𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Friday, October 01, 2021
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Generated Sat 2 Oct 02:39:58 BST 2021
Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖)
Full hyperlinks for navigation omitted but are fully available in the originals
The corresponding HTML versions are at 𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈
Latest in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕 and older bulletins can be found at 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕-𝒂𝒓𝒄𝒉𝒊𝒗𝒆𝒔
Full IPFS index in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔 and as plain text in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔/𝒕𝒙𝒕
Gemini index for the day: gemini://gemini.techrights.org/2021/10/01/


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

QmUnQ1KgLk5TqpmioRpKSTQMgTjk8uPKTKhNxDBwtV545z
QmUPLCS39mA6XaZmdzwh1WbF8ry8hiVAzuaf4P9A1AmKbd
QmNdAU6bFwZMUbnvK1m3e7aSwoHNFY97JdqWjpMVzvVT6V
QmSDxEDkdmunKoZmMNVwhKaEKpJYVPqrdqPnbEGhNadE9g
QmU3Cc6hMhpsNzFQ82J5uqhtgrCrh67mKLmWhYadentK2o
QmQacCjdmHDTi18CHZHhTZoQaq1qFiasj5iWoMZ8Fehf5q
QmPWMxYuC9jpqYMEsNWeqP6frZMUpZi99XXbWkJNBJUKoi
QmVJRjPH1YsZzKy3abfyBSCWdBy7Pfm7cEB8d1g1cQQyfd
QmNUSEXDbUxbW6m6ooyVZNdN7ZyhMjh1q1VNUXyw4WUQ3i
QmXigVXDZA7wuFXWn1ieyB6Z3Vz1jBDVuLsbFcmJW29g7k
QmPEfsYcyS2TDHQVY6rC6oShWGQQA9zzKSLEsWg34fRiPT
QmZvjyhZs3sJdozDCTLX1fbmAMdwoGgJqcPT97hYdb4eS8
QmP3ZqUhWLtsoNk9e1XZbKMU4hB7Z4XET8rdm3utr2x9y9
QmRJGaosMaTsLMaPkXt42c3eUm2cmGbMQsiWbqwfSj4rFV
QmVpm9hDw5gu77p5GNGaG5DU2W7uzy83mFBbqknJREAU3w
QmV3rmUZyHKRZr4HLVsZHXH3SyMh5Xz6dwshz5vRFuVMAD
QmSoYJzJX4ejm4LRdPXhN6F7YBjLvbCRnrxdhaDSj8iaNC
QmbpQyjzfhZNaWnZ1L6GHyRzDA6B5RojnHgAGKGeJKMiyn
QmZjNRnDnEWPhNuhKXBvuyovU32qnjESR1UG1T8emS6oy2
QmSjHyfej3iKcBfRyB2EGPkqcfwQ3z51X2Qz89CbQ1D5GX
QmRXKRPosZ7Bz2MggcSzikrb6U91AxeDNghC3nQk4eD4fh


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

⦿ IRC Proceedings: Thursday, September 30, 2021 | Techrights

⦿ [Meme] Over-the-Web JavaScript Itself is the Problem (Someone Else’s Server Running Code on Someone Else’s PC) | Techrights

⦿ With Microsoft, Security Breaches Are Presumed | Techrights

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
		http://techrights.org/2021/10/01/irc-log-300921/#comments
		http://techrights.org/2021/10/01/js-is-the-problem/#comments
		http://techrights.org/2021/10/01/microsoft-azure-is-a-security-breach/#comments

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
		http://techrights.org/2021/10/01/gemini-migrations/#comments
		http://techrights.org/2021/10/01/ghostbsd-21-09-29-iso/#comments
		http://techrights.org/2021/10/01/llvm-13/#comments
		http://techrights.org/2021/10/01/xfce-update/#comments

                    ䷩ 𝚕𝚒𝚗𝚎 56

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/10/01/irc-log-300921/#comments
    Gemini version at gemini://gemini.techrights.org/2021/10/01/irc-log-300921/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 10.01.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ IRC_Proceedings:_Thursday,_September_30,_2021⠀✐


Posted in Site_News at 2:53 am by Needs Sunlight


Also available via the Gemini protocol at:


    * gemini://gemini.techrights.org/tr_text_version/irc-log-techrights-
      300921.txt
    * gemini://gemini.techrights.org/tr_text_version/irc-log-300921.txt
    * gemini://gemini.techrights.org/tr_text_version/irc-log-social-300921.txt
    * gemini://gemini.techrights.org/tr_text_version/irc-log-techbytes-
      300921.txt
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
 Qmd9ygn4gGEK7rTg8GZft7VHcYfkMJcEnPCXzhxipKxPh7 #boycottnovell  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell
 Qmf8okkFW8ybyX61qSZi9pbQFb8UdyLxdNk1P9NXrb4sB3 (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
                                                 #boycottnovell-
 QmecFeoDDPtHJD7HYMkMzyCmWv9ixiB9kxFK8iaWZuWMsP social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell-
 QmWExioLPiQ8iVYroH7HwaL7tEni4Mpr3HTWbTH4oQFi6p social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 (full IRC log
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 QmZt8ZTaKy2TJeuLT7Gz3krB9FtkUAfM6Dsa7Mrhck3WKF #techbytes      🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techbytes
 QmUWhsMaDi7Y4zNZYmALtj7167guEnrAWbZN44Vrs7Dv1L (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 QmZgMVVVp4zC9XoGgC9BYobrrRYQZNkyFV5tVaZBiDF1Mo #techrights     🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techrights
 QmeAFyt44V5vahpGxwEogEbJMozJ9rdU1BmE7h5aSxU6YK (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈


§ Bulletin for Yesterday⠀➾


Local_copy | CID (IPFS): QmRXKRPosZ7Bz2MggcSzikrb6U91AxeDNghC3nQk4eD4fh



                    ䷩ 𝚕𝚒𝚗𝚎 185

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/10/01/js-is-the-problem/#comments
    Gemini version at gemini://gemini.techrights.org/2021/10/01/js-is-the-problem/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 10.01.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_Over-the-Web_JavaScript_Itself_is_the_Problem_(Someone_Else’s_Server
Running_Code_on_Someone_Else’s_PC)⠀✐


Posted in Free/Libre_Software, FSF at 3:19 am by Dr. Roy Schestowitz


Alex Oliva et al (including Richard Stallman) mentioning Gemini: Alexandre
Oliva:_The_WWWorst_App_Store


Yesterday (by FSF): FSF_announces_JShelter_browser_add-on_to_combat_threats
from_nonfree_JavaScript | Keeping_your_freedom_intact_when_registering_or
renewing_as_a_DMCA_agent


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇I told you. Just move to Gemini. I've made more JS.⦈
Workarounds are not solutions. Maybe another approach is, let’s get off the Web
(to the extent possible). There are also benefits for the environment and that
  scales well for residential connections (hosting from home, self-hosting).


                 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Gemini_near_1700_October⦈_
 Gemini near 1,700 known capsules now. It’s growing_fast. More of us adopt it
                                    [1, 2].


Summary: JavaScript as a concept (Web sites running code on someone else’s
computer) is flawed; for more things we need to adopt and spread something like
Gemini (where such a mindset is strongly and actively discouraged)


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⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡆⠀⠀⠀⠀⠀⠀⣼⠄⠀⠹⠋⣉⣙⢻⡟⠀⠘⢻⡿⠍⠀⠙⡄⠀⣿⡟⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣧⣽⡿⣯⣽⡿⣿⢻⣿⣿⣟⣿⣿⣹⣯⣿⣷⣼⣿⣿⡇⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠚⣿⣷⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡟⣿⢸⡯⣿⠁⣿⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡏⣿⣿⡇⣀⠀⠘⢙⠃⠀⠀⠀⣠⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⠚⠁⠀⠀⠀⠀⠀⢸⠙⡂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡇⣿⢸⣇⣿⣶⣿⣿⣏⣿⣷⣿⣿⣟⣿⣿⣿⣿⣿⣻⡅⠙⠛⠁⠉⠀⠀⠿⠨⢄⣀⢘⡻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣿⣟⣛⣿⣟⣒⢻⣿⢿⣿⣿⢿⡟⣯⣯⣿⡟⢹⣿⡿⢹⡿⣿⢿⢱⡟⣷⢸⣟⣻⣿⣿⣿⣿⣿⢻⣧⣿⢸⡇⣿⡄⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⡃⢹⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⢹⣿⠆⠀⢻⣏⣸⡇⣿⣹⢸⡗⣾⣸⣿⡃⣿⣿⣿⡏⣿⢸⡿⣿⢸⣇⣿⣿⠂⠀⠀⠀⠀⠀⠸⢻⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⣿⢶⣿⣿⢸⣿⣿⣿⣿⣿⣿⡟⢿⣿⣧⣿⣿⣼⣿⣶⣼⣾⣿⣿⣿⣿⣾⡏⠛⠛⠙⠋⠁⢉⡍⣈⡥⠉⠈⠁⠑⣶⣶⣷⣻⣄⣀⣀⡀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠉⠈⠉⠁⠈⠉⠁⠀⢰⠀⢠⠖⢱⣿⣿⣿⣿⣿⣿⣿⣌⡁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⣿⣿⣿⠇⣿⣿⠟⠀⠄⣀⠤⠄⣲⣖⡢⡤⣄⡭⡈⠦⠿⢿⠿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⢵⣿⣿⣿⣿⣿⣿⣿⣿⢯⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⢿⣟⣿⠌⠀⠠⣢⡷⠻⠐⠉⡁⢹⣯⣿⣿⣮⣯⡾⡢⡈⢃⠷⣿⣿⡟⠉⠉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣿⠌⡰⡕⠋⠈⠀⠀⠑⢤⣾⣿⣿⣿⣿⣿⣿⣯⣎⠄⢢⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢜⠟⠀⠑⠁⠀⠀⠀⠀⠀⢾⠁⣿⣿⣿⣿⣿⣿⠘⠟⡞⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡍⠀⠀⠀⠀⠀⠀⠀⠀⣴⡺⠀⣿⣿⣿⣿⣿⣟⢠⣦⡇⡅⢸⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⡄⢀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠻⠡⣾⣿⣿⣿⣿⣿⡇⠃⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢁⡇⠈⠀⣤⣴⠞⠳⡁⠉⠀⠀⠀⠈⠈⠈⠻⢿⣿⡿⢿⠀⣀⠛⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠈⣿⠇⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠲⣜⠴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣴⣶⣾⣿⣿⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢻⣿⣿⣇⣴⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣽⣿⣿⣾⣿⢸⣿⣼⣿⣿⣿⣿⣿⣿⣇⣿⢿⣷⢸⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⢸⣿⣻⣿⣿⣿⢿⡟⣿⣿⣿⢾⣿⢸⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⢩⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣽⣾⣷⣯⣿⣽⣾⣽⣿⣽⣿⣿⣿⣯⡍⠀⠀⠀⠀⠀⠘⣨⠁⠀⠀⢀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣏⣿⣿⢹⣿⣿⣿⢻⣿⢿⣿⢹⣿⢿⣿⡏⣿⡏⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢠⣛⢸⣶⠀⠙⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢸⣿⣿⣿⢸⣿⢾⣟⢸⣿⣾⣿⡇⣿⡇⠻⣿⣾⣿⣿⣿⠀⠀⠀⠀⠀⢀⣬⣾⡿⠀⠈⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⢿⡇⣿⢸⣿⣿⣿⣸⣿⢸⣿⢸⣿⣼⢻⣧⣿⡇⣿⣯⣿⢿⣿⣿⠀⠀⠀⠀⠀⠸⡿⢿⡇⠀⠀⢿⣿⣿⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣷⣶⣷⣾⣶⣿⣿⣿⣿⣷⣶⣷⣶⣷⣶⣶⣿⣿⣾⣷⣿⣿⣿⣿⣾⣿⠀⠀⠀⠀⠀⠀⡇⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⠝⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⡇⣿⡇⠀⠀⢘⠽⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⡿⠟⢁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⡇⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠇⡀⠀⠀⠀⠀⣀⣀⢀⡀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢰⡏⠉⠰⢶⣦⢰⡴⣦⢠⣶⠆⣶⢰⡆⣿⢠⡶⣦⢰⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠷⠴⠸⠯⠿⢸⡧⠟⠰⠽⠇⠿⠼⠇⠿⠸⠯⠭⠬⠽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠐⡖⠀⡄⡠⡀⡀⡀⠀⠀⡀⡠⡠⡀⠠⡄⣄⠠⣠⢠⡀⠀⠀⠠⡀⡠⣀⠄⡀⡀⡆⠀⢀⠄⠀⢠⣠⠀⡠⡀⢀⠄⡀⢀⠀⡠⢀⢄⠠⢀⠄⡴⡀⡀⡆⣆⢀⠀⡠⢀⢄⢀⠄⡀⡀⡠⣀⠄⡄⡠⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠃⠛⠀⠀⠛⠀⠘⠃⠃⠙⠃⠀⠃⠓⠙⠚⠐⠂⠈⠒⠛⠃⠗⠑⠛⠓⠃⠃⠛⠐⠃⠂⠘⠃⠃⠛⠀⠐⠃⠓⠈⠒⠑⠊⠛⠘⠓⠛⠀⠑⠃⠃⠃⠏⠀⠓⠚⠚⠘⠀⠃⠃⠛⠘⠒⠓⠙⠃⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀
⠀⢰⢣⡜⡀⡖⢢⢴⡒⢺⠂⠀⡖⠂⡖⢢⢰⢲⠒⡄⡖⡖⢢⢰⠒⡄⡖⡆⠀⢰⠒⢐⣲⢰⠒⡆⢖⡂⡆⢰⢸⢠⣒⡄⢖⡂⠀⡗⢢⢰⢠⠀⢰⠖⡆⡆⢰⢰⠒⡔⡆⡗⢲⢠⣒⡄⡖⠀⢠⠒⡔⡗⠀⢰⡰⢰⢰⠒
⠀⠘⠈⠁⠃⠑⠋⠐⠊⠘⠂⠀⠑⠂⠑⠃⠘⠘⠀⠁⠃⠃⠘⠈⠚⠁⠃⠁⠀⠈⠒⠘⠊⠸⠓⠁⠒⠃⠑⠘⠘⠊⠓⠀⠒⠃⠀⠓⠊⠠⠏⠀⠈⠀⠃⠑⠚⠘⠀⠁⠃⠓⠊⠈⠒⠀⠃⠀⠈⠒⠁⠃⠀⠈⠃⠋⠈⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⡲⢰⠂⡖⡖⡄⢰⢲⢸⠀⡗⡔⢤⠒⠐⠂⡖⠀⣖⢾⢲⢸⠲⠂⢠⢒⢰⠢⡲⠀⠀⠀⡎⡆⡋⢴⢱⠈⠁⠀⡇⡇⣯⠂⠀⠰⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠈⠁⠁⠁⠁⠈⠈⠈⠁⠉⠈⠀⠉⠀⠀⠁⠀⠚⠃⠈⠈⠉⠁⠁⠉⠈⠐⠛⠀⠀⠀⠈⠀⠉⠀⠁⠈⠁⠀⠉⠀⠁⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⣴⢰⡄⡆⡆⡆⢰⢰⢰⡀⣆⢠⡆⣇⡆⣦⢐⣄⣇⣤⡆⠒⢀⢸⢸⠆⡂⠈⡇⣉⢾⣸⢈⡁⣇⡇⢸⣀⢸⢸⢸⡀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⣀⠀⡀⠀⡀⡀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⢝⠸⡃⠏⡏⠆⠸⢹⠸⠀⡏⢎⠇⣏⠇⠂⣏⠇⣉⠺⠸⡱⡹⠸⠱⠀⢏⠸⡱⠀⡇⠇⠪⠀⠈⡺⢘⠞⡳⠛⠺⠀⢇⠇⡗⠅⣇⢘⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⢀⠀⠀⡀⢀⢀⠀⢀⠀⣠⠀⡀⢀⠀⢀⠀⡀⠀⢀⢀⠀⢀⢀⠀⢀⢀⢀⢀⠀⡀⠀⠀⡀⣀⢀⠀⡀⡀⠀⢀⢠⢠⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠾⠸⠣⠷⠧⠸⠄⠇⠦⠇⠤⠸⠼⠰⠥⠇⠇⠥⠸⠆⠄⠤⠢⠅⠇⠇⠮⠀⠈⠜⠨⠅⠯⠪⠀⠡⠋⠜⠠⠃⠥⠁⠸⠼⠸⠣⠠⠬⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/10/01/microsoft-azure-is-a-security-breach/#comments
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Gemini_version_available_♊︎


