𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Saturday, July 30, 2022
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Generated Sun 31 Jul 02:39:39 BST 2022
Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖)
Full hyperlinks for navigation omitted but are fully available in the originals
The corresponding HTML versions are at 𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈
Latest in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕 and older bulletins can be found at 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕-𝒂𝒓𝒄𝒉𝒊𝒗𝒆𝒔
Full IPFS index in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔 and as plain text in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔/𝒕𝒙𝒕
Gemini index for the day: gemini://gemini.techrights.org/2022/07/30/


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

QmP3Nw5usXTHPhcMx8yZ9TYsWzwSKRw9BNnbjhkoJ88gpe
QmNt7g1pzLJJDE5MHZ21wEEuyos1W3DFP2LTSjB2FLPJPi
QmXniW6uykwhxPzQFCih3ywbRTbNtozdD9MTkKJWNUUis7
Qmba4Ap4JVU96TSWT1jJZfQAasTyweA1EFu92C6ULqfYVF
QmQDNYLCxwvKJsAAbaMfkydsH6iMivVs54xVt3e1WhRa4V
QmZrgDSeEPr5Tk1kd6ixcTH5gK8gVF6UWZ8USDWkwExtL2
QmdVCZ22xUbZkpsSDmSDMrnFTMypCGWw1f2punvumLq2NJ
QmXJTu6CfqTRzBWfbZAfQFS2Je8PJA65YsoWMZp6Z3WV8Z
QmXptQogxzP3vUxmf2ttL7Vyb5aAwUT9Ux3nmXxPkuNRNp
QmYTKahqtmH46iM3ZthdPvDKojc39tpTCiyk2GGs8Y29DU
QmRRSvTcmYGSSCvpvxz5PTAHRT4fdRHip9uhxwcQXMWp9G
QmQpoFyQcBb3KsKSZ3VzsMZsMmgcTqXq1zThATBh2bp3Yp
QmZrQzFnwRoF6P9gTMQfqokg7GSmtCyoyEMWxV7jZxDsZn
QmRgX3FU5tqoWu74D2LUMC84rvb5VBXutGnvudD9rbAAgn
QmNocWiFPVNdoZoPJy1s4vZQryq4BWRJMou5WsNScHuuMt
QmWkLbREwUBZdex6qeeh1UyUD3GwnNihMfEE28VhuPZYAK
QmUmo6iUYY6LPz7rMxVJXtYjzryXZaVK76GtZjE3wXnAbk
QmTcjQcpQmc33H6tVYxaBQP4SYQnHTEnFzA1HJRmbELhh3
Qmd5sSa6zctA8RcuhbgaMD5PKt4K2aGr7vwBWUT9GrkoLL
QmXggz4ZzdoNrnyGD87xZXV7EnECHikMc7N5PUE6qSiZ7Y
QmcHk17nfvFbsgxkAzX3fqiG6CVs1EHd6jwajhUb1wWHkg


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

⦿ IRC Proceedings: Friday, July 29, 2022 | Techrights

⦿ Goodbye to Unnecessary Bloat (We’re Getting There!) | Techrights

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
		http://techrights.org/2022/07/30/irc-log-290722/#comments
		http://techrights.org/2022/07/30/unnecessary-bloat/#comments

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
		http://techrights.org/2022/07/30/4mlinux-40-released/#comments
		http://techrights.org/2022/07/30/links-30072022-easyos-4-3-graft-for-hardware-giants/#comments

                    ䷩ 𝚕𝚒𝚗𝚎 51

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/07/30/irc-log-290722/#comments
    Gemini version at gemini://gemini.techrights.org/2022/07/30/irc-log-290722/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.30.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ IRC_Proceedings:_Friday,_July_29,_2022⠀✐


Posted in IRC_Logs at 2:06 am by Needs Sunlight


Also available via the Gemini protocol at:


    * gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-290722.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-290722.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-social-290722.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-290722.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
 QmSU1UzGUtZeE3NBaUA6MVBMQkfQprFcLZ5sMSZc85kX5b #boycottnovell  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell
 QmREV3CsKVj3E6puZCcc7GWeERfpt6J3MVBA1DUbJAmj1R (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
                                                 #boycottnovell-
 QmbuCVaK9hafZuoV4nz6GXRqTFmdtpzmQBw3xL52rXR1FR social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell-
 QmTYFJdUPqjeoGih7jcJMcsdS4vWUZN763WLDtnNZQX2eU social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 (full IRC log
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 QmSmdRTsZsb3zGrpqFAn2Hhb94Pk8cyzFtBDr7Pc8FKHSS #techbytes      🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techbytes
 QmPDCQoWhUY382gb9BAUYRhZccLS5XoscX6fbyx9iTGvpT (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 QmR87wzdDNyCpuPSp7sypvRQS6RPei7oTbB1RzPm8UefR6 #techrights     🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techrights
 QmWMtApq7Fa4LiugKXdFDpzPapdGkrYiLeP4igP3Dh8ieQ (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈


§ Bulletin for Yesterday⠀➾


Local_copy | CID (IPFS): QmcHk17nfvFbsgxkAzX3fqiG6CVs1EHd6jwajhUb1wWHkg



                    ䷩ 𝚕𝚒𝚗𝚎 178

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/07/30/unnecessary-bloat/#comments
    Gemini version at gemini://gemini.techrights.org/2022/07/30/unnecessary-bloat/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.30.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Goodbye_to_Unnecessary_Bloat_(We’re_Getting_There!)⠀✐


Posted in Site_News at 8:38 pm by Dr. Roy Schestowitz


Video_download_link | md5sum 143e801136254f28e3b384afae31a7be
Progress on Moving the Sites
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/migration-to-static-sites.webm


Summary: In an effort to reduce complexity and lessen the technical debt we’ve
developed our content management system (CMS), which now has some rudimentary
support for images and file uploads


THIS weekend has been somewhat of an exception in the sense that it was mostly
about organisation and maintenance (upgrades, backups, development). We’ve made
further strides towards taking the sites “static”, serving requests from
prepared files rather than querying the databases. It’ll be a long journey
given the sizes of the sites in question (about a quarter million pages in
total), but that needs to be done to secure the sites’ future and lower the
complexity of maintaining them.


“Some of us just want to deliver text to people without all this unnecessary
overhead.”The summer months are generally slower (less news, a lot fewer
announcements are made), so we’re hoping to be finished with the lion’s share
of migration by the end of August. European Patent Office (EPO) affairs are of
strategic importance to us (tacking software_patents_in_Europe and EPO
corruption in general), but also have two series about Microsoft running at the
moment. We’ve paced them down for improved if not maximal impact.


The video above explains what we’ve been up to so far this weekend and then
resorts to the typical rants about the World Wide Web and the state of Web
browsers. The bloat is a mutual relationship between Web ‘standards’ (like
DRM), Web sites, and Web browsers. Bloat in the CMS sense contributes to this
too. Some of us just want to deliver text to people without all this
unnecessary overhead. The operating system we’re moving to is Alpine. It should
be absolutely fine for most sites, Git repositories, IRC networks and so on.
It’s minimalist and reliable. █


