𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Friday, December 24, 2021
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Generated Sat 25 Dec 02:42:51 GMT 2021
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/2021/12/24/


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

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

⦿ The EPO ’Mafia’ | Techrights

⦿ [Meme] The Most Inclusive Greeting We Can Think of | Techrights

⦿ IRC Proceedings: Thursday, December 23, 2021 | Techrights

⦿ Alexandre Oliva’s Open Letter on Richard Stallman | Techrights

⦿ The Car Drives You  -  Part III  -  The Very Concept of a Car Has Changed | Techrights

⦿ The Car Drives You  -  Part IV  -  Today’s Cars Come With Up to 3,000 Chips and Security Isn’t of Concern | Techrights

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
		http://techrights.org/2021/12/24/epo-mafia-culture/#comments
		http://techrights.org/2021/12/24/inclusive-greetings/#comments
		http://techrights.org/2021/12/24/irc-log-231221/#comments
		http://techrights.org/2021/12/24/lxo-rms/#comments
		http://techrights.org/2021/12/24/on-car-owners/#comments
		http://techrights.org/2021/12/24/unnecessary-complexity-in-cars/#comments

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
		http://techrights.org/2021/12/24/jami-taranis/#comments
		http://techrights.org/2021/12/24/sway-1-7-rc/#comments

                    ䷩ 𝚕𝚒𝚗𝚎 63

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/12/24/epo-mafia-culture/#comments
    Gemini version at gemini://gemini.techrights.org/2021/12/24/epo-mafia-culture/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.24.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ The_EPO_‘Mafia’⠀✐


Posted in Europe, Patents at 8:12 pm by Dr. Roy Schestowitz


Video_download_link | md5sum ca81779d727fd48c518e5be02bc689a9


http://techrights.org/videos/epo-italy.webm


Summary: When nations are run by well-organised_cartels or what some have
dubbed “mafias” we should not expect the legal system to curtail illegal
operations; today’s video takes stock of Slovenia and then Italy — the subjects
of last night’s articles


THERE is no intention to publish much today, but last night we published a
couple of articles, the primary of which concerned Italy’s relationship with
the EPO, whose notorious dictator_had_an_Italian_name (despite the French
nationality) and his French_successor had a Portuguese name because of his
father, who had died decades ago under tragic circumstances.


“Internally, the EPO has long been characterised as a “Mafia” (by people who
work there!), so maybe a country like Italy should not be expected to tackle
the problem as much as perpetuate it.”This sort of Mediterranean era of the EPO
has been an epic failure; patent quality was abandoned in order to turn_the_EPO
into_some_kind_of_a_bank and a banker represented Italy at the EPO since 2006
despite lack of a track record in patents. So this kind of kakistocracy
jeopardises the legitimacy of the patent system not just in Europe but
internationally; of course, Team UPC doing all sorts of illegal and
unconstitutional things won’t help either. Internally, the EPO has long been
characterised as a "Mafia" (by people who work there!), so maybe a country like
Italy should not be expected to tackle the problem as much as perpetuate it. █



                    ䷩ 𝚕𝚒𝚗𝚎 115

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/12/24/inclusive-greetings/#comments
    Gemini version at gemini://gemini.techrights.org/2021/12/24/inclusive-greetings/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.24.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_The_Most_Inclusive_Greeting_We_Can_Think_of⠀✐


Posted in Site_News at 11:15 am by Dr. Roy Schestowitz


Unless you’re in the southern hemisphere!


       🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Happy_turkey_day_(unless_you're_vegetarian)⦈_


Summary: Techrights will be posting as usual after dinner


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

                    ䷩ 𝚕𝚒𝚗𝚎 1314

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

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✐ IRC_Proceedings:_Thursday,_December_23,_2021⠀✐


Posted in IRC_Logs at 2:36 am by Needs Sunlight


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✐ Alexandre_Oliva’s_Open_Letter_on_Richard_Stallman⠀✐


Posted in Free/Libre_Software, FUD, GNU/Linux, GPL at 9:21 am by Guest
Editorial Team


                     🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Alexandre Oliva⦈
                                 Image_source


Summary: The person whom many consider to be the ‘heir’ of RMS responds to
common accusations, which are sadly not based on actual facts


The other day, I sent email to a celebrated feminist leader in the FLOSS
community, letting her know about some good news I’d just come across that I
thought would be of her interest, and congratulating her for some of her
accomplishments. My email signature, pointing to https://stallmansupport.org,
caught her attention, and she mentioned her disagreement with it in her kind
and respectful response. I thought a lot about how to respond, and I’ve finally
sent her the following response.


I’m sorry it seems to have been the most relevant part of my email to you. I
almost took it out, suspecting you might differ and be offended, but I ended up
leaving it there because I didn’t think you deserved dishonesty from me. This
has been in my signature in emails I’ve sent out since May 3rd, and removing it
didn’t feel honest.


I’ve been close to RMS for over 25 years. I, my wife and my daughter have
hosted him a number of times, and arranged for others to host him a larger
number of times. People who admire him, and people who hardly knew him. He was
never easy to deal with, he’s persistent and often obsessed about issues that
catch his attention. But harassment?


Harassment, to me, is ganging up on someone in a hate letter to bring them
down. A hate letter that attempts to disguise its actual motivations by
resorting to a bunch of shocking but false accusations, exaggerations and
misrepresentations.


As for the experiences and reports you got… An FSF board committee whose
members AFAICT all wanted RMS out investigated reports about RMS for over two
years, before and after RMS resigned, and despite all the second-hand rumors,
they could never get to any concrete findings. I have independently
investigated various claims and invariably came to dead ends. Given how many
false reports and ad hominem attacks on Free Software he’s been targeted with,
it wasn’t at all unthinkable to conclude that this was yet another character
assassination attack without substance.


He, clumsy, obsessive, meltdown-prone and sometimes harsh, as our shared
condition makes us, has always been an easy target for this kind of
discrimination. Besides, the movement he started and leads threatens various
powerful monopolies, which makes him more of a target of such attacks. It’s
easy and disappointing to see how his supposed offenses don’t seem to motivate
action when committed by actual celebrities who work for the corporate forces
who lead and who are served by the attacks on him.


Of course none of this proves him innocent, but that’s what’s suggested by the
absence of credible evidence and the exclusivity of dead-end second-hand
hearsay and fabrications. In case the people you know personally who have
alleged harassment by RMS would like to report it to me, my opinion may change,
and if they’re willing, I may pass it on to the FSF board. But, so far, what
I’ve seen has been limited to false and dehumanizing allegations to support the
discrimination of a person who fights for freedom and justice untiringly,
without regard for much else, and with some traits that are hard for
neurotypicals to understand or like.


I’m disappointed that someone like you, who purports to fight for justice and
against discrimination, would join the beating up, let alone to label him a
celebrity to further dehumanize him. But then, I have only my experiences to go
by, not yours, and certainly not the reports you heard and chose to believe.
Not knowing what they are, I can’t tell whether they justify mistreating him.


I can, howvever, tell that nothing justifies lying in false and exaggerated
accusations: if the facts are not shocking enough to support that amount of
mistreatment, fabricating alternative facts to carry it out doesn’t make them
so. It rather makes the attack itself unjustified, disproportional and
dishonest.


Subscribing ot the letter might be understandable in the height of emotions,
but refraining from revoking the signature once it becomes clear that it’s no
more than a collection of lies speaks a lot more about the moral alignment of
the subscriber than about that of the target of the hate letter.


I hope these words and facts will find ressonance in your conscience and bring
you to align your behavior with the rightful pursuit of justice and fight
against the various forms of discrimination. Undoing the injustice you’ve been
part of would be a long-overdue first step, even if other unrelated reasons
remain to seek and pursue justice for or against this one person.


Happy holidays, and keep up the fights for good,


–
Alexandre Oliva, happy hacker https://FSFLA.org/blogs/lxo/
Free Software Activist GNU Toolchain Engineer
Disinformation flourishes because many people care deeply about injustice
but very few check the facts. Ask me about https://stallmansupport.org


So blong █


===============================================================================
Copyright 2007-2021 Alexandre Oliva


Permission is granted to make and distribute verbatim copies of this entire
document worldwide without royalty, provided the copyright notice, the
document’s_official_URL, and this permission notice are preserved.


The following licensing terms also apply to all documents and postings in this
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assumed to be held by Alexandre Oliva.


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                    ䷩ 𝚕𝚒𝚗𝚎 1619

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/12/24/on-car-owners/#comments
    Gemini version at gemini://gemini.techrights.org/2021/12/24/on-car-owners/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.24.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ The_Car_Drives_You_—_Part_III_—_The_Very_Concept_of_a_Car_Has_Changed⠀✐


Posted in DRM, Free/Libre_Software at 12:55 am by Dr. Roy Schestowitz


                       🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Car in Cuba⦈
 Sometimes it feels like “dumb” cars are the smarter choice because they take
                      instructions from their true owners


Summary: The debate or the conversation about what it means to be car “owners”
relates to issues discussed since the 1980s in the context of software (or
code-sharing/code-altering practices)


SO IN Part_I and in Part_II we focused on loss of ownership and cost/price
hikes associated with car ‘ownership’. These issues are closely connected;
they’re intertwined because when few vendors control the car you supposedly
bought (paid for) they can keep bilking and milking. They’re constantly in
control or something they supposedly gave away in exchange for a fee (price of
purchase). It wasn’t always this bad as only when repairs were needed the
vendors became potentially needed (just potentially because with simpler and
standardised components one could work around them, whereas proprietary
components make “support” or “maintenance” a monopoly or merely a small set of
shared, price-fixing monopolies).


“They’re constantly in control or something they supposedly gave away in
exchange for a fee (price of purchase).”As cars are becoming more computerised
(their technical composition or breakdown may be the subject of future parts),
especially in the software sense (not mechanics), these reasonably old issues
are fast becoming issues pertaining to software freedom.


Last week we shared_a_video_of_what_Toyota_had_begun_doing. Here it is again:


Video_download_link


http://techrights.org/videos/toyota-thinks-they-own-your-car.webm


This got the ball rolling.


“I realized what they were doing,” Ryan wrote last week. “They tried selling it
as a “feature”. Like, it could see the size of the Keurig logo and figure out
whether you were brewing a cup or a carafe of coffee. But there was no need to
trademark that. What they were doing was making it so nobody could copy the
icon that it was looking for, so it would refuse to work at all if you used a
physically compatible coffee pod. And many of the alternative pods use far less
non-biodegradable mass. Gordon’s Food Service sells theirs in bulk and it’s
just a lid along with a filter full of coffee. There’s no hard plastic at all
in the pod. And those never worked with the K 2.0. The 2.0 machines were a
total disaster and it wasn’t long before they all got clearanced out. They blew
up right in Keurig’s face. And the whole thing came about when Keurig’s patent
on the coffee pod expired, because trademarks on the logo that tells it to brew
don’t expire like patents do.


“Notice the similarity between DRM in appliances (physical things like pods and
cartridges), information/multimedia, and cars.”“So they were trying to extend
their monopoly using whatever part of the law they could in order to keep out
competitors who drive prices down. The market refusal of the K 2.0 machines was
an unexpected success against DRM. But people put up with behavior like this in
an iPhone. Why? It’s so expensive to develop software for any of Apple’s
products that unless you already have a Mac laying around that’s new enough and
don’t mind wasting $100 per year to keep your developer account current,
there’s no way you think about developing freeware.


“F-Droid’s model obviously doesn’t work this way at all. The iPhone is pretty
much a meme. And we’re in the higher points of the bubble at this point because
they’re getting so ungodly expensive that they’re losing marketshare. They say
they’re fine with that, and maybe they are. Selling $2,000 phones that cost
them $200 to produce to 70% of the people who would buy them at a lower price
is effectively being paid to produce less. But at some point, they drive so
much of the market over to Android that developers no longer see the economic
incentives of having a huge base of customers on the iPhone.”


Notice the similarity between DRM in appliances (physical things like pods and
cartridges), information/multimedia, and cars. The agenda sort of converges
across domains and the methods are similar. Ultimately, the buyer suffers.


“I don’t like any of the new features, including “self-drive”,” Ryan said. “The
driver is still liable in civil and criminal matters regarding what the
software does, including if it causes an at-fault accident. But now, you also
have to spend $80 a year subscribing to a remote starter that’s already on the
car, if you buy a Toyota, or else it will stop working. This is like Windows
“Anytime Upgrade”, where all of the features are there, but Microsoft disables
them unless you buy a new activation code. If you have the Toyota for 15 years,
it costs $1200 to have the remote starter work and previously it cost $200 or
so to have a good one put on the car that works forever. But now, you also have
to spend $80 a year subscribing to a remote starter that’s already on the car,
if you buy a Toyota, or else it will stop working. They like to slip “little
things” in past you that don’t register while you’re buying the car. Who is
thinking about a remote starter that costs them $1200-1600 over the life of the
car? What if you buy the car and then they raise the price later?”


“The ironic thing is, with plate readers seemingly everywhere (but covert;
they’re barely visible) you nowadays get better privacy as a passenger in a
taxi than as driver of ‘your’ ‘own’ car, especially if that car was made in
recent years.”Never mind the increasing costs of increasingly-complex repairs
they_prevent_you_from_doing_on_your_own. If you cannot repair your own thing,
is it your own at all? And if you cannot drive privately, are you being
babysat? Today’s cars are being made hostile (towards the buyer) by default;
“new ones have always-on GPS + “blackbox” recorders,” one associate noted.
“Even though you don’t own a car, you have a stake in the outcome of the
consultation[s]. Thus I would encourage you to send them a few words at least.”


The British_consultation_ended_last_month, but it is still possible to contact
politicians. We need to tackle these issues before they become more widespread
(like DRM on printers and coffee machines) and thus irreversible. We need to
contact people who can put an end to it, legally, as “that’s how it works on
both sides of the Atlantic,” the associate noted. “That’s one of the reason
Louis [from the video above] has collected money to buy his own lobbyists for
the Fight to Repair work…”


The ironic thing is, with plate readers seemingly everywhere (but covert;
they’re barely visible) you nowadays get better privacy as a passenger in a
taxi than as driver of ‘your’ ‘own’ car, especially if that car was made in
recent years. In the next part we’ll look at what nowadays makes up a “modern”
car. █


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⢹⠠⢻⣷⡏⠶⡎⠲⢠⠳⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣾⠀⠀⠀⠀⠀⠓⠊⡿⠟⠛⠛⣿⡟⠛⠛⠛⠛⠁⠀⡟⡄⠈⢸⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⢻⣟⠟⠲⡟⠀⠘⣿⣢⣠⠀⠈⡀⡙⠛⠟⠇⠁⡕⡈
⡟⢶⡀⡀⠐⠋⠇⠈⠀⠀⢈⣯⡡⢙⣿⣿⣿⡿⠀⠃⠀⠃⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠇⢁⢰⣴⣟⢿⡀⣿⣿⣿⣿⡿⢷⡿⠘⠤⠁⠈⠉⡀⠀⠉⠂⠀⠠⣴⠀⢠⡢⠉⠀⢀⣑⠄⣶⣤⣔
⠃⠐⢾⣾⣿⣄⠤⡀⠀⣱⣲⡿⠫⡼⡆⢈⢿⣅⣠⣤⣤⣤⣤⣤⣤⠤⣤⣤⣿⣭⣭⣭⣿⣿⣿⣿⣖⣄⣀⣀⣀⣠⢴⠋⠉⠉⡿⠃⢸⣿⣯⠉⠘⠑⠋⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠤⢠⣂⠌⠀⠈⠀⢠⡄⣀⠉⠛⡩
⠈⠒⠽⢈⡂⠆⢦⡔⠒⠿⣿⣿⣌⣉⣽⣽⢷⣿⣿⣿⣿⣿⣿⣿⣿⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢁⣥⣶⡿⣿⢻⣀⣠⣶⣿⣦⣅⠡⠤⢠⣁⡀⠀⠀⠀⠀⡡⠀⢐⣐⢬⡆⠈⠁⡀⠀⠘⣿⡄⠀⠀⠀
⡡⠀⠋⢿⣗⣀⣾⡌⢷⣞⡀⣹⣿⣿⣿⣿⣮⡿⢿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡳⢿⣿⢣⠟⢈⢹⣿⣿⣿⣿⣿⣿⣾⡜⠛⠁⠀⠀⠀⡀⢀⡤⠉⠀⣁⣹⢁⢠⠂⣀⡈⢉⣶⠀⠀⠀
⢠⠰⢒⣿⣁⡾⠚⠀⢈⣿⣷⣿⣿⣿⣿⣿⣿⣷⣌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢰⣿⣿⣼⠀⣾⣿⣿⣿⣿⡛⠻⢿⣿⡿⠀⠀⠀⠀⠠⠝⣍⠋⠀⣩⠎⠀⣂⡀⢈⣽⣷⢼⣷⠀⠀⠀
⢀⣈⡙⠀⠮⠄⠀⠠⢟⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣰⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣤⣤⣶⣤⠀⢮⣒⠀⠀⠀⠁⠁⠿⣟⠨⠋⠘⢀⡵⣋⢠⣇
⠠⠀⠠⠀⠀⡠⠁⠰⢓⣋⣠⠁⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣄⢸⣯⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠿⠟⣩⢭⠻⠃⢀⣿⠁⣿⣽⣿⣿⣿⣿⣿⣟⣿⡛⢿⣿⣿⢀⣀⡥⡄⠀⠀⠀⠀⢀⠀⠶⠂⢀⠀⠈⠈⡛⠃⠉
⠀⠃⠀⠀⠀⠀⠁⠀⠙⠓⠉⠀⠈⣽⣿⣬⣭⣭⣭⣭⣭⣍⣉⣉⣩⣛⣛⣛⣛⣛⣻⣿⣿⣿⣾⣿⣿⡆⢻⣤⢠⠇⠀⢸⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣗⠄⠴⢿⡿⣛⠧⠡⠀⠀⠂⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⠀⠠⢶⠂⠀⠀⢠⣤⣀⣀⣈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠙⠻⠿⠟⠟⠻⡏⠇⠀⠈⠁⠀⠀⠘⢠⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡗⠀⠀⠶⢴⡓⠦⢀⡐⠀⡀⠀⠀⠀⠀⠑⠀
⠦⢤⠅⠈⠁⠀⢒⠁⢨⡀⢂⣈⡉⠉⠉⠉⠉⠉⠉⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠓⠓⠒⠒⠒⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⡿⠛⠸⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠴⠏⠀⠀⠀⠹
⠤⠈⣀⣴⣷⣾⣿⣦⣤⣤⣤⣄⣀⣒⣒⣂⠀⠀⠤⠀⢤⠤⡤⡤⣤⡤⣄⣀⣀⣀⡀⠀⠀⠤⠤⢄⣥⠤⠀⠠⠒⠀⣀⣤⢸⣿⣿⣿⣿⣿⣿⣿⡝⢿⡿⠙⠂⠙⠻⡧⠒⠀⡄⠀⠄⠀⠀⠐⡂⠀⠊⠀⠀⠀⠀⠀⠀⢈
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣤⢼⣼⣯⣷⢷⣽⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠈⠉⠉⠀⠈⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠑⠛⠛⠛⠛⠛⠉⠋⠁⠉⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣟⡋⢁⠀⠀⠀⠀⠀⠀⠠⠌⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⣍⡉⠔⠀⢐⠀⠀⠀⠐⢊⡤⠐⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡷⡄⠤⠂⠠⣀⣀⣋⡑⢢⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣶⣤⣶⣶⣶⣦⣦⣤⣶⣴⣶⣶⣶⣶⣶⣖⣶⣶⣶⣶⣦⣤⣤⣴⣶⣶⣶⣶⣀⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⡏⣊⡵⣥⡴⠠⡁⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠿⠟⣿⠛⠿⡟⠟⡯⣽⢭⣭⣭⣟⡶⣠⣷⡾⡿⠉⣻⣿⣤⣤⣿⣀⣀⠠⣀⣀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 1794

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/12/24/unnecessary-complexity-in-cars/#comments
    Gemini version at gemini://gemini.techrights.org/2021/12/24/unnecessary-complexity-in-cars/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.24.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ The_Car_Drives_You_—_Part_IV_—_Today’s_Cars_Come_With_Up_to_3,000_Chips_and
Security_Isn’t_of_Concern⠀✐


Posted in Free/Libre_Software, Security at 9:10 pm by Dr. Roy Schestowitz


 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Consulting firm Deloitte Touche Tohmatsu Limited estimates
    that as of 2017, some 40% of the cost of a new car can be attributed to
    semiconductor-based electronic systems, a cost doubling since 2007. It
 estimates this total will approach 50% by 2030. The company further predicts
that each new car today has about $600 worth of semiconductors packed into it,
                consisting of up to 3,000 chips of all types.⦈
 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Further, internal and external vehicle communications have
   exploded in the past decade. In 2008, there were an estimated 2,500 data
 signals being exchanged among the ECUs in a luxury car. Volvo’s Antinyan says
   that today more than 7,000 external signals connect the 120 ECUs in Volvo
 vehicles, and the number of internal vehicle signals being exchanged are two
orders of magnitude greater. Consulting firm McKinsey & Company estimates this
        information can easily surpass 25 gigabytes of data an hour.⦈
                           Article from 2021 (IEEE)


Summary: The concept of software freedom inside cars has become a distant
fantasy; the cars that are being manufactured nowadays disregard security and
embrace unnecessary complexity


ABOUT a week ago we started this series. We looked at a consultation right here
in the UK — a misguided bit of text which characterises modifying one’s own car
as “tampering”. Shades of “sideloading” in the context of software…


Demonising those who exercise control over a device they bought?