✐ With_Microsoft,_Security_Breaches_Are_Presumed⠀✐


Posted in Deception, Microsoft, Security at 10:18 am by Dr. Roy Schestowitz


Video_download_link | md5sum 90baecb5d2c9d010cbd33c5e9a387984


http://techrights.org/videos/azure-is-a-breach.webm


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇They migrated to Azure for 'security'⦈ Summary: A video
about the current media coverage about Azure being inherently bad when it comes
to security


LAST night we republished an article from a Microsoft_whistleblower who had
seen from the inside how insecure Azure really is. Nothing has improved since
then and days ago it made the news, highlighting a longstanding issue that
Microsoft refuses to address. Microsoft’s own clients complained about it years
ago.


“Nothing says it better like Microsoft’s own words. When it talks honestly.”The
video above concerns this whole matter and some broader issues, knowing that
Microsoft does not actually care about the security of Azure ‘tenants’ (that’s
what they are; they pay rents to be controlled and even neglected by
Microsoft). Nothing says it better like Microsoft’s own words. When it talks
honestly. █


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


                                          –Brian Valentine, Microsoft executive


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

                    ䷩ 𝚕𝚒𝚗𝚎 1538

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 10.01.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_1/10/2021:_More_Gemini_Migrations,_Proton_6.3-7⠀✐


Posted in News_Roundup at 6:45 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o § Instructionals/Technical⠀➾


                # ⚓ Gemini:_the_misaligned_incentives⠀⇛


                       How does gemtext suck? Let me count the ways: [...]


                # ⚓ Going_From_A_Domain_Name_to_IP_Address_in_DNSDB:_Some_“Pro
                  Tips”_To_Keep_In_Mind⠀⇛


                       Virtually every DNSDB user makes domain name to IP
                       address queries. Often that will be quite straight
                       forward, but today we’re going to talk about some
                       of the times when you may run into surprises – and
                       how you can easily deal with them.


                # ⚓ Setting_up_a_Gemini_server⠀⇛


                       I could not get agate to start correctly, it would
                       not bind to the ipv4 port 1965. After some
                       desultory troubleshooting I used gemserv instead.


                       I didn’t bother compiling gemserv to use GGI, just
                       static content.


                # ⚓ Pimping_My_Type_–_Improving_My_Website’s_Typography⠀⇛


                       Anyway, since doing the research for the typography
                       post, I discovered Oliver’s YouTube channel and
                       newsletter, Pimp My Type. He’s a professional
                       typographer, so when I learned that he offers free
                       website typography reviews, I was on that like a
                       tramp on chips!


                # ⚓ [Old] An_Introduction_to_JQ⠀⇛


                       However, some things never stick in my head, nor my
                       fingers, and I have to google them every time. jq
                       is one of these.


                       I know it’s a powerful tool, but I always end up
                       back at Google and then copying and pasting a
                       solution from somewhere. So I solve my problem but
                       never learn the tool.


                       It’s time to fix that. In this article, I’m going
                       to go over the basics building blocks of jq in
                       enough depth that you will be able to understand
                       how jq works. Of course, you still might
                       occasionally need to head to google to find a
                       function name or check your syntax, but at least
                       you’ll have a firm grounding in the basics.


          o § Games⠀➾


                # ⚓ Why_D&D_over_other_RPGs?⠀⇛


                       It’s true that our version of D&D is modified
                       beyond recognition. Which is fine since it’s an
                       open source game.


                       It’s true that I’m a fan of D&D as a brand, as a
                       shorthand, as a community, whereas I don’t touch
                       “gamer” stuff with the proverbial ten-foot pole.


                       It’s not true that this is out of ignorance with
                       other systems. “Just play Fiasco” we went from
                       Fiasco to D&D after trying both. And, we’ve mashed
                       in stuff from Fiasco into “our” D&D.


                       I had read around 200 core books until finally
                       giving the much maligned D&D a shot. I had believed
                       the anti-hope of haters on Usenet and TBP. “AC
                       doesn’t make sense”, “Levels don’t make sense”,
                       “It’s so unrealistic” etc. And I felt so dumb for
                       looking at it last because it was exactly what I
                       had been longing for all this time.


                # ⚓ Valve_Releases_Proton_6.3-7_with_Support_for_Life_is
                  Strange:_True_Colors,_DXVK_1.9.2⠀⇛


                       Coming about five weeks after Proton 6.3-6, the
                       Proton 6.3-7 release is here to add support for the
                       Life is Strange: True Colors, Quake Champions,
                       Divinity: Original Sin 2, eFootball PES 2021,
                       EVERSLAUGHT VR, as well as WRC (World Rally
                       Championship) 8, 9 and 10 video games.


                       This means that you’ll now be able to play these
                       games on your Linux-powered computer using the new
                       Proton version. However, it should be noted the
                       fact that the Quake Champions and Divinity:
                       Original Sin 2 games will apparently brake after a
                       game update, so you shouldn’t update them yet.


          o § Desktop Environments/WMs⠀➾


                # ⚓ Greyscale_screens_for_anxiety⠀⇛


                       One thing I didn’t expect to work so well was
                       having my computer screen set to greyscale mode the
                       past few days. I’d enabled it to test the
                       accessibility and contrast of a design I was
                       working on and… I didn’t turn it off.


          o § Distributions⠀➾


                # § IBM/Red Hat/Fedora⠀➾


                      # ⚓ Fedora_Linux_declared_a_‘digital_public_good’⠀⇛


                             Fedora Linux has been recognized as a
                             “digital public good” by the Digital Public
                             Goods Alliance (DPGA), a strategy group set
                             up by UNICEF to promote sustainable
                             development through open-source solutions
                             that contribute to an equitable world.


          o § Devices/Embedded⠀➾


                # § Open Hardware/Modding⠀➾


                      # ⚓ Machine_Learning_Prosthetic_Arm_|_The_MagPi_#110⠀⇛


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


                # § SaaS/Back End/Databases⠀➾


                      # ⚓ YottaDB_Continuous_Integration_/_Continuous
                        Delivery⠀⇛


                             At YottaDB we have a network of a couple
                             dozen machines that include all Supported
                             platforms, ranging from Raspberry Pi Zeroes
                             to x86_64 servers. We run the YottaDB test
                             system across these machines most weekends,
                             and frequently overnight as well. The normal
                             run checks out the current master source
                             code, builds it, and runs it on these
                             machines against the current master test
                             system. The source code is built and tested
                             two ways, “DBG” builds with asserts that
                             detect error and out-of-design conditions for
                             us to debug, and “PRO” builds that are built
                             the way binary distributions are delivered,
                             and which invoke the recovery code for these
                             error and out-of-design conditions. The tests
                             involve extensive simulated crashes and
                             recovery. They also randomly vary a number of
                             parameters to test the various permutations
                             and combinations of operating conditions.


                # § FSF⠀➾


                      # § Licensing/Legal⠀➾


                            # ⚓ Can_Radio_Benefit_From_An_Open_Source
                              Society?⠀⇛


                                   Radio has never been on the leading
                                   edge as an industry full of tech
                                   oriented companies so open source can
                                   be a solution that allows these
                                   companies to focus on what they are
                                   good at – delivering amazing content.


                                   Isn’t that the name of the game?


                                   Collaboration in the spirit of open-
                                   source could be an engine for much
                                   needed growth as well.


                # § Programming/Development⠀➾


                      # ⚓ Common_mistakes_when_using_libcurl⠀⇛


                             I’ve been traveling this road for a while.
                             Here’s my collection of 15 of the most common
                             mistakes and issues people will run into when
                             writing applications and services that use
                             libcurl. I’ve also done recorded
                             presentations on this topic that you can
                             watch if you prefer that medium.


                      # ⚓ Things_unlearned⠀⇛


                             This post is part of a series, starting at
                             Reflections on a decade of coding.


                             This is one of my favorite questions to ask
                             people: what are some things that you used to
                             strongly believe but have now changed your
                             mind about?


                             I want to focus especially on ideas that I
                             wasted a lot of time on, or that got in the
                             way of success.


                      # ⚓ Fun_with_glibc_and_the_ctype.h_functions⠀⇛


                             I got really bored tonight and went down some
                             rabbit holes and turned up something from
                             about a year ago. If you follow the latest
                             Linux type stuff, you probably remember this,
                             but if not, this might seem new to you. It’s
                             just something dumb and amusing.


                      # ⚓ CHERI_Software_Release_for_Summer_2021⠀⇛


                             The CHERI protection model provides
                             architectural primitives to protect computer
                             systems from widely-exploited security
                             vulnerabilities. CHERI revises the hardware/
                             software architectural interface with
                             hardware support for capabilities that can be
                             used for fine-grained memory protection and
                             scalable software compartmentalization.
                             Supported by DARPA (the US Defense Advanced
                             Research Projects agency) as well as UKRI (UK
                             Research and Innovation) and its Digital
                             Security by Design (DSbD) program, CHERI is
                             the work of a large research team at the
                             University of Cambridge, SRI International,
                             Arm and many industrial and academic
                             collaborators throughout the world.


                      # ⚓ Understanding_AWK⠀⇛


                             It turns out Awk is pretty simple. It has
                             only a couple of conventions and only a small
                             amount of syntax. As a result, it’s
                             straightforward to learn, and once you
                             understand it, it will come in handy more
                             often than you’d think.


                             So in this article, I will teach myself, and
                             you, the basics of Awk. If you read through
                             the article and maybe even try an example or
                             two, you should have no problem writing Awk
                             scripts by the end of it. And you probably
                             don’t even need to install anything because
                             Awk is everywhere.


