𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Monday, July 25, 2022
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Generated Tue 26 Jul 02:39:50 BST 2022
Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖)
Full hyperlinks for navigation omitted but are fully available in the originals
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Gemini index for the day: gemini://gemini.techrights.org/2022/07/25/


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

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QmajcAdRfWtgWFRoBM7yDJL3X8EJ5w8Wxf6CNnraP2EQo6
QmateHRg7s96CyDx4BcnezZSfn66P9YWrKiMv5VvFfNyEU
QmehYSPymw58ozer2trPYvEomCKmEguPNgE3qdCbXcmNW9
QmP3Nw5usXTHPhcMx8yZ9TYsWzwSKRw9BNnbjhkoJ88gpe
QmNt7g1pzLJJDE5MHZ21wEEuyos1W3DFP2LTSjB2FLPJPi
QmXniW6uykwhxPzQFCih3ywbRTbNtozdD9MTkKJWNUUis7
Qmba4Ap4JVU96TSWT1jJZfQAasTyweA1EFu92C6ULqfYVF
QmQDNYLCxwvKJsAAbaMfkydsH6iMivVs54xVt3e1WhRa4V
QmZrgDSeEPr5Tk1kd6ixcTH5gK8gVF6UWZ8USDWkwExtL2
QmdVCZ22xUbZkpsSDmSDMrnFTMypCGWw1f2punvumLq2NJ
QmXJTu6CfqTRzBWfbZAfQFS2Je8PJA65YsoWMZp6Z3WV8Z
QmXptQogxzP3vUxmf2ttL7Vyb5aAwUT9Ux3nmXxPkuNRNp
QmYTKahqtmH46iM3ZthdPvDKojc39tpTCiyk2GGs8Y29DU
QmRRSvTcmYGSSCvpvxz5PTAHRT4fdRHip9uhxwcQXMWp9G
QmQpoFyQcBb3KsKSZ3VzsMZsMmgcTqXq1zThATBh2bp3Yp
QmZrQzFnwRoF6P9gTMQfqokg7GSmtCyoyEMWxV7jZxDsZn
QmRgX3FU5tqoWu74D2LUMC84rvb5VBXutGnvudD9rbAAgn
QmNocWiFPVNdoZoPJy1s4vZQryq4BWRJMou5WsNScHuuMt
QmWkLbREwUBZdex6qeeh1UyUD3GwnNihMfEE28VhuPZYAK


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

⦿ EPO Monday: A Carnival of Law-Breaking Fluff, Even Celebration of Crime | Techrights

⦿ [Meme] Sneak Preview: EPO Chain Gang Movie | Techrights

⦿ [Meme] The EPO’s Unprecedented Surge | Techrights

⦿ IRC Proceedings: Sunday, July 24, 2022 | Techrights

⦿ [Meme] The EPO’s Great Leap Forward | Techrights

⦿ Inside the Minds of Microsoft’s Media Operatives — Part III — Attacking Real Security, Promoting Lies and Fake ’Security’ | Techrights

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
		http://techrights.org/2022/07/25/celebration-of-epo-crime/#comments
		http://techrights.org/2022/07/25/epo-sadists/#comments
		http://techrights.org/2022/07/25/epo-unprecedented-surge-animation/#comments
		http://techrights.org/2022/07/25/irc-log-240722/#comments
		http://techrights.org/2022/07/25/magampinos-great-leap-forward/#comments
		http://techrights.org/2022/07/25/nontechnical-security-talking-points/#comments

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
		http://techrights.org/2022/07/25/berlin-mini-guadec-2022/#comments
		http://techrights.org/2022/07/25/mozilla-firefox-103/#comments
		http://techrights.org/2022/07/25/postmarketos-considering-sourcehut/#comments

                    ䷩ 𝚕𝚒𝚗𝚎 64

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/07/25/celebration-of-epo-crime/#comments
    Gemini version at gemini://gemini.techrights.org/2022/07/25/celebration-of-epo-crime/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.25.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ EPO_Monday:_A_Carnival_of_Law-Breaking_Fluff,_Even_Celebration_of_Crime⠀✐


Posted in Courtroom, Deception, Europe, Law, Patents at 12:00 pm by Dr. Roy
Schestowitz


Video_download_link | md5sum 2943763a7338f9b045165608738928ed
Lobbyists Run the Official EPO Site
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/epo-org-by-lobbyists.webm


Summary: Today, as before [1, 2, 3, 4], we’re once again seeing EPO.org turned
into Russian-like propaganda apparatus of Team UPC and their puppets on a
string; the EPO actively glorifies illegal actions and celebrates the
perpetrators’ actions while based on the staff_survey this site does not even
remotely represent the views of EPO staff, only those who captured the
organisation to oppress_the_staff


TWO decades ago the EPO.org Web site was was mostly OK. Less than a decade ago
I ceased to be shocked upon seeing that the site became a shrine of an
antipathic crook, Benoît_Battistelli, who had cheated his way into a position
of power (in tandem with António_Campinos, a fellow Frenchman who would later
inherit that position at the EPO).


“Today’s EPO amounts to little but organised crime. Why is it allowed to have
diplomatic immunity while ILOAT keeps ruling against it? End the crime,
prosecute the culprits already.”We recently (Sunday) finished the series about
the plot to boost European_software_patents, in violation of the European
Patent Convention of 1973 (EPC). Watch how the the_EPO_keyword-stuffs_“EPC”
[PDF] while promoting the illegal UPC, as it also did in this_new_site_update,
stating: “The Committee’s next meeting will take place in October 2022 in the
margins of the 172nd meeting of the Administrative Council.”


It’s likely that something major will happen before that.


As also shown in the video above, the site published this_Campinos_puff_piece_a
few_hours_ago. [PDF]


What is the purpose of the EPO’s site? It does not inform anybody, it just
pushes utterly illegal things, it’s lying about staff, lying about quality (the
staff has been very clear about this), and it pretends to value privacy when
the_exact_opposite_is_true.


Today’s EPO amounts to little but organised crime. Why is it allowed to have
diplomatic immunity while ILOAT keeps_ruling_against_it? End the crime,
prosecute the culprits already. █



                    ䷩ 𝚕𝚒𝚗𝚎 136

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/07/25/epo-sadists/#comments
    Gemini version at gemini://gemini.techrights.org/2022/07/25/epo-sadists/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.25.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_Sneak_Preview:_EPO_Chain_Gang_Movie⠀✐


Posted in Europe, Patents at 9:39 am by Dr. Roy Schestowitz


                     🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇EPO_-_Chain_Gang⦈_
 Sneak preview of a soon-to-be-released EPO movie based on the 1932 classic “I
                       Am_a_Fugitive_from_a_Chain_Gang”.


Summary: The sad or sadist future of EPO patent granting, in particular
European_software_patents under António_Campinos


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

                    ䷩ 𝚕𝚒𝚗𝚎 262

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/07/25/epo-unprecedented-surge-animation/#comments
    Gemini version at gemini://gemini.techrights.org/2022/07/25/epo-unprecedented-surge-animation/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.25.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_The_EPO’s_Unprecedented_Surge⠀✐


Posted in Europe, Patents at 7:49 am by Dr. Roy Schestowitz


    🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇European_Patent_Office;_European_Patent_Convention;
                             Unprecedented_surge⦈_
                Maybe the girl_should_borrow_her_dad's_immunity


Summary: As EPO presidents, Benoît_Battistelli and António_Campinos have
figured out a way to print more monopolies


