𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Tuesday, December 20, 2022
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Generated Wed 21 Dec 02:42:35 GMT 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/2022/12/20/


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

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QmdWUusNqJMS57MytvSBqcKNCLRPfimgbePGhjNYNCrwrs
QmbPTsZioPtTXeNWAZ3ALomNL4TBHGpogkpqcBMt1XfHcK
QmYfN5RSjFSUavYPSs8WzFFWaWumk8hYAfuw6kpmXGe13e
QmW2j2ckzmovo3T5PVVEPyCDY6cxTKFEYB2dhVvwPkm1n7
QmTyKJ8ueXdR2ThkLMDuN6zbrTdYNb2WE4A3bWb3nThabk
QmUT1CDXsiCQqLRdwHpHpoJJqSGBqjbHvUXKGRHpv1w5gX
QmXRyhQvsYF5K1BmNnXd3xbo53qK3sj8L46ar78ZSMZE11
Qme6wheEKimQwauNrUa2HdWuHW39unWrCNHkenNBZynvWf
QmQHZvL9iG7GQCdxV1Zkr1SFySsQJaamRJ7AYK9BphiEMQ
QmcFHsyQGaiMfwHfdP4bVFof2wQaKcG3nTnFVodehzsUrf
QmRDqLW6m2gg8NR4aFbzPgtLMjZfkcdrwfoBbBrENHTXKj
Qmcj5EHanYd6dSt2degUEWTEyqqoyygQduM5qxSoUY9tbQ
QmdRJwsbsXgydBbvrvinQ8ybSqJWBJpS39D3VBcY5DSd3G
Qmb4EjHKEYahRXurhmzoyhxRGEPvXqTA7AcQPuzLrKfJGh
QmeFrf4tqX8a5FgfN4cMTHFas3gdjg8g34A9iryCnBvtMG
QmVK3bkZbD5g3xuJVLcQEb4nbz82bgKPeuhqrZfSGDbnWj
QmcMmjkkKEkp8tPhvcRuQqQEthfDb2Nksw3RYrGfjUfw3Q
QmfQQhspUHkt3SuJBA5fzqjRPqzZGW5MrbYgrDoP7udz1f
QmVUTRpCU7PcTDC7kj2yHWWkV5Mhg6XD2yLq9ekqQv4xj5
QmVwJZvv6r7xzdhVLH4kTyoCkuFgsArexoVuFbayx9A5N5


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

⦿ IRC Proceedings: Monday, December 19, 2022 | Techrights

⦿ Former Executive Director John Sullivan Has Left the Free Software Foundation (FSF) | Techrights

⦿ Sirius ‘Open Source’ Outsourcing Confidential Information to Spying Companies in Another Continent | Techrights

⦿ [Meme] Denying Security Breaches, Excuses No-one | Techrights

⦿ This Shell Game Gives ’Open Source’ a Bad Name | Techrights

⦿ EPO Writing About Unitary Patent From One Year in the Future! | Techrights

⦿ [Meme] Seven Years After Battistelli Said It Would Start | Techrights

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
		http://techrights.org/2022/12/20/irc-log-191222/#comments
		http://techrights.org/2022/12/20/john-sullivan-leaves-fsf/#comments
		http://techrights.org/2022/12/20/sirius-open-source-outsources-everything/#comments
		http://techrights.org/2022/12/20/the-mickey-mouse-model/#comments
		http://techrights.org/2022/12/20/uk-us-shell-game/#comments
		http://techrights.org/2022/12/20/unitary-patent-future/#comments
		http://techrights.org/2022/12/20/upc-no-time-to-talk/#comments

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
		http://techrights.org/2022/12/20/banana-pi/#comments
		http://techrights.org/2022/12/20/netbsd-10-0-beta/#comments
		http://techrights.org/2022/12/20/tails-5-8-released/#comments

                    ䷩ 𝚕𝚒𝚗𝚎 67

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/12/20/irc-log-191222/#comments
    Gemini version at gemini://gemini.techrights.org/2022/12/20/irc-log-191222/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.20.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ IRC_Proceedings:_Monday,_December_19,_2022⠀✐


Posted in IRC_Logs at 2:55 am by Needs Sunlight


Also available via the Gemini protocol at:


    * gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-191222.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-191222.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-social-191222.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-191222.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
 QmZYnABqNziBZ6BYQFNrp553oDPqcuWUFJuPG8WrpfhqUU #boycottnovell  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell
 QmS35BiAbyzKwDPR17wEoK4ZDkyFbLqWezjWMurC5QBCG7 (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
                                                 #boycottnovell-
 QmVvPAUDYrn69iamv9LiXo1o5853yyzcxA32VaUegFJfdn social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell-
 QmPi7yT1RknRg3kAMXaF2JDt5hqPEp6SdXw8g12FrgKNnh social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 (full IRC log
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 QmTa9s4BDQEpQWUK6kYfLamL4bNXhheXanU1o3cit1dciw #techbytes      🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techbytes
 QmPpCY6c4uffv4gXkJZjdE44XSEZrnW4W1iZYKfY2Baoc2 (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 QmP2H8YNnxCGMeNRERDxoPYZYjejiCwfYdYAGp6ZaWYsyb #techrights     🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techrights
 QmNb1JXTukGDA1Q2aCk8E1n11WTi1HbjwouvPSyfdf5WrT (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈


§ Bulletin for Yesterday⠀➾


Local_copy | CID (IPFS): QmVwJZvv6r7xzdhVLH4kTyoCkuFgsArexoVuFbayx9A5N5



                    ䷩ 𝚕𝚒𝚗𝚎 194

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/12/20/john-sullivan-leaves-fsf/#comments
    Gemini version at gemini://gemini.techrights.org/2022/12/20/john-sullivan-leaves-fsf/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.20.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Former_Executive_Director_John_Sullivan_Has_Left_the_Free_Software_Foundation
(FSF)⠀✐


Posted in Free/Libre_Software, FSF at 10:21 am by Dr. Roy Schestowitz


2021 (after he had been pressured_by_an_online_mob, became “outgoing” but
remained ad interim for a graceful_transition and advising the successor):


       🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇FSF_executive_director_John_Sullivan_in_2021⦈_


Months ago:


 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇FSF_executive_director_John_Sullivan_and_Kooyman_in_2022⦈_


Today:


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


Hours ago:


                  🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇December's_FSF_opening⦈_


Summary: Former FSF executive director John Sullivan, who served in this role
for many years, has left completely, based on the “staff” page, the Internet
Archive (Wayback Machine), and a new job opening


⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠃⠈⠑⠉⠘⠐⠀⠀⠂⠂⠘⠀⠃⠘⠀⠋⠐⠃⠁⠈⠀⠀⠀⠃⠂⠁⠘⠀⠑⠀⠃⠐⠂⠀⠘⠀⠃⠊⠀⠃⠘⠂⠋⠈⠈⠊⠘⠁⠓⠀⠀⠃⠁⠈⠂⠚⠐⠃⠀⠂⠁⠈⠂⠀⠐⠈⠊⠃⠘⠀⠃⠘⠀⠃⠘
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⢿⣿⣿⡿⢿⣿⣿⣿⣿⢿⡿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣗⣋⣐⣀⣶⣸⣇⣸⣆⣕⣸⣟⣨⣂⣀⣅⣖⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣟⡿⣟⣛⣟⡟⡟⣻⢟⢻⣟⣿⢿⢟⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻
⡟⠟⠿⠿⢿⠛⠿⢿⢿⠿⠟⢻⠿⠿⢿⡿⠿⡿⠿⢿⡿⢟⡿⡿⠿⠿⢿⠿⠿⡿⠿⡻⡟⠿⣿⠻⠿⠿⡟⠻⠟⢻⠿⠿⠿⢿⠛⠿⢿⠿⠿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⣷⣷⣶⣾⣾⣶⣶⣾⣾⣶⣿⣾⣶⣷⣾⣷⣷⣷⣾⣾⣷⣿⣷⣿⣷⣷⣿⣾⣷⣿⣾⣿⣾⣶⣿⣷⣷⣷⣷⣾⣶⣿⣶⣶⣾⣾⣾⣾⣾⣿⣾⣾⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡏⢹⢹⠛⡋⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣇⣀⣷⣅⣸⣆⣅⣀⣿⣌⣄⣨⣮⣻⣄⣯⣂⣩⣢⣹⣀⣎⣇⣹⣐⣄⣰⣀⣕⣔⣀⣐⣿⣔⣯⣨⣰⣔⣯⣭⣧⣢⣀⣔⣀⣕⣅⣀⣕⣸⣿⠛⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣻⣿⣿⣟⣟⣿⣹⣹⣿⣽⣽⣿⣿⣻⣹⣿⣹⣿⣿⣽⣿⣿⣿⣏⣿⣽⣽⣿⣙⣻⣿⣍⣙⣻⣿⣿⣿⣽⣽⣹⣙⣹⣿⣿⣉⣹⣿⣿⣿⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⣿⣿⣿⣿⠿⣿⣿⢿⡿⣿⡿⣿⡿⣿⣿⣿⡿⣿⣿⣿⡿⢿⡿⠿⡿⣿⠿⣿⣿⣿⣿⣿⣿⠿⣿⣿⢿⣿⣿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠙⠑⠂⠀⠀⠀⠀⣿⣷⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡷⣶⣶⣿⢿⣶⣶⣶⣶⣼⠶⢷⢶⢶⣶⣷⢾⠾⣶⣶⡽⣶⣿⣿⣷⣶⡶⢿⣾⠷⢷⠾⣶⠶⣿⣶⡶⣾⣷⣶⣾⢷⣶⣿⣶⣾⣷⣿⣿⣿⣿⠈⠀⠀⠀⠀⠘⠀⠀⠀⣤⣴⡄⠀⠀⠀⣿⡿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡷⢶⣿⣷⣶⣾⣾⣶⣿⣿⡿⣶⣿⣾⣶⣷⣾⣶⣶⣾⣷⣶⡾⢾⣿⣶⡷⣶⣾⡾⢾⣿⣾⣶⣶⣾⣿⣶⡶⢿⣶⢮⣿⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⢉⣧⠀⠀⠀⠿⠃⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡷⣶⡾⡷⣤⢶⣿⣶⣾⣾⡶⢷⣽⠶⣿⣶⣶⣷⡶⡶⡿⢷⣶⣶⢾⣷⣷⣷⣶⣿⣶⣷⠶⣿⣷⢶⣿⣷⣷⣶⣶⣮⠾⢽⣿⡿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⠙⢻⠄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⡷⣶⣶⢷⣶⣾⣷⣶⣽⣷⣦⣧⡾⢦⣤⣿⣶⣧⣯⡧⡿⢽⣶⣶⣾⣯⣶⣿⣶⣶⣾⣶⣶⣾⣾⣶⣮⣶⣷⣶⣾⣶⣾⣶⣿⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣲⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣶⣦⣾⣶⣮⣾⣷⣶⣶⣷⣧⣷⣷⣶⣾⣷⣦⣶⣿⣵⣷⣥⣶⣾⣼⣷⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣟⣿⣻⣿⣛⣟⡛⣛⣻⣿⣋⣿⣻⣻⣟⣙⣻⢻⣻⣏⣝⣛⣿⣟⣛⣛⣿⣉⣙⣟⢿⣛⣻⣿⣛⣛⣏⣉⣋⣏⣿⣍⣛⣩⣻⡻⣟⣻⣻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣏⣛⣻⣟⡟⣟⣛⣻⣟⣻⣙⣹⣟⣻⣉⣋⣹⣛⣟⣏⡛⣿⣙⣛⣿⣟⣻⣙⣛⣻⣟⣛⣻⣟⡻⣛⣛⣻⣻⡛⣿⣟⣿⣛⣻⣻⣙⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣟⣻⣛⣹⣿⣻⣟⣿⢛⣻⡟⣻⣻⢻⣟⣹⣛⣏⣹⡛⣟⡿⣛⣛⣛⣟⣋⣟⢛⣻⢋⣛⢟⣻⣿⡛⣟⡙⣟⢻⣛⣹⣋⡛⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡯⡿⣛⣛⣛⢟⣙⣻⢻⣋⣛⣿⣛⢫⢻⣙⣛⢟⣛⣻⢻⣛⡿⡛⣋⡻⢛⡟⡻⣏⢉⣋⢿⣉⣛⣛⣻⢻⣛⢛⣛⡟⣯⡟⣻⣉⡛⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⣟⡛⢻⣻⡟⡛⡻⣟⡋⡏⡏⣉⣙⣿⢛⡻⣿⠟⣻⣻⣿⢛⡛⢛⢻⢛⢛⡙⣏⡛⡟⡛⣛⢛⡟⣹⢿⣟⡙⣟⢛⡿⢛⣟⣟⢛⡛⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⡿⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣴⡤⣾⣤⣷⣷⣦⣷⣧⣼⣧⢤⡾⣿⢦⣦⣤⣥⡦⣧⣤⣧⣿⣥⣾⣦⣤⣼⣤⣴⣭⣤⣤⣯⣼⣤⣤⣿⣦⣯⣯⣮⣤⣶⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣯⣦⣤⣼⣦⣼⣯⣥⣦⣼⣤⣤⣼⣦⣬⣤⣬⣧⣤⣧⣯⣤⣦⣯⣴⣷⣦⣾⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣜⣉⣁⣯⣅⣏⣹⣇⣈⣮⣀⣁⣽⣈⣰⣈⣑⣠⣇⣻⣇⣈⣨⣏⣈⣨⣾⣂⣍⣄⣁⣃⣁⣠⣇⣿⣤⣕⣀⣀⣿⣍⣈⣠⣂⣇⣁⣕⣅⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢉⣡⣤⣍⠻⣿⣿⣿⣿⣿⣟⣛⣻⣿⣛⣛⡏⣉⣟⣹⣛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡏⣴⣿⡿⠿⠿⠀⠘⣿⣿⣿⣿⡿⠿⡿⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⢿⢿⡿⡿⣿⠿⡿⡿⡿⡿⣿⠿⡿⡿⣿⣿⣿⡿⣿⢿⢿⢿⣿⢿⢿⡿⣿⠿⢿⡿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⢠⠀⠀⣀⠄⠀⢸⣿⣿⣿⣿⣶⣿⣾⣾⣶⣿⣾⣾⣾⣾⣷⣿⣿⣶⣿⣿⣷⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣾⣷⣿⣿⣿⣷⣶⣾⣾⣷⣶⣿⣶⣾⣿⣷⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠈⠀⢻⣿⣿⣟⢛⡻⣟⠛⢻⣛⡟⢻⡟⣟⢟⡛⢻⢿⣟⡛⡿⡛⠹⣿⣛⠛⣻⡟⣻⣛⣛⣻⡹⠉⣿⣛⣿⡛⡛⣻⣟⢻⢛⠋⣛⢛⢻⢛⡛⠛⣻⡛⣛⢻⢻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡻⢟⠿⢛⣛⡟⠻⣟⡋⣛⡻⢛⠛⢟⠟⢻⢻⣟⢹⢛⢛⡛⣛⠛⡛⡛⡏⢛⢻⢛⠛⡟⠹⣻⡏⢛⣻⢛⢋⠛⠛⢛⢻⣛⡛⠛⢿⠟⠛⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡏⠙⣻⢛⢻⢻⣻⢛⠛⢹⠛⢿⢻⡛⡛⠙⡿⡛⣛⢛⠛⢛⠛⡿⠛⡟⢙⢻⢉⢹⣹⢻⡿⠉⡋⡏⢿⢛⣟⢻⢛⡛⣛⡛⠛⢛⢿⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⡟⣛⠙⣻⡏⣛⢛⡛⠛⠛⡟⠛⣻⡛⠛⡟⠛⠛⠛⣻⡟⢻⢽⢽⠛⢻⣟⡟⡟⢻⡟⠻⢻⡟⠻⠟⡛⡏⣻⣟⡛⠛⠛⢛⡟⡏⢻⠛⠛⢛⡟⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⡟⣻⡛⡟⠙⢻⡛⠛⢛⠛⠻⣛⡟⣫⣟⡛⠛⡟⠛⡟⢛⣻⠛⡛⢛⣛⠟⣻⣛⡏⡟⠟⠛⢛⢻⢛⢟⣿⠟⡻⠛⣻⢻⢙⣟⣟⠛⣟⡟⠛⣻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠛⠛⡟⡛⡿⠛⠛⡏⢛⠿⣿⠻⡟⠛⢻⠛⠛⢻⠛⣟⠟⡿⢻⡛⠻⡟⣟⠛⢛⠛⣛⣟⠛⣻⠻⡟⠛⡿⠻⢻⠛⠻⡛⠛⢿⠛⣟⢻⠛⠛⢛⣻⢟⠛⠛⣟⡟⠛⢛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠛⢻⠿⡟⢛⣿⠿⠿⡿⢻⡟⢻⠿⡿⠿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣵⣮⣶⣷⣾⣷⣵⣾⣧⣾⣧⣵⣮⣧⣶⣷⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⣍⣧⣿⣭⣿⣽⣧⣭⣭⣯⣧⣭⣿⣿⣯⣬⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯
⣏⣉⣉⣉⣹⣉⣝⣹⣉⣉⣉⡹⣏⣙⣉⣉⣍⣟⣉⣽⣹⣫⣙⣉⣉⣫⣙⣟⣹⣙⣹⣉⣉⣉⣉⠉⣏⣉⣉⣉⣉⣋⣫⣙⣏⣩⣏⣉⣉⣏⣭⣙⣙⣏⣋⣩⣉⣙⣙⣍⣻⣙⣉⣉⣉⣉⣉⣙⣉⣙⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⢿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣗⣈⣐⣀⣇⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣟⢻⠿⠛⡿⢟⠿⠿⠿⠿⠿⡿⠿⢿⣿⠛⠿⡿⠿⠿⠿⠟⠿⠿⢿⢛⠟⠿⠿⠿⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣶⣶⣶⣷⣶⣶⣶⣦⣶⣾⣶⣶⣮⣿⣶⣶⣶⣶⣶⣾⣶⣶⣶⣾⣶⣶⣾⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣯⣤⣮⣽⣶⣬⣿⣤⣽⣽⣽⣦⣽⣽⣽⣮⣾⣼⣽⣤⣼⣾⣼⣾⣽⣤⣼⣾⣴⣵⣽⣵⣼⣴⣽⣴⣾⣵⣽⣮⣤⣮⣼⣧⣼⣽⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠟⠛⢛⣛⠟⠛⡟⠛⡻⠛⢻⠛⠛⡟⣛⢻⢻⠻⢛⣛⠛⢻⡛⡟⡛⠛⠛⠛⠛⠛⢛⣿⣟⠻⢻⡿⠛⣿⠛⠛⠛⡛⠟⣻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣟⠻⠛⡚⠟⠟⢻⠛⢻⠛⠻⠟⣻⡟⢻⠛⠛⢛⠛⢻⠛⣻⢛⠟⠛⠟⡟⠟⠛⢛⠛⠛⢻⠛⠛⢻⠛⠻⣛⠛⠛⢚⠟⠛⠛⠛⠛⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⢟⠛⡟⠓⠟⠻⣛⠛⡟⠛⢻⠛⠛⠛⠻⡛⡛⠚⡟⡟⠛⠛⠛⢻⠛⢻⡛⠛⢛⠿⠛⣛⡿⡟⠟⢟⡿⠻⢻⠻⡛⠛⠛⢛⣻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣟⠻⠛⡛⠟⠟⢻⡟⢟⠛⡟⠛⢻⠛⠛⣿⡛⢟⡟⠛⣟⠟⠛⣿⡛⢛⠛⡛⠻⡟⠛⡟⠚⠛⢛⠟⠛⠛⠛⢻⢻⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠻⠛⢛⠗⠛⠛⢛⠛⡟⢻⠛⡛⢻⢻⡛⠛⠛⢻⠻⡟⠛⠛⡻⠛⠛⣛⡟⠛⡛⡛⠛⢛⠟⠛⢿⠛⠛⠛⡻⠛⢛⠛⡟⢟⠛⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠻⠛⢻⡛⢻⠛⠛⡿⠛⢟⠛⠛⠛⡻⠛⢻⡛⢛⠛⡛⠛⢛⡿⠛⠻⡛⡟⠟⢛⠛⢻⠟⠛⠻⠛⢿⣳⡻⢻⢟⢿⠓⢻⢛⠟⢛⠛⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠟⠛⡟⡛⠚⢛⠻⡛⠻⢻⢛⠛⢻⠛⡟⠛⢻⠛⠛⠛⡻⢻⢛⢛⡻⠟⢻⠛⢛⢛⠛⠛⠛⠛⢻⣟⡟⠛⠛⡟⠛⡛⡟⠛⠿⠻⡟⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠛⢻⠛⠛⠛⠛⡟⢛⢛⡛⢻⠻⠛⢛⡿⢻⢛⢻⠛⠻⡛⠛⢛⡛⢛⡿⠛⠛⢻⠛⢛⢛⢛⠛⢻⢻⢓⢛⡻⠛⢛⢿⠛⢛⡟⡻⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⢛⡻⢻⠛⠻⠛⠛⣿⠛⠛⡿⠛⠛⢟⡟⠛⡛⡟⠚⠛⣿⣛⠛⡟⠛⡛⢻⠟⠛⢛⠟⠛⢻⠛⣻⢻⠻⠛⡛⠛⡟⢛⡟⡟⠛⡻⠛⠛⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⡛⠛⠛⡟⣟⠟⠚⠛⠛⠛⠛⡻⢻⠛⡻⢻⢛⠟⠛⠛⠟⢛⠟⡟⠛⠟⢛⠛⡺⠛⠟⡟⢟⡟⠛⠻⠛⡛⠛⠛⡟⠛⠛⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠟⠛⠛⠛⠛⢻⡚⠛⠓⠛⢿⠻⡺⢻⠻⡟⢻⡟⠛⠛⡛⡟⠳⢟⠻⠛⠟⠛⢻⡟⠛⠛⡛⢻⠛⢻⢛⠛⠛⠛⠛⠛⢻⣛⠛⢛⠟⠟⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣟⠛⠛⡛⠛⢛⠟⠛⢻⠛⡻⢻⠛⢛⠟⣟⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣶⣥⣼⣤⣼⣤⣤⣤⣷⣤⣧⣼⣷⣦⣼⣶⣤⣿⣧⣤⣼⣦⣦⣬⣧⣤⣤⣬⣔⣼⣼⣧⣄⣷⣄⣾⣤⣤⣤⣴⣤⣤⣤⣤⣼⣤⣤⣤⣤⣴⣤⣤⣤⣼⣠⣦⣭⣤⣶⣷⣦⣤⣤⣅⣤⣾⣬⣦⣼⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣮⣤⣤⣼⣤⣦⣤⣤⣤⣴⣿⣤⣤⣼⣮⣤⣯⣤⣴⣮⣤⣤⣼⣦⣦⣤⣼⣤⣼⣧⣧⣤⣧⣤⣤⣼⣦⣸⣤⣤⣤⣤⣤⣤⣰⣽⣤⣮⣼⣬⣤⣬⣤⣧⣥⣤⣤⣤⣿⣦⣤⣬⣴⣥⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⢟⠛⢟⣛⠟⠻⣟⠟⠛⠛⡟⣿⠻⠛⣟⠟⠛⢟⡟⢻⠛⠛⠻⡟⠛⠛⡛⠟⡟⣻⡟⠛⠟⠛⢿⠛⠛⢻⢻⣿⠛⠛⠛⡟⠛⠛⡟⡟⠿⢛⠛⢻⣻⡛⡿⠛⠛⢿⡟⡟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⣛⢛⠚⢟⠟⠛⢛⢟⡟⢟⢟⡟⣛⢻⠛⢟⠻⠛⠛⢟⣿⠛⡟⠻⢻⠺⢛⡻⢛⢟⡟⠛⠟⠟⠛⣿⡻⠛⠛⣟⡛⢟⣻⠛⠛⣿⣟⡛⢛⠻⡛⢛⢿⠟⢻⠻⣛⡟⠛⢟⡻⠛⠛⣿⡻⠛⠛⣿⣻⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠻⢻⡿⠟⠛⠛⣟⠟⠛⠛⢻⡟⢛⠛⣟⠟⢻⡟⢛⠻⢻⢛⣿⠛⡿⠛⣻⢟⠻⡷⡛⠛⠛⢳⠛⡻⣻⠛⠟⢛⠛⠟⡟⠻⣟⠛⢻⡛⡻⠟⠛⠟⡞⠟⠛⢻⣛⠟⡛⣟⠛⡟⠻⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠟⠛⠛⡻⠛⠛⢻⡟⢟⠟⢻⡟⠛⣿⣟⡟⢛⢻⠛⠟⠻⡛⠛⡿⠛⡻⡻⢻⠛⠟⡟⢻⢛⢻⡻⠻⢻⢛⠻⢻⠻⣟⠟⠛⠻⡟⠛⠛⡛⡟⢻⢛⡟⢛⠛⡿⠛⢿⠟⢻⠻⠛⢻⡻⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣟⠟⠻⠟⠛⡟⢟⡟⡛⢟⠟⢛⢻⠲⠛⡿⠛⢛⣿⡟⡟⠛⠿⠛⡛⡟⠛⣟⠞⢻⠻⣻⠟⠓⠿⠛⠛⠛⡛⡿⠛⠛⠛⡻⠛⠻⡟⠛⠛⣿⠛⡟⠛⠛⣿⡻⡟⢟⡻⡟⠛⡻⢻⡟⢟⢓⡟⠛⢿⣛⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠛⠿⠟⢻⠻⢿⠛⢟⠛⡛⠻⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠻⡿⢿⠟⡿⠟⢻⠻⠿⠿⠿⣿⡟⠿⠻⡿⠻⠿⢿⢿⡟⣻⠻⠿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⡵⡶⡾⣷⣾⣶⣷⣶⣾⢶⣶⢶⢷⢾⣶⢶⢾⣾⣶⢶⢾⣿⣷⢾⢶⣶⢷⣾⢿⣿⣿⣿⢿⢿⣿⣿⣿⢿⢿⡿⣿⣿⢿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠁⡀⠀⠀⡇⣿⣯⣷⣮⣿⣤⣯⣿⣮⣾⣬⣽⣼⣽⣬⣾⣼⣾⣼⣿⣼⣭⣤⣿⣵⣽⣽⣾⣧⣼⣾⣾⣴⣽⣼⣾⣦⣬⣼⣽⣧⣯⣮⣽⣧⣦⣽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⢈⣡⠀⠀⠁⣿⡟⠛⢛⣿⡟⠛⣛⡟⠛⢻⠛⠟⠛⠛⠛⡟⠛⢛⠛⠛⠛⡟⢛⢛⡟⠝⢻⢿⣟⠛⠛⠻⡟⠛⠛⡟⣛⢻⠛⡛⠛⡏⠟⠛⠛⡟⠛⢻⠙⠛⢛⡟⠛⠛⢻⣻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣿⡟⢻⢿⢟⠻⠻⡟⡛⠛⢻⠛⠛⠛⠻⡛⠛⢻⡛⢻⡟⠛⠛⡟⣻⣛⠛⠛⢛⡛⡟⢟⠟⡟⡛⠛⠛⠛⠻⣟⠛⡟⠛⠛⣻⡟⠛⠻⠛⠛⢻⡛⡛⢻⡛⠛⣟⢻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣿⣛⠛⠛⡿⠟⠛⠛⠛⡟⠛⠛⡟⣻⠛⠛⠟⠛⠻⡟⠛⠛⠛⢛⠛⡟⢟⡟⠻⡛⡛⠟⢻⣻⠛⢋⢻⡛⢻⠛⠛⢻⠟⢛⡛⠛⢛⠟⢻⢛⢻⠛⠛⠛⠛⡻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠟⠛⢛⠛⠛⣿⠟⠛⢻⢛⠛⡿⠻⠛⠓⢿⢛⡿⠻⡟⡿⢿⠛⠛⠛⡟⡟⠛⢻⠛⠛⡟⠟⢛⠛⠛⠻⠛⡟⠛⠛⠛⠛⠛⡟⢛⠛⢛⡛⠛⢛⡿⡛⠛⡛⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠻⡟⠛⢟⠛⠛⠛⣻⠛⡟⠛⠛⣛⢛⠛⢛⠛⢿⠛⠛⡟⠛⡻⡛⠛⡟⡟⡟⡟⠛⠛⠛⠛⡛⡟⠟⠛⠛⠛⠛⡟⠛⠛⣿⠛⠟⠛⢛⣿⠛⠻⡿⣿⢛⠛⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⡟⢿⠛⠟⠛⢻⠞⢛⢿⢛⠛⠛⡛⠛⠛⠟⡟⢻⠟⠛⢟⠛⠛⠛⠛⢻⣛⠻⢻⠛⠛⠛⢻⠛⠛⡟⢛⡟⠛⠛⠛⠛⡟⠛⠻⠛⠛⠛⢿⢛⢛⡿⠛⢛⠛⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⢛⡛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣏⡹⢹⠛⢉⢹⡟⢻⡛⢛⣿⣏⠙⡛⠛⣟⢛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣾⣾⣶⣾⣾⣷⣾⣷⣶⣿⣷⣾⣾⣶⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣧⣷⣷⣦⣦⣧⣶⣾⣾⣴⣾⣷⣵⣴⣦⣼⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣇⣤⣩⣡⣻⣀⣉⣹⣡⣋⣥⣜⣇⣍⣍⣽⣁⣏⣥⣏⣠⣍⣉⣇⣩⣉⣙⣏⣯⣍⣿⣩⣡⣯⣭⣹⣭⣩⣉⣉⣈⣉⣉⣹⣩⣼⣀⣉⣹⣠⣍⣉⣽⣨⣩⣄⣉⣍⣭⣩⣧⣍⣍⣉⣁⣉⣀⣍⣉⣻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠿⢿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣧⣴⣬⣤⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡛⡛⠻⢻⡟⠻⡻⠛⠻⢛⠻⠛⢛⢿⡟⢻⢟⠛⢟⠻⠛⢛⢟⠛⡟⡛⠛⡛⠻⡛⡛⢻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡶⡶⠾⡾⣷⣶⣾⢶⠷⠾⣶⢶⣾⠶⣷⢶⠷⡶⣶⠶⡷⡾⣾⠶⡷⡾⡶⡷⡾⡾⡶⠾⡿⡿⡿⢿⡿⠿⣿⠿⣿⡿⣿⠿⡿⡿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣾⣷⣷⣷⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⣿⣷⣿⣷⣷⣶⣿⣿⣷⣷⣿⣿⣷⣶⣶⣿⣷⣶⣿⣶⣿⣷⣶⣾⣿⣾⣶⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣉⢛⢟⢛⣛⢛⣻⠹⣛⡛⡻⣏⣝⣛⣏⣛⠛⣫⢙⣫⠟⠛⣛⢻⣋⢛⢟⡛⡙⣻⡛⣛⣿⣩⢉⣝⡟⢻⡿⣛⠛⢻⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣛⠛⢛⡛⠛⢛⣿⣛⡯⡯⡏⢉⢿⣻⡟⢿⡟⠛⠛⣻⠋⡟⡻⡻⠉⢿⠛⢏⣛⣛⢟⠛⣿⠛⠻⣹⠟⣻⣟⣛⠛⣛⡻⢛⢟⠛⠛⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠛⢻⡟⠛⢻⠛⠛⢻⡉⡛⢻⠻⠛⡻⠛⠋⢛⢻⢻⣛⠛⠿⢟⣿⠛⣏⡛⢙⡟⡛⢛⢻⢹⠭⠩⠹⣏⠛⡟⣻⢟⠛⠛⣛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢛⠛⢛⠟⠛⢛⣿⡟⠙⢻⠙⠻⡏⢙⠛⣏⠉⢹⡛⢻⠛⢛⣛⣿⢛⠟⣻⠟⢻⡙⣻⠟⠉⠛⢛⢻⠛⠛⡛⡟⢛⡋⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠛⢟⠛⠛⠙⠻⡟⠛⢻⠛⢻⢛⡛⡟⢛⢛⠛⠛⡟⢿⢛⡛⢉⠟⠛⠛⢻⠛⢛⣋⠛⡛⠛⠛⠻⡟⣛⠛⠛⠻⠋⣛⢻⠛⣛⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠙⠛⡛⠙⠛⣟⢟⠛⡟⠛⠛⡙⢛⠛⠛⡛⡏⢛⣻⢟⢛⠛⢻⢛⠛⢛⢻⠻⠉⠫⡫⡿⠉⠫⡏⣿⣯⣝⠛⡯⠋⡋⡫⡟⠻⠛⠛⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣛⡛⠛⡟⠛⣛⠛⠛⠛⠛⡟⠛⠛⢻⢻⠻⠟⠛⠛⠛⠋⠟⣟⠛⡛⠟⠋⡟⠛⠛⠙⣛⠛⠛⡟⡏⡛⡟⠛⠻⢋⢛⢻⠋⠛⠟⢻⠛⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠛⡛⢻⠛⡛⠟⢻⠛⢹⠛⠛⡟⠝⢟⠛⠙⡿⠏⡟⠛⠛⠛⠛⠛⢻⠻⡟⠛⠛⡟⠛⠛⠛⡛⠛⠛⡟⣻⡛⠿⠛⡻⡟⠛⣻⠛⠛⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠛⠛⠛⣿⠛⠛⡛⠻⡟⠟⠛⢛⣛⠛⢻⡟⠛⠛⠛⠛⠛⡟⡻⢻⠛⢛⠟⠛⠛⠛⠛⠛⡛⡟⢋⡟⡟⠛⢛⠛⢻⠛⢻⠛⡛⠛⠛⠛⠛⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡛⠛⠟⠛⢻⠛⠛⣞⠛⠛⡛⠚⠛⢿⠛⠛⣿⠛⢻⡛⠛⠛⠛⢻⡟⠛⠛⠛⢛⠟⠛⢻⠛⢻⠛⡛⠛⢛⠛⡟⢻⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠛⠛⢛⢛⠻⡛⡗⠛⠻⠞⢻⡟⠗⠛⡿⠛⠛⢻⠛⡛⡛⠛⡟⠚⠛⡛⠛⠛⠛⢻⠛⠛⢛⠛⡟⠓⡟⠟⠛⠛⡻⠛⠛⣟⡛⠛⠛⠻⠛⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢛⠛⣛⠿⠛⠛⠛⡛⣻⠛⠛⣿⡻⠛⢻⡛⠟⠻⡛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣴⣤⣬⣾⣦⣧⣦⣤⣦⣮⣸⣤⣼⣤⣥⣧⣧⣵⣽⣤⣤⣼⣤⣼⣼⣬⣤⣤⣥⣮⣧⣽⣦⣠⣮⣦⣧⣧⣠⣬⣮⣤⣤⣥⣤⣯⣦⣤⣤⣤⣴⣤⣤⣤⣇⣴⣌⣥⣴⣾⣶⣤⣬⣤⣠⣴⣧⣵⣤⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣥⣴⣤⣦⣇⣴⣬⣤⣥⣦⣼⣷⣵⣥⣷⣥⣦⣷⣥⣤⣤⣵⣤⣶⣼⣦⣥⣧⣤⣤⣤⣿⣾⣤⣥⣤⣷⣅⣧⣤⣤⣤⣤⣤⣄⣎⣧⣤⣥⣧⣴⣵⣥⣼⣨⣧⣤⣤⣼⣷⣤⣤⣵⣮⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠛⠿⣻⠟⠿⠻⣻⠻⡻⠟⢻⠿⡟⠛⢟⠻⠛⠿⣻⡛⡻⠻⢻⢻⡻⠻⠛⠻⢻⠛⢿⠛⠿⡻⠿⡟⡟⠟⡟⣻⠟⠿⠻⢿⠻⠻⢻⢻⡿⠟⡟⠛⢟⣟⢻⠟⠛⠿⣿⢻⠛⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠛⠿⠟⠿⠿⡟⣛⠿⢿⠟⠿⠛⡟⠿⠟⠿⠿⡛⣻⠿⠿⣟⢻⠛⠿⢷⠚⠿⠟⠿⣻⠻⠿⠻⡻⢿⣟⢟⠛⢿⡻⠿⣛⡟⠻⠿⣿⢛⠻⠟⢿⠛⡻⡿⠟⡟⢟⡻⠟⠿⣛⠿⠿⢿⡟⠿⠿⢿⣟⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢛⡿⢿⠛⠿⣿⠿⠟⢿⡿⠻⣿⠿⡻⢿⠻⠿⢿⠿⠿⢿⡟⠿⡿⠿⠿⠿⢿⡿⠿⢾⢻⡿⠿⡾⠷⢿⡿⠿⡿⡻⠿⣿⠻⢿⡿⠿⢿⢻⠿⠻⠿⢷⠿⠿⠿⣿⡿⠿⢿⡿⢿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢿⠿⡟⡻⠾⢿⡳⢿⡾⠿⠗⠟⠿⣿⠾⠿⡞⠻⢿⠿⠷⠿⢿⠷⡿⠻⠾⢿⡞⠳⠿⡿⠿⡶⣟⠛⠷⢿⠿⠾⡿⢿⡾⠿⠿⢿⠿⠻⠿⠾⠟⡟⣿⢛⠾⢿⠟⢿⡾⠟⡾⠿⠗⣷⠿⠟⡿⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠷⠾⠿⣿⢷⠿⢻⠷⠷⠞⠾⣿⡿⢾⢿⠺⢻⢷⡿⢷⠾⠶⠿⠿⢷⠿⠿⣗⡿⡿⠾⢿⠷⠳⠿⠾⠳⠿⠿⣷⠿⠺⢺⠾⠶⢿⠿⠾⢺⡾⢶⠻⠿⠿⣟⢾⠺⡞⣾⠞⠷⠿⣿⠷⡷⠺⠶⢿⡿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠻⡶⠶⠿⡞⠷⢿⡟⢷⠶⡾⢿⣷⣷⣷⣷⣿⣶⣿⣾⣾⣿⣷⣿⣾⣷⣾⣿⣾⣿⣾⣿⣾⣾⣷⣿⣶⣾⣾⣷⣷⣶⣶⣷⣶⣿⣾⣷⣾⣷⣿⣾⣶⣾⣷⣷⣿⣾⣿⣶⣾⣷⣾⣾⣷⣿⣾⣾⣿⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣷⣿⣾⣷⣶⣿⣶⣾⣶⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⠿⡿⡿⣿⡿⡿⠿⢿⠿⡿⣿⠿⠿⠿⡿⠿⡿⣿⡿⢿⢿⠿⢿⢿⢿⡿⠿⠿⠿⠿⠿⠿⡿⢿⠿⡿⠿⠿⡿⠿⢿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣧⣮⣤⣤⣶⣤⣦⣼⣧⣤⣶⣤⣤⣾⣤⣼⣤⣬⣼⣦⣽⣧⣴⣴⣤⣴⣵⣼⣧⣤⣤⣴⣥⣤⣶⣤⣼⣴⣤⣤⣾⣧⣤⣼⣴⣤⣧⣴⣥⣤⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣠⣴⣶⣆⠙⢿⣿⣿⣿⣿⣧⣽⣵⣿⣭⣭⣇⣤⣯⣼⣭⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠚⠻⠛⠛⠃⠀⠈⢿⣿⣿⣿⣟⠛⣟⢿⠿⠿⣿⡟⣻⡻⡛⡿⡟⡟⣟⡟⣟⣿⢻⣟⡟⢛⣻⡟⡟⣛⢻⡟⢛⣻⢻⣟⢻⢻⢻⣻⢻⢻⢻⢻⠻⠛⢿⢻⡻⠻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠐⠀⠀⠤⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣧⣩⣍⣩⣉⣹⣉⣋⣹⣏⣇⣉⣉⣹⣩⣭⣉⣏⣍⣈⣩⣍⣉⣉⣏⣝⣟⣭⣹⣸⣀⣼⣏⣭⣍⣩⣹⣬⣹⣉⣉⣩⣉⣹⣍⣙⣩⣉⣈⣩⣝⣉⣿⣿⣿⣿⣿
⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣴⣴⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⡟⣛⢛⡻⠋⣩⣭⣿⣿⠩⡝⠝⡏⢽⠩⣿⡏⠽⣫⠛⠩⣯⢩⡹⠹⡙⢻⠩⢻⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡆⠶⠶⢟⣃⣄⣒⣲⣿⡞⣳⡗⣳⣾⡖⣿⠷⣾⡖⢺⣿⢻⣾⢳⣷⣷⡖⣺⣾⠖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣥⣅⣿⣴⣿⣧⣦⣬⣧⣿⣿⣧⣬⣬⣤⣤⣥⣴⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠔⠸⠄⠦⠰⠀⠇⠀⠀⠄⠄⠰⠀⠆⠰⠀⠆⠠⠀⠆⠐⠄⠀⠸⠀⠆⠀⠂⠰⠀⠰⠀⠆⠴⠀⠀⠆⠰⠠⠂⠰⠀⠇⠒⠀⠆⠢⠐⠀⠆⠐⠀⠀⠆⠆⠐⠄⠐⠀⠆⠀⠄⠂⠐⠄⠀⠐⠀⠴⠀⠆⠰⠀⠆
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⡮⠚⢐⣿⡏⢽⠍⣿⠍⠩⠋⢝⠍⢩⠩⠹⣯⠁⡭⡙⡯⣿⠾⡉⢹⠍⠹⠉⠝⣹⡯⠀⣯⠋⠋⠍⠍⢽⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⢿⣿⠿⡷⡿⡿⠿⡿⢿⡾⡷⡿⣿⠿⡿⢿⢿⢿⣿⡾⢿⡿⢿⡿⡿⢿⡿⢿⢷⠿⢿⣿⢿⣿⠿⣿⣿⠿⢿⡿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡷⣿⣿⣷⢷⣷⣷⣷⢾⣾⢷⣿⣷⣾⣷⡷⣿⣾⣿⡿⣿⣷⣷⣾⣾⡷⡾⡷⣿⣶⣿⣾⢾⣶⣷⣷⣾⢾⣾⣾⣾⣾⣾⡷⡿⡿⡿⣿⡿⣿⢿⣿⢿⣿⡿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⡿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣦⣤⣧⣦⣦⣦⣧⣤⣤⣦⣤⣤⣴⣼⣷⣤⣤⣤⣤⣤⣤⣤⣤⣿⣷⣦⣴⣧⣽⣬⣷⣤⣤⣤⣥⣤⣤⣤⣤⣴⣤⣤⣧⢤⣤⣥⣼⡤⣥⣼⣤⢤⣤⡤⣤⣼⣦⣤⢤⣼⣤⣧⣴⣤⣦⢤⣤⣤⣤⣼⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣤⣴⣿⣤⣼⣤⣤⣤⣤⣤⣼⣤⣤⣤⣤⣬⣦⣤⣼⣤⣤⣤⣼⣤⣦⣤⣤⣧⣤⣬⣧⣤⣤⣤⣤⣧⣼⣤⣤⣤⣴⣤⣤⣤⣤⣧⣤⣤⣼⣤⣤⣤⣤⣤⣤⣼⣤⣤⣤⣤⣤⣼⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣦⣤⣤⣤⣤⣧⣤⣧⣤⣼⣤⣤⣼⣶⣥⣼⣦⣤⣤⣼⣧⣤⣥⣤⣦⣰⣧⣤⣦⣤⣦⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⡛⠛⢛⡿⣻⡛⡏⣛⡿⣙⢻⡛⣻⢛⠿⡻⡛⠛⡿⣛⡛⢻⠿⣿⣟⣛⡛⡟⡙⠛⠛⠛⣟⠋⣛⠛⣛⠛⡟⠋⢻⠛⣿⢻⢻⣟⣟⠟⣻⣟⠋⢛⣟⣻⢛⣟⠛⣻⣿⡛⡏⠙⢛⡛⠛⡻⡛⡛⠻⡻⡛⠋⣿⣿⣿
⣿⣿⡟⠛⢛⠟⠛⠹⣛⡟⢋⣟⡛⢛⡿⠛⠛⡟⡿⡛⠛⢻⡟⠛⠻⣿⠟⠛⡛⠛⡛⢻⣟⠛⠛⡿⡛⠛⠻⣏⣝⡛⢿⢟⠛⣏⠛⢛⢻⠛⠟⠙⡛⢻⠛⠙⠙⣟⠛⠻⡟⠛⢻⢛⡛⡟⠛⠛⢻⡏⢻⠋⠙⢛⣛⠛⣿⣿
⣿⣿⡿⠙⡛⠛⡿⠟⠋⢟⠛⡛⢛⠙⣻⢛⠻⣿⡛⡛⢻⢛⠛⠛⡛⠉⣛⢻⡋⢙⠛⠛⠛⠻⣯⣝⡛⡏⢛⠛⠋⡿⠛⠛⢟⠋⠛⠛⡟⢻⡻⠛⣟⣻⠛⡛⢛⠛⡟⢛⠛⠛⠿⢻⢻⡛⡋⠙⡟⢛⢛⠛⠛⢻⣿⣿⣿⣿
⣿⣿⡟⠙⠙⢛⢻⠛⢻⣛⠟⠛⢛⠛⢻⣛⠻⡛⠙⢛⢻⠛⠛⡛⠙⠛⡿⠛⠙⢛⠛⡛⠻⡟⢛⠋⡟⠻⠋⠟⠛⠛⡛⠛⠛⢿⠟⠙⡟⠛⢟⡿⠛⠛⠛⠛⠛⠛⡟⠛⡟⡛⠛⠛⡿⠛⠛⢹⣟⠛⠛⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡆⡄⡍⢸⠉⣿⣭⠉⢸⠉⣿⠈⢹⡇⡌⢹⢩⡏⢙⠍⢩⠉⡋⢉⢍⢉⠋⢹⡏⠙⡅⢹⠉⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣭⣿⣽⣩⣍⣹⣟⣍⣭⣫⣩⣏⣟⣭⣫⣻⣿⣍⣧⣭⣝⣏⣽⣿⣣⣯⣟⣭⣬⣍⣼⣫⣭⣩⣇⣭⣣⣭⣝⣭⣍⣉⣯⣭⣽⣿⣍⣯⣭⣍⣭⣫⣩⣽⣣⣧⣭⣻⣭⣜⣍⣍⣼⣾⣩⣩⣈⣽⣯⣝⣿⣿⣿⣿⣿
⣿⣿⣿⠿⣿⠿⡿⠿⢿⡿⢻⣿⠿⢿⡿⣿⠿⠿⡿⠿⣿⡿⠿⠿⠿⡿⢻⢿⠿⠿⡟⠿⠟⠿⠿⣿⠿⠿⡿⡟⠿⠿⠛⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣾⣶⣿⣾⣾⣶⣿⣷⣿⣾⣷⣶⣶⣷⣾⣾⣿⣶⣷⣿⣷⣶⣿⣿⣶⣿⣿⣶⣾⣾⣿⣶⣶⣷⣿⣷⣶⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣭⣿⣨⣉⣉⣽⣉⣹⣩⣍⣸⣩⣙⣬⣭⣹⣋⣉⣏⣍⣍⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠿⣿⠻⡿⢿⠿⠟⠿⠿⠿⡿⠿⠟⠿⠿⠿⡿⠟⠿⠿⠿⠿⣿⠿⣿⠿⠿⢻⠿⠿⠿⠿⢿⡿⠿⢿⡿⠟⠿⢿⠻⡿⠛⠿⠿⠿⢿⠿⠿⢿⡟⠿⠿⢿⠿⠿⡿⠿⢿⠿⠿⢻⠿⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣿⣶⣷⣾⣷⣷⣶⣾⣷⣷⣶⣶⣶⣶⣶⣿⣶⣶⣷⣶⣶⣷⣷⣾⣶⣷⣾⣶⣷⣷⣶⣾⣾⣶⣾⣶⣶⣾⣾⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣷⣿⣶⣶⣷⣶⣾⣶⣶⣾⣾⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠉⠿⠩⠛⠉⠹⠉⠉⠉⠝⠉⠛⠉⠉⠹⠍⠩⠉⠉⠋⠙⠉⠍⠉⠯⠉⠽⠙⠝⠹⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