    * § Leftovers⠀➾


          o ⚓ You_Are_Enough⠀⇛


          o ⚓ The_Holiness_of_Degradation⠀⇛


                 with a title and a line from Leslie Jamison


                 Anne says, what if you are notsick or bad, what if you
                 are Katie?


          o ⚓ Instituting_Liberty:_Contested,_Changing,_Conflicted
            Definitions⠀⇛


                 Records of UT administrators describe an institute that
                 would be “dedicated to the study and teaching of
                 individual liberty, limited government, private
                 enterprise and free markets” and promote “intellectual
                 diversity.” Most people, myself included, support
                 individual liberty. The remaining phrases are highly
                 ideological and should be in scare quotes.


                 Does “limited government” enhance individual liberty, or
                 does it really mean using government power to protect
                 concentrated wealth and limit our collective ability to
                 create a decent society? Does “private enterprise” really
                 mean allowing corporations to use that concentrated
                 wealth to undermine democratic decision-making? Do those
                 corporations champion “free markets” only as long as they
                 can extract profit, running to the government for
                 bailouts when they fail?


          o ⚓ Desire_in_Our_Times:_A_Conversation_With_Amia_Srinivasan⠀⇛


                 What is it about sex that makes talking about it with
                 political and moral honesty so difficult? It’s so easy to
                 fixate on its purely political aspects, relying on the
                 simplicity of a relationship with black-and-white
                 consequences. It’s so tempting to reduce it to the
                 absolutely personal, just someone’s preference, beyond
                 anyone else’s understanding or judgment. Even among
                 feminists, the tensions between the intimacy of sex, its
                 potential for violence, and the fact that its
                 participants, limitations, and consequences often fall
                 under the supervision of public authorities are perennial
                 sources of conflict.


          o ⚓ Misquoting_Einstein_Is_Fast_And_Stupid,_But_Not_Accurate⠀⇛


                 I was writing something a while ago, and had reason to
                 quote the famous aphorism “Computers are incredibly fast,
                 accurate, and stupid; humans are incredibly slow,
                 inaccurate, and smart.” I’ll bet you’ve heard a variation
                 on that quote before, and probably have seen a meme or
                 two with it. It’s usually attributed to Einstein.


          o ⚓ A_Time_of_Plague_in_an_Era_of_Corruption,_Mistrust_and
            Irrationality⠀⇛


                 That so many are willing to take the word of any
                 contrarian rather than that of peer reviewed science is
                 astonishing. But after decades of government and
                 corporate malfeasance and abuses, it isn’t too difficult
                 to understand the roots for this skepticism. Indeed,
                 government agencies and business institutions have
                 constructed this atmosphere of distrust. Just one look at
                 the CIA, the military, or the tobacco and fossil fuel
                 industries and we get a litany of lies, crimes, and the
                 obfuscation of those crimes. Indeed, most drug companies
                 have gotten away with the many crimes they have
                 committed, with the recent opioid scandal and the Sackler
                 family coming to mind. But there is also a kind of
                 collective fear and a legacy of anti-scientific credulity
                 that is common in far-right political circles that goes
                 beyond justified criticism of and opposition to the
                 crimes of the powerful.


                 None of this is especially original. Climate change
                 deniers have long latched on to the proclamations of a
                 small, but loud, group of scientists who confirm their
                 narrative. A major part of this is thanks to a well
                 funded campaign of disinformation by the fossil fuel
                 industry who began lying to the public about the damaging
                 effects of burning fossil fuels decades ago. And there
                 are dozens of think tanks in Washington whose sole
                 purpose it to peddle corporate propaganda to politicians
                 on the dole and a public that is already inclined to be
                 against any scientific warning that may alter the Western
                 lifestyle. But there is also a conspiratorial way of
                 thinking about these things. The very real and
                 existential issue of climate catastrophe has been linked
                 to crackpot theories about a tyrannical “one world
                 government.” Those who have been alienated from society
                 often become targets for this kind of delusion. And
                 social media amplifies it all through echo chambers of
                 confirmation bias, connecting the alienated with one
                 another, albeit in a very superficial manner.


          o ⚓ China’s_Fortune_Cookie_Crumbles⠀⇛


                 Ross Ashcroft Michael Hudson, always great to have you
                 back on Renegade Inc.


                 Michael Hudson It’s good to be back here. Thanks for
                 having me.


          o ⚓ The_rise_of_dark_web_design:_how_sites_manipulate_you_into
            clicking⠀⇛


                 Dark design has proven to be an incredibly effective way
                 of encouraging web users to part with their time, money
                 and privacy. This in turn has established “dark
                 patterns”, or sets of practices designers know they can
                 use to manipulate web users. They’re difficult to spot,
                 but they’re increasingly prevalent in the websites and
                 apps we use every day, creating products that are
                 manipulative by design, much like the persistent, ever-
                 present pop-ups we’re forced to close when we visit a new
                 website.


          o § Science⠀➾


                # ⚓ Teaching_an_algorithm_to_identify_cancer_from_sequence
                  data⠀⇛


                       Algorithms have been used to identify cells in
                       sectional images of tissue samples. For instance,
                       if tissue cells appear atypical, the algorithm will
                       spot this and determine if the cells are cancerous.
                       DNA sequence data from tumours is now being used
                       along with imaging data to identify cancers.


          o § Health/Nutrition⠀➾


                # ⚓ ‘Eye-Popping_Rip-Off’:_Americans_Pay_Nearly_Double_Rest_of
                  World_Combined_for_Top_Meds⠀⇛


                       As public health advocates fumed over efforts by
                       right-wing congressional Democrats to water down
                       prescription drug pricing reforms proposed in their
                       own party’s flagship Build Back Better package, a
                       report published Thursday by a leading progressive
                       advocacy group revealed that Americans are paying
                       nearly twice as much for the 20 bestselling
                       medications as the rest of the world combined.


                       “Empowering Medicare to push back against inflated
                       drug prices is the responsible and commonsense way
                       to stand up to the industry’s greed.”—Rick
                       Claypool,Public Citizen


                # ⚓ ‘Let_Them_Know_How_You_Feel,’_Voters_Urged_as_Pharma-Backed
                  Dems_Tank_Drug_Cost_Plan⠀⇛


                       Supporters of drug pricing reform expressed alarm
                       Wednesday at efforts by right-wing congressional
                       Democrats—including some of the biggest recipients
                       of Big Pharma campaign contributions—to water down
                       progressive-led efforts to lower the world’s
                       highest prescription medication costs.


                       Mirroring key items on Big Pharma’s wishlist,
                       corporate Democrats are taking aim at proposed drug
                       pricing reforms in the $3.5 trillion Build Back
                       Better budget reconciliation package. According to
                       Politico:


                # ⚓ University_in_‘Europe’s_Oil_Capital’_Votes_to_Divest_from
                  Fossil_Fuels⠀⇛


                       A Scottish university in “Europe’s oil and gas
                       capital” has voted to sell all of its fossil fuel
                       investments over the next four years.


                       The University of Aberdeen, which has strong ties
                       with the North Sea oil and gas industry, announced
                       today that its governing body had voted to exclude
                       fossil fuel extraction companies from its £52.7
                       million investment portfolio by 2025. It currently
                       has an estimated £3.1 million invested in fossil
                       fuels, according to campaigners.


                # ⚓ Sickening,_Indeed:_the_Horrors_of_Big_Pharma⠀⇛


                       For this reason, there is good cause to expect that
                       his new book, Sickening: How Big Pharma Broke
                       American Health Care and How We Can Repair It,
                       would make a substantial contribution to the
                       current debate over controlling drug prices.
                       (Unfortunately, its publication date is not until
                       February.) The book is indeed useful in documenting
                       the failures of the pharmaceutical industry, but it
                       comes up painfully short in the remedies.


                       The first part of the book goes over some of the
                       major scandals of the pharmaceutical industry over
                       the last three decades. It notes the overuse of
                       statins, a drug designed to lower cholesterol.
                       Abramson points out that statins are often
                       prescribed for women, based on clinical trials
                       showing their effectiveness for men. In spite of
                       the lack of evidence of benefit, expensive statins
                       have been prescribed for millions of women over the
                       last three decades.


                # ⚓ ‘You_Should_Get_the_Vaccine_Despite_the_Media_Telling_You
                  You_Should’⠀⇛


                       Janine Jackson interviewed Jim Naureckas about
                       Covid and corporate media  for the September 24,
                       2021, episode of CounterSpin. This is a lightly
                       edited transcript.


                # ⚓ ‘Not_Ashamed’:_Democratic_Congresswomen_Testify_About_Their
                  Personal_Abortion_Stories⠀⇛


                # ⚓ Opinion_|_These_Pfizer-Backed_GOP_Lawmakers_Are_Heading_to
                  Q-Anon_Anti-Vax_Summit⠀⇛


                # ⚓ House_Oversight_Won’t_Hurt,_But_the_Fight_for_Abortion_Is
                  Waged_at_Grassroots⠀⇛


                # ⚓ With_Infrastructure_on_the_Brink,_Manchin_Refuses_to
                  Negotiate⠀⇛


                # ⚓ Critics_Slam_Manchin_for_Invoking_‘Brutal_Fiscal_Reality’
                  to_Defend_Tanking_of_Biden_Agenda⠀⇛


                       Just ahead of Sen. Joe Manchin’s Thursday
                       declaration that $1.5 trillion is his topline
                       number for the reconciliation bill, the corporate
                       Democrat referred to the United States’ so-called
                       “brutal fiscal reality” on Wednesday to defend his
                       opposition to the Democratic Party’s 10-year, $3.5
                       trillion package—a justification progressives
                       criticized as baseless and a threat to Americans’
                       future well-being.


                       “While I am hopeful that common ground can be found
                       that would result in another historic investment in
                       our nation, I cannot—and will not—support trillions
                       in spending or an all or nothing approach that
                       ignores the brutal fiscal reality our nation
                       faces,” Manchin (D-W.Va.) said Wednesday night in a
                       statement, adding that he wants to “pass on a
                       better America to the next generation.”


                # ⚓ Manchin:_If_You_Want_to_Save_the_Planet,_Elect_More
                  Progressives_in_2022⠀⇛


                       Sen. Joe Manchin said Thursday that securing
                       sweeping climate legislation to safeguard the
                       planet for future generations requires electing
                       more progressives—unlike him—in 2022.


                       The corporate Democrat’s assertion came as he
                       announced to a crowd of reporters that his topline
                       number for the broad reconciliation bill is $1.5
                       trillion—a fraction of the $3.5 trillion demanded
                       by progressive lawmakers for the 10-year Build Back
                       Better plan that includes investments to strengthen
                       the safety net and tackle the climate emergency.


                # ⚓ Manchin_Admits_Getting_His_Bill_Passed_and_Then_Tanking
                  Progressive_Package_Was_Always_the_Plan⠀⇛


                       Sen. Joe Manchin admitted Thursday, ahead of a
                       scheduled House vote on the Senate-passed
                       bipartisan infrastructure bill, that it had been
                       corporate Democrats’ plan all along to first secure
                       passage of their fossil fuel-friendly legislation
                       and then undermine the party’s more ambitious
                       reconciliation package that proposes investing up
                       to $3.5 trillion over a decade in clean energy and
                       the social safety net.


                       The conservative West Virginia Democrat told
                       reporters Thursday that on July 28, he secured a
                       signed agreement (pdf) from Senate Majority Leader
                       Chuck Schumer (D-N.Y.) outlining his conditions for
                       voting on the final reconciliation bill.


                # ⚓ Manchin_Goes_After_Abortion_Rights_in_Latest_Reconciliation
                  Bill_Opposition⠀⇛


                # ⚓ Relying_on_Public-Private_Partnerships_Has_Weakened
                  America’s_Pandemic_Response⠀⇛


                       As the United States continues to record thousands
                       of cases of Covid infection and as many as 2,000
                       deaths per day, many Americans are scrambling to
                       get rapid tests for extra reassurance as they
                       return to school, work and start to travel. But
                       rapid tests are hard to find on stores shelves
                       across the country—and when you finally track them
                       down, they cost from $10 to $15 per test. As it
                       happens, that’s because there’s a nationwide
                       shortage of rapid tests. Meanwhile, other countries
                       have plentiful amounts of tests—in Germany, for
                       instance, rapid testing, along with vaccination,
                       has become the bedrock of their plan to live with
                       the virus. There, rapid testing is widely used and
                       available outside of restaurants and gyms and other
                       facilities. Why is something that could be so
                       instrumental to managing the pandemic so hard for
                       Americans to get their hands on?


                # ⚓ Being_“Pro_NBA_Player”_Means_Being_Pro-Vaccine⠀⇛


                       Many of America’s pro athletes are union workers,
                       albeit union workers with a decidedly distorted
                       social position, relative to organized working-
                       class people more broadly. They benefit greatly
                       from collective bargaining. As is the case for all
                       workers, unions are a pro athlete’s best friend.
                       Just do your own investigation into what conditions
                       and wages were like before unions—pro sports were
                       part playground, part sweatshop.


                # ⚓ YouTube_cracks_down_on_anti-vax_misinformation⠀⇛


                       The new policy builds on existing rules against
                       COVID-19 vaccine misinformation, which have led to
                       the removal of 130,000 videos since October.
                       YouTube says it has taken down more than 1 million
                       videos for violating its overall COVID-19 medical
                       misinformation policy.


