𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Tuesday, May 21, 2024
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Generated Wed 22 May 02:49:19 BST 2024
Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖)
Full hyperlinks for navigation omitted but are fully available in the originals
The corresponding HTML versions are at 𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈
Latest in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕 and older bulletins can be found at 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕-𝒂𝒓𝒄𝒉𝒊𝒗𝒆𝒔
Full IPFS index in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔 and as plain text in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔/𝒕𝒙𝒕
Gemini index for the day: gemini://gemini.techrights.org/2024/05/21/


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

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QmdLsuRLzrwb58dZaSmJah6oCmNNZ6cW4ick4chqJmHjmY
QmTNR3uqcbMYjPAbbHjBqyNJb3ib8kytQvdFnATzkBFVvo
QmfCHrqMLfMsHXYnQeAvVuNYt91Zw2AmMJ5mx4RqsrWy3b
QmR2rr1yXDANjQBEz2oGtd2UMgy9U37FHdjpUhPfAk7h5z
QmWE6ucdKk9Q1pi6ce3ko9xPWd9Y4BjpLij3W7tJ5TMjG3
QmaoEDiALTYYZdaq3SQ86aQpMwUji1nqCeLbXAoszFRYvJ
QmSTkZUY74BcgbgqS6JKwwNbVnbzY5uqwpgWtYonGJua8s
QmXZcp3rXLYa24pYd7jUu6sPDrhziRCNCok875WLJTLysP
QmUE7nd24kx2soZFbSYKDsb1ik1wpirFTRTBhDTj6w9sjh
QmdKeWBhfnjgQLYU48wto7DdStpXsB5mE1yEEnWcxQ53vu
QmfSnnTnjcAe3YvtRsVgAwUJfpcEk1dM5J5yjJLyv7MxqM
QmQ16CkpxBbMzPZ6wZcuKBUcxH1RZ8uAEhcvdBsPRpVZe9
QmT3gTQRv33wEDtJveL8DiqiacGeRaxEbRFDUyVSJEAvDL
QmTs9qcwghZPs5oBh9qzsu8a11T4s6xHrJjVNyk5miFy3X
Qmdqd6mb8mj27qVvQZRR7sjshrXYYirWm9vRttLkNB5rW6
QmSjY85vxbu9nNFHUMmuK7CxRame2VYuhb523CJaK5zRkj
QmZwah9nZHVvSzbJWEAMxumYDpanFPqTahnqoNP83tuZbx
QmQWSrGfeYwgf6HE9N3742DJrJwq8uNSCUAz469CnuUFGe
QmcgTTyseF5zFd4MLquM4PtJZzkFcBEqaUbqDe4eaUx6Na
QmZMEFKvpgvjxAcV9Pwu7yF74LYZwS7ktdLFdYb988Ncfu


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

⦿ Techrights  -  Canonical and Red Hat Are Not Competing With Microsoft Anymore

⦿ Techrights  -  GNU/Linux Growing Worldwide (the Story So Far!)

⦿ Techrights  -  GNU/Linux in Honduras: From 0.28% to 6%

⦿ Techrights  -  Good News From Manchester and London, Plus High Productivity in Techrights

⦿ Techrights  -  Internal Memos/Communications Hinting at "a New, But Masked, Round of Layoffs" at Red Hat

⦿ Techrights  -  IRC Proceedings: Monday, May 20, 2024

⦿ Techrights  -  [Meme] Money In, No Money Out (Granting Loads of Invalid European Patents)

⦿ Techrights  -  Nigeria: Windows Down to 6%, Android at All-Time High of 77%

⦿ Techrights  -  Over at Tux Machines...

⦿ Techrights  -  Pursuing a Case With No Prospects (Because It's "Funny")

⦿ Techrights  -  Staff Representation at the EPO Has Just Explained to Heads of Delegations (National Delegates) Why the EPO's Financial Study is Another Hoax

⦿ Techrights  -  [Video] Microsoft's Attack on Education

⦿ Techrights  -  [Video] The 'Linux' Foundation Cannot be Repaired Anymore (It Sold Out)

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
https://techrights.org/n/2024/05/21/Canonical_and_Red_Hat_Are_Not_Competing_With_Microsoft_Anymore.shtml
https://techrights.org/n/2024/05/21/GNU_Linux_Growing_Worldwide_the_Story_So_Far.shtml
https://techrights.org/n/2024/05/21/GNU_Linux_in_Honduras_From_0_28_to_6.shtml
https://techrights.org/n/2024/05/21/Good_News_From_Manchester_and_London_Plus_High_Productivity_in_.shtml
https://techrights.org/n/2024/05/21/Internal_Memos_Communications_Hinting_at_a_New_But_Masked_Round.shtml
https://techrights.org/n/2024/05/21/IRC_Proceedings_Monday_May_20_2024.shtml
https://techrights.org/n/2024/05/21/Meme_Money_In_No_Money_Out_Granting_Loads_of_Invalid_European_P.shtml
https://techrights.org/n/2024/05/21/Nigeria_Windows_Down_to_6_Android_at_All_Time_High_of_77.shtml
https://techrights.org/n/2024/05/21/Over_at_Tux_Machines.shtml
https://techrights.org/n/2024/05/21/Pursuing_a_Case_With_No_Prospects_Because_It_s_Funny.shtml
https://techrights.org/n/2024/05/21/Staff_Representation_at_the_EPO_Has_Just_Explained_to_Heads_of_.shtml
https://techrights.org/n/2024/05/21/Video_Microsoft_s_Attack_on_Education.shtml
https://techrights.org/n/2024/05/21/Video_The_Linux_Foundation_Cannot_be_Repaired_Anymore_It_Sold_O.shtml

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
https://techrights.org/n/2024/05/21/Gemini_Links_21_05_2024_Caesar_II_for_MS_DOS_and_Reinventing_th.shtml
https://techrights.org/n/2024/05/21/Gemini_Links_21_05_2024_Losing_Fats_and_Modern_XMPP.shtml
https://techrights.org/n/2024/05/21/Gemini_Links_21_05_2024_New_Gemini_Reader_and_Gemini_Games.shtml
https://techrights.org/n/2024/05/21/Links_21_05_2024_Hating_Apple_Goes_Mainstream_Lots_of_Coverage_.shtml
https://techrights.org/n/2024/05/21/Links_21_05_2024_Tesla_Layoffs_and_Further_Free_Speech_Perils_O.shtml

                    ䷩ 𝚕𝚒𝚗𝚎 87

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/05/21/Canonical_and_Red_Hat_Are_Not_Competing_With_Microsoft_Anymore.shtml
    Gemini version at https://techrights.org/n/2024/05/21/Canonical_and_Red_Hat_Are_Not_Competing_With_Microsoft_Anymore.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Canonical and Red Hat Are Not Competing
With Microsoft Anymore⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on May 21, 2024


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


What a shame they hired so_many_people from Microsoft...


THE news sites, pointing to this_authoritative_source, say that "Google_goes
for_Microsoft's_jugular", but Google is proprietary software and hardly a
modest solution to the real problem, which ranges from bad privacy to
unnecessarily high cost. Heck, Google is in_some_sense_becoming_another
Microsoft, so do we even want to root for it?


We said the same thing about IBM roughly 15 years ago when it was pushing Lotus
and Symphony at the expense of Microsoft. Those are all proprietary and not
what we the Free software community ought to advocate for.


An associate of ours pointed out that Google is promoting alternatives to
Microsoft Office. "This is the kind of marketing that Red Hat and Canonical
ought to be doing at scale," the associate said. "Except offering a standards
based FOSS solution."


Well, Canonical and Red Hat keep pushing Microsoft. We gave_a_new_example
yesterday or as recently as about 20 hours ago.


Windows is not doing well, so why don't Canonical and Red Hat take advantage
and promote GNU/Linux for desktops and laptops? They hardly do. In IRC,
psydroid tells us that he has seen "lots of Qualcomm spam too as if the dying
OS [Windows] is suddenly relevant when switching to new hardware..."


Anyway, we'll continue to express our disappointment with Canonical and Red
Hat. The latter_helped_Microsoft_boot-lock_PCs_(for_Windows_monopoly) and it is
still_doing_this. How can we forget and forgive when it remains_a_growing
problem?


Our associate argues that "Canonical and IBM [Red Hat] have actively
facilitated infiltration by microsofters so as to subvert and weaken the two
companies. Within living memory, IBM used to be a heavy investor in Linux and
they liked the money they made rapidly though their Linux investments."


Well, today's IBM is a different company and there's a_rumour that this week,
shortly before a public holiday, it'll lay off many Red Hat employees.


Red Hat works for IBM. IBM does not work for the community, it's often trying
to cancel the community. Look_what_it_did_to_RHEL_last_summer. █




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⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡱⠂⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣡⣿⣿⡿⠿⢟⣾⣿⣿⣿⣿⣿⣼⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⠀⠀⢀⣷⣄⡀⣽⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣧⡀⠈⢿⣧⣠⣽⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡆⠀⠀⠀⠀⠀⠉⠻⣿⣷⣿⣻⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠼⣿⣵⣾⣿⣿⣟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⡈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣠⣶⣾⣿⣤⣾⣿⣿⣿⣿⣿⣯⢥⣺⣇⣪⣅⣀⣛⣯⡝⠚⠩⡭⠉⠈⠉⠉⠗⠛⠿⠿⠇⠈⢻⠿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣽⣿⣿⣿⣿⣿⣿⣿⣿⣭⣍⣿⡿⣿⣿⣿⣻⣿⠯⠳⢿⣿⣿⣿⣿⣷⣿⢿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡯⠿⣷⣶⣦⣉⣴⡀⠀⠀⠀⠀⠀⠀⣀⠀⢙⢿⠛⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⣛⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣓⣢⣀⠀⠀⠈⠁⢉⣻⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⢿⣵⣥⣤⡀⡀⠐⣢⣯⣦⣿⣾⣾⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣝⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 184

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/05/21/GNU_Linux_Growing_Worldwide_the_Story_So_Far.shtml
    Gemini version at https://techrights.org/n/2024/05/21/GNU_Linux_Growing_Worldwide_the_Story_So_Far.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ GNU/Linux Growing Worldwide (the Story So
Far!)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on May 21, 2024,
updated May 21, 2024


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


Taking the complete_(global)_data from statCounter, then averaging over a 6-
month sliding window, we can see the global "market share" of GNU/Linux
fluctuating between 6 and 7 percent. That's for desktops and laptops, at the
very least, and it ought to be noted upfront that statCounter probably does not
correctly capture some GNU/Linux clients. We wrote_about_that_yesterday_in
relation_to_China_with_its_homegrown_operating_systems.


What's pleasing about the image below is, caveats notwithstanding about the
absolute rather than relative numbers, the trends speak volumes. From 0.6 -
0.7% we've moved to 6 - 7%. Microsoft is unable to stop GNU/Linux. Many people
publicly moan about Vista 11 and then delete it. But installing GNU/Linux can
be harder if not impossible because of UEFI_'secure'_boot, still an outstanding
competition crime of Microsoft. It has no real purpose other than obstructing
the installation of alternatives to Windows. This needs to be properly
challenged in court. █


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




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠛⠛⠙⠛⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⣿⣿⣿
⣿⣿⣿⣿⣿⠿⠟⢿⡿⣿⡿⡻⢿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⠀⠀⠀⠀⢤⣤⣤⣤⣶⣦⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠀⠀⠀⠈⠄⣀⡐⠂⠤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣔⠂⢀⠀⣀⠀⢈⠀⡝⢐⠂⠀⠬⠅⠒⡒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉
⠹⣿⠋⠈⠀⢿⣧⢘⠀⣗⢸⠀⠀⠁⠀⢰⠄⢐⡁⢩⠁⡂⠸⠁⠋⠃⠙⠃⠘⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⠇⠸⠇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣠⣤⣤⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣴⣤⣶⣶⣶⣤⣠⣠⣀⣀⠀⠠⠀⠠⠠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⠿⢻⣿⣛⡿⢿⠝⢹⠻⡍⠉⡀⠀⠋⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⢹⣿⣯⢩⣯⢹⣏⢛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢛⡽⢿⡿⠛⡿⣻⣿⣟⣛⡒⢒⡛⠷⠔⠾⡟⢊⡟⠀⠀⠀⠠⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣘⣿⣸⣿⡘⣿⣸⣿⣿⣿⣿⡿⣿⣿⣿⣽⣛⢷⡳⠷⢿⠹⡳⢁⠿⠇⣪⠙⠈⠁⠀⠈⠈⠋⠂⠀⠀⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠛⠛⠟⠻⣿⣿⣿⣿⣿⣿⣿⣷⡞⡿⢟⣻⢛⡻⣁⢈⡑⠀⢀⠠⢂⠂⠘⠠⠳⠂⠀⠀⠀⠀⠃⠐⠀⠐⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⢙⣟⣿⣿⣿⠿⣿⣿⢷⣿⣵⢆⢉⣥⢦⣉⠃⠀⠈⠠⠜⢄⠀⠀⠁⢀⣄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣈⣟⣟⣿⢟⡿⠿⣿⢖⡏⣄⢳⡆⡱⣿⣿⢁⣢⡄⢶⡧⣀⣀⠄⣀⢈⠀⠘⡀⠐⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⢿⡿⢿⣿⣿⣽⣬⡛⢩⡹⠶⡯⢴⠭⠛⣿⠷⣤⡅⢛⠉⠒⠀⠰⠯⡄⢀⡌⠈⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠤⠒⠈⣣⠂⡁⠀⠉⢀⡉⢒⡌⡖⢶⠃⠀⠀⠀⠙⠀⠈⠙⠆⡐⠓⠑⠓⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠃⠂⠀⠈⠁⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠲⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡏⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⣿⡏⠹⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⣿⣿⣵⣬⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢹⣿⣿⣿
⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣾⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⡇⠀⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⡇⠀⣿⣿⣿⣘⣀⣇⣿⡀⣌⣀⣿⣼⣳⣿⣸⣻⣾⣇⣇⣇⣇⣷⣐⣿⣽⣇⣿⣆⣆⣷⣰⣎⣶⣇⣰⣉⣤⣇⣷⣕⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⢟⣿⢟⣿⣿⡿⠿⢿⠿⡿⡿⣿⢻⡟⡿⣿⣿⣿⠿⡿⡿⢿⠿⡿⠿⢿⠿⣿⠿⣿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣼⣷⣷⣿⣶⣧⣿⣠⣿⣄⣿⣻⣼⣇⣟⣿⣿⣯⣧⣿⣴⣧⣷⣟⣸⣯⣧⡇⡓⣧⣷⣿⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢹⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣻⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠹⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢸⡟⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠈⠛⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣽⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⡇⠀⣿⠿⠟⠛⠛⠉⠁⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⠿⣿⣿⣿⢿⣿⢻⣿⢿⡿⣿⣿⣿⠿⣿⣟⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣟⢿⡿⣿⢿⣿⣿⣿⢿⣿⢿⣿⣿⣿⢿⡿⣿⣿⣿⣟⣿⡟⣿⡿⣿⣿⣿⣻⣿⢻⣿⣻⣿⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣞⣯⣞⣽⣿⣽⣿⣿⣻⣯⣫⣿⣯⣾⣿⣼⢿⣟⣹⣿⣵⣿⣿⡿⣿⣋⣶⣯⣿⣿⣿⣿⣟⣿⣟⣽⣿⣽⣿⣷⣻⣿⣫⣿⣯⣿⣿⣞⣟⣞⣿⣿⣿⣿⣿⡿⣯⡻⣯⣛⣿⣿⣾⣿⣾⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 300

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/05/21/GNU_Linux_in_Honduras_From_0_28_to_6.shtml
    Gemini version at https://techrights.org/n/2024/05/21/GNU_Linux_in_Honduras_From_0_28_to_6.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ GNU/Linux in Honduras: From 0.28% to
6%⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on May 21, 2024


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


Moments ago in the sister site: From_0.5%_to_Nearly_5%:_How_GNU/Linux_Has_Fared
in_Mexico


Honduras, based in_central_America with a_population_of_over_10_million, was
mentioned_here_a_year_ago_because_of_a_fast-growing_share_of_GNU/Linux_users.
Looking at these_latest_numbers (ODF) from statCounter, Honduras remains
somewhat of a hotspot. See the graph below. █


 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Desktop Operating System Market Share Honduras: Feb 2009 -
                                  May 2024⦈




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⣿⣿⡿⢿⡿⣿⡿⡿⠛⠛⠛⠋⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹⣿⠳⢶⣿⠉⠉⠛⠛⠗⠿⣿⢯⢿⡿⠻⡿⠉⠛⠁⠀⠀⠀⠀⢀⣠⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠄⣴⣶⣿⡇⢰⢷⣿⣿⡿⡶⣦⣄⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠰⣯⠀⣄⣤⡆⢀⣨⢯⣿⣗⢺⣿⣿⣦⣴⣦⠄⠀⠀⠀⠀⣘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠈⢘⣹⣿⡿⠈⠘⠁⠈⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠷⠃⢹⠽⢳⡗⠀⠉⠟⠿⣿⡿⠃⠙⠉⠑⠋⠋⠁⠀⠙⠀⠀⠀⠀⠀⢸⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣀⠰⣾⣶⡆⢾⣧⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠆⠀⣄⣠⣦⣾⣿⣼⣶⣿⣿⣿⣿⣤⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⡟⣱⣿⡏⣔⡮⣿⣿⣿⡟⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⣿⣿⣿⣿⡲⣿⣿⣿⣻⡿⠿⢻⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣾⡆⠄⠆⢸⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣾⣯⠀⣼⣿⣿⣿⣿⣷⣿⣿⣿⡿⠇⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⡀⠀⢀⠀⠠⣺⣿⣿⣿⡿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣿⣿⡏⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃
⠀⠀⠀⠀⠀⠰⢢⠴⣾⣷⣿⡿⠿⢻⢿⡿⣿⡿⣿⣿⣿⢙⣿⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⢮⣼⣤⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⡗⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠮⡼⢿⣿⣿⡿⡄⠀⢠⡄⠁⣏⠴⣿⡿⡿⣿⣿⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⠦⠷⠌⢼⣿⣿⣿⢷⣿⣿⣿⣿⣿⣿⡿⠿⠏⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡺⠻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⠰⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⢘⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣝⠁⠈⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠇⠸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⢸⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁⠀⠈⠈⠁⠈⠉⠿⠍⠁⢹⣽⣿⣿⠀⣿⣴⣽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⢿⠏⠀⠁⠀⠀⠀⠈⠉⠉⠭⢿⡿⠍⠉⠉⠁⠈⠭⠭⠍⠭⠭⠿⡿⢿⡇⠀⠙⠋⠁⠀⠙⠁⠀⠀⠀⠀⠀⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠣⠀⠀⠓⠛⣿⣿⠀⠀⠙⠉⠛⣿⣿⣿⡟⣿⣿⢿⠟⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣽⠀⠀⠀⠀⠀⠀⡐⡀⢀⣄⠀⠀⣠⣾⣇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡀⢰⣿⣮⣐⣿⡯⡿⡟⠊⠉⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⣹⡇⠀⠀⠀⠀⠀⢀⣀⣾⡿⠻⣄⢰⡟⡫⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠉⢻⣿⡇⢈⣿⣿⣇⠿⠉⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⣿⢀⠂⢠⣶⣷⣿⣿⣿⣿⣯⣿⣿⣾⣗⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠰⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠈⢿⡇⢸⢿⣿⡿⠧⠵⠐⠖⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⢸⡿⠓⠛⡞⠛⢟⣿⠟⠛⡻⣿⢻⠟⠟⠋⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣰⣿⣱⣻⣷⡂⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⢸⡇⠀⠉⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣸⣿⣷⣾⣿⣿⣾⣷⣿⣼⣿⣿⣿⡇⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢰⣾⣿⣿⣿⣿⣿⣷⢠⠀⠀⠀⠀⠀⢾⠟⠀⠀⠀⠀⠐⡏⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠛⠆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢘⣿⣿⣿⣿⣿⣿⣏⠈⡆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡠⡀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠺⡏⣀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⣿⠿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢹⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣍⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡿⢻⠿⣿⣿⣿⣿
⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿
⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿
⣿⡿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⢿⣿⣿⣿
⣿⣷⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⢸⣿⣿⣿
⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⠿⢿⢿⢿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⠁⠀⠀⢸⣿⣿⣿
⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣠⣌⣤⣆⣨⣬⣦⣥⣤⣤⣄⣻⣽⣷⣴⣤⣤⣤⣬⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⢹⣿⣿
⣿⣏⡇⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠰⣾⣿
⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡃⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⣛⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡿⠿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⡇⠈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣏⡇⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠒⠒⠒⠂⠀⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿
⣿⣷⢻⡿⣻⣿⣿⢿⡟⣿⣟⡟⣿⢟⣿⣻⡟⣿⢻⡟⣿⢻⡟⣻⣿⡿⣿⡟⣿⢻⡟⣿⢛⣿⣻⢟⣿⣻⡿⣿⢻⡟⣿⣟⡿⣻⢟⣿⢿⡿⣿⢛⣿⣻⢟⡿⣻⡟⣿⢻⡟⣿⢻⡟⣿⢟⣿⣿⡟⣿⢻⡿⣿⢻⣿⣿⣿⣿
⣿⣵⣏⣼⣣⣟⣿⣹⣮⣶⣥⣿⣭⣯⣽⣹⣎⣷⣹⣎⣿⣭⣿⣩⣟⣽⣹⣞⣷⣵⣯⣾⣯⣿⣥⣏⣷⣹⣎⣷⣹⣮⣽⣏⣽⣩⣏⣷⣻⣎⣷⣵⣾⣵⣯⣼⣡⣎⣵⣡⣎⣴⣥⣿⣭⣏⣽⣡⣞⣼⣡⣯⣴⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 391

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/05/21/Good_News_From_Manchester_and_London_Plus_High_Productivity_in_.shtml
    Gemini version at https://techrights.org/n/2024/05/21/Good_News_From_Manchester_and_London_Plus_High_Productivity_in_.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Good News From Manchester and London, Plus
High Productivity in Techrights⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on May 21, 2024


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


THIS past Monday (yesterday) we published 29_pages/articles and 3_videos. It's
not an all-time high, but it is close. We're generally very productive and
still jubilant over the local team's season achievement (following Sunday's
victory on a very sunny day at home). Yes, that's Manchester City.


Here in Techrights we strive not to merely relay some news, such as distro
releases. That's what Tux Machines is for. This site is different.


Techrights explores mostly suppressed or unreported issues, not only with
analysis or commentary where actual evidence (such as leaks) became available.
We want to put in the public domain material that can improve people's
understanding of the world, including the patent and Free software spheres. Of
course those whom we expose try to prevent us from doing so. It's sometimes
easier to attack and try to demoralise the messenger (than to actually try to
refute the message).


Later today, probably in the evening, we shall release a video ("Microsoft's
Attack on Education") and also, seeing that the UK sort of changed its stance
on Julian Assange (this outcome surprised us for the better!) we're in high
spirits, extremely happy and having a good time. Thankfully we don't live in a
society or country like Russia. Press protections exist here, and not only for
those who back the dictators.


Let's hope Manchester City can win another cup, the FA Cup, next week in
London. We look forward to this "away derby". █


                 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Manchester City's Rodri⦈




⢟⣿⣽⣿⣿⠟⠏⠀⠀⢠⠀⠀⢀⡀⢿⣴⡖⠀⠉⠃⠀⢦⠀⠀⠀⢠⢀⠀⢸⡦⠀⢠⠉⠁⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣽⣷⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⠯⠹⣿⣿⣿⣿⣿⣿
⣼⣿⡟⢉⣿⣄⡆⠀⠀⠘⠀⠀⣿⠁⢸⣿⣿⠀⢠⠀⢀⣿⠆⠐⠒⠝⠉⠀⣸⡟⣀⢈⡀⠀⠀⣿⣿⣿⣿⣿⠿⣿⣿⣯⢹⣿⣿⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣽⣿⣯⣿⠗⠤⣿⣿⣿⣿⣿⣿
⣿⣹⣧⣾⣿⢿⡇⠀⠀⠀⠀⠀⣿⠀⠈⢻⣿⡴⣇⠀⠀⣿⡃⠀⠀⣵⣠⠀⣾⣿⣿⣿⣤⡆⣴⣿⣯⣿⣿⣿⣾⣿⣿⣿⢹⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠⣿⣿⢈⣿⡀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣼⡇⠀⢤⡆⠀⠀⠁⠀⢼⣿⣿⣷⣿⠀⠀⢑⣇⣠⡀⣿⣿⣎⣿⣿⣷⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣀⣿⣷⠭⣞⠀⣴⣿⣿⣿⣿⣿⣿
⣿⢿⣿⣿⣿⣿⡇⠀⠈⣷⠀⠀⠀⠀⣤⣿⣿⣿⣿⣶⣶⣾⣿⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼⣿⣿⣖⣿⣿⢉⣿⡅⣡⣿⣿⠿⣿⣿⣿
⡇⢸⣿⣿⣿⣿⣷⣠⣷⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢼⣿⣿⣿⣿⣿⣿⠉⠉⠉⢿⣿⣿⣿⣿⣿
⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢋⣉⠉⠉⠀⠀⠀⠘⣿⣿⣝⣿⣿⡏⠀⠀⠀⢽⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⠙⣿⣿⣿⡇⢸⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⡇⠉⠙⠉⠁⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡧⠀⠀⠀⢨⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠇⣽⣿⡟⠛⠒⠛⠛⠛⠛⠻⠿⠿⢿⠿⠿⠿⠟⠛⢋⠉⠉⠉⠛⠛⠛⠋⠙⠁⠀⠀⠀⠀⠀⠀⡀⡀⠀⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⠀⠀⠀⠈⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢹⣿⣿⠀⠁⢻⣷⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⣿⣿⣻⢿⣿⣿⣧⢀⠀⠘⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⣿⡆⣄⣸⣿⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠛⠛⠛⠓⠛⠛⠋⠉⠁⠨⠏⠉⠈⠉⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣟⣷⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢹⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠠⢤⠀⣀⢀⣠⣄⣤⣀⠡⠤⠄⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡄⠀⠀⠀⠀⠀⢰⣿⣿⣿⣟⣿⣾⣿⣿⡿⢷⣷⣾⣿⣿
⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣄⠀⠀⠀⠀⠀⠀⠠⣶⡞⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢷⠈⡽⣿⣿⣿
⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢠⣿⣽⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣿⢿⣿⣿⣿⣿⣿⣿⡝⠄⡒⢿⣿⢝
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢈⣾⣿⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⢸⡿⣿⢿⣳⡿⣿⣿⣿⣇⠩⠃⠐⣹⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢀⡀⠀⠀⢸⣾⣿⣇⠀⣿⡇⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⠀⠀⠀⠀⠀⢸⣿⣯⣿⣿⣿⣿⣿⣿⣗⣺⡃⠸⢹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢸⣿⣿⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡿⣿⣟⣿⣟⠛⠛⡋⡻⡉⠀⠀⠀⠀
⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣯⣿⣦⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡄⠀⠀⠀⠀⠘⠓⠉⡏⠿⣿⢸⣇⣷⣿⣿⣦⠀⠀⠀
⣀⣾⣟⡋⠉⣿⡝⠛⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠀⠀⠀⢀⠉⠉⠛⣿⣿⣿⢸⣰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠤⡴⡊⠇⢒⢸⣿⣿⣿⣿⣿⣇⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣧⣸⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠃⠀⠀⠈⠀⠀⠀⣿⣟⣻⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠠⠀⠃⠂⠈⢘⣿⣿⣿⣿⣿⣷⠀⠀
⠈⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⢈⠀⢸⠻⣿⣿⣿⠞⡻⠀⠀
⠒⠈⠁⠁⠙⡛⠛⠻⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠐⠛⠘⠁⠀⠀⠸⠟⠿⢄⣀⠀⠀
⠠⠤⢧⣀⡀⠀⠀⠀⠆⠀⢠⠀⣛⡛⢻⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢀⣀⣀⣠⣤⣀⣀⠀⢸⢸⣿⠛⣿⠿⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣦⣤⣄⣈⠉⠑⠚⠳⠤⢄⣀⣈⡘⢺⡇⢻⠑⣏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣬⣤⣶⣶⣿⣿⣿⣿⣲⣶⣶⢤⣤⣤⣀⣀⢀⣿⡇⠀⠀⠀⠀⠀⣿⣷⠶⣶⣦⢤⣤⣄⠀⢀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣄⣀⠉⠉⢙⣻⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣦⡈⠻⠁⠀⠀⠀⠀⠀⠉⠀⠀⠹⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣄⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣦⠹⠋⣹⡏⢠⠀⠀⣀⡀⠀⢤⡄⠀⠀⢀⠀⠀⠀⠁⠘⠛⠛⠻⢿⡿⣿⣿⣿⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿
⢿⣷⣾⣧⣶⣿⡶⢲⡟⠁⣰⡿⢰⡷⠆⢉⣄⡀⢀⠠⠀⢀⠀⠀⠀⠀⠉⠙⠑⠿⠿⣿⣿⣿⣷⣶⣤⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿
⠀⠀⠉⠙⠛⠿⢿⣿⣷⣾⣿⣾⣽⣿⣷⣿⠿⣿⣞⣳⣦⢤⣟⣶⢄⣤⠀⠀⠀⠀⠀⠀⠈⠈⠛⠙⠽⢿⣿⣿⣷⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣷⣶⣦⣈⢲⣦⣤⢠⣀⢀⣀⠀⠀⠉⠉⠛⠿⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣾⣷⣷⣶⣬⣤⣴⣀⠶⠀⠀⣀⠀⠀⠀⠀⣶⣤⣄⣀⣀⠀⢀⣴⡆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⣿⣟⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀⣀⠀⠀⠀⠀⠀⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣦⣿⣲⠖⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡾⣋⡻⣿⣿⣾⣿⣿⣿⣿⣭⣿⣿⣿⣿⣶⣶⣤⣀⣀⡀⠀⠀⠀⠉⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠂⠀⣸⣶⣦⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣵⣿⣤⣼⡟⣿⣟⣻⣿⣿⣶⣦⣤⣄⣀⠀⠀⠀⠉⠉⢻⡿⠿⣿⣿⣿⣿⣽⣿⣿⣿⣿⠋⠉⠁⠈⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡦⡀⠉⠉⠋⠱⠿⣿⢿⣶⣤⣄⣀⠀⠀⠀⠀
⣾⣷⠉⠛⣿⣷⡿⣿⣿⣿⣻⣯⡿⢯⣽⣿⣿⣷⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣶⣶⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣷⣆⡀⠒⠀⢰⣿⡇⠀⠀⠀⠙⠛⢿⣿⣿⣿⣶⣶⣶⡂⠀⠀⠀⠈⠉⠛⠿⠿⣿⣷⣶⣤
⠀⠀⠀⠉⠀⠙⠣⢶⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⢿⣴⣾⣏⣘⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⣀⣠⡄⣈⣸⣿⣿⣿⣿⣿⣿⣿⣷⣬⣈⣐⣀⣄⣰⣿⡿⣯⣽⣿⣿⣿⣿⣦⣈⡷⣦⣀⠐⠀⠀⠈⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⢿⣿⣿⣿⣿⣬⣿⣟⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢛⣿⣿⣷⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⢆⣠⣄
⣧⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⣿⣝⣿⣷⣶⣾⣽⣿⣏⠑⢝⣟⣿⣿⣿⣿⡿⢿⡿⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⢷⣾⣟⣼⣟⣶⣾⣿⣦⣤⣠⣦⣤⣄⣤⣤⣤⣄⣤⣤⡤⢀⡼⠻⣿⣿⡿⢿⣿⣿⣿⣯⡟⣾⣿⣿⡏⠀⡀⣹⣿⡞⠻⡟⠋⠉⢛⣀⢀⠈⡾⠿⢿⣿⣥⢀⣾⣿⣷⣦⣄⣀⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⢹⣻⣿⣿⢹⣯⣻⣿⣿⣿⣿⣿⣿⣿⣏⣻⣧⣟⣽⣴⣼⣯⣉⣭⣀⣠⢾⣠⣴⣿⣿⢧⣿⣿⣿⣿⣧⣿⣏⢻⣷⡿⢀⣤⣦⣝⡿⠗⠞⠨⣁⣸⣏⠙⣫⣿⣿⣿⣿⣿⣿⣷⣦⣤⣄⣀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿
⠀⢸⠰⣿⣿⣿⣼⣿⣿⣇⣿⣿⣿⣿⣿⣯⣿⠛⣿⣿⠿⣿⣿⣳⣅⣰⣦⣿⣾⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⣿⣿⣿⣏⡔⣅⡀⠀⠙⠦⠄⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣄⣀⠁⠉
⠀⢸⡾⢿⣿⡿⢻⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⠇⣿⣇⠺⣿⡛⢸⡷⣿⣿⣿⣿⣿⣿⣿⡟⠀⢿⣿⣿⣿⣿⣿⣿⠟⠉⣟⣿⢿⣿⣿⠁⠈⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣯⡿⢿⣿⣶⣶
⠀⣼⠀⢺⣿⡇⢸⣿⣿⡷⣿⣿⣿⣿⣿⣏⣿⣤⣿⣦⠁⣿⠋⠈⡱⠿⢿⣷⠻⡛⠇⠋⠁⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⣸⠽⠀⠀⠃⠀⠀⠀⠀⠀⠁⠀⠉⠙⠉⠉⠙⠛⠛⠛⠉⠉⠉⠀⠀⠀⠿⣿⣿⣿⣷⣬⡁⢹⡟
⠀⢻⠀⢸⣿⡇⠘⢿⡿⠃⠿⢛⣛⣛⣫⢩⣭⣽⣶⡞⠉⣿⠀⠰⠃⠀⠀⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠃⣶⠎⠡
⠀⢼⠀⠈⣽⣶⡄⢰⣿⣿⡀⣿⣿⣿⣿⣼⣿⣿⣿⣷⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠂⠀
⠀⣸⠀⢸⣿⣿⡏⣿⣟⣿⡇⣿⣿⣿⣿⣿⡿⣿⣿⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠰⢄⡀⠀⠀⠀⠀⠀⠀⠀
⠀⣻⠀⠈⠻⠿⠃⠿⠏⠿⠷⠿⠿⠸⠿⠿⠇⠿⠿⠿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠭⠅⣣⠀⠀⠀⠀⠀⢀⠸⣷⣤⠐⠃⠀⠀⠀
⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡈⠀⠈⣼⠀⠀⠀⠀⠀⠃⠀⠂⠁⠛⠃⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 494

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/05/21/Internal_Memos_Communications_Hinting_at_a_New_But_Masked_Round.shtml
    Gemini version at https://techrights.org/n/2024/05/21/Internal_Memos_Communications_Hinting_at_a_New_But_Masked_Round.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Internal Memos/Communications Hinting at "a
New, But Masked, Round of Layoffs" at Red Hat⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█
⌧


posted by Roy Schestowitz on May 21, 2024


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


A negative outlook ahead of a long weekend.


In The Register right now:


    * ⚓ Red_Hat_middleware_takes_a_back_seat_in_strategic_shuffle⠀⇛


           Red Hat is slowing or stopping development of some of its
           middleware software, a situation which could result in some
           staff layoffs.


           The Register has seen what purports to be an internal email
           from the IBM subsidiary's vice president of Middleware
           Engineering, Mark Little, revealing that development and
           maintenance of several of the company's products will be
           slowed, stopped, or – using one of everyone's favorite bits of
           corporate euphemism – "rightsized."


           Apparently the changes are part of the company's "strategic
           realignment," which is assessing the Hat's products and
           services "to identify those that no longer aligned with our
           long-term strategy." The goal is double-digit growth, but it's
           possible it is a new, but masked, round of layoffs. We are sure
           this has nothing whatsoever to do with Red Hat retaining
           McKinsey & Company a couple of months ago.