                    ䷩ 𝚕𝚒𝚗𝚎 395

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/12/20/sirius-open-source-outsources-everything/#comments
    Gemini version at gemini://gemini.techrights.org/2022/12/20/sirius-open-source-outsources-everything/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.20.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Sirius_‘Open_Source’_Outsourcing_Confidential_Information_to_Spying_Companies
in_Another_Continent⠀✐


Posted in Free/Libre_Software, Security at 11:32 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Putin_koala:_I_got_all_of_his_passwords!_Not_my_fault!⦈_


Summary: The Sirius_‘Open_Source’ management made the decision (without any
consultation with the staff affected) to outsource key operations to foreign,
third-party entities that are subjected_to_the_US_government's_prying_eyes_and
several_of_the_National_Security_Agency's_programs; this affected clients as
well (usually without their awareness, let alone consent)


THIS is the last part of the third section of a report I left with the company
before leaving at the start of this month. There will be a lot more information
about this scandal next month. Recent E-mails are appended below (with certain
stuff redacted for privacy’s sake).


I cautioned about this repeatedly (for about 4 years) and suffered retribution,
threats, and more. Nothing has improved since then.


As just a little sample, please see the E-mails at the bottom (recent); shared
in the future will be some longer E-mails about this issue.


But first… the report.


===============================================================================
The morale around that time was low, set aside COVID-19 becoming a growing
problem, along with lock-downs. Roy noted that in order to comply with the law
he cannot post clients’ details on the Slack network. So he chose to obey the
regulations and the law, in line with security standards. Stuff like “hi” is
probably considered OK and safe enough for Slack, but not addresses, passwords
etc. Things have not improved since, as the final section notes again (with
examples).


This long section, along with written messages as evidence, is very important.
Bad leadership worsened the corporate climate and changed how people viewed the
company from within, if not from the outside as well.


This document now proceeds to a discussion about the latest and maybe the final
blow. The company already had capacity issues (not enough staff to cover
shifts) and now it’s even worse.


Roy and Rianne hoped to prevent a ‘death spiral’ and ironically enough it seems
like the company wants to accelerate its own ‘death spiral’, due to tactless,
insensitive remarks. █


===============================================================================
One of many messages to that effect — messages which I was sending for_years to
highlight the problem. Of course nothing was done about this; usually there was
not even as much as a reply. Hush hush as a company-wide policy…


This one is from August of this year:


     Date: Tue, 30 Aug 2022 09:00:50 +0100
     MIME-Version: 1.0
     User-Agent: Mozilla/5.0 (X11; U; Linux i686; en-US; rv:1.7.6) Gecko/
     20050317
      Thunderbird/1.0.2 Mnenhy/0.7.4.0
     From: Roy Schestowitz
     Subject: Handover to Shift 2 (30/08/22)
     To: [whole team]

     [...]

     https://www.darkreading.com/cloud/lastpass-data-breach-source-code-
     stolen

     users need to change all the passwords they have there and not keep
     them
     there if they value real security not paper mills.
Another one from August of this year:


     Date: Thu, 11 Aug 2022 03:10:53 +0100
     MIME-Version: 1.0
     User-Agent: Mozilla/5.0 (X11; U; Linux i686; en-US; rv:1.7.6) Gecko/
     20050317
      Thunderbird/1.0.2 Mnenhy/0.7.4.0
     Content-Language: en-US
     From: Roy Schestowitz
     Subject: Slack admits to leaking hashed passwords for five years
     To: [whole team]
     Content-Type: text/plain; charset=UTF-8
     Content-Transfer-Encoding: 7bit

     https://nakedsecurity.sophos.com/2022/08/08/slack-admits-to-leaking-
     hashed-passwords-for-three-months/

     Does not surprise me at all. They only admit this because they got
     caught, hence they need to spin this somehow, belittling the
     severity,
     just as LastPass did after several blunders (it had suffered a
     breach).
     The way forward is self-hosting and encrypting things (on server one
     controls, not leasing).
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠟⠛⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⢉⣀⣠⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣈⣉⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡿⠛⠉⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣈⠉⠛⠿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⡏⢹⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡉⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣾⡏⢠⠧⡜⢁⠌⣛⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢰⣿⣿⣿⣿⠉⡟⢻⠿⣿⣿⣷⣶⣿⣇⣘⢠⡃⡘⢀⡿⠀⣿⣿⠃⠀⣿⠉⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡇⢠⠀⡎⢠⡃⢀⣸⣿⠟⠛⢿⣿⣷⣶⣾⣧⣼⣿⠇⣈⠀⡇⢸⡟⢠⣿⡿⢁⠌⢹⠙⢛⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣦⣧⣴⣁⣞⠹⠀⣿⡟⢀⣃⡜⢠⢠⡏⢩⢙⡿⠻⢿⣿⣶⣦⣬⣅⣘⣿⡇⠸⢀⠇⢈⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⡿⣿⣿⣿⣿⠿⠋⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣧⣼⣿⣁⡅⢸⠳⡈⢻⣄⠳⣼⢀⠋⢹⠛⡿⠿⢿⣿⣶⣾⣤⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠳⠆⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⢐⡖⣺⣿⣿⣇⣴⣖⣉⣀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣦⣤⣧⣘⣀⡇⠈⡄⠀⣰⠁⡎⢰⠃⡈⢹⠟⡛⢿⡿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠈⢿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣤⣯⣐⣁⡞⢠⠂⡞⢀⠇⣸⠀⢦⣹⠉⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣧⣌⣠⡏⠱⢀⣇⣸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⠟⣻⣿⡿⠋⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣀⣠⣾⣿⠟⠀⣠⣾⣿⡿⠿⠿⠛⠛⠉⣉⣀⣀⡉⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢽⡌⢿⣿⣿⣿⣿⣿⣟⣍⣉⣋⣛⣛⣛⣻⣿⡍⠁⠀⠘⠉⠁⠀⠀⠀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⣉⠉⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠙⠄⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠁⠼⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠙⠳⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢄⢀⡀⢀⣰⣷⡤⣐⣿⢿⡽⣿⣟⢛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠝⢿⣟⠻⢿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣾⣾⣿⣿⣿⣿⣷⣿⣿⣿⣯⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣶⣶⣤⣄⣰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣟⣿⡻⡿⢥⠨⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡛⠛⢿⣶⣦⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣷⣃⠷⠅⡄⠀⢹⣿⣿⣿⣿⣿⣿⣿⣟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡏⠉⠉⠙⠛⢾⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⢛⢛⣿⢿⢿⠟⡛⠁⢲⣶⣿⣿⣿⣿⣿⣿⣝⣾⡟⣁⢹⠅⣥⣼⣿⣿⣿⣿⣿⣿⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠃⠀⣠⣤⡤⡶⠿⣿⣿⣿⣿⣿⣿⣽⠈⢠⣾⠯⠈⠃⢛⠛⢪⣤⠽⢿⣿⣿⣿⣿⣷⣿⣿⣿⢿⣿⣎⠛⠋⣿⣿⣿⣿⣿⣿⣯⡀⡤⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⡽⠿⢨⠥⠛⢻⡄⠀⠁⢀⡀⠀⢹⠼⣾⣿⣀⣠⣿⢿⣿⣿⠯⡽⣷⡟⡏⣿⣦⣶⣿⣿⣿⣿⣯⢿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠈⠉⠀⠀⠊⠀⡀⡆⣕⣿⠛⡋⠛⡏⢹⣿⣯⣯⣿⣻⣶⣿⣿⣿⣿⣿⠻⡿⠹⡏⠈⠛⠟⠉⠰⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣦⡆⣆⣾⣺⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣼⣗⢖⠟⠀⠀⠀⠀⠠⣷⣞⣳⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⣇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣼⣿⡟⢠⣀⠡⡀⠽⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀
⡏⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣦⣿⣿⡟⣲⣼⣯⣵⠃⠀⠀⡙⡏⠓⣿⣿⣿⠿⠉⠹⣿⠟⠉⠀⠀⠀⠈⠉⠛⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀
⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣟⢻⣿⣿⣿⣿⣳⣾⣻⣿⣿⣿⣿⣦⣶⣢⠌⠁⢻⠟⣁⣸⢣⣊⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⣀⣤⣤⣴⣦⣄⠀⠀⠀⠉⠉⠀⠹⠿⢋⡿⣭⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠯⠉⠄⠠⠤⡫⢑⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⢀⣩⣵⣿⣿⣿⣗⣿⣤⣦⣄⣀⣄⡀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⡿⠋⡀⡖⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡇⠀⠀⠀⣀⣤⣤⣶⣤⣤⣀⠀⣠⣿⣿⡇⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣖⢀⠨⠙⠛⣙⠿⢛⣛⢟⣶⠉⠄⠨⡁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠇⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠈⠉⠈⠉⠉⠁⠀⠈⠉⠙⠛⠛⢿⣿⣿⣿⣦⣰⡄⠈⠈⠋⠗⢃⠅⡰⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⠏⢠⣾⡏⠉⢿⠉⡟⠉⡍⠙⣏⠉⢉⣹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢶⡕⡤⢆⠁⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⢠⣿⣿⡇⠀⠈⠀⡇⠀⡇⠀⣿⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣿⣿⣿⡇⠀⡆⠀⣇⠀⠇⢀⣿⠀⢸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠀⠀⡇⠀⢸⡀⠛⢀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠀⡄⠁⡆⢸⣧⠀⣸⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣀⣧⣠⣇⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢿⣿⣿⡿⣿⣿⡿⠿⡿⢿⡿⠿⣿⠿⠿⠿⣿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣽⡏⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⢰⣼⠀⡀⢸⡇⠀⡇⠀⡇⠀⣿⣤⠀⢠⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠶⣿⣿⣿⢱⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⢠⡼⠀⠇⠈⡇⠀⡇⠀⡇⠀⣿⣿⠀⢸⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⢤⣈⠉⢛⣸⡇⠀⠀⠀⠀⠀⠀⠀
⣿⣀⣸⣇⣀⣆⣀⣧⣀⣁⣰⣇⣀⣉⣿⣀⣸⣿⣉⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣀⣀⣠⣼⣿⣷⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠁⠙⠛⠻⢿⣿⣿⣿⡿⠳⠔⠛⡳⡄⠀⠀⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣶⣦⣄⣈⡀⠀⢰⠾⠛⠁⠀⠀⠀⣠⣀⠉⢸⡀⠀⠀⠀
⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠙⠛⠛⠛⡿⠷⠂⠀⠀⠁⠀⠘⠿⠈⠁⢸⠇⠀⠀⠀
⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀
⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⡴⠶⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 571

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/12/20/the-mickey-mouse-model/#comments
    Gemini version at gemini://gemini.techrights.org/2022/12/20/the-mickey-mouse-model/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.20.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_Denying_Security_Breaches,_Excuses_No-one⠀✐


Posted in Free/Libre_Software, Security at 12:00 pm by Dr. Roy Schestowitz


 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇We_outsourced_all_the_passwords_to_spying_firms;_but_added
                                 2FA_on_top⦈_
                   “It seemed like a good idea at_the_time…”


Summary: The ‘Mickey Mouse’ security at Sirius_‘Open_Source’ followed the staff
exodus or the management’s infinitely admirable ability to drive away essential
technical staff


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


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

                    ䷩ 𝚕𝚒𝚗𝚎 1592

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/12/20/uk-us-shell-game/#comments
    Gemini version at gemini://gemini.techrights.org/2022/12/20/uk-us-shell-game/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.20.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ This_Shell_Game_Gives_‘Open_Source’_a_Bad_Name⠀✐


Posted in Deception, Finance at 12:41 am by Dr. Roy Schestowitz


Video_download_link | md5sum 2559ad3e58655ae8f53c6926a800bc30
The Sirius Open Source Shell Game
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/sirius-shell-games.webm


Summary: Sirius_‘Open_Source’ is trying to dodge liabilities; in the process it
misleads staff and bullies staff, leading some colleagues to abrupt departures
and others into mental and physical health problems


THE company that my wife and I left earlier this month no longer has an office
and no longer pretends to have an office, either. About 7 weeks ago the address
was changed for the second time in a month. The current address isn’t even the
company’s own.


The legal status of the company is unclear or barely verifiable. People who ask
about it receive evasive if not aggressive replies. The video above goes
through the latest 3 posts about the company. This hopefully serves as a bit of
a cautionary tale. Do not work for companies like these. Spot the signs. █



                    ䷩ 𝚕𝚒𝚗𝚎 1637

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/12/20/unitary-patent-future/#comments
    Gemini version at gemini://gemini.techrights.org/2022/12/20/unitary-patent-future/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.20.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ EPO_Writing_About_Unitary_Patent_From_One_Year_in_the_Future!⠀✐


Posted in Europe, Patents at 1:08 am by Dr. Roy Schestowitz


Video_download_link | md5sum 4ed054291037e914e53a719bc16a1963
EPO Stuck in the Future
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/epo-in-time-machine.webm


Summary: The Unified Patent Court (UPC) is illegal and the thugs who promote
this illegal_system are resorting to Public Relations tourism*; sadly for the
EPO, many people know what’s going on, including the EPO’s own staff; “we are
proud of what we have achieved and we are confident that our successes will
continue in the New Year,” the staff union said this week, adding that members
will be “continuing our work together in the New Year.”


THE EPO‘s Web site contains some ludicrous things this week**. António_Campinos
went on a photo ops expedition in Africa while the EPO promotes illegal things,
in effect inciting politicians to break the law based on some bizarre
expectation that the constitutions of European Union member states will be
violated next year.


The reality is, as_usual, far from what the EPO keeps pretending it is. As a
reminder, below is a clip of Benoît_Battistelli saying that the UPC would
commence in 2016. █


Video_download_link | md5sum 5bcecd2426b605307e71fa1af9e13983


http://techrights.org/wp-content/uploads/2022/12/battistelli-epo-2016.webm


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


_____________
* Travel with no purposes other than optics; it’s trying to misframe issues of
corporate corruption in terms like racism.
** Almost everything published in epo.org is a lie, as we noted many times in
the past, e.g. [1, 2, 3, 4, 5].


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⡿⣿⣿⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⣿⣇⡇⣿⢸⢸⢸⢷⡇⣿⣾⡞⢧⣿⣿⣿⣧⡗⣿⢸⢸⣱⣷⣿⣾⣾⣾⣷⣿⣿⢨⣭⡏⣿⢸⢰⡇⣿⢹⣾⢿⡗⣿⣿⣿⢾⣎⣧⣿⣿⢰⡇⣿⢼⢸⡇⡇⣿⢸⢾⣯⣧⣗⡇⣿⣿⣾⣾⣱⡷⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣿⣿⣿⣿⣿⣿
⣿⡟⡿⢿⢿⡿⡿⣿⢿⢿⣿⣿⣿⡯⡿⣿⣿⢿⢿⡿⡿⣿⣿⣿⢿⣿⡿⣿⢿⢿⣿⡿⡿⣿⣿⣿⣿⡿⣿⢿⢿⣿⡿⣿⣿⢿⢿⣿⡿⡿⡿⣿⢿⣿⢿⣿⣿⣿⢿⢿⢿⢿⢹⣿⡿⡏⢿⢿⢹⢿⡿⣿⣿⣿⣿⣿⣿⣿
⣿⣇⣇⣿⣹⣇⣇⣿⣸⣾⣽⣿⣿⣇⣟⣿⣼⣸⣿⣿⣟⣿⣿⣿⣸⣷⣿⣧⣿⣿⣹⣇⣗⣯⣻⣻⣿⣿⣯⣿⣿⣻⣏⣿⣿⣿⣸⣸⣗⣧⣳⣜⣾⣿⣹⣇⣷⣯⣟⣿⣸⣸⣸⣹⣇⣇⣿⣸⣸⣸⣗⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⣿⣿⣿⢿⣿⣿⢿⣿⣿⡿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⣟⢻⣿⣿⣿⣿⡿⢻⣿⣿⣿⢻⣿⢟⣿⣿⣟⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 1716

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/12/20/upc-no-time-to-talk/#comments
    Gemini version at gemini://gemini.techrights.org/2022/12/20/upc-no-time-to-talk/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.20.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_Seven_Years_After_Battistelli_Said_It_Would_Start⠀✐


Posted in Europe, Patents at 1:27 am by Dr. Roy Schestowitz


No time to talk! No time to check compliance.


           🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Interstellar 7 years: December 2023⦈
               Anything to perpetuate the illusion of “progress”


Summary: The EPO, writing_about_the_Unitary_Patent_from_one_year_in_the_future
(!!), says it’ll start next year (they always say “next year”)


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⢿⠿⡿⢿⣿⡟⢿⢿⣿⡿⣿⣿⣻⣿⣿⠻⢟⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡏⡿⡏⣿⢁⡿⣿⣹⣋⣿⣨⣽⣤⣇⣽⣺⣿⣟⣿⣿⣶⣿⣿⣼⣿⣧⣷⣽⣿⣮⣾⣿⣿⣿⣿⣿⣷⣿⣾⣷⣿⣾⣿⣿⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⡿⢿⠿⡟⣿⡿⡿⢿⢿⡿⣟⡿⡟⣟⠿⢻⢟⣿⣻⣟⡿⢟⢟⣿⡟⡿⡻⡉⣿⠏⡿⢸⠁⡿⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⣷⣿⣼⣿⣟⣽⣿⣼⣿⣿⣿⣦⣧⣿⣿⣧⣮⣷⣷⣿⣶⣷⣿⣾⣾⣷⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⠒⠒⠒⠀⠀⠠⠀⠀⠀⠀⠉⠉⠛⢋⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠉⣿⣼⣆⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡙⠿⠀⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⠆⠐⠿⡿⢿⣿⡿⠿⢿⡿⠿
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⣤⡾⠃⠀⠀⢀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢤⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢀⣤⠀⠀⠀⠀⠀⣠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠘⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⣄⣴⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠟
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⣠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠂⠐⠀⡆⡆⢰⠀⡖⠀⠀⡇⢰⢠⠦⠆⠐⠀⠦⠤⠀⡀⡆⠦⡀⠀⠀⡰⠀⠀⠰⢠⢠⠆⠆⡀⢰⠀⠂⠰⢀⠀⠂⠂⢰⢰⠀⡆⠉⢠⠦⠆⠀⢰⠀⠂⢸⠀⠐⠀⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠁⠁⠈⠀⠁⠀⠀⠁⠈⠀⠁⠀⠀⠀⠁⠀⣀⣀⡁⠀⠁⠀⠀⠁⠀⠀⣀⠇⠀⠁⠀⠁⠈⠀⠀⠀⠈⠀⠀⠁⠈⠈⠀⠀⠀⠀⠁⠀⠁⠈⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 1769

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.20.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_20/12/2022:_Kodi_Nexus_RC_1_and_$96+_Banana_Pi⠀✐


Posted in News_Roundup at 4:32 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Server
          o Audiocasts/Shows
          o Graphics_Stack
          o Applications
          o Instructionals/Technical
          o Desktop_Environments/WMs
                # GNOME_Desktop/GTK
    * Distributions_and_Operating_Systems
          o Fedora_and_Red_Hat
          o Debian_Family
          o Devices/Embedded
          o Mobile_Systems/Mobile_Applications
    * Free,_Libre,_and_Open_Source_Software
          o Web_Browsers/Web_Servers
                # Mozilla
          o FSFE
          o Programming/Development
                # Perl_/_Raku
                # Python
                # Shell/Bash/Zsh/Ksh
                # Rust
    * Leftovers
          o Hardware
          o Pseudo-Open_Source
                # Openwashing
          o Security
          o AstroTurf/Lobbying/Politics
    * Gemini*_and_Gopher
          o Personal
          o Technical
    * § GNU/Linux⠀➾


          o ⚓ Chris Hannah ☛ One_of_Those_Linux_Evenings⠀⇛


                 It’s an interesting story, and he takes you through the
                 various stages of the debugging process. But I had to
                 share the part where he eventually discovered the fix on
                 an online forum: [...]


          o § Server⠀➾


                # ⚓ Kubernetes Blog ☛ Kubernetes_1.26:_Introducing_Validating
                  Admission_Policies_|_Kubernetes⠀⇛


                       In Kubernetes 1.26, the 1st alpha release of
                       validating admission policies is available!


