𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Friday, July 29, 2022
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Generated Sat 30 Jul 02:39:44 BST 2022
Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖)
Full hyperlinks for navigation omitted but are fully available in the originals
The corresponding HTML versions are at 𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈
Latest in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕 and older bulletins can be found at 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕-𝒂𝒓𝒄𝒉𝒊𝒗𝒆𝒔
Full IPFS index in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔 and as plain text in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔/𝒕𝒙𝒕
Gemini index for the day: gemini://gemini.techrights.org/2022/07/29/


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

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QmP3Nw5usXTHPhcMx8yZ9TYsWzwSKRw9BNnbjhkoJ88gpe
QmNt7g1pzLJJDE5MHZ21wEEuyos1W3DFP2LTSjB2FLPJPi
QmXniW6uykwhxPzQFCih3ywbRTbNtozdD9MTkKJWNUUis7
Qmba4Ap4JVU96TSWT1jJZfQAasTyweA1EFu92C6ULqfYVF
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QmZrgDSeEPr5Tk1kd6ixcTH5gK8gVF6UWZ8USDWkwExtL2
QmdVCZ22xUbZkpsSDmSDMrnFTMypCGWw1f2punvumLq2NJ
QmXJTu6CfqTRzBWfbZAfQFS2Je8PJA65YsoWMZp6Z3WV8Z
QmXptQogxzP3vUxmf2ttL7Vyb5aAwUT9Ux3nmXxPkuNRNp
QmYTKahqtmH46iM3ZthdPvDKojc39tpTCiyk2GGs8Y29DU
QmRRSvTcmYGSSCvpvxz5PTAHRT4fdRHip9uhxwcQXMWp9G
QmQpoFyQcBb3KsKSZ3VzsMZsMmgcTqXq1zThATBh2bp3Yp
QmZrQzFnwRoF6P9gTMQfqokg7GSmtCyoyEMWxV7jZxDsZn
QmRgX3FU5tqoWu74D2LUMC84rvb5VBXutGnvudD9rbAAgn
QmNocWiFPVNdoZoPJy1s4vZQryq4BWRJMou5WsNScHuuMt
QmWkLbREwUBZdex6qeeh1UyUD3GwnNihMfEE28VhuPZYAK
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QmTcjQcpQmc33H6tVYxaBQP4SYQnHTEnFzA1HJRmbELhh3
Qmd5sSa6zctA8RcuhbgaMD5PKt4K2aGr7vwBWUT9GrkoLL
QmXggz4ZzdoNrnyGD87xZXV7EnECHikMc7N5PUE6qSiZ7Y


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

⦿ Microsoft Bribing Everyone: Canonical, ’Linux’ Foundation, OSI... (Those That Should Push Back Against Microsoft Crimes) | Techrights

⦿ [Meme] “Truly a Landmark Occasion” | Techrights

⦿ IRC Proceedings: Thursday, July 28, 2022 | Techrights

⦿ GNOME (IBM/Red Hat Staff) Promoting Microsoft’s ’Security’ Scam With the ‘Secure’ Boot Sham | Techrights

⦿ EPO VP4 Nellie Simon: 24/7 Day and Night, Only One Hour to Speak to EPO Staff | Techrights

⦿ Windows Has Had a Very Tough Year (That’s Why Microsoft Starts to Block GNU/Linux With ’Secure’ Boot) | Techrights

⦿ Microsoft Windows in Chinese Desktops/Laptops Down to 80% (Hence Microsoft Started Blocking GNU/Linux From Even Booting, as China’s Lenovo Demonstrates) | Techrights

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
		http://techrights.org/2022/07/29/bribing-the-rivals/#comments
		http://techrights.org/2022/07/29/epo-landmark-occasion/#comments
		http://techrights.org/2022/07/29/irc-log-280722/#comments
		http://techrights.org/2022/07/29/richard-hughes-secure-boot-sham/#comments
		http://techrights.org/2022/07/29/too-busy-to-get-real-work-done/#comments
		http://techrights.org/2022/07/29/tough-windows-year/#comments
		http://techrights.org/2022/07/29/windows-in-china/#comments

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
		http://techrights.org/2022/07/29/linux-foundation-greenwashing-microsoft/#comments
		http://techrights.org/2022/07/29/sysadmin-appreciation-day/#comments

                    ䷩ 𝚕𝚒𝚗𝚎 66

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/07/29/bribing-the-rivals/#comments
    Gemini version at gemini://gemini.techrights.org/2022/07/29/bribing-the-rivals/

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Gemini_version_available_♊︎


✐ Microsoft_Bribing_Everyone:_Canonical,_‘Linux’_Foundation,_OSI…_(Those_That
Should_Push_Back_Against_Microsoft_Crimes)⠀✐


Posted in Antitrust, Deception, Microsoft at 3:01 am by Dr. Roy Schestowitz


From yesterday’s “news” alone:


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Openwashing_and_greenwashing_as_a_service_diluting_the_brand
'Linux'_for_Microsoft⦈_


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇What_is_an_Open_Source_Program_Office_and_why_you_should
have_one:_The_openwashing_hive_known_as_OSI_is_now_more_closely_connected_to_LF
via_TODO_Group;_these_are_proprietary_people⦈_


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Let’s_get_confidential!_Canonical_Ubuntu_Confidential_VMs
are_now_generally_available_on_Microsoft_Azure:_When_did_you_sell_to_Microsoft
and_how_much_for,_Mark_Shuttleworth_(MS)?_a_division_of_Microsoft?_exclamation
mark_on_a_LIE⦈_


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Ubuntu_Confidential_Virtual_Machines_come_to_Microsoft
Azure:_Layoffs,_failure;_Azure_is_surveillance;_company_that_blocks_Linux⦈_


Summary: Don’t expect the Linux_Foundation or OSI to speak out against
Microsoft’s latest crimes [1, 2, 3]; heck, even Ubuntu no longer competes with
Windows because Microsoft paid the parent company to become a partner instead
of competitor (hence WSL); this is what antitrust laws exist for! But nobody
enforces them anymore, except when Microsoft lobbyists ask regulators to focus
on other companies, weaponising_enforcement_to_basically_protect_an_abusive
monopolist


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⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣾⣶⣴⣶⣷⣶⣾⣷⣷⣷⣦⣶⣶⢾⣶⣷⣶⣶⣷⣶⣷⣶⣶⣶⣷⣶⣶⣧⣶⣦⣶⣶⣶⣾⣶⣷⣷⣿⣾⣷⣶⣴⣾⣿⣷⣶⣷⣶⣾⣶⣷⣾⣶⣶⣶⣷⣷⣶⣶⣶⣾⣶⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣧⣴⣦⣤⣥⣧⣵⣧⣤⣦⣲⣿⣦⣤⣼⣥⣦⣢⣷⣥⣴⣽⣤⣎⣮⣬⣴⣵⣶⣵⣥⣧⣤⣼⣽⣼⣷⣷⣥⣄⣤⣮⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⢿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⣿⣿⣿⢿⣿⣿⡿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣥⣠⣤⣤⣽⣦⣾⣼⣬⣴⣵⣼⣤⣤⣤⣤⣼⣤⣤⣧⣤⣤⣤⣾⣴⣤⣤⣆⣈⣧⣦⣤⣼⣸⣤⣦⣤⣤⣤⣼⣤⣤⣞⣧⣤⣤⣤⣤⣼⣤⣤⣦⣥⣤⣤⣴⣦⣥⣤⣤⣷⣥⣬⣤⣰⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣭⣋⣉⣙⣏⣍⣉⣉⣩⣩⣹⣉⣹⢉⣩⡫⣿⣫⣉⣙⣽⣋⣉⣉⣫⣋⣉⣙⣏⣩⢉⣉⣙⣽⣋⣹⣉⣉⣫⣉⣍⣉⡝⣿⣉⢉⣙⣍⢏⣽⣏⣏⣋⣉⣹⣹⣉⣻⣝⣉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⡟⠛⠟⠿⡟⠿⣟⠟⠻⠿⠿⣟⢻⠿⠿⡛⠟⠿⠿⣻⠻⠿⠟⠻⠿⡛⡿⠿⠿⠿⠿⠿⠻⠟⠿⣟⠿⡟⠿⡻⡿⠟⡿⣻⠛⠿⢿⠻⠻⠿⠻⢿⠛⠿⠟⠻⠟⡟⠟⢿⡿⠻⠿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣾⢶⣶⣷⡷⣷⣾⣷⣿⣶⣶⣶⣷⣿⣶⣾⣷⣷⣷⣶⣾⣶⠶⣷⣶⠿⢾⡷⣷⣶⣾⣶⣶⣾⣷⣶⣷⡷⢿⡾⣾⡾⣶⢿⡾⣶⣶⢾⣾⣶⣶⣾⣾⣶⡶⣶⣶⣷⣷⣷⣾⣿⣶⣷⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣵⣧⣴⣤⣤⣥⣮⣦⣤⣤⣴⣼⣤⣤⣥⣯⣦⣤⣤⣬⣶⣽⣤⣰⣤⣤⣤⣤⣤⣸⣥⣧⣤⣤⣤⣤⣶⣧⣤⣤⣤⣦⣤⣤⣧⣬⣴⣼⣤⣤⣧⣧⣤⣤⣤⣥⣤⣼⣤⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣭⣉⣉⣉⣉⣉⣍⣈⣉⣉⣏⣩⣁⣁⣉⣍⣉⣋⣉⣯⣊⣉⣉⣁⣀⣀⣽⣈⣙⣁⣁⣉⣍⣹⣉⣉⣩⣹⣈⣀⣉⣉⣉⣹⣉⣏⣈⣉⣹⣉⣉⣈⣉⣹⣉⣉⣉⣉⣈⡉⣩⣩⣉⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⡟⠛⠛⠛⡙⡛⠛⡟⡛⡻⡛⠛⠛⠛⣟⡛⡟⡻⢻⠛⡛⠛⢻⠟⠛⠛⡛⡟⠛⠋⣟⠛⠛⠛⠟⣛⠛⠛⠛⠛⢟⢻⠛⠙⢟⠛⠛⢛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢹⡛⢻⠛⣛⠛⠛⠛⢛⠟⠛⡟⠝⠛⠛⠋⠋⡙⢻⠛⡟⠛⡟⠛⠛⡟⠙⢻⠛⠋⠛⠛⠛⠛⣻⠛⠛⡟⡟⢛⢛⢻⠛⢿⠛⠛⠛⠙⢛⠛⠛⡟⢻⣛⠛⢛⠛⠛⡟⢙⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⠿⠿⢿⠿⢿⠿⢿⡿⠿⠿⠿⡿⡿⢿⠿⢿⠿⢿⠿⠿⠿⡿⠿⠿⡿⡾⠿⠿⠿⠿⢿⠿⠿⠿⠿⣿⠿⡿⠷⠿⠿⣿⡿⠿⠿⡿⠿⠿⠿⠿⠿⢿⢿⠿⠿⠿⠿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣶⣷⣷⣿⣶⣶⣶⣶⣶⣶⣷⣷⣶⣶⣾⣶⣷⣶⣷⣶⣷⣶⣶⣷⣾⣷⣷⣶⣶⣿⣶⣶⣾⣤⣼⣶⣴⣶⣶⣿⣾⣿⣶⣶⣿⣶⣶⣶⣶⣶⣾⣵⣿⣶⣶⣶⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣕⣅⣉⣌⣹⣔⣝⣡⣁⣉⣨⣪⣼⣨⣁⣇⣕⣝⣾⣁⣉⣉⣏⣉⣈⣦⣅⣸⣉⣈⣆⣔⣌⣉⣡⣕⣸⣉⣌⣺⣾⣨⣃⣧⣅⣨⣉⣭⣮⣉⣹⣀⣉⣨⣁⣉⣸⣸⣉⣁⣕⣅⣈⣹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢿⢛⠟⠛⠋⢻⠏⠛⠉⠛⡟⠛⠛⠙⠛⣻⠛⡋⠛⢻⣯⡍⠛⣟⠛⠛⢻⡟⢻⠛⣛⠛⠛⠛⠛⡛⠛⠛⡛⠛⠻⡟⢿⠛⢛⢛⠛⢛⠻⡛⠛⠙⢻⠛⡛⢹⢹⠛⠙⢛⡻⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠻⠿⠿⡿⠻⠿⡿⠿⠿⠿⠿⡿⠿⠿⠟⡿⢿⠿⠿⢿⠟⠿⠿⠿⠾⢿⠿⠿⠿⠿⠿⠿⠿⢿⠟⠿⡟⠻⠿⠿⠿⢿⣛⠿⡿⠿⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣷⣶⣶⣷⣾⣶⣦⣤⣷⣶⣶⣶⣶⣾⣶⣷⣾⣷⣶⣶⣶⣾⣾⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣷⣶⣶⣿⣬⣾⣿⣷⣾⣶⣶⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡟⡿⠿⠿⠟⠿⠿⡿⠿⠿⢿⡻⠿⠿⠿⠿⡟⡛⢟⡿⡿⠿⠿⡿⠿⠿⠻⠻⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣤⣤⣤⣤⣤⢤⣄⣷⣾⢶⣶⣴⣶⣶⣷⣷⣷⣾⣶⣶⣷⣶⣷⣷⣶⣷⣷⣷⣶⡶⣷⢶⣶⣶⣾⣦⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠋⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣀⣄⡀⠀⠀⠘⢿⠿⠻⠿⠿⠟⠿⢿⠿⠿⠛⡿⠻⠟⠿⠻⠿⡿⠻⠟⠿⠿⠟⠿⠿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠻⡿⠃⠀⠀⢀⣤⣧⣥⣴⣭⣤⣤⣼⣦⣵⣴⣧⣥⣴⣦⣤⣦⣯⣤⣬⣴⣤⣤⣤⣥⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣆⠀⠀⣰⣷⡀⠀⢀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣶⣿⣿⣷⣶⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⢿⠿⣿⠿⡿⠿⠿⣿⡿⢿⢿⣿⢿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⣿⣿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣽⣬⣴⣱⣯⣬⣢⣹⣥⣯⣬⣵⣿⣯⣽⣦⣴⣤⣼⣥⣤⣮⣤⣬⣦⣦⣴⢰⣤⣧⣦⣴⣤⣤⣧⣬⣴⣤⣼⣽⣧⣴⣶⣤⣤⣮⣤⣵⣿⣿⣤⣴⣶⣤⣦⣴⣦⣴⣤⣧⣤⣥⣼⣦⣤⣧⣦⣾⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿
⡉⣹⡏⢉⣿⠉⣩⢹⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⠸⢣⡄⠟⣼⣿⢠⣶⢸⡧⠖⠈⣷⢰⣾⣿⣦⢸⡇⠢⣿⣿⡧⠖⢸⣧⢠⣦⢸⣿⣿⠀⣿⣿⡷⢸⡆⣴⣆⢹⠁⣒⣘⡆⣰⡆⢹⣿⡿⣄⡉⢻⡏⣴⡆⢱⠀⣷⠀⣷⠈⣤⠋⣴⣤⠋⣐⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣆⣾⣷⣰⣿⣯⣬⣯⣬⣧⣩⣄⣽⣌⣽⣿⣭⣬⣯⣡⣼⣿⣧⣩⣌⣭⣬⣯⣬⣿⣿⣧⣬⣉⣥⣾⡇⣌⣡⣼⣤⣉⣽⣥⣼⣥⣼⣿⣧⣬⣩⣼⣧⣍⣥⣾⣦⣩⣄⣭⣬⣿⣧⣍⣭⣧⣍⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡛⢛⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣛⠻⣿⡿⢛⠛⣉⣙⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⢹⣿⣿⣿⣿⣿⣿⡋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⢘⣃⣬⠉⣥⡍⣩⣍⢻⠉⡬⢡⣭⢉⣭⣉⠌⢹⡍⣩⡌⢩⡌⢹⣿⣿⢰⣿⣿⡇⢸⡅⣭⠀⣭⠉⡟⣩⣌⡟⠉⠈⣻⣿⣏⠤⢹⡏⢩⣍⢹⡏⣥⡅⢸⣿⣯⠉⠏⢻⢉⡇⢨⣌⢹⡍⢹⢍⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣃⣘⣿⣟⣀⣻⣧⣘⣋⣼⠅⣀⠛⣟⣘⣿⣀⣣⣘⣃⣹⣃⣸⣇⣘⣿⣿⣦⣙⣛⣡⣾⣃⣛⣀⣛⣀⣧⣘⣋⣧⣘⣋⣿⣿⣅⣊⣘⣃⣘⣟⣘⣧⣙⣃⣸⣿⣿⣆⣼⣄⣾⣃⣘⣟⣘⣿⠌⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣭⣴⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⣿⣟⠛⣿⣿⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡉⣽⢍⡝⣩⡍⢻⡍⣿⡍⣿⣿⡏⢍⣿⠀⣩⡉⣿⢋⣭⠙⡏⢹⡏⢹⡇⣿⠋⣭⡁⣿⣿⡇⢈⣍⢻⣏⡍⢹⡍⢹⠍⡝⠩⠍⢻⣿⡟⣩⡍⢻⡉⣩⡉⣿⠋⠍⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⠈⣼⣇⡙⢋⣸⣇⠛⡁⢻⣿⣏⠂⣸⠀⢻⠃⢳⡘⠛⣡⣧⠘⢃⠘⠃⢻⣌⠛⡃⢻⣿⡇⠘⡟⠘⡁⢒⠘⣿⡈⣼⣧⡘⢛⣻⣿⣇⡛⢃⣼⠃⢻⠃⢻⡈⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣭⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢛⠿⢿⣿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⣿⡿⢿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⡿⢿⠿⣿⠿⡿⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⢿⣿⡿⣿⠿⢿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣹⣰⣀⣃⣺⣑⣨⣔⣂⣑⣂⣁⣸⣇⣀⣿⣐⣄⣢⣰⣄⣢⣚⣐⣄⣣⣐⣀⣅⣢⣏⣂⠍⣼⣏⣇⣚⣄⣃⣐⣃⣿⣊⣈⣆⣂⣘⡀⣂⢻⣇⣂⣰⣸⣗⣃⣂⣀⣟⣁⣇⣢⣀⣠⣐⣄⣂⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⣿⣿⣿⡿⣿⢿⢿⢿⢿⡿⡿⣿⣿⢿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣂⣴⠐⢠⣂⣤⣧⣈⣢⣂⣇⣠⣂⣰⣸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⢠⣉⣉⡙⢻⣿⣿⡛⡟⢻⡻⣿⠛⢻⣟⢻⢛⣯⣏⢏⣿⡟⡟⢛⠛⣻⡝⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⢻⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣟⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡟⣿⢻⣿⡿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⢸⣿⡏⣒⣸⣷⣾⣿⣕⡾⣿⡯⣶⢸⣓⣒⣹⢰⣾⣿⢵⣶⢱⣶⢹⢰⣶⣿⣶⣾⣿⣶⡆⡏⣒⣊⡇⣶⢹⣷⣾⢸⢗⡂⡇⣿⢸⣿⡷⣿⣿⢗⣒⣿⣶⡎⡏⣶⡎⡇⣶⣾⣿⡯⣶⡾⣒⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣮⣭⣷⣯⣿⣿⣽⣿⣯⣷⣿⣗⣾⣸⣷⣭⣿⣮⣿⣿⣮⣽⣷⣽⣾⣾⣿⣿⣿⣿⣿⣮⣵⣿⣮⣽⣷⣿⣾⣿⣽⣾⣮⣵⠷⣿⣼⣿⣷⣮⣽⣾⣭⣿⣿⣷⣿⣮⣷⣷⣿⣿⣿⣷⣭⣷⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⢻⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢟⣛⣿⣿⣿⣿⣿⣿⡟⣭⣻⣿⣿⢹⣿⣿⣿⣿⣿⡟⣿⣟⣿⣿⣿⠉⠀⢹⣿⡟⡟⢿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⢸⣿⣿⡇⣿⣾⣿⣿⢸⢰⣷⣿⣶⣿⣿⡇⣿⣇⣿⣿⡏⣾⡎⡇⣿⣾⣷⣾⢸⣳⣷⢸⢑⣓⣿⣾⡆⡇⣶⡇⡟⣓⢸⢰⠀⣦⢻⣱⡇⣎⢏⡦⣧⣚⢿⣿⣚⡊⡇⣿⢑⣓⣹⣿⢰⣷⣿⢴⣷⣧⠿⡈⡟⣿⣿⣿
⣿⣿⣷⣿⣾⣷⣷⣾⣷⣿⣾⣾⣿⣿⣾⣾⣾⣷⣿⣿⣶⣷⣿⣾⣾⣷⣿⣿⣿⣿⣾⣷⣿⣾⣷⣷⣿⣿⣷⣿⣾⣷⣷⣿⣾⣾⠀⣿⣷⣿⣷⣿⣿⣷⣷⣷⣾⣿⣾⣷⣷⣿⣷⣿⣿⣿⣾⣿⣿⣶⣷⣿⣷⣿⣾⣿⣿⣿
⣿⣿⣿⢿⣿⡿⢿⣿⠿⣿⣿⠿⣿⡿⢿⡿⣿⡏⡏⣿⣿⣿⣿⡿⢿⣿⣿⣿⡿⣿⣟⡏⣿⠿⣿⣿⢿⣿⢹⣿⠿⣿⣿⣿⢿⣿⠀⢿⣿⣿⠻⣿⡿⢻⣟⣿⠿⣿⠿⣿⡿⣿⣿⢿⣿⠿⣿⣯⣭⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⢰⣿⣿⢾⣧⡇⣿⡎⡇⣿⣼⢸⣿⣻⡟⡇⡇⣧⢻⣸⣿⢻⡇⣧⠿⣼⣻⡇⡇⡇⡿⣻⣾⣷⣿⢼⢸⡳⣿⣼⣿⢱⣿⢸⠀⣷⣿⣿⢸⡽⣱⢸⡇⡷⣿⡇⣿⡧⣿⣞⣬⡛⡷⣿⢞⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣓⣒⣿⣶⣶⣷⣿⣷⣿⣶⣾⣾⣿⣶⣶⣷⣷⣞⣣⣿⣿⣶⣶⣿⣶⣿⣶⣶⣷⣿⣾⣶⣾⣷⣶⣿⣷⣷⣶⣾⣿⣷⣶⣿⠀⣿⣿⣿⣾⣿⣿⣿⣿⣷⣶⣶⣿⣿⣶⣾⣶⣶⣿⣶⣾⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡻⣿⠿⠿⡿⣿⣿⡿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⢓⣓⣹⣟⣵⡇⣿⢸⣿⣿⢨⣥⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣶⣶⣿⣶⣾⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣘⣽⣺⣇⣷⣰⣇⣗⣈⣺⣾⣷⣰⣇⣷⣬⣿⣺⣆⣏⣸⣟⣛⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠛⣛⠛⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠀⢺⣿⡇⠈⣿⣿⢿⣇⣁⣽⣗⣺⣻⣸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣿⣿⣿⣼⣿⣿⢿⢿⡿⠿⣿⢿⡿⣿⡿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣶⣿⣿⣿⣼⣾⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⡿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⡇⡇⣶⢹⣿⢸⣵⣽⢰⣿⡇⣿⡷⣿⡏⣶⢹⣵⢹⢰⢸⣵⢼⢑⣹⢰⡎⢰⡏⢗⣺⢸⣿⡸⣱⢸⢱⣦⡇⣿⠹⣒⡇⣿⡇⡹⡁⡟⡊⡏⣶⣯⡎⡏⣯⡎⡏⣊⣗⡺⣿⢱⣾⣵⢽⣵⢱⣾⢑⣊⣿⢰⡯⡮⣿⣿
⣿⣷⣾⣷⣶⣿⣶⣾⣿⣿⣶⣷⣶⣉⡁⣀⣀⣀⣈⣉⣈⣈⣈⣀⣈⣀⣈⠀⠀⣀⣀⣀⣀⣈⣿⣷⣿⣾⣾⣷⣶⣶⣶⣶⣷⣿⣷⣷⣷⣷⣶⣿⣶⣿⣷⣷⣿⣷⣷⣶⣷⣾⣿⣷⣾⣶⣾⣿⣾⣿⣷⣾⣿⣷⣷⣶⣿⣿
⣿⠘⡟⢸⢸⣩⡍⣭⢫⡝⡫⢽⣩⣹⢨⢨⣿⡟⠞⣯⢩⢹⡏⣏⣽⠭⠛⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⣼⣾⣼⣮⠗⣿⣮⣵⣯⣾⣮⣾⡞⠊⠛⠘⠛⠀⠉⠊⠑⠛⠛⠊⠒⠆⢰⡾⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢻⢿⣿⠛⠏⠀⠹⢻⣿⣿⡟⡟⡟⣧⠀⠄⡄⡄⡄⡄⡄⡄⢀⣀⣤⣤⠀⢸⡇⠿⠓⢱⠛⡯⠎⡇⡆⡆⢺⢿⣷⣾⠒⡇⣿⠸⢿⢰⡇⢊⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣿⢻⣿
⣿⣿⣿⣿⣿⣤⠀⣀⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿
⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠛⠛⠛⠛⠋⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣿⣿⣿⣿⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⢀⣀⣠⡄⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠟⡛⡟⣟⠛⢻⢙⠛⣟⢛⡟⢛⡻⠛⢛⠁⠹⠛⢛⠛⡻⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡟⡛⠻⡛⠛⠻⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣾⣶⣾⣷⣾⣶⣶⣷⣾⣶⣿⣷⣷⣾⣶⣾⣶⣾⣾⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠞⠾⠿⢷⠺⠺⠿⠞⠿⢿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⢀⣀⠤⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣥⣤⣤⣽⣤⣤⣴⣥⣤⣼⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠤⡚⠀⠀⢙⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣇⣃⣲⣉⣀⣸⡇⠀⢸⣿⣿⣿⡇⠀⢸⣿⡇⠀⠁⣀⣀⡀⠈⠻⣿⣿⠀⠀⣿⣿⣿⡇⠀⢸⣿⡏⠀⢀⣀⣀⡀⠈⠻⣿⣿⠀⠀⣀⣀⣀⣸⡇⠀⢸⣿⣿⣿⠀⠀⣿⣧⡀⠘⠠⠔⡌⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⡇⠀⢸⣿⡇⠀⣿⣿⣿⣿⡆⠀⢹⣿⠀⠀⣿⣿⣿⡇⠀⢸⣿⡇⠀⢸⣿⣿⣿⡀⠀⣿⣿⠀⠀⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⣿⣿⣿⣦⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢸⣿⣿⣿⡇⠀⢸⣿⡇⠀⣿⣿⣿⣿⡇⠀⢸⣿⠀⠀⣿⣿⣿⡇⠀⢸⣿⡇⠀⢸⣿⣿⣿⡇⠀⣿⣿⠀⠀⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠻⠿⠿⠇⠀⢸⣿⡇⠀⠿⢿⠿⠟⠁⢀⣾⣿⡄⠀⠻⠿⠿⠇⠀⢸⣿⡇⠀⢸⣿⣿⣿⡇⠀⣿⣿⡀⠀⠿⠿⠿⢿⣧⠀⠘⠿⠿⠿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⣀⣀⣤⣼⣿⣧⣄⣀⣀⣀⣠⣴⣿⣿⣿⣿⣦⣄⣀⣀⣀⣠⣼⣿⣧⣀⣸⣿⣿⣿⣇⣀⣿⣿⣷⣤⣀⣀⣀⣼⣿⣷⣤⣀⣀⣀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 228

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/07/29/epo-landmark-occasion/#comments
    Gemini version at gemini://gemini.techrights.org/2022/07/29/epo-landmark-occasion/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.29.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_“Truly_a_Landmark_Occasion”⠀✐


Posted in Europe, Patents at 3:49 am by Dr. Roy Schestowitz


Context: Banana_EPO:_Montenegro,_With_Population_134_Times_Smaller_Than
Germany’s,_Will_Get_a_Vote_as_Powerful_as_Germany’s | [Meme]_Voting_Fodder_and
Faking_Concern_for_the_European_Patent_Convention_(EPC)


            🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Just_one_European_Patent_per_year⦈_
                      Source_page (warning: epo.org link)


                    🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Montenegro_and_EPO⦈_
   Cannot contain the excitement of being able to buy more delegates to back
                              criminal behaviour


Summary: With about 1 patent application in 100,000, Montenegro is truly a
cause for celebration for EPO presidents like Benoît_Battistelli and António
Campinos, who simply buy_votes


⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢸⣿⣿⣿⡿⢿⠿⠿⢿⣿⣿⣿⣿⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣥⣤⣤⣤⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⣿⣿⣿⣿⠿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠿⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⣀⣀⣠⣀⣀⣄⣄⣀⣸⣀⣄⣀⣄⣠⣀⣇⣀⣀⣀⣀⣄⣄⣀⣀⣀⣆⣀⣇⣠⣀⣼⣄⣄⣄⣀⣤⣀⣀⣮⣠⣰⣄⣄⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⢿⠿⠿⠿⡿⠿⠿⢿⠿⠿⠿⡿⠿⡿⡿⠿⠿⡿⠿⠿⠿⠿⠿⡿⢿⠿⠿⠿⠿⠿⡿⠿⣿⠿⢿⠿⠿⠿⢿⡿⠿⠿⠿⠿⠿⠿⡿⠿⠿⢿⠿⠿⡿⠿⠿⠿⠿⢿⣿⣿
⣿⣶⣶⣤⣶⣴⣶⣶⣦⣶⣶⣶⣦⣴⣦⣴⣦⣶⣶⣶⣦⣶⣷⣶⣶⣾⣶⣶⣦⣶⣶⣦⣶⡶⣶⣷⣤⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣼⣶⣾⣶⣶⣶⣦⣷⣶⣶⣶⣶⣶⣶⣷⣾⣶⣾⣶⣴⣶⣤⣶⣦⣶⣿⣿⣿
⣧⣤⣤⣤⣤⣧⣤⣧⣠⣤⣤⣤⣠⣤⣤⣤⣄⣤⣤⣥⣤⣤⣤⣤⣠⣤⣤⣤⣄⣤⣤⣄⣤⣴⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⠿⠿⣏⢉⣉⣉⣉⡋⣍⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣦⣼⣶⣤⠿⣛⣫⠭⠽⠶⠶⠮⠭⣝⣛⠿⣿⣐⣄⣣⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣤⣨⣰⣬⡿⢋⡵⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢮⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡻⣿⣿⠿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡹⣧⣦⣼⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⣹⣉⡉⢹⡟⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⢻⡿⠿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢸⣧⣤⣾⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢸⣇⣉⣛⣠⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⢿⠿⢻⠟⠿⠿⢿⠛⡿⠿⠿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣾⠋⠛⠛⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣧⠶⠶⠶⡶⠾⡶⢾⠶⠶⡶⠦⠶⢶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣱⡟⢓⡓⠓⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣶⣤⣥⣤⣤⣇⣤⣤⣟⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢟⣼⠿⠷⡾⠶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠟⠛⠛⢿⣮⣓⢦⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢚⣵⣿⣿⣶⣶⣧⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣭⣟⣓⣒⣒⣛⣫⣭⣴⣾⠀⣀⢉⣹⢀⠠⠂⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣾⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣛⣛⣛⣛⣛⣛⣛⣛⠀⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛
⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣏⣉⠉⢹⠀⠉⣿⣿⣇⣸⢉⡉⡏⡉⠉⠉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣈⣏⡉⣉⣋⢉⣉⢉⡏⡉⠉⡉⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣉⣉⣹⣉⣉⣏⢉⣉⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣉⣍⣉⣸⡉⣉⣈⣉⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣇⣸⣀⣠⣐⣈⣁⣉⣈⣉⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣇⣀⣸⣀⣘⣉⣈⣁⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣀⣄⣅⣠⣬⣁⣁⣈⣀⣀⣌⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣔⣀⣨⣉⣁⣈⣉⣈⣉⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣟⣛⣛⣛⠀⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠛⠛⠛⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⡟⠋⠛⢛⣯⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠙⠋⢿⣿⣿⣿⣿⣿⡟⠙⠛⠛⠛⠛⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠿⠿⠿⠀⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠾⢿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠟⠿⠆⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡷⠶⠶⠶⠀⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿
⣿⣿⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡷⠶⠶⠶⠶⠶⠦⠶⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣛⣻⣿⣿⠿⣿⠿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⠿⢿⢿⢿⣿⣿⣿⣿
⣿⣿⣿⣿⢀⠃⠀⠁⡆⠁⢰⢰⢰⠀⡂⡇⡆⠈⢐⢈⢰⠄⠀⡎⢰⠈⣿⠡⡆⡃⣶⢸⣿⢰⢰⢐⠊⣿⡘⢁⠇⠇⡂⣇⠛⣼⣷⢰⢰⡆⣿⡇⣶⠈⢐⢈⢱⡮⠡⡆⡇⡆⢰⢸⢐⡊⣿⡷⣍⢠⢙⢈⢰⢠⡆⣿⣿⣿
⣿⣿⣿⣿⣾⣶⣶⣷⣶⣷⣾⣾⣶⣶⣶⣷⣷⣶⣶⣾⣀⣠⣶⣷⣶⣾⣿⣷⣶⣷⣿⣾⣿⣾⣶⣶⣶⣿⣷⣾⣾⣶⣶⣞⣰⣿⣿⣶⣶⣶⣿⣷⣶⣾⣶⣾⣶⣶⣷⣶⣷⣷⣾⣾⣶⣶⣿⣷⣶⣾⣶⣾⣶⣾⣷⣿⣿⣿
⣶⣾⣿⣿⢉⣉⡏⣉⡙⡟⣩⣙⣿⡟⣩⣉⡿⠛⢿⠛⠻⠛⡿⢻⠛⢿⠟⠻⠛⠭⠿⠛⡿⠻⢻⣿⠋⣍⡛⢻⠟⢻⠛⡿⠛⢿⣿⠟⠻⠻⠻⣿⣿⡉⣿⣿⢋⣭⡙⡿⠻⠏⠻⠛⢿⠙⠻⠟⠻⡟⢻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠐⠒⣇⣶⣶⣇⠛⢋⣿⣇⡙⢋⣇⠛⣸⢸⣇⡘⡃⣏⠐⡘⡘⢛⡘⣀⣸⡇⡇⢛⢸⣿⡑⠒⣠⢘⠐⡘⡀⣇⠒⣺⣿⡘⢃⢸⡇⣿⡟⠃⢻⣿⣌⠛⣣⣇⢛⡇⢃⠛⣸⠘⢃⡐⢒⡇⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠴⣸⢰⡆⣧⠖⣸⠴⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣬⣭⣦⣥⣧⣭⣽⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠻⢻⡿⠻⠟⢿⢿⠻⠻⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣼⣼⣯⣤⣤⣢⣿⣬⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠟⠻⠿⠟⠿⠿⠿⠿⠿⠿⡟⠿⡿⠿⡿⠿⡿⠿⡟⠿⠿⠿⠿⠿⠿⢿⠛⠿⢿⡟⢟⠟⠻⡿⠿⠿⠿⠿⠻⠿⢿⡿⠿⠿⠿⢿⠿⢻⠿⠿⠿⡟⠻⣿⠿⠿⠿⢿⠿⠿⡟⠻⠿⠿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣶⣮⣶⣤⣤⣴⣦⣬⣴⣤⣧⣤⣷⣴⣴⣴⣧⣴⣧⣴⣴⣵⣵⣿⣦⣾⣤⣶⣼⣯⣦⣦⣤⣧⣾⣦⣾⣧⣤⣦⣼⣧⣦⣤⣤⣾⣦⣾⣧⣷⣴⣧⣵⣽⣧⣤⣴⣴⣤⣧⣧⣾⣤⣤⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣏⢆⣩⠍⠉⠉⠈⠉⠁⢈⠉⣽⣿⠒⣩⢹⠼⠀⣟⢈⢋⠉⢻⠀⣍⢹⡯⡩⡙⠉⠁⠩⢻⡏⠉⡩⡩⣩⠉⠉⠀⢉⡍⠉⡉⣏⢭⡉⣹⠀⡉⢉⢸⠉⢈⢉⢽⡏⢉⢉⡉⢩⡉⡉⣏⠉⢍⢍⢉⢁⣩⠉⢹⣿⣿
⣿⣿⣿⡿⠿⣿⠟⠿⢿⠛⠻⠿⠿⠿⠿⠿⠿⢿⢛⠿⠟⠿⠿⢿⣟⡻⠿⠿⡿⠿⠿⠛⠿⠿⡿⡛⠛⡻⢛⡻⡟⠿⢿⠿⠿⡿⠿⠿⠟⠟⠿⠿⡟⠻⢿⠻⠿⠟⠿⣿⠿⠿⠿⠟⡿⠿⢻⠿⠿⠿⠿⠿⠿⠻⠿⢿⣿⣿
⣿⣿⣿⣿⣮⣿⣴⣤⣼⣬⣥⣤⣦⣮⣦⣦⣤⣼⣴⣧⣤⣤⣴⣾⣧⣴⣵⣿⣴⣴⣦⣤⣤⣼⣷⣥⣥⣾⣮⣦⣧⣤⣾⣦⣦⣮⣦⣦⣶⣴⣧⣤⣧⣤⣼⣤⣤⣤⣼⣽⣿⣤⣤⣦⣷⣵⣿⣤⣴⣴⣴⣤⣴⣮⣶⣤⣿⣿
⣿⣿⣿⡟⡘⢉⡏⢹⢉⢉⢉⠋⡩⢿⠘⢈⠉⣍⠉⣉⠉⠉⠉⡉⣉⢹⡏⠉⡩⡉⡉⡉⣉⢍⡍⡏⣉⣀⣏⠉⢏⠉⣹⠉⠀⡉⡉⣹⡩⣩⣹⠸⣏⢆⡉⢈⢁⢍⢉⣽⠀⡐⡁⡕⢽⣻⠉⡹⣯⢉⠋⠉⢩⣹⣉⢍⣿⣿
⣿⣿⣿⣿⢻⠟⠻⠟⠿⣿⢻⠻⡻⠛⢛⣿⠛⢛⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣦⣴⣴⣤⣤⣯⣴⣵⣴⣤⣬⣿⣭⣴⣷⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⡛⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⡟⠿⠿⠿⠿⠿⠿⠿⡿⠻⠿⡟⠛⠛⢟⣻⡿⡿⠿⢻⠻⠻⠿⠿⠻⠿⠿⠿⠿⠿⢿⠿⠻⠿⠿⠿⠟⡟⠿⡟⠻⡻⡻⡛⣿⠿⠟⠿⠿⢿⠟⠿⠿⡿⠟⠿⠻⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣵⣦⣶⣴⣤⣤⣴⣤⣵⣵⣧⣧⣴⣴⣶⣴⣴⣴⣷⣧⣦⣤⣷⣭⣴⣦⣼⣧⣵⣤⣼⣤⣶⣵⣦⣤⣤⣴⣤⣤⣧⣼⣤⣤⣤⣧⣴⣤⣧⣤⣧⣴⣵⣵⣼⣼⣴⣶⣤⣤⣿⣧⣷⣴⣧⣤⣤⣴⣼⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢩⣍⢍⡍⠉⡉⡉⣯⢭⠉⢹⡱⡀⠀⠉⠉⣏⢉⣼⡩⢹⡍⢉⡉⢨⣯⠩⣹⢉⢉⠉⡉⠈⠉⢈⢹⡏⢩⢹⠠⢍⡉⢉⡍⠉⡈⡉⢹⣁⠫⣯⠉⡉⢩⣝⢉⡍⢸⣉⡁⢭⢹⠀⣍⢹⡇⠄⣪⡰⡙⣿⣿⣿⣿
⣿⣿⣿⣟⢛⠿⠿⡿⠟⠿⠿⠻⠿⢿⡿⠟⡟⠻⠿⣿⠻⠿⠿⠿⠿⠿⠿⠿⠿⢿⠿⣿⡛⠛⠛⠛⣿⠿⠿⠿⠻⠻⠿⢿⠻⠿⠿⠿⠻⠿⠿⠿⠿⠿⢿⠿⢿⡿⠿⠟⠿⡟⠻⠿⣿⠿⠿⠿⠿⠿⡿⠿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣼⣧⣤⣧⣤⣤⣼⣤⣦⣽⣯⣾⣧⣤⣦⣯⣦⣤⣴⣴⣴⣧⣴⣤⣷⣿⣾⣿⣬⣴⣤⣦⣷⣴⣧⣤⣤⣤⣤⣼⣶⣶⣴⣤⣤⣤⣶⣴⣥⣦⣼⣶⣽⣯⣤⣤⣦⣧⣼⣦⣿⣴⣤⣬⣤⣤⣷⣴⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢍⢍⢁⢹⠠⢍⡉⢉⡍⠉⠈⡉⢹⡡⡊⠉⢈⢹⡉⢯⠉⢸⠉⠈⡉⡉⣩⢋⢉⢹⠉⣩⡯⡍⠉⡇⠴⣀⡱⣠⠉⡟⡘⠁⡍⠁⠉⠈⠁⢉⠉⢍⢋⢹⡇⢊⢍⠏⡉⠉⢸⡏⠉⣹⠉⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢻⡿⠟⠿⠿⠟⢿⣟⢟⠟⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣼⣷⣦⣤⣴⣤⣿⣧⣧⣦⣥⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠛⠻⠟⠟⡿⠿⠿⠿⠿⢿⠻⠟⠿⢿⡿⠿⠿⣟⢛⢻⡟⢿⠿⢿⡛⢟⠟⡟⢻⡟⠟⠿⠿⠟⠿⠿⠿⠿⠿⠿⡟⠿⠿⠿⠿⠟⠻⢿⠿⠿⠿⡿⠿⠿⠿⠿⢻⠻⢿⡿⠿⠿⠿⠿⠻⢿⠻⢿⡿⠻⠿⣿⣿⣿
⣿⣿⣿⣿⣶⣦⣴⣶⣯⣶⣶⣶⣷⣾⣶⣶⣶⣦⣷⣶⣷⣷⣶⣾⣶⣶⣮⣾⣶⣶⣶⣶⣦⣷⣶⣶⣶⣶⣶⣶⣶⣤⣾⣶⣷⣶⣾⣿⣶⣶⣦⣿⣶⣶⣴⣶⣶⣶⣶⣶⣾⣶⣾⣷⣶⣶⣶⣶⣶⣾⣶⣾⣷⣷⣶⣿⣿⣿
⣿⣿⣿⣿⣀⣠⣕⣚⣯⣒⣩⣹⣘⣀⣇⣂⣉⣈⣁⣉⣉⣽⣂⣑⣃⣃⡘⣇⣈⣉⣟⣈⣉⣩⣍⣩⣏⣉⣩⣉⣀⣩⣉⣇⣒⣉⣉⣩⣉⣁⣏⣁⣾⣨⣉⣹⣀⣙⣉⣉⢉⣉⣉⣩⣹⣠⣍⣉⣉⣉⣸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⡛⠿⠿⠿⠿⠻⠿⠟⠻⠿⢿⠿⠟⠻⠿⡿⡟⠿⡟⠿⠿⠛⠿⠿⣿⠻⠻⠿⠟⠿⠿⠿⠿⠿⠿⢿⠿⢿⠿⠿⠿⠿⠟⠿⣿⠿⢿⠛⠿⢿⡟⠛⠻⣛⣿⡟⠿⡿⠿⠿⠿⡿⡟⢛⢛⡟⢻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣶⣾⣤⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣥⣷⣾⣷⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣦⣴⣶⣾⣶⣾⣶⣶⣶⣶⣶⣶⣿⣶⣾⣶⣷⣾⣷⣶⣿⣶⣿⣷⣷⣷⣶⣶⣯⣼⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣏⣁⣉⣉⣙⣉⣉⣉⣉⣍⣹⣏⣉⣩⣉⣉⣉⣉⣍⣉⣉⣁⣏⣉⣽⣀⣍⣉⣏⣉⠉⣈⣁⣉⣀⣩⣉⣏⣁⣉⣉⣍⢉⣉⣉⣏⣉⣉⣙⣉⣍⣉⣸⣈⣹⣏⣉⣩⣍⢉⡈⣹⣉⣁⣩⣹⣀⣍⣹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠿⠿⠿⠿⠿⠟⠿⠿⠿⡿⠿⠻⠿⠿⠿⣿⠻⠿⠿⢿⠟⣿⢻⡿⠿⠿⠿⠟⠿⠿⠿⠟⠟⠿⡿⠿⡿⠿⠿⢿⠛⣿⠿⠿⠿⠿⠿⠿⢿⠛⠿⠟⠿⠿⢻⢟⠻⠿⠿⠿⠟⠿⠿⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣶⣶⣶⣴⣶⣶⣶⣶⣶⣷⣶⣷⣶⣾⣤⣿⣿⣶⣶⣿⣷⣾⣾⣿⣷⣶⣶⣶⣶⣶⣷⣶⣶⣴⣷⣶⣿⣾⣶⣾⣶⣶⣾⣶⣴⣶⣶⣾⣾⣾⣶⣶⣶⣶⣾⣶⣶⣧⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣤⣩⣉⣁⡍⢹⣏⣩⣹⣂⣀⣇⣂⣉⣉⣉⣩⣍⣉⣉⣹⣂⣕⣀⣐⡛⣇⣨⣉⣹⣤⣉⣩⣈⣉⣉⣉⣉⣉⣏⣉⣼⣈⣈⣉⣁⣉⣩⣉⡉⢉⣉⣹⣉⣉⢉⣉⣉⣩⣉⣁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠛⠻⠿⠟⠿⠿⠿⠿⠿⠿⡻⢿⠿⠿⠿⠿⠿⠿⠻⠿⢿⠻⠿⡿⠿⠿⡟⢛⠛⢟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣤⣴⣶⣷⣾⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣷⣷⣶⣷⣶⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠛⠿⠿⠿⣿⠿⠿⠿⠿⠿⡟⠿⢿⠿⠿⡟⠿⠿⡿⠟⠿⠻⠿⢿⡿⢿⡟⡟⢛⢛⢻⠿⠿⡟⠛⢻⠿⠿⠿⠿⠿⠿⠿⣿⠿⡿⠿⠿⠿⡿⠿⢿⠿⢟⣟⣿⢛⠿⠟⠿⠻⠿⠿⣟⠛⢛⢛⢻⣿⠟⠿⢿⣿⣿
⣿⣿⣿⣿⣿⣷⣶⣿⣷⣶⣶⣾⣶⣶⣷⣶⣶⣾⣶⣷⣷⣤⣷⣶⣶⣶⣶⣾⣷⣿⣷⣶⣾⣿⣿⣶⣶⣷⣶⣾⣶⣷⣾⣿⣶⣶⣶⣷⣶⣶⣶⣶⣶⣷⣶⣾⣶⣾⣷⣾⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣾⣿⣾⣶⣾⣿⣿
⣿⣿⣿⣿⣀⣉⣉⣉⣉⣉⣉⣉⣇⣤⣉⣈⣉⣍⣻⣒⣩⠉⣉⣫⣉⣉⣉⣉⣉⣍⣇⣉⣉⣹⢉⣩⣉⣩⣉⣉⣇⣉⣿⣈⣉⣏⣹⣉⣙⣉⣉⣉⣉⣉⣏⣉⣉⣩⢉⣏⣁⣇⣩⣉⣉⣍⣉⣁⣈⣉⣝⣉⣿⣉⣉⣹⣿⣿
⣿⣿⣿⡿⠿⠿⠿⠿⠟⠻⠿⢿⡿⠿⠿⢻⠛⠻⠿⠿⠿⠿⠿⠿⢿⠻⠿⠿⠿⠿⠿⠛⠿⠿⣿⡿⠿⢿⠿⠿⠻⠟⠿⠿⡿⠿⠿⠿⠿⡟⠿⠿⠿⠿⠿⠟⠻⠿⢿⠿⠿⠿⢻⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣷⣶⣦⣴⣶⣶⣶⣾⣾⣷⣦⣿⣷⣶⣦⣶⣾⣤⣷⣶⣶⣶⣶⣷⣾⣾⣶⣶⣷⣶⠒⠚⠚⠒⠚⠒⠚⠒⠒⠒⠒⠒⠚⠓⢲⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡏⢉⣍⣉⣉⣁⣙⣇⣂⣀⣌⣁⣉⣀⢉⣏⣉⣉⣈⣉⣉⣉⣈⡍⢹⣀⣁⣉⣉⣈⣉⣉⣉⠉⣉⣹⣋⣉⣿⣍⣉⣉⣩⣈⣉⣩⣏⣁⣉⣈⣹⣏⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⠿⢿⠛⠿⢿⡿⠿⠿⠿⠿⠿⡿⠟⡟⠿⠿⢿⠛⣿⠿⠿⠿⠿⠿⡿⢿⠛⠿⠿⠿⠿⢻⢛⠻⠿⠿⠿⠟⠿⠿⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣼⣾⣾⣶⣶⣾⣿⣶⣶⣶⣾⣴⣷⣶⣷⣾⣶⣾⣶⣶⣾⣶⣴⣶⣶⣾⣾⣾⣷⣶⣶⣶⣾⣶⣶⣧⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 367

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(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/07/29/irc-log-280722/#comments
    Gemini version at gemini://gemini.techrights.org/2022/07/29/irc-log-280722/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.29.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ IRC_Proceedings:_Thursday,_July_28,_2022⠀✐


Posted in IRC_Logs at 2:43 am by Needs Sunlight


Also available via the Gemini protocol at:


    * gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-280722.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-280722.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-social-280722.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-280722.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
 QmXq7okL1guAj1GorFGd1YdPt5voPhaTm2oUpCXJu59m6u #boycottnovell  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell
 QmdVRDyQyPo88irw6wmx42Doo26VbJY5iite8UqxXWSZT6 (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
                                                 #boycottnovell-
 QmTEwugEAQxuUM8kvrEo4qSKTgpkYgvnaDE56XvLaaxwH8 social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell-
 QmXDhTi8xGgUTNz8Zatgh3o7xqKrV2bR8wyeYbEdy35g2e social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 (full IRC log
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 QmS7vcAD5cjFQ71qrvc9PR1x841mEfk9Gysoih97dL6UYg #techbytes      🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techbytes
 QmWAtbYnLUpaPjNQTxjQUgKYTvqvRTvSZhBS6oNXESdyNV (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 Qmck9ci8N2xUhzyXNRj6QmLf4Fz5bTk6ThactiMoDF1ypX #techrights     🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techrights
 QmZ1Hs5nJnkAFfWgpSsgrCBxdiP6psYAnNvcMWnHUoaanA (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈


§ Bulletin for Yesterday⠀➾


Local_copy | CID (IPFS): QmXggz4ZzdoNrnyGD87xZXV7EnECHikMc7N5PUE6qSiZ7Y



                    ䷩ 𝚕𝚒𝚗𝚎 494

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/07/29/richard-hughes-secure-boot-sham/#comments
    Gemini version at gemini://gemini.techrights.org/2022/07/29/richard-hughes-secure-boot-sham/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.29.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ GNOME_(IBM/Red_Hat_Staff)_Promoting_Microsoft’s_‘Security’_Scam_With_the
‘Secure’_Boot_Sham⠀✐


Posted in IBM, Microsoft, Red_Hat at 8:38 pm by Dr. Roy Schestowitz


IBM/Red Hat, which paid Garrett to vandalise_Linux [1, 2], is shilling
Microsoft's_vendor_lockin (a ploy to force people to use NSA_back-doored
Windows, misleadingly and disingenuously disguised as “security”)


  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Emulated host profiles in fwupd; Windows is malicious; A
                     system you control is not 'threats'⦈
          Who chose these wordings? Richard Hughes or his paymasters?


    🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Reply to GNOME and Red Hat developers are working on
  integrating firmware security tips and recommendations into the desktop for
warning users about platform/firmware security issues like if UEFI Secure Boot
  is disabled and other possible avenues their system could be exploited...⦈
    🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Reply to GNOME and Red Hat developers are working on
  integrating firmware security tips and recommendations into the desktop for
warning users about platform/firmware security issues like if UEFI Secure Boot
  is disabled and other possible avenues their system could be exploited...⦈

The comments_in_Phoronix (those two examples are from page_1) reveal that very
                few GNU/Linux users have fallen for these lies


Summary: Sponsored by IBM and the ‘Linux’_Foundation (James_Zemlin and Sheela
Microsoft, who reject Linux), Richard insinuates that protecting_Microsoft's
monopoly_(Windows) is protecting “against malicious software when the device
starts”


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


  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇We need to slaughter Novell before they get stronger….If
  you’re going to kill someone, there isn’t much reason to get all worked up
about it and angry. You just pull the trigger. Any discussions beforehand are a
   waste of time. We need to smile at Novell while we pull the trigger. ~Jim
             Allchin, Microsoft's Platform Group Vice President⦈