⠀⠀⠀⠀⠀⠀⠐⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠐⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠠⡀⠀⡀⠀⠀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢈⠀⠀⡇⠀⠀⠀⠨⡇⠀⠀⠀⠀⣅⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡾⣸⠀⠀⠀⠀⠀⢰⡆⠀⢀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢸⠀⠂⠇⠀⢨⠀⠈⡇⠀⠀⠀⠐⡁⠀⠀
⠀⠀⠀⠀⠀⠀⣤⣼⣥⣿⣄⢠⡤⡄⢠⣼⣅⢠⡤⣄⢠⡤⠀⣤⣝⢠⡄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢀⣦⡆⠀
⣦⣶⣶⣿⣶⡆⣿⡏⣾⣿⣟⢸⡷⣏⢸⣿⣿⢸⡧⠟⢺⡷⢠⡏⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⣀⣀⣀⣀⣀⢀⣀⣄⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡄⣤⡄⠀⢀⠀⠈⢫⣷⠀
⣻⣿⣿⣿⣿⣧⣿⡦⣙⣿⡻⠺⠇⠟⠘⠿⠟⡸⠇⠀⣻⠷⠸⣏⣿⣸⣏⢿⣐⣀⣀⣀⣀⣀⣀⣐⣠⣤⣤⣠⣀⣀⣤⣡⣤⣬⣭⣭⣬⣀⣩⣭⣩⣬⣭⣤⣀⣀⣲⣶⣗⣒⣚⣓⣻⣶⣦⡈⡉⣁⣰⣖⣮⣆⣠⣐⣛⣲
⢿⣿⣿⣿⣿⣯⢒⣤⣭⢡⣤⡖⣶⢲⣶⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣟⣿⣻⣿⣿⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠽⢰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢈⣿⡿⠇⣾⣿⣶⢼⣟⣿⣯⡧⣿⣾⣿⣹⣿⣿⣿⡇⣿⢸⣿⠇⣿⡿⣿⣿⣿⢿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠠⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢠⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣧⣿⣿⣿⣾⣿⣿⣿⣧⣿⣽⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡀⠀⠀⡀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿
⢈⡙⠛⠛⢻⣿⣿⡿⠿⢿⣫⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣇⠀⠀⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠘⣿⣨⣸⣆⢹⣿⣿⠿⠟⠚⠞⠛⠿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣭⣙⣻⠿⠘⣿⣾⡆⠒⠂⠀⠛⠛⠀⠶⢽⣿⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣾⣿⡄⠸⢿⣿⣿⣿⣿⣿⣿⣿
⢴⣾⣶⣶⣾⣿⣿⣯⣥⡄⡄⠀⠀⠀⠀⠐⠛⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣯⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿
⠙⠟⠻⣿⠛⢿⠟⠹⠿⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠆⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢰⠀⠀⡀⠀⢰⡀⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⡇⠀⢀⠀⢸⡆⠀⠁⠀⢸⡄⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⡄⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠂⡇⠀⠸⠀⢸⠃⠀⠁⠀⠐⡡⠀⠀
⠀⠀⠀⠀⠀⠀⣤⢤⣯⣼⣧⢠⣤⡄⢠⡤⣇⢠⡤⣄⣤⡤⠀⣤⣜⢠⡄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⣯⡄⠀
⣰⣶⣾⣿⣷⣶⣿⡞⣿⣿⣯⢸⡷⣏⢸⣇⣿⢸⡧⠟⣻⡷⢠⡇⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⣀⣀⣀⣀⣠⣀⣀⢀⣤⣀⡤⠀⠀⠀⠰⠀⠀⠀⠀⣀⣟⠀⢠⡄⣦⡀⠀⢀⠀⠸⢿⡷⠀
⣿⣿⣿⣿⣿⣟⣿⣷⣝⣾⡋⠻⠇⠟⠘⠿⢛⣸⡇⣀⣻⣷⠸⣏⣿⣸⣏⣿⣐⣁⣀⣀⣀⣀⣀⣘⣠⣤⣤⣤⣤⣤⣤⣤⣤⣠⣭⣭⣬⣥⣭⣭⣬⣾⣭⣤⣄⣠⣲⣿⣟⣟⣛⣓⣛⣷⣶⣄⢉⢁⣲⣶⣯⣀⣀⣘⣓⣲
⢿⣻⣿⣿⢻⣿⢿⣦⣬⢡⣤⡔⣾⣶⣾⣿⣿⣻⣿⣿⣿⣿⣿⡟⣿⣟⣿⣻⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠫⢇⡾⣻⣿⣿⣿⣿⣿⣿⣿⣿
⠈⣿⣿⣷⣾⣹⣾⣿⣿⣿⣿⣧⣿⣾⣿⣼⣿⣿⣿⡇⣿⢸⣿⡇⣿⣽⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠄⣱⣿⣿⣿⣿⣿⣿⣿⣿
⢴⢿⣿⣷⣿⣿⣿⣾⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣧⣿⣽⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⠀⠀⢀⢠⣷⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣤⣄⡉⡉⡙⢿⣿⣿⣟⣻⡯⣶⣶⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡄⠀⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⢸⠿⣯⣬⣽⡄⣿⣿⡿⠛⠋⠑⢋⡛⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣟⣷⣿⠩⠟⠃⢸⣿⣷⠈⠁⠀⠈⠉⠁⠘⢆⣿⣏⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⢠⣾⡄⠸⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣶⣶⣿⣿⣿⣿⣿⣿⣶⣶⡰⠀⠀⠀⠀⠀⠉⠉⠈⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣬⣿⣿⣤⣴⣿⣿⣿⣿⣿⣿⣿
⠘⠟⠻⣿⠋⢿⠝⠹⠽⠿⠏⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠐⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⡀⠀⠀⠀⠀⡆⠀⣀⠀⠀⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⡀⠀⣺⠀⠀⠀⠀⡇⠀⠘⠀⠀⣇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⡟⡆⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠹⠀⠀⠀⠀⡇⠀⠀⠀⠀⣳⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣤⡾⣤⣧⣤⢠⡤⡄⢠⣼⣄⢠⡤⣄⢤⡤⠀⣤⡇⢠⡄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠁⠀⠀⠀⠃⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⢠⣿⣄⠀⢐
⢶⣶⣿⣿⣶⡆⣿⠇⣿⣿⣏⢸⡷⣏⢸⣿⣿⢸⡧⠟⣸⡷⢠⣏⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢠⣄⢀⣀⣀⣀⣀⡀⣄⣀⡀⠠⣀⡠⠀⠀⠀⠀⡀⠀⠀⣀⢀⣦⡀⠄⣆⣰⣄⠀⣀⡀⠘⠿⣿⠂⢸
⣹⣿⣿⣿⢿⣧⣿⡶⠹⣿⠋⠻⠇⠟⠘⠿⣟⣸⣇⣀⣻⣷⣸⣏⣿⣸⣏⣿⣈⣀⣀⣀⣀⣄⣠⣥⣤⣤⣤⣤⣤⣤⣤⣦⣤⣬⣥⣤⣤⣤⣥⣤⣶⣦⣦⣤⣤⣐⣶⣿⣻⣟⣛⣊⣻⣧⣦⣀⣁⣒⣲⣿⣆⣐⣐⣿⣒⣾
⢻⣿⣿⡯⢻⣿⢻⣿⣤⢠⣴⡞⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣟⣿⢻⣿⣿⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⢫⢕⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⢨⣿⣿⢧⣿⣹⣾⣾⣿⣿⣯⡷⣿⣾⣿⣸⣿⣿⣿⡇⣿⣸⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠠⠄⣺⣿⣿⣷⣿⣿⣿⣿⣿
⢰⠿⢿⣗⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣧⣿⣼⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣰⣶⣿⣿⣿⣿⣿⣿⣿⣿
⣇⢠⣤⣄⣉⣉⡙⢿⣿⣟⣛⣫⢴⢶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡀⠀⠉⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢻⠀⡭⢷⣶⣦⣷⢸⣿⢿⠛⠋⠁⠉⣉⣛⠿⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⡿⠶⠬⢍⣛⣀⣿⣿⠏⠉⠁⠀⠈⠁⠀⢓⣨⣯⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⣦⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣖⠆⠀⠀⠀⠀⠉⠀⡀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠘⠟⠻⣿⠉⢿⠍⠹⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠰⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⡆⡀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡂⠀⠀⠀⠀⡆⠀⡂⠀⠀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠁⡁⠀⠀⠄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠠⠀⠸⡄⠀⣗⠀⠐⠀⠐⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⡿⡆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠝⠀⠐⠀⠀⡇⠀⠀⠀⠀⡧⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣼⠥⣯⣤⣤⢠⣤⡄⢸⡤⣄⢠⡤⣄⣤⡤⠀⣧⣄⢠⡄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠄⠀⠀⠀⠐⠀⢠⣷⣆⠀⣤⠀
⣶⣿⣿⣶⡆⢠⣿⠆⣿⣹⣿⢸⡷⣏⣿⡇⣿⢸⡧⠟⣽⡷⢰⣏⣿⢸⣿⣿⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢤⣤⢤⠤⣤⣄⠤⢔⡤⡤⠀⠀⠀⠠⣠⣄⣀⣀⢀⣦⣂⣄⣧⡷⠆⠀⣠⡀⠈⠛⡿⠈⣿⣷
⣻⣿⣿⣿⣧⣬⣿⣶⣙⡿⠛⠺⠇⠟⠙⣷⣟⣸⣇⣀⣻⣷⣸⣏⣿⣸⣏⣿⣀⣠⣀⣠⣤⣤⣥⣤⣴⣤⣶⣦⣤⣶⣶⣤⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣦⣤⣬⣿⣯⣭⣭⣭⣭⣿⣧⣥⡄⠁⣭⣽⣿⣥⣤⣬⣭⣽⣿⣶
⢿⣿⣿⡋⢩⣦⢘⣿⣿⣷⣼⣗⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣻⡉⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿
⢈⣿⣿⣇⣾⢻⣦⣼⣿⣿⣿⣟⣿⣾⣿⣾⣿⣿⣿⡇⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠉⢈⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣏⣿⡿⠿⠿⣿⣿⣿⣧⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠀⣦⣤⠤⢤⣍⢻⣿⣿⣟⣋⣺⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡀⠀⠒⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣀⣽⢻⡶⣶⣿⠈⣿⣻⠋⠉⠀⠉⣭⣉⠛⡻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⢿⡿⠿⠿⣖⣛⣉⣁⣿⣿⠧⠉⠁⠀⠀⠀⠀⣉⣼⡷⠬⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⡇⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠘⠟⠻⣿⠉⢶⠄⠰⠴⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠆⠀⣶⠆⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⢲⠀⡐⡀⠀⠀⠀⢰⠀⠀⡀⠀⢰⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠅⠀⢠⠀⠂⡇⠀⢁⠀⢸⠀⠀⡀⠀⢸⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⢇⡇⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠁⠃⠀⠈⠀⢸⠀⠀⠀⠀⢠⠰⡀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣯⠼⣥⣤⣤⢠⡤⡄⣧⡤⣄⢠⡤⣄⢤⡤⠈⣧⡄⢠⡄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⣀⠀⠀⠀⠀⠞⣷⡄⡀⣄⠀
⣾⣿⣿⣶⡀⡼⣿⠎⣿⣽⣿⢸⡷⣏⣿⡇⣿⢸⡧⠟⣿⡷⢰⣏⣿⢸⣿⣿⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢤⠄⠀⠠⡤⡤⠤⠴⣤⡤⠀⢶⠤⠆⠀⠀⠀⢠⣀⣠⣀⡀⣼⣷⣄⣴⣎⠿⠄⢀⢤⠀⠘⢻⠏⢑⣿⠠
⣽⣿⡿⣿⡧⡥⣿⣶⣙⡿⠛⠸⠃⠟⣙⣷⣟⣸⣇⣄⣻⣷⣸⣏⣿⣸⣏⣿⣀⣤⣄⣠⣤⣬⣤⣤⣤⣤⣶⣤⣴⣶⣦⣴⣶⣶⣶⣶⣶⣶⣦⣿⣶⣶⣴⣤⣽⣿⣯⣯⣭⣭⣽⣿⣬⣥⡄⢉⣽⣽⣯⣤⣤⣭⣽⣽⣷⣴
⡹⣿⣿⡁⢰⣤⢉⣭⣽⢻⣿⣟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣟⣿⣻⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⢻⡉⣿⣿⣿⢿⣿⣿⣽⣿⣿⣿
⢈⣿⣿⣧⣿⢹⣾⣾⣧⣿⣿⣧⣿⣾⣿⣼⣿⣿⣿⡇⣿⢸⣿⡇⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠉⠈⠰⢻⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⡿⠟⠿⠿⣿⣿⣿⣿⣿⣏⣿⡿⠿⠿⠿⣿⣿⣧⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⢰⣶⡤⠄⠤⡌⢻⣿⣿⣿⣶⣜⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠐⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣷⣈⣀⢿⢿⣶⣿⠸⣿⣛⢉⣁⠈⠠⣬⡍⢛⡻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⢿⣿⣿⣟⣛⣒⣓⣬⣤⣿⡿⡃⠀⠀⠀⠀⠀⠀⡩⠾⠷⠭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠏⠃⠀⠀⠀⠀⠀⠠⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠘⠟⠻⣷⠁⠶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠂⠀⣶⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠀⡆⠠⣰⠀⠀⡄⠀⢰⠀⢐⠀⠀⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⡧⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠠⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠀⢸⠀⠀⠃⠀⢿⠀⠀⠀⠀⠗⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡼⢹⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⣘⠀⠀⠃⠀⠸⠀⠀⠀⠀⢰⢢⠀⠀⠀⠀
⠀⠀⡀⠀⠀⢸⣧⡼⣤⣤⣄⢠⣤⣼⣧⡤⣄⢠⡤⣄⣤⡤⠘⣤⡄⢠⡄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⢀⠄⠀⠀⠀⠐⢾⣾⢤⢠⣇⠀
⢿⣿⣿⣿⢀⡟⣿⠎⣿⣼⣿⢸⡷⣿⣿⡇⣿⢸⡧⠟⣿⡷⢸⣏⣿⢸⣿⣿⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠤⡤⠄⠦⠢⡆⠴⠐⠶⠶⠃⠈⠀⢀⣔⣠⣀⣤⡀⣶⣷⣔⣼⡸⢓⣀⣀⠆⢀⠘⣿⣀⣸⣷⠶
⢿⣿⣿⢿⡦⠖⣿⡶⢿⣿⣋⡸⡇⣟⣙⣷⣟⣸⣧⣄⣿⣷⣸⣯⣿⣸⣏⣿⣤⣤⣤⣴⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣷⣾⣷⣾⣶⣶⣮⣿⣿⣶⣿⣭⣦⣾⣷⣭⣤⣄⢉⣭⣿⣶⣶⣶⣶⣾⣷⣷⣶
⢮⣻⣮⡀⢨⣤⢀⣤⣤⢩⣽⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣻⠁⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿
⢠⣿⣿⢷⣿⢹⣾⣽⣷⣾⣿⡏⣿⣾⣿⣾⣿⣿⣿⣇⣿⢸⣿⡇⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢈⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⣼⣿⣿⡟⠿⠻⠿⠿⠿⣿⣿⣿⣿⣿⠟⣻⢟⡿⢿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣄⣺⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⢹⡿⣖⣒⠒⡌⢻⣿⣿⣿⡯⢻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠐⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢻⣿⣿⣧⣼⣖⣻⠻⣿⣿⠸⣯⣯⠁⡀⠀⠰⠶⠎⢩⡑⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣛⣛⣛⣻⣿⣭⣭⣤⣶⣿⣟⣃⢀⠀⠀⠀⠀⠠⠶⠟⠓⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠛⠸⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠟⠻⣶⠀⠶⠄⠠⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣢⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠐⠀⠐⡶⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⢀⠀⠀⡆⡤⣠⠀⠀⠀⠀⡆⠀⢀⠀⠀⡆⠂⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⢸⢇⠀⠀⠀⠀⠀⢀⡀⠠⢀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⠀⠀⡇⢈⢿⠀⠀⡀⠀⡇⠀⠂⠀⠀⠇⠂⠀⠀⠀⠇
⠀⠀⠀⠀⠀⢠⡟⣸⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠘⣎⠀⠀⠃⠀⠇⠀⠀⠀⠀⣗⣷⢀⢀⠀⠀
⣀⣀⡀⠀⠀⣾⣥⡽⣤⣤⡄⢠⡤⣼⢡⡤⣄⢠⡤⣄⣤⣤⠘⣤⡄⢠⡄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣹⠀⠀⣠⡀⡅⠀⠀⠀⠈⢻⣿⡠⣼⡥⠀
⣿⣿⣿⣧⢰⠇⣿⢎⣿⣿⣷⢸⡷⣿⢸⡇⣿⢸⡧⠟⣿⡷⢸⣏⣿⢸⣿⣿⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠐⠖⠀⠀⠰⠶⠔⠲⠳⡶⠶⣺⠗⠚⠁⠀⢀⣠⣷⣬⣲⣶⣰⣿⣧⣖⠿⠟⣛⣀⣞⡆⠀⢈⣿⣈⣽⠧⠒
⢿⣿⣿⢿⠺⢂⡿⠶⠛⢿⣯⣸⡇⢿⣜⣷⣿⣸⣧⣤⣿⣷⣸⣯⣿⣸⣏⣿⣴⣶⣶⣶⣶⣶⣾⣿⣷⣾⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣶⣶⣶⣶⣾⣷⣤⣶⣦⣀⣿⣿⣶⣶⣷⣾⣷⣿⣿⣿
⢹⣫⣥⡀⢡⣤⣠⣤⣴⢠⣭⣝⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⡭⢀⠽⢿⣿⣿⣿⣿⣿⣿⣿⣿
⢴⣿⣿⣿⣿⢻⣾⣾⣿⣾⣷⣿⣿⣾⣿⣿⣿⣿⣿⡇⣿⣸⣿⡗⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠠⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⠿⠻⠟⠻⠿⠿⢿⣿⣿⣿⡿⠻⣟⣛⣻⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠰⢆⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡄⠿⢿⣟⣈⡒⡎⢻⣿⣷⡿⠗⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠈⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢻⣿⣿⣿⣷⣾⣼⣛⣻⡿⠧⢸⣯⣧⠀⠄⠀⠒⠒⠂⢬⢑⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣭⣭⣭⣴⣶⣶⣾⣿⣻⣤⢀⠀⠀⠀⠀⠐⠛⠋⠙⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⡿⠿⠟⠛⠛⠛⠛⠛⠛⠘⠛⠁⠀⠀⠀⠀⠀⠀⠂⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠆⠲⣶⠀⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣮⣢⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⡦⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠆⡆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠰⠀⠀⢄⠀⡀⠀⢰⠠⣆⡦⠀⣰⠀⢰⡄⠀⡆⠀⢰⠀⡂⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣾⡄⠀⠀⠀⠁⠀⢀⠀⡇⠄⠀⠀⠄⠀⢸⡁⠀⠆⠀⢠⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣇⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠃⠀⢸⡇⢿⡇⠀⣺⠀⢸⡇⠀⠅⠀⠸⡆⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣸⠃⡇⠀⠀⠀⠀⠀⣼⠀⠁⠃⠀⠀⠀⠀⠘⡇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢽⣇⠀⠘⠀⠈⠃⠀⠀⠀⢐⣷⡇⡀⡀⠀⠀
⣀⣠⠀⡀⢠⡟⣤⡇⣤⣤⡄⢠⡤⣿⢠⡤⣄⢠⡤⣄⣤⡤⠁⣤⡄⢠⡄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠀⡀⡀⠀⠀⢈⣿⠀⢠⣄⣴⠀⠀⠀⠀⣑⣿⣧⣇⣿⡆⠀
⣿⣿⣿⡇⠾⠁⣿⠇⣿⣿⣧⢸⡷⣿⢸⡇⣿⢸⡧⢟⣿⡷⢱⣏⣿⢸⣿⣿⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠸⠆⠐⠐⠲⠖⠲⠾⠺⣶⢄⣛⢛⠛⠀⠀⣀⣼⣧⣵⣶⣦⣾⣿⣶⡿⠷⠏⢩⣥⡜⠀⠀⢹⠧⡤⠿⠟⢃
⣽⣿⡿⠷⡚⣂⠿⠶⠛⣿⣋⣸⣧⣿⣜⣷⣿⣼⣧⣴⣿⣷⣸⣯⣿⣸⣯⣿⣴⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣿⣿⣿⣷⣶⣶⣦⣀⢾⣿⣷⣾⣿⣿⣿⣿⣿⣿
⢞⣯⣤⡀⢠⣤⣤⣶⣾⣻⣿⡀⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢯⢄⠼⢻⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⢻⣾⣾⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣧⣿⣸⣿⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠏⡹⢏⠹⠿⠟⢿⣿⣿⡿⣏⣩⣽⣧⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠰⢆⣸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⣿⣫⣥⣌⣲⡄⣽⣿⣿⠟⠙⠟⠛⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿
⢻⣿⣿⣿⣿⣯⣶⣾⣿⣧⣿⡻⠇⢹⣷⣷⠐⠀⠈⠉⠉⠐⠶⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣭⣿⣿⣿⣿⣽⣿⣶⣶⣾⣿⣿⣿⡿⣶⣤⠄⠀⠀⠀⠀⠊⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣘⠛⠿⠿⠿⠿⠟⠛⠛⠙⠋⠉⠉⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠆⠲⣶⠠⠶⠄⠰⠶⠶⠆⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⡾⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⢶⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⡄⠀⢰⢰⣆⡆⠀⡄⠀⢰⠀⠐⡆⠀⢰⡐⠀⠀⠄⢀⠀
⠀⠀⠀⠀⠀⢀⡟⡄⠀⠀⠀⠁⠀⣀⠀⠀⡄⠀⠀⠀⠀⢸⡁⠀⠆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠀⠀⠸⠀⠃⠀⢹⡈⢿⡇⠀⢣⠀⢸⠀⠀⠇⠀⢸⡘⠀⡀⠀⠈⠀
⠀⠀⠀⠀⠀⣼⢣⡇⠀⠀⠀⠀⠀⣿⠀⠁⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢿⡇⠀⢸⠀⢸⠀⠀⠀⠀⢸⣿⡆⡄⡀⠀⠀
⣀⣠⢀⠀⢰⡇⣬⡇⣤⣤⡄⢠⣤⣏⢠⡤⣄⢠⡤⣄⣤⣤⠁⣤⡄⢠⡄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⡀⡀⠀⠀⢸⣇⠀⢠⣠⣸⠀⠀⠁⠀⠻⣿⣇⢽⣿⡄⠀
⣿⣿⣟⡇⠿⠀⣿⠆⣿⣿⣷⢸⡷⣏⢸⡇⣿⢸⡧⢟⣿⡷⢰⣏⣿⢸⣿⣿⠀⠀⠀⠠⢠⠀⠠⠀⠀⠀⠀⠛⠂⡐⠒⠦⠖⠲⠞⠺⡆⢀⣛⢚⠛⠀⠀⣀⣼⣧⣵⣶⢆⢾⣿⣶⡿⠷⠝⢩⣤⣳⠀⡄⡹⠧⡭⠿⠞⢃
⣿⣿⠿⢗⡛⡂⠿⠖⠛⣿⡋⣸⣧⣿⣼⣷⣿⣸⣧⣴⣿⣷⣸⣯⣿⣸⣯⣿⣴⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣧⣶⣦⣦⣀⣻⣿⣷⣾⣿⣿⣿⣿⣿⣿
⠚⣭⣤⣀⣠⣤⣴⣶⣾⣿⣿⣟⣤⢩⣽⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢫⢅⡸⡿⣟⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⢻⣾⣾⣿⣿⣯⣿⣿⣾⣿⣽⣿⣿⣿⣧⣿⣼⣿⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⠸⢏⡹⠿⠟⠿⢿⣿⣿⣿⣯⣽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠶⣠⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⡟⣻⣥⣄⣲⡄⣝⠿⢿⠟⠙⠛⠛⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡄⠀⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭⠿⠟⠃⣸⣿⣷⠀⠀⠈⠉⠉⠐⢃⣿⣏⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣯⣿⣿⣿⣶⣾⣶⣶⣾⣿⣿⣿⣿⡟⣾⣆⠄⠀⠀⠀⠀⠉⠉⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣬⣽⠛⠛⠻⠿⠿⠛⠛⠉⠉⠉⠉⠉⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢈⡉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⡇⠲⣶⠀⠶⠆⠰⠶⠶⠆⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⣾⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠂⠀⣶⠂⠀⠀⠀⠀⠀⠀⢀⣰⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⡂⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⡄⠀⢲⢰⣤⡆⠀⡆⠀⢰⠀⢰⡆⠀⢰⠐⠀⠀⠄⠀⠀
⠀⠀⠀⠀⠀⢠⡟⡀⠀⠀⠀⠀⠀⣀⠰⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠁⠀⢽⠈⣿⡇⠀⣇⠀⢻⠀⠀⠃⠀⠸⡠⠀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⡾⢱⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⠃⢿⡇⠀⠸⠀⢸⠀⠀⠀⠀⢸⣿⡆⠄⡀⠀⠀
⣀⣄⢀⠀⢸⠇⣼⡅⣤⣤⣤⢠⣤⡇⢠⡤⣄⢠⡤⣄⣠⣬⠁⣤⡄⢠⡄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⢇⡀⠀⠀⠀⢸⣇⠀⢠⢠⣼⠀⠀⠀⠀⢻⣿⣗⢼⣿⢤⠀
⣿⣿⣿⡄⠟⠀⣿⠆⣿⣿⣷⢸⡿⣏⢸⡇⣿⢸⡧⢟⣿⡷⢰⣏⣿⢸⣿⣿⠀⠀⠀⠠⢤⠀⠀⠀⠀⠀⠀⠿⠂⠆⠒⠶⠒⠖⡛⢺⡞⣘⣛⢛⡃⠀⠀⣀⣼⣶⣴⣶⢆⣾⣿⣾⡿⠻⠙⢭⣤⣣⠀⠄⡽⢧⡨⠿⠞⣊
⣻⣿⠿⢟⡛⠂⠿⠖⢛⣿⡋⣸⣇⣿⣼⣷⣿⣸⣧⣶⣿⣷⣸⣯⣿⣸⣯⣿⣶⣶⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣶⣦⣤⡀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⣩⣤⣀⣠⣤⣴⣶⣿⣻⣿⡿⣯⢠⣄⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⡩⡨⠯⣟⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⢻⣾⣿⣿⣿⣿⣧⣿⣿⣿⣿⡿⣿⣿⣧⣿⣼⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢀⠀⢼⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⠇⡸⠿⠍⠿⠻⢿⣿⣿⣿⣿⣧⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⣸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣵⣧⣤⣩⡆⣽⢿⡿⠋⠙⢛⣛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣇⠀⠘⠀⣽⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⠧⠿⣟⣃⣸⣿⡧⠈⠀⠈⠉⠁⠘⣂⣿⣍⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿
⣸⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣖⠆⠀⠀⠀⠀⠉⠁⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡯⠉⠛⠛⠛⠛⠛⠉⠉⠉⠉⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⠷⣶⠀⠶⠔⠰⠶⠶⠆⠀⠀⡠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣟⣾⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⡖⠀⠀⠀⢀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠰⢰⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠆⠀⠀⡀⢀⡀⠀⡆⢴⣴⠂⠀⡄⠀⣶⠀⢰⠀⠀⡆⢐⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣸⢷⠀⠀⠀⠀⠀⢀⡄⢸⠰⠀⠀⢘⠀⠀⣿⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡻⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⣿⢸⣿⠀⠠⡇⠀⢿⠀⠐⠀⠀⠇⡌⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⡏⣼⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠿⠐⢿⡆⠀⠀⠀⠸⠀⠀⠀⢀⢼⣿⢀⢀⡀⠀⠀
⣤⣦⣤⠀⡿⠀⣽⠄⣤⣤⣤⢠⣼⡇⢠⡤⣄⢠⡤⣄⣤⣬⠀⣤⡄⢠⡄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⢀⠀⡀⠀⠀⠋⢠⢐⠀⠀⠀⢸⡇⠀⣠⣄⢆⠀⠀⡀⠈⣽⣿⣟⣸⣿⠀⠀
⣿⣿⣽⢘⣃⠀⣿⠆⣿⣿⣿⢸⡿⣏⢸⡇⣿⢸⡷⠟⣿⡿⢸⣏⣿⢸⣿⣿⠀⠀⠀⠐⠦⣀⣀⡀⢀⣀⣈⣉⣃⣀⣉⣛⣋⣛⣉⣛⣉⣩⣟⣙⣁⣐⣠⣤⣽⠶⠷⠾⠮⢿⡷⡿⠛⠛⠭⠥⣼⠥⠠⠠⠿⡤⣼⣟⣙⣈
⣿⡛⠛⠫⠩⠓⠿⠶⣹⣿⣇⣸⣗⡿⠟⠷⣿⣸⣷⣿⣿⣷⣺⣿⣿⣸⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣴⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣠⣤⣤⣰⣶⢾⣿⣿⣻⣿⣿⣿⣧⣄⣴⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⡭⣀⠯⣽⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⢻⣿⣿⡿⢿⡿⠷⣿⣿⣿⣿⣷⣿⣿⡧⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣇⠸⠷⠆⠿⠻⢏⠹⣿⣿⣿⣧⣿⣾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣷⣿⣿⣶⣾⡆⣿⣻⠛⡁⠉⢩⣭⡛⢛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡇⠀⠈⠁⢹⣿⣿⣿⣿⣿⣿⣿
⣽⣿⣿⣿⠿⣿⣿⣿⣻⣿⣟⣛⣛⣶⣬⣤⣿⡿⡇⠀⠀⠀⠀⠀⢈⣵⡿⠬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿
⣻⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⡿⠿⠿⠏⠂⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⠃⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣶⠀⠶⠄⠰⠴⠶⠆⠀⠀⢠⣖⣶⡄⠀⠀⣀⠀⣀⡀⠀⠀⠀⠀⣿⡹⣾⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢰⡂⠀⠀⠀⠀⠀⠀⠀⡆⠆⠀⠀⠀⠀⢰⡆⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢲⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⢰⠀⢐⡆⣦⣴⠀⢠⠀⠀⡆⠀⢦⠀⠀⡆⡆⠀⠰⠀⠀⠀
⠀⠀⠀⠀⢀⡿⡅⠀⠀⠀⠀⠀⢠⠀⡇⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⠀⠸⡇⢹⣿⠀⢸⡀⠈⡇⠀⠉⠀⠀⢧⡂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣼⠁⡇⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠘⣿⠀⠀⠃⠀⡇⠀⠀⠀⢀⣿⣷⠠⢀⠀⠀⠀
⣴⣤⡄⢰⡏⠀⣧⠄⣤⣤⣤⢠⣿⡄⢠⡤⣄⢠⡤⣄⣤⣥⠀⣤⣄⢠⡄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣀⢀⠀⠂⠀⠑⡀⠀⠀⠀⠀⣻⡀⢀⣦⣴⣇⡀⢈⠀⠸⣿⣿⠦⣿⡇⠀⠀
⣿⣿⣇⣛⣀⠀⣿⠆⣿⣿⡿⢸⡿⣏⢸⡇⣿⢸⡷⠟⣿⡷⢸⣏⣿⢸⣿⣿⠀⠀⣀⣂⣆⣀⣀⣀⣀⣀⣈⣁⣀⣀⣙⣓⣙⣋⣙⣉⣁⣬⣍⣍⣀⣀⣠⣴⣽⡶⣷⠿⢼⣿⣷⠿⠛⠋⠭⠴⠮⠄⠠⠠⢿⣴⣾⣟⣉⣉
⢞⠟⠛⠍⠙⠓⠿⣶⣻⣾⣧⣸⣷⣿⣝⠿⠟⢻⣷⣿⣿⣷⣻⣿⣿⣸⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣄⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣠⣤⣴⣶⣾⢿⣿⣿⣿⣿⡿⣿⢿⣿⣦⣤⣾⣟⣿⣿⣿⣿⡟⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢭⢄⠼⢽⣿⣿⣿⣿⣿⣿⣿
⣸⣿⣿⣿⣿⣻⣿⣿⣿⣿⡿⠗⣿⣿⡿⢿⣿⣿⣿⣇⣿⢻⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠠⠄⠀⢻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠆⠿⣻⠇⠸⠇⢹⣿⣧⣿⠾⡿⣿⣿⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⢐⣶⣄⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⣼⣿⣿⢻⣷⣿⠘⣯⣏⠁⠀⠀⠶⠬⠉⣍⢽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣽⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣽⣭⣽⣶⣶⣿⣿⣀⢀⠀⠀⠀⠀⠴⠿⠛⠚⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠰⠀⣸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⡿⠿⠿⠟⠛⠛⠻⠛⠘⠛⠊⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⡄⣹⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣢⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢻⣿⣿⣿⣿⠶⠄⠠⠶⠶⠆⠀⠀⠀⠀⣔⣽⣵⡄⠀⠀⠄⠠⠤⠀⠀⠀⠀⠸⣷⣿⠇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⢰⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⡂⡂⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠐⠀⠐⠂⠀⡦⠀⢰⠰⣦⡆⠀⣦⠀⢰⡆⠀⡆⠀⢰⠀⠀⠀⠀⢠⠀⠀
⠀⠀⠀⠀⢰⢏⡀⠀⠀⠀⠀⠀⣤⠀⠂⡆⠀⠀⠀⠀⢸⡀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠸⡇⣿⡇⠀⢹⠀⢘⡇⠀⠁⠀⠈⣠⡂⠄⠀⠀⠀⠀
⠀⠀⠀⢀⡟⢸⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡁⠀⠀⠘⠇⠻⣧⠀⠀⠀⠘⠃⠀⠀⠀⣤⣿⡧⡆⣄⠀⠀⠀
⣶⣤⠀⣼⠁⠈⣥⠄⣤⣤⣤⢠⣧⡄⢠⡤⣄⢠⡤⣄⣤⣥⠀⣤⣄⢠⡄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡀⠀⠀⡀⠀⢀⢠⣀⡀⣀⣀⣀⣤⠀⠄⠈⢠⡆⠄⠀⠀⣠⣿⠀⣠⣧⣶⣄⡀⣀⠀⠈⣿⡿⠇⣿⠇⣃⡀
⣻⣿⣂⣃⣀⡀⣿⢆⣿⣿⡿⢸⡷⣏⢸⣗⣿⣸⡷⠟⣿⡷⢸⣏⣿⢸⣿⣿⢀⡀⡀⣘⣂⣠⣀⣀⣀⣀⣈⣀⣀⣀⣹⣭⣀⣉⣩⣌⣍⣽⣭⣈⣀⣀⣦⣾⣿⣻⡿⢓⣻⣿⡿⠛⡉⣓⠴⠒⠋⢀⢀⣜⣓⣒⣿⣋⣁⣉
⡱⠙⠣⠉⠛⠉⣿⣶⣿⣾⣿⣾⣿⣿⣽⣷⠟⠹⢿⣿⣿⣿⣺⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡠⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣤⣤⣶⣶⣿⣿⣿⣿⣻⣿⡟⣿⢿⣿⣿⣤⣤⣿⣿⣿⣿⣿⡟⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠰⠢⠜⠿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⠅⣿⣿⡿⢿⡿⢿⣿⣧⣿⢼⣿⡗⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⠀⠐⠆⡀⠙⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠿⢿⣗⣸⠇⡄⢹⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡐⠖⢀⠈⢿⣶⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣼⣟⣻⡿⠿⢸⣿⡏⠀⠀⠐⠒⠂⠩⡕⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠀⢿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣽⣭⣭⣭⣿⣶⣶⣾⣿⣭⣄⡀⠀⠀⠀⠀⠚⠛⠛⢚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⢰⡀⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣛⠛⠿⠿⣿⣿⡿⠿⠟⠛⠛⠛⠛⠛⠋⠛⠋⠀⠀⠀⠀⠀⠀⠂⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣧⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣮⣶⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢽⣿⣿⣿⣿⣷⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⣮⢿⣵⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠻⣾⡿⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢰⡆⠀⠀⠀⠠⠀⠀⠀⡰⠂⠀⠀⠀⠀⠀⡦⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⢐⢰⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⠀⡆⠀⢶⢰⣶⡆⠄⡆⠀⣲⠀⠐⡆⠀⢰⢐⠀⠄⠂⠀⠀⡀
⠀⠀⠀⠀⣾⢡⠀⠀⠀⠀⠀⢠⡄⢸⢰⠀⠀⠀⠀⠀⣧⠀⠈⠀⠀⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢘⡗⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠝⠀⠀⠀⣿⠀⣿⡇⠀⢧⠀⢸⠀⠀⠀⠀⢸⣄⡀⠆⠀⠈⠀⠀
⠀⠀⠀⣸⠃⣿⠀⠀⠀⠀⠀⢸⠁⠀⠈⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⢀⠄⠀⠻⠈⢿⡇⠀⠨⠀⢸⠀⠀⡀⠀⣼⣿⡇⢆⣄⠀⠀⠀
⣤⡄⢀⡏⠀⡯⣤⠤⣤⢠⣄⣸⣤⣄⢠⡤⣄⢠⡤⣄⣬⣤⠀⣤⣄⢠⡄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡅⡀⢀⣀⡀⣀⣀⣀⣀⠀⢀⣤⣀⡆⠀⠀⠀⣡⠀⡀⠀⡀⣸⣧⢀⣼⣶⣾⣠⡀⣀⠀⠹⢿⡧⢶⣿⢑⣀⡄
⢽⣇⣘⣀⢀⠐⣿⠆⣿⣿⡿⢻⣷⣏⣼⡇⣿⣸⣷⣟⣿⡷⣹⣏⣿⢸⣿⣿⢀⣀⣈⣓⣠⣤⣤⣠⣥⣄⣩⣭⣍⣨⣯⣥⣭⣭⣬⣭⣬⣯⣥⣄⣠⣐⣶⣿⣛⣛⣛⣓⣻⣿⣿⣋⣙⣒⡖⠂⠑⢀⣂⣻⣷⣞⣿⣫⣠⣠
⠚⠛⠭⠙⠓⢉⣿⣶⣿⣿⣿⣾⣿⣿⣾⣷⡟⠸⠟⣿⣿⣿⣻⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠤⢾⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣤⣶⣶⣾⣿⣿⣿⣿⣻⣿⣟⣿⣿⣿⣿⣷⣦⣾⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠐⠃⠞⠻⣿⣿⣿⣿⣿⣿⣿
⣺⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⡏⣿⣿⡟⢻⡿⠿⣿⣷⣿⣼⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⢀⡀⢂⣄⢘⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠿⡿⣷⣸⡇⣠⡘⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⠈⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣛⣿⡿⠇⢿⣿⡀⠂⠀⠚⠒⠂⠴⢼⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣷⣶⣶⣶⣾⣿⣧⣠⡀⠀⠀⠀⠐⠛⠉⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢰⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡟⠻⠿⠿⣿⣿⠿⠿⠛⠛⠛⠛⠛⠛⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢹⣇⠘⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣯⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡆⠰⠶⠶⠆⠀⠀⠀⠀⠀⢰⡿⢟⣧⠀⠀⠐⠀⠒⠀⠀⠀⠀⠘⠽⡿⠃⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡀⠀⠀⣶⠀⠀⠀⠀⠄⠀⠀⠀⠖⠀⠀⠀⠀⠀⢰⡆⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⣀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⢰⠀⠰⡆⢶⣴⠀⢰⠀⠀⡆⠀⡰⠀⠀⡆⠀⠀⠀⠀⡄⠀⠀
⠀⠀⠀⢰⣏⡄⠀⠀⠀⠀⠀⣴⠀⡇⡅⠀⠀⠀⠀⢸⡇⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡇⢸⣿⠀⠸⡆⠀⡇⠀⠈⠀⠀⣷⣼⠐⠀⠀⠁⠀⠀
⠀⠀⢀⡟⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⠰⠀⠀⠋⠈⣿⠀⠀⢀⠀⡃⠀⠠⠀⢠⣿⣿⣸⢰⣄⡀⠀⠀
⣤⠀⣸⠁⢸⡇⣤⡄⣤⣤⣤⣧⣤⡄⢠⡤⣄⢠⡤⣄⣤⣤⠀⣤⣄⢠⡄⣤⠀⠀⠀⠀⠀⠀⠀⠠⠀⢨⣀⠀⢀⣀⣀⣀⣀⣄⣀⣀⣤⣄⣰⠀⠀⠀⠁⣶⣀⡀⣀⢀⣿⡄⣠⣿⣾⣧⠤⢠⡄⠘⢿⣿⠻⢿⡏⣤⣤⡀
⣽⣃⣋⣀⣀⠂⣿⠆⣿⢿⡟⢻⡷⣏⣺⣇⣿⢸⣧⣟⣿⣿⣸⣏⣿⢸⣿⣿⢀⣀⣁⣂⣤⣤⣤⣤⣤⣠⣥⣭⣤⣼⣭⣬⣭⣬⣥⣤⣾⣤⣤⣤⣤⣔⣾⣿⣿⣿⣻⣼⣿⣿⣟⣥⣉⣐⣟⡁⠀⢐⣤⣿⣿⣭⣭⣤⣤⣤
⠘⠫⠍⠛⠋⣁⣿⣶⣿⣿⣿⣾⣿⣿⣿⣿⣿⠸⠏⢹⣿⣿⣻⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠐⢻⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣴⣶⣶⣻⣿⣿⣿⣿⣻⣿⣟⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠈⠁⠊⠹⣿⣿⣿⣿⣿⣿⣿
⣼⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣾⡏⢸⡟⠻⢿⣿⣿⢿⣿⡍⣿⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠠⠶⢱⣤⣼⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⢿⣼⣇⣢⣞⢿⣿⣿⠟⠛⠿⠻⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠤⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣽⣽⣟⠿⠈⣿⣆⠒⠀⠈⠙⠁⠀⢎⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣯⣭⣿⣿⣶⣶⣿⣿⣿⣽⣤⠄⠀⠀⠀⠀⠉⠉⠉⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣧⠀⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣭⠟⠛⠿⠿⠿⠿⠟⠛⠛⠛⠉⠉⠙⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⡆⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⢿⣷⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⣾⣖⣿⡆⠀⠐⠀⠈⠉⠀⠀⠀⠀⠺⠿⠟⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⡂⠂⠀⠀⠀⠀⠰⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⡀⢰⠀⠀⡆⠔⣴⠀⢰⠀⠀⣆⠀⠐⠀⠀⣆⠀⠀⠀⠀⡀⠀⠀⠀
⠀⠀⢀⡿⡇⠀⠀⠀⠀⠀⢰⠀⠁⢀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⣿⠘⣿⠀⠰⡃⠀⡑⠀⠈⠀⠀⢡⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣼⠁⡧⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠠⠀⠀⠋⠈⢿⠀⠀⢀⠀⡁⠀⠠⠀⢀⣾⣿⢈⢰⣄⠀⠀⢀⠀
⡄⢰⡏⠀⡷⠀⣤⠄⣤⣤⣿⢠⣤⣄⢠⡤⣄⢠⡤⣤⣤⡤⠀⣤⡄⢠⡄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⣀⣀⣀⣀⣄⣀⡀⢠⣄⣠⠄⠀⠀⠁⣲⣐⡀⣀⢀⣮⣇⣠⣾⣾⣷⠄⢠⡄⠘⠺⣿⠛⢿⣇⣠⣠⡀⣀
⢃⣚⣀⡀⡐⠒⣿⠆⣿⢿⣿⢸⡷⣏⣺⡇⣿⢸⡷⣿⣿⣷⣰⣏⣿⢸⣿⣿⣀⣀⣃⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣤⣥⣬⣥⣤⣴⣮⣤⣤⣤⣴⣾⣿⣿⣿⣋⣸⣿⣿⣿⣥⣁⣐⣻⣛⠀⠈⣠⣿⣿⣭⣭⣤⣤⣴⣶
⠘⠅⠉⠋⣉⣀⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⠈⣻⣿⣺⣿⣿⣸⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣠⣶⣶⣿⣻⣿⣿⣿⣿⣻⣿⣟⣿⢿⣿⣿⣿⣿⣿⣶⣿⣻⣿⡟⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠙⠑⠉⢿⣿⣿⣿⣿⣿⣿⣿
⣸⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣾⣏⢸⡏⠛⢻⡿⣿⣾⡿⠷⣿⣭⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⣤⣈⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡸⣧⣥⣺⣧⢿⣿⡿⠛⠿⠛⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠛⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠽⠿⠛⢀⣷⣦⠀⠀⠀⠉⠉⠀⢃⣿⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⢷⣶⡢⠀⠀⠀⠀⠉⠁⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣸⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⡏⠙⠛⠛⠛⠛⠋⠉⠉⠉⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢻⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢄⠀⠀⠀⠀⠀⣀⠀⠀⠀⢜⣞⣾⡧⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⡶⠶⠆⠀⠀⠀⠀⠀⠀⠀⢾⣏⣿⡇⠀⠈⠁⠀⠀⠀⠀⠀⠈⠓⠛⠁⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⢰⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⡆⡂⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢒⠀⡦⠀⢰⡤⢶⡆⠄⣶⠀⢰⡆⢀⡆⠀⢰⡆⡆⠀⠀⢀⠀⠀⠀⠀
⠀⠀⢰⣟⡄⠀⠀⠀⠀⠀⣤⠀⠀⡄⠀⠀⠀⠀⢸⡆⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡇⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠸⡇⠁⠀⢸⡇⣿⡇⠀⢻⠀⠨⠇⠀⠁⠀⠈⣧⡇⠂⠀⠀⠀⠘⠀⠀
⠀⢀⡟⢸⡇⠀⠀⠀⠀⠀⡏⠀⠁⠁⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠤⠀⠸⠇⢹⣷⠀⠀⠄⠘⠃⠀⠀⠀⣤⣿⣟⡆⣶⡀⠀⠀⡀⠀
⠀⣼⠁⢸⠆⠀⣤⠄⣤⣠⣧⢠⣤⣄⢠⡤⣄⢠⡤⣅⣤⡤⠀⣤⡄⢠⡄⣤⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⣀⣀⢀⣀⣠⣀⣀⣀⢤⣄⡤⠀⠄⠈⢱⣆⡇⠀⠀⣠⣽⢀⣰⣷⣾⣦⣀⢠⠀⠀⣿⣿⠿⣿⣇⡄⣠⢁⣀
⣀⣇⣀⣀⠒⠖⣿⠆⣿⢿⣿⢸⡷⣟⢸⡇⣿⢸⡷⣟⣿⣷⣰⣏⣿⢸⣿⣿⣀⣘⣀⣤⣄⣠⣄⣠⣀⣬⣬⣡⣙⣭⣭⣭⣭⣯⣄⣽⣭⣭⣀⣁⣲⣿⣟⣻⣛⣓⣻⣿⣟⣏⣉⣁⣶⣶⠎⠂⠂⣚⣛⣲⣿⣯⣦⣤⣬⣶
⠠⠉⠛⠉⣁⣀⣿⣶⣿⣿⣯⣿⣿⣿⣿⣿⣿⣾⣷⠀⠻⢿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣄⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣠⣶⣶⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⢿⣿⣿⣿⣻⣿⣷⣾⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠶⠢⠻⣿⣿⣿⣿⣿⣿⣿⣿
⣸⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣾⡇⢸⡏⠙⢻⡟⣿⣿⣿⠟⣿⣍⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠠⡀⠈⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣸⣷⣯⣼⣧⡿⣿⣿⠟⠿⠛⢿⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣀⠀⠀⣻⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠿⠟⠃⣸⣷⡆⠀⠀⠈⠉⠁⠘⣸⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠈⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣺⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡷⣶⣖⠄⠀⠀⠀⠈⠉⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⡀⠀⠀⠀⠀⢀⡀⠀⠀⢰⣽⣳⢿⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢹⣿⣿⣿⣿⣿⣿⣿⣷⠶⠆⠀⠀⠀⠀⠀⠀⠀⢸⢾⣵⡿⠀⠀⠉⠀⠀⠀⠀⠀⠈⠓⠛⠋⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣖⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⢀⡆⠀⣶⢰⣶⠆⠀⡆⢀⣰⠀⢐⡄⠀⢰⢰⠀⠀⠂⠀⠀⠀⠀⠀
⠀⠀⣼⢻⠀⠀⠀⠀⠀⠀⡆⠸⢸⠀⠀⢈⠀⠀⢿⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠸⠀⠇⠀⢻⠌⣿⡇⠀⣧⠀⢻⠀⠈⠁⠀⢸⣾⡄⠀⠀⠀⠀⠃⠀⠀
⠀⢰⡇⣽⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡄⠀⠿⠓⣿⡇⠀⢸⠀⢸⠀⠀⠀⢀⣸⣻⣦⢠⣄⠀⠀⠀⠀⠀
⢀⡿⠀⢹⠀⠀⣤⠄⣤⣼⡇⢠⣤⣄⢠⡤⣄⢠⡬⣄⣤⡤⠀⣤⡄⢠⡄⣤⠀⠀⠀⠀⠀⠀⠀⠀⣁⡀⠀⠀⠀⠀⡀⣀⢀⢀⣀⣀⣀⡄⠀⠀⠘⢹⡄⠀⡀⠀⣸⣧⠀⣸⣶⣾⣀⢀⡄⠀⢘⣿⣿⣿⣿⣽⡀⡄⠀⠄
⢘⣁⣀⢘⠰⡆⣿⠆⣿⢻⣿⢸⡷⣏⢸⡇⣿⢸⡷⡟⣿⣷⣸⣏⣿⢸⣿⣿⢘⣐⣀⣄⣀⣀⣠⣀⣉⣁⣁⣁⣓⣉⣛⣋⣹⣉⣨⣭⣈⣁⣀⣀⢴⣿⣿⣿⠿⣣⣿⣿⣿⣟⢛⣭⣴⡾⡵⠀⠄⣾⣷⣞⣟⣫⣌⣁⣼⣿
⠨⠉⠛⢉⣁⣀⣿⣶⣿⣿⣯⣿⣿⣿⣿⣷⣿⣼⣿⡟⠻⠿⣻⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣶⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣟⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⣩⠤⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣸⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣾⡏⢸⡏⣉⣹⡟⣿⣿⣿⠝⣿⠿⣿⣽⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢈⠀⠙⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣇⣿⣽⣧⣿⢸⣿⡿⠿⠉⠿⣛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠅⠀⠀⠀⢷⣄⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠯⠿⢛⣀⣿⣷⠉⠁⠀⠉⠉⠀⢓⣽⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠀⠀⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⢶⣶⡲⠀⠀⠀⠀⠉⠉⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢰⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣄⠀⠀⠀⠀⢀⣀⠀⠀⠀⣮⣞⡷⡧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠛⠁⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣰⡆⠀⠀⠀⠀⠀⠀⠀⡔⠂⠀⠀⠀⠀⢰⡶⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢰⢠⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠆⠀⠰⡆⢰⠀⠀⣆⢶⣶⠰⢰⡀⠠⡆⠀⣲⠀⠀⣆⣖⢠⠐⠀⡄⠀⠂⠀⠀
⠀⢀⡿⣇⠀⠀⠀⠀⠀⢰⠀⠁⢤⠀⠀⠀⠀⠀⣧⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢸⣸⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠁⠀⠀⣷⠘⠀⢐⣿⢺⣿⠀⢸⡇⠀⡯⠀⠘⠀⠀⣿⣾⠸⠀⠀⠁⠀⠁⠀⠀
⠀⣼⠁⡿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡠⠆⠐⠟⠘⣿⡄⠸⢅⠀⡇⠀⢠⠀⢠⣿⣿⣰⣰⣄⡀⠀⠀⠀⠀
⢰⠇⠀⡟⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⠀⢀⣀⣀⣀⣀⣄⣀⣀⣰⣤⣠⠄⢐⠀⠋⣦⣴⣐⣀⢁⣿⣇⣠⣾⣿⣧⣄⣤⡀⠘⠿⣿⠿⢿⣿⣧⣠⠀⢠⡀
⢩⣤⣀⣉⡻⠷⠃⠀⠀⠙⣀⣀⣌⣃⣀⣐⣁⣀⣀⣠⣫⣤⣿⣀⣀⣀⣀⣄⣉⣣⣤⣥⣤⣤⣤⣤⣬⣬⣥⣬⣭⣭⣭⣬⣯⣭⣽⣯⣭⣤⣤⣴⣾⣿⣿⣿⣿⣺⣿⣿⣿⣉⣙⣶⣶⣿⡣⠰⣘⣿⣷⣿⣟⣯⣬⣥⣽⣧
⠐⠈⢉⣀⣤⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⣽⢬⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣤⣠⣬⠭⠉⢻⣿⣯⣉⡙⣳⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣈⠀⠹⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣸⣿⣿⣿⣷⡆⣿⣿⣛⣉⠈⢉⣍⡛⢛⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣷⡀⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡿⣿⣿⣗⣚⣛⣡⣽⡿⠗⠀⠀⠀⠀⠀⢈⣵⡿⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠐⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠿⠯⠃⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣤⣌⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣶⡄⠀⠀⣀⠀⠤⠄⠀⠀⠸⣻⣽⣾⠂⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣷⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢁⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣶⠀⠀⠀⠀⠆⠀⠀⠀⡖⠀⠀⠀⠄⠀⢰⡆⠀⡄⠀⢰⡀⠀⠀⠀⠀⠀⠀⢲⠀⠀⠀⠀⣤⡆⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢲⡆⣶⠀⢰⡤⣶⡖⠄⣖⠀⣰⡆⠀⡦⠀⢰⣆⡆⠀⠀⢠⠀⠀⠀⡀⠀
⠀⣸⢷⡇⠀⠀⠀⠀⠀⣾⠀⡇⡇⠀⠀⠄⠀⢸⡇⠀⠁⠀⠸⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢸⡇⠹⠀⢺⡇⣿⡧⠨⣿⠀⢸⡇⠀⠃⠀⢸⣷⡇⠂⠀⠈⠀⠘⠀⠀⠀
⢠⡏⢸⡇⠀⠀⠀⠀⠀⣿⠀⠁⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢨⣧⡗⠀⡸⢃⢻⣷⠀⠉⡇⢸⠇⠀⠀⠀⢼⣿⣟⣆⣦⡀⠀⠀⠀⠀⠀
⣾⠁⠸⠇⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⢺⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸⣄⣀⣀⣄⣀⣀⣠⣠⣀⡀⣤⣤⣴⠀⡇⠈⢙⣧⣇⣆⣀⣰⣽⣀⣴⣿⣿⣦⢀⣤⠀⠹⣿⣿⠿⣿⣷⣇⣠⠃⣀⠀
⢤⣤⣤⣉⠻⠚⠀⠀⢈⣁⣀⣀⣽⣀⣀⣈⣄⣀⣀⣸⣍⣀⢷⣦⣄⣄⣠⣀⣭⣧⣤⣤⣤⣤⣤⣤⣤⣵⣤⣭⣭⣿⣭⣬⣯⣤⣿⣵⣧⣤⣥⣶⣿⣿⣿⣿⣟⣿⣿⣿⣿⣉⣱⣶⣶⣟⠂⠒⢺⣟⣿⣿⣿⣧⣭⣬⣿⣶
⠈⢉⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⢼⢒⠿⣿⣿⣿⣿⣿⣿⣿⣿
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣤⣄⢤⢉⠹⣿⣷⣌⣉⣙⢶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠠⠀⢹⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣿⣿⢿⣿⡆⢿⣿⣟⣉⡀⠉⣭⡭⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣟⣛⣻⣭⣥⣼⣿⣟⡀⠀⠀⠀⠀⠀⡩⠾⠷⠭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⠀⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠙⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣷⣆⠀⠀⠀⠀⠠⠤⠀⠀⠀⢯⡯⣿⡗⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣉⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⢰⢠⠀⠀⠰⠀⠀⣶⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢠⠄⠀⠐⠀⠀⠀⠀⠀⠀⢶⠀⡆⠀⢶⢰⣶⡆⠄⣆⠀⢰⠀⢰⡆⠀⢰⢰⠀⡄⠂⠀⠀⠀⠀⡀⠀
⢀⡿⣿⠀⠀⠀⠀⠀⢀⡇⠸⠘⠀⠀⠠⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢸⠀⠃⠐⣺⡇⣿⡇⠘⢿⠀⢸⠀⠀⠃⠀⢸⣶⡇⠆⠀⠈⠀⠛⠀⠀⠀
⣼⠃⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢨⣦⠆⠀⠛⢀⢻⡇⠀⢸⠀⢸⠀⠀⡄⠀⣾⣿⣇⢶⣦⣠⠀⠀⠀⠀⠀
⠏⠀⢹⢀⡀⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⣷⠀⢀⡀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠃⠀⢤⢄⣀⣤⣄⣠⣄⣤⣤⣠⣠⣦⣤⡖⠀⠀⠈⢸⣦⣤⣇⡀⣼⣷⣠⣾⣿⣿⡤⣠⡆⠀⠻⢿⡾⠿⣿⣿⣄⡆⢀⢆⠀
⢲⣴⡤⠽⠛⣛⠀⣀⣈⣡⣄⣤⣥⣤⣤⣭⣤⣤⣤⣭⣤⣬⠵⢶⣤⣤⣤⣤⣬⣤⣦⣦⣤⣴⣤⣴⣶⣶⣤⣽⣴⣧⣥⣼⣧⣼⣶⣴⣤⣤⣤⣾⣿⣿⣿⣻⣷⣿⣿⣿⣯⣉⣶⣶⣿⡿⠀⠂⢿⣛⣿⣿⣿⣴⣥⣼⣿⣶
⢀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣄⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠁⠾⠢⠺⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢠⣄⡠⡀⡈⢻⣿⣶⣬⣌⣹⣾⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠠⠀⣼⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣿⡿⢿⣿⠘⣿⣿⡏⠥⡀⠡⠬⠝⢛⡫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢠⡀⠀⠀⣀⣷⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣭⣥⣴⣿⣟⣋⣀⡀⠀⠀⠀⠠⠿⠿⠶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠟⠻⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣖⣤⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣵⡄⠀⠀⠤⠀⠠⠀⠀⠀⠸⣾⣽⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠫⣿⠿⠁⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣉⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠆⡀⠀⠀⠀⠀⠰⡖⠀⢰⠀⠀⡄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢰⢰⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠄⠀⠐⣆⢰⡆⠂⣦⢠⣶⠴⢰⡆⢠⣶⠀⣲⠀⠀⣦⣔⠀⠀⠀⡄⠀⠀⠀⠀⠀
⢰⡿⣇⠀⠀⠀⠀⠀⢸⠀⠀⠸⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⡸⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠁⠀⠀⣿⢈⠆⠀⣿⢸⣿⠀⣽⡇⠀⡯⠀⠘⠀⠀⣫⣾⠰⠀⠀⠁⠀⠃⠀⠀⠀
⡾⠀⡷⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣰⠄⢈⠿⠈⢿⡆⠈⠁⠀⡏⠀⠀⠀⢠⣾⣿⣰⣰⡀⠀⠀⠀⠀⠀⠀
⠁⠀⠏⣀⡀⠀⠀⠀⣿⠀⠀⠀⡀⠀⠀⠀⠀⠀⠸⣇⠀⢠⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢠⣇⠀⢀⣀⣀⣀⣀⣆⣀⣀⣠⣤⣠⡄⢸⠀⠉⣮⣸⡠⢀⢀⣽⣇⣠⣿⣾⣷⣄⣀⡀⠈⢽⣿⣿⢿⣿⣠⣀⠄⠀⠀⠀
⢠⣤⡬⠝⠛⠃⠀⣀⣉⣠⣤⣬⣥⣤⣤⣥⣠⣠⣤⣭⣄⣉⡀⢶⣦⣤⣤⣤⣥⣴⣦⣤⣤⣤⣤⣤⣬⣤⣬⣭⣥⣭⣭⣭⣭⣿⣯⣯⣥⣬⣴⣾⣿⣿⣟⣟⣾⣿⣿⣿⣉⣛⣶⣶⣿⡣⠐⠈⣟⣶⣾⣟⣯⣭⣥⣽⣷⣼
⢀⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣠⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠠⠿⡢⠿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣤⢠⣈⠙⣿⣿⣤⣭⣈⣽⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣤⠀⣼⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣸⣿⡿⣿⡇⢻⣿⣿⡋⣀⠈⠥⡭⠛⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢠⠀⠀⠀⢈⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣯⣥⣤⣼⣿⣟⡃⡀⠀⠀⠀⠀⡩⠿⠿⠮⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠈⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠟⠿⠿⠙⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣾⣟⣆⠀⠀⠠⠀⠠⠤⠀⠀⠀⢻⣯⣿⡟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠏⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣉⣉⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣶⡄⠀⠀⠀⠀⠀⠀⠀⡆⡀⠀⠀⠂⠀⢰⡆⠀⡆⠀⢠⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠠⠀⠀⢐⡆⣶⠀⢰⡆⣶⣶⠀⣲⠀⢴⡆⠀⣶⠀⢰⡦⡆⠄⠀⢠⠀⠀⠀⠀⠀⠀
⣼⢻⡇⠀⠀⠀⠀⠀⣿⠀⠇⠇⠀⠀⠇⠀⢸⡇⠀⠆⠀⠘⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣿⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠱⠀⢺⡷⣻⡿⠐⣻⡀⢸⡇⠀⠁⠀⠸⣽⡗⠂⠀⠀⠀⠘⠀⠀⠀⠀
⠇⢸⡇⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠈⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⣇⡶⡀⢸⠃⠹⣿⠀⠀⡇⢀⡇⠀⠄⠀⣶⣿⣿⣇⣶⣀⡀⠀⡀⠀⠀⠀
⠀⠘⣃⣀⢀⠀⠀⢀⡇⠀⠀⢀⠀⠀⢀⠀⠀⠆⢹⡀⠀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠠⠀⠼⣤⡀⣤⣤⣤⣤⣴⣤⣤⣤⣶⣦⣴⠀⡇⠘⣸⣷⣧⣁⣀⣤⣿⣄⣴⣿⣿⣧⠄⣴⠀⠻⠿⣿⠟⣿⣧⣧⣰⠁⢠⠀⠀
⢠⡶⠬⠙⣉⡀⣀⣀⣠⣤⣤⣮⣦⣤⣬⣤⣤⣤⣬⣤⣤⣥⣤⠘⠷⣶⣤⣬⣷⣶⣷⣶⣶⣶⣶⣶⣶⣦⣾⣶⣶⣶⣶⣷⣦⣾⣶⣦⣤⣤⣷⣿⣿⣿⣟⣯⣿⣿⣿⣫⣍⣕⣿⣿⣟⠆⠓⠚⣟⣻⣿⣽⣶⣴⣤⣿⣿⣾
⢀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⠰⠃⠔⠻⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣰⢀⣦⡄⢻⣿⣷⣶⣤⠮⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠰⠦⢠⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣽⣟⠻⢿⠈⣿⣿⣿⠤⠄⠀⠦⠍⢩⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣰⠀⠀⢀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣯⣭⣭⣽⣶⣶⣿⣟⣭⣀⡀⠀⠀⠀⠠⠾⠟⠛⠺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠈⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⢿⣿⡿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠃⠁⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣶⣦⡈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢾⢿⣳⠀⠀⠀⠀⠀⠒⠂⠀⠀⠘⢿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡁⠀⠀⠀⠀⠀⠀⠀⠻⠯⠟⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣄⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡶⡄⠀⠀⠀⠀⠀⠀⠀⡆⡄⠀⠀⡂⠀⢰⡆⠀⠄⠀⢰⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⢴⠀⢰⡆⢶⣶⠠⢰⠀⢴⡆⠀⣶⠀⠐⡦⡆⠀⠐⠀⠀⠀⠀⠀⠀⠀
⣸⢫⡇⠀⠀⠀⠀⠀⣿⠀⡇⠇⠀⠀⠃⠀⢸⡇⠀⠀⠀⠸⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢽⢴⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠇⠘⡇⠸⠀⢐⡇⢺⡿⠀⢸⡄⠘⡇⠀⠀⠀⠀⣷⡷⠀⠈⠀⠀⠘⠀⠀⠀⠀
⡏⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⡶⠀⠸⠃⠘⣿⠀⠀⡇⢀⡇⠀⠠⠀⢰⣿⣿⣦⣶⡀⡄⠀⠀⠀⠀⠀
⠀⠠⠇⣀⠀⠀⠀⠀⡟⠀⠀⢀⠀⠀⠀⠀⠀⠄⢸⡄⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠀⢸⢤⣀⣤⣤⣤⣤⣤⣤⣤⣤⣴⣦⣼⠀⠀⠈⢑⣧⣤⣜⣀⢤⣿⣆⣤⣿⣿⡧⠄⣼⠀⠋⠿⣿⠿⣿⣧⣧⣰⠀⣰⡀⠀
⢠⣤⠌⠛⠛⠂⢀⣀⣁⣄⣠⣬⣤⣄⣬⣀⣤⣤⣬⣥⣤⣭⣤⣤⣤⠚⢿⣷⣥⣶⣥⣴⣶⣦⣶⣶⣶⣦⣼⣶⣶⣤⣴⣷⣤⣶⣶⣶⣤⣤⣶⣿⣿⣿⣿⣯⣾⣿⣿⣛⣍⣁⣿⣿⣷⣡⠐⠞⢿⣿⣿⣽⣶⣶⣶⣾⣿⣶
⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⡽⢄⠼⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣢⣌⢻⣿⣷⣾⣤⡬⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠠⠀⢰⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣗⠻⠿⢸⣿⣽⣷⠥⠤⠀⠦⠍⢩⡫⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿
⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣽⣶⣶⣶⣿⣯⣭⣀⡀⠀⠀⠀⠠⠾⠛⠓⠺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⠀⠀⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠘⠛⠃⠁⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿
⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣲⣦⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢰⣿⢾⣧⠀⠀⠀⠀⠀⠒⠂⠀⠀⠘⣽⣞⡿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠘⠯⠿⠋⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣶⡄⠀⠀⠀⠀⠀⢀⠀⡆⡆⠀⠀⡂⠀⢰⡆⡄⠆⠀⢰⠄⠀⠀⠀⠀⠆⠀⡒⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡂⣰⠀⠰⡆⢶⣶⢐⢰⠀⠰⡆⠀⣶⠀⠀⡶⡆⠀⠐⠀⠀⢠⡀⠀⠀⠀
⣸⢣⡇⠀⠀⠀⠀⠀⣿⠀⠃⠇⠀⠀⠃⠀⠘⡇⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠘⡇⠘⡀⢡⡷⢸⣿⠀⠚⡂⠀⡇⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠈⠀⠀⠀⠀
⡏⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣧⡾⠀⢸⠃⠜⣿⠀⢀⡇⢀⡇⠀⢰⠀⢲⣿⣿⣮⣴⡄⡄⠀⠀⠀⠀⠀
⠀⠈⣃⣀⡀⠀⠀⢀⣿⠀⠀⢀⠀⠀⢀⠀⠀⠃⢘⣄⠀⣰⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠰⠀⢰⠦⠠⠤⣤⣤⠤⣤⢦⣤⡤⡲⣶⡾⠄⠃⠈⠹⣷⣶⣼⣤⢰⣿⣦⣾⣿⡿⠧⠢⣾⡀⠘⠟⣿⠛⢿⣷⡿⣼⣀⣴⡄⢀
⢠⡢⠮⠙⣋⣁⣀⣀⣈⣤⣤⣤⣤⣤⣬⣤⣤⣤⣬⣥⣤⣥⣤⣤⣤⡴⠙⢻⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣷⣶⣶⣼⣿⣿⣽⣯⣭⣿⣿⣿⣽⣤⣭⣽⣿⣿⣥⡬⠬⠩⣽⣽⣷⣷⣶⣶⣿⣷⣿
⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⣹⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⢻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢩⠅⡨⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣑⣄⢻⣿⣷⡶⣶⠤⢯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠠⠄⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡘⠿⢸⣿⣷⣿⠓⠂⠀⠒⠊⢩⣝⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣶⣶⣶⣷⣿⣿⣧⣤⣠⡀⠀⠀⠀⠐⠚⠛⠛⠚⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠀⠀⠚⠈⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⠻⠿⠛⠛⠛⠉⠉⠉⠉⠛⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣵⣦⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿
⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢬⣟⡶⡧⠀⠀⠐⠂⠀⠒⠀⠀⠀⠘⢿⣾⠞⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠈⠚⠛⠁⠀⢀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣶⡄⠀⠀⠀⠀⠀⢀⠀⡆⡄⠀⠀⡂⠀⢰⡆⡄⠄⠀⢰⠄⠀⠀⠀⠀⠄⠀⡒⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⢰⠀⢐⣦⢶⣶⠐⢰⡀⠲⡆⠀⢶⠀⠀⣶⣆⠀⠐⠀⡆⢠⡀⠀⠀⠀