                       Validating admission policies use the Common
                       Expression Language (CEL) to offer a declarative,
                       in-process alternative to validating admission
                       webhooks.


                       CEL was first introduced to Kubernetes for the
                       Validation rules for CustomResourceDefinitions.
                       This enhancement expands the use of CEL in
                       Kubernetes to support a far wider range of
                       admission use cases.


                       Admission webhooks can be burdensome to develop and
                       operate. Webhook developers must implement and
                       maintain a webhook binary to handle admission
                       requests. Also, admission webhooks are complex to
                       operate. Each webhook must be deployed, monitored
                       and have a well defined upgrade and rollback plan.
                       To make matters worse, if a webhook times out or
                       becomes unavailable, the Kubernetes control plane
                       can become unavailable. This enhancement avoids
                       much of this complexity of admission webhooks by
                       embedding CEL expressions into Kubernetes resources
                       instead of calling out to a remote webhook binary.


          o § Audiocasts/Shows⠀➾


                # ⚓ David Revoy ☛ Overview_of_my_Krita_Digital_Painting
                  Workflow_−_end_2022_–_David_Revoy⠀⇛


                       These steps make it easier to make my Digital
                       Painting at the end of 2022, and you’ll see many of
                       my artworks with a similar process: a large sketch
                       or storyboard, then a thin temporary line-art, then
                       a silhouette on multi layer, then a color flat, a
                       shading and to finish with a paint-over and post-
                       effect. This is a tutorial doesn’t dive into the
                       details, but keeps an overview of the workflow, the
                       goal is to give an idea of the full path and to
                       give tips on the way. I hope showing my recipe will
                       inspire you to start a drawing to test something
                       you’ll find interesting and find your own path.


                # ⚓ Late_Night_Linux_–_Episode_208_–_Late_Night_Linux⠀⇛


                       It’s our 2022 in review episode which features
                       Linux in space, gaming wins and fails, Raspberry Pi
                       drama, the year of user-facing AI, Canonical and
                       Microsoft, the rise of Mastodon, and more.


                # ⚓ Video ☛ The_SCREEN_Act_and_Why_It_is_the_WRONG_Solution_–
                  Invidious⠀⇛


                       Today we talk about the newly proposed SCREEN act
                       and why it is not a good solution to protecting
                       kids online.


          o § Graphics Stack⠀➾


                # ⚓ Khronos_Group_Welcomes_Inseye_as_Associate_Member⠀⇛


                # ⚓ Khronos_Finalizes_Vulkan_Video_Extensions_for_Accelerated
                  H.264_and_H.265_Decode⠀⇛


                       In April 2021, the Vulkan® Working Group at
                       Khronos® released a set of provisional extensions ,
                       collectively called ‘Vulkan Video’, for seamlessly
                       integrating hardware-accelerated video compression
                       and decompression into the Vulkan API. Today,
                       Khronos is releasing finalized extensions that
                       incorporate industry feedback and expose core and
                       decode Vulkan Video functionality to provide fully
                       accelerated H.264 and H.265 decode.


                # ⚓ Collabora ☛ Jason_Ekstrand_is_a_2022_Khronie_Award
                  recipient! [Ed: Awards from corporations to corporations]⠀⇛


                       With such a talented team contributing to various
                       realms of software development, it is a gratifying
                       moment when one of our teammates receives
                       recognition. This year, our fellow colleague Jason
                       Ekstrand is the recipient of a Khronie Award from
                       the Khronos Group!


                       “The Khronie Awards are presented to individuals
                       who have made significant contributions in
                       advancing the work of Khronos Working Groups
                       towards their goals.”


          o § Applications⠀➾


                # ⚓ OpenSource.com ☛ Explore_the_features_of_the_Linux_Double
                  Commander_file_manager_|_Opensource.com⠀⇛


                       Double Commander is a graphical dual-pane file
                       manager for Linux, in the tradition of Midnight
                       Commander (mc). While Midnight Commander (like the
                       DOS application Norton Commander before it) has its
                       fans, its audience is limited by the fact that it
                       only runs in a terminal window. Not everyone wants
                       to use a “flat” interface embedded in a terminal to
                       browse their file system, and so Double Commander
                       provides a similar interface in a way that feels
                       familiar to many desktop users.


                # ⚓ Kodi Foundation ☛ Kodi_Nexus_RC_1⠀⇛


                       Here we go folks, ramping things up and we have the
                       first Release Candidate (RC) for Kodi “Nexus”.


                       As always, thanks go out to all contributors for
                       their work. We are nearing 4,000 commits since v19
                       “Matrix” was first released on February 19th 2021.
                       For everyone that has contributed, both those in
                       Team Kodi and all other devs that choose to roll up
                       their sleeves and fix an issue. Everyone
                       appreciates you for making Kodi better.


                       We also want to thank all those users who provide
                       endless support on the forums, we appreciate you,
                       and all the support anyone provides to our users.


          o § Instructionals/Technical⠀➾


                # ⚓ TecAdmin ☛ df_Command_–_Check_Disk_Space_in_Linux_–
                  TecAdmin⠀⇛


                       Do you use Linux? If so, then you know that it is a
                       powerful operating system with a lot of tools and
                       options to help you manage your system. One of the
                       most useful tools that Linux provides is the df
                       command, which allows you to check your disk space.
                       In this blog, we will take a look at how to use the
                       df command to check your disk space in Linux.


                # ⚓ TecMint ☛ 30_Most_Commonly_Asked_Linux_Interview
                  Questions⠀⇛


                       If you have already achieved your Linux
                       certification and are looking forward to securing a
                       Linux job, it pays a great deal to prepare for an
                       interview that tests your knowledge of the ins and
                       outs of Linux.


                       In this guide, we present to you some of the most
                       commonly asked questions in Linux interviews and
                       answers.


                # ⚓ It’s FOSS ☛ How_to_Downgrade_Flatpak_Packages_in_Linux_–
                  It’s_FOSS⠀⇛


                       Technically, minor or point release updates are
                       released to solve issues. But things may get worse
                       when some updates break your current workflow.


                       Whether a Flatpak package or Snap, everything
                       breaks at some point when there is an issue. Being
                       a sandboxed packaging solution, it may not affect
                       the entire system, but if you encounter a bug that
                       makes your app experience worse, you may regret the
                       update.


                       For example, the previous update of Black Box was
                       bundled with certain bugs, and I could not select
                       text! Developers have solved this issue now, but
                       until they did not, I downgraded that specific
                       package to make things work.


                # ⚓ nixCraft ☛ How_to_add_Mastodon_verification_for_the
                  Discourse_forum⠀⇛


                       Discourse is a free and open-source Internet forum
                       software. Mastodon is also free and open-source
                       software for running self-hosted social networking
                       services such as Twitter. Let us see how to add a
                       Mastodon verification link to your forum. Here is
                       how it looks when verification is done correctly:


                # ⚓ DebugPoint ☛ How_to_Find_Out_Ubuntu_Version:_6_Methods⠀⇛


                       A simple guide, showing five methods to find the
                       installed Ubuntu version of your desktop and
                       servers via GUI and CLI methods.


                       Usually, if you are well-known about the Ubuntu
                       release cycle, you probably know what Ubuntu
                       desktop or server version you are running in your
                       system. Generally, there are two Ubuntu versions
                       per year and one LTS (long-term support) version
                       every two years.


                       Having said that, it’s always a good idea to check
                       what version you are running for development
                       projects and compatibilities. Here’s how to find
                       the Ubuntu version.


                # ⚓ “most”_is_an_advanced_alternative_for_the_less_command⠀⇛


                       The pager programs like more, less, and “most” are
                       often used to fit the output of a particular
                       command that is too big to fit on one screen. So,
                       what is the difference between them?


                # ⚓ DebugPoint ☛ Linux_Command_Learning_Series#4:_How_to_Find
                  Out_Ubuntu_Version:_6_Methods⠀⇛


                       Usually, if you are well-known about the Ubuntu
                       release cycle, you probably know what Ubuntu
                       desktop or server version you are running in your
                       system. Generally, there are two Ubuntu versions
                       per year and one LTS (long-term support) version
                       every two years.


                       Having said that, it’s always a good idea to check
                       what version you are running for development
                       projects and compatibilities. Here’s how to find
                       the Ubuntu version.


                # ⚓ Linux Capable ☛ How_to_Install_Linux_Kernel_6.1_on_CentOS
                  Stream_EL9/EL8⠀⇛


                       On December 11, 2022, Linux Kernel 6.1 was released
                       with a significant new addition – initial Rust
                       language support in mainline Kernel. Users of
                       CentOS Stream 9 or 8 may find upgrading to the
                       latest Kernel will bring better performance due to
                       hardware possibly not supported on the existing
                       Kernel or through improvements in code on existing
                       hardware support, amongst other features. The
                       following tutorial will teach you how to upgrade
                       your Linux Kernel using the ELRepo repository.


                # ⚓ IT Pro Today ☛ How_to_Use_AppImage_to_Distribute_Software
                  on_Linux⠀⇛


                       The open source AppImage tool enables developers to
                       make their Linux software available for all Linux
                       distributions. Here’s a look at how AppImage works.


                # ⚓ VMware_vSphere_Virtual_Machine_Snapshots_Explained_–
                  buildVirtual⠀⇛


                       VMware snapshots are a feature in VMware
                       virtualization software that allows administrators
                       to create a point-in-time copy of a virtual machine
                       (VM). Snapshots allow administrators to roll back
                       the VM to a previous state if something goes wrong.


                # ⚓ UNIX Cop ☛ How_To_Install_Glances_on_Ubuntu_20.04_|_22.04
                  LTS⠀⇛


                       Glances is a cross-platform system monitoring tool
                       written in Python. Glances is developed by an
                       awesome community. If you want to join us, please
                       open|find an opened issue scheduled in the next
                       release. Add a simple message in the issue to
                       inform the community that you want to contribute.


                # ⚓ UNIX Cop ☛ How_To_Install_BleachBit_on_Ubuntu_20.04_|_22.04
                  LTS⠀⇛


                       BleachBit is a free and open-source disk space
                       cleaner, privacy manager, and computer system
                       optimizer. The BleachBit source code is licensed
                       under the GNU General Public License version 3.


                       It can do identifying and removing Web cache, HTTP
                       cookies, URL history, temporary files log files and
                       Flash cookies for Firefox, Opera, Safari, APT and
                       Google Chrome


                # ⚓ UNIX Cop ☛ How_To_Install_gThumb_on_Ubuntu_20.04_|_22.04
                  LTS⠀⇛


                       In this small guide, we will show you how to
                       install gThumb on Ubuntu systems.


                       gThumb is a free and open-source image viewer and
                       image organizer with options to edit images. It is
                       designed to have a clean and simple user interface
                       and follows GNOME HIG, it integrates well with the
                       GNOME desktop environment.


                # ⚓ UNIX Cop ☛ How_To_Install_TagSpaces_on_Ubuntu_20.04_|_22.04
                  LTS⠀⇛


                       In this guide, we will show you how to install
                       TagSpaces on Ubuntu systems


                       TagSpaces is an open-source data manager and file
                       navigator. It helps organize files on local drives
                       by adding tags to files. Users get the same user
                       interface to manage their files on different
                       platforms. TagSpaces is compatible with Windows,
                       Linux, Mac, Android, iPhone, Firefox and Chrome.
                       The application requires neither internet
                       connection, nor user’s registration to run both on
                       desktop and portable devices.


                # ⚓ UNIX Cop ☛ How_to_install_Shotwell_on_Ubuntu_20.04_|_22.04
                  LTS⠀⇛


                       In this guide, we will show you how to install
                       Shotwell on Ubuntu systems.


                       Shotwell is an image organizer designed to provide
                       personal photo management for the GNOME desktop
                       environment. In 2010, it replaced F-Spot as the
                       standard image tool for several GNOME-based Linux
                       distributions, including Fedora in version 13 and
                       Ubuntu in its 10.10 Maverick Meerkat release.


                # ⚓ UNIX Cop ☛ How_To_Install_Chkrootkit_on_Ubuntu_20.04_|
                  22.04_LTS⠀⇛


                       In this guide, we will show you how to install
                       Chkrootkit in Ubuntu systems.


                       chkrootkit (Check Rootkit) is a common Unix-based
                       program intended to help system administrators
                       check their system for known rootkits. It is a
                       shell script using common UNIX/Linux tools like the
                       strings and grep commands to search core system
                       programs for signatures and for comparing a
                       traversal of the /proc filesystem with the output
                       of the ps (process status) command to look for
                       discrepancies.


                # ⚓ DebugPoint ☛ Writing_a_Macro_in_LibreOffice_Calc:_Getting
                  Started⠀⇛


                       Planning to automate stuff in LibreOffice? Start
                       writing your first LibreOffice Calc macro using
                       this guide.


                       LibreOffice provides a way to write your macro to
                       automate various repetitive tasks in your office
                       application. You can use Python or basic for your
                       macro development. This tutorial focuses on writing
                       a macro in LibreOffice with a ‘Hello World’ macro
                       in the Basic programming language.


                # ⚓ TecAdmin ☛ The_stream_or_file_“/var/www/html/storage/logs/
                  laravel.log”_could_not_be_opened:_failed_to_open_stream:
                  Permission_denied_–_TecAdmin⠀⇛


                       One of my Laravel applications started showing the
                       following error after I restarted the instance.


                # ⚓ Linux Capable ☛ How_to_Install_EPEL_on_CentOS_Stream_EL9/
                  EL8⠀⇛


                       EPEL, which stands for Extra Packages for
                       Enterprise Linux, is an open-source and free
                       repository that provides extra packages for
                       Enterprise Linux which can be beneficial on CentOS
                       Stream 9 or 8 distributions. The following tutorial
                       will teach you how to install and enable EPEL on
                       your CentOS Stream system.


                # ⚓ Linux Capable ☛ How_to_Increase_DNF_Speed_on_Rocky_Linux
                  EL9/EL8⠀⇛


                       DNF is a package manager for RPM-based
                       distributions such as CentOS Stream, Fedora, Red
                       Hat Enterprise Linux (RHEL), and Rocky Linux. The
                       following tutorial will cover how to increase DNF
                       performance, centering around download speed by
                       adding parallel downloads and configuring the
                       fastest mirrors.


                # ⚓ Linux Shell Tips ☛ DNF_vs_YUM_Commands:_What’s_the
                  Difference?⠀⇛


                       This article guide explains the nature and
                       differences between the Yum package manager and the
                       DNF package manager in Fedora and Red Hat-based
                       Linux distributions.


                       The first step to being a Linux user is choosing a
                       preferred Linux operating system distribution. A
                       key identifier in each Linux distribution is the
                       package manager used to perform operating system
                       tasks like installing, updating, upgrading, and
                       removing packages or software collections.


                       Some popular package managers include APT (Advanced
                       Packaging Tool) for Debian and Ubuntu
                       distributions, ZYPPER for SUSE Linux Enterprise,
                       and PACMAN for Arch Linux distribution.


          o § Desktop Environments/WMs⠀➾


                # § GNOME Desktop/GTK⠀➾


                      # ⚓ GStreamer_1.20.5_stable_bug_fix_release⠀⇛


                             The GStreamer team is pleased to announce
                             another bug fix release in the stable 1.20
                             release series of your favourite cross-
                             platform multimedia framework!


                             This release only contains bug fixes. It
                             should be safe to update from 1.20.x.


    * § Distributions and Operating Systems⠀➾


          o § Fedora and Red Hat⠀➾


                # ⚓ Fedora Project ☛ My_Experience_as_a_Fedora_Intern_–_Fedora
                  Community_Blog⠀⇛


                       As my internship with Fedora comes to an end, I
                       reflect on my experiences over the past five
                       months. I began my internship in May, applying to a
                       Community Architect position posted through Red
                       Hat. I was unfamiliar with the Fedora community,
                       but was eager to learn and contribute to the
                       communities. Marie Nordin, the former Fedora
                       Community Action and Impact Coordinator guided me
                       the whole way. She taught me about the passion and
                       enthusiasm the open source community respects
                       within community involvement.


                       Marie and I began the internship preparing for the
                       summer’s Fedora Hatch events. We put together
                       promotional content for the Hatches taking place
                       around the globe. Marie guided me through the
                       process of ensure each Hatch was properly promoted.
                       I communicated with the organizers to ensure that
                       the promotional tweets and Community Blog posts
                       were all agreed upon. The Hatches allowed me to
                       acquaint myself with the involved Fedora
                       contributors. This allowed me to feel more
                       confident and comfortable within the community.


                # ⚓ Red Hat ☛ GitOps_Cookbook:_Kubernetes_automation_in
                  practice_|_Red_Hat_Developer⠀⇛


                       With the advent of practices such as infrastructure
                       as code (IaC), software development has pushed the
                       boundaries of platforms where you can run
                       applications. This becomes more frequent with
                       programmable, API-driven platforms such as public
                       clouds and open source infrastructure solutions.
                       While some years ago developers were only focusing
                       on application source code, today they also have
                       the opportunity to code the infrastructure where
                       their application will run. This gives control and
                       enables automation, which significantly reduces
                       lead time.


                       A good example is with Kubernetes, a popular open
                       source container workload orchestration platform
                       and the de facto standard for running production
                       applications, either on public or private clouds.
                       The openness and extensibility of the platform
                       enables automation, which reduces risks of delivery
                       and increases service quality. Furthermore, this
                       powerful paradigm is extended by another
                       increasingly popular approach called GitOps.


                # ⚓ Red Hat ☛ Stream_processing_with_ksqlDB_in_OpenShift
                  Streams_for_Apache_Kafka_|_Red_Hat_Developer⠀⇛


                       This is the first article in a three-part regarding
                       existing solutions to manipulate Kafka stream data
                       with SQL, the well-known query language widely used
                       to manipulate relational databases.


                # ⚓ Red Hat ☛ How_to_contribute_to_LLVM_|_Red_Hat_Developer⠀⇛


                       LLVM is a collection of compiler toolchain
                       technologies that underpins many modern programming
                       languages, including Rust, Julia, and Swift. The
                       LLVM community is welcoming to new contributors and
                       a great place to get into compiler development.


                       This article is a fairly detailed guide for LLVM
                       contributions. Generally speaking, it’s fine to
                       just put up a patch, and somebody will be happy to
                       guide you through the more idiosyncratic parts of
                       the LLVM contribution process. However, a lot of
                       the early patch review feedback tends to be the
                       same, and this article should help you avoid some
                       of the common issues.


                # ⚓ A_quarter_on_the_Red_Hat_OSCI_and_Testing_Farm_team_–
                  Martin_Pitt⠀⇛


                       For the last quarter I have worked in Red Hat’s
                       Testing Farm (TFT) and “Operating System CI” (OSCI)
                       and teams, on a temporary rotation. TFT develops
                       and runs the Testing Farm (TF) infrastructure, an
                       API which you tell “go run a test with $these
                       parameters, it allocates a bunch of cloud
                       instances, sets them up, runs your test, and
                       returns the result. OSCI builds upon this to
                       implement Fedora’s and RHEL’s gating tests for
                       package updates, image builds, upgrades, and so on.
                       Everytime you look at Fedora’s bodhi and see these,
                       you are looking at results provided by these teams…


          o § Debian Family⠀➾


                # ⚓ Utkarsh Gupta ☛ FOSS_Activites_in_November_2022_·
                  utkarsh2102⠀⇛


                       Here’s my (thirty-eighth) monthly but brief update
                       about the activities I’ve done in the F/L/OSS
                       world.


          o § Devices/Embedded⠀➾


                # ⚓ CNX Software ☛ $96+_Banana_Pi_BPI-M2S_Amlogic_A311D/S922X
                  SBC_offers_dual_GbE,_optional_PoE_and_WiFi_5⠀⇛


                       The company provides more information and Android
                       9, Ubuntu 20.04, and Debian 10 OS images in the
                       wiki. But note that, as usual, some of the
                       information is wrong or incomplete, for instance,
                       they shamelessly copied the preliminary
                       specifications from the first CNX Software article,
                       which stated there are three buttons based on the
                       3D renders, while there are now only two buttons
                       following a small design change, and did not update
                       the info. Also worth noting is that the Linux BSP
                       hosted on GitHub relies on U-boot 2015.1 & Linux
                       kernel 4.9.236.


          o § Mobile Systems/Mobile Applications⠀➾


                # ⚓ Linux On Mobile ☛ LINMOB.net_–_Weekly_GNU-like_Mobile_Linux
                  Update_(50/2022):_postmarketOS_22.12_and_the_PineTab2⠀⇛


                       Sailfish OS approaching daily-drivability on
                       PinePhone, gtk-file-chooser memes coming to an end
                       and more.


                # ⚓ TechRadar ☛ Hundreds_of_Android_apps_found_leaking_API
                  keys,_putting_users_at_risk_|_TechRadar⠀⇛


                # ⚓ Phone Arena ☛ Nokia_XR20_and_Nokia_G50_getting_Android_13
                  updates_–_PhoneArena⠀⇛


                # ⚓ SamMobile ☛ US_unlocked_Galaxy_Note_20_series_gets_Android
                  13_One_UI_5_update_–_SamMobile⠀⇛


                # ⚓ SamMobile ☛ With_Android_13,_the_last_Galaxy_Note_models
                  are_now_on_life_support_–_SamMobile⠀⇛


                # ⚓ Giz China ☛ Xiaomi_12S_/_Ultra_series_start_to_push_the
                  Android_13_/_MIUI_14_stable_version_–_Gizchina.com⠀⇛


                # ⚓ Dignited ☛ What’s_new_with_Android_TV_13_and_How_to_Get_it
                  –_Dignited⠀⇛


                # ⚓ The Register UK ☛ Google_melds_Indian_government_cloud
                  storage_into_Android_•_The_Register⠀⇛


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


          o § Web Browsers/Web Servers⠀➾


                # § Mozilla⠀➾


                      # ⚓ Installing_Windows_(2022)_|_Will’s_Blog⠀⇛


                             I work at Mozilla. We get a laptop refresh
                             periodically. I got a new laptop that I was
                             going to replace my older laptop with. I’m a
                             software engineer and I work on services that
                             are built using Docker and tooling that runs
                             on Linux.


                             This post covers my attempt at setting up a
                             Windows laptop for software development for
                             the projects I work on after having spent the
                             last 20 years predominantly using Linux and
                             Linux-like environments.


                             Spoiler: This is a failed attempt and I gave
                             up and stuck with Linux.


                      # ⚓ The Register UK ☛ Google,_Mozilla_to_collaborate_with
                        Apple_on_fresh_Webkit_browser_benchmark [Ed: Mozilla
                        does not compete with Google, it works for Google; sort
                        of like Canonical and Microsoft]⠀⇛


                             Apple, Google and Mozilla are teaming up to
                             develop a new version of the Speedometer
                             browser benchmark that they say will score
                             web browser performance in a novel way: one
                             that reflects user journeys, not under-the-
                             hood streamlining.


                             Speedometer was originally released in 2014
                             by Apple’s WebKit team and measures web app
                             responsiveness; version 2 was released in
                             2018. The WebKit, Chrome and Mozilla
                             Developer teams confirmed in tweets they’re
                             now collaborating on version 3.


                             The Speedometer project’s page states that
                             its goal is to build a benchmark in which
                             higher scores indicate an actual user
                             benefit. “Historically benchmarks haven’t
                             done a great job at this and have actively
                             competed for attention with the needs of real
                             sites,” Mozilla’s developer account said in a
                             tweet.


                             Speedometer originally included
                             implementations of todo apps in vanilla
                             Javascript as well as the Ember, Backbone,
                             AngularJS, jQuery, Flight and React
                             frameworks. Version 2 added support for
                             additional modern JavaScript frameworks and
                             libraries.


          o § FSFE⠀➾


                # ⚓ FSFE ☛ FSFE_is_hiring_an_office_coordinator [Ed: They still
                  say “Free Software Foundation Europe” despite trademark
                  issues (the_FSF_does_not_like_this)]⠀⇛


                       We are looking for an office coordinator for 25-35
                       hours per week in our Berlin office. As part of our
                       office management team you will be the
                       administrative backbone of our operations. Our
                       ideal candidate has experience as an office
                       administrator, secretary, event organiser, or
                       another relevant administrative role.


          o § Programming/Development⠀➾


                # ⚓ Daniel Miessler ☛ Would_You_Put_AI_Art_In_Your_House?⠀⇛


                       What about you? Does your brain instantly rebel
                       against this idea? And if so, do you think there’s
                       a justifiable reason? Or are you letting society
                       tell you what to like? If you have a real reason
                       this isn’t real art I’m willing to be that kind of
                       enthusiast. But it’d have to be a real reason, not
                       one based on gatekeeping or peer pressure.


                # ⚓ Bootlin ☛ Updated_Buildroot_support_for_STM32MP1_platforms,
                  ST_BSP_v4.1_–_Bootlin’s_blog⠀⇛


                       Back in December 2021, we announced the buildroot-
                       external-st project, which is an extension of the
                       Buildroot build system with ready-to-use
                       configurations for the STMicroelectronics STM32MP1
                       platforms. Later on, in July 2022, we updated it to
                       the lastest Buildroot LTS 2022.02 and version 4.0
                       of ST BSP version.


                       More specifically, this project is a BR2_EXTERNAL
                       repository for Buildroot, with a number of
                       defconfigs that allow to quickly build embedded
                       Linux systems for the STM32MP1 Discovery Kit
                       platforms. It’s a great way to get started with
                       Buildroot on those platforms.


                # ⚓ KDAB ☛ The_Top_100_QML_Resources_by_KDAB⠀⇛


                       If you’re a reader of this blog, you probably know
                       that we have a huge amount of quality material on
                       QML and Qt Quick, among other topics. In fact,
                       there is so much material that it can be hard to
                       find what you need.


                       If that sounds familiar, you’ll want to bookmark
                       this page! This blog captures a snapshot of the top
                       100 resources we offer on QML and Qt Quick. This
                       mix of blogs, instructional videos, and other
                       resources has been organized into simple, easy-to-
                       understand categories with simple descriptions
                       added when necessary.


                # § Perl / Raku⠀➾


                      # ⚓ Rakulang ☛ Day_20:_Sigils_are_an_underappreciated
                        programming_technology_–_Raku_Advent_Calendar⠀⇛


                             Sigils – those odd, non-alphabetic prefix
                             characters that many programmers associate
                             with Bash scripting; the  $  in  echo $USER 
                             – have a bit of a bad reputation. Some
                             programmers view them as “old fashioned”,
                             perhaps because sigils are used in several
                             languages that first gained popularity last
                             millennium (e.g. BASIC, Bash, Perl, and PHP).
                             Other programmers just view sigils as rather
                             pointless, as “just a way of encoding type
                             information” in variable names – basically a
                             glorified version of apps Hungarian notation
                             (which isn’t even the good kind of Hungarian
                             notation).


                             Maybe sigils served a purpose in the bad old
                             days, these critics say, but modern IDEs and
                             editors give us all the type information we
                             could want, and these tools have made sigils
                             obsolete. Now that we have VS Code, we don’t
                             have any reason to take the risk that someone
                             might use sigils to write code that bears a
                             suspicious resemblance to line noise, or
                             perhaps to an extremely angry comic strip
                             character.


                      # ⚓ Rakulang ☛ 2022.51_Hijacking_D3_–_Rakudo_Weekly
                        News⠀⇛


                             Anton Antonov has published another video,
                             this time about their excellent new module
                             Javascript::D3 to create beautiful graphs
                             with Raku in Jupyter notebooks, or just even
                             in HTML. It also comes with a blog post and
                             comments on /r/rakulang. Check it out!


                # § Python⠀➾


                      # ⚓ Didier Stevens ☛ New_tool:_teeplus.py⠀⇛


                             This new tool, teeplus.py, is an extension of
                             the tee command.


                             The tools takes (binary) data from stdin, and
                             sends it to stdout, while also writing the
                             data to a file on disk.


                             While the tee command requires a filename as
                             argument, teeplus.py takes no arguments (only
                             options).


                      # ⚓ Adafruit ☛ The_Python_on_Hardware_Newsletter:_Over10k
                        subscribers,_subscribe_now!_#CircuitPython_#Python
                        #RaspberryPi_@micropython_@ThePSF⠀⇛


                             The Python on Microcontrollers newsletter is
                             the place for the latest news involving
                             Python on hardware (microcontrollers AND
                             single board computers like Raspberry Pi).


                      # ⚓ OpenSource.com ☛ How_I_use_Artipie,_a_PyPI_repo_|
                        Opensource.com⠀⇛


                             While developing with Python as a student, I
                             found that I needed some private centralized
                             storage. This was so I could store binary and
                             text data files, as well as Python packages.
                             I found the answer in Artipie, an open source
                             self-hosted software repository manager.


                             At university, my colleagues and I conducted
                             research and worked with a lot of data from
                             experimental measurements. I used Python to
                             process and visualize them. My university
                             colleagues at the time were mathematicians
                             and didn’t have experience with software
                             development techniques. They usually just
                             passed data and code on a flash drive or over
                             email. My efforts to introduce them to a
                             versioning system like Git were unsuccessful.


                      # ⚓ Linux Hint ☛ SciPy_Differential_Evolution⠀⇛


                             This article is about SciPy Differential
                             Evolution (DE). SciPy is the library of the
                             Python language, and Differential Evolution
                             is the method or function of the SciPy
                             library. Most people have been learning
                             Python, whether they are developers or not,
                             since Python’s numerous libraries and
                             functions make it very secure and reliable.
                             SciPy is frequently used for solving
                             differential and algebraic equations,
                             interpolation, optimization, etc. Here, we
                             are discussing SciPy DE usage to help you
                             understand how to implement the SciPy
                             differential evolution function in Python
                             applications.


                # § Shell/Bash/Zsh/Ksh⠀➾


                      # ⚓ University of Toronto ☛ My_dmenu_wrapper_script_and
                        what_it_will_invoke_for_me⠀⇛


                             Dmenu needs a wrapper script in order to do
                             something useful, because all it does by
                             itself is read autocompletion entries from
                             standard input and write your selection to
                             standard output. The traditional basic
                             wrapper script runs a command found in your
                             $PATH, or perhaps does some other single
                             purpose action like passing a URL you entered
                             to a browser. My wrapper script has always
                             been a little more complicated, and has
                             evolved to primarily do three different
                             things: run commands (using a custom $PATH
                             for dmenu), pass ‘URLs’ to my primary Firefox
                             session, and start terminal sessions to local
                             hosts, possibly using alternate usernames.


                # § Rust⠀➾


                      # ⚓ Diziet ☛ diziet_|_Rust_for_the_Polyglot_Programmer,
                        December_2022_edition⠀⇛


                             I have reviewed, updated and revised my short
                             book about the Rust programming language,
                             Rust for the Polyglot Programmer.


                             It now covers some language improvements from
                             the past year (noting which versions of Rust
                             they’re available in), and has been updated
                             for changes in the Rust library ecosystem.


                             With (further) assistance from Mark Wooding,
                             there is also a new table of recommendations
                             for numerical conversion.


    * § Leftovers⠀➾


          o § Hardware⠀➾


                # ⚓ CNX Software ☛ Pinecil_V2_Bluetooth_LE_soldering_iron_gets
                  a_web_interface_–_CNX_Software⠀⇛


                       It’s now possible to make use of the Pinecil V2
                       soldering iron‘s Bluetooth LE connectivity through
                       a web-based interface used to monitor and/or set
                       the temperature and power of the RISC-V soldering
                       iron.


                       When the Pinecil V2 soldering iron was launched
                       with a Bouffalo Lab BL706 RISC-V Bluetooth
                       microcontroller last summer, we were told there
                       were main potential cases to make use of the
                       Bluetooth LE features: OTA firmware upgrade and
                       remote telemetry and control. The latter is now
                       being taken care of by Joric who has written a web
                       application to visualize telemetry data and even
                       control the temperature of the soldering iron.


          o § Pseudo-Open Source⠀➾


                # § Openwashing⠀➾


                      # ⚓ TechRepublic ☛ Acceldata_launches_new_open-source
                        data_observability_platform⠀⇛


                             Acceldata has announced the release of a new
                             open-source version of its data platform.
                             Unlike many traditional data platforms, this
                             new release is multidimensional, promising
                             integrated insights from data pipelines, data
                             quality tools and data systems.


          o § Security⠀➾


                # ⚓ FOSSLife ☛ Ethical_Hacking_Insights_from_HackerOne_Report⠀⇛


                       Today’s ethical hackers are motivated by the desire
                       to learn, to earn money, and to protect and defend,
                       according to HackerOne’s 2022 Hacker-Powered
                       Security Report. In fact, 92 percent of hackers say
                       they can find vulnerabilities that scanners can’t,
                       the report says.