                # ⚓ Zero_tolerance:_YouTube_blocks_all_anti-vaccine_accounts⠀⇛


                       The company said that while accounts will be taken
                       down, so will any posts which express unfounded
                       concerns about vaccines or falsely state that some
                       vaccines cause autism or cancer or something else
                       the vaccine has never been proven to cause.


          o § Integrity/Availability⠀➾


                # ⚓ DoS_Attacks_against_our_Online_Game⠀⇛


                       Based on the rising player number the urge to deal
                       with the DoS problem is larger than ever. A few
                       months ago for example we organized a Tournament
                       for everyone in the community to participate.
                       Unfortunately the event was the continuous target
                       of DoS attacks for multiple hours, with players
                       fleeing from one server to the next, trying to find
                       a safe refuge. These bandwidth graphs for our
                       servers in Netherlands and Germany respectively
                       illustrate the problem: [...]


                # § Proprietary⠀➾


                      # ⚓ Ransomware_contractor_paints_a_different_picture_of
                        the_genre [iophk: Windows TCO]⠀⇛


                             A threat actor, who claims to have worked for
                             the REvil ransomware group among others, has
                             cast doubt on the common tendency to
                             associate individuals from a particular
                             country who do such work as acting for the
                             governments of the same countries.


                      # ⚓ Apple_‘Still_Investigating’_Unpatched_and_Public
                        iPhone_Vulnerabilities⠀⇛


                             Tokarev reported the vulnerabilities to Apple
                             between March 10 and April 29, but the last
                             time he heard back from Apple about the three
                             vulnerabilities was August 6, August 12, and
                             August 25, respectively. Then the researcher
                             said he told Apple on September 13 he would
                             publish details of the bugs unless he heard
                             back.


                             It was only after he went public with details
                             about the unpatched bugs that Apple reached
                             out, according to Tokarev, who shared Apple’s
                             email with Motherboard.


                      # ⚓ Apple’s_fortress_of_secrecy_is_crumbling_from_the
                        inside⠀⇛


                             The tension might have stayed at a low simmer
                             were it not for a Slack channel — #remote-
                             work-advocacy — created in September 2020 to
                             promote a more flexible working environment.
                             By the summer of 2021, it had reached roughly
                             2,800 members, with conversations growing
                             increasingly lively. After Cook made his
                             announcement, employees knew they had to send
                             a message. It was a small push back against
                             management that would lay the groundwork for
                             months of employee organizing and perhaps
                             change the Apple workforce forever.


                      # § Security⠀➾


                            # § Privacy/Surveillance⠀➾


                                  # ⚓ Facebook’s_Latest_Scandals:_The_Banality
                                    Of_Hubris;_The_Messiness_Of_Humanity⠀⇛


                                         Over the last few weeks, the WSJ
                                         has run a series of posts
                                         generally called “The Facebook
                                         Files,” which have exposed a
                                         variety of internal documents
                                         from Facebook that are somewhat
                                         embarrassing. I do think some of
                                         the reporting is overblown — and,
                                         in rather typical fashion
                                         regarding the big news
                                         publications and their reporting
                                         on Facebook, presents everything
                                         in the worst possible light. For
                                         example, the report on how
                                         internal research showed that
                                         Instagram made teen girls feel
                                         bad about themselves downplays
                                         that the data actually shows a
                                         significantly higher percentage
                                         of teens indicated that Instagram
                                         made them feel better:


                                  # ⚓ CIA,_NSA_Block_Ads_Network-Wide_To
                                    Protect_Agencies._Ron_Wyden_Says_Rest_Of
                                    Gov’t_Should_Do_The_Same.⠀⇛


                                         Not everyone uses an ad-blocker.
                                         But most people do. And no matter
                                         how much online publications
                                         claim ad blocking is the same
                                         thing as stealing, it really
                                         isn’t. If they’re bent out of
                                         shape about it, it’s because they
                                         assault users with ads, burying
                                         content behind a wall of
                                         uncurated virtual salesmen. If it
                                         bleeds, it leads, the old saying
                                         goes, but now it refers to
                                         readers’ processing power and
                                         data allotments.


                                  # ⚓ Hillicon_Valley_—_Presented_by_Ericsson_—
                                    Senators_gear_up_for_Facebook_hearing⠀⇛


                                         Facebook’s head of global safety
                                         will face off with members of the
                                         Senate Commerce consumer
                                         protection subcommittee on
                                         Thursday as part of the panel’s
                                         first in a series of hearings
                                         focused on kids’ safety. As
                                         criticism of the tech giant heats
                                         up following recent bombshell
                                         reports, the panel will convene
                                         again next week to hear testimony
                                         from a Facebook whistleblower.


                                  # ⚓ Face_detection_for_my_leaf_blower⠀⇛


                                         The short of it: I have a face
                                         detection algorithm running
                                         which, when a certain individual
                                         enters the field of the Pi’s
                                         vision, triggers a servo that
                                         powers on the blower, releasing a
                                         powerful air blast.


                                  # ⚓ Apple_AirTag_Zero-Day_Weaponizes
                                    Trackers⠀⇛


                                         An unpatched stored cross-site
                                         scripting (XSS) bug in Apple’s
                                         AirTag “Lost Mode” could open up
                                         users to a cornucopia of web-
                                         based attacks, including
                                         credential-harvesting, click-
                                         jacking, malware delivery, token
                                         theft and more.


                                         That’s according to Bobby Rauch,
                                         an independent security
                                         researcher who said that it’s
                                         possible to use the zero-day to
                                         fully weaponize an AirTag, with
                                         the ability to attack random
                                         strangers (or specific targets)
                                         should they interact with it.


                                         Stored XSS, also known as
                                         persistent XSS, occurs when a
                                         malicious script is injected
                                         directly into a vulnerable web
                                         application. An attack then only
                                         requires that a victim visit a
                                         compromised web page.


          o § Defence/Aggression⠀➾


                # ⚓ They_Fled_the_Taliban._Now_They’re_in_a_Tent_City_in_New
                  Mexico.⠀⇛


                       In late August, 26-year-old Abul Ahmed was heading
                       to his university in Kabul to fill out some
                       paperwork when he got a call from a friend. “Don’t
                       go to your house, because it’s dangerous. The
                       Taliban are there,” Abul recalled being told. Abul
                       said he wasn’t going to leave his family, but after
                       the Taliban took over Kabul, he knew they couldn’t
                       stay at home. “The Taliban broke into our compound,
                       and they stole our car,” he told me. “They beat up
                       my uncle and searched our stuff.”


                # ⚓ Jan_6_Committee_Subpoenas_11_Individuals_Who_Organized
                  Trump_Rally_That_Day⠀⇛


                # ⚓ Open_for_Military_Business:_Ebola_Research_at_Canada’s_Only
                  BSL-4_Lab⠀⇛


                       By the time Qiu started work on Ebola, the
                       mishandling of the SARS epidemic by China’s
                       leadership was well-known worldwide. Officials had
                       been fired for misbehavior. China had called upon
                       leading scholars in the US, like W. Ian Lipkin, and
                       Chinese scholars with significant success abroad,
                       such as George Gao, to help reorganize its public
                       health system, especially its disease surveillance
                       methods. That year, a group of scientists from
                       Guangdong, the centre of the SARS pandemic, arrived
                       in Winnipeg to tour the Canadian Science Centre for
                       Human and Animal Health, which includes both the
                       NML, now managed by PHAC (Public Health Agency of
                       Canada), and the animal diseases lab managed by the
                       Canadian Food Inspection Agency. China was
                       negotiating its agreement with France, which led to
                       the construction of the BSL-4 at the Wuhan
                       Institute of Virology.


                       Natalie Salat, a reporter for Legion, a magazine
                       about Canada’s military history, came to Winnipeg
                       to write about the facility after the visitors from
                       China had come and gone. Their attendance was
                       presented to her as a mark of the NML’s global
                       importance. Salat was told that the NML had
                       partnerships with the Department of National
                       Defence, the University of Manitoba, the US Centers
                       for Disease Control and Prevention, the US
                       Bioterrorism Response Network, etc. Stefan Wagener,
                       whom Salat identified as the centre’s scientific
                       director for biosafety and environment, told her
                       that everyone who worked at the lab for more than
                       ten days had to have a rigorous security clearance.
                       He jokingly said that if he told her anything else
                       about the detailed security measures in place, he’d
                       “have to kill her.”227


                # ⚓ The_Untold_Story_of_Why_Palestinians_Are_Divided⠀⇛


                       Palestinian political disunity is tied to the fact
                       that the issue of representation in Palestinian
                       society has always been an outcome of one party
                       trying to dominate all others. This dates back to
                       Palestinian politics prior to the establishment of
                       Israel on the ruins of historic Palestine in 1948,
                       when various Palestinian clans fought for control
                       over the entire Palestinian body politic.
                       Disagreements led to conflict, often violent,
                       though, at times, it also resulted in relative
                       harmony – for example, the establishment of the
                       Arab Higher Committee (AHC) in 1936.


                       These early years of discord duplicated themselves
                       in later phases of the Palestinian struggle. Soon
                       after Egyptian leader, Jamal Abdel Nasser,
                       relinquished his influential role over the
                       Palestine Liberation Organization (PLO) following
                       the humiliating Arab defeat in 1967, the relatively
                       new Fatah Movement – established by Yasser Arafat
                       and others in 1959 – took over. Since then, Fatah
                       has mostly controlled the PLO, which was declared
                       in Rabat, in 1974, to be the “sole legitimate
                       representative of the Palestinian people”.


                # ⚓ Who_Lost_Afghanistan?_H.R.⠀⇛


                       What it does not show, and what Pentagon leaders
                       don’t seem to understand, is why.


                       Whitlock’s book reads like a synopsis of the many
                       essays, books and cartoons I produced over 20
                       years, which were rejected by most newspapers and
                       news websites because editors and producers refused
                       to publish content that criticized the war.


                # ⚓ What_Are_The_Prospects_For_Peace?_An_Interview_With_Coleen
                  Rowley⠀⇛


                       Coleen Rowley is an attorney, peace activist and
                       whistleblower. She’s a retired FBI Special Agent
                       and former FBI Minneapolis Division Legal Counsel.
                       For her exposure of the FBI’s pre-911 failures, she
                       was named one of Time Magazine’s “Persons of the
                       Year” in 2002. We are extremely honored that she
                       took the time to talk to us and share her views.
                       Her responses below are exactly as she provided.


                       The questions here are not philosophical or
                       abstract. They focus on the realities of the
                       international power struggle unfolding in real
                       time. They directly address the role of the U.S. in
                       the escalating tensions and its capacity to reduce
                       them. We also probe the role of everyday citizens
                       in affecting the relationship the U.S. now has and
                       will have with the rest of the world community.


                # ⚓ Survey_Confirms_Los_Angeles_Sheriff’s_Department_Is_Still
                  Home_To_Dangerous_Gangs,_Has_No_Solid_Plan_To_Eliminate
                  Them⠀⇛


                       The Los Angeles Police Department has spent years
                       compiling a “gang database.” The term “compile” is
                       used loosely, because the LAPD decides people are
                       gang members just because they know gang members,
                       or are related to them, or live in the same
                       buildings, or work near them, or pass through gang-
                       controlled neighborhoods, or go to school with gang
                       members, or just (as non-gang people are wont to
                       do) wear clothes, shoes, and hats. It’s ridiculous.


                # ⚓ Opinion_|_Good_Riddance_to_the_Horrible_Failures_of
                  CENTCOM⠀⇛


                       The bad news stemming from the ill-planned and ill-
                       managed U.S. evacuation of the Afghan capital just
                       kept coming in. The Washington Post put it this way
                       in blowing the whistle on the culminating disaster:
                       “U.S. military admits ‘horrible mistake’ in Kabul
                       drone strike that killed 10 Afghans.”


                # ⚓ The_Myth_of_a_New_“Cold_War”_Between_the_U.S._and_China/
                  Russia⠀⇛


                       Outraged French President Emmanuel Macron denounced
                       the Biden-approved agreement as blatant “Trumpism”
                       and withdrew the French ambassador to the U.S., the
                       first and only such termination of diplomatic
                       relations with France in some 250 years. “Trumpism”
                       has in recent years come to be defined as “America
                       First” or “MAGA,” Make America Great Again,
                       including the imposition of U.S. tariffs not only
                       against China but against Western European nations
                       and Canada. At the time Democrats and leading U.S.
                       corporate think tanks, including the Council on
                       Foreign Relations, pilloried Trump’s tariffs but
                       the Biden administrations has largely maintained
                       them all and indeed, expanded their scope and
                       impact. No doubt, there are always major divisions
                       within the U.S. ruling class – not to mention among
                       and between their international counterparts – when
                       their base economic interests are in conflict.


                       Pivot to Asia


                # ⚓ Constructive_Criticism_Rooted_in_Respect:_A_View_from
                  Vietnam⠀⇛


                       In other words, because Mr. Pierre has the passport
                       of a former colonial power that brutally exploited
                       Vietnam and its people until it was decisively
                       defeated at the Battle of Điện Biên Phủ in 1954, he
                       doesn’t have the right to constructively criticize
                       anything that is happening here in 2021.


                       Vietnam and presumably other countries that France
                       colonized get an unlimited pass on any societal
                       problem, big or small. What does that have to do
                       with the existential problem of air and water
                       pollution? You guessed it: absolutely nothing.


