𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Thursday, July 31, 2025
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Generated Fri 1 Aug 02:49:23 BST 2025
Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖)
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Latest in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕 and older bulletins can be found at 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕-𝒂𝒓𝒄𝒉𝒊𝒗𝒆𝒔
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Gemini index for the day: gemini://gemini.techrights.org/2025/07/31/


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

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QmZMEFKvpgvjxAcV9Pwu7yF74LYZwS7ktdLFdYb988Ncfu


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

⦿ Techrights  -  A Lot of Supposedly "Successful" Businesses Are Just Debt-Racking Vessels Without Any Prospects of Financial Sustainability

⦿ Techrights  -  An Illusion and Cult Worship of Magnitude (Ubiquity as "Victory")

⦿ Techrights  -  Google: From Pointing to Relevant Sites to Pointing to Social Control Media to Actually Parroting Social Control Media as "Facts"

⦿ Techrights  -  IRC Proceedings: Wednesday, July 30, 2025

⦿ Techrights  -  Moving on in Techrights, Geeks Gonna Geek

⦿ Techrights  -  Over at Tux Machines...

⦿ Techrights  -  Sabotaging Linux on Behalf of Microsoft With UEFI 'Secure' Boot (De Facto Remote 'Kill Switch'), Then Defaming, Stalking and Harassing Critics of 'Secure' Boot for 12 Years, Then SLAPPing Their Spouses and Them

⦿ Techrights  -  Slopwatch: Google News Has Lost the Plot

⦿ Techrights  -  theregister.com: The Voice of Microsoft US?

⦿ Techrights  -  Yes, You Can Love and Adore Things Whilst Also Criticising Them

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
https://techrights.org/n/2025/07/31/A_Lot_of_Supposedly_Successful_Businesses_Are_Just_Debt_Racking.shtml
https://techrights.org/n/2025/07/31/An_Illusion_and_Cult_Worship_of_Magnitude_Ubiquity_as_Victory.shtml
https://techrights.org/n/2025/07/31/Google_From_Pointing_to_Relevant_Sites_to_Pointing_to_Social_Co.shtml
https://techrights.org/n/2025/07/31/IRC_Proceedings_Wednesday_July_30_2025.shtml
https://techrights.org/n/2025/07/31/Moving_on_in_Techrights_Geeks_Gonna_Geek.shtml
https://techrights.org/n/2025/07/31/Over_at_Tux_Machines.shtml
https://techrights.org/n/2025/07/31/Sabotaging_Linux_on_Behalf_of_Microsoft_With_UEFI_Secure_Boot_D.shtml
https://techrights.org/n/2025/07/31/Slopwatch_Google_News_Has_Lost_the_Plot.shtml
https://techrights.org/n/2025/07/31/theregister_com_The_Voice_of_Microsoft_US.shtml
https://techrights.org/n/2025/07/31/Yes_You_Can_Love_and_Adore_Things_Whilst_Also_Criticising_Them.shtml

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
https://techrights.org/n/2025/07/31/Gemini_Links_31_07_2025_Fake_Money_and_Gemini_Diaries.shtml
https://techrights.org/n/2025/07/31/Links_31_07_2025_Australia_Restricts_YouTube_Access_Personal_Pr.shtml
https://techrights.org/n/2025/07/31/Links_31_07_2025_Spotify_Collapses_and_Spotify_Now_Forcing_Some.shtml
https://techrights.org/n/2025/07/31/Links_31_07_2025_War_in_Ukraine_Security_News_and_Cyberattacks_.shtml

                    ䷩ 𝚕𝚒𝚗𝚎 77

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/07/31/A_Lot_of_Supposedly_Successful_Businesses_Are_Just_Debt_Racking.shtml
    Gemini version at gemini://gemini.techrights.org/n/2025/07/31/A_Lot_of_Supposedly_Successful_Businesses_Are_Just_Debt_Racking.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ A Lot of Supposedly "Successful" Businesses
Are Just Debt-Racking Vessels Without Any Prospects of Financial
Sustainability⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jul 31, 2025


Older: Sheela_Zemlin's_Company_Has_Hit_All-Time_Low,_Lost_More_Than_90%_of
'Market_Value'_in_Only_Months | Linux_Foundation_Revenue_Plunges_($18,000,000
Decrease_in_One_Year)_and_Jim_Zemlin's_Wife_Has_Her_Company_Sued_for_Securities
Fraud_(Class_Action)


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Claude_Code_weekly_rate_limits;_Read:_our_bills_are_too_high
         and_we're_running_out_of_money_without_prospects_of_income⦈_


The probability of bankruptcy of any business is more than 0%. I've lived long
enough to see businesses which one year claimed to be worth absolutely
astounding sums and vanished from this planet just months later. They basically
defrauded whoever bankrolled them. Where did all the money go? Who stood the
benefit? Was anyone sentenced to prison? Heck, even the wife of Jim Zemlin from
the Linux_Foundation did_that. In recent years we saw companies like Workday
Inc (WDAY) announcing "success" while getting rid of many workers - a
contradictory message/signal for sure. In the case of "Open" "hey hi"
(basically a Microsoft 'offshoot'), the company privately admits_it's_spinning
out_of_control,_drowning_in_an_ocean_of_debt. Publicly, however, Scam Altman
behaves_like_he_and_this_'company'_are_worth_trillions. He's a scammer. Heck,
his_sister_sued_him_for_sexual_abuse, yet the media doesn't seem too bothered
about that. Yes, trust that guy!


Earlier today we wrote about Microsoft, which laid off about 30,000 workers so
far this year and whose debt_continues_to_skyrocket (despite those mass
layoffs). So on_what_basis_does_the_Wall_Street_media_assert_that_it's_the
second-most_valuable_company_in_the_world? We see a ton of fake news today. In
the case of NVIDIA, the ascent was temporary as it's strictly tied to a_giant
bubble_(rebranding_GPUs_as_"hey_hi_chips"_and_asserting_that_slop_is_the
future).


Don't be so shocked to see fallen giants. Intel is just one example. It failed
to fake. The faking didn't last long enough. █


    * theregister.com:_The_Voice_of_Microsoft_US?
    * Links_31/07/2025:_Spotify_Collapses_and_Spotify_Now_Forcing_Some_Users_to
      Undergo_Face-Scanning


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⡟⠛⠛⡛⠛⡟⠛⠛⣟⠟⠛⠛⠛⠛⠛⠋⢙⠻⡟⢉⠙⠛⢹⠉⡋⠻⡟⠛⠛⠚⠛⢻⣯⢿⣿⢛⢟⠟⣿⣉⡻⠻⢹⠛⠻⠛⠓⢿⠛⠛⢻⡍⡟⣞⠏⢟⠞⢻⠛⠛⡛⡟⠁⠉⠛⠛⠛⠛⠟⠻⡏⡍⠛⢻⣿⣿⣿⣿
⣯⣉⡉⣉⡩⡙⣿⣋⣩⣉⡍⣏⢉⡋⣟⢙⠁⣙⠍⣙⢙⢍⡯⢙⡏⡿⡯⡯⡫⣫⢽⢉⡉⢉⣩⢘⣿⢝⢙⣉⣹⡉⢉⢙⡏⡫⣫⢝⠉⣹⢫⢝⢟⣽⢉⣙⡉⡉⣩⠍⣾⣏⣙⢉⡉⣏⣋⢙⣻⡯⣛⣿⢿⢙⢉⡍⣿⣿
⣏⣍⣉⣹⣉⣉⢉⣉⣹⣿⣸⣍⣈⣗⣅⣉⣹⣈⣉⣉⣉⣹⣉⣸⣐⣉⣉⣉⣉⣹⣅⣏⣉⣉⣸⣎⣀⣟⣀⣸⣈⣉⣉⣹⣻⣉⣸⣑⣍⣙⣙⣿⣸⣍⣁⣁⣁⣉⣏⣈⣉⣈⣯⣉⣉⣉⣸⡟⣏⣯⣻⣉⣿⣿⣿⣿⣿⣿
⣿⣉⣰⣁⣁⣻⣨⣅⢅⣍⣭⣧⢪⢪⣻⣸⣍⣉⣈⣌⣽⣉⣀⣷⣿⣅⣩⣪⣸⣕⣍⣁⣍⣈⣉⣹⣨⣸⣅⣹⣖⣌⣪⣨⣸⣱⣫⣾⣮⣵⣕⣯⣶⣟⣷⣺⣪⢅⣯⣲⣇⣝⡕⣅⣯⣪⣪⣪⣸⢏⣎⣀⣉⣁⣕⣉⣸⣿
⣿⢴⣇⣦⣤⣶⣧⣴⢼⡤⣾⢿⡴⣤⣧⠶⣵⣾⣾⣼⡶⣵⣦⣷⢤⣤⣤⣤⣦⣿⣤⣤⣽⡴⣤⡤⢧⣤⢤⣤⣤⣀⣴⣧⣤⡧⠦⣤⣤⡷⣿⣆⣤⣤⣴⣧⣤⣤⣦⣼⣦⣤⣦⣤⣦⣧⣵⣌⣶⣴⣤⣴⣧⣮⣿⣿⣿⣿
⣿⠴⠼⠭⡼⡌⠤⡿⢧⡴⠼⢬⡤⡤⠼⠤⢷⠤⠥⠼⠤⠤⠬⡧⢤⡤⠤⠿⡤⠤⠷⠵⠥⣥⡠⣷⠤⣤⠧⡤⠧⡥⠤⠤⠤⣤⠤⡦⡦⠧⠭⢷⠤⠄⠄⠤⣤⢯⠼⢎⠿⠮⡼⣄⡶⢧⠤⢤⠼⠧⢡⠯⠤⣦⣿⣿⣿⣿
⡷⡷⢾⡶⠳⠳⢿⢾⠶⠷⠇⢶⢷⣞⡶⣾⠾⠶⠴⡶⠶⠶⠷⢷⣶⣷⣶⣾⣷⣶⣶⣶⣿⣿⣿⣾⣿⣿⣾⣶⣶⣿⣶⣾⣶⣽⣶⣾⣾⣶⣶⣾⣶⣷⣶⣷⣾⣶⣶⣾⣶⣾⣿⣾⣷⣾⣶⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿
⣷⣷⣿⣶⣶⣶⣾⣶⣶⣷⣶⣾⣾⣿⣾⣿⣶⣾⣾⣧⣷⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⠙⡉⣟⠉⠛⢙⣏⠛⠻⢝⢝⣽⠏⠛⡏⢩⠛⡹⡫⡿⣯⢫⠫⢻⠍⠋⢹⡏⠛⠛⢛⢻⠛⠛⠋⡛⠋⢿⠛⠛⠙⡙⣿⡝⢹⢛⢹⡋⣫⡫⠛⠛⠛⢙⠙⡋⡫⣟⠙⢛⡛⠋⠛⢹⢛⠋⠉⠋⡛⣩⠝⣿⢹⣝⢽⣿⣿
⡏⣝⣍⣅⣉⣉⣉⣉⣉⣩⣩⣿⣩⣉⣉⣍⣿⣍⣉⣭⣍⣩⣇⣉⣍⣍⣹⣉⣭⣫⣩⣩⡫⣯⣭⣻⣼⣹⣭⣍⣩⣙⣽⣉⣍⣏⢉⣁⣽⣁⢍⣏⣩⣹⣙⣝⣩⣁⣉⣩⣿⣯⣯⣫⣿⣉⣀⣸⣹⣝⣍⣽⣽⣟⣽⣿⣿⣿
⣿⣩⣫⣋⣏⣉⣙⣩⡙⣹⣉⣏⣹⣿⣉⣍⣉⣩⣏⣹⡝⣿⣉⣙⣋⣉⣹⣝⣍⣉⣹⣘⣯⣩⣟⣉⣉⣅⣉⡉⣏⣘⡩⣍⣻⣹⣏⣻⣏⣉⣉⣁⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⣿⣿⢿⣿⠿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣼⣤⣤⣤⣧⣯⣬⣷⣽⣷⣼⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 165

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/07/31/An_Illusion_and_Cult_Worship_of_Magnitude_Ubiquity_as_Victory.shtml
    Gemini version at gemini://gemini.techrights.org/n/2025/07/31/An_Illusion_and_Cult_Worship_of_Magnitude_Ubiquity_as_Victory.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ An Illusion and Cult Worship of Magnitude
(Ubiquity as "Victory")⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jul 31, 2025,
updated Jul 31, 2025


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇GNU⦈_


Size of companies? Size of their_debt (how much they're able to borrow with so-
called "credit")? Where does this lunacy end?


From Appeal to Popular Opinion By Douglas Walton


   🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇GNU_has_been_around_for_over_40_years_and_it'll_likely
               continue_to_exist_for_another_40_(in_some_form)⦈_


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


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


Some companies want us to think that their large(r) size implies merit. Or that
projects with many contributors/coders can use magnitude as evidence of
"success".


One common example of this is Linux. Another is Microsoft.


Linux has many contributors. It's also bloated. Microsoft has hundreds of
thousands of workers. Its software is still bloated and unreliable. And no, I
don't need a program that sucks up one gigabyte of RAM to write a simple
letter.


There are Latin terms for all sorts of fallacies (one is detailed above; there
are others). Those are logical fallacies that piggyback misconceptions. One
example of that is Wayland being "new" (it's actually not!) and hence "better".
Somehow the most valuable (or highly valued) artwork is centuries old. Why is
that?


Now consider GNU. Its core tools are not overly complex. Nor should they be.
There are similar tools in the BSDs and there are some Rust cultists (read:
lovers of Microsoft's proprietary GitHub) who try to replace them in the name
of... God knows what (certainly not security).


A lot of people out there prefer simple tools, simple protocols, and simple
workflows for a simpler life. I myself still use IRC - the same thing I used in
the early and mid-nineties. Moments ago I connected again to the same IRC
networks that I connected to when I was a kid. They still work. Not much has
changed, except the people and the irdc (IRC daemon) at the back end.


We need to get rid of this dumb, shallow notion that something being newer,
bigger, more "advanced" necessarily makes it better. It just doesn't work that
way. Many people still use the same toaster or kettle technology we had 50
years ago. It's good enough to get the job done. Due to relative simplicity,
repair work is also ranging from trivial to feasible.


This past week Microsoft and IBM both pretended to be doing OK [1, 2] and
Microsoft's propagandist (and source burner) Todd Bishop is again spreading the
"headcount" propaganda that we debunked here about half a dozen times before.
It goes something along the lines of, yes, we lay off many people, but we add
the same number of people. It's a lie. Those companies get smaller while, for
investors' sake, pretend to become "more efficient" or "equally big".


Size isn't everything. Size can be a liability when salaries in IT are high and
lesser-paid workers are inexperienced. Right now it looks like Microsoft_cannot
keep_up_with_salaries (payroll), hence almost 30,000 layoffs so far this year.


GNU has been around for over 40 years and it'll likely continue to exist for
another 40 (in some form). It doesn't need to allocate millions or billions in
budget for "workers". █


    * Google:_From_Pointing_to_Relevant_Sites_to_Pointing_to_Social_Control
      Media_to_Actually_Parroting_Social_Control_Media_as_"Facts"
    * Gemini_Links_31/07/2025:_Fake_Money_and_Gemini_Diaries