⣸⢣⡇⠀⠀⠀⠀⠀⣿⠀⠃⠃⠀⠀⠃⠀⠘⡇⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠂⠀⠗⠘⡂⢩⣿⢸⣿⠀⢚⡇⠀⡇⠀⠈⠀⠀⣿⣿⢈⠀⠀⠀⠀⠀⠀⠀⠀
⡏⠸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠧⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡞⠀⢨⠃⠌⣿⠀⠈⣧⣠⡇⠀⢰⠀⢸⣿⣿⣼⣾⣄⡆⠀⠀⠀⠀⠀
⠀⠀⣃⣀⣀⠀⠀⠀⣿⠀⠀⢀⠀⠀⢀⡀⠀⠃⠐⣤⠀⣴⠀⠀⠀⠀⠀⣄⣄⡀⡀⠀⠘⠀⠰⠦⠠⡴⢴⣤⣴⡴⡖⠶⠶⠾⠶⠞⠆⠁⠀⢩⣷⣴⣼⣤⢰⣿⣧⣶⣿⡿⡿⣂⡴⡄⠐⠚⣿⣛⣻⣷⠿⠾⠀⠼⡄⡀
⢰⠦⠮⠙⣉⣁⣀⣀⣠⣤⣴⣶⣶⣤⣤⣶⣴⣶⣴⣶⣦⣶⣶⣶⣶⣶⣦⠉⠹⣿⣶⣶⣷⣶⣶⣾⣷⣷⣶⣶⣾⣶⣶⣷⣾⣿⣷⣶⣶⣶⣼⣿⣿⣾⣿⣿⣿⣿⣿⣯⣶⣶⣿⣿⣿⣷⡬⠉⠃⢿⣿⣷⣿⣷⣶⣿⣷⣿
⢠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⢨⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠛⠛⢿⣿⣿⣿⠿⡿⢿⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⡵⢠⠿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢀⢵⡆⣻⣿⣿⡿⡶⠖⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢠⠀⢾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢿⠉⠛⢸⣿⣶⠿⠓⠂⠀⠓⠂⠰⢕⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣴⣶⣤⡄⠀⠀⠀⠐⠋⠉⠙⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠉⢸⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠈⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣪⢭⣦⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⡷⣟⢿⡇⠀⠀⠀⠀⠈⠉⠀⠀⠀⠘⠯⡾⠞⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⢀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣶⡆⠀⠀⠀⠀⠀⢠⠀⡆⡆⠀⠀⠂⠀⢰⡆⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡂⢰⠀⠀⣆⢴⣶⠀⢐⡆⠀⡆⠀⠲⠀⠀⠖⠀⠀⠀⠀⠆⠠⠀⠀⠀⠀
⣼⢁⡇⠀⠀⠀⠀⠀⣾⠀⠀⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢈⠀⠀⡟⠸⣿⠀⠀⡇⠀⡇⠀⠀⠀⢀⣿⣿⢀⢀⠀⠀⠀⠀⠀⠀⠀
⠇⠘⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠓⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠷⡀⠀⠀⠀⠀⡻⡀⠀⣣⢄⡅⠀⠸⠀⢘⢿⣿⣼⣿⡇⡆⢀⠀⢀⠀⠀
⠀⠀⠥⣤⣄⠀⠀⠀⢿⠀⠀⠠⠀⠀⠠⠀⠀⠀⠈⠦⠀⠴⠀⠀⠀⠀⠀⠀⣤⣤⣄⠀⠀⠀⠘⠓⠐⠒⠲⠖⠒⠶⠓⠖⠋⣚⡓⡋⠀⠀⢀⣤⣿⢶⣶⠶⢸⣿⣷⣾⠟⠟⣋⣥⣞⡆⢀⢉⠿⣬⣽⡗⠓⠚⠀⣂⣆⢀
⠰⠴⠒⠈⣡⣄⣄⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣷⣶⣾⣶⣿⣾⣿⣯⢀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⣶⣿⣿⣷⣷⣶⣾⣿⣿⣾⣷⢂⠈⠘⣿⣿⣿⣿⣿⣿⣿⣿
⢠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠐⢻⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠈⠉⡉⠻⣿⣿⣿⣛⠟⠻⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡶⣶⣷⣶⣞⣿⣿⢻⣿⣶⣶⢰⡗⢺⢶⣷⣾⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣺⡆⣿⡿⠿⣟⡿⠋⠙⡚⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣟⣿⣿⣾⡯⣿⠉⢸⣏⣾⢾⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⣿⣿⣶⣈⣁⣸⣿⠿⠛⠉⠁⠀⠉⠁⠚⣪⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣀⡀⠀⢀⢠⣾⣿⣿⣿⣿⣿⣿
⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⡶⠄⠀⠀⠀⠈⠈⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⣷⣼⠈⣿⣿⣿⣿⣿⣿⣿
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠒⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠄⠇⠿⣀⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣤⣲⣦⡀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢸⣽⣳⢷⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣧⢠⣧⣤⣿⣿⣿⣿⣿⣿⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠄⠀⠀⠀⠀⠀⢽⣟⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣻⣿⣿⣹⣿⡟⣿⣾⣿
⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣆⣀⣀⠀⠀⠀⠀⠀⠉⢀⣀⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣽⣿⣿⣿⣿⣽⣿⣿⣿
⢠⣶⡆⠀⠀⠀⠀⠀⢠⠀⠆⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⣦⠠⢰⠀⠰⡆⠀⡆⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⠠⡇⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠛⠘⠱⠀⠀⠇⠀⡃⠀⠀⠀⢠⣷⣇⠰⣠⠀⠀⠀⠀⠀⠀⠀
⠃⠈⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣃⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⣠⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⣰⣢⡅⠀⢀⠀⠨⣽⣿⢯⣿⡇⣠⢀⠀⠠⠀⠀
⠀⠀⠃⠶⣦⠀⠀⠀⠻⠀⠀⠐⠀⠀⠠⠀⠀⠀⠀⠑⠀⠐⠀⠀⠀⠀⠀⠂⠂⣀⠶⢶⣦⡀⣀⣉⣀⣈⣙⣋⣉⣙⣛⣋⣃⣼⣍⣍⣀⣈⡠⣴⣾⢶⣿⠟⠼⢿⡷⠷⠛⠋⢡⡶⣮⣇⣠⣠⡛⠶⢾⣇⣍⣍⣤⣥⣧⣦
⠘⠛⢉⢀⣤⣦⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⢈⣿⣿⣿⣿⣿⣿⣿
⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠩⢙⡅⣽⣿⣿⣿⣿⣿⣿
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠙⣿⣿⣿⣯⣛⡙⣻⢼⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣷⣶⣞⣿⣿⢻⣿⣶⢲⢰⡖⢰⣶⣵⣾⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡄⠸⡇⣿⣟⣛⣫⣿⡁⢈⣙⡛⠿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢸⣏⣼⢾⣿⣿⣿⣿⣿⣿
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡭⣭⣭⣭⣤⣤⣾⣿⢛⡛⠀⠈⠀⠀⠀⢙⣼⣿⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣧⡆⠀⠀⠴⢸⣿⣿⣿⣿⣿⣿
⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡿⠿⠿⠟⠛⠛⠛⠛⠛⠻⠟⠟⠿⠿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡇⣷⣼⠈⡏⣿⣿⣿⣿⣿⣿
⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢄⠁⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⢇⣿⠀⢷⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢰⣿⢽⣦⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⣟⣟⣷⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣧⢠⣿⣿⡄⣿⢿⣿⣿⣿⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠂⠀⠀⠀⠀⠘⠯⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼⣿⣿⣿⣿⣿⣧⣿⣿⣟⣿⣿⣿⣿⣾⣿⢸⣿⡏⣿⣾⣿
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣧⣄⣀⣀⣀⣀⣀⣀⣤⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣾⣿⣽⣿⣿⣿⣿⣽⣿⣿⣽
⢠⡖⡆⠀⠀⠀⠀⠀⢰⠀⠄⠄⠀⠀⡀⠀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⢰⠀⠀⡂⠀⡆⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡾⢀⡇⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠛⠀⠰⠀⠀⠀⠀⠃⠀⢀⠀⠀⣳⣅⠀⣠⠀⠀⠀⠀⠀⠀⠀
⠃⠀⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⠀⠀⡀⡀⣀⣀⣄⣀⣀⣠⣀⣠⠀⠀⠀⠐⠀⠀⠀⠀⢀⢄⡀⠀⣠⢤⣀⠀⢀⡀⠈⢩⣿⠪⢹⡇⣀⠀⠀⠠⠀⠀
⠀⠀⡒⢲⡦⠄⠀⠀⠛⠀⠀⡐⠀⠀⠀⠀⠀⠀⢀⡀⠀⠐⢀⠀⠀⢀⣀⣀⣂⣀⣀⠲⢶⣶⣄⣩⣨⣈⣙⣫⣅⣉⣉⣍⣅⣽⣍⣭⣀⣀⣐⣶⣶⣒⣺⣛⣚⣻⣿⠷⣉⣉⣰⣶⣮⣅⣀⣀⣛⠲⠞⣇⣍⣬⣥⣵⣧⣵
⠘⠊⣉⣀⣴⣶⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢤⡀⣹⣿⣿⣿⣿⣿⣿
⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠋⠉⣩⢰⢿⣿⣿⣿⣿⣿
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠙⣿⣿⣿⣭⣯⣩⣿⣲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣷⣶⣾⣿⣿⢻⣿⣶⢳⢰⡖⢰⢶⢰⣾⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⡸⠈⣿⣿⣛⣽⣿⡁⠨⣭⠛⡛⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢸⣏⣼⢼⣾⣿⣿⣿⣿⣿
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣷⣶⣶⣶⣿⣿⣛⡋⡀⠀⠀⠀⠀⡩⠼⠿⠭⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⡆⠀⠀⠐⢂⣿⣿⣿⣿⣿⣿
⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡻⠿⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣷⣸⡈⡏⣿⣿⣿⣿⣿⣿
⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⢄⠁⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢇⣿⡇⠇⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣮⡞⡾⡆⠀⠀⠀⠤⠀⠤⠄⠀⠀⠀⣿⣯⣯⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣿⣧⢠⣿⣿⡇⣼⢿⣿⣿⣿⢿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠁⠀⠀⠀⠀⠙⠻⠟⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠉⣉⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼⣿⣿⣿⣿⣿⣷⣿⣿⣟⣿⣿⣿⣽⣾⣿⢸⣿⡏⣿⣾⣿
⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣤⣀⣠⣤⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣽⣿⣿⣿⣿⣵⣿⣿⣽
⢰⡦⡆⠀⠀⠀⠀⠀⣶⠀⡂⠄⠀⠀⠄⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠐⠀⠀⣆⠠⣰⠀⠐⡂⠀⡆⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⢰⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠁⠀⠀⠂⠀⠃⠀⠀⠀⢠⣧⣇⢠⣠⣀⠀⠀⠀⠀⠀⠀
⠁⠀⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣀⣀⣀⣄⣀⣀⢠⣄⣠⠀⠀⠀⠀⠆⠀⠀⠀⢀⣤⡀⠀⣶⢤⣄⠀⢈⡀⠈⠺⣿⠺⢿⡏⣀⢠⠀⠀⡀⠀
⠀⣀⡒⢳⠴⠄⠀⠀⠃⢀⣀⣒⠀⠀⢐⣀⣀⣀⣀⡂⠀⣚⣀⣀⣀⣀⣀⣀⣃⣠⣤⣠⠚⢻⣷⣤⣬⣤⣬⣥⣥⣭⣬⣥⣭⣽⣥⣥⣤⣠⣐⣶⣿⣛⣒⣛⣚⣿⣟⣛⣉⣁⣒⣒⣷⣂⣐⣐⣛⠒⠞⣏⣥⣦⣤⣾⣧⣵
⠘⠉⣁⣠⣶⣶⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⢈⣿⣿⣿⣿⣿⣿
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡟⠩⢙⡡⣿⣿⣿⣿⣿⣿
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢹⣿⣿⣿⣵⣯⣉⣿⣲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣾⣿⢻⣿⣾⣿⢰⡖⢰⢶⠀⣾⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⢸⣿⣭⣭⣷⢿⡀⠨⠭⢛⡻⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢸⣏⣼⢾⣦⣟⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣾⣿⣟⣉⣁⡀⠀⠀⠀⠀⠭⠾⠿⠬⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣧⣴⡀⠀⠀⠖⣿⣿⣿⣿⣿⣿
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⠋⠉⠉⠉⠉⠉⠙⠛⠙⠙⠛⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⠈⡏⣿⣿⣿⣿⣿⣿
⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣄⠑⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠇⣿⡇⠇⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢠⣷⣻⣼⡄⠀⠀⠀⠀⠀⠒⠂⠀⠀⠸⣽⢽⣿⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢠⣼⣿⡇⣤⢿⣿⣿⣿⢿⣻
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣛⠛⠁⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⣀⣀⡀⠀⣀⣀⣈⣉⣁⣀⣬⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣧⣿⣿⣟⣿⣿⣿⣿⣷⣿⢸⣿⡇⣿⣾⣿
⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣾⣿⣽⣿⣿⣿⣿⣵⣿⣿⣽
⣰⢦⡄⠀⠀⠀⠀⠀⣶⠀⡀⠄⠀⠀⠄⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⢀⠀⠀⡆⠀⢶⠀⠀⡂⠀⡆⠀⠀⠀⠀⡄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡏⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠰⠀⠀⠀⠀⠁⠀⠀⠀⢠⣷⣇⠀⣤⡀⡀⠀⠀⠀⠀⠀
⠁⠘⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣄⠀⢀⣀⣀⣀⣀⣄⣀⡀⢤⣄⣴⠀⠀⠐⠈⠀⢀⠀⢀⢀⣤⡄⡀⡆⣠⡄⠀⢈⡀⠸⠳⣿⠨⣿⣇⣄⣀⠀⣐⡀⠀
⢀⣀⡒⢻⠶⠀⠀⠈⠃⣀⠀⣚⣀⠀⣐⣀⣀⣀⣐⡂⢀⣊⣀⣀⣀⣀⣀⣈⣣⣤⣤⣤⣬⠙⢻⣿⣭⣤⣬⣭⣥⣭⣭⣥⣥⣷⣦⣦⣤⣤⣰⣷⣿⣻⣿⣛⣞⣿⣿⣟⣉⣁⣒⣾⣷⣢⣐⣐⣛⣖⠼⢥⣶⣶⣶⣶⣧⣶
⠈⢉⣀⣠⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣄⠀⣻⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡿⠛⠟⡋⢼⣿⣿⣿⣿⣿
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣶⣥⡭⢽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣷⣶⣾⣿⣽⣻⣿⣿⣿⢱⡒⢰⢷⡁⣾⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢸⣿⣯⣭⡷⠿⠀⠠⠭⢛⡻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢸⣏⣾⢾⣆⣿⣿⣿⣿⣿
⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣶⣟⣿⣫⣭⣁⡀⠀⠀⠀⠀⠽⠾⠷⠬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣧⣰⡆⠀⠀⠤⢺⣿⣿⣿⣿⣿
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠛⠉⠉⠉⠉⠉⠉⠙⠃⠙⠘⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣸⠈⡏⢹⣿⣿⣿⣿⣿
⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢤⡈⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠇⠿⡄⠇⣼⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⢸⣾⣻⣵⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⢺⡾⣽⡽⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢧⣤⣿⡇⣤⢿⣿⣿⣿⢿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠉⠁⠀⠀⠀⠈⠛⠚⠁⠀⠀⠀⢀⣀⣀⣀⢀⣀⣀⣀⣉⣉⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣧⣿⣿⣟⣿⣿⣿⢺⣷⣿⢼⣿⡇⣿⣾⣿
⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣶⣴⣶⣶⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣷⣿⣿⣿
⡶⢰⠀⠀⠀⠀⠀⠀⡆⠐⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠰⠀⢰⡆⢀⡆⠀⢰⠀⢰⡆⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⢾⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠀⠂⠀⠈⠁⠐⠓⠀⠀⡀⠀⠁⠀⠀⠀⠂⣷⡆⢀⣦⠀⠀⠀⠀⠀⠀⠀
⠀⢸⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣀⣀⡄⣀⣠⣠⡠⡤⡀⠀⣤⡤⡦⠀⡇⠂⠀⠀⠀⢀⡀⣄⣬⣀⢠⣖⡾⠄⠀⢠⠀⠠⣿⡟⠂⣿⣧⡄⣐⢁⣠⠀⢀
⢀⣀⡘⠿⠞⠀⠀⠈⢃⣀⣀⣉⣀⣀⣀⣀⣀⣀⣴⣀⣀⣁⣀⣀⣀⣤⣤⣬⣥⣤⣤⣤⣤⣤⡌⠉⢻⣿⣭⣭⣬⣥⣬⣤⣴⣾⣴⣦⣤⣥⣶⣿⣯⣽⣟⣭⣿⣿⣝⣛⣌⣤⣷⣿⣷⣦⣧⣬⣭⣍⣼⠥⣴⣶⣶⣿⣶⣶
⠈⣁⣄⣴⣯⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣠⡀⢸⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠓⣛⠩⣿⣿⣿⣿⣿
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢹⣿⣿⣿⣿⣾⣦⠬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣶⣶⣶⣾⣿⣿⢻⣿⣷⣿⢱⡖⢰⢾⢈⣦⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠘⣿⣷⣾⣶⡿⠯⠀⠦⠉⣙⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⣿⣿⠏⢸⣏⣾⢾⡎⣟⣿⣿⣿⣿
⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⢻⣯⣭⡥⣄⠀⠀⠀⠀⠤⠿⠿⠦⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣤⣶⠀⠀⠀⠔⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⡏⠁⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣤⢄⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠿⡀⠇⣠⣿⣿⣿⣿⣿
⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢸⣽⣻⣻⠀⠀⠀⠐⠒⠀⠒⠂⠀⠀⠘⣟⣭⣻⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣧⣤⡇⣤⢿⣿⣿⣿⢿⣿
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⡉⠁⠀⠀⠀⠀⠙⠛⠁⠀⠀⢀⣀⣀⣀⣀⣀⣄⣠⣤⣨⣉⣡⣤⣴⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣧⣿⣿⣟⣿⣿⣿⢾⣾⣿⣾⣿⡇⣿⣾⣿
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣽⣿⣿⣮⣿⣷⣿⣿⣽
⠒⣤⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢰⠀⠀⡆⠀⠰⠀⢰⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢾⣶⡀⢁⣆⠀⠀⠀⠀⠀⠀⠀
⠀⠟⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⣀⣤⡤⣀⣤⡤⠠⠠⠤⣤⣤⡂⠀⠀⠀⠀⠀⠀⣀⡀⣴⣤⣀⣰⣀⠦⠀⠀⡄⠀⠐⢺⡅⠺⣿⢠⠀⡄⢀⣀⠀⢀
⠠⣈⠉⠓⠃⠀⠀⠉⢀⣀⣠⣁⣀⣀⣁⣀⣀⣤⣤⣀⣈⣥⣤⣄⣄⣤⣬⣬⣤⣦⣦⣴⣤⣤⣤⡌⠉⢻⣿⣴⣶⣦⣿⣶⣴⣶⣶⣤⣤⣤⣿⣿⣭⣭⣭⣵⣽⣯⣎⣠⣄⣤⣾⣿⣮⣤⣥⣭⣭⣥⡶⠴⣴⣶⣶⣿⣶⣶
⢀⣠⣤⣼⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣠⣀⢈⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⢿⣿⣿⣿⣿⡿⠿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⢙⠅⡿⣿⣿⣿⣿
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣿⣿⣿⣿⣾⢿⡤⠸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⢻⣿⣷⣿⢱⡖⢰⢶⢠⣦⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⢹⣿⣷⣶⣾⠛⠧⠐⠖⢩⡝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⣿⣿⣿⣿⣸⣿⣿⡏⢸⣏⣼⢾⡆⣟⣿⣿⣿⣿
⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣯⣤⣤⡄⠀⠀⠀⠠⠒⠛⠛⠆⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣧⣾⢆⠀⠀⠐⣾⣿⣿⣿⣿
⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡏⠁⠀⠀⠀⠀⠉⠉⠁⠈⠈⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠊⡏⢡⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣔⣦⠄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠇⣸⣿⣿⣿⣿⣿
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢷⢯⣟⡗⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠸⣽⣜⡟⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣿⣿⣿⣿⣧⡄⣴⢿⣿⣿⣿⢿⣻
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣀⠀⠀⠀⠀⠈⠉⠉⠀⠀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣌⣥⣤⣤⣾⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡟⣧⣿⣿⣟⣿⣿⣿⣺⣷⣿⢸⣿⡇⣿⣾⢿
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣾⣿⣽⣿⣿⣮⣿⣵⣿⣿⣽
⢢⡆⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⢐⠀⠀⠀⠀⢴⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣴⡀⢸⡄⠀⠀⠀⠀⠀⠀⠀
⠀⡇⣀⠀⠀⠀⠀⣿⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠠⢠⣤⣤⣤⣤⠦⡤⠤⠐⣴⡴⠂⠰⠀⠀⠀⣀⣀⣤⢠⣴⣄⣀⣼⣰⠦⠀⠀⠆⠀⠛⣻⡕⢸⣿⠤⠠⠄⠀⠄⠀⠀
⢀⠬⠉⠛⠀⠀⣀⣈⣤⣤⣬⣥⣄⣬⣥⣤⣤⣤⣥⣤⣭⣤⣤⣤⣤⣤⣤⣭⣶⣶⣶⣶⣶⣶⣶⣶⡌⡉⣿⣷⣶⣶⣾⣶⣿⣷⣷⣶⣶⣮⣿⣿⣽⣭⣭⣯⣽⣿⣋⣤⣤⣬⣿⣽⣭⣾⣭⣿⣭⣥⠕⠒⢶⣿⣾⣷⣶⣷
⢀⣤⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡴⣄⡨⢿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⢿⣿⣿⣿⣿⡿⢿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠩⠂⠝⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣷⡄⠺⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣷⣶⣾⣿⣿⢿⣿⣷⣿⢱⡒⢰⢶⠠⣦⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣓⣀⣀⣿⣿⣷⣶⡟⠛⠇⠒⠂⢭⡛⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣼⣿⣿⡟⢸⣏⣼⢾⡤⡟⣿⣿⣿⣿
⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⠸⡯⣶⣦⢦⠀⠀⠀⠀⠐⠛⠛⠓⠢⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⣾⢧⠀⠀⠘⣽⣿⣿⣿⣿
⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⡏⢱⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⠤⣲⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡦⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢇⣾⣿⣿⣿⣿⣿
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠂⠀⠀⠸⣟⣼⣻⠀⠀⠀⠀⠉⠀⠉⠁⠀⠀⠀⢷⣗⡿⠃⠀⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡄⣼⢻⣿⣿⣿⢻⣿
⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣄⣀⡀⠀⠀⠈⠉⠀⢀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣾⣿⣟⣿⣿⢸⣿⣿⣿⣿⡟⣧⣿⣿⣟⣿⣿⣿⣾⣷⣿⢸⣿⡇⣿⣾⢻
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣽⣿⣿⣯⣿⣽⣿⣿⣿
⢰⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠂⠀⠀⠀⠀⡆⠀⠀⠀⠀⡆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠘⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠠⠁⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠇⣇⠠⣶⡀⠀⠀⠀⠀⠀⠀⠀
⢸⢀⣀⠀⠀⠀⢸⡇⠀⠀⣀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠰⢆⠠⠤⣤⣤⣴⡴⢤⠤⠀⢲⠦⠖⠀⠀⠀⣀⣀⣀⣠⣤⢠⣶⣠⣠⣇⡾⠆⣀⡰⠀⠈⢓⣿⠐⢿⡧⠖⠤⠀⠠⠄⠀⠠
⠠⠍⠛⠋⠀⢀⣀⣡⣤⣤⣭⣤⣤⣥⣤⣤⣤⣼⣤⣤⣤⣤⣤⣤⣴⣦⣼⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⢀⢹⣿⣷⣶⣶⣶⣿⣾⣷⣶⣶⣿⣽⣿⣿⣯⣷⣯⣿⣯⣯⣦⣶⣿⣿⣿⣷⣼⣿⣶⣯⡿⠒⠒⢲⣿⣿⣿⣿⣿
⣠⣤⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣄⠀⢿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠻⣿⣿⣿⣷⣾⠿⡿⢿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠸⠂⠜⢻⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣿⣿⣿⣿⡿⣿⣷⠐⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣶⣶⣶⣾⣿⣿⣻⣿⣿⣿⢱⡒⢰⢶⠰⣦⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣛⣛⣛⣃⣀⡸⣿⣿⣷⣾⠟⠛⠐⠓⠠⠮⣳⣿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣸⣿⣿⡟⢸⣏⣼⢾⡦⣟⣿⣿⣿⣿
⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⡇⢿⢵⣶⡴⡄⠀⠀⠀⠀⠚⠋⠛⠓⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⣿⢷⠀⠀⠈⣼⣿⣿⣿⣿
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⡏⢱⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣠⣲⡶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣮⣵⢆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠇⣾⣿⣿⣿⣿⣿
⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠀⠀⠀⢯⣷⣻⠇⠀⠀⠀⠈⠁⠈⠉⠀⠀⠀⠘⢿⡾⠎⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣧⡄⣤⢻⣿⡿⣿⢻⣿
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡿⣧⣿⣿⣟⣿⣿⣿⣾⣷⣿⢸⣿⡏⣿⣾⣻
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣽⣿⣿⣯⣿⣽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⠀⢰⠀⠀⠀⠀⡆⠀⠀⠀⠀⡆⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠐⠀⠀⠀⠀⠄⠀⠐⠀⠰⠷⣿⡄⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⠀⠀⠀⢸⡇⠀⠀⣀⠀⠀⢀⠀⠀⠂⢘⠄⢀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠐⠀⠰⠶⠠⠀⢶⠴⣴⣴⣶⡶⠖⢾⠶⠚⠀⠀⢀⣀⣤⣔⣠⣤⢠⣶⣥⣴⠯⠞⣓⣀⡰⠀⢀⢉⣿⣘⣻⠇⠶⠰⠀⢄⡄⠀⡀⠤
⠀⠉⣉⡀⣀⣀⣠⣤⣴⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣦⣶⣴⣶⣶⣶⣶⣶⣿⣶⣶⣷⣷⣶⣿⣿⣾⣿⣾⢀⣉⣿⣷⣾⣿⣿⣿⣷⣶⣶⣿⣷⣶⣶⣶⣶⣿⣷⣥⣶⣶⣾⣿⣿⣾⣶⣶⣶⣶⣾⡶⠒⠛⢿⣿⣿⣿⣿⣿
⢴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣷⣢⣄⠜⢿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⣿⣿⣿⣷⡿⣛⡻⠿⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠴⠪⠞⠿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠿⢿⣷⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣷⣶⣾⣿⣿⢿⣿⣶⣿⢱⡒⢰⢶⠰⣦⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⠹⣿⠿⠿⠿⠟⠛⠊⠉⠰⢎⣹⣿⠻⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣸⣿⣿⡏⢸⣏⣾⢾⡦⣟⣿⣾⣿⣿
⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠿⠿⠿⠿⠿⠂⠿⣶⣿⡿⠆⠀⠀⠀⠈⠉⠉⠉⠉⠚⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⣿⢷⠀⠀⠈⢹⣿⣿⣿⣿
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠠⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡮⡏⠁⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢠⢮⢭⣶⡀⠀⠀⠀⣀⡀⣀⣀⠀⠀⠀⣼⡿⣯⡆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠇⠀⣿⣿⣿⣿⣿
⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠉⠀⠀⠈⠿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠷⠁⠀⣸⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⣿⣤⡌⣤⢸⣿⡻⣿⢿⣿
⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣦⣴⣴⣶⣶⣶⣶⣶⣾⣿⣷⣿⣽⢸⣿⣿⣿⣿⣿⣧⣿⣿⣟⣿⣿⣿⣹⣿⣿⢸⣿⡇⣿⣾⣻
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣽⣿⣿⣾⣿⣼⣿⣿⣾⣿⣽⣿⣿⣽
⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠐⠀⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠆⠀⡂⠀⠐⠀⠰⠄⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠸⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⢿⣇⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⡀⠀⠀⠀⣸⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⡂⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠲⠂⠠⠰⠖⠴⢲⣾⣴⣶⠖⡳⠶⠇⠀⠀⣀⣀⢀⣀⣠⡄⣾⣶⣤⡸⠧⢗⣒⣀⡰⠀⡈⢹⣇⡁⣿⠲⠆⠆⠠⣠⠀⠀⠠⠠
⠈⢋⣁⠀⡀⣀⣤⣤⣴⣤⣦⣶⣶⣴⣤⣴⣶⣶⣤⣴⣤⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣷⣶⣶⣶⣷⣇⢀⢹⣿⣾⣿⣿⣶⣶⣶⣷⣿⣷⣶⣶⣶⣶⣿⣧⣴⣶⣶⣿⣿⣷⣶⣶⣦⣶⣶⣿⣶⠛⠚⢿⣿⣿⣿⣿⣿
⢴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣷⣦⣀⠸⢿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⢿⣿⣿⣿⣿⢽⣛⡟⢿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠽⠢⠜⢿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢸⣿⣿⡿⡿⠟⣻⣇⢉⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠶⣶⣷⣶⣾⣾⣿⢻⣿⣶⣿⢱⡒⢰⢶⠰⣦⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣯⣯⣭⣭⣤⡌⣿⡿⠿⠿⠟⠙⠓⠉⠁⢓⣹⣿⡟⠿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡿⣿⣿⣼⣿⣿⡏⢸⣏⣼⢾⡆⡟⣿⣾⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠛⠛⠛⠿⠟⠿⠿⠇⠸⠿⠿⢯⠷⠀⠀⠀⠀⠁⠁⠀⠉⠑⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣦⣾⢷⠀⠀⠚⠘⣿⣿⣿⣿
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡏⠁⢠⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣔⡿⣭⡆⠀⠀⠀⢀⣀⢀⣀⡀⠀⠀⢰⣧⢾⣵⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠇⠀⣼⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠉⠀⠀⠹⠽⠷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠿⠊⠀⢀⡿⣿⣿⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⣿⣧⡌⣤⢸⣿⡻⣿⢿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⣀⣀⣀⣀⣀⣠⣄⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣖⣶⣶⣿⣿⣿⣿⢸⣿⣿⣿⣿⣟⣧⣿⣾⣟⣿⣿⣿⢾⣷⣿⢸⣿⡇⣿⣾⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿
⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠂⠀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⢀⠀⠀⠀⠀⠲⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⡻⣾⡀⢸⣦⠀⠀⢀⠀⠄⠀⠀⠀⠀
⢀⠀⠀⠀⢀⡇⠀⠀⢀⠀⠀⢀⠀⠀⠀⠐⡀⠀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠰⠶⠠⠄⠰⡦⠴⠖⣵⣤⣴⡺⡶⠾⠂⠸⢀⣀⣀⣀⣀⣤⢐⣵⣧⠄⠾⠼⢓⣀⣀⠆⠀⠉⣿⣋⣸⡟⠶⠐⠄⢄⡄⠀⠀⠄⠅
⠈⣉⡀⢀⣀⣠⣴⣤⣤⣴⣤⣶⣦⣦⣤⣶⣦⣦⣤⣤⣶⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣿⣶⣶⣷⣷⣾⡀⣈⣿⣿⣿⣿⣶⣶⣾⣽⣿⣶⣶⣶⣶⣿⣿⣴⣴⣶⣶⣿⣾⣷⣾⣶⣶⣶⣶⣿⣷⠖⠓⢿⣿⣾⣿⣿⣿
⢸⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣧⣦⣀⡘⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣯⣿⣿⣿⠫⣝⣻⡻⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⢭⢐⡼⢿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⣿⣿⣿⣿⠿⢿⣿⡈⡹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⣶⣷⣶⣾⣿⣿⢻⣿⣾⣿⢱⡖⢰⢶⢠⣦⣶⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣭⣭⣭⣭⣥⣤⢻⣿⢟⠿⠿⠋⠛⠊⠁⠘⣪⣿⣟⠻⢿⣿⣿⣿⣿⣷⣿⣿⣿⡿⣿⣿⣸⣿⣿⡏⢸⣏⣾⢾⡄⡟⣿⣨⣿⣿
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⠛⠛⠛⠛⠛⠿⠿⠘⠟⠿⠷⡿⠇⠀⠀⠀⠈⠈⠀⠉⠉⠚⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣤⣾⢧⠀⠀⠔⠒⣿⣿⣿⣿
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡎⡏⠁⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢰⣭⢿⣢⠀⠀⠀⠀⣀⠀⣀⣀⠀⠀⠀⣾⡾⣯⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠇⠀⣠⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠛⠁⠀⠘⠾⠯⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠀⠀⡺⣿⣿⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣯⡄⣤⢸⣽⣻⣿⢻⣿
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⢸⣿⣿⣿⣿⣟⣧⣿⣹⣟⣿⣿⣿⣸⣷⣿⢸⣿⡇⣿⣾⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣾⣿⣼⣿⣿⣾⣿⣵⣿⣿⣽
⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡂⠀⠐⠀⠀⡆⠀⠀⠀⠀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠸⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⢷⣇⠀⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⣸⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠲⠦⠄⠀⢖⠤⠔⠞⢒⣤⣤⣲⠆⠒⠀⠂⡀⣀⢀⣀⣠⣄⣠⣾⣤⣠⠧⡞⢒⣀⡰⠀⡀⢙⣟⣁⣿⠣⠆⠤⠀⢤⠀⠀⠠⠨⠀
⠈⣁⠀⠀⣀⣡⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣆⢀⢹⣿⣾⣷⣶⣶⣼⣽⣷⣶⣷⣶⣿⣿⣯⣥⣦⣴⣿⣷⣷⣶⣶⣶⣶⣴⣶⣶⣶⠖⠓⢿⣿⣿⣿⣿⣿
⢰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣧⢦⡀⡸⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⣿⣽⣿⣿⡞⢯⣛⣟⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⢩⢔⡸⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⠿⣿⣃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠶⣶⣶⣶⣶⣿⣿⢻⣿⣶⣿⢱⡖⢰⢶⢠⣦⣶⢿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣤⡝⣿⡻⡿⡶⠟⠛⠛⠉⠐⢓⣹⣿⡛⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣼⣿⣿⡏⢸⣍⣾⢾⡆⡟⣿⣘⣿⣿
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠟⠛⠛⠛⠛⠿⠿⠗⠿⢶⣿⠞⠗⠀⠀⠀⠈⠉⠀⠉⠉⠑⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣤⣾⢇⠀⠀⠔⠒⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠃⠀⠀⠀⢀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡌⡏⠁⠀⢻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣪⢽⣳⡀⠀⠀⠀⣀⡀⢀⣀⠀⠀⠀⣴⣷⢿⡂⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠇⣀⣠⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠃⠀⠈⠺⠯⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠝⠃⠀⠘⣿⣿⢿⣿⣿⣿⣿⣿⡿⣿⢻⣿⣿⣻⣿⣿⡄⣤⢻⣿⡻⣿⢿⣿
⢸⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣤⣄⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣧⣿⣿⢸⣿⣿⣿⣿⡟⣧⣿⣸⣟⣿⣿⣿⣼⣦⣿⢸⣿⡇⣿⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣽⣿⣿⣿⣿⣼⣿⣿⣯⣿⣵⣿⣿⣿
⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⢰⠀⠀⠀⠀⠆⠀⠀⠀⠀⡆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠘⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠨⠗⣗⠀⣾⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⢁⠀⢀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠰⠖⠀⠀⢲⠠⠴⠒⠶⠦⢆⣶⣶⣎⠀⠀⢀⣀⣠⣀⣠⣤⢰⣷⣥⡄⠿⠞⢂⣀⡰⠂⢀⢉⣿⣈⡹⠇⠦⠠⠀⢄⡄⠀⠀⢠⢀⢀
⢈⠀⠀⣀⣁⣴⣤⣤⣤⣤⣤⣤⣤⣤⣴⣴⣤⣀⣴⣶⣦⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣷⣶⣿⣿⣷⣷⣶⣶⣎⠀⢻⣿⣶⣶⣾⣽⣷⣶⣾⣶⣶⣿⣶⣬⣶⣦⣮⣷⣿⣶⣶⣶⣴⣶⣶⣶⣶⣿⠗⠚⠳⣾⣿⣿⣿⣿
⢸⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⢿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣿⣿⣿⣿⡞⣮⣛⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠨⠖⠔⢻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⣿⣿⣿⣿⣿⡿⢿⣓⠹⣿⣿⣿⣿⣿⣿⣿⣿⣶⠶⣶⣷⣶⣾⣿⣿⣻⣿⣷⣿⢳⡖⢰⢶⠰⣦⣶⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣭⣭⣭⣭⣭⣭⣤⢹⣿⠻⡿⣶⠷⠚⠛⠉⠰⢮⣱⣿⠻⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣼⣿⣿⠏⢸⣏⣼⢾⡄⡟⣿⣨⣿⣿
⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠛⠛⠛⠛⠻⠿⠿⠿⠿⣷⣶⡾⠖⠀⠀⠀⠈⠉⠉⠉⠉⠒⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣶⣾⢷⠀⠀⠒⠈⢹⣿⣿⣿
⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠈⡏⣧⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢰⣻⢭⣦⠀⠀⠀⠀⣀⡀⣀⣀⠀⠀⠀⣞⡿⡷⡄⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢧⡟⠀⣴⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠿⢟⠿⠟⠃⠀⠘⠯⠿⠎⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠀⠹⠯⠟⠁⠀⣸⣿⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢻⣿⣧⡄⣿⢣⣤⡹⣿⢻⣻
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣦⣤⣄⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣢⣶⣶⣶⣶⣶⣿⣹⢸⣿⡿⣿⣿⡟⣧⣿⣽⣟⣿⣿⣿⢸⣦⣿⢸⣿⡇⣿⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣽⣿⣿⣾⣿⣽⣿⣿⣿⣿⣵⣿⣿⣽
⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⡂⠀⠐⠀⠰⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠛⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠋⢿⡇⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠂⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠐⡆⠆⠖⠖⠲⠔⠰⣲⣶⣃⠀⠀⣀⣀⣄⣀⣠⣄⣾⣾⣤⡸⠧⣓⣂⣀⣒⠀⡀⣹⣇⣁⣿⠰⠂⠂⠀⣰⠀⣀⢠⣄⣀⣀
⢀⠀⢀⡀⣤⣤⣦⣤⣤⣤⣦⣤⣤⣴⣶⣤⣤⣤⣶⣶⣤⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣿⣶⣷⣿⣿⣾⣶⣾⣷⣾⠁⠙⣿⣷⣶⣮⣿⣶⣶⣶⣶⣶⣿⣧⣴⣶⣶⣿⣾⣷⣶⣶⣶⣶⣶⣿⣾⣾⣾⠖⠉⠙⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣷⣖⣦⡀⠻⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿⣿⣷⢻⣝⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠖⠥⠛⣿⣿⣿
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⠿⣟⣈⢼⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣷⣶⣿⣿⣿⣻⣿⣿⣿⢱⡖⢰⢶⠀⣦⣶⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣭⣭⣭⣭⣥⡈⣿⡟⠿⣶⡾⠗⠛⠋⠀⢖⣹⣿⡛⠿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⣿⣿⠏⢸⣟⣼⢾⡆⡟⣿⣨⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠛⠛⠛⠻⠛⠿⠿⠷⠻⠻⢾⠞⠷⠂⠀⠀⠀⠁⠉⠀⠉⠑⠲⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⣿⢿⠀⠀⠘⠁⠸⣿⣿⣿
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠈⡏⣵⡄⠀⣹⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣪⢯⣵⡀⠀⠀⠀⣀⡀⢀⣀⡀⠀⠀⢰⣹⢯⡆⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⣷⣿⡇⠀⣿⣿⣿
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⢿⡿⠿⠿⠛⠀⠈⠯⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠿⠿⠃⠀⣠⣽⢟⣿⣿⣿⣿⣿⡿⣿⣻⣿⣿⣻⣿⣤⡔⣿⢿⣥⡀⣿⢻⣻
⢸⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣶⣶⣔⣶⣶⣶⣶⣶⣦⣿⣻⢸⣿⡷⣿⣿⡟⣧⣿⣽⣟⣿⣿⣿⢸⣴⣿⢸⣿⡇⣿⣾⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣾⣿⣼⣽⣿⣿⣿⣽⣿⣿⣿
⠀⠀⢰⡆⠀⠀⠀⠀⠐⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠰⠀⠀⡂⠀⠆⠀⠀⠀⠀⡂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠸⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⣀⠀⠀⠀⠀⠀⠸⠿⣿⠀⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣸⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠰⡆⠀⠠⢤⣤⢴⠴⠶⢤⠔⠲⢦⣶⣀⠀⠀⢀⣀⣀⣀⣤⢰⣶⣤⣄⣇⡼⠆⣀⡰⠄⢀⢃⣿⣐⣻⠧⠦⠤⠀⢄⡄⠠⠠⠤⢀⢀⣀
⠀⠀⢈⣠⣤⣄⣥⣠⣤⣥⣤⣤⣤⣯⣤⣬⣥⣤⣤⣤⣴⣤⣼⣵⣿⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣿⡏⠙⣿⣷⣾⣽⣷⣾⣯⣵⣿⣿⣿⣭⣦⣴⣭⣿⣿⣷⣾⣶⣴⣾⣾⣶⣶⣷⣶⠟⠓⠛⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡠⠹⣿⣿⣿⣿
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⣿⣿⣿⣿⡼⣾⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠨⠗⠤⠛⣿⣿⣿
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⣿⣿⣿⣿⣷⡾⣿⡃⢹⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣷⣶⣾⣿⣿⢻⣿⣾⣿⢱⡖⢰⢶⠀⣦⣶⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣿⣿⣯⣥⡀⢿⣿⠿⣿⣶⡗⠛⠛⠁⠶⣝⣾⡟⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣼⣿⣿⠉⢸⣟⣼⢾⡆⡟⣿⣨⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⡷⡾⢿⣶⣶⢶⠖⠀⠀⠀⠈⠉⠉⠉⠑⠲⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢿⠀⠀⠒⠋⢸⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠆⠀⠀⠀⠀⠁⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⡏⣧⡀⠀⢻⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣖⣭⣒⡄⠀⠀⠀⢀⡀⢀⣀⡀⠀⠀⢠⣮⢯⣦⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⣿⣿⣷⠀⢸⣿⣿
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠿⠿⠀⠀⠯⣷⡽⠃⠀⠀⠀⠂⠀⠀⠀⠐⠂⠀⠈⠿⠿⠏⠀⣠⣿⢟⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⢻⡧⣤⡼⣿⢿⣿⡀⣼⢿⣻
⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣧⣤⣄⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣶⣤⣤⣤⣤⣤⣤⣤⣿⣹⢸⣿⣟⣿⣿⡟⣧⣿⣽⣟⣿⣿⣷⢸⣵⣿⢸⣿⡇⣿⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣽⣿⣿⣿⣿⣼⣿⣿⣮⣿⣿⣿⣿⣿
⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠐⠀⠀⢂⠀⢰⠀⠀⠀⠀⢰⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⣾⠀⢠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢥⠀⠀⡠⣄⣤⣤⣦⣤⢤⠤⣄⢤⣆⣰⠀⠀⠀⠀⠀⣀⡠⣤⣆⡀⣼⣰⠦⠀⠀⡄⠀⠒⢺⠅⢺⣿⣤⠠⡄⢀⣀⠀⠀⣀⡆⠀⠀⠀
⠀⠈⢃⣀⣀⣈⢀⣀⡠⣄⣀⣀⣤⣠⣀⢉⣀⣀⣀⣀⣤⣤⣥⣴⣤⣤⣤⣤⣤⣤⣾⣤⣤⣷⣦⣦⣤⣴⣦⣴⣷⡖⠙⢻⣿⣽⣿⣭⣭⣭⣽⣿⣿⣯⣤⣨⣬⣿⣽⣮⣬⣥⣽⣭⣯⣷⣽⣶⣶⣾⡷⠾⠷⣶⣶⣷⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡾⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⡀⠀⢿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣿⣻⣿⣿⡞⣟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢙⡥⣀⠿⣿⣿⣿
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢹⣿⣿⣿⣷⣷⢿⣆⢪⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣵⣾⣿⣿⣿⢳⣿⣶⣾⢲⡖⢰⢶⢠⣦⣶⠹⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣛⣛⣛⣋⡀⢻⣿⢿⣿⣿⡶⠸⠿⠃⢭⡙⣿⡿⢿⡿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣸⣿⣿⠉⢸⣟⣼⢾⡆⡟⣿⣀⣻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣧⢸⣿⣶⣮⢶⡤⠀⠀⠀⠐⠙⠛⠛⠲⠭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⣾⣿⢇⠀⠀⠴⠒⢻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠁⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣏⡅⠀⠘⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣤⣒⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣖⣶⣢⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠿⢀⣿⣿⣆⠀⢸⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠀⠀⢯⣧⣿⠇⠀⠀⠀⠈⠉⠀⠉⠁⠀⠀⠘⢯⣾⠟⠀⣠⣼⢟⣿⣿⣿⣿⣿⡿⣿⣻⣿⣿⢿⡥⣤⡞⣿⢻⣿⡂⣬⢻⣻
⢸⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣦⣄⠀⠀⠀⠉⡀⢀⣀⣀⣀⣄⣠⣤⣤⣤⣠⣤⣤⣤⣤⣠⡄⣿⣩⢸⣿⡟⣿⣿⡟⣧⣿⣿⣞⣿⣿⣧⢸⢲⣿⢸⣿⡇⣿⣾⣹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣾⣷⣿⣿⣽⣿⣿⣾⣿⣼⣿⣿⣾⣿⣽⣿⣿⣽
⢰⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⡆⠀⠐⠀⠰⡆⠀⠀⠀⠀⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⢄⣯⡏⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣀⣀⢀⣠⣀⣀⠀⢄⣀⡤⠀⠀⡀⠀⠀⠀⠀⠀⡀⣀⠀⠀⡆⣮⡀⠀⢀⠀⠀⠿⡗⠀⣿⣆⡀⡀⠀⢀⠀⠀⠀⢠⠀⠀⠀⠀⠀
⠁⢀⠀⠀⠀⠀⡐⠂⢀⠀⣀⣂⠀⠒⢀⡀⣀⣀⣀⣀⣑⣀⣄⣤⣀⣤⣀⣠⣥⣤⣠⣭⣭⣭⣥⣬⣭⣈⣾⣥⣄⣤⠛⢻⣿⣟⣚⣚⣓⣻⣿⣋⢊⣉⣁⣒⣒⣖⣂⣂⣘⣓⣒⣽⣬⣤⣤⣤⣾⣤⣶⣮⣾⣶⣴⣶⣦⣶
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠙⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⠤⠀⠻⣿⣿⣿⣿
⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣬⣶⡭⠝⢿⣿⣿⣿⣿⣿⣿⣶⢲⣶⣷⣾⣟⣿⣽⢳⣿⣶⣿⢱⡖⢱⢶⠰⣎⣶⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠿⠿⠿⠿⠿⠋⠀⢸⣿⢿⣯⣭⣭⠸⢿⠎⣽⡻⣽⣿⣿⣿⣿⣿⣷⣿⣻⣿⣿⣿⣿⣾⡿⣿⠉⢸⣍⣼⢾⡶⡟⣿⢈⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⡧⢸⣯⣦⣝⣭⡍⠄⠀⠀⠬⠲⠿⠷⠬⣙⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣶⣾⣿⠇⠀⡀⡀⢀⣿⣷⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣦⣀⠀⠀⠀⠈⠉⠁⠀⠉⠉⠉⠈⡇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⠈⡏⠁⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣠⣤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣠⡀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠿⢀⣿⡄⠀⠸⣿⣿⣿
⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⣾⢯⣿⠇⠀⠀⠀⠐⠒⠀⠒⠂⠀⠄⠸⣿⢽⡿⠀⣠⣄⢟⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⢫⡀⣤⡞⣿⢿⣤⡀⣽⢿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⡀⠀⠀⠈⠉⠁⠀⠀⢀⣀⣀⣀⡀⣀⣀⣀⣀⣀⠈⠉⠀⠀⣿⣉⢸⣿⡿⣿⣿⡟⣧⣿⣾⣞⣿⣿⣧⣸⣿⣿⢸⣿⡇⣿⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣾⣷⣿⣿⣽⣿⣿⣾⣿⣽⣽⣿⣮⣿⣷⣿⣿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⠀⠶⠀⠐⠀⠀⡆⠀⠀⠀⠀⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠠⠨⠀⠀⠀⠀⠃⠀⠀⠀⢠⣧⣥⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣀⠀⠀⣀⢀⡀⣀⠀⣀⣀⣀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡆⢠⡄⠀⢀⠀⠈⠥⣟⠠⣿⡇⣀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡂⠀⠀⠂⠀⠀⢀⣂⠀⠐⠂⠀⠀⠀⢀⢀⣐⣀⣄⣀⣀⣠⣀⣀⣠⣄⣈⣐⣈⣉⣉⣈⣌⣀⣽⣥⣍⣀⣀⠚⢽⣿⣖⣚⣛⣚⣿⣟⡛⡉⢁⣲⣖⣿⣂⣐⣐⣓⣲⣾⣍⣁⣈⣤⣽⣥⣴⣦⣮⣴⣶⣶⣦⣶⣦
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⢿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡄⠸⣿⣿⣿⣿⣿
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣿⣿⣿⣿⣬⣭⣏⠩⣻⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣾⣿⣽⢷⣿⣶⣿⢱⡖⢱⢶⡠⣶⣶⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⡿⡿⣿⣿⠿⠟⠀⢸⣿⣿⣿⣿⣩⢉⣷⠞⡛⠿⣻⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣼⠿⣿⠉⢸⣏⣾⢼⣦⡟⣿⠙⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣧⢸⣿⣯⣙⣿⣍⡀⠀⠀⠨⠷⠿⠧⢍⡛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣶⣾⣿⠇⢀⣀⠀⠀⣿⣦⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⡀⠈⠉⠉⠉⠉⠁⠈⠉⠛⠛⠈⡇⠀⠀⠀⠀⠀⠀⠄⠀⠈⠉⠛⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠈⡟⠓⠈⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⡠⣤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠿⠀⣷⠀⠀⢿⣿⣿⣿
⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠰⡶⣯⣿⠆⠀⠀⠀⠐⢒⠐⠒⠂⣀⠀⢸⣽⣽⡳⠀⣠⣄⢘⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢫⣠⣤⡾⣿⢷⣤⡀⣿⢿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⡁⠀⠀⠉⠛⠉⠀⠀⠀⠀⣀⡀⣀⡀⣀⡀⠀⠀⠉⠋⠁⠀⣷⣉⢸⣿⣟⣿⣿⡟⣧⣿⣾⣏⣿⣿⣇⣸⣿⣿⢺⣿⡇⣿⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣽⣯⣮⣿⣷⣿⣾⣿⣿⣿⣽⣿⣿⣾⣿⣼⣼⣿⣮⣿⣵⣿⣿⣽
⠀⠀⠀⠀⠠⠀⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⢰⠀⢀⡂⠀⣶⠀⠀⠀⠀⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠰⠀⠀⠀⠀⠉⠀⠀⠀⠠⣼⣿⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⢀⠀⡀⡀⢀⣀⣀⣀⡄⠠⠀⠀⠀⠀⠀⠀⢀⣔⡀⠀⣠⢠⡀⠀⠀⡀⠀⡩⣿⢄⢸⣷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠠⠀⠀⠂⠀⠀⠀⢀⠀⠐⡂⣠⣀⣀⣈⣀⢈⣉⣈⣈⣙⣊⣉⣉⣈⣛⣁⣩⣍⣍⣀⣈⣀⠜⠿⣷⡶⠟⠚⣿⣿⠷⢋⠋⠠⢶⣦⣅⣰⣀⣛⠶⣎⣇⣉⣈⣅⣩⣇⣀⣤⣭⣥⣬⣦⣦⣶⣦⣴
⢸⣿⣿⣿⣷⣾⣾⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠻⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣦⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣠⠀⢿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣬⣯⣍⡹⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣶⣾⣿⣿⣻⣿⣾⣿⢱⡖⣴⢶⠰⣾⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡿⠟⠀⢰⣿⣿⣿⣟⣛⣉⣿⡖⣛⢿⣻⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣸⡿⣿⠉⢸⣏⣾⢼⡆⡟⣿⢿⣿⣿
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣷⣿⣿⣿⣿⣿⣿⡇⢰⣿⣥⣛⣛⣛⠁⠈⠀⡩⡵⠿⣯⣙⡛⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⣴⣶⣿⠀⢀⣀⠀⢸⣶⣄⣽⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡉⠉⠉⠉⠉⠙⠃⠈⠃⠛⠛⠙⢿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⠈⡿⠑⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠿⢀⣇⠀⠘⣿⣿⣿⣿
⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠰⡷⣟⢾⠆⠀⠀⠀⠀⢀⢀⠤⢄⠀⠀⢸⣽⣻⠷⠀⣠⣄⢘⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢫⡄⣤⡾⣿⢆⢤⡸⣿⢿⣿
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⣷⣉⢸⣿⡇⣿⣿⡟⣧⣿⢽⣟⣿⣿⣯⢸⣿⣿⢸⢸⡇⣿⣾⣻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣽⣯⣮⣿⣿⣿⣾⣿⣿⣿⣽⣿⣿⣾⣿⣼⣵⣿⣾⣿⣥⣿⣿⣽
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠰⡆⠀⡂⠀⢰⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠆⠀⠀⠀⠘⠀⠀⠀⠀⣼⣼⡀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣃⠀⠀⠀⠀⠀⠀⡀⡀⠀⢀⣀⢀⠄⠘⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⢠⠠⣆⠀⠀⡂⠀⠭⣽⡦⣸⣷⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢒
⠀⠂⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣀⣀⣀⣀⣀⣀⣉⣐⣀⣑⣛⣑⣋⣋⣛⣉⣨⣍⣍⣁⣀⣀⢴⡖⠿⣷⣞⠣⠛⣷⡶⢞⠈⠩⠴⣶⣥⡀⣀⣚⡣⣶⣉⣉⣉⣁⣨⣮⣤⣤⣥⣵⣤⣴⣤⣴⣴⣴⣶
⢸⣷⣿⣷⣷⣿⣿⣿⣿⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣮⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⢿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣿⣿⣿⣶⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡄⠸⣿⣿⣿⣿⣿⣿
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢹⣿⣿⣿⣏⣋⣙⡛⢿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣷⣶⣾⣿⣿⣻⣿⣶⣿⢱⣶⢶⣶⢲⣾⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⠟⠀⠠⣿⣿⣿⣟⣛⡉⣻⡶⠶⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣸⡿⣿⠉⢸⣏⣼⢼⡆⡟⣿⣿⣿⣿
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣷⣷⣒⣂⠀⣿⣧⡻⣟⣛⢁⠈⠀⢙⣦⣿⣯⡙⠻⠙⣿⣿⣿⣿⣿⣿⣿⣿⣧⡤⣶⣾⡇⢀⢀⣀⠀⣷⣤⣼⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡉⠉⠉⠉⠉⠋⠃⠀⠃⠛⠛⠙⢿⠀⠀⠀⠀⠀⠀⢀⠀⠙⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣸⠘⡟⠋⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠿⣰⡇⠀⢿⣿⣿⣿⣿
⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠰⣿⣟⣯⠆⠀⠀⠀⠠⠤⠀⠤⠄⠀⠀⢰⣷⣳⣷⠀⣠⣄⢀⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⡀⣴⡿⣧⢀⢬⣿⣿⢿⣿
⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠀⣧⣉⢸⡗⡯⣿⣿⡟⣧⣿⣽⢟⣿⣿⡇⢻⣿⣿⢸⣼⡇⣿⣾⣽
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣦⣽⣯⣮⣿⣷⣿⣾⣿⣿⣷⣽⣿⣿⣾⣿⣼⣾⣿⣮⣿⣽⣿⣿⣽
⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⡆⠀⣰⠀⢰⡆⠀⠀⠀⢐⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠁⠇⠀⠀⠀⠘⠃⠀⠀⠀⢀⣮⡄⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⡄⣤⡀⠀⢀⠀⢀⢽⡧⡀⣿⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⣒⣒
⠀⠀⠠⠀⠀⠀⠨⠀⠀⠴⠀⠀⠀⠀⠀⠀⠦⠀⡀⡀⠀⠀⠀⣙⣁⣉⠉⢛⣋⣋⣉⣛⣉⡁⣭⣉⣀⢀⡁⠤⣦⡶⡾⠻⣷⣿⢿⣖⠖⠓⠋⠥⢴⡬⠄⠄⠱⠯⢤⣟⣉⣅⣉⣀⣬⣀⣠⣤⣬⣤⣦⣤⣤⣤⣦⣤⣶⣶
⢰⣶⣷⣷⣿⣿⣿⣷⣿⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣦⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣷⣹⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡦⠀⠘⢿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠐⣿⣿⣿⣧⣙⣿⠿⡿⣿⣿⣿⣿⣿⣿⣾⢿⣶⣷⣶⣞⣿⣿⢻⣿⣷⣶⢰⡶⢰⢶⢳⣾⣶⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡿⠀⠀⣿⣿⣿⣿⡟⡛⢹⣵⠾⣶⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣸⠇⣿⡉⢸⣏⣾⢼⡖⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⡆⠀⡿⣿⡹⣿⣿⠃⡉⠁⠒⣈⣿⣟⠛⠿⡟⢿⣿⣿⣿⣿⣿⣿⣷⣴⡾⣿⡇⡀⠀⠀⣐⣬⣽⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣭⡉⠉⠉⠉⠛⠛⠋⠀⠃⠿⠿⠙⢻⡅⠀⠀⠈⠈⠉⠉⠉⠲⠶⠜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣹⠈⣏⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠇⢿⠀⠟⣿⣿⣿⣿⣿⣿
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⣱⣓⣟⠄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢠⣮⢽⣂⠀⣠⣄⢀⣼⣿⣿⣿⣿⡿⣿⣿⣿⣿⢧⡀⣿⡆⣤⢹⣿⣿⣿⢿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠙⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠯⠏⠀⣇⣉⢸⣏⡇⣿⣿⡟⣧⡿⣻⢟⣿⣿⡇⢸⠇⣿⢸⣿⡇⣿⣾⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣮⣾⣿⣿⣷⣾⣶⣶⣶⣶⣤⣤⣤⣤⣽⣯⣮⣿⣿⣿⣼⣷⣿⣷⣽⣿⣿⣼⣷⣼⣴⣿⣮⣿⣵⣿⣿⣽
⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⡆⠀⢰⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⢆⠀⠀⠀⠘⠃⠀⠀⠀⣄⣏⡃⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⡄⠀⡀⠀⠀⠀⠀⠀⠀⢀⣠⠀⢀⡄⣄⡀⠀⠀⠀⢈⣽⡧⡀⣿⡄⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠗⣒⣒⣂
⠀⠠⠀⠀⠀⠨⠀⠀⠤⠀⠀⠀⠀⠀⠀⠤⠀⣀⡀⣀⡀⢀⣙⣁⣀⢉⣋⣋⣉⣈⣛⣉⣠⣭⣡⣀⣀⡃⠤⣶⡒⣲⡾⠻⣷⣿⢖⠞⠓⠉⢥⣶⣬⣄⣄⣴⣧⣦⣿⣈⣥⣭⣬⣭⣤⣬⣬⣬⣴⣴⣶⣶⣦⣦⣴⣷⣷⣾
⢰⣶⣶⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡋⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⣿⣿⣷⣹⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠂⠘⠿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⣿⣿⣿⣧⣙⣿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣵⣶⣾⣿⣿⢻⡟⣶⣶⢱⡖⢱⢶⣷⣾⣷⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⣿⣿⢿⣿⡟⠀⢠⣿⣿⣿⣟⣛⡋⢫⣥⣴⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⢿⣸⣇⣿⠉⢸⣏⣼⢾⣾⣟⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⡆⢰⣿⣿⡹⣿⡿⠃⡉⠁⠲⣙⣾⡟⠿⣿⠻⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣇⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡉⠉⠉⠉⠉⠛⠃⠈⠋⠿⠿⠙⢫⡆⠀⠀⠈⠉⠉⠛⠒⠶⠧⢾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⣿⣹⠈⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠇⠿⠀⢿⣿⣿⣿⣿⣿⣿
⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣼⣳⢿⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢠⣦⣴⠄⠀⣠⣄⢀⣾⣿⣿⣿⣿⡿⣿⣻⣿⣿⢠⡠⣧⡄⣼⣿⣿⣿⣿⢻⣻
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠈⠓⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⣺⠇⠀⣇⣉⢸⡇⡇⣿⣿⡟⣧⣿⣿⣟⣿⣿⡇⢻⠀⣿⢹⣿⡏⣿⣾⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣕⣾⣾⣾⣿⣷⣷⣶⣶⣦⣤⣤⣤⣤⣽⣯⣮⣿⣿⣿⣾⣿⣿⣿⣽⣿⣿⣼⣧⣼⣴⣿⣯⣿⣽⣿⣿⣿
⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢀⢶⠀⠀⡆⠀⡆⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠃⠀⠠⠀⠀⠀⠀⠃⠀⠀⠀⢠⣮⣯⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⡀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⡀⠀⣤⢤⣀⠀⠀⡀⠀⡨⣿⢀⢽⡇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢒⢂⣤⠌⠀
⠀⠀⠀⠸⠄⠀⠤⠀⠀⠀⠀⠀⠀⠠⢀⡀⣀⢀⣀⣀⣉⣁⣊⣈⣚⣙⣹⣁⣛⣋⣃⣬⣙⣅⣀⣀⢠⣴⣶⣒⣶⠿⠛⢿⣷⡾⠛⡋⢡⠶⣮⣅⢰⣰⣛⣲⣮⣇⣭⣬⣥⣭⣧⣢⣮⣽⣥⣮⣶⣶⣷⣶⣼⣾⣿⣿⣿⣿
⢰⣿⣾⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⡎⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠴⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢿⣿⣿⣿⣜⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣵⣶⣾⣿⣿⢳⡆⣶⢲⢰⡖⢳⣶⣿⣾⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣿⣿⣿⣿⡿⠀⠀⣾⣿⣿⣿⣛⣋⠹⣯⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡟⣿⢸⣸⠇⣿⠉⢸⣏⣾⢾⣿⣟⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣷⣶⣖⣶⣶⣶⣶⣆⠀⣿⣻⡙⣿⣿⠟⠈⠉⠰⢈⣷⣟⠿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⡀⠀⡀⣐⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣭⣉⠉⠉⠉⠉⠛⠛⠀⠋⠿⠿⠝⠛⡵⠀⠀⠀⠉⠉⠛⠓⠲⠴⢼⡻⣿⣿⣿⣿⣿⣿⣿⣿⡇⣯⠉⣿⣸⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠄⠇⠿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢰⣷⣛⣾⠄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⣶⣶⣄⠀⠀⣠⣄⢰⣿⣿⣿⣿⣿⡿⣿⣻⣿⣠⢠⡄⣤⣿⣿⣿⣿⣿⣿⢿⣻
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣺⠟⠀⠀⣷⣉⢸⣧⡧⣿⣿⡟⣧⣿⣿⢟⣿⢿⡇⢸⢻⣿⢾⣿⡇⣿⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾⣾⣿⣿⣿⣷⣶⣶⣦⣤⣤⣤⣤⣤⣤⣽⣯⣮⣿⣿⣿⣾⣷⣿⣷⣽⣿⣿⣼⣷⣼⣽⣿⣯⣿⣽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢶⠀⠀⡄⠀⡆⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠠⠀⠀⠀⠀⠃⠀⠀⠀⠠⣫⣶⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠀⠀⠀⡀⠀⠀⢀⣀⠀⢀⣀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡄⢀⣤⢰⣄⠀⠀⡀⠀⠬⣿⠠⢼⡗⣀⢀⡀⠈⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠚⠭⠡⠤⢭⣉⡩⠩
⠀⠰⠔⠀⠐⠀⠀⠀⠀⠀⠀⠢⢀⡀⣀⢀⣀⣀⣉⣃⣋⣈⣛⣙⣊⣁⣙⣋⣀⣭⣁⣌⣀⣀⢠⢶⣿⣒⣶⣛⣞⠛⢿⣿⣍⡁⣰⣖⣶⣃⣐⣐⣛⣒⣾⣯⣍⣴⣄⣴⣧⣦⣶⣶⣴⣶⣶⣶⣶⣶⣴⣾⣿⣿⣿⣿⣿⣿
⢸⣿⣷⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡋⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⣿⣿⣿⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣹⣿⣿⣿⣼⣿⡿⡿⣿⣽⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣷⡞⣿⣵⢲⡗⣶⢳⢱⣶⣷⣶⣿⣾⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⣿⠟⠀⠀⣿⣿⣿⣿⣛⣋⢹⣷⠶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣻⠃⣏⣷⣿⣸⠇⣿⠝⢸⣿⣿⢾⣿⣟⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣷⣦⠀⣿⣿⣝⣿⣛⡋⡈⠁⠲⣌⣿⣟⠛⠿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⣀⣀⣾⢿⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣍⠉⠉⠉⠉⠉⠋⠀⠃⠛⠛⠙⠋⡷⠀⠀⠀⠈⠉⠉⠑⠲⠶⠼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⣯⠁⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠷⠄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡷⣻⢾⠀⠀⠀⠀⠠⠀⠀⢀⡀⠀⠀⢠⣺⢷⡄⠀⠀⠀⣠⣤⢟⣿⣿⣿⣿⣿⡟⣿⣧⡄⢠⢠⣼⣿⡿⣿⢿⣿⡿⣿⢿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣾⠇⠀⠀⠀⣿⣉⢸⣯⡇⣿⣿⡟⣧⡿⣿⠂⣼⢿⣿⢸⣿⣿⢹⣿⣇⣿⣾⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣶⣦⣴⣿⣾⣶⣷⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣴⣶⣽⣯⣮⣿⣿⣿⣾⣷⣿⣷⣼⣿⣿⣾⣿⣽⣿⣿⣾⣿⣵⣿⣿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⡀⠀⠐⠆⠀⡆⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠳⣷⠀⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⡀⠀⠠⠀⠠⠤⠤⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠀⠀⠤⣄⣤⠤⢴⣤⣤⢤⢦⠤⠖⠀⠂⠀⠀⣀⣠⢀⣀⢠⣦⣄⣤⣿⣺⠦⣀⡠⠄⢀⠈⣿⡁⣸⡗⠶⠠⠄⠄⡄⠀⠀⠀⠄⣀⣀⣀⣀⣀⢀⣀⣬⣨⣤⣤⣬⣤⣥⣤⣬⣬
⠀⡀⣀⣀⣀⣄⣤⣥⣤⣤⣤⣤⣤⣤⣴⣦⣦⣴⣷⣶⣶⣴⣴⣶⣶⣾⣶⣶⣴⣶⣭⣿⣿⣭⣭⣭⣭⣽⣯⢀⢹⣿⣿⣽⣯⣥⣼⣾⣵⣿⣶⣶⣷⣷⣾⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣟⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⠉⣿⣿⣿⣇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣂⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣤⣽⣿⣿⣿⣾⣿⠏⠋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⣶⢱⡆⡟⣶⢹⢻⣿⣾⣿⢻⡿⣿⣿⣿⣿⣷⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣏⣉⣋⣛⣛⣛⣁⠀⢸⣿⣿⣿⣿⣧⡦⠼⠟⡛⢿⣻⣿⣿⣿⣿⣿⣿⣿⣉⣿⣁⣿⣼⠇⡏⣷⢼⣸⣿⣿⣿⣸⣟⣾⢾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⢾⢿⡇⢸⣿⣿⣮⣿⡭⢅⠀⠀⠩⠶⠿⢦⣙⣉⠀⢹⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⢸⡿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡦⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⡟⠀⠀⠀⠀⠀⢄⠀⠉⠉⠙⠊⣿⣿⣿⣿⣿⣿⡿⢸⢹⠈⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣰⣖⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠿⢹⡆⠿⣹⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠳⣷⣺⠏⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⣾⢞⣿⡄⠀⠀⠀⠀⠀⣻⣿⢿⣿⣿⣿⣧⣠⡜⣧⢠⣿⣿⢿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣀⣀⣀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⢀⣀⡄⣿⣙⢸⣿⡇⣿⣿⡟⣧⣏⢸⣞⣿⣿⣿⣸⣿⣿⣻⣿⡏⣿⣿⣻
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣯⣮⣿⣿⣿⣼⣷⣿⣿⣽⣿⣿⡾⣿⣽⣿⣿⣮⣿⣵⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣛⣧⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡠⢀⣀⠒⠀⠒⠒⠂⠀⢐⣂⣐⡒
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠰⠴⠐⠖⠔⠆⠆⢀⡓⢒⠁⠀⠀⣀⣀⣤⣤⣤⢄⣦⣿⣶⣼⢷⣿⣥⣠⣜⠀⠀⠨⠿⡬⠝⠃⠃⡘⣀⢲⡂⡀⣀⣐⣀⣤⣤⣤⣤⣄⣠⣤⣶⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾
⢠⣤⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣾⣿⣷⣶⣶⣶⣶⣾⣷⣇⣄⣾⣿⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⣿⣿⣿⡎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣡⠄⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣴⣶⣿⣿⣿⡿⠿⣿⣦⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣷⠂⣶⢱⡂⡖⣾⣻⢻⣿⣶⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣦⣤⣴⣿⣭⣥⢤⠀⣿⣿⡿⣿⣷⣶⠆⠚⢩⡙⢯⣿⠿⣿⢿⠿⣿⣿⣄⣠⣤⣿⣇⢿⣸⠃⡏⣷⣿⣸⣿⣿⣿⣸⣿⣿⣾⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡛⠛⠛⠛⠛⠻⠿⠀⠻⢿⣿⡾⠿⢗⡀⠀⠀⠚⠛⠛⠦⠬⣄⣄⣽⣿⣿⣿⣿⣿⣿⠀⢀⣤⠤⢸⣿⣿⡿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠄⠀⠀⠀⠉⠸⣿⣿⣿⣿⣿⡆⣯⣿⢸⢹⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢠⣾⡿⡷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡃⠇⢸⡿⠹⣾⣿⣿⣷⣿⣏⣿⣟⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠻⠯⠟⠁⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠘⣿⡽⡿⠀⠀⠀⠀⠀⠀⠹⣿⣿⢟⣿⡇⣠⢸⣧⡄⣿⢻⣿⣿⢻⣿⣿⡟⣿⢿⣿⡿⣿⢻⢻
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣄⣀⣠⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⠀⠈⠉⢁⢀⣀⣀⣄⣤⣾⡇⣿⣙⢸⣏⣇⣿⣿⡟⣧⣿⣿⣟⣿⣿⣿⣿⢿⣿⢸⣿⡇⣿⣾⣸
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣾⣿⣿⣿⣼⣷⣿⣟⣽⣿⣽⣾⣿⣽⣽⣿⣿⣿⣵⣿⣿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣰⠄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⢀⣄⡀⠀⡀⠀⠀⢼⡇⠔⣿⢀⡀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠭⠤⢤⣁⡀⢉⢩⣁⣀⢀⣀⣀⣀⣀⣀
⠀⠀⠄⠀⠀⠀⠀⠀⠀⢉⣁⣀⠁⣓⣉⣀⣉⣈⣓⣀⣬⣍⣀⣀⣀⡀⠴⣖⡒⣲⠟⠂⠻⢟⠁⣩⠛⠻⣷⣶⣁⣀⣂⣚⣓⣂⣉⣨⣠⣤⣤⣶⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⢻⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣈⣻⡿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠡⠖⡀⠲⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⢛⢿⡿⠗⠀⠰⣿⣿⣿⣿⣟⣛⢉⡿⠶⣾⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠀⡀⣶⠂⣶⢰⡆⡞⣿⣿⢻⣿⣶⣿⢱⣿⣿⣶⣿⣾⣷⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣟⣻⡆⢠⣿⣿⣛⣿⣿⡟⠈⠁⠒⣌⣿⡟⠛⠟⠛⠹⣿⣶⣶⣾⣿⣷⣿⣁⢿⣹⢣⡏⣿⣿⣸⣿⣿⣿⣾⣿⣿⣾⣿⣟⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣥⣌⠉⠉⠉⠉⠙⠃⠀⠋⠻⠛⠙⠋⢱⠆⠀⠀⠉⠉⠉⠑⠶⠖⠠⡟⣿⣿⣿⣿⣿⡀⠀⠒⠈⠸⣿⣿⣿⣿⡿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⢠⣯⡿⣻⢿⣿⣿⣷⣿⣿⣿⣿⣾⣟⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢼⣽⣻⣳⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢰⣮⣶⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡆⠀⢸⡿⠀⢿⣿⣿⣿⣿⣷⣏⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⡺⠃⠀⠀⠀⠀⠀⠀⣿⡿⣿⣿⢇⡤⡜⣯⢠⣨⡟⣿⢻⣿⣿⢿⣿⣿⡿⣿⢿⣿⡻⣿⢻⢻
⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣠⣤⣤⣤⣴⣷⣿⣿⡇⣿⣹⢸⣧⡧⣿⣿⣟⣧⡿⣿⣟⣿⣿⣿⣸⣼⣿⢸⣿⡇⣿⣾⢽
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣮⣿⣵⣿⣼⣧⣿⣧⣼⣿⣿⣼⣿⣼⣿⣿⣮⣿⣥⣿⣿⣼
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⠀⢀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣀⣀⠀⡀⣀⠀⠀⢤⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣀⡀⡤⣠⣄⣀⠀⡄⠀⠀⢿⠁⢸⣗⣤⠀⡀⠀⠀⠀⠀⠀⠄⠀⠀⢀⢀⡀⠈⠐⣂⣒⣶⡤⣠⣀⣤⣤⣄⣠⣤⣤⣤⣤⣤⣦⣤
⠀⠀⣀⣀⣀⣀⣀⣨⣠⣄⣈⣭⣤⣄⣀⣤⣤⣀⣬⣤⣄⣄⣄⣐⣒⣎⣙⣛⣋⣈⣙⣋⣑⣠⣌⠉⢻⣿⣇⣤⣤⣭⣭⣥⣤⣤⣶⣴⣶⣷⣶⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣯
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠁⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⡅⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠄⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣀⣺⣿⣿⣿⣬⣿⡟⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠐⠋⠄⠙⠽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠻⠟⠿⠟⠁⠀⢸⣿⣿⣿⣿⣫⡅⣸⠛⢿⣾⣿⣿⣿⣿⣿⣿⠛⠉⢁⣀⡄⠀⠀⣶⠂⣶⢰⣶⣞⣾⣵⢻⣿⣾⣿⢱⣶⣷⣶⣿⣾⣶⣿⣿⣿
⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣽⣿⣿⣿⠀⢸⣻⣿⣽⣿⣿⡁⠀⠈⣰⣼⣿⣉⠙⠉⠉⠺⣿⣿⣿⣿⣿⠀⠀⣿⣁⢿⣹⣿⡏⣷⣿⣸⣿⣿⣿⣿⣿⣾⣾⣿⣟⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣦⡀⠀⠀⠈⠉⠉⠀⠈⠘⠛⠃⠉⠁⡿⠀⠀⠀⠀⠀⡁⠙⠛⠓⠺⠝⣿⣿⣿⣿⡄⠀⠉⠀⠀⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⡠⣤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢹⣿⣿⣿⠇⠀⢰⡄⠀⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣷⢯⣟⠇⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⣞⡿⣧⠀⠀⠀⠀⠀⠀⠺⢿⣿⣿⡇⠀⢼⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣏⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠀⠀⠀⠀⠀⣀⣀⣾⣿⠿⣤⣄⢈⡭⡄⣠⢻⣿⡟⣿⢻⣿⣿⢿⣿⣿⡿⣿⢿⣭⡻⣿⢻⢻
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣷⣶⣶⣶⣶⣶⣶⣤⣴⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣷⣾⣿⣿⣿⣇⣿⣽⢸⣷⣧⣿⣿⡟⣧⡿⢾⢟⣿⣿⣿⣸⣿⣿⢸⣿⡇⣿⣾⣸
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣽⣯⣮⣿⣿⣿⣿⣷⣿⣷⣼⣿⣿⣾⣿⣼⣽⣿⣮⣿⣵⣿⣿⣽
⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣦⠀⢴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠄⠀⠤⠀⠤⠤⠤⠀⠀⠀⠀⠐⠀⠀⠀⠀⠤⠄⡀⠀⠀
⠀⠀⢤⡀⡀⠀⢀⣀⠀⠠⢀⠄⠠⠤⡤⠄⠀⠀⠀⠀⠀⡀⠀⢀⡀⣄⣤⣀⢠⣇⡴⠄⣀⣤⣄⣀⠋⢿⣐⣻⠇⠤⠠⠀⢄⡄⠀⠀⠀⠄⣀⣀⣄⣄⣀⣀⣩⣥⣭⣽⣂⣤⣤⣴⣦⣤⣶⣶⣶⣶⣾⣿⡶⣶⣶⣿⣷⣾
⢀⣀⣠⣤⣤⣄⣨⣥⣤⣤⣤⣤⣤⣶⣶⣤⣤⣤⣤⣍⣿⣭⣭⣭⣭⣬⣭⣅⣡⣤⣤⣭⡇⡀⢹⣿⣶⣶⣦⣶⣶⣶⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢏⣒
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⡀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⠉⣿⣿⣿⡄⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠖⡀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣤⣤⣿⣿⣿⣷⣶⡿⣝⠸⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠋⠒⠈⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢛⣉⣉⣛⣛⣛⣃⡀⠀⣿⣿⣿⣿⣯⣵⠤⠜⡛⠿⣟⣿⣿⣿⣿⣉⣁⣠⣤⣦⠀⠀⠀⠤⠀⣸⣶⠦⣶⢲⣶⣾⣿⣿⢻⣿⣶⣿⢱⣶⣷⣶⣿⣾⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠿⢿⣿⣿⣿⡧⠀⡟⣾⣷⣽⣿⡭⠀⠀⠩⠴⠿⠧⢈⡋⠀⠀⢻⣿⣿⣿⡆⠀⢀⣀⠠⣿⣿⣳⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣾⣿⣾⢾⣿⣟⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣦⠀⠀⠀⠀⠈⠁⠀⠀⠉⠉⠈⠀⠈⡇⠀⠀⠀⠀⠠⡀⠉⠉⠀⠒⠹⣿⣿⡇⠀⠈⠀⠀⣿⣾⣿⣿⣾⣿⣿⣿⣿⣿⡿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢠⣐⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⢸⣆⠀⠘⣿⣿⣿⣿⣿⣿⢻⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠸⣽⣼⡟⠀⠀⠀⠀⠐⠒⠐⠒⠂⠀⠀⢸⣞⣻⡄⠀⠀⠀⠀⠀⠀⠻⣿⠇⠀⢾⣿⡆⠀⢻⣿⣏⢿⣿⣿⣿⣿⣿⣟⣿⣏⣇⡿⣋⣟⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⢀⡀⣠⢻⡀⠀⣬⡥⣤⣄⢒⣯⡿⣿⢿⣿⡿⣿⣻⣿⣿⣿⣿⣿⡿⣿⢿⣿⡿⣿⢻⢻
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣽⢸⡟⡇⣿⣿⡟⣧⣿⣾⣟⣿⣿⣿⢽⣿⣿⢸⣿⡇⣿⣾⣸
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣷⣿⣼⣿⣿⣿⣼⣿⣿⣾⣿⣼⣿⣿⣮⣿⣵⣿⣽⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣆⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠄⠀⠀⠀⠶⠔⠀⠀⠐⡀⣀⠂⠀⠀⠀⠀⡴⠠⠀⠀⠄⠀⠀
⠀⠀⠀⠀⣀⠀⠠⠠⠄⠀⠀⠢⠠⠐⠀⠀⠀⠀⢀⣀⣀⣀⡀⣴⣦⣀⢰⢦⠖⢂⣀⣴⣤⣤⣉⣏⣀⢿⠃⠆⠐⠀⣀⡄⠀⣀⠐⣀⣠⣀⣄⣤⣄⣠⣭⣤⣤⣖⣲⣶⣶⣶⣶⣦⣶⣶⣿⣿⣿⣿⠿⢾⣿⣻⣿⣿⠿⠽
⢠⣤⣤⣤⣴⣤⣴⣤⣤⣶⣤⣼⣶⣦⣤⣤⣮⣽⣿⣤⣭⣭⣤⣤⣽⣭⣥⣤⣤⣭⣷⡇⡀⣿⣿⣶⣶⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣑⠲⢝⠒
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣛⢾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣴⣤⣠
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠁⠨⣿⣿⣿⠘⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠒⡀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠄⢠⣤⣬⣿⣿⣿⣷⠾⢯⣉⢺⣿⣿⣿⣿⣿⡿⡿⠋⠁⠀⠋⠐⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣋⣉⣘⣛⣛⣋⣁⠀⢸⣿⣿⣿⣿⣷⣶⠴⢉⡙⢾⣿⣿⣿⣿⢁⠀⣤⣤⣶⠀⠀⠀⠤⠀⣰⣿⣿⣶⠶⣶⣷⣾⣾⣿⣿⢻⣿⣶⣿⢱⡶⢷⣶⣿⣾⣶⣿⣿⣿
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⠿⠿⠿⠿⠾⣿⣿⠇⢸⢷⣿⡿⣿⣿⠥⡀⠀⠉⠾⠿⠦⢈⡀⡀⠈⣻⣿⣿⡇⠀⢀⣀⠤⢿⣿⣿⣿⣳⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣾⣟⣾⣾⣿⣟⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡦⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢸⠁⠀⠀⠀⠀⢤⠀⠈⠁⠀⠂⠹⣿⣷⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿
⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣠⣒⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⡀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⢈⣦⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣷⣿⣿⣿⣼⡞⡯⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢿⣷⣿⠇⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⣿⣟⣷⠀⠀⠀⠀⠀⠀⠀⠿⠁⠀⢺⣿⡇⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠏⢇⡿⣃⠟⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⢀⢀⣌⣀⣀⣠⣨⣤⡄⣾⣿⢟⣿⣿⣿⢿⣿⡟⣿⣻⣿⣿⢻⣿⣿⡟⣿⢿⣿⡟⣿⢻⢻
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⣿⣉⢸⡿⡇⣿⣿⡟⣧⡿⢾⢟⣿⣿⣿⢸⣿⣿⢸⣿⡇⣿⣾⢸
⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣮⣿⣿⣿⣼⣿⣿⣿⣼⣿⣿⣾⣿⣼⣬⣿⣮⣿⣥⣿⣽⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⣆⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢦⢀⣀⣒⠀⠒⠒⢒⠀⣂⡂⣐⠀⠀⠀⠀⠀⠖⠢⠀⠀⣄⢀⣀⣀⣀
⠀⠀⢠⡠⠤⠐⠀⠀⠀⠢⠆⠔⠀⠀⠀⢀⣠⣀⣀⣤⡀⣴⣦⠤⠸⠦⠛⣂⣀⣐⣠⣴⣭⣏⣁⢻⠗⠂⡒⡀⣒⣂⢐⣐⣐⣀⣠⣤⣤⣦⣄⣤⣤⣶⣴⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠾⠿⠝⠫⡙
⢠⣤⣶⣢⣶⣶⣶⣶⣶⣿⣶⣷⣶⣶⣮⣽⣷⣶⣿⣧⣶⣶⣷⣥⣴⣦⣴⣾⣵⣷⣆⣄⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣡⠯⠟⠃⠀⠑
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣁⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⣤⣤⣤⣤
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠉⠁⢸⣿⣿⣷⠘⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠓⡂⢈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠔⢦⣤⣼⣿⣿⣿⡷⠾⣏⣃⢻⣿⣿⣿⣿⣿⠿⠛⠉⠀⠉⠐⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣉⣉⣐⣛⣉⣉⣀⠀⢸⣿⣿⣿⣿⣷⡶⠶⢩⡙⢿⣿⣿⣿⣗⠠⢤⣴⣶⡄⠀⠀⠤⠄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⠿⠷⠾⢿⡿⣿⠆⢸⢽⣿⡿⣿⡿⠆⡀⠀⠰⠾⠿⠤⣀⡀⡀⠈⣻⣿⣿⠀⢀⣀⠠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠘⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠻⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣔⣖⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢀⣷⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢷⣷⣷⠃⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠰⣿⣻⡇⠀⠀⠀⠀⠀⠀⠐⠃⠀⢸⣿⡇⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣾⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣾⣿⣷⣾⣶⣶⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣽⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣆⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢆⢀⣀⣒⠀⠒⠒⠒⠐⢀⠒⠀⠀⠀⠀⢀⠀⠶⠂⠄⠀⢄⠀⣀⣀⣀⣀⣀
⠠⠤⠠⠐⠀⠠⠀⠢⠆⠜⠀⠀⠀⢀⡠⣀⣀⣤⡄⣬⣦⢤⠸⠧⠛⣂⣀⣐⡀⣠⣿⣷⣄⢛⠓⠂⠚⠀⣂⣆⣀⣀⣐⣢⣠⣤⣤⣤⣄⣤⣴⣦⣤⣶⣷⣶⣶⣾⣶⣶⣿⣿⣿⣿⣿⣿⣟⣿⣿⣻⣿⠿⠿⠟⠫⡍⢈⠝
⢰⣖⣶⣶⣶⣶⣶⣾⣶⣷⣶⣶⣦⣭⣿⣦⣶⣦⣴⣦⣷⣤⣴⣦⣶⣶⣶⣿⣶⣇⡄⣻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣰⠭⠺⠉⠀⠉⠋⠀
⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⡀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣤⣤⣤⣤⣤⣤
⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠉⠀⢸⣿⣿⣿⠘⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠟⢂⠀⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠒⣢⣤⣼⣿⣿⣿⡷⠾⣏⣃⢿⣿⣿⣿⣿⡿⠛⠃⠀⠈⠁⠂⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣉⣁⣀⣛⣋⣉⣀⠀⢸⣿⣿⣿⣿⣶⡶⠖⢩⡹⣯⣿⣿⣿⣧⠤⠰⣶⣧⠀⠀⠡⠄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠿⠿⠿⠿⢶⡷⣿⠆⢸⢽⣷⡿⣿⡿⠆⡀⠀⠐⠾⠿⠤⣀⠀⡀⠀⢻⣿⠀⠀⣀⠠⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠘⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠁⠹⠂⠀⡀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⣴⣖⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⢿⣳⡯⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠸⣿⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⢀⣀⣀⣠⣔⣶⣤⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣶⣿⣷⣾⣶⣿⣶⣿⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣲⡄⠰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⣂⣀⣐⡂⠐⠒⠒⠂⠂⠂⠀⠀⠀⠀⠀⡀⠰⠒⠠⢀⢀⣀⣀⣀⣀⣀⣠⣀⣀⠠⣤
⠠⠲⠀⠐⠂⠆⠂⠀⠀⠀⣀⢀⣀⣀⣤⠠⣴⣤⢄⠿⠼⢒⣀⣀⣂⠀⡀⣸⡧⣷⣿⣔⠂⠒⡐⣀⡀⣀⣐⣐⣀⣠⣤⣤⣤⣤⣤⣴⣶⣾⣯⣵⣶⣶⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠏⠚⢭⡉⡠⠊⠁⠀⠘
⢰⣶⣶⣾⣿⣶⣶⣶⣶⣮⣭⣷⣶⣶⣴⣴⣬⣷⣤⣶⣶⣶⣾⣾⣷⣶⣶⣾⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢑⡤⠥⠏⠁⠀⠑⠁⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡝⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣤⣤⣤⣤⣤⣦⣶⣶⣶
⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠁⠀⢸⣿⣿⣧⠘⣾⣿⣿⢿⣻⣿⣿⣿⣿⠟⠚⣋⠀⣘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢒⣦⣧⣾⣿⣿⣿⠶⠾⣛⣺⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣉⣁⣈⣛⣋⣀⠀⠸⣿⣿⣿⣿⣿⣶⡶⢨⡝⢿⣽⣿⣿⣿⣄⠶⢷⠀⠀⠒⠄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠿⠿⠿⢿⢿⣿⣿⡗⠠⣿⣿⡿⣿⣿⠷⢄⠀⠐⠾⠿⠦⣌⡀⢀⠀⠘⠀⠀⡄⠤⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡦⠀⠀⠀⠀⠈⠀⠀⠀⠉⠉⠈⠀⠀⠁⠀⠀⠀⠀⢤⡀⠉⠉⠀⠀⠀⠀⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⢲⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢿⣫⣝⡇⠀⠀⠀⠀⠐⠂⠐⠒⠀⠀⠀⣷⣟⣷⠀⠀⠀⠀⠀⠀⠀⠐⠻⠃⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯
⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⣀⣀⣀⣦⣤⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣷⣶⣿⣶⣶⣿⣿⣾⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢐⢰⢶⡀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⡀⣀⣐⠂⠐⠒⠒⠂⠀⠒⢀⡀⠀⠀⠀⠀⠰⠒⠄⡀⠠⣀⣀⣀⣀⣀⣀⣀⠀⢠⣤⣤
⢀⠄⠐⠠⠴⠀⠀⠀⠀⡀⣄⣀⣠⣄⢠⣾⣤⠄⠧⠜⢓⣀⣀⠂⠀⠈⣹⣊⠼⣿⣾⡔⡂⢐⣀⡀⣀⣀⣒⣀⣤⣤⣠⣤⣠⣤⣴⣴⣼⣭⣶⣶⣶⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣻⣟⣻⢿⠟⠛⠋⢭⢁⡬⠊⠀⠉⠋⠉
⢰⣶⣶⣷⣶⣶⣶⣴⣭⣯⣶⣴⣯⣤⣤⣾⣿⣤⣴⣶⣶⣷⣾⣶⣶⣶⣶⣿⣠⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣁⡬⠕⠏⠁⠈⠘⠀⠀⡠⠀⠐⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣾⣿⣿⡕⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣀⡀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣮⣤⣤⣴⣤⣤⣤⣶⣶⣶⣶
⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⡁⠀⣿⣿⣿⡆⢻⣾⣿⣿⣿⣿⣿⣿⣿⠟⠓⡋⠀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠤⣶⣤⣶⣿⣿⣿⣷⠶⢿⣑⣿⣿⣿⣿⠿⠁⠀⠈⠀⠁⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡛⠉⠁⠐⠚⠃⠀⠀⢿⣿⣿⣿⣿⣷⣶⠆⣉⠱⣞⣿⣿⣿⣧⣲⠆⠀⠀⠒⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢿⢿⣿⣯⣭⣽⣭⠀⢾⣽⣯⢿⣿⣭⠥⠀⠈⠳⠾⠧⣄⣁⠈⠀⠀⠀⠠⠤⠔⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⠈⠉⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣄⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⡠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠸⣟⣭⢾⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢸⣞⣻⡄⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⡌
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣤⣾⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡀⠀⠀⠀⠀⢐⠒⣶⠀⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⣀⣀⣐⡀⠒⣒⠒⠀⣐⢒⠀⡂⠀⠀⠀⠀⠴⠂⢄⣀⣀⣀⣀⣀⣀⣀⣀⡀⡀⢠⣤⣤⣤
⢀⠀⠤⠔⠀⠀⠀⠀⢀⣀⣀⣠⡄⣤⣾⣤⠰⠧⠞⢒⣀⡐⡂⢀⢉⣿⣈⣸⢷⣾⣴⡂⢂⣂⠀⣂⣂⣂⣐⣤⣤⣤⣤⣠⣤⣦⣴⣾⣵⣶⣶⣶⣷⣶⣿⣿⣿⣿⣿⣿⡿⣿⣿⣻⣿⠿⠿⠛⠫⡍⢁⠜⠋⠀⠁⠋⢽⣤
⢰⣾⣶⣶⣶⣤⣤⣽⣿⣦⣼⣯⣤⣦⣿⣷⣥⣦⣤⣼⣵⣿⣶⣶⣶⣶⣶⣿⣠⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣁⠭⠝⠏⠀⠈⠚⠀⠀⠀⠀⠂⠈⠣
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠳⣿⣿⣿⣿⣿⣿⣿⣿⣇⣄⣀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣧⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣿
⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⡉⡁⠀⣿⣿⣿⡀⢻⣿⣿⡿⣿⣿⣿⣿⠟⠛⡚⠁⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢠⣴⣲⣴⣤⣿⣿⣷⣷⣾⠯⢱⣿⣿⣿⡿⠃⠀⠀⠀⠁⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠿⠿⠂⠀⠰⣿⣿⣿⣿⣿⣷⡦⢔⡛⢷⣻⣿⣿⣿⣴⡶⠀⠀⠐⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣛⡆⠀⣿⣿⣿⣯⣭⣭⡅⠀⠡⡾⣿⣏⡉⠉⢃⠀⠀⠀⠤⠴⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣦⡀⠈⠉⠉⠙⠁⠀⠁⠛⠛⠉⠉⠀⠈⠀⠀⠀⠀⢀⡉⠙⠛⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢾⣻⣻⡥⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⣿⡞⣧⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⡌⠐
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠈⠛⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠋⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣿⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣴⣶⣾⣿⣿⣿⣿⣟⢿⣛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⢲⣦⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢂⢀⣀⡒⡀⠒⣒⠒⠀⢐⠒⢀⠂⠀⠀⠀⠀⠶⠂⠄⠀⢄⣀⡀⣀⣀⢀⣀⣀⠀⢤⣤⣤⣤⣤
⠠⠠⠖⠀⠀⠀⠀⢠⣀⣀⣤⡄⣼⣾⣤⡸⠧⠟⣒⣀⡰⡀⢀⢉⣿⣈⣹⣧⢶⣶⣤⣂⠂⠀⣂⣂⣂⣐⣤⣤⣠⣀⣠⣤⣦⣤⣴⣦⣶⣶⣶⣷⣶⣷⣿⣿⣿⣿⣿⡿⣿⣟⣻⣿⠿⠟⠕⠫⡍⢁⠕⠁⠀⠀⠉⢽⡤⠾
⢸⣶⣦⣤⣦⣬⣭⣽⣤⣼⣥⣤⣤⣯⣭⣥⣦⣤⣼⣵⣿⣶⣶⣶⣶⣷⣾⣧⣤⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⣡⠭⠿⠋⠀⠉⠋⠀⢀⠀⠀⠂⠈⠇⣒
⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⡇⣤⡠⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣥⣤⣤⣤⣤⣴⣴⣶⣶⣶⣶⣿⣿
⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠁⢸⣿⣿⢷⠀⣿⣿⣿⡿⣿⣿⣿⠟⠛⣛⢁⠨⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⢲⣶⣦⣤⣼⣿⣿⣿⣶⣼⠏⢶⣿⣿⡿⠃⠀⠀⠀⠈⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣉⡸⠿⠟⠀⠀⢸⣿⣿⣿⣿⣿⣷⡤⣚⢫⣎⣿⣿⣿⣇⡶⠄⠀⠀⠈⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣻⣷⣦⠀⢸⢻⣿⣿⣭⣭⣭⠀⠉⢥⢿⣿⣉⠙⠛⡁⠀⠀⠀⠶⠒⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣍⠈⠉⠉⠋⠋⠀⠈⠘⠛⠋⠛⠉⠀⠁⠀⠀⠀⠀⣈⠙⠛⠛⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠⣿⣗⣟⡄⠀⠀⠀⠀⠤⠄⠤⠤⠀⠀⢸⣷⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣩⠈⠒⡑
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠙⠓⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣬⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣷⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣶⣶⣤⣤⣶⣶⣾⣿⣿⣿⣟⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢐⠀⠀⡀⢀⡀⠀⠀⠀⠠⣰⣶⢄⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢒⡒⢒⢐⠀⠐⠒⠀⠀⠠⠤⠤⢄⣀⣀⣀⣀⡒⣂⣂⣀⣐⣀⣀⣀⣤⡤⣤⣤⣠⢠⣤⣤⣦⣴⣦⣴
⠐⠀⠀⠀⣀⣀⢤⢤⣴⡆⡲⣿⣤⣤⠧⠚⢋⣤⣔⡃⠠⠀⠿⢥⠼⡋⠘⢨⠵⣾⣦⣄⣀⣠⣱⣤⣤⣤⣴⣤⣤⣶⣾⣶⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⠿⠛⡓⠋⢬⢁⢖⠁⠀⠅⠤⢝⣮⠾⠼⣭
⢸⣷⣶⣾⣾⣿⣷⣶⣶⣶⣶⣿⣯⣴⣿⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⠌⠒⠍⠁⠈⠚⠀⠀⠐⠀⠀⠀⢛⣁⣒⣀
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣯⠰⣿⣿⣿⣿⣿⣿⣇⣴⣔⡦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣶⣶⣴⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢁⠀⢸⣿⣿⢿⠀⣿⣿⡿⢿⣿⣿⡿⠉⠁⠆⠸⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⠿⣿⣤⣿⣾⣿⣿⣿⠶⠾⡁⢨⣿⣿⡿⠀⠀⠀⠡⠐⢣⠀⢫⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠘⠛⠃⠀⠀⣿⣿⣿⡿⣿⣿⣶⠆⡉⢵⣞⣿⣿⣿⣧⣞⠀⠀⠀⢀⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣽⣿⣿⣿⣿⣟⣃⠄⡟⣿⣿⣿⣿⣭⡥⠀⠩⠶⠿⣧⣉⠉⣻⡁⠀⠀⠀⠉⠁⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⡄⠀⠈⠉⠙⠁⠀⠀⠙⠛⠈⠉⠀⠀⠀⠀⠀⠀⢀⡈⠙⠛⠓⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⡀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡾⣻⢶⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⣾⣟⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡅⢀⠈⠑⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠋⠀⠀⠀⠀⠀⠀⢀⢀⣀⣴⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣾⣾⣿⣿⣿⣿⣷⣿⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⢀⠀⣀⠀⠀⠀⠀⠦⢰⡦⡀⣶⠆⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⠤⠤⢤⣄⣀⢀⢀⡀⠠⣄⣀⣀⣀⣀⣀⣐⣀⣐⣤⣄⣤⣠⢤⣤⣤⠠⢦⡠⢀⠶⣶⡶⠶⢶⣶⣶
⠀⠀⠀⢀⣤⡤⠤⢤⠶⠀⢾⡷⠲⠞⠚⠩⠥⣤⡭⠀⠄⠸⠧⣤⣛⣈⣁⣉⠔⠻⣷⣦⣈⣬⣥⣴⣶⣶⣶⣦⣶⣾⣿⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣛⢉⡉⠲⡄⡔⠉⠀⠀⡐⠐⢳⡞⠓⠾⡻
⢸⣿⣿⣿⣶⣿⣿⣿⣶⣾⣾⣿⣷⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣿⢽⣿⣿⣿⣿⣿⡟⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠖⢊⠛⠀⠀⠈⠁⠀⠀⠀⠀⠀⢈⣢⣥⣴⣲
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⠅⣿⣿⣿⣿⣿⣿⣇⣸⣺⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁⢀⣀⠠⣿⣿⣻⠀⢻⣿⠿⣛⣿⣿⡿⠀⠀⠙⠘⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡇⠘⠻⣯⣿⣷⣿⣿⡿⡿⠿⢿⡃⢁⣿⣛⣿⣂⢀⠀⠀⠂⠑⢄⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣋⣡⠤⢀⠙⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⠆⣍⢺⣽⣿⣿⣿⣿⣮⠀⠀⠀⣀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡧⠀⡟⣷⣿⣿⣶⣶⠶⠀⠀⠲⠿⠧⣄⣉⣹⡄⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡦⠀⠀⠀⠈⠁⠀⠀⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠠⡄⠉⠉⠉⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⡠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠋⢻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠸⣿⣽⢾⠀⠀⠀⠀⠀⠒⠀⠒⠂⠀⠀⣾⣟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣷⡶⣀⡉⠉⠀⠀
⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⢀⣀⣀⣀⣤⣴⣿⣯⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣷⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⢶⠄⢰⡶⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠤⠤⠄⠀⠀⠀⠀⣀⠀⢀⣀⣀⣀⣀⣤⣀⣀⣠⣠⣤⢠⣤⡄⣤⢆⡀⠤⡤⠀⡠⠶⣶⠖⠶⢶⡶⢶
⠀⠀⠀⢀⣤⠠⠤⠴⠆⠰⢻⠖⠒⠓⠊⠩⠤⢤⠅⠀⠀⠘⠠⢈⣁⣉⣈⣁⡀⠛⢿⣶⣄⣥⣤⣴⣶⣴⣴⣴⣶⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣟⣛⣿⣟⣏⣩⣵⡬⡝⢃⠀⣌⡁⢢⢠⠪⠀⠀⠀⠒⠪⣴⡚⠚⠞⠋
⢨⣿⣶⣶⣾⣿⣷⣷⣶⣶⣷⣶⣶⣾⣴⣯⡿⣿⣿⣿⣿⣿⠿⣿⢿⣿⣿⣿⣷⣶⣼⠿⣿⣿⣿⣿⣿⣿⠛⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡴⠂⡑⠂⠀⠀⠉⠀⠀⠀⠀⠀⡀⣁⣠⣭⣄⣤
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⡍⢺⣿⣿⣿⣿⣿⣧⡀⣟⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁⠀⣀⠀⣿⣿⣿⡇⢘⣾⠿⣛⣿⣿⡿⠃⠀⠈⡂⢋⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠇⠈⠚⣠⣴⣶⣿⣿⣿⠿⠛⢛⡃⢀⣺⣿⣿⣃⠀⠀⠀⠐⠈⢢⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣋⢉⠠⠀⠀⠀⠀⠀⢻⣿⣿⣿⢿⣿⣿⠏⣉⠺⣽⣿⣿⣿⣯⣯⠁⠀⠀⢀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠼⢿⡿⠿⠿⠭⢭⠁⠀⢸⣿⣿⢿⣷⣶⠶⠀⠀⠒⠳⠦⠄⣉⣉⡆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⡦⠀⠀⠀⠈⠁⠀⠀⠈⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⣄⠈⠉⠉⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡿⡿⣿⣿⣯⣽⣿⣿⣿⣿⣯⣾
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⡠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠿⠋⠉⠠⠀⢨⠑⠘⢻⣿⣿⣿⠿⠛⠛⡉⣭⣿
⣻⣿⣿⣿⡿⠿⡿⠿⡿⢿⣿⠿⢿⠿⠿⠇⠐⣯⡏⣯⠀⠀⠀⠀⠀⠒⠀⠒⠒⠀⠀⢸⡾⣳⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⠿⢿⠿⠿⡿⠿⠿⢯⣉⢼⡋⣠⡍⣥⠀⠖⠈⠒⡈⠂⠀⢄⣺⡿⣿⠷⠆⠀⠀⠉⢀⠀
⣼⣿⣿⣿⣿⣿⢻⣿⣻⣿⡏⣿⣾⣿⡟⣿⡄⣿⡟⣿⡆⣿⡟⠃⢰⣿⢹⣷⢀⣿⠛⠀⣿⡟⣿⡆⢸⣿⠛⢸⣿⣤⣿⢸⣻⣿⢛⢹⣿⣿⣿⣿⢻⣿⣽⣿⣾⣟⠿⠏⣸⣿⢸⣿⢿⣿⣿⣿⡈⣿⡟⣿⡾⣿⣟⠋⠠⣿
⢹⣿⣿⣿⣿⣿⣺⣿⣻⣿⣿⣿⣻⣿⣷⣿⣇⣿⡟⣿⣧⣿⡿⣗⣺⣿⣬⣝⢸⣿⣿⡆⣿⣧⣿⡧⣾⣿⣗⣽⣿⣿⣿⢨⢸⣿⣸⣸⣿⣿⣿⣿⢠⣿⣿⣿⢾⡻⣿⣟⢻⣿⢸⣿⢿⣿⣿⣯⠂⣿⡿⣶⡞⣿⣿⣇⣠⣥
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣿⣿⣿⣿⣾⣿⣾⡏⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣼⣿⣿⣿⣿⣼⡿⣻⣿⡿⣧⣿⢟⣼⣿⣼⣿⣿⣿⠿⣿⢀⢿⣧⢿⡇⣿⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⢴⡂⠀⣶⢀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠄⣀⣀⣀⠀⣀⣀⣀⣐⣂⣤⣤⣤⣤⣄⣠⣤⣤⣤⣤⡤⢤⡴⡖⠰⡶⠄⡀⠶⢶⠖⠲⠦⣶⣶⡶
⠀⠀⠤⠤⠄⠤⠤⠖⠐⠺⠗⠢⠛⠊⠩⠴⢦⡥⠀⢀⡘⠓⢒⣉⣈⣀⣀⣠⡔⠛⢽⣷⣤⣤⣴⣶⠤⢶⣶⣶⣾⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣽⣙⣻⣿⣭⣭⣵⣦⠜⢋⠈⣌⡁⠺⢠⠎⠀⠀⠂⢐⠀⢯⢛⠛⠶⠊⠈
⢸⣿⣶⣾⣯⣽⣭⣿⣿⣶⣿⣶⣶⣯⣽⣽⣿⣯⣿⣿⣿⡟⢿⢿⣿⣿⣿⣿⣷⣦⡾⢽⣿⣿⣿⣿⣿⣿⠟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡴⠊⣉⠀⠀⠀⠈⠀⠀⠀⣀⣀⣀⣈⣤⣬⣤⣤⣽
⢸⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⣽⣿⣿⣿⣿⡿⠟⠻⣿⣿⣿⠂⢻⣿⣿⣿⣿⣿⣿⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⡀⣠⣄⠀⣿⣿⣾⡇⢰⡿⠟⣯⣽⣿⡿⠏⠀⠈⢁⢻⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠇⠈⠚⣦⣶⣼⣿⣿⣟⡛⠛⣛⠘⣴⣽⣭⣽⣅⢀⠀⠀⠀⠂⢣⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣋⣁⣤⣀⢀⣀⠀⠀⣿⣿⣿⣟⢿⣿⡿⠋⠅⠻⣽⣿⣿⣿⣿⠶⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠰⠿⡻⠿⠿⠭⣭⠀⠀⡏⣾⣿⢿⣿⠷⠖⠀⠀⠚⠛⠦⠄⣀⣙⡄⡀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡦⠀⠀⠀⠈⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠉⠉⠉⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣯⣽⣿⣿⡿⠿⣿⣿⣿⣿⣿⣽⣾⣿⣿⣿⣾
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⡠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡿⠛⠉⠁⠀⠀⠘⠋⢉⣿⣿⣛⡛⠋⡛⣉⢹⣿⠟
⢿⣿⣿⣿⡿⠿⡿⠿⣿⠿⣿⠿⢿⠿⠿⠀⠸⣿⢭⣿⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⢸⢾⣳⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠿⠿⠟⠿⠿⠿⠯⠭⢅⣰⣯⡠⢩⡼⡤⠘⠊⠈⠁⡉⠠⠤⢽⣿⡿⣷⠃⣀⠐⠀⠀⠀⠀
⣺⣿⣿⣿⣿⣿⢸⣿⣹⣿⡟⣿⢿⣿⡟⣿⡄⣿⡟⣿⡆⣿⡟⠃⢰⣿⢹⣷⢠⣿⠛⠀⣿⡟⣿⡆⢸⣿⢛⢸⣿⣴⣿⣸⢻⣿⢻⢸⣿⣿⣿⣿⢻⣿⣽⣿⣾⣟⠿⠇⢸⣿⢸⣿⣾⣿⣿⣿⡀⣿⡟⣿⣏⣿⡟⠃⣼⣿
⢻⣿⣿⣿⣿⣿⣼⣿⣼⣿⣿⣿⣿⣿⣷⣿⡃⣿⡟⣿⣵⣿⡿⣗⢼⣿⣎⣉⢾⣿⢿⣆⣿⡇⣿⡧⣾⣿⣗⣿⣿⣿⣿⢸⣺⣿⣾⣸⣿⣿⣿⣿⢴⣿⣿⡿⢾⡻⣿⣟⢸⣿⢸⣿⢻⣿⣿⣯⠂⣿⡿⣶⡿⣿⣿⣇⣤⣿
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣷⣯⣿⣿⣿⣿⣼⣿⣿⡇⣿⣧⣿⣯⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣾⣸⣿⣿⣾⣿⣼⡿⢻⣿⡻⣧⣿⣟⡼⣿⣼⣿⣿⣿⡿⣿⢄⢿⣧⢿⡇⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⢠⣀⠀⠀⡀⠀⠐⢴⡂⢰⣶⢀⠀⡀⢀⢀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠐⠂⠒⢒⡒⢀⣀⣀⣀⣀⣀⣄⣤⣤⣤⣴⣤⣤⣴⣤⣶⡴⣶⢖⡶⠖⠄⢒⠔⠀⠀⡲⢶⠒⢒⠶⢖⣲⢖⡒
⠀⠤⠤⡐⠴⠶⠓⠘⠻⠷⠀⢉⠉⢀⣒⣲⣀⣀⣀⣚⣒⣒⣅⣠⣠⣤⣀⣂⡆⠉⢺⣿⣶⣶⣾⣾⣾⣶⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣯⣥⣴⣶⡶⠞⠩⢅⠤⠄⠱⣰⠁⠀⠀⠁⠉⠉⡾⢍⠙⠋⠅⣈⡠
⢸⣿⣿⣯⣿⣭⣿⣿⣿⣷⣾⣿⣿⣿⣝⣿⣿⣿⣿⣿⣛⣻⣻⣿⣿⣿⣿⣿⣿⣿⠾⣓⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣞⣉⡉⠁⠀⢀⠀⠀⢀⣀⣀⣀⣀⣬⣤⣶⣧⣶⣿⣿
⢸⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠿⠛⢻⣿⣿⣿⠀⠹⣿⣿⣿⣿⣿⣿⣿⡅⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⢁⢀⡤⣄⣸⣿⣿⣼⣀⣼⣟⣿⣿⣿⣿⣿⣿⠛⠉⠉⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠀⠛⢛⣼⣶⣿⣿⣿⣿⣉⣉⡥⣹⣿⣾⣿⣿⡿⡁⠀⠀⠀⠀⠌⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠠⠀⢀⡀⠀⠈⣿⣿⣿⣟⠿⠿⠟⠠⡘⠳⣿⠿⢿⢿⣶⠓⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠯⠭⠭⡭⠭⣍⠀⠀⡇⣿⣟⢿⡿⠟⠃⠀⠈⠉⠛⠒⠠⣤⣼⡤⢤⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⠈⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡿⠿⠿⠛⣿⣿⣷⣾⣿⣿⣿⣿⣿⣾⡿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⡠⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⠟⠉⠉⠀⠀⡀⠈⠁⢹⣿⣿⡿⠛⢉⡉⡀⠾⠿⠏⠛
⢿⣿⣿⣿⡿⠿⠿⢿⡿⠿⣿⠿⢿⠿⠿⠃⠸⣷⢭⢿⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⢸⣻⣹⡅⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡫⠯⠿⠿⠿⡯⠯⠤⣼⣥⣤⣤⣵⡤⢉⠀⠉⠠⠤⡤⠤⠽⠿⡿⠮⣃⠄⡀⠀⠀⠀⠀⠀
⣼⣿⣿⣿⣻⣿⢽⣿⣽⣿⡟⣿⣿⣿⡟⣿⡆⣿⡟⣿⡆⣿⡟⠃⢰⣿⢹⣷⢠⣿⠛⠀⣿⡟⣿⡆⢸⣿⣛⣸⣿⣴⣿⠜⢻⣿⣻⢸⣿⣿⣿⣿⢻⣿⡽⣿⣾⣟⠿⠏⢸⣿⢸⣿⣾⣿⣿⣿⡈⣿⡟⣿⡦⣿⡟⣛⣏⠐
⢺⣿⣿⣿⣿⣿⣼⣿⣼⣿⣿⣿⣿⣿⣷⣿⡇⣿⡟⣿⣵⣿⡿⣗⣼⣿⢎⣻⢾⣿⣿⡆⣿⡧⣿⣧⣾⣿⣷⣽⣿⣿⣿⣰⣼⣿⣿⢿⣿⢿⣺⣿⢰⣿⣿⠟⢿⡻⣷⣝⢹⣿⢸⣿⢻⣿⣿⣯⡃⣿⡿⣷⡆⣿⣿⣇⡿⣼
⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣿⣿⣿⣿⣾⣿⣾⡇⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⢻⣿⣼⣿⣻⣿⡿⣧⣿⣟⡼⣿⣼⣿⣻⣿⢷⣿⣁⣿⣧⢿⡇⣿⣿⣯⣷⣾
⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⡀⣤⡀⠀⢀⠀⠀⠠⣶⠠⢰⡆⣀⢀⠀⠀⡀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠐⠐⠒⢒⠀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣴⣴⣦⢐⡲⢒⠶⠶⠀⣂⠖⠠⠐⠲⠖⠐⡒⠶⢒⡶⣒⣂
⠀⠤⢤⡂⠰⠾⠃⠓⠿⠞⠈⡁⠁⢰⢒⣦⣀⣐⣐⣛⣒⣊⣡⣀⣄⣤⣀⣤⣶⠉⠐⣿⣦⣶⣷⢾⣶⣖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣭⣤⣶⣶⡶⠃⠭⡰⠤⠈⠇⡜⠁⠀⠈⠈⠁⢸⠯⠉⡛⠋⢀⣁⠬
⢸⣿⣿⣭⣯⣿⣿⣿⣿⣷⣿⣿⣯⣭⣻⣿⣽⣿⣿⣿⣛⣟⣿⣿⣿⣿⣿⣿⣿⣿⠾⣓⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣦⣚⣉⡌⠀⠀⡀⠀⡀⣐⣀⣀⣀⣀⣤⣶⣾⣽⣾⣿⣿
⢸⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣭⣿⣿⣿⣿⣿⡿⠿⠛⢛⣿⣿⣿⠁⠹⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣰⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⣀⢄⠤⠤⣀⣿⣿⣼⣄⣸⢟⣯⣿⣿⣿⣿⣿⣿⠷⠐⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠂⠘⠋⣴⣶⣾⣿⣿⣿⣍⣍⡩⢜⣿⣿⣿⣿⣿⣟⠢⠀⠀⠀⠀⢹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⢀⣀⣀⣀⠀⠀⣿⣿⣿⣿⡻⠿⠿⠀⡀⠻⠾⠿⠿⠿⢿⠓⠀⠀⠀⠀⠀⢀⣈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠰⠿⠿⠿⣿⡿⣭⠁⠂⠯⣿⣿⢿⡿⠟⠋⠀⠀⠉⠛⠓⠢⣤⣬⡧⠤⡄⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⡦⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣭⣿⠿⠿⠟⢿⣿⣿⣶⣿⣿⣿⣿⣿⣷⣿⠿⠷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⡠⢤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⣿⣿⣿⣿⡿⣿⣿⢿⣿⡿⠛⠉⠀⠀⢀⠀⠉⠈⣹⣻⣿⠿⠛⢉⢁⡠⠾⠿⠋⠛
⢽⣿⣿⣿⡿⠿⡿⢿⡿⠿⣿⠿⢿⠿⠿⠇⠀⢿⢯⣿⠆⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠘⣿⡭⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹⠻⠿⠿⠿⡥⠤⠤⢫⣤⣤⡤⣤⡴⢁⠁⠀⠤⠤⡤⠬⠽⢿⠿⠼⣠⠀⠠⠀⠀⠀⠀⠀
⢼⣿⣿⣿⣻⣿⣿⣿⣽⣿⡿⣿⣿⣿⡟⣿⡆⣿⡟⣿⡆⣿⡟⠃⢰⣿⢹⣷⢠⣿⠛⠀⣿⡟⣿⡆⢸⣿⣛⣸⣿⣴⣿⠞⢻⣿⣻⢸⣿⣻⣾⣿⠻⣿⣽⣿⣾⣟⠿⠇⢸⣿⢸⣿⣾⣿⣿⣿⡈⣿⡟⣿⡆⣿⡟⣛⠁⠀
⢺⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣿⡇⣿⡟⣿⣽⣿⡿⣇⢼⣿⢞⣫⣾⣿⢿⡆⣿⡧⣿⣧⣿⣿⣷⣾⣿⣿⣿⢰⣼⣿⣿⢾⣿⣿⣾⣿⢸⣿⡿⢻⢿⡻⣷⣟⢸⣿⢸⣿⣻⣿⣿⣯⠃⣿⡿⣶⡆⣿⣿⣇⢷⣶
⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣿⣿⣿⣾⣿⣽⣿⣾⡇⣿⣯⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣸⣿⣿⣿⣿⣼⡿⣻⣿⡿⣧⣿⢟⡼⣿⣼⣿⣹⣿⡿⣿⣁⢿⣧⢿⣇⣿⣿⣯⣷⣾
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⠀⣄⠀⠀⣀⠀⠀⠴⡆⠄⣶⢀⡀⣀⠀⡀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣦⣴⣤⣒⡖⡲⠶⠆⠐⡢⠂⠀⢐⠶⡆⢒⡲⠖⣒⣖⣒⡀
⠠⠤⢄⠂⠴⠟⠈⠺⢷⠃⢈⠈⠀⡰⢒⣄⣀⣂⣘⣓⣒⣩⣤⣠⣠⣤⣦⣤⣶⠉⠐⣿⣶⣷⣷⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣓⣿⣿⣥⣤⣶⣶⠖⠋⢍⠢⠄⠙⢄⠎⠀⠀⠁⠈⠈⢫⠍⢉⠛⠁⢀⣂⠍
⢸⣿⣿⣭⣭⡿⣿⣿⣿⣶⣿⣯⣭⣭⣻⣿⣽⣿⣿⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⠾⢓⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣊⣡⠁⠀⠀⠀⢀⣀⣂⣀⣁⣠⣠⣤⣶⣾⣶⣾⣿⣷
⢸⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣽⣿⣿⣿⣿⣿⣿⠿⠛⠛⣿⣿⣿⡇⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⢉⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⢁⣤⡤⣤⣄⣿⣿⣯⣧⣠⡿⣻⣿⣿⣿⣿⣿⣿⣿⣇⠠⢾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠇⠀⠓⢠⣶⣾⣿⣿⣿⣍⡍⣩⢥⣻⣿⣿⣿⣿⣿⣿⠉⠂⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣉⣀⣀⣀⣀⡀⠀⢹⣿⣿⣿⡻⠿⠿⠃⢄⠘⠷⡿⠿⠿⢿⡟⠋⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠾⠿⠿⠷⣾⢿⡁⠀⠸⢸⣷⡿⣿⠿⠛⠀⠀⠉⠙⠓⠂⢤⣤⣵⡠⣄⠀⠀⠀⠀⢸⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣽⢿⠿⢿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠿⠗
⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢠⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢿⣿⣿⣿⡿⣿⣿⢽⣿⡿⠛⠉⠀⣀⠀⠨⠁⠉⣷⣿⡿⠟⠋⡉⣁⠹⠿⠿⠙⠓
⣼⣿⣿⣿⡿⠿⡿⠿⡿⠿⣿⠿⢿⠿⠿⠿⠀⢻⣫⡽⡇⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⢾⣽⣹⡱⠀⠀⠀⠀⠀⠀⠀⠀⢀⠽⠸⠿⠽⠯⠦⠤⠔⢭⣤⣤⣬⣶⡋⣀⠈⠩⠤⠤⠴⠭⠿⢿⢷⠟⣤⠄⠀⠀⠀⠀⠀⠀
⢼⣿⣿⣿⣿⣿⢿⣿⣽⣿⡟⣿⣿⣿⡟⣿⡆⣿⡟⣿⡆⣿⡟⠃⢰⣿⢹⣷⢠⣿⠛⠀⣿⡟⣿⡇⢸⣿⣛⣸⣿⣴⣿⠺⢻⣿⣻⣸⣿⣿⢾⣿⠻⣿⣽⣿⣿⣟⠿⠇⢸⣿⢸⣿⣿⣿⣿⣿⡉⣿⣟⣿⡆⣿⣟⣛⠀⠀
⢹⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣷⣿⡇⣿⡟⣿⣵⣿⡿⣇⣸⣿⢚⣭⢼⣿⢿⡆⣿⡧⣿⣧⣿⣿⣷⣾⣿⣿⣿⣰⣼⣿⣿⢿⣿⣿⣾⣿⢸⣿⡟⢟⢿⡻⣷⣝⢸⣿⢸⣿⢿⣿⣿⣯⠂⣿⡿⣶⡆⣿⣿⡇⡧⢤
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣯⣿⣿⣾⣿⣾⣿⣾⡇⣿⣯⣿⢿⣿⣿⣿⣿⣿⣿⣿⣻⣾⣿⣟⢸⣿⣿⢿⣿⣼⡿⣻⣿⡻⣧⣿⢟⡼⣿⣼⣿⣹⣿⣯⣿⣁⣿⣧⢿⣇⣿⣷⣿⣶⣾
⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⢠⠀⣀⠀⠀⡀⠀⠀⢴⡆⠄⣶⢀⡀⡀⠀⢀⠀⢀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠂⠒⡒⡂⠀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣦⡄⢤⠆⡲⠶⠄⢐⡤⠀⠀⠐⠶⠒⢒⠲⠖⣲⢖⣒⠀
⠠⠤⡖⠒⠦⠗⠘⠺⢷⠡⢉⠈⠀⠔⣲⣅⡀⣂⣚⣒⣒⣉⣀⣠⣠⣤⣦⣤⣶⠉⠑⣿⣷⣶⣾⣷⣶⣻⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣪⣿⣯⣤⣤⣶⡶⠞⠸⢅⠦⠄⠹⢠⠋⠀⠀⠁⢉⠁⡿⠍⠙⠛⠁⣀⡀⠁
⢸⣿⣯⣭⣽⠿⣻⣿⣿⣶⣿⣿⣭⣝⣿⣿⣿⣿⣿⡛⣿⣻⣿⣿⣿⣿⣿⣿⣿⣾⡶⢗⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣔⣋⡡⠁⠀⢀⠀⢀⢀⣂⣀⣀⣀⣠⣤⣶⣧⣷⣿⣿⣶
⢸⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⣽⣿⣿⣿⣿⣿⣿⡿⠿⠛⢻⣿⣿⡇⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡉⣀⣠⣤⡀⣼⣿⣿⣿⣠⣿⢟⣯⣿⣿⣿⣿⣿⣿⣿⣧⡀⣰⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠂⠐⢐⣴⣶⣿⣿⣿⣟⣛⢉⣩⢽⣿⣿⣿⣿⣿⣿⣿⡟⠁⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣉⣀⣀⣀⣀⣀⠀⠈⣿⣿⣿⡿⠿⣿⠟⠠⡑⠻⢽⠿⢿⣿⣿⠛⠁⠐⡀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠐⠒⠺⠿⢿⠿⣏⠀⠀⡇⣿⣾⢿⡿⠟⠂⠀⠀⠙⠛⠢⢤⣤⣼⣆⠀⠀⠁⠀⠀⠀⢠⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⣿⣿
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠆⠀⠀⠀⠈⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣯⡽⠿⠿⠿⠻⣿⣿⣷⣾⣿⣽⣿⣿⣿⣿⡿⠿⠖
⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢀⣄⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⢿⣿⣿⣿⢿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠈⠀⠩⣾⣿⡿⠟⠋⡉⣀⠿⠿⠟⠙⠃
⣼⣿⣿⣿⡿⠿⡿⠿⡿⠿⣿⠿⢿⠿⠿⠿⡀⠸⣽⡭⣾⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠰⣼⣏⣟⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⠿⠻⠯⠤⠤⠸⢥⣠⣤⡤⢤⡉⣁⠈⠡⠤⠤⠤⠭⠿⠿⢯⠇⣄⠀⠀⠀⠀⠀⠀⡀
⣸⣿⣿⣿⣿⣿⣿⣿⢹⣿⡟⣿⣿⣿⡟⣿⡆⣿⡏⣿⡇⣿⡟⠃⢰⣿⢹⣷⢠⣿⠛⠀⣿⡟⣿⡏⢸⣿⣛⣸⣿⣴⣿⠹⢻⣿⣻⢸⣿⣿⢾⣿⠻⣿⣽⣿⣾⣟⠿⠇⢸⣿⢸⣿⣿⣿⣿⣿⠉⣿⡟⣿⡆⣿⡿⡋⠀⠈
⢻⣿⣿⣿⣿⣿⣼⣿⣾⣿⣿⣿⣿⣿⡷⣿⡇⣿⡟⣿⣵⣿⡿⣇⢸⣿⢾⣭⢼⣿⢿⡆⣿⡧⣿⡧⣿⣿⣷⣾⣿⣿⣿⣸⢻⣿⣿⢼⣿⣿⣾⣿⢀⣿⣟⣻⢿⡻⣷⣝⢸⣿⢸⣿⣿⣿⣿⣯⠂⣿⡿⣶⣆⣿⣿⡇⣥⠶
⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣯⣿⣿⣼⣿⣾⣿⣾⡇⣿⣯⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣟⢸⣿⣿⣽⣿⣼⡿⣻⣿⡻⣧⣿⢟⡼⣿⣼⣿⣻⣿⠯⣿⣁⢿⣧⢿⣇⣿⣿⣿⣶⣾
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⡀⢀⡀⠀⠀⠀⠀⠠⣖⠠⢰⡆⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠠⠀⠀⣄⣀⣀⡀⡀⣀⣀⢐⣐⣠⣤⣤⣤⣤⣀⣤⣤⣤⣠⣤⠤⡤⢖⠀⢒⠄⠀⠐⠶⠖⠒⠶⠶⣒⣲⢒⡂⠀
⢠⣤⠤⠤⠴⠆⠒⡿⠖⠔⠓⠋⠡⠤⠬⠀⠠⠀⠛⠀⢈⣁⣉⣈⣀⢤⣤⣀⣤⠚⠋⢹⣶⣦⠤⣶⣶⣶⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣯⣏⣹⣿⣭⣤⣤⣴⡴⠚⠩⢠⣉⡈⢇⡔⠁⠀⠀⠀⡂⠸⡍⡉⠛⠝⠀⠙⠫⠀
⢰⣾⣟⣾⣷⣶⣶⢾⣷⣶⣷⣴⣾⢛⣿⣿⣿⣿⣿⠻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣦⣦⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⠔⢈⡁⠀⠀⠀⠀⠀⠐⢀⣀⣀⣀⣡⣤⣬⣭⣬⣿⣷⣦
⢸⣿⣿⣷⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣷⠂⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⣁⣀⣀⡀⣿⣿⣿⣇⢨⣿⠿⣻⣯⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠇⠀⠀⣴⣾⣾⣿⣿⠿⠟⠛⣫⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣉⣁⣀⣀⣀⣀⠀⠀⣿⣿⣿⣿⣿⣿⡷⢈⡁⢻⣽⣿⣿⣿⣿⠿⠋⣿⣿⣿⠛⠋⠈⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⠿⠿⠿⠾⢽⢏⠀⠀⡏⣾⣾⢿⣾⠿⠃⠀⠀⠒⠻⠦⠄⣀⣸⡄⠀⠀⢿⣿⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡆⠀⠀⠀⠈⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⣷⣤⣀⣹⣿⣿⣿⣿⣻⣿⣭⣿⣿⠿⠿⢿⣿⣿⣷⣿⣯⣿⣿⣿⣷⣷⡾⠷⠴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢀⣤⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⢿⣿⣟⠿⠿⡟⠏⣽⣿⠟⠋⠁⠀⠀⠀⠉⠈⢹⣿⣿⡟⠛⢉⣋⡉⢿⠿⠏⠚⠀
⣿⣿⣿⣿⡿⠿⡿⡿⡿⠿⣿⠿⢿⠿⠿⣿⡿⠀⠸⣾⢽⢿⠀⠀⠀⠀⠀⠒⠀⠒⠀⠀⠀⢰⣷⣛⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⠀⣀⣀⡡⢄⡈⢉⠈⠀⠀⠠⠤⠽⠿⠿⠮⠃⣀⠀⠀⠀⠀⠀⠀⠀
⣺⣿⣿⢿⣿⣿⣻⣿⢿⣿⡟⣿⣿⣿⡟⣿⡆⣿⡏⣿⡏⣿⡟⠃⢰⣿⢹⣷⢀⣿⠛⠀⣿⡏⣿⡟⢻⣟⠋⢸⣿⣤⣿⠘⢻⣿⢛⢸⣿⣿⣾⣿⠛⣿⣼⣾⣾⣟⠿⠏⢸⣿⢸⣿⢻⣿⣿⣿⠀⣿⡟⣿⡆⣿⡟⠋⠀⠀
⢿⣿⣿⣿⣿⣿⣹⣿⣼⣿⣿⣿⣾⣿⡷⣿⡃⣿⡟⣿⣵⣿⡿⣇⢸⣿⢎⣍⢼⣿⢿⡂⣿⡇⣿⡇⣼⣿⣷⢼⣿⣿⣿⢸⢸⣿⣿⢸⣿⣷⣾⣿⠘⣿⠿⢿⢟⡻⣷⡍⢸⣿⢸⣿⣿⣿⣿⣯⠂⣿⡷⣶⣆⣿⡿⣇⣴⣄
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣯⣿⣷⣿⣯⣿⣿⣿⣷⣿⣿⣿⣼⣿⣿⣿⣾⡇⣿⣯⣿⢧⣿⣿⣿⣿⣿⣿⣿⣽⣾⣿⣻⢺⣿⣿⣽⣿⣼⡿⣻⣿⡻⣧⣿⢟⡼⣿⣼⣟⣽⣿⢯⣿⢁⢿⣧⢿⡇⣿⣿⣷⣶⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⢀⠀⡶⢀⣲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠤⠄⡀⠀⠀⠀⡀⠀⢀⣀⣀⣀⣀⣀⣠⣀⣀⣠⣄⠤⣤⢤⣤⣄⠠⢆⠄⢀⠤⢶⡖⠢⠦⣶⡶⡶⠖⠂⠀
⢀⣠⠀⣠⡤⠄⠦⣧⠴⡐⠑⠋⢁⡤⡌⠀⠀⠠⠯⠤⢘⠁⡉⣈⣀⡡⣅⣀⣀⡜⠛⠹⣶⢤⢴⣤⡴⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⢉⣿⣿⣉⣁⣭⣧⡬⠗⡀⢡⣉⠐⡆⡔⠅⠀⠐⠐⠂⢩⣞⠓⠳⠞⠉⠙⠿⠀
⢨⣾⣒⣒⣖⡲⣤⢶⣧⣴⣶⣖⣒⣶⡿⣺⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣢⣴⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣄⠖⢈⠓⠀⠀⠀⠁⠀⠀⠀⠀⣀⣈⣠⣬⣥⣥⣼⣿⣦⣄
⢸⣿⣿⣷⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣛⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢉⡉⣀⠀⢸⢿⣯⣷⠈⣿⣿⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⠀⠨⢯⣭⣯⣾⣿⣿⡿⠟⢛⣃⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢰⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁⠀⣀⣀⡀⠀⢸⣿⣿⡿⣿⣿⣷⡆⠉⠱⣯⣿⣿⣿⣿⡿⠟⢹⣿⣿⣿⡿⢾⣛⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠾⠿⠿⠿⠭⢭⡁⠀⢸⢳⣿⡿⣾⣿⠿⢀⠈⠑⠲⠶⢄⣈⣈⣣⠀⡠⠽⣿⣿⡇⠀⠈⠁⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⠀⠀⠀⠀⠉⠀⠀⠈⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⢀⠈⠉⠉⠁⠀⠀⠈⠉⠀⠀⠀⠀⣤⡀⠉⢿⣿⣿⣿⠻⣿⣙⣿⣿⣿⠿⠿⣿⣿⣭⣽⣭⣷⣿⣿⣾⣶⡯⠭⠬
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢠⣤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⡀⣴⠿⠿⠦⠴⠟⢻⣿⠏⠉⠀⠀⠀⠀⠀⠈⢹⣿⣟⣛⠟⠛⢋⠩⣽⡿⠓⠢⠀
⣿⣿⣿⣿⡿⢿⣿⡿⣿⠿⣿⡿⢿⢿⢿⣿⡿⠇⠀⢷⡯⣿⡇⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⣾⣾⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠠⠀⠿⠿⢿⠖⠀⣀⠀⠀⠀⠀⠀⠀⠀
⣸⣿⣿⣿⣿⣿⣻⣿⢿⣿⡟⣿⣿⣿⡟⣿⡆⣿⡏⣿⡟⣿⡟⠃⢰⣿⢹⣷⢀⣿⠛⠀⣿⡏⣿⡾⢿⡟⠋⢸⣿⣀⣿⠘⢻⣿⢻⣸⣿⡻⣼⣿⠻⣿⣴⣶⣾⣟⠿⠇⢸⣿⢸⣿⢺⣿⣿⣿⡄⣿⡟⣿⡆⣿⡟⠓⠀⠀
⢻⣿⣿⣿⣿⣿⣸⣿⣼⣿⣿⣿⢽⣿⡷⣿⡗⣿⡟⣯⣥⣿⡿⣇⢸⣿⢌⣉⢸⣿⢿⡂⣿⡇⣿⡇⣸⣿⣷⣸⣿⣿⣿⢰⢼⣿⣽⢹⣿⣿⣼⣿⠀⣿⡿⢿⢟⡻⣷⣝⢸⣿⢸⣿⢿⣿⣿⣯⠂⣿⡷⣶⡆⣿⣿⢇⣀⣀
⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣿⣧⣿⣯⣿⣿⣿⣷⣯⣿⣿⣼⣿⣾⣿⣾⡇⣿⣧⣿⢧⢿⣿⣿⣼⣿⣿⣿⣼⣼⣿⢹⢸⣿⣿⢹⣿⣴⡿⢻⣎⠻⣧⣾⢟⡼⣿⣼⡿⣾⣿⡇⣿⠀⢿⣧⢿⡇⣿⣷⣦⣶⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣂⡦⢀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠒⠀⠄⠀⠀⠀⠀⠀⠀⠄⠀⠀⣀⣀⣀⣀⣀⢀⣐⣀⡀⢀⣠⢤⣤⡄⠠⢤⠄⠀⠰⣶⠶⠶⢢⣖⠶⡶⠶⠂⠀
⢀⡠⠀⣀⣤⠄⠾⣧⢤⡸⠅⠋⣁⡤⡘⠀⠀⠠⠯⠤⠝⠃⢃⡈⡀⠡⣅⢀⣀⣠⠚⠛⣶⣄⣤⣤⣴⣶⣶⣶⣮⣥⣿⣿⣿⣿⣷⣿⣿⠻⣿⣟⣉⣉⣉⣭⣭⠟⣈⢁⡋⠰⡀⡔⠁⠀⠀⠀⠐⣖⠚⠓⠴⡛⠕⠯⡒⠀
⢠⣾⣒⣒⣶⣶⣦⣴⣦⣤⣶⣶⣶⣶⣷⣶⣶⣿⡾⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣤⣽⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⠄⠒⠑⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⣀⣡⣔⣢⣼⣷⣦⡀
⢸⣿⣿⣿⣧⣷⣿⣿⣿⣿⣿⣿⣿⣾⣿⣙⣛⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣯⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁⡀⠀⣻⣿⡿⡆⠩⣿⣿⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠻⣽⣭⣵⣿⣿⣿⡿⠿⢛⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⡀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣶⠄⡉⠾⣻⣿⣿⣿⣿⡿⠟⢿⣿⣿⣿⣿⡆⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⠿⠿⠯⠭⠭⢭⠁⠀⢸⢷⣿⢿⣿⣿⠏⡀⠁⠲⠾⢧⣀⣉⣙⡆⠀⡨⣿⣿⣿⡟⠀⠻⡤⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡤⠀⠀⠀⠈⠁⠀⠀⠈⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⡀⠉⠉⠉⠉⠁⠀⠙⠿⠫⠀⠀⠀⠈⠐⠿⣿⣿⡿⢿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣭⣟⣟⣿⣿⣿⣭⣿⣿⣭⠭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⡠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠼⠦⠀⠘⣻⣿⠟⠛⠉⠁⠁⠀⠂⠚⣻⢿⣿⡿⠟⠛⠋⢻⣿⣿⠢⠦⠀
⣻⣿⣿⣿⡿⠿⡿⠿⡿⠿⣿⠿⢿⣿⣿⣿⣿⠿⠇⠰⣷⢯⣿⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⣾⡶⣇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⢀⡂⠀⠂⠀⠀⠀⠐⠿⠿⢯⣲⠀⣉⠉⠀⠀⠀⠀⠀⠀
⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⡟⣿⡆⣿⡟⣿⡍⣿⡟⠃⢰⣿⢹⣷⠀⣿⠛⠀⣿⡏⣿⡟⢿⡿⠋⢸⣿⣀⣿⠘⢻⣿⢛⢸⣿⣻⣼⣿⠛⣿⣴⣾⣾⣟⠿⠏⢸⣿⢸⣿⢺⣿⣻⣿⡄⣿⡏⣿⡆⣿⡟⠃⠀⠀
⢽⣿⣿⣿⣿⣿⣹⣿⣼⣿⣿⣿⣽⣿⡷⣿⡗⣿⡟⣯⣥⣿⡿⣇⢸⣿⣈⣉⢸⣿⢿⡂⣿⣇⣿⡇⣸⣿⣷⢸⣿⣿⣿⢰⣸⣿⣺⢸⣿⣿⣽⣿⠀⣿⣿⣿⢛⡻⣷⣝⢸⣿⢸⣿⢾⣿⣿⣯⠂⣿⡷⣶⡎⣿⡿⣇⣄⣠
⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣷⣿⣧⣿⣿⣿⣿⣿⣷⣯⣾⣿⣼⣿⣾⣿⣾⡆⣿⣧⣿⢧⢿⣿⣿⣹⣿⣿⣿⣼⣼⣿⢹⢸⣿⣿⢿⣿⣴⡿⣺⡞⠻⣧⣾⢟⣼⣿⣼⡿⣾⣿⠏⣿⠀⢿⣧⢿⡇⣿⣷⣯⣵⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣂⡦⢀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠒⠀⠄⠀⠀⠀⠀⠀⠀⠄⠀⠄⣀⣀⣀⣀⣀⣀⣐⣀⣀⠀⣠⢤⣤⠤⠠⢤⡀⠀⠒⣶⠶⠖⢶⣔⢶⣶⠶⠂⠀
⢀⡠⠀⣀⣠⠀⠶⣧⢤⡸⠑⠋⣁⡤⡘⠀⠀⠠⠯⠤⠝⠃⠃⡈⡀⠡⡅⠀⣀⣀⡔⠛⢳⣦⣤⣤⣴⣶⣶⣶⣯⣵⣿⣿⣿⣿⣿⣿⣿⠿⣿⣟⣙⣉⣉⣍⣭⠟⣀⢁⡊⠰⡀⡔⠁⠀⠀⠀⠀⣗⠞⠂⠜⡛⠕⠯⡖⠀
⢠⣾⣒⣒⣶⢶⣶⣴⣦⣤⣶⣲⣲⢶⣶⣶⣶⣿⡾⢷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣬⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⠄⠒⠙⠈⠀⠈⠁⠀⠀⠀⠀⠀⠈⣀⣁⣖⣢⣴⣷⣦⡀