                # ⚓ Black_Residents_of_Minneapolis_Say_They_Need_More_Cops—Not
                  Fewer⠀⇛


                       Minneapolis, Minn.—On a quiet Sunday afternoon, Don
                       Samuels emerged from his home on the northern wing
                       of this city, wearing a black hoodie with “Pratt”
                       printed on the chest. Clinging to his iPhone,
                       Samuels sat on the porch as he typed the final
                       words of a message he had been writing to a woman.


                # ⚓ Mali_junta’s_sovereignty_push_arouses_hope,_fear_amid
                  troubled_anti-jihadist_struggle⠀⇛


                       “But even though many Malians like the emphasis on
                       national sovereignty, they are also concerned about
                       where it may lead,” Tounkara continued. “If private
                       security companies and Malian troops achieve
                       military victories, that may well strengthen anti-
                       French sentiment. On the other hand, if Bamako cuts
                       ties to France and to its regional allies, it risks
                       finding itself ostracised in the anti-jihadist
                       struggle in the Sahel, without reliable partners to
                       support it. That would be enormously disappointing
                       to the Malian people.”


                # ⚓ Arson_attack_on_house_of_critic_of_Islam_in_Dresden,
                  Germany⠀⇛


                       The so-called Molotov cocktail was thrown onto the
                       balcony on the first floor of the shell of the
                       building in the street Brückenstraße at around 3:30
                       a.m. last Saturday. As a result, a fire broke out.
                       The resulting damage to property cannot yet be
                       quantified. The Police Counter-Terrorism and
                       Counter-Extremism Centre has taken over the
                       investigation.


          o § Transparency/Investigative Reporting⠀➾


                # ⚓ Scientist:_Mysterious_beacons_source_of_MS_Estonia_survey
                  interference⠀⇛


                       A scientist says he believes he has found the
                       source of mysterious interference experienced in
                       sonar and other devices during an investigation
                       into the wreck of the MS Estonia, which sank in
                       1994 with the loss of 852 lives. The scientist, a
                       hydrographer called Peeter Ude, says the source is
                       transmitter beacons installed on the sea-bed and
                       close to the wreck, but who placed them there, why
                       and when remains unclear, he says.


          o § Environment⠀➾


                # ⚓ 50_years_of_Greenpeace:_Looking_back_and_looking_forward⠀⇛


                       Some observers object, claiming that “there is no
                       limit to growth,” or “no limit to human ingenuity,”
                       but the lessons of the natural world tell us
                       otherwise. Some extreme technology-obsessed
                       billionaires imagine that we’ll colonize other
                       planets and leave the depleted Earth behind.


                       I ask this question to myself virtually every day:
                       How do we change the human trajectory, away from
                       growth, chaos, and collapse? What path will lead us
                       toward genuine sustainability? I suspect that our
                       progeny — and all other species — will be far
                       better off if we embrace our relationship with the
                       living Earth, learn from nature itself, consciously
                       contract, slow our economies, and allow wild,
                       untrammeled natural habitats to expand.


                # ⚓ Joe_Manchin,_America’s_Climate_Decider_in_Chief,_Is_a_Coal
                  Baron⠀⇛


                       This story originally appeared in The Guardian and
                       is republished here as part of Covering Climate
                       Now, a global journalism collaboration cofounded by
                       The Nation and Columbia Journalism Review to
                       strengthen climate coverage.


                # ⚓ ‘Be_Our_Climate_President’:_Biden_White_House_to_Face_Full
                  Week_of_Protests⠀⇛


                       Climate justice campaigners plan to descend on
                       Washington, D.C. in October to protest outside the
                       White House for a week straight, calling on
                       President Joe Biden to declare a climate emergency
                       and end all new fossil fuel projects.


                       The Build Back Fossil Free coalition announced the
                       People Vs. Fossil Fuels: Biden’s Test
                       demonstrations, to be held October 11-15, in a
                       statement Thursday. The week of action will come
                       just before COP 26, a United Nations climate summit
                       scheduled to begin in Scotland at the end of next
                       month.


                # ⚓ The_New_‘Con’_in_Conservation:_Why_the_Proposed_Voluntary,
                  Paris_Agreement-Style,_‘30×30’_Target_for_Protected_Areas
                  Won’t_Save_the_World’s_Biodiversity⠀⇛


                       Proposals to protect a third of the Earth for
                       wildlife (or even ‘half Earth’, as suggested by
                       some extremist conservationists) have been around
                       for decades, but the idea has only been taken up as
                       a serious proposition over the last couple of
                       years. A target of 30% by 2030 has been included in
                       a new draft action plan for 2020 to 2030 under the
                       global Convention on Biological Diversity. A
                       coalition of 60 governments led by France and Costa
                       Rica is lobbying heavily for the idea.


                       During the World Conservation Congress just
                       finished in Marseille, I asked the French
                       government’s co-coordinator of this so-called ‘High
                       Ambition Coalition’ how they foresaw the target
                       working in practice. Key issues are not clear.
                       Would each country have to designate 30% of its
                       territory for conservation, or would it be a global
                       target and, if so, how would it be determined which
                       countries protected what, bearing in mind that
                       biodiversity is very unevenly distributed around
                       the planet?


                # § Energy⠀➾


                      # ⚓ PennEast_Pipeline_Cancelation_Could_Signal_‘End_of_an
                        Era’_for_Unnecessary_Fossil_Fuel_Projects⠀⇛


                             A major natural gas pipeline in Pennsylvania
                             was canceled this week in the face of a
                             thicket of legal obstacles and intense local
                             opposition. The cancelation may punctuate
                             what could be the end of a decade-long
                             pipeline building frenzy in the U.S. as
                             federal regulators begin to heed calls from
                             activists and local communities to increase
                             scrutiny over unneeded pipelines
                             crisscrossing the country. 


                             The PennEast pipeline would have carried
                             Marcellus shale gas from Luzerne County,
                             Pennsylvania, across the Delaware River and
                             to Mercer County, New Jersey. But the
                             developers of the project canceled it on
                             September 27, citing its inability to obtain
                             state-level water quality permits from New
                             Jersey. The decision came three months after
                             the company won a case before the U.S.
                             Supreme Court related to the corporation’s
                             ability to seize state land using eminent
                             domain authority.


                      # ⚓ Head_of_California_Utility_Regulator_Resigns_Less
                        Than_One_Year_Into_Six-Year_Term⠀⇛


                             The head of California’s powerful utility
                             regulator announced to staff that she would
                             be leaving her position at the end of the
                             year, less than one year into a six-year
                             term.


                      # ⚓ Oil_Production_To_Grow_Over_the_Next_Five_Years,_OPEC
                        Says⠀⇛


                             In that year, the planet will have 9.5
                             billion people who will consume 108 mbd of
                             crude oil, although the diffusion of energy
                             efficient technologies could reduce the oil
                             demand by over 8 mbd. Despite this, oil “will
                             continue to be the fuel with the largest
                             share in the world energy basket.”


                # § Wildlife/Nature⠀➾


                      # ⚓ Wild_Birds_Will_Be_Protected_Once_Again,_As_U.S.
                        Resumes_Enforcing_Rules_On_Companies⠀⇛


                             The Biden administration said Wednesday it
                             will draft rules to govern the killing of
                             wild birds by industry and resume enforcement
                             actions against companies responsible for
                             deaths that could have been prevented, a
                             longstanding practice that ended under
                             President Donald Trump.


                             The move came as North American bird numbers
                             have plummeted drastically in recent decades.
                             That decline was punctuated by news Wednesday
                             that the famed ivory-billed woodpecker and 22
                             other species of flora and fauna have gone
                             extinct.


                # § Overpopulation⠀➾


                      # ⚓ Religion,_religiosity,_fertility_and_contraception_in
                        Sub-Saharan_Africa_–_Part_1,_Introduction_to_studies_of
                        religion⠀⇛


                             How important is religion and belief in the
                             supernatural for family life, contraceptive
                             use, fertility, and family size? Presumably
                             many of our readers have considered the role
                             played in high-fertility societies by the
                             belief that “children are God’s will”. In
                             this blog series based on a literature
                             review1, we focus on Sub-Saharan Africa (SSA)
                             and summarize much evidence about the
                             importance of religion and religiosity. SSA
                             has the highest degree of religiosity and
                             highest fertility rate in the world. In part
                             1 below, we give background on scientific
                             research into religion – an active field with
                             intriguing theories and findings.


                      # ⚓ We_Used_Up_All_the_Earth’s_Resources_on_July
                        29th—Here’s_What_That_Means_for_the_Planet_(and_Us)⠀⇛


                             This year, Earth Overshoot Day fell on July
                             29th, which means humans currently use 74%
                             more resources than what the planet can
                             regenerate. In this episode of Good Together,
                             Brightly’s co-founder and CEO, Laura Wittig,
                             spoke with Sarah Baillie, the population and
                             sustainability organizer at the Center for
                             Biological Diversity, about how our everyday
                             consumption plays a role and what we can do
                             to ensure our resources are sustained.


                      # ⚓ Over-population:_Threat_to_mankind⠀⇛


                             Finding a long-term solution to
                             overpopulation is bringing down the human
                             population which our earth can support and
                             living with decent conditions is all that’s
                             needed. If the equilibrium doesn’t maintain
                             it creates a misbalance on the environment
                             and economy. It’s a fancy issue for those
                             that don’t know the way overpopulation could
                             be a threat to mankind and our earth evolved
                             changes within the past few decades.
                             Somewhere the population increasing with the
                             speed of sunshine and somewhere it’s minimal.


                             Overpopulation is an alarming threat and if
                             not taken into control, it will cause severe
                             consequences in the future. Literacy and
                             poverty are the two main causes that should
                             be taken in control with the right steps to
                             avoid the misbalance. Overpopulation is the
                             evil root for climate change, poverty,
                             unemployment, and conflicts. There are a
                             million children who don’t have family their
                             adoption is an option and home or shelter
                             will be provided to them and collectively as
                             humans, we have the power to make a world a
                             better place to live in.


          o § Finance⠀➾


                # ⚓ Progressives_Deliver_Message_to_Democrats_on
                  Infrastructure:_‘Don’t_F**k_This_Up’⠀⇛


                       The progressive activists in the stands at
                       Wednesday night’s congressional baseball game held
                       up a series of banners, one of which said “Dems
                       Don’t Fuck This Up,” and another that read “Our
                       Lives Are a Game: Pass $3.5T.” A third banner
                       declared: “Reconciliation First / Hold the Line.”


                       “We are going to make sure we deliver the entirety
                       of the president’s agenda, because… 96% of
                       Democrats in the House and Senate agree that that’s
                       the right thing to do.” —Rep. Pramila Jayapal


                # ⚓ Progressives_Remain_United_on_Holding_Democrats_to
                  Infrastructure_Promises⠀⇛


                # ⚓ Opinion_|_Close_This_Perverse_Tax_Loophole_in_Order_to_Save
                  Jobs_and_Fund_Infrastructure⠀⇛


                       The multi-trillion-dollar budget reconciliation
                       bill moving through Congress represents an enormous
                       opportunity to invest in unmet human and
                       environmental needs. It’s also the best chance we
                       have to close loopholes that help the wealthy avoid
                       their fair share of taxes.


                # ⚓ Opinion_|_When_the_New_York_Times_Colludes_With_the
                  Billionaire_Class⠀⇛


                       According to a White House analysis (9/23/21), the
                       country’s 400 wealthiest families have an effective
                       tax rate of just over 8%. At the New York Times (9/
                       23/21), reporter Jim Tankersley was quick to cast
                       doubt on the figure.


                # ⚓ “A_Moral_Crisis”:_Reverend_William_Barber_on_Why_Congress
                  Must_Pass_$3.5_Trillion_Bill⠀⇛


                       Activists continue to call on Democratic leaders to
                       pass the $3.5 trillion Build Back Better Act, which
                       expands the social safety net and includes measures
                       to address the climate crisis. Progressives remain
                       resolute in their opposition to passing a
                       bipartisan $1 trillion infrastructure bill unless
                       it is paired with the larger package. The Build
                       Back Better Act represents “economic investment in
                       the lives of poor and low-wealth people in this
                       country,” says Reverend William Barber, co-chair of
                       the Poor People’s Campaign. “The question here is
                       not ‘What will it cost if we do this?’ What will it
                       cost if we don’t do this?”


                # ⚓ Schumer_Announces_Deal_Reached_With_GOP_Senators_to_Fund
                  Government_Through_Dec⠀⇛


                # ⚓ Utilities_Took_$1.25_Billion_in_Pandemic_Aid_Then_Shut_Off
                  Power_to_Households_Nearly_1_Million_Times:_Report⠀⇛


                       Over a dozen leading U.S. utility companies took
                       more than a billion dollars of publicly-funded
                       pandemic bailout money while pulling the plug on
                       power to vulnerable households nearly a million
                       times, according to a new report out Thursday.


                       “It is clear that private utilities prioritize
                       profits and shareholder satisfaction over all else,
                       including customer health and the climate.”—Chris
                       Kuveke, BailoutWatch


                # ⚓ “In_Those_Pictures,_You_Can_See_the_Community”⠀⇛


                       In East and West Garfield Park, Chicago, we sought
                       out residents’ archives to shed light on a
                       neighborhood the city neglected.