                # ⚓ Computer World ☛ The_trials_and_tribulations_of_Microsoft’s
                  KB5012170_patch [Ed: ‘Secure’_boot_is_the_opposite_of
                  security]⠀⇛


                       KB5012170 is many things to many Windows users.
                       First, it’s a patch that either installs with no
                       problems or leads to a blue screen of death (BSOD).
                       It can also be an indicator we have a problem
                       getting updated drivers on our systems. It can
                       demonstrate how users don’t keep up with Bios
                       updates. And it shows that some OEMs enable
                       Bitlocker on the systems they sell (not necessarily
                       in a good way).


                       In short, it’s a problematic patch that just keeps
                       rearing its head.


                       Also known as “Security Update for Secure Boot
                       DBX,” KB5012170 was released earlier this year and
                       makes improvements to the Secure Boot Forbidden
                       Signature Database (DBX). Windows devices that have
                       Unified Extensible Firmware Interface (UEFI)-based
                       firmware have Secure Boot enabled. It ensures only
                       trusted software can be loaded and executed on
                       during the boot process by using cryptographic
                       signatures to verify the integrity of the process
                       and the software being loaded.


                # ⚓ Bleeping Computer ☛ Microsoft:_KB5021233_causes_blue
                  screens_with_0xc000021a_errors⠀⇛


                       Microsoft is investigating a known issue leading to
                       Blue Screen of Death (BSOD) crashes with 0xc000021a
                       errors after installing the Windows 10 KB5021233
                       cumulative update released during this month’s
                       Patch Tuesday.


                       The company warned over the weekend that “after
                       installing KB5021233, some Windows devices might
                       start up to an error (0xc000021a) with a blue
                       screen.”


                       This known issue is likely caused by a mismatch
                       between the file versions of hidparse.sys in
                       system32 and system32/drivers in the Windows
                       folder, “which might cause signature validation to
                       fail when cleanup occurs.”


                       The list of affected platforms includes only client
                       Windows 10 versions, from Windows 10 20H2 to the
                       latest release, Windows 10 22H2.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ [Old]_Points_worth_noting_in_the_Estonia_i-voting_report_|
                  Stop_at_Zona-M⠀⇛


                       Back in 2019, the OSCE Office for Democratic
                       Institutions and Human Rights (ODIHR) deployed an
                       Election Expert Team (EET) to observe the 3 March
                       parliamentary elections in Estonia. That team
                       focused its assessment on the work of the election
                       administration, the implementation of Internet
                       voting, and the participation of national
                       minorities in the electoral process. The final
                       report, published in June 2019, contains some
                       considerations and recommendations that anybody who
                       still thinks online voting in actual political
                       elections makes sense consider carefully….


    * § Gemini* and Gopher⠀➾


          o § Personal⠀➾


                # ⚓ Santa_Claus,_Coca-Cola,_Sprite,_and_vast_amounts_of
                  cookies⠀⇛


                       I was wrong when I mentioned that Coca-Cola created
                       our modern image of Santa Claus [1]— it goes back
                       into the mid-to-late 1800s [2]. But Coca-Cola’s
                       Santa Claus advertising *might* have been the
                       inspiration for Sprite.


                       And speaking of Santa and food products, here’s a
                       video that answers the question no one bothered to
                       ask, how many cookies does Santa Claus consume on
                       Christmas? [3] It’s amazing he even survives the
                       trip.


          o § Technical⠀➾


                # ⚓ initial_thoughts_on_stable_diffusion’s_dataset⠀⇛


                       i’ve come across this little article about stable
                       diffusion’s training dataset [2]. unlike dall-e’s
                       openAI, stability is rather transparent about this
                       stuff, which is great. so. i wanna talk about the
                       dataset — or rather, the fraction of the dataset
                       [3] that’s been organized and can be browsed. read
                       the article first and then come back so i don’t
                       have to paraphrase it all lmao


                       the fraction we can browse is composed of 12
                       million image-caption pairs, or “2% of the 600
                       million images used to train the most recent three
                       checkpoints”. so it’s a lot but doesn’t even
                       scratch the surface.


                # ⚓ Change_the_default_character_limit_on_your_Mastodon
                  instance⠀⇛


                       For the sake of this post, we’ll assume we want to
                       change the default character limit to 2000
                       characters.


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



                    ䷩ 𝚕𝚒𝚗𝚎 3038

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.20.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_20/12/2022:_NetBSD_10.0_Beta,_SystemRescue_9.06,_and_DietPi_8.12⠀✐


Posted in News_Roundup at 9:40 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Desktop/Laptop
          o Server
          o Audiocasts/Shows
          o Kernel_Space
          o Graphics_Stack
          o Benchmarks
          o Applications
          o Instructionals/Technical
    * Distributions_and_Operating_Systems
          o New_Releases
          o BSD
          o SUSE/OpenSUSE
          o Fedora_Family_/_IBM
          o Debian_Family
          o Mint/Ubuntu_Family
          o Devices/Embedded
          o Open_Hardware/Modding
          o Mobile_Systems/Mobile_Applications
    * Free,_Libre,_and_Open_Source_Software
          o Web_Browsers/Web_Servers
                # Mozilla
          o SaaS/Back_End/Databases
          o FSF
          o GNU_Projects
          o Programming/Development
                # Perl_/_Raku
                # Python
    * Leftovers
          o Proprietary
          o Linux_Foundation
          o Security
                # Privacy/Surveillance
          o AstroTurf/Lobbying/Politics
                # Misinformation/Disinformation/Propaganda
          o Internet_Policy/Net_Neutrality
          o Monopolies
    * Gemini*_and_Gopher
          o Personal
          o Technical
                # Programming
    * § GNU/Linux⠀➾


          o ⚓ ZDNet ☛ Linux-based_tablets:_Pine64_says_its_PineTab_2_tablet_is
            a_‘complete’_redesign_|_ZDNET⠀⇛


                 Pine64 has announced it is making the Linux-based PineTab
                 2, which is the successor to the original PineTab that
                 didn’t make it through the post-pandemic chip shortage.


                 Pine64, which makes numerous developer-friendly pieces of
                 kit, is billing the PineTab 2 as much more than just a
                 specifications upgrade due to its new design, including a
                 metal chassis that has two “snap-tabs” for easily
                 releasing the back to access internals for repairs and
                 upgrades.


          o § Desktop/Laptop⠀➾


                # ⚓ Make Use Of ☛ The_3_Best_Christmas-Themed_Wallpaper
                  Collections_for_Linux⠀⇛


                       Get into the holiday spirit by finding a Christmas-
                       themed, high-quality wallpaper for your Linux
                       desktop.


                       With the holiday season in full swing, it is a good
                       time to refresh the Christmas-themed wallpapers on
                       your Linux PC.


                       When you have so many wallpaper websites to choose
                       from, how do you know which sites have high-quality
                       images with wintry themes featuring magical views
                       outdoors to full-blown Christmas scenes showing off
                       the lights and action of the big city?


                       You’ll have no trouble finding a perfect desktop
                       background image to suit your Linux PC with these
                       wallpaper collections.


          o § Server⠀➾


                # ⚓ Netcraft ☛ December_2022_Web_Server_Survey_|_Netcraft_News
                  [Ed: Microsoft is down sharply again, from 5.43% in busiest
                  sites to just 5.37% in one single month]⠀⇛


                       In the December 2022 survey we received responses
                       from 1,125,374,532 sites across 271,238,722 domains
                       and 12,234,425 web-facing computers. This reflects
                       a loss of 9.7 million sites, 450,421 domains, and
                       72,200 web-facing computers.


                       Cloudflare continues its growth, gaining 1.5
                       million sites (+1.44%) and 309,670 domains
                       (+1.21%). Cloudflare now accounts for 9.14% of
                       sites and 9.57% of domains seen by Netcraft, up by
                       0.21pp and 0.13pp respectively.


                       Apache lost 7.4 million sites (-3.03%) and 15,439
                       web-facing computers (-0.46%). However, it saw a
                       modest gain of 52,986 domains (+0.09%). nginx also
                       saw significant loss of 5.5 million sites (-1.84%),
                       1.3 million domains (-1.77%), and 82,128 web-facing
                       computers (-1.71%).


                       The largest percentage growth this month comes from
                       LiteSpeed, with it gaining 1.1 million sites
                       (+2.01%) and 170,873 domains (+2.03%). OpenResty
                       also saw a significant growth of 1.1 million sites
                       (+1.20%) but lost 135,748 domains (-0.34%).


                       In the top million busiest sites, Cloudflare
                       continues its upward trend – gaining 809 of the top
                       million sites, which increases its market share by
                       0.08pp to 21.08%. The gap between Cloudflare and
                       the leader Apache, which lost 784 sites and 0.08pp
                       market share, is down to just 0.51pp. In second
                       place, nginx gained a modest 428 sites and 0.04pp
                       market share.


          o § Audiocasts/Shows⠀➾


                # ⚓ Video ☛ Linux_SUCKS_at_these_5_day_to_day_tasks…_–
                  Invidious⠀⇛


                # ⚓ Video ☛ Ubuntu_Unity_22.10_Quick_overview_#shorts_–
                  Invidious⠀⇛


                       A Quick Overview Ubuntu Unity 22.10.


                # ⚓ Video ☛ How_to_install_Manjaro_21.3.7_KDE_Plasma_Edition_–
                  Invidious⠀⇛


                       In this video, I am going to show how to install
                       Manjaro 21.3.7 KDE Plasma Edition


                # ⚓ Tux Digital ☛ 72:_How_It’s_Made:_Rare_Earth_Minerals_and
                  Chip_Manufacturing_Wonders!_–_Hardware_Addicts_–_TuxDigital⠀⇛


                       Welcome to Hardware Addicts, a proud member of the
                       TuxDigital Network. Hardware Addicts is the podcast
                       that focuses on the physical components that powers
                       our technology world.


                       In this episode, we’re going to be talking about
                       TSMC’s new fabrication facility in the US and why
                       this is such an important endeavor for technology
                       enthusiasts along with a discussion on rare earth
                       minerals. Then we head to Camera Corner where Wendy
                       will discuss the Camera Corner Gift Guide.


                # ⚓ Video ☛ Atom_Code_Editor_Is_Dead:_Long_Live_Its_Successors
                  –_Invidious [Ed: Microsoft kills Open Source to make sure you
                  adopt its proprietary spyware instead]⠀⇛


                       All the way back it June it was announced that the
                       Atom code editor was being discontinued in favour
                       of Visual Studio Code but no matter because 2
                       projects now exist to keep that legacy going,
                       Pulsar and Zed.


                # ⚓ Video ☛ World_Leaders_Bully_Apple_With_Regulations_–
                  Invidious⠀⇛


                       In this video I discuss some of the actions that
                       governments like the EU, Brazil and India are doing
                       to protect their citizens who consume Apple
                       products from the companies abusive practices.


          o § Kernel Space⠀➾


                # ⚓ The Register UK ☛ Kernel_6.2_promises_multiple_filesystem
                  improvements_•_The_Register⠀⇛


                       The forthcoming Linux kernel 6.2 should see
                       improved filesystem handling, including performance
                       gains for SD cards and USB keys, as well as FUSE.
                       As for the next-gen storage subsystems… not so
                       much.


                       For a mature OS kernel, there are still
                       considerable improvements being made in Linux’s
                       handling of existing disk formats, and this should
                       improve when kernel 6.2 appears at some point in
                       early 2023.


                       A patch from Sony engineer Yuezhang Mo makes it
                       quicker to create new files or directories on an
                       exFAT disk with lots of files on it – and the more
                       files there are, the bigger the improvement. This
                       follows the same programmer’s earlier patch to
                       improve exFAT handling, in March.


                # ⚓ InfoQ ☛ Linux_6.1_Officially_Adds_Support_for_Rust_in_the
                  Kernel⠀⇛


                       After over two years in development, support for
                       using Rust for kernel development has entered a
                       stable Linux release, Linux 6.1, which became
                       available a couple of weeks ago.


                       Previous to its official release, Rust support has
                       been available in linux-next, the git tree
                       resulting from merging all of the developers and
                       maintainers trees, for over a year. With the stable
                       release, Rust has become the second language
                       officially accepted for Linux kernel development,
                       along with C.


                       Initial Rust support is just the absolute minimum
                       to get Rust code building in the kernel, say Rust
                       for Linux maintainers. This possibly means that
                       Rust support is not ready yet for prime-time
                       development and that a number of changes at the
                       infrastructure level are to be expected in coming
                       releases. Still, there has been quite some work
                       work going on on a few actual drivers that should
                       become available in the next future. These include
                       a Rust nvme driver, a 9p server, and Apple Silicon
                       GPU drivers.


          o § Graphics Stack⠀➾


                # ⚓ Collabora ☛ State_of_Monado’s_visual-inertial_tracking⠀⇛


                       After a two-year hiatus, FOSS XR took place in
                       Minneapolis this past October. Besides being a
                       wonderful place to come together and meet many
                       different awesome people working on open-source XR,
                       the conference held several talks directly related
                       to Monado, our open-source OpenXR runtime. In this
                       post, I’ll focus on summarizing some of the key
                       points of the “Visual-inertial tracking for Monado”
                       talk as an overview of its current state.


                       In my last blog post, I took a more in-depth look
                       at the details of integrating visual-inertial
                       tracking solutions with Monado and why it was an
                       important component to build. The gist is that new
                       headsets have been coming with only cameras and
                       IMUs as their sensors for tracking, and there
                       hasn’t been a clear alternative to their
                       proprietary tracking solutions. Although still not
                       meant for final users, thanks to this module (and
                       thanks to Basalt in particular), we can now get
                       OpenXR apps tracked on a totally open-source
                       software stack on Linux.


          o § Benchmarks⠀➾


                # ⚓ WCCF Tech ☛ AMD_EPYC_Genoa_CPUs_Showcase_Strong_Performance
                  Improvement_With_AVX-512_At_The_Same_Power⠀⇛


                       AMD’s EPYC 9004 Genoa CPUs have been tested in
                       various AVX-512 benchmarks by Phoronix and it looks
                       like the latest Zen 4 parts deliver a big boost in
                       performance while retaining the same power.


          o § Applications⠀➾


                # ⚓ OMG Ubuntu ☛ Use_’Corluma’_to_Control_Hue,_LIFX_–_Nanoleaf
                  Lights_on_Ubuntu_–_OMG!_Ubuntu!⠀⇛


                       If you’re rocking some luscious LED smart lights in
                       your home and you want to be able to control them
                       from your Ubuntu desktop, check out Corluma.


                       Corluma is a cross-platform light controller app
                       available for macOS, iOS, Android, and — of
                       interest to those of you reading this — Ubuntu-
                       based Linux distributions. While the mobile and Mac
                       versions of the app are paid software the Ubuntu
                       version is free (as in beer).


                       The aim of the app is to allow you to control all
                       your lights from one app, without having to
                       configure IFTT, smart assistant integrations, etc.
                       For some of these lights, there aren’t other
                       options for controlling them on Ubuntu.


                       So if you’ve LIFX lights, or those pricey (but
                       pretty) NanoLeaf tiles, you can control all of them
                       from within one app, at the same time — an
                       undoubted boon. Better yet, the app works over the
                       local Wi-Fi network so there are no cloud services
                       to sign up to, or logins to faff around with.


                       Now, I don’t have any smart lights that are
                       compatible with this app for me to test, so I can’t
                       illuminate (sorry) this post with much first-hand
                       perspective. While I have written about how to
                       control Hue lights on Ubuntu before Corluma is the
                       first tool I’ve seen that encompasses support for
                       more than just Hue.


                # ⚓ Linux Links ☛ 5_Best_Free_and_Open_Source_Address_Book
                  Managers⠀⇛


                       Address books allow easy access to the user’s
                       friends, family, business associates and others by
                       maintaining their email and other contact details
                       on their computer.


                       This article focuses on standalone software.
                       CardOver is tightly integrated with Thunderbird but
                       it can also run independently.


                # ⚓ LWN ☛ GnuPG_2.4.0_released⠀⇛


                       Exactly 25 years ago the very first release of
                       GnuPG was published. We are pleased to take this
                       opportunity to announce the availability of a new
                       stable GnuPG release: version 2.4.0.


                       This release has a few new features and the binary
                       releases come with an updated Libksba to fix
                       another vulnerability related to CVE-2022-3515.


                # ⚓ Ubuntu Handbook ☛ MuseScore_4_Released!_New_Mixer,_Accent
                  Colors_&_Muse_Sounds_Plugin_|_UbuntuHandbook⠀⇛


                       Free and open-source music notation software
                       MuseScore 4 is out after more than 2 year since the
                       last major release.


                       MuseScore 4 now have a modern look UI with both
                       light and dark mode, as well as 7 accent colors. It
                       provides a setup dialog to choose between them on
                       first launch, though user can re-configure them
                       along with fonts, background and paper colors by
                       going to Preferences -> Appearances.


          o § Instructionals/Technical⠀➾


                # ⚓ Make Tech Easier ☛ LibreOffice_Calc_Keyboard_Shortcuts_–
                  Make_Tech_Easier⠀⇛


                       LibreOffice Calc is a free, open-source spreadsheet
                       program for Linux, Windows, and MacOS. Like
                       Microsoft Excel, LibreOffice Calc provides a simple
                       yet powerful interface that you can use to record
                       and manipulate data tables. LibreOffice Calc can
                       also produce complex tables and analyze them
                       through its extensive built-in wizards.


                # ⚓ ExplainShell:_The_Best_Alternative_for_Linux_Man_Pages⠀⇛


                       Look at the following command and tell me what each
                       part of it does:


                       $ find . -type f -printf ‘%s %p\n’ | sort -nr |
                       head -10 | numfmt –to=iec-i –suffix=B
                       –format=”%.3f”
                       You might be full of confidence if you are a pro
                       Linux user, but things are not that easy for
                       beginners, and even for advanced users, there will
                       be some commands that put them in a loop of
                       confusion.


                       Now, you might be thinking there are two ways to
                       break down the above command: first, by directly
                       searching for it on the internet, and second, by
                       manually checking each part of the command on the
                       manual page.


                       For now, we will keep the first way aside (because
                       you will rarely find the command’s explanation on
                       the internet); however, the second way, manually
                       checking on the manual page, can be too boring,
                       mentally painful, and time consuming for a Linux
                       user.


                       But what if I told you that there is an amazing
                       web-based tool known as ExplainShell, an
                       alternative to the traditional manual page, that
                       can quickly decode each part of the specified
                       commands and give you a beautiful hierarchy with an
                       explanation of each part?


                # ⚓ Ubuntubuzz ☛ How_To_Import_and_Use_Microsoft_PowerPoint
                  Templates_on_LibreOffice_Impress⠀⇛


                       This tutorial will help you importing and using
                       Microsoft PowerPoint templates on LibreOffice
                       Impress. This way, you can immediately create
                       beautiful presentations you really need and want
                       just instantly. From this article, you can download
                       a lot of both academic and general purpose
                       templates including those from Oxford, Harvard, and
                       MIT available for free on the net in PowerPoint
                       PPTX format to later import, save, and convert them
                       to Impress ODP format if you wish. Now let’s
                       practice!


                # ⚓ Make Use Of ☛ How_to_Create_a_Winter_Wonderland_on_Linux
                  With_GNOME_Extensions⠀⇛


                       Whether you view the snow and cold weather as havoc
                       to winter drivers, naughty words, aching backs, or
                       a delightful way to have a hot beverage in hand,
                       there are three straightforward ways to add a bit
                       of joy to your Linux PC.


                # ⚓ Linux Nightly ☛ How_to_Install_PyCharm_on_Ubuntu_22.04_–
                  Linux_Nightly⠀⇛


                       PyCharm is an IDE developed by JetBrains. It’s used
                       for programming in the Python language, and comes
                       with some convenient features like the ability to
                       connect to a database, create virtual environments,
                       and more. In this tutorial, we will learn how to
                       install PyCharm on Ubuntu 22.04. You will see how
                       to install with Snap package, the official
                       download, flatpak, and with GUI.


                # ⚓ TechRepublic ☛ How_to_create_a_Linux_distribution_within
                  your_web_browser_with_Instantbox⠀⇛


                       If you’re a developer — especially one who works
                       with container or cloud-native deployments — you
                       work with Linux. Even though Linux might not be
                       your desktop operating system of choice, it
                       certainly is your container or cloud environment.
                       Because of that, you need to have easy access to a
                       native Linux operating system to serve as your
                       development environment.


                       For that, you can always log in to your Docker or
                       Kubernetes server and spin up a new container based
                       on any given Linux image. You could also go the
                       virtual machine route or even use a tool like
                       Multipass.


                # ⚓ Make Use Of ☛ How_to_Manage_Logitech_Unifying_Receiver_and
                  Devices_on_Linux⠀⇛


                       Do you have a Logitech device and want to use a
                       unifying receiver instead of Bluetooth but struggle
                       to manage it on Linux?


                       Solaar is a great tool for managing Logitech
                       devices on Linux. You can use the Logitech Unifying
                       or Bolt Receiver and connect up to six devices on a
                       single unifying receiver.


                # ⚓ HowTo Forge ☛ How_to_Install_and_Configure_GoCD_on_Ubuntu
                  22.04⠀⇛


                       GoCD is an open-source continuous delivery and
                       automation system.


                # ⚓ HowTo Forge ☛ How_to_deploy_Ghost_CMS_on_Rocky_Linux_9⠀⇛


                       Ghost is an open-source blogging platform to help
                       you create a professional-looking blog.


                # ⚓ How_to_Empty_a_File_in_Linux⠀⇛


                       The more we use a PC, the more files we collect.
                       Some of them are important, while others aren’t,
                       and it’s important to know how (and when) to remove
                       them.


                       If you want to empty a file on Linux but don’t want
                       to remove it entirely, you can try a couple of
                       methods. Using the Linux terminal, you can make
                       changes to the contents of a file, stripping it of
                       content.


                       The file will remain, allowing you to reuse it for
                       other things. If you want to know how to empty a
                       file in Linux, follow these steps.


                # ⚓ Video ☛ How_to_install_Zoom_on_KDE_Neon_–_Invidious⠀⇛


                       In this video, we are looking at how to install
                       Zoom on KDE Neon.


                # ⚓ UNIX Cop ☛ How_To_Install_Zlib_on_Ubuntu_20.04_|_22.04
                  LTS⠀⇛


                       In this guide, we will show you how to install zlib
                       on Ubuntu systems.


                       zlib is a software library used for data
                       compression. zlib was written by Jean-loup Gailly
                       and Mark Adler and is an abstraction of the DEFLATE
                       compression algorithm used in their gzip file
                       compression program. zlib is also a crucial
                       component of many software platforms, including
                       Linux, macOS, and iOS. It has also been used in
                       gaming consoles such as the PlayStation 4,
                       PlayStation 3, Wii U, Wii, Xbox One and Xbox 360.


                       zlib is designed to be a free, general-purpose,
                       legally unencumbered — that is, not covered by any
                       patents — lossless data-compression library for use
                       on virtually any computer hardware and operating
                       system. The zlib data format is itself portable
                       across platforms. Unlike the LZW compression method
                       used in Unix compress(1) and in the GIF image
                       format, the compression method currently used in
                       zlib essentially never expands the data. (LZW can
                       double or triple the file size in extreme cases.)
                       zlib’s memory footprint is also independent of the
                       input data and can be reduced, if necessary, at
                       some cost in compression.


                # ⚓ UNIX Cop ☛ How_To_Install_RustDesk_on_Ubuntu_20.04_|_22.04
                  LTS⠀⇛


                       In this tutorial, we will illustrate how to install
                       RustDesk into your Ubuntu systems.


                       RustDesk is a remote access and remote control
                       software, allowing maintenance of computers and
                       other devices.


                       The RustDesk client is available for different
                       operating systems. RustDesk has the aspiration to
                       be an open source alternative for Remote desktop
                       software like TeamViewer or AnyDesk. Therefore,
                       RustDesk is able to function without additional
                       tools like VPNs or port forwardings, even behind
                       firewalls or NATs. RustDesk used to be based on the
                       proprietary Sciter UI runtime library, but in 2022
                       plans started to replace it with Flutter.


                # ⚓ UNIX Cop ☛ How_To_Install_Gatsby_Node_Framework_on_Ubuntu
                  20.04_|_22.04_LTS⠀⇛


                       In this tutorial, we will show you how to install
                       and use Gatsby.js on Ubuntu


                       Gatsby is an open-source static site generator
                       built on top of Node.js using React and GraphQL. It
                       provides over 2500 plugins to create static sites
                       based on sources as Markdown documents, MDX
                       (Markdown with JSX), images, and numerous Content
                       Management Systems such as WordPress, Drupal and
                       more. Since version 4 Gatsby also supports Server-
                       Side Rendering and Deferred Static Generation for
                       rendering dynamic websites on a Node.js server.
                       Gatsby is developed by Gatsby, Inc. which also
                       offers a cloud service, Gatsby Cloud, for hosting
                       Gatsby websites.


                # ⚓ Video ☛ Install_Linux_Without_Losing_Your_Windows_OS_–
                  Invidious⠀⇛


                       If you purchased a new laptop recently and want to
                       replace the Windows OS with Linux. In this video I
                       walk through how save the windows OS you paid for
                       incase you ever want to go back. You paid for
                       Windows, so why not keep it.


                # ⚓ Linux Made Simple ☛ How_to_install_RStudio_on_a
                  Chromebook⠀⇛


                       Today we are looking at how to install R-base and
                       RStudio on a Chromebook.


                # ⚓ RoseHosting ☛ How_to_Install_Odoo_16_on_Ubuntu_22.04_–
                  RoseHosting⠀⇛


                       Take a look at our tutorial and learn more about
                       how to install Odoo 16 on Ubuntu 22.04. Let’s dive
                       right in!


                # ⚓ TecAdmin ☛ How_to_Change_Redis_Max_Memory_–_TecAdmin⠀⇛


                       To configure the maximum amount of memory that
                       Redis will use, you can use the `maxmemory`
                       directive in the Redis configuration file
                       (`redis.conf`). This directive takes an integer
                       value, representing the maximum number of bytes
                       that Redis will use to store data in memory.


                # ⚓ How_to_Exclude_Words_and_Patterns_in_Grep_–_buildVirtual⠀⇛


                       Grep is a powerful command-line tool that allows
                       you to search for specific patterns or words in a
                       file or group of files. It is widely used by
                       programmers, system administrators, and analysts to
                       search for specific patterns in logs, configuration
                       files, and other types of data.


                       One useful feature of grep is the ability to
                       exclude certain words or patterns from the search.
                       This can be useful if you want to focus on specific
                       patterns or if you want to exclude certain types of
                       information from the search results.


                # ⚓ Red Hat Official ☛ Top_10_Ansible_automation_guides_of_2022
                  |_Enable_Sysadmin⠀⇛


                       Boost your productivity by automating your most
                       frequent and monotonous tasks with Ansible.


                # ⚓ ifconfig_–_command_not_found_!_–_buildVirtual⠀⇛


                       If you’ve ever tried to use the ifconfig command on
                       a Linux or Unix-based system, you may have
                       encountered the error message “ifconfig: command
                       not found”. This error occurs when the ifconfig
                       command is not recognized by the system, and can be
                       frustrating if you’re not sure how to fix it.


                       In this blog post, we’ll take a look at why the
                       “ifconfig: command not found” error occurs and how
                       to troubleshoot and fix it.


                # ⚓ A_Terraform_Learning_Plan_–_buildVirtual⠀⇛


                       Terraform is a powerful tool for building,
                       changing, and managing infrastructure as code. It
                       allows you to define infrastructure in a high-level
                       configuration language, and then use those
                       configurations to create and manage resources
                       across a variety of cloud providers and on-premises
                       environments. This article aims to detail a
                       Terraform learning plan for those getting started
                       with this great tool.


                       Learning Terraform can be a valuable addition to
                       your skill set, as it can help you automate the
                       provisioning and management of infrastructure,
                       making it easier to deploy and maintain
                       applications and services. It is also a key tool in
                       the realm of infrastructure as code, which is
                       becoming increasingly important in modern cloud-
                       based environments.


                # ⚓ AddictiveTips ☛ How_to_use_the_Signal_chat_app_on_a
                  Chromebook⠀⇛


                       Singal is a privacy-centric chat application for
                       Linux, Mac OS, Windows, and mobile devices. With
                       it, users can expect encrypted chat messages and
                       many other privacy-respecting features. Here’s how
                       you can use the Signal chat app on your Chromebook.


                # ⚓ ID Root ☛ How_To_Install_VMware_Tools_on_Ubuntu_22.04_LTS_–
                  idroot⠀⇛


                       In this tutorial, we will show you how to install
                       VMware Tools on Ubuntu 22.04 LTS. For those of you
                       who didn’t know, VMware Tools is a suite of
                       utilities that enhances the performance of the
                       virtual machine’s guest operating system and
                       improves the management of the VM. It includes a
                       number of tools, such as a virtual network driver
                       to improve network performance, a time
                       synchronization utility to keep the guest operating
                       system’s clock synchronized with the host, and a
                       utility to improve the display resolution and
                       colors of the guest operating system.


                       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 VMware Tools 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.


                # ⚓ grep_cheat_sheet_–_buildVirtual⠀⇛


                       Grep is a command-line tool that allows you to
                       search for specific patterns or words in a file or
                       group of files. It is commonly used by programmers,
                       system administrators, and analysts to search for
                       specific patterns in logs, configuration files, and
                       other types of data.


                       To use grep, you specify the pattern you want to
                       search for and the file or files you want to search
                       in. Grep will then output all lines that contain
                       the pattern.


                # ⚓ LinuxConfig ☛ How_to_Install_etcd_on_Ubuntu⠀⇛


                       Etcd is a free and open-source distributed and
                       secure key-value store used to store the most
                       critical information of a given distributed system.
                       Etcd is written in Go making it extremely fast in
                       distributed systems without incurring a performance
                       overhead from clustered machines. In this guide,
                       you discover the basics of installing and setting
                       up an etcd cluster on Ubuntu systems.


                # ⚓ LinuxConfig ☛ How_to_retrieve_hardware_information_with
                  dmidecode_on_Linux⠀⇛


                       Dmidecode is a free and open source utility we can
                       use to retrieve hardware information on Linux. The
                       tool is available in the repositories of all the
                       major Linux distributions, and is able to inspect
                       and dump the content of the SMBIOS table.


                       In this tutorial we learn how to install dmidecode,
                       and how to use it to retrieve information about the
                       hardware configuration on Linux.


                # ⚓ How_to_Find_the_Most_Used_Commands_in_Your_Linux_System⠀⇛


                       As a Linux administrator or a normal user, you
                       often have to execute multiple commands in your
                       terminal emulator like Gnome Terminal or Konsole
                       for different purposes.


                       But have you ever wondered which command you are
                       executing repeatedly without being aware of it? So,
                       don’t worry if this thought did not come to your
                       mind before or until you found this article.


                       In this article, you will learn how to find and
                       list the most (including least) used commands in
                       your Linux system.


                # ⚓ How_to_Find_and_List_the_Largest_Files_in_Your_Linux
                  System⠀⇛


                       Hardly, 10 GB of disk space is used for the Linux
                       operating system, and the rest of the space is
                       occupied by your own files when you set up a new
                       Linux system.


                       Sadly, more disk space is consumed over time when
                       your system gets cluttered with a lot of
                       unnecessary files, mostly due to large log or
                       backup files.


                       However, you have the find and du commands that can
                       help you estimate the file size in your current
                       working directory or whole system, and by piping
                       another command, you can list them based on their
                       size.


                       In this tutorial, you will learn how to find and
                       list the largest files and directories in your
                       Linux system using the “find” and “du” commands.


                # ⚓ How_to_Grep_Files_Recursively_–_buildVirtual⠀⇛


                       Grep is a powerful command-line tool that allows
                       you to search for specific patterns within text
                       files. It’s a staple of many Linux and Unix-based
                       systems, and is widely used by system
                       administrators, developers, and others who need to
                       search through large volumes of text data. In this
                       article you will learn how to grep files
                       recursively.


                       One common use case for grep is the need to search
                       through multiple files, including files within sub-
                       directories. In this blog post, we’ll take a look
                       at how to grep files recursively, including how to
                       search through sub-directories, how to search for
                       an exact match, how to only search within certain
                       file extensions, and how to use the find command
                       instead of grep.


    * § Distributions and Operating Systems⠀➾


          o ⚓ The Register UK ☛ SystemRescue_9.06_is_here_with_the_shiny_new
            Xfce_4.18⠀⇛


                 SystemRescue 9.06 may only be a point release, but it has
                 some good stuff including the newly released Xfce,
                 MemTest86+ version 6, and a new USB-key-writing tool.


                 We took at look at SystemRescue 9 when it appeared,
                 nearly a year ago now. While version 9.06 isn’t a hugely
                 different version number, it actually has some
                 significant changes which merit a fresh look.


          o ⚓ DebugPoint ☛ EndeavourOS:_Your_Search_for_Perfect_Arch_Distro
            Ends_Here⠀⇛


                 A lot went into developing the distribution, which is
                 quite evident if you have ever tried it out. The motto of
                 this distro is to be a “general purpose” Arch Linux
                 distribution for the masses, discarding the Arch Linux
                 installation fear for new users and the superiority of
                 using Arch.


                 If you ever tried EndeavourOS, you must have “felt” how
                 “easy” things are to perform on a desktop for the end
                 user, being an Arch distro.