We then looked at what Toyota had begun doing, published Part_I about the
issue, and then — several days later — expanded in Part_II and in last night’s
Part_III. We’ve meanwhile, in parallel, studied just what amount of computing
had crept into today’s cars (gradually over the years). The data isn’t entirely
secret, but there are not many publications about it; more importantly, there
seems to be no public debate about software freedom in that context. We wish to
change that.


“The data isn’t entirely secret, but there are not many publications about it;
more importantly, there seems to be no public debate about software freedom in
that context.”Last week we wrote that in today’s cars there’s “not just a
computer onboard but several”; a person contacted us to say “not just a
computer onboard but many“…


OK, but just how many exactly? Obviously that depends on the car, but there are
many overlaps across models and brands.


I am not clueless about today’s cars; I did drive in the past and a decade ago
I went to a car agency (that was the last time). Even in 2011 things were
already starting to look grim. It was a Toyota agency.


“Most car fanatics I know consider the car a single system and ignore the many
microcontrollers,” an associate noted a week ago. “I have the feeling that on
top of that most of the information is proprietary…”


Certainly, in my experience, the media does not inform people about the
situation; I only realised how big an issue it was when supply chain woes
caused price spikes and critical shortages; it was getting too hard to get all
the bits to assemble new cars [1, 2].


So we decided to study a number authoritative pages about the number of
processors and the nature of the tasks they perform. I already knew about the
“micro” (processors) ones, which aren’t exactly new and are installed at the
ends/edges, but was not sure how they qualify with respect to “computer” (the
components and their complexity may vary in definition).


As our associate put it, “there are many microcontrollers, I guess based on
activities, and at least two full computers.” There are publications[PDF] and
full_articles_about_it (not necessarily new). As our associate explained,
“another site, with a comment going to a dead MIT link, suggests 50 to 70
“Electronic Control Units” in cars as of ten years ago.”


That’s the last time I went to a car agency. It has certainly increased a lot
since then.


“That’s even older” than this (“More Auto Computers Means More Complicated,
Costly and Longer Repairs” according to this article from 2016), the associated
noted, quoting various bits. This page says “high-end cars have as many as 100,
and they’re accompanied by 60 to 100 different electronic sensors…”


And these parts are controlled by computers: “Engine control, Exhaust control,
Heating/cooling, Fuel pump, Water pump, Transmission, Power steering, Brakes,
Traction control, Airbags, Collison warning, Parking assist, Backup monitoring,
Door and trunk locks, Power windows, Climate control, Power seats, Wipers,
Charging system, Interior lighting, Brake lights, turn signals, Headlamps/
daytime running lamps, Navigation, Car audio, and GPS…”


And “add side- and rear-view mirrors to that long list above,” our associate
noted.


“There are security/safety implications, as we covered earlier this year (in
summer)…”Remember that these are all proprietary, some go decades back, but now
they get connected to the Internet and more (e.g. Bluetooth connectivity with
another device, which may be compromised). So some are connected less directly
to the Net, e.g. their local (car) mother ship, which is in turn controlled by
a bigger mother ship (vendor/government/cracker).


There are security/safety implications, as we covered_earlier_this_year (in
summer), and articles_like_“How_a_Hacker_Could_Hijack_Your_Car_While_You_Drive”
(Tom’s Guide) that deal with the main question.


“It’s largely ignored because, as mentioned, car fans see the vehicle as a
physical object still when in reality most of it is software,” our associate
said. “Yes, all proprietary and restricted so as to lock out independent repair
shops and mechanics. There was a lot of attention to this about 10 years ago in
the various security conferences. Then a burst of information as some of the
embargoes were lifted. I presume the quietness on that front means that more of
the researchers are under NDAs again. Shmoocon, DefCon, and BlackHat usually
have automative tracks.”


We hope the conversation will be resumed and extended to the Free software
world. We need to do more to highlight the dangers and tackle the problem.


“General-purpose computing is niche nowadays,” our associate said, “and that
niche has been shrinjing. The multinationals also appear to be aiming to
eliminate it eventually. UEFI, TPM, DRM etc…”


“We hope the conversation will be resumed and extended to the Free software
world. We need to do more to highlight the dangers and tackle the
problem.”Well, almost nobody covers these issues, so it’s a vacuum we can fill
in the coming weeks/months. We invite groups like the FSF (even SFC and OSI) to
do the same.


More than a decade ago we still saw people saying that software was eating the
world (citing famous old words), but nowadays people talk about “apps” and
“clown computing” and all sorts of other nonsense. Not too long ago an article
entitled “How_Software_Is_Eating_the_Car” was published in IEEE Spectrum. To
quote: “Predictions of lost global vehicle production caused by the ongoing
semiconductor shortage continue to rise. In January, analysts forecast that 1.5
million fewer vehicles would be produced as a result of the shortage; by April
that number had steadily climbed to more than 2.7 million units, and by May, to
more than 4.1 million units. The semiconductor shortage has underscored not
only the fragility of the automotive supply chain, but placed an intense
spotlight on the auto industry’s reliance on the dozens of concealed computers
embedded throughout vehicles today.”


Get ready for some numbers that are more recent: “The company further predicts
that each new car today has about $600 worth of semiconductors packed into it,
consisting of up to 3,000 chips of all types.”


“The IEEE article above speaks of “7,000 external signals”, “120 ECUs” and so
on. They say “Electronic Control Unit” (as euphemism for a computer).”Up to
3,000.


As our associated noted, “security has to be part of the design process, but it
hasn’t been, thus we end up with not just CAN but with everything integrated
with it.”


The IEEE article above speaks of “7,000 external signals”, “120 ECUs” and so
on. They say “Electronic Control Unit” (as euphemism for a computer).


In the next part we’ll continue this discussion. One growing concern is, the
lobbyists of car-making giants are trying to pass new laws mandating all sorts
of things which eventually take “old” or “dumb” cars off the road (even if some
manufacturers produce new alternatives that opt out of this whole mess). █


⣿⠿⢿⣿⣿⣿⣿⡿⢿⢿⣿⣿⡿⢿⣿⣿⣿⡿⠿⣿⢿⣿⢿⠿⣿⣿⠿⢿⣿⣿⣿⢿⣿⣿⠿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⢿⣿⣿⢿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿
⣧⣙⣅⣀⣆⣀⣀⣃⣸⣀⣘⢐⣇⣚⣰⣀⣸⣇⣣⣐⣘⣀⣸⣀⣂⣺⣇⣇⣠⣃⣐⣐⣁⣺⣇⣇⣀⣂⣐⣂⣀⣔⣀⣀⣿⣘⣁⣀⣂⣠⣂⣂⣘⣇⣂⣀⣃⣀⣂⣀⣔⣐⣀⣧⣂⣨⣀⣸⣇⣀⣸⣔⣅⣿⣿⣿⣿⣿
⣿⡛⢛⠟⣟⣻⡿⠿⠿⠿⠿⢿⡿⠛⡛⠛⢻⡿⢿⢛⠿⠻⡿⢿⠿⠿⠿⠟⣿⠿⠛⡿⢿⠿⠿⠿⠿⢿⠿⠿⠿⣿⠿⠿⠿⣿⠻⡿⢿⠿⠻⠻⠟⠻⠿⢿⠻⢿⠟⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⣬⣬⣦⣥⣯⣧⣤⣬⣥⣴⣽⣷⣴⣵⣷⣤⣧⣵⣼⣮⣬⣤⣽⣬⣮⣦⣤⣿⣥⣬⣧⣼⣬⣤⣼⣤⣿⣬⣤⣥⣷⣽⣤⣤⣽⣤⣮⣿⣤⣬⣤⣥⣮⣦⣬⣤⣵⣥⣧⣥⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠻⠛⠛⡻⠙⡻⡛⠛⢟⠙⡛⢛⠛⡛⢛⠿⠙⠛⡟⠛⠛⢹⡟⠋⠛⢟⡛⢛⢛⠟⠋⢟⣻⠛⠛⠛⡛⠛⢛⠛⠛⣿⡟⢿⢛⢛⠟⠛⡿⡋⢛⠟⠋⡛⠉⡛⠛⢻⡟⡋⢛⢟⡛⢻⡭⡏⠙⡍⡍⣿⣭⢻⣿⣿⣿⣿⣿
⣷⣾⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣷⣶⣶⣷⣶⣶⣶⣷⣶⣶⣾⣶⣵⣶⣷⣶⣶⣶⣶⣼⣶⣾⣶⣶⣷⣶⣿⣶⣶⣷⣶⣶⣶⣶⣦⣼⣷⣶⣶⣶⣶⣾⣶⣶⣾⣶⣷⣾⣶⣾⣿⣿⣿⣿⣿
⣟⠙⠉⠩⠏⠩⠏⠉⠉⠋⢹⠩⠈⠸⠹⡏⠫⠋⠏⠃⣏⠉⡅⠰⢿⠉⠩⠋⠩⠙⠝⠉⠩⢨⢹⠔⡱⢠⠈⢻⠨⠋⣹⠗⠅⠼⠊⠰⡻⣷⢰⠈⠋⢹⠩⠫⠋⠩⠋⠹⠹⠉⡝⣽⢀⠏⢩⠩⠈⠋⡏⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⡿⣿⣷⣿⣿⣿⠿⡿⣿⢿⠿⣿⣿⣿⣿⣿⡿⣿⣿⣷⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢂⣰⣀⣑⣀⣑⣐⣀⣇⣂⣘⣘⣸⣁⣁⣁⣂⣎⣇⣸⣈⣠⣸⣗⣂⣀⣾⣐⣀⣑⣀⡠⣹⣇⣘⣸⣘⣇⣀⣪⣀⣘⣀⣿⣀⣐⣁⣪⣀⣷⣀⣌⣪⣰⣀⣎⣇⣺⣸⣁⣁⣅⣀⣏⣐⣑⣅⣈⣂⣀⣑⣃⣑⣁⣆⣻⣿
⣿⣿⡿⡿⡟⢿⢿⠟⡿⣿⡿⡿⣿⣿⢿⣿⢿⣿⣿⣿⠿⡿⡿⢿⣿⡿⣿⢿⢟⣿⢿⣿⡿⣿⣿⢟⣿⠿⡟⠿⡻⣿⠟⣿⢻⢿⡿⣿⢿⢛⡿⡟⢻⡿⢿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣠⣤⣬⣤⣤⣤⣧⣧⣿⣤⣯⣼⣼⣌⣧⣥⣤⣼⣤⣤⣤⣧⣼⣧⣀⣷⣥⣼⣧⣼⣧⣧⣧⣼⣵⣍⣤⣮⣤⣧⣧⣥⣧⣄⣧⣤⣧⣧⣼⣽⣤⣼⣯⣢⣿⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢛⠻⠿⠿⠟⢿⢿⢿⡟⡿⠿⠿⡿⠿⠿⢟⢻⠿⠿⡿⢻⡿⠿⠿⡿⡿⠿⠿⠟⣿⠿⠿⠻⡟⠿⢻⢿⡿⠿⠿⠿⠿⠿⠿⢿⠿⢿⠿⠿⠿⠻⠿⠿⠿⡟⢿⠿⠿⠿⣿⠿⠿⠿⡟⠿⡿⠻⠿⢻⡟⠿⣿⠟⢿⠿⣿⣿
⣿⣴⣧⣤⣧⣥⣤⣬⣌⣧⣥⣤⣤⣤⣧⣬⣬⣼⣤⣬⣤⣼⣤⣥⣥⣤⣤⣥⣤⣤⣿⣴⣤⣬⣤⣬⣤⣼⣯⣥⣤⣥⣤⣧⣤⣭⣤⣤⣭⣤⣬⣤⣤⣥⣤⣧⣥⣤⣶⣤⣷⣤⣬⣨⣦⣤⣬⣤⣤⣬⣧⣬⣽⣤⣧⣤⣿⣿
⣿⢛⠟⠛⠛⡿⡋⠛⢛⡟⠟⠙⢻⣿⠙⡛⣯⠙⡍⢩⠋⢹⣟⡋⣻⠛⠛⠛⡟⠛⠛⡛⠛⣿⠻⠛⡿⠛⠛⠋⡟⠛⡟⠟⠛⢟⢹⡍⣿⡩⢩⢫⢹⢟⠙⠛⡛⢻⠛⠙⢛⠛⠛⡍⠛⡏⠻⢻⠙⢻⢛⣿⣿⣿⣿⣿⣿⣿
⣿⣴⣷⣶⣶⣿⣶⣶⣷⣷⣶⣶⣾⣿⣶⣶⣷⣾⣶⣶⣷⣶⣿⣶⣶⣶⣾⣶⣿⣷⣷⣶⣶⣿⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣷⣾⣶⣷⣾⣶⣷⣾⣷⣶⣶⣶⣾⣶⣦⣴⣶⣶⣶⣶⣷⣾⣾⣶⣦⣴⣿⣿⣿⣿⣿⣿⣿
⣿⠩⠍⠩⡅⠉⠩⠍⠉⡩⡫⢸⠉⠩⠉⡩⡋⠉⠩⡇⢨⠉⢽⠠⢂⠶⡰⢨⢹⡇⠉⣿⠉⡇⡩⠏⢉⠽⢩⢩⡏⠍⠩⠽⣷⢡⠩⡃⢉⠩⡇⢹⢇⠹⠉⡩⠈⡍⢩⠉⢩⢹⠉⠉⡍⡉⣯⠁⡍⠉⢸⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣿⡿⣿⣿⣿⣿⣶⣿⣿⣿⣿⠿⣿⣿⣿⣷⠾⡿⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⡿⡿⠿⢿⡿⢿⠿⠿⡿⣿⡿⣿⣾⢿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣬⣢⣤⣇⣀⣼⣴⣀⣔⣄⣔⣾⣀⣆⣀⣰⣼⣵⣣⣤⣣⣜⣼⣴⣀⣆⣴⣰⣠⣇⣀⣧⣀⡂⣂⣠⣨⣀⣼⣔⣔⣄⣰⣆⣴⣔⣔⣧⣇⣠⣺⣇⣏⣤⣳⣇⣪⣜⣥⣣⣠⣇⣶⣸⣧⣦⣪⣧⣦⣸⣿⣿⣿⣿⣿⣿⣿
⣿⠿⠿⠿⠟⢿⢿⠿⠿⣿⠿⢿⠿⢻⡟⢻⠿⢿⠿⡿⠿⡿⠟⠿⠿⢿⡿⠟⣽⠻⡿⠻⠿⠿⡿⠿⢻⢿⠿⠟⢿⠿⠟⠿⡿⠿⣿⠿⢿⡿⠻⢿⢻⠿⠟⢿⠿⢿⠿⠿⣿⠟⠿⢿⠿⠿⠿⠿⢹⠿⡿⠿⣿⣿⣿⣿⣿⣿
⣿⣶⣶⣾⣶⣶⣾⣶⣶⣼⣶⣾⣶⣾⣷⣾⣶⣾⣶⣷⣶⣷⣶⣷⣶⣾⣷⣶⣿⣶⣷⣶⣶⣷⣷⣶⣾⣷⣷⣶⣾⣶⣶⣶⣷⣶⣵⣵⣶⣷⣶⣾⣾⣶⣶⣾⣦⣼⣶⣶⣷⣶⣶⣾⣶⣴⣶⣶⣾⣶⣷⣶⣿⣿⣿⣿⣿⣿
⣿⢩⠉⡙⢝⡏⠋⡝⠘⠙⠙⢹⡫⠋⣾⠉⠹⠙⠉⢩⠃⠩⠋⠫⠏⢻⠉⢫⠋⠋⡏⠋⢩⢿⠱⠝⢝⠉⠋⠹⠃⠹⠉⢹⠍⡏⢸⢹⠙⢹⡏⠋⡫⠇⡱⠘⡝⠉⠋⡙⣿⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣶⣿⣿⣿⢿⡿⣿⡿⣶⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⢿⣾⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⢿⡿⣿⣿⣿⣿⣿
⣿⣘⣂⣪⣀⡰⢀⣀⣐⡠⣸⣁⣁⣆⣐⣂⣘⣐⣀⣀⣸⣐⣀⣃⣀⣇⣰⣁⣑⣁⣆⣀⣃⣁⣈⣂⣰⣹⣐⣀⣰⣹⣀⣀⣃⣋⡠⣼⣁⣜⣀⡆⣘⣘⣘⣘⣏⣐⣹⠇⢀⠀⣂⣓⡠⣠⣂⣀⣸⣑⣅⣏⣂⣀⣐⣈⣿⣿
⣿⠿⠿⢿⠻⡿⠿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣬⣼⣤⣬⣤⣭⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 2020

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.24.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_24/12/2021:_Darktable_3.8_and_Jami_“Taranis”⠀✐


Posted in News_Roundup at 11:51 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Distributions
          o Devices/Embedded
    * Free_Software/Open_Source
    * Leftovers
    * § GNU/Linux⠀➾


          o § Server⠀➾


                # ⚓ 9_Hot_Free_and_Open_Source_Java_Application_Servers_–
                  LinuxLinks⠀⇛


                       An application server is computer software which
                       provides the business logic for an application
                       program. It offers services such as management of
                       large distributed systems, data services, load
                       balancing, transaction support, and network
                       security. The application server is one part of a
                       three-tier application, consisting of a graphical
                       interface server, an application (business logic)
                       server, and a database / transaction server. Many
                       application servers support the Java platform, but
                       they can be found in other environments.


                       There are good reasons to deploy an application
                       server in a corporate environment. At a high level,
                       an application server enables updates and upgrades
                       to applications to be distributed to all users.
                       System administrators also benefit from the fact
                       that changes to application configuration can take
                       place centrally, which greatly simplifies technical
                       support and ultimately the end user experience.
                       Application servers also simplify user management,
                       avoiding the need to set up and maintain user-
                       management systems for applications. This type of
                       software also enhances scalability and resource
                       usage, and exposes business components via
                       different deployment wrappers.


                       Java is a general-purpose, concurrent, class-based,
                       object-oriented, high-level programming language
                       and computing platform first released by Sun
                       Microsystems in 1995. It’s related in some ways to
                       C and C++, in particular with regard to its syntax,
                       and borrows a few ideas from other languages.


                       Here’s our recommended Java application servers,
                       captured in a legendary LinuxLinks chart.


          o § Applications⠀➾


                # ⚓ darktable_3.8:_Winter_Release_2021_|_darktable⠀⇛


                       The darktable team is proud to announce the second
                       feature release of 2021.


                # ⚓ Darktable_3.8.0_released⠀⇛


                       Version 3.8.0 of the Darktable photo-processing
                       application has been released. Significant changes
                       include a new keyboard shortcut system, a new
                       diffuse-or-sharpen module, a new “scene-referred”
                       blurs module “to synthesize motion and lens blurs
                       in a parametric and physically accurate way”,
                       support for the Canon CR3 raw format, and more.


                # ⚓ Darktable_3.8_Released_with_Huge_Set_of_Changes,_New
                  Modules_+_More⠀⇛


                       Major improvements are on offer in the latest
                       release of Darktable, an open source alternative to
                       Adobe Lightroom.


                       This pro photography tool traditionally issues a
                       new stable release on December 24 and 2021 is no
                       exception. Those unfamiliar with this highly-
                       regarded tool will find more details on its
                       capabilities in the comprehensive online manual.