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⡍⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣴⣿⢿⣰⣶⣤⣤⡉⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⡇⠿⠿⠿⠛⠻⠿⢿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⣾⣿⣿⠿⠟⡛⠛⡛⠁⢿⢆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠹⡯⢸⣿⣾⣿⣮⣷⡄⡄⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣥⣴⢾⡧⢋⠄⣊⣴⣦⣺⣗⣦⡅⠘⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣄⢻⠅⢾⣿⣿⣿⣿⠿⠟⠛⠿⣿⣿⡈⣿⡿⣫⢄⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⠏⢐⣵⡿⣿⣿⣯⠾⠟⢿⣵⡸⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢿⠀⠀⠀⠀⠈⠙⠻⣎⠟⠶⣰⡌⠟⣵⡴⢚⣡⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡁⠂⢫⢯⣶⣮⠋⠆⢿⣿⣿⣿⡇⢋⣴⠖⠲⢒⣀⣭⡻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢮⡇⠀⠐⠘⠂⠀⠀⣦⣄⠐⠒⠾⠇⣰⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢠⣿⡽⢟⣾⣟⣪⣿⡿⠟⠀⠀⠀⠈⠀⠀⠙⠃⠀⣀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠘⡦⣄⣀⣀⠤⣼⣿⠟⠀⢀⠄⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣬⣤⣤⣟⣛⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⢸⣿⣿⣿⣿⣿⣿⣿⣟⠟⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢻⣿⣿⡿⢿⣭⣄⣷⡀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⢀⡄⠈⠉⠋⢉⣭⡍⣩⠙⢁⣎⢻⣿⣻⡶⡔⣩⣭⣀⠲⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣅⠀⡀⣀⣀⣤⣤⣄⣈⣉⣀⡀⠀⠀⠀⠀⠀⠈⡹⣿⡿⠋⠀⠀⠀⠈⠁⠀⠀⠀⠀⡀⠀⠀⠹⡇⣿⠘⣿⣿⣷⡌⣛⢛⠁⣼⠿⠿⡗⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡻⠣⠿⠛⢛⣛⣛⠛⠛⠛⠿⠿⢿⣶⣦⡄⣠⣾⢸⣿⡇⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⣿⢸⣿⣿⣟⠈⢿⣿⠀⣾⣾⣿⣷⢸⣿⣿⣿⢟⣵⡶⡷⣶⣾⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡻⡿⠇⢀⣻⠿⣶⣿⣿⡇⣰⣤⣿⣿⢶⣂⣭⡌⠋⣱⣿⣿⡇⠀⠀⢀⣀⣤⣤⣄⢀⣤⣤⡤⠤⠤⠀⠀⣿⠸⣿⣿⡇⣿⣜⢿⡆⣱⡾⠓⣒⢈⠟⣻⣯⣞⣿⣿⣿⣻⣯⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⢿⡿⣫⣽⣿⣷⣿⣻⣿⣿⣿⣿⣿⣻⣭⣿⣶⣦⣝⠟⢻⡇⠀⢐⡢⢤⣤⢹⣿⣿⣿⣀⣒⣒⣈⠁⠀⢸⠰⣩⢂⡃⣿⢹⡈⠁⣤⠖⣛⠧⠀⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠛⠻⢿⣿⣿⣿⣿⣷⡇⠉⢉⣛⣛⣿⣽⣿⣿⣿⣿⣿⠟⠶⠹⠿⠛⣵⣶⣾⣃⠀⠦⢾⣿⡿⢙⣿⣿⣿⡘⠳⣿⡿⠟⠀⠈⣸⣿⣬⡖⢨⢠⠰⣿⡆⢋⣷⠂⢀⡻⣫⣶⣶⣾⣼⣿⣿⣿⣼
⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠇⡄⠘⣿⣿⣿⣿⠷⣶⡟⣿⣿⣿⣿⠇⠀⣼⢿⣿⣿⣿⡇⠀⠂⠲⣶⣺⣫⢽⣿⡿⣿⣷⠂⠉⠀⠀⣿⣿⣟⣿⣆⣚⠣⢋⣴⣄⢻⢸⡜⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠸⣶⣆⠈⠻⢿⣿⣧⣭⣴⣿⣿⡿⠋⢀⣼⢱⡼⡟⡏⣿⡆⠀⠀⠈⠈⠙⠛⢿⡟⠛⠉⠀⠀⠀⡀⣤⢹⣾⣿⣿⡟⡃⠺⢸⣿⣿⣮⣼⡇⢿⣿⣿⣿⣿⣿⠟⠉⠛⠿
⣿⣿⣿⡇⠀⠀⠀⠀⣐⡒⢀⣀⠀⠠⠄⠸⣿⡇⡟⢻⢿⢠⡀⠀⡹⣛⣛⣛⠉⠁⣠⠴⢙⣡⠹⣷⢠⣶⣦⢁⠀⠰⢄⡀⠀⠀⠘⠇⠀⣀⠀⢢⣬⢹⣯⣈⣭⣩⣶⣶⣿⡧⣈⠅⣼⣿⣟⣾⣿⣿⣿⠉⠉⠁⠀⠀⠀⠀
⣿⣿⣿⡃⠀⠀⠀⠬⢇⣒⠂⠃⠘⣣⡭⢡⣿⣷⣵⣾⠴⣚⣉⢸⣾⣿⣿⣿⠐⢿⠟⣴⣿⡿⠿⠛⡛⢿⣿⡇⠄⣄⢰⣿⡾⢷⡀⠠⢐⢿⠇⠞⠻⠿⢿⣿⣿⣿⣿⣿⣿⣮⣥⢸⣿⢿⡞⣿⣿⣻⡁⡀⠴⠒⠒⠂⠀⠀
⣿⣿⣿⣧⡀⠀⠠⡂⠉⣭⢀⣿⣿⡗⠂⠀⢟⣝⣏⢴⣿⣿⣏⢣⣙⠿⣿⠿⠀⠶⢰⠿⠛⣋⣉⣀⣈⠀⢘⣷⠀⣿⡀⡽⢞⣾⣿⡆⢰⡗⣢⣴⣶⣤⠸⢿⣿⣿⡯⢕⣒⣒⠨⠈⠁⣼⣿⣯⣿⣿⣿⡅⠀⠀⣠⣤⣶⠶
⣿⣿⣿⣿⣤⢠⣤⣈⡙⠿⢸⣿⣾⡇⢁⡀⡸⠾⠿⢸⣾⣿⣿⣷⣽⣿⣶⣾⠘⠀⠺⢿⡾⣿⣿⣿⣷⡆⢸⡇⠀⣠⢅⣿⣿⣿⣿⡇⠘⣈⠁⠀⢲⣿⡖⣸⣿⣿⠰⠖⠩⣭⣛⠀⠸⣿⣿⣇⢻⣾⣿⣷⠠⢞⢋⠁⠘⣿
⣿⣿⣿⣿⣿⢠⡍⠿⢿⡷⢈⣿⣿⡇⠹⠃⡉⣿⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⡆⠮⣶⣥⡈⠈⠉⠛⠃⢀⣴⣶⣶⡪⣼⣿⣿⣿⣿⡧⢸⣮⣀⡀⠚⣭⣾⣛⣿⣻⣆⡀⠠⡿⠿⠃⣴⣿⣿⣿⢱⣿⣿⣍⠴⢿⣯⡤⠾⣻
⣿⣿⣿⣿⡏⢸⣿⠿⠆⢲⠸⣿⣿⡇⢶⠆⡃⠠⢘⡟⣿⣿⣿⣿⣿⣿⣟⣿⡿⠦⢻⣿⣷⣽⣷⡆⠀⠀⢿⣿⣿⣷⡝⣿⣿⣿⣿⣿⡌⣙⣛⠳⠘⢿⣇⣈⡋⢅⣿⣷⣤⠞⣠⣾⣿⣿⣿⢏⢸⣟⣿⣿⣿⡿⣿⣿⣛⣿
⣿⣿⣿⣿⡇⠐⠿⠂⣴⢸⡄⡺⢾⣷⢸⠀⣤⠉⣘⠿⣿⣷⢈⠹⣿⣿⣿⡏⢰⣶⡄⠻⣿⣿⢛⠙⣂⣾⣷⣯⣛⠿⣿⣞⢿⣿⠏⣴⣲⣼⡙⡏⡿⣦⣝⠛⠲⠾⠟⣋⢡⠈⣿⣿⣿⣿⣿⢿⣯⠷⣟⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⢰⠀⣦⣏⢸⡆⣿⣿⣿⢸⡆⢠⡀⠄⠉⢲⣶⣸⣧⡌⠻⡟⢀⣼⡏⣔⡒⢦⠡⣌⠃⡤⡝⢿⣿⣿⣷⣿⡻⢾⣿⣆⢛⡛⣿⠁⠳⠋⠛⠋⠸⣿⣿⣀⠉⠛⠀⠹⠟⢿⣿⣿⡏⣽⣿⣿⣿⣿⣿⡿⢟⣛⣽
⣿⣿⣿⣿⡇⠘⢠⢹⣶⢸⡆⣿⣿⣿⠸⣿⢸⣻⣷⣌⡲⢟⣋⣭⢐⣀⠀⢾⣿⡷⠙⡃⠀⠘⠎⠒⠶⠈⡌⢻⣿⣿⣿⣿⣿⣿⣿⠸⠷⣿⢐⢊⣥⢰⢠⣌⡙⢛⣡⡾⠘⠐⠦⣅⠘⢿⣿⡇⣿⣿⣻⣿⣿⣿⢳⣿⣿⣿
⣿⣿⣿⣿⣷⠀⠌⣸⣿⣿⢸⣿⣿⣿⢸⣿⢸⣯⣜⢿⣿⣿⣿⣿⡘⣿⣷⠈⢿⠁⠀⣿⣧⡄⠀⠄⠖⡀⣿⠘⣿⣿⣿⣿⣿⣿⣿⠠⠖⠠⠄⣾⡇⣾⢸⣿⣿⣿⢰⣶⣾⣿⣿⢸⡈⡆⣿⣿⣿⡿⣿⣿⣿⣿⣞⠟⡛⣭
⣿⣿⣿⣿⡇⠨⣿⣿⣿⣿⠰⣿⣿⣿⢎⣿⠈⢿⣿⣷⣬⡻⢿⣿⡇⢻⣿⣷⠆⣸⢀⣿⣿⣑⣂⣴⣿⣷⣬⡀⢹⣿⣿⣿⣿⣿⡟⢀⡊⠆⢰⣿⣄⢿⠸⣿⣿⣿⣘⣿⠿⠿⣛⣸⡇⣷⠸⣿⣿⡇⠻⣿⣿⣿⣿⢠⠇⣿
⣿⣿⣿⡿⠁⣶⡿⠭⠟⢛⣷⢹⣿⡏⠺⠿⢟⣒⣬⣝⢻⣿⣦⡙⣿⣬⢉⣁⡴⠧⢸⣿⣿⣹⣿⠂⠙⢷⣟⣳⣆⠂⠀⠒⠂⣿⢁⣿⠍⣶⠸⣭⣿⡎⣇⢻⣋⣼⣯⣿⠘⢠⣿⡻⠁⣿⡀⣿⣿⣇⠀⣰⣿⠿⡿⠯⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⡿⢿⣿⣿⣿⣿⢿⣿⣿⣿⡿⣿⣿⢿⡿⣿⣿⣿⢿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣏⢉⢿⡇⡭⢈⠍⡉⢩⣏⠁⡍⠩⣽⢫⠸⠉⣾⢣⡅⡉⢍⠙⡍⢩⠉⢉⢹⡇⠍⣿⡸⢇⠉⠩⠩⢸⡏⠩⢹⡇⡙⠄⠍⠍⠹⠉⠍⠹⠁⠍⠋⠩⢽⡰⠷⡈⠍⠩⠉⠏⠩⠉⠍⠉⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣯⢩⠹⠿⣿⢿⡿⠿⠿⣿⠿⡿⠿⢹⠿⢿⢹⢿⠿⣿⠏⠯⠿⡿⡏⡿⢿⡿⠿⠿⣿⠫⠏⢹⡯⢿⠿⠿⣿⠿⠿⢿⢿⢿⠹⠿⠿⠿⢿⣯⢩⡍⠿⢿⡟⠟⠿⠿⠹⣿⠛⡿⠿⢿⠿⠿⢿⣿⠿⠿⠿⣿⣿⣿⣿
⣿⣿⣿⣿⣾⣶⡶⣿⡶⣶⣶⡶⣿⠶⣶⣶⣶⣶⣶⣾⣶⣶⣿⣶⣶⣶⣷⣶⣷⣶⣴⢶⣶⣿⢶⣶⣶⣷⣶⣶⣶⣿⣾⣶⣶⣾⣶⣶⣶⣶⣶⣶⣿⣶⣷⣶⣾⣾⣶⣶⣾⣶⣿⣶⣶⣶⣶⣶⣦⣾⣷⣶⣶⣶⣿⣿⣿⣿
⣿⣿⣿⣏⣉⣉⣃⣏⣃⣉⣹⣸⣉⣀⣉⣍⣋⣏⡉⢹⣏⣉⣉⣹⣏⣉⣉⣉⣹⣏⣁⣿⣉⣁⣇⣋⣉⣉⣏⣉⣉⣩⣉⢉⣿⣈⣏⡉⢍⣉⡉⡉⣹⡇⣘⣏⣉⣉⣉⣯⣙⣢⣺⣉⣉⣉⣸⣉⣋⠹⣸⣉⣩⣩⣿⣿⣿⣿
⣿⣿⣿⡿⠿⠿⠿⠿⠿⠟⠿⢿⢿⠟⡿⡟⠿⢿⠿⠿⠿⡿⠟⡽⢿⠿⠿⠿⠿⠻⠟⡟⠿⠿⠿⢻⡿⠟⡿⠟⠿⠿⠿⠿⠿⢿⡿⠳⠿⠿⡿⠾⠿⠿⠿⠟⠿⡟⠿⡿⢿⡿⠿⠿⢿⠿⠻⢻⠿⢻⡿⠿⠿⠿⣿⣿⣿⣿
⣿⣿⣿⣷⣶⣶⣶⣶⣼⣶⣶⣾⣾⣶⣷⣷⣶⣾⣶⣶⣾⣷⣶⣷⣾⣶⣰⣾⣾⣶⣶⣷⣾⣶⣶⣾⣷⣶⣿⣷⣶⣷⣾⣶⣶⣿⣷⣶⣶⣾⣷⣆⣆⣶⣷⣶⣶⣷⣶⣷⣾⣾⣶⣶⣷⣶⣶⣶⣷⣾⣷⣶⣶⣼⣿⣿⣿⣿
⣿⣿⣿⣏⣩⣹⣩⣈⣩⣿⣉⣉⣩⣩⣩⣉⣉⣟⣍⣸⣏⣈⣩⣿⣩⣉⣉⣉⣩⡸⣏⣉⣙⢅⣈⣍⣉⢍⡝⣿⣉⣩⡏⠉⡍⣉⠉⢍⣏⣅⠉⠉⣿⠈⣹⠉⠁⡩⡏⣩⢩⡉⡩⠸⣿⠈⡹⠉⡩⠉⡁⣿⡉⢩⣿⣿⣿⣿
⣿⣿⣿⡿⠿⠿⢿⠟⠿⡿⠿⠻⢿⠿⡿⠟⠿⢿⡿⡿⠿⠿⠿⠿⠿⠿⠿⢿⡿⠿⢿⣿⠟⠿⢿⡟⠿⠿⢿⢿⡟⠿⣷⠾⣿⠻⠷⠺⠿⢿⠿⢿⢻⣿⢿⢿⡿⠿⠿⢿⡿⠟⠟⠿⠟⣿⠿⠿⠿⢿⡿⠻⡿⠿⣿⣿⣿⣿
⣿⣿⣿⣷⣷⣶⣷⣤⣮⣮⣿⣤⣾⣨⣷⣥⣴⣽⣧⣤⣀⣦⣦⣤⣮⣤⣯⣼⣷⣤⣧⣿⣤⣴⣽⣧⣴⣤⣴⣽⣧⣼⣼⣧⣿⣤⣥⣤⣤⣥⣵⣵⣭⣷⣵⣼⣧⣶⣴⣵⣦⣤⣥⣬⣤⣿⣶⣦⣄⣾⣧⣤⣥⣮⣿⣿⣿⣿
⣿⣿⣿⡏⠩⠃⠉⠈⡩⡇⢙⢽⡩⠈⡉⡩⠋⠅⠉⣽⠉⢹⡨⡫⣟⠅⠝⠙⠉⠉⠍⡫⢩⠈⡩⠈⣽⠉⢠⡏⠩⠹⠉⠉⠝⢙⠅⡏⠘⠅⠰⢝⠹⠉⠉⠘⢝⠉⣏⠉⢹⠋⠙⠉⠍⠉⡏⠋⢹⠘⠉⡹⠋⠿⣿⣿⣿⣿
⣿⣿⣿⡿⠻⡿⢶⠿⠿⢿⢿⠻⢿⢿⠿⠟⡷⡾⡿⠿⣿⢿⢿⠛⡟⣻⠛⢿⡿⠿⢿⠿⠿⣿⠻⢿⠿⡿⡿⢿⠿⣿⢿⢿⡟⣿⢻⢻⠿⣿⢻⣿⡟⢿⢿⢿⢿⢿⣿⣿⣻⣿⣿⣿⢿⣿⣿⣿⣿⢿⣿⠟⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣥⣤⣽⣔⣱⣬⣤⣬⣬⣼⣮⣤⣤⣤⣧⣬⣾⣴⣵⣤⣤⣬⣄⣾⣀⣤⣵⣤⣨⣾⣤⣤⣤⣤⣤⣼⣤⣿⣤⣤⣤⣽⣤⣤⣤⣿⣤⣲⣧⣥⣤⣤⣤⣥⣤⣤⣬⣤⣀⣯⣴⣤⣥⣲⣯⣤⣽⣤⣥⣤⣿⣿⣿⣿
⣿⣿⣿⡟⠙⠝⠹⡿⠁⠃⠋⣿⠏⠉⠫⢸⡏⠙⠙⠍⠫⠙⢫⠊⠙⢹⡏⠇⠛⢻⡏⠫⠛⠛⠯⠛⠛⠋⠻⠛⠑⠫⠛⢻⡟⠛⠻⣟⠇⠛⠋⣿⠛⠚⠘⢻⡗⠛⢿⠛⠻⠋⠘⠿⠛⠚⠛⠏⠚⢿⡟⠛⠛⠇⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⣿⣿⠟⡿⣿⡿⡻⢿⢿⣷⡿⣿⡿⢿⢷⣾⡛⡓⢾⢿⡿⣛⣟⢻⣿⣶⣿⣿⣿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣤⣦⣤⣼⣇⣠⣬⣦⣴⣤⣄⣸⣧⣥⣤⣤⣥⣬⣿⣧⣧⣥⣼⣯⣥⣥⣤⣤⣦⣼⣧⣤⣿⣬⣤⣤⣤⣼⣧⣥⣤⣤⣬⣿⣤⣤⣤⣬⣿⣤⣤⣬⣿⣤⣤⣤⣤⣽⣧⣤⣿⣬⣦⣾⣭⣤⣿⣬⣥⣤⣿⣿⣿⣿
⣿⣿⣿⡟⠛⠻⡛⠛⠻⠛⠛⠋⣿⠊⠛⠛⠀⣾⠘⠻⠟⣿⠛⢻⡇⠛⢟⠛⣿⠚⢿⠛⢿⡿⠛⠛⠃⢿⠻⠟⡟⢻⡟⠟⠛⠛⠛⠟⢻⡟⢸⠛⠻⠛⢻⠛⠛⢸⣟⠛⠛⠛⣿⠛⢻⡟⠛⠛⠟⠛⠃⣿⠛⠟⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⡿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣴⣤⣤⣬⣧⣤⣤⣼⣤⣤⣥⣤⣤⣦⣼⣤⣼⣥⣿⣥⣬⣤⣤⣤⣽⣣⣢⣤⣬⣄⣼⣦⣤⣤⣤⣦⣤⣤⣬⣿⣠⣤⣤⣦⣤⣤⣦⣧⣤⣤⣦⣤⣤⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢏⠃⢹⡟⠘⠛⡟⡛⠃⠛⠛⣻⠛⠛⠛⠛⢻⡟⢛⠛⠃⠛⠛⡋⡟⠛⣿⠃⠛⣻⡃⠛⠛⢻⣛⠛⠛⢛⡟⠋⣺⠃⠛⣻⢛⢙⠛⢛⠛⢛⢛⣿⣿⢛⠙⠛⢻⡛⠻⡟⡟⠛⡟⢛⢻⢛⡛⢛⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡟⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⠛⣿⣿⣿⣿⣿⣿⣿⡿⡿⢛⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡻⡛⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣤⣤⣥⣧⣤⣽⣤⣤⣥⣥⣤⣤⣿⣳⣷⣿⣧⣤⣤⣿⣤⣤⣬⣼⣤⣧⣥⣤⣤⣤⣦⣤⣤⣿⣬⣤⣤⣤⣽⣧⣧⣤⣼⣤⣤⣐⣤⣴⣤⣤⣤⣤⣼⣧⣤⣤⣬⣼⣤⣮⣧⣴⣤⣤⣤⣧⣥⣤⣤⣤⣿⣿⣿⣿
⣿⣿⣿⡟⠃⢸⡟⠸⠟⠟⠛⡟⢻⡟⠛⠛⠻⠛⠟⠃⠛⢻⡏⠺⠛⠛⡟⠟⠻⣿⢙⠛⠻⠻⢿⠋⡟⠛⢛⡟⠟⠟⠛⠟⠃⠛⠛⢻⡟⢻⠻⠛⠛⠛⠛⠻⠛⡟⠛⠛⠛⠛⠛⣻⡟⠘⠛⢻⡟⠛⡛⠛⡛⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡟⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣤⣤⣤⣽⣧⣤⣿⣤⣦⣤⣼⣰⣤⣤⣤⣿⣤⣦⣧⣼⣇⣥⣥⣤⣧⣤⣥⣤⣤⣿⣠⣰⣤⣤⣠⣬⣿⣤⣴⣧⣤⣦⣰⣤⣤⣤⣾⣦⣤⣦⣤⣿⣤⣤⣤⣯⣤⣤⣦⣤⣼⣇⣤⣤⣬⣤⣤⣤⣤⣴⣿⣿⣿⣿
⣿⣿⣿⡟⢛⠛⠛⡟⠛⠛⡻⢿⡟⠛⠛⠛⠛⠛⠻⡟⠛⢻⡇⠛⠛⢿⠛⠛⠛⠛⠛⠛⠛⢻⡟⢻⡟⠛⠛⡛⠛⠛⢻⠙⡟⣿⠛⠛⠛⠛⠛⠛⠛⡛⠛⠛⣿⢟⢹⠛⠛⣿⠛⡛⠛⠻⣿⡉⠛⠛⠛⠛⠋⡿⣿⣿⣿⣿
⣿⣿⣿⣷⡟⣿⣷⣿⣿⣿⣾⣾⣿⡟⣻⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⢻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⡟⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⢻⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣧⣤⣤⣧⣇⣆⣤⣼⣼⣤⣧⣤⣆⣢⣤⣦⣤⣤⣤⣿⣤⣥⣤⣤⣤⣽⣤⣤⣿⣤⣼⣤⣤⣤⣤⣬⣤⣿⣤⣼⣧⣼⣤⣤⣴⣤⣤⣤⣤⣤⣤⣼⣧⣴⣤⣤⣹⣧⣤⣤⣴⣤⣤⣤⣤⣸⣇⣤⣤⣧⣿⣿⣿⣿
⣿⣿⣿⡏⡟⠘⠛⣿⠛⠛⠛⠛⠛⠛⠇⠛⠛⢻⡟⠋⣾⠃⡟⠛⡟⠛⠛⠻⠛⠛⠛⢻⠛⢹⡟⢹⠛⠛⠋⠻⢸⠛⠻⠻⠛⠛⢻⡟⢸⠛⢻⡟⠛⢻⠛⠛⠛⠛⠛⢻⠛⢻⠛⠛⡟⡟⠛⠛⣻⠙⢻⢻⠛⠻⣿⣿⣿⣿
⣿⣿⣿⡿⣾⣿⣿⣿⣿⣿⣾⣿⡿⣿⣿⣿⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⡟⣿⣿⣾⣿⣿⢻⣿⣿⡿⣿⣿⣿⣿⣿⣾⣿⣿⢿⡿⣿⡷⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⣿⢿⣿⡟⣿⣿⣿⣿
⣿⣿⣿⣧⣤⣤⣤⣌⣧⣤⣼⢰⣤⣼⣤⣤⣥⣤⣤⣹⣼⣤⣧⣤⣼⣤⣤⣤⣦⣴⣤⣤⣤⡄⣺⣦⣤⣤⣼⣧⣤⣧⣤⣤⣤⣤⣤⣤⣴⣤⣴⣧⣤⣴⣷⣥⣦⣤⣷⣦⣼⣤⣴⣴⣴⢠⣔⣬⣿⣤⣽⣼⣤⣴⣿⣿⣿⣿
⣿⣿⣿⡟⡋⠛⣻⡟⠛⡛⡛⠛⢛⠛⡛⠛⡛⣿⣻⠛⢛⠋⣿⡏⠛⣿⡟⢙⠛⣻⡏⢹⠛⢛⣿⠛⡛⠛⠛⢛⢻⡟⡻⢹⡿⡛⠛⢛⠛⣿⢻⠛⢻⣟⠛⢻⣿⢛⠛⠋⣿⡏⠛⢟⠙⡟⠋⠙⡻⢛⣿⢛⠙⢛⣿⣿⣿⣿
⣿⣿⣿⡿⢿⣿⣿⣿⢿⡧⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠿⣿⢿⣿⣿⣿⣿⢿⡿⣦⣾⣿⣿⣤⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣟⣀⣠⠠⣃⣀⣄⣀⣔⣴⣸⣔⣀⣠⣺⣜⣠⣂⣆⣠⣢⣄⣧⣘⣼⣀⣀⣤⣐⣇⣰⣁⣸⡅⣐⣰⣀⣆⣀⣸⣠⣢⣀⣆⣀⣀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡏⢻⡟⠛⠛⠋⢟⢹⢙⢟⣿⡟⠛⣿⠛⠛⡋⢹⣟⡋⠛⠛⣻⢋⡻⢛⡟⣙⠛⢛⢛⣿⡋⠻⡛⢛⠛⠹⣛⠋⣿⢛⢻⠛⡛⣿⠙⢻⡟⢙⢟⣿⠉⢟⠛⣻⢟⢹⠛⠛⡿⡻⢩⡟⢟⠛⠛⠿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣾⣷⣶⡷⣶⣷⡾⣶⣷⣿⣷⣶⢿⡾⣷⡶⣶⣿⣶⣶⣶⣾⣶⣶⣾⣷⣶⣶⣷⣶⣷⣶⣾⢶⣶⣷⣶⣶⣶⣿⣶⣶⣶⣶⠿⣶⣾⡷⡶⣶⢿⣶⣶⣾⡾⣷⣶⣶⢷⣿⣾⣾⣷⣶⡤⣶⣿⣿⣿⣿⣿
⣿⣿⣿⣏⣂⣉⣀⣀⣂⣟⣀⣁⣀⣏⣊⣈⣡⣸⣇⣐⣋⣸⣐⣈⣐⣈⣘⣀⣻⣈⣰⡇⣘⣀⣒⣘⣀⣊⣇⣀⣾⣈⡈⢀⣋⣀⣈⣀⣊⣘⣿⣀⣈⣁⣇⣐⣇⣐⣁⢊⣾⣁⣑⣝⣇⣐⣁⣻⢀⣐⣨⣊⣁⣈⣿⣿⣿⣿
⣿⣿⣿⡏⢿⢿⡿⢿⠽⠿⡿⡿⠟⣽⠋⡿⠿⡏⠽⢿⠿⢿⠿⣿⠽⡿⡟⣽⠿⢿⠿⠽⠿⠿⢿⣿⠿⠿⠿⡯⢿⡿⢿⠿⠿⠿⡿⡏⠝⢩⠽⡿⠏⢿⡟⢿⢿⠽⠹⠿⡿⠫⢫⢿⣿⠿⡿⠏⣿⠿⠿⡿⡏⡿⣿⣿⣿⣿
⣿⣿⣿⣷⣶⠶⣶⣶⣶⣶⣶⣷⣶⣿⣶⣶⣶⣷⣶⣶⣶⣶⣶⣾⣶⣶⡷⣶⣶⣾⣤⢾⣶⣶⣾⣷⣶⣶⣶⣷⣶⣷⣶⣶⣶⢶⣿⣶⣶⡶⢶⣶⣶⢶⣷⣶⣿⣶⣶⣶⢶⣶⣮⣴⣷⣶⣶⣶⣿⣶⠶⠶⢶⣶⣿⣿⣿⣿
⣿⣿⣿⣏⣋⣸⣙⣉⣉⣏⣉⢉⢙⣉⣉⣉⣹⣉⣉⣈⣙⣉⣹⣙⣉⣉⣁⣿⣉⣹⣙⣈⣉⣏⣋⣉⣉⣏⣉⣏⣏⣉⣉⣍⣹⣈⣉⣋⣋⣃⡈⣹⣹⣈⣉⣉⣋⣉⣙⣉⣸⣹⣉⣏⣉⣉⣋⣉⣉⣹⣟⣸⣈⣉⣿⣿⣿⣿