                       🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇EME_and_W3C⦈_


                         🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Web_2030⦈_


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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠤⣶⣶⣴⣷⢷⣶⣤⣻⣶⣾⣭⣽⣿⣴⣶⣿⣿⣾⣾⣿⡶⢶⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢁⣀⠀⢀⠀⠀⣒⢡⠆⠀⠀⠀⠀⣀⣠⣀⡀⠀⣤⣤⣄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠊⢛⣿⠟⠛⠈⠛⡛⠛⠙⠚⡟⠛⠿⣿⡿⠿⣿⣿⠟⠛⠋⡙⠻⠂⢊⣁⣠⣶⣿⣿⣿⣿⣿⣿⣟⣉⣶⣶⣶⣿⣿⣴⢂⣺⣷⣶⣤⠠⠶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡀⠈⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀
⠏⠍⢛⡀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢩⣤⣶⣤⣤⣀⣠⣰⢎⣰⣤⣼⣿⣿⣿⣿⣿⣿⡿⠛⠒⢃⣀⣉⣿⣿⣿⣿⣷⣷⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣂⠀⣠⣀⣀⣭⣧⣤⣤⡐⠀
⠀⢤⣵⣆⠀⠀⠀⠀⠀⠀⠀⣤⣿⣵⣿⣿⣿⣿⣿⣿⡧⣖⣾⣿⣿⣿⣿⣿⣿⣿⣉⣥⡄⢐⣲⣿⣿⣿⣿⣿⣿⡏⠟⣏⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠍⣅⢭⣝⠻⠟⠻⠿⠏⠹⠯⢰
⠚⠋⠃⠂⠠⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣛⣿⣧⣬⣽⣿⣿⣿⣿⣿⡿⠛⠛⠛⠻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣷⠷⡟⢟⣿⣿⡷⣫⣿⣿⣿⠿⢿⣟⣿⣿⣽⣿⠏⠛⠹⠿⠷⠎⠁⠐⠓⠋⠀⠀⠂⠀⠀⠀⠑
⠠⠴⣶⡴⢀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣯⣽⣭⣤⣤⣤⣴⣶⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⣝⣓⢃⣸⣿⡟⣿⡏⠋⠛⠙⠀⠛⠺⢻⢅⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠈⠁⠃⠀⠈⣰⢀⣾⣿⣿⣯⣿⣮⣻⣿⣿⡛⠋⠸⣿⢿⣿⣿⣿⣿⣿⣯⣏⠉⢻⣻⡞⠟⢹⣿⣿⣿⣿⣿⣿⣿⢯⣽⠿⠟⢳⡿⠭⠋⠁⠀⠀⠀⣠⣤⣶⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀
⠀⡀⠀⠀⠀⣻⣶⠿⠍⢢⡈⠩⠏⡈⢅⠀⠁⠀⠉⠉⠛⣟⢯⠘⠻⠫⢿⠁⠀⠂⠀⠀⠀⠀⠿⠿⣿⣿⣿⢿⠟⡨⢊⡂⣐⣼⡲⠚⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀
⣿⣶⣶⣤⣴⣿⣯⣿⣷⣦⣶⣞⡉⠬⢲⢥⣤⠀⠀⣐⣌⠀⠀⠀⠀⡀⠀⠄⣄⣀⡀⠑⢒⠚⣤⣭⣿⣿⡿⠹⠃⢀⠄⠐⠫⣻⣅⠀⠀⠀⠀⠀⠀⠈⠋⠉⠁⠀⠀⢈⠽⡀⠀⢐⡀⠀⠀⠀⠀⠀⠀⠠⣶⣷⣶⣽⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣴⡈⣠⣤⣄⣴⣾⣼⣿⣾⣯⣷⡛⡳⠿⠛⡗⢘⢻⡶⠄⠤⠒⠻⠅⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⣠⣤⣶⣿⣿⣾⣿⣶⡤⠀⠐⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣭⣾⠿⣥⣲⣾⣿⣿⣼⣿⣿⣇⠈⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣘⣿⣿⣿⣿⠙⠿⣿⡇⢽⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠫⠙⣿⡶⣻⣾⡾⠃⠀⠀⠁⠀⠀⠀⠀⠀⣀⡠⡤⢿⣿⣿⡟⡄⠀⢹⡇⠀⢸⣿⣿⣿⣟⡿⠏⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⠓⠛⠁⢖⣷⡅⠀⣠⡀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣾⣿⣿⣿⣷⠀⠘⣷⠀⢸⢿⣿⡿⠯⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⢀⠈⢺⣿⣣⣖⠐⠆⡀⠀⠀⠀⠀⠀⠀⠘⣿⠿⢿⣿⣿⣿⣧⡀⣸⠁⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⢿⠿⠃⠀⠁⠁⢷⠬⢾⠷⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⣠⣿⣿⣿⣿⣧⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠙⠛⠉⠙⠛⠋⠉⠛⠛⠁⠀⠁⠀⠈⠙⠉⠉⠉⠉⠀⠓⡳⠁⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⢿⣵⣷⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠀⠀⠀⠀⠀⠀⠄⠒⠀⠐⠂⠀⠀⠀⠀⠀⠄⠀⠀⢠⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⡀⢀⡧⡿⢽⣿⣧⢲⣶⣶⡶⣶⣤⣤⣤⣤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⡤⡯⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣀⡄⢀⠀⠀⠀⠀⠀⠀⠸⠿⠛⠛⠉⠁⠀⠀⠀⠈⢋⢟⣯⣿⣿⣿⡷⣺⣶⣿⣭⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠀⠀⠀⠀⠄⠂⠈⠀⠀⢂⣤⠐⠂⠀⠀⠀⠀⡘⣿⣿⣨⣵⣶⡖⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣀⡀⣼⣿⣿⣿⣿⣿⣭⣭⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠐⠛⢿⡿⠛⡛⠛⠋⠀⠀⠀⠀⢀⣰⣦⠀⠙⠻⠟⠃⠀⠄⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣟⣿
⠀⠀⠀⠂⠀⢀⢐⢁⣀⣄⡀⡀⣄⡰⣒⣖⣲⣷⣦⣦⣄⡦⡈⠙⠀⢠⢠⣼⣆⣀⣀⣀⣔⣀⡇⠀⢀⢄⡀⠀⠀⡠⠤⠖⠉⠆⠽⠕⠀⠀⠀⠀⠀⠀⣀⣁⣥⣷⡤⠀⠒⢀⠂⠀⠘⠛⠻⠿⢿⣛⣛⣟⣿⣿⣷⣿⣿⡷
⠀⠀⡀⠀⡪⠬⣿⡿⣿⣾⣧⣿⣿⣿⣿⣷⣿⣿⡿⣿⣿⣟⡁⣔⠀⢀⣸⡿⠉⠉⠉⠐⠒⠐⠀⠀⠀⠀⠀⠀⠈⠁⢉⢈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣶⣶⣶⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠀⠀⠀⢠⣙⠹⣏⣿⣿⢺⣿⣿⡿⣯⣿⠾⠇⠛⠛⠻⠟⠉⠁⠼⡿⠷⠶⠶⣶⠷⠶⠾⢷⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⡿⠿⢿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⢆⣅⠲⠿⠙⠈⢠⡖⢓⠟⠀⣿⣿⡆⣿⣿⣇⣸⣿⡟⣿⣿⣿⣿⢸⣿⣿⣿⣷⣎⣿⣿⣳⣿⡿⣿⣿⡛⣿⣿⢿⣿⣮⢱⣿⣿⢿⣿⡞⢿⣿⡿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠁⠀⠀⠠⠰⠀⠀⠐⠀⠀⠀⠀⠀⣈⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣂⢸⣿⣿⣸⣿⡿⣴⣿⣛⣛⢣⣿⣿⢳⣿⣿⢸⣿⣿⢸⣟⣿⣼⣿⠏⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⣿⣿⣿⢿⣿⣿⣿⠃⣿⣿⡿⢿⢸⣿⣿⢻⣿⣷⢩⣿⣿⣣⣿⣿⠯⣾⣿⣿⢸⣿⣿⢸⣯⣿⢻⣿⣧⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣧⣭⢸⣿⣿⣼⣿⣿⣸⡿⣳⣿⣿⣥⣤⠈⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⡿⢸⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡛⣛⣋⣠⣿⣻⣫⣤⣿⣿⣿⣿⣼⣿⣻⣿⣿⣽⣿⣿⣛⣿⣿⣿⣻⣾⣮⣿⣟⣿⣷⣶⣽⣿⣿⣿⣿⣿⣽⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠶⣶⠏⢶⠆⠰⠶⠶⠶⠀⣤⣤⣤⣤⡀⢀⠀⢙⣋⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡤⣶⣶⣶⣶⣷⣶⣤⣻⣶⣾⣽⣿⣿⣼⣾⣿⣿⣿⣿⣿⡶⣷⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢁⣄⠄⠀⠀⣠⣁⣱⡦⡀⠀⠀⡀⣄⣤⣤⡄⠀⣦⣴⣄⠀⠀⠀⢀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢚⣻⣿⠟⠻⠈⠛⠛⠻⠙⠚⡟⢛⠿⣿⡿⠿⣿⣟⠿⠛⠋⣙⠻⠂⢊⣁⣠⣶⣿⣿⣿⣿⣿⣿⣟⣉⣶⣶⣿⣿⣿⣶⢒⣿⣿⣶⣶⠢⢻⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠈⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀
⠏⠝⢛⡀⠀⠀⠀⠀⠐⠀⠀⢀⣤⢩⣤⣷⣤⣬⣤⣦⣰⣎⣶⣬⣽⣿⣾⣿⣿⣿⣿⡿⠛⠒⢋⣀⣉⣿⣿⣿⣿⣷⣷⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣢⠀⣀⣀⣐⣿⣧⣤⣴⡔⠂
⠀⢤⣵⣖⠄⠀⠀⠀⠀⠀⠀⣴⣿⣵⣿⣿⣿⣿⣿⣿⡧⣖⣾⣿⣿⣿⣿⣿⣿⣿⣉⣥⡄⢐⣲⣿⣿⣿⣿⣿⣿⡏⠟⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠭⣅⣯⣽⠻⡟⢿⡿⠏⠻⠯⢠
⠚⠛⠃⠒⠤⠀⠀⠀⠀⢀⣺⣿⣿⣿⣿⣿⣿⣻⣿⣧⣮⣿⣿⣿⣿⣿⣿⡿⠛⠛⢛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠶⣿⣟⣿⣿⡿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣽⣿⠿⠿⠹⡿⠷⠎⠁⠘⠛⠋⠁⠀⠂⠀⠀⠀⠓
⠀⠴⣶⣦⢀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣯⣽⣭⣥⣤⣤⣴⣶⢾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣇⢠⣝⣓⢇⣸⣿⣟⣿⡓⠋⠛⠙⠀⠙⠻⡻⣔⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠂
⠈⢁⠓⠈⠈⣰⢀⣾⣿⣿⣿⣿⣯⣽⣿⣿⣟⠋⠸⣿⢿⣿⣿⣿⣿⣿⣿⣏⠋⢻⣿⡿⡟⢹⣿⣿⣿⣿⣿⣿⣿⠯⣿⠻⣟⡻⣿⠭⠋⠁⠀⠀⢀⣠⣴⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀
⠁⣄⠀⠀⠀⣻⣶⠿⠍⢳⡨⠩⠇⡀⢅⠀⠁⠀⠩⠉⠛⣛⢿⠚⠻⠯⡿⠁⠀⠂⠀⠀⠀⠀⠿⠿⣿⣿⣿⢿⡟⡬⢛⡂⣐⣼⡿⠚⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀
⣿⣶⣶⣴⣴⣿⣯⣿⣷⣦⣾⣾⡉⠬⢳⢥⣤⠀⠀⣐⣌⠀⠀⠀⠀⡀⠠⠄⣄⣀⡀⠑⢒⡺⣦⣭⣿⣿⡿⠹⠣⢀⠄⠐⠫⣻⣅⠄⠀⠀⠀⠀⠀⠈⠋⠉⠁⠀⠀⢘⠽⣀⡀⢐⡀⡀⠀⠀⠀⠀⠀⠠⣶⣷⣶⣿⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣴⡊⣠⣤⣤⣴⣾⣼⣿⣾⣯⣿⡛⣿⠿⠛⡗⣘⢻⡾⠇⡤⢒⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⣠⣤⣶⣿⣿⣾⣿⣷⣥⠄⠰⢾⣷⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣾⠯⣥⣶⣾⣿⣿⣾⣿⣿⣇⡈⠀⢀⡀⠀⠀⠀⠀⠀⠀⢈⣘⣿⣿⣿⣿⠹⠿⣿⣇⢽⣿⣿⣿⣿⣿⣿⣽⣿⡟⠋⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠫⠙⣿⡷⣿⣾⡞⠃⠀⠈⠁⠀⠀⠀⠀⠀⣀⡠⡤⢿⣿⣿⡟⡄⠀⢹⡇⠀⢸⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⠓⠛⠑⢾⣷⡅⠀⣠⡄⠀⠀⠀⠀⠀⠀⣀⣤⣤⣾⣿⣿⣿⣷⠂⠘⣷⠀⢸⢿⣿⡿⡯⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⢀⠈⢺⣿⣫⣿⠲⠄⡀⠀⠀⠀⠀⠀⠀⠘⣿⠿⢿⣿⣿⣿⣧⡀⣸⠁⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⢿⠿⠃⠀⠁⠁⣷⠬⣾⠷⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⣬⣿⣿⣿⣿⣧⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠙⠛⠉⠙⠛⠋⠉⠛⠛⠁⠈⠁⠀⠈⠙⠉⠉⠉⠉⠀⠓⡷⠁⠀⠀⠀⠈⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⢿⣵⣷⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡉⠙⠉⠀⠀⠀⠀⠀⠀⠄⠒⠀⠐⠂⠈⠀⠀⠀⠀⠄⠀⠀⢠⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡀⢀⡧⡿⢷⣿⣧⣶⣶⣶⡶⣶⢤⣤⣴⡦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠠⡤⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣀⡄⢀⠀⠀⠀⠀⠀⠀⠸⠿⠟⠛⠋⠁⠀⠠⠀⠈⢋⢟⣯⣿⣿⣿⡿⣺⣶⣽⣽⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠐⠀⠀⠀⠀⡀⠄⠂⠈⠀⠀⢢⣤⠐⠒⠀⠀⠀⠀⡘⣿⣿⣬⣵⣶⡖⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⠀⠀⠀⣠⡀⣼⣿⣿⣿⣿⣿⣭⣭⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠐⠛⢿⡿⠛⡙⠛⠋⠀⠀⠀⠀⢀⣸⣧⠀⠙⠻⠟⠃⠀⠄⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣟⣿
⠀⠀⠀⠂⠀⢀⢰⢄⣂⣄⡀⡠⣔⣲⣺⣾⣲⣷⣦⣦⣄⡦⡈⠙⠀⢠⢠⣼⣦⣀⣀⣴⡆⣒⡇⠀⢀⢀⡀⢀⡀⠠⣤⡏⠙⠆⠿⠕⠀⠀⠀⠀⠀⠀⣀⣉⣭⣷⡦⠠⠒⢀⠂⠀⠘⠛⠿⠿⢿⣛⣛⣟⣿⣿⣷⣿⣿⡷
⠄⠀⡀⠀⡚⠬⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⡿⣿⣿⣟⡉⣔⠁⢀⣸⡿⠉⠉⠉⠐⠒⠒⠀⠀⠀⠀⠀⠀⠈⠉⠉⢊⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣶⣶⣶⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠀⠀⠀⢠⣙⠻⣏⣿⣿⢺⣿⣿⡿⣿⠿⠾⠓⠛⠛⠻⠟⠋⠃⠾⡿⠷⠷⠶⢶⣶⠶⠶⢿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡿⠿⢿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⠀⠀⠀⠀⠐⢖⣅⡳⠿⠝⡈⢠⡖⢣⠟⠀⣿⣿⡆⣿⣿⡇⣸⣿⡟⣿⣿⣿⣿⢸⣿⣿⣿⣿⣎⣿⣿⣳⣿⡿⣿⣿⡛⣿⣿⢿⣿⣮⢱⣿⣿⢿⣿⡿⢿⣿⡿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠁⠀⠀⠠⠴⠀⠉⠐⠀⠀⠀⠀⠀⣈⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣢⢸⣿⣿⣸⣿⡿⣴⣿⣛⣛⢣⣿⣿⢳⣿⣿⣼⣿⣿⢸⣿⣿⣼⣿⠏⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⣿⣿⣿⢿⣿⣿⣿⠃⣿⣿⡿⣿⢸⣿⣿⢻⣿⣷⢩⣿⣿⣣⣿⣿⠿⣾⣿⣿⣸⣿⣿⢸⣯⣿⢻⣿⣧⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣧⣭⢸⣿⣿⣼⣿⣿⣸⡿⣷⣿⣿⣥⣤⠌⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⣿⢸⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠛⣛⣋⣬⣻⣛⣏⣤⣿⣿⣿⣿⣼⣿⣿⣿⣿⣽⣿⣿⣛⣿⣿⣿⣻⣾⣮⣿⣟⣿⣷⣶⣽⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠶⣶⠯⢶⠦⠰⠶⠶⠶⠀⣤⣤⣤⣤⡄⢀⡀⢛⣋⣛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡤⣶⣶⣾⣶⢷⣶⣤⣻⣶⣾⣭⣯⣿⣼⣾⣿⣿⣾⣿⣿⡶⣷⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢁⣄⠀⠀⡀⣄⣛⠻⠦⠀⠀⠀⢀⡀⣤⣤⡀⠀⣤⣤⣤⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢊⣛⣿⠟⡟⠀⠛⡛⠻⠝⠚⡟⢛⠿⣿⡿⢿⣿⣟⠿⡛⠋⣙⠻⠂⢊⣁⣤⣶⣿⣿⣿⣿⣿⣿⣟⣁⣶⣶⣷⣿⣿⣶⢒⣻⣿⣷⣦⠪⢿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⠈⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀
⠏⠝⢛⡀⠀⠀⠀⠀⠐⠀⠀⢀⣄⢩⣤⣷⣤⣤⣤⣦⣸⣎⣴⣬⣽⣿⣿⣿⣿⣿⣿⡿⠟⠓⣋⣀⣉⣿⣿⣿⣿⣷⣷⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣂⠀⣀⣀⣐⣯⣧⣤⣴⣔⠀
⠀⢤⣵⣖⠄⠀⠀⠀⠀⠀⠀⣴⣿⣵⣿⣿⣿⣿⣿⣿⣧⣖⣾⣿⣿⣿⣿⣿⣿⣿⣋⣤⡄⢐⣲⣿⣿⣿⣿⣿⣿⡏⡟⣟⣟⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠭⣇⢯⣽⠻⠟⡻⡿⠏⠻⠯⢠
⠚⠋⠃⠂⠤⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣻⣿⣷⣬⣿⣿⣿⣿⣿⣿⡿⠛⠛⢛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⠶⡿⢟⣿⣿⡿⣯⣿⣿⣿⣿⠿⣿⣿⣿⣽⣿⠿⠻⠹⡿⠷⠎⠁⠘⠓⠋⠁⠀⠂⠀⠈⠀⠑
⠀⠴⣶⡶⢀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣯⣽⣭⣥⣤⣤⣴⣶⢾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣇⢠⣝⣛⣃⣸⣿⡟⣿⡟⠋⠋⠉⠀⠛⠻⣻⣜⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂
⠈⠁⠓⠊⠈⣰⢀⣾⣿⣿⣿⣿⣯⣻⣿⣿⣛⠋⠸⣿⢿⣿⣿⣿⣿⣿⣿⣍⠋⢻⣿⡾⡟⢹⣿⣿⣿⣿⣿⣿⣿⠯⢿⠿⢿⣻⡿⠭⠋⠁⠀⠀⠀⣠⣴⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀
⠁⣄⠄⠀⠀⣻⣶⠿⠍⢳⡬⠩⠇⠀⢅⠀⠁⠀⠫⠉⠛⣟⢿⠘⠿⠿⡿⠁⠀⠂⠀⠀⠈⠀⠿⠿⣿⣿⣿⢿⡟⡌⢚⡂⣰⣿⡷⠚⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡠
⣿⣶⣶⣤⣴⣿⣯⣿⣷⣦⣶⣾⡙⠬⢳⢥⣤⠀⠀⣐⣌⠀⠀⠀⠀⡀⠠⠄⣄⣀⡀⠑⢒⡺⣦⣭⣿⣿⡿⠹⠧⢁⠄⠚⠉⣿⣅⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⢈⠿⡀⠀⢐⡀⠀⠀⠀⠀⠀⠀⠠⣶⣷⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣴⡊⣠⣤⣄⣼⣾⣼⣿⣾⣯⣿⡻⣿⠿⠛⡗⣙⠻⡾⠇⠤⣒⡻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⣠⣤⣶⣿⣿⣾⣿⣷⣦⠄⠴⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣭⣾⠿⣥⣶⣾⣿⣿⣾⣿⣿⣇⡈⠀⢀⡀⠀⠀⠀⠀⠀⠀⢈⣹⣿⣿⣿⣿⠹⠿⣿⣇⢽⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠫⠙⣿⣶⣻⣾⡾⠃⠀⠀⠁⠀⠀⠀⠀⠀⣀⡠⡤⢿⣿⣿⡿⡄⠀⢹⡇⠀⢸⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠛⠛⠑⢿⣷⡅⠀⣠⡀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣾⣿⣿⣿⣷⠂⠘⣷⠀⢸⢿⣿⡿⡯⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⢀⠈⢿⣿⣷⣾⠖⡆⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⢿⣿⣿⣿⣦⡀⣼⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⢿⠿⢃⠀⠁⠁⢷⠭⢾⠿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⣨⣿⣿⣿⣿⣧⣿⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠙⠛⠉⠙⠛⠋⠉⠛⠛⠁⠈⠀⠀⠈⠙⠉⠉⠉⠉⠈⠗⡷⠁⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⡿⢿⣽⣷⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠁⠀⡉⠝⠉⠀⠀⠀⠀⠀⠀⠄⠒⠀⠐⠂⠈⠀⠀⠀⠀⠄⠀⠀⢠⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡀⢀⡧⡽⢽⣿⣧⢲⣶⣶⣶⣶⣤⣤⣴⡤⢔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣀⡄⢀⠀⠀⠀⠀⠀⠀⠸⠿⠛⠛⠋⠁⠀⠠⠀⠈⢋⢟⣯⣿⣿⣿⡷⣺⣴⣵⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠐⠀⠀⠀⠀⡠⠄⠂⠈⠁⠀⢢⣤⠀⠖⠀⠀⠀⠀⡘⣿⣿⣨⣵⣶⡖⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⠀⠀⠀⣢⡀⣼⣿⣿⣿⣿⣿⣭⣭⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠑⠉⠀⠀⠀⠀⠀⠐⠛⢿⡿⠛⡛⠻⠋⠀⠀⠀⠀⢀⣰⣦⠀⠙⠹⠟⠂⠀⠄⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣟⣿
⠀⠀⠀⠂⠀⢀⢐⢄⣂⣄⡀⡀⣔⡲⣳⣶⣺⣷⣦⣦⣆⡦⡈⠙⠀⢠⠠⣼⣦⣀⣀⣔⡌⣂⡗⡀⢀⠄⡀⢀⣀⠠⢦⣇⠙⠆⠽⠝⠂⠀⠀⠀⠀⠀⣀⣁⣭⣷⡤⠤⠖⣄⠂⠀⠘⠛⠻⠿⢿⣛⣛⣟⣿⣿⣷⣿⣿⣷
⠄⠠⡐⠁⡊⠬⣿⡿⣿⣾⣷⣿⣿⣿⣿⣷⣿⣿⡿⣿⣿⣟⡁⣔⠁⢀⣸⡿⠉⠉⠉⠀⠒⠓⠀⠀⠀⠀⠀⠀⠈⠉⢉⣉⣀⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣠⣤⣤⣦⣶⣶⣶⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠀⠀⠂⠠⣉⠿⣇⣿⣿⢺⣿⣿⡿⣿⡿⠾⠃⠛⠛⠻⠟⠋⠁⠾⡿⠷⠷⠶⣶⣷⠾⠶⢿⣾⣿⣿⣿⣿⢿⢿⣿⣿⣿⡿⠿⢿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⠀⠀⠀⠈⠐⢆⣅⡳⠿⠛⡈⢤⣖⢲⠟⠀⣿⣿⡆⣿⣿⣇⣸⣿⡟⣿⣿⣿⣿⢸⣿⣿⣿⣿⣎⣿⣿⣳⣿⡿⣿⣿⡛⣿⣿⢿⣿⣮⢱⣿⣿⢿⣿⡟⢿⣿⡿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠁⠀⠀⠠⠴⠄⠈⠐⠀⠀⠀⠀⠀⢈⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣢⢸⣿⣿⣸⣿⡿⣴⣷⣛⣛⢣⣿⣿⢳⣿⣿⣼⣿⣿⢸⣿⣿⣼⣿⠏⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⣿⣿⣿⢿⣿⣿⣿⠃⣿⣿⡿⢿⢸⣿⣿⢻⣿⣷⢩⣿⣿⣣⣿⣿⠯⣾⣿⣿⢹⣿⣿⢸⣯⣿⢻⣿⣧⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣧⣭⢸⣿⣿⣼⣿⣿⣸⡿⣷⣿⣿⣥⣤⠌⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⣿⣸⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡛⣛⣛⣨⣻⣛⣛⣤⣿⣿⣿⣿⣼⣿⣻⣿⣿⣿⣿⣿⣛⣿⣿⣿⣻⣾⣮⣿⣟⣿⣷⣶⣽⣿⣟⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠶⣶⠯⢶⠦⠰⠶⠶⠶⠀⣤⣤⣤⣤⣄⢠⠀⢛⣋⣛⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠤⣶⣶⣾⣶⢷⣶⣤⣻⣾⣿⣭⣯⣷⣼⣾⣿⣿⣾⣿⣿⡶⣷⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢁⣄⠄⠀⠀⣀⣋⠱⠆⠀⠀⠀⢀⡀⣤⣤⡄⠀⣢⣴⣄⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢚⣛⣿⠟⡋⠈⠛⡙⠻⠙⢚⡿⠛⠿⣿⡿⢿⣿⣿⠿⠟⠋⡙⠻⠂⢊⣁⣤⣶⣿⣿⣿⣿⣿⣿⣟⣁⣶⣶⣿⣿⣿⣴⢒⣸⣿⣶⡦⠦⢶⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠈⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀
⠏⠝⢛⡀⠀⠀⠀⠀⠐⠀⠀⢀⣤⢩⣤⣷⣦⣨⣤⣦⣰⣎⣴⣬⣼⣿⣿⣿⣿⣿⣿⡿⠛⠒⢋⣀⣙⣿⣿⣿⣿⣷⣷⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣢⠀⣀⣀⣀⣭⣧⣤⣴⣔⠀
⠀⣤⣵⣆⠀⠀⠀⠀⠀⠀⠀⣴⡿⣴⣿⣿⣿⣿⣿⣿⡷⣖⣾⣿⣿⣿⣿⣿⣿⣿⣉⣥⡄⢐⣲⣿⣿⣿⣿⣿⣿⡏⡟⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭⢇⣭⣽⠻⡟⢛⠿⠉⠹⠯⠠
⠚⠋⠃⠂⠤⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⡿⠛⠛⢛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣷⠷⣟⢟⣿⣿⡷⣯⣿⣿⣿⡿⢿⣿⣿⣿⣽⣿⠟⠻⠹⡿⠶⠏⠁⠘⠓⠋⠁⠀⠂⠀⠀⠀⠙
⠀⠴⣶⣶⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣯⣿⣭⣤⣤⣤⣴⣶⠾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣇⢨⣝⣓⢃⣲⣿⡟⣿⡛⠛⠋⠉⠀⠛⠿⠻⣜⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠈⠁⠓⠀⠈⣰⢀⣾⣿⣿⣿⣿⣯⣽⣿⣿⡛⠋⠸⣿⢿⣿⣿⣿⣿⣿⣿⣍⠋⢻⣿⡿⡟⢽⣿⣿⣿⣿⣿⣿⣿⢯⣿⠿⢟⣻⣿⠩⠋⠁⠀⠀⢀⣠⣴⣶⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀
⠀⡄⠀⠀⠀⣺⣶⠿⠍⢳⡨⠩⠏⠀⢅⡀⠁⠀⠉⠉⠛⣟⢯⠘⠻⠯⣯⠁⠀⠂⠀⠀⠀⠀⠿⢿⣿⣿⣿⢿⡟⡬⢚⡂⣰⣿⡿⠞⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀
⣿⣶⣶⣤⣶⣿⣯⣿⣷⣦⣲⣞⡙⠬⠲⠥⣤⠀⠀⣐⣌⠀⠀⠀⠀⡀⠀⠄⣄⣀⡀⠑⢒⡒⣦⣭⣿⣿⡿⠙⠧⢁⠀⠚⠋⣻⡅⠀⠀⠀⠀⠀⠀⠘⠉⠉⠉⠀⠀⣸⠧⡀⡀⣐⡀⠀⠀⠀⠀⠀⠀⠠⣶⣷⣶⣽⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣴⡊⣠⣤⣤⣴⣾⣼⣿⣾⣯⣿⡟⡿⠿⠛⡗⢚⠻⡾⠅⠤⠂⢿⠕⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⣠⣤⣶⣿⣿⣿⣿⣶⡤⠤⢄⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣭⣸⢿⣥⡶⣾⣿⣾⣾⣿⣿⣇⡈⠀⢠⡀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣿⣿⠹⠿⣿⣄⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠩⠙⣿⡾⣿⣾⡾⠃⠀⠀⠁⠀⠀⠀⠀⠀⣀⣠⡤⢿⣿⣿⡿⡄⠀⢻⡇⠀⢸⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠛⠛⠓⢿⣷⡅⠀⣠⡀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣾⣿⣿⣿⣷⠂⠘⣷⠀⢸⢿⣿⡿⡯⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⢀⠀⢿⣿⣷⣾⣦⡦⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⣿⣿⣿⣿⣦⡀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⢿⠿⠃⠀⠈⠁⢷⠵⢾⠷⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣤⣿⣿⣿⣿⣧⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠙⠛⠋⠙⠛⠋⠉⠛⠛⠁⠈⠁⠀⠈⠙⠉⠉⠉⠉⠀⠓⡳⠁⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⢿⣱⣷⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠀⠀⠀⠀⠀⠀⠄⠖⠀⠐⠂⠈⠀⠀⠀⠀⠄⠀⠀⢠⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡀⢀⡧⡿⢾⣿⣇⣶⣶⣶⣶⡶⣤⣤⣤⡤⢔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣿⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⣀⡄⢀⠀⠀⠀⠀⠀⠀⠸⠿⠛⠛⠋⠁⠀⠀⠀⠈⢋⣏⣽⣿⣿⣿⡷⣺⣴⣽⣽⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠐⠀⠀⠀⠀⡠⠄⠂⠈⠉⠀⢢⣤⠐⢖⠀⠀⠀⠀⡘⣿⣿⣨⣵⣶⡖⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⠀⠀⣠⡀⣾⣿⣿⣿⣿⣿⢭⣭⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠐⠛⠿⣿⠛⣛⠛⠋⠀⠀⠀⠀⢀⣸⣧⠀⠙⢻⠟⠃⠀⠄⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣟⣿
⠀⠀⠀⠀⠀⢀⢰⢄⣢⣄⡔⡀⣔⡲⣻⣔⣶⣷⣦⣧⣄⡦⡈⠙⠀⢠⠀⣼⣦⣄⣄⣔⡆⣒⡶⠀⢀⠄⡀⠀⣀⣠⣴⡏⡙⠎⠽⠽⠂⠀⠀⠀⠀⠀⣀⣉⣭⣷⡦⠠⠖⢀⠂⠀⠘⠛⠻⠿⢟⣛⣛⣿⣿⣿⣷⣿⣿⡷
⠤⠀⡄⠀⡨⠬⣿⡿⣷⣽⣧⣿⣿⣿⣿⣿⣿⣾⡿⣿⣿⣟⡉⣄⠁⢀⣸⡿⠍⠉⠉⠐⠒⠒⠀⠀⠀⠀⠀⠐⠈⠉⠈⣋⣁⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣶⣶⣶⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠒⠀⠂⢠⣙⠻⣏⣿⣿⢺⣿⣿⡿⣿⡿⠾⠇⠛⠛⠻⠟⠋⠃⠿⡿⠷⠷⠶⣷⣿⠶⠶⢶⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠐⢦⣅⡳⠿⠛⠈⢴⡦⢯⠟⠁⣿⣿⡆⣿⣿⣇⣸⣿⡟⣿⣿⣿⣿⢸⣿⣿⣿⣿⣎⣿⣿⣳⣿⡿⣿⣿⡛⣷⣿⢿⣿⣮⢹⣿⣿⢿⣿⡞⢿⣿⡿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠁⠀⠀⠠⠴⠆⠉⠐⠀⠀⠀⠀⠀⣈⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣢⢸⣿⣿⣸⣿⡿⣴⣷⣛⣛⢣⣿⣿⢳⣿⣿⢸⣿⣿⢸⣿⣿⣼⣿⠏⢸⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⣿⣿⣿⢿⣿⣿⣿⠃⣿⣿⡿⣿⢸⣿⣿⢻⣿⣷⢹⣿⣿⣣⣿⣿⠯⣾⣿⣿⢸⣿⣿⢸⣯⣿⢻⣿⣧⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣧⣭⢸⣿⣿⣼⣿⣿⣸⡿⣷⣿⣿⣥⣤⠌⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⣿⢸⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣛⣛⣛⣬⣻⣻⣻⣤⣿⣿⣿⣿⣼⣿⣻⣿⣿⣿⣿⣿⣛⣿⣿⣿⣻⣾⣮⣿⣟⣿⣷⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠶⣶⠯⢶⠶⠰⠶⠶⠶⠀⢤⣤⣤⣤⣀⢠⡈⣙⣛⣛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠤⣶⣶⣾⣶⢷⣶⣤⣻⣿⣿⣭⣯⣿⣼⣾⣿⣿⣾⣿⣿⡶⣷⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢁⣄⠄⠀⠀⣀⣋⠱⠆⠀⠀⠀⢀⣀⣤⣄⡄⠀⣤⣴⣄⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢚⣛⣿⠟⡻⠈⠛⠙⠻⠙⠚⡿⠛⠿⣿⡿⢿⣿⣟⠿⡟⠋⡙⠻⠂⢋⣁⣤⣶⣿⣿⣿⣿⣿⣿⣟⣁⣶⣶⣾⣿⣿⣴⢒⣺⣿⣶⣦⠦⢶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⠈⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀
⠯⠝⢛⡀⠀⠀⠀⠀⠐⠀⠀⢀⣤⢩⣬⣦⣦⣨⣠⣦⣰⣎⣶⣬⣽⣿⣿⣿⣿⣿⣿⡿⠛⠒⢋⣀⢙⣿⣿⣿⣿⣷⣷⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⠀⣀⣀⣀⣯⣧⣤⣴⡔⠂
⠀⢤⣴⡖⠀⠀⠀⠀⠀⠀⠀⣴⣿⣴⣿⣿⣿⣿⣿⣿⡧⣖⣾⣿⣿⣿⣿⣿⣿⣿⣉⣥⡄⢐⣺⣿⣿⣿⣿⣿⣿⡏⡟⣏⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⡬⣇⢭⣝⠻⠟⠛⠿⠉⠹⠧⠠
⠚⠋⠃⠂⠠⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⡿⠛⠛⢛⠻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣿⠷⣿⢟⣿⣿⡷⣯⣿⣿⣿⡿⢿⣿⣿⣿⣽⣿⠟⠻⠹⡿⠷⠎⠁⠘⠓⠋⠁⠀⠂⠀⠀⠀⠘
⠀⠴⣶⣶⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣯⣽⣭⣤⣤⣤⣴⣶⠾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣇⢨⣝⣓⠃⣲⣿⡟⣿⠏⠛⠋⠉⠀⠛⠻⢿⡜⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂
⠈⢁⠓⠀⠈⣰⢀⣾⣿⣿⣿⣿⣯⣹⣿⣿⣛⠋⠸⣿⢿⣿⣿⣿⣿⣿⣿⣍⠋⢻⣿⡾⡟⠽⣿⣿⣿⣿⣿⣿⣿⢯⣿⠻⣟⣻⣿⠩⠋⠁⠀⠀⢀⣠⣴⣶⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀
⠀⡄⠀⠀⠀⣺⣶⠿⠍⠳⡨⠩⠗⡈⢁⠀⠁⠀⠉⠉⠛⣛⢯⠘⠻⠯⣟⠁⠀⠂⠀⠀⠀⠀⠿⢿⣿⣿⣿⢿⡏⡈⢈⡂⣰⣿⡶⠒⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣶⣶⣦⣶⣿⣯⣿⣷⣦⣲⣞⡹⠬⢳⠥⣤⠀⠀⣐⣌⠀⠀⠀⠀⡀⠄⠄⣄⣀⡀⢑⣒⡾⣦⣭⣿⣿⡿⠙⠣⢁⠀⠚⠹⣻⡅⠀⠀⠀⠀⠀⠀⠸⠉⠉⠉⠀⠀⣸⠇⡀⡀⣐⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣶⣿⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣤⡊⣠⣤⣤⣴⣾⣼⣿⣾⣯⣿⡿⡻⠾⠙⡇⢚⠻⡾⠄⠤⠂⣾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⣠⣤⣶⣿⣿⣿⣿⣷⡦⠤⢤⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣭⣺⢿⣡⡶⣾⣿⣿⣾⣿⣿⣆⡈⠀⢠⡀⠀⠀⠀⠀⠀⠀⢈⣹⣿⣿⣿⣿⠻⡿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠫⠙⢿⡾⣿⣾⡾⠃⠀⠂⠂⠀⠀⠀⠀⠀⣀⣠⣤⣿⣿⣿⣿⡀⠀⢻⡇⠀⢸⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠛⠛⠑⢿⣷⡅⠀⣠⡀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣾⣿⣿⣿⣷⠂⢸⣧⠀⢸⣿⣿⡿⡯⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⢀⠀⢿⣿⣧⣾⣦⠦⠀⠀⠀⠀⠀⠀⠀⠸⣿⠿⣿⣿⣿⣿⣦⢀⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⢿⠿⠃⠀⠉⠁⢷⠽⢾⠷⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣥⣿⣿⣿⣿⣇⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠙⠛⠉⠙⠛⠋⠉⠛⠛⠁⠈⠁⠀⠈⠙⠉⠉⠉⠉⠀⠓⡷⠁⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⢿⣩⣷⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠝⠉⠀⠀⠀⠀⠀⠀⠄⠖⠀⠐⠂⠈⠀⠀⠀⠀⠄⠀⠀⢠⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡀⢀⠧⡿⢾⣿⡇⣶⣶⣶⣶⡶⣤⣤⣴⡤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣿⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣀⡄⠀⡀⠀⠀⠀⠀⠀⠸⠿⠟⠛⠉⠁⠀⠀⠀⠈⢫⣋⣽⣿⣿⣿⡗⣺⣴⣷⣭⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠐⠀⠀⠀⠀⠠⠄⠂⠈⠁⠀⢢⣤⠔⢖⠀⠀⠀⠀⡚⣟⣿⣨⣵⣶⡖⠀⠀⠀⠀⠀⢀⡀⠀⣀⡀⠀⠀⠀⣢⡀⣾⣿⣿⣿⣿⣿⣯⣭⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠐⠛⢿⡿⠛⡟⢻⠋⠀⠀⠀⠀⢀⣼⡦⠀⠙⢻⠟⠂⠀⠤⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣟⣿
⠀⠀⠀⠀⠀⢀⢰⣀⣂⣀⡄⡀⣄⡲⣻⣶⣺⣷⣦⣷⣴⣦⡈⠙⠀⢠⠠⣬⣦⣀⣄⣔⣆⣄⡶⠠⢀⠄⡀⠀⣀⠠⣮⣏⡙⠆⠽⠽⠂⠑⠀⠀⠀⠀⣀⣉⣤⣶⡶⠠⠒⢀⠂⠀⠘⠛⠻⠿⢟⣛⣛⣿⣿⣿⣷⣿⣿⣷
⠄⠀⡀⠀⡲⠬⣿⣿⣽⣿⣷⣿⣿⣿⣿⣷⣿⣿⡿⣿⣿⣟⣉⣄⠁⢀⣸⡿⠍⠉⠉⠀⠒⠓⠀⠀⠀⠀⠀⠀⠈⠉⠈⢋⣁⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣦⣶⣶⣶⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠐⠐⠂⠀⠂⢠⣙⠿⣏⣿⣿⢺⣿⣿⡿⣿⡿⠾⠇⠛⠛⠻⠟⠉⠃⢿⡿⠷⠶⠶⣷⣿⠾⠾⢷⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠿⢿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⢶⣅⠳⠿⠛⡂⢠⣶⢋⠟⠁⣿⣿⡆⣿⣿⣇⣸⣿⡿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣎⣿⣿⣻⣿⡿⣿⣿⡛⣷⣿⢿⣿⣮⢹⣿⣿⢿⣿⡟⢯⣿⡿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠁⠀⠀⠠⠴⠂⠈⠀⠀⠀⠐⠀⠈⣈⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣂⢸⣿⣿⣸⣿⡿⣶⣷⣛⣛⢣⣿⣿⢳⣿⣿⢸⣿⣿⢸⣿⣿⣼⣿⠏⢸⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⣿⣿⣿⢿⣿⣿⣿⠃⣿⣿⡿⣿⢸⣿⣿⢻⣿⣷⢹⣿⣿⣣⣿⣿⠯⣾⣿⣿⢸⣿⣿⢸⣯⣿⢻⣿⣧⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣧⣭⢸⣿⣿⣼⣿⣿⣸⡿⣷⣿⣿⣥⣤⠌⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⣿⣸⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡛⣛⣛⣬⣻⣻⣋⣤⣿⣿⣿⣿⣼⣿⣻⣿⣿⣽⣿⣿⣛⣿⣿⣿⣻⣾⣮⣿⣟⣿⣷⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠶⣶⠯⢶⠦⠰⠶⠶⠶⠀⢤⣤⣤⣤⣄⢠⡀⣛⣋⣛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠤⣶⣶⣾⣶⢷⣶⣤⣻⣷⣿⣿⣯⣷⣼⣾⣿⣿⣿⣿⣿⡶⣷⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⣄⠄⠀⠀⣄⣩⡹⠦⠀⠀⠀⢀⡀⢤⣤⠀⠀⣤⣴⣄⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢚⣻⣿⠟⠋⠈⠛⡛⠻⠙⠚⡻⠛⠿⣿⡿⠿⣿⣟⠿⡟⠋⣙⠻⠂⢋⣁⣤⣶⣿⣿⣿⣿⣿⣿⣿⣉⣶⣶⣿⣿⣿⣴⢒⣻⣿⣶⡶⠢⢶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣀⠈⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀
⠫⠝⢛⡀⠀⠀⠀⠀⠐⠀⠀⢀⣤⢩⣤⣶⣦⣤⣤⣦⣰⣎⣴⣬⣼⣿⣿⣿⣿⣿⣿⡿⠛⠒⢋⣀⣉⣿⣿⣿⣿⣷⣷⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣢⠀⣀⣀⣀⣯⣧⣤⣴⣔⠂
⠀⢤⣵⡆⠄⠀⠀⠀⠀⠀⠀⣴⣿⣴⣿⣿⣿⣿⣿⣿⣷⣖⣾⣿⣿⣿⣿⣿⣿⣿⣉⣤⡄⢐⣲⣿⣿⣿⣿⣿⣿⡏⡟⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠍⣇⣭⣽⠻⡟⢛⡿⠋⠹⠯⠰
⠚⠋⠃⠂⠠⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⣬⣿⣿⣿⣿⣿⣿⡿⠛⠛⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠶⣿⣿⣿⣿⡷⣿⣿⣿⣿⡿⢿⣿⣿⣿⣽⣿⠿⠻⠹⡿⠷⠏⠁⠐⠓⠋⠀⠀⠂⠀⠀⠀⠙
⠠⠴⣶⣦⢀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣯⣿⣭⣥⣤⣤⣴⣶⠾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣇⢨⣝⣛⢃⣱⣿⡟⣿⠃⠛⠋⠉⠈⠛⢊⣽⣴⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂
⠈⢁⠓⠀⠈⣰⢀⣾⣿⣿⣿⣿⣿⣽⣿⣿⣛⠋⠸⣿⢿⣿⣿⣿⣿⣿⣿⣍⠋⢻⣿⡿⡟⢽⣿⣿⣿⣿⣿⣿⣿⢯⣿⠿⣟⣳⣿⡭⠉⠁⠀⠀⢀⣠⣴⣶⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠀⣀⠀⠀⠀⣺⣶⠿⠍⠳⡨⠩⠟⡀⢅⡀⠁⠀⠉⠉⠛⣟⢯⠚⠻⠯⡟⠁⠀⠂⠀⠀⠀⠀⠿⢿⣿⣿⣿⢿⡏⡄⢚⡂⣰⣿⡾⠒⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀
⣿⣶⣶⣴⣶⣿⣯⣿⣷⣦⣲⣞⡉⠤⢳⢥⣤⠀⠀⣐⣌⠀⠀⠀⠀⡀⠠⠄⣄⣀⡀⠑⣒⡺⣦⣭⣿⣿⡿⠙⠣⢁⠀⠚⠩⣻⡅⠀⠀⠀⠀⠀⠀⠸⠉⠉⠉⠀⠀⡹⢇⡀⡀⣰⠀⠀⠀⠀⠀⠀⠀⠠⣦⣷⣶⣿⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣴⡎⣠⣤⣤⣴⣾⣼⣿⣾⣯⣿⡟⡿⠿⠛⡗⢚⠻⡾⠀⠠⢒⢾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⣶⣦⠤⢴⢾⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣩⣺⢿⣥⡶⣾⣿⣿⣾⣿⣿⣆⡈⠀⢠⡀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⠻⢿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠫⠙⣿⣾⣿⣾⡾⠃⠀⡂⠃⠀⠀⠀⠀⠀⣀⣠⣤⣿⣿⣿⣻⡀⠀⢻⠁⠀⢸⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠛⠛⠑⢿⣷⡇⠀⣠⡀⠀⠀⠀⠀⠀⠀⢉⣤⣤⣾⣿⣿⣯⣧⠆⢸⣧⠀⢸⣿⣿⡿⡯⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⢀⠈⢽⣿⣿⣾⠧⠆⠀⠀⠀⠀⠀⠀⠀⢹⣿⠿⣿⣿⣿⣿⣦⢀⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⢿⠿⠃⠀⠈⠃⢷⠬⣾⠷⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣡⣿⣿⣿⣿⣇⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⠙⠛⠉⠙⠛⠋⠉⠛⠛⠁⠈⠁⠀⠈⠙⠉⠉⠉⠉⠀⠓⡷⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⢿⣸⣧⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠝⠉⠀⠀⠀⠀⠀⠀⠄⠒⠀⠐⠂⠈⠀⠀⠀⠀⠄⠀⠀⢠⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣯⠀⢀⠯⡿⢾⣿⡇⣴⣶⣶⣶⣶⣤⣤⣤⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠠⢤⣿⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠱⠿⠟⠛⠉⠁⠀⠀⠀⠘⣫⣋⣽⣿⣿⣿⡧⣸⣤⣽⣭⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠐⠀⠀⠀⠀⠠⠄⠂⠈⠉⠀⢢⣤⠴⢖⠀⠀⠀⠀⡚⣟⣿⣨⣵⣶⡖⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀⠀⠀⠀⣂⡀⣾⣿⣿⣿⣿⣿⣭⣭⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢀⠀⠀⠀⠀⠀⢀⡠⠀⠈⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠐⠛⢿⣿⠻⡟⠿⠋⠀⠀⠀⠀⣀⣼⡧⠀⠙⠻⠟⠂⠀⠤⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣟⣿
⠀⠀⠀⠂⠀⢀⢰⢄⣢⣄⡀⠀⣔⡲⣻⣴⣳⣷⣦⣧⣖⡦⡈⠙⠀⢠⠠⣬⣦⣄⣄⣐⡦⣀⡷⠠⢀⠄⡀⢀⣀⡠⣴⠎⠙⠎⠽⠽⠂⠑⠀⠀⢀⠀⣀⣁⣤⣶⡶⠠⠒⣂⠒⠀⠘⠛⠻⠿⢟⣛⣛⣿⣿⣿⣷⣿⣿⣿
⠤⠠⡀⠁⡺⠬⣿⡿⣷⣿⣧⣿⣿⣿⣿⣷⣿⣿⡿⣿⣿⣟⣉⣔⠁⢀⣸⡿⠅⠉⠉⠐⠒⠃⠀⠀⠀⠀⠀⠐⠀⠉⠉⣋⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣈⣀⣀⣀⣤⣤⣤⣦⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠀⠀⠂⢠⣙⠻⣏⣿⣿⢺⣿⣿⡿⣿⡿⠾⠇⠛⠛⠻⠟⠉⠃⠿⡿⠿⠶⠶⣶⡿⠶⠾⢿⣾⣿⣿⣿⣿⡿⢿⣿⣿⣿⡿⠿⢿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠐⢶⣅⠳⠿⠛⡈⢰⣦⢶⠟⠁⣿⣿⡆⣿⣿⡇⣸⣿⡟⣿⣿⣿⣿⢸⣿⣿⣿⣿⣎⣿⣿⣻⣿⡿⣿⣿⡛⣷⣿⢿⣿⣮⢹⣿⣿⢿⣿⡞⢯⣿⡿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠁⠀⠀⠀⠴⠀⠉⠀⠀⠀⠀⠀⠀⣈⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣂⢸⣿⣿⣸⣿⡿⣶⣿⣛⣛⢣⣿⣿⢳⣿⣿⢸⣿⣿⢸⣿⣿⣼⣿⠏⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⣿⣿⣿⢿⣿⣿⣿⠃⣿⣿⡿⣿⢸⣿⣿⢻⣿⣷⢹⣿⣿⣣⣿⣿⠯⣿⣿⣿⢸⣿⣿⢸⣯⣿⢻⣿⣧⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣧⣭⢸⣿⣿⣼⣿⣿⣸⣿⣷⣿⣿⣥⣴⠈⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⣿⢸⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡛⣛⣛⣬⣿⣻⣫⣤⣿⣿⣿⣿⣼⣿⣻⣿⣿⣽⣿⣿⣛⣿⣿⣿⣻⣾⣮⣿⣟⣿⣷⣶⣽⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠶⣶⠯⢶⠦⠰⠶⠶⠶⠀⢤⣤⣤⣤⣄⢠⡀⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠤⣶⣶⣾⣶⢷⣶⣤⣻⣿⣿⣭⣯⣿⣼⣾⣿⣿⣾⣿⣿⡶⣷⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢁⣄⠄⠀⢀⢀⣛⠹⠆⡀⠀⠀⢀⡄⣠⣤⡄⠀⣢⣴⣄⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢚⡻⣿⠟⡻⠈⠛⡙⠻⠙⢚⡿⠛⠿⣿⡿⢿⣿⣟⠿⡟⠋⡙⠻⠂⢋⣁⣤⣶⣿⣿⣿⣿⣿⣿⣟⣁⣶⣶⣿⣿⣿⡴⢓⣺⣿⣶⣶⠦⢶⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠈⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀
⠏⠝⢛⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢩⣬⣶⣦⣨⣤⣦⣰⣎⣶⣬⣼⣿⣿⣿⣿⣿⣿⡿⠛⠒⢋⣀⣉⣿⣿⣿⣿⣷⣷⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣢⠀⣀⣀⣀⣯⣧⣤⣴⣘⠂
⠀⢤⣵⣖⠀⠀⠀⠀⠀⠀⠀⣤⣿⣵⣿⣿⣿⣿⣿⣿⡧⣖⣾⣿⣿⣿⣿⣿⣿⣿⣉⣤⡄⢐⣺⣿⣿⣿⣿⣿⣿⡏⡟⢏⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭⢇⣯⣝⠿⡟⣻⠿⠍⠹⠯⠠
⠚⠋⠃⠂⠠⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣨⣿⣿⣿⣿⣿⣿⡿⠛⠛⢛⠻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣏⣾⣿⠶⣿⢟⣿⣿⡷⣯⣿⣿⣿⡿⢿⣿⣿⣿⣽⣿⠾⠻⠹⡿⠷⠎⠁⠘⠓⠋⠁⠀⠂⠀⠀⠀⠛
⠀⠴⣶⣶⢀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣯⣽⣭⣥⣤⣤⣴⣶⠾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣇⢨⣝⣓⢃⣺⣿⡟⣿⠛⠛⠋⠉⠘⠻⢟⢽⡄⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂
⠈⢁⠃⠀⠈⣰⢀⣾⣿⣿⣿⣿⣯⣽⣿⣿⡛⠋⠸⣿⢿⣿⣿⣿⣿⣿⣿⣏⠋⢻⣿⡿⡟⢽⣿⣿⣿⣿⣿⣿⣿⢯⣿⠿⣟⣓⣿⡭⠋⠁⠀⠀⢀⣠⣴⣾⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀
⠀⣄⠀⠀⠀⣺⣶⠿⠉⢲⡨⠩⠟⡈⢅⠀⠁⠀⠉⠉⠛⣟⢯⠘⠻⠯⡏⠁⠀⠂⠀⠀⠀⠀⠿⢿⣿⣿⣿⢿⡏⡌⢊⡈⣰⣿⡟⠂⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣶⣶⣤⣶⣿⣯⣿⣷⣦⣲⣞⡹⠤⠳⢥⣤⠀⠀⣐⣌⠀⠀⠀⠀⡀⠀⠄⣄⣀⡀⠑⢒⡺⣦⣭⣿⣿⡿⠙⠣⢁⠀⠚⠹⣻⡅⠀⠀⠀⠀⠀⠀⠩⠙⠉⠁⠀⠀⡹⢇⡀⢀⣐⠀⠀⠀⠀⠀⠀⠀⠠⣶⣷⣷⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣤⡊⣠⣤⣤⣴⣾⣼⣿⣾⣯⣿⡟⡿⠿⠛⡗⢘⠻⡾⠄⠤⠒⢺⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣷⣿⣿⣶⠆⠤⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣭⣺⢿⣥⡶⣾⣿⣿⣾⣿⣿⣆⡈⠀⡠⡀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⡏⡿⢿⣿⡨⣿⣾⣿⣾⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠫⠙⣿⡾⣿⣾⡞⠃⠀⠐⠁⠀⠀⠀⠀⠀⢀⣠⣬⣿⣿⣿⣳⠀⠀⢿⠀⠀⢹⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠓⠛⠑⢿⣷⡇⠀⣠⠀⠀⠀⠀⠀⠀⠀⣉⣀⣤⣾⣿⣿⣿⡇⠂⢸⣇⠀⡹⣿⣿⡿⡯⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⢀⠀⢿⣿⣿⣾⡦⡦⠀⠀⠀⠀⠀⠀⠀⢹⣿⠿⣿⣿⣿⣿⣤⢀⣍⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⢿⠿⠃⠀⠈⠁⢷⠽⢾⠷⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣭⣿⣿⣿⣿⣏⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠙⠛⠉⠙⠛⠋⠉⠛⠛⠁⠈⠁⠀⠈⠙⠉⠉⠉⠉⠀⠓⡷⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡿⢿⢰⣧⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠀⠀⠀⠀⠀⠀⠄⠒⠀⠐⠂⠈⠀⠀⠀⠀⠄⠀⠀⢠⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣯⠀⢀⠯⡽⢾⣿⡇⣶⣶⣶⣶⡶⣤⣤⢴⡦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣿⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣀⡄⠀⡀⠀⠀⠀⠀⠀⠹⠿⠟⠛⠉⠁⠀⠀⠀⠘⠫⣫⣽⣿⣿⣿⡷⣺⣴⣿⣭⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠐⠀⠀⠀⠀⠠⠄⠂⠈⠁⠀⢢⣤⠔⢖⠀⠀⠀⠀⡚⣿⣿⣨⣵⣶⡖⠀⠀⠀⠀⠀⠀⡄⠀⣀⡀⠀⠀⠀⣢⡀⣾⣿⣿⣿⣿⣿⣭⣭⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠄⢀⠀⠀⠀⠀⠀⢁⡠⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠐⠛⢿⡿⠻⡟⠻⠋⠀⠀⠀⠀⣠⣼⡧⠀⠙⢹⠟⠂⠀⠤⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣟⣿
⠀⠀⠀⠂⠀⢀⣰⢄⣢⣄⡀⡀⣄⡰⣻⣶⣲⣷⣦⣧⣤⣦⡈⠙⠀⢠⠀⣼⣦⣀⣄⣔⣖⣂⡶⠠⢀⡄⡀⢀⣄⠠⣴⣏⠙⡎⠽⠽⠂⠁⠀⠀⢀⠀⣀⣩⣤⣶⠖⠠⠒⣀⠒⠀⠘⠛⠻⠿⢛⣛⣛⣿⣿⣿⣷⣿⣿⡿
⠤⠀⡀⠁⡰⠬⣿⡯⣷⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⣉⣔⠁⢀⣸⡿⠍⠉⠉⠀⠒⠒⠀⠀⠀⠀⠀⠐⠈⠋⠉⣋⣁⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣦⣶⣶⣶⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠂⠀⠂⢡⣙⠻⣇⣿⣿⢻⣿⣿⡿⣿⡿⠾⠃⠛⠛⠻⠟⠋⠁⠾⡿⠷⠶⢶⣷⡿⠶⠶⢷⣾⣿⣿⣿⣿⠿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⢶⣅⡳⠿⠛⣈⢤⣧⢊⠟⠁⣿⣿⡆⣿⣿⡇⣸⣿⡟⣿⣿⣿⣿⢸⣿⣿⣿⣷⣎⣿⣿⣳⣿⡿⣿⣿⡛⣷⣿⢿⣿⣮⢹⣿⣿⢿⣿⡟⢯⣿⡿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠁⠀⠀⠀⠴⠀⠉⠐⠀⠀⠀⠀⠈⣈⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣂⢸⣿⣿⣸⣿⡿⣶⣿⣛⣛⢣⣿⣿⢳⣿⣿⢸⣿⣿⢸⣿⣿⣼⣿⠏⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⣿⣿⣿⢿⣿⣿⣿⠃⣿⣿⡿⣿⢸⣿⣿⢻⣿⣷⢹⣿⣿⣣⣿⣿⠯⣾⣿⣿⢸⣿⣿⢸⣯⣿⢻⣿⣧⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣧⣭⢸⣿⣿⣼⣿⣿⣸⡿⣷⣿⣿⣥⣤⠈⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⣿⢸⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡛⣛⣛⣬⣿⣟⣯⣤⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣻⣾⣮⣿⣟⣿⣷⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠶⣶⠯⢶⠦⠰⠶⠶⠶⠀⣤⣤⣤⣤⣄⣠⡈⣛⣉⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠤⣶⣶⣾⣶⢷⣶⣤⣻⣾⣿⣭⣯⣷⣼⣾⣿⣿⣾⣿⣿⡶⣷⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⣄⠄⠀⢀⣀⢉⠿⠆⠀⠀⠀⠀⠀⣠⣄⡄⠀⣤⣴⣄⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢚⡻⣿⠟⠋⠈⠛⡙⠻⠙⢚⡿⠛⠿⣿⡿⢿⣿⣿⠿⠟⠋⡙⠻⠂⢊⣁⣤⣶⣿⣿⣿⣿⣿⣿⣟⣁⣶⣶⣿⣿⣿⣴⢓⣼⣿⣷⣦⠦⢿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡀⠈⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀
⠏⠝⢻⡀⠀⠀⠀⠀⠐⠀⠀⢀⣤⢩⣤⣷⣆⣬⣤⣦⣰⣎⣴⣬⣼⣿⣿⣿⣿⣿⣿⡿⠛⠒⢋⣀⣉⣿⣿⣿⣿⣷⣷⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⢠⠀⣀⣀⢀⣭⣧⣤⣴⣔⠀
⠀⢤⣵⡖⠄⠀⠀⠀⠀⠀⠀⣤⣿⣵⣿⣿⣿⣿⣿⣿⡧⣖⣾⣿⣿⣿⣿⣿⣿⣿⣉⣤⡄⢐⣲⣿⣿⣿⣿⣿⣿⡏⡟⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠭⢅⣯⣽⠻⡟⠛⠿⠋⠹⠯⠠
⠚⠋⠃⠀⠠⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⣬⣿⣿⣿⣿⣿⣿⡿⠛⠛⢛⠻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣿⠶⡿⣟⣿⣿⡷⣯⣿⣿⣿⡿⢿⣿⣿⣿⣽⣻⠯⠻⠹⡿⠷⠏⠁⠘⠓⠋⠀⠀⠂⠀⠀⠀⠘
⠠⠴⣶⡶⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣯⣿⣭⣥⣤⣤⣴⣶⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢠⣝⣛⢃⣺⣿⡟⣿⠏⠛⠙⠉⠘⠛⠆⣽⡔⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂
⠈⠁⠓⠀⠈⣰⢀⣾⣿⣿⣿⣿⣯⣹⣿⣿⡛⠋⠸⣿⢿⣿⣿⣿⣿⣿⣿⣍⠋⢻⣿⡾⡟⢽⣿⣿⣿⣿⣿⣿⣿⠯⣽⠿⣟⣳⣿⡍⠉⠁⠀⠀⣀⣠⣴⣾⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠀⡄⠀⠀⠀⣺⣶⠿⠍⠳⡨⠩⠏⡀⢅⡀⠁⠀⠉⠉⠛⣟⢯⠘⠻⠯⣏⠁⠀⠊⠀⠀⠀⠀⠿⢿⣿⣿⣿⢿⡏⡬⢚⡊⣱⣿⡖⠂⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀
⣿⣶⣶⣤⣴⣿⣯⣿⣷⣦⣲⣞⡉⠬⢲⢥⣤⠀⠀⣐⣌⠀⠀⠀⠀⡀⠤⠄⣄⣀⡀⢕⣒⡺⣦⣭⣿⣿⡿⠙⠣⢁⠀⠐⠉⣻⠅⠀⠀⠀⠀⠀⠀⠏⠛⠉⠁⠀⠀⡻⢄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣷⣷⣽⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣤⡎⣠⣤⣤⣴⣾⣼⣷⣾⣯⣿⡿⣻⠾⠛⡗⢘⠻⡾⠄⠤⠒⠟⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⣠⣴⣾⣿⣷⣿⣿⣶⣦⠤⠴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣩⣺⢿⣥⡶⣾⣿⣿⣾⣿⣿⣆⡈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠊⣿⣿⣿⣿⡏⠿⢿⣿⡈⡿⣿⣿⣾⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠙⣿⡼⣿⣾⡞⠃⠀⠘⠀⠀⠀⠀⠀⠀⢈⣡⣼⣿⣿⣿⢧⠀⠈⣿⠀⠀⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠛⠛⠁⢾⣷⡇⠀⣠⡀⠀⠀⠀⠀⠀⠀⡉⣀⣤⣿⣿⣿⣿⡆⠀⢻⣇⠀⡿⣿⣿⡿⡯⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⢈⠀⢿⣿⣷⣻⡶⣆⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⣿⣿⣿⣿⣄⢀⡍⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⢿⠿⠃⠀⠀⠁⠷⠵⢾⠷⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⣽⣿⣿⣿⣿⣎⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠙⠛⠉⠙⠛⠋⠉⠛⠛⠁⠈⠀⠀⠈⠙⠉⠉⠉⠉⠀⠓⡷⠁⠀⠀⠀⠈⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠿⢿⢹⣧⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠖⠀⠐⠂⠈⠀⠀⠀⠀⠄⠀⠀⢠⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣇⠀⢈⢿⡿⢿⣿⡇⣴⣶⣶⣶⣶⣤⣤⣤⡤⢔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠠⢤⣯⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣠⡄⡀⡀⠀⠀⠀⠀⠀⠹⠿⠟⠛⠉⠁⠀⠀⠀⠘⡩⣫⣽⣿⣿⣿⡷⣺⣴⣽⣭⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠐⠀⠀⠀⠀⡠⠄⠂⠈⠉⠀⢢⣤⠔⢖⠀⠀⠀⠀⠚⣿⣿⣨⣵⣾⡆⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⠀⠀⣦⠀⣾⣿⣿⣿⣿⣿⣭⣭⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠓⠉⠀⠀⠀⠀⠀⠐⠛⠿⣿⠋⡛⠟⠋⠀⠀⠀⠀⣠⣾⡧⠀⠙⠹⠟⠂⠀⠤⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣟⣿
⠀⠀⠀⠂⠀⢀⢐⣄⣂⣄⡄⡠⣄⡰⣳⣴⣳⣷⣦⣷⣄⡦⡈⠙⠀⢠⠠⣼⣦⣠⣄⣔⣆⣀⡷⠀⢀⡄⡀⠀⣀⠠⢴⣎⡙⡊⠿⠽⠂⠀⠀⠀⢀⠀⣀⣩⣤⠶⠖⠠⠒⢂⠒⠀⠘⠛⠻⠿⢛⣛⣛⣿⣿⣿⣷⣿⣿⡷
⠤⠀⡀⠁⡚⠬⣿⡿⣵⣿⣷⣿⣿⣿⣿⣷⣿⣿⡿⣿⣿⣟⣉⣄⠁⢀⣸⡿⠍⠉⠉⠀⠒⠒⠀⠀⠀⠀⠀⠐⠈⠉⠈⢊⣁⣁⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣦⣶⣶⣶⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠀⠀⠂⢠⣙⠿⣇⣿⣿⢺⣿⣿⣿⣿⣿⠾⠃⠛⠛⠻⠟⠉⠃⠼⡿⠿⠷⢶⣶⡿⠶⠶⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⠿⢿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠐⢖⣅⠳⠿⠛⡈⢠⡶⢎⠟⠁⣿⣿⡆⣿⣿⣇⣸⣿⡟⣿⣿⣿⣿⢸⣿⣿⣿⣷⣎⣿⣿⣻⣿⡿⣿⣿⡛⣷⣿⢿⣿⣮⢹⣿⣿⢿⣿⡞⢯⣿⡿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠁⠀⠀⠀⠴⠀⠉⠀⠀⠀⠀⠀⠈⣈⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣢⢸⣿⣿⣸⣿⡿⣶⣿⣛⣛⢣⣿⣿⢳⣿⣿⢸⣿⣿⢸⣿⣿⣼⣿⠏⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⣿⣿⣿⢿⣿⣿⣿⠃⣿⣿⡿⣿⢸⣿⣿⢻⣿⣷⢹⣿⣿⣣⣿⣿⠯⣾⣿⣿⢸⣿⣿⢸⣯⣿⢻⣿⣧⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣧⣭⢸⣿⣿⣼⣿⣿⣸⡿⣷⣿⣿⣥⣤⠌⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⣿⢸⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣛⣛⣛⣬⣿⣻⣫⣤⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣻⣾⣮⣿⣟⣿⣷⣶⣽⣿⣻⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠶⣶⠯⢶⠶⠰⠶⠶⠶⠀⣤⣤⣦⣤⣄⢠⡀⣻⣙⣛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡤⣶⣶⣾⣶⢷⣶⣤⣻⣶⣾⣭⣯⣿⣼⣾⣿⣿⣾⣿⣿⡶⣷⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢁⣄⡀⠀⡀⣄⣛⠻⠦⠀⠀⠀⢀⣀⣤⣤⡀⠀⣦⣴⣄⡀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢚⣻⣿⠟⡛⠀⠛⡛⠻⠙⠚⡟⠛⠿⣿⣿⠿⣿⣟⠿⡛⠋⡙⠻⠂⢉⣁⣤⣶⣿⣿⣿⣿⣿⣿⣟⣁⣶⣶⣿⣿⣿⣶⢒⣹⣿⣷⣶⠪⢿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⠈⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀
⠏⠝⢛⡀⠀⠀⠀⠀⠐⠀⠀⢀⣄⢩⣤⣷⣦⣤⣤⣦⣸⣎⣴⣬⣼⣿⣿⣿⣿⣿⣿⡿⠛⠓⢋⣀⣉⣿⣿⣿⣿⣷⣷⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⢂⠀⣀⣀⣐⣯⣧⣤⣴⡔⠂
⠀⢤⣵⣖⠄⠀⠀⠀⠀⠀⠀⣴⣿⣵⣿⣿⣿⣿⣿⣿⣧⣖⣾⣿⣿⣿⣿⣿⣿⣿⣋⣤⡄⢐⣲⣿⣿⣿⣿⣿⣿⡏⡟⣏⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠭⣇⣯⣽⠻⡟⠛⡿⠋⠻⠯⢰
⠚⠙⠃⠂⠤⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣻⣿⣧⣬⣿⣿⣿⣿⣿⣿⡿⠛⠛⢛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⠾⡿⣿⣿⣿⡷⣯⣿⣿⣿⡿⢿⣿⣻⣿⣽⣿⠿⠛⠹⡿⠷⠏⠁⠘⠓⠋⠁⠀⠂⠀⠈⠀⠑
⠠⠶⣶⡶⢀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣯⣽⣭⣥⣤⣤⣴⣶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢠⣝⣛⢃⣸⣿⡟⣿⠟⠛⠋⠉⠛⠷⡏⣿⣦⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂
⠈⠀⡓⠈⠈⣰⢀⣾⣿⣿⣿⣿⣯⣽⣿⣿⡛⠋⠸⣿⢿⣿⣿⣿⣿⣿⣿⣍⠋⢻⣿⡾⡟⣹⣿⣿⣿⣿⣿⣿⣿⠯⢿⠿⣿⣻⣿⠍⠋⠀⠀⠀⣀⣠⣶⣾⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀
⠁⣄⠄⠀⠀⣹⣶⠿⠍⢳⡨⠩⠇⡈⢅⠀⠁⠀⠩⠉⠛⣟⢯⠚⠿⠿⡿⠁⠀⠂⠀⠀⢀⠀⠿⠿⣿⣿⣿⢿⡟⡤⢚⡂⣰⣿⡚⠂⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀
⣿⣶⣶⣴⣴⣿⣯⣿⣷⣦⣲⣾⡹⠬⢳⢥⣤⠀⠀⣐⣌⠀⠀⠀⠀⡀⠀⠄⣄⣀⡀⠑⢒⡚⣦⣭⣿⣿⡿⠑⠣⢁⠄⠘⠉⣻⠅⠀⠀⠀⠀⠀⠘⠏⠛⠉⠁⠀⠈⡿⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣷⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣤⡊⣠⣤⣤⣼⣾⣼⣿⣾⣯⣿⡿⣿⠾⠛⡗⢙⠻⡾⠄⠤⢐⠿⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⣠⣴⣾⣿⣿⣿⣿⣶⠤⠤⠶⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣩⣺⢿⡥⡶⣾⣿⣿⣼⣿⣿⣆⠈⠀⣄⠀⠀⠀⠀⠀⠀⠀⠒⣿⣿⣿⣿⡟⠿⢿⣧⠸⡽⢿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠫⠙⣿⣜⣿⣾⡾⠃⢠⠈⠀⠀⠀⠀⠀⠀⠈⣉⣽⣿⣿⣿⣇⠀⠈⣿⠀⠀⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠛⠛⠑⢾⣷⡗⠀⣀⠀⠀⠀⠀⠀⠀⠈⡉⣀⣤⣿⣿⣿⣿⡔⠀⢹⡆⠀⡿⣿⣿⡿⡯⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⢈⠀⢾⣿⣧⣳⣦⡆⠀⠀⠀⠀⠀⠀⠈⢿⡿⠿⣿⣿⣿⣷⣄⢀⡏⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⢿⠿⠃⠀⠉⠁⣷⠥⢿⠿⠀⠀⠀⠀⠀⠀⠀⠘⣷⢀⣼⣿⣿⣿⣿⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠙⠛⠉⠙⠛⠋⠉⠛⠛⠁⠈⠁⠀⠈⠙⠉⠉⠉⠉⠈⠓⡷⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠿⢿⢻⣆⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⡉⠙⠉⠀⠀⠀⠀⠀⠀⠄⠒⠀⠐⠂⠈⠀⠀⠀⠀⠄⠄⠀⢠⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣇⠀⢨⢾⡟⢿⣿⣇⡴⣶⣶⣶⣶⣤⣤⣤⡤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠠⠤⣯⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠛⠉⠀⠀⠀⠀⠘⣩⣫⣿⣾⣿⣿⡧⣺⣴⣵⣽⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠐⠀⠀⠀⠀⡠⠆⠂⠈⠁⠀⢦⡤⠀⠖⠀⠀⠀⠀⠘⣟⣿⣨⣵⣶⡆⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⠀⠀⠀⣦⠀⣾⣿⣿⣿⣿⣯⣭⣭⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢁⡠⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠀⠀⠀⠀⠀⠐⠛⠿⣿⠋⡛⠿⠃⠀⠀⠀⠀⣀⡼⡧⠀⠙⠹⠛⠂⠀⠤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿
⠀⠀⠀⠂⠀⢀⣰⢄⣢⣄⡀⡀⣄⡲⣻⣶⣲⣷⣦⣦⡤⡦⡈⠙⠀⢠⢀⣼⣦⣀⣄⣔⡆⣀⡦⡀⢀⡄⡀⢀⣀⠠⣴⡂⡙⠂⠹⠽⠂⠀⠀⠀⠀⠀⣈⣠⣴⠿⠖⠠⠒⢀⠂⠀⠘⠛⠿⠿⢛⣛⣙⣿⣿⣿⣷⣿⣿⣷
⠄⠀⡀⠁⡚⠬⣿⡿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣟⡁⣔⠁⢀⣸⡿⠉⠉⠉⠀⠒⠂⠀⠀⠀⠀⠀⠀⠈⠉⠀⣊⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣦⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠐⠀⠀⠀⢠⣉⠹⣇⣿⣿⢺⣿⣿⡿⣿⠿⠾⠃⠛⠛⠻⠟⠉⠁⠼⡿⠿⠷⢶⣶⠾⠶⠶⢾⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⡿⠿⢿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⠀⠀⠀⠀⠐⢆⣅⠳⠿⠛⠈⢤⣖⢃⠟⠀⣿⣿⡆⣿⣿⡇⣸⣿⡟⣿⣿⣿⣿⢸⣿⣿⣿⣷⣎⣿⣿⣻⣿⡿⣿⣿⡛⣿⣿⢿⣿⣮⢹⣿⣿⢿⣿⡟⢿⣿⡿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⠴⠀⠈⠐⠀⠀⠀⠀⠈⣈⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣢⢸⣿⣿⣸⣿⡿⣶⣷⣛⣛⢣⣿⣿⢳⣿⣿⢼⣿⣿⢸⣿⣿⣼⣿⠏⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⣿⣿⣿⢿⣿⣿⣿⠃⣿⣿⡿⣿⢸⣿⣿⢻⣿⣷⢩⣿⣿⣣⣿⣿⠯⣾⣿⣿⢸⣿⣿⢸⣯⣿⢻⣿⣧⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣧⣭⢸⣿⣿⣼⣿⣿⣸⡿⣷⣿⣿⣥⣤⠌⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⣿⢸⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡛⣛⣛⣬⣻⣻⣋⣤⣿⣿⣿⣿⣼⣿⣻⣿⣿⣿⣿⣿⣛⣿⣿⣿⣻⣾⣮⣿⣟⣿⣷⣶⣽⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠶⣶⠯⢶⠦⠰⠶⠶⠶⠀⢤⣤⣤⣤⡄⢠⠀⢛⣋⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡤⣶⣶⣾⣶⢷⣶⣤⣻⣷⣾⣭⣿⣿⣼⣾⣿⣿⣿⣿⣿⡶⣷⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢁⣄⠄⠀⠀⣀⣛⠻⠦⠀⠀⠀⢀⣀⣤⣤⡀⠀⣦⣴⣄⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢊⣛⣿⠟⠛⠀⠛⡛⠻⠝⠚⡟⢛⠿⣿⡿⢿⣿⣟⠿⡛⠋⡙⠻⠂⢉⣁⣤⣶⣿⣿⣿⣿⣿⣿⣟⣉⣶⣶⣷⣿⣿⣶⢒⣻⣿⣷⣶⠪⢷⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⠈⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀
⠏⠝⢛⡀⠀⠀⠀⠀⠐⠀⠀⢀⣄⢩⣤⣷⣦⣬⣠⣢⣸⣎⣶⣬⣼⣿⣿⣿⣿⣿⣿⡿⠛⠓⢋⣀⢉⣿⣿⣿⣿⣷⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣂⠀⣀⣀⣐⣯⣧⣤⣴⣜⠂
⠀⢤⣵⣖⠄⠀⠀⠀⠀⠀⠀⣴⣿⣵⣿⣿⣿⣿⣿⣿⣷⣖⣾⣿⣿⣿⣿⣿⣿⣿⣉⣤⡄⢐⣲⣿⣿⣿⣿⣿⣿⡏⡿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠭⣇⢯⣽⠻⠟⡛⡿⠋⠻⠯⢰
⠚⠋⠃⠂⠠⠈⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣻⣿⣧⣮⣿⣿⣿⣿⣿⣿⡿⠛⠛⢛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⠾⣿⣟⣿⣿⡷⣯⣿⣿⣿⡿⠿⣿⣿⣿⣽⣿⠿⠛⠹⡿⠷⠎⠁⠘⠓⠋⠁⠀⠂⠀⠈⠀⠙
⠀⠴⣶⡶⢀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣯⣽⣭⣥⣤⣤⣴⣶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢠⣝⣛⢃⣸⣿⡟⡿⠟⠛⠉⠉⠻⠦⣿⣿⡔⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂
⠈⢁⠓⠈⠈⣰⢀⣾⣿⣿⣿⣿⣯⣹⣿⣿⣛⠋⠸⣿⢿⣿⣿⣿⣿⣿⣿⣏⡋⢻⣿⡾⡟⣹⣿⣿⣿⣿⣿⣿⣿⠯⣿⠻⣿⣻⣿⠉⠉⠀⠀⠀⣀⣤⣶⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀
⠁⣄⠄⠀⠀⣻⣶⠿⠍⢳⡨⠩⠇⡀⢅⠀⠁⠀⠩⠉⠛⣟⢯⠚⠿⠿⡿⠁⠀⠊⠀⠀⠀⠀⠿⠿⣿⣿⣿⢿⡏⡬⢚⡈⣰⣿⡷⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀
⣿⣶⣶⣶⣴⣿⣯⣿⣷⣦⣲⣞⡩⠬⢳⢥⣤⠀⠀⣐⣌⠀⠀⡀⠀⡀⠠⠄⣄⣀⡀⠑⣒⡺⣦⣭⣿⣿⡿⠑⠧⢁⠄⠐⢹⣫⠀⠀⠀⠀⠀⠀⠸⠛⠛⠉⠁⠀⢘⡿⣀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠠⣶⣷⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣴⡊⣠⣤⣄⣽⣾⣽⣿⣾⣯⣿⡛⣿⠿⠛⡗⢘⢻⡾⠄⠠⢐⡗⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⣠⣴⣾⣿⣾⣿⣷⣲⢂⠤⢶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣭⣺⠯⣥⡶⣾⣿⣿⣼⣷⣿⣦⡈⢀⢀⠀⠀⠀⠀⠀⠀⠀⠒⣿⣿⣿⣿⢹⠿⣿⣇⠼⢵⢿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠋⠙⣿⣜⣿⣾⡞⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⣉⣽⣿⣿⣟⡄⠀⠸⣏⠀⠈⣾⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠛⠛⠓⢾⣷⡕⠀⣀⠀⠀⠀⠀⠀⠀⠈⣉⣀⣬⣿⣿⣿⣿⠐⠀⣿⡄⠀⣿⣿⣿⡿⡯⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⢈⠈⢶⣿⣧⣷⣦⡀⠀⠀⠀⠀⠀⠀⠉⢿⣿⢿⣿⣿⣿⣷⡄⢀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⢿⠿⠃⠀⠉⠁⠷⠽⢾⠷⠀⠀⠀⠀⠀⠀⠀⠸⣧⠈⣹⣿⣿⣿⣿⣼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠙⠛⠋⠙⠛⠋⠉⠛⠛⠁⠈⠁⠀⠈⠙⠉⠉⠉⠉⠀⠓⡷⠁⠀⠀⠀⠈⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠿⢯⢶⣆⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠉⠁⠁⠀⠀⠀⠀⠀⠀⠁⠀⡙⠙⠉⠀⠀⠀⠀⠀⠀⠄⠒⠀⠐⠂⠀⠀⠀⠀⠀⠄⠄⠀⢠⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣇⠀⣸⢼⡗⢿⣿⣆⣶⣶⣶⣶⡶⣤⣤⣴⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠠⠤⣯⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠛⠿⠟⠛⠉⠀⠀⠀⠀⠘⣭⣫⣾⣿⣿⣿⡷⣺⣴⣵⣯⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠀⠀⠀⡠⠆⠂⠈⠁⠀⢦⣤⠀⠖⠀⠀⠀⠂⠘⣿⣿⣨⣵⣶⡂⠀⠀⠀⠀⠀⢀⡀⠀⢀⡄⢀⠀⠀⣦⢀⣾⣿⣿⣿⣿⢭⣭⣭⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⡄⢀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠓⠉⠀⠀⠀⠀⠀⠐⠛⠿⣟⠋⣛⠛⠃⠀⠀⠀⠀⣠⣼⡧⠀⢙⠹⠛⠀⠀⠤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿
⠀⠀⠀⠂⠀⢀⢐⢄⣂⣄⡀⡀⣄⡲⣻⣶⣺⣷⣦⣦⣦⣦⡈⠙⠀⢠⢠⣼⣧⣀⣄⣔⡆⣀⡦⡀⡀⡄⡀⢀⣀⠠⣶⢎⡙⠂⠽⠽⠂⠀⠀⠀⠀⠀⣈⣡⡴⠿⠗⠀⠒⣀⠀⠀⠘⠛⠿⠟⢛⣋⣙⣿⣿⣿⣷⣿⣿⡷
⠄⠠⡀⠀⡊⠬⣿⡿⣿⣾⣷⣿⣿⣿⣿⣷⣿⣿⡿⣿⣿⣟⡉⣔⠀⢀⣸⡿⠉⠁⠉⠀⠒⠂⠂⠀⠀⠀⠀⠀⠈⠉⠉⢊⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣦⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠐⠀⠀⠀⢠⣙⠻⣏⣿⣿⢺⣿⣿⡟⣿⡿⠾⠓⠛⠛⠻⠟⠋⠁⠾⡿⠿⠷⠲⣶⡾⠶⠶⣾⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⡿⠿⢿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠐⢆⣅⠳⠿⠛⡈⢠⣖⢊⠟⠀⣿⣿⡆⣿⣿⡇⣸⣿⡟⣿⣿⣿⣿⢸⣿⣿⣿⣷⣎⣿⣿⣻⣿⡿⣿⣿⡛⣷⣿⢿⣿⣮⢱⣿⣿⢿⣿⡿⢿⣿⡿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠁⠀⠀⠠⠴⠀⠈⠐⠀⠀⠀⠀⠈⡈⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣂⢸⣿⣿⣸⣿⡿⣶⣷⣛⣛⢣⣿⣿⢳⣿⣿⢸⣿⣿⢸⣿⣿⣼⣿⠏⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⣿⣿⣿⢿⣿⣿⣿⠃⣿⣿⡿⢿⢸⣿⣿⢻⣿⣷⢩⣿⣿⣣⣿⣿⠯⣾⣿⣿⢸⣿⣿⢸⣯⣿⢻⣿⣧⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣧⣭⢸⣿⣿⣼⣿⣿⣸⣿⣷⣿⣿⣥⣤⠌⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⣿⢸⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡛⣛⣛⣬⣿⣻⣻⣤⣿⣿⣿⣿⣼⣿⣻⣿⣿⣽⣿⣿⣛⣿⣿⣿⣻⣾⣮⣿⣿⣿⣷⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠶⣶⠯⢶⠦⠰⠶⠶⠶⠀⣤⣤⣤⣤⣄⢠⠀⢛⣋⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡤⣶⣶⣾⣶⢷⣶⣤⣻⣶⣾⣭⣯⣿⣼⣾⣿⣿⣾⣿⣿⡶⣷⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢁⣀⡀⠀⠐⣀⣛⠻⠦⠀⠀⢀⢀⡀⣤⣤⡀⠀⣦⣴⣄⡀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢊⣻⣿⠟⡟⠈⠛⡛⠻⠝⢚⡟⢛⠿⣿⣿⢿⣿⣟⠿⡛⠋⡙⠻⠂⢋⣁⣤⣶⣿⣿⣿⣿⣿⣿⣟⣉⣶⣶⣿⣿⣿⣶⢒⣻⣿⣶⣦⠮⢷⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⠈⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀
⠏⠝⢛⡀⠀⠀⠀⠀⠐⠀⠀⢀⣤⢩⣤⣷⣤⣤⣤⣦⣸⣎⣴⣬⣼⣿⣿⣿⣿⣿⣿⡿⠛⠒⣋⣀⢙⣿⣿⣿⣿⣷⣷⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣂⡀⣀⣀⣀⣯⣧⣤⣴⣔⠂
⠀⢤⣵⣖⠄⠀⠀⠀⠀⠀⠀⣴⣿⣵⣿⣿⣿⣿⣿⣿⣧⣶⣾⣿⣿⣿⣿⣿⣿⣿⣋⣤⡄⢐⣲⣿⣿⣿⣿⣿⣿⡏⡟⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠭⣇⣯⣽⠻⡟⡻⡿⠏⠻⠯⢠
⠚⠋⠃⠂⠤⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣻⣿⣷⣮⣿⣿⣿⣿⣿⣿⡿⠛⠛⢛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⠶⣿⣿⣿⣿⡷⣯⣿⣿⣿⡿⠿⣿⣿⣿⣽⣿⠿⠻⢹⡿⠷⠎⠁⠘⠓⠋⠁⠀⠂⠀⠈⠀⠑
⠠⠴⣶⡶⢀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣯⣽⣭⣥⣤⣤⣴⣶⠾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣇⢠⣝⣛⢃⣸⣿⡟⡿⠟⠛⠉⠘⠧⠵⣿⣿⡖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂
⠉⠁⠓⠈⠈⣰⢀⣾⣿⣿⣿⣿⣯⣹⣿⣿⡛⠋⠸⣿⢿⣿⣿⣿⣿⣿⣿⣏⠋⢻⣿⡾⡟⢽⣿⣿⣿⣿⣿⣿⣿⠯⣿⠿⣿⣛⣿⠍⠁⠀⠀⠀⣀⣤⣶⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠁⣄⠄⠀⠀⣻⣶⠿⠍⢳⡬⠩⠇⠀⣅⡠⠁⠀⠩⠉⠛⣟⢿⠚⠿⠿⠯⠁⠀⠊⠀⠀⠀⠀⠿⠿⣿⣿⣿⢿⡏⡤⢚⡂⣰⣿⠖⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀
⣿⣶⣶⣤⣴⣿⣯⣿⣷⣦⣲⣾⡙⠬⢳⢥⣤⠀⠀⣐⣌⠀⠀⠀⠀⡀⠠⠄⣀⣀⡀⠑⢒⡺⣦⣭⣿⣿⡿⠙⠧⢀⠄⠐⢈⣫⠀⠀⠀⠀⠀⠀⢻⠛⠛⠙⠁⠀⢹⠇⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣷⣶⣿⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣴⡊⣠⣤⣄⣿⣾⣼⣿⣾⣯⣿⡻⣿⠾⠛⡗⢚⢻⡾⠄⠠⣐⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣾⣿⣶⢒⡦⠤⠖⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣭⣺⠿⣥⡶⣾⣿⣿⣼⣷⣿⣆⡈⢀⡀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⣿⣿⠻⡿⣿⡅⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠋⢙⣿⣜⣿⣾⡞⠁⠄⠃⠀⠀⠀⠀⠀⠐⠂⣉⣿⣿⣿⡿⡄⠀⢹⡇⠀⢸⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠛⠛⠓⠾⣷⡕⠀⣀⠀⠀⠀⠀⠀⠀⠈⢁⣉⣸⣿⣿⣿⣷⠀⠀⣷⡀⢈⢿⣿⣿⡿⡯⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⢀⠀⢤⣿⣷⣲⣆⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣧⡀⣈⡁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⢿⠿⠃⠀⠉⠑⡿⠭⢾⠷⠀⠀⠀⠀⠀⠀⠀⢹⣆⢘⣹⣿⣿⣿⣿⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⠙⠛⠉⠙⠛⠋⠙⠛⠛⠁⠈⠁⠀⠈⠙⠉⠉⠉⠉⠈⠓⡷⠁⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠿⣇⢾⡆⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡉⠙⠉⠀⠀⠀⠀⠀⠀⠄⠂⠀⠐⠂⠈⠀⠀⠀⠀⠄⠄⠀⢠⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢿⣿⣿⣿⡇⠀⠸⢼⠗⣿⣿⣖⣶⣶⣶⣶⣶⣤⣤⣴⡤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠠⠤⣯⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠞⠿⠿⠛⠋⠀⠀⠀⠀⠘⣭⣽⣼⣿⣿⣿⡗⣚⣤⣽⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠀⠀⠀⡠⠆⠂⠈⠁⠀⢦⣤⠀⠖⠀⠀⠀⠀⠘⣿⣿⣠⣵⣶⠂⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀⢀⠀⠀⣦⢀⣾⣿⣿⣿⣿⣯⣭⣭⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠑⠉⠀⠀⠀⠀⠀⠐⠛⠿⣿⠋⣛⠻⠃⠀⠀⠀⠀⣠⣿⡧⠀⠙⠹⠛⠀⠀⠤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿
⠀⠀⠀⠀⠀⢀⣰⢄⣂⣄⡀⡀⣔⡲⣺⣶⣲⣷⣦⣦⣤⡦⡈⠙⠀⢠⢠⣼⣦⣠⣄⣔⣄⣀⡶⠀⣀⡄⡀⢀⣀⡠⢶⣎⡙⠂⠽⠽⠒⠀⠀⠀⠀⠀⣈⣤⠴⠿⠛⠠⠒⣀⠀⠀⠘⠛⠻⠟⢛⣋⣛⣿⣿⣿⣷⣿⣿⣿
⠄⠠⡐⠀⡚⠬⣿⡿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⡿⣿⣿⣟⡁⣔⠀⢀⣸⡿⠉⠀⠉⠀⠒⠒⠂⠀⠀⠀⠀⠐⠈⠉⠈⣃⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣦⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠀⠀⠀⠠⣉⠿⣏⣿⣿⢺⣿⣿⡿⣿⡽⠾⠓⠛⠛⠻⠟⠋⠃⠾⡿⠷⠶⠶⢶⠾⠶⠶⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⡿⠿⢿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⠀⠀⠀⠀⠐⢖⣅⡲⠿⠛⠈⢠⡶⢃⠟⠁⣿⣿⡆⣿⣿⡇⣸⣿⡟⣿⣿⣿⣿⢸⣿⣿⣿⣷⣎⣿⣿⣻⣿⡿⣿⣿⡛⣿⣿⢿⣿⣮⢱⣿⣿⢿⣿⡞⢿⣿⡿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠁⠀⠀⠠⠴⠀⠈⠐⠀⠀⠀⠀⠀⢈⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣢⢸⣿⣿⣸⣿⡿⣶⣿⣛⣛⢣⣿⣿⢣⣿⣿⢼⣿⣿⢸⣿⣿⣼⣿⠏⢸⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⣿⣿⣿⢿⣿⣿⣿⠃⣿⣿⡿⣿⢸⣿⣿⢻⣿⣷⢩⣿⣿⣣⣿⣿⠯⣾⣿⣿⢹⣿⣿⢸⣯⣿⢻⣿⣧⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣧⣭⢸⣿⣿⣼⣿⣿⣸⣿⣷⣿⣿⣥⣤⠌⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⣿⢸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡛⣛⣛⣬⣿⣻⣋⣤⣿⣿⣿⣿⣼⣿⣻⣿⣿⣿⣿⣿⣛⣿⣿⣿⣻⣾⣮⣿⣟⣿⣷⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠶⣶⠯⢶⠦⠰⠶⠶⠶⠀⣤⣤⣤⣤⣀⢠⡀⢙⣋⣛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡤⣶⣶⣾⣶⣷⣶⣤⣻⣶⣾⣭⣭⣷⣼⣾⣿⣿⣿⣿⣾⡶⣷⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢁⢀⡄⢀⠀⡄⣃⢱⣦⠀⡀⢀⢀⣀⣄⣀⠀⢀⣤⣴⣄⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢊⠿⣿⠟⡛⠨⠛⠛⠻⠝⢚⡿⠟⠿⣟⣿⢿⣿⣿⠿⡛⠋⡙⠿⠂⢊⣡⣤⣶⣿⣿⣿⣿⣿⣿⣟⣉⣴⣶⣷⣿⣿⣶⢂⣿⣿⣶⣧⠂⢷⣎⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡅⠈⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀
⠯⠝⢛⡀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢩⣬⣧⣦⣬⣤⣦⣸⣎⣷⣤⣽⣿⣿⣿⣿⣿⣿⡟⠛⠓⣃⣀⣉⣿⣿⣿⣿⡷⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠃⠂⣠⣀⢔⣽⣶⣦⣤⣖⠀
⠀⢤⣵⣖⠄⠀⠀⠀⠀⠀⠀⣤⣿⣷⣿⣿⣿⣿⣿⣿⡧⣖⣾⣿⣿⣿⣿⣿⣿⣿⣉⣤⡄⢐⣲⣿⣿⣿⣿⣿⣿⡏⠟⣏⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⡟⡭⢅⣬⣽⠿⡟⠻⡿⠋⠙⠯⠨
⠚⠋⠃⠒⠠⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣿⣿⣿⣿⣿⣿⡿⠛⠛⢛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⠶⣿⣿⣿⣿⡷⣯⣿⣿⣿⣿⠿⣿⣿⣿⢽⣿⠾⠻⢹⡿⠷⠎⠁⠘⠓⠋⠀⠀⠖⠀⠀⠀⠋
⠠⠴⣶⡤⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⣽⣭⣥⣤⣤⣴⣶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢠⣟⣟⢇⣹⣿⡟⡿⠟⠙⠙⠫⠷⣶⣿⣿⣖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂
⠈⡁⠓⠂⠈⡰⢀⣾⣿⣿⣿⣿⣯⣽⣿⣿⡟⠋⠸⣿⢿⣿⣿⢿⣿⣿⣿⣍⠋⢻⣿⡿⡟⢽⣿⣿⣿⣿⣿⣿⣿⢯⠿⠿⣿⣻⡟⠉⠀⠀⠀⠀⣀⣴⣾⣿⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀
⠁⡄⠀⠀⠀⣻⣶⠿⠍⠲⡌⠩⠗⣀⢅⠠⠁⠀⠩⠉⠟⣟⢯⠚⠻⠿⡿⠁⠀⠊⠀⠁⠀⠀⠿⢿⣿⣿⣿⢿⡏⡌⢈⡊⣱⡟⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣶⣶⣴⣴⣽⣭⣾⣷⣦⣴⣼⡩⠬⢳⢥⣤⠀⠀⢐⣌⠀⠀⠀⠀⡀⠀⠄⣀⣀⡀⡁⠒⡪⣦⣭⣿⣿⡿⠑⠧⢁⠄⠐⠛⡃⠀⠀⠀⠀⠀⠸⠿⠿⠛⠋⠁⠘⡿⣠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢰⣦⣷⣶⣿⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣴⡋⣠⣤⣤⣶⣾⣽⣿⣿⣯⣿⣻⣿⠿⠛⡗⢘⠻⡾⡄⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣨⣶⣿⣷⣿⣷⡎⣶⡦⠰⢲⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣭⣺⣿⡥⣶⣾⣿⣾⣼⣿⣿⣇⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⡟⠿⣿⣯⠸⡿⣶⢾⣿⣾⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠋⢙⣿⡜⣿⣿⡾⠀⠘⠀⠀⠀⠀⠀⠀⠀⠐⢻⣿⣿⣿⢧⠀⠘⣿⠀⠀⢽⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠛⠑⢾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⢉⣻⣿⣿⣟⡆⠀⢸⣇⠀⠹⢿⣿⣿⡿⡯⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⢈⠀⢸⣿⣧⣺⠆⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣄⠀⣩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⢿⠿⠃⠀⠍⠁⣷⠽⢾⠆⠀⠀⠀⠀⠀⠀⠈⢿⠀⢋⣿⣿⣿⣿⣧⣿⡆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⠙⠛⠉⠙⠛⠋⠙⠛⠛⠁⠈⠀⠀⠈⠙⠉⠉⠉⠉⠀⠓⡳⠁⠈⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⣾⣿⣿⣿⣿⠿⡕⣾⡄⢐⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⡙⠙⠉⠀⠀⠀⠀⠀⠀⠄⠄⠐⠒⠂⠈⠀⠀⠀⠀⠀⠀⠀⢠⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⣿⣿⣿⡁⠀⡹⢭⠚⣿⣿⣠⣰⣶⣶⣶⣶⣤⣤⣴⡤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠠⢄⣯⡻⠁⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣠⡄⢀⠀⠀⠀⠀⠀⠐⣽⠿⠿⠟⠋⠀⠀⠀⠀⠙⣌⣴⣿⣿⣿⣿⡷⣺⣶⣽⣭⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠐⠀⠀⠀⠀⡠⠄⠂⠈⠈⠀⢢⢄⠐⠖⠀⠀⠀⠀⡸⣟⣿⣤⣵⣶⠂⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⠀⠀⠀⣄⢀⣿⣿⣿⣿⣿⣿⣭⣽⢽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⢀⡠⠀⠈⠀⠀⠀⠀⠀⠀⠓⠉⠀⠀⠀⠀⠀⠐⠛⠿⣿⠋⡟⠻⠁⠀⠀⠀⠀⣴⢿⣇⡀⢙⠹⠟⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿
⠀⠀⠈⠂⠀⠀⢐⣔⣐⣄⡄⡀⣄⡲⢻⣶⣺⣷⣦⣷⣤⡆⡈⠉⠀⠠⠀⣼⣦⣀⣄⣄⣆⣀⡤⠠⡀⡀⡀⠀⢀⡠⣼⡄⠉⠂⠻⠽⠒⠁⠀⠀⠀⠀⣈⡥⠾⠛⠃⠀⠂⢀⠀⠀⠘⠛⠻⠟⣻⣟⣛⣿⣿⣿⣷⣿⣿⣷
⠄⠠⡀⠀⡢⠬⣽⡿⣿⣷⣧⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⡁⣄⠁⢀⣸⡿⠉⠈⠉⠐⠒⠒⠂⠀⠀⠀⠀⠀⠈⠉⠉⢈⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣤⣬⣴⣴⣶⣶⣶⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠀⠀⡂⠠⣙⠻⣯⣻⣿⢻⣿⣿⡿⣿⣿⠾⠇⠻⠛⠻⠟⠉⠃⢽⡿⠷⡶⠶⣶⣿⠶⠾⢾⣾⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⠿⢿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⠀⠀⠀⠀⠐⢖⡅⢳⠿⠟⠈⢠⣖⢫⠟⠁⣿⣿⡆⣿⣿⣇⣸⣿⡟⣿⣿⣿⣿⢸⣿⣿⣿⣷⣎⣿⣿⣳⣿⡿⣿⣿⡛⣿⣿⢿⣿⣮⢱⣿⣿⢿⣿⡞⢿⣿⡿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠁⢀⠀⠠⠴⠀⠈⠀⠀⠀⠀⠀⠀⣈⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣢⢸⣿⣿⣸⣿⡿⣴⣷⣛⣛⢣⣿⣿⢳⣿⣿⣼⣿⣿⢸⣿⣿⣼⣿⠏⢸⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢸⣿⣿⣿⢿⣿⣿⣿⠃⣿⣿⡿⣿⢸⣿⣿⢻⣿⣷⢩⣿⣿⣣⣿⣿⠯⣾⣿⣿⢹⣿⣿⢸⣯⣿⢻⣿⣧⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣧⣭⢸⣿⣿⣼⣿⣿⣸⣿⣷⣿⣿⣥⣴⠌⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⣿⢸⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢈⠛⣛⣛⣬⣿⣻⣫⣤⣿⣿⣿⣿⣼⣿⣻⣿⣿⣽⣿⣟⣛⣿⣿⣿⣻⣾⣮⣿⣟⣿⣷⣶⣽⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠶⣶⠯⢶⠦⠰⠶⠶⠶⠀⣤⣤⣤⣤⣄⢀⠀⢙⣙⣛⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡤⣶⣶⣾⣶⣷⣶⣤⣻⣶⣾⣿⣭⣷⣼⣾⣿⣿⣿⣿⣾⡶⣷⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢁⣠⡄⢀⢐⢄⣃⢱⡆⠀⡀⢀⢀⣠⣄⣀⠀⢄⣦⣴⣀⡀⠀⠀⢀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢚⠿⣿⠟⡛⠈⠛⠛⠻⠝⢺⡟⠟⠿⣿⣿⢿⣿⣿⠿⣟⠋⡙⠻⠂⢊⣡⣤⣶⣿⣿⣿⣿⣿⣿⣟⣉⣴⣶⣿⣿⣿⣶⢒⣿⣿⣷⣧⠪⢷⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀
⠯⠝⢚⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢩⣬⣵⣦⣬⣤⣶⣰⣆⣴⣤⣽⣿⣿⣿⣿⣿⣿⡿⠛⠒⣃⣀⣙⣿⣿⣿⣿⡷⣿⣿⡿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣆⠂⣀⣀⢔⣽⣷⣦⣤⣖⠀
⠀⢤⣵⡖⠄⠀⠀⠀⠀⠀⠀⣤⣿⣷⣿⣿⣿⣿⣿⣿⡧⣖⣾⣿⣿⣿⣿⣿⣿⣿⣁⣤⡄⢐⣲⣿⣿⣿⣿⣿⣿⡏⡟⣏⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⡭⢅⣭⣼⠿⡟⠻⠿⠏⠙⠯⠸
⠚⠋⠃⠒⠠⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣟⣿⣷⣬⣿⣿⣿⣿⣿⣿⡿⠛⠛⢛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⠶⣿⣿⣿⣿⡷⣯⣿⣿⣿⡿⠿⣿⣿⣿⢽⣿⠾⠿⢻⡿⢷⠎⠁⠘⠓⠋⠀⠀⠆⠀⠈⠀⠛
⠠⠴⣶⡶⡀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⣽⣭⣥⣤⣤⣴⣶⢾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣇⢠⣟⣛⣇⣹⣿⡟⠿⠋⠋⠻⠹⢷⣾⣿⣿⡜⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂
⠈⠁⠃⠀⠈⡰⢀⣾⣿⣿⣿⣿⣿⣹⣿⣿⡟⠋⠸⣿⢿⣿⣿⢿⣿⣿⣿⣍⠋⢻⣻⡾⠟⢽⣿⣿⣿⣿⣿⣿⣿⢯⠽⠿⣿⣻⡟⠉⠀⠀⠀⠀⣠⣴⣿⣿⣆⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀
⠁⡠⠀⠀⠀⣺⣶⠿⠍⠲⡬⠩⠗⣀⢅⠠⠁⠀⠩⠉⠛⣟⢯⠚⠻⠿⡿⠁⠀⠊⠀⠁⠀⠀⠿⢿⣿⣿⣿⢿⡏⡄⢊⡊⣰⠇⠀⠀⠀⠀⢲⣿⣿⣿⣿⣿⣿⣷⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣶⣶⣴⣴⣽⣭⣿⣷⣦⣶⣞⡉⠬⢲⢥⣤⠀⠀⢐⣌⠀⠀⠀⠀⡀⠠⠄⣄⣀⡀⡁⣒⡪⣦⣭⣿⣿⡿⠙⢧⢁⠄⠐⠛⠀⠀⠀⠀⠀⠀⡿⢿⠿⠛⠉⠀⢻⡇⡀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⢰⣦⣷⣶⣿⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣴⡍⣠⣤⣄⣷⣾⣽⣿⣿⣯⣿⣻⣿⠿⠛⡗⢘⠻⡾⡄⠠⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣬⣾⣿⣶⣿⣶⣐⣶⡤⠀⢶⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣺⣿⡡⣴⣾⣿⣿⣼⣷⣿⣇⣈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⠻⡿⣿⣇⠹⢵⣻⢶⣿⣾⣿⣿⣿⣿⡿⡟⠋⠀⠈⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢙⣿⡼⢿⣾⡾⠋⠄⠀⠀⠀⠀⠀⠀⠤⠐⢿⣿⣿⡿⡄⠀⠙⡟⠀⠀⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠛⠛⠑⢾⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⢛⣿⣿⣿⣹⡀⠀⢻⡄⠀⡿⢿⣿⣿⡿⡯⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⢈⠀⢲⣿⣧⣺⡄⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⣷⣄⢈⣉⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⢿⠿⠃⠀⠉⠁⢷⠭⢶⠄⠀⠀⠀⠀⠀⠀⠘⣏⠁⠛⣿⣿⣿⣿⣎⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⣻⠛⠛⠉⠙⠛⠋⠙⠛⠛⠁⠀⠁⠀⠈⠙⠋⠉⠉⠉⠀⠓⡳⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣿⣿⣿⣿⣿⢿⡔⣶⡀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠄⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡁⠀⡧⠿⠸⣿⡿⣠⣶⣶⣶⣶⣶⣤⣤⣴⡴⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠤⣯⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣠⡄⠀⠀⠀⠀⠀⠀⠐⣻⣿⠿⠟⠃⠀⠀⠀⠀⠋⣬⣾⣿⣿⣿⣿⡷⣺⣦⣵⣭⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠐⠀⠀⠀⠀⡠⠄⠂⠈⠈⠀⢢⣄⠔⠖⠀⠀⠀⠂⡸⣿⣿⣨⣵⣶⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⠀⠀⠐⣄⢰⣿⣿⣿⣿⣿⣯⣽⣽⢽⣿⣿⣿
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠓⠉⠀⠀⠀⠀⠀⠐⠙⢿⣿⠋⡛⠻⠁⠀⠀⠀⠀⣼⢿⣇⡀⢙⠹⠟⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿
⠀⠀⠀⠂⠀⢀⢐⣌⣀⣄⡄⡁⣄⣲⣻⣶⣺⣷⣮⣷⣤⡦⡈⠙⠀⢠⠠⣼⣦⣀⣄⣀⣆⣀⡄⠠⠀⡀⡀⢀⢀⡠⣴⡄⠙⠂⠹⠽⠐⠀⠀⠀⠀⠀⣈⡴⠾⠛⠃⠠⠆⢀⠀⠀⠘⠛⠿⠟⣿⣟⣛⣿⣿⣿⣷⣾⣿⣷
⠄⠠⡐⢀⡫⠬⣿⡿⣿⣿⣦⣿⣿⣿⣿⣯⣿⣿⡿⣿⣿⣟⡁⣄⠁⢀⣸⡿⠉⠈⠉⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣤⣤⣴⣴⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠀⠀⡂⠀⣉⢿⣏⣿⣿⢻⣿⣿⡿⣿⡿⠾⠃⠻⠛⠻⠟⠋⠃⢽⡿⠷⡶⠶⣶⣿⡶⠶⢿⣾⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⠿⢿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⠀⠀⠀⠀⠐⢶⣅⢳⠿⠟⠌⢠⣖⣋⠟⠁⣿⣿⡆⣿⣿⡇⣸⣿⡟⣿⣿⣿⣿⢸⣿⣿⣿⣷⣎⣿⣿⣳⣿⡿⣿⣿⡛⣷⣿⢿⣿⣮⢱⣿⣿⢿⣿⡞⢿⣿⡿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⠴⠀⠈⠀⠀⠀⠀⠀⠀⢈⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣲⢸⣿⣿⣸⣿⡿⣴⣿⣛⣛⢣⣿⣿⢳⣿⣿⢸⣿⣿⢸⣿⣿⣼⣿⠏⢸⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⣿⣿⣿⢿⣿⣿⣿⠃⣿⣿⡿⣿⢸⣿⣿⢻⣿⣷⢩⣿⣿⣣⣿⣿⠯⣾⣿⣿⢸⣿⣿⢸⣯⣿⢻⣿⣧⢸⣿⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣧⣭⢸⣿⣿⣼⣿⣿⣸⣿⣷⣿⣿⣥⣴⠈⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⣿⢸⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢈⠛⣛⣛⣬⣿⣻⣯⣤⣿⣿⣿⣿⣼⣿⣻⣿⣿⣽⣿⣟⣛⣿⣿⣿⣻⣾⣮⣿⣟⣿⣷⣶⣽⣿⣻⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠶⣶⠯⢶⠦⠰⠶⠶⠶⠀⣤⣤⣤⣤⣀⡀⠀⢙⣙⣛⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡤⣶⣶⣾⣶⣷⣶⣤⣻⣶⣾⣭⣭⣷⣼⣾⣿⣿⣿⣿⣾⡶⣷⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢁⢀⡄⠀⣐⣄⣁⢱⡦⠀⠀⢀⠀⣀⣄⣀⡀⢀⣦⣤⣀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢊⠿⣿⠟⡛⠈⠛⠛⠻⠝⢚⡿⠟⠿⣟⡿⢿⣿⣿⠿⡛⠋⡙⠿⠂⢊⣡⣤⣶⣿⣿⣿⣿⣿⣿⣟⣉⣴⣶⣷⣿⣿⣶⢂⣿⣿⣶⣧⠪⢲⣞⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠈⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀
⠯⠝⢛⡀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢩⣬⣧⣦⣬⣤⣶⣰⣆⣴⣤⣽⣿⣿⣿⣿⣿⣿⡿⠛⠒⣃⣀⣉⣿⣿⣿⣿⣷⣷⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀⠀⣀⣀⢔⣹⣦⣤⣤⣖⠀
⠀⢤⣵⣖⠄⠀⠀⠀⠀⠀⠀⣤⣿⣷⣿⣿⣿⣿⣿⣿⡦⣖⣾⣿⣿⣿⣿⣿⣿⣿⣉⣤⡄⢐⣲⣿⣿⣿⣿⣿⣿⡏⠟⣏⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⡿⡭⢅⣭⣼⠿⡟⠻⡿⠋⠙⠯⠸
⠚⠋⠃⠒⠠⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣿⣿⣿⣿⣿⣿⡿⠛⠛⢛⠫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⠶⣿⣿⣿⣿⡷⣯⣿⣿⣿⡿⠿⣿⣿⣿⢽⣿⠿⠿⢻⡿⠶⠎⠁⠘⠓⠋⠀⠀⠆⠀⠀⠀⠚
⠠⠴⣶⡴⡀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⣽⣭⣥⣤⣤⣴⣶⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢠⣟⣛⣇⣹⣿⡟⠿⠏⠹⠏⢽⣷⣾⡿⣽⣆⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂
⠈⠁⠃⠀⠈⣰⢀⣾⣿⣿⣿⣿⣿⣹⣿⣿⡟⠋⠸⣿⢿⣿⣿⢿⣿⣿⣿⣍⡋⢻⢿⠾⠟⢽⣿⣿⣿⣿⣿⣿⣿⢯⠿⠿⣿⢻⠛⠉⠀⠀⠀⢀⣠⣾⣷⣾⡑⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀
⠁⡄⠀⠀⠀⣺⣶⠿⠍⠳⡬⠩⠗⢈⢅⠠⠁⠀⠩⠉⠛⣟⢯⠚⠻⠿⡯⠁⠀⠊⠀⠁⠀⠀⠿⢿⣿⣿⣿⢿⡟⡄⢈⡂⡰⠁⠀⠀⠀⠠⣶⣿⣿⣿⣿⣿⣿⣖⣦⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣷⣶⣶⣴⣴⣽⣭⣾⣷⣦⣴⣞⡉⠨⢲⢥⣠⠀⠀⢐⣌⠀⠀⠀⠀⠀⠀⠄⣄⣀⡀⡁⣒⠪⣦⣭⣿⣿⡿⠑⠧⢁⠄⠐⠁⠀⠀⠀⠀⠀⢹⣿⣿⡿⠟⠋⠙⢿⢔⠂⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠰⣦⣷⣶⣿⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⡊⣠⣤⣤⣶⣾⣽⣿⣾⣯⣿⣻⣿⠿⠛⡗⢘⠻⡾⠄⠰⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⣵⣿⣷⣾⣷⣇⣻⣶⠄⠀⢲⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣭⣺⣿⡡⣲⣾⣿⣿⣼⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡟⢿⢿⣿⡉⢯⢖⣶⢾⣿⣾⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⢙⣿⡝⣿⣾⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣿⣿⣷⠀⠈⢻⡇⠀⢸⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠓⠛⠑⢾⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢻⣿⣿⣧⢇⠀⠈⣷⡀⢈⠿⠿⣿⣿⡿⡯⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄⢈⠀⢺⣿⣧⣂⠀⠀⠀⠀⠀⠀⠀⠴⣶⣿⣿⣿⣿⣿⣦⡀⢉⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⢿⠿⠃⠀⠉⠁⣷⠭⣷⠄⠀⠀⠀⠀⠀⠀⠹⡏⠉⢻⣿⣿⣿⣿⣜⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⣻⠋⠛⠉⠙⠛⠋⠙⠛⠛⠁⠈⠀⠀⠈⠙⠋⠉⠉⠉⠈⠓⡲⠁⠈⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣿⣿⣿⣿⣿⣿⢰⣧⠀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⡙⠙⠉⠀⠀⠀⠀⠀⠀⠄⠄⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⠀⠀⡇⠿⠸⣿⡷⡤⣶⣶⣶⣶⣶⣤⣤⣤⡤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⢤⣯⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣠⡄⠀⠀⠀⠀⠀⠀⠡⢿⣿⠿⠟⠃⠀⠀⠀⠀⠣⣤⣾⣿⣿⣿⣿⣷⣺⣴⣵⣭⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠐⠀⠀⠀⠀⡠⠄⠂⠈⠁⠀⢢⢤⠐⢖⠀⠀⠀⠀⡸⣟⣿⣨⣵⣶⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⠀⠀⠐⡄⢰⣿⣿⣿⣿⣿⣭⣭⣭⢽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠓⠉⠀⠀⠀⠀⠀⠐⠛⢿⣿⠋⡛⠻⠀⠀⠀⠀⠀⣼⢿⣦⡄⢙⠹⠗⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿
⠀⠀⠀⠂⠀⢀⢐⣅⣀⣀⡄⡀⣄⡲⢺⣶⣺⣷⣦⣷⣤⡦⡈⠙⠀⢠⢠⣴⣦⣀⣄⣄⣆⣀⡤⠠⡀⡀⡀⢀⢀⡠⣴⡀⡉⡂⠽⠝⠒⠁⠀⠀⠀⠀⣀⡴⠞⠛⠁⠠⠂⢀⠀⠀⠘⠛⠻⠟⣟⣟⣛⣿⣿⣿⣷⣿⣿⣷
⠄⠀⡐⠀⡣⠭⣽⡿⣿⣷⣧⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⡁⣄⠁⢀⣸⡿⠁⠈⠙⠐⠒⠚⠀⠀⠀⠀⠀⠀⠈⠉⠉⢁⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣤⣬⣤⣴⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠂⠈⡂⢠⣉⠻⣭⣻⣿⢺⣿⣿⡟⣯⡿⠾⠇⠻⠛⠻⠟⠉⠃⢽⡿⠷⡶⠶⣶⣿⡾⠾⢷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⠀⠀⠀⠀⠐⢖⣥⢳⠿⠛⠈⢠⣆⢏⠟⠀⣿⣿⡆⣿⣿⣇⣸⣿⡟⣿⣿⣿⣿⢸⣿⣿⣿⣷⣎⣿⣿⣳⣿⡿⣿⣿⡛⣿⣿⢿⣿⣮⢱⣿⣿⢿⣿⡞⢿⣿⡿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠁⠀⠀⠠⠴⠀⠈⠀⠀⠀⠐⠀⠀⣈⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣢⢸⣿⣿⣸⣿⡿⣴⣷⣛⣛⢣⣿⣿⢳⣿⣿⢼⣿⣿⢸⣿⣿⣼⣿⠏⢸⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢸⣿⣿⣿⢿⣿⣿⣿⠃⣿⣿⡿⣿⢸⣿⣿⢻⣿⣷⢩⣿⣿⣣⣿⣿⠯⣾⣿⣿⢹⣿⣿⢸⣯⣿⢻⣿⣧⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣧⣭⢸⣿⣿⣼⣿⣿⣸⣿⣷⣿⣿⣥⣴⠈⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⡿⢸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢈⠛⣛⣛⣬⣿⣻⣫⣤⣿⣿⣿⣿⣼⣿⣻⣿⣿⣽⣿⣟⣛⣿⣿⣿⣻⣾⣮⣿⣟⣿⣷⣶⣽⣟⣻⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠲⣶⠯⢶⠦⠰⠶⠶⠶⠀⣤⣤⣦⣤⣄⣀⡀⢙⣛⣛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡤⣶⣶⣾⣶⣷⣶⣤⣻⣶⣾⣭⣭⣷⣼⣾⣿⣿⣿⣿⣾⡶⣷⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢁⣤⡄⢀⢐⡄⣃⢱⡦⠀⡀⢀⢀⣀⣄⣀⠀⠀⣦⣴⣄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢊⠿⣿⠟⡛⠈⠛⠛⠻⠝⢚⡿⠛⠿⣟⣿⢿⣿⣿⠿⡛⠋⡙⠿⠂⢊⣡⣤⣶⣿⣿⣿⣿⣿⣿⣟⣉⣴⣶⣿⣿⣿⣶⢂⣿⣿⣶⣧⠪⢶⣞⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡅⠈⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀
⠯⠝⢚⠀⠀⠀⠀⠀⠐⠀⠀⢀⣄⢩⣬⣷⣆⣬⣤⣶⣰⣦⣵⣤⣽⣿⣿⣿⣿⣿⣿⡿⠛⠒⢃⣀⢉⣿⣿⣿⣿⡷⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡂⠂⣀⣀⢔⣽⣧⣦⣬⣖⠀
⠀⢤⣵⣖⠄⠀⠀⠀⠀⠀⠀⣤⣿⣷⣿⣿⣿⣿⣿⣿⡧⣖⣾⣿⣿⣿⣿⣿⣿⣿⣉⣤⡄⢐⣲⣿⣿⣿⣿⣿⣿⡏⠟⣟⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⡭⢅⣭⣼⠿⡟⠿⡿⠏⠙⠯⠨
⠚⠟⠃⠒⠠⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣟⣿⣷⣬⣿⣿⣿⣿⣿⣿⡿⠛⠛⢛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⠶⣿⣿⣿⣿⡷⣯⣿⣿⣿⡿⠿⣿⣿⣿⢽⣿⠿⠿⢻⡿⢷⠎⠁⠘⠛⠋⠀⠀⠖⠀⠈⠀⠛
⠠⠴⣶⡴⡀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣯⣽⣍⣥⣤⣤⣴⣶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢠⣟⣛⣇⣽⣿⣟⠿⠛⢿⢯⣿⣥⣾⠿⣿⣞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂
⠈⠁⠃⠀⠈⣰⢀⣾⣿⣿⣿⣿⣿⣹⣿⣿⡟⠋⠸⣿⢿⣿⣿⢿⣿⣿⣿⣍⠋⢻⣿⡿⡟⢽⣿⣿⣿⣿⣿⣿⣿⢯⠿⠿⣿⠻⠛⠁⠀⠀⠀⢀⣠⣿⣦⣜⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀
⠡⡄⠀⠀⠀⣺⣶⠿⠍⠱⡌⠩⠗⣈⢅⠠⠁⠀⠩⠉⠛⣟⢯⠚⠻⠿⡿⠁⠀⠊⠀⠁⠀⠀⠿⢿⣿⣿⣿⢿⡏⡄⢈⡂⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣦⢰⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣷⣶⣶⣤⣴⣽⣭⣾⣷⣦⣴⣞⡩⠨⢻⠥⣤⠀⠀⢐⣌⠀⠀⠀⠀⡀⠠⠄⣄⣀⡀⡁⢒⡪⣦⣭⣿⣿⡿⠑⠧⢁⠄⠒⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠟⠉⢿⡧⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣷⣶⣿⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣴⡋⣠⣤⣤⣶⣾⣽⣿⣾⣯⣿⣻⣿⠿⠛⡗⢘⠻⡾⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⢀⣵⣿⣶⣶⣶⡈⠉⣒⠦⠠⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣺⣿⡥⣶⣾⣿⣿⣼⣷⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣏⠹⡵⣒⡖⢾⣿⣾⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠋⢙⣿⡝⢿⣶⡞⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡇⠀⠹⣿⠀⠀⢿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠛⠑⢾⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⢿⣿⣿⡼⡄⡀⠸⣆⠀⢸⠿⢿⣿⣿⡿⠯⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⢈⠀⢸⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣄⠀⢙⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⢿⠿⠃⠀⠉⠁⣷⠯⢦⠀⠀⠀⠀⠀⠀⠀⢿⠉⠹⢿⣿⣿⣿⣷⣹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⣻⠛⠛⠉⠙⠛⠋⠙⠛⠛⠁⠈⠀⠀⠈⠙⠋⠉⠉⠉⠀⠓⡶⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⣧⣠⣾⣿⣿⣿⣿⣯⢸⣆⠀⣲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⡉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠔⠐⠒⠂⠀⠀⠀⠀⠀⠄⠀⠀⢠⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣿⣿⣿⣿⣟⠀⢈⠎⠍⢻⣿⡇⡆⣶⣶⣶⣶⣶⣤⣤⣤⡤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣯⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣠⡄⠀⠀⠀⠀⠀⠀⢃⣻⣿⡿⠟⠂⠀⠀⠀⠀⠡⣷⣷⣿⣿⣿⣿⡷⣺⣦⣵⣭⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠐⠀⠀⠀⠀⡠⠄⠂⠈⠈⠀⠢⠄⠔⢖⠀⠀⠀⠀⡘⣟⣿⣨⣵⡖⠀⠀⠀⠀⠀⠀⣁⠀⠀⢀⡀⠀⠀⠐⡄⣸⣿⣿⣿⣿⣿⣯⣭⣭⢽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠁⠀⠀⠀⠀⠀⠀⠓⠉⠀⠀⠀⠀⠀⠐⠛⢿⣿⠋⡟⠻⠀⠀⠀⠀⠀⡼⢿⣤⡄⢉⠹⠗⠀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿
⠀⠀⠀⠂⠀⠀⢐⣄⣀⣀⡄⡁⣄⡢⢺⣶⣺⣷⣦⣷⡤⡆⡈⠙⠀⠠⢠⣴⣦⣀⡄⣄⣆⣀⡤⠀⠀⠄⡀⢀⢀⣠⣴⡄⡉⡂⠻⠝⠒⠁⠀⠀⠀⠀⣠⡴⠛⠛⠁⠠⠂⢀⠀⠀⠘⠛⠿⠿⣿⣟⣛⣿⣿⣿⣷⣿⣿⣷
⠄⠠⡐⠀⡢⠤⣹⡿⣿⣷⣦⣿⣿⣿⣿⣿⣯⣿⡿⣿⣿⣟⡃⣔⠁⢀⣹⡿⠀⠈⠘⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠁⠉⢉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣬⣤⣴⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠐⠀⡂⠠⣉⢿⣏⣻⣿⢻⣿⣿⡟⣯⣿⠾⠇⠻⠛⠻⠟⠉⠃⢼⡿⠷⠶⢶⣶⠿⠶⠶⢷⣶⣾⣿⣿⣿⣿⢿⣿⣿⣿⡿⠿⢿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⠀⠀⠀⠈⠐⢆⣥⢲⠿⠟⡊⢠⣆⢋⠟⠁⣿⣿⡆⣿⣿⡇⣸⣿⡟⣿⣿⣿⣿⢸⣿⣿⣿⣷⣎⣿⣿⣳⣿⡿⣿⣷⡛⣿⣿⢿⣿⣮⢱⣿⣿⢿⣿⡞⢿⣿⡿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠀⠀⠴⠀⠈⠀⠀⠀⠐⠀⠀⣈⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣢⢸⣿⣿⣸⣿⡿⣴⣷⣛⣛⢣⣿⣿⢣⣿⣿⣸⣿⣿⢸⣿⣿⣼⣿⠏⢸⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢸⣿⣿⣿⢿⣿⣿⣿⠃⣿⣿⡿⣿⢸⣿⣿⢻⣿⣷⢩⣿⣿⣣⣿⣿⠯⣾⣿⣿⢸⣿⣿⢸⣯⣿⢻⣿⣧⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣧⣭⢸⣿⣿⣼⣿⣿⣸⣿⣷⣿⣿⣥⣶⠌⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⣿⢸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠛⣛⣛⣬⣿⣻⣫⣤⣿⣿⣿⣿⣼⣿⣻⣿⣿⣽⣿⣟⣛⣿⣿⣿⣻⣾⣮⣿⣟⣿⣷⣶⣽⣿⣻⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠶⣶⠯⢶⠆⠰⠶⠶⠶⠀⣤⣤⣤⣤⣀⢀⡀⣉⣛⣛⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡤⣶⣶⣾⣶⣷⣶⣤⣻⣶⣾⣭⣭⣷⣼⣾⣿⣿⣿⣿⣾⡶⣷⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢁⢤⡄⠀⢀⡄⣁⢡⡆⠀⠀⠀⠀⢀⣀⣀⠀⡀⣤⣤⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢊⠿⣿⠟⡛⠈⠛⠛⠻⠝⢺⡟⠛⠿⣟⣿⢿⣿⣿⠿⣛⠋⡙⠿⠂⢊⣡⣤⣶⣿⣿⣿⣿⣿⣿⣟⣉⣴⣶⣿⣿⣿⣴⢂⣿⣿⣶⣧⠢⢲⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡅⠈⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀
⠯⠝⢛⡀⠀⠀⠀⠀⠐⠀⠀⢀⣄⢩⣬⣷⣦⣬⣤⣶⣰⣮⣵⣤⣽⣿⣿⣿⣿⣿⣿⡟⠛⠒⢃⣀⢉⣿⣿⣿⣿⡷⣷⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀⠀⣀⣀⢐⣹⣧⣦⣤⣖⠂
⠀⢤⣵⣖⠄⠀⠀⠀⠀⠀⠀⣤⣿⣷⣿⣿⣿⣿⣿⣿⡧⣖⣾⣿⣿⣿⣿⣿⣿⣿⣉⣤⡄⢐⣲⣿⣿⣿⣿⣿⣿⡏⠟⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⡟⡭⢅⣬⣽⠿⠗⠿⡿⠏⠙⠯⠨
⠚⠋⠃⠒⠠⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣟⣿⣷⣬⣿⣿⣿⣿⣿⣿⡿⠛⠛⢛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⠶⣿⣿⣿⣿⡷⣯⣿⣿⣿⣿⠿⣿⣿⣿⢽⣿⠾⠟⢻⡿⢷⠏⠁⠘⠛⠋⠀⠀⠆⠀⠈⠀⠛
⠠⠴⣶⡦⡀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⣽⣍⣥⣤⣤⣴⣶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢠⣝⣛⣇⣹⣿⡟⣿⠿⣟⣿⣿⡣⡶⠿⣿⣞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂
⠈⠁⠃⠀⠈⣰⢀⣾⣿⣿⣿⣿⣿⣹⣿⣿⡟⠋⠸⣿⢿⣿⣿⢿⣿⣿⣿⣍⡋⢻⣿⡿⡟⢽⣿⣿⣿⣿⣿⣿⣿⢯⠿⠿⢿⠟⠛⠁⠀⠈⠀⣠⣿⣩⠁⠘⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀
⠡⣤⠀⠀⠀⣺⣶⠿⠍⠳⡈⠩⠗⣈⢅⠠⠁⠀⠩⠉⠻⣟⢯⠚⠛⠿⠿⠁⠀⠊⠀⠁⠀⠀⠿⢿⣿⣿⣿⢿⡟⡄⠈⠂⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⡄⠀⠠⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣷⣶⣶⣴⣴⣽⣭⣾⣷⣦⣴⣞⡩⠬⢳⠥⣤⠀⠀⢐⣌⠀⠀⠀⠀⠀⠀⠄⣄⣀⡀⡁⢒⡪⣦⣭⣿⣿⡿⠙⠧⢁⠄⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⠿⣿⡞⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣶⣶⣿⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣋⣠⣤⣴⣶⣾⣽⣿⣾⣯⣿⣻⣿⠿⠛⡗⢘⠻⡶⠄⠀⠀⠀⠀⠀⠘⠿⠿⠟⠋⠀⠀⠐⣹⣿⣯⣴⣴⡂⠀⠙⢲⠦⠀⢶⢾⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣭⣺⣿⡡⣴⣾⣿⣺⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡟⢻⣣⠲⣶⣛⢿⣿⣾⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⢙⣿⡼⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡈⠋⢻⣿⠀⠁⢿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠛⠛⠓⢮⡅⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣿⣿⣿⡱⡀⠀⢹⣄⠀⢘⠿⠿⢿⣿⣿⡿⠯⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄⢈⠀⢰⣷⡀⠀⠀⠀⠀⠀⠀⠐⠈⢉⣹⣿⣿⣷⣱⡀⠀⠻⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⢿⠿⠃⠀⠍⠁⣷⠄⠀⠀⠀⠀⠀⠀⠘⢩⡼⠿⣿⣿⣿⣿⣷⡀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⣻⠛⠛⠉⠙⠛⠋⠙⠛⠛⠁⠈⠁⠀⠈⠙⠋⠉⠉⠉⠀⠓⡶⠁⠈⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⢢⠀⢨⣿⣿⣿⣿⣿⡠⣱⡀⢐⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⡉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠄⠐⠒⠂⠀⠀⠀⠀⠀⠄⠀⠀⢠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢫⣿⣿⣿⠋⠀⢳⠉⠁⢿⡿⢰⢀⣶⣶⣶⣶⢶⣤⣤⣴⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣯⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣠⡄⠀⠀⠀⠀⠀⠈⠈⣻⣿⣿⠷⠀⠀⠀⠀⠘⢰⣾⣿⣿⣿⣿⣿⣶⣺⣶⣵⣭⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠐⠀⠀⠀⠀⡠⠄⠂⠈⠉⠀⢢⠄⠐⠖⠀⠀⠀⠀⡘⣟⣿⣮⣵⡆⠀⠀⠀⠀⠀⠀⠀⠉⠀⣀⡀⠀⠀⢠⡀⣸⣿⣿⣿⣿⣿⢯⣭⣽⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠑⠉⠀⠀⠀⠀⠀⠐⠛⠿⣿⠋⡛⠋⠀⠀⠀⠀⢠⠿⣿⡿⠀⠉⢻⠒⠀⠀⢸⣾⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣟⣿
⠀⠀⠀⠂⠀⢀⢐⣜⣐⣄⡀⡀⣄⡲⢻⣶⣺⣷⣮⣷⣤⡆⡈⠙⠀⠠⠠⣴⣦⣀⣄⣔⣄⣀⡄⠀⠄⠀⡀⢀⣀⣠⣴⡂⡙⠂⠹⠽⠂⠀⠀⠀⠀⠀⣠⠾⠉⠛⠀⠠⠂⢀⠀⠀⠘⠛⠻⠿⣿⣟⣛⣿⣿⣿⣷⣿⣿⣷
⠄⠠⡐⠀⡢⠤⣹⡿⣽⣿⣦⣿⣿⣿⣿⣯⣿⣿⡿⣿⣿⣟⡃⣄⠀⢀⣸⡿⠁⠁⠈⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠉⠉⠊⣁⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣤⣬⣤⣤⣶⣶⣶⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠀⠀⠂⢠⣉⠻⣏⣻⣿⢺⣿⣿⡟⣿⡿⠾⠇⠻⠛⠻⠟⠉⠃⢼⡿⠷⠶⢶⣶⡿⠶⠶⢶⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠿⢿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⠀⠀⠀⠀⠐⢆⣅⠳⠿⠟⠈⢠⣎⢏⠛⠁⣿⣿⡆⣿⣿⣇⣸⣿⡟⣿⣿⣿⣿⢸⣿⣿⣿⣷⣎⣿⣿⣳⣿⡿⣿⣿⡛⣿⣿⢿⣿⣮⢱⣿⣿⢿⣿⡞⢿⣿⡿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⠴⠀⠈⠀⠀⠀⠐⠀⠀⣈⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣠⢸⣿⣿⣸⣿⡿⣴⣷⣛⣛⢣⣿⣿⢣⣿⣿⢼⣿⣿⢸⣿⣿⣼⣿⢏⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢸⣿⣿⣿⢿⣿⣿⣿⠃⣿⣿⡿⣿⢸⣿⣿⢻⣿⣷⢩⣿⣿⣣⣿⣿⠯⣾⣿⣿⢹⣿⣿⢸⣯⣿⢻⣿⣧⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣧⣭⢸⣿⣿⣼⣿⣿⣸⣿⣷⣿⣿⣥⣴⠈⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⣿⢸⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠛⣛⣛⣬⣿⣻⣫⣤⣿⣿⣿⣿⣼⣿⣻⣿⣿⣿⣿⣟⣛⣿⣿⣿⣻⣾⣮⣿⣿⣿⣷⣶⣽⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠶⣶⠯⢶⠦⠰⠶⠶⠶⠀⣤⣤⣦⣤⣄⣀⡀⣙⣛⣛⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡤⣶⣶⣾⣶⣷⣶⣤⣻⣶⣾⣿⣭⣷⣼⣾⣿⣿⣿⣿⣾⡶⣷⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢁⣄⡄⠀⢀⡄⣁⢱⡠⠀⠀⢀⠀⢀⣀⣀⠀⠀⣤⣤⣄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢚⢿⣿⠟⡛⠈⠛⠉⠻⠝⢺⡻⠛⠿⣿⡿⢿⣿⢿⠿⡛⠋⡙⠿⠂⢋⣁⣤⣶⣿⣿⣿⣿⣿⣿⣟⣉⣴⣶⣷⣿⣿⣶⢂⣿⣿⣶⣥⠪⠲⣮⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⡅⠈⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀
⠯⠍⢚⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢩⣬⣵⣦⣤⣠⣶⣰⣆⣴⣤⣽⣿⣿⣿⣿⣿⣿⡟⠛⠒⣃⣀⢉⣿⣿⣿⣿⡷⣿⣿⡿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀⠀⣀⣀⢀⣹⣦⣦⣤⣖⠀
⠀⢤⣵⣆⠀⠀⠀⠀⠀⠀⠀⣤⣿⣵⣿⣿⣿⣿⣿⣿⡧⣖⣾⣿⣿⣿⣿⣿⣿⣿⣉⣤⡄⢐⣲⣾⣿⣿⣿⣿⣿⡏⡟⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⡿⡋⡭⢅⣬⣜⠫⠗⠻⠿⠋⠉⠯⠨
⠚⠋⠃⠂⠠⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⡿⠛⠛⢛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⠶⣿⣿⣿⣿⡷⣯⣿⣿⣿⣿⢿⣿⣿⣿⢽⣿⠿⠟⢻⡿⠷⠎⠁⠘⠓⠋⠀⠀⠆⠀⠀⠀⠛
⠠⠴⣶⡤⡀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⣽⣭⣥⣤⣤⣴⣶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢠⣿⣟⢇⣹⡿⣿⣿⣿⣿⣻⣿⡧⣶⠿⣿⣔⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠈⠀⠃⠈⠈⣰⢀⣾⣿⣿⣿⣿⣯⣹⣿⣿⡛⠋⠸⣿⢿⣿⣿⢿⣿⣿⣿⣍⠋⢻⣷⠾⡟⢽⣿⣿⣿⣿⣿⣿⣿⢯⢿⢿⢿⠛⠛⠀⠙⠉⢁⣺⢽⣫⣥⠜⠁⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠁⡀⠀⠀⠀⣺⣶⠿⢉⠳⠨⠩⠇⣀⢅⠀⠀⠀⠉⠉⠛⣟⢯⠚⠻⠿⡏⠁⠀⠂⠀⠁⠀⠀⠻⢿⣿⣿⣿⢿⡟⡌⡘⠂⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡀⠀⡀⣠⣾⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣶⣶⣶⣶⣿⣿⣾⣷⣦⣰⣾⡉⠼⢲⠥⣠⠀⠀⢐⣄⠀⠀⠀⠀⠀⠀⠄⣄⣀⡀⡁⢒⡪⣮⣭⣿⣿⡿⠑⠧⠁⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣶⣶⣷⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⡍⣢⣶⣤⣶⣾⣽⣿⣾⣯⣿⡿⣿⠿⠛⡗⢘⠻⡎⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⠛⠀⠈⢍⣿⣿⣿⣴⡤⠐⠈⠉⢒⠠⠰⢖⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣭⣺⣿⡥⣴⣾⣿⣺⣼⣷⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⣠⣾⣿⣿⣿⠿⣷⡀⢰⣶⣲⣾⣿⣾⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠋⠙⣿⡼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡏⠿⢻⣿⡆⠉⠸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠛⠛⠁⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⣿⣿⡗⡀⠀⠹⣧⠀⠀⠿⠿⠿⢿⣿⣿⡿⡯⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄⢀⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⣿⣿⣿⡄⡄⠀⠹⢷⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⢿⠿⠃⠀⠉⠁⣆⠀⠀⠀⠀⠀⠀⠀⠴⢊⣿⣿⣿⣿⣿⣶⣄⢈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⠛⠛⠉⠙⠛⠋⠉⠛⠛⠁⠈⠁⠀⠈⠙⠋⠉⠉⠉⠀⠓⡶⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠈⢹⣿⣿⣿⣿⣇⢈⣆⠀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠄⠐⠐⠂⠈⠀⠀⠀⠀⠆⠀⠀⢠⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⡛⣿⣿⣿⠋⠉⡆⠉⠰⣿⠟⢞⢀⣲⣶⣶⣶⣶⣤⣤⣴⡤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠤⣯⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣠⡄⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⠦⠀⠀⠀⠀⠈⢴⣿⣿⣿⣿⣿⣿⣗⣺⣶⣽⣭⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠐⠀⠀⠀⠀⡠⠄⠂⠈⠉⠀⢦⠤⠄⠆⠀⠀⠀⠀⡘⣟⣿⣮⣵⠂⠀⠀⠀⠀⠀⠀⠀⢉⠁⣀⠀⠀⠀⢠⠀⣿⣿⣿⣿⣿⡿⢿⣽⣭⢽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⢀⡠⠀⠁⠀⠀⠀⠀⠀⠀⠓⠉⠀⠀⠀⠀⠀⠐⠛⢿⣿⠛⡝⠃⠀⠀⠀⠀⢰⢟⣿⠿⠀⢉⠳⠇⠀⠈⢸⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣟⣿
⠀⠀⠀⠂⠀⢀⢐⣄⣂⣀⡄⡀⣄⡢⢻⣶⣺⣷⣦⣧⣴⡆⡌⠉⠀⢠⠠⣼⣦⣀⣄⣔⣆⣀⡦⠐⠀⠄⡀⢀⣀⣠⣴⡂⡉⡂⠹⠍⠒⠀⠀⠀⠀⠀⣠⠟⠉⠓⠀⠰⠎⢀⠀⠀⠘⠛⠿⠿⣿⣞⣛⣿⣿⣿⣷⣾⣿⣷
⠄⠀⡀⢁⡳⠬⣽⡿⣿⣿⣧⣿⣿⣿⣿⣯⣿⣿⡿⣿⣿⣟⣋⣤⠁⢀⣸⡿⠁⠈⠙⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠉⠁⠊⣁⣀⣀⣀⣀⣀⣠⣀⣀⣈⣀⣀⣀⣀⣤⣤⣤⣤⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠐⠀⠂⢀⣉⠿⣏⣿⣿⢺⣿⣿⡿⣿⡿⠾⠇⠻⠛⠻⠟⠉⠃⢾⡿⠷⠶⢶⣶⣿⡶⠶⣷⣾⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⠿⢿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⠀⠀⠀⠀⠐⠶⣥⢳⠿⠟⡢⢥⣷⢯⠟⠁⣿⣿⡆⣿⣿⡇⣸⣿⡟⣿⣿⣿⣿⢸⣿⣿⣿⣷⣎⣿⣿⣳⣿⡿⣿⣿⡛⣷⣿⢿⣿⣮⢱⣿⣿⢿⣿⡞⢿⣿⡿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠁⢀⠀⠠⠴⠀⠈⠀⠀⠀⠐⠀⠁⢈⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣒⢸⣿⣿⣸⣿⡿⣴⣿⣛⣛⢣⣿⣿⢣⣿⣿⢸⣿⣿⢸⣿⣿⣼⣿⠏⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢸⣿⣿⣿⢿⣿⣿⣿⠃⣿⣿⡿⣿⢸⣿⣿⢻⣿⣷⢩⣿⣿⣣⣿⣿⠯⣾⣿⣿⢸⣿⣿⢸⣯⣿⢻⣿⣧⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣧⣭⢸⣿⣿⣼⣿⣿⣸⣿⢷⣿⣿⣥⣴⠌⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⣿⢸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢈⠛⣛⣛⣬⣿⣻⣫⣤⣿⣿⣿⣿⣼⣿⣻⣿⣿⣽⣿⣟⣛⣿⣿⣿⣻⣾⣮⣿⣟⣿⣷⣶⣽⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠲⣶⠯⢶⠦⠰⠶⠶⠶⠀⣤⣤⣦⣤⣄⣠⠈⣙⣛⣛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡤⣶⣶⣾⣶⣷⣶⣤⣻⣶⣾⣽⣭⣷⣼⣾⣿⣿⣿⣿⣾⡶⣷⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢁⣤⡄⢀⢀⢔⣁⢱⡆⠀⠀⠀⠀⣠⣄⣀⠀⢠⣤⣤⣄⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢊⢿⣿⠟⡻⠈⠛⠛⠻⠝⢺⡟⠛⠿⣟⣿⢿⣿⣿⠿⣟⠋⡙⠿⠂⢋⣡⣤⣶⣿⣿⣿⣿⣿⣿⣟⣉⣶⣶⣷⣿⣿⣴⢂⣿⣿⣶⣧⠢⢳⣞⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡅⠈⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀
⠯⠝⢛⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢩⣬⣧⣦⣬⣤⣶⣸⣮⣽⣤⣽⣿⣿⣿⣿⣿⣿⡟⠛⠛⣃⣀⢙⣿⣿⣿⣿⡷⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⣀⣀⢀⣹⣦⣦⣤⣖⠀
⠀⢤⣵⣖⠄⠀⠀⠀⠀⠀⠀⣴⣿⣵⣿⣿⣿⣿⣿⣿⡧⣖⣾⣿⣿⣿⣿⣿⣿⣿⣁⣤⡄⢐⣲⣿⣿⣿⣿⣿⣿⡏⠟⣏⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⡟⡭⢇⣬⣾⠿⡟⠻⡿⠋⠙⠯⠨
⠚⠏⠃⠒⠠⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣟⣿⣷⣴⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⠶⣿⣿⣿⣿⣷⣯⣿⣿⣿⣿⠿⣿⣿⣿⣽⣿⠿⠿⢻⡿⠷⠏⠁⠘⠓⠋⠀⠀⠆⠀⠀⠀⠛
⠠⠴⣶⡶⣀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⣿⣭⣥⣤⣤⣴⣶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢨⣝⣟⢇⣹⣿⡿⣿⣟⣿⣻⣿⣧⣷⠿⣿⣞⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂
⠈⡁⠓⠐⠈⣰⢄⣾⣿⣿⣿⣿⣿⣹⣿⣿⡟⠋⠸⣿⢿⣿⣿⢿⣿⣿⣿⣍⡋⢻⣿⡾⡟⢽⣿⣿⣿⣿⣿⣿⣿⢯⢿⢿⢿⡛⠙⢿⠉⡋⣃⠾⣿⣯⣭⠈⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠀⠀⠀
⠁⡠⠀⠀⠀⣻⣶⠿⠍⠳⡬⠩⠗⣈⢅⠠⠁⠀⠉⠉⠿⣟⢯⠚⠻⠿⠿⠁⠀⠊⠀⠁⠀⠀⠿⢿⣿⣿⣿⢿⡟⣄⠘⠂⠀⠀⠀⠀⠀⣼⣷⣾⣼⠁⠂⠀⡀⣰⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣶⣶⣴⣴⣿⣭⣾⣷⣦⣴⣞⡉⠨⢳⢥⣤⠀⠀⢐⣌⠀⠀⠀⠀⡀⠠⠄⣄⣀⡀⡑⣒⠪⣮⣭⣿⣿⡿⠑⠧⠁⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣄⠀⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣶⣶⣿⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⡋⣠⣤⣔⣶⣾⣽⣿⣾⣯⣿⡿⣿⠿⠛⡗⢚⠻⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⠏⠚⢻⣾⣾⣿⣿⡄⡤⠀⠈⠉⢒⡠⠠⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣺⣿⡡⣴⣾⣿⣿⣜⠀⠀⠀⠀⠀⠀⠛⠛⠿⠋⠀⠀⠀⣱⣿⣿⣿⡿⣿⡤⠄⢰⣶⣺⣾⣿⣿⣿⣿⣿⣿⣿⡟⠋⠈⠈⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢙⣿⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⢿⣿⣿⡧⠘⠛⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠛⠛⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠀⠀⠙⣿⠀⠀⢻⣿⠿⠿⢿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣄⢄⠀⠘⣷⡄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⢿⠿⠃⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢼⣿⣿⣿⣾⣦⣄⡀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⠛⠛⠉⠙⠛⠋⠙⠛⠛⠁⠈⠁⠀⠈⠙⠋⠉⠉⠉⠀⠓⡶⠁⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠛⢿⣿⣿⣿⣷⡄⣱⡀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⡉⠙⠉⠀⠀⠀⠀⠀⠀⠄⠄⠐⠐⠂⠀⠀⠀⠀⠀⠄⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⡿⠋⠹⡈⠉⢺⣿⠃⣇⣀⣶⣶⣶⣶⡶⣤⣤⣴⡴⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠠⢤⣯⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣠⡀⠀⠀⠀⠀⠀⠀⠚⢿⣿⣷⡄⠀⠀⠀⠀⠃⣾⣿⣿⣿⣿⣿⣿⣷⣺⣶⣵⣭⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠐⠀⠀⠀⠀⡠⠄⠂⠈⠉⠀⢢⢄⠒⠒⠀⠀⠀⠂⡸⣿⣿⣬⣵⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⢀⡀⠀⠀⢀⠀⣿⣿⣿⣿⣿⠿⣻⣭⣭⢿⣿⣿⣿
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠓⠉⠀⠀⠀⠀⠀⠐⠛⢿⣿⠋⣟⠃⠀⠀⠀⠀⠰⢲⣿⠧⠀⠙⠳⠆⠀⠀⢼⣿⣿⣿⣟⣿⣶⣾⣿⣿⣿⣿⣟⣿
⠀⠀⠈⠂⠀⢀⢐⣕⣒⣄⡄⡀⣔⡲⣺⣶⣺⣷⣦⣷⣔⡦⡈⠙⠀⢠⠠⣾⣆⣀⣄⣔⣆⣀⡄⠀⠄⠄⡀⠀⣀⣠⣴⣆⡉⡂⠹⠍⠂⠀⠀⠀⠀⠀⡴⠋⠉⠓⠀⠴⠂⠀⠀⠀⠘⠛⠻⠿⣿⣟⣛⣟⣿⣿⣷⣿⣿⣷
⠄⠠⡀⠀⡫⠬⣽⡿⣿⣷⣧⣿⣿⣿⣿⣿⣿⣾⡿⣿⣿⣟⡃⣄⠁⢀⣸⡿⠉⠈⠈⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠉⠁⠋⣀⣁⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣤⣤⣤⣤⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠀⠈⡂⠠⣉⠿⣏⣻⣿⢺⣿⣿⡿⣿⣿⠾⠗⠻⠛⠻⠟⠉⠋⠼⡿⠷⠶⠶⣶⣷⠶⠶⣶⣶⣶⣷⣿⣿⡿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⠀⠀⠀⠀⠐⢦⣥⢳⠿⠟⠊⢠⣖⢫⠟⠁⣿⣿⡆⣿⣿⣇⣸⣿⡟⣿⣿⣿⣿⢸⣿⣿⣿⣷⣎⣿⣿⣳⣿⡿⣿⣿⡛⣿⣿⢿⣿⣮⢱⣿⣿⢿⣿⡞⢯⣿⡿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠁⢀⠀⠠⠴⠀⠈⠀⠀⠀⠐⠀⠀⣈⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣲⢸⣿⣿⣸⣿⡿⣴⣿⣛⣛⢣⣿⣿⢣⣿⣿⣼⣿⣿⢸⣿⣿⣼⣿⠏⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢸⣿⣿⣿⢿⣿⣿⣿⠃⣿⣿⡿⣿⢸⣿⣿⢻⣿⣷⢩⣿⣿⣣⣿⣿⠯⣾⣿⣿⢸⣿⣿⢸⣯⣿⢻⣿⣧⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣧⣭⢸⣿⣿⣼⣿⣿⣸⣿⣷⣿⣿⣥⣴⠌⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⣿⢸⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢈⠛⣛⣛⣬⣿⣻⣋⣤⣿⣿⣿⣿⣼⣿⣻⣿⣿⣿⣿⣟⣛⣿⣿⣿⣻⣾⣮⣿⣟⣿⣷⣶⣽⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠲⣶⠯⢶⠦⠰⠶⠶⠶⠀⣤⣤⣤⣤⣄⣀⡀⢙⣛⣛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡤⣶⣶⣾⣶⣷⣶⣤⣻⣶⣾⣿⣭⣷⣼⣾⣿⣿⣿⣿⣾⡶⣷⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢁⣄⡄⢀⢐⣔⣡⢱⡦⠀⡀⢀⢀⣀⢄⣄⠀⢤⣦⣴⣤⡀⠀⠀⢀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢚⢿⣿⠟⡻⠈⠛⠛⠻⠝⢺⡛⢛⠿⣿⣿⢿⣿⣿⠿⣛⠋⡙⠿⠂⢋⣡⣤⣶⣿⣿⣿⣿⣿⣿⣿⣉⣴⣶⣿⣿⣿⣶⣂⣿⣿⣷⣷⠪⢿⣮⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠈⠁⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀
⠯⠝⢛⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢩⣬⣵⣦⣬⣤⣶⣸⣮⣿⣤⣽⣿⣿⣿⣿⣿⣿⡟⠛⠓⣋⣀⣩⣿⣿⣿⣿⡷⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣅⠂⣀⣀⣐⣽⣷⣦⣤⣖⠂
⠀⢤⣵⣖⠄⠀⠀⠀⠀⠀⠀⣴⣿⣷⣿⣿⣿⣿⣿⣿⡧⣖⣾⣿⣿⣿⣿⣿⣿⣿⣁⣤⡄⢐⣲⣿⣿⣿⣿⣿⣿⡏⠟⣏⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⡭⣇⣯⣼⠿⡟⠿⡿⠋⠙⠯⢨
⠚⠟⠃⠒⠤⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣟⣿⣷⣬⣿⣿⣿⣿⣿⣿⡿⠛⠛⢛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⠶⣿⣿⣿⣿⡷⣯⣿⣿⣿⣿⠿⣿⣿⣿⣽⣿⠿⠿⢹⡿⢷⠏⠁⠘⠓⠋⠀⠀⠆⠀⠈⠀⠛
⠠⠶⣶⡤⢀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⣿⣭⣥⣤⣤⣴⣶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢨⣟⣟⢇⣻⣿⡟⣿⡟⣿⣻⣽⡧⣷⠿⣿⣖⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂
⠈⡁⠃⠈⠈⣰⢄⣾⣿⣿⣿⣿⣿⣹⣿⣿⡟⠋⠸⣿⢿⣿⣿⢿⣿⣿⣿⣍⡛⢻⣷⡿⡟⢽⣿⣿⣿⣿⣿⣿⣿⢯⣽⢿⣿⣻⣿⡿⡋⣙⣃⠞⣝⣫⣭⠘⠁⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀
⠡⡠⠀⠀⠀⣻⣶⠿⢍⠳⡬⠩⠗⣈⢅⠠⠁⠀⠩⠉⠿⣟⢯⠚⠻⠿⡿⠁⠀⠂⠀⠁⠀⠀⠿⢿⣿⣿⣿⢿⡏⣌⠚⠊⢐⡽⠟⠞⢿⣶⣟⠦⠘⠁⠀⠀⡀⡰⣦⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣷⣶⣶⣴⣴⣽⣯⣾⣷⣦⣶⣞⡉⠸⢺⢥⣤⠀⠀⢐⣌⠀⠀⠀⠀⡀⠠⠄⣄⣀⡀⡁⣒⡪⣮⣽⣿⣿⡿⠙⠧⠁⠀⠀⠈⠁⠀⣾⣿⣶⣌⠁⠀⠀⠐⠀⣿⣿⣿⡆⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠰⣦⣷⣶⣿⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣷⣶⣶⡏⣢⣦⣶⣶⣾⣽⣿⣿⣯⣿⡻⣿⠿⠛⡗⠘⠁⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⣄⠀⠀⢐⣿⣿⣿⢜⡦⠁⠈⠍⢳⡦⠶⢖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣭⣺⣿⡥⣴⣶⣟⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡿⠋⢿⣿⣿⣿⣿⣿⣿⣤⠧⠔⠰⣶⣺⣿⣿⣾⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠫⠝⠀⠀⠀⠀⠀⠈⠻⣿⢿⣿⠟⠁⠀⢈⣿⣿⣿⣿⢿⣿⣿⢻⣧⣽⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⣿⣿⣿⠂⠁⠹⣿⣿⡿⠿⠿⢿⣿⣿⡿⡯⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠇⠀⠈⠻⣧⡀⠀⢹⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⢿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⠻⣿⣧⡀⠀⠀⠘⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⠛⠛⠉⠙⠛⠋⠙⠛⠛⠁⠈⠁⠀⠈⠙⠋⠉⠉⠉⠀⠓⡷⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣶⣶⣶⣄⡐⠀⠀⠀⢴⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡙⠙⠉⠀⠀⠀⠀⠀⠀⠄⠔⠐⠒⠂⠀⠀⠀⠀⠀⠄⠀⠀⢠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣿⣽⣿⠷⡀⠑⢠⣿⡇⣯⣤⣤⣶⣶⣶⣶⡶⣤⣤⣴⡴⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠠⢤⣯⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡁⠀⠃⠀⠀⠉⢰⣿⣿⣿⣿⣿⣿⣿⣷⣺⣦⣵⣭⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠐⠀⠀⠀⠀⡠⠆⠂⠈⠉⠀⢦⣤⠖⠖⠀⠀⠀⠀⡸⣟⣿⣪⡄⠀⠀⠀⠀⠀⠀⠀⠰⠿⠁⢀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠿⢿⣻⣯⣭⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⢀⡠⠀⠈⠀⠀⠀⠀⠀⠀⠓⠋⠀⠀⠀⠀⠀⠐⠛⢿⣿⠋⡇⠀⠀⠀⠀⠀⢄⣤⣶⠤⠄⢙⢻⠀⠀⠀⣦⣿⣿⣿⣋⣯⣶⣾⣿⣿⣿⣿⣟⣿
⠀⠀⠀⠀⠀⢀⣐⣌⣢⣄⡄⡁⣄⡲⣻⣶⣺⣿⣮⣷⣤⡶⡈⠙⠀⢠⢠⣾⣆⣀⣄⣔⣦⣉⡦⠐⠄⠄⡀⠀⣀⡠⣴⣂⡻⡂⠿⠩⠀⠀⠀⠀⠀⠀⡞⠍⠉⠒⠀⠴⠆⠀⠀⠀⠘⠛⠿⢿⣟⣟⣛⣟⣿⣿⣷⣿⣿⣿