                 We review the recent release of EndeavourOS “Cassini” and
                 the distro overall.


          o § New Releases⠀➾


                # ⚓ It’s FOSS ☛ EndeavourOS_‘Cassini’_Releases_With_New
                  Features_and_Linux_Kernel_6.0⠀⇛


                       ndeavourOS is a popular Arch-based Linux
                       distribution that aims to make the Arch experience
                       easy.


                       Code-named ‘Cassini’, it signifies a new phase in
                       EndeavourOS’s development that aims to make the OS
                       better than its previous iterations.


                       Similar to a previous release, this release is also
                       named after one of NASA’s projects.


                       Let’s see what makes this release so unique.


                # ⚓ Neowin ☛ Arch-based_EndeavourOS_gets_22.12_‘Cassini’
                  release_bringing_official_Pinebook_Pro_support_–_Neowin⠀⇛


                       The second-most popular Linux distribution,
                       according to DistroWatch, has got a new update
                       today. EndeavourOS 22.12 ‘Cassini’ is here and
                       ready for installation, it includes updated
                       software such as Linux kernel 6.0.12 and brings
                       official support for the Pinebook Pro – a Linux-
                       first laptop from Pine64. For those unaware,
                       EndeavourOS is based on Arch Linux and uses a
                       rolling release model rather than point releases
                       that we get for Ubuntu and Linux Mint.


                       Development of EndeavourOS began in 2019 following
                       the discontinuation of Antergos – a distro aimed at
                       making Arch easy to install and use.


                # ⚓ DietPi_8.12_Released⠀⇛


                       The December 17th, 2022 release of DietPi v8.12
                       comes with a new image for the NanoPi R6S and the
                       Radxa ROCK 5B and a couple of improvements and bug
                       fixes.


          o § BSD⠀➾


                # ⚓ NetBSD ☛ NetBSD_10.0_BETA_available⠀⇛


                       After nearly 3 whole years of development (work
                       started on NetBSD 10 in late 2019), BETA snapshots
                       have finally been published for interested users to
                       test. More changes will be backported from the
                       development branch over the next few months before
                       we tag a final release, so the BETA images will
                       keep getting updated.


                       While NetBSD 10.0 is expected to be a major
                       milestone on performance, especially on multi-core
                       systems, currently the BETA builds have some extra
                       kernel diagnostics enabled that may reduce
                       performance somewhat.


          o § SUSE/OpenSUSE⠀➾


                # ⚓ SUSE’s Corporate Blog ☛ ALP_is_moving_to_its_next_peak:
                  Punta_Baretti_|_SUSE_Communities⠀⇛


                       ALP is the next generation of Linux, an
                       application-centric, secure and flexible platform
                       designed to focus on workloads while abstracting
                       from the hardware and the application runtime
                       layers.


                       Punta Baretti is one of the prototypes based on ALP
                       where we implemented features, approaches and
                       relevant changes. There will be also other
                       deliverables builds all based on ALP to come!


                       The products and solutions based on ALP use
                       containerized workloads to isolate different
                       processes at the application layer. These are
                       managed using K3s for Kubernetes-based workloads or
                       Podman for non-k8s workloads. This approach adds
                       extra flexibility while keeping the deployment and
                       management of workloads persistent, easy and
                       stable.
                       ALP’s ‘Zero-Touch’ approach makes systems
                       management, patching, and upgrading more stable,
                       reliable and secure.


          o § Fedora Family / IBM⠀➾


                # ⚓ Fedora Project ☛ Changes/Unified_Kernel_Support_Phase_1_–
                  Fedora_Project_Wiki [Ed: systemd creeping deeper into the
                  stack; see Phoronix ☛ comments_here]⠀⇛


                       The goal is to move away from initrd images being
                       generated on the installed machine. They are
                       generated while building the kernel package
                       instead, then shipped as part of a unified kernel
                       image.


                       A unified kernel image is an all-in-one efi binary
                       containing kernel, initrd, cmdline and signature.
                       The secure boot signature covers everything,
                       specifically the initrd is included which is not
                       the case when the initrd gets loaded as separate
                       file from /boot.


                       Main motivation for this move is to make the distro
                       more robust and more secure.


                       Switching the whole distro over to unified kernels
                       quickly is not realistic though. Too many features
                       are depending on the current workflow with a host-
                       specific initrd (and host-specific kernel command
                       line), which is fundamentally incompatible with
                       unified kernels where everybody will have the same
                       initrd and command line. Thats why there is ‘Phase
                       1′ in title, so we can have more Phases in future
                       releases


                # ⚓ Enterprisers Project ☛ IT_hiring_strategies_–_and_5
                  illuminating_interview_questions_to_ask_candidates_in_2023⠀⇛


                       Finding the right talent – and keeping it – is
                       critical to the health and success of IT
                       organizations today. With the new year comes an
                       opportunity to reflect on how your organization’s
                       hiring practices have served you to date: Is hiring
                       taking too long? Are you asking the right questions
                       during interviews? Can you promote from within
                       instead of opening a new role?


                # ⚓ Enterprisers Project ☛ Digital_transformation:_5_trends_to
                  watch_in_2023⠀⇛


                       The history of digital transformation is layered
                       and has determined business processes for years.
                       From automated technologies to AI-driven data
                       insights, business leaders must understand the
                       past, present, and future of digital
                       transformation.


          o § Debian Family⠀➾


                # ⚓ Linuxiac ☛ Tails_5.8_Comes_with_a_Wholly_Redesigned
                  Persistent_Storage⠀⇛


                       Tails 5.8 OS now ships with a complete redesign of
                       the Persistent Storage, Wayland by default, and a
                       better Unsafe Browser.


                       Tails (The Amnesic Incognito Live System) is a
                       Debian-based distro that differs from all other
                       Linux distributions in that it is a live system
                       solely focused on privacy. It is intended for
                       security paranoids looking for maximum personal
                       security and anonymity on the Internet. But, of
                       course, this has its drawbacks.


                       For example, because Tails is pre-configured to run
                       everything through the Tor network, the speed of
                       operations requiring a network connection is much
                       slower than on a regular Linux distro.


                       Today, the Tails Project has announced the general
                       availability of Tails 5.8 with yet another dose of
                       novelties. So, let’s have a look at them.


                # ⚓ Tails ☛ Tails_–_Tails_5.8_is_out⠀⇛


                       Tails 5.8 is the most important release of Tails in
                       years. It includes both major redesign of existing
                       features, important usability improvements, and
                       hardened security.


                       This work has been made possible by donations from
                       users like you. If you like these changes and want
                       more, donate now to fund our work in 2023.


                # ⚓ Neowin ☛ Tails_5.8_now_available_with_much_improved
                  Persistent_Storage_–_Neowin⠀⇛


                       The Tails Project has announced the availability of
                       Tails 5.8. The team has said that this release is
                       the most important one in years as it brings a
                       “major redesign of existing features, important
                       usability improvements, and hardened security.”
                       Perhaps the most notable change is the complete
                       redesign of Persistent Storage, which hasn’t
                       changed that much since 2012.


                       With the new Persistent Storage update, you no
                       longer have to restart after creating a Persistent
                       Storage space or when you activate a new feature.
                       You can change your Persistent Storage password
                       with the updated application, and you can choose to
                       create a Persistent Storage space from the Welcome
                       Screen if one isn’t yet set up.


                # ⚓ ID Root ☛ Debian_vs._Ubuntu_Comparison_–_idroot⠀⇛


                       In this tutorial, we will show you the differences
                       between Debian and Ubuntu. For those of you who
                       didn’t know, Debian and Ubuntu are two popular
                       open-source operating systems that are widely used
                       on servers and other computer systems. While both
                       distributions have many similarities, there are
                       also some key differences between them that may
                       make one a better choice for a particular use case.
                       Overall, Ubuntu and Debian are a popular choices
                       for users who value open-source software, community
                       support, and frequent updates. It is suitable for a
                       wide range of use cases, including desktop
                       computing, server administration, and embedded
                       systems development.


          o § Mint/Ubuntu Family⠀➾


                # ⚓ Beta News ☛ You_should_replace_Windows_11_with_Linux_Mint
                  21.1_on_grandma’s_PC_this_Christmas⠀⇛


                       Grandmothers can be great ladies, but let’s be
                       honest — they aren’t very good at using computers.
                       It’s not their fault though — they didn’t grow up
                       with them. That’s why every time you visit grandma
                       for Christmas, she asks you to fix her computer.


                       If you are sick of removing malware from grandma’s
                       PC, there is a simple solution — install Linux!
                       Yes, by formatting grandma’s hard drive and
                       replacing Windows with Linux, she will have the
                       best Christmas ever.


                       But what Linux distribution should you install on
                       grandma’s computer? Well, Linux Mint 21.1 was
                       officially released earlier today and it is a great
                       option for beginners. The latest version of the
                       operating system, code-named “Vera,” is based on
                       Ubuntu 22.04 and uses Linux kernel 5.15. Best of
                       all, Linux Mint 21.1 will be supported until 2027.


                # ⚓ Make Use Of ☛ Linux_Mint_21.1_Released_With_Decluttered
                  Desktop,_Other_Improvements⠀⇛


                       The Linux Mint development team has announced the
                       release of Linux Mint 21.1, codenamed “Vera.” The
                       release will likely be a welcome holiday gift for
                       its users.


                # ⚓ Neowin ☛ Linux_Mint_21.1_out_now_with_a_theme_overhaul_and
                  more_–_Neowin⠀⇛


                       At the start of the month, Neowin wrote that Linux
                       Mint 21.1 Beta was available with a new theme and
                       that the final release would come out around
                       Christmas. Living up to that promise, the Mint team
                       has now released the final stable version of Linux
                       Mint 21.1 ‘Vera’ in Cinnamon, MATE, and Xfce
                       editions. Those running the Beta can just apply
                       updates to get to the final version while those on
                       Linux Mint 21 will be able to upgrade soon.


                       If you want to see the new theme and mouse cursor,
                       check out the coverage from the Beta release. Those
                       are not the only new features in this update,
                       however. With this update, the Driver Manager has
                       been made more friendly. You no longer need to type
                       your password to launch it and it will display
                       dedicated screens if you’re in offline mode or if
                       it detects installation media. The Driver Manager
                       now also lists dummy packages with “exotic
                       dependencies” and test mode to help developers
                       troubleshoot issues.


                # ⚓ DebugPoint ☛ Linux_Mint_21.1_“Vera”_is_Officially_Released.
                  This_is_What’s_New⠀⇛


                       Linux Mint 21.1 “Vera” is officially out and it is
                       available to download and upgrade.


                       Following a successful BETA release, the Linux Mint
                       team officially released the first point release of
                       Linux Mint 21 series. Being a first point release,
                       it brings all the initial bug fixes since the major
                       release earlier this year and some interesting
                       customizations.


                       Let’s brief the release highlights.


                # ⚓ Linuxiac ☛ Linux_Mint_21.1_Vera:_The_Best_Mint_Release
                  Yet⠀⇛


                       Linux Mint 21.1 “Vera” has just been released,
                       boasting numerous new features and a polished
                       design. It’s the best Mint release yet – see why.


                       Linux Mint is a free and open-source Ubuntu-based
                       distro designed to be easy to use and provide a
                       comfortable, modern computing experience. Mint is a
                       popular choice for beginners and experienced users
                       because of its simplicity, stability, and user-
                       friendly interface.


                       Each new release strengthens Linux Mint’s
                       reputation as the best desktop-oriented Linux
                       distribution. However, its latest release, Linux
                       Mint 21.1, has exceeded all users’ expectations.
                       Here’s why.


                # ⚓ Linux Mint ☛ Linux_Mint_21.1_‘Vera’_Xfce_released!_–_The
                  Linux_Mint_Blog⠀⇛


                       Linux Mint 21.1 is a long term support release
                       which will be supported until 2027. It comes with
                       updated software and brings refinements and many
                       new features to make your desktop even more
                       comfortable to use.


                # ⚓ Linux Mint ☛ Linux_Mint_21.1_‘Vera’_MATE_released!_–_The
                  Linux_Mint_Blog⠀⇛


                       Linux Mint 21.1 is a long term support release
                       which will be supported until 2027. It comes with
                       updated software and brings refinements and many
                       new features to make your desktop even more
                       comfortable to use.


                # ⚓ Linux Mint ☛ Linux_Mint_21.1_‘Vera’_Cinnamon_released!_–
                  The_Linux_Mint_Blog⠀⇛


                       Linux Mint 21.1 is a long term support release
                       which will be supported until 2027. It comes with
                       updated software and brings refinements and many
                       new features to make your desktop even more
                       comfortable to use.


                # ⚓ It’s FOSS ☛ Linux_Mint_21.1_Arrives_with_a_Ton_of_Visual
                  Changes_and_Improvements⠀⇛


                       This release is similar to the usual point
                       releases. However, it includes various changes to
                       the look, feel, and features that could look subtle
                       but will affect the user experience.


                       Let’s take a look at the major highlights. We focus
                       on Linux Mint’s Cinnamon edition.


                # ⚓ LWN ☛ Linux_Mint_21.1_(“Vera”)_released_[LWN.net]⠀⇛


                       Linux Mint has announced the release of version
                       21.1 of the distribution in three editions:
                       Cinnamon (what’s new), MATE (what’s new), and Xfce
                       (what’s new). Mint 21.1 is based on Ubuntu 22.04
                       and uses kernel version 5.15.


                # ⚓ Ghacks ☛ Linux_Mint_21.1_Long_Term_Support_Release_is_out⠀⇛


                       The releases share some of the improvements while
                       others are environment-specific. Generally
                       speaking, users of the Linux distribution may
                       notice “cleaner and more modern looks”. The team
                       highlights more vibrant accent colors and that it
                       cleaned up the desktop to only show essential
                       icons. The computer, trash and network icons were
                       removed, but remain accessible via the File
                       Manager. The home folder has been removed from the
                       desktop as well. It can be accessed via the main
                       menu or by using the keyboard shortcut Super-E.


                       As far as colors are concerned, use of accent
                       colors on the panel was removed and the team
                       decided to switch to yellow folders instead of the
                       classic green color used in previous versions of
                       the Linux distribution. Linux Mint users may pick
                       their favorite desktop color to customize the look.


                       Linux Mint users who prefer the classic look may
                       enable the Mint-Y-Legacy theme in the theme options
                       to restore it. This restores the Linux Mint 20.2
                       look and feel.


                       Another change that users may notice is that there
                       is a new default mouse pointer theme. It is called
                       Bibata, and designed to “give a fresh new look to
                       the operating system”. Traditional DMZ-White and
                       DMZ-Black mouse pointer themes are available next
                       to a alternative pointer themes such as GoogleDot-
                       Black, GoogleDot-White, or XCursor Pro. Speaking of
                       icons, Linux Mint 21.1 includes alternative icon
                       themes. Next to Mint-X, Mint-Y and Ming Legacy
                       themes, users may choose one of four installed
                       alternative icon themes: Breeze, Papirus, Numix and
                       Yaru.


                # ⚓ Ubuntu ☛ Manage_Debian,_Ubuntu,_and_derivative_Linux
                  distributions_with_Landscape_Scripts_|_Ubuntu⠀⇛


                       What are you tinkering with over your vacation?
                       Perhaps you have ambitions to have a beautiful
                       homelab, launch pet projects on a public cloud, or
                       build do it yourself home automation. Ubuntu has
                       broad community and commercial support, making it
                       the logical choice when you need to provision
                       machines and containers with a mix of proprietary
                       and open source software. Once your homelab, home
                       automation, or public cloud projects are running,
                       you can deploy Landscape beta. Landscape beta is a
                       Linux dashboard which can be deployed on Oracle
                       Cloud Infrastructure’s Always Free tier in 5
                       minutes, and manage machines anywhere. This self-
                       hosted Linux systems management software can
                       administer a variety of Linux distributions.
                       Canonical maintains a Landscape Scripts Github
                       repository where we aggregate community scripts for
                       common tasks in any language. If you write shell
                       scripts that make managing your Raspberry Pis or
                       virtual machines easier, consider forking the
                       Landscape Scripts repository and contributing to
                       open-source software by submitting a Pull Request
                       with your own scripts or script ideas.


                # ⚓ Ubuntu ☛ See_for_yourself:_the_benefits_of_chiselled_Ubuntu
                  images_in_action_with_an_ASP.NET_shop_demo [Ed: Now it truly
                  looks as though Microsoft bought Canonical, based on how
                  Canonical_is_behaving]⠀⇛


          o § Devices/Embedded⠀➾


                # ⚓ Linux_and_software_containers_in_the_vehicle_…⠀⇛


                       Why automakers are borrowing software technology
                       from commercial IT


          o § Open Hardware/Modding⠀➾


                # ⚓ CNX Software ☛ T-Camera_S3_–_An_ESP32-S3_board_with_camera,
                  display,_PIR_motion_sensor,_and_microphone_–_CNX_Software⠀⇛


                       LilyGO has launched a new ESP32-S3 WiFi & BLE
                       camera board with the T-Camera S3 also featuring a
                       small display, a PIR motion sensor, and a
                       microphone, as well as an optional plastic shell.


                # ⚓ Arduino ☛ The_Infineon_team’s_XXL_Chatbot_offers_you
                  yuletide_greetings_|_Arduino_Blog⠀⇛


                       Infineon is one of the world’s largest
                       semiconductor manufacturers, but the company is
                       made up of regular people like any other. Many of
                       those people just happen to be engineers and they
                       like to build gadgets and gizmos like the rest of
                       us. Following a water cooler discussion about who
                       had the biggest 3D printer, the Infineon team
                       decided to build this delightful XXL Chatbot to
                       offer yuletide greetings.


                       The adorable robot was designed after the Infineon
                       Chatbot avatar that offers virtual assistance on
                       the Infineon website. While that internet Chatbot
                       can respond to natural language questions, this XXL
                       Chatbot can only emote through its animated eyes
                       and chest-mounted RGB LED matrix. The team 3D-
                       printed the robot’s body in several sections on a
                       Creality Ender-5 Plus and the assembled figure is
                       quite large, hence the “XXL” designation.


          o § Mobile Systems/Mobile Applications⠀➾


                # ⚓ Sportskeeda ☛ 5_best_Android_games_like_Minecraft⠀⇛


                # ⚓ And_The_Top_Android_Phone_of_2022_is…⠀⇛


                # ⚓ Future Publishing Limited ☛ OnePlus_11_benchmarks_just
                  leaked_–_could_this_be_the_best_Android_phone_yet?_|_T3⠀⇛


                # ⚓ Hacker News ☛ Beware:_Cybercriminals_Launch_New_BrasDex
                  Android_Trojan_Targeting_Brazilian_Banking_Users⠀⇛


                # ⚓ Express ☛ New_Samsung_Galaxy_S23_faces_stiff_competition
                  from_one_Android_rival_|_Express.co.uk⠀⇛


                # ⚓ SamMobile ☛ Google_and_Samsung’s_Health_Connect_could_be
                  integrated_into_Android_14_–_SamMobile⠀⇛


                # ⚓ Notebook Check ☛ RedMagic_8_Pro_teased_as_a_premium_Android
                  device_with_a_radical_design_overhaul_on_launch_date
                  announcement_–_NotebookCheck.net_News⠀⇛


                # ⚓ SlashGear ☛ Why_Your_Android_Phone_Is_Freezing_And_How_To
                  Fix_It⠀⇛


                # ⚓ Express ☛ New_Samsung_Galaxy_S23_faces_stiff_competition
                  from_one_Android_rival_|_Express.co.uk⠀⇛


                # ⚓ Tech Advisor ☛ Android_14:_Everything_You_Need_To_Know_–
                  Tech_Advisor⠀⇛


                # ⚓ SamMobile ☛ Samsung_Galaxy_S10_Lite_gets_new_update_in_the
                  US,_and_it’s_not_Android_13_–_SamMobile⠀⇛


                # ⚓ Android Police ☛ Nothing_Phone_1_Android_13_beta_hands-on:
                  Less_buggy_than_Android_12_already⠀⇛


                # ⚓ The Sun ☛ People_are_just_noticing_simple_Android_hack_that
                  instantly_boosts_battery_life_|_The_Sun⠀⇛


                # ⚓ Android Authority ☛ The_best_custom_Android_home_screens_of
                  2022⠀⇛


                # ⚓ EIN Presswire ☛ Radix_to_launch_a_new_version_of_its
                  Android_TV_Manager_at_CES_2023_–_EIN_Presswire⠀⇛


                # ⚓ 9to5Google ☛ YouTube_on_Android_testing_video_progress_bar
                  that_isn’t_always_red⠀⇛


                # ⚓ CNET ☛ What_Android_Needs_in_2023_to_Overcome_iPhone’s
                  Dominance_–_CNET⠀⇛


                # ⚓ Ghacks ☛ Some_Android_app_APIs_have_been_putting_users_at
                  risk⠀⇛


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


          o ⚓ Libre Arts ☛ Libre_Arts_–_Hugin_2022⠀⇛


                 New annual release of Hugin, free/libre panorama maker,
                 has arrived with UX improvements.


                 It’s been a long time since Hugin has seen active
                 development. However, the few people still working on
                 this project do make regular releases with useful
                 changes. This release (see the official notes here)
                 mostly got contributions from Thomas Modes, JohnsWork,
                 and Bruno Postle.


                 The most user-visible changes in this release are split
                 buttons in the Assistant mode. They provides a kind of
                 presets to simplify accomplishing particular tasks.


          o § Web Browsers/Web Servers⠀➾


                # § Mozilla⠀➾


                      # ⚓ Mozilla ☛ Mozilla_to_Explore_Healthy_Social_Media
                        Alternative⠀⇛


                             In early 2023, Mozilla will stand up and test
                             a publicly accessible instance in the
                             Fediverse at Mozilla.Social. We’re eager to
                             join the community in growing, experimenting,
                             and learning how we can together solve the
                             technical, experience, and trustworthiness
                             challenges inherent in hyper-scale social
                             systems. Our intention is to contribute to
                             the healthy and sustainable growth of a
                             federated social space that doesn’t just
                             operate but thrives on its own terms,
                             independent of profit- and control-motivated
                             tech firms. An open, decentralized, and
                             global social service that puts the needs of
                             people first is not only possible, but it’s
                             absolutely necessary.


                             Our Pledge for a Healthy Internet describes
                             our hopes for the Internet, and what it can
                             become: a powerful tool for promoting civil
                             discourse and human dignity. One that
                             elevates critical thinking and reasoned
                             argument, that honors shared experience and
                             individual expression and brings together
                             diverse and global communities to work
                             together for the common good. Today we see
                             the rising tide of the Fediverse, through
                             Mastodon, Matrix, Pixelfed, and many others
                             as a promising next step in that direction.
                             Together we have an opportunity to apply the
                             lessons of the past to build a social
                             experience for humanity that is healthy,
                             sustainable, and sheltered from the
                             centralized control of any one entity.


          o § SaaS/Back End/Databases⠀➾


                # ⚓ PostgreSQL ☛ PostgreSQL:_pgAdmin_4_v6.18_Released⠀⇛


                       The pgAdmin Development Team is pleased to announce
                       pgAdmin 4 version 6.18. This release of pgAdmin 4
                       includes 13 bug fixes and new features. For more
                       details please see the release notes.


                       pgAdmin is the leading Open Source graphical
                       management tool for PostgreSQL. For more
                       information, please see the website. Notable
                       changes in this release include:


                # ⚓ PostgreSQL ☛ PostgreSQL:_pg_ivm_1.4_released⠀⇛


                       IVM Development Group is pleased to announce the
                       release of pg_ivm 1.4.


                # ⚓ Will_Kahn-Greene:_NormConf_2022_thoughts⠀⇛


                       I went to NormConf 2022, but didn’t attend the
                       whole thing. It was entirely online as a YouTube
                       livestream for something like 14 hours split into
                       three sessions. It had a very active Slack
                       instance.


                       I like doing post-conference write-ups because then
                       I have some record of what I was thinking at the
                       time. Sometimes that’s useful for other people.
                       Often it’s helpful for me.


                # ⚓ Data_Scientist_×_Data_Analyst_–_Avi_Alkalay⠀⇛


                       Analysts inform, explain and visualize DATA THAT
                       EXISTS in order to help business executives make
                       strategic decisions. Thus, data analysts live in
                       business meetings, talk to a lot of people and
                       create data visualizations to help others
                       understand what is going on. Tools: SQL, BI,
                       spreadsheets, PowerPoint.


                       Scientists infer and calculate INFORMATION THAT
                       STILL DOESN’T EXIST, such as the future, usually in
                       order to optimize each and every business
                       transaction. Example: if you like this one product,
                       you might also like that other product. Example:
                       according to data from surroundings, this house
                       price should be around $X. Example: I learned how
                       cars look like, so there is 98% chance there is a
                       car in this photo. Thus, they create or improve
                       digital products using machine learning and applied
                       statistics. To create such improved user
                       experiences, first data scientists use advanced
                       exploratory data analysis techniques, create data
                       visualization only for themselves, only for their
                       better comprehension of what is going on. Tools:
                       SQL, Pandas, math and statistics, git, programing,
                       containers, Linux.


          o § FSF⠀➾


                # ⚓ FSF ☛ FSF_job_opportunity:_Deputy_director⠀⇛


                       The Free Software Foundation (FSF), a Massachusetts
                       501(c)(3) charity with a worldwide mission to
                       protect computer user freedom, seeks a motivated
                       and talented Boston-based individual to be our
                       full-time deputy director.


                       Reporting to the executive director, the deputy
                       director plays a critical role in ensuring the
                       value-added execution of key operational and
                       business functions. This position assists with
                       leading the organization in close partnership with
                       the executive director. The ideal candidate is calm
                       under pressure with proven ability to manage
                       multiple moving priorities and stakeholders, all
                       with attention to detail and rigor.


          o § GNU Projects⠀➾


                # ⚓ GNU ☛ GNU_Common_Lisp_–_News:_GCL_2.6.13_is_released_
                  [Savannah]⠀⇛


                       Greetings! The GCL team is happy to announce the
                       release of version 2.6.13, the latest achievement
                       in the ‘stable’ (as opposed to ‘development’)
                       series. Please see http://www.gnu.org/software/gcl
                       for downloading information.


                       This release consolidates several years of work on
                       GCL internals, performance and ansi compliance.


                       Garbage collection has been overhauled and
                       significantly accelerated. Contiguous block
                       handling is now as fast as or perhaps faster than
                       relblock handling, leading to the now implemented
                       promotion of relblock data to contiguous after a
                       surviving a number of gc calls. Relblock is only
                       written once during gc. Heap allocation is fully
                       dynamic at runtime and controllable with
                       environment variables without recompilation. While
                       SGC is supported, it is found in practice to be
                       less useful with modern large memory cores and is
                       off by default.


                       GCC on several platforms defaults to code which
                       must lie within a common 2Gb space, now an issue
                       with heaps routinely larger than this. Error
                       protection for code address overflow is in place on
                       most machines. The variable si::*code-block-
                       reserve* can be set to a static array of element
                       type ‘character to preallocate a code block early
                       within an acceptable range. On amd64, compile-file
                       takes a :large-memory-model-p keyword (with
                       compiler::*default-large-memory-model-p*) to
                       compile somewhat slower code which can be loaded at
                       an arbitrary address.


                       The COMMON-LISP package is fixed to the ansi
                       standard. A CLTL1-COMPAT package is defined to
                       support earlier applications, and is used in non-
                       ansi builds.


                # ⚓ GNU ☛ GNU_Parallel_–_News:_GNU_Parallel_20221222_(-
                  #039;ChatGPT')_released_[Savannah]⠀⇛


                       GNU Parallel 20221222 (‘ChatGPT’) has been
                       released. It is available for download at: lbry://
                       @GnuParallel:4


                       Quote of the month:


                       GNU Parallel absolutely rocks.
                       — Austin Mordahl@Stackoverflow


                       - New in this release:


                       - –results works on more file systems (e.g. fat)
                       Joblog gives the same exit code as bash.


                       News about GNU Parallel:


                       - Programação Shell Linux: Paralelismo de processos
                       com GNU parallel https://www.youtube.com/
                       watch?v=duheTWLIrp8


                       - Talk Python: Data Science from the Command Line
                       https://talkpython.fm/episodes/show/392/data-
                       science-from-the-command-line


                       GNU Parallel – For people who live life in the
                       parallel lane.


                       If you like GNU Parallel record a video
                       testimonial: Say who you are, what you use GNU
                       Parallel for, how it helps you, and what you like
                       most about it. Include a command that uses GNU
                       Parallel if you feel like it.


          o § Programming/Development⠀➾


                # ⚓ Barry Kauler ☛ Meta-quirky_Kirkstone_git_repository_created
                  [Ed: Outsourcing to Microsoft proprietary prison some more]⠀⇛


                       This is based on the Kirkstone 4.0 release of
                       OpenEmbedded/Yocto, iteration 4.0.5.


                       As reported, it took four 24-hour days and three
                       hours, a long time, but more experimenting is
                       planned to reduce that.


                       Anyway, won’t have to do a complete recompile for
                       awhile. If any individual package needs to be
                       recompiled, or a new package added, it can be done
                       without a complete recompile.


                # ⚓ Git_Commands_Cheatsheet_–_buildVirtual⠀⇛


                       Welcome to my Git Commands Cheatsheet!


                # ⚓ SpiderMonkey_Newsletter_(Firefox_108-109)_|_SpiderMonkey
                  JavaScript/WebAssembly_Engine⠀⇛


                       SpiderMonkey is the JavaScript engine used in
                       Mozilla Firefox. This newsletter gives an overview
                       of the JavaScript and WebAssembly work we’ve done
                       as part of the Firefox 108 and 109 Nightly release
                       cycles.


                # ⚓ OpenSUSE ☛ Good_Commit_Messages_Give_Devs_Meaning,_Purpose
                  –_openSUSE_News⠀⇛


                       Adding clarity to commit messages significantly
                       helps fellow developers, and this short blog will
                       share some best practices for writing quality
                       commit messages for openSUSE and open-source
                       contributions.


                       Commit messages communicate vital information
                       between team members, and since open-source
                       software is one big team focusing on open
                       collaboration, it’s imperative to communicate
                       context in these messages.


                       Why?


                       The “Why?” may be obvious to you now, but it might
                       not be to others; especially those who might not
                       even be involved yet with your code. Well-crafted
                       commit messages help developers remember aspects of
                       a previous commit and help future developers
                       understand what changed and the purpose for the
                       change.


                # ⚓ Godot Engine ☛ Godot_Engine_–_Status_of_the_OpenGL_3
                  renderer⠀⇛


                       Last year we announced that we were planning on
                       creating an OpenGL-based renderer to complement the
                       current Vulkan-based renderers. At that time, we
                       thought that we wouldn’t have it ready until 4.1.
                       However, we are now confident that we will be
                       shipping 4.0 with an OpenGL-based renderer; it just
                       won’t be feature complete. As a reminder, an
                       OpenGL-based renderer is still crucial so we can
                       support older platforms, and Web export. There is a
                       Vulkan-like web API called WebGPU in development,
                       but it currently isn’t widely supported yet, so
                       WebGL remains the best option for targetting web
                       games.


                       At the time of writing this article, all planned 2D
                       features and most basic 3D functionalities are now
                       supported by the OpenGL 3 renderer. As it is much
                       newer, the OpenGL 3 renderer hasn’t been tested as
                       widely as the Vulkan-based renderer. We expect it
                       will have more bugs for the time being.


                       Our goal is for the OpenGL 3 renderer to have broad
                       compatibility and good performance on a wide range
                       of hardware. Accordingly, it won’t receive all the
                       fancy new features that the Vulkan-based renderers
                       bring.


                # ⚓ TecAdmin ☛ How_to_Set_Session_Timeout_in_PHP:_A_Guide_for
                  Newbies_–_TecAdmin⠀⇛


                       As a web developer, you might need to create
                       websites with user logins, comment sections, and
                       other features that require users to keep their
                       accounts active. As such, it’s important to
                       implement a way of limiting the time that users can
                       spend on your website. This is called setting
                       session timeout in PHP. Without this restriction,
                       users can stay logged in on your website
                       indefinitely.


                       This blog post will explain what session timeout in
                       PHP is and why you would need it. Then we’ll
                       provide step-by-step instructions for implementing
                       session timeout in your own website projects. So
                       keep reading to learn more!


                # ⚓ More_Flexibility_for_Workflows_in_the_OBS_and_SCM
                  Integration_–_Open_Build_Service⠀⇛


                       Right in time for the holiday season, we have
                       prepared you a gift for the continuous integration
                       between OBS and SCMs. We are introducing
                       placeholder variables and for your workflows
                       configuration files, a customizable location. Let’s
                       see how this new flexibility helps you in your
                       work.


                       [...]


                       Whenever a webhook event comes in, OBS downloads
                       the workflows configuration file and parses it.
                       This was previously static, but you can now use
                       placeholder variables to tell OBS to replace them
                       with data from the webhook event payload.


                # ⚓ Dirk Eddelbuettel ☛ Dirk_Eddelbuettel:_RcppDE_0.1.7_on
                  CRAN:_Several_Updates⠀⇛


                       RcppDE is a “port” of DEoptim, a popular package
                       for derivative-free optimisation using differential
                       evolution optimization, from plain C to C++. By
                       using RcppArmadillo the code becomes a lot shorter
                       and more legible. Our other main contribution is to
                       leverage some of the excellence we get for free
                       from using Rcpp, in particular the ability to
                       optimise user-supplied compiled objective functions
                       which can make things a lot faster than repeatedly
                       evaluating interpreted objective functions as
                       DEoptim does (and which, in fairness, most other
                       optimisers do too). The gains can be quite
                       substantial.