                # ⚓ When_Will_the_US_Break_Free_from_the_Clutches_of_Its
                  Grifters?⠀⇛


                       Thus it surprises nobody to discover that when
                       Donald Trump and the people around him learned, in
                       mid-November of 2020, that there was absolutely no
                       meaningful voter fraud in that month’s election,
                       they chose, instead of acknowledging the truth, to
                       go ahead with a plan to raise over $200 million
                       dollars (and counting).  That even today “President
                       Trump” is sending out one or two fundraising emails
                       a day, each one with the tiny “make this a
                       recurring donation” box pre-checked.


                       Republican appointees on the US Supreme Court
                       cracked open the door for professional grifters in
                       1976 when, for the first time in American history,
                       the Court redefined politicians taking money from
                       billionaires away from being “political corruption”
                       and “bribery” — what such behavior had been called
                       since the beginning of the republic — to instead
                       say it was a mere “exercise of free speech” on the
                       part of the morbidly rich.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ When_Democrats_Go_Small,_They_Lose_Big⠀⇛


                       President Franklin Delano Roosevelt taught
                       Democrats how to keep power by enacting bold
                       programs that spoke to the pressing needs of
                       working-class Americans. Unfortunately, the heirs
                       to what is still referred to as “the party of FDR”
                       have spent the better part of 75 years trying to
                       unlearn that lesson.


                # ⚓ Social_Media_Regulation_In_African_Countries_Will_Require
                  More_Than_International_Human_Rights_Law⠀⇛


                       There has been a lot of focus on moderation as
                       carried out by platforms—the rules social media
                       companies base their decision on what content
                       remains online. There has however been limited
                       attention on how actors other than social media
                       platforms, in this case governments, seek to
                       regulate these platforms. 


                # ⚓ Progressives_Hold_the_Line_as_‘Manchema’_Side_With
                  Oligarchy_Against_Biden_Agenda⠀⇛


                       Political observers predicted three options late
                       Thursday as it remained unclear whether Speaker of
                       the House Nancy Pelosi would still hold a vote on
                       the Bipartisan Infrastructure Framework, or BIF,
                       which has stirred a Capitol Hill fight between a
                       small band of corporate Democrats in Congress and
                       the rest of the party anchored by the Congressional
                       Progressive Caucus.


                       As of this writing, there was no final word other
                       than promises earlier in the day by Pelosi that a
                       vote would come—even though fresh public comments
                       from Sen. Joe Manchin (D-W.V.) made it clear that a
                       chasm remains between his opposition and that of
                       Sen. Kyrsten Sinema (D-Ariz.) and House Democrats 
                       on the $3.5 trillion Build Back Better Act that
                       must ultimately be passed via the bicameral
                       reconciliation process.


                # ⚓ Donald_J._Trump:_Traitor⠀⇛


                       “There is an unfolding assault taking place in
                       America today,” President Biden said in
                       Philadelphia on July 13. “An attempt to suppress
                       and subvert the right to vote in fair and free
                       elections, an assault on democracy, an assault on
                       liberty, an assault on who we are — who we are as
                       Americans.”


                       All the world knows who is leading that assault:
                       Donald Trump. Why then isn’t the President, or
                       Democrats, or liberal and progressive opinion
                       writers calling Trump and his high-ranking
                       followers traitors? Not just “fascists” and
                       “autocrats” but traitors. Aren’t the Trumpists
                       committing treason by actively subverting
                       constitutional democracy, the very fabric of our
                       political system?


                # ⚓ Most_Americans_Want_Dems_in_Charge_of_Congress_Next_Year,
                  Polling_Data_Shows⠀⇛


                # ⚓ In_Anti-Reconciliation_Blitz,_Exxon_Spent_$275,000_on
                  Facebook_Ads_in_One_Week⠀⇛


                # ⚓ Biden’s_Immigration_Policy_Picks_Up_Where_Trump_Left_Off⠀⇛


                       Mass opposition to Donald Trump began with
                       immigration. His racist rhetoric and barbaric
                       policies around immigrants and asylum-seekers are
                       what first fueled outrage among liberals, as well
                       as among people who were otherwise apolitical.
                       Politicians, pundits, and rank-and-file Democratic
                       voters alike rightfully decried Trump’s migrant
                       policies, with some going as far as to compare the
                       administration to the Nazi regime.


                # ⚓ YouTube_Deletes_RT_German-Language_Channels_Over_COVID-19
                  ‘Misinformation’⠀⇛


                       Video-sharing platform YouTube has deleted two
                       German-language channels managed by Russia’s state-
                       owned media company RT, prompting Moscow to blast
                       the company for “censorship” and vow retaliation.


                # ⚓ Keynote_Speech_by_President_of_the_Republic_of_Finland,
                  Sauli_Niinistö,_at_the_FIIA_Forum,_Helsinki,_29_September
                  2021⠀⇛


                       An important legacy of the original Conference on
                       Security and Cooperation in Europe, held here in
                       Helsinki in 1975, was the spirit of that meeting.
                       The willingness of competitors and adversaries to
                       sit at the same table, despite their disagreements.
                       Such a spirit is in high demand today, on the
                       global level.


                       We urgently need to respond to fundamental
                       questions of war and peace, climate change and
                       biodiversity loss, pandemics and the challenges of
                       new technologies. We can only succeed in that
                       together. It is a question of our common human
                       responsibilities. What kind of a world will we
                       leave to future generations?


                       Above all, these are not some distant global
                       issues, somehow detached from our national
                       interests. They are at the heart of our own
                       security. And therefore, they reside at the very
                       centre of Finland’s foreign and security policy.


          o § Censorship/Free Speech⠀➾


                # ⚓ U.S._Supreme_Court_Upholds_Public_School_Students’_Off-
                  Campus_Speech_Rights⠀⇛


                       The case, Mahanoy Area School District v. B.L.,
                       involved a public high school student who was
                       placed on the junior varsity cheerleading squad
                       after failing to make varsity. Out of frustration,
                       Brandi Levy (later identified by her full name
                       since she is no longer a minor) shared a “snap”
                       with her middle finger raised and text that said,
                       among other things, “fuck cheer.” The message was
                       posted on a Friday night from a local convenience
                       store. The cheerleading coaches suspended Levy from
                       the J.V. squad for a year after one of her Snapchat
                       connections took a screen shot of the message and
                       shared it with them.


                       The school justified the punishment of Levy’s off-
                       campus speech by invoking the Supreme Court’s
                       opinion in Tinker v. Des Moines Independent
                       Community School District (1969), which held that
                       students may not be punished for their on-campus
                       speech unless the speech “materially and
                       substantially” disrupted the school day or invaded
                       the rights of others. The school further justified
                       Levy’s suspension on the ground that social media
                       posts generated off campus can easily be brought
                       onto campus given the widespread use of cell phones
                       and the internet. We argued that Tinker should not
                       be used to punish off-campus speech—including
                       social media speech.


                       In ruling in favor of Levy, the Supreme Court did
                       not go as far as we had hoped. The Court held that
                       Tinker may sometimes justify restrictions to off-
                       campus speech: “[W]e do not believe the special
                       characteristics that give schools additional
                       license to regulate student speech always disappear
                       when a school regulates speech that takes place off
                       campus.”


                # ⚓ Leader_of_Prestigious_Yale_Program_Resigns,_Citing_Donor
                  Pressure⠀⇛


                       Four months of wrangling over the program later,
                       Professor Gage resigned after the university
                       administration informed her that a new advisory
                       board it was creating to oversee the course under
                       previously ignored bylaws would be dominated by
                       conservative figures of the donors’ choosing,
                       including, against her strong objections, Henry A.
                       Kissinger, the former secretary of state under
                       President Richard M. Nixon.


                       Her resignation, which Yale has not yet made
                       public, raises the question of where universities
                       draw the line between honoring original agreements
                       with donors and allowing them undue sway in
                       academic affairs. It’s a question that can become
                       turbocharged when colliding political visions, and
                       the imperatives of fund-raising, are involved.


                # ⚓ Iranian_Singer_Googoosh_Raises_Her_Voice_To_Keep_Her
                  Nation’s_Culture_Alive⠀⇛


                       She was forbidden from participating in any type of
                       public gathering. “They tried hard to erase me—I
                       mean, erase my name, erase my position, erase my
                       songs, erase my face, erase the memory of me,” she
                       says. “But they couldn’t.”


                       At the peak of her career, Googoosh was forced to
                       live in silence for 21 years. Then, in July of
                       2000, the government granted her permission to
                       visit her family in Los Angeles, and she left. Her
                       first stop was in Toronto. At the Air Canada Center
                       Arena, 18,000 fans waited for her return with open
                       arms.


                       Reminiscing about that auspicious day when she
                       returned to the stage, Googoosh tears up. “I was
                       speechless, and then I had fear,” she explains. “I
                       didn’t know if I can take care of these people. But
                       it happened.”


                # ⚓ In_Hong_Kong,_access_to_online_museum_about_Tiananmen
                  Square_appears_blocked⠀⇛


                       Hong Kong users have not been able to access the
                       website from the city since Thursday without using
                       virtual private networks. Internet service provider
                       PCCW declined to comment. Providers HKBN and 3HK
                       did not respond to requests for comment.


                       “This is a disgraceful act to erase historical
                       memory,” the online museum said in a statement.


                       Police officers take away a cardboard featuring the
                       image of Goddess of Democracy from the June 4th
                       museum in Hong Kong on Sept. 9, 2021.Kin Cheung /
                       AP Hong Kong police said they could not comment on
                       individual cases, but said national security
                       legislation states that “police may require service
                       providers to take actions to prohibit electronic
                       messages posted on electronic platforms that are
                       likely to endanger national security.”


                # ⚓ Govt_wants_to_impose_centralised_censorship_office:_RSF⠀⇛


                       In a statement issued on Wednesday, the Reporters
                       Without Borders (RSF) said that along with its
                       Pakistani partner, the Freedom Network, it is
                       supporting the campaign that Pakistani journalists
                       have launched against the proposed legislation.


                       The draconian proposed law was unveiled in June and
                       would create a powerful new entity called the
                       Pakistani Media Development Authority (PMDA).


                # ⚓ Woman_gets_death,_fine_for_blasphemy_in_Lahore⠀⇛


                       The judge, after going through the statements of
                       the witnesses and their cross examination, observed
                       that the oral and material evidence proved beyond
                       reasonable doubt that the suspect wrote and
                       distributed the writings attributed to her.


                # ⚓ Xiaomi_censorship_allegations_may_cloud_its_global
                  ambitions,_expansion_plans⠀⇛


                       Last week, a report by the Lithuanian defence
                       ministry’s National Cyber Security Centre (NCSC)
                       alleged that Xiaomi’s Mi 10T 5G smartphone, which
                       is widely sold in Europe, has a built-in ability to
                       detect and censor terms such as “Free Tibet”, “Long
                       live Taiwan independence” or “democracy movement”.


                # ⚓ First_look:_Rick_Scott_probes_LinkedIn,_Microsoft_on
                  censoring_U.S._journalists_in_China⠀⇛


                       Sen. Rick Scott (R-Fla.) sent a letter to Microsoft
                       and LinkedIn leadership on Thursday questioning why
                       LinkedIn censored the profiles of U.S. journalists
                       from the company’s China-based platform this week,
                       according to a letter obtained by Axios.


                       Driving the news: LinkedIn — which is owned by
                       Microsoft — notified several U.S. journalists this
                       week, including Axios’ Bethany Allen-Ebrahimian,
                       that their accounts will no longer be viewable in
                       China due to “prohibited content” on their profile.


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


                # ⚓ Inside_the_CIA_plot_to_kidnap,_kill_Julian_Assange⠀⇛


                # ⚓ Australian_visitors_to_Assange_demand_answers⠀⇛


                # ⚓ Report_On_CIA_Plans_To_Kidnap_Or_Kill_Assange_Show_Clearest
                  Evidence_Yet_Of_Improper_Pressure_On_Prosecutors⠀⇛


                       Though District Judge Vanessa Baraitser ruled
                       against the United States’ extradition request, she
                       rejected the argument from the legal team for
                       WikiLeaks founder Julian Assange that hostility
                       within U.S. intelligence agencies “translated into
                       improper pressure on federal prosecutors to bring
                       charges.”


          o § Civil Rights/Policing⠀➾


                # ⚓ This_Supreme_Court_Term,_Conservatives_Have_One_Aim:_Stop
                  Progress⠀⇛


                       On the first Monday in October, the Supreme Court,
                       the most powerful government body controlled by
                       conservatives, returns to work. Democrats have the
                       White House and both chambers of Congress;
                       Republicans, who have lost the popular vote in
                       seven of the last eight presidential elections, are
                       currently confined to the unelected, unaccountable
                       branch of government.1


                # ⚓ “Language”_Arguments_Against_Immigration_Freedom_are_a
                  Tower_of_Babble⠀⇛


                       The simplest, and most appropriate response to that
                       argument comes from comedian Doug Stanhope: “Then
                       don’t talk to ’em.” Problem solved. But I can’t get
                       a whole column out of that response, so let’s take
                       apart the fake “issue” in a little more detail.