⠄⠀⡐⢀⡺⠭⣿⡿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⡁⣄⡁⢀⣸⡿⠀⠈⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠊⠀⣁⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣠⡤⣥⣤⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠀⠀⡂⢀⣉⢿⣯⣿⣿⢺⣿⣿⡿⣿⡿⠾⠗⠻⠛⠻⠟⠉⠃⢼⡿⠷⠶⢶⣶⡿⠶⠶⣶⣶⣶⣿⣶⣿⡿⢿⣿⣿⣿⣿⠿⢿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⠀⠀⠀⠀⠐⢶⣅⢳⠿⠿⠌⢠⣶⢋⠟⠁⣿⣿⡆⣿⣿⣇⣸⣿⡟⣿⣿⣿⣿⢸⣿⣿⣿⣷⣎⣿⣿⣳⣿⡿⣿⣿⡛⣿⣿⢿⣿⣮⢱⣿⣿⢿⣿⡞⢿⣿⡿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠁⢀⠀⠠⠴⠀⠈⠀⠀⠀⠐⠀⠁⣈⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣢⢸⣿⣿⣸⣿⡿⣴⣷⣛⣛⢣⣿⣿⢣⣿⣿⣼⣿⣿⢸⣿⣿⣼⣿⠏⢸⣿⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⣿⣿⣿⢿⣿⣿⣿⠃⣿⣿⡿⣿⢸⣿⣿⢻⣿⣷⢩⣿⣿⣣⣿⣿⠯⣾⣿⣿⣹⣿⣿⢸⣯⣿⢻⣿⣧⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣧⣭⢸⣿⣿⣼⣿⣿⣸⣿⣷⣿⣿⣥⣴⠌⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⣿⣸⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢈⠛⣛⣛⣬⣿⣻⣫⣤⣿⣿⣿⣿⣼⣿⣻⣿⣿⣽⣿⣟⣛⣿⣿⣿⣻⣾⣮⣿⣟⣿⣷⣶⣽⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠶⣶⠯⢶⠦⠰⠶⠶⠶⠀⣤⣤⣦⣤⣄⣀⡀⣙⣛⣛⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡤⣶⣶⣾⣶⣷⣶⣤⣻⣷⣾⣿⣭⣿⣼⣾⣿⣿⣿⣿⣾⡶⣷⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢁⣠⡄⢀⢐⡔⣁⣱⡤⠀⡀⠀⢀⣠⣤⡀⠀⢤⣤⣤⣄⡀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢚⢿⣿⠟⡛⠨⠛⠛⠻⠝⢺⡿⠟⠿⣿⣿⢿⣿⣿⠿⡟⠋⡙⠿⠂⢋⣡⣤⣶⣿⣿⣿⣿⣿⣿⣟⣉⣶⣶⣾⣿⣿⣶⣂⣻⣿⣷⣧⠪⢲⣞⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠈⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀
⠯⠍⢛⡀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢩⣬⣵⣦⣬⣤⣶⣰⣮⣵⣤⣽⣿⣿⣿⣿⣿⣿⡟⠛⠒⣃⣀⣩⣿⣿⣿⣿⣷⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠂⠀⣀⣀⣐⣽⣧⣦⣬⣖⠂
⠀⢤⣵⣆⠄⠀⠀⠀⠀⠀⠀⣤⣿⣷⣿⣿⣿⣿⣿⣿⣦⣖⣾⣿⣿⣿⣿⣿⣿⣿⣉⣥⡄⢐⣲⣾⣿⣿⣿⣿⣿⡏⣟⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⡭⢇⣯⣿⠻⡟⠻⠿⠏⠙⠯⠸
⠚⠟⠃⠂⠠⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⡿⠛⠛⢛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⠶⣿⣿⣿⣿⣷⣯⣿⣿⣿⣿⠿⣿⣿⣿⢽⣿⠿⠿⢻⡿⠷⠎⠁⠘⠓⠋⠀⠀⠆⠀⠈⠀⠛
⠠⠴⣶⡤⡀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⣿⣍⣥⣤⣤⣴⣶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢠⣟⣛⢇⣻⣿⡟⣿⡿⣻⣻⣿⡧⣶⢿⣿⣞⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠈⠁⠃⠀⠈⣰⢀⣾⣿⣿⣿⣿⣿⣽⣿⣿⣛⠋⠸⣿⢿⣿⣿⣿⣿⣿⣿⣍⠛⢻⣿⡿⣟⢽⣿⣿⣿⣿⣿⣿⣿⢯⣿⢿⢿⣻⣿⡿⡋⣙⣓⠜⣝⣫⣍⠜⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠁⣀⠀⠀⠀⣺⣶⠿⠍⢳⡭⠩⠗⣈⢅⠀⠁⠀⠩⠉⠿⣟⢯⠘⠻⠿⡯⠁⠀⠊⠀⠁⠀⠀⠿⢿⣿⣿⣿⢿⡏⣌⢋⡚⣳⣿⣟⢖⣯⣼⡛⠖⠘⠁⠀⠁⡀⣰⣦⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣷⣶⣶⣴⣴⣿⣯⣿⣷⣦⣰⣾⡉⠸⢲⢥⣤⠀⠀⣐⣌⠀⠀⠀⠀⠀⠠⠄⣄⣀⡀⡑⣒⡪⣯⣭⣿⣿⣿⠙⢧⠙⠀⢚⠛⠿⣽⣾⡿⠃⠐⠀⠀⠀⠐⠠⣿⣿⣿⡆⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠰⣦⣶⣶⣿⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⡊⣢⣶⣤⣶⣾⣽⣿⣾⣯⣿⡿⣿⠿⠛⡷⠜⠋⠀⠀⠁⠀⢨⣿⣿⣷⣤⡀⠀⠀⠀⠀⢐⣿⣿⣿⢌⡤⠉⠀⠉⢲⠦⠴⢖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡭⣺⣿⡭⡶⣾⡟⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⣦⣤⣰⣯⣿⣿⣿⣿⣵⠧⠄⠸⣶⣲⣻⣿⣾⣿⣿⣿⣿⣿⠟⠋⠉⠈⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡿⠈⢻⣿⣿⣯⣿⣿⣿⣿⣿⠿⣧⣾⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠘⠛⠿⣿⣿⠟⠁⠀⠀⣿⣿⣿⣿⠛⠾⢿⣿⣿⣿⣿⠿⠿⠿⣿⣿⡿⡯⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠿⢻⣿⣇⠀⠀⠻⠻⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⢿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡇⠀⠀⠙⢿⣤⡀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠛⠛⠉⠙⠛⠋⠛⠛⠛⠁⠈⠀⠀⠈⠙⠋⠉⠉⠉⠈⠓⡳⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠏⢿⣿⣦⡀⠀⠀⠙⠛⠀⠀⠀⢄⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⠙⠙⠉⠀⠀⠀⠀⠀⠀⠄⠄⠐⠒⠂⠀⠀⠀⠀⠀⠆⠀⠀⢠⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢿⣿⣷⣿⣿⣶⡀⠐⠄⣰⣿⢚⣶⣶⣶⣶⣶⣶⣶⡶⣤⣤⣤⡦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣯⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣿⡿⠁⠈⠀⠀⠈⠃⣼⣿⣿⣿⣿⣿⣿⣿⣖⣺⣴⣽⣭⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠐⠀⠀⠀⠀⡠⠖⠂⠈⠉⠀⢦⡤⠖⠖⠀⠀⠀⠀⡸⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢙⡷⠄⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⢟⣯⣭⣭⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠓⠋⠀⠀⠀⠀⠀⠐⠛⢿⣿⠛⡂⠀⠀⠀⠀⠀⢀⣀⣤⠤⠌⠙⠳⠀⠀⠀⣎⣿⣿⡿⣙⣯⣶⣾⣿⣿⣿⣿⣟⣿
⠀⠀⠀⠂⠀⢀⢐⣅⣒⣄⡔⡃⣔⣢⣻⣶⣺⣷⣮⣧⣴⡆⡌⠙⠀⢠⠠⣾⣦⣀⣄⣔⣦⣉⡦⠰⠀⠄⡀⠀⣀⡠⣶⣂⡻⡚⠻⠽⠂⠀⠀⠀⠀⠀⠟⠉⠉⠛⠂⠴⠂⠀⠀⠀⠘⠛⠿⢿⣿⣟⣛⣟⣿⣿⣷⣾⣿⣷
⠤⠀⡀⢁⡺⠬⣿⡿⣿⣿⣧⣿⣿⣿⣿⣯⣿⣿⡿⣿⣿⣟⡅⣤⡁⢘⣸⡿⠀⠈⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠁⠊⠁⢀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣤⣤⣥⣤⣴⣶⣶⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠄⠀⡂⢁⣉⠿⣍⣿⣿⢺⣿⣿⣿⣿⣿⠾⠇⠻⠛⠻⠟⠉⠋⢿⡿⠷⣶⠶⣶⣷⡶⠶⢶⣶⣶⣶⣶⣿⡿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⠀⠀⠀⠈⠐⢶⣅⢳⠿⠟⠈⢤⣿⢫⠟⠁⣿⣿⡆⣿⣿⣇⣸⣿⡟⣿⣿⣿⣿⢸⣿⣿⣿⣷⣎⣿⣿⣻⣿⡿⣿⣿⡛⣿⣿⢿⣿⣮⢹⣿⣿⢿⣿⡞⢯⣿⡿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠁⢀⠀⠠⠴⠀⠉⠀⠀⠀⠐⠀⠀⣈⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣒⢸⣿⣿⣸⣿⡿⣴⣿⣛⣛⢣⣿⣿⢳⣿⣿⢸⣿⣿⢸⣿⣿⣼⣿⠏⢸⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⣿⣿⢿⣿⣿⣿⠃⣿⣿⡿⣿⢸⣿⣿⢻⣿⣷⢩⣿⣿⣣⣿⣿⠯⣾⣿⣿⢹⣿⣿⢸⣯⣿⢻⣿⣧⢸⣿⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣧⣭⢸⣿⣿⣼⣿⣿⣸⣿⣷⣿⣿⣥⣴⠌⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⣿⣸⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢌⡛⣛⣛⣬⣿⣻⣫⣤⣿⣿⣿⣿⣼⣿⣻⣿⣿⣽⣿⣿⣛⣿⣿⣿⣻⣾⣮⣿⣿⣿⣷⣶⣽⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠲⣶⠯⢶⠆⠰⠶⠶⠶⠀⣤⣤⣤⣤⣄⣠⡈⣙⣛⣛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡤⣶⣶⣾⣶⣷⣶⣤⣻⣶⣾⣿⣭⣷⣼⣾⣿⣿⣿⣿⣾⡶⣷⣾⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⠛⢁⢀⠄⢀⠀⡄⣁⣱⡄⡀⠀⢀⢀⠀⣀⡀⠀⡀⣤⣤⣄⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢊⠿⣿⠟⡛⠈⠛⠉⠻⠝⢺⡻⠛⠿⣿⡿⢿⣿⣿⠿⡟⠋⡙⠿⠂⢊⣁⣤⣶⣿⣿⣿⣿⣿⣿⣟⣁⣴⣶⣷⣿⣿⣴⢂⣿⣿⣶⣥⠢⠢⣮⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣷⡅⠈⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀
⠯⠍⢚⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢩⣤⣷⣦⣬⣄⣦⣰⣎⣴⣤⣽⣿⣿⣿⣿⣿⣿⡟⠛⠒⢁⣀⢙⣿⣿⣿⣿⡷⣷⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡂⠀⣀⣀⢀⣹⣶⣤⣤⣖⠀
⠀⢤⣵⣆⠄⠀⠀⠀⠀⠀⠀⣤⣿⣵⣿⣿⣿⣿⣿⣿⡧⣖⣾⣿⣿⣿⣿⣿⣿⣿⣁⣤⡄⢐⣲⣾⣿⣿⣿⣿⣿⡏⡟⣏⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⡏⡉⢅⣬⣜⠻⠟⠻⠿⠋⠙⠏⠨
⠚⠋⠃⠒⠠⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣟⣿⣧⣤⣿⣿⣿⣿⣿⣿⡿⠛⠛⢛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⠷⣿⣿⣿⣿⡷⣯⣿⣿⣿⣿⠿⣿⣿⣿⢽⣿⠿⠛⢹⡿⠧⠎⠁⠘⠓⠋⠀⠀⠆⠀⠀⠀⠚
⠠⠴⣶⡤⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⣽⣭⣥⣤⣤⣴⣶⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢨⣿⣛⢇⣻⣿⡟⣿⡿⣿⣻⣽⡧⣶⠿⣿⡞⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂
⠈⠀⠂⠈⠈⣐⢀⣾⣿⣿⣿⣿⣯⣽⣿⣿⢟⠋⠸⣿⢿⣿⣿⢿⣿⣿⣿⣍⠉⢻⢿⠾⢟⢽⣿⣿⣿⣿⣿⣿⣿⢯⣿⢿⢿⣻⣿⡿⠋⣙⡃⠐⣕⣫⢅⠈⠋⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠁⡀⠀⠀⠀⣻⣶⠿⠍⠳⠨⠩⠇⣀⢁⠠⠀⠀⠉⠉⠛⣛⢯⠘⠛⠯⠯⠁⠀⠂⠀⠁⠀⠀⠿⢿⣿⣿⣿⢿⡏⣜⢛⡖⣱⣿⡟⠞⣯⣼⡟⠂⠘⠁⠀⠁⡀⡰⣦⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣶⣶⣴⣴⣽⣯⣾⣷⣦⣰⣐⡉⠨⢲⠤⣤⠀⠀⢐⣌⠀⠀⠀⠀⠀⠀⠄⣄⣀⡀⡀⢒⡪⣦⣭⣿⣿⡿⠙⠧⢓⠀⠘⠛⣻⣤⣺⠼⠉⠐⠀⠀⠀⠐⠠⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣶⣿⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣴⠋⣠⣦⣤⣴⣾⣽⣿⣾⣯⣿⡿⣿⠽⠛⡗⢜⠛⡾⢄⠠⢢⡿⠙⠃⠀⠀⠀⠀⠀⠀⠀⢰⣿⣯⣿⠌⡤⠁⠀⠉⢂⠦⠔⢶⢾⣿⡿⣿⣿⣿⣿⣿⣿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣭⣺⣿⡭⣶⣾⡿⠒⠈⠀⠁⠀⣸⣿⣶⣦⣄⡀⠀⠀⠀⠰⣿⣻⣯⣿⣿⣥⠦⠔⠰⣖⣳⣾⣷⣾⣿⣿⣿⣿⣿⠟⠋⠀⠈⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡟⠋⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⣶⣖⣊⣈⣽⣿⣿⣿⡿⠿⣥⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠘⢻⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⡿⡯⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠾⢿⣿⣿⡿⠃⠀⠀⣿⣿⣿⣿⡛⠛⠻⣿⠿⠻⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⢿⠟⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡿⠻⠿⣿⣧⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⣻⠛⠛⠉⠙⠛⠋⠉⠛⠛⠁⠈⠀⠀⠈⠙⠋⠉⠉⠉⠈⠓⡲⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣇⠀⠀⠉⠻⣧⣤⡀⠁⠀⡀⣤⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠂⠀⠀⠀⠀⠀⠄⠀⠀⢠⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⣄⣀⡀⣈⣙⠁⠀⠀⠀⣿⡗⢷⣶⣷⣶⣷⣶⣶⣶⣶⣤⣤⣤⡤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣯⡻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⡿⠓⠀⠀⠈⠻⠁⣿⣿⣿⣿⣿⣿⣿⣿⠖⣺⣤⣽⣭⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠀⠀⠀⡀⠄⠂⠈⠉⠀⢢⣤⠖⠖⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠅⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡹⡿⣿⣩⣭⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠘⠛⢿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠙⠢⠀⠀⠀⡘⣿⣿⡟⣉⣯⣶⣾⣿⣿⣿⣿⣟⣿
⠀⠀⠀⠀⠀⢀⢐⣄⣀⣄⡄⠁⣄⡢⢻⣖⣺⣷⣮⣧⡴⡤⡈⠉⠀⢠⠠⣼⣦⣀⣄⣔⣦⣂⡤⠰⠄⠄⡀⠀⢄⠠⣴⣀⡝⡚⠻⠟⠀⠀⠀⠀⠀⢀⠀⠀⠉⠛⠂⢤⠂⠀⠀⠀⠈⠛⠿⠿⣿⣟⣛⣿⣿⣿⣵⣾⣿⣷
⠤⠀⡀⢀⡫⠬⣿⡯⣵⣵⣦⣿⣿⣿⣽⣯⣿⣿⡿⣿⣿⣟⡃⣤⠁⢀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣀⠀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣠⡤⣥⣤⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠄⠀⡂⢀⣉⠿⣏⣿⣿⢺⣿⣿⡿⣿⡿⠾⠃⠻⠛⠻⠟⠉⠃⢽⡿⠷⠤⢶⣶⣶⠶⠶⢶⣶⣶⣶⣶⣶⡾⢿⣿⣿⣿⡿⠿⢿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⢦⡄⢳⠿⠟⠈⢡⣆⢋⠛⠁⣿⣿⡆⣿⣿⡇⣸⣿⡟⣿⣿⣿⣿⢸⣿⣿⣿⣷⣎⣿⣿⣳⣿⡿⣿⣿⡛⣷⣿⢿⣿⣮⢹⣿⣿⢿⣿⡞⢯⣿⡿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠁⢀⠀⠀⠴⠄⠈⠀⠀⠀⠀⠀⠀⣈⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣠⢸⣿⣿⣸⣿⡿⣴⣷⣛⣛⢣⣿⣿⢳⣿⣿⢸⣿⣿⢸⣿⣻⣼⣿⠏⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢸⣿⣿⣿⢿⣿⣿⣿⠃⣿⣿⡿⣿⢸⣿⣿⢻⣿⣷⢩⣽⣿⣣⣿⣿⠯⣾⣿⣿⢸⣿⣿⢸⣯⣿⢻⣿⣧⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣧⣭⢸⣿⣿⣼⣿⣿⣸⣿⣶⣿⣿⣥⣤⠈⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⡿⢸⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢈⠛⣛⡛⣬⣿⣻⣫⣤⣿⣿⣿⣿⣼⣿⣻⣿⣿⣽⣿⣟⣛⣿⣿⣿⣻⣾⣮⣿⣟⣿⣷⣶⣽⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠲⣶⠯⢶⠶⠰⠶⠶⠶⠀⣤⣤⣦⣤⣀⣀⠀⢙⣛⣛⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡤⣶⣶⣾⣶⣷⣶⣤⣻⣶⣾⣯⣭⣷⣼⣾⣿⣿⣿⣿⣾⡶⣷⣾⣿⣷⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢁⢄⡄⠀⢐⠔⣃⢱⡆⠀⡀⠀⠀⣄⣄⣀⡀⠀⣤⣤⣄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢒⠿⣿⠟⡛⠈⠛⠛⠻⠝⢚⡻⠛⠿⣟⡿⢿⣿⣟⠟⣟⠋⡘⠻⠂⢋⣡⣤⣶⣿⣿⣿⣿⣿⣿⣟⣁⣴⣶⣷⣿⣿⣶⢂⣿⣿⣶⣧⠪⢶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣷⡅⠈⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀
⠯⠝⢛⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢩⣬⣵⣦⣬⣤⣶⣰⣎⣴⣤⣽⣿⣿⣿⣿⣿⣿⡟⠛⠒⢃⣀⢙⣿⣿⣿⣿⡷⣿⣿⡿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡂⠀⣀⣀⢄⣽⣧⣦⣴⣖⠂
⠀⢤⣵⣖⠄⠀⠀⠀⠀⠀⠀⣤⣿⣷⣿⣿⣷⣿⣿⣿⡦⣖⣾⣿⣿⣿⣿⣿⣿⣿⣉⣥⡄⢐⣲⣾⣿⣿⣿⣿⣿⡏⡟⣏⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⡟⡍⢅⣭⣽⠻⡟⠿⠿⠋⠙⠯⠨
⠚⠋⠃⠂⠠⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⠶⣿⣿⣿⣿⡷⣿⣿⣿⣿⣿⢿⣿⣿⣿⣽⣿⠯⠻⠹⡿⠷⠎⠁⠘⠓⠋⠀⠀⠆⠀⠈⠀⠒
⠠⠴⣶⡴⢀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⣿⣭⣥⣤⣤⣴⣶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢠⣟⣛⣇⣸⣿⣟⣿⡟⣿⣿⣿⣧⣷⢿⣿⣍⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠈⠀⠃⠈⠈⡰⢄⣾⣿⣿⣿⣿⣿⣹⣿⣿⡛⠋⠸⣿⢿⣿⣿⢿⣿⣿⣿⣍⠛⢻⣿⠿⢟⢽⣿⣿⣿⣿⣿⣿⣿⢯⣿⢿⢿⣻⣿⡿⣋⣹⣷⣔⣕⣫⣌⠘⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀
⠀⡀⠀⠀⠀⣺⣶⠿⠉⠳⡬⠩⠗⡀⢅⠀⠁⠀⠉⠉⠟⣟⢯⠘⠻⠯⠏⠁⠀⠊⠀⠁⠀⠀⠿⢿⣿⣿⣿⢿⡏⣄⣘⡚⣴⣿⡿⢟⣿⣼⡛⠋⠈⠁⠀⠁⡀⡰⣾⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣷⣶⣶⣤⣴⣿⣭⣿⣷⣦⣲⣜⡉⠼⢲⢥⣤⠀⠀⢐⣌⠀⠀⠀⠀⠀⠀⠄⣄⣀⡀⡀⢒⠪⣮⣭⣿⣿⣿⠙⡷⢃⠀⠚⠻⣿⣭⣾⠔⠁⠐⠀⠀⠀⠀⠠⣻⢿⣿⠇⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣶⣶⣿⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣷⣦⣶⠋⣠⣦⣤⣴⣾⣽⣿⣿⣯⣿⡟⣻⠿⠛⡧⢜⢻⡾⠆⣠⣂⡿⠝⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⣯⣿⡼⡤⠉⠨⠉⢂⠤⠴⢴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣬⣺⣿⣭⣶⣾⣿⣿⣾⣿⣿⣧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣽⣿⣿⣿⣥⠤⠄⠰⣶⣳⢾⣷⣾⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⠫⠙⠷⠸⠟⠚⢚⣇⣀⣀⡀⠀⠀⠀⠰⣶⠈⡈⣿⣿⣿⣿⣿⠻⣭⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣷⣦⣄⠸⠂⣛⣛⣭⡽⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⡿⡯⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠹⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠟⠟⠃⠀⠀⢀⣿⣿⣿⣿⡟⠀⠈⢿⣿⣿⣿⡿⠟⠛⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⣻⠉⠛⠉⠙⠛⠋⠙⠛⠛⠁⠈⠀⠀⠉⠙⠋⠉⠉⠉⠈⠓⡒⠀⠀⠀⠀⠀⠈⠛⠙⠛⠛⠁⠀⠀⠠⣿⣿⣿⣇⠀⠀⠈⣻⠆⣀⡀⢀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠉⠀⠀⠀⠀⠀⠀⠀⠄⠐⠐⠂⠈⠀⠀⠀⠀⠄⠀⠀⢠⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠙⠿⣷⣤⣄⠀⠀⠘⢿⣿⢻⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⣤⣴⡤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⣄⡀⠀⠀⡀⣻⣏⡀⠀⠀⠸⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣺⣤⣽⣭⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠐⠀⠀⠀⠀⠀⠆⠂⠈⠉⠀⢢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠇⢹⠋⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⡟⡿⣿⣯⣭⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠹⣿⣿⠟⣋⣯⣶⣾⣿⣿⣿⣿⣟⣿
⠀⠀⠀⠀⠀⠀⢐⢔⣀⣄⡄⠀⣄⡒⢻⣶⣲⣷⣦⣧⡴⡤⡌⠙⠀⢠⠠⣼⡦⣀⡀⣔⠦⣂⡦⠄⠄⠄⡂⠀⢀⠀⢴⡄⠙⠲⠿⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠴⠂⠀⠀⠀⠀⠙⠿⢿⣿⣟⣛⣿⣿⣿⣷⣿⣿⡷
⠤⠀⡀⠁⡲⠭⣽⡿⣷⣷⣧⣿⣿⣿⣿⣯⣿⣿⡿⣿⣿⣟⡉⣄⠀⢀⣸⡟⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣈⣀⣀⣀⣀⣠⡤⣤⣤⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠂⠀⠂⢁⣉⢿⣏⣿⣿⢻⣿⣿⡿⣿⡿⠾⠇⠻⠛⠻⠟⠉⠃⢾⡿⠷⠦⠶⣶⡶⠶⠶⣶⣶⣶⣶⣶⣶⠶⢾⣿⣿⣿⡿⠿⢿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⢶⡥⢳⠿⠟⡀⢡⠇⢋⠛⠁⣿⣿⡆⣿⣿⡇⣸⣿⡟⣿⣿⣿⣿⢸⣿⣿⣿⣷⣎⣿⣿⣳⣿⡿⣿⣿⡛⣷⣿⢿⣿⣮⢻⣿⣿⢿⣿⡞⢯⣿⡿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠁⢀⠀⠠⠴⠀⠈⠀⠀⠀⠐⠀⠀⣈⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣂⢸⣿⣿⣸⣿⡿⣴⣿⣛⣛⢣⣿⣿⢣⣿⣿⢸⣿⣿⢸⣟⣿⣼⣿⠏⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⣿⣿⢿⣿⣿⣿⠃⣿⣿⡿⢿⢸⣿⣿⢻⣿⣷⢩⣿⣿⣣⣿⣿⠯⣾⣿⣿⢸⣿⣿⢸⣯⣿⢻⣿⣧⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣧⣭⢸⣿⣿⣼⣿⣿⣸⡿⣷⣿⣿⣥⣴⠌⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⡿⢸⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢈⠛⣛⡛⣤⣿⣻⣫⣤⣿⣿⣿⣿⣼⣿⣻⣿⣿⣽⣿⣟⣛⣿⣿⣿⣻⣾⣮⣿⣟⣿⣷⣶⣽⣿⣛⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠲⣶⠮⢶⠦⠰⠶⠶⠶⠀⣤⣤⣤⣤⣀⣀⠀⡙⣛⣛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡤⣶⣶⣾⣴⣷⣶⣤⣻⣶⣾⣿⣭⣷⣼⣾⣿⣿⣿⣿⣾⡶⣷⣾⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⠛⢁⢀⠄⢀⠀⢄⣁⢡⠄⡀⠀⠀⠀⣀⢀⣀⡀⠀⣄⣤⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢚⠿⣿⠟⡛⠈⠛⠋⠻⠙⠺⡻⠛⠿⣟⡿⢿⣿⢟⠿⡛⠋⡘⠻⠂⢉⣁⣤⣶⣿⣿⣿⣿⣿⣿⣟⣉⣴⣶⣷⣿⣿⣴⢂⣯⣿⣶⣥⠀⢲⣎⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣺⣷⡀⠈⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀
⠏⠍⢚⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢩⣬⣵⣦⣤⣤⣦⣰⣎⣶⣤⣽⣿⣿⣿⣿⣿⣿⡟⠛⠒⢃⣀⢉⣿⣿⣿⣿⡷⣷⣿⡿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀⠀⣀⣀⢀⣹⣷⣤⣤⣒⠀
⠀⢤⣵⣆⠀⠀⠀⠀⠀⠀⠀⣤⣽⢵⣿⣿⣿⣿⣿⣿⡦⣖⣾⣿⣿⣿⣿⣿⣿⣿⣉⣤⡄⢐⣲⣾⣿⣿⣿⣿⣿⡏⡟⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⡏⡉⢅⣬⣜⠫⠟⠻⠿⠉⠉⠯⠠
⠚⠉⠃⠀⠠⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣟⣿⣧⣤⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣷⠶⣿⣿⣿⣿⡷⣯⣿⣿⣿⣿⢿⣿⣿⣿⣽⣿⠯⠛⠹⡿⠷⠎⠁⠘⠓⠋⠀⠀⠂⠀⠀⠀⠒
⠠⠴⣶⡤⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣽⣭⣥⣤⣤⣴⣶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢠⣿⣛⣃⣾⣿⣟⣿⡟⣿⣻⣿⡧⣷⢾⣻⣏⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂
⠈⠀⠃⠀⠈⡐⢄⣾⣿⣿⣿⣿⣿⣽⣿⣿⡛⠋⠸⣿⢿⣿⣿⢿⣿⣿⣿⣍⠉⢻⢿⠾⡟⢽⣿⣿⣿⣿⣿⣿⣿⢯⣿⢿⢿⣿⣿⡿⡋⣋⣣⡄⣝⣫⡌⠘⠃⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠁⡀⡀⠀⠀⢺⣶⠿⠉⠱⠈⠩⠇⠀⢅⠀⠁⠀⠉⠉⠛⣛⢯⠘⠛⠯⠍⠁⠀⠂⠀⠁⠀⠀⠿⢿⣿⣿⣿⢿⡏⣍⣚⡚⣰⣿⡿⠟⣿⣼⡛⠋⠀⠁⠀⠁⡀⡰⣼⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣶⣶⣤⣴⣿⣭⣿⣷⣦⣲⣔⡉⠤⢲⠥⣤⠀⠀⢐⣄⠀⠀⠀⠀⠀⠀⠄⣄⣀⡀⡁⢒⡪⣦⣭⣿⣿⣿⠙⡷⢃⠀⠘⢻⣿⡤⢺⠜⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⣶⣶⣿⣶⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣴⡏⣢⣦⣤⣴⣾⣼⣿⣾⣯⣿⡟⡻⠿⠛⡷⢘⢻⡾⠆⣠⡶⡿⠝⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⣯⣿⡄⠀⠉⠈⠉⢒⠂⠔⠒⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣭⣸⣿⣥⣾⣾⣿⣿⣾⣿⣿⣇⡈⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⣙⣭⣿⣿⣡⠤⠄⠐⣶⢓⢺⣷⣾⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠫⠙⣿⣼⢿⣾⡾⠁⠀⠀⠀⠀⠀⠀⠐⡲⠊⡉⣿⣿⣿⣿⡿⠋⣥⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠓⠛⠑⣿⣿⣅⢀⣠⣀⣀⠀⢃⣄⠀⠨⠂⣋⣛⣭⡽⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⡿⡯⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⢈⠀⣿⣿⣷⢷⣾⡷⣷⣾⣿⣻⣶⡶⠿⠋⣿⣿⣿⢿⠟⠹⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⢿⠿⠃⠀⠬⣤⣭⣛⢶⣿⣶⣶⣶⣶⣷⣦⣤⣤⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⣛⠙⠛⠉⠙⠛⠋⠙⠛⠛⠁⠈⠁⠀⠉⠙⠋⠉⠉⠉⠈⠓⡓⠁⠀⠀⣰⣾⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⢠⣤⣤⣴⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠘⠀⠀⠀⠈⢿⣿⣿⣿⣮⡦⠘⢻⣿⣿⣿⣿⣿⣿⡯⢿⣿⣿⣶⣶⣶⡞⢿⣿⣿⣿⣯⠀⣶⣶⣶⣶⣶⣤⣤⣴⡤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠀⠀⠘⢻⣿⣿⣿⠀⠀⠀⠁⠥⠤⠥⢽⣿⢸⣿⣿⣿⣿⣷⣽⣿⣿⣿⡿⣺⣴⣽⣭⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠐⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠛⠿⠟⠀⠀⠀⠈⠃⠻⣿⣦⣤⣤⣤⠀⠀⠀⠸⠃⠘⣿⣿⣿⣿⣿⣿⡿⠿⣿⣫⣭⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠛⡛⠛⠋⠀⠀⠀⠀⠀⠀⠙⢿⣿⡿⠉⣙⣯⣶⣾⣿⣿⣿⣿⣟⣿
⠀⠀⠀⠀⠀⠀⢐⣄⣀⣄⡄⡀⣀⡠⢻⣶⣺⣷⣦⣷⣤⡤⡈⠉⠀⢠⠠⣼⡦⣀⣄⣔⡆⣗⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠐⠊⠶⠀⠀⠀⠀⠀⠻⠿⢿⣿⣟⣛⣿⣿⣿⣷⣿⣿⡷
⠀⠀⡀⢀⡲⠬⣽⡿⣽⣿⣧⣿⣿⣿⣿⣯⣿⣿⡿⣿⣿⣟⡁⣄⠀⢀⣸⡿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡥⣤⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠀⠀⡀⠀⣉⢿⣏⣿⣿⢻⣿⣿⡿⣿⡿⠿⠇⠻⠛⠻⠟⠉⠃⠾⡿⠷⠦⠲⣶⠶⠶⠶⣶⣶⣶⣶⣶⣦⠶⣶⣶⣶⣶⡿⠿⠿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⢦⣅⢳⠿⠟⠠⢥⠧⢫⠛⠁⣿⣿⡆⣿⣿⣇⣸⣿⡟⣿⣿⣿⣿⢸⣿⣿⣿⣷⣎⣿⣿⣳⣿⡿⣿⣿⡛⣷⣿⢿⣿⣮⢹⣿⣿⢿⣿⡞⢯⣿⡿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠀⠠⠴⠀⠈⠀⠀⠀⠐⠀⠁⣈⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣂⢸⣿⣿⣸⣿⡿⣶⣿⣛⣛⢣⣿⣿⢣⣿⣿⢸⣿⣿⢸⣿⣿⣼⣿⠏⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⣿⣿⢿⣿⣿⣿⠃⣿⣿⡿⣿⢸⣿⣿⢻⣿⣷⢩⣿⣿⣣⣿⣿⠯⣾⣿⣿⢸⣿⣿⢸⣯⣿⢻⣿⣧⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣧⣭⢸⣿⣿⣼⣿⣿⣸⡿⣷⣿⣿⣥⣴⠈⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⡿⢸⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢈⠛⣛⡛⣤⣿⣻⣫⣤⣿⣿⣿⣿⣼⣿⣻⣿⣿⣵⣿⣟⣛⣿⣿⣿⣻⢼⣮⣿⣟⣿⣷⣶⣽⣿⣛⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠲⣶⠯⢶⠆⠰⠶⠶⠶⠀⣤⣤⣤⣤⣀⡀⠀⡙⣛⣛⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡤⣶⣶⣾⣴⣷⣶⣤⣻⣶⣾⣽⣭⣷⣼⣾⣿⣿⣷⣿⣾⡶⡷⣾⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⠛⢁⣀⠀⠀⠀⠀⣀⢠⠀⠀⠀⠀⠀⢀⢀⡀⡀⠀⣀⣤⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠿⣿⠟⡛⠈⠉⠋⠛⠙⢚⡻⠛⠿⣟⡿⠿⣿⢟⠿⡛⠋⡘⠻⠂⢈⣁⣠⣶⣿⣿⣿⣿⣿⣿⣏⣁⣴⣶⣶⣿⣧⣴⢂⣭⣻⣖⣥⠠⢰⣌⣦⣿⣿⣿⣷⣿⣿⣿⣿⣿⣯⣧⣺⣤⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀
⠏⠍⢚⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢡⣤⣥⣆⣤⣤⣠⣰⡆⣔⣤⣽⣿⣿⣿⣿⣿⣿⡟⠛⠐⢁⣀⢉⣿⣿⣿⣿⡷⣷⣿⡿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⣀⣀⢀⣹⣦⣤⣤⣆⠀
⠀⢤⣵⡆⠀⠀⠀⠀⠀⠀⠀⣠⣽⣵⣿⣿⣳⣿⣿⣿⡦⣖⣾⣿⣿⣿⣿⣿⣿⣿⣉⣤⡄⢐⣲⣾⣿⣿⣿⣿⣿⡏⠟⣏⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⡿⡃⠈⠄⣤⡜⠻⠟⠻⠿⠋⠙⠯⠠
⠒⠉⠃⠀⠠⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣟⣿⣧⣤⣽⣿⣿⣿⣿⣿⡿⠛⠛⠛⠫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣶⣿⠶⣿⣿⣿⣿⡷⣯⣿⣿⣿⣿⢿⣿⣿⣿⣽⣿⠯⠛⠹⡿⠧⠌⠁⠘⠓⠋⠀⠀⠂⠀⠈⠀⠂
⠀⠴⢶⡤⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⣽⣭⣤⣤⣤⣴⣶⢺⣯⣿⣿⣿⣿⣿⣿⣿⣿⣇⢠⣟⣛⢃⣸⣿⡟⣿⡟⢛⣿⣽⡧⣶⢾⣿⡍⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠈⠀⠃⠀⠈⡐⠀⣾⣿⣿⣿⣿⣯⣹⣿⣿⠛⠋⠸⣿⢿⣿⣿⢿⣿⣿⣿⣍⠉⢻⢿⠾⠟⢽⣿⣿⣿⣿⣿⣿⣿⢯⣽⢿⢿⣻⣿⡿⢉⣉⣣⡄⣕⣫⡍⠘⠃⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠀⡀⠀⠀⠀⢺⣴⠿⠉⠰⠌⠉⠇⠀⢅⠀⠁⠀⠉⠉⠙⣛⢯⠈⠛⠿⠍⠁⠀⠀⠀⠁⠀⠀⠿⢿⣿⣿⣿⢿⡏⣌⣚⡒⣠⣿⡿⠟⣯⣼⡛⠃⠀⠀⠀⠁⡀⡰⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⣶⣶⣤⣴⣿⣭⣾⣷⣦⣒⣐⠉⠠⢲⠤⢠⠀⠀⢐⣄⠀⠀⠀⠀⡀⠀⠄⣄⣀⡀⡀⢒⠢⣦⣭⣿⣿⣿⠙⡷⢁⠀⠘⠻⣿⡄⠘⠐⠑⠀⠀⠀⠀⠀⠀⣿⣿⣹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣦⣴⣵⣶⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣴⡈⣀⣤⣄⣴⣾⣽⣿⣾⣯⣿⡛⡻⠿⠛⡗⢘⢻⡾⠄⣢⢒⡟⠕⠁⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣯⠌⠀⠉⠀⠉⢐⠠⠀⠰⣶⣽⣿⣽⣿⣿⣿⣿⣿⣟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣭⣸⡯⡥⣶⣾⣿⣿⣾⣿⣿⣇⡈⠀⠀⠀⠀⠀⠀⠀⠀⠰⢯⣛⣯⣿⣿⣁⠤⠀⠰⣶⢓⢺⣶⣾⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⠫⠙⣿⣜⢿⣾⡾⠁⠀⠀⠀⠀⠀⠀⠐⡲⠈⠈⣩⣿⣿⣿⡯⠉⣥⣹⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⠓⠛⠁⣿⣷⡄⠀⣀⣀⣀⠀⢁⣀⠀⠨⠂⢋⣛⣭⡽⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⡿⡯⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⢈⠀⠾⣿⡷⢲⣶⡯⡧⢮⣹⣳⣶⠶⠟⠉⣽⣿⣿⢿⠟⠹⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⢿⠿⠃⠐⣶⣶⣮⣝⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⣛⠉⠛⠉⠙⠛⠋⠉⠛⠛⠁⠈⠀⠀⠈⠙⠉⠉⠉⠉⠀⠓⡒⠀⠀⣠⣾⣿⣿⡿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠹⣿⣿⣿⣿⣶⠀⠙⠿⣿⣿⣿⣿⡿⠭⠈⢿⣿⡿⢿⣿⣿⡍⣿⣿⣿⣿⣇⡀⢲⣶⣶⣶⣦⣤⣤⣴⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠙⣿⣿⣿⡀⠀⠀⠀⠐⠒⠐⠒⢻⡇⢸⣿⣿⣿⣿⡶⣼⣿⣿⢿⠷⣪⣤⣭⣭⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠐⠀⠀⠀⠀⡠⠄⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠋⠀⠀⠀⠀⠉⠈⢿⣷⣶⣶⣶⡆⠀⠀⠀⠋⠁⠸⣿⣽⣿⣿⣿⡿⠛⢿⣟⣩⣭⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢉⣉⠉⠩⠁⠀⠀⠀⠀⠀⠀⠈⠿⣿⡏⠁⣙⣯⣶⣼⣿⣿⣿⣿⣟⣿
⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⡀⠀⣄⡂⢺⣖⣲⣷⣦⣧⣤⡤⡈⠙⠀⢀⠠⣴⡦⣠⣀⣔⣶⣖⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⡄⠀⠀⠀⢀⢀⣼⠿⢿⣿⣟⣛⣿⣿⣿⣷⣾⣿⡷
⠀⠀⡀⠀⡢⠬⣹⣿⣽⣷⣦⣿⣾⣿⣿⣧⣿⣿⡿⣿⣿⣟⡁⣄⠀⢀⣸⡟⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡭⣤⣤⣤⣶⣶⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠀⠀⡂⠁⣉⠿⣍⣿⣿⢻⣿⣿⡿⣻⡿⠾⠗⠻⠛⠻⠟⠉⠃⢼⡿⠷⠦⠲⢶⡶⠶⠶⢶⣶⣶⣶⣶⣦⠶⢶⣶⣶⣾⡿⠿⠿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⢦⡄⢳⠿⠛⠈⢡⠆⢌⠛⠀⣿⣿⡆⣿⣿⡇⣸⣿⡟⣿⣿⣿⣿⢸⣿⣿⣿⣷⣎⣿⣿⣳⣿⡿⣿⣿⡛⣷⣿⢿⣿⣮⢻⣿⣿⢿⣿⡞⢯⣿⡿⣿⣷⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠀⠀⠴⠀⠈⠀⠀⠀⠀⠀⠀⡈⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣂⢸⣿⣿⣸⣿⡿⣴⣿⣛⣛⢣⣿⣿⢣⣿⣿⢸⣿⣿⢸⣿⣻⣼⣿⠏⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⣿⣿⢿⣿⣿⣿⠃⣿⣿⡿⣿⢸⣿⣿⢻⣿⣷⢩⣿⣿⣡⣿⣿⠯⣾⣿⣿⢸⣿⣿⢸⣯⣿⢻⣿⣧⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣧⣭⢸⣿⣿⣼⣿⣿⣸⡿⢷⣿⣿⣥⣤⠈⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⡿⢸⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠛⣛⡛⣤⣛⣻⣫⣤⣿⣿⣿⣿⣼⣿⣻⣿⣿⣽⣿⣟⣛⣿⣿⣿⣻⣼⣮⣿⣟⣿⣷⣶⣽⣿⣛⣿⣿⣿⣽⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠲⣶⠎⢶⠦⠰⠶⠶⠶⠀⣤⣤⣤⣤⣀⡀⠀⠙⡛⡋⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡤⣶⣶⣾⣶⣷⣶⣤⣻⣶⣾⣭⣭⣷⣼⣾⣾⣿⣿⣿⣾⡶⢶⣾⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⠛⢁⣀⡀⢀⠀⠀⡂⢱⡄⠀⠀⠀⠀⣀⣄⣀⠀⠀⣤⣤⣄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢊⠿⣿⠟⡛⠈⠛⠙⠛⠙⠺⡻⠟⠿⣿⡿⠿⣟⣟⠟⡛⠋⡙⠻⠂⢈⣁⣤⣶⣿⣿⣿⣿⣿⣿⣟⣁⣴⣶⣶⣿⣿⣴⢂⣻⣷⣶⣥⠀⠶⣎⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣧⡄⠈⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀
⠏⠍⢛⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢩⣬⣷⣦⣤⣤⣤⣰⣎⣔⣤⣽⣿⣿⣿⣿⣿⣿⡟⠛⠒⢃⣀⢉⣿⣿⣿⣿⡷⣷⣿⡿⣿⣽⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⣀⣀⢀⣹⣶⣤⣤⣖⠀
⠀⢤⣵⡆⠀⠀⠀⠀⠀⠀⠀⣠⣽⣵⣿⣿⣷⣿⣿⣿⡦⣖⣾⣿⣿⣿⣿⣿⣿⣿⣁⣤⡄⢐⣲⣾⣿⣿⣿⣿⣿⡏⡟⣏⣛⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⡿⡇⡈⢅⣬⣕⠻⠟⠻⡿⠋⠉⠯⠠
⠚⠋⠃⠂⠠⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣟⣿⣧⣬⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣷⣿⠶⣟⣟⣿⣿⡷⣯⣿⣿⣿⣿⢿⣿⣿⣿⢽⣻⠯⠛⠹⡿⠶⠈⠁⠘⠓⠋⠀⠀⠆⠀⠈⠀⠒
⠠⠴⣶⡤⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⣽⣭⣥⣤⣤⣴⣶⠺⣯⢿⣿⣿⣿⣿⣿⣿⣿⣇⢠⣟⣛⣇⣾⣿⣟⣿⡟⣛⣻⣽⡦⡶⢿⣿⣅⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠈⠀⠃⠀⠈⡐⠀⣾⣿⣿⣿⣿⣯⣹⣿⣿⠛⠋⠸⣿⢿⣿⣿⢿⣿⣿⣿⣍⠉⢻⢿⠾⠟⢽⣿⣿⣿⣿⣿⣿⣿⠯⣿⢿⣿⣻⣿⡿⠉⣉⣳⡄⣕⣋⡍⠘⠋⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠀⡀⠀⠀⠀⢺⣶⠿⠉⠵⠬⠉⠇⢀⢅⠠⠁⠀⠉⠈⠛⣛⢯⠘⠛⠏⠍⠁⠀⠂⠀⠀⠀⠀⠿⠿⣿⣿⣿⢿⡏⣌⣚⡒⣰⣿⡟⠞⣯⣼⡛⠃⠀⠀⠀⠁⡀⡰⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣷⣶⣶⣤⣶⣿⣭⣿⣷⣦⣲⣔⠉⠤⠲⠤⣠⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠄⣄⣀⡀⠀⠒⠪⣦⣭⣿⣿⣿⠙⡷⢃⠀⠘⢻⣿⣤⠨⠘⠉⠀⠀⠀⠀⠀⠀⣿⢿⡽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣶⣶⣿⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣴⡊⣠⣦⣄⣤⣾⣽⣿⣾⣯⣿⡛⡻⠾⠛⡗⢘⢻⡾⠄⣠⣖⡟⠕⠁⠀⠀⠀⠀⠀⠀⠀⣰⣿⣯⣯⠄⠀⠉⠈⠉⢀⠠⠀⠶⢾⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣭⣸⣿⡥⣶⣾⣿⣿⣾⣿⣿⣇⡈⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣛⣭⣿⣿⡁⠤⠄⠰⣶⣳⢾⣷⣾⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠫⠙⣿⣼⢿⣾⡾⠃⠀⠀⠀⠀⠀⠀⢐⣲⠈⡨⣻⣿⣿⣿⡯⠉⣥⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠛⠛⠑⣿⣷⡄⢀⣠⣀⣀⠀⢃⣀⠀⠨⠂⣛⣋⣭⡽⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⡿⠯⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠈⠀⢿⡿⠣⣾⣶⣿⣯⢮⣻⣳⣶⡶⠿⢋⣽⣿⣿⡿⠿⠹⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⢿⠿⠃⣶⣶⣦⣍⣻⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⠙⠛⠉⠙⠛⠋⠉⠛⠛⠁⠈⠀⠀⠉⠙⠉⠉⠉⠉⠀⠓⡓⠀⢠⣾⣿⣿⡿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⢠⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠀⠀⠀⠀⠄⠀⠀⠀⠘⠈⠀⠘⣿⣿⣿⣿⣾⡖⠊⠿⣿⣿⣿⣿⣿⢯⠤⢽⣿⣿⣿⡿⣷⣯⢻⣿⣿⣿⣿⣀⡀⢶⣶⣶⣶⣶⣤⣤⣴⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡇⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠒⠀⠘⠘⣿⠀⣿⣿⣿⣿⣷⠾⣾⣿⣿⣿⡯⣺⣤⣽⣭⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠛⠛⠁⠀⠀⠀⠘⠉⢻⣿⣶⣤⣤⡤⠀⠐⠀⠐⠋⠀⢻⣿⣿⣿⣿⣿⣿⠙⢿⣿⣩⣭⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⣉⡙⠉⠍⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡯⠉⣙⣯⣶⣾⣿⣿⣿⣿⣟⣿
⠀⠀⠀⠀⠀⠀⢐⢄⣀⣄⡄⠀⣔⡂⣻⣶⣺⣷⣦⣧⣴⡦⡈⠙⠀⢠⠠⣼⡦⣀⣤⣔⣶⣲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠠⣆⠀⠀⡀⢀⣠⣽⠿⢿⣷⣿⣛⣿⣿⣿⣷⣿⣿⡷
⠠⠀⡀⠁⡲⠬⣽⡯⣿⣿⣦⣿⣾⣿⣿⣯⣯⣿⡿⣿⣿⣟⡋⣄⠀⢀⣸⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣭⣤⣤⣴⣶⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠄⠀⡂⢀⣉⢿⣏⣻⣿⢻⣿⣿⡿⣿⡿⠾⠇⠛⠛⠻⠟⠉⠃⢼⡿⠷⠶⠲⣶⡷⠶⠶⢶⣶⣶⣶⣶⣤⠶⣶⣶⣶⣶⡶⠾⢿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⢶⣄⢳⠿⠟⡈⢥⢖⢫⠟⠁⣿⣿⡆⣿⣿⣇⣸⣿⡟⣿⣿⣿⣿⢸⣿⣿⣿⣷⣎⣿⣿⣳⣿⡿⣿⣿⡛⣷⣿⢿⣿⣮⢻⣿⣿⢿⣿⡞⢯⣿⡿⣿⣷⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠀⠀⠴⠀⠈⠀⠀⠀⠐⠀⠁⣈⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣂⢸⣿⣿⣸⣿⡿⣶⣿⣛⣛⢣⣿⣿⢳⣿⣿⢸⣿⣿⢸⣿⣿⣼⣿⠏⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⣿⣿⢿⣿⣿⣿⠃⣿⣿⡿⣿⢸⣿⣿⢻⣿⣷⢩⣿⣿⣣⣿⣿⠯⣾⣿⣿⢸⣿⣿⢸⣯⣿⢻⣿⣧⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣧⣭⢸⣿⣿⣼⣿⣿⣸⡿⣷⣿⣿⣥⣤⠈⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⣿⢸⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢌⠛⣛⡛⣤⣿⣻⣫⣤⣿⣿⣿⣿⣼⣿⣻⣿⣿⣽⣿⣟⣛⣿⣿⣿⣻⣼⣮⣿⣟⣿⣷⣶⣽⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠲⣶⠏⢶⠆⠰⠶⠶⠶⠀⣤⣤⣦⣤⣄⡠⠀⢙⣛⣋⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡤⣶⣶⣾⣶⣷⣶⣤⣻⣶⣾⣭⣭⣷⣼⣾⣾⣿⣿⣿⣾⡶⢶⣾⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⠛⢁⣀⡀⢀⠀⠀⡂⢱⡄⠀⠀⠀⠀⣀⣄⣀⠀⠀⣤⣤⣄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢊⠿⣿⠟⡛⠈⠙⠋⠛⠝⢺⡻⠟⠿⣿⡿⠿⣟⣟⠟⡛⠋⡙⠻⠂⢈⣁⣤⣶⣿⣿⣿⣿⣿⣿⣟⣁⣴⣶⣶⣿⣿⣴⢂⣿⣿⣶⡥⠀⠶⣎⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣧⡄⠈⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀
⠏⠍⢛⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢩⣤⣢⣦⣤⣤⣤⣰⣎⣔⣤⣽⣿⣿⣿⣿⣿⣿⡟⠛⠒⢋⣀⢉⣿⣿⣿⣿⡷⣷⣿⡿⣿⣽⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⣀⣀⢀⣹⣷⣤⣤⣖⠀
⠀⢤⣵⡆⠀⠀⠀⠀⠀⠀⠀⣠⣽⣷⣿⣿⣷⣿⣿⣿⡦⣖⣾⣿⣿⣿⣿⣿⣿⣿⣁⣤⡄⢐⣲⣾⣿⣿⣿⣿⣿⡏⠟⢏⣛⣿⡿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⣏⡍⣅⣬⣝⠻⠟⠻⠿⠉⠉⠯⠠
⠚⠉⠃⠂⠠⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣟⣿⣧⣬⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣶⠖⣿⣿⣿⣿⡷⣯⣿⣿⣿⣿⠿⣿⣿⣿⢹⣿⠮⠛⠹⡿⠶⠌⠁⠘⠓⠋⠀⠀⠆⠀⠀⠀⠒
⠠⠴⣶⡤⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⣿⣭⣥⣤⣤⣴⣶⢾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣇⢠⣟⣋⣃⣶⣿⣟⣿⡟⣛⣻⣽⡦⡶⠷⣿⡅⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠈⠀⠃⠈⠈⡐⢀⣾⣿⣿⣿⣿⣯⣹⣿⣿⡛⠋⠸⣿⢿⣿⣿⢿⣿⣿⣿⣍⠋⢻⢿⠾⠟⢸⣿⣿⣿⣿⣿⣿⣿⠯⣿⢿⢿⣻⣿⡿⢋⣉⣳⡄⣕⣋⣍⠘⠉⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠀⡄⠀⠀⠀⢺⣶⠿⠉⠳⠬⠉⠇⢀⢅⠠⠀⠀⠉⠈⠛⣛⢯⠘⠛⠯⠍⠁⠀⠊⠀⠀⠀⠀⠿⢿⣿⣿⣿⢿⡏⣌⣋⡒⣡⣿⡟⠞⣯⣼⡛⠋⠠⠀⠀⠁⡀⡰⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣶⣶⣤⣶⣿⣭⣿⣷⣦⣶⣔⠉⠤⢲⠤⣠⠀⠀⢀⣄⠀⠀⠀⠀⡀⠀⠄⣄⣀⡀⠀⣒⠪⣦⣭⣿⣿⣿⠙⡷⢃⠀⠘⢻⣻⣤⢼⠘⠉⠀⠀⠀⠀⠀⠠⣷⢽⡽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣶⣶⣿⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣴⡊⣀⣤⣄⣤⣾⣽⣿⣾⣯⣿⣟⡻⠿⢛⡷⢘⠻⡾⠇⣠⣖⡿⠕⠁⠀⠀⠀⠀⠀⠀⠀⣰⣿⣯⣯⠄⠀⠉⠀⠉⢐⠠⠤⠶⢾⣽⣿⣿⣿⣿⣿⡿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣭⣸⣿⡥⣶⣾⣿⣾⣾⣿⣿⣇⡈⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣛⣭⣿⣿⣅⠤⠄⠰⣶⣓⠺⣷⣾⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠫⢙⣿⣼⢿⣾⡾⠃⠀⠀⠀⠀⠀⠀⠐⣶⠈⡨⣻⣿⣿⣿⡯⠩⣥⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠑⣿⣷⡄⢀⣀⣀⣀⠀⢁⣀⠀⠨⠂⣛⣛⣭⡽⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⡿⠯⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⢈⠀⢿⣿⣷⣿⣦⣮⣵⣾⣹⣳⣶⡶⠿⢋⣽⣿⣿⢿⠿⠹⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠟⠿⡃⣤⣬⣝⡻⣿⣿⣷⣶⣶⣶⣶⣶⣦⣤⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⠙⠛⠉⠙⠛⠋⠉⠛⠛⠁⠈⠀⠀⠉⠙⠋⠉⠉⠉⠈⠓⡒⠀⣠⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢰⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠘⠀⠐⢿⣿⣿⣿⣮⡦⠈⢻⣿⣿⣿⣿⣿⣏⡋⠙⣿⣿⣿⣶⣶⣤⡛⢿⣿⣿⣿⣧⣀⡐⣶⣶⣶⣶⡶⣤⣤⣴⡠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠀⠀⠘⢻⣿⣿⣿⠀⠀⠀⠉⠩⠭⠩⠧⢿⡇⢸⣿⣿⣿⣿⣿⣶⣽⣿⣿⣿⡿⣺⣤⣽⣭⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠙⠙⠛⠿⠛⠀⠀⠀⠘⠛⠻⣿⣦⣤⣠⣤⠄⠀⠀⠀⠸⠃⠘⣿⡿⣿⣿⣿⣿⡿⡙⡿⣯⣩⣭⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠉⠛⠛⠛⢻⠂⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡨⠁⣙⣯⣶⣼⣿⣿⣿⣿⣟⣿
⠀⠀⠀⠀⠀⠀⢐⢄⣀⣀⡄⠀⣄⣲⢻⣶⣺⣷⣦⣦⡴⡦⡈⠙⠀⢠⠠⣴⡦⣠⣄⣴⣒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢀⠛⠲⡀⠀⠀⠀⢀⣈⣻⠿⢿⣿⣟⣛⣿⣿⣿⣷⣾⣿⡷
⠠⠀⡀⢁⡪⠬⣽⡯⣿⣷⣦⣿⣿⣿⣿⣯⣿⣿⡿⣿⣿⣟⡃⣄⠀⢀⣸⡟⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡭⣤⣤⣤⣶⣶⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠀⠀⡂⢀⣉⠻⣏⣿⣿⢻⣿⣿⡿⣿⡿⠾⠇⠛⠛⠻⠟⠋⠃⢼⡿⠷⠶⢲⣶⡶⠶⠶⢶⣶⣶⣶⣶⣢⠶⣶⣶⣶⣶⡶⠾⢿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⢶⣅⢳⠿⠟⡀⢥⢗⢫⠛⠁⣿⣿⡆⣿⣿⣇⣸⣿⡟⣿⣿⣿⣿⢸⣿⣿⣿⣷⣎⣿⣿⣳⣿⡿⣿⣿⡛⣷⣿⢿⣿⣮⢹⣿⣿⢿⣿⡞⢯⣿⡿⣿⣷⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠁⢀⠀⠀⠴⠀⠉⠀⠀⠀⠐⠀⠁⢈⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣂⢸⣿⣿⣸⣿⡿⣴⣿⣛⣛⢣⣿⣿⢣⣿⣿⢸⣿⣿⢸⣿⣿⣼⣿⠏⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⣿⣿⣿⢿⣿⣿⣿⠃⣿⣿⡿⣿⢸⣿⣿⢻⣿⣷⢩⣿⣿⣣⣿⣿⠯⣾⣿⣿⢸⣿⣿⢸⣯⣿⢻⣿⣧⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣧⣭⢸⣿⣿⣼⣿⣿⣸⡿⢷⣿⣿⣥⣤⠌⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⣿⢸⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢌⠛⣛⡛⣄⣿⣻⣫⣤⣿⣿⣿⣿⣼⣿⣻⣿⣿⣽⣿⣟⣛⣿⣿⣿⣻⣼⣮⣿⣟⣿⣷⣶⣽⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠲⣶⠮⢶⠦⠰⠶⠶⠶⠀⣤⣤⣤⣤⣄⠠⠀⡙⣛⣛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡤⣶⣶⣾⣴⣷⣶⣤⣳⣶⣾⣭⣥⣷⣤⣾⣷⣿⣷⣿⣶⡶⡶⣾⣿⣖⣟⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⡿⠛⢁⣀⠀⠀⠀⠀⣀⢡⡄⠀⠀⠀⠀⣀⠀⢀⠀⠀⢄⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠻⣿⠟⡛⠈⠋⠋⠛⠙⠚⡛⠛⠟⣟⠿⠿⣟⣟⠟⡛⠋⡘⠻⠂⢈⣁⣤⣶⣿⣿⣿⣿⣿⣿⣟⣁⣴⣶⣶⣷⣯⣴⢂⣬⣶⣶⣥⠀⠰⣌⣦⣾⣾⣿⣿⣿⣿⣿⣿⣷⣧⣗⣾⣇⡀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀
⠏⠍⢚⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢨⣤⣵⣆⣤⣀⣢⣰⣆⣔⣤⣽⣽⣿⣿⣿⣿⣿⡟⠛⠒⢃⣀⢉⣿⣿⣿⣿⡷⣵⣿⡿⣿⣽⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⣀⣀⢀⣹⣦⣤⣤⣂⠀
⠀⢤⣵⡆⠀⠀⠀⠀⠀⠀⠀⣤⣽⣵⣿⣿⣻⣿⣿⣿⡦⣖⣾⣿⣿⣿⣿⣿⣿⣿⣁⣤⡄⢐⣲⣾⣿⣿⣿⣿⣿⡏⠟⠋⣻⣿⡿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡿⡏⡉⢅⢤⣼⠻⠟⠛⠿⠋⠉⠯⠠
⠚⠉⠃⠀⠠⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣛⣿⣧⣠⣹⣿⣿⣿⣿⣿⡿⠛⠛⠛⠫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⢷⣶⠖⣝⣟⣿⣿⡷⣯⣿⣿⣿⡿⠿⣟⣿⣿⢹⣻⠮⠛⠹⡿⠶⠌⠁⠘⠓⠋⠀⠀⠂⠀⠈⠀⠒
⠠⠴⢦⡤⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣯⣽⣭⣤⣤⣤⣴⣶⠺⣿⢽⣿⣿⣿⣿⣿⣿⣿⣇⢠⣕⣃⣃⣰⣿⡟⣿⡇⣿⣻⣽⡦⣶⠷⣻⡅⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠈⠀⠂⠀⠈⡐⢀⣾⣿⣿⢯⣿⣭⣹⣿⣿⠛⠋⠸⣿⢿⣿⣿⢿⣿⣿⣿⡍⠋⢻⢳⠾⠘⢸⣿⣿⣿⣿⣿⣿⣿⠯⣽⠽⢿⣛⣻⡷⠉⣉⡣⡐⣕⣋⡄⠈⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠀⡀⠀⠀⠀⢺⣴⠟⠉⠱⠈⠩⠇⠀⢅⠀⠁⠀⠉⠉⠛⣛⢯⠘⠛⠏⠉⠁⠀⠊⠀⠁⠀⠀⠻⠿⣿⣿⣿⢿⡏⣄⣈⡒⣠⣽⡚⠖⣯⢴⡛⠃⠀⠀⠀⠁⡀⠐⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⣶⣶⣤⣴⣿⣭⣾⣧⣦⣒⣐⠉⠤⠲⠤⣠⠀⠀⢐⢄⠀⠀⠀⠀⠀⠀⠄⣄⣀⡀⠁⢒⠪⣦⣭⣿⣿⣿⠐⡧⢁⠄⠈⢺⣫⠄⠸⠘⠁⠀⠀⠀⠀⠀⠠⡳⢾⡹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣶⣴⣷⣶⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣴⡊⣀⣤⣤⣤⣾⣼⣿⣾⣯⢿⡓⡻⠿⠛⡗⢘⠻⡾⠄⡠⢒⡔⠔⠁⠀⠀⠀⠀⠀⠀⠀⣐⣿⣯⣏⠄⠀⠉⠀⠉⢀⠄⠄⠆⢶⣰⣶⣿⣿⣿⣿⡿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⡬⣸⡯⡥⣶⣾⣿⣖⣾⣿⣿⣆⡈⠀⠀⠀⠀⠀⠀⠀⠀⠰⢯⣙⣭⣿⣿⡄⠠⠄⠐⣶⣓⠾⣶⣾⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡟⠫⠙⣷⣔⢻⣾⡞⠁⠀⠀⠀⠀⠀⠀⠐⡒⠈⡠⣻⣿⣿⣿⡿⠉⣥⣽⣻⣿⣾⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⠛⠛⠁⣟⣶⡅⠀⣀⢀⣀⠀⢁⣀⠀⠨⠂⡋⣛⣩⡽⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⡻⡯⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⢈⠀⢷⣿⣧⣢⣄⣐⣔⣮⣋⣳⣶⠶⠟⠋⣽⢿⡟⢿⠿⠹⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠟⠿⠣⣤⣬⣙⠿⣿⣿⣷⣶⣶⣶⣶⣷⣦⣤⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⣛⠙⠛⠉⠙⠛⠋⠉⠛⠛⠁⠈⠀⠀⠈⠙⠋⠉⠉⠉⠀⠓⡓⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢠⣤⣤⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠘⠀⠘⣿⣿⣿⣿⣜⡄⠬⢿⣿⣿⣿⣿⣿⡟⠿⠻⣿⣿⣷⣶⣦⣤⠾⣿⣿⣿⣿⣿⣀⡀⣴⣶⣶⣶⡶⣤⡤⣤⡠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠈⠹⢿⣿⣿⡿⠉⠁⠀⠉⢉⡉⢙⣉⣿⡇⢸⣿⣿⣿⣿⣻⡦⣽⣿⣿⢿⠗⣺⣤⣵⣭⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠋⠉⠛⠿⠃⠀⠀⠀⠘⠏⢿⣿⣄⡀⣀⣀⠀⠀⠀⠀⡼⠃⢸⣿⢿⣿⣿⣾⣿⡟⠛⠿⣏⣩⣭⠽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠧⠿⠿⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡟⠌⠉⣙⣯⣶⣼⣿⣿⣿⣿⣟⣿
⠀⠀⠀⠀⠀⠀⢀⢀⢀⡀⡄⡀⣀⣒⢲⣴⣲⣷⣢⣦⡄⡄⡈⠉⠀⠀⠠⣼⢆⣠⣠⣔⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠒⠢⡀⠀⠀⠀⠈⠻⣿⠿⢿⣿⣿⣛⣷⣿⣿⣷⣾⣿⡷
⠀⠀⡀⠀⡂⠤⣹⡯⣽⣶⣦⣿⣿⣿⣽⣧⣯⣿⡻⣿⣿⣟⡁⣄⠀⢀⣸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡥⣠⣤⣤⣴⣴⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠀⠀⠂⠀⣉⠹⢍⣻⡯⠺⣿⣿⡟⣫⡿⠞⠇⠙⠛⠻⠟⠉⠁⢸⡿⠷⠴⠲⡶⠷⠶⠶⢶⣶⣶⣶⣶⣠⠶⢶⣶⣶⣶⡶⠾⠿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⢆⡀⠲⠿⠋⠀⢠⢖⢁⠛⠀⣿⣿⡆⣿⣿⡇⣸⣿⡟⣿⣿⣿⣿⢸⣿⣿⣿⣷⣎⣿⣿⣳⣿⡿⣿⣿⡛⣷⣿⢿⣿⣮⢱⣿⣿⢿⣿⡞⢯⣿⡿⣿⣷⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠀⠀⠴⠀⠈⠀⠀⠀⠀⠀⠀⣈⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣂⢸⣿⣿⣸⣿⡿⣴⣿⣛⣛⢣⣿⣿⢣⣿⣿⢸⣿⣿⢸⣟⣻⣼⣿⠏⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⣿⣿⢿⣿⣿⣿⠃⣿⣿⡿⢿⢸⣿⣿⢻⣿⣷⢩⣽⣿⣡⣿⣿⠯⣾⣿⣿⢸⣿⣿⢸⣯⣿⢻⣿⣧⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣧⣭⢸⣿⣿⣼⣿⣿⣸⡿⢷⣿⣿⣥⣤⠌⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⡿⢸⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣛⡛⣤⣟⣻⣋⣤⣿⣿⣿⣿⣼⣿⣻⣿⣿⣵⣿⣟⣛⣿⣿⣿⣻⣾⣮⣿⣟⣿⣵⣶⣽⣿⣛⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠲⣶⠮⢶⠄⠰⠶⠶⠶⠀⣤⣤⣤⣤⣀⠀⠀⠙⠛⡛⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡤⣶⣶⣾⣴⣷⣶⣤⣳⣶⣾⣭⣥⣷⣤⣾⣷⣿⣷⣿⣶⡶⡶⣾⣿⣖⣟⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⡿⠛⢁⣀⠀⠀⠀⠀⣀⢡⡄⠀⠀⠀⠀⣀⠀⢀⠀⠀⢄⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠻⣿⠟⡛⠈⠋⠋⠛⠙⠚⡟⠛⠟⣟⠿⠿⣟⡟⠟⡛⠋⡘⠻⠂⢈⣁⣤⣶⣿⣿⣿⣿⣿⣿⣟⣁⣴⣶⣶⣷⣯⣴⢂⣼⣶⣶⣥⠀⠰⣎⣦⣾⣾⣿⣿⣿⣿⣿⣿⣷⣧⣷⣾⣷⡀⠈⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀
⠏⠍⢚⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢨⣤⣥⣆⣤⣄⣢⣰⢆⣔⣤⣽⣿⣿⣿⣿⣿⣿⡟⠛⠒⠃⣀⢉⣿⣿⣿⣿⡷⣷⣿⡿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⣀⣀⢀⣹⣦⣤⣤⣂⠀
⠀⢤⣵⡆⠀⠀⠀⠀⠀⠀⠀⣠⣽⣴⣿⣿⣳⣿⣿⣿⡦⣖⣾⣿⣿⣿⣿⣿⣿⣿⣁⣤⡄⢐⣲⣾⣿⣿⣿⣿⣿⡏⠛⠏⣻⣿⡿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⡏⡉⢅⢤⣼⠻⠟⠛⠿⠋⠉⠯⠠
⠚⠋⠃⠀⠠⠀⠀⠀⠀⠀⣨⣿⣷⣿⣿⣿⣿⣟⣿⣧⣠⣹⣿⣿⣿⣿⣿⡿⠛⠛⠛⠫⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⣶⣶⠖⣟⣿⣿⣿⡷⣯⣿⣿⣿⢿⠿⣟⣿⣿⢽⣻⠮⠛⠹⡿⠶⠌⠁⠘⠓⠋⠀⠀⠂⠀⠈⠀⠒
⠠⠴⢦⡤⠀⠀⠀⢀⣴⣿⣿⣿⣿⣯⣿⣿⣿⣿⠿⣿⣿⣿⣿⣯⣽⣭⣤⣤⣤⣴⣶⠺⣿⢽⣿⣿⣿⣿⣿⣿⣿⣇⢠⣕⣂⣃⣰⣿⡟⣿⡏⣿⣛⣽⡦⣶⠷⢻⡅⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠈⠀⠂⠀⠈⡐⢀⣾⣿⣿⢯⣿⣭⣹⣿⣿⠟⠋⠸⣿⢿⣿⣿⢿⣿⣿⣯⣍⡉⢻⢳⠾⠘⢸⣽⣿⣿⣿⣿⣿⣿⢯⣽⠽⢿⣻⣹⡷⢉⣉⣣⡀⣝⣃⡄⠈⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠀⡀⠀⠀⠀⢻⣴⠿⠉⠱⠈⠩⠇⠀⢅⠀⠀⠀⠉⠉⠛⣛⢯⠘⠛⠏⠉⠁⠀⠀⠀⠁⠀⠀⠻⠿⣿⣿⣿⢿⡏⣄⢈⡒⣠⣼⡛⠖⣯⣼⡛⠃⠀⠀⠀⠁⡀⡰⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣷⣶⣶⣤⣴⣿⣭⣾⣷⣤⣒⣐⠉⠠⠲⠤⣤⠀⠀⢐⣄⠀⠀⠀⠀⠀⠀⠄⣄⣀⡀⡁⠒⠪⣤⣭⣿⣿⡿⠑⡷⢀⠀⠀⠸⣫⠄⠸⠜⠁⠀⠀⠀⠀⠀⠠⣳⢽⡹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣶⣶⣵⣶⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣴⡊⣀⣤⣤⣤⣾⣼⣿⣾⣯⣿⡓⡻⠾⠛⡗⢘⠻⡾⠄⣠⢒⡔⠔⠁⠀⠀⠀⠀⠀⠀⠀⣐⣿⣯⣏⠄⠀⠈⠀⠉⢀⠀⠔⠖⢶⣷⣿⣷⣿⣿⣿⡿⣿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡬⣸⡯⡥⣶⣾⣿⣖⣾⣿⣿⣆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠰⢯⣛⣭⣿⣿⡅⠤⠄⠰⣶⣓⢺⣾⣾⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡟⠫⡙⣿⣔⣿⣾⡾⠁⠀⠀⠀⠀⠀⠀⢐⣲⠈⡨⣻⣿⣿⣿⡿⠹⣥⣽⣿⣿⣾⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠋⠛⠑⣛⣶⡄⠀⡀⢀⣀⠀⢁⣀⠀⠨⠂⡊⣋⣩⡽⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⡿⠯⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠈⠀⢷⣿⣷⢢⣄⣲⣔⣮⣛⣳⣶⡶⠞⠋⣽⢿⣟⢿⠿⠹⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠟⠿⣣⣠⣬⣝⡻⣿⣿⣷⣶⣶⣶⣶⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⣛⠉⠛⠉⠙⠛⠋⠉⠛⠛⠁⠈⠀⠀⠈⠙⠋⠉⠉⠉⠀⠓⡒⢀⣠⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠘⠂⢘⣿⣿⣿⣿⣏⡄⠀⢿⣿⣿⣿⣿⣿⣿⠟⠛⣿⣿⣿⣶⡦⣤⡴⣿⣿⣿⣿⣿⣀⠀⢴⣶⣶⣶⡶⣤⣤⣔⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⠀⠀⠸⢻⣿⣿⣿⠋⠉⠉⠛⢛⡛⠛⠍⣿⡇⢸⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣇⣺⣤⣵⣭⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠪⠛⠀⠀⠀⠘⠟⢿⣿⣀⡀⠀⠀⠀⠀⠀⠀⣸⠇⢸⣿⣿⣿⣿⣿⣿⣿⠛⠟⣯⣩⡭⠽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠿⠿⠀⠀⠀⠀⠀⠀⠐⢿⣾⣿⣿⡌⠉⣙⣯⣶⣼⣿⣿⣿⣿⣟⣿
⠀⠀⠀⠀⠀⠀⢐⠀⢀⣀⡄⠀⣀⣠⢲⣴⣲⣷⣢⣧⡄⡄⡈⠙⠀⠀⠠⣼⢆⣠⣤⣔⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠚⠠⠀⠀⠀⠀⠙⢿⣿⠿⢿⣷⣟⣛⣿⣿⣿⣷⣾⣿⡷
⠀⠀⡀⠀⡂⠤⡹⡯⣽⣷⣦⣿⣾⣟⣽⣧⣧⣺⡻⣿⣿⣟⡁⣄⠀⠀⣸⡟⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡤⣠⣤⣤⣤⣴⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠀⠀⠀⠀⣉⠙⣉⣻⣿⠺⣿⣿⡟⣿⣿⠞⠃⠛⠛⠻⠟⠉⠁⢼⡿⠷⠤⠲⡶⢷⠶⠶⢶⣶⣶⣶⣶⣠⠶⢶⣶⣶⣶⡶⠾⠿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⠀⠀⠀⠀⠐⢖⣄⠲⠿⠋⠀⢠⢄⠂⠛⠀⣿⣿⡆⣿⣿⣇⣸⣿⡟⣿⣿⣿⣿⢸⣿⣿⣿⣷⣎⣿⣿⣳⣿⡿⣿⣿⡛⣷⣿⢿⣿⣮⢱⣿⣿⢿⣿⡞⢯⣿⡿⣿⣷⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⠰⠀⠈⠀⠀⠀⠀⠀⠀⢈⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣂⢸⣿⣿⣸⣿⡿⣴⣿⣙⣛⢣⣿⣿⢣⣿⣿⢸⣿⣿⢸⣟⣻⣼⣿⠏⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⣿⣿⢿⣿⣿⣿⠃⣿⣿⡿⢿⢸⣿⣿⢻⣿⣷⢩⣿⣿⣣⣿⣿⠯⣾⣿⣿⢸⣿⣿⢸⣯⣿⢻⣿⣧⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣧⣭⢸⣿⣿⣼⣿⣿⣸⡿⢷⣿⣿⣥⣤⠈⣿⣿⣸⣿⣿⠸⣿⣿⣸⣿⡿⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣛⡋⣤⣿⣻⣫⣤⣿⣿⣿⣿⣼⣿⣻⣿⣿⣵⣿⣟⣛⣿⣿⣟⣻⢾⣮⣿⣟⣿⣷⣶⣽⣿⣻⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠲⣶⠮⢶⠄⠰⠶⠶⠶⠀⣤⣤⣤⣤⡀⠀⠀⠉⠋⡛⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡤⣶⣶⣾⣴⣷⣶⣤⣓⣶⣾⣭⣭⣷⣴⣾⣷⣿⣷⣿⣶⡶⣷⣾⣿⣖⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⢀⠀⠀⠀⠄⣀⢡⡄⠀⠀⠀⠀⣀⠀⢀⠀⠀⢤⣤⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢂⠻⡿⠟⡓⠈⠛⠋⠛⠙⠚⡛⠛⠿⣟⠿⢿⣟⢟⠟⡛⠋⡘⠻⠂⢈⣁⣤⣶⣿⣿⣿⣿⣿⣿⣟⣁⣴⣶⣶⣿⣿⣴⢂⣻⣷⣶⡥⠀⠲⣎⣦⣾⣿⣿⣿⣿⣿⣽⣿⣷⣧⣷⢽⣷⡄⠈⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀
⠏⠍⢚⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢨⣤⣥⣆⣤⣄⣢⣰⠆⣴⣤⣹⣿⣿⣿⣿⣿⣿⡟⠛⠒⢋⣀⢉⣿⣿⣿⣿⡷⣷⣿⡿⣿⣽⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⣀⣀⢀⢹⣧⣤⣤⣆⠀
⠀⢤⣵⡆⠀⠀⠀⠀⠀⠀⠀⣤⣿⣵⣿⣿⣻⣿⣿⣿⡦⣖⣾⣿⣯⣿⣿⣿⣿⣿⣁⣤⡄⢐⣲⣿⣿⣿⣿⣿⣿⡏⠟⢋⣻⣿⠿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⡿⡋⡍⢅⢤⣼⠿⡟⠻⠿⠋⠉⠯⠠
⠚⠉⠃⠀⠠⠀⠀⠀⠀⠀⣸⣿⣷⣿⣿⣿⣿⣛⣿⣧⣤⣽⣿⣿⣿⣿⣷⡿⠛⠛⠛⠫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣷⣶⠖⣽⣟⣿⣿⡗⣫⣿⣿⣿⠿⠿⣟⣿⣿⢽⣿⠮⠛⠹⡿⠶⠌⠁⠘⠓⠋⠀⠀⠆⠀⠈⠀⠒
⠠⠴⢦⡤⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣯⣽⣭⣤⣤⣤⣴⣶⠺⣯⢽⣿⣿⣿⣿⣿⣿⣿⣇⢠⣝⣋⣃⣲⣿⡟⣿⡏⣟⣙⣽⡦⡶⠷⣿⡅⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠈⠀⠂⠀⠈⡐⢄⣾⣿⣿⢿⣿⣭⣹⣿⣿⠛⠋⠸⣿⢿⣿⣿⢿⣿⣿⣿⣍⠉⢻⢳⠾⠚⢹⣿⣿⣿⣿⣿⣿⣿⢯⢽⢽⢟⣻⣹⡧⠉⣉⠥⡀⢕⣋⢌⠈⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠀⡀⠀⠀⠀⢺⣶⠿⠉⠴⠈⠩⠇⠀⢅⠠⠀⠀⠉⠉⠛⣛⢯⠘⠛⠏⠉⠁⠀⠂⠀⠁⠀⠀⠿⠿⣿⣿⣿⢿⡏⣄⢛⡚⣠⣼⡚⠖⢯⣼⡛⠃⠠⠀⠀⠁⡀⡰⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣷⣶⣶⣤⣴⣿⣭⣾⣷⣦⣒⣐⠉⠤⢲⠤⣠⠀⠀⢐⣄⠀⠀⠀⠀⠀⠀⠄⣄⣀⡀⡁⠒⠪⣤⣭⣿⣿⣿⠐⡧⢀⠄⠀⢸⣫⠄⠸⠜⠁⠀⠀⠀⠀⠀⠠⡳⢼⡽⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣶⣶⣷⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣴⡊⢀⣤⣤⣴⣾⣼⣿⣾⣯⣿⡛⡹⠼⠛⡗⢘⠻⡾⠄⣠⢒⡖⠔⠁⠀⠀⠀⠀⠀⠀⠀⣐⣿⣯⣏⠀⠀⠉⠀⠉⢀⠠⠄⠴⢶⣴⣷⣷⣿⣿⣿⡿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣬⣸⡿⡥⣶⣾⣿⣟⣾⣿⣿⣇⡈⠀⠀⠀⠀⠀⠀⠀⠀⠰⢯⣙⣭⣿⣿⡅⠠⠄⠐⣶⢓⢾⣾⣾⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡟⠫⠙⣿⣼⢿⣾⡾⠁⠀⠀⠀⠀⠀⠀⢰⣒⠈⡠⣻⣿⣿⣿⡿⠙⣥⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠛⠛⠁⣻⣷⡄⠀⡀⢀⣐⠀⢃⣀⠀⠨⠂⡚⣋⣩⡽⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⡿⠯⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⢈⠀⢶⣿⣷⣲⣌⣂⣗⣮⣛⣳⣶⡶⠟⠋⣽⢿⣟⡿⠿⠩⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠟⠿⣣⣠⣤⣍⡻⣿⣿⣷⣶⣶⣶⣶⣶⣶⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⣛⠉⠛⠉⠙⠛⠋⠉⠛⠛⠁⠀⠀⠀⠈⠙⠋⠉⠉⠉⠀⠓⡒⠀⣠⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⣀⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⢀⢿⣿⣿⣿⣏⣆⠀⠿⣿⣿⣿⣿⣿⣿⢛⡛⣻⣿⣿⣶⣶⣤⡤⣿⣿⣿⣿⣿⣇⠀⢰⣶⣶⣶⡦⣤⣤⣴⡠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠀⠀⠙⢿⣿⣿⣿⠛⠋⠉⠛⠛⠛⠛⠎⢿⡷⢰⣿⣿⣿⣿⣿⡧⣼⣿⣿⣿⠇⣺⣤⣴⣭⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠡⠛⠀⠀⠀⠘⡿⢿⣿⣀⡀⠀⠀⠈⠉⠉⠉⢸⡇⢸⣿⣿⣿⣿⣿⣿⡟⠙⠿⣯⣩⣭⠽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣻⣹⡿⠁⠀⠀⠀⠀⠀⠀⢿⣮⣿⡿⢄⠈⣙⣯⣶⣼⣿⣿⣿⣿⣟⣿
⠀⠀⠀⠀⠀⠀⢀⢀⢀⣀⡄⡀⣀⣒⢒⣴⣺⣷⣠⣦⡄⡄⡈⠉⠀⠠⠠⣼⣦⣠⣠⣔⣖⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⠢⠀⠀⠀⠀⠻⣿⣿⠿⢿⣷⣟⣛⣿⣿⣿⣷⣾⣿⡷
⠀⠀⡀⠀⡂⠠⣽⡯⣽⣵⣦⣿⣾⡿⣽⣧⣧⣾⡻⣿⣿⣟⡁⣄⠀⢀⣸⡟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡤⣠⣤⣤⣤⣾⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠀⠀⡀⠀⢉⠹⣅⣻⣿⢻⣿⣿⡟⣿⡿⠬⠁⠛⠛⠻⠏⠉⠀⠼⡿⠷⠦⠲⢶⣷⠶⠶⢶⣶⣶⣶⣶⣠⠶⢶⣶⣶⣶⡶⠶⠿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⢆⡅⠲⠿⠍⠀⠠⢄⢊⠛⠀⣿⣿⡆⣿⣿⣇⣸⣿⡟⣿⣿⣿⣿⢸⣿⣿⣿⣷⣎⣿⣿⣳⣿⡿⣿⣿⡛⣷⣿⢿⣿⣮⢹⣿⣿⢿⣿⡞⢯⣿⡿⣿⣷⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠴⠀⠈⠀⠀⠀⠀⠀⠀⣈⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣂⢸⣿⣿⣸⣿⡿⣴⣿⣘⣛⢣⣿⣿⢣⣿⣿⢸⣿⣿⢸⣟⣻⣼⣿⠏⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⣿⣿⢿⣿⣿⣿⠃⣿⣿⡿⢿⢸⣿⣿⢻⣿⣷⢩⣽⣿⣡⣿⣿⠯⣾⣿⣿⢸⣿⣿⢸⣯⣿⢻⣿⣧⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣧⣭⢸⣿⣿⣼⣿⣿⣸⡿⢳⣿⣿⣥⣤⠈⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⡿⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣛⡛⣄⣿⣻⣋⣤⣿⣿⣿⣿⣼⣿⣻⣿⣿⣵⣿⣟⣛⣿⣿⣟⣻⣾⣮⣿⣟⣿⣵⣶⣽⣿⣛⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠲⣶⠎⢶⠆⠰⠶⠶⠶⠀⣤⣤⣤⣤⣀⠀⠀⠙⠛⡛⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡤⣶⣶⣾⣴⣷⣶⣤⣳⣶⣾⣭⣭⣷⣼⣾⣾⣿⣿⣿⣾⡶⢶⣾⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⠛⢁⢀⠀⠀⠀⠀⡀⠱⡄⠀⠀⠀⠀⢀⣄⣀⠀⠀⡤⣤⣄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢂⠻⣿⠟⠓⠈⠓⠉⠛⠙⢺⡻⠛⠿⣟⡿⠿⣟⣟⠟⠟⠋⡘⠻⠂⢈⣁⣤⣶⣿⣿⣿⣿⣿⣿⣏⣉⣴⣶⣶⣿⣿⣴⢂⣺⣿⣶⣥⠀⠲⣾⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣷⣿⣼⣥⡀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀
⠏⠍⢚⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢨⣤⣵⣆⣤⣤⣤⣰⣆⣴⣤⣽⣿⣿⣿⣿⣿⣿⡟⠛⠒⢃⣀⢉⣿⣿⣿⣿⡷⣷⣿⡿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⣀⣀⢀⣩⣧⣤⣤⣖⠀
⠀⢤⣵⡆⠀⠀⠀⠀⠀⠀⠀⣠⣽⣴⣿⣿⣿⣿⣿⣿⡦⣖⣾⣿⣿⣿⣿⣿⣿⣿⣁⣤⡄⢐⣲⣿⣿⣿⣿⣿⣿⡏⠟⣏⣛⣿⡿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⡏⠉⢅⣬⣝⠻⠗⠻⠿⠉⠉⠯⠠
⠚⠋⠃⠀⠠⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣟⣿⣧⣬⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣷⣶⠶⣿⣿⣿⣿⡷⣯⣿⣿⣿⡿⠿⣟⣿⣿⢹⣿⠮⠛⠹⡿⠧⠊⠁⠘⠓⠋⠀⠀⠆⠀⠈⠀⠂
⠀⠴⣶⡤⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⣽⣭⣥⣤⣤⣴⣶⠺⣯⣿⣿⣿⣿⣿⣿⣿⣿⣇⢠⣿⣋⣃⣸⣿⡟⣿⡏⣛⣻⣽⡦⣶⠷⣻⡅⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠈⠀⠃⠀⠈⡐⠀⣾⣿⣿⢿⣿⣯⣹⣿⣿⡛⠋⠸⣿⢿⣿⣿⢿⣿⣿⣿⣍⠋⢻⢿⠾⠟⢽⣿⣿⣿⣿⣿⣿⣿⠯⣽⢿⢿⣻⣿⡷⢋⣙⡷⡐⣕⡏⡄⠘⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠀⡀⠀⠀⠀⣺⣶⠿⠉⠴⠨⠉⠃⠀⢁⠀⠀⠀⠈⠈⠛⣛⢯⠘⠛⠏⠍⠁⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⢿⡏⣌⢋⡒⣰⣿⡻⠖⣯⢼⡛⠋⠀⠁⠀⠁⡀⡰⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣷⣶⣶⣤⣴⣿⣭⣾⣷⣦⣶⣔⡉⠤⢲⠤⣠⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠄⣄⣀⡀⡀⢒⠪⣦⣭⣿⣿⣿⠙⡷⢃⠀⠐⢻⣻⡄⠸⠜⠁⠀⠀⠀⠀⠀⠠⣿⣾⡽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣶⣴⣿⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣴⡊⣠⣤⣄⣤⣾⣼⣿⣾⣯⣿⡛⡻⠿⠛⡗⢜⠻⡾⠅⣠⠒⡜⠄⠁⠀⠀⠀⠀⠀⠀⠀⣠⣿⣯⣏⠄⠀⠉⠀⠉⢀⠤⠤⠶⢾⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣬⣸⡿⡥⣶⣾⣿⣿⣾⣿⣿⣇⡈⠀⠀⠀⠀⠀⠀⠀⠀⠰⢯⣙⣭⣿⣿⡅⠤⠄⠐⣶⣓⢾⣾⣾⣿⣿⣿⣿⡿⠟⠃⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠫⠙⣿⣼⣿⣾⡾⠁⠀⠀⠀⠀⠀⠀⢐⣲⠈⡨⣫⣿⣿⣿⡯⠹⣥⣽⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⠛⠛⠑⣻⣶⣄⠀⣀⡀⣀⠀⢁⣀⠀⠨⠂⣊⣛⣭⡽⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⡿⡯⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⢈⠀⢾⣿⣧⣲⣮⣆⣗⣾⣛⣳⣶⡶⠿⠋⣽⣿⣟⡿⠿⠹⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠟⠿⣃⣠⣬⣍⡻⣿⣿⣿⣶⣶⣾⣷⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⣛⠙⠛⠉⠙⠛⠋⠉⠛⠛⠁⠈⠀⠀⠉⠙⠋⠉⠉⠉⠀⠓⡒⠀⣰⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠂⠀⣻⣿⣿⣿⣯⣃⡀⠹⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣶⣶⣤⣤⣾⣿⣿⣿⣿⣇⡀⢴⣶⣶⣶⡦⣤⣤⣤⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠀⠀⠉⢿⣿⣿⣿⠟⠛⠀⠚⠛⠛⠛⠛⢿⣷⠀⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⢗⣪⣤⣽⣭⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠘⠉⠛⠵⠙⠀⠀⠀⠈⡿⢿⣿⡀⠀⠀⠀⠈⠉⠈⠉⢹⡏⠀⣿⣿⣿⣿⣿⣿⡿⠽⢿⣯⣩⣭⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣼⣿⠁⠀⠀⠀⠀⠀⠀⢿⣮⣿⣿⣔⠍⣛⣯⣶⣼⣿⣿⣿⣿⣟⣿
⠀⠀⠀⠀⠀⠀⢐⢄⢀⣀⡀⠀⣀⡂⢺⣶⣲⣷⣦⣦⡤⡤⡈⠙⠀⢀⠠⣼⣦⣠⣠⣔⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠚⠢⠀⠀⠀⠀⠻⣿⣿⠿⢿⣿⣟⣛⣿⣿⣿⣷⣾⣿⡷
⠀⠀⡀⠁⡪⠬⣽⡯⣿⣿⣦⣿⣾⣿⣿⣯⣿⣿⡿⣿⣿⣟⡁⣄⠀⢀⣸⡟⠀⠈⠈⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡤⣠⣤⣤⣤⣼⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠀⠀⡂⠀⣉⠿⢍⣿⣯⢻⣿⣿⡿⣻⡿⠞⠃⠛⠛⠻⠟⠉⠃⠼⡿⠷⠶⠲⣶⡷⠶⠶⣶⣶⣶⣶⣶⣦⠶⢶⣶⣶⣶⡶⠾⢿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⠶⡄⢲⠿⠟⠈⢤⢇⢪⠛⠁⣿⣿⡆⣿⣿⡇⣸⣿⡟⣿⣿⣿⣿⢸⣿⣿⣿⣷⣎⣿⣿⣳⣿⡿⣿⣿⡛⣷⣿⢿⣿⣮⢹⣿⣿⢿⣿⡞⢯⣿⡿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠁⢀⠀⠀⠰⠀⠈⠀⠀⠀⠐⠀⠀⣈⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣂⢸⣿⣿⣸⣿⡿⣴⣿⣛⣛⢣⣿⣿⢣⣿⣿⢸⣿⣿⢸⣟⣻⣼⣿⠏⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⣿⣿⣿⢿⣿⣿⣿⠃⣿⣿⡿⣿⢸⣿⣿⢻⣿⣷⢩⣽⣿⣣⣿⣿⠯⣾⣿⣿⢸⣿⣿⢸⣯⣿⢻⣿⣧⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣧⣭⢸⣿⣿⣼⣿⣿⣸⡿⢷⣿⣿⣥⣴⠈⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⡿⢸⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢈⠛⣛⡋⣬⣿⣻⣫⣤⣿⣿⣿⣿⣼⣿⣻⣿⣿⣽⣿⣟⣛⣿⣿⣿⣻⣾⣮⣿⣟⣿⣷⣶⣽⣿⣛⣿⣿⣿⣽⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠲⣶⠮⢶⠦⠰⠶⠶⠶⠀⣤⣤⣤⣤⣀⡀⠀⡙⣛⡛⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠤⣶⣶⣶⣤⣷⣶⣤⣓⣶⣾⣭⣭⣶⣴⣾⣷⣿⣷⣿⣶⡶⡶⣾⣿⣖⣟⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⡿⠛⠁⢀⠀⠀⠀⠄⢀⢡⡀⠀⠀⠀⠀⠀⢄⢀⠀⠀⡄⢤⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢂⠻⣿⠟⡃⠈⠋⠋⠛⠙⠚⡛⠛⠟⣟⠿⠿⣟⡟⠿⠛⠋⡘⠻⠂⢈⣁⣤⣶⣿⣿⣿⣿⣿⣿⣏⣁⣴⣦⣶⣿⣿⣔⠀⣿⣶⣖⣥⠀⠰⣌⣦⣾⣶⣿⣿⣿⣿⣿⣿⣿⣧⣷⣾⣇⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀
⠏⠍⢚⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢨⣤⣥⣆⣠⣄⣢⣰⡆⣔⣤⣭⣷⣿⣿⣿⣿⣿⡏⠛⠐⢁⣀⢉⣿⣿⣿⣿⡷⣷⣿⡿⣿⣽⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⢀⣀⢀⣹⣤⣤⣤⣂⠀
⠀⢤⣵⡆⠀⠀⠀⠀⠀⠀⠀⣠⣽⣴⣿⣿⣻⣿⣿⣿⡦⣂⣾⣿⣿⣿⣿⣿⣿⣿⣁⣤⡄⢐⣲⣼⣿⣿⣿⣿⣽⡏⠟⢋⣻⣿⠿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⡿⡏⠉⢅⢬⢜⠫⠟⠻⠻⠉⠉⠯⠠
⠚⠉⠃⠀⠠⠀⠀⠀⠀⠀⣨⣿⣷⣿⣿⣿⣿⣛⣿⣧⣤⣹⣿⣿⣿⣿⣿⡿⠛⠛⠛⠫⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⢷⣶⠶⣽⢟⣿⣿⡷⣯⣿⣿⣿⠿⠿⣿⣿⣿⢽⣻⠮⠻⠹⡿⠦⠌⠁⠘⠓⠋⠀⠀⠂⠀⠀⠀⠒
⠠⠴⣶⡤⠀⠀⠀⢀⣴⣿⣿⣿⣿⣯⣿⣿⣿⣿⠿⣿⣿⣿⣿⣯⣽⣍⣤⣤⣤⣴⣶⠺⣯⢽⣿⣿⣿⣿⣿⣿⣿⣇⢠⣕⣒⣃⣸⣿⡟⣿⡗⣓⣛⣽⡦⡶⠶⢿⡏⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠈⠀⠂⠀⠈⡐⢄⣾⣿⡿⢯⣿⣭⣹⣿⣿⠛⠋⠸⣿⢿⣿⣿⢿⣿⣿⣯⣍⠉⢻⢳⠾⠘⢸⣻⣿⣿⣿⣿⣿⣿⢯⢿⢿⢿⣛⣿⡯⡉⢉⣣⠀⣕⡯⣤⠘⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠀⡀⠀⠀⠀⢺⣴⠿⠉⠠⠈⠩⠃⠀⢅⠀⠁⠀⠉⠈⠛⣛⢯⠘⠛⠏⠉⠁⠀⠊⠀⠁⠀⠀⠻⠿⣿⣿⣿⢿⡏⡄⢚⡒⣵⣽⡷⠖⢯⣼⡛⠂⠸⠁⠀⠁⡀⡰⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣷⣶⣶⣤⣴⣿⣭⣾⣷⣤⣲⣐⠉⠠⠲⠤⣠⠀⠀⢐⣄⠀⠀⠀⠀⠀⠀⠄⣄⣀⡀⠁⠒⠪⣤⣭⣿⣿⡿⠑⢧⢀⠄⠘⢛⣟⡤⡸⠄⠁⠐⠀⠀⠀⠀⠠⣷⣾⣽⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣲⣶⣷⣶⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣴⡈⣀⣤⣄⣤⣾⣼⣿⣾⣯⣿⡓⣳⠿⠛⡷⢘⠻⡾⠄⡠⢂⡷⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⣯⣟⡄⠀⠀⠠⠉⢒⠄⠄⢤⢾⣵⣿⣷⣿⣿⣿⡿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⡬⢸⢿⢥⣴⣾⣿⣷⣾⣿⣿⣇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⢯⣙⣭⣿⣿⡥⠄⠀⠐⣶⣳⢺⣾⣾⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡟⠫⡙⣿⣼⢿⣾⡞⠁⠀⠀⠀⠀⠀⠀⠰⣒⠈⡈⣉⣿⣿⣿⡿⠘⣥⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠛⠛⠉⣿⣷⡇⠀⣠⠀⣀⠀⢁⢀⠀⠺⠂⡊⣛⣭⡽⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⡿⡯⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄⢀⠀⢲⣿⣯⣚⣢⣶⣗⣎⣻⣳⣶⡾⠿⠩⣿⣿⣿⡿⠿⠙⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢃⣠⣤⣭⡛⢿⣿⣿⣶⣶⣾⣾⣶⣶⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⣛⠉⠛⠉⠙⠛⠋⠙⠛⠛⠁⠈⠀⠀⠈⠙⠋⠉⠉⠉⠈⠓⡓⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢀⣠⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣻⣿⣿⣿⣯⢫⣀⣹⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣿⣶⣦⣤⣤⣾⣿⣿⣿⣿⣇⡀⣴⣶⣶⣶⡶⣤⡤⢤⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠀⠀⠉⣿⣿⣿⣿⡟⠒⠀⠚⠛⠛⠛⠛⢻⣷⠀⣿⣿⣿⣿⣿⣶⣼⣿⣿⣿⠏⣪⣤⣴⣭⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠐⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠙⠃⠹⠀⠀⠀⠀⣿⢿⣿⡄⠀⠀⠀⠀⠉⠀⠉⢩⡟⠀⣿⣿⣿⣿⣿⣿⡿⢯⠟⣯⣩⣭⠽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⢿⣾⣿⠃⠀⠀⠀⠀⠀⠀⢿⣯⣿⣿⡀⠢⢛⣯⣶⣼⣿⣿⣿⣿⣟⣿
⠀⠀⠀⠀⠀⠀⢀⢀⢀⣀⡀⠀⣀⣠⢒⣴⣲⣷⣢⣧⡄⡄⡈⠙⠀⢠⠠⣴⣦⣠⣤⣴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⠂⠀⠀⠀⠀⠻⣿⣿⢿⢿⣿⣿⣛⣿⣿⣿⣷⣿⣿⡷
⠀⠀⡀⠀⡂⠤⡹⡯⣵⣷⣦⣿⣿⣿⣿⣧⣽⣾⡿⣿⣿⣟⡁⣄⠀⢀⣸⡟⠀⠈⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡥⣠⣤⣤⣤⣼⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠀⠀⠂⠠⣉⠽⢉⣺⣿⠺⣟⣿⡟⣫⡽⠬⠁⠙⠛⠻⠟⠉⠃⢼⡿⠷⠦⠶⠶⡶⠶⠶⢶⣶⣶⣶⣶⣤⠶⢶⣶⣶⣶⡶⠶⢿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⠆⡁⢰⠿⠋⠀⢠⣄⢊⠛⠀⣿⣿⡆⣿⣿⡇⣸⣿⡟⣿⣿⣿⣿⢸⣿⣿⣿⣷⣎⣿⣿⣱⣿⡿⣿⣿⡛⣷⣿⢿⣿⣮⢹⣿⣿⢿⣿⡞⢯⣾⡿⣿⣷⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠴⠀⠈⠀⠀⠀⠀⠀⠀⠈⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣂⢸⣿⣿⣸⣿⡿⣴⣷⣚⣛⢣⣿⣿⢣⣿⣿⢸⣿⣿⢘⣟⣿⣼⣿⠏⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⣿⣿⢿⣿⣿⣿⠃⣿⣿⡿⢿⢸⣿⣿⢻⣿⣷⢩⣿⣿⣣⣿⣿⠯⣾⣿⣿⢸⣿⣿⢸⣯⣿⢻⣿⣧⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣧⣭⢸⣿⣿⣼⣿⣿⣸⡿⢷⣿⣿⣥⣴⠈⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⡿⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣛⡛⣤⣟⣻⣋⣤⣿⣿⣿⣿⣼⣿⣻⣿⣿⣵⣿⣟⣛⣿⣿⣟⣻⢾⣮⣿⣟⣿⣵⣶⣽⣟⣛⣿⣿⣿⣽⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠲⣶⠎⢶⠆⠰⠶⠶⠶⠀⣤⣤⣤⣤⣀⠀⠀⠙⠉⡋⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡤⣶⣶⣾⣤⣷⣶⣤⣻⣶⣾⣭⣭⣶⣴⣾⣿⣿⣷⣿⣶⡶⡶⣾⣿⣖⣟⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⢀⠀⠀⠀⠄⣀⢡⡄⠀⠀⠀⠀⠀⢄⢀⠀⠀⡤⣠⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢂⠿⣿⠟⡓⠈⠛⠉⠛⠙⠺⡛⠛⠟⣟⠿⠿⣟⣟⠿⠛⠋⡘⠻⠂⢈⣁⣄⣶⣿⣿⣿⣿⣿⣿⣏⣁⣴⣶⣶⣿⣯⣴⠀⣻⣶⣶⣥⠀⠲⣎⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣗⣿⣧⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀
⠏⠍⢚⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢨⣤⣷⣆⣠⣄⣢⣰⢄⣔⣤⣼⣷⣿⣿⣿⣿⣿⡟⠛⠒⢃⣀⣁⣿⣿⣿⣿⡷⣷⣿⡿⣿⣽⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⢀⣀⢀⣹⣦⣤⣤⣒⠀
⠀⢤⣵⡆⠀⠀⠀⠀⠀⠀⠀⣤⣽⣴⣿⣻⣻⣿⣿⣿⡦⣖⣾⣿⣿⣿⣿⣿⣿⣿⣁⣤⡄⢐⣒⣼⣿⣿⣿⣿⣿⡏⠟⣋⣻⣿⢿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⡽⡋⡉⢅⣬⣜⠻⠗⠻⠻⠉⠉⠯⠠
⠚⠉⠃⠀⠠⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣛⣿⣧⣤⣻⣿⣿⣿⣿⣷⡿⠛⠛⠛⠫⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⣷⣶⠶⣿⣿⣿⣿⡷⣯⣿⣿⣿⠿⠿⣟⣿⣿⢽⣿⠮⠻⠹⡿⠶⠌⠁⠘⠓⠋⠀⠀⠆⠀⠀⠀⠒
⠀⠴⣦⡤⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣯⣽⣍⣥⣤⣤⣴⣶⠺⣯⢿⣿⣿⣿⣿⣿⣿⣿⣇⢠⣝⣂⢃⣸⣿⡟⣿⡗⢓⣛⣽⡦⡶⠶⢿⡏⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠈⠀⠂⠀⠀⡐⢀⣾⣿⣿⣿⣿⣭⣹⣿⣿⠛⠋⠸⣿⢿⣿⣿⢿⣿⣿⣿⣍⡋⢻⢳⠾⠘⢸⣿⣿⣿⣿⣿⣿⣿⢯⢿⢿⢿⣻⣿⡯⣋⠉⣣⠐⣕⡯⣤⠈⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠀⡀⠀⠀⠀⢺⣴⠿⠉⠰⠨⠩⠃⠀⢅⠀⠁⠀⠉⠈⠛⣛⢯⠘⠛⠏⠉⠁⠀⠀⠀⠁⠀⠀⠻⠿⣿⣿⣿⢿⡏⡌⢚⡒⣵⢼⡿⠖⢯⣼⡛⡃⠨⠁⠀⠁⡀⡰⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣶⣶⣤⣴⣿⣭⣾⣷⣦⣲⣔⠩⠴⠲⠤⣠⠀⠀⢐⣄⠀⠀⠀⠀⠀⠀⠄⣄⣀⡀⠁⢒⠪⣦⣭⣿⣿⡿⠑⢧⢀⠄⠘⢚⣯⡤⣘⠔⠁⠐⠀⠀⠀⠀⠠⣷⣼⣽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣶⣶⣷⣶⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣴⡊⢀⣤⣄⣤⣾⣼⣿⣾⡯⣿⡓⣻⠽⠛⡷⢘⢻⡾⡄⡠⣒⡿⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⣯⣟⡄⠂⠀⠀⠉⢀⠄⠄⢠⢾⣷⣿⣿⣿⣿⣿⡿⢿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣬⢺⢿⣡⣶⣾⣿⣷⣾⣿⣿⣇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⢯⣙⣭⣿⣿⡥⠄⠀⠀⣶⣓⢺⣾⣾⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⢩⡝⣿⣼⢿⣾⡞⠁⠀⠀⠀⠀⠀⠀⠰⣲⠈⣈⣩⣿⣿⣿⡿⠛⣥⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠛⠛⠙⢻⣷⡇⠀⣠⠀⣀⠀⢀⢀⠀⠨⠂⡊⣛⣭⡽⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⡿⠯⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄⠀⠀⢺⣿⣧⣒⣦⣶⣇⣎⣹⣻⣶⡿⠿⠩⣿⣿⣯⠻⠿⠙⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢃⣠⣤⣭⡛⢿⣿⣿⣶⣶⣾⣾⣷⣶⣄⣄⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⣛⠉⠛⠉⠙⠛⠋⠉⠛⠛⠁⠈⠀⠀⠈⠙⠋⠉⠉⠉⠈⠓⡓⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢀⣠⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣻⣿⣿⣿⣯⢫⣀⣹⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣿⣶⣦⣤⣤⣾⣿⣿⣿⣿⣇⣀⣴⣶⣶⣶⡶⣤⡤⣔⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠀⠀⠉⣿⣿⣿⣿⡟⠒⠐⠚⠛⠛⠛⠛⢻⣷⠀⣿⣿⣿⣿⣿⡦⣽⣿⣿⢿⠏⣪⣤⣴⣭⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠐⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠯⠻⠀⠀⠀⠀⣿⢿⣿⡀⠀⠀⠀⠀⠉⠀⠉⢩⠟⠀⣿⣿⣿⣿⣿⣿⡿⠿⡟⣋⣩⣭⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⢿⢾⣿⠃⠀⠀⠀⠀⠀⠀⢿⣯⣿⣿⡄⠈⢛⣯⣶⣼⣿⣿⣿⣿⣟⣿
⠀⠀⠀⠀⠀⠀⢀⢀⢀⡀⡄⠀⣄⣲⢒⣴⣲⣷⣠⢦⡄⡄⡈⠙⠀⢠⠠⣾⣦⣀⣤⣴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⠂⠀⠀⠀⠀⠻⣿⣿⠿⢿⣿⣿⣛⣿⣿⣿⣷⣾⣿⡷
⠀⠀⠀⠀⡂⠤⡹⡯⣽⣶⣦⣟⣿⣿⣿⣧⣽⣾⡟⣿⣿⣏⡁⣄⠀⢀⣸⡟⠈⠈⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡥⣠⣤⣤⣤⣼⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠀⠀⠀⠠⣉⠩⢉⣺⣿⠺⣿⣿⡟⣫⡽⠜⠁⠛⠛⠻⠟⠉⠁⠼⡿⠷⠦⠶⡶⠶⠶⠶⢶⣶⣶⣶⣶⣦⠶⢶⣶⣶⣶⡶⠶⢿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⠆⡀⢱⠿⠋⠀⢠⢄⢁⠛⠀⣿⣿⡆⣿⣿⡇⣸⣿⡟⣿⣿⣿⣿⢸⣿⣿⣿⣷⣎⣿⣿⣳⣿⡿⣿⣿⡛⣷⣿⢿⣿⣮⢹⣿⣿⢿⣿⡞⢯⣿⡿⣿⣷⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⠴⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣀⢸⣿⣿⣸⣿⡿⣴⣷⣛⣛⢣⣿⣿⢣⣿⣿⢸⣿⣿⢘⣟⣻⣼⣿⠏⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⣿⣿⢿⣿⣿⣿⠃⣿⣿⡿⢿⢸⣿⣿⢻⣿⣷⢩⣿⣿⣡⣿⣿⠯⣾⣿⣿⢸⣿⣿⢸⣯⣿⢻⣿⣧⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣧⣭⢸⣿⣿⣼⣿⣿⣸⣿⢷⣿⣿⣥⣤⠈⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⡿⢸⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣛⡛⣠⣛⣛⣫⣤⣿⣿⣿⣿⣼⣿⣻⣿⣿⣵⣿⣟⣛⣿⣿⣟⣻⢾⣮⣿⣟⣿⣵⣶⣽⣟⣛⣿⣿⣿⣽⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠲⣶⠎⢶⠄⠰⠶⠶⠶⠀⣤⣤⣤⣤⣀⢀⠀⠙⠙⠋⢉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡤⣶⣶⣾⣤⣷⣶⣤⣻⣶⣾⣭⣭⣶⣴⣾⣿⣿⣷⣿⣶⡶⡶⣾⣿⣖⣟⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⣀⠀⠀⠀⠄⣀⢡⡄⠀⠀⠀⠀⠀⢀⣀⠀⠀⡠⣤⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢂⠿⣿⠟⡓⠈⠋⠋⠛⠙⠚⡛⠛⠟⣟⠿⠿⣟⣟⠿⠛⠋⡘⠻⠂⢈⣁⣠⣶⣿⣿⣿⣿⡿⣿⣏⣁⣴⣦⣶⣿⣯⣴⠀⣻⣶⣶⣥⠀⠲⣄⣢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣥⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀
⠏⠍⢚⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢨⣤⣵⣆⣠⣄⣢⣰⢆⣴⣤⣭⣿⣿⣿⣿⣿⣿⡟⠛⠒⢁⣀⢉⣿⣿⣿⣿⡷⣷⣿⡿⣿⣽⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⢀⣀⢀⣩⣤⣤⣤⣂⠀
⠀⢤⣵⡆⠀⠀⠀⠀⠀⠀⠀⣠⣽⣵⣿⣿⣻⣿⣿⣿⡦⣖⣾⣿⣿⣿⣿⣿⣿⣿⣁⣤⡄⢐⣲⣼⣿⣿⣿⣿⣽⡏⠟⢏⣻⣿⠿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⡿⡏⠉⢅⣬⢜⠿⠟⠛⠿⠉⠉⠯⠨
⠒⠉⠃⠂⠠⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣛⣿⣧⣠⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠫⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⣷⣶⠶⣿⣿⣿⣿⡷⣯⣿⣿⣿⠿⠿⣿⣿⣿⢽⣿⠯⠛⠹⡿⠶⠌⠁⠘⠓⠋⠀⠀⠆⠀⠈⠀⠐
⠠⠴⣦⡤⠀⠀⠀⢀⣴⣿⣿⣿⣿⣯⣿⣿⣿⣿⠿⣿⣿⣿⣿⣯⣽⣭⣥⣤⣤⣴⣶⠺⣯⢽⣿⣿⣿⣿⣿⣿⣿⣇⢠⣕⣂⣇⣼⣿⡟⣿⡗⢛⣛⣽⡦⡶⠷⢿⡌⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠈⠀⠂⠀⠈⡐⢀⣾⣿⣿⢿⣿⣭⣹⣿⣿⠛⠋⠸⣿⢿⣿⣿⢿⣿⣿⣿⡍⠋⢻⢳⠾⠛⢸⣿⣿⣿⣿⣿⣿⣿⢯⢿⢿⢿⣻⣿⡿⣋⢉⣣⠐⣕⡏⣄⠌⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠀⡀⠀⠀⠀⢺⣴⠿⠉⠰⠈⠩⠃⠀⢅⠀⠁⠄⠉⠉⠙⣛⢯⠘⠛⠏⠉⠁⠀⠀⠀⠁⠀⠀⠿⠿⣿⣿⣿⢿⡏⡜⢚⣒⣷⣼⡷⠖⢯⣼⡛⠃⠸⠁⠀⠁⡀⡰⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣷⣶⣶⣤⣴⣿⣭⣾⣷⣤⣲⣔⠉⠠⠲⠤⢠⠀⠀⢐⣄⠀⠀⠀⠀⠀⠀⠄⣄⣀⡀⠁⠒⠪⣦⣭⣿⣿⡿⠑⢧⢀⠄⠘⠻⣏⡥⣸⠔⠁⠐⠀⠀⠀⠀⠠⣷⣾⣽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣶⣴⣷⣶⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣴⡈⢀⣤⣄⣴⣾⣼⣿⣾⣯⣿⡛⣻⠽⠛⡷⢘⠻⡾⡄⡠⣒⡿⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⣯⣿⡄⠂⠈⠠⠉⢐⠄⠄⢠⢶⣷⣿⣿⣿⣿⣿⡿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣬⢺⢿⣡⣴⣾⣿⣷⣾⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣙⣭⣿⣿⡵⠄⠀⠠⣶⣒⣺⣾⣾⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡟⢫⡝⣿⣼⢿⣾⡞⠁⠀⠀⠀⠀⠀⠀⠰⣲⠈⡨⣹⣿⣿⣿⣿⠛⣥⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠛⠛⠙⣿⣷⡇⠀⣰⢀⢀⡀⢑⢀⠀⠸⠂⣋⣛⣭⡽⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⡿⠯⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄⠀⠀⢲⣿⣧⣒⣦⣶⣗⣞⣹⣳⣶⡾⠿⠉⣿⣿⣿⠻⠿⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣃⣤⣤⣭⡻⣿⣿⣿⣶⣶⣾⣶⣶⣶⣄⣄⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⣛⠉⠛⠉⠙⠛⠋⠉⠛⠛⠁⠈⠀⠀⠈⠙⠋⠉⠉⠉⠈⠓⡓⠀⣰⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢀⣠⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠀⠀⠀⠀⠀⠀⠄⠀⠐⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣻⣿⣿⣿⣯⢃⣀⡹⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣿⣶⣦⣤⣤⣾⣿⣿⣿⣿⣇⣀⣴⣶⣶⣶⡶⣤⡤⢴⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠀⠀⠉⢿⣿⣿⣿⠟⠒⠀⠘⠛⠛⠛⠛⢻⣷⠀⣿⣿⣿⣿⣿⣶⣽⣿⣿⣿⠯⣊⣤⣴⣭⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠏⠻⠀⠀⠀⠈⣿⢿⣿⡀⠀⠀⠀⠀⠉⠀⠉⢹⠟⠀⣿⣿⣿⣿⣿⣿⡿⠻⠿⣿⣩⣭⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣼⣿⠃⠀⠀⠀⠀⠀⠀⢿⣮⣿⣿⡀⠋⢛⣯⣶⣼⣿⣿⣿⣿⣟⣿
⠀⠀⠀⠀⠀⠀⢀⠄⢀⣀⡀⠀⣀⣐⢒⣴⣺⣷⣢⣦⡄⡄⡈⠙⠀⠠⠠⣾⣦⣠⣤⣴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⠂⠀⠀⠀⠀⠻⣿⣿⠿⢿⣿⣿⣛⣿⣿⣿⣷⣾⣿⡷
⠀⠀⡀⠀⡂⠬⣹⡯⣽⣴⣦⣟⣾⣿⣿⣧⣿⣾⠻⣿⣿⣟⡁⣄⠀⢀⣸⡟⠈⠈⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡥⣠⣤⣤⣤⣼⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠀⠀⠂⠠⣉⠹⢍⣺⣿⠺⣿⣿⡟⣫⡽⠜⠁⠛⠛⠻⠟⠉⠃⢼⡿⠷⠶⠶⡶⡶⠶⠶⢶⣶⣶⣶⣶⣤⠶⢶⣶⣶⣶⡶⠶⠿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⠆⣀⠲⠿⠋⠀⢠⢖⠊⠛⠀⣿⣿⡆⣿⣿⡇⣸⣿⡟⣿⣿⣿⣿⢸⣿⣿⣿⣷⣎⣿⣿⣳⣿⡿⣿⣿⡛⣷⣿⢿⣿⣮⢹⣿⣿⢿⣿⡞⢫⣿⡿⣿⣷⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠴⠀⠈⠀⠀⠀⠐⠀⠀⣈⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣂⢸⣿⣿⣸⣿⡿⣴⣷⣛⣛⢣⣿⣿⢣⣿⣿⢸⣿⣿⢘⣟⣿⣼⣿⠏⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⣿⣿⣿⢿⣿⣿⣿⠃⣿⣿⡿⢿⢸⣿⣿⢻⣿⣷⢩⣿⣿⣡⣿⣿⠯⣾⣿⣿⢸⣿⣿⢸⣯⣿⢻⣿⣧⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣧⣭⢸⣿⣿⣼⣿⣿⣸⡿⢳⣿⣿⣥⣴⠈⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⡿⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣛⡛⣤⣟⣻⣋⣤⣿⣿⣿⣿⣼⣿⣻⣿⣿⣵⣿⣟⣛⣿⣿⣟⣻⢾⣮⣿⣟⣿⣵⣶⣽⣿⣛⣿⣿⣿⣽⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠲⣶⠎⢶⠆⠰⠶⠶⠶⠀⣤⣤⣤⣤⣀⠀⠀⠙⡙⡛⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡤⣶⣶⣾⣴⣷⣶⣤⣻⣶⣾⣭⣭⣶⣴⣾⣿⣿⣷⣿⣶⡶⣷⣾⣿⣶⣟⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡿⠛⠁⣀⠀⠀⠀⠄⣀⢡⡄⠀⠀⠀⠀⠀⢀⣀⠀⠀⡠⣤⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢂⠿⣿⠟⡛⠈⠛⠋⠛⠙⢺⡛⠛⠿⣟⠿⠿⣿⡟⠟⠛⠋⡘⠻⠂⢈⣁⣤⣶⣿⣿⣿⣿⣿⣿⣟⣁⣴⣶⣶⣿⣯⣴⠀⣻⣶⣶⣥⠀⠲⣄⣢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣥⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀
⠏⠍⢚⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢨⣤⣥⣆⣤⣄⣢⣰⣎⣴⣤⣽⣿⣿⣿⣿⣿⣿⡏⠛⠒⢁⣀⢉⣿⣿⣿⣿⡷⣷⣿⡿⣿⣽⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⢀⣀⢀⣹⣆⣤⣤⣐⠀
⠀⢤⣵⡆⠀⠀⠀⠀⠀⠀⠀⣠⣽⣵⣿⣻⣻⣿⣿⣿⡦⣖⣾⣿⣿⣿⣿⣿⣿⣿⣁⣤⡄⢐⣒⣼⣿⣿⣿⣿⣿⡏⠟⣋⣻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⡿⡏⡉⢄⣬⢜⠻⠗⠛⠿⠉⠉⠯⠠
⠚⠉⠃⠀⠠⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣛⣿⣧⣬⣻⣿⣿⣿⣿⣿⡿⠛⠛⠛⠫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣶⠖⣿⣿⣿⣿⡷⣯⣿⣿⣿⠿⠿⣿⣿⣿⢽⣿⠯⠟⠹⡿⠶⠎⠁⠘⠓⠋⠀⠀⠆⠀⠈⠀⠐
⠀⠴⢶⡤⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣯⣽⣍⣥⣤⣤⣴⣶⠺⣯⢿⣿⣿⣿⣿⣿⣿⣿⣇⢠⣝⣂⣃⣺⣿⡟⣿⡗⣛⣛⣽⡦⣶⠷⢿⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠈⠀⠂⠀⠈⡐⢀⣾⣿⣿⢿⣿⣭⣹⣿⣿⠟⠋⠸⣿⢿⣿⣿⢿⣿⣿⣿⣍⠋⢻⢱⠾⠙⢸⣿⣿⣿⣿⣿⣿⣿⢯⢿⢿⢿⣻⣿⡯⣋⣙⣧⠐⣕⡏⣤⠜⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠀⡀⠀⠀⠀⣺⣴⠿⠉⠰⠈⠉⠃⠀⢁⠠⠀⠄⠉⠉⠛⣛⢯⠘⠛⠏⠉⠁⠀⠂⠀⠁⠀⠀⠿⠿⣿⣿⣿⢿⡏⡌⢛⡒⣵⣼⡿⠖⢯⣼⡻⠃⠨⠁⠀⠁⡀⡰⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣷⣶⣶⣤⣴⣿⣭⣾⣷⣤⣰⣜⠉⠴⠲⠤⣠⠀⠀⢐⣄⠀⠀⠀⠀⠀⠀⠄⣄⣀⡀⠁⠒⡪⣦⣭⣿⣿⡿⠑⢧⢀⠄⠚⢻⣿⡥⣸⠔⠁⠐⠀⠀⠀⠀⠠⣷⣾⣽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⣴⣽⣶⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣴⡊⣀⣤⣤⣴⣾⣼⣿⣾⣯⣿⡛⣻⠾⠛⡷⢘⠻⡾⡅⡠⣂⡿⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⣯⣯⡄⡂⠀⠀⠉⢀⠄⠄⢠⣾⣷⣿⣷⣿⣿⣿⡿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣬⢸⣿⢭⣼⣾⣿⣷⣾⣿⣿⣇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣙⣭⣿⣿⡱⠄⠈⠐⣶⣒⢺⣶⣾⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⠫⡝⣿⣼⢿⣿⡞⠁⠀⠀⠀⠀⠀⠀⠰⡲⠈⣨⣻⣿⣿⣿⡿⠛⣥⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠛⠛⠙⣿⣷⡇⠀⣰⢀⠠⠀⢀⣀⠀⠰⠂⣚⣋⣩⡽⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⡿⠯⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠈⠀⢲⣿⣧⣳⣦⣶⣗⣟⣹⣳⣶⡾⠿⠩⣿⣿⣿⢻⠿⠛⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⠿⣣⣠⣤⣍⡻⣿⣿⣷⣶⣶⣾⣾⣷⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⣛⠉⠛⠉⠙⠛⠋⠉⠛⠛⠁⠀⠀⠀⠈⠙⠋⠉⠉⠉⠈⠓⡓⠀⣰⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠈⣿⣿⣿⣿⣏⣇⡀⠻⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣶⣦⣤⣤⣿⣿⣿⣿⣿⣇⡀⣶⣶⣶⣶⡶⣤⣤⢴⡠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠀⠀⠉⢿⣿⣿⣿⠟⠛⠁⠛⠛⠛⠛⠛⢿⣷⠨⣿⣿⣿⣿⣿⣦⣽⣿⣿⣿⠯⣊⣤⣴⣭⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠯⠻⠀⠀⠀⠘⡿⢿⣿⡀⠀⠀⠀⠈⠉⠈⠉⢹⠏⢀⣿⣿⣿⣿⣿⣿⡿⠏⠿⣯⣩⣭⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣹⣽⡿⠁⠀⠀⠀⠀⠀⠀⢿⣮⣿⣿⣄⠋⢛⣯⣶⣼⣿⣿⣿⣿⣟⣿
⠀⠀⠀⠀⠀⠀⢀⢄⢀⡀⡄⠀⣄⣢⢚⣴⣲⣷⣢⣦⡄⡄⡈⠙⠀⢠⠠⣾⣦⣠⣤⣴⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⠂⠀⠀⠀⠀⠻⣿⣿⠿⢿⣿⣿⣛⣿⣿⣿⣷⣾⣿⡷
⠀⠀⡀⠀⡊⠤⣽⡯⣽⣷⣦⣟⣾⣿⣿⣧⣿⣾⡿⣿⣿⣟⡁⣄⠀⢀⣸⡟⠈⠈⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡥⣠⣤⣤⣤⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠀⠀⠀⠠⣉⠩⣉⣺⣯⠺⣿⣿⡟⣫⡿⠾⠃⠛⠛⠻⠟⠋⠁⢼⡿⠷⠦⠶⢶⡶⠶⠶⢶⣶⣶⣶⣶⣤⠶⢶⣶⣶⣶⡶⠶⢿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⠆⡄⠰⠿⠋⠀⢠⠆⢈⠛⠀⣿⣿⡄⣿⣿⡇⣸⣿⡟⣿⣿⣿⣿⢸⣿⣿⣿⣷⣎⣿⣿⣳⣿⡿⣿⣿⡛⣿⣿⢿⣿⣮⢹⣿⣿⢿⣿⡾⢫⣾⡿⣿⣷⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠴⠀⠈⠀⠀⠀⠀⠀⠀⢈⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣂⢸⣿⣿⣸⣿⡿⣴⣿⣛⣛⢣⣿⣿⢣⣿⣿⢸⣿⣿⢘⣿⣻⣼⣿⠏⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⣿⣿⢿⣿⣿⣿⠃⣿⣿⡿⢿⢸⣿⣿⢻⣿⣷⢩⣿⣿⣣⣿⣿⠯⣾⣿⣿⢸⣿⣿⢸⣯⣿⢻⣿⣧⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣧⣭⢸⣿⣿⣼⣿⣿⣸⡿⢷⣿⣿⣥⣤⠈⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⡿⢸⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣛⡋⣤⣿⣻⣋⣤⣿⣿⣿⣿⣼⣿⣻⣿⣿⣵⣿⣟⣛⣿⣿⣿⣻⢾⣮⣿⣟⣿⣵⣶⣽⣟⣻⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠲⣶⠎⢶⠆⠰⠶⠶⠶⠀⣤⣤⣤⣤⣀⢀⠀⠙⡛⡋⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠤⣶⣶⣶⣤⣷⣶⣤⣛⣶⣾⣭⣭⣶⣴⣾⣷⣿⣷⣿⣶⡶⢶⣾⣿⣖⣟⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⢀⠀⠀⠀⠄⣀⢡⡄⠀⠀⠀⠀⠀⢄⢀⠀⠀⠤⣤⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢂⠿⣿⠟⡓⠈⠛⠉⠛⠙⠺⡛⠛⠿⣟⠿⠿⣟⣟⠛⠛⠋⡘⠻⠂⢈⣁⣄⣶⣿⣿⣿⣿⣿⣿⣏⣁⣴⣦⣶⣿⣿⣴⠀⣻⣶⣶⣥⠀⠰⣎⣦⣿⣶⣿⣿⣿⣿⣿⣿⣿⣧⣗⣿⣧⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀
⠏⠍⢚⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢨⣤⣵⣆⣠⣄⣢⣰⣆⣴⣤⣭⣷⣿⣿⣿⣿⣿⡏⠛⠒⢁⣀⣉⣿⣿⣿⣿⡷⣷⣿⡽⣿⣽⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⢀⣀⢀⣹⣤⣤⣤⣒⠀
⠀⢤⣵⡆⠀⠀⠀⠀⠀⠀⠀⣤⣽⣵⣿⣿⣻⣿⣿⣿⡦⣆⣾⣿⣿⣿⣿⣿⣿⣿⣁⣤⡄⢐⣲⣼⣿⣿⣿⣿⣿⡏⠟⢋⣻⣿⠿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡿⡋⡉⢅⢬⣜⠫⠗⠻⠻⠉⠉⠯⠠
⠒⠉⠃⠀⠠⠀⠀⠀⠀⠀⣨⣿⣷⣿⣿⣿⣿⣛⣿⣧⣨⣻⣾⣿⣿⣿⣿⡿⠛⠛⠛⠫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⣷⣶⠖⣿⣿⣿⣿⡷⣯⣿⣿⣿⠿⠿⣿⣿⣿⢽⣿⠮⠛⠹⡷⠦⠌⠁⠘⠓⠋⠀⠀⠆⠀⠀⠀⠐
⠠⠴⣦⡤⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⣽⣍⣥⣤⣤⣴⣶⠺⣿⢽⣿⣿⣿⣿⣿⣿⣿⣇⢠⣕⣂⣃⣸⣿⡟⣿⡗⣛⣛⣽⡦⡖⠶⢻⡍⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠈⠀⠂⠀⠈⡐⢀⣾⣿⣿⢿⣿⣭⣹⣿⣿⡛⠋⠸⣿⢿⣿⣿⢿⣿⣿⣯⣍⠋⢻⢳⠾⠚⢹⣿⣿⣿⣿⣿⣿⣿⠯⢿⢿⢿⣻⣿⡯⡋⠙⣧⠀⣕⣯⣄⠌⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠀⡀⠀⠀⠀⣺⣴⠿⠉⠱⠨⠩⠃⠀⢅⠀⠁⠀⠉⠉⠙⣛⢯⠘⠛⠯⠉⠁⠀⠂⠀⠁⠀⠀⠻⠿⣿⣿⣿⢿⡏⡄⢚⡒⣰⣴⡟⠖⣯⣼⡛⡃⠨⠁⠀⠁⠀⡰⡼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣶⣶⣤⣴⣿⣭⣾⣷⣦⣲⣔⠉⠤⢲⠤⣠⠀⠀⢐⢄⠀⠀⠀⠀⠀⠀⠄⣄⣀⡀⡀⠒⠪⣦⣭⣿⣿⡿⠙⢧⢀⠄⠘⢻⣏⡥⣼⠔⠁⠐⠀⠀⠀⠀⠠⣷⣿⣽⠆⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠠⣦⣶⣴⣶⣶⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣴⡊⣀⣤⣤⣴⣾⣼⣿⣾⣯⣿⡃⣻⠼⠛⠷⢘⠻⡾⠅⡠⣂⡿⠆⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⣯⣯⡄⠆⠀⠨⠉⢀⠄⠄⢠⢾⣵⣿⣿⣿⣿⣿⡿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣬⣺⣿⢥⣶⣾⣿⣷⣾⣿⣿⣇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣙⣭⣿⣿⡥⠄⠀⠐⣖⣒⢺⣶⣾⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢫⠝⣿⣾⢿⣾⡞⠁⠀⠀⠀⠀⠀⠀⠰⣳⠊⡈⣫⣿⣿⣿⣿⠉⣥⣿⣻⣶⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠙⠛⠑⣿⣷⡇⠀⣰⢀⠀⠀⢐⢀⠀⠨⠂⣋⣛⣩⡽⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⡿⠯⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄⠈⠈⢺⣿⣧⢳⣦⣶⣗⣟⣹⣳⣶⡶⠿⠩⣿⣿⡿⢻⠿⠙⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⠿⣣⣤⣤⣝⡻⣿⣿⣿⣶⣶⣾⣾⣷⣶⣠⣀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⣛⠉⠛⠉⠙⠛⠋⠙⠛⠛⠁⠈⠀⠀⠈⠙⠋⠉⠉⠉⠈⠓⡓⢀⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⣀⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⡉⠙⠉⠀⠀⠀⠀⠀⠀⠄⠀⠐⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⢘⣿⣿⣿⣿⣏⣄⠀⢿⣿⣿⣿⣿⣿⣿⠛⠛⣿⣿⣿⣶⣶⣤⡤⣿⣿⣿⣿⣿⣃⡀⣶⣶⣶⣶⡦⣤⣤⢤⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⠀⠀⠘⢿⣿⣿⣿⠛⠋⠉⠛⠛⠛⠛⠏⢿⡇⢸⣿⣿⣿⣿⣿⣶⣽⣿⣿⣿⡧⣪⣤⣼⣭⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠐⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠛⠨⠻⠀⠀⠀⠸⠟⢿⣿⣀⡀⠀⠀⠀⠉⠈⠉⠸⡇⢸⣿⣿⣿⣿⣿⣿⡿⠋⠟⣿⣩⣭⠽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣻⣻⡿⠁⠀⠀⠀⠀⠀⠀⢿⣾⣿⣟⡌⠫⢛⣯⣶⣼⣿⣿⣿⣿⣟⣿
⠀⠀⠀⠀⠀⠀⢐⢄⢀⡀⡄⠀⣀⣢⢲⣴⣲⣷⣢⣤⣄⡄⡈⠙⠀⢠⠠⣾⣦⣠⣤⣔⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⠂⠀⠀⠀⠀⠙⣿⣿⠿⢿⣿⣿⣛⣿⣿⣿⣷⣿⣿⡷
⠀⠀⡀⠀⡢⠤⣹⡿⣽⣶⣦⣿⣿⣿⣿⣧⣿⣾⡻⣿⣿⣟⡁⣄⠀⢀⣸⡟⠉⠈⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡥⣠⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠀⠀⠂⠠⣉⠽⢉⣻⣿⢻⣿⣿⡿⣻⡿⠜⠃⠛⠛⠻⠟⠉⠃⢼⡿⠷⠴⠶⡶⠶⠶⠶⢶⣶⣶⣶⣶⣤⠶⢶⣶⣶⣶⡶⠶⠿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⠆⣁⠰⠿⠋⠀⢠⢄⢊⠛⠀⣿⣿⡆⣿⣿⡇⣸⣿⡟⣿⣿⣿⣿⢸⣿⣿⣿⣷⣎⣿⣿⣳⣿⡿⣿⣿⡛⣷⣿⢿⣿⣮⢹⣿⣿⢿⣿⡞⢯⣿⡿⣿⣷⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⢈⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣢⢸⣿⣿⣸⣿⡿⣴⣿⣙⣛⢣⣿⣿⢳⣿⣿⢸⣿⣿⢘⣟⣻⣼⣿⠏⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⣿⣿⣿⢿⣿⣿⣿⠃⣿⣿⡿⢿⢸⣿⣿⢻⣿⣶⢩⣿⣿⣣⣿⣿⠯⣾⣿⣿⢸⣿⣿⢸⣯⣿⢻⣿⣧⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣧⣭⢸⣿⣿⣼⣿⣿⣸⡿⢳⣿⣿⣥⣴⠌⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⡿⢸⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣛⡛⣤⣿⣻⣋⣤⣿⣿⣿⣿⣼⣿⣻⣿⣿⣵⣿⣟⣛⣿⣿⣟⣻⢾⣮⣿⣟⣿⣷⣶⣽⣿⣛⣿⣿⣿⣽⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠲⣶⠯⢶⠆⠰⠶⠶⠶⠀⣤⣤⣤⣤⣀⠀⠀⢙⡛⡛⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠤⣶⣶⣞⣤⢷⣶⣤⣳⣶⣾⣭⣭⣶⣴⣾⣷⣿⣷⣿⣶⡶⢶⣾⣿⣖⣟⣿⣿⣾⣿⣶⣿⣿⣿⣿⣿⡿⠛⠁⢀⠀⠀⠀⠄⢀⢡⠄⠀⠀⠀⠀⠀⢀⢀⠀⠀⡄⢤⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢂⠻⣿⠟⡓⠈⠛⠉⠛⠙⠚⡛⠛⠿⣟⠿⠿⣟⣟⠟⠛⠋⡘⠻⠂⢈⣁⣤⣶⣿⣿⣿⣿⣿⣿⣟⣁⣴⣶⣶⣿⣿⣔⠀⣫⣶⣶⣤⠀⠰⣌⣦⣾⣶⣿⣿⣿⣿⣿⣿⣿⣧⣇⣾⣅⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀
⠏⠍⢚⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢨⣤⣡⣆⣤⣀⣢⣰⡆⣔⣤⣭⣽⣾⣿⣿⣿⣿⡏⠛⠐⢃⣀⢉⣿⣿⣿⣿⡷⣷⣿⡿⣿⣽⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⢀⣀⢀⢩⣤⣤⣤⣒⠀
⠀⢤⣵⡆⠀⠀⠀⠀⠀⠀⠀⣠⣽⣴⣿⣿⣻⣿⣿⣿⡦⣂⣶⣿⣿⣿⣿⣿⣿⣿⣁⣤⡄⢐⣲⣼⣿⣿⣿⣿⣿⡏⠛⢋⣻⣿⠿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡟⡿⡋⠉⢅⢤⢜⠻⠗⠻⠻⠉⠉⠯⠠
⠚⠋⠃⠂⠠⠀⠀⠀⠀⠀⣨⣿⣷⣿⣿⣿⣿⣛⣿⣧⣨⣹⣿⣿⣿⣿⣿⡿⠛⠛⠛⠫⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⣷⣶⠖⡿⢟⣿⣿⡷⣯⣿⣿⣿⠿⠿⣿⣿⣿⢽⣻⠮⠫⠹⡷⠦⠈⠁⠘⠓⠋⠀⠀⠂⠀⠀⠀⠒
⠀⠴⣦⡤⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣯⣽⣍⣤⣤⣤⣴⣶⠺⣯⢽⣿⣿⣿⣿⣿⣿⣿⣇⢠⣕⣃⣇⣸⣿⡟⣿⡗⣛⣛⣽⡦⡶⠷⢻⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠈⠀⠃⠀⠈⡐⢀⣾⣿⣿⢯⣽⣭⣹⣿⣿⠛⠋⠸⣿⢿⣿⣿⢿⣿⣿⣯⣍⡋⢻⢻⠾⠚⢸⣽⣿⣿⣿⣿⣿⣿⠯⢿⢿⢿⣛⣿⡯⠋⢙⡇⠔⣕⡯⣄⠌⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠀⡀⠀⠀⠀⢺⣴⠿⠉⠲⠈⠩⠃⠀⢅⠀⠁⠀⠉⠉⠛⣛⢯⠘⠛⠏⠉⠁⠀⠊⠀⠀⠀⠀⠻⠿⣿⣿⣿⢿⡏⡄⢘⡒⣱⢼⡞⠒⢯⢼⡛⠃⠐⠁⠀⠀⡀⡰⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣷⣶⣶⣤⣴⣿⣭⣾⣷⣦⣲⣔⠁⠤⠲⠤⢠⠀⠀⢐⢄⠀⠀⠀⠀⡀⠀⠄⣄⣀⡀⠀⠒⠪⣤⣭⣿⣿⡿⠑⢧⢀⠄⠘⢻⣻⡥⣼⠔⠅⠐⠀⠀⠀⠀⠠⣷⣾⣽⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⣶⣴⣷⣶⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣴⡈⢀⣤⣄⣴⣾⣼⣿⣾⣯⢿⡛⡳⠿⠛⡷⢘⠻⡾⠁⡠⣂⡿⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⣯⣯⠄⠀⠀⠠⠉⢀⠄⠄⢠⢶⣴⣿⣿⣿⣿⣿⡿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣏⣬⢸⣿⢥⣴⣾⣷⣷⣾⣿⣿⣇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣙⣭⣿⣿⡥⠄⠀⠐⣶⢒⢺⣶⣾⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⢫⠝⣿⣾⢿⣾⡞⠁⠀⠀⠀⠀⠀⠀⠰⣲⠊⣈⣩⣿⣿⣿⡿⠊⣥⣿⣿⣾⣾⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠛⠛⠙⢿⣷⡅⠀⣰⢀⠀⠀⢀⢀⠀⠨⠂⡊⣛⣩⡽⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⡿⠯⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠈⢾⣿⢧⣺⣦⣶⣗⣎⣹⣳⣶⡾⠿⠉⣿⢿⡿⠻⠿⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⣣⣠⣬⣝⡻⣿⣿⣷⣶⣶⣿⣾⣷⣶⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⣛⠉⠛⠉⠙⠛⠛⠉⠛⠛⠁⠀⠀⠀⠈⠙⠋⠉⠉⠉⠈⠓⡓⢀⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⣀⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⢘⣿⣿⣿⣿⣏⣄⠀⢿⣿⣿⣿⣿⣿⣿⠟⠛⣿⣿⣿⣶⣶⣤⡴⣿⣿⣿⣿⣿⣁⡀⣶⣶⣶⣶⡦⣤⡤⣴⡠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⠀⠀⠸⢿⣿⣿⣿⠋⠋⠉⠛⠛⠛⠛⠏⢿⡇⢸⣿⣿⣿⣿⣿⡶⣽⣿⣿⢿⢷⣚⣤⣴⣭⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠐⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⠛⠍⠋⠀⠀⠀⠸⠟⢿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠸⡇⢸⣿⣿⣿⣿⣿⣿⡿⠟⠿⣟⣩⡭⠽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣛⣻⡿⠀⠀⠀⠀⠀⠀⠀⢿⣾⣿⣟⡌⠂⢛⣯⣶⣼⣿⣿⣿⣿⣟⣿
⠀⠀⠀⠀⠀⠀⢀⢀⢀⣀⡄⠀⣀⢒⢲⣰⣲⣷⣠⣦⡄⡆⡈⠉⠀⢀⠠⣼⣆⣠⣤⣴⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠚⠂⠀⠀⠀⠀⠙⣿⣿⠿⠿⣿⣿⣛⣿⣿⣿⣷⣾⣿⡷
⠀⠀⡀⠀⡂⠤⡹⡯⣵⣴⣦⣟⣿⡟⣿⣧⣿⣾⡻⣿⣿⣟⡁⣄⠀⠀⣸⡟⠈⠈⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡥⣠⣤⣤⣤⣼⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠀⠀⠀⠀⣉⠽⢁⣺⣿⠺⣟⣿⡟⣻⡿⠜⠃⠛⠛⠫⠟⠉⠁⠼⡿⠷⠴⠲⢶⡶⠶⠶⢶⣶⣶⣶⣶⣤⠶⢶⣶⣶⣶⡶⠶⠿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⠄⡄⢰⠿⠋⠀⢠⢆⢃⠛⠀⣿⣿⡆⣿⣿⡇⣸⣿⡟⣿⣿⣿⣿⢸⣿⣿⣿⣷⣎⣿⣿⣳⣿⡿⣿⣿⡛⣷⣿⢿⣿⣮⢹⣿⣿⢿⣿⡞⢯⣿⡿⣿⣷⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠰⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣀⢸⣿⣿⣸⣿⡿⣴⣿⣛⣛⢣⣿⣿⢣⣿⣿⢸⣿⣿⢘⣿⣿⣼⣿⠏⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⣿⣿⢿⣿⣿⣿⠃⣿⣿⡿⢿⢸⣿⣿⢻⣿⣶⢩⣿⣿⣡⣿⣿⠯⣾⣿⣿⢸⣿⣿⢸⣯⣿⢻⣿⣧⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣧⣭⢸⣿⣿⣼⣿⣿⣸⡿⢳⣿⣿⣥⣤⠌⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⡿⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣛⡛⣤⣟⣻⣫⣤⣿⣿⣿⣿⣼⣿⣻⣿⣿⣵⣿⣟⣛⣿⣿⣿⣻⣾⣮⣿⣟⣿⣵⣶⣽⣟⣛⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠲⣶⠮⢶⠆⠰⠶⠶⠶⠀⣤⣤⣤⣤⣀⠀⠀⠙⠙⡋⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡤⣶⣶⣾⣴⣷⣶⣤⣻⣶⣾⣭⣭⣶⣴⣾⣷⣿⣷⣿⣶⡶⣷⣾⣿⣶⣟⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡿⠛⠁⢀⠀⠀⠀⠄⣀⢡⡄⠀⠀⠀⠀⠀⢄⢀⠀⠀⠤⣤⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢂⠿⣿⠟⡓⠈⠛⠛⠛⠙⠚⡛⠛⠿⣟⠿⠿⣿⡟⠟⡛⠋⡘⠻⠂⢈⣁⣤⣶⣿⣿⣿⣿⣿⣿⣟⣁⣴⣶⣶⣿⣿⣴⢂⣻⣶⣶⣥⠀⠰⣎⣦⣾⣶⣿⣿⣿⣿⣿⣿⣷⣧⣷⢿⣧⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀
⠏⠍⢚⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢨⣤⣱⣆⣠⣄⣢⣰⢄⣔⣤⣭⣿⣿⣿⣿⣿⣿⡏⠛⠒⢃⣀⢉⣿⣿⣿⣿⡷⣷⣿⡿⣿⣽⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⢀⣀⢀⣹⣤⣤⣤⣒⠀
⠀⢤⣵⡆⠀⠀⠀⠀⠀⠀⠀⣠⣽⣵⣿⣿⣻⣿⣿⣿⡦⣖⣾⣿⣿⣿⣿⣿⣿⣿⣁⣤⡄⢐⣲⣼⣿⣿⣿⣿⣿⡏⠟⢋⣛⣿⡿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡟⡿⡋⡉⢄⢤⣜⠻⠗⠛⠿⠉⠉⠯⠠
⠚⠉⠃⠀⠠⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣟⣿⣧⣨⣻⣿⣿⣿⣿⣿⡿⠛⠛⠛⠫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣷⣶⠖⣿⣟⣿⣿⡷⣯⣿⣿⣿⠿⠿⣟⣿⣿⢽⣻⠯⠻⠹⡿⠦⠎⠁⠘⠓⠋⠀⠀⠆⠀⠀⠀⠐
⠠⠴⣶⡤⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣯⣽⣭⣤⣤⣤⣴⣶⠺⣯⢽⣿⣿⣿⣿⣿⣿⣿⣇⢠⣕⣂⣃⣺⣿⡟⣿⡗⣛⣛⣽⡦⡶⠷⢻⡏⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠈⠀⠂⠀⠈⡐⢀⣾⣿⣿⣿⣿⣭⣹⣿⣿⠛⠋⠸⣿⢿⣿⣿⢿⣿⣿⣿⣍⠉⢻⢳⠾⠙⢹⣿⣿⣿⣿⣿⣿⣿⠯⢿⢿⢟⣻⣿⡯⣋⢉⣧⠀⣕⡯⣄⠌⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠀⡀⠀⠀⠀⣺⣴⠿⠉⠰⠈⠩⠃⠀⢅⠠⠁⠀⠉⠉⠛⣛⢯⠘⠛⠏⠉⠁⠀⠈⠀⠁⠀⠀⠻⠿⣿⣿⣿⢿⠏⡌⢚⡒⣵⣽⡟⠖⢯⣼⡻⠂⠈⠁⠀⠀⠀⡰⣬⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣶⣶⣤⣴⣿⣭⣾⣷⣦⣲⣔⠉⠤⠲⠤⣠⠀⠀⢐⣄⠀⠀⠀⠀⠀⠀⠄⣄⣀⡀⡀⠒⠪⣦⣭⣿⣿⡿⠑⣧⢀⠄⠘⢻⣏⡥⣬⠔⠍⠐⠀⠀⠀⠀⠠⣷⣾⣽⠆⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⣤⣶⣶⣷⣶⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣴⡊⢀⣤⣄⣴⣾⣽⣿⣾⣯⣿⡛⣻⠿⠛⡷⢘⠻⡾⡅⠠⣀⡿⠀⠁⠀⠀⠀⠀⠀⠀⠀⣐⣿⣯⣯⠄⠀⠀⠀⠉⢀⠄⠄⢤⢾⣱⣿⣷⣿⣿⣿⡿⣿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣭⣸⣿⢥⣼⣾⣿⣿⣾⣿⣿⣇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣙⣭⣿⣿⡤⠄⠀⠐⣶⣒⢺⣾⣾⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢫⠝⣿⣾⢿⣾⡾⠁⠀⠀⠀⠀⠀⠀⠐⣲⠊⣌⣫⣿⣿⣿⡿⠉⣥⣿⣿⣾⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠛⠛⠙⣻⣷⡇⠀⣠⢀⢠⡀⢑⢀⠀⠸⠂⡊⣛⣩⡽⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⡿⠯⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄⠈⠈⢺⣿⣷⣺⣦⡶⣗⣏⣫⣳⣶⡾⠿⢉⣿⢿⡯⢻⠿⠙⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣣⣤⣬⣝⡻⣿⣿⣷⣶⣶⣾⣾⣷⣶⣠⣀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⣛⠋⠛⠉⠙⠛⠋⠉⠛⠛⠁⠈⠀⠀⠈⠙⠋⠉⠉⠉⠈⠓⡓⢀⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⣀⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⢘⣿⣿⣿⣿⣏⣄⠠⢿⣿⣿⣿⣿⣿⣿⠛⠛⣿⣿⣿⣶⡶⣤⡴⣿⣿⣿⣿⣿⣁⣀⣰⣶⣶⣶⡶⣤⡤⣤⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⠀⠀⠸⢿⣿⣿⣿⠋⠋⠉⠛⠛⠛⠛⠏⢿⡇⢸⣿⣿⣿⣿⣿⣶⣽⣿⣿⢿⠧⣪⣤⣴⣭⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠐⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⠛⠞⠋⠀⠀⠀⠸⠟⢿⣿⣂⡀⠀⠀⠀⠀⠀⠀⠸⠇⢸⣿⣿⣿⣿⣿⣿⡿⢋⠿⣻⣩⣭⠽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣟⣻⠿⠀⠀⠀⠀⠀⠀⠈⢿⣾⣿⣷⡬⠋⢛⣯⣶⣼⣿⣿⣿⣿⣟⣿
⠀⠀⠀⠀⠀⠀⢀⢀⢀⣀⡀⠀⣀⣐⢲⣴⣲⣷⣠⣦⣄⡄⡈⠙⠀⢠⠠⣾⣆⣠⣤⣴⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠚⠂⠀⠀⠀⠀⠙⣿⣿⠿⢿⣿⣿⣛⣿⣿⣿⣷⣿⣿⡷
⠀⠀⡀⠀⡂⠬⣽⡯⣵⣴⣦⣿⣾⣟⣿⣧⣿⣾⡿⣿⣿⣟⡁⣄⠀⢀⣸⡟⠈⠈⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡥⣠⣤⣤⣤⣾⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠀⠀⠂⠠⣉⠽⣍⣺⣿⠺⣿⣿⡟⣻⡿⠞⠃⠛⠛⠻⠟⠉⠁⢼⡿⠷⠴⠲⠶⡶⠶⠶⢶⣶⣶⣶⣶⣤⠶⢶⣶⣶⣶⡶⠶⠿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⠀⠀⠀⠀⠐⠆⡄⢰⠿⠋⠀⢠⢄⢊⠛⠀⣿⣿⡆⣿⣿⡇⣸⣿⡟⣿⣿⣿⣿⢸⣿⣿⣿⣷⣎⣿⣿⣳⣿⡿⣿⣿⡛⣷⣿⢿⣿⣮⢻⣿⣿⢿⣿⡞⢯⣿⡿⣿⣷⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⠰⠀⠈⠀⠀⠀⠀⠀⠀⣈⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣂⢸⣿⣿⣸⣿⡿⣴⣿⣛⣛⢣⣿⣿⢣⣿⣿⢸⣿⣿⢘⣿⣿⣼⣿⠏⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⣿⣿⢿⣿⣿⣿⠃⣿⣿⡿⢿⢸⣿⣿⢻⣿⣷⢩⣿⣿⣡⣿⣿⠯⣾⣿⣿⢸⣿⣿⢸⣯⣿⢻⣿⣧⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣧⣭⢸⣿⣿⣼⣿⣿⣸⡿⢲⣿⣿⣥⣤⠌⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⡿⢸⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠛⣛⡋⣤⣿⣻⣋⣤⣿⣿⣿⣿⣼⣿⣻⣿⣿⣽⣿⣟⣛⣿⣿⣿⣻⣾⣮⣿⣟⣿⣷⣶⣽⣿⣛⣿⣿⣿⣽⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠲⣶⠏⢶⠆⠰⠶⠶⠶⠀⣤⣤⣤⣤⣀⠀⠀⠙⠛⡋⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠤⣶⣶⣶⣤⢷⣶⣤⣻⣶⣾⣭⣭⣶⣴⣾⣷⣿⣷⣿⣶⡶⠶⣾⣿⣶⣟⣿⣿⣾⣿⣶⣿⣿⣿⣿⣿⡿⠛⠁⢀⠀⠀⠀⠄⢀⢡⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠠⡠⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢂⠿⣿⠟⡓⠈⠛⠉⠛⠙⠚⡛⠛⠿⣟⠿⠿⣟⡟⠟⠛⠋⡘⠻⠂⢈⣁⣤⣶⣿⣿⣿⣿⣿⣿⣟⣁⣴⣶⣶⣿⣿⣴⠂⣻⣶⣖⣤⠀⠰⣌⣦⣾⣶⣿⣿⣿⣿⣿⣿⣷⣧⣷⢿⣅⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀
⠏⠍⢚⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢨⣤⣱⣆⣠⣄⣢⣰⠄⣔⣤⣬⣿⣿⣿⣿⣿⣿⡏⠛⠒⢃⣀⢉⣿⣿⣿⣿⡷⣷⣿⡿⣿⣽⣿⣟⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⢀⣀⢀⣹⣤⣤⣤⣒⠀
⠀⢤⣵⡆⠀⠀⠀⠀⠀⠀⠀⣠⣽⣵⣿⣿⣻⣿⣿⣿⡦⣖⣾⣿⣿⣿⣿⣿⣿⣿⣁⣤⡄⢐⣲⣼⣿⣿⣿⣿⣿⡏⠟⢋⣛⣿⠿⣿⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡟⡿⡋⠉⢄⢤⣜⠻⠗⠛⠻⠉⠉⠯⠠
⠚⠉⠃⠀⠠⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣟⣿⣧⣨⣹⣿⣿⣿⣿⣿⡿⠛⠛⠛⠫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⣶⣶⠖⡿⢟⣿⣿⡷⣯⣿⣿⣿⠿⠿⣟⣿⣿⢹⣻⠯⠻⠹⡿⠦⠊⠁⠘⠓⠋⠀⠀⠂⠀⠀⠀⠐
⠀⠴⣶⡤⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⣽⣍⣤⣤⣤⣴⣶⠺⣯⢿⣿⣿⣿⣿⣿⣿⣿⣇⢠⣕⣂⣃⣸⣿⡟⣿⡗⣛⣛⣽⡢⡶⠷⢻⡅⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠈⠀⠂⠀⠈⡐⢀⣾⣿⣿⢿⣿⣭⣹⣿⣿⠛⠋⠸⣿⢿⣿⣿⢿⣿⣿⣿⣍⠉⢻⢳⠾⠙⢸⣽⣿⣿⣿⣿⣿⣿⠯⢿⢿⢿⣛⣿⡭⡋⢉⡧⠄⣕⡏⡄⠈⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠀⡀⠀⠀⠀⢺⣴⠿⠉⠰⠈⠉⠁⠀⢁⠀⠁⠀⠉⠉⠙⣛⢯⠘⠛⠏⠉⠁⠀⠊⠀⠀⠀⠀⠿⠿⣿⣿⣿⢿⡏⡄⢚⡒⣱⢿⡟⠖⣯⢴⣛⠃⠐⠀⠀⠀⠀⡰⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣷⣶⣶⣤⣴⣿⣭⣾⣷⣤⣰⣔⠉⠤⠲⠤⢠⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠄⣄⣀⡀⠀⠒⠪⣦⣭⣿⣿⡿⠑⢧⢀⠄⠘⢹⣿⡥⣬⠔⠅⠀⠀⠀⠀⠀⠠⣷⣾⣩⠂⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⣦⣶⣶⣵⣶⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣴⡈⢀⣤⣄⣤⣾⣼⣿⣾⣯⢿⡛⣳⠾⠛⡷⢘⠻⡾⡅⡠⣐⡟⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣮⡄⠀⠀⠠⠉⢀⠀⠄⢠⢶⣵⣿⣿⣿⣿⣿⡿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⡬⢸⢿⢥⣼⣾⣿⣷⣾⣷⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣙⣭⣿⣷⡠⠤⠀⠐⣖⣲⠺⣶⣾⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⠫⠝⣿⣜⢿⣾⡞⠁⠀⠀⠀⠀⠀⠀⠰⣲⠊⣨⣩⣿⣿⣿⣿⠋⣥⣿⣻⣶⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠛⠛⠑⣽⣷⡇⠀⣠⢀⢠⠀⢀⢀⠀⠸⠂⣚⣛⣭⡽⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⡿⠯⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄⠈⠈⢸⣿⣧⣺⣆⡶⣗⣎⣫⣳⣶⡶⠿⢉⣿⢿⣟⠻⠿⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣣⣠⣬⣝⡻⣿⣿⣷⣶⣶⣶⣶⣶⣶⣠⣀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⣛⠉⠛⠉⠙⠛⠋⠉⠛⠛⠁⠈⠀⠀⠈⠙⠉⠉⠉⠉⠈⠓⡓⢀⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⣀⣤⣄⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⢘⣿⣿⣿⣿⣏⣄⠠⢿⣿⣿⣿⣿⣿⣿⠛⠛⣿⣿⣿⣶⡶⣤⡴⢿⣿⣿⣿⣿⣁⣀⢰⣶⣶⣶⡶⣤⣤⣤⡠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⠀⠈⠸⢻⣿⣿⣿⠋⠋⠉⠛⠛⠛⠛⠏⢿⡇⢸⣿⣿⣿⣿⢻⡦⣽⣿⣿⣿⠧⣺⣤⣴⣭⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠐⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⠛⠎⠋⠀⠀⠀⠸⠏⢿⣿⣂⡀⠀⠀⠀⠀⠀⠀⠸⡇⢸⣿⣿⣿⣿⣿⣿⡿⢛⠿⣫⣩⣭⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣟⣻⠿⠀⠀⠀⠀⠀⠀⠐⢿⣾⣿⣟⡌⠋⢛⣯⣶⣼⣿⣿⣿⣿⣟⣿
⠀⠀⠀⠀⠀⠀⢀⢀⢀⡄⡀⠀⣀⡀⢲⣔⣺⣷⣠⢦⡄⡄⡈⠙⠀⢀⠠⣾⣦⣠⣤⣔⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠚⠂⠀⠀⠀⠀⠙⣿⣿⠿⠿⣿⣿⣛⣿⣿⣿⣷⣿⣿⡷
⠀⠀⡀⠀⡂⠬⣹⡯⣵⣴⣦⣟⣾⣟⣽⣧⣿⣾⡿⣿⣿⣏⡁⣄⠀⠀⣸⡟⠉⠈⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡥⣠⣤⣤⣤⣼⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠀⠀⠂⠠⣉⠽⢍⣺⣿⠺⣿⣿⡟⣫⡿⠞⠃⠛⠛⠻⠟⠉⠁⢼⡿⠷⠤⠲⠶⡶⠶⠶⢶⣶⣶⣶⣶⣤⠶⢶⣶⣶⣶⡶⠾⠿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⠆⡄⠲⠿⠋⠀⠠⢆⠊⠛⠀⣿⣿⡆⣿⣿⡇⣸⣿⡟⣿⣿⣿⣿⢸⣿⣿⣿⣷⣎⣿⣿⣳⣿⡿⣿⣿⡛⣷⣿⢿⣿⣮⢹⣿⣿⢿⣿⡞⢯⣿⡿⣿⣷⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⣈⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣂⢸⣿⣿⣸⣿⡿⣴⣿⣙⣛⢣⣿⣿⢣⣿⣿⢸⣿⣿⢸⣟⣻⣼⣿⠏⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⣿⣿⢿⣿⣿⣿⠃⣿⣿⡿⢿⢸⣿⣿⢻⣿⣷⢩⣿⣿⣡⣿⣿⠯⣾⣿⣿⢸⣿⣿⢸⣯⣿⢻⣿⣧⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣧⣭⢸⣿⣿⣼⣿⣿⣸⡿⢷⣿⣿⣥⣤⠈⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⡿⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣛⡛⣤⣟⣻⣫⣤⣿⣿⣿⣿⣼⣿⣻⣿⣿⣵⣿⣟⣛⣿⣿⣿⣻⢾⣮⣿⣟⣿⣵⣶⣽⣿⣛⣿⣿⣿⣽⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠲⣶⠏⢶⠆⠰⠶⠶⠶⠀⣤⣤⣤⣤⡀⠀⠀⠉⡛⡋⢉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠤⣶⣶⣾⣤⣷⣶⣤⣻⣶⣾⣭⣭⣶⣴⣾⣷⣿⣷⣿⣶⡶⠶⣾⣿⣖⣟⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⠛⢁⢀⠀⠀⠀⠀⡀⢡⡄⠀⠀⠀⠀⠀⣀⣀⠀⠀⣠⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢂⠿⣿⠟⡃⠈⠛⠛⠛⠙⠚⡛⠛⠿⣟⠿⢿⣟⣟⠛⠛⠋⠘⠻⠂⢈⣁⣤⣶⣿⣿⣿⣿⣿⣿⢏⣁⣴⣶⣶⣿⣿⣴⢂⣿⣶⣶⣤⠀⠴⣎⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣇⣽⣶⡄⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀
⠏⠍⢚⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢨⣤⣵⣆⣤⣄⣢⣰⡄⣔⣤⣽⣿⣿⣿⣿⣿⣿⠏⠓⠒⢁⣀⢉⣿⣿⣿⣿⡷⣷⣿⡿⣿⣽⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⢀⣀⢀⣹⣤⣤⣤⣒⠀
⠀⢤⣵⡆⠀⠀⠀⠀⠀⠀⠀⣠⣽⣴⣿⣻⣻⣿⣿⣿⠦⣖⣾⣾⣿⣿⣿⣿⣿⣿⣁⣤⡄⢐⣲⣼⣿⣿⣿⣿⣿⡏⠛⣋⣻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⡋⡉⢅⢬⣜⠻⠏⠻⠻⠉⠉⠯⠨
⠚⠉⠃⠀⠠⠀⠀⠀⠀⠀⣨⣿⣷⣿⣿⣿⣿⣛⣿⣧⣬⣽⣿⣿⣿⣿⣿⡿⠛⠛⠛⠫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⣷⣶⠖⣿⣟⣿⣿⡷⣯⣿⣿⣿⠿⠿⣟⣿⣿⢹⣻⠌⠛⠹⡷⠦⠎⠁⠘⠓⠋⠀⠀⠆⠀⠀⠀⠒
⠀⠴⣶⡤⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣯⣽⣍⣤⣤⣤⣴⣶⢺⣯⢿⣿⣿⣿⣿⣿⣿⣿⣇⢠⣕⣂⣃⣸⣿⡟⣿⡗⢛⣛⣽⡦⡖⠷⢻⡄⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠈⠀⠂⠀⠈⡐⢄⣾⣿⡿⢿⣿⣯⣹⣿⣿⠛⠋⠸⣯⢿⣿⣿⢿⣿⣿⣿⡍⠋⢻⢳⠾⠘⢸⣽⣿⣿⣿⣿⣿⣿⢯⢿⢿⢟⣻⣿⡯⠋⢉⣣⠔⣕⡏⡄⠘⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠀⡀⠀⠀⠀⣺⣴⠿⠉⠱⠈⠉⠃⠀⢅⠠⠁⠀⠉⠉⠙⣛⢯⠘⠛⠏⠉⠁⠀⠂⠀⠁⠀⠀⠿⠿⣿⣿⣿⢿⠏⡄⢛⡒⣰⣾⡗⢞⣯⣼⡛⠃⠀⠀⠀⠀⠀⡰⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣷⣶⣶⣤⣴⣽⣭⣾⣷⣦⣲⣘⠉⠤⢲⠤⣠⠀⠀⢐⣄⠀⠀⠀⠀⠀⠀⠄⣄⣀⡀⡀⠒⠪⣦⣭⣿⣿⡿⠙⢧⢀⠄⠘⢻⣯⡥⣜⠔⠍⠐⠀⠀⠀⠀⠠⣷⣾⣭⠆⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⣦⣲⣴⣽⣶⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣴⡊⣀⣤⣤⣴⣾⣽⣿⣾⣯⣿⡋⣳⠾⠛⡷⢘⠻⡾⡄⡠⣒⡿⠄⠁⠀⠀⠀⠀⠀⠀⠀⣀⣿⣯⣯⠄⠂⠀⠀⠉⢀⠄⠄⢰⢶⣵⣿⣿⣿⣿⣿⡿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣋⡬⢸⣿⢥⣴⣾⣿⣷⣼⣷⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣙⣭⣿⣿⡠⠤⠔⠐⣖⣲⠺⣶⣾⣿⣿⣿⣿⠿⠟⠃⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⠫⠝⣿⣾⢿⣾⡞⠁⠀⠀⠀⠀⠀⠀⠰⣲⠊⣨⣫⣿⣿⣿⡯⠉⣥⣽⣿⣶⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠛⠛⠙⣻⣷⣇⠀⣠⢀⢐⡀⢀⢀⠀⠸⠂⡚⣛⣭⡽⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⡿⠯⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄⢀⠈⢲⣿⣧⣳⣦⡶⣗⣎⣫⣳⣶⡶⠿⠋⣻⢿⡿⠻⠿⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⣣⣤⣬⣝⡻⣿⣿⣿⣶⣶⣶⣶⣷⣶⣠⣀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⣛⠉⠛⠉⠙⠛⠋⠉⠛⠛⠁⠈⠀⠀⠈⠙⠋⠉⠉⠉⠈⠓⡓⢀⣰⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⣀⣠⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⢘⣿⣿⣿⣿⣏⣆⠀⢿⣿⣿⣿⣿⣿⣿⢛⡛⣻⣿⣿⣶⣶⣤⡤⣿⣿⣿⣿⣿⣃⣀⠲⣶⣶⣶⣶⣤⣤⣤⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠀⠀⠸⢿⣿⣿⣿⠋⠋⠉⠛⠛⠛⠛⠏⢿⡷⢸⣿⣿⣿⣿⣿⡦⣽⣿⣿⣿⡧⣺⣤⣴⣭⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠋⠋⠻⠾⠿⠀⠀⠀⠸⠟⢿⣿⣂⡀⠀⠀⠈⠉⠉⠁⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⢟⠿⣻⣩⣭⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣛⣻⡿⠁⠀⠀⠀⠀⠀⠀⢿⣾⣿⣷⡬⠛⢛⣯⣶⣼⣿⣿⣿⣿⣟⣿
⠀⠀⠀⠀⠀⠀⢐⢀⢀⣄⡀⠀⣀⣐⢒⣴⣺⣷⣢⣦⣄⡄⡈⠙⠀⢠⠀⣾⣦⣠⣤⣴⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠚⠂⠀⠀⠀⠀⠻⣿⣿⢿⠿⣿⣿⣛⣿⣿⣿⣷⣾⣿⡷
⠀⠀⡀⠀⡂⠤⣹⡿⣽⣶⣦⣿⣿⣟⣿⣧⣿⣾⡿⣿⣿⣟⡁⣄⠀⢀⣸⡟⠈⠉⠀⠀⠒⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡥⣠⣤⣤⣤⣼⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠀⠀⠂⠠⣉⠻⣉⣺⣿⠻⣿⣿⡟⣿⡿⠞⠃⠙⠛⠻⠟⠉⠃⠼⡿⠷⠶⠲⣶⡶⠶⠶⢶⣶⣶⣶⣶⣤⠶⢶⣶⣶⣶⡶⠶⠿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⠖⡄⢲⠿⠋⠀⢠⢄⠋⠛⠀⣿⣿⡆⣿⣿⡇⣸⣿⡟⣿⣿⣿⣿⢸⣿⣿⣿⣷⣎⣿⣿⣳⣿⡿⣿⣿⡛⣷⣿⢿⣿⣮⢹⣿⣿⢿⣿⡞⢯⣿⡿⣿⣷⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠴⠀⠈⠀⠀⠀⠀⠀⠀⣈⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣂⢸⣿⣿⣸⣿⡿⣴⣿⣛⣛⢣⣿⣿⢣⣿⣿⢸⣿⣿⢸⣿⣿⣼⣿⠏⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⣿⣿⣿⢿⣿⣿⣿⠃⣿⣿⡿⢿⢸⣿⣿⢻⣿⣷⢩⣿⣿⣡⣿⣿⠯⣾⣿⣿⢸⣿⣿⢸⣯⣿⢻⣿⣧⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣧⣭⢸⣿⣿⣼⣿⣿⣸⡿⢳⣿⣿⣥⣤⠈⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⡿⢸⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣛⡋⣤⣟⣻⣫⣤⣿⣿⣿⣿⣼⣿⣻⣿⣿⣵⣿⣟⣛⣿⣿⣟⣻⢾⣮⣿⣟⣿⣷⣶⣽⣿⣛⣿⣿⣿⣽⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠲⣶⠎⢶⠆⠰⠶⠶⠶⠀⣤⣤⣤⣤⣀⠀⠀⠉⠙⡋⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠤⣶⣶⣾⣴⣷⣶⣤⣻⣶⣾⣭⣭⣶⣴⣾⣷⣿⣷⣿⣶⡶⢶⣾⣿⣖⣟⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⠛⢁⢀⠀⠀⠀⠀⡀⢡⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢂⠿⣿⠟⡓⠈⠛⠛⠛⠙⠚⡛⠛⠿⣟⠿⢿⣟⣟⠛⠛⠋⡘⠻⠂⢈⣁⣤⣶⣿⣿⣿⣿⣿⣿⢏⣁⣴⣶⣶⣷⣿⣴⢂⢿⣶⣶⣤⠀⠴⣎⣦⣿⣾⣿⣿⣿⣿⣿⣿⣿⣧⣇⣽⣶⡄⠈⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀
⠏⠍⢚⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢨⣤⣵⣆⣤⣄⣢⣰⡄⣔⣤⣭⣿⣿⣿⣿⣿⣿⡏⠛⠒⢃⣀⢉⣿⣿⣿⣿⡷⣷⣿⡿⣿⣽⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⢀⣀⢀⣩⣆⣤⣤⣒⠀
⠀⢤⣵⡖⠀⠀⠀⠀⠀⠀⠀⣤⣽⣵⣿⣿⣻⣿⣿⣿⠦⣖⣾⣿⣿⣿⣿⣿⣿⣿⣉⣤⡄⢐⣲⣼⣿⣿⣿⣿⣿⡏⠟⢋⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⡿⡋⠉⢅⢤⣜⠻⠗⠻⠻⠉⠉⠯⠠