                       [...]


                       There’s also a new ‘Diffuse or Sharpen’ module, and
                       a new scene-referred blurs module to create motion
                       and lens blurring in a ‘physically-accurate’ way.


                       The ‘Perspective Correction’ module is now called
                       ‘Rotate and Perspective’ and lets users “manually
                       define correction settings by drawing lines or
                       rectangles on the image”, and ‘Scopes’ is the new
                       name for the ‘Histogram’ module.


                # ⚓ Darktable_3.8_Open-Source_RAW_Image_Editor_Released_as_a
                  Massive_Update⠀⇛


                       Darktable 3.8 comes with major changes like a
                       completely revamped keyboard shortcut system with
                       support for controlling the app with other devices,
                       such as game controllers or MIDI devices, a new
                       diffuse or sharpen module that lets users simulate
                       or revert diffusion processes to reconstruct
                       images, as well as a new scene-referred blurs
                       module that lets you accurately synthesize motion
                       and lens blurs.


                       Other major changes include support for multiple
                       images in the print view, Aa new LMMSE demosaic
                       algorithm, support for the Canon CR3 RAW image
                       format, and the global availability of the
                       composition guides from the crop module across the
                       entire app.


                # ⚓ Darktable_3.8_Released_For_This_Great_Open-Source
                  Alternative_To_Adobe_Lightroom⠀⇛


                       Just in time for dealing with any holiday photos,
                       Darktable 3.8 is out today as the latest shiny
                       feature update to this open-source RAW photography
                       post-production software.


                       Darktable 3.8 has seen nearly four thousand commits
                       since the prior v3.6 feature release with more some
                       265 issues closed, and more than 500 pull requests.


                # ⚓ ticker_–_terminal_stock_ticker_–_LinuxLinks⠀⇛


                       While it can be a struggle to make ends meet, it’s
                       possible to make life easier through better money
                       management. Financial management is about planning
                       income and expenditure and making informed
                       decisions that enable you to survive financially.
                       With today’s financial pressures, it’s even more
                       important to look after your finances, if only to
                       make sure there are no nasty surprises when you
                       receive your next bank statement.


                       One way of staying alert regarding your financial
                       position is to use a stock ticker. This is software
                       that provides live updates of stock prices and
                       enables you to easily monitor your investments.


                       As its name suggests, ticker is software that
                       performs this function. And it offers this tracking
                       without straying from the command-line. It’s free
                       and open source software written in Go.


                       Command-line software is light on system resources
                       (very useful on low specified machines), can be
                       faster and more efficient than their graphical
                       counterparts, they do not stop working when X is
                       restarted, and are great for scripting purposes.


                # ⚓ 4_Tools_/_Extensions_to_Add_Falling_Snow_Effect_on_Ubuntu
                  20.04_/21.10_Desktop_|_UbuntuHandbook⠀⇛


                       XSnow is till in active development. It enables
                       falling snow effects in GNOME, XFCE, KDE, LXDE,
                       OPENBOX, etc. Which means, user may run it in
                       Ubuntu, XUbuntu, KUbuntu, Debian, and other based
                       Linux distributions. It also works on RPM based
                       Linux (e.g., Fedora) though the package from
                       system’s own repositories.


                       Snow by default is falling on top of opened app
                       windows and screen bottom. So, you won’t see
                       snowflakes if there’s a window maximized.


                       XSnow provides an user interface to configure how
                       many snowflakes, size, color, etc. And, it also may
                       display Santa, Scenery, birds and more.


                       The app provides modern 64-bit (amd64), old 32-bit
                       (i386), and arm64/armhf (e.g., for Raspberry Pi)
                       deb packages for Debian and Ubuntu based systems.
                       Just select download the latest package from the
                       link below:


          o § Instructionals/Technical⠀➾


                # ⚓ How_to_install_and_configure_Minikube_on_Ubuntu_21.10_–
                  NextGenTips⠀⇛


                       Minikube is a tool that makes it easy to run
                       Kubernetes locally. Minikube runs a single-node
                       Kubernetes cluster inside a VM on your local
                       machine. Kubernetes quickly set up a local
                       Kubernetes cluster on Linux, Windows, and macOS.


                       It is always advisable before diving into
                       Kubernetes, you will need a minimal Kubernetes
                       setup. Such a setup should spin up fast and
                       integrate well with other tools.


                # ⚓ 2_Ways_to_Install_Homebrew_on_Debian_11_Bullseye_Linux_–
                  Linux_Shout⠀⇛


                       Learn the commands to install Homebrew on Debian 11
                       Bullseye to install and manage various packages via
                       “formulas” and “casks” on your Linux.


                       Homebrew is an open-source project for providing a
                       package manager to macOS because there is no
                       default package manager, unlike Linux systems.
                       However, the Homebrew is also present for Linux,
                       popularly known as Linux brew.


                       The homebrew was started by Max Howell. In 2009 the
                       first version of Homebrew was released. To use it
                       the user either has to be on Linux or Mac. However,
                       using homebrew on Linux doesn’t make sense because
                       all of them almost come with their package manager.


                       Nevertheless, Homebrew does several things, it can
                       be used to install, uninstall and update software.


                # ⚓ FreeAptitude_–_Playing_with_DBus_and_KDE_applications_(Part
                  2)⠀⇛


                       In a previous article I introduced the DBus
                       technology and provided some examples built around
                       the Klipper service to integrate the clipboard area
                       within our scripts. In this article, we will see
                       other useful DBus services and how to take
                       advantage of them within our scripts.


                # ⚓ Debian_11_is_broken⠀⇛


                       Debian 11 is switching around device names like /
                       dev/sda and /dev/sdb on each boot, as you can see
                       for yourself, if you so wish, or by having a look
                       at my video:


                       https://youtu.be/MhZLLoR4Y80


                       This means that your Debian 11 system will
                       regularly fail to boot.


                       [...]


                       P.S.: can you imagine a Microsoft Windows person
                       who would find it conceivable that the system
                       drive, aka (C:), would change its drive letter on
                       each boot? Debian can!


                # ⚓ ThingsBoard_and_Raspberry_PI_(part_2):_Add_Device_telemetry
                  by_MTTQ_and_Python⠀⇛


                       Creating a tenant and adding a first device is the
                       next step once you installed ThingsBoard on
                       Raspberry PI. A simple monitoring task is by
                       checking internal CPU temperature


                       In this tutorial, I’m going to show you how to
                       create a tenant, add a device and configure it to
                       message by MTTQ and Python with Thingsboard on
                       Raspberry PI. We’ll start from a fresh ThingsBoard
                       installation, according to my ThingsBoard and
                       Raspberry PI: getting a Professional IoT dashboard
                       tutorial.


          o § Desktop Environments/WMs⠀➾


                # § K Desktop Environment/KDE SC/Qt⠀➾


                      # ⚓ Krita_5.0_Is_Out_as_a_New_Major_Release_With_a_Lot_of
                        Changes⠀⇛


                             Without doubt Krita 5.0 is a big release,
                             with a lot of new features and improvements.
                             With their latest version, it should get more
                             exciting for all the users across multiple
                             platforms.


                             Krita is a well known digital painting
                             program, available for Windows, Mac, and
                             Linux, but is primarily known for its Linux
                             side. It’s a professional free and open-
                             source raster graphics editor designed
                             primarily for digital painting and 2D
                             animation.


                             Today all digital artists and art lovers have
                             reason to rejoice, because almost four years
                             since the Krita 4.x branch first saw the
                             light of day, Krita 5.0 has been released.


                             So without further ado, let’s dive into
                             what’s new in version 5.


                      # ⚓ 2021_KDE_Eco_Sprint_|_KDE.news⠀⇛


                             On 11 December 2021, KDE Eco held the first
                             of many planned Sprints. The Sprint was
                             originally intended to be an in-person event
                             to set up a community measurement lab, but
                             Corona had other ideas. Nevertheless, the
                             community deployed its usual resourcefulness,
                             and we met online instead.


                             We discussed the next steps in KDE’s Eco
                             project, and the day’s conversation was
                             varied, covering topics such as setting up a
                             team space for the project (achieved),
                             completing the Blauer Engel application for
                             Okular (submitted), along with several
                             technical issues related to energy-
                             consumption measurements in the lab,
                             including Standard Usage Scenarios,
                             replicable reference systems, standardizing
                             data output, budget vs. professional power
                             meters, and more. See the minutes for
                             details.


                             A more detailed summary of the discussion
                             will be published at the KDE Eco blog (coming
                             soon), so keep an eye out for updates there!


                # § GNOME Desktop/GTK⠀➾


                      # ⚓ [Video]_GNOME_42_Demo_in_Nightly_GNOME_OS⠀⇛


                             We give you the first look at GNOME 42
                             desktop in GNOMS OS Nightly.


          o § Distributions⠀➾


                # ⚓ 7_Linux_Distro_Versions_Released_This_Christmas_Season_–
                  It’s_FOSS_News⠀⇛


                       In this holiday season, are you looking forward to
                       trying out new distributions on your Linux system?


                       Fret not, we have you covered. Here, I shall be
                       listing some of the latest Linux distribution
                       releases.


                # § New Releases⠀➾


                      # ⚓ Debian-Based_siduction_2021.3_Distro_Released_with
                        Linux_Kernel_5.15_LTS,_PipeWire⠀⇛


                             Dubbed “Wintersky,” siduction 2021.3 comes
                             about five months after the 2021.2 update and
                             brings some interesting changes, such as the
                             use of PipeWire as default sound system,
                             replacing PulseAudio and JACK, as well as the
                             iNet Wireless Daemon (iwd) for handling Wi-Fi
                             networks on the KDE Plasma, LXQt, and Xfce
                             editions, replacing wpa_supplicant.


                             As a matter of fact, siduction 2021.3 only
                             comes with KDE Plasma, LXQt, and Xfce
                             editions as live media, alongside the
                             standard Xorg (uses the Fluxbox window
                             manager) and noX (text-mode only) editions,
                             as the development team decided to drop
                             support for the Cinnamon, LXDE, and MATE
                             editions due to lack of time.


                # § SUSE/OpenSUSE⠀➾


                      # ⚓ openSUSE_Tumbleweed_–_Review_of_the_week_2021/50_&
                        51⠀⇛


                             Unfortunately, I missed writing up the weekly
                             review last week, so I am spanning once again
                             two weeks here. And Tumbleweed has been so
                             stable for the last weeks, even the snapshot
                             count shows this. For example, in the period
                             from snapshot 1116 to 1222, only a total of
                             three snapshots were not released (1204,
                             opneQA issues, and 1216 & 1217 due to a new
                             pango version having an impact on the
                             rendering, which required a lot of needles to
                             be created, which we could not do in time
                             before the next snapshots reached QA).
                             looking only at the time since my last weekly
                             review, we have published 12 snapshots
                             (1209..1215 & 1218..1222). Despite the
                             holiday season, there seem still to be ample
                             changes incoming (but it is getting less, as
                             the look at the Staging dashboard reveals at
                             the moment).


                # § IBM/Red Hat/Fedora⠀➾


                      # ⚓ Irving_Wladawsky-Berger:_New_Ways_of_Understanding
                        Human_Behavior⠀⇛


                             “It is often said that no person is an island
                             and it takes a village to raise a child, but
                             psychology has largely lacked the scientific
                             evidence to quantify and characterize these
                             aphorisms,” wrote MIT professor Alex (Sandy)
                             Pentland in Contextualizing Human Psychology,
                             – an article published in the August, 2020
                             issue of Technology, Mind and Behavior, a
                             journal of the American Psychological
                             Association. “As a result, experimental focus
                             is usually on more easily quantifiable
                             individual traits and behaviors.”


                             “In the last decade, however, digital data
                             from online interactions, cell phones, and
                             credit cards have allowed us to precisely
                             quantify large-scale social behavior at a
                             very fine level of detail. The little data
                             breadcrumbs that we leave behind as we move
                             around in the world are enabling new ways of
                             understanding human behavior, giving rise to
                             the emerging discipline of computational
                             social science. “[T]hese new tools can help
                             relate individual traits to the surrounding
                             social context and thus better explain life
                             outcomes and societal characteristics.”


                             The article illustrated the advances and
                             challenges of data-driven predictions by
                             discussing a 2017 mass collaboration
                             experiment. The experiment asked each of 160
                             academic teams to predict six life outcomes,
                             – such as a child’s grade point average and
                             whether a family would be evicted from their
                             home, – by analyzing development data of over
                             4.200 at-risk children from the Fragile
                             Families and Child Wellbeing Study. These
                             data had been collected by interviewing
                             primary caregivers over more than 15 years,
                             as well as other assessments including early
                             childhood education and the children’s scores
                             on a variety of standard tests. Additional
                             information was provided on the parents,
                             including medical, employment, and
                             incarceration histories, religion, and child
                             care practices. Almost 13,000 measurements
                             were made for each child and their family.


                      # ⚓ 10_of_our_favorite_sysadmin_stories_from_2021_|
                        Enable_Sysadmin⠀⇛


                             In the Special Theory of Relativity, Albert
                             Einstein popularized the concept that “time
                             is relative” or that “time is a (persistent)
                             illusion.”


                             In a more prosaic way, we all have the
                             feeling that time appears to move slowly when
                             we are bored and quickly when we are having
                             fun.


          o § Devices/Embedded⠀➾


                # ⚓ 10_best_mood_tracker_apps_for_Android_–_Android_Authority⠀⇛


                # ⚓ Huawei_gets_patent_for_technology_related_to_Android
                  applications_migration⠀⇛


                # ⚓ L-Launcher_is_a_free_launcher_app_for_non-Wear_OS_Android
                  smartwatches⠀⇛


                # ⚓ Top_3_reasons_why_Android_is_at_18GB_RAM_and_iOS_is_at_6GB
                  RAM⠀⇛


                # ⚓ Galaxy_S20_owners,_brace_yourselves_for_an_upcoming_Android
                  12_update_–_PhoneArena⠀⇛


                # ⚓ How_to_customize_your_Android_12_phone’s_Material_You
                  theme⠀⇛


                # ⚓ Google_explains_how_Android’s_Private_Compute_Core_works⠀⇛


                # § Open Hardware/Modding⠀➾


                      # ⚓ Becky_Stern’s_machine_brings_the_NYC_hot_dog
                        experience_to_you_|_Arduino_Blog⠀⇛


                             For her gift to Colin Furze as a participant
                             in this year’s YouTube Makers Secret Santa
                             event, Becky Stern opted to bring the street
                             food of New York City in the form of a mostly
                             automatic hot dog dressing machine. It was
                             designed with the intention of letting a user
                             set down a hot dog at the top of a small
                             roller ramp and then have it slide along as
                             it gets covered in various authentic
                             toppings.


                             An Arduino Uno is responsible for controlling
                             all three servo motors via a single PCA9685
                             driver module and the attached Adafruit Sound
                             Board, which is loaded with sounds that Stern
                             recorded around Manhattan. A separate
                             Adafruit Pro Trinket sits at the base and
                             sends commands to an RGB LED matrix in order
                             to scroll text across the display.


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


                # ⚓ 13_Website_copiers_that_help_you_keep_offline_mirrored
                  versions_of_websites⠀⇛


                       Ever wanted to save a copy of a certain website to
                       review it later when offline?


                       In the early 2000s, we used to copy a whole website
                       into a static HTML format with images and scripts
                       assets, in order to have access to them when
                       disconnected.


                       Believe it or not, for many reasons, some are still
                       doing this.


                       To have a copy of a website, you need to use a
                       special web crawler, called a website copier that
                       copies all the website into static HTML files
                       alongside its images, styles, and JavaScript files.


                # ⚓ Top_20_free,_Open-source_Icon_packs_for_your_project⠀⇛


                       Finding the right icons for your project, is not an
                       easy task, especially when you are looking for
                       something specific to give your project a
                       distinguished appearance and match its
                       specifications, and standards.


                       You can find many free icons sets out there,
                       however, some of them are not truly open-source or
                       come with a limitation for commercial use.


                       In this article, we present you with a list of
                       open-source icon fonts, which you can use freely in
                       your personal, and commercial projects.


                # ⚓ Jrnl:_Create_your_personal_journals_with_style⠀⇛


                       Jrnl is a command-line journal and note-taking
                       application for all old-school nerds who value the
                       terminal.


                       Jrnl is created and maintained by several
                       contributors who like the project and packed by
                       many supporters.


                       Unlike other personal journaling systems, Jrnl
                       comes with no constraints to a user interface, all
                       it is required is: typing your journals, tagging
                       them, encrypting them, and searching them with
                       simple commands.


                       [...]


                       Jrnl is released as free and open-source software
                       under GPL-3.0 License.


                # ⚓ MedicLog:_The_personal_health_logger_that_everyone_needs⠀⇛


                       The application and source code is licensed under
                       GPL-3.0 License.


                # ⚓ Another_ASRock_Sandy_Bridge_/_Ivy_Bridge_Motherboard_Ported
                  To_Open-Source_Coreboot_–_Phoronix⠀⇛


                       Another aging Intel motherboard is now supported by
                       Coreboot for those wanting to free your system down
                       to the BIOS.


                       The ASRock H77 Pro4-M is the latest board picked up
                       by mainline Coreboot. Like with many of the
                       consumer desktop motherboards supported by
                       Coreboot, it’s an old Sandy Bridge / Ivy Bridge era
                       motherboard. The ASRock H77 Pro4-M is a micro-ATX
                       motherboard that supports LGA-1155 Sandy/Ivy Bridge
                       processors, four DDR3 slots, one PCI Express 3.0
                       x16 slot, Gigabit Ethernet, and other usual
                       features for its age.


                # § FSF⠀➾


                      # § GNU Projects⠀➾


                            # ⚓ Taranis,_a_major_release_of_Jami⠀⇛


                                   Taranis is the new major stable release
                                   of Jami, and so we invite all Jami
                                   users to upgrade their version of Jami
                                   to this newest release now. Taranis,
                                   the Gallic and Celtic god of the sky,
                                   lightning and thunder, will be the
                                   baptismal name of this new version of
                                   Jami.


                            # ⚓ Jami_“Taranis”_released⠀⇛


                                   The Jami communication tool has
                                   released a major new stable version
                                   called “Taranis”; the blog post
                                   announcement explains: “Taranis, the
                                   Gallic and Celtic god of the sky,
                                   lightning and thunder, will be the
                                   baptismal name of this new version of
                                   Jami.


                            # ⚓ GNU_Jami_Taranis_Released_For_Free_Software
                              Conferencing,_Peer-To-Peer_Communication_–
                              Phoronix⠀⇛


                                   GNU Jami “Taranis” has been released as
                                   a major update to this free software
                                   project for peer-to-peer communication
                                   and SIP-based messaging. GNU Jami is
                                   what previously started out as SFLphone
                                   and then GNU Ring for initially being
                                   focused on softphones.


                                   Taranis is the name of the new GNU Jami
                                   release, which they describe as a major
                                   update. Jami sums itself up as “a GNU
                                   package for universal communication
                                   that respects the freedom and privacy
                                   of its users. Jami is an end-to-end
                                   encrypted secure and distributed voice,
                                   video, and chat communication platform
                                   that requires no central server, and
                                   leaves the power of privacy and freedom
                                   in the hands of users.”


                            # ⚓ Jami_Taranis_released⠀⇛


                                   The Jami team is pleased to announce a
                                   major release of Jami, Taranis.
                                   You can read the full announcement
                                   article on the Jami blog:

                                   https://jami.net/taranis-a-major-
                                   release-of-jami

                                   What is Jami?
                                   -------------

                                   Jami is a GNU package for universal
                                   communication that respects the
                                   freedom and privacy of its users.  Jami
                                   is an end-to-end encrypted
                                   secure and distributed voice, video,
                                   and chat communication platform
                                   that requires no central server, and
                                   leaves the power of privacy and
                                   freedom in the hands of users.