      Also: (ongoing)


      🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Strategic redhat coding is not going anywhere outside
      the US. IBM has way too much invested in the strategic code and will not
       risk letting it get pilfered. Sustain code on the other hand can easily
                         go to a lower cost coding center⦈


      And this:


      🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Anyone know what segments to be affected by potential
                                     layoffs?⦈




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠛⠛⠛⠛⢉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠙⠉⠉⠉⠙⠛⠛⠟⠟⠛⠛⠛⠙⠋⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠅
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣴⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣴⣶⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠐⠚⠉⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣦⣶⢂⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠃⠀⠀
⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⠙⠂⠁⠈⠀⠀
⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⢝⣀⠀⠀⠀⠀⠀
⣯⣠⣼⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⠁⠁⠀⠀⢀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢉⣽⣿⣿⣿⣿⣿⣿⡓⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠳⢶⡖⠢⠀⠀⡒⡀⠀
⣿⡿⢿⣭⠛⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠙⢿⣿⡿⣿⢻⣯⣿⣇⢠⣴⢾⡉⠉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢅⡀⠀⠀⠁⠀⡀⠘⠃⠀⠇
⠯⠙⠩⢴⠶⠶⠛⢻⣿⠿⠿⣿⣯⣭⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⢯⣽⣿⣿⣿⡻⡵⢾⣿⡁⠹⡧⠸⠋⠹⠋⠟⠋⣑⡻⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢆⣌⠀⠀⠁⠆⣀⡀⡀⠀⢬⠈⠉⠙⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⢀⣽⡟⠙⡶⠀⣨⠛⢀⠀⠀⠀⠠⠀⣀⢀⠉⠙⠀⢠⡈⣩⣿⡟⠻⣿⣿⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠙⢓⡤⢤⢎⢁⡐⠚⠊⣘⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⡿⠷⠇⠐⢠⣿⣿⠶⠈⢀⠹⣧⠈⠑⢀⡄⢤⠀⡉⠙⣴⠳⠾⠷⠾⠿⠿⠛⠀⠎⠙⡻⠏⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠀⠀⠀⠀⠁⠀⠈⠀⠀⢰⠄⡐⠄⠙⠁⣩⣳⠙⢍⣿⠋⠂⠀⢠⣍⣳⣯⣛⠛⠀⠳⣤⣠⡀⢿⣷⡜⠤⠀⠁⠀⠀⠀⠀⠀⠀⠀⡤⡴⡞⠈⢀⡠⠦⠀⠬⠉⠀⠤⠀⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀
⠂⠀⢀⠀⠀⠀⠀⠀⠀⢹⣲⢶⠤⠘⠖⠈⠈⠙⣠⣿⡏⠀⠀⠀⠈⠁⢹⡻⠏⠁⢐⢢⣚⠋⠁⠀⠈⡁⠀⠀⠀⠀⠀⢀⢠⣄⢀⠅⠀⠳⠤⠐⢒⠀⣀⡀⠁⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠀⠈⠠⠀⠀⠀⠀⠀
⠀⠀⠠⠀⠀⠀⠀⠀⠠⠀⠀⣠⡄⠀⠢⠀⠞⢛⣏⢧⠥⢀⢀⠀⠀⠢⠒⠋⢀⣠⡘⠸⢭⣵⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠹⠛⠃⠀⠀⡀⠰⡤⢁⠈⠻⠒⠀⠁⠉⠀⠙⢂⣠⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠂⠀⠀⠀
⠈⣀⢐⢀⡀⠀⡀⠈⣦⡀⡆⠠⠀⠄⠀⠠⡉⡤⠁⠘⢐⠂⠁⠻⠂⡀⢀⣾⣿⣿⣿⣦⡀⠈⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣢⠀⠰⣷⣿⣦⠀⠈⠒⠓⠢⠀⠀⣿⣇⠀⠀⠉⠁⠄⠀⠀⠀⡁⠀⠀⠁⠀⠢⠀⠀⠀
⢨⠟⠉⠉⠸⠏⠋⠉⠂⠀⠠⠈⢰⣶⣾⡄⡙⡀⠀⠀⠀⠠⠀⠀⡁⢠⣿⣿⣿⣿⣿⣿⣿⠀⠸⢿⡷⠀⠀⠀⠀⠀⠈⢀⡀⠔⠃⠀⠀⠂⠛⠛⠈⠀⠿⠇⠀⠙⠄⣿⣗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀
⠄⠐⠁⠈⠂⠀⠀⢀⡂⢀⣐⠛⠟⠻⡿⢣⡀⣧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⣿⣿⣄⣀⡄⠈⡷⠀⠀⠀⠀⢀⠔⠟⠀⢀⡀⠀⠎⠀⠀⠀⠀⠀⠀⠀⣀⢠⣝⣂⡀⠀⠀⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢄⡑⢀⠂⠐⠂⠠⠐⠃⡉⠅⠀⠀⢀⡃⢠⣌⡉⠄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⣼⣿⣿⡟⠛⠻⠿⠿⠿⠶⢶⣶⣶⣷⣤⣭⣦⣄⣶⣀⣀⡀⠀⢀⣦⣤⠄⠈⠈⠉⠀⠀⠹⠐⠀⠀⠀⠀⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀
⠘⠉⢉⠃⣌⠠⠀⡀⠠⠎⠈⠈⡱⠁⠀⠈⠀⠁⡄⠀⠀⠀⠢⢀⢀⣴⣿⣿⣿⡇⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠿⠿⠿⠿⠷⣾⣿⣶⣶⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣎⡀⡉⠀⠀
⠁⣈⠗⠀⠀⠀⠀⠐⠒⠀⠀⠀⢻⣿⣿⠀⠀⠀⠁⠀⠀⠀⣦⣴⣿⣿⣿⣿⣿⣇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠻⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣟⣛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⢻⣻⣿⣿⣿⡿⣿⢻⣛⣻⡛⣿⠟⣿⡛⣿⣿⣿⣿⣿⣿⢛⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠿⡿⢸⢸⢰⣆⢅⡣⠸⡰⠾⣿⠶⣆⠥⡇⠣⠇⠅⡇⣮⠺⢸⢸⢸⠸⠘⢼⣿⢸⠷⢎⠷⣌⡆⣿⡇⡣⡸⡞⣼⡺⣸⢸⠶⡧⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣧⣼⣤⣤⣥⣀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠛⢛⣻⣿⣿
⣿⣿⣿⣿⣿⣿⡟⡭⢻⣿⣿⡟⢻⠿⡿⠿⠿⢿⡿⠿⢿⠟⡿⢿⠿⠻⡿⠿⠿⠿⠿⠿⢿⠿⠿⠻⡿⡿⠟⠿⡿⢿⡿⠿⢿⠿⢿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢩⡉⡇⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡥⢿⣿⣿⣯⣴⣭⣯⣬⣤⣽⣧⣧⣵⣭⣭⣭⣤⣬⣯⣷⣭⣤⣯⣼⣯⣤⣽⣬⣭⣭⣧⣼⣅⣈⣧⣯⣴⣥⣧⣧⣽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣶⣧⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⠦⣼⣿⣿⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⡿⢿⢿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡏⠧⣹⣿⣿⣧⣤⣄⣤⣼⣍⣦⣶⣬⣦⣬⣤⣤⣴⣤⣐⣤⣦⣴⣾⣤⣤⣤⣳⣥⣤⣭⣜⣽⣭⣜⣾⣴⣝⣶⣦⣤⣟⣳⣤⣤⣛⣠⣴⣷⣮⣤⣜⣣⣤⣤⣤⣤⣴⣬⣤⣦⣌⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⡟⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣀⣽⣬⣻⣘⣉⣹⣿⣇⣀⣿⣿⣿
⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣏⢍⣿⢛⡟⢻⢛⢻⢙⡿⠛⡟⢻⡟⠿⢿⡿⣿⠿⢻⡿⠿⡿⢿⡿⣿⠿⣿⣿⠿⠿⢿⡟⡿⡿⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣧⣥⣿⣼⣯⣽⣨⣼⣬⣵⣭⣯⣼⣧⣭⣼⣥⣽⣤⣮⣯⣽⣭⣮⣧⣽⣭⣯⣿⣬⣧⣭⣧⣥⣵⣨⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⢛⡛⣽⣿⣿
⣿⣿⣿⣿⣿⣿⣧⡖⣽⣿⣿⡏⠛⠛⠋⠛⠛⠙⢿⡛⠛⣝⠟⡻⡟⠛⠋⠙⠛⣻⠛⣟⠛⠛⡟⡛⠛⡛⢻⠛⡛⢛⠛⢙⠛⠛⢻⠛⠛⠙⢻⢻⢻⠋⣻⢻⠹⣉⢿⢩⢩⠋⡏⠛⡟⣟⢛⢛⢻⣿⣿⣿⣘⣂⡇⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠟⣿⣿⣿⡟⠿⠿⡿⠿⣶⠟⢿⠻⠿⠿⠿⠿⠿⢻⠻⢿⠗⠾⢿⠿⠿⠿⠷⠾⠿⢿⠾⠿⢿⢾⠿⠿⢿⡿⠟⠛⡿⠿⠿⡿⠿⠿⣟⠿⠻⣿⢿⢿⠻⡿⠿⠟⡿⢟⠛⠷⠿⠿⣿⣷⣶⣶⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡛⣿⣿⣿⡷⣶⣶⢿⡾⣾⣶⣿⣶⣾⣷⣶⣶⠶⣾⣾⣾⡶⣶⣾⡶⣾⣾⣶⣦⣷⣾⣶⣶⣾⡾⣶⣶⣾⣷⣶⣶⣿⢶⣶⣷⣷⣶⣿⣶⡾⣾⣿⣼⣶⣧⣴⣶⣧⣾⣾⣾⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣧⣓⣼⣿⣿⣧⣬⣤⣬⣤⣤⣧⣬⣬⣥⣧⣤⣼⣤⣤⣼⣴⣥⣤⣤⣧⣤⣭⣬⣽⣥⣤⣼⣤⣤⣬⣧⣇⣠⣼⣥⣼⣼⣥⣴⣶⣬⣿⣤⣥⣤⣧⣤⣮⣭⣯⣸⣤⣤⣬⣥⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡭⣽⣿⣿
⣿⣿⣿⣿⣿⣿⣏⡖⣹⣿⣿⡟⠛⠛⠛⠻⣿⢻⠟⠛⣟⢛⠟⢛⣛⡟⣻⠿⠻⢻⠻⠟⢻⠟⠟⢛⠻⢟⢛⠛⠛⠛⢟⡟⠟⡟⠛⠛⠛⣿⣛⢿⠻⠛⢛⢿⣻⠟⡟⢻⣛⠟⢛⠛⠻⠻⣻⣿⣿⣿⣿⣿⡰⠅⡇⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠶⣿⣿⣿⡿⡿⡶⣶⡶⡷⠾⡶⡾⠷⠶⡷⡿⡶⡦⣿⠷⡶⠾⡾⠶⡾⠷⡷⠿⡶⡷⡴⠶⡶⡶⠶⡷⡷⡷⢶⠶⡶⠾⣶⡿⠾⢶⣦⣿⣶⣶⣷⣷⣴⣷⣾⣶⣾⣾⣾⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠶⣿⣿⣿⣯⣮⣮⣭⣥⣧⣥⣥⣄⣤⣤⣦⣦⣧⣥⣷⣭⣦⣯⣧⣴⣬⣤⣀⣜⣿⣯⣷⣭⣦⣧⣤⣬⣦⣯⣥⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣏⠧⣹⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢹⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠟⠛⡟⡛⡟⣓⢸⣿⢛⡻⠛⢻⢛⡛⢟⡻⡛⣛⢟⡂⡇⣟⢛⢻⢟⡛⣻⣷⠴⢹⠟⠛⡟⣓⣿⣿⠰⠷⢸⢛⢻⢛⣻⣷⢸⢛⢛⢻⣛⢟⡛⡏⣒⢐⡞⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣌⣫⣅⣂⣇⣋⣸⣿⣘⣧⣙⣹⢀⡚⣔⣀⣇⣿⣌⣃⣃⣛⣸⣘⢅⡒⣿⣏⣳⣜⣌⣫⣎⣋⣻⣿⣘⣟⣸⣐⣘⣌⣽⣟⣸⣐⣸⡇⣼⣌⣣⣇⣻⣸⣗⣢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿
⣉⣉⣏⣩⣏⣀⣉⣉⠉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⣛⣻⣿⣿
⣿⡏⣿⡟⠛⣟⢟⢛⣉⡉⠛⣟⣻⢛⢿⣝⡻⠛⢿⡟⢛⣛⡟⡛⣟⣻⢻⢛⣛⡟⣻⠛⠟⡋⣿⢙⢙⢛⡝⢻⣟⠟⣟⠛⠟⠻⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠤⢸⣿⣿⣿
⣿⣧⣥⣮⣜⣼⣮⣮⣭⣥⣵⣿⣴⣮⣾⣧⣼⣮⣾⣮⣼⣭⣥⣧⣧⣼⣮⣬⣭⣵⣵⣮⣶⣥⣿⣴⣼⣬⣥⣼⣿⣴⣾⣮⣷⣵⣴⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣽⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣇⣏⣉⡽⡩⣿⣫⣉⡉⢹⣩⣝⣭⣭⣡⣽⣉⣹⣧⣀⣉⣍⣿⣏⣸⣨⣩⣿⣩⣽⣉⣉⣹⣯⣉⣍⣉⣼⣆⣆⣉⣭⣍⣫⣈⡉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⡉⣹⣗⡩⣿⡩⡝⢻⣿⣏⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢩⢹⢸⢸⢉⣹⡉⢿⡏⡏⣭⣹⢩⠋⠭⢩⣿⢩⢋⡙⣍⢋⣹⢩⡏⣽⡟⡝⣭⣹⣯⣽⣩⠋⡍⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣰⣾⣾⣾⣶⣾⣶⣿⣧⣷⣶⣶⣶⣷⣾⣶⣿⣾⣷⣾⣶⣷⣾⣶⣾⣾⣷⣾⣶⣶⣿⣾⣶⣧⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⣛⣻⣿⣿
⣿⡟⠿⣿⠿⣿⡿⠿⡟⠿⣿⡿⠿⣿⠿⠟⠿⠟⣿⠿⠿⡿⣿⠿⠿⠟⡿⣟⡿⢿⢻⠿⣿⢿⡛⠿⢿⢻⠿⠟⡟⠿⢿⣿⢿⠟⠿⣿⣿⡻⠟⣿⠿⠿⢿⢟⠻⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠤⢸⣿⣿⣿
⣿⣷⣶⣿⣴⣶⣶⣶⣷⣶⣶⣾⣶⣿⣶⣷⣶⣶⣾⣶⣦⣴⣶⣶⣶⣶⣶⣿⣶⣾⣶⣷⣿⣶⣶⣶⣶⣶⣶⣶⣷⣮⣾⣵⣶⣶⣶⣾⣶⣶⣶⣷⣶⣵⣶⣾⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣽⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡟⡛⢿⣽⣿⣿
⣿⡇⠉⠉⡭⠀⣉⡏⠩⡭⠍⢉⢙⢝⠙⠅⠉⠩⡭⠉⠁⢿⠈⢽⠭⠩⠍⡇⠩⣍⢉⠉⣽⠩⠋⠋⠍⡭⢈⡉⢹⠩⣩⠉⠉⠹⡯⡯⠉⡍⠉⠍⠏⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣇⣚⣸⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 675

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/05/21/IRC_Proceedings_Monday_May_20_2024.shtml
    Gemini version at https://techrights.org/n/2024/05/21/IRC_Proceedings_Monday_May_20_2024.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ IRC Proceedings: Monday, May 20,
2024⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on May 21, 2024


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


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


                                              #techrights_log                                                                                           #boycottnovell_log


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


                                         #boycottnovell-social_log                                                                                        #techbytes_log


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


                          Enter_the_IRC_channels_now




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

                    ䷩ 𝚕𝚒𝚗𝚎 901

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

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    Gemini version at https://techrights.org/n/2024/05/21/Meme_Money_In_No_Money_Out_Granting_Loads_of_Invalid_European_P.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ [Meme] Money In, No Money Out (Granting
Loads of Invalid European Patents)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on May 21, 2024


Context: Staff_Representation_at_the_EPO_Has_Just_Explained_to_Heads_of
Delegations_(National_Delegates)_Why_the_EPO's_Financial_Study_is_Another_Hoax


                      🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇EPO production⦈




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

                    ䷩ 𝚕𝚒𝚗𝚎 1387

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/05/21/Nigeria_Windows_Down_to_6_Android_at_All_Time_High_of_77.shtml
    Gemini version at https://techrights.org/n/2024/05/21/Nigeria_Windows_Down_to_6_Android_at_All_Time_High_of_77.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Nigeria: Windows Down to 6%, Android at
All-Time High of 77%⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on May 21, 2024


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Rower⦈_


Google is becoming the "new_monopoly" in some places


MICROSOFT recently had mass_layoffs_in_Nigeria (confirmed_by_Microsoft) and it
is_losing_share_all_across_the_board. We're talking about by_far_the_largest
population_in_Africa, so the chart below ought to alarm Microsoft. Windows is
already a dying breed, especially in countries where mobile devices are widely
used. █


          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Operating System Market Share Nigeria⦈




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

                    ䷩ 𝚕𝚒𝚗𝚎 1492

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/05/21/Over_at_Tux_Machines.shtml
    Gemini version at https://techrights.org/n/2024/05/21/Over_at_Tux_Machines.gmi

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


posted by Roy Schestowitz on May 21, 2024


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


⚓  Updated This Past Day⠀⇛


   1. ⚓ GNU/Linux_in_Oman:_From_0.03%_to_5%! [original]⠀⇛


           Incredible!


   2. ⚓ MX_Linux_23.3_“Libretto”_Released_with_Linux_Kernel_6.8_and_Updated
      Components⠀⇛


           The MX Linux team announced today the release and general
           availability of MX Linux 23.3 as the third stable update to the
           latest MX Linux 23 “Libretto” series.


   3. ⚓ Never_Criticize_The_Linux_Foundation_Expenses⠀⇛


           new video


   4. ⚓ Explained:_What_is_a_Tiling_Window_Manager_in_Linux?⠀⇛


           Learn what a tiling window manager is, and the benefits that
           come along with it


   5. ⚓ Today_in_Techrights⠀⇛


           Some of the latest articles


      ⚓  New⠀⇛


   6. ⚓ HandBrake_1.8_Video_Transcoder_Adds_GTK4_Port_on_Linux,_FFmpeg_7.0
      Support⠀⇛


           HandBrake 1.8 open-source and free video transcoding
           application is now available for download with a GTK4 port for
           Linux users, as well as numerous other new features and
           enhancements.


   7. ⚓ Perl_Programming:_This_week_in_PSC,_LPW_2024,_and_Perl_Weekly
      Challenge⠀⇛


           Some programming news


   8. ⚓ IceWM_3.5_Lightweight_Window_Manager_Released_with_New_Features⠀⇛


           IceWM 3.5 lightweight window manager has been released today as
           a major update that introduces several new features, options,
           commands, improvements, and bug fixes.


   9. ⚓ today's_leftovers⠀⇛


           5 more links


  10. ⚓ Videos_and_Shows:_COSMIC_DE,_Linus_and_Dirk,_Free_Software_Security
      Podcast,_LINUX_Unplugged⠀⇛


           New videos or shows


  11. ⚓ Postgres:_PGDay_Israel_2024_and_Pgpool-II_Releases⠀⇛


           Some PSQL news


  12. ⚓ today's_howtos⠀⇛


           3 howtos


  13. ⚓ GNOME:_Sam_Thursfield,_Pablo_Correa_Gomez,_and_Endless_OS_6_Review⠀⇛


           Some GNOME related news


  14. ⚓ Fedora_Elections_(Interviews_With_Candidates)⠀⇛


           Some upcoming elections


  15. ⚓ Android_Leftovers⠀⇛


           Wow! A lot of people still don't know about this seven year old
           Android feature


  16. ⚓ Fwupd_1.9.20_Firmware_Updater_Adds_Support_for_FPC_FF2_Fingerprint
      Devices⠀⇛


           Fwupd maintainer Richard Hughes released today fwupd 1.9.20 as
           a new maintenance update to this firmware updating utility for
           Linux-based operating systems that brings support for new
           hardware and other changes.


  17. ⚓ Try_Image_Classification_Running_In_Your_Browser,_Thanks_To_WebGPU⠀⇛


           When something does zero-shot image classification, that means
           it’s able to make judgments about the contents of an image
           without the user needing to train the system beforehand on what
           to look for


  18. ⚓ Fwupd_1.9.20_Enhances_Support_for_FPC_FF2_Fingerprint_Devices⠀⇛


           The latest fwupd 1.9.20 firmware update daemon fixes bugs, adds
           more hardware support, and enhances security for firmware
           updates


  19. ⚓ Programming_Leftovers⠀⇛


           Programming links


  20. ⚓ Ventoy_1.0.98_Fixes_Boot_Issues⠀⇛


           Ventoy 1.0.98, an open-source tool for creating a bootable USB
           drive to load multiple ISO files, brings a few important fixes


  21. ⚓ Ubuntu_24.04_Now_Runs_on_the_Nintendo_Switch_(Unofficially)⠀⇛


           There are plenty of fun things you can do on a Nintendo Switch


  22. ⚓ Best_Free_and_Open_Source_Software⠀⇛


           We only feature open source goodness


  23. ⚓ Collections_of_Different_Linux_Distributions⠀⇛


           Ultramarine Linux is a Linux-based operating system designed
           for your own personal workstation (or battlestation)


  24. ⚓ Review:_Archcraft_2024.04.06⠀⇛


           I want to acknowledge right up front that I like what Archcraft
           is trying to do


  25. ⚓ today's_howtos⠀⇛


           first batch of howtos for today


  26. ⚓ 9to5Linux_Weekly_Roundup:_May_19th,_2024⠀⇛


           The 188th installment of the 9to5Linux Weekly Roundup is here
           for the week ending on May 19th, 2024.


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


                          Span from 2024-05-14 to 2024-05-20
      1179 /n/2024/05/14/
           Manjaro_Linux_24_0_Wynsdey_Officially_Released_with_Linux_Kerne.shtml


      979  /n/2024/05/15/
           Security_Patches_and_Linux_FUD_Blaming_Everything_on_Linux_Agai.shtml




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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠹⣿⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠
⠙⠻⣿⣿⣿⣿⣿⣿⠟⠋⠀⠉⠙⢻⣿⣿⣿⣏⡁⠀⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠋
⠀⠀⠙⠻⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣶⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣦⣤⣤⣴⣾⣿⣯⡁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠉⠛⠿⡿⠿⠿⠿⠛⠛⠿⠛⠉⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡅⢬⣻⣿⣿⣿⣿⣛⢰⡆⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠁⢘⣿⣿⣿⣿⣿⣿⣧⣤⣾⣿⣿⣿⡄⠄⠂⠀⢀⡤⢺⠷⢦⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣶⣿⣥⣄⣬⣿⣿⣶⣦⣀⠀⠀⢹⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣰⣾⣶⣄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⠏⠀⠀⣻⣿⣿⣿⣿⡄⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⣿⣿⣿⢹⣿⣿⢻⡏⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁⠄⣰⡖⠋⠙⣿⣿⣿⡿⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠟⠙⢿⣿⣿⣿⠛⠻⠋⠈⠉⠹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣂⡈⣿⣿⣿⣆⢻⡁⢨⠆⠘⠟⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⢰⣿⣥⣤⣾⣿⣿⡟⠁⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣾⣿⣿⣿⣆⣳⣿⣦⡀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠀⣸⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠙⣿⣿⣿⣿⣿⣿⠁⠀⠀⠛⠛⢿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⢀⣤⣾⣷⣶⠆⠀⠀⠀⠀⠼
⠀⠀⠀⠀⠰⢟⣿⣿⣿⣿⣶⣶⣄⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⣾⣿⣿⣿⡿⠃⠀⠀⠀⠀⢰⣿⣿⢿⠋⠀⠀⠀⠀⠀⠀⠠⣴⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀
⠀⠀⠀⠀⠚⠛⠿⣿⣿⢿⢿⣿⣿⡆⠀⠀⢩⠩⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢹⣿⣿⡻⠇⠀⠀⠀⠀⠀⠈⢿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠙⠋⠉⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠿⡅⠀⠀⠙⢿⠏⠀⢰⡇⠀⡀⠀⠀⠻⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠹⣿⣿⣇⠀⠀⠈⡛⢉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣄⣐⣂⠀⠀⠀⠀⠀
⡤⠀⠀⠀⠀⠀⠀⠀⠙⠈⠁⠀⠠⠐⠀⢸⣀⠡⠂⠀⠀⠀⢰⢿⣿⡿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠹⣿⠏⠀⣰⣾⣿⣿⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠘⠁⠀⠀⠀⠀⠀⠂⢀⣿⡧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣠⣄⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷⡦⠀⠀⠀⠀⣴⣿⣷⣶⣶⣶⣤⡀⠈⠛⢿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⡀⠀⠀⠀⠀⠀⠊⣹⣿⣧⣶⣿⣿⣿⣿⣿⣿⣿⣏⣩⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠀⠀⠙⠛⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣷⣤⡄⢀⠀⠀⠀⠷⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢻⣿⣿⣿⠁⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠈⠉⠁⠙⠛⠑⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠈⠛⠉⠉⠀⠀⣠⣿⣿⣿⣿⣷⠆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠘⣿⣿⣿⣿⠿⠿⠿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣙⣿⣿⣅⡀⠀⠀⠀⠀⠀⠀
⠀⠀⣾⣷⡄⠀⠀⡄⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣻⣿⣿⣏⠀⠀⠀⠀⢈⣿⣿⠟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀
⠀⢠⣤⣭⣤⡄⠀⠀⢀⡦⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢘⠉⣠⣆⣀⡠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠙⠿⢿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠘⣿⣿⠟⠋⡀⠀⠈⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣟⠈⡿⠉⢹⣿⣷⡀⠀⠶⠀⠐⢻⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⣤⣤⣤⣤⣠⣤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠀⢠⣾⣷⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡿⣷⣶⣾⣿⣿⣿⡇⠐⠂⠠⡆⠶⡖⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠃⢀⣼⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⢀⣴⣾

                    ䷩ 𝚕𝚒𝚗𝚎 1740

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/05/21/Pursuing_a_Case_With_No_Prospects_Because_It_s_Funny.shtml
    Gemini version at https://techrights.org/n/2024/05/21/Pursuing_a_Case_With_No_Prospects_Because_It_s_Funny.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Pursuing a Case With No Prospects (Because
It's "Funny")⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on May 21, 2024


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


What next, a chatbot? Import/export of "justice" (cross-continental)?


TODAY we continue explaining an ongoing campaign of aggravated_harassment
against my wife; this involved illegal behaviour directed at her, with casual
attempts at provocation. It is a familiar modus operandi - aiming at people
higher than oneself (e.g. Stallman, Moglen, Torvalds, Wright) in pursuit of
legitimacy where none_is_deserved, seeking to compensate for one's lack of
suitable qualifications and/or achievements.


The perpetrators are trying_to_exploit_the_US as a safe haven for their decade
or so of ritual_defamation against people with actual computer-related degrees
and credentials. Trying to tear them down by humiliation - i.e. classic_crab
mentality, then threaten them any time they open their mouth in self-defence.
It's projection at its finest - defame people endlessly, then try to blackmail
those people using threats of defamation lawsuits while constantly stalking
them and provoking them. This isn't the behaviour of mentally sound human
beings but of con artists. This went on for years, not days, weeks, or months.


Speaking of con artists, it's totally permissible for me to say that I spoke to
people and all of them say - having looked at the claims - that it's a futile,
ridiculous "case", or a case of flinging lots of low-quality crap at the wall,
praying something can somehow stick. A lot was identified as "boilerplate
text", i.e. copypasta, to keep this "funny"_move (or stunt) "on budget".


The "phonebooks" sent to us are about 80% our own text, our own articles, our
own work. Maybe that's just what we should expect from a 'mule' carrying
Microsoft's anti-Linux, anti-freedom agenda/code (to be put in Linux_to
restrict_PCs_or_let_Microsoft_control_them_remotely_from_the_moment_they're
powered_on).


Adding insult to injury, the perpetrators are taking a firm that's considered
notorious. They're notorious for picking up any case, irrespective of how weak
the merits or how low the chances of winning may be (unverifiable and baseless
claims), as_long_as_they_get_paid. Their reputation is already tarnished by
virtue of doing so and their track record shows a considerable rate of losses.
█




⠀⠀⠀⢀⠦⠀⠉⠁⠁⠀⠀⡀⠀⠂⡊⡸⢼⡆⠁⠁⢠⡤⠀⠀⣐⠀⡉⠀⠀⠠⢼⡿⣶⠶⠀⣤⣀⡉⠓⠾⠼⠩⡨⢋⡀⠀⠀⠈⠉⢄⣴⣿⣿⠃⢽⣿⣷⣤⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾
⠀⠀⠀⠀⠀⠰⡀⠘⠣⡆⠀⣀⡄⣴⣿⣬⣼⣿⡿⣼⢿⡇⠀⠀⢙⠁⠀⠀⠄⠀⢀⡶⠤⠆⠀⠈⠀⠙⠛⠉⣹⢛⢾⣿⠁⠀⠀⢀⡆⠀⡈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⢿⣿
⠀⢀⠀⢰⠀⠘⢿⣿⣼⣇⠀⣟⣿⡹⣩⣿⣿⣿⣧⠛⣿⣿⡄⠀⠀⢐⣀⢞⣠⠤⠒⠂⢉⠭⢀⠭⠉⡉⡒⠂⠤⣈⠙⠻⠢⢄⠀⠈⢳⢸⣿⣾⣿⣿⣿⣿⣧⣽⣿⣿⣿⣷⣷⣠⠀⢀⠀⠀⠀⠀⠀⣶⣠⣀⢀⣴⣤⣶
⠀⠈⠀⠀⠀⠀⠋⠂⠉⠁⢰⠛⢻⣿⡻⠋⢿⣿⢟⣿⣏⠈⣁⣶⣽⣿⠞⢩⡔⡄⠀⠠⡈⡓⡆⠙⠆⢱⠁⠀⣴⠀⡉⡂⠄⠀⠀⠀⣘⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⢉⣲⣓⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢆⡄⠰⣠⣾⣿⡀⢤⣼⣿⣿⣿⣿⣶⢋⡿⢋⣄⠺⣄⢻⠽⠂⣀⣤⠴⠶⠶⠲⠶⠦⢤⣘⠚⢱⠓⠁⢀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣓⣺⣶⠦⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠰⠤⢳⠠⣿⣤⣿⡁⢈⠈⣹⣿⣿⣿⣿⠞⡱⠂⠘⠙⠈⠁⠐⢈⠁⠀⠀⢀⣴⣴⣲⣲⣤⡀⠉⠳⢤⡀⢠⠇⢀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⠋⢫⣉⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⠀⠰⢿⣿⣷⣿⣿⣿⣟⢛⣫⠏⠀⠙⢯⠜⣠⠎⢠⠅⢁⠀⠀⢠⡿⡽⠊⢽⣋⢷⡗⣷⡀⠀⠙⢦⡰⢛⡴⠀⠈⢻⣿⣿⣿⣿⣿⣿⣏⣩⣿⣿⣿⣿⣿⣿⣗⡀⠈⠀⠀⢹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣷⣿⣷⢰⣸⣿⡿⠿⣿⣿⣿⣸⣿⠏⠀⠀⠀⠀⡴⢇⠀⠀⠐⡏⠀⠀⢼⢹⣵⢧⣟⣞⣿⣽⡸⣾⡦⠀⠀⠙⣌⠴⡟⡄⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⠦⢤⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣤⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡏⠀⠸⠇⠀⡜⠈⠓⢦⡀⠈⠋⡦⠀⠸⡾⣟⢟⣞⢾⣽⢯⡗⡅⣀⣛⡄⠀⠈⢮⠃⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡧⣭⣯⣹⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣤⣴⣿⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣸⢁⠀⠀⠀⢮⡑⢌⠁⠑⢀⠻⣟⡧⣘⣴⣵⣿⣽⣤⣾⣟⣡⣶⠶⠈⣧⢀⡄⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠯⢾⡄⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢂⡞⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⣀⣀⢀⣿⡇⡀⠀⠀⠁⠈⢐⠀⠀⠀⠑⡍⣛⣻⡟⠽⣯⠟⢋⣽⣿⣿⣟⠀⠀⠘⡆⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣉⠙⠇⠀⢸⣿⣿⣿⣿⣿⣿
⠈⠃⠀⠀⠀⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢏⣉⢉⢸⣧⣲⡁⠀⠀⠀⠀⠁⢆⡀⡵⠐⢐⢻⢹⣿⡇⢹⣖⣿⣿⣿⣿⣽⠄⠀⠀⢿⠀⠀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⢐⡈⠙⠃⣾⣿⣿⣿⣿⣿⣿⣿⣷⣼⡿⠛⢿⡇⣄⠀⣨⢸⣿⠿⢇⠀⠀⠀⢠⣤⢰⠀⣥⠀⠀⡼⣾⣿⣷⡾⠁⢹⣿⣿⣿⡷⠀⠀⠀⢸⠰⠿⡁⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠤⣿⣤⡄⠀⠈⣿⣿⣿⣿⣿⣿
⢀⣾⣌⣀⣁⣬⣽⣿⣿⣏⣿⣿⣿⣿⣹⣷⣤⣾⡇⢠⣾⣡⢸⡇⠀⠨⣗⡆⠀⢘⣿⣞⢧⠣⠀⢸⣿⣿⣿⣿⣦⣄⣾⣿⣿⣿⣱⠀⡀⠀⢸⢱⠂⠄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⡟⣆⠀⠀⠀⣿⣿⣿⣿⣿⣿
⢿⠋⠉⠉⣽⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣷⣿⣷⢠⣤⡤⡎⡇⠀⠠⠍⡥⡀⠀⠨⣺⣪⣌⠢⢸⣿⣿⣿⣿⣿⣿⣿⣷⡿⠋⢀⣐⣿⠀⢸⢈⡛⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⡄⠘⠦⠀⠀⣿⣿⣿⣿⣿⣿
⣷⠦⣠⣼⣻⣟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣻⠀⠀⣀⣲⠰⢀⢰⣴⡆⡧⣶⣤⠀⠳⠻⡳⢸⣿⣿⣿⣿⣿⣿⡿⠋⠁⢠⢛⣿⡼⠂⡾⣬⣉⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿
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⡿⢿⣿⣿⣿⣿⣿⣿⣾⠟⣿⣿⣿⣷⣾⣿⡆⢺⣿⡿⣯⣿⣦⠙⠄⠞⠀⠈⠳⡀⠀⠈⠃⠀⠈⠁⠻⣻⡾⣿⠵⠁⠀⠈⠙⢃⠜⢡⣈⠩⠅⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣯⣌⠉⠁⠀⢸⣿⣿⣿⣿⣿
⠀⢾⣏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣛⠘⣿⣿⣿⣿⣿⣿⣆⠀⠀⢰⡁⢄⡁⠺⢿⣶⣠⣀⠁⠘⣇⣯⡄⠢⣀⡤⢞⡡⠀⠀⡎⠃⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⡿⠋⠻⣿
⠀⠈⠉⠸⢟⣿⣻⣿⣿⡷⠿⣯⠿⣡⣯⣱⣤⠀⢸⣿⢻⣿⣿⣿⣿⣷⢌⠠⠃⢀⠏⠆⣠⢉⣙⠓⠒⠶⠖⡒⠚⠋⣱⠲⡌⢿⠂⡠⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣇⡴⠷⡆⠀⢸⣿⠃⠀⠀⠙
⠖⢊⠀⠀⣺⠁⢍⠋⠉⠗⠋⣟⣿⣿⣿⣿⣯⡄⡸⣿⣿⣿⣼⣿⣿⣿⣿⣷⣆⡙⠀⠌⢺⠀⡜⠀⢸⠍⠘⠦⡅⠀⠘⠄⢃⠤⢊⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠞⡜⢸⣙⡇⠀⠘⣿⣠⣴⣴⣴
⠄⠉⠀⠀⡏⠀⠀⠀⢶⡤⢀⣿⣟⣻⣿⣿⣷⣤⠲⢻⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣶⣦⢤⣥⣀⣈⣀⣈⣑⣡⠤⣒⣫⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣇⢸⣒⡆⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠸⡇⠀⠀⡦⠬⠞⠛⣿⣿⣿⣿⣿⣿⡟⠐⢺⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣉⣘⠉⠁⠀⠀⣿⣛⣿⢻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢲⠷⠻⠛⠟⠛⠟⠃⠀⢠⢀⠀⠠⢉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠿⢸⣿⣹⡅

                    ䷩ 𝚕𝚒𝚗𝚎 1829

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/05/21/Staff_Representation_at_the_EPO_Has_Just_Explained_to_Heads_of_.shtml
    Gemini version at https://techrights.org/n/2024/05/21/Staff_Representation_at_the_EPO_Has_Just_Explained_to_Heads_of_.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Staff Representation at the EPO Has Just
Explained to Heads of Delegations (National Delegates) Why the EPO's Financial
Study is Another Hoax⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on May 21, 2024


                 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇EPO Financial Study 2023⦈


ABOUT half a decade ago the staff representation at the EPO put a lot of effort
into explaining why the so-called "study" (Financial 'Study') was in fact a
"hoax", to quote the word they kept using [1, 2]. It started less than a year
after António_Campinos had joined. Here we are again 5 years later and the
Central Staff Committee, i.e. elective representatives, write the following to
staff:


     Dear Colleagues,


     The Office is asking for the opinion of the Budget and Finance
     Committee (BFC) on two documents: Financial Study Phase II (CA/23/24)
     and the Office opinion on the recommendations (CA/39/24). The staff
     representation was not involved in the drafting of the mandate of the
     consultants.


     The Financial Study supports the funding of EPO benefit liabilities:
     family allowances (unfunded) and tax compensation (marginally
     funded), and long-term care insurance, health insurance and pensions
     (currently funded). This proposal appropriately goes into the
     direction of solving long-standing issues of liabilities.


     However, the Financial Study Phase II relies on a base scenario with
     overconservative layers of assumptions and targets which are used to
     justify several measures at the expense of staff and the patent
     system:


         * A steady increase in productivity of 2.1% per annum on average
           is foreseen over the period until 2030. The Office will
           therefore increase the production pressure on DG1 staff and
           seems to have given no consideration for any impact on patent
           quality (the word “quality” is notably absent from both
           documents).
         * The Office refers to the bundle of measures of the previous
           financial study (CA/18/20) and announces that it will explore
           ways to address post-employment liabilities and will make
           proposals to address the principle of shared effort. This
           statement is already a matter of concern. We can only strongly
           advise against any adversarial change to the pension benefits,
           tax compensation, family allowances, healthcare insurance and
           long-term care insurance.
     In this open letter to the Budget and Finance Committee, we provide
     our comments.


     Sincerely yours,


     The Central Staff Committee


Here's the letter they had sent less than a week ago and then circulated among
staff:


     European Patent Office
     80298 Munich
     Germany


     Central Staff Committee
     Comité central du personnel
     Zentraler Personalausschuss


     centralSTCOM@epo.org


     Reference: sc24027cl


     Date: 16/05/2024


     European Patent Office | 80298 MUNICH | GERMANY


     To: Heads of Delegation in the Budget and
     Finance Committee


     Cc: Mr António Campinos
     President of the EPO


     By email:
     council@epo.org
     president@epo.org


     § OPEN LETTER⠀➾


     Comments from the staff representation on Financial Study Phase II


     Dear Heads of Delegations,


     The Office is asking for the opinion of the Budget and Finance
     Committee (BFC) on two documents: Financial Study Phase II (CA/23/24)
     and the Office opinion on the recommendations (CA/39/24). The staff
     representation was not involved in the drafting of the mandate of the
     consultants. The Pensioner’s Association has neither been invited to
     a meeting nor informed about the present documents although many
     proposals are centred on the pension scheme, the healthcare insurance
     and the long-term care insurance which are of paramount interest to
     pensioners.


     The Financial Study supports the funding of EPO benefit liabilities:
     family allowances (unfunded) and tax compensation (marginally
     funded), and long-term care insurance, health insurance and pensions
     (currently funded). This proposal appropriately goes into the
     direction of solving long-standing issues of liabilities.


     However, the Financial Study Phase II relies on a base scenario with
     overconservative layers of assumptions and targets.


     First, the Office intends to opt for a target funding ratio of 105%
     for all benefit liabilities. However, the Actuarial Advisory Group
     (AAG) considers that overfunding shall trigger measures to reduce the
     asset to a suitable funding target1 and even views that a funding
     level of 96.5% does not lead to a recommendation of an action to be
     taken2. The target funding ratio of 105% is hence a conservative
     target.


     Second, the Office considers a margin for allowing the coverage of
     short- term fluctuations in the funding ratio. It intends to set
     aside a cash buffer corresponding to 12 months of the Office’s
     operational cash requirement plus the amount of non-current prepaid
     fees. This constitutes an additional layer of conservative target.


     Third, the Financial Study assumes a low discount rate set at 4.6%3
     in nominal terms (including consumer price inflation) as a
     consequence of the proposal to increase the probability of reaching
     the overfunding level at 66%4 instead of the current target of 50%5
     of the AAG. Indeed, the AAG Study6 opted for a discount rate of 3.25%
     in real terms which amounts in nominal terms (when considering +2.03%
     consumer price inflation) to 5.28%. The chosen discount rate is below
     the expected yearly return rate of the RFPSS until 2042 of 6.07%
     according to PPC metrics and further below the RFPSS 20-year
     annualised performance of 6.4%7. This constitutes a further layer of
     conservative assumption.


     Fourth, the Financial Study takes into account a one-off increase of
     the fees in 2024 and no increase of the fees thereafter until 20308.
     This constitutes yet another layer of conservative assumption.


     The overconservative layers of assumptions and targets are used to
     justify several measures at the expense of staff and the patent
     system.


     First, a steady increase in productivity of 2.1% per annum on average
     is foreseen over the period until 20309. The Office will therefore
     increase the production pressure on DG1 staff and seems to have given
     no consideration for any impact on patent quality (the word “quality”
     is notably absent from both documents). This measure is difficult to
     reconcile with the latest Engagement Survey 202410 by Willis Towers
     Watson showing that the largest decline of –12% since 2022 related to
     the perception of the EPO’s reputation for the quality of products
     and services.


     Furthermore, any deviation from the annual production target will be
     tightly monitored via the DG1 management dashboard to ensure that it
     is kept at no more than –2%. Therefore, EPO staff can expect
     increased micro-management.


     Second, the Office refers to the bundle of measures of the previous
     financial study (CA/18/20) and announces that it will explore ways to
     address post-employment liabilities and will make proposals to
     address the principle of shared effort. This statement is already a
     matter of concern among staff. The latest Engagement Survey 2024
     results show that wellbeing and change fatigue remain a challenge at
     the EPO11. In this context, we can only strongly advise against any
     adversarial change to the pension benefits, tax compensation, family
     allowances, healthcare insurance and long-term care insurance.


     Sincerely yours


     Derek Kelly
     Chairman of the Central Staff Committee


     __________


     1 CA/52/23, p. 63/64


     2 CA/52/23, p. 31/70, par. 133


     3 CA/39/24, p. 4/14, par. 5


     4 CA/23/24, p. 28/97


     5 CA/39/24, p. 8/14, par. 12


     6 CA/52/23, p. 22/70, par. 90 and 92


     7 CA/42/23, p. 3/21


     8 CA/23/24, p. 44/97


     9 CA/39/24, p. 6/14, par. 8


     10 Engagement Survey 2024, Willis Towers Watson, p. 12/35


     11 Engagement Survey 2024, Willis Towers Watson, p. 4/35


As we explained here before, the Budget and Finance Committee (BFC) is a major
facilitator of EPO corruption [1, 2], yet the media never talks about it. █




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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠈⠁⠉⠈⠁⠁⠁⠈⠀⠉⠁⠉⠈⠁⠁⠁⠀⠈⠉⠁⠈⠁⠉⠉⠈⠉⠁⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢠⡄⢤⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠘⠓⠛⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀
⢰⠒⠒⠒⠒⠒⠒⡗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢲⠒⠒⢒⠲⠶⣶⣖⣒⣶⣖⣶⣒⡒⠖⠒⢺⠒⠒⠒⠒⠒⠒⠒⡗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒
⢠⠀⠀⠀⠀⠀⠀⡇⠀⡆⡄⢠⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣾⣿⣻⣾⣟⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣷⣶⣶⣔⡄⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢰⠀⠀⠀⠀⠀
⢨⠀⠀⠀⠀⠀⠀⡇⠀⡇⡇⢸⣿⣿⣭⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⢀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣖⣧⡀⡀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⢸⠀⠀⢸⠀⠀⠀⠀⠀
⣰⠀⠀⠀⠀⠀⠀⡇⠀⣇⡇⢸⣯⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠶⠦⠧⠄⡀⠨⢛⣪⣈⣻⠀⠀⢸⠀⠀⠀⠀⠀
⠸⠀⠀⠀⠀⠀⠀⡇⠀⡧⡇⢸⣿⣿⣿⣿⣇⡄⢀⡇⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣹⣿⣧⣿⡀⠀⢸⢀⣀⡀⠀⠀
⠸⠀⠀⡤⡆⣢⢰⣇⣆⡇⡇⢸⣿⣿⣿⣿⣷⡇⣴⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣼⠐⠛⢃⠀⡜
⢀⠠⠈⢸⠀⠊⣄⣯⠛⡇⣧⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⢵⣶⣾⣟⣴
⠈⠉⠉⢹⠈⠉⢯⣯⠉⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣯⣿⣿⣳
⠀⣀⣤⣼⠦⣰⣿⣿⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡟⠏⣿⣧⣶⣮⣿⣿⠍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡛
⣾⣿⣿⣿⠀⣁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡈⣀⠊⠙⣹⣿⡿⣿⣿⣿⢿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣛⣿⠿⢿⣿⣿⣿⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧
⣿⣿⣿⣿⣦⣬⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⣷⡿⢿⣿⣿⣿⣙⠿⠻⣿⡽⠟⣿⣿⣿⣿⡿⡿⠻⣿⢿⣿⢿⡫⢳⡿⣁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠉⠊⢛⠿⡈⣽⣿⣿⣟⠞⢷⣂⠉⠸⣿⣿⣿⣿⣿⣿⣿⣿⢯⣉⢴⠿⣇⠀⢸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠖⢀⡒⠒⠏⢃⠈⡣⢜⠺⠓⢏⠉⣿⣿⣿⣿⣿⡟⠻⢯⠍⠙⠈⠙⡧⡀⠐⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣄⢂⡆⡜⠈⠘⢱⢁⠅⡄⠀⠀⣀⠀⠚⣿⣿⣿⣿⣯⣿⣿⣿⡇⠀⠘⠌⠢⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⡄⢏⣿⢻⢧⣺⣆⠠⠦⠌⠁⠀⠈⠉⣽⣿⣿⣿⣿⣿⠛⠋⠉⠃⠀⠀⠀⠈⠄⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠐⠄⢐⢠⣽⢚⡐⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣆⠀⠀⣠⣾⣿⣿⣶⠘⠡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡡⢸⣴⡔⠬⢲⠄⡂⠀⠀⠀⠀⠀⠀⠀⣀⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠺⣿⣥⣟⠣⠀⠀⢤⠀⠀⠀⠀⠀⠂⠄⠻⣿⣿⣿⣿⣿⣿⣿⠿⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢿⣒⢠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠉⠋⠋⠉⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⢷⣉⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣶⡀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠁⠈⠀⠉⠙⡛⢛⠈⠋⠙⠲⠤⢄⢀⠀⡀⢀⣀⣀⠀⠀⠀⡐⠒⡇⠈⠉⠀⠀⠐⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿
⣿⣿⣿⣥⣾⡿⣫⡽⣿⣿⣻⣻⣿⢿⣟⢽⡟⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠟⢹⡟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⢻⢻⢺⢺
⠙⢻⢿⢼⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠃⠀⢰⣿⡿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣺⢻⢸⠈
⣄⣴⣤⣄⠀⠀⢀⡟⠉⠉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣦⣦⣦⣠⣤⣤⣀⣠⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣤⣤⣴⣤⣠⣤⣄⣴⣀⣠⣦⣴⣄⣀⣬⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼⣿⢼⡀⣘⠀⠈
⡿⣽⡝⢿⣿⡯⣏⣯⣏⣭⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⠹⠉⢹⠹⢹⣙⢉⡉⠉⠉⢉
⠉⠩⠙⠻⠻⠹⣷⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⡉⠉⠉⠉⠉⠉⠉⣉⢻⡯⣽⢻⣿⣿⣿⣿⢛⡛⠙⠝⠏⠉⢝⣿⣿⣿⣿⣽⣿⣻⣻⣿⣯⡻⣿⣿⣟⣻⣿⣿⣟⣩⠽⣿⣿⣻⣿⡿⠉⠁⠈⠀⠛⠛⢛⠫⣄⠨⣻
⠀⠀⠀⠀⠀⠈⠉⠛⠙⠳⠿⠛⠻⠋⠁⠀⠀⢏⣏⠉⢭⢹⠏⠉⠀⠉⠿⠾⠟⠹⠋⠛⠛⠋⠛⠘⠛⠉⠉⠉⠉⠉⠉⠛⠻⠿⠿⠿⠾⠾⠛⠉⠉⠉⠉⠉⠉⠹⣵⠻⢛⢴⡿⠛⠁⠉⠀⣔⡙⠿⣉⠷⠀⠘⠲⠛⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠁⠉⠉⠉⠈⠈⠉⠉⠈⠉⠁⠀⠀⠀⠁⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠁⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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                    ䷩ 𝚕𝚒𝚗𝚎 2128

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/05/21/Video_Microsoft_s_Attack_on_Education.shtml
    Gemini version at https://techrights.org/n/2024/05/21/Video_Microsoft_s_Attack_on_Education.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ [Video] Microsoft's Attack on
Education⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on May 21, 2024,
updated May 21, 2024


Video_download_link | md5sum 9229497ed0631c14c1b2f269c35717a2
Microsoft_and_Education_Cannot_Mix
Creative Commons Attribution-No Derivative Works 4.0


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


TODAY we cover a topic/theme that I primarily address in the form of video
because it is in some sense easier this way. There's a lot to be said about
Microsoft's cult-like activities and overt entryism. It impacts us directly.
They keep targeting us in IRC too, and sometimes they get_arrested_later.