⢸⣿⣿⣿⣧⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣛⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡥⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠁⢀⢘⣿⣿⣻⠀⢽⣿⡿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠⠯⣯⣬⣷⣿⣿⣿⠿⠛⣛⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣛⢉⣁⣀⣀⣀⠀⠀⣿⣿⣿⢿⣿⣷⡶⠈⠫⢾⣻⣿⣿⣿⣿⡿⠋⣿⣿⣿⣿⣿⣿⠋⠁⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠸⠿⠿⠿⠿⠿⣍⠀⠀⡏⣾⣿⢿⣿⡿⠅⠀⠀⠲⠾⢤⣈⣉⣹⡄⢀⡥⣿⣿⣿⣿⡿⢀⡲⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠄⠀⠀⠀⠈⠀⠀⠀⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⢀⡀⠉⠉⠉⠉⠁⠀⠙⣿⡿⠀⠀⠀⡦⢬⣿⣿⡿⢿⣟⣻⣿⣿⣿⡿⣿⣿⣿⣭⣿⣛⣿⣿⣷⣽⣿⣿⣭⠭
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢀⠤⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠋⣽⠿⠟⠛⠉⠁⠁⠀⠂⠘⣻⣿⣿⡿⠟⠛⠋⢻⣿⣿⠲⠦⠀
⣻⣿⣿⣿⡿⠿⣿⡿⣿⢿⣿⠿⢿⢿⣿⣿⣿⠿⠿⠀⢸⡿⣽⠿⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⢠⠷⠾⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠤⢀⡀⠀⠀⠀⠀⠀⡐⠿⠿⢯⡲⠀⣉⠌⠀⠀⠀⠀⠀⠀
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⡟⣿⡆⣿⡟⣿⡄⣿⡟⠃⢰⣿⢹⣷⠀⣿⠛⠀⣿⡏⣿⡆⢻⡿⠟⢸⣿⡀⣿⠘⢻⣿⢛⢸⣿⣻⣼⣿⠻⣿⣴⣶⣾⣟⠿⠏⢸⣿⢸⣿⢾⣿⣿⣿⡄⣿⡏⣿⡆⣿⡟⠃⠠⠀
⢿⣿⣿⣿⣿⣿⣹⣿⣾⣿⣿⣿⢽⣿⡷⡿⡟⣿⡟⣿⣥⣿⡿⣇⢸⣿⣈⣉⢸⣿⢿⡂⣿⣇⣿⡇⣸⣿⣶⣸⣿⣿⣿⢰⣸⣿⣾⢸⣿⣿⣽⣿⠠⣿⡿⣿⢻⡻⣷⣟⢸⣿⢸⣿⢾⣿⣿⣯⠂⣿⡷⣶⡎⣿⡿⣇⣄⣔
⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣷⣿⣧⣿⣿⣿⣿⣿⣷⣯⣼⣿⣼⣿⣾⣿⣾⡇⣿⣧⣿⣧⣿⣿⣿⣻⣿⣿⣿⣼⣼⣿⢹⢸⣿⣿⢿⣿⣴⡿⣻⡞⠻⣧⣾⢟⡼⣿⣼⡿⣿⣿⠟⣿⠀⢿⣧⢿⣇⣿⣷⣯⣥⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣂⡦⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⣀⣀⣀⡀⣀⣐⣀⡀⠄⣀⢀⣤⠤⠠⢄⡄⠀⠒⣶⠶⠖⣦⡰⠶⡶⠶⠀⠀
⢀⡠⠀⣀⡦⠄⠶⣧⢄⠘⠑⠋⣀⠤⡘⠀⠀⠠⠯⠤⠝⠁⠁⠈⡀⠁⡁⢀⣀⣈⣀⡔⠛⠹⣶⢤⣴⣶⣶⣶⣦⣥⣿⣿⣿⣿⣿⣿⣿⠛⢿⣟⣉⣉⣉⣍⡭⠍⡀⢁⡂⠲⡀⡔⠁⠀⠀⠀⠀⣖⠚⠢⢞⡛⠔⠯⡂⠀
⢨⣶⣒⣒⣖⢲⣤⣶⣤⣴⣶⣲⣒⢶⣾⣲⣶⣿⡾⠶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣰⣠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⠄⠒⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⢈⣈⣀⣐⣢⣴⣷⣤⡀
⢸⣿⣿⣷⣦⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠘⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠁⢠⡄⣻⣿⣽⡆⠸⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠔⢡⣵⣶⣾⣿⣿⠿⠛⢛⣭⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⣉⣁⣀⣀⣀⡀⠀⢸⣿⣿⣿⣿⣿⣶⠆⣉⠹⣯⣿⣿⣿⣿⡿⠟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠞⠛⠻⠿⠿⢿⡅⠀⢸⢱⣷⡿⣾⡿⠟⢀⠈⠑⠒⠶⠤⢀⣨⣳⣀⣠⠼⣿⣿⣿⣿⣿⣿⡿⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡦⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠉⠉⠀⠉⠀⠈⢻⣿⣿⣿⠛⠀⠀⡀⠀⢿⣟⣻⢿⣿⣿⡿⣿⣿⣿⣽⣿⣻⣿⣿⣷⣽⣿⣿⣭⠩
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠠⠄⠉⠿⠟⠋⠁⠀⠀⠀⠀⠊⣹⣿⣿⡿⠟⠻⠋⢹⣿⣿⠲⠦⠀
⢿⣿⣿⣿⡿⠿⣿⡿⣿⡿⣿⠿⢿⣿⣿⣿⣿⠿⠿⠿⠇⠀⢯⣯⢷⡇⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢼⡺⢺⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢀⡀⠀⠀⠀⠀⠀⠐⠿⠿⢯⡲⠀⣉⠉⠀⠀⠀⠀⠀⠀
⣺⣿⣿⣿⣿⣿⣿⣿⢻⣿⡟⣿⣿⣿⡟⣿⡆⣿⡟⣿⡆⣿⡟⠋⢹⣿⢹⣷⠀⣿⠛⠀⣿⡏⣿⡆⢸⡟⠻⢿⣿⡀⣿⠘⢻⣿⢛⢸⣿⣻⣼⣿⠻⣿⣤⣤⣾⣟⠿⠏⢸⣿⢸⣿⢺⣿⣿⣿⠀⣿⡏⣿⡆⣿⡟⠃⠀⠀
⢻⣿⣿⣿⣿⣿⣹⣿⣼⣿⣿⣿⣽⣿⡷⣿⡗⣿⡟⣯⣵⣿⡿⣇⢸⣿⢈⣉⢸⣿⢿⡆⣿⣇⣿⡇⣸⣿⣷⣸⣿⣿⣿⢰⣸⣿⣾⢸⣿⣿⣼⣿⠀⣿⠿⣿⢛⡻⣷⣕⢸⣿⢸⣿⢾⣿⣿⣯⠂⣿⡷⣶⡎⣿⡿⢇⣀⢀
⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣷⣿⣧⣿⣿⣿⣿⣿⣷⣯⡼⣿⣼⣿⣾⣿⣶⡆⣿⣧⣿⢧⣿⣿⣿⣸⣿⣻⣿⣼⣼⣿⢸⢸⣿⣿⢻⣿⣴⡿⣸⡎⠻⣧⣾⢟⣼⣿⣼⡿⣽⣿⠏⣿⠂⢿⣧⢿⡇⣿⣷⣮⣥⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣂⡦⢀⣲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠒⠀⠀⠀⠀⠀⠠⠀⠀⠤⠠⠄⢀⣀⣀⣀⠐⢀⣐⣀⡀⠀⣀⢄⡤⠤⠠⢤⡄⠀⠲⣶⠶⠖⢦⡴⠶⡶⠶⠂⠀
⢀⡠⠀⣀⣠⠄⠦⣦⠤⡸⠇⠊⣀⡤⣜⠀⠠⠠⠿⠤⠝⠃⠁⡈⡀⠠⡅⠀⣀⣀⣤⣤⠔⠋⠷⣦⢴⣶⣶⣶⣯⣵⣿⣿⣿⣿⣿⣿⣻⠻⣿⣿⣉⣉⣉⣍⣭⠝⣀⢀⠊⠰⡄⡔⠂⠀⠀⠠⠀⣓⠖⠢⢞⡛⠑⠻⡆⠀
⢠⣶⣒⣒⣶⣶⣦⣴⣤⣴⣴⣲⣒⢶⣷⣶⣷⣿⡾⢷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣂⣸⢯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⠤⠒⠉⠈⠀⠈⠁⠀⠀⠀⠈⠀⠈⣈⣀⣂⣂⣴⣷⣦⡀
⢸⣿⣿⣿⣧⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣛⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⢁⣤⡘⣿⣿⣿⡀⠸⣿⡿⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣰⣥⣴⣾⣿⣿⠿⠛⢻⡝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠀⢀⣀⡀⠀⢹⣿⣿⣿⣿⣷⣶⠆⣉⠻⣯⣿⣿⣿⣿⡿⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠰⠯⠭⠭⠿⠭⣭⡁⠀⢸⢱⣿⡿⣿⡿⠏⢀⠈⠐⠒⠶⠤⢀⣠⣳⣀⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣄⠀⠀⠀⠀⠁⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠁⠀⠈⣿⣿⣿⣿⡿⠟⠉⠈⠙⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣭⣿⣽⣍⢉
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣠⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠏⠁⢀⡀⠂⠀⠀⠈⠉⠁⠁⠈⠀⠘⣹⣿⣿⡿⢿⠻⡛⢛⣿⣿⠦⠦⠀
⣻⣿⣿⣿⣿⠿⡿⡿⡿⠿⣿⡿⢿⢿⣿⣿⣿⠿⠿⢿⡿⠇⠀⣯⣏⣿⡇⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⢼⡽⢺⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢀⡀⠀⠀⠀⠀⠀⡐⠾⠿⢯⡰⠀⣉⠌⠀⠉⠀⠀⠀⠀
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⡟⣿⡆⣿⡟⣿⡆⣿⡟⠋⢻⣿⢹⣷⠀⣿⠛⠀⣿⡏⣿⡆⢸⡟⠛⢻⣿⡁⣿⠘⢻⣿⠛⢸⣿⣛⣼⣿⠛⣿⣤⣶⣾⣟⠿⠏⢸⣿⢸⣿⣾⣿⣿⣿⡀⣿⡟⣿⡆⣿⡟⠃⠀⠀
⢿⣿⣿⣿⣿⣿⣹⣿⣼⣿⣿⣿⣽⣿⡷⣿⡟⣿⡟⣯⣵⣿⡿⣇⢸⣿⢈⣉⢸⣿⢿⡂⣿⡇⣿⡇⢼⣿⣷⣸⣿⣿⣿⢰⣸⣿⣸⢸⣿⣿⣽⣿⠰⣿⡿⣿⢟⡻⣷⣕⢸⣿⢸⣿⢾⣿⣿⣯⡂⣿⡿⣶⡎⣿⡿⣇⣀⣀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣷⣿⣧⣿⣿⣿⣿⣿⣷⣯⣼⣿⣼⣿⣾⣿⣾⡆⣿⣧⣿⢇⣿⣿⣿⣻⣿⣿⣿⣼⣼⣿⢸⢸⣿⣿⢹⣿⣴⡿⣻⡎⠻⣧⣿⣟⡼⣿⣼⠿⣼⣿⠏⣿⠀⢿⣧⢿⡇⣿⣷⣮⣥⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⣖⠀⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣒⠀⣀⡒⠀⠒⠒⠐⠀⠀⠀⠀⠀⠀⢀⣀⠐⠒⣐⣀⡀⢂⣀⣀⣠⠠⢤⣄⡀⠀⠠⣤⡤⠤⣤⣤⢤⣴⡶⠆⠀
⢀⢠⣀⣀⣠⡄⣤⣧⠤⡰⠦⠛⣂⣀⣔⠀⠀⢀⠟⠈⠘⠃⠓⠘⠂⢀⣀⠀⠀⣀⣀⣀⣤⠶⠛⢲⣤⢤⣶⣤⣭⣥⣾⣷⣿⣿⣶⣿⣿⠛⢿⣿⡛⠋⣛⣏⣙⠯⠁⣈⠊⠡⡈⡰⠊⠀⠈⠠⠤⣓⠤⠦⢭⡴⠓⠲⡦⠀
⢨⣵⣶⣴⣤⣤⣦⣴⣤⣤⣦⣤⣶⣴⣶⣶⣶⣶⣶⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣄⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣀⡤⠑⠬⠉⠀⠁⠃⠀⠀⠀⠀⠀⠘⢈⣐⣂⣀⣰⣶⣤⡀
⢸⣿⣿⣿⣯⣽⣷⣾⣿⣿⣿⣿⣿⣾⣿⣛⣻⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡅⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣦⣤⣤⣦⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢉⡉⣀⢸⣿⣿⣧⠀⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠌⣠⣥⣼⣾⣿⣿⠿⠿⣛⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠉⠁⠀⠀⣿⣿⣿⣿⣿⣶⣴⠌⠉⠾⣽⣿⣿⣿⣿⠿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⠿⠿⠭⠭⢭⣭⠁⠀⢿⣵⣯⢿⣿⡿⠇⡀⠀⠐⠲⠶⠄⣈⣈⣇⣀⣔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡀⠀⠀⠀⠈⠁⠀⠈⠈⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⢄⠈⠉⠉⠀⠁⠀⠘⣿⣿⣿⠿⠿⠿⠿⠿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣽⣿⣿⣟⣯⣟⣟⣛
⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠈⢀⡀⠀⠀⠀⠈⠋⠉⠉⠉⠀⠙⢻⣿⡿⡿⡿⠿⠟⠛⣿⣿⠦⢄⠀
⣿⣿⣿⣿⡿⣿⡿⣿⡿⢿⣿⡿⢿⣿⣿⣿⣿⢿⠿⠿⡿⠿⠇⠰⣯⣟⣟⠄⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⣬⡴⢯⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⡀⠀⠀⠀⠀⠀⠐⠿⠿⢿⡽⠀⣀⠈⠀⠉⠁⠀⠀⠀
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡟⣿⡆⣿⡟⣿⣆⣿⡟⠃⢹⣿⢻⣷⠀⣿⠛⠀⣿⡏⣿⡆⢸⡟⠋⢸⣿⡽⣿⠘⢻⣿⠛⢸⣿⢛⣸⣿⠻⣿⣤⣤⣾⣟⠿⠇⢸⣿⢸⣿⣼⣿⣻⣿⡀⣿⡟⣿⡆⣿⡟⠃⠠⠠
⢻⣿⣿⣾⣿⣿⣻⣿⣼⣿⣿⣿⣽⣿⡷⣿⡷⣿⡟⣯⣵⣿⡿⣇⢸⣿⢈⣉⢰⣿⢷⡂⣿⡇⣿⡇⢸⣿⣷⢸⣿⣿⣿⢠⣸⣿⣶⢸⣿⣷⣹⣿⠀⣿⣿⣿⢿⡻⣷⣖⢸⣿⢸⣿⣾⣿⣿⣯⠂⣿⡷⣶⡆⣿⣿⣇⣀⣠
⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣿⣏⣿⣗⣿⣿⣿⣷⣯⡼⣿⣼⣿⣾⣿⣾⡇⣿⣧⣿⣧⢿⣿⣿⣺⣿⣻⣿⣼⣼⣿⢹⢼⣿⣿⣻⣿⣴⣿⣳⡟⠻⣧⣿⣟⣸⣿⣼⡿⣼⣿⠟⣿⠂⢿⣧⢿⡇⣿⣷⣯⣭⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣦⠀⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⣀⡐⠀⠐⢒⣂⠀⠐⠂⠀⠀⠀⠀⠀⠠⠒⠠⠀⠀⠀⢀⣀⣀⣀⢀⣀⠀⠀⠠⣄⣤⣤⣤⣠⣤⣤⣤⡄⠀
⠀⢀⣀⣀⣠⡄⣬⣧⣤⢰⠆⠗⢂⣀⡐⠀⢀⢀⣷⣈⡹⠇⠒⠐⠀⢂⡂⠀⠀⠐⣂⣀⣀⣠⠶⠒⣦⣤⣤⣤⣖⣢⣶⣶⣶⣶⣶⣶⣶⠿⣿⣿⠻⠛⠛⡛⣛⡷⠄⠉⠜⠡⡀⡠⠜⠁⠀⠀⠈⢤⡤⠎⣭⠶⠣⢔⠄⠀
⢈⣵⠤⡬⣥⣤⣄⣽⣆⣀⣤⣤⡬⣵⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣿⣶⣿⣿⣿⣿⣿⣧⢠⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⡿⠉⣀⠭⠚⠑⠀⠑⠃⠀⠀⠀⠀⠀⠙⠄⠂⡀⢅⣠⣦⣅⠀
⢸⣿⣿⣯⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⣥⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⡋⠉⠀⢿⣿⣿⡆⠩⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠁⣠⣤⣼⣿⣿⣿⠶⠿⣃⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠉⠁⠀⠘⣿⣿⣿⣿⣿⣤⡤⠈⠋⢿⣹⣿⣿⣿⣿⠿⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣐⣒⣒⣒⣛⣛⣛⠀⠀⡟⣿⣿⣿⣿⡿⠁⠀⠁⠒⠶⠦⢄⣁⣜⣆⣠⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣄⠀⠀⠀⠈⠙⠂⠀⠁⠛⠛⠈⠁⠀⠈⠀⠀⠀⠀⠀⢀⠈⠉⠉⠈⠁⠀⢻⣿⣿⣿⠿⢿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣟⣿⣿⣟⣛
⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠿⠅⠁⡀⢀⠀⠀⠉⠋⠉⠋⠉⠥⠘⢛⣿⣿⣿⡿⢿⠟⢿⣿⣿⢭⣅⠀
⢿⣿⣿⣿⡿⢿⣿⢿⣿⢿⣿⠿⢿⢿⢿⣿⣿⡿⢿⣿⣿⠿⠿⠀⢰⣽⣳⡷⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⣾⡴⢧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⢾⣟⣥⠀⣒⠐⠈⠉⠉⠀⠀⠀
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡟⣿⡎⣿⡟⣿⡆⣿⡟⠃⢸⣿⢿⣿⠀⣿⠛⠀⣿⡏⣿⡆⢸⡟⠛⢸⣿⡾⣿⠙⢻⣿⠛⢸⣿⠛⢸⣿⠛⣿⣀⣀⣼⣏⠿⠇⢸⣿⢸⣿⣼⣿⣿⣿⠀⣿⡟⣿⡆⣿⡟⠃⠀⠤
⣽⣿⣿⣾⣿⣿⢹⣿⣽⣿⣿⣿⣻⣿⡷⣿⡷⣿⡟⣯⣥⣿⡿⣇⢸⣿⢈⣉⢰⣿⢶⡂⣿⡇⣿⡇⢸⣿⣖⢸⣿⣷⣿⢠⢸⣿⣴⢸⣿⣷⣸⣿⠀⣿⣿⣿⢿⡻⣷⣄⢸⣿⢸⣿⣽⣿⣿⣯⡂⣿⡷⣶⡆⣿⡿⠇⠀⠀
⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢿⣿⣷⣿⣇⣿⣷⣿⣿⣿⣷⣯⡼⣿⣼⣿⣾⣿⣾⡇⣿⣧⣿⣧⢾⣿⣿⢸⣿⣽⣿⣼⣹⣿⢹⢸⣿⣿⢹⣿⣴⣿⣱⡼⠻⣧⣾⣟⡼⣿⣼⡿⣸⣿⠟⣿⠁⢿⣧⢿⡇⣿⣿⣿⣋⣿
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢲⣆⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠠⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⣠⡀⠀
⢀⡀⠄⣀⣤⠐⢵⣦⢄⠼⠬⠓⣀⣠⣂⠀⡀⣨⡇⣁⠟⠐⠂⠒⠀⣂⡂⠀⠀⠐⣀⢀⣀⣠⣠⠶⠚⣦⣤⣤⣒⣢⣶⣶⣶⣶⣦⣶⣶⢾⣿⣿⠿⠿⠾⡟⠿⣧⠈⠏⠽⣋⠂⢈⠝⠁⠂⢉⠙⣅⣨⡙⣋⡭⢋⣭⡀⠀
⢰⣶⣶⣒⣲⣶⣶⣴⣤⣴⣴⣶⢶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣶⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣽⣿⣀⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣶⣿⡿⠋⣁⡢⠓⠂⠈⠲⠃⠀⠀⠀⠀⠀⠻⠀⠀⢉⡂⢀⣍⡃⠀
⢸⣿⣿⣿⣧⣽⣿⣿⣿⣿⣿⣿⣿⣾⣟⣛⣿⣿⣶⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣴⣄⣀⣀⣀⣀⣠⣤⣤⣤⣴⣴⣶⣿⣷⣿⣿⣿⣿⣦
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠁⢿⣿⣿⡇⠹⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠨⣠⣬⣼⣿⣿⣿⠷⠟⣋⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⠁⠀⠘⣿⣿⣿⣿⣿⣤⡦⠎⡉⠿⣽⣿⣿⣿⣿⠟⠙⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣰⣶⣖⣒⣒⣛⣛⠀⠀⣿⣽⣿⢿⣿⣿⠅⠀⠀⠐⠛⠷⠤⣠⣤⣷⣤⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣉⠀⠀⠈⠀⠙⠃⠀⠁⠙⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⢿⣿⣿⡿⠿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠈⠀⠉⠉⠉⠙⠟⠛⠛⠛⡉⠿⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣛⡋⠉
⣺⣿⣿⣿⡿⢿⣿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠿⠿⡿⠿⠟⠿⠃⢠⣯⡾⣿⡄⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⢸⢺⠺⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⢿⠿⣋⠁⣄⠤⠘⠛⠛⠈⠁⠀
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡟⣿⡎⣿⡟⣿⣆⣿⡟⡃⢰⣿⢻⣿⠿⣿⠛⠀⣿⡏⣿⡆⢸⡟⠛⢸⣿⡈⣿⠿⢻⣿⠛⢸⣿⠛⢸⣿⠛⣿⣉⣀⣼⣏⠿⠇⢸⣿⢸⣿⣸⣿⣿⣿⡈⣿⡏⣿⡦⣿⡟⠃⠀⢀
⢿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣹⣿⡷⣿⡷⣿⡟⣿⣽⣿⡿⣇⢼⣿⢈⣉⢰⣿⢶⡀⣿⡇⣿⡇⣼⣿⡖⢸⣿⣷⣿⢀⢸⣿⣠⢸⣿⠿⣸⣿⠀⣿⣿⣿⢾⡻⣷⣄⢸⣿⢸⣿⣼⣿⣿⣯⠂⣿⡷⣶⡆⣿⣿⡇⠉⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣇⣿⣷⣿⣿⣿⣷⣯⣼⣿⣼⣿⣾⣿⣾⡇⣿⣧⣿⢧⣾⣿⣿⢺⣿⣽⣿⣹⣹⣿⢻⢸⣿⣿⣿⣿⣴⣿⣉⣵⡻⣧⣿⢟⡼⣿⣼⡿⣽⣿⠿⣿⢁⢿⣧⢿⡇⣿⣿⣶⠞⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⢐⣲⠄⢰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⢀⣀⠂⠀⠒⡒⠀⠀⢒⣀⡀⠀⠀⠀⠀⠤⠄⠄⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⢀⣠⠀⠀
⢀⠠⠤⣴⠦⠰⢿⡶⠄⠃⠚⢁⣤⣄⡃⠀⠄⠸⠁⠬⠛⠘⠀⠂⠀⣔⠀⠀⡐⣀⣀⣠⣤⣠⣤⡔⠛⢷⣦⣴⣒⣴⣶⣶⣶⣶⣶⣶⡶⢿⣿⡿⠿⠳⢟⠛⢿⡇⠙⠯⠟⣉⠂⡨⠋⠀⠂⠉⣛⢁⣩⣹⣋⠽⣫⡍⡀⠀
⢸⣷⣒⣷⣶⣶⣶⣧⣤⣶⣶⣖⣶⣿⣷⣶⣶⣷⠶⡾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣄⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣿⣿⠏⢋⣐⢌⡓⠂⠘⠸⠀⠀⠀⠀⠀⠀⢟⠠⠈⣑⠀⣠⣙⠀⠀
⢸⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣛⣻⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡅⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣦⣄⣀⣠⣀⣠⣤⣤⣤⣤⣤⣴⣶⣿⣶⣿⣿⣿⣷⣄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⠀⢹⣿⣿⣷⠈⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣡⣤⣼⣾⣿⣿⠟⠛⣫⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠋⠀⠀⣿⣿⣿⣿⣿⣶⣴⠆⠉⠘⠷⠿⠿⢿⣿⣟⠁⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢁⣒⣒⣒⣚⣛⣛⡃⠀⢸⢱⣿⡿⣿⡿⠇⠀⠀⠀⠙⠛⠓⠢⢴⣾⠦⠾⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣁⠀⠀⠀⠀⠈⠃⠀⠈⠈⠉⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣟⣿⣿⣿⣿⣿⡿⠿⠿
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠷⠚⠛⠛⢉⠉⠿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⣛⠃⠀
⢿⣿⣿⣿⡿⠿⡿⠿⣿⠿⣿⡿⢿⠿⡿⣿⣿⡿⠿⠿⠿⠿⠟⠻⠋⠀⣼⢶⢻⡥⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣯⡟⣟⠆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡰⠿⢿⢟⡉⠠⣅⠤⠛⠛⠃⠉⠁⠀
⣽⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣽⣿⡟⣿⡎⣿⡟⣿⣎⣿⡟⡋⢸⣿⢹⣿⠿⣿⠛⠀⣿⡏⣿⡆⢸⡟⠋⢸⣿⡀⣿⠛⢻⣿⠛⢸⣿⠛⢸⣿⠛⣿⠀⠀⣼⣟⠿⠇⢸⣿⢸⣿⢺⣿⢿⣿⠁⣿⡏⣿⡦⣿⡟⠃⡀⣀
⢻⣿⣿⣿⣿⣿⣹⣿⣾⣿⣿⣿⢹⣿⡷⣿⡟⣿⡟⣿⣽⣿⡿⣇⢸⣿⢈⣉⢰⣿⢷⡂⣿⡇⣿⡇⣼⣿⡖⢸⣿⣿⣿⢀⢸⣿⠀⢸⣿⣷⣸⣿⠀⣿⣿⣿⢾⡻⣷⣄⢸⣿⢸⣿⣾⣿⣿⣯⠂⣿⡷⣶⡆⣿⣿⠇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣿⣇⣿⣿⣿⣿⣿⣷⣯⡼⣿⣾⣿⣼⣿⣾⡇⣿⣧⣿⢇⢾⣿⣿⣺⣿⣽⣿⣸⣺⣿⣳⢸⣿⣿⢿⣿⣴⡿⣩⢧⡻⣧⣿⢟⡸⣿⣼⡿⢼⣿⠿⣿⢁⢿⣧⢿⡇⣿⣷⣶⢲⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⣶⠀⢰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠄⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⡀⡀⢀⣀⠀⠀
⢀⡦⢀⣠⡄⠠⣷⡤⣤⠧⠜⢓⣀⣀⠃⠀⠈⣸⣂⡈⠟⠘⠒⠂⠐⡔⠀⠀⠀⢀⣀⢀⣠⣠⣤⣀⠾⠛⣦⣄⣒⣲⣦⣴⣶⣶⣴⣶⣶⣶⣶⡾⠾⠷⠶⠶⢿⣞⡻⢫⠟⡋⠁⣉⠟⠀⠀⠙⢫⣉⣙⣛⢿⡻⣛⣉⡀⠀
⢰⣖⣒⣒⣶⣶⣦⣦⣤⣴⣶⣶⣶⣾⣶⣶⣶⣶⣶⣾⣿⣿⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣶⣿⣿⠿⠋⣐⡐⡒⠀⠙⠼⠁⠀⢀⠀⠍⠐⣏⠌⢉⣚⠁⣀⣙⠁⠀
⢸⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣠⣄⣀⣀⣀⣀⣀⣀⣥⣤⣤⣤⣴⣶⣶⣾⣿⣿⣿⣷⡄
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠉⠉⣿⣿⣿⡆⢹⣿⡿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢘⣸⣧⣽⣿⣿⣿⠿⢛⣥⢝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠃⠀⠘⣿⣿⣿⣿⣷⣦⡖⠂⠀⠛⠾⠿⠿⢿⢿⡋⠜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣡⣶⣶⣒⣒⣚⣛⠀⠀⣟⣿⣿⢿⣿⡿⠅⡀⠀⠈⠉⠙⠒⠲⠶⠿⠴⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⡉⠈⠀⠀⠉⠙⠂⠀⠉⠙⠋⠁⠁⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡤⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠷⠞⠟⠛⣛⣻⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠛⠒⠂
⣿⣿⣿⣿⣿⢿⣿⣿⣿⠿⣿⣿⢿⣿⣿⣿⣿⡿⠿⠿⣿⠿⠿⠿⠿⠇⠀⡾⡶⢟⡆⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠸⣾⢹⣿⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⡰⡿⠿⢟⡍⠨⣭⠄⠿⠟⠋⠉⠂⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡟⣿⡏⣿⡟⣿⣞⣿⡟⣃⢸⣿⢹⣿⠿⣿⠛⠀⣿⡏⣿⡆⢸⡟⠛⢸⣿⡀⣿⠙⢻⣿⠛⢸⣿⠛⢸⣿⠙⣿⡁⠀⣼⣟⠿⠇⢸⣿⢸⣿⣺⣿⣿⣿⡁⣿⡏⣿⡆⣿⡟⠃⠀⠀
⢿⣿⣿⣿⣿⣿⣻⣿⣽⣿⣿⣿⣻⣿⡷⣿⡗⣿⣟⣿⣽⣿⡿⣇⢸⣿⢈⣉⢰⣿⢷⠂⣿⡇⣿⡇⣼⣿⠖⢸⣿⣿⣿⢀⢸⣿⠀⢸⣿⢷⣸⣿⠀⣿⣿⣾⢾⡻⣷⣌⢸⣿⣸⣿⣿⣿⣿⣯⠂⣿⡷⣶⡆⣿⣿⠇⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣿⣇⣿⣿⣿⣿⣿⣷⣯⣽⣿⣼⣿⣾⣿⣾⡇⣿⣧⣿⢧⣾⣿⣷⣺⣿⣽⣿⣹⣽⣿⣶⢸⣿⣿⣿⣿⣴⡿⣹⣿⡻⣧⣿⢟⡸⣿⣼⡿⣽⣿⠿⣿⢀⢿⣧⢿⡇⣿⣷⣶⢶⣷
⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠒⡶⢀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣐⢀⢀⣐⠀⣐⠒⠒⠀⠐⠒⢀⠀⠀⠀⠠⠀⠐⠀⠀⠀⠄⠀⠀⠀⣀⡀⣀⠀⠀⢀⣀⣀⣀⣠⢀⣀⣀⣤⡤⠀⠀
⢀⠤⠤⠤⠆⠾⡷⠒⠘⠃⠊⠡⡤⡌⠀⠠⠠⠿⠤⠼⠃⠛⡀⠀⠀⣄⠀⠀⣀⣀⣄⣤⣤⣠⣄⣠⠜⠋⠳⣦⣤⣴⣶⣶⣶⣶⣶⣶⡾⣿⣿⡿⠟⠚⢛⢛⣿⠤⠟⠭⠋⡕⢀⠔⠋⢐⢀⡉⢫⣈⣭⣟⣋⠝⠥⣥⡀⠀
⢰⣗⣾⣶⡲⡶⢶⣦⣶⣶⣶⣖⢾⣿⣷⣾⣿⡾⢷⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣄⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠋⣑⠬⢜⠒⠂⠑⠎⠀⠀⠀⠀⠀⠉⠗⠀⠌⣁⢠⣤⣑⠀⠀
⢸⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣦⣤⣀⣤⣤⣤⣤⣤⣴⣴⣴⣾⣿⣿⣿⣿⣿⣿⣷⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⠉⠀⢹⣿⣿⣳⣈⣿⣿⢻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣤⣤⣾⣿⣿⡿⠟⠋⣵⢶⡿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⠛⠛⠋⠀⠀⢿⣿⣿⣿⣿⣷⡶⠁⠠⢈⣙⣛⡋⠛⠛⢯⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢁⣶⣒⣒⣻⣿⣯⡁⠀⢸⢱⣿⡽⣿⠿⠃⡀⠀⠀⠀⠀⠈⠉⠛⠛⠓⠛⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣀⠀⠀⠀⠈⠁⠁⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⢿⠿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⣿⣿⡿⣿⣿⣿⠿⠻
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣶⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠋⠛⠉⠍⠹⢿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣟⣛⠉⠁
⢻⣿⣿⣿⡿⡿⡿⣿⣿⠿⣿⡿⢿⣿⡿⢿⣿⠿⠿⠿⢿⠿⠛⠿⠿⢛⠀⢸⣺⢺⣳⠀⠀⠀⠀⠀⠐⠀⠒⠒⠀⠀⠀⢿⣣⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡼⠿⠷⢛⠉⠠⡰⠐⠛⠓⠀⠉⠀⠀
⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣟⣿⡆⣿⡟⣿⣎⣿⡟⣃⢹⣿⢹⣿⠻⣿⠛⠀⣿⡏⣿⡆⢸⡟⠋⢸⣿⡀⣿⠘⢻⣿⠛⢸⣿⠛⢸⣿⠛⣿⡀⠀⣼⣟⠿⠇⢸⣿⢸⣿⣻⣿⣿⣿⠀⣿⡏⣿⡆⣿⡟⠃⠀⣀
⢾⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⢹⣿⡷⣿⡇⣿⡟⣿⣽⣿⡿⣇⢺⣿⣈⣉⢰⣿⢷⡂⣿⡇⣿⣧⣺⣿⠗⢸⣿⣿⣿⢀⢸⣿⠀⢸⣿⣷⣸⣿⠀⣿⣿⡿⢾⡻⣷⣄⢸⣿⢸⣿⣿⣿⣿⣯⠂⣿⡷⣶⡆⣿⡿⠇⠀⠀
⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣿⣇⣿⣿⣿⣿⣿⣷⣯⡼⣿⣾⣿⢾⣿⣾⡇⣿⣧⣿⣧⣿⣿⣾⣺⣿⣽⣿⣸⣹⣿⣸⢸⣿⣿⣽⣿⣴⣿⡉⣮⡻⣧⣿⢟⡸⣿⣼⡿⣼⣿⠟⣿⠠⢿⣧⢿⡇⣿⣷⣦⣶⣶
⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠐⣶⠀⢰⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢒⣂⣀⣒⠀⠐⠒⡒⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠂⠄⠀⠀⠀⢀⢀⣀⡀⣀⠀⠀⠠⣀⣀⣤⣠⢄⣀⣀⣠⣄⠀⠀
⠀⠤⢤⡴⠆⠴⣷⠖⠐⠃⠊⠡⠤⢌⠀⠠⠀⠿⠤⠜⠃⠉⡀⠀⠠⢄⡀⢀⣀⣁⣀⣠⣤⣠⣄⣠⣤⡜⠋⠙⣳⣶⣶⣶⣷⣶⡶⡾⡟⣿⣿⠿⠛⠓⢛⢛⣻⠄⠝⠥⠫⡕⢀⠔⠉⠐⠀⡀⢡⢬⣯⣝⣓⠝⠥⣤⡀⠀
⢸⣗⣾⣷⡒⢦⢶⣦⣤⣶⣶⣖⠾⣿⣟⣶⣿⡷⠷⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣾⣿⣧⣤⣤⢾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⣀⠬⠘⠃⠂⠉⠊⠀⠀⠀⠀⠂⠈⠇⠂⠬⡅⢠⣤⣁⠀⠀
⢸⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣻⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣦⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡄
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁⡀⢘⣿⣿⣟⣄⣻⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣠⣤⣴⣿⣿⠿⠛⠉⠵⢶⣬⢿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⠊⠀⠐⢈⣿⣏⣉⠙⣙⣆⢈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⣰⣖⣒⣚⣿⣿⣍⠀⠀⡇⣿⣿⡻⡿⠛⢠⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠋⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿
⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢈⡁⠀⠈⠀⠀⠈⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⠛⠛⠿⠿⣿⣿⣿⣿⡿⣿⣿⡿⣿⡿⣿⣿⣿⡿⣟⣟⠿⠿⠻
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣖⣶⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠛⠋⠉⠙⢿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣟⡉⠉⠁
⢻⣿⣿⣿⡿⠿⡿⡿⣿⣿⣿⡿⢿⣿⡿⢿⣿⠿⠿⠿⢿⠿⠛⠻⠿⢿⡿⠇⠀⡯⡟⡾⠆⠀⠀⠀⠀⠐⠂⠀⠐⠂⠀⠀⠈⢯⣶⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠼⠿⠷⢳⡀⠀⣑⠂⠛⠓⠀⠈⠀⠀
⢼⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣟⣿⡆⣿⡟⣿⣎⣿⡟⣇⢹⣿⢹⣷⠀⣿⠿⠟⣿⡏⣿⡆⢸⡟⠋⢸⣿⡀⣿⠘⢻⣿⠛⢸⣿⠛⢸⣿⠛⣿⠀⠀⣼⣟⠿⠇⢸⣿⢸⣿⣾⣿⢿⣿⠄⣿⡟⣿⡆⣿⡟⠃⠀⣀
⢺⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣻⣿⡷⣿⡇⣿⡟⣯⣽⣿⡿⣗⢸⣿⢊⣉⢰⣿⢷⡂⣿⡇⣿⡧⣺⣿⠗⢸⣿⣿⣿⢀⢸⣿⠀⢸⣿⣷⣸⣿⠀⣿⣿⠿⢾⡻⣷⣄⢸⣿⢸⣿⣿⣿⣿⣯⠂⣿⡷⣶⡆⣿⡿⠇⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣷⣯⡼⣿⣽⣿⢼⣿⣾⡇⣿⣧⣿⢇⣿⣿⣾⣺⣿⣽⣿⣼⣸⣿⣬⢸⣿⣿⢻⣿⣴⣿⡉⣮⡻⣧⣾⢟⡸⣿⣼⡿⣽⣿⠿⣿⠄⢿⣧⢿⡇⣿⣿⣦⣶⣾
⠀⠀⠀⠀⠀⠀⣀⠀⠀⣠⢠⡀⠀⠀⠀⠀⠀⢰⡂⠀⣶⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢤⣤⣤⡀⠀⠄⠀⠠⠠⠀⠄⣀⣀⣀⣀⡐⢂⣂⣀⣐⣀⣀⣀⣄⠀⠄⢀⠀⢀⠤⣤⠤⣄⣠⣤⣤⣤⡶⠀⠀
⢠⡔⠢⠶⠒⠘⠺⣗⠢⠋⠈⠠⠴⠦⠅⠀⠀⡘⠁⠒⣉⣈⣁⣀⢈⣠⣀⣀⣀⣤⣤⣴⣴⣤⣦⣤⣴⣶⡎⢁⠈⣽⣿⣿⣿⣿⣿⣿⡟⠻⣿⣟⣋⣉⣩⣉⡫⠍⠉⡑⠈⢤⢁⠔⠁⠀⠁⠤⢜⡠⠴⢬⡥⠞⠒⢂⠄⠀
⢸⣭⣭⣽⢝⣹⣲⣶⣶⣾⣯⣿⡟⣿⣿⣿⣿⣿⠛⢟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⡠⠌⠂⠍⠁⠈⠘⠀⠀⠐⠀⠀⠀⠋⡁⣂⡤⣀⣶⣤⣀⠀
⢸⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣧⠹⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣦⣦⣴⣴⣶⣶⣶⣶⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣦
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠁⠀⠀⢸⣿⣿⣮⣤⣿⡿⠑⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣴⣶⣿⣿⣿⣛⣉⢀⠚⠻⣾⣻⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠋⢉⣉⣀⠀⢸⣿⣿⢿⣿⣿⡿⠀⠀⠀⠠⠿⠧⠄⣉⣬⣦⣠⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣒⣿⠯⠭⠭⠽⢅⠀⠀⡇⣿⣿⠻⠟⠉⠴⠀⠀⠀⠀⠀⢀⠈⠉⠉⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣻⣿⣿⣿⣿⣿⣿⣿
⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠟⢿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣯⣿⣿⣟⣿⣿⣿⣛⡙
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢀⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣮⡽⣗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠁⠀⠛⣿⣿⣿⣿⠿⠿⠛⣻⣿⡯⣭⡀⠀
⢿⣿⣿⣿⡿⠿⡿⠿⡿⡿⣿⠿⢿⠿⡿⣿⡿⠿⠿⠿⣿⠿⠯⠟⣛⢛⡻⠿⠄⠀⣷⢟⡷⡇⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠳⢷⠽⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠸⠶⠿⢫⠅⠀⣐⠂⠉⠉⠁⠀⠀⠀
⢿⣿⣟⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣟⣿⣎⣿⡟⣿⣮⣿⡟⣇⢹⣿⢹⣷⢰⣿⠛⠛⣿⡏⣿⡆⢸⡟⠋⢸⣿⡀⣿⠘⢻⣿⠛⢸⣿⠛⢸⣿⠛⣿⢀⣀⣼⣏⠿⠇⢸⣿⢸⣿⢼⣿⣻⣿⠀⣿⡏⣿⡆⣿⡟⠃⠀⠤
⢻⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣹⣿⡷⣿⡟⣿⡟⣯⣿⣿⡿⣇⢸⣿⢌⣉⢼⣿⢿⡂⣿⡇⣿⡇⢾⣿⡗⢸⣿⣿⣿⢠⢸⣿⣀⢸⣿⣷⣸⣿⠀⣿⣿⠷⢾⡻⣷⣔⢸⣿⢸⣿⢽⣿⣿⣯⠀⣿⡷⣶⡆⣿⡿⠇⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢿⣿⣿⣿⣧⣿⣯⣿⣷⣿⣷⣯⡼⣿⣾⣿⣾⣿⣶⣆⣿⣧⣿⢇⢻⣿⣿⣹⣿⣽⣿⣼⢽⣿⢼⢸⣿⣿⢹⣿⣴⣿⡠⠲⠻⣧⣾⢟⡸⣿⣼⡟⢸⣿⠗⣿⠀⢿⣧⢿⡇⣿⣷⣯⣱⣽
⠀⠀⠀⠀⠀⠀⢀⡂⠀⢠⠀⣤⡀⠀⣀⠀⠀⠰⡆⠀⣶⠄⡀⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠂⠠⠀⢠⣴⢤⣀⠀⢀⢀⠀⠀⣀⣀⣀⣀⣂⣀⣀⣀⣀⣀⠤⠠⢄⡤⠄⠠⢄⠀⠀⠀⢦⠤⠖⣐⡰⠶⡦⠶⠂⠀
⠐⣊⣒⣒⠛⢀⠛⠛⠑⢉⠉⠀⡒⣒⣆⣀⣂⣐⣓⣒⣀⣀⣀⣤⣀⣤⣄⣄⣤⣤⣴⣴⣶⠦⠶⣶⣖⣾⣷⡇⢀⢀⣿⣿⣿⣿⣿⣿⡿⢙⣿⣟⣉⣉⣉⣭⡭⠃⡂⣀⡁⢲⣀⠔⠁⠀⠀⠀⠀⣖⠚⠲⢜⠟⠐⢶⡆⠀
⢸⣷⣶⣶⡿⢝⣶⣿⣿⣿⣿⣿⣯⣻⣿⣿⣿⣿⣋⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⡠⠔⢂⠁⠀⠀⠈⠀⠀⠄⠀⠈⠀⢘⣈⣀⣒⣀⣲⣦⣄⡀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⣿⣿⣿⣧⠹⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⣼⣿⣿⣿⣾⠿⢟⣈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣶⣿⣿⣿⣿⣭⣄⣠⠛⡻⠿⣽⡿⢿⣿⣿⠫⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⢉⣉⣀⣠⣤⠀⢸⡿⣛⣹⣿⣿⣟⠀⠀⠀⠒⠒⠒⠤⢤⣬⣧⠴⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠭⠭⠽⠿⠶⠲⢦⠀⠘⠏⠿⠿⠙⠋⠁⡾⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⡻⢿⣿⣿⠿⣿⣿⣿⣿⣿⣻⣽⣿⣷⣩⣽⣿⣛⡉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⡠⢤⢄⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠠⡷⡖⣎⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⡿⣿⣿⠿⠟⢿⠛⢻⣿⡿⠤⡄⠀
⢾⣿⣿⣿⡿⠿⡿⠿⡿⠿⣿⠿⢿⠿⠿⣿⡿⠿⠿⠿⣿⠿⠯⠽⣝⢏⡹⠿⠿⠀⠀⣿⢯⡷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠟⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠒⠿⠿⢧⠆⠀⣡⠁⠈⠉⠀⠀⠀⠀
⢿⣿⣟⣻⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣟⣿⣎⣿⡟⣿⣶⣿⡟⣿⢸⣿⢹⣷⢸⣿⠛⠉⣿⡏⣿⡆⢸⣟⠋⢸⣿⡀⣿⠘⢻⣿⠛⢸⣿⠛⢸⣿⠛⣿⠀⣀⣼⣏⠿⠇⢸⣿⢸⣿⢼⣿⣿⣿⠀⣿⡏⣿⡆⣿⡟⠃⠀⠠
⢹⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣺⣿⣷⣿⡏⣿⡟⣯⣿⣿⡿⣇⢸⣿⢎⣍⢾⣿⢿⠂⣿⡇⣿⡇⣺⣿⡗⣸⣿⣿⣿⢠⣼⣿⢀⢸⣿⣷⣸⣿⠀⣿⠿⡛⢚⡻⣷⣔⢸⣿⢸⣿⢺⣿⣿⣯⠂⣿⡷⣶⡆⣿⡿⡇⡀⢀
⢺⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣷⣿⣷⣿⣿⣿⣷⣯⣾⣿⣼⣿⣽⣿⣾⡇⣿⣧⣿⢇⢽⣿⣿⣿⣿⣽⣿⣾⢺⣿⢰⢸⣿⣿⢹⣿⣴⡿⣰⠘⠻⣧⣾⢟⡼⣿⣼⡟⢸⣿⠓⣿⠀⢿⣧⢿⡇⣿⣿⣯⣽⣾
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡆⢠⣄⠀⠀⡀⠀⠠⢶⠠⢰⡆⢀⢀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠦⣄⡀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⢀⠤⣠⠄⠀⠤⡀⠀⠀⠠⡦⠦⢀⣀⠄⢤⠶⠆⠀
⠐⣒⣐⣒⡚⠃⠈⠛⡋⠉⠁⡁⢐⢒⣒⣀⣀⣀⣚⣒⣂⣠⣄⣀⣀⡀⣀⣀⣠⣤⣤⣦⡴⡶⠴⣴⡴⣲⣾⣾⡏⠀⠄⣺⣿⣿⣿⣿⣯⡋⣻⣽⣉⣉⣉⣡⠨⠍⢀⢀⣈⠐⣆⡠⠊⠀⠀⠀⠀⢰⡒⠓⠾⡻⠓⠺⡴⠀
⢸⣿⣷⣲⡖⠋⢒⣚⣿⣿⣿⣶⡯⡉⣿⣿⣿⣿⣟⣙⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⠤⠒⡑⠀⠀⠀⠁⠀⠠⠀⠀⠁⠈⣂⣁⣀⣒⣰⣶⣀⣀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⣿⣿⣿⢷⠸⣽⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⣼⣿⣿⣷⡶⠿⢟⣀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢴⣿⣿⣿⣿⣭⣤⢠⠍⠋⠻⣽⠿⠿⢿⣿⡋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⣉⣁⣀⣤⠀⢸⡿⣻⡙⣿⣿⣟⠀⠀⠀⠐⠛⠒⠂⠤⣶⣷⠴⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠬⠭⠭⠿⠶⠶⢦⡀⠀⠇⠿⠿⠝⠋⠁⢾⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠊⠛⠛⢿⣿⣿⡿⡛⢿⣿⣋⣟⣛⣯⣿⣧⣌⣭⣫⣛⣋
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢠⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣗⡗⣻⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢿⣿⡿⠿⠻⠟⠛⣿⣿⠧⢄⠀
⢿⣿⣿⣿⡿⠿⣿⠿⡿⠿⣿⠿⢿⠿⠿⣿⡿⠿⠿⠿⣟⠿⠿⠯⣭⢟⡋⢿⡿⠿⠇⠀⢟⢯⡵⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⠿⢯⡰⠀⣉⠌⠀⠉⠁⠀⠀⠀
⢿⣿⣿⣟⢿⣿⢿⣿⢽⣿⡿⣿⢿⣿⡿⣿⣆⣿⡟⣿⡆⣿⡟⣛⢹⣿⢹⣷⢸⣿⠛⠀⣿⡟⣿⡇⢸⣟⠃⢸⣿⡀⣿⠘⢻⣿⠛⢸⣿⠛⢸⣿⠙⣿⠀⢀⣼⣏⠿⠇⢸⣿⢸⣿⢸⣿⣻⣿⠀⣿⡏⣿⡆⣿⡟⠃⠀⠀
⢹⣿⣿⣿⣿⣿⣾⣿⢿⣿⣿⣿⣿⣿⣷⣿⡋⣿⣟⣯⣿⣿⡿⣇⢸⣿⢮⣉⢼⣿⢿⠂⣿⡇⣿⡇⢸⣿⣷⢸⣿⣿⣿⢀⢸⣿⢀⢸⣿⢷⣸⣿⠀⣿⠀⠟⢚⡻⣷⡔⢸⣿⢸⣿⢾⣿⣿⣯⠂⣿⡷⣶⡆⣿⡿⢇⢀⠀
⣸⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣷⣿⣷⣿⣷⣿⣷⣯⣿⣿⣼⣿⣿⣿⣾⡄⣿⣧⣿⢇⢾⣿⣿⣼⣿⣽⣿⢾⢾⣿⢸⢸⣿⣾⢹⣿⣴⡿⣰⡀⠸⣧⣾⢟⡸⣿⣼⠟⢸⣿⠃⣿⠀⢿⣧⢿⡇⣿⣷⣮⣭⣤
⠀⠀⠀⠀⠀⠀⡀⠀⣠⡄⡀⣰⢀⠤⠀⠀⠄⠀⠀⢰⡄⠀⣶⢠⡄⠄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠒⠒⠀⣰⠶⠶⣄⡀⢀⣀⣂⣤⣤⣤⣤⣄⣠⣤⣤⡀⠠⠄⣤⠰⡂⠄⡢⠀⡀⠒⣤⠆⠀⠤⠦⢶⠶⠶
⢀⣀⣛⣩⢉⢩⢉⣁⠉⣩⠀⢀⣀⣀⣋⣉⣂⣄⣠⣬⣉⣩⣤⣤⣤⣄⣀⣠⣄⣤⣤⣶⣴⣶⣒⣒⣒⣓⣻⣾⣿⣿⣿⡅⣠⣀⣟⣯⣿⣯⣍⣉⣳⣭⣤⣄⣤⡤⠔⢂⠀⣌⡀⢲⢠⠊⠀⠀⠀⠒⠊⣴⡚⠪⠖⠋⠈⠑
⢸⣿⣿⣷⣾⣳⡀⣈⣭⣽⣿⣿⣷⣶⣆⡹⡷⢿⣿⣿⣍⣫⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡔⠂⡁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢁⣄⣤⣂⣦⣿⣤
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢻⣿⣿⢿⢇⢻⣿⡿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢐⣿⣿⣿⣿⠿⢿⣋⡨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠀⠀⣿⣿⣿⣿⣶⣦⡆⠴⠉⡝⠛⠾⠛⠻⠿⢿⠑⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⣁⣀⣠⣤⡄⠀⢹⣟⣯⣛⣿⣿⡇⠀⠀⠀⠈⠉⠉⠐⠲⠶⠷⠺⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠⠭⠽⠷⠒⠒⠒⠦⠀⠘⠟⠿⠟⠙⠁⠘⡇⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣭⣿⣿⣿⣿⣿⣿
⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⠤⢀⠀⠀⠀⠀⠀⠀⠉⠻⠿⡿⠿⠿⢟⣻⣭⣽⣟⣳⣾⣷⣆⣬⣍⣩
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⡤⣒⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣏⣟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢽⣿⣿⠿⠛⠛⠉⣽⣿⡗⠤
⢻⣿⣿⣿⡿⠿⡿⠿⡿⠿⣿⠿⢿⠿⠿⢿⡿⠿⠿⠿⣿⠿⠩⠿⣷⢾⡭⠭⡽⠿⠟⠟⠻⠀⠀⣯⡯⢷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠚⢿⢿⠔⣆⠈⠈⠁⠀⠀⠀⠀
⣿⣿⣿⣿⣽⣿⢻⣿⢾⣿⡟⣿⣼⣿⡟⣿⡆⣿⣿⣿⣎⣿⡟⣃⢹⣿⢹⣷⢹⣿⠛⡃⣿⡏⣿⡎⢹⣟⣃⢸⣿⡀⣿⠘⢻⣿⠛⢸⣿⠛⢸⣿⠙⣷⠀⠀⢸⣏⠿⠇⢸⣿⢸⣿⢸⣿⣿⣿⠀⣿⡟⣿⡆⣿⡟⠃⠀⠀
⣸⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⢽⣿⣷⣿⣇⣿⡟⣯⣽⣿⡿⣗⣸⣿⢊⣙⢾⣿⢿⡂⣿⡇⣿⡇⢸⣿⣗⢽⣿⣿⣿⠠⢸⣿⣠⢸⣿⠗⢸⣿⠀⣿⠀⠀⢘⡻⣷⡄⢸⣿⢸⣿⢺⣿⢻⣯⠂⣿⡷⣶⡎⣿⡿⡇⢂⠀
⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣯⡿⣿⣿⣿⣼⣿⣾⡄⣿⣧⣿⣇⢿⣿⣿⣸⣿⣽⣿⣸⢼⣿⣺⢸⣿⣶⢸⣿⣴⡿⠰⢦⡻⣧⣾⠟⡸⣿⣼⠟⠸⣿⠁⣿⠀⢿⣧⢿⡇⣿⣷⣦⢠⣥
⠀⠀⠀⠀⠀⠀⢀⠀⢀⣤⢀⠀⡄⠠⠄⠀⠀⠄⠀⠀⢲⠀⠰⣆⢠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠂⠀⣀⡶⠖⣄⡀⢀⢀⣠⣤⣤⣤⣤⢀⣠⣤⣤⠀⡠⠄⣀⢒⠀⠐⡦⢀⠐⢲⡴⠂⠦⣴⠖⢶⠶
⢀⣀⢒⣒⣀⣈⣛⣉⠈⠙⡍⠀⢀⢀⣐⣋⣑⣀⣀⣀⣍⣉⣡⣠⣄⣤⣄⣀⡤⣄⢤⣤⣦⣤⣚⣒⣐⣚⣒⣯⣼⣿⣷⣿⣏⢀⣄⣼⣿⣿⣯⣉⣉⣿⣭⣤⣤⣤⠤⠐⡂⢀⣉⠐⠇⡰⠁⠀⠀⠀⠂⢸⣐⠓⠰⠖⠁⠈
⢸⣿⣿⣿⣶⣦⣞⠂⣸⢭⣿⣿⣿⣶⣦⠉⢷⠶⣿⣿⣿⣉⣩⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠔⠈⡑⠀⠀⠀⠁⠀⠠⠀⠀⠀⠀⣡⣠⣥⣀⣬⣟
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠻⣿⣿⣿⣳⢹⣽⣿⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣷⡿⠿⣛⣁⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢸⣿⣿⣿⣾⣦⣤⠠⠎⠉⠛⠻⠟⠛⠿⠿⡁⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⢉⣀⣀⣤⣤⠀⠘⡿⣻⣝⣻⣿⡟⠀⠀⠀⠀⠉⠉⠁⠒⠶⠾⠚⠏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠭⠭⠽⠗⠒⠒⠲⡄⠀⠃⠿⠿⠊⠋⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣭⣽⣿⣿⣿⣿⣿
⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⡀⠀⠀⠀⠀⠀⠙⢿⢿⠿⠿⠽⣿⣿⣭⣽⣛⣶⣿⣷⣤⣭⣥
⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢠⣔⣢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡾⣹⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽⣿⡿⠟⠛⠋⢩⣿⣿⠢
⢺⣿⣿⣿⡿⠿⡿⠿⡿⠿⣿⠿⢿⠿⠿⢿⣿⠿⠿⠿⡿⠿⠯⠽⣿⢶⡯⢭⠭⠿⠿⠷⠻⠿⠇⠀⢷⡿⢽⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⡿⠯⣲⠀⠉⠈⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢹⣿⢿⣿⡟⣿⣹⣿⡿⣿⡶⣿⣿⣿⡮⣿⡟⣣⢹⣿⢹⣷⢹⣿⢛⡃⣿⡟⣿⡆⢸⣟⠋⣸⣿⡀⣿⠘⢻⣿⠛⢸⣿⠛⢸⣿⠙⣷⠀⠀⢸⣏⠿⠇⢸⣿⢸⣿⢸⣿⢻⣿⠀⣿⡏⣿⡆⣿⡟⠃⠀⠀
⣹⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⢻⣿⣷⣿⣇⣿⡟⣯⣽⣿⡿⣏⣼⣿⢎⣉⢾⣿⢿⡂⣿⡇⣿⡇⢸⣿⢟⢸⣿⣿⣿⢀⢸⣿⢠⢸⣿⠗⢸⣿⠀⣿⠀⠀⢈⡻⣷⡄⢸⣿⢸⣿⢺⣿⠻⣯⠂⣿⡷⣶⡆⣿⡿⣇⡀⡀
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣏⣿⣿⣿⣷⣿⣷⣯⣿⣿⣽⣿⣼⣿⣾⡅⣿⣧⣿⢧⢼⣿⣿⣼⣿⣽⣿⢼⢹⣿⣾⢸⣿⣶⢹⣿⣴⡿⠸⠶⡺⣧⣾⢟⠸⣿⣼⡟⡸⣿⠀⣿⠀⢿⣧⢿⡇⣿⣷⣯⡠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⢀⢠⡄⠤⠄⠀⢠⠀⠀⠀⣦⠀⢰⡆⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠀⠀⣀⡶⠶⢦⡀⡀⣒⣠⣤⣤⣄⡄⣀⣤⣤⠄⢀⠤⢀⡐⡒⠠⢒⠄⠀⠐⢄⠖⠲⠤⡤⠒⡤
⢠⣀⣐⠒⢒⣁⢘⣋⡁⡉⢛⠋⠈⢀⣀⣒⣛⣃⣀⣀⣠⣉⣈⣠⣤⣤⣤⣀⡀⡄⢄⣤⣤⣴⣴⣒⣀⢂⣒⣚⣥⣿⣽⣷⣾⣿⠀⣠⣠⣿⢽⣽⣉⣹⣮⣥⣠⡤⣄⠤⠒⡀⣠⣁⠘⣄⡞⠀⠀⠀⠐⠀⢥⢚⠓⠶⠊⠀
⢰⣶⣿⣷⣷⡖⣔⡒⢀⡩⣿⣿⣿⣿⣶⢢⠡⣧⢿⣿⣿⣏⣙⣙⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣭⣿⣿⣿⣿⣿⣿⣾⣿⣿⣭⡤⠒⢉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢈⣤⣬⣴⣠⣽
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⣿⣿⣿⡟⡜⣯⣿⣿⣟⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣸⣿⣿⣿⣷⠿⢟⣁⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠰⣿⣿⣿⣶⣿⣴⡄⠴⠩⠙⠳⠿⠛⠻⠟⢏⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⣁⣀⣠⣤⠄⠀⣿⢿⣟⢻⣿⣿⠀⠀⠀⠀⠉⠉⠁⠒⠶⠾⠖⠿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠨⠭⠽⠷⠒⠒⠒⠆⠀⠸⠸⠿⠗⠙⠁⢻⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡿⢭⣭⣽⣿⢿⣿⣿
⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡠⠤⠀⠀⠀⠀⠀⠀⠸⠿⣿⠿⠭⠻⣻⣯⣭⣟⣻⣶⣿⣶⣭⣭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⣄⣂⣄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠰⡶⣋⡾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡨⣿⣻⡿⠛⠛⠉⣩⣿⡗
⢻⣿⣿⣿⡿⠿⡿⠿⡿⠿⣿⠿⢿⠿⠿⣿⣿⠿⠿⣿⣿⠿⠿⠯⣽⢿⡶⢯⡭⠽⠿⠿⠾⠿⠿⡿⠀⠸⣾⢭⢯⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢛⠿⣗⠆⠀⠁⠉⠀⠀⠀
⣻⣿⣿⣿⣿⣿⢹⣿⢻⣿⡟⣿⣸⣿⡟⣿⡟⣿⣿⣿⣾⣿⡟⣃⢺⣿⢻⣷⢹⣿⢛⡃⣿⡟⣿⡆⢸⣟⠋⢹⣿⡀⣿⠘⢻⣿⠛⢸⣿⠛⢸⣿⠙⣷⠀⠀⢸⣏⠿⠇⢸⣿⢸⣿⢸⣿⢿⣿⠀⣿⡏⣿⡆⣿⡟⠃⠈⠂
⣹⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢾⣿⣷⣿⣇⣿⣟⣯⣵⣿⡿⣷⢸⣿⢎⣍⢺⣿⢿⡂⣿⡇⣿⡇⢸⣿⠗⢻⣿⣷⣿⢀⢸⣿⠀⢸⣿⠗⢸⣿⠀⣿⡀⠀⠈⠻⣷⡄⢸⣿⢸⣿⢺⣿⢻⣯⠂⣿⡷⣶⡆⣿⡿⠇⢀⠄
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣟⣿⣿⣿⣿⣿⣷⣯⣽⣿⣿⣿⣼⣿⣾⡅⣿⣧⣿⣷⢾⣿⣷⣼⣿⣽⣿⢼⢼⣿⣶⢸⣿⣶⢸⣿⣴⡿⠘⠗⠹⣧⣼⢗⡸⣿⣼⠟⢼⣿⠀⣿⠀⢿⣧⢿⡇⣿⣷⣦⢃⠤
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⣀⡀⢠⢀⠦⠀⠀⠠⠀⠀⠲⡆⠀⢶⠠⠄⠄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠒⠐⠒⠀⠀⢀⣰⠶⠢⣄⢀⣠⣤⣤⣤⣤⣀⣠⣤⣤⡀⠀⠄⣐⠒⡒⠐⡠⠀⠀⠲⢴⠂⠠⠤⡐⠶
⠠⣀⣠⣀⣚⣣⢁⠩⢁⠀⠉⢋⠀⢀⣀⣀⣙⣭⣢⣤⣁⣬⣉⣁⣄⣤⣤⣄⣀⣀⣀⡀⣤⣶⣤⢴⢓⣒⡓⣂⣹⣾⣿⣿⣿⣿⣿⡁⣀⣀⣿⣰⣆⣈⣳⣤⣤⡤⣄⡄⠐⠀⠄⡌⡀⠱⢠⠊⠀⠀⠀⠒⠠⣇⡙⠚⠴⠊
⢸⣿⣿⣿⣿⢳⣊⣴⠂⢈⠬⣭⣿⣿⣿⣖⣀⣹⠾⢿⣿⣷⣍⣉⣍⣿⣿⣿⣿⣿⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣿⣾⣿⣯⣥⡔⢊⡡⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⢈⣤⣬⣬⣤
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⢻⣿⣿⣿⢇⢻⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢘⣿⣿⣿⣿⠿⢿⣋⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⠀⠀⢿⣿⣿⣿⣶⣦⡦⠰⠊⠅⠛⠾⠟⠛⠻⠻⠑⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⢉⣀⣀⣤⣤⠤⠀⢸⣟⣯⡛⣿⣿⡇⠀⠀⠀⠈⠉⠉⠁⠐⠶⠶⠚⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠⠭⠿⠒⠒⠒⠛⠣⠀⠈⠋⠿⠛⠊⠉⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣯⢭⣭⣽⡿⣿⣿
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⢤⡄⡀⠀⠀⠀⠀⠈⠿⠿⠟⠿⠹⣻⣬⣽⣍⣲⣾⣶⣦⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⡠⣲⣢⡀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⢿⢿⡹⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣟⣛⠛⠛⠋⠉⣽⣿
⢻⣿⣿⣿⡿⢿⡿⠿⡿⠿⣿⠿⢿⠿⠿⣿⣿⠿⠿⢿⣿⠿⠿⠿⠭⢿⡶⢶⡭⠭⠽⠟⠾⠟⠿⠿⠿⠀⠀⢿⠣⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⠒⠂⠀⠈⠀⠀⠀
⢻⣿⣿⣿⣿⣿⣽⣿⢹⣿⡟⣿⢻⣿⡿⣿⣿⣿⡿⣿⣾⣿⡟⣃⢸⣿⢹⣷⢹⣿⢛⡃⣿⡟⣿⡆⢸⣿⠃⢸⣿⡉⣿⠘⢻⣿⠛⢸⣿⠛⢸⣿⠙⣷⠀⠀⢸⣏⠻⠇⢸⣿⢸⣿⢸⣿⠛⣿⠀⣿⡏⣿⡎⣿⡟⠃⠀⠉
⣽⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⢸⣿⣷⣿⣧⣿⣟⣯⡽⣿⡿⣗⢼⣿⣞⣉⢺⣿⢿⡂⣿⡇⣿⡇⢸⣿⡗⢸⣿⣿⣿⠀⢸⣿⠀⢸⣿⡷⢸⣿⠀⣿⢠⡀⠈⠻⣷⡍⢸⣿⢸⣿⢸⣿⠻⣯⠀⣿⡷⣶⡞⣿⡿⠇⢀⣤
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣿⣿⣿⣿⣾⣿⣾⡇⣿⣧⣿⢧⢼⣿⣿⣾⣿⣹⣿⣴⢼⣿⣾⢸⣿⣶⢸⣿⣴⡿⠨⠓⠻⣧⣾⠟⡸⣿⣼⠟⣼⣿⠀⣿⢀⢿⣧⢿⡇⣿⣷⣦⡉⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣄⣀⢀⣆⠶⠀⠀⠠⠀⠀⠀⡶⠀⠰⠆⠤⠠⠀⠄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⣀⡶⠖⠦⣤⣤⡤⢤⣤⠀⠀⠤⣤⠄⠠⠶⠐⠐⠆⠀⡠⠂⠀⠀⠶⠒⠒⠠⠆
⠀⣀⠠⠤⢀⡉⠩⠌⠬⠍⠀⠀⢉⣀⣁⣀⢀⠉⣭⣧⣤⣬⣬⣨⣭⣤⣤⣠⣤⣄⣄⣀⣄⣰⣶⣤⣴⣛⣁⣚⣣⣨⣼⣿⣯⣿⣿⣿⣿⣿⣀⣐⣨⣇⣀⣡⣥⣤⣤⡄⡦⠒⠀⠄⡠⠄⠙⢄⠎⠀⠀⠀⢀⠀⢯⢉⠑⠣
⢸⣿⣿⣿⣿⣿⣏⢆⣧⢇⣀⡽⠎⡿⣿⣿⣷⣆⢐⠊⠾⢿⣷⣦⣬⣉⣭⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢵⣿⣿⣿⣾⣿⣽⣯⣥⣔⣊⣡⠁⠀⠀⠀⠀⠀⠂⣀⡀⣀⣈⣤⣤⣬
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠙⣿⣿⣿⣏⡞⣿⣿⢿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢀⣿⣿⣿⣿⡿⢟⣛⣅⣥⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠃⠀⠀⣿⣿⣿⣿⣶⣶⡄⠰⠉⠍⠛⠞⠛⠻⠟⢏⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⣀⣀⣠⡤⠤⠤⠆⠀⢹⢿⣭⣻⣿⣿⢀⠀⠀⠀⠈⠉⠉⠐⠲⠶⠖⠳⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠐⠒⠒⠒⠚⠛⠉⠣⠀⠘⠙⠛⠛⠈⠁⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⢿⣿⣟⣶⡾⢿⣿⢿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢀⠀⠀⠀⠀⠀⠻⠟⠈⢩⣿⣧⣤⣩⣵⣾⣶⣶
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠁⢀⣔⣶⡢⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣗⣏⣻⡅⠀⠀⠀⠀⠀⠀⠀⠀⣘⣛⡛⡛⠋⠛⡉⣭
⢹⣿⣿⣿⡿⠿⡿⠿⡿⠿⣿⠿⢿⠿⠿⣿⣿⠿⠿⠿⣿⠿⠿⠛⡿⢥⡿⢷⡶⠶⠶⠾⠿⠟⠟⠻⠿⠿⠟⠓⠀⠘⣟⣧⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠚⠁⠀⠀⠀⠀⠀⠀⠀⠈⣻⠟⠂⠃⠀⠀⠀⠀
⢾⣿⣿⣿⣿⣿⣿⣿⢸⣿⡟⣿⢼⣿⣿⣿⣖⣿⡟⣿⣾⣿⡟⣧⢹⣿⣻⣷⢻⣿⢻⠃⣿⡟⣿⡆⢸⣿⠛⢸⣿⣀⣿⠙⢻⣿⠛⢸⣿⠛⢸⣿⠙⣷⠀⠀⢸⣏⠻⠆⢸⣿⢸⣿⢰⣿⢛⣿⠀⣿⡏⣿⡆⣿⡟⠃⠀⠀
⣽⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣯⣿⣟⣯⣵⣿⡿⣇⢸⣿⣿⣿⣼⣿⠿⠂⣿⡧⣿⡇⢸⣿⠗⣸⣿⣷⣿⠂⢸⣿⠀⢸⣿⡗⣸⣿⠀⣿⢀⢠⢈⡻⣷⡄⢸⣿⢸⣿⢸⣿⠻⣯⠀⣿⡷⣶⡆⣿⡿⠇⠀⢀
⣹⣿⣿⣿⣿⣿⣽⣿⣿⣿⣾⣿⢾⣿⣿⣿⣿⣿⣯⣿⡿⣿⣷⣿⣿⣿⣼⡿⣽⣿⣾⣆⣿⣧⣿⣧⣸⣿⣿⢹⣿⣹⣿⣰⣾⣿⣿⢸⣿⣿⣹⣿⣴⡿⠀⠹⠹⣧⣾⠇⠸⣿⣼⠟⡸⣿⠂⣿⠀⢿⣧⢿⡇⣿⣷⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⣰⣀⠰⠀⠀⠠⠀⠀⠐⡆⠀⠶⠠⠄⠄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠒⠀⢀⣀⣀⣀⣰⠶⠢⣤⠤⠤⢤⣄⠀⡀⣤⣄⠀⠀⠄⣐⠢⠂⠠⡠⠀⠀⠰⢔⠐⠀⠴
⢰⠠⠀⠤⠄⣈⣉⡡⠄⠭⠉⠀⠈⣉⣀⢀⡀⢀⢉⣩⣧⣤⣅⣌⣩⣭⣤⣄⣤⣤⣄⣀⡠⣠⣴⣶⡤⣖⠒⣒⣫⣃⣡⣾⣿⣭⣿⣿⣿⣿⣿⡇⣀⣆⣟⣀⣢⢤⣤⡄⢄⡄⠀⠠⠄⡌⠀⠱⢰⠋⠀⠀⠀⡒⠨⡝⡙⠒
⢸⣿⣿⣿⣿⣿⣿⣓⣪⠤⠁⡀⠭⣭⡿⣿⣻⣳⢠⣰⠶⠿⣿⣷⣥⣉⣍⣭⣽⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣿⣿⣤⡔⢊⡁⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣡⣤⣬
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣟⣿⣿⣯⣿⣿⣿⣿⣿⣿⡿⠟⠉⣿⣿⣿⣿⢣⣻⣿⡿⢻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣸⣿⣿⣿⣿⠿⣿⣋⣈⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠋⠓⠀⠀⢸⣿⣿⣿⣶⣦⡆⠠⠮⠉⠙⠫⠿⠿⠿⠿⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢁⣀⣀⣀⣤⠤⠤⠀⠘⡿⣧⣝⣿⣿⡇⠀⠀⠀⠁⠒⠓⠒⠀⢴⡶⠾⠝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠶⠒⠒⠒⠒⠛⠻⠀⠀⠋⠻⠟⠊⠉⢹⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠯⣭⣭⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠿⠟⠍⠙⣿⣭⣍⣉⣶⣾⣶
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⡠⣒⣶⠄⠀⠀⠀⠀⠀⠀⠀⣀⠃⠀⠀⠀⢰⣲⢚⣞⠀⠀⠀⠀⠀⠀⠀⠀⣙⣛⣛⠟⠛⢋⠉
⢾⣿⣿⣿⡿⠿⡿⠿⡿⠿⣿⠿⢿⠿⠿⣿⣿⠿⠿⢿⡿⠿⠿⠟⡿⢯⡯⢿⡶⠶⠼⠵⠻⠿⠿⠿⠿⠿⠿⠿⠛⠀⠀⢯⣿⠜⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⠛⠀⠀⠀⠀⠀⠀⠀⣈⠿⠟⠒⠀⠀⠈⠀
⣿⣿⣿⣿⣿⣿⣿⣿⢼⣿⡟⣿⢺⣿⡟⣿⡶⣿⡟⣿⣾⣿⡟⡧⢹⣿⣻⣷⢹⣿⢻⡇⣿⡟⣿⡆⢸⣿⠛⢸⣿⡀⣿⠘⢻⣿⠛⢸⣿⠛⢸⣿⠙⣷⠀⠀⢸⣏⠻⠆⢸⣷⢸⣿⢠⣿⠛⣿⠀⣿⡏⣿⡆⣿⡟⢃⠀⠀
⣽⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣼⣿⡷⣿⣇⣿⣟⣯⣷⣿⡿⣇⢸⣿⣿⣿⣾⣿⢿⠂⣿⣷⣿⡇⢸⣿⡗⢸⣿⣿⣿⠑⢸⣿⢀⢸⣿⢷⣼⣿⠀⣿⠠⢄⢈⡻⣷⡄⢸⣿⢸⣿⢸⣿⠻⣯⠀⣿⡧⣶⡆⣿⡿⠇⠀⠀
⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣿⣿⣿⣿⣿⣿⣾⣄⣿⣯⣿⢇⢸⣿⣿⢾⣿⣽⣿⢸⣸⣿⣾⢸⣿⣿⣹⣿⣴⡿⠸⠈⡹⣧⣾⠗⠸⣿⣼⠟⠾⣿⠂⣿⠀⢿⣧⢿⡇⣿⣷⣦⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣠⣀⡀⣄⡐⠦⠀⠀⠄⠀⠀⢰⠄⠐⠦⠠⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠂⠀⠀⢀⣀⣀⣀⡴⠶⢤⣤⠤⣤⣄⢀⡠⣤⡄⠀⠠⠀⡖⢒⠂⢄⠤⠀⠀⠤⡠⠀⠠
⢠⡲⠤⠀⠤⢤⣉⠉⡤⠨⠭⠁⠀⠈⣁⣈⣀⡀⡈⣉⣽⣠⣄⣠⣍⣭⣡⣤⣀⣤⣖⣀⣀⠤⣠⣴⣦⢤⡞⢊⣒⢋⣍⣥⣿⣿⣯⣿⣿⣿⣿⣽⣿⢀⣰⣰⣃⣦⣤⣤⠀⢠⠤⠀⠠⢀⣉⠈⠇⡐⠁⠀⠀⠀⠂⠸⣜⠛
⢸⣿⣿⣿⣿⣿⣿⣿⡱⡲⡔⢀⠨⠭⣽⣿⣟⣿⡢⠄⡖⠾⢿⣿⣦⣤⣩⣩⣭⣿⣻⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣹⣿⣷⣷⣿⣿⣯⣤⠒⢈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣁⣠
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢿⣿⣿⣿⡟⢸⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣾⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⡿⠿⣟⣁⣡⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠚⠃⠀⠀⣿⣿⣿⣷⣶⣶⠀⠬⠏⠋⠻⠽⠿⠿⠿⡏⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⣀⣀⣂⠤⠤⠤⠆⠀⢻⢿⣜⣻⣿⣟⠀⠀⠀⠀⠐⠒⠒⠀⢤⣤⡼⠯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠐⠒⠒⠒⠛⠛⠋⠃⠀⠘⠸⠿⠓⠙⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⡿⣿⣿⠯⣭⣭⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠺⠋⠉⢻⣭⣭⣌⣓⣦⣧
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢀⢔⣒⣤⠀⠀⠀⠀⠀⠀⠀⢀⣚⠀⠀⠀⠀⣞⡖⢺⠂⠀⠀⠀⠀⠀⠈⠀⢿⣛⡻⠟⠛⠉
⢾⣿⣿⣿⡿⠿⡿⠿⡿⠿⣿⠿⢿⠿⠿⢿⣿⠿⠿⢿⣿⠿⠿⠿⣻⢿⡯⢽⡿⠶⠶⠼⠜⠿⠿⠿⠿⠿⠿⠿⠟⠋⠁⠀⠸⣼⠬⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠃⠀⠀⠀⠀⠀⣀⠘⠻⠇⠒⠀⠁⠁
⢹⣿⣿⣿⣿⣿⣿⣿⣽⣿⡏⣿⠸⣿⡟⣿⡦⣿⡿⣿⣿⣿⡟⣧⢸⣿⣹⣷⢻⣿⢛⡧⣿⡟⣿⡆⢸⣿⠛⢸⣿⡄⣿⠘⢻⣿⠛⢸⣿⠛⢸⣿⠙⣷⠀⠀⢸⣏⠻⠆⢸⣿⢸⣿⢠⣿⠛⣿⠀⣾⡏⣿⡆⣿⡟⠃⡀⠀
⢼⣿⣿⣿⣿⣿⣽⣿⣾⣿⣿⣿⣺⣿⣷⣿⡟⣿⣟⣯⣵⣿⡿⣇⢸⣿⢾⣿⣾⣿⢿⠂⣿⣧⣿⡇⢸⣿⠗⢸⣿⣿⣿⢪⢺⣿⠀⢸⣿⠗⣼⣿⠀⣿⠀⡠⢨⡻⣷⡄⢸⣿⢸⣿⢸⣿⠻⣯⠀⣿⡷⣶⡆⣿⡿⠇⠀⠀
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣾⣿⣿⣿⣿⣿⣾⡅⣿⣧⣿⢇⢼⣿⣿⣾⣿⣹⣿⢰⣸⣿⣶⢸⣿⣿⣹⣿⣴⡿⢐⠄⠹⣧⣾⠟⡸⣿⣼⠟⠸⣿⠄⣿⠀⢿⣧⢿⡇⣿⣷⣤⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⣀⣄⣀⢀⣆⠠⠆⠀⠠⠀⠀⠀⡦⠀⠲⠆⠄⠠⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⣀⣀⣀⣀⣀⣰⠶⠦⣤⣤⣤⠄⣀⢤⡤⡀⠀⠄⢀⠐⡒⠰⠠⠄⠀⠀⢠⠆⠰
⢠⣔⡦⠀⠀⠤⣈⠉⣫⠌⠭⠍⠁⠄⢉⣀⣁⣀⣀⣉⣩⣧⣤⣄⣬⣉⣩⣤⣤⣠⣤⣂⣀⡠⠤⣤⡤⣦⢠⠉⣐⠂⣁⣸⣼⣿⣯⣽⣿⣿⣿⣿⣿⣿⣁⣀⣀⣟⣠⣤⡤⢄⡠⠄⠀⠀⣈⡁⠸⣀⠞⠀⠀⠂⠐⠀⢧⡚
⢸⣿⣿⣿⣿⣿⣿⣿⡋⢎⢵⢂⡀⡩⢭⣿⣿⣻⣳⢀⠙⠂⠿⣿⣷⣤⣉⣉⣍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣩⣿⣶⣾⣿⣿⣥⡴⠂⣉⠂⠀⠀⠈⠀⠀⠀⠀⠂⠀⠈⣀
⢸⣿⣿⣿⣿⣟⣿⣿⢿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⣿⣿⣿⣿⢟⢿⣿⣿⠿⣺⣿⣿⣿⣿⣿⣷⣶⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢸⣿⣿⢿⣿⡿⠿⣟⣊⣉⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠚⠛⠉⠀⠀⢾⣿⣿⣷⣶⣶⠀⢠⡝⠛⠻⢏⡿⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⣀⣀⣐⣒⣤⠤⠤⠀⢸⡿⣊⣻⣿⣿⠀⠀⠀⠈⠀⠐⠒⠢⠄⣤⣤⢏⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠐⠶⠖⠒⠒⠒⠚⠢⠀⠘⠇⠿⠿⠙⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢿⣿⠿⢭⣭⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠭⠹⣻⣭⣍⣝⣳⣼
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣠⣒⡠⡀⠀⠀⠀⠀⠀⠀⢀⣒⡀⠀⠀⠀⣐⣱⢺⢦⠀⠀⠀⠀⠀⠀⠸⣿⣿⠿⠛⠟
⢺⣿⣿⣿⡿⠿⡿⠿⣿⠿⣿⠿⢿⠿⠿⢿⣿⠿⠿⢿⣿⠿⠿⠿⣿⢟⡿⢭⡿⠷⠶⠬⠭⠿⠿⣿⠟⠿⠿⠿⠿⠿⠉⠉⠀⠀⣶⠯⣯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠯⠿⠞⠀⠀⠀⠀⢀⠀⠛⠯⠔⠂⠈⠈
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⣿⠸⣿⡟⣿⣦⣿⣿⣿⣿⣿⡟⣧⢼⣿⣹⣷⢻⣿⢛⡃⣿⡟⣿⡆⢸⣿⣛⢸⣿⡤⣿⣘⢻⣿⠛⢹⣿⠛⢸⣿⠙⣷⠀⠀⢸⣏⠻⠇⢸⣿⢸⣿⢠⣿⠛⣿⠀⣾⡏⣿⡆⣿⡟⠃⠀⠀
⢼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⢸⣿⡷⣿⣟⣿⣟⣯⣷⣿⡿⣇⢸⣿⣿⣿⣾⣿⢿⡂⣿⡇⣿⡇⢿⣿⠗⢸⣿⣿⣿⢒⢹⣿⢀⢸⣿⠗⢸⣿⠀⣿⠀⠀⢈⡻⣷⡄⢸⣿⢸⣿⢸⣿⠻⣯⠀⣿⡷⣶⡆⣿⡿⠇⠄⠀
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣿⣿⣿⣿⣼⣿⣾⡇⣿⣧⣿⢧⢸⣿⣿⣾⣿⣹⣿⣠⢸⣿⣶⢸⣿⣾⣿⣿⣴⡿⠠⣨⠸⣧⣿⠗⠸⣿⣼⠟⠸⣿⠄⣿⠀⢿⣧⢿⡇⣿⣷⣦⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣄⣀⢠⣀⠢⠄⠀⠠⠀⠀⠐⡆⠀⢶⠀⠄⠤⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠐⠒⠀⠀⢀⣀⣀⣀⣀⡀⣂⣴⠤⣤⣄⠀⣀⢠⣤⠀⢀⠠⢀⡠⡀⠀⢀⠄⠀⠐⠄⠖
⢠⣤⣴⠦⠀⠀⠤⣌⠉⣣⠌⠩⠍⠁⠀⣩⣀⣀⣀⣀⢉⣉⣃⣤⣄⣬⣉⣍⣄⣤⣤⣄⣂⣀⣠⣤⡤⣴⣶⡖⢂⡐⠃⢃⢺⣬⣿⣫⣶⣶⣾⣿⣿⣿⣿⣽⣏⣀⡠⣸⣡⣀⢀⡄⠄⢀⡀⣄⡁⢲⢀⠖⠁⠀⠀⠀⠀⣖
⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⣏⢼⠋⠀⠭⠭⣿⣿⣿⣶⠀⠰⠆⠿⢿⣷⣥⣉⣉⣋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣵⣟⣏⣚⣧⡠⠒⢈⠂⠀⠀⠈⠀⠀⠄⠀⠈⠀⠁
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢹⣿⣿⡿⢿⣿⡿⢿⠆⠚⢻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠉⠉⠉⠉⠁⠀⠿⣿⣿⣿⣶⣶⡄⠉⣩⡜⠟⢿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠤⠤⣤⣤⣐⣒⣒⣀⡀⢤⣿⢎⡛⣛⣿⠁⠀⠀⠀⠐⠀⠠⣍⡉⠉⠈⡿⣿⣿⣿⣿⣿⣿⣿
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠮⠞⠒⠒⠒⠒⠒⠀⠀⠿⢻⠿⠎⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢻⡿⣿⣿⠿⣭⣽
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⣯⣉⡉⢙⣠
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢀⢤⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⢀⢐⣤⣢⡀⠀⠀⠀⠀⠹⠿⡿⠿⠻
⢼⣿⣿⣿⡿⠿⡿⠿⡿⠿⣿⠿⢿⠿⠿⢿⣿⠿⠿⣿⣿⠿⠿⠿⣿⢿⡻⠿⡽⠿⠶⠶⠽⠭⠹⣿⠿⠿⠿⡿⠿⡿⠟⠏⠉⠉⠀⠀⢶⠮⣹⢻⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠘⢮⣶⣯⠃⠀⠀⠀⠐⠻⠯⠰⠀⠈
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⢘⣿⡟⣿⣆⣿⣿⣿⣿⣿⡟⣯⢽⣿⢹⣷⢻⣿⢻⣃⣿⡟⣿⡎⣸⣿⣛⢸⣿⡼⣿⠘⣻⣿⠛⢸⣿⠛⢻⣿⠙⣷⠀⠀⢸⡏⠹⠆⢸⣷⢸⣿⢀⣿⠙⣷⠀⣾⡏⣿⡆⣿⡟⠃⠀⠀
⣽⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢸⣿⣷⣿⡇⣿⣟⣯⣿⣿⡿⣇⢸⣿⢟⣿⣿⣿⢿⡂⣿⡗⣿⡇⣾⣿⠗⢸⣿⣿⣿⢘⢺⣿⢀⢸⣿⠗⢸⣿⠀⣿⠀⠀⢨⡻⣷⡄⢸⣿⢸⣿⢸⣿⠻⣯⠀⣿⡷⣶⡆⣿⡿⡇⠲⠀
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⣯⣾⣿⣿⣿⣿⣿⣾⡇⣿⣧⣿⢧⢼⣿⣯⣾⣿⣹⣿⣠⢸⣿⣴⢸⣿⣿⣾⣿⣴⡿⢰⡄⠹⣧⣾⠗⠸⣿⣼⠟⠼⣿⠂⣿⠀⢿⣧⢿⡇⣿⣷⣦⠀⠀
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡄⠀⠄⠀⠀⡀⠀⠀⢠⠂⢰⡆⢠⢀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⣤⣤⣀⡀⠀⡀⣀⡀⠀⠀⠀⢀⠤⠀⡀⡀⠀⠀⢀⡤
⢠⣄⣀⡤⠀⠀⣀⣀⢒⢒⣀⡐⡚⠉⠈⠛⡉⠐⢁⢀⣐⣚⣑⣀⣀⣀⣈⣀⣀⣠⡄⣀⣀⠀⠀⡀⡀⢤⣀⡀⠔⠀⠄⠒⡐⣢⣽⣖⣒⣶⣶⣿⣟⣯⣿⠯⣯⣿⠁⢀⢼⣁⣈⣀⠨⠄⣀⢀⠀⠑⡄⡠⠊⠀⠀⠠⠄⣰
⢸⣿⣿⣿⣷⣶⣶⣾⣵⡾⢒⢐⡒⠀⠀⠬⣿⣿⣻⣶⡆⠈⠥⢲⣿⣯⣏⣉⢛⣛⣛⣿⡿⣿⣿⣿⣟⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣲⣶⣋⣀⠄⠒⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣴⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣶⣶⣶⣶⣶⣶⣶⣷⣶⣾⣾
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣹⣿⣿⡿⢿⣿⣿⣿⡯⠠⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠉⠉⠉⠉⠁⠀⡿⣿⣿⣿⣶⣤⡄⠐⠒⣐⠾⢿⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠤⠤⠤⠤⣤⣤⣐⣂⢡⣿⡏⠛⢻⡿⠃⠀⠈⠉⠀⠈⢁⡙⠛⠛⠙⢿⣿⣿⣿⣿⣿⣿
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠰⠭⠿⠷⠤⠤⠤⠄⢘⢻⢹⣿⣞⠿⠆⢀⠀⠀⠀⠀⠀⠀⠉⠐⠲⠋⠿⣿⣿⢿⣛⣛
⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢼⣏⣉⠒⠫
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⡠⢀⠤⡀⠀⠀⠀⠘⡿⠿⢿⠿
⣹⣿⣿⣿⡿⠿⡿⠿⡿⠿⣿⠿⢿⠿⠿⢿⡿⠿⠿⢿⣿⠿⠿⠿⣿⢿⡿⠿⠭⠟⠧⠼⠭⠯⠽⣿⠿⠿⠿⡿⠿⡽⠿⠛⠋⠉⠋⠀⠀⢨⢾⠹⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣞⣯⢿⡇⠀⠀⠀⠲⠿⠩⠅⠀
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⣿⢘⣿⡿⣿⡆⣿⣿⣿⣾⣿⡟⣧⣹⣿⢹⣷⢺⣿⢻⡇⣿⡟⣿⡎⢸⣿⣻⢸⣿⡽⣿⠘⢻⣿⠛⢸⣿⠛⢙⣿⠛⣷⠀⠀⢸⡏⠹⠆⢸⣿⢸⣿⠀⣿⠙⣿⠉⣾⡏⣿⡆⣿⡟⠃⠀⠀
⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿⣿⣿⢺⣿⣷⣿⡧⣿⣟⣯⣽⣿⡿⣇⢼⣿⣾⣿⢾⣿⢿⡂⣿⡇⣿⡇⢸⣿⡗⢸⣿⣿⣿⠀⢻⣿⠄⢸⣿⠖⢸⣿⠀⣿⠀⠀⠈⡻⣷⡄⢸⣿⢸⣿⢸⣿⠻⣯⠀⣿⡧⣶⡆⣿⡿⢇⠠⡀
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣯⣾⣿⣾⣿⣿⣿⣾⡇⣿⣧⣿⢇⢹⣿⣾⢸⣿⣼⣿⣠⢸⣿⣤⢸⣿⣷⣸⣿⣴⡿⡰⡤⠸⣧⣼⠟⠸⣿⣼⠟⠸⣿⠀⣿⠀⢿⣧⢿⡇⣿⣷⣤⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢠⠀⢄⡀⠀⣀⠀⠀⢰⡆⠀⣶⢀⡀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠠⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⣀⣀⡀⠐⢂⢂⣀⠐⠀⡀⣀⡀⠀⢀⢄⡀⠀⠤⡤
⢀⣄⣀⣠⡄⠀⢀⡀⠐⠒⣂⡀⢒⠓⠀⠋⠛⠑⠈⠉⠀⠒⢒⢆⣀⢂⣘⠓⡂⣀⣀⢀⡠⠀⠀⠀⡀⣀⣤⣀⠀⠄⠠⠄⠄⢒⣴⣶⣖⣴⣤⣵⣿⣻⣿⣟⣻⣿⡿⠋⠉⣹⡊⠁⢉⡁⠀⠀⡐⠈⢄⢁⠔⠁⠀⠀⠄⠀
⢸⣿⣿⣿⣷⣶⣶⣶⣷⣶⣖⣐⣒⠂⠀⣒⣻⣷⣾⣧⢅⠈⠹⢭⣿⣯⣯⡉⠛⢛⡛⣻⣿⣿⣿⣿⣞⣿⣿⣿⣾⣶⣶⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣶⠾⢷⡽⣁⣠⠌⠂⠉⠁⠈⠚⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣾⣾⣶⣤⣿⣿⣿⣿⣶⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣯⣿⣿⣿⣷⣶⣷⣤⣤⣴⣤⣴⣶⣶⣶⣶⣶
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣟⡋⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠉⠉⠉⠉⠉⠁⢸⣿⣿⣿⣦⣍⡍⠭⢭⠀⣼⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠣⠤⠤⠤⠤⠤⠤⠤⠀⢸⢹⡟⠻⠿⠿⡏⠀⠀⠛⠀⠈⠛⠸⠿⢿⢿⣿⣿⣿⣿⣿⣿
⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠐⠾⠭⠭⠭⠭⠭⠍⠙⢸⡯⣾⣞⢷⡆⠀⠀⠀⠀⠀⠈⠁⠂⠠⠄⢾⣿⣿⣿⣟⣛
⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣛⠓⠒⠝
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⡀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡀⢤⣄⠀⠀⠀⠀⣻⣿⣷⡿
⣽⣿⣿⣿⡿⠿⡿⠿⡿⠿⣿⠿⢿⠿⠿⢿⣿⠿⠿⢿⣿⠿⠿⠿⣿⢿⡿⢿⡟⠻⠯⢭⠭⠻⠛⣿⠿⠿⠿⡿⠿⡿⠿⠿⠟⠛⠛⠉⠀⠀⢘⢺⠹⣬⠄⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠰⡿⣏⢷⡇⠀⠀⠰⠶⠎⢠⠀
⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⢘⣿⡿⣿⡆⣿⣟⣿⣿⣿⡟⣧⣻⣿⢽⣷⢸⣿⢻⡋⣿⣟⣿⡎⢹⣿⢻⢼⣿⡽⣿⠘⢻⣿⠛⢸⣿⠛⢸⣿⠛⣿⠀⠀⢸⡏⠹⠇⢸⣷⢸⣿⢀⣿⠙⣿⠛⣿⡋⣿⡆⣿⡟⠃⠀⠀
⢻⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⢾⣿⣷⣿⡷⣿⣟⣯⣿⣿⡿⣇⢸⣿⣞⣿⢾⣿⢿⡂⣿⡏⣿⡇⣼⣿⠗⢹⣿⣿⣿⢀⢸⣿⡄⢸⣿⠗⢸⣿⠀⣿⠀⠀⠈⡻⣷⡄⢸⣿⢸⣿⢸⣿⠻⣯⠀⣿⡧⣶⡆⣿⡿⠇⠀⠄
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢾⣿⣿⣿⣧⣿⣿⣿⣿⣿⣷⣯⣾⣿⣼⣿⣿⣿⣾⡇⣿⣧⣿⢯⢻⣿⣿⢸⣿⣽⣿⢠⢸⣿⣤⢸⣿⣶⢼⣿⣴⡿⢠⣤⡸⣧⣾⠟⡼⣿⣼⠟⠸⣿⠀⣿⠀⢿⣧⢿⡇⣿⣷⣦⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠠⠀⢠⡀⠀⢀⠀⠀⠠⣖⠀⢴⡀⡀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠂⠤⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠂⡐⡀⡀⠀⣀⢀⢀⠀⠀⠀⡀⠄⠄⠠
⢀⣀⣀⣀⠄⠀⠀⣀⡀⠒⣒⡀⢐⡚⠀⠉⠛⠉⠈⠉⠀⠒⢒⣆⣀⡀⣐⠓⣒⣀⣀⢀⣀⠄⠀⠀⢀⣀⣠⢀⠀⠄⠀⠄⠠⢐⣠⣶⣖⣰⣤⣥⣿⣻⣿⣳⣳⣛⢋⣿⠟⠉⢻⡁⠈⡁⠀⠀⠀⠊⢥⠁⡤⠊⠀⠀⠀⠈
⢸⣿⣿⣿⣿⣶⣾⣶⣯⣶⠗⡒⣀⠂⠀⢒⣙⣷⣾⢷⡴⠈⠩⢭⣿⣿⣯⣉⠙⣛⡻⣻⣿⣿⣿⣷⣾⣿⣿⣿⣷⣶⣶⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣶⣦⡽⡿⣇⢠⠬⠑⠍⠁⠀⠘⠀⠀⡀⠀⠐⠀
⢸⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣾⣾⣶⣿⣶⣦⣾⣿⣾⣿⣶⣼⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣯⣿⣿⣷⣶⣾⣤⣤⣤⣤⣤⣤⣴⣶⣦⣶
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⢹⣿⣿⣿⣿⣿⣾⣿⣿⢛⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠋⠀⢸⣿⣿⣿⣭⣙⡛⣩⡍⠩⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠒⣒⣒⣒⣒⣒⣀⣀⡀⢻⡟⠿⣿⣿⡷⠀⠀⠛⠀⠈⠛⠹⠿⡿⣿⣿⣿⣿⣿⣿
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠂⠘⠒⠒⠒⠒⠒⠒⠀⠀⢸⢷⣶⣆⢶⡄⠀⠀⠀⠀⠀⠉⠉⠂⠠⠠⣿⣿⣿⣿⠛
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⠛⠒⠽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⢄⢀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡤⣀⠀⠀⠀⢻⣿⣷⣿
⣽⣿⣿⣿⡿⠿⡿⠿⡿⠿⣿⠿⢿⠿⠿⢿⣿⠿⠿⢿⣿⠿⠿⠿⣿⢿⡿⢿⠟⠿⠿⠭⠭⠻⠛⢿⠿⠿⠿⡿⠿⡿⠽⠿⠛⠋⠋⠉⠀⠀⠀⢠⢿⢹⣽⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⢸⣻⡹⣾⠀⠀⠀⠶⠖⢱⠀
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⢘⣿⡿⣿⡆⣿⣟⣿⣿⣿⡟⣧⣹⣿⢽⣷⢸⣿⢛⡃⣿⡟⣿⡎⢸⣿⠛⢼⣿⡽⣿⠘⢻⣿⠛⢸⣿⠛⢸⣿⠙⣿⠁⠀⢸⡏⠹⠆⢸⣧⢸⣿⢀⣿⠙⣿⠙⣿⡋⣿⡄⣿⡟⠃⠀⠀
⢿⣿⣿⣿⣿⣿⣼⣿⣽⣿⣿⣿⢼⣿⣷⣿⡧⣿⡟⣯⣿⣿⡿⣇⢸⣿⣞⣻⢾⣿⢿⡂⣿⡏⣿⡇⢽⣿⣗⢹⣿⣿⣿⢀⢸⣿⣤⢸⣿⠗⢸⣿⠀⣿⠀⠀⠈⡻⣷⡄⢸⣿⢸⣿⢸⣿⠻⣯⠀⣿⡧⣶⡆⣿⡿⠇⠀⡄
⢽⣿⣿⣿⣿⣿⣽⣿⣿⣿⣾⣿⢾⣿⣿⣿⣧⣿⣿⣿⣿⣿⣷⣯⣾⣿⣾⣿⣾⣿⣾⡇⣿⣧⣿⢧⢻⣿⣴⣸⣿⣼⣿⢠⢸⣿⣤⢸⣿⣶⣸⣿⣴⡿⢠⣤⡸⣧⣼⠗⠸⣿⣼⠟⠸⣿⠀⣿⠀⢿⣧⢿⡇⣿⣷⣤⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 1677