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


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


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


http://techrights.org/videos/video-red-hat-microsoft.webm


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⣿⣿⣿⣷⣼⣷⣼⣏⣿⣼⣿⣾⣼⣿⣽⣴⣼⣿⣧⣶⣥⣿⣧⣲⣿⣿⣬⣿⣴⣥⣿⣿⣿⣼⣦⣿⣿⣼⣿⣿⣿⣿⣿⣼⣿⣿⣥⣿⣿⣿⣷⣼⣇⣼⣿⣿⣬⣿⣾⣿⣧⣼⣿⣿⣿⣯⣧⣿⣤⣾⣿⣼⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⢿⢻⣿⢟⣿⣿⠟⣿⣟⣿⣿⠿⣿⡿⡟⢿⣿⣿⢿⢻⢿⣿⣿⡿⢿⡿⣿⡿⣻⠿⣿⣟⢻⣿⣿⣿⠻⣿⡟⢿⡿⣿⣿⣿⣿⡿⢻⣿⠿⣿⣿⢻⣿⣿⡟⣿⣟⣿⢿⣿⡿⢻⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣹⣿⣿⣉⣿⣏⣩⣿⣿⣋⣿⣿⣿⣿⣿⣉⣿⣿⣿⣸⣹⣿⣏⣿⣇⣽⣿⣿⣿⣿⣽⣄⣽⣧⣟⣏⣿⣿⣹⣿⣯⡏⣿⣿⣉⣽⣿⣏⣽⣿⣙⣿⣏⣩⣿⣿⣿⣿⣏⣿⣿⣿⣯⣩⣿⣿⡏⣻⣏⣿⣿⣽⣿⣿
⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣿⣷⣷⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡛⢛⠛⠛⠛⢻⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤⠄⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣾⣷⣮⣬⣿⣿⣦⣤⣷⣷⣾⣷⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣥⣦⣯⣤⣷⣧⣼⣼⣾⣿⣧⣯⣾⣦⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣀⣀⣀⣀⣠⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿
⣿⠿⡿⡿⣿⠿⠿⢿⡿⢿⢿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣶⣦⣷⣼⣶⣶⣾⣿⣶⣷⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣥⣿⣿
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣶⣇⣅⣔⣣⣦⣸⣠⣠⣤⣸⣄⣷⣶⣅⣿⣠⣮⣺⣅⣤⣗⣅⣽⣨⣸⣠⣼⣨⣨⣂⣠⣶⣎⣇⣴⣅⣴⣧⣴⣦⣱⣗⣕⣅⣀⣤⣖⣇⣂⣪⣠⣾⣫⣡⣣⣇⣌⣅⣤⣇⣝⣔⣅⣅⣵⣼⣤⣷⣧⣺⣸⣿⣿⣿⣿⣿
⣿⣉⣋⣉⣉⣩⣆⣨⣉⣉⣇⣍⣉⣻⣉⣉⣉⣍⣹⣈⣏⣁⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢸⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣧⣤⣤⣤⣤⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿
⣿⣿⡿⢿⠿⠿⡿⣿⡿⡿⠿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿
⣿⣿⣶⣾⣶⣷⣶⣶⣶⣷⣿⣶⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣼⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⣿⡿⡿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣴⣴⣾⣤⣤⣤⣄⣰⣦⣿⣦⣤⣤⣤⣤⣧⣤⣤⣧⣤⣤⣧⣥⣢⣧⣴⣦⣤⣦⣧⣥⣤⣤⣬⣧⣦⣦⣤⣧⣤⣧⣴⣼⣴⣦⣬⣧⣼⣤⣤⣤⣴⣾⣦⣤⣧⣥⣤⣼⣤⣤⣴⣼⣤⣤⣤⣤⣦⣼⣿⣿⣿⣿
⣿⣿⣕⣌⣁⣸⣁⣀⣸⣰⣁⣨⣢⣌⣈⣌⣘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠹⠙⡛⠛⠛⠋⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠙⠋⠂⠛⠛⠛⣿⣿⣿⣾
⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮
⣛⣛⣛⣛⣛⣛⣛⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⡟⠙⠛⠋⠻⣻⠙⠋⠛⠛⡟⠛⢹⠋⠛⠙⠛⠛⠛⠛⡏⠙⠛⠋⡛⠛⠻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠀⠀⠙⣿⡗⠾⠶⡖⠾⠿⣾⣶⣶⣷⣷⣷⣿⣶⣾⣾⣷⣶⣶⣷⣷⣶⣶⣶⣷⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣷⣶⣶⣷⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣅⣩⣽⣀⣀⣀⣿⣽⣌⣍⣉⣉⣁⣿⣟⣸⣩⣉⣩⣹⣸⣉⣉⣭⣍⣍⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡿⠿⠟⠿⢿⣿⠻⠟⠿⠟⡟⡻⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣶⣶⣷⣷⣶⣾⣶⣶⣿⣶⣦⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣇⣈⣹⣀⣹⣀⣜⣀⣙⣁⣬⣈⣸⣊⣀⣱⣇⣅⣀⣄⣅⣗⣅⣩⣀⣸⣪⣠⣇⣼⣀⣈⣺⣨⣉⣘⣿⣈⣤⣇⣈⣸⣹⣊⣀⣌⣁⣁⣹⣤⣉⣵⣌⣀⣬⣀⣇⣵⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣩⣉⣉⣉⣉⣏⣉⣁⣹⣉⣏⣈⣙⣘⣡⣠⡸⣇⣍⣉⣉⡉⣉⣀⣈⣻⡉⣉⣉⣉⣩⣏⣉⣈⣩⣁⣉⣉⣹⣈⣩⡋⣉⣏⣩⣉⣏⣉⣉⣏⣉⣁⣉⣉⣉⣹⣉⣩⣹⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡛⣙⠛⠛⡻⠛⠙⢛⢛⠙⢻⡙⣻⠉⢿⢹⠛⡛⢻⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⡿⠿⠟⠿⢿⠿⠿⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⠿⢿⠿⡿⠿⠿⢿⡿⠿⠿⠿⠿⠿⠿⡿⠿⠟⠿⠿⢿⢻⠿⠿⠿⠟⠿⠿⠿⠿⠟⠿⠿⠿⠿⢻⠿⠿⠿⠿⠿⠛⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡶⡾⣷⢶⣶⢾⡾⣶⣾⢷⣿⡶⣶⣶⣾⣿⢶⣶⣶⣶⣾⣾⣿⣷⡶⣦⡷⣶⣶⣶⣶⢶⢶⡷⣾⢦⣶⣶⣾⣾⣶⣾⣶⣷⣶⣶⢶⣶⢶⣶⣶⡧⢼⣷⢶⣶⣶⣶⣶⣶⣦⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣦⣧⣮⣬⣼⣴⣶⣦⣤⣴⣤⣤⣤⣤⣴⣶⣦⣤⣤⣷⣤⣬⣿⣦⣤⣽⣧⣼⣤⣤⣤⣤⣤⣧⣾⣤⣤⣤⣠⣤⣾⣦⣤⣶⣼⣤⣤⣦⣤⣤⣧⣶⣤⣤⣤⣤⣴⣤⣤⣬⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣥⣧⣤⣶⣦⣦⣤⣧⣤⣧⣤⣴⣼⣤⣮⣤⣴⣷⣦⣬⣤⣤⣾⣴⣥⣤⣦⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠄⢸⡏⢝⢉⠋⠉⠙⠙⠙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣶⠓⠀⢸⡟⢻⠿⡛⠻⡟⡞⠻⢿⠿⠟⠟⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣬⣬⣤⣼⡷⡾⡿⡶⣾⡷⢷⣷⣷⣶⣶⣾⠶⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣬⣬⣤⣷⣧⣶⣤⣤⣷⣼⣾⣬⣶⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠟⢟⠋⠛⣻⡿⠛⠟⠛⠋⡟⠟⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⡿⠿⣷⢿⢿⡿⡿⢿⣿⣿⣷⡿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⠿⢿⡿⣿⢿⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣧⣤⣼⣥⣶⣤⣧⣦⣤⣤⣤⣤⣤⣴⣧⣼⣼⣤⣤⣾⣧⣴⣤⣦⣧⣴⣠⣤⣤⣤⣤⣤⣤⣦⣦⣤⣷⣽⣦⣦⣴⣼⣤⣤⣇⣠⣤⣤⣧⣤⣦⣦⣼⣥⣤⣬⣶⣦⣼⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣌⣉⣍⣹⣻⣈⣩⣉⣨⣍⣇⣸⣁⣏⣩⣉⣙⣹⣉⣀⣍⣩⣉⣡⣌⣉⣉⣏⣏⣉⣉⣉⣝⣀⣉⣸⣉⣀⣀⣌⣉⣉⣧⣪⣇⣈⣩⣉⣩⣬⣉⣉⣋⣙⣀⣀⣹⣀⣁⣼⣀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠟⠛⠿⢿⣿⣿⠿⠛⠛⠛⠛⠛⢿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢠⢀⣄⡈⣨⣤⢠⠄⢰⣄⣴⢦⢨⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣫⣾⣿⣿⢧⣿⣿⣎⠿⣿⣿⠿⣟⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣟⣻⣥⣼⣿⣿⣿⣯⣹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠿⣿⣿⣿⣋⡉⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣏⣙⡛⢉⣭⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⣶⣶⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠋⠀⠐⠒⢒⡂⠂⠉⠻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⣰⣿⣷⣿⣿⡷⠀⣼⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣾⡁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣵⣾⣿⣿⡟⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣟⣿⣿⣿⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠐⢶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿
⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠉⠉⠉⠉⠉⠉⠛⠛⠿⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣀⣫⣼⣟⣿⣿⣯⣿⣿⣽⣻⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⢨⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠈⢿⣿⣿⣤⣤⣾⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⣾⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⣸⣿⠻⢻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⢿⣿⣿⣿⡿⣋⣩⠻⢿⣏⣿⣽⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⣿⣿⣚⣺⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠈⣿⣿⣿⣿⣿⣿⠀⠀⠙⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠸⣿⡿⢿⣿⣿⡄⠀⠀⠈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿
⣿⣿⣿⣿⣿⣟⡻⣿⣷⣦⡀⠘⣿⣿⣿⣿⠿⠯⣿⣿⣿⣿⠀⠀⢻⠷⠠⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣇⠀⠀⠀⢸⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣾⣿⣵⣿⣿⣾⣿⣿⣿⣷⣒⣚⣻⢟⣿⣿⠀⠀⠀⣷⣾⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣸⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢹⣿⣿⣿⣿⣿⠀⠀⢻⣿⣿⣿⣿⡟⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠻⣿⡿⢿⢿⣿⣿⣿⣿⠀⠀⠀⠈⣿⣿⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣦⣭⣶⣾⡎⣿⣿⣿⣿⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠿⢿⣿⣿⣿⣿⣇⢹⣿⣿⣿⠀⠀⠀⠀⠘⣿⣿⣿⣿⡇⠀⠘⣿⣿⣿⣿⡇⠀⠀⢰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢈⣉⣉⢙⣐⠀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠙⠻⢿⣿⣷⣾⣷⣿⣿⣿⡿⠇⠀⠀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⢻⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⡉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣤⢀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⢻⡇⠀⠀⠐⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣽⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⠘⠰⠆⠀⣠⠀⠛⣿⢿⡿⡿⠛⠀⠀⠀⠀⠀⢹⣿⣿⣿⠛⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣰⣿⣶⣄⠀⠈⠁⠀⠀⠀⢀⣤⠀⠀⠘⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⡋⠙⠻⠷⣦⣄⣉⣉⣭⡵⠟⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠛⠛⠀⠀⠀⢸⣶⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⡇⠀⠉⠉⠛⠛⠓⠀⠀⠀⠉⠉⠉⠡⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⡇⠀⠀⠛⢰⣾⡶⡄⠀⡖⣦⡶⢰⠆⣶⠀⠀⢺⢢⢲⠀⠀⢶⢰⣦⢺⠈⡇⡴⡄⠀⣰⡆⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⡇⠀⠀⣀⠀⠀⠈⠀⠀⢀⠀⡀⠀⠁⠀⢀⠀⢠⣀⣁⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢈⠀⡀⠀⠀⢀⢀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⡇⠀⠀⠿⠸⠝⠳⠙⠾⠸⠄⠧⠀⠀⠾⠻⠹⠹⣿⣿⣿⣷⠄⠱⠞⠿⠅⠀⡯⠟⠼⠘⠄⠣⠀⠀⠹⠼⠹⠻⠇⠀⠘⠅⠏⠈⠧⣫⠟⣽⠻⠇⠏⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⡇⠀⠀⠀⢀⡀⣦⡦⡆⡠⠄⡤⢠⡄⣤⢠⢤⢴⢿⣿⣿⣯⣤⠀⠀⣖⠖⡆⣤⡤⡦⢰⠆⣤⣾⠤⣤⡄⠀⡔⡂⡤⢠⡄⣤⢠⢤⠀⠰⣰⢰⠀⡤⢠⣄⠀⢰⡲⢠⢄⣤⢠⡄⣶⢠⢴⣤⣤⢤⢴⠄⠀⠀⠀⢸⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠁⠁⠉⠈⠁⠁⠈⠁⠉⠈⠉⠈⡀⠉⡉⠉⢉⡀⠀⠁⠀⠉⠉⠁⠉⠈⠀⠙⢩⡄⠉⠁⠀⠈⠁⠁⠈⠁⠉⠘⠉⠀⠀⠁⠈⠁⠉⠈⠁⠀⠈⠀⠈⠀⠉⠈⠁⠈⠈⠉⠉⠉⠈⠈⠁⠀⠀⠀⢸⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢷⢿⡯⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣇⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣯⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢖⣶⣤⣴⣾⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⡛⣛⡋⠛⠛⠁⠀⠀⠀⠸⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⡈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⡝⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠄⢠⣄⠴⡶⠦⣄⣰⢠⣦⠀⠀⣦⣠⡄⢰⡄⢠⡶⣄⢰⠶⢤⡆⠀⣤⠀⠀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣿⡛⣿⣏⣻⣿⣭⡽⣽⣧⣮⣦⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣽⣇⡿⢿⡄⡇⠀⢸⡇⡾⠾⡆⠀⡏⢻⣇⡿⢿⣸⣧⡾⢸⣭⡌⣧⣤⣿⣤⢰⠷⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣂⢴⣶⣶⠆⣶⢲⣲⣶⣲⣰⡒⡶⡔⣖⢰⣦⢶⠖⣔⣲⣲⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣵⣦⠫⣷⡔⣼⣰⣮⡗⡗⠁⠀⠀⠁⠁⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠁⠉⠉⠈⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣰⢿⣿⣿⣿⣿⣛⠛⡯⠁⢻⡇⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⣾⣿⢸⣿⣿⣿⣿⣿⣿⣿⣾⣿⣇⣴⣿⣿⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠋⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⠉⠉⠉⠉⠉⠉⠋⢉⣉⡉⡉⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣄⣰⣿⡿⠏⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣶⠀
⣀⣀⠀⠀⠀⠀⠀⠀⢀⣰⣶⣶⡶⠂⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⣀⣀⣠⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠈⠹⠿⠿⠏⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣟⠋⠉⠓⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠷⠂⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⣤⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠹⣿⣽⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⡄⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣠⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠐⠀⠈⠻⠇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢙⣿⣿⠛⠛⠁⠀⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⠇⠀⠀⠀⠀⠀⢹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠋⠀⠀⠀⠀⠀⠀⢠⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⣶⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣸⣿⣷⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⢰⣿⣿⣿⣦⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⢀⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣿⣆⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡀⢀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣀⣀⣀⣿⣿⣇⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠹⢿⣿⣿⣿⠉⠉⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡑⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠦⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠻⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⡡⠀⡀⠈⠛⠿⠏⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠙⡿⠛⠛⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⣽⣿⣿⣿⣿⣿⠏⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠆⠀⠀⢀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣠⣾⣿⣿⠟⠛⠛⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣦⠀⠀⠀⣀⣀⡀⠀⠀⠠⠤⣠⠀⣠⠀⣠⠄⠀⠀⣀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⡆⢀⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣦⡀⠀⣿⣿⣿⣾⣷⣴⡟⣿⠀⣿⠶⣿⣺⣿⡞⣿⠃⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⢸⢿⣼⣿⣿⣶⠓⣶⣶⠛⡶⣾⣲⠓⡖⡟⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠊⠻⢿⣿⣿⣷⣿⣿⡇⠀⠛⠈⠛⠛⠛⠈⠛⠛⠀⠛⠂⠛⠛⠛⠃⠛⠓⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⣿⣿⡿⣿⣿⠇⠘⠉⠃⠛⠛⠙⠛⠛⠊⠛⠋⠛⠉⠛⠃⠃⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣶⣶⣶⣶⣶⣿⣶⣶⣶⣾⣿⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⣿⣿⣿⣿⣇⠘⣿⣿⣿⡽⠿⠋⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠉⠘⠋⣿⣿⣿⠇⠀⠉⠛⠛⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣠⡄⠀⠰⠟⠁⢿⠀⠀⠠⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣉⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠟⣿⣿⣿⣿⣿⡻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⡄⠉⠀⠀⢈⠃⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⢈⣱⣾⣿⣙⣿⣿⣿⡗⠀⠽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢰⣶⡟⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠈⠛⠛⢿⣿⣿⠿⠙⠓⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⠀⠀⣌⣡⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣟⣁⠐⠉⢁⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣧⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠸⣿⣷⡀⠰⡀⠀⠀⠀⢠⡄⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠘⠿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠀⠀⠹⣿⡀⠀⠁⠀⠀⠀⠘⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣧⣀⠀⠀⠀⠀⠀⠈⠉⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠉⠙⢙⣽⣿⣟⠋⠀⠀⠈⠹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣟⠙⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠋⠻⢟⣉⡙⠛⠻⣿⡏⠉
⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⠀⠀⢀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣠⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡁⠀⠀⠈⠛⠋⠁⢀⣽⡆⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠓⣷⡆⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣿⣤⣀⣀⣀⣀⣀⣀⣰⣿⡇⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⣿⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠈⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠟⠿⠟⠛⠛⠛⠛⠛⠛⠛⠟⠉⠺⣿⣇⠠
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣽⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣸⣿⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣋⣛⣃⣘⣠⣿⣿⣿⣿⣿⣀

                    ䷩ 𝚕𝚒𝚗𝚎 847

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/07/29/too-busy-to-get-real-work-done/#comments
    Gemini version at gemini://gemini.techrights.org/2022/07/29/too-busy-to-get-real-work-done/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.29.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ EPO_VP4_Nellie_Simon:_24/7_Day_and_Night,_Only_One_Hour_to_Speak_to_EPO
Staff⠀✐


Posted in Europe, Patents at 6:50 am by Dr. Roy Schestowitz


Video_download_link | md5sum 6e06b34d85f0c4e3c0d0847053795671
EPO VP4 Too Busy to Speak to Staff
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/vp4-snubbing-epo-staff.webm


Summary: The president’s sidekick Nellie Simon isn’t fulfilling her Office
duties; staff isn’t amused


THE corruption at the EPO deepens, as do the stress_levels. European_software
patents, as we recently showed, are_being_promoted under false pretenses and
buzzwords while staff gets treated very poorly. No wonder there's_a_recruitment
and_retention_crisis.


“No wonder there’s a recruitment and retention crisis.”The document discussed
above and shown below (as HTML) reminds us of the lack of dialogue — an issue
for which EPO management is entirely to blame. It can barely devote an hour a
month to discussion about pressing issues, including worrisome deviations from
the rules/laws.


Here’s the full text:


     Örtlicher Personalausschuss München Innenstadt, Haar und Brüssel
     Local Staff Committee Munich City, Haar and Brussels
     Le Comité local du Personnel de Munich ville, Haar et Bruxelles


     Munich/München,28.07.2022
     sc22018mp


     § Report on the meeting of the Local Staff Committee Munich City with
     the Site Manager of Munich City, VP4 Nellie Simon⠀➾


     On 12 July 2022 the Local Staff Committee Munich City, Haar and
     Brussels (LSC Munich) met the Site Manager of Munich City, VP4 Nellie
     Simon, for the first time in 2022 to discuss a number of prevailing
     local matters, notably the Bringing Teams Together project and the
     planned move of the BoA Unit to PH 7 in a virtual meeting which had
     been scheduled, as had the previous ones last year, for one hour,
     only.


     Since on some topics no progress had been made, we had requested the
     administration to put them on the agenda again.


     The agenda was as follows:
     1. Bringing Teams Together Project
     2. BoA Unit re-location to PH VII (see also Intranet announcement by
     BoA 05.04.2022)
     3. Proposal for a Conference on the possible building occupancy
     4. DE Kindergeld vs. EPO Dependants’ allowance
     5. Dependency status
     6. Lack of Consultation of LOHSEC


     Topics which were not discussed


     i. Ongoing problems with tools and associated issues
     ii. Compensation for extra-ordinary inflation
     iii. Data-protection issues regarding on-call colleagues and personal
     mobile phones


     We had agreed with the administration in advance that any topic left
     out would be dealt with by the administration in writing. Topic (i)
     was submitted as “Kleine Anfrage”, due to be answered by VP4 by the
     end of the summer break.


     Present for the administration: Nellie Simon (VP4), Edda Franz (PD
     44), Fiona Dullenkopf (President’s Office); Steve Rowan (VP1), Jan
     Boulanger (in part) (Director HR Essential Services) and Frédéric
     Brunelle (Director Planning and Construction)


     =====================================================================
     ⚓  1. Bringing Teams Together Project⠀⇛


     For the project, we noted that a prime motivation appeared to be the
     plan to gradually empty the offices_in_the_PH_I-IV_buildings due to
     structural problems, as seen e.g. by the rusting of the reinforcing
     steel of the concrete in the underground_garage. We inquired how long
     these repairs would last. We were especially curious why the works
     weren’t well underway, some closed off areas being in the same
     corroded state since February 2021, the date shown on the closing-off
     notice in the garage. We specifically asked whether the long
     announced tender for fixing the concrete reinforcements in the
     underground garage PH I-IV had been completed and repair work
     started.


     In this connection we also inquired what would happen if, in addition
     to staff from PH I-IV, staff from PH VII would also be moved
     elsewhere, due to the planned move of the BoA to PH VII (see also
     next agenda item). Presently foreseen is only PH V, VI, VIII and the
     ISAR building.


     While the emptying out of PH I-IV was neither confirmed nor denied,
     the administration was adamant with regard to repair_work having in
     fact started. It assured us that the underground garage was
     structurally sound. It further explained that at the moment it was
     collecting information about workspace relocation and the underground
     garage. In the garage, measurements were being made to make a 3D
     digital twin of it, to enable efficient working on the needed
     repairs.


     Regarding the planning of future office use within the project, we
     stressed that staff needed to know what they should do to have an
     allocated_fixed_office. In essence, we inquired whether it would be
     sufficient just to ask for a fixed office in order to get one, no
     matter whether for one day per week or e.g. if a whole team would
     like to come in four to five days per week, or if further factors
     were involved.


     The administration gave various “peripheral” replies amounting to (1)
     the need for discussion_within_the_teams, with the line_manager
     deciding based on the information gained, but that everybody’s
     preference would be accepted, with (2) chances being higher if
     increased_presence is sought (e.g. two days per week), but (3) there
     was no_“one_solution_fits_all”_approach. Responding to an explicit
     question, VP4 said a whole team wishing to come in four to five days
     per week on a regular basis would be “perfect[ly]” accommodated with
     an allocated fixed offices for each team member.


     In this connection it was pointed out that VP1 was currently asking
     Team Managers how we could make staff come back to the EPO. However,
     unsurprisingly, it turned out that a workplace for the day was
     unattractive to many. We strongly urged the administration to clarify
     its plans, i.e. whether to motivate staff to come back or to keep
     them out as much as practically possible by demotivating their
     return.


     VP1 replied that the plan was neither. The question should actually
     be “What do I do?” The New Ways of Working scheme gave “incredible
     flexibility and treated everyone with trust”. Surely there were
     people who needed an office, but others who rarely came would not.
     The idea was to give people an adult_choice how they want to manage
     their time.


     We found it bizarre to have on one hand a security awareness campaign
     but on the other an open door policy with absence_of_keys even for
     allocated fixed offices. The administration stressed that security
     was not seen as an issue. Staff did not have keys in The Hague either
     and Munich should not


     =====================================================================
     be treated differently. In any case, papers should not be left on
     desks and with proper discipline there would not be a problem.


     ⚓  2. BoA Unit re-location to PH VII⠀⇛


     We inquired about the time frame of planned movements of DG1 staff
     actually situated in PH VII, noting that the President of the BoA had
     stated that the relocation would be completed in 2025-26. In
     particular we sought clarification as to when the removals would
     start and to which building the DG1 staff concerned would move.


     The administration confirmed that 2025-2026 was correct. However no
     concrete plans for a starting date had yet been made. With regard to
     staff moving out of PH VII, it was reiterated that it was most
     important to bring_teams_together. Again no confirmation was given
     that PH I-IV would be emptied (and no denial). With respect to the
     planned investment into Oral Proceedings facilities on the side of
     BoA, including F2F facilities, not being foreseen anymore save for
     very exceptional cases in DG1, the administration could not give any
     specific assessment, being aware, as was everyone, of the Oral
     Proceedings rooms in PH I-VI.


     With respect to our assumption that there would be free movement
     possible between the BoA building and PH I-VI and VIII (e.g. Sky bar,
     tunnel, bike cages), as well as the rooms in PH VII not being used
     for the BoA, the administration could not refer to any concrete plans
     as of now.


     (N.B. After the meeting with VP4, an update by the BoA Unit appeared
     on the intranet on 20.07. 2022; inter alia free access of the Sky-bar
     to all EPO staff was mentioned)


     ⚓  3. Proposal for a Conference on the possible building occupancy⠀⇛


     In context with the removal topics of the preceding agenda items, we
     wished to discuss our proposal of a conference with, inter alia, the
     Presidium of the BoA Unit, the MSC and the site managers of Munich
     Haar and Munich City, and Facility Management, in order to discuss
     the future of BT7 and related matters of building_occupancy. We
     further noted that a conference was the gold standard of
     consultation.


     VP4 essentially replied that the word “conference” sent shivers down
     her spine. In her experience, conferences were often a waste of time.
     It was still early, and she hadn’t seen any plans about 2025-2026.
     However, there would be full communication, which would be low key
     and efficient. She didn’t like the idea of a conference, but she
     understood our point that transparency was needed. As for the “wish
     list” of the President of the BoA, it was too early for any detailed
     discussion. Even if consultation wasn’t possible she agreed that
     information should be provided to the people. She understood that
     staff representatives needed to know what was happening.


     ⚓  4. DE Kindergeld vs EPO Dependants’ allowance⠀⇛


     The German “Kindergeldgesetz” and “Einkommensteuergesetz” contain a
     passage stating that Kindergeld is not paid if it can be received
     from an International Organisation, cf. Bundeskinder-geldgesetz:


          § 4 Andere Leistungen für Kinder, (1) Kindergeld wird nicht
          für ein Kind gewährt, für das eine der folgenden Leistungen
          zu zahlen ist oder bei entsprechender Antragstellung zu
          zahlen wäre: …3. Leistungen für Kinder, die von einer
          zwischen-_oder_überstaatlichen_Einrichtung gewährt werden
          und dem Kindergeld vergleichbar sind


     =====================================================================
     This is not in line with the EPO’s handling of the Kindergeld, which
     merely deducts it from the dependants’ allowance, as possible under
     previous DE law. However, this situation is now illegal under the
     current DE law quoted above, hence colleagues unaware of this change
     in law and still collecting the German Kindergeld first and the
     remainder from the EPO second are liable for DE fraud charges,
     regardless of the fact that the EPO would be the beneficiary of this
     fraud. So we inquired once again (after 23 June and 28 October 2021)
     about any office measures to inform and/or help affected colleagues.


     The administration was aware of the situation and would assess the
     extent of the problem based on case numbers, noting that staff had to
     take individual responsibility too, in view of the complex multi-
     national and interlocutory situation. If the numbers are sufficiently
     high, VP4 offered to have a communication sent to alert colleagues to
     this important regulatory change. If not, following our suggestion,
     the affected colleagues would be contacted individually.


     ⚓  5. Dependency status Article 69 (3) vs 69 (4) and the implementing
     Circular 82.⠀⇛


     We informed the administration anew that their systematic confusion
     of Article 69(3) ServRegs with Article 69(4) ServRegs was detrimental
     to staff. Thus the administration was confusing the dependency_status
     of a child with granting it an allowance. This confusion had great
     implications for all children between 18–26 years irrespective if
     these children are in vocation training or not.


     The administration argued that only a handful of staff were affected.
     We pointed out that this was demonstratively not true.


     We explained how the two articles must be considered in order to
     avoid misinterpretation.


     Step 1:


     Article 69(3) ServRegs


     This article deals solely with establishing if a child is dependent.
     Once this has been established that child is automatically in receipt
     of the health_insurance under the parent’s policy (Cigna).


     Step 2:


     Article 69(4) ServRegs


     This article deals solely with granting a child a dependency
     allowance according to a couple of rules one of which is: if the
     child is in receipt of vocational_or_educational_training. This
     article has nothing to do with the health insurance (Cigna) or
     dependency status. It is purely the basis for granting an allowance.


     The problem is with Circular_No._82 which deals with the
     implementation_of_Article_69(3) (dependency status) and not with
     Article 69(4) (Granting of an allowance), but contains provisions of
     the latter:


     Rule_1


     (1) Subject to paragraph (2), a legitimate, natural or adopted child
     (Art. 69(3(a) ServRegs) shall be assumed to be mainly and
     continuously supported by the employee or his spouse if the child is:
     (a) not gainfully employed (Rule 3) and
     (b) is under 18 years of age, or has not reached the age of twenty-
     six and is receiving educational or vocational training, or
     (c) prevented by serious illness or invalidity from earning a
     livelihood, irrespective of age.


     Hence this circular introduces unallowable restrictions (in bold and
     red above) into Article 69(3) from Article 69(4). For instance, it
     introduces the restriction that a child has_to_be_receiving
     educational_or_vocational_training_in_order_to_be_considered
     dependant. This requirement is not found in Article 69(3) ServRegs
     which Circular No. 82 is meant to implement.


     In a nutshell: the Administrative Council of the Organisation, by
     adopting Article 69 ServRegs as is, has decided that dependent
     children should still receive health insurance (Cigna), even without
     undergoing educational or vocational training. The President of the
     Office, by adopting Circular No. 82 as is, has taken that away again.
     However, it is beyond his powers to do so (ultra vires). This is why
     it is an unallowable_restriction.


     This unallowable restriction causes considerable anxiety for ALL
     staff having children between the age of 18-26, because they are left
     unsure_how_the_administration_will_interpret_the_rules. For instance,
     all children finishing the baccalaureate are, according to the
     administration not_health_insured_(Cigna) unless the parents can
     prove that within a very limited time frame the child continues with
     their vocational or educational training. This situation may even
     lead to retroactive_loss_of_coverage and is clearly wrong since there
     is no such requirement in Article 69(3) ServRegs.


     Should the Office insist on such an interpretation, the staff should
     ask for a written confirmation of the Article of the ServRegs (not
     the Circular) indicating the basis of such a requirement. The
     Circular is of a lower ranking law which cannot supersede the
     ServRegs.


     We insisted on this during the meeting until VP4 instructed the
     Director of HR Essential Services to delve further into the matter.
     We have also been promised by the President that should there be a
     systemic problem with implementing the Rules of the Codex this would
     be addressed immediately. There is no better example of systematic
     wrongful implementation of the ServRegs than this present case. We
     look forward to seeing swift_implementation of an appropriate
     amendment to the provisions of Circular No. 82.


     ⚓  6. Lack of Consultation of LOHSEC⠀⇛


     We explained that on 2 June 2022 there had been a publication on the
     intranet in the “Life” channel about a new terrace outside the
     cafeteria in the ISAR building. LOHSEC had not been informed about
     this, nor other staff representatives. On 9 June 2022 the LOHSEC
     members of the MSC presented this issue to all LOHSEC members, asking
     to put the topic of the terrace and the lack of consultation of the
     LOHSEC on the next agenda, since safety and health aspects were
     clearly involved. We found


     =====================================================================
     the reply by the LOHSEC Chairwoman unsatisfactory, that the project
     had been mentioned months before and thus the topic could have been
     raised before.


     We further inquired when and how consultation should start, in
     particular with the LOHSEC. At the same time we were curious to know
     whether the PschorrHöfe Buildings would also have outdoor terraces.


     The administration sided with the LOHSEC Chairwoman, noting further
     that safety aspects had been considered by facility management staff
     and working conditions did not change, hence the Staff Representation
     did not need to be involved.


     We noted that the initial publication was on a side-line of the Life
     channel, hence of low visibility. Moreover, Staff Representatives
     should not have to hunt for information, rather the Administration_in
     control_of_this_knowledge should be approaching Staff Representatives
     with it. That is what consultation was about. The absence in this
     case was furthermore seen as symptomatic of how “consultation” is
     presently carried out in the Office. Lastly the difference between
     Article 38 Service Regulations, defining when the Staff
     Representation is to be consulted, and Article 38a Service
     Regulations, defining when the LOHSEC is to be consulted, was
     explained, as well as between considering (something) and consulting
     (someone).


     This issue and the pertinent procedural and legal questions was
     furthermore submitted as “Kleine_Anfrage” to VP4, due to be answered
     after the summer break.


     ⚓  Conclusion⠀⇛


     While the meeting may be said to be well organized and efficiently
     conducted, one hour per half year is not enough. Consider this: A
     working year has about 2000 hours. The Site Manager of Munich City is
     spending 0,1% of her working time on consultation with us. It is not
     nearly enough for one half year of topics, of both broad scope and
     great impact, requiring normally lengthy discussions. The latter
     applies especially to the complex Bringing Teams Together project,
     the apparently desperately needed PH 1-4 building repairs, or to
     properly follow the dynamics of a pandemic.


     Your


     Local Staff Committee Munich City, Haar and Brussels


     [...]


With a dire situation such as this, no wonder many workers are protesting and
engaging in industrial action. As noted_the_other_day, quoting the union: “770
staff members participated in the ballot on the “Work-to-Rule” actions among
which 90% voted in favour.”


It’ll carry on for at least 2 more months.


“A working year has about 2000 hours,” the above notes. “The Site Manager of
Munich City is spending 0,1% of her working time on consultation with us. It is
not nearly enough for one half year of topics, of both broad scope and great
impact, requiring normally lengthy discussions.”


She wants people to work all day long (it's_illegal_by_the_way) while she fails
to_fulfil_her_own_role. She’s busy doing pinkwashing_photoshoots to distract
from the fact she’s not qualified for this job and got it through nepotism as a
former colleague of António_Campinos. █



                    ䷩ 𝚕𝚒𝚗𝚎 1332

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/07/29/tough-windows-year/#comments
    Gemini version at gemini://gemini.techrights.org/2022/07/29/tough-windows-year/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.29.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Windows_Has_Had_a_Very_Tough_Year_(That’s_Why_Microsoft_Starts_to_Block_GNU/
Linux_With_‘Secure’_Boot)⠀✐


Posted in Antitrust, Microsoft at 2:35 am by Dr. Roy Schestowitz


Yesterday: Antitrust_Action_Against_Microsoft_is_Well_Overdue


Two days ago: Microsoft’s_Crimes_Against_the_Competition,_Notably_BSD_and_GNU/
Linux,_Persist_Albeit_Disguised_as_‘Security’_(UEFI_‘Secure’_Boot,_TPM,
Pluton…)


                🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Monopoly_vs_Free_software⦈_
                   Microsoft knows_exactly_what's_happening


                 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇2022_Android_and_Windows⦈_
               Android and Windows. Notice the trends this year.


Summary: Microsoft is just blatantly trying to obstruct BSD and Linux from even
booting on new desktops/laptops, having simply resorted to illegal tactics
while bribing those who would otherwise deposit a complaint with the
authorities


Background: Aside from the links above, consider that Lenovo (probably more
OEMs to come) has become outright blocking Linux from even booting on some new
laptops. They’re not just preloading Windows, they force people to keep it and
use it. They’re using the_false_pretence_of_“security”.