⣿⣿⣿⣿⠿⠟⡿⠿⠿⠿⡿⠹⠿⠿⡿⡿⠿⠿⠿⠿⢿⠿⠿⢿⢿⠿⠿⠏⣿⠿⢿⡟⠿⠿⡟⢿⢿⠿⠿⠿⢿⡿⠟⣽⠿⠿⠿⠿⣿⡿⠿⠿⠹⠿⡿⡿⢿⠿⣿⠿⠿⠿⡿⠿⠿⠹⠿⢿⠿⠿⠿⢿⠿⡿⣿⣿⣿⣿
⣿⣿⣿⣷⣶⣶⣧⣶⣦⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣴⣶⣾⣶⣶⣶⣶⣿⣶⣾⣷⣶⣶⣶⢾⣾⣼⡴⣶⣶⣷⣶⣿⣶⣶⣶⣶⣿⣶⣷⣶⣶⣶⣷⣷⣾⣶⣿⣴⣶⣶⣷⣶⣶⣶⣶⣿⣶⣶⣦⣿⣶⣶⣿⣿⣿⣿
⣿⣿⣿⣏⣍⣉⣉⣉⢭⣉⣁⣉⣉⣩⣏⡉⣍⣉⣉⣩⣉⣉⣹⣿⣈⣹⣇⣉⣉⣅⣹⣇⣁⣩⣉⣈⣹⣉⣡⣏⣉⣉⣉⣉⢻⣏⣈⣉⣿⢉⣩⣩⣉⣉⣉⣩⣏⣍⣸⣍⣉⢩⡉⣉⣉⣉⣉⣸⡏⣉⣁⣍⣀⣉⣿⣿⣿⣿
⣿⣿⣿⡿⠿⠿⠻⠿⠿⠿⢿⡿⠿⢿⠿⠿⠿⠟⠿⠿⠿⠿⠿⡟⠿⡿⠿⠿⠿⢻⠿⠿⡟⠿⠟⠿⠿⡿⠻⡿⢿⠿⠿⠿⠿⠿⠿⠟⠟⠺⠿⠿⡿⠿⢻⠿⡿⠿⠿⠿⠿⠿⡷⠻⠿⢿⠿⠿⠿⠿⠿⢿⠿⠟⣿⣿⣿⣿
⣿⣿⣿⣷⣷⣰⣶⣾⣶⣶⣾⣷⣶⣿⣶⣷⣷⣶⣾⣷⣾⣶⣾⣷⣶⣷⣾⣶⣾⣾⣶⣷⣷⣾⣶⣾⣾⣷⣾⣾⣿⣶⣶⣷⣇⣷⣶⣶⣶⣾⣶⣴⣷⣷⣾⣶⣇⣱⣶⣶⣷⣷⣷⣶⣶⣷⣷⣷⣶⣾⣶⣿⣾⣶⣿⣿⣿⣿
⣿⣿⣿⣏⣉⣍⣍⣍⣉⢻⣏⣉⣽⣩⣉⣿⣉⡉⠩⠉⣭⣉⣿⣙⣅⣉⠩⡋⢈⣝⠩⣏⣹⡏⡉⢉⣩⢈⡍⠁⣉⣩⣯⣁⡫⣍⡉⢍⢍⠈⣩⢹⣿⢔⠉⣩⡈⣿⠉⠉⣿⠈⢉⡈⡍⣩⠉⡩⣩⣯⠉⡉⡁⣛⣿⣿⣿⣿
⣿⣿⣿⣿⠿⠟⠻⠿⡿⡿⠻⠿⠿⣿⠻⠿⠿⠿⡾⢾⢿⡿⠻⡿⣿⠿⠾⠿⠿⠿⢾⠿⢿⢷⡿⠟⣻⠿⠿⠻⡟⠻⢿⡿⡿⠟⠷⡟⠿⠿⣿⠻⢿⢻⢿⡿⠿⠿⢻⡿⠿⣿⢿⢿⠿⢿⢿⡟⠟⠿⡿⢳⡿⡟⣻⣿⣿⣿
⣿⣿⣿⣷⣥⣤⣔⣾⣧⣤⣼⣦⣧⣿⣴⣾⣼⣴⣥⣴⣽⣧⣤⣮⣿⣴⣧⣥⣼⣤⣴⣥⣭⣼⣮⣦⣿⣰⣤⣮⣦⣴⣽⣮⣆⣦⣬⣥⣴⣤⣿⣤⣾⣰⣵⣤⣤⣥⣼⣧⣮⣾⣴⣵⣤⣴⣽⣧⣥⣤⣬⣼⣮⣦⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡟⢻⢻⢻⢻⠛⠻⠛⡛⢻⢻⡟⡟⢻⠻⣿⢻⢻⢻⢻⠿⢟⣟⠛⠛⣿⣿⣿⡟⠟⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣾⣾⣶⣶⣾⣷⣶⣾⣾⣿⣶⣿⣾⣿⣶⣿⣾⣶⣶⣷⣷⣶⣾⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡏⡉⠩⡉⣉⡉⡍⢈⣉⣽⡏⠩⣭⡉⣍⠉⣀⣩⢉⢁⣉⣩⣻⡩⣩⣿⣈⣁⡩⣉⢍⣍⣉⣭⣏⣉⣉⣉⣍⣉⣉⣽⣩⣈⣉⣹⣇⣉⣉⣅⣹⣏⣉⣍⣋⣉⣩⣸⣉⣿⣩⣉⣉⣫⣈⣏⣁⣩⣋⣙⣿⣿⣿⣿⣿⣿
⣿⣿⣛⢛⠲⠷⡿⠿⠿⠟⠿⢿⢳⠻⠻⠿⠟⣿⠿⢻⡿⠿⠿⠿⡟⠿⡿⠿⢿⢿⠿⠿⠻⠿⠿⢿⠿⠻⠿⡿⠿⠿⠻⢻⠿⢿⠿⠿⠿⠿⠻⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⢻⡟⢿⡿⠿⢿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿
⣿⣿⣯⣼⣤⣼⣷⣧⣃⣦⣮⣤⣾⣴⣵⣧⣤⣷⣵⣼⣮⣶⣴⣽⣧⣴⣷⣶⣶⣽⣷⣾⣶⣾⣶⣿⣧⣶⣾⣟⣱⣶⣾⣾⣾⣿⣶⣸⣾⣷⣶⣶⣷⣷⣷⣆⣶⣾⣶⣶⣷⣾⣷⣾⣷⣶⣾⣷⣾⣶⣶⣾⣿⣿⣿⣿⣿⣿
⣿⣿⡏⡉⠁⢝⠀⢩⡏⢍⢉⠀⡩⢉⣿⠈⢍⠉⡩⢿⡏⡩⣻⡩⠈⠉⢹⡏⢨⠫⣽⡩⡉⣩⡫⣅⠋⢁⡫⡉⢹⡏⡹⠉⠍⠩⣍⣉⢍⢸⣇⣍⣿⢁⣉⣉⣽⣩⣈⣩⣉⣽⣇⣉⣏⣹⡏⣍⣏⣈⣀⣩⣿⣿⣿⣿⣿⣿
⣿⣿⡶⠿⡿⠿⠿⠿⡷⠾⠿⣿⠟⠾⠿⢿⡿⠟⠿⢿⡿⠿⢿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠟⣿⡿⠿⠿⠿⠷⠷⠿⠿⠿⣿⠟⠿⠿⣿⡻⠿⠿⠿⠿⠿⢟⣻⡿⠿⢿⡿⠿⠓⠻⠟⠿⠛⠿⣿⣿⣿⣿⣿⣿
⣿⣿⣮⣮⣦⣤⣮⣼⣤⣤⣥⣿⣦⣧⣤⣼⣷⣥⣤⣿⣧⣮⣤⣤⣧⣤⣮⣴⣦⣿⣾⣦⣰⣴⣽⣦⣮⣦⣿⣷⣾⣰⣶⣽⣦⣷⣶⣷⣿⣶⣷⣾⣿⣷⣵⣷⣷⣾⣾⣾⣿⣷⣷⣾⣷⣷⣶⣶⣷⣶⣶⣴⣿⣿⣿⣿⣿⣿
⣿⣿⡏⠩⡉⡉⡩⡉⡩⡫⢸⣉⡉⠉⣹⡉⢩⡏⢈⢅⠏⠉⢹⡩⡈⠈⠉⠩⣹⢉⡫⣉⣩⣷⠆⣆⠉⣽⠈⣩⡉⡁⣈⠍⠉⢈⢝⡉⣇⣍⣏⣅⠉⠋⣯⡉⣉⣩⡫⣿⢭⢅⣁⣩⣉⣸⣩⣉⣈⣽⣩⣉⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠶⠷⠿⠿⠿⢻⡿⠿⠟⡟⠷⡿⡟⢿⢿⢿⡿⠿⠷⢾⢿⠻⡿⠷⠾⣿⠿⠿⠿⠿⠿⠿⠿⠟⣿⠿⡿⣷⠿⠿⢿⠿⠟⠿⠿⡿⠟⣿⡿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠟⠿⠿⢿⡿⣿⠿⠿⠿⠻⠟⣿⣿⣿⣿⣿⣿
⣿⣿⣇⣨⣬⣤⣥⣤⣼⣇⣴⣥⣥⣝⣼⣧⣥⣬⣼⣧⣴⣵⣦⣿⣬⣮⣮⣤⣿⣥⣨⣂⣦⣮⣶⣮⣦⣿⣮⣦⣿⣴⣤⣶⣵⣥⣴⣤⣮⣦⣿⣧⣵⣿⣴⣇⣦⣮⣷⣼⣦⣶⣾⣄⣸⣧⣼⣷⣶⣾⣦⣴⣿⣿⣿⣿⣿⣿
⣿⣿⡏⠉⠉⠍⠉⣷⢘⠙⠉⠍⢸⡫⡋⢹⠩⡻⠁⠁⢘⢽⠫⠉⠩⠋⠩⠉⠉⠉⢹⡫⠍⠩⡋⠩⠉⠁⠉⠉⣯⠅⠉⢽⠉⠉⠩⡋⠉⣉⠩⠁⣯⠉⠍⡉⣏⠍⣹⠨⡫⠨⠋⠍⡩⢿⡪⡸⠉⡅⢹⠉⣿⣿⣿⣿⣿⣿
⣿⣿⡿⡿⡿⢿⠟⠿⡿⠻⠿⢿⡟⡿⣿⢿⠾⢿⣿⠿⢿⢿⠿⢻⡿⠿⠿⠟⢻⠟⠟⢿⢿⠲⣿⠿⣿⠿⡿⠶⠿⢿⠿⡿⡟⣾⠺⢿⣿⠟⢿⢿⡿⠿⡿⠾⠿⠿⠿⣿⢿⢛⡿⡿⢿⡟⠿⢿⠿⢿⡿⡟⣻⣿⣿⣿⣿⣿
⣿⣿⣮⣬⣦⣤⣥⣤⣤⣤⣤⣼⣧⣤⣯⣥⣤⣬⣧⣤⣤⣤⣤⣼⣧⣥⣅⣤⣤⣥⣤⣡⣿⣬⣦⣤⣿⣴⣥⣀⣀⣬⣤⣬⣤⣽⣤⣥⣿⣤⣤⣽⣧⣬⣦⣤⣬⣥⣬⣷⣵⣼⣧⣬⣼⣧⣤⣦⣤⣽⣮⣦⣿⣿⣿⣿⣿⣿
⣿⣿⡻⠫⠋⠋⠫⠛⣉⠛⠙⠝⢽⡏⢻⠃⠞⠁⠋⠫⠑⠫⠏⢸⡫⠫⠋⠋⠋⠉⠹⢿⠈⡙⣿⠙⡏⠙⠍⠛⠍⠋⢹⡏⠁⣾⠈⠩⠋⠁⠘⠍⠋⠉⠏⠉⡏⡆⠖⠩⠫⠋⣿⢉⢩⢙⠁⢿⡷⢰⠈⠫⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢻⣶⣿⣿⣿⡟⣿⣿⣻⣿⣿⣿⣻⣿⢿⢻⣿⢿⣿⣿⣿⡿⣿⢾⣟⡿⣷⣿⣿⡟⣻⢿⣿⡟⢿⢿⣿⣿⣷⡿⢿⣿⠻⡿⡿⠿⣿⡿⠿⡿⡿⡿⢿⡷⡗⣿⠻⣿⢿⡿⠻⡿⣿⣿⣿⣿⣿⣿
⣿⣿⣥⣤⣨⣠⣠⣬⣤⣤⣼⣧⣥⣤⣤⣥⣬⣤⣤⣥⣤⣿⣤⣿⣬⣤⣤⣼⣧⣼⣧⣤⣤⣤⣤⣬⣼⣇⣤⣤⣤⣕⣼⣧⣬⣤⣽⣧⣤⣴⣦⣿⣤⣤⣤⣤⣿⣥⣨⣈⣦⣬⣦⣤⣤⣿⣬⣢⣿⣧⣤⣤⣿⣿⣿⣿⣿⣿
⣿⣿⡟⠛⠃⠟⠘⠻⠟⠛⡟⢻⠛⠟⠟⠛⠻⠓⢿⠟⠟⠛⠛⠛⠟⠛⠛⢻⠛⠛⠛⠛⠚⠛⡟⡏⠘⠛⠻⡗⠛⠻⠛⠐⠛⢻⠻⠘⠛⢹⠛⠛⠟⡻⠛⠛⢻⠛⠻⡋⡇⠪⠂⠸⠛⢛⠚⠙⢻⡏⠘⠛⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣿⢿⣿⣿⣿⡟⣿⣾⣿⣿⣿⡻⣿⡟⣿⣿⣿⣿⣿⣿⣾⣿⣿⡟⢻⢻⣿⣿⣿⣿⠖⢻⣿⣿⣿⣿⡿⣿⣿⣿⣟⣿⢻⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣄⣤⣬⣤⣦⣬⣼⣤⣤⣤⣤⣬⣧⣤⣧⣤⣤⣤⣬⣼⣤⣥⣤⣤⣬⣤⣤⣧⣬⣧⣤⣤⣤⣤⣦⣤⣠⣧⣤⣼⣤⣿⣬⣤⣤⣥⣤⣥⣼⣿⣤⣼⣧⣤⣤⣤⣤⣤⣥⣤⣼⣴⣤⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡏⡇⠛⣻⢛⠛⠛⢘⠋⠛⡛⢻⠛⢛⠛⠛⡛⢛⡏⢚⠛⠛⢻⡟⠘⡟⢻⠘⡟⠛⠃⡟⠟⢰⢻⠛⠛⠓⠛⠛⠛⡛⠛⠛⢿⠛⠘⠛⡛⠛⡻⡇⢛⢻⢻⠛⠐⠛⠛⠛⠻⠛⡏⠞⠛⠻⠛⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⢟⣿⣿⣿⢿⢻⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⣿⣿⣿⣿⣿⡟⣿⢺⣿⣿⣿⣿⡿⣿⣿⣷⣿⣿⣿⣿⣿⡟⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣽⣰⣤⣴⣤⣼⣤⣴⣯⣤⣼⣇⣤⣦⣤⣤⣴⣿⣤⣠⣤⣦⣤⣤⣼⣧⣤⣷⣤⣤⣤⣿⣤⣾⣤⣤⣴⣿⣴⣤⣾⣬⣤⣤⣤⣿⣤⣢⣿⣠⣴⣤⣤⣤⣤⣤⣤⣤⣹⣧⣤⣤⣤⣤⣄⣄⣥⣤⣌⣿⣿⣿⣿⣿⣿
⣿⣿⡟⢛⠛⢛⢛⠛⠛⠛⢛⠛⢛⢻⡟⡛⠛⠛⡛⢛⡟⠛⢛⠛⠛⠻⡟⡛⢻⢙⠛⡻⠛⠛⢛⠛⠛⢛⣟⠛⢙⠛⢻⡛⠛⠛⠛⠛⣟⠛⢻⢛⠛⠛⠛⠛⡛⠛⠘⠛⢛⡟⠛⣻⠛⣻⠀⠛⢛⠛⢛⢛⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⡿⣿⣿⣧⣾⡿⣿⣿⢿⣿⣿⢿⣿⡿⣳⣿⣿⣿⣿⢷⣿⣿⣿⣾⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣿⣿⡿⣿⣿⢿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣦⣸⣧⣢⣤⣮⣄⣤⣴⣴⣿⣧⣴⣿⣄⣹⣿⣤⣼⣧⣤⣴⣴⣻⣧⣴⣵⣿⣧⣤⣤⣤⣼⣿⣤⣴⣤⣴⣤⣤⣬⣦⣦⣼⣧⣦⣼⡇⣤⣦⡄⣤⡄⣠⣤⣤⣦⣼⣿⣧⣴⣿⣤⣿⣦⣤⣴⣿⣿⣿⣿⣿⣿
⣿⣿⡟⠛⢹⠉⠛⠛⡋⠛⠛⡿⡛⢹⢙⠛⠛⡛⡛⠛⠛⡛⢹⢻⠛⢛⢛⠋⠙⣻⠛⢛⠛⠛⠙⠛⡻⡟⠛⡏⠛⠋⠙⠻⡛⡛⠛⣻⣛⠛⠛⠛⢻⠙⢛⠙⠛⠛⠙⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣾⣷⢶⣾⢿⣶⣾⣶⣿⣾⣾⣾⣷⣦⣦⡼⣾⣾⣾⣶⣿⣼⣿⣷⣿⣿⣿⣿⣼⣿⣿⣿⢿⣿⣷⣿⣿⣿⣿⣿⣿⢿⣿⢿⢾⣿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣠⣺⣀⣼⣰⣐⡀⣼⣤⣢⣇⣔⣕⣇⣂⣠⣤⣼⢐⣕⣔⣰⡇⣄⣔⣦⣠⣂⣠⣾⣐⣼⣀⡇⣪⣢⣤⣔⣴⣠⣺⣼⣀⣴⣀⣄⣔⣠⣕⣔⣯⣢⣄⣧⣦⣤⣾⣔⣕⣴⣥⣮⣮⣢⣴⣕⣤⣿⣿⣿⣿⣿⣿
⣿⣿⡟⢟⠙⠋⢟⠛⡻⡛⢻⠛⣿⣯⢩⠙⢟⠛⣻⠛⠛⠛⠛⣻⢛⠛⣿⠙⢛⠙⠛⡻⢛⡟⡛⢻⡟⠛⠛⢛⠙⡛⠋⠛⢛⡟⠛⡛⠛⠛⡛⢻⡏⠛⡛⡛⠟⠛⢛⣿⢋⡛⢛⢛⡟⢙⢛⢹⡟⡋⠛⠛⣿⣿⣿⣿⣿⣿
⣿⣿⣷⢶⣶⢶⣷⣾⣾⣶⢶⣶⣿⣿⣾⣶⢷⣵⣿⣿⡷⡶⣾⣾⣷⡾⣿⣾⣶⣶⣶⣶⣴⢿⣶⣿⣧⣷⣶⣷⣶⣷⣶⣶⠾⣧⢴⣷⣷⣦⣼⣾⡷⡿⣾⣷⣶⣶⢷⣿⣷⢷⣾⢾⣿⣷⣷⢾⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿
⣿⣿⣇⣀⣁⣘⣸⠀⣑⣅⣘⣸⣕⣀⣀⣿⣠⣐⣇⣀⣂⣀⣑⣤⣀⣀⣻⣕⣅⣟⣀⣀⣀⣨⣺⣃⣀⣀⣐⣸⡇⣠⣈⣀⣀⣪⣀⣾⣠⣪⣇⣀⣂⣀⣐⣤⣰⣻⣐⢄⣾⣠⣐⣀⣀⡈⢐⣀⡀⢸⣔⣠⣿⣿⣿⣿⣿⣿
⣿⣿⡟⠻⢟⢙⢿⠻⡟⠻⡻⠛⠛⢹⠛⣻⠛⠛⡻⠟⠛⣿⡍⠙⢻⢻⠛⠉⡿⡛⢹⠛⠛⡟⠟⢟⡏⢻⠟⢛⡟⠟⡟⠛⠛⢟⠟⢛⢛⠉⠋⢟⡟⡛⢻⢛⠙⠙⢻⢙⠙⠻⡋⡟⠛⣹⠻⠛⠛⢟⠛⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣾⣶⢧⣾⣦⣼⡶⣶⡶⣿⣤⣾⣾⣶⣴⢾⣶⣶⢶⣾⣶⣶⣿⡶⣾⢶⣶⣷⣶⢷⣧⣷⡶⣶⣷⡶⣷⡶⣶⣷⡷⣴⣷⣶⣶⠷⣿⣶⢾⡶⣶⣶⣿⢶⣶⣶⣶⡷⣶⣿⣦⡼⣴⢷⣶⣶⣿⣿⣿⣿⣿⣿
⣿⣿⣇⣋⣅⣑⣹⣔⣀⣑⣝⡁⢁⣸⣇⣘⣇⣐⣁⢁⣾⣐⣅⣿⣈⣀⣁⣯⣰⣁⣑⣀⣃⣀⣿⣀⣊⣧⣂⣈⣸⣇⣀⣂⣀⣠⣄⣁⣐⣯⣪⣸⣇⣑⣀⣀⣔⣸⣇⣐⣁⣁⣸⣇⣀⣿⣈⣀⣁⣈⣀⣨⣿⣿⣿⣿⣿⣿
⣿⣿⣟⠟⢟⠟⠛⣿⡍⢝⢿⠙⢟⡿⡻⢻⠻⡛⡋⠛⠻⡋⡿⠛⢻⠙⢟⠙⡻⠛⡏⢟⠉⣻⠛⢻⠟⡿⡻⢩⠟⣿⠛⠛⠛⠛⡛⢋⠛⢹⣿⠛⢛⢛⠟⠹⠟⢛⠛⡋⠛⠛⣿⢟⠙⠛⡛⠏⠛⠟⢛⠟⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣷⣶⣶⣾⣿⢷⣷⣿⣶⣷⣧⡼⢾⡾⣶⣷⣿⢾⣶⢿⣶⣿⡶⣷⣶⣶⣤⣷⣷⣾⢾⣷⣷⣷⣿⣾⣾⣷⣯⣼⣾⣿⣿⠷⣶⣶⡶⣿⣶⣷⣾⣶⣾⠷⣾⣾⡶⣶⣤⣾⡷⣾⣶⣷⣶⣶⣷⡾⣶⣿⣿⣿⣿⣿⣿
⣿⣿⡇⢀⣔⣜⡀⣼⣰⣼⣠⣀⣔⣠⣀⣔⣠⣇⣀⣨⣸⣕⣠⣆⠆⣄⢠⣧⡀⢢⣠⣢⣖⣀⡈⢐⣆⣤⣧⣄⡴⣠⣪⣀⣴⣿⣄⣕⣽⣀⣬⣺⣦⣀⡀⣪⣀⣰⣰⣂⣤⣰⣽⣀⣼⣠⣺⣤⣠⣕⣷⣀⣿⣿⣿⣿⣿⣿
⣿⣿⡟⠛⢛⠛⢛⠙⢛⠛⢛⢟⠛⠛⣻⠛⢉⡟⠛⡛⡻⡛⢛⠙⢙⢿⠛⠛⢙⠋⠙⣻⠛⢛⠏⠛⠹⡻⠛⣿⢛⠛⢻⠛⡛⠛⠻⣻⡻⠛⠛⡻⡛⠛⡛⡟⠛⣿⠛⠛⠛⢛⢛⢻⢟⠋⡟⡛⡟⠙⠉⢟⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⢿⣿⣿⣿⡿⣿⣷⣿⢿⡿⣿⡿⣿⣿⣧⡿⣿⣿⣿⢿⣿⣼⣿⡷⣿⣿⣿⡿⣴⣿⣿⣿⣾⣿⡾⣷⣿⣿⢾⣾⢿⣿⣿⢿⣿⣧⣾⢾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣷⠿⣧⣿⣿⣾⣿⡿⢿⣿⣿⣿⣿⣿
⣿⣿⡇⣤⣤⣬⡶⣰⣧⣦⣤⣤⣾⣴⣥⣤⣤⣦⣿⣴⣤⣴⣴⣤⣼⣯⣦⣬⣦⣴⣼⣧⣤⣾⣵⣦⣴⣴⣠⣦⣤⣰⣿⣤⣴⣤⣤⣤⣤⣦⣜⣿⣤⣿⣤⣿⢰⣵⣤⣤⣴⣤⣼⣤⣿⣤⣤⣦⣤⣿⣵⣤⣿⣿⣿⣿⣿⣿
⣿⣿⡟⠛⡛⠛⠛⠛⠛⢛⠛⠻⣟⠛⠛⠛⠛⡛⠛⠙⡻⢛⡏⠛⠛⠛⡛⡛⠛⠻⡋⢛⠛⢛⡟⡿⡋⡛⠻⠛⠛⢛⡏⢛⣿⠛⠛⢛⡝⡟⡛⠛⡛⠛⠛⡏⠛⢛⠛⡛⠛⠛⡟⠛⠛⠛⠋⠋⡏⡻⣻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣿⣿⡿⠿⣿⣿⣿⣿⣷⣿⣿⡧⣤⣴⣿⣿⢿⢿⣴⣿⣿⢿⣿⣧⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣤⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⢿⡿⢿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣧⣧⣤⣾⣦⣴⣤⣦⣤⣴⣿⢠⣴⣤⣤⣬⣦⣶⣼⣤⣼⣴⣤⣤⣾⣠⣤⣤⣯⣦⣤⣴⣯⣦⣼⣵⣤⣦⣴⣤⣦⣤⣤⣧⣤⠀⣷⣤⣦⣤⣤⣿⢠⣤⣴⣤⣤⣾⣴⠰⣤⣤⣤⣦⣤⣷⣤⣿⣿⣿⣿⣿⣿
⣿⣿⢟⠛⢻⡟⢛⠛⠛⢛⣿⠙⠛⠛⢛⣿⡏⢛⣿⠙⣿⠛⡿⡋⠛⡛⡛⢛⢻⡟⠛⠛⢹⡟⢛⠛⠛⢛⣿⠛⡛⠙⢛⢛⣿⢛⢛⠛⢙⠽⡛⡛⢻⡟⠋⣻⠋⢛⠛⡛⡛⠛⡋⠛⠙⡻⢛⣟⠛⡋⠛⠛⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⢿⣿⣿⡿⡿⣿⢿⣿⣿⢿⣿⣧⣽⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⣼⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣴⣿⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣕⣔⣤⣤⣦⣤⣦⣤⣤⣮⣼⣦⣠⣴⣄⣀⣤⣿⣠⣴⣧⣠⣆⣤⣴⣄⣧⣆⣄⣴⣄⣷⣄⣠⣂⣼⣇⣿⢠⣤⣲⣆⣀⣠⣲⣇⣄⣾⣀⣬⣺⣇⣤⣤⣔⣦⣀⣔⣀⣔⣧⣀⣾⣀⡇⣢⣃⣠⣀⣕⣿⣿⣿⣿⣿⣿
⣿⣿⢟⠛⠋⢛⠋⠛⢛⣿⣯⢩⠙⢟⠛⣛⡟⠛⢛⣿⢛⠛⢛⢿⠛⠛⠛⠛⢻⠛⢛⡟⡛⠛⠛⠋⢛⠟⠋⠛⠋⡛⠛⢻⡟⠛⠋⡻⠉⢛⡿⡛⡛⠙⠋⢟⠟⢻⡟⠛⣻⢛⠟⠙⡻⢛⡏⢛⣿⠛⢻⠟⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣧⣷⢿⣶⡾⢾⡿⣿⣾⣾⣷⡿⣾⣷⣶⣷⠿⣾⣿⣷⢿⣿⣷⣦⣷⡿⣷⣾⣷⣿⠶⡶⣶⣤⡷⣶⣶⣶⣾⣦⣼⢥⣷⣾⣾⣶⣾⣿⣮⣼⣶⣶⣷⣷⣾⣷⣶⣿⣷⣶⣶⣦⣤⡷⢷⣷⢶⣿⣶⣿⣿⣿⣿⣿⣿
⣿⣿⣇⣀⣔⣼⣇⣄⣮⣂⣠⣢⡂⢢⣀⣄⣤⣘⣧⣛⣄⣠⣺⣀⣸⣠⣪⡇⢀⣤⣰⣇⣹⣀⣀⣠⣺⣇⣀⡀⢢⣠⣂⣀⣀⣀⣎⣇⣀⣾⣤⣄⣔⣅⡀⢸⣀⣀⣀⣔⣐⣈⣐⣀⣰⣕⣀⣷⣀⣒⣁⣁⣿⣿⣿⣿⣿⣿
⣿⣿⡟⠛⠋⡻⠉⢛⡿⡻⠛⠙⠋⢟⠟⢻⡏⢛⣿⠉⡻⢻⡟⡛⡛⢛⠛⠛⠹⣻⣿⠙⠛⣿⠛⠛⠙⠛⢻⡟⢿⢛⢟⠋⢹⡟⠙⡟⢛⡏⢟⠟⠏⠛⣻⠛⣛⠝⡟⠟⠙⡉⢛⡏⡻⠛⢻⡏⢻⠛⢻⡟⣿⣿⣿⣿⣿⣿
⣿⣿⡥⡷⡶⣾⢶⣶⣿⢮⡼⣶⣶⡶⠷⢾⣷⣾⣾⣾⠾⣾⣷⣶⣶⣶⣶⢴⣶⣶⡿⢶⣵⡿⢶⢶⣶⣦⣼⣷⢾⡤⡷⣶⣾⣷⣶⠶⣶⡷⣷⡷⣶⣶⣾⣶⣶⣶⣶⣶⡶⣶⣶⣷⣾⣶⣾⣷⡶⢶⠾⣶⣿⣿⣿⣿⣿⣿
⣿⣿⣇⣀⣁⣑⣀⣂⣸⣐⣅⣈⣘⣿⣸⣐⣁⣿⢀⣁⣀⣁⣈⣂⣂⣷⣀⣐⣁⣸⣑⣐⣹⣐⣊⣀⣿⣀⣊⣀⣈⣂⣇⣈⣸⣕⣃⣀⣁⣁⣻⣀⣈⣸⡇⣁⣁⣈⣀⣊⣀⣁⣈⣸⣈⣪⡇⣀⣋⣈⣀⣑⣿⣿⣿⣿⣿⣿
⣿⣿⢟⠟⠋⢟⠏⠛⢛⣿⣯⠉⠻⠟⣿⠋⡻⢻⡿⡻⠋⠻⠛⣻⡻⢟⠛⢿⡿⡻⢩⡟⠛⡟⢛⡏⠛⠻⢽⠻⡋⠛⠟⣿⢟⠿⠋⠋⡿⣻⡿⡻⠻⠙⠻⢟⠟⢻⡟⢟⢿⢟⢟⠟⠟⢟⠿⠝⣿⡏⡽⠹⣿⣿⣿⣿⣿⣿
⣿⣿⡷⣦⣶⣶⣶⣶⣶⢶⣿⣶⣶⣶⢿⡶⣶⣶⡿⢾⣶⣶⣶⣿⣷⣶⣦⢾⣷⣶⢾⣷⣶⣶⣶⢶⣴⣶⢶⣶⣶⣶⣤⢽⣴⣷⣶⣶⣶⣾⣷⡦⣴⣶⣶⣶⣶⣾⣷⣶⣾⣷⣶⣶⣶⣶⣶⣶⢾⣶⣶⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣇⣈⣚⣁⣁⣭⣭⣐⡉⣼⣃⣉⣉⣂⣉⣈⣂⣀⡈⢸⡇⣪⣈⣪⢈⣈⣹⣗⣈⣉⣉⣉⠉⣐⣹⣑⣈⣙⣁⢑⣅⣩⣉⣹⣏⣉⣉⣿⣉⣸⣏⣉⠏⢉⣉⣙⣉⣉⣁⣉⣙⣉⣉⣹⣭⣭⣉⣻⣟⣉⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠿⠿⣿⠋⠿⢿⣿⡍⢿⠿⠿⣿⠻⢿⡏⠿⠿⠿⢿⠏⠿⠿⠿⠿⠿⠿⠿⠿⠏⣿⠿⠏⠿⠟⣿⠿⢿⢹⠏⠽⣿⢿⢿⠯⠿⡿⡿⠿⣿⠽⣿⡯⠿⣿⠿⠿⡏⠿⢿⡿⠿⣿⠿⠿⢿⠿⠿⡿⡿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣿⣶⣶⢾⣷⣶⣶⣶⣶⣿⢶⣾⣷⣶⣶⠷⣾⣶⣶⣶⣶⡶⣶⢶⣶⣶⣶⣿⣶⣷⠶⣶⣿⣴⣶⢶⣶⣶⣾⣶⣦⣶⣶⣶⢶⣶⣿⣶⣾⣷⣶⣿⣶⡶⣶⣶⣾⣷⣶⣯⣦⣶⣾⣶⡶⣦⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣝⣉⣉⣹⣏⣩⣈⣉⣽⣙⣉⣉⣿⣈⣉⣿⣉⣁⣃⣉⣉⣉⣙⣉⣁⣿⣈⢩⣿⣋⡏⣋⣋⣀⣿⣉⣹⣏⣘⣉⣉⣩⣏⣋⣋⣉⣙⣈⣉⣋⣉⣉⣉⣿⣋⣉⣁⢻⣏⣹⣹⢙⣙⣉⣉⣙⣙⣁⣉⣙⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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                    ䷩ 𝚕𝚒𝚗𝚎 419