                       Often, the argument starts off with fake tones of
                       sympathy. Those poor immigrants — how will they
                       ever get jobs and “assimilate” if they don’t know
                       “the national language?” Send them back for their
                       own good!


                # ⚓ Democratic_Congresswomen_Testify_About_Their_Personal
                  Abortion_Stories⠀⇛


                # ⚓ Media_Fixate_on_Missing_White_Women_and_Ignore_Black,_Brown
                  and_Indigenous_Women⠀⇛


                # ⚓ As_Canada_Honors_Indigenous_Children,_Judge_Rejects_Trudeau
                  Challenge_to_Compensation⠀⇛


                # ⚓ Abattoir_labour_shortage_sees_Yorkshire_farmer_kill
                  piglets⠀⇛


                # ⚓ ‘A_Stunning_About-Face’:_Rights_Group_Lambast_Biden_for
                  Expanded_For-Profit_Immigrant_Detention⠀⇛


                       Human rights organizations on Wednesday criticized
                       the Biden administration over an expansion of
                       privatized immigration detention they said
                       represented an “inexcusable” walk-back of a
                       campaign promise.


                       “When will Biden act on his promise to bring
                       justice and fairness to the immigration
                       system?”—Setareh Ghandehar, Detention Watch Network


                # ⚓ Warning_of_‘Looming_Harsh_Winter,’_IFRC_Calls_for_Urgent
                  Humanitarian_Aid_for_Afghan_People⠀⇛


                       “After living through decades of fleeing and
                       fighting, Afghans now face a severe drought which
                       has devastated food production, leaving millions
                       hungry and destitute.”—Alexander Matheou, IFRC


                # ⚓ ‘Appalled’_UN_Human_Rights_Experts_Urge_Immediate_Release,
                  Compensation_for_Steven_Donziger⠀⇛


                       Ahead of Steven Donziger’s sentencing scheduled for
                       Friday, five United Nations human rights experts
                       ruled that the American attorney who won a
                       multibillion-dollar judgment against Chevron in
                       Ecuadorian courts has been “arbitrarily” detained
                       in the U.S. for 787 days.


                       “The appropriate remedy would be to release Mr.
                       Steven Donziger immediately and accord him an
                       enforceable right to compensation and other
                       reparations.”—UN Experts


                # ⚓ Missing_White_Woman_Syndrome:_Media_Obsess_Over_Some_Cases
                  as_Black,_Brown_&_Indigenous_Women_Ignored⠀⇛


                       Wall-to-wall coverage of the case of Gabby Petito —
                       a 22-year-old white woman and blogger who went
                       missing while traveling with her fiancé Brian
                       Laundrie and whose remains were found in a national
                       park in Wyoming — has renewed attention on what
                       some call “missing white woman syndrome,” the
                       media’s inordinate focus on white female victims
                       and the disparity in coverage for women of color.
                       We host a roundtable discussion with Amara Cofer,
                       host and executive producer of the podcast “Black
                       Girl Gone”; Mary Kathryn Nagle, a citizen of the
                       Cherokee Nation and lawyer focused on tribal
                       sovereignty; and Melissa Jeltsen, a freelance
                       reporter who covers violence against women. “There
                       is an underrepresentation of Black women, of women
                       of color in these stories,” says Cofer.


                # ⚓ Australia_returns_world’s_oldest_tropical_forest_to
                  indigenous_owners⠀⇛


                       Listed as a UNESCO World Heritage Site since 1988,
                       the Daintree National Park was handed back to the
                       Eastern Kuku Yalanji people in a ceremony in the
                       remote town of Bloomfield on Wednesday.


                       The 135-million-year-old tropical rainforest is
                       famed for its rich biodiversity – from a giant
                       clawed cassowary bird to plants that have existed
                       since the age of the dinosaurs. But it has come
                       under sustained pressure from climate change and
                       industries such as logging.


                       In striking a new deal to manage the rainforest,
                       Queensland said the Daintree would be returned to
                       the traditional owners of the land.


                # ⚓ UK_police_officer_sentenced_to_life_in_jail_for_woman’s
                  murder⠀⇛


                       The judge said that Couzens’ use of his police
                       status to carry out the “grotesque” offences
                       warranted the highest penalty, a rare whole-life
                       jail term for which there is no possibility of
                       parole.


                # ⚓ The_Lancet:_More_than_half_of_police_killings_in_USA_are
                  unreported_and_Black_Americans_are_most_likely_to_experience
                  fatal_police_violence⠀⇛


                       To examine the extent of under-reporting,
                       researchers compared NVSS data to three non-
                       governmental, open-source databases on police
                       violence: Fatal Encounters, Mapping Police
                       Violence, and The Counted [2]. These databases
                       collate information from news reports and public
                       record requests. When compared, the researchers’
                       new estimates highlight the extent to which deaths
                       from police violence are under-reported in the NVSS
                       and the disproportionate effect of police violence
                       on Black, Hispanic, and Indigenous people in the
                       USA.


                # ⚓ Study:_Police_kill_more_people_in_this_state_than_any
                  other._And_many_deaths_go_unreported.⠀⇛


                       About 84% of police killings in the state from 1980
                       to 2018 were unreported or misclassified in
                       official government reports, according to the peer-
                       reviewed study in The Lancet, one of the world’s
                       oldest and most renowned medical journals.


                # ⚓ UAE:_Tolerance_Narrative_a_Sham⠀⇛


                       Domestic critics are routinely arrested and, since
                       at least 2015, UAE authorities have ignored or
                       denied requests for access to the country by United
                       Nations experts, human rights researchers, and
                       critical academics and journalists. The
                       government’s pervasive domestic surveillance has
                       led to extensive self-censorship by UAE residents
                       and UAE-based institutions; and stonewalling,
                       censorship, and possible surveillance of the news
                       media by the government.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ Google,_NBC_Bring_Dumb_Cable_TV_Blackout_Feuds_To
                  Streaming⠀⇛


                       For years cable TV has been plagued by retrans
                       feuds and carriage disputes that routinely end with
                       users losing access to TV programming they pay for.
                       Basically, broadcasters will demand a rate hike in
                       new content negotiations, the cable TV provider
                       will balk, and then each side blames the other for
                       failing to strike a new agreement on time like
                       reasonable adults. That repeatedly results in
                       content being blacked out for months, without
                       consumers ever getting a refund. After a few
                       months, the two sides strike a new confidential
                       deal, your bill goes up, and nobody much cares how
                       that impacts the end user. Rinse, wash, repeat.


                # ⚓ My_changing_(citation)_style_of_external_links_here_on
                  Wandering_Thoughts⠀⇛


                       Instead, the growing amount of information I
                       include about the link is a quiet reaction to the
                       unfortunate fact that over time, an increasing
                       number of URLs will stop working. More and more
                       I’ve come to feel that the more information I
                       include about a URL, the better for the future,
                       both for me and for other people. If I put in the
                       full title and even the name the author uses,
                       there’s a higher chance that some copy of the page
                       can be found in search engines, even if the domain
                       changes, the site is restructured, the form of the
                       URLs all change, and so on.


                # ⚓ Open_Access_Model_Can_Leverage_Historic_Funding_to_Drive
                  Broadband_Expansion⠀⇛


                       The model comes with several inherent benefits over
                       conventional approaches, the conference heard.
                       “When a community owns [the infrastructure] they’re
                       going to build it to the specs they need,” McKinley
                       explained. “Private [carriers] will employ cost-
                       cutting methods wherever they can.”


          o § Monopolies⠀➾


                # ⚓ Google_Urges_EU_Judges_to_Slash_‘Staggering’_$5_Billion
                  Fine⠀⇛


                       The search-giant’s power over mobile phones is the
                       focus of a week-long court hearing. Google’s
                       lawyers are arguing that the European Commission
                       blundered by demanding changes to allegedly anti-
                       competitive contracts with suppliers of phones
                       running its Android operating system — the engine
                       room for the vast majority of mobile devices in the
                       region.


                # § Patents⠀➾


                      # ⚓ How_to_respond_to_China’s_bid_to_join_the_CPTPP⠀⇛


                             The CPTPP is largely an agreement to treat
                             companies equally, regardless of the country
                             they come from. Importantly, it is intended
                             to be a ‘high quality’ agreement. So, for
                             instance, while Article 2.4 focuses on the
                             elimination of customs duties, China has
                             recently demonstrated a willingness to use
                             informal trade restrictions, such as
                             unofficial instructions to simply not process
                             goods coming from Australia. Such moves would
                             certainly be against the spirit of the CPTPP.


                # § Copyrights⠀➾


                      # ⚓ Eddy_Grant_Copyright_Infringement_Lawsuit_Against
                        Donald_Trump_Moves_Forward⠀⇛


                             Eddy Grant filed the lawsuit in New York in
                             September 2020 after the campaign used his
                             work in an online video. The clip features a
                             fast train mean to represent the Trump
                             campaign, while Joe Biden trails along in a
                             manually operated vehicle. Twitter removed a
                             viral copy of the video following a copyright
                             claim from Grant.


                             Eddy Grant is just one of many artists who
                             pushed back against the Trump campaign using
                             his music. Other artists who objected to
                             their music being featured in political
                             campaigns include Neil Young, The Rolling
                             Stones, Panic! at the Disco and many more.


                      # ⚓ Disney_and_Scarlett_Johansson_have_settled_their
                        lawsuit⠀⇛


                             Terms of the settlement weren’t disclosed


                      # ⚓ YouTube_TV_and_NBCUniversal_agree_to_‘short’
                        extension_to_avoid_channels_disappearing⠀⇛


                             According to NBCUniversal, the standoff over
                             carriage — which has become all too common in
                             the streaming wars, particularly when it
                             comes to regional sports programming —
                             involved a demand for what an NBCUniversal
                             source close to the matter described as a
                             fair rate relating to marketplace terms. A
                             spokesperson for YouTube, meanwhile, said
                             that the company was negotiating for terms
                             that it sees as fair based on industry
                             standards and the size of its service. The
                             spokesperson also said that NBCUniversal
                             asked YouTube TV to bundle Peacock, which the
                             spokesperson claimed would result in users
                             paying twice for the same content.


                      # ⚓ Cloudflare_Books_Partial_Victory_in_‘Thothub’_Piracy
                        Lawsuit⠀⇛


                             Cloudflare has booked a partial victory in a
                             piracy lawsuit filed by several models whose
                             photos leaked online. The CDN provider
                             previously offered its proxying service to
                             the now-defunct website ‘Thothub’. The court
                             agreed with Cloudflare that there’s no
                             evidence for direct infringement, but the
                             contributory copyright infringement claim
                             remains intact.


                      # ⚓ Accused_Pirate_Asks_Court_to_Dismiss_Lawsuit_from
                        Suspended_‘Copyright_Troll’⠀⇛


                             An accused pirate has asked a Texas federal
                             court to dismiss a copyright lawsuit filed by
                             Malibu Media. The adult entertainment
                             company, which has sued thousands of people
                             over the years, is currently suspended by
                             California’s Franchise Tax Board. The defense
                             argues that, due to this suspension, the
                             company is not allowed to maintain a lawsuit.


                      # ⚓ Copyright_Continues_To_Be_Abused_To_Censor_Critics_By
                        Entities_Both_Big_And_Small⠀⇛


                             We’ve talked far too many times about how the
                             DMCA takedown processes across internet
                             industries as they stand are wide, wide open
                             for abuse. From churches wielding copyright
                             to attempt to silence critics engaging in
                             protected speech, to lawyers using copyright
                             to try to silence critics engaging in
                             protected speech, to freaking political
                             candidates abusing YouTube’s DMCA notice
                             process to silence critics engaging in
                             protected speech… well, you get the idea. The
                             point is that we’ve known for a long, long
                             time that the current method by which the
                             country and companies currently enforce
                             copyright law tilts so heavily towards the
                             accuser that it’s an obvious avenue for
                             misuse.



                    ䷩ 𝚕𝚒𝚗𝚎 3813

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 10.01.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_1/10/2021:_GhostBSD_21.09.29_ISO,_Free_Software_Foundation_(FSF)_Vs_JS
Mess⠀✐


Posted in News_Roundup at 2:05 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o § Desktop/Laptop⠀➾


                # ⚓ The_4_Invaluable_Benefits_of_Switching_to_Linux⠀⇛


                       Linux is an operating system used in everything
                       from phones to cars and complex supercomputers, yet
                       you can also use it to power your personal
                       computer. The desktop may not be the space where
                       you’re most likely to encounter Linux, but it’s
                       more than worth your consideration.


                       Far from being merely another tool for the job,
                       there are several big benefits that come from
                       taking the time to try out, learn, and maybe even
                       stick with using the Linux desktop. Here are four
                       advantages of switching to Linux:


                       1. A Free Course in Digital Ethics


                       The free and open-source community views software
                       differently from what you encounter on commercial
                       operating systems. On Windows, macOS, Android, and
                       iOS, most apps come exclusively as binaries whose
                       code you don’t have access to. This binary, though
                       sometimes available for free, is generally a
                       product that you pay for.