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/07/25/irc-log-240722/#comments
    Gemini version at gemini://gemini.techrights.org/2022/07/25/irc-log-240722/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.25.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ IRC_Proceedings:_Sunday,_July_24,_2022⠀✐


Posted in IRC_Logs at 2:11 am by Needs Sunlight


Also available via the Gemini protocol at:


    * gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-240722.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-240722.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-social-240722.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-240722.gmi
Over HTTP:


                                      🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H                                     🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇HTML5_logs⦈_


                                         #techrights_log_as_HTML5                                                                                  #boycottnovell_log_as_HTML5


                                      🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H                                     🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇HTML5_logs⦈_


                                    #boycottnovell-social_log_as_HTML5                                                                               #techbytes_log_as_HTML5


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


                                          #techrights_log_as_text                                                                                   #boycottnovell_log_as_text


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


                                     #boycottnovell-social_log_as_text                                                                                #techbytes_log_as_text


                          Enter_the_IRC_channels_now


===============================================================================
§ IPFS Mirrors⠀➾


CID                                              Description     Object type


                                                 IRC log for
 QmP4JowkXk9VxR8aaBVyXt4SUdQqxC5DT3pM4x39Na4ZA3 #boycottnovell  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell
 QmTY4ow6rnBu2QimJkNhMJ9T1EwJ2jREBxXt3f4HBSAuYZ (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
                                                 #boycottnovell-
 QmU97zzfi9sMfM5rY4HiSkzPoyZqvyyHNMkFvSnKTXremf social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


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§ Bulletin for Yesterday⠀➾


Local_copy | CID (IPFS): QmWkLbREwUBZdex6qeeh1UyUD3GwnNihMfEE28VhuPZYAK



                    ䷩ 𝚕𝚒𝚗𝚎 1804

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/07/25/magampinos-great-leap-forward/#comments
    Gemini version at gemini://gemini.techrights.org/2022/07/25/magampinos-great-leap-forward/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.25.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_The_EPO’s_Great_Leap_Forward⠀✐


Posted in Europe, Patents at 7:31 am by Dr. Roy Schestowitz


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


Summary: As seen in our latest EPO series, the EPO cannot distinguish/
differentiate a patent office from a bank


⡿⣽⣿⣿⣽⣽⣿⣽⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣯⣿⣟⣿⣝⣯⣿⣿⣿⡟⣯⢿⡝⣯⢿⢹⢹⢹⢻⣯⡿⠛⠉⠁⣀⠀⠀⠀⠀⠙⠿⣿⡗⡟⡟⡶⣶⣶⣶⣲⢲⢖⣖⡶⣶⡶
⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣾⣿⣽⣿⣿⣿⢿⡻⣿⣻⣽⣧⢿⡽⡞⣏⣏⣿⣿⡞⠀⣴⣿⣿⣿⣿⣿⣶⣦⠀⠀⢹⣿⢿⢿⢷⢿⢳⢷⢯⣏⢿⣟⣾⣼⡽
⣿⣷⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢷⣿⣯⡿⣿⢧⡿⣟⣿⣿⣞⣯⢷⣻⣹⣽⣽⣿⡇⢀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣾⡾⣟⣟⣯⢯⢯⢿⢯⢯⣾⢿⣾⣿
⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢩⢬⣓⡮⣝⡺⣽⠿⣿⣟⢯⣿⣽⣾⢿⡽⣞⣯⢿⢯⢷⣿⣿⣿⣼⣿⣅⣉⣿⣏⣁⣀⣹⡇⢀⣾⣷⢿⣻⣽⣞⢯⣯⣯⣫⣿⣫⣻⣿⣿
⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡩⢺⢽⣿⣷⣹⣷⢻⣿⣿⡷⣽⣾⣿⣻⣽⣞⣯⢿⣟⣾⣿⣿⣿⣿⣿⣿⡿⠟⣿⣿⣿⢟⣾⣿⣽⣯⢷⣽⣮⢯⣫⡻⣷⣷⣟⣿⣿⣿
⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⠿⡯⠻⠿⡆⠉⡻⣿⣾⣮⣿⣿⣿⣞⣞⣿⣾⣿⣿⣿⣿⣿⣿⣯⣍⠁⠈⠿⠏⢺⣿⣿⣿⣿⣳⣽⣯⡳⡿⣽⣿⣾⡻⣯⡿⣯
⣟⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡇⠀⣿⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣔⠀⡑⠀⠻⢦⣙⠻⢿⣿⣿⣿⣿⣿⣿⡿⠿⢛⣭⣿⠏⠛⢿⠿⠁⠀⢀⣨⡍⡛⠿⣿⣿⣮⣷⣽⢿⡺⣿⣿⣿⣿⣿⣷
⣏⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡇⠀⣿⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⣿⣿⣿⣯⣿⢿⡿⣿⣿⣿⡇⠈⠀⠀⠀⠀⠑⠙⠦⢀⠉⡙⢛⣫⠕⠪⠾⠟⠋⠁⠀⠀⠈⠂⠀⠀⠩⠉⠚⠿⠃⡀⠉⠻⣿⣿⣿⣿⣿⣝⣗⣿⣿⣿
⣧⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣧⣤⣿⣿⣿⣤⣼⣿⣿⣤⣼⣿⣿⣿⣿⣿⣷⣯⣷⢿⣻⣿⣿⣧⣄⠀⢀⣴⣶⣶⣶⣶⣶⣶⡾⣿⣷⣶⣶⣶⣶⣶⣶⢦⠀⠒⠀⠆⠀⠀⠀⠀⠀⠈⠙⠙⢦⢹⣿⣿⣿⣿⣿⣿⣿⣿⣟
⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡿⣿⣿⡿⣻⣿⡯⣿⢽⡿⣿⣿⢸⣿⣾⣶⣷⣾⣷⣾⡶⣷⣿⣿⣿⣶⣷⣶⣷⣾⡇⢰⣶⣶⣖⣶⠆⠀⠀⠀⠀⠋⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿⡷
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡯⣿⣿⣿⣿⣿⣿⡵⣿⣫⢗⣽⣫⣻⢿⢸⣿⣿⣿⣵⡷⠿⢷⡷⡾⡶⣿⣷⣿⣿⣿⣿⣿⡇⠸⠿⠿⠗⠐⠒⠀⠀⠀⠀⠀⠀⠀⣿⣿⣵⣿⣿⡿⣿⣿⣯
⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⡿⣻⣯⣯⣿⣾⡵⣿⢸⣿⣿⣿⣿⣷⣿⢾⣷⣷⣿⣿⣿⡿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣾
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣯⣿⣯⡾⣽⣯⣟⣿⣿⣸⣿⣾⣷⣿⣿⣶⢶⠿⠿⣶⠾⡿⣷⣷⣾⣿⣿⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿
⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢿⣽⣟⣿⣿⣿⣿⣷⣝⡿⠿⠿⠿⠿⠿⠿⠷⠷⠾⠿⠿⠿⠿⠿⠛⠁⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣻⣿⣾
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢱⢸⣿⣿⣿⡁⠀⠀⠨⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⣾⣿⣿⣿⣿⣿⣿⣿⡅⣀⣀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠟⠛⠿⣯⣿⣿
⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠘⢈⢿⣿⢉⣟⣻⣿⣀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠉⠘⠻⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⡄⠣⠀⢡⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠇⠛⠇⠁⠀⠈⣯⣿
⡿⣿⣿⣿⣿⣇⢧⢻⣿⣿⣿⡿⠗⠄⠘⢫⡻⠑⣿⣿⣿⡛⣿⣿⢯⠈⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⠿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣽⣯⣭⡅⢀⠁⠀⠀⠠⠀⠀⠀⣀⣀⠀⠀⠀⠐⠀⠀⠀⢸⢿⡆⠄⠀⠀⠀⠀⠛⣿
⣯⣿⣿⡩⢻⣿⣷⢱⡮⡻⣿⣿⢩⡧⣠⠈⠱⢀⠩⠙⢋⡕⣬⠑⠉⠇⠘⡉⢛⠀⠀⢸⢛⣿⡬⠿⣳⠓⠆⠫⠿⣿⡟⠿⠟⠛⠙⣿⣯⠿⡀⠚⠖⠆⣀⡀⠤⠀⠀⡉⠿⡿⣶⣶⣶⣶⠀⠀⠈⠛⠳⠄⠀⠀⠀⠀⠀⠈
⡷⢾⣿⣿⣻⢻⡅⡅⣙⢷⢮⠉⠠⠑⠈⢓⡀⡆⠀⠀⠒⠀⢣⠿⡷⣌⠰⠂⢀⣀⣀⢛⠁⠁⠀⢀⣮⢉⣴⠀⠀⠈⠀⠀⠀⠀⣰⣿⢁⡾⠀⠀⠀⠀⠀⣴⢡⡶⠋⠀⠀⠀⠐⢦⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣟⣻⣿⣿⣿⡜⠑⣚⢼⡭⡪⠀⠀⠀⠀⠸⢿⢇⠦⠶⠶⠈⡦⡰⡈⠋⢷⣅⠙⠑⡸⠇⠀⠀⠀⣼⡟⢸⣿⠀⠀⠀⠀⠀⠀⢠⣿⣿⣼⠇⠀⣀⠀⡴⣣⣳⠏⠀⠀⠀⠀⢀⠀⠀⣿⣿⣿⣷⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡔⠹⠦⠧⣮⠀⠀⠀⠀⠀⠘⡸⠀⡀⡀⣄⣨⡈⢠⠀⠹⣿⢗⠀⠁⠀⣠⣤⣾⣿⣿⣾⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠀⠈⠀⠐⠟⢹⠁⢀⠀⠀⠀⠀⠀⠀⠀⠽⣿⠟⡟⣼⡀⠁⠀⠀⠀⠀⠀⠀⠀
⣿⢿⣿⣿⣿⣿⣿⡀⠀⠀⠘⣷⠀⠀⠀⠀⢰⠋⠦⠀⢉⣩⡽⣷⠀⠀⠂⠀⣸⣤⣤⣒⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣾⣿⣿⣿⠁⠀⠀⠀⢀⡄⠀⠀⠿⠀⠀⠀⠀⠒⢳⠀⠈⡤⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 1853

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/07/25/nontechnical-security-talking-points/#comments
    Gemini version at gemini://gemini.techrights.org/2022/07/25/nontechnical-security-talking-points/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.25.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Inside_the_Minds_of_Microsoft’s_Media_Operatives_—_Part_III_—_Attacking_Real
Security,_Promoting_Lies_and_Fake_‘Security’⠀✐


Posted in Deception, Microsoft, Security at 9:35 am by Dr. Roy Schestowitz


Series parts:


   1. Inside_the_Minds_of_Microsoft’s_Media_Operatives_—_Part_I_—_Bishops_in
      Rooks
   2. Inside_the_Minds_of_Microsoft’s_Media_Operatives_—_Part_II_—_Justifying_a
      Career_as_a_Microsoft_Mouthpiece_That_Destroys_Lives_of_People_With
      Actual_Facts
   3. YOU ARE HERE ☞ Attacking Real Security, Promoting Lies and Fake
      ‘Security’
                 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Microsoft_dirty_tactics⦈_


Summary: Nontechnical talking points from Microsoft ‘suits’ and paid ‘analysts’
are promoted by veiled media operatives which saturate the pool of news and end
up reducing the signal-to-noise ratio, in effect spreading disinformation (fake
news) on behalf of Microsoft so as to hide from very simple (albeit
uncomfortable) facts; habitually they also misplace blame (offloading
culpability for malware to “Linux”) in order to shift the public’s attention,
partly because GNU/Linux and BSD are optimal alternatives for security-minded
governments/enterprises


A number of days ago we published Part_II, which was read by a lot of people. A
lot more than expected anyway. We’re running two Microsoft series at the moment
(at the same time), so we expect this current one to take a fortnight or so
longer before it’s entirely over. In Part II, for those who have missed it, we
explained (or rather showed strong evidence) that Microsoft whistleblowers are
fighting with Microsoft operatives who work in so-called “tech” (myth) media,
challenging them not just over the lies they help spread, by and for Microsoft.
As it turns out, those Microsoft operatives are moreover burning sources, in
effect smoking them out or sniffing them up for Microsoft. This is not
acceptable and we need to talk about it. We must, at the very least, raise
awareness. This is not just unethical but a breach of journalists’ professional
standards. It is misconduct. Microsoft is replacing actual journalism with
churnalism (more on that in Part IV when it’s ready).


Today, in Part III, we’ll focus on security aspects and how Microsoft
operatives in the media warp the debate to deflect or distract from Microsoft’s
extreme incompetence and abject failures. We’ll mostly quote the whistleblower,
without interjecting any of our own interpretation (Edward_Snowden’s_leaks
helped_prove_that_Microsoft_does_not_at_all_strive_to_ensure_security; real
security is not the ultimate objective).


We’d like to point out (in case it’s a recurring pattern) that the so-called
‘journalists’ (Microsoft mouthpieces in “reporter” clothing) go out of their
way to pretend they’re objective, unbiased, fair etc. Don’t fall for it. They
pretend to be all nice and welcoming. So upfront, we’d like to quote the
“source burner” (pretending to be abundantly cordial after destroying someone’s
career to suck up to his masters at Microsoft, who reward or reciprocate with
“access” and money*): “We can’t promise to publish anything without seeing it
first, and we rarely publish guest commentaries, but I’d be happy to hear more
about what you’d like to write, or take a look at a draft. I would need to go
back and find our specific guidelines, but some of the basics are that they
need to be relevant and valuable to the broader community of readers, grounded
in provable fact, not self-promotional, not libelous, etc. Please let me know
what you have in mind.”


To put it in very simple terms, what he’s saying is, they’ll weed out anything
Microsoft and its mindset don’t agree with, in the name of “facts”. As if
Microsoft was ever known for uttering facts…


An associate explains that “weed out” (as worded above) “is the wrong verb
there, since it looks like they are not weeding out anything Microsoft but
weeding out anything disfavorable to Microsoft.”


“That’s totally fair and I wasn’t expecting otherwise,” the whistleblower said,
but “I’ve actually been working on a continuation of Strassmann’s and later my
own work on Microsoft’s present state of complexity, defect, and consequent
monopoly on ransomware infections/zero days as a national security threat. I’d
also like to highlight that Microsoft’s architecture is not only expensive to
mange and vulnerable to exploit due to their sheer complexity and level of
defect but that it’s grown to a place where we don’t have enough nearly experts
to implement, manage, support, and secure it.”


Knowing it from first-hand experience, having also witnessed incidents that
Microsoft attempted to cover up or simply lied about (after the public found
out).


To quote further: “I can support this empirically with the sheer amount of
vacant IT jobs in this country (600,000 for cybersecurity alone), Microsoft’s
major uptick in non-feature updates over the years, and with Microsoft’s hyper-
monopoly on <insert any major threat vector here>. And I can approach it a
priori by way of the fundamentals of defect density (thermodynamics) as this
outcome is actually predictable, but it may take 2,000-2,500 words due to
having to backfill readers on a few fundamental aspects of IT finance and
software engineering.”


There’s more coming about this and we’ve published articles on the subject in
the distant past.


“Alternatively,” the whistleblower said, “I can write an article about how
Microsoft’s partners and consultants seem to operate on a conflict of interest
by recommending defective products that generate their long-term necessity the
most while avoiding solutions that benefit their clients more while naturally
necessitating less of their services. I can also highlight_where_Microsoft_has
publicly_instructed_it’s_partners_to_deploy_their_services,_create_stickiness
to_be_exact,_so_as_to_entrench_their_services_and_maximize_switching_costs_and
highlight_how_they_deleted_this_after_I_reported_on_this_before.”


Readers can guess if this resulted in an actual article published in the
Microsoft-affiliated site. It’s all pretence. They’re not open to new/opposing/
factual ideas. “Especially if it contradicts Microsoft or its agenda,” as an
associate adds. It’s like religion, not science.