The topic deals with education versus training (or indoctrination) and it's far
from the first time we cover the issue. However, there are new examples of it.


There are various projects like OLPC which started as educational, got hijacked
by Microsoft, then destroyed completely. There are many examples of the same,
including Nokia_in_Finland. Many of today's examples deal with Finland, but the
common denominator being education.


For instance, an associate tells us that "microsofters are not even donating
actual resources, but merely using RPi [Raspberry Pi Foundation] to print money
through software 'donations', see "In-kind_support" [as we_covered_here_last
week_when_Raspberry_Pi_confirmed_it_would_go_public]."


The associate argues that: "1) Microsoft doesn't have to spend a cent on that,
yet 2) it can deduct it multiple places financially, 3) all the while infecting
the RPi ecosystem (E.E.E.)" (see the Halloween_Documents_in_Geminispace).


The associate further notes that Microsoft resellers "don't have to be
competent in anything other than making a sale for Redmond. Apropos sales and
politics, microsofters get all butthurt when it is pointed out that there are
moles inside RPF on the board (members and trustees) and, especially, on the
staff. There are some really good people there but mixed in there are some
turds."


Some years ago we showed how they censored critics of Microsoft's abusive
behaviour, dismissing or blocking them under the flag/banner of "Microsoft
bashing" (what a ridiculous concept).


Now consider what happens in universities, starting with an example from
Finland, courtesy of Sami_Tikkanen ("Sompi" in IRC).


He shared with us this_video and said: "This is how the school login page looks
now..."


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


It's all Microsoft. Take a look. Ridiculous.


"And randomly it looks like this," he said.


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


"They say that I have the "verification with text messages" switched on," he
explained, "so it should not force me to install Microsoft Authenticator, but
for some reason it still does that and I don't have a supported phone." (It's a
Microsoft sign-in that makes ludicrous assumptions)


He said that "Finnish universities use Microsoft for everything nowadays [and]
this has made my studying impossible [as] literally nothing works."


So it seems like the university is infiltrated by "microsofters"; if it's not
run by Microsoft staff, then it's run by their enablers, i.e. people who work
for Microsoft but receive salaries from taxpayers or students' tuition fees.


I told Sompi, "they are salaried by you, not by Redmond," to which he agreed.
Where's the student consent in all this? They virtually force everyone to
accept inexcusable terms from another continent.


Sompi added that "they say that criticizing their outsourcing choices is
"politics" and should not be discussed."


An associate of ours commented by noting that: "Even the Parliament was taken
down by those moles. The news distracts the public with the Vastaamo fall guy
but he was only one of the many and there are also those who set up the
Microsoft gimmicks into production on purpose, as well as the managers who
arranged it."


Sompi told me that "the technical support team of the school is not even aware
of the fact that reppu.savonia.fi redirects to microsoft sharepoint login [...]
I don't understand how they can be so totally incompetent, it's almost like
they have never even tested the system at all or just don't pay attention to
even the most obvious details."


"They say that I'm the only one who has problems but I don't believe that," he
added.


"I found that it was a standard like to accuse people of being the only ones
encountering problems with the Microsoft products." our associate remarked on
it. "There is a lot of word-bending too, to just carefully tread around who is
saying what."


"Don't read anything into what they say. It's almost all lies when they can but
I'm not sure how the Finnish culture survives being based on so many lies, it's
not just around Microsoft products but about everything all day every day even
on topics it's neither necessary nor convenient to lie about," he argues.
"Microsoft did not attack Finland directly but hired Quislings to sell out
Finland from the inside. These are not 'foreigners' who have broken the school
system and rolled out bugdoors for the Russians but actual home grown
"Kotiryssä" smiling slickly while hollowing out national preparedness. MSFT?
Double-tap to be sure!"


"Microsoft really seems to have attacked the Finnish education system," Sompi
said, "and it has attacked it hard. And it has won. Our tax money goes to
Microsoft and the education system has became crap."


2 years ago Andy wrote a series about this [1, 2, 3, 4], having taught at a
Finnish university for a number of years.


"I think Finland is targeted by those corporations," Sompi said, "because 1)
Finland is the homeland of many competing free software technologies like IRC,
Linux, SSH and many others and 2) those corporations are mostly from USA and
Finland is in the center of hybrid warfare because of its geopolitical
situation. That's why Finland gets more of that crap than other countries."