                                   Jami supports the following key
                                   features:

                                   - One-to-one conversations
                                   - File sharing
                                   - Audio/video calls and conferences
                                   - Screen sharing in video calls and
                                   conferences
                                   - Recording and sending audio/video
                                   messages
                                   - Functioning as a SIP phone software


                                   Jami Taranis release highlights
                                   -------------------------------

                                   The highlights of the Taranis release
                                   of Jami include:

                                   - Windows 11 support
                                   - Phase one of Swarms: synchronized 1-
                                   to-1 conversations
                                     - The first phase of Swarm support in
                                   Jami is now available
                                       across all platforms.
                                     - Swarms are fully distributed, peer-
                                   to-peer chats with conversation
                                       histories synchronized across your
                                   devices, and the potential to
                                       be expanded into group chats in
                                   upcoming future releases of Jami.
                                       See our earlier article Swarm: a
                                   new generation of group
                                       conversations[1] to learn more
                                   about Swarms.
                                     - In the first phase of Swarm
                                   support, Swarms enable synchronization
                                       of 1-to-1 conversations across
                                   multiple devices associated with
                                       the same account.  See the full
                                   release announcement linked above
                                       for more details.
                                   - Improvements to conferences and
                                   rendezvous points:
                                     - fine-grained moderation tools for
                                   conferences,
                                       such as 'moderator mute' and
                                   'kick';
                                     - 'raise hand' feature for indicating
                                   intention to speak; and
                                     - enhanced screen-sharing now
                                   allowing sharing individual windows,
                                       in addition to the already-
                                   available options of sharing the entire
                                       desktop or a selected screen area.
                                     - Read more about these enhancements
                                   and new features for
                                       conferences and rendezvous points
                                   in our recent article
                                       The Jami conferencing system[2].
                                   - New Android call interface and
                                   improved mobile connectivity

                                   For a detailed changelog see[3].

                                   [1] https://jami.net/swarm-introducing-
                                   a-new-generation-of-group-conversations
                                   [2] https://jami.net/the-jami-
                                   conferencing-system
                                   [3] https://git.jami.net/
                                   savoirfairelinux/jami-client-gnome/-/
                                   wikis/changelog


                                   Download Jami Taranis
                                   ---------------------

                                   Pre-built Jami binaries/packages for
                                   various GNU/Linux distributions
                                   and other platforms can be downloaded
                                   from https://jami.net/download.
                                   If you had previously installed Jami
                                   from the repositories of your
                                   GNU/Linux distribution of choice and it
                                   has not been updated for a
                                   while, you can instead install Jami
                                   following the instructions at the
                                   above link for regularly-updated Jami
                                   packages.

                                   Here are the compressed sources:
                                     https://ftp.gnu.org/gnu/jami/jami-
                                   20211223.2.37be4c3.tar.gz   (53MB)
                                     https://ftp.gnu.org/gnu/jami/jami-
                                   20211223.2.37be4c3.tar.xz   (51MB)

                                   Here are the GPG detached signatures
                                   [*]:

                                   https://ftp.gnu.org/gnu/jami/jami-
                                   20211223.2.37be4c3.tar.gz.sig


                                   https://ftp.gnu.org/gnu/jami/jami-
                                   20211223.2.37be4c3.tar.xz.sig

                                   Use a mirror for higher download
                                   bandwidth:

                                   https://www.gnu.org/order/ftp.html

                                   Here are the SHA1 and SHA256 checksums:

                                   81bcdaadbc9a96c76f9238908ce2cdc4a3f797b8
                                   jami-20211223.2.37be4c3.tar.gz
                                   ee92877382287a6b8d6772effd54773249b8ed54
                                   jami-20211223.2.37be4c3.tar.xz
                                   5d70265d0010a7c4ace4e4f3a417c8be293f55bdd0cdbc3dfa610f18fb633b74

                                   jami-20211223.2.37be4c3.tar.gz
                                   fef0e9cd1f60a71011f08a152c490f412c786f9525ca2bb8a180f2bdbb91f44c

                                   jami-20211223.2.37be4c3.tar.xz

                                   [*] Use a .sig file to verify that the
                                   corresponding file (without the
                                   .sig suffix) is intact.  First, be sure
                                   to download both the .sig file
                                   and the corresponding tarball.  Then,
                                   run a command like this:

                                     gpg --verify jami-
                                   20211223.2.37be4c3.tar.gz.sig

                                   If that command fails because you don't
                                   have the required public key,
                                   then run this command to import it:

                                     gpg --keyserver pgp.mit.edu --recv-
                                   keys
                                   BE6273738E616D6D1B3A08E8A21A020248816103

                                   and rerun the 'gpg --verify' command.
                # § Programming/Development⠀➾


                      # ⚓ The_Most_Excellent_Non-Programming_Books_for_Coders⠀⇛


                             Learning always goes on in absolute swing for
                             learners and developers. Coding has picked up
                             as a great career opportunity, and that is
                             happening coders also have to be on their
                             best learning to provide high-quality
                             performance at work.


                             Programming is also a fast-moving technique
                             and thus requires one to be on their learning
                             curve to stay relevant and crucial for
                             developers to stay updated. Books are an
                             excellent source for knowledge bearing and
                             the same stands for programmers and coders.


                      # ⚓ Top_Programming_Languages_for_Data_Science⠀⇛


                             Data science is an important instrument in
                             the modern world. A lot of computers gather a
                             lot of bytes of information about users
                             behavior, weather, results of sports games
                             and all other kinds of content that appears
                             every second. However, there are a lot of
                             questions about the quality of conclusions
                             that are built according to the analysis of
                             such data. For instance, some respectable
                             magazine created a list of top universities
                             in the country according to their special
                             scoring.


                      # ⚓ Jussi_Pakkanen:_This_year_receive_the_gift_of_a_free
                        Meson_manual⠀⇛


                             About two years ago, the Meson manual was
                             published and made available for purchase.
                             The sales were not particularly stellar and
                             the bureaucracy needed to keep the sales
                             channel going took a noticeable amount of
                             time and effort. The same goes for keeping
                             the book continually up to date.


                             Thus it came to pass that sales were shut
                             down a year ago. At the time there were some
                             questions on whether the book could be made
                             freely available. This was not done, as it
                             would not really have been fair to all the
                             people who paid actual money to get it. So
                             the book has been unavailable since.


                      # § Perl/Raku⠀➾


                            # ⚓ [Perl]_Monthly_Report_–_November⠀⇛


                                   I started the 1000 days FREE T-shirt
                                   campaign. I am so grateful for all the
                                   support that I received so far. It
                                   feels great. I decided to gift FREE
                                   specially designed T-shirt to all the
                                   champions of The Weekly Challenge. I am
                                   done with the most difficult phase of
                                   the campaign i.e. collecting funds.
                                   Thanks to all the sponsors, we have
                                   collected £1029.64 in total. The fund
                                   is enough to cover the cost of T-shirt
                                   printing and international delivery as
                                   per my own estimation.


                                   As of today, I have received 32
                                   confirmations out of 53 eligible
                                   members. I am not in a rush to be
                                   honest. I would want to gift each and
                                   every eligible members unless anyone
                                   says the opposite. I am hoping after
                                   the holiday break they will find time
                                   to respond to my email request. You can
                                   find the regular update to the campaign
                                   in the blog here.


    * § Leftovers⠀➾


          o § Integrity/Availability⠀➾


                # § Proprietary⠀➾


                      # § Security⠀➾


                            # ⚓ Security_updates_for_Friday⠀⇛


                                   Security updates have been issued by
                                   Debian (webkit2gtk and wpewebkit),
                                   Fedora (httpd and singularity), Mageia
                                   (ldns, netcdf, php, ruby, thrift/
                                   golang-github-apache-thrift,
                                   thunderbird, and webkit2), openSUSE
                                   (go1.16, go1.17, libaom, and p11-kit),
                                   and SUSE (go1.16, go1.17, htmldoc,
                                   libaom, libvpx, logstash, openssh-
                                   openssl1, python3, and runc).


                            # § Privacy/Surveillance⠀➾


                                  # ⚓ We_take_action_against_Hack-for-Hire_firm
                                    Belltrox_#SaveOurPrivacy⠀⇛


                                         The surveillance-for-hire
                                         industry has been in the eye of
                                         the storm in 2021 and it is
                                         essential that these entities are
                                         held accountable for their
                                         illegal actions. Following a new
                                         report from Meta (Facebook) on
                                         the surveillance activities of an
                                         Delhi-based company Belltrox, we
                                         have filed a criminal complaint
                                         with the Cyber Crime Cell of the
                                         Delhi Police asking them to take
                                         appropriate action.


                                         [...]


                                         In July, the activities of
                                         Israel’s NSO Group, especially
                                         its spyware Pegasus, became the
                                         focus of media and public ire
                                         over allegations of hacking and
                                         misuse. However, the NSO Group
                                         isn’t the only entity engaged in
                                         surveillance activities. While
                                         Pegasus is a spyware which is
                                         sold for use by its clients,
                                         there are also entities engaged
                                         in the (self-explanatory)
                                         surveillance-for-hire activities.
                                         These entities targeted people
                                         across the world, including
                                         journalists and human rights
                                         activists.


                                         On December 16, 2021, Meta, which
                                         is the parent company of
                                         Facebook, issued a press release
                                         titled, “Taking Action Against
                                         the Surveillance-For-Hire
                                         Industry”. This press release was
                                         on the basis of and accompanied
                                         by a threat report titled,
                                         “Threat Report on the
                                         Surveillance-for-Hire Industry”.
                                         The report was authored by Mike
                                         Dvilyanski, Facebook’s Head of
                                         Cyber Espionage Investigations,
                                         David Agranovich, Facebook’s
                                         Director of Threat Disruption,
                                         and Nathaniel Gleicher,
                                         Facebook’s Head of Security
                                         Policy. At the end of a months-
                                         long investigation, seven
                                         entities were identified as
                                         engaging in surveillance-for-hire
                                         activities and subsequently
                                         removed from Meta’s platforms.



                    ䷩ 𝚕𝚒𝚗𝚎 3154

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

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Gemini_version_available_♊︎


✐ Links_24/12/2021:_Sway_1.7_RC,_Systemd_250⠀✐


Posted in News_Roundup at 5:22 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Distributions
          o Devices/Embedded
    * Free_Software/Open_Source
    * Leftovers
    * § GNU/Linux⠀➾


          o § Server⠀➾


                # ⚓ How_to_Use_the_Kubectl_Top_Command⠀⇛


                       Whenever we set a different Kubernetes cluster,
                       there are specific things we have to do. We have to
                       be assured that the node pool has an accurate size.
                       We have to be assured that the application is in
                       the correct namespace. And also, we are assured
                       that we are properly observing the cluster. This
                       may be a chore for inexperienced users. Kubernetes
                       can monitor numerous things, such as pods and
                       namespaces, that may be difficult to track.


                       This article covers the essentials of CPU and
                       memory usage. There’s a lot to discuss about
                       monitoring, but we have to be assured that the
                       metrics are observed and checked. There are various
                       techniques to monitor the resources and several
                       methods to approach them. Thus, it is important to
                       ensure that the application utilizes only the
                       proposed number of resources to avoid running out
                       of space.


                       Though, it is simple to establish the auto-scaling
                       in Kubernetes. Hence, we have to observe the
                       metrics while we always ensure the cluster has
                       sufficient nodes to handle the workload. One more
                       reason to monitor the CPU and memory usage
                       indicators is to be conscious of abrupt changes in
                       enactment. A sudden surge in memory usage occurs.
                       This may indicate a memory escape. A sudden surge
                       in CPU usage occurs. This can be an indication of
                       an unlimited loop. These metrics are absolutely
                       useful. These are the reasons why we need to
                       observe the metrics. We have operated the commands
                       on the Linux system and used the top command. Once
                       we understand the commands, we can efficiently
                       utilize them in Kubernetes.


                       For running the commands in Kubernetes, we install
                       Ubuntu 20.04. Here, we use the Linux operating
                       system to implement the kubectl commands. Now, we
                       install the Minikube cluster to run Kubernetes in
                       Linux. Minikube offers an extremely smooth
                       understanding as it provides an efficient mode to
                       test the commands and applications.


                # ⚓ What_Kubernetes_taught_me_about_development_|
                  Opensource.com⠀⇛


                       As a full-stack developer, especially a front-end
                       developer, DevOps technologies and the way DevOps
                       developers think were always a mystery to me. When
                       the company I work for launched a new command-line
                       interface (CLI) application called Gatekeeper, I
                       jumped into the world of DevOps and Kubernetes, and
                       what I learned turned out to be very valuable. I
                       now have a much better understanding of Kubernetes
                       and the DevOps pipeline, and I can better explain
                       how our CLI application supports them both.


          o § Audiocasts/Shows⠀➾


                # ⚓ Xsnow:_Brings_Snow_To_A_Poor_Aussie_Linux_User_–
                  Invidious⠀⇛


                       I’ve never seen snow before so how about I bring it
                       to my Linux desktop with xsnow.


          o § Kernel Space⠀➾


                # ⚓ systemd_250_Released_With_A_Huge_Number_Of_New_Features,
                  Improvements_–_Phoronix⠀⇛


                       Systemd 250 is the latest major open-source
                       software project release for those trying to get
                       out their releases before year’s end… Simply put,
                       systemd 250 is a very big feature release.


                       Systemd 250 has a lot in store that has accumulated
                       over the past half-year. Following the release
                       candidates the past few weeks, systemd 250 formally
                       shipped this afternoon.


                # ⚓ Systemd_250_released_[LWN.net]⠀⇛


                       Systemd 250 has been released. To say that the list
                       of new features is long would be a severe
                       understatement; the developers have clearly been
                       busy.


                # ⚓ Intel_Prepares_More_DG2_+_XeHP_Bits_For_Linux_5.17_–
                  Phoronix⠀⇛


                       Intel on Thursday submitted a final drm-intel-gt-
                       next pull of new material slated for introduction
                       in the upcoming Linux 5.17 cycle.


                       Previous pull requests to DRM-Next of new feature
                       work for Linux 5.17 has included Raptor Lake S
                       enablement, Ice Lake VRR support, privacy screen
                       support, Alder Lake P graphics now considered
                       stable, hang fixes, and a lot of other low-level
                       work.


                       This week’s batch of Intel GT material for Linux
                       5.17 is mostly focused on bug fixes but does bring
                       more DG2/Alchemist enablement as well as for the
                       software development vehicle (SDV) around XeHP.
                       This latest — and final — pull for Linux 5.17 on
                       the Intel kernel driver front also includes a
                       performance optimization around GuC microcontroller
                       log access, speedier at GuC firmware loading,
                       sanity checking of memory regions on load, a
                       “i915.memtest=1″ option to force a full memory
                       test, and an assortment of other low-level driver
                       work.


                # § Graphics Stack⠀➾


                      # ⚓ Sway_1.7-rc1_Has_Better_Zero-Copy_Direct_Scanout,
                        Drops_“–my-next-gpu-wont-be-nvidia”_–_Phoronix⠀⇛


                             The first release candidate of the Sway 1.7
                             Wayland compositor is now available for
                             testing.


                             Sway 1.7 is working towards release as
                             another exciting update for this i3-inspired
                             Wayland compositor. Sway 1.7-rc1 has improved
                             zero-copy direct scanout support for full-
                             screen windows thanks to integrating support
                             for the Linux DMA-BUF surface feedback
                             extension.


                             Sway 1.7 has also been working on support for
                             virtual reality (VR) headsets via DRM
                             leasing, tabs can now be dragged with the
                             mouse, hit bit depth composition, Wayland-
                             native urgency using xdg-activation-v1
                             protocol, and a variety of other improvements
                             and new features.


          o § Applications⠀➾


                # ⚓ Audacity_Delivers_an_Early_Xmas_Present:_50x_Faster_Project
                  Loading⠀⇛


                       Major performance improvements are wrapped inside
                       of the latest update to Audacity, the premiere open
                       source audio editing suite.


                       Loading in projects is said to be as much as 50x
                       faster in Audacity 3.1.3 compared to the Audacity
                       3.1.0 release outed back in October (a release
                       which delivered a bevy of performance boosts
                       itself).


                       Elsewhere, a couple of new shortcuts are introduced
                       in Audacity 3.1.3: shift + L to set loop to
                       selection, and alt + shift + L to clear loop.
                       They’ve also made it harder to accidentally create
                       loop regions when attempting to use Timeline Quick
                       Play — something I’ve done a lot.


          o § Instructionals/Technical⠀➾


                # ⚓ Truncation_and_neat_terminal_output⠀⇛


                       I like things neat and orderly, and this does not
                       include output from commands where each line is
                       wrapped beyond the width of the current terminal
                       I’m in. It’s not the end of the world but it does
                       make things more difficult to read.


                       Here are a couple of examples. The first is the
                       default that you get from a docker ps invocation (I
                       actually prefer the equivalent docker container ls
                       command, but that’s a story for another time):
                       [...]


                # ⚓ The_many_methods_for_using_SVG_icons⠀⇛


                       Recently at work, I ran into a situation where we
                       had to revisit how SVG icons were being implemented
                       on our pages. And that gave me the opportunity to
                       dig into the myriad of options we have for doing
                       so. I thought this was worth documenting for future
                       me (and maybe some of you who actually read this
                       blog), because there are a LOT of options.


                # ⚓ How_to_Install_Go_on_Ubuntu_20.04_–_buildVirtual⠀⇛


                       Go is a modern programming language developed by
                       Google and has been used to write many well known
                       applications such as Docker, Terraform and
                       Kubernetes. This short article covers how to
                       install Go on Ubuntu so that you can get up and
                       running with Go!


                # ⚓ How_does_virtual_computing_work?⠀⇛


                       The corporate world has witnessed a dramatic
                       transformation in the last two years, where most of
                       the global workforce was operating from their
                       homes. As organizations began embracing the work-
                       from-home culture, technology became the backbone
                       of the new normal. Virtual computing is one such
                       technology that has largely facilitated the smooth
                       functioning of several businesses.


                       Hybrid work cultures may become standard for many
                       companies, including yours. Now is the time to plan
                       for dynamic technology that benefits your business
                       processes. In this article, we shall walk you
                       through different aspects of virtual computing and
                       enable you to make an informed decision.


                # ⚓ Get_started_with_Zyn-Fusion,_an_open_source_synthesizer_|
                  Opensource.com⠀⇛


                       A wall of synth. That’s what I dream of. Given the
                       chance, on one wall of my office, I’d have a
                       modular synthesizer that only Bob Moog himself
                       could truly ever understand. Until I realize this
                       dream, I make do with a very good approximation:
                       Zyn-Fusion.


                # ⚓ AppImage_Pool_standalone_App_Store_for_AppImages_–_TREND
                  OCEANS⠀⇛


                       Short Story: Now we have AppImage Pool, a
                       standalone GUI app store to Find and Manage
                       AppImages.


                       In Linux, we have many different ways to install
                       applications like Snap, Flatpak, AppImages, and
                       default package manager.


                       The common thing in them they all provide their
                       custom app store or platform to Find, Manage,
                       Install Apps except AppImages.


                       For newbies, AppImages is a bundle of any
                       application. Inside, a single-bundle application
                       provides all required tools with required
                       dependencies.


                # ⚓ How_to_Repair_File_System_Errors_in_Linux_Mint⠀⇛


                       Using Linux Mint makes Linux a user-friendly
                       operating system environment for all the right
                       reasons. Whether you are interested in gaming,
                       multimedia, graphic design, or improving your
                       productivity, Linux Mint is fully equipped with all
                       the apps you might need. It is a user-centered and
                       community-centric Linux distribution.


                       The Linux Mint community and its development team
                       have a great bond that turns user feedback into
                       prime system updates and bug fixes. On top of being
                       open-source, Linux Mint is famed for low memory
                       usage and feature-rich software sources.


                # ⚓ How_to_Install_MATE_Desktop_on_CentOS_8_Stream⠀⇛


                       For those not familiar with MATE Desktop
                       Environment, it is the continuation of GNOME 2. It
                       is famous for being lightweight, fast, and stable
                       that runs on Linux and most BSD operating systems.
                       MATE is also an excellent choice for a lower-end
                       system or those looking to remain efficient on
                       system resources.


                       In the following tutorial, you will have learned
                       how to install the MATE Desktop environment on
                       CentOS 8 Stream.


                # ⚓ How_To_Install_pgAdmin_4_On_Rocky_Linux/Alma_Linux_8_–
                  Citizix⠀⇛


                       PGAdmin is a web-based GUI tool used to interact
                       with the Postgres database sessions, both locally
                       and remote servers as well. It is an open-source,
                       powerful, and feature-rich graphical user interface
                       (GUI) administration and management tool for the
                       PostgreSQL database. It provides a powerful user
                       interface that enables you to easily create,
                       manage, maintain and use database objects, by both
                       beginners and experienced Postgres users alike.


                       pgAdmin 4 supports PostgreSQL 9.2 or later, and
                       runs on Unix and its variants such as Linux, Mac OS
                       X as well as Windows operating systems.