A day passed and the source burner just said (direct quote): “This is a lot to
digest. I’m going to need to spend more time reading it, and exploring some of
the links you’ve referenced. Since you raise the security issue, have you read
this story? [Linking to his own Microsoft puff piece about Microsoft] I’d be
interested in hearing how this squares with your perception of [redacted]‘s
coverage of the company. What did I miss? Do you feel that I let the company
off too easily? How would you have approached a story on this topic?”


So he barely bothered reading what was actually said (it “is a lot to digest”).
Instead, he pushed his own new article, a new pile of fluff (redacted to avoid
names becoming too obvious). They’re impenetrable to dissent, they just keep
parroting their own (and Microsoft’s) lies. This is what keeps them at this
job, Public Relations and source burning spun as “journalism”.


A response came a day later: “I’ve actually danced around this topic
extensively over the past 4 or so years. It’s actually a major problem given
Microsoft’s reach and lack of adequate response [1, 2, 3, 4, 5, 6] (no idea
what Hackernoon was thinking with that high contrast/bright green background
btw, I have no control over this)”.


Unlike the fake “journalist” (Microsoft operative), the whistleblower did in
fact read what was sent and responded in great length:


     With regard to your article:


     It still reads like executive fan fiction to some degree if I’m being
     honest. Like many other articles, it seems to overlook how much
     influence corporate counsel has at this level; execs tend to be
     figureheads that do as they’re told and this is especially true at
     Microsoft. And even when that isn’t the case, executives at this
     level are too crippled by plausible deniability to lead effectively;
     you never see them out in the halls interacting with the commoners or
     getting their hands dirty. It looks mostly like leadership theater to
     me where the people less likely to be hands on with any problem are
     being presented as champions of said problems. In reality their orgs
     are probably hanging on by a thread made of a few competent vendors
     that they probably can’t put a name or a face to.


     I’m also not sure how geriatrics in the technology space are viewed
     as its saviors and leaders. Just like American politics where the
     least fit and capable of us seem to rise to the top, the same is true
     of tech monopoly leadership; not just as Microsoft. But I digress.


     Secondly, Windows is old, defect density/software_entropy are things,
     and there are no shortages throughout the Windows ecosystem to
     correlate their defect density going out of control. A few obvious
     examples besides the aforementioned IT labor shortage (40 million+ IT
     professionals globally isn’t enough apparently) can be found in their
     their non-feature update velocity which has skyrocketed by 5x over
     the past 6 years (135 in Win 7 SP1 in 2015 vs. 1000+ in 2021).
     Windows rate of exploit has also skyrocketed while its stability has
     plummeted and it’s TCO has consequently skyrocketed even further
     beyond <insert any flavor of linux here) or MacOS which are already
     1/3 of what Microsoft is.


     Most don’t argue with this but they also don’t always realize the
     implications of this. These aren’t just problems that can be
     engineered out of existence. One problem with bugs is that they are
     50-10000x more expensive for software firms to remedy once they hit
     production as opposed to when they’re caught in pre-production by QA
     and peer review. In other words, Microsoft has a mountain of
     technical debt and its highly likely that its more cost effective and
     prudent to rebuild Windows from the ground up than fix it. This is
     why I’ve speculated in the past that they’re likely working on their
     own flavor of Linux to replace Windows as this would satisfy this
     exact need while further explain them joining of OIN. A good visual
     on the lifespan of software can be found below: [redacted]


     Most software engineers overlook defect density as it’s a rare/
     abstract area of study but I can’t because I have an applied
     understanding of it from my work with it at Microsoft. And it is not
     my expectation of journalists to know much, if anything about it.
     Meanwhile, few entities in the world know more about it than
     Microsoft which is where I learned about it; it’s not even covered in
     academia and was pioneered by Capers Jones and others at IBM.


     Another roadblock in the way of Microsoft addressing its defective
     ways is its partner-centric business model that heavily incentivizes
     them to let their defect density run out of control. 95% of
     Microsoft’s commercial revenue comes from their partners who resell
     Microsoft solutions due to them having the highest resale margins
     while also driving the most revenue for their firms (IT consulting &
     Managed Services Providers) after purchase in the form of
     implementation, management, and support services. Meanwhile, simpler,
     less defective, more secure solutions generate less revenue after
     purchase and are consequently given less priority among Microsoft
     partners because they’re less profitable. As such and so long as
     businesses continue to trust the opinions of Microsoft partners,
     Microsoft has little to no incentive besides governmental pressure to
     stop printing its own checks so to speak by letting it’s defect
     density spiral out of control.


     Strassmann’s article relating Microsoft’s monopoly to the same
     problems mono croppers experience linked in my previous [above] email
     is still as relevant to this matter today as it was in 1998.


     Additionally and when looking at their defective and clumsy nature,
     lots of people look at Microsoft take Microsoft for buffoon on face
     value. But they’re overlooking the fact that Microsoft has such a
     profound understanding of business, lock-in, partner strategy, and
     software that they found a way to monetize defective software while
     not having to worry much about quality. This is why their market cap
     can increase in proportion to their defect density.


     And I’m also not exactly seeing any specific commitments or
     strategies in this article, let alone any that are going to help
     Microsoft make headway against their defect and consequent security
     issues. Most of it is just hollow promises from a bunch of industry
     relics who probably can’t even tell you what information or
     technology is. Nor has their trajectory changed in the time since
     this article was published; almost like it’s the same company as
     before.


“Strassman’s_most_famous_article ought to be highlighed more,” an associate
concludes. Strassman was very high profile. He already explained these issues
two and a half decades ago. His article rattled Microsoft so badly that Bill
Gates went to see him in person and refused to even pay for his own lunch, as
Strassman recalls! █


“Our products just aren’t engineered for security.”


                                          –Brian Valentine, Microsoft executive


_____
* As someone put it, Microsoft “tends to freeze out “journalists” that don’t
toe the line, so over time they become more obedient and compromised until they
are so bad that they lose credibility and then they are discarded.” Techrights
showed a lot of evidence of it in past years.


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Gemini_version_available_♊︎


✐ Links_25/07/2022:_Berlin_Mini_GUADEC_2022,_DebConf23_Dates_Announced⠀✐


Posted in News_Roundup at 5:58 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Audiocasts/Shows
          o Kernel_Space
          o Applications
          o Instructionals/Technical
    * Distributions_and_Operating_Systems
          o SUSE/OpenSUSE
          o Fedora_Family_/_IBM
          o Devices/Embedded
    * Free,_Libre,_and_Open_Source_Software
          o Events
    * Leftovers
          o Freedom_of_Information_/_Freedom_of_the_Press
          o Digital_Restrictions_(DRM)
    * § GNU/Linux⠀➾


          o ⚓ Hacker Noon ☛ An_Overview_of_the_Linux_Operating_System_for
            Beginners_|_HackerNoon⠀⇛


                 Linux is an open-source operating system that is used for
                 computers, servers, mainframes, mobile devices, and
                 embedded devices. Linux is one of the most widely
                 supported operating systems as it is available on almost
                 every major computer platform, including x86, ARM, and
                 SPARC.


                 There are several Linux OS versions available: each
                 version manages hardware resources, launches and handles
                 applications, and provides some sort of user interface.
                 Linux has been used in different ways for web servers,
                 network operations, specific computing tasks, running
                 databases, endpoint computing, and running mobile devices
                 with OS versions like Android.


          o § Audiocasts/Shows⠀➾


                # ⚓ Jupiter Broadcasting ☛ The_Read_Only_Scenario_|_LINUX
                  Unplugged_468⠀⇛


                       A fundamental change is coming to desktop Linux,
                       and Silverblue might be our hint at where things
                       are going.


          o § Kernel Space⠀➾


                # ⚓ InfoQ ☛ New_Asahi_Linux_Release_Brings_Support_for_Apple_M1
                  Ultra_and_M2_CPUs⠀⇛


                       When Apple adopted their new ARM-based CPUs
                       collectively dubbed Apple Silicon, it made all
                       existing Linux distributions incompatible with its
                       most recent hardware. This is changing thanks to
                       the hard work of the Asahi Linux team, that
                       recently introduced preliminary support for Apple
                       M1 Ultra and M2 CPUs.


                       The new release follows closely the first alpha
                       made available last March for M1, M1 Pro, and M1
                       Max machines. Being alpha, that release did not
                       support all features you usually take for granted
                       in a kernel, including GPU, Bluetooth, HDMI, Touch
                       Bar, and others.


          o § Applications⠀➾


                # ⚓ Medevel ☛ 12_Open-source_Free_LAN_Chat_and_Messenger_Apps
                  for_Windows,_Linux,_macOS,_and_Android⠀⇛


                       While working on a local network, network users
                       often want to communicate locally, without the need
                       of an internet connection.


                       In this case, they will need a LAN messenger, that
                       allows network users to exchange messages and files
                       locally, without the need of a centralized server.


                       In this article, we offer you several open-source
                       free LAN messenger that can be installed, and used
                       totally free of charge for anyone.


                # ⚓ Its FOSS ☛ Koodo_is_an_All-in-one_Open_Source_eBook_Reader
                  for_Linux⠀⇛


                       There are several ebook readers available for
                       desktop Linux users.


                       Almost all distributions come with a document
                       reader that can open PDF files. It may also support
                       other file formats like epub or Mobi, but that’s
                       not guaranteed.


                       This is why specialized applications like Foliate
                       and Calibre are needed to read and manage ebooks in
                       various formats.


                       Recently, I came across another open source
                       software that boasts several exciting features for
                       an ebook reader.


                # ⚓ Linux Links ☛ Best_Free_and_Open_Source_Alternatives_to
                  Oracle_Business_Intelligence⠀⇛


                       
                       The company co-develops the OpenJDK, an open source
                       implementation of the Java Platform Standard
                       Edition, and Btrfs, a B-tree file system. They also
                       open source the Oracle Coherence Community Edition,
                       NetBeans, and produce Oracle Linux which is a Linux
                       distro compiled from Red Hat Enterprise Linux
                       source code.


                       While Oracle develops and distributes open source
                       software, they have many different business models.
                       The majority of their products are published under
                       a proprietary license. This series looks at free
                       and open source alternatives to Oracle’s products.


          o § Instructionals/Technical⠀➾


                # ⚓ ID Root ☛ How_To_Install_uGet_Download_Manager_on_Ubuntu
                  22.04_LTS_–_idroot⠀⇛


                       In this tutorial, we will show you how to install
                       uGet Download Manager on Ubuntu 22.04 LTS. For
                       those of you who didn’t know, uGet is a free,
                       lightweight, and open-source download manager for
                       Linux users that speeds up the download process.
                       It’s a perfect utility for those who want to
                       download large files on their system. It can easily
                       download multiple files at a time and gives you the
                       option to queue them for faster downloading. It is
                       a popular multi-platform application that supports
                       various operating systems like Mac, Windows, Linux,
                       and also the Mobile phone.


                       This article assumes you have at least basic
                       knowledge of Linux, know how to use the shell, and
                       most importantly, you host your site on your own
                       VPS. The installation is quite simple and assumes
                       you are running in the root account, if not you may
                       need to add ‘sudo‘ to the commands to get root
                       privileges. I will show you the step-by-step
                       installation of the uGet Download Manager on Ubuntu
                       22.04 (Jammy Jellyfish). You can follow the same
                       instructions for Ubuntu 22.04 and any other Debian-
                       based distribution like Linux Mint, Elementary OS,
                       Pop!_OS, and more as well.


                # ⚓ Red Hat Official ☛ How_to_generate_a_Red_Hat_Enterprise
                  Linux_9_image_with_MicroShift_|_Enable_Sysadmin⠀⇛


                       I was involved in a demo of Red Hat Enterprise
                       Linux (RHEL) for Edge, using MicroShift and
                       ImageBuilder, and I experienced some problems with
                       the network driver for Raspberry Pi 4 in RHEL 8. To
                       solve this problem, I decided to create a custom
                       image based on RHEL 9 instead, and in my previous
                       article, I explain how I did that. If you haven’t
                       read that article, please read it before continuing
                       with this article.


                       (Note: At the time of this writing, there is no
                       RHEL version for Raspberry Pi. RHEL for ARM is
                       available only for larger 64-bit ARMv8 platforms.
                       However, this is based on a demo, and if you need a
                       supported Linux system, try Fedora on Raspberry Pi.
                       Fedora 29 and later supports the Raspberry Pi Model
                       2B- and 3-series of devices, including the 3B, 3B+,
                       3A+, 3CM and 3CM+.)


                # ⚓ H2S Media ☛ How_to_install_Supertuxkart_Game_on_Ubuntu
                  22.04_LTS⠀⇛


                       Install SuperTuxKart on Ubuntu 22.04 LTS Jammy
                       JellyFish using the command terminal to start
                       playing the game on your Linux.


                       SuperTuxKart is a free 3D kart racing game more
                       about fun than realism. The goal of the game
                       remains to be the first to cross the finish line if
                       possible. There are 12 race tracks, time, single,
                       and Grand Prix races as well as a multiplayer mode
                       via split screen, via the Internet, and in the
                       local network available. In addition, there are
                       plenty of additional karts and tracks as add-ons.


                       It is an enhanced version or a fork of an earlier
                       developed game called the TuxKart racing game. In
                       comparison to the TuxKart comparison, it adds more
                       new roles and the race route, a new interface, as
                       well as some small graphical improvements. It’s a
                       fun competitive game that focuses on fun and ease
                       of use.


                # ⚓ Simple_Fix_No_Sound_Issue_in_Ubuntu_22.04_with_ESSX8336
                  Sound_Card_–_LateWeb.Info⠀⇛


                       Sound does not work in your Ubuntu 22.04, and
                       happen to have Everest ESSX8336 sound card in your
                       machine? This tutorial may help!


                       ESSX8336 is one of the common used chips in recent
                       laptops and tablets, such as Huawei Matebook
                       D14~16, Gemini Lake laptop, and Chuwi Hi10X tablet.
                       But, the current Linux Kernel does not support this
                       sound card, though there seems to have patches
                       (here and here) for it.


                       Until Linux Kernel officially adds the device
                       support, you may build Kernel manually with the
                       patch. Or use yangxiaohua’s custom kernel files to
                       fix the issue.


    * § Distributions and Operating Systems⠀➾


          o § SUSE/OpenSUSE⠀➾


                # ⚓ SUSE’s Corporate Blog ☛ Navigating_the_rapidly_evolving
                  world_of_retail_|_SUSE_Communities⠀⇛


                       In today’s highly competitive post-Covid retail
                       landscape, efficient operations which enable
                       retailers to deliver the most competitive prices
                       and enhance customer experience, have become
                       essential to the sector.


                       Retail organisations that can adapt quickly to
                       market changes and enhance customer services,
                       whilst reducing operating costs, are the companies
                       that will grow and prosper – whilst other market
                       participants risk crumbling under increased
                       competition from online retailers.


          o § Fedora Family / IBM⠀➾


                # ⚓ Enterprisers Project ☛ Who_is_buying_edge_computing?_These
                  6_key_roles⠀⇛


                       It’s long been recognized that IoT and edge
                       computing require more than just Information
                       Technology (IT) involvement. After all, the data
                       being collected, analyzed, and driving decisions as
                       part of an edge architecture is associated with an
                       organization’s physical assets – whether the
                       machine is on a factory floor or components of an
                       electric utility delivery system. As a result, it
                       has become common to talk about IoT as a
                       partnership between IT and their Operational
                       Technology (OT) counterparts.


                       However, just talking about IT/OT oversimplifies
                       how edge solutions are approached, evaluated, and
                       selected within an organization. In practice, there
                       are many stakeholders. To explore this topic at a
                       more granular level, Red Hat commissioned a survey
                       by Frost & Sullivan of over 1,000 decision-makers
                       across discrete, process, and automobile
                       manufacturing – as well as oil/natural gas and
                       utilities – to better understand their involvement
                       in the role or persona in edge computing. The
                       respondents were drawn from North America, Germany,
                       China, India, and Japan.


                # ⚓ Enterprisers Project ☛ Digital_transformation:_8_guiding
                  principles⠀⇛


                       Since COVID-19, the shift to remote work has
                       influenced many organizations to invest in digital
                       transformation initiatives at warp speed. With
                       little to no time for strategic planning or
                       preparation, the onset of the pandemic served as an
                       accelerator for companies and CIOs to establish new
                       business models that prioritize and deliver
                       efficiency, flexibility, and speed.


                       With remote and hybrid work now considered the
                       norm, more enterprises are adjusting to this new
                       reality by adopting a digital service mindset and
                       embracing forward-thinking ways to stay ahead and
                       future-proof their business. Even with businesses
                       optimistically moving forward to keep up with the
                       rapid pace of digital transformations, 70 percent
                       of these initiatives unfortunately still fail.


          o § Devices/Embedded⠀➾


                # ⚓ CNX Software ☛ EM_PRO_mini_–_An_AMD_Ryzen_Embedded_R1102G
                  fanless_mini_PC_–_CNX_Software⠀⇛


                       E.E.P.D. EM PRO mini “eNUC-BoxPC” is a mini PC
                       powered by a 6-watt AMD Ryzen Embedded R1102G dual-
                       core processor and designed for a variety of
                       applications such as thin client, network
                       monitoring, production data acquisition, digital
                       signage, point-of-sale, building management
                       systems, and so on.


                       The embedded fanless mini PC ships with up to 16 GB
                       DDR4 RAM, supports M.2 SATA or NVMe storage, and
                       offers two mini DisplayPort video outputs, three
                       USB 3.1 ports, and two Gigabit Ethernet ports, as
                       well as serial ports. The mini PC offers 8V to 32V
                       input voltage suitable for automotive applications
                       and can operate in the 0°C to 50°C temperature
                       range, although a wider range can be worked on upon
                       request.


                # ⚓ CNX Software ☛ Compact3566_–_A_Rockchip_RK3566_SBC_that
                  closely_follows_Raspberry_Pi_3_form_factor⠀⇛


                       
                       We’ve very recently written about Geniatech XPI-
                       3566 SBC powered by Rockchip RK3566 CPU that
                       somewhat follows the Raspberry Pi 3 Model B form
                       factor. Boardcon Compact3566 offers similar
                       features, but it appears to keep exactly the same
                       port assignment as the Raspberry Pi SBC, so it
                       should be compatible with more accessories.


                       The Compact3566 SBC ships with up to 8GB LPDDR4 and
                       128GB eMMC flash, features Gigabit Ethernet & WiFi
                       5, four USB 3.0/2.0 ports, HDMI 2.0 output, MIPI
                       DSI and CSI interfaces, the 40-pin GPIO header, as
                       well as extra built-in features such as an M.2
                       socket for storage, RTC with battery, and a built-
                       in microphone.


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


          o ⚓ Document Foundation ☛ Community_Member_Monday:_Juan_C._Sanz_–_The
            Document_Foundation_Blog⠀⇛


                 Today we’re chatting with Juan C. Sanz, who helps out in
                 many LibreOffice projects: documentation, translations,
                 user help and more…


                 Tell us a bit about yourself!


                 I live in the city of Logroño, in the autonomous
                 community of La Rioja (famous for its wines), in the
                 north of Spain. Although I like reading a lot, my main
                 passion is computers in general.


                 Almost all the time I have been working as a helicopter
                 engineer, but due to my passion, while I was working, I
                 studied to get a degree in Computer Science (Programming)
                 and I was working as a programmer for a while without
                 leaving my main job with helicopters.


                 When did you join the LibreOffice community, and how was
                 the experience?


                 I like to say that I have been collaborating with
                 LibreOffice since before LibreOffice existed and it is
                 really true, how is that possible?


                 Well, my history with LibreOffice started, like many of
                 us, in OpenOffice.


                 When I discovered the existence of OpenOffice I loved
                 both the program and the possibility of getting it for
                 free (then I didn’t know about FLOSS – I thought only
                 about “gratis”). But at the same time, I realized that
                 there was no documentation available in Spanish. While
                 searching, I came across that phrase, which I don’t
                 remember exactly, but it says something like “if you
                 can’t find what you want, collaborate to make it”, so I
                 joined the OpenOffice documentation team at ODFAuthors
                 and there, together with a mini-team (I don’t think there
                 were more than a couple of active collaborators at that
                 time) I started translating the Getting Started Guide
                 into Spanish.


          o § Events⠀➾


                # ⚓ Berlin_Mini_GUADEC_2022_|_Adrien_Plazas⠀⇛


                       Wow it’s been ages since I last attended a
                       conference in-person and since I last blogged.


                       I’m on my way back form Berlin Mini GUADEC 2022,
                       and it was delightful! I’ve been able to meet pals,
                       colleagues and comrades, old and new! The location
                       was great, it’s a really cool hackerspace called c-
                       base, decorated like a sci-fi spaceship with a
                       gigantic 40×16px screen made out of old bottles of
                       Club Mate.


                # ⚓ Berlin_Mini_GUADEC_2022⠀⇛


                       The GUADEC is back!


                       This year, the famous GNOME developers meeting
                       event, the GUADEC, gets back to “normal” after the
                       last year global COVID-19 situation. And when I say
                       normal, I’m talking about people meeting in one
                       place to share knowledge and to build a great
                       community around this great software project.


                       This year the even was in Guadalajara, Mexico, and
                       that’s great, but a bit far to go from Spain… But
                       thankfully, some of GNOME folks who can’t go to
                       Mexico organized a parallel event to attend
                       remotely in Berlin, Europe, that’s the Berlin Mini
                       GUADEC.


                # ⚓ DebConf22_closes_in_Prizren_and_DebConf23_dates_announced_–
                  Bits_from_Debian⠀⇛


                       On Sunday 24 July 2022, the annual Debian
                       Developers and Contributors Conference came to a
                       close. Hosting more than 210 attendees from 38
                       different countries over a combined 91 event talks,
                       discussion sessions, Birds of a Feather (BoF)
                       gatherings, workshops, and activities, DebConf22
                       was a large success.


                       The conference was preceded by the annual DebCamp
                       held 10 July to 16 July which focused on individual
                       work and team sprints for in-person collaboration
                       towards developing Debian. In particular, this year
                       there have been sprints to advance development of
                       Mobian/Debian on mobile, reproducible builds and
                       Python in Debian, and a BootCamp for newcomers, to
                       get introduced to Debian and have some hands-on
                       experience with using it and contributing to the
                       community.


                       The actual Debian Developers Conference started on
                       Sunday 17 July 2022. Together with activities such
                       as the traditional ‘Bits from the DPL’ talk, the
                       continuous key-signing party, lightning talks and
                       the announcement of next year’s DebConf (DebConf23
                       in Kochi, India), there were several sessions
                       related to programming language teams such as
                       Python, Perl and Ruby, as well as news updates on
                       several projects and internal Debian teams,
                       discussion sessions (BoFs) from many technical
                       teams (Long Term Support, Android tools, Debian
                       Derivatives, Debian Installer and Images team,
                       Debian Science…) and local communities (Debian
                       Brasil, Debian India, the Debian Local Teams),
                       along with many other events of interest regarding
                       Debian and free software.


    * § Leftovers⠀➾


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


                # ⚓ uni Oxford ☛ As_many_journalists_come_under_attack,_TRF
                  launches_a_free_tool_to_monitor_online_abuse_|_Reuters
                  Institute_for_the_Study_of_Journalism⠀⇛


                       Brazilian journalist Daniela Pinheiro will never
                       forget the moment when a troll army managed to get
                       her daughter’s photographs and posted them online.
                       An award-winning reporter and the first woman who
                       became editor-in-chief of a national publication,
                       Pinheiro became the target of a vicious harassment
                       campaign after publishing a story about Jair
                       Bolsonaro’s daughter-in-law. As a result, she
                       resigned from her position at Época magazine along
                       with some of her colleagues in September 2019.


                       “When you are under threat, you are always nervous
                       and super alert, and you can’t do your work or live
                       your life normally,” Pinheiro said. “They called me
                       a whore and a cow, and terrible names to imply some
                       kind of sexual connections. For some time, I didn’t
                       allow my daughter to get out of the house. And for
                       almost two years, I stopped writing. I couldn’t
                       write.”


                       A few months after her resignation, Pinheiro spent
                       a few months in Oxford as a Journalist Fellow of
                       the Reuters Institute and tried to figure out what
                       to do next. Was it really worth writing again about
                       what was happening in Brazil? She decided it was.
                       But she left her home country and started a new
                       life abroad. “I keep receiving attacks, but I feel
                       more protected because I’m living in Portugal,” she
                       said. “I decided to move here because of the
                       attacks.”


                # ⚓ Gizmodo ☛ Experts_Blast_Meta_Human_Rights_Report_as
                  ‘Propaganda’⠀⇛


          o § Digital Restrictions (DRM)⠀➾


                # ⚓ Trend Oceans ☛ Watching_Netflix_on_Linux_with_Chrome/
                  Firefox_–_TREND_OCEANS⠀⇛


                       Netflix is a popular video streaming platform,
                       hosting more than 3,600+ movies and 1,800 TV shows.
                       Currently, Netflix has the highest number of
                       subscribers among its counterparts, Prime and Hulu.


                       To watch the movies or shows on Netflix, you
                       usually download an Android app, and Windows users
                       have a standalone application on the Microsoft
                       store. What about Linux users?


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



                    ䷩ 𝚕𝚒𝚗𝚎 2789

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⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.25.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_25/07/2022:_Mozilla_Firefox_103_and_GNU_poke_2.4⠀✐


Posted in News_Roundup at 4:22 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Desktop/Laptop
          o Server
          o Audiocasts/Shows
          o Applications
          o Instructionals/Technical
          o Desktop_Environments/WMs
                # K_Desktop_Environment/KDE_SC/Qt
                # GNOME_Desktop/GTK
    * Distributions_and_Operating_Systems
          o Fedora_and_IBM
          o Debian_Family
          o Devices/Embedded
          o Open_Hardware/Modding
          o Mobile_Systems/Mobile_Applications
    * Free,_Libre,_and_Open_Source_Software
          o Web_Browsers
                # Mozilla
          o GNU_Projects
          o Programming/Development
                # Perl_/_Raku
                # Shell/Bash/Zsh/Ksh
    * Leftovers
          o Science
          o Proprietary
          o Security
                # Privacy/Surveillance
    * Gemini*_and_Gopher
          o Personal
          o Technical
                # Programming
    * § GNU/Linux⠀➾


          o ⚓ The Register UK ☛ Upgrading_what_might_be_the_world’s_oldest
            running_Linux_install⠀⇛


                 There are some complexities involved in upgrading what
                 the Reg FOSS desk suspects may be the world’s oldest
                 running Linux installation: an OS install dating back to
                 1993.


                 The machine called chiark.greenend.org.uk appears to be a
                 relatively ordinary webserver, hosting a bunch of home
                 pages, a few mailing lists, usenet groups and things.
                 People with no links to Cambridge University may have
                 encountered it only if they downloaded the PuTTY SSH
                 client for Windows from the author’s own site.


                 What’s remarkable about Chiark is that it was originally
                 installed with Debian Linux 0.93R5 in 1993, and the same
                 installation of the OS is now running Debian 11
                 “Bullseye”, the x86-64 version, freshly upgraded from an
                 x86-32 installation of Debian 8 “Jessie”.


          o § Desktop/Laptop⠀➾


                # ⚓ Linux Magazine ☛ System76_Refreshes_Their_Popular_Oryx_Pro
                  Laptop_with_a_New_CPU⠀⇛


                       The makers at System76 are never one to rest on
                       their laurels and are always trying to improve the
                       already outstanding hardware they offer. This time
                       around, they gave the Oryx Pro, one of their most
                       popular laptops, a bit of a refresh. This machine
                       is an outstanding option for gaming as well as AI/
                       ML. And with the new 12th Gen CPU (boasting 14
                       cores and 20 threads running between 1.7 to 4.7
                       GHz), you’ll have more power than you need to run
                       the software you require.


                       But this new update isn’t just about the CPU.
                       System76 has also made it so you can configure the
                       Oryx Pro with either NVIDIA RTX 2070 Ti or 3080 Ti
                       graphics (along with the RTX 3070 and 3080 that
                       were previously available).


                # ⚓ Wired ☛ HP_Dev_One_Linux_Laptop_Review:_The_Best_for
                  Linux⠀⇛


                       
                       HP’s latest Linux laptop sees the computer maker
                       collaborating with erstwhile competitor (or at
                       least, fellow Linux laptop maker) System76. It
                       seems like an odd combo, given that System76 makes
                       its own competing laptops, but the collaboration
                       works.


                       The Dev One is a very nice Linux machine that packs
                       enough punch for developers or creatives without
                       hitting top-tier laptop prices. Even more
                       impressive is the work HP and System76 have put
                       into making Linux work perfectly with the AMD
                       chipset.


                       Combining HP’s hardware capabilities and industry
                       experience with System76′s Pop!_OS desktop has
                       produced the best all-around Linux laptop you can
                       buy right now.


          o § Server⠀➾


                # ⚓ Kubernetes_Troubleshooting:_Finding_the_Right_Monitoring
                  Solution_–_Container_Journal⠀⇛


                       Kubernetes is revolutionizing application
                       development because it is designed for ease of use,
                       flexibility and scalability. In spite of these
                       compelling advantages, however, troubleshooting
                       Kubernetes problems can be a formidable challenge.
                       Once you are alerted to an error, just knowing
                       where to begin can even be overwhelming.


                       Imagine you are developing an app in a Kubernetes-
                       based development environment and you get an alert
                       for a container error that you do not recognize.
                       First, you ask your colleagues if they have seen
                       this before. Next, you search multiple blogs to see
                       what other developers are saying about this error.
                       Maybe you check multiple dashboards and logs; try
                       to dig up any information you can find. The whole
                       process can take hours and involve multiple teams.
                       Ultimately, you end up back at the command line,
                       trying to solve a problem that you do not really
                       understand. Does this frustrating scenario sound
                       familiar? This is a hit-or-miss approach to
                       Kubernetes troubleshooting that does not benefit
                       the development process or the business.


          o § Audiocasts/Shows⠀➾


                # ⚓ Video ☛ Speed_Up_Linux_–_Invidious [Ed: Although many GNU/
                  Linux channels have slowed down, it's part of the trend in
                  YouTube at large]⠀⇛


                # ⚓ E44:_Open_Source_Auth-as-a-Service_by_Aserto⠀⇛


                # ⚓ Episode_36:_Beginner’s_Guide_to_Contributions_2.0_–
                  WordPress_News⠀⇛


                       In the thirty-sixth episode of the WordPress
                       Briefing, Josepha Haden Chomphosy revisits the
                       Beginner’s Guide to Contributions to the WordPress
                       open source project.


                # ⚓ Video ☛ WARNING:_Don’t_Toast_your_Steam_Deck_(plus_other
                  Deck_news)_–_Invidious⠀⇛


                # ⚓ Video ☛ Manjaro_21.3.0_Xfce_Edition_Quick_overview_#linux
                  #Manjaro_–_Invidious⠀⇛


                       A Quick overview of Manjaro 21.3.0 Xfce Edition


                # ⚓ Video ☛ Using_nmap_to_scan_networks_(Awesome_Linux_Tools)_–
                  Invidious⠀⇛


                       nmap is a network mapping utility that you can use
                       to gather information regarding the nodes on your
                       network. With nmap, you can perform port scanning,
                       OS fingerprinting, and more! In this tutorial,
                       you’ll learn the basics of using nmap.


          o § Applications⠀➾


                # ⚓ CPU-X_The_Best_Linux_Alternative_Of_CPU-Z⠀⇛


                       For those want to check PC hardware specs in Linux,
                       CPU-X is a good choice for user switching from
                       Microsoft Windows.


                       It’s a free open-source system profiling and
                       monitoring application, that looks quite similar to
                       CPU-Z for Windows. With it, you can check your CPU
                       specification, vendor, codename, clocks, and L1/L2/
                       L3 caches.


                       CPU-Z is a freeware that gathers information on
                       some of the main devices of your system :
                       Processor name and number, codename, process,
                       package, cache levels.
                       Mainboard and chipset.
                       Memory type, size, timings, and module
                       specifications (SPD).
                       Real time measurement of each core’s internal
                       frequency, memory frequency.


                # ⚓ OMG Ubuntu ☛ TopHat_is_a_Nifty_System_Monitor_for_GNOME
                  Shell_–_OMG!_Ubuntu! [Ed: Another extension limited to GNOME/
                  GTK crowd because of integration]⠀⇛


                       Want to keep an eye on your system resources
                       without pulling up a terminal or launching GNOME’s
                       System Monitor tool?


                       Check out TopHat.


                       TopHat is a new system monitor GNOME extension that
                       puts a top-level overview of active CPU, RAM, and
                       network usages in the GNOME Shell top bar.


                       There are, of course, ample system monitor GNOME
                       extensions out there. Heck, I feel like I’ve
                       written about them all at some point. But most tend
                       to be singular, putting a wealth of system resource
                       info within a two column table.


                # ⚓ OSNote ☛ Seafile_–_Sync_and_Share_Your_Files_Ubuntu_–
                  OSNote⠀⇛


                       Seafile is the high-performance open-source cross-
                       platform software for file sharing and sync. The
                       stored file can be synchronized from various
                       devices from the central server through built-in
                       file encryption. Before syncing the files to the
                       server files are encrypted. The Seafile core is
                       built using C programming which may be small but
                       has fantastic performance. Files can be organized
                       into libraries that can be encrypted by the
                       password set by the user itself.
                       Seafile provides similar functionality just like
                       other file hosting services like dropbox, google
                       drive, etc. but seafile is a self-hosted file
                       sharing service. If you are curious about how we
                       can sync and share files from self-hosted Seafile
                       this article is for you. All the procedures in this
                       article are performed on the Ubuntu 20.04 LTS
                       system.
                       Before continuing the installation we need to pre-
                       install the Nginx, Mysql, and Python along with
                       additional Python modules.


                # ⚓ Ubuntu Handbook ☛ Findex_–_A_Super_Fast_Tool_to_Search_&
                  Launch_Your_Apps_in_Linux_|_UbuntuHandbook⠀⇛


                       Looking for an alternative app launching tool for
                       your Linux? Findex is one with highly customizable
                       interface and fast performance.


                       The app runs silently in the background. Once you
                       hit the shortcut key, a search box pop-up in screen
                       center allows to quickly search and open desired
                       applications.


          o § Instructionals/Technical⠀➾


                # ⚓ HowTo Forge ☛ Linux_nm_Command_Tutorial_for_Beginners_(10
                  Examples)⠀⇛


                       This is a tutorial for Linux users who do system-
                       level software development. Learn more in this
                       Linux nm command tutorial for beginners.


                # ⚓ TechRepublic ☛ How_to_easily_open_files_with_sudo
                  privileges_in_the_GNOME_File_Manager_|_TechRepublic⠀⇛


                       Not all Linux file managers are created equal. Some
                       file managers have more bells and whistles than the
                       average user will ever need, while other file
                       managers are as inflexible as cold, hard steel.
                       There are also those that ship with a bare minimum
                       of features but allow users to extend the feature
                       set with add-ons.


                       Given how we so often take the file manager for
                       granted, once you find a feature that could really
                       make your daily life a bit more efficient, you
                       realize just how important the tool is. Such is the
                       case with the GNOME File Manager. Out of the box,
                       it works great and includes enough features to get
                       you by for a while. Eventually, however, you’ll
                       find some features that could make things a bit
                       easier.


                # ⚓ AddictiveTips ☛ How_to_watch_Live_TV_on_the_Linux_desktop
                  with_Hypnotix⠀⇛


                       Want to watch free TV on your Linux desktop? With
                       Hypnotix, you can! The Hypnotix application gives
                       you access to tons of free, legal live TV channels
                       right on the Linux desktop. Here’s how to use it.


                # ⚓ ID Root ☛ How_To_Install_Java_on_Rocky_Linux_9⠀⇛


                       In this tutorial, we will show you how to install
                       Java on Rocky Linux 9. For those of you who didn’t
                       know, Java is a popular programming language and
                       software platform that allows you to run many
                       server-side applications. The general purpose of
                       the Java programming language is to let developers
                       write programs or applications once, but the
                       application itself can be run on any system across
                       multiple operating systems.


                       This article assumes you have at least basic
                       knowledge of Linux, know how to use the shell, and
                       most importantly, you host your site on your own
                       VPS. The installation is quite simple and assumes
                       you are running in the root account, if not you may
                       need to add ‘sudo‘ to the commands to get root
                       privileges. I will show you the step-by-step
                       installation of Java programming language on Rocky
                       Linux. 9.


                # ⚓ RoseHosting ☛ How_to_Install_Netdata_Monitoring_Tool_on
                  Ubuntu_22.04⠀⇛


                       In this tutorial, we are going to explain how to
                       install Netdata Monitoring Tool on the latest
                       Ubuntu 22.04.


                       Netdata Monitoring tool is an open-source software
                       developed to track and show the statistic of server
                       usage. System Administrators, Developers, or even
                       non-technical users are using this software to
                       check the CPU usage, RAM usage, available DISK
                       space, Network bandwidth and etc. Netdata
                       Monitoring tool is mainly written in C, JavaScript,
                       and Python and can be installed on various
                       operating systems such as Ubuntu, Debian, and
                       CentOS.


                       Installing the Netdata Monitoring tool on Ubuntu
                       22.04 can take up to 10 minutes. Let’s get started!


                # ⚓ MakeTech Easier ☛ What_is_the_Rc_Shell_and_How_to_Install
                  It_in_Linux_–_Make_Tech_Easier⠀⇛


                       The rc shell is a simple and innovative command
                       interpreter built for the Plan 9 family of
                       operating systems. It is currently a part of
                       plan9port, which is a suite of Plan 9 software that
                       is available for Linux.


                       Rc aims to improve on the default UNIX shell and it
                       introduces a cleaner syntax for writing scripts. It
                       is also built to be as simple to understand as
                       possible. This makes rc a good program for someone
                       that wants to learn how a shell works.


                # ⚓ How_to_Install_DokuWiki_with_Nginx_on_Ubuntu_22.04⠀⇛


                       DokuWiki is a free and open-source wiki software
                       written in PHP that allows users to create and edit
                       pages using a web browser. It is easy to install
                       and use, and doesn’t require a database since it
                       works on plain text files. Using a very familiar
                       interface, allows you to easily scale and optimize
                       using many advanced features.


                       The installation is quite simple and assumes you
                       are running in the root account, if not you may
                       need to add ‘sudo‘ to the commands to get root
                       privileges.


                # ⚓ TecAdmin ☛ How_to_declare_boolean_variable_in_shell
                  script⠀⇛


                       he shell (bash) script doesn’t offer any data type
                       with the variables. So we can’t specifically
                       declare a variable of type boolean in shell
                       scripts.


                       But, you can still use the variable like a boolean
                       in shell scripts. Store a sample string “true” to a
                       variable and match it with the if condition. This
                       works similarly to boolean.


                # ⚓ Trend Oceans ☛ How_to_Copy_the_contents_of_a_file_into_the
                  clipboard_without_displaying_its_contents_–_TREND_OCEANS⠀⇛


                       While working on the terminal, we copy a lot of
                       text from the file content to the clipboard and
                       then paste the content where it needs to be pasted.


                       If I ask you how do you copy the content of the
                       file from your terminal to your clipboard, you may
                       say that I usually display the content of the file
                       using the cat command and then I select the text
                       that I want to copy.


                       Absolutely correct, and nothing is wrong with the
                       approach, but why make an unnecessary effort when
                       you can use the xclip command to copy the content
                       of a file directly into the clipboard?


                # ⚓ ID Root ☛ How_To_Install_MySQL_Workbench_on_Ubuntu_22.04
                  LTS_–_idroot⠀⇛


                       In this tutorial, we will show you how to install
                       MySQL Workbench on Ubuntu 22.04 LTS. For those of
                       you who didn’t know, The MySQL Workbench is a GUI
                       application for administrators’ and developers’
                       databases. Its graphical interface provides
                       database architects and administrators with an
                       easier way to model data, build and run SQL
                       queries, and maintain a database. MySQL Workbench
                       is available on Windows, Linux, and macOS.


                       This article assumes you have at least basic
                       knowledge of Linux, know how to use the shell, and
                       most importantly, you host your site on your own
                       VPS. The installation is quite simple and assumes
                       you are running in the root account, if not you may
                       need to add ‘sudo‘ to the commands to get root
                       privileges. I will show you the step-by-step
                       installation of the MySQL Workbench on Ubuntu 22.04
                       (Jammy Jellyfish). You can follow the same
                       instructions for Ubuntu 22.04 and any other Debian-
                       based distribution like Linux Mint, Elementary OS,
                       Pop!_OS, and more as well.


                # ⚓ Vitux ☛ How_to_Install_AWS-CLI_on_Ubuntu⠀⇛


                       Since Linux users are more comfortable working with
                       command line interfaces, Amazon Web Services
                       introduced the AWS CLI to manage all these services
                       from a single platform. With this tool, you can
                       manage multiple services at once, easily and
                       conveniently. In this guide, we’ll show you how to
                       install the AWS CLI on Ubuntu Linux.


                # ⚓ dwaves.de ☛ GNU_Linux_–_how_to_allow_sftp_file_access_to
                  webserver_only_–_lock_sftp_user_to_/var/www_–_bad_ownership
                  or_modes_for_chroot_directory_component⠀⇛


                # ⚓ dwaves.de ☛ GNU_Linux_Bash_–_simple_backup_web_root_and
                  mysql_mariadb_database_in_one_go_script⠀⇛


          o § Desktop Environments/WMs⠀➾


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


                      # ⚓ psifidotos:_Latte_Dock_|_Farewell…⠀⇛


                             Unfortunately I would like to inform kde
                             community that I am stepping away from Latte
                             development. No time,motivation or interest
                             from my part is the main reason. I hope that
                             this will give free space and air for new
                             developers/maintainers to step in and move
                             Latte forward.


                             I hoped that I would be able to release Latte
                             v0.11 but unfortunately I can not. Releasing
                             Latte v0.11 it would mean that someone would
                             maintain it afterwards and that is no more
                             the case.


                # § GNOME Desktop/GTK⠀➾


                      # ⚓ Liam Proven ☛ liam_on_linux_|_On_GNOME_advocacy⠀⇛


                             The odd things for me, having tried more or
                             less every single Linux desktop under the
                             sun, including several that no longer exist,
                             is that there’s no one definition of “user
                             friendly” that holds true for everyone.


                             In this story’s comments, there are people
                             saying Windows is the best, others saying
                             certain particular versions are best, others
                             saying they find it unusable or at least
                             hard.


                             Yet this has been the best-selling desktop OS
                             in history for about 35 years now, used by
                             _billions_ of people, so it must be getting
                             *something* right.


                             Counter to that, there are also people
                             castigating Macs and macOS. That’s normal;
                             there are as many biased fanboys *against* as
                             there are *for*.


                             And yet, again, for nearly 40 years now,
                             Apple has been *THE ONE COMPANY* to resist
                             the rise of Microsoft, and has a
                             fantastically loyal fan base and makes a lot
                             of money.


                             I also have a number of blind friends, and
                             they mostly tell me that Windows is the most
                             accessible OS there is, that it has the best
                             selection of assistive tech, that the apps
                             are more accessible, and so on.


                             Some favour macOS. What macOS provides out of
                             the box is *way* better, it’s true. If you’re
                             a casual computer user — bit of surfing, bit
                             of online chat, very occasionally write a
                             letter — it’s better for blind users than
                             Windows.


                             If you have a job to do, in business, and
                             need rich powerful apps, and need them to be
                             accessible, my working blind mates tell me
                             Windows easily trounces the Mac.


                             I am not blind so I must take their word for
                             it.


                             But I can make Windows and macOS and my
                             preferred Linux desktops, Unity and Xfce,
                             stand on their heads and do back handsprings
                             for me. I regularly read people telling me
                             that any of these OSes just can’t do X or
                             can’t do Y, when X and Y are things I do on a
                             daily basis.


                             What this really means is: they don’t know
                             how to do X or Y, and they haven’t bothered
                             to look for instructions or guidance. It
                             doesn’t do it — whatever “it” is, it varies a
                             lot — and so they decide it can’t, it doesn’t
                             work, and they move on.


                      # ⚓ Berlin_Mini_GUADEC⠀⇛


                             The Berlin hackfest and conference wasn’t a
                             polished, well organized experience like the
                             usual GUADEC, it had the perfect Berlin
                             flavor. The attendance topped my expectations
                             and smaller groups formed to work on
                             different aspects of the OS.


                             GNOME shell’s quick settings, the mobile form
                             factor, non-overlapped window management,
                             Flathub and GNOME branding, video subsystems
                             and others.


    * § Distributions and Operating Systems⠀➾


          o ⚓ DebugPoint ☛ Feren_OS_Review:_Clever_KDE_Distro_for_Easy
            Migration_from_Windows⠀⇛


                 An in-depth review of Feren OS, which is based on Ubuntu
                 LTS and KDE Plasma desktop with an unique way to help
                 Windows users to migrate.


          o ⚓ HaikuOS ☛ [GSoC_2022]_Ham:_Status_Update⠀⇛


                 Hello everyone. This is a brief update on the Ham project
                 – a drop in replacement for the Jam build system. For
                 those more curious about the technical details, there
                 will be a larger blog post on Ham’s action modifier
                 implementation coming soon.


          o § Fedora and IBM⠀➾


                # ⚓ Network World ☛ Rocky_Linux_9_arrives_with_Peridot⠀⇛


                       Release 9 of Rocky Linux just made its public
                       appearance on July 14, and the big news is
                       something called Peridot, which anyone (yes,
                       anyone) can use to reproduce Rocky Linux 9 from
                       scratch on their own. This is a truly exciting turn
                       for the Linux community.


                       If you’re not familiar with Rocky Linux, don’t be
                       too surprised that it made it to Release 9 and
                       you’re just now tuning in. “Release 9” doesn’t mean
                       that Rocky has gone through eight prior major
                       releases. Instead, the name indicates its
                       connection to RHEL 9. Rocky Linux began life as
                       Release 8.3 in April 2021 as a replacement for
                       CentOS, which was EOL’ed in December 2020.


                # ⚓ Linuxiac ☛ Nobara_Is_a_Fedora-Based_Linux_Distro_with
                  Gamers_in_Mind⠀⇛


                       Nobara is a new user-friendly distribution with a
                       modified GNOME aimed at new Linux users with gaming
                       affinities.


                       Fedora is a distribution that improves with each
                       new version. As a result, it is becoming a more
                       attractive choice for developing new ones based on
                       it.


                       The fact that Fedora comes with a vanilla GNOME
                       opens up many possibilities for developers to build
                       on. This is the case with a relatively new
                       distribution that attempts to make GNOME more user-
                       friendly for novice Linux users, particularly those
                       who enjoy gaming. Please, meet Nobara.


                # ⚓ LWN ☛ Fedora_to_disallow_CC0-licensed_code_[LWN.net]⠀⇛


                       The Creative Commons CC0 license is essentially a
                       public-domain declaration (or as close as is
                       possible in jurisdictions that lack a public
                       domain). The Fedora project has allowed the
                       distribution of code under this license, but, as
                       announced by Richard Fontana, that policy is
                       changing and CC0 will no longer be allowed for
                       code…


                # ⚓ Power10_Entry_Machines:_The_Power_S1022s⠀⇛


                       Software-based replication surfaced in the 1990s
                       and continues to be a very popular choice for IBM i
                       shops of all sizes, across an array of industry
                       sectors. But what are the benefits of using
                       software solutions versus hardware alternatives for
                       HA/DR? There are a number of benefits that are an
                       outgrowth of an HA/DR strategy that go beyond HA/DR
                       and where the software approach is better than the
                       hardware approach.


                # ⚓ The_Case_For_Software-Based_IBM_i_HA/DR⠀⇛


                       Software-based replication surfaced in the 1990s
                       and continues to be a very popular choice for IBM i
                       shops of all sizes, across an array of industry
                       sectors. But what are the benefits of using
                       software solutions versus hardware alternatives for
                       HA/DR? There are a number of benefits that are an
                       outgrowth of an HA/DR strategy that go beyond HA/DR
                       and where the software approach is better than the
                       hardware approach.


                # ⚓ No_Plan_To_Bring_.NET_To_Power,_IBM_Says⠀⇛


                # ⚓ IBM_i_PTF_Guide,_Volume_24,_Number_30⠀⇛


          o § Debian Family⠀➾


                # ⚓ LWN ☛ Debian.community_domain_name_seized⠀⇛


                       The Debian project, Debian.ch, and Software in the
                       Public Interest recently filed a WIPO action to
                       take control of the “debian.community” domain name,
                       which has been used by Daniel Pocock to attack the
                       Debian project and its members. Red Hat had made a
                       similar attempt to take control of WeMakeFedora.org
                       earlier this year, but that attempt failed. The
                       Debian action succeeded, though; on July 19, WIPO
                       decided in favor of the action and ordered the
                       domain name transferred. That domain name can no
                       longer be used, but the attacks seem certain to
                       continue.


          o § Devices/Embedded⠀➾


                # ⚓ CNX Software ☛ Rakwireless_introduces_WisBlock_modular
                  power_supply,_IP65_enclosures,_and_more_sensor_modules_–_CNX
                  Software⠀⇛


                       Rakwireless Wisblock modular IoT prototyping system
                       will get new modules about once every quarter and
                       the latest Wisblock Summer 2022 event brings some
                       RAK190xx base boards and power modules to support
                       various power sources from solar panels to PoE, two
                       IP65-rated “Unify” enclosures, as well as four new
                       Wisblock sensor modules.


          o § Open Hardware/Modding⠀➾


                # ⚓ Arduino ☛ Reviving_a_vintage_secondary_split-flap_clock
                  with_Arduino_|_Arduino_Blog⠀⇛


                       In the world of computing, many interfaces utilize
                       a primary/secondary model of asymmetric
                       communication, in which a primary host device
                       controls one or more secondary client devices. This
                       model is, for example, common among PATA and SATA
                       hard drive arrangements. It is also common in clock
                       networks, with a central time server updating
                       several client clocks. iSax had a unique example of
                       such a client clock with a vintage split-flap
                       display, and made it useful again by retrofitting
                       an Arduino board.


                       This clock likely came from a set of many, which
                       would have been used in a government building,
                       train station, or similar application. It would
                       have received a signal from a primary clock and set
                       its time accordingly. In the original setup, that
                       signal came in the form of a 1Hz alternating square
                       wave that drove a motor for the clockwork gears.
                       Instead of attempting to reverse-engineer and
                       replicate that signal, iSax chose to drive the
                       motor with an Arduino Nano board that keeps its own
                       time with an RTC (real-time clock) module.


                # ⚓ Arduino ☛ Now_you_can_make_shawarma_at_your_desk_|_Arduino
                  Blog⠀⇛


                       If you’ve ever been lucky enough to visit a country
                       in the Middle East or around the Mediterranean Sea,
                       then you’ve probably seen street food vendors
                       cutting slices off of a big ol’ hunk of slowly
                       rotating meat. This delicious delicacy is called
                       shawarma and is a form of vertical rotisserie. The
                       meat can be beef, lamb, chicken, or even turkey —
                       the cooking process is what is important. And now,
                       thanks to a tutorial from Roni Bandini, you can
                       perform that cooking process on your desktop with
                       this Micro Shawarma machine.


                       This machine is exactly what it sounds like: a tiny
                       vertical rotisserie machine that sits on a desktop.
                       It is sure to make your coworkers jealous in the
                       hours leading up to lunchtime. Like its traditional
                       full size cousins, this Micro Shawarma machine is
                       open-air and has a spit that spins on a vertical
                       axis. Offset to one side of the spit, there is a
                       heating element that continuously roasts the meat.
                       Anytime you get a hankering for some protein, you
                       can slice off some meat. The machine even hosts its
                       own web app, so you can operate everything from
                       your smartphone.


          o § Mobile Systems/Mobile Applications⠀➾


                # ⚓ Notebook Check ☛ First_MIUI_14_signs_based_on_Android_13
                  emerge_alongside_unofficial_eligibility_list_with_nearly_125
                  devices_–_NotebookCheck.net_News⠀⇛


                # ⚓ Gadgets Now ☛ Google_brings_AR_support_to_these_phones_to
                  make_better_use_of_cameras,_sensors_and_more_|_Gadgets_Now⠀⇛


                # ⚓ Android Police ☛ How_to_use_Android_TV⠀⇛


                # ⚓ SlashGear ☛ Why_You_Probably_Need_To_Stop_Using_Your
                  Android_Phone’s_Built-In_Browser⠀⇛


                # ⚓ Android Headlines ☛ Most_Android_Users_Use_Budget_Phones_In
                  2022⠀⇛


                # ⚓ Android Headlines ☛ Google_Selects_NowSecure_For
                  Independent_Security_Reviews_Of_Android_Apps⠀⇛


                # ⚓ Top_10_Ways_to_Fix_Camera_Focus_Not_Working_on_Android_–
                  Guiding_Tech⠀⇛


                # ⚓ Phone Arena ☛ T-Mobile_launches_new_Android_tablet,_offers
                  it_for_free_–_PhoneArena⠀⇛


                # ⚓ TechRadar ☛ OnePlus_defends_decision_to_remove_popular
                  feature_from_next_Android_phone_|_TechRadar⠀⇛


                # ⚓ The Verge ☛ Google_is_paying_some_much-needed_attention_to
                  its_Android_tablet_apps_–_The_Verge⠀⇛


                # ⚓ Android Police ☛ The_best_Android_projectors_in_2022⠀⇛


                # ⚓ Fresh_Android_13_Beta_Arrives_for_Pixel_Phones⠀⇛


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


          o § Web Browsers⠀➾


                # § Mozilla⠀➾


                      # ⚓ 9to5Linux ☛ Mozilla_Firefox_103_Is_Now_Available_for
                        Download,_This_Is_What’s_New⠀⇛


                             
                             Firefox 103 has been in beta since June 27th,
                             2022, and it introduces improved WebGL
                             performance on Linux systems when using the
                             NVIDIA binary drivers via DMA-Buf, improved
                             performance on high-refresh rate monitors of
                             120Hz or higher, and stronger security due to
                             the removal of the configuration option that
                             allows SHA-1 signatures in certificates


                      # ⚓ OMG Ubuntu ☛ Firefox_103_Available_to_Download,_But
                        Promised_Swipe_Gesture_is_MIA⠀⇛


                             
                             Mozilla Firefox 103 features another clutch
                             of conservative changes aimed at improving
                             the overall experience of using the browser
                             rather than dramatically reinventing it.