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢸⡿⠛⠈⠈⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡷⣼⠁⠀⠀⠀⠈⠃⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣿⣿⣿⣿⣿⣿⢿⣿⡗⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠟⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢿⣿⣿⣿⣧⠈⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣴⣿⣿⣿⠃⠹⣿⣿⠛⣻⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢰⠘⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⢻⣿⣿⣿⡿⢻⣦⣾⣿⣿⣿⣿⣿⡇⢠⣿⡏⠀⠤⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠋⠀⠀⠀⠀⠉⠛⠏⠉⠙⠻⣧⣾⠟⠀⠀⠀⠈⠻⠟⣿⣿⣿⣿⣿⡿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠉⣿⡟⣻⡇⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆⢰⣶⡆⢰⡖⢲⣆⢰⣶⠀⣶⠀⣴⡟⣷⡄⢰⣶⢶⡆⢠⣶⢲⣦⢸⣿⡇⢸⣿⣿⣿⣿⣿⣭⣉⡛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠠⣿⠁⢾⡂⢰⢈⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡾⣿⡇⢸⡇⢸⣿⢸⣿⣧⣿⠀⣿⡇⣿⡇⢸⣿⣼⠇⢸⣿⢸⣿⠈⣿⡟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠉⠀⣿⠀⢸⠇⢺⣟⠈⠀⣀⠀⠀⣷⠀⠀⢸⡇⢹⡇⣿⡇⢸⣇⣸⡿⢸⣿⢹⣿⠀⣿⡇⣿⡇⢸⣿⠀⠀⢸⣿⢸⣿⠀⣿⣀⠀⢼⣿⠉⠉⠀⣀⣉⣙⣵⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠈⢹⡇⠀⠀⢹⠀⠨⠀⠠⠴⠀⢸⣿⠀⢠⣿⣷⠀⠈⠉⠈⠁⠉⠁⠀⠉⠉⠁⠈⠉⠀⠉⠀⠈⠉⠉⠀⢈⣉⠀⠀⠀⠉⠉⠁⠀⠉⠉⠀⠈⠉⠀⠀⠀⠀⠈⣿⢙⡛⡹⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⡇⠀⠀⢸⠀⠀⠀⠠⠄⠀⢸⣿⡇⣼⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣷⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠓⠀⠀⠀⠀⠐⢘⣿⣦⣸⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⢨⣉⠁⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠈⠉⠐⠺⠭⠍⠉⠀⠉⠉⠉⠹⣿⡟
⠀⠀⠀⠀⠀⠐⠀⠀⠤⠀⠀⠉⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣥⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠘⠚⠲⠶⠿⠷
⠀⠀⠄⠀⢰⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠋⠙⠻⠿⠿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣷⣧⡤⠜⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⠿⠟⠛⠛⠛⠋⢠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡼⠟⠉⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⠀⠀⠀⢀⠀⠀⠀⠀⢈⣻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠅⠀⠀⠂⠀⠀⣈⣤⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠐⠆⠀⠀⠀⠀⠀⠀⠈⠁⠨⠍⢉⣀⣀⠀⠀⠀
⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠀⠀⠀⠀⠀⠀⠻⠧⠀⣠⣈⣤⣶⣶⣶⡶⠀⣤⣄⣀⣀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⢤⣤⣀⠀⠀⠀⠀⠀⠀⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠁⠀⠀⠙⢻⣿⠛⣿⣿⣧⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⣀⣀⣴⣲⣷⣶⣥⣶⣾⣶⡶⠿⠛⠛⠛⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠙⢿⣿⣯⣼⡷⠢⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠙⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣀⣈⣻⣿⣟⣉⣤⣀⠀⠀⠀⣀⣀⣀⣼⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⣀⠀⣲⣾⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡍⣿⣿⣿⡏⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠀⠀⢀⣀⣀⢀⣀⡄⣾⣿⣿⣿⣿⣾⣧⢀⡀⡀⢀⣤⣀⣴⣞⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢸⡿⠛⠈⠁⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⣾⠃⠀⠀⠀⠀⠃⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣿⣿⣿⣿⣿⣿⢿⣿⡗⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⠟⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣣⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢇⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠉⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣀⣼⣿⣿⣿⠃⠻⣿⣿⠻⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢐⠘⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⢻⣿⣿⣿⡿⢿⣦⣾⣿⣿⣿⣿⣿⡇⢰⣿⠏⠀⠄⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢠⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠋⠀⠀⠀⠀⠉⠙⠏⠉⠙⠻⣧⣾⠟⠀⠀⠀⠈⠻⠟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠉⣿⡟⣿⡇⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆⢰⣶⡆⢰⡖⢲⣆⢰⣶⠀⣶⠀⣴⡟⣷⡄⢰⣶⢶⡆⢠⣶⢲⣦⢸⣿⡇⢸⣿⣿⣿⣿⣿⣍⣉⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠰⣿⠁⢻⡆⢰⢴⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡾⣿⡇⢸⡇⢸⣿⢸⣿⣧⣿⠀⣿⡇⣿⡇⢸⣿⣼⠇⢸⣿⢸⣿⠈⣿⡟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠁⠀⣿⠀⢸⠇⢺⣇⠉⢀⣀⠀⠀⣷⠀⠀⢸⣿⢸⡇⣿⡇⢸⣇⣸⡿⢸⣿⢹⣿⠀⣿⡇⣿⡇⢸⣿⠀⠀⢸⣿⢸⣿⠀⣿⣀⠀⢼⣿⠉⠉⠀⣀⣭⣉⣽⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠈⢹⡇⠀⠀⢻⠀⠨⠄⠠⢶⠀⢸⣿⠀⢠⣿⣷⠀⠈⠉⠈⠁⠉⠁⠀⠉⠉⠀⠈⠉⠀⠉⠀⠈⠉⠉⠀⢈⣉⠀⠀⠀⠉⠉⠁⠀⠉⠉⠀⠈⠉⠀⠀⠀⠀⠹⣯⢹⡟⡻⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⡇⠀⠀⢸⠀⠀⠀⠠⠄⠀⢸⣿⠇⣼⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣷⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠖⠀⠀⠒⠁⠰⣹⣿⣦⣼⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⢨⣍⠁⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠐⠺⠯⠍⠉⠀⠉⠉⠉⠹⣿⡟
⠀⠀⠀⠀⠀⠐⠀⠀⠤⠀⠀⠉⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣥⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠚⠲⠶⠿⠷
⠀⠀⠀⠀⢰⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠋⠙⠻⠿⠿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣷⣧⡤⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⡿⠟⠛⠛⠛⠋⢠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡼⠟⠉⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⠀⠀⠀⢀⠀⠀⠀⠀⢀⣻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠂⠀⠀⣈⣤⣾⡿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠐⠆⠀⠀⠀⠀⠀⠀⠈⠁⠨⠌⠉⣀⣀⠀⠀⠀
⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠈⠻⠗⠀⣠⣈⣤⣶⣶⣷⡶⠀⣤⣄⣀⣀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠐⠀⠠⠤⠤⢤⣤⣀⠀⠀⠀⠀⠈⠀⠠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠁⠀⠀⠙⢻⣿⠛⣿⣿⣧⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⣀⣀⣴⣲⣷⣾⣥⣶⣾⣶⡶⠿⠛⠛⠛⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠙⢿⣿⣯⣼⡷⠢⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠙⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣀⣈⣻⣿⣟⣉⣤⣀⠀⠀⠀⣀⣀⣈⣼⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⣀⠀⣲⣿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡉⢿⣿⣿⡏⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠀⠀⢀⡀⣀⢀⣀⣄⣾⣿⣿⣿⣿⣾⣧⣀⡀⡀⢄⣤⣀⣴⣞⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢸⡿⠛⠀⠉⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡾⡳⣾⠂⠀⠀⠀⠀⠃⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣿⣿⣿⣿⣿⣿⢿⣿⡇⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⠟⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠊⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣠⣼⣿⣿⣿⠃⠻⣿⣿⠻⣛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢰⠘⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⢻⣿⣿⣿⡿⢿⣦⣾⣿⣿⣿⣿⣿⡇⢰⣿⠏⠀⠤⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠋⠀⠀⠀⠀⠉⠙⠏⠉⠙⠻⣧⣾⠟⠀⠀⠀⠈⠻⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠉⣿⡟⣿⡇⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆⢰⣶⡆⢰⡖⢲⣆⢰⣶⠀⣶⠀⣴⡟⣷⡄⢰⣶⢶⡆⢠⣶⢲⣦⢸⣿⡇⢸⣿⣿⣿⣿⣿⣏⣉⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠰⣿⠁⢼⡆⢐⢤⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡾⣿⡇⢸⡇⢸⣿⢸⣿⣧⣿⠀⣿⡇⣿⡇⢸⣿⣼⠇⢸⣿⢸⣿⠈⣿⡟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠁⠀⣿⠀⢸⠇⢺⣇⠉⢀⣀⠀⠀⣷⠀⠀⢸⣇⢸⡇⣿⡇⢸⣇⣸⡿⢸⣿⢹⣿⠀⣿⡇⣿⡇⢸⣿⠀⠀⢸⣿⢸⣿⠀⣿⣀⠀⢼⣿⠁⠉⠁⣠⣭⣉⣭⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠈⢹⡇⠀⠀⢻⠀⠨⠀⠠⠔⠀⢸⣿⠀⢠⣿⣷⠀⠈⠁⠈⠁⠉⠁⠀⠉⠉⠁⠈⠉⠀⠉⠀⠈⠉⠉⠀⢈⣉⠀⠀⠀⠉⠉⠁⠀⠉⠉⠀⠈⠉⠀⠀⠀⠀⠹⣯⢹⡟⡛⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⡇⠀⠀⢸⠀⠀⠀⠠⠄⠀⢸⣿⡇⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⣆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠚⠀⣘⣙⣿⣦⣸⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⢨⣍⠁⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠉⠉⠁⠐⠺⠏⠍⠉⠀⡉⠉⠉⠹⣿⡟
⠀⠀⠀⠀⠀⠐⠀⠀⠤⠀⠀⠉⠁⠀⠀⠀⢿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣥⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠐⠚⠺⠷⠿⠷
⠀⠀⠀⠀⢰⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠋⠙⠻⠿⠿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣷⣦⡤⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⠟⠛⠛⠛⠋⢤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡼⠟⠉⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠅⠀⠀⠂⠀⠀⣈⣄⣿⡿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠐⠆⠀⠀⠀⠀⠀⠀⠈⠀⠨⠌⠉⣀⣀⠀⠀⠀
⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠛⠀⠀⠀⠀⠀⠈⠻⠇⠀⣠⣀⣤⣶⣶⣷⡶⠀⣤⣄⣀⣀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⢤⣤⣁⠀⠀⠀⠀⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠁⠀⠀⠙⢻⣿⠛⣿⣿⣯⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠀⠀⣀⣀⣴⣲⣷⣾⣥⣶⣾⣶⡶⠿⠛⠛⠛⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠙⢿⣿⣯⣼⡷⠢⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠙⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣀⣈⣻⣿⣛⣉⣤⡀⠀⠀⠀⣀⣀⣈⣼⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⣀⠀⣲⣿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡉⢿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠀⠀⢀⣀⣀⢀⣀⣄⢶⣿⣿⣿⣿⣾⣧⣀⡀⡀⢀⣤⣀⣴⣞⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢸⡿⠛⠀⠉⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡾⠷⣼⠀⠀⠀⠀⠀⠃⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣿⣿⣿⣿⣿⣿⢿⣿⡇⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⠋⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣢⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢿⣿⣿⣿⣧⠛⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣠⣼⣿⣿⣿⠁⠹⣿⣿⠛⡛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣽⣿⣿⣿⡇⢐⠘⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠈⢻⣿⣿⣿⡿⢻⣶⣾⣿⣿⣿⣿⣿⡇⢰⣿⠏⠀⠄⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⠈⢠⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠋⠁⠀⠀⠀⠉⠛⠏⠉⠉⠛⣷⣾⠟⠀⠀⠀⠘⠻⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠁⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠉⣿⡟⢿⡇⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆⢰⣶⡆⢰⡖⢲⣆⢰⣶⠀⣶⠀⣴⡞⣷⡄⢰⣶⢶⡆⢠⣶⢲⣦⢸⣿⡇⢸⣿⣿⣿⣿⣿⣏⣉⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠠⣿⠁⢼⡆⢐⢤⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡾⣿⡇⢸⡇⢸⣿⢸⣿⣧⣿⠀⣿⡇⣿⡇⢸⣿⣼⠇⢸⣿⢸⣿⠈⣿⡟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠁⠀⣿⠀⢸⠇⢺⡇⠉⢀⣀⠀⠀⣷⠀⠀⢸⣇⢸⡇⣿⡇⢸⣇⣸⡿⢸⣿⢹⣿⠀⣿⡇⣿⡇⢸⣿⠀⠀⢸⣿⢸⣿⠀⣿⣀⠀⢼⣿⠉⠉⠀⣠⣭⣉⣭⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠉⢹⡇⠀⠀⢹⠀⠸⠀⠠⢰⠀⢸⣿⠀⢠⣿⣷⠀⠈⠉⠈⠁⠉⠁⠀⠉⠉⠁⠈⠉⠀⠉⠀⠈⠉⠉⠀⢈⣉⠀⠀⠀⠉⠉⠁⠀⠉⠉⠀⠈⠉⠀⠀⠀⠀⢹⣯⠹⡏⡛⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⡇⠀⠀⠸⠀⠀⠀⠠⠄⠀⢸⣿⡇⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣷⣆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠒⠀⣘⣛⣿⣶⣸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⢨⣉⠁⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠉⠉⠉⠐⠺⠯⠍⠉⠀⠉⠩⠉⠹⣿⣟
⠀⠀⠀⠀⠀⠐⠀⠀⠤⠀⠀⠉⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣡⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠚⠲⠶⠿⠷
⠀⠀⠀⠀⢰⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠋⠙⠻⠿⠿⣿⣿⢿⠿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣷⣦⡤⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⢿⠟⠛⠛⠛⠋⢤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡼⠟⠉⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡅⠀⠀⠂⠀⠀⣈⣤⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠐⠆⠀⠀⠀⠀⠀⠀⠈⠁⠨⠌⠉⣀⣀⠀⠀⠀
⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠛⠀⠀⠀⠀⠀⠀⠻⠇⠀⣠⣈⣤⣶⣶⣷⡶⠀⣤⣄⣀⣀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⢤⣤⣀⠀⠀⠀⠀⠀⠀⠠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠁⠀⠀⠙⢻⣿⠛⣿⣿⣯⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠀⠀⣀⣀⣴⣲⣷⣮⣥⣶⣾⣶⡶⠿⠛⠛⠛⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠙⢿⣿⣯⣼⡷⠢⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠙⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣀⣈⣻⣿⣛⣉⣤⡀⠀⠀⠀⣀⣀⣈⣼⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣲⣾⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡉⢿⣿⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠀⠀⢀⡀⣀⢀⣀⣄⣾⣿⣿⣿⣿⣾⣧⣀⡀⡀⢀⣤⣀⣴⣞⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢸⡿⠛⠀⠉⢿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⠷⣼⠂⠀⠀⠀⠀⠃⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣿⣿⣿⣿⣿⣿⢿⣿⡇⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⠋⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⢹⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢿⣿⣿⣿⡧⠛⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣠⣼⣿⣿⣿⡁⠹⣿⣿⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⠘⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⢻⣿⣿⣿⡿⢻⣶⣾⣿⣿⣿⣿⣿⡇⢰⣿⠏⠈⠄⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠟⠉⠀⠀⠀⠉⠙⠟⠉⠉⠙⢷⣾⠟⠀⠀⠀⠈⠻⠝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠁⢭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠉⣿⡟⣿⡇⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆⢰⣶⡆⢰⡖⢲⣆⢰⣶⠀⣶⠀⣴⡾⣷⡄⢰⣶⢶⡆⢠⣶⢲⣦⢸⣿⡇⢸⣿⣿⣿⣿⣿⣍⣍⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠠⣿⠁⢾⡆⢰⠤⣇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡾⣿⡇⢸⡇⢸⣿⢸⣿⣧⣿⠀⣿⡇⣿⡇⢸⣿⣼⠇⢸⣿⢸⣿⠈⣿⡟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠁⠀⣿⠀⢸⠇⢺⡇⠉⢀⣀⠀⠀⣷⠀⠀⢸⣧⢸⡇⣿⡇⢸⣇⣸⡿⢸⣿⢹⣿⠀⣿⡇⣿⡇⢸⣿⠀⠀⢸⣿⢸⣿⠀⣿⣀⠀⢼⣿⠁⠈⠀⣀⣩⣉⣭⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠉⢹⡇⠀⠀⢻⠀⠸⠀⠠⠔⠀⢸⣿⠀⢠⣿⣷⠀⠈⠁⠈⠁⠉⠁⠀⠉⠉⠀⠈⠉⠀⠉⠀⠈⠉⠉⠀⢈⣉⠀⠀⠀⠉⠉⠁⠀⠉⠉⠀⠈⠉⠀⠀⠀⠀⢙⣯⠹⡟⡻⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⡇⠀⠀⠸⠀⠀⠀⠠⠄⠀⢸⣿⡇⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⣆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⠀⠀⠐⠀⣘⣛⣿⣶⣸⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⢨⣍⠁⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠉⠉⠉⠐⠺⠯⠍⠉⠀⡉⠩⠉⠹⣿⣟
⠀⠀⠀⠀⠀⠐⠀⠀⠤⠀⠀⠉⠁⠀⠀⠀⢿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣥⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠚⠺⠲⠿⠷
⠀⠀⠀⠀⢰⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠋⠙⠻⠿⠿⣿⣿⣿⠿⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣷⣦⡤⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⡿⣿⠟⠛⠛⠛⠃⢤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡼⠟⠉⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡅⠀⠀⠂⠀⠀⣈⣄⣾⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠐⠆⠀⠀⠀⠀⠀⠀⠈⠁⠨⠌⠉⣀⣀⠀⠀⠀
⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⢻⠇⠀⣠⣀⣤⣶⣶⣶⡶⠀⣤⣄⣀⣀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⢤⣤⣀⠀⠀⠀⠀⠁⠀⠠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠁⠀⠀⠙⢻⣿⠛⣿⣿⣯⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠀⠀⣀⣀⣴⣲⣷⣮⣥⣶⣾⣶⡶⠿⠛⠛⠛⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠙⢿⣿⣯⣼⡷⠂⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠙⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣀⣈⣻⣿⣛⣉⣤⡀⠀⠀⠀⣀⣀⣈⣼⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⠀⠂⠀⠀⠀⠀⠀⣀⠀⣲⣿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡍⣿⣿⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠀⠀⢀⡀⣀⢀⣀⣄⣾⣿⣿⣿⣿⣾⣧⣀⡀⡀⢀⣤⣀⣴⣞⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣏⢸⠗⠓⠀⠀⢿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⠳⣸⠀⠀⠀⠀⠀⠃⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣿⣿⣿⣿⣿⣿⢿⣿⡇⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⠋⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣯⣿⣿⣿⣿⡿⢃⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠙⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢿⣿⣿⣿⡧⠛⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣼⣿⣿⣿⡁⠘⣿⣿⠟⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢐⠘⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠈⢻⣿⣿⣿⡿⢻⣦⣾⣿⣿⣿⣿⣿⡇⢠⣿⡏⠈⠄⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠛⠁⠀⠉⠉⠉⠻⠁⠉⠉⢻⣾⠟⠀⠀⠀⠈⠻⠝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠁⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠉⣿⡟⣿⡇⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆⢰⣶⡆⢰⡖⢲⣆⢰⣶⠀⣶⠀⣴⡾⣷⡄⢰⣶⢶⡆⢠⣶⢲⣦⢸⣿⡇⢸⣿⣾⣿⣿⣿⣭⣉⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠠⣿⠁⢞⡂⢰⠤⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡾⣿⡇⢸⡇⢸⣿⢸⣿⣧⣿⠀⣿⡇⣿⡇⢸⣿⣼⠇⢸⣿⢸⣿⠈⣿⡟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠁⠀⣿⠀⢸⠇⢺⡆⠈⢀⣀⠀⠀⣷⠀⠀⢸⣇⢹⡇⣿⡇⢸⣇⣸⡿⢸⣿⢹⣿⠀⣿⡇⣿⡇⢸⣿⠀⠀⢸⣿⢸⣿⠀⣿⣀⠀⢼⣿⠁⠈⠀⣠⣉⣉⣭⡍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠈⢹⡇⠀⠀⢹⠀⠨⠀⠠⢐⠀⢸⣿⠀⢠⣿⣧⠀⠈⠉⠈⠁⠉⠁⠀⠉⠉⠁⠈⠉⠀⠉⠀⠈⠉⠉⠀⢈⣉⠀⠀⠀⠉⠉⠁⠀⠉⠉⠀⠈⠉⠀⠀⠀⠀⠸⣮⠹⡟⡛⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⡇⠀⠀⠸⠀⠀⠀⠠⠄⠀⢸⣿⡆⣾⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣷⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠧⠀⠀⠟⠀⣘⣛⣿⣶⣸⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⢨⣍⠁⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠉⠉⠉⠐⠾⠯⠍⠉⠀⠉⢉⠉⠹⣿⡟
⠀⠀⠀⠀⠀⠐⠀⠀⠤⠀⠀⠉⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣩⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠚⠲⠶⠿⠷
⠀⠀⠀⠀⢰⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠋⠉⠻⠿⠿⣿⣿⣿⠿⣶⠶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣷⣦⡤⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⣿⡿⠟⠛⠛⠛⠃⢤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡼⠟⠈⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡅⠀⠀⠂⠀⠀⣈⣤⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠐⠆⠀⠀⠀⠀⠀⠀⠈⠁⠨⠌⠉⣀⣀⠀⠀⠀
⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⢻⠇⠀⣠⣀⣤⣶⣶⣷⡶⠀⣤⣄⣀⣀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⢤⣤⣀⠀⠀⠀⠀⠁⠀⠠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠁⠀⠀⠙⢻⣿⠛⣿⣿⣯⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠀⠀⣀⣀⣴⣲⣷⣮⣥⣶⣾⣶⡶⠿⠛⠛⠛⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠙⢻⣿⣯⣼⡿⠢⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠙⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣀⣈⣻⣿⣛⣉⣤⡀⠀⠀⠀⣀⣀⣈⣼⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣲⣿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡉⢿⣿⣿⡏⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠀⡀⣀⡀⣀⢀⣀⡄⣾⣿⣿⣿⣿⣾⣧⣀⠀⡀⢀⣤⣀⣴⣞⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢸⡟⠛⠈⠁⢿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⠳⣼⠂⠀⠀⠀⠀⠃⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣿⣿⣿⣿⣿⣿⢿⣿⡇⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⠿⠋⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢃⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠁⠉⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢿⣿⣿⣿⣧⠋⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣼⣿⣿⣿⡇⠈⣿⣿⡿⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⠘⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠈⢻⣿⣿⣿⣿⢻⣦⣶⣿⣿⣿⣿⣿⣿⢀⣿⡏⠈⠄⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠿⠟⠃⠘⠛⠉⠉⠛⠁⠈⠉⠻⣿⠟⠀⠀⠀⠈⠻⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠈⣿⡟⣻⣇⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆⢰⣶⡆⢰⡖⢲⣆⢰⣶⠀⣶⠀⣴⡾⣷⡄⢰⣶⢶⡆⢠⣶⢳⣦⢸⣿⡇⢸⣿⣿⣿⣿⣿⣭⣉⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠠⣿⠀⢚⡆⢰⠤⣇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡾⣿⡇⢸⡇⢸⣿⢸⣿⣧⣿⠀⣿⡇⣿⡇⢸⣿⣼⠇⢸⣿⢸⣿⠈⣿⡟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣿⡟⠁⠀⣿⠀⢸⠇⢺⡇⠉⢀⣀⠀⠀⣷⠀⠀⢸⣇⢸⡇⣿⡇⢸⣇⣸⡿⢸⣿⢹⣿⠀⣿⡇⣿⡇⢸⣿⠀⠀⢸⣿⢸⣿⠀⣿⣀⠀⢼⣿⠁⠉⠀⣠⣉⣉⣭⡍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠈⢹⡇⠀⠀⢻⠀⠨⠀⠠⢲⠀⢸⣿⠀⢀⣿⣧⠀⠈⠉⠈⠁⠉⠁⠀⠉⠉⠁⠈⠉⠀⠉⠀⠈⠉⠉⠀⢈⣉⠀⠀⠀⠉⠉⠁⠀⠉⠉⠀⠈⠉⠀⠀⠀⠀⠘⣯⢹⡟⡻⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⡇⠀⠀⠸⠀⠀⠀⠠⠄⠀⢸⣿⡆⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣷⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠗⠀⠀⠟⠀⣘⣻⣿⣶⣸⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⢨⣉⠁⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠉⠉⠉⠐⠾⠯⠍⠉⢀⡉⠩⠉⠹⣿⡟
⠀⠀⠀⠀⠀⠐⠀⠀⠤⠀⠀⠉⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣩⡕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠐⠒⠲⠲⠿⠷
⠀⠀⠀⠀⢰⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠋⠉⠻⠿⠿⢿⣿⡿⠷⠶⠶⢶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠰⣷⣦⡤⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠟⠛⠛⠛⠃⢤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡼⠟⠈⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡍⠀⠀⠂⠀⠀⣈⣤⣾⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠐⠆⠀⠀⠀⠀⠀⠀⠈⠁⠨⠌⠉⢀⣀⠀⠀⠀
⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠻⠇⠀⣠⣀⣤⣶⣶⣷⡶⠀⣤⣄⣀⣀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⢤⣤⣁⠀⠀⠀⠀⠁⠀⠠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠁⠀⠀⠙⢻⣿⠛⣿⣿⣯⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⣀⣀⣴⣲⣷⣮⣥⣶⣾⣶⡶⠿⠛⠛⠛⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠙⢻⣿⣯⣼⡿⠂⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠙⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣀⣈⣻⣿⣛⣉⣤⡀⠀⠀⠀⣀⣀⣀⣼⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⠀⠂⠀⠀⠀⠀⠀⣀⠀⣲⣾⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡉⢿⣿⣿⡏⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠀⠀⢀⡀⣀⢀⣀⡄⣾⣿⣿⣿⣿⣾⣧⣀⠀⡀⢄⣤⣀⣴⣞⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢸⡟⠛⠈⠁⢿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⠳⣼⠂⠀⠀⠀⠀⠃⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣿⣿⣿⣿⣿⣿⢿⣿⡇⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⠿⠋⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣟⣿⣿⣿⣿⡿⢃⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠁⠉⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢿⣿⣿⣿⣧⠊⢸⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣼⣿⣿⣿⡇⠈⣿⣿⡿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢐⠘⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⢻⣿⣿⣿⣿⢻⣦⣶⣿⣿⣿⣿⣿⣿⢀⣿⡏⠈⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠟⠃⠘⠛⠉⠉⠛⠁⠈⠉⠻⣿⠟⠀⠀⠀⠈⠻⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠁⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠈⣿⡟⣻⣇⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆⢰⣶⡆⢰⡖⢲⣆⢰⣶⠀⣶⠀⣴⡾⣷⡄⢰⣶⢶⡆⢠⣶⢳⣦⢸⣿⡇⢸⣿⣿⣿⣿⣿⣭⣉⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠠⣿⠀⢚⡆⢰⠤⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⡾⣿⡇⢸⡇⢸⣿⢸⣿⣧⣿⠀⣿⡇⣿⡇⢸⣿⣼⠇⢸⣿⢸⣿⠈⣿⡟⠿⢿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠁⠀⣿⠀⢸⠇⢺⣇⠈⢀⣀⠀⠀⣷⠀⠀⢸⣇⢸⡇⣿⡇⢸⣇⣸⡿⢸⣿⢹⣿⠀⣿⡇⣿⡇⢸⣿⠀⠀⢸⣿⢸⣿⠀⣿⣀⠀⢼⣿⠁⠉⠀⣠⣍⣉⣭⡍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠈⢹⡇⠀⠀⢹⠀⠨⠀⠠⢰⠀⢸⣿⠀⢀⣿⣧⠀⠈⠉⠈⠁⠉⠁⠀⠉⠉⠁⠈⠉⠀⠉⠀⠈⠉⠉⠀⢈⣉⠀⠀⠀⠉⠉⠁⠀⠉⠉⠀⠈⠉⠀⠀⠀⠀⠙⣯⢹⡟⡻⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⡇⠀⠀⠸⠀⠀⠀⠠⠄⠀⢰⣿⡆⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣷⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠇⠀⠀⠟⠀⣘⣻⣿⣦⣸⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⢨⣍⠁⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠉⠉⠉⠐⠺⠯⠉⠉⠀⠉⠩⠉⠹⣿⡟
⠀⠀⠀⠀⠀⠐⠀⠀⠤⠀⠀⠉⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣭⡕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠐⠖⠲⠶⠿⠷
⠀⠀⠀⠀⢴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠋⠉⠻⠿⠿⢿⣿⣿⠷⠶⠶⢶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠰⣷⣦⡤⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠟⠛⠛⠛⠃⢤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡼⠟⠈⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡅⠀⠀⠂⠀⠀⣈⣄⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠐⠆⠀⠀⠀⠀⠀⠀⠈⠀⠨⠌⠉⣀⣀⠀⠀⠀
⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠋⠀⠀⠀⠀⠀⠀⠻⠇⠀⣠⣀⣤⣶⣶⣷⡶⠀⣤⣄⣀⣀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⢤⣤⣁⠀⠀⠀⠀⠀⠀⠠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠁⠀⠀⠙⢻⣿⠛⣿⣿⣯⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⣀⣀⣴⣲⣷⣮⣥⣶⣾⣶⡶⠿⠛⠛⠛⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠙⢻⣿⣯⣼⡿⠢⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠙⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣀⣈⣻⣿⣛⣉⣤⡀⠀⠀⠀⣀⣀⣈⣼⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⠀⠂⠀⠀⠀⠀⠀⣀⠀⣲⣾⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡉⢿⣿⣿⡏⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠀⠀⢀⡀⣀⢀⣀⣄⣾⣿⣿⣿⣿⣾⣧⣀⡀⡀⢄⣤⣀⣴⣞⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣏⢸⠗⠓⠀⠀⢿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠚⠡⣼⠀⠀⠀⠀⠀⠃⠀⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣿⣿⣿⣿⣿⣿⢿⣿⡇⣇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠿⠋⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡃⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠈⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢿⣿⣿⣿⡧⠊⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣀⣴⣿⣿⣿⣇⠀⣿⣿⡿⢛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢐⠘⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⢻⣿⣿⣿⣿⢟⣷⣶⣿⣿⣿⣿⣿⣿⢀⣿⡏⠈⠄⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⢠⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠚⠟⠃⠈⠉⠃⠀⠀⠙⣿⠟⠀⠀⠀⠀⠹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠈⣿⡟⣻⡇⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆⢰⣶⡆⢰⡖⢲⣆⢰⣶⠀⣶⠀⣴⡟⣷⡄⢰⣶⢶⡆⢠⣶⢳⣦⢸⣿⡇⢸⣿⣾⣿⣿⣿⣭⣉⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠠⣿⠁⢚⡧⢰⡄⡧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⡾⣿⡇⢸⡇⢸⣿⢸⣿⣧⣿⠀⣿⡇⣿⡇⢸⣿⣼⠇⢸⣿⢸⣿⠈⣿⡟⠿⢿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣿⡟⠁⠀⣿⠀⢸⠇⢺⠆⠉⢀⣀⠀⠀⣧⠀⠀⢸⣇⢸⡇⣿⡇⢸⣇⣸⡿⢸⣿⢹⣿⠀⣿⡇⣿⡇⢸⣿⠀⠀⢸⣿⢸⣿⠀⣿⣀⠀⢼⣿⠁⠉⠁⣀⣭⣙⣽⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠈⢹⡇⠀⠀⢹⠀⠨⠀⠠⠔⠀⢸⣿⠀⢀⣿⣆⠀⠈⠉⠈⠁⠉⠁⠀⠉⠉⠁⠈⠉⠀⠉⠀⠈⠉⠉⠀⢈⣉⠀⠀⠀⠉⠉⠁⠀⠉⠉⠀⠈⠉⠀⠀⠀⠀⠸⣯⢹⡟⡻⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⡇⠀⠀⠸⠀⠀⠀⠠⠄⠀⢰⣿⡆⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣷⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠇⠀⠀⠓⠀⣘⣛⣿⣦⣸⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⢨⣍⠁⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠉⠉⠁⠐⠾⠯⠍⠉⠀⠉⢩⠉⠹⣿⣟
⠀⠀⠀⠀⠀⠐⠀⠀⠤⠀⠀⠉⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣯⣩⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠖⠲⠲⠿⠷
⠀⠀⠀⠀⢰⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠋⠙⠻⠿⠿⢿⣿⣿⠷⠶⠶⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠰⣷⣦⡤⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠟⠛⠙⠛⠋⢤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡼⠟⠈⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⠀⠀⠀⢀⠀⠀⠀⠀⢀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡍⠀⠀⠂⠀⠀⣈⣄⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠐⠆⠀⠀⠀⠀⠀⠀⠈⠀⠨⠌⠈⣀⣀⠀⠀⠀
⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠛⠀⠀⠀⠀⠀⠀⢻⠇⠀⣠⣀⣤⣶⣶⣶⡶⠀⣤⣄⣀⣀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤⢤⣤⣀⠀⠀⠀⠀⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠁⠀⠀⠙⢻⣿⠛⣿⣿⣯⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠀⠀⣀⣀⣴⣲⣷⣮⣥⣶⣾⣶⡶⠿⠛⠛⠛⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠙⢻⣿⣯⣼⡷⠢⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠙⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣀⣈⣻⣿⣛⣉⣤⡀⠀⠀⠀⣀⣀⣈⣼⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣲⣿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡉⢿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠀⡀⢀⡀⣀⢀⣀⣄⣾⣿⣿⣿⣿⣾⣧⣀⠀⡀⠄⣤⣀⣰⣖⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡏⢸⡟⠛⠈⠁⢿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡺⠣⣼⠄⠀⠀⠀⠀⠃⠀⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣿⣿⣿⣿⣿⣿⢿⣿⡇⣗⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⠿⠋⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠈⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠊⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣶⣿⣿⣿⣧⠀⣿⣿⡿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢐⠘⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠊⢻⣿⣿⣿⣿⢟⣷⣶⣿⣿⣿⣿⣿⣿⣀⣿⡏⠈⠄⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠿⠿⠺⠿⠃⠀⠉⠃⠀⠀⠈⣿⠟⠀⠀⠀⠈⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠉⣿⡟⣻⣇⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆⢰⣶⡆⢰⡖⢲⣆⢰⣶⠀⣶⠀⣴⡟⣷⡄⢰⣶⢶⡆⢠⣶⢲⣦⢸⣿⡇⢸⣿⣿⣿⣿⣿⣭⣉⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠠⣿⠁⢞⡧⢰⡤⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡾⣿⡇⢸⡇⢸⣿⢸⣿⣧⣿⠀⣿⡇⣿⡇⢸⣿⣼⠇⢸⣿⢸⣿⠈⣿⡟⠿⢿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠁⠀⣿⠀⢸⠇⢺⣆⠉⢀⣀⠀⠀⣧⠀⠀⢸⣧⢸⡇⣿⡇⢸⣇⣸⡿⢸⣿⢹⣿⠀⣿⡇⣿⡇⢸⣿⠀⠀⢸⣿⢸⣿⠀⣿⣀⠀⢼⣿⠡⠉⠁⣀⣭⣙⣽⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠈⢹⡇⠀⠀⢹⠀⠨⠀⠠⠴⠀⢸⣿⠀⢠⣿⣇⠀⠈⠉⠈⠁⠉⠁⠀⠉⠉⠁⠈⠉⠀⠉⠀⠈⠉⠉⠀⢈⣉⠀⠀⠀⠉⠉⠁⠀⠉⠉⠀⠈⠉⠀⠀⠀⠀⠘⢯⢹⡟⡻⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⡇⠀⠀⠸⠀⠀⠀⠠⠄⠀⢰⣿⡆⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣷⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠇⠀⠀⠺⠀⣘⣛⣿⣶⣸⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⢨⣉⠁⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠉⠉⠉⠐⠿⠯⠍⠉⠀⠉⠉⠉⢹⣿⣿
⠀⠀⠀⠀⠀⠐⠀⠀⠤⠀⠀⠉⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣩⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠐⠖⠲⠶⠿⠷
⠀⠀⠀⠀⢰⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠋⠙⠻⠿⠿⠿⣿⣿⠶⠶⠶⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣷⣦⡤⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠟⠛⠙⠛⠋⢤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡼⠟⠉⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡍⠀⠀⠂⠀⠀⣈⣴⣾⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠐⠆⠀⠀⠀⠀⠀⠀⠈⠀⠨⠌⠉⣀⣀⠀⠀⠀
⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠛⠀⠀⠀⠀⠀⠀⢿⠧⠀⣰⣀⣤⣶⣶⣶⡶⠀⣤⣄⣀⣀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⢤⣤⣅⠀⠀⠀⠀⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠁⠀⠀⠙⢿⣿⠛⣿⣿⣯⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠀⠀⣀⣀⣴⣲⣷⣮⣥⣶⣾⣶⡶⠿⠛⠛⠛⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠙⢿⣿⣯⣼⡷⠂⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠙⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣀⣈⣻⣿⣛⣉⣤⡀⠀⠀⠀⣀⣀⣈⣼⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⠀⠂⠀⠀⠀⠀⠀⣀⠀⣲⣿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡩⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠀⡀⢀⡀⣀⢀⣀⣄⣾⣿⣿⣿⣿⣾⣧⣀⠀⡀⢄⣤⣀⣴⣖⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⡟⠛⠈⠁⢿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡾⠳⣾⠀⠀⠀⠀⠀⠃⠀⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣿⣿⣿⣿⣿⣿⢿⣿⡇⣇⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠿⠋⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣷⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣟⣿⣿⣿⣿⡿⠂⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠊⢸⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣴⣿⣿⣿⣧⠀⣿⣿⡿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢐⠘⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⢻⣿⣿⣿⣿⠟⣷⣾⣿⣿⣿⣿⣿⣿⣀⣿⡏⠈⠄⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⠻⠿⠿⠿⠃⠰⠉⠁⠀⠀⠈⣿⠟⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠉⣿⡟⣿⣇⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆⢰⣶⡆⢰⡖⢲⣆⢰⣶⠀⣶⠀⣴⡟⣷⡄⢰⣶⢶⡆⢠⣶⢲⣦⢸⣿⡇⢸⣿⣿⣿⣿⣿⣭⣍⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠠⣿⠁⢞⡧⢰⣤⡧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡾⣿⡇⢸⡇⢸⣿⢸⣿⣧⣿⠀⣿⡇⣿⡇⢸⣿⣼⠇⢸⣿⢸⣿⠈⣿⡟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠁⠀⣿⠀⢸⠇⢺⢷⠁⢀⣀⠀⠀⣧⠀⠀⢸⣷⢸⡇⣿⡇⢸⣇⣸⡿⢸⣿⢹⣿⠀⣿⡇⣿⡇⢸⣿⠀⠀⢸⣿⢸⣿⠀⣿⣀⠀⢼⣿⢡⠉⠁⣀⣭⣹⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠈⢹⡇⠀⠀⢹⠀⠸⠀⠨⢶⠀⢸⣿⠀⢠⣿⣇⠀⠈⠉⠈⠁⠉⠁⠀⠉⠉⠁⠈⠉⠀⠉⠀⠈⠉⠉⠀⢈⣉⠀⠀⠀⠉⠉⠁⠀⠉⠉⠀⠈⠉⠰⠀⠀⠀⠹⣯⢹⡟⡻⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⡇⠀⠀⠸⠀⠀⠀⠠⠄⠀⢰⣿⡆⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠃⠀⠀⠻⠁⣘⣛⣿⣶⣸⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⢨⣍⠁⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠉⠉⠁⠐⠿⠯⠍⠉⣀⠉⠉⠉⠹⣿⣿
⠀⠀⠀⠀⠀⠐⠀⠀⠤⠀⠀⠉⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠐⠞⠲⠶⠿⠷
⠀⠀⠀⠀⢰⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠋⠙⠻⠿⠿⢿⣿⣿⠶⠶⠶⢤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣷⣦⡤⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠟⠛⠉⠛⠉⢤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡼⠟⠉⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣷⠀⠀⠀⢀⠀⠀⠀⠀⢀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡍⠀⠀⠂⠀⠀⣈⣴⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠐⠆⠀⠀⠀⠀⠀⠀⠈⠀⠨⠍⠉⣀⣀⠀⠀⠀
⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠿⠷⠀⣠⣀⣤⣶⣶⣶⡶⠀⣤⣄⣀⣀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠐⠂⠠⠤⠤⢤⣤⣅⠀⠀⠀⠀⠁⠀⠠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠁⠀⠀⠙⢿⣿⠛⣿⣿⣯⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠀⠀⣀⣀⣴⣲⣷⣮⣥⣶⣾⣶⡶⠿⠋⠛⠛⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠙⢿⣿⣯⣼⡿⠂⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠙⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣀⣈⣻⣿⣛⣉⣤⡀⠀⠀⠀⣀⣀⣈⣼⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⠀⠂⠀⠀⠀⠀⠀⣀⠄⣲⣿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡩⣿⣿⣿⡯⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠀⡀⣀⡀⣀⢀⣀⣄⣾⣿⣿⣿⣿⣾⣧⢀⠀⡀⠄⣤⣀⣴⣖⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡏⢸⠟⠛⠀⠁⢿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡞⠓⣾⠂⠀⠀⠀⠀⠃⠀⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣿⣿⣿⣿⣿⣿⢿⣿⡇⣗⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢻⣿⠿⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡃⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣏⣿⣿⣿⣿⣿⣿⣿⡿⠂⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢿⣿⣿⣿⡧⠛⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣾⣿⣿⣿⣧⠀⣿⣿⣿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⠘⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⢹⣿⣿⣿⣿⢟⣷⣾⣿⣿⣿⣿⣿⣿⣀⣿⡟⠀⠄⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣾⣯⣿⣿⣿⣿⣿⣇⠈⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⠿⠿⠦⠶⠉⠃⠀⠀⠈⣿⠟⠀⠀⠀⠈⠹⡿⣿⣿⣿⣿⣿⡿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⠁⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠘⣿⡟⣻⣇⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆⢰⣶⡆⢰⡖⢲⣆⢰⣶⠀⣶⠀⣴⡟⣷⡄⢰⣶⢶⡆⢠⣶⢲⣦⢸⣿⡇⢸⣿⣾⣿⣿⣿⣍⣉⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠰⣿⠁⢻⡧⢰⡤⡧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡾⣿⡇⢸⡇⢸⣿⢸⣿⣧⣿⠀⣿⡇⣿⡇⢸⣿⣼⠇⢸⣿⢸⣿⠈⣿⡟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣿⡟⠁⠀⣿⠀⢸⠇⢺⣆⠁⢀⣀⠀⠀⣧⠀⠀⢸⣇⢸⡇⣿⡇⢸⣇⢸⡿⢸⣿⢹⣿⠀⣿⡇⣿⡇⢸⣿⠀⠀⢸⣿⢸⣿⠀⣿⣀⠀⢼⣿⠡⠙⠁⣤⣏⣽⣽⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠈⢹⡇⠀⠀⢹⠀⠈⠀⠸⠶⠀⢸⣿⠀⢠⣿⣇⠀⠈⠉⠈⠁⠉⠁⠀⠉⠉⠁⠈⠉⠀⠉⠀⠈⠉⠉⠀⢈⣉⠀⠀⠀⠉⠉⠁⠀⠉⠉⠀⠈⠉⠀⠀⠀⠀⠘⠫⢻⡟⡻⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⡇⠀⠀⠸⠀⠀⠀⠠⠄⠀⢰⣿⡆⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⠀⠀⠘⠀⣘⣻⣿⣶⣸⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⢨⣉⠁⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠉⠉⠉⠐⠾⠯⠉⠉⢀⠉⢩⠉⠹⣿⣿
⠀⠀⠀⠀⠀⠐⠀⠀⠤⠀⠀⠉⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣏⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠘⠞⠲⠲⠿⠷
⠀⠀⠀⠀⢴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠋⠉⠻⠿⠿⠿⣿⢿⠶⠶⠶⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣷⣧⡤⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠟⠛⠉⠛⠉⢤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⠟⠉⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡍⠀⠀⠂⠀⠀⣈⣤⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠐⠆⠀⠀⠀⠀⠀⠀⠈⠀⠨⠍⠉⢀⣀⠀⠀⠀
⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠋⠀⠀⠀⠀⠀⠐⠻⠷⠉⣠⣈⣤⣶⣶⣶⡶⠀⣤⣄⣀⣀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠐⠀⠠⠤⠤⢤⣤⣅⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣠⣾⣿⣿⣿⣿⣿⣿⠁⠀⠀⠙⢻⣿⠛⣿⣿⣿⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠀⠀⣀⣀⣴⣲⣷⣮⣥⣶⣾⣶⡶⠿⠋⠛⠛⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠙⢿⣿⣯⣼⡿⠂⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠙⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣀⣈⣻⣿⣛⣉⣤⡀⠀⠀⠀⣀⣀⣈⣼⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⠀⠂⠀⠀⠀⠀⠀⣀⠀⣲⣿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡩⣿⣿⣿⡏⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠀⡀⢀⣀⣀⢀⣀⣄⢾⣿⣿⣿⣿⣾⣧⢀⠀⡀⠄⣤⣀⣠⣔⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡷⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣏⢸⠿⠛⠈⠉⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡞⠁⣺⠃⠀⠀⠀⠀⠃⠀⠋⠻⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣿⣿⣿⣿⣿⣿⢿⣿⡗⣇⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠿⠋⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⡇⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣽⣿⣿⣿⡿⢃⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠛⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⣠⣾⣿⣿⣿⣧⠀⣿⣿⣟⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢰⠘⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⢻⣿⣿⣿⣿⢿⣷⣾⣿⣿⣿⢿⣿⣿⣀⣿⡟⠀⠆⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⠿⠿⠧⠶⠉⠁⠀⠀⢈⣿⠟⠀⠀⠀⠈⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠁⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠙⣿⡟⣻⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆⢰⣶⡆⢰⡖⢲⣆⢰⣶⠀⣶⠀⣴⡞⣷⡄⢰⣶⢶⡆⢠⣶⢲⣦⢸⣿⡇⢸⣿⣾⣿⣿⣿⣇⣉⡙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠠⣿⠁⢸⡧⢰⡤⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡾⣿⡇⢸⡇⢸⣿⢸⣿⣧⣿⠀⣿⡇⣿⡇⢸⣿⣼⠇⢸⣿⢸⣿⠈⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣿⡟⠁⠀⣿⠀⢸⠇⢸⣳⠁⢀⣀⠀⠀⣧⠀⠀⢸⣿⢹⡇⣿⡇⢸⣇⣸⡿⢸⣿⢹⣿⠀⣿⡇⣿⡇⢸⣿⠀⠀⢸⣿⢸⣿⠀⣿⣀⠀⢼⣿⠉⠹⠁⢄⣭⣽⣽⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠈⢹⡇⠀⠀⢻⠀⠈⠀⠸⠱⠀⢸⣿⠀⢠⣿⣇⠀⠈⠉⠈⠁⠉⠁⠀⠉⠉⠁⠈⠉⠀⠉⠀⠈⠉⠉⠀⢈⣉⠀⠀⠀⠉⠉⠁⠀⠉⠉⠀⠈⠉⠀⠀⠀⠀⢈⠩⠹⣟⡽⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⡇⠀⠀⠸⠀⠀⠀⠠⠄⠀⢸⣿⡄⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠇⠀⠀⠩⠀⣐⣻⣿⣶⣸⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⢈⣉⠁⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠉⠉⠉⠐⠻⡯⠉⢉⠀⠉⢉⢩⠿⣿⣟
⠀⠀⠀⠀⠀⠐⠀⠀⠄⠀⠀⠉⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣏⣭⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠀⠐⠚⠳⠾⠿⠿
⠀⠀⠀⠀⢰⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠋⠉⠛⠿⠿⢿⣿⣿⠶⠶⠆⢤⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣷⣦⡤⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠿⠿⠿⠟⠛⠛⠛⠁⢠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⠟⠈⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣷⠀⠀⠀⢀⠀⠀⠀⠀⢀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡅⠀⠀⠂⠀⠀⣈⣠⣿⡿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠐⠆⠀⠀⠀⠀⠀⠀⠈⠀⠨⠭⠉⣀⣀⠀⠀⠀
⠶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠛⠀⠀⠀⠀⠀⠀⠿⠷⠀⣠⣀⣤⣶⣶⣶⣶⠀⣤⣄⣀⣀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠂⠀⠤⠤⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠁⠀⠈⠙⢿⣿⠛⣿⣿⣿⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠀⠀⣀⣀⣤⣒⣷⣾⣧⣴⣾⣶⡶⠿⠛⠻⠛⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠙⢻⣿⣯⣼⡿⠂⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠙⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣀⣈⣻⣿⣛⣉⣤⡀⠀⠀⠀⣀⣀⣈⣽⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⣀⠀⣲⣿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡭⣿⣿⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠀⠀⢀⣀⣀⢀⣀⣔⣾⣿⣿⣿⣿⣾⣧⢀⡀⣀⠀⡤⣠⣠⣎⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣕⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣏⢸⠿⠓⠈⠉⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡞⠁⣰⠃⠀⠀⠀⠀⠃⠀⠋⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣿⣿⣿⣿⣿⣿⢿⣿⡇⣏⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠿⠋⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⡇⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣿⣟⣹⣿⣿⣿⡟⠃⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢿⣿⣿⣿⡇⠛⢸⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⣠⣾⣿⣿⣿⣧⠀⣿⣿⣟⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢰⠘⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⢻⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣀⣿⡟⠀⠄⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢠⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠷⠷⠉⠁⠀⠀⢈⣿⠟⠀⠀⠀⠈⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣯⣿⡧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠁⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠛⣿⡟⣿⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆⢰⣶⡆⢰⡖⢲⣆⢰⣶⠀⣶⠀⣴⡞⣷⡄⢰⣶⢶⡆⢠⣶⢳⣦⢸⣿⡇⢸⣿⣾⣿⣿⣿⣗⣉⡙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠠⣿⠁⢸⡇⢰⠤⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡾⣿⡇⢸⡇⢸⣿⢸⣿⣧⣿⠀⣿⡇⣿⡇⢸⣿⣼⠇⢸⣿⢸⣿⠈⣿⡟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣿⡟⠁⠀⣿⠀⢸⠇⢻⡓⠁⢀⣀⠀⠀⣧⠀⠀⢸⣿⢹⡇⣿⡇⢸⣇⣸⡿⢸⣿⢹⣿⠀⣿⡇⣿⡇⢸⣿⠀⠀⢸⣿⢸⣿⠀⣿⣀⠀⢼⣿⠉⠹⠁⢄⣭⣽⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠈⢹⡇⠀⠀⢻⠀⠈⠀⠸⠲⠀⢸⣿⠀⢠⣿⣇⠀⠈⠉⠈⠁⠉⠁⠀⠉⠉⠁⠈⠉⠀⠉⠀⠈⠉⠉⠀⢈⣉⠀⠀⠀⠉⠉⠁⠀⠉⠉⠀⠈⠉⠀⠀⠀⠐⢈⠩⠽⣟⡻⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⡇⠀⠀⠸⠀⠀⠀⠠⠄⠀⢸⣿⡅⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠀⠈⠀⣐⣻⣿⣶⡸⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⢈⡍⠁⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠉⠉⠁⠐⠻⠯⠉⢉⠀⠉⢉⢉⠿⣿⣟
⠀⠀⠀⠁⠀⠐⠀⠀⠄⠀⠀⠉⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣏⣭⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠁⠐⠚⠳⠾⠿⠿
⠀⠀⠀⠀⢰⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠋⠉⠛⠿⠿⢿⣿⣿⠶⠶⠆⢤⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢐⣷⣶⡤⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠿⠿⠿⠟⠛⠙⠛⠉⢠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⠟⠈⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡅⠀⠀⠂⠀⠀⣈⣠⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠐⠆⠀⠀⠀⠀⠀⠀⠈⠀⠨⠭⠉⣀⣀⠀⠀⠀
⠶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠛⠀⠀⠀⠀⠀⠀⠿⠷⠀⣠⣀⣤⣶⣶⣶⣶⠀⣤⣄⣀⣀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠂⠠⠤⠤⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠁⠀⠈⠙⢿⣿⠛⣿⣿⣿⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠀⠀⣀⣀⣴⣒⣷⣾⣧⣴⣾⣶⡶⠿⠛⠻⠛⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠙⢻⣿⣯⣼⡿⠆⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠙⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣀⣈⣻⣿⣛⣉⣤⡀⠀⠀⠀⣀⣀⣈⣽⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⣀⠀⣲⣿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡭⣿⣿⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠀⠀⢀⡀⣀⢀⣀⣄⣾⣿⣿⣿⣿⣾⣧⢀⡀⣀⠀⡤⣠⣠⣄⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣕⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣏⢸⠿⠛⠈⠉⢿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡜⠁⣠⠇⠀⠀⠀⠀⠃⠀⠛⠻⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣿⣿⣿⣿⣿⣿⢿⣿⡇⣇⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠿⠋⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣺⣿⣿⣿⣿⣿⣿⣿⣿⡇⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣹⣿⣿⣿⡟⢃⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠋⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⣠⣾⣿⣿⣿⣧⠀⣿⣿⡿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢰⠘⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⢻⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⢿⣿⣿⣀⣿⡟⠀⠄⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⡿⠻⠟⠻⠿⠉⠁⠀⠀⢉⣿⠟⠀⠀⠀⠈⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣯⣿⡧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠘⣿⡟⣻⡇⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆⢰⣶⡆⢰⡖⢲⣆⢰⣶⠀⣶⠀⣴⡞⣷⡄⢰⣶⢶⡆⢠⣶⢳⣦⢸⣿⡇⢸⣿⣾⣿⣿⣿⣇⣉⡙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠠⣿⠁⢹⡧⢰⡤⡧⠀⠀⠀⠀⠀⠀⠀⢸⡿⣷⡾⣿⡇⢸⡇⢸⣿⢸⣿⣧⣿⠀⣿⡇⣿⡇⢸⣿⣼⠇⢸⣿⢸⣿⠈⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣿⡟⠁⠀⣿⠀⢸⠇⢺⡃⠁⢀⣀⠀⠀⣧⠀⠀⢸⣿⢹⡇⣿⡇⢸⣇⣸⡿⢸⣿⢹⣿⠀⣿⡇⣿⡇⢸⣿⠀⠀⢸⣿⢸⣿⠀⣿⣀⠀⢼⣿⠉⠩⠁⢠⣭⣽⣽⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠈⢹⡇⠀⠀⢻⠀⠈⠀⠸⠐⠀⢸⣿⠀⢠⣿⣇⠀⠈⠉⠈⠁⠉⠁⠀⠉⠉⠁⠈⠉⠀⠉⠀⠈⠉⠉⠀⢈⣉⠀⠀⠀⠉⠉⠁⠀⠉⠉⠀⠈⠉⠀⠀⠀⠀⢙⠭⠽⣟⡿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⡇⠀⠀⠸⠀⠀⠀⠠⠄⠀⢸⣿⡄⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠇⠀⠀⠀⠀⣐⣻⣿⣦⡸⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⢈⣉⠁⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠉⠉⠁⠐⠾⠯⠉⢉⠁⠉⢉⠉⠿⣿⣟
⠀⠀⠀⠀⠀⠐⠀⠀⠄⠀⠀⠉⠁⠀⠀⠀⢿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣏⣭⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠁⠒⠚⠳⠾⠿⠿
⠀⠀⠀⠀⢰⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠋⠉⠻⠿⠿⢿⣿⣿⠶⠶⠦⣤⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⣷⣦⡤⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠿⠿⠟⠛⠙⠛⠁⢠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⠟⠈⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡅⠀⠀⠂⠀⠀⣈⣀⣿⡿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠐⠆⠀⠀⠀⠀⠀⠀⠈⠀⠨⠭⠉⣀⣀⠀⠀⠀
⠶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠝⠀⠀⠀⠀⠀⠀⠻⠷⠀⣠⣀⣤⣶⣶⣶⣶⠀⣤⣄⣀⣀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠐⠂⠀⠤⠤⢤⣤⣀⠀⠀⠀⠀⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠁⠀⠈⠙⢿⣿⠛⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠀⠀⣀⣀⣤⣒⣷⣾⣧⣴⣾⣶⡶⠾⠛⠻⠛⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠙⢻⣿⣯⣼⡿⠢⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠙⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣀⣈⣻⣿⣛⣉⣤⡀⠀⠀⠀⣀⡀⣈⣽⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⣀⠀⣲⣿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡭⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠀⠀⢀⡀⣀⢀⣀⣄⣾⣿⣿⣿⣿⣾⣧⣀⡀⣀⠀⡤⣠⣴⣄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡏⢹⠿⠛⠈⠙⣿⣯⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡾⠡⣼⠃⠀⠀⠀⠀⠃⠀⠋⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣿⣿⣿⣿⣿⣿⢿⣿⡇⣏⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠿⠋⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣺⣿⣿⣿⣿⣿⣿⣿⣿⡇⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣿⣿⣹⣿⣿⣿⡿⢃⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠈⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠋⢸⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⣠⣾⣿⣿⣿⣇⠀⣿⣿⡿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢰⠘⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⢻⣿⣿⣿⣿⢿⣷⣾⣿⣿⣿⣿⣿⣿⣀⣿⡟⠀⠄⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣽⣿⣿⣿⣿⡇⠀⢠⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠛⠛⠻⠿⠉⠁⠀⠀⢉⣿⠟⠀⠀⠀⠈⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣯⣿⡧⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠈⠀⡀⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠙⣿⡿⣻⣇⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆⢰⣶⡆⢰⡖⢲⣆⢰⣶⠀⣶⠀⣴⡞⣷⡄⢰⣶⢶⡆⢠⣶⢳⣦⢸⣿⡇⢸⣿⣾⣿⣿⣿⣇⣉⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠠⣿⠁⢺⡧⢰⣤⡧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡾⣿⡇⢸⡇⢸⣿⢸⣿⣧⣿⠀⣿⡇⣿⡇⢸⣿⣼⠇⢸⣿⢸⣿⠈⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠁⠀⣿⠀⢸⠇⢻⡛⠃⢀⣀⠀⠀⣧⠀⠀⢸⣯⢹⡇⣿⡇⢸⣇⣸⡿⢸⣿⢹⣿⠀⣿⡇⣿⡇⢸⣿⠀⠀⢸⣿⢸⣿⠀⣿⣀⠀⢼⣿⠉⠩⠁⢀⣭⣽⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠈⢹⡇⠀⠀⢻⠀⠘⠀⠸⠛⠀⢸⣿⠀⢠⣿⣇⠀⠈⠉⠈⠁⠉⠁⠀⠉⠉⠀⠈⠉⠀⠉⠀⠈⠉⠉⠀⠈⣉⠀⠀⠀⠉⠉⠁⠀⠉⠉⠀⠈⠉⠀⠀⠀⠀⠙⠯⠝⣟⡻⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⡇⠀⠀⠸⠀⠀⠀⠠⠄⠀⢸⣿⡄⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠈⠁⣐⢻⣿⣶⡸⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⢈⡉⠁⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠀⠀⠀⠉⠉⠉⠐⠾⡯⠉⢉⠉⠉⢉⠉⠿⣿⣟
⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣏⣭⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠉⠓⠖⠲⠾⠿⠿
⠀⠀⠀⠀⢰⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠋⠙⠻⠿⠿⣿⣿⣿⠶⠶⠦⢤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢐⣷⣦⡤⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠿⠿⠟⠛⠙⠛⠉⢠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⠟⠈⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣷⠀⠀⠀⢀⠀⠀⠀⠀⢀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡅⠀⠀⠂⠀⠀⣈⣠⣿⡿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠐⠆⠀⠀⠀⠀⠀⠀⠈⠀⠨⠭⠉⣀⣀⠀⠀⠀
⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡉⠀⠀⠀⠀⠀⠐⠻⠷⠀⣠⣀⣤⣶⣶⣶⣶⠀⣤⣄⣀⣀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠐⠂⠀⠤⠤⢤⣤⣀⠀⠀⠀⠀⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠁⠀⠈⠙⢿⣿⠛⣿⣿⣿⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠀⠀⣀⣀⣴⣚⣷⣾⣥⣴⣾⣶⡶⠾⠛⠻⠛⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠙⢻⣿⣯⣸⡿⠢⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠙⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣀⣈⣻⣿⣛⣉⣤⡀⠀⠀⠀⢀⡀⣈⣽⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠚⠀⠀⠀⠀⠀⣀⠀⣲⣿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡭⣿⣿⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠀⠀⠀⡀⣀⢀⣀⣄⣾⣿⣿⣿⣿⣾⣧⠀⠀⣀⢀⡤⣀⣤⣔⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣏⢹⠿⠛⠈⠉⢿⣯⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⡱⣲⠁⠀⠀⠀⠀⠃⠀⠋⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣇⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠿⠋⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣿⣟⣽⣿⣿⣿⡿⢃⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠈⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢿⣿⣿⣿⣇⠋⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣾⣿⣿⣿⣇⠈⣿⣿⡿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢰⠘⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⢻⣿⣿⣿⣿⢿⣷⣾⣿⣿⣿⣿⣿⣿⢠⣿⡟⠀⠴⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣽⣿⣿⣿⣿⡇⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠟⠙⠛⠻⠿⠉⠁⠀⠀⢙⣿⠟⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠈⠀⠁⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠙⣿⡟⣿⡇⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆⢰⣶⡆⢰⡖⢲⣆⢰⣶⠀⣶⠀⣴⡞⣷⡄⢰⣶⢶⡆⢠⣶⢲⣦⢸⣿⡇⢸⣿⣾⣿⣿⣿⣇⣈⡙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠠⣿⠁⢻⡃⢰⡤⡧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡾⣿⡇⢸⡇⢸⣿⢸⣿⣧⣿⠀⣿⡇⣿⡇⢸⣿⣼⠇⢸⡯⢸⣿⠈⣿⡟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣿⡟⠁⠀⣿⠀⢸⠇⢻⡫⠁⢀⣀⠀⠀⣧⠀⠀⢸⣿⢹⡇⣿⡇⢸⣇⣸⡿⢸⣿⢹⣿⠀⣿⡇⣿⡇⢸⣿⠀⠀⢸⣿⢸⣿⠀⣿⣀⠀⢼⣿⠉⠉⠁⢀⣭⣽⣽⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠈⢹⡇⠀⠀⢻⠀⠸⠀⠸⠀⠀⢸⣿⠀⢠⣿⣇⠀⠈⠉⠈⠁⠉⠁⠀⠉⠉⠀⠈⠉⠀⠉⠀⠈⠉⠉⠀⠈⣉⠀⠀⠀⠉⠉⠁⠀⠉⠉⠀⠈⠉⠠⠀⠀⠀⠙⠭⠽⣟⡻⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⡇⠀⠀⠸⠀⠀⠀⠠⠄⠀⢸⣿⡅⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠇⠀⠀⠈⠀⣐⡻⣿⣦⡸⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⢨⣉⠁⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠉⠉⠉⠐⠺⡯⠉⠉⠈⠉⢉⠉⠽⣿⣟
⠀⠀⠀⠀⠀⠐⠀⠀⠄⠀⠀⠉⠀⠀⠀⠀⢿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣏⣭⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠉⠒⠖⠲⠶⠿⠿
⠀⠀⠀⠀⢰⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠋⠙⠻⠿⠿⢿⣿⣿⠶⠶⠆⢤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢐⣷⣦⡤⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠿⠿⠟⠛⠙⠛⠉⢠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⠟⠈⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣷⠀⠀⠀⢀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡅⠀⠀⠂⠀⠀⣈⣠⣾⣾⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠐⠆⠀⠀⠀⠀⠀⠀⠈⠀⠨⠭⠉⡀⣀⠀⠀⠀
⠶⠞⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠀⠀⠀⠀⠀⠐⠿⠷⠀⣢⣈⣥⣶⣶⣶⣶⠀⣤⣄⣀⢀⣀⣀⣠⠀⠀⠀⠀⠀⠀⠐⠂⠠⠤⠤⣤⣤⣀⠀⠀⠀⠀⠈⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠁⠀⠈⠙⢿⣿⠛⣿⣿⣦⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠀⠀⣀⣀⣤⣚⣷⣾⣥⣴⣾⣶⡶⠾⠛⠻⠛⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠛⢻⣿⣯⣸⡿⠢⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠄⠀⠋⠀⠀⠀⠙⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀⣈⣻⣿⣛⣉⣤⡀⠀⠀⠀⢀⡀⣈⣽⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠒⠀⠀⠀⠀⠀⢀⠀⣲⣿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡩⣿⣿⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠀⠀⠀⡀⣀⢀⣀⣄⣶⣿⣿⣿⣿⣾⣦⢀⡀⣀⠀⡤⢠⣠⡄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡟⢹⠿⠛⠈⠙⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡞⠡⣴⠃⠀⠀⠀⠀⠃⠀⠋⠻⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣿⣿⣿⣿⣿⣿⢿⣿⡇⣗⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠿⠋⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣹⣿⣿⣿⡿⢃⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠈⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢿⣿⣿⣿⣧⠋⢸⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣾⣿⣿⣿⡇⠈⣿⣿⡟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢰⠘⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⢻⣿⣿⣿⣿⢿⣷⣿⣿⣿⡿⣿⣿⣿⢠⣿⡟⠀⠦⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣽⣿⣿⣿⣿⡇⠈⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠟⠙⠋⠛⠛⠉⠀⠀⠀⢙⣿⠟⠀⠀⠀⠈⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣯⣿⡧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠈⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠙⣿⡟⣻⡇⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆⢰⣶⡆⢰⡖⢲⣆⢰⣶⠀⣶⠀⣴⡞⣷⡄⢰⣶⢶⡆⢠⣶⢲⣦⢸⣿⡇⢸⣿⣾⣿⣿⣿⣃⣉⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠠⣿⠁⢻⡧⢰⡤⡧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡾⣿⡇⢸⡇⢸⣿⢸⣿⣧⣿⠀⣿⡇⣿⡇⢸⣿⣼⠇⢸⣿⢸⣿⠈⣿⡟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣿⡟⠁⠀⣿⠀⢸⠇⢺⡫⠁⢀⣀⠀⠀⣧⠀⠀⢸⣿⢹⡇⣿⡇⢸⣇⣸⡿⢸⣿⢹⣿⠀⣿⡇⣿⡇⢸⣿⠀⠀⢸⣿⢸⣿⠀⣿⣀⠀⢼⣿⠉⠙⠁⢀⣍⣽⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠈⢹⡇⠀⠀⢻⠀⠸⠀⠸⢳⠀⢸⣿⠀⢠⣿⣇⠀⠈⠉⠈⠁⠉⠁⠀⠉⠉⠁⠈⠉⠀⠉⠀⠈⠉⠉⠀⠈⡉⠀⠀⠀⠉⠉⠁⠀⠉⠉⠀⠈⠉⠀⠀⠀⠀⠙⠯⠿⡗⡻⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⡇⠀⠀⠸⠀⠀⠀⠠⠄⠀⢸⣿⡄⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠃⠀⠀⠈⠀⣀⠹⣿⣦⣼⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⢈⣉⠁⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠀⠈⠉⠉⠉⠁⠐⠾⡯⠉⢉⠀⠉⢉⠉⠿⣿⣟
⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣏⣭⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠉⠓⠚⠳⠾⠿⠿
⠀⠀⠀⠀⢰⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠋⠙⠛⠿⠿⢿⣿⣿⠶⠶⠆⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢐⣷⣦⡤⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿⠿⠟⠛⠙⠛⠉⢠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⠟⠈⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣷⠀⠀⠀⢀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡅⠀⠀⠂⠀⠀⣈⣠⣾⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠐⠆⠀⠀⠀⠀⠀⠀⠈⠀⠨⠍⠉⡀⣀⠀⠀⠀
⠶⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡉⠀⠀⠀⠀⠀⠐⠿⠷⠀⣠⣀⣥⣶⣶⣶⣶⠀⣤⣄⣀⢀⣀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠂⠠⠤⠤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣠⣾⣿⣿⣿⣿⣿⣿⠁⠀⠈⠙⢿⣿⠛⣿⣿⣦⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠀⠀⣀⣀⣤⣺⣷⣮⣥⣴⣾⣶⡶⠾⠛⠻⠛⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠛⢿⣿⣿⣸⡿⠢⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠄⠀⠋⠀⠀⠀⠙⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀⣈⣻⣿⣛⣉⣤⡀⠀⠀⠀⢀⡀⣈⣽⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡀⠂⠀⠀⠀⠀⠀⣀⠀⣲⣿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡍⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠀⠀⢀⡀⣀⢀⣀⣄⣶⣿⣿⣿⣿⣾⣦⠀⡀⣀⠀⡤⢠⣤⣄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⡗⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢹⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡇⠀⠀⠀⠘⠛⠈⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢿⣿⠿⠋⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⣱⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⡇⠀⠀⠀⢆⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⢈⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣴⣿⣿⣿⣿⡇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⠸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⢠⣿⡏⠙⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⢸⣏⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠋⠉⠉⠛⠛⠉⠀⠀⠀⢹⣿⠟⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠟⠉⠉⡁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣻⣿⡿⣿⣗⢀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢠⣤⣿⣶⣾⣿⣿⣋⣛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠿⣿⠧⢿⡧⢰⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠋⠀⣿⡀⣸⠇⣿⣿⠛⢀⣀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢩⣭⣽⠁⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠁⠉⢻⡇⠀⠀⢻⠀⠸⠀⢽⣿⠀⢸⣿⠀⢰⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣀⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣧⠀⠀⢸⠀⠀⠀⢠⡴⠀⢸⣿⡧⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣷⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣷⣼⣿⣿⣞⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡏⠀⠀⠀⠀⠀⠄⢀⣄⠀⢨⣍⡁⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠨⠯⠉⠉⠉⠉⠉⠉⠛⢿⣯⠟⣹⣫⣭⣽⣿⣿⣿⣿
⠀⠀⠀⠁⠀⠰⠀⠠⠤⠀⠈⠉⠉⠀⠀⠀⢿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣾⣿⣿⣿⣿⣿⣿⣿⣯⣯⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⠻⠿⠿⠿⠿⠿
⠀⠀⡂⠀⢴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠋⠙⠻⠿⣿⣿⣿⣿⣷⣶⠶⣤⣶⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣷⣤⠜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⣿⢿⠿⠟⠛⠛⠋⢤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⡟⠉⠆⠀⠀⡈⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣷⠄⠀⠀⣀⡀⠀⠀⠀⣨⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠋⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡏⠀⠐⠆⠀⢀⣈⣼⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠐⠆⠀⠈⠀⠀⠀⡌⠈⠀⡹⣭⣍⣥⣃⡈⡀⠀
⠾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁⠀⠀⠀⠓⠸⢿⠿⠉⣿⣉⣯⣶⣶⣶⣶⠀⣤⣄⣀⣀⣀⣀⣠⠀⠀⠀⠀⠀⠀⠐⠒⠴⠤⠤⣤⣤⣭⡀⠀⠀⠀⠙⠀⠡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣠⣾⣿⣿⣿⣿⣿⣿⠁⠀⠈⠙⢿⣿⠟⣿⣿⣿⣾⣃⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢉⡀⠀⠀⠀⠀⠠⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠀⠀⣀⣀⣴⣾⣷⣾⣧⣷⣾⣶⣶⠾⠛⠻⠻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠛⢿⣿⣿⣼⡿⠮⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠄⠀⠋⠀⠀⠀⠙⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣀⣈⣻⣿⣟⣋⣤⣀⠀⠀⠀⢀⡀⣈⣽⣧⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡀⠚⠀⠀⠀⠀⠀⣀⠄⣲⣿⣯⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⠀⠄
⠀⢀⠀⠉⠀⡀⢀⣀⣀⣀⣀⣴⣾⣿⣿⣿⣿⣾⣧⣀⣀⣠⢄⣤⣠⣴⣞⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠦⠀⠀⠄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢹⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡇⠀⠀⠀⠘⠛⠈⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⠿⠋⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⡵⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⡇⠀⠀⠀⢆⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⢨⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣴⣿⣿⣿⣿⡇⠈⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⠸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠋⢻⣿⣿⣿⣿⣻⣿⣿⣿⣿⠿⠿⣿⣿⢠⣿⡏⠙⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⢴⡇⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠋⠉⠉⠛⠛⠉⠀⠀⠀⣹⣿⠏⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⡍⡉⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣻⣿⡿⣿⣗⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢠⣤⣿⣷⣾⣿⣿⣋⡟⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠷⣿⠧⢿⡧⢰⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠋⠀⣿⡀⣸⠇⣿⣿⠛⢀⣀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢩⣭⣽⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠁⠉⢹⡇⠀⠀⢻⠀⠸⠀⢽⣿⠀⢸⣿⠀⢠⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⡀⢼⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣧⠀⠀⢸⠀⠀⠀⢠⡴⠀⢸⣿⡇⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣷⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣷⣼⣿⣿⣞⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡏⠀⠀⠀⠀⠀⠄⢀⣄⠀⢨⣍⡁⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠠⠯⠉⠉⠉⠉⠉⠉⠛⢿⣯⠟⣻⣫⣭⣭⣯⣿⣿⣿
⠀⠀⠀⠃⠀⠐⠀⠠⠤⠀⠈⠉⠉⠀⠀⠀⢿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣾⣿⣿⣿⣿⣿⣿⣿⣯⣯⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⠻⠿⠿⠿⠿⠿
⠀⠀⡆⠀⢴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠋⠙⠻⠿⡿⣿⣿⣿⣷⣶⠶⣶⣶⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣷⣤⠜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⣿⢿⠿⠟⠛⠛⠋⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⡟⠉⠆⠀⠀⡈⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣷⠄⠀⠀⣀⡀⠀⠀⠀⣸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢀⡀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠋⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡏⠀⠐⠆⠀⢠⣈⣼⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠐⠆⠀⠈⠀⠀⠀⠌⠈⡀⡹⣭⣍⣥⣃⡈⡀⠀
⠾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡿⠁⠀⠀⠀⠓⠸⣿⠿⠉⣿⣉⣯⣶⣶⣶⣶⠀⣤⣄⣀⢀⣀⣀⣠⠀⠀⠀⠀⠀⠀⠐⠒⠶⠤⠤⣤⣤⣭⠀⠀⠀⠀⠙⠀⠡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣠⣾⣿⣿⣿⣿⣿⣿⠁⠀⠈⠙⢿⣿⠟⣿⣿⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⡀⠀⠀⠀⠀⠠⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠀⠀⣀⣀⣴⣾⣷⣾⣧⣷⣾⣶⣶⠾⠛⠻⠻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠛⢿⣿⣿⣼⡿⠮⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠄⠀⠋⠀⠀⠀⠛⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀⣈⣻⣿⣟⣋⣤⣀⠀⠀⠀⢀⡀⣈⣽⣧⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡀⠚⠀⠀⠀⠀⠀⢀⠄⣲⣿⣯⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀
⠀⢀⠀⠉⠀⡀⢀⣀⣀⣀⣀⣵⣾⣿⣿⣿⣿⣾⣧⣀⣀⣠⢄⣤⣠⣴⣖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠦⠀⠀⠄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⠛⠋⠙⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠇⠀⠀⠀⠘⠛⠈⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⠟⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣗⠿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣗⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢹⣿⡇⠀⠀⠀⢂⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠁⠀⢸⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢸⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⣴⣿⣿⣿⣿⡄⠘⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢰⠸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠋⢿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠿⢿⣿⣇⣸⣿⠏⠘⢿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⢠⡇⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠟⠃⠉⠉⠛⠋⠉⠀⠀⠀⣹⣿⠏⠀⠀⠀⠙⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⢭⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣻⣿⡿⣿⣇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢀⣤⣿⣶⣾⣿⣿⣋⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠶⣿⡅⢿⡧⢰⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠋⠀⣿⠀⢸⠇⢻⣿⠋⢀⣀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠉⡭⣹⠁⣸⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⢹⡇⠀⠀⢻⠀⠸⠀⢸⢿⠀⢸⣿⠀⢠⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣧⡀⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⣧⠀⠀⢸⠀⠀⠀⠠⡄⠀⢸⣿⡇⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣷⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡧⣤⣿⣷⣞⣿⣿⣾⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⣀⠀⢨⣍⡁⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠡⢏⠉⠉⠉⠉⠉⠉⠛⢿⣯⠟⢻⣩⣍⢩⣯⢿⣿⣿
⠀⠀⠀⠁⠀⠐⠀⠠⠤⠀⠈⠉⠉⠀⠀⠀⢿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣾⣿⣿⣿⣿⣿⣿⣿⣯⣯⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⠻⠟⠻⠾⠿⠿
⠀⠀⠂⠀⢴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠋⠛⠻⠿⠿⣿⣿⣿⣷⣶⠶⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣷⣷⣤⠜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⣿⢿⠿⠛⠛⠻⠋⢤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⠟⠉⠄⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣷⠄⠀⠀⣀⡀⠀⠀⠀⣠⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠋⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡏⠀⠀⠂⠀⢀⣈⣼⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠐⠆⠀⠀⠀⠀⠀⠀⠈⠀⠩⡭⢉⣁⣀⡀⡀⠀
⡾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠃⠸⠿⠷⠉⣿⣉⣭⣶⣶⣶⣶⠀⣤⣄⣀⢀⣀⣀⣠⠀⠀⠀⠀⠀⠀⠐⠒⠤⠤⠤⣤⣤⣭⠀⠀⠀⠀⠉⠀⠡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣠⣾⣿⣿⣿⣿⣿⣿⠁⠀⠈⠙⢿⣿⠟⣿⣿⣿⣾⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠀⠀⣀⣀⣴⣾⣷⣾⣥⣶⣾⣶⣶⠾⠛⠻⠻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠛⢿⣿⣿⣼⡿⠮⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠄⠀⠋⠀⠀⠀⠛⣿⣾⣿⣿⣿⣿⣿⣿⡿⣿⢃⣀⡀⣀⣈⣛⣿⢟⣋⢤⣀⡀⣀⣀⣀⣀⢈⡹⣧⢀⡀⢀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡀⠚⠀⠀⠀⠀⠀⢀⠄⣲⣿⣯⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡇⣷⣹⣿⡇⡿⣹⣿⣿⢟⢾⢺⣿⡇⣷⣁⣿⣿⣿⢧⡟⣾⣷⢸⢼⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠀⠀⢀⣀⣀⢀⣀⣴⣾⣿⣿⣿⣿⣾⣧⢀⣀⣀⢀⡤⣠⣴⣖⣻⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣯⣧⣿⣿⣿⣿⣿⣾⣮⣿⣿⣧⣿⣿⣯⣿⣾⡇⢯⠝⠘⠘⠈⠛⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠆⠀⠀⠄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠟⠹⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠇⠀⠀⠀⠘⠛⠈⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠟⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠿⠱⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣗⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣿⡇⠀⠀⠀⢂⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⢹⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣠⣴⣿⣿⣿⣿⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢳⠸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠋⢿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠿⢿⣿⡇⣸⣿⠏⠘⣿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⢰⡇⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠟⠁⠉⠉⠛⠋⠁⠀⠀⠈⣿⣿⠏⠀⠀⠀⠛⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⢭⡁⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣻⣿⡿⣿⣇⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢀⣴⣿⣷⣾⣿⣿⣋⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠶⣿⠇⢿⡧⢰⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠋⠀⣿⠀⣼⠇⢿⣿⠛⢀⣀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠩⣭⣽⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠈⢹⡇⠀⠀⢻⠀⠸⠀⢸⣿⠀⢸⣿⠀⢰⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣧⣀⢹⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⣧⠀⠀⢸⠀⠀⠀⢨⡔⠀⢸⣿⡇⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣷⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣽⣼⣿⣿⣜⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡏⠀⠀⠀⠀⠀⠄⢀⣄⠀⢨⣍⡁⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠨⠯⠉⠉⠉⠉⠉⠉⠛⢿⣯⠏⣻⣫⣍⣩⣯⢿⣿⣿
⠀⠀⠀⠁⠀⠐⠀⠠⠤⠀⠈⠉⠉⠀⠀⠀⢿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣯⣯⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⠻⠟⠻⠾⠿⠿
⠀⠀⠂⠀⢴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠛⠛⠻⠿⠿⣿⣿⣿⣷⣶⠶⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣷⣤⠜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⣿⢿⠿⠛⠛⠻⠋⢤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⠟⠉⠄⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣷⠄⠀⠀⣀⡀⠀⠀⠀⣸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢋⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡏⠀⠐⠆⠀⢀⣈⣴⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠐⠆⠀⠈⠀⠀⠀⠀⠈⡀⡩⣭⣉⣡⣂⡀⡀⠀
⡾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠑⠘⢿⠿⠉⣿⣉⣭⣶⣶⣶⣶⠀⣤⣄⣀⢀⣀⣀⣠⠀⠀⠀⠀⠀⠀⠐⠒⠤⠤⠤⣤⣤⣭⠀⠀⠀⠀⠉⠀⠡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣠⣾⣿⣿⣿⣿⣿⣿⠁⠀⠈⠙⢿⣿⠟⣿⣿⣿⣾⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠀⠀⣀⣀⣴⣶⣷⣾⣧⣷⣾⣶⣶⠾⠛⠻⠻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠛⢿⣿⣿⣼⡿⠮⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠄⠀⠋⠀⠀⠀⠛⣿⣾⣿⣿⣿⣿⣿⣿⡿⣿⢃⣀⡀⣀⣈⣛⣻⣟⣋⢤⣀⡀⣀⣀⣀⣀⢉⣹⣧⢀⡀⢀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡀⠚⠀⠀⠀⠀⠀⢀⠄⣲⣿⣯⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣹⣿⡇⡿⣹⣿⣿⢟⢾⢺⣿⡇⣷⣁⣿⣿⣿⢧⡟⣾⣷⢸⢼⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀
⠀⢀⠀⠉⠀⠀⢀⣀⣀⣀⣀⣵⣾⣿⣿⣿⣿⣾⣧⣀⣀⣀⢄⡤⣠⣴⣖⣻⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣯⣧⣿⣿⣿⣿⣿⣾⣮⣿⣿⣧⣿⣿⣯⣿⣾⡧⢯⠝⠘⠘⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠹⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠇⠀⠀⠀⠘⠛⠀⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⠟⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠿⠱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢱⡿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣗⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣿⡇⠀⠀⠀⠂⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⣹⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣠⣾⣿⣿⣿⣿⡀⢸⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢱⠸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⢿⣿⣿⣿⣟⣿⣿⣿⣿⡿⠿⢿⣿⡇⣸⣿⠏⠘⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⢰⡇⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠟⠟⠁⠉⠉⠛⠋⠁⠀⠀⠈⣿⣿⠏⠀⠀⠀⠛⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠟⠉⠭⠁⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣻⣿⡿⣿⣗⠀⢸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢠⣤⣿⣴⣾⣿⣿⣋⡛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠷⣿⠅⢿⡧⢰⣾⣷⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠋⠀⣿⠀⣸⠇⢿⣿⠋⢀⣀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠉⣭⣹⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠉⢹⡇⠀⠀⢻⠀⠸⠀⢸⣿⠀⢸⣿⠀⢠⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣧⣀⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣧⠀⠀⢸⠀⠀⠀⢠⡌⠀⢸⣿⡇⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣷⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⣵⣼⣿⣷⣜⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⢀⣄⠀⢨⣉⡁⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠨⢯⠉⠉⠉⠉⠉⠉⠛⢿⣿⠟⢻⣫⣍⣩⣯⢿⣿⣿