                       In this article, we will learn how to install
                       pgadmin 4 on Rocky Linux 8 server. This guide
                       assumes that you already have Postgres 9.2
                       installed and set up. If not checkout How to
                       Install and Configure Postgres 14 on Rocky Linux/
                       Centos 8.


                # ⚓ How_to_publish_your_content_using_GitHub_Pages_and_Jekyll
                  [Ed: Fedora Magazine is shilling Microsoft's proprietary
                  software on Xmas Eve]⠀⇛


                # ⚓ Unleashing_Accelerated_Speeds_with_RAM_Drives⠀⇛


                       Time is money, and sometimes that means you need a
                       faster way to process data. Solid state drives
                       (SSDs) and, more specifically, non-volatile memory
                       express (NVMe) devices have helped alleviate the
                       burden of processing data to and from a backing
                       store. However, at times, even SSD technology is
                       not quite fast enough, which is where the RAM drive
                       comes into the picture.


                       Typically, the RAM drive is used as temporary
                       storage for two reasons: Its capacities tend to be
                       lower (because the technology is more expensive),
                       and more importantly, it is a volatile technology;
                       that is, if the system were to lose power or go
                       into an unstable state, the contents of that RAM
                       drive would disappear. Depending on the type of
                       data being processed, the reward can often outweigh
                       the risks, which is why the RAM drive can
                       potentially be the better option.


                       In this article, I rely on the RapidDisk suite to
                       create and manage RAM drives. The RapidDisk
                       software project [1] provides an advanced set of
                       Linux kernel RAM drive and caching modules with
                       which you can dynamically create and remove RAM
                       drives of any size or map them as a temporary read
                       cache to slower devices.


                       The system used in this article is an older system
                       with limited memory clocked at a slow speed. More
                       modern and faster systems with faster memory will
                       produce significantly different results than those
                       found here. The dmidecode command summarizes the
                       configuration and capabilities of memory DIMMs and
                       revealed that my system has four DDR3 RAM devices
                       of 2048MB configured at speeds of 1333MTps (mega
                       transfers per second).


                # ⚓ How_to_play_Age_of_Empires_IV_on_Linux⠀⇛


                       Age of Empires IV is a real-time strategy video
                       game developed by Relic Entertainment and published
                       by Xbox Game Studios for Microsoft Windows. Here’s
                       how you can play Age of Empires IV on Linux.


                # ⚓ How_to_play_PlanetSide_2_on_Linux⠀⇛


                       Age of Empires IV is a real-time strategy video
                       game developed by Relic Entertainment and published
                       by Xbox Game Studios for Microsoft Windows. Here’s
                       how


                # ⚓ How_does_Oracle_VM_Virtualbox_work?⠀⇛


                       VirtualBox is a general-purpose virtualization
                       program for x86 and x86-64 hardware that lets users
                       and administrators run several guests operating
                       systems on a single host. It intendes for the
                       server, desktop, and embedded applications
                       VirtualBox is a graphical user interface (GUI) and
                       command-line program for virtualizing servers,
                       desktops, and embedded operating systems. A single
                       VirtualBox host may run as many guest virtual
                       machines as the host hardware allows.


                       VirtualBox has two types of users: hosts and
                       guests. The host is where the VirtualBox software
                       is kept, from whence the guests may be deployed.
                       Any compatible operating system running as a
                       virtual machine is referred to as a guest.
                       VirtualBox hosts can run Linux, Windows, or macOS,
                       while guests may run any Linux distribution,
                       Solaris, macOS, BSD, IBM OS/2, or Windows. To run
                       macOS or Windows as a virtual machine, you’ll need
                       a licensed copy of the operating system.


                       Administrators can deploy hosts using ISO images or
                       VDI/VMDK/VHD images when using VirtualBox as the
                       host platform. When guests are deployed from an ISO
                       image, the guest operating system is installed
                       normally, but only as a virtual machine. It is
                       possible to quickly deploy a virtual appliance
                       using VDI/VMDK/VHD images without having to go
                       through the procedures of installing the operating
                       system as the guest. TurnKey Linux is an excellent
                       source to get virtual appliances for VirtualBox.


                       The VirtualBox Extension Pack adds support for USB
                       2.0 and USB 3.0 devices, VirtualBox RDP, disc
                       encryption, NVMe, and PXE boot for Intel GPUs to
                       make VirtualBox even more desirable. The Guest
                       Additions adds mouse pointer integration, shared
                       folders (between guest and host), better video
                       support, seamless windows, generic host/guest
                       communication channels, time synchronization,
                       shared clipboard, and automatic logins to the
                       VirtualBox feature set.


                # ⚓ How_to_install_MyWebSQL_on_Ubuntu_20.04?_–_Unixcop_the_Unix
                  /_Linux_the_admins_deams⠀⇛


                       Hello, friends. Today, you will learn how to
                       install MyWebSQL on Ubuntu 20.04.


                       MyWebSQL is a web application created with PHP that
                       allows us to manage an instance of MariaDB / MySQL,
                       PostgreSQL or SQLite.


                       Being compatible with these tools can be of great
                       help in many projects.


                       So, with MyWebSQL you can create, modify and delete
                       data, tables, and databases all from a comfortable
                       web interface. Let’s get started.


          o § Games⠀➾


                # ⚓ Polychromatic_0.7.3_Released_With_New_Razer_Device_Support,
                  8000Hz_Polling_–_Phoronix⠀⇛


                       Polychromatic as the open-source GUI front-end for
                       working in turn with OpenRazer for configuring
                       Razer peripherals under Linux is out with a new
                       holiday release.


                       Polychromatic works with the open-source,
                       community-maintained OpenRazer for supporting Razer
                       peripherals and other devices under Linux for
                       managing RGB lighting and various device settings
                       under Linux where there isn’t any official support
                       from Razer Inc.


                # ⚓ The_Fusion_Pro_Controller_by_PowerA:_Ergonomic_Goodness_on
                  Linux_–_Boiling_Steam⠀⇛


                       If you’ve read my previous gamepad reviews, you
                       know I just can’t help it when it comes to buying
                       more. So after noticing a controller on sale from
                       my r/consoledeals feed, I’ve added yet another to
                       my collection: the PowerA Fusion Pro for Xbox One/
                       PC. Got it on sale at Best Buy for $30, rather than
                       the $80 MSRP. And let me tell you, that $30 was
                       most certainly a steal.


                       The kit that you get with the controller is a nice
                       black carrying case, made of polyurethane,
                       polyester, and ethylene-vinyl, that can open and
                       close with the zipper, a 9.8-foot braided micro USB
                       cable, two extra thumbsticks, a pair of extra
                       tension rings, and a four-button paddle set.


                # ⚓ Ogre_2.3_Released_With_Vulkan_Render_Support,_Other_Engine
                  Updates_–_Phoronix⠀⇛


                       Ogre 2.3 is out for a holiday release as the newest
                       feature release of the Ogre-Next open-source 3D
                       rendering engine code used both for games and
                       applications.


                       Significant to Ogre-Next’s Ogre 2.3 release is the
                       introduction of the Vulkan rendering system
                       support. Merged last year for this Ogre 2.3 release
                       is initial Vulkan API support, which has been
                       ongoing for more than two years now. The Vulkan
                       support is now in good shape as an alternative to
                       OpenGL.


          o § Desktop Environments/WMs⠀➾


                # § GNOME Desktop/GTK⠀➾


                      # ⚓ GNOME’s_Mutter_Lands_Some_Fixes_For_Hybrid_Laptop
                        Graphics_Crashes_–_Phoronix⠀⇛


                             For those making use of the GNOME desktop and
                             running a laptop with dual-GPU hybrid
                             graphics, Mutter has landed some fixes that
                             may help if you have been experiencing
                             crashes.


                             Red Hat’s Jonas Ådahl has been working on
                             some fixes for hybrid graphics crashes seen
                             under GNOME. One of the issues now resolved
                             stems from a left-over cursor that had
                             troubles freeing itself when the dedicated
                             GPU is deactivated, which is now fixed by
                             invalidating that GPU data in the cursor
                             renderer upon GPU deactivation. The other is
                             an issue with a page-flip callback from the
                             dedicated GPU being involed after that GPU
                             was deactivated, which is now fixed by
                             delaying the deactivation until ensuring that
                             callback has been invoked.


          o § Distributions⠀➾


                # § IBM/Red Hat/Fedora⠀➾


                      # ⚓ Leadership:_How_to_show_empathy_to_hybrid_work_teams
                        |_The_Enterprisers_Project⠀⇛


                             As we adapt to a new hybrid work style that
                             jumps between virtual and in-person, teams
                             that were used to working in shared spaces
                             now collaborate mainly via online tools. The
                             physical distance can add a degree of
                             difficulty to complex technology projects
                             that normally would benefit from frequent
                             personal interactions to spur creative
                             problem-solving.


                             Even though team members are distributed,
                             expectations for the quality of their work
                             remain the same. As leaders, it’s up to us to
                             tap into our emotional intelligence (EQ) to
                             ensure that team members know we understand
                             their challenges and are proactively seeking
                             ways to help them stay productive and
                             motivated.


                      # ⚓ 10_reasons_to_love_Linux_in_2021_|_Opensource.com⠀⇛


                             Opensource.com published well over 150
                             articles about Linux in 2021. From articles
                             about small utilities for desktop Linux users
                             to tutorials about working with Linux as a
                             server operating system and everything in
                             between, these articles have covered many
                             facets of the Linux ecosystem. It is well
                             worth your time to check out all of them, but
                             here are ten great articles published this
                             year to get you started.


                # § Debian Family⠀➾


                      # ⚓ Release_Notes_for_siduction_2021.3.0_»Wintersky«⠀⇛


                             Just before the holidays, we present you
                             siduction 2021.3.0. This edition is called
                             “Wintersky”. User and password for the live
                             session are siducer/live.


                             With that out of the way, we need to inform
                             you of some changes. Those who have read our
                             call for collaboration in the forum know that
                             we lack the time to adequately maintain
                             siduction in its current incarnation.
                             Therefore, we have decided to stop publishing
                             some desktop variants for the official
                             release for the time being. We will stop
                             shipping Cinnamon and LXDE in addition to
                             MATE, which was already missing in the last
                             release, and concentrate on KDE Plasma, LXQt,
                             Xfce, Xorg and noX.


          o § Devices/Embedded⠀➾


                # ⚓ $35_Orange_Pi_3_LTS_SBC_comes_with_2GB_RAM,_8GB_flash,
                  AW859A_WiFi_5_and_Bluetooth_5.0_module_–_CNX_Software⠀⇛


                       Orange Pi 3 LTS is a cost-down, more compact
                       version of Orange Pi 3 SBC launched in 2019 with
                       Allwinner H6 quad-core Cortex-A53 processor,
                       Gigabit Ethernet, four USB 3.0 ports, and mPCIe
                       socket with a PCIe x1 Gen2 lane. AFAICR, the latter
                       never really worked well due to a botched
                       implementation in the SoC.


                       The new slimmed-down Orange Pi 3 LTS is sized like
                       a business card, loses the mostly useless mPCIe
                       socket from the original board, comes with 2GB
                       LPDDR3 RAM (no more 1GB RAM option), a lower number
                       of USB ports, USB Type-C power input, and an
                       Allwinner AW859A WiFi and Bluetooth module replaces
                       the Ampak AP6256 module from the original board.


                # § Open Hardware/Modding⠀➾


                      # ⚓ Manufacturing_samples_of_Xassette-Asterisk_open-
                        source_hardware_board⠀⇛


                             We covered Xassette-Asterisk open source-
                             hardware Allwinner D1s RISC-V Linux SBC last
                             October. But it will most likely never be
                             mass-manufactured since SdtElectronics, the
                             designer, has no resources and time for
                             production. So I thought I should give it a
                             try, and I managed to get 10 boards
                             manufactured and assembled.


                             Time for a little disclaimer. While the post
                             is not sponsored in the sense I did not get
                             paid for it, NextPCB agreed to cover all
                             costs, aka sponsor, and manufacture ten
                             boards. Today, I’ll report my experience
                             manufacturing an open-source hardware board,
                             but I had no time to check whether any of the
                             boards worked.


                      # ⚓ Newt_2.7-inch_wireless_display_offers_high_refresh
                        rate_with_SHARP’s_Memory-in-Pixel_(MiP)_technology_
                        (Crowdfunding)_–_CNX_Software⠀⇛


                             Newt is a battery-powered, always-on, ESP32-
                             S2 wireless display with a 2.7-inch display
                             leveraging SHARP’s Memory-in-Pixel (MiP)
                             technology to provide an experience similar
                             to E-Ink displays but with a much faster
                             refresh rate.


                             The wireless display can connect to the
                             Internet to retrieve weather, calendars,
                             sports scores, to-do lists, quotes, and
                             whatever you’d like. Since it is powered by
                             an ESP32-S2 microcontroller you can program
                             with the ESP-IDF framework, Arduino,
                             MicroPython, or CircuitPython.


                      # ⚓ Christmas_Light_Display_2021_–_CubicleNate’s
                        Techpad⠀⇛


                             The lights are sequenced to music using
                             Falcon Player running on a BeagleBone Black
                             with the Kulp Lights F8-B Cape and a Pixel2AC
                             board. The sequence was programmed using
                             xLights on openSUSE Tumbleweed.


                      # ⚓ Raspberry_Pi_holds_its_own_against_low-cost_ARM_NAS⠀⇛


                             Well, ASUSTOR introduced a new lower-cost
                             NAS, the $329 Drivestor 4 Pro (model
                             AS3304T—pictured above), and sent me one to
                             review against the Raspberry Pi, since it
                             make for a better matchup—both have 4-core
                             ARM CPUs and a more limited PCI Express Gen 2
                             bus at their heart.


                             Around the same time, Radxa also sent me
                             their new Taco—a less-than-$100 Raspberry Pi
                             Compute Module 4 carrier board with 5x SATA
                             ports, 1 Gbps and 2.5 Gbps Ethernet, an M.2
                             NVMe slot, and an M.2 A+E key slot. (The Taco
                             will soon be available as part of a kit with
                             a CM4 and case for around $200.)


                # § Mobile Systems/Mobile Applications⠀➾


                      # ⚓ Clear_your_Android_phone’s_browser_cookies_and_cache
                        already_–_CNET⠀⇛


                      # ⚓ Android_13_“Tiramisu”_First_Look_and_Upcoming
                        Features_Leaked_–_MySmartPrice⠀⇛


                      # ⚓ Samsung_One_UI_4_/_Android_12_rollout_paused_in_Korea
                        to_fix_Google_Play_bugs_–_Android_Authority⠀⇛


                      # ⚓ Oppo_Android_12_(ColorOS_12)_update_tracker:_Eligible
                        devices,_release…⠀⇛


                      # ⚓ Samsung_One_UI_4.0_(Android_12)_update_tracker:
                        Eligible_devices_&_more⠀⇛


                      # ⚓ Vivo_Android_12_(Funtouch_OS_12/OriginOS/iQOO_UI_3.0)
                        update_tracker⠀⇛


                      # ⚓ Nokia_X10_is_receiving_Android_12_update_–
                        GSMArena.com_news⠀⇛


                      # ⚓ Hisense_ULED_Class_U8G_Android_4K_Smart_TV_and_more
                        TVs_are_on_sale_–_Pocketnow⠀⇛


                      # ⚓ Moto_G31_gets_December_Android_security_patch_with
                        latest_update_|_Technology⠀⇛


                      # ⚓ 10_best_mood_tracker_apps_for_Android_–_Android
                        Authority⠀⇛


                      # ⚓ Interesting_rumor_suggests_Samsung_could_be_planning
                        to_ditch_Android_in_the_future_–_Phandroid⠀⇛


                      # ⚓ I_switched_from_my_iPad_to_an_Android_tablet_—_here’s
                        what_happened_|_Tom’s_Guide⠀⇛


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


                # § SaaS/Back End/Databases⠀➾


                      # ⚓ Firebird_Project_is_happy_to_announce_general
                        availability_of_Firebird_4.0.1⠀⇛


                             Firebird Project is happy to announce general
                             availability of Firebird 4.0.1 — the first
                             point release in the Firebird 4.0 series.


                      # ⚓ PostgreSQL:_PostgreSQL_Core_Team_Report:_June_2019_–
                        December_2021⠀⇛


                             The PostgreSQL Core Team has published its
                             activity report for the period between June
                             2019 through December 2021


                # § Productivity Software/LibreOffice/Calligra⠀➾


                      # ⚓ Best_Wishes_from_TDF_–_The_Document_Foundation_Blog⠀⇛


                             Dear community members, TDF members, Advisory
                             board members, team members, membership
                             committee and board!


                             Another year marked by the global pandemic is
                             coming to an end these days. In addition to
                             all the depressing news and circumstances
                             that affect us all, there are also pleasing
                             and uplifting developments.


                             Apart from the painfully missed opportunity
                             to meet in person, be it in the local
                             communities or at our annual conference, we
                             have nevertheless achieved so much together,
                             worked together and brought our foundation
                             forward, so that we can already say that it
                             was one of the most successful years for and
                             with our project.


                             I would like to thank all of you on behalf of
                             our project. Everyone has contributed to the
                             success story in different ways. All the
                             contributions intertwine, and without these
                             individual parts the whole thing would not be
                             possible and so successful. Especially in
                             these times. Thank you very much again for
                             this.


                # § FSF⠀➾


                      # ⚓ Last_minute_gift_ideas:_give_an_FSF_membership_and
                        other_free_software_gifts⠀⇛


                             With a gifted membership, your friends and
                             loved ones will be joining a vibrant movement
                             for software freedom, and helping us to
                             amplify the free software message everywhere.
                             Each new member exponentially increases our
                             reach, and our ability to make change. A
                             gifted membership will count towards our
                             year-end goal of 500 new members, and keep us
                             fighting the good fight for computer users’
                             freedom in 2022.


                             Your friend, colleague, or loved one will be
                             able to redeem their membership from the
                             moment your donation is complete. After
                             donating, you’ll receive a code and a
                             printable page so that you can present your
                             gift as a physical object, if you like. The
                             membership is valid for one year, and
                             includes the many benefits that come with an
                             FSF associate membership, including a USB
                             member card, email forwarding, access to our
                             Jitsi Meet videoconferencing server and
                             member forum, discounts in the FSF shop and
                             on ThinkPenguin hardware, and many more.


                             Looking for more gifts? You can also check
                             out the latest FSF Giving Guide, or have a
                             look at the great list of potential gifts our
                             operations assistant Davis Remmel made for
                             this very purpose!


                             Finally: don’t forget that you don’t have to
                             spend money to give people the gift of
                             freedom: Now is the perfect time to revisit
                             and share our ShoeTool video, and our list of
                             free software tools for staying in touch –
                             and use them as a conversation-starter to
                             explain software freedom to your family.
                             Share the video on your social media using
                             the #UserFreedom hashtag – you can also use
                             the short URL https://u.fsf.org/shoetool.


                      # § Licensing/Legal⠀➾


                            # ⚓ TikTok_is_accused_of_violating_GPL_with_new
                              livestreaming_software⠀⇛


                                   TikTok’s latest video-production tool
                                   is said to be violating open-source
                                   licenses: The company’s new Live Studio
                                   Windows app, which launched last week,
                                   is using code from the Open Broadcaster
                                   Software project’s popular OBS Studio
                                   app and other open-source projects
                                   without adhering to the respective
                                   open-source licensing terms, according
                                   to allegations that first surfaced on
                                   Twitter late last week.


                                   Open Broadcaster Software business
                                   development manager Ben Torell
                                   confirmed that his team had found
                                   “clear evidence” for these violations
                                   when contacted by Protocol. Torell said
                                   the project had already reached out to
                                   TikTok, but hadn’t gotten a response
                                   yet.


                                   A TikTok spokesperson didn’t
                                   immediately respond to Protocol’s
                                   request for comment.


                                   TikTok released its Live Studio app
                                   without much fanfare last week. The
                                   Windows-based app is supposed to help
                                   people produce high-quality
                                   livestreams, and allows broadcasters to
                                   incorporate video game streams, image
                                   and text overlays and more. The app is
                                   currently only available to a few
                                   thousand users in a couple of markets,
                                   the company told TechCrunch.