⠚⠋⠃⠀⠠⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣛⣿⣧⣬⣻⣿⣿⣿⣿⣿⡿⠛⠛⠛⠫⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⣷⣶⠖⣿⣟⣿⣿⡷⣯⣿⣿⣿⠿⠿⣟⣿⣿⢹⣿⠮⠙⠹⡷⠦⠌⠁⠘⠓⠋⠀⠀⠆⠀⠀⠀⠒
⠀⠴⢶⡤⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣯⣽⣭⣥⣤⣤⣴⣶⠺⣯⢽⣿⣿⣿⣿⣿⣿⣿⣇⢠⣝⣂⣃⣸⣿⡟⣿⡗⢛⣛⣽⡦⡖⠷⢻⡌⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠈⠀⠂⠀⠈⡐⢀⣾⣿⡿⢿⣿⣯⣹⣿⣿⠛⠋⠸⣯⢿⣿⣿⢿⣿⣿⣿⡍⠋⢻⢳⠾⠛⢹⣿⣿⣿⣿⣿⣿⣿⠯⢿⢿⢿⣛⣿⡯⡋⢙⣧⠔⢕⡏⡄⠈⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀
⠀⡀⠀⠀⠀⣻⣴⠿⠉⠰⠈⠩⠃⠀⢅⠠⠁⠀⠉⠈⠛⣛⢯⠘⠛⠯⠉⠁⠀⠂⠀⠁⠀⠀⠻⠿⣿⣿⣿⢿⠏⡄⢚⡒⣰⣽⡟⢖⢯⣴⡛⠃⠐⠀⠀⠀⡀⡰⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣷⣶⣶⣤⣴⣿⣭⣾⣷⣦⣲⣒⡉⠤⠲⠤⣠⠀⠀⢐⣄⠀⠀⠀⠀⠀⠀⠄⣄⣀⡀⠀⠒⠪⣦⣭⣿⣿⡿⠑⢧⢠⠄⠘⢻⣯⡥⣌⠔⠅⠐⠀⠀⠀⠀⠠⣳⣾⣽⠂⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⣦⣶⣶⣷⣶⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣴⡊⣀⣤⣤⣴⣾⣼⣿⣾⣯⣿⡛⣻⠿⠛⡷⢘⠻⡾⡅⡠⣖⡷⠀⠁⠀⠀⠀⠀⠀⠀⠀⢐⣿⣯⣯⠄⠂⠈⠠⠉⢀⠄⠔⢴⢾⣵⣿⣷⣿⣿⣿⡿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⡬⢸⢿⢥⣼⣾⣿⣶⣾⣷⣿⣇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣙⣭⣿⣿⡠⠄⠐⠐⣖⣲⠺⣶⣾⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢫⡝⣿⣾⢿⣾⡞⠁⠀⠀⠀⠀⠀⠀⠰⣲⠊⣨⣋⣿⣿⣿⡯⠋⣥⣽⣿⣶⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠛⠛⠙⣻⣷⡇⠀⣠⣀⢀⠀⢀⢀⠀⠨⠂⣚⣛⣭⡽⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⡿⠯⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄⢈⠈⢳⣿⣧⣲⣎⡶⣗⣎⣫⣳⣶⡶⠿⠋⣿⢿⣯⠻⠿⠙⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠟⠿⣣⣤⣬⣝⡻⣿⣿⣿⣶⣶⣾⣶⣷⣶⣤⣀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⣛⠉⠛⠉⠙⠛⠋⠙⠛⠛⠁⠈⠀⠀⠈⠙⠋⠉⠉⠉⠈⠓⡓⢀⣰⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠂⢈⣿⣿⣿⣿⣏⣆⠀⢿⣿⣿⣿⣿⣿⣿⢻⣟⣻⣿⣿⣶⣶⣤⡤⣿⣿⣿⣿⣿⣇⣀⢰⣶⣶⣶⡶⣤⡤⢤⡠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠀⠀⠘⢿⣿⣿⣿⠛⠋⠉⠛⠛⠛⠛⠋⢿⡷⢸⣿⣿⣿⣿⣿⡦⣽⣿⣿⣿⡷⣪⣤⣴⣭⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠐⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠛⠉⠛⠮⠿⠀⠀⠀⠘⠿⢿⣿⣀⡀⠀⠀⠈⠉⠉⠉⢸⡇⢸⣿⣿⣿⣿⣾⣿⡿⠟⠿⣏⣩⣭⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣻⣽⡿⠁⠀⠀⠀⠀⠀⠀⢿⣾⣿⣿⡜⠋⢛⣯⣶⣼⣿⣿⣿⣿⣟⣿
⠀⠀⠀⠀⠀⠀⢐⢀⢀⡄⡀⠀⣀⣀⢒⣴⣺⣷⣢⣦⣄⡄⡈⠙⠀⢠⠠⣾⣦⣠⣤⣴⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⠂⠀⠀⠀⠀⠻⣿⣿⠿⠿⣿⣿⣛⣿⣿⣿⣵⣾⣿⡷
⠀⠀⡀⠀⡂⠤⣽⡯⣽⣷⣦⣿⣾⣿⣽⣧⣿⣾⡿⣿⣿⣏⡁⣄⠀⢀⣸⡟⠉⠉⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡥⣠⣤⣤⣤⣼⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠀⠀⠂⠠⣉⠫⣇⣺⣿⢻⣿⣿⡟⣻⡿⠞⠃⠙⠛⠻⠟⠉⠁⠼⡿⠷⠤⠲⣶⡶⠶⠶⢶⣶⣶⣶⣶⣤⠶⢶⣶⣶⣶⡶⠶⠿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⠆⡅⢲⠿⠋⠈⠠⢄⠊⠛⠀⣿⣿⡆⣿⣿⡇⣸⣿⡟⣿⣿⣿⣿⢸⣿⣿⣿⣷⣎⣿⣿⣱⣿⡿⣿⣿⡛⣷⣿⢿⣿⣮⢹⣿⣿⢿⣿⡞⢯⣿⡿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠴⠀⠈⠀⠀⠀⠀⠀⠀⢈⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣠⢸⣿⣿⣸⣿⡿⣴⣷⣛⣛⢣⣿⣿⢣⣿⣿⢸⣿⣿⢘⣟⣻⣼⣿⠏⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⣿⣿⣿⢿⣿⣿⣿⠃⣿⣿⡿⢿⢸⣿⣿⢻⣿⣷⢩⣽⣿⣣⣿⣿⠯⣾⣿⣿⢸⣿⣿⢸⣯⣿⢻⣿⣧⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣧⣭⢸⣿⣿⣼⣿⣿⣸⡿⣳⣿⣿⣥⣤⠈⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⡿⢸⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣛⡛⣄⣿⣻⣫⣤⣿⣿⣿⣿⣼⣿⣻⣿⣿⣵⣿⣟⣛⣿⣿⣿⣻⢾⣮⣿⣟⣿⣵⣶⣽⣿⣻⣿⣿⣿⣽⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠲⣶⠮⢶⠆⠰⠶⠶⠶⠀⣤⣤⣤⣤⣀⠀⠀⠙⠛⡛⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡤⣶⣶⣾⣤⣶⣶⣤⣻⣶⣾⣭⣭⣶⣴⣾⣾⣿⣷⣿⣶⡶⡶⣾⣿⣷⣟⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⢀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠿⣿⠟⠓⠀⠉⠉⠫⠙⠚⡛⠛⠟⡟⡿⠿⣟⣟⠛⠛⠋⠘⠻⠂⢈⣁⣀⣴⣿⢿⣿⣿⣿⣿⢏⣁⣴⣦⣴⣷⡧⣄⠀⡮⣲⣶⡥⠠⠰⣌⣢⣤⣶⣮⣷⣿⣿⣿⣿⣶⣦⣶⢼⣤⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀
⠋⠌⢚⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢨⣤⣥⣄⣄⣀⣠⣰⡄⣰⣤⣼⣷⣿⣿⣿⣿⣿⡟⠛⠒⢁⣀⢉⣿⣿⣿⣿⡷⣧⣿⡽⣿⣽⣿⣷⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⣀⡀⠀⣠⣤⣤⣤⣂⠀
⠀⢤⣵⡆⠀⠀⠀⠀⠀⠀⠀⣠⣽⣴⣿⣻⣒⣿⣿⣿⡦⣐⣾⣿⣿⣿⣿⣿⣿⣿⣁⣤⡄⢐⣲⣾⣿⣿⣿⣿⣿⡏⠛⢋⣛⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠍⡫⠋⠀⢄⢤⣜⠻⠗⠻⠿⠉⠉⠏⠠
⠚⠉⠃⠀⠠⠀⠀⠀⠀⠀⣸⣿⣷⣿⣿⣿⣿⣟⣯⣧⣠⣹⣿⣿⣿⣿⣿⡿⠛⠛⠛⠫⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⣶⣶⠖⣿⢿⣿⣿⡷⣯⣿⣿⣿⠿⠿⣿⣿⣿⢽⣟⠮⠙⢹⠿⠦⠀⠁⠘⠓⠋⠀⠀⠂⠀⠀⠀⠂
⠀⠴⢤⡤⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣯⣽⣭⣤⣤⣤⣴⣶⢺⣯⣿⣿⣿⣿⣿⣿⣿⣿⣇⢠⣕⣃⢃⣸⣿⡟⣿⡟⣛⣛⣽⡦⣶⠟⣻⡔⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠈⠀⠃⠀⠈⡐⠀⣾⣿⣿⣯⣿⣭⣹⣿⣿⠛⠋⠸⣿⢿⣿⣿⢿⣿⣿⣿⣍⠋⢻⢫⠾⠛⢹⣿⣿⣿⣿⣿⣿⣿⠯⢽⢿⢿⣛⣿⡯⠋⠉⣧⠐⢕⡯⡭⠈⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠀⡀⠀⠀⠀⢺⣶⠿⠉⠐⠈⠉⠁⠀⢅⠀⠀⠀⠉⠈⠛⣛⢏⠘⠛⠏⠉⠁⠀⠂⠀⠀⠀⠀⠻⠿⣿⣿⣿⢿⡏⡄⢘⠒⣡⣿⡾⠖⣯⣼⣛⠃⠘⠀⠀⠀⡀⡰⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣷⣶⣶⣤⣴⣿⣭⣾⣷⣦⣰⣐⠁⠤⢲⠤⢠⠀⠀⢐⢄⠀⠀⠀⠀⠀⠀⠄⣄⣀⡀⡀⠒⠢⣦⣩⣿⣿⡿⠹⢧⢀⠀⠘⠛⣫⣅⣼⠜⠁⠀⠀⠀⠀⠀⠠⣷⣾⣿⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣦⣴⣷⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣴⡈⣀⣤⣄⣴⣾⣽⣿⣾⣯⣿⡛⣳⠾⠛⡷⢙⠻⡾⠄⡀⠄⡘⠘⠃⠀⠀⠀⠀⠀⠀⠀⣀⣽⣯⣯⠀⡀⠀⠀⠉⢀⠀⠀⠀⢶⣴⢶⣵⣿⣿⣿⡿⠿⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣬⣸⣿⡭⣴⣾⣿⣷⣼⣿⣿⣆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⣙⣭⣿⣿⡁⠠⠀⠐⣖⣒⠲⣾⣾⣿⣿⣯⣯⡿⠟⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⠫⠙⣿⣖⢿⣿⡾⠁⠀⠀⠀⠀⠀⠀⠰⣴⠀⠈⣻⣿⣿⣿⡯⠂⣄⣌⣿⣿⣾⣿⣿⣿⣿⠿⠏⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠛⠛⠙⣻⣷⡄⠀⣠⣀⢠⠀⢁⣄⠀⠨⠂⣈⣛⣭⡿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⠿⡯⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄⢈⠀⢺⣿⣧⣷⣦⡤⣵⣮⣉⣻⣶⡶⠟⠋⣻⣿⣯⣿⠯⠙⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠿⠿⣣⣤⣬⣝⡻⣿⣿⣿⣶⣶⣾⣶⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⣛⠉⠛⠉⠙⠛⠋⠙⠛⠛⠁⠈⠀⠀⠉⠙⠋⠉⠉⠉⠀⠓⡖⢀⣰⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠄⠀⠀⠐⠐⠂⠈⣿⣿⣿⣿⣏⣇⡀⠻⣿⣿⣿⣿⣿⣿⢻⡟⣻⣿⣿⣶⣶⣤⡤⣿⣿⣿⣿⣿⣇⠀⣰⣶⣶⣶⣶⣤⡤⢴⡠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠀⠀⠙⢿⣿⣿⣿⠟⠛⠁⠛⠛⠛⠛⠇⢿⣷⢸⣿⣿⣿⣿⣿⡧⣿⣹⣿⢿⠷⣺⣤⣥⣭⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠛⠀⠀⠀⠘⠿⢿⣿⡀⠀⠀⠀⠈⠉⠉⠉⢹⡇⢀⣿⣿⣿⣿⣿⣿⡿⡻⣿⣋⣫⣭⢽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣻⣿⡿⠁⠀⠀⠀⠀⠀⠀⢿⣮⣿⣿⡆⠞⢛⣯⣶⣼⣿⣿⣿⣿⣟⣿
⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⡀⠀⣀⡒⢳⣶⣲⣷⣦⣤⡤⡄⡈⠙⠀⢀⠀⣴⣦⣠⣄⣴⣢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠂⠀⠀⠀⠀⠻⣿⣿⢿⢿⣿⣟⣛⣿⣿⣿⣷⣾⣿⡷
⠀⠀⡀⢀⡣⠬⣻⡯⣽⣿⣦⣿⣿⣿⣿⣿⣯⣿⡿⣿⣿⣟⡁⣄⠀⢀⣸⡟⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡤⣠⣤⣤⣤⣼⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠀⠀⡀⠀⢉⢿⣍⣻⣿⠻⣿⣿⡿⣿⡿⠾⠇⠛⠛⠻⠟⠉⠃⠸⡿⠷⠶⠶⣶⡶⠶⠶⣶⣶⣶⣶⣶⣴⠶⣶⣶⣶⣶⡶⠾⢿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⢆⡀⢳⠿⠟⠈⢥⠆⢋⠛⠀⣿⣿⡆⣿⣿⡇⣸⣿⡟⣿⣿⣿⣿⢸⣿⣿⣿⣷⣎⣿⣿⣳⣿⡿⣿⣿⡛⣷⣿⢿⣿⣮⢻⣿⣿⢿⣿⡞⢿⣿⡿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠴⠀⠈⠀⠀⠀⠐⠀⠀⠈⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣂⢸⣿⣿⣸⣿⡿⣶⣿⣙⣛⢣⣿⣿⢣⣿⣿⢸⣿⣿⢸⣿⣻⣼⣿⠏⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⣿⣿⣿⢿⣿⣿⣿⠃⣿⣿⡿⢿⢸⣿⣿⢻⣿⣷⢩⣿⣿⣣⣿⣿⠯⣾⣿⣿⢸⣿⣿⢸⣯⣿⢻⣿⣧⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣧⣭⢸⣿⣿⣼⣿⣿⣸⡿⢷⣿⣿⣥⣴⠈⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⡿⢸⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠛⣛⡛⣄⣟⣻⣫⣤⣿⣿⣿⣿⣼⣿⣻⣿⣿⣵⣿⣟⣛⣿⣿⣿⣻⣼⣮⣿⣟⣿⣷⣶⣽⣿⣛⣿⣿⣿⣽⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠲⣶⠯⢶⠆⠰⠶⠶⠶⠀⣤⣤⣤⣤⣀⠀⠀⠙⣛⣛⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡤⣶⣶⣾⣴⠷⣶⣤⣛⣶⣾⣭⣭⣶⣴⣾⣷⣿⣷⣿⣶⡶⣶⣾⣿⣗⣟⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⠛⢁⢀⠀⢀⠀⠄⣀⢡⠄⠀⠀⠀⠀⣀⣄⣀⠀⠀⣠⣤⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢊⠻⣿⠟⠓⠀⠛⠋⠛⠝⢚⡛⠛⠿⣟⠿⢿⣿⡿⠟⡛⠋⡘⠻⠂⢈⣁⣤⣶⣿⣿⣿⣿⣿⣿⢟⣁⣴⣶⣶⣿⣿⣴⢂⣻⣾⣶⡥⠀⢰⣌⣶⣭⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⢾⣥⡄⠈⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀
⠏⠍⢚⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢨⣤⣡⣆⣠⣄⣢⣰⡆⣴⣤⣭⣽⣾⣿⣿⣿⣿⡏⠛⠒⢁⣀⢉⣿⣿⣿⣿⡷⣿⣿⡿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⣀⣀⢀⣩⣤⣤⣤⣒⠀
⠀⢤⣵⡆⠀⠀⠀⠀⠀⠀⠀⣤⣽⣵⣿⣿⣳⣿⣿⣿⡦⣖⣾⣿⣿⣿⣿⣿⣿⣿⣁⣤⡄⢐⣲⣼⣿⣿⣿⣿⣿⡏⠟⢏⣛⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡿⡏⠉⢅⣤⣼⠻⡟⠻⠻⠉⠉⠯⠠
⠚⠉⠃⠀⠠⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣛⣿⣧⣬⣹⣿⣿⣿⣿⣷⡿⠛⠛⠛⠫⣾⣿⣿⣽⣿⣿⣿⣿⣿⡇⣷⣷⠶⣽⢿⣿⣿⡷⣯⣿⣿⣿⡿⠿⣟⣿⣿⣹⣿⠮⠙⠹⡿⠶⠎⠁⠘⠓⠋⠀⠀⠆⠀⠈⠀⠒
⠀⠴⣶⡤⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣯⣽⣭⣥⣤⣤⣴⣶⢺⣿⢽⣿⣿⣿⣿⣿⣿⣿⣇⢠⣝⣊⣃⣸⣿⡟⣿⡗⢛⣛⣹⡦⣶⠖⣿⢄⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠈⠀⠂⠀⠈⡐⢀⣾⣿⣿⢿⣿⣭⣹⣿⣿⠛⠋⠸⣿⢿⣿⣿⢿⣿⣿⣿⡍⠋⢻⢳⠾⠛⢸⣿⣿⣿⣿⣿⣿⣿⠯⢿⠿⣿⣛⣿⡯⡃⠉⡇⠐⣕⡯⣤⠈⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠀⡀⠀⠀⠀⢺⣶⠿⠉⠰⠨⠩⠁⠀⢅⠀⠀⠀⠉⠉⠛⣛⢯⠘⠛⠏⠋⠁⠀⠊⠀⠁⠀⠀⠻⠿⣿⣿⣿⢿⡏⡄⢘⠒⣠⣾⡺⠖⣯⣴⣛⠃⠘⠀⠀⠀⠀⡰⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣶⣶⣤⣴⣽⣭⣾⣷⣦⣲⣔⠉⠤⠲⠥⣠⠀⠀⢐⢄⠀⠀⠀⠀⠀⠀⠄⣄⣀⡀⡁⠒⠪⣦⣭⣿⣿⡿⠑⣧⢀⠀⠘⠛⣫⠅⣌⠔⠁⠀⠀⠀⠀⠀⠠⣷⣾⣽⠆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣶⣶⣽⣶⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣴⡋⣀⣤⣄⣴⣾⣽⣿⣾⣯⣿⣛⣽⠾⠛⡷⢙⢻⡾⠅⡠⢄⡹⠘⠃⠀⠀⠀⠀⠀⠀⠀⣀⣿⣯⣯⠀⡀⠁⠀⠉⢐⠀⠀⢶⢶⣸⣿⣿⣿⣿⣿⡿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⡬⢸⣿⡭⣴⣶⣿⣗⣼⣿⡿⣇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣝⣭⣿⣿⡁⠤⠄⠐⣖⣓⠾⣾⣾⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⠫⠙⣿⣞⣿⣾⡞⠁⠀⠀⠀⠀⠀⠀⠰⣶⠊⠈⣋⣿⣿⣿⡯⠨⣥⣏⣿⣿⣾⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠛⠛⠑⣻⣷⡄⠀⣠⢀⣠⠀⢁⣀⠀⠨⠂⡊⣛⣭⡽⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⠿⡯⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⢈⠈⢸⣿⣧⣣⣮⡷⣿⣮⣻⣻⣶⡶⠟⠋⣻⣿⣯⠿⠿⠙⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠿⠿⣣⣤⣤⣝⡻⣿⣿⣿⣶⣶⣾⣶⣷⣶⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⣛⠉⠛⠉⠙⠛⠋⠉⠛⠛⠁⠀⠀⠀⠈⠙⠋⠉⠉⠉⠀⠓⡛⠀⣰⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠘⠂⠈⣿⣿⣿⣿⣏⣃⣀⠻⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣶⣶⣤⡤⣿⣿⣿⣿⣿⣇⠀⣶⣶⣶⣶⣶⣤⣤⢄⡠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠀⠀⠙⢿⣿⣿⣿⠟⠛⠁⠛⠛⠛⠛⠇⢿⣷⠸⣿⣿⣿⣿⣿⡶⣽⣿⣿⣿⠗⣺⣤⣴⣭⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠐⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠈⠙⠀⠀⠀⠈⠿⢿⣿⡀⠀⠀⠀⠈⠉⠉⠉⢹⡏⢀⣿⣿⣿⣿⣿⣿⡿⠟⢿⣏⣩⣭⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣹⣽⡿⠁⠀⠀⠀⠀⠀⠀⢿⣮⣿⣿⡎⠏⢛⣯⣶⣼⣿⣿⣿⣿⣟⣿
⠀⠀⠀⠀⠀⠀⢐⢄⣀⣀⡀⠀⣀⣀⢲⣶⣺⣷⣢⣧⡄⡄⡈⠙⠀⢠⠠⣼⣦⣤⣤⣴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⠂⠀⠀⠀⠀⠻⣿⣿⢿⢿⣿⣿⣛⣿⣿⣿⣷⣾⣿⡷
⠀⠀⡀⠀⡂⠬⣽⡯⣽⣿⣦⣿⣾⣿⣿⣯⣿⣿⡻⣿⣿⣟⡁⣄⠀⢀⣸⡟⠀⠈⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡡⢠⣤⣤⣤⣼⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠀⠀⠀⠀⢉⠿⣍⣺⣿⢻⣿⣿⡟⣻⡿⠞⠃⠛⠛⠻⠟⠉⠃⠸⡿⠷⠶⠲⡶⡶⠶⠶⢶⣶⣶⣶⣶⣦⠶⢶⣶⣶⣶⡶⠾⠿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⢆⡅⢲⠿⠋⠀⢠⣖⢋⠛⠀⣿⣿⡆⣿⣿⡇⣸⣿⡟⣿⣿⣿⣿⢸⣿⣿⣿⣷⣎⣿⣿⣱⣿⡿⣿⣿⡛⣷⣿⢿⣿⣮⢻⣿⣿⢿⣿⡞⢯⣿⡿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠴⠀⠈⠀⠀⠀⠀⠀⠀⢈⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣂⢸⣿⣿⣸⣿⡿⣴⣿⣙⣛⢣⣿⣿⢳⣿⣿⢸⣿⣿⢘⣿⣿⣼⣿⠏⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⢸⣿⣿⣿⢿⣿⣿⣿⠃⣿⣿⡿⢿⢸⣿⣿⢻⣿⣷⢩⣽⣿⣣⣿⣿⠯⣾⣿⣿⢸⣿⣿⢸⣯⣿⢻⣿⣧⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣧⣭⢸⣿⣿⣼⣿⣿⣸⡿⢷⣿⣿⣥⣤⠈⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⡿⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣛⡛⣤⣟⣻⣋⣤⣿⣿⣿⣿⣼⣿⣻⣿⣿⣽⣿⣟⣛⣿⣿⣟⣻⢾⣮⣿⣟⣿⣷⣶⣽⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠲⣶⠯⢶⠆⠰⠶⠶⠶⠀⣤⣤⣄⣤⡀⠀⠀⠙⡛⡋⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠤⣶⣶⣶⣤⠷⣶⣤⣻⣶⣾⣭⣭⣶⣴⣾⣷⣿⣷⣿⣶⡶⡶⣾⣿⣗⣛⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⡿⠛⠁⢀⠄⠀⠀⠄⡁⢡⡄⠀⠀⠀⠀⠀⢀⢀⠀⠀⡠⠤⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢂⠻⣿⠟⠓⠀⠋⠋⠛⠙⠺⡛⠛⠿⣟⠿⠿⣟⡟⠿⠛⠋⡘⠻⠂⢈⣁⣤⣶⣿⣿⣿⣿⣿⣿⢏⣁⣴⣦⣶⣿⣿⣴⢀⣻⣶⣶⡥⠀⠰⣄⣦⣾⣶⣿⣷⣿⣿⣿⣿⣷⣧⣷⣾⣥⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀
⠏⠍⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢨⣤⣤⣆⣠⣀⣢⣰⠄⣰⣤⣬⣴⣾⣯⣿⣿⣿⡏⠛⠒⠁⣀⢉⣿⣿⣿⣿⡷⣷⣿⡿⣿⣽⣿⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⢀⣀⢀⣨⣤⣤⣤⣒⠀
⠀⢤⣵⡆⠀⠀⠀⠀⠀⠀⠀⣠⣽⢴⣿⣻⣳⣿⣿⣿⡦⣖⣾⣿⣿⣿⣿⣿⣿⣿⣁⣤⡄⢐⣲⣼⣿⣿⣿⣿⣿⡏⠚⢋⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡿⡏⠍⢅⢬⣜⠻⠗⠛⠻⠉⠉⠯⠠
⠚⠉⠃⠀⠠⠀⠀⠀⠀⠀⣨⣿⣷⣿⣿⣿⣿⣛⣿⣧⣠⣻⣿⣿⣿⣿⣿⡿⠛⠛⠛⠫⣾⣿⣿⣽⣿⣿⣿⣿⣿⡇⢷⣶⠖⣿⢿⣿⣿⡷⣧⣿⣿⣿⡿⠿⣟⣿⣿⢽⣻⠮⠙⠹⡿⠶⠌⠁⠘⠓⠋⠀⠀⠂⠀⠈⠀⠐
⠀⠴⢦⡤⠀⠀⠀⢀⣴⣿⣿⣿⣿⣯⣿⣿⣿⣿⠿⣿⣿⣿⣿⣯⣽⣍⣤⣤⣤⣴⣶⠚⣿⢽⣿⣿⣿⣿⣿⣿⣿⣇⢠⣕⣂⢃⣰⣿⡟⣿⡗⢋⣛⣹⡦⣶⠖⣻⡄⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠈⠀⠂⠀⠈⡐⢀⣾⣿⡿⢯⣿⣭⣹⣿⣿⠛⠋⠘⣿⢿⣿⣿⢿⣿⣿⣿⡍⡋⢻⢳⠞⠚⢸⣿⣿⣿⣿⣿⣿⣿⠯⢽⠿⢿⣛⣿⡯⠋⢉⡇⠐⢕⡋⣥⠈⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠀⡀⠀⠀⠀⣺⣴⠿⠉⠠⠈⠩⠃⠀⢁⠀⠁⠀⠉⠈⠛⣛⢯⠘⠛⠏⠉⠁⠀⠊⠀⠁⠀⠀⠻⠿⣿⣿⣿⢿⡏⡄⢐⠂⣠⢾⡚⠖⣯⣼⡚⠂⠘⠀⠀⠁⡀⡰⣤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣶⣶⣤⣴⣽⣭⣾⣧⣤⣰⣔⠩⠤⠲⠤⣠⠀⠀⢐⢄⠀⠀⠀⠀⠀⠀⠄⣄⣀⡀⡑⠒⠪⣦⣭⣿⣿⡿⠑⢧⢀⠀⠘⠙⡋⡅⣬⠔⠁⠀⠀⠀⠀⠀⠠⣷⢾⣽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⣴⣵⣶⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣴⡊⣀⣤⣄⣴⣾⣼⣿⣾⣯⣿⡛⣹⠾⠛⡷⢙⠻⡾⠄⡠⠄⡛⠜⠃⠀⠀⠀⠀⠀⠀⠀⣀⣿⣯⣏⠀⡀⠁⠀⠉⢀⠀⠀⢐⢶⣼⣾⣷⣿⣿⣿⡿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⡬⣸⣯⠭⣴⣾⣿⣷⣼⣿⣿⣇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣛⣭⣿⣿⡁⠀⠀⠀⣖⣒⠶⣾⣾⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⠫⠙⣿⣖⣿⣾⡞⠃⠀⠀⠀⠀⠀⠀⠰⣒⠊⠈⣻⣿⣿⣿⡯⠈⣥⣾⣿⣿⣾⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠛⠛⠑⢻⣷⡄⠀⣠⡀⣀⠀⢁⢀⠀⠨⠀⡚⣛⣭⡽⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⠿⡯⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⢈⠈⢲⣿⣧⣲⣦⡶⣿⣎⣻⣳⣶⡶⠟⠉⣻⢿⣯⡿⠟⠙⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠿⠿⣣⣤⣤⣝⡻⣿⣿⣿⣶⣶⣾⣶⣷⣶⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⣛⠉⠛⠉⠙⠛⠋⠙⠛⠛⠁⠈⠀⠀⠈⠙⠋⠉⠉⠉⠀⠓⡒⠀⣰⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠈⣿⣿⣿⣿⣏⣇⡀⠻⣿⣿⣿⣿⣿⣿⢻⣟⣿⣿⣿⣶⣶⣤⡤⣿⣿⣿⣿⣿⣇⠀⣴⣶⣶⣶⡶⣤⣤⢤⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠀⠀⠙⢿⣿⣿⣿⠟⠛⠁⠛⠛⠛⠛⠇⢿⣷⠸⣿⣿⣿⣿⣿⡶⣽⣿⣿⣿⡷⣺⣤⣵⣭⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠙⠀⠀⠀⠈⠿⢿⣿⡀⠀⠀⠀⠈⠉⠉⠉⢹⡇⢀⣿⣿⣿⣿⣿⣿⡿⠟⢿⣏⣩⣭⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣹⣽⡿⠁⠀⠀⠀⠀⠀⠀⢿⣮⣿⣿⡏⠏⢛⣯⣶⣼⣿⣿⣿⣿⣟⣿
⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀⡀⡀⣀⣠⢲⣴⣲⣷⣢⣦⡄⡄⡈⠙⠀⢠⠠⣴⣦⣤⣤⣴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠂⠀⠀⠀⠀⠻⣿⣿⢿⢿⣿⣿⣛⣿⣿⣿⣷⣾⣿⡷
⠀⠀⡀⠀⡂⠤⣽⡯⣽⣷⣦⣿⣾⣿⣿⣧⣿⣿⡻⣿⣿⣟⡁⣄⠀⠀⣸⡿⠀⠉⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡤⢠⣤⣤⣤⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠀⠀⠀⠀⣉⠙⣋⣾⣿⠻⣿⣿⠟⣛⠿⠎⠃⠛⠛⠻⠟⠁⠃⠸⡿⠷⠶⠲⠶⡶⠶⠶⣶⣶⣶⣶⣶⣶⠶⢶⣶⣶⣶⡶⠾⢿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⠆⡄⠲⠿⠋⠀⠠⢄⠊⠛⠀⣿⣿⡆⣿⣿⡇⣸⣿⡟⣿⣿⣿⣿⢸⣿⣿⣿⣷⣎⣿⣿⣱⣿⡿⣿⣿⡛⣷⣿⢿⣿⣮⢻⣿⣿⢿⣿⡞⢯⣿⡿⣿⣷⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣂⢸⣿⣿⣸⣿⡿⣴⣿⣚⣛⢣⣿⣿⢣⣿⣿⢸⣿⣿⢘⣿⣿⣼⣿⠏⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⣿⣿⣿⢿⣿⣿⣿⠃⣿⣿⡿⢿⢸⣿⣿⢻⣿⣷⢩⣿⣿⣣⣿⣿⠯⣾⣿⣿⢸⣿⣿⢸⣯⣿⢻⣿⣧⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣧⣭⢸⣿⣿⣼⣿⣿⣸⡿⣳⣿⣿⣥⣤⠌⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⡿⢸⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣛⡛⣠⣿⣻⣋⣤⣿⣿⣿⣿⣼⣿⣻⣿⣿⣵⣿⣟⣛⣿⣿⣟⣻⣾⣮⣿⣟⣿⣷⣶⣽⣟⣻⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠲⣶⠮⢶⠄⠰⠶⠶⠶⠀⣤⣤⣤⣤⡀⠀⠀⠙⡉⠋⢉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡤⣶⣶⣾⣴⢷⣶⣤⣻⣶⣾⣭⣭⣶⣴⣾⣷⣿⣷⣿⣶⡶⡷⣾⣿⣷⣟⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⢀⠀⠀⠀⠄⡀⢡⠄⠀⠀⠀⠀⢀⣄⡀⠀⠀⡠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢊⠻⣿⠟⡃⠈⠛⠉⠋⠙⠚⡛⠛⠟⣟⠿⠿⣿⣟⠟⠛⠋⡘⠻⠂⢈⣁⣀⣶⣿⣿⣿⣿⣿⣿⢏⣁⣴⣦⣶⣷⣧⣴⢀⣿⣶⣶⣥⠀⠰⣄⣦⣴⣾⣿⣷⣿⣿⣿⣿⣿⣧⣷⣽⣷⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀
⠋⠍⢚⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢨⣤⣱⣆⣠⣄⣢⣰⣆⣐⣤⣬⣷⣾⣿⣿⣿⣿⡏⠓⠒⠁⣀⢉⣿⣿⣿⣿⡷⣷⣿⡿⣿⣽⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⢀⣀⢀⣹⣤⣤⣤⣐⠀
⠀⢤⣵⡆⠀⠀⠀⠀⠀⠀⠀⣠⣽⣴⣿⣻⣻⣿⣿⣿⠦⣖⣾⣿⣿⣿⣿⣿⣿⣿⣁⣤⡄⢐⣲⣾⣿⣿⣿⣿⣿⡏⠛⢋⣛⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⡽⡃⠁⢅⢬⣜⠫⠗⠛⠟⠉⠉⠯⠨
⠚⠉⠁⠂⠠⠀⠀⠀⠀⠀⣸⣿⣷⣿⣿⣿⣿⣟⣿⣧⣤⣻⣿⣿⣿⣿⣿⡿⠛⠛⠛⠫⣾⣿⣿⣿⣿⣿⣿⣿⣿⡧⣷⣶⠖⣿⢿⣿⣿⡷⣯⣿⣿⣿⡿⠿⣿⣿⣿⣽⣻⠯⠙⠹⠽⠦⠌⠁⠘⠓⠋⠀⠀⠆⠀⠈⠀⠒
⠠⠴⣦⡤⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣯⣽⣭⣤⣤⣤⣴⣶⠚⣯⢽⣿⣿⣿⣿⣿⣿⣿⣇⢀⣕⣋⣃⣰⣿⡟⣿⡇⢛⣫⣽⡧⡶⠞⣹⡄⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠈⠀⠃⠀⠈⡐⢀⣾⣿⣿⢿⣿⣯⣹⣿⣿⠛⠋⠘⣿⢿⣿⣿⢿⣿⣿⣯⣍⠉⢻⢳⠾⠞⢸⣿⣿⣿⣿⣿⣿⣿⠯⢽⠿⢿⣛⣿⡯⢋⢙⣇⠐⢕⡋⣥⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠀⡀⠀⠀⠀⢺⣶⠿⠉⠰⠈⠩⠁⠀⢅⠀⠁⠀⠉⠉⠙⣛⢯⠘⠛⠯⠍⠁⠀⠂⠀⠁⠀⠀⠻⠿⣿⣿⣿⢿⠏⡄⢘⠒⣠⢾⡿⠖⣯⣼⡛⠃⠘⠁⠀⠀⡀⡰⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣷⣶⣶⣤⣴⣽⣭⣾⣷⣆⣒⣔⠉⠠⠲⠤⣠⠀⠀⢐⣄⠀⠀⠀⠀⠀⠀⠄⣄⣀⡀⡁⠒⠪⣦⣭⣿⣿⡿⠹⢧⢀⠀⠘⠛⣋⡥⠼⠔⠁⠀⠀⠀⠀⠀⠠⣷⣾⣽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣶⣶⣿⣶⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣔⡈⢀⣤⣄⣴⣾⣼⣿⣾⣯⣿⡓⣿⠾⠻⡷⢙⠻⡾⠄⡠⢔⡝⠜⠃⠀⠀⠀⠀⠀⠀⠀⣀⣿⣯⣯⠀⠀⠁⠀⠉⢀⠄⠄⢔⢶⣼⣿⣷⣿⣿⣿⡿⡿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⡬⢸⢿⡥⣴⣾⣟⣷⣾⣿⡿⣆⠊⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣝⣭⣿⣿⡡⠀⠄⠐⣖⣓⢲⣾⣾⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⠫⠙⣿⣞⢿⣾⡞⠁⠀⠀⠀⠀⠀⠀⠰⡶⠊⠈⣻⣿⣿⣿⡯⠨⣤⣞⣿⣿⣾⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠛⠛⠑⢻⣷⡄⠀⣠⠀⣀⠀⢁⣀⠀⠠⠂⡊⣛⣭⡽⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⠿⠯⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⢈⠀⢶⣿⣷⣣⣦⡶⣷⣮⣛⣻⣶⡶⠟⠋⣻⢿⣿⣿⠟⠙⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠿⣣⣤⣬⣝⡻⣿⣿⣿⣶⣶⣾⣶⣷⣶⣠⣀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⣻⠙⠛⠉⠙⠛⠋⠉⠛⠛⠁⠈⠀⠀⠈⠙⠋⠉⠉⠉⠈⠓⡓⠀⣰⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠈⣿⣿⣿⣿⣏⣇⡀⢻⣿⣿⣿⣿⣿⣿⢻⡿⣿⣿⣿⣶⣶⣤⡤⣿⣿⣿⣿⣿⣇⠀⢴⣶⣶⣶⡶⣤⡤⣤⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠀⠀⠙⢿⣿⣿⣿⠟⠛⠁⠛⠛⠛⠛⠇⢿⣷⠸⣿⣿⣿⣿⣿⡦⣽⣿⣿⣿⠷⣺⣤⣴⣭⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠊⠛⠀⠀⠀⠈⠿⢿⣿⡀⠀⠀⠀⠈⠉⠉⠉⢹⠇⢀⣿⣿⣿⣿⣿⣿⡿⠛⠿⣋⣩⣭⢽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣽⡿⠁⠀⠀⠀⠀⠀⠀⢿⣮⣿⡿⣄⠎⢛⣯⣶⣼⣿⣿⣿⣿⣟⣿
⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀⡀⠀⣀⣐⣲⣰⣺⣷⣢⣦⣄⡄⡈⠙⠀⢠⠠⣴⣦⣠⣤⣔⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⠂⠀⠀⠀⠀⠻⣿⣿⣿⢿⣿⣿⣛⣿⣿⣿⣷⣾⣿⡷
⠀⠀⡀⠀⡂⠤⣽⡯⣽⣿⣧⣟⣾⣿⣿⣧⣿⣾⡻⣿⣿⣟⡁⣄⠀⠀⣸⡿⠈⠈⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⢠⣤⣤⣤⣼⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠀⠀⠀⠀⢉⠽⣍⣾⣿⠺⣿⣿⡿⣻⡿⠼⠃⠛⠛⠻⠟⠉⠁⠼⡿⠷⠦⠲⡶⡶⠶⠶⢶⣶⣶⣶⣶⣦⠶⢶⣶⣶⣶⡶⠶⢿⣿⣷⣿⠿⠿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⠄⡅⢲⠿⠋⠀⢠⢄⠂⠛⠀⣿⣿⡆⣿⣿⡇⣸⣿⡟⣿⣿⣿⣿⢸⣿⣿⣿⣷⣎⣿⣿⣳⣿⡿⣿⣿⡛⣷⣿⢿⣿⣮⢻⣿⣿⢿⣿⡞⢯⣿⡿⣿⣷⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠴⠀⠈⠀⠀⠀⠀⠀⠀⣈⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣀⢸⣿⣿⣸⣿⡿⣴⣷⣙⣛⢣⣿⣿⢣⣿⣿⢸⣿⣿⢸⣿⣻⣼⣿⠏⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⣿⣿⢿⣿⣿⣿⠃⣿⣿⡿⢿⢸⣿⣿⢻⣿⣷⢩⣿⣿⣣⣿⣿⠯⣾⣿⣿⢸⣿⣿⢸⣯⣿⢻⣿⣧⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣧⣭⢸⣿⣿⣼⣿⣿⣸⡿⣳⣿⣿⣥⣤⠈⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⡿⢸⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣛⡛⣠⣻⣻⣋⣤⣿⣿⣿⣿⣼⣿⣻⣿⣿⣵⣿⣟⣛⣿⣿⣟⣻⢾⣮⣿⣟⣿⣵⣶⣽⣟⣛⣿⣿⣿⣽⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠲⣶⠎⢶⠆⠰⠶⠶⠶⠀⣤⣤⣄⣤⣀⠀⠀⠙⡙⠋⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠤⣶⣶⣶⣴⢷⣶⣤⣻⣶⣾⣭⣭⣶⣴⣾⣷⣿⣷⣿⣶⡶⡷⣾⣿⣗⣟⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⢀⠀⠀⠀⠄⣁⢡⡄⠀⠀⠀⠀⢀⢀⣀⠀⠀⡤⢤⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢂⠻⣿⠟⡃⠀⠛⠛⠛⠙⠺⡛⠛⠿⣟⠿⠿⣿⡟⠻⡛⠋⡘⠻⠂⢈⣁⣄⣶⣿⣿⣿⣿⣿⣿⣏⣁⣴⣦⣶⣿⣿⣴⢂⣽⣾⣶⣤⠀⠰⣎⣶⣴⣶⣿⣿⣿⣿⣿⣿⣿⣧⣿⣾⣧⡄⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀
⠏⠍⢚⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢨⣤⣥⣆⣤⣄⣢⣰⠆⣴⣤⣬⣿⣿⣷⣿⣿⣿⡏⠛⠒⢁⣀⢉⣿⣿⣿⣿⡷⣷⣿⡿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⢀⣀⢀⣹⣆⣤⣤⣐⠀
⠀⢤⣵⡆⠀⠀⠀⠀⠀⠀⠀⣠⣽⣴⣿⣻⣳⣿⣿⣿⡦⣖⣾⣿⣿⣿⣿⣿⣿⣿⣁⣤⡄⢐⣲⣼⣿⣿⣿⣿⣿⡏⠟⢋⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡿⡋⠉⢅⢬⣜⠻⠗⠛⠻⠉⠉⠯⠨
⠚⠉⠃⠀⠠⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣟⣿⣧⣨⣻⣿⣿⣿⣿⣷⡿⠛⠛⠛⠫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣷⣶⠶⣿⢿⣿⣿⡷⣯⣿⣿⣿⡿⠿⣟⣿⣿⣽⣻⠮⠙⠹⡿⠦⠌⠁⠘⠓⠋⠀⠀⠆⠀⠀⠀⠒
⠀⠴⣶⡤⠀⠀⠀⢀⣴⣿⣿⣿⣿⣯⣿⣿⣿⣿⠿⣿⣿⣿⣿⣯⣽⣍⣥⣤⣤⣴⣶⠚⣿⣽⣿⣿⣿⣿⣿⣿⣿⣇⢠⣝⣃⣃⣰⣿⡟⣿⡇⢛⣫⣽⡧⡶⠗⢹⡄⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠈⠀⠂⠀⠈⡐⢀⣾⣿⣿⢯⣿⣭⣹⣿⣿⠟⠋⠸⣿⢿⣿⣿⢿⣿⣿⣿⣍⠋⢻⢲⠾⠛⢹⣿⣿⣿⣿⣿⣿⣿⠯⢽⠿⢿⣛⣿⡯⢉⢙⣃⠐⣕⣫⣥⠈⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠀⡀⠀⠀⠀⣺⣴⠿⠉⠰⠈⠩⠃⠀⢅⠀⠁⠀⠉⠉⠛⣛⢯⠘⠛⠏⠍⠁⠀⠂⠀⠁⠀⠀⠻⠿⣿⣿⣿⢿⡏⡄⢚⠓⣠⣾⡚⠖⣯⣼⡛⠃⠘⠀⠀⠀⡀⡰⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣶⣶⣤⣴⣽⣭⣾⣷⣦⣲⣔⡉⠤⠲⠤⣠⠀⠀⢐⣄⠀⠀⠀⠀⠀⠀⠄⣄⣀⡀⠑⠒⡪⣦⣭⣿⣿⡿⠑⢧⢀⠀⠘⠝⡋⣥⠼⠔⠁⠀⠀⠀⠀⠀⠀⣷⣾⣽⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣶⣶⣵⣶⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣴⡋⢠⣤⣤⣴⣾⣼⣿⣾⣯⣿⡛⣽⠿⠛⡷⢙⠻⡾⠄⣠⢖⠙⠜⠁⠀⠀⠀⠀⠀⠀⠀⣀⣿⣯⣯⠀⠀⠉⠀⠉⢀⠄⠄⢴⢶⣬⣿⣿⣿⣿⣿⡿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⡬⣸⣷⠭⣴⣾⣿⣖⣼⣿⣿⣆⡈⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣟⣭⣿⣿⡁⠄⠀⠐⣖⣓⠲⣾⣾⣿⣿⣿⣿⡿⠟⠃⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⠫⠙⣿⣾⣿⣾⡞⠃⠀⠀⠀⠀⠀⠀⠰⡶⠈⠈⣫⣿⣿⣿⡯⠪⣥⣞⣻⣿⣾⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠛⠛⠑⢹⣶⡆⠀⣠⢀⢀⠀⢁⣀⠀⠠⠂⡚⣛⣭⡽⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⠿⠯⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄⢈⠈⢲⣿⣷⣧⣦⡷⣯⣮⣋⣻⣶⡶⠟⠉⣻⣿⣯⢻⠟⠙⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⠿⣣⣤⣬⣝⡻⣿⣿⣿⣶⣶⣾⣶⣷⣶⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⣛⠉⠛⠉⠙⠛⠋⠙⠛⠛⠁⠈⠀⠀⠈⠙⠋⠉⠉⠉⠀⠓⡗⠀⣰⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠂⠈⣿⣿⣿⣿⣏⣇⡀⢻⣿⣿⣿⣿⣿⣿⢛⣟⣻⣿⣿⣶⣶⣤⡤⣿⣿⣿⣿⣿⣇⠀⣴⣶⣶⣶⡶⣤⣤⣴⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠀⠀⠙⢿⣿⣿⣿⠛⠛⠁⠛⠛⠛⠛⠋⢿⡷⢸⣿⣿⣿⣿⣿⣦⣿⣷⣿⢿⠷⣸⣤⣵⣭⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠐⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠂⠛⠀⠀⠀⠘⠿⢿⣿⡀⠀⠀⠀⠈⠉⠉⠉⢹⡇⢀⣿⣿⣿⣿⣿⣿⡿⠻⠿⣋⣩⣭⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣽⡿⠁⠀⠀⠀⠀⠀⠀⢿⣮⣿⣿⡌⠃⣛⣯⣶⣼⣿⣿⣿⣿⣟⣿
⠀⠀⠀⠀⠀⠀⣀⢀⣀⡀⡀⠀⣀⣒⢳⣴⣲⣷⣠⣦⡄⡄⡈⠙⠀⢠⠠⣴⣦⣠⣤⣴⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠃⠀⠀⠀⠀⠻⣿⣿⣿⠿⣿⣿⣛⣿⣿⣿⣷⣾⣿⡷
⠀⠀⡀⠀⡂⠬⡽⡯⣽⣷⣧⣿⣾⣿⣿⣧⣿⣾⡻⣿⣿⣟⡁⣄⠀⢀⣸⡿⠈⠉⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡠⣠⣤⣤⣤⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠀⠀⠀⠀⣉⠙⣍⣻⣿⠻⣿⣿⡿⣻⡿⠬⠃⠙⠛⠻⠟⠉⠃⠼⡿⠷⠶⠲⡶⡶⠶⠶⣶⣶⣶⣶⣶⣦⠶⢶⣶⣶⣶⡶⠶⠿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⠆⡄⠲⠿⠛⠀⢠⡄⠂⠛⠀⣿⣿⡆⣿⣿⡇⣸⣿⡟⣿⣿⣿⣿⢸⣿⣿⣿⣷⣎⣿⣿⣳⣿⡿⣿⣿⡛⣷⣿⢿⣿⣮⢻⣿⣿⢿⣿⡞⢯⣿⡿⣿⣷⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠰⠀⠈⠀⠀⠀⠀⠀⠀⣈⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣂⢸⣿⣿⣸⣿⡿⣴⣿⣙⣛⢣⣿⣿⢳⣿⣿⢸⣿⣿⢘⣿⣻⣼⣿⠏⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⣿⣿⢿⣿⣿⣿⠃⣿⣿⡿⢿⢸⣿⣿⢻⣿⣶⢩⣿⣿⣡⣿⣿⠯⣾⣿⣿⢸⣿⣿⢸⣯⣿⢻⣿⣧⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣧⣭⢸⣿⣿⣼⣿⣿⣸⡿⣶⣿⣿⣥⣴⠈⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⡿⢸⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣛⡛⣤⣿⣻⣫⣤⣿⣿⣿⣿⣼⣿⣻⣿⣿⣵⣿⣟⣛⣿⣿⣿⣻⢾⣮⣿⣟⣿⣷⣶⣽⣟⣛⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠲⣶⠎⢶⠆⠰⠶⠶⠶⠀⣤⣤⣤⣤⣀⡀⠀⠙⠛⡋⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠤⣶⣶⣶⣤⠷⣶⣤⣻⣶⣾⣭⣭⣶⣴⣾⣷⣿⣷⣿⣶⡶⡷⣾⣿⣗⣛⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⢀⠄⠀⠀⠄⡁⢡⡄⠀⠀⠀⠀⠀⢀⢀⠀⠀⡠⢤⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢂⠻⣿⠟⡃⠀⠋⠛⠛⠙⠺⡛⠛⠿⣟⠿⠿⣿⡟⠿⠛⠋⡘⠻⠂⢈⣁⣤⣶⣿⣿⣿⣿⣿⣿⢏⣁⣴⣦⣶⣿⣿⣴⢀⣻⣶⣶⡥⠀⢰⣄⣦⣾⣶⣿⣷⣿⣿⣿⣿⣷⣧⣷⣾⣥⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀
⠏⠍⢚⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢨⣤⣵⣆⣠⣄⣢⣰⡄⣰⣤⣬⣽⣾⣯⣿⣿⣿⡟⠛⠒⠃⣀⢉⣿⣿⣿⣿⡷⣷⣿⡿⣿⣽⣿⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⢀⣀⢀⣸⣆⣤⣤⣖⠀
⠀⢤⣵⡆⠀⠀⠀⠀⠀⠀⠀⣤⣽⢵⣿⣿⣳⣿⣿⣽⡦⣖⣾⣿⣿⣿⣿⣿⣿⣿⣁⣤⡄⢐⣲⣼⣿⣿⣿⣿⣿⡏⠟⢋⣻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡿⡋⠌⢅⢬⣼⠻⠗⠻⠿⠉⠉⠯⠠
⠚⠉⠃⠀⠠⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣛⣿⣧⣤⣻⣿⣿⣿⣿⣿⡿⠛⠛⠛⠫⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⣷⣶⠖⣿⢿⣿⣿⡷⣯⣿⣿⣿⡿⠿⣿⣿⣿⣽⣻⠮⠙⠹⡿⠦⠌⠁⠐⠓⠋⠀⠀⠂⠀⠈⠀⠐
⠀⠴⢶⡤⠀⠀⠀⢀⣴⣿⣿⣿⣿⣯⣿⣿⣿⣿⠿⣿⣿⣿⣿⣯⣽⣍⣤⣤⣤⣴⣶⠚⣯⣽⣿⣿⣿⣿⣿⣿⣿⣇⢠⣕⣃⢃⣸⣿⡟⣿⡗⢛⣋⡹⡦⡶⠒⠻⡄⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠈⠀⠂⠀⠈⡐⢀⣾⣿⡿⢿⣿⣭⣹⣿⣿⠛⠋⠸⣿⢿⣿⣿⢿⣿⣿⣯⣍⡋⢻⢳⠾⠚⢸⣿⣿⣿⣿⣿⣿⣿⠯⢽⠿⢿⣛⣿⡯⠉⢙⣃⠀⣕⡋⢥⠈⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠀⡀⠀⠀⠀⣺⣴⠿⠉⠰⠈⠩⠃⠀⢁⠀⠁⠀⠉⠉⠙⣛⢯⠘⠛⠏⠉⠁⠀⠂⠀⠁⠀⠀⠿⠿⣿⣿⣿⢿⡏⡄⣘⠂⣰⣾⡚⠖⣯⣼⡛⠂⠘⠀⠀⠀⠀⡠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣶⣶⣤⣴⣽⣭⣾⣷⣦⣰⣔⠉⠤⠲⠤⣠⠀⠀⢐⣄⠀⠀⠀⠀⠀⠀⠄⣄⣀⡀⠁⠒⠪⣦⣭⣿⣿⡿⠙⢧⢀⠀⠘⠙⡻⣥⠬⠔⠁⠀⠀⠀⠀⠀⠀⣳⣾⣽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⣶⣿⣶⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣴⡋⢀⣤⣤⣴⣾⣼⣿⣾⣯⣿⡛⣽⠾⠛⡷⢘⠻⡾⠄⣠⢄⡙⠜⠃⠀⠀⠀⠀⠀⠀⠀⣀⣾⣯⣯⠀⠀⠉⠀⠉⢀⠀⠄⢰⢾⣽⣿⣿⣿⣿⣿⡿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⡬⣸⣿⠭⣴⣾⣟⣶⣾⣿⣿⣇⡈⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣛⣭⣿⣿⡡⠀⠀⠐⣖⣒⢶⣾⣾⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⠫⠙⣿⣾⣿⣾⡾⠃⠀⠀⠀⠀⠀⠀⠰⡲⠊⠈⣋⣯⣿⣯⡮⠊⣥⣎⣿⣿⣾⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠛⠛⠑⢻⣶⡄⠀⣠⣀⢠⡀⢁⣀⠀⠠⠂⡚⣛⣭⡽⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⠿⠯⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⢈⠈⢲⣿⣧⣣⣶⡗⡶⣮⣫⣳⣶⡶⠟⠋⣻⢿⣯⢻⠟⠙⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠟⠿⣣⣤⣤⣝⡻⣿⣿⣿⣶⣶⣾⣶⣷⣶⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⣛⠉⠛⠋⠙⠛⠋⠉⠛⠛⠁⠈⠀⠀⠈⠙⠋⠉⠉⠉⠀⠓⡗⠀⣰⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠂⢈⣿⣿⣿⣿⣏⣆⠀⠿⣿⣿⣿⣿⣿⣿⢛⡟⣻⣿⣿⣶⣶⣤⡤⣿⣿⣿⣿⣿⣇⠀⣴⣶⣶⣶⣶⣤⣤⣴⡠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠀⠀⠘⢿⣿⣿⣿⠛⠛⠉⠛⠛⠛⠛⠋⢿⡷⢸⣿⣿⣿⣿⣻⣦⣽⣷⣿⣿⠷⣺⣤⣵⣭⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠐⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠚⠛⠀⠀⠀⠸⢿⢿⣿⡀⠀⠀⠀⠈⠉⠉⠉⢹⡇⢸⣿⣿⣿⣿⣿⣿⡿⠛⠿⣯⣩⣭⢽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣻⣽⡿⠁⠀⠀⠀⠀⠀⠀⢿⣾⣿⡿⡌⠊⢛⣯⣶⣼⣿⣿⣿⣿⣟⣿
⠀⠀⠀⠂⠀⠀⣀⢀⢀⣀⡀⠀⣀⡒⢲⣴⣺⣷⣠⣦⡄⡄⡈⠙⠀⢠⠠⣴⣦⣠⣤⣴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠂⠀⠀⠀⠀⠻⣿⣿⠿⠿⣿⣟⣛⣿⣿⣿⣷⣿⣿⡷
⠀⠀⡀⠀⡂⠤⣽⡯⣵⣷⣧⣿⣾⣟⣿⣧⣯⣿⡻⣿⣿⣟⡁⣄⠀⢀⣸⡿⠉⠈⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡡⣠⣤⣤⣤⣼⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠀⠀⡀⠀⣉⠽⣍⣺⣿⠻⣿⣿⡟⣫⡿⠬⠅⠛⠛⠻⠟⠉⠃⠼⡿⠷⠴⠲⠶⠶⠶⠶⢶⣶⣶⣶⣶⣦⠶⢶⣶⣶⣶⡶⠿⠿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⠄⡄⠲⠿⠋⠀⢠⢄⢊⠛⠀⣿⣿⡆⣿⣿⡇⣸⣿⡟⣿⣿⣿⣿⢸⣿⣿⣿⣷⣎⣿⣿⣱⣿⡿⣿⣿⡛⣷⣿⢿⣿⣮⢻⣿⣿⢿⣿⡞⢿⣿⡿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠴⠀⠈⠀⠀⠀⠀⠀⠀⢈⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣂⢸⣿⣿⣸⣿⡿⣴⣿⣙⣛⢣⣿⣿⢳⣿⣿⢸⣿⣿⢘⣿⣻⣼⣿⠏⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⣿⣿⢿⣿⣿⣿⠃⣿⣿⡿⣿⢸⣿⣿⢻⣿⣶⢩⣿⣿⣡⣿⣿⠯⣾⣿⣿⢸⣿⣿⢸⣯⣿⢻⣿⣧⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣧⣭⢸⣿⣿⣼⣿⣿⣸⡿⣳⣿⣿⣥⣤⠈⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⡿⢸⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣛⡛⣠⣟⣻⣫⣤⣿⣿⣿⣿⣼⣿⣻⣿⣿⣵⣿⣟⣛⣿⣿⣿⣻⢾⣮⣿⣟⣿⣷⣶⣽⣿⣛⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠲⣶⠮⢶⠦⠰⠶⠶⠶⠀⣤⣤⣄⣤⡀⠀⠀⠙⣛⡋⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠤⣶⣶⣶⣤⢷⣶⣤⣻⣶⣾⣭⣭⣶⣴⣾⣷⣿⣷⣿⣶⡶⡷⣾⣿⣗⣟⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⢀⠀⠀⠀⠄⣁⢡⡄⠀⠀⠀⠀⢀⢀⣀⠀⠀⡤⢤⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢂⠻⣿⠟⡓⠀⠛⠛⠛⠙⠺⡛⠛⠿⣟⠿⠿⣿⡟⠿⠛⠋⡘⠻⠂⢈⣁⣤⣶⣿⣿⣿⣿⡿⣿⣏⣁⣴⣦⣶⣿⣿⣴⢂⣼⣾⣶⣤⠀⠰⣎⣶⣴⣶⣿⣿⣿⣿⣿⣿⣿⣧⣿⣾⣧⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀
⠏⠍⢚⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢨⣤⣥⣆⣠⣄⣢⣰⡄⣔⣤⣬⣾⣾⣿⣿⣿⣿⡟⠛⠐⢁⣀⢉⣿⣿⣿⣿⡷⣷⣿⡿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⢀⣀⢀⣹⣦⣤⣤⣒⠀
⠀⢤⣵⡆⠀⠀⠀⠀⠀⠀⠀⣠⣽⢵⣿⣿⣳⣿⣿⣽⡦⣒⣾⣿⣿⣿⣿⣿⣿⣿⣁⣤⡄⢐⣲⣼⣿⣿⣿⣿⣿⡏⠟⣋⣻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡿⡋⠉⢅⢬⢜⠻⠗⠻⠻⠉⠉⠯⠠
⠚⠉⠃⠂⠠⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣟⣿⣧⣨⣻⣿⣿⣿⣿⣷⡿⠛⠛⠛⠫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⢷⣶⠖⣿⢿⣿⣿⡷⣯⣿⣿⣿⡿⠿⣟⣿⣿⢽⣿⠮⠙⠹⡿⠦⠌⠁⠘⠓⠋⠀⠀⠆⠀⠀⠀⠒
⠀⠴⣦⡴⠀⠀⠀⢀⣴⣿⣿⣿⣿⣯⣿⣿⣿⣿⠿⣿⣿⣿⣿⣯⣽⣍⣤⣤⣤⣴⣶⠚⣯⢽⣿⣿⣿⣿⣿⣿⣿⣇⢠⣕⣋⣃⣰⣿⡟⣿⡗⢛⣫⡽⡧⡶⠖⠻⣄⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠈⠀⠂⠀⠈⡐⢀⣾⣿⣿⢿⣿⣯⣹⣿⣿⠛⠋⠸⣿⢿⣿⣿⢿⣿⣿⣿⡍⡋⢻⢳⠞⠚⢸⣿⣿⣿⣿⣿⣿⣿⠯⢽⠿⢿⣛⣟⡯⣁⢙⣃⠀⢕⡫⣤⠈⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠀⡀⠀⠀⠀⣺⢴⠿⠉⠱⠈⠩⠃⠀⢅⠀⠀⠀⠉⠉⠛⣛⢯⠘⠛⠏⠍⠁⠀⠈⠀⠁⠀⠀⠻⠿⣿⣿⣿⢿⡏⡄⢓⡂⣰⣾⡚⠖⣯⣴⡛⠂⠐⠁⠀⠀⡀⡰⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣶⣶⣤⣴⣽⣭⣾⣷⣤⣲⣐⠉⠤⠲⠤⣠⠀⠀⢐⣄⠀⠀⠀⠀⠀⠀⠄⣄⣀⡀⡁⠒⠪⣦⣭⣿⣿⡿⠑⢧⢀⠀⠘⠙⡛⣥⣬⠔⠁⠀⠀⠀⠀⠀⠀⣻⣿⣽⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⣶⣾⣶⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣴⡊⣠⣤⣄⣴⣾⣽⣿⣾⣯⢿⡓⣹⠾⠛⡷⢙⠻⡾⠄⡠⣄⡛⠜⠃⠀⠀⠀⠀⠀⠀⠀⣀⣾⣯⣿⠀⠀⠈⠀⠉⢀⠀⠀⢐⢾⣿⣷⣿⣿⣿⣿⡿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⣬⢸⢧⠭⣴⣾⣟⣖⢼⣿⣿⣆⡈⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣝⣭⣿⣿⡁⠄⠔⠐⣖⢒⢶⣶⣾⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⠫⠙⣿⣾⢿⣾⡾⠁⠀⠀⠀⠀⠀⠀⠰⡶⠈⢈⣋⣿⣿⣯⡮⠊⣥⣾⣻⣯⣾⣿⣿⣿⣿⠿⠏⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠛⠛⠑⢽⣧⡄⠀⣠⣀⢀⠀⢁⣄⠁⠠⠂⡛⣛⣭⡽⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⠿⠯⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⢘⠀⢻⣿⣧⣲⣆⡞⣶⣮⣫⣳⣶⡶⠟⠋⣻⢿⣯⠻⠿⠙⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠿⣣⣤⣬⣝⡻⣿⣿⣿⣶⣶⣾⣶⣷⣶⣠⣀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⣻⠉⠛⠉⠙⠛⠋⠙⠛⠛⠁⠈⠀⠀⠈⠙⠋⠉⠉⠉⠀⠓⡗⢀⣰⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠂⢈⣿⣿⣿⣿⣏⣆⠀⢻⣿⣿⣿⣿⣿⣿⢛⡟⣻⣿⣿⣶⣶⣤⡤⣿⣿⣿⣿⣿⣇⠀⣶⣶⣶⣶⣶⣤⣤⢴⡠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠀⠀⠘⢿⣿⣿⣿⠛⠋⠉⠛⠛⠛⠛⠋⢿⡷⢸⣿⣿⣿⣿⣻⡦⣽⣿⣿⣿⡷⣚⣤⣴⣭⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠐⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠈⠋⠛⠒⠻⠀⠀⠀⠸⠿⢿⣿⡀⠀⠀⠀⠈⠉⠉⠉⢹⡇⢸⣿⣿⣿⣿⣿⣿⡿⠛⠿⣯⣩⣭⢽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣻⣽⡿⠁⠀⠀⠀⠀⠀⠀⢿⣾⣿⣿⡌⠇⢛⣯⣶⣼⣿⣿⣿⣿⣟⣿
⠀⠀⠀⠀⠀⠀⢀⢀⣀⣄⡀⠀⣄⣒⢲⣲⣲⣷⣢⣦⡄⡄⡈⠙⠀⢠⠠⣴⣦⣠⣤⣴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠂⠀⠀⠀⠀⠻⣿⣿⠿⢿⣿⣿⣛⣿⣿⣿⣷⣾⣿⡷
⠀⠀⡀⢀⡢⠬⣽⡯⣽⣷⣦⣿⣿⣿⣿⣧⣧⣾⡿⣿⣿⣟⡁⣄⠀⢀⣸⡿⠀⠈⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡡⣠⣤⣤⣤⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠀⠀⠂⠀⣉⠙⣉⣺⣿⢻⣿⣿⡿⣿⠿⠾⠃⠙⠛⠻⠟⠉⠃⠸⡿⠷⠶⠲⠶⣶⠶⠶⣶⣶⣶⣶⣶⣦⠶⢶⣶⣶⣶⡶⠾⠿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⠆⡄⢲⠿⠋⠀⠠⢄⠊⠛⠀⣿⣿⡆⣿⣿⡇⣸⣿⡟⣿⣿⣿⣿⢸⣿⣿⣿⣷⣎⣿⣿⣱⣿⡿⣿⣿⡛⣷⣿⢿⣿⣮⢻⣿⣿⢿⣿⡞⢯⣿⡿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠴⠀⠈⠀⠀⠀⠐⠀⠀⣈⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣂⢸⣿⣿⣸⣿⡿⣶⣷⣙⣛⢣⣿⣿⢣⣿⣿⢸⣿⣿⢘⣟⣻⣼⣿⠏⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⣿⣿⢿⣿⣿⣿⠃⣿⣿⡿⢿⢸⣿⣿⢻⣿⣷⢩⣽⣿⣡⣿⣿⠯⣾⣿⣿⢸⣿⣿⢸⣯⣿⢻⣿⣧⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣧⣭⢸⣿⣿⣼⣿⣿⣸⡿⣲⣿⣿⣥⣴⠈⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⡿⢸⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣛⡛⣤⣟⣻⣫⣤⣿⣿⣿⣿⣼⣿⣻⣿⣿⣵⣿⣟⣛⣿⣿⣿⣻⢾⣮⣿⣟⣿⣷⣶⣽⣿⣛⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠲⣶⠎⢶⠆⠰⠶⠶⠶⠀⣤⣤⣤⣤⣀⠀⠀⠙⠓⡋⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠤⣶⣶⣶⣤⢷⣶⣤⣻⣶⣾⣭⣭⣶⣴⣾⣷⣿⣷⣿⣶⡶⠶⣾⣿⣖⣛⣿⣿⣾⣿⣶⣿⣿⣿⣿⣿⡿⠛⠁⢀⠄⠀⠀⠀⡀⢡⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⡠⠤⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢂⠻⣿⠟⡃⠀⠋⠉⠛⠙⠚⡛⠛⠿⣟⠿⠿⣟⡟⠿⠛⠋⡘⠻⠂⢈⣁⣤⣶⣿⣿⣿⣿⡿⣿⢏⣁⣴⣦⣶⣿⣧⣴⢀⣻⣶⣖⡤⠀⠰⣄⣦⣾⣶⣿⣷⣿⣿⣿⣿⣷⣧⣷⣾⣥⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀
⠏⠍⢚⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢨⣤⣠⣆⣠⣄⣢⣰⡄⣐⣤⣬⣶⣾⣿⣿⣿⣿⡟⠛⠐⠁⣀⢉⣿⣿⣿⣿⡷⣷⣿⡿⣿⣽⣿⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⢀⣀⢀⣨⣄⣤⣤⣒⠀
⠀⢤⣵⡆⠀⠀⠀⠀⠀⠀⠀⣠⣽⢴⣿⣻⣳⣿⣿⣽⡤⣒⣾⣿⣿⣿⣿⣻⣿⣿⣁⣤⡄⢐⣲⣼⣿⣿⣿⣿⣿⡏⠛⠋⣛⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡿⡋⠌⢅⢨⣜⠻⠗⠻⠻⠉⠉⠏⠠
⠚⠉⠃⠀⠠⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣛⣿⣧⣠⣹⣿⣿⣿⣿⣷⡿⠛⠛⠛⠫⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⣷⣶⠖⣿⢿⣿⣿⡷⣯⣿⣿⣿⠿⠿⣟⣿⣿⢽⣻⠮⠙⠹⡿⠦⠈⠁⠐⠓⠋⠀⠀⠂⠀⠀⠀⠐
⠀⠴⢦⡤⠀⠀⠀⢀⣴⣿⣿⣿⣿⣯⣿⣿⣿⣿⠿⣿⣿⣿⣿⣯⣽⣍⣤⣤⣤⣴⣶⢚⣿⢽⣿⣿⣿⣿⣿⣿⣿⣇⢠⣝⣋⢃⣸⣿⡟⣿⡗⢛⣋⣽⡧⡶⠲⠹⡄⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠈⠀⠂⠀⠈⡐⢀⣾⣿⡿⢯⣿⣭⣹⣿⣿⠛⠋⠘⣿⢿⣿⣿⢿⣿⣿⣿⣍⠉⢻⢳⠾⠚⢸⣿⣿⣿⣿⣿⣿⣿⠯⢽⠿⢿⣛⣿⡯⡉⢙⣃⠐⣕⡏⣤⠈⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠀⡀⠀⠀⠀⢺⣴⠿⠉⠠⠈⠩⠁⠀⢁⠀⠀⠀⠉⠈⠛⣛⢯⠘⠛⠏⠉⠁⠀⠂⠀⠀⠀⠀⠻⠿⣿⣿⣿⢿⡏⡄⢓⡂⣰⣾⡚⠖⣯⣼⡛⠂⠐⠀⠀⠀⠀⡰⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣶⣶⣤⣴⣽⣭⣾⣧⣤⣰⣔⠉⠤⠲⠤⣠⠀⠀⢀⣌⠀⠀⠀⠀⡀⠀⠄⣀⣀⡀⠑⠒⡪⣦⣭⣿⣿⡿⠙⢧⢀⠀⠐⠙⡋⢥⢼⠔⠁⠀⠀⠀⠀⠀⠀⣳⣿⣽⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣶⣴⣵⣶⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣴⡈⢀⣤⣄⣴⣾⣼⣿⣾⣯⢿⡊⣳⠿⠛⡷⢙⠻⡾⠄⡠⣔⠙⠜⠁⠀⠀⠀⠀⠀⠀⠀⣀⣾⣯⣯⠀⠀⠈⠀⠉⢀⠀⠀⢐⢾⣸⣷⣿⣿⣿⣿⡿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⡬⣸⣧⠭⡴⣾⣟⣷⣾⣿⣿⣆⡈⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣛⣭⣿⣿⡁⠀⠔⠐⣖⢓⢶⣾⣾⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⠫⠙⣿⣾⢿⣾⡞⠁⠀⠀⠀⠀⠀⠀⠰⡲⠊⡈⣋⣯⣿⣯⡯⠈⣥⣎⣿⣾⣾⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠛⠛⠑⢽⣦⡄⠀⡠⢀⢀⠀⢁⣀⠀⠠⠂⡚⣛⣭⡽⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⡿⠯⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⢘⠀⢾⣿⣧⣳⣆⡶⣶⣮⣫⣳⣶⡶⠟⠋⣻⢿⣯⠻⠟⠙⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠟⣃⣤⣬⣝⡻⣿⣿⣿⣶⣶⣶⣶⣷⣶⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⣛⠉⠛⠉⠙⠛⠋⠉⠛⠛⠁⠈⠀⠀⠈⠙⠋⠉⠉⠉⠀⠓⡗⢀⣰⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠚⠂⢈⣿⣿⣿⣿⣏⣆⠀⢿⣿⣿⣿⣿⣿⣿⢛⡛⣻⣿⣿⣶⣶⣤⡤⣿⣿⣿⣿⣿⣇⠀⠶⣶⣶⣶⡶⣤⡤⢴⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠀⠀⠘⢿⣿⣿⣿⠛⠋⠉⠛⠛⠛⠛⠋⢿⡷⢸⣿⣿⣿⣿⣻⡦⣽⣿⣿⣿⠷⣚⣤⣥⣥⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠈⠋⠛⠚⠛⠀⠀⠀⠸⠿⢿⣿⡀⠀⠀⠀⠈⠉⠉⠉⢸⡇⢸⣿⣿⣿⣿⣿⣿⡿⠛⠿⣫⣩⣭⢽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣻⣽⡿⠁⠀⠀⠀⠀⠀⠀⢿⣾⣿⡿⡄⠂⢛⣯⣶⣼⣿⣿⣿⣿⣟⣿
⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⡀⠀⣀⡂⢲⣰⣲⣷⣠⢦⡄⡄⡈⠙⠀⢠⠠⣴⢦⣠⣄⣴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠂⠀⠀⠀⠀⠻⣿⣿⠿⠿⣿⣿⣛⣻⣿⣿⣷⣾⣿⡶
⠀⠀⡀⠀⡂⠤⣽⡯⣵⣷⣧⣷⣾⡟⣿⣧⣯⣾⡻⣿⣿⣟⡁⣄⠀⠀⣸⡿⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡡⣠⣤⣤⣤⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠀⠀⠀⠀⣉⠹⢍⣺⣯⠻⣿⣿⡟⣿⡿⠼⠃⠙⠛⠻⠏⠉⠁⢸⡿⠷⠶⠲⠶⡶⠶⠶⢶⣶⣶⣶⣶⣦⠶⢶⣶⣶⣶⡶⠾⠿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⠄⣁⠲⠿⠉⠀⢠⠄⠊⠛⠀⣿⣿⡆⣿⣿⡇⣸⣿⡟⣿⣿⣿⣿⢸⣿⣿⣿⣷⣎⣿⣿⣳⣿⡿⣿⣿⡛⣷⣿⢿⣿⣮⢹⣿⣿⢿⣿⡞⢫⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⠴⠀⠈⠀⠀⠀⠀⠀⠀⡈⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣂⢸⣿⣿⣸⣿⡿⣴⣿⣘⣛⢣⣿⣿⢣⣿⣿⢸⣿⣿⢘⣿⣿⣼⣿⠏⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⣿⣿⢿⣿⣿⣿⠃⣿⣿⡿⢿⢸⣿⣿⢻⣿⣷⢩⣿⣿⣣⣿⣿⠯⣾⣿⣿⢸⣿⣿⢸⣯⣿⢻⣿⣧⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣧⣭⢸⣿⣿⣼⣿⣿⣸⡿⣳⣿⣿⣥⣴⠈⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⡿⢸⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣛⡋⣤⣟⣻⣫⣤⣿⣿⣿⣿⣼⣿⣻⣿⣿⣵⣿⣟⣛⣿⣿⣟⣻⢾⣮⣿⣟⣿⣷⣶⣽⣿⣻⣿⣿⣿⣽⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠲⣶⠎⢶⠆⠰⠶⠶⠶⠀⣤⣤⣤⣤⣀⠀⠀⡙⠛⡛⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠤⣶⣶⣶⣤⢷⣶⣤⣻⣶⣾⣭⣭⣶⣴⣾⣷⣿⣷⣿⣶⡶⠶⣾⣿⣗⣟⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⡿⠛⠁⢀⠀⠀⠀⠄⣁⢡⡀⠀⠀⠀⠀⢀⢀⣀⠀⠀⡤⢤⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢂⠻⣿⠟⡃⠀⠛⠋⠛⠙⠺⡛⠛⠿⣟⠿⠿⣟⡟⠻⠛⠋⡘⠻⠂⢈⣁⣤⣶⣿⣿⣿⣿⡿⣿⣏⣁⣴⣦⣶⣿⣿⣴⢂⣸⣾⣖⣤⠀⠰⣎⣦⣴⣶⣿⣿⣿⣿⣿⣿⣿⣧⣟⣾⣧⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀
⠏⠍⢚⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢨⣤⣤⣆⣠⣄⣠⣰⠆⣔⣤⣬⣴⣾⣿⣿⣿⣿⡟⠛⠐⢁⣀⢉⣿⣿⣿⣿⡷⣷⣿⡿⣿⣽⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⢀⣀⢀⣹⣦⣤⣤⣐⠀
⠀⢤⣵⡆⠀⠀⠀⠀⠀⠀⠀⣤⣽⣴⣿⣿⣳⣿⣿⣿⡤⣖⣾⣾⣿⣿⣿⣿⣿⣿⣁⣤⡄⢐⣲⣼⣿⣿⣿⣿⣿⡏⠛⢋⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡿⡋⠉⢅⢬⢜⠻⠗⠻⠻⠉⠉⠯⠨
⠚⠉⠃⠀⠠⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣛⣿⣧⣨⣹⣿⣿⣿⣿⣷⡿⠛⠛⠛⠫⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⢶⣶⠖⣿⢿⣿⣿⡷⣧⣿⣿⣿⡿⠿⣟⣿⣿⢽⣻⠮⠙⠹⡿⠦⠌⠁⠘⠓⠋⠀⠀⠂⠀⠀⠀⠐
⠀⠴⣶⡤⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣯⣽⣭⣤⣤⣤⣴⣶⠚⣿⢿⣿⣿⣿⣿⣿⣿⣿⣇⢠⣝⣃⢃⣰⣿⡟⣿⡇⢛⣋⡽⡧⡶⠒⠹⡄⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠈⠀⠂⠀⠈⡐⢀⣾⣿⡿⢯⣿⣭⣹⣿⣿⠛⠋⠸⣿⢿⣿⣿⢿⣿⣿⣿⡍⡋⢻⢳⠾⠘⢸⣿⣿⣿⣿⣿⣿⣿⠯⢽⠿⣟⣻⣟⠯⠉⢙⣃⠐⣕⡏⣤⠈⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠀⡀⠀⠀⠀⢺⢴⠿⠉⠢⠈⠉⠁⠀⢅⠀⠀⠀⠉⠈⠛⣛⢯⠘⠛⠏⠉⠁⠀⠂⠀⠁⠀⠀⠿⠿⣿⣿⣿⢿⡏⡄⢑⡂⣰⣾⡚⠖⣯⣼⡛⠂⠀⠁⠀⠀⡀⡰⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣶⣶⣤⣴⣽⣭⣾⣷⣤⣲⣔⠉⠤⠲⠤⣠⠀⠀⢐⣄⠀⠀⠀⠀⡀⠀⠄⣄⣀⡀⡁⠒⠪⣦⣭⣿⣿⡿⠑⠧⢀⠀⠐⠙⡋⢥⣬⠔⠁⠀⠀⠀⠀⠀⠰⣳⣾⣽⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣶⣴⣷⣶⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣴⡊⣀⣠⣄⣴⣾⣼⣿⣾⣯⣿⡊⣵⠿⠛⡷⢘⠻⡾⠄⡠⣖⡙⠜⠁⠀⠀⠀⠀⠀⠀⠀⣀⣾⣯⣏⠄⠀⠉⠀⠉⢀⠀⠀⢴⢾⣽⣷⣿⣿⣿⣿⡿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⡬⢸⣷⠭⣴⣾⣟⣶⢼⣿⣿⣇⡈⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣙⣭⣿⣿⡀⠀⠔⠐⣖⢒⢲⣾⣾⣿⣿⣿⣽⣿⠟⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⠫⠙⣿⣾⣿⣾⡾⠁⠀⠀⠀⠀⠀⠀⠰⡲⠊⢈⣋⣯⣿⣯⡯⠊⣥⣞⣿⣾⣾⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠛⠛⠑⢹⣦⡄⠀⣠⠀⢀⡀⢁⣀⠀⠨⠂⡋⣛⣭⡽⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⡿⠯⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⢘⠀⢯⣿⣧⣣⣆⡞⣶⣦⣛⣳⣶⡶⠟⠋⣻⢿⣯⠻⠟⠙⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠿⣣⣤⣬⣝⡻⣿⣿⣿⣶⣶⣾⣶⣷⣶⣠⣀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⣛⠉⠛⠉⠙⠛⠋⠉⠛⠛⠁⠈⠀⠀⠈⠙⠋⠉⠉⠉⠀⠓⡗⠀⣰⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠘⠂⢈⣿⣿⣿⣿⣏⣆⠀⢿⣿⣿⣿⣿⣿⣿⢛⡟⣻⣿⣿⣶⣶⣤⡤⣿⣿⣿⣿⣿⣇⠀⢶⣶⣶⣶⣶⣤⡤⣤⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠀⠀⠘⢿⣿⣿⣿⠛⠋⠉⠛⠛⠛⠛⠋⢿⡷⢸⣿⣿⣿⣿⣻⡦⣽⣿⣿⣿⠷⣺⣤⣤⣥⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠐⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠚⠟⠀⠀⠀⠘⠿⢿⣿⡀⠀⠀⠀⠈⠉⠉⠉⢹⠇⢸⣿⣿⣿⣿⣿⣿⡿⠛⠿⣫⣩⣭⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣻⣽⡿⠁⠀⠀⠀⠀⠀⠀⢿⣾⣿⡿⡄⠆⢛⣯⣶⣼⣿⣿⣿⣿⣟⣿
⠀⠀⠀⠀⠀⠀⢀⠄⣀⣀⡀⠀⣀⡠⢲⣴⣲⣷⣢⣦⡄⡄⡈⠙⠀⢠⠠⣴⣦⣠⣤⣴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠂⠀⠀⠀⠀⠻⣿⣿⠿⢿⣿⣿⣛⣿⣿⣿⣷⣾⣿⡷
⠀⠀⡀⠀⡂⠤⡽⡯⣽⣶⣧⣿⣾⣟⣿⣧⣿⣾⡻⣿⣿⣟⡁⣄⠀⢀⣸⡿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡡⣠⣤⣤⣤⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠀⠀⡀⠀⢉⠉⣍⣺⣯⠺⣿⣿⡿⣻⡿⠌⠃⠙⠛⠻⠏⠉⠃⢸⡿⠷⠶⠲⣶⡶⠶⠶⢶⣶⣶⣶⣶⣦⠶⢶⣶⣶⣶⡶⠶⠿⣿⣷⣿⠿⠿⣿⣿⣿⣿⣿⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⠄⡅⠲⠿⠋⠈⠠⠄⢋⠛⠀⣿⣿⡆⣿⣿⡇⣸⣿⡟⣿⣿⣿⣿⢸⣿⣿⣿⣷⣎⣿⣿⣳⣿⡿⣿⣿⡛⣷⣿⢿⣿⣮⢻⣿⣿⢿⣿⡞⢯⣿⡿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠴⠀⠈⠀⠀⠀⠐⠀⠀⣈⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣂⢸⣿⣿⣸⣿⡿⣴⣷⣙⣛⢣⣿⣿⢣⣿⣿⢸⣿⣿⢘⣟⣿⣼⣿⠏⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⣿⣿⢿⣿⣿⣿⠃⣿⣿⡿⢿⢸⣿⣿⢻⣿⣷⢩⣿⣿⣡⣿⣿⠯⣾⣿⣿⢸⣿⣿⢸⣯⣿⢻⣿⣧⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣧⣭⢸⣿⣿⣼⣿⣿⣸⡿⢳⣿⣿⣥⣤⠌⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⡿⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣛⡋⣠⣟⣻⣋⣤⣿⣿⣿⣿⣼⣿⣻⣿⣿⣵⣿⣟⣛⣿⣿⣿⣻⣾⣮⣿⣟⣿⣷⣶⣽⣿⣛⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠲⣶⠮⢶⠄⠰⠶⠶⠶⠀⣤⣤⣤⣤⡀⠀⠀⠙⡙⡋⢉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡤⣶⣶⣾⣤⠶⣶⣤⣳⣶⣾⣯⣭⣷⣼⣾⣾⣿⣷⣾⣾⡶⠶⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢁⢀⠄⠀⠀⠄⣀⢱⠄⠀⠀⠀⠀⢀⠄⡀⠀⠀⢀⣤⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠿⣿⠟⠃⠀⠃⠉⠛⠙⠚⡛⠛⠟⣟⡿⠿⣿⢟⠟⠛⠋⡙⠻⠂⢉⣁⣠⣶⣿⣿⣿⣿⣿⣿⢏⣁⣴⣶⣶⣿⣯⣴⢂⣫⣷⣖⡥⠀⠐⣎⣦⣮⣶⣿⣷⣿⣿⣽⣿⣿⣷⣶⣾⣤⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀
⠏⠌⢚⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢠⣤⣥⣆⣤⣄⣂⣰⣆⣴⣤⣨⣾⣾⣿⣿⣿⣿⠟⠛⠐⠁⣀⢉⣿⣿⣿⣿⡷⣷⣿⡿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⢀⣀⢀⣹⣄⣤⣤⡐⠀
⠀⢤⣴⡆⠀⠀⠀⠀⠀⠀⠀⣠⣽⣴⣿⣿⣷⣿⣿⣿⡦⣖⣾⣿⣿⣿⣿⣿⣿⣿⣁⣤⡄⢐⣲⣾⣿⣿⣿⣿⣿⡏⠟⣋⣛⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⡹⠋⠀⠄⣤⣜⠫⠗⠻⠻⠉⠉⠯⠠
⠚⠋⠁⠀⠠⠀⠀⠀⠀⠀⣸⣿⣷⣿⣿⣿⣿⣟⣿⣧⣤⣹⣿⣿⣿⣿⣷⡿⠛⠛⠛⠫⣾⣿⣿⣿⣿⣿⣿⣿⣿⡧⣶⣶⠖⣿⢿⣿⣽⣧⣯⣿⣿⣿⠿⠿⣿⣿⣿⣽⣻⠯⠹⠹⠽⠦⠊⠁⠈⠓⠋⠀⠀⠂⠀⠀⠀⠐
⠀⠴⢴⡤⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣯⣿⣭⣤⣤⣤⣰⣶⠺⣯⢿⣿⣿⣿⣿⣿⣿⣿⣇⢠⣝⣋⢃⣸⣿⡟⣿⡟⢛⣫⣽⡢⡶⠲⠿⡕⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠈⠀⠃⠀⠈⡀⠀⣾⣿⣿⣿⣽⣯⣹⣿⣿⠛⠋⠸⣿⢿⣿⣿⢿⣿⣿⣿⡍⠋⢻⢿⠾⠝⢼⣿⣿⣿⣿⣿⣿⣿⢯⢽⢿⢿⣛⣿⡯⡋⣙⡣⠐⢕⡏⣥⠈⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠀⠀⠀⠀⠀⣸⣴⠿⠉⠰⠈⠉⠃⠀⢅⠀⠀⠀⠈⠉⠛⣛⢯⠘⠛⠏⠉⠁⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⣿⢿⡏⡄⣚⡂⣰⣿⡒⠖⣯⢼⡻⠊⠐⠁⠀⠁⡀⡐⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣷⣶⣶⣤⣴⣿⣭⣾⣷⣦⣰⣐⡉⠤⠲⠤⣠⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠄⣄⣀⡀⠐⠒⡪⣦⣩⣿⣿⡿⠙⢧⢁⠀⠘⠹⣿⡥⣤⠔⠁⠀⠀⠀⠀⠀⠠⠷⣽⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣦⣶⣵⣶⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣴⡈⣠⣤⣄⣴⣾⣼⣿⣾⣯⣿⡟⣽⠾⠛⡷⢘⠻⡾⠁⡠⠖⡟⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣯⣿⠄⡀⠀⠀⠉⢠⠄⠀⢠⣶⣷⣿⣷⣿⣿⣿⡿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣬⣸⣷⠭⡴⣾⣿⣶⣾⣿⣿⣆⡈⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣛⣭⣿⣿⡠⠄⠂⠰⣖⢒⢺⣾⣾⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⠋⠛⣿⣶⣿⣶⡾⠁⠀⠀⠀⠀⠀⠀⢰⠶⠈⡀⣹⣿⣿⣯⡯⠊⣥⣿⣿⣾⣾⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠓⠛⠁⣾⣷⡄⠀⣠⣀⣀⡀⢁⣀⠀⠨⠀⣚⣉⣭⣽⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⠿⠯⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⢐⠀⢺⣿⣡⣩⣆⡿⣷⣆⣋⣳⣶⡶⠟⠋⣻⢿⣿⣻⠿⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠟⠿⣣⣤⣬⣝⡻⣿⣿⣷⣶⣶⣶⣶⣶⣶⣠⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⣛⠙⠛⠉⠙⠛⠋⠉⠛⠛⠁⠀⠀⠀⠉⠙⠋⠉⠉⠉⠀⠓⡖⠀⣰⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠂⠈⣿⣿⣿⣿⣏⣆⠀⠻⣿⣿⣿⣿⣿⣿⢛⣟⣿⣿⣿⣶⣶⣤⡤⣿⣿⣿⣿⣿⣇⢀⡴⣶⣶⣶⢶⣤⡤⢴⡠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠀⠀⠘⢿⣿⣿⣿⠟⠋⠉⠛⠛⠛⠛⠋⢿⡷⢸⣿⣿⣿⣿⣻⣷⣽⣿⣿⣿⠇⣺⣤⣵⣭⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠀⠹⠀⠀⠀⠸⠿⢿⣿⡀⠀⠀⠀⠈⠉⠉⠉⢹⡇⢸⣿⣿⣿⣿⣿⣿⣿⠛⠿⣋⣩⣭⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣽⡿⠁⠀⠀⠀⠀⠀⠀⢿⣾⣿⡿⡔⠁⢛⣯⣶⣼⣿⣿⣿⣿⣟⣿
⠀⠀⠀⠀⠀⠀⢐⢀⣀⣀⡄⠀⣀⡂⢺⣖⣲⣷⣦⣦⡤⡤⡈⠉⠀⠠⠠⣴⣦⣤⣤⣴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠂⠀⠀⠀⠀⠻⣿⣿⠿⢿⣿⣿⣛⣿⣿⣿⣷⣾⣿⡷
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⠀⠐⠄⠀⠀⠀⣉⠿⣍⣻⣿⢻⣿⣿⡟⣿⡿⠎⠃⠛⠛⠻⠟⠉⠃⢸⡿⠷⠦⠶⢶⡶⠶⠶⢶⣶⣶⣶⣶⣶⠶⢶⣶⣶⣶⡶⠶⠿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣧⣭⢸⣿⣿⣼⣿⣿⣸⡿⣷⣿⣿⣥⣤⠈⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⡿⢸⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⠀⠖⠲⣶⠏⢶⠆⠰⠶⠶⠶⠀⣤⣤⣤⣤⣀⠀⠀⠙⣙⣛⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 1706