                             This release was expected to add a big new
                             feature: two finger horizontal swipe to move
                             back/forward between pages on Linux, with
                             accompanying animation/OSD indication – as
                             this gif demos…


                      # ⚓ Thunderbird ☛ Thunderbird_Time_Machine:_A_Look_Back
                        At_Thunderbird_0.1⠀⇛


                             Let’s take a walk down memory lane to the
                             summer of 2003. Cinemas are dominated by
                             sequels like Iron Man 3 and Fast & Furious 6.
                             Linkin Park, 50 Cent, and Evanescence have
                             top-selling new albums. Apple’s iPod hasn’t
                             even sold 1 million units. Mozilla’s brand
                             new web browser is still called Firebird. And
                             a new cross-platform, open-source application
                             called Thunderbird has debuted from the
                             foundations of Mozilla Mail…


                             Because the entirety of Thunderbird’s
                             releases and corresponding release notes have
                             been preserved, I’ve started a self-guided
                             tour of Thunderbird’s history. Why? A mixture
                             of personal and technical curiosity. I used
                             Thunderbird for a couple years in the mid-
                             2000s, and again more recently, but there are
                             giant gaps in my experience. So I’m
                             revisiting every single major version to
                             discover the nuances between releases; the
                             changes big and small.


                             (If you ever get the craving to do the same,
                             I’ve found the easiest operating system to
                             use is Windows, preferably inside a virtual
                             machine. Early versions of Thunderbird for
                             Macs were built for PowerPC architecture,
                             while early Linux versions were 32-bit only.
                             Both may cause you headaches with modern PC
                             hardware!)


          o § GNU Projects⠀➾


                # ⚓ GNU ☛ poke_–_News:_GNU_poke_2.4_released_[Savannah]⠀⇛


                       I am happy to announce a new release of GNU poke,
                       version 2.4.


                       This is a bugfix release in the poke 2.x series.


                       See the file NEWS in the distribution tarball for a
                       list of issues fixed in this release.


                       The tarball poke-2.4.tar.gz is now available at


                       https://ftp.gnu.org/gnu/poke/poke-2.4.tar.gz.


                       > GNU poke (http://www.jemarch.net/poke) is an
                       interactive, extensible editor for binary data. Not
                       limited to editing basic entities such as bits and
                       bytes, it provides a full-fledged procedural,
                       interactive programming language designed to
                       describe data structures and to operate on them.


                       Happy poking!


          o § Programming/Development⠀➾


                # ⚓ KDE ☛ Measurement_Lab_Follow-Up:_Sprint_Achievements_And
                  To-dos_–_KDE_Eco⠀⇛


                       On Saturday 16 July 2022 KDE Eco held the second
                       in-person Sprint to work on the community
                       measurement lab at the KDAB office in Berlin. The
                       Sprint is one of several planned follow-up events.


                # ⚓ GSoC_update:_Draw_Ellipses_in_Krita⠀⇛


                       I’ve been working on Krita’s ellipse tool as my
                       GSoC project. Here’s a status update and demo of
                       what I have till now. I’m trying to improve the
                       reading experience by using no code and reducing
                       technical details in the post; if you are
                       interested in those details, just visit the merge
                       request page.


                       If you have ever tried to draw an ellipse of small
                       size in Krita, you must have noticed that the
                       ellipse is asymmetric and twisted. These minor
                       errors can be negligible when drawing ellipses of
                       larger size, but it became annoying when trying to
                       draw some small-sized ellipses for pixel arts. To
                       fully understand the cause, let’s look at how Krita
                       draws the ellipse.


                # ⚓ Drew DeVault ☛ Code_review_at_the_speed_of_email⠀⇛


                       I’m a big proponent of the email workflow for patch
                       submission and code review. I have previously
                       published some content (How to use git.sr.ht’s
                       send-email feature, Forks & pull requests vs email,
                       git-send-email.io) which demonstrates the
                       contributor side of this workflow, but it’s nice to
                       illustrate the advantages of the maintainer
                       workflow as well. For this purpose, I’ve recorded a
                       short video demonstrating how I manage code review
                       as an email-oriented maintainer.


                # ⚓ Make Use Of ☛ The_6_Best_Vim_Plugin_Managers⠀⇛


                       Vim is one of the best command-line text editors
                       you can lay your hands on. It comes preinstalled by
                       default on Linux, macOS, and other Unix-like
                       systems.


                       Vim plugins allow you to extend Vim’s functionality
                       according to your workflow and preferences. But
                       you’ll need a good plugin manager to install and
                       manage your Vim plugins.


                       Here are some of the best plugin managers for Vim
                       that will make your life a bit easier.


                # § Perl / Raku⠀➾


                      # ⚓ Rakulang ☛ Rakudo_Weekly_News:_2022.30_What⠀⇛


                             Someone with the nick MicrowaveOven86 asked a
                             question on /r/rakulang: What do yall use
                             raku for? With some nice, insightful,
                             revealing and funny answers. Maybe more
                             answers can be given by the readers of the
                             Rakudo Weekly News?


                # § Shell/Bash/Zsh/Ksh⠀➾


                      # ⚓ Guru:_Regular_Expressions,_Part_1_–_IT_Jungle⠀⇛


                             In the first part of this series, I will show
                             how to replace characters in a string using
                             SQL and regular expressions. I know I can
                             replace characters using RPG or SQL, and they
                             work great, but there are some cases where I
                             find using regular expressions is a bit
                             easier.


                             For the examples I’ll show, I’m using the
                             REGEXP_REPLACE function. REGEXP_REPLACE
                             allows me to search for a particular value
                             within a string and replace it with another
                             value.


                             In the first example (Figure 1), I want to
                             search a string that has both letters and
                             digits and I want to extract the just digits
                             or periods. To accomplish this objective, I
                             use REGEXP_REPLACE to replace characters that
                             are not digits.


    * § Leftovers⠀➾


          o § Science⠀➾


                # ⚓ Bloomberg ☛ BCI_Startup_Implants_First_Device_in_U.S.
                  Patient⠀⇛


                # ⚓ IEEE ☛ This_Car_Charger_Bot_Will_Also_Hold_Your_Spot⠀⇛


                       The vision of Ziggy, a mobile EV charger designed
                       to tool around parking lots like a plug-wielding
                       valet, raises an important question: Do robots take
                       tips?


                       EV owners may be happy to toss Ziggy a fiver if it
                       can hold an open parking spot and deliver electrons
                       to fill up the car’s battery, with no worries over
                       fixed chargers being occupied by other cars. As
                       importantly, site operators could lease turnkey
                       robo-chargers without the pricey hassles of charger
                       installation, or setting aside precious real estate
                       for chargers that are often underutilized.


                # ⚓ Blockchain_not_just_for_bitcoin:_It_can_secure_and_store
                  genomes,_too⠀⇛


                       Blockchain is a digital technology that allows a
                       secure and decentralized record of transactions
                       that is increasingly used for everything from
                       cryptocurrencies to artwork. But Yale researchers
                       have found a new use for blockchain: they’ve
                       leveraged the technology to give individuals
                       control of their own genomes.


                       Their findings are published June 29 in the journal
                       Genome Biology.


          o § Proprietary⠀➾


                # ⚓ Liam Proven ☛ liam_on_linux_|_Why_MS_Word_jumped_from
                  version_2_to_version_6⠀⇛


                       There were three products all called MS Word, only
                       peripherally related:


                       Word for DOS, which I first saw at version 3, and
                       of which I used 3, 4, 5, 5.5 (when it suddenly
                       switched to CUA menus), and 6 (like WordPerfect,
                       the last and best version).


                       Word for Mac, which I first saw at version 4, and
                       which in generally-held opinion peaked at v5.1.


                       Word for Windows, AKA WinWord, which went v1, v2,
                       v6.


                       But there were legit reasons.


                       MS was making an effort to harmonise and coordinate
                       its versions.


                       IIRC the story is that Gates met Paul Brainerd
                       (founder of Aldus) at some event, and Brainerd told
                       him that Aldus (creators of PageMaker, the ultimate
                       DTP app in its day and the product that made the
                       Mac a big success) was working on a wordprocessor
                       for Windows, because there wasn’t a good one. The
                       product was codenamed “Flintstone” and was nearly
                       ready for alpha test.


                       Gates panicked, lied to Brainerd that they
                       shouldn’t waste their time because MS was almost
                       ready to launch its and it’d be a killer app.


                       Brainerd went back to base and cancelled
                       Flintstone. Gates went back to base and told his
                       team to write a Windows word-processor ASAP because
                       Aldus was about to kill them.


          o § Security⠀➾


                # ⚓ LWN ☛ Security_updates_for_Monday [Ed: Some patches,
                  deprecation etc.]⠀⇛


                       Security updates have been issued by Debian
                       (chromium, djangorestframework, gsasl, and openjdk-
                       11), Fedora (giflib, openssl, python-ujson, and
                       xen), Mageia (virtualbox), SUSE (git, gpg2, java-
                       1_7_1-ibm, java-1_8_0-ibm, java-1_8_0-openjdk,
                       mozilla-nspr, mozilla-nss, mozilla-nss, python-
                       M2Crypto, and s390-tools), and Ubuntu (php8.1).


                # ⚓ Red Hat Official ☛ Enhancing_RHEL_Security:_Understanding
                  SHA-1_deprecation_on_RHEL_9⠀⇛


                       While Red Hat Enterprise Linux 9 (RHEL 9)
                       deprecated SHA-1 for signing for security reasons,
                       it is still used by many for signing packages. In
                       this article, I’ll go over some typical problems
                       users may face with Fedora SHA-1 status (including
                       some possible workarounds), and how you can update
                       your infrastructure to use a more secure SHA-256.


                # ⚓ Trend_Micro_Tightens_Container_Security_Integration_in
                  Cloud_Platform_–_Container_Journal⠀⇛


                       Trend Micro today extended its Trend Micro Cloud
                       One platform to more tightly integrate its
                       container security offering.


                       Mike Milner, vice president of cloud technology for
                       Trend Micro, said the latest edition of Trend Micro
                       Cloud One eliminates the need to separately deploy
                       a container security platform. Instead, the
                       company’s container security capabilities are now
                       deployed as part of the larger Trend Micro Cloud
                       One platform—making container security
                       administration simpler at a time when the number of
                       container applications running in production
                       environments that need to be secured continues to
                       steadily increase.


                       In addition, Trend Micro has simplified the
                       deployment and management of its cloud intrusion
                       prevention system.


                # § Privacy/Surveillance⠀➾


                      # ⚓ Zach Flower ☛ Anonymity_and_Pseudonymity_|
                        flower.codes⠀⇛


                             Being anonymous on the internet isn’t
                             impossible, but it sure as hell isn’t easy
                             either. You have a name, a face, and email
                             address, a phone number… these things, and
                             more, are being asked of us all the time to
                             prove our legitimacy on countless websites.


                             [...]


                             A not-insignificant number of apps and
                             websites have decided that emails and
                             passwords are “bad,” so they’ve moved to
                             using pin-based logins that get texted to
                             your phone number—nevermind the fact that SIM
                             swapping makes using a phone number as a
                             login method a laughable instance of security
                             theater.


                             While you can always generate a single
                             pseudonymous phone number using Google Voice,
                             a more “on rails” solution is https://
                             www.burnerapp.com/, a mobile app that can be
                             used to generate (and destroy) multiple
                             temporary phone numbers at once. I don’t
                             personally use this service, but I like the
                             idea behind it.


                      # ⚓ Trust ☛ Doxxing:_a_new_tool_of_repression_against
                        Arab_women⠀⇛


    * § Gemini* and Gopher⠀➾


          o § Personal⠀➾


                # ⚓ SpellBinding:_ABLOPTY_Wordo:_NASAL⠀⇛


          o § Technical⠀➾


                # ⚓ FreeBSD_Firewall⠀⇛


                # ⚓ figlet_test⠀⇛


                # ⚓ DIY_Macro-keyboard⠀⇛


                       Using a short Python script, an extra keyboard can
                       easily be configured to serve as custom macro-
                       keyboard.


                       The script relies on the `evdev`package that
                       provides and interface for passing events generated
                       in the kernel directly to userspace. Simulating key
                       presses (and controlling the mouse) can be done
                       with `xdotool`(which allows access to all keys –
                       binded or not), or with Python’s
                       `pyautogui`package.


                # ⚓ IPFS_Quickstart⠀⇛


                       This is just a short pointer on how to use IPFS to
                       access the care list, for anyone who doesn’t know
                       and/or isn’t interested in learning more about it
                       right now. To learn more you should go to the
                       official website or search around.


                # ⚓ ipfs.scm⠀⇛


                       I wrote a CHICKEN Scheme egg to control a Kubo node
                       through its RPC API.


                # § Programming⠀➾


                      # ⚓ Programming_languages⠀⇛


                             I have a little clock app that I use on my
                             Raspberry Pi 0. It is written in Go. The Pi0
                             is a slow machine, so compiling Go code is
                             actually pretty painful, despite the language
                             having a reputation for fast compile times.


                             An older version written in C acquitted
                             itself rather well compile-time wise, and
                             seemed AT LEAST as good as Go. Go has
                             excellent cross-compile support, so my new
                             strategy is to compile on my arm64, and copy
                             the program to the Pi.


                             C++ is of course very slow to compile on the
                             Pi. Cross-compiling is more difficult.
                             There’s a library that I’m thinking of
                             linking to, and I haven’t yet fathomed out
                             how I’m going to do it.


                      # ⚓ Petri_Nets_Log_#003⠀⇛


                             It has to be a real programming language, not
                             a modelling one!


                             [...]


                             In this net acc may start empty, but bound
                             must have a single token. When a token is
                             produced to input, either kons or default-acc
                             is enabled. If there’s no token in acc, then
                             there must be a token in bound, and in that
                             case default-acc is enabled; if there’s a
                             token in ac, then there’s no token in bound,
                             and in that case kons is enabled. kons
                             behaves as before. On the other hand, peek
                             may consume the token from acc at any time,
                             but does not put it back, and instead puts a
                             dummy token in bound. This place bound is
                             only used to “signal” that acc has no tokens,
                             so that default-acc may move one there.
                             default-acc simply moves an input token to
                             acc to initialize the accumulator.


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



                    ䷩ 𝚕𝚒𝚗𝚎 4243

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.25.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_25/07/2022:_postmarketOS_Considering_SourceHut⠀✐


Posted in News_Roundup at 3:08 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Instructionals/Technical
    * Distributions_and_Operating_Systems
          o Devices/Embedded
    * Free,_Libre,_and_Open_Source_Software
          o Productivity_Software/LibreOffice/Calligra
          o Programming/Development
    * Leftovers
          o Hardware
          o Proprietary
          o Security
          o Defence/Aggression
          o Environment
                # Wildlife/Nature
          o Finance
          o AstroTurf/Lobbying/Politics
          o Civil_Rights/Policing
          o Digital_Restrictions_(DRM)
          o Monopolies
                # Copyrights
    * Gemini*_and_Gopher
          o Personal
          o Technical
                # Science
                # Internet/Gemini
    * § GNU/Linux⠀➾


          o ⚓ 9to5Linux ☛ 9to5Linux_Weekly_Roundup:_July_24th,_2022⠀⇛


                 
                 This week has been a bit slow in Linux news and releases
                 due to the GUADEC 2022 and DebConf22 conferences. Still,
                 we saw the launch of two new Linux laptops, Dell’s XPS 13
                 Plus Developer Edition with Ubuntu 22.04 LTS and
                 System76’s Oryx Pro, as well as new major FFmpeg, Qt
                 Creator, and VirtualBox releases.


                 On top of that, early adopters got their hands on the
                 alpha version of the upcoming GNOME 43 desktop
                 environment and LibreOffice 7.3 office received a new
                 bugfix release. Below, you can enjoy these and much more
                 in 9to5Linux’s Linux weekly roundup for July 24th, 2022.


          o § Instructionals/Technical⠀➾


                # ⚓ Trend Oceans ☛ How_to_Change_MAC_Address_in_Linux⠀⇛


                       MAC (Media Access Control Address) address is one
                       of the most physical identifiers assigned to your
                       network interface controller. Every device has its
                       own unique mac address, which is set at
                       manufacturing but can be changed using a few tools.


                # ⚓ Linux Capable ☛ How_to_Install_Wine_(WineHQ)_on_Debian_11
                  Bullseye⠀⇛


                       Wine is a free and open-source compatibility layer
                       that enables Windows applications to run on POSIX-
                       compliant operating systems such as Linux, FreeBSD,
                       and macOS. Wine translates each system call your
                       application makes into an equivalent POSIX function
                       used across all platforms, which can be very
                       helpful if you don’t support specific features
                       available in Microsoft’s Windows operating systems.


                       One of the great features of Wine is the Wine
                       AppDB. This database contains lists of confirmed
                       applications that can be run under Wine without
                       errors. This program saves the trouble for Linux
                       users who want to use Windows-based programs on
                       their UNIX systems, but not all programs will work
                       in this way; some may have strange bugs or crashes
                       when run with no warnings beforehand. Despite this,
                       many popular programs such as Microsoft Office and
                       Adobe Photoshop work well under Wine with few to no
                       issues. Overall, the Wine AppDB is a handy tool for
                       anyone looking to use Windows-based programs on
                       Linux.


                       In the following tutorial, you will learn how to
                       install and configure Wine on Debian 11 Bullseye
                       using the command line terminal by importing the
                       official WineHQ repository and installing the
                       latest stable or next release titled development
                       for those eager to try the latest bleeding-edge
                       version of Wine for your windows compatibility
                       needs.


                # ⚓ UNIX Cop ☛ How_to_install_Microsoft_PowerShell_on_Ubuntu
                  22.04 [Ed: How to destroy GNU/Linux.]⠀⇛


                # ⚓ Linux Shell Tips ☛ How_to_Find_a_String_in_a_tar.gz_Archive
                  File_in_Linux⠀⇛


                       Archiving files is another important aspect of
                       Linux file management, which helps in organizing
                       and managing your project-related files and also
                       saves on disk space to let your Linux OS
                       accommodate more files and be more performant.


                       A common file archiving tool for seasoned Linux
                       users is the GNU tar archiving program, which not
                       only lets us store multiple files in a single file
                       archive but also gives Linux users the privilege of
                       manipulating the same archives.


                       This tutorial however seeks to explore the
                       possibility of grepping an already existing tar.gz
                       archive.


                # ⚓ Linux Shell Tips ☛ How_to_View_Files_in_Linux_Using_cat,
                  more,_or_less_Commands⠀⇛


                       Linux has numerous file viewing tools at its
                       disposal and these tools give Linux users the
                       flexibility of scanning or going through already
                       existing files with the objective of fact-checking
                       or simply retrieving specific information. Three
                       in-built file viewing commands are availed in
                       Linux, namely, cat, more, and less commands.


                       These three commands will comfortably let you view
                       targeted files under the Linux operating system
                       environment. Despite this shared commonality
                       between the three commands, the functional
                       originality defined for each of them is different.


                # ⚓ Linux Shell Tips ☛ The_History_of_Manjaro_Linux
                  Distribution⠀⇛


                       Based on Arch Linux, Manjaro Linux is a desktop-
                       oriented and user-friendly Linux distribution
                       designed for desktop lovers and Linux users with a
                       keen eye for an exciting UI experience.


                       Manjaro is a rolling release and is entirely open
                       source and free to download. It is a versatile
                       distribution that can be used for gaming, app
                       development, and even for basic desktop tasks at
                       home or in the office. It is easy to install and
                       provides basic applications out-of-the-box to help
                       you get started.


                       In this guide, we explore the journey that Manjaro
                       had taken from when it was first released to where
                       it is currently.


                # ⚓ Barry Kauler ☛ Install_Limine_to_PC_with_mainline_Linux
                  distros⠀⇛


                       This is a continuation of case-studies, using
                       Limine Installer to install Limine to computers
                       with different hardware and software setups.
                       In this case, installing to my “HP Tower” PC. I
                       bought this secondhand, many years ago. The guy I
                       bought it from had built it from various parts,
                       including a Hewlett Packard motherboard. It is one
                       of the early UEFI motherboards.
                       Originally, it had Windows, that I removed, and
                       currently has two frugal installations, EasyOS and
                       VanillaDpup, and three mainstream-Linux
                       installations, Debian, Mint and Manjaro. The
                       mainstream distros all installed GRUB2, though, the
                       end result has become a bit confused.


                # ⚓ ELinux ☛ How_to_set_max_open_files_in_MariaDB_/_MySQL_in
                  CentOS_7⠀⇛


                # ⚓ LinuxTechi ☛ How_to_Install_Kubernetes_Cluster_on_Ubuntu
                  22.04⠀⇛


                       Are you looking for an easy guide on how to install
                       Kubernetes Cluster on Ubuntu 22.04 (Jammy
                       Jellyfish)?


                       The step-by-step guide on this page will show you
                       how to install Kubernetes cluster on Ubuntu 22.04
                       using Kubeadm command step by step.


                       Kubernetes is a free and open-source container
                       orchestration tool, it also known as k8s. With the
                       help of Kubernetes, we can achieve automated
                       deployment, scaling and management of containerized
                       application.


                       A Kubernetes cluster consists of worker nodes on
                       which application workload is deployed and a set up
                       master nodes which are used to manage worker nodes
                       and pods in the cluster.


    * § Distributions and Operating Systems⠀➾


          o § Devices/Embedded⠀➾


                # ⚓ Linux Gizmos ☛ ESP32-based_PoE+_board_designed_for_home
                  automation_applications⠀⇛


                       The Espoir is a Power over Ethernet (PoE+) board
                       built around the ESP32-MINI-1 microcontroller and
                       it includes a mikroBUS socket for additional
                       peripherals. This tiny device is OSHWA certified
                       and it was designed for applications such as
                       gardening, home automation, etc.


                       The Espoir is a four-layer board that features the
                       ESP32-MINI-1 which is a dual core processor with
                       maximum frequency of 240MHz. This ESP32
                       microcontroller includes 4MB of flash and 520KB of
                       SRAM. For connectivity, there is one GbE LAN port
                       in addition to the 802.11b/g/n Wi-Fi and Bluetooth
                       4.2 support.  


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


          o ⚓ OpenSource.com ☛ The_secret_to_making_self-organized_teams_work
            in_open_source⠀⇛


                 Managers and executives are in the business of managing
                 people and resources. Because many of our models for
                 organization are built with the assumption that there’s a
                 manager involved, there’s an expectation that there’s
                 some level of control over all the moving parts of the
                 mechanisms we build. And for that reason, when you
                 propose the idea of self-organizing teams to a manager,
                 the response is often that it’s just not possible. Surely
                 everything will spin out of control. Surely the only way
                 to maintain momentum and direction is through the
                 guidance of a project manager and a technical manager.


                 It’s not just management that gets confounded by the
                 concept of self-organizing teams, though. It can give
                 pause to team members, too. After all, in traditional
                 organizations a developer only needs to deal with the
                 technical manager. However, in a self-organizing team, a
                 developer has to face at least seven or eight pairs of
                 eyes (their team members.) That can be a pretty
                 overwhelming prospect.


                 Is it possible for self-organizing teams to thrive?


                 Take the example of a team I have coached. One day at a
                 daily standup meeting, a technical manager stood behind
                 the team without saying a word.


          o § Productivity Software/LibreOffice/Calligra⠀➾


                # ⚓ OpenSource.com ☛ Tour_Collabora_Online,_an_open_source
                  alternative_to_Google_Workspace⠀⇛


                # ⚓ OpenSource.com ☛ How_to_use_LibreOffice_Writer_templates⠀⇛


                       A staple in any office software suite is the word
                       processor. Whether your needs are small or large,
                       from jotting down a note to writing a book, the
                       word processor gets the job done. Most Linux
                       distributions include the LibreOffice suite, and I
                       use LibreOffice Writer as my word processor.


                       LibreOffice Writer provides lots of flexibility
                       through its toolbar, keyboard shortcuts, and menus.
                       But if you just want to start a document without
                       too much hassle, you can use one of the pre-loaded
                       templates. Here’s how to use LibreOffice Writer
                       templates to make your work easier.


          o § Programming/Development⠀➾


                # ⚓ postmarketOS_//_Considering_SourceHut⠀⇛


                       It’s important to us that the software we use could
                       be selfhosted. But there’s a lot of maintenance
                       effort that comes with running a selfhosted
                       instance of pretty much any code hosting or CI
                       infrastructure related software: making sure it is
                       constantly available, has no unpatched
                       vulnerabilities, doesn’t run into performance
                       problems etc. All the time we would spend on that
                       is time we can’t spend actually hacking on phones.
                       We would very much like to avoid that.


                       So platforms where we would need to selfhost either
                       the whole code forge or CI for it are out of the
                       picture. As you can guess from the title, SourceHut
                       is the prime candidate right now and there we could
                       just use the official instance at sr.ht for
                       everything, including CI. In fact, we have been
                       using the CI component already since end of 2019 to
                       build all packages and images.


    * § Leftovers⠀➾


          o ⚓ India Times ☛ Uber_admits_covering_up_2016_[cracking],_avoids
            prosecution_in_U.S._settlement⠀⇛


                 Hinds said the decision not to criminally charge Uber
                 reflected new management’s prompt investigation and
                 disclosures, and Uber’s 2018 agreement with the FTC to
                 maintain a comprehensive privacy program for 20 years.


                 The San Francisco-based company is also cooperating with
                 the prosecution of a former security chief, Joseph
                 Sullivan, over his alleged role in concealing the
                 [cracking].


          o ⚓ Hackaday ☛ Turn_Drone_Into_A_Large_Propeller_To_Increase_Hover
            Efficiency⠀⇛


                 Multirotor drones are significantly more popular than
                 conventional helicopter designs for many reasons, which
                 do not include efficiency. Making use of the aerodynamic
                 effects behind this, [Nicholas Rehm] was able to
                 significantly increase the efficiency of his experimental
                 tricopter by turning it into one large spinning
                 propeller.


          o ⚓ Hackaday ☛ Stackable_3D-Printed_Gearbox_For_Brushless_Motor⠀⇛


                 Affordable brushless motors are great for a variety of
                 motion applications, but often require a gearbox to tame
                 their speed. [Michael Rechtin] decided to try his hand at
                 designing a stackable planetary gearbox for a brushless
                 motor that allows him to add or remove stages to change
                 the gear ratio.


          o § Hardware⠀➾


                # ⚓ Hackaday ☛ A_’70s_TV_With_’20s_Parts⠀⇛


                       Keeping older technology working becomes
                       exponentially difficult with age. Most of us have
                       experienced capacitor plague, disintegrating wire
                       insulation, planned obsolescence, or even the
                       original company failing and not offering parts or
                       service anymore. To keep an antique running often
                       requires plenty of spare parts, or in the case of
                       [Aaron]’s vintage ’70s Sony television set, plenty
                       of modern technology made to look like it belongs
                       in a machine from half a century ago.


                # ⚓ Hackaday ☛ Interesting_Optics_Make_This_Laser_Engraver_Fit
                  In_A_Pocket⠀⇛


                       We’re going to start this post with a stern
                       warning: building a laser engraver that can fit in
                       your pocket is probably not a wise idea. Without
                       any safety interlocks and made from lightweight
                       components as it is, this thing could easily tip
                       over and sear a retina before you’d even have time
                       to react. You definitely should not build this, or
                       even be in the same room with it. Got it?


                # ⚓ Hackaday ☛ Automated_Hotend_Swapping_For_Less_Wasteful
                  Multicolor_Printing⠀⇛


                       Multicolor printing on FDM machines can be tricky
                       to get working flawlessly, and purging hotends when
                       changing colors can end up wasting a lot of
                       filament and material. To solve this problem for
                       the popular Prusa i3 and Ender 3 printers,
                       [BigBrain3D] developed the Swapper3D, an automated
                       system that swaps the entire hotend when the
                       material is changed, eliminating the need for
                       purging almost entirely. Video after the break.


                # ⚓ Hackaday ☛ Complex_Movements_From_Simple_Inflatables,
                  Thanks_To_Physics⠀⇛


                       Inflatable actuators that change shape based on
                       injected pressure can be strong, but their big
                       limitation is that they always deform in the same
                       way.


          o § Proprietary⠀➾


                # ⚓ The Register UK ☛ AWS_sales_boss_claims_Microsoft’s
                  softened_cloud_licensing_regime_is_a_sham⠀⇛


                       A senior exec at Amazon Web Services has accused
                       Microsoft of making cosmetic licence changes to
                       appease regulators, but continuing to ensure its
                       wares are more expensive when run in rivals’
                       clouds.


                       Matt Garman, a senior vice president for sales and
                       market at AWS took to LinkedIn to share his opinion
                       that “Customers and policy makers around the world
                       increasingly see MSFT’s recent licensing rhetoric
                       as a troubling admission of the same anti-
                       competitive tactics that many companies have been
                       raising with them for years, but went unheeded
                       until they were put before the European
                       Commission.”


          o § Security⠀➾


                # ⚓ Windows Latest ☛ Microsoft:_KB5015882,_KB5015814_updates
                  break_Start_menu_in_Windows_11⠀⇛


                       The last two cumulative updates for Windows 11 –
                       KB5015882 and KB5015814 – are causing major issues
                       for some users, according to several reports and
                       Microsoft’s own documentation. The latest round of
                       updates could make the Start menu disappear as soon
                       as you try to open it, thanks to a bug in the
                       operating system.


          o § Defence/Aggression⠀➾


                # ⚓ Foreign Policy ☛ Can_This_Brussels_Neighborhood_Shake_Its
                  Jihadi_Reputation?⠀⇛


                       But while Washington has pivoted away from the
                       Middle East, withdrawing from Afghanistan and
                       reducing its troop presence in Iraq, and the
                       Islamic State’s popularity has waned amid its
                       territorial defeats, local factors in Molenbeek
                       remain that extremist groups could now exploit. In
                       particular, unemployment in Molenbeek is 21
                       percent, three times the national average. Economic
                       despair has coincided with crime increasing in the
                       neighborhood, especially in drug trafficking over
                       the past couple years. “For more than 40 years,
                       [Molenbeek] was a drug trafficking line from
                       Morocco to the Netherlands, but drug trafficking
                       has exploded recently mainly because the pandemic
                       reduced earnings,” Leman said. “It has become a
                       business model for many families.”


                # ⚓ Algemeiner ☛ In_Belgium,_Jihadists,_Guns,_and_(Drug)
                  Money⠀⇛


                       Molenbeek, Belgium, you may recall, was the
                       Brussels neighborhood that was home to almost half
                       of the jihadists responsible for the 2015 Paris
                       attacks and several subsequent terror attacks in
                       Belgium. The bomber of a train at Brussels Central
                       Station in 2017, for instance, lived in Molenbeek.
                       Mehdi Nemmouche, who shot and killed four people at
                       Brussels’ Jewish Museum in 2014, had previously
                       lived in Molenbeek. The mastermind of the Paris
                       killings, Abdelhamid Abboud, grew up and still
                       lived in Molenbeek.


                # ⚓ Counter Punch ☛ The_War_‘Diplomat’:_How_Borrell,_the_West
                  Lost_the_‘Global_Battle_of_Narratives’⠀⇛


                       “The global battle of narratives is in full swing
                       and, for now, we are not winning,” Borrell
                       admitted. The solution: “As the EU, we have to
                       engage further to refute Russian lies and war
                       propaganda,” the EU’s top diplomat added.


                       Borrell’s piece is a testimony to the very
                       erroneous logic that led to the so-called ‘battle
                       of narratives’ to be lost in the first place.


                # ⚓ Common Dreams ☛ Opinion_|_The_War_‘Diplomat’:_How_Borrell
                  and_the_West_Lost_the_‘Global_Battle_of_Narratives’⠀⇛


                       In a blog entry reflecting on the G20 Foreign
                       Ministers’ meeting in Bali, Indonesia on July 7-8,
                       the High Representative of the European Union,
                       Josep Borrell, seems to have accepted the painful
                       truth that the West is losing what he termed “the
                       global battle of narratives.”


          o § Environment⠀➾


                # ⚓ Counter Punch ☛ Paper_Straws_Are_Not_Enough⠀⇛


                       According to Monbiot: “Paper straws are not enough.
                       Only System Change can halt the climate crisis.” Of
                       course, System Change can only mean throwing out
                       the neoliberal brand of capitalism in favor of
                       almost anything else.


                       Adam Smith would be spinning in his grave with
                       today’s crony capitalism. Interestingly, “the term
                       ‘capitalism’ appears nowhere in Smith’s writings.”
                       (Source: Jesse Norman, Adam Smith, Penguin Random
                       House/UK 2018, pgs. 265-66)


                # ⚓ TruthOut ☛ Roads_Are_Literally_Melting_in_Europe_During
                  Unprecedented_Heat_Wave⠀⇛


                # ⚓ TruthOut ☛ Biden_Mulls_Climate_Emergency_Declaration_as
                  Wildfire_Sweeps_California⠀⇛


                # ⚓ Counter Punch ☛ The_Fateful_Fist_Bump⠀⇛


                       Perhaps Joe Biden’s advisors thought that a fist
                       bump between the president and Saudi leader
                       Mohammed bin Salman (MbS) would also somehow avoid
                       the appearance of contamination and embarrassment,
                       in this case of the political variety. Certainly,
                       they were worried about the near-radioactivity of
                       MbS. The crown prince is responsible for the murder
                       of a Washington Postjournalist, the ongoing war in
                       Yemen, and innumerable human rights abuses in Saudi
                       Arabia. Indeed, on the campaign trail, Biden had
                       promised to turn the Saudi autocrat into a
                       veritable “pariah.”


                       Shaking hands with such a devil seemed
                       inconceivable for a president determined to
                       distance himself from the callous disregard for
                       human rights of his predecessor. But perhaps a fist
                       bump…?


                # ⚓ Common Dreams ☛ Opinion_|_The_Fist_Bump_Was_Bad,_But
                  Biden’s_Middle_East_Policies_Are_Worse⠀⇛


                # ⚓ Counter Punch ☛ Back_to_the_Future:_Biden_in_the_Middle
                  East⠀⇛


                       Biden did what all presidents do: He gave priority
                       to strategic and economic interests ahead of human
                       rights. His main accomplishment is that he
                       discarded some of the worst features of Trump’s
                       Middle East policy.


                       Suspending Human Rights


                # ⚓ Counter Punch ☛ By_the_Givers_of_Jordan⠀⇛


                       Towards the end of last year, I wrote a piece for
                       CounterPunch on the Hashemite kingdom, using
                       personal memories and anecdotes from my time there
                       during what I called the foothills of Gulf War One.
                       These were pitted against a recent barrage of
                       coordinated barbs and criticism directed against
                       the kingdom. I suggested that this was not only
                       wearisome for the reader but counter-productive to
                       peace and security in the region. Since then, and
                       this is the great surprise, there has actually been
                       a change in attitude towards Jordan, that for me is
                       like watching someone come back from the dead.


                       I see it in all sorts of ways, global food crises
                       or tightening of oil markets or not. The now
                       completed, and sometimes befuddled, visit by US
                       President Biden to the region, when Biden was met
                       on Jeddah tarmac by Prince Bandar bin Sultan,
                       deputy governor of Mecca, and not by Saudi Crown
                       Prince Mohammed bin Salman, has not been the only
                       show in town. The crown prince, or MBS as he is
                       known — to be fair, not exactly rehabilitated later
                       by Biden’s visit — held recent talks with Jordan’s
                       King Abdullah II at Al Husseiniya Palace in the
                       capital Amman. This was the first such visit by the
                       de facto ruler of Saudi Arabia in years. This new
                       phase of cooperation, with its openly declared
                       enthusiasm for good relations, was a genuine
                       surprise. MBS was granted the Order of al-Hussein
                       bin Ali, the highest in Jordan. All those tense
                       past few years, due to contrasting views on local
                       hostilities and pledges of aid not followed
                       through, evaporated like a desert haze. Colossal
                       funding projects of at least $3 billion promised by
                       Saudi Arabia could now be unblocked. It was like
                       watching a desert rock at sundown change colour
                       last minute. ‘There are large investments in Jordan
                       that we are keen to actively participate in and
                       such investments will bring benefits to both
                       countries,’ said MBS. (‘What are the Saudis up to?’
                       one observer exclaimed to me about this.) Despite
                       Biden later refusing to make Saudi Arabia a ‘pariah
                       state’, at the same time as blaming MBS for being
                       personally responsible for the killing of Saudi
                       journalist Jamil Khashoggi, not even he was treated
                       with such largesse. (They say MBS in quick reply to
                       mention of Khashoggi accused Washington of
                       hypocrisy by not investigating the killing of
                       Palestinian-American journalist Shireen Abu Aqleh,
                       and for allowing Abu Ghraib prisoners to be
                       abused.)


                # ⚓ Counter Punch ☛ Creating_the_Capitalocene:_Endless
                  Accumulation⠀⇛


                       “ . . . why does the early modern period come
                       across as the new era of progress and humanism (?)
                       . . . The reason for cultivating this myth is
                       obvious: it is crucial to the West’s narrative of
                       being the bearer of progress throughout the history
                       of mankind. But what if our present system was
                       actually built on a nightmare, born of naked
                       violence and sheer despair? . . . What if
                       civilization did not make progress, but
                       systematized barbarism instead?”


                       It is that system which threatens to plunge the
                       world into final nightmares as we confront the
                       consequences, of warfare and ecological
                       destruction.  “  . . . we must thoroughly question
                       the foundations of our economy, our state and much
                       more,” Scheidler writes in his recent work, The End
                       of the Megamachine: A Brief History of a Failing
                       Civilization.


                # ⚓ Common Dreams ☛ Opinion_|_Greenland_Loses_6_Billion_Tons_of
                  Ice_in_3_Days,_Harbinger_of_Unprecedented_Coastal_Flooding⠀⇛


                       CNN and The Independent reported this week on a
                       massive ice melt in Greenland, with on the order of
                       6 billion tons of ice lost in three days. The
                       melting was because of a heat wave at the top of
                       the world, caused by our burning coal, gasoline,
                       and methane gas and spewing billions of tons of the
                       dangerous heat-trapping gas carbon dioxide into the
                       atmosphere.


                # § Wildlife/Nature⠀➾


                      # ⚓ Common Dreams ☛ California_Oak_Fire_Rages_Out_of
                        Control_as_Biden_Mulls_Climate_Emergency⠀⇛


                             Thousands of emergency workers in California
                             struggled to fight a rapidly growing wildfire
                             near Yosemite National Park on Sunday as
                             President Joe Biden continued to mull whether
                             to declare a national climate emergency, a
                             move that campaigners say is needed to
                             respond to the immediate threat of extreme
                             weather and lay the groundwork for a livable
                             future.


                             Dubbed the Oak Fire, the California blaze was
                             completely uncontained as of Sunday
                             afternoon, having tripled in size since it
                             began on Friday. The fire has now burned more
                             than 14,000 acres, making it California’s
                             largest wildfire of the season.


          o § Finance⠀➾


                # ⚓ TruthOut ☛ Amid_Eviction_Crisis,_Organizers_Win_Right_to
                  Legal_Representation_for_Tenants⠀⇛


                # ⚓ TruthOut ☛ Federal_Minimum_Wage_Hasn’t_Been_Raised_in_13
                  Years⠀⇛


                # ⚓ Common Dreams ☛ On_13th_Anniversary_of_Last_Minimum_Wage
                  Hike,_Dems_Urged_to_Raise_‘Deplorable’_$7.25_Floor⠀⇛


                       Marking the 13-year anniversary of the last federal
                       minimum wage increase in the U.S.—a meager boost
                       from $5.15 to $7.25 in 2009—progressive campaigners
                       on Sunday urged congressional Democrats to make
                       another push to raise the national pay floor as
                       inflation continues to diminish workers’ purchasing
                       power.


                       “Congress must act to raise wages for the tens of
                       millions of workers who are struggling just to get
                       by.”


                # ⚓ Counter Punch ☛ Why_Trader_Joe’s_Workers_Are_Joining_the
                  Fight_to_Unionize⠀⇛


                       Modern companies like Apple, Google, Starbucks,
                       and Trader Joe’s perpetrated this lie, obscuring
                       their business practices with a veneer of
                       progressive ideals and referring to staff with
                       euphemistic titles like “partners,” “associates,”
                       or “crew members.” Indeed, many workers employed
                       within this slice of the American corporate world
                       were often relatively content—until now. Alongside
                       the recent pro-union activity at more than 150
                       Starbucks cafés across the United States is a
                       newfound awareness among some workers at the Trader
                       Joe’s grocery chain that a union may also be in
                       their best interest.


                       Unlike corporations like Starbucks or Amazon where
                       attempts to unionize have a long history, Trader
                       Joe’s workers have traditionally been content. In
                       2003, when tens of thousands of grocery store
                       workers in Southern California—home of the original
                       Trader Joe’s—went on strike for better working
                       conditions and pay, Trader Joe’s workers, who were
                       not unionized, sat out the labor strife.


                # ⚓ Common Dreams ☛ Opinion_|_The_World_Burns_and_the_Richest
                  Profit._It_Doesn’t_Have_to_Be_This_Way⠀⇛


                       The last time prices rose this fast was 41 years
                       ago. The last time the UK got through prime
                       ministers this fast was the mid-1970s. The last
                       time there was open war between major European
                       powers was in 1945. The last time the Northern
                       Hemisphere was this hot was probably 125,000 years
                       ago.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Telex (Hungary) ☛ Orbán’s_key_word_for_the_season_ahead:
                  staying_out⠀⇛


                       The Bálványos Free Summer University and Student
                       Camp (more commonly known as Tusványos) has been
                       organised in Transylvania since 1990. It has become
                       a large-scale intellectual workshop of the
                       Carpathian Basin, with tens of thousands in
                       attendance. It was originally intended to promote
                       cross-border cooperation, Romanian-Hungarian
                       dialogue and a cultured Hungarian-Hungarian
                       political exchange. According to critics, in recent
                       years it has become a place where members of the
                       Budapest government and representatives of the
                       intellectual establishment close to them express
                       their ideas without substantive debate. It was here
                       that Viktor Orbán first spoke about building an
                       “illiberal democracy’ in 2014, and his speeches
                       have become the highlight of the event and are
                       largely considered to be marking the direction of
                       Fidesz’ politics for the year ahead. This year’s
                       speech was no different.


                # ⚓ Craig Murray ☛ The_Forde_Report_and_the_Labour_Right⠀⇛


                       Nobody can accuse the authors of the Forde report
                       of having a low opinion of themselves. Its lofty
                       tone reflects profound disdain for the views and
                       actions of mere mortals, and it utters judgments
                       with an air of deep profundity. This is amusing as
                       it is banal in the extreme.


                # ⚓ TruthOut ☛ Political_Polarization_Is_Pushing_Evangelicals
                  to_a_Historic_Breaking_Point⠀⇛


                # ⚓ Scheerpost ☛ What_Does_the_Future_Between_the_US_and_China
                  Look_Like?⠀⇛


                       As China ascends economically and politically, its
                       struggle with the US has grown fiercer. Huang
                       Renwei points out the inherent weakness of the US
                       power structure and argues that, starting in 2020 …


                # ⚓ Common Dreams ☛ Major_Missouri_Newspaper_Calls_Josh_Hawley
                  a_‘Laughingstock’_for_Fleeing_Jan._6_Mob⠀⇛


                       Missouri’s second-largest newspaper by circulation
                       derided home-state Sen. Josh Hawley in a scathing
                       editorial on Saturday, calling him a
                       “laughingstock” and a “coward” after the House
                       panel investigating the January 6 Capitol attack
                       showed previously unseen security footage of the
                       GOP lawmaker fleeing the violent right-wing
                       insurrectionists that he helped embolden.


                       “Hawley has become one of the defining figures of
                       that day,” notes The Kansas City Star’s editorial
                       board. “A famous photo captured by Francis Chung
                       shows him raising a fist in solidarity with the
                       crowds that would soon break through doors, loot
                       offices, and assault law enforcement.”


                # ⚓ Counter Punch ☛ By_Denying_Proven_Failures_in_Tory
                  Government,_Sunak_and_Truss_Will_Repeat_Them⠀⇛


                       I was reminded of this Chinese fable when watching
                       Liz Truss and Rishi Sunak, one of whom will be the
                       next British prime minister come September, pretend
                       to a control over events past and present that is
                       just as fictitious as anything imagined by the
                       Chinese beetle.


                       Governments at all times log anything good that
                       happens as their own achievement and disclaim
                       responsibility for anything bad. There is nothing
                       new in this behaviour, but the Truss/Sunak fantasy
                       picture of what has happened in Britain from
                       Margaret Thatcher to Boris Johnson requires a
                       radical rewrite of history.


                # ⚓ Counter Punch ☛ Scott_Morrison_Awaits_the_Apocalypse⠀⇛


                       This may well have been the case with Scott
                       Morrison, the accidental of Australia’s prime
                       ministers.  In 2019, he won an election deemed
                       unwinnable.  In 2022, he lost in the formidable
                       face of a third of voters who preferred to go for
                       alternative parties.  Refusing to read the smoke
                       signals from a Liberal heartland worried about
                       political integrity, climate change and violence
                       against women, his party was carved by the stormy
                       arrival of independents and minor parties.


                       Put out to lean, undernourished pasture, there was
                       little reason to expect him to slide into
                       respectable obscurity.  The lecture circuit
                       beckoned, and his debut came in his July 14 address
                       to the Asian Leadership Conference in Seoul.  In
                       it, he emerges enlightened, quoting from yet
                       another pop-historical tract from historian Niall
                       Ferguson, this time on pandemics.  His account is
                       free of failures and full of praise, much of it for
                       achievements not his own.


                # ⚓ Counter Punch ☛ Yellen’s_Noble_Efforts_Come_to_Naught⠀⇛


                # ⚓ Counter Punch ☛ America_as_Panopticon:_You_are_Being
                  Watched,_Even_if_No_One_is_Looking_for_You⠀⇛


                       Most Americans are aware of video surveillance of
                       public spaces. Likewise, most people know about
                       online tracking – and want Congress to do something
                       about it. But as a researcher who studies digital
                       culture and secret communications, I believe that
                       to understand how pervasive surveillance is, it’s
                       important to recognize how physical and digital
                       tracking work together.


                       Databases can correlate location data from
                       smartphones, the growing number of private cameras,
                       license plate readers on police cruisers and toll
                       roads, and facial recognition technology, so if law
                       enforcement wants to track where you are and where
                       you’ve been, they can. They need a warrant to use
                       cellphone search equipment: Connecting your device
                       to a mobile device forensic tool lets them extract
                       and analyze all your data if they have a warrant.


          o § Civil Rights/Policing⠀➾


                # ⚓ Pro Publica ☛ Richard_Glossip_Set_to_Be_Executed_in
                  Oklahoma_Amid_Innocence_Claims⠀⇛


                       In the parking lot outside the Oklahoma State
                       Penitentiary, I stood on my toes in a throng of
                       reporters, straining to hear death row inmate
                       Richard Glossip’s words through the speaker of a
                       phone his friend held aloft.


                       It was 3:45 p.m. on Sept. 30, 2015, and Glossip
                       should have been dead by now from a cocktail of
                       lethal drugs pumped into his body.


                # ⚓ Common Dreams ☛ Opinion_|_Biden_Backs_Off_Anti-Abortion
                  Judicial_Nominee—Because_GOP_Senator_Objects⠀⇛


                # ⚓ TruthOut ☛ We_Can’t_Build_Real_Power_by_Defending
                  Democrats._We_Must_Organize_From_Below.⠀⇛


                # ⚓ Linux Gizmos ☛ ATX_board_integrates_12th_Gen_Intel
                  processors,_dual_2.5GbE,_quad-displays_and_5G/LTE_support⠀⇛


                       A few days ago, IBASE unveiled an ATX motherboard
                       debuting the 12th Gen Intel Core processors. The
                       MBB-1000 supports up to 128GB DDR4 RAM, four SATA
                       ports, eight USB 3.1 ports and several other
                       peripherals.


                       The MBB-1000 motherboards feature an LGA 1700
                       socket compatible with the latest Intel’s Alder
                       Lake processors that integrate up to 8 P-cores and
                       E-cores. According to the product page, the
                       chipsets supported will be the R680E, Q670E and the
                       W680. See this link to see the chipsets comparison.


          o § Digital Restrictions (DRM)⠀➾


                # ⚓ Computer World ☛ Netflix_to_launch_ad-supported_tier_with
                  Microsoft_in_2023⠀⇛


                       Netflix chief operating officer Greg Peters told
                       analysts during the company’s earnings call
                       yesterday that “all of the ads that are served on
                       our ad-supported offering will come through
                       Microsoft. So that’s an exclusive arrangement with
                       them.”


                # ⚓ The Verge ☛ Streaming_video_apps_all_look_the_same_now⠀⇛


                       Based on the comments on our story and comments
                       I’ve seen across Twitter, Reddit (1, 2, 3), and
                       elsewhere, people don’t seem to mind the
                       similarities. This interface has gradually become
                       the de facto standard across Netflix, Disney Plus,
                       HBO Max, and now Prime Video. And consistency goes
                       a long way here; we’re fundamentally using all of
                       these services to reach the entertainment on each
                       one, and having a samey interface between them
                       should make doing so easier for everyone.


          o § Monopolies⠀➾


                # § Copyrights⠀➾


                      # ⚓ Torrent Freak ☛ Sony_Flags_Its_Own_Website_for_Repeat
                        Copyright_Infringements⠀⇛


                             Takedown notices can be a useful tool for
                             rightsholders to protect their content but
                             it’s less productive when companies start to
                             report their own websites as piracy havens,.
                             This is precisely what an Indian branch of
                             Sony Pictures did recently, and they’re not
                             alone either.


    * § Gemini* and Gopher⠀➾


          o § Personal⠀➾


                # ⚓ Hadestown_and_How_Having_Power_Sucks⠀⇛


                       This moment in the show is absolutely brilliant.
                       When you see it actually staged, Orpheus stamps his
                       feet in time with the “keeps his head low” line,
                       mimicking the choreography from the workers’ chant.
                       It’s a fantastic, beautiful reversal of the theme,
                       showing how Hades is just as trapped as his
                       workers.


                       Being on top of an oppressive hierarchy is awesome
                       from a resources and power standpoint. You have all
                       the power, money, food, everything you could
                       possibly want, at the expense of everyone
                       underneath you. But beyond that, from an emotional
                       — or perhaps even, a spiritual — perspective, there
                       are no winners in the game of oppression. Being at
                       the bottom sucks worst of all because you fear for
                       your survival, your basic needs. But the top of the
                       pile is a terrifying, lonely, impossibly stressful
                       place as well.


                       I say this not to say “Oh, think of the poor
                       billionaires, managing a company from their yacht
                       parties must be so stressful! :(” but rather to
                       point out that *everyone* is worse off under
                       oppressive hierarchies, even when those hierarchies
                       seem to explicitly benefit them. We are not meant
                       to hold so much power. We are not meant to
                       constantly watch our backs, fearful someone will
                       take away our position at the top.


                # ⚓ zine-making,_and_the_benefits_it_provides_(in_my_eyes)⠀⇛


                       I compile a zine, a “per-zine” (personal zine)
                       every so often. Usually every couple of months, and
                       it always is the most rewarding and fulfilling
                       thing I do when I am online. It’s a creative
                       initiative, it’s motivating, it’s 100% *BY* me, and
                       I am glad to keep it going.


                       It’s also a direct response to a *lack* of
                       motivation and creativity I succumbed to when I was
                       on social media for all those years (10 years).
                       Everything was a “do X in order to arrive at the
                       same result as anyone else who ‘does X’”, which was
                       to: gain attention > try to gain followers > try to
                       get reaction/engagement, etc. – when all I ever
                       wanted to do was to feel *personally* satisfied/
                       fulfilled with whatever I was doing. Not need to
                       run it through a vanity filter to vindicate/justify
                       that, “yes, I DO need to feel significant, needed,
                       wanted, fulfilled and satisfied”. So the zine
                       offers that personal gratification.


                # ⚓ Plants_and_Food⠀⇛


                       We may have become a bit plant obsessed as of late.
                       This weekend we picked up the following plants for
                       our yard and future garden…


                       [...]


                       We are hoping to be able to cultivate a nice
                       collection of edibles on our property over time. So
                       far we have 7 different plants that are edible,
                       maybe 8 if you count Hibiscus. Right now the
                       edibles we have are 2 guava trees, 2 varieties of
                       mint, basil, cocoplum, prickly pear, lime and
                       calamondin. Plus, our neighbor on one side has a
                       big avocado tree that produces tons of avocadoes
                       and on the other side they have a huge walnut tree.
                       I’m not sure what else we’ll get in the future but
                       some likely possibilties are some of the many
                       varieties of banana that grow well here, maybe a
                       dwarf variety of orange or maybe some other edible
                       natives like blueberry and mulberry. There are some
                       other native and non-native edibles that grow well
                       in our climate too so we’ll see.


          o § Technical⠀➾


                # ⚓ Ask_advices_about_smartphone_changing_when_you_try_to
                  remove_Google_of_your_life⠀⇛


                       Today, I have a OnePlus Nord since mostly two
                       years, and I am almost satisfied. I have Android
                       smartphones since about ten years today, and I
                       change my phone almost every two years. I want to
                       keep my current phone longer, this time (for
                       ecological reason). My first problem is the
                       software update (with security fixes) seems to be
                       over in one year, and I don’t like to have a phone
                       without security fixes. My second problem is I try
                       to remove maximum Google usage in my (personal)
                       life, and I am not sure if that to keep a
                       “standard” Android phone is a good thing here.


                # ⚓ On_telling_users_to_write_the_documentation_themselves⠀⇛


                       i occasionally encounter a situation in which foss
                       users, noting or complaining about the lack of
                       documentation for a piece of software – whether an
                       end-user application or a developer library – get
                       told by the software dev(s) to write it themselves.


                       This feels _ridiculous_ to me. Someone reaching for
                       documentation is doing so because _they don’t know_
                       how to use some software, whether an application or
                       a library. Since _they don’t know_ how to use the
                       software, they are _not able to document how to use
                       it_!


                # § Science⠀➾


                      # ⚓ Bad_news_for_the_pub⠀⇛


                             People aged under 40 should not drink alcohol
                             and consumption guidelines should be changed,
                             study says


                      # ⚓ Putting_ourselves_out_of_business⠀⇛


                             I’ve started reading Patrick Stuart’s blog
                             post about artificial intelligence and art,
                             and I immediately thought of a post by Judd
                             Karlmann I recently saw on Mastodon.


                # § Internet/Gemini⠀➾


                      # ⚓ Re:_Gemlog_and_internet_time⠀⇛


                             I received a nice email from Ernst, but
                             something’s not right with the account so I
                             can’t send a response. So instead, I’ll just
                             publish my reply here.


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


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