My own thoughts are in the video at the top. █




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⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣗⠷⣶⢶⡖⣶⢚⡒⢒⢒⡦⠀⠀⡀⢨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠄⠀
⠀⠨⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⢗⡶⢾⣷⡶⡷⠚⢶⠺⡞⠁⠀⠢⠄⠬⠀⠀⢀⠀⠀⢀⠀⠀⠀⠁⠀⠐⠀⠠⠀⠀
⠀⠀⠀⣦⡔⢨⢠⠀⡤⢠⢠⢀⡀⡄⡄⡎⡆⠀⣀⡄⡤⠄⡄⠄⠀⡦⠄⡄⡄⡄⠀⡄⠀⣀⡄⠀⣅⠄⡄⠄⡄⢠⠊⠀⣄⡄⡄⡄⡄⡄⡄⡄⡆⠀⡷⡰⣎⠠⡠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠁⠀⠈⠈⠀⠁⠈⠈⠀⠁⠁⠁⠁⠁⠀⠁⠅⠁⠀⡁⠁⠀⠁⠀⠁⠁⠁⠁⠉⠁⠉⠁⠁⠁⠉⠁⠀⣥⣤⣭⣥⡍⠁⠁⢡⣡⡥⠩⠁⢁⣤⣥⢀⣭⣬⣬⣼⣿⣟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⣾⡍⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⡲⢲⣾⣿⣿⣿⣿⣿⣿⣧⠫⢻⠿⠿⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⣽⣦⠉⠂⠖⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢶⣤⣇⣠⣺⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢼⡧⣥⠀⢈⠀⠑⠠⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠠⢺⣿⣿⣿⣿⣿⣿⣿⡟⢲⣤⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠸⡧⢾⡷⢄⠀⡀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⣽⣿⣯⣹⣽⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢀⠀⠉⠘⠿⡦⠑⠀⡀⠀⡁⢀⠀⠀⠀⠀⠀⡀⢀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣝⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⢀⠀⠀⠀⡾⠋⠐⠀⠀⠀⡀⠀⠀⠀⠀⠈⡰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠸⣷⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢡⡀⣾⠓⣿⢚⡄⠀⡀⠈⠄⢠⡄⠠⣠⣮⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠙⢿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣶⣲⣲⠶⣶⣶⣶⣶⣶⣶⢲⣖⣲⡖⢠⣀⣿⡛⠻⢛⣿⡻⡗⢂⡄⢠⡄⢠⣭⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣯⣙⡛⠿⢿⣿⡿⢫⣴⣾⣿⣿⣟⣤⠀⠀⠙⠛⠻⣷⣼⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣟⡟⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⢿⡁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣹⣶⣨⣽⣟⡻⠿⣿⣿⣿⣿⣁⡄⠀⠀⠠⡦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠂⠀⢒⠆⢠⢀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⢿⣟⣈⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣵⣆⣩⣙⠛⠿⣿⣤⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢍⠃⠀⠠⠠⠿⠄⠀⠀⣑⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠇⠝⢿⣸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣮⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠿⠇⠐⠀⠀⢀⠁⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣽⣽⡛⡿⢿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠀⠓⠐⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⢾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⡟⢘⡃⢀⡀⢘⡃⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⡽⡇⠀⠀⠀⠀⢀⠀⠐⠀
⣿⣿⣿⣿⣿⣹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣑⣼⣇⢘⡁⢉⠁⢀⠀⣉⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢏⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣾⣇⣉⡀⣈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⣿⢿⣿⢀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠟⣿⣋⣛⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⠿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡐⣽⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠅⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠋⠐⠻⡻⣿⢿⡿⡿⣿⣿⣿⠿⢯⠋⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⣬⠀⣥⢀⣤⠀⠄⢀⠀⠀⠀⢹⡀⠦⠀⠘⠀⠂⠀⠄⠀⠀⠀⠀⠐⠀⠠⠀
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣗⠷⣶⢶⡖⣶⢚⡒⢒⢒⡦⠀⠀⡄⢨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠄⠀
⠀⠨⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⢗⡶⢾⣷⡶⡷⠚⢶⠺⡞⠁⠀⠢⠄⠬⠀⠀⢀⠀⠀⢀⠀⠀⠀⠁⠀⠐⠀⠠⠀⠀
⠀⠀⠀⣦⡐⢠⢠⠤⡤⢠⢤⢠⡄⡤⡄⡦⡦⠀⢠⡄⡤⠄⡤⠄⠀⡆⠀⡤⡄⡄⠀⡤⠄⣤⡤⠄⣄⠤⡄⠤⡄⢠⠒⠂⣤⡄⡤⡄⡤⡄⡤⡤⡦⠀⡶⡰⣦⠠⡠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠁⠀⠈⠈⠀⠁⠈⠈⠀⠀⠁⠁⠁⠁⠀⠁⠅⠁⠀⡁⠁⠀⠁⠀⠁⠁⠁⠁⠁⠀⠀⠁⠁⠁⠁⠁⠀⣥⣤⣵⣤⡅⠁⠁⢡⣡⡥⠁⠁⠁⢠⣥⢁⣭⣬⣬⣴⣿⣟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⣾⡍⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⡢⢰⣾⣿⣿⣿⣿⣿⣿⣆⠫⢛⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⣽⣦⠉⠂⠖⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣑⡀⢸⣿⣿⣿⣿⣿⣿⣿⣟⠐⠀⢶⣦⣦⢠⣺⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢼⡧⣥⠀⢈⠀⠑⠠⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠠⢺⣿⣿⣿⣿⣿⣿⣿⡟⢲⣤⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠸⡧⢾⡷⢄⠀⡀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣼⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⣽⣿⣯⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀⠀⠉⠘⠿⡦⠑⠀⡀⠀⡁⢀⠀⠀⠀⠀⠀⡀⢀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣝⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⢀⠀⠀⠀⡾⠋⠐⠀⠀⠀⡀⠀⠀⠀⠀⠈⡰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢡⡀⣾⠓⣿⢚⡄⠀⡀⠈⠄⢠⡄⠠⣠⣮⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠙⢿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣤⣲⣲⠶⣶⣶⣶⣶⣶⣶⢲⣖⣲⡖⢠⣀⣿⡛⠻⢛⣿⡻⡗⢂⡄⢠⡄⢠⣭⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣯⣙⡛⠿⢿⣿⡿⢫⣴⣾⣿⣿⣟⣤⠀⠀⠙⠛⠻⣷⣼⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣟⡿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⢿⡃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣹⣶⣨⣽⣟⡻⠿⣿⣿⣿⣿⣁⡄⠀⠀⠠⡦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠂⠀⢐⠆⠠⢀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣯⢿⣟⢨⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣵⣆⣩⣙⠛⠿⣿⣤⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⢛⠁⠀⠀⠀⠿⠄⠀⠈⢑⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣻⢗⠙⢿⣸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣮⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠿⠇⠐⠀⠀⢀⠈⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣽⣽⡛⡿⢿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠀⠓⠐⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⢾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⡟⢘⡃⢀⡀⢘⡃⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⡽⡇⠀⠀⠀⠀⢀⠀⠐⠀
⣿⣿⣿⣿⣿⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣑⣼⣇⢘⡁⢉⠁⢀⠀⣉⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢏⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣾⣇⣉⡀⣈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⣿⢿⣿⢀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠟⣿⣋⣚⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⠿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡐⣽⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠅⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠋⠘⢙⡿⢿⡿⡿⡿⢿⣿⣿⠿⢿⠫⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⣬⠀⣥⢀⣤⠀⠄⢀⠀⠀⠀⢹⡀⠦⠀⠘⠀⠂⠀⠄⠀⠀⠀⠀⠐⠀⠠⠀
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣗⠷⣶⢶⡖⣶⢚⡒⢒⢒⡦⠀⠀⡄⢨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠄⠀
⠀⠨⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢵⢗⡶⢾⣷⡶⡷⠚⢶⠺⡞⠃⠀⠢⠄⠬⠀⠀⢀⠀⠀⢀⠀⠀⠀⠁⠀⠐⠀⠠⠀⠀
⠀⠀⠀⣦⡐⢰⢠⠤⡤⢤⢤⢠⠄⡤⡄⡦⡦⠀⢠⡄⡤⠄⡠⠄⠀⡖⠒⡤⡆⡄⠀⡠⠄⣤⡠⠤⣆⠤⡀⠤⡀⢀⠒⠂⣤⡄⡤⡄⡤⡄⡤⡤⡦⠀⣶⡰⡶⠠⡠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠃⠁⠘⠈⠂⠃⠈⠊⠐⠂⠑⠁⠃⠑⠀⠑⠁⠃⠀⡑⠀⠀⠑⠒⠑⠁⠑⠁⠑⠂⠒⠃⠒⠃⠒⠁⠀⣡⣤⣵⣦⡇⠁⠁⢡⣡⡅⠁⠁⠁⢄⣡⢁⣻⣼⣴⣼⣿⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⣾⡍⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⡂⢰⣾⣿⣿⣿⣿⣿⣿⣆⠣⢻⠿⠿⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⣽⣦⠉⠂⠖⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣱⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⣦⣦⣦⣠⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⢼⡧⣥⠀⢈⠀⠑⠠⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠡⢺⣿⣿⣿⣿⣿⣿⣿⡟⢲⣦⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠸⡧⢾⡷⢄⠀⡀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣼⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⣽⣽⣿⣹⣽⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⠀⠉⠘⠿⡦⠑⠀⡀⠀⡁⢀⠀⠀⠀⠀⠀⡀⢀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣝⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⢀⠀⠀⠀⡾⠋⠐⠀⠀⠀⡀⠀⠀⠀⠀⠈⡰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢡⡀⣾⠓⣿⢚⡄⠀⡀⠈⠄⢠⡄⠠⣠⣮⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠙⢿⣿⠿⢛⠋⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣶⣲⣲⠶⣶⣶⣶⣶⣶⣶⢲⣖⣲⡖⢠⣀⣿⡛⠻⢛⣿⡻⡗⢂⡄⢠⡄⢠⣭⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣯⣙⡛⠿⢿⣿⡿⢫⣴⣾⣿⣿⣟⣤⠀⠀⠙⠛⠻⣷⣼⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣟⡟⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⢿⡣
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣹⣶⣨⣽⣟⡻⠿⣿⣿⣿⣿⣁⡄⠀⠀⠠⡦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠖⠀⠀⢰⠆⠠⢄⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⢨⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣵⣆⣩⣙⠛⠿⣿⣤⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠩⠁⠀⠀⠀⠀⠀⠀⢍⠁⠀⠀⠠⠸⠄⠀⠤⢔⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠇⠙⣿⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣮⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠿⠇⠐⠀⠀⢀⠉⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣽⣽⡛⡿⢿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠀⠓⠐⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⢾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⡟⢘⡃⢀⡀⢘⡃⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⡽⡇⠀⠀⠀⠀⢀⠀⠐⠀
⣿⣿⣿⣿⣿⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣑⣼⣇⢘⡁⢉⠁⢀⠀⣉⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢏⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣽⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣾⣇⣉⡀⣈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⣿⢿⣿⢀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠟⣿⣋⣚⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⠿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡐⣽⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠅⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠋⠘⠙⡟⣿⡿⡿⡿⢿⢿⣿⠿⢻⠋⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⣬⠀⣥⢀⣤⠀⠄⢀⠀⠀⠀⢹⡀⠦⠀⠘⠀⠂⠀⠄⠀⠀⠀⠀⠐⠀⠠⠀
⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣗⠷⣶⢶⡖⣶⢚⡒⢒⢒⡦⠀⠀⡄⢨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠄⠀
⠀⠨⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢵⢗⡶⢾⣶⡶⡷⠚⢶⠺⡞⠁⠀⠢⠄⠬⠀⠀⢀⠀⠀⢀⠀⠀⠀⠁⠀⠐⠀⠠⠀⠀
⠀⠀⠀⣦⡰⢰⢀⠄⡄⢄⢄⠠⠄⡠⡀⡶⡦⠀⠠⠄⡄⠄⡠⡀⠀⣖⣒⡠⡆⡄⠀⡠⠄⠠⡠⠤⡆⠤⡀⠠⡀⢀⠖⠂⠤⡀⡤⡀⡤⡀⡤⡠⡤⠀⣦⠰⣶⠠⡠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠃⠁⠘⠘⡒⠃⠘⠚⠐⠃⠓⠃⠃⠓⠀⠓⠂⠃⠀⡑⠂⠀⠓⠒⠓⠃⠑⠂⠑⠂⠓⠃⠒⠋⠒⠑⠀⣃⣈⣒⣂⡃⠃⠁⢡⣁⣇⢁⠁⡡⢄⠃⢁⣛⣐⣑⣸⣯⡏⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⣾⡍⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⡔⣴⣾⣿⣿⣿⣿⣿⣿⣄⠧⢻⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⣽⣦⠉⠂⢖⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⠀⣧⣦⣶⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢼⡧⣥⠀⢈⠀⠑⠠⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⣿⣿⣿⣿⣿⣿⣿⣿⡇⢤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠸⡧⢾⡷⢄⠀⡀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣼⣿⣿⣿⣿⣿⣿⣿⣧⣄⣼⣛⣽⣯⣹⣽⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⠀⠉⠘⠿⡦⠑⠀⡀⠀⡁⢀⠀⠀⠀⠀⠀⡀⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣝⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⠀⠀⠀⡾⠋⠐⠀⠀⠀⡀⠀⠀⠀⠀⠈⡰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢡⡀⣾⠓⣿⢚⡄⠀⡀⠈⠄⢠⡄⠠⣠⣮⣻⣾⣻⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠙⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣶⣲⣲⠶⣶⣶⣶⣶⣶⣶⢲⣖⣲⡖⢰⣀⣿⡛⠻⢛⣿⡻⡗⢂⡄⢠⡄⢠⣭⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣯⣙⡛⠿⢿⣿⡿⢫⣵⣾⣿⣿⣟⣤⠀⠀⠙⠛⠻⣷⣼⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣟⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⢿⡖
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣹⣶⣨⣽⣟⡻⠿⣿⣿⣿⣿⣁⡄⠀⠀⠠⡶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠖⠀⠶⠂⢤⢀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⢿⣟⢨⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣵⣆⣩⣙⠛⠿⣿⣤⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠕⠒⠀⠤⠤⠿⠀⠀⢀⡑⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠗⠙⢿⣸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣮⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠿⠇⠐⠀⠀⢀⠉⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣽⡛⡿⢿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠀⠓⠐⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⢾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡔⡟⢘⡃⢀⡀⢘⡃⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⡽⡇⠀⠀⠀⠀⢀⠀⠐⠀
⣿⣿⣿⣿⣿⣹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣑⣼⣇⢘⡁⢉⠁⢀⠀⣉⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢏⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣾⣇⣉⡀⣈⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠼⣿⢿⣿⢀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠟⣿⣋⣛⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡐⣽⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠅⠄⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠋⠐⠻⡛⣿⣿⡿⡿⣿⣿⣿⠿⢿⠋⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⣬⠀⣥⢀⣤⠀⠄⢀⠀⠀⠀⢹⡀⠮⠀⠘⠀⠂⠀⠄⠀⠀⠀⠀⠐⠀⠠⠀
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣗⠷⣶⢶⡖⣶⢚⡒⢒⢒⡦⠀⠀⡄⢨⠁⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠤⠀
⠀⠨⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢵⢗⡶⢾⣷⡶⣷⠚⢶⠺⡞⠁⠀⠢⠄⠬⠀⠀⢀⠀⠀⢀⠀⠀⠀⠁⠀⠐⠀⠠⠀⠀
⠀⠀⠀⣆⡰⢐⢀⠀⡀⢀⢀⠀⠀⡀⡀⡖⡄⠀⠀⡀⡀⡀⡀⡀⠀⣔⡒⡀⡄⡀⠀⡀⠀⠀⡀⠄⡂⡀⡀⡀⡀⢀⠔⠀⡠⡁⡠⡀⡠⡁⡨⡉⡍⠉⣯⠹⡟⢩⢩⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠋⠁⠘⠘⠒⠃⠘⠚⠘⠃⠓⠃⠃⠓⠀⠛⠃⠃⠀⡓⠂⠀⠓⠂⠓⠃⠓⠂⠓⠂⠛⠃⠂⠋⠒⠓⠀⣃⣈⣒⣂⡋⠃⠁⢣⣁⡅⠃⠁⢁⠀⣡⢁⣛⣐⣑⣰⣿⣏⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⣾⡍⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⡶⡔⢴⣾⣿⣿⣿⣿⣿⣿⣆⢣⢻⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⣽⣦⠉⠂⢖⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠙⠂⢶⣤⣦⣠⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢼⡧⣥⠀⢈⠀⠑⠠⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠍⠡⢺⣿⣷⣿⣿⣿⣿⣿⡟⢶⣤⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠸⡧⢾⡷⢄⠀⡀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣼⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣛⣽⣯⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢀⠀⠉⠘⠿⡦⠑⠀⡀⠀⡁⢀⠀⠀⠀⠀⠀⡀⢀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣝⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⢀⠀⠀⠀⡾⠋⠐⠀⠀⠀⡀⠀⠀⠀⠀⠈⡰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢡⡀⣾⠛⣿⢚⡄⠀⡀⠈⠄⢠⡄⠠⣠⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠙⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣶⣲⣲⠶⣶⣶⣶⣶⣶⣶⢲⣖⣲⡖⢰⣀⣿⡛⠻⢛⣿⡻⡗⢂⡄⢠⡄⢠⣭⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣯⣙⡛⠿⢿⣿⡿⢫⣵⣾⣿⣿⣟⣤⠀⠀⠙⠛⠻⣷⣼⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣟⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⢿⡏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣹⣶⣨⣽⣟⡻⠿⣿⣿⣿⣿⣁⡄⠀⠀⠠⡶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠒⠂⢐⠆⢤⢀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⢿⣿⢨⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣵⣆⣩⣙⠛⠿⣿⣤⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠇⠒⠀⠤⠀⠸⠀⠀⢀⡑⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠗⠙⣷⣸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣮⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠿⠇⠐⠀⠀⢀⠉⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣽⡛⡿⢿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠀⠓⠐⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⢾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡔⡟⢘⡃⢀⡀⢘⡃⣑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⡽⡇⠀⠀⠀⠀⢀⠀⠐⠀
⣿⣿⣿⣿⣿⣹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣑⣼⣇⣘⡁⢉⠁⢀⠀⣉⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢏⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣾⣇⣉⡀⣈⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠼⣿⢿⣿⢀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠟⣿⣋⣛⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡖⣽⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠅⠄⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠋⠐⠻⡛⣿⣿⡿⡿⣿⣿⣿⠿⢿⠫⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⣬⠀⣥⢀⣤⠀⠄⢀⠀⠀⠀⢹⡀⠮⠀⠘⠀⠂⠀⠄⠀⠀⠀⠀⠐⠀⠠⠀
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣗⠷⣶⢶⡖⣶⢚⡒⢒⢒⡦⠀⠀⡄⢨⠁⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠤⠀
⠀⠨⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢗⡶⢾⣷⡶⣷⠚⢶⠺⡞⠃⠀⠢⠄⠬⠀⠀⢀⠀⠀⢀⠀⠀⠀⠁⠀⠐⠀⠠⠀⠀
⠀⠀⠀⣄⠠⢐⢀⠀⣀⢀⢀⢀⠀⡀⡀⡔⡄⠀⠀⡀⣀⡀⡀⡀⠀⣄⡀⡀⡀⡀⠀⣀⡀⣀⡀⡀⡂⣀⡀⣀⡉⢉⠍⠍⣉⡉⣉⡉⣉⡉⣉⡉⣍⠉⣭⢩⣝⢉⢉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠋⠁⠘⠘⣀⠃⠘⠘⠈⠃⠃⠃⠃⠃⠀⠊⠃⠃⠀⡃⠂⠀⠃⠀⠃⠃⠃⠂⠃⠀⠋⠃⠂⠋⠂⠃⠀⣃⣈⣂⣂⡋⠃⠁⠣⣁⣇⢁⠁⢁⣠⣡⢁⣛⣐⣑⣸⣯⣏⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⣾⡍⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⡔⢰⣾⣿⣿⣿⣿⣿⣿⣄⠷⢻⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⣽⣦⠉⠂⠖⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⠀⣽⣿⣿⣿⣿⣿⣿⣿⡗⠀⠂⢦⣦⣾⠴⣺⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢼⡧⣥⠀⢈⠀⠑⠠⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠠⢿⣿⣿⣿⣿⣿⣿⣿⡗⢴⣴⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠸⡧⢾⡷⢄⠀⡀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣼⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿⣹⣽⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⠀⠉⠘⠿⡦⠑⠀⡀⠀⡁⢀⠀⠀⠀⠀⠀⡀⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣝⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⠀⠀⠀⡾⠋⠐⠀⠀⠀⡀⠀⠀⠀⠀⠈⡰⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢡⡀⣾⠓⣿⢚⡄⠀⡀⠈⠄⢠⡄⠠⣠⣮⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠙⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣶⣲⣲⠶⣶⣶⣶⣶⣶⣶⢲⣖⣲⡖⢠⣀⣿⡛⠻⢛⣿⡻⡗⢂⡄⢠⡄⢠⣭⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣯⣙⡛⠿⢿⣿⡿⢫⣴⣾⣿⣿⣟⣤⠀⠀⠙⠛⠻⣷⣼⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣟⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⢿⡂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣹⣶⣨⣽⣟⡻⠿⣿⣿⣿⣿⣁⡄⠀⠀⠠⡦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠖⠀⢲⠂⢤⢀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⢿⣿⣿⢈⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣵⣆⣩⣙⠛⠿⣿⣤⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠇⠓⠀⠤⠠⠿⠀⠀⠀⡑⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣻⠗⠙⣿⣸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣮⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠿⠇⠐⠀⠀⢀⠉⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣽⣽⡛⡿⢿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠀⠓⠐⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⢾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⡟⢘⡃⢀⡀⢘⡃⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⡽⡇⠀⠀⠀⠀⢀⠀⠐⠀
⣿⣿⣿⣿⣿⣹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣑⣼⣇⢘⡁⢉⠁⢀⠀⣉⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢏⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣾⣇⣉⡀⣈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⣿⢿⣿⢀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠟⣿⣋⣛⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡐⣽⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠅⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠋⠐⠻⡛⣿⣿⡿⡿⣿⣿⣿⠿⢿⠋⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⣬⠀⣥⢀⣤⠀⠄⢀⠀⠀⠀⢹⡀⠦⠀⠘⠀⠂⠀⠄⠀⠀⠀⠀⠐⠀⠠⠀
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣷⠷⣶⢶⡖⣶⢚⡒⢒⢒⡤⠀⠀⡄⢨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠄⠀
⠀⠨⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢵⢗⡶⢾⣷⡶⡷⠚⢶⠺⡞⠁⠀⠢⠄⠬⠀⠀⢀⠀⠀⢀⠀⠀⠀⠁⠀⠐⠀⠠⠀⠀
⠀⠀⠀⣄⠠⢠⢀⣉⣀⣀⣀⢀⡀⣀⡀⣄⣄⠀⢀⡀⣀⡀⢀⡀⠀⡤⠤⣀⡄⡀⠀⢀⡀⣀⢀⣀⡄⣀⠀⣀⠉⢉⠭⠍⣉⡉⣉⡉⣉⡉⣉⣉⣍⠉⣭⢩⣭⢉⢉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠏⠃⠸⠘⠄⠇⠘⠜⠨⠁⠣⠃⠇⠣⠀⠪⠃⠇⠀⠣⠂⠀⠣⠤⠣⠃⠣⠂⠣⠄⠍⠇⠄⠏⠢⠓⠀⣇⣈⣢⣄⡏⠁⠁⠣⣁⡇⠁⠃⢁⣠⣯⢁⣻⣰⣱⣰⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⣾⡍⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⡶⡔⢰⣾⣿⣿⣿⣿⣿⣿⣆⢣⢻⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⣽⣦⠉⠂⠖⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣑⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠙⠀⢶⣶⣶⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢼⡧⣥⠀⢈⠀⠑⠠⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠠⢺⣿⣷⣿⣿⣿⣿⣿⣿⢶⣤⣾⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠸⡧⢾⡷⢄⠀⡀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⣿⣿⣿⣿⣿⣿⣿⣧⣌⣬⣩⣽⣯⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠉⠘⠿⡦⠑⠀⡀⠀⡁⢀⠀⠀⠀⠀⠀⡀⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢻⣿⣿⣿⣿⣿⣿⣝⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⠀⠀⠀⡾⠋⠐⠀⠀⠀⡀⠀⠀⠀⠀⠈⡰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢡⡀⣾⠓⣿⢚⡄⠀⡀⠈⠄⢠⡄⠠⣠⣮⣻⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠙⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣴⣲⣲⠶⣶⣶⣶⣶⣶⣶⢲⣖⣲⡖⢠⣠⣿⡛⠻⢛⣿⡻⡗⢂⡄⢠⡄⢠⣭⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣯⣙⡛⠿⢿⣿⡿⢫⣴⣾⣿⣿⣟⣤⠀⠀⠙⠛⠻⣷⣼⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣟⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⢿⡢
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣹⣶⣨⣽⣟⡻⠿⣿⣿⣿⣿⣁⡄⠀⠀⠠⡦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠒⠂⢑⠂⢤⢀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⢿⣟⢨⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣵⣆⣩⣙⠛⠿⣿⣤⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢇⠒⠀⠤⠀⠸⠀⠀⠀⡐⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣻⢗⠹⣿⣸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣮⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠿⠇⠐⠀⠀⢀⠉⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣽⣽⡛⡿⢿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠀⠓⠐⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡻⠄⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⢾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⡟⢘⡃⢀⡀⢘⡃⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⡽⡇⠀⠀⠀⠀⢀⠀⠐⠀
⣿⣿⣿⣿⣿⣹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣼⣑⣼⣇⢘⡁⢉⠁⢀⠀⣉⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢏⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣾⣇⣉⡀⣈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⣿⢿⣿⢀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠟⣿⣋⣛⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⠿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⡐⣽⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⠅⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠋⠐⠻⡛⣿⣿⡿⡿⣿⣿⣿⠿⢿⠫⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⣬⠀⣥⢀⣤⠀⠄⠀⠀⠀⠀⢹⡀⠦⠀⠘⠀⠂⠀⠄⠀⠀⠀⠀⠐⠀⠠⠀
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣗⠷⣶⢶⡖⣶⢚⡒⢒⢒⡦⠀⠀⡀⢨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠄⠀
⠀⠨⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⢗⡶⢾⣷⡶⡷⠚⢶⠺⡞⠁⠀⠢⠄⠬⠀⠀⢀⠀⠀⢀⠀⠀⠀⠁⠀⠐⠀⠠⠀⠀
⠀⠀⠀⣄⢠⢠⠉⣀⣀⡀⡀⢀⡀⢀⠀⣤⣄⠀⢀⡀⣀⡀⢀⡀⠀⡤⠤⢀⡄⡀⠀⢀⡀⣀⢀⣀⡄⣀⠀⣀⠉⠉⡭⠍⣉⠉⣉⠉⣉⠉⣉⢉⣉⠉⣍⢩⣭⢉⢉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠏⠃⠸⠸⠤⠇⠸⠼⠠⠆⠧⠇⠇⠧⠀⠢⠄⠇⠀⠣⠄⠀⠯⠥⠣⠇⠣⠆⠣⠄⠦⠇⠤⠗⠤⠃⠀⠇⠘⠦⠄⠦⠃⠁⠧⢅⡇⠥⠃⠥⢄⣯⠁⠿⠠⠣⢸⣯⡏⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⣾⡍⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⡶⣤⣶⣾⣿⣿⣿⣿⣿⣿⡄⡎⠛⠿⠿⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡣⣽⣦⠉⠂⠖⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣍⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⠀⣮⣦⣦⣴⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢼⡧⣥⠀⢈⠀⠑⠠⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⡗⣦⣶⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠸⡧⢾⡷⢄⠀⡀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣻⣽⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⠀⠉⠘⠿⡦⠑⠀⡀⠀⡁⢀⠀⠀⠀⠀⠀⡀⢀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣝⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⢀⠀⠀⠀⡾⠋⠐⠀⠀⠀⡀⠀⠀⠀⠀⠈⡰⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢡⡀⣾⠓⣿⢚⡄⠀⡀⠈⠄⢠⡄⠠⣠⣮⣻⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣴⣲⣲⠶⣶⣶⣶⣶⣶⣶⢲⣖⣲⡖⢠⣀⣿⡛⠻⢛⣿⡻⡗⢂⡄⢠⡄⢠⣭⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣯⣙⡛⠿⢿⣿⡿⢫⣴⣾⣿⣿⣟⣤⠀⠀⠙⠛⠻⣷⣼⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣟⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣹⣶⣨⣽⣟⡻⠿⣿⣿⣿⣿⣁⡄⠀⠀⠠⡦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠒⠀⠲⠂⢤⢀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⢿⣟⢨⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣵⣆⣩⣙⠛⠿⣿⣤⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠇⠒⠀⠄⠄⠿⡀⠀⠀⣱⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣻⠗⠙⢿⣸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣮⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠿⠇⠐⠀⠀⢀⠉⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣽⣽⡛⡿⢿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠀⠓⠐⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡻⠄⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⢾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⡟⢘⡃⢀⡀⢘⡃⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⡽⠇⠀⠀⠀⠀⢀⠀⠐⠀
⣿⣿⣿⣿⣿⣹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣼⣑⣼⣇⢘⡁⢉⠁⢀⠀⣉⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢏⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣾⣇⣉⠀⣈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⣿⢿⣿⢀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠟⣿⣋⣛⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⠿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⡐⣽⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⠅⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠋⠐⠻⡛⣿⣿⡿⡿⣿⣿⣿⠿⢿⠫⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⣬⠀⣥⢀⣤⠀⠄⠀⠀⠀⠀⢹⡀⠦⠀⠘⠀⠂⠀⠄⠀⠀⠀⠀⠐⠀⠠⠀
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣗⠷⣶⢶⡖⣶⢚⡒⢒⢒⡦⠀⠀⡀⢨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠄⠀
⠀⠨⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⢗⡶⢾⣷⡶⡷⠚⢶⠺⡞⠁⠀⠢⠄⠬⠀⠀⢀⠀⠀⢀⠀⠀⠀⠁⠀⠐⠀⠠⠀⠀
⠀⠀⠀⣄⢠⢠⠀⡀⡀⠀⡀⠀⡀⢀⠀⣤⣀⠀⢀⠀⠀⡀⢀⠀⠀⡠⠤⢀⠄⠀⠀⢀⠀⢀⠀⡀⡄⢀⠀⢀⠉⠉⡩⠍⢉⠉⣉⠉⣉⠉⢉⢉⣉⠉⣍⢩⣍⢉⢉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠏⠃⠸⠸⠤⠇⠸⠼⠠⠆⠧⠇⠇⠧⠀⠶⠆⠇⠀⠧⠅⠀⠯⠭⠧⠇⠧⠄⠧⠄⠦⠇⠤⠗⠥⠃⠁⠇⠘⠤⠄⠆⠇⠁⠧⢅⡇⠅⠁⠥⠄⣯⠀⠿⠨⠣⢸⣯⡏⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⣾⡍⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⡶⡔⣴⣾⣿⣿⣿⣿⣿⣿⣄⡎⢛⠿⠻⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⣽⣦⠉⠂⠖⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⣾⣿⣿⣿⣿⣿⣿⣿⡟⠑⠀⣤⣴⣦⢤⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢼⡧⣥⠀⢈⠀⠑⠠⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⢿⣿⣿⣿⣿⣿⣿⣿⡗⢶⣤⣿⡿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠸⡧⢾⡷⢄⠀⡀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣼⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣽⣿⣯⣹⣽⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠉⠘⠿⡦⠑⠀⡀⠀⡁⢀⠀⠀⠀⠀⠀⡀⢀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣝⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⠀⠀⠀⡾⠋⠐⠀⠀⠀⡀⠀⠀⠀⠀⠈⡰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢡⡀⣾⠓⣿⢚⡄⠀⡀⠈⠄⢠⡄⠠⣠⣮⣻⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠙⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣴⣲⣲⠶⣶⣶⣶⣶⣶⣶⢲⣖⣲⡖⢠⣀⣿⡛⠻⢛⣿⡻⡗⢂⡄⢠⡄⢠⣭⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣯⣙⡛⠿⢿⣿⡿⢫⣴⣾⣿⣿⣟⣤⠀⠀⠙⠛⠻⣷⣼⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣟⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⢿⡉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣹⣶⣨⣽⣟⡻⠿⣿⣿⣿⣿⣁⡄⠀⠀⠠⡦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠒⠒⠶⠆⢤⢀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⢿⣟⣨⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣵⣆⣩⣙⠛⠿⣿⣤⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⢃⠓⠀⠤⠠⠿⠀⠀⠀⡑⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⢿⠇⠝⢿⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣮⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠿⠇⠐⠀⠀⢀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣽⣽⡛⡿⢿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠀⠓⠐⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡻⠄⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⢾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⡟⢘⡃⢀⡀⢘⡃⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⡽⡇⠀⠀⠀⠀⢀⠀⠐⠀
⣿⣿⣿⣿⣿⣹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣼⣑⣼⣇⢘⡁⢉⠁⢀⠀⣉⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢏⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣾⣇⣉⡀⣈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⣿⢿⣿⢀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠟⣿⣋⣛⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⠿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⡐⣽⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⠅⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠋⠐⠻⡛⣿⣿⡿⡿⣿⣿⣿⠿⢻⠫⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⣬⠀⣥⢀⣤⠀⠄⠀⠀⠀⠀⢹⡀⠦⠀⠘⠀⠂⠀⠄⠀⠀⠀⠀⠐⠀⠠⠀
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣗⠷⣶⢶⡖⣶⢚⡒⢒⢒⡦⠀⠀⡀⢨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠄⠀
⠀⠨⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢵⢗⡶⢾⣶⡶⡷⠚⢶⠺⡞⠁⠀⠢⠄⠬⠀⠀⢀⠀⠀⢀⠀⠀⠀⠁⠀⠐⠀⠠⠀⠀
⠀⠀⠀⡀⢀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠉⠉⡩⡉⠉⠛⠙⠋⠛⠛⠛⠛⡛⠛⣟⢛⡻⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠟⠃⠸⠸⠀⠏⠸⠸⠘⠆⠇⠇⠇⠇⠀⠔⠇⠏⠁⠇⠅⠀⠏⠁⠇⠇⠇⠄⠧⠀⠶⠇⠄⠗⠥⠇⠁⠇⠘⠄⠄⠇⠁⠁⠧⢅⡇⠅⠁⠥⠠⣭⠀⠿⠨⠪⢸⣯⡛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⣾⡍⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⡶⣴⣾⣿⣿⣿⣿⣿⣿⣄⡎⠿⠿⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣽⣦⠉⠂⠖⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⡀⣻⣿⣿⣿⣿⣿⣿⣿⡏⠈⠸⣾⣤⣶⢤⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢼⡧⣥⠀⢈⠀⠑⠠⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⠁⢻⣿⣿⣿⣿⣿⣿⣿⡟⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠸⡧⢾⡷⢄⠀⡀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣼⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣽⣽⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢀⠀⠉⠘⠿⡦⠑⠀⡀⠀⡁⢀⠀⠀⠀⠀⠀⡀⢀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢻⣿⣿⣿⣿⣿⣿⣝⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⢀⠀⠀⠀⡾⠋⠐⠀⠀⠀⡀⠀⠀⠀⠀⠈⡰⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⢸⣯⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢡⡀⣾⠓⣿⢚⡄⠀⡀⠈⠄⢠⡄⠠⣠⣮⣺⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣴⣲⣲⠶⣶⣶⣶⣶⣶⣶⢲⣖⣲⡖⢠⣀⣿⡛⠻⢛⣿⡻⡗⢂⡄⢠⡄⢠⣭⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣯⣙⡛⠿⢿⣿⡿⢫⣴⣾⣿⣿⣟⣤⠀⠀⠙⠛⠻⣷⣼⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣟⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣹⣶⣨⣽⣟⡻⠿⣿⣿⣿⣿⣁⡄⠀⠀⠠⡦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠒⠂⢐⠂⠤⢀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⢿⣟⢨⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣵⣆⣩⣙⠛⠿⣿⣤⣷⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢇⠂⠀⠤⠀⠸⠀⠀⠀⢱⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⢿⢇⠙⢿⣸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣮⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠿⠇⠐⠀⠀⢀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣽⣽⡛⡿⢿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠀⠓⠐⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡻⠄⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⢾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⡟⢘⡃⢀⡀⢘⡃⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⡽⡇⠀⠀⠀⠀⢀⠀⠐⠀
⣿⣿⣿⣿⣿⣹⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣼⣑⣼⣇⢘⡁⢉⠁⢀⠀⣉⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢏⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣾⣇⣉⡀⣈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⣿⢿⣿⢀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠟⣿⣋⣛⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⡐⣽⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⠅⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠋⠐⠻⡛⣿⣿⡿⣿⣿⣿⣿⠿⢿⠫⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⣬⠀⣥⢀⣤⠀⠄⠀⠀⠀⠀⢹⡀⠦⠀⠘⠀⠂⠀⠄⠀⠀⠀⠀⠐⠀⠠⠀
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣗⠷⣶⢶⡖⣶⢚⡒⢒⢒⡦⠀⠀⡀⢨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠄⠀
⠀⠨⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⢗⡶⢾⣷⡶⡷⠚⢶⠺⡞⠁⠀⠢⠄⠬⠀⠀⢀⠀⠀⢀⠀⠀⠀⠁⠀⠐⠀⠠⠀⠀
⠀⠀⠀⡀⢀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣛⡛⠛⠛⠛⠛⠛⠛⠛⠛⡛⠛⣛⢛⡛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠟⠂⠸⠸⡉⠏⠹⠹⠘⠃⢏⠇⠏⠏⠀⢜⠇⠏⠁⢏⠅⠀⢇⡀⠏⠇⠇⠄⠏⠁⠛⠎⠅⠗⠍⠇⠉⠇⠘⢄⠀⠟⠁⠉⠥⣍⡅⠉⠋⠩⢄⣯⠈⠿⠨⢪⢸⣿⡋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣤⣶⡄⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⡶⡄⣶⣾⣿⣿⣿⣿⣿⣿⣈⠎⠻⠻⠿⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣣⣽⣦⠉⠂⠖⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⣴⣤⣦⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢼⡧⣥⠀⢈⠀⠑⠠⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⠃⠷⣾⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠸⡧⢾⡷⣄⠀⡀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣼⣿⣿⣯⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢌⠀⠉⠘⠿⡦⠑⠀⡀⠀⡁⢀⠀⠀⠀⠀⠀⡀⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣝⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⠀⠀⠀⡾⠋⠐⠀⠀⠀⡀⠀⠀⠀⠀⠈⡰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢡⡀⣾⠓⣿⢚⡄⠀⡀⠈⠄⢠⡀⠀⣠⣮⣻⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠙⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣤⣲⡶⠶⣶⣶⣶⣶⣶⣶⢲⣖⣲⡖⢢⣠⣿⡛⠻⢛⣿⡻⡗⢂⡄⢠⡄⢠⣭⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣯⣙⡛⠿⢿⣿⡿⢫⣴⣾⣿⣿⣟⣤⠀⠀⠙⠛⠻⣷⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⢿⡂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣹⣶⣨⣽⣟⡻⠿⣿⣿⣿⣿⣁⡄⠀⠀⠠⡦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠲⠀⠀⡰⠇⠠⢄⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣯⢿⣟⣈⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣵⣆⣭⣙⠛⠿⣿⣄⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢍⠁⠀⠀⠄⠇⠄⠀⠤⢵⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣻⠇⠙⢿⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣮⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⢀⠈⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣽⣝⡛⠿⢿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠀⠓⠐⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⢾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⡟⢘⡃⢀⡀⢘⡃⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⡽⠇⠀⠀⠀⠀⢀⠀⠐⠀
⣿⣿⣿⣿⣿⣹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣼⣑⣼⣇⢘⡁⢉⠁⢀⠀⣉⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣻⢏⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣾⣅⣉⠀⣈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⣿⢿⣿⢀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠟⣿⣋⣛⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⡐⣽⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⠅⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠋⠐⠙⡻⣿⣿⡿⡿⢿⣿⣿⠿⢻⠋⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⣬⠀⣥⢀⣤⠀⠄⠀⠀⠀⠀⢹⡀⠦⠀⠈⠀⠂⠀⠄⠀⠀⠀⠀⠐⠀⠠⠀
⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣗⠷⣶⢶⡖⣶⢚⡒⢒⢒⡦⠀⠀⡀⢨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠄⠀
⠀⢨⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⢗⡶⢾⣷⡶⡷⠚⢶⠺⡞⠃⠀⠢⠄⠬⠀⠀⢀⠀⠀⢀⠀⠀⠀⠁⠀⠐⠀⠠⠀⠀
⠀⠀⠀⡀⢀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠛⠛⣛⡛⠛⠛⠛⠛⠛⠛⠛⠛⡛⠛⡛⢛⣛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡟⠎⢸⢸⣉⡏⢹⡱⢘⡅⣎⡆⡏⣏⠀⢜⡃⡏⠁⢎⡁⠀⣗⣂⢎⡇⢇⡄⢎⡁⣙⡎⣉⡷⣉⠞⠉⡆⠐⣅⡀⡍⠄⠍⡧⣍⡇⣉⠊⠩⠄⡍⠎⡻⢈⢎⢸⣷⣗⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣤⣶⡄⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣔⣶⣶⣶⣶⣶⣾⣿⣿⣆⠷⠹⠿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣣⣽⣦⠉⠂⠖⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢤⠀⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣣⣦⣦⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢼⡧⣥⠀⢈⠀⠑⠠⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠀⢿⣿⣿⣿⣿⣿⣿⣿⡏⠲⢶⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠸⡧⢾⡷⣄⠀⡀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣼⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣙⣽⣯⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢌⠀⠉⠘⠿⡦⠑⠀⡀⠀⡁⢀⠀⠀⠀⠀⠀⡀⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢻⣿⣿⣿⣿⣿⣿⣭⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⠀⠀⠀⡾⠋⠐⠀⠀⠀⡀⠀⠀⠀⠀⠈⡰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢡⡀⣾⠓⣿⢚⡄⠀⡀⠈⠄⢠⡀⠀⣠⣮⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠙⢿⣿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣤⣲⡲⠶⣶⣶⣶⣶⣶⣶⢲⣖⣲⡖⢢⣀⣿⡛⠻⢛⣿⡻⡗⢂⡄⢠⡄⢠⣭⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣯⣙⡛⠿⢿⣿⡿⢫⣴⣾⣿⣿⣟⣤⠀⠀⠙⠛⠻⣷⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣹⣶⣨⣽⣟⡻⠿⣿⣿⣿⣿⣁⡄⠀⠀⠠⡦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠐⠂⠀⠶⠆⠠⠄⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⢿⣿⣟⢨⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣵⣆⣭⣙⠛⠿⣿⣄⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢇⠒⠀⠂⠄⠿⠄⠀⠨⠌⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣻⢗⠙⢿⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣮⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⢀⠉⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣽⣝⡛⠿⢿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠀⠓⠐⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⢾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⡟⢘⡃⢀⡀⢘⡃⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⡽⡇⠀⠀⠀⠀⢀⠀⠐⠀
⣿⣿⣿⣿⣿⣹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣑⣼⣇⢘⡁⢉⠁⢀⠀⣉⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣻⢏⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣾⣅⣉⡀⣈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⣿⢿⣿⢀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠟⣿⣋⣚⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡐⣽⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠅⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⡿⠋⠐⢙⣻⣿⠿⡿⣿⢿⣿⣿⠿⢿⠋⠉⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⣬⠀⣥⢀⣤⠀⠄⢀⠀⠀⠀⢹⡀⠦⠀⠈⠀⠂⠀⠄⠀⠀⠀⠀⠐⠀⠠⠀
⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣗⠷⣶⢶⡖⣶⢚⡒⢒⢒⡦⠀⠀⡀⢨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠄⠀
⠀⢨⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⢗⡶⢾⣷⡶⡷⠚⢶⠺⡞⠃⠀⠢⠄⠬⠀⠀⢀⠀⠀⢀⠀⠀⠀⠁⠀⠐⠀⠠⠀⠀
⠀⠀⠀⡀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠛⠛⣛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡛⢛⣛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡟⠎⢸⢰⣁⡇⢱⣱⢈⡅⣎⡆⡏⣏⠀⣌⡀⡇⠁⢎⡂⠀⣗⣒⣎⡆⣇⡀⢎⡁⣌⡎⣁⡧⣈⠆⠈⡆⠰⣁⡀⡍⠀⠍⡤⣍⡆⣉⠊⣉⠀⣯⠈⣷⢘⢎⢸⣿⣿⠈⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣤⣶⡄⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠔⢴⣶⣶⣶⣶⣾⣿⣿⣧⠹⠊⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡣⣽⣦⠉⠂⠖⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠐⣾⣿⣿⣿⣿⣿⣿⣿⣿⢀⠁⢣⣤⣷⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢼⡧⣥⠀⢈⠀⠑⠠⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠠⢻⣿⣿⣿⣿⣿⣿⣿⡏⠸⠻⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠸⡧⢾⡷⣄⠀⡀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣼⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣭⣿⣯⣹⣽⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢌⠀⠉⠘⠿⡦⠑⠀⡀⠀⡁⢀⠀⠀⠀⠀⠀⡀⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢻⣿⣿⣿⣿⣿⣿⣯⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⠀⠀⠀⡾⠋⠐⠀⠀⠀⡀⠀⠀⠀⠀⠈⡰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢡⡀⣾⠓⣿⢚⡄⠀⡀⠈⠄⢠⡀⠀⣠⣮⣻⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠙⢿⣿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣦⣲⡲⠶⣶⣶⣶⣶⣶⣶⢲⣖⣲⡖⢢⣀⣿⡛⠻⢛⣿⡻⡗⢂⡄⢠⡄⢠⣭⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣯⣙⡛⠿⢿⣿⡿⢫⣴⣾⣿⣿⣟⣤⠀⠀⠙⠛⠻⣷⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⢿⡃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣹⣶⣨⣽⣟⡻⠿⣿⣿⣿⣿⣁⡄⠀⠀⠠⡦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠶⠀⢐⠆⠠⡄⡀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⢿⣟⢈⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣵⣆⣭⣙⠛⠿⣿⣄⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢂⠒⠂⠤⠤⠼⠠⠀⠀⠬⠄⠀⠀⣰⣿⣿⣿⣿⣿⣿⣻⠗⠙⢿⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣮⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⢀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣽⣝⡛⠿⢿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠀⠓⠐⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⢾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⡟⢘⡃⢀⡀⢘⡃⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⡽⠇⠀⠀⠀⠀⢀⠀⠐⠀
⣿⣿⣿⣿⣿⣹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣼⣑⣼⣇⢘⡁⢉⠁⢀⠀⣉⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣻⢏⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣾⣅⣉⠀⣈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⣿⢿⣿⢀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠟⣿⣋⣚⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⠿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⡐⣽⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⠅⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠋⠐⢙⣻⣿⠿⡿⣿⢿⣿⣿⠿⢻⠫⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⣬⠀⣥⢀⣤⠀⠄⠀⠀⠀⠀⢹⡀⠦⠀⠈⠀⠂⠀⠄⠀⠀⠀⠀⠐⠀⠠⠀
⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣗⠷⣶⢶⡖⣶⢚⡒⢒⢒⡦⠀⠀⡀⢨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠄⠀
⠀⢨⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⢗⡶⢾⣷⡶⡷⠚⢶⠺⡞⠁⠀⠢⠄⠬⠀⠀⢀⠀⠀⢀⠀⠀⠀⠁⠀⠐⠀⠠⠀⠀
⠀⠀⠀⡀⢈⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠛⠟⢛⠛⠛⠿⠻⠟⠿⠿⠿⠿⠿⠿⡿⢿⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡷⠎⢰⢰⣀⡆⢰⣰⢠⡄⣆⡆⡇⣇⠀⣤⡆⡆⠂⣆⡂⠀⣗⡂⣆⡆⣆⡀⣆⡀⣤⡆⡁⡦⣂⡆⠂⡆⠰⣁⡀⡆⠄⠀⡤⣌⡆⡈⠀⡁⡠⣯⠈⣳⢐⢔⢸⣟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣤⣶⡄⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣖⣤⣶⣶⣶⣶⣶⣾⣿⣧⡸⠊⠟⠻⠿⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣣⣽⣦⠉⠂⠖⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢉⢹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠁⢰⣦⣦⣖⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢼⡧⣥⠀⢈⠀⠑⠠⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⡿⢿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠸⡧⢾⡷⣄⠀⡀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣠⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣭⣿⣿⣹⣽⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢌⠀⠉⠘⠿⡦⠑⠀⡀⠀⡁⢀⠀⠀⠀⠀⠀⡀⢀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣽⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⠀⠀⠀⡾⠋⠐⠀⠀⠀⡀⠀⠀⠀⠀⠈⡰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢡⡀⣾⠓⣿⢚⡄⠀⡀⠈⠄⢠⡀⠀⣠⣮⣻⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠙⢿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣦⣲⡲⠶⣶⣶⣶⣶⣶⣶⢲⣖⣲⡖⢢⣀⣿⡛⠻⢛⣿⡻⡗⢂⡄⢠⡄⢠⣭⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣯⣙⡛⠿⢿⣿⡿⢫⣴⣾⣿⣿⣟⣤⠀⠀⠙⠛⠻⣷⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡟⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⢿⡁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣹⣶⣨⣽⣟⡻⠿⣿⣿⣿⣿⣁⡄⠀⠀⠠⡦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠶⠀⠀⢠⠓⠠⢄⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⢿⣟⢈⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣵⣆⣭⣙⠛⠿⣿⣄⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⢋⠁⠀⠂⠠⠿⠄⠀⠤⢔⠀⠀⠀⣰⣽⣿⣿⣿⣿⣿⣿⢗⠝⢿⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣮⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⢀⠈⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣽⣝⡛⠿⢿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠀⠓⠐⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⢾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⡟⢘⡃⢀⡀⢘⡃⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⡽⡇⠀⠀⠀⠀⢀⠀⠐⠀
⣿⣿⣿⣿⣿⣹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣼⣑⣼⣇⢘⡁⢉⠁⢀⠀⣉⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣻⢏⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣾⣅⣉⡀⣈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⣿⢿⣿⢀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠟⣿⣋⣛⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⠿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⡐⣽⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⠅⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⡿⠋⠐⠙⡿⣿⡿⣿⠿⢿⣿⣿⠿⢿⠋⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⣬⠀⣥⢀⣤⠀⠄⠀⠀⠀⠀⢹⡀⠦⠀⠈⠀⠂⠀⠄⠀⠀⠀⠀⠐⠀⠠⠀
⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣗⠷⣶⢶⡖⣶⢚⡒⢒⢒⡦⠀⠀⡀⢨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠄⠀
⠀⢨⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⢗⡶⢾⣷⡶⡷⠚⢶⠺⡞⠁⠀⠢⠄⠬⠀⠀⢀⠀⠀⢀⠀⠀⠀⠁⠀⠐⠀⠠⠀⠀
⠀⠀⠀⠀⠈⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡷⠌⢰⢰⠂⡖⢰⢰⠰⠄⡆⡆⡇⡇⠀⡰⡆⡖⠂⡖⡂⠀⡗⠂⡆⡆⡆⡀⡖⠂⡶⡆⡂⡦⡒⡖⠒⡆⠰⡁⡁⡆⠀⠂⡤⣆⡄⠀⡀⠁⢠⣭⠈⣷⢐⢔⢸⣷⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡄⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣔⣶⣶⣶⣶⣶⣾⣿⣧⡘⠊⠟⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡣⣽⣦⠉⠂⠖⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢉⢹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠁⢐⣦⣤⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢼⡧⣥⠀⢈⠀⠑⠠⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠸⣿⣿⣿⣿⣿⣿⣿⣿⠁⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠸⡧⢾⡷⣄⠀⡀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣾⣹⣽⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠀⠉⠘⠿⡦⠑⠀⡀⠀⡁⢀⠀⠀⠀⠀⠀⡀⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣝⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⠀⠀⠀⡾⠋⠐⠀⠀⠀⡀⠀⠀⠀⠀⠈⡰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢡⡀⣾⠓⣿⢚⡄⠀⡀⠈⠄⢠⡀⠀⣠⣮⣻⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣦⣲⡲⠶⣶⣶⣶⣶⣶⣶⢲⣖⣲⡖⢢⣀⣿⡛⠻⢛⣿⡻⡗⢂⡄⢠⡄⢠⣭⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣯⣙⡛⠿⢿⣿⡿⢫⣴⣾⣿⣿⣟⣤⠀⠀⠙⠛⠻⣷⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⢿⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣹⣶⣨⣽⣟⡻⠿⣿⣿⣿⣿⣁⡄⠀⠀⠠⡦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⠔⠂⠶⠂⢤⢀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⢿⡿⢨⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣵⣆⣭⣙⠛⠿⣿⣄⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠗⠒⠀⠤⠀⠿⠀⠀⠀⡐⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣻⠗⠙⣿⣸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣮⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⢀⠈⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣽⣝⡛⠿⢿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠀⠓⠐⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⢾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⡟⢘⡃⢀⡀⢘⡃⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⡽⠇⠀⠀⠀⠀⢀⠀⠐⠀
⣿⣿⣿⣿⣿⣹⡿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣼⣑⣼⣇⢘⡁⢉⠁⢀⠀⣉⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣻⢏⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣾⣅⣉⠀⣈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⣿⢿⣿⢀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠟⣿⣋⣚⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⡐⣽⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⠅⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠋⠐⢙⣻⣿⠿⡿⣿⢿⣿⣿⠿⢿⠋⠉⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⣬⠀⣥⢀⣤⠀⠄⠀⠀⠀⠀⢹⡀⠦⠀⠈⠀⠂⠀⠄⠀⠀⠀⠀⠐⠀⠠⠀
⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣗⠷⣶⢶⡖⣶⢚⡒⢒⢒⡦⠀⠀⡀⢨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠄⠀
⠀⢨⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⢗⡶⢾⣷⡶⡷⠚⢶⠺⡞⠁⠀⠢⠄⠬⠀⠀⢀⠀⠀⢀⠀⠀⠀⠁⠀⠐⠀⠠⠀⠀
⠀⠀⠀⠀⠀⠘⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡷⡜⢸⢰⠒⡖⢲⢲⠰⠂⡖⡆⡟⡗⠀⡰⠆⡖⠂⡔⠂⠀⡯⠍⡔⡆⡆⡀⡔⠂⠲⡔⠒⣧⠒⡔⠒⡄⠰⡉⠁⡒⠀⠔⡤⣔⡄⠐⡄⠃⠄⣧⠘⣿⢐⡔⢸⣟⠙⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠁⠀⠈⠀⠁⠁⠈⠁⠈⠁⠈⠀⠁⠉⠀⠈⢁⣥⣤⡌⡡⠀⠉⠉⠈⠁⠈⠁⠈⠁⠉⠁⠉⠁⠉⠀⠀⣥⣤⣭⣥⣥⣤⣤⣤⣴⣶⣶⣴⣤⢠⣤⣶⣿⣾⣾⣾⣿⣧⡱⠘⡛⠿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢣⣽⣦⠉⠂⠖⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢉⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠑⢱⣦⣤⣦⡤⣺⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣧⢼⡧⣥⠀⢈⠀⠑⠠⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⢸⣿⣿⣿⣿⣿⣿⣿⣿⠐⣶⣾⣿⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠸⡧⢾⡷⣄⠀⡀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣾⣫⣽⣯⣹⣽⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢌⠀⠉⠘⠿⡦⠑⠀⡀⠀⡁⢀⠀⠀⠀⠀⠀⡀⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⡝⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⠀⠀⠀⡾⠋⠐⠀⠀⠀⡀⠀⠀⠀⠀⠈⡰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⣾⠓⣿⢚⡄⠀⡀⠈⠄⢠⡀⠀⣠⣮⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠈⠻⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣦⣲⡲⠶⣶⣶⣶⣶⣶⣶⢲⣖⣲⡖⢠⣀⣿⡛⠻⢛⣿⡻⡗⢀⡄⢠⡄⢠⣭⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣯⣙⡛⠿⢿⣿⡿⢫⣵⣾⣿⣿⣟⣤⠀⠀⠙⠛⠻⣷⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⢿⡃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣹⣶⣨⣽⣟⡻⠿⣿⣿⣿⣿⣁⡄⠀⠀⠠⡶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠐⠂⠀⠠⡄⡀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠿⣟⢨⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣵⣆⣭⣙⠛⠿⣿⣄⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⡐⠂⠰⠤⠄⡿⠀⠀⣀⡡⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣽⠗⠙⢿⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣮⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⢀⠉⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣽⣝⡛⠿⢿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠀⠓⠐⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⢾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠔⡟⢘⡃⢀⡀⢘⡃⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⡽⡇⠀⠀⠀⠀⢀⠀⠐⠀
⣿⣿⣿⣿⣿⣹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣑⣼⣇⢘⡁⢉⠁⢀⠀⣉⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣻⢏⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣾⣅⣉⡀⣈⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠼⣿⢿⣿⢀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠟⣿⣋⣚⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡐⣽⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠅⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⡿⠋⠐⢙⣻⣿⠿⣿⣿⢿⣿⣿⠿⢻⠋⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⣬⠀⣥⢀⣤⠀⠄⢀⠀⠀⠀⢹⡀⠦⠀⠈⠀⠂⠀⠄⠀⠀⠀⠀⠐⠀⠠⠀
⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣷⠷⣶⢶⡖⣶⢚⡒⢒⢒⡦⠀⠀⡀⢨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠄⠀
⠀⢨⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢵⢗⡶⢾⣶⡶⡷⠚⢶⠺⡞⠁⠀⠢⠄⠬⠀⠀⢀⠀⠀⢀⠀⠀⠀⠁⠀⠐⠀⠠⠀⠀
⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡷⡜⢸⢠⠂⡖⢢⢢⠐⡂⡔⡄⡟⡗⠀⡐⠂⡖⠂⡔⠀⠀⡯⠭⡔⡆⡆⠀⡔⠂⡒⡔⠒⣇⠒⡄⠐⡄⢠⠋⠁⡂⡀⠄⡤⣄⡄⠀⡄⠀⠄⣧⠘⡿⠐⡔⢸⣏⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠁⠀⠈⠈⠉⠁⠈⠉⠈⠁⠉⠁⠁⠉⠀⠈⢁⣥⣤⡌⡡⠀⠉⠉⠈⠁⠈⠁⠈⠁⠉⠁⠉⠁⠉⠀⠀⣥⣤⣭⣥⣥⣥⣤⣥⣤⣥⣬⣤⣥⢠⣤⣤⣭⣬⣬⣼⣿⣦⠑⠙⡛⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠣⣽⣦⠉⠂⠖⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢋⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠁⢡⣴⣤⣦⣰⣺⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⢼⡧⣥⠀⢈⠀⠑⠠⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠸⡧⢾⡷⣄⠀⡀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣾⣛⣽⣿⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢌⠀⠉⠘⠿⡦⠑⠀⡀⠀⡁⢀⠀⠀⠀⠀⠀⡀⢀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣝⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⠀⠀⠀⡾⠋⠐⠀⠀⠀⡀⠀⠀⠀⠀⠈⡰⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢡⡀⣾⠓⣿⢚⡄⠀⡀⠈⠄⢠⡀⠀⣠⣮⣻⣬⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣦⣲⡲⠶⣶⣶⣶⣶⣶⣶⢲⣖⣲⡖⢠⣀⣿⡛⠻⢛⣿⡻⡗⢂⡄⢠⡄⢠⣭⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣯⣙⡛⠿⢿⣿⡿⢫⣴⣾⣿⣿⣟⣤⠀⠀⠙⠛⠻⣷⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⢿⡂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣹⣶⣨⣽⣟⡻⠿⣿⣿⣿⣿⣁⡄⠀⠀⠠⡦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⠒⠒⠀⠂⣄⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣯⠿⣟⢨⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣵⣆⣭⣙⠛⠿⣿⣄⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠕⠒⠀⠤⠄⠾⠀⠀⢀⣱⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣻⢓⠙⢻⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣮⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⢀⠈⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣽⣝⡛⠿⢿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠀⠓⠐⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⢾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⡟⢘⡃⢀⡀⢘⡃⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⡽⠇⠀⠀⠀⠀⢀⠀⠐⠀
⣿⣿⣿⣿⣿⣹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣼⣑⣼⣇⢘⡁⢉⠁⢀⠀⣉⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣻⢏⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣾⣅⣉⠀⣈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⣿⢿⣿⢀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠟⣿⣋⣛⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⠿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⡐⣽⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⠅⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠋⠐⠙⡿⣿⡿⣿⠿⢿⣿⣿⠿⢿⠋⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⣬⠀⣥⢀⣤⠀⠄⠀⠀⠀⠀⢹⡀⠦⠀⠈⠀⠂⠀⠄⠀⠀⠀⠀⠐⠀⠠⠀
⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣗⠷⣶⢶⡖⣶⢚⡒⢒⢒⡦⠀⠀⡀⢨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠄⠀
⠀⢨⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⢗⡶⢾⣷⡶⡷⠚⢶⠺⡞⠃⠀⠢⠄⠬⠀⠀⢀⠀⠀⢀⠀⠀⠀⠁⠀⠐⠀⠠⠀⠀
⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡷⡜⢸⢠⠂⡄⢠⢢⠀⡂⡔⡄⡟⡖⠀⣐⡀⡄⠂⡔⠄⠀⡮⠭⡔⡇⡄⠀⡔⠀⡐⡔⠂⣇⠔⡄⠔⡄⢠⠊⠁⡀⡀⠄⡤⣄⡄⠀⡄⠀⠠⣧⠘⣮⠰⡴⢸⣏⢙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠁⠀⠈⠈⠉⠁⠈⠉⠈⠁⠉⠁⠁⠉⠀⠉⢁⣥⣤⡍⡡⠀⠉⠉⠉⠁⠉⠁⠉⠁⠉⠁⠁⠁⠉⠀⠀⣥⣤⣭⣥⣥⣥⣤⣥⣤⣤⣥⣤⣤⢠⣤⣤⣭⣬⣬⣼⣿⣦⠑⠙⡻⠿⠿⠿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢧⣽⣦⠉⠂⠖⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢋⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠁⢣⣶⣶⣧⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⢼⡧⣥⠀⢈⠀⠑⠠⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⢸⣿⣷⣿⣿⣿⣿⣿⣿⠐⢾⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠸⡧⢾⡷⣄⠀⡀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣝⣽⣯⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢈⠀⠉⠘⠿⡦⠑⠀⡀⠀⡁⢀⠀⠀⠀⠀⠀⡀⢀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣝⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⠀⠀⠀⡾⠋⠐⠀⠀⠀⡀⠀⠀⠀⠀⠈⡰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⢸⣽⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢡⡀⣾⠓⣿⢚⡄⠀⡀⠈⠄⢠⡀⠀⣠⣮⣻⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣦⣲⡲⠶⣶⣶⣶⣶⣶⣶⢲⣖⣲⡖⢠⣀⣿⡛⠻⢛⣿⡻⡗⢂⡄⢠⡄⢠⣭⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣯⣙⡛⠿⢿⣿⡿⢫⣴⣾⣿⣿⣟⣤⠀⠀⠙⠛⠻⣷⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⢿⡆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣹⣶⣨⣽⣟⡻⠿⣿⣿⣿⣿⣁⡄⠀⠀⠠⡦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠠⠀⠀⠀⠀⠀⢀⠠⠀⠒⠂⠂⠂⣄⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠿⣟⣨⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣵⣆⣭⣙⠛⠿⣿⣄⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠕⠒⠀⠤⠄⢿⠀⠀⢀⣱⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣻⠏⠻⢿⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣮⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⢀⠈⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣽⣝⡛⠿⢿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠀⠓⠐⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⢾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⡟⢘⡃⢀⡀⢘⡃⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⡽⡇⠀⠀⠀⠀⢀⠀⠐⠀
⣿⣿⣿⣿⣿⣻⡿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣼⣑⣼⣇⢘⡁⢉⠁⢀⠀⣉⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣻⢏⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣽⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣾⣅⣉⡀⣈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⣿⢿⣿⢀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠟⣿⣋⣚⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⡐⣽⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⠅⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⡿⠋⠘⠙⣿⣿⡿⡿⡿⢿⣿⣿⠿⢿⠋⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⣬⠀⣥⢀⣤⠀⠄⠀⠀⠀⠀⢹⡀⠦⠀⠈⠀⠂⠀⠄⠀⠀⠀⠀⠐⠀⠠⠀
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣗⠷⣶⢶⡖⣶⢚⡒⢒⢒⡦⠀⠀⡀⢨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠄⠀
⠀⢨⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢵⢗⡶⢾⣷⡶⡷⠚⢶⠺⡞⠁⠀⠢⠄⠬⠀⠀⢀⠀⠀⢀⠀⠀⠀⠁⠀⠐⠀⠠⠀⠀
⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣦⡔⢨⢠⠀⡤⢠⢠⢀⡀⡄⡄⡎⡆⠀⢀⡄⡤⠄⡄⠄⠀⡦⠄⡄⡆⡄⠀⡄⠀⣀⡄⠀⣅⠄⡄⠄⡄⢠⠂⠂⡄⠀⠄⡤⣄⡄⠄⡄⠀⢄⣧⠐⣦⠠⡠⢸⣗⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠁⠀⠈⠈⠀⠁⠈⠈⠀⠁⠁⠁⠁⠁⠀⠁⢁⣥⣤⡅⡡⠀⠁⠀⠁⠁⠁⠁⠁⠀⠉⠁⠁⠁⠁⠁⠀⣥⣤⣥⣥⣥⣤⣤⣥⣤⣥⣤⣤⣤⢠⣥⣤⣭⣬⣬⣼⣿⣧⠸⠊⠟⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣧⣽⣦⠉⠂⠖⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢉⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⢰⣦⣤⣔⣠⣺⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢼⡧⣥⠀⢈⠀⠑⠠⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⢸⣿⣿⣿⣿⣿⣿⣿⣿⠐⠬⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠸⡧⢾⡷⣄⠀⡀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣾⣽⣿⣯⣹⣽⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢈⠀⠉⠘⠿⡦⠑⠀⡀⠀⡁⢀⠀⠀⠀⠀⠀⡀⢀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣽⣿⣿⣿⣿⣿⣝⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⠀⠀⠀⡾⠋⠐⠀⠀⠀⡀⠀⠀⠀⠀⠈⡰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢡⡀⣾⠓⣿⢚⡄⠀⡀⠈⠄⢠⡀⠀⣠⣮⣻⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣦⣲⡲⠶⣶⣶⣶⣶⣶⣶⢲⣖⣲⡖⢠⣀⣿⡛⠻⢛⣿⡻⡗⢂⡄⢠⡄⢠⣭⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣯⣙⡛⠿⢿⣿⡿⢫⣴⣾⣿⣿⣟⣤⠀⠀⠙⠛⠻⣷⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣹⣶⣨⣽⣟⡻⠿⣿⣿⣿⣿⣁⡄⠀⠀⠠⡦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠐⠐⡤⠀⣄⡀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠿⣿⣨⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣵⣆⣭⣙⠛⠿⣿⣄⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠕⠒⠀⠤⠀⠏⠀⠀⢀⡁⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣹⠗⠘⢿⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣮⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⢀⠉⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣽⣝⡛⠿⢿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠀⠓⠐⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⢾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⡟⢘⡃⢀⡀⢘⡃⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⡽⡇⠀⠀⠀⠀⢀⠀⠐⠀
⣿⣿⣿⣿⣿⣹⡿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣼⣑⣼⣇⢘⡁⢉⠁⢀⠀⣉⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣻⢏⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣾⣅⣉⡀⣈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⣿⢿⣿⢀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠟⣿⣋⣛⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⠿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⡐⣽⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⠅⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⡿⠋⠐⠙⡿⣿⠿⣿⣿⢿⣿⣿⠿⢿⠋⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⣬⠀⣥⢀⣤⠀⠄⠀⠀⠀⠀⢹⡀⠦⠀⠈⠀⠂⠀⠄⠀⠀⠀⠀⠐⠀⠠⠀
⠀⠀⠀⠀⠉⠀⠀⠀⠈⠀⠀⠀⠀⠄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣗⠷⣶⢶⡖⣶⢚⡒⢒⢒⡦⠀⠀⡀⢨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠄⠀
⠀⢨⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⢗⡶⢾⣷⡶⡷⠚⢶⠺⡞⠃⠀⠢⠄⠬⠀⠀⢀⠀⠀⢀⠀⠀⠀⠁⠀⠐⠀⠠⠀⠀
⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣦⡐⢰⢠⠤⡤⢤⢤⢠⠄⡤⡄⡦⡦⠀⢠⡄⡤⠄⡠⠄⠀⣖⡒⡠⡆⡄⠀⡠⠄⣤⡠⠤⣆⠤⡀⠤⡀⢠⠒⠂⡄⠀⠄⡠⣤⡄⠤⡄⡠⠄⡦⡰⣶⠠⡠⢸⣇⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠃⠁⠘⠈⠂⠃⠈⠊⠐⠂⠑⠁⠃⠑⠀⠑⢀⣃⣀⡑⡀⠀⠓⠒⠑⠁⠑⠁⠑⠂⠒⠃⠒⠃⠒⠁⠀⣧⣤⣵⣦⣷⣦⣦⣧⣦⣧⣶⣥⣒⢠⣦⣥⣿⣼⣵⣼⣿⣦⠘⠊⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣽⣦⠉⠂⠖⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⣙⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠁⢰⣦⣤⣇⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢼⡧⣥⠀⢈⠀⠑⠠⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠃⢹⣿⣿⣿⣿⣿⣿⣿⣿⠐⠹⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠸⡧⢾⡷⣄⠀⡀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣾⣽⣿⣿⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢌⠀⠉⠘⠿⡦⠑⠀⡀⠀⡁⢀⠀⠀⠀⠀⠀⡀⢀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣝⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⠀⠀⠀⡾⠋⠐⠀⠀⠀⡀⠀⠀⠀⠀⠈⡰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢡⡀⣾⠓⣿⢚⡄⠀⡀⠈⠄⢠⡀⠀⣠⣮⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠈⠻⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣦⣲⡲⠶⣶⣶⣶⣶⣶⣶⢲⣖⣲⡖⢠⣀⣿⡛⠻⢛⣿⡻⡗⢂⡄⢠⡄⢠⣭⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣯⣙⡛⠿⢿⣿⡿⢫⣴⣾⣿⣿⣟⣤⠀⠀⠙⠛⠻⣷⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⢿⡃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣹⣶⣨⣽⣟⡻⠿⣿⣿⣿⣿⣁⡄⠀⠀⠠⡦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠲⠀⡲⠀⢤⡀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠿⣿⣈⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣵⣆⣭⣙⠛⠿⣿⣄⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠕⠒⠀⠄⠀⠇⠀⠀⢀⣡⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠗⡙⢿⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣮⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⢀⠈⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣽⣝⡛⠿⢿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠀⠓⠐⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⢾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⡟⢘⡃⢀⡀⢘⡃⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⡽⡇⠀⠀⠀⠀⢀⠀⠐⠀
⣿⣿⣿⣿⣿⣹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣑⣼⣇⢘⡁⢉⠁⢀⠀⣉⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣻⢏⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣾⣅⣉⡀⣈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⣿⢿⣿⢀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠟⣿⣋⣛⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡐⣽⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠅⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⡿⠋⠐⠙⡿⣿⡿⣿⠿⢿⣿⣿⠿⢿⠋⠉⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⣬⠀⣥⢀⣤⠀⠄⢀⠀⠀⠀⢹⡀⠦⠀⠈⠀⠂⠀⠄⠀⠀⠀⠀⠐⠀⠠⠀
⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣗⠷⣶⢶⡖⣶⢚⡒⢒⢒⡦⠀⠀⡀⢨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠄⠀
⠀⢨⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢵⢗⡶⢾⣷⡶⡷⠚⢶⠺⡞⠃⠀⠢⠄⠬⠀⠀⢀⠀⠀⢀⠀⠀⠀⠁⠀⠐⠀⠠⠀⠀
⠀⠀⠀⠀⠉⠘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣦⡰⢰⢠⠤⡤⢤⢄⢠⠄⡠⡠⡶⡦⠀⢠⡄⡤⠄⡠⠄⠀⣖⡒⡠⡆⡄⠀⡠⠄⢤⡠⠤⣆⠤⡀⠤⡀⢠⠖⠂⠄⠀⠠⡠⣤⡄⠠⡄⠤⠀⣦⠰⣶⠠⡠⢸⣟⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠃⠁⠘⠘⠒⠃⠘⠊⠐⠃⠓⠃⠃⠓⠀⠑⢂⣃⣀⡑⡂⠀⠓⠒⠑⠃⠑⠃⠑⠂⠒⠃⠒⠋⠒⠉⠀⣃⣀⣓⣂⣓⣃⣂⣂⣂⣃⣒⣁⣒⢀⣃⣁⣛⣐⣑⣸⣿⣆⠛⠘⡛⠻⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣽⣦⠉⠂⠖⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢉⣰⣸⣿⣿⣿⣿⣿⣿⣿⣟⠀⠁⣡⣦⣦⣆⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢼⡧⣥⠀⢈⠀⠑⠠⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⠃⢹⣿⣾⣿⣿⣿⣿⣿⡏⠸⠻⣿⣿⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠸⡧⢾⡷⣄⠀⡀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣛⣿⣯⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢌⠀⠉⠘⠿⡦⠑⠀⡀⠀⡁⢀⠀⠀⠀⠀⠀⡀⢀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⡝⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⢀⠀⠀⠀⡾⠋⠐⠀⠀⠀⡀⠀⠀⠀⠀⠈⡰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢡⡀⣾⠓⣿⢚⡄⠀⡀⠈⠄⢠⡀⠀⣠⣮⣻⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠹⣿⡿⠿⡛⠁⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣦⣲⡲⠶⣶⣶⣶⣶⣶⣶⢲⣶⣲⡖⢠⣀⣿⡛⠻⢛⣿⡻⡗⢂⡄⢠⡄⢠⣭⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣯⣙⡛⠿⢿⣿⡿⢫⣴⣾⣿⣿⣟⣤⠀⠀⠙⠛⠻⣷⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⢿⡁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣹⣶⣨⣽⣟⡻⠿⣿⣿⣿⣿⣁⡄⠀⠀⠠⡦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠠⠀⠀⠀⠀⠀⣠⠀⠶⠀⠀⡐⠆⠤⡀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⢿⣿⢨⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣵⣆⣭⣙⠛⠿⣿⣄⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢌⠁⠐⠀⠀⠧⠄⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣽⠗⠙⢿⣸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣮⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⢀⠈⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣽⣝⡛⠿⢿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠀⠓⠐⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⢾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⡟⢘⡃⢀⡀⢘⡃⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⡽⡇⠀⠀⠀⠀⢀⠀⠐⠀
⣿⣿⣿⣿⣿⣻⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣼⣑⣼⣇⢘⡁⢉⠁⢀⠀⣉⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣻⢏⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣽⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣾⣅⣉⡀⣈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⣿⢿⣿⢀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠟⣿⣋⣚⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⡐⣽⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⠅⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⡿⠋⠘⠙⣿⣿⡿⡿⡿⢿⣿⣿⠿⢿⠋⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⣬⠀⣥⢀⣤⠀⠄⠀⠀⠀⠀⢹⡀⠦⠀⠈⠀⠂⠀⠄⠀⠀⠀⠀⠐⠀⠠⠀
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣗⠷⣶⢶⡖⣶⢚⡒⢒⢒⡦⠀⠀⡀⢨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠄⠀
⠀⢨⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⢗⡶⢾⣷⡶⡷⠚⢶⠺⡞⠁⠀⠢⠄⠬⠀⠀⢀⠀⠀⢀⠀⠀⠀⠁⠀⠐⠀⠠⠀⠀
⠀⠀⠀⠀⠀⠈⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣦⡰⢰⢀⠄⡀⢀⢄⠠⠄⡠⡀⡶⡦⠀⠠⠄⡄⠄⡠⡀⠀⣖⣒⡠⡆⡄⠀⡠⠄⠠⡠⠤⡆⠠⡀⠠⡀⢀⠖⠂⠀⠀⠀⡠⣠⡄⠀⡄⠠⡠⣤⠰⣲⢠⡠⢸⣷⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠃⠁⠘⠘⠒⠃⠘⠚⠐⠃⠓⠃⠃⠓⠀⠓⢂⣃⣀⡑⡂⠀⠓⠒⠓⠃⠓⠂⠑⠂⠓⠃⠒⠋⠒⠁⠀⣃⣈⣒⣂⣓⣂⣂⣃⣂⣃⣒⣂⢒⢀⣃⣀⣋⣐⣑⣸⣿⣷⠘⠊⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡣⣽⣦⠉⠂⠖⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢐⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠁⢐⣦⣦⣆⣀⣺⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢼⡥⣥⠀⢈⠀⠑⠠⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠸⡧⢾⡷⣄⠀⡀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣽⣽⣯⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢈⠀⠉⠘⠿⡦⠑⠀⡀⠀⡁⢀⠀⠀⠀⠀⠀⡀⢀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣝⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⡾⠋⠐⠀⠀⠀⡀⠀⠀⠀⠀⠈⡰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢡⡀⣾⠓⣿⢚⡄⠀⡀⠈⠄⢠⡀⠀⣠⣮⣻⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣦⣲⡲⠶⣶⣶⣶⣶⣶⣶⢲⣶⣲⡖⢠⣀⣿⡛⠻⢛⣿⠻⡗⢂⡄⢠⡀⢠⣭⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⣯⣙⡛⠿⢿⣿⡿⢫⣴⣾⣿⣿⣟⣤⠀⠀⠙⠛⠻⣷⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⢿⡂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣹⣶⣨⣽⣟⡻⠿⣿⣿⣿⣿⣁⡄⠀⠀⠠⡦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠠⠀⠀⠀⠀⠀⠀⠤⠀⠒⠆⠶⠀⢄⡀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠿⣿⢨⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣵⣆⣭⣙⠛⠿⣿⣄⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠕⠒⠀⠤⠀⠿⠀⠀⢀⣡⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣻⠗⠹⢿⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣮⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⢀⠈⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣽⣝⡛⠿⢿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠀⠓⠐⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⢾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⡟⢘⡃⢀⡀⢘⡃⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⡽⠇⠀⠀⠀⠀⢀⠀⠐⠀
⣿⣿⣿⣿⣿⣹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣼⣑⣼⣇⢘⡁⢉⠁⢀⠀⣉⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣻⢏⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣾⣅⣉⠀⣈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⣿⢿⣿⢀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠟⣿⣋⣛⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⠿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⡐⣽⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠋⠐⠙⡿⣿⡿⣿⠿⢿⣿⣿⠿⢿⠋⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⣬⠀⣥⢀⣤⠀⠄⠀⠀⠀⠀⢹⡀⠦⠀⠈⠀⠂⠀⠄⠀⠀⠀⠀⠐⠀⠠⠀
⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣗⠷⣶⢶⡖⣶⢚⡒⢒⢒⡦⠀⠀⡀⢨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠄⠀
⠀⢨⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⢗⡶⢾⣷⡶⡷⠚⢶⠺⡞⠁⠀⠠⠄⠬⠀⠀⢀⠀⠀⢀⠀⠀⠀⠁⠀⠐⠀⠠⠀⠀
⠀⠀⠀⠀⠀⠩⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣆⡰⢐⢀⠀⡀⢀⢀⠀⠀⡀⡀⡖⡄⠀⠀⡀⡀⡀⡀⡀⠀⣔⡂⡀⡄⡀⠀⡀⠀⠀⡀⠄⡂⡀⡀⡀⡉⢉⠝⠉⡉⠉⡉⡩⣉⡍⠉⡉⢉⢩⣥⠠⣄⢀⢀⢸⣇⠉⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠋⠁⠘⠘⠂⠃⠘⠘⠘⠃⠓⠃⠃⠃⠀⠛⢃⣃⣀⡓⡂⠀⠓⠂⠓⠃⠓⠂⠓⠂⠛⠃⠂⠋⠒⠃⠀⣃⣈⣒⣂⣓⣃⣂⣃⣂⣂⣒⣂⢂⢀⣃⣀⣛⣐⣑⣸⣿⣧⠘⠊⠿⠿⠿⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣽⣦⠉⠂⠖⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢈⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⢰⣦⣄⣦⣐⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢼⡧⣥⠀⢈⠀⠑⠠⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⠐⠹⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠸⡧⢾⡷⣄⠀⡀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣽⣿⣯⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢈⠀⠉⠘⠿⡦⠑⠀⡀⠀⡁⢀⠀⠀⠀⠀⠀⡀⢀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣝⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⠀⠀⠀⡾⠋⠐⠀⠀⠀⡀⠀⠀⠀⠀⠈⡰⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢡⡀⣾⠓⣿⢚⡄⠀⡀⠈⠄⢠⡀⠀⣠⣮⣻⣮⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠈⠻⣿⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣤⣲⡲⠶⣶⣶⣶⣶⣶⣶⢲⣖⣲⡖⢠⣠⣿⡛⠻⢛⣿⡻⡗⢂⡄⢠⡄⢠⣭⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣯⣙⡛⠿⢿⣿⡿⢫⣴⣾⣿⣿⣟⣤⠀⠀⠙⠛⠻⣷⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⢿⡃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣹⣶⣨⣽⣟⡻⠿⣿⣿⣿⣿⣁⡄⠀⠀⠠⡦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠠⠀⠀⠀⠀⠀⠀⠤⠀⠒⠂⡢⠀⠄⡀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⢿⠿⣟⣨⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣵⣆⣭⣙⠛⠿⣿⣄⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠑⠒⠠⠤⠀⠟⠀⠀⢀⣡⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣻⠟⠘⢻⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣮⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⢀⠈⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣽⣝⡛⠿⢿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠀⠓⠐⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⢾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⡟⢘⡃⢀⡀⢘⡃⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⡽⡇⠀⠀⠀⠀⢀⠀⠐⠀
⣿⣿⣿⣿⣿⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣑⣼⣇⢘⡁⢉⠁⢀⠀⣉⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣻⢏⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣽⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣾⣅⣉⡀⣈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⣿⢿⣿⢀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠟⣿⣋⣚⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡐⣽⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠅⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⡿⠋⠘⠙⣿⣿⡿⡿⡿⢿⣿⣿⠿⢿⠋⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⣬⠀⣥⢀⣤⠀⠄⢀⠀⠀⠀⢹⡀⠦⠀⠈⠀⠂⠀⠄⠀⠀⠀⠀⠐⠀⠠⠀
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣗⠷⣶⢶⡖⣶⢚⡒⢒⢒⡦⠀⠀⡀⢨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠄⠀
⠀⢨⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢵⢗⡶⢾⣷⡶⡷⠚⢶⠺⡞⠁⠀⠢⠄⠬⠀⠀⢀⠀⠀⢀⠀⠀⠀⠁⠀⠐⠀⠠⠀⠀
⠀⠀⠀⠀⠀⠩⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣄⠠⢠⢀⣁⣀⣀⣀⢀⡀⣀⡀⣄⣄⠀⢀⡀⣀⡀⢀⡀⠀⡤⠤⣀⡄⡀⠀⢀⡀⣀⢀⣀⡄⣀⠀⣀⠉⢉⠭⠍⡉⠉⡉⠩⣉⡍⣉⡍⣉⠍⣥⢠⣭⢉⢉⢹⣇⠙⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠏⠃⠸⠘⠄⠃⠘⠜⠨⠀⠣⠃⠇⠣⠀⠪⠃⠇⠀⠣⠂⠀⠣⠤⠣⠃⠣⠂⠣⠄⠍⠇⠄⠏⠠⠃⠀⣇⣈⣢⣄⣧⣇⣆⣇⣆⣇⣢⡃⢦⢀⣆⣂⣿⣰⣳⣸⣿⣦⠘⠊⡟⠻⠿⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣽⣦⠉⠂⠖⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢉⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⣰⣬⣤⣦⣤⢺⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢼⡧⣥⠀⢈⠀⠑⠠⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⠘⠹⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠸⡧⢾⡷⣄⠀⡀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣙⣿⣯⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢌⠀⠉⠘⠿⡦⠑⠀⡀⠀⡁⢀⠀⠀⠀⠀⠀⡀⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡝⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⢀⠀⠀⠀⡾⠋⠐⠀⠀⠀⡀⠀⠀⠀⠀⠈⡰⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢡⡀⣾⠓⣿⢚⡄⠀⡀⠈⠄⢠⡀⠀⣠⣮⣺⣼⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠿⠻⠁⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣦⣲⡲⠶⣶⣶⣶⣶⣶⣶⢲⣖⣲⡖⢠⣀⣿⡛⠻⢛⣿⡻⡗⢂⡄⢠⡄⢠⣭⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣯⣙⡛⠿⢿⣿⡿⢫⣴⣾⣿⣿⣟⣤⠀⠀⠙⠛⠻⣷⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣹⣶⣨⣽⣟⡻⠿⣿⣿⣿⣿⣁⡄⠀⠀⠠⡦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠒⠂⡢⢠⡄⡀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⢿⢿⣟⣈⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣵⣆⣭⣙⠛⠿⣿⣄⡷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡐⠂⠰⠤⠀⠇⠀⠀⣀⣠⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣻⠇⠹⢿⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣮⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⢀⠈⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣽⣝⡛⠿⢿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠀⠓⠐⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⢾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⡟⢘⡃⢀⡀⢘⡃⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⡽⡇⠀⠀⠀⠀⢀⠀⠐⠀
⣿⣿⣿⣿⣿⣹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣼⣑⣼⣇⢘⡁⢉⠁⢀⠀⣉⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣻⢏⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣾⣅⣉⡀⣈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⣿⢿⣿⢀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠟⣿⣋⣛⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⠿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⡐⣽⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⠅⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⡿⠋⠐⠙⡿⣿⡿⣿⠿⢿⣿⣿⠿⢿⠋⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⣬⠀⣥⢀⣤⠀⠄⠀⠀⠀⠀⢹⡀⠦⠀⠈⠀⠂⠀⠄⠀⠀⠀⠀⠐⠀⠠⠀
⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣗⠷⣶⢶⡖⣶⢚⡒⢒⢒⡦⠀⠀⡀⢨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠄⠀
⠀⢨⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢵⢗⡶⢾⣷⡶⡷⠚⢶⠺⡞⠁⠀⠢⠄⠬⠀⠀⢀⠀⠀⢀⠀⠀⠀⠁⠀⠐⠀⠠⠀⠀
⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣄⢠⢠⢀⣈⣀⣀⡀⢀⡀⣀⡀⣤⣄⠀⢀⡀⣀⡀⢀⡀⠀⡤⠤⢀⡄⡀⠀⢀⡀⣀⢀⣀⡄⣀⠀⣀⠉⢉⠭⠍⣉⠉⢉⠩⣉⡍⣉⡍⣉⠍⣭⢠⣬⢉⢁⢹⣏⠙⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠏⠃⠸⠸⠤⠇⠸⠜⠨⠄⠣⠃⠇⠧⠀⠪⠅⠇⠀⠣⠄⠀⠯⠥⠣⠇⠣⠆⠣⠄⠬⠇⠤⠟⠤⠃⠀⠇⠈⠦⠄⠦⠇⠆⠇⠆⡇⣦⠃⠦⠀⠇⢂⣿⣰⣣⣸⣿⣧⡙⠘⡛⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⣽⣦⠉⠂⠖⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⣉⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠁⢣⣬⣤⣶⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢼⡧⣥⠀⢈⠀⠑⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠋⢸⣿⣷⣿⣿⣿⣿⣿⣿⠁⣶⣾⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠸⡧⢾⡷⣄⠀⡀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣻⣿⣯⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠉⠐⠿⡦⠑⠀⡀⠀⡁⢀⠀⠀⠁⠀⠀⡀⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⡝⠻⠿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⢀⠀⠀⠀⡾⠋⠐⠀⠀⠀⡀⠀⠀⠀⠀⠈⡰⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢡⡀⣾⠓⣿⢚⡄⠀⡀⠈⠄⢠⡀⠀⣠⣮⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⠻⠁⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣶⣲⡲⠶⣶⣶⣶⣶⣶⣶⢲⣖⣲⡖⢠⣠⣿⡛⠻⢛⣿⡻⡗⢂⡄⢠⡄⢠⣭⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣯⣙⡛⠿⢿⣿⡿⢫⣴⣾⣿⣿⣟⣤⠀⠀⠙⠛⠻⣷⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⢿⡅
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣹⣶⣨⣽⣟⡻⠿⣿⣿⣿⣿⣁⡄⠀⠀⠠⡦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠠⠀⠀⠀⠀⠀⢀⠠⠄⠀⠀⠀⢦⠀⡀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡿⣟⣨⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣵⣆⣭⣙⠛⠿⣿⣄⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⡐⠂⠰⠤⠀⢿⠀⠀⣀⣠⠀⠀⠀⣰⣽⣿⣿⣿⣿⣿⣻⢗⡙⢿⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣮⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠿⠇⠐⠀⠀⢀⠈⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣽⣝⡛⠿⢿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠀⠓⠐⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣵⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⢾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⡟⢘⡃⢀⡀⢘⡃⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⣿⡿⡽⡇⠀⠀⠀⠀⢀⠀⠐⠀
⣿⣿⣿⣿⣿⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣑⣼⣇⢘⡁⢉⠁⢀⠀⣉⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣻⢏⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣽⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣾⣅⣉⡀⣈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⣿⢿⣿⢀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠟⣿⣋⣚⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡐⣽⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠅⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⡿⠋⠘⠙⣿⣿⡿⡿⡿⢿⣿⣿⠿⢿⠋⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⣬⠀⣥⢀⣤⠀⠄⢀⠀⠀⠀⢹⡀⠦⠀⠈⠀⠂⠀⠄⠀⠀⠀⠀⠐⠀⠠⠀
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣷⠷⣶⢶⡖⣶⢚⡒⢒⢒⡦⠀⠀⡀⢨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠄⠀
⠀⢨⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢵⢗⡶⢾⣶⡶⡷⠚⢶⠺⡞⠁⠀⠢⠄⠬⠀⠀⢀⠀⠀⢀⠀⠀⠀⠁⠀⠐⠀⠠⠀⠀
⠀⠀⠀⠀⠀⠠⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣄⢠⢠⠀⡀⣀⡀⡀⢀⡀⢀⠀⣤⣄⠀⢀⡀⣀⡀⢀⠀⠀⡤⠤⢀⡄⡀⠀⢀⡀⣀⢀⣀⡄⣀⠀⢀⠉⠉⡭⠍⡉⠉⠉⠩⣉⡍⠉⡍⡩⠩⣭⢡⣠⢉⢉⢹⣇⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠏⠃⠸⠸⠤⠇⠸⠼⠠⠆⠧⠇⠇⠧⠀⠢⠄⠇⠀⠣⠄⠀⠯⠭⠣⠇⠣⠄⠣⠄⠦⠇⠤⠗⠤⠣⠀⠇⠘⠤⠄⠦⠆⠆⠇⠆⠇⠦⠇⠦⠀⠆⠂⠿⠠⠣⢸⣿⣦⠙⠚⡛⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⣽⣦⠉⠂⠖⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣍⢹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠁⢰⣦⣤⣶⣔⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢼⡧⣥⠀⢈⠀⠑⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠃⢹⣿⣿⣿⣿⣿⣿⣿⣿⠐⢾⣿⣿⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠸⡧⢾⡷⣄⠀⡀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣿⣽⣽⣯⣹⣽⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠉⠐⠿⡦⠑⠀⡀⠀⡁⢀⠀⠀⠁⠀⠀⡀⢀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⡝⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⢀⠀⠀⠀⡾⠋⠐⠀⠀⠀⡀⠀⠀⠀⠀⠈⡰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢡⡀⣾⠓⣿⢚⡄⠀⡀⠈⠄⢠⡀⠀⣠⣮⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣦⣲⡲⠶⣶⣶⣶⣶⣶⣶⢲⣖⣲⡖⢠⣠⣿⡛⠻⢛⣿⡻⡗⢂⡄⢠⡄⢠⣭⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣯⣙⡛⠿⢿⣿⡿⢫⣴⣾⣿⣿⣟⣤⠀⠀⠙⠛⠻⣷⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⢿⡁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣹⣶⣨⣽⣟⡻⠿⣿⣿⣿⣿⣁⡄⠀⠀⠠⡦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠠⠀⠀⠀⠀⠀⠀⠤⠀⠐⠒⡠⢠⡀⡀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠿⣟⢨⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣵⣆⣭⣙⠛⠿⣿⣄⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⡐⠒⠰⠤⠀⠏⠀⠀⣀⣠⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣻⣗⠙⢻⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣮⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠿⠇⠐⠀⠀⢀⠈⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣽⣝⡛⠿⢿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠀⠓⠐⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⢾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⡟⢘⡃⢀⡀⢘⡃⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⡽⡇⠀⠀⠀⠀⢀⠀⠐⠀
⣿⣿⣿⣿⣿⣹⡿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣑⣼⣇⢘⡁⢉⠁⢀⠀⣉⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣻⢏⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣾⣅⣉⡀⣈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⣿⢿⣿⢀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠟⣿⣋⣛⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡐⣽⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠅⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⡿⠋⠐⢙⡻⣿⣿⡿⡿⢿⣿⣿⠿⢿⠋⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⣬⠀⣥⢀⣤⠀⠄⢀⠀⠀⠀⢹⡀⠦⠀⠈⠀⠂⠀⠄⠀⠀⠀⠀⠐⠀⠠⠀
⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣗⠷⣶⢶⡖⣶⢚⡒⢒⢒⡦⠀⠀⡀⢨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠄⠀
⠀⢨⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⢗⡶⢾⣷⡶⡷⠚⢶⠺⡞⠃⠀⠢⠄⠬⠀⠀⢀⠀⠀⢀⠀⠀⠀⠁⠀⠐⠀⠠⠀⠀
⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣄⢠⠠⠀⡉⠀⠀⡀⠀⠀⢀⠀⡤⣀⠀⠀⠀⠀⠀⢀⠀⠀⡠⠤⢀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠀⠀⢀⠉⠉⡩⠍⠉⠉⠉⠩⣉⡍⠉⡍⠩⢍⣭⢡⡨⢉⢉⢹⣗⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠟⠃⠸⠸⠤⠇⠸⠼⠠⠆⠧⠇⠇⠧⠀⠶⠇⠇⠀⠣⠅⠀⠯⠭⠧⠇⠧⠄⠧⠄⠶⠇⠄⠗⠥⠃⠁⠇⠘⠤⠄⠶⠆⠆⠆⠆⠇⠦⠇⠦⠀⠇⠂⠿⠨⠫⢸⣿⣧⡸⠊⡟⠿⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⣽⣦⠉⠂⠖⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢉⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢰⣦⣦⣦⡰⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢼⡧⣥⠀⢈⠀⠑⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢾⣾⣿⡿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠸⡧⢾⡷⣄⠀⡀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣾⣻⣽⣯⣹⣽⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠉⠐⠿⡦⠑⠀⡀⠀⡁⢀⠀⠀⠁⠀⠀⡀⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣝⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⢀⠀⠀⠀⡾⠋⠐⠀⠀⠀⡀⠀⠀⠀⠀⠈⡰⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢡⡀⣾⠓⣿⢚⡄⠀⡀⠈⠄⢠⡀⠀⣠⣮⣻⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠈⠻⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣶⣲⡲⠶⣶⣶⣶⣶⣶⣶⢲⣖⣲⡖⢠⣠⣿⡛⠻⢛⣿⡻⡗⢂⡄⢠⡄⢠⣭⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣯⣙⡛⠿⢿⣿⡿⢫⣴⣾⣿⣿⣟⣤⠀⠀⠙⠛⠻⣷⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⢿⡃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣹⣶⣨⣽⣟⡻⠿⣿⣿⣿⣿⣁⡄⠀⠀⠠⡦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠠⠀⠀⠀⠀⠀⠀⠤⠀⠔⠖⡠⢠⡀⡀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡻⣟⢈⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣵⣆⣭⣙⠛⠿⣿⣄⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⡐⠂⠠⠤⠀⠇⠀⠀⣀⣠⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣻⣗⠸⢻⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣮⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠿⠇⠐⠀⠀⢀⠈⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣽⣝⡛⠿⢿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠀⠓⠐⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⢾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⡟⢘⡃⢀⡀⢘⡃⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⡽⡇⠀⠀⠀⠀⢀⠀⠐⠀
⣿⣿⣿⣿⣿⣹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣼⣑⣼⣇⢘⡁⢉⠁⢀⠀⣉⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣻⢏⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣾⣅⣉⡀⣈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⣿⢿⣿⢀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠟⣿⣋⣛⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⠿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⡐⣽⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⠅⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⡿⠋⠐⠹⣿⣿⡿⡿⡿⣿⣿⣿⡿⢻⠋⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⣬⠀⣥⢀⣤⠀⠄⠀⠀⠀⠀⢹⡀⠦⠀⠈⠀⠂⠀⠄⠀⠀⠀⠀⠐⠀⠠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣷⠷⣶⢶⡖⣶⢚⡒⢒⢒⡦⠀⠀⡀⢨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠄⠀
⠀⢨⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⢗⡶⢾⣷⡶⡷⠚⢶⠺⡞⠃⠀⠢⠄⠬⠀⠀⢀⠀⠀⢀⠀⠀⠀⠁⠀⠐⠀⠠⠀⠀
⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣛⡛⠋⠉⠉⠩⣉⡍⠉⡉⠩⠍⡉⢑⡚⠛⠛⢻⣇⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡟⠂⠸⠸⡉⠏⠹⡹⠘⠃⢏⠇⡏⢏⠀⢜⠇⠏⠁⢏⠅⠀⢇⡀⢏⠇⢇⠄⢏⠁⠛⠎⠍⡗⢍⠟⠉⠆⠘⢄⠀⢗⡆⡆⡆⡆⡆⢇⠆⣆⠀⡏⠎⢯⢨⢪⢸⣿⣧⠹⠚⡟⠻⠻⠟⠻⢻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⣴⣦⠀⠂⠖⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⢩⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠁⢰⣦⣤⣖⣠⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⢼⡧⣥⠀⢈⠀⠑⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⠑⠾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠸⡧⢾⡷⣄⠀⡀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣯⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠉⠐⠿⡦⠑⠀⡀⠀⡁⢀⠀⠀⠁⠀⠀⡀⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣝⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⠀⠀⠀⡾⠋⠐⠀⠀⠀⡀⠀⠀⠀⠀⠈⡰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢡⡀⣾⠓⣿⢚⡄⠀⡀⠈⠄⢠⡀⠀⣠⣮⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠻⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣴⣲⡲⠶⣶⣶⣶⣶⣶⣶⢲⣖⣲⡖⢠⣠⣿⡛⠻⢛⣿⡻⡗⢂⡄⢠⡄⢠⣭⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣯⣙⡛⠿⢿⣿⡿⢫⣴⣾⣿⣿⣟⣤⠀⠀⠙⠛⠻⣷⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⢿⡋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣹⣶⣨⣽⣟⡻⠿⣿⣿⣿⣿⣁⡄⠀⠀⠠⡦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠠⠀⠀⠀⠀⠀⡀⠄⠐⠒⠂⡲⠀⣄⡀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⢿⢿⣟⢨⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣵⣆⣭⣙⠛⠿⣿⣄⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡀⠒⠰⠤⠄⠇⠀⠀⣀⣠⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡗⠘⢿⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣮⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠿⠇⠐⠀⠀⢀⠈⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣽⣝⡛⠿⢿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠀⠓⠐⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⢾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⡟⢘⡃⢀⡀⢘⡃⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⡽⡇⠀⠀⠀⠀⢀⠀⠐⠀
⣿⣿⣿⣿⣿⣻⡿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣑⣼⣇⢘⡁⢉⠁⢀⠀⣉⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣻⢏⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣽⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣾⣅⣉⡀⣈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⣿⢿⣿⢀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠟⣿⣋⣚⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⠿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡐⣽⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠅⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⡿⠋⠘⠙⣿⣿⡿⡿⡿⢿⣿⣿⠿⢻⠋⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⣬⠀⣥⢀⣤⠀⠄⢀⠀⠀⠀⢹⡀⠦⠀⠈⠀⠂⠀⠄⠀⠀⠀⠀⠐⠀⠠⠀
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣷⠷⣶⢶⡖⣶⢚⡒⢒⢒⡦⠀⠀⡀⢨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠄⠀
⠀⢨⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢵⢗⡶⢾⣷⡶⡷⠚⢶⠺⡞⠃⠀⠢⠄⠬⠀⠀⢀⠀⠀⢀⠀⠀⠀⠁⠀⠐⠀⠠⠀⠀
⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡀⢀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠛⠛⣛⡛⠋⠉⠉⠩⢉⡍⠉⡍⠉⠉⣩⢐⣚⠛⠓⢻⣧⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡟⠆⢸⠸⡉⡏⠹⡹⢘⡁⢏⠇⡏⢏⠀⢜⠃⡏⠁⢎⡁⠀⣗⣂⢎⡇⢇⠄⢎⡁⣛⡎⣉⡗⣉⠦⠉⡂⠘⢄⡀⣟⡆⡎⡆⡎⡆⣆⠆⣆⠀⡞⠎⣿⢨⢮⢸⣿⣷⡘⠊⠟⠿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⣴⣦⡀⠂⢖⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣰⢰⣿⣿⣿⣿⣿⣿⣿⣿⡁⠉⢘⣾⣤⣦⣠⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⢾⡷⣥⡀⢈⠈⠑⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⢹⣿⣷⣿⣿⣿⣿⣿⣿⠓⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡷⢾⡷⣄⠀⡀⠀⠀⠀⠐⠐⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣾⣿⣿⣯⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢌⠠⠉⠒⠿⡦⠑⠀⡀⠀⡁⢀⠀⠀⠁⠀⠀⡀⢀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⡝⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⢈⠀⠀⡀⣾⠋⠒⠀⡀⠀⡀⠀⠀⠀⠀⡪⣰⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢱⡀⣾⡛⣿⢚⡄⠀⡀⠈⠄⢠⡀⠠⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣴⣶⡲⢶⣶⣶⣶⣶⣶⣶⣲⣖⣲⡖⢲⣀⣿⡛⠻⢟⣿⣻⡷⢂⡄⢠⣄⣠⣭⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣯⣙⣟⠿⣿⣿⡿⢻⣵⣾⣿⣿⣟⣤⠀⠀⠙⠛⠿⣷⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣹⣶⣨⣿⣿⡻⠿⣿⣿⣿⣿⣇⡄⠀⢴⠠⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡄⠀⠀⡀⠢⡀⡀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⢨⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣵⣦⣭⣙⠛⠿⣿⣦⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡐⠂⠰⠤⠄⠟⠀⠀⣀⣠⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠗⠝⣻⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠿⠇⠐⠀⠀⢀⠁⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣟⡛⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠀⠛⠘⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣟⢘⡃⢀⡀⢘⡃⣛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⡿⡇⠀⠀⠀⠀⢀⠀⠐⠀
⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣼⣇⣜⡁⣉⠁⢀⠀⣉⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣻⢏⡿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣉⡀⣉⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠼⣿⢿⣿⢀⠇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀
⣿⣿⠟⣿⣋⣚⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣽⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠍⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠄
⡿⠋⠘⢛⣿⣿⡿⣿⣿⢿⣿⣿⠿⢿⠋⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄⣬⠀⣥⢀⣤⠀⠄⢀⡄⠀⠀⢹⣁⠯⠀⠋⠀⠆⠀⠄⠀⠀⠀⠀⠐⠀⠠⠀
⠀⠀⠀⠈⠉⠈⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠷⣶⢶⡖⣶⢚⡒⢒⢒⡦⠀⠀⣀⢨⠁⠔⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠤⠀
⠀⢨⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢗⣶⢾⣷⣶⣷⠺⣶⠺⡞⠁⠀⠲⠄⠼⠀⠀⢀⠀⠀⢀⠀⠀⠀⠁⠀⠐⠀⠠⠀⠀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡀⢀⢀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠛⠛⣛⡛⠋⠉⠉⠩⢉⡍⠉⡍⠉⡉⣩⢑⣚⠚⠚⢻⣷⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡟⠎⢸⢸⣉⡏⢹⡱⢘⡅⣎⡆⡏⣏⠀⢌⡃⡏⠁⢎⡁⠀⣗⣂⢎⡇⢇⡄⢎⡁⣉⡎⣉⡷⣉⠖⠉⡆⠐⣅⡀⣕⡆⡆⡆⡆⡆⣆⡆⣇⠀⡗⠎⣿⢈⢎⢸⣿⣧⠨⠊⠿⠿⠿⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⣴⣦⡀⠂⢖⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣆⢠⢰⣶⣶⣶⣶⣶⣾⣿⣿⠀⠀⢘⣶⣤⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢾⡷⣥⡀⢈⠈⠑⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿⠀⡧⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡛⠻⡷⢾⡷⣄⠀⡀⠀⠀⠀⠐⠐⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣾⣿⣿⣯⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢌⠀⠉⠒⠿⡦⠑⠀⡀⠀⡁⢀⠀⠀⠁⠀⠀⡀⢀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⡝⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢈⠀⠀⡀⣾⠋⠒⠀⡀⠀⡀⠀⠀⠀⠀⡪⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢱⡀⣾⡛⣿⢚⡄⠀⡀⠈⠄⢠⡀⠠⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣶⣶⡲⢶⣶⣶⣶⣶⣶⣶⣲⣖⣲⡖⢲⣀⣿⡛⠻⢟⣿⣻⡷⢂⡄⢠⣄⣠⣭⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⢟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣯⣙⣟⠿⣿⣿⡿⢻⣵⣾⣿⣿⣟⣤⠀⠀⠙⠛⠿⣷⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⢿⡃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣹⣶⣨⣿⣿⡻⠿⣿⣿⣿⣿⣇⡄⠀⢄⠠⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠠⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⡠⠠⡀⡀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⢿⢿⣟⢨⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣵⣦⣭⣙⠛⠿⣿⣦⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⡐⠂⠠⠤⠀⠇⠀⠀⣀⣠⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡗⡹⢿⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠿⠇⠐⠀⠀⢀⠉⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣟⡛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠀⠛⠘⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣟⢘⡃⢀⡀⢘⡃⣛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⡿⡇⠀⠀⠀⠀⢀⠀⠐⠀
⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣛⣼⣇⣜⡁⣉⠁⢀⠀⣉⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣻⢏⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣉⡀⣉⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠼⣿⢿⣿⢀⠇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀
⣿⣿⠟⣿⣋⣛⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣽⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠍⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠄
⡿⠋⠘⢛⡿⣿⣿⣿⣿⢿⣿⣿⠿⢿⠋⠉⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄⣬⠀⣥⢀⣤⠀⠄⢀⡄⠀⠀⢹⣁⠯⠀⠋⠀⠆⠀⠄⠀⠀⠀⠀⠐⠀⠠⠀
⠀⠀⠀⠈⠉⠊⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠷⣶⢶⡖⣶⢚⡒⢒⢒⡦⠀⠀⣀⢨⠁⠔⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠤⠀
⠀⢨⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢗⣶⢾⣷⣶⣷⠺⣶⠺⡞⠁⠀⠲⠄⠼⠀⠀⢀⠀⠀⢀⠀⠀⠀⠁⠀⠐⠀⠠⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡀⢀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠛⠛⢛⡛⠋⠉⠉⠩⣉⡍⠉⡍⠉⢩⣩⢉⣛⠚⠓⢺⣿⣟⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡟⠎⢸⢰⡁⡇⢱⣱⢈⡅⣎⡆⡏⣏⠀⣌⡀⡇⠁⢎⡂⠀⣗⣒⣎⡆⣇⡀⢎⡁⣌⡎⣁⡧⣊⠆⠈⡆⠰⣁⡀⣄⡆⡆⡆⡆⡆⣆⡆⣆⠀⡖⠌⣟⢘⢎⢸⣿⣿⣆⡷⠹⠿⠿⠿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⣴⣦⠀⠂⢖⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣆⣄⡀⣶⣶⣶⣶⣶⣾⣿⣿⡿⠈⠀⢿⣤⣦⠄⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⢾⡷⣥⡀⢈⠈⠑⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⢳⣴⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡷⢾⡷⣄⠀⡀⠀⠀⠀⠐⠐⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⣽⣿⣯⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢌⠀⠉⠒⠿⡦⠑⠀⡀⠀⡁⢀⠀⠀⠁⠀⠀⡀⢀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣝⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⢀⠀⠀⠀⣾⠋⠒⠀⡀⠀⡀⠀⠀⠀⠀⡊⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⢺⣟⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⣾⠛⣿⢚⡄⠀⡀⠈⠄⢠⡀⠠⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣴⣲⡲⠶⣶⣶⣶⣶⣶⣶⣲⣖⣲⡖⢢⣀⣿⡛⠻⢛⣿⣻⡷⢂⡄⢠⣄⣠⣭⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣯⣙⣟⠿⣿⣿⡿⢻⣵⣾⣿⣿⣟⣤⠀⠀⠙⠛⠿⣷⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣹⣶⣨⣿⣟⡻⠿⣿⣿⣿⣿⣃⡄⠀⢄⠠⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡄⠀⠀⢀⢦⠀⡀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⢨⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣵⣦⣭⣙⠛⠿⣿⣦⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⡑⠂⠀⠤⠀⢹⠀⠀⢀⡠⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡗⠍⢻⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠿⠇⠐⠀⠀⢀⠉⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣟⡛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠀⠛⠐⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⢾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣟⢘⡃⢀⡀⢘⡃⣙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⡽⡇⠀⠀⠀⠀⢀⠀⠐⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣙⣼⣇⣘⡁⢉⠁⢀⠀⣉⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣻⢏⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣅⣉⡀⣉⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠼⣿⢿⣿⢀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠟⣿⣋⣚⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣽⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠅⠄⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠄
⡿⠋⠘⠛⣿⣿⡿⡿⣿⢿⣿⣿⠿⢿⠋⠉⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄⣬⠀⣥⢀⣤⠀⠄⢀⡄⠀⠀⢹⣁⠯⠀⠈⠀⠂⠀⠄⠀⠀⠀⠀⠐⠀⠠⠀
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣗⠷⣶⢶⡖⣶⢚⡒⢒⢒⡦⠀⠀⡀⢨⠁⠔⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠤⠀
⠀⢨⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢗⣶⢾⣷⣶⣷⠺⢶⠺⡞⠃⠀⠲⠄⠼⠀⠀⢀⠀⠀⢀⠀⠀⠀⠁⠀⠐⠀⠠⠀⠀
⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠿⠿⠿⠿⠏⠉⠉⠩⣩⡭⠉⠉⠉⠍⣩⠹⢷⠾⠷⢾⣿⡏⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡷⠌⢰⢰⠒⡖⢰⢲⠰⠆⡖⡆⡇⡗⠀⡰⡆⡖⠂⡖⡂⠀⡗⠂⡖⡇⡆⡀⡖⠂⠶⡆⡂⡦⡒⡆⠒⡆⠰⡁⡁⡶⡆⡖⡆⡖⡆⡖⡖⡖⠀⡗⡜⣷⢐⢔⢸⣿⣿⣄⠎⢛⠿⠟⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⣴⣦⠀⠂⢖⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣖⣒⠀⣶⣶⣶⣶⣾⣾⣿⣿⡇⠉⠠⣴⣤⣶⡤⢺⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⢾⡷⣥⡀⢈⠈⠑⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠃⠀⣿⣷⣿⣿⣿⣿⣿⣿⡇⣶⣶⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡛⠻⡷⢾⡷⣄⠀⡀⠀⠀⠀⠐⠐⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢌⠀⠉⠒⠿⡦⠑⠀⡀⠀⡁⢀⠀⠀⠁⠀⠀⡀⢀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⡝⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⢀⠀⠀⠀⣾⠋⠒⠀⡀⠀⡀⠀⠀⠀⠀⡊⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⣾⡛⣿⢚⡄⠀⡀⠈⠄⢠⡀⠠⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠈⠻⣿⣿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣶⣲⡲⠶⣶⣶⣶⣶⣶⣶⣲⣖⣲⡖⢲⣠⣿⡛⠻⢛⣿⣻⡷⢂⡄⢠⣄⣠⣭⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣯⣙⣟⠿⣿⣿⡿⢻⣵⣾⣿⣿⣟⣤⠀⠀⠙⠛⠿⣷⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⢿⡎
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣹⣶⣨⣿⣟⡻⠿⣿⣿⣿⣿⣇⡄⠀⢄⠠⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠠⠀⠀⠀⠀⠀⠀⢤⠀⠖⠒⡠⠠⡄⡀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣟⢨⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣵⣦⣭⣙⠛⠿⣿⣦⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⡐⠂⠰⠤⠀⠗⠀⠀⣀⣠⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣗⣹⣿⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠿⠇⠐⠀⠀⢀⠁⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣟⡛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠀⠛⠐⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣟⢘⡃⢀⡀⢘⡃⣛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⡽⡇⠀⠀⠀⠀⢀⠀⠐⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣛⣼⣇⣘⡁⢉⠁⢀⠀⣉⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣻⢏⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣽⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣅⣉⡀⣉⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠼⣿⢿⣿⢀⠅⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀
⣿⣿⠟⣿⣋⣛⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⠿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣽⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠄⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠄
⡿⠋⠘⠛⣿⣿⡿⡿⣿⢿⣿⣿⠿⢻⠋⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄⣬⠀⣥⢀⣤⠀⠄⢀⡄⠀⠀⢹⣁⠯⠀⠈⠀⠂⠀⠄⠀⠀⠀⠀⠐⠀⠠⠀
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣷⠷⣶⢶⡖⣶⢚⡒⢒⢒⡦⠀⠀⡀⢨⠁⠔⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠤⠀
⠀⢨⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢗⣶⢾⣷⣶⣷⠺⣶⠺⡞⠁⠀⠲⠄⠼⠀⠀⢀⠀⠀⢀⠀⠀⠀⠁⠀⠐⠀⠠⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠏⠉⠉⠩⣩⡭⠩⠉⠉⠭⣩⠱⠿⠿⠿⢿⣿⣶⠛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡷⡌⢸⢰⠒⡖⢲⢲⠰⠂⡖⡆⡗⡗⠀⡰⡆⡖⠂⡔⡂⠀⡏⠉⡖⡇⡆⡀⡔⠂⠶⡔⠒⡧⠒⡄⠒⡄⠰⡉⠁⡶⡆⡖⡆⡖⡆⡖⡖⡖⠀⡷⡜⣿⢐⣔⢸⣿⣿⡄⠿⠙⠻⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠁⠀⠈⠀⠁⠁⠀⠁⠈⠀⠈⠀⠁⠈⠀⠈⣠⣥⣤⡈⠀⢄⡨⠉⠈⠀⠈⠀⠈⠁⠁⠁⠁⠁⠈⠀⠀⣷⣶⣾⣷⣿⣷⣷⣷⣷⣷⣿⣶⢭⠀⣧⣴⣿⣾⣾⣾⣿⣿⡇⠈⠀⣳⣤⣦⣴⢾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⢾⡷⣥⡀⢈⠈⠑⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠈⣿⣿⣿⣿⣿⣿⣿⣿⡇⠗⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡷⢾⡷⣄⠀⡀⠀⠀⠀⠐⠐⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣽⣿⣯⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠀⠉⠒⠿⡦⠑⠀⡀⠀⡁⢀⠀⠀⠁⠀⠀⡀⢀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣍⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢈⠀⠀⡀⣾⠋⠒⠀⡀⠀⡀⠀⠀⠀⠀⡪⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠈⡻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⣾⡛⣿⢚⡄⠀⡀⠈⠄⢠⡀⠠⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣶⣶⡲⢶⣶⣶⣶⣶⣶⣶⣲⣖⣲⡖⢲⣠⣿⡛⠻⢟⣿⣻⡷⢂⡄⢠⣄⣠⣭⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣯⣙⣟⠿⣿⣿⡿⢻⣵⣾⣿⣿⣟⣤⠀⠀⠙⠛⠿⣷⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⢿⡃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣹⣶⣨⣿⣿⡻⠿⣿⣿⣿⣿⣇⡄⠀⢄⠠⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠠⠀⠀⠀⠀⠀⢀⠀⣤⠀⠀⡀⠤⡀⡀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⢿⣿⣨⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣵⣦⣭⣙⠛⠿⣿⣦⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡑⠄⠀⠄⠀⠇⡀⠀⣀⡑⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣽⡇⠜⢻⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠿⠇⠐⠀⠀⢀⠈⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣟⡛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠀⠛⠘⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣟⢘⡃⢀⡀⢘⡃⣛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⡿⡇⠀⠀⠀⠀⢀⠀⠐⠀
⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣛⣼⣇⣜⡁⣉⠁⢀⠀⣉⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣻⢏⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣉⡀⣉⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠼⣿⢿⣿⢀⠇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀
⣿⣿⠟⣿⣋⣚⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣽⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠍⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠄
⡿⠋⠘⢛⣿⣿⡿⣿⣿⢿⣿⣿⠿⢿⠋⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄⣬⠀⣥⢀⣤⠀⠄⢀⡄⠀⠀⢹⣁⠯⠀⠋⠀⠆⠀⠄⠀⠀⠀⠀⠐⠀⠠⠀
⠀⠀⠀⠈⠉⠈⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠷⣶⢶⡖⣶⢚⡒⢒⢒⡦⠀⠀⣀⢨⠁⠔⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠤⠀
⠀⢨⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢗⣶⢾⣷⣶⣷⠺⣶⠺⡞⠁⠀⠲⠄⠼⠀⠀⢀⠀⠀⢀⠀⠀⠀⠁⠀⠐⠀⠠⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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                    ䷩ 𝚕𝚒𝚗𝚎 3102