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.30.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_30/07/2022:_KMyMoney_5.1.3_and_4MLinux_40_Released⠀✐


Posted in News_Roundup at 6:46 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Desktop/Laptop
          o Audiocasts/Shows
          o Applications
          o Instructionals/Technical
          o Desktop_Environments/WMs
                # K_Desktop_Environment/KDE_SC/Qt
                # GNOME_Desktop/GTK
    * Distributions_and_Operating_Systems
    * Debian_Family
    * Mobile_Systems/Mobile_Applications
    * Free,_Libre,_and_Open_Source_Software
          o Programming/Development
                # Perl_/_Raku
    * Leftovers
          o Environment
          o Finance
          o AstroTurf/Lobbying/Politics
                # Misinformation/Disinformation
          o Freedom_of_Information_/_Freedom_of_the_Press
          o Internet_Policy/Net_Neutrality
    * Gemini*_and_Gopher
          o Personal
          o Technical
                # Science
                # Internet/Gemini
    * § GNU/Linux⠀➾


          o § Desktop/Laptop⠀➾


                # ⚓ Hacker Noon ☛ Calling_All_Linux_Lovers:_Answer_These_Simple
                  Questions_to_Win_from_$3,000!_|_HackerNoon⠀⇛


                       Today, Linux powers most of the internet; in fact,
                       it is being used everywhere – from your laptops to
                       cars to mobile devices. What makes it a preferable
                       choice for so many users? Why is it everyone’s
                       favorite?


                       Here at HackerNoon, we are looking for some
                       interesting stories on your experiences and journey
                       with Linux. Take a moment to think of everything
                       you love about Linux and answer some of these
                       questions we have curated for you.


                # ⚓ Linux Links ☛ Linux_Around_The_World:_USA_–_Washington_–
                  LinuxLinks⠀⇛


                       We cover events and user groups that are running in
                       the US state of Washington. This article forms part
                       of our Linux Around The World series.


                # ⚓ Slashdot ☛ The_Story_Behind_Google’s_In-house_Desktop_Linux
                  –_Slashdot⠀⇛


                       “For more than a decade, Google has been baking and
                       eating its own homemade Linux desktop
                       distribution,” writes Computerworld.


                # ⚓ Android Police ☛ What_is_a_Chromebook?⠀⇛


                       While Chromebooks might not be as popular as they
                       were in 2020, they’re still a handy piece of
                       hardware. However, since it’s a newcomer to the PC
                       market, many people aren’t even sure what a
                       Chromebook is. Simply put, a Chromebook is Google’s
                       answer to both the Windows PC and the Mac computer.
                       It’s a device, usually a laptop or tablet, that
                       runs on Google’s Chrome OS. All-in-one desktops
                       using Chrome OS, called Chromebases, are also
                       available.


          o § Audiocasts/Shows⠀➾


                # ⚓ mintCast Pocast ☛ 391.5_–_The_Subscription_Service_Rabbit
                  Hole_–_mintCast⠀⇛


                       0:42 Linux Innards
                       1:24:06 Vibrations from the Ether
                       1:28:30 Check This Out
                       1:30:45 Housekeeping and Announcements


                       In our Innards section, we discuss the subscription
                       services we’re using.


                       And finally, the feedback and a couple of
                       suggestions


                # ⚓ Video ☛ COPR:_Fedora’s_Answer_To_The_Arch_User_Repository_–
                  Invidious⠀⇛


                       The Arch User Repository is the main reason I keep
                       using Arch but it’s not the only user repository
                       out there, Fedora has there own solution this one
                       called COPR the Cool Other Package Repo


                # ⚓ Video ☛ Linux_Lite_6:_A_Performance_Packed_Linux
                  Distribution_PERFECT_For_Windows_Users_(For_2022!)_–
                  Invidious⠀⇛


                       Linux Lite is a High-Performance Linux distro made
                       for WINDOWS Users and for people looking to get a
                       Boosted Performance out of their computers. Why I
                       am particularly excited about Linux Lite is because
                       it delivers impressive performance while also
                       giving us an elegant user interface and a set of
                       power tools that enable even the newest of Linux
                       newcomers to use Linux for their daily life very
                       easily or tweak under the hood and customize it
                       like they own it.


                # ⚓ Video ☛ Configuring_Neovim_With_Lua_(It’s_Easy!)_–
                  Invidious⠀⇛


                       Although I’m mostly an Emacs user these days,
                       viewers of the channel have been asking me to do
                       more videos about Neovim, especially how to
                       configure Neovim using Lua. So a few days ago, I
                       decided to convert my existing Neovim config
                       (init.vim) over to Lua (init.lua).


          o § Applications⠀➾


                # ⚓ Make Use Of ☛ Build_a_Gemini_Server_on_Linux_and_Join_the
                  Web_That_Might_Have_Been⠀⇛


                       Gopher is an internet protocol that existed in the
                       early 1990s but ultimately lost out to HTML and the
                       World Wide Web. It still exists today and Gemini is
                       its spiritual successor, with improved security,
                       and thousands of independent servers (known as
                       capsules) running on low-cost hardware.


                       The numbers are insignificant when compared with
                       the web we know and love, but with a small amount
                       of effort, you can swell the capsule ranks by one.
                       Read on to find out how to set up your own Gemini
                       server.


          o § Instructionals/Technical⠀➾


                # ⚓ Linux Host Support ☛ How_to_Install_and_Secure_PhpMyAdmin
                  on_AlmaLinux_|_LinuxHostSupport⠀⇛


                       In this tutorial we are going to explain in step-
                       by-step detail how to install and secure PhpMyAdmin
                       on AlmaLinux.


                       PhpMyAdmin is a free and open-source tool written
                       in PHP used for managing MySQL databases via
                       browser. It provides a very easy and user-friendly
                       interface, that allows users to easily create
                       databases, create users, tables columns and etc in
                       no time. In this blog post, we are going to install
                       PhpMyAdmin with the LAMP stack.


                       Installing and securing PhpMyAdmin on AlmaLinux is
                       a straightforward process and may take up to 15
                       minutes. Let’s get started!


                # ⚓ TecAdmin ☛ How_to_run_a_command_or_function_on_error_in
                  Bash_Script_–_TecAdmin⠀⇛


                       We can use the trap command to catch the error
                       signal system by the system during script
                       execution. Then you can execute a shell command or
                       call a function. In this way, you can execute your
                       custom script code on an error that occurred in a
                       bash script.


                       This can be helpful to revert any partial changes,
                       close database connections, or email status to the
                       concerned persons, etc. You can use trap command
                       with ERR signal like:


                       trap 'on_error_function' ERR


                       When an error is generated in a shell script, it
                       will execute a function named ‘on_error_function’
                       of your shell script. Instead of calling a
                       function, you can simply run a command as well.


                # ⚓ TecAdmin ☛ (Resolved)_Unknown_collation:
                  utf8mb4_unicode_520_ci_–_TecAdmin⠀⇛


                       A collation is a set of rules that defines how to
                       compare and sort character strings in a database
                       server. In this tutorial, we are discussing an
                       error faced during database restoration on another
                       server.


                # ⚓ Linux Cloud VPS ☛ 10_Useful_firewall-cmd_Commands_in_Linux
                  |_LinuxCloudVPS_Blog⠀⇛


                       In this blog post, we are going to explain 10
                       useful firewall-cmd commands in Linux with real
                       examples.


                       The firewall-cmd is the command-line client used to
                       manage the runtime configurations. It is a firewall
                       solution as an alternative to the iptables service.
                       We know that a properly configured firewall is the
                       only weapon that can defend the server from attacks
                       caused by internal influences. The firewall-cmd is
                       part of the firewalld application that can be used
                       for managing the firewall.


                       In this blog post, we are going to use Ubuntu 22.04
                       as Linux OS. You can use any Linux distribution.
                       Let’s get started!


                # ⚓ ID Root ☛ How_To_Install_Memtest_on_Ubuntu_22.04_LTS_–
                  idroot⠀⇛


                       In this tutorial, we will show you how to install
                       Memtest on Ubuntu 22.04 LTS. For those of you who
                       didn’t know, Memtests are memory-testing programs
                       that check for faults in the RAM of your system.
                       Memtest or Memtest86+ reads data, writes the memory
                       address patterns, and checks the errors. It can
                       output a list of bad RAM regions usable by the
                       BadRAM kernel patch so that you can still use your
                       old RAM with one or two bad bits.


                       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 Memtest 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.


                # ⚓ AddictiveTips ☛ How_to_play_Craft_The_World_on_Linux⠀⇛


                       Craft The World is a sandbox strategy game
                       developed by Dekovir Entertainment and published by
                       Black Maple Games. In this guide, we’ll show you
                       how you can play Craft The World on Linux.


                # ⚓ Ubuntubuzz ☛ How_To_Download_YouTube_Videos_for_Everyone⠀⇛


                       This is a simple tutorial to download YouTube
                       videos for everyone, in every computer and phone
                       device at no cost. This is good for your software
                       freedom as well as privacy. Now let’s download
                       some!


                # ⚓ Its FOSS ☛ How_to_Install_Latest_Vim_9.0_on_Ubuntu_&_Linux
                  Mint⠀⇛


                       Vim is one of the most popular terminal-based text
                       editors. However, it is not installed by default on
                       Ubuntu.


                       Ubuntu uses Nano as the default terminal editor.
                       Nano is also an excellent tool and I am not going
                       into Nano vs Vim debate.


                       If you have already spent some time mastering the
                       Vim shortcuts, you don’t have to forget them and
                       start using a new editor.


                # ⚓ Easy_Way_to_Extend_KVM_Virtual_Machine_Disk_Size_–
                  kifarunix.com⠀⇛


                       This is a simple tutorial about an easy way to
                       extend KVM virtual machine disk size. Disk usage in
                       a VM is among the limited resources which sometimes
                       require to be increased/reduced. It is possible to
                       resize the disk in KVM using QEMU.


                # ⚓ Barry Kauler ☛ A_new_fault_in_the_5.15.x_kernel⠀⇛


                       It did eventually “come good”, but that was many
                       releases after 5.15.16.


                       EasyOS has 5.15.57 kernel, and there is a new
                       problem. It was in the previous version used in
                       Easy, 5.15.53 I think, don’t recall if had the
                       problem before that. Anyway, it is recent.


                       I found that if plug in a USB-stick, sometimes its
                       partitions are not recognized. If the stick is, for
                       example, /dev/sdb with two partitions, then /sys/
                       block/sdb is created, but not /sys/block/sdb/sdb1
                       and sdb2.


          o § Desktop Environments/WMs⠀➾


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


                      # ⚓ KMyMoney_5.1.3_released⠀⇛


                             
                             This is a maintenance release as part of the
                             ongoing effort to support our users and fix
                             bugs and annoyances. If you think you can
                             support the project with some code changes or
                             your artistic or writing talent, please take
                             a look at the some low hanging fruits at the
                             KMyMoney junior job list. Any contribution is
                             welcome.


                             Despite the ongoing permanent testing we
                             understand that some bugs may have slipped
                             past our best efforts. If you find one of
                             them, please forgive us, and be sure to
                             report it, either to the mailing list or on
                             bugs.kde.org.


                      # ⚓ DebugPoint ☛ 10_Easy_Kdenlive_Features_for_Beginner’s
                        for_Faster_Video_Editing⠀⇛


                             In this article, I will show you how easy to
                             learn Kdenlive features and create awesome
                             videos.


                             Kdenlive is a free and open-source video
                             editor for Linux, Windows and macOS. It’s a
                             KDE application and is considered one of the
                             best feature-rich video editors. Although
                             other excellent contenders exist in the free
                             video editor space, such as Blender and Da
                             Vinci Resolve, Kdenlive is the “OG” of all. I
                             think it has all the features you get for
                             free instead of buying costly licenses from
                             commercial video editors.


                             Basic video editing in Kdenlive is easy if
                             you know how to do it. Each of these Kdenlive
                             features probably takes less than a minute to
                             learn.


                             In this article, I will show you some basic
                             video editing operations in Kdenlive in the
                             easiest way.


                      # ⚓ KStar Development ☛ Jasem’s_Ekosphere:_KStars_v3.6.0
                        Released⠀⇛


                             KStars v3.6.0 is released on 2022.07.30 for
                             MacOS, Linux, and Windows. It’s a bi-monthly
                             bugfix release with a couple of exciting
                             features.


                             Linear 1 Pass Algorithm


                             John Evans contributed a new Focus algorithm:
                             The Linear 1 Pass Algorithm. When using this
                             algorithm, Ekos initially performs like the
                             Linear algorithm in establishing the first
                             pass V-Curve and fitting a curve to it to
                             find the solution. Then, however, it moves
                             directly to the calculated minimum.


                # § GNOME Desktop/GTK⠀➾


                      # ⚓ Berlin_Mini_GUADEC_2022_–_Space_and_Meaning⠀⇛


                             Given the location of this year’s GUADEC many
                             of us couldn’t make it to the real event (or
                             didn’t want to because of the huge
                             emissions), but since there’s a relatively
                             large local community in Berlin and nearby
                             central Europe, we decided to have a new
                             edition of our satellite event, to watch the
                             talks together remotely.


                             This year we were quite a few more people
                             than last year (a bit more than 20 overall),
                             so it almost had a real conference character,
                             though the organization was a lot more
                             barebones than a real event of course.


    * § Distributions and Operating Systems⠀➾


          o ⚓ Its FOSS ☛ SpiralLinux:_New_Distro_Making_Debian_Easier_for
            Beginners⠀⇛


                 
                 I like the imagination of the developer. GeckoLinux is
                 based on openSUSE. Since openSUSE logo/mascot is a
                 chameleon, the developer named it Gecko (a type of
                 lizard).


                 The logo of Debian is a swirl, so the developer named the
                 Debian variant SpiralLinux.


                 Both have the intention of simplifying the experience of
                 their popular parent distro.


          o § New Releases⠀➾


                # ⚓ Beta News ☛ 4MLinux_40.0_achieves_stable_status,_but_does
                  anyone_actually_care?⠀⇛


                       You know what annoys me most about the Linux
                       comuniuty? There are too many gosh darn operating
                       systems based on the Linux kernel. And yes, too
                       much choice can be a bad thing. You see, new Linux
                       users often find themselves overwhelmed with the
                       number of distributions from which to choose. Even
                       worse, having many distros causes resources to be
                       spread too thin. Desktop Linux would be better off
                       if developers worked together on just a handful of
                       operating systems (such as Debian and Fedora).


                       But no. The Linux community can’t operate as a
                       cohesive unit. Instead, it must be fragmented and
                       confusing. Such is life, I suppose. With all of
                       that said, version 40.0 of 4MLinux — an operating
                       system that probably doesn’t need to exist — is now
                       available for download. The lightweight
                       distribution has officially achieved stable status,
                       and the developers are hopeful you will choose
                       their offering over the plethora of alternatives.


                       “The status of the 4MLinux 40.0 series has been
                       changed to STABLE. Edit your documents with
                       LibreOffice 7.3.5 and GNOME Office (AbiWord 3.0.5,
                       GIMP 2.10.32, Gnumeric 1.12.52), share your files
                       using DropBox 143.4.4161, surf the Internet with
                       Firefox 103.0 and Chromium 103.0.5060.53, send
                       emails via Thunderbird 91.12.0, enjoy your music
                       collection with Audacious 4.1, watch your favorite
                       videos with VLC 3.0.17.3 and mpv 0.34.0, play games
                       powered by Mesa 21.3.8 and Wine 7.12. You can also
                       setup the 4MLinux LAMP Server (Linux 5.18.7, Apache
                       2.4.54, MariaDB 10.8.3, PHP 5.6.40 and PHP 7.4.30).
                       Perl 5.34.1, Python 2.7.18, and Python 3.9.12 are
                       also available,” explains the development team.


          o ⚓ 9to5Linux ☛ 4MLinux_40_Distro_Released_with_Linux_Kernel_5.18,
            Improved_3D_Support,_and_More⠀⇛


                 
                 4MLinux 40.0 comes a little over four months after
                 4MLinux 39 and ships with a newer kernel, namely Linux
                 5.18, for better hardware support, a newer graphics
                 stack, namely Mesa 21.3.8, improved 3D support for both
                 bare-metal and virtual machines, and initial support for
                 the NVMe (NVM Express) interface, which appears to work
                 well in VirtualBox for now.


                 To make the operating system more versatile, the 4MLinux
                 40.0 release also introduces legacy MPlayer with MEncoder
                 software for playing and decoding/encoding media, as well
                 as several new apps pre-installed by default.


          o ⚓ 4MLinux Blog ☛ 4MLinux_Releases:_4MLinux_40.0_STABLE_released.⠀⇛


                 The status of the 4MLinux 40.0 series has been changed to
                 STABLE. Edit your documents with LibreOffice 7.3.5 and
                 GNOME Office (AbiWord 3.0.5, GIMP 2.10.32, Gnumeric
                 1.12.52), share your files using DropBox 143.4.4161, surf
                 the Internet with Firefox 103.0 and Chromium
                 103.0.5060.53, send emails via Thunderbird 91.12.0, enjoy
                 your music collection with Audacious 4.1, watch your
                 favorite videos with VLC 3.0.17.3 and mpv 0.34.0, play
                 games powered by Mesa 21.3.8 and Wine 7.12. You can also
                 setup the 4MLinux LAMP Server (Linux 5.18.7, Apache
                 2.4.54, MariaDB 10.8.3, PHP 5.6.40 and PHP 7.4.30). Perl
                 5.34.1, Python 2.7.18, and Python 3.9.12 are also
                 available.


    * § Debian Family⠀➾


          o ⚓ Death_of_Michael_Anthony_Bordlee,_New_Orleans,_Louisiana [Ed:
            Link may be broken]⠀⇛


                 On 17 June 2022, information was published for the first
                 time confirming the suicide of Frans Pop and linking it
                 to the history of cyberbullying Pop experienced in the
                 Debian open source project.


                 Two days later, on 19 June 2022, an open-source VR
                 artist, Michael Bordlee, passed away, age 29, in New
                 Orleans. The cause of death has not been disclosed at
                 this stage.


                 There is a tribute page for Michael. The cause of death
                 is not mentioned.


                 We found that Michael had previously worked on a VR
                 simulator to help people understand depression. There is
                 a news article about it. The news article notes that
                 Michael was himself a victim of bullying, much like Frans
                 Pop. There is no statement connecting this to the death.


                 There have been a number of similar deaths in 2021,
                 including the suspected suicide of 18 year old Redox OS
                 developer Samuel (jd91mzm2 / LEGOlord208) and in Japan,
                 the confirmed suicide of BSNES creator Near ( Byuu /
                 Dave). Both Samuel and Near had described experiences of
                 bullying.


    * § Mobile Systems/Mobile Applications⠀➾


          o ⚓ GSM Arena ☛ Samsung_Galaxy_Z_Flip_5G_gets_August_2022_Android
            security_patch_–_GSMArena.com_news⠀⇛


          o ⚓ CNET ☛ Your_Android_Phone’s_Cookies_and_Cache_Build_Up_Fast._How
            to_Clean_Them_Out_–_CNET⠀⇛


          o ⚓ Indian Express ☛ ExpressBasics:_How_to_force_landscape_mode_on
            any_Android_tablet,_phone_|_Technology_News,The_Indian_Express⠀⇛


          o ⚓ FOSSBytes ☛ How_To_Take_A_Screenshot_On_Android?⠀⇛


          o ⚓ Best_Android_PSP_emulator:_What_is_the_best_PSP_emulator_on
            Android?⠀⇛


          o ⚓ Nokia Mob ☛ Nokia_5.4_apparently_receiving_Android_12_update?_|
            Nokiamob⠀⇛


          o ⚓ Android Authority ☛ 5_Android_apps_you_shouldn’t_miss_this_week_–
            Android_Apps_Weekly⠀⇛


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


          o § Programming/Development⠀➾


                # ⚓ Matt Rickard ☛ Presentation_Next_to_Code⠀⇛


                       We’re taught to separate presentation logic from
                       code. Multi-tiered architectures, data layers,
                       control planes, and service layers.


                       But maybe there’s some merit to sometimes putting
                       presentation right next to the code.


                       CSS-in-JS – More expressive, more reusable. You
                       could view this as part of the wider movement to
                       mix markup and logic in the frontend stack (e.g.,
                       JSX and React). CSS-in-JS, while ugly sounding, is
                       a better solution than preprocessors with ever-
                       increasing complexity.


                       Notebooks – Faster iteration between changes.
                       Iteration speed is critical in the earliest phases
                       of analysis – cleaning data, training small models,
                       and calculating metrics.


                # ⚓ glandium.org_»_Announcing_git-cinnabar_0.5.10⠀⇛


                       Git-cinnabar is a git remote helper to interact
                       with mercurial repositories. It allows to clone,
                       pull and push from/to mercurial remote
                       repositories, using git.


                # ⚓ Ubuntu Pit ☛ Scala_vs_Java:_Things_You_Should_Know_About⠀⇛


                       Object-oriented languages are in demand for their
                       security, flexibility, and abstraction. Java and
                       Scala are two user favorites among these languages
                       and are seen as competitions often. This article
                       compares Scala vs. Java and discusses the things
                       you should know about them before diving into the
                       programming aspects.


                       Although programming languages have many common
                       grounds, object-oriented languages tend to prepare
                       learners to solve real-world problems. They are
                       also easier to learn compared to structured
                       languages such as C. Hopefully; you’ll have a more
                       precise concept of OOP languages by the end of it –
                       so keep reading!


                # ⚓ Medevel ☛ 21_Free_Open-source_React_Dashboards_and_Control
                  Panel_Templates⠀⇛


                       React is an amazing framework for building scalable
                       apps. It also has a growing supportive community of
                       passionate developers all around the world.


                       In terms of templates, and UI components, React
                       does not have any shortage, thanks to its active
                       community.


                       As we reviewed the best Vue dashboard and control
                       panel templates in this list, It is time to do the
                       same to our React collection.


                # § Perl / Raku⠀➾


                      # ⚓ Swarming_Sundays_|_Playing_Perl_6␛b6xA_Raku⠀⇛


                             To not miss any Sundays, PWC 175 is asking us
                             to find them. Raku helps us a great deal,
                             because we can easily find the last day in a
                             month, calculate it’s distance to the next
                             Sunday and turn the clock back by that many
                             days.


    * § Leftovers⠀➾


          o § Environment⠀➾


                # ⚓ The Conversation ☛ What_is_a_heat_dome?_An_atmospheric
                  scientist_explains_the_weather_phenomenon_baking_large_parts
                  of_the_country⠀⇛


                       A heat dome occurs when a persistent region of high
                       pressure traps heat over an area. The heat dome can
                       stretch over several states and linger for days to
                       weeks, leaving the people, crops and animals below
                       to suffer through stagnant, hot air that can feel
                       like an oven.


                       Typically, heat domes are tied to the behavior of
                       the jet stream, a band of fast winds high in the
                       atmosphere that generally runs west to east.


                       Normally, the jet stream has a wavelike pattern,
                       meandering north and then south and then north
                       again. When these meanders in the jet stream become
                       bigger, they move slower and can become stationary.
                       That’s when heat domes can occur.


          o § Finance⠀➾


                # ⚓ Ruben Schade ☛ CNBC_on_why_Starbucks_failed_in_Australia⠀⇛


                       CNBC ran a story and video back in 2018 about why
                       Starbucks failed in Australia. This was pre-COVID
                       pandemic, and more Starbucks stores have opened
                       since, but the general message still applies.


          o § AstroTurf/Lobbying/Politics⠀➾


                # § Misinformation/Disinformation⠀➾


                      # ⚓ John Gruber ☛ Instagram_Walks_Back_Recent_Changes_
                        (But_the_Whole_Thing_Is_Still_Going_to_Shit,_Don’t
                        Worry)⠀⇛


                             If you haven’t been paying attention to
                             Instagram lately, they’ve been steadily
                             dialing up the algorithmic content users see
                             in their feeds, especially video. More stuff
                             in your feed from accounts you don’t follow,
                             selected by machine learning algorithms, at
                             the expense of stuff from people and brands
                             you have chosen to follow. To top it off,
                             they recently rolled out a limited test to a
                             small — but not that small — number of users
                             that turned those users’ timelines into
                             something basically like TikTok: full-screen
                             videos (and some images) that you go through
                             one at a time. This did not go over well.


                      # ⚓ 🚨_Instagram_walks_back_its_changes_–_by_Casey
                        Newton⠀⇛


                             Instagram will walk back some recent changes
                             to the product following a week of mounting
                             criticism, the company said today. A test
                             version of the app that opened to full-screen
                             photos and videos will be phased out over the
                             next one to two weeks, and Instagram will
                             also reduce the number of recommended posts
                             in the app as it works to improve its
                             algorithms.


                             “I’m glad we took a risk — if we’re not
                             failing every once in a while, we’re not
                             thinking big enough or bold enough,”
                             Instagram chief Adam Mosseri said in an
                             interview. “But we definitely need to take a
                             big step back and regroup. [When] we’ve
                             learned a lot, then we come back with some
                             sort of new idea or iteration. So we’re going
                             to work through that.”


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


                # ⚓ John Pilger ☛ THE_US_IS_‘CLOSE_TO_GETTING_ITS_HANDS_ON
                  JULIAN_ASSANGE’._AN_INTERVIEW_WITH_JOHN_PILGER⠀⇛


                       In an interview with Oscar Grenfell of the World
                       Socialist Website, John Pilger explains the latest
                       manoeuvres by the US and UK authorities to
                       extradite Julian Assange, journalist and publisher,
                       to the US where he faces 175 years in prison for
                       the crime of journalism.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ Ish Sookun ☛ S._Moonesamy_writes_to_the_Data_Protection
                  Office_regarding_the_alleged_data_capture_at_the_Baie_Jacotet
                  Submarine_Cable_Landing_Station⠀⇛


                       The Data Protection Office of Mauritius operates
                       under the aegis of the Ministry of Technology,
                       Communication and Innovation, since February 2009
                       when the Data Protection Act 2004 came into force.
                       ​This office aims at protecting privacy rights of
                       individuals.


    * § Gemini* and Gopher⠀➾


          o § Personal⠀➾


                # ⚓ SpellBinding:_BCEILVN_Wordo:_LOINS⠀⇛


                # ⚓ Friendships⠀⇛


                       It is a fact of life that nothing lasts forever.
                       You might want something to last forever, but it
                       won’t, because such is the fact of life.


                       Did it ever happen to you that on a non-busy day
                       you sat in your room alone, your thoughts wandering
                       – wondering – how is that person doing?


                       That person, who you used to be best friends with,
                       until you weren’t. That person, or, these persons.


                       You may have great friends now, but inevitably, at
                       some random times, you will glance into that mirror
                       of time, where your past is.


                       You’re lucky if you smile looking into that mirror.
                       Good memories, firmly categorized as _memories_.


          o § Technical⠀➾


                # ⚓ Let’s_Encrypt_with_OpenBSD_and_Rex⠀⇛


                       In short, it gives away TLS certificates for your
                       website – for free! The catch is, that the
                       certificates are only valid for three months. So it
                       is better to automate certificate generation and
                       renevals.


                # § Science⠀➾


                      # ⚓ Quanta Magazine ☛ Quanta_Magazine:_Can_Computers_Be
                        Mathematicians?⠀⇛


                             How do you teach mathematics to an artificial
                             intelligence? AI has already bested humans at
                             problem-solving tasks that include games like
                             chess and Go. But before any task can be
                             tackled by a machine, it must be
                             reinterpreted as directions in a language
                             that computers can understand. For the last
                             few years, researchers and amateurs all over
                             the world have worked together to translate
                             the essential axioms of mathematics into a
                             programming language called Lean. Armed with
                             this knowledge, theorem-proving programs that
                             understand Lean have begun helping some of
                             the world’s greatest mathematicians verify
                             their work. Steven Strogatz speaks with Kevin
                             Buzzard, professor of pure mathematics at
                             Imperial College London, about the effort to
                             “teach” math to Lean — and how projects like
                             this one could shape the future of
                             mathematics.


                      # ⚓ George ☛ Eating_Boogers_–_by_George_–_Epistemink⠀⇛


                             The most plausible story we could craft here
                             is one where eating dry nasal mucus might
                             provide some headway for adaptive immunity
                             against pathogens we might later ingest in
                             larger quantities and better-preserved
                             states. This is very far-fetched but fine,
                             what does the literature have to say?


                # § Internet/Gemini⠀➾


                      # ⚓ WordPress_to_Gemini⠀⇛


                             I was surprised by the response in the poll
                             about [which link mode would feel the most
                             natural for Gemini?], there were several
                             options and to put links at the end of the
                             article was almost the least popular answer.


                             Some time ago I’ve started to organize my
                             articles in the same way. I had been adding
                             links in the Gopher style, with numbering
                             them like [1], [2], [3], …, [n], and puting
                             the index of links at the end of the article.
                             But then Przemek said, that he had an idea to
                             put descriptions of the links, instead of
                             their occurrence number. And I liked that
                             idea. It’s better when we can read an article
                             without looking at the links, and after that
                             to look at the index of every link with their
                             description. So we can process an article, or
                             an index in a separate way.


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



                    ䷩ 𝚕𝚒𝚗𝚎 2703

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.30.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_30/07/2022:_EasyOS_4.3,_Graft_for_Hardware_Giants⠀✐


Posted in News_Roundup at 10:20 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Server
          o Kernel_Space
          o Instructionals/Technical
          o Games
          o Desktop_Environments/WMs
                # K_Desktop_Environment/KDE_SC/Qt
    * Distributions_and_Operating_Systems
          o New_Releases
          o Fedora_Family_/_IBM
          o Open_Hardware/Modding
          o Mobile_Systems/Mobile_Applications
    * Free,_Libre,_and_Open_Source_Software
          o Programming/Development
                # Python
    * Leftovers
          o Hardware
          o Health/Nutrition/Agriculture
          o Proprietary
          o Security
                # Privacy/Surveillance
          o Defence/Aggression
          o Transparency/Investigative_Reporting
          o Environment
                # Energy
                # Wildlife/Nature
                # Overpopulation
          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
                # Trademarks
                # Copyrights
    * Gemini*_and_Gopher
          o Personal
          o Technical
                # Science
                # Internet/Gemini
                # Programming
    * § GNU/Linux⠀➾


          o § Server⠀➾


                # ⚓ ZDNet ☛ Mirantis_releases_Lens_Pro_Kubernetes_IDE_|_ZDNet⠀⇛


                       Lens, the most popular Kubernetes Integrated
                       Development Environment (IDE), is still open-source
                       software under the new name OpenLens. But, its
                       parent company, Mirantis, is seeking to profit from
                       it with the release of Lens Pro. This has a revised
                       end-user license and includes new features for
                       enterprise users.


          o § Kernel Space⠀➾


                # ⚓ LWN ☛ Linux_5.18.15⠀⇛


                # ⚓ LWN ☛ Linux_5.15.58⠀⇛


                # ⚓ LWN ☛ Linux_5.10.134⠀⇛


                # ⚓ LWN ☛ Linux_5.4.208⠀⇛


                # ⚓ LWN ☛ Linux_4.19.254⠀⇛


                # ⚓ LWN ☛ Linux_4.14.290⠀⇛


                # ⚓ LWN ☛ Linux_4.9.325⠀⇛


          o § Instructionals/Technical⠀➾


                # ⚓ HowTo Forge ☛ How_to_Install_Cacti_Monitoring_Tool_on
                  Ubuntu_22.04⠀⇛


                       Cacti is an open-source network monitoring and
                       graphing tool written in PHP. Learn how to install
                       the Cacti monitoring tool on Ubuntu 22.04 here.


                # ⚓ TecAdmin ☛ How_to_list_all_collections_in_MongoDB_database
                  –_TecAdmin⠀⇛


                       Question – How do I list all the collections
                       available in the MongoDB database?


                       MongoDB is a NoSQL database, that stores documents
                       in JSON format. A collection is an entity in
                       MongoDB (ie similar to a table in RDBMS databases)
                       that stores JSON documents.


                       You can use one of the below options to list
                       collections in a MongoDB database.


                # ⚓ TecAdmin ☛ Mongodb_–_Get_the_last_record_from_collection_–
                  TecAdmin⠀⇛


                       MongoDB find() method is used to select documents
                       from a specified collection. It also set the cursor
                       position to the selected document.


                       The default find() method gets the documents from
                       the start of the collection. In some situations, we
                       need to fetch the last record from a collection.
                       Use the following query to get the last records
                       from a MongoDB collection.


                # ⚓ Medium ☛ How_to_create_a_Linux_bootable_USB_|_by_Nithil
                  Krishnaraj_|_Jul,_2022_|_Medium⠀⇛


                       If you own and use a computer, there’s a big chance
                       it’s running Windows. However, there’s a better
                       alternative to Windows. It’s called Linux. Unlike
                       Windows, where there’s only one type, there are
                       more than 600 Linux distributions or distro for
                       short. You can think of these as different flavors
                       and each flavor targets a certain audience. For
                       example, Edubuntu, a Linux distro, is targeted
                       toward students and educators. Since there are so
                       many different ones, there’s probably a distro
                       that’s probably tailored for your needs. Also, due
                       to its small user base, it’s less targeted by
                       hackers, making it more secure and better in
                       performance. You can install a distro onto a USB
                       and try it out without replacing your current
                       operating system. In this article, you’ll learn how
                       to create a USB that can be used to install Linux
                       onto any computer. For the sake of simplicity,
                       we’ll be installing the Pop!_OS distribution.


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


                       In this tutorial, we will show you how to install
                       Pantheon Desktop Environment on Ubuntu 22.04 LTS.
                       For those of you who didn’t know, Pantheon Desktop
                       Environment is the default desktop environment for
                       Elementary OS developed by Elementary OS developers
                       using the GTK3 toolkit and Vala. Pantheon offers an
                       amazingly pretty user interface with a rich set of
                       features, programs, and apps needed in day-to-day
                       use.


                       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 Pantheon Desktop Environment 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.


                # ⚓ ID Root ☛ How_To_Install_Papirus_Icon_Theme_on_Ubuntu_22.04
                  LTS_–_idroot⠀⇛


                       In this tutorial, we will show you how to install
                       Papirus Icon Theme on Ubuntu 22.04 on Ubuntu 22.04
                       LTS. For those of you who didn’t know, Papirus is
                       an icon theme that has been developed using the
                       GTK+ library, so it is compatible with GNOME and
                       its derivative. It is a huge icon set, encompassing
                       close to a thousand icons in its bundle. Papirus is
                       well-known for its polished and stylish look. The
                       Papirus icon theme has three versions, dark, white
                       and simple theme.


                       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 Papirus Icon Theme 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.


                # ⚓ AddictiveTips ☛ How_to_play_Minion_Masters_on_Linux⠀⇛


                       Minion Masters is a free-to-play tower-defense card
                       game. It was developed and published by BetaDwarf
                       for Mac OS and Windows. Here’s how you can play
                       Minion Masters on your Linux PC.


                # ⚓ Trend Oceans ☛ How_to_Mount_and_Unmount_an_ISO_Image_in
                  Linux⠀⇛


                       In this beginner’s guide, you will learn how to
                       mount and unmount ISO image files on the Linux
                       system temporarily and permanently without any
                       applications.


          o § Games⠀➾


                # ⚓ GamingOnLinux ☛ OUTRIDERS_officially_gets_a_Playable_Steam
                  Deck_rating⠀⇛


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


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


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


                # ⚓ GamingOnLinux ☛ Proton_Experimental_brings_support_for
                  Unravel_Two,_fixes_up_Civilization_IV⠀⇛


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


                # ⚓ GamingOnLinux ☛ Modern_Diablo_game_engine_devilutionX_sees
                  new_release,_how_to_get_it_on_Steam_Deck⠀⇛


                       Do you want to play the classic Diablo RPG? Well,
                       not only does GOG have it and the Hellfire
                       expansion but the Native Linux devilutionX game
                       engine can make it even better. Here’s how to get
                       it working on Steam Deck (and Linux desktop!).


                # ⚓ GamingOnLinux ☛ Yars:_Recharged_from_Atari_launches_August
                  23rd⠀⇛


                       Yars: Recharged is the latest remake from Atari
                       with developers Adamvision Studios and SneakyBox
                       and it’s launching on August 23rd with Native Linux
                       support. This is the latest entry in the Recharged
                       series following Missile Command: Recharged,
                       Centipede: Recharged, Black Widow: Recharged,
                       Asteroids: Recharged and Breakout: Recharged. No
                       doubt they have more planned too.


                # ⚓ GamingOnLinux ☛ Valve_speeds_up_Steam_Deck_production_some
                  more,_all_existing_reservations_this_year⠀⇛


                       Valve has announced that they’ve sorted out various
                       issues with their Steam Deck supply chain, so they
                       will get through reservations much faster than
                       expected now. This means a lot of people will be
                       bumped up the list a bit getting their Steam Deck
                       purchase email a lot sooner.


                # ⚓ GamingOnLinux ☛ The_Humble_Amazing_Adventures_Bundle_has
                  some_gems_in_it⠀⇛


                       Need some new games for the weekend? Humble Bundle
                       have put up the Amazing Adventures Bundle and there
                       are a couple of gems in it so let’s take a look. As
                       usual I’ll let you know what you can expect from
                       them on Linux desktop and Steam Deck, along with
                       ProtonDB rating if needed.


                # ⚓ Linux Links ☛ 10_Fun_Free_and_Open_Source_Role-Playing
                  Games_–_Part_2⠀⇛


                       
                       A role-playing game (RPG) is a genre of video game
                       where the gamer controls a fictional character (or
                       characters) that undertakes a quest in an imaginary
                       world. RPG video games originate from tabletop or
                       pen-and-paper RPGs, such as Rolemaster or Dungeons
                       & Dragons — a type of game in which the players
                       impersonate their characters by actively describing
                       their actions and thoughts.


                       It’s difficult to define an RPG given that modern
                       games often contain elements from another genre.
                       Traditional RPGs often let you improve your
                       character as you play and interact with elements of
                       the environment or storyline. You may have a menu-
                       based combat system, and a central quest.


          o § Desktop Environments/WMs⠀➾


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


                      # ⚓ Nate Graham ☛ This_week_in_KDE:_Lots_of_work_on
                        Discover_–_Adventures_in_Linux_and_KDE⠀⇛


                             This week, Aleix Pol Gonzalez put a ton of
                             work into Discover, which you’ll see
                             throughout the post! Beyond that, it was a
                             Plasma-heavy week, with developers adding
                             several useful new features, polishing the
                             UI, and fixing a large number of high-
                             priority issues.


                      # ⚓ Volker Krause ☛ June/July_in_KDE_Itinerary⠀⇛


                             After the necessary foundational work has
                             been finished, Itinerary now has a completely
                             new integration with the corresponding system
                             calendar on Android and Linux.


                             So far it was only possible to import events
                             created by KMail’s itinerary plugin from the
                             Android calendar. This is now not only also
                             possible on Linux, but is also no longer
                             restricted to those specific events.


                             Instead, events that the travel document
                             extractor recognizes as e.g. train trip due
                             to being provided by an iCal file from the
                             corresponding train operator or booking agent
                             can now also be imported. You can also import
                             arbitrary events as such.


                             Events are also no longer imported
                             automatically and from all calendars, but you
                             can now select which calendar to import from,
                             and which events exactly to import. This also
                             avoids ending up with trips in your timeline
                             from other people’s shared calendars.


    * § Distributions and Operating Systems⠀➾


          o § New Releases⠀➾


                # ⚓ EasyOS_Dunfell-series_4.3⠀⇛


                       EasyOS was created in 2017, derived from Quirky
                       Linux, which in turn was derived from Puppy Linux
                       in 2013. Easy is built in woofQ, which takes as
                       input binary packages from any distribution, and
                       uses them on top of the unique EasyOS
                       infrastructure.
                       Throughout 2020, the official release for x86_64
                       PCs was the Buster-series, built with Debian 10.x
                       Buster DEBs.
                       EasyOS has also been built with packages compiled
                       from source, using a fork of OpenEmbedded (OE).
                       Currently, the Dunfell release of OE has been used,
                       to compile two sets of binary packages, for x86_64
                       and aarch64.
                       The latter have been used to build EasyOS for the
                       Raspberry Pi4, and first official release, 2.6.1,
                       was in January 2021.
                       The page that you are reading now has the release
                       notes for EasyOS Dunfell-series on x86_64 PCs, also
                       debuting in 2021.
                       Ongoing development is now focused on the x86_64
                       Dunfell-series. The last version in the x86_64
                       Buster-series is 2.6.2, on June 29, 2021, and that
                       is likely to be the end of that series. Releases
                       for the Pi4 Dunfell-series are still planned but
                       very intermittent.
                       The version number is for EasyOS itself,
                       independent of the target hardware; that is, the
                       infrastructure, support-glue, system scripts and
                       system management and configuration applications.
                       The latest version is becoming mature, though Easy
                       is an experimental distribution and some parts are
                       under development and are still considered as beta-
                       quality. However, you will find this distro to be a
                       very pleasant surprise, or so we hope.


                # ⚓ Barry Kauler ☛ EasyOS_Dunfell-series_version_4.3_released⠀⇛


          o § Fedora Family / IBM⠀➾


                # ⚓ Hackaday ☛ Why_Fedora_Decided_To_Give_CC0_Licensed_Code_The
                  Boot⠀⇛


                       The term “open source” can be tricky. For many
                       people, it’s taken to mean that a particular piece
                       of software is free and that they can do whatever
                       they wish with it. But the reality is far more
                       complex, and the actual rights you’re afforded as
                       the user depend entirely on which license the
                       developers chose to release their code under. Open
                       source code can cost money, open source code can
                       place limits on how you use it, and in some cases,
                       open source code can even get you into trouble down
                       the line.


                # ⚓ Fedora Project ☛ Friday’s_Fedora_Facts:_2022-30_–_Fedora
                  Community_Blog⠀⇛


                       Here’s your weekly Fedora report. Read what
                       happened this week and what’s coming up. Your
                       contributions are welcome (see the end of the
                       post)!


          o § Open Hardware/Modding⠀➾


                # ⚓ Tom’s Hardware ☛ Raspberry_Pi_4_Drives_Open_Source_MIDI
                  Controller_and_Sequencer_|_Tom’s_Hardware⠀⇛


                       If you’re looking for a cool Raspberry Pi project
                       to jam out with this summer, take a close look at
                       this open-source MIDI controller and sequencer
                       created by maker and musician Niisse. It’s 100%
                       driven by a Raspberry Pi 4 and features handmade
                       modules that handle special effects as well as
                       input controls for real-time jam sessions.


                # ⚓ Gizmodo ☛ Analogue_OS_v1.1_Update_Now_in_Beta,_Full_Release
                  by_September⠀⇛


                       Library, Memories, Game Boy Camera Support, and
                       Spacewar!


                # ⚓ Tom’s Hardware ☛ Alien-Themed_Raspberry_Pi_Motion_Tracker
                  Monitors_for_Facehuggers_|_Tom’s_Hardware⠀⇛


                       Bill O’Sullivan uses a Raspberry Pi to drive a
                       custom Alien-themed motion tracking handheld that
                       works using ultrasonic sensors.