                # § Perl / Raku⠀➾


                      # ⚓ Rakulang ☛ Day_21:_Raku_and_I:_Journey_begin_…_–_Raku
                        Advent_Calendar⠀⇛


                             It has been ages since I last blogged about
                             Raku. The only time, I have blogged about
                             when I took part in The Weekly Challenge .
                             But then this also changed recently as I
                             finally found time to contribute to the
                             weekly fun challenges but no blogging still.


                             I would say it is all about my mental state,
                             since I have so much to talk about. Recently
                             I was approached by a very dear friend and
                             senior member of Raku Community if I am
                             interested in contributing to the Raku Advent
                             Calendar 2022 . So as you guessed it rightly
                             so, I have a compelling reason to get back to
                             blogging.


                # § Python⠀➾


                      # ⚓ Video ☛ This_Python_Code_Should_Be_Illegal,_Do_This
                        Instead_–_Invidious⠀⇛


                             Writing Python code like this is bad
                             practice, use list comprehensions instead


                      # ⚓ TecAdmin ☛ Python_–_How_to_find_local_IP_address_–
                        TecAdmin⠀⇛


                             An IP address is a unique identifier that
                             computers use to communicate with each other
                             on a network. It stands for Internet
                             Protocol, and it’s a set of numbers that
                             identify each device connected to a network.
                             Without an IP address, your computer wouldn’t
                             be able to access the internet. It’s
                             essential for communication between computers
                             and networks, as it helps to direct data to
                             the right place. An IP address is like a
                             street address for your computer — it’s how
                             computers can find each other. Every computer
                             on the internet has a unique IP address,


    * § Leftovers⠀➾


          o ⚓ Please_help_me_share_my_NEXT_million_words_in_2023_|_Stop_at
            Zona-M⠀⇛


                 As of today, this blog contains almost one million, two
                 hundred twenty thousand words, in about 2200 posts all
                 100% free of charge, advertising or tracking.


          o ⚓ Dedoimedo ☛ Dedoimedo_–_A_Place_to_Learn_a_Lot_About_a_Lot⠀⇛


                 After fourteen years, I have moved dedoimedo.com to a new
                 hosting provider. Why, you ask? Well, it’s a long story.
                 In the past year, I noticed a whole bunch of problems
                 with my previous hosting provider. Namely, there were SSL
                 termination issues, about which I already wrote. Then,
                 the provider deprecated their ticketing system in favor
                 of a “live” chat thing. Except, you end up sitting there
                 like a monkey, waiting for hours for someone to respond.
                 The site performance dropped after a migration to a “new”
                 infrastucture. Weird redirections pointing to a problem
                 with the loadbalancers or such. And worst of all, half of
                 my pages suddenly had become de-indexed on search
                 engines, as the the provider seems to be blocking Google
                 crawler and alike. Enough.


          o § Proprietary⠀➾


                # ⚓ Climate_Contradiction:_Microsoft_Invests_$1_Billion_In
                  Climate_Innovation,_$2_Billion_In_Oil,_Coal-Fired_Utilities
                  [Ed: And yet, TFIR keeps shilling Microsoft and keeps
                  perpetuating climate lies for Microsoft, as Spamnil did no
                  more than a year ago]⠀⇛


                       Microsoft shareholders voted on an As You Sow
                       resolution asking the company to disclose how the
                       company’s 401(k) retirement funds manage the
                       growing systemic risk created by investing in
                       companies contributing significantly to climate
                       change. The proposal earned an 11.2% vote last week
                       at Microsoft’s annual general meeting, achieving
                       the threshold needed to continue dialog with the
                       company and resubmit the resolution next year, if
                       necessary.


                       [...]


                       Rather than addressing growing employee concern
                       about climate change across its full range of
                       investment options, the company offers a difficult-
                       to-use alternative of a self-directed option, which
                       charges additional fees, and outsources investment
                       risk to employees.


          o § Linux Foundation⠀➾


                # ⚓ BGR ☛ Google_Maps_just_got_a_new_competitor_from_Linux,
                  Amazon,_Meta,_Microsoft,_and_TomTom [Ed: They_keep_conflating
                  Linux_with_‘Linux’_Foundation, which in many ways even harms
                  Linux adoption and misrepresents GNU/Linux users]⠀⇛


                       There’s no question that Google Maps is the most
                       popular navigation app on mobile devices. Google
                       Maps has two big rivals: Waze, which Google owns,
                       and Apple Maps, available only on iPhone. But if
                       some of Google’s biggest competitors have their
                       way, Google Maps might soon get a decent
                       alternative that could make the entire geo-location
                       industry more interesting.


                       The Linux Foundation unveiled the Overture Maps
                       Foundation a few days ago. The project aims to
                       develop an open-source mapping system that could
                       become the backbone of other mapping services that
                       compete against Google Maps.


                #      The Linux Foundation has formed the Overture Maps
                       Foundation, “a collaborative effort to develop
                       interoperable open map data as a shared asset.”


                       Overture Maps aims to create an “easy-to-use
                       ecosystem of map data,” according to the website.
                       And, through development of a Global Entity
                       Reference System, Overture will work to “simplify
                       interoperability” and “combine resources to build
                       map data that is complete, accurate, and refreshed
                       as the physical world changes,” the announcement
                       says.


                # ⚓ PR Newswire ☛ The_Linux_Foundation’s_AgStack_Project_to
                  Build_World’s_First_Global_Dataset_of_Agricultural_Field
                  Boundaries [Ed: 'Linux' Foundation as front group for IBM et
                  al, misusing the name of a kernel]⠀⇛


                       The Linux Foundation, a global nonprofit
                       organization enabling innovation through open
                       source, today announced that its AgStack project
                       will host a new open source code base, alongside a
                       fully automated, continuous computation engine, to
                       create, maintain and host a global dataset of
                       boundaries’ “registry” for agricultural fields to
                       aid in such things as food traceability, carbon
                       tracking, crop production, and other field-level
                       analytics.


                # ⚓ PR Newswire ☛ Automotive_Grade_Linux_Showcases_Open_Source
                  Technology_and_Software_Defined_Vehicle_at_CES_2023⠀⇛


                       Automotive Grade Linux (AGL), a cross-industry
                       effort developing an open source platform for all
                       connected car technologies, will be at CES 2023 in
                       the Las Vegas Convention Center, West Hall Booth
                       #4141 from January 5-8, 2023.


          o § Security⠀➾


                # ⚓ PIA ☛ Do_You_Still_Need_an_Antivirus?_–_PIA_VPN_Blog [Ed:
                  Poorly composed.]⠀⇛


                       Last, but certainly not least is Linux, an open-
                       source operating system that renders it
                       intrinsically safe and transparent. Malware which
                       targets Linux systems is exceedingly rare, so if
                       you’re considering a safer OS for your next
                       machine, you might want to check it out.


                       Linux, by design, uses the principle of least
                       privilege, wherein every user can only enter
                       specific areas of the system. This limits
                       catastrophic disruption in the event of a malware
                       attack since the malicious code will be barred
                       entry in sensitive system areas.


                       Even if Linux malware infects the system, it
                       shouldn’t be able to affect the OS core, not
                       without help. Linux is the least common OS among
                       everyday users, compared to Windows and macOS,
                       making it less attractive as a target for attacks.


                       That said, Linux is still the de-facto OS used in
                       enterprise and mission-critical environments.
                       Servers running Linux distros are constantly hit by
                       DDoS (Distributed Denial of Service) attacks,
                       viruses, spyware, ransomware, and worms. Zero-day
                       attacks are also recorded.


                # ⚓ Bruce Schneier ☛ Trojaned_Windows_Installer_Targets_Ukraine
                  –_Schneier_on_Security [Ed: Every country, including Ukraine,
                  should not be using Windows at all]⠀⇛


                       Mandiant is reporting on a trojaned Windows
                       installer that targets Ukrainian users. The
                       installer was left on various torrent sites,
                       presumably ensnaring people downloading pirated
                       copies of the operating system…


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


                       Security updates have been issued by Fedora (mujs)
                       and SUSE (kernel and thunderbird).


                # ⚓ CISA ☛ CISA_Releases_Six_Industrial_Control_Systems
                  Advisories_|_CISA⠀⇛


                       CISA released six Industrial Control Systems (ICS)
                       advisories on December 20, 2022. These advisories
                       provide timely information about current security
                       issues, vulnerabilities, and exploits surrounding
                       ICS.


                # § Privacy/Surveillance⠀➾


                      # ⚓ Make Tech Easier ☛ Epic_Games_to_Pay_Record_FTC_Fine
                        for_Children’s_Privacy_Violations_–_Make_Tech_Easier⠀⇛


                             Epic Games will have to start changing its
                             tune. After making Apple the bully in its
                             fight against the App Store ecosystem, the
                             FTC has fined Epic Games $275 million for
                             violating the children’s privacy law with
                             Fortnite and will have to refund $245 million
                             for practices that tricked users into paying
                             unwanted charges.


                             [...]


                             The Depart of Justice on behalf of the FTC
                             filed two separate settlements and is forcing
                             Epic Games to create strong privacy settings
                             for minors. Along with accusing the FTC of
                             tricking minors into unwanted charges and
                             retaining children’s information without
                             parental consent, it also left voice and text
                             chat open on the Fortnite game by default.


          o § AstroTurf/Lobbying/Politics⠀➾


                # § Misinformation/Disinformation/Propaganda⠀➾


                      # ⚓ Public Knowledge ☛ Election_Disinformation_2022:_The
                        Battlefield_Shifts_Again_–_Public_Knowledge⠀⇛


                             After the presidential election in 2020,
                             Public Knowledge reported on how effectively
                             digital platforms had countered the “election
                             misinformation war,” meaning the torrent of
                             election misinformation flowing across their
                             platforms. We concluded, as we did during the
                             COVID-19 pandemic, that “in a high-stakes and
                             high-visibility situation, platforms will
                             develop new standards and solutions to
                             problems they previously claimed were
                             impossible to solve.” Days after that
                             election, we theorized that the dominant
                             platforms had taken sufficient accountability
                             for the content on their platforms that
                             Americans could safely get to the polls and
                             vote. But we warned of a new risk: that an
                             extended vote-counting period – due in part
                             to COVID-19 precautions that encouraged early
                             and mail-in voting – would allow
                             misinformation to erode trust in the results
                             after the election.


                             We published that blog post two months before
                             the insurrection at the U.S. Capitol on
                             January 6. On that day and in the weeks
                             since, we have learned a great deal about the
                             potential for violence stemming directly from
                             election-related networked disinformation.
                             (Misinformation – that is, false information
                             that isn’t deliberately misleading – holds
                             the potential for harm. However, because of
                             its role in elections, in particular, we will
                             focus here on networked disinformation:
                             deliberately false information seeded and
                             spread in the interest of power or profit, in
                             this case to influence elections.) We have
                             seen how election-related conspiracy theories
                             and disinformation, long after the actual
                             election, can be used to justify a record-
                             breaking number of new laws designed to
                             suppress voting or distort the electoral
                             process, and to further the campaigns of
                             election-denying political candidates seeking
                             to take over the administration of elections.
                             We’ve also seen harassment, intimidation, and
                             threats directed at the people – including
                             volunteers – that administer U.S. elections.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ Internet Freedom Foundation ☛ 2022_Year_In_Review:_A_recap
                  of_how_sustained_legal_efforts_advanced_digital_rights⠀⇛


                       The legal team at IFF has been working hard to
                       address important digital rights issues, such as
                       internet shutdowns, mandatory imposition of Aarogya
                       Setu, illegal website blocking, unlawful spying and
                       use of facial recognition technology. In 2020 and
                       2021, we brought these issues to the attention of
                       Constitutional Courts. This year, we are seeing the
                       fruits of our labour, with positive outcomes from
                       cases filed in previous years and additional
                       victories that have advanced the digital rights of
                       every Indian. For example, Mr. Tanul Thakur’s case
                       against the illegal ban on his website was filed in
                       2019 and saw positive outcomes in 2022.
                       Additionally, our sustained efforts have resulted
                       in 5 more important victories this year, all of
                       which we have summarised in this post below.


                       Clearly, litigation is a process that requires
                       patience and sustained support over the years. If
                       you believe in the efforts that we describe, please
                       support us. Our members enable us to perform the
                       important task of defending digital freedoms in
                       courts. We are grateful to the litigants for
                       trusting us with their cases and our network of
                       collaborating lawyers who spent countless hours
                       working pro bono.


          o § Monopolies⠀➾


                # ⚓ Public Knowledge ☛ Public_Knowledge_Responds_to_Omnibus
                  Spending_Package_–_Public_Knowledge⠀⇛


                       Today, Congressional leadership unveiled a roughly
                       $1.7 trillion deal to fund the U.S. government
                       through fiscal year 2023. The package includes
                       provisions that would benefit consumers by taking
                       steps towards promoting adoption of broadband
                       through device access and assisting greater
                       antitrust enforcement, but, unfortunately, abandons
                       popular antitrust bills designed to rein in Big
                       Tech. Public Knowledge looks forward to working
                       with the new Congress next year to promote a
                       competitive marketplace for Big Tech, help close
                       the digital divide, and better protect consumers.


    * § Gemini* and Gopher⠀➾


          o § Personal⠀➾


                # ⚓ Star_Log_2022-12-19_Evening_(Fairbanks,_AK,_US)⠀⇛


                       Last night my family and I visited some relatives
                       for a movie party. The skies were clear, and the
                       location was about 20 miles outside of the
                       Fairbanks light pollution. So, while everybody else
                       watched the movie, I snuck outside for some
                       stargazing. I did not have any astronomy equipment
                       with me, so it was a naked-eye session. It was also
                       -17 ℉ (-27 ℃), but fortunately I had brought most
                       of my cold-weather gear, and I was able also to
                       warm up in the Suburban when necessary.


          o § Technical⠀➾


                # § Programming⠀➾


                      # ⚓ Don’t_Quote_Me⠀⇛


                             Another option (at the cost of time,
                             complexity, and other drawbacks) would be to
                             use a YAML library to modify test.yml. An
                             advantage is that the substitutions can be
                             better controlled; if test.yaml were ever
                             modified (and how would you know?) to have a
                             key such as EXAMPLE_MAIL_CONTACT_FILE, this
                             new key would be mangled by the simple
                             substitution on EXAMPLE_MAIL_CONTACT. This
                             would not be the case with the substitutions
                             confined to non-key portions of the YAML.


                             On the other hand, YAML libraries can be
                             complicated and may do undesirable things
                             such as to reorder your carefully organized
                             Ansible configuration stanzas. In that case,
                             I’ve used simple regex modifications, similar
                             to the above, combined with a very careful
                             review of the diff. This was suitable for a
                             one-time bulk edit of the YAML.


                      # ⚓ Embedding_Wren,_pt2⠀⇛


                             It’s Xmas time, which, amongst other things,
                             means I have no guilt about working on the
                             side project for a few days…


                             So I’m back on the EH500!


                             The last time I picked this up was in the
                             Summer, so I decided to finish embedding Wren
                             and get the rest of the “console” exposed to
                             script.


                      # ⚓ GCC_code_generation_quirks⠀⇛


                             I’ve been stuck upside down in a peculiar pit
                             of hell, a strange combination of pure joy
                             and absolute frustration. Some of you know
                             I’ve succumbed to a monumental bucket list
                             project, trying to harness and integrate a C
                             compiler (gcc for now) into a Forth/Lisp/
                             Smalltalk-like interactive environment, with
                             function-level compilation and immediate
                             linking, image, sources integration, and all
                             the good stuff.


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



                    ䷩ 𝚕𝚒𝚗𝚎 5573

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.20.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_20/12/2022:_Epic_Games_Fined_Over_Privacy_Abuse,_Tails_5.8_Released⠀✐


Posted in News_Roundup at 7:52 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Applications
          o Instructionals/Technical
          o Games
    * Distributions_and_Operating_Systems
          o BSD
          o Debian_Family
          o Devices/Embedded
          o Open_Hardware/Modding
    * Free,_Libre,_and_Open_Source_Software
          o Content_Management_Systems_(CMS)
          o GNU_Projects
    * Leftovers
          o Science
          o Education
          o Hardware
          o Health/Nutrition/Agriculture
          o Security
                # Integrity/Availability/Authenticity
                # Privacy/Surveillance
                # Confidentiality
          o Defence/Aggression
          o Transparency/Investigative_Reporting
          o Environment
                # Energy
                # Wildlife/Nature
          o Finance
          o AstroTurf/Lobbying/Politics
          o Censorship/Free_Speech
          o Freedom_of_Information_/_Freedom_of_the_Press
          o Civil_Rights/Policing
          o Internet_Policy/Net_Neutrality
          o Monopolies
                # Patents
                # Copyrights
    * Gemini*_and_Gopher
          o Personal
    * § GNU/Linux⠀➾


          o § Applications⠀➾


                # ⚓ TecMint ☛ 16_Best_Microsoft_Teams_Alternatives_For_Linux⠀⇛


                       Brief: In this guide, we explore the best Microsoft
                       Teams alternatives for Linux that you can use to
                       streamline your workflows and collaborate with your
                       friends and colleagues.


          o § Instructionals/Technical⠀➾


                # ⚓ Terence Eden ☛ You_Don’t_Need_HTML!⠀⇛


                       And I thought… do you even need HTML to make a
                       website?


                       A few hours later, I launched the NO-HT.ML website.
                       Proving, once and for all, that you don’t need HTML
                       to make a beautiful1 responsive2, and useful3
                       website which everyone will love4.


                # ⚓ Mark ☛ Migrating_My_Blog_to_a_New_Host_with_no_Downtime⠀⇛


                       My blog is finally running on a new host! I learned
                       a lot about DNS and SSL certificates during the
                       transition and it tickled the curious part of my
                       brain that loves puzzles and problems. I love doing
                       things the “right way” and “the hard way” to learn
                       and I hope this might educate or be a good
                       reference in the future. I aimed to do my migration
                       with no downtime, but my website did go down for a
                       few minutes. For that, I explained what I did wrong
                       and what I believe is the better method.


          o § Games⠀➾


                # ⚓ GamingOnLinux ☛ Epic_Games_to_pay_$520_million_for_privacy
                  violations_and_unwanted_charges⠀⇛


                       The FTC announced that Epic Games has agreed to pay
                       $520 million, due to “violating children’s privacy
                       laws” and “tricking users into making unwanted
                       charges”.


                # ⚓ GamingOnLinux ☛ Neon_Prime_from_Valve_is_reportedly_a
                  third-person_shooter_close_to_release⠀⇛


                       Neon Prime isn’t here yet, and there’s nothing
                       actually confirmed about it, but data miner and
                       leaker Tyler McVicker gave a fresh overview on what
                       to expect.


    * § Distributions and Operating Systems⠀➾


          o § BSD⠀➾


                # ⚓ APNIC ☛ Be_careful_with_that_ping,_FreeBSD⠀⇛


                       Out of the blue, an interesting Common
                       Vulnerabilities and Exposures (CVE), formally
                       called CVE-2022-23093 has emerged, which exploits
                       one of the fundamental tools of the Internet stack:
                       Ping, the command that implements the Internet
                       Control Message Protocol (ICMP) as it’s universally
                       known.


          o § Debian Family⠀➾


                # ⚓ 9to5Linux ☛ Privacy-Focused_Tails_5.8_Enables_Wayland_by
                  Default,_Adds_New_Persistent_Storage⠀⇛


                       The Debian-based Tails 5.8 privacy-focused Linux
                       distribution has been released today and it’s a
                       major update that brings exciting new features and
                       better security for those who want to stay
                       anonymous while browsing the Internet.


                       The biggest change in Tails 5.8 is the fact that
                       Wayland is now used as the default display system
                       instead of X.Org Server for an extra layer of
                       security. For Tails specifically, the switch to
                       Wayland reenables the Unsafe Browser, which was
                       disabled a few releases ago due to a security
                       vulnerability in X11.


          o § Devices/Embedded⠀➾


                # ⚓ Doug Brown ☛ Upgrading_my_old_Chumby_8_Linux_kernel_part_1:
                  U-Boot⠀⇛


                       As I mentioned in my last post, I spent a good
                       chunk of my spare time over the past 6 months
                       working on a project I’ve been thinking about for
                       over a decade. I bought a Chumby 8 in 2011. It’s an
                       8″ touchscreen device powered by the Marvell PXA166
                       processor. It is essentially a souped-up digital
                       picture frame with extra capabilities like
                       speakers, a microphone, and Wi-Fi. There are a
                       bunch of little Flash-based “apps” you can install
                       for stuff like pictures, music, sports scores,
                       weather, games, etc. I have no idea how many of the
                       apps still work these days. Chumby actually went
                       out of business a few months after I bought mine,
                       although one of the founders stepped up to keep the
                       service running. A variant of this device was also
                       created for Insignia, which was called the Infocast
                       8″ Internet Media Display.


                # ⚓ Mark Allen Group ☛ Open-Source,_Reusable_Software_Stack
                  Enables_Real-Time_Processing_and_Algorithm_Development_for
                  CbM⠀⇛


                       The CN0549 CbM platform provides system flexibility
                       and a myriad of software resources to designers
                       when developing their applications. A deep dive
                       into the software stacks has been provided with
                       discussions around how the different components can
                       be leveraged for CbM and predictive maintenance
                       (PdM) developments. Due to the openness of the
                       software, HDL, schematics, and integrations with
                       data science tools, designers can leverage the
                       components they need for their end system
                       throughout the entire stack. In summary, this
                       condition monitoring design offers an easy to use
                       out-of-the-box solution, complete with open-source
                       software and hardware, to provide flexibility and
                       allow designers to achieve better, customized
                       results in less time.


          o § Open Hardware/Modding⠀➾


                # ⚓ Andrew Hutchings ☛ Acorn_RiscPC:_Upgrades_Part_4⠀⇛


                       What is likely the final batch of upgrades has
                       arrived for my RiscPC. This is exciting stuff as I
                       got some games running on it too. Let’s get into
                       it.


                # ⚓ Kian Ryan ☛ The_Rough_And_Ready_Guide_To_Getting_Your
                  RC2014_Pro_Online⠀⇛


                       Back in t’day (drops 20p in t’swear jar), before
                       the advent of the Internet as we know it in its
                       current form, computers talked to each other using
                       BBS software and terminal programs. You dialled the
                       remote machine, the modem on the other side would
                       pick up and a conversation would ensue, machine to
                       machine.


                       The internet abstracted all this away, and we moved
                       towards a model where your computer connected to an
                       Internet Service Provider, and then all your
                       traffic is routed over a global network of
                       connected machines.


                # ⚓ Meduza ☛ Foreign_manufacturers_stop_delivering_‘Russian’
                  Baikal_and_Elbrus_microchips_to_Russia_—_Meduza⠀⇛


                       The foreign producers of the nominally “Russian”
                       Baikal and Elbrus CPUs have stopped delivering them
                       to Russia.


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


          o ⚓ SANS ☛ Hunting_for_Mastodon_Servers⠀⇛


                 The problem with this decentralized platform, the number
                 of servers keeps growing, and there are many domain names
                 to track to detect Mastodon traffic. Hopefully, it’s
                 possible to generate the list of servers through an API
                 call.


          o § Content Management Systems (CMS)⠀➾


                # ⚓ Mark ☛ Why_does_my_blog_HTTP_503_Service_Unavailable_when_I
                  click_around_using_Firefox_on_iPhone?⠀⇛


                       After migrating my blog to a new host, I noticed my
                       website would crawl to a halt while I clicked
                       around. I would see hangs ranging from 4 seconds to
                       15 seconds. If I click enough, I’d eventually see
                       HTTP 503 Service Unavailable. Why was visiting my
                       website causing it to hang? Here’s my debugging
                       story.


                       It was strange. In my previous post, I shared some
                       tests measuring my website’s response times and the
                       numbers were beautifully performant. Yet, I was
                       seeing and feeling something very different. CURL
                       would return within one second, but my real-world
                       experience was terrible. So what was the
                       difference?


          o § GNU Projects⠀➾


                # ⚓ TecMint ☛ Progress_–_Show_Percentage_of_Copied_Data_for_
                  (cp,_mv,_dd,_tar)_Commands⠀⇛


                       Progress, formerly known as Coreutils Viewer, is a
                       light C command that searches for coreutils basic
                       commands such as cp, mv, tar, dd, gzip/gunzip, cat,
                       grep, etc currently being executed on the system
                       and shows the percentage of data copied, it only
                       runs on Linux and Mac OS X operating systems.


                       Additionally, it also displays important aspects
                       such as estimated time and throughput and offers
                       users a “top-like” mode.


    * § Leftovers⠀➾


          o ⚓ Hackaday ☛ Mouse_Whisperer_Keeps_You_Working,_Even_When_You_Need
            A_Break⠀⇛


                 When life hands you lemons, you make lemonade, right?
                 What about when life hands you annoyingly intrusive work-
                 from-home policies that require you to physically stay at
                 your computer even though you really, REALLY need to go
                 to the bathroom, but can’t be trusted to act like a
                 responsible adult who won’t get diverted by TV or the
                 fridge on the way back? In that case, you build something
                 like the Mouse Whisperer — because malicious compliance
                 is the best kind of compliance.


          o ⚓ Common Dreams ☛ News_Sites_Took_Nearly_$1_Million_From_Consultant
            Pushing_Power_Companies’_Agenda:_Report⠀⇛


                 Alabama Power and Florida Power & Light hired a political
                 consulting firm that paid six news websites in the two
                 states nearly a million dollars as they attacked
                 officials seeking to hold the polluting utilities
                 accountable, an investigation revealed Monday.


                 “Matrix sought to ensure much coverage was secretly
                 driven by the priorities of its clients.”


          o ⚓ The Nation ☛ A_Gift_Guide_for_the_Whole_Planet⠀⇛


                 My husband and I stopped exchanging gifts a few years
                 ago. Instead, we make donations and do something fun,
                 like see a play. It’s great: no shiny new books to add to
                 the teetering tower of unread tomes, no scarves to add to
                 the overflowing basket of same, and especially no
                 complicated kitchen equipment to gaze up reproachfully
                 from next to that never-used air fryer I got from a
                 neighbor on Freecycle. Whether or not you give presents
                 to your loved ones, here are some suggestions for your
                 end-of-year donations.


          o § Science⠀➾


                # ⚓ Hackaday ☛ Laser_Fusion_Ignition:_Putting_Nuclear_Fusion
                  Breakthroughs_Into_Perspective⠀⇛


                       This month the media was abuzz with the
                       announcement that the US National Ignition Facility
                       (NIF) had accomplished a significant breakthrough
                       in the quest to achieve commercial nuclear fusion.
                       Specifically, the announcement was that a net
                       fusion energy gain (Q) had been measured of about
                       1.5: for an input of 2.05 MJ, 3.15 MJ was produced.


          o § Education⠀➾


                # ⚓ Telex (Hungary) ☛ Hungarian_Teachers’_Unions_demand
                  resignation_of_minister_in_charge_of_public_education⠀⇛


          o § Hardware⠀➾


                # ⚓ Hackaday ☛ Photography,_The_Stereo_Way⠀⇛


                       Most consumer-grade audio equipment has been in
                       stereo since at least the 1960s, allowing the
                       listener to experience sounds with a three-
                       dimensional perspective as if they were present
                       when the sound was originally made. Stereo
                       photography has lagged a little behind the stereo
                       audio trend, though, with most of the technology
                       existing as passing fads or requiring clumsy
                       hardware to experience fully. Not so with the DIY
                       stereoscopic cameras like this one produced by this
                       group of 3D photography enthusiasts, who have also
                       some methods to view the photos in 3D without any
                       extra hardware.


                # ⚓ Hackaday ☛ Snail_Mail_Notifier’s_Simple_Power_Management_To
                  Maximize_Battery_Life⠀⇛


                       There are no weird, specialized components nor
                       esoteric sleep mode tricks behind the long battery
                       life of [Zak]’s WiFi mail slot watcher. Just some
                       sensible design and clever focus on the device’s
                       purpose: to send an HTTP request whenever it
                       detects that the front door’s mail slot has been
                       opened. The HTTP request is what kicks off useful
                       notifications, but it’s the hardware design that’s
                       really worth a peek.


                # ⚓ Hackaday ☛ IO_Connected_Radio_Alarm_Clock⠀⇛


                       [CoreWeaver] creates an alarm clock that includes
                       features one might expect in such a project,
                       including an FM radio, snooze button inputs and a
                       display, but goes beyond the basic functionality to
                       include temperature sensing and a PC connection,
                       opening the way for customizable functionality.


                # ⚓ Hackaday ☛ It’s_Ethernet,_From_An_SPI_Interface⠀⇛


                       Over the years as microcontrollers have become fast
                       enough to do the heavy lifting, we have become used
                       to 10 megabit Ethernet being bit-banged from
                       interfaces it was never meant to emerge from. We
                       think however that we’ve never seen one driven from
                       an SPI interface, so this one from [Ivan] may be a
                       first. With a cleverly designed transceiver using
                       logic chips, it even offers a chance to understand
                       something about the timing of an Ethernet
                       interface, too.


                # ⚓ Hackaday ☛ 35mm_Film_Restoration_Process_Explained⠀⇛


                       For a large part of the 20th century, motion
                       pictures were distributed on nitrate film. Although
                       cheaper for the studios, this film was highly
                       flammable and prone to decay. On top of that, most
                       film prints were simply discarded once they had
                       been through their run at the cinema, so a lot of
                       film history has been lost.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ Common Dreams ☛ Upending_of_Daily_Life_During_Pandemic_Led
                  to_Traumatic_Stress_Among_US_Mothers:_Study⠀⇛


                       A study by the National Institute of Health in the
                       first 16 months of the coronavirus pandemic found
                       that mothers in the U.S. were especially likely to
                       report high levels of stress during the public
                       health crisis if they experienced major disruptions
                       to their daily lives at work, their children’s
                       schools, or in their interactions with their
                       communities—as the majority of people surveyed said
                       they did.


                       The NIH’s Environmental Influences on Child Health
                       Outcomes (ECHO) program surveyed more than 11,000
                       mothers between April 2020 and August 2021—the
                       largest study to date regarding how mothers
                       experienced the pandemic.


                # ⚓ Counter Punch ☛ The_Meat_Industry_Has_Created_a_False
                  Dichotomy_That_Pits_People_Against_Animals⠀⇛


                       This narrative has made it easy for the meat
                       industry to create a false dichotomy that pits
                       people against animals: “Do you care more about a
                       pig than my family’s livelihood?”


                       It’s now been decades with factory farming as the
                       dominant industry, but have rural communities
                       actually experienced their purported economic
                       benefits? Has factory farming made life easier for
                       the people in small towns?


                # ⚓ TruthOut ☛ West_Virginia_Officials_Hamper_Public_Health
                  Measures_Amid_Local_HIV_Outbreak⠀⇛


                # ⚓ Common Dreams ☛ Just_in_Time_for_Holidays,_Dems_May_Embrace
                  GOP_Plan_to_Boot_Millions_Off_Medicaid⠀⇛


                       With congressional leadership expected to
                       imminently release the text of omnibus government
                       funding legislation, Politico revealed Monday that
                       Democrats are preparing to join with Republicans
                       who have demanded an end to Medicaid policies
                       enacted because of the Covid-19 pandemic.


                       As part of pandemic relief legislation passed in
                       2020, Congress boosted Medicaid funding to states
                       but imposed a “continuous coverage” requirement,
                       barring them from cutting off most enrollees from
                       the government healthcare program until after the
                       public health emergency (PHE) officially ends.


                # ⚓ US Dept Of Health and Human Services ☛ Use_of_Online
                  Tracking_Technologies_by_HIPAA_Covered_Entities_and_Business
                  Associates⠀⇛


                       Tracking technologies are used to collect and
                       analyze information about how users interact with
                       regulated entities’ websites or mobile applications
                       (“apps”). For example, a regulated entity may
                       engage a technology vendor to perform such analysis
                       as part of the regulated entity’s health care
                       operations.5 The HIPAA Rules apply when the
                       information that regulated entities collect through
                       tracking technologies or disclose to tracking
                       technology vendors includes protected health
                       information (PHI).6 Some regulated entities may
                       share sensitive information with online tracking
                       technology vendors and such sharing may be
                       unauthorized disclosures of PHI with such
                       vendors.7Regulated entities are not permitted to
                       use tracking technologies in a manner that would
                       result in impermissible disclosures8 of PHI to
                       tracking technology vendors or any other violations
                       of the HIPAA Rules. For example, disclosures of PHI
                       to tracking technology vendors for marketing
                       purposes, without individuals’ HIPAA-compliant
                       authorizations, would constitute impermissible
                       disclosures.9


                # ⚓ The Guardian UK ☛ TikTok_self-harm_study_results_‘every
                  parent’s_nightmare’⠀⇛


                       The Center for Countering Digital Hate (CCDH) found
                       that the video-sharing site will promote content
                       including dangerously restrictive diets, pro-self-
                       harm content and content romanticising suicide to
                       users who show a preference for the material, even
                       if they are registered as under-18s.


                # ⚓ India Times ☛ TikTok_bans_hit_more_U.S._states;_security
                  firm_says_most_access_blocked_globally⠀⇛


                       TikTok on Monday reiterated a statement, saying the
                       company was “disappointed that so many states are
                       jumping on the political bandwagon to enact
                       policies based on unfounded falsehoods about TikTok
                       that will do nothing to advance the national
                       security of the United States.”Some 19 of the 50
                       U.S. states have now at least partially blocked
                       access on government computers to TikTok, which is
                       owned by Beijing-based ByteDance Ltd. Most of the
                       restrictions came within the past two weeks.