                # § Programming/Development⠀➾


                      # ⚓ Lisp_In_436_Bytes_|_Hackaday⠀⇛


                             You would assume that any programming
                             language available back in the 1960s would be
                             small enough to easily implement on today’s
                             computers. That’s not always true though,
                             since old languages sometimes used multiple
                             passes. But in some cases, you can implement
                             what would have been a full language decades
                             ago in a tiny footprint. A case in point is a
                             pretty good implementation of Lisp —
                             including garbage collection — in 436 bytes.


                             SectorLISP claims to be the tiniest real
                             language, beaten only by toy languages that
                             are not really very useful. If you want to,
                             you can try it in your browser, but that
                             version has better error messages and
                             persistent bindings, so it hogs up a whole
                             509 bytes.


                      # ⚓ Welcome_to_our_Qt_Champions_for_2021!⠀⇛


                             It is now finally time to report that
                             @SGaist, @mrjj, @aha_1980 and Orgad Shaneh
                             representing the Qt Lifetime Champions have
                             now come to a consensus on the Qt Champions
                             of 2021! A special thank you to all of you
                             for your help in this regard!


                             Before getting into the winners of this year,
                             I want to take the time to thank everyone for
                             their nominations and to everyone’s
                             contributions from the Qt Community in making
                             2021 a great year for Qt!


                      # ⚓ All_about_property_bindings_in_Qt_6.2⠀⇛


                             Qt 6 introduced bindable properties a while
                             ago. Based on our experience and feedback we
                             got after the 6.0 release, we further
                             improved the underlying engine. In this post
                             we will give the overview of the bindable
                             properties, see what has changed since our
                             last update on property bindings, and discuss
                             why you may want to use the new property
                             bindings in your C++ code.


                      # ⚓ OpenCV_Knows_Where_Your_Hand_Is_|_Hackaday⠀⇛


                             We have to say, [Murtaza]’s example game in
                             his latest video isn’t very exciting.
                             However, the OpenCV technique he uses to
                             track a hand and determine its distance from
                             a single camera is pretty interesting. The
                             demo shows a random button on the screen and
                             you have to use your hand to press the button
                             which then moves so you can try again. The
                             hand measurement seems accurate to a few
                             centimeters which is good enough for many
                             applications.


                             The Python code is actually quite
                             straightforward. Essentially, the software
                             tracks your hand and by estimating its
                             relative size to determine how far away it
                             is. Of course, your hand might also rotate,
                             and [Murtaza] works through all the cases
                             step-by-step. If we wanted to know a
                             distance, we’d probably turn to ultrasonics
                             or a time of flight sensor. The problem is,
                             those sensors can’t tell your hand from
                             anything else that happens to be in front of
                             it. The use of a single camera to track and
                             locate is pretty impressive.


                      # ⚓ LLVM_Clang_Lands_Initial_SPIR-V_Toolchain_Support_–
                        Phoronix⠀⇛


                             An exciting LLVM development has landed in
                             time for Christmas! Complementary to the LLVM
                             SPIR-V back-end work that could soon be
                             mainlined, Clang has now merged the initial
                             SPIR-V toolchain support. This allows going
                             from Clang to the SPIR-V intermediate
                             representation that is conformant to the
                             OpenCL environment specification — such as
                             for compiling OpenCL kernels into SPIR-V.


                             Without the LLVM SPIR-V back-end itself being
                             merged yet, the Clang SPIR-V toolchain relies
                             upon the external LLVM to SPIR-V translator
                             (llvm-spirv) for the conversion process. Once
                             that big SPIR-V back-end is merged and in
                             good standing, it can transition to using
                             that within the LLVM code-base rather than
                             requiring the external llvm-spirv tool.


                      # ⚓ Test_Your_Product_on_a_Crappy_Laptop⠀⇛


                             There is a huge and ever-widening gap between
                             the devices we use to make the web and the
                             devices most people use to consume it. It’s
                             also no secret that the average size of a
                             website is huge, and it’s only going to get
                             larger.


                             What can you do about this? Get your hands on
                             a craptop and try to use your website or web
                             app.


                      # ⚓ Hunting_Bugs_with_Bisect⠀⇛


                             A bug was introduced at some point in the
                             last month. You know how to test for its
                             existence, but don’t know what code
                             introduced it. What’s the most effective way
                             to find where the bug was created?


                             Most computer scientists have had to
                             implement binary search – it’s one of the
                             more simple and intuitive algorithms that’s
                             also fast. But few utilize one of its more
                             practical manifestations: git bisect. The
                             algorithm goes like this: find the latest
                             revision where the code works, and pick the
                             middle revision between that and now. If that
                             works, then the bug was introduced in a later
                             revision, if it doesn’t, the bug was
                             introduced in an earlier revision. Continue
                             until you find the bug – O( log n ) time
                             complexity.


                      # § Perl/Raku⠀➾


                            # ⚓ Raku_Advent_Calendar:_Day_24_–_Packaging_and
                              unpackaging_real_good⠀⇛


                                   After all Rakuing along all Christmas,
                                   Santa realizes it’s a pretty good idea
                                   to keep things packed and ready to ship
                                   whenever it’s needed. So it looks at
                                   containers. Not the containers that
                                   might or might not actually be doing
                                   all the grunt work for bringing gifts
                                   to all good boys and girls in the
                                   world, but containers that are used to
                                   pack Raku and ship it or use it for
                                   testing. Something you need to do
                                   sooner or later, and need to do real
                                   fast.


                            # ⚓ My_Favorite_Warnings:_ambiguous⠀⇛


                                   … computer language design is just like
                                   a stroll in the park. Jurassic Park,
                                   that is. — Larry Wall


                                   Perl’s grammar is inherently ambiguous.
                                   That is, it is possible for a
                                   syntactically correct chunk of Perl to
                                   have more than one valid
                                   interpretation. Maybe this is because
                                   Larry Wall is a linguist? After all,
                                   natural languages are full of
                                   ambiguity.


                                   The ambiguous warning is part of the
                                   group syntax; that is to say, use
                                   warning ‘syntax’; enables ambiguous, as
                                   well as other warnings in that group.
                                   Of course, if appropriate you can just
                                   use warning ‘ambiguous’; if more
                                   precision is justified. Both warnings
                                   go back to Perl 5.6, when the warnings
                                   pragma itself was introduced.


                            # ⚓ Rakudo_compiler,_Release_#152_(2021.12)⠀⇛


                                   On behalf of the Rakudo development
                                   team, I’m very happy to announce the
                                   December 2021 release of Rakudo #152.
                                   Rakudo is an implementation of the
                                   Raku1 language.


    * § Leftovers⠀➾


          o ⚓ Opinion_|_3_Reasons_to_Be_Hopeful_as_This_Pretty_Shitty_Year
            Comes_to_an_End⠀⇛


                 There’s no getting around it: 2021 has been a tough year.
                 As with 2020, many of us are glad to see its back end. Do
                 let the door hit you on the way out.


          o ⚓ Opinion_|_Do_We_Dare_Stop_Being_Afraid_of_Ourselves?⠀⇛


                 What’s your story?


          o ⚓ Opinion_|_A_Look_Back_on_a_Not_So_Happy_Year⠀⇛


                 Whether the pandemic that’s swept the world started from
                 a bat or not, as 2021 ends, I think it’s safe to say that
                 we’re all far battier than we were when it began.


          o ⚓ Resolution_for_2022:_Dare_to_Build_Your_Own_Opinions_and_Then
            Defend_Them!⠀⇛


                 The military-industrial-financial complex in the US,
                 Canada, UK, EU is hell bent on full spectrum cognitive
                 control and inundates the population with plausible
                 “narratives” based on fake news, fake history, fake law,
                 fake diplomacy and fake democracy. We are literally
                 swimming in an ocean of lies – but, remarkably, most
                 people are not conscious of the fact that they are
                 systematically manipulated by governments, corporate
                 media, compliant think tanks and universities. The power
                 of “political correctness” surrounds us in direct and
                 subliminal ways. Most accept it as the “new normal”, as
                 long as they continue having Hollywood entertainment and
                 lots of sports on television. The classical panem et
                 circensis (Juvenal).


                 A particularly worrisome phenomenon is the gradual
                 emergence of a “human rights industry” that
                 systematically subverts and weaponizes human rights.  The
                 holistic approach to civil, political, economic, social
                 and cultural rights advocated by Eleanor Roosevelt has
                 been quietly denatured, dismantled, discarded.  We see
                 how the “industry” transforms the individual and
                 collective entitlement to assistance, protection, respect
                 and solidarity — based on our common human dignity  —
                 into a hostile arsenal to target competitors and
                 political adversaries.


          o ⚓ This_Holiday_Season,_Give_the_Gift_of_a_Habitable_Planet⠀⇛


                 Confession time: This year, I don’t want to buy my kids
                 anything for Christmas. Big one, right? Okay, let me
                 soften that just a bit. I have bought a few modest,
                 useful things. But that’s it! No new games, no new toys,
                 no new clothes (other than socks)… nothing. They already
                 have too much. We have too much. Our nation is drowning
                 in stuff and, in reality, need almost none of it.


          o ⚓ Founding_Godfathers⠀⇛


                 They called him a lot of things: “Momo,” “Mooney,” “Sam
                 the Cigar.” But in the 1960s, maybe they should have
                 called Sam Giancana “the real president of the United
                 States.”


          o ⚓ Facing_the_Winter_of_the_Soul⠀⇛


                 The darkness of the times is in our face. The Big Lie
                 campaign around the “stolen election” has resulted in
                 democracy-killing measures passed in numerous state
                 legislatures, suppressing voting and effectively giving
                 legislatures the power to nullify election results. Along
                 with radical gerrymandering, these measures seem likely
                 to hand Congress to the Republicans in 2022 and the White
                 House in 2024, with Trump’s return a high probability.


                 Meanwhile, one coal state senator has blocked legislation
                 that would deal with climate disruption and increasing
                 social inequity, even as the top ranks accumulate wealth
                 to an astounding degree, and climate extremes intensify.
                 Just in recent weeks, storms drenched Southeast Asia and
                 unprecedented windstorms shredded Midwest towns. We just
                 learned that the ice shelf which corks the flow of
                 central West Antarctic glaciers is nearing break-up, with
                 10 or more feet of sea level rise in prospect.


          o ⚓ Video_Game_‘Hades’_Makes_History_As_First_Video_Game_To_Win_A
            Hugo_Award⠀⇛


                 While arguing that video games are a form of art and
                 should be respected as such has been a personal drum I’ve
                 enjoyed beating for a decade, it’s worth acknowledging
                 just how far the public has come in its acceptance. While
                 I spent a great deal of time ten years ago trying to get
                 people, especially older folks, to see the light on this
                 topic, the idea that video games are an artform has
                 become far less controversial. As more people experience
                 games, they’ve come to recognize better that games
                 exhibit all the traditional hallmarks of an artform:
                 creativity, political and ideological expression, efforts
                 at preservation, and fights over expression in the
                 courthouse.


          o ⚓ Ring_In_The_New_Year_With_DIY_Bagpipes_|_Hackaday⠀⇛


                 Remember early on in the pandemic when people would don
                 protection just short of a full hazmat suit to go out,
                 and wore rubber gloves to the grocery store? Was that
                 just us? The point is, we are surely not alone in having
                 an excess of latex gloves left over, and pitifully few
                 uses for them aside from the usual — gross jobs around
                 the house, and making hand-shaped ice cubes.


          o ⚓ FlyBrainLab:_Google_Earth_But_For_A_Drosophila_Fly’s_Brain_|
            Hackaday⠀⇛


                 In biology there are a couple of truly crucial model
                 animals and insects. Not that they’re particularly good
                 students, or pick up their own trash, but in the sense
                 that they have become standard model organisms for
                 research. Aside from genetic research, the FlyEM project
                 seeks to fully map a little fly’s brain’s neural
                 connections. This common fly, called drosophila
                 melanogaster (or ‘lesser fruit fly’) has been the subject
                 of a lot of genetic studies, but this study of its brain
                 structure may provide insights in how our brain works as
                 well.


                 Based on electron microscope images of thin slices of a
                 drosophila brain, the three-dimensional structure of this
                 tiny brain is reconstructed to not only determine the
                 location of each neuron, but also their connections with
                 other neurons. We know that about two-thirds of their
                 brain is dedicated to processing the visual information
                 from their relatively advanced compound eyes, but a lot
                 is still unknown about how this is done, or how the
                 brain’s structure develops.


                 If it’s always been your dream to tinker with a little
                 fruit fly’s brain, you can do so yourself using the open
                 source FlyBrainLab tool provided, along with the freely
                 available data sources.


          o § Science⠀➾


                # ⚓ Tea_contest_in_central_Taiwan_uses_DNA_sequencing_to_oust
                  fraudsters⠀⇛


                       The Lugu Farmers’ Association in Nantou County on
                       Monday (Dec. 20) published the list of the winners
                       in this year’s winter tea contest along with the
                       information of five participants who were
                       disqualified for allegedly competing with imported
                       teas, per the Liberty Times.


                       Using a DNA sequencing technique, tea leaf
                       submissions by the suspected fraudsters — two from
                       Nantou County, two from Chiayi County, and one from
                       Changhua County — were determined to have been
                       cultivated overseas. The samples were destroyed,
                       and the perpetrators risk permanent
                       disqualification from the competition as well as
                       prosecution on charges of fraud and breach of trust
                       if they commit the offense again, TVBS citing the
                       association as saying.


                       The technology was used for the first time in the
                       45-year history of the tea contest to ensure fair
                       play. It has become a much-coveted award, as
                       winning teas can receive a boost in prices.


          o § Hardware⠀➾


                # ⚓ Fixing_A_Freezer_Design_Flaw_With_A_Little_Bit_Of_Heat_|
                  Hackaday⠀⇛


                       As a shining example of the law of unintended
                       consequences, [Lou] demonstrates how certain types
                       of freezer/refrigerator combinations fail to work
                       in a cold environment, such as a garage during the
                       winter. As [Lou] points out in his video (also
                       linked after the break) – using the freezer unit in
                       his own garage – the problem lies with devices that
                       put the temperature sensor in the refrigerator
                       section, but circulate cold air starting in the
                       freezer section.


                       This works great in a home environment with a room
                       temperature comfortable for humans, as the
                       refrigerator will constantly warm up slightly due
                       to heat from the outside, triggering the cooling
                       cycle and ensuring the freezer section will stay
                       nice and cold. When placed in, say, a garage when
                       it’s around freezing, the refrigerator section will
                       not warm up, and thus no more cooling cycle gets
                       triggered.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ Opinion_|_Who_Saw_Omicron_Coming?_Many,_in_Fact⠀⇛


                       “Nobody saw it coming. Nobody in the whole world.
                       Who saw it coming?” That was President Joe Biden
                       speaking on ABC Wednesday about the COVID-19
                       Omicron variant. In fact, many people saw it
                       coming. Global health experts and activists have
                       been warning for more than a year that aggressive
                       variants of the virus are essentially guaranteed as
                       long as much of the world’s population remains
                       unvaccinated.


                # ⚓ As_Patients_Caught_COVID_Inside_Hospitals,_Government
                  Oversight_Fell_Short⠀⇛


                # ⚓ Getting_Ready_for_the_Next_Pandemic⠀⇛


                       At the most basic level, we need an explicit
                       recognition that patent monopolies are just one
                       possible mechanism for financing research. This
                       should have always been obvious, but the pandemic
                       should have hit us over the head with this simple
                       but important fact.


                       The bulk of the research developing mRNA technology
                       was done on the government’s dime. When it came to
                       developing the Moderna vaccine, the government put
                       up almost a billion dollars for the research and
                       clinical testing. It also provided the company with
                       insurance against failure, with a large advance
                       purchase agreement that would have required it to
                       buy hundreds of millions of doses even if it was
                       not the best available vaccine.


                # ⚓ The_Pandemic_Shows_Why_We_Need_Universal_Health_Care⠀⇛


                       The United States has just passed a grim milestone
                       of 800,000 official deaths from Covid-19, more than
                       in any other country, with the actual death toll
                       likely much higher. As the nation has faced over
                       100 days in which more than 100 people have died
                       and now faces the prospect of a more infectious
                       variant that may weaken vaccine efficacy, it must
                       be asked: How exactly did the richest country in
                       the world get here? There are a number of reasons,
                       but the primary one is that the United States does
                       not have a free, universal health care system. The
                       lack of a national health insurance program affects
                       everything from vaccine hesitancy to the ability to
                       get a test to how we manage the virus going
                       forward.


                # ⚓ The_Low-and-Slow_Approach_to_Food_Safety_Reform_Keeps_Going
                  Up_in_Smoke⠀⇛


                       For Nancy Donley, the fight for safer food started
                       one agonizing summer night in 1993.


                       She and her family had hamburgers for dinner, and
                       soon after, her 6-year-old son Alex complained of a
                       stomachache. Within hours, he had curled himself
                       into a ball and was begging his mother for comfort.


                # ⚓ Vaccinated_Isn’t_Enough:_Omicron_Carries_the_Risk_of_Long
                  Covid⠀⇛


                       But in reality, the president’s message didn’t give
                       it to anyone straight, or even accurately. That’s
                       because Long Covid — a dizzyingly lengthy list of
                       new, returning, or ongoing health problems some
                       people experience for months (and in some cases,
                       close to two years) following their initial
                       infection — wasn’t mentioned as one of the
                       potential outcomes of Omicron infection. In fact,
                       Biden didn’t mention Long Covid at any point during
                       his speech. Here’s why that’s a problem.


          o § Integrity/Availability⠀➾


                # ⚓ Don’t_trust_hotel_Wi-Fi_during_holiday_travel._Here’s_how
                  to_keep_your_info_safe⠀⇛


                       But you still want to stay connected on the go,
                       especially if you’ve brought along a tablet or
                       laptop. You’ve got a couple of choices for the sake
                       of safety: using a VPN service, or connecting to
                       your phone’s mobile connection wirelessly. Both
                       have advantages and drawbacks.


                # § Proprietary⠀➾


                      # ⚓ MS_Teams:_1_feature,_4_vulnerabilities⠀⇛


                             We reported the issues to Microsoft in March
                             2021, who has only remediated one so far


                      # ⚓ Harris_calls_for_‘cyber_doctrine’_to_address
                        increasing_attacks [iophk: Windows TCO]⠀⇛


                             Vice President Harris is calling for a “cyber
                             doctrine” and greater international
                             coordination to address cybersecurity
                             concerns after a year of mounting attacks.


                             “I do believe that it is important for us to
                             have a cyber doctrine,” Harris said as part
                             of an upcoming interview on CBS’s ‘Face the
                             Nation,” airing later this week, when asked
                             whether cyberattacks should be considered
                             acts of terror.


                             Harris pointed to her work as chair of the
                             National Space Council in stressing the need
                             to work towards enhancing international
                             cybersecurity efforts, noting the importance
                             of the “role and the responsibility that we
                             have to work with our partners and allies
                             around international norms and rules.”


                      # § Security⠀➾


                            # § Fear, Uncertainty, Doubt/Fear-mongering/
                              Dramatisation⠀➾


                                  # ⚓ Open_Unlocks_the_World’s_Potential⠀⇛


                                         Given the relative prominence it
                                         was given and add to that zero
                                         commentary or inputs or
                                         counterpoints from anyone here in
                                         Singapore, shows a stunning lack
                                         of credibility on the part of the
                                         editors of the Straits Times (no
                                         real surprise here though,
                                         sadly).


                                         This clickbait-y article has to
                                         be responded to and given how the
                                         editors of the Straits Times
                                         butcher and paraphrase letters to
                                         the editor (yeah, learned this
                                         the hard way over the years), I
                                         wrote in with a tight and to the
                                         point letter – and it got
                                         published pretty much verbatim,
                                         today 24 December 2021…


                            # § Privacy/Surveillance⠀➾


                                  # ⚓ Detective_Tesla_videos_itself_being
                                    keyed⠀⇛


                                         The Tesla’s onboard cameras
                                         recorded a woman scratching the
                                         car’s passenger door at a retail
                                         park in Poole, Dorset


                                  # ⚓ Tesla_on-board_cameras_show_woman_keying
                                    car⠀⇛


                                         “The front camera caught the
                                         woman walking towards our car.
                                         The camera on the wing mirror
                                         showed her putting stuff in the
                                         passenger side of her car before
                                         she keyed the car.”