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/07/31/Google_From_Pointing_to_Relevant_Sites_to_Pointing_to_Social_Co.shtml
    Gemini version at gemini://gemini.techrights.org/n/2025/07/31/Google_From_Pointing_to_Relevant_Sites_to_Pointing_to_Social_Co.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Google: From Pointing to Relevant Sites to
Pointing to Social Control Media to Actually Parroting Social Control Media as
"Facts"⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jul 31, 2025


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


Over time Google is only increasing_the_amount_of_slop and making it harder to
turn_off. It's basically a giant bubble waiting_too_explode/implode and "AI
Overviews_[are]_cutting_publisher_clickthrough_rates_by_50%,_new_report_finds".


This will discourage real journalism. The future is put at risk as plagiarists
and crackpots misuse terms like "hey hi".


Social Control Media misinformation, according to this_short_report, is now
being magnified and amplified by Google, which will in turn lead to more people
(who use Google) to spreading such misinformation. We wrote about this
yesterday and it's good to see more examples affirming there's a giant problem
here.


Google has_become_a_misinformation_company. Google_"AI_Overview"_is_not
intelligence_but_a_parrot (a real parrot is in fact vastly smarter than this).
It is being falsely marketed or sold as wisdom, sheltering trust that it does
not deserve. █


    * Over_at_Tux_Machines...
    * An_Illusion_and_Cult_Worship_of_Magnitude_(Ubiquity_as_"Victory")


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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣩⣉⣹⣉⣉⣈⣉⣈⣏⣉⣉⣁⣉⣩⣈⣉⣉⣉⣉⣉⣏⣹⣉⣉⠉⣁⣉⣉⣈⣏⣉⢉⣍⣉⣉⣭⣉⣋⣏⡈⢉⢉⣈⣉⣉⡹⣉⣉⣉⣁⣉⣉⣉⣉⡉⢍⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣈⣉⣉⣙⣯⣈⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣝⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣠⣬⣦⣬⣤⣿⣬⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣹⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣶⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 485

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/07/31/IRC_Proceedings_Wednesday_July_30_2025.shtml
    Gemini version at gemini://gemini.techrights.org/n/2025/07/31/IRC_Proceedings_Wednesday_July_30_2025.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ IRC Proceedings: Wednesday, July 30,
2025⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jul 31, 2025


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Sysupgrade⦈_


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


    * How_to_Report_Apple_Layoffs_Without_Saying_the_"L"_Word
    * Over_at_Tux_Machines...


⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⠿⠿⣿⠿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⣛⣛⠛⠁⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠉⠙⠻⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠙⢿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⢸⣿⣿⣿⡟⠁⠀⠀⠀⢀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀
⣤⣀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠈⠛⣻⣷⣿⠄⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣶⣦⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣤⣼⣿⠋⠉⠀⠀⠀⣠⣴⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀
⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣠⣾⣿⣿⠋⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣠⣾
⣠⣤⡀⢀⣈⡛⢿⣿⣿⣿⣿⣿⣷⣴⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣾⣿⣿
⣿⣿⣿⣿⡿⠻⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡟⠋⣠⣾⣿
⣿⣿⣿⣿⡀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠋⢠⣾⡿⠛⠁
⠉⠉⠛⠛⢿⡆⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⡿⠋⠀⢠⣿⠇⠀⠀⣴
⠀⠀⠀⠀⠘⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⣠⣾⣿⡿⠋⠀⠀⢀⠾⠁⠀⠀⢸⠏
⠀⠀⠀⠀⠀⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⣿⣿⠀⣠⣾⣿⣿⡿⠋⠀⠀⠀⠀⠈⠀⠀⠀⠘⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠋⠙⢿⡆⠀⠈⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⢀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀
⣿⠃⠀⠀⠀⠀⠀⠀⠀⠛⠻⠏⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⠛⠛⠁⠀⠀⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀
⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠀⠀⠀⠀⠀⠈⠛⠛⠛⠿⠿⠋⣀⣤⣴⣶⣦⣄
⣿⣿⣆⠀⠀⠀⡄⠣⣄⠀⠀⠀⠀⠀⢀⣾⣟⠀⠀⠀⢀⣠⣴⣶⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣟⣿⣿⣿
⣿⣿⣿⡄⠀⠀⠀⠀⠈⠻⣷⣦⣤⣴⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣟⣤⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣷⣾
⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⣿⣿⣿⣿⣿⠀⠻⢿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣿⣿⣿⣿⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠹⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠈⠻
⠀⠀⢸⣷⡄⠀⠀⠀⠀⣰⣷⠀⣠⣾⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣾⣿⣿⠏⠀⠀⠀⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡛⠛
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⣴⣿⣿⣧⣄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⠀⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⢿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⣼⣿⡿⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡏⠀⠀⠀⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠛⢻⣿⣧⣀⣤⣶⣿⣿⡀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠿⢷⡄⠀⠀⠀⠀⠈⠉⠙⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠛⠛⠉⠀⠁⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⣤⣤⣀⡀⠀⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣠⣿⣿⣿⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠉⠙⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣼⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠈⢻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢀⣾⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿
⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛
⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀
⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢀⣤⣴⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀
⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⣤⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠒⠒⠒⠚
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠈⢿⣿⣿⣿⠁⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠻⣿⣿⠀⠸⣿⣿⣿⣿⠀⠀⠀⢀⣠⣴⣦⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠈⠁⠀⠀⢿⣿⣿⣯⣤⣴⣾⣿⡿⠟⠋⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣽⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢾⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⣾⡿⠿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠑⡆⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡿⠛⢿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⣴⣷⡀⠀⢀⣀⠀⠀⠀⢀⣿⣿⡅⠀⠀⠙⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⣾⣿⣿⣶⣤⣾⣿⠿⣿⠀⠀⠀⠀⠙⠿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠐⠂⠀⠀⠀⠘⠟⠁⠀⣸⣿⣿⣿⣿⣿⣿⣿⠂⠉⠀⠀⠀⠀⠀⠀⢹⠿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿
⣠⣤⣴⣦⣤⣤⣀⠀⠀⢀⣠⣾⡿⠛⠻⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⡀⠀⢀⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣯⣄⣀⣀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣿⣿⣿⣿⣿⣿⠇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⠉⠙⠛⠿⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡏⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣦⣤⣀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢿⣿⣿⣿⣿⣿⣿⠋⠉⠻⣿⣿⡏⠉⠻⢿⣿⠇⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠂⠀⠀
⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⢀⣠⣤⣤⣴⣶⣶⣶⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀
⣿⡿⠿⠋⠁⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶
⣄⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣄⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣦⣄⡀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣶⣿⣿⡆⠀⠀⠀⠀⠀⠀⣠⣾⠏⠁⠀⢻⣿⣿⣿
⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣴⣿⣿⣧⣤⣤⣿⣿⣿⡿
⠀⠈⠙⠻⢿⡿⠛⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠐⠻⠛⠿⠿⠿⠿⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠛⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠏⠙⠻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣼⣿⣿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠃⠀⠀
⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠁⠀⠀⠀
⠀⢀⣴⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 812

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

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⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Moving on in Techrights, Geeks Gonna
Geek⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jul 31, 2025


Earlier today:


 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Richard_Stallman_reminds_me_of_the_age_when_tech_guys_were
   loveable_and_good_hearted_geeks_who_lived_amongst_us_mere_mortals_not_the
                   billionaire_greed_machines_they_became.⦈_


And added_some_hours_ago, "I told you Stallman was alpha."


This past week we published loads_of_articles. We had gotten tired of wasting
our time on Microsofters and their SLAPPs, which are basically driving straight
into a concrete wall and are, at best, deadlocked.


So we expect to spend the future wasting less time talking about their ordeals
(dumb lawsuits they should never have started) and instead write technical
articles about technical issues.


It's a shame that 18 months were spent dealing with over 5_KG_of_legal_papers
instead of being focused on our core topics.


In the coming weeks we plan to focus (as we explained last week) on patents,
GNU/Linux issues, and the occasional philosophical essays. That's what we like
to do and would rather do. █


    * Slopwatch:_Google_News_Has_Lost_the_Plot
    * Sabotaging_Linux_on_Behalf_of_Microsoft_With_UEFI_'Secure'_Boot_(De_Facto
      Remote_'Kill_Switch'),_Then_Defaming,_Stalking_and_Harassing_Critics_of
      'Secure'_Boot_for_12_Years,_Then_SLAPPing_Their_Spouses_and_Them


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⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
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⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⡀⢀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢃⠌⣠⠁⡁⠐⢸⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢄⢸⣿⣒⡒⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠉⡜⠸⢀⠈⠀⣸⣿⣿⣿⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⢠⡄⢠⢠⡤⢤⡤⣤⠤⣤⠄⠀⠀⠀⢀⠄⡀⠀⣰⡊⠈⠛⠓⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣖⡲⢰⠀⣶⢰⡖⢾⣿⣿⣿⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠭⠽⠘⠧⠼⠸⠇⠸⠇⠸⠀⠿⠀⠀⢀⣴⣾⣶⣿⠇⠅⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠛⠘⠓⠛⠘⠃⢸⣿⣿⣿⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠛⠒⠛⠁⠀⠐⠒⠑⠊⠛⢻⣿⣿⣿⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⣿⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 892

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/07/31/Over_at_Tux_Machines.shtml
    Gemini version at gemini://gemini.techrights.org/n/2025/07/31/Over_at_Tux_Machines.gmi

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


posted by Roy Schestowitz on Jul 31, 2025


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Shrug.opus⦈_


⚓  Updated This Past Day⠀⇛


   1. ⚓ Programming_Leftovers⠀⇛


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      ⚓  New⠀⇛


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   9. ⚓ Web_Browsers:_Curl,_Webrings,_and_Numbers_Station_Simulator⠀⇛


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  19. ⚓ 5_Linux_KDE_Plasma_Features_that_Completely_Changed_How_I_Use_My_PC⠀⇛


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  20. ⚓ Euphonica_–_Cool_New_GTK4_MPD_Client_Work_in_Process⠀⇛


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  21. ⚓ Free_and_Open_Source_Software,_howtos_and_Installations⠀⇛


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  23. ⚓ DietPi_July_2025_Update_Adds_Orange_Pi_3_Support_and_Prepares_for
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           The July 2025 release of DietPi v9.15 introduces support for
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  24. ⚓ Welcoming_New_Faces_to_the_Thunderbird_Community_Team⠀⇛


           Thunderbird is (and has always been) powered by the people


  25. ⚓ XDA_and_Storage_With_GNU/Linux_at_home⠀⇛


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  27. ⚓ HowTo_Geek_on_Batch_Renaming,_Daemons,_Distros,_and_More⠀⇛


           4 recent articles


  28. ⚓ Jack_Wallen_on_Distributions_and_Operating_Systems⠀⇛


           a pair of articles


  29. ⚓ Linux_Kernel_Bits_and_Linux_Foundation_Still_Tarnishing_the_"Linux"
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  30. ⚓ PCLinuxOS_Magazine's_Latest⠀⇛


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           Some of the latest articles


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      1064 /n/2025/07/25/This_Laptop_Has_a_Raspberry_Pi_inside.shtml


      1056 /n/2025/07/28/Linux_6_16.shtml


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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣠⣴⣶⣶⣿⣿⣿⡿⣿⣿⣿⠿⣿⢛⣻⡟⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣴⣿⡯⣽⣿⠯⣿⢩⣻⡾⣧⣛⣿⣈⣻⣧⣺⣿⣧⣿⣽⣿⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⣿⣿⣷⢾⣿⣬⣿⣾⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⢻⠛⣿⣎⡇⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠛⠛⠛⠋⠉⠀⢹⣿⡏⣾⣡⣼⣴⣼⣿⣿⣾⣿⣾⣬⣿⣯⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⠿⠟⠛⢻⡿⠛⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣻⣟⣿⢿⡿⡷⢶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣭⣼⣤⣸⢉⣽⢽⣹⢫⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣶⣿⣬⣼⣻⡷⠶⡙⠙⣿⣷⣦⣤⣀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⠿⠛⠀⠀⠀
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                    ䷩ 𝚕𝚒𝚗𝚎 1159

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/07/31/Sabotaging_Linux_on_Behalf_of_Microsoft_With_UEFI_Secure_Boot_D.shtml
    Gemini version at gemini://gemini.techrights.org/n/2025/07/31/Sabotaging_Linux_on_Behalf_of_Microsoft_With_UEFI_Secure_Boot_D.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Sabotaging Linux on Behalf of Microsoft
With UEFI 'Secure' Boot (De Facto Remote 'Kill Switch'), Then Defaming,
Stalking and Harassing Critics of 'Secure' Boot for 12 Years, Then SLAPPing
Their Spouses and Them⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jul 31, 2025,
updated Jul 31, 2025


The sorts of stubborn_lunatics we've been dealing_with for 18 months (since
February_2024)


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Brett_Wilson_LLP;_Meanwhile_in_America:_US_police_and_Brett
                             Wilson_LLP_customer⦈_


Microsoft is very_deep_in_debt. By the end of this week the latest figures will
go public, revealing (albeit quietly) by how much that debt grew. See,
Microsoft isn't selling much except buzzwords and hype (rebranding existing
things as "hey hi", then claiming growth in "hey hi"). Sales of Windows are
down ("licences" for use of Windows are not sales per se). There are no new
products, just lots of shutdowns (even whole divisions and offices).


Quite frankly, contrary to what the media claims this week, Microsoft has
serious_problems.


Now they sabotage GNU/Linux some more and try to tell us, "this is OK!"


We said we'd bring up this topic at least once a week, hence this exception to
the_rule [1, 2].


Pointing to this_journal, a reader quotes a comment about certificates in UEFI
'secure'_boot_poised_to_'expire': "This should be on the front page. Can't you
just roll the computer's clock back a few years before each boot up?"


People are very angry at enablers of this. One reader told us, "time to mention
[insult omitted] matt and his [insult omitted] there with his role in deploying
Microsoft shim in place of a platform independent solution which could have
avoided vendor lock-in".


The said thread is dated Monday and it's entitled "Too Old For This Nonsense":


     I need to slow down, to take some time off. My brain has melted.


     I'm a bit stuck with bootloaders. Since UEFI came along, it looks
     like you just need a file in the right directory called BOOT.X64 at
     the bare minimum to get something running. I need to install GRUB.
     Why do I need to do command-line-fu? Can I not just drop a binary
     into the right subdir and a .conf file?


     Some years ago (about 7) I used the tools in ISOLINUX to boot a USB
     stick. Of course, I never wrote down what I did. That was on a UEFI
     system too.


     I know that you sometimes need to register the bootloader with the
     firmware, in the menus, by browsing the filesystems and selecting the
     binary.


"Alternatively," said one comment jokingly, "give up Linux (and watch TikTok/YT
or do whatever you enjoy)."


A later comment spoke of "UEFI and its time bomb payload", saying: "Wait. The
best is yet to come."


Here is the explanation with a diverse set of press links:


     The mini OS known as UEFI has more than bug doors and other problems:
     it's payload of an expired key will raise its ugly head in September
     of this year. So unless you've gone through the trouble of making and
     self-signing your own keys, then restricted_boot_systems_will_cease
     to_start_at_that_time [tomshardware.com]. We were warned_back_in_2012
     [archive.org].


     In other words, a_great_many_GNU/Linux_desktop_and_laptop_systems
     will_expire_soon [lwn.net], thanks to M$ payload in UEFI:


          Linux users who have Secure Boot enabled on their systems
          knowingly or unknowingly rely on a key from Microsoft that
          is set to expire in September. After that point, Microsoft
          will no longer use that key to sign the shim first-stage
          UEFI bootloader that is used by Linux distributions to boot
          the kernel with Secure Boot. But the replacement key, which
          has been available since 2023, may not be installed on many
          systems; worse yet, it may require the hardware vendor to
          issue an update for the system firmware, which may or may
          not happen. It seems that the vast majority of systems will
          not be lost in the shuffle, but it may require extra work
          from distributors and users.


                — Linux_and_Secure_Boot_certificate_expiration
                [lwn.net]
So this is a problem for all of us to "look forward" to (like last_August).
Thanks, Microsoft. █


    * Moving_on_in_Techrights,_Geeks_Gonna_Geek
    * next


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

                    ䷩ 𝚕𝚒𝚗𝚎 2406

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

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⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Slopwatch: Google News Has Lost the
Plot⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jul 31, 2025


The frequency or the prominence of LLM slop seems to have grown in Google News.
The slop is drowning out the signal. It's really bad. We'll come to that in a
moment.


So Google News links to Linux Journal, which based on the structure alone gives
away its misuse of bots:


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Veil_of_Vigilance:_Tails_6.0’s_New_Frontiers_in_Surveillance
                                 Resistance⦈_


Pure nonsense. Same as LinuxSecurity with LLM slop, i.e. the usual:


 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Hardening_Open-Source_Web_Applications:_Best_Practices_for
                           Security_Professionals⦈_


Bland headline and pointless text. The wrong output of a lazy "prompt
engineer"?


Then there's this relatively new slopfarm in Google News:


 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Linux_Kernel_6.16_Released._New_Features_and_Improvements
                          Without_Much_Woww_Effect⦈_


It's slop, as usual:


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Last_weekend_the_final_version_of_the_Linux_kernel_6.16_was
                                  released⦈_


Google News is also promoting FUD.


Consider this latest_misdirection. Now a pair of slopfarms run by the same
people and containing only slop images are propped up by Google News:


  🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Gunra_Ransomware’s_New_Linux_Variant_Uses_100_Encryption
                   Threads_and_Partial_Encryption_Feature⦈_


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Gunra_Ransomware_New_Linux_Variant_Runs_Up_To_100_Encryption
                 Threads_With_New_Partial_Encryption_Feature⦈_


Fake articles about what's really (originally) a Windows issue.


Also boosted by Google News today... at least 4 fake articles about "Linux".
This is all from a slopfarm containing slop images and fake author names:


    🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇_Linux_Kernel_6.17_Drops_Uniprocessor_Builds_for_SMP
                                Optimization⦈_


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇_Lyon_Switches_to_Linux,_Open-Source_from_Microsoft_by_2026⦈


   🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇_Sparky_Linux_7.8_‘Orion_Belt’:_Lightweight_Windows_11
                                 Alternative⦈_


               🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇AMD_Ryzen_Threadripper_9970X⦈_


So basically it has been a bad day in Google News. Almost the majority of
articles returned for "Linux" are fakes. █


    * Links_31/07/2025:_Australia_Restricts_YouTube_Access,_Personal_Privacy_at
      Risk
    * Moving_on_in_Techrights,_Geeks_Gonna_Geek


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

                    ䷩ 𝚕𝚒𝚗𝚎 2798

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/07/31/theregister_com_The_Voice_of_Microsoft_US.shtml
    Gemini version at gemini://gemini.techrights.org/n/2025/07/31/theregister_com_The_Voice_of_Microsoft_US.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ theregister.com: The Voice of Microsoft
US?⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jul 31, 2025


theregister.com, formerly theregister.co.uk or The Register UK, is now_run
mostly_by_Americans. Hence, we sometimes call it The Register US or The
Register MS. Since I woke up at around 3AM and until now (8:30AM) the front
page of The Register US has persistently been_"Microsoft_sez":


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


I know enough and have heard enough about the_Editor_in_Chief and how he was
put in charge by Chris, his successor, who became_GAFAM_(US)_staff.


My trust in this publisher is rapidly waning. It basically sold_out. Instead of
"biting the hand that feeds IT" it was fed to that hand. █


    * Yes,_You_Can_Love_and_Adore_Things_Whilst_Also_Criticising_Them
    * A_Lot_of_Supposedly_"Successful"_Businesses_Are_Just_Debt-Racking_Vessels
      Without_Any_Prospects_of_Financial_Sustainability


⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠰⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⡿⢿⣿⢿⢿⢿⢿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣽⠀⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣵⣮⣴⣿⣼⣴⣽⣧⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠰⢄⡘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣿⣯⣫⣿⣉⣿⣉⣹⣿⣻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠞⣠⣾⣾⣿⣦⣄⠙⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠂⡀⣿⣿⣿⣿⣿⣿⠓⠢⠀⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢭⣿⠿⠿⢿⡿⣿⠟⠻⠿⠿⣿⠿⣿⠿⠛⠀⠀⠀⣽⣿⣿⣿⣿⣽⣿⡀⡆⠀⢼⣿⣿⣟⣿⣭⣽⣥⣤⣬⣩⣯⣬⣯⣭⣭⣿⣥⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⣶⣿⣷⣶⣶⣾⣿⣿⣿⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⣿⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣛⣿⣟⡛⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠿⢿⣟⣿⢿⣿⡿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣯⣵⡆⢀⣒⣿⣿⣷⣶⢿⢾⣾⣳⣛⣀⠀⢻⣿⠻⡙⣻⠿⠿⢿⣿⣛⣻⣿⣛⣿⣿⠿⢿⣯⣟⣿⣿⣿⢿⢿⣿⣿⣿⣿⢿⢿⠿⣿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⠲⠶⢿⣿⣿⣟⢻⣿⣿⣿⢯⣭⢟⢻⠿⣻⣶⣿⣇⢸⣿⣿⣯⣿⣿⡑⣠⡆⠈⡯⡍⠰⠈⠏⠨⠗⢻⣿⣿⣿⢿⣥⣥⣾⣿⣿⠿⢾⣧⣾⣽⣿⣽⣿⣬⣦⣥⣤⣧⣽⣴⣼⣧⣿⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢩⠥⢔⣛⣻⣿⣿⣿⣿⠧⣴⣶⠯⢩⣗⠳⠶⣿⣮⣷⣶⡶⠨⣥⡭⠭⣿⣽⠀⠀⠁⢀⣧⣀⡀⠀⠘⠒⠚⠛⠉⠛⠀⠉⣿⣿⣿⣿⣛⣿⣿⣿⢿⣿⣿⣿⣿⣐⣍⣽⡉⣹⣯⣉⣋⣿⣤⣋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠁⠙⠒⠛⠁⠐⠉⠉⠉⠙⠛⠚⠋⡉⠡⠛⠋⠩⢛⠟⠏⠨⠭⣯⣙⡿⢿⣆⡑⠋⠻⢷⣦⡯⠉⡒⢦⡤⡶⠶⠾⠿⠟⠛⠉⢙⣟⣿⣿⣭⣿⣿⢤⡯⢽⣿⠛⢿⣿⣿⠿⣿⣿⡿⣿⠿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠀⠀⠀⠀⠂⠠⠠⣐⡢⠄⠡⣗⡂⢬⣬⣤⠤⢀⣀⣦⣝⠤⣓⢠⡄⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢿⡳⣾⣝⡛⠏⠙⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠄⠀⠀⠀⠒⠒⠒⠒⠂⠀⠂⠈⠁⣆⠁⠑⢐⡽⠛⠻⠿⡻⠘⢧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠉⠈⠉⠂⠛⠃⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠈⠉⠀⠀⠀⠘⠃⠚⠉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠢⡶⢐⢲⠰⡂⡶⢖⢸⠂⢰⠲⠂⡄⠖⠄⣰⢐⢺⠂⢖⠐⢲⠐⠀⠆⢖⠀⡇⡀⡖⢐⠇⢐⠆⢻⠀⠴⣰⠀⢐⠢⡠⡖⢐⠆⢐⡧⡀⠆⢰⠆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⡀⢀⠀⢀⡀⠀⣀⠀⣀⠀⢀⡀⠀⡄⢀⠀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣠⣟⣉⣟⡉⣻⣯⣯⣻⣳⣃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠀⠈⠈⠀⠈⠀⠈⠀⠀⠀⠀⠁⠈⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠙⢿⡟⠛⣻⢟⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠰⠀⠀⠀⠦⠀⠀⠀⠰⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⣾⡿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣾⣿⣿⣿⣿⣶⣿⣶⣾⣷

                    ䷩ 𝚕𝚒𝚗𝚎 2859

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/07/31/Yes_You_Can_Love_and_Adore_Things_Whilst_Also_Criticising_Them.shtml
    Gemini version at gemini://gemini.techrights.org/n/2025/07/31/Yes_You_Can_Love_and_Adore_Things_Whilst_Also_Criticising_Them.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Yes, You Can Love and Adore Things Whilst
Also Criticising Them⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jul 31, 2025


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇BSD_and_UNIX⦈_


Criticising something and disliking some things aren't opposites (as concepts/
attitudes). There are famous sayings along the lines of, when you stop
criticising something or give up offering ways to improve, then that means
you've given up on that something (or someone, sometimes). The idea that you're
attached to something is key. If you care about something or someone, then
you'll very much care about the destination of that something or someone,
right? If you quit caring, and thus quit criticising, that's not the same as
acceptance. It might even be a sign of apathy, maybe rejection.