⠀⠀⠀⠁⠀⠐⠀⠠⠤⠀⠈⠉⠉⠀⠀⠀⢿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣯⣭⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⠻⠟⠻⠾⠿⠿
⠀⠀⠆⠀⢴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠛⠛⠻⠿⠿⣿⣿⣿⣷⣶⠶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣷⣷⣤⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⡿⢿⠟⠛⠛⠿⠋⢤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⡟⠍⠅⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣷⠄⠀⠀⢀⡀⠀⠀⠀⣸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢋⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡏⠀⠐⠆⠀⢀⣈⣴⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠐⠆⠀⠈⠀⠀⠀⠄⠈⠀⡩⣭⣉⣁⣂⡀⡀⠀
⡾⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠓⠸⢿⠷⠉⣿⣉⣭⣶⣶⣶⣶⠀⣤⣄⣀⣀⣀⣀⣠⠀⠀⠀⠀⠀⠀⠐⠒⠴⠤⠤⣤⣤⣭⠀⠀⠀⠀⠙⠀⠡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣠⣾⣿⣿⣿⣿⣿⣿⠁⠀⠈⠙⢿⣿⠟⣿⣿⣿⣾⣃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠀⠀⣀⣀⣴⣶⣷⣾⣧⣷⣾⣶⣶⠾⠛⠻⠻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠛⢿⣿⣿⣼⡿⠮⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠄⠀⠋⠀⠀⠀⠛⣿⣾⣿⣿⣿⣿⣿⣿⡿⣿⢃⣀⡀⣀⣈⣛⣿⣟⣋⢤⣀⡀⣀⣀⣀⣀⢉⡹⣧⢀⡀⢀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡀⠚⠀⠀⠀⠀⠀⢀⠄⣲⣿⣯⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣹⣿⡇⡿⣹⣿⣿⢝⢾⢺⣿⡇⣷⣁⣿⣿⣿⢧⡟⣾⣷⢸⢼⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀
⠀⢀⠀⠉⠀⠀⢀⣀⣀⣀⣀⣴⣾⣿⣿⣿⣿⣾⣧⣀⣀⣀⣄⡤⢠⣴⣖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣯⣧⣿⣿⣿⣿⣿⣾⣮⣿⣿⣧⣿⣿⣯⣿⣾⡧⢯⠝⠘⠘⠈⠛⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠦⠀⠀⠄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⠟⠋⠹⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠇⠀⠀⠀⠘⠋⠀⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⠟⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣗⠿⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢰⡯⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣗⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣇⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⣹⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣠⣶⣿⣿⣿⣿⠀⢹⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢲⠸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⣿⣿⣿⣿⣟⣿⣿⣿⣿⡿⠿⣿⣿⡇⣸⣿⠏⠘⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⢠⡏⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠏⠉⠉⠉⠛⠉⠁⠀⠀⠉⣿⣿⠏⠀⠀⠀⠘⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠭⡁⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣻⣿⡿⣿⣇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣠⣤⣿⣴⣼⣿⣿⣋⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠴⣿⠅⢿⡧⢰⣴⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠋⠀⣿⠀⢸⠇⢻⣿⠋⢀⣀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠉⡭⣹⠁⣸⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠈⢹⡇⠀⠀⢻⠀⠸⠀⢸⢿⠀⢸⣿⠀⢠⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣁⣀⢘⢿⣿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⡧⠀⠀⠸⠀⠀⠀⢠⡄⠀⢸⣿⡇⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣷⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⣳⡼⣽⣧⣔⣿⣿⣶⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⣀⠀⢨⣍⡁⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠠⠏⠉⠈⠉⠉⠉⠉⠛⢿⣯⠍⢛⣩⣍⣩⣯⢿⣿⣿
⠀⠀⠀⠁⠀⠐⠀⠠⠤⠀⠈⠉⠉⠀⠀⠀⢿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣯⣭⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⠻⠟⠻⠾⠿⠿
⠀⠀⡂⠀⢴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠛⠛⠻⠿⢿⣿⣿⣿⣷⣶⠶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣷⣷⣤⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⣿⢿⠟⠛⠙⠻⠋⢤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⠟⠉⠅⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣾⣷⠄⠀⠀⢀⡀⠀⠀⠀⣨⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡏⠀⠐⠆⠀⢀⣈⣤⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠐⠆⠀⠈⠀⠀⠀⠄⠈⡀⠩⡭⣉⣡⣂⡀⡀⠀
⡾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠁⠰⢿⠷⠉⣿⣉⣩⣶⣶⣶⣶⠀⣤⣄⣀⢀⣀⣀⣠⠀⠀⠀⠀⠀⠀⠐⠒⠤⠤⠤⣤⣤⣭⠀⠀⠀⠀⠉⠀⠡⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣠⣾⣿⣿⣿⣿⣿⣿⠁⠀⠈⠙⢿⣿⠟⣿⣿⣿⣾⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠀⠀⣀⣀⣤⣶⣷⣾⣧⣷⣾⣶⣶⠾⠛⠻⠻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠛⢿⣿⣿⣼⡿⠮⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠄⠀⠋⠀⠀⠀⠛⣿⣾⣿⣿⣿⣿⣿⣿⡿⣿⢃⣀⡀⣀⣈⣛⣻⢛⣋⢄⣀⡀⣀⣀⣀⣀⢉⡹⣧⢀⡀⢀⣁⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡀⠚⠀⠀⠀⠀⠀⢀⠀⣲⣿⣯⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡇⣷⣹⣿⡇⡿⣹⣿⣿⢝⢾⢺⣿⡇⣷⣁⣿⣿⣿⢧⡟⣾⣷⢸⢼⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠀⠀⢀⣀⣀⣀⣀⣴⣾⣿⣿⣿⣿⣶⣦⣀⣀⣀⣄⣤⢀⣠⣖⣻⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣯⣧⣿⣿⣿⣿⣿⣾⣮⣿⣿⣧⣿⣿⣯⣿⣾⡇⢯⠙⠘⠘⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⡇⠀⠀⠀⠈⠋⠈⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠟⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢰⣟⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣇⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣇⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣹⣿⡇⠀⠀⠀⠂⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⣻⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢸⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣠⣴⣿⣿⣿⣿⠀⢹⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢱⠸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⣿⣿⣿⣿⣟⣿⣾⣿⣿⣿⣿⣿⣿⠀⣸⣿⠏⠘⣯⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⢠⡏⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⠏⠉⠉⠙⠛⠉⠁⠀⠀⠉⣷⣿⠏⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⢸⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⣟⡁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢻⣿⡿⣿⣇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣠⣿⣴⣾⣿⣯⣉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠶⣿⠥⢿⡧⢰⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠋⠀⣿⠁⢸⠇⢿⣿⠏⢀⣀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡭⡽⠋⣼⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠈⢹⡇⠀⠀⢻⠀⠸⠀⢸⣿⠀⢸⣿⠀⢠⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⣀⣀⢸⢿⡿⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⡧⠀⠀⢸⠀⠀⠀⢠⡄⠀⢸⣿⡇⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣷⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣽⡾⣿⣿⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⢈⣉⠁⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠱⠯⠁⠉⠉⠙⠉⠉⠓⢿⣿⡿⢻⣯⡍⣉⣻⣿⣿⣿
⠀⠀⠀⠁⠀⠰⠀⠀⠄⠀⠈⠉⠁⠀⠀⠀⢿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣯⣭⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⠻⠗⠻⠶⠿⠿
⠀⠠⠀⠀⢤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣷⣧⡤⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⣿⠿⠿⠟⠛⠛⠋⢤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⡟⠉⠁⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣷⠄⠀⠀⢀⡀⠀⠀⠀⢨⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡏⠀⠀⠆⠀⢀⣈⣠⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠐⠆⠀⠀⠀⠀⠀⠀⠉⡀⡹⣭⣍⣡⢂⠀⠀⠀
⡾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠐⠸⣿⠷⠉⣾⣙⣽⣶⣶⣶⣶⠀⣤⣄⣀⢀⣀⣀⣠⠀⠀⠀⠀⠀⠀⠐⠒⠦⠤⢤⣤⣤⣏⠀⠀⠀⠀⠉⠀⠡⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⣾⣿⣿⣿⣿⣿⣿⠃⠀⠈⠙⢿⣿⠟⣿⣿⣿⣾⣂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠀⠀⢀⣀⣤⣶⣷⣾⣧⣴⣾⣶⣶⠾⠟⠻⠻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠛⢻⣿⣿⣼⡿⠮⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠄⠐⠋⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢃⣀⡀⣀⣈⣛⣻⢛⣋⢄⣀⡀⣀⣀⣀⣀⢉⡹⣧⢀⡀⢀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡀⠚⠀⠀⠀⠀⠀⢀⠠⣶⣿⣯⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣹⣿⡇⡿⣹⣿⣿⢝⢾⢺⣿⡇⣷⣁⣿⣿⣿⢧⡟⣾⣷⢸⢼⢸⡧⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀
⠀⢀⠀⠉⠀⠀⠀⢀⣀⣀⣀⣭⣾⣿⣿⣿⣿⣶⣧⣀⣀⣀⣄⣠⢠⣤⣖⣻⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣯⣧⣿⣿⣿⣿⣿⣾⣮⣿⣿⣧⣿⣿⣯⣿⡾⡧⢯⠙⠘⠘⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠦⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⢹⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⡇⠀⠀⠀⠘⠏⠀⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠟⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠟⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣇⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣹⣿⡇⠀⠀⠀⠢⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⣻⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢹⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣠⣴⣿⣿⣿⣿⠀⢹⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⠸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⣿⣿⣿⣿⣟⣿⣾⣿⣿⣿⣿⣿⣿⠂⣸⣿⠏⠸⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⢰⡏⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠏⠉⠉⠙⠛⠉⠁⠀⠀⠙⣷⣿⠏⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⡟⡉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡻⣿⡿⣿⣇⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣠⣷⣴⣾⣿⣯⣋⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠾⣿⡥⢿⣧⢰⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠋⠀⣿⠁⢸⠇⢿⣿⠋⢀⣀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⣭⣽⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠉⢻⡇⠀⠀⢻⠀⠸⠀⢹⣿⠀⢼⣿⠀⢠⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣁⣄⢸⣿⣿⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣧⠀⠀⢸⠀⠀⠀⢠⡌⠀⢸⣿⡇⣾⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣷⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣾⡾⣿⣿⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⢈⣉⡁⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠹⠯⠁⠉⠉⠙⠉⠉⠓⢿⣿⡿⢹⣯⡍⣩⣻⣿⣿⣿
⠀⠀⠀⠁⠀⠰⠀⠀⠄⠀⠈⠉⠁⠀⠀⠀⢿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣯⣭⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⠿⠟⠻⠶⠿⠿
⠀⠠⠂⠀⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣷⣧⡤⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⣿⡿⠿⠟⠛⠛⠋⢤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⡟⠉⠅⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣷⠄⠀⠀⢀⡀⠀⠀⠀⣸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡟⠀⠀⠖⠀⢀⣈⣠⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠐⠆⠀⠀⠀⠀⠀⠀⠉⡀⣹⣭⣍⣡⢂⠀⠀⠀
⡾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠐⠸⣿⢿⠋⣿⣙⣽⣶⣶⣶⣶⠀⣤⣄⣀⣀⣀⣀⣠⠀⠀⠀⠀⠀⠀⠐⠒⠶⠤⢤⣤⣤⣏⠀⠀⠀⠀⠉⠀⢡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⣾⣿⣿⣿⣿⣿⣿⠃⠀⠈⠙⢿⣿⠛⣿⣿⣿⣾⣂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠀⠀⢀⣀⣤⣶⣷⣾⣧⣴⣾⣶⣶⡾⠟⠻⠻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠛⢻⣿⣿⣼⡿⠮⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠄⠀⠋⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢃⣀⡀⣀⣈⣛⣻⢛⣋⢤⣀⡀⣀⣀⣀⣀⢉⡹⣧⢀⡀⢀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡀⠚⠀⠀⠀⠀⠀⢀⠠⣶⣿⣯⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣹⣿⡇⡿⣹⣿⣿⢝⢾⢺⣿⡇⣷⣁⣿⣿⣿⢧⡟⣾⣷⢸⢼⢸⡧⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀
⠀⢀⠀⠉⠀⠀⠀⣀⣀⣀⣀⣭⣾⣿⣿⣿⣿⣶⣧⣀⣀⣀⣄⣤⢀⣤⣖⣻⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣯⣧⣿⣿⣿⣿⣿⣾⣮⣿⣿⣧⣿⣿⣯⣿⡾⡧⢯⠙⠘⠘⠈⠛⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠦⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⡇⠀⠀⠀⠘⠋⠀⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠟⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠿⠘⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣇⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⣿⡇⠀⠀⠀⠂⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⣻⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠟⢸⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣠⣴⣿⣿⣿⣿⠀⢹⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢰⠸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⠀⣸⣿⠇⠘⣷⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⢠⡇⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠏⠉⠉⠙⠛⠉⠁⠀⠀⠙⣷⣿⠏⠀⠀⠀⠚⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⡟⡁⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣻⣿⡿⣿⣇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣠⣷⣴⣾⣿⣿⣉⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠾⣿⠅⢿⡧⢰⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠃⠀⣿⠁⢸⠇⢻⣿⠋⢀⣀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣭⢽⠉⣨⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠈⢹⡇⠀⠀⢻⠀⠸⠀⢸⣿⠀⢼⣿⠀⢠⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⣀⣄⣼⢿⣿⢿⣟⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⡧⠀⠀⢸⠀⠀⠀⢠⡄⠀⢸⣿⡇⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣷⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣼⡿⣿⢿⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⢈⣉⡁⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠹⠯⠁⠉⠉⠙⠉⠉⠒⢿⣯⠿⢻⣯⡍⣉⣻⣿⣿⣿
⠀⠀⠀⠁⠀⠰⠀⠀⠄⠀⠈⠉⠁⠀⠀⠀⢿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣯⣭⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⠻⠗⠻⠶⠿⠿
⠀⠠⠀⠀⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠛⠛⠻⠿⢿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣷⣧⡤⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⣿⠿⠿⠟⠛⠛⠋⢤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⡟⠉⠁⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣷⠄⠀⠀⢀⡀⠀⠀⠀⣸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡟⠀⠀⠆⠀⢀⣈⣠⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠐⠆⠀⠀⠀⠀⠀⠀⠉⡀⣽⣭⣉⣡⢂⠀⠀⠀
⠶⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠸⣿⢿⠉⣿⣙⣽⣶⣶⣶⣶⠀⣤⣄⣀⢀⣀⣀⣠⠀⠀⠀⠀⠀⠀⠐⠒⠶⠤⢤⣤⣤⣏⠀⠀⠀⠀⠉⠀⠡⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⣾⣿⣿⣿⣿⣿⣿⠃⠀⠈⠙⢿⣿⠛⣿⣿⣾⣾⣃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠀⠀⢀⣀⣤⣶⣷⣾⣧⣴⣾⣶⣶⡾⠟⠻⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠛⢻⣿⣯⣼⡿⠮⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠄⠀⠋⠀⠀⠀⠛⣿⣾⣿⣿⣿⣿⣿⣿⡿⣿⢃⣀⡀⣀⣈⣛⣻⢛⣋⣄⣀⡀⣀⣀⣀⣀⢉⡹⣧⢀⡀⢀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡀⠒⠀⠀⠀⠀⠀⢀⠠⣶⣿⣯⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣹⣿⡇⡿⣹⣿⣿⢝⢾⢺⣿⡇⣷⣁⣿⣿⣿⢧⡟⣾⣷⢸⢼⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠉⠀⠀⠀⢀⣀⣀⣀⣭⣾⣿⣿⣿⣿⣶⣧⣀⣀⣀⣀⣠⢀⣤⣖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣯⣧⣿⣿⣿⣿⣿⣾⣮⣿⣷⣧⣿⣿⣯⣿⡾⡧⢯⠙⠘⠘⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠹⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⡇⠀⠀⠀⠈⠋⠈⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠟⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠿⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢰⡟⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣇⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢹⣿⡇⠀⠀⠀⠢⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⠈⣻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠟⢸⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣠⣶⣿⣿⣿⣿⠀⢹⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⠸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⠀⣼⣿⠇⠸⣿⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠌⢠⡏⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠏⠉⠉⠙⠛⠉⠁⠀⠀⠙⣿⣿⠏⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⡟⡉⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣻⣿⡿⣿⣇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣠⣷⣴⣾⣿⣿⣋⣛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠾⣿⠥⢿⡧⣰⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠋⠀⣿⠁⢸⠇⢻⣿⠋⢀⣀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⣭⢽⠁⣨⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠈⢻⡇⠀⠀⢻⠀⠸⠀⢸⣿⠀⢼⣿⠀⢠⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢽⣀⣄⣼⣿⣿⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⡧⠀⠀⠸⠀⠀⠀⢠⡄⠀⢸⣿⡇⣾⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣷⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣽⣾⣿⣿⣼⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⢈⣉⡁⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠠⠯⠁⠉⠉⠙⠉⠙⠓⢿⣿⠿⢻⣯⡍⣩⣻⢿⣿⣿
⠀⠀⠀⠁⠀⠰⠀⠀⠄⠀⠈⠉⠁⠀⠀⠀⢿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣯⣭⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⠻⠗⠻⠶⠿⠿
⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠛⠛⠻⠿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣷⣧⡤⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢿⣿⣿⠿⠟⠛⠛⠋⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⡟⠉⠁⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣷⠄⠀⠀⢀⡀⠀⠀⠀⣸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢃⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡏⠀⠀⠖⠀⢀⣈⣠⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠐⠆⠀⠀⠀⠀⠀⠀⠉⡀⣹⣭⣍⣁⣃⠀⠀⠀
⡾⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠑⠸⣿⠿⠋⣿⣙⣵⣶⣶⣶⣶⠀⣤⣄⣀⢀⣀⣀⣠⠀⠀⠀⠀⠀⠀⠐⠒⠤⠤⢤⣤⣤⣏⠀⠀⠀⠀⠁⠀⠡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⣾⣿⣿⣿⣿⣿⣿⠃⠀⠈⠙⢿⣿⠛⣿⣿⣾⣾⣁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠀⠀⢀⣀⣤⣶⣷⣾⣧⣴⣾⣶⣶⡾⠛⠻⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠛⢿⣿⣯⣼⡿⠮⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠄⠐⠋⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢃⣀⡀⣀⣈⣛⣻⢛⣋⢄⣀⡀⣀⣀⣀⣀⢉⡹⣧⢀⡀⢀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡀⠚⠀⠀⠀⠀⠀⢀⠠⣶⣿⣯⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣹⣿⡇⡿⣹⣿⣿⢟⢾⢺⣿⡇⣷⣁⣿⣿⣿⢧⡟⣾⣷⢸⢼⢸⡧⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠉⠀⠀⠀⢀⣀⣀⣀⣭⣾⣿⣿⣿⣿⣾⣧⠀⡀⢀⣀⣤⢀⣤⣖⣻⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣯⣧⣿⣿⣿⣿⣿⣾⣮⣿⣷⣧⣿⣿⣯⣿⡾⡧⢯⠙⠘⠘⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠙⢿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⡇⠀⠀⠀⠈⠋⠈⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡿⠏⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣧⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⡇⠀⠀⠀⠢⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡏⠋⠀⠀⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠟⢸⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⣠⣾⣿⣿⣿⣯⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⠸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠀⣼⣿⠁⠸⢿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⢠⡏⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠋⠉⠉⠙⠛⠈⠁⠀⠀⢙⣿⣿⠋⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⡍⡉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣻⣿⡿⣿⣇⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣠⣷⣴⣾⣿⣿⣉⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠾⣿⠥⢿⡧⢰⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠃⠀⣿⠁⢸⠇⢺⣿⠋⢀⣀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣭⢽⠁⣨⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠈⢻⡇⠀⠀⢻⠀⠸⠀⢸⣿⠀⢸⣿⠀⢠⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣤⣄⣸⣿⣿⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⡧⠀⠀⠸⠀⠀⠀⢠⡄⠀⢸⣿⡇⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣷⣆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣽⣮⣿⣿⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⢈⣉⠁⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠠⠯⠁⠉⠉⠉⠉⠉⠓⢿⣿⠿⢻⣯⡏⣉⣻⣿⣿⣿
⠀⠀⠀⠁⠀⠰⠀⠀⠄⠀⠈⠉⠁⠀⠀⠀⢿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣯⣭⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠛⠻⠗⠻⠶⠿⠿
⠀⠠⠀⠀⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠛⠛⠻⠿⢿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣷⣧⡤⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⠿⠟⠛⠛⠋⢠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⡟⠉⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣾⣷⠄⠀⠀⢀⡀⠀⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡏⠀⠀⠖⠀⢀⣘⣠⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠐⠆⠀⠀⠀⠀⠀⠀⠈⡀⡹⣭⣉⣁⢂⡀⠀⠀
⡾⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡟⠀⠀⠀⠀⠑⠸⡿⢿⠙⣿⣘⣵⣶⣶⣶⣶⠀⣤⣄⣀⣀⣀⣀⣠⠀⠀⠀⠀⠀⠀⠐⠒⠦⠤⢤⣤⣤⣭⠀⠀⠀⠀⠁⠀⠡⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⣾⣿⣿⣿⣿⣿⣿⠃⠀⠈⠙⢿⣿⠛⣿⣿⣷⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠀⠀⢀⣀⣤⣶⣷⣾⣧⣴⣾⣶⣶⡾⠛⠿⠻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠙⢻⣿⣯⣼⡿⠮⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠄⠀⠋⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⢃⣀⡀⣀⣈⣛⣻⢛⣋⣄⣀⡀⣀⣀⣀⣀⢉⡹⣧⢀⡀⢀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡀⠒⠀⠀⠀⠀⠀⢀⠠⣶⣿⣯⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡇⣷⣹⣿⡇⡿⣹⣿⣿⢟⢾⢺⣿⡇⣷⣁⣿⣿⣿⢧⡟⣾⣷⢸⢼⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⢀⠉⠀⠀⠀⢀⣀⣀⣀⣥⣾⣿⣿⣿⣿⣶⣦⡀⡀⣀⠀⣠⢀⣤⡖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣯⣧⣿⣿⣿⣿⣿⣾⣮⣿⣷⣧⣿⣿⣯⣿⡾⡧⢯⠙⠘⠘⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⡇⠀⠀⠀⠈⠋⠈⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡿⠋⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣇⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣸⣿⡇⠀⠀⠀⠢⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠀⠀⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢹⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⣠⣾⣿⣿⣿⣯⠀⢻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢰⠸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠀⣼⣿⠁⠸⣿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠌⢠⡏⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠋⠉⠉⠛⠳⠈⠁⠀⠀⢙⣿⡿⠃⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⡍⡉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣻⣿⡿⣿⣇⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣠⣷⣴⣾⣿⣿⣉⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠾⣿⠥⢿⡯⢰⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠃⠀⣿⠀⣸⠇⢿⣿⠋⢀⣀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⣭⢽⠉⣨⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠈⢻⡇⠀⠀⢻⠀⠸⠀⢸⣿⠀⢸⣿⠀⢠⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣤⣄⢼⣿⣿⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⡧⠀⠀⢸⠀⠀⠀⢠⡄⠀⢸⣿⡇⣾⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣷⣆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣺⣿⣿⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⢈⣉⡁⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠠⠯⠁⠉⠉⠉⠉⠉⠓⢿⣿⡿⢻⣯⡏⣉⣻⢿⣿⣿
⠀⠀⠀⠁⠀⠰⠀⠠⠄⠀⠈⠉⠁⠀⠀⠀⢿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣯⣭⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⠻⠗⠻⠶⠿⠿
⠀⠠⠀⠀⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠛⠛⠻⠿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣷⣧⡤⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⠿⠟⠛⠛⠋⢠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⡟⠉⠁⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣷⠄⠀⠀⢀⡀⠀⠀⠀⣸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢃⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡟⠀⠀⠖⠀⢀⣘⣠⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠐⠆⠀⠀⠀⠀⠀⠀⠉⡀⡹⣭⣍⣁⢀⡀⠀⠀
⣾⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡟⠀⠀⠀⠀⠐⠸⡿⢿⠙⣿⣈⣭⣶⣶⣷⣶⠀⣤⣄⣀⣀⣀⣀⣠⠀⠀⠀⠀⠀⠀⠐⠒⠦⠤⢤⣤⣤⣍⠀⠀⠀⠀⠁⠀⠡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⣾⣿⣿⣿⣿⣿⣿⠃⠀⠈⠙⢿⣿⠛⣿⣿⣷⣾⣂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠀⠀⣀⣀⣤⣶⣷⣾⣧⣶⣾⣶⣶⡾⠟⠿⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠙⣿⣿⣧⣼⡿⠮⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠄⠐⠋⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢃⣀⡀⣀⣉⣛⣻⢛⣋⣄⣀⡀⣀⣀⣀⣀⢈⡹⣧⢀⡀⢀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡀⠒⠀⠀⠀⠀⠀⢀⠄⣶⣿⣯⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡇⣷⣹⣿⡇⡿⣹⣿⣿⢝⢾⢺⣿⡇⣷⣁⣿⣿⣿⢧⡟⣾⣷⢸⢼⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠀⠀⠀⢀⣀⣀⣀⣭⣾⣿⣿⣿⣿⣶⣦⡀⡀⣀⣄⣠⢠⣤⡖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣯⣧⣿⣿⣿⣿⣿⣾⣮⣿⣷⣧⣿⣿⣯⣿⡾⡧⢯⠙⠘⠘⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⢹⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⡇⠀⠀⠀⠈⠋⠈⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠋⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠿⠘⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣧⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣸⣿⡇⠀⠀⠀⢆⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠀⠀⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠛⢸⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⣠⣾⣿⣿⣿⣯⠀⢻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣱⠸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⠀⣼⣿⠁⠸⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⢠⡏⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠛⠛⠛⠿⠷⠈⠁⠀⠀⢙⣿⡿⠃⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢸⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⡍⡉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣻⣿⡿⣿⣇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣠⣷⣶⣾⣿⣿⣉⡻⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢾⣿⠅⢿⡧⢰⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠃⠀⣿⡁⣸⠇⢿⣿⠏⠀⣀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⣭⣽⠁⣨⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠈⢹⡇⠀⠀⢻⠀⠸⠀⢸⣿⠀⢼⣿⠀⢠⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⣄⣼⣿⣿⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣧⠀⠀⢸⠀⠀⠀⢠⡄⠀⢸⣿⡇⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣷⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⣿⣿⣿⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⢈⣉⡁⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠠⠿⠁⠉⠉⠙⠉⠉⠓⢿⣿⠿⢻⣯⡍⣩⣻⣿⣿⣿
⠀⠀⠀⠁⠀⠐⠀⠀⠄⠀⠈⠉⠁⠀⠀⠀⢿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣯⣭⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⠻⠗⠻⠶⠿⠿
⠀⠠⠂⠀⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠛⠛⠻⠿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣷⣧⡤⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⠿⠟⠛⠛⠋⢤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⡟⠉⠁⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣷⠄⠀⠀⢀⡀⠀⠀⠀⣸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡏⠀⠀⠖⠀⢀⣈⣸⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠐⠆⠀⠀⠀⠀⠀⠀⠉⠀⡹⣭⣍⣡⣂⡀⠀⠀
⡾⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡟⠀⠀⠀⠀⠑⠸⢿⢿⠉⣯⣹⣭⣶⣶⣷⡶⠀⣤⣄⣀⣀⣠⣤⣤⠀⠀⠀⠀⠀⠀⠐⠒⠤⠤⢤⣤⣤⣏⠀⠀⠀⠀⠉⠀⠡⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣠⣾⣿⣿⣿⣿⣿⣿⠃⠀⠀⠉⠻⣿⣩⣿⣿⣿⣾⣃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠀⠀⢀⣀⣤⣶⣷⣮⣧⣶⣾⣶⣶⡾⠛⠿⠻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⢿⣿⣧⣼⡿⠮⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠄⠐⠋⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢃⣀⡀⣀⣉⣛⣛⢛⣉⣄⣀⡀⣀⣀⣀⣀⢀⡩⣄⢀⡀⢀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡀⠒⠀⠀⠀⠀⠀⢀⠀⣶⣿⣯⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣹⣿⡇⡿⣹⣿⣿⢟⢾⢺⣿⡇⣷⣁⣿⣿⣿⢧⡟⣾⣷⢸⢼⢸⡧⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠉⠀⠀⠀⣀⣀⣀⣀⣥⣾⣿⣿⣿⣿⣶⣦⡀⡀⣀⡄⣠⢠⣤⡖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣯⣧⣿⣿⣿⣿⣿⣾⣮⣿⣷⣯⣿⣿⣯⣿⡾⡧⢯⠙⠘⠘⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⠛⠋⠹⢿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⡇⠀⠀⠀⠈⠋⠀⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣷⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠋⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡧⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⡇⠀⠀⠀⠂⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠀⠀⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠛⢸⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣠⣾⣿⣿⣿⣿⠀⢹⣿⣿⣻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⠸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⠀⣾⣿⠁⠸⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⢠⡏⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠛⠛⠻⠿⣯⠉⠁⠀⠀⢉⣿⡿⠃⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⡍⡉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠻⣿⡿⣿⣇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣠⣷⣴⣾⣿⣯⣉⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢶⣿⠅⢿⡧⢰⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠃⠀⣿⠁⣸⠇⢾⣿⠋⠀⣀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣭⢽⠁⣨⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠈⢹⡇⠀⠀⢻⠀⠸⠀⢸⣿⠀⢸⣿⠀⢠⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⡀⢸⣿⣿⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⡧⠀⠀⠸⠀⠀⠀⢠⡄⠀⢸⣿⡇⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⣷⣆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡥⣜⣿⣿⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⢈⣉⡁⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠠⠯⠁⠉⠉⠉⠉⠉⠒⢿⣯⠿⢻⣯⡍⣉⣻⣿⣿⣿
⠀⠀⠀⠁⠀⠐⠀⠀⠄⠀⠈⠉⠁⠀⠀⠀⢿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣯⣭⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠛⠻⠷⠻⠶⠿⠿
⠀⠀⠂⠀⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠛⠛⠻⠿⣿⣿⣿⣶⠶⡶⢤⣴⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣷⣧⡤⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⠿⠟⠛⠛⠋⢤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⡟⠉⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣾⣷⠄⠀⠀⢀⡀⠀⠀⠀⢈⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡏⠀⠀⠖⠀⠀⣈⣠⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠐⠆⠀⠀⠀⠀⠀⠀⠈⡀⡩⣭⣉⣁⢂⡀⠀⠀
⡾⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡟⠀⠀⠀⠀⠐⠸⠿⢿⠙⣯⣹⣭⣶⣶⣶⡶⠀⣤⣤⣀⣀⣤⣤⣤⠀⠀⠀⠀⠀⠀⠐⠒⠴⠤⢤⣤⣤⣍⠀⠀⠀⠀⠉⠀⠡⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⣾⣿⣿⣿⣿⣿⣿⠁⠀⠀⠉⢻⣿⣸⣿⡿⢿⣿⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠀⠀⢀⣀⣤⣶⣷⣾⣧⣶⣾⣶⣶⡾⠛⠻⠻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠻⣿⣧⣾⠿⠨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠄⠀⠋⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢃⣀⡀⣀⣈⣛⣛⢉⣉⢄⣀⡀⣀⣀⣀⣀⢀⡠⣄⢀⡀⢀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡀⠒⠀⠀⠀⠀⠀⢀⠀⣶⣿⣯⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡇⣷⣹⣿⡇⡿⣹⣷⣿⢝⢾⢺⣿⡇⣷⣁⣿⣿⣿⢧⡟⣾⣷⢸⢼⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠀⠀⠀⣀⣀⣀⣀⣥⣶⣿⣿⣿⣿⣶⣦⡀⡀⣀⡄⣠⢠⣤⡖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣯⣧⣿⣿⣿⣿⣿⣾⣮⣿⣷⣧⣿⣿⣯⣿⡾⡧⢯⠙⠘⠘⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣽⡿⠛⠋⠙⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⡇⠀⠀⠀⠈⠋⠀⠋⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣷⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠿⠋⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⠿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⡇⠀⠀⠀⢦⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⣽⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠟⢸⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣴⣿⣿⣿⣿⠀⢹⣿⡿⢿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢰⠸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠙⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡇⣼⣿⠁⠘⣷⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⢰⡏⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠛⠿⠿⣿⣿⣿⠿⠯⠀⠀⠉⣿⡿⠃⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠋⠉⠏⠉⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢻⣿⡿⣿⣇⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣠⣷⣤⣾⣿⣯⣉⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠶⣿⠅⢿⡧⢰⣶⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠃⠀⣿⠀⢸⠇⢻⣿⠋⢀⣀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣭⢹⠁⣨⣯⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠈⢹⡇⠀⠀⢻⠀⠸⠀⢸⢿⠀⣸⣿⠀⢠⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣀⡀⠸⢿⣿⢿⣟⣻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⡧⠀⠀⠸⠀⠀⠀⢠⡄⠀⢸⣿⡇⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡯⡄⣜⣿⣿⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⢈⣉⠁⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠠⡯⠁⠉⠉⠉⠉⠉⠓⢿⣯⠿⢛⣯⡍⣉⣻⢿⣿⣿
⠀⠀⠀⠁⠀⠐⠀⠀⠄⠀⠈⠉⠁⠀⠀⠀⢿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣭⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠛⠻⠗⠻⠶⠿⠿
⠀⠀⠀⠀⢤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠛⠛⠻⠿⣿⣿⣷⣶⠶⠠⠄⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣷⣧⡤⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⠿⠟⠛⠛⠋⢠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⡟⠉⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣾⣷⠄⠀⠀⢀⡀⠀⠀⠀⢘⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡏⠀⠀⠖⠀⢀⣈⣠⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠐⠆⠀⠀⠀⠀⠀⠀⠉⡀⡩⣭⣍⣡⢃⡀⠀⠀
⡶⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡟⠀⠀⠀⠀⠐⠸⡿⢿⠉⣯⣹⣯⣶⣶⣶⡆⠠⣤⣤⣤⡶⣶⣷⣦⠀⠀⠀⠀⠀⠀⠐⠂⠤⠤⢤⣤⣄⣍⠀⠀⠀⠀⠁⠀⠡⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠙⠿⢷⣿⣿⣉⣿⣿⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠀⠀⢀⣀⣤⣶⣷⣮⣧⣴⣾⣶⣶⠿⠙⠛⠻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⠛⠿⠛⣽⠭⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠄⠀⠋⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢂⣀⡀⣀⣉⣛⣛⢉⣉⢄⣀⡀⣀⣀⣀⣀⢀⡀⣄⢀⡀⢀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡀⠒⠀⠀⠀⠀⠀⢀⠀⣶⣿⣯⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡇⣷⣹⣿⡇⡿⣹⣿⣿⢝⢾⢺⣿⡇⣷⣁⣿⣿⣿⢧⡟⣾⣷⢸⢼⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠀⠀⠀⢀⣀⣀⣀⣥⣶⣿⣿⣿⣿⣶⣦⡀⡀⣀⡄⣠⢀⣤⡖⣻⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣯⣧⣿⣿⣿⣿⣿⣾⣮⣿⣷⣧⣿⣿⣯⣿⡾⡧⢯⠙⠘⠘⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⡿⠙⠋⠙⢿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⡇⠀⠀⠀⠈⠋⠀⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠟⠋⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣇⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⢸⣿⡇⠀⠀⠀⠠⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⣹⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠛⢸⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣰⣿⣿⣿⣿⠀⢸⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢰⠸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠙⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣇⣼⣿⠁⠘⣷⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⢠⡏⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠿⠿⣿⣿⣿⣿⠿⠉⠉⠉⣻⡿⠁⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠏⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢹⣿⡿⣿⣇⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣠⣶⣤⣾⣿⣏⣉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠶⣿⠅⢿⡧⢰⣦⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠃⠀⣿⠀⢸⠇⢿⣿⠋⠀⣀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⣭⢹⠁⣨⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠁⠈⢻⡇⠀⠀⢻⠀⠸⠀⢸⢿⠀⢸⣿⠀⢠⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⡀⢸⣿⣿⢿⣟⣻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣧⠀⠀⠸⠀⠀⠀⢠⡄⠀⢸⣿⡇⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⣼⣿⣿⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⢈⣉⠁⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠠⡯⠁⠉⠉⠉⠉⠉⠒⢿⣯⠿⢻⣯⡍⣉⢻⢿⣿⣿
⠀⠀⠀⠁⠀⠐⠀⠀⠄⠀⠈⠉⠁⠀⠀⠀⢿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣩⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⠻⠗⠻⠶⠿⠿
⠀⠀⠀⠀⢤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠛⠛⠻⠿⣿⣿⣷⡶⠀⠀⠀⢤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣷⣧⡤⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⠿⠟⠛⠛⠋⢠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⡟⠉⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣾⣷⠄⠀⠀⢀⡀⠀⠀⠀⠸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡏⠀⠀⠖⠀⠀⣈⣠⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠸⠆⠐⠆⠀⠀⠀⠀⠀⠀⠈⡀⡩⣭⣉⣁⢂⠀⠀⠀
⡶⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡟⠀⠀⠀⠀⠐⠸⡿⢿⠉⣯⣹⣭⣶⣶⣶⠆⠰⣶⣴⣶⢻⣿⣿⣦⡄⠀⠀⠀⠀⠀⠐⠀⠤⠤⢤⣤⣄⣉⠀⠀⠀⠀⠁⠀⠡⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠙⠿⢿⣿⣧⣼⣿⣿⣂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠀⠀⢀⣀⣤⣶⣷⣮⣧⣴⣾⣶⣶⠟⠙⠛⠻⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠉⠻⠏⢰⣦⠨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠄⠀⠋⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⢀⣀⡀⣀⣙⣛⣛⢉⣉⢄⣀⡀⣀⣀⣀⣀⢀⡐⣖⢀⡀⢀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡀⠒⠀⠀⠀⠀⠀⢀⠀⣲⣾⣯⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡇⣷⣹⣿⡇⡿⣹⣿⣿⢝⢾⢺⣿⡇⣷⣁⣿⣿⣿⢧⡟⣾⣷⢸⢼⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠀⠀⠀⠀⣀⣀⣀⣥⣶⣿⣿⣿⣿⣶⣦⡀⢀⣀⡀⡠⢀⣠⡖⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣯⣧⣿⣿⣿⣿⣿⣾⣮⣿⣷⣧⣿⣿⣯⣿⡾⡧⢯⠙⠘⠘⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣹⡿⠙⠋⠙⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡾⡿⣿⡇⠀⠀⠀⠈⠋⠀⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢏⢸⣿⡇⠀⠀⠀⠢⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⣹⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠛⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣠⣿⣿⣿⣿⡀⢸⣿⡿⣿⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢰⠸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠙⢿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣇⣼⣿⠁⠘⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⢠⡏⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⢿⣿⣿⣿⣿⡿⠉⠉⠉⣹⠿⠁⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠋⠉⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠹⣿⡿⣿⣇⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣠⣾⣤⣼⣿⣟⣋⠻⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠾⣿⠅⢿⡇⢰⣦⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠃⠀⣿⠀⢸⠇⢻⣿⠋⠀⣀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡭⢽⠉⣨⣯⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠈⢹⡇⠀⠀⢻⠀⠸⠀⢸⢟⠀⢸⣿⠀⢠⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣀⠀⢸⣽⣿⢿⣟⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⡧⠀⠀⠸⠀⠀⠀⢠⡄⠀⢸⣿⡇⣾⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⡁⣨⣿⣷⣄⣸⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⢈⣉⠁⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⡯⠉⠉⠉⠉⠉⠁⠒⢿⣯⠿⢹⣯⠍⣉⣛⢿⣿⣿
⠀⠀⠀⠁⠀⠐⠀⠀⠄⠀⠈⠉⠁⠀⠀⠀⢿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣯⣩⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠛⠻⠷⠿⠶⠿⠿
⠀⠀⠀⠀⢤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠛⠛⠻⠿⣿⣿⣷⡦⠀⠄⠀⢤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣷⣧⡤⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⡿⠿⠟⠛⠛⠋⢠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⡟⠉⠁⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣾⣷⠄⠀⠀⢀⡀⠀⠀⠀⠸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡏⠀⠀⠖⠀⠀⣘⣠⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⢠⣶⣶⣄⠀⠀⠀⠸⠆⠐⠆⠀⠀⠀⠀⠀⠀⠈⡀⠹⣍⣉⣁⢂⠀⠀⠀
⣾⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡟⠀⠀⠀⠀⠐⠸⠿⠿⠉⣺⣈⣯⣶⣶⡶⠀⠶⢾⣿⣾⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠐⠒⠠⠤⢤⣤⣄⣉⠀⠀⠀⠀⠁⠀⠡⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠉⢻⣿⣿⣿⣻⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠀⠀⢀⣀⣤⣶⣷⣮⣧⣤⣶⣶⡾⠟⠉⠉⠹⣿⣿⣿⣿⣇⠀⠀⠀⠀⠐⠛⠻⣿⣯⣿⣯⠬⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠄⠀⠋⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⢀⣀⡀⣀⣈⣛⣛⢛⣉⢄⣀⡀⣀⣀⣀⣀⢁⡰⣟⢁⡀⢀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡀⠒⠀⠀⠀⠀⠀⢀⠀⣴⣿⣯⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡇⣷⣹⣿⡇⡿⣹⣿⣿⢝⢾⢺⣿⡇⣷⣁⣿⣿⣿⢧⡟⣾⣷⢸⢼⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠀⠀⠀⢀⣀⣀⣀⣥⣶⣿⣿⣿⣿⣶⣦⠀⠀⡀⡀⣠⢀⣠⡖⢻⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣯⣧⣿⣿⣿⣿⣿⣾⣮⣿⣷⣧⣿⣿⣯⣿⡾⡧⢯⠙⠘⠘⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢽⠿⠛⠋⠙⠿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⡿⣿⡇⠀⠀⠀⠈⠋⠀⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠟⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣺⣿⣿⣿⣿⣿⣿⣿⣿⡇⠟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⢹⣿⣿⣿⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠛⢸⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣠⣿⣿⣿⣿⡀⢸⣿⡿⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢰⠸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠉⢿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣇⣼⡿⠁⠘⣷⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠈⢠⡏⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⢹⠟⠁⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠏⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⣍⠉⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠹⣿⡿⣿⣇⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣠⣷⣤⣼⣿⣟⣉⠻⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠶⣿⠅⢻⡧⢰⣶⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠃⠀⣿⠀⢸⠇⢻⣿⠋⠀⣀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⣭⢽⠁⣨⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠁⠈⢹⡇⠀⠀⢻⠀⠸⠀⢸⢟⠀⢸⣿⠀⢠⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⢃⡀⢘⣽⣿⢿⣟⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⡧⠀⠀⠸⠀⠀⠀⢠⡄⠀⢸⣿⡇⣾⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠅⡤⣽⣟⣔⣼⣿⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⢈⣉⠁⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠠⠯⠉⠉⠉⠉⠉⠉⠒⢿⣯⡿⢻⣯⡍⢉⣛⣿⣿⣿
⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⢿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣩⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠛⠻⠷⠷⠶⠿⠿
⠀⠀⠀⠀⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠛⠛⠻⠿⣿⣿⣷⡦⠠⠀⠀⢤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣷⣦⡤⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⡿⠿⠟⠛⠛⠋⢠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⡟⠉⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣷⠄⠀⠀⢀⡀⠀⠀⠀⠸⣿⣿⣿⡄⠀⠀⠀⠀⢠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡏⠀⠀⠆⠀⠀⣘⣀⣿⣿⣿⣿⠋⠀⠀⠀⢀⣀⢸⣿⣿⣿⣿⣆⠀⠀⠸⠆⠐⠆⠀⠀⠀⠀⠀⠀⠈⠀⡸⣭⣉⣁⢀⡀⠀⠀
⣶⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡟⠀⠀⠀⠀⠀⠘⠿⠷⠁⣩⣨⣽⣿⣿⡇⠘⠛⠛⠿⠻⠿⠿⠋⢡⠀⠀⠀⠀⠀⠀⠐⠂⠤⠤⢤⣤⣄⣀⠀⠀⠀⠀⠁⠀⠡⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⣤⣦⣤⣶⣄⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠀⠀⢀⣀⣤⣶⣷⣮⣧⣤⣶⣶⡾⠛⠁⠈⠈⢿⣿⣿⣿⣇⠀⠀⠀⠀⠙⠻⣿⣿⣯⣿⣯⠭⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠄⠀⠋⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⡿⣓⢀⣀⡀⣀⣈⣙⣛⢛⣁⢄⣀⡀⣀⣀⣀⣈⢙⡻⣟⢁⡀⢀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡀⠒⠀⠀⠀⠀⠀⢀⠄⢴⣿⣯⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡇⣷⣹⣿⡇⡷⣹⣿⣿⢝⢾⢺⣿⡇⣷⣁⣿⣿⣿⢧⡟⣾⣷⢸⢼⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠀⠀⠀⢀⣀⣀⣀⣥⣶⣿⣿⣿⣿⣶⣦⠀⢀⣀⣄⣠⢀⣠⡖⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣯⣧⣿⣿⣿⣿⣿⣾⣮⣿⣷⣧⣿⣿⣯⣿⡾⡧⢯⠙⠘⠘⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⡿⠙⠋⠙⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡇⠀⠀⠀⠈⠏⠀⠛⠻⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠟⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⡿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠀⠀⢹⣿⣿⣿⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠛⢹⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣿⣿⣿⣿⡄⢸⣿⡿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢰⠸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠉⢿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣧⣼⡿⠁⠘⣧⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⢠⡏⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⡍⠈⠉⢹⠟⠁⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠋⠉⠍⠁⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢻⣿⡿⣿⣇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣠⣷⣤⣾⣿⣯⣉⡻⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠴⣿⠅⢿⡧⢸⣦⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠃⠀⣿⠀⢸⠇⢻⣿⠋⠀⣀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⣭⢽⠋⣨⣟⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⢹⡇⠀⠀⢻⠀⠸⠀⢸⣿⠀⢸⣿⠀⢠⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⢂⡀⠨⣽⣻⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣧⠀⠀⢸⠀⠀⠀⢠⡤⠀⢸⣿⡇⣾⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⡁⣤⣸⣧⣬⣿⣿⣦⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⢈⣉⠁⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠠⡍⠉⠉⠉⠉⠉⠙⠲⢿⣿⣿⠋⣩⡍⢙⡛⢿⣿⣿
⠀⠀⠀⠁⠀⠰⠀⠠⠀⠀⠈⠉⠁⠀⠀⠀⢿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣟⣭⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠛⠳⠷⠷⠶⠿⠿
⠀⠀⡀⠀⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠛⠛⠻⠿⣿⣿⣷⣦⠠⠀⠀⢤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣷⣧⣄⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⢿⣿⣿⠿⠟⠛⠛⠋⢤⣤⣤⡀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⡿⠉⠁⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣶⣷⠄⠀⠀⢀⠀⠀⠀⠀⠈⣿⣿⣿⡀⠀⠀⠀⠰⣿⣿⡏⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡏⠀⠀⠖⠀⠀⣘⣐⣿⣿⣿⣿⣋⣁⡀⣠⣴⣦⣿⣿⣿⡿⠇⠀⠀⠀⠸⠆⠐⠆⠀⠀⠀⠀⠀⠀⠈⠀⠩⢉⣉⣁⢂⠀⠀⠀
⣾⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡟⠀⠀⠀⠀⠀⠐⠿⠷⠉⣠⣭⣿⣿⣿⠁⠀⠉⠉⠁⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠐⠂⠤⠤⢤⣤⣠⣌⠀⠀⠀⠀⠁⠀⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣰⣶⣦⣴⣶⣄⣾⣂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠀⠀⢀⣀⣤⣶⣷⣾⣧⣴⣶⡶⡿⠟⠉⠀⠀⠘⢿⣿⣿⣷⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⠮⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠄⠀⠋⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡷⣛⢂⣀⡀⣀⣀⣈⣉⢉⣁⢄⣀⡀⣀⣀⣀⣉⢛⡿⣟⢁⡀⢀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡀⠒⠀⠀⠀⠀⠀⢀⠀⢴⣾⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡇⣷⣹⣿⡇⡷⣹⣿⣿⢝⢾⢺⣿⡇⣷⣁⣿⣿⣿⢧⡟⣾⣷⢸⢼⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠀⠀⠀⠀⣀⣀⣀⣥⣶⣿⣿⣿⣿⣶⣦⠀⢀⣀⣄⣠⢀⣤⡔⢻⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣯⣧⣿⣿⣿⣿⣿⣾⣮⣿⣷⣧⣿⣿⣯⣿⡾⡧⢯⠙⠘⠘⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣏⣻⣿⠛⠋⠙⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠿⣿⡇⠀⠀⠀⠈⠃⠀⠋⠻⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠟⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣺⣿⣿⣿⣿⣿⣿⣿⣿⡇⠿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣇⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⢹⣿⣿⣿⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢹⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣾⣿⣿⣿⡄⢸⣿⡿⠻⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢠⠸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠈⢻⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣧⣼⡿⠁⠘⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠈⢠⡏⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⢿⣿⣿⣿⣿⣿⣿⠏⠉⠉⢹⠟⠁⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⠈⠉⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⠉⣅⠁⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠹⣿⡿⣿⣇⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣠⣯⣴⣾⣿⣯⣉⠻⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠶⣿⠥⢿⡧⢰⣦⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠃⠀⣿⠀⢸⠇⢻⣿⠋⠀⣀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⣭⢽⠃⣨⣏⣻⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠉⢻⡇⠀⠀⢻⠀⠸⠀⢸⢿⠀⢸⣿⠀⢠⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣀⡀⠨⣿⣿⢿⡿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣧⠀⠀⢸⠀⠀⠀⢠⡄⠀⢸⣿⡇⣾⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣇⣔⣻⣫⣼⣿⣿⣦⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⢈⣉⠁⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠠⡭⠉⠉⠉⠉⠉⠉⠱⢿⣿⣿⠋⣩⡉⣙⡛⣿⣿⣿
⠀⠀⠀⠁⠀⠰⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⢿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣟⣭⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠛⠿⠷⠷⠶⠿⠿
⠀⠀⠀⠀⢠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠛⠛⠻⠿⣿⣿⣷⣦⠀⠀⠀⢤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣷⣧⡄⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⢿⣿⣿⠿⠟⠛⠛⠋⢤⣤⣤⡀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⡿⠉⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣷⠄⠀⠀⢀⠀⠀⠀⠀⠈⣿⣿⣿⡀⠀⠀⠀⠀⣾⣿⣿⡛⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡏⠀⠀⠖⠀⠀⣘⣀⣿⣿⣿⣿⣏⣁⣀⢠⣴⣾⣦⣽⣿⣿⣿⠁⠀⠀⠸⠆⠐⠆⠀⠀⠀⠀⠀⠀⠈⠀⠭⢉⣉⣀⢂⠀⠀⠀
⣾⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡟⠀⠀⠀⠀⠀⠘⠿⠗⢉⣦⣬⣿⣿⣿⣯⠀⠈⠉⠉⠁⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠐⠂⠤⠤⢤⣤⣤⣈⠀⠀⠀⠀⠁⠀⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠠⣶⣦⣴⣶⣄⣾⣂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠀⠀⠀⣀⣤⣶⣷⣾⣧⣴⣾⣶⣿⡿⠿⠟⠉⠀⠘⣿⣿⣿⡧⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⠮⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠄⠈⠁⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⢲⣂⡀⣀⣀⣀⢈⢉⣉⢄⣀⡀⣀⣀⣀⣙⢛⡿⣟⢁⡀⢀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡀⠒⠀⠀⠀⠀⠀⢀⠀⢴⣾⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡇⣷⣹⣿⡇⡷⣹⣷⣿⢝⢾⢺⣿⡇⣷⣁⣿⣿⣿⢧⡟⣾⣷⢸⢼⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠀⠀⠀⢀⣀⣀⣀⣥⣶⣿⣿⣿⣿⣾⣦⠀⢀⣀⡄⣠⢀⣤⡔⢻⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣯⣧⣿⣿⣿⣿⣿⣾⣮⣿⣷⣧⣿⣿⣯⣿⣾⡧⢯⠙⠘⠘⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣟⢻⠿⠙⠋⠉⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡼⠿⣾⡇⠀⠀⠀⠈⠇⠀⠋⠻⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣺⣿⣿⣿⣿⣿⣿⣿⣿⡇⠟⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡗⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠛⢹⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠈⣿⣿⣿⡇⠙⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢠⠸⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠈⢻⣿⣿⣿⣿⣿⣇⠀⠀⣠⣿⣿⣿⣷⠀⣿⡿⠛⢠⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⢠⡏⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣦⣶⣿⣿⣿⣿⣿⡆⠛⠁⠀⠀⠚⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠏⠿⣿⣿⡟⠛⢿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠛⠈⠁⠁⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠹⣿⡿⣿⣇⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣠⣥⣴⣼⣿⣋⣉⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠤⣿⠁⢻⡧⢰⣦⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠃⠀⣿⠀⢸⠇⢻⣿⠃⠀⣀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢭⢽⠃⣈⣋⣹⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⢙⡇⠀⠀⢻⠀⠸⠀⠸⠙⠀⢸⣿⠀⢠⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢀⡀⠈⢿⣿⢛⡟⠿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⡧⠀⠀⢸⠀⠀⠀⢠⡄⠀⢸⣿⡇⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠁⠤⠘⣇⣬⣽⣿⣦⣹⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⢈⡉⠁⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠠⠍⠉⠉⠉⠉⠉⠉⠰⢾⣯⠝⠉⢉⠉⢉⡛⢿⣿⣿
⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⢿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣟⣭⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠳⠶⠶⠶⠿⠿
⠀⠀⠂⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠙⠛⠻⠿⠟⠀⠀⠀⠀⠀⢤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠰⣷⣦⡀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⡿⠿⠛⠋⠉⠛⠉⢠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⡟⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡷⠀⠀⠀⠠⠀⡀⠀⣤⣼⣿⣿⣷⠀⠀⠀⠀⠀⠀⢀⣴⣶⣄⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠐⠂⠀⠤⡨⠹⢛⠻⢿⠿⠁⣀⣀⡀⢀⣤⣴⣜⢿⣿⣿⢻⡷⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠨⠉⣉⡀⢂⠀⠀⠀
⣶⠞⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡟⠀⠀⠀⠀⠀⠀⠁⠀⢀⣤⣤⣴⣿⣿⣿⡇⠈⠉⠛⠻⠟⠿⠿⠿⠃⠀⠀⠀⠀⠀⠐⠂⠤⠤⢤⣤⣠⣌⠀⠀⠀⠀⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠠⢤⣴⣶⣤⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣀⣤⣶⣷⣾⣧⣤⣾⣿⣿⠛⠛⠻⠋⠀⠀⢻⣿⣿⡷⠀⠀⠀⠀⠀⠀⢹⣍⣽⣧⠬⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡀⠀⠀⢀⣀⣉⣉⣄⡀⠀⡀⠀⢀⣉⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠐⠀⠀⠀⠀⠀⢀⠀⢴⣾⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠍⣿⣿⣿⣿⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠀⠀⠀⢀⣀⣀⣀⣥⣶⣿⣿⣿⣿⣶⣦⣀⣠⣤⣄⣤⢀⣤⡔⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⡷⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡟⢹⠿⠛⠋⠉⠿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠿⣾⠇⠀⠀⠀⠈⠃⠀⠋⠻⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣷⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⡇⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠉⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣦⠀⠀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠛⢸⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢐⠘⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⠟⠛⢻⣿⣿⣿⠻⣿⣿⣦⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠈⢠⡇⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠁⠀⠀⠀⣿⣿⣿⠀⣿⡟⠀⠊⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠃⠀⠀⣀⣾⣿⣿⣿⡆⠈⠀⠀⠀⠀⠀⠈⠀⠋⠀⠁⠁⠩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠹⣿⡿⣿⣇⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣼⣿⣋⣉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠶⣿⠁⢿⡇⢰⣴⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠑⠿⠿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠃⠀⣿⠀⢸⠇⢻⣿⠃⠀⡀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠭⢙⠉⣈⣉⣹⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠈⢛⡇⠀⠀⢻⠀⠨⠀⢸⠿⠀⢸⣿⠀⢰⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠈⢿⣛⢛⡗⠻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣧⠀⠀⠸⠀⠀⠀⢠⠄⠀⢸⣿⡆⣾⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠄⢁⣃⣬⣹⣿⣦⣸⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⢈⡉⠁⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠍⠉⠉⠉⠉⠉⠉⠰⢿⣯⠝⠉⣉⠉⢉⡛⠿⣿⣿
⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢿⣿⣿⠿⢿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠛⠳⠶⠶⠶⠾⠿
⠀⠀⠀⠀⢠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠰⣷⣦⡀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⠉⠉⠁⠀⠀⠀⠀⠀⣰⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⡟⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠠⠀⠈⠀⠘⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠨⢉⣉⠀⠀⠀⠀⠀
⣾⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣶⣾⣿⣿⠀⠘⠻⢿⣿⣽⣿⣿⣻⣷⠀⠀⠀⠀⠐⠀⠤⠤⠤⣠⣠⣌⠀⠀⠀⠀⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢠⢶⣶⣶⣿⣿⡿⠿⢿⣿⣿⣿⠂⠀⠀⠀⠉⠙⢿⣿⣿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣺⣷⣾⣧⣡⣾⣶⡿⠃⠀⠙⠋⠀⠀⠘⣿⣿⡿⠀⠀⠀⠀⠀⠀⠠⠈⢡⣀⠨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣄⠀⠀⠀⣀⣈⣉⣄⣀⠀⠀⠀⠀⢀⣶⣶⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⢀⠀⢰⣾⣿⣭⢰⣤⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⣿⣿⣿⣯⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠀⠀⠀⠀⣀⣀⣀⣥⣶⣿⣿⣿⣿⣿⣿⣿⣾⣷⣖⣶⢀⣰⡞⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⡗⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡿⢹⠻⠉⠉⠉⠿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡜⠷⣾⡇⠀⠀⠀⠈⠃⠀⠛⠻⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣷⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⡇⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⢻⣿⣿⣿⣿⣿⣇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢏⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣦⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠙⢸⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⡿⠿⠛⠿⢿⣿⣧⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢠⠘⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⢠⡇⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⠛⣿⣿⣿⡿⣿⡟⠈⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⠏⠁⠀⠀⢈⣿⣿⠁⠺⠁⠀⠀⠀⠈⠀⠋⠈⠁⠁⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠹⣿⡿⣿⣇⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠟⠀⠀⠀⣰⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣼⣿⣋⣉⠻⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠴⣿⠁⢻⡇⢰⣴⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠑⠿⠿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠁⠀⣿⠀⢸⠇⢻⣏⠃⠀⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠋⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠭⠝⠃⣈⣉⣹⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠈⢙⡇⠀⠀⢻⠀⠸⠀⢸⠛⠀⢸⣿⠀⢠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠈⠿⣻⢻⡟⠻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣧⠀⠀⠸⠀⠀⠀⢠⠄⠀⢸⣿⡇⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⣄⣀⣀⠀⠀⣼⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠁⡄⢈⣃⣌⣻⣿⣦⣸⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⢈⡉⠁⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣶⣿⣿⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠍⠉⠉⠉⠉⠉⠉⠰⢿⣯⡝⠋⢉⠉⢉⡛⢿⣿⣿
⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⠋⠁⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠛⠳⠷⠶⠶⠾⠿
⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⢀⣤⣤⡀⣢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢐⣷⣦⡀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡶⠀⠀⠀⠀⠀⣸⣿⠛⠉⢙⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣸⡟⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠻⠃⠀⠀⠀⠀⡀⠈⠆⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⢉⣉⡁⢀⠀⠀⠀
⣶⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⢀⣴⣶⣶⣶⣿⣿⣿⡗⠀⠻⢷⣶⣶⢿⣿⣷⣄⠀⠀⠀⠀⠐⠂⠤⠤⢄⣄⣠⣈⠀⠀⠀⠀⠁⠀⠠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⣴⢶⣿⠿⢿⣿⡿⠟⠻⣿⣿⣿⡇⠀⠀⠀⠙⠿⣿⣿⣇⣹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢠⣧⣱⣾⣶⡿⠫⠀⠀⠉⠀⠀⠀⢻⣿⣿⠃⠀⠀⠀⠀⠀⠈⠙⠛⠉⠁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣶⣶⣄⠀⠀⠀⠀⣀⣀⣄⣀⠀⡀⠀⠀⠈⣷⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢴⣿⣿⣭⣿⣿⣿⣶⣶⠀⣄⢀⡀⣀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣟⠉⣿⣿⣿⣯⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠀⠀⠀⢀⣀⣀⣀⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣵⢪⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⡷⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣟⢹⠿⠙⠋⠉⠿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⠳⣿⡇⠀⠀⠀⠈⠃⠀⠋⠻⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣷⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⡇⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣽⣿⣿⣿⡿⢇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠉⢸⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠟⠻⢿⣿⣿⡏⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⡀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢠⠘⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⢠⡇⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠀⠋⠈⠀⠁⠩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠻⣿⡟⣿⣇⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡿⠋⠁⠀⠈⣿⣿⠇⡿⠃⠀⠀⠀⠀⠀⣠⣤⣤⣼⣿⣋⣉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠶⣿⠅⢻⡇⢰⣶⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⠆⠀⠀⢠⣾⣿⣿⡀⠀⠀⠀⠀⠀⠁⠿⠿⣿⣿⣿⣿⣟⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠃⠀⣿⠀⢸⠇⢺⣿⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠃⣈⣍⣫⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠈⢙⡇⠀⠀⢻⠀⠨⠀⢸⠻⠀⢈⣿⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⡿⠟⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣛⢛⡗⠻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣧⠀⠀⠸⠀⠀⠀⢠⠄⠀⢸⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⢈⡃⣌⣽⣿⣦⣸⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⢈⡉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⣿⣶⣦⡄⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠍⠉⠉⠉⠉⠉⠉⠰⢿⣯⠝⠉⡩⠉⢉⡛⠿⣿⣿
⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠛⠳⠶⠶⠶⠾⠿
⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢐⣷⣦⡀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡇⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣸⡟⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠨⠉⣉⠀⢀⠀⠀⠀
⣶⠞⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⢀⣴⣶⣶⣶⣿⣿⣿⣟⠀⠙⠿⣿⣿⣹⣿⡿⢿⡯⠴⠂⠀⠐⠀⠠⠤⠄⣠⣠⣄⠀⠀⠀⠀⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⢶⣿⡿⣿⣿⣿⣿⠿⢿⣿⣿⡟⠀⠀⠀⠈⠛⢿⣿⣷⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⣤⣾⣵⡿⠋⠀⠀⠙⠛⠀⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⢀⣠⣀⠀⢀⠀⠀⠈⣳⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠐⠀⠀⠀⠀⠀⢀⠀⢴⣿⣿⣯⣿⣿⣿⣿⣿⢿⣧⢦⡄⣠⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣟⠉⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠀⠀⠀⢀⣀⣀⣀⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣵⢪⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⡗⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡏⢹⠻⠉⠉⠉⠾⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡜⠿⣾⠇⠀⠀⠀⠈⠃⠀⠋⠻⠻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣞⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⡅⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣟⣿⣿⣿⣹⣿⣿⣿⡿⢇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠈⣿⣿⣿⣿⣿⡏⠉⠉⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠙⢸⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢐⠘⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⣿⣿⣿⣷⡄⢀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⢠⡏⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠀⠋⠈⠍⠁⠩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠹⣿⡟⣿⣇⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡿⠛⠀⠘⣿⣿⡟⢹⡇⠀⠀⠀⠀⠀⣠⣤⣤⣼⣿⣋⣉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠠⣿⠁⢻⡇⢰⢤⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣯⠀⠀⠀⣠⣿⣿⠁⠋⠀⠀⠀⠀⠀⠻⠿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣻⣿⡟⠁⠀⣿⠀⢸⠇⢻⣧⠃⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⣠⣤⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠁⣈⣉⣩⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠈⢛⡇⠀⠀⢻⠀⠸⠀⠸⠚⠀⢈⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡻⢻⡗⠻⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣧⠀⠀⠸⠀⠀⠀⢠⠄⠀⢸⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⣈⣽⣿⣦⣸⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⢈⠉⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠘⠾⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠐⢿⣯⠝⠉⠉⠉⢉⠛⠿⣿⣿
⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣾⣶⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠛⠲⠶⠶⠶⠾⠿
⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢐⣷⣦⡀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣸⡟⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣶⣶⣦⣄⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠉⣉⠀⠀⠀⠀⠀
⣶⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣴⣾⣿⣿⡀⠉⠛⠿⣿⣼⣿⣿⣹⣿⡯⠴⠂⠀⠐⠀⠠⠤⠄⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠉⠻⢿⡟⢹⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣾⣷⡿⠩⠉⠛⢿⡿⠋⠈⢻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠉⢉⣀⡀⣀⠀⠀⠈⣿⣶⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢴⣿⣿⣯⣿⣿⣿⣿⣿⢿⣧⢦⡄⣠⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣟⠉⣿⣿⣿⡯⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠀⠀⠀⢀⣀⣀⣀⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣵⢨⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⡷⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣏⢹⠻⠙⠉⠉⠿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⠿⣾⡇⠀⠀⠀⠈⠃⠀⠋⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣗⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⡇⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢏⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠙⣿⣿⣿⣿⣿⡟⠛⠛⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠙⢸⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢐⠘⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣇⠀⠀⢀⣠⣼⣿⣿⣿⣿⣿⣿⣦⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣽⣿⣿⣿⣿⡯⠀⢠⡇⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠀⠛⠉⠉⠁⠽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠹⣿⡟⣿⡇⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡿⠛⠉⢻⣿⣿⡟⢹⡇⠀⠀⠀⠀⠀⣠⣥⣤⣾⣿⣉⣉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠤⣿⠁⢻⡇⢰⣴⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣟⠀⠀⠀⣠⣿⣿⠁⠾⠁⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠁⠀⣿⠀⢸⠇⢻⡯⠂⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠛⠃⣀⣤⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⠉⣈⣉⣩⣿⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠈⢙⡇⠀⠀⢻⠀⠸⠀⠸⠂⠀⠈⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣿⡻⢻⡟⠻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣧⠀⠀⢸⠀⠀⠀⠠⠄⠀⢰⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢈⣹⣿⣦⣸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⢈⠉⠈⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠉⠐⢿⣯⠝⠋⠉⠉⢉⠛⠿⣿⣿
⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣆⣀⣸⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠛⠳⠶⠶⠶⠾⠿
⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢐⣷⣦⡀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣸⡟⠉⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⠾⣿⣷⢦⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢉⣉⠀⠀⠀⠀⠀
⣶⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣴⣾⣿⡆⠈⠛⠻⢿⣶⣿⣿⣦⣿⣿⠯⢴⠂⠀⠐⠀⠤⠤⠄⣀⣠⣄⠀⠀⠀⠀⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠉⣻⣄⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⣭⣾⣿⣿⡿⠿⢿⣿⡿⠋⠙⣿⣿⣿⠄⠀⠀⠀⠀⢀⣠⠈⣹⣦⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣿⣿⣿⣿⣿⣤⣤⣀⠉⠀⠀⠀⠈⠉⢉⣀⡀⣀⠀⠀⠈⣿⣾⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠀⢴⣿⣿⣯⣿⣿⣿⣿⣿⣿⣷⣧⣄⣤⣄⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣟⠏⣿⣿⣿⡯⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠀⠀⠀⢀⣀⣀⣀⣡⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⢮⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⡷⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡏⢹⠻⠙⠉⠉⠾⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡜⠿⣾⠇⠀⠀⠀⠈⠃⠀⠋⠻⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣖⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⡇⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠙⢿⣿⣿⣿⣿⣿⡿⠿⠛⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠙⢸⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢰⠘⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣇⡀⠀⠀⣀⣤⣿⣿⣿⣿⣿⣿⣿⡄⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⢠⡇⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠈⠀⠛⠈⠍⠁⠍⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠹⣿⡟⣿⡇⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⡿⠟⠛⣿⣿⣿⡟⣿⡇⠀⠀⠀⠀⠀⣀⣥⣤⣾⣿⣋⣉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠤⣿⠁⢻⡇⢰⡤⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠏⠀⠀⠀⣸⣿⡟⢀⡿⠁⠀⠀⠀⠀⠀⠙⠟⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠁⠀⣿⠀⢸⠇⢻⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠀⣀⣤⣾⣿⣿⡧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⣈⣉⣩⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠈⢙⡇⠀⠀⢻⠀⠸⠀⠸⠳⠀⢈⣿⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠻⢛⡗⠻⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⡧⠀⠀⠸⠀⠀⠀⢠⠄⠀⢸⣿⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠋⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⣤⣸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⢈⠉⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠐⢾⣯⠝⠉⢉⠉⢉⠛⠿⣿⣿
⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⣾⣷⣀⣘⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠛⠳⠶⠶⠶⠾⠿
⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣷⣦⡀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡟⠛⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣸⡟⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⡟⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡴⣿⣿⡷⣤⣄⣄⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠨⠉⣉⡀⠀⠀⠀⠀