                                  # ⚓ 4th_Advent_Reading:_Facebook_fully
                                    ignores_“Schrems”_rulings_by_Court_of
                                    Justice⠀⇛


                                         In the last “Advent Reading” in
                                         protest against the Irish DPC’s
                                         removal of noyb from a procedure,
                                         we will discuss Facebook’s
                                         discarding of the European Court
                                         of Justice (CJEU) rulings on EU-
                                         US data transfers, in an
                                         allegedly “confidential” 86 pages
                                         “Transfer Impact Assessment”.
                                         Since 2013, the issue of
                                         Facebook’s cooperation with US
                                         government agencies on mass
                                         surveillance is pending before
                                         the Irish Data Protection
                                         Commission (“DPC”). A first
                                         decision by the Irish DPC is not
                                         even in sight – 8.5 years after
                                         the initial complaint and 1.5
                                         years after the second
                                         clarification by the CJEU.
                                         Schrems: “Facebook fully ignores
                                         the Court of Justice, despite two
                                         explicit rulings.”


                                  # ⚓ Third_noyb_“Advent_Reading”_from
                                    Facebook/DPC_Documents⠀⇛


                                         In its third “Advent Reading” (in
                                         protest of the DPC unlawfully
                                         removing noyb from a pending
                                         procedure) noyb is publishing
                                         Facebook’s main GDPR compliance
                                         document: Facebook’s “Record of
                                         Processing Activities” under
                                         Article 30 GDPR (short: “ROPA”).
                                         Such legally required document
                                         should allow to easily assess
                                         Facebook’s compliance with the
                                         GDPR, but in fact it only has a
                                         laughable four pages. Usually
                                         such documents otherwise have
                                         hundreds of pages. Schrems:
                                         “Facebook’s core GDPR compliance
                                         document is symptomatic of their
                                         ignorance of the law – it only
                                         has four pages. Usually such a
                                         document would be hundreds of
                                         pages. The Irish DPC knows about
                                         the lack of documentation since
                                         2018, but did not take action.”


                                  # ⚓ Google-Analytics⠀⇛


                                         Being ubiquitous, Google
                                         Analytics raises privacy
                                         concerns. When someone visits a
                                         website that uses Google
                                         Analytics, Google uses your IP
                                         address to track who you visit in
                                         order to determine your
                                         approximate geographic location.


                                  # § Confidentiality⠀➾


                                        # ⚓ Another_Illinois_Appeals_Court
                                          Handles_Compelled_Password
                                          Production,_Says_There’s_No_Fifth
                                          Amendment_Issue_Here⠀⇛


                                               The Fifth Amendment
                                               implications of compelled
                                               password production has
                                               reverted from “somewhat
                                               settled” to “not settled at
                                               all” in the state of
                                               Illinois.


                                        # ⚓ OpenPGP_Card_Support_In_Sequoia⠀⇛


                                               Over the last months we’ve
                                               worked on adding support
                                               for OpenPGP card hardware
                                               tokens to Sequoia. OpenPGP
                                               cards (like the free Gnuk
                                               implementation, or e.g.
                                               Nitrokey and YubiKey
                                               devices) are great when you
                                               want to use an OpenPGP key,
                                               but don’t want the private
                                               key material stored on your
                                               computer. Advanced OpenPGP
                                               users have come to expect
                                               their software to support
                                               them.


                                               Earlier this month, we
                                               connected a set of physical
                                               cards to our continuous
                                               integration (CI) machine
                                               and configured a job to run
                                               a test suite on these
                                               cards. This setup ensures
                                               that every change to our
                                               code is tested on a set of
                                               physical OpenPGP cards. The
                                               ability to test against
                                               multiple cards is
                                               essential, as cards
                                               implement different
                                               versions of the
                                               specification, and, on top
                                               of that, many have various
                                               quirks.


          o § Defence/Aggression⠀➾


                # ⚓ The_Fear_of_Those_Still-Secret_CIA_Records_on_the_JFK
                  Assassination⠀⇛


                       What’s up with that? Surely, lone-nut theorists
                       don’t really buy into the “national security”
                       rationale for keeping 58-year-old records relating
                       to the assassination secret from the American
                       people. I don’t know of anyone who really buys into
                       that rationale. After all, what do they think will
                       happen if those records are suddenly disclosed —
                       that the Cuban communist army will invade Miami and
                       start moving up the coast toward Washington? 


                       I’ll tell you why those lone-nut theorists don’t
                       demand immediate disclosure of those documents?
                       They’re scared. Very scared. They fear, at least on
                       a subconscious level, that those remaining records
                       include powerful circumstantial evidence
                       establishing that what happened on November 22,
                       1963, was a regime-change operation on the part of
                       the national-security establishment. Why else would
                       they still be hiding those records? No, the Cuban
                       army isn’t not going to invade Miami and start
                       moving north toward Washington.


                # ⚓ A_Million_Afghan_Children_Could_Starve_This_Winter._Are_US
                  Sanctions_to_Blame?⠀⇛


                       On a warm day in late August, 22-year-old Samim was
                       navigating the streets of Kabul for the last time.
                       In the waning days of their 20-year occupation, the
                       Americans were transporting Afghans out of the
                       country from Kabul’s airport, and Samim was
                       desperate to make it onto a flight.


                # ⚓ Trump_Asks_Supreme_Court_to_Block_Presidential_Records_From
                  Jan._6_Committee⠀⇛


                # ⚓ Chomsky:_Outdated_US_Cold_War_Policy_Worsens_Ongoing
                  Russia-Ukraine_Conflict⠀⇛


                # ⚓ January_6_Committee_Requests_That_Jim_Jordan_Speak_With
                  Them⠀⇛


                # ⚓ How_Awesome_is_‘Awesome,’_America’s_Underperforming
                  Military⠀⇛


                       Of course, war is not a game. The stakes on the
                       battlefield are infinitely higher than on the
                       playing field. When wars go wrong, “We’ll show ’em
                       next year — just you wait!” is seldom a
                       satisfactory response.


                       At least, it shouldn’t be. Yet somehow, the
                       American people, our political establishment, and
                       our military have all fallen into the habit of
                       shrugging off or simply ignoring disappointing
                       outcomes. A few years ago, a serving army officer
                       of unusual courage published an essay — in Armed
                       Forces Journal no less — in which he charged that
                       “a private who loses a rifle suffers far greater
                       consequences than a general who loses a war.”


                # ⚓ When_Whiny,_Incompetent_Nazis_Lost_Big⠀⇛


                       Charlottesville, Va.—There is a through line from
                       the violent white supremacist Unite the Right rally
                       that took place here in August 2017 to the January
                       6 Capitol insurrection that sought to overturn the
                       valid election of Joe Biden in favor of the twice-
                       impeached Donald Trump.1


                # ⚓ America’s_Foreign_Policy_Death_Spiral⠀⇛


                       The paradigm that ensnares American diplomacy
                       cemented some 75 years ago with World War II and
                       the Cold War. Those cataclysmic events forged an
                       enduring American national security state
                       characterized by unlimited global intervention,
                       cultivation of an ever-metastasizing “military-
                       industrial complex,” and endless and often
                       racialized enemy-othering followed by highly
                       destructive yet ultimately losing wars replete with
                       devastating blowback on the “homeland.”


                       Urgently needed is a new foreign policy paradigm of
                       cooperative internationalism centered on combating
                       climate change, population control, control of
                       infectious disease, investment to deal effectively
                       with poverty and global migration, dramatic
                       demilitarization, and renunciation of arms as well
                       as human trafficking. The United States should take
                       the lead in resurrecting and strengthening the
                       United Nations to better enable it to pursue the
                       mission of promoting global security, anti-racism,
                       and universal human rights.


                # ⚓ Opinion_|_A_$778_Billion_Pentagon_Budget_Is_Our_Lump_of
                  Coal⠀⇛


                       What if you wanted less child poverty, better
                       health care, more help with child care and elder
                       care, and at least a gesture toward a solution to
                       the climate crisis? And what if instead you got a
                       $778 billion check for war profiteering?


                # ⚓ Pentagon_Clamps_Down_on_Extremism_&_White_Supremacy_After
                  Dozens_of_Jan._6_Rioters_Had_Military_Ties⠀⇛


                       The Pentagon has announced new rules to slow the
                       spread of extremism in the military, one of which
                       will discipline soldiers for liking or resharing
                       white nationalist and other extremist content on
                       social media. The Pentagon announcement comes just
                       two weeks before the first anniversary of the
                       January 6 insurrection, where more than 80 of the
                       700 individuals charged with the attack had ties to
                       the U.S. military. Director of the Southern Poverty
                       Law Center’s Intelligence Project Susan Corke says
                       these rule changes are welcomed by her organization
                       but don’t go far enough to stop extremism in the
                       armed forces. “It shouldn’t have taken January 6 to
                       rouse us to really address the problem of extremism
                       in the military,” says Corke.


                # ⚓ Trump_ally_and_Pennsylvania_Republican_Scott_Perry’s_House
                  committee_collision_course⠀⇛


                       On Monday night, Rep. Bennie Thompson, D-Miss., the
                       chair of the select committee, wrote a letter to
                       Perry seeking his “voluntary cooperation.” The
                       letter also informed him that the panel had
                       received evidence from multiple witnesses,
                       including then-acting Attorney General Jeffrey
                       Rosen and then-acting Deputy Attorney General
                       Richard Donoghue, that Perry played “an important
                       role” in efforts to install Trump loyalist Jeffrey
                       Clark as acting attorney general. In addition, last
                       week the committee revealed that it had evidence
                       that Perry was the lawmaker who had sent a text
                       message to then-White House chief of staff Mark
                       Meadows the day after the 2020 election pushing an
                       “AGRESSIVE (sic) STRATEGY” for three state
                       legislatures to ignore the will of their voters and
                       deliver their states’ electors to Trump.


                # ⚓ ‘Let’s_turn_this_page’_Putin_talks_tensions_over_Ukraine,
                  prison_torture,_and_Santa_Claus_in_annual_marathon_press
                  conference⠀⇛


                       Vladimir Putin held his yearly marathon press
                       conference for the seventeenth time on Thursday,
                       December 23. Around 500 journalists were invited to
                       attend; the Russian president fielded 55 questions
                       in just under four hours, taking few questions from
                       the foreign press and no questions from the
                       “foreign agent” media outlets present (Meduza
                       included). Putin commented on a number of pressing
                       issues, including tensions with the U.S. and NATO
                       over Ukraine, this past year’s crackdown on
                       dissent, systemic abuse in the Russian prison
                       system, and, in the holiday spirit, his feelings
                       about Santa Claus. Meduza sums up the key takeaways
                       here. 


          o § Transparency/Investigative Reporting⠀➾


                # ⚓ Telex’s_third_transparency_report⠀⇛


          o § Environment⠀➾


                # ⚓ The_Trap_of_Climate_Optimism⠀⇛


                       There’s a very specific kind of writing on climate
                       change that we’ve probably all read, a realistic
                       and pragmatic science journalism about the future
                       we must stop from happening. It gives us facts,
                       projections, and stirring rhetoric; it delicately
                       balances fear with hope, measuring the dire
                       consequences of what could be against what we must
                       do to prevent it. Most of all, it has an activist’s
                       faith: Because we must, we will.1


                # ⚓ 2021’s_Climate_Disasters_Revealed_an_East-West_Weather
                  Divide,_With_One_Side_of_the_Country_Too_Wet,_the_Other
                  Dangerously_Dry⠀⇛


                       Extreme rainstorms turned to raging flash floods
                       that swept through mountain towns in Europe,
                       killing over 200 people. Across Asia, excessive
                       rainfall inundated wide areas and flooded subway
                       stations in China. Heat waves shattered records in
                       the Pacific Northwest, Europe and the Arctic.
                       Wildfires swept through towns in California,
                       Canada, Greece and Australia. And those were only a
                       few of the extremes.


                       In the U.S. alone, damage from the biggest climate
                       and weather disasters is expected to total well
                       over US$100 billion in 2021.


                # § Energy⠀➾


                      # ⚓ Texas_Regulators_Learned_Nothing_From_February’s
                        Carnage,_Prepare_To_Repeat_The_Cycle⠀⇛


                             Texas consumers recently learned the hard way
                             that regulatory capture can prove to be
                             fatal. Texas energy companies (and the
                             regulators and lawmakers who love them)
                             ignored a decade-plus of warnings that they
                             needed to harden their utility infrastructure
                             in the face of climate change. As a result,
                             we’re still measuring the casualties. Not
                             only did 700 Texans die after they lost power
                             during a brutal cold snap last February, but
                             a new report by ProPublica found that an
                             additional 1,400 Texans were hospitalized,
                             and at least 7 died.


                      # ⚓ Belgium_to_close_all_existing_nuclear_power_plants⠀⇛


                             The seven-party coalition has wrangled for
                             weeks over the issue. The Greens insisted the
                             government adhere to a 2003 law on Belgium’s
                             exit from nuclear power.


                             Meanwhile, public broadcasters RTBF and VRT
                             said the country’s francophone liberals
                             wanted the two newest nuclear reactors kept
                             open.


                             A core group of ministers agreed on a deal
                             after talks that went into Thursday morning.
                             The last existing nuclear power plants are to
                             close in 2025, local media said, in
                             accordance with a 2003 law.


                      # ⚓ SUVs_conquer_Earth⠀⇛


                             Why it matters: SUVs are heavier than typical
                             passenger cars and hence use more fuel, which
                             generates more CO2.


                             IEA’s analysis has this wild stat: “If SUVs
                             were an individual country, they would rank
                             sixth in the world for absolute emissions in
                             2021, emitting over 900 million tonnes of
                             CO2.”


                # § Wildlife/Nature⠀➾


                      # ⚓ What’s_Working:_The_Revelator’s_12_Favorite_Solutions
                        Stories_of_2021⠀⇛


                # § Overpopulation⠀➾


                      # ⚓ Forecasters:_New_Mexico_should_brace_for_worsening
                        drought⠀⇛


                             The association is planning a series of
                             meetings among acequia leaders to talk about
                             the year ahead in terms of sharing
                             observations about the drought, dealing with
                             scarcity and conflicts, and addressing the
                             need for more water-sharing agreements for
                             those areas that will need it most.


          o § Finance⠀➾


                # ⚓ What_Columbia_Student_Workers_Are_Asking_For⠀⇛


                       In early November, student workers at Columbia
                       University in New York City went on strike in
                       response to the university administration’s
                       continued failure to bargain over the workers’
                       contract in good faith. Student Workers of
                       Columbia–United Auto Workers (SWC-UAW, of which I
                       was a member until June 2020) represents over 3,000
                       graduate and undergraduate student workers. GSOC-
                       UAW has been asking the university to make
                       meaningful concessions in the areas of
                       compensation, health care, child care and parental
                       leave, nondiscrimination, and union security. As
                       the strike enters its eighth week, the union has
                       presented a new package of proposals to a
                       university administration that has repeatedly met
                       the bargaining committee’s efforts with the same,
                       unrevised contract that was voted down by the unit
                       this past April.


                # ⚓ Sanders_Urges_Biden_to_Demand_DeJoy’s_Resignation_Over_USPS
                  “Sabotage”⠀⇛


                # ⚓ Sanders_Urges_Biden_to_Demand_DeJoy’s_Resignation_Over
                  Postal_Service_‘Sabotage’⠀⇛


                       Sen. Bernie Sanders on Thursday urged President Joe
                       Biden to immediately request the resignation of
                       Postmaster General Louis DeJoy, citing the
                       Republican megadonor’s ongoing “sabotage” of the
                       U.S. Postal Service and potential conflicts of
                       interest.


                       “We need a postmaster general who will strengthen
                       and expand the Postal Service.”


                # ⚓ ‘This_Is_a_Big_Deal’:_Amazon_Settlement_With_NLRB_Could
                  Ease_Worker_Unionization_Efforts⠀⇛


                       As Amazon faces growing criticism over working
                       conditions and its response to employee organizing,
                       the online retail giant this week finalized a
                       settlement with a federal labor agency that’s
                       expected to make it easier for workers in the
                       United States to unionize.


                       “This is a big deal,” Service Employees
                       International Union (SEIU) Local 1021 tweeted
                       Thursday.


                # ⚓ “It’s_a_Win_for_Us”:_Striking_Kellogg’s_Workers_Get_Raises,
                  Improved_Benefits_&_Avoid_Two-Tier_System⠀⇛


                       In a major victory for labor rights, 1,400
                       unionized Kellogg’s workers have ended their nearly
                       three-month strike across four states after
                       approving a new contract that provides a wage
                       increase and enhanced benefits for all. The prior
                       agreement that Kellogg’s tried to bargain only
                       offered wage increases and improved benefits to
                       longtime workers, whereas the new agreement ensures
                       newer workers have a guaranteed option to receive
                       the same improvements. We speak with Kellogg’s
                       worker Kevin Bradshaw, who will return to work on
                       Monday alongside his co-workers. “We didn’t have
                       any takeaways and no concessions, so I would say
                       that, in essence, that we did win,” says Bradshaw.


                # ⚓ A_Mother_Needed_Welfare._Instead,_the_State_Used_Welfare
                  Funds_to_Take_Her_Son.⠀⇛


                       It was getting dark when Arianna Bermudez caught
                       her first glimpse of the Phoenix skyline, that
                       evening in 2018, as her 2-year-old son, David,
                       murmured peacefully in the back seat. But to
                       Bermudez, it felt like a new day. This vast,
                       rapidly growing city, stretching out before them
                       after a long drive from California, offered her and
                       David a genuine chance — perhaps not to have the
                       easy middle-class existence of so many other recent
                       transplants to Arizona, but to be safe and happy
                       together as mother and child.


                # ⚓ On_Non-Fungible_Tokens,_Faces_of_Our_Leadership,_and
                  Supporting_Artists⠀⇛


                       We were certainly surprised this week to be told
                       that we (Karen and Bradley) were “for sale” at
                       approximately US$200 each. It’s not us personally
                       that’s for sale, of course. Rather, the sale is for
                       financial derivative products that are based on
                       digital images of us. Because of the connection to
                       these financial derivative products (called NFT) to
                       our work on ethical technology and FOSS generally,
                       we share herein our analysis of the situation. And,
                       in the unlikely event you were thinking about
                       buying one of these risky financial derivatives —
                       we give our recommendation for an alternative way
                       that you fund both Software Freedom Conservancy and
                       the artist who took the photographs in question
                       while avoiding derivative products entirely.


                       [...]


                       On 2017-03-04, we (Karen and Bradley) sat for a
                       photo shoot with a photographer named Peter Adams,
                       who later released one photo from each of our
                       shoots as part of a larger work called “Faces of
                       Open Source”. We were surprised to learn that we
                       were the only FOSS leaders (among those who had
                       been photographed at that point) to raise the
                       question of FOSS licensing for the photographs
                       themselves. Sadly, Adams was not interested in
                       licensing the series under a Free license. We
                       nearly declined to continue with the photo shoot,
                       but Karen had a compromise idea: if Adams agreed to
                       license one good photo of each of us back to us
                       under CC-BY-SA, we would agree to sit for the photo
                       shoot.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Opinion_|_A_Few_Astounding_Wins_That_People-Powered
                  Movements_Won_in_2021⠀⇛


                       It would be easy to survey the end of 2021 and see
                       another year in wreckage. There’s the pandemic that
                       won’t end. Rising inflation. Climate disasters. A
                       democracy that looks creakier by the day.


                # ⚓ The_Meaning_of_Boric’s_Victory_in_Chile⠀⇛


                       In times that have seen the alarming rise of
                       authoritarianism worldwide, it is a cause for
                       celebration that Chilean voters rejected not only
                       Boric’s opponent, the ultraconservative faux-
                       populist, José Antonio Kast—an admirer of the
                       country’s former dictator, Gen. Augusto
                       Pinochet—but also Kast’s anti-immigrant,
                       traditionalist, anti-abortion, law-and-order
                       message of fear and intolerance.


                       Just as significant globally is that my compatriots
                       chose in Boric a leader who, at 35, will be the
                       youngest president in Chilean history, someone who
                       embodies the emergence of a new generation on our
                       troubled planet. The causes he believes in are
                       those youth everywhere have been increasingly
                       fighting for across the globe: gender equity, the
                       empowerment of women and indigenous peoples, an end
                       to police brutality and neoliberal economic
                       policies, a deepening of democracy and civil rights
                       and, above all, urgent action on climate change.