                       Some members of Congress last week proposed a
                       nationwide ban, which would follow countries such
                       as India that have already prohibited its use.


          o § Security⠀➾


                # § Integrity/Availability/Authenticity⠀➾


                      # ⚓ APNIC ☛ Securing_NTP_against_MITM_attacks⠀⇛


                             The Network Time Protocol (NTP) is one of the
                             oldest Internet protocols that is still
                             widely used. The protocol has no security
                             mechanisms, communication is unencrypted, and
                             there is no authentication between client and
                             server or safeguards against manipulation of
                             network packets. Attacks against NTP can have
                             a serious impact because other protocols are
                             dependent on the accuracy of the system time,
                             such as DNSSEC, Kerberos, and TLS.


                # § Privacy/Surveillance⠀➾


                      # ⚓ NYOB ☛ Statement_on_EU_Comission_adequacy_decision_on
                        US⠀⇛


                             Today, the European Commission issued a new
                             adequacy decision replacing the “Privacy
                             Shield” decision, that was previously
                             invalidated by the Court of Justice of the EU
                             (CJEU) over US surveillance. The CJEU
                             required (1) that US surveillance is
                             proportionate within the meaning of Article
                             52 of the Charter of Fundamental Rights (CFR)
                             and (2) that there is access to judicial
                             redress, as required under Article 47 CFR.
                             Updated US law (Executive Order 14086) seems
                             to fail on both requirements, as it does not
                             change the situation from the previously
                             applicable PPD-28. There is continuous “bulk
                             surveillance” and a “court” that is not an
                             actual court. Therefore, any EU “adequacy
                             decision” that is based on Executive Order
                             14086 will likely not satisfy the CJEU.


                      # ⚓ Citizen Lab ☛ Mass_Iris_Scan_Collection_in_Qinghai⠀⇛


                             Of the 189 publicly available sources we
                             uncovered, 53 contained figures for the
                             number of iris scans police had collected.
                             Based on our analysis of these 53 reports, we
                             estimate that between March 2019 and July
                             2022, police may have collected between
                             roughly 1,248,075 and 1,452,035 iris scans,
                             representing between one fifth (21.1%) and
                             one quarter (25.6%) of Qinghai’s total
                             population (5.9 million). The number of
                             irises scanned would make mass iris scan
                             collection in Qinghai the largest known
                             program conducted in China relative to
                             population, with the possible exception of an
                             earlier program in the Xinjiang Uyghur
                             Autonomous Region.


                      # ⚓ Krebs On Security ☛ Hacked_Ring_Cams_Used_to_Record
                        Swatting_Victims⠀⇛


                             Two U.S. men have been charged with hacking
                             into the Ring home security cameras of a
                             dozen random people and then “swatting” them
                             — falsely reporting a violent incident at the
                             target’s address to trick local police into
                             responding with force. Prosecutors say the
                             duo used the compromised Ring devices to
                             stream live video footage on social media of
                             police raiding their targets’ homes, and to
                             taunt authorities when they arrived.


                      # ⚓ Techdirt ☛ Surprise:_Telehealth_Startups_Playing_Fast
                        And_Loose_With_Sensitive_User_Medical_Data⠀⇛


                             From the Internet of very broken
                             things to telecom networks, the state of U.S.
                             privacy and user security is arguably
                             pathetic. It’s 2022 and we still don’t have
                             even a basic privacy law for the Internet
                             era, in large part because over-collection of
                             data is too profitable to a wide swath of
                             industries, which, in turn, lobby Congress to
                             do either nothing, or the wrong thing.


                # § Confidentiality⠀➾


                      # ⚓ SequoiaPGP ☛ The_Sequoia_GnuPG_Chameleon_0.1_Is
                        Released⠀⇛


                             We are pleased to announce the first release
                             of the Chameleon, Sequoia’s reimplementation
                             of the GnuPG interface. This is a technology
                             preview, but we encourage developers who
                             integrate GnuPG into their software to see
                             whether it works with the Chameleon.


                             The Chameleon is a re-implementation and
                             drop-in replacement of gpg and gpgv using the
                             Sequoia OpenPGP implementation.


          o § Defence/Aggression⠀➾


                # ⚓ The Nation ☛ DOJ_Lawyers_Are_Cowards_if_They_Don’t_Indict
                  Trump⠀⇛


                       As many have noted: these criminal referrals
                       legally mean jack squat. Congress is not a law
                       enforcement body. Congress can write the laws, but
                       it’s up to others to determine if those laws have
                       been violated. That’s a good thing, and the next
                       two years of Kevin McCarthy and the Republican
                       Congress hunting Hunter Biden’s penis pics will
                       prove the wisdom of having at least nominal
                       separation of powers between our political bodies
                       and our law enforcement apparatus.


                       Unfortunately, Merrick Garland’s Department of
                       Justice is the law enforcement body responsible for
                       holding the people who attacked the country
                       accountable. Whether Trump is actually charged for
                       the crimes the Select Committee laid out is, and
                       has always been, up to the discretion of Garland
                       and the DOJ.


                # ⚓ ADF ☛ Fears_Of_Islamic_State_Presence_Grow_In_South
                  Africa⠀⇛


                       In November, less than a week after the United
                       States and other countries issued a terror alert in
                       South Africa, the U.S. Treasury Department filed
                       sanctions against four Durban men who allegedly
                       procure weapons and money for ISIS.


                # ⚓ Quartz ☛ The_UK_can_deport_asylum_seekers_to_Rwanda,_the
                  high_court_has_ruled⠀⇛


                       “On the evidence before this court, the government
                       has made arrangements with the government of Rwanda
                       which are intended to ensure that the asylum claims
                       of people relocated to Rwanda are properly
                       determined in Rwanda,” read part of a summary of
                       the judgement by Lord Justice Lewis, who oversaw
                       the high court case.


                # ⚓ Common Dreams ☛ UK_Court_Upholds_‘Inhumane’_Plan_to_Send
                  Asylum-Seekers_to_Rwanda⠀⇛


                       Human rights advocates on Monday vowed to continue
                       fighting the United Kingdom’s plan to deport
                       asylum-seekers to Rwanda if they arrive in the U.K.
                       after crossing the English Channel by boat, after
                       the country’s High Court ruled that the
                       Conservative Party’s plan is lawful.


                       “If the government moves ahead with these harmful
                       plans, it would damage the U.K.’s reputation as a
                       country that values human rights.”


                # ⚓ JURIST ☛ UK_plan_to_deport_asylum_seekers_to_Rwanda_lawful,
                  judges_rule⠀⇛


                       One of the judges, Lord Justice Lewis, said, “The
                       court has concluded that it is lawful for the
                       government to make arrangements for relocating
                       asylum seekers to Rwanda and for their asylum
                       claims to be determined in Rwanda rather than in
                       the United Kingdom.” But he added that the home
                       secretary “has not properly considered” eight
                       individual cases, meaning the decisions to send
                       these people to Rwanda will now be returned to the
                       Home Office.


                # ⚓ France24 ☛ UK_plan_to_deport_asylum-seekers_to_Rwanda_is
                  legal,_court_rules⠀⇛


                       More than 44,000 people have arrived in Britain
                       across the Channel this year, and several have died
                       in the attempt, including four last week when a
                       boat capsized in freezing weather.


                # ⚓ The Nation ☛ Defense_Contractors_Are_Escorting_Us_Down_the
                  Path_to_Armageddon⠀⇛


                       Hey, cheer up because it truly is a beauty! I’m
                       talking about this country’s latest “stealth
                       bomber,” the B-21 Raider, just revealed by Northrop
                       Grumman, the company that makes it, in all its
                       glory. With its striking bat-winged shape and its
                       ability to deliver a very big bang (as in nuclear
                       weapons), it’s our very own “bomber of the future.”
                       As Secretary of Defense Lloyd Austin put it at its
                       explosive debut, it will “fortify America’s ability
                       to deter aggression, today and into the future.”
                       Now, that truly makes me proud to be an American.


                # ⚓ Counter Punch ☛ A_Blueprint_For_Peace_In_Ukraine⠀⇛


                       My blueprint for peace is simple.  1. Ceasefire
                       based on the UN Charter, 2. A ban on deliveries of
                       weapons to the belligerents, 3. UN organized
                       international assistance to all populations
                       suffering because of the war, lack of energy, lack
                       of food, etc. 4. UN organized and monitored
                       referenda in Crimea and Donbas, 5. Lifting of
                       sanctions that have nullified the benefits of
                       globalization, broken supply chains, upset
                       international trade, endangered food security, 6.
                       Drafting of a new security architecture for Europe
                       and the world, 7. Establishment of a Truth and
                       Reconciliation Commission to hear the grievances
                       from all sides, 8. Punishment of war crimes by the
                       respective governments, e.g. Ukrainian crimes to be
                       investigated and prosecuted by Ukrainian judges,
                       Russian crimes to be investigated and punished by
                       Russian tribunals.


                       There is no valid binary analysis or division of
                       the world into “good guys” and “bad guys”.  There
                       has always been good in the bad and bad in the
                       good.  A binary analysis is only possible if one
                       refuses to consider the opinions of all
                       belligerents, and of the rest of humanity — as it
                       watches this tragedy unfold.  There are root causes
                       of the catastrophe that we are witnessing, and if
                       we want to formulate a viable blueprint for peace,
                       we must not look at it exclusively from the
                       “Western” perspective, but also take into account
                       the views of 1.5 Billion Chinese, 1.5 Billion
                       Indians, 240 million Pakistanis, 170 million
                       Bangladeshis, 280 million Indonesians, 220 million
                       Nigerians, 220 million Brazilians, 140 million
                       Mexicans etc.  The stakes are too high, and we
                       Americans and Europeans have no right to risk the
                       survival of the planet because of an internal
                       European querelle.  For the average African, Asian
                       or Latin American, it is wholly irrelevant whether
                       Crimea is in Russia or in Ukraine.  A nuclear war
                       must not be fought over this.


                # ⚓ Telex (Hungary) ☛ BKV_donates_15_scrapped_but_functioning
                  buses_to_Ukraine⠀⇛


                # ⚓ Counter Punch ☛ Can_the_Left_Disagree_Without_Being
                  Disagreeable?⠀⇛


                       There is no war that I have experienced that has
                       been as devastating as the war on Iraq, which
                       snatched the lives of millions, devastated the
                       lives of the entire population, and left the
                       country scarred beyond belief. No doubt other
                       reporters who are in Ukraine will come with their
                       own stories. There is no comparison of warzones,
                       one more deadly than the other, although the sheer
                       destruction of Iraq compares to the pain inflicted
                       on Hiroshima and Nagasaki by the atomic bombs.


                       Wars are to be opposed and every effort must be
                       made to prevent wars and to end wars.


                # ⚓ Counter Punch ☛ Will_Ukraine_Become_Another_Ceaseless
                  War?⠀⇛


                       Refugees who are at first warmly accepted as
                       victims of tyranny may outstay their welcome and
                       become resented and even hated. This is what
                       happened to the five million Syrians who fled to
                       Turkey and one million to Lebanon after 2011. The
                       wars in Somalia and Yemen are not only endless, but
                       are escalating.


                       Will the Ukraine conflict become another of these
                       ceaseless wars? It is difficult to see why it
                       should not, since neither Moscow nor Kyiv is likely
                       to win a decisive victory but they still hope to
                       improve their political and diplomatic position on
                       the battlefield. The Russians are using precision-
                       guided missiles and drones to destroy the Ukrainian
                       infrastructure and the Ukrainians are beginning to
                       fire missiles back at ostensibly military targets.
                       It may not be long before they decide that if they
                       are going to sit in the dark, so too will the
                       Russians.


                # ⚓ Counter Punch ☛ Biden’s_National_Security_Team_is_Trailing
                  Badly_at_Halftime⠀⇛


                       Conversely, the preoccupation with Ukraine has kept
                       the Biden team from pursuing alternatives to the
                       feckless dual containment policy against Russia and
                       China; the maximalist (and similarly feckless)
                       denuclearization policies against Iran and North
                       Korea; the emphasis on increased military spending;
                       and the unwillingness to pursue arms control and
                       disarmament measures.  A dialogue is needed with
                       North Korea, and Biden should have returned to the
                       Iran nuclear accord.  But the Biden team doesn’t
                       even include a disarmament specialist!


                       Although Biden can claim credit for ending the
                       “forever wars” in Iraq and Afghanistan, the record
                       spending on defense, which includes an $80 billion
                       increase over last year’s spending as well as the
                       emphasis on costly weapons systems points to
                       business as usual.  The increase in spending alone
                       is far more than Russia spending on its entire
                       defense budget.  In fact, with the exception of
                       China, this year’s increase is greater than every
                       defense budget in the global community. The
                       mainstream media approved the unrestrained defense
                       spending, and merely highlighted the fact that the
                       defense bill rescinded the Pentagon mandate
                       regarding the coronavirus vaccine.


                # ⚓ TruthOut ☛ January_6_Committee_Unanimously,_Formally
                  Accuses_Trump_of_Insurrection⠀⇛


                # ⚓ Common Dreams ☛ Opinion_|_Arming_Robots_Is_Too_Dangerous⠀⇛


                       San Francisco was embroiled in controversy earlier
                       this month over a proposal to allow police to
                       deploy robots armed with deadly weapons. After
                       initially greenlighting the technology, the Board
                       of Supervisors reversed course due to widespread
                       public outcry. For the time being, killer robots
                       are banned in San Francisco, but the controversy
                       there has put the issue in the national spotlight.
                       People are increasingly aware that this technology
                       exists and that some police departments want to
                       deploy it.


                # ⚓ Common Dreams ☛ ‘Time_to_Prosecute’:_Jan._6_Panel
                  Unanimously_Refers_Trump_to_DOJ_for_Criminal_Charges⠀⇛


                       The congressional committee probing the January 6
                       attack on the U.S. Capitol on Monday concluded its
                       proceedings by unanimously voting to recommend that
                       Attorney General Merrick Garland and the Justice
                       Department investigate former President Donald
                       Trump and some of his associates for four crimes in
                       connection with the deadly insurrection.


                       “Donald Trump knowingly and corruptly repeated
                       election fraud lies, which incited his supporters
                       to violence on January 6.”


                # ⚓ Counter Punch ☛ Challenging_the_Fake_Antiwar_Left_on
                  Ukraine⠀⇛


                       This time Eric takes on some of the arguments put
                       forward by those on the Left who advocate for
                       immediate negotiation as they claim to be the voice
                       of the authentic “antiwar” Left. Eric addresses
                       claims about NATO, US arms to Ukraine, the
                       objectives of the Biden Administration, Putin’s
                       justifications for the war, and much more.


                # ⚓ Common Dreams ☛ Opinion_|_Where_Is_the_Debate_Over_This
                  Bloated,_Immoral_Pentagon_Budget?⠀⇛


                       Congress is on track in the coming week to give
                       final approval to a national military budget for
                       the fiscal year that is expected to reach about
                       $858 billion—or $45 billion more than President
                       Biden had requested and 8 percent more than last
                       year.


                # ⚓ Scheerpost ☛ Congress_Just_Passed_$858_Billion_Military
                  Budget,_But_GOP_Is_Blocking_$12_Billion_to_Fight_Child
                  Poverty⠀⇛


                       “This isn’t using our taxpayer dollars wisely,”
                       said one analyst. “It’s robbing programs that we
                       need.”


                # ⚓ Meduza ☛ Saving_Private_Alexey_A_Russian_prisoner_joins_a
                  private_military_company_to_follow_his_conscripted_twin_to
                  Ukraine,_but_his_brother_dies_and_now_the_mercenary_is
                  missing_—_Meduza⠀⇛


                       In September, a Russian prisoner named Alexey who
                       had just a few months left on his sentence decided
                       to sign a contract with the Wagner private military
                       company (PMC) after learning that his twin brother,
                       Konstantin, had been drafted to fight in Ukraine.
                       Now Konstantin is dead, and the twins’ family is
                       desperately lobbying the Wagner Group to return
                       Alexey, who has been out of contact since early
                       November. But their pleas are being ignored.


                # ⚓ Meduza ☛ Putin_issues_decree_to_grant_veterans_free_land
                  plots_in_Moscow_region_and_Crimea_—_Meduza⠀⇛


                       Vladimir Putin has signed a decree instructing
                       authorities in the Moscow region, Crimea, and
                       Sevastopol to pass legislation to grant plots of
                       land to veterans of the war in Ukraine free of
                       charge.


          o § Transparency/Investigative Reporting⠀➾


                # ⚓ The Dissenter ☛ How_NSA_Whistleblower_Reality_Winner_Came
                  To_Support_Prison_Abolition⠀⇛


          o § Environment⠀➾


                # ⚓ RTL ☛ EU_reaches_deal_on_major_carbon_market_reform⠀⇛


                       EU member states and parliamentarians on Sunday
                       announced an agreement for a major reform to the
                       bloc’s carbon market, the central plank of its
                       ambitions to reduce emissions and invest in
                       climate-friendly technologies.


                       The deal aims to accelerate emissions cuts, phase
                       out free allowances to industries and targets fuel
                       emissions from the building and road transport
                       sectors, according to a European Parliament
                       statement.


                # ⚓ RTL ☛ France_bans_disposable_packaging,_utensils_in_fast-
                  food_restaurants⠀⇛


                       Restaurants have been preparing for months to
                       implement a rule that comes into force on January
                       1, which for many has upended business models based
                       on single-use packaging and utensils, both for
                       eating in and for take-out.


                       The roughly 30,000 fast-food outlets in France
                       serve six billion meals a year, generating an
                       estimated 180,000 tons of waste.


                # ⚓ Helsinki Times ☛ HS:_Finland_contributes_to_warming_as_much
                  as_it_did_in_early_1990s⠀⇛


                       The turnaround is attributable to the adoption of
                       more accurate calculation methods at the Natural
                       Resources Institute Finland (Luke). The updated
                       calculations reveal that the carbon sink of forests
                       has eroded so much in the past decade that it has
                       undone the otherwise commendable emission
                       reductions and, as a result, jeopardises the
                       government-stated objective of becoming carbon
                       neutral by 2035.


                       The objective is inscribed in the newly adopted
                       climate act.


                # ⚓ Common Dreams ☛ A_‘Weak’_Global_Biodiversity_Pact_Approved
                  at_COP15_Despite_Objections_of_African_Nations⠀⇛


                       Over the objections of the Democratic Republic of
                       Congo and frustrations by other African nations, a
                       final draft of The Kunming-Montreal Global
                       Biodiversity Framework was adopted in the early
                       hours of Monday that conservationists say is not
                       strong enough to prevent industries and corporate
                       behemoths from continuing their destructive,
                       profit-driven attacks on the natural world and
                       vulnerable species.


                       “The draft agreement is weak,” said An Lambrechts,
                       leader of Greenpeace International’s delegation at
                       the summit, following the release of the final
                       draft text on Sunday. “This is an open invitation
                       to greenwash. In its present shape, it won’t halt
                       biodiversity loss, much less reverse it.”


                # ⚓ TruthOut ☛ Global_Biodiversity_Pact_Draft_Is_an_“Open
                  Invitation_to_Greenwash,”_Critics_Say⠀⇛


                # § Energy⠀➾


                      # ⚓ Helsinki Times ☛ LUT_is_planning_the_first_advanced
                        research_microreactor_in_Finland⠀⇛


                             LUT University and Seattle-based Ultra Safe
                             Nuclear Corporation have signed a Memorandum
                             of Understanding (MOU) aiming to deploy a
                             micro-modular reactor (MMR®) as a research
                             and test reactor in the city of Lappeenranta,
                             Finland. The planned project will also
                             involve local authorities and stakeholders.


                      # ⚓ Zimbabwe ☛ Zimbabwe’s_current_load_shedding
                        explained⠀⇛


                             Zimbabwe’s power demand sits at 2100MW and at
                             the time I am writing this we are producing
                             501MW of power. Less than 25% of the national
                             demand. Is it a case that we don’t have
                             enough power-generating stations to meet this
                             demand?


                      # ⚓ New York Times ☛ Sam_Bankman-Fried_Said_to_Agree_to
                        Extradition_After_Chaotic_Hearing⠀⇛


                             The disgraced cryptocurrency mogul Sam
                             Bankman-Fried has agreed to be extradited to
                             the United States, one of his lawyers said on
                             Monday, after a chaotic morning of legal
                             maneuvering in which Mr. Bankman-Fried was
                             shunted back and forth between court and
                             prison in the Bahamas.


                             Mr. Bankman-Fried is facing fraud charges in
                             the United States related to the collapse of
                             his cryptocurrency exchange, FTX, which was
                             based in the Bahamas. Jerone Roberts, a local
                             defense lawyer for Mr. Bankman-Fried, told
                             reporters that his client had agreed to
                             extradition voluntarily, defying “the
                             strongest possible legal advice.”


                      # ⚓ The Nation ☛ The_Crypto_Scandal_Is_Also_an
                        Opportunity_for_the_Left⠀⇛


                             Sam Bankman-Fried’s empire of fraud was
                             protected by the disguise of philanthropy,
                             with the ideology of effective altruism used
                             as justification for his once-immense
                             fortune, estimated recently, at its peak, at
                             over $26 billion. That fortune, always
                             largely imaginary and speculative, is now
                             gone. The Bahamas-based crypto exchange
                             Bankman-Fried founded, FTX, is bankrupt.
                             Bankman-Fried himself is facing a variety of
                             criminal charges on fraud in both the Bahamas
                             and the United States. Bankman-Fried’s
                             philanthropy was always a shifty business
                             (despite having prominent neoliberal
                             apologists), since it was so clearly a
                             vehicle for keeping cryptocurrency
                             deregulated.1


                      # ⚓ Common Dreams ☛ ‘Listen_to_Oregon’:_Merkley,_Wyden
                        Urge_FERC_to_Deny_Expansion_of_Gas_Pipeline⠀⇛


                             U.S. Democratic Sens. Jeff Merkley and Ron
                             Wyden on Monday pressured federal regulators
                             to reject a Canadian company’s attempt to
                             expand a fracked gas pipeline, citing
                             President Joe Biden’s climate promises,
                             threats to Oregon’s frontline communities,
                             and efforts by their state to fight the
                             planetary crisis.


                             “Rather than helping Americans, GTN Xpress
                             would be supporting a market for dirty fossil
                             gas from a foreign country.”


                # § Wildlife/Nature⠀➾


                      # ⚓ Hollywood Reporter ☛ Steven_Spielberg_Says_He_“Truly”
                        Regrets_‘Jaws’_Influence_on_the_“Decimation_of_the
                        Shark_Population”⠀⇛


                             “Thousands of fishers set out to catch trophy
                             sharks after seeing Jaws,” he told the
                             outlet, while suggesting — similar to other
                             published studies — that the shark population
                             was notably impacted by the release of the
                             movie. “It was good blue-collar fishing. You
                             didn’t have to have a fancy boat or gear — an
                             average Joe could catch big fish, and there
                             was no remorse since there was this mind-set
                             that they were man-killers.”


                             For that reason, Benchley spent parts of his
                             life after the book’s publishing working to
                             campaign to save the oceanic creatures his
                             book had vilified. “Jaws was entirely a
                             fiction,” he reportedly told the London Daily
                             Express in 2006. “Knowing what I know now, I
                             could never write that book today.”


          o § Finance⠀➾


                # ⚓ ABC ☛ Mom_warns_parents_after_son_charges_$16K_on_in-app
                  game_purchases⠀⇛


                       Johnson, a real estate broker and mother of two,
                       said that on July 9, she noticed the same charge of
                       $106.34 appear on her bank statement 12 times in a
                       row. In a transaction report shared by Johnson with
                       “GMA,” there were also lesser charges of $53.16 and
                       several more in the $200 to $600 range.


                # ⚓ EFF ☛ EFF_Receives_$250k_Grant_from_Craig_Newmark
                  Philanthropies⠀⇛


                       This generous support will help EFF educate
                       journalists about, and protect them from, digital
                       and legal threats. It also will help us do public
                       education, build coalitions, and conduct research
                       into the disciplinary technologies that
                       corporations, schools, and individuals use to
                       violate people’s autonomy and privacy. 


                       This grant, for work to be conducted through April
                       2023, is the latest in a series of grants made to
                       EFF by the Craig Newmark Philanthropies, created by
                       the founder of Craigslist to support causes
                       including building networks to help protect the
                       country in the cybersecurity world, defending
                       against disinformation warfare, and fighting online
                       harassment as well as support for ethical and
                       trustworthy journalism, particularly in underserved
                       communities. 


                       EFF, founded in 1990, is the leading nonprofit
                       organization defending civil liberties in the
                       digital world, championing user privacy, free
                       expression, and innovation through impact
                       litigation, policy analysis, grassroots activism,
                       and technology development. Newmark is a member of
                       EFF’s advisory board. 


                # ⚓ Common Dreams ☛ Opinion_|_10_Ways_We_Helped_Dent_Inequality
                  in_2022⠀⇛


                       Congratulations to everyone who worked to move the
                       country and the world towards greater equity in
                       2022. Herewith are 10 of the most inspiring
                       economic inequality victories of the year.


                # ⚓ Meduza ☛ Demand_for_foreign_real_estate_more_than_doubled
                  in_Russia,_compared_to_2021_—_Meduza⠀⇛


                       The Russian buyers’ demand for foreign real estate
                       has increased by a factor of 2.3, compared to 2021.
                       Compared to the 2019 pre-pandemic demand for
                       properties abroad, this is a 1.7-fold increase.


                # ⚓ Counter Punch ☛ How_Colombia_Will_Tax_the_Wealthy⠀⇛


                # ⚓ FAIR ☛ Media_Prescribe_More_‘Pain’_for_Workers_as
                  Inflation’s_Only_Cure⠀⇛


                       Federal Reserve chair Jerome Powell is profit’s
                       prophet and the corporate media are his cultish
                       devotees, joining hands to sacrifice working
                       people. In this cult, profit is sacrosanct.


                # ⚓ Common Dreams ☛ Biden_Unveils_Plan_to_Reduce_Homelessness
                  25%_by_2025⠀⇛


                       The Biden administration on Monday released a plan
                       that seeks to eventually eradicate homelessness in
                       the United States, starting with a 25% reduction in
                       the number of people suffering from a lack of
                       reliable access to safe housing over the next two
                       years.


                       “My plan offers a roadmap for not only getting
                       people into housing but also ensuring that they
                       have access to the support, services, and income
                       that allow them to thrive,” President Joe Biden
                       said in a statement. “It is a plan that is grounded
                       in the best evidence and aims to improve equity and
                       strengthen collaboration at all levels.”


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Techdirt ☛ As_Many_Suspected,_Elon’s_Claims_Of_Jet_Account
                  Helping_His_Stalker_Turned_Out_To_Be_Bogus⠀⇛


                       That said, reporters Taylor Lorenz and Drew
                       Harwell, both excellent tech reporters who were
                       both suspended from Musk’s Twitter over the last
                       few days, have a more complete story of the
                       stalker, including talking to the guy. And it’s
                       pretty damn clear that it has literally nothing to
                       do with the ElonJet account, which did not dox him,
                       nor help the crazed guy.


                # ⚓ Scheerpost ☛ Matt_Taibbi_and_Russell_Brand_Expose_Twitter
                  Policy⠀⇛


                       “The Twitter Files with Matt Taibbi, who has been
                       releasing internal documents from before Elon Musk
                       purchased Twitter. Here Matt reveals everything we
                       need to know about these revelations.”


                # ⚓ TruthOut ☛ Warren:_Musk_Is_Using_Tesla_to_Prop_Up_Twitter’s
                  Debts_and_Failures⠀⇛


                # ⚓ Common Dreams ☛ ‘I_Will_Abide’:_In_Self-Imposed_Survey,
                  57.5%_of_Twitter_Say_Musk_Should_Step_Down_as_CEO⠀⇛


                       Update: After twelve hours of voting—and over 17.5
                       million accounts casting a digital response—the
                       results of Elon Musk’s survey question on whether
                       or not he should “step down” as head of Twitter
                       determined the answer was resounding: Yes.


                       With 17,502, 391 total votes, 57.5% said he should
                       step aside while just 42.5% said he should not.


                # ⚓ Techdirt ☛ I_Speak_Fluent_‘New_Social_Media_CEO_Who’s_In
                  Over_Their_Head’;_Let_Me_Translate_The_Last_Few_Days_Of
                  Twitter_Policy⠀⇛


                       The last few days on Twitter have been, well,
                       chaotic, I guess? Beyond the blocking of the
                       ElonJet account, followed by the blocking of the
                       @JoinMastodon account, then the blocking of
                       journalists asking about all this and the silly
                       made up defense of it, over the weekend, Twitter
                       announced a new policy banning linking to or even
                       displaying usernames on a whole host of other
                       social media platforms:


                # ⚓ Common Dreams ☛ Campaigners_Declare_‘No…_Democracy_With
                  Oligarchy’_at_Twitter_HQ⠀⇛


                       Dozens of artists, labor advocates, and climate
                       campaigners answered a call from Climate Justice
                       Arts on Sunday, arriving at Twitter’s headquarters
                       in San Francisco to paint the company’s famed bird
                       logo on the street outside along with pro-democracy
                       messages.


                       “Sick of billionaires, wealthy corporations, and
                       their politicians mismanaging, profiteering, and
                       wrecking our communities and planet?” read the
                       invitation to community members. “Join us speaking
                       out against oligarchy by painting a guerrilla
                       street mural directly in front of San Francisco
                       Twitter headquarters.”


                # ⚓ The Nation ☛ Citizen_Musk⠀⇛


                       Elon, we knew ye all too well. Elon Musk, the
                       failed emperor of Twitter, will apparently be
                       stepping down from his lofty perch after issuing a
                       user poll asking whether he should remain head of
                       the company. The poll appeared after yet another
                       series of deranged miscalls and abuses on the
                       site—from the random suspension of the accounts of
                       Musk-critical journalists on the fabricated charge
                       of doxxing Musk’s real-time whereabouts to an
                       abrupt ban on promotional links to other social
                       media platforms—which alienated even his previous
                       supporters. It was scarcely surprising that the
                       vote landed firmly in the “Leave” column.


                # ⚓ Scheerpost ☛ Dangerous_“Kids_Online_Safety_Act”_Does_Not
                  Belong_in_Must-Pass_Legislation⠀⇛


                       Every year, Congress must follow through on an
                       enormous and complicated task: agreeing on how to
                       fund the government for the following year. The
                       wrangling over spending often comes down to the
                       wire, and this year, some Senators are considering
                       shoehorning a controversial and unconstitutional
                       bill, the Kids Online Safety Act (KOSA), into the
                       must-pass legislation. Make no mistake: KOSA is bad
                       enough on its own, but putting KOSA into the
                       “omnibus package” is a terrible idea.


                # ⚓ Michael Geist ☛ Elon_Musk’s_Twitter_Linking_Restrictions
                  May_Have_Been_Short-Lived,_But_Bill_C-18_is_Based_on_a
                  Similar_Approach_to_Links⠀⇛


                       The policy may have been short-lived – last night
                       the company’s tweets on point were removed – but
                       the policy on linking remains particularly notable
                       because it bears a striking resemblance to the
                       Canadian government’s Online News Act, known as
                       Bill C-18. While some responded to a tweet I wrote
                       that the comparison is a stretch, the parallels are
                       obvious. In Twitter’s case, the company took the
                       position that certain links posted by users –
                       namely links to rival services – create unfair
                       competition since Twitter is competing with
                       services such as Instagram for the same user base
                       and the same advertisers. In response, the company
                       said that the links would either be blocked or
                       could remain with compensation (ie. paid
                       advertising).


                # ⚓ RTL ☛ Meta_‘breached_EU_antitrust_rules’_on_Facebook_ads⠀⇛


                       Monday’s announcement was about “suspected
                       violations” of EU antitrust rules and gives Meta a
                       chance to respond to the commission’s formal
                       Statement of Objections.


                       Those concerns focus on the way Meta gives Facebook
                       users automatic access to Facebook Marketplace
                       “whether they want it or not”.


                # ⚓ The Nation ☛ Hunting⠀⇛


                # ⚓ Common Dreams ☛ Opinion_|_The_Crazy_Code_Behind_the_Far
                  Right’s_Success⠀⇛


                       Arizona is ground zero for the wackiest theories
                       and craziest political candidates.


                # ⚓ Counter Punch ☛ Beyond_Razor_Wire:_A_Connected_Planet⠀⇛


                       OK, he’s a politician — Doug Ducey, the exiting
                       governor of Arizona, who recently began erecting
                       “hundreds of double-stacked shipping containers
                       topped by razor wire” along Arizona’s eastern
                       border with Mexico, including through the Coronado
                       National Forest. Is this not his right: to blather,
                       lie and give his constituents an enemy? And what
                       keeps us safer from that enemy than a wall,
                       especially one topped with razor wire?


                       No matter the wall doesn’t really keep desperate,
                       fleeing migrants out. It keeps out ocelots and
                       jaguars, bighorn sheep and spotted owls. It keeps
                       out, or rather, imperils the life of the western
                       yellow-billed cuckoo. It endangers the survival of
                       70+ plant and animal species. The wall is a
                       monument to racism, according to Daniel Lombroso,
                       director of “American Scar,” and what it
                       accomplishes is ecocide.


                # ⚓ Counter Punch ☛ New_Era_of_China-Saudi_Ties_Riles_Iran⠀⇛


                       The “three-in-one” conveyed a big signal that Saudi
                       Arabia stands at the heart of China’s Arab world
                       diplomacy. It is in sharp contrast with the
                       transactional relationship that the historic U.S.-
                       Saudi alliance has been reduced to.