There are all sorts of projects and companies that we criticise here all the
time. Criticising is OK. It ought to be welcomed sometimes. I too read
criticisms of myself, my sites, my articles. I view some of those as
constructive and some as mean-spirited attacks, depending on who or what does
the criticism (which implies the "whys").


Decades ago (maybe too much yearning for the 1990s, that's a giveaway) we were
able to disagree with people, even in the open. Even with employers! On many
occasions I openly criticised my bosses, sometimes to their face (even as a
teenager). Before I quit Sirius I confronted my bosses for a number of years,
preferably over the phone (where making excuses and preparing carefully-crafted
lies would be harder). E-mail criticism was easier to deflect, in my
experience.


By 2022 it was already becoming very hard to criticise bosses. Doing so was
feasible, but they would just not listen. Lots of that foolish, infantile,
"either you're with us, or..."


Regarding politics, which isn't our focus in this site, back in the old days we
could argue with people - even close colleagues - without words like "Woke" or
"communist" or "fascist" being tossed around.


Is society being divided and groomed/primed to be resistant to constructive
criticism?


For what it's worth, it's OK to argue with BSD folks (the operating systems or
the licences); it's like brothers and sisters having arguments. Our overall
goals are pretty much the same, even if not 100% overlapping. A lot of our
"blood" (code) is also overlapping, as we stand to benefit from kinship.
Opinionated people can have fierce arguments with siblings and parents and
still love them deeply. █


    * Links_31/07/2025:_War_in_Ukraine,_Security_News,_and_Cyberattacks_Against
      Journalists_on_the_Rise
    * theregister.com:_The_Voice_of_Microsoft_US?


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                    ䷩ 𝚕𝚒𝚗𝚎 2959

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Gemini Links 31/07/2025: Fake Money and
Gemini Diaries⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jul 31, 2025


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Core_dumped⦈_


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o § Personal/Opinions⠀➾


                # ⚓ Entity_Observation_Diary⠀⇛


                       Today I was blessed with tips from two additional
                       members of my beloved advisory council.


                # ⚓ ~hammie's_Tiny_gemlog⠀⇛


                       Where does the time go? Today I cleaned up some odd
                       test pages here and updated my books page. My
                       manager recently went to Scotland and brought back
                       some Tunnock's Caramel Log bars, which are very
                       rare in the south of England.


          o § Technology and Free Software⠀➾


                # ⚓ Cryptocurrency⠀⇛


                       When Bitcoin was first emerging I was still at
                       school. It seemed interesting, right up until I
                       found out that just to set up a wallet you needed
                       to complete a huge download which would have
                       completely blown the family internet data quota and
                       filled up a good chunk of my storage. Now of course
                       I realise I just needed to hold onto some coin for
                       a few years and it would have eventually increased
                       in value enough to easily cover the cost of the
                       internet excess and a new HDD. But even then I
                       could only find places in Melbourne as the nearest
                       to actually convert Bitcoin with AUD anyway, so the
                       wallet probably would have stayed empty.


                       Plus investment wasn't really on my mind anyway. I
                       was keen on an alternative to Credit Cards and
                       PayPal, which had fees, and equally important back
                       then, 18+ age restrictions. Since then, Bitcoin
                       went insanely volitile and the trickle of services
                       accepting it for payment shrank back again, taking
                       my interest away with it. So I was slow to discover
                       there are now "stablecoins", and PayPal even has
                       one itself. In theory these do seem easier to use,
                       except I've never seen anyone but my VPS provider
                       accept them (and even their PayPal payment option
                       has been broken for years (though I reported it to
                       support), so I rather doubt that it works). Plus
                       I've since developed misgivings about
                       cryptocurrency which I've struggled to fully
                       express.


                # § Internet/Gemini⠀➾


                      # ⚓ Strange_Goings-On_At_Ultimatum_Labs⠀⇛


                             Strange goings-on because it's strange that
                             I'm still obsessing over some of this stuff.
                             Nevertheless, there are some related Gemini-
                             related updates to report.


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


    * An_Illusion_and_Cult_Worship_of_Magnitude_(Ubiquity_as_"Victory")
    * Links_31/07/2025:_War_in_Ukraine,_Security_News,_and_Cyberattacks_Against
      Journalists_on_the_Rise



                    ䷩ 𝚕𝚒𝚗𝚎 3068

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 31/07/2025: Australia Restricts
YouTube Access, Personal Privacy at Risk⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jul 31, 2025


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Gopher⦈_


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * Leftovers
          o Science
          o Career/Education
          o Hardware
          o Health/Nutrition/Agriculture
          o Proprietary
                # Artificial_Intelligence_(AI)_/_LLM_Slop_/_Plagiarism
                # Social_Control_Media
          o Security
                # Privacy/Surveillance
                # Confidentiality
          o Defence/Aggression
          o Environment
                # Energy/Transportation
                # Wildlife/Nature
                # Overpopulation
          o Finance
          o AstroTurf/Lobbying/Politics
          o Censorship/Free_Speech
          o Civil_Rights/Policing
          o Internet_Policy/Net_Neutrality
          o Monopolies/Monopsonies
                # Patents
                # Copyrights
    * § Leftovers⠀➾


          o § Science⠀➾


                # ⚓ Science Alert ☛ 'Bad_Omen':_An_Ancient_Pyramid_in_Mexico
                  Collapsed_Into_A_Pile_of_Rubble⠀⇛


                       Extreme weather triggered a tragedy.


                # ⚓ Science Alert ☛ Mysterious_2,500-Year-Old_'Gift_to_The
                  Gods'_Finally_Identified⠀⇛


                       It's still enjoyed today.


                # ⚓ Science Alert ☛ This_Potent_Psychedelic_Mysteriously_Echoes
                  Near-Death_Experiences⠀⇛


                       Fascinating similarities, but differences too.


                # ⚓ Science Alert ☛ Engineers_Weigh_Up_Returning_to_Ancient
                  Roman_Concrete_Recipes⠀⇛


                       The ancients might have been onto something.


                # ⚓ Science Alert ☛ Study_Reveals_The_Shocking_Amount_of
                  Plastic_We_Breathe_in_Every_Day⠀⇛


                       It's a lot.


          o § Career/Education⠀➾


                # ⚓ JURIST ☛ UCLA_reaches_$6.13_million_settlement_with_Jewish
                  plaintiffs⠀⇛


                       The University of California, Los Angeles (UCLA)
                       announced on Tuesday that it has reached a
                       settlement agreement in a lawsuit brought by a
                       Jewish faculty member and students. The initial
                       complaint, filed in June 2024, emphasized that
                       Jewish students were unlawfully prevented from
                       “accessing the heart of campus,” including
                       classroom buildings and the main library.


                # ⚓ NYPost ☛ Brown_University_strikes_deal_with_Convicted_Felon
                  administration_to_restore_half_a_billion_dollars_in_federal
                  funding⠀⇛


                       “The Forrest Dump Administration is successfully
                       reversing the decades-long woke-capture of our
                       nation’s higher education institutions,” Education
                       Secretary Linda McMahon said.


                # ⚓ Pro Publica ☛ Idaho_Schools_Are_Breaking_Special_Education
                  Laws,_Failing_Students_With_Disabilities⠀⇛


                       Kali Larsen sat at her desk at Fruitland Elementary
                       School in Idaho earlier this year, trying to read
                       the test questions as her classmates silently
                       worked around her. Her anxiety climbed as she
                       stared at the paper. She asked to use the bathroom
                       and left the room.


                       Her mother, Jessica Larsen, had been substitute
                       teaching that day when she received a call from the
                       front office, notifying her that her 9-year-old
                       daughter was having a panic attack. Kali, now 10,
                       has dyslexia and struggles with reading and
                       writing, Larsen said.


          o § Hardware⠀➾


                # ⚓ Atlantic Council ☛ To_secure_reprogrammable_chips,_the_US
                  must_address_supply_chain_risks⠀⇛


                       This policy brief analyzes the FPGA supply chain
                       for US firms and the trade-offs these companies
                       make among risks to cost, availability, and
                       security; assesses how those trade-offs will change
                       given a shifting global environment; and recommends
                       policy interventions for the US government.


                # ⚓ Tom's Hardware ☛ Chinese_CPUs_are_closing_the_gap_on_AMD_—
                  next-gen_Zhaoxin_chips_feature_96_cores,_12-channel_DDR5
                  memory,_and_128_PCIe_5.0_Lanes⠀⇛


                       Zhaoxin has announced the new KaiXian KX-7000N and
                       Kaisheng KH-50000 processors at the World
                       Artificial Intelligence Conference 2025.


                # ⚓ Hackaday ☛ The_LumenPnP_Pasting_Utility:_Never_Buy_Solder
                  Stencils_Again?⠀⇛


                       Over on his YouTube channel the vivacious [Stephen
                       Hawes] tells us that we never need to buy solder
                       stencils again!


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ Federal News Network ☛ NIH_director_talks_grant
                  terminations_controversy,_Bethesda_Declaration,_making
                  America_healthy⠀⇛


                       "We haven't yet achieved the mission of the NIH,
                       which is research that improves the health and
                       longevity of the American people," Jay Bhattacharya
                       said.


                # ⚓ New York Times ☛ Canada’s_Measles_Cases_Surpass_U.S.,
                  Alberta_Officials_Push_for_State_of_Emergency⠀⇛


                       Some doctors in Alberta have criticized officials
                       for not declaring a health emergency in the western
                       province where measles infections are surging.


                # ⚓ Federal News Network ☛ How_Healthcare.gov’s_botched_rollout
                  led_to_a_digital_services_revolution_in_government⠀⇛


                       The botched rollout of a federal website 12 years
                       ago became a turning point for digital services
                       across government.


                # ⚓ Federal News Network ☛ Dihydroxyacetone_Man_administration
                  is_launching_a_new_private_health_tracking_system_with_Big
                  Tech’s_help⠀⇛


                       The Forrest Dump administration is pushing for
                       Americans to upload personal health data to new
                       apps run by private tech companies.


          o § Proprietary⠀➾


                # § Artificial Intelligence (AI) / LLM Slop / Plagiarism⠀➾


                      # ⚓ Security Week ☛ Flaw_in_Vibe_Coding_Platform_Base44
                        Exposed_Private_Enterprise_Applications⠀⇛


                             Base44 owner Wix quickly patched a critical
                             authentication bypass vulnerability
                             discovered by researchers at Wiz.


                      # ⚓ Zimbabwe ☛ You’ve_Seen_These_Hey_Hi_(AI)_Features
                        Before,_Now_Google’s_Putting_Them_in_Search [Ed: Slop
                        is not Hey Hi (AI)]⠀⇛


                # § Social Control Media⠀➾


                      # ⚓ France24 ☛ Australia_widens_teen_social_control_media
                        ban_to_YouTube,_scraps_exemption⠀⇛


                             Australia said on Wednesday it will add
                             YouTube to sites covered by its world-first
                             ban on social control media for teenagers,
                             reversing an earlier decision to exempt the
                             Alphabet-owned video-sharing site and
                             potentially setting up a legal challenge.


                      # ⚓ New Yorker ☛ Getting_in_Marc_Maron’s_Head⠀⇛


                             The podcast host recommends three recent
                             favorites—about the gentrification of punk,
                             what makes a great actor, and the corrosive
                             influence of social-media platforms.


          o § Security⠀➾


                # § Privacy/Surveillance⠀➾


                      # ⚓ Purism ☛ AI_Puts_Your_Personal_Privacy_at_Risk⠀⇛


                             For government agencies and enterprise
                             systems, the implications are even more
                             grave. When models trained on third-party
                             datasets begin interfacing with federal
                             workflows, without strict
                             compartmentalization, they become backdoors
                             to national infrastructure. If private
                             contractors or cloud-hosted models absorb
                             classified or sensitive personal data, the
                             exposure isn’t hypothetical—it’s systemic.
                             Just like we saw with large platforms failing
                             to wall off classified systems, AI introduces
                             another vector for data leakage and
                             manipulation. The challenge isn’t simply
                             technical; it’s philosophical.


                # § Confidentiality⠀➾


                      # ⚓ Michael Geist ☛ Commentary:_Ensuring_the_Sovereignty
                        and_Security_of_Canadian_Health_Data⠀⇛


                             Following on our earlier Globe_and_Mail_op-ed
                             and Law_Bytes_podcast, I am pleased to co-
                             author a commentary_on_health_data
                             sovereignty_and_security with Kumanan_Wilson
                             and Mari_Teitelbaum in the Canadian Medical
                             Association Journal.


          o § Defence/Aggression⠀➾


                # ⚓ France24 ☛ Palestinian_activist_Owdeh_Hathaleen_killed_by
                  Israeli_settler_in_West_Bank,_witness_says⠀⇛


                       Palestinian activist and teacher Owdeh Hathaleen
                       was killed during an attack by Israeli settlers in
                       the occupied West Bank village of Umm al-Khair and
                       several witnesses say that settler Yinon Levi is
                       responsible for his death. The FRANCE 24 Observers
                       team spoke to Mattan Berner-Kadish, a friend of the
                       victim who was present during the incident on July
                       28.


                # ⚓ Bruce Schneier ☛ Measuring_the_Attack/Defense_Balance⠀⇛


                       “Who’s winning on the internet, the attackers or
                       the defenders?”


                       I’m asked this all the time, and I can only ever
                       give a qualitative hand-wavy answer. But Jason
                       Healey and Tarang Jain’s latest Lawfare piece has
                       amassed_data.


                # ⚓ Pro Publica ☛ Venezuelan_Men_Sent_to_CECOT_on_What_They
                  Endured_and_Reuniting_With_Their_Families⠀⇛


                       Now that he’s free, Leonardo José Colmenares
                       Solórzano, a 31-year-old Venezuelan, wants the
                       world to know that he was tortured over four months
                       in a Salvadoran prison. He said guards stomped on
                       his hands, poured filthy water into his ears and
                       threatened to beat him if he didn’t kneel alongside
                       other inmates and lick their backs.


                       Now that he’s free, Juan José Ramos Ramos, 39,
                       insists he’s not who President Donald Trump says he
                       is. He’s not a member of a gang or an international
                       terrorist, just a man with tattoos whom immigration
                       agents spotted riding in a car with a Venezuela
                       sticker on the back.


                # ⚓ The Strategist ☛ The_case_for_South_Korea-Australia_defence
                  industrial_cooperation⠀⇛


                       Strategic convergence between South Korea and
                       Australia is accelerating, but defence industrial
                       cooperation remains underdeveloped.


                # ⚓ New York Times ☛ Dihydroxyacetone_Man_Administration_Told
                  Taiwan’s_President_to_Avoid_U.S._Stopover⠀⇛


                       The Taiwanese leader canceled U.S. transit visits
                       after being urged to change his plans, two
                       officials said. Washington has been in talks with
                       Beijing over trade and a possible summit.


                # ⚓ The Straits Times ☛ China_calls_for_more_engagement_with
                  US,_warns_against_confrontation⠀⇛


                       China-US relations exert a “profound impact” on
                       international dynamics, said Foreign Minister Wang
                       Yi.


                # ⚓ New York Times ☛ A_Seaside_Refuge_in_Gaza,_Torn_Apart_by_an
                  Israeli_Strike⠀⇛


                       The Israeli military said it killed at least three
                       Hamas operatives at Al-Baqa Cafe. It also killed a
                       journalist, an artist and two best friends
                       reconciling after a fight.


                # ⚓ JURIST ☛ Drone_strikes_on_Iraq_oil_fields_threaten
                  essential_public_services⠀⇛


                       Drone strikes that have damaged oil fields in the
                       Kurdistan region of Iraq potentially threaten
                       public services that impact human rights including
                       healthcare and education, according to a Tuesday
                       release from Human Rights Watch. They also risk
                       escalating an ongoing dispute between the regional
                       and national government over oil revenues, the
                       organization said.


                # ⚓ France24 ☛ At_least_22_killed_in_Angola_fuel_hike_unrest⠀⇛


                       Unrest in Angola following protests against a fuel
                       price hike has killed 22 people since Monday, the
                       interior minister said, as calm returned to the
                       capital. Sporadic gunfire was heard across Luanda
                       and several other cities on Monday and Tuesday as
                       people looted shops and clashed with police when
                       violence erupted during a taxi strike.


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


                      # ⚓ LRT ☛ Lithuania_is_not_considering_easing_sanctions
                        against_Belarus,_quite_the_contrary_–_FM⠀⇛


                             Lithuania’s government is not looking into
                             easing sanctions on Belarus, Foreign Minister
                             Kęstutis Budrys has stated, amid a proposal
                             from Birių Krovinių Terminalas (BKT), a
                             Klaipėda-based bulk cargo terminal controlled
                             by Igor Udovickij, to withdraw its lawsuit
                             filed at the EU Court if the government
                             allows Belarusian fertiliser shipments to
                             resume through Lithuania.


                      # ⚓ JURIST ☛ Russian_journalist_sentenced_to_12_years_for
                        ties_to_Navalny’s_Anti-Corruption_Foundation⠀⇛


                             A Russian court sentenced journalist Olga
                             Komleva to 12 years in prison on Tuesday for
                             cooperation with the Anti-Corruption
                             Foundation and the dissemination of false
                             information about the Russian military’s
                             actions.


                      # ⚓ Meduza ☛ Russia_adds_Navalny’s_posthumous_memoir_to
                        list_of_banned_‘extremist’_materials_—_Meduza⠀⇛


                      # ⚓ Atlantic Council ☛ Ukraine’s_democracy_is_the_key_to
                        the_country’s_Euro-Atlantic_integration⠀⇛


                             While Ukraine currently faces a range of
                             unique challenges, this cannot justify
                             neglecting democratic principles. On the
                             contrary, defending the democratic gains of
                             recent decades is vital if further progress
                             toward Euro-Atlantic integration is to be
                             achieved, writes Alyona Getmanchuk.


                      # ⚓ RFERL ☛ Zelenskyy_Says_US_Arms_Deal_Set_As_Parliament
                        Prepares_To_Hear_Key_Anti-Graft_Bill⠀⇛


                             Ukrainian President Volodymyr Zelenskyy said
                             he had approved key principles of "large-
                             scale" US weapons agreements, while Ukrainian
                             lawmakers geared up for a crucial vote on a
                             bill designed to restore the independence of
                             two agencies that fight graft.


                      # ⚓ Meduza ☛ A_political_crisis_that_could_weaken_the_war
                        effort_itself_What_Zelensky’s_anti-corruption_U-turn
                        means_at_a_‘precarious_moment’_for_Ukraine_—_Meduza⠀⇛


                      # ⚓ France24 ☛ Ukraine_will_'fix'_controversial_anti-
                        graft_law,_FM_says_on_eve_of_vote⠀⇛


                             Ukraine's government will "fix" anti-graft
                             legislation that ignited rare mass protests
                             in the war-ravaged country after critics
                             accused President Volodymyr Zelensky of
                             trying to meddle with corruption probes
                             against senior government officials, Foreign
                             Minister Andriy Sybiga said Wednesday.
                             Parliament will vote on an amended bill on
                             Thursday.


                      # ⚓ RFERL ☛ Kolomoyskiy,_Once_Powerful_Ukraine_Tycoon,
                        Loses_$1.9_Billion_Fraud_Case⠀⇛


                             The High Court of Justice in London has ruled
                             against two of Ukraine's former tycoons in a
                             landmark case involving the siphoning of
                             nearly $2 billion from Privatbank, the
                             country’s largest lender.


                      # ⚓ NYPost ☛ Senate_Majority_Leader_John_Thune_readying
                        Russia_sanctions_as_deadline_for_Ukraine_cease-fire
                        shortens_to_10_days⠀⇛


                             "He's somebody who is animated largely by
                             trying to get to a peaceful solution," the
                             Republican leader said of Convicted Felon.
                             "We want to be a good partner in that and so
                             like I said, we've been, I made it clear
                             we're available to move on that whenever
                             they're ready to have us do it."


                      # ⚓ France24 ☛ Dihydroxyacetone_Man_imposes_25%_tariff,
                        'penalty'_on_India_over_Russia_ties⠀⇛


                             US President The Insurrectionist on Wednesday
                             hit India with a 25 percent tariff on its
                             imports, as well as a flurry of other duty
                             hikes and an undefined "penalty" for its
                             dealings with Russia, as the US ramps up its
                             efforts to force an end to Moscow's war on
                             Ukraine.


                      # ⚓ Meduza ☛ Trump_announces_‘penalty’_tariff_on_India
                        over_purchases_of_Russian_energy_resources_and_weapons
                        —_Meduza⠀⇛


                      # ⚓ Meduza ☛ Russia_claims_capture_of_Chasiv_Yar_in
                        eastern_Ukraine_—_Meduza⠀⇛


                      # ⚓ RFERL ☛ Russia,_Pacific_Coastlines_Appear_To_Avoid
                        Major_Damage_After_Massive_Earthquake⠀⇛


                             A powerful 8.8-magnitude earthquake struck
                             off the coast of Russia's Kamchatka Peninsula
                             early on July 30, triggering tsunami waves,
                             widespread evacuations, and emergency
                             declarations around the Pacific Rim, although
                             the regions appeared to avoid major
                             casualties or damages.


                      # ⚓ Meduza ☛ ‘We_just_kept_doing_our_job’:_Doctors_in
                        Russia’s_Kamchatka_steady_patient_mid-surgery_as
                        earthquake_hits,_complete_operation_safely_—_Meduza⠀⇛


                      # ⚓ The Straits Times ☛ Huge_earthquake_rocks_Russia’s
                        far_east,_triggering_tsunami_warnings_around_Pacific⠀⇛


                             Several people were injured in the remote
                             Russian Kamchatka region, while much of
                             Japan’s eastern seaboard was ordered to
                             evacuate.


                      # ⚓ New York Times ☛ Dihydroxyacetone_Man_Threatens_India
                        With_Steep_Tariffs,_Including_Penalty_Over_Russian
                        Oil⠀⇛


                             The president said Wednesday that imports
                             from India would be subject to a 25 percent
                             tariff as of Friday, as trade talks between
                             the countries hit a stumbling block.


                      # ⚓ New York Times ☛ Brennan_and_Clapper:_The_Forrest
                        Dump_Administration_Is_Rewriting_History_of_Russia_and
                        2016⠀⇛


                             We want to set the record straight and also
                             sound a warning.


                      # ⚓ New York Times ☛ Why_Did_Such_a_Powerful_Earthquake
                        Generate_Such_a_Weak_Tsunami?⠀⇛


                             The quake in Russia on Wednesday was among
                             the strongest ever recorded — but in many
                             places, the resulting wave was small.


                      # ⚓ New York Times ☛ Powerful_Earthquake_Rattles_Russia’s
                        Far_East_But_Causes_Little_Damage⠀⇛


                             A 8.8-magnitude earthquake shook the remote,
                             sparsely populated Kamchatka region and set
                             off tsunami waves. No serious injuries were
                             reported, officials said.


                      # ⚓ New York Times ☛ In_Kamchatka,_Epicenter_of_the
                        Russian_Earthquake,_Seismic_Activity_Is_Common⠀⇛


                             Tremors are regularly reported in this remote
                             Russian peninsula dotted with volcanoes, some
                             of which erupt every year.


                      # ⚓ New York Times ☛ Russia’s_Far_East_Suffers_Some
                        Damage_From_Earthquake_and_Tsunami⠀⇛


                             Regional authorities in one region declared
                             an emergency after a tsunami hit the Kuril
                             Islands, and the Kamchatka Peninsula was
                             watching for volcanic activity.