⣶⠞⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⣿⣷⠀⠙⠛⠿⣷⣿⣿⣧⣿⢟⣿⠯⢴⠂⠀⠐⠀⠤⠤⠄⣀⣀⣀⠀⠀⠀⠀⠁⠀⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠉⢙⣧⣼⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣩⣿⣿⣿⡾⢿⣿⣿⡿⠋⠻⣿⣿⣷⠀⠀⠀⠀⠀⣀⣠⣉⣹⣦⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⣿⣿⣯⣀⣀⡈⠉⠀⠀⠀⠈⠉⢁⣀⠀⣀⠀⠀⠈⣿⣾⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⠀⢴⣿⣿⣭⣿⣿⣿⣿⣿⣿⣷⢦⡀⣠⣄⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⣟⠏⣻⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠀⠀⠀⢀⣀⣀⣀⣁⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣾⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⡗⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⡏⢹⡻⠉⠉⠉⠾⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡜⠱⣾⠇⠀⠀⠀⠈⠃⠀⠋⠻⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣖⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⡇⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣽⣿⣿⣿⡿⢇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠙⣿⣿⣿⣿⣿⣿⡟⠛⠉⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠉⢸⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣇⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢐⠘⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣇⡀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⡆⢤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⢠⡇⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠛⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠈⠀⠉⠈⠉⠁⠩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠹⣿⡟⣿⣇⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠿⠋⠙⢿⣿⣿⠏⢻⡇⠀⠀⠀⠀⠀⠀⢠⣤⣤⣼⣿⣉⣉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠰⣿⠁⢻⡇⢰⡤⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠃⠀⠀⢀⣼⣿⡏⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠁⠀⣿⠀⢸⠇⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠀⣀⣴⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢈⣉⣩⣯⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠈⢙⡇⠀⠀⢻⠀⠸⠀⠸⠂⠀⢈⣿⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠓⢻⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⡧⠀⠀⠸⠀⠀⠀⠠⠄⠀⢸⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⠉⢩⣴⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣸⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠉⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠠⠾⣯⠉⠉⢉⠉⢉⠛⠿⣿⣿
⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣤⣤⣿⣿⣿⣶⣿⣾⣿⣿⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠛⠢⠶⠶⠶⠾⠿
⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⣷⣦⡀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⡟⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣦⣤⣤⣤⣤⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠨⢉⣉⠀⢀⠀⠀⠀
⣶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⡆⠘⠛⠿⣿⣤⣿⣿⣹⣿⢿⣿⠯⢴⠂⠀⠐⠀⠀⠤⠄⣀⣠⣀⠀⠀⠀⠀⠁⠀⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠉⠙⠛⠿⣁⣾⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣼⣧⣦⣿⣿⣿⣿⡿⠛⢿⣿⣿⡄⠀⠀⠀⠀⠀⢀⣠⣋⣿⣯⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⣶⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣛⣉⣉⡙⠋⠀⠀⠀⠉⠉⢀⣀⠀⢀⠀⠀⠈⣿⣾⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠀⢴⣿⣿⣭⣿⣿⣿⣿⣿⢹⣤⣄⡀⣀⣀⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⣟⠉⣿⣿⣿⡯⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠀⠀⠀⢀⣀⣀⣀⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⡗⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣏⢹⠿⠉⠋⠉⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡼⠹⣾⠇⠀⠀⠀⠈⠃⠀⠋⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣶⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⡇⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡧⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢏⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⢹⣿⣿⣿⣿⣿⡏⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠛⢸⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡀⠀⢀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢠⠘⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣤⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⡀⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⢠⡏⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠙⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠀⠉⠈⠉⠁⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠹⣿⡟⣿⣇⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⠟⠋⠀⠙⣿⣿⡟⢘⡿⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣼⣿⣋⣉⠻⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠰⣿⠁⢻⡅⢰⣤⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡅⠀⠀⢀⣴⣿⣿⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠁⠀⣿⠀⢸⠇⢻⡇⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⣤⣴⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠹⢿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠈⢹⡇⠀⠀⢻⠀⠨⠀⢸⢓⠀⠨⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣧⠀⠀⠸⠀⠀⠀⢠⠄⠀⢸⣿⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢠⣴⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠰⢿⣯⠟⠋⢉⠉⢉⡛⠿⣿⣿
⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠈⠉⠁⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠛⠳⠶⠶⠶⠾⠿
⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⣷⣦⡀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⡿⠉⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣦⣄⣤⣤⣤⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠨⢉⣉⡀⠀⠀⠀⠀
⣶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⡆⠘⠛⠿⣿⣤⣿⣿⣹⣿⢿⣿⠯⢴⠂⠀⠐⠀⠤⠤⠄⣀⣠⣀⠀⠀⠀⠀⠉⠀⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠉⠙⠛⠿⣁⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣽⣴⣧⣆⣿⣿⣿⣿⡿⠛⢿⣿⣿⡄⠀⠀⠀⠀⠀⣀⣠⣋⣿⣯⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⣶⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣛⣉⣈⡙⠋⠀⠀⠀⠉⠉⢀⣀⠀⣀⠀⠀⠈⣿⣾⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠄⢴⣿⣿⣯⣿⣿⣿⣿⣿⣹⣦⣄⡀⣠⣀⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⣟⠩⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠀⠀⠀⢀⣀⣀⣀⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⡗⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⡇⢻⡻⠙⠉⠉⠿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡞⠿⣾⠇⠀⠀⠀⠈⠃⠀⠋⠻⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣖⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⡇⠟⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠛⢸⣿⡗⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣧⡀⢀⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢠⠘⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣶⣄⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣷⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⢠⡏⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠙⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠃⠀⠁⠁⢩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠹⣿⡟⣿⣇⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠟⠁⠀⠀⢻⣿⡿⠁⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣼⣿⣉⣉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠴⣿⠁⢻⡇⢰⣄⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⣿⠀⠀⢀⣴⣿⣿⣧⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣟⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠁⠀⣿⠀⢸⠇⢻⡇⠋⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠉⠁⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠈⢙⡇⠀⠀⢻⠀⠸⠀⠸⠐⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠿⠿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣧⠀⠀⠸⠀⠀⠀⢠⠄⠀⢰⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⣸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠰⢿⣯⠍⠉⢉⠉⢉⡛⠿⣿⣿
⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠳⠶⠶⠶⠾⠿
⠀⠀⡀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠰⣷⣦⡀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⡿⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⡆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣦⣄⠀⣤⣤⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠨⠉⣉⡁⠀⠀⠀⠀
⡶⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣾⡆⠘⠛⠿⣿⣤⣿⣿⣹⣿⢿⣿⠯⢴⠂⠀⠐⠀⠠⠤⠄⣀⣠⣀⠀⠀⠀⠀⠁⠀⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠉⠙⠛⠿⣁⣼⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣧⣇⣿⣿⣿⣿⡿⠛⢿⣿⣿⡄⠀⠀⠀⠀⠀⣀⣠⣋⣿⣿⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⣶⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⣿⣿⣟⣉⣉⡙⠋⠀⠀⠀⠉⠉⢀⣀⠀⣀⠀⠀⠈⣿⣾⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠀⢴⣿⣿⣽⣿⣿⣿⣿⣿⢭⣶⢦⡀⣠⣄⣤⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⣟⠍⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⠀⠉⠀⠀⠀⢀⣀⣀⣀⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⡗⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣹⡿⠛⠋⠉⠿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡻⡿⣿⡇⠀⠀⠀⠈⠃⠀⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣷⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣺⣿⣿⣿⣿⣿⣿⣿⣿⡇⠟⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣧⣸⣷⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⢻⣿⣿⣿⣿⣿⣿⠿⠿⠋⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣻⣿⡇⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠟⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣄⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢰⠸⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢹⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠈⢠⡏⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⢿⣿⡆⠀⠀⠀⠀⠀⠈⠃⠈⠁⠉⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢙⣿⡿⣿⣇⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡟⠁⠀⠀⢨⣿⣿⠇⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣤⣾⣿⣏⣉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠴⣿⠅⢻⡇⢰⣤⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠇⠀⢀⣴⣿⣿⣿⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠃⠀⣿⠀⢸⠇⢻⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⢹⡇⠀⠀⢻⠀⠘⠀⠸⢓⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣧⠀⠀⠸⠀⠀⠀⢠⡄⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⢙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠲⢿⣯⠟⠉⢩⠉⢉⡛⠿⣿⣿
⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠉⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣄⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠲⠖⠶⠶⠿⠿
⠀⠀⠀⠀⢠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠋⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣷⣦⣀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⠟⠋⠉⠀⠀⠀⢀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⡿⠉⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⠇⠀⠀⠀⠀⠀⠲⠗⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⣀⠀⢀⣤⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣉⡀⠀⠀⠀⠀
⣾⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣶⣾⡆⠘⠛⠿⣿⣴⣿⣿⣹⣿⢿⣿⠯⢴⠂⠀⠐⠀⠤⠤⢤⣠⣠⣄⠀⠀⠀⠀⠉⠀⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠉⠛⠻⠿⣁⡼⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣼⣧⡃⣿⣿⣿⣿⡿⠛⢿⣿⣿⡄⠀⠀⠀⠀⠀⣀⣠⣛⣿⣿⠥⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⣶⣄⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣛⣉⡙⠛⠀⠀⠀⠉⠋⢠⣀⡀⣀⠀⠀⠈⣻⣾⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣯⣿⣿⣿⣿⣿⢭⣤⢦⡀⣠⣄⣤⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣿⣿⣿⣟⠍⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠀⠀⠀⠀⣀⣀⣀⣅⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⡗⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡏⢹⠿⠋⠋⠉⠾⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡸⠿⣿⡇⠀⠀⠀⠀⠃⠀⠛⠻⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣗⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⡇⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣇⣸⣷⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⢿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣽⣿⣿⣿⡿⢃⢻⣿⡇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡄⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠛⢸⣿⡇⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣆⢀⣾⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢰⠸⣿⡗⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣷⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠩⣿⣷⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠈⢠⡏⢁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠈⠲⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⠿⠛⢿⣿⣿⡿⢻⣿⠄⠀⠀⠀⠀⠀⠈⠈⠋⠈⠁⠁⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠹⣿⡿⣿⣇⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡏⠀⠀⠀⢨⣿⣿⠃⢰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣼⣿⣋⣉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠶⣿⠅⢻⡁⢰⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⣿⠇⠀⣀⣴⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⣟⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠃⠀⣿⠀⢸⠇⢺⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠉⠻⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠈⢹⡇⠀⠀⢻⠀⠸⠀⠸⠿⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠋⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠻⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⡧⠀⠀⠸⠀⠀⠀⢠⡄⠀⢰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣷⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠰⢿⣯⠛⠋⢉⠉⢙⡛⠿⣿⣿
⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣄⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠳⠖⠶⠶⠿⠿
⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣷⣦⡀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⡟⠉⠁⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠉⣉⠀⠂⠀⠀⠀
⡶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠐⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣶⣶⡄⠘⠿⢿⣿⣹⣿⣿⢻⣶⣿⣿⠯⢤⠂⠀⠐⠀⠄⠄⢤⣠⣠⣄⠀⠀⠀⠀⠁⠀⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠙⠛⠿⠿⠿⢋⣼⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⣾⣧⡃⣿⣿⣿⣿⡿⠛⢿⣿⣿⡀⠀⠀⠀⠀⠀⢀⣠⣟⣿⣿⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣋⡙⠋⠁⠀⠀⠉⠋⢠⣀⡀⣀⠀⠀⠈⣹⣾⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢴⣿⣿⣽⣿⣿⣿⣿⣿⣩⣤⢄⡀⣠⣄⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⣟⠉⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠀⠀⠀⠀⣀⣀⣀⣅⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⡷⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡶⣿⣿⣿⣿⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⡀⢹⣿⣿⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢻⣿⣿⣦⠀⠈⠃⢸⣿⡏⠀⠀⢀⣤⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⢸⠟⠁⠀⣿⣿⣿⣿⣷⣶⡶⠟⠋⠀⠀⣶⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⢀⠀⢀⣠⣿⣿⣿⠟⠋⠁⠀⠀⠀⣀⣼⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠤⠀⣸⣾⣶⣿⣿⣿⡏⠀⠀⠀⠀⢀⣤⣼⣿⢿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⠿⠿
⠀⠀⠀⠀⠀⣶⣄⣀⣴⣿⣿⣿⡟⢴⣿⡇⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢾⡿⣿⠙⠀⠀
⠀⠀⠀⠀⣸⣿⣿⠿⣿⣿⣿⣿⣿⣶⣿⡇⢠⡞⢉⣉⢿⣿⣿⣿⣻⣿⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣷⣴⣖⠈⣿
⠀⠀⠀⣰⣿⡟⠀⠀⠈⢿⣿⣿⣿⡿⢿⡇⢸⣇⡙⠋⣸⣿⣿⣿⣿⣿⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣻⣿⣷⣏⣰⣿
⠀⠀⢀⣿⣿⣇⠀⠛⢀⣼⣿⣿⣿⣶⣾⡇⢸⣿⣿⣿⣿⣿⣿⣿⡿⡿⠀⠀⠀⠸⢿⣿⣿⡿⠿⢿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣯⡶⠉⢻
⠀⠀⣼⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⢟⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠛⣷⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠉⠉⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⣿⣿⣿⣤⠀⠐
⠀⠀⣿⣿⡿⣋⡉⣉⣉⡛⢻⣿⣿⣶⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠀⠀
⠀⢸⣿⣿⡇⣋⣿⣿⣿⣿⢹⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⠗⠀⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡄⠀⠰
⠀⢸⣿⣿⡇⠿⢿⠿⢿⢿⣸⣿⣿⣿⣿⡇⠸⣿⣿⣩⣛⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠐⢶⣆⠀⠀⠉⠀⠀⢰⣾⣿⣿⣿⣿⡿⠛⠁⢈⣻⣿⠀⠀⠀⣰⣿⣷⡈⣿⣿⣿⡛⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣾⣷
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⣿⣿⣿⣿⠚⣿⡿⠀⠀⠀⠀⠀⠀⠀⢿⡂⠙⡇⠀⠀⠀⠀⠀⠙⠛⢛⡏⢀⡀⠀⠀⠸⣿⣿⡄⣠⣴⣿⣿⣿⣿⣿⣿⡟⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣴⣿⣿⣿⣿⣿⣟⣭⣛⣿⣿⣿⣿⠋⣿⣿⣿⣿⣿⣛⣄⠀⣿⣷⣶⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⠀⠙⠀⠀⠀⠀⢀⡜⠁⣸⡇⠀⠀⠀⢹⣿⣿⡿⠙⣿⣿⣿⣿⣿⡿⢷⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿
⣿⣿⣿⣿⡿⢛⡟⣻⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⢈⣿⠀⠙⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢀⣹⡁⠀⠀⠀⢸⣿⣿⡇⠀⢿⣿⣿⣿⡟⢠⣿⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⡃⠀⣿⣿⣿
⣿⣿⣿⣿⡏⢼⢷⠿⣿⢿⣿⣿⣿⠀⣿⣿⣿⣿⣯⣯⣿⡾⠏⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⠙⠀⢸⣿⣿⠀⠀⠀⠘⣿⣿⣿⡆⠘⣿⣿⡟⢀⣼⡟⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⣿⠃⠀⣿⣿⣿
⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡟⠛⠛⠛⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⣿⣿⡷⠀⠀⠀⢠⣿⣿⣿⣷⠀⢻⣿⢳⣿⣿⣿⠀⠀⣤⠀⠀⣿⣿⣿⣿⣿⣆⠀⠀⢀⣿⣿⣿
⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⡟⠉⠁⠁⠀⠀⠀⠂⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⢸⣿⣿⣿⣿⡀⠀⠀⣸⣿⣿⣿⡇⠀⣿⠀⠀⣿⣿⣿⣿⣿⣿⢠⡤⠾⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣿⣤⣤⣾⣿⣿⣿⠀⣿⣿⡇⢀⠀⠀⠀⠀⡆⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣿⠿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣷⣄⠀⣿⣿⣿⣿⡇⠐⣯⡀⠀⠈⣵⣿⣿⣿⣿⠠⣧⢀⣹⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⠉⠁⢀⠀⠀⠀⠀⠄⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⢀⣀⣀⣸⣿⣿⣿⣿⣿⡿⢰⣿⣿⣿⣿⡇⢸⣿⣧⠀⠀⠑⠂⠈⠉⠀⠀⣅⠈⢻⣿⣿
⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠘⠲⠄⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⢁⣸⣿⣿⣿⣿⠃⢸⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⡭⠀⣸⣿⣿
⢸⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⢳⣿⣿⣿⣿⣿⡟⠀⠀⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣶⣶⣿⣿⣿
⠀⣿⣿⣿⣿⣸⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠈⠂⠀⠀⠀⣿⣿⣿⣿⣿⣿⢫⣿⣿⣿⣿⣿⣿⠁⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⢿⡟⢻⣿⣿
⠀⢹⣿⣿⣿⢘⡋⢻⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣏⣉⠛⠁⠈⣿⣿⣷⣤⡈⠛⠀⣄⠀⠀⠏⠻⠇⠀⠀⠀⠀⠀⠀⢾⡏⣙⣿⣿
⠀⠘⣿⣿⣿⢠⣤⣬⠭⣭⡭⣿⣿⣶⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⢸⣿⣿⣿⡧⠀⠀⢻⣧⣼⣿⣿⣦⡄⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠉⠹⣿
⠀⠀⢹⣿⣿⠘⠁⠀⠀⢾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠺⠿⠀⠀⠀⠀⠀⠸⠿⠛⠉⠁⣄⠀⠘⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢸⢣⡄⠀⢿
⠀⠀⠀⠙⣿⣄⣀⣀⣀⣀⣩⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡴⠾⠀⠀⠀⠀⠀⠀⡄⠀⠀⢰⣿⠀⠀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⣿⣿⣿⣿⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⡀⢹⣿⣿⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢙⣿⣷⣦⠀⠈⠁⢸⣿⡏⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠠⠟⠁⠀⣾⣿⣿⣿⣷⣶⡶⠟⠋⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣟⢀⠀⠀⢠⣿⣿⣿⠟⠉⠁⠀⠀⠀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠄⠀⢸⣶⣶⣿⣿⣿⡏⠀⠀⠀⠀⢀⣤⣼⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢿⣿⣿⣿⠿⠿
⠀⠀⠀⠀⠀⣴⣄⣀⣴⣿⣿⣿⡏⢴⣿⡇⠀⠀⢠⣴⣾⣿⣿⣷⣻⣿⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⣾⡿⣿⢕⠀⠀
⠀⠀⠀⠀⣸⣿⣿⠿⣿⣿⣿⣿⣿⣶⣿⡇⢠⡞⢉⣉⢿⣿⣿⣿⣛⣿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣷⣴⣖⠀⣻
⠀⠀⠀⣰⣿⡟⠀⠀⠈⢿⣿⣿⣟⠿⢻⡇⢸⣇⠙⠋⣸⣿⣿⣿⣿⣿⠀⠀⠘⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣷⡏⣰⣿
⠀⠀⢀⣿⣿⣇⠀⠛⢀⣼⣿⣿⣿⣶⣾⡇⢸⣿⣿⣿⣿⣿⣿⣿⡾⡿⠀⠀⠀⢿⣿⣿⣿⣗⠘⠿⣿⣿⠏⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⣯⡖⠀⠻
⠀⠀⣼⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⢛⣻⡇⢸⣿⣿⣿⣿⣿⣿⣿⠛⣷⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠈⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⣿⣿⣿⣥⠀⠀
⠀⠀⣿⣿⡿⣋⠋⣉⣉⡙⢻⣿⣿⣶⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠠⠄⢹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠈⢉⡛⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀
⠀⢸⣿⣿⡇⡃⣾⣿⣿⣿⢸⣿⣿⢿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇⢸⣿⡟⠀⠀⢀⣀⡙⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⡄⠀⠠
⠀⢸⣿⣿⡇⠿⢿⠿⢿⠿⣸⣿⣿⣿⣿⡇⠸⢻⣿⣉⣛⢻⣿⣟⠁⠀⠀⠀⠀⠀⠀⠐⣶⣆⠀⠀⠉⠀⠀⠰⣾⣿⣿⣿⣿⡿⠟⠃⢘⣿⠇⠀⠀⣾⣿⣿⣈⣿⣿⣿⣿⠟⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣷
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⣿⣿⣿⣿⠘⣻⡿⠀⠀⠀⠀⠀⠀⠀⢿⡂⠙⡇⠀⠀⠀⠀⠀⠙⠛⢙⡍⢀⡃⠀⠀⠸⣿⣷⣤⠀⣿⣿⣿⣿⣿⣿⣿⣟⡁⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣴⣿⣿⣿⣿⣿⣛⣩⣛⣿⣿⣿⣿⠋⣿⣿⣿⣿⣿⣫⣁⠀⣿⣧⣤⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⠀⠙⠀⠀⠀⠀⢀⡜⠁⢰⡇⠀⠀⠀⢹⣿⡿⠀⡿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⡾⠛⣿⣿⣿
⣿⣿⣿⣿⡿⢛⡏⣻⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⠀⣯⠀⠙⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢀⣙⡁⠀⠀⠀⢸⣿⣿⢸⡃⢸⣿⣿⣿⣿⡟⢹⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡃⠀⣿⣿⣿
⣿⣿⣿⣿⡇⢸⠷⠿⠿⢿⣿⣿⣿⠀⣿⣿⣿⣿⣯⣯⣍⡘⠋⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠀⠘⠀⢸⣿⣿⠀⠀⠀⠸⣿⣿⣿⣷⠈⣿⣿⣿⠏⣠⣼⠆⠀⠀⣾⠀⢹⣿⣿⣿⣿⡿⣿⠇⠀⣿⣿⣿
⣿⣿⣿⣿⣏⣽⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡟⠛⠛⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣾⣿⡧⠀⠀⠀⢀⣿⣿⣿⣿⠀⢻⣿⣿⣾⣿⣿⠀⠀⢠⣿⡀⢈⣿⣿⣿⣿⣆⠀⠀⢀⣿⣿⣿
⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⡟⠈⠁⠁⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⡀⠈⠛⢹⣿⣿⣿⣆⠀⣸⠟⠁⢸⣿⣿⣿⣿⣿⠠⡤⠾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣤⣤⣾⣿⣿⣿⠀⣿⣿⡇⠀⡀⠀⠀⠀⠄⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⡿⠿⠁⠀⠀⠀⢸⣿⣿⣿⣿⣧⡀⠀⣾⣿⣿⣿⡿⠀⣦⣾⠀⠈⣵⣿⣿⣿⣿⠠⣧⠀⣹⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡀⠀⣼⣿⣿⣿⣿⣿⡇⢀⣿⣿⣿⣿⡇⢸⣿⣿⡀⠀⠐⠂⠈⠉⠁⠀⣄⠈⢻⣿⣿
⢿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠘⠲⠀⠀⣿⣿⣂⣿⣿⣿⣿⣿⡟⢀⣸⣿⣿⣿⣿⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠍⠀⣸⣿⣿
⢸⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⢛⣰⣿⣿⣿⣿⣿⣿⠀⠀⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣶⣶⣿⣿⣿
⠀⣿⣿⣿⣿⢰⣶⣿⣿⣿⣿⣿⣿⣯⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠉⠂⠀⠀⠈⣿⠿⣿⣿⣿⢻⣼⣿⣿⠛⠛⣿⣿⡇⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⢿⡟⢻⣿⣿
⠀⢹⣿⣿⣿⠈⡋⢻⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⡀⠉⠁⠈⣿⣿⣿⣶⣦⠀⠙⢻⣆⠀⠀⠛⠿⠇⠀⠀⠀⠀⠀⠀⢺⡏⣙⣿⣿
⠀⠘⣿⣿⣿⢠⣤⡬⠭⢭⡭⣿⣿⣆⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆⠀⠹⣿⣯⣿⣿⣿⣦⣤⡽⠆⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢸⣇⠉⠸⣿
⠀⠀⢹⣿⣿⠈⠀⠀⠀⠲⣯⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠺⠿⠀⠀⠀⠀⠀⠸⠟⠋⠻⢍⡆⠀⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢣⡄⠀⢿
⠀⠀⠀⠉⣿⣄⣀⣀⣀⣀⣩⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠾⠀⠀⠀⠀⠀⠀⡀⠀⠀⢻⣷⠀⢐⣿⣿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡲⣿⣿⣿⣿⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⡀⢹⣿⣿⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢹⣿⣷⣦⠀⠈⠃⢸⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⢰⠛⠁⠀⣿⣿⣿⣿⣷⣶⡶⠟⠋⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⢀⠀⠀⢀⣿⣿⣿⠟⠋⠁⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠄⠀⣸⣾⣶⣿⣿⣿⡏⠀⠀⠀⠀⢀⣤⣼⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⠿⠿
⠀⠀⠀⠀⠀⣶⣄⣀⣴⣿⣿⣿⡏⢴⣿⡇⠀⠀⢠⣴⣾⣿⣿⣿⣻⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢛⣿⣿⣿⣿⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣾⡿⣿⢉⠀⠀
⠀⠀⠀⠀⣸⣿⣿⠿⣿⣿⣿⣿⣿⣶⣿⡇⢠⡞⢉⣉⢿⣿⣿⣿⣻⣿⡅⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣷⣴⣖⠀⣿
⠀⠀⠀⣰⣿⡟⠀⠀⠈⢻⣿⣿⣯⠿⢿⡇⢸⣇⠙⠋⣸⣿⣿⣿⣿⣿⠀⠀⢿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣷⡏⣰⣿
⠀⠀⢀⣿⣿⣇⠀⠛⢀⣼⣿⣿⣿⣶⣾⡇⢸⣿⣿⣿⣿⣿⣿⣿⡾⡿⠀⠀⠸⣿⣿⣿⣿⡿⠘⠛⢿⣿⠏⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣯⡖⠍⠻
⠀⠀⣼⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⢛⣻⡇⢸⣿⣿⣿⣿⣿⣿⣿⠛⣷⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⣿⣿⣿⣤⠀⠐
⠀⠀⣿⣿⡿⣋⡉⣉⣉⡙⢻⣿⣿⣶⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠠⠄⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢘⣿⠻⢿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠀⠀
⠀⢸⣿⣿⡇⣃⣾⣿⣿⣿⢸⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇⢸⣿⠋⠀⠀⢀⣉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡄⠀⠰
⠀⢸⣿⣿⡇⠿⢿⠿⢿⠿⣸⣿⣿⣿⣿⡇⠸⢻⣿⣉⣙⢻⣿⣟⠁⠀⠀⠀⠀⠀⠀⠐⣶⣆⠀⠀⠉⠀⠀⠠⣾⣿⣿⣿⣿⡿⠟⠃⠸⡏⠀⠀⢠⣿⣿⣿⢸⣿⣿⣿⣿⡿⠛⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣷
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⣿⣿⣿⣿⠘⣻⠿⠀⠀⠀⠀⠀⠀⠀⢿⡀⠙⡇⠀⠀⠀⠀⠀⠙⠛⢛⡏⢀⡃⠀⠀⠸⣿⠦⡄⠈⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣴⣿⣿⣿⣿⣿⣟⣽⣟⣿⣿⣿⣿⠋⣿⣿⣿⣿⣿⣛⣅⠀⣿⣷⣴⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⠀⠙⠀⠀⠀⠀⢀⡞⠁⢸⡇⠀⠀⠀⢹⣧⡄⠀⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿
⣿⣿⣿⣿⡿⢛⡏⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⢀⣿⠀⠙⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢀⣹⡃⠀⠀⠀⢸⣿⠃⠀⡟⢻⣿⣿⣿⣿⣿⢿⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⡃⠀⣿⣿⣿
⣿⣿⣿⣿⣇⢹⠷⠿⠿⢿⣿⣿⣿⠀⣿⣿⣿⣿⣯⣭⣯⡼⠏⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠀⠘⠀⢸⣿⣿⠀⠀⠀⢸⣿⡆⢠⣷⠈⣿⣿⣿⡿⠁⣸⡄⠀⠀⢸⡆⢿⣿⣿⣿⣿⡿⣿⠇⠀⣿⣿⣿
⣿⣿⣿⣿⡏⣽⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡟⠛⠛⠓⠋⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣾⣿⡷⠀⠀⠀⠠⣿⣿⣿⣿⡇⢻⣿⣿⣵⣾⣿⠁⠀⠀⣾⡇⠀⣿⣿⣿⣿⣆⠀⠀⢀⣿⣿⣿
⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⡟⠈⠁⠁⠀⠀⠀⠂⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⡇⠘⣿⣿⣿⣿⣿⣄⠀⠀⠛⡃⠀⣿⣿⣿⣿⣿⠀⡤⠾⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣿⣤⣬⣼⣿⣿⣿⠀⣿⣿⡇⠀⠀⠀⠀⠀⡆⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⡿⠿⠂⠀⠀⠀⢸⣿⣿⣿⣿⣇⠀⠀⢸⣿⣿⣿⡟⠀⣴⣾⡇⠀⢹⣿⣿⣿⣿⠠⡧⠀⣹⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⣼⣿⣿⣿⣿⣿⡆⠀⣾⣿⣿⣿⡇⢠⣿⣿⡇⠀⠘⠂⠈⠉⠁⠀⣄⠈⣻⣿⣿
⢿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠘⠲⠀⠀⣿⣿⢠⣿⣿⣿⣿⣿⡟⢀⣸⣿⣿⣿⣿⠀⢸⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⡍⠀⣸⣿⣿
⢸⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⢛⣰⣿⣿⣿⣿⣿⣿⠀⠈⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣶⣶⣿⣿⣿
⠀⣿⣿⣿⣿⢸⣶⣾⣿⣿⣿⣿⣿⣭⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠉⠂⠀⠀⠘⠿⣿⣿⣿⣿⢟⣼⣿⣿⣿⣿⣿⣿⡟⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⢿⡟⢻⣿⣿
⠀⢹⣿⣿⣿⢈⡋⢻⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠋⠉⢺⣿⣿⣿⣥⡝⠿⣿⣷⣄⠀⠀⠙⢿⡇⠀⠀⠀⠀⠀⠀⢺⡏⣙⣿⣿
⠀⠘⣿⣿⣿⢠⣤⣬⠽⠭⡽⣿⣿⣶⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⢸⣶⣶⣤⡤⠀⢻⣿⣯⣿⣿⣦⣄⡘⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠉⠹⣿
⠀⠀⢹⣿⣿⠘⠁⠀⠀⠺⣯⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠺⠿⠀⠀⠀⠀⠀⠸⠟⠛⢿⣇⡀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢣⡄⠐⢿
⠀⠀⠀⠛⣿⣄⣀⣀⣀⣀⣩⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡴⠾⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⣷⠀⢘⣿⣿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡰⣿⣿⣿⣿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⡀⢹⣿⣿⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢙⣿⣷⣦⠀⠈⠃⢸⣿⡏⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠰⠛⠁⠀⣿⣿⣿⣿⣷⣶⡶⠟⠋⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠀⠀⠀⢠⣿⣿⣿⠟⠋⠁⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠄⠀⣸⣶⣶⣿⣿⣿⡏⠀⠀⠀⠀⢀⣤⣴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⣿⣿⣿⣿⠻⠿
⠀⠀⠀⠀⠀⣶⣄⣀⣤⣿⣿⣿⡏⢴⣿⡇⠀⠀⢠⣴⣾⣿⣿⣷⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣾⡿⣿⢕⠀⠀
⠀⠀⠀⠀⣸⣿⣿⠿⣿⣿⣿⣿⣿⣶⣿⡇⢠⡞⢉⣉⢿⣿⣿⣿⣛⣿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣷⣴⣖⠀⣻
⠀⠀⠀⣰⣿⡟⠀⠀⠈⢻⣿⣿⣿⡿⢿⡇⢸⣇⠙⠋⣸⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣷⡏⣰⣿
⠀⠀⢀⣿⣿⣇⠀⠛⢀⣼⣿⣿⣿⣶⣾⡇⢸⣿⣿⣿⣿⣿⣿⣿⡾⡿⠀⠀⢻⣿⣿⣿⣿⡿⠛⠛⢿⣿⠏⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣯⡖⠋⢻
⠀⠀⣼⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⢟⣻⡇⢸⣿⣿⣿⣿⣿⣿⣿⠛⣷⠀⠀⠀⠀⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣿⣿⣿⣥⠀⠐
⠀⠀⣿⣿⡿⣋⣋⣉⣉⡙⢻⣿⣿⣶⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠄⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢸⣿⣿⠿⣿⣿⣩⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀
⠀⢸⣿⣿⡇⣋⣿⣿⣿⣿⢸⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣇⢸⡟⠁⠀⠀⢈⣙⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡄⠀⠠
⠀⢸⣿⣿⡇⠿⢿⠿⢿⠿⣸⣿⣿⣿⣿⡇⠸⢻⣯⣉⣛⢻⣿⣟⠁⠀⠀⠀⠀⠀⠀⠐⣶⣄⠀⠀⠉⠀⠀⠠⣾⣿⣿⣿⣿⡿⠟⠋⣾⠃⠀⠀⢠⣿⣿⣿⢸⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣷
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⣿⣿⣿⣿⠚⣻⠿⠀⠀⠀⠀⠀⠀⠀⢿⡀⠙⡆⠀⠀⠀⠀⠀⠙⠛⢛⣏⢁⡀⠀⠀⢹⣦⣤⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣴⣿⣿⣿⣿⣿⣟⣽⣟⣿⣿⣿⣿⠋⣿⣿⣿⣿⣿⣋⣅⠀⣿⣧⣤⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⠀⠛⠀⠀⠀⠀⣀⡜⠁⢸⡇⠀⠀⠀⢰⣬⠀⠀⣾⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿
⣿⣿⣿⣿⡿⠟⡏⣻⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡿⠀⣿⠀⠙⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢀⣹⡃⠀⠀⠀⢸⡟⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⣿⣿⣿
⣿⣿⣿⣿⡇⢸⠷⠿⠿⢿⣿⣿⣿⠀⣿⣿⣿⣿⣯⣭⣯⡼⠋⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠀⠘⠀⢸⣿⣿⠀⠀⠀⠈⣧⠀⠀⢸⠈⣿⣿⣿⣿⡟⢻⡄⠀⠀⠀⠹⣿⣿⣿⣿⣿⡿⣿⠃⠀⣿⣿⣿
⣿⣿⣿⣿⡏⣽⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡿⠻⠛⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣾⣿⡧⠀⠀⠀⢀⣿⣇⣠⣾⡇⢻⣿⣿⣿⣴⣿⡇⠀⠀⢰⡀⠹⣿⣿⣿⣿⣇⠀⠀⢀⣿⣿⣿
⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢨⣟⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⢘⡃⠀⣿⣿⣿⣿⣿⢠⡤⠾⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣿⣤⣤⣼⣿⣿⣿⠀⣿⣿⡇⠀⡀⠀⠀⠀⡂⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⡿⠿⠆⠀⠀⠀⠐⣼⣿⣿⣿⡇⠀⠛⢻⣿⣿⣿⣿⠀⢀⣾⣧⠀⢱⣿⣿⣿⣿⠠⣧⠀⣹⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡄⠀⣼⣿⣿⣿⡟⢀⣾⣿⣿⠀⠐⠂⠈⠉⠁⠀⣄⠈⣻⣿⣿
⢿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠘⠶⠀⠀⣿⡇⠀⣿⣿⣿⣿⣿⣿⠃⢠⣿⣿⣿⣿⠃⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠍⠀⣸⣿⣿
⢸⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⢻⣿⣼⣿⣿⣿⣿⡿⢃⣠⣿⣿⣿⣿⣿⠀⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣶⣶⣿⣿⣿
⠀⣿⣿⣿⣿⢰⣶⣿⣿⣿⣿⣿⣿⣯⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠉⠀⠀⠀⠸⣿⣿⣿⣿⣿⠟⣳⣿⣿⣿⣿⣿⣿⡇⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⢿⡟⢻⣿⣿
⠀⢹⣿⣿⣿⢘⠋⢻⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠏⠁⢼⣿⣿⣇⡀⠻⢿⣿⣷⡄⠀⠈⠻⣿⡗⠀⠀⠀⠀⠀⠀⢺⡏⣙⣿⣿
⠀⠘⣿⣿⣿⢀⣤⣬⠭⢭⡭⣿⣿⣖⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠈⢿⣿⣿⣿⣦⣀⠀⢻⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠉⠸⣿
⠀⠀⢹⣿⣟⠈⠁⠀⠀⢰⣯⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠸⠟⠛⣿⡀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢣⡄⠐⢿
⠀⠀⠀⠋⣿⣄⣀⣀⣀⣀⣨⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠴⠾⠀⠀⠀⠀⠀⠀⠀⠀⠉⢺⣆⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⣩⣶⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣈⠀⡀⠀⠀⡀⢹⣿⣿⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢻⣿⣿⣦⡀⠈⠃⢸⣿⡏⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣆⢸⡟⡗⠀⣿⣿⣿⣿⣷⣶⡶⠟⠋⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⢠⠀⢰⣠⣿⣿⣿⠟⠋⠁⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠠⠤⠀⣹⣿⣷⣿⣿⣿⡏⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⢿⣿
⠀⠀⠀⠀⠀⣴⣄⣀⣴⣿⣿⣿⡟⢵⣿⡇⠀⠀⣤⣴⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣾⣷⣾⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠁⣾⣿⣿⡭⠈⢐
⠀⠀⠀⠀⣸⣿⣿⠿⣿⣿⣿⣿⣿⣶⣿⡇⢠⡞⢉⣉⢿⣿⣿⣿⣻⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣻⣿⣿⣿⣿⣿⡖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣷⣵⣶⡘⣿
⠀⠀⠀⣸⣿⡟⠀⠀⠈⢿⣿⣿⣿⡿⢻⡇⢸⣇⠛⠋⣸⣿⣿⣿⣿⣿⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠉⠛⣿⣿⣿⣿⣿⣿⣿⡟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣲⣿
⠀⠀⢀⣿⣿⣇⠀⠛⢀⣾⣿⣿⣿⣷⣾⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢻⣿⣿⣿⡿⠟⠉⠋⢹⣿⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣻⣦⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣯⡾⠟⣻
⠀⠀⣼⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⢟⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠛⣷⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⣿⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣥⠀⠚
⠀⠀⣿⣿⡿⣛⣛⣉⣙⡛⢿⣿⣿⣶⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⡄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⢸⣿⣿⣿⣿⣿⣫⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢀
⠀⢸⣿⣿⡇⣯⣿⣿⣿⣿⢺⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣧⢸⡉⠉⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡖⠁⠼
⠀⢸⣿⣿⣇⠿⢿⡿⣿⣿⣸⣿⣿⣿⣿⡇⠸⣿⣿⣩⣛⣻⣿⣟⠁⠀⠀⠀⠀⠀⠀⠐⣶⣄⠀⠀⠋⠀⠀⠠⣾⣿⣿⣿⣿⣿⠟⢻⣿⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿
⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⣿⣿⣿⣿⠺⣿⡿⠀⠀⠀⠀⠀⠀⠀⢿⡂⠙⡆⠀⠀⠀⠀⠄⠙⠻⢻⡯⢉⡂⠀⠊⢹⣤⡀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣴⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠋⣿⣿⣿⣿⣿⣻⣥⢐⣿⣿⣶⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⠀⠛⠀⠀⠀⠀⢐⡟⠁⣸⡇⠀⠀⠀⢀⡀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣟⡇⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣏⠘⠻⣿⣿⣿
⣿⣿⣿⣿⡿⣟⡟⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣨⣿⠂⠙⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢠⣽⡃⠀⠀⠀⠸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣿⣿⣿
⣿⣿⣿⣿⣟⢽⢿⠿⣿⢿⣿⣿⣿⠀⣿⣿⣿⣿⣯⣿⣿⣿⠿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠀⠙⠀⢸⣿⣿⠀⠀⠀⠀⣄⠀⠀⢸⠿⣿⣿⣿⣿⣿⢿⡆⠀⠀⠈⣿⣿⣿⣿⣿⣿⡿⣿⠇⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⠿⠻⠟⠛⠫⠧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⢀⠀⣿⣿⣿⠀⠀⠀⠀⣿⣄⠀⢸⣧⣿⣿⣿⣿⣃⣼⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⠀⠀⢀⣿⣿⣿
⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⡿⠉⠁⠁⠀⠀⠈⡂⠂⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⡏⠭⣵⣿⣿⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⢠⣤⢾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣤⣭⣭⣿⣿⣿⠀⣿⣿⡟⢰⡀⠀⠀⠀⡎⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⡿⠿⠃⠀⠀⠀⠀⢁⣾⣿⣿⣿⠈⢿⣿⣿⣿⣿⣿⠀⠀⣼⡄⠈⢹⣿⣿⣿⣿⠠⣧⢀⣹⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⡻⠃⢀⠀⠀⠀⠀⡀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⡉⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡄⠀⣿⣿⣿⣿⣿⠀⣠⣿⣷⠀⠘⠂⠈⠉⠁⠀⣇⠈⣻⣿⣿
⢿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣧⣀⠁⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠘⠶⣀⠀⣿⡄⠀⣼⣿⣿⣿⣿⣿⠇⢠⣿⣿⣿⣿⡏⢰⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⡭⠀⣸⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⢿⣯⣰⣿⣿⣿⣿⣿⠟⢀⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣶⣶⣿⣿⣿
⠀⣿⣿⣿⣿⣸⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠁⠂⠀⠀⢸⣿⣿⣿⣿⣿⡿⢇⣴⣿⣿⣿⣿⣿⡟⠀⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⡟⢻⣿⣿
⠀⢹⣿⣿⣿⢘⡛⢻⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⡿⠋⣠⣿⣿⡁⠹⢿⣿⣿⣇⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⢾⡏⣙⣿⣿
⠀⠘⣿⣿⣿⢠⣤⣬⢭⢭⣽⣿⣿⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⠋⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣦⣀⠉⠁⣿⣷⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⣇⠋⠸⣿
⠀⠀⢹⣿⣿⠘⠋⠀⠈⢳⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠸⠿⡿⣿⡇⠀⠘⣿⣿⣿⣿⣿⣿⣿⠁⠀⢲⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⢫⡄⠐⢿
⠀⠀⠀⠛⣿⣄⣈⣁⣀⣀⣩⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡴⠾⠀⠀⠀⠀⠀⠀⠀⠈⠛⣻⣄⠀⢸⣿⣿⣿⣿⣿⣿⡆⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠍⡡⣭⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢅⣉⠫⡐⠁⠀⡀⢹⣿⣿⢀⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡗⠪⣿⣿⣿⣦⠀⠈⠃⢸⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣆⣺⡟⡷⣄⣿⣿⣿⣿⣷⣶⣶⠟⠋⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣵⡽⣢⣼⣿⣿⣿⠿⠋⠉⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠠⡤⠀⢹⣿⣷⣿⣿⣿⡏⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣶⣄⣀⣤⣿⣿⣿⡟⢷⣿⡇⠀⠀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⢰⣦⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠁⣾⣿⣿⣽⢿⢗
⠀⠀⠀⠀⣸⣿⣿⢿⣿⣿⣿⣿⣿⣶⣿⡇⢠⡞⢉⣉⢿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣏⣽⣿⣿⣿⣿⣿⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣵⣶⡚⣿
⠀⠀⠀⣸⣿⡟⠁⢀⠈⢿⣿⣿⣿⡿⢿⡇⢸⣇⠛⠋⣸⣿⣿⣿⣿⣿⠉⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠙⠛⠻⣿⣿⡿⠃⣻⣿⡟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿
⠀⠀⢀⣿⣿⣇⠀⠛⢀⣾⣿⣿⣿⣶⣾⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⢻⣿⠿⢿⡏⠉⠀⠀⢹⠿⠋⠛⢿⣿⣿⣿⠹⣿⣿⣿⣇⣶⣦⣤⣾⣿⣿⣷⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⡾⡿⣿
⠀⠀⣼⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠛⣷⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣧⣽⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⠭⢾
⠀⢀⣿⣿⡿⣛⡛⣙⣛⡛⢿⣿⣿⣶⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⡄⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⡟⠻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣕⢜
⠀⢸⣿⣿⡇⣯⣿⣿⣿⣿⢻⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣷⡘⠛⠋⠀⠀⠘⣿⣧⣄⣀⣼⣿⣿⣿⠛⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⠧⢽
⠀⢸⣿⣿⣇⠿⢿⣿⣿⣿⣺⣿⣿⣿⣿⡇⠸⣿⣿⣻⣟⣻⣿⣿⠁⠀⠀⠀⠀⠀⠀⠐⣶⣄⠀⠀⠋⠀⠀⠠⣾⣿⣿⣿⣿⣿⠿⣿⡏⠀⠀⠀⠀⠸⣿⡿⣿⣿⣿⣿⣿⠟⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⣿⣿⣿⣿⠾⣿⡿⠀⠀⠀⠀⠀⠀⠀⢿⡂⠙⡆⠀⠀⠀⠀⠀⠙⠿⣿⡯⢩⡃⠈⠛⠁⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣿⣿⣿⣿⣿⣿⣯⢸⣿⣿⣶⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⠀⠛⠀⠀⠀⠀⣐⡟⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠛⣿⣿⣿
⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣹⣿⠃⠛⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢠⣿⡃⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣯⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⢽⢿⠿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠀⠛⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⣿⠃⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡿⠿⠿⠿⠿⠷⢡⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠨⣇⠀⣿⣿⣿⠀⠀⠀⠀⣦⠀⠀⢸⡏⣿⣿⣿⣿⠋⣿⡇⠀⠀⠀⠙⣿⣿⣿⣿⣿⣇⠀⠀⢀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⠙⢡⠩⠇⠀⡦⡪⠋⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡀⠀⠈⠀⣿⣿⡟⠀⠀⠀⠀⡏⢨⣶⣾⣧⣿⣿⣿⣷⣶⡟⠃⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⢠⣤⢾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣤⣭⣽⣿⣿⣿⠀⣿⣿⣟⢰⣚⣈⡁⠀⡏⠀⣀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣿⠿⠇⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⢱⣿⣿⣿⣿⠨⣧⢀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠹⣻⠇⢈⡗⠀⠀⠀⣯⠇⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏⠻⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠁⠈⠉⠁⠀⣏⠈⣻⣿⣿
⢿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣧⣈⠙⠀⠀⠀⠀⠀⠀⠓⠛⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠘⠷⣄⠀⣆⠀⠀⢠⣿⣿⣿⣿⣿⡇⢀⣿⣿⣿⣿⣿⡇⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⡯⠆⣸⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀⢻⣇⢀⣾⣿⣿⣿⣿⣿⠇⣸⣿⣿⣿⣿⣿⢠⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿
⠀⣿⣿⣿⣿⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠙⠂⠀⠀⣸⣿⣿⣿⣿⣿⣿⡿⠋⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⡟⢻⣿⣿
⠀⢻⣿⣿⣿⢹⣛⢿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⠿⠋⣡⣾⡿⣿⣿⣿⣿⡿⠀⢻⣿⣿⣿⣷⠂⠀⠀⠀⠀⠀⢾⡏⣹⣿⣿
⠀⠘⣿⣿⣿⢠⣤⣬⢿⣯⣽⣿⣿⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠋⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⣾⣿⣿⣦⠈⠛⠻⠿⣿⠀⠘⣿⠿⠉⠁⠀⠀⠀⠀⠀⠀⢸⣇⠋⢸⣿
⠀⠀⢹⣿⣿⠘⠛⡾⡞⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠺⠿⠀⠀⠀⠀⠀⠠⣤⡤⣤⣄⠈⢿⣿⣿⣿⣶⣤⣤⣽⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢫⡄⠐⢿
⠀⠀⠀⠻⣿⣄⣉⣁⣁⣉⣩⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡴⢾⠀⠀⠀⠀⠀⠀⠈⠻⢿⢿⡀⠀⢻⣿⣿⣿⣿⣿⣿⡆⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢮⣽⣻⣿⣿⣿⣿⣿⣿⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣯⣿⣯⡻⠁⢀⡀⢹⣿⣿⢀⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣮⣿⠿⣿⣿⣿⣧⡀⠘⠃⢸⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣮⣻⣿⣿⣤⣿⣿⣿⣿⣷⣶⣶⠟⠋⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣻⣿⣿⣿⣿⠿⠋⠉⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠠⡤⠀⣹⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣶⣄⣀⣤⣿⣿⣿⡟⢿⣿⡇⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⢰⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⣾⣿⣿⣽⣿⣿
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡇⢠⡾⢉⣉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣏⣽⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣵⣾⣿⣿
⠀⠀⠀⣸⣿⡿⠁⢀⠈⢿⣿⣿⣿⣿⣿⡇⢸⣇⠛⠋⣸⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡿⠟⠋⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⠏⠙⠛⢿⣿⣿⣇⢀⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢠⣿⣿⣇⠀⠛⢀⣾⣿⣿⣿⣷⣾⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⠛⠛⠋⠉⣡⠀⠀⠀⠸⠿⠊⠛⢻⣿⣿⣿⠸⣿⣿⣿⣷⣾⣦⣤⣾⣿⡛⢋⣤⣿⣿⡇⠙⢿⡄⠈⣿⣿⣿⣿⣿⣿⣿⠋⣿⣿⣿⣿⣿⣿
⠀⠀⣾⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠟⣿⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣧⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠇⠀⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿
⠀⢠⣿⣿⡿⣛⣛⣙⣛⡛⢿⣿⣿⣶⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⡄⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠋⠀⠙⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿
⠀⢸⣿⣿⣇⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣟⣻⣿⣿⠁⠀⠀⠀⠀⠀⠀⠐⣶⣄⠀⠀⠛⠀⠀⠠⣼⣿⣿⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣼⣿⣿⣿⣿⠿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢿⡆⠻⣧⠀⠀⠀⠀⠀⠘⠿⣿⣏⢩⡅⠀⠆⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣍⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣿⣿⣿⣿⣿⣿⣯⣼⣿⣿⣾⠀⠀⠀⣄⠀⠀⠀⠃⠀⠘⠀⠚⠀⠀⠀⠀⣸⡟⠁⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠃⠈⠛⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⣻⡃⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡀⠛⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⡷⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡿⠿⠿⠿⠻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠹⣷⡆⣿⣿⣿⠀⠀⠀⠀⠆⠀⢀⡘⡟⣿⣿⣿⡿⢿⣿⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣇⠀⠀⢀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⠹⣿⣿⡇⠀⡿⡫⠛⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡀⠀⠉⠁⣿⣿⡿⠀⠀⠀⠀⠐⣸⣾⣧⣽⣿⣿⣿⣇⣘⠿⠃⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⢠⣤⢾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣤⣭⣽⣿⣿⣿⠀⣿⣿⣿⢸⣛⣉⡁⠀⣿⡇⢠⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⣿⠿⠗⠀⠀⠀⠀⣰⣿⣿⣋⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠨⣧⣄⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠹⣿⣏⣨⣿⠂⡸⠀⣿⡇⢀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⡍⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠁⠈⠉⠁⠀⣏⠉⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣧⣈⠙⠋⠈⠉⠀⠀⠀⠓⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠘⠿⣅⠀⢀⠀⠀⠀⣿⣿⣿⣿⣿⡇⢨⣿⣿⣿⣿⣿⡇⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡯⠆⣹⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⠀⠀⡀⠀⠀⠀⢹⣆⠀⣴⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⢠⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⣿⣿⣿
⠀⣿⣿⣿⣿⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠉⠂⠀⠀⣨⣿⣾⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢻⣿⣿
⠀⢻⣿⣿⣿⢹⣻⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⡿⢋⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⢾⡟⣹⣿⣿
⠀⠘⣿⣿⣿⢠⣤⣬⢿⣿⣿⣿⣿⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠋⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠈⠻⠋⠀⣶⣿⣿⡍⠛⠿⢿⣿⠇⠘⢿⣿⠿⠏⠁⠀⠀⠀⠀⠀⠀⢸⣇⠛⢻⣿
⠀⠀⢻⣿⣿⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠺⠿⠀⠀⠀⠀⠀⢠⣤⣤⣤⡄⠈⢿⣿⣿⣶⣤⣄⣠⣤⢀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⢫⡄⠸⢿
⠀⠀⠈⢻⣿⣄⣉⣉⣉⣉⣩⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡴⢾⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡀⠈⢻⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢮⣿⣻⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣯⣿⣯⡻⠁⢀⡀⢹⣿⣿⢀⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠿⣿⣿⣿⣧⡀⠘⠃⢸⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣻⣿⣿⣤⣿⣿⣿⣿⣷⣶⣶⠿⠛⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠠⡤⠀⣹⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣶⣄⣀⣤⣿⣿⣿⡟⢿⣿⡇⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⢰⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⠈⠁⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡇⢠⡾⢉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣼⣿⣷⣿⣿⣵⣾⣿⣿
⠀⠀⠀⣸⣿⡿⠁⢀⠈⢿⣿⣿⣿⣿⢿⡇⢸⣇⠛⠋⣸⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡿⠿⠟⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠙⠛⢻⣿⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢠⣿⣿⣇⠀⠛⢀⣾⣿⣿⣿⣷⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⠛⠛⠉⢀⡀⠠⠀⠀⠺⠿⠂⠛⢻⣿⣿⣿⠸⣿⣿⣿⣿⣾⣦⣤⣿⣿⣿⡆⢿⣿⡟⠁⠉⢻⣿⣿⣛⣿⣿⣿⣿⣿⣿⠉⣿⣿⣿⣿⣿⣿
⠀⠀⣾⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠟⣿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⣿⣧⣽⣿⣿⣿⣿⣿⣿⣿⣯⣍⣴⣿⣿⡇⠀⠀⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣽⣿
⠀⢀⣿⣿⡿⣛⣛⣛⣛⡛⢿⣿⣿⣾⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⢠⠄⠘⠟⠛⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾
⠀⢸⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⣷⣦⡀⠻⠟⢹⣿⣿⣿⠋⠉⣸⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣇⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣟⣻⣿⣿⠁⠀⠀⠀⠀⠀⠀⡐⣶⣄⠀⠀⠛⠀⠀⠠⣼⣿⣿⣿⣿⣦⣀⡸⠿⠿⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣼⣿⣿⣿⣿⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢿⡂⢻⣧⡀⠀⠀⠀⠀⠘⠿⣿⣯⢭⡅⠀⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣿⣿⣿⣿⣿⣿⣯⣼⣿⣿⣼⠀⠀⠀⣄⠀⠀⠀⠃⠀⠹⠇⠚⠀⠀⠀⠀⣸⡿⠁⣸⡇⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣟⠀⢀⣿⣿⣿⣿⣿⣿⣿⡿⠃⠈⠛⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣽⣿⡏⠛⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢰⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠁⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡀⠛⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⠄⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠒⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡿⠿⠿⠿⠻⣿⣷⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠫⣷⡄⣿⣿⣿⠀⠀⠀⠀⠆⠀⢀⡈⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⡇⠀⠀⢀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⡿⢙⣍⣽⡇⠀⡯⡻⠃⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡀⠀⠉⠁⣿⣿⡿⠁⠀⠀⠀⠑⣿⣿⣇⠻⣿⣿⣿⠏⠿⡿⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⢠⣤⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣤⣭⣽⣿⣿⣿⠀⣿⣿⡟⢹⣟⣙⡃⠀⣿⣦⣠⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⣿⠿⠗⠀⠀⠀⠀⣴⣿⣿⡃⢸⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠨⣧⢄⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢹⣿⣏⢨⡽⠆⠰⠀⣿⡇⢀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠸⠁⠈⠉⠁⠀⣏⠈⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣧⣈⠙⠋⠈⠁⠀⠀⠀⠛⠟⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠘⠿⣅⠀⢀⠈⠀⠘⣿⣿⣿⣿⣿⣿⠙⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠆⣻⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⠀⠀⠀⠀⠀⠀⢹⡄⠀⣰⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⠇⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⣿⣿⣿
⠀⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠉⠂⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⢻⣿⣿
⠀⢻⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⡿⠛⣡⣴⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⠄⠀⠀⠀⠀⠀⢾⡟⣽⣿⣿
⠀⠘⣿⣿⣿⢠⣤⣬⣿⣿⣿⣿⣿⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠋⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠈⠿⠟⠀⣴⣿⣿⣟⠻⢿⣿⣿⣿⣿⣿⣿⡿⠏⠉⠀⠀⠀⠀⠀⠀⢸⣇⠛⢻⣿
⠀⠀⢻⣿⣿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠺⠿⠀⠀⠀⠀⠀⠲⣶⣶⣶⣦⠘⢿⣿⣿⣷⣦⣄⣀⣀⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⢫⡤⠸⢿
⠀⠀⠈⢻⣿⣄⣉⣉⣉⣉⣩⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⢾⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡄⠈⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢾⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣻⠁⢀⡀⢻⣿⣿⢀⣍⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠿⣿⣿⣿⣷⡀⠘⠃⢸⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣻⣿⣿⣤⣿⣿⣿⣿⣷⣶⣶⠿⠛⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣻⣿⣿⣿⣿⠿⠋⠉⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠠⡤⠀⣹⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣶⣄⣀⣤⣿⣿⣿⡟⢿⣿⡇⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⣴⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡇⢠⡾⢉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣧⠀⣼⣿⣵⣾⣿⣿
⠀⠀⠀⣸⣿⡿⠁⢀⠈⢿⣿⣿⣿⣿⣿⡇⢼⣇⠛⠋⣸⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⡿⠿⠛⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿
⠀⠀⢠⣿⣿⣇⠀⠛⢀⣾⣿⣿⣿⣷⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠛⢛⠁⢀⡔⠂⠀⠀⠀⠉⠀⠛⠿⣿⣿⣿⠸⣿⣿⣿⣿⣾⣶⣤⣿⣿⠋⢻⣿⣿⡟⠛⠛⠻⢿⣿⣿⣷⣨⣿⣿⣿⣿⠁⣿⣿⣿⡿⣿⣿
⠀⠀⣾⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠿⣿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣧⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⠛⣿⣿⡆⠀⠀⠀⠀⠙⣻⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣽⣿⡿
⠀⢀⣿⣿⡿⣛⣛⣛⣛⡛⢿⣿⣿⣶⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⣠⠄⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣾⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⣷⣞⠻⠛⠁⣿⣿⣿⡿⠟⠋⢉⣿⣿⣿⣿⣷⡄⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣇⠿⢿⣿⣿⣿⣾⣿⣿⣿⣿⡇⠸⣿⣿⣿⣟⣻⣿⣿⠁⠀⠀⠀⠀⠀⠀⡐⣶⣄⠀⠀⠛⠀⠀⠀⣼⣿⣿⣿⣷⣤⡼⣿⠿⠿⠁⠀⠀⣸⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣼⣿⣿⣿⣿⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢿⡆⢻⣧⡀⠀⠀⠀⠀⠸⠿⣿⣟⢛⡀⠈⠃⢸⠄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣿⣿⣿⣿⣿⣿⣯⣼⣿⣿⣼⠀⠀⠀⣄⠀⠀⠀⠃⠀⠻⡇⠚⠄⠀⠀⠀⣼⡿⠁⣸⡇⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣶⣦⠄⠀⣿⣿⣿⣿⣿⣿⣿⡿⠃⠈⠛⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⠀⢠⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡋⠃⠀⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡀⠛⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⣀⡀⢿⣿⣿⣿⣿⣿⣿⣷⠒⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡿⠿⠿⠿⠻⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠻⣷⡄⣿⣿⣿⠀⠀⠀⠀⠄⠀⣠⠀⣿⣿⣿⣿⣿⣿⣿⠉⠁⠂⠈⠛⢻⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⠽⣭⣿⡇⠀⣿⡿⠿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡀⠀⠉⠁⣿⣿⡿⠁⠀⠀⠀⠐⣿⣿⡂⢻⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⢀⣤⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣤⣭⣽⣿⣿⣿⠀⣿⣿⣿⢹⣟⣛⡁⠀⣿⣇⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⣿⠿⠗⠀⠀⠀⠀⣾⣿⣿⡇⢈⣿⣿⣿⣯⣽⡃⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣷⠨⣧⣄⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢻⣿⣟⣸⣿⠂⠻⠀⣿⣇⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⢀⣿⣿⣿⣇⣠⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠨⠅⠈⠉⠉⠀⣏⠉⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣧⣈⠙⠋⠈⠠⠀⠀⠀⠛⠟⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠘⠿⣅⠀⢀⠈⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠇⣻⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⠀⠀⡀⠀⠀⠀⢹⣄⣀⣠⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⣿⣿⣿
⠀⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠙⠂⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣇⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⣿⣿
⠀⢻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠟⢋⣠⣿⣿⣿⣿⣿⣿⣿⣿⣀⣠⡤⠀⠀⠀⠀⠀⠀⢾⡟⣝⣿⣿
⠀⠘⣿⣿⣿⢠⣤⣬⣿⣿⣿⣿⣿⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠋⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣀⣀⣻⣯⠀⣴⣾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢸⣇⠛⢻⣿
⠀⠀⢻⣿⣿⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠺⠿⠀⠀⠀⠀⠀⠹⣿⣿⣿⣧⠘⣿⣿⣿⣿⣷⣤⡉⢙⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢫⣤⠸⣿
⠀⠀⠈⢻⣿⣄⣉⣉⣉⣉⣩⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⢾⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡄⠘⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⠁⢀⡀⢻⣿⣿⢀⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠿⣿⣿⣿⣧⡀⠘⠃⢸⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣻⣿⣿⣤⣿⣿⣿⣿⣷⣶⣶⠿⠛⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠠⡦⠀⣹⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣶⣄⣀⣴⣿⣿⣿⣟⢿⣿⡇⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣴⣦⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡇⢠⡾⢉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿⣿⣿⣷⣋⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⡿⣽⣿⣽⣿⣿⣿
⠀⠀⠀⣸⣿⡿⠁⢀⠉⢿⣿⣿⣿⣿⣿⡇⢼⣇⠛⠋⣸⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⢿⠿⠛⠋⠈⠿⣿⢯⠙⢿⣿⣿⣿⢻⣿⣿⣿⣿⠇⠙⠛⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿
⠀⠀⢠⣿⣿⣧⠀⠛⢀⣾⣿⣿⣿⣷⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠈⠙⠙⠁⢀⠀⠐⠀⠀⠠⠄⠀⠀⠸⣿⣿⣿⠸⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣭⣽⣿⣿⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣾⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⣿⣿⣿⣆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⡅⣿⣿⣿⣿⣿⣿
⠀⢠⣿⣿⡿⣛⣛⣛⣛⣛⢿⣿⣿⣶⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡿⠉⠉⠉⠙⠻⣿⣿⣷⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣀⣛⣛⣛⣿⣿⣧⡈⣿⣿⣿⡀⠀⠀⠀⠀⠉⣩⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣇⠿⢿⣿⣿⣿⣾⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣻⣿⣿⠁⠀⠀⠀⠀⠀⠀⠐⣶⣄⠀⠀⠛⠀⠀⠀⣴⣿⣿⣿⣿⠋⠀⣾⣿⣿⡿⠿⠟⠛⠻⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣼⣿⣿⣿⣿⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢿⡆⢻⣧⡀⠀⠀⠀⠀⠸⢿⣿⣿⢻⡀⠀⠿⢻⠟⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⣄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣿⣿⣿⣿⣿⣿⣯⣾⣿⣷⣼⠀⠀⠐⣄⠀⠀⠀⠃⠀⠻⡇⠺⠄⠀⠀⠀⣨⡟⠁⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢈⣿⣿⣿⣿⣿⣿⡿⠃⠈⠙⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠻⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⠁⢰⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠀⠻⠀⣼⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣷⠂⢸⣿⣿⣿⣿⣿⣿⡷⠒⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡿⠿⠿⠿⠻⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠳⣷⡄⣿⣿⡏⠀⠀⠀⠀⠀⢀⣄⠀⡀⢸⣿⣿⣿⣿⣿⣿⣿⠃⠘⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⢹⣿⣽⣇⠀⣿⡻⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡀⠀⠉⢹⣿⣿⡗⠀⠀⠀⠀⠀⣾⣿⡄⢹⣾⣿⣿⣿⣿⣿⣿⡯⠀⠀⢿⣿⣿⣿⣿⣿⡿⢀⣤⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣤⣭⣽⣿⣿⣿⠀⣿⣿⣿⢹⣿⣛⡃⠀⣿⣇⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠘⣿⡿⠇⠀⠀⠀⠀⣾⣿⣿⠃⣸⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢹⣿⣿⣿⣷⠨⣧⣄⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢻⣿⣏⣸⣿⠋⡾⠀⣿⣇⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢸⣏⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇⠉⢿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠸⠅⠈⠉⠀⠀⣏⠉⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣧⣈⠙⠋⠀⠉⠀⠀⠀⠛⠟⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠺⢿⡀⠀⡀⠈⠀⢸⣿⣿⣿⣧⡀⢀⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠗⢻⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠒⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃⠀⠀⠀⠀⠀⠘⣿⠀⢀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⣿⣿⣿
⠈⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠒⠀⠀⠀⠸⣷⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⣿⣿
⠀⢻⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⣽⣿⣿
⠀⠘⣿⣿⣿⢠⣤⣭⣿⣿⣿⣿⣿⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠋⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢠⣤⣀⣘⣿⢁⣀⣾⣿⠻⢿⣿⣿⣿⣟⣠⣾⡿⠀⠲⠀⠀⠀⠀⠀⠀⢸⣇⠛⢹⣿
⠀⠀⢻⣿⣿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠺⠿⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠹⣿⣿⣿⣿⣦⡙⢻⠛⠛⠋⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣤⠸⣿
⠀⠀⠈⢻⣿⣄⣉⣉⣉⣉⣩⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⢶⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠄⢹⣿⣿⣿⣿⣿⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡿⠁⢀⡀⢻⣿⣿⢀⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠿⣿⣿⣿⣷⡀⠘⠃⢸⣿⡿⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣤⣿⣿⣿⣿⣷⣶⣶⠿⠋⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣽⣿⣿⣿⣿⠿⠋⠉⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠠⡤⠀⣹⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⢀⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣴⣄⣀⣤⣿⣿⣿⡟⢿⣿⡇⠀⢀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣰⣦⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡇⢠⡾⢉⣙⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢿⣿⣿⣿⣷⣏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣿⣿⣿⢿⣿⣽⣾⣿⣿
⠀⠀⠀⣸⣿⡟⠁⡀⠉⢿⣿⣿⣿⣿⣿⡇⢼⣇⠛⠛⣸⣿⣿⣿⣿⣿⡿⢿⣿⣿⡿⠿⠿⠛⠉⠈⠻⡿⠃⠉⢹⣿⣿⣿⢻⣿⣿⣿⣿⠇⠙⠛⠻⣏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢠⣿⣿⣇⠀⠛⢀⣾⣿⣿⣿⣷⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂⢸⣿⣿⣿⢸⣿⣿⣿⣿⣾⣦⣴⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣾⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣷⣿⣿⣏⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣿⣿⡿⣛⣛⣛⣛⡛⢿⣿⣿⣶⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⣤⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⡀⣸⣿⣿⣿⡿⣿⣿⣿⡿⣯⣹⣿⣿⣿⣿⣿
⠀⢸⣿⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣰⣼⣿⣿⣿⣿⣿⣿⠉⣉⣛⡋⢹⣿⣿⣿⣿⣿⣿⠋⠉⠘⠻⠿⣿⣿⣿⡈⢻⣯⣶⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣇⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣟⣻⣿⣿⠁⠀⠀⠀⠀⠀⠀⠐⣶⣄⠀⠀⠉⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⠀⠀⠈⣿⣿⠉⢿⣿⣿⡄⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣼⣿⣿⣿⣿⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢿⡎⢻⣧⡀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣾⣿⣿⣿⣼⣿⣿⣿⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣿⣿⣿⣿⣿⣿⣯⣽⣿⣷⣶⠀⠀⠐⣄⠀⠀⠀⠁⠀⠹⡇⠺⠄⠀⠀⠀⣀⡟⠋⣾⡟⠃⠀⠹⣿⣿⠋⠁⠀⢀⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡟⠃⠈⠙⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣿⠁⢐⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⣿⣿⣿⣿⣿⣿⡄⠀⠀⠈⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠃⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡿⠿⠿⠿⠻⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⠀⣿⣿⣿⠀⠀⠀⠀⠀⢀⣄⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣹⣿⣿⣷⠀⡿⡫⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⢰⣿⣿⡇⠀⠀⠀⠀⢠⣿⣿⠀⠙⠹⣿⣿⣿⣿⣿⣿⣿⠇⠀⣿⣿⣿⣿⣿⣿⡿⢀⣤⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣤⣭⣭⣿⣿⣿⠀⣿⣿⣿⢹⣟⣙⣁⠀⣿⣃⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠸⣿⡿⠃⠀⠀⠀⠀⣿⣿⣿⠁⡼⣸⣿⣿⣿⣿⣿⣿⣿⡄⠀⢸⣿⣿⣿⣿⣿⣷⠨⣷⣄⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢻⣿⡟⣸⣿⠊⣸⡅⣿⣇⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢾⣟⠀⠀⠀⠀⠀⠀⢙⣿⣿⡄⠉⢿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠈⠙⠻⠅⠉⠉⠀⠀⣏⠉⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣧⣈⠙⠇⠀⠀⠀⠀⠀⠟⠾⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠿⢿⠀⢀⡀⠀⠀⠠⣾⣿⣿⣧⡀⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠗⣻⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⣿⣿⣿⣿⣇⣈⡿⣿⣿⣿⣧⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⣿⣿⣿
⠈⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠈⠂⠀⠀⠀⢻⣦⣴⠟⠻⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢻⣿⣿
⠀⢻⣿⣿⣿⢿⣿⣻⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡟⣙⣿⣿
⠀⠘⣿⣿⣿⢨⣥⣽⣿⣿⣽⣿⣿⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠋⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢿⣦⣤⣀⡸⠟⢫⣿⣿⢿⣿⣿⣿⣿⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠛⢹⣿
⠀⠀⢻⣿⣿⢸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⢸⠿⣿⣿⣧⠀⣾⣿⣿⣷⡈⢿⣿⡟⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⡄⠰⣿
⠀⠀⠈⢻⣿⣄⣉⣉⣈⣉⣩⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢶⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⢰⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡿⠁⢀⡀⢻⣿⣿⢀⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠿⣿⣿⣿⣧⡀⠘⠃⢸⣿⡿⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣤⣿⣿⣿⣿⣷⣶⣶⠿⠋⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠠⡤⠀⣹⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢀⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣴⣄⣀⣤⣿⣿⣿⡟⣿⣿⡇⠀⢀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣦⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡇⢠⡾⢉⣙⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢻⣿⣿⣿⣷⣏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣾⣻⣿
⠀⠀⠀⣸⣿⡿⠁⡀⠉⢿⣿⣿⣿⣿⣿⡇⢼⣇⠛⠛⣸⣿⣿⣿⣿⣿⡿⢿⣿⣿⡿⠿⠿⠛⠉⠈⠻⠿⠋⠙⢹⣿⣿⣿⢻⣿⣿⣿⣿⠇⠙⠛⠻⣏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢠⣿⣿⣇⠀⠛⢀⣾⣿⣿⣿⣷⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠋⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂⠸⣿⣿⣿⢸⣿⣿⣿⣿⣾⣦⣴⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿
⠀⠀⣾⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣏⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿
⠀⢀⣿⣿⡿⣛⣛⣛⣛⡛⢿⣿⣿⣶⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⣤⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⣿⣿⣿⡿⣿⣿⣿⡿⣯⣹⣿⣿⣿⣷⣿
⠀⢸⣿⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣰⣼⣿⣿⣿⣿⣿⣿⠉⣉⡛⠋⢹⣿⣿⣿⣿⣿⣿⠋⠉⠘⠻⠿⣿⣿⣷⡈⢻⣯⣶⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣇⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣟⣻⣿⣿⠁⠀⠀⠀⠀⠀⠀⡐⣶⣄⠀⠀⠉⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⠀⠀⠈⣿⣿⠉⢿⣿⣿⡄⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⣿⣿⣿⣿⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢿⡎⢻⣧⡀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣶⣿⣿⣿⣼⣿⣿⣿⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣿⣿⣿⣿⣿⣿⣯⣽⣿⣷⣶⠀⠀⠐⣄⠀⠀⠀⠁⠀⠹⡇⠰⠄⠀⠀⠀⣀⡟⠉⣾⡟⠃⠀⠹⣿⣿⠋⠁⠀⢀⣿⣿⣿⣿⣿⣆⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟⠃⠈⠙⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣿⠁⢐⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⣿⣿⣿⣿⣿⣿⡄⠀⠀⠈⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠃⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡿⠿⠿⠿⠻⣻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⠀⣿⣿⡿⠀⠀⠀⠀⠀⢀⣄⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣹⣯⣿⣷⠀⡿⡫⠛⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⢰⣿⣿⡇⠀⠀⠀⠀⢠⣿⣿⠀⠙⠹⣿⣿⣿⣿⣿⣿⣿⠇⠀⣿⣿⣿⣿⣿⣿⡿⢀⣤⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣤⣭⣭⣿⣿⣿⠀⣿⣿⣿⢹⣿⣋⣑⠀⣿⣃⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠸⣿⡿⠃⠀⠀⠀⠀⣿⣿⣿⠃⡼⣸⣿⣿⣿⣿⣿⣿⣿⡀⠀⢸⣿⣿⣿⣿⣿⣷⠨⣷⣄⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢻⣿⡯⣨⣿⠂⣺⠁⣿⡇⢀⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢺⣟⠀⠀⠀⠀⠀⠀⠙⣿⣿⡄⠉⢿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠈⠙⠻⠅⠉⠉⠀⠀⣏⠉⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣧⣈⠙⠇⠠⠀⠀⠀⠀⠟⠞⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠿⠿⠀⢀⡀⠀⠀⠠⣾⣿⣿⣧⡀⢹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠗⢻⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⣿⣿⣿⣿⣇⣈⡿⣿⣿⣿⣧⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⣿⣿⣿
⠀⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠈⠂⠀⠀⠀⢻⣦⣴⠟⠻⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢻⣿⣿
⠀⢻⣿⣿⣿⢽⣻⣻⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡟⣙⣿⣿
⠀⠘⣿⣿⣿⢨⣥⣼⣿⣿⣽⣿⣿⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠋⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢿⣦⣤⣀⡸⠟⢫⣿⣿⢿⣿⣿⣿⣿⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡛⢹⣿
⠀⠀⢻⣿⣿⢹⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⢸⠿⣿⣿⣧⠀⣾⣿⣿⣷⡈⢿⣿⡟⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⢼⣿⡄⠰⢿
⠀⠀⠈⢻⣿⣄⣉⣉⣉⣉⣩⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢶⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⢰⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡿⠁⢀⡀⢻⣿⣿⢀⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠿⣿⣿⣿⣷⡀⠘⠃⢸⣿⡿⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣤⣿⣿⣿⣿⣷⣶⣶⠿⠛⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠠⡤⠀⣹⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣶⣄⣀⣤⣿⣿⣿⡟⣿⣿⡇⠀⢀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡇⢠⡾⢉⣙⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣷⣏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣻⣿
⠀⠀⠀⣸⣿⡿⠁⡀⠉⢿⣿⣿⣿⣿⣿⡇⢼⣧⠛⠛⣸⣿⣿⣿⣿⣿⡟⢿⣿⣿⡿⠿⠿⠛⠉⠈⠿⡿⠃⠉⣹⣿⣿⣿⢿⣿⣿⣿⣿⠇⠙⠛⠻⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢠⣿⣿⣇⠀⠛⢀⣾⣿⣿⣿⣷⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠃⠚⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂⢸⣿⣿⣿⢸⣿⣿⣿⣿⣿⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣾⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⣿⣿⣿⣿⣿
⠀⢀⣿⣿⡿⣛⣛⣋⣛⣛⢿⣿⣿⣶⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⣠⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⡇⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿
⠀⢸⣿⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⠉⢉⡛⢻⠛⣿⣿⣷⣾⣿⣿⣿⣿⣷⣄⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣿
⠀⢸⣿⣿⣇⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣟⣻⣿⣿⠁⠀⠀⠀⠀⠀⠀⡐⣶⣄⠀⠀⠉⠀⠀⠠⣼⣿⣿⣿⣿⣿⣿⣿⣴⣷⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠻⠿⢿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⣿⣿⣿⣿⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢿⡎⢻⣧⡀⠀⠀⠀⠀⠹⢿⣿⣿⣿⠟⠹⠏⣿⡯⠀⠀⠈⢿⣿⠿⣿⣿⣿⡇⠀⠀⠀⠈⠛⣿⣿⣿⣬⣿⣿⣿⡿⣿⣿⣿⣿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣿⣿⣿⣿⣿⣿⣯⣽⣿⣷⣶⠀⠀⠐⣄⠀⠀⠀⠁⠀⠹⡇⠰⠄⠀⠀⠀⣀⡟⠁⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣦⣈⣿⣿⣿⡀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⡟⠃⠈⠙⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣿⠀⠀⢿⠁⠀⠀⠀⠀⢀⡀⠘⠛⠛⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⠀⠀⠈⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠁⠘⢸⣿⣧⡀⣠⣤⠀⠸⢳⠂⠀⢸⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡿⠿⠿⠿⠻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠈⠉⠀⠀⢀⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣸⣿⣿⣿⣿⣿⡄⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⢙⣿⣿⣧⠀⡿⡻⠛⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⣶⣿⡿⠀⠀⠀⠀⢀⣿⣿⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣿⣿⣿⣿⣿⣿⡟⢀⣤⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣤⣭⣭⣿⣿⣿⠀⣿⣿⣿⢹⣿⣙⣛⠀⣿⣧⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢸⣿⡿⠃⠀⠀⠀⢀⣾⣿⣿⠇⡼⠟⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⡷⠨⣷⣄⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢻⣿⡏⢸⣿⠆⣸⠇⣿⣇⢀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢻⣿⠁⠀⠀⠀⠀⢰⣿⣿⣿⡄⠉⢀⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⡿⠅⠉⠉⠀⠀⣏⠉⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣧⣈⠙⠇⠀⠀⠀⠀⠀⠟⠟⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠿⠯⠀⢀⠀⠐⠀⢸⣿⣿⣿⣇⡀⣾⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠏⠀⠀⠀⠀⠀⠀⡿⠗⣻⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠒⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⠛⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠈⠂⠀⠀⠀⠁⠀⠀⠀⠻⢿⣿⣿⣧⣜⠘⣿⣿⣿⣅⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢻⣿⣿
⠀⢻⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⢹⣿⣿⣿⣤⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡿⣙⣿⣿
⠀⠘⣿⣿⣿⢨⣥⣭⣿⣿⣽⣿⣿⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠋⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣿⣇⣤⣄⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡛⢽⣿
⠀⠀⢻⣿⣿⢸⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⢫⣿⣿⣿⣯⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡄⠰⣿
⠀⠀⠀⢻⣿⣄⣉⣉⣉⣉⣩⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢶⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣦⠻⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⢸
⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⢿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⢼⣿⡧⣿⢩⣬⢻⠩⠌⢿⣡⣼⠥⢽⡅⣭⢹⡏⣥⣽⡏⡤⢩⣿⣇⣛⠻⡹⡟⣉⠡⢽⢨⣽⠩⠌⣿⣡⡌⣥⢹⣿⣿⢈⢿⢣⢸⡯⠬⣿⢩⣼⠸⢫⡏⠥⢹⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣌⣛⣡⣿⢘⣋⣾⣜⣛⣿⣿⣧⣛⣽⣇⣛⣸⣇⣿⣿⢃⣀⣹⣿⣟⣛⣡⡷⢱⣏⣛⣸⣞⣻⣜⣛⣿⣿⣇⣿⣼⣿⣿⣼⣄⣿⣸⣜⣫⣿⣸⣿⣸⣎⣧⣛⣻⣏⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⢛⡛⡟⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⠟⣿⡟⣿⣷⣶⣾⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣌⡛⡇⣴⡆⡿⠒⣺⡇⣴⡇⠒⢸⣿⣧⠻⣴⠹⢸⢡⣶⢸⣧⣶⣿⡇⣶⣼⡏⡏⡘⢃⣿⡇⣶⡄⡏⠒⠊⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣯⣭⣥⣧⣿⣧⣧⣭⣼⣧⣿⣧⣭⣽⣿⣿⣤⣿⣧⣿⣦⣭⣼⣿⣿⣿⣧⣭⣼⣿⣼⣧⣼⣿⣧⣭⣤⣧⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⡟⣿⣿⣿⡟⡛⣿⢛⢿⢟⡻⡟⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⠘⣒⢸⢰⡆⣿⣟⣻⣿⢸⢸⡇⡇⡜⢧⣿⡿⢣⡇⢿⢾⡿⣡⡿⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣉⣾⣶⣾⣾⣷⣿⣿⣿⣏⣼⣶⣶⣷⣋⣾⣿⣷⣶⣾⣶⣾⣶⣶⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣏⢹⡍⡉⠙⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣷⣾⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⡿⠿⡛⠛⠛⠋⠍⠉⠉⠻⠂⣀⣀⣀⣀⣀⣀⣀⣘⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⢟⠛⠛⠋⠉⠉⠉⠻⣃⣀⣀⣀⣀⣀⣀⣤⣬⣥⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⡿⢻⠛⠻⢿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠛⢿⠏⠉⠉⠀⢀⣀⣀⣀⣨⣥⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣧⣤⣥⣦⣤⣿⠖⣀⣀⣈⣠⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠃⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⢿⣿⣿⣧⣥⣤⣄⣀⣀⣀⣀⣀⡀⠐⠈⠉⠉⠁⠀⠀⠀⠉⠡⠄⠀⠀⠿⠏⠀⡅⢼⠁⠸⠠⠌⠤⡍⠤⢹⠸⢸⢨⡌⡄⢜⠀⢹⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⡇⣘⢂⣄⣈⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣅⠀⠀⠈⠀⠀⠀⢀⣤⣤⣀⣀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠉⠀⠈⢈⡁⠁⠈⠠⠬⠬⠭⠭⠭⢉⠩⠭⢭⣭⣭⣭⣭⣭⣭⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣦⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣄⣀⣀⣀⠀⠈⠉⠩⠌⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⡯⠉⠍⡉⠙⣿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣷⣾⣶⣷⣶⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇⢂⣀⡀⠀⠀⠈⠉⠉⠉⠰⠈⠉⠉⠉⠉⠉⠉⠙⠋⡍⠋⠉⠉⠉⠉⠉⠁⠀⣐⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣐⣀⣀⣀⣀⣀⣀⣀⣀⣨⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⡟⠻⠛⠛⢻⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣯⣤⣥⣦⣤⣿⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⢡⣄⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⠐⠂⠀⠀⠉⠉⠉⠉⠉⠉⠰⠈⠉⠉⠉⠉⠉⠉⠉⠉⠍⠛⠛⠛⠛⠛⠛⠛⠛⢋⠛⠛⠛⠛⠛⠛⠛⠛⢛⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢛⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⢿⢿⢿⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣇⢂⣄⡈⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 3263