                # ⚓ Tom’s Hardware ☛ How_to_Connect_Your_Raspberry_Pi_Pico_W_to
                  Twitter_via_IFTTT_|_Tom’s_Hardware⠀⇛


                       Connecting the $6 Raspberry Pi Pico W to Twitter is
                       a breeze using IFTTTs free service. In this how-to,
                       we send live sensor data to Twitter using IFTTT and
                       MicroPython.


                # ⚓ Tom’s Hardware ☛ Unique_Raspberry_Pi_Gaming_Rig_Uses
                  Complex_Shapes_and_Circular_LCD_Screens_|_Tom’s_Hardware⠀⇛


                       Developer and woodworker Mw33212 has created
                       another beautiful Pi-powered gaming rig—this time
                       with two round LCD displays in a handmade
                       tridiminished rhombicosidodecahedron-shaped case.


                # ⚓ Tom’s Hardware ☛ Raspberry_Pi_Pico_Emulates_6502_Computer
                  and_Runs_Loderunner_|_Tom’s_Hardware⠀⇛


                       Eric Badger is emulating the 8-bit 6502 computer on
                       the Raspberry Pi Pico and demonstrates its ability
                       to run Loderunner.


                # ⚓ Tom’s Hardware ☛ Embedded_Raspberry_Pi_Compute_Module_4_KVM
                  Card_Offers_Full_Remote_Control_|_Tom’s_Hardware⠀⇛


                       Putting a computer inside a computer may seem like
                       something Xzibit may have done in the early 2000s.
                       But this awkwardly named Blicube BLiKVM PCIe (Pi
                       CM4) is a PCIe card bearing a Raspberry Pi Compute
                       Module 4


          o § Mobile Systems/Mobile Applications⠀➾


                # ⚓ CNX Software ☛ Allwinner_H618_processor_powers_Android_12
                  TV_boxes_–_CNX_Software⠀⇛


                # ⚓ Notebook Check ☛ Lenovo_Legion_Y700_Ultimate_Edition_8-inch
                  Android_tablet_with_color-changing_glass_back_launched_in
                  China_for_3,299_yuan_–_NotebookCheck.net_News⠀⇛


                # ⚓ Android Police ☛ Android_tablets_and_Chromebooks_struggle
                  for_market_share_amid_tumbling_shipments⠀⇛


                # ⚓ Android Central ☛ Google’s_game_dashboard_could_soon_expand
                  to_select_Android_13_phones_|_Android_Central⠀⇛


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


          o § Programming/Development⠀➾


                # § Python⠀➾


                      # ⚓ Medevel ☛ FastAPI_is_an_Open-source_Enterprise-grade
                        API_Framework⠀⇛


                             FastAPI is a modern, fast (high-performance),
                             web framework for building APIs with Python
                             3.6+ based on standard Python type hints.


                             It plays well with other Python libraries as
                             requests, multipart, ujson, pyyaml, and
                             others.


    * § Leftovers⠀➾


          o ⚓ Common Dreams ☛ Opinion_|_The_Cynics’_Monkey_Wrench⠀⇛


                 If you depart from an “us vs. them” philosophy of life,
                 your first confrontation is likely to be with the cynics.


          o ⚓ The Verge ☛ Kylie_Jenner_can’t_save_Instagram_forever⠀⇛


                 In early May, the Meta executive in charge of Instagram,
                 Adam Mosseri, shared some news: the social media app’s
                 main feed would start looking dramatically different to
                 some users.


                 For those in a small test group, the feed they’d been
                 using for a decade would be replaced with an “immersive
                 viewing experience” containing full-screen photos and
                 videos with many posts coming from people they weren’t
                 following. In other words, Instagram would start to look
                 and feel even more like TikTok, the short-form video app
                 that Meta sees as its fiercest competition.


          o ⚓ Tedium ☛ Lava_Me_3_Review:_A_Carbon_Fiber_Guitar_With_a
            Touchscreen⠀⇛


                 So, I bought a new guitar over the fourth of July
                 weekend. I’m not sure why. Perhaps it was the sudden
                 increase in my credit line or the sudden appearance of
                 one at my favorite music store that drove me toward the
                 purchase. From the day I saw Mary Spender review the
                 guitar on her YouTube channel, I decided to get one
                 sometime. I didn’t realize it would happen a mere six
                 months later. In today’s Tedium, we’re doing something a
                 little different and reviewing the Lava Me 3 from Lava
                 Music. Now, let’s talk about this phenomenal guitar.


          o ⚓ Scheerpost ☛ Donkey_Punch⠀⇛


                 “Donkey Punch,” a new original cartoon by the inimitable
                 Mr. Fish, looks at the fundamental disconnect between
                 true progressivism and the DNC.


          o ⚓ Hackaday ☛ Hackaday_Prize_2022:_Modern_Plug-in_Gives_TRS-80_Its
            Voice_Back⠀⇛


                 Like artificial intelligence, speech synthesis was one of
                 those applications that promised to revolutionize
                 computing in the 1980s, only to fizzle out after people
                 realized that a robotic voice reading out predefined
                 sentences was not actually that useful. Nevertheless,
                 computer manufacturers didn’t want to miss out on the
                 hype and speech synthesizers became a relatively common
                 add-on for a typical home computer.


          o § Hardware⠀➾


                # ⚓ Hackaday ☛ CV_Based_Barking_Dog_Keeps_Home_Secure,_Doesn’t
                  Need_Walking⠀⇛


                       Meet [Tanner]. [Tanner] is a hacker who also
                       appreciates the security of their home while
                       they’re out of town. After doing some research
                       about home security, they found that it doesn’t
                       take much to keep a house from being broken into.
                       It’s true that truly determined burglars might be
                       more difficult to avoid. But, for the opportunistic
                       types who don’t like having their appendages
                       treated like a chew toy or their face on the local
                       news, the steaks are lowered.  All it might take is
                       a security camera or two, or a big barking dog to
                       send them on their way. Rather than running to the
                       local animal shelter, [Tanner] used parts that were
                       already sitting around to create a solution to the
                       problem: A computer vision triggered virtual dog.


                # ⚓ Hackaday ☛ Toddler_EV_Gets_Big_Boy_Battery_Upgrade⠀⇛


                       No matter the type of vehicle we drive, it has a
                       battery. Those batteries wear out over time. Even
                       high end EV’s have batteries with a finite life.
                       But when your EV uses Lead Acid batteries, that
                       life is measured on a much shorter scale. This is
                       especially true when the EV is driven by a driver
                       that takes up scarcely more space in their EV than
                       a stuffed tiger toy! Thankfully, the little girl in
                       question has a mechanic:


                # ⚓ Hackaday ☛ When_[Carl]_Says_Jump,_PCBs_Say_“How_High?”⠀⇛


                       We’ve noticed that [Carl Bugeja] likes flexible
                       PCBs. His latest exploit is to make PCB-based
                       springs that combine with some magnets to create
                       little devices that jump. We aren’t sure what
                       practical use these might have, but they are
                       undeniably novel and you can see them — um —
                       jumping around, in the video, below.


                # ⚓ CNX Software ☛ Allwinner_H618_processor_powers_Android_12
                  TV_boxes_–_CNX_Software⠀⇛


                       Allwinner H618 processor has started to show up in
                       several TV boxes running Android 12, and capable of
                       playing 6K/4K VP9 and H.265 videos with devices
                       such as T95Z Plus and T95 Max, which may be
                       confusing, as companies are reusing those model
                       numbers over and over.


                       Featuring a quad-core Cortex-A53 processor, an Arm
                       Mali-G31 MP2 GPU, and 6K video support, the
                       Allwinner H618 looks exactly like the Allwinner
                       H616 processor except it can run the more recent
                       Android 12 operating system.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ TruthOut ☛ Prison_Health_Expert_Warns_Monkeypox_Could
                  “Dramatically_Increase”_Behind_Bars⠀⇛


                # ⚓ Democracy Now ☛ Prison_Health_Expert_Warns_Monkeypox_Could
                  “Dramatically_Increase”_Behind_Bars,_Calls_for_CDC_Action⠀⇛


                       The first case of monkeypox behind bars was
                       reported in Chicago this week, and health experts
                       are warning that jails could accelerate the spread
                       as they are dangerously unprepared to combat
                       against a virus that spreads through close physical
                       contact. We speak with Dr. Homer Venters, the
                       former chief medical officer for New York City’s
                       Correctional Health Services, whose new op-ed for
                       The Hill is headlined ”CDC must act to prevent
                       monkeypox explosion in prisons.”


                # ⚓ Pro Publica ☛ New_York_Polio_Case_Linked_to_Virus_Traces
                  Found_in_UK,_Israel⠀⇛


                       Public health officials’ international hunt for
                       clues in the case of polio that paralyzed a New
                       York man has turned up a big one: The virus that
                       infected him matches the genetic fingerprint of
                       poliovirus found in sewage samples taken in London
                       and in the Jerusalem area, officials at the Centers
                       for Disease Control and Prevention and the World
                       Health Organization told ProPublica on Friday.


                       It is not yet clear how the virus moved from one
                       place to another or where it was first.


                # ⚓ Common Dreams ☛ Opinion_|_The_Paranoid_Nature_of_American
                  Foreign_and_Domestic_Policy⠀⇛


                       I have a brother with chronic schizophrenia. He had
                       his first severe catatonic episode when he was 16
                       years old and I was 10. Later, he suffered from
                       auditory hallucinations and heard voices saying
                       nasty things to him. I remember my father
                       reassuring him that the voices weren’t real and
                       asking him whether he could ignore them. Sadly,
                       it’s not that simple.


                # ⚓ Common Dreams ☛ Big_Pharma_Flooding_Airwaves_With
                  Disinformation_to_Kill_Drug_Price_Reform⠀⇛


                       While its thousands of lobbyists work fervently on
                       Capitol Hill, the pharmaceutical industry is
                       flooding the airwaves in several states with
                       deceptive ads in a last-ditch campaign to block
                       Senate Democrats’ plan to curb the unchecked
                       pricing power of drug corporations.


                       Included as part of a reconciliation package
                       negotiated by Sen. Joe Manchin (D-W.Va.) and Senate
                       Majority Leader Chuck Schumer (D-N.Y.), the
                       proposal would require Medicare to negotiate the
                       prices of a small number of drugs directly with
                       pharmaceutical companies, which can currently drive
                       up costs as they please—boosting their profits at
                       the expense of patients.


          o § Proprietary⠀➾


                # ⚓ India Times ☛ AWS_now_has_$79_bn_annual_sales_run_rate_as
                  top_Cloud_provider⠀⇛


                       Amazon Web Services (AWS), the Cloud arm of Amazon,
                       now represent an annualised sales run rate of
                       nearly $79 billion that has made it the leading
                       Cloud provider once again.


                       AWS reported $19.7 billion net sales in the June
                       quarter, up 33 per cent year over year. The
                       operating income of AWS was $5.7 billion in Q2.


                # ⚓ India Times ☛ Apple_now_has_over_860_mn_paid_subscriptions
                  across_services⠀⇛


                       Tech giant Apple has announced that it now has over
                       860 million paid subscribers across all of its
                       services, which includes Apple Music, Apple TV+,
                       Apple News, iCloud, and more.


          o § Security⠀➾


                # ⚓ Diffoscope ☛ diffoscope_220_released⠀⇛


                       The diffoscope maintainers are pleased to announce
                       the release of diffoscope version 220. This version
                       includes the following changes:


                       * Support Haskell 9.x series files and update the
                       test files to match. Thanks
                         to Scott Talbert for the relevant info about the
                       new format.
                         (Closes: reproducible-builds/diffoscope#309)
                       * Fix a regression introduced in diffoscope version
                       207 where diffoscope
                         would crash if one directory contained a
                       directory that wasn't in the
                         other. Thanks to Alderico Gallo for the report
                       and the testcase.
                         (Closes: reproducible-builds/diffoscope#310)
⚓ Security Week ☛ Microsoft_Connects_USB_Worm_Attacks_to_‘EvilCorp’_Ransomware
Gang_|_SecurityWeek.Com [Ed: Microsoft blames others for its vulnerable
software, as usual]⠀⇛


     Cybersleuths at Microsoft have found a link between the recent
     ‘Raspberry Robin’ USB-based worm attacks and EvilCorp, a notorious
     Russian ransomware operation sanctioned by the U.S. government.


⚓ Krebs On Security ☛ 911_Proxy_Service_Implodes_After_Disclosing_Breach⠀⇛


     911[.]re, a proxy service that since 2015 has sold access to hundreds
     of thousands of Microsoft Windows computers daily, announced this
     week that it is shutting down in the wake of a data breach that
     destroyed key components of its business operations. The abrupt
     closure comes ten days after KrebsOnSecurity published an in-depth
     look at 911 and its connections to shady pay-per-install affiliate
     programs that secretly bundled 911’s proxy software with other
     titles, including “free” utilities and pirated software.


    * § Privacy/Surveillance⠀➾


          o ⚓ The Verge ☛ NJ_police_used_baby_DNA_to_investigate_crimes,
            lawsuit_claims⠀⇛


                 According to the lawsuit, parents and the public at large
                 are unaware that blood samples taken from their children
                 could be used in this way. “The New Jersey Monitor
                 believe the public would be shocked by what has occurred
                 in OPD’s client’s case and that law enforcement agencies
                 are skirting warrant requirements in this way,” a section
                 of the lawsuit reads. “It also believes that parents in
                 particular would be shocked to learn that their
                 children’s blood samples are being stored by the
                 Department of Health for more than twenty years and are
                 being accessed by law enforcement agencies without their
                 knowledge or consent so that their DNA could be
                 analyzed.”


          o ⚓ Newborn_screening_program_used_to_aid_criminal_investigation,
            public_defender_says⠀⇛


                 Blood drawn as part of a mandatory New Jersey newborn
                 testing program could end up as evidence in the hands of
                 law enforcement.


                 The state Office of the Public Defender is alleging law
                 enforcement in New Jersey obtained blood taken as part of
                 the program and used it to charge the child’s father with
                 a crime, an allegation that has led to cries of alarm
                 from civil liberties advocates.


          o ⚓ Techdirt ☛ San_Francisco_Mayor_Wants_PD_To_Be_Able_To_Commandeer
            Cameras_Owned_By_Residents_Because_Reasons⠀⇛


                 Ring has been bedding down as many law enforcement
                 partners as possible, turning cops into brand evangelists
                 with the implicit (and sometimes, explicit) promise
                 they’ll have access to private citizens’ recordings. Ring
                 likes this because it increases its market share. Cops
                 like it because it gives them more camera coverage in the
                 areas they patrol, at least theoretically.


§ Defence/Aggression⠀➾


    * ⚓ Medforth ☛ Anti-Semitic_Imam_expelled_from_France⠀⇛


           The file put together by the Northern Prefecture on Hassan
           Iquioussen convinced the Commission for the Expulsion of
           Foreigners, presided over by the President of the Lille Court.
           It gave a positive opinion on the expulsion on June 22. The
           decision was not a foregone conclusion. With five children,
           fifteen grandchildren and all his assets declared in France,
           Hassan Iquioussen could claim to be integrated in his very own
           way. At the meeting of the departmental commission on
           expulsion, the minutes of which Le Point has read, the prefect
           of the Nord department travelled in person to address the case
           before the judges, receiving the full support of the Minister
           of the Interior, Gérald Darmanin.


    * ⚓ Jerusalem Post ☛ Turkey_accused_of_killing_Kurdish_female_commander_in
      Syria⠀⇛


           A Kurdish commander in the Syrian Democratic Forces, the US-
           backed group that helped defeat ISIS, was murdered in a
           targeted assassination by a drone strike in Syria on July 22.


    * ⚓ Firstpost ☛ Hindus_are_under_attack_in_Bangladesh:_Why_it_is_right_time
      for_Indian_Muslims_to_stand_up_and_protest⠀⇛


           The Economist recounted how innocent Hindus were targeted by
           frenzied mobs shouting “Hang the culprits”. It was Durga Puja
           day and people were looking forward to celebrating it but were
           instead caught up in a wave of violent protests. There was
           Dilip Das, a washerman, who set out for his local temple to
           take part in the festivities.


    * ⚓ Bangladesh_witnessing_steep_rise_in_persecution_of_Hindus⠀⇛


           According to the data released, apart from 79 Hindus being
           killed this year alone, 620 of them have been threatened, 183
           of them injured in “targeted” quarrels and fights, 32 of them
           are missing and more than 145 of them have faced attempt to
           murder like situation across Bangladesh.


           Not only this, the Hindu Mahajot also claims that more than 130
           Hindu families have been rendered homeless, 77 Hindus have been
           kidnapped, while 501 incidents of “organised” attacks on Hindus
           have been reported. The Hindu Mahajot also claims that this
           year alone, 95 cases of forced conversion have been documented
           in the country in the last six months.


    * ⚓ Jerusalem Post ☛ Children_in_Houston_sing_religious_anthem_associated
      with_Iranian_regime⠀⇛


           The video was posted on Tuesday on the “Houston Azadari”
           channel which has been active since October 2011 and has over
           12,000 subscribers. Azadari, meaning “mourning,” refers to a
           set of commemoration rituals practiced mostly by Shi’ite
           Muslims to mourn the death of Imam Husayn ibn Ali in the Battle
           of Karbala.


    * ⚓ Medforth ☛ Muslim_randomly_stabs_train_passengers_in_Germany:_He
      intended_to_rid_Germany_of_“non-Muslims”⠀⇛


           Now a psychiatric examination came to the conclusion: the man
           was acting with full consciousness and was not mentally
           impaired at the time of the crime. In the course of the
           investigation, IS propaganda had been found on the
           Palestinian’s person.


    * ⚓ The Nation ☛ Trump_Might_Face_Prison,_but_Bolton_and_Kissinger?
      Never!⠀⇛


           John Bolton made a staggering admission recently. Speaking to
           CNN’s Jake Tapper earlier this month, Bolton denied that what
           Donald Trump tried to do after the election was a “carefully
           planned coup d’etat.” When Tapper replied that “one doesn’t
           have to be brilliant to plan a coup,” Bolton pushed back—and
           drew on his credentials as Trump’s national security adviser
           and George W. Bush’s ambassador to the UN. “I disagree with
           that,” Bolton said, “as someone who has helped plan coups
           d’etat, not here, but, you know, other places. It takes a lot
           of work…”


    * ⚓ Meduza ☛ At_least_53_Ukrainian_POWs_feared_dead_after_missile_strike_on
      prison_camp_near_Donetsk_—_Meduza⠀⇛


           Ukraine and Russia traded accusations on Friday after a missile
           strike on a prison camp in Olenivka, a village outside of
           Donetsk, reportedly killed dozens of Ukrainian prisoners of
           war.


    * ⚓ Scheerpost ☛ Is_America’s_Destiny_Manifest?⠀⇛


           One of the GODFATHER’s most dramatic episodes is the ‘Day of
           the Long Knives.’


    * ⚓ Common Dreams ☛ Records_Show_There_Are_More_Missing_Jan._6_Texts_That
      DHS_Watchdog_Failed_to_Mention⠀⇛


           It was revealed Thursday that additional text messages sent and
           received by Department of Homeland Security officials before
           and during the January 6, 2021 assault on the U.S. Capitol are
           missing—something the DHS inspector general has known for more
           than five months but unlawfully failed to disclose to Congress.


           On top of the Secret Service texts from January 5 and 6 that
           were deleted after the DHS inspector general’s office requested
           the agency’s electronic communications records, messages sent
           to and from three high-ranking Trump administration officials
           at DHS in early January 2021 are missing, according to an
           internal agency record obtained by the Project On Government
           Oversight (POGO) and congressional sources.


    * ⚓ Techdirt ☛ Training_And_Expertise:_Denver_Cops_Hit_Five_Bystanders
      While_Shooting_At_‘Felony_Menacing’_Suspect⠀⇛


           Sometimes you’ve got to shoot a few civilians to make the
           public safe. (h/t Maggie McNeill)


    * ⚓ Common Dreams ☛ Opinion_|_Republicans_Who_Testified_Had_No_Business
      Acting_Surprised_by_Trump’s_Incitements_to_Violence_on_Jan_6⠀⇛


           The overarching narrative presented by the House January 6
           Committee is that the violence of January 6 was the culmination
           of a long process: that Trump laid the groundwork to undermine
           the election long before November 2020; promoted the Big Lie
           every day since the election; invited the mob to the Ellipse on
           January 6; incited them on that day; urged them to march on the
           Capitol; and then stood by approvingly while they did what he
           told them to do.


    * ⚓ Common Dreams ☛ Anti-War_Voices_Warn_Against_‘Insanely_Provocative’
      Pelosi_Visit_to_Taiwan⠀⇛


           As U.S. House Speaker Nancy Pelosi departs Friday for an Asian
           trip that may include a stop in Taiwan, anti-war voices are
           sounding the alarm over a visit they say would needlessly
           provoke China during a time of already heightened global
           tensions from Russia’s invasion of Ukraine.


           “Chinese officials have warned of serious consequences should
           Pelosi make the trip.”


§ Transparency/Investigative Reporting⠀➾


    * ⚓ Techdirt ☛ The_Case_Against_Reality_Winner_Was_A_Travesty⠀⇛


           Ever since Reality Winner was arrested, we’ve written about the
           ridiculousness of her case. It was yet another in a long line
           of cases using the Espionage Act to go after whistleblowers who
           aren’t spies, but are actively trying to do the right thing —
           and, as per the Espionage Act — not even allowed to give the
           context to the court. And, as we noted, the information that
           Winner “leaked” and for which she was sentenced to five years
           in prison, was publicly revealed by other government agencies
           anyway, which seems to completely erase any claim that the
           leaking of the documents caused some sort of harm to national
           security.


§ Environment⠀➾


    * ⚓ Common Dreams ☛ Climate_Crisis_Linked_to_Deadly_Kentucky_Floods⠀⇛


           The planetary crisis was linked to at least 15 deaths in
           Kentucky Friday as heavy rains triggered what Gov. Andy Beshear
           called “one of the worst, most devastating flooding events” in
           the state’s history.


           “As we keep kicking the can on climate solutions, more lives
           will be lost in climate-based tragedies. We must act now.”


    * ⚓ Democracy Now ☛ Behind_the_Scenes_of_the_Senate_Climate_Bill_&_What
      Finally_Pushed_Joe_Manchin_to_Make_a_Deal⠀⇛


           President Biden is hailing a Senate bill negotiated by Joe
           Manchin and Chuck Schumer as “the most significant legislation
           in history to tackle the climate crisis.” While it faces
           hurdles before passage, the so-called Inflation Reduction Act
           would invest $369 billion into renewable energy and other
           measures to reduce reliance on fossil fuels. Leah Stokes, a
           professor of environmental politics who advised Senate
           Democrats on the legislation, says that while the bill is not
           perfect, it represents a major step forward. “We just do not
           have another decade left to wait if we really want to be on
           track to cut carbon pollution in half this decade,” says
           Stokes.


    * ⚓ Common Dreams ☛ Advocates_Slam_$0_for_Child_Care_in_Manchin_Anti-
      Inflation_Package⠀⇛


           Advocates for children and parents on Friday highlighted what
           they say is a major oversight in the Inflation Reduction Act,
           the climate and tax bill introduced this week after months of
           negotiations between Sen. Joe Manchin and Democratic leaders,
           as the package included no funding to help shore up struggling
           child care facilities across the United States.


           “There is unanimous frustration that Congress continues to push
           child care to the side, threatening small businesses, keeping
           parents out of the workforce and putting childrens’ development
           at risk.”


    * ⚓ TruthOut ☛ 369_Groups_Tell_Biden_to_Reject_Manchin’s_Big_Oil_“Handouts”
      in_Reconciliation⠀⇛


    * ⚓ FAIR ☛ Vivek_Shandas_on_Climate_Disruption_&_Heat_Waves,_Jamie_Kalven
      on_Laquan_McDonald_Coverup⠀⇛


    * ⚓ TruthOut ☛ Climate_Deal_Is_Making_McConnell_Gag_on_His_Own_Tactics_—
      But_It’s_Not_Done_Yet⠀⇛


    * ⚓ DeSmog ☛ Ireland’s_Agri_Lobby_Has_Dodged_Its_Climate_Commitments
      Through_Special_Pleading_and_Dubious_Science⠀⇛


           After months of protracted and often bitter wrangling,
           Ireland’s coalition government yesterday published emissions
           budgets for each part of the economy, in a bid to meet its
           ambitious climate goals.


           They take us a step further to achieving the 51 percent
           emissions cut by 2030 enshrined in legislation, but leave much
           to be desired. For a start, when all the sectoral targets are
           tallied up, they represent – at best – a 43 per cent reduction,
           according to the government’s own Climate Change Advisory
           Council (CCAC). 


    * ⚓ The Nation ☛ Gavin_Newsom’s_Letter_to_Biden_Urges_Climate_Action⠀⇛


    * ⚓ The Nation ☛ This_Year,_It_Was_New_Mexico’s_Turn_to_Burn⠀⇛


           Firefighters don’t normally allude to early English epics, but
           in a briefing on the massive Hermits Peak/Calf Canyon Fire in
           northern New Mexico, a top field chief said, “It’s like
           Beowulf: It’s not the thing you fear, it is the mother of the
           thing you fear.” He meant that the flames you face may be
           terrifying, but scarier yet are the conditions that spawned
           them, perhaps enabling new flames to erupt behind you with no
           escape possible. The lesson is a good one and can be taken
           further. If tinder-dry forests and high winds are the mother of
           the thing we fear, then climate change is the grandmother.


    * ⚓ DeSmog ☛ Climate_Protesters_Delay_Congressional_Baseball_Game⠀⇛


           The Congressional Baseball Game is an annual tradition that
           dates back to 1909. It’s supposed to be a time for both sides
           of the political system to come together and join in a peaceful
           nine innings of the national pastime. 


           But this year’s game, held on Thursday, July 28 at the
           Washington Nationals’ ballpark in Washington, D.C., was less
           sleepy than the average baseball game. Now or Never, a group of
           justice, faith, and climate organizations, held a protest in an
           attempt to disrupt the event and draw attention to the urgent
           need for large-scale climate action. 


    * ⚓ The Nation ☛ Red_Hot_Summer_In_America⠀⇛


    * ⚓ Democracy Now ☛ “Hellholes”:_Heat_Waves_Worsen_Conditions_in_Prisons
      with_No_Air_Conditioning,_Understaffing⠀⇛


           As tens of millions of people in the United States live under
           heat alerts this summer, we look at conditions faced by those
           in prisons and jails with poor cooling systems and lack of
           access to running water. “Although heat has been an ongoing
           issue in Texas, this year it’s exacerbated by a staffing crisis
           that’s been years in the making,” says Keri Blakinger, the
           first formerly incarcerated reporter for The Marshall Project.
           “This is a drastically underappreciated problem,” adds Dr.
           Homer Venters, the former chief medical officer for New York
           City’s Correctional Health Services.


    * ⚓ Democracy Now ☛ “Our_Lives_Depend_on_Passing_Climate_Policy”:_Meet
      Congressional_Staffer_Arrested_in_Senate_Protest⠀⇛


           Before a deal emerged this week on a bill to address the
           climate emergency, six congressional staffers were arrested
           Monday on Capitol Hill as they held a nonviolent civil
           disobedience protest inside the office of Senate Majority
           Leader Chuck Schumer, urging him to reopen negotiations on the
           bill. We speak with Saul Levin, one of the staffers who was
           arrested, and discuss the role the action had in pushing the
           bill forward. “Our lives depend on passing climate policy this
           year,” says Levin. “We hope that this had an impact.” We’re
           also joined by Leah Stokes, a professor of environmental
           politics who advised Senate Democrats on the legislation.


    * ⚓ Common Dreams ☛ Mediterranean_Sea_Ecosystem_Threatened_by_Heat-Induced
      ‘Marine_Wildfire,’_Scientists_Warn⠀⇛


           Scientists are warning this week that the prolonged and above-
           average temperatures gripping the Mediterranean Sea are causing
           a “marine wildfire” that could permanently alter the ecosystem
           and cause species extinction.


           David Diaz of the Spanish oceanographic institute told Le Monde
           such ocean heatwaves were “the equivalent of underwater
           wildfires, with fauna and flora dying just as if they had been
           burned.”


    * § Energy⠀➾


          o ⚓ FAIR ☛ Nightly_News_Fails_to_Connect_Gas_Price_Surge_and_Climate
            Crisis⠀⇛


                 Gas prices hit an all-time high in June, with the
                 national average surpassing $5 per gallon. A shortage of
                 Russian oil due to sanctions imposed by the European
                 Union, United States and others is largely to blame, and
                 in response President Biden has urged US oil companies
                 and other producers—like Saudi Arabia and the United Arab
                 Emirates—to increase their production to fill the gap.


          o ⚓ DeSmog ☛ When_Extreme_Weather_Reigns,_Disinformation_Pours⠀⇛


                 Recent extreme weather across the globe is showing us how
                 rapidly the climate is changing in an increasingly
                 warming world. Heatwaves are scorching Europe, the United
                 States, North Africa, Siberia, and some parts of the
                 Middle East and China. Last month, the worst heatwave
                 ever recorded hit Japan. In Brazil, more than 20,000
                 people were displaced after heavy rainfall in May
                 triggered floods and landslides. The month before,
                 extreme rainfall and floods in South Africa killed more
                 than 400 people. In Europe, Spain and Portugal are
                 battling wildfires, while Italy is suffering from the
                 worst drought in the past 70 years, with many
                 municipalities rationing water.


          o ⚓ TruthOut ☛ ExxonMobil_Is_Counting_on_Trump-Chosen_Judge_to
            Undermine_Right_to_Sue_Polluters⠀⇛


          o ⚓ Common Dreams ☛ Price_Gouging_at_the_Pump_Results_in_235%_Profit
            Jump_for_Big_Oil:_Analysis⠀⇛


                 As fossil fuel giants this week reported record profits
                 for the second quarter, an analysis out Friday
                 highlighted how eight oil companies have raked in nearly
                 $52 billion over the past three months “while Americans
                 continue to struggle at the pump.”


                 The review by the watchdog group Accountable.US revealed
                 that from April through June, Chevron, Equinor,
                 ExxonMobil, Hess Corp, Phillips 66, Shell, and TechnipFMC
                 “saw their profits skyrocket from the same time period
                 last year, with income shooting up 235%.”


          o ⚓ Common Dreams ☛ Climate_Coalition_to_Biden_and_Schumer:_Reject
            ‘Fossil_Fuel_Expansion’_in_Manchin_Deal⠀⇛


                 A climate justice coalition sent a letter Friday
                 imploring President Joe Biden and Senate Majority Leader
                 Chuck Schumer to reject any proposed fossil fuel
                 expansion during negotiations over the latest iteration
                 of the Democratic Party’s reconciliation bill.


                 “The unnecessary fracked gas Mountain Valley Pipeline and
                 further drilling in Alaska and the Gulf are not foregone
                 conclusions.”


          o ⚓ Common Dreams ☛ Major_Handouts_in_Manchin_Deal_‘Delighting’_Oil
            and_Gas_Industry⠀⇛


                 The U.S. oil and gas industry is openly lauding elements
                 of a reconciliation package that includes historic
                 renewable energy investments, a response likely to
                 heighten climate advocates’ wariness of the bill as
                 Democrats look to push it through the Senate as soon as
                 next week.


                 The legislation, whose scope and ambitions were dictated
                 by fossil fuel industry ally Sen. Joe Manchin (D-W.Va.),
                 includes components “that are helpful to our
                 business,” Rich Walsh of Valero said during the fossil
                 fuel giant’s earnings call on Thursday, referring to tax
                 credits in the 725-page bill that could benefit the
                 company.


    * § Wildlife/Nature⠀➾


          o ⚓ Counter Punch ☛ The_NYT_Promotes_Logging_in_Yosemite⠀⇛


                 The article states without qualification, “many experts
                 say there is a consensus among scientists and political
                 leaders on the need to thin and burn forests more
                 proactively.”


                 The article suggests that humans always managed the
                 landscapes in Yosemite and elsewhere. And that there is
                 consensus that Indian burning kept the forests open. This
                 view has been challenged but is not acknowledged in the
                 NYT piece.


          o ⚓ Nepal’s_tiger_population_reaches_355⠀⇛


                 Nepal has successfully achieved its goal of doubling the
                 tiger population by 2022, as per its commitment, along
                 with 12 other tiger range countries, the first tiger
                 summit in 2010 in St Petersburg.


                 In 2010, there were 121 tigers in Nepal. The number rose
                 to 198 in 2013 and 235 in 2018.


                 Nepal has now easily surpassed its commitment to increase
                 the number to 250 in 2022, as 355 tigers were counted
                 during the last census in December.


          o ⚓ The Washington Post ☛ In_much_of_Asia,_tiger_populations_are
            rebounding⠀⇛


                 Tiger researchers, while optimistic, warn that the fierce
                 hunter remains under threat from both poaching and
                 encroachment into its remaining habitat. And nations are
                 struggling to reach their collective goal of doubling the
                 population of wild tigers worldwide between 2010 and
                 2022, the last two years assigned to the tiger in the
                 Chinese zodiac.


          o ⚓ Nepal_Nearly_Doubles_Its_Wild_Tiger_Population⠀⇛


                 With fewer than 4,000 wild tigers left in the world, more
                 must be done to ensure tiger numbers keep trending
                 upwards. “Every tiger counts, for Nepal and the world,”
                 said Dr. Ghana S. Gurung, Country Representative of WWF-
                 Nepal. “While Nepal is but a few tigers away from our
                 goal to double tiger numbers by 2022, this survey
                 underscores the continued need to ensure protection and
                 improved and contiguous habitats for the long-term
                 survival of the species.”


          o ⚓ BBC ☛ Nepal:_Return_of_the_tigers_brings_both_joy_and_fear⠀⇛


                 Nepal’s zero-poaching approach has worked to protect the
                 tigers. The military units support the national park
                 teams. And in buffer zones next to the park, community
                 anti-poaching units monitor nature corridors that allow
                 tigers to roam safely.


    * § Overpopulation⠀➾


          o ⚓ Newsweek ☛ It’s_Earth_Overshoot_Day,_and_Future_Generations_Are
            Calling⠀⇛


                 July 28 is Earth Overshoot Day. As of that day, for the
                 rest of 2022, human economic activity will be using the
                 planet’s resources beyond its capacity to renew them.
                 Humans now consume things like wood, water, and soil at
                 nearly twice the rate the planet can support.


                 We’re also fast approaching climate overshoot, beyond 1.5
                 degrees Celsius of warming, by 2030. The Climate
                 Overshoot Commission will meet several times this year to
                 discuss ways to keep that from happening. Meanwhile the
                 World Meteorological Organization calculates a 50 percent
                 chance of touching the 1.5 degree threshold by 2026.
                 Recent intensified storms, fires, floods, and droughts
                 are all symptoms of the fever.


                 The dominoes are falling. Resource consumption drives
                 climate change, and the biggest driver of consumption is
                 population growth. Strategies for perpetual economic
                 growth demand ever increasing consumption, requiring more
                 and more people, pushing us into overshoot.


          o ⚓ Health_Minister_Offers_Absurd_Solution_to_Control_Pakistan’s
            Population⠀⇛


                 A recent UN report titled ‘World Population Prospects
                 2022’ revealed that Pakistan’s population will jump to
                 366 million by 2050. To put into perspective, it will be
                 an increase of 56% in the country’s current 220 million
                 population.


                 Instead of taking holistic measures after the publication
                 of the UN report, Federal Health Minister, Abdul Qadir
                 Patel, has come up with an absurd solution to rein in the
                 rapidly rising population of Pakistan.


          o ⚓ Qadir_Patel’s_out-of-the-box_advice_to_people_wanting_more
            children⠀⇛


                 Federal Minister for Health Abdul Qadir Patel Monday gave
                 an out-of-the-box solution to couples who want more
                 children.


                 Presenting a solution to them, the federal minister said
                 during an event that if couples want to have more
                 children, they can go to a country where there are fewer
                 Muslims — so that the Muslim population increases there.


          o ⚓ Dawn Media ☛ The_people_bomb⠀⇛


                 We are now faced with a perfect storm. Inadequate
                 investment in education and poor economic growth have
                 generated enormous resentment and anger among a youth
                 cohort that sees few prospects for advancement amid
                 contracting employment opportunities. The effects of
                 climate change are bearing down unmistakably upon us, and
                 making scarce resources even more so. Unpredictable
                 weather patterns and rising temperatures are adversely
                 affecting harvests and exacerbating food insecurity.
                 Population pressures also leave us much more vulnerable
                 to international developments such as the ongoing Russia-
                 Ukraine war that disrupt global supply chains. Shortages
                 of water and electricity have already begun to spark
                 unrest; the smallest provocation, it seems, is enough to
                 trigger mob violence in a people whose patience has been
                 stretched thin by poor governance, rising inflation and
                 urban crime. This is not how a country’s future is
                 secured.


          o ⚓ Daily Times ☛ Pakistan’s_population_to_double_in_next_30_years
            burdening_its_resources:_Turner⠀⇛


                 British High Commissioner on Tuesday observed that
                 Pakistan’s population was going to double in the next 30
                 years putting a huge burden on its resources that
                 demanded a proper response to address the pressing issue.


                 The British envoy made these remarks during a ceremony to
                 commemorate World Population Day, a collaborative event
                 conducted here in a joint effort of the United Nations
                 Population Fund (UNFPA) Pakistan, British High
                 Commission, Ministry of National Health Services,
                 Regulations & Coordination (NHSRC), and Population
                 Programme Wing (PPW), the event revolved around the
                 theme” A world of 8 billion: Towards a resilient future
                 for all – Harnessing opportunities and ensuring rights
                 and choices for all,” a news release said.


          o ⚓ Rapid_growth_in_Pakistan’s_population_warrants_head-on_response:
            UK_HC⠀⇛


                 While addressing the ceremony, Dr Christian Turner said,
                 “The business-as-usual approach needs to stop. It is
                 important to talk about family planning. The UK is the
                 largest donor on Family Planning in Pakistan and has been
                 supporting the country since 2012. Delivering Accelerated
                 Family Planning in Pakistan (DAFPAK) is a £90 million
                 programme that has so far reached 7 million family
                 planning users mostly from marginalised communities. The
                 UK remains committed to support Pakistan.” While
                 addressing the World Population Day event via a video
                 testimonial, President Dr Arif Alvi expressed concern
                 over the constant population growth and the meager
                 resources available in Pakistan.


§ Finance⠀➾


    * ⚓ Counter Punch ☛ American_Diplomacy_as_a_Tragic_Drama⠀⇛


           Confronted with China’s industrial prosperity based on self-
           financed public investment in socialized markets, U.S.
           officials acknowledge that resolving this fight will take a
           number of decades to play out. Arming a proxy Ukrainian regime
           is merely an opening move in turning Cold War 2 (and
           potentially/or indeed World War III) into a fight to divide the
           world into allies and enemies with regard to whether
           governments or the financial sector will plan the world economy
           and society.


           What is euphemized as U.S.-style democracy is a financial
           oligarchy privatizing basic infrastructure, health and
           education. The alternative is what President Biden calls
           autocracy, a hostile label for governments strong enough to
           block a global rent-seeking oligarchy from taking control.
           China is deemed autocratic for providing basic needs at
           subsidized prices instead of charging whatever the market can
           bear. Making its mixed economy lower-cost is called “market
           manipulation,” as if that is a bad thing that was not done by
           the United States, Germany and every other industrial nation
           during their economic takeoff in the 19th and early 20th
           century.


    * ⚓ Meduza ☛ The_film_industry_gets_creative_Russian_movie_theaters’_last-
      ditch_effort_to_survive_Hollywood’s_boycott_—_Meduza⠀⇛


           Russia’s movie theater industry is on the brink of collapse.
           After the country launched its full-scale war against Ukraine,
           Hollywood’s largest studios were quick to pull out of the
           market. Russian distributors initially thought they could make
           up for the lost movies by showing Indian and Latin American
           films, but filling theater seats has turned out to be harder
           than they anticipated. Now, the industry is discussing
           “solutions” such as the parallel import of foreign films,
           “compulsory licenses” issued by the Russian government, and the
           “non-contractual use of rights” to new films. Some theaters
           have already screened the latest Top Gun and Doctor Strange
           films illegally, and industry experts say illegal showings will
           only become more common as theaters fight to stay open. Meduza
           weighs the future of going to the movies in Russia.


    * ⚓ TruthOut ☛ 4_Companies_Filed_Nearly_15,000_Eviction_Actions_in_COVID’s
      First_16_Months⠀⇛


    * ⚓ Scheerpost ☛ Massachusetts_Trader_Joe’s_Becomes_First_to_Unionize_in
      Huge_Workers’_Victory⠀⇛


           Brett Wilkins reports on how grocery store workers in Hadley,
           Mass. organized and won a huge labor victory despite anti-union
           moves.


    * ⚓ Common Dreams ☛ Opinion_|_Debunking_Four_Myths_About_Inflation⠀⇛


           The truth about inflation is getting covered up by countless
           myths spewed by corporations and their political lackeys.


    * ⚓ Techdirt ☛ 76%_Of_U.S._Voters_Don’t_Know_Congress_Passed_A_Huge
      Infrastructure_Bill⠀⇛


           You might recall that John Oliver bit years ago about how
           Americans fall asleep when they hear the word “infrastructure.”
           We’ll obsess for hours over Elon Musk showmanship, or the
           innovative potential of NFTs, but the U.S. press in particular
           falls into a lazy stupor any time actual, essential
           infrastructure is mentioned. It’s a problem for a species
           facing an historic climate destabilization that heavily
           targets… infrastructure.


    * ⚓ Common Dreams ☛ Opinion_|_Interest_Rate_Hikes_Will_Not_Fix_Inflation⠀⇛


           In prescribing cures for inflation, economists rely on the
           diagnosis of Nobel laureate Milton Friedman: inflation is
           always and everywhere a monetary phenomenon—too much money
           chasing too few goods. But that equation has three variables:
           too much money (“demand”) chasing (the “velocity” of spending)
           too few goods (“supply”). And “orthodox” economists, from
           Lawrence Summers to the Federal Reserve, seem to be focusing
           only on the “demand” variable. 


    * ⚓ Common Dreams ☛ Opinion_|_The_Fed_Will_Be_to_Blame_if_the_Economy
      Crashes_Into_a_Recession⠀⇛


           The Federal Reserve’s interest rate policy is one of the most
           important economic decisions that our government makes. If it
           were more widely understood, and the Fed were held more
           accountable, Fed officials would probably be more careful about
           the downside risks of raising interest rates too much.


§ AstroTurf/Lobbying/Politics⠀➾


    * ⚓ The Nation ☛ Missouri_Senate_Hopeful_Lucas_Kunce_Battles_Big_Money_in
      Both_Parties⠀⇛


           There is a good debate to be had about whether newspaper
           endorsements still carry the weight in political races that
           they once did. But if Missouri Democrats are serious about
           winning the race for that state’s open US Senate seat, they
           will pay close attention to the reasoning of the St. Louis
           Post-Dispatch editorial board than they do to ads from
           millionaire candidates and special-interest groups that are
           flooding the state’s airwaves.


    * ⚓ The Nation ☛ We_Sing,_We_Dance⠀⇛


    * ⚓ TruthOut ☛ ALEC_Focuses_on_“Woke_Capitalism,”_Bodily_Autonomy_and_More
      at_Annual_Meeting⠀⇛


    * ⚓ Democracy Now ☛ Why_Is_AIPAC_Spending_Millions_in_Primary_to_Defeat
      Rep._Andy_Levin,_a_Former_Synagogue_President?⠀⇛


           As the American Israel Public Affairs Committee (AIPAC) invests
           millions in Democratic primaries to defeat progressives who
           support Palestine, we speak to one of the candidates: Michigan
           Congressmember Andy Levin, whose primary is on Tuesday. He is a
           self-described Zionist who supports a two-state solution, but
           earlier this year a former president of AIPAC described him as
           “arguably the most corrosive member of Congress to the U.S.-
           Israel relationship.” “What you have here is a real threat to
           the Democratic Party being able to choose our own nominees that
           we send to the general election in November,” says Levin. Levin
           was among 17 House Democrats arrested Tuesday in a pro-abortion
           protest outside the U.S. Supreme Court.


    * ⚓ Scheerpost ☛ Fun_Fun_Fun!⠀⇛


           “Fun Fun Fun,” a new original cartoon by the inimitable Mr.
           Fish, considers the altruistic side of the Republican Party.


    * ⚓ Common Dreams ☛ Following_Trump’s_Lead,_GOP_Pushes_Bill_to_Make_Federal
      Workers_Fireable_‘At_Will’⠀⇛


           U.S. Rep. Chip Roy’s introduction Friday of a bill to make
           federal bureaucratic personnel at-will employees further stoked
           fears that marginalized workers will suffer discriminatory
           firings under a future Republican administration or even GOP-
           controlled Congress.


           “This is obviously a huge and major change, an effort to gear
           up a major assault on the federal employment system.”


    * ⚓ Scheerpost ☛ Katie_Halper:_Trump_‘Broke_Liberals’_Brains’⠀⇛


           The comedian and host of two popular progressive podcasts
           offers her take on why the American left keeps getting things
           wrong.


    * ⚓ TruthOut ☛ Warnock,_Abrams_in_Close_Races_With_Republicans_in_Georgia
      Races⠀⇛


    * § Misinformation/Disinformation⠀➾


          o ⚓ NBC ☛ In_a_California_town,_a_militia_is_welcomed_by_some,
            cautioned_by_others⠀⇛


                 “There is a wide open park with a shade filled pavilion.
                 Completely empty. You would figure that would be the
                 perfect area for evacuees to eat and unwind, but no, they
                 chose a couple parking lots in the middle of town, highly
                 visible, so they could advertise,” a commenter responded.


                 “They have no authority. They are in costume and they
                 want attention. That is all. Otherwise they would move
                 their charade to a place that makes sense.”


          o ⚓ India Times ☛ Meta_to_no_longer_fund_its_news_publishers_in_US:
            Report⠀⇛


                 Tech giant Meta has started informing its news partners
                 that the company will stop paying publishers for their
                 content to run on Facebook’s News Tab in the US.


                 According to Axios, as the company is moving forward with
                 sweeping changes to the Facebook experience, news has
                 become less of a priority.


          o ⚓ NBC ☛ Elon_Musk_countersues_Twitter,_but_details_of_the_suit_are
            confidential⠀⇛


                 It wasn’t clear why Musk asked the court to keep details
                 of his countersuit confidential when the billionaire, who
                 is also the CEO of SpaceX, had been vocally critical of
                 Twitter on social media and in press interviews in recent
                 months.


          o ⚓ The Hill ☛ Musk_confidentially_countersues_Twitter_over_nixed
            acquisition_bid:_reports⠀⇛


                 Tesla CEO Elon Musk confidentially filed a countersuit
                 against Twitter after the company sued him for
                 terminating a deal to buy the social media platform for
                 $44 billion earlier this month, according to multiple
                 news reports.


          o ⚓ Reuters ☛ Elon_Musk_files_countersuit_under_seal_vs_Twitter_over
            $44_bln_deal⠀⇛


                 Elon Musk countersued Twitter Inc (TWTR.N) on Friday,
                 escalating his legal fight against the social media
                 company over his bid to walk away from the $44 billion
                 purchase, although the lawsuit was filed confidentially.


                 While the 164-page document was not publicly available,
                 under court rules a redacted version could soon be made
                 public.


          o ⚓ Axios ☛ Scoop:_Meta_officially_cuts_funding_for_U.S._news
            publishers⠀⇛


                 Catch up quick: Facebook brokered a slew of three-year
                 deals with publishers in 2019. At the time, the company
                 was ramping up its investment in news and hired
                 journalists to help direct publisher traffic to its new
                 tab for news.


                 The deals were worth roughly $105 million in the U.S.,
                 sources told Axios. In addition to that, the company
                 spent around $90 million on news videos for the company’s
                 video tab called “Watch.”


          o ⚓ Axios ☛ Reality_crashes_down_on_Meta⠀⇛


                 Driving the news: The tech giant told investors Wednesday
                 that it’s planning to cut costs, slow investments and
                 reduce head count as it braces for what CEO Mark
                 Zuckerberg called a “downturn” that has already begun to
                 wreak havoc on its business.


§ Censorship/Free Speech⠀➾


    * ⚓ WSWS ☛ WSWS_readers_defend_Zero-COVID_advocate_Dr_David_Berger⠀⇛


           The WSWS continues to receive statements in defence of Dr David
           Berger, a respected Australian physician and dedicated zero-
           COVID advocate who is being threatened with deregistration by
           the Australian Health Practitioner Regulation Agency (AHPRA)
           over his social media condemnations of the government’s “let it
           rip” coronavirus policies.


    * ⚓ YLE ☛ Turkey_again_requests_legal_assistance_against_Tampere_man_that
      insulted_Erdoğan⠀⇛


           The man is accused by Turkey of posting derogatory pictures of
           the President and derogatory comments about him on Facebook,
           according to the prosecutor. The man from Tampere has
           repeatedly denied the crime [sic].


    * ⚓ RFERL ☛ Iranian_Actress_Nazanin_Bahrami_Reportedly_Detained,
      Whereabouts_Unknown⠀⇛


           Bahrami was one of some 800 women to recently sign a statement
           denouncing the “systematic” sexual harassment and violence
           against women in the Iranian film industry and had called for a
           mechanism to ensure those responsible were dealt with.


           Her relatives said Bahrami was returning home in the capital
           from work when she was surrounded by plainclothes police and
           taken into custody.


           Her whereabouts are not known and officials have not commented
           on the situation.


    * ⚓ Frontpage Magazine ☛ Death_for_‘Blasphemers’_in_Pakistan⠀⇛


           The problem with this law is not so much that its sentencing is
           extreme and irrevocable but rather that Muslims regularly
           exploit it to settle personal grudges against non-Muslim
           minorities in Pakistan, as in this case. The fact is,
           Pakistan’s non-Muslim minorities, mostly Christians and Hindus,
           know better than to say anything that can be misconstrued as
           offensive to the Muslim prophet—being, as they are, well
           acquainted with the dire repercussions. They are taught from
           youth to exhibit nothing but deference for Islam’s prophet. But
           that does not stop Muslims from falsely accusing those
           “infidels” they have a grudge against of vocally insulting
           Muhammad.


    * ⚓ [Old] Amnesty International ☛ Pakistan:_Use_and_abuse_of_the_blasphemy
      laws⠀⇛


           AI is concerned that a number of people facing charges of
           blasphemy, or convicted on such charges have been detained
           solely for their real or imputed religious beliefs. Most of
           those charged with blasphemy belong to the Ahamdiyya community
           but Christians have increasingly been accused of blasphemy,
           among them a 13-year-old boy accused of writing blasphemous
           words on the walls of a mosque despite being totally
           illiterate. The following case histories are supplied: Anwar
           Masih, a Christian prisoner; Arshad Javed, reportedly mentally
           ill, sentenced to death; Gul Masih, a Christian, sentenced to
           death; Tahir Iqbal, a convert to Christianity, died in jail
           while on trial; Sawar Masih Bhatti, a Christian prisoner; Dr
           Akhtar Hameed Khan, Muslim social activist; Chand Barkat, a
           Christian acquitted of blasphemy but continuously harassed;
           Hafiz Farooq Sajjad, stoned to death; Salamat Masih, Manzoor
           Masih and Rehmat Masih, three Christians.


    * ⚓ Techdirt ☛ Trump_Says_It’s_Defamation_To_Call_His_Lying_About_The
      Results_Of_The_2020_Election_‘The_Big_Lie’⠀⇛


           Donald Trump, whose supporters still pretend is a “free speech”
           champion, has regularly been known to sue news organizations
           that are mildly critical of him. You may recall that back in
           2020 he hired notorious-lawyer-for-suing-media-companies (yes,
           he once was the lawyer in a case against us), Charles Harder,
           and sued both the NY Times and the Washington Post. The NY
           Times case was dismissed easily. The Washington Post case
           appears to somehow still be alive, though not much has happened
           in a while. It was, initially, assigned to Judge Ketanji Brown
           Jackson, who has since received two separate promotions, which
           took her off the case. Somewhere along the way, Harder left the
           case and was replaced by Harmeet Dhillon, who has been a
           favorite lawyer of perpetually aggrieved culture warriors.


§ Freedom of Information / Freedom of the Press⠀➾


    * ⚓ The Nation ☛ David_Moberg,_1943–2022⠀⇛


           In September 1965, David Moberg, a 22-year-old reporter in
           Newsweek’s Los Angeles bureau, interviewed Bob Dylan, who had
           just begun using electric instruments in his recordings and
           concerts, which upset fans who preferred a more traditional,
           acoustic sound. He asked the singer if there was a “new” Bob
           Dylan. Dylan responded, “How would you like it if somebody
           introduced you as the ‘new’ David Moberg?”


§ Civil Rights/Policing⠀➾


    * ⚓ BBC ☛ Iran:_Ex-child_bride_among_three_women_executed_in_one_day_–
      report⠀⇛


           Rights groups report that Iran also executes more women than
           any other country, the majority of whom are thought to have
           been found guilty of killing their husbands.


           On Wednesday, the Iran Human Rights Group says former child
           bride Soheila Abadi was hanged in prison after being convicted
           of killing her husband after marrying him 10 years previously
           when she was 15 years old.


    * ⚓ Internet Freedom Foundation ☛ Hey_CM_leave_those_kids_alone!⠀⇛


           In the latest edition of the Delhi Government’s CCTV saga,
           parents will now be able to livestream CCTV footage of the
           children who study in Delhi govt. schools. Concerned about
           potential misuse, we wrote to the Chief Minister’s Office
           urging them to recall the scheme.


           Why should you care?


           CCTV surveillance has risen exponentially in the national
           capital. According to a report titled, “Delhi, Chennai among
           most surveilled in the world, ahead of Chinese cities”,
           published on the Forbes India website on August 26, 2021, Delhi
           is the most surveilled city in the world with 1,826.6 cameras
           per square mile. While we were concerned after seeing this
           report, the Government of Delhi on the other hand seemed to
           take it as an achievement. Now, the Government of Delhi is
           planning to livestream CCTV footage from government schools to
           the parents of their children. It is essential that we resist
           the urge to normalise these levels of surveillance, especially
           because increasing surveillance fails to fulfil its primary
           promise, a corresponding increase in security.


    * ⚓ TruthOut ☛ Michigan_High_Court:_Anti-Discrimination_Law_Applies_to
      LGBTQ_Residents⠀⇛


    * ⚓ The Nation ☛ After_Dobbs,_Republicans_Offer_Few_Ideas_for_Increasing
      Support_for_Children_and_Families⠀⇛


           The conservative movement that has worked for a half century to
           overturn the 1973 Supreme Court decision Roe v. Wade has
           finally succeeded: As of the Supreme Court’s decision in the
           Dobbs case in June, abortion is no longer a constitutional
           right guaranteed across the country.


    * ⚓ TruthOut ☛ Alito_Gloats_and_Taunts_Critics_of_His_Anti-Abortion
      Ruling⠀⇛


    * ⚓ Common Dreams ☛ Biden_Applauded_for_Nominating_‘Distinguished’_Abortion
      Rights_Lawyer_to_Federal_Court⠀⇛


           Reproductive freedom advocates on Friday praised President Joe
           Biden’s nomination of an abortion rights attorney to the
           federal bench in the wake of the U.S. Supreme Court reversing
           Roe v. Wade.


           “This important nomination… could not come at a more important
           time in the fight for reproductive freedom.”


    * ⚓ TruthOut ☛ Massachusetts_Trader_Joe’s_Workers_Celebrate_Forming
      Company’s_First-Ever_Union⠀⇛


§ Internet Policy/Net Neutrality⠀➾


    * ⚓ Techdirt ☛ Comcast_Loses_500k_Video_Customers,_Fails_To_Add_Broadband
      Users_For_First_Time_In_History⠀⇛


           Comcast had a particularly ugly second quarter, according to
           the company’s latest earnings report. The nation’s biggest
           cable giant not only lost half a million pay TV subscribers as
           the cord cutting trend continued, it failed to add any new
           broadband customers for the first time in company history.


§ Monopolies⠀➾


    * ⚓ The Verge ☛ FTC_staff_reportedly_recommended_against_suing_Meta⠀⇛


           The FTC’s latest suit targets the specific category of VR
           fitness apps. But a key claim is that buying Within has a
           larger purpose for Meta: “building, and ultimately controlling,
           a VR ‘metaverse.’” It asserts that by buying the fitness
           studio, Meta is removing competition that could spur it to keep
           improving its own software offerings, including the fitness-
           adjacent rhythm game Beat Saber. “As early as 2015, Mr.
           Zuckerberg instructed key Facebook executives that his vision
           for ‘the next wave of computing’ was control of apps and the
           platform on which those apps were distributed,” it says. “A key
           part of this strategy was for his company to be ‘completely
           ubiquitous in killer apps.’”


    * § Trademarks⠀➾


          o ⚓ Techdirt ☛ Rapper_IDK_Calls_Out_Popeyes_Over_Trademark_Because
            He’s_Trademark_Illiterate⠀⇛


                 I’ll preface this post with this short bit of throat-
                 clearing: no writer or reader of this site should expect
                 the average person on the street to understand the
                 nuances of intellectual property at the same level of
                 those of us interested in the topic. The law is
                 complicated and nuanced, and the layperson is simply not
                 going to have the background that some of us have.


    * § Copyrights⠀➾


          o ⚓ Torrent Freak ☛ Piracy_Lawsuit_Triggers_Dispute_Over_‘Hollywood
            Style_Quality’_of_Adult_Films⠀⇛


                 Piracy lawsuits should be pretty straightforward.
                 Rightsholders must provide solid evidence that someone
                 shared a copy of their content without permission.
                 However, in a piracy case filed by adult entertainment
                 company Strike 3 the purported “Hollywood style quality”
                 of the porn videos is now a topic of contention.


§ Gemini* and Gopher⠀➾


    * § Personal⠀➾


          o ⚓ Equalizer_Baduk_variant⠀⇛


                 Players take turns saying a number or passing. You can’t
                 say a number higher or the same as what’s already been
                 said. It’s an action and who bids lowest is the
                 equalizer.


                 The equalizer sits on black’s left side and white’s
                 right. East, if black is north and white is south.


          o ⚓ How_to_Watch_Terminator⠀⇛


                 I’ve re-watched all the Terminator movies in the past few
                 days, trying to determine how they fit together in some
                 sort of watch order. (A small disclaimer is in order: I
                 haven’t seen a single episode of the Sarah Connor
                 Chronicles. This post is about the movies only.)


                 It’s not… easy. Almost all those following Terminator:
                 Judgment Day are reboots or rewrites of the storyline.
                 Although they do take advantage of the confusing
                 mechanics of time travel to sort of make it work.


                 So how do we do this? Let’s attempt to make some sense to
                 it. Here’s what I choose to call the School Bus Approach
                 to Terminator (stupid name, sure, but I’m just now re-
                 watching the scene in Genisys where a school bus tumbles
                 around on the Golden Gate Bridge).


          o ⚓ The_Martian_and_Project_Hail_Mary⠀⇛


                 I rewatched The Martian some weeks back and had the idea
                 to read the book by Andy Weir it was based on. I ended up
                 liking it enough to also check out Andy Weir’s most
                 recent book, Project Hail Mary. And it’s a good thing I
                 did since that one, in my opinion, is even better.


                 I won’t go too into detail but the two books are pretty
                 similar. If you like one you’ll almost certainly enjoy
                 the other. But they each also feel different and unique
                 which I appreciate having read the two back to back.


          o ⚓ Washington,_Oklahoma,_Kansas/Missouri⠀⇛


                 My wife and I took our first ever real vacation in the 17
                 years we have been married.


          o ⚓ Saniĝanta_kaj_pensanta_pri_teĥnologio_senkomprena⠀⇛


                 I’ve recovered from whatever illness I had before.
                 Perhaps it was food poisoning, or some side-effect of jet
                 lag, or some virus or bacterium. Whatever it was, it’s
                 done.


                 I’m taking a couple days vacation with my family in The
                 Windy City before I start working for the nonprofit. We
                 drove here 2 days ago and spent yesterday at a car
                 dealership looking at folkloric shirts (it’s a long
                 story). Today we’re going to visit museums.


          o ⚓ Travel_Fatigue_and_US_hospitality⠀⇛


                 Greetings fellow pub-goers, it’s been a while and I’m all
                 traveled out.


                 Maybe it was an attempt to make up for the lack of going
                 anywhere over the last two years, or just a yearning for
                 being anywhere else — but after visiting my family
                 earlier this year, going to a wedding in a hot country
                 last month, and spending three weeks just now in the US —
                 I can safely say that I’m done.


                 There is only so much walking under the midday summer sun
                 in a hot country that I am willing to do, and I think I’m
                 well past any healthy limit. Plus, I just can’t handle
                 takeoff’s and landings anymore. It’s gotten to the point
                 that I automatically revert into a meditative state where
                 I hum a song to myself with my hands clasped lightly
                 together until the plane levels out.


    * § Technical⠀➾


          o ⚓ I_Just_Left_Feedly!⠀⇛


                 Running FreshRSS has been a great experience. So much so
                 that I almost forgot that I had Feedly account, despite
                 using it for more than a decade.


                 I’m subscribing to more feeds now. Adding new
                 subscriptions no longer feels like a dumb idea; reading
                 posts on Feedly was starting to become so annoying I just
                 didn’t want more there.


                 Because I’ve locked my FreshRSS instance between HTTP
                 Auth (it’s only for me, after all) it can’t do WebSub
                 (formerly PubSubHubub). But that’s okay. It just meant
                 that the initial import from the OPML file I got from
                 Feedly threw a few errors. It quickly adapted.


          o ⚓ Two_Weeks_With_the_Snail⠀⇛


                 Most of the time, I focus on one or two applications (a
                 browser or a text editor and a browser), and everything
                 else (like the IRC client) is packed neatly in the stack
                 area. Therefore, I’m fine with this limitation. I tried
                 to tune the formula to allow 3 tall windows in the master
                 area even with a 16:9 monitor, but they’re just too
                 narrow. A high-resolution display doesn’t help, because
                 many UIs (especially IDEs with sidebars) don’t work well
                 when they’re so narrow.


                 I find the snail layout very nice to use when I combine
                 it with “workspaces”. I have one tag with my coding setup
                 (text editor, browser, IRC client, two general-use
                 terminals) and another for everything else (audio mixer,
                 Bluetooth settings, etc’). The former has room for two
                 tall windows in the master area, and the latter is always
                 a mess with “temporary” windows I forgot to close, and
                 changes constantly.


          o § Science⠀➾


                # ⚓ Hackaday ☛ Testing_Antennas_With_WSPR⠀⇛


                       There are many ways to test HF antennas ranging
                       from simulation to various antenna analyzers and
                       bridges. However, nothing can replace simply using
                       the antenna to see how it works. Just as —
                       supposedly — the bumblebee can’t fly, but it does
                       so anyway, it is possible to load up some bed
                       springs and make contacts. But it used to be
                       difficult — although fun — to gather a lot of
                       empirical data about antenna performance. Now you
                       can do it all with WSPR and [TechMinds] suggests a
                       moderately-priced dedicated WSPR transmitter to do
                       the job. You can see a video about the results of
                       this technique below.


                # ⚓ Hackaday ☛ Calculus_Made_Easy_In_The_Car⠀⇛


                       If you had the traditional engineering education,
                       you’ve made your peace with calculus. If you
                       haven’t, you may have learned it on your own, but
                       for many people, calculus has a reputation for
                       being super difficult. While some of the details
                       can be very tricky, the core concepts are actually
                       simple and [Mathologer] has a very simple
                       explanation along with some good graphics that can
                       help you get started on calculus mastery if you’ve
                       been putting it off. Using a car on the highway as
                       the prototypical example, he covers quite a bit of
                       ground in the 30 minute video that you can see
                       below.


          o § Internet/Gemini⠀➾


                # ⚓ New_Lagrange_Fontpack:_W95FA⠀⇛


                       I’ve packaged W95FA for the Lagrange gemini browser
                       as a bit of fun.


          o § Programming⠀➾


                # ⚓ I_can’t_stand_developer_interviews_with_algorithms_(Or,_why
                  I’m_learning_APL)⠀⇛


                       I’ve been contacted by several HR people who are
                       looking for a software engineer. It’s good. I’m
                       always looking for new challenges. What I can’t
                       stand is a large portion of the company decides
                       that they should test the candidate’s algorithm
                       skill. Sorry, what? You just said you want to hire
                       a senior GPU developer. Instead of interviewing
                       with actual related domain knowledge and writing
                       code that runs on the GPU. You decided if I want
                       the potision, I should spend time on LeetCode and
                       write algorithm questions. You are waisting my
                       time. And so I’ll have my revenge.


                # ⚓ Unmaintained_packages⠀⇛


                       I’m a strong advocate of downstream packaging,
                       however, one of the downsides I neglected to
                       mention is when a package becomes unmaintained
                       (i.e, orphaned). I’ve seen this happen with both
                       traditional package management and also on Flathub.


                       In the latter case, the update for an app and a PR
                       was available for months, but the maintainer was
                       inactive. I e-mailed the Flathub admins and they
                       manually intervened. It was for an emulator, so not
                       a big deal and I didn’t plan on using it for long
                       anyway. As another example, arc-theme (a GTK theme)
                       was outdated for months as the original upstream
                       was no longer maintained. It took a while for the
                       package for a new maintainer to adopt the package
                       and switch to the new upstream.


                # ⚓ moving_forward⠀⇛


                       So I got let go from Google Summer of Code, it’s
                       unfortunate, but the project just involved
                       different skillsets than I expected, and I wasn’t
                       able to hack it. I have enough money to probably
                       get me through August and into the period of time I
                       go to houston to visit family.


                       I originally saw these as two seperate projects,
                       but in the process of writing them, I have realized
                       that they can be completed in sequence.


                       Start a personal project, see if it gets big, then
                       either go to houston and work on it there for free
                       for a while, or come back after going there for a
                       few weeks and work on it here. Coming back would be
                       preferable, but I probably would have to get a
                       “regular job” to pay for myself until I could get
                       it out.


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


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