                      # ⚓ Meduza ☛ ‘An_extraordinary_event’_Tsunami_waves_hit
                        Kamchatka_after_historic_earthquake_strikes_off_Russian
                        coast_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ Volcano_erupts_in_Russia’s_Kamchatka,_hours
                        after_massive_earthquake_triggers_tsunami_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ Russian_overnight_strike_on_Kyiv_kills_at
                        least_six,_including_child_—_Meduza⠀⇛


          o § Environment⠀➾


                # ⚓ Science Alert ☛ Giant_Earthquake_Off_Russian_Coast_Triggers
                  Mass_Evacuations_as_Far_as_Hawaii⠀⇛


                       One of the largest earthquakes ever recorded.


                # ⚓ France24 ☛ Tsunami_alerts_due_to_Russian_quake_downgraded
                  in_several_nations⠀⇛


                       A powerful magnitude 8.8 earthquake struck off
                       Russia’s Kamchatka Peninsula on July 30, 2025,
                       triggering tsunami warnings across the Pacific
                       rim—including Japan, Hawaii, Alaska, and several
                       Central and South American countries. While initial
                       alerts led to evacuations, many were later
                       downgraded after no major damage was reported.
                       Monitoring continues due to potential aftershocks.


                # ⚓ Mexico News Daily ☛ No_damages_reported_from_tsunami
                  effects;_8_ports_remain_closed⠀⇛


                       The president ruled out damages but warned of
                       rising sea levels along Mexico’s Pacific coast
                       after an 8.8-magnitude earthquake in Russia
                       prompted a tsunami warning on Wednesday morning.


                # § Energy/Transportation⠀➾


                      # ⚓ Hackaday ☛ One_Man’s_Trash…_Bicycle_Edition⠀⇛


                             [Remy van Elst] found an obsolete bike
                             navigation system, the Navman Bike 1000, in a
                             thrift store for €10. The device was a
                             rebadged Mio Cyclo 200 from 2015. Can a
                             decade-old GPS be useful? Well, the answer
                             depends on a little reverse engineering.


                # § Wildlife/Nature⠀➾


                      # ⚓ BIA Net ☛ Court_case_reveals_security,_oil-driven
                        deforestation_in_Şırnak⠀⇛


                             Commenting on the findings revealed through
                             the legal process led by the Lawyers for
                             Freedom Association, lawyer İpek Sarıca said,
                             “It is clear that this deforestation is also
                             harming the peace process.”


                # § Overpopulation⠀➾


                      # ⚓ Meduza ☛ ‘You’ll_want_to_do_it_again!’_On_Pregnant
                        Women’s_Day,_Russia_reframes_childbearing_as_a
                        patriotic_duty_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ Russian_convent_hands_out_plastic_fetuses_to
                        women_in_anti-abortion_campaign_—_Meduza⠀⇛


          o § Finance⠀➾


                # ⚓ The Straits Times ☛ Dihydroxyacetone_Man_says_US_will
                  impose_15%_tariff_on_South_Korean_imports⠀⇛


                       South Korean President Lee Jae Myung will visit the
                       White House “within the next two weeks”, Convicted
                       Felon said.


                # ⚓ The Straits Times ☛ China_earmarks_$16_billion_budget_for
                  2025_childcare_subsidies⠀⇛


                       It is reported to be 3,600 yuan per year for every
                       child, until they reach the age of three.


                # ⚓ The Straits Times ☛ China_and_US_are_still_key_trade
                  partners:_Chinese_commerce_minister⠀⇛


                       US and Chinese officials agreed to seek an
                       extension of their 90-day tariff truce on July 29.


                # ⚓ France24 ☛ Angola:_Deadly_protests_erupt_over_fuel_price
                  hikes⠀⇛


                       Deadly protests have swept across Angola following
                       a sharp rise in fuel prices. Demonstrators took to
                       the streets of Luanda and other cities in July to
                       protest soaring costs and worsening living
                       conditions. Police responded with force, leaving at
                       least four dead and over 500 arrested. Human rights
                       groups have condemned the crackdown and called for
                       respect of peaceful assembly. An internet blackout
                       during the protests raised further concerns over
                       repression.


                # ⚓ Latvia ☛ Latvia_and_17_other_countries_ask_for_loan_from
                  European_Security_Action_Fund⠀⇛


                       Latvia and 17 other European Union (EU) Member
                       States have requested €127 billion in loans from
                       the newly created Security Action Fund for Europe
                       (SAFE), the European Commission (EC) announced on
                       Wednesday.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Scoop News Group ☛ Senate_Democrats_call_Convicted_Felon
                  admin’s_focus_on_state_voter_rolls_a_pretext_for
                  disenfranchisement⠀⇛


                       Sen. Alex Padilla and other Democrats say the GOP
                       is pressing inflated concerns about noncitizen
                       voting to justify legal and legislative challenges
                       to eligible voters. 


                # ⚓ JURIST ☛ US_lawmakers_sue_Convicted_Felon_over_detention
                  facility_visit_restrictions⠀⇛


                       US lawmakers initiated a lawsuit against the
                       Convicted Felon administration on Wednesday,
                       challenging the administration’s new policy
                       regarding visitation procedures for members of
                       Congress visiting detention facilities.
                       Representative Joe Neguse announced that he would
                       be leading a group of lawmakers in challenging this
                       policy on Wednesday.


                # ⚓ France24 ☛ France_prepares_law_to_fast-track_return_of_art
                  looted_during_imperial_conquests⠀⇛


                       France's government on Wednesday discussed a bill
                       that would streamline the process of returning
                       artworks and cultural artefacts looted from the
                       country's former colonies over more than a century
                       of imperial rule. Under current laws, the return of
                       each item in France's extensive national collection
                       must be voted on individually.


          o § Censorship/Free Speech⠀➾


                # ⚓ New York Times ☛ Pro-Palestinian_Group_Can_Appeal_U.K._Ban,
                  Judge_Rules,_Citing_Free_Speech⠀⇛


                       A High Court judge in London said that Palestine
                       Action had the right to challenge the British
                       government’s decision to ban it as a terrorist
                       group.


                # ⚓ RFERL ☛ Iran_Withdraws_'Fake_News'_Bill_After_Public
                  Outcry⠀⇛


                       The Iranian government has withdrawn a
                       controversial legislation meant to counter fake
                       news after critics charged that it would gut the
                       already restricted freedom of expression in Iran.


                # ⚓ JURIST ☛ Russia_warned_of_escalating_state_control_over
                  internet_and_digital_repression⠀⇛


                       Human Rights Watch (HRW) on Wednesday released a
                       report highlighting the alarming extent of the
                       Russian government’s increasing technological
                       control over internet infrastructure and digital
                       communication across the country.


          o § Civil Rights/Policing⠀➾


                # ⚓ ACLU ☛ Your_Questions_Answered:_The_Supreme_Court's_Impact
                  On_Our_Rights⠀⇛


                       The Supreme Court's most recent term reshaped the
                       legal landscape on immigration, transgender rights,
                       and free speech. But behind the decisions,
                       procedural shifts like limits on nationwide
                       injunctions and expanded use of the emergency
                       docket signal a court increasingly driven by
                       politics.


                       At the ACLU we believe that information is power,
                       and that informed opinions make a more perfect
                       union. That’s why we’ve taken a hard look inside
                       this Supreme Court term and analyzed what the
                       court’s cases reveal about its values, and how its
                       direction and influence impacts our civil
                       liberties.


                       To help us all better understand the civil rights
                       and civil liberties issues at hand this Supreme
                       Court term, our series, “Your Questions Answered,”
                       brings your questions directly to ACLU experts for
                       informed answers. In this installment, our legal
                       director, Cecillia Wang, answers your most pressing
                       questions on the Supreme Court.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ Hackaday ☛ Legally_Distinct_Space_Invaders_Display_WiFi
                  Info⠀⇛


                       In the early 00s there was a tiny moment before the
                       widespread adoption of mobile broadband, after the
                       adoption of home WiFi, and yet before the
                       widespread use of encryption. For this brief time a
                       unique practice arose called wardriving — where
                       people would drive around, document, and use these
                       open wireless networks.


      § Monopolies/Monopsonies⠀➾


          o § Patents⠀➾


                # ⚓ Dennis Crouch/Patently-O ☛ Federal_Circuit_Steps_Into
                  Apple-Fintiv_Discovery_Fight_Days_Before_August_4_Trial⠀⇛


                       In an unusual move, the Federal Circuit on July 29,
                       2025, ordered Fashion Company Apple to respond to
                       Fintiv's petition for writ of mandamus seeking to
                       halt the upcoming August 4 trial date over
                       unresolved discovery disputes. In re Fintiv, Inc.,
                       Docket No. 25-00142 (Fed. Cir. July 29, 2025). 
                       Fintiv Petition.


                # ⚓ Unified Patents ☛ Malikie_MPEG-DASH_related_patent_monopoly
                  challenged⠀⇛


                       On July 28, 2025, Unified Patents filed an ex parte
                       reexamination proceeding against U.S._Patent
                       8,392,598, owned and asserted by Malikie
                       Innovations Limited, an NPE and entity of Key
                       Patent_Innovations_Limited. The '598 patent
                       monopoly is generally directed to streaming media
                       content to user devices, and allowing the user
                       devices to control the format of the media
                       downloaded based on conditions such as available
                       bandwidth.


                # ⚓ Unified Patents ☛ Dominion_Harbor_entity,_Arlington
                  Technologies,_Wi-Fi_patent_monopoly_challenged⠀⇛


                       On July 28, 2025, continuing in the ongoing efforts
                       in the new SEP_Wi-Fi_Zone, Unified filed an ex
                       parte reexamination proceeding against U.S._Patent
                       7,193,986, owned and asserted by Arlington
                       Technologies LLC, an NPE and entity of the Dominion
                       Harbor_Group. The ‘986 patent monopoly is generally
                       directed to communications between a master
                       wireless network device and one or more slave
                       network devices using a medium access protocol such
                       as the MAC protocol.


          o § Copyrights⠀➾


                # ⚓ Digital Music News ☛ IFPI,_CISAC,_and_Many_More_Call_Out
                  Hey_Hi_(AI)_Act_Implementation_Measures:_‘A_Missed
                  Opportunity_to_Provide_Meaningful_Protection_of_Intellectual
                  Property_Rights’⠀⇛


                       The IFPI, CISAC, IMPALA, and others are taking aim
                       at the EU’s Hey Hi (AI) Act implementation, which
                       they’re criticizing as “a missed opportunity to
                       provide meaningful protection of intellectual
                       property rights.” Those entities, besides United
                       Voice Artists, the European Federation of
                       Journalists, and many more, voiced their qualms in
                       a release that was emailed to DMN.


                # ⚓ Public Domain Review ☛ Breaking_the_Celestial_Ceiling:_Now
                  and_Then_#4⠀⇛


                       Female astronomical first, in 2025 and 1787.


                # ⚓ Public Domain Review ☛ Flowers_of_Fealty:_Wilhelm_Dilich’s
                  Commemoration_of_the_Christening_of_Elisabeth_of_Hesse_
                  (1598)⠀⇛


                       Commemorative featuring illustrations of pageants,
                       costumes, and fireworks, later further illustrated
                       by a separate artist, with floral motifs.


    * Links_31/07/2025:_Spotify_Collapses_and_Spotify_Now_Forcing_Some_Users_to
      Undergo_Face-Scanning
    * Slopwatch:_Google_News_Has_Lost_the_Plot



                    ䷩ 𝚕𝚒𝚗𝚎 4049

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 31/07/2025: Spotify Collapses and
Spotify Now Forcing Some Users to Undergo Face-
Scanning⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jul 31, 2025


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Bhyve⦈_


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * Leftovers
          o Career/Education
          o Health/Nutrition/Agriculture
          o Proprietary
          o Security
                # Integrity/Availability/Authenticity
                # Privacy/Surveillance
          o Defence/Aggression
          o Environment
                # Energy/Transportation
                # Wildlife/Nature
                # Overpopulation
          o AstroTurf/Lobbying/Politics
          o Censorship/Free_Speech
          o Freedom_of_Information_/_Freedom_of_the_Press
          o Civil_Rights/Policing
          o Digital_Restrictions_(DRM)
          o Monopolies/Monopsonies
    * § Leftovers⠀➾


          o ⚓ The Guardian UK ☛ ‘Everybody_was_fondling_underwater!’:_the_Rocky
            Horror_Picture_Show_at_50_–_an_oral_history⠀⇛


                 It remains the longest-running theatrical release in film
                 history and still plays in cinemas today. We look back
                 with the cast and crew to find out how the film became
                 such a cult phenomenon.


          o § Career/Education⠀➾


                # ⚓ Noel Rappin ☛ Programming_Proverbs_in_1975_and_2025⠀⇛


                       I thought I would read this book and do a big
                       compare and contrast as to how best practice advice
                       has changed. As it happens, most of the book is
                       worked out examples, and there’s really only one
                       big way in which practices have changed that colors
                       all the other advice in the book.


                       To explain that, I need to give you the context of
                       1975. I’m not quite old enough to have professional
                       memories of 1975, so this is a mixture of research
                       and extrapolation. (If you think this was an excuse
                       to research what programming was like in 1975… I
                       can’t really argue with that.)


                # ⚓ Robert Birming ☛ Less_time,_more_blog⠀⇛


                       Sometimes, less is more. Sometimes, limits unlock
                       flow.


                # ⚓ Kev Quirk ☛ How_Do_You_Take_Notes?⠀⇛


                       I need a better way of organising my notes, to-dos
                       and tasks. I have crap all over the place at the
                       moment, so if you have a system, I'd love to know
                       what it is.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ Omicron Limited ☛ Measurements_suggest_we_inhale_68,000
                  lung-penetrating_microplastics_daily_in_our_homes_and_cars⠀⇛


                       New measurements of fine microplastic particles
                       suspended in the air in homes and cars suggest that
                       humans may be inhaling far greater amounts of lung-
                       penetrating microplastics than previously thought.
                       Nadiia Yakovenko and colleagues at the Université
                       de Toulouse, France, present these findings in the
                       open-access journal PLOS One.


                # ⚓ Canadian Medical Association Journal ☛ Ensuring_the
                  sovereignty_and_security_of_Canadian_health_data_|_CMAJ⠀⇛


                       Health data are critical to health systems in
                       Canada, but the potential of these data to be
                       accessed and used by foreign entities for
                       surveillance purposes without consent is
                       concerning. Furthermore, advances in artificial
                       intelligence (AI) have increased the economic value
                       of these data, creating new risks.1 Serious
                       privacy, security, and economic risks arise when
                       companies in other countries hold and use Canadian
                       data. Given the rapidly changing political climate
                       in the United States, preserving the sovereignty of
                       Canada’s health data — notably, ensuring that the
                       data are subject to Canadian laws and legal systems
                       — requires renewed focus.


          o § Proprietary⠀➾


                # ⚓ Tim Bray ☛ De-Google_Project_Update⠀⇛


                       I introduced this family project in the spring of
                       2024. I won’t reproduce those arguments for why
                       we’re working on this, but in the current climate I
                       feel like I hardly need to. Since that post, our
                       aversion to Google dependency has only grown
                       stronger. Progress has been non-zero but not fast.


                # ⚓ Clayton Errington ☛ The_Invasion_of_Advertising⠀⇛


                       Over the last few weeks I’ve seen an increase in
                       advertising in places that appear new and where I
                       haven’t seen it before. Along with new places,
                       there has been a massive increase in others. I’d
                       like to take a quick tour through these areas.


                # § Artificial Intelligence (AI) / LLM Slop / Plagiarism⠀➾


                      # ⚓ Futurism ☛ In_Disturbing_Demo,_Video_Game_Characters
                        Panic_When_Told_They're_Just_Code⠀⇛


                             Others in the industry are calling for
                             keeping humans at the heart of video games,
                             or citing concerns that an LLM-powered NPC
                             could lead to all kinds of unpredictable —
                             and potentially unsavory — behavior.


                      # ⚓ Pivot to AI ☛ CSIRO_posts_AI-fake_climate_article
                        with_made-up_quotes⠀⇛


                             David Ho is an oceanographer at the
                             University of Hawai’i. Cosmos posted an
                             article about removing carbon from the
                             oceans. Professor Ho was quite surprised the
                             article had a quote from him and a pile of
                             stuff he didn’t actually think — particularly
                             when he hadn’t spoken to Cosmos at all. The
                             article read just like AI slop.


                      # ⚓ Futurism ☛ People_Are_Becoming_"Sloppers"_Who_Have_to
                        Ask_AI_Before_They_Do_Anything⠀⇛


                             For instance, Foster pointed to one viral
                             video in which a man recounted going on a
                             first date with a woman — but was surprised
                             when she pulled out ChatGPT on her phone and
                             asked it what she should order off the menu.
                             ("There was no second date," he concluded.)


                             The term "AI slop" has become synonymous with
                             often garbled low-effort content online, from
                             ChatGPT's weird way of talking to a barrage
                             of junk littering platforms like Facebook and
                             Pinterest. Turning it into a noun evokes the
                             "glassholes" who were lampooned for walking
                             around with Google's head-mounted Glass
                             cameras more than a decade ago — and puts the
                             focus on how new technology is changing the
                             way we relate to others, and even now perhaps
                             to ourselves.


                      # ⚓ Digital Music News ☛ Tyler,_the_Creator’s_'Don’t_Tap
                        the_Glass'_Drowned_Out_By_AI⠀⇛


                             Tyler, the Creator’s ninth studio album,
                             Don’t Tap the Glass, was set up for a massive
                             summer impact. But the album release has been
                             overshadowed by an AI song with the same name
                             on TikTok.


                      # ⚓ Terence Eden ☛ Winners_don’t_use_ChatGPT⠀⇛


                             This isn't that essay. I'm too lazy to write
                             something amazing, and too aware of the
                             limitations of outsourcing my thinking.


                             But I see the pattern in myself.


                # § Windows TCO / Windows Bot Nets⠀➾


                      # ⚓ The Register UK ☛ Ingram_Micro_attackers_threaten_3.5
                        TB_data_leak_this_week⠀⇛


                             Although Ingram Micro previously said it had
                             contained the incident, its appearance on
                             SafePay's website suggests that – if it was
                             being extorted as per the ransomware playbook
                             – it did not pay up.


                      # ⚓ Cyble Inc ☛ U.S._Data_Breach_Costs_Rise_As_Global
                        Average_Falls⠀⇛


                             Data breaches in the U.S. are getting more
                             costly even as they’re getting cheaper in the
                             rest of the world.


                             That was one of the conclusions in the new
                             IBM-Ponemon Institute 2025 Cost of a Data
                             Breach report, which also found that AI is
                             playing a significant role in cybersecurity,
                             both as an attack vector and as a defensive
                             measure.


                      # ⚓ Press Gazette ☛ Cyberattacks_target_email_accounts_of
                        senior_journalists⠀⇛


                             Phishing remains the most common method of
                             attack, with media groups targeted both by
                             ‘hacktivists’ and for-profit ransomware
                             gangs.


          o § Security⠀➾


                # § Integrity/Availability/Authenticity⠀➾


                      # ⚓ Krebs On Security ☛ Scammers_Unleash_Flood_of_Slick
                        Online_Gaming_Sites⠀⇛


                             Fraudsters are flooding Discord and other
                             social media platforms with ads for hundreds
                             of polished online gaming and wagering
                             websites that lure people with free credits
                             and eventually abscond with any
                             cryptocurrency funds deposited by players.
                             Here’s a closer look at the social
                             engineering tactics and remarkable traits of
                             this sprawling network of more than 1,200
                             scam sites.


                      # ⚓ Silicon Angle ☛ Lazarus_turns_open_source_into_a
                        weapon_in_its_latest_global_espionage_push⠀⇛


                             Like many similar groups, Lazarus over the
                             years has shifted tactics. Today, instead of
                             simply attacking financial institutions
                             directly, the group has become more sneaky by
                             targeting developers and deployment
                             environments. It plants malware in widely
                             used open-source repositories such as npm and
                             PyPI. The malicious packages from Lazarus are
                             designed to mimic trusted libraries, often
                             through typosquatting or combo-squatting, to
                             trick developers into unknowingly installing
                             backdoors into their systems.


                # § Privacy/Surveillance⠀➾


                      # ⚓ Papers Please ☛ Palantir_breaks_new_ground_in
                        algorithmic_surveillance_and_control⠀⇛


                             One of the biggest beneficiaries of the
                             expansion of the homeland-security industrial
                             complex since the second inauguration of
                             Donald Trump has been Palantir.  Shares of
                             Palantir stock have doubled in value since
                             Trump’s re-election.


                             Both the Department of Defense and the
                             Department of Homeland Security have expanded
                             their contracts with Palantir for data
                             aggregation, data mining, algorithmic
                             profiling, predictive “pre-crime” policing
                             and preemptive war, and automated decision-
                             making.


                             But is Palantir just doing more of what it
                             has been doing since at least the first Trump
                             presidency? Or is it (also) doing something
                             new? We think it’s doing both.


                      # ⚓ The Gray Zone ☛ Israeli_spyware_firms_are_fueling_the
                        global_surveillance_state⠀⇛


                      # ⚓ EFF ☛ EFFector_37.9_-_Featured_Story:_Amazon_Ring
                        Cashes_in_on_Techno-Authoritarianism⠀⇛


                             Why the sudden about-face on privacy? One
                             clue: These days, there are billions of
                             dollars to be made by tech companies willing
                             to work with police or the defense sector to
                             trample on our civil liberties.


                      # ⚓ Scoop News Group ☛ Senate_Democrats_want_total_audit
                        of_DOGE_[sic]_access_to_agency_systems⠀⇛


                             The Pick Up After Your DOGE [sic] Act from
                             Sens. Sheldon Whitehouse of Rhode Island, Ron
                             Wyden of Oregon and Elizabeth Warren of
                             Massachusetts would require the administrator
                             of the Elon Musk-created tech collective to
                             provide a full accounting to the U.S.
                             comptroller general of all the agencies and
                             IT systems that DOGE [sic] accessed. Those
                             systems would then be subject to
                             comprehensive performance and security
                             audits.


                             “The DOGE [sic]-boys have weaseled their way
                             into Americans’ most sensitive data systems,
                             claiming to hunt ‘waste, fraud, and abuse,’
                             while actually creating waste, fraud, and
                             abuse. They’re destroying Americans’ trust in
                             once-reliable government systems and could be
                             hawking your stolen data to their friends in
                             Big Tech and AI,” Whitehouse said in a press
                             release. “The Pick Up After Your DOGE [sic]
                             Act protects seniors and all Americans by
                             fixing any bugs or backdoors that DOGE [sic]
                             may have purposefully or negligently created
                             in Social Security, Medicare, and other
                             highly sensitive government data systems.”


                      # ⚓ OpenRightsGroup ☛ [Repeat]_Google_Refuses_to_Deny_UK
                        Encryption_Demands⠀⇛


                             “When my office asked Google about backdoor
                             demands from the U.K., the company did not
                             answer the question, only stating that if it
                             had received a technical capabilities notice,
                             it would be prohibited from disclosing that
                             fact.”


                             In response to the letter, Jim Killock,
                             Executive Director of Open Rights Group said:
                             [...]


                      # ⚓ The Washington Post ☛ Wyden_wants_Gabbard_to_press
                        the_UK_on_encryption_backdoors⠀⇛


                             In the letter, Wyden reported that Google
                             said it could not tell him whether the
                             British government had demanded special
                             “backdoor” access to users’ private data on
                             its services. That seemed to raise the
                             possibility that Apple, which has said it
                             received such a demand, was not alone.


                      # ⚓ The Record ☛ Schools_are_next_for_Flock_Safety’s
                        automatic_license_place_reader_cameras⠀⇛


                             "There is a pattern when schools adopt such
                             technologies: parents aren’t consulted or
                             asked for consent, vulnerable student
                             populations are impacted and already limited
                             resources are diverted without actually
                             achieving the intended goal,” said Kristin
                             Woelfel, policy counsel in the Center for
                             Democracy and Technology’s Equity in Civic
                             Technology division.


                             “Schools are meant to be places of learning,
                             not expansion points for police
                             surveillance.”


                      # ⚓ 404 Media ☛ Spotify_Is_Forcing_Users_to_Undergo_Face
                        Scanning_to_Access_Explicit_Content⠀⇛


                             Spotify is requiring users in the UK to
                             verify they’re over 18 to view "certain age
                             restricted content," and users are reporting
                             seeing a popup on Spotify to verify their
                             ages following the enactment of the UK's
                             Online Safety Act last week, which forced
                             platforms to verify the ages of everyone who
                             tries to access certain kinds of content
                             deemed harmful to children.


                      # ⚓ Don Marti ☛ personalized_advertising_is_an_adult
                        custom⠀⇛


                             Cool, cool, all makes sense, I can see
                             they’re trying to get teens to develop
                             healthy online habits, and…hold on a minute,
                             go back to that first one. "Showing only non-
                             personalized ads" is a "protection" now?