                # ⚓ Start_the_Steal⠀⇛


                # ⚓ Biden_Says_He’s_Running_for_Reelection_in_2024,_With_a_Big
                  “If”_Added⠀⇛


                # ⚓ Trump’s_2024_Campaign_Will_Likely_Be:_“I_Did_the_Vaccines
                  All_by_Myself!”⠀⇛


                # ⚓ Stop_Blaming_Progressives_For_Right_Wing_Corporatism⠀⇛


                       I am finding it really hard to believe that it’s
                       the progressive Democrats who are to blame for the
                       botched Build Back Better negotiations. I am
                       wondering who on earth could be making such an
                       argument in good faith. It’s very similar to the
                       Force The Vote episode by Jimmy Dore and co.


                       While I am more than open to a critique of
                       progressives from the left it seems to me a
                       fundamentally right-wing to hold them responsible
                       for the problems in Washington right now.


                # ⚓ Tea_Party_Redux:_How_the_Koch_Network_Funds_and_Fuels_the
                  Anti-Lockdown_Movement⠀⇛


                       A new report titled “How The Koch Network Hijacked
                       The War On COVID” reveals how a right-wing network
                       linked to billionaire Charles Koch has played a key
                       role in fighting public health measures during the
                       pandemic, including mask and vaccine mandates,
                       contact tracing and lockdowns. The groups include
                       the American Legislative Exchange Council (ALEC),
                       the American Institute for Economic Research
                       (AIER), Donors Trust, the Hoover Institution and
                       Hillsdale College. We speak about the contents of
                       the report with co-author Walker Bragman, who says
                       the right-wing network’s attack on public health is
                       designed to “maintain corporate profit at the
                       expense of human life.”


                # ⚓ ‘Pressure_Works’:_Senate_Told_to_Act_on_Voting_Rights_Bills
                  After_Biden_Backs_Filibuster_Exception⠀⇛


                       Progressive activists and lawmakers frustrated by
                       GOP gerrymandering and voter suppression efforts
                       celebrated on Thursday after U.S. President Joe
                       Biden clearly signaled that he supports making an
                       exception to the Senate filibuster to pass federal
                       voting rights legislation.


                       “The Senate should heed President Biden’s call and
                       act immediately in the new year to reform the
                       filibuster and pass the Freedom to Vote Act and the
                       John Lewis Voting Rights Advancement Act before
                       it’s too late.”


                # ⚓ 800+_Faith_Leaders_Tell_Biden,_Dems_Voting_Rights_Must_Be
                  ‘Number_One_Priority’_in_2022⠀⇛


                       Citing “extraordinary challenges” to American
                       democracy in 2021, over 800 faith leaders on
                       Wednesday urged President Joe Biden and the U.S.
                       Senate to make passage of comprehensive voting
                       rights legislation their “number one priority” for
                       the coming year.


                       “It’s time to stop lamenting the state of our
                       democracy and take action to address it.”


                # ⚓ West_Virginians_Give_Manchin_a_Lump_of_Coal_for_Christmas⠀⇛


                       When West Virginia Senator Joe Manchin rocked
                       Washington with his announcement that he would
                       oppose President Biden’s Build Back Better agenda,
                       he offered a sort of explanation. “If I can’t go
                       home and explain it to the people of West Virginia,
                       I can’t vote for it. And I cannot vote to continue
                       with this piece of legislation. I just can’t,”
                       Manchin told Fox News Sunday. “I’ve tried
                       everything humanly possible. I can’t get there.”


                # ⚓ 21_Million+_Going_Hungry_in_US_as_Manchin_Tanks_Expanded
                  Child_Tax_Credit⠀⇛


                       Data released Wednesday by the U.S. Census Bureau
                       shows that more than 21 million people across the
                       country live in households where there was
                       “sometimes or often not enough to eat in the last
                       seven days,” a five-month high.


                       “We’re going to keep pushing for an extension of
                       the CTC until it happens. Child hunger is too high
                       a price to pay.”


                # ⚓ University_of_Hong_Kong_removes_Tiananmen_‘Pillar_of_Shame’
                  statue⠀⇛


                       The totem pole-like tower of naked human figures
                       commemorates the protesters killed by the Chinese
                       military during its 1989 crackdown. It stood on the
                       campus for 24 years and was reportedly among few
                       public Tiananmen Square memorials in Hong Kong.


                       Recent photos taken by pedestrians showed the site
                       obscured behind plastic tarpaulins and tall yellow
                       barriers. Inside, workers wrapped up the statue and
                       packed it into a shipping container.


                       The move comes in a year in which Hong Kong
                       students have clashed with university
                       administrators, with arrests of numerous pro-
                       democracy protesters. Many have criticised what
                       they described as an environment that restricts
                       academic freedom and speech critical of Beijing.


          o § Censorship/Free Speech⠀➾


                # ⚓ State_Department_Report_Repeats_Talking_Points_From_Group
                  Who_Wants_To_Ban_All_Porn⠀⇛


                       Last week the State Department released its United
                       States Advisory Council on Human Trafficking Annual
                       Report 2021, and it’s… a weird document in so many
                       ways. Anti-human trafficking policy making is one
                       of those issues that just seems to attract some
                       very, very bizarre people — as you might have
                       noticed from the world of Pizzagate and Q-Anon.
                       Human trafficking is (1) a very real problem, (2) a
                       very serious problem, (3) just generally horrific
                       for all the reasons you know, but (4) happens way
                       less than most people think (especially given how
                       much people focus on it). Obviously, continued
                       efforts to prevent all human trafficking are
                       important, and so I can understand why the State
                       Department set up this advisory council. However,
                       they seemed to staff it with a bunch of folks who
                       have a very clear incentive to play up the issue as
                       much bigger and more threatening than it really is.


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


                # ⚓ ‘It’s_even_good_for_your_health’_Why_were_journalists
                  attending_Vladimir_Putin’s_annual_press_conference_sprayed
                  with_silver_particles?⠀⇛


                       Around 500 journalists were invited to attend
                       Vladimir Putin’s 2021 marathon press conference at
                       the Moscow Manege on Thursday, December 23. But
                       even those with invitations couldn’t just waltz
                       right inside. First, they had to pass through a
                       disinfection booth installed at the entrance, which
                       sprayed attendees with silver particles. Then, they
                       had to don special protective masks treated with an
                       “antibacterial solution of nanosilver.”


                # ⚓ Stella_Moris_statement_on_Julian_Assange’s_Supreme_Court
                  appeal⠀⇛


                       The High Court’s ruling in USA v Assange raises
                       three points of law of general public importance
                       that have an impact on the procedural and human
                       rights safeguards of a wide range of other types of
                       cases.


                # ⚓ Jailed_Belarusian_Journalist_Kuznechyk_Faces_Criminal
                  Charges⠀⇛


                       A jailed freelance journalist who has worked for
                       RFE/RL’s Belarus Service, is facing unspecified
                       criminal charges, his relatives told RFE/RL on
                       December 23.


                       Andrey Kuznechyk was not released from jail last
                       week even though his second consecutive jail term
                       he was handed on a controversial hooliganism charge
                       ended.


                       His relatives told RFE/RL that they were officially
                       informed that the journalist will be transferred
                       from the notorious Akrestsina detention center,
                       where many inmates have said they were tortured, to
                       another detention center in Minsk as a criminal
                       case on unspecified charges had been launched
                       against him.


                # ⚓ Belarus_–_“We_cannot_give_up_our_struggle_for_freedom_of
                  the_press”⠀⇛


                       On 18 May 2021, the Belarusian authorities blocked
                       access to the TUT.BY website, raided its offices
                       and arrested 15 members of its staff, who are still
                       in prison. This dark day, the culmination of a long
                       period of harassment of TUT.BY because of its
                       reporting, forced some of its journalists to flee
                       abroad. They include Aleksandra Pushkina, one of
                       the founders of Zerkalo.io, literally the TUT.BY
                       “mirror.” She has recounted these events in a video
                       for RSF.


          o § Civil Rights/Policing⠀➾


                # ⚓ All_They_Want_for_the_Holidays_Is_for_Their_Loved_Ones_to
                  Come_Home_From_Prison⠀⇛


                # ⚓ The_Black_Core_of_the_Culture_War⠀⇛


                       US politics has been deluged by heated debates
                       surrounding cancel culture, “wokeness,” and
                       critical race theory. What do these three topics
                       have in common? Some would say that they are all
                       ostensibly progressive ideas that seek
                       understanding and accountability regarding
                       histories of oppression. Others might argue they
                       are all facets of an illiberal and regressive left
                       trying to shame everyone into submission. Yet if
                       you ask most people (regardless of their political
                       background) to define these terms, you would likely
                       get Justice Potter Stewart “I know it when I see
                       it”–type answers.


                # ⚓ Ten_Of_The_Best_Protest_Albums_Of_2021⠀⇛


                       *The following is a collection of some of the best
                       albums of protest music released in 2021. They were
                       selected by Kevin Gosztola and C.J. Baker, who
                       publishes writing regularly at Ongoing History Of
                       Protest Songs. They are in alphabetical order by
                       artist.


                       **Full playlist with each album on Spotify


                # ⚓ Opinion_|_Tornados_Can_Kill._So_Does_Amazon’s_Business
                  Model⠀⇛


                       Old-school home-improvement contractors have a
                       piece of folk wisdom they love to share with
                       prospective clients.


                # ⚓ 2021_Year_in_Review⠀⇛


                       We’re thankful for our roughly 38,000 members who
                       not only support us financially but spring into
                       action whenever it’s needed. It allowed us to build
                       on what we did in 2020, to meet the new challenges
                       brought by this new era.


                       Our biggest action this year was a powerful
                       pushback against Apple when it announced that it
                       was reneging on its promise to provide us with
                       secure devices. In the summer, Apple announced it
                       would be scanning some images on our devices in a
                       poorly-conceived strategy aimed at child safety.
                       With 25,000 of your signatures, we delivered a
                       single, simple message to Apple: don’t scan our
                       phones. We sponsored a protest at Apple stores and
                       an alternative event to make sure that Apple heard
                       from those, especially children, who have first-
                       hand experience with the real dangers of device
                       insecurity. We even flew a plane over Apple’s
                       headquarters during its major product launch to
                       make sure its employees and executives got our
                       message. Our message was received.  Apple first
                       delayed and then agreed not to scan iMessage and
                       send notifications to parents. This was a first
                       victory, but a big one, and it was only made
                       possible by your contributions. Of course, we’ll
                       keep pushing until all your devices are secure and
                       answer only to you. 


                       We also stood up with parents and students against
                       the increased surveillance of students. This year,
                       Dartmouth accused medical students of cheating
                       based on a flawed understanding of how technology
                       works. Our experts dug into the data and showed
                       that what looked like cheating was just
                       applications working as they should. After first
                       doubling down and also instituting a policy
                       preventing students from speaking out on social
                       media, news coverage fueled by EFF’s technical and
                       activism work finally convinced Dartmouth to admit
                       its error and drop its allegations. We also brought
                       litigation to protect a student who faced copyright
                       claims after demonstrating the extent of
                       surveillance conducted by student surveillance
                       company Proctorio. 


                # ⚓ Electronic_Frontier_Alliance_Defending_Local_Communities:
                  2021_in_Review⠀⇛


                       The Electronic Frontier Alliance (EFA) is an
                       information-sharing network of local groups that
                       span a range of organizational models. Some are
                       fully volunteer-run, some are affiliated with a
                       broader institution (such as student groups), and
                       others are independent non-profit organizations.
                       What these groups all share in common is an
                       investment in local organizing, a not-for-profit
                       model, and a passion for five guiding principles:


                       Since first forming in 2016, the alliance has grown
                       to 73 member groups across 26 states. It’s not
                       possible to review everything these grassroots
                       groups have accomplished over the last year, but
                       this post highlights a number of exemplary
                       victories. We hope they will inspire others to take
                       action in the new year.


                       EFA members have been vital in the fight against
                       government use of face recognition technology. This
                       type of biometric surveillance comes in many forms,
                       and is a special menace to civil liberties. Since
                       2019, when San Francisco became the first city to
                       ban government use of this technology, more than a
                       dozen municipalities nationwide have followed suit,
                       including Portland and Boston last year. In 2021,
                       these victories continued with the passage of bans
                       in Minneapolis and Kings County, Washington, which
                       were won by a close collaboration between EFA
                       members, local ACLU chapters, other local community
                       groups, and the support of EFF.


                # ⚓ Kim_Potter,_ex-Minnesota_officer,_found_guilty_of
                  manslaughter_in_death_of_Daunte_Wright⠀⇛


                       Potter, a former Brooklyn Center officer, showed no
                       emotion as the Hennepin County jury found her
                       guilty of first-degree manslaughter, meaning she
                       improperly used “such force and violence that death
                       of or great bodily harm to any person was
                       reasonably foreseeable.”


                # ⚓ ‘Small_Win_for_Police_Accountability’_as_Kim_Potter_Found
                  Guilty_of_Manslaughter_in_Daunte_Wright_Killing⠀⇛


                       This is a breaking news story… Check back for
                       possible updates…


                       After four days of deliberation, a Hennepin County,
                       Minnesota jury on Thursday found former Brooklyn
                       Center police officer Kim Potter guilty of first-
                       and second-degree manslaughter for fatally shooting
                       Daunte Wright, an unarmed 20-year-old Black father,
                       during an April 11 traffic stop.


                # ⚓ Tiananmen_Square:_What_happened_in_the_protests_of_1989?⠀⇛


                       In 1989 Beijing’s Tiananmen Square became the focus
                       for large-scale protests, which were crushed by
                       China’s Communist rulers.


                       The events produced one of the most iconic photos
                       of the 20th Century – a lone protester standing in
                       front of a line of army tanks.


                       The events remain a highly sensitive topic in China
                       and one of the few remaining public memorials in
                       Hong Kong has now been removed.


                # ⚓ Complaint_filed:_Help!_My_recruiter_is_an_algorithm!⠀⇛


                       noyb has filed a complaint with the Luxembourg data
                       protection authority (the CNPD) against Amazon
                       because of their dubious e-recruiting practices on
                       their Mechanical Turk platform. In particular,
                       Amazon uses automated decision-making to accept or
                       reject workers – with no possibility for the
                       applicants to understand the criteria behind such
                       an automated decision, or to challenge it.


                # ⚓ Tibetan_political_prisoners_denied_family_visits_over
                  ‘COVID_concerns’⠀⇛


                       Authorities in western China’s Sichuan and Qinghai
                       provinces are barring family visits for Tibetan
                       prisoners held in political cases, citing concerns
                       over the spread of COVID-19, Tibetan sources say.


                       The restriction remains in force even though no
                       cases of infection have been reported for more than
                       a year in Sichuan’s Mianyang prison or the
                       detention center in Minyak Yak-nga (in Chinese,
                       Ya’an), a prefecture-size city in the western part
                       of the province, a family member of two political
                       prisoners said.


                       Prisoners in the past have been able to meet with
                       relatives separated by a glass wall, and their
                       families could bring in goods that had been
                       inspected by prison authorities, RFA has learned.


                # ⚓ Toronto_police_used_Clearview_AI_facial_recognition
                  software_in_84_investigations⠀⇛


                       Toronto police used Clearview AI facial recognition
                       software to try to identify suspects, victims and
                       witnesses in 84 criminal investigations in the
                       three and a half months officers utilized the
                       controversial technology before their police chief
                       found out and ordered them to stop.


                       The revelations are contained in an internal police
                       document recently obtained by CBC News through an
                       appeal of an access to information request.


                # ⚓ Explained:_Who_Is_Julian_Assange_And_What_Is_The_Case
                  Against_Him⠀⇛


                       If there is any one case which brings the US under
                       the radar of most criticism with regards to the
                       freedom of expression or press it is Julian Assange
                       case. Be it the Russian President Vladimir Putin
                       asking, “Why is Mr Assange in prison?….Is this
                       democracy?”, or the Brazilian President backing
                       Assange or the Azerbaijan President reminding a
                       western reporter of Assange’s treatment.


                # ⚓ Belarusian_prosecutors_seek_11-year_prison_sentence_for
                  Russian_national_Yegor_Dudnikov⠀⇛


                       State prosecutors in Belarus have asked a Minsk
                       court to sentence 21-year-old Russian national
                       Yegor Dudnikov to 11 years in prison, reports BBC
                       News Russian.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ Another_Report_Shows_U.S._5G_Isn’t_Living_Up_To_The_Hype⠀⇛


                       Despite the relentless hype leading up to the
                       deployment of 5G, and all the lopsided favors
                       regulators gave wireless carriers on behalf of 5G,
                       and all the lobbying and DC rhetoric about how the
                       U.S. was engaged in a “race with China” over 5G —
                       U.S. 5G continues to be… largely mediocre.


          o § Monopolies⠀➾


                # § Patents⠀➾


                      # ⚓ WHO_Chief_Says_Vaccine_Inequity_Is_‘Giving_the_Virus
                        More_Opportunity_to_Spread_and_Mutate’⠀⇛


                             With Omicron now officially the dominant
                             coronavirus variant in several countries, the
                             head of the World Health Organization warned
                             Wednesday that new—and potentially more
                             dangerous—mutations will continue to emerge
                             and spread widely as long as much of the
                             global population is denied access to
                             vaccines.


                             “The global priority must be to support all
                             countries to reach the 40% target as quickly
                             as possible.”


                      # ⚓ No_One_Is_Safe_Until_Everyone_Is_Safe:_Oxfam_on
                        Vaccine_Equity_&_Taking_On_Moderna⠀⇛


                             Oxfam America has accused Moderna of
                             misleading its investors about an ongoing
                             dispute over whether it needs to share
                             vaccine patent rights with the U.S.
                             government. Oxfam filed a shareholders
                             complaint against Moderna with the Securities
                             and Exchange Commission over the company’s
                             resistance to recognizing the role played by
                             three scientists with the National Institutes
                             of Health in developing the vaccine. We speak
                             with Robbie Silverman, senior corporate
                             advocacy manager at Oxfam America, who says
                             the federal government owns a right to
                             license the vaccine to manufacturers. “It is
                             simply not sufficient just to vaccinate the
                             U.S. or just to vaccinate rich countries,
                             because the virus knows no national
                             boundaries,” says Silverman, who claims
                             Moderna is “essentially doing almost nothing
                             to vaccinate low-income countries, and that
                             has negative impacts for all of us.”


                      # ⚓ Oxfam_Takes_On_Moderna_in_Fight_for_Vaccine_Equity⠀⇛


                # § Copyrights⠀➾


                      # ⚓ Court:_Ad_Agency_Must_Pay_Damages_For_Placing_Adverts
                        on_Pirate_Manga_Site⠀⇛


                             The Tokyo District Court has ordered two
                             advertising companies to pay damages to a
                             cartoonist whose work was offered illegally
                             on now-defunct pirate manga site, Mangamura.
                             The Court found that by posting adverts on
                             the site, the agencies assisted in the
                             copyright infringements of the site’s former
                             operator.


                      # ⚓ Pirate_Party_Fills_Three_Ministerial_Positions_in_New
                        Czech_Government⠀⇛


                             The Czech Pirate Party has booked several
                             election wins over the years, including the
                             European Parliament election. With yet
                             another milestone achievement following the
                             national elections, the Pirates are now ready
                             to govern. The Pirates will fill three
                             ministerial positions in the new government,
                             a breakthrough achievement for the political
                             movement.


                      # ⚓ Russia_fines_GitHub_for_failing_to_delete_Navalny’s
                        ‘Smart_Vote’_endorsements⠀⇛


                             Moscow’s Tagansky District Court has fined
                             GitHub 1 million rubles ($13,630) for failing
                             to delete the list of “Smart Vote”
                             endorsements uploaded by Alexey Navalny’s
                             team ahead of the Russian State Duma
                             elections in September.


                      # ⚓ Tanzania’s_Abuse_Of_US_Copyright_Law_To_Silence
                        Critics_On_Twitter_Should_Be_A_Warning_For_Regulators
                        Looking_To_Mess_With_Content_Moderation⠀⇛


                             We were just highlighting how rules that
                             enable the easy takedown of content on social
                             media will always lead to over-blocking, and
                             this is why we should be quite careful about
                             government attempts to mandate content
                             removal — like those of Senator Amy Klobuchar
                             to require websites to remove “health
                             misinformation.” It’s not like we don’t have
                             tremendous evidence of this. Daphne Keller
                             over at Stanford has been keeping tabs on
                             studies of “over-removal”, with the key
                             culprit being copyright law.


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