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/07/29/windows-in-china/#comments
    Gemini version at gemini://gemini.techrights.org/2022/07/29/windows-in-china/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.29.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Microsoft_Windows_in_Chinese_Desktops/Laptops_Down_to_80%_(Hence_Microsoft
Started_Blocking_GNU/Linux_From_Even_Booting,_as_China’s_Lenovo_Demonstrates)⠀✐


Posted in Asia, Microsoft, Windows at 7:27 am by Dr. Roy Schestowitz


Background: Windows_Has_Had_a_Very_Tough_Year_(That’s_Why_Microsoft_Starts_to
Block_GNU/Linux_With_‘Secure’_Boot) | Antitrust_Action_Against_Microsoft_is
Well_Overdue | Microsoft’s_Crimes_Against_the_Competition,_Notably_BSD_and_GNU/
Linux,_Persist_Albeit_Disguised_as_‘Security’_(UEFI_‘Secure’_Boot,_TPM,
Pluton…)


Minutes ago: (Source)


                      🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇china-windows⦈_
 Windows loses its grip on the biggest market; the reasons for migrating away
 from Microsoft are both control and security; furthermore, all countries can
                 realise those benefits by ditching Microsoft


Summary: China’s official policy is that it'll_migrate_away_from_Windows; so
far this year the effect can be seen and Microsoft seems to have responded by
technical sabotage


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣟⡛⠻⣿⣿⣿⣿⣿⣿⢻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡟⣿⣿⣿⣿⣿⣿⣿⡿⣛⢻⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡷⡏⠐⠊⣇⠒⢾⠘⢵⡆⣾⢱⣶⢹⢰⣶⢹⣿⡇⣿⣿⢸⣧⣶⣼⠃⠒⢸⢠⣾⠖⡂⡇⣶⡇⡇⣶⣾⡇⠶⢰⣿⣧⣉⢻⡸⡏⣆⠒⢶⢰⡏⠒⠊⡇⣶⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣯⣭⣴⣷⣬⣭⣯⣭⣼⣼⣦⣧⣽⣮⣭⣾⢨⣭⣾⣿⣷⣬⣭⣾⣧⣭⣼⣧⣭⣽⣼⣿⣬⣥⣷⣭⣧⣧⣿⣿⡧⠭⢽⣿⣯⣭⣼⠇⣼⣯⣭⣼⣬⣵⣭⣽⣧⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡏⢿⣿⠉⡿⠿⢿⡿⠿⣿⡿⢿⠿⢿⠟⢿⣿⡏⣭⣹⠹⠿⢿⠿⠿⣿⠿⢿⠿⢿⣿⣿⢋⣭⣹⠹⠿⣿⢹⠿⠿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡜⢃⡇⡟⣩⢸⣧⣿⣏⡐⡇⣉⣈⡇⣿⣿⣷⣬⢹⢰⣿⢸⢋⡁⣿⢸⡇⢈⣁⣿⣧⢻⣿⣿⢸⣿⢸⢸⢸⣿⢸⢋⡥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣾⣷⣷⣶⣾⣿⣿⣿⣿⣾⣶⣾⣷⣾⣿⣷⣶⣾⣾⣿⣾⣶⣶⣿⣾⣿⣶⣶⣿⣿⣷⣶⣾⣾⣿⣾⣾⣾⣿⣾⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢹⠟⢿⡿⠻⣿⣿⣿⣿⢹⢿⡿⡏⢿⡿⣿⣯⡍⡟⣭⢻⣭⢽⣭⡍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢸⠁⣂⣿⣿⣿⣧⣼⣿⢸⡘⠃⡇⡏⢱⣿⠋⠐⣇⠛⣸⠃⠚⠋⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣠⣌⣖⣄⣽⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣘⠛⠛⠛⠛⠛⠿⠿⠿⠿⣛⠻⠿⠟⠛⠛⠛⠛⠛⠛⢩⠛⠛⠛⠛⠛⠛⠛⠛⠛⢋⠛⠛⠻⠿⠿⠿⠿⠿⠿⠟⠻⠿⠿⠿⠿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣀⣀⣀⣈⣀⠉⠙⠛⠻⠿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⣀⠉⢉⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢍⠍⣋⠋⢿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⠿⠿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣾⣶⣷⣷⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠃⠈⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣾⣿⡆⠀⠀⠀⣿⣏⠉⡅⢨⠍⠉⠀⡝⢡⡝⢩⠉⠉⡏⠉⠉⢩⢨⡍⢉⡉⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⡿⡿⠿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠉⠋⠁⠀⢀⣦⣿⣷⣶⣷⣶⣶⣶⣶⣾⣶⣾⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣟⣂⣄⣔⣄⣽⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣤⣀⠀⠀⠀⣠⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡉⢉⢉⠉⢿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣶⣶⣷⣷⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢿⠿⠿⠿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣘⣀⣐⣄⣽⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠁⣀⣈⢡⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡟⣘⠛⠛⠛⠛⠛⠛⠛⠛⠛⣋⠛⠛⠛⠿⠿⠿⠿⠿⠿⠛⠿⠿⠿⠿⠿⣿⣿⠿⠿⢛⠻⠿⠿⠿⠿⠿⠿⠿⠿⢛⠻⠛⠛⠛⠛⠛⠛⠛⠋⠩⠍⠁⣀⣠⣤⣶⣾⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡗⡀⠒⠒⠒⠒⠒⠒⠒⠒⠒⢠⠐⠂⠀⠀⠀⠀⠀⠀⠀⠭⠀⠀⠀⠀⣴⣿⠋⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠉⠉⣹⣿⣿⣿⠋⠉⠩⠌⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠉⠋⠉⢏⠒⠉⠉⠉⠉⠉⠉⠉⠉⠉⠐⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⢩⣿⡟⠉⠉⠉⠉⠉⠡⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⣰⣾⡿⠋⠉⠉⠉⠉⠉⠉⠑⠊⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣶⣶⣶⣾⣶⣾⣶⣾⣶⣾⣾⣶⣾⡖⡛⢶⣾⣶⣾⣾⣶⣾⣶⡞⡒⣾⣿⣿⣷⣶⣾⣶⣾⡖⡚⠷⣾⣶⣾⣶⣶⣾⣶⡾⡓⡾⣷⣾⣶⣶⣾⣶⣾⣿⡿⠿⣾⣷⣶⣶⣶⣾⣶⣾⠓⠾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠄⢃⣾⣿⣿⣿⣿⣿⣿⠿⢠⣿⣿⣿⣿⣿⣿⣿⣿⠿⠠⠑⣼⣿⣿⣿⣿⣿⣿⡿⠰⠑⣴⣿⣿⣿⣿⣿⣿⡿⠻⠙⣰⣿⣿⣿⣿⣿⣿⡿⠡⠘⣰⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⢡⣿⣿⣿⣿⣿⣿⣿⣏⣠⣿⣿⣿⣿⣿⣿⣿⣿⣏⡄⢡⣼⣿⣿⣿⣿⣿⣿⣏⡅⢅⣼⣿⣿⣿⣿⣿⣿⣟⡁⠍⣼⣿⣿⣿⣿⣿⣿⣿⣁⠌⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠩⢱⣿⣿⣿⣿⣿⣿⣿⡟⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⢳⣾⣿⣿⣿⣿⣿⣿⡿⠃⡙⣾⣿⣿⣿⣿⣿⣿⡿⠉⢙⣾⣿⣿⣿⣿⣿⣿⡟⠃⡙⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠩⢀⣡⣿⣿⣿⣿⣿⣿⣿⠣⣼⣿⣿⣿⣿⣿⣿⣿⣿⣏⢀⣀⣻⣿⣿⣿⣿⣿⣿⠧⠁⣠⣶⣿⣿⣿⣿⣿⣿⡿⢁⢰⣾⣿⣿⣿⣿⣿⣿⣟⡁⢂⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣍⢿⡏⠏⠏⠙⡛⢛⠹⠛⠻⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣭⠹⣿⢹⡏⢛⠋⠛⠛⠟⡛⠟⠟⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣿⣿⣼⣼⣤⣧⣦⣴⣤⣦⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⣿⣤⣴⣼⣤⣦⣿⣤⣴⣴⣤⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 3360

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.29.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_29/07/2022:_‘Linux’_Foundation_is_Greenwashing_Microsoft⠀✐


Posted in News_Roundup at 1:37 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Audiocasts/Shows
          o Applications
          o Instructionals/Technical
          o Games
    * Distributions_and_Operating_Systems
          o Fedora_Family_/_IBM
          o Canonical/Ubuntu_Family
          o Devices/Embedded
          o Open_Hardware/Modding
          o Mobile_Systems/Mobile_Applications
    * Free,_Libre,_and_Open_Source_Software
          o Web_Browsers
                # Mozilla
          o SaaS/Back_End/Databases
          o Programming/Development
                # Shell/Bash/Zsh/Ksh
                # Rust
          o Standards/Consortia
    * Leftovers
          o Hardware
          o Health/Nutrition/Agriculture
          o Proprietary
          o Linux_Foundation
          o Security
                # Integrity/Availability/Authenticity
                # Privacy/Surveillance
          o Defence/Aggression
          o Transparency/Investigative_Reporting
          o Environment
                # Energy
                # Wildlife/Nature
          o Finance
          o AstroTurf/Lobbying/Politics
          o Censorship/Free_Speech
          o Civil_Rights/Policing
          o Internet_Policy/Net_Neutrality
          o Monopolies
                # Patents
                # Software_Patents
                # Copyrights
    * Gemini*_and_Gopher
          o Personal
          o Politics
          o Technical
                # Science
                # Internet/Gemini
                # Programming
    * § GNU/Linux⠀➾


          o § Audiocasts/Shows⠀➾


                # ⚓ Video ☛ Welcome_to_SCaLE_19x_–_Invidious⠀⇛


                       Preview of just some of the coverage coming to
                       LearnLinuxTV for #SCaLE19x.


                # ⚓ Video ☛ Valve’s_a_distro_maintainer,_now._They_need_a
                  “patch_Tuesday.”_–_Invidious⠀⇛


                # ⚓ Video ☛ Unlocking_the_Steam_Deck_–_Invidious⠀⇛


                       This shows how to unlock the steam deck and the
                       HOLO OS that comes with it. This makes the ENTIRE
                       OS writable and so you can install any program that
                       you want.


                # ⚓ Video ☛ Sysadmins_are_Super_Heroes!_(System_Administrator
                  Appreciation_Day_2022)_–_Invidious⠀⇛


                       System Administrators keep our servers running, and
                       they do this so well that you might not even be
                       aware that there were ever problems that needed
                       solving. On System Administrator Appreciation Day,
                       we celebrate the people out there that spend
                       countless hours installing patches, resetting
                       passwords, monitoring reliability, saving their
                       companies from the latest cyber threats, and more!


                # ⚓ Video ☛ Enterprise_Linux_Security_Episode_37_–_System
                  Administrator_Appreciation_Day_2022_–_Invidious⠀⇛


                       System Administrators are the heroes we need, and
                       in today’s episode of Enterprise Linux Security, we
                       celebrate Sysadmin Day 2022 and the many people
                       that work tirelessly to keep our servers running.


          o § Applications⠀➾


                # ⚓ Its FOSS ☛ 7_Docks_to_Customize_Your_Linux_Desktop_in
                  2022⠀⇛


                       A dock has been an important part of the Linux
                       desktop experience for decades. It provides a handy
                       way of quickly accessing your favorite, frequently
                       used applications.


                       Unfortunately, the popular desktop environment
                       GNOME doesn’t provide a dock.


                       Fret not. You can always install a Docking
                       application on your Linux desktop.


                       And this is not just limited to GNOME. If you don’t
                       like the dock provided by your distribution and the
                       desktop environment, you can replace it with
                       another one of your choices.


                       Speaking of choices, let me share some of my
                       favorite docks that will help you change the
                       default look of your desktop Linux.


                # ⚓ Make Use Of ☛ The_Top_10_Most_Popular_AppImage_Apps_for
                  Linux⠀⇛


                       
                       It may not be as popular as Snap or FlatPak, but
                       there are some great AppImage Linux apps.


                       While most of you probably know of Flatpaks and
                       Snaps, you may not have heard much about AppImage.
                       It might even surprise you to know that it’s been
                       around quite a bit longer than the other Linux
                       universal package formats.


                       When apps are released as Snaps or Flatpaks,
                       there’s usually accompanying articles, videos, and
                       social media posts, whereas when apps release as
                       AppImage, there seems to be little to no fanfare.


                # ⚓ Linux Links ☛ Best_Free_and_Open_Source_Alternatives_to
                  Apple_Dictionary⠀⇛


                       
                       Apple Dictionary is a small utility that lets users
                       easily get definitions of words and phrases from a
                       variety of sources.


                       While Apple Dictionary free to use, it’s
                       proprietary software and not available for Linux.
                       We recommend the best free and open source
                       alternatives.


          o § Instructionals/Technical⠀➾


                # ⚓ uni Toronto ☛ What_ZFS_‘individual’_and_‘aggregated’_IO
                  size_statistics_mean⠀⇛


                       On all of the machines that I can readily get
                       statistics for, individual IO seems more common by
                       count and to be responsible for more IO size than
                       aggregated IO. However, aggregated IO is often
                       large enough in both count and especially size to
                       matter; it’s clear to me that you can’t just ignore
                       aggregated IO. Asynchronous writes seem to
                       especially benefit from aggregation. All of this is
                       on SSD based pools, often using large files, and I
                       don’t understand how the non-rotating aggregation
                       limit is interacting with the 128 KB default ZFS
                       recordsize.


                # ⚓ TecMint ☛ Installation_of_Manjaro_21_(GNOME_Edition)
                  Desktop⠀⇛


                       Manjaro 21, codenamed ‘Ruah‘ is the latest release
                       of Manjaro which is a Linux distribution based on
                       Arch Linux. It features major improvements and
                       enhancements including new versions of desktop
                       environments – Xfce, GNOME, and KDE.


                       In this guide, we walk you through the installation
                       of Manjaro 21 GNOME Edition.


                # ⚓ TecMint ☛ Useful_Tips_For_VLC_Player_Users_in_Linux
                  Desktop⠀⇛


                       The VLC media player is arguably one of the most
                       widely used media players. It is a multi-platform
                       media player and framework that supports a wide
                       range of multimedia files and streaming protocols.


                       In this tutorial, we will show you how to install
                       VLC and examine some of the tips you can use to
                       make the most out of the popular and feature-rich
                       VLC media player on the Linux desktop.


                # ⚓ TecMint ☛ Ebook:_Introducing_Learn_Linux_In_One_Week_and_Go
                  from_Zero_to_Hero⠀⇛


                       After the success of our RHCSA / RHCE and LFCS /
                       LFCE certification books, we are now happy to
                       present “Learn Linux In One Week”.


                       This ebook will walk you through the beginnings of
                       Linux and the contributions of Linus Torvalds and
                       Richard Stallman to performing secure file
                       transfers over a network. You’ll learn how to
                       manage users and groups, and to write shell scripts
                       to help automate system administration tasks.


                # ⚓ ID Root ☛ How_To_Install_Barrier_on_Ubuntu_22.04_LTS_–
                  idroot⠀⇛


                       In this tutorial, we will show you how to install
                       Barrier on Ubuntu 22.04 LTS. For those of you who
                       didn’t know, The barrier is free and open-source
                       making it easy to share a mouse & keyboard, over a
                       local network, between machines running Windows,
                       Linux, and macOS. The barrier was forked from
                       Symless’s Synergy 1.9 codebase. Synergy was a
                       commercialized reimplementation of the original
                       CosmoSynergy written by Chris Schoeneman.


                       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 Barrier 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.


                # ⚓ ByteXD ☛ How_to_Use_Steam_Proton_&_ProtonDB_to_Play_Games
                  on_Linux⠀⇛


                       Playing games on Linux has never been easier than
                       it is now because of Steam Play support for Linux
                       and tools like Steam Proton.


                       Previously there was no way for Linux users to play
                       Windows games unless developers had developed a
                       Linux native version. But, with Steam Proton, Linux
                       users can download and play Windows games.


                       Some of these games will run natively and some will
                       need minor tweaks to run on Linux based system.
                       Steam Proton has an associated community website
                       that displayed data collected from users about the
                       compatibility status of different games with
                       Proton. Users share exactly the system
                       configurations they used to run a game so you can
                       find out if you are in a position to try and run a
                       game with tweaks or not.


                # ⚓ ID Root ☛ How_to_Install_Citra_Nintendo_3DS_Emulator_on
                  Ubuntu_22.04_LTS_–_idroot⠀⇛


                       In this tutorial, we will show you how to install
                       Citra Nintendo 3DS Emulator on Ubuntu 22.04 LTS.
                       For those of you who didn’t know, Citra is an
                       experimental open-source Nintendo 3DS emulator/
                       debugger written in C++. This emulator has been
                       developed keeping in mind that it has portability
                       since it has actively maintained compilations for
                       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 Citra Nintendo 3DS Emulator 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.


                # ⚓ Citizix ☛ How_to_create_a_Digitalocean_Managed_Database
                  cluster_using_terraform⠀⇛


                       Terraform is an open-source, infrastructure as
                       code, software tool created by HashiCorp. Users
                       define and provide data center infrastructure using
                       a declarative configuration language known as
                       HashiCorp Configuration Language, or optionally
                       JSON.


                       Terraform codifies cloud APIs into declarative
                       configuration files. It allows you to compose
                       infrastructure as code in a Terraform file using
                       HCL to provision resources from any infrastructure
                       provider.


                # ⚓ Linux.org ☛ VirtualBox_Explored_(Part_1)_|_Linux.org⠀⇛


                       Many people that use VirtualBox, at some point come
                       across a problem they have not encountered before.


                       In this article, I want to cover as many issues
                       that may arise and how to fix them. This may be hum
                       drum to some, but I’m sure there may be some
                       tidbits in here that can be useful. The first part
                       of the article is more basic than the second part.


                # ⚓ Video ☛ How_to_install_LeoCAD_on_Pop!_OS_22.04_–
                  Invidious⠀⇛


                       In this video, we are looking at how to install
                       LeoCAD on Pop!_OS 22.04.


                # ⚓ Linux Made Simple ☛ How_to_install_Godot_Game_Engine_on_a
                  Chromebook_in_2022⠀⇛


                       Today we are looking at how to install Godot Game
                       Engine on a Chromebook. Please follow the video/
                       audio guide as a tutorial where we explain the
                       process step by step and use the commands below.


                # ⚓ Trend Oceans ☛ How_to_install_and_start_an_SSH_server_in
                  Fedora_36_–_TREND_OCEANS⠀⇛


                       Once you have installed the Fedora system on your
                       VirtualBox or hardware, there may be a possibility
                       you will access your system remotely through the
                       SSH service, and when you try to access it, you may
                       find the error “ssh: connect to host 192.168.40.120
                       port 22: No route to host.”


                       And when you try to check the status of the SSH
                       service in your Fedora, you may get another error:
                       “Unit ssh.service could not be found.”


                       If you are also facing a similar kind of issue or
                       you want to install an OpenSSH server on Fedora,
                       then this article can be helpful to fix the above
                       issue.


                # ⚓ Linux Shell Tips ☛ How_to_Swap_Contents_of_Two_Files_in
                  Linux⠀⇛


                       The handy tools and commands provided by the Linux
                       operating system make it possible to achieve/
                       accomplish numerous file manipulation objectives.
                       Under Linux file management, you might need to swap
                       two files for one reason or another.


                       When we talk of swapping two files on a Linux
                       operating system environment, it does not exactly
                       translate to swapping/exchanging the location of
                       these two files but their actual content.


                       To better understand the objective of this
                       tutorial, consider the existence of the following
                       files under a Linux operating system environment.


                # ⚓ Linux Shell Tips ☛ How_to_Edit_Binary_Files_on_Linux
                  Command_Line⠀⇛


                       If a file stores data in contiguous bytes format, a
                       program trying to read this file will need to be
                       instructed on how to read it since such files do
                       not directly define a compatible method for reading
                       their associated content.


                       This type of file is called a binary file. Opening
                       such a file on a normal text editor program will
                       only display unreadable characters. It is because
                       binary data store data as bytes and not as textual
                       characters.


                       The headers of a binary file are accompanied by an
                       instruction set that reveals how its stored data
                       should be read. Since binary files can store any
                       data type, we can broadly classify all file types
                       as either binary or text.


                # ⚓ FOSSLinux ☛ How_to_install_LXDE_GUI_in_Debian_11_Bullseye_|
                  FOSS_Linux⠀⇛


                       The LXDE (Lightweight X11 Desktop Environment) is a
                       program that aims to create a lightweight and fast
                       desktop environment. This software is a meta-
                       package that relies on the LXDE’s core and
                       recommended components such as lxde-core,
                       lxappearance, lxinput, lxsession-edit, gpicview,
                       mousepad, lxterminal, galculator, lxrandr, and
                       xarchiver. LXDE is optimized for devices with
                       limited resources, including older resource-
                       constrained PCs, newer netbooks, and other compact
                       computers.


                       This tutorial guide will illustrate how to install
                       LXDE on an existing Debian 11 Bullseye
                       installation. Therefore, to learn more, keep
                       reading this article guide.


                # ⚓ FOSSLinux ☛ How_to_install_Thunar_file_manager_on_Debian_|
                  FOSS_Linux⠀⇛


                       Thunar is an X11 file manager based on the GTK+ 2
                       widget toolkit. Since version 4.4, it has been the
                       primary file manager in Xfce. Thunar is a
                       contemporary, lightweight file manager that ships
                       with the Xfce desktop environment as the default
                       file manager. It was created to be quicker and more
                       responsive than existing file managers for Linux
                       computers. Thunar is a simple and easy-to-use user
                       interface that may be expanded with plugins.


                       This tutorial guide will demonstrate how to
                       download, install, set up, and use the Thunar file
                       manager on Debian 11 Bullseye. Below are the
                       essential features of Thunar that you ought to
                       know.


                       On Debian 11, there are three ways to install the
                       Thunar file manager. Apt-get, apt, and aptitude.
                       Each method will be described in detail in the
                       sections that follow. You may select one of them
                       that suits you more.


                # ⚓ UNIX Cop ☛ How_to_kill_all_Python_processes_on_Linux⠀⇛


                       This tutorial guide will demonstrate how to
                       download, install, set up, and use the Thunar file
                       manager on Debian 11 Bullseye.


                # ⚓ Ubuntubuzz ☛ Fixing_Telegram_Opens_PDFs_with_Wrong
                  Applications⠀⇛


                       When you receive PDF files in Telegram Desktop, you
                       might be disappointed when it opens in the wrong
                       application not in your PDF reader. For example, in
                       Kubuntu, it wrongly opens PDF with LibreOffice
                       Draw, while it should be Okular. In other cases, it
                       may instead opens PDF with web browser. We will
                       show you how to fix this issue quickly.


          o § Games⠀➾


                # ⚓ GamingOnLinux ☛ GE-Proton_7-27_has_the_Halo_Infinite
                  campaign_and_videos_working_on_Steam_Deck_&_Linux⠀⇛


                       Recently I showed off Halo Infinite running quite
                       nicely online on the Steam Deck and now GE-Proton
                       7-27 that just went up makes the process even
                       smoother and the campaign and videos now work too.
                       This is another great step forwards.


                # ⚓ GamingOnLinux ☛ Wine_manager_app_Bottles_makes_rolling_back
                  configs_real_easy⠀⇛


                       Bottles is the free and open source app that allows
                       you to easily manage Wine, the Windows
                       compatibility layer on Steam Deck and Linux.
                       Another new version is live, with a whole new
                       versioning system to help you roll back changes.


                # ⚓ Boiling Steam ☛ Starship_Troopers:_Terran_Command._Finally
                  a_Great_Video_Game_After_the_Movie!_–_Boiling_Steam⠀⇛


                       Starship Troopers is back! While I’m probably more
                       of a fan of Robocop when it comes from the same
                       director, Paul Verhoeven, I have to admit that
                       Starship Troopers was brilliantly made back when it
                       was released. Fighting aliens on other planets is
                       one thing (Avatar anyone?), but when the enemy is a
                       truly insect-like alien, things get scary really
                       fast as swarms of them attack your human forts and
                       dismember everyone in sight. In a sense, this is
                       the ultimate merciless enemy: insects have no
                       remorse, no feelings, and no individuality.
                       Starship Troopers demonstrates that humans would
                       fare very poorly against such adversaries even with
                       superior firepower and technology.


                # ⚓ Nikita Prokopov ☛ GMTK_Game_Jam_2022:_Dice_Out⠀⇛


                       Using a game engine helps a lot. It solves a lot of
                       problems that you don’t want to deal with in 48
                       hours or, probably, never.


                       I chose Godot and liked it a lot: Python-like
                       language seems like a better fit for casual
                       scripting than C#, and apparently it has much
                       better HTML export than Unity.


                # ⚓ GamingOnLinux ☛ Voodoo_Detective_is_a_Monkey_Island
                  inspired_point-and-click_adventure⠀⇛


                       One we apparently missed that arrived with Native
                       Linux support back in May, Voodoo Detective is a
                       Monkey Island inspired point-and-click adventure
                       from Short Sleeve Studio. It has a Very Positive
                       user rating on Steam, so seems like it’s worth a
                       highlight if you’re after something new.


                # ⚓ GamingOnLinux ☛ Detective_adventure_Lord_Winklebottom
                  Investigates_is_out_now⠀⇛


                       Cave Monsters has released their detective
                       adventure game Lord Winklebottom Investigates with
                       Native Linux support. Inspired by Agatha Christie
                       and Sherlock Holmes, you will find a classic
                       British murder mystery set in the 1920s. Setting
                       itself apart, it features a quirky animal cast with
                       the protagonist being a giraffe detective.


                # ⚓ GamingOnLinux ☛ Proton_Experimental_brings_support_for
                  Unravel_Two,_fixes_up_Civilization_IV⠀⇛


                       Valve has released the latest update to Proton
                       Experimental, the special version of Proton you can
                       use that has the latest updates bringing more game
                       compatibility to Linux and Steam Deck.


                # ⚓ GamingOnLinux ☛ You_can_now_play_DOOM_as_the_Cat_from
                  Stray⠀⇛


                       Yes this is a real thing, DOOM modders will quite
                       literally do anything and I’m here loving it. You
                       can now play DOOM as the cat from Stray.


                # ⚓ GamingOnLinux ☛ Just_King_blends_Vampire_Survivors_action
                  with_Slay_the_Spire_progression⠀⇛


                       Just King is going to be my next game to be fixated
                       on. It’s ridiculously cheap and offers up gameplay
                       where you keep wanting to come back for more. Note:
                       personal purchase.


                # ⚓ GamingOnLinux ☛ itch.io_has_another_Creator_Day_live_with
                  100%_going_to_developers⠀⇛


                       The game store itch.io is running another Creator
                       Day, this is where they don’t take any cut from
                       developers. Developers will then get all of the
                       proceeds from each sale (minus any required fees
                       and taxes).


                # ⚓ GamingOnLinux ☛ OUTRIDERS_officially_gets_a_Playable_Steam
                  Deck_rating⠀⇛


                       Looking for your next RPG-shooter hybrid with
                       online co-op? OUTRIDERS from People Can Fly
                       recently released the WORLDSLAYER expansion and
                       it’s now actually Playable on the Steam Deck (and
                       Linux desktop too). Previously it had problems with
                       Easy Anti-Cheat but that is no longer an issue.


    * § Distributions and Operating Systems⠀➾


          o § Fedora Family / IBM⠀➾


                # ⚓ DaemonFC (Ryan Farmer) ☛ Fedora_removes_Creative_Commons
                  CC0-licensed_software;_leaves_Fraunhofer_AAC._Bonus:_Use_Opus
                  instead_of_AAC._–_BaronHK’s_Rants⠀⇛


                       Fraunhofer is a member of the MPEG-LA patent troll,
                       and other patent trolls. It is a patent troll.


                       They are giving you software and threatening to see
                       you in court if you use it without paying a ransom
                       to someone. This is blackmail.


                       You may remember Fraunhofer from the late 90s and
                       early 2000s threat letters sent out around the time
                       that Napster made MP3 popular, which said that they
                       intended to collect royalties from or sue people
                       for using MP3 or offering people encoders (such as
                       LAME) or decoders which could play the files back.


                       They specifically demanded “$25,000 per year” in
                       one case, from one open source MP3 encoder project
                       called 8hz MP3, knowing it would ruin them, and
                       that they would decide to shut down the project
                       instead.


                       (Although the article plays up MP3 “Pro” and
                       Microsoft WMA, nobody took them seriously. The only
                       serious usage WMA ever got was some music “stores”
                       that failed and destroyed your entire library with
                       the Digital Restrictions Malware when they did.
                       Walmart even had one!)


                       This resulted in a number of responses.


          o § Canonical/Ubuntu Family⠀➾


                # ⚓ HowTo Geek ☛ What’s_New_in_Linux_Mint_21_“Vanessa”⠀⇛


                       
                       Linux Mint 21, codenamed “Vanessa,” is a major
                       update coming to Mint users in summer 2022. The
                       first beta release was on July 14, 2022. Here’s a
                       rundown of what’s new in this version—the changes,
                       improvements, and new features.


                       Vanessa is the first release of the Linux Mint 21
                       “V” series, having a long-term support plan lasting
                       till 2027. As you’ll see, the coming improvements
                       and new updates make the latest Linux Mint more
                       efficient and advanced than its predecessors.


          o § Devices/Embedded⠀➾


                # ⚓ CNX Software ☛ SolidRun_introduces_SolidWAN_software-
                  defined_edge_network_hardware_with_NXP_LX_16-core_Cortex-A72
                  SoCs⠀⇛


                       SolidRun has launched two SolidWAN Linux-based
                       system-level solutions for software-defined wide
                       area networks and network security applications
                       with the SolidWAN Single LX2162 based on NXP LX2162
                       16-core Cortex-A72 SoC designed for small offices
                       (SoHo) and SMBs, and the SolidWAN Dual LX2160
                       equipped with two NXP LX2160A 16-core Cortex-A72
                       networking processors targetting enterprise and
                       edge data center applications.


                       The compact SolidWAN LX2162A features SolidRun LX2-
                       Lite system-on-module with the NXP CPU, memory, and
                       storage, and targets applications such as Secure
                       Access Service Edge (SASE) or WAN Edge Gateways in
                       small offices or home offices. Alternatively,
                       SolidRun also offers the earlier quad-core Clearfog
                       CN9130 Base and Clearfog CN9130 Pro fanless
                       solutions with 1GbE/2.5GbE/10GbE software-defined
                       dedicated Ethernet ports that are now part of the
                       SolidWAN offerings. More details about LX2162A can
                       be found on SolidRun’s documentation website, but
                       somehow there’s no info about the software yet.


                # ⚓ Stacy on IoT ☛ Forget_sleep_and_wake;_it’s_time_to_embrace
                  ambient_mode⠀⇛


                       Forget binary sleep and wake. When we ask a fitness
                       tracker to measure heart rate or a battery-powered
                       earbud to have an always-on listen mode without
                       requiring a fresh charge every hour, we’re taking
                       advantage of ambient mode. As we are when we
                       leverage the face detection sensors on our phones
                       that wait until our face is detected before “waking
                       up” a primary processor for the heavy lifting of
                       facial recognition. Its use cases like these that
                       are driving the rise of “ambient mode” in
                       processors.


                # ⚓ Linux Gizmos ☛ SeeedStudio_launches_carrier_boards_for
                  Jetson_Nano/Xavier_NX/TX2_NX⠀⇛


                       SeeedStudio has unveiled the reComputer J101 and
                       J202 which are compatible with the 260-pin SODIMM
                       modules from NVIDIA. The company specified the J101
                       and the J202 feature a similar functional design
                       and the same size as the NVIDIA development kits.


                       According to the product page, the design of
                       reComputer J101 it’s based on the NVIDIA Jetson
                       Nano Developer Kit while the reComputer J202
                       mirrors the design of the NVIDIA Jetson Xavier
                       Developer Kit. 


                # ⚓ Ubuntu ☛ The_State_of_IoT_–_June_&_July_2022⠀⇛


                       Welcome to the June & July combined edition of the
                       monthly State of IoT series.


                       Let’s dive straight into the most prominent news
                       across the IoT landscape from the last two months.


          o § Open Hardware/Modding⠀➾


                # ⚓ Raspberry Pi ☛ Pico_PlayStation_MemCard⠀⇛


                       The goal of this project was to provide a solid
                       alternative at a very low price, says Daniele.
                       “Raspberry Pi Pico understands the protocol used to
                       communicate with memory cards and convinces the
                       PlayStation into believing an original memory card
                       is plugged in. Development boards, such as these
                       ones, were particularly interesting because they
                       were quite powerful yet very cheap, and allowed me
                       to set up my personal server to test all sorts of
                       applications.”


                # ⚓ Björn Wärmedal ☛ PICO-8_and_TIC-80⠀⇛


                       Now TIC-80 is open source. Well, at least the basic
                       version. There’s a PRO version too, though I don’t
                       know that I’d ever need it. The main problem is
                       documentation and, from an ideological standpoint,
                       opacity regarding guardianship. I’ve looked around
                       the website and have been left with questions.


                # ⚓ peppe8o ☛ MQTT_and_Raspberry_PI_Pico_W:_Start_with
                  Mosquitto_(MicroPython)⠀⇛


                       Raspberry PI Pico W brings connectivity to your
                       projects. Mosquitto is one of the most reliable,
                       simple and fast communications for IoT projects.
                       For this reason, MQTT and Raspberry PI Pico W will
                       surely give you great flexibility for your Smart
                       Things projects


          o § Mobile Systems/Mobile Applications⠀➾


                # ⚓ 9to5Google ☛ Pixel_6a_gets_day_one_update,_Android_13
                  coming_–_9to5Google⠀⇛


                # ⚓ Android Police ☛ Google_confirms_its_Game_Dashboard_is
                  coming_to_other_‘select_devices’_with_Android_13⠀⇛


                # ⚓ SamMobile ☛ Samsung_shows_everyone_who’s_the_king_of
                  Android_updates_–_SamMobile⠀⇛


                # ⚓ Notebook Check ☛ HarmonyOS_3:_Huawei’s_Android_alternative
                  promises_improved_battery_life,_responsiveness_and_new
                  features_–_NotebookCheck.net_News⠀⇛


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


          o § Web Browsers⠀➾


                # § Mozilla⠀➾


                      # ⚓ 9to5Linux ☛ Firefox_104_Enters_Beta_Testing_with_Two-
                        Finger_Swipe_Back/Forward_Gesture_on_Linux⠀⇛


                             Firefox 104 doesn’t look like a big release,
                             but it may be an important release for Linux
                             laptop users as it enables a long-anticipated
                             feature, namely a two-finger horizontal swipe
                             gesture to navigate forward and backward
                             using a touchpad, which now works out-of-the-
                             box without holding down the Alt key.


                             The two-finger swipe back/forward gesture was
                             available in the Firefox web browser since
                             version 4.0, which was released back in 2011
                             as the first 64-bit build for Linux, but you
                             needed to hold down the Alt key to use it.


                      # ⚓ Firefox_Nightly:_These_Weeks_In_Firefox:_Issue_121⠀⇛


          o § SaaS/Back End/Databases⠀➾


                # ⚓ Vincent Bernat ☛ Vincent_Bernat:_ClickHouse_SF_Bay_Area
                  Meetup:_Akvorado⠀⇛


                       Here are the slides I presented for a ClickHouse SF
                       Bay Area Meetup in July 2022, hosted by Altinity.
                       They are about Akvorado, a network flow collector
                       and visualizer, and notably on how it relies on
                       ClickHouse, a column-oriented database.


          o § Programming/Development⠀➾


                # ⚓ Matt Rickard ☛ Lisp_and_Spreadsheets⠀⇛


                       What if you could use a Lisp inside a spreadsheet?
                       Or another functional language? Or maybe even a
                       general purpose language?


                # ⚓ Seth Michael Larson ☛ Help_us_test_system_trust_stores_in
                  Python⠀⇛


                       If you’re an IT or software team that uses Python
                       along with corporate system certificates, an
                       internal CA, or internal PyPI repository: please
                       read on to help improve Python. If you know one or
                       more teams that fits this description: forward them
                       this article! We need lots of people to try the new
                       pip feature to test our implementation of system
                       trust stores in Python.


                # ⚓ Rlang ☛ Posit_–_Why_Rstudio_is_changing_its_name⠀⇛


                       For the past few years, Posit (formerly RStudio)
                       has been shifting from R-exclusive tooling to a
                       language agnostic ecosystem. Much to our enjoyment,
                       we’ve seen the RStudio IDE grow to be more Python-
                       friendly and the Posit data science ecosystem
                       become “A Single Home for R & Python.”


                # ⚓ Rlang ☛ RStudio_is_becoming_Posit⠀⇛


                       So while you will see our name change in a bunch of
                       places (including our main corporate website), we
                       are still continuing on the same path. That path
                       has widened as we have succeeded in the original
                       mission, and we are excited at the chance to bring
                       what we all love so much about the R community to
                       everyone.


                # § Shell/Bash/Zsh/Ksh⠀➾


                      # ⚓ OpenSource.com ☛ Fix_bugs_in_Bash_scripts_by_printing
                        a_stack_trace⠀⇛


                             No one wants to write bad code, but
                             inevitably bugs will be created. Most modern
                             languages like Java, JavaScript, Python,
                             etc., automatically print a stack trace when
                             they encounter an unhandled exception, but
                             not shell scripts. It would make it much
                             easier to find and fix bugs in shell scripts
                             if you could print a stack trace, and, with a
                             little work, you can.


                             Shell scripts can span multiple files, and
                             well-written code is further broken down into
                             functions. Tracing issues when something goes
                             wrong in a shell script can be difficult when
                             these scripts get large enough. A stack trace
                             that walks the code backward from the error
                             to the beginning can show you where your code
                             failed and give you a better understanding of
                             why so you can fix it properly.


                             To implement the stack trace, I use the trap
                             in the following manner at the beginning of
                             my script:


                             This example accomplishes a few things, but
                             I’ll address the second one, trap
                             ‘ERRO_LINENO=$LINENO’ ERR, first. This line
                             ensures the script traps all commands that
                             exit with a non-zero exit code (i.e., an
                             error), and saves the line number of the
                             command in the file where the error was
                             signaled. This is not captured on exit.


                # § Rust⠀➾


                      # ⚓ OpenSource.com ☛ Learn_Rust_by_debugging_Rust⠀⇛


                             In my previous article about rustup, I showed
                             you how to install the Rust toolchain. Well,
                             what good is the toolchain if you won’t be
                             using it to get more hands-on with Rust?
                             Learning any language involves reading
                             existing code and writing a lot of sample
                             programs. That’s a good way to become
                             proficient in a language. However, there’s a
                             third way: debugging code.


                             Learning through debugging involves trying to
                             compile a pre-written (buggy) sample program,
                             understanding the errors generated by the
                             compiler, fixing the sample code, and then
                             re-compiling it. Repeat that process until
                             the code successfully compiles and runs.


                             Rustlings is an open source project by the
                             Rust team that helps you learn Rust through
                             the process of debugging. It also provides
                             you with a lot of hints along the way. If
                             you’re a beginner to Rust and have either
                             started or completed reading the Rust book,
                             then rustlings is the ideal next step.
                             Rustlings helps you apply what you’ve learned
                             from the book, and move to working on bigger
                             projects.


          o § Standards/Consortia⠀➾


                # ⚓ Jim Nielsen ☛ HTML_Emails:_A_Rant⠀⇛


                       I’ve wanted to share these thoughts for a while,
                       but stitching them into a coherent piece of writing
                       seemed too much to overcome. However, with some
                       prodding I decided to go ahead and hit “publish”.


                       I’ve been in the world of HTML emails lately so the
                       wounds are still fresh — maybe too fresh. Perhaps
                       these are more feelings than thoughts. But I don’t
                       care, it’s how I feel.


                       Maybe you do too.


    * § Leftovers⠀➾


          o ⚓ Buttondown ☛ Information_camouflage⠀⇛


                 I do a lot of research for my job and over time built a
                 vocabulary for researching concepts. This one comes up a
                 lot so I figured I’d get it written down.


                 Information camouflage is when piece of information A has
                 a name similar to another, very different, much more
                 popular piece B. This makes searching for A difficult
                 because you always get results for B instead.


          o ⚓ Counter Punch ☛ Train_I_Ride,_Five_Coaches_Long⠀⇛


                 The change in the landscape is subtle as one travels from
                 Burlington to the New York suburbs. The woods and fields
                 of Vermont are occasionally interrupted by small and
                 smaller towns along the track, Indeed, it isn’t until one
                 is south of Greenfield, Massachusetts that industrial
                 structures and houses began to dominate the scenery. Even
                 then, there are still enough woods on both sides of the
                 train a passenger can ignore the impending aesthetic
                 dissonance that describes the dystopian reality of the
                 eastern seaboard. A similar phenomenon can be seen in the
                 passengers boarding at each stop. The styles become more
                 urban. Fades in the haircuts, a brutal razor’s edge taken
                 to the skull in an attempt to reflect or blend in to an
                 urban architecture defined by angles or just an attempt
                 to blend in with a fad I’m unaware of, I’m not certain.
                 Conversations become louder and one cannot help but hear
                 personal issues they might rather not. It’s almost like
                 riding a city bus where neighbors play out their disputes
                 and their affairs, teenagers their loves and nonsense,
                 and people complain about the weather no matter what it
                 is. By the time the train is in the tunnel that leads
                 into Manhattan’s Penn Station, the ride is more like a
                 ride on the D Train heading north from West 4th than an
                 interstate train collecting and dispersing its human
                 cargo up and down the coast.


                 Certain towns along the way take one back to how it used
                 to be. Bellows Falls, VT is one such place. The waters of
                 the Connecticut River slowed by the walls that fence it
                 in through the town, one can almost hear the water wheels
                 turning crushing grain or powering looms. The industrial
                 revolution that moved New Englanders off the farms and
                 out of the shacks to fill the pockets of the bankers down
                 river with more money then the workers would ever see in
                 a dozen lifetimes of wage slavery. It turned the towns
                 upside down, fed the tavern owners, freed the children
                 from the structures of home and church and replaced them
                 with the oppression of capitalism and its measly rewards
                 the bosses call a payday—a ritual they begrudgingly go
                 along with despite the greed capitalism encourages.


          o § Hardware⠀➾


                # ⚓ IT Wire ☛ iTWire_–_Global_smartphone_sales_take_a_hit_for
                  fourth_quarter_running⠀⇛


                       Global smartphone sales fell to 287 million units
                       in the second quarter of 2022, a drop of 9% year-
                       on-year and the lowest figure since the second
                       quarter of 2020 when the pandemic first hit, the
                       technology analyst firm Canalys says.


                       Another company, IDC, said the figure was 286
                       million units and represented a drop of 8.7%, about
                       3.5% lower than forecast.


                       Canalys said Samsung (61.8 million units, 21%
                       share) led the market followed by Apple (49.5
                       million units, 17% share) and Xiaomi (39.6 million
                       units). Oppo and vivo made up the top five, with
                       27.3 million units and 25.4 million units
                       respectively.


                       “What started out as a supply-constrained industry
                       earlier this year has turned into a demand-
                       constrained market,” said Nabila Popal, research
                       director with IDC’s Worldwide Tracker team.


                       {loadposition sam08}”While supply improved as
                       capacity and production was ramped up, roaring
                       inflation and economic uncertainty has seriously
                       dampened consumer spending and increased inventory
                       across all regions.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ Common Dreams ☛ Opinion_|_The_Corporate_Oligarchs_Have_Put
                  Humanity_on_a_Path_Toward_Self-Annihilation⠀⇛


                       The world today is on the verge of a major food
                       emergency, provoked in part by Russia’s attack on
                       Ukraine but more broadly by the damage heat from
                       global warming is doing to crops worldwide. This is
                       both a crisis and an opportunity.


                # ⚓ Common Dreams ☛ Opinion_|_On_Their_57th_Anniversary,
                  Medicare_and_Medicaid_Remain_Under_Threat⠀⇛


                       You may wonder why former President Harry Truman is
                       sitting close by while President Lyndon B. Johnson
                       signs Medicare and Medicaid into law in the iconic
                       1965 photograph. Or why Harry Truman received the
                       first-ever Medicare card. The reason is that Truman
                       first proposed a Medicare-like system in 1945—but
                       it took two decades, another Democratic president,
                       and a Democratic supermajority in Congress to
                       overcome opposition from political conservatives
                       and the health industry. As we celebrate 57 years
                       of Medicare and Medicaid successes on July 30th, it
                       is vexing that these two vital programs continue to
                       be in the cross-hairs of GOP opponents. 


                # ⚓ Common Dreams ☛ Opinion_|_Four_Ways_to_Improve_Anxiety_and
                  Despair_Amid_Never-Ending_Bad_News⠀⇛


                       The bad news keeps coming, seemingly at an ever-
                       increasing rate: The war in Ukraine; frequent mass
                       shootings; global heating with its concomitant
                       fires and droughts; high rates of overdose deaths
                       and suicide; the overturning of Roe v. Wade and all
                       it portends for women’s autonomy and rights;
                       inflation; the persistence of COVID variants; and
                       growing extinction rates (even the Monarch
                       Butterfly has been listed as an endangered
                       species), to name a few.


                # ⚓ Techdirt ☛ Colorado_Appeals_Court_Again_Reminds_Cops_That
                  Marijuana_Legalization_Means_Their_Drug_Dogs_Are_Mostly
                  Useless⠀⇛


                       Colorado legalized recreational marijuana use in
                       2012. That’s an entire decade ago. Who knew the
                       learning curve for cops would be so extreme?


          o § Proprietary⠀➾


                # ⚓ CBC ☛ Shopify_laying_off_10%_of_staff_as_explosive_pandemic
                  growth_fizzles⠀⇛


                       According to regulatory filings, the company had
                       about 10,000 employees at the end of 2021, twice
                       the amount they had before the pandemic. The cuts
                       amount to 10 per cent of the company’s workforce.


                # ⚓ Earthly ☛ S3_Terraform_Backend⠀⇛


                       In the previous article I ported all my AWS
                       infrastructure to Terraform. But in doing so, I was
                       left tracking all my Terraform state in a
                       terraform.tfstate file. This has a number of
                       problems.