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/05/21/Video_The_Linux_Foundation_Cannot_be_Repaired_Anymore_It_Sold_O.shtml
    Gemini version at https://techrights.org/n/2024/05/21/Video_The_Linux_Foundation_Cannot_be_Repaired_Anymore_It_Sold_O.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ [Video] The 'Linux' Foundation Cannot be
Repaired Anymore (It Sold Out)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on May 21, 2024


Video_download_link | md5sum 98d742ded30e038b1ca62d024606ac1d
They_Do_Not_Care_About_Linux...
Creative Commons Attribution-No Derivative Works 4.0


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


THIS is a response to the detailed video about the Linux_Foundation, published
(with our_transcript_of_it) earlier this week in Australia.


I try not to be overly cynical or critical; I just try to expand on (or
correct) what the vlogger - a man called Brodie (and whom_I_sometimes_disagree
with - asserted. I mostly agree with his supposition that Linux Foundation (LF)
does not care about "desktop" GNU/Linux; the idea that it somehow would (given
more pressure) may be misguided because of the funding model and corporate
infiltration at all important levels, not just the_board.


We might need to accept that the Linux Foundation lost its way and we need to
create (or support) something else.


An associate of ours explained that he would consider it "not too cynical that
there is the possibility that the members of the_GPL-infringers_club are there
to ensure that as little as possible of the Foundation's money is spent on
actual Linux. It's about 2% - 3% depending on the year and, as Brodie and the
others point out, there is 0% spent on desktop Linux. In part because that
treads on the toes on Microsoft and its partners in the LF. But the overall
matter is one caused by NSA, FSB, GCHQ, etc who don't care what the fuck
happens to computers as long as they themselves continue to have an easy time
accessing via backdoors and bugdoors."


He further noted that "those backdoor and bugdoors are the_core_of_Microsoft
Windows_and_not_feasible_with_desktop_GNU/Linux." █




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

                    ䷩ 𝚕𝚒𝚗𝚎 3906

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Gemini Links 21/05/2024: Caesar II for MS-
DOS and Reinventing the Assertion Wheel⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on May 21, 2024


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Empty_Tables⦈_


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o § Games/Personal/Opinions⠀➾


                # ⚓ Retro_Replay:_Caesar_II_for_MS-DOS_(1995)⠀⇛


                       I remember getting hold of a shareware cd
                       containing Caesar II and playing the demo
                       endlessly. It's one of the few games out of the
                       90's that I still fire up on a regular basis, time
                       as an adult does seem to fly by faster and faster,
                       so regular in my case seems to indicate every 2
                       months or so.


                       I came across a local listing selling the complete
                       boxed copy of the game for only €5! So I jumped on
                       the opportunity to get a physical copy of the game
                       I've been adoring for over 29 years.