                      # ⚓ CoryDoctorow ☛ Pluralistic:_Delta’s_AI-based_price-
                        gouging⠀⇛


                             Data-brokers hold all kinds of data on you,
                             from the "legitimate" information about
                             everywhere your car has driven, to everywhere
                             point in space that the Bluetooth radios on
                             your phone and headphones have passed, to
                             everything you've bought, to every website
                             you've visited and every search you've
                             performed. They also buy data that has been
                             straight up stolen from you by spyware
                             implanted on your phone:


                             https://www.404media.co/a-startup-is-selling-
                             data-hacked-from-peoples-computers-to-debt-
                             collectors/


                             All of this can be merged into a single file
                             that you have no right to scrutinize, let
                             alone redact. Biden's Consumer Finance
                             Protection Bureau passed a rule banning all
                             this shit, but Trump illegally killed off
                             that rule: [...]


                      # ⚓ Deccan Chronicle ☛ YouTube_To_Use_AI_To_Detect
                        Viewers_Under_18⠀⇛


                             “We will use AI to interpret a variety of
                             signals that help us to determine whether a
                             user is over or under 18. These signals
                             include the types of videos a user is
                             searching for, the categories of videos they
                             have watched, or the longevity of the
                             account,” YouTube said in a blog post.


                      # ⚓ Nick Heer ☛ Tea_Spilled⠀⇛


                             R Street is a think tank that stands for
                             “free markets and limited, effective
                             government”, so they will not say this, but
                             privacy legislation would help protect users
                             from these kinds of abuses. It was probably a
                             bad idea for Tea to be collecting so much
                             personal information in the first place. Yet
                             this kind of data is routinely used in some
                             industries, and it is unrealistic to expect
                             individuals to figured out and monitor the
                             privacy practices of individual services.
                             Policies that limit data collection and
                             retention, along with public auditing or
                             other compliance-checking methods, can allow
                             us to be more confident and provide remedies
                             for bad practices and misuse.


          o § Defence/Aggression⠀➾


                # ⚓ ADF ☛ Terrorists_in_Mozambique_Use_Child_Abductions_to_Grow
                  Ranks⠀⇛


                       Islamic State-Mozambique is one of many terrorist
                       groups in Africa using child abduction as a weapon
                       of war.


                # ⚓ SBS ☛ YouTube_to_be_included_in_Australia's_social_media
                  ban._Here's_what_you_need_to_know⠀⇛


                       Under-16s won't be allowed to have active YouTube
                       accounts or subscribe to YouTube channels when the
                       federal government's social media ban comes into
                       effect.


                # ⚓ India Times ☛ TikTok_asks_users_to_help_police
                  misinformation⠀⇛


                       With a new feature, Footnotes, TikTok will let a
                       select group of users add context and background
                       information to some of the short videos on the app,
                       along with links to the information's sources.


                # ⚓ US News And World Report ☛ Islamic_State_and_Al-Qaida
                  Threat_Is_Intense_in_Africa,_With_Growing_Risks_in_Syria,_UN
                  Experts_Say⠀⇛


                       The experts monitoring sanctions against the two
                       groups said “the organization’s pivot towards parts
                       of Africa continued" partly because of Islamic
                       State losses in the Middle East due to
                       counterterrorism pressures. There are also
                       “increasing concerns about foreign terrorist
                       fighters returning to Central Asia and Afghanistan,
                       aiming to undermine regional security,” they said.


                       The Islamic State also continues to represent “the
                       most significant threat” to Europe and the
                       Americas, the experts said, often by individuals
                       radicalized via social media and encrypted
                       messaging platforms by its Afghanistan-based
                       Khorasan group.


                # ⚓ Deccan Chronicle ☛ Australia_Widens_Teen_Social_Media_Ban
                  To_YouTube⠀⇛


                       Since the government said last year it would exempt
                       YouTube due to its popularity with teachers,
                       platforms covered by the ban, such as Meta's
                       Facebook and Instagram, Snapchat and TikTok, have
                       complained


                # ⚓ The Register UK ☛ Australia_bans_kids_from_signing_up_for
                  YouTube_accounts⠀⇛


                       The decision, announced today by Prime Minister
                       Anthony Albanese, alters the 2024 decision to
                       exclude YouTube from the regime that will require
                       Facebook, Instagram, Snapchat, TikTok, and X to use
                       age verification technology to ensure that kids
                       cannot sign up for accounts.


                       Australia’s plan, which comes into force in
                       December, is not to ban kids from using social
                       media. The nation’s leaders instead want to stop
                       social media services from tracking kids through
                       their accounts.


                # ⚓ [Old] Michael Hudson ☛ The_End_of_Western_Civilization⠀⇛


                       As I have sought to emphasize, oligarchic control
                       of government has been a major distinguishing
                       feature of Western civilization ever since
                       classical antiquity. And the key to this control
                       has been opposition to strong government – that is,
                       civil government strong enough to prevent a
                       creditor oligarchy from emerging and monopolizing
                       control of land and wealth, making itself into a
                       hereditary aristocracy, a rentier class living off
                       land rents, interest and monopoly privileges that
                       reduce the population at large to austerity.


                       The unipolar U.S.-centered order hoping to “end
                       history” reflected a basic economic and political
                       dynamic that has been a characteristic of Western
                       civilization ever since classical Greece and Rome
                       set off along a different track from the Near
                       Eastern matrix in the first millennium BC.


                # ⚓ The Telegraph UK ☛ They_tried_to_break_Lucy_Connolly,_but
                  the_decent people_of_Britain_will_never_desert_her⠀⇛


                       The blood-curdling savagery of the attack and the
                       choice of target – young girls dancing to a pop
                       singer who had been singled out for death threats
                       that summer by Islamic State – told anyone who
                       cared to think about it that Axel Rudakubana had
                       spent time in Islamist chatrooms. (This has never
                       been confirmed, but parallels with the 2017 suicide
                       bombing of young pop fans at the Ariana Grande
                       concert at the Manchester Arena are undeniable.)


          o § Environment⠀➾


                # ⚓ The Nation ☛ The_Great_Salt_Lake_Is_a_Ticking_Time_Bomb⠀⇛


                       This would spell catastrophe for Utah. The New York
                       Times says the Great Salt Lake’s disappearance
                       would constitute an “environmental nuclear bomb.”
                       Water supplies would dwindle, and ecosystems would
                       perish: from the brine shrimp in the lake to the
                       over 10 million migratory birds that refuel in its
                       marshes each year. Utah’s population may vanish
                       with them.


                       When Utah industrialized, mines began dumping waste
                       into the lake, polluting it with heavy metals like
                       arsenic. As a terminal lake, the Great Salt Lake
                       has inlets but no outlets other than evaporation.
                       All the metals that have ever been poured into the
                       Great Salt Lake have accumulated in its lakebed
                       over time, with no way out.


                       Now, retreating water levels are exposing stretches
                       of cracked, arsenic-laden lakebed. Windstorms have
                       begun to blow across the lakebed, picking up clouds
                       of poisonous dust. They carry it into the Wasatch
                       Front, which houses 2.8 million of Utah’s 3.4
                       million residents.


                # ⚓ Deseret Media ☛ Great_Salt_Lake_drops_back_to_a_'really
                  bad'_level,_but_expert_sees_'silver_lining'_for_now⠀⇛


                       Brine shrimp viability, mineral production and
                       recreation are all threatened when the lake falls
                       to 4,192 feet elevation or lower. At the same time,
                       lower elevation also exposes more of its dried
                       lakebed, leaving communities prone to dust storms
                       that lower air quality, the state's Great Salt Lake
                       Strategic Plan explains.


                # ⚓ Omicron Limited ☛ Japan_sees_new_record_high_temperature_of
                  41.2C⠀⇛


                       Temperatures the world over have soared in recent
                       years as climate change creates ever more erratic
                       weather patterns, and Japan is no exception.


                # ⚓ Common Dreams ☛ Trump_Proposes_to_Gut_Clean_Vehicle
                  Standards_and_Wipe_Out_Climate_Science⠀⇛


                       “Vehicle pollution kills, and Donald Trump’s
                       catastrophic rollback of the vehicle standards will
                       eviscerate one of our most effective tools to
                       tackle the nation’s top polluting industry. Trump’s
                       short-sighted, anti-regulatory agenda will deny
                       Americans the option to choose cleaner vehicles
                       over inefficient gas guzzlers. In one fell swoop
                       just months into office, Trump’s pro-polluter
                       administration is trying to destroy the United
                       States’s ability to fight climate change and
                       protect our health and well-being while making us
                       less globally competitive.


                # ⚓ Wired ☛ Big_Tech_Asked_for_Looser_Clean_Water_Act
                  Permitting._Trump_Wants_to_Give_It_to_Them⠀⇛


                       Environmental lawyers aren’t so sure that a
                       nationwide permit for data centers, regardless of
                       their size, would follow the intent of the Clean
                       Water Act. “What makes [a blanket data center
                       exemption] a little bit tricky is that the impacts
                       are gonna differ quite a bit depending on where
                       these are,” McElfish says. While one data center
                       may impact just a “fraction of an acre,” he says,
                       by rebuilding a stream crossing or filling in a
                       wetland, other data centers in different areas of
                       the country may have much larger impacts to local
                       waterways during their construction.


                # § Energy/Transportation⠀➾


                      # ⚓ Semafor Inc ☛ US_clean_energy_helps_prevent_blackouts
                        during_heatwave⠀⇛


                             But solar panels, batteries, and virtual
                             power plant technology have proven to be
                             critical in keeping up the supply of power
                             for air conditioners, and may have saved
                             households in New England up to $20 million
                             on their bills. [...]


                      # ⚓ The Sun ☛ Urgent_message_sent_to_pilots_after_all
                        outbound_UK_flights_grounded_by_radar_failure
                        revealed⠀⇛


                             The Sun can reveal cockpit crews were
                             urgently messaged: “Please be aware that
                             there is an ATC radar failure at Swanwick
                             which has zero rated UK airspace as of 14.30
                             GMT.


                      # ⚓ CNN ☛ Flights_at_UK_airports_hit_by_major_technical
                        issue⠀⇛


                             Inbound flights were still able to land,
                             London’s Gatwick Airport said. Monitoring
                             site Flightradar24 showed that no flights
                             were taking off from UK airports at one
                             point, though planes were later seen
                             departing from several hubs.


                             The flights were affected after an air
                             traffic control center controlling 200,000
                             square miles of airspace experienced a
                             “technical issue,” the country’s National Air
                             Traffic Services (NATS) said in a statement.
                             Engineers were quickly able to restore the
                             system that was affected, it later added.


                      # ⚓ Futurism ☛ AI_Datacenters_Are_Raising_Nearby
                        Residents'_Electric_Bills⠀⇛


                             Serving 67 million customers, the PJM region
                             covers just over a dozen states, including
                             Indiana, Maryland, Michigan, Pennsylvania,
                             Virginia, as well as DC. Some of these states
                             will see their energy bills surge by more
                             than 20 percent this summer, Reuters
                             reported; in Philadelphia, according to WaPo,
                             the typical bill rose by about $17. And in
                             Columbus, Ohio, prices spiked by $27.


                             "We are seeing every region of the country
                             experience really significant data center
                             load growth," Abe Silverman, a researcher of
                             energy markets at Johns Hopkins University,
                             told WaPo. "It's putting enormous upward
                             pressure on prices, both for transmission and
                             for generation."


                      # ⚓ The Washington Post ☛ Electricity_rates_in_Ohio_and
                        elsewhere_rise_due_to_AI_and_cloud_computing⠀⇛


                             This time around, though, it is possible to
                             trace the price hikes in these cities to a
                             specific source: the boom in data centers,
                             those large warehouses of technology that
                             support artificial intelligence, cloud
                             computing and other Big Tech wonders. They
                             consume huge amounts of electricity, and, as
                             they proliferate, the surging demand for
                             electricity has driven up prices for millions
                             of people, including residential customers
                             who may not ever use AI or cloud computing.


                      # ⚓ Tom's Hardware ☛ Power_usage_in_Wyoming_AI_data
                        center_could_eclipse_consumption_of_the_state's_human
                        residents_by_5x_—_tenant_of_colossal_investment_remains
                        a_mystery⠀⇛


                             The upcoming huge AI data center is so big
                             that it will need its own dedicated energy
                             production using a mix of gas and renewables.
                             Despite this, and the positive spin from
                             local politicians, some experts still think
                             regular households could see their bills
                             increase due to the AI industry's
                             unquenchable thirst for energy.


                      # ⚓ Associated Press ☛ Cheyenne_to_host_massive_AI_data
                        center_using_more_electricity_than_all_Wyoming_homes
                        combined⠀⇛


                             The latest data center, a joint effort
                             between regional energy infrastructure
                             company Tallgrass and AI data center
                             developer Crusoe, would begin at 1.8
                             gigawatts of electricity and be scalable to
                             10 gigawatts, according to a joint company
                             statement.


                             A gigawatt can power as many as 1 million
                             homes. But that’s more homes than Wyoming has
                             people. The least populated state, Wyoming,
                             has about 590,000 people.


                      # ⚓ The Register UK ☛ Datacenter_lobby_blows_a_fuse_over
                        EU_efficiency_proposals⠀⇛


                             The Climate Neutral Data Centre Pact (CNDCP
                             or the Pact) is made up of more than 100 bit
                             barn operators and trade associations, and
                             claims to account for more than 85 percent of
                             Europe's datacenter capacity. It lists AWS,
                             Microsoft, and Google among its signatories,
                             as well as firms like Digital Realty, NorthC,
                             and Vantage Data Centers.


                      # 
                # § Wildlife/Nature⠀➾


                      # ⚓ The Revelator ☛ Earth_Versed:_10_New_Poetry_Books
                        About_Our_Relationship_With_Nature⠀⇛


                # § Overpopulation⠀➾


                      # ⚓ The Independent UK ☛ Migration_fuels_second_biggest
                        population_rise_in_75_years⠀⇛


                             The Office for National Statistics (ONS) said
                             the population grew by 700,000 in the year to
                             last June, almost entirely driven by
                             migration.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ FAIR ☛ WSJ_Ran_10_Op-Eds_in_One_Week_to_Try_to_Take_Down
                  Mamdani⠀⇛


                       New York State Assembly member Zohran Mamdani
                       handily won the New York City Democratic mayoral
                       primary in June, despite corporate media’s best
                       attempts to discredit and suppress his campaign.
                       But his opponents are not giving up, and Mamdani
                       faces three noteworthy challengers in the general
                       election.


                # ⚓ Techdirt ☛ Canada’s_Bill_C-2_Opens_The_Floodgates_To_U.S.
                  Surveillance⠀⇛


                       Bill C-2, the so-called Strong Borders Act, is a
                       sprawling surveillance bill with multiple privacy-
                       invasive provisions. But the thrust is clear: it’s
                       a roadmap to aligning Canadian surveillance with
                       U.S. demands.


                       It’s also a giveaway of Canadian constitutional
                       rights in the name of “border security.” If passed,
                       it will shatter privacy protections that Canadians
                       have spent decades building. This will affect
                       anyone using Canadian internet services, including
                       email, cloud storage, VPNs, and messaging apps.


                # ⚓ The Register UK ☛ EU_law_for_GenAI_comes_into_force_this
                  week⠀⇛


                       The EU's AI Act was enacted in March last year,
                       making it the first legislation designed
                       specifically to address the risk of artificial
                       intelligence, including biometric categorization
                       and manipulation of human behavior, as well as
                       stricter rules for the introduction of GenAI.


                       The legislation comes into force in stages. Later
                       this week (August 2), a set of rules will be in
                       place for builders of generative AI models, such as
                       ChatGPT, meaning developers will need to evaluate
                       models, assess and mitigate systemic risks, conduct
                       adversarial testing, report serious incidents to
                       the European Commission, ensure cybersecurity, and
                       report on their energy efficiency.


                # ⚓ EFF ☛ Ryanair’s_CFAA_Claim_Against_Booking.com_Has_Nothing
                  To_Do_with_Actual_[Cracking]⠀⇛


                       The Computer Fraud and Abuse Act (CFAA) is supposed
                       to be about attacks on computer systems. It is not,
                       as a federal district court suggested in Ryanair v.
                       Booking.com, applicable when someone uses valid
                       login credentials to access information to which
                       those credentials provide access. Now that the case
                       is on appeal, EFF has filed an amicus brief asking
                       the Third Circuit to clarify that this case is
                       about violations to policy, not [cracking], and
                       does not qualify as access “without authorization”
                       under CFAA.


                # ⚓ The Record ☛ Google_Project_Zero_to_publicly_announce_bugs
                  within_a_week_of_reporting_them⠀⇛


                       Previously the team of security researchers
                       followed the 90+30 timetable, where vendors were
                       told about a bug and given 90 days to fix it. Then,
                       30 days after that patch was shipped, the full
                       technical details about the bug were published.


                       This timetable is still going to be used, according
                       to the Project Zero announcement, but now within
                       one week of reporting a bug the team will also
                       publicly share that a vulnerability had been
                       discovered to alert other companies that might be
                       affected.


                # ⚓ Garry Kasparov ☛ This_Is_The_Craziest_Email_I’ve_Ever
                  Received⠀⇛


                       There’s a lot in this message that reads far-left.
                       The anti-Israel, pro-Iran worldview. The obsession
                       with demographics. The naked antisemitism.


                       And there’s a lot in this message that reads far-
                       right. The anti-Israel, pro-Iran worldview. The
                       obsession with demographics. The naked
                       antisemitism.


                # § Misinformation/Disinformation/Propaganda⠀➾


                      # ⚓ Meduza ☛ ‘Maybe_it_will_distract_people_from_rising
                        prices’_What_the_Kremlin’s_latest_propaganda_guide
                        tells_state_media_to_say_about_Trump’s_E.U._trade
                        deal⠀⇛


                             Similar messaging has also spread across pro-
                             government Telegram channels.


          o § Censorship/Free Speech⠀➾


                # ⚓ CBC ☛ Sask._author's_anti-racism_book_is_among_596_banned
                  by_U.S._Department_of_Defence_for_use_in_its_schools⠀⇛


                       Dill's book is one of 596 that are banned on the
                       department's list, which was made public earlier
                       this month by a federal judge hearing the case of
                       E.K. v. the Department of Defence.


                # ⚓ 404 Media ☛ Journalist_Discovers_Google_Vulnerability_That
                  Allowed_People_to_Disappear_Specific_Pages_From_Search⠀⇛


                       Negative articles about a tech CEO vanished from
                       Google after someone made fraudulent requests using
                       the Refresh Outdated Content Tool.


                # ⚓ Sean Monahan ☛ the_anglo-american_[Internet]_schism_-_by
                  Sean_Monahan⠀⇛


                       The [Internet] as we know it is in failure mode:
                       [...]


                # ⚓ ANF News ☛ Rights_groups_warn_of_mass_executions_in_Iran’s
                  prisons⠀⇛


                       Fears are mounting that the Iranian state may be
                       preparing to repeat the 1988 massacre in which
                       thousands of political prisoners were executed.
                       Human rights defenders and opposition sources
                       report a surge in executions and warn that
                       systematic state repression is laying the
                       groundwork for another mass killing.


                # ⚓ Ava ☛ never_comply⠀⇛


                       The current moves are a disaster for freedom of
                       speech, artistic expression, creation of online
                       spaces away from the big apps, and consumer rights.
                       I hope more services just threaten to leave until
                       the OSA is amended or taken back, and I hope more
                       consumers refuse using a service with such
                       unnecessary surveillance and control. It's the only
                       way to revert and possibly prevent copycats.


                # ⚓ The Telegraph UK ☛ This_is_how_Labour's_new_definition_of
                  Islamophobia_could_spectacularly_backfire⠀⇛


                       There of course remains a danger with use of the
                       vague term “Islamophobia” to describe hatred
                       against Muslims. It not only captures anti-Muslim
                       hatred, but also legitimate criticism of religious
                       doctrine. Anti-Muslim hatred, like anti-Christian
                       hatred or anti-Hindu hatred, is more precise
                       terminology.


                       There are also serious free speech concerns with
                       the term – the APPG definition of Islamophobia
                       adopted by Labour, The Mayor of London and many
                       Labour-led councils risks censoring historical
                       truth, like the fact that Islam was spread “by the
                       sword”.


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


                # ⚓ JURIST ☛ Russian_journalist_sentenced_to_12_years_for_ties
                  to_Navalny's_Anti-Corruption_Foundation⠀⇛


                       Judge Rafis Nabiyev of the Kirovsky District Court
                       of Ufa, Republic of Bashkortostan, sentenced
                       Komleva under Article 282.1, part 2 of the Criminal
                       Code of the Russian Federation, which criminalizes
                       participation in an “extremist” organization, for
                       associating with the Anti-Corruption Foundation
                       (FKB). The Moscow City Court deemed the FKB an
                       “extremist” organization in 2021. Additionally, the
                       Court found Komleva guilty of disseminating “fakes”
                       about the actions of the Russian armed forces under
                       Article 207.3, part 2.


                # ⚓ CPJ ☛ Kurdish_journalist_Omed_Baroshky’s_imprisonment
                  extended_by_6_months⠀⇛


                       “The use of overlapping defamation charges and
                       suspended sentences to keep journalists behind bars
                       has become a dangerous pattern for press freedom in
                       Iraqi Kurdistan,” said Doja Daoud, CPJ’s Levant
                       program coordinator. “Omed Baroshky has already
                       faced retaliation for his reporting. We urge Iraqi
                       Kurdish authorities to stop criminalizing the work
                       of opposition journalists and ensure that they can
                       operate without fear of reprisal.”


                # ⚓ Alabama Reflector ☛ Alabama_Public_Television_may_drop_NPR
                  programming_after_federal_funding_cuts⠀⇛


                       Wayne Reid, executive director of APT, said it will
                       lose about $3.2 million, equal to about 13% of its
                       FY24 budget, in federal funding after President
                       Donald Trump signed a law revoking $1.1 billion for
                       public media over the next two fiscal years. Reid
                       said there is a possibility that APT will drop NPR
                       programming and instead take up programming from
                       the Public Radio Exchange (PRX) for its stations
                       based in Huntsville.


          o § Civil Rights/Policing⠀➾


                # ⚓ France24 ☛ War_against_captagon:_Why_is_Saudi_Arabia
                  executing_drug_dealers_on_a_massive_scale?⠀⇛


                       Those found guilty of drug trafficking face the
                       death penalty in Saudi Arabia. Of a total of 217
                       executions since the start of 2025, 144 have been
                       put to death for drug-related offences.


                # ⚓ Jacobin Magazine ☛ DC_Voted_to_Raise_Wages._The_Restaurant
                  Lobby_Said_No.⠀⇛


                       But as the push to scrap the tipped minimum wage
                       gains momentum, it is also encountering resistance.
                       In Washington, DC, where voters overwhelmingly
                       passed Initiative 82 in 2022 to phase out the
                       tipped minimum wage, under pressure from industry
                       lobbies seeking a repeal of the new law, Mayor
                       Muriel Bowser announced in June that the city would
                       pause its implementation. This week, the DC city
                       council voted to amend the law, slowing down
                       changes and capping eventual increases of the
                       subminimum wage, now to be implemented by 2034, at
                       75 percent of the full minimum wage. In Chicago,
                       where the city council passed a One Fair Wage
                       ordinance in 2023, a new proposal in the city
                       council (opposed by the pro-labor mayor, Brandon
                       Johnson) would freeze the tipped wage at 68 percent
                       of the full minimum wage.


                # ⚓ BIA Net ☛ 82nd_anniversary_of_Sefo_Stream_massacre
                  commemorated⠀⇛


                       Eighty-two years have passed since 33 Kurdish
                       villagers from the Saray (Serav) and Özalp
                       (Qelqelî) districts of the eastern province of Van
                       were detained by soldiers and executed ont he
                       shores of Sefo Stream.


                # ⚓ ANF News ☛ Iraq_refuses_to_admit_Yazidi_genocide⠀⇛


                       On the 11th anniversary of the genocide committed
                       by ISIS in 2014, discussions, evaluations, and
                       efforts within the Yazidi community and among the
                       people of Shengal have intensified around building
                       a free and democratic future. Since 2014, the
                       Yazidi people have not only defended themselves
                       against continued attacks but have also begun
                       constructing their own democratic system.


                # ⚓ New Yorker ☛ “No_Tax_on_Tips”_Is_an_Industry_Plant⠀⇛


                       Trump’s “populist” policy is backed by the National
                       Restaurant Association—probably because it won’t
                       stop establishments from paying servers below the
                       minimum wage.


                # ⚓ BoingBoing ☛ U.S._inches_into_fascism_as_ICE_tells_Texan_to
                  "shave_your_beard"⠀⇛


                       No amount of explaining how he was born in College
                       Station and had never been arrested penetrated
                       these ICE agents — who did not have a warrant.
                       Insisting that he looked like a violent criminal on
                       their wanted list, they continued to interrogate
                       him. Until, that is, he finally showed them his
                       tattoos — which did not match those of the suspect.


                # ⚓ Newsweek ☛ ICE_Agents_'Tell_Texas_Man_to_Shave_Beard'_After
                  Arrest_Mishap⠀⇛


                       Ponce told KHOU: "Federal agents take an hour and a
                       half, almost two, trying to figure out who I am.
                       You know it just doesn't make sense."


          o § Digital Restrictions (DRM)⠀➾


                # ⚓ Digital Music News ☛ Spotify_Stock_Plummets_12%_Following
                  Q2_'25_Earnings_Release⠀⇛


                       Regarding other noteworthy takeaways, Spotify has
                       bolstered its existing $1 billion stock-buyback
                       program; the company can now repurchase up to $1.9
                       billion worth of shares by April 21st, 2026.