                       Indeed, the nearly three dozen energy and
                       investment deals during Xi’s visit will preserve
                       the core of the strategic interests of Saudi Arabia
                       and China. They encompass frontier areas such as
                       information technology, green energy, cloud
                       services, infrastructure and health and inject a
                       greater sense of alignment between Riyadh’s
                       economic diversification pivot (known as Vision
                       2030) and China’s Belt and Road Initiative (BRI)-
                       driven development of smart industries and high
                       quality infrastructure, including digital
                       infrastructure, which has the potential to
                       undergird regional connectivity in the coming
                       decades.


                # ⚓ The Nation ☛ Democrats_Could_Have_Won_the_House_if_They’d
                  Had_Their_Act_Together⠀⇛


                       House minority leader Kevin McCarthy, the most
                       inept congressional leader of the modern age, is
                       struggling to pull together enough assurances from
                       members of the House Republican Caucus to secure
                       his election as speaker of the House in January. He
                       may get the votes he needs, but the fact that he
                       does not have them yet offers a measure of just how
                       miserable the next two years will be for McCarthy
                       and his partisan allies.


                # ⚓ Common Dreams ☛ Opinion_|_Judge_the_Far-Right_by_Their
                  Hideous_Heroes⠀⇛


                       You can learn a lot about the people who make up a
                       political party by identifying their heroes. So,
                       who are the heroes of today’s Republicans? If your
                       first thought was Ronald Reagan, you’re showing
                       your age. Reagan was the answer of an earlier time,
                       when we had a different, although not wholly
                       dissimilar, Republican Party. Saint Ronnie, as he
                       was sometimes called back then, was the patron
                       saint of the GOP. Their answer to every question.


                # ⚓ Common Dreams ☛ WATCH_LIVE:_Criminal_Referrals_for_Trump
                  Expected_During_Final_Jan._6_Committee_Hearing⠀⇛


                       The final public hearing of the Select Committee to
                       Investigate the January 6th Attack on the United
                       States Capitol will be held Monday afternoon, a
                       televised session that will include a vote on
                       issuing criminal referrals against former president
                       Donald Trump to the U.S. Department of Justice.


                       In public statements and interviews over recent
                       days, committee members have made clear their
                       shared belief that Trump is guilty of criminal
                       conduct related to his involvement in the lead up
                       to the insurrection that took place on January 2,
                       2021 and his behavior on that day.


                # ⚓ Meduza ☛ New_Russian_children’s_and_youth_organization
                  named_‘Movement_of_the_First’_—_Meduza⠀⇛


                       The first congress of the new state-sponsored
                       Russian children’s and youth organization has voted
                       on the organization’s name. TASS, RIA Novosti, and
                       RBC report that the organization will operate as
                       the “Movement of the First.”


                # § Misinformation/Disinformation/Propaganda⠀➾


                      # ⚓ NPR ☛ In_the_Southeast,_power_company_money_flows_to
                        news_sites_that_attack_their_critics⠀⇛


                             After winning, Dunn says, a top lobbyist for
                             the utility took him aside and promised he
                             could hold his roughly $100,000-a-year
                             position on the commission for years — as
                             long as he remained a team player. (Alabama
                             Power declined to make the executive
                             available to address the accusation; the
                             utility and its corporate parent, Southern
                             Company, declined all comment for this
                             story.)


                             “They didn’t take me [seriously],” Dunn says
                             now.


                             Dunn, a Republican and Tea Party
                             conservative, plowed ahead. And soon enough,
                             he found himself the target of a political
                             pressure campaign, replete with character
                             assassinations and online smears.


                      # ⚓ Meduza ☛ ‘I_hope_this_won’t_influence_viewers’_In
                        their_own_words,_actors_in_Russian_pro-war_videos
                        explain_why_they_accepted_roles_in_invasion_propaganda
                        —_Meduza⠀⇛


          o § Censorship/Free Speech⠀➾


                # ⚓ FMG Inc ☛ Should_Artists_Facing_Censorship_Head_to
                  OnlyFans?⠀⇛


                       Hartlauer notes that beyond driving tourism, the
                       campaign aimed to start discussions about the power
                       social media companies wield regarding censorship
                       and illuminate the challenges some artists face in
                       promoting their more provocative work. The message
                       clearly resonated—the video landed a coveted Cannes
                       Golden Lion award this year. “We question this kind
                       of censorship because we believe it’s not a good
                       idea to let an algorithm determine our cultural
                       legacy,” Hartlauer tells NPR. “It might lead to
                       some unconscious self-censorship when artists make
                       art differently because they know a tool as strong
                       as social media would not show or promote certain
                       types of art. This is quite frightening.”


                       While Vienna found success in leveraging OnlyFans
                       as an inclusive venue for uninhibited artistic
                       expression, observers note that artists have yet to
                       follow the city’s lead. The reason may lie in the
                       website’s stigma as a platform for sex workers and
                       performers—in 2020 alone it experienced growth from
                       7.5 million subscribers to 85 million. (Some say
                       Beyoncé is partially responsible for shouting it
                       out in her “Savage” remix.) Though OnlyFans hosts
                       family-friendly accounts for cooking, gardening,
                       and fitness, it has yet to shake its X-rated
                       reputation, especially after a botched attempt to
                       ban pornography in 2021 garnered widespread
                       ridicule.


                # ⚓ Teen Vogue ☛ American_Library_Association_President:
                  Librarians_Are_Facing_Harassment⠀⇛


                       Book bans are only one of the issues that public
                       libraries are currently facing. In Tennessee,
                       lawmakers want to force librarians to list all the
                       materials they offer and to conduct periodic
                       reviews to make sure the materials are “age-
                       appropriate,” a measure many librarians told
                       Chalkbeat is unnecessary and beyond the scope of
                       their job. Across the country, several librarians
                       have been attacked or doxxed for standing up for
                       books that are deemed controversial or worthy of
                       being banned.


                       The American Library Association (ALA), the oldest
                       and largest library association in the world, is a
                       nonprofit that promotes libraries and public
                       education across the United States. Teen Vogue
                       spoke with the organization’s president, Lessa
                       Kanani’opua Pelayo-Lozada, about the consequences
                       of book bans, the importance of public libraries as
                       community spaces, and how the ALA is fighting back
                       against censorship across the country.


                # ⚓ RFERL ☛ Rights_Group_Says_Tortured_Iranian_Protester_Dies
                  In_Hospital⠀⇛


                       Hengaw, a Norway-based group that monitors rights
                       violations in Iran’s Kurdish regions, said on
                       December 19 that Mohammad Haji Rasoulpour was
                       arrested on October 1 during nationwide protests
                       over the death of Mahsa Amini in September while in
                       police custody for allegedly wearing a head scarf
                       improperly.


                # ⚓ Journal of Free Speech Law ☛ Public_Calls_For_Censorship_As
                  Bad_Speech⠀⇛


                       Responsible speakers avoid trafficking in bad
                       speech, that is, speech that they have reason to
                       believe causes or constitutes net harm. Moreover,
                       third parties have prima facie reason to suppress
                       such speech. As recent events have made salient
                       just how harmful speech can be, there has been a
                       corresponding increase in calls to suppress or
                       censor such speech. This article argues that there
                       are three mechanisms by which calls to suppress bad
                       speech themselves tend to cause or constitute harm.
                       Paradoxically, then, those most concerned about the
                       pernicious effects of bad speech ought to be
                       especially reluctant to call for its suppression.


                # ⚓ The Hindu ☛ Relationship_between_writer_and_society_should
                  not_be_one_of_censorship,_says_Geetanjali_Shree⠀⇛


                       Delivering the first M.R. Narayana Kurup memorial
                       lecture at Government College, Madappally, here on
                       Monday on ‘A writer’s responsibility’, the author
                       of Tomb of Sand ( Ret Samadhi) said writing, for a
                       writer, was as natural as breathing. “How can I
                       breathe when the atmosphere is so polluted? But I
                       have to find strategies to do it even in such a
                       condition,” she said, adding that censorship
                       crushed the story and limited knowledge and that
                       the curbs to freedom should come from within the
                       writer.


                       Ms. Shree explained, through several anecdotes, how
                       most people thought that writing was not a
                       profession that had something to covet, that
                       writing in a regional language was not necessary
                       when the writer was educated and were often
                       surprised to find an educated writer writing in his
                       or her mother tongue.


                # ⚓ EFF ☛ No_Nudity_Allowed:_Censoring_Naked_Yoga⠀⇛


                       One recent illustration is the censorship of True
                       Naked Yoga—a platform providing online naked yoga
                       videos. In August 2022, payment processor Stripe
                       banned True Naked Yoga, calling it a “restricted
                       business,” which contravened Stripe’s service
                       agreement. Stripe gave True Naked Yoga just four
                       days’ notice before the account was closed.


                       Stripe had reviewed the site in December 2021 and
                       did not flag any problems, nor did it give True
                       Naked Yoga any warning that the terms of service
                       had changed. The abrupt ban forced True Naked Yoga
                       to shut down for more than one month until it could
                       find a new payment processor.


                # ⚓ Salon ☛ Elon_Musk’s_censorship_spree_exposes_the
                  fundamental_flaw_in_the_right’s_definition_of_“free_speech”⠀⇛


                       The simplest explanation for Musk’s ever-more-
                       hilarious self-contradictory behavior as the new
                       boss of Twitter is that the man is a narcissist and
                       a hypocrite. Like his right wing brethren (no, his
                       politics are not “complicated”), Musk subscribes to
                       a “free speech for me, but not for thee”
                       philosophy, which of course means he never believed
                       in free speech at all.


                       But it’s worth digging a little deeper, because
                       this entire (extremely entertaining) debacle also
                       helps reveal quite a bit about the right wing
                       mythology around “free speech” that colonized
                       Musk’s mind. It goes further than plain old
                       hypocrisy and into the psychology of the right,
                       especially the self-serving tale of their own
                       alleged victimhood.


                # ⚓ Quillette ☛ The_Radicalization_of_the_Film_Canon⠀⇛


                       The winner of the 2022 critics’ poll, on the other
                       hand, raised more than a few eyebrows. Belgian
                       director Chantal Akerman’s 1975 film Jeanne
                       Dielman, 23 Quai du Commerce, 1080 Bruxelles is a
                       202-minute work of glacial minimalism, which
                       painstakingly dramatises the daily routine of a
                       middle-aged woman who earns money by selling
                       herself. It’s deeply admired by the few people who
                       have seen it, but it’s rarely discussed today. Even
                       its most ardent admirers would, I think, struggle
                       to argue that it has had a fraction of the cultural
                       impact of Vertigo or Citizen Kane. Dielman’s surge
                       from #36 in the 2012 poll to #1 in 2022 only really
                       makes sense as a political statement rather than an
                       assessment of artistic importance. This is, after
                       all, the first time that a film directed by a woman
                       has topped Sight and Sound’s poll, and the film’s
                       status as a feminist portrait of a sex worker
                       appears to meet the demand for a more progressive
                       canon, inclusive of previously marginalized voices.


                       This has led some observers to suspect that the
                       results had been massaged to produce a politically
                       desirable outcome. In a characteristically blunt
                       post on his Facebook page the day after the poll
                       results were published, the veteran American
                       screenwriter and director Paul Schrader spoke for
                       many skeptics when he wrote the following: [...]


                # ⚓ Meduza ☛ ‘Inappropriate_for_screening’:_Documentary_about
                  1920s_famine_released_online_after_Russia’s_Culture_Ministry
                  revokes_theatrical_license_—_Meduza⠀⇛


                       “Famine,” a new documentary film from the U.S.-
                       government-funded media outlet Current Time about
                       the famine that ravaged Russia in the early 1920s,
                       has been released on YouTube after the Russian
                       Culture Ministry revoked its theatrical
                       distribution certificate.


                # ⚓ Meduza ☛ ‘Murderers,_you_bombed_it_to_rubble’:_Graffiti
                  prompts_removal_of_St._Petersburg_display_celebrating_city’s
                  ‘brotherhood’_with_Mariupol_—_Meduza⠀⇛


                       A decorative display with two hearts — the greater
                       one inscribed “St. Petersburg,” and the one beside
                       it “Mariupol” — had to be removed from the Palace
                       Square, after a 16-year-old girl scrawled on it in
                       black paint: “Murderers, you bombed it to rubble.
                       Judases.”


                # ⚓ Meduza ☛ From_Jean_Genet_to_Sarah_Waters:_Moscow_libraries
                  told_to_‘recycle’_books_that_fail_‘LGBT_propaganda’_test_—
                  Meduza⠀⇛


                       Moscow libraries have received a government-issued
                       list of books that must be written off and
                       “recycled,” due to content that runs against the
                       grain of Russia’s new law against “LGBT
                       propaganda.” This information was published by the
                       journalist and literary critic Sergey Lebedenko, on
                       Telegram.


                # ⚓ Netblocks ☛ TikTok_restricted_in_Jordan_amid_fuel_price
                  protests⠀⇛


                       Network data confirm the restriction of social
                       video platform TikTok in the Hashemite Kingdom of
                       Jordan on multiple internet providers on Friday 16
                       December 2022. The incident comes amid protests
                       over high fuel prices which have spread to multiple
                       cities.


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


                # ⚓ Deutsche Welle ☛ Swedish_court_stops_extradition_of_Turkish
                  journalist⠀⇛


                       The court said there were “several hindrances” to
                       the extradition of Kenes, the former editor-in-
                       chief of the Zaman daily newspaper, including the
                       fact that some of the accusations against him are
                       not crimes in Sweden.


                       This, along with his refugee status and the
                       political nature of his case, made the extradition
                       impossible, it added.


                       “There is also a risk of persecution based on this
                       person’s political beliefs. An extradition can
                       thusly not take place,” Judge Petter Asp said in a
                       statement.


                # ⚓ Craig Murray ☛ Not_a_Fit_and_Proper_Person⠀⇛


                       After a two year process, the NUJ Executive have
                       finally rejected the renewal of my NUJ membership
                       based on social media posts I allegedly made which
                       they refuse to show me and of content and subject
                       of which I genuinely have not a clue.


                       But apparently these social media posts make me not
                       a fit and proper person to be a member of the NUJ.


                       Murdoch employees are fit and proper persons. The
                       Guardian journalists who produced the front page of
                       lies about Manafort meeting Assange are fit and
                       proper persons. The security service mouthpieces at
                       the BBC are fit and proper persons.


                       The NUJ even accepts for membership copywriters for
                       corporations working in PR companies. All these
                       people are fine.


                # ⚓ Don’t Extradite Assange ☛ Sakharov_award_ceremony_at_the
                  European_Parliament⠀⇛


                       Julian Assange was selected as one of three
                       finalists for the prestigious Sakharov Prize for
                       Freedom of Thought, awarded each year by the
                       European Union Parliament. More than 40 MEPs
                       nominated Julian Assange for this year’s Sakharov
                       Prize long list. Julian Assange’s wife Stella
                       Assange addressed a meeting in Brussels on Tuesday,
                       October 11th, in which she made the case for Julian
                       Assange winning the award.


                # ⚓ Eesti Rahvusringhääling ☛ Postimees_and_Õhtuleht_chiefs
                  expect_Eesti_Päevaleht_to_also_drop_Mondays⠀⇛


                       The editors-in-chief of two of Estonia’s leading
                       daily newspapers, Postimees and Õhtuleht, believe
                       that Eesti Päevaleht will eventually follow them in
                       opting not to publish paper editions on Mondays.
                       Postimees and Õhtuleht will discontinue their
                       Monday editions from January due to rising costs
                       announced by state-owned delivery service Omniva.


          o § Civil Rights/Policing⠀➾


                # ⚓ Meduza ☛ Sevastopol_court_gives_Russian_man_12-year_prison
                  sentence_for_alleged_spying_—_Meduza⠀⇛


                       A Sevastopol court has sentenced a Russian citizen
                       to 12 years in a high-security penal colony on
                       treason charges after finding him guilty of
                       gathering information for Ukrainian intelligence
                       services, Interfax reported on Monday, citing the
                       Russian FSB. The man, whose name is Yevgeny
                       Petrushin, was also reportedly fined 100,000 rubles
                       (about $1,480).


                # ⚓ Meduza ☛ Greek_citizen_arrested_in_Austria_on_suspicion_of
                  spying_for_Russia_—_Meduza⠀⇛


                       A Greek citizen whose father is a former employee
                       of the Russian General Staff and former diplomat
                       has reportedly been arrested in Vienna. The unnamed
                       man is suspected of spying for Russia and faces up
                       to five years in prison if convicted, Deutsche
                       Welle reported Monday.


                # ⚓ Scheerpost ☛ Scott_Ritter:_A_Lexicon_for_Disaster⠀⇛


                       Russia seeks arms control agreements to prevent
                       dangerous escalation. But the U.S. seeks only
                       unilateral advantage. This risks all out conflict
                       unless this changes.


                # ⚓ Counter Punch ☛ Changing_the_‘World_as_It_Is’_into_the
                  ‘World_as_it_Should_Be’⠀⇛


                       Over the past half-century, some of the most
                       prominent community organizing networks in the
                       United States — ranging from the Gamaliel
                       Foundation to Faith In Action to the Industrial
                       Areas Foundation, or IAF — have taught about this
                       divide as a key part of their introductory
                       trainings, using it as a means of orienting new
                       organizers to their approach to organizing. Over
                       the years, the framework has been invoked by Barack
                       Obama, Saul Alinsky and countless rank-and-file
                       organizers. For advocates of this concept,
                       understanding the “two worlds” dichotomy is
                       fundamental to developing the type of people who
                       can effectively produce change: namely, realistic
                       radicals.


                       So what is the origin of this idea? And why might
                       it be useful for us today?


                # ⚓ Common Dreams ☛ Dutch_Slavery_Apology_Dismissed_by_Black
                  Activists_as_‘Neocolonial_Belch’⠀⇛


                       While many activists welcomed Monday’s official
                       apology by Netherlands Prime Minister Mark Rutte
                       for his country’s 250-year history of enslaving
                       Africans, some Dutch advocates of African ancestry
                       called the gesture ill-timed and insufficient.


                       “For centuries, the Dutch state and its
                       representatives stimulated, preserved, and profited
                       from slavery,” Rutte, who represents the center-
                       right People’s Party for Freedom and Democracy,
                       declared during a speech in The Hague. “For
                       centuries, in the name of the Dutch state, human
                       beings were made into commodities, exploited, and
                       abused. For centuries, under Dutch state authority,
                       human dignity was violated in the most horrific way
                       possible.”


                # ⚓ Pro Publica ☛ Congress_and_Industry_Leaders_Call_for
                  Crackdown_on_Hospice_Fraud⠀⇛


                       Less than three weeks after ProPublica and the New
                       Yorker published an exposé of hospice fraud,
                       members of Congress have called on the Department
                       of Health and Human Services to “immediately
                       investigate this situation.”


                       In a letter sent Friday to the Centers for Medicare
                       and Medicaid Services and the Office of Inspector
                       General, the bipartisan leaders of the
                       Comprehensive Care Caucus wrote that “Medicare
                       fraud cannot be tolerated, especially when it is
                       being perpetrated on our nation’s most vulnerable
                       patients.”


                # ⚓ Democracy Now ☛ Morocco’s_Occupation_of_Western_Sahara_Is
                  at_Center_of_Growing_European_Parliament_Bribery_Scandal⠀⇛


                       A corruption scandal involving Qatar and Morocco is
                       rocking the European Union, with authorities in
                       Belgium earlier this month raiding the homes and
                       offices of multiple European Parliament lawmakers
                       for allegedly accepting bribes from the two
                       governments. The raids recovered hundreds of
                       thousands of euros in cash. Among those arrested
                       was European Parliament Vice President Eva Kaili,
                       who in the lead-up to the World Cup repeatedly
                       defended Qatar against critics. Ana Gomes, a
                       retired Portuguese diplomat who was a member of the
                       European Parliament from 2004 to 2019, says that
                       while the investigation was initially focused on
                       Qatar, “it looks more and more that Morocco should
                       be the center of the investigation.” We also speak
                       with Francesco Bastagli, a former United Nations
                       special representative for Western Sahara, who
                       notes that Morocco has cultivated a sophisticated
                       network of “friends” in Europe who have helped the
                       country in trade agreements and in gaining
                       acceptance for its illegal occupation of Western
                       Sahara.


                # ⚓ Democracy Now ☛ Judge_Orders_Philly_DA_to_Disclose_All
                  Evidence_in_Mumia_Abu-Jamal_Case._Could_It_Lead_to_New
                  Trial?⠀⇛


                       Supporters of imprisoned journalist Mumia Abu-Jamal
                       are celebrating a decision by a Philadelphia judge
                       on Friday to order the Philadelphia District
                       Attorney’s Office to share all of its files on the
                       case with Abu-Jamal’s defense team. Judge Lucretia
                       Clemons gave prosecutors and the defense 60 days to
                       review the files, including many that Abu-Jamal’s
                       team has never seen. The judge is then expected to
                       rule on whether to hold a new trial for the former
                       Black Panther, who has been imprisoned for over 40
                       years for his 1982 conviction in the murder of
                       police officer Daniel Faulkner. His supporters have
                       long claimed prosecutors withheld key evidence and
                       bribed or coerced witnesses to lie, and documents
                       found in the DA’s office in 2019 show Abu-Jamal’s
                       trial was tainted by judicial bias and police and
                       prosecutorial misconduct. For more on the case, we
                       speak with Johanna Fernández, an associate
                       professor of history at CUNY’s Baruch College and
                       one of the coordinators of the Campaign to Bring
                       Mumia Home. “We have enough evidence here to
                       clearly give Mumia at least an evidentiary hearing,
                       a new trial or set him free,” says Fernández. She
                       is the executive producer and writer of the film
                       “Justice on Trial: The Case of Mumia Abu-Jamal” and
                       is also the editor of “Writing on the Wall:
                       Selected Prison Writings of Mumia Abu-Jamal.”


                # ⚓ Techdirt ☛ Court_Reminds_St._Louis_City_Council_That
                  Blocking_Taxpayers_On_Social_Media_Violates_1st_Amendment⠀⇛


                       No matter what you may have heard on certain social
                       media outlets, this is how the First Amendment
                       actually works.


                # ⚓ Techdirt ☛ Independent_Journalist_Sues_Deputy_Who_Arrested
                  Him_For_Filming_Officers_Responding_To_A_Call⠀⇛


                       Maybe if enough cases pile into the federal court
                       system, the Supreme Court might decide to actually
                       establish a First Amendment right to record public
                       officials as they engage in their public duties.
                       Until then, we’re stuck with a patchwork of
                       precedent that recognizes this right only in
                       certain parts of the nation.


                # ⚓ Democracy Now ☛ As_Title_42_Nears_End,_El_Paso_Declares
                  Emergency_over_Influx_of_Asylum_Seekers⠀⇛


                       The Democratic mayor of El Paso, Texas, has
                       declared a state of emergency over concerns the
                       city won’t be able to provide shelter and resources
                       to the thousands of asylum seekers arriving at the
                       U.S.-Mexico border. This comes as the Biden
                       administration is expected on Wednesday to stop
                       enforcing Title 42, the Trump-era pandemic policy
                       that has been used by the U.S. government to block
                       over 2 million migrants from seeking asylum in the
                       country. Many asylum seekers now at the border are
                       sleeping outdoors in freezing temperatures while
                       the infrastructure to welcome them is sorely
                       lacking, says Fernando García, the founder and
                       executive director of the Border Network for Human
                       Rights based in El Paso. “This is what I consider
                       the perfect storm happening right now at the
                       border,” he says. “If we don’t have long-term
                       fixes, if we don’t have immigration reform fixing
                       the asylum process, which has been broken and
                       damaged by the previous administration, I think we
                       are going to continue seeing these crises.”


                # ⚓ TruthOut ☛ El_Paso_Declares_Emergency_Over_Influx_of_Asylum
                  Seekers_Amid_Freezing_Weather⠀⇛


                # ⚓ Common Dreams ☛ Chief_Justice_Grants_GOP_Request_to_Halt
                  End_of_‘Inhumane’_Title_42_Policy⠀⇛


                       In a move that outraged migrant rights advocates,
                       U.S. Supreme Court Chief Justice John Roberts on
                       Monday granted a request from 19 GOP-led states to
                       temporarily stop the Biden administration from
                       winding down the Title 42 policy used to swiftly
                       expel asylum-seekers during the Covid-19 pandemic.


                       “It’s an inhumane policy that misuses public health
                       to unjustly—and unlawfully—expel asylum-seekers.”


                # ⚓ TruthOut ☛ Israel_Deports_Palestinian_Human_Rights_Lawyer
                  Who_Sent_War_Crimes_Case_to_ICC⠀⇛


                # ⚓ TruthOut ☛ Zionism_Made_Hanukkah_About_Israel,_But_It’s
                  Always_Been_a_Holiday_of_Diaspora⠀⇛


                # ⚓ TruthOut ☛ House_Passes_Bill_to_Allow_Puerto_Ricans_to_Vote
                  on_Statehood_or_Independence⠀⇛


                # ⚓ TruthOut ☛ Over_25,000_People_in_Prison_Await_Decisions_on
                  Their_Clemency_Applications⠀⇛


                # ⚓ Counter Punch ☛ Kate_Brown_Finally_Finds_the_Courage_of_Her
                  Convictions⠀⇛


                       It’s not that Williamson supports the death
                       penalty. Unlike most “conservative” commentators,
                       he considers the outcome good. His complaint is
                       that “executive unilateralism of the sort being
                       practiced here by Gov. Brown is an invitation to
                       chaos.”


                       He does, in a minor way, support his claim. After
                       court decisions eviscerated the death penalty as
                       practiced, Oregon’s voters remedied the situation
                       with a constitutional amendment specifically
                       providing for its narrower use, and the legislature
                       has since tailored that use. “If Gov. Brown wants
                       to change the laws of Oregon,” Williamson opines,
                       “she should run for the state legislature.”


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ Zimbabwe ☛ Facebook’s_fiber_has_landed_in_South_Africa_and
                  it’s_the_world’s_longest_undersea_cable_at_45000km⠀⇛


                       Meta’s Facebook is joining the telecoms space and
                       they have decided to come out of the gates with the
                       longest undersea fiber optic cable at 45000km. To
                       make this all happen they formed the 2Africa group
                       which comprises other telecom operators. China
                       Mobile International, Djibouti Telecom, Meta
                       (Facebook), MTN GlobalConnect, Orange, Saudi
                       Telecom Company (STC), Telecom Egypt, Vodafone, and
                       WIOCC is the full list of the consortium.


                # ⚓ APNIC ☛ Why_kids_need_to_be_involved_in_Internet_governance
                  discussions⠀⇛


                       I see firsthand both the huge opportunities and
                       damaging effects of the Internet for kids. It can
                       be a huge enabler for education, it gives us access
                       to information for living, it connects us globally,
                       and it is also a place to advocate for ourselves
                       and share our voices.


                # ⚓ Common Dreams ☛ Tim_Berners-Lee_Wants_to_Enable_Internet
                  Users_to_Own_Their_Personal_Data⠀⇛


                       The creator of the World Wide Web is on a mission
                       to reinvent it and protect personal data from Big
                       Tech.


                       “I think the public has been concerned about
                       privacy—the fact that these platforms have a huge
                       amount of data, and they abuse it,” Tim Berners-
                       Lee, who developed the concept of the web in 1989,
                       told CNN on Friday. “But I think what they’re
                       missing sometimes is the lack of empowerment. You
                       need to get back to a situation where you have
                       autonomy, you have control of all your data.”


          o § Monopolies⠀➾


                # ⚓ India Times ☛ EU_warns_Meta_over_Facebook_Marketplace
                  antitrust_breach⠀⇛


                       The European Commission on Monday said it has
                       warned Facebook parent company Meta that it is
                       breaching EU antitrust laws by distorting
                       competition in markets for online classified
                       advertising and abusing its dominant position.


                       The Commission said in a preliminary view that it
                       would further investigate and that it could impose
                       a fine of up to 10% of the company’s annual global
                       turnover, if there is sufficient evidence of an
                       infringement of European Union rules.


                # ⚓ India Times ☛ Twitter_bans_all_links_to_FB,_Insta,_Mastodon
                  &_other_rivals_on_its_platform⠀⇛


                       The company said that it will remove accounts
                       created solely for the purpose of promoting other
                       social platforms and content that contains links or
                       usernames for the following platforms: Facebook,
                       Instagram, Mastodon, Truth Social, Tribel, Nostr
                       and Post.


                       Twitter will still allow cross-posting content from
                       any social media platform.


                # ⚓ Counter Punch ☛ Corporate_Monopoly_Power:_a_Main_Driver_of
                  Inflation⠀⇛


                       Large U. S. multinational corporations are,
                       however, major drivers of inflation by price
                       gouging.  An analysis by the House Subcommittee on
                       Economic and Consumer Policy included these
                       findings between 2019 and 2021:


                       According to Rakeen Mabud, chief economist and
                       managing director of policy and research at the
                       Groundwork Cooperative, 3


                # § Patents⠀➾


                      # ⚓ Teen Vogue ☛ The_Artificial_Christmas_Tree_Was
                        Invented_By_Jewish_World_War_II_Pilot_Si_Spiegel⠀⇛


                             But things didn’t go as planned. After a
                             string of legal patent challenges, design
                             flaws, and competition, American Brush
                             Machinery was ready to give up. “When they
                             didn’t do too well and wanted to close up,”
                             said Spiegel in an interview with the New
                             York State Military Museum, “I asked them to
                             let me run it.” So, the higher-ups gave him a
                             shot.


                             Spiegel decided to take a different approach.
                             He brought in real trees to study and then
                             made corresponding tweaks to the brush
                             machines. With more tinkering, Spiegel
                             eventually crafted the perfect artificial
                             tree that was set to take over American
                             homes. And with the influx of plastic
                             products following World War II, Spiegel had
                             the right materials to make his vision a
                             reality.


                # § Copyrights⠀➾


                      # ⚓ Walled Culture ☛ How_to_redeem_big,_bad_music
                        streaming_so_that_it_serves_artists,_fans_–_and_local
                        communities⠀⇛


                             Music streaming services are great – for
                             listeners, who gain access to huge quantities
                             of music, even if they don’t end up owning
                             any of it. But it’s hardly a secret that
                             streaming services produce very little income
                             for the musicians involved – even the big
                             names earn a pittance – with most of the
                             money ending up with the recording companies.
                             That doesn’t mean that streaming services are
                             beyond redemption. It just requires a little
                             imagination to think of ways in which they
                             can be great for artists and audience alike.
                             Take this idea, for example, reported on
                             Vice: [...]


                      # ⚓ Vice Media Group ☛ Libraries_Are_Launching_Their_Own
                        Local_Music_Streaming_Platforms⠀⇛


                             That prototype has become the open source
                             program MUSICat, which is now being used by a
                             number of libraries in North America. Artists
                             whose music is included in one of the local
                             streaming collections are paid an honorarium
                             of at least $200 per licensed album. That
                             means they get money up front, not in barely
                             visible dribs and drabs over years, as with
                             the mainstream streaming services.


                      # ⚓ Torrent Freak ☛ UK_Govt:_Netflix_Password_Sharing_is
                        Illegal_&_Potentially_Criminal_Fraud⠀⇛


                             The UK Government’s Intellectual Property
                             Office published new piracy guidance today,
                             and it contains a small, easily missed
                             detail. People who share their Netflix,
                             Amazon Prime, or Disney+ passwords are
                             violators of copyright law. And it gets
                             worse. The IPO informs TorrentFreak that
                             password sharing could also mean criminal
                             liability for fraud.


                      # ⚓ Creative Commons ☛ Patrick_J._McGovern_Foundation
                        Funds_New_CC_Initiative_to_Open_Large_Climate
                        Datasets⠀⇛


                             Today, Creative Commons (CC) is excited to
                             announce one million US dollars in new
                             programmatic support from the Patrick J.
                             McGovern Foundation (PJMF) to help open large
                             climate datasets. The twelve-month grant will
                             enable CC to conduct key climate data
                             landscape analyses and expand our work,
                             bringing people together to create policy and
                             practices to open data that advances climate
                             research and innovation.


                      # ⚓ Creative Commons ☛ CC_Publishes_Global_Open_Culture
                        Call_to_Action_to_Policymakers⠀⇛


                             Today, we are proud at CC to announce the
                             publication of Towards better sharing of
                             cultural heritage — A Creative Commons Call
                             to Action to Policymakers, a simple, concise,
                             and accessible resource that aims to support
                             policymakers with key arguments to reform
                             policy — in particular copyright — to achieve
                             better sharing of cultural heritage in the
                             public interest. 


                      # ⚓ Techdirt ☛ Can_AI_Text_Writers_Help_People_Impacted
                        By_Copyright_Law_To_Better_Weigh_In_On_Copyright?⠀⇛


                             One of the reasons that copyright is so
                             unbalanced in favor of companies, especially
                             Big Content, is that the process of bringing
                             in new copyright laws is hard for ordinary
                             members of the public to engage with.
                             Typically, new laws come about after
                             government consultations. Although these are
                             public in the sense that they are not secret,
                             and anyone can take part, their questions and
                             format are at best intimidating, and at worst
                             incomprehensible for ordinary people.


    * § Gemini* and Gopher⠀➾


          o § Personal⠀➾


                # ⚓ 🔤SpellBinding:_ETGIOSF_Wordo:_SAWED⠀⇛


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


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