                # ⚓ Traditional_Latin_Mass_-_Propers_of_the_Mass:_May_21,_2024
                  -_Pentecost_Tuesday_(R)⠀⇛


                # ⚓ Hope⠀⇛


                       Hope... [static] ...nyone... [garbled]
                       ...resources... [distorted] ...unknown...
                       [incomplete] ...g for response... [nonsense]


          o § Technology and Free Software⠀➾


                # ⚓ Converting_from_teensy_to_arduino⠀⇛


                       For the past few days, I have been converting my
                       weather station firmware to use an Arduino
                       Atmega328P chip instead of a teensy Arm Cortex M7
                       chip. In my last post, I found that the teensy is
                       significantly overpowered for the job and it could
                       be contributing to why the temperature readings are
                       consistently so high.


                # ⚓ Reinventing_the_Assertion_Wheel_(go_test)⠀⇛


                       Like many developers, I like to reinvent the wheel.
                       Like many Go developers, I created my own assertion
                       package...


                       For a couple of months it lived as an internal
                       package, but prompted by a discussion on lobste.rs,
                       I finally decided to make it a dedicated package.


                # § Internet/Gemini⠀➾


                      # ⚓ Profectus_Now_On_Flathub!⠀⇛


                             P.S. Apparently apps that use subdomains
                             cannot be verified, because they require the
                             user own the main domain, with exceptions for
                             source code repo sites. My experience with
                             Flathub has been pretty infuriating, with
                             rude comments, extremely slow responses, and
                             unnecessarily restrictive rules to follow. My
                             biggest complaint, however, is the fact that
                             you cannot use subdomains, and that I wasn't
                             really told this before the app got merged.
                             In the future I will probably change the app
                             id to something under gitlab or github and
                             move the HTTP website over to there so that I
                             can verify the app, but I won't be doing this
                             for a while.


                      # ⚓ Music_Spotlight:_Pure_Hex_—_Spilling⠀⇛


                             As part of a double LP the bay area shoegaze
                             band Pure Hex released part 1 as their EP
                             "Spilling". This album came out on Friday,
                             May 17th, and I've not stopped listening to
                             it since.


                      # ⚓ Writing_around_writing⠀⇛


                             ❦ Finding it difficult to write is not an
                             uncommon occurrence it seems, on a platform
                             focussed around a textual medium. I've read
                             plenty of gemlogs, vowing to publish on their
                             capsule morefrequently or to take it less
                             seriously. For me sometimes the problem can
                             be starting to write, the classic writers
                             block. How do I want to write about this
                             topic; a short informative piece, a long
                             meandering essay, or is it time to have a go
                             at poetry (the reader will be glad to note I
                             do not make my poetry debut here). Sometimes
                             it's other ideas that are the problem, a new
                             and shiny topic can be a big distraction. For
                             better or worse there's no shortage of
                             inspiration in this vast space. If you are
                             reading this then this gemtext managed to
                             avoid the fate of those in my growing
                             collection of shelved drafts.


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





                    ䷩ 𝚕𝚒𝚗𝚎 4059

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Gemini Links 21/05/2024: Losing Fats and
Modern XMPP⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on May 21, 2024


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Beautiful_sand_dunes_in_Lithuania._Sun_and_shadows_play.
Horizontal_format⦈_


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o § Personal/Opinions⠀➾


                # ⚓ Intentional_weight_loss⠀⇛


                       Straying out of my wheelhouse into new topics is
                       always a li’l scary, especially controversial
                       topics. This one is a mess because it's both
                       politically contentious & also unsually personal &
                       oversharey for this capsule.


                # ⚓ 🔤SpellBinding:_GIYORVL_Wordo:_COALS⠀⇛


                # ⚓ new_magic_sprout⠀⇛


                       for the first time in a long while i've gotten an
                       inkling of a spiritual/magical ... thing. concept.
                       way. for a long time i've been Trying. and that
                       counts but it's not that inspiring organic feeling
                       where the right thing comes along. my Trying has
                       mostly consisted of mantra meditation and the
                       aramaic prayer as gratitude and a magical formula,
                       and i'm sure they'll keep serving me in various
                       situations.


          o § Technology and Free Software⠀➾


                # ⚓ First_past_the_post⠀⇛


                       You know how in number guessing games, where you
                       win if you guess closest, so if Alice guesses say
                       254 and I think it’s closer to a thousand, I’m
                       still better off guessing 255 because if it is
                       actually 626, that’s closer to 254 than it is to
                       1000 so I would’ve lost if I had said 1000?


                # ⚓ Modern_XMPP⠀⇛


                       I’m glad XMPP is getting some love. It’s a protocol
                       that has some advantages over Matrix and
                       ActivityPub and even over IRC. (even though adding
                       OMEMO to IRC might be possible, the way XMPP
                       federates is a li’l more flexible than how IRC
                       federates). Not that I’m ready to take all my
                       proverbial eggs out of the ActivityPub, email, or
                       IRC baskets just yet. Email is my doll my dear my
                       darling♥︎ but ultimately from a user perspective,
                       choosing a protocol is about the people on it. I
                       find a lot of awesome stuff on email, on
                       ActivityPub, on IRC and on XMPP so they’re all
                       great in terms of what’s on it. Philosophically is
                       where it doesn’t make sense to keep spending time
                       developing a protocol when there’s a better
                       protocol for the same thing and I don’t know yet
                       which of these four li’l creatures is the best one.
                       I suspect email is the best♥︎


                # § Internet/Gemini⠀➾


                      # ⚓ Inter⠀⇛


                             A new addition in the Sans collection: Inter.


                      # ⚓ First_of_All;_I'm_Sorry...⠀⇛


                             Have you ever heard of zenity? It's a widget
                             library for bash scripts. Not a GUI library,
                             mind you; a widget library. If you have a
                             script that needs user input you can make it
                             a little prettier by adding a dialogue box, a
                             calendar for date choice, a list, or similar.


                             There is no reactivity in this. The chosen
                             value is read when the user clicks "OK" and
                             the widget closes. Great UX for collecting
                             some user input!


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





                    ䷩ 𝚕𝚒𝚗𝚎 4188

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Gemini Links 21/05/2024: New Gemini Reader
and Gemini Games⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on May 21, 2024


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇1492_And_The_Unveiling_Epoch⦈_


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o § Personal/Opinions⠀➾


                # ⚓ I'm_not_dead_I_just_feel_that_way⠀⇛


                       With stuff like the hole in my bathroom ceiling
                       half the size of me, and several online
                       acquaintances having crises of everything, and just
                       general malaise at the entire universe (have you
                       seen the rest of the universe lately?) ...


                # ⚓ anthology_of_accumulated_short_notes⠀⇛


                       maybe some day I'll go back to spending more than 5
                       minutes writing about the same thing -.-


                # ⚓ Why_are_you_doing_this?_Why_are_you_here?⠀⇛


                       You could ask this question in the title regarding
                       any kind of online platform or forum etc. where you
                       are active, any association/club, any NGO, any
                       company, any project... why are you doing this? Why
                       are you here?


                       It is about the exchange, of thoughts, ideas,
                       feelings, of adventures/experiences, of insights.
                       Maybe also a bit about coping with trauma, ego,
                       other mental health issues etc.


                       All of this, can be said, is energy and so your
                       engagement on online platforms, associations etc.
                       is an exchange of energy. (So, ultimately, life is
                       an ongoing exchange of energies.)


                # ⚓ Acronymification⠀⇛


                       So one may observe a Power Organizing Module (POM)
                       and a European Service Module (ESM) among other
                       such TLA and may be left wondering what, exactly, a
                       ESM or a POM actually is and does—a battery?—a "I
                       can't believe it's not Socialism!" jobs
                       program?—other? Oh well, back to grazing from this
                       Nutrient Source Container (a bowl with a lot of
                       lentils, a roma tomato that got the worst of the
                       encounter, some olive oil, etc).


          o § Science⠀➾


                # ⚓ How_solarpunk_has_affected_me_so_far⠀⇛


                       Welcome to Futurism! I thought it would be nice to
                       start Futurism, my solarpunk-themed gemlog, with a
                       few thoughts about how the ideology of solarpunk
                       has influenced my life and my thinking so far.


          o § Technology and Free Software⠀➾


                # ⚓ so_just_a_quick_update⠀⇛


                       I had entirely forgotten why online games are so
                       great honestly. this is what AAA developers don't
                       get. just give us some guns so we can run around
                       and shoot each other; then, more importantly, a
                       chat where all the actual fun happens. anyway yeah,
                       where have the last 2 hours gone.


                # ⚓ How_to_Clean_a_Flashlight_Lens⠀⇛


                       Here are the steps I follow to clean the glass
                       lenses on my flashlights.


                # § Internet/Gemini⠀➾


                      # ⚓ Naming_the_gemini_reader⠀⇛


                             I want this project to have a name. It helps
                             me keep track of it in my head. Keeping with
                             the gemini protocol tradition of naming stuff
                             after Gemini mission things or space things,
                             I'd like it to be related to the Gemini
                             missions. Something about the launch vehicle
                             (because it gets you to Gemini) or command/
                             control of the spacecraft.


                      # ⚓ More_AuraGem_Search_Updates:_Detection_of_Duplicates
                        and_Mirrors⠀⇛


                             AuraGem search is now able to detect
                             duplicate documents across all of the
                             supported smallnet protocols (scroll, gemini,
                             nex, and spartan). The search engine has
                             already been storing hashes of documents from
                             the very beginning, since 2021, so detecting
                             duplicates is as simple as comparing hashes.


                      # ⚓ It's_nice_to_be_noticed⠀⇛


                             Just today I stumbled upon a post on
                             tfurrows' zaibatsu phlog[1] which was
                             entirely about me being back on the gopher.


                             We don't do our phlogs for them audiences, if
                             we did, we would be on TikTok doing viral
                             videos, but it is really nice to be noticed!


                      # ⚓ Mental_Gymnastics:_Hacking_Up_Simple_Gemini_Games⠀⇛


                             Surprize! 'Simple' things turn out to be much
                             more complicated than they should be.


                             This is my second go around: first time was
                             spellbinding, which I implemented it as a
                             specialized CGI program with a bunch of
                             adjacent programs and scripts. While that
                             worked, it required keeping track of a lot of
                             details, scripts and cron jobs, and is so
                             specialized that it's entirely useless for
                             anything else.


                             So this time around I was going to be smart.
                             I separated the game logic, the CGI script,
                             from the database that stores the game state.
                             Ideally the database should know nothing
                             about the game itself it just serves data for
                             each session.


                      # ⚓ AuraGem_Search_Crawls_Spartan,_Profectus_Beta_1.2.1,
                        AuraGem_Server_Update⠀⇛


                             AuraGem Search now crawls the spartan
                             protocol. An interface to search just
                             spartanspace will be added later.


                # § Programming⠀➾


                      # ⚓ Eyeing_awk⠀⇛


                             I use Linux on my home computers as well as
                             at my job. I've learned how to use a lot of
                             tools along the way, but there are many
                             tricks and programs that I still don't know
                             much about. One of those programs is awk.


                             Most of my computing activities take place in
                             the terminal, and as such, I work with text
                             almost all the time. When I write scripts,
                             the bulk of the commands simply print, parse,
                             perform actions on, and prettify text. I
                             first learned how to work with text in Linux
                             using grep and sed, and to this day, those
                             are the tools I reach for first when I need
                             to process textual data.


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





                    ䷩ 𝚕𝚒𝚗𝚎 4414

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 21/05/2024: "Hating Apple Goes
Mainstream", Lots of Coverage About Julian Assange
Ruling⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on May 21, 2024


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o ⚓ France24 ☛ Japanese_town_erects_barrier_to_block_Mount_Fuji_view
            from_tourists⠀⇛


                 A Japanese town mounted a large mesh barrier at a popular
                 viewing spot for Mount Fuji on Tuesday, in an attempt to
                 deter photo-taking by an ever-growing number of tourists.


          o ⚓ Lykolux ☛ Onepage_website_architecture⠀⇛


                 A simple and small entire website can be seen as one
                 structured document. Such website can be reduced to one
                 web document, i.e. one page!


          o ⚓ Lykolux ☛ A_nav_menu_as_webpage⠀⇛


                 I’ve had an idea for a menu navigation in the back of my
                 mind for days.


                 A menu that would be an entire HTML document: a site map
                 for the user. This menu is a summary of the site. It
                 allows the content to be viewed quickly.


          o ⚓ Michael Bburkhardt ☛ Go_Away⠀⇛


                 Occasionally, the would-be salesman attempts to counter.
                 Time for the heater: “Have a great day! Thanks again!” I
                 smile and wave before turning to go back inside.


          o ⚓ James G ☛ Blog_of_the_Day⠀⇛


                 A few months ago, I had the idea to start a website that
                 chooses one blog a day to be featured as the "blog of the
                 day." The site would broadcast an RSS feed of the blog of
                 the day, offering a new way for you to passively find new
                 websites. I was excited by the serendipity this would
                 offer: you may find the featured blog in your RSS feed
                 resonates with you and becomes your next favourite blog.
                 This project was designed to work at a slow pace: you
                 should never feel overwhelmed with too many things to
                 explore.


          o ⚓ Barry Sampson ☛ Barry_Sampson_|_Blogging_Fatigue⠀⇛


                 When I started this challenge, I set out to write a post
                 every day for 31 days - and at the moment I'm still
                 planning to do that - but it's getting harder. It's not a
                 lack of things to wrote about that's getting in the way.
                 I've got quite few ideas for thing to write about, but
                 they'll be long posts and they need time to plan and
                 write.


          o ⚓ Lykolux ☛ URLs_for_blog_posts⠀⇛


                 Let’s imagine you have a blog. You are posting on this
                 saturday 17th mai 2024 “State of the HTML 2024”.


                 How the URL can be?


          o ⚓ Johnny Decimal ☛ Which_apps_do_I_use?⠀⇛


                 Peter asks on Discord, what apps do you use to organise
                 yourself and your website and your business life?


                 I’m in-between tools at the moment; part of the
                 ‘organisational bankruptcy’. But I’ll give a run-down of
                 what I’ve used in the past, and where I’m leaning for the
                 future.


          o ⚓ Rach Smith ☛ Some_observations_after_journaling_every_day_this
            year⠀⇛


                 My main goal for this year was to journal something about
                 my day, every day. Some observations: [...]


          o ⚓ Stefan Zweifel ☛ Migrating_from_Laravel_to_Eleventy⠀⇛


                 Instead of finishing the many blog post drafts I have in
                 iA Writer, I've spent the last couple of days/weeks
                 replacing the tech stack that runs this website.


                 As of May 12th 2024, stefanzweifel.dev now runs on
                 Eleventy and is hosted on Cloudflare Pages.


          o § Standards/Consortia⠀➾


                # ⚓ [Old] Tim Bray ☛ Life_Is_Complicated⠀⇛


                       Having said that, I still think OOXML is totally
                       bogus; ECMA shouldn’t have gone near it and neither
                       should ISO. The world does not need two ways to say
                       “This paragraph is in 12-point Arial with 1.2em
                       leading and ragged-right justification”. As I
                       argued in 2005, if you want to capture MS-Office-
                       specific semantics (not a bad thing in principle)
                       the right way to do it is a namespaced layer on top
                       of ODF.


                # ⚓ [Old] Groklaw ☛ Groklaw_-_Deadline_Looms_to_Express
                  Concerns_about_ECMA_376_Office_Open_XML⠀⇛


                       Judging from my email and the project input, some
                       are worried about Ecma 376 Office Open XML's
                       complexity. It is over 6,000 pages long, excluding
                       supporting material. Is a fast track appropriate
                       for a document of such length? Why, others ask, do
                       we need a duplicative standard, when we already
                       have ISO/IEC 26300, the Open Document Format? If
                       there is a need to address Microsoft legacy
                       documents, why not replace Ecma 376 by a
                       specification that extends ISO 26300 with whatever
                       new tags are needed to cover the additional
                       functionality? Is that something that could be
                       done?


                       First, Tim Bray, co-lead developer of the W3C XML
                       1.0 recommendation, has advocated the same
                       solution, Microsoft developers have reportedly told
                       the Commonwealth of Massachusetts it would be
                       "trivial" for Microsoft to implement OpenDocument
                       in Microsoft Office, and Microsoft's Alan Yates,
                       General Manager, Microsoft Information Worker
                       Business Strategy, predicted that ODF and its
                       competing standard would in fact one day be
                       harmonized:


                       "I would say, in the future, some time, you know,
                       at some point, there will be convergence.
                       Convergence does happen over a period of time. Or
                       there will be incorporation, there will be
                       subsetting, supersetting. You know, the wireless
                       standard, the A version merged into the B version,
                       merged into the G version over a period of time to
                       give better performance and functionality over a
                       period of time. ... So, good news, I think, on that
                       front is that this problem will be solved in time."


          o § Science⠀➾


                # ⚓ Science Alert ☛ Physicists_Finally_Confirm_Einstein's
                  Stunning_Prediction_About_Black_Holes⠀⇛


                       Beyond the point of no return.


          o § Education⠀➾


                # ⚓ Baldur Bjarnason ☛ The_deskilling_of_web_dev_is_harming_the
                  product_but,_more_importantly,_it's_damaging_our_health_–
                  this_is_why_burnout_happens_– Baldur_Bjarnason⠀⇛


                       Even before the web developer job market became as
                       dire as it is today, I was regularly seeing
                       developers burn out and leave the industry. Some
                       left for good; some only temporarily. Many have
                       outright destroyed their health through anxiety and
                       burnout.


                       The only other industry I’m familiar with that has
                       the same levels of physically-demanding anxiety and
                       worker churn is trade publishing – and that’s an
                       industry famous for literally paying below-
                       subsistence wages for the cities they’re based in.


                       “Maybe I should try to find a job that doesn’t
                       involve web development?"


                # ⚓ Tracy Durnell ☛ My_current_work-life_“rules”⠀⇛


                       A lot of entrepreneurs go in for hustle culture,
                       seemingly working 60-80-hour weeks, but I’ve been
                       trying to create a sustainable practice. To help
                       myself take time to rest and give myself a break
                       from work, these are the guidelines I’ve developed
                       for myself over the past year and a half.


                # ⚓ Peter Norvig ☛ Teach_Yourself_Programming_in_Ten_Years⠀⇛


                       Malcolm Gladwell has popularized the idea, although
                       he concentrates on 10,000 hours, not 10 years.
                       Henri Cartier-Bresson (1908-2004) had another
                       metric: "Your first 10,000 photographs are your
                       worst." (He didn't anticipate that with digital
                       cameras, some people can reach that mark in a
                       week.) True expertise may take a lifetime: Samuel
                       Johnson (1709-1784) said "Excellence in any
                       department can be attained only by the labor of a
                       lifetime; it is not to be purchased at a lesser
                       price." And Chaucer (1340-1400) complained "the lyf
                       so short, the craft so long to lerne." Hippocrates
                       (c. 400BC) is known for the excerpt "ars longa,
                       vita brevis", which is part of the longer quotation
                       "Ars longa, vita brevis, occasio praeceps,
                       experimentum periculosum, iudicium difficile",
                       which in English renders as "Life is short, [the]
                       craft long, opportunity fleeting, experiment
                       treacherous, judgment difficult." Of course, no
                       single number can be the final answer: it doesn't
                       seem reasonable to assume that all skills (e.g.,
                       programming, chess playing, checkers playing, and
                       music playing) could all require exactly the same
                       amount of time to master, nor that all people will
                       take exactly the same amount of time. As Prof. K.
                       Anders Ericsson puts it, "In most domains it's
                       remarkable how much time even the most talented
                       individuals need in order to reach the highest
                       levels of performance. The 10,000 hour number just
                       gives you a sense that we're talking years of 10 to
                       20 hours a week which those who some people would
                       argue are the most innately talented individuals
                       still need to get to the highest level."


                # ⚓ Terence Eden ☛ It_isn’t_who_you_know_–_it’s_who_knows_you⠀⇛


                       I realise that asking lottery-winners for advice on
                       how to pick your numbers is not a reliable method
                       for becoming a millionaire - but I'd like to
                       explain how I network and where it has got me.


          o § Hardware⠀➾


                # ⚓ The Drone Girl ☛ Chevron_Technology_Ventures_invests_in
                  SwissDrones_Series_B⠀⇛


                       You might know Chevron as the company that enables
                       you to put gas in your cars. But right now, Chevron
                       has its eyes on drones — uncrewed helicopters to be
                       exact. Chevron Technology Ventures was one of a
                       handful of investors to toss over more money this
                       month to SwissDrones. SwissDrones primarily bills
                       itself as an aerial intelligence company.


                # ⚓ [Repeat] Tedium ☛ How_Optical_Mice_Came_To_Dominate_Input
                  Devices⠀⇛


                       Today in Tedium: Here’s something that you, as a
                       computer user, likely have not had to do in a long
                       time: Open up the mouse, and clean out the grime
                       that had built up on the rollers over the last
                       couple of months, revealing that no, your desk is
                       not as clean as you believe it to be. No, it’s not
                       because your desk got cleaner. Rather, it’s because
                       we figured out that optical mice were significantly
                       better designs, because they could work in many
                       more settings, in fact, without even requiring a
                       mouse pad. So, what was the aha moment where the
                       ball mouse lost out to the optical one? And how did
                       it happen? Today’s Tedium ponders a mouse-design
                       murder. — Ernie @ Tedium


                # ⚓ Jason Burk ☛ Buying_Weird_Old_Digital_Cameras⠀⇛


                       Regarding technology, you generally want the newest
                       possible version of a given item, as technology
                       changes rapidly and improves dramatically along
                       with those changes. For most people, this is
                       typically true with digital cameras as well. This
                       is why I would never recommend these to the average
                       person looking for a digital camera. On to the
                       oddities!


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ US News And World Report ☛ 2024-05-17_[Older]_Canada_Asks
                  Chemical_Plants_to_Check_Pollution_After_Leaks_Hit_Indigenous
                  Community⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-05-16_[Older]_'No_evidence'_of_H5N1
                  bird_flu_spreading_among_people⠀⇛


                # ⚓ CBC ☛ 2024-05-15_[Older]_Next_generation_of_Prince_Edward
                  Islanders_could_be_hit_with_tobacco_ban_—_no_ifs,_ands_or
                  butts⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-05-16_[Older]_Spanish_tourism
                  industry_under_pressure_amid_record_drought⠀⇛


                # ⚓ CBC ☛ 2024-05-13_[Older]_Water_in_N.W.T.'s_Great_Slave_Lake
                  is_now_so_low,_some_houseboats_won't_float⠀⇛


                # ⚓ CBC ☛ 2024-05-15_[Older]_Buying_and_selling_water_is_a
                  reality_in_Alberta_—_sometimes_for_big_money⠀⇛


                # ⚓ CBC ☛ 2024-05-12_[Older]_Nurses_in_special_911_response
                  program_help_take_pressure_off_ambulances_and_hospital_ERs⠀⇛


                # ⚓ Video ☛ Confirmed_horrifying_scandal⠀⇛


                # ⚓ The Telegraph UK ☛ Britain’s_‘day_of_shame’_as_full_scale
                  of_infected_blood_scandal_revealed⠀⇛


                # ⚓ Russell Coker ☛ Respect_and_Children⠀⇛


                       I attended the school Yarra Valley Grammer (then
                       Yarra Valley Anglican School which I will refer to
                       as “YV”) and completed year 12 in 1990. The school
                       is currently in the news for a spreadsheet some
                       boys made rating girls where “unrapeable” was one
                       of the ratings. The school’s PR team are now making
                       claims like “Respect for each other is in the DNA
                       of this school”. I’d like to know when this DNA
                       change allegedly occurred because respect
                       definitely wasn’t in the school DNA in 1990! Before
                       I go any further I have to note that if the school
                       threatens legal action against me for this post it
                       will be clear evidence that they don’t believe in
                       respect. The actions of that school have wronged
                       me, several of my friends, many people who aren’t
                       friends but who I wish they hadn’t had to suffer
                       and I hadn’t had to witness it, and presumably
                       countless others that I didn’t witness. If they
                       have any decency they would not consider legal
                       action but I have learned that as an institution
                       they have no decency so I have to note that they
                       should read the Wikipedia page about the Streisand
                       Effect [1] and keep it in mind before deciding on a
                       course of action.


                       I think it is possible to create a school where
                       most kids enjoy being there and enjoy learning,
                       where hardly any students find it a negative
                       experience and almost no-one finds it traumatic.
                       But it is not possible to do that with the way
                       schools tend to be run.


                       When I was at high school there was a general
                       culture that minor sex crimes committed by boys
                       against boys weren’t a problem, this probably
                       applied to all high schools. Things like ripping a
                       boy’s pants off (known as “dakking”) were
                       considered a big joke. If you accept that ripping
                       the pants off an unwilling boy is a good thing (as
                       was the case when I was at school) then that leads
                       to thinking that describing girls as “unrapeable”
                       is acceptable. The Wikipedia page for “Pantsing”
                       [2] has a reference for this issue being raised as
                       a serious problem by the British Secretary of State
                       for Education and Skills Alan Johnson in 2007. So
                       this has continued to be a widespread problem
                       around the world. Has YV become better than other
                       schools in dealing with it or is Dakking and
                       Wedgies as well accepted now as it was when I
                       attended? There is talk about schools preparing
                       kids for the workforce, but grabbing someone’s
                       underpants without consent will result in instant
                       dismissal from almost all employment. There should
                       be more tolerance for making mistakes at school
                       than at work, but they shouldn’t tolerate what
                       would be serious crimes in other contexts. For work
                       environments there have been significant changes to
                       what is accepted, so it doesn’t seem unreasonable
                       to expect that schools can have a similar change in
                       culture.


                # ⚓ CBC ☛ 2024-05-16_[Older]_Ontario_warns_Toronto_to_drop_drug
                  decriminalization_request⠀⇛


                # ⚓ CBC ☛ 2024-05-14_[Older]_Frito_Lay_Canada_recalls_2_of_its
                  most_popular_snacks_for_possible_salmonella_contamination⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-05-17_[Older]_Germany:_New_online
                  atlas_compares_1,700_hospitals'_services⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-05-14_[Older]_Fentanyl_smuggled_into
                  US_at_highest_rates_ever⠀⇛


                # ⚓ CBC ☛ 2024-05-17_[Older]_Manitoba_post-secondary_schools
                  should_track_student_suicides,_experts_say,_but_most_don't⠀⇛


                # ⚓ CBC ☛ 2024-05-17_[Older]_Ontario_child's_death_from_measles
                  is_1st_in_province_since_1989,_public_health_says⠀⇛


                # ⚓ The_Washington_Post_flubs_it_with_an_advertorial_on_IV
                  drips⠀⇛


                       Last week, I wrote about a poorly framed article in
                       the New York Times by Apoorva Mandavilli about
                       people who thought they were vaccine-injured,
                       pointing out how it seemed to downplay vaccine
                       benefits versus tiny risks while putting front-and-
                       center an unfortunate woman who seems to believe
                       that her health problems were caused by a
                       “contaminated batch” of the Johnson & Johnson
                       COVID-19 vaccine and has been drifting into
                       quackery while making rookie mistakes discussing
                       the vaccine safety monitoring system in the US. At
                       the time, there was another, even worse, article
                       about health published in The Washington Post on
                       the same weekend, but I left it aside because
                       discussing COVID-19 vaccines seemed more important
                       than discussing IV drips of minerals and vitamins.
                       Basically, in a way, The Washington Post flubbed
                       science even wore than the NYT did.


                # ⚓ Futurism ☛ Neuralink_Jamming_Wires_Deeper_Into_Second
                  Patient's_Brain⠀⇛


                       While it's good that things haven't gone worse for
                       Arbaugh, it's clear now that Neuralink is applying
                       Silicon Valley's "move fast and break things"
                       adage, coined by Musk's nemesis Mark Zuckerberg, to
                       its approach to human test subjects.


                # ⚓ The Register UK ☛ FDA_gives_Neuralink_another_shot_at_brain
                  chip_–_report⠀⇛


                       The N1 chip itself uses hair-thin wires inserted
                       into the brain, which can come loose – and that's
                       apparently what happened to the upstart's first
                       human patient, Noland Arbaugh.


                       It's said 85 percent of the wires connecting the
                       prototype N1 to Arbaugh's brain came loose, leaving
                       just nine or ten of the original 64, greatly
                       reducing the capabilities of the chip. Neuralink
                       did not disclose this in its initial report about
                       the loose wires, only saying that some had come
                       out.


                # ⚓ Futurism ☛ Man_Drinks_Poison_Oak_Smoothie_in_Bid_to_Develop
                  Resistance⠀⇛


                       At the end of his experiment, Horwitz says he could
                       rub a poison oak leaf on his skin and not
                       experience any rash breakouts.


                       "My poison-oak salad days are over, but I do intend
                       to nibble a few leaves here and there when hiking
                       around the Bay Area in an effort to maintain my
                       resistance on a permanent basis," he wrote.


                       Horwitz got his idea from reading about how
                       California's indigenous tribes would make tea from
                       poison oak roots and eat the leaves to develop
                       immunity. He also read online forums where outdoors
                       enthusiasts discussed noshing on poison ivy or
                       poison oak helped them develop a resistance, though
                       much of literature he consulted warned not to eat
                       the plants.


                # ⚓ Science Alert ☛ This_New_Clue_May_Signal_Alzheimer's_Before
                  You_Have_Symptoms⠀⇛


                       A test to show the disease approaching?


                # ⚓ Science Alert ☛ Testosterone_Supplements_Can_Be_Dangerous.
                  Here's_Why_Some_Take_The_Risk.⠀⇛


                       A shocking revelation.


                # ⚓ Federal News Network ☛ EPA_warns_of_increasing_cyberattacks
                  on_water_systems,_urges_utilities_to_take_immediate_action⠀⇛


                       The Environmental Protection Agency warns that
                       cyberattacks against water utilities around the
                       U.S. are becoming more frequent and more severe.
                       The agency on Monday issued an alert urging water
                       systems to take immediate actions to protect the
                       nation's drinking water. The EPA said about 70% of
                       utilities inspected by federal officials over the
                       past year violated standards meant to protect
                       cyberattacks. They cited basic errors such as
                       failing to change default passwords or cut off
                       system access to former employees. The EPA says
                       nations including Russia, China and Iran are
                       actively seeking the ability to disable critical
                       U.S. infrastructure.


          o § Proprietary/Artificial Intelligence (AI)⠀➾


                # ⚓ US News And World Report ☛ 2024-05-15_[Older]_Now_Armed
                  With_AI,_America's_Adversaries_Will_Try_to_Influence
                  Election,_Security_Officials_Warn⠀⇛


                # ⚓ Screen Rant ☛ Xbox_Is_Making_A_Huge_Mistake_Putting_Call_Of
                  Duty_On_Game_Pass⠀⇛


                       Call of Duty is expected to come to Xbox Game Pass,
                       but this choice might not be the best decision for
                       Xbox. It's not guaranteed that subscriptions to
                       Game Pass will increase, and this move could end up
                       hurting Xbox financially at a time when console
                       exclusives are already struggling with sales.
                       Additionally, studio closures and layoffs are being
                       seen throughout the game industry, meaning that
                       this could be a dangerous time to make this kind of
                       financial move.


                # ⚓ Mike Rockwell ☛ Hating_Apple_Goes_Mainstream⠀⇛


                       I would say the downfall started more than five
                       years ago. I would look at the 2015 introduction of
                       the butterfly keyboard as the beginning of this
                       era. An era where they would continue to sell these
                       awful keyboards for around five years, failing to
                       resolve the issue through at least two iterations
                       of the product before finally moving back to
                       scissor switches.


                # ⚓ 37signals LLC ☛ Hating_Apple_goes_mainstream⠀⇛


                       That's because Apple has lost its presumption of
                       good faith over the last five years with an ever-
                       larger group of people, and now we've reached a
                       tipping point. A year ago, I'm sure this awful ad
                       would have gotten push back, but I'm also sure we'd
                       heard more "it's not that big of a deal" and "what
                       Apple really meant to say was..." from the stalwart
                       Apple apologists the company has been able to count
                       on for decades. But it's awfully quiet on the fan-
                       boy front.


                # ⚓ Cory Dransfeldt ☛ AI-free_products⠀⇛


                       You build the tool, keep it as simple as possible
                       and it does what you set out for it to do. Your
                       customers see the value and use it accordingly.


                # ⚓ Reason ☛ AI_Regulations_Are_Crony_Capitalism_in_Action⠀⇛


                       Because of ChatGPT's seemingly vast powers, Altman
                       called for government regulation to "mitigate the
                       risks of increasingly powerful AI systems" and
                       recommended that U.S. or global leaders form an
                       agency that would license AI systems and have the
                       authority to "take that license away and ensure
                       compliance with safety standards." Major AI players
                       around the world quickly roared approval of
                       Altman's "I want to be regulated" clarion call.


                       Welcome to the brave new world of AI and cozy crony
                       capitalism, where industry players, interest
                       groups, and government agents meet continuously to
                       monitor and manage investor-owned firms.


                # ⚓ Derek Kędziora ☛ New_tech_that’s_actually_interesting⠀⇛


                       For now AI is overhyped FOMO. Apple is the new
                       Microsoft, which means it’s good enough and kind of
                       works but not antthing to get excited about.


                       But that doesn’t mean there aren’t interesting
                       things going on in the tech world.


                # ⚓ Tech Central (South Africa) ☛ Workspace_vs_Office_-_Google
                  goes_for_Microsoft's_jugular⠀⇛


                       Google is betting Microsoft’s very public
                       cybersecurity failures — along with deep discounts
                       — will persuade corporate and government customers
                       to use the search giant’s productivity software
                       rather than Office.


          o § Security⠀➾


                # § Integrity/Availability/Authenticity⠀➾


                      # ⚓ Deutsche Welle ☛ 2024-05-13_[Older]_Germany:
                        Cybercrime_by_foreign_actors_rose_by_28%_in_2023⠀⇛


                      # ⚓ CBC ☛ 2024-05-14_[Older]_RBC_customer's_cheque_was
                        cashed_twice._He_says_his_bank_shouldn't_have_let_it
                        happen⠀⇛


                      # ⚓ CBC ☛ 2024-05-17_[Older]_Calgary_lawyer_resigns_from
                        firm_after_sending_'disturbing'_and_'misogynistic'
                        email⠀⇛


                # § Privacy/Surveillance⠀➾


                      # ⚓ Deutsche Welle ☛ 2024-05-17_[Older]_AI_Lexicon:_F_is
                        for_facial_recognition [Ed: Well, nothing to do with
                        "AI"; This kind of media needs to stop pumping this
                        hype-driven Ponzi scheme around valuation and fictional
                        prospects]⠀⇛


                      # ⚓ EFF ☛ Shots_Fired:_Congressional_Letter_Questions_DHS
                        Funding_of_ShotSpotter⠀⇛


                             The seven page letter, from Senators Ed
                             Markey, Ron Wyden and Elizabeth Warren, and
                             Representative Ayanna Pressley, begins by
                             questioning the “accuracy and effectiveness”
                             of ShotSpotter, and then outlines some of the
                             latest evidence of its abysmal performance,
                             including multiple studies showing false
                             positive rates—i.e. incorrectly classifying
                             non-gunshot sounds as gunshots—at 70% or
                             higher. In addition to its ineffectiveness,
                             the Congress members voiced their serious
                             concerns regarding ShotSpotter’s contribution
                             to discrimination, civil rights violations,
                             and poor policing practices due to the
                             installation of most ShotSpotter sensors in
                             overwhelmingly “Black, Brown and Latin[e]
                             communities” at the request of local law
                             enforcement. Together, the inefficacy of the
                             technology and the placements can result in
                             the deployment of police to what they expect
                             to be a dangerous situation with guns drawn,
                             increasing the chances of all-too-common
                             police violence against civilians in the
                             area.


                             In light of the grave concerns raised by the
                             use of ShotSpotter, the lawmakers are
                             demanding that DHS investigate its funding,
                             and whether it’s an appropriate use of
                             taxpayer dollars. We agree: DHS should
                             investigate, and should end its program of
                             offering grants to local law enforcement
                             agencies to contract with SoundThinking. 


                             The letter can be read in its entirety here.


                      # ⚓ EFF ☛ Georgia_Prosecutors_Stoke_Fears_over_Use_of
                        Encrypted_Messengers_and_Tor⠀⇛


                             “Indeed, communication among the Defend the
                             Atlanta Forest members is often cloaked in
                             secrecy using sophisticated technology aimed
                             at preventing law enforcement from viewing
                             their communication and preventing recovery
                             of the information” the indictment reads.
                             “Members often use the dark web via Tor, use
                             end-to-end encrypted messaging app Signal or
                             Telegram.”


                             The secure messaging app Signal is used by
                             tens of millions of people, and has hundreds
                             of millions of global downloads. In 2021,
                             users moved to the nonprofit-run private
                             messenger en masse as concerns were raised
                             about the data-hungry business models of big
                             tech. In January of that year, former world’s
                             richest man Elon Musk tweeted simply “Use
                             Signal.” And world-famous NSA whistle-blower
                             Edward Snowden tweeted in 2016 what in
                             information security circles would become a
                             meme and truism: “Use Tor. Use Signal.”


                # § Confidentiality⠀➾


                      # ⚓ 404 Media ☛ Nonconsensual_AI_Porn_Maker_Accidentally
                        Leaks_His_Customers'_Emails⠀⇛


                             A popular Patreon account that created
                             nonconsensual AI-generated sexual images of
                             celebrities for his paying subscribers has
                             leaked a list of his clients’ emails to other
                             clients and to 404 Media.


          o § Defence/Aggression⠀➾


                # ⚓ Air Force Times ☛ Bud_Anderson,_America’s_last_World_War_II
                  ‘triple_ace,’_dies_at_102⠀⇛


                       Over the course of the war, the Mustang was
                       credited with downing nearly 600 enemy planes —
                       including a record 17 of Nazi Germany’s
                       Messerschmitt Me-262 jets — and destroying more
                       than 100 aircraft on the ground. It also produced a
                       record 42 aces, including Anderson, who at the end
                       of the war had 16.25 victories to his credit.
                       (Pilots are awarded a fraction of a “kill” if
                       multiple airmen contributed to a plane’s downfall.)


                # ⚓ The Register UK ☛ DoJ_and_ByteDance_ask_court_to_speed_up
                  ruling_on_TikTok_ban⠀⇛


                       The Act defines ByteDance and TikTok as foreign
                       adversary-controlled applications and gives US
                       presidents the power to name more. The concern
                       among US lawmakers is that the company is beholden
                       to requests from Beijing whether that be to snoop
                       on Americans, alter algorithms to push propoganda
                       or otherwise.


                # ⚓ Digital Music News ☛ TikTok,_U.S._Gov't_Jointly_Move_to
                  Fast-Track_Ban_Lawsuit⠀⇛


                       Ahead of a quick-approaching deadline for ByteDance
                       to divest from or shut down TikTok in the U.S., a
                       joint motion has been filed to fast-track the
                       appropriate legal challenges.


                # ⚓ YLE ☛ Finland_and_UK_sign_strategic_partnership_deal⠀⇛


                       According to the Finnish Foreign Ministry, the
                       strategic partnership between Finland and the UK
                       will deepen cooperation in many areas, including
                       global and multilateral issues, such as the
                       economy, migration, security and defence.


                # ⚓ Deutsche Welle ☛ Israel-Hamas_war:_Biden_says_Gaza
                  offensive_'not_genocide'⠀⇛


                       "The simultaneous application for arrest warrants
                       against the Hamas leaders on the one hand and the
                       two Israeli officials on the other has given the
                       false impression of equivalence," a Foreign
                       Ministry spokesman said in a statement.


                # ⚓ VOA News ☛ Rwanda_deploying_another_2500_soldiers_to_help
                  Mozambique_fight_Cabo_Delgado_insurgency⠀⇛


                       Rwanda is deploying an additional 2,500 soldiers to
                       help Mozambique fight resurgent attacks by Islamic
                       State insurgents in the oil-rich Cabo Delgado
                       province. Attacks have been on the rise in the area
                       as a force known as SAMIM, deployed by the Southern
                       African Development Community, prepares to
                       withdraw.


                # ⚓ Federal News Network ☛ Navy_grapples_with_at-sea_shortages
                  as_recruiting_lags⠀⇛


                       Although retention remains strong, the Navy has
                       thousands of vacancies in its afloat community
                       because of the recruiting slowdown.