                # ⚓ Jeff Geerling ☛ Starlink’s_current_problem_is_capacity⠀⇛


                       This blog post is a lightly edited transcript from
                       my most recent YouTube video, in which I explain
                       some of Starlink’s growing pains: slower speeds due
                       to oversubscription, design challenges with their
                       v2 hardware, and a major bet on much larger v2 sats
                       and a rocket (Starship) that has yet to complete an
                       orbital flight.


                # ⚓ Matt Rickard ☛ Don’t_Be_Scared_of_Cloud_Lock-in⠀⇛


                       Technology companies were right to care so much
                       about vendor lock-in in the last two decades. In
                       the past, developers were burned by IBM, Microsoft,
                       and Oracle services, often with few alternatives
                       and price gouging. But to align your strategy so
                       vehemently against the same type of lock-in in the
                       cloud era would be wrong.


                       Vendor lock-in still exists (switching costs will
                       always be one core driver of competitive
                       advantage), but the calculation is much different.
                       Lock-in is a trade-off between portability/
                       optionality and velocity.


          o § Linux Foundation⠀➾


                # ⚓ Linux Foundation’s Site/Blog ☛ What_is_the_OpenGEH_(Green
                  Energy_Hub)_Project [Ed: More greenwashing_PR to dilute/harm
                  the brand “Linux”; Linux Foundation is not misusing the brand
                  “Linux” to spread lies for Microsoft and it’s_like
                  ClearlyDefined_in_OSI; LF became a GPL violators’ force of
                  occupation against Linux and against the GPL. If the LF’s
                  mission isn’t to kill Linux, it’s to kill the original
                  owners/ownership of Linux, handing over control of the
                  project to its enemies.]⠀⇛


                       OpenGEH ( GEH stands for Green Energy Hub ) enables
                       fast, flexible settlement and hourly measurements
                       of production and consumption of electricity.
                       OpenGEH seeks to help utilities to onboard
                       increased levels of renewables by reducing the
                       administrative barriers of market-based
                       coordination. By utilizing a modern DataHub, built
                       on a modular and microservices architecture,
                       OpenGEH is able to store billions of data points
                       covering the entire workflow triggered by the
                       production and consumption of electricity.


                       [...]


                       Initially built in partnership with Microsoft,
                       Energinet


          o § Security⠀➾


                # ⚓ Matthew Garrett ☛ Matthew_Garrett:_UEFI_rootkits_and_UEFI
                  secure_boot [Ed: Microsoft_apologists_at_it_again. The person
                  who caused the problems now pretends to be the rescuer
                  offering redemption.]⠀⇛


                       Kaspersky describes a UEFI-implant used to attack
                       Windows systems. Based on it appearing to require
                       patching of the system firmware image, they
                       hypothesise that it’s propagated by manually
                       dumping the contents of the system flash, modifying
                       it, and then reflashing it back to the board. This
                       probably requires physical access to the board, so
                       it’s not especially terrifying – if you’re in a
                       situation where someone’s sufficiently enthusiastic
                       about targeting you that they’re reflashing your
                       computer by hand, it’s likely that you’re going to
                       have a bad time regardless.


                # ⚓ Linux Shell Tips ☛ The_History_of_Kali_Linux_[Penetration
                  Testing]_Distribution⠀⇛


                       In cybersecurity and digital forensics, penetration
                       testing plays a crucial role in identifying and
                       mitigating exploitable vulnerabilities in a system.
                       A number of tools have been developed to help
                       pentesters efficiently conduct penetrations tests,
                       one of which is Kali Linux.


                # ⚓ Ghacks ☛ LibreOffice_security_update_fixes_macro_execution
                  bypass_and_potential_password_leaking_–_gHacks_Tech_News⠀⇛


                       The developers of LibreOffice have released updates
                       for the open source Office suite to patch three
                       security issues.


                # § Integrity/Availability/Authenticity⠀➾


                      # ⚓ David Rosenthal ☛ The_Internet_Archive’s_“Long_Tail”
                        Program⠀⇛


                             In 2018 I helped the Internet Archive get a
                             two-year Mellon Foundation grant aimed at
                             preserving the “long tail” of academic
                             literature from small publishers, which is
                             often at great risk of loss. In 2020 I wrote
                             The Scholarly Record At The Internet Archive
                             explaining the basic idea: [...]


                # § Privacy/Surveillance⠀➾


                      # ⚓ Free Press Journal ☛ Law_can_be_stretched_to
                        stonewall_questions_on_Pegasus⠀⇛


                             The law of contempt, like the criminal law,
                             can be stretched to save those who chastise
                             judges for flaying Nupur Sharma in their
                             court rooms while ignoring the unjustified
                             comments in the judgment which resulted in
                             the arrest of activists like Teesta Setalvad.


                             Predictably, this is why the attorney general
                             of India KK Venugopal refused to sanction the
                             prosecution of those dignitaries for
                             criticising Justice Surya Kant for his so-
                             called intemperate remarks against Nupur
                             Sharma, which is a gross violation of the
                             fundamental rights in Part III of the
                             Constitution.


                      # ⚓ Krebs On Security ☛ Breach_Exposes_Users_of
                        Microleaves_Proxy_Service⠀⇛


                             Microleaves, a ten-year-old proxy service
                             that lets customers route their web traffic
                             through millions of Microsoft Windows
                             computers, recently fixed a vulnerability in
                             their website that exposed their entire user
                             database. Microleaves claims its proxy
                             software is installed with user consent, but
                             data exposed in the breach shows the service
                             has a lengthy history of being supplied with
                             new proxies by affiliates incentivized to
                             distribute the software any which way they
                             can — such as by secretly bundling it with
                             other titles.


                      # ⚓ EFF ☛ Federal_Preemption_of_State_Privacy_Law_Hurts
                        Everyone⠀⇛


                             The debate around the ADPPA’s preemption
                             provisions has centered largely on whether or
                             not it’s stronger than current state privacy
                             laws, therefore lowering the bar for the
                             country right now. But that’s only part of
                             the issue: we must also look to the future.
                             So the ADPPA’s current preemption language is
                             bad for everyone in the country—not only
                             those who happen to live in one of the states
                             that have passed data privacy statutes.


                             At least five states have enacted
                             comprehensive consumer data privacy statutes
                             in the past few years: Connecticut, Utah,
                             Colorado, Virginia, and California. Like
                             ADPPA, these laws govern how companies can
                             collect, use, store, or share data, and they
                             allow people to access, delete, or stop sale
                             of their data. EFF wanted more from these
                             laws, but they nonetheless demonstrate the
                             ongoing commitment of state legislators to
                             protect their residents’ data privacy. Some
                             provisions of these state laws are stronger
                             than parallel features of ADPPA. But the
                             ADPPA would preempt them all.


                             Of course, current state and local protection
                             of data privacy extends far beyond these
                             recent comprehensive statutes. For example,
                             ADPPA would roll back rights to data privacy
                             that states have enshrined in their state
                             constitutions. Based on the text of the
                             current bill, ADPPA also endangers state
                             privacy rules that address just some types of
                             businesses, such as broadband providers or
                             data brokers.


                      # ⚓ Wired ☛ How_Tor_is_fighting—and_beating—Russian
                        censorship⠀⇛


                             For years, the anonymity service Tor has been
                             the best way to stay private online and dodge
                             web censorship. Much to the ire of
                             governments and law enforcement agencies, Tor
                             encrypts your web traffic and sends it
                             through a chain of computers, making it very
                             hard for people to track you online.
                             Authoritarian governments see it as a
                             particular threat to their longevity, and in
                             recent months, Russia has stepped up its
                             long-term ambition to block Tor—although not
                             without a fight.


                             In December 2021, Russia’s media regulator,
                             Roskomnadzor, enacted a 4-year-old court
                             order that allows it to order internet
                             service providers (ISPs) to block the Tor
                             Project website, where the Tor Browser can be
                             downloaded, and restrict access to its
                             services. Since then, censors have been
                             locked in a battle with Tor’s technical team
                             and users in Russia, who are pushing to keep
                             the Tor network online and allow people to
                             access the uncensored web, which is otherwise
                             heavily restricted in the country.


                             Russia’s efforts to block Tor come in two
                             flavors: the technical and the political. So
                             far, Tor has had some success on both fronts.
                             It has found ways to avoid Russian blocking
                             efforts, and this month, it was removed from
                             Russia’s list of blocked websites following a
                             legal challenge. (Although this doesn’t mean
                             blocking efforts will instantly end.)


          o § Defence/Aggression⠀➾


                # ⚓ JNS ☛ The_Israeli_journalist_who_visited_Mecca_should_be
                  worried⠀⇛


                       The legal prohibition on non-Muslims visiting Mecca
                       is based on a Koranic injunction (Surah 9, verse
                       28). Since Muslims believe that the Koran is the
                       word of God, no human authority, whether religious
                       or political, can change this ruling. Non-Muslims
                       who enter Mecca are therefore defiling Islam’s most
                       important holy place, as Tamary did.


                       To complicate matters, Islam has no pope-like
                       central figure. So, even if the Saudis decided to
                       table the issue for the time being, others—such as
                       a “lone wolf” terrorist—perhaps opposed to the
                       Saudi regime, could take up the charge to defend
                       the honor of Islam. Indeed, throughout the history
                       of Islam, individual Muslims and sects have
                       interpreted the Koran as they chose, resulting in
                       insurrections and assassinations that have often
                       threatened Muslim regimes. This means that
                       extremists might try to take revenge against Tamary
                       personally.


                # ⚓ Meduza ☛ Rumor_has_it_Did_Zelensky_strip_Ukrainian_oligarch
                  Ihor_Kolomoisky_of_his_citizenship?_—_Meduza⠀⇛


                       Last week, Ukrainian lawmaker Serhiy Vlasenko
                       published what appeared to be a scan of a
                       presidential decree depriving ten people of
                       citizenship. The fact that billionaire oligarch
                       Ihor Kolomoisky was included on the list caused a
                       sensation. The Ukrainian authorities have yet to
                       provide clear confirmation as to whether the
                       document is real. Regardless, journalist Konstantin
                       Skorkin, a contributor for the Carnegie Endowment
                       for International Peace, believes that the document
                       speaks to a behind-the-scenes struggle in the
                       highest echelons of power in Kyiv. Indeed, when he
                       was elected in 2019, Zelensky’s critics dubbed him
                       “Kolomoisky’s puppet.” But in the years since, he
                       has been working consistently to rid Ukrainian
                       politics of oligarchic influence — all while
                       strengthening his personal power. 


                # ⚓ Meduza ☛ ‘He_walks_the_walk’_How_United_Russia_General
                  Secretary_Andrey_Turchak_turned_the_‘party_of_power’_into_the
                  party_of_war_—_Meduza⠀⇛


                       After Russia launched its full-scale invasion of
                       Ukraine, it didn’t take United Russia General
                       Secretary Andrey Turchak long to realize that
                       Vladimir Putin’s obsession with the Donbas region
                       was here to stay. In a bid to secure his own
                       political future as well as that of the party
                       — whose approval ratings are in decline — Turchak
                       decided to go all-in on consolidating United
                       Russia’s influence in Ukraine’s occupied
                       territories.


                # ⚓ Pro Publica ☛ Turkish_TB2_Drones:_Federal_Lawmakers_Demand
                  Investigation⠀⇛


                       As countries around the globe add armed drones to
                       their arsenals, federal lawmakers are pressing the
                       Biden administration to investigate how U.S. parts
                       and technology ended up in what has fast become one
                       of the most popular models on the world market:
                       Turkey’s TB2.


                       Manufactured by the Turkish firm Baykar Technology,
                       the TB2 can hover high above a battlefield and
                       strike targets with laser-guided missiles. Baykar
                       has maintained that the TB2s are domestically
                       produced, with nearly all of the parts coming from
                       within Turkey. But, as ProPublica reported this
                       month, wreckage from downed drones in multiple
                       conflicts has shown otherwise. A range of
                       components were made by manufacturers in the U.S.,
                       Canada and Europe.


                # ⚓ Democracy Now ☛ Ukraine_Invasion:_Russian_Opposition_to_War
                  Has_Been_Smashed,_with_Many_Dissidents_Fleeing_Abroad⠀⇛


                       We look at how the Russian war in Ukraine is
                       impacting the Russian people, with many Russian
                       dissidents who oppose the invasion choosing to flee
                       abroad after facing violent crackdowns at home.
                       Ilya Budraitskis is a Russian historian and
                       political writer who left his home in Moscow after
                       the war in Ukraine began, and recently launched the
                       media outlet Posle. Meanwhile, Putin’s Russia looks
                       like an extremely “conformist” society, where “some
                       200 kilometers from your home you have a full-scale
                       war with the army of your country that started this
                       war, and you pretend not to follow the news, not to
                       disturb your normal way of life with this
                       terrifying information,” says Budraitskis.


                # ⚓ Counter Punch ☛ Donald_Trump_is_in_Trouble⠀⇛


                # ⚓ The Nation ☛ Calls_for_a_Diplomatic_Settlement_in_Ukraine
                  Are_Misplaced⠀⇛


                       The war in Ukraine has lasted for more than five
                       months. As the bloodletting and destruction
                       continue, the West faces rising inflation, and many
                       economists warn that recessions may be coming. With
                       winter coming, Europe is panicking about gas
                       supplies. And on the military front, there are
                       fears that the war could spread or escalate,
                       spiraling into a clash between the world’s two
                       nuclear superpowers.


                # ⚓ Counter Punch ☛ Letter_From_Crimea:_the_Bridge⠀⇛


                       The overnight train from Novocherkassk to Crimea
                       left just before 6 p.m. I had an early dinner at my
                       guest house and set off on the bicycle for the
                       station, which, while in no way busy, was still in
                       a state of confusion. The electronic departure
                       board was not working, and the dispatcher
                       announcing the trains kept changing the platform
                       for my train, as if calling a Square Dance.


                       Twice I had to drag my bike and bags up the
                       staircases and over the tracks until I finally came
                       back to the original platform. When the long string
                       of Pullmans (well, the Russian equivalent) pulled
                       into the station, I was at the wrong end of the
                       platform, which meant another sprint while pushing
                       the bicycle to get to my sleeping car.


                # ⚓ Counter Punch ☛ Gun_Violence:_an_International_Educator’s
                  Moral_Quandary⠀⇛


                       He posted: “It is days like today in the USA when I
                       have an internal ethical struggle with my job … the
                       job I’ve had for 20+ years … the job I love and
                       find so rewarding … the job that has shown me the
                       world and taught me so much about life –
                       outreaching to and recruiting international
                       students to come to this country for a powerful
                       educational experience and a valuable higher
                       education degree.


                       “I feel guilty sometimes, working with students and
                       families in their pursuit to come to America to
                       experience our culture. Why would anyone want to
                       come here right now? We have some major issues to
                       work out as a society and as a country that the
                       entire world is watching closely.”


          o § Transparency/Investigative Reporting⠀➾


                # ⚓ The Dissenter ☛ Whistleblower_Testimony_Shows_BOP_Director
                  Ignored_Rampant_Abuse_And_Corruption_At_Atlanta_Prison⠀⇛


                       Two whistleblowers who worked at United States
                       Penitentiary Atlanta testified at a US Senate
                       hearing and described rampant abuse and corruption
                       that has plagued the medium-security prison in
                       Georgia for several years.The hearing on July 26
                       was part of an investigation by the Senate Homeland
                       Security and Government Affairs Permanent
                       Subcommittee on Investigations into USP Atlanta,
                       which is a facility for pretrial detainees. So far,
                       the investigation has focused on civil rights
                       violations, prison staff misconduct, the flow of
                       contraband and narcotics, and the high rate of
                       suicides. According to Georgia Senator Jon Ossoff,
                       who is the chair of the subcommitee, “The
                       investigation has revealed that gross misconduct
                       persisted at this facility for at least nine years,
                       and that much of the damning information revealing
                       misconduct, abuse, and corruption was known to BOP
                       and accessible to BOP leadership during that
                       period.”The subcommittee invited outgoing BOP
                       Director Michael Carvajal to testify, but the
                       Justice Department initially declined to make
                       Carvajal available. Only after the subcommittee
                       issued a subpoena, which was later withdrawn, did
                       the BOP director agree to appear before senators.


                       Terri Whitehead worked for BOP for 30 years before
                       she was forced into retirement in December 2021.
                       She was a staff member at USP Atlanta from August
                       2020 until she retired.There are around 600 beds in
                       the Detention Center Unit. When Whitehead arrived
                       at USP Atlanta, she noticed the unit had “mold on
                       the ceilings and walls, an infestation of roaches
                       and rats, cats roaming the hallways, holes in the
                       ceiling (ceiling tiles and drywall missing),
                       graffiti on the walls, elevators not working, three
                       inmates sleeping in two-man cells, inadequate food
                       portions, not enough laundry (jump suits, towels,
                       rags, underwear, socks), standing water on the
                       floor, and no assigned COVID-19 isolation or
                       quarantine areas.”In early 2021, Whitehead became
                       the USP Atlanta’s acting associate warden. “I was
                       appalled to learn of USP Atlanta’s repeated
                       bureaucratic failures to deal with infestations of
                       rodents in food preparation areas,” Whitehead
                       recalled [PDF]. “I was contacted, via email, by the
                       Southeast Regional Office food service
                       administrator, who indicated someone had reported
                       cats and rats inside of inmate food preparation
                       areas.”“I then met with the food service staff
                       management who told me rat infestation had been a
                       recurring problem and food service staff
                       intentionally left doors open so that cats could
                       catch the rats. Rats were getting into inmate
                       food.”Whitehead added, “I was told USP Atlanta had
                       no professional pest control program because two
                       management officials did not agree which department
                       budget would pay for the pest control service.” She
                       does not know if officials at the prison ever took
                       care of the rodents—or the cats.A major incident
                       occurred in July 2021 when “over 700 cell phones
                       and numerous hard contraband items and illegal
                       drugs were found inside USP-Atlanta.” Detainees
                       were moved to other prisons, and according to
                       Whitehead, “approximately 40 management officials”
                       were transferred as well. Yet none of the 432 staff
                       members were apparently punished.  Whitehead wrote
                       discipline memos urging investigations into
                       misconduct by other institutions, but they went
                       nowhere. She was “rewarded” for her efforts to
                       enforce policies and procedures with a dismissal.
                       The BOP tried to relocate her to Texas so she
                       retired earlier than she had planned.


          o § Environment⠀➾


                # ⚓ Common Dreams ☛ From_‘Poison_Pills’_to_‘Transformative’
                  Funding,_Climate_Groups_Grapple_With_Manchin_Deal⠀⇛


                       More than 700 pages of legislative text negotiated
                       principally by Sen. Joe Manchin—one of the fossil
                       fuel industry’s closest allies in Congress—are
                       bound to contain provisions that are appalling to
                       climate advocates and communities on the frontlines
                       of the planetary emergency.


                       That is certainly the case with the newly revealed
                       Inflation Reduction Act of 2022, which green groups
                       characterized as a mixture of potentially
                       “transformative investments” in renewable energy
                       and alarming giveaways to the fossil fuel industry,
                       the primary driver of the climate crisis. The
                       combination has left climate groups grappling with
                       whether the good outweighs the bad—a question with
                       massive implications for the planet.


                # ⚓ Common Dreams ☛ After_Manchin_Deal,_Advocates_Say_‘We_Still
                  Need_Biden_to_Declare_a_Climate_Emergency’⠀⇛


                       Climate advocates made clear Thursday that they
                       have no intention of dropping their calls for U.S.
                       President Joe Biden to declare a climate emergency
                       after Democratic leaders cut a legislative deal
                       with Sen. Joe Manchin that includes tens of
                       billions of dollars in green energy investments.


                       “The climate doesn’t give out prizes for getting
                       70% of the way there,” said Fossil Free Media
                       director Jamie Henn, referring to estimates that
                       Senate Democrats’ newly proposed bill, if passed,
                       would bring the U.S. significantly closer to
                       meeting Biden’s goal of cutting the nation’s
                       greenhouse gas emissions in half by the end of the
                       decade.


                # § Energy⠀➾


                      # ⚓ David Rosenthal ☛ Regulating_“Digital_Assets”⠀⇛


                             I’m a retired software engineer so I focus
                             here on the technological risks. I have no
                             positions in cryptocurrencies or related
                             companies. Nearly a quarter-century ago I
                             started work at Stanford on a decentralized
                             peer-to-peer consensus system using Proof-of-
                             Work. It won a Best Paper award five years
                             before Satoshi Namakoto published the Bitcoin
                             protocol.


                             This discussion is badly framed; the term
                             “digital asset” is counter-productive. My
                             checking accounts are digital assets. What
                             you want to talk about are “cryptocurrencies”
                             or “digital ledger technologies” or
                             “blockchains”, but these terms cover two
                             completely different technologies: [...]


                      # ⚓ DeSmog ☛ Murky_World_of_Carbon_Offsets_Faces_Greater
                        Scrutiny⠀⇛


                             Proposals to boost transparency in the carbon
                             offset market could shine a light on brokers
                             who buy credits cheaply from Indigenous
                             communities before selling them to companies
                             at inflated prices. 


                             The measures form part of a wide-ranging
                             package drafted by the Integrity Council for
                             the Voluntary Carbon Market, a governance
                             body aiming to boost the quality of carbon
                             offsets. The proposals were published this
                             week, beginning a 60-day public consultation.


                      # ⚓ Site36 ☛ Airbus‘_„Zephyr“:_Stratospheric_drone_beats
                        own_record⠀⇛


                             Airbus‘ unmanned glider has been flying for
                             42 days without landing; no aircraft has been
                             in the air without refueling for such a long
                             time. As a flying Internet node, the drone
                             could replace 250 cell towers. But there is
                             interest mainly from the military.


                      # ⚓ DeSmog ☛ Pennsylvania_County_Bans_Fracking_in_Area
                        Parks⠀⇛


                             Eight years after allowing a shale gas
                             company to drill beneath Deer Lakes County
                             Park for methane gas, the Pennsylvania county
                             home to Pittsburgh has banned all industrial
                             activity in the area’s eight other parks —
                             despite a veto from the county executive.


                             It’s the first such move at the county level
                             in the state, one fracking opponents term a
                             milestone in a state where the fracking
                             industry almost always gets its way.


                      # ⚓ Common Dreams ☛ Since_2021,_Big_Oil_Has_Spent_Over
                        $200_Million_to_Sabotage_Climate_Action:_Analysis⠀⇛


                             The oil and gas industry, one of the most
                             powerful corporate forces in American
                             politics, has spent more than $200 million
                             over the past year and a half to stop
                             Congress from slashing carbon emissions as
                             evidence of their catastrophic impact—from
                             deadly heatwaves to massive
                             wildfires—continues to accumulate in stunning
                             fashion.


                             That topline estimate of the fossil fuel
                             industry’s lobbying outlays and congressional
                             election spending in the U.S. was calculated
                             by Climate Power, which provided its findings
                             exclusively to Common Dreams.


                      # ⚓ Common Dreams ☛ Opinion_|_With_Referendum_Off_Until
                        2024,_California_Lawmakers_Must_Act_on_$18_Minimum
                        Wage⠀⇛


                             Californians may have gotten temporary relief
                             recently when gas prices finally fell to
                             about $6 a gallon this month, down from as
                             high as $8 per gallon in June in Los Angeles
                             County. Inflation has rocked the economy,
                             soaring 9.1% from a year ago in June.


                      # ⚓ Common Dreams ☛ Big_Oil’s_Record_Profits_and_Buyback
                        Splurge_Spotlight_‘Broken_Energy_System,’_Critics_Say⠀⇛


                             Economic and climate justice advocates on
                             Thursday reiterated their demands for far-
                             reaching energy reforms after Europe’s two
                             biggest fossil fuel corporations reported
                             more than $21 billion in combined second-
                             quarter profits and announced plans to buy
                             back a combined $8 billion in shares in the
                             third quarter—all while continuing to receive
                             billions in public subsidies each year to
                             wreck the planet.


                             British venture Shell posted a record-
                             breaking $11.5 billion in profits from April
                             through June, more than doubling its Q2
                             earnings compared with 2021 ($5.5 billion)
                             and surpassing the previous quarterly high of
                             $9.1 billion set during the first three
                             months of 2022, which was nearly triple last
                             year’s Q1 net income of $3.2 billion.


                      # ⚓ Counter Punch ☛ Energy_is_Eternal_Delight⠀⇛


                             I was on the banks of a pond off Mount
                             Tremper, in the Catskill Mountains of New
                             York, with my daughters Josie and Léa and
                             Josie’s friend Ito, on a Sunday not long ago,
                             a day of high wind and pouring sun in big
                             blue sky.


                             The sunlight, the wind on the pond, the
                             shifting breezes threw the surface of the
                             water this way and that, so that the rippling
                             liquid burst in traceries of fire, golden
                             treasures, scintillations, waves of diamonds
                             and crystals one after the other as if in
                             rhythms of the sea.


                # § Wildlife/Nature⠀➾


                      # ⚓ The Revelator ☛ A_New_Way_to_Count_African_Forest
                        Elephants:_DNA_From_Dung⠀⇛


                      # ⚓ Counter Punch ☛ Breakdown_of_the_Marine_Food_Web⠀⇛


                             It’s a disturbing discovery, but first a look
                             at the marine food web, starting with the
                             lowest organisms: (1) phytoplankton – plant-
                             like plankton: green algae, diatoms, and
                             dinoflagellates eaten by (2) zooplankton –
                             microorganisms: crustaceans, rotifers, insect
                             larvae and mites eaten by (3) small fish:
                             anchovies, sardines, shrimp, squid, krill
                             eaten by (4) bigger fish: sturgeon, sunfish,
                             sharks, manta rays eaten by (5) mammals:
                             seals, dolphins, polar bears, and last but
                             certainly not least, humans at an
                             increasingly wobbly end of the food chain.


                             At the bottom of the food web phytoplankton
                             generically serves as the most significant
                             resource of marine life simply because
                             nothing else eats if phytoplankton doesn’t
                             exist. Moreover, phytoplankton performs
                             photosynthesis, converting sunrays to energy,
                             absorbs CO2, and serves as a major source,
                             producing oxygen for the biosphere.


          o § Finance⠀➾


                # ⚓ Common Dreams ☛ Opinion_|_Noam_Chomsky:_We_Can_Free
                  Ourselves_from_State_Capitalism⠀⇛


                       The following interview originally appeared in
                       German at Telepolis but this is the first
                       publication of the English translation.


                # ⚓ Common Dreams ☛ Report_Details_‘Abusive’_Eviction_Tactics
                  by_Corporate_Landlords_During_Height_of_Pandemic⠀⇛


                       Four large corporate landlords filed nearly 15,000
                       eviction actions in the first 16 months of the
                       pandemic, with some executives and property
                       managers engaging in harassment and deception of
                       their tenants and deliberately inflicting cruelty
                       on people who had been unable to pay their rent.


                       The U.S. House Select Subcommittee on the
                       Coronavirus Crisis released a new report Thursday
                       following a yearlong investigation into the
                       eviction practices of Pretium Partners, Invitation
                       Homes, Ventron Management, and the Siegel Group,
                       all of which were thriving financially when the
                       committee began examining its practices.


                # ⚓ Counter Punch ☛ Roaming_Charges:_Tell_Tom_Joad_the_News⠀⇛


                       + Ticket prices for Springsteen’s Born to Run tour
                       in 1975 averaged about $8 for general admission.
                       ($7.50 in Upper Darby, PA, when he played venues
                       that small.) The minimum wage was $2.10 per hour.
                       So a kid had to work less than half a day to earn
                       enough to go to the gig. Today the minimum wage is
                       a miserly $7.25 an hour. But the price of tickets
                       for this fall’s Springsteen tour ranges from $100
                       to more than $5000 a piece. The cheapest price I
                       could find for the Portland show was a restricted
                       view seat from behind the stage selling for
                       $136–which means that a Springsteen fan who works
                       at a minimum wage job (assuming he has any left)
                       would have to work nearly 3 full days to buy a
                       crappy ticket. Landau said the absurd ticket prices
                       were “a fair price to see someone universally
                       regarded as among the very greatest artists of his
                       generation.” They call him the boss for a reason.
                       Now go tell Tom Joad the news.


                       + Given the extortionate price of these tickets, it
                       might be fair to ask just how much more money does
                       Springsteen need? Forbes calculated his yearly
                       income while touring at $81 million. And  that was
                       before he sold his entire catalogue to Sony for
                       $550 million.


                # ⚓ Counter Punch ☛ The_Semi-Conductor_Bill_and_the_Moderna
                  Billionaires⠀⇛


                       To be clear, the bill does some good things. It has
                       funding both to subsidize manufacturing capacity
                       for semiconductors in the United States and also
                       for further research in developing better chips in
                       the future. Both of these are positive developments
                       even if the benefits of the former are overstated.


                       It was common in the pandemic days to tout the
                       supply chain problems as evidence that we needed
                       more manufacturing in the United States in a
                       variety of areas. However, that story ignored
                       several factors.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Free Press Journal ☛ Media_must_carry_out_some_soul-
                  searching⠀⇛


                       Chief Justice of India NV Ramana has pointed to
                       mediocrity and mischief in the media which pose a
                       grave threat to democracy. He said, “New media
                       tools have enormous amplifying ability but appear
                       incapable of distinguishing between the right and
                       the wrong, the good and the bad and the real and
                       the fake. Media trials cannot be a guiding factor
                       in deciding cases. Of late, we see the media
                       running kangaroo courts, at times on issues even
                       experienced judges find difficult to decide. Ill-
                       informed and agenda-driven debates on issues
                       involving justice delivery are proving detrimental
                       to the health of democracy.” Along with the
                       additional pressures created by social media, the
                       Chief Justice unambiguously said, “biased views
                       being propagated by the media are affecting the
                       people, weakening democracy, and harming the
                       system.” It is absolutely impossible to differ with
                       the honourable Chief Justice, as the media’s
                       character has doubtless changed for the worse — and
                       dangerously so. Mediocrity can be explained in
                       terms of inadequate resources, but what about
                       mischief? [...]


                # ⚓ The Nation ☛ Biden’s_Misguided_International_Crusade⠀⇛


                       Biden’s on a mission! He’s working the phones,
                       twisting arms, giving speeches, and otherwise
                       campaigning for a cause. Only it’s not abortion
                       rights or climate survival, stopping gun violence,
                       or protecting voter rights. Rather, he’s busy
                       creating a Cold War–like network of alliances to
                       defend the “rules-based world order” against rogue
                       states like Russia and China.


                # ⚓ Counter Punch ☛ Donation_Politics:_Biden’s_Global_Hypocrisy
                  Starts_at_Home⠀⇛


                       The approach became even more personal a day or two
                       later when the same lure line was attributed to
                       Jill Biden, cast in the role of a political party
                       team player. The First Lady went on to expatiate
                       upon the cynical view that Democrats are so
                       desperate for a chance to interact with the
                       President that they would fall for any come on,
                       however absurd. In her  astonishing words:
                       “Throughout the years, I’ve learned that there are
                       at least three things that can make Joe smile from
                       ear to ear: Our kids and grandkids, chocolate chip
                       ice cream, and getting to talk one-on-one with
                       Americans like you, Richard.”


                       And continues, “Having the chance to hear your
                       hopes and dreams grounds Joe and motivates him to
                       keep fighting the hard battles. That’s why Joe
                       would love nothing more than to give you a call
                       soon.” Then come what the message was really
                       about—nothing more or less than a crass appeal for
                       money coupled with a sly ‘confession’ that, after
                       all, receiving a call from Biden was as unlikely as
                       Donald Trump committing civil disobedience as a
                       consequence of becoming an ardent anti-nuclear
                       activist.


                # ⚓ Common Dreams ☛ ‘These_Motherf*ckers’:_Jon_Stewart_Goes_Off
                  on_GOP_Turning_Back_on_Sick_Veterans⠀⇛


                       Liberal comedian Jon Stewart chastised the GOP on
                       Thursday, less than 24 hours after Senate
                       Republicans tanked a bill that would have expanded
                       healthcare access for U.S. military veterans
                       exposed to Agent Orange and toxic burn pits—a move
                       that was made in retaliation for Democrats reviving
                       their reconciliation package following the passage
                       of bipartisan legislation designed to boost
                       domestic semiconductor chip manufacturing.


                       “Fuck the Republican caucus and their empty promise
                       to our veterans.”


                # ⚓ Counter Punch ☛ Washington_is_the_Problem,_Not_the
                  Solution⠀⇛


                       Political and diplomatic platitudes aside, the
                       current American administration has done the exact
                       opposite as indicated in Biden’s words and actions.
                       Alleging that the US commitment to a two-state
                       solution “has not changed”, Biden dismissed his
                       Administration’s interest in trying to achieve such
                       a goal by declaring that the “ground is not ripe”
                       for negotiations.


                       Considering that the Palestinian Authority of
                       Mahmoud Abbas has repeatedly announced its
                       readiness to return to negotiations, one can only
                       assume that the process is being stalled due to
                       Israel’s intransigence. Indeed, none of Israel’s
                       top leaders or major parties champion negotiations,
                       or the so-called peace process, as a strategic
                       objective.


                # ⚓ Counter Punch ☛ It’s_the_Corruption,_Stupid!⠀⇛


                       They don’t all chat; and those who do don’t always
                       follow my leads into politics and society. But
                       enough of the 8,000-plus passengers I’ve driven in
                       four years have gone with me that I can draw some
                       firm conclusions.


                       First, I can say with 100% certainty that, when
                       conversations do turn political, they all respond
                       with reflexive nods of recognition when I say: “The
                       overriding problem in America today is that all of
                       the resources go to the handful at the top, and the
                       rest of us are left to fight for the scraps.”


                # § Misinformation/Disinformation⠀➾


                      # ⚓ NPR ☛ A_Georgia_monument_was_destroyed._Locals_blame
                        conspiracy_theories.⠀⇛


                             Conspiracy theories aren’t a new phenomenon,
                             and neither is people acting out on them in
                             real life. But Jared Holt, an extremism
                             researched with the Institute for Strategic
                             Dialog, said the Guidestones are a perfect
                             example of how pervasive conspiracy thinking
                             has become.


          o § Censorship/Free Speech⠀➾


                # ⚓ Free Press Journal ☛ Proposed_bill_to_control_digital_media
                  is_worrying⠀⇛


                       The Press and Registration of Books (PRB) Act,
                       1867, which regulates newspapers and printing
                       presses in India, is intended to be replaced by
                       this proposed bill. The cabinet, chaired by Prime
                       Minister Narendra Modi, is reportedly expected to
                       pass this bill soon. Since there is currently no
                       procedure in place to register digital news portals
                       like newspapers, this bill intends to do so with
                       the Press Registrar General, which would be the
                       equivalent of India’s current Registrar of
                       Newspapers. It is intended to require digital news
                       providers to submit an application for registration
                       within 90 days of the law taking effect. For the
                       first time in India, there will be rules governing
                       digital media, which will be under the Ministry of
                       Information and Broadcasting if the bill is
                       approved.


                # ⚓ Reuters ☛ Ex-journalist_fined_again_for_discrediting
                  Russian_army_over_Ukraine⠀⇛


                       Former Russian TV journalist Marina Ovsyannikova
                       was fined 50,000 roubles ($820) on Thursday after
                       being found guilty of discrediting the country’s
                       armed forces in social media posts condemning
                       Russia’s actions in Ukraine.


                       The ruling was passed after a short hearing in a
                       Moscow administrative court. Ovsyannikova rejected
                       the proceedings against her as “absurd”.


                # ⚓ [Old] RFERL ☛ Russian_TV_Journalist_Who_Protested_War_On-
                  Air_Arrested⠀⇛


                       Ovsyannikova published a post on Instagram saying
                       she was taken to the police station in the
                       capital’s Krasnoselsky district.


                       She later wrote she had been charged with
                       “discrediting the actions of the army of Russia”
                       during an interview she gave near the Basmanny
                       Court of Moscow in support of opposition politician
                       Ilya Yashin, who is being held in pretrial
                       detention for allegedly spreading false information
                       about the Russian military.


                # ⚓ The Independent UK ☛ Russia_finds_former_state_TV
                  journalist_guilty_of_discrediting_army_in_‘absurd’_trial⠀⇛


                       Now she has appeared in court over subsequent
                       social media posts in which she said that those
                       responsible for the invasion of Ukraine should be
                       standing in the dock before an international
                       tribunal.


                       During the trial, Ms Ovsyannikova said she did not
                       understand why she was on trial, telling the court:
                       “What’s going on here is absurd. War is horror,
                       blood and shame.”


                # ⚓ RTE ☛ Russian_court_fines_Ukraine_protest_TV_journalist⠀⇛


                       In March, Ms Ovsyannikova shot to prominence for
                       interrupting a live TV broadcast to denounce
                       Russia’s military intervention in Ukraine.


                       After sending troops to Ukraine, Moscow adopted
                       laws imposing sentences of up to 15 years in prison
                       for spreading information about the military deemed
                       false by the authorities.


                # ⚓ Free Press Journal ☛ Prophet_row:_Rajasthan_man_offers
                  house,_property_to_anyone_who_beheads_Nupur_Sharma⠀⇛


                       After the heinous beheading of Kanhiya Lal in
                       Udaipur, the incidents of death threats and
                       controversial posts on social media are being
                       reported in various parts of Rajasthan. Five
                       persons have been arrested in the Hanumangarh
                       district for circulating objectional content on
                       social media.


                       The [Internet] services were suspended in the state
                       for three days after the Udaipur incident. Internet
                       and other services were restored in a phased manner
                       on Monday, however, as soon as they were restored,
                       the cases of threats and objectionable content also
                       started coming to the fore on social media


                # ⚓ Techdirt ☛ Devin_Nunes_Drops_SLAPP_Case_He_Lost_Against_Guy
                  He_Claims_Is_The_Husband_Of_The_Satirical_Tweeting_Cow_Who
                  Mocks_Him⠀⇛


                       Last month, we wrote about how Devin Nunes had lost
                       yet another of his many, many SLAPP suits against
                       various critics online for being mildly critical of
                       the former congressman, who seems to have the
                       thinnest skin imaginable. As you’ll recall, Nunes’
                       chronic SLAPP infatuation began a little over three
                       years ago with a lawsuit against a satirical online
                       cow who mocked him. While most people don’t realize
                       it, that lawsuit is still going on (other
                       defendants, namely Twitter and Liz Mair have gotten
                       out of it), but technically the suit against the
                       cow lives on, in part because Nunes and his lawyer,
                       Steven Biss, have claimed they’re unable to
                       identify the cow.


                # ⚓ EFF ☛ Abortion_Information_Is_Coming_Down_Across_Social
                  Media._What_Is_Happening_and_What_Next.⠀⇛


                       As reported by Vice and followed up on by Wired,
                       posts about abortion receive intense scrutiny
                       online. The difference, one activist told Vice, is
                       simply that more people are seeing their posts
                       removed than before.


                       Vice found that the truthful sentence “abortion
                       pills can be mailed” triggered a flag as violating
                       Facebook’s rules about “buying, selling, or
                       exchanging non-medical drugs.” A moderator running
                       a group on Facebook connecting people seeking
                       information about abortions told Wired she has
                       always had to carefully monitor posts to avoid the
                       group being removed entirely, with clear rules
                       about what can be posted—any links are banned, for
                       instance.


                       The moderator expressed a frustration we’ve heard
                       constantly about community guidelines: that they
                       have no idea what the lines actually are and find
                       things suddenly shifting with no warning.


                # ⚓ Democracy Now ☛ Nina_Khrushcheva:_“Don’t_Cancel_Russian
                  Culture.”_Collective_Punishment_“Plays_into_Putin’s_Hands.”⠀⇛


                       As the Russian invasion of Ukraine continues, many
                       in Western countries are expressing their
                       opposition to the war by becoming hostile to
                       Russian culture. Nina Khrushcheva argues that
                       Russian music, films, books and art are not the
                       right targets for antiwar activism in her latest
                       article, “Don’t Cancel Russian Culture.” If
                       Russians feel that the West is inhibiting Russian
                       culture, “they will blame the West more than they
                       blame the oppressive regime that is there in
                       Russia,” says Khrushcheva, professor at The New
                       School and great-granddaughter of former Soviet
                       Premier Nikita Khrushchev. Meanwhile, Russia is
                       cracking down on cultural producers who dare to
                       oppose the invasion.


          o § Civil Rights/Policing⠀➾


                # ⚓ Pro Publica ☛ Help_Us_Investigate_Termination_of_Parental
                  Rights_in_the_Child_Welfare_System [Ed: ProPublica pretends
                  to care about children while bagging bribes from Bill Gates,
                  who helped Epstein smuggle thousands of underage girls for
                  sexual exploitation]⠀⇛


                       Journalists at ProPublica and NBC News would like
                       to connect with people whose parental rights have
                       been terminated in the past decade.


                       We want to understand how your case was handled by
                       your state’s child welfare agency and courts, and
                       what types of services you were provided to help
                       reunite your family.


                # ⚓ Techdirt ☛ Kansas_Police_Officer_Who_Killed_Innocent_Man
                  During_A_Swatting_Denied_Qualified_Immunity⠀⇛


                       Swatting is truly heinous. People angry about video
                       game playing somehow believe they’re justified in
                       attempting to end their opponents’ lives,
                       literally. Toxic sub-humans who can’t handle losing
                       turn to secondhand killing to get their revenge.
                       Absolutely abhorrent behavior that plays into law
                       enforcement’s shoot-first, handcuff-the-corpse-
                       later warrior mentality.


                # ⚓ Counter Punch ☛ Organized_Labor_and_the_Crisis_of
                  Democracy⠀⇛


                       There is, however, at least one glimmer of hope for
                       democracy, and it comes from a source that might
                       initially, to many people, seem rather unrelated: a
                       renascent labor movement.


                       Given that the primary role of unions is to
                       advocate for the interests of their members on the
                       job, one might wonder how they could play an
                       essential part in protecting and revitalizing the
                       very different institution of political democracy.
                       How can organizations with such a particular
                       mission, a seemingly narrow economic one, serve as
                       a buttress for the universal interest of democracy
                       itself? Actually, according to polls, two thirds of
                       Americans approve of labor unions, suggesting they
                       understand what a constructive force unions are. If
                       people knew the real history of organized labor,
                       however, the number would probably be close to 90
                       percent.


                # ⚓ Pro Publica ☛ Liberty_University’s_Online_Programs_Are
                  Source_of_Veterans’_Complaints⠀⇛


                       When an Army veteran was looking for somewhere to
                       get an online aviation degree a couple of years ago
                       in hopes of becoming a pilot, Liberty University
                       advertised having the speed and flexibility she
                       needed: accelerated eight-week courses with start
                       times throughout the year and 52 affiliated flight
                       schools around the country where she could get the
                       required flight training. She signed up for the
                       program, paying with the GI Bill benefits that have
                       made military veterans such a reliable source of
                       revenue for Liberty and other universities with
                       large online programs.


                       But when her husband, who was still on active duty,
                       learned he would be transferred from Georgia to
                       Hawaii, she discovered that the lone Liberty flight
                       affiliate on Oahu, George’s Aviation Services in
                       Honolulu, did not offer the accelerated courses
                       Liberty had touted. This meant that it would take
                       her double the time to complete her program, two
                       years rather than one, and would cost U.S.
                       taxpayers more along the way, she stated in a
                       complaint she filed with the Department of Veterans
                       Affairs.


                # ⚓ Techdirt ☛ City_Of_Chicago,_Chicago_PD_Officers_Sued_Over
                  Their_Use_Of_Questionable_ShotSpotter_Technology⠀⇛


                       ShotSpotter has made a name for itself (and not a
                       good one!) by telling cops its sensors and mics can
                       convert soundwaves into actionable intel. It has
                       become beloved by some cops, perhaps in part for
                       being willing to alter its reports to reflect what
                       cops want to believe happened, rather than what
                       actually may have happened.


                # ⚓ Democracy Now ☛ Taliban_Rule_an_“Epic_Failure”_for
                  Afghanistan_with_Widespread_Poverty,_Crackdown_on_Women_&
                  Girls⠀⇛


                       As next month marks one year since the United
                       States officially withdrew from Afghanistan, we
                       look at the Taliban-ruled country’s devastating
                       economic and humanitarian crisis that has unfolded
                       since. Afghan journalist Bilal Sarwary describes
                       the dire situation as “an epic failure by the
                       Taliban as the de facto rulers in terms of not
                       stopping their crackdown against the Afghan people”
                       while they cope with flash floods, food shortages
                       and more. He adds that the U.S. exit deal with the
                       Taliban “completely sidelined the previous
                       government” and failed to kickstart a peace
                       process, contributing to instability in the
                       country.


                # ⚓ The Nation ☛ They_Don’t_Know_Us._But_They_Hate_Us.⠀⇛


                       Are you fucking kidding me?


                # ⚓ Common Dreams ☛ Opinion_|_Fox_News_Seeks_Allies_Across_the
                  Political_Spectrum_to_Defend_Neoliberal_Bolsonaro⠀⇛


                       “Particularly since the 1930s, the connection of
                       PSYOP with ideology and mass communication has made
                       it a constant strategic element of international
                       politics.” — An Overview of Psychological
                       Operations (PSYOP), Federal Research Division,
                       Library of Congress (1989)


                # ⚓ The Nation ☛ Pete_Seeger_Outlasted_the_Bastards⠀⇛


                       Newport, Rhode Island—Pete Seeger was one of the
                       handful of visionaries who started the Newport Folk
                       Festival in 1959, at a time when elite venues
                       refused to allow the father of American folk music
                       anywhere near a microphone. So it was only fitting
                       that the US Postal Service issued a stamp featuring
                       Seeger last week on the eve of the festival, in a
                       special ceremony where musicians and fans honored
                       the singer for his music and his activism.


                # ⚓ Common Dreams ☛ Petition_Demanding_Clarence_Thomas
                  Impeachment_Reaches_1.2_Million⠀⇛


                       U.S. Reps. Jamaal Bowman and Ilhan Omar joined
                       progressive groups outside the Supreme Court on
                       Thursday to deliver over 1.2 million petition
                       signatures demanding the impeachment of Justice
                       Clarence Thomas.


                       “This issue is even bigger than impeaching Thomas.
                       We need to reform this broken court.”


                # ⚓ Common Dreams ☛ Opinion_|_The_Dual_Population_Problem:
                  People_and_Things⠀⇛


                       As we careen from one crisis to the next, focused
                       on political struggles that seem to rarely produce
                       even short-term solutions, it’s easy to avoid big
                       questions that have no easy answers. Here’s a good
                       one: What is the sustainable carrying capacity of
                       the planet for Homo sapiens?


                # ⚓ Common Dreams ☛ Propelled_to_Victory_by_Dem_Leaders,
                  Cuellar_Says_$7.25_Too_Much_for_Millions_of_Workers⠀⇛


                       Labor experts and advocates on Wednesday expressed
                       disbelief and outrage as the details of an
                       “unconscionable” new bill purporting to expand
                       “flexibility and choice” in workplaces came to
                       light, condemning Democratic co-sponsor Rep. Henry
                       Cuellar for proposing the gutting of minimum wage
                       protections.


                       “This bill would allow employers to trample on the
                       rights of an untold numbers of workers.”


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ Extra_icanhazip_services_going_offline_::_Major_Hayden⠀⇛


                       Every great thing has its end, and the extra
                       services I launched along with icanhazip.com are no
                       exception. I started icanhazip.com way back in 2009
                       and detailed much of the history when I transferred
                       ownership to Cloudflare.


                       The extra services, such as icanhazptr.com,
                       icanhaztrace.com, and icanhaztraceroute.com, came
                       online in 2013 and they weren’t part of the
                       Cloudflare transfer. These services add extra
                       challenges since they need IPv6 connectivity and
                       they don’t play well with containers. Relative to
                       icanhazip.com, these services receive very little
                       traffic.


                       As much as I’d like to keep running these sites,
                       the extra services will go offline on August 17,
                       2022.


                # ⚓ Techdirt ☛ U.S._ISPs_That_Ripped_Out_Huawei_Gear_After
                  Promise_Of_FCC_Funding_Now_Struggle_To_Get_FCC_Funding⠀⇛


                       You might recall that the FCC under both Trump and
                       Biden has made a big deal about forcing U.S.
                       telecoms to rip out Huawei gear from their
                       networks, under the allegation that the gear is
                       used to spy on Americans. You’re to ignore, of
                       course, that the United States spies on everyone,
                       constantly.


                # ⚓ Techdirt ☛ The_NFL’s_New_Streaming_Offering…_Kind_Of_Sucks
                  Thanks_To_Legacy_Broadcasting_Rights⠀⇛


                       I’ve spilled many words on these pages talking
                       about the outsized importance live sports has on
                       the adoption of streaming as a primary
                       entertainment platform compared with traditional
                       cable. While cord-cutting is very much a thing, the
                       vine that terrestrial cable is clinging to keeping
                       it all from falling over the cliff remains live
                       sports. Major sporting leagues in America have
                       typically woven a complicated web of broadcasting
                       rights, whether with local broadcast stations,
                       cable channels, or even with some teams that own
                       their own channels. That complicated web is what
                       keeps blackout rules for MLB.TV in place, as well
                       as what keeps the implementation of true streaming
                       of everything impossible.


          o § Monopolies⠀➾


                # ⚓ Techdirt ☛ Chuck_Schumer_Admits_What’s_Been_Obvious_For_A
                  While:_There_Just_Aren’t_Enough_Votes_To_Pass_Sketchy
                  Antitrust_Bill_Targeting_Tech_Companies⠀⇛


                       Advocates for the problematic American Innovation
                       and Choice Online Act (AICOA) (which includes
                       groups and organizations I often agree with and
                       work with) keep insisting that they have the votes
                       to pass the bill and demanding that Senator Chuck
                       Schumer bring it to the floor for a vote. Schumer,
                       who correctly has no interest in wasting floor time
                       on a controversial bill that won’t pass, has now
                       admitted that the votes just aren’t there to pass
                       it.


                # § Patents⠀➾


                      # ⚓ Common Dreams ☛ Vaccine_Equity_Activists_Denounce
                        Pfizer’s_‘Obscene’_Pandemic_Windfall⠀⇛


                             Health equity campaigners on Thursday called
                             for a fairer system of developing and
                             distributing Covid-19 medications after
                             pharmaceutical company Pfizer announced
                             record second-quarter revenue, more than half
                             of which is attributable to sales of
                             coronavirus vaccines and treatments that
                             remain out of reach for much of the Global
                             South.


                             “Millions of people in low- and middle-income
                             countries faced death and devastation without
                             access to vaccines while Pfizer sold doses to
                             the highest bidders.”


                # § Software Patents⠀➾


                      # ⚓ TechCrunch ☛ LOT,_the_anti-patent-troll_group,
                        launches_Adapt_to_tackle_inclusion_in_the_world_of_IP
                        [Ed: This is about inclusion in a software patents
                        racket; they are not “anti-troll group”, they include
                        trolls like Microsoft, so AOL now issues paid-for fluff
                        for bad_people]⠀⇛


                # § Copyrights⠀➾


                      # ⚓ Torrent Freak ☛ Record_Labels_and_ISP_Bright_House_go
                        to_Trial_over_Pirating_Subscribers⠀⇛


                             ISP Bright House and several music companies
                             go to trial next week. In preparation, a
                             Florida federal court has set some rules for
                             what can and what can’t be brought up before
                             the jury. Among other things, the ISP is
                             allowed to argue that terminating accounts of
                             persistent pirates is disproportional.
                             However, the ISP can’t freely argue that
                             Internet access is a human right.


                      # ⚓ Torrent Freak ☛ Pirate_IPTV:_Five_Charged_Following
                        RCMP_Cybercrime_Investigation⠀⇛


                             Following an investigation by the Royal
                             Canadian Mounted Police, five people have
                             been charged with distributing pirate IPTV
                             services. RCMP officers raided GaloTV (Soltv)
                             in 2021, seizing hundreds of set-top boxes,
                             receivers and broadcasting devices. One of
                             the men was previously sued by DISH and
                             agreed to settle a civil suit for more than
                             half a billion dollars.


    * § Gemini* and Gopher⠀➾


          o § Personal⠀➾


                # ⚓ TTRPGs,_PDFs,_and_a_Very_Cheap_Tablet⠀⇛


                       I’ve been wanting to start playing tabletop role
                       playing games (TTRPGs) again. I used to play them a
                       lot in high school and college, but until I joined
                       a remote game for a podcast a few years ago, it had
                       been close to 20 years since I had played one.
                       COVID lockdowns gave me the urge to play remotely,
                       but I was so busy at home I didn’t ever get around
                       to it, though I did buy some TTRPG products, in
                       digital media form.


                       The thing about TTRPG rulebooks and supplements,
                       which has been true since the 90s, AD&D 2d edition,
                       and the White Wolf World of Darkness games, is that
                       they are mostly printed on glossy paper, with lots
                       of color illustrations and really intensive layout.
                       Two columns of text, interrupted in fancy shapes by
                       illustrations running in from the sides. Some
                       independent games are simpler, but this is the
                       standard that most games aspire to, and with D&D
                       5e, it’s especially intense.


                # ⚓ SpellBinding:_AYNRSWC_Wordo:_SCRIP⠀⇛


                # ⚓ You_Wanna_Help_My_Plant?⠀⇛


                       I’ve spoken a lot about AstroBotany on here. It’s
                       awesome.


                       My plant is currently getting increasingly closer
                       to 600th generation, and I can and do harvest it
                       several times a day. But harvesting is a pretty big
                       operation with many gemini requests, each one
                       carrying with it a TLS handshake.


          o § Politics⠀➾


                # ⚓ What’s_up_with_this_recession?_(Unemployment)⠀⇛


                       There seems to be a lot of arguing in the
                       mainstream news about what we are experiencing.


                       Is this a recession? Macro numbers seem to indicate
                       yes. And yet, unemployment is not going through the
                       roof, as it should. In fact, businesses of all
                       kinds cannot hire enough employees. Salaries and
                       wages are going through the roof too, contributing
                       to the final, more obvious stages of monetary
                       inflation (started with the massive money-dump
                       directly into billionaires’ pockets). And yet, the
                       world is running out of employees.


                       So some are saying “no, this is not a recession —
                       look at unemployment numbers”. I don’t think this
                       is a valid argument, as mainstream statistics are
                       completely off-mark.


                       In the US, the numbers come from those claiming
                       unemployment benefits from the government. After a
                       while, many give up and are no longer counted. What
                       do these people do? They don’t crawl under a rock
                       and die, right?


          o § Technical⠀➾


                # ⚓ Why_Not_Oberon?⠀⇛


                       “Why not?” indeed. The language has been called an
                       “overlooked gem” and it is both a low-level
                       language, capable of building operating systems,
                       and a high-level language, defined in terms of
                       basic data types and operations that are not
                       inherently bound to machine sizes such as 32-bit
                       and so on. CHARs typically are thought of as 8-bit,
                       but the language doesn’t require that; a particular
                       implementation could use unicode-able CHARs (the
                       JVC ‘oberonc’ compiler does, for instance).


                       It explicitly has the Dijkstra “DO Guard -
                       > Statement { [] Guard -> Statement } OD”
                       construct, visible within Oberon(07)’s WHILE
                       statement!


                # ⚓ There’s_(gonna_be)_an_AI_for_that!⠀⇛


                       Yup, any day now, it’ll be “there’s an AI for
                       that!” instead of last decade’s “there’s an App for
                       that!”.


                # ⚓ Just_Writing⠀⇛


                       Two years ago I wrote about writing. I thought the
                       main barrier that kept most people from writing was
                       environmental distractions. I claimed “stress,
                       anxiety, sleep deprivation, or other mental issues”
                       played a role, but often the issue was “whether or
                       not you chose the right font, whether that section
                       should be in italics, or if that paragraph should
                       be colored red for emphases [sic]“. Those might
                       have been my excuses for not writing then, but its
                       far from my main inhibition now.


                # ⚓ NUU_F4L⠀⇛


                       Dumbphones are becoming extremely hard to come by
                       in the US. 3G networks were shut down, so an entire
                       class of devices are obsolete here. Many carriers
                       are selling Kyocera and other dumbphone devices at
                       extreme prices ($200+), while giving away overkill
                       smartphones for free (one can only imagine that
                       there is some kind of incentive structure at play
                       there…).


                       KaiOS devices are a bit scary, as KaiOS has huge
                       Google investment, and they are becoming almost
                       functional smartphones with quite a lot of
                       functionality and apps – distractions and news are
                       what we’re trying to get away from.


                # ⚓ How_to_start_an_unencrypted_chat_on_Matrix_(Element)⠀⇛


                       This is nice and easy because encryption is the
                       default. On the “people” section on the left side,
                       click the plus icon. Search for a person’s name, or
                       enter their full @username:matrix.org handle into
                       the box. Click Go. All done!


                       If you like encryption – most people do – then you
                       don’t need to read the rest of this post.


                # ⚓ NVIDIA_with_Wayland_on_GNOME⠀⇛


                       Your immediate thought may be why I’m trying to use
                       an NVIDIA card with Wayland. The simple answer is
                       I’ve been stuck with a GTX 1060 for the past 5
                       years with no money to buy an AMD card. Nouveau is
                       a non-starter as the Pascal series of cards does
                       not support reclocking and will occasionally lock
                       up the system.


                       As of driver version 515.57 with GNOME 42, I have a
                       mostly stable experience on Wayland. Emphasis on
                       “mostly”. Going from not being able to even log
                       into the desktop to a functional experience is a
                       major improvement, however I semi-regularly
                       experience freezes with perplexing errors…


                # § Science⠀➾


                      # ⚓ Meduza ☛ Halting_another_‘brain_drain’:_Officials
                        moved_against_Jewish_Agency_of_Israel_partly_to_protect
                        Russia’s_‘economic_prospects,’_says_new_BBC_report_—
                        Meduza⠀⇛


                             The Jewish Agency for Israel predates the
                             existence of the modern state of Israel.
                             Established in 1929, the organization focuses
                             primarily on fostering the immigration of
                             Jews in diaspora to the Land of Israel. The
                             agency has had a presence in Russia since
                             1989, before the USSR’s collapse. Today, it
                             operates branches in nine cities, including
                             Moscow and St. Petersburg. But rising
                             hostility to foreign entities and growing
                             concerns about the loss of its highest-
                             skilled laborers now threatens the Jewish
                             Agency’s future in Russia. Meduza summarizes
                             a new report by the BBC about the
                             organization’s troubles in the country.


                # § Internet/Gemini⠀➾


                      # ⚓ Hello!⠀⇛


                             Growing up I was very active, but very
                             cautious, on the internet of the late 90′s/
                             early 00′s. I was anonymous in the extreme. I
                             didn’t give any demographic or location
                             information whatsoever. But I had some really
                             interesting conversations online… religion,
                             science, anything and everything. People were
                             interesting, and interested.


                             Then I grew up some more, shrugged off the
                             anonymity, signed up for Facebook when it
                             expanded to some more .edu’s early on. Things
                             started getting weird online, though. Hard to
                             put your finger on, but, strange. I deleted
                             Facebook a couple years in, avoided most of
                             the other services, and let my online
                             presence eventually turn into just… a sort of
                             resume. Things got weirder online, and the
                             weirdness and negativity leaked into the real
                             world too. I turtled more, became a hermit
                             online. Didn’t want to get pulled into all
                             that.


                      # ⚓ Some_Boring_Analysis_on_TLGS_Index_(and_messing_with
                        CERN’s_ROOT_analysis_framework)⠀⇛


                             Lupa[1] provides constant basic statistics
                             about the Gemini network. Stats like how many
                             servers are online, number of virtual hosts,
                             TLS distribution, etc.. It’s a really cool
                             project. It got me asking.. what kinds of
                             information can I extract from TLGS’ index?
                             Furthermore, I want to provide some more
                             information for Gemini users. Helping us to
                             understand the network we love.


                             [...]


                             First, I need to get the index from
                             PostgreSQL into SQLite. ROOT’s RDataFrame
                             should support PostgreSQL in the future. But
                             for now SQLite is the best option we have.
                             The table format can be directly extracted
                             from the source code of `tlgs_ctl` and use
                             with minimal modification. Dumping the actual
                             data is more complicated. What’s generated by
                             `pg_dump` is quite close to what SQLite can
                             handle. But some changes are needed. I ended
                             creating my own command to remove unsupported
                             commands. And generates “dump.sql” as output.


                # § Programming⠀➾


                      # ⚓ Re_Error_Handling⠀⇛


                             At it’s simplest, an enum is almost an
                             algabraic data type. In C however enums are
                             little more than an integer constant. If one
                             looks at Zig’s error handling, we see that
                             errors are implemented as error unions. That
                             is, the function is able to return either the
                             intended return value or the error. Zig also
                             has tagged unions, which in code look like an
                             enum wrapping a union. This is what is really
                             meant by the term Algabraic Data Types. A
                             type that can be one of several things with a
                             tag to determine unequivically what type it
                             is


                      # ⚓ Hacking_osu!lazer_for_fun_and_fun⠀⇛


                             The circles mode in osu! is a somewhat fun
                             game. I want to play it casually from time to
                             time, and enjoy myself, without taking it
                             seriously. But the game has always fought
                             back against me whenever I’ve tried to play
                             it more. The life bar is strangely aggressive
                             on some songs and the scoring system places a
                             huge amount of emphasis on combo, to the
                             point where accidentally missing a single
                             note will make your score worthless, no
                             matter what else happened in that attempt.