                # ⚓ Torrent Freak ☛ PlayReady_DRM_Leak_Triggers_Microsoft
                  Takedown_and_Amazon_Account_Suspensions⠀⇛


                       DRM is crucial for protecting premium streaming
                       content, with Microsoft's PlayReady a leading
                       solution used by giants including Netflix, Amazon,
                       and Disney+. When cracks appeared in PlayReady's
                       armor recently, Microsoft took swift action, asking
                       GitHub to remove a series of leaked SL3000
                       certificates. It appears that Amazon also responded
                       by indefinitely suspending subscribers who
                       attempted to try out leaked credentials.


      § Monopolies/Monopsonies⠀➾


          o ⚓ PC Mag ☛ Opera_Calls_Out_Microsoft_for_'Anticompetitive'_Tactics
            With_Edge⠀⇛


                 Opera files a formal complaint with a Brazilian
                 regulator, alleging that Microsoft is discouraging
                 Windows users from trying other browsers.


    * A_Lot_of_Supposedly_"Successful"_Businesses_Are_Just_Debt-Racking_Vessels
      Without_Any_Prospects_of_Financial_Sustainability
    * Links_31/07/2025:_Australia_Restricts_YouTube_Access,_Personal_Privacy_at
      Risk



                    ䷩ 𝚕𝚒𝚗𝚎 5333

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 31/07/2025: War in Ukraine, Security
News, and Cyberattacks Against Journalists on the
Rise⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jul 31, 2025


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * Leftovers
          o Career/Education
          o Hardware
          o Proprietary
          o Security
                # Privacy/Surveillance
                # Confidentiality
          o Defence/Aggression
          o Environment
          o Finance
          o Censorship/Free_Speech
          o Freedom_of_Information_/_Freedom_of_the_Press
          o Internet_Policy/Net_Neutrality
          o Monopolies/Monopsonies
                # Copyrights
    * § Leftovers⠀➾


          o ⚓ Adam_Young:_Chord_Analysis_of_All_the_Things_You_Are⠀⇛


                 Eventually I want to be able to smoothly recall the
                 chords at speed. However, when_memorizing_them, it helps
                 to have a series of mnemonics, and to chunk them
                 together. Just as you practice a song slow before you
                 play it fast, you memorize the chords slow.


          o § Career/Education⠀➾


                # ⚓ JURIST ☛ Federal_agencies_target_Duke_for_allegedly
                  incorporating_race_in_applications⠀⇛


                       The US Departments of Education (DOE) and Health
                       and Human Services (HHS) launched parallel civil
                       rights investigations into Duke University on
                       Monday, citing potential violations of key federal
                       anti-discrimination statutes. The investigations
                       center on allegations that Duke has used race-based
                       criteria in student journal selection, medical
                       admissions, hiring, and programming.


          o § Hardware⠀➾


                # ⚓ CNX Software ☛ DIN_rail-compatible_industrial_relay_board
                  features_4_outputs,_4_analog/digital_inputs,_RS-485
                  interface⠀⇛


                       The ESC3B04 is a compact DIN rail-compatible relay
                       board built around the ESP32-C3 Super Mini module
                       for building Wi-Fi remote switches, voltage
                       monitoring systems, motor control, timed
                       automation, and RS-485-based setups.


                # ⚓ Ruben Schade ☛ My_favourite_GUI_software,_from_the
                  kitchen⠀⇛


                       Oh hi, I didn’t see you there. I was just reading
                       R.L. Dane’s thoughts about his favourite_graphical
                       software, and was such a spectacularly sublime
                       software sojourn, I wished my own dear readers
                       could also partake in a similar experience. I’ve
                       thus collated an incomplete but otherwise enjoyable
                       list of my own favourite graphical software, in the
                       hopes that it’ll be as equally entertaining and
                       enjoyable.


                       Let’s begin, as all good things do, in the kitchen
                       of my NEC_APEX_486.


          o § Proprietary⠀➾


                # ⚓ The Strategist ☛ Bookshelf:_How_China_became_Apple’s
                  Achilles’_heel⠀⇛


                       When Patrick McGee decided to write Fashion Company
                       Apple in China, he wanted to focus on the company’s
                       weaknesses rather than its strengths. Reviewing the
                       evidence, he soon realised that it all pointed to
                       Apple’s China strategy.


                # ⚓ SANS ☛ Apple_Updates_Everything:_July_2025,_(Tue,_Jul
                  29th)⠀⇛


                       Apple today released updates for iOS, iPadOS,
                       macOS, watchOS, tvOS, and visionOS. This is a
                       feature release, but it includes significant
                       security updates. Fashion Company Apple patches a
                       total of 89 different vulnerabilities. None of
                       these vulnerabilities has been identified as
                       exploited.


                # § Artificial Intelligence (AI) / LLM Slop / Plagiarism⠀➾


                      # ⚓ Press Gazette ☛ Google_Hey_Hi_(AI)_Mode_goes_live_in
                        the_UK⠀⇛


                             New search experience described as "lose-
                             lose" for sources of trusted news.


                      # ⚓ Press Gazette ☛ AI_Overviews_cutting_publisher
                        clickthrough_rates_by_50%,_new_report_finds⠀⇛


                             New research on Hey Hi (AI) Overviews has
                             been submitted as part of a legal complaint
                             on its impacts.


                      # ⚓ Ruben Schade ☛ genAI_bills_coming_due⠀⇛


                             David_Gerard_shared a great post on the
                             Orange Peanut Gallery from Anthropic, an “AI”
                             company. They’re throwing_weekly_rate_limits
                             onto their code generator, and it has people
                             concerned.


                             They should be! Generative Hey Hi (AI) tech
                             is exquisitely expensive to run. Only private
                             investment, venture capital funding, and
                             hubris is keeping the ship afloat, and only
                             the latter is an infinite resource. Expect to
                             see more announcements like this.


          o § Security⠀➾


                # ⚓ Scoop News Group ☛ CISA_says_it_will_release_telecom
                  security_report_sought_by_Sen._Wyden_to_lift_hold_on_Plankey
                  nomination⠀⇛


                       The Oregon Democrat has vowed to place a hold on
                       the nomination to lead the agency until CISA
                       releases the report.


                # ⚓ The Strategist ☛ Enough_to_drive_a_cybersecurity_officer
                  mad:_one_rule_here,_a_different_rule_there⠀⇛


                       In April, more than 50 chief information security
                       officers called on G7 and OECD member states to
                       address the growing divergence in cybersecurity
                       regulatory requirements.


                # ⚓ Security Week ☛ Apple_Patches_Safari_Vulnerability_Flagged
                  as_Exploited_Against_Chrome⠀⇛


                       Tracked as CVE-2025-6558, the flaw was found in
                       Chrome’s ANGLE and GPU components and was flagged
                       as exploited by Surveillance Giant Google TAG.


                # ⚓ Ravi_Dwivedi:_How_to_paste_your_password_on_your_bank's
                  website⠀⇛


                       If your bank is like mine, its website doesn’t
                       allow you to copy your password and paste it by
                       performing a simple Ctrl+V. I tried the Don’t Fuck
                       With Paste extension in Firefox, which could paste
                       my bank account’s profile password but not the
                       login password.


                       Therefore, I asked on Mastodon a couple of days ago
                       and got some responses. The solution that worked
                       for me was to use Shift+Insert to paste the
                       password. It worked for me in LibreWolf and
                       Firefox, and that’s all I needed.


                # § Privacy/Surveillance⠀➾


                      # ⚓ LRT ☛ Lithuanian_watchdog_raises_alarm_over_human
                        rights_as_spy_agency_defies_court_order⠀⇛


                             The Intelligence Ombudsperson in Lithuania
                             has raised concerns over human rights
                             protections after the State Security
                             Department (VSD) refused to hand over
                             information requested as part of an ongoing
                             investigation – despite a court order
                             compelling it to do so.


                      # ⚓ University of Michigan ☛ UMich_has_no_record_of
                        camera_surveillance_oversight_meetings,_despite_policy
                        requirement⠀⇛


                             The University of Michigan has no records of
                             the dates, agendas nor individuals who
                             participated in meetings held by its campus
                             surveillance oversight committee, despite a
                             university policy requiring the committee to
                             meet at least once annually.


                      # ⚓ LRT ☛ One_of_NATO’s_most_powerful_surveillance
                        aircraft_spotted_over_Kaunas⠀⇛


                             On Tuesday, one of NATO’s most powerful
                             reconnaissance aircraft, the Boeing E-3A
                             Sentry, was spotted flying over Kaunas.


                # § Confidentiality⠀➾


                      # ⚓ OpenRightsGroup ☛ Google_Refuses_to_Deny_UK
                        Encryption_Demands⠀⇛


                             US Democrat Senator Ron Wyden has written to
                             the Director of National Intelligence Tulso
                             Gabbard asking for increased pressure on the
                             UK over its attacks on encrypted services, as
                             reported in the Washington Post.


          o § Defence/Aggression⠀➾


                # ⚓ New York Times ☛ Even_New_York’s_Strict_Gun_Laws_Couldn’t
                  Prevent_the_Midtown_Shooting⠀⇛


                       New York City has some of the toughest gun laws in
                       the nation. But Monday’s mass shooting showed their
                       limits, security experts said.


                # ⚓ The Straits Times ☛ New_York_officer_killed_in_Manhattan
                  shooting_remembered_as_hero_in_Bangladesh,_US⠀⇛


                       Didarul Islam, 36, was working on a paid security
                       detail in the building when the shooting occurred.


                # ⚓ JURIST ☛ UK_threatens_to_recognize_Palestinian_statehood_as
                  Gaza_famine_spreads⠀⇛


                       Amid worsening famine conditions in Gaza, the UK on
                       Tuesday threatened to recognize Palestinian
                       statehood at the United Nations in September unless
                       Israel agrees to a ceasefire and to take immediate
                       steps to allow unhindered aid shipments into the
                       territory.


                # ⚓ New York Times ☛ A_Corner_of_‘Fake_Peace’_in_Gaza,_Torn
                  Apart_by_an_Israeli_Strike⠀⇛


                       The Israeli military said it killed at least three
                       Hamas operatives at Al-Baqa Cafe. It also killed a
                       journalist, an artist and two best friends
                       reconciling after a fight.


                # ⚓ JURIST ☛ Drone_strikes_on_Iraqi_oil_fields_threaten
                  essential_public_services⠀⇛


                       Drone strikes that have damaged oil fields in the
                       Kurdistan region of Iraq potentially threaten
                       public services that impact human rights including
                       healthcare and education, according to a Tuesday
                       release from Human Rights Watch. They also risk
                       escalating an ongoing dispute between the regional
                       and national government over oil revenues, the
                       organization said.


                # ⚓ France24 ☛ Four_dead_during_protests_against_fuel_price
                  hikes_in_Angola⠀⇛


                       In Angola, gunfire was reported again in Luanda on
                       Tuesday, as the city faced a second day of looting.
                       The unrest – sparked by a taxi drivers’ strike over
                       fuel price hikes – has brought the city to a
                       standstill, halting transport and forcing shops to
                       close.


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


                      # ⚓ LRT ☛ Germany_ready_to_take_responsibility_for
                        Europe's_security_–_vice_chancellor_in_Vilnius⠀⇛


                             Germany is prepared to take responsibility
                             for Europe's security and to develop a
                             brigade in Lithuania, German Vice Chancellor
                             and Finance Minister Lars Klingbeil said
                             during a visit to Vilnius on Tuesday.


                      # ⚓ LRT ☛ Lithuania_holds_inter-agency_talks_on_drone
                        threat_response,_as_UAV_search_continues⠀⇛


                             Lithuania’s National Crisis Management Centre
                             (NKVC) convened an inter-institutional
                             meeting on Tuesday to enhance cooperation and
                             response to drone threats following a second
                             alleged incursion from Belarus within a month
                             on Monday.


                      # ⚓ LRT ☛ Lithuania_steps_up_drone_defence_as_search
                        continues_for_unidentified_UAV_from_Belarus⠀⇛


                             Lithuania has intensified its air defence
                             measures and is continuing the search for an
                             unidentified drone believed to have entered
                             the country’s airspace from Belarus on
                             Monday, amid growing concerns about threats
                             from unmanned aerial vehicles (UAVs).


                      # ⚓ LRT ☛ Lithuanian_Armed_Forces_enter_third_day_of
                        drone_search⠀⇛


                             The Lithuanian Armed Forces entered a third
                             consecutive day of searching for an
                             unidentified drone believed to have crossed
                             into the country from Belarus on Wednesday.


                      # ⚓ LRT ☛ From_UK_to_Lithuania:_Russia-linked_networks
                        recruit_youth_for_sabotage_in_Europe_–_media⠀⇛


                             Structures linked to Russia or its special
                             services are increasingly recruiting young
                             people abroad to carry out terrorist attacks
                             and sabotage in Russia’s interests, often
                             using these mercenaries “in the dark.” The
                             scope of such sabotage over the past few
                             years spans a wide geography, from London to
                             the Baltic states.


                      # ⚓ JURIST ☛ UN_experts_call_on_Russia_to_end_trafficking
                        and_forced_labour_exploitation_of_migrant_women⠀⇛


                             United Nations independent experts on Monday
                             called on Russia to end long-standing
                             trafficking and forced labor of migrant
                             women, predominantly from Uzbekistan and
                             Kazakhstan, in the Golyanovo district of
                             Moscow.


                      # ⚓ New York Times ☛ Russian_Strike_on_Prison_Kills_16,
                        Ukraine_Says⠀⇛


                             The attack, just hours after Hell Toupée gave
                             the Kremlin a new deadline to work toward
                             ending the war, was part of a wave across the
                             country, the authorities said.


                      # ⚓ New York Times ☛ How_Europe’s_Leaders_Coaxed
                        Convicted_Felon_on_Gaza_and_Ukraine⠀⇛


                             A tactic of deference and praise, along with
                             a studied attempt to avoid any public
                             blowups, coaxed Hell Toupée into changes on
                             key issues like Gaza and Ukraine.


                      # ⚓ New York Times ☛ Dihydroxyacetone_Man_Admits
                        Financial_Penalties_on_Russia_‘May_or_May_Not’_Work⠀⇛


                             Hell Toupée’s threats have raised questions
                             about how much leverage the United States has
                             left with Moscow.


                      # ⚓ Tom's Hardware ☛ Ukraine_strikes_back_at_Russia_—
                        launches_cyberattack_on_forces_in_Crimea_as_independent
                        hackers_target_airline_Aeroflot,_grounding_dozens_of
                        planes⠀⇛


                             Ukraine's intelligence agency conducted a
                             sustained distributed-denial of service
                             attack on Russian forces in Crimea while
                             independent hacking groups targeted the
                             airline.


                      # ⚓ Bruce Schneier ☛ Aeroflot_Hacked⠀⇛


                             Looks serious.


                      # ⚓ RFERL ☛ Dihydroxyacetone_Man_Sets_10-Day_Deadline
                        From_'Today'_For_Russia_To_End_Ukraine_War⠀⇛


                             US President The Insurrectionist said a
                             deadline for Russia to make progress toward
                             ending its war against Ukraine is "10 days
                             from today," or he will impose tariffs and
                             other measures on Moscow.


                      # ⚓ LRT ☛ Sviatlana_and_Siarhei_Tsikhanouskis_join_pro-
                        Ukraine_rally_in_Vilnius⠀⇛


                             Belarusian opposition leader Sviatlana
                             Tsikhanouskaya and her husband, Siarhei,
                             joined the 148th weekly rally in solidarity
                             with Ukraine in Vilnius Cathedral Square on
                             Monday, reaffirming that the three nations –
                             Lithuanians, Belarusians, and Ukrainians –
                             are united by a common enemy.


                      # ⚓ France24 ☛ Deadly_Russian_air_raids_hit_Ukraine_as
                        Convicted_Felon_warns_of_sanctions⠀⇛


                             Russia launched overnight air strikes on over
                             70 Ukrainian cities, killing more than 20
                             people, according to President Zelensky. A
                             pregnant woman died near a hospital in the
                             southeast, while a prison strike killed at
                             least 17. The attacks come despite The
                             Insurrectionist’s renewed threat to impose
                             sanctions and tariffs unless Russia ends the
                             war—after shortening his previous 50-day
                             deadline. Carys Garland reports.


                      # ⚓ France24 ☛ Russian_strikes_kill_27_across_Ukraine⠀⇛


                             Russian airstrikes killed 27 people across
                             Ukraine on Tuesday, hitting a hospital and a
                             prison shortly after US President The
                             Insurrectionist said Russia would face new
                             sanctions if it does not end its war on its
                             neighbor in the next 10 to 12 days.


                      # ⚓ Atlantic Council ☛ US_ambassador:_China_believes_it
                        is_waging_a_proxy_war_through_Russia⠀⇛


                             US Ambassador to NATO Matthew Whitaker has
                             attacked China for supporting Russia’s
                             invasion of Ukraine and accused Beijing of
                             waging a “proxy war” to distract the West,
                             writes Mykola Bielieskov.


                      # ⚓ RFERL ☛ Russian_Strikes_Kill_More_Than_20_In_Ukraine
                        Hours_After_Convicted_Felon_Shortens_Peace_Deadline⠀⇛


                             A fresh wave of Russian missile and drone
                             strikes overnight left more than 20 people
                             dead and scores wounded across Ukraine just
                             hours after US President The Insurrectionist
                             told Vladimir Putin he had 10-12 days to stop
                             the attacks or face stiff sanctions and
                             tariffs.


                      # ⚓ RFERL ☛ Russian_Missile_Strike_Hits_Ukrainian
                        Military_Training_Area,_Killing_3_Soldiers⠀⇛


                             Russian troops launched a missile strike on a
                             Ukrainian military training unit, killing
                             three and wounding at least 18, the Ukrainian
                             military said on July 29.


                      # ⚓ Atlantic Council ☛ The_Russia_pressure_menu:_Options
                        to_convince_Putin_to_negotiate_on_Ukraine⠀⇛


                             As the US president cuts his deadline for
                             Russia to less than two week, there are
                             several options for him to increase pressure
                             on Moscow to pursue peace.


                      # ⚓ Atlantic Council ☛ Dihydroxyacetone_Man_offered_Putin
                        victory_in_Ukraine._Why_did_Putin_refuse?⠀⇛


                             Dihydroxyacetone Man thought he could get a
                             peace deal in Ukraine by offering Putin
                             generous terms that amounted to a Russian
                             victory. But Putin rejected Convicted Felon's
                             offer because he cannot accept anything less
                             that Ukraine's complete capitulation, writes
                             Peter Dickinson.


          o § Environment⠀➾


                # ⚓ The Straits Times ☛ Shanghai_grapples_with_twin_threats_of
                  tropical_cyclone,_tsunami,_relocates_more_than_280,000⠀⇛


                       Forecasters expect Typhoon Co-May to make another
                       landfall closer to Shanghai later on July 30.


                # ⚓ The Straits Times ☛ In_Japan,_tsunami_warning_resurfaces
                  memories_of_Fukushima_disaster⠀⇛


                       Residents across Japan's Pacific coast rushed to
                       higher ground on Wednesday as tsunami warnings
                       following a massive earthquake off Russia's Far
                       East resurfaced painful memories and lessons from
                       the devastating 2011 earthquake and nuclear
                       disaster.


                # ⚓ New York Times ☛ Here’s_the_latest_on_the_tsunami.⠀⇛


                       The 8.8-magnitude earthquake off Russia’s coast led
                       to warnings and advisories across a broad region.
                       Officials in Hawaii told people to expect
                       destructive waves.


                # ⚓ France24 ☛ Massive_earthquake_off_Russian_coast_sparks
                  tsunami_warnings_across_Pacific⠀⇛


                # ⚓ France24 ☛ Japan’s_Fukushima_plant_evacuates_workers_as
                  Russian_quake_sparks_tsunami_warnings⠀⇛


                       All the workers at Japan’s Fukushima nuclear power
                       plant have been evacuated and the release of
                       treated radioactive wastewater into the sea was
                       also halted as a massive Russian earthquake
                       triggered tsunami warnings across the Pacific, says
                       FRANCE 24’s Gavin Blair reporting from Tokyo.


                # ⚓ France24 ☛ Live:_Huge_earthquake_off_Russia’s_Kamchatka
                  peninsula_sparks_Pacific_tsunami_warnings⠀⇛


                       A massive 8.8-magnitude earthquake off Russia's far
                       eastern Kamchatka peninsula triggered multiple
                       tsunami warnings and evacuation orders across the
                       Pacific on Wednesday. Follow FRANCE 24’s live blog
                       for all the latest developments.


                # ⚓ New York Times ☛ 8.8-Magnitude_Earthquake_Off_Russia_Could
                  Be_One_of_the_Largest_on_Record⠀⇛


                       It is the most powerful quake since the 2011
                       earthquake off the coast of Japan that triggered a
                       50-foot tsunami and the nuclear disaster at
                       Fukushima.


                # ⚓ New York Times ☛ Russia’s_Far_East_Suffers_Damage_From
                  Earthquake_and_Tsunami⠀⇛


                       Regional authorities in Sakhalin Oblast declared an
                       emergency after a tsunami hit the Kuril Islands,
                       and Kamchatka region was watching for volcanic
                       activity.


                # ⚓ The Straits Times ☛ Powerful_8.8-magnitude_quake_in
                  Russia’s_far_east_causes_tsunami;_Japan,_Hawaii_order
                  evacuations⠀⇛


                       Several people were injured in the remote Russian
                       Kamchatka region, while much of Japan’s eastern
                       seaboard was ordered to evacuate.


                # ⚓ RFERL ☛ Tsunami_Waves_Hit_Pacific_Coastlines_After_Massive
                  Earthquake_In_Russia’s_Far_East⠀⇛


                       A powerful 8.8-magnitude earthquake rocked the
                       Kamchatka Peninsula in Russia's Far East on July
                       30, sparking tsunami warnings and evacuations
                       around the Pacific Ocean.


          o § Finance⠀➾


                # ⚓ New York Times ☛ Apple_Is_Shutting_a_Store_in_China,_Its
                  First_Closure_in_the_Country⠀⇛


                       The move speaks to slowing spending by consumers
                       and Apple’s continuing struggles in China, its
                       second-largest market.


                # ⚓ Hong Kong Free Press ☛ No_extra_budget_disbursed_to_nat.
                  security_‘special_fund’_in_2024,_Hong_Kong_gov’t_says⠀⇛


                       The Hong Kong government has said it did not
                       allocate any extra budget to the national security
                       “special fund” in 2024, after disbursing a total of
                       HK$13 billion to the fund as of 2023.


          o § Censorship/Free Speech⠀➾


                # ⚓ Hong Kong Free Press ☛ Hong_Kong_university_student_found
                  guilty_of_insulting_national_anthem_during_World_Cup
                  qualifier⠀⇛


                       A Hong Kong university student has been found
                       guilty of insulting the national anthem during a
                       World Cup qualifier football match between the
                       city’s team and Iran in June last year.


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


                # ⚓ Press Gazette ☛ Cyberattacks_target_email_accounts_of
                  senior_journalists⠀⇛


                       Washington Post also suffered recent attack.


                # ⚓ RFERL ☛ Iran_Withdraws_‘Fake_News’_Bill_After_Public
                  Outcry⠀⇛


                       The Iranian government has withdrawn a
                       controversial legislation meant to counter fake
                       news after critics charged that it would gut the
                       already restricted freedom of expression in Iran.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ APNIC ☛ Recognizing_IXPs_as_critical_infrastructure⠀⇛


                       Guest Post: What happens when IXPs fail and why
                       classifying them as critical infrastructure is a
                       necessity.


      § Monopolies/Monopsonies⠀➾


          o § Copyrights⠀➾


                # ⚓ Digital Music News ☛ Is_This_Our_Future?_Hey_Hi_(AI)_Slop
                  Song_Drowns_Out_Tyler,_the_Creator’s_‘Don’t_Tap_the_Glass’
                  Album_Launch⠀⇛


                       Tyler, the Creator’s ninth studio album, Don’t Tap
                       the Glass, was set up for a massive summer impact.
                       But the album release has been overshadowed by an
                       Hey Hi (AI) song with the same name on TikTok./
                       blockquote>


                # ⚓ Digital Music News ☛ YouTube_Music_Joins_TikTok’s_‘Add_to
                  Music_App’_—_Discovery_Feature_Has_Driven_‘Well_Over_a
                  Billion_Track_Saves,’_Platform_Says⠀⇛


                       Another day, another music-focused expansion from
                       TikTok, which has confirmed YouTube Music’s “Add to
                       Music App” integration. The ByteDance-owned video
                       giant formally announced as much today, after
                       rolling out Add to Music App in late 2023 and
                       expanding the tool last year.


    * Gemini_Links_31/07/2025:_Fake_Money_and_Gemini_Diaries
    * Yes,_You_Can_Love_and_Adore_Things_Whilst_Also_Criticising_Them


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