                # ⚓ Deutsche Welle ☛ 2024-05-13_[Older]_Congo:_Can_SADC_troops
                  defeat_M23_rebels?⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-05-13_[Older]_Grave_of_German
                  politician_Wolfgang_Schäuble_desecrated⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-05-17_[Older]_US:_30_years_for_man
                  who_attacked_Nancy_Pelosi's_husband⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-05-13_[Older]_India:_How_a_year_of
                  ethnic_violence_changed_Manipur⠀⇛


                # ⚓ US News And World Report ☛ 2024-05-14_[Older]_Missouri_Man
                  Pleads_Guilty_to_Crashing_Truck_Into_White_House_Security
                  Barriers⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-05-14_[Older]_Iran_hopes_to_boost
                  security_with_Afghan_border_wall⠀⇛


                # ⚓ US News And World Report ☛ 2024-05-17_[Older]_Violence_in
                  New_Caledonia_Subsides_Slightly_as_France_Sends
                  Reinforcements_for_Security [Ed: China's TikTok inflaming
                  conflict]⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-05-15_[Older]_New_Caledonia:_France
                  declares_state_of_emergency_amid_riots⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-05-13_[Older]_Catalonia:_Separatists
                  lose_majority_as_Socialists_make_gains [Ed: Violence incited
                  by TikTok]⠀⇛


                # ⚓ The Local SE ☛ 2024-05-17_[Older]_Sweden_boosts_security
                  for_Israeli_interests_after_gunfire_near_embassy [Ed: The
                  country is overrun by Muslims, 20% by some estimates (many
                  undocumented)]⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-05-17_[Older]_Robert_Fico_shooting
                  highlights_Slovakia's_deep_polarization⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-05-18_[Older]_Slovakia:_'We_have_to
                  stop_this_hatred'⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-05-17_[Older]_Slovakia:_PM_Fico_in
                  'serious'_state_after_another_operation⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-05-16_[Older]_Slovakia:_PM_Fico_able
                  to_speak,_'lone_wolf'_suspect_charged⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-05-15_[Older]_Slovakia:_PM_Fico_shot
                  in_'an_attack_on_democracy'⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-05-15_[Older]_Slovakia:_PM_Fico_shot,
                  in_'life_threatening_condition'⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-05-16_[Older]_Netherlands:_New
                  coalition_pitches_'strictest'_asylum_policy⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-05-16_[Older]_Sudan_facing_'inferno
                  of_brutal_violence':_UN⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-05-16_[Older]_Switzerland:_Police
                  arrest_knife_attack_suspect⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-05-15_[Older]_Switzerland:_'Several'
                  wounded_in_knife_attack⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-05-17_[Older]_Iran:_Police_arrest
                  some_260_people_at_'satanist'_gathering⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-05-13_[Older]_Armenia_detains_scores
                  of_Azerbaijan_land_deal_protesters⠀⇛


                # ⚓ CBC ☛ 2024-05-17_[Older]_Alberta_RCMP_link_four_Calgary
                  murders_in_1970s_to_American_serial_killer⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-05-17_[Older]_French_police_kill_man
                  who_tried_to_set_fire_to_synagogue⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-05-14_[Older]_Germany:_Court_fines
                  AfD_politician_Höcke_over_Nazi_slogan⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-05-14_[Older]_Germany:_Far-right
                  leader_Björn_Höcke_suffers_defeat_in_court⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-05-14_[Older]_Germany's_far-right_AfD
                  under_mounting_pressure⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-05-14_[Older]_Italy:_Police_arrest
                  over_100_mafia_members_in_mass_raid⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-05-18_[Older]_Afghanistan:_Three
                  Spanish_tourists_killed_in_shootout⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-05-15_[Older]_Netherlands:_Right-wing
                  parties_to_form_government⠀⇛


                # ⚓ Democracy Now ☛ Trita_Parsi_on_Future_of_Iran_After
                  President_&_Foreign_Minister_Die_in_Helicopter_Crash⠀⇛


                       Iranian President Ebrahim Raisi and Foreign
                       Minister Hossein Amir-Abdollahian were killed on
                       Sunday in a helicopter crash along with several
                       other officials and crew. Wreckage of the
                       helicopter was found early Monday in a mountainous
                       region of the country’s northwest following an
                       overnight search in blizzard conditions. Raisi was
                       returning from inaugurating a new dam built jointly
                       with Azerbaijan along the two countries’ border.
                       Raisi, 63, was elected in 2021 in a vote that saw
                       the lowest-percentage turnout in the Islamic
                       Republic’s history after major opposition
                       candidates were disqualified from taking part.
                       Analyst Trita Parsi says the president’s death will
                       have little impact on the Islamic Republic’s
                       policies, including barring dissident candidates
                       from running for office. “Now the regime is going
                       to have to try to whip up and mobilize voters and
                       excitement for an election within 50 days,” he
                       says. “And it has to make a decision: Is it
                       actually going to allow other candidates to stand,
                       or is it going to continue on the path that it has
                       set out for itself in which these elections
                       increasingly become rather meaningless in terms of
                       actual democratic value?”


                # ⚓ Deutsche Welle ☛ 2024-05-15_[Older]_Can_China_resolve
                  Niger-Benin_border_dispute?⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-05-15_[Older]_Chinese_planes
                  'increasingly_provocative'_to_Taiwan⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-05-15_[Older]_Germany:_Man_jailed_for
                  life_for_train_knife_attack⠀⇛


                # ⚓ New York Times ☛ Iran_President_Raisi_Is_Latest_Prominent
                  Figure_to_Die_in_a_Helicopter_Crash⠀⇛


                       Officials from Ukraine, Kenya and Sudan are just
                       some of the others who have also died in crashes.


                # ⚓ France24 ☛ Reactions_pour_in_after_death_of_Iranian
                  President_Raisi_in_helicopter_crash⠀⇛


                       Iran's powerful allies on Monday mourned the death
                       of its President Ebrahim Raisi in a helicopter
                       crash, while regional militants hailed him as a
                       supporter of the Palestinian cause. The United
                       States expressed its condolences but said the
                       deceased ultraconservative leader "had blood on his
                       hands", Russia and China called him a "friend", and
                       Iran's arch-foe Israel slammed the United Nations
                       Security Council's decision to hold a minute of
                       silence in a mark of respect. Read the live blog to
                       see how events developed.


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


                      # ⚓ Deutsche Welle ☛ 2024-05-15_[Older]_Georgia:_EU,_NATO
                        condemn_passing_of_'foreign_agent'_law⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-05-15_[Older]_Georgia's
                        president_plans_foreign_agent_law_veto_as_'symbol'⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-05-14_[Older]_Georgia
                        parliament_passes_divisive_'foreign_influence'_bill⠀⇛


                      # ⚓ LRT ☛ A_Ukrainian_fought_and_died_among_Lithuanian
                        partisans._His_story_remains_a_mystery⠀⇛


                             Amid a sea of crosses bearing Lithuanian
                             tricolours, one stood out. Marked with a
                             blue-yellow trident, it carried the name of
                             the only Ukrainian volunteer to fight and die
                             alongside Lithuania‘s anti-Soviet partisans –
                             Ivan Resekovski.


                      # ⚓ Latvia ☛ Protesters_rally_again_against_EP_election
                        debates_in_Russian⠀⇛


                             The issue of pre-election debates in Russian
                             in the public media continues to be a hot
                             topic. A few days ago there was a protest in
                             front of the Public Electronic Mass Media
                             Council, and on Monday there is another one.


                      # ⚓ teleSUR ☛ Ramstein_Group_to_Reinforce_Ukraine's_Air
                        Defense⠀⇛


                             This group consists of the European Union and
                             56 countries, including 32 NATO member
                             states.


                      # ⚓ CS Monitor ☛ Can_Ukraine_attack_inside_Russia?_Kyiv
                        wants_US_to_say_yes.⠀⇛


                             U.S. military aid is reaching Ukraine with
                             much-needed ammunition and air defense
                             systems. Kyiv wants to use Western weapons to
                             hit inside Russia.


                      # ⚓ New York Times ☛ For_Old_Ukrainians,_Russia’s
                        Invasion_Echoes_World_War_II_Trauma⠀⇛


                             The oldest Ukrainians whose towns have been
                             bombarded and overrun by Russia’s invasion
                             have memories of similar miseries at the
                             hands of Nazi Germany in World War II.


                      # ⚓ RFERL ☛ Appeal_By_Woman_Imprisoned_For_Killing_Pro-
                        Kremlin_Blogger_Rejected⠀⇛


                             A military appeals court in St. Petersburg on
                             May 20 rejected a motion filed by Darya
                             Trepova against the 27-year prison term she
                             was handed after she was found guilty for her
                             role in the killing of prominent pro-Kremlin
                             blogger Vladlen Tatarsky, a fervent proponent
                             of Russia's war in Ukraine.


                      # ⚓ New York Times ☛ Faced_With_a_Russian_Onslaught,
                        Ukraine_Struggles_to_Keep_the_Lights_On⠀⇛


                             The government has for the first time ordered
                             nationwide rolling blackouts for Monday night
                             to conserve energy.


                      # ⚓ JURIST ☛ Finland_parliament_to_vote_on_controversial
                        Russia_border_migration_law:_PM⠀⇛


                             Finnish Prime Minister Petteri Orpo announced
                             on Sunday plans to introduce a draft law
                             introducing temporary measures to combat
                             instrumentalized migration at the Finnish-
                             Russian border, in an interview with Finnish
                             media. The controversial law which
                             potentially breaches international law
                             commitments on asylum, will be proposed later
                             this week.


          o § Transparency/Investigative Reporting⠀➾


                # ⚓ Jason Kratz ☛ Why_I'm_Unplugging_from_Tech_Media_-_A_Rant
                  on_Misinformation⠀⇛


                       I’ve reached my breaking point with the tech media.
                       You might have seen the recent story that people
                       were having deleted photos reappear on their
                       iPhones after Apple released the latest update, iOS
                       17.5. One Reddit user posted that photos they had
                       deleted had reappeared on an a device they had
                       wiped and sold. No real proof was given but the
                       story spread in the tech press anyhow.


                       The story didn’t hold up under scrutiny (the user
                       deleted the post and their account soon after
                       posting and they had a very short posting history)
                       and has only gotten worse with the release of iOS
                       17.5.1 today which fixes the bug but with an
                       admittedly inadequate explanation.


                # ⚓ The Register UK ☛ Boeing_union_holds_whistleblower-rights
                  training_for_workers⠀⇛


                       A union representing Boeing employees held a
                       training session last week on whistleblower
                       protection rights, suggesting the troubled
                       jetmaker's problems may be far from over.


          o § Environment⠀➾


                # ⚓ JURIST ☛ Amnesty_International_says_South_Korea_ruling_on
                  climate_change_case_could_set_human_rights_precedent⠀⇛


                       The four cases were first heard in April by the
                       court and involve approximately 200 people, 60 of
                       whom are children. The plaintiffs are suing the
                       South Korean government due to an alleged failure
                       to adequately protect people against the harms of
                       climate change, claiming the state is violating the
                       right to life in Article 34 and the right to a
                       healthy environment in Article 35 of the
                       Constitution of the Republic of Korea.


                # ⚓ The Kent Stater ☛ Air_Quality_Alert_issued_for_northeast
                  Ohio⠀⇛


                       The current air quality index in Kent is at 126,
                       which is unhealthy for sensitive groups.


                # ⚓ Deutsche Welle ☛ 2024-05-17_[Older]_Extreme_weather_batters
                  world_in_2024⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-05-17_[Older]_Germany:_Floods_hit
                  large_parts_of_Saarland⠀⇛


                # § Energy/Transportation⠀➾


                      # ⚓ Deutsche Welle ☛ 2024-05-15_[Older]_Is_India_taking_a
                        risk_with_Iran_Chabahar_port_deal?⠀⇛


                      # ⚓ CBC ☛ 2024-05-16_[Older]_Ontario's_'Crypto_King'
                        arrested_after_18-month_investigation⠀⇛


                      # ⚓ CBC ☛ 2024-05-15_[Older]_Ontario's_'Crypto_King'_and
                        his_associate_arrested,_charged_with_fraud⠀⇛


                      # ⚓ CBC ☛ 2024-05-17_[Older]_Minister_suggests_Canada_is
                        considering_tariffs_on_Chinese_EVs_following_U.S.
                        move⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-05-16_[Older]_Benin_gives_green
                        light_for_Niger's_oil_exports_to_China⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-05-16_[Older]_India:_Is_the
                        Tata_Group's_Air_India_revamp_working?⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-05-14_[Older]_US_announces
                        higher_China_tariffs,_including_100%_for_EVs⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-05-14_[Older]_US-China_trade
                        war:_Why_Joe_Biden_has_raised_the_stakes⠀⇛


                      # ⚓ CBC ☛ 2024-05-13_[Older]_Canada's_next_EV_supply
                        chain_plant_landing_in_Port_Colborne,_Ont.⠀⇛


                      # ⚓ CBC ☛ 2024-05-14_[Older]_$1.6B_EV_battery_separator
                        plant_to_open_in_Ontario's_Niagara_Region_in_2027_will
                        'boost'_the_city,_mayor_says⠀⇛


                      # ⚓ CBC ☛ 2024-05-15_[Older]_Ontario_plans_to_toughen
                        penalties_for_impaired_drivers⠀⇛


                      # ⚓ CBC ☛ 2024-05-14_[Older]_Ontario_to_suspend_driver's
                        licences_of_convicted_auto_thieves⠀⇛


                      # ⚓ CBC ☛ 2024-05-17_[Older]_Quebec_to_force_gas_stations
                        to_report_their_prices._Will_it_lower_fuel_costs?⠀⇛


                      # ⚓ DeSmog ☛ ‘Hydrogen_Highway’_Network_of_Refueling
                        Stations_to_Span_Alberta_Cities⠀⇛


                      # ⚓ The Revelator ☛ Burning_Trees:_As_the_Biomass
                        Industry_Grows,_Its_Carbon_Emissions_Go_Uncounted⠀⇛


                      # ⚓ Connor Tumbleson ☛ I_hate_flying⠀⇛


                             So I started changing my life to avoid
                             flights unless absolutely needed - driving
                             everywhere when possible and declining trips
                             as a flight was involved. When a flight was
                             not avoidable I forced myself to find a
                             direct flight to cut down on the possibility
                             of getting sick on the plane.


                      # ⚓ Rob Knight ☛ Do_You_Not_Fear_Death,_Sir?⠀⇛


                             It was fine, no one died, we made it back in
                             one piece. Still. The man clearly has no
                             fear.


                      # ⚓ YLE ☛ Google's_planned_Finnish_data_centre_expansion
                        to_create_100_new_jobs⠀⇛


                             The firm has operated the centre in the
                             southern city since 2011 and has expanded the
                             facility a number of times.


                             Google currently employs around 400 people in
                             Hamina and it is expected that the new
                             expansion will create about 100 new jobs.


                      # ⚓ India Times ☛ Google_invests_1_billion_euros_in
                        Finnish_data_centre_to_drive_AI_growth⠀⇛


                             In recent years, many data centres have been
                             located in the Nordic countries because of
                             the region's cooler climate, tax breaks and
                             abundant availability of renewable power.


                # § Wildlife/Nature⠀➾


                      # ⚓ US News And World Report ☛ 2024-05-12_[Older]_Western
                        Canada_Blazes_Cause_Evacuation_Orders,_Air_Quality
                        Concerns⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-05-16_[Older]_Canada:
                        Evacuations_as_wildfire_closes_in_on_oil_sands_town⠀⇛


                      # ⚓ US News And World Report ☛ 2024-05-14_[Older]
                        Explainer-Canada_Wildfire_Season_Is_Heating_Up:_Here's
                        What_to_Know⠀⇛


                      # ⚓ US News And World Report ☛ 2024-05-14_[Older]_A
                        Wildfire_in_Western_Canada_Is_Growing._More_People
                        Nearby_Are_Told_to_Leave⠀⇛


                      # ⚓ CBC ☛ 2024-05-17_[Older]_B.C._man_who_was_tracking_a
                        bear_airlifted_to_hospital_after_grizzly_attack⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-05-14_[Older]_Roadkill_on_the
                        menu:_Can_highways_become_wildlife_friendly?⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-05-14_[Older]_Animal_crossing:
                        How_wildlife-safe_highways_stop_roadkill⠀⇛


          o § Finance⠀➾


                # ⚓ Deutsche Welle ☛ 2024-05-12_[Older]_How_Germany_plans_to
                  end_homelessness⠀⇛


                # ⚓ CBC ☛ 2024-05-14_[Older]_WATCH_|_Are_you_boycotting_Loblaw?
                  We_asked_people_across_Canada⠀⇛


                # ⚓ CBC ☛ 2024-05-17_[Older]_Shoppers_Drug_Mart_'volunteer'_job
                  posting_was_an_error:_Loblaw⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-05-16_[Older]_Germany_faces_challenge
                  as_2025_tax_forecast_sinks⠀⇛


                # ⚓ The Verge ☛ She_sold_her_bathwater_—_PayPal_took_her
                  profits⠀⇛


                       Belle Delphine, the woman who went viral in 2019
                       for selling jars of her bathwater, revealed earlier
                       this month that the stunt earned her $90K in
                       profits. In a thread on X, the adult content
                       creator and model also explained that because of
                       PayPal, the payment processing system she used for
                       the sale, she never saw a dime of that money.


                       “PayPal, without any warning closed my PayPal
                       account and took the $90,000 that I earned from
                       selling my bathwater,” Belle Delphine wrote.


                # ⚓ Business Insider ☛ Belle_Delphine_Got_$90K_From_PayPal
                  Years_After_Selling_Her_Bathwater⠀⇛


                       She made about $90,000, but PayPal froze her
                       account and kept the money as a fine for each sale.


                # ⚓ Deutsche Welle ☛ 2024-05-16_[Older]_Have_the_Germans_become
                  lazy_at_work? [Ed: More victim-blaming in a failing system?
                  Well, victim-blaming never solves problems and it barely
                  delays solution seeking, it just offends the victims and then
                  exacerbates things by virtue of suppressed rage that can
                  "explode".]⠀⇛


                # ⚓ Deccan Herald ☛ Pandemic-era_college_kids_face_job_market
                  that_doesn’t_want_them [Ed: Lots of victim-blaming going on
                  these days]⠀⇛


                       The class of 2024 - tainted by the pandemic, this
                       outgoing class of seniors had anything but a
                       typical college experience. Most are ready to enter
                       the “real world”. Yet the class is - again -
                       needing to adjust their expectations.


                # ⚓ CBC ☛ 2024-05-17_[Older]_Semi-detached_Toronto_home
                  renovation_sparks_bitter_feud_among_neighbours⠀⇛


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Deutsche Welle ☛ 2024-05-14_[Older]_Kuwait's_unique
                  democratic_experiment_could_be_at_an_end⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-05-13_[Older]_German_court_upholds
                  AfD_'suspected'_extremist_status⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-05-13_[Older]_Germany:_Angela
                  Merkel's_memoirs_to_be_published_in_November⠀⇛


                # ⚓ CBC ☛ 2024-05-15_[Older]_4th_man_appears_in_court_on
                  charges_of_killing_B.C._Sikh_leader⠀⇛


                # ⚓ Modern Diplomacy ☛ 2024-05-16_[Older]_Sikh_Killings_and
                  Strained_Canada-India_Relations⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-05-16_[Older]_North_Macedonia_name
                  dispute_reignites_spat_with_Greece⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-05-16_[Older]_Protests_in_Pakistan-
                  ruled_Kashmir_expose_long-standing_grievances⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-05-14_[Older]_Protests_in_Pakistan-
                  held_Kashmir_end_after_aid_deal_offer⠀⇛


                # ⚓ Federal News Network ☛ VA_should_admit_failure_of_its_new
                  e-health_record_system⠀⇛


                       Despite this skepticism, there does not appear to
                       be even the smallest consideration that this
                       program should be reevaluated, even though the VA
                       has not been able to show any — even the slightest
                       — benefit to veterans, clinicians or the American
                       taxpayer after six years and $10 billion worth of
                       effort. The best that VA Secretary Denis McDonough
                       could say about the program is that “VA is seeing
                       incremental, but accelerating progress as it
                       addresses the issues that clinicians and other end
                       users are experiencing.”


                       This decision to move forward, even though every
                       known metric for this system is negative — and many
                       are tragically negative — is incomprehensible.


                # ⚓ Silicon Angle ☛ Google_to_invest_€1B_in_Finland_data_center
                  expansion⠀⇛


                       Google LLC will invest €1 billion, or $1.1 billion,
                       to expand a data center campus it built in southern
                       Finland more than a decade ago.


                # ⚓ The Verge ☛ Google_plans_to_reuse_heat_after_expanding_a
                  data_center_for_AI⠀⇛


                       Already energy-hungry data centers are now even
                       more energy-intensive when used for AI. Reusing the
                       server heat is one way to mitigate the effects that
                       AI has on the power grid and environment. After
                       all, if Google isn’t careful, its scramble to
                       inject AI into Search and other products could
                       derail the company’s climate goals and place added
                       pressure on energy systems where it operates.


                # ⚓ Jacobin Magazine ☛ Worker_Co-Ops_Have_a_Role_to_Play_in
                  Socialist_Strategy⠀⇛


                       There’s another benefit to building up the
                       cooperative economy: it is a proven way to combat
                       the atomization of modern society which, many of us
                       now recognize, has made it harder for the Left to
                       win elections and union drives. Without a sense
                       that our well-being depends on the well-being of
                       others, not only is it harder to mobilize the votes
                       needed for left candidates to win — it is harder to
                       convince voters that left policies are even
                       desirable. As Gabriel Winant has lamented, “Eugene
                       Debs could rise from the dead and would get little
                       traction.”


                # ⚓ RTL ☛ Social_media_platform:_Parent_company_of_Trump's
                  Truth_Social_posts_$328_mln_loss⠀⇛


                       Trump Media and Technology Group, which owns former
                       US president Donald Trump's social media platform
                       Truth Social, lost more than $300 million in the
                       first quarter of 2024, it said Monday.


                       TMTG, which recently went public, posted a net loss
                       of $327.6 million from January to March, compared
                       with $210,300 in net losses for the same period
                       last year, according to a company statement.


                # ⚓ New Yorker ☛ What_Asian_America_Meant_to_Corky_Lee⠀⇛


                       A new anthology by Chinatown’s omnipresent
                       documentarian, who captured half a century of
                       shifting identities, activism, and daily life.


                # § Misinformation/Disinformation/Propaganda⠀➾


                      # ⚓ Deutsche Welle ☛ 2024-05-12_[Older]_Fake_news_on_the
                        rise_leading_up_to_EU_election⠀⇛


                      # ⚓ NL Times ☛ Doctors_increasingly_have_to_dissuade
                        patients_from_medical_misinformation_found_online⠀⇛


                             Doctors are facing more and more medical
                             misinformation in their practices. They
                             increasingly have to dissuade patients from
                             false claims they heard on social media like
                             that whooping cough is beneficial for a
                             child’s development, deodorant can make you
                             sick, and sunscreen is carcinogenic, NOS
                             reports after surveying 670 doctors with the
                             doctors’ federation KNMG.


                             Over half (55 percent) of the surveyed
                             doctors speak to a misinformed patient at
                             least once a week. For 14 percent, it’s a
                             daily occurrence. Misinformation about
                             vaccinations, allergies, vitamins, and
                             contraception is most common, according to
                             the respondents.


                      # ⚓ The Local SE ☛ Inside_Sweden:_Why_[astroturfer]
                        factory_won't_spark_a_government_crisis⠀⇛


                             News that the Sweden Democrats are operating
                             a far-right [astroturfer] factory – which
                             among other things the party uses to smear
                             political opponents as well as its supposed
                             allies – has caused probably the biggest rift
                             yet between them and the three other parties
                             that make up Sweden’s ruling coalition.


                      # ⚓ New York Times ☛ In_China,_Deepfakes_of_‘Russian’
                        Women_Point_to_‘Nationalistic_Sexism’⠀⇛


                             A.I.-manipulated videos on Chinese sites use
                             young, supposedly Russian women to promote
                             China-Russia ties, stoke patriotism — and
                             make money.


                      # ⚓ Mozilla ☛ Sneha_Revanur_on_empowering_youth_voices_in
                        AI,_fighting_for_legislation_and_combating_deepfakes
                        and_disinformation⠀⇛


                             At Mozilla, we know we can’t create a better
                             future alone, that is why each year we will
                             be highlighting the work of 25 digital
                             leaders using technology to amplify voices,
                             effect change, and build new technologies
                             globally through our Rise 25 Awards. 


          o § Censorship/Free Speech⠀➾


                # ⚓ Deutsche Welle ☛ 2024-05-12_[Older]_Dresden_Peace_Prize
                  goes_to_the_late_Alexei_Navalny⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-05-13_[Older]_Key_witness_Cohen_says
                  Trump_told_him_to_pay_hush_money⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-05-14_[Older]_Roman_Polanski:_French
                  court_acquits_director_in_libel_trial⠀⇛


                # ⚓ International Business Times ☛ UK_Cracks_Down_On_'Just_Stop
                  Oil':_Will_Force_Org_To_Pay_For_Being_Disruptive_And_Make_It
                  Easier_to_Sue_Them⠀⇛


                       Per a conversation between The Telegraph and a
                       source from the Home Office, the new guidelines
                       will make it easier to sue JSO. This could occur
                       when they set up a roadblock preventing people from
                       arriving on time to work or making a hospital
                       appointment.


                # ⚓ Futurism ☛ Sam_Altman_Clearly_Freaked_Out_by_Reaction_to
                  News_of_OpenAI_Silencing_Former_Employees⠀⇛


                       The optics were especially appalling because both
                       had been working on OpenAI's team dedicated to
                       controlling any future superintelligent AI the
                       company might create, with one of the two harshly
                       criticizing OpenAI's purported lack of commitment
                       in that domain. And then things got even more
                       embarrassing for the company when Vox reported that
                       any workers leaving OpenAI had to sign a draconian
                       nondisclosure agreement to retain their equity
                       stipulating, among other things, that they could
                       never criticize the company in the future.


                # ⚓ Meduza ☛ A_Ukrainian_student_escaped_Russia_after_his
                  arrest_for_anti-war_posts._Meduza’s_sources_say_his_friends
                  asked_Putin’s_daughter_for_help.⠀⇛


                       For nearly two years, he managed to avoid any
                       trouble from the authorities. In March 2024,
                       however, he received a Telegram message from an
                       acquaintance warning him that some of his
                       classmates had screenshotted his anti-war posts and
                       were planning to report him.


                       “I probably should have left [Russia] at that
                       point, but my thesis defense was coming up, my
                       state exams were just around the corner, and I
                       decided to stay,” he says.


                # ⚓ New Eastern Europe ☛ Georgia_has_now_reached_a_crucial
                  moment⠀⇛


                       Enforcing the law may serve several purposes. These
                       include the government’s desire to control and
                       weaken opposition organizations; to entrench the
                       political system and maintain power; to mobilize
                       its own electorate; or to divert attention from
                       Georgia’s other problems. The parliamentary
                       elections will be held in Georgia this October. The
                       attempt to maintain the power is the main driving
                       force behind the Georgian Dream policy. And the
                       future success remains uncertain. While it is true
                       that Georgia has managed to improve some
                       macroeconomic indicators since the outbreak of the
                       full-scale war in Ukraine, mainly by restoring
                       economic relations with sanctioned Russia, the
                       country still faces problems. These include an
                       unemployment rate of around 15 per cent, corruption
                       and a huge wave of emigration. This coincides with
                       the simultaneous arrival of Russians, their
                       purchase of property and the influx of Russian
                       capital into Georgia. This is causing justifiable
                       resentment in Georgian society, as around 20 per
                       cent of the country’s territory remains outside
                       Tbilisi’s control as a result of the 2008 war with
                       Russia. At the same time some part of the society
                       benefits from the situation.


                # ⚓ RFA ☛ Chinese_agents_highly_active_in_democratic_Taiwan,
                  dissidents_say⠀⇛


                       He believes the ruling Chinese Communist Party
                       under Xi Jinping is now focusing closely on
                       "cleaning up" opposition voices overseas, and has
                       spotted people he believes to be Chinese agents a
                       number of times at public events in democratic
                       Taiwan.


                       According to a former Chinese agent who spoke
                       recently to Australian broadcaster ABC, this is
                       exactly what's going on. Former Chinese spy "Eric"
                       told the station that he has been involved in
                       surveillance, abductions and the silencing of
                       targets around the world since 2008.


                # ⚓ RFA ☛ Conform_or_be_canceled⠀⇛


                       Taiwanese TV and movie actor Wu Mu-hsuen was
                       recently forced to sign a pledge to support China's
                       claim that democratic Taiwan is a part of China, or
                       her the online drama "Hey! Come a bit closer" would
                       never be aired. [...]


                # ⚓ RFERL ☛ Trial_Of_Theater_Director_Berkovich,_Playwright
                  Petriichuk_Starts_In_Moscow⠀⇛


                       A military court in Moscow has started the trial of
                       theater director Yevgenia Berkovich and playwright
                       Svetlana Petriichuk, who are charged with
                       justifying terrorism.


                # ⚓ RFERL ☛ YouTube_Blocks_4_Videos_At_Russia's_Request⠀⇛


                       The YouTube online video-sharing platform has
                       blocked four videos after a request from Russia's
                       Roskomnadzor media watchdog, Agentsvo Telegram
                       channel reported on May 20.


                # ⚓ RFERL ☛ Russian_Anti-War_Activist_Gets_25_Years_In_Prison
                  On_Treason_Charge⠀⇛


                       A court in Siberia on May 20 sentenced anti-war
                       activist Ilya Baburin to 25 years in prison on a
                       high-treason charge that stemmed from allegations
                       that the 24-year-old planned to set several
                       military recruitment centers on fire.


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


                # ⚓ CPJ ☛ 2024-05-15_[Older]_CPJ_urges_India_to_ensure_freedom
                  for_3_journalists_granted_bail_in_security_cases⠀⇛


                # ⚓ Democracy Now ☛ British_High_Court_Grants_WikiLeaks_Founder
                  Julian_Assange_the_Right_to_Appeal_U.S._Extradition⠀⇛


                       WikiLeaks founder Julian Assange on Monday won the
                       right to appeal his extradition to the United
                       States. Assange’s lawyers argued before the British
                       High Court that the U.S. government provided
                       “blatantly inadequate” assurances that Assange
                       would have the same free speech protections as an
                       American citizen if extradited from Britain.
                       Assange has spent more than a decade facing the
                       threat of extradition to the U.S., where he faces
                       up to 175 years in prison for publishing classified
                       documents exposing U.S. war crimes in Iraq and
                       Afghanistan. “This is a victory for Julian Assange
                       in that he lives on to fight another day, his case
                       lives on to fight another day. But he’s not out of
                       Belmarsh [Prison] yet, and he’s not in the clear
                       yet,” says Chip Gibbons, policy director of
                       Defending Rights & Dissent. “This could still end
                       in him being sent to the U.S. And the person who
                       can stop this is Joe Biden and Merrick Garland.”


                # ⚓ The Dissenter ☛ US_Effort_To_Extradite_Assange_Hits
                  Roadblock⠀⇛


                       Assange, an award-winning journalist, faces a
                       maximum of 175 years in prison for his role in
                       receiving and publishing classified materials
                       relating to the Iraq and Afghanistan wars,
                       Guantanamo Bay detainee files, and diplomatic
                       cables. No other individual or press organization
                       which participated in the publications of these
                       very documents, including the New York Times,
                       Washington Post and The Guardian, have faced
                       criminal charges.


                       Throughout Assange’s extradition case, the U.S.
                       government has argued that he would not be
                       permitted to argue that his publications were
                       protected under the First Amendment — because he is
                       a non-U.S. citizen whose activities occurred
                       outside the U.S.


                # ⚓ RFA ☛ Head_of_embattled_Hong_Kong_journalists'_union_to
                  step_down⠀⇛


                       Ronson Chan, an outspoken critic of diminishing
                       press freedom who currently chairs the embattled
                       Hong Kong Journalists' Association, has said he
                       won't run again for office in union elections at
                       the end of next month, saying he had been told that
                       the organization would continue to be targeted by
                       the authorities if he didn't step down.


                # ⚓ Daniel Pocock ☛ Fact_check:_relation_to_Julian_Assange,
                  founded_Wikileaks_at_University_of_Melbourne_and_Arjen
                  Kamphuis⠀⇛


                       Arjen Kamphuis is notable for his collaboration
                       with the UK Centre for Investigative Journalism and
                       his work on the book Information Security for
                       Journalists and for his subsequent disappearance.
                       It is not clear if Arjen was very close to
                       Wikileaks or just one of many people with a similar
                       interest in the security of journalists.


                # ⚓ The Register UK ☛ Julian_Assange_can_appeal_extradition
                  from_UK_to_US⠀⇛


                       Manning gave Assange various collections of
                       classified data, including hundreds of thousands of
                       US diplomatic cables that formed the basis of the
                       Cablegate series on WikiLeaks, and details about
                       the Pentagon's actions in Iraq and Afghanistan
                       including potential war crimes committed by
                       American forces.


                # ⚓ El País ☛ London_court_rules_WikiLeaks_founder_Assange_can
                  appeal_against_an_extradition_order_to_the_US⠀⇛


                       “The U.S. response has been to say that Assange
                       will always be able to use the First Amendment in
                       his defense, but that it will be the court that
                       must decide whether to admit it or not. That is no
                       guarantee, quite the opposite. It does not clarify
                       anything about what may happen if he is eventually
                       extradited to the United States,” Jennifer
                       Robinson, the Australian publisher’s lawyer,
                       explained last week at a briefing in London with
                       the Foreign Press Association.


                # ⚓ France24 ☛ WikiLeaks’_Assange_wins_UK_court_bid_to_appeal
                  extradition_to_US⠀⇛


                       Assange is wanted by Washington for publishing
                       hundreds of thousands of secret US documents from
                       2010 as head of the whistle-blowing website
                       WikiLeaks.


                # ⚓ New York Times ☛ Assange_Can_Appeal_U.S._Extradition,
                  English_Court_Rules⠀⇛


                       Two High Court judges said they would allow an
                       appeal to be heard on a limited number of issues.


                # ⚓ NYPost ☛ WikiLeaks_founder_Julian_Assange_can_appeal_US
                  extradition_order⠀⇛


                       Commuters emerging from a Tube stop near the
                       courthouse couldn’t miss a large sign bearing
                       Assange’s photo and the words, “Publishing is not a
                       crime. War crimes are.” Scores of supporters
                       gathered outside the neo-Gothic Royal Courts of
                       Justice chanting “Free Julian Assange” and “Press
                       freedom, Assange freedom.”


                       Some held a large white banner aimed at President
                       Biden, exhorting: “Let him go Joe.”


                # ⚓ Hindustan Times ☛ WikiLeaks_founder_Julian_Assange_can
                  appeal_against_extradition_to_US,_rules_UK_court⠀⇛


                       Assange's lawyers argued that the U.S. provided
                       “blatantly inadequate” assurances the whistleblower
                       would have free press protections if extradited to
                       America to face espionage charges.


                # ⚓ Press Gazette ☛ Julian Assange wins_bid_to_bring_appeal
                  against_extradition⠀⇛


                       At a hearing on Monday, the two judges granted
                       permission to appeal over the freedom of speech and
                       nationality points, meaning Assange will be able to
                       bring the appeal.


                # ⚓ Wired ☛ WikiLeaks'_Julian_Assange_Can_Appeal_His
                  Extradition_to_the_US,_British_Court_Says⠀⇛


                       Following a two-hour hearing, at which Assange was
                       not present due to health issues, the judges
                       allowed Assange to appeal his extradition on
                       freedom of speech and freedom of expression
                       grounds. The decision, the latest in a years-long
                       legal battle, follows a UK High Court ruling in May
                       that asked the US government to provide more
                       “assurances” about the conditions Assange would
                       face if he was extradited. In that instance, the
                       court said it required more convincing that Assange
                       would have free speech protections, his Australian
                       nationality would not prejudice him in any trial,
                       and he would not later be sentenced to death.


                # ⚓ Deutsche Welle ☛ Julian_Assange_given_permission_to_appeal
                  US_extradition⠀⇛


                       Assange's wife, Stella, said outside the court the
                       US should "read the situation" and drop the case.


                       "As a family we are relieved but how long can this
                       go on?" she said. "This case is shameful and it is
                       taking an enormous toll on Julian."


                # ⚓ Amnesty International ☛ UK/USA:_Long_lasting_damage_to
                  global_media_freedom_as_Julian_Assange_back_in_UK_court_ahead
                  of_possible_extradition_to_USA⠀⇛


                       Following the adjournment of court on 26 March, the
                       High Court in the UK has confirmed a hearing on 20
                       May, having received renewed diplomatic assurances
                       from the USA on 16 April.


                # ⚓ Hong Kong Free Press ☛ Hong_Kong_media_mogul_Jimmy_Lai’s
                  lawyers_to_argue_no_case_to_answer_at_national_security
                  trial⠀⇛


                       Lawyers for Hong Kong media mogul Jimmy Lai have
                       said they will argue the tycoon has no case to
                       answer in his national security trial, in which he
                       faces three conspiracy charges involving foreign
                       collusion and sedition.


          o § Civil Rights/Policing⠀➾


                # ⚓ Deutsche Welle ☛ 2024-05-12_[Older]_Germany:_Tesla_protests
                  end_with_arrests_and_dismantled_camp⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-05-16_[Older]_Tesla:_Court_win_for
                  German_protesters_amid_expansion_vote⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-05-15_[Older]_Thai_PM_promises
                  investigation_after_activist_dies_in_jail⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-05-15_[Older]_Ousman_Sonko:_Swiss
                  court_convicts_Gambia_ex-minister⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-05-15_[Older]_Pakistan:_Why_are_there
                  so_few_female_judges?⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-05-17_[Older]_US:_Mercedes-Benz
                  plants_in_Alabama_remain_union-free⠀⇛


                # ⚓ CBC ☛ 2024-05-13_[Older]_Workers_can_form_union_at_Amazon
                  warehouse_in_Laval,_Que.,_a_first_in_Canada⠀⇛


                # ⚓ CBC ☛ 2024-05-15_[Older]_Calls_for_evictions,_threats_of
                  vigilantism_over_drug_activity_at_Kenora,_Ont.,_apartment
                  building⠀⇛


                # ⚓ CBC ☛ 2024-05-15_[Older]_Van_passenger_in_Ontario_highway
                  wrong-way_crash_was_barred_from_liquor_store_after_alleged
                  theft⠀⇛


                # ⚓ CBC ☛ 2024-05-14_[Older]_Immigrant_workers_say_future_in
                  limbo_as_government_ranking_system_scores_soar⠀⇛


                # ⚓ EFF ☛ Podcast_Episode:_Chronicling_Online_Communities⠀⇛


                # ⚓ CoryDoctorow ☛ Pluralistic:_The_new_globalism_is_global
                  labor⠀⇛


                       That meant that each level of the system – primary,
                       junior, secondary – was about to go through a
                       whipsaw, in which low numbers of students would be
                       followed by large numbers. For a unionized
                       education workforce, this presented a crisis:
                       normally, a severe contraction in student numbers
                       would trigger layoffs, on a last-in, first-out
                       basis. That meant that layoffs loomed for junior
                       teachers, who would almost certainly end up
                       retraining for another career. When student numbers
                       picked up again, those teachers wouldn't be in the
                       workforce anymore, and worse, a lot of the senior
                       teachers who got priority during layoffs would be
                       retiring, magnifying the crisis.


                # ⚓ The Register UK ☛ Police_caught_circumventing_city_bans_on
                  face_recognition⠀⇛


                       Police in multiple major US cities have figured out
                       a trick to circumvent bans on facial recognition
                       technology. Just ask a friend in a city without any
                       such restrictions to do it for you.


                       It's not immediately clear how widespread such
                       side-stepping of facial recognition restrictions in
                       the US may be. According to the Washington Post's
                       review of police documents in Austin, Texas, and
                       San Francisco, California, however, it's definitely
                       something that's gone on in at least two major US
                       metropolitan areas.


                # ⚓ ACLU ☛ We_Fought_for_Deaf_People_on_Probation_and_Parole_in
                  Georgia_—_and_Won⠀⇛


                       A five-year effort to get equal access for deaf and
                       hard-of-hearing people on parole and probation in
                       Georgia has ended in victory. The American Civil
                       Liberties Union and our legal partners reached a
                       groundbreaking settlement that requires the Georgia
                       agency responsible for supervising people on
                       probation and parole – the Georgia Department of
                       Community Supervision or “GDCS” – to dismantle the
                       discriminatory hurdles that make it harder for deaf
                       and hard-of-hearing people to avoid prison and live
                       safely in their communities. We hope that other
                       states look to this agreement when determining what
                       is required for their supervision agencies to
                       comply with the Americans with Disabilities Act and
                       Section 504 of the Rehabilitation Act.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ EFF ☛ Sunsetting_Section_230_Will_Hurt_Internet_Users,_Not
                  Big_Tech⠀⇛


                       The House Energy and Commerce Committee is holding
                       a hearing on Wednesday on a bill that would end 47
                       U.S.C. § 230 (“Section 230”) in 18 months. The
                       authors of the bill argue that setting a deadline
                       to either change or eliminate Section 230 will
                       force the Big Tech online platforms to the
                       bargaining table to create a new regime of
                       intermediary liability.  


                       As EFF has said for years, Section 230 is essential
                       to protecting individuals’ ability to speak,
                       organize, and create online. 


                       Congress knew exactly what Section 230 would do –
                       that it would lay the groundwork for speech of all
                       kinds across the internet, on websites both small
                       and large. And that’s exactly what has happened.  


      § Monopolies/Monopsonies⠀➾


          o ⚓ Deutsche Welle ☛ 2024-05-13_[Older]_EU_says_Booking.com_is_tech
            'gatekeeper,'_set_to_rule_on_X⠀⇛


          o § Trademarks⠀➾


                # ⚓ TTAB Blog ☛ TTAB_Finds_CINNAMON_DONUT_STOUT_to_be_Generic
                  for_._._._Guess_What?⠀⇛


                       I don't drink a lot of beer - I want to keep my
                       weigh down. But I don't think I would ever want a
                       glass of CINNAMON DONUT STOUT. The Board was not
                       enamored with the idea, either. It affirmed a
                       refusal to register, on the Supplemental Register,
                       the term CINNAMON DONUT STOUT for "beer" [STOUT
                       disclaimed], finding it to be generic for the goods
                       under Sections 23(c) and 45. Examining Attorney
                       Raul Cordova "proffered clear and convincing
                       evidence that beer is offered in a variety of
                       flavors that describe the central, or key, aspect
                       of the beer." In_re_Blake_Farms_Hard_Fashion
                       Company_Apple_Cider,_LLC, Serial No. 90504414 (May
                       16, 2024) [not precedential] (Opinion by Judge
                       Melanye K. Johnson).