                             Something I love to do in rhythm games is
                             improve upon my past scores, but the combo
                             system makes this difficult and frustrating.
                             “Improving” in the circles mode of osu! means
                             “getting lucky and not missing for longer
                             chains”. Some people may find satisfaction in
                             playing easier songs and striving for a full
                             combo, but I find it much more fun to play
                             more difficult and intense songs and try to
                             get a certain % score on them.


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



                    ䷩ 𝚕𝚒𝚗𝚎 6475

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.29.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_29/07/2022:_End_of_SysAdmin_Appreciation_Day⠀✐


Posted in News_Roundup at 8:00 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Server
          o Audiocasts/Shows
          o Instructionals/Technical
          o WINE_or_Emulation
          o Desktop_Environments/WMs
                # K_Desktop_Environment/KDE_SC/Qt
                # GNOME_Desktop/GTK
    * Distributions_and_Operating_Systems
          o Fedora_/_Red_Hat_/_IBM
          o Debian_Family
          o Canonical/Ubuntu_Family
          o Devices/Embedded
    * Free,_Libre,_and_Open_Source_Software
          o Events
          o Web_Browsers
                # Mozilla
          o Programming/Development
    * Leftovers
          o Science
          o Hardware
          o Health/Nutrition/Agriculture
          o Linux_Foundation
          o Security
          o Defence/Aggression
          o Environment
                # Energy
                # Wildlife/Nature
          o Finance
          o AstroTurf/Lobbying/Politics
          o Freedom_of_Information_/_Freedom_of_the_Press
          o Civil_Rights/Policing
          o Monopolies
                # Copyrights
    * Gemini*_and_Gopher
          o Technical
                # Science
    * § GNU/Linux⠀➾


          o ⚓ Linux Foundation’s Site/Blog ☛ People_of_Open_Source:_Neville
            Spiteri,_Wevr_–_Linux_Foundation⠀⇛


                 Linux and Python were my best friends in 2000.


          o ⚓ Linux Links ☛ Linux_Around_The_World:_Slovenia_–_LinuxLinks⠀⇛


                 Slovenia is a country in Central Europe. It is bordered
                 by Italy to the west, Austria to the north, Hungary to
                 the northeast, Croatia to the southeast, and the Adriatic
                 Sea to the southwest.


          o § Server⠀➾


                # ⚓ Happy_SysAdmin_Appreciation_Day!_»_ADMIN_Magazine⠀⇛


                       To celebrate System Administration Appreciation Day
                       and to honor the tireless work of IT professionals
                       around the world, ADMIN Network & Security and
                       TuxCare are proud to present the 2022 edition of 10
                       Terrific Tools for the Busy Admin.


                # ⚓ FOSSLife ☛ Special_Offer_to_Celebrate_SysAdmin_Appreciation
                  Day⠀⇛


                       For a limited time, you can download this free
                       collection of articles covering useful tools for IT
                       pros.


                # ⚓ Using_Kubernetes_to_Secure_Data_–_Container_Journal⠀⇛


                       Data loss and ransomware are two of the biggest
                       threats to data security today, especially as
                       malicious actors turn their attention to the cloud.
                       Even with security perimeters in place, bad actors
                       are determined to map out new methods and tactics
                       to penetrate these cloud-based environments.


                       Although it’s impossible to predict or prevent
                       every attack, there are security measures and
                       practices that can help reduce the risk. Cloud-
                       native development practices can help your
                       organization ensure that these solutions are more
                       resistant to attack. Kubernetes, for example, is a
                       tool that can help.


          o § Audiocasts/Shows⠀➾


                # ⚓ Red Hat Official ☛ Are_Big_Mistakes_That_Big_Of_A_Deal?
                  Part_2⠀⇛


                       Mistakes are part of growth. If we’re lucky, we’re
                       in an environment where they’re not punished
                       harshly. That lets us fix the problem, learn to do
                       better, and move on—but also to tell the story once
                       the sting has passed.


                       Last episode, we heard three stories of people
                       blundering into trouble and coming out the other
                       side a little bit wiser. This episode adds three
                       more stories of mistakes being made—but the culprit
                       isn’t always as clear.


                # ⚓ Jupiter Broadcasting ☛ Linux_Action_News_251⠀⇛


                       Red Hat hints at its future direction, why realtime
                       might finally come to Linux after all these years,
                       and our reaction to Google’s ambitious new
                       programing language.


                # ⚓ Jupiter Broadcasting ☛ Solid_as_a_Rock_|_Self-Hosted_76⠀⇛


                       Alex runs us through his new and improved off-site
                       backup setup, and Chris is trying out some Shelly
                       devices.


          o § Instructionals/Technical⠀➾


                # ⚓ TecAdmin ☛ Running_a_Cron_Every_10,_20_or_30_Minutes_–
                  TecAdmin⠀⇛


                       Cron is a service that runs tasks at specified
                       intervals in Unix/Linux systems. It’s commonly used
                       for operational tasks like cleaning log files or
                       backing up databases. But for our purposes, we can
                       also use it to automate applications to perform
                       some tasks at regular intervals.


                # ⚓ Make Use Of ☛ How_to_Make_Your_Linux_Terminal_More_Colorful
                  With_lolcat⠀⇛


                       The terminal can seem a little boring compared to
                       flashier graphical Linux apps. lolcat is a program
                       that adds some flair to your Linux terminal
                       sessions. Here’s how to install and use lolcat on
                       Linux.


                # ⚓ Network World ☛ Repeating_commands_on_Linux_with_or_without
                  changes_|_Network_World⠀⇛


                       Life on the command line on Linux is clearly
                       something most of us enjoy, but typing the same
                       command again and again can become tiresome. To
                       avoid that boredom, this post explains a number of
                       ways that you can make repeating commands – or
                       repeating commands but with some changes – a lot
                       easier than you might expect.


                # ⚓ Linux Made Simple ☛ How_to_install_Toontown_Rewritten_on_a
                  Chromebook_–_Updated_Tutorial⠀⇛


                       Today we are looking at how to install Toontown
                       Rewritten on a Chromebook. Please follow the video/
                       audio guide as a tutorial where we explain the
                       process step by step and use the commands below.


                       Please take note that the fonts are currently not
                       visible, as seen in the video. We hope it will be
                       fixed soon.


                       This tutorial will only work on Chromebooks with an
                       Intel or AMD CPU (with Linux Apps Support) and not
                       those with an ARM64 architecture CPU.


          o § WINE or Emulation⠀➾


                # ⚓ WINE Project (Official) ☛ WineHQ_–_Wine_Announcement_–_The
                  Wine_development_release_7.14_is_now_available.⠀⇛


                       The Wine development release 7.14 is now available.


                       What’s new in this release:
                       – More progress on syscall interface for USER32.
                       – Improved font fallbacks in DirectWrite.
                       – Some fixes for socket shutdowns.
                       – Various bug fixes.


                       The source is available at:


                       https://dl.winehq.org/wine/source/7.x/wine-
                       7.14.tar.xz


                       Binary packages for various distributions will be
                       available from:


                       https://www.winehq.org/download


                       You will find documentation on https://
                       www.winehq.org/documentation


                       You can also get the current source directly from
                       the git
                       repository. Check https://www.winehq.org/git for
                       details.


                       Wine is available thanks to the work of many
                       people. See the file
                       AUTHORS in the distribution for the complete list.


          o § Desktop Environments/WMs⠀➾


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


                      # ⚓ Adriaan de Groot ☛ Mini-Talks_Published⠀⇛


                             At work-work there are educational sessions
                             for the software team. They last about 2
                             hours, generally filled with a mix of
                             watching a talk, discussing how the talk
                             applies to the codebase, and individual
                             developers presenting something. Typical
                             conference talks might come from CPP on Sea).
                             Discussion might go on about vocabulary types
                             – what are the things in our system?
                             Presentations are whatever somebody feels is
                             interesting, and I’ve written up two 20-
                             minute talks so far.


                             There’s CMake Domain-Specific-Languages,
                             which was written to talk about how we (at
                             work-work) can update our CMake
                             infrastructure to be less repetetive and to
                             express better the kinds of things we build.
                             It’s based on my experience with Calamares
                             (which has CMake code to support writing
                             Calamares modules) and ARPA2CM (similar, also
                             for things like “build all the kinds of
                             libraries you can from these sources”). The
                             slides have been sanitized of any internal
                             bits.


                # § GNOME Desktop/GTK⠀➾


                      # ⚓ This Week in GNOME ☛ #54_More_Portings_·_This_Week_in
                        GNOME⠀⇛


                             Update on what happened across the GNOME
                             project in the week from July 22 to July 29.


                      # ⚓ Barry Kauler ☛ GTK3_CUPS_printing_fixed⠀⇛


                             Amazing, how long ago since the Dunfell-
                             series had the first release? In all of that
                             time, have not been able to from from GTK3-
                             based apps.
                             For Firefox, I always print to PDF, then use
                             Evince PDF viewer to print the PDF. Evince,
                             being GTK2-based can print.
                             Yes, I discovered that the ‘gtk+3′ package in
                             OpenEmbedded defaults to not having CUPS
                             support. I modified the recipe, and
                             recompiled it, and tested the result. Voila,
                             FF now prints!


                      # ⚓ Linuxiac ☛ Dash_to_Dock_vs._Dash_to_Panel:_Which_One
                        Extension_is_Better?⠀⇛


                             Let’s compare the two most popular GNOME
                             extensions providing dock functionality, Dash
                             to Dock vs. Dash to Panel. Which one is
                             better?


                             Unlike other modern desktop environments,
                             GNOME sticks to a different philosophy than
                             the commonly accepted traditional user
                             experience. But we will not comment here on
                             whether this approach helps or degrades the
                             GNOME desktop environment.


                             However, one thing is certain: the average
                             computer user has specific expectations about
                             how the user interface appears and functions.
                             And more precisely, elements and behaviors
                             that he is familiar with embraced through
                             time and is at ease with.


                             The dock panel is an essential component of
                             almost every desktop environment. It is the
                             element with which the user interacts the
                             most, providing for quick and easy
                             application launching, quick switching
                             between them, a list of currently running
                             ones, and so on. Furthermore, other features
                             like the start menu, system tray, and others
                             are integral.


    * § Distributions and Operating Systems⠀➾


          o ⚓ Digital Trends ☛ The_best_Linux_distros_for_gaming_|_Digital
            Trends⠀⇛


                 You’ve heard all the accusations. Gaming on Linux is
                 crazy, right? Gamers should use a Windows PC and be done
                 with it. Linux is all terminal commands and Firefox
                 stuff. Valve would like a word with you. After all, the
                 Valve Steam Deck runs on Linux. Steam is available on
                 Linux, with more than 6,000 titles available. Many game
                 developers have begun building for Linux systems as well.


          o ⚓ H2S Media ☛ 4_Best_Linux_Distros_for_Android_Studio_Developers_–
            Linux_Shout⠀⇛


                 Among the popular operating systems, Linux has always
                 been the first choice of many programmers and developers
                 because they don’t have to pay for it. Moreover being an
                 open source licensed software it is easy for programmers
                 to customize Linux as per their needs. Furthermore, Linux
                 also supports a wide range of programming languages,
                 including C, C++, Perl, Ruby, PHP, and more.


                 Even Linux is now a backbone of the internet, cloud
                 hosting, Android, smartphones, routers, and other many
                 devices. Hence, system administrators and developers need
                 to learn how to operate a Linux system. There was a time
                 when it was only a cup of tea for coders, but now even
                 common desktop users can learn and operate Linux easily
                 because of attractive and intuitive graphical desktop
                 environments.


          o § Fedora / Red Hat / IBM⠀➾


                # ⚓ Containerization_Executive_Q&A_|_ESF⠀⇛


                       Containerization is a key technology for
                       enterprises that need to frequently transport
                       critical applications between different
                       environments and operating systems. To maintain
                       operations, they have to launch and move those
                       applications within a short time frame. The
                       technology gives businesses a more flexible
                       application infrastructure.


                # ⚓ Video ☛ In_the_Clouds_(E26)_|_Cloud_Ecosystem_–_Invidious⠀⇛


                       The cloud native ecosystem has grown far beyond
                       Kubernetes. The hundreds of projects show the
                       innovation in open source, and the challenge for
                       anyone to keep up with current technology. Red Hat
                       Senior Director, Technical Marketing & Field PM,
                       Cloud Platforms Chris Morgan joins host Stu Miniman
                       to discuss the evolution of the cloud-native
                       ecosystem. Chris was intimately involved in
                       development of OpenShift and its partnerships with
                       many key vendors.


                # ⚓ Richard_Hughes:_Emulated_host_profiles_in_fwupd [Ed: IBM is
                  shilling Microsoft_vendor_lockin_disguised_as_“security”]⠀⇛


                       As some as you may know, there might be firmware
                       security support in the next versions of Plymouth,
                       GNOME Control Center and GDM. This is a great
                       thing, as most people are running terribly insecure
                       hardware and have no idea. The great majority of
                       these systems can be improved with a few settings
                       changes, and the first step in my plan is showing
                       people what’s wrong, giving some quick information,
                       and perhaps how to change it. The next step will be
                       a “fix the problem” button but that’s still being
                       worked on, and will need some pretty involved
                       testing for each OEM. For the bigger picture
                       there’s the HSI documentation which is a heavy and
                       technical read but the introduction might be
                       interesting. For other 99.99% of the population
                       here are some pretty screenshots:


                # ⚓ Fedora Project ☛ Fedora_Community_Blog:_Important_changes
                  to_software_license_information_in_Fedora_packages_(SPDX_and
                  more!)⠀⇛


                       On behalf of all of the folks working on Fedora
                       licensing improvements, I have a few things to
                       announce!


                # ⚓ Fedora Project ☛ Fedora_Community_Blog:_CPE_Weekly_Update_–
                  Week_30_2022⠀⇛


                       Purpose of this team is to take care of day to day
                       business regarding CentOS and Fedora Infrastructure
                       and Fedora release engineering work.


                # ⚓ Red Hat ☛ Red_Hat_Developer_roundup:_Best_of_July_2022_|
                  Red_Hat_Developer⠀⇛


                       Welcome to our monthly article recap, where we
                       round up the latest popular content from Red Hat
                       Developer in one helpful place. Like last month,
                       GitOps, Go, and Kubernetes security topics were in
                       high demand from our readers. Without further ado,
                       let’s dive into the July highlights.


                # ⚓ Red Hat Official ☛ Modernization:_Building_a_modernization
                  project_team⠀⇛


                       In this article, I discuss a proposal to build a
                       success-primed team to modernize a portfolio of
                       applications. We will take into account our points
                       for alignment from our previous blog post. It’s
                       important to remember this might not be a team that
                       will be long running or one that will become a key
                       part of the enterprise culture. As we discussed in
                       the previous article, there will be a set budget
                       and timeframe to get the work done. What is being
                       proposed in this article is building a team to get
                       results under these constraints.


                # ⚓ Enterprisers Project ☛ Workplace_culture:_4_ways_to_foster
                  healthy_conflict⠀⇛


                       Especially as CIOs and IT departments begin to
                       rethink the way they interact with IT and business,
                       the idea that conflict is unproductive and
                       detrimental to workplace culture – and the notion
                       that organizations should avoid conflict entirely –
                       is based on a false premise: that all conflicts are
                       unhealthy and unproductive.


                       That claim falls flat when we broaden our
                       perspective on what the term “conflict”
                       encompasses.


                       Healthy conflict allows room for treating people
                       with respect, listening to others’ ideas, and
                       considering those ideas during collaborative,
                       iterative, and agile processes. Maintaining a
                       diversity of thought and experience is crucial to
                       building a healthy, fair, and inclusive company
                       culture.


                # ⚓ Red Hat Official ☛ Happy_Sysadmin_Appreciation_Day:_2022′s
                  top_articles_for_sysadmins_|_Enable_Sysadmin⠀⇛


                       Thank you to all of the system administrators who
                       keep our systems up and running, patched, and
                       deployed every day of the year. Check out our most
                       popular articles for sysadmins.


                # ⚓ Enterprisers Project ☛ Future-proof_your_IT_organization_by
                  focusing_on_these_5_priorities⠀⇛


                       The past two years of rapid digital transformation
                       have reshaped the role of IT teams. More
                       enterprises and workloads have shifted to the
                       cloud, digital user experience (UX) has become more
                       important than ever, and once-siloed IT
                       professionals are now a central part of business
                       decision-making. But understandably, many
                       organizations are struggling to keep pace with
                       these changes.


                       The organizations coming out on top are the ones
                       retooling IT operations to adapt to shifts in
                       today’s market. These companies – we’ll call them
                       the leaders of today’s IT world – are steps ahead
                       of those that haven’t narrowed their focus on what
                       really matters.


                       Innovation and growth – rather than just staying
                       afloat – must be a top priority to maintain a
                       competitive advantage in 2022 and beyond.


          o § Debian Family⠀➾


                # ⚓ New_Debian_Developers_and_Maintainers_(May_and_June_2022)⠀⇛


                       The following contributors got their Debian
                       Developer accounts in the last two months:


                       Geoffroy Berret (kaliko)
                       Arnaud Ferraris (aferraris)


          o § Canonical/Ubuntu Family⠀➾


                # ⚓ 9to5Linux ☛ Linux_Mint_21_“Vanessa”_Is_Now_Available_for
                  Download,_This_Is_What’s_New⠀⇛


                       Linux Mint 21 “Vanessa” has been in development for
                       the past five months and it’s the new major series
                       of Linux Mint after Linux Mint 20 “Ulyana”,
                       shipping with a brand-new Ubuntu base powered by
                       Linux kernel 5.15 LTS and derived from Ubuntu 22.04
                       LTS (Jammy Jellyfish), and supported for the next
                       five years, until 2027.


                       Linux Mint 21 comes in three flavors, with the
                       Cinnamon 5.4, Xfce 4.16, and MATE 1.26 desktop
                       environments. All three flavors include the same
                       under-the-hood improvements, as well as numerous
                       other changes!


          o § Devices/Embedded⠀➾


                # ⚓ CNX Software ☛ Pinecil_V2_soldering_iron_gets_BL706
                  Bluetooth_LE_RISC-V_MCU,_USB_PD_EPR_support_–_CNX_Software⠀⇛


                       PINE64 is about to launch the second generation
                       Pinecil RISC-V soldering iron with the Pinecil V2
                       featuring a new Bouffalo Lab BL706 RISC-
                       V microcontroller with Bluetooth LE connectivity,
                       optimizations for higher power levels, as well as
                       tentative support for the new USB PD EPR standard
                       (Extended Power Range) working at up to 28V.


                # ⚓ CNX Software ☛ Altium_Designer_adds_3D_PCB_layout_tool_–
                  CNX_Software [Ed: Red flag if they use Microsoft (LinkedIn)
                  and Facebook to promote this]⠀⇛


                       While we like open-source tools such as KiCAD,
                       Altium has added a pretty cool feature to the
                       Altium Designer program with a 3D layout tool,
                       which as its name implies, allows the design of 3D
                       PCBs…


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


          o ⚓ Apache Blog ☛ Launch_of_the_2022_ASF_Community_Survey_:_The
            Apache_Software_Foundation_Blog⠀⇛


                 This week, we are excited to launch the 2022 ASF
                 Community Survey, which will gather scientific data that
                 allows us to understand our community better, both in its
                 demographic composition and collaboration styles and
                 preferences. We want to find areas where we can continue
                 to do great work and others where we need to provide more
                 support so that our projects can keep growing healthy and
                 diverse. This joint effort was long overdue: our last
                 surveys of this kind were implemented in 2016 [1] and
                 2020 [2], which means we are finally in a position to see
                 trends over time.


                 For this new version of the survey, we worked with
                 Bitergia to design it. Bitergia is an expert in analyzing
                 open source communities and other types of software
                 development teams. They have deep experience running this
                 type of survey and research in open source communities.
                 Among other studies, their previous work includes an
                 analysis in gender diversity in technical contributions
                 for OpenStack [3]. The 2022 ASF Community Survey is the
                 first part of a two-stage research project. The second
                 part consists of interviews with people who have
                 contributed to the ASF in order to assess their
                 experience. We’ll share more on this second part of the
                 project soon.


          o ⚓ Apache Blog ☛ The_Apache_News_Round-up:_week_ending_29_July_2022
            :_The_Apache_Software_Foundation_Blog⠀⇛


                 Farewell, July –we’re wrapping up the month with another
                 great week. Here are the latest updates on the Apache
                 community’s activities…


          o § Events⠀➾


                # ⚓ Allan_Day:_BBerlin_mini-GUADEC_–_Form_and_Function⠀⇛


                       As I write this post, I’m speeding through the
                       German countryside, on a high speed train heading
                       for Amsterdam, as I make my way home from the
                       GUADEC satellite event that just took place in
                       Berlin.


                       The event itself was notable for me, given that it
                       was the first face-to-face GNOME event that I’ve
                       participated in since the Covid pandemic set in.
                       Given how long its been since I physically met with
                       other contributors, I felt that it was important to
                       me to do a GNOME event this summer, but I wasn’t
                       prepared to travel to Mexico for various reasons
                       (the environment, being away from family), so the
                       Berlin event that sprang up was a great
                       opportunity.


                       I’d like to thank the local Berlin organisers for
                       making the event happen, C-Base for hosting us, and
                       the GNOME Foundation for providing sponsorship so I
                       could attend.


                # ⚓ Linux Plumbers Conference (LPC) ☛ LPC_2022_Schedule_is
                  posted!_–_Linux_Plumbers_Conference_2022⠀⇛


                       The schedule for when the miniconferences and
                       tracks are going to occur is now posted at: https:/
                       /lpc.events/event/16/timetable/#all


                       The runners for the miniconferences will be adding
                       more details to each of their schedules over the
                       coming weeks.


                # ⚓ Qubes_OS_Summit_2022:_September_9-11_in_Berlin_|_Qubes_OS⠀⇛


                       In conjunction with 3mdeb, the fourth edition of
                       our Qubes OS Summit will be held live this year
                       from September 9 to 11 in Berlin, Germany! For more
                       information about this event, including the CFP
                       (which is open until August 29), please see: https:
                       //qubesos.3mdeb.com


          o § Web Browsers⠀➾


                # § Mozilla⠀➾


                      # ⚓ Mozilla ☛ Performance_Tools_Newsletter_(H1_2002)_–
                        Mozilla_Performance⠀⇛


                             As the Perf-Tools team, we are responsible
                             for the Firefox Profiler. This newsletter
                             gives an overview of the new features and
                             improvements we’ve done in the first half of
                             2022.


                             You can find the previous newsletter here
                             which was about the Q4 2021. This newsletter
                             contains updates related to work done in the
                             first half of 2022.


                             Here are some highlights.


                      # ⚓ Mozilla ☛ L10n_Report:_July_2022_Edition_|_Mozilla
                        L10N⠀⇛


                             While the last months have been pretty quiet
                             in terms of new content for Firefox, we’re
                             approaching a new major release for 2022, and
                             that will include new features and dedicated
                             onboarding.


                      # ⚓ Mozilla ☛ Riot_Games’_head_of_player_community,_known
                        as_‘Aureylian’_to_game_streaming_fans,_on_her_favorite
                        corners_of_the_internet [Ed: Proprietary software again
                        in Mozilla's blog]⠀⇛


          o § Programming/Development⠀➾


                # ⚓ arc4random_–_are_you_sure_we_want_these?⠀⇛


                       Hi glibc developers,

                       I learned about the addition of the arc4random
                       functions in glibc this
                       morning, thanks to Phoronix. I wish somebody would
                       have CC'd me into
                       those discussions before it got committed, but here
                       we are.

                       I really wonder whether this is a good idea,
                       whether this is something
                       that glibc wants, and whether it's a design worth
                       committing to in the
                       long term.

                       Firstly, for what use cases does this actually
                       help? As of recent
                       changes to the Linux kernels -- now backported all
                       the way to 4.9! --
                       getrandom() and /dev/urandom are extremely fast and
                       operate over per-cpu
                       states locklessly. Sure you avoid a syscall by
                       doing that in userspace,
                       but does it really matter? Who exactly benefits
                       from this?

                       Seen that way, it seems like a lot of complexity
                       for nothing, and
                       complexity that will lead to bugs and various
                       oversights eventually.
                # ⚓ GCC ☛ GCC_12.1.1_Status_Report_(2022-07-27)⠀⇛


                       The gcc-12 branch is open for regression and
                       documentation fixes.

                       It is time for a GCC 12.2 release, we are
                       comparatively late with it
                       already.  The plan is to create a GCC 12.2 release
                       candidate on
                       August 12th which should give plenty of time to
                       backport or implement
                       important regression fixes.

                       Please make sure your primary and secondary targets
                       are in good
                       shape for this release.
    * § Leftovers⠀➾


          o ⚓ Scheerpost ☛ Patrick_Lawrence:_The_Causes_of_Things⠀⇛


                 Over a summer sup on the back lawn the other night, a
                 Times-reading, MSNBC–watching, NPR–listening neighbor…


          o ⚓ Counter Punch ☛ The_Cynics’_Monkeywrench⠀⇛


                 Last week, for instance, I wrote about the weekend I
                 spent, a decade ago, getting handgun training from the
                 NRA — and what I learned, which is that the things you
                 need to fear are endless, and when one of them pops up in
                 your life you’d better be prepared to kill it. One reader
                 said he wondered “if Robert has ever truly felt as though
                 his life or those he values were threatened” and quickly
                 answered his own question: Of course not! And then he
                 crooned, oh so tenderly: “Must be nice for Robert to live
                 in such an insulated bubble.”


                 Issue solved! Everyone needs a gun, except for the
                 utterly naïve.


          o ⚓ Hackaday ☛ Foam_Cutter_Moves_Like_A_Hot_Knife_Through_Butter⠀⇛


                 Make enough attempts to cut foam using whatever you’ve
                 got — utility knife, hacksaw, serrated plastic knife —
                 and you’ll wish hard for something that cuts cleaner,
                 faster, and better. While there are all sorts of ways to
                 build a hot wire foam cutter, this design from
                 [jasonwinfieldnz] is both interesting and imitable.


          o ⚓ Hackaday ☛ Love_Is_A_Burning_Flame,_And_So_Is_This_Underwater
            Burning_Ring_Of_Fire⠀⇛


                 When Johnny Cash wrote “Ring of Fire”, he was talking
                 about love. But when an unnamed follower of
                 [TheBackyardScientist] took it literally and suggested
                 making actual rings of fire — underwater —  they rose to
                 the challenge as you can see in the video below the
                 break.


          o ⚓ Counter Punch ☛ Encounters_With_Sinead_O’Connor⠀⇛


                 Speaking with her, reminded me how much I loved listening
                 to her music which I’d listened to very little in the
                 previous decade, though she had been featured several
                 times in CounterPunch “Best Of” articles. Her haunting
                 voice was just as powerful as it had seemed to me when I
                 first heard her in the late 80s. I wasn’t an MTV fanatic
                 like my older sister, but I’d stop to watch Sinead’s
                 videos a long with a handful of others.


                 I recalled the night she tore up the photo of Pope John
                 Paul II and said “Fight the Real Enemy”. I thought she
                 was bold and beautiful and brave and I had deep
                 admiration for her. And I didn’t understand why the fuck
                 anybody in my surroundings cared at all that she’d done
                 this. That is to say, the Mormon capital of the world,
                 Happy Valley, Utah. I defended her and questioned them.
                 It’s the Catholic pope… why should it bother any of them?
                 It’s not as if it’s the president of the Mormon church. I
                 wouldn’t have torn up a photo of him then, but I did
                 question the abuse of men in the church from years before
                 that. It was only two before then that I had three
                 different men, two bishops and an older member of the
                 priesthood, tell me that because I was then pregnant and
                 getting married, it was now my duty to please my husband
                 however he saw fit, whether I wanted to or not. Their
                 orders were eerily similar. They all told me that I had
                 tempted  my soon to be husband and spread my legs for him
                 and got myself pregnant and ruined his life and from then
                 forward I should continued spreading my legs (yes they
                 said those exact words) and if I didn’t want to have sex
                 then I should at least give him a hand-job. All three of
                 them asked me if I knew how to do that and offered
                 instruction. I was 17. These were men between 45-65. So
                 as Sinead made her statement about PJ11 which brought
                 about a war against her by the music industry, that
                 profited from her and still does, and the entire world
                 still ignoring for another decade the abuses committed by
                 the Catholic church, the seeds of escaping Mormonism were
                 already sprouted in the back of my mind. She was an
                 inspiration even if I can’t carry a tune. Shortly after
                 her photo destruction, I shaved my head and escaped
                 Mormonism.


          o ⚓ The Nation ☛ Encounters_With_Adélia_Prado⠀⇛


                 My impulse to live and toil and evolve inside someone
                 else’s words is sparked by a desire for intimacy. Living
                 in Brazil for 18 months in the late 1970s, I haunted
                 bookstores and combed through literary journals, aching
                 to find a voice that was irresistible, larger, different
                 than mine, one that challenged me to find a way to haul
                 it—still fully alive—into English.


          o § Science⠀➾


                # ⚓ Jurassic_vampire_squid_were_active_predators⠀⇛


                       When you think Jurassic Park, you probably imagine
                       a chomping T-Rex, or even a giant snapping
                       Mosasaurus. But how about vampire squid?


          o § Hardware⠀➾


                # ⚓ Hackaday ☛ A_Customizable_Macropad_To_Make_Anyone’s_Tail
                  Wag⠀⇛


                       [Gili Yankovitch] has always wanted some kind of
                       macro keypad for all those boss-slaying combos he
                       keeps up the sleeve of his wizard robe while
                       playing WoW. Seventeen years later, he finally
                       threw down the gauntlet and built one. But really,
                       this is an understatement, because Paws is kind of
                       the customizable macropad to end all customizable
                       macropads.


                # ⚓ Hackaday ☛ Hackaday_Prize_2022:_A_Functional_Commodore_PET
                  Tribute⠀⇛


                       The C64 may be the best-selling computer of all
                       time, but Commodore made several machines before
                       that, too. [Mjnurney] always loved the Commodore
                       PET, and set about building some new machines in
                       the PET’s unique all-in-one form factor.


                # ⚓ Hackaday ☛ New_OS_For_Commodore_64_Adds_Modern_Features⠀⇛


                       The Commodore 64 was a revolutionary computer for
                       its day and age. After four decades, though, it
                       gets harder and harder to use these computers for
                       anything more than educational or hobby electronics
                       projects. [Gregory Nacu] is fiercly determined to
                       challenge this idea, though, and has gone to great
                       extremes to make this hardware still relevant in
                       the modern age by writing a completely new
                       operating system for the Commodore machines.


                # ⚓ Hackaday ☛ PERSEUS-9,_The_Dual-6502_Portable_Machine_That
                  Should_Have_Been⠀⇛


                       A question: does anyone who was around in the early
                       days of the 8-bit computer revolution remember a
                       dual-CPU 6502 portable machine like this one? Or
                       just a dual-CPU machine? Or even just a reasonably
                       portable computer? We don’t, but that begs a
                       further question: if [Mitsuru Yamada] can build
                       such a machine today with parts that were available
                       in the era, why weren’t these a thing back then?


                # ⚓ Petros Koutoupis ☛ Intel_to_Kill_its_Optane_Business?_–
                  Random_[Tech]_Stuff⠀⇛


                       It is a shame too because it was a solid
                       technology. The problem was always: lack of
                       adoption. The technology was confined and limited
                       to Intel. This is yet another case of history
                       repeating itself and I am saddened to read this
                       news.


                # ⚓ The Next Platform ☛ Intel_Let_The_Chips_Fall_Where_They
                  Might⠀⇛


                       This day always comes. It is the nature of monopoly
                       and hubris.


                       It came for IBM. It came for Microsoft, and it is
                       coming for Facebook. It will come for Google and,
                       even though it is hard to believe, it will come for
                       Amazon. And it is most assuredly coming for Intel
                       right now, and it is probably going to get worse.
                       Maybe not as bad as IBM in the early 1990s –
                       because nothing was worse than that self-inflicted
                       and self-described “near-death experience,” where
                       Big Blue had the biggest write-offs in corporate
                       history and eventually had to lay off half of its
                       400,000 workforce – but most assuredly for Intel,
                       bad nonetheless.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ Counter Punch ☛ The_Weaponization_of_Food⠀⇛


                       International outcry against the Russian bombing of
                       Odesa—as with its earlier strikes on shopping
                       malls, train stations, and hospitals—has been
                       fierce. “Striking a target crucial for grain export
                       a day after the signature of Istanbul agreements is
                       particularly reprehensible & again demonstrates
                       Russia’s total disregard for international law &
                       commitments,” tweeted Josep Borrell Fontelles, who
                       coordinates the European Union’s foreign policy.


                       Despite Russia’s action, the agreement on grain
                       exports will likely hold. After all, Russia didn’t
                       technically violate the accord. The Kremlin
                       promised only to avoid hitting the ships carrying
                       food to the outside world.


                # ⚓ Counter Punch ☛ Climate_Change_is_Reshaping_America’s_Most
                  Iconic_Landscapes⠀⇛


                       I see constellations at night instead of smog. I’ve
                       summited rock formations that left me breathless
                       and humbled with sweeping views, reminding me to
                       tread lightly on the sacred and ancestral lands of
                       the Cahuilla, Chemehuevi, Serrano, and Mojave
                       peoples.


                       Millions have also shared memorable experiences
                       like these at our long-treasured national parks.
                       But as climate change caused by human activities
                       brings more heat, drought, and fire, it now
                       threatens natural wonders across the country.


                # ⚓ TruthOut ☛ GOP_Opposition_to_Drug_Pricing_Bill_Shows_Scope
                  of_Big_Pharma’s_Grip_on_Congress⠀⇛


          o § Linux Foundation⠀➾


                # ⚓ Reuters ☛ OS_Climate_launches_climate_planning_tools_for
                  companies,_investors [Ed: Linux Foundation buys greenwashing
                  puff pieces from tycoon-owned media]⠀⇛


                       Non-profit OS Climate on Wednesday launched the
                       first in a series of free tools to drive climate-
                       friendly decision making by companies, financial
                       institutions and governments.


                       As a project of the Linux Foundation, a non-profit
                       technology consortium founded in 2000 that builds
                       open-source software, OS Climate aims to help fill
                       the gaps in data currently preventing capital
                       flowing to the right projects.


          o § Security⠀➾


                # ⚓ LWN ☛ Security_updates_for_Friday_[LWN.net]⠀⇛


                       Security updates have been issued by Fedora (xorg-
                       x11-server and xorg-x11-server-Xwayland), SUSE
                       (aws-iam-authenticator, ldb, samba, libguestfs,
                       samba, and u-boot), and Ubuntu (firefox, intel-
                       microcode, libtirpc, linux, linux-aws, linux-kvm,
                       linux-lts-xenial, linux-azure, linux-bluefield,
                       linux-gcp-5.4, linux-gke-5.4, mysql-5.7, and mysql-
                       5.7, mysql-8.0).


                # ⚓ Bruce Schneier ☛ Microsoft_Zero-Days_Sold_and_then_Used
                  [Ed: There are so many Microsoft Zero-Days and Microsoft even
                  shares them with the NSA (back doors)]⠀⇛


                       Yet another article about cyber-weapons arms
                       manufacturers and their particular supply chain.
                       This one is about Windows and Adobe Reader zero-day
                       exploits sold by an Austrian company named DSIRF.


                # ⚓ 0-days_sold_by_Austrian_firm_used_to_hack_Windows_users,
                  Microsoft_says [Ed: Microsoft claiming to value security is
                  an outright lie; it's just another blame game]⠀⇛


                       Multiple news outlets have published articles like
                       this one, which cited marketing materials and other
                       evidence linking DSIRF to Subzero, a malicious
                       toolset for “automated exfiltration of sensitive/
                       private data” and “tailored access operations
                       [including] identification, tracking and
                       infiltration of threats.”


                # ⚓ USCERT ☛ CISA_Adds_One_Known_Exploited_Vulnerability_to
                  Catalog [Ed: Microsoft and Windows still dominate this list
                  of “Known Exploited Vulnerabilit[ies]“]⠀⇛


                       CISA has added one new vulnerability to its Known
                       Exploited Vulnerabilities Catalog, based on
                       evidence of active exploitation. These types of
                       vulnerabilities are a frequent attack vector for
                       malicious cyber actors and pose significant risk to
                       the federal enterprise.


                # ⚓ Efficient_Infrastructure_Testing_|_Pen_Test_Partners⠀⇛


                       Before we start let’s set the scene regarding
                       vulnerability assessment. It is imperative that
                       enterprises conduct their own continuous automated
                       scanning, to have up-to-date assessments of threats
                       that their networks may be susceptible to.
                       Infrastructure penetration testing (discussed in
                       this blog post) should be then used to delve
                       further to expose issues and attack chains using
                       manual testing that would have not been uncovered
                       by automated techniques.


                       To go one step further, mature environments with
                       well-formed patch management policies and good
                       security practice, should then consider Red Team
                       engagements to assess response and detection
                       against emulated real-world adversaries.


                       On several infrastructure tests I’ve found myself
                       performing vulnerability assessments on expansive
                       networks. While Nessus and other scanning tools
                       have their place, it is crucial to be able to work
                       efficiently to provide much more value on an
                       engagement rather than providing tool output that
                       clients can run themselves (and should be doing,
                       regularly).


                # ⚓ Ubuntu ☛ Multipass_1.10_brings_new_instance_modification
                  capabilities_|_Ubuntu [Ed: Canonical_prioritising_Microsoft
                  again?]⠀⇛


                       The 1.10 update brings some other nice features,
                       particularly for Windows users. Windows Pro
                       machines can now take advantage of generation 2
                       virtual machines through Hyper-V. These new VMs
                       support a variety of boot features, including UEFI,
                       secure boot, and more.


          o § Defence/Aggression⠀➾


                # ⚓ Counter Punch ☛ The_Paranoid_Nature_of_American_Foreign_and
                  Domestic_Policy⠀⇛


                       That conversation between my father and brother has
                       been on my mind, as I’ve been experiencing
                       America’s increasingly divided, almost schizoid,
                       version of social discourse. It’s as if this
                       country were suffering from some set of collective
                       auditory hallucinations whose lead feature was
                       nastiness.


                       Take cover! We’re being threatened by a revived red
                       (dish) menace from a “rogue” Russia! A “Yellow
                       peril” from China! Iran with a nuke! And then there
                       are the alleged threats at home. “Groomers”! MAGA
                       kooks! And on and on.


                # ⚓ Scheerpost ☛ The_Nasty_Voices_in_Our_Heads⠀⇛


                       The Paranoid Nature of American Foreign and
                       Domestic Policy.


                # ⚓ Scheerpost ☛ Lee_Camp:_The_Shadow_Bank_That_Owns_The
                  World⠀⇛


                       BlackRock’s power is growing — and that’s not a
                       good thing.


                # ⚓ Counter Punch ☛ Liberalism_and_the_Morality_of_War⠀⇛


                       On the other hand, journalist Gerard Colby-
                       Zilg—also identifying progressivism with corporate
                       liberalism—defines the first as an “instrument of
                       conservatism,” in the sense that it is the
                       “rationalization of the old order to meet the needs
                       of the new monopolistic order.” This radical view
                       presupposes a psychological derivation of the idea
                       of progress in terms of political ideology, as in
                       Karl Polanyi: “Hope—the vision of
                       perfectibility—was distilled out of the nightmare
                       of population and wage laws, and was embodied in a
                       concept of progress so inspiring that it appeared
                       to justify the vast and painful dislocations to
                       come.” This interpretation locates a cynicism at
                       the heart of the modern liberal project, a dark
                       twin to its much-vaunted idealism, and would
                       therefore read the original progressive rhetoric
                       for empire as textbook delusions of grandeur. These
                       delusions would be leveraged to crush indigenous
                       initiatives toward self-sufficiency around the
                       world while hiding behind platitudes of support for
                       the self-determination of all peoples.


                       Consider that the archetypal elements of American
                       Third World thuggery emerge fully formed—like
                       Athena from the head of Zeus—in the period 1898-
                       1901, between the dust-up to the Spanish-American
                       War and the defeat of the Filipino insurrection:


                # ⚓ Counter Punch ☛ Wake_up_Stupid!_Biden_Wants_War_with_Iran
                  Too⠀⇛


                       Talks have been dragging on for months and leading
                       nowhere. Iran’s demands are simple and remain
                       virtually the same since day one, save for a few
                       concessions that they’ve made to the Biden
                       Administration; knock it off with the fucking
                       sanctions that crazed orange orangutan gagged us
                       with and we’ll offer you back our nuclear program
                       on the same silver platter we awarded to Obama back
                       in 2015. But somehow this simple message is two
                       fucking complicated for Biden’s people, who let’s
                       not forget are essentially just Obama’s people in
                       new ties. America won’t even meet with Iran
                       directly. We send them coded messages in a bottle
                       through EU intermediaries at drop sites in Doha or
                       Vienna and they fucking put up with it! Yet
                       somehow, the simplest snafu to undue in imperial
                       history continues to be derailed by a never-ending
                       procession of tripwires and landmines.


                       Iran offers to return to the JCPOA, and Biden
                       demands they make concessions to the maximum
                       pressure ransom note of the same ginger asshole who
                       continues to insist Joe stole the fucking election.
                       Iran offers to return to the JCPOA, and their
                       scientists are assassinated in broad daylight by
                       hired guns who do everything but wave an Israeli
                       flag over their bodies after dropping the gat to
                       announce who sent them. Iran offers to return to
                       the goddamn JCPOA, and America hijacks their oil
                       tankers on the high seas like Blackbeard with
                       battleships. Iran finally caves to the crazy
                       concessions Trump made and Biden demands, and talks
                       are put on hold. Iran finally loses their shit with
                       these honky whack jobs and raises their plutonium
                       enrichment to well beneath the threshold necessary
                       for nuclear weapons to even be an option and
                       suddenly they’re the crazy brown rogue state
                       swinging a saber at the wilting Western World.


                # ⚓ Counter Punch ☛ The_Reserves_of_the_DA_Afghanistan_Bank
                  Belong_to_Afghanistan⠀⇛


                       This waking nightmare is a policy choice. When the
                       Taliban became the de facto government in August
                       2021, the Biden administration decided to deny
                       Afghanistan’s central bank, Da Afghanistan Bank
                       (DAB), access to most of its international
                       reserves, more than $7 billion that are deposited
                       in the US. Without access to foreign reserves, it
                       is virtually impossible for DAB to fulfill its
                       basic central banking functions. And without a
                       functioning central bank, economic collapse was
                       nearly inevitable.


                       The blocking of DAB assets, and the subsequent
                       executive order setting aside half for potential
                       compensation for victims of the September 11
                       attacks, have been widely condemned by lawmakers,
                       economists, UN human rights experts, civil society
                       organizations, 9/11 victims’ families, and everyday
                       Afghans alike. After months of pressure, there are
                       now reports that the Biden administration is in
                       talks with the Taliban for an as-yet-undetermined
                       mechanism for using half the assets to help address
                       the crisis.


                # ⚓ TruthOut ☛ Trump_Claims_“Absolute_Immunity”_Protects_Him
                  Against_Jan._6_Civil_Lawsuits⠀⇛


                # ⚓ TruthOut ☛ The_Justice_Department_Obtains_a_Warrant_to
                  Search_John_Eastman’s_Phone⠀⇛


                # ⚓ TruthOut ☛ Putin’s_Repression_Is_Driving_Many_Antiwar
                  Russians_Abroad⠀⇛


                # ⚓ TruthOut ☛ Republican_Senators_Reject_Bill_to_Provide
                  Veterans_Care_for_Toxic_Exposure⠀⇛


                # ⚓ Counter Punch ☛ On_Schedule_(for)_F(ascism):_the_Dithering
                  Dems_and_the_Radical_Republicans⠀⇛


                       I once watched a small youth soccer game pitting
                       two teams of four and five-year-olds against each
                       other. One of the teams had an aggressive thirty-
                       something buzz-cut white dad coach who egged his
                       team down the field until they somehow managed to
                       nudge the ball though their opponents’ goal posts.
                       Winning was a big deal to him. He was a local
                       Republican and general all-around pain in the ass –
                       the kind of guy who fouls you a lot during noontime
                       basketball at the Y.


                       The other team was coached by a laid-back Democrat,
                       a decent young man with shoulder-length hair and a
                       tie-dye t-shirt. I liked him. For him, the game was
                       about fun and sharing. He’d yell out “good job” and
                       “great kick” whenever one of his kids almost made a
                       decent play. When the other team scored, as it did
                       over and over, he’d call out “nice try” to his
                       goalie, a five-year-old girl who had little idea
                       where the goal was.


                # ⚓ Counter Punch ☛ Get_Brittney_Griner_Back?_Sure,_But_Release
                  Her_Counterparts_in_America,_Too⠀⇛


                       Griner, currently on trial, faces a ten-year
                       sentence if convicted of possessing cannabis. She
                       was arrested at Moscow’s Sheremetyevo International
                       Airport on February 17 after officials allegedly
                       found vape cartridges containing “hash oil” in her
                       possession.


                       I’d personally like to see Griner released. I
                       suspect most Americans agree with me. But the
                       political outrage over her arrest feels quite
                       manufactured given that hundreds of thousands of
                       Americans get treated like Griner every year by
                       their own governments.


                # ⚓ Democracy Now ☛ Ukrainian_Feminist:_We_Need_Western
                  Solidarity_in_Fighting_Russian_Imperialism⠀⇛


                       We speak to Oksana Dutchak, a Ukrainian feminist
                       and co-editor of the leftist journal Spilne, who
                       fled to Germany because of the “inability to live
                       under the constant pressure of fear” as Russian
                       invaded. She says Western leftists and feminists
                       who have misgivings about Western military support
                       for Ukraine often overlook that Ukrainians are
                       fighting for self-determination and against
                       imperialism. “What does it mean to stop the war?
                       How it should be stopped? There are questions which
                       should be in the center if you want to give a
                       political answer to the challenges Ukrainian
                       society is facing,” she adds.


          o § Environment⠀➾


                # ⚓ TruthOut ☛ Manchin’s_Climate_Reversal_Comes_With_Major
                  Caveat:_Expanding_Oil_and_Gas⠀⇛


                # § Energy⠀➾


                      # ⚓ TruthOut ☛ Big_Oil_Has_Spent_Over_$200_Million_in_1.5
                        Years_to_Sabotage_Climate_Action⠀⇛


                # § Wildlife/Nature⠀➾


                      # ⚓ Counter Punch ☛ The_King_and_the_Queen_of_the
                        Endangered_Monarch_Butterfly:_A_Story_of_Proactive
                        Environmentalism⠀⇛


                             There were an estimated ten million monarchs
                             in the 1980s. In July 2022, the International
                             Union for Conservation of Nature issued a
                             report that said the population has declined
                             by an estimated 99.9 percent. The species was
                             originally described by Carl Linnaeus in
                             his Systema Naturae in 1758.


                             Black, orange and white, as though painted by
                             an artist, and with a wingspan of about
                             three-and-a-half inches by four inches, the
                             monarchs are easily recognizable, even by
                             those who aren’t lepidopterists and don’t
                             study butterflies and moths. “I’m not sure I
                             deserve the title of monarch queen,” Weber
                             tells me. “But Ole definitely deserves the
                             title of monarch king.”


                      # ⚓ Counter Punch ☛ The_Forests_of_the_Midwest_Lost
                        Midwest_8,000_Years_of_Stored_Carbon_in_Just_150
                        Years⠀⇛


                             The primary reason for this arboreal zeal is
                             to capitalize on the power of trees to remove
                             excess carbon dioxide from the atmosphere and
                             turn it into wood, safely locking carbon away
                             for decades to centuries.


                             That’s the theory, anyway.


          o § Finance⠀➾


                # ⚓ Counter Punch ☛ It’s_Time_to_Crackdown_on_the_Excessive_Pay
                  of_CEO’s⠀⇛


                       Big company CEOs have enjoyed soaring pay, even as
                       their employees have been struggling to keep their
                       families safe and their bills paid.


                       Look at Target, for example. Last year, the median
                       Target worker salary did not even keep pace with
                       inflation, rising by less than 4 percent to
                       just $25,501.


                # ⚓ Common Dreams ☛ Recession_Fears_Spark_Calls_to_Stop_Hiking
                  Interest_Rates_and_Rein_In_Corporate_Greed⠀⇛


                       As new government data on Thursday stoked fears of
                       a looming recession—and even led to some claims
                       that the nation is already experiencing
                       one—progressives renewed calls for the Federal
                       Reserve to stop hiking interest rates and
                       policymakers to take on the corporate profiteering
                       driving inflation.


                       “Reining in corporate greed is the key to bringing
                       down costs for families and kickstarting economic
                       growth.”


                # ⚓ Common Dreams ☛ ‘This_Victory_Is_Historic’:_Massachusetts
                  Trader_Joe’s_Becomes_First_to_Unionize⠀⇛


                       Workers at a Massachusetts Trader Joe’s on Thursday
                       voted to become the first of the supermarket
                       chain’s more than 500 locations to unionize, a
                       historic development that comes amid a nationwide
                       labor organizing wave.


                       “Our crew needs to be represented by an entity that
                       is solely dedicated to our best interests.”


                # ⚓ Counter Punch ☛ The_West_Can’t_Stop_Pillaging_Other
                  Countries’_Bank_Accounts⠀⇛


                       See a pattern? Leave your nation’s money in a
                       western bank, and it might not be yours for very
                       long, especially if you in any way bother western
                       politicos, like having an economic system they
                       disapprove of, or sending them packing when they
                       invade your country, or telling NATO where to get
                       off when it threatens to absorb a neighboring
                       nation and plant missiles there. In this last
                       instance, it would have been far better had Moscow
                       waged economic war on NATO countries, instead of an
                       actual war on Kiev. But as it happened, Ukraine got
                       clobbered militarily and dreadfully, and the west
                       launched an economic blitzkrieg on Moscow,
                       accidentally firing all its financial missiles at
                       itself.


                       The west’s larcenous behavior erodes trust in its
                       financial system, to understate matters. Keep your
                       savings in dollars or in western banks and you
                       could lose them, if say, you don’t let NATO invade
                       your country and topple your government, or
                       balkanize your country, or even if you don’t
                       privatize your ports, or worse, you let China
                       invest in them. Not saying these last two have
                       happened, but if the past is precedent, they sure
                       could. All over the world, in recent months,
                       countries finally got the message, and some feel
                       vulnerable. So things have begun to change in ways
                       that do not bode well for Washington’s global
                       financial hegemony. It is certainly likely, for
                       example, that Chinese leaders look at their more
                       than one trillion dollars in U.S. debt and now
                       think “Gee, maybe that’s not such a great idea.”
                       Indeed, compared to May, 2021, China’s holdings in
                       U.S. treasury securities this year fell by 9
                       percent.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Counter Punch ☛ Beidaihe_Closed_Doors:_China_Plots_Its
                  Future⠀⇛


                       Beidaihe, a coastal resort some 280 km north of
                       Beijing, does not see the country’s leading
                       politicians taking the plunge into the blue, to
                       escape the sultry heat, but it does see them
                       testing the political waters for two weeks from the
                       beginning of August.  The jostling for position and
                       power brokers doing deals may be reminiscent of
                       political conclaves the world over but this is in a
                       league of its own. One showpiece event will focus
                       their minds this year.


                       In November central Beijing will cordon off its
                       roads, and close it subway stations as the
                       quinquennial 20th National Congress of the
                       Communist Party takes place. President Xi Jinping
                       wants to take this opportunity to be chosen for an
                       unprecedented third term as party secretary and get
                       his allies into top positions. Xi’s hope was that
                       the political atmosphere could be summed up, ahead
                       of the congress, as steady as she goes. That hope
                       has vanished, evaporated like mist in the glare of
                       an unforgiving sun.


                # ⚓ Counter Punch ☛ Chaff_Candidates:_The_Race_for_the_UK_Tory
                  Leadership⠀⇛


                       No leader with such a destructive sense of presence
                       could do anything but impair those who followed
                       him. But that impairment lingers in the contenders
                       who are seeking to replace him, and it shows.


                       In a system that is admirably daft, the governing
                       party, namely the Conservatives, have given
                       themselves a remarkable span of time to pick
                       Johnson’s successor. A number of candidates
                       initially put their name forth, a chaff-wheat
                       separation exercise that eventually led to the
                       selection of chaff.


                # ⚓ Scheerpost ☛ Ralph_Nader:_Keep_Calling_Powerful
                  Players–Even_If_They_Won’t_Answer⠀⇛


                       I am confident in saying that members of Congress
                       and their staff have never been more unresponsive
                       to serious petitions (letters, calls, emails and
                       old-fashioned petitions) on important issues than
                       today.


                # ⚓ TruthOut ☛ Clarence_Thomas_Bows_Out_of_Teaching_at_GWU
                  After_Students_Demand_His_Dismissal⠀⇛


                # ⚓ Telex (Hungary) ☛ The_hothead_of_Karcag_who_organized_the
                  American_light_cavalry_in_the_War_of_Independence⠀⇛


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


                # ⚓ Common Dreams ☛ House_Dems_and_Shireen_Abu_Akleh’s_Family
                  Urge_US_to_‘Hold_Her_Killers_Accountable’⠀⇛


                       Progressive U.S. lawmakers on Thursday joined
                       relatives of Shireen Abu Akleh in demanding the
                       Biden administration thoroughly and transparently
                       investigate the Israeli military’s killing of the
                       Palestinian-American journalist, with one
                       congressman introducing a bill that would require
                       such a probe.


                       “From Day One the Israeli government has denied
                       Shireen’s murder. There is no reason for them to be
                       conducting an investigation.”


          o § Civil Rights/Policing⠀➾


                # ⚓ Counter Punch ☛ The_Growing_Danger_of_Anti-Abortion
                  Extremism⠀⇛


                       Far-fetched? Not the way things are going. When it
                       comes to extremism, Republican politicians are
                       racing each other to the bottom.


                       Once we thought that otherwise anti-choice
                       Republicans favored allowing girls and women who
                       were victims of rape or incest to get abortions.
                       But there are no such exceptions in the laws
                       Republican legislatures have recently enacted.


                # ⚓ TruthOut ☛ Kansas_GOP_Seeks_to_Remove_Abortion_Rights_From
                  State_Constitution_in_Primaries⠀⇛


                # ⚓ The Nation ☛ Erasing_the_Constitution⠀⇛


                # ⚓ The Nation ☛ As_the_World_Burns,_Organizers_Are_Burning
                  Out⠀⇛


                       Political organizing is challenging work. You’re
                       expected to keep up with the metrics and goals of
                       your parent organization while convincing people,
                       one by one, to help you push political leaders to
                       make positive change. All the while, climate change
                       continues, justices and Republicans strip people’s
                       reproductive rights, and the news from Washington
                       is relentlessly bad. It’s no wonder organizers are
                       burning out.


                # ⚓ Common Dreams ☛ ‘Truly_Disgusting’:_Alito_Mocks_Critics_of
                  Anti-Abortion_Ruling_as_Pregnant_People_Suffer⠀⇛


                       As horror stories abound of the impact his Dobbs
                       ruling is having on pregnant people across the
                       United States, Supreme Court Justice Samuel Alito
                       used his keynote address Thursday at Notre Dame’s
                       Religious Liberty Summit in Rome to mock critics of
                       the opinion, which ended constitutional protections
                       for abortion and endangered a plethora of other
                       rights.


                       “I had the honor this term of writing I think the
                       only Supreme Court decision in the history of that
                       institution that has been lambasted by a whole
                       string of foreign leaders who felt perfectly fine
                       commenting on American law,” Alito said in his
                       first public address since the ruling, which was
                       joined by the high court’s five other right-wing
                       justices.


                # ⚓ Insight Hungary ☛ Orban_causes_outrage_for_opposing_‘mixed
                  race’_society_in_Hungary⠀⇛


                       Hungary’s Prime Minister Viktor Orban is facing
                       backlash after a speech arguing that Europeans
                       should not become people of ‘mixed race’. Orban
                       held his annual speech in Băile Tuşnad, Romania,
                       where he spoke about racial purity among Europeans.
                       This year’s event (a Summer University often
                       referred to as ‘Tusványos’) was the first since the
                       coronavirus pandemic started. Băile Tuşnad is where
                       Orbán usually assesses current political events and
                       sets the tone for future communication.


                       When Orbán started his speech, leader of Romanian
                       nationalist Calea Neamului Mihai Tîrnoveanu and
                       another individual held up a poster that read “Ceva
                       este etern: Transilvania, pământ românesc!” meaning
                       “Something is eternal: Transylvania is Romanian
                       land!” Orban supporters quickly gathered around
                       them and hid the message with umbrellas. The two
                       protesters were escorted out of the event.


                # ⚓ The Nation ☛ Philip_Guston’s_Philosophy_of_Doubt⠀⇛


                       At the entrance to the Philip Guston exhibition at
                       the Museum of Fine Arts in Boston, one might pick
                       up a card bearing a statement that reads: emotional
                       preparedness for “philip guston now.” On the verso,
                       one finds the trigger warning—“The content of this
                       exhibition is challenging”—and the wise observation
                       that while “it is human to shy away or ignore what
                       makes us uncomfortable…this practice
                       unintentionally causes harm.” Viewers are invited
                       to “lean into the discomfort of confronting racism
                       on an experiential level as you view art that
                       wrestles with America’s past and present racial
                       tensions.” But maybe you shouldn’t lean too far:
                       “Identify your boundaries and take care of
                       yourself.”


                # ⚓ TruthOut ☛ Republican_Blocks_Contraception_Access_Bill_From
                  Coming_to_Vote_in_Senate⠀⇛


                # ⚓ AccessNow ☛ Meta_must_disclose_India’s_Human_Rights_Impact
                  Assessment_–_Access_Now⠀⇛


                       Meta is deflecting accountability in India, and
                       perpetuating human rights harms, by refusing to
                       disclose findings from the independent Human Rights
                       Impact Assessment (HRIA).


                       Meta’s first-ever human rights report has a mere
                       four pages on Facebook’s impact on India, most of
                       which is merely descriptive rather than providing
                       detailed substantive information. It also shifts
                       the blame to third parties, and emphasizes that
                       Meta does not agree with its findings. It fails to
                       include the assessor’s analysis, conclusions, or
                       recommendations, and Meta does not make any
                       commitments on next steps. In private briefings,
                       Meta has made it clear that it will not release any
                       further information, wholly rejecting the calls by
                       civil society to release the full report.


                       HRIAs are supposed to show that a company is
                       seriously committed to understanding and addressing
                       its impacts on human rights. Investors also look to
                       HRIAs to evaluate whether the companies in their
                       portfolios are meeting their responsibility to
                       respect human rights. Under the U.N. Guiding
                       Principles on Business and Human Rights, Meta has a
                       duty to “provide information that is sufficient to
                       evaluate the adequacy of an enterprise’s response
                       to the particular human rights impact involved” –
                       one that it is failing to fulfill.


          o § Monopolies⠀➾


                # § Copyrights⠀➾


                      # ⚓ Heather J Meeker ☛ Victory_for_FireTek_in_the
                        PyroTechnics_Case_–_Copyleft_Currents⠀⇛


                             About a year ago, I wrote about a copyright
                             case involving fireworks firing codes. This
                             case did not get a lot of attention at the
                             time, and it was yet another example of a
                             plaintiff using copyright law as unexploded
                             ordinance (if you will forgive the pun) to
                             harass its competitors, rather than to
                             protect works of authorship.


                             Fortunately, the Third Circuit recently
                             vacated a prior injunction in the case, for
                             lack of likelihood of success on the merits,
                             and remanded to the district court with an
                             order to to dismiss the claim with prejudice.


                             The court analyzed the copyright protection
                             of both Pyrotechnics’ digital message format,
                             and the digital messages created with it. The
                             opinion linked above provides interesting
                             detail on how the messages worked.


    * § Gemini* and Gopher⠀➾


          o § Technical⠀➾


                # § Science⠀➾


                      # ⚓ Hackaday ☛ Inca_Knots_Inspire_Quantum_Computer⠀⇛


                             We think of data storage as a modern problem,
                             but even ancient civilizations kept records.
                             While much of the world used stone tablets or
                             other media that didn’t survive the
                             centuries, the Incas used something called
                             quipu which encoded numeric data in strings
                             using knots. Now the ancient system of
                             recording numbers has inspired a new way to
                             encode qubits in a quantum computer.


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


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