                # § Right of Publicity⠀➾


                      # ⚓ RTL ☛ Synthetic_voice:_OpenAI_to_'pause'_voice_linked
                        to_Scarlett_Johansson⠀⇛


                             "I was shocked, angered, and in disbelief
                             that Mr. Altman would pursue a voice that
                             sounded so eerily similar to mine that my
                             closest friends and news outlets couldn't
                             tell the difference," Johannson said in a
                             statement.


                      # ⚓ Wired ☛ Scarlett_Johansson_Says_OpenAI_Ripped_Off_Her
                        Voice_for_ChatGPT⠀⇛


                             On Monday, Johansson issued a statement
                             claiming to have forced that reversal, after
                             her lawyers demanded OpenAI clarify how the
                             new voice was created.


                      # ⚓ The Verge ☛ Scarlett_Johansson_told_OpenAI_not_to_use
                        her_voice_—_and she’s not_happy_they_might_have
                        anyway⠀⇛


                             Johansson says she was “shocked, angered and
                             in disbelief” over how “eerily similar” the
                             voice of Sky sounded to herself. OpenAI said
                             the voice comes from an actor who they hired
                             who is speaking in their normal speaking
                             voice. The company declined to share the
                             actor’s name, citing privacy concerns.


                      # ⚓ NPR ☛ Scarlett_Johansson_says_she_is_'shocked,
                        angered'_over_new_ChatGPT_voice⠀⇛


                             "After much consideration and for personal
                             reasons, I declined the offer," Johansson
                             wrote.


                             Just two days before the new ChatGPT was
                             unveiled, Altman again reached out to
                             Johansson's team, urging the actress to
                             reconsider, she said.


                             But before she and Altman could connect, the
                             company publicly announced its new, splashy
                             product, complete with a voice that she says
                             appears to have copied her likeness.


                             To Johansson, it was a personal affront.


                      # ⚓ Hindustan Times ☛ Scarlett_Johansson_vs_OpenAI:_Actor
                        says_ChatGPT_voice_is_'eerily_similar'_to_hers._5
                        points_to_know_about_controversy⠀⇛


                             In a personal claim, Scarlett Johansson
                             stated that OpenAI initially approached her
                             to use her voice in their project. However,
                             after careful consideration, she declined the
                             offer to voice the chatbot herself. On May
                             20, the actor accused the tech company of
                             using a voice that was strikingly similar to
                             hers.


                      # ⚓ NDTV ☛ Scarlett_Johansson_"Angered"_By_OpenAI_Chatbot
                        Voice_That_Sounds_"Eerily"_Like_Her⠀⇛


                             Ms Johansson added that she declined the
                             offer but was taken aback when she heard the
                             demo. "When I heard the released demo, I was
                             shocked, angered and in disbelief that Mr.
                             Altman would pursue a voice that sounded so
                             eerily similar to mine that my closest
                             friends and news outlets could not tell the
                             difference. Mr Altman even insinuated that
                             the similarity was intentional, tweeting a
                             single word "her" - a reference to the film
                             in which I voiced a chat system, Samantha,
                             who forms an intimate relationship with a
                             human."


                             Ms Johansson stated that the circumstances
                             "forced her to hire legal counsel," and as a
                             result, her attorney sent two letters to Mr
                             Altman and OpenAI requesting an explanation
                             of the chatbot's voice's creation process.
                             She added that OpenAI then "reluctantly
                             agreed" to remove the voice from the
                             platform.


                      # ⚓ Variety ☛ Scarlett_Johansson_Reacts_to_OpenAI_Sky
                        Voice:_'Shocked'_and_'Angered'⠀⇛


                             Actor Scarlett Johansson said she turned down
                             OpenAI‘s request for her to lend her voice to
                             a conversational ChatGPT system — and that
                             she was “shocked” and “angered” that the
                             company went ahead and used a voice that
                             sounded very similar to hers anyway.


                      # ⚓ Rolling Stone ☛ Scarlett_Johansson_'Angered'_After
                        ChatGPT_Used_'Eerily_Similar'_Voice⠀⇛


                             In her statement, Johansson says Altman
                             “insinuated that the similarity [of the
                             voice] was intentional” when he tweeted the
                             word “her” in reference to the film and the
                             new ChatGPT model.


                             “Two days before the ChatGPT 4.0 demo was
                             released, Mr. Altman contacted my agent,
                             asking me to reconsider. Before we could
                             connect, the system was out there,” she
                             wrote.


                      # ⚓ TMZ ☛ Scarlett_Johansson_Hired_Lawyers_Over_OpenAI's
                        ChatGPT_Voice⠀⇛


                             As it turns out ... Scarlett claims that she
                             was actually approached by OpenAI's head
                             honchos in September -- including CEO Sam
                             Altman -- who she says wanted to hire her to
                             voice the current ChatGPT 4.0 model. SJ says
                             she considered it ... but ultimately
                             declined.


                             Fast-forward to December, and OpenAI's "Sky"
                             was rolled out ... with just about everyone
                             saying it reminded them of ScarJo -- and she
                             thought so too, which is why she lawyered up.


                      # ⚓ Axios ☛ Scarlett_Johansson_says_lawyers_got_OpenAI_to
                        shut_down_"Her"_voice⠀⇛


                             Why it matters: The dispute between the maker
                             of ChatGPT and a performer famous for
                             representing AI will further spook creative
                             artists already suspicious that AI could
                             dilute the value of their work.


                      # ⚓ New York Times ☛ Scarlett_Johansson_Said_No,_but
                        OpenAI’s_Virtual_Assistant_Sounds_Just_Like_Her⠀⇛


                             Last week, the company released a chatbot
                             with an option that sounded like the actress,
                             who provided the voice of an A.I. system in
                             the movie “Her.”


                      # ⚓ New York Times ☛ Scarlett_Johansson’s_Statement_About
                        Her_Interactions_With_Sam_Altman⠀⇛


                             “Last September, I received an offer from Sam
                             Altman, who wanted to hire me to voice the
                             current ChatGPT 4.0 system. He told me that
                             he felt that by my voicing the system, I
                             could bridge the gap between tech companies
                             and creatives and help consumers to feel
                             comfortable with the seismic shift concerning
                             humans and A.I. He said he felt that my voice
                             would be comforting to people. After much
                             consideration and for personal reasons, I
                             declined the offer. Nine months later, my
                             friends, family and the general public all
                             noted how much the newest system named ‘Sky’
                             sounded like me.


                      # ⚓ US News And World Report ☛ Scarlett_Johansson_Says
                        OpenAI_Chatbot_Voice_'Eerily_Similar'_to_Hers⠀⇛


                             "When I heard the released demo, I was
                             shocked, angered and in disbelief that Mr.
                             Altman would pursue a voice that sounded so
                             eerily similar to mine that my closest
                             friends and news outlets could not tell the
                             difference."


          o § Copyrights⠀➾


                # ⚓ Torrent Freak ☛ WOW_Asks_Court_to_Throw_Out_Filmmakers'
                  Expanded_Piracy_Liability_Lawsuit⠀⇛


                       Internet provider WOW has asked a Colorado federal
                       court to dismiss an expanded piracy liability
                       complaint filed by several film companies earlier
                       this year. The ISP says there is no evidence to
                       show that it received any piracy notices for the
                       300 new works added to the lawsuit. In addition, it
                       believes that recent court verdicts support a
                       dismissal of at least some of the claims in the
                       multimillion dollar lawsuit.


                # ⚓ Torrent Freak ☛ MPA_Ramps_Up_Efforts_to_Disrupt_Pirate
                  Sites'_Use_of_Internet_Intermediaries⠀⇛


                       A major hire at the Motion Picture Association, to
                       a new senior position that until recently did not
                       exist, offers a glimpse into part of Hollywood's
                       global anti-piracy strategy. Jesse Martin, former
                       senior attorney at The Software Alliance (BSA),
                       joins the MPA with a brief to combat and disrupt
                       pirates' use of intermediaries. The MPA speaks of
                       "intermediary outreach" and "voluntary initiatives"
                       but if cooperation isn't forthcoming, preparations
                       will have been made.





                    ䷩ 𝚕𝚒𝚗𝚎 6878

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 21/05/2024: Tesla Layoffs and Further
Free Speech Perils Online⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on May 21, 2024


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Forest_Walk⦈_


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o § Science⠀➾


                # ⚓ The Conversation ☛ 2024-05-15_[Older]_Fossil_captures
                  starfish_splitting_itself_in_two_–_showing_this_has_been
                  happening_for_155_million_years⠀⇛


                # ⚓ The Conversation ☛ 2024-05-16_[Older]_Why_so_many_animals
                  have_a_third_eyelid,_including_our_pets_–_yet_humans_don’t⠀⇛


                # ⚓ The Conversation ☛ 2024-05-16_[Older]_From_silent_dialogues
                  to_vivid_memories_– here’s_how_the_science_of_inner
                  experience_could_transform_gaming⠀⇛


                # ⚓ The Conversation ☛ 2024-05-17_[Older]_How_newborn_chicks
                  are_helping_to_settle_a_centuries-old_debate_about_cognition
                  and_our_senses⠀⇛


          o § Proprietary/Artificial Intelligence (AI)⠀➾


                # ⚓ The Cyber Show ☛ Robert_Thomas:_AI_in_Music⠀⇛


                       Andy talks to Rob Thomas about creativity, AI,
                       generative and reactive music. How will music
                       evolve as an art form?


                # ⚓ Square_Enix_Announces_Major_Layoffs_in_North_America_and
                  Europe⠀⇛


                       Square Enix, the Japanese gaming giant behind
                       franchises like Final Fantasy and Tomb Raider, has
                       announced significant workforce reductions at its
                       North American and European operations.


                       In a statement, Square Enix revealed plans to lay
                       off hundreds of employees across its studios and
                       offices in the West. The cuts are part of a major
                       restructuring effort aimed at improving
                       profitability and shifting resources towards live
                       service and mobile game development.


                # ⚓ Tesla_Layoffs_To_Continue_Through_June,_Morale_Low_Among
                  Workers⠀⇛


                       employees are fearful as the rolling layoffs are
                       expected to continue through at least June.


                       Over a month into CEO Elon Musk's plan to cut at
                       least 10% of the workforce, the process is ongoing,
                       causing employees to anxiously check their messages
                       daily, uncertain of their job security.


                # ⚓ Some_Tesla_employees_worry_that_layoffs_are_coming⠀⇛


                       Some Tesla employees are concerned that layoffs are
                       imminent, possibly as soon as this weekend.


                       Rumors are circling at Tesla's offices that cuts
                       are on the horizon, seven engineers — including
                       from the Austin gigafactory and the Fremont factory
                       — told Business Insider. While there has not been
                       any official communication to teams, some workers
                       said they'd heard cuts could begin as soon as
                       Sunday.


                       Two other workers said they hadn't heard the
                       chatter about layoffs, while others said they
                       weren't taking them too seriously.


                # ⚓ Tesla_to_make_job_cuts_through_June,_leaving_workers_in
                  limbo⠀⇛


                       Over a month into Chief Executive Officer Elon
                       Musk’s plans to slash at least 10% of the company’s
                       workforce, he’s still not done. This means anxious
                       employees wake up each day to check their messages,
                       wondering if they still have a job. The rolling job
                       cuts are likely to extend through at least June,
                       according to people familiar with the matter, who
                       weren’t authorized to speak publicly about the
                       layoffs.


                       “It’s difficult to imagine the feeling of walking
                       on eggshells every day at work, uncertain whether
                       or not you’ll be able to pay your bills or feed
                       your family,” Michael Minick, a former Tesla sales
                       representative who was laid off in April, wrote on
                       LinkedIn. “It would be a relief to know that they
                       can breathe and focus on their work, without the
                       gray cloud of uncertainty looming over.”


                # ⚓ Head Topics ☛ What’s_Even_The_Point_Of_Xbox_Game_Pass
                  Now?⠀⇛


                       On May 7, Microsoft closed down four first-party
                       development studios it had acquired from Zenimax
                       Media in 2021 including Tango Gameworks , developer
                       of The Evil Within series and 2023’s surprise hit
                       Hi-Fi Rush. It’s the latest round of layoffs and
                       closures that the gaming industry, and Xbox
                       specifically, has seen in recent months.


                # ⚓ International Business Times ☛ 2024-05-17_[Older]_Microsoft
                  Allegedly_Willing_To_Transfer_800_AI_Workers_From_China_To
                  US,_Ireland_Or_Australia⠀⇛


                # ⚓ US News And World Report ☛ 2024-05-17_[Older]_UK_Watchdog
                  Decides_Not_to_Investigate_Microsoft's_AI_Partnership_With
                  France's_Mistral⠀⇛


                # ⚓ Gizmodo ☛ 2024-05-16_[Older]_Samsung_Mocks_Apple_Over_iPad
                  Commercial_Fiasco⠀⇛


                # ⚓ Daniel Miessler ☛ 2024-05-12_[Older]_One_Apple_Fanboy's
                  White-hot_Anger_at_the_iPad_Commercial⠀⇛


                # ⚓ Gizmodo ☛ 2024-05-13_[Older]_Apple_Could_Face_Its_First
                  Retail_Strike⠀⇛


                # ⚓ US News And World Report ☛ 2024-05-12_[Older]_Apple_Store
                  Employees_in_Maryland_Vote_to_Authorize_a_First_Strike_Over
                  Working_Conditions⠀⇛


                # ⚓ GeekWire ☛ Recruiting_software_company_SeekOut_lays_off
                  employees_in_another_round_of_cuts⠀⇛


                       SeekOut, a Seattle-area startup that sells
                       recruiting software and raised $115 million in
                       2022, is trimming its workforce for the second time
                       in the past eight months.


                       TechCrunch, which first reported on the layoffs,
                       reported that 30% of SeekOut’s workforce was let
                       go. The cuts were announced last week, according to
                       LinkedIn posts from affected workers.


                # ⚓ TechCrunch ☛ SeekOut,_a_recruiting_startup_last_valued_at
                  $1.2_billion,_lays_off_30%_of_its_workforce⠀⇛


                       SeekOut, an eight-year-old recruiting startup that
                       uses AI to find candidates, cut about 30% of its
                       workforce this past Thursday, TechCrunch has
                       learned.


                       “Lately, we have been spending roughly $2 to earn
                       $1, and this last fiscal year, we incurred
                       significant cash burn,” SeekOut’s CEO Anoop Gupta
                       and CTO Aravind Bala wrote in a letter to
                       employees. “Unfortunately, to put us on a
                       sustainable trajectory, we must make significant
                       employee reductions.”


          o § Defence/Aggression⠀➾


                # ⚓ Deutsche Welle ☛ 2024-05-10_[Older]_Germany_stands_by
                  Israel_as_its_'reason_of_state'_—_with_caveats⠀⇛


                # ⚓ US News And World Report ☛ 2024-05-17_[Older]_The_Slovak
                  Assassination_Attempt_Photo_That_Nearly_Got_Away⠀⇛


                # ⚓ US News And World Report ☛ 2024-05-14_[Older]_American
                  Sought_After_‘So_I_Raped_You’_Facebook_Message_Detained_in
                  France_on_2021_Warrant⠀⇛


                # ⚓ US News And World Report ☛ 2024-05-17_[Older]_Canada
                  Security_Intelligence_Chief_Warns_China_Can_Use_TikTok_to_Spy
                  on_Users,_CBC_Reports⠀⇛


                # ⚓ Vox ☛ 2024-05-17_[Older]_When_TikTok_therapy_is_more
                  lucrative_than_seeing_clients⠀⇛


                # ⚓ Gizmodo ☛ 2024-05-16_[Older]_France_Bans_TikTok_in_Island
                  Territory_After_Pro-Independence_Protests_Turn_Violent⠀⇛


                # ⚓ Gizmodo ☛ 2024-05-15_[Older]_Billionaire_Real_Estate_Mogul
                  Hopes_to_Turn_TikTok_Into_His_Utopian_Internet_Dream⠀⇛


                # ⚓ US News And World Report ☛ 2024-05-15_[Older]_Billionaire
                  Frank_McCourt_Says_He's_Putting_Together_a_Consortium_to_Buy
                  TikTok⠀⇛


                # ⚓ NL Times ☛ 2024-05-17_[Older]_Amsterdam_can't_limit_TikTok
                  famous_french_fry_shop's_line_to_less_than_10_people:_court⠀⇛


                # ⚓ US News And World Report ☛ 2024-05-14_[Older]_TikTok
                  Content_Creators_Sue_the_U.S._Government_Over_Law_That_Could
                  Ban_the_Popular_Platform [Ed: Suing for Beijing]⠀⇛


                # ⚓ Gizmodo ☛ 2024-05-14_[Older]_Raw_Milk_Sales_Skyrocket_as
                  Idiots_Believe_Drinking_Bird_Flu_Will_Give_Them_'Immunity'⠀⇛


                # ⚓ Counter Punch ☛ 2024-05-14_[Older]_The_Blue_Homeland_of
                  Turkey_Threatens_War_Against_Greece⠀⇛


                # ⚓ US News And World Report ☛ 2024-05-15_[Older]_Greece
                  Arrests_Suspected_Criminal_Gang_Leader_Wanted_by_Turkey⠀⇛


                # ⚓ CBC ☛ 2024-05-12_[Older]_Politicians_keep_getting_more
                  threats._The_head_of_the_RCMP_says_new_tools_might_be_needed
                  to_protect_them⠀⇛


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


                      # ⚓ The Age AU ☛ 2024-05-13_[Older]_Vladimir_Putin
                        removes_defence_minister_in_major_shake-up_of_Kremlin
                        security_team⠀⇛


                      # ⚓ CPJ ☛ 2024-05-16_[Older]_Ukrainska_Pravda_staff,_lead
                        investigative_reporter_Mykhailo_Tkach_receive_threats⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-05-18_[Older]_Ukraine_war:_The
                        trillion_dollar_cost_to_the_West⠀⇛


                      # ⚓ US News And World Report ☛ 2024-05-17_[Older]_Ukraine
                        Restores_Consular_Services_for_Military-Age_Men
                        Abroad⠀⇛


                      # ⚓ US News And World Report ☛ 2024-05-17_[Older]_Ukraine
                        Allows_Some_Convicts_to_Join_Armed_Forces_in_Manpower
                        Push⠀⇛


                      # ⚓ US News And World Report ☛ 2024-05-16_[Older]_IMF_to
                        Launch_New_Ukraine_Mission_to_Review_Loan,_Latest
                        Economic_Developments⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-05-15_[Older]_Putin_in_China
                        seeking_support_for_Ukraine_war_effort⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-05-15_[Older]_Ukraine_updates:
                        Kyiv_withdraws_some_forces_around_Kharkiv⠀⇛


                      # ⚓ US News And World Report ☛ 2024-05-15_[Older]_Blinken
                        Says_U.S._Rushing_Ammunition,_Weapons_to_Ukraine_Amid
                        Fierce_New_Fighting⠀⇛


                      # ⚓ US News And World Report ☛ 2024-05-15_[Older]
                        Blinken's_Guitar_Performance_in_Ukraine_Seen_as_Tone-
                        Deaf_by_Some⠀⇛


                      # ⚓ US News And World Report ☛ 2024-05-15_[Older]_Dozens
                        of_Countries_Signing_up_for_Ukraine_Peace_Summit,
                        Switzerland_Says⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-05-14_[Older]_Ukraine:
                        Kharkiv's_strategic_importance⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-05-14_[Older]_Ukraine_updates:
                        Blinken_arrives_in_Kyiv_to_show_US_support⠀⇛


                      # ⚓ US News And World Report ☛ 2024-05-14_[Older]
                        Blinken,_Guitar_in_Hand,_Tells_Ukraine_to_Keep_'Rockin'
                        in_the_Free_World'⠀⇛


                      # ⚓ US News And World Report ☛ 2024-05-14_[Older]_Ireland
                        to_Slash_Payments_to_Ukrainian_Refugees_in_State
                        Accommodation⠀⇛


                      # ⚓ Counter Punch ☛ 2024-05-13_[Older]_US_Is_Losing_In
                        Ukraine. _Blame_China,_Says_Blinken⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-05-13_[Older]_Germany's_Scholz
                        and_Nordic_leaders_call_for_more_Ukraine_aid⠀⇛


                      # ⚓ US News And World Report ☛ 2024-05-13_[Older]
                        Ukrainian_Commander,_Defence_Minister_Discussed_Aid,
                        Frontline_With_US_Officials⠀⇛


                      # ⚓ US News And World Report ☛ 2024-05-13_[Older]_UK's
                        Labour_Pledges_'Ironclad'_Commitment_to_Ukraine_During
                        Kyiv_Visit⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-05-12_[Older]_Ukraine_updates:
                        Putin_appoints_Shoigu_to_security_council⠀⇛


                      # ⚓ US News And World Report ☛ 2024-05-12_[Older]
                        Ukraine's_First_Lady_Makes_Her_Premier_Visit_to
                        Belgrade⠀⇛


                      # ⚓ Modern Diplomacy ☛ 2024-05-11_[Older]_French-Speaking
                        African_States_Under_Kremlin’s_Politico-Military
                        Influence⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-05-12_[Older]_Lithuania:
                        Security_issues_dominate_presidential_election⠀⇛


                      # ⚓ US News And World Report ☛ 2024-05-15_[Older]_EU
                        Ambassadors_Agree_to_Place_Four_Russian_Media_Outlets
                        on_Sanctions_List⠀⇛


                      # ⚓ US News And World Report ☛ 2024-05-17_[Older]_EU_Bans
                        Distribution_of_Four_Russian_News_Outlets⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-05-15_[Older]_How_China_is
                        helping_keep_the_Russian_economy_afloat⠀⇛


                      # ⚓ US News And World Report ☛ 2024-05-16_[Older]_Russia
                        Declares_Independent_News_Outlet_SOTA_an_'Undesirable'
                        Organisation⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-05-18_[Older]_Ukraine_updates:
                        Russia_may_try_taking_Kharkiv—_Zelenskyy⠀⇛


                      # ⚓ Modern Diplomacy ☛ 2024-05-17_[Older]_Russian
                        Travellers_and_Tourists_squeezed_between_Asia_and
                        Europe⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-05-17_[Older]_Ukraine_updates:
                        Kyiv_partially_halts_Russian_offensive_in_Kharkiv⠀⇛


                      # ⚓ US News And World Report ☛ 2024-05-17_[Older]_US
                        Lukewarm_on_G7_Russian_Diamond_Ban_After_Industry
                        Backlash⠀⇛


                      # ⚓ US News And World Report ☛ 2024-05-17_[Older]_Fire_at
                        Russia's_Mineralnye_Vody_Airport_Has_Been_Put_Out,_Say
                        Officials⠀⇛


                      # ⚓ US News And World Report ☛ 2024-05-17_[Older]_Russian
                        Guided_Bombs_Kill_Three,_Injure_28_in_Ukraine's
                        Kharkiv⠀⇛


                      # ⚓ US News And World Report ☛ 2024-05-17_[Older]
                        Russia's_Novorossiisk_Resumes_Partial_Loadings_After
                        Drone_Attack,_Sources_Say⠀⇛


                      # ⚓ US News And World Report ☛ 2024-05-17_[Older]_Ukraine
                        Braces_for_Heavy_Battles_as_Putin_Says_Russia_Carving
                        Out_'Buffer_Zone'⠀⇛


                      # ⚓ US News And World Report ☛ 2024-05-17_[Older]_Yellen
                        to_Push_G7_on_Bond_for_Ukraine_Backed_by_Frozen_Russian
                        Asset_Profits⠀⇛


                      # ⚓ Modern Diplomacy ☛ 2024-05-16_[Older]_Borell:
                        Georgia’s_‘Russian_law’_should_be_removed⠀⇛


                      # ⚓ CBC ☛ 2024-05-16_[Older]_How_the_West's_plan_to
                        punish_Russian_oil_backfired_|_About_That⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-05-16_[Older]_Ukraine_updates:
                        US_sanctions_Russia,_North_Korea_arms_deals⠀⇛


                      # ⚓ US News And World Report ☛ 2024-05-16_[Older]_Russia
                        Says_It_Destroys_Five_Ukraine-Launched_ATACMS_Missiles
                        Over_Crimea⠀⇛


                      # ⚓ US News And World Report ☛ 2024-05-16_[Older]_G7_to
                        Back_EU_Line_on_Frozen_Russian_Assets,_Italian_Official
                        Says⠀⇛


                      # ⚓ US News And World Report ☛ 2024-05-16_[Older]_Russia
                        Expels_UK_Defence_Attache_in_Retaliatory_Move⠀⇛


                      # ⚓ US News And World Report ☛ 2024-05-16_[Older]_Russia
                        Ramps_up_Strike_Drone_Use_on_Kharkiv_Front,_Ukrainian
                        Artillery_Crew_Says⠀⇛


                      # ⚓ US News And World Report ☛ 2024-05-16_[Older]
                        Scrambles_of_NATO_Jets_Against_Russian_Aircraft_up_More
                        Than_20%,_Source_Says⠀⇛


                      # ⚓ US News And World Report ☛ 2024-05-16_[Older]_Top
                        NATO_Commander_Says_Russian_Troop_Numbers_Insufficient
                        for_Kharkiv_Breakthrough⠀⇛


                      # ⚓ US News And World Report ☛ 2024-05-16_[Older]_US
                        Announces_New_Sanctions_Over_North_Korea-Russia_Arms
                        Transfers⠀⇛


                      # ⚓ Modern Diplomacy ☛ 2024-05-15_[Older]_U.S.,_Russia,_&
                        South_Asian_Elections:_A_Diplomatic_Chessboard⠀⇛


                      # ⚓ NL Times ☛ 2024-05-15_[Older]_MH17_convict_Igor
                        Girkin_in_court_for_appeal_against_extremism_conviction
                        in_Russia⠀⇛


                      # ⚓ The Conversation ☛ 2024-05-15_[Older]_Ukraine_war:
                        why_the_Russian army_is_still_using_morse_code_more
                        than_a_century_after_its_invention⠀⇛


                      # ⚓ CBC ☛ 2024-05-15_[Older]_Zelenskyy_postpones_foreign
                        travel_amid_Russian_offensive_in_northeast_Ukraine⠀⇛


                      # ⚓ The Age AU ☛ 2024-05-15_[Older]_‘Betraying_our
                        future’:_Georgia’s_parliament_passes_‘Russian_law’_bill
                        sparking_public_fury⠀⇛


                      # ⚓ US News And World Report ☛ 2024-05-15_[Older]
                        Blinken's_Kyiv_Song_Choice_Raises_Eyebrows_as_Ukraine
                        Fights_Fierce_Russian_Attacks⠀⇛


                      # ⚓ US News And World Report ☛ 2024-05-15_[Older]_Estonia
                        Parliament_Backs_Using_Frozen_Russian_Assets_for
                        Ukraine_Reparations⠀⇛


                      # ⚓ US News And World Report ☛ 2024-05-15_[Older]_Finland
                        Plans_to_Use_Reservists_to_Patrol_Border_With_Russia⠀⇛


                      # ⚓ US News And World Report ☛ 2024-05-15_[Older]
                        Moldova's_Justice_Ministry_Seeks_Temporary_Ban_on_Pro-
                        Russian_Party_Activities⠀⇛


                      # ⚓ US News And World Report ☛ 2024-05-15_[Older]_Putin
                        Says_Advance_of_Russian_Forces_in_Ukraine_Is_Going_to
                        Plan⠀⇛


                      # ⚓ US News And World Report ☛ 2024-05-15_[Older]_Who_Is
                        Robert_Fico,_the_Populist_Slovak_Prime_Minister_Wounded
                        in_a_Shooting?⠀⇛


                      # ⚓ US News And World Report ☛ 2024-05-15_[Older]_Russian
                        Air_Strikes_Injure_at_Least_25_in_Ukraine's_South,_Say
                        Local_Officials⠀⇛


                      # ⚓ US News And World Report ☛ 2024-05-15_[Older]_Russian
                        Troops_Leave_Karabakh,_Now_Back_Under_Azerbaijan's
                        Control⠀⇛


                      # ⚓ Modern Diplomacy ☛ 2024-05-14_[Older]_Putin’s_Russia:
                        A_Tabula_Rasa_for_Sociological_Transformations⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-05-14_[Older]_Who_is_Russia's
                        new_defense_minister_Andrei_Belousov?⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-05-14_[Older]_Why_Kharkiv_is_an
                        important_city_in_Russia's_war_in_Ukraine⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-05-14_[Older]_Why_Putin_chose
                        an_economist_as_Russia's_defense_minister⠀⇛


                      # ⚓ International Business Times ☛ 2024-05-14_[Older]
                        Russian_Women_Speaking_Mandarin,_Looking_For_Chinese
                        Husbands_Go_Viral_-_With_A_Catch⠀⇛


                      # ⚓ US News And World Report ☛ 2024-05-14_[Older]_Biden
                        Signs_Ban_on_Imports_of_Russian_Nuclear_Reactor_Fuel
                        Into_Law⠀⇛


                      # ⚓ US News And World Report ☛ 2024-05-14_[Older]_Russian
                        General_Detained_in_Suspected_Criminal_Prosecution,
                        Tass_Says⠀⇛


                      # ⚓ Copenhagen Post ☛ 2024-05-13_[Older]_Prime_Minister
                        warns_of_Russian_hybrid_attack⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-05-13_[Older]_Georgia_poised_to
                        adopt_'Russian_law'_despite_mass_protests⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-05-13_[Older]_Ukraine_updates:
                        Russia_making_'tactical'_gains_in_Kharkiv⠀⇛


                      # ⚓ US News And World Report ☛ 2024-05-12_[Older]
                        Lithuania's_Incumbent_Nauseda_Ahead_in_Presidential
                        Election⠀⇛


                      # ⚓ US News And World Report ☛ 2024-05-12_[Older]
                        Ukraine-Launched_Drone_Sparks_Fire_at_Russia's
                        Volgograd_Refinery,_Regional_Governor_Says⠀⇛


                      # ⚓ US News And World Report ☛ 2024-05-12_[Older]
                        Apartment_Building_Partially_Collapses_in_a_Russian
                        Border_City_After_Shelling._at_Least_13_Killed⠀⇛


                      # ⚓ US News And World Report ☛ 2024-05-12_[Older]
                        Exclusive-Before_Arrest_in_Russia,_US_Soldier's
                        Relationship_With_Russian_Girlfriend_Turned_Bloody,
                        Wife_Says⠀⇛


                      # ⚓ US News And World Report ☛ 2024-05-12_[Older]
                        Lithuanians_Vote_in_a_Presidential_Election_as
                        Anxieties_Rise_Over_Russia_and_the_War_in_Ukraine⠀⇛


                      # ⚓ US News And World Report ☛ 2024-05-12_[Older]_Putin
                        in_Cabinet_Shakeup_Moves_to_Replace_Defense_Minister_as
                        He_Starts_His_5th_Term_in_Office⠀⇛


                      # ⚓ US News And World Report ☛ 2024-05-12_[Older]_Russian
                        Forces_Bear_Down_on_Ukraine_Border_Town_in_Kharkiv
                        Region⠀⇛


                      # ⚓ US News And World Report ☛ 2024-05-12_[Older]_Nine
                        Killed_in_Ukrainian_Missile_Strike_on_Russian_Apartment
                        Block,_Russia_Says⠀⇛


          o § Environment⠀➾


                # ⚓ Green Party UK ☛ 2024-05-15_[Older]_Joint_Statement_with
                  Lord_Mann [Ed: Green Party issues statement to belittle its
                  issue of rampant BDS]⠀⇛


                # ⚓ Green Party UK ☛ 2024-05-13_[Older]_Green_Party_reaction_to
                  Sunak's_Policy_Exchange_speech⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-05-18_[Older]_Munich_airport
                  disrupted_due_to_climate_protesters⠀⇛


                # ⚓ US News And World Report ☛ 2024-05-18_[Older]_Munich
                  Airport_Faces_Delays_After_Climate_Activists_Breach_Runway⠀⇛


                # ⚓ Counter Punch ☛ 2024-05-17_[Older]_Local_News_Is_Vital:_Can
                  We_Survive_the_Climate_Crisis_Without_It?⠀⇛


                # ⚓ US News And World Report ☛ 2024-05-17_[Older]_With_Hunger,
                  Climate_Cuts,_US_House_Farm_Bill_Proposal_Faces_Slim_Senate
                  Odds⠀⇛


                # ⚓ TruthOut ☛ 2024-05-16_[Older]_Ron_DeSantis_Signs_Bill
                  Weakening_Climate_Regulations,_Expanding_Fossil_Fuel_Use⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-05-16_[Older]_Germany:_Climate
                  lawsuit_against_federal_government_opens⠀⇛


                # ⚓ New Yorker ☛ 2024-05-15_[Older]_It’s_a_Climate_Election
                  Now⠀⇛


                # ⚓ Scheerpost ☛ 2024-05-14_[Older]_Local_Newspapers_Are
                  Lifelines_for_Climate-Disaster_Communities⠀⇛


                # ⚓ US News And World Report ☛ 2024-05-15_[Older]_Community
                  Colleges_Offer_Clean_Energy_Training_as_Climate-Related_Jobs
                  Expand_Across_America⠀⇛


                # ⚓ US News And World Report ☛ 2024-05-15_[Older]_DeSantis,
                  Amid_Criticism,_Signs_Florida_Bill_Making_Climate_Change_a
                  Lesser_State_Priority⠀⇛


                # ⚓ TruthOut ☛ 2024-05-14_[Older]_Climate_Crisis-Driven
                  Wildfires_in_Canada_Prompt_Air_Quality_Warnings_in_US⠀⇛


                # ⚓ TruthOut ☛ 2024-05-14_[Older]_Flash_Flooding_Kills_More
                  Than_300_in_Climate-Vulnerable_Afghanistan⠀⇛


                # ⚓ The Age AU ☛ 2024-05-14_[Older]_End_to_a_secret_deal_that
                  locked_in_coal_exports_and_Sydney_truck_traffic⠀⇛


                # ⚓ NL Times ☛ 2024-05-13_[Older]_Staff_shortages_too
                  widespread_to_achieve_2050_climate-neutral_goal:_EIB⠀⇛


                # ⚓ Vox ☛ 2024-05-14_[Older]_How_to_prepare_for_another_season
                  of_wildfire_smoke⠀⇛


                # ⚓ Vox ☛ 2024-05-14_[Older]_Something_weird_is_happening_with
                  tornadoes⠀⇛


                # ⚓ Scheerpost ☛ 2024-05-13_[Older]_Climate_Extremes_Slammed
                  Latin_America_and_the_Caribbean_Last_Year._A_New_UN_Report
                  Details_the_Impacts_and_Costs⠀⇛


                # ⚓ Counter Punch ☛ 2024-05-13_[Older]_Local_Newspapers_Are
                  Lifelines_for_Climate-Disaster_Communities⠀⇛


                # ⚓ TruthOut ☛ 2024-05-12_[Older]_Unprecedented_Climate-Fueled
                  Flooding_May_Force_a_Political_Reckoning_in_Brazil⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-05-15_[Older]_The_race_to_fix
                  Africa's_poor_weather_forecasting⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-05-13_[Older]_Carbon_capture:_How_to
                  turn_air_into_clean_fuel⠀⇛


                # § Energy/Transportation⠀➾


                      # ⚓ Gizmodo ☛ 2024-05-15_[Older]_Scientist_Trap_Sunlight
                        to_Reach_Temps_of_Nearly_2,000_Degrees_Fahrenheit⠀⇛


                      # ⚓ TruthOut ☛ 2024-05-15_[Older]_New_Rule_to_Overhaul
                        Electric_Grids_Could_Boost_Transition_to_Renewable
                        Energy⠀⇛


                      # ⚓ US News And World Report ☛ 2024-05-14_[Older]
                        Maryland_Sets_Course_for_Offshore_Wind_Energy_Expansion
                        With_New_Legislation⠀⇛


                      # ⚓ US News And World Report ☛ 2024-05-13_[Older]_US
                        Energy_Panel_Approves_Rule_to_Expand_Transmission_of
                        Renewable_Power⠀⇛


          o § Finance⠀➾


                # ⚓ Counter Punch ☛ 2024-05-10_[Older]_The_Parallels_Between
                  Archaic_Entrepots_and_Modern_Offshore_Banking_Centers⠀⇛


                # ⚓ The Age AU ☛ 2024-05-17_[Older]_‘I_still_hate_the_man’:_Why
                  Wall_Street’s_billionaires_are_crawling_back_to_Trump⠀⇛


                # ⚓ The Age AU ☛ 2024-05-15_[Older]_The_code-breaking_maths
                  whiz_who_built_a_$48_billion_fortune⠀⇛


                # ⚓ US News And World Report ☛ 2024-05-17_[Older]_Vindicated_by
                  Supreme_Court,_CFPB_Director_Says_Bureau_Will_Add_Staff,
                  Consider_New_Rules_on_Banks⠀⇛


                # ⚓ CBC ☛ 2024-05-13_[Older]_Customer_who_filed_complaint
                  against_TD_Bank_refuses_to_sign_gag_order_to_get
                  compensation⠀⇛


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Deutsche Welle ☛ 2024-05-12_[Older]_Projections_show
                  separatists_losing_majority_in_Catalonia⠀⇛


          o § Censorship/Free Speech⠀➾


                # ⚓ US News And World Report ☛ 2024-05-17_[Older]_Portuguese
                  Speaker_Defends_Lawmaker's_Race_Remarks_as_Free_Speech⠀⇛


                # ⚓ Project Censored ☛ 2024-05-15_[Older]_Free_People_Read
                  Freely⠀⇛


                # ⚓ Project Censored ☛ 2024-05-13_[Older]_The_Threat_to_Press
                  Freedom_in_Congress_and_Beyond⠀⇛


                # ⚓ US News And World Report ☛ 2024-05-15_[Older]_Independent
                  UN_Experts_Say_Radical_Saudi_Arabia_Scholar_Held_for_Years
                  Should_Be_Tried_or_Released⠀⇛


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


                # ⚓ BIA Net ☛ 2024-05-15_[Older]_RSF:_Turkey’s_new_'espionage
                  bill'_threatens_media_supported_by_international_funds⠀⇛


                # ⚓ BIA Net ☛ 2024-05-14_[Older]_Reports:_Turkey_to_include
                  ‘influence_operations’_in_anti-espionage_legislation⠀⇛


                # ⚓ CPJ ☛ 2024-05-17_[Older]_Syrian_journalist_Mahmoud_Ibrahim
                  arrested_after_post_on_anti-Assad_protests⠀⇛


          o § Civil Rights/Policing⠀➾


                # ⚓ Counter Punch ☛ 2024-05-15_[Older]_Why_African_Homophobia
                  is_Still_the_Real_Western_Import⠀⇛


                # ⚓ HRW ☛ 2024-05-16_[Older]_Japan:_Press_Saudi_Arabia_on_Human
                  Rights⠀⇛


                # ⚓ International Business Times ☛ 2024-05-17_[Older]_Newcastle
                  City_Council_Urged_to_Address_Human_Rights_Concerns_Amid
                  Saudi_Investment_Controversy⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-05-11_[Older]_Spy_scandal:_Why_did_a
                  Polish_judge_'defect'_to_Belarus?⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-05-11_[Older]_Georgia:_Thousands
                  protest_'foreign_agent'_bill_in_Tbilisi⠀⇛


                # ⚓ Project Censored ☛ 2024-05-16_[Older]_Promises_to_Women
                  Health_Activists_in_India_Not_Yet_Met_Despite_ASHA_Strike
                  Suspension⠀⇛


                # ⚓ Project Censored ☛ 2024-05-16_[Older]_Demand_for_University
                  by_Women_in_One_of_India’s_Poorest_Districts⠀⇛


      § Monopolies/Monopsonies⠀➾


          o § Patents⠀➾


                # ⚓ 2024-05-14_[Older]_The_USPTO's_Proposed_Terminal_Disclaimer
                  Rule:_A_Litigator's_Perspective⠀⇛


                # ⚓ 2024-05-12_[Older]_USPTO_Proposed_Rule_Change_to_Terminal
                  Disclaimer_Practice⠀⇛


                # § Kangaroo Courts⠀➾


                      # ⚓ IP Kat ☛ 2024-05-12_[Older]_[UPCKat]_Access_to
                        confidential_information_by_parties_and_the_public_in
                        the_UPC [Ed: UPC is illegal and unconstitutional, but
                        its longtime shill is trying to legitimise this crime
                        for profit, which is a travesty]⠀⇛


                      # ⚓ IP Kat ☛ 2024-05-13_[Older]_Stretching_the_cheese:
                        Contradictory_evidence_for_a_purported_technical_effect
                        relied_on_for_inventive_step_(T_0629/22) [Ed: EPO
                        kangaroo courts giving the impression of lawfulness
                        again]⠀⇛


                      # ⚓ IP Kat ☛ 2024-05-17_[Older]_DABUS_in_China:_So_far,
                        it_is_0–2 [Ed: "DABUS" is just trolling the system with
                        buzzwords, hype, and misnomers]⠀⇛


          o § Trademarks⠀➾


                # ⚓ IP Kat ☛ 2024-05-12_[Older]_Italian_Supreme_Court_refers
                  questions_to_CJEU_on_conflicts_between_GIs_and_trade_marks⠀⇛


                # ⚓ IP Kat ☛ 2024-05-14_[Older]_Louis_Vuitton_successful
                  against_knock-off_trade_mark [Ed: Europe's richest man gets
                  the courts' nod]⠀⇛


                # ⚓ IP Kat ☛ 2024-05-15_[Older]_[Guest_post]_Conference_Report
                  –_Fashion_Reborn:_The_Age_of_AI⠀⇛


                # ⚓ IP Kat ☛ 2024-05-15_[Older]_NOT_MILK_IS_NOT_DISTINTICTVE,
                  SAYS_THE_GENERAL_COURT⠀⇛




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