                       The Linux world doesn’t focus on the binary but on
                       the code itself. This code is a language, and the
                       only way to know what it’s doing is to read it. If
                       you (or other Linux users) can’t read the code, you
                       have no way to know what it’s actually doing. You
                       can only have the developer’s word.


                       Free software is based on the four freedoms. Here
                       they are, as defined by the Free Software
                       Foundation…


          o § Audiocasts/Shows⠀➾


                # ⚓ Arch_Guided_Installer_Is_Finally_Amazing!!!_–_Invidious⠀⇛


                       A few months back I did a video about the Arch
                       Guided Installer and at the time it was an absolute
                       train wreck but I gave it a few months and I have
                       to admit it’s now become an amazing piece of
                       software.


          o § Kernel Space⠀➾


                # ⚓ Linux_5.14.9⠀⇛


                       I'm announcing the release of the 5.14.9 kernel.

                       All users of the 5.14 kernel series must upgrade.

                       The updated 5.14.y git tree can be found at:
                       	git://git.kernel.org/pub/scm/linux/kernel/git/
                       stable/linux-stable.git linux-5.14.y
                       and can be browsed at the normal kernel.org git web
                       browser:

                       https://git.kernel.org/?p=linux/kernel/git/stable/
                       linux-s...

                       thanks,

                       greg k-h
                # ⚓ Linux_5.10.70⠀⇛


                # ⚓ Linux_5.4.150⠀⇛


                # ⚓ New_AMD_Linux_Audio_Driver_Patches_Posted_–_Aimed_For
                  Enhancing_Chromebook_Support_–_Phoronix⠀⇛


                       In addition to Linux 5.15 adding a new AMD audio
                       driver for “Van Gogh” APUs such as found in the
                       forthcoming Steam Deck, AMD’s open-source Linux
                       driver engineers have also been working on other
                       audio improvements — this time on the Chromebook
                       front.


                       A set of eight AMD Linux audio patches were sent
                       out today. These audio patches of relevance to
                       Renoir and Cezanne platforms seems to be driven by
                       the Google Chromebook “Guybrush” board but may
                       prove relevant to other hardware moving forward.
                       That Guybrush Zen 3 Chromebook has been known since
                       the end of last year when it began appearing in
                       Chromium OS sources.


                # ⚓ Microsoft_Bluetooth_Mouse_Loves_Linux._A_GNU/Linux_review
                  of_the_mouse_that_wants_a_better_home.⠀⇛


                       When I bought this laptop last year, I needed a
                       Bluetooth mouse. Nothing fancy, nothing that would
                       break the bank. Amazon had a “Microsoft Bluetooth
                       Mouse” in Warehouse Deals for $9.99!


                       In fact, for that $10, you got a Bluetooth 5.0 LE
                       device, no less, with battery life that goes on for
                       months and months of constant use.


                       The problem I kept hitting was that it just doesn’t
                       work very well with Windows 10. In fact, despite
                       all of the “This works great with Windows 10!”
                       nonsense on Amazon, from Microsoft, the facts are
                       that it is very frustrating due to the Bluetooth
                       stack on Windows being utter crap.


                # § Intel⠀➾


                      # ⚓ Intel_Announces_Loihi_2,_Lava_Software_Framework_For
                        Advancing_Neuromorphic_Computing⠀⇛


                             Lava will be available as open-source on
                             GitHub under BSD-3 and LGPLv2.1 licensing.


                      # ⚓ Intel_Exploring_CPU+GPU_Synchronized_Priority
                        Scheduling_For_Linux_–_Phoronix⠀⇛


                             Intel’s open-source Linux graphics driver
                             engineers are evaluating possible
                             improvements to the Linux kernel for
                             accommodating CPU and GPU synchronized
                             priority scheduling.


          o § Applications⠀➾


                # ⚓ KDiskMark⠀⇛


                       There is a new application available for Sparkers:
                       KDiskMark


                # ⚓ Best_Harddisk_Cloning_Tools_For_Linux⠀⇛


                       Let’s have a look at the list of the best hard disk
                       cloning tools for Linux-based operating systems.


          o § Instructionals/Technical⠀➾


                # ⚓ How_to_Install_Snort_on_Ubuntu_20.04⠀⇛


                       Snort is an open-source lightweight network
                       Intrusion Prevention System for running a network
                       intrusion detection system (NIDS). Snort is used to
                       monitor the package data sent/received through a
                       specific network interface. Network intrusion
                       detection systems can catch threats targeting your
                       system weakness and vulnerabilities using
                       signature-based detection and protocol analysis
                       technologies.


                       When NIDS software is installed and configured
                       correctly, can identify different kinds of attack
                       and suspicions things like CGI attacks, network
                       policy violations, SMB probes, malware infections,
                       a compromised system, stealth port scan, etc.


                # ⚓ How_to_Install_MERN_Stack_for_JS_Based_Applications_on
                  Ubuntu_20.04⠀⇛


                       MERN stack is a combination of MongoDB, Express,
                       React, Node. All of them are based on Javascript
                       and the stack is used to build modern web
                       applications. It is comprising the front-end
                       (React), back-end (Node and Express), and database
                       components (MongoDB).


                # ⚓ How_to_Install_Magento_on_Rocky_Linux_and_AlmaLinux⠀⇛


                       Written in PHP, Magento is a popular open-source,
                       and versatile eCommerce platform that provides
                       businesses with an online shopping cart. It
                       leverages various PHP frameworks such as Symfony
                       and Laminas to enhance its functionality and
                       usability.


                       Magento provides you with an Administrator’s
                       control panel that helps you create your online
                       shop, manage product catalog, monitor transactions
                       and invoices, and keep track of customers’ purchase
                       behavior among many other tasks.


                # ⚓ How_to_install_ZOOM_client_on_Debian_11_Bullseye_Linux⠀⇛


                       Zoom is a popular video conferencing software
                       available for multiple operating systems including
                       Linux. Here we learn the simplest way to install
                       Zoom client on Debian 11 Bullseye Linux.


                       Zoom as a conferencing software can be used to
                       perform telephone and video conferences. The basic
                       functions of Zoom can be used free of charge and
                       registration is not absolutely necessary. Zoom is
                       available both as a program for the computer and as
                       an app for all Android and iOS devices.


                       Even if the use of Zoom is basically free of
                       charge, not all functions of the program are
                       available to you in the basic free version. Not
                       only is the number of participants in a conference
                       limited to 100 people, but also its duration. If
                       there are more than two people, the maximum
                       conversation limit will be up to 40 minutes.


                # ⚓ How_to_Install_and_Use_Telnet_on_Debian_11_Bullseye_–
                  LinuxCapable⠀⇛


                       Telnet is a protocol that allows you to connect to
                       remote computers (called hosts) over a TCP/IP
                       network using a client-server protocol to establish
                       a connection to Transmission Control Protocol port
                       number 23


                       In the following tutorial, you will learn how to
                       install Telnet on a Debian 11 Bullseye operating
                       system.


                # ⚓ How_to_Install_The_Lounge_IRC_Client_on_Debian_11_Bullseye
                  –_LinuxCapable⠀⇛


                       The Lounge is a web-based IRC client written in
                       Node.js and can be installed and then accessed from
                       any modern browser for a native-like experience
                       without having a dedicated application installed.


                # ⚓ How_to_Backup_Linux_Filesystem_Using_dump_Command⠀⇛


                       On a Linux operating system environment, mastering
                       how to create and restore backups is a very
                       important skill set. It is easier for well-versed
                       Linux user to attain their data backup goals from
                       the terminal environment without the need for a
                       GUI-oriented application package.


                       The Linux dump utility is effective in creating
                       filesystem backups on an availed storage device.
                       However, the filesystem supported by this backup
                       utility disregards the likes of ReiserFS and FAT.


                # ⚓ How_To_Install_WordPress_with_LEMP_(Nginx,_MariaDB,_and
                  PHP)_on_Debian_11_Bullseye_–_LinuxCapable⠀⇛


                       WordPress is the most dominant content management
                       system written in PHP, combined with MySQL or
                       MariaDB database. You can create and maintain a
                       site without any prior knowledge in web development
                       or coding. The first version of WordPress was
                       created in 2003 by Matt Mullenweg and Mike Little
                       and is now used by 70% of the known web market,
                       according to W3Tech. WordPress comes in two
                       versions: the free open source WordPress.org and
                       WordPress.com, a paid service that starts at $5 per
                       month up to $59. Using this content management
                       system is easy and often seen as a stepping stone
                       for making a blog or similar featured site.


                       In the following tutorial, you will learn how to
                       install self-hosted WordPress using the latest
                       Nginx, MariaDB, and PHP versions available.


                # ⚓ How_to_Install_&_Configure_Wine_on_Pop!_OS_20.04_–
                  LinuxCapable⠀⇛


                       Wine is an open-source compatibility layer that
                       allows you to run Windows applications on Unix-like
                       operating systems like Linux, FreeBSD, and macOS.
                       It is an interface that translates Windows system
                       calls into equivalent POSIX calls used by Linux and
                       other Unix-based operating systems.


                       For Linux users, Wine is a savior when running
                       Windows-based applications on UNIX systems.
                       However, not all Windows applications will run in
                       Wine and may have strange crashes or bugs. The Wine
                       AppDB is a database containing a list of
                       applications that have been tested and confirmed to
                       work under Wine.


                # ⚓ How_to_Install_&_Use_PHP_Composer_on_Debian_11_Bullseye_–
                  LinuxCapable⠀⇛


                       Composer is an application-level package manager
                       for the PHP programming language similar to NPM for
                       Node.Js or PIP for Python. Composer provides a
                       standard format for managing all dependencies of
                       PHP software and the required libraries by
                       downloading all the required PHP packages of your
                       project and managing them for you. It is used by
                       most modern PHP frameworks such as Laravel, Drupal,
                       Magento, and Symfony.


                       In the following tutorial, you will learn how to
                       download and install composer, along with some
                       essential how to work with composer on Debian 11
                       Bullseye.


                # ⚓ How_to_Install_Discord_on_Debian_11_Bullseye_–
                  LinuxCapable⠀⇛


                       Discord is a free voice, video, and text chat app
                       used by tens of millions of people ages 13+ to talk
                       and hang out with their communities and friends.
                       Users communicate with voice calls, video calls,
                       text messaging, media, and files in private chats
                       or as part of communities called “servers.” Discord
                       is available on Windows, macOS, and Linux Distros.


                       In the following tutorial, you will learn how to
                       install Discord client on Debian 11 Bullseye.


                # ⚓ How_to_Install_Opera_Browser_on_Debian_11_Bullseye_–
                  LinuxCapable⠀⇛


                       Opera is a freeware, cross-platform web browser
                       developed by Opera Software and operates as a
                       Chromium-based browser. Opera offers a clean,
                       modern web browser that is an alternative to the
                       other major players in the Browser race. Its famous
                       Opera Turbo mode and its renowned battery saving
                       mode are the best amongst all known web browsers by
                       quite a margin, along with a built-in VPN and much
                       more.


                       In the following tutorial, you will learn how to
                       install Opera Browser on Debian 11 Bullseye.


                # ⚓ How_to_Install_Python_3.9_on_Debian_11_Bullseye_–
                  LinuxCapable⠀⇛


                       Python is one of the most popular high-level
                       languages, focusing on high-level and object-
                       oriented applications from simple scrips to complex
                       machine learning algorithms. The Python language
                       was created by Guido van Rossum and released in
                       1991, Python 2 in 2000, and Python 3 in 2008.
                       Currently, the latest series in Python is 3.9
                       brings forward significant changes to language
                       features, and how the language is developed along
                       with a performance boost in new string functions,
                       dictionary union operators, and more consistent and
                       stable internal APIs.


                # ⚓ How_to_Install_Slack_on_Debian_11_Bullseye_–_LinuxCapable⠀⇛


                       Slack is one of the most popular collaboration
                       communication platforms in the world. From it was
                       initial launch in 2013, it has grown. It is now
                       favored amongst development teams and corporations
                       to integrate so many services, run groups, and
                       meetings, amongst other things. The way Slack works
                       is to create channels for your teams, topics,
                       customers, or co-workers. Slack also features voice
                       and video calls, file sharing.


                       In the following tutorial, you will know how to
                       install the Slack communication platform on Debian
                       11 Bullseye.


                # ⚓ How_to_Install_Snap_&_Snap-Store_(Snapcraft)_on_Debian_11
                  Bullseye_–_LinuxCapable⠀⇛


                       By default, Debian does not come with Snap or Snap
                       Store installed as this is a feature that was built
                       by developed by Canonical as a faster and easier
                       way to get the latest versions of software
                       installed on Ubuntu systems, and Snap packages are
                       installed from a central SNAP server operated by
                       Canonical.


                       Given that Ubuntu is based on Debian, Snap can be
                       installed and, for the most part, work with most
                       packages. There are a few conflicts with specific
                       packages, especially when Debian spits out a new
                       release, luckily Debian stable releases are few and
                       far between. The issue with Snaps VS APT package
                       manager is that Snaps are self-contained, which
                       results in an increased .snap due to having all its
                       dependencies included. In contrast, APT is much
                       lighter than its snap counterpart because it
                       doesn’t need to bundle dependencies.


                # ⚓ How_to_Install_Steam_on_Debian_11_Bullseye_–_LinuxCapable⠀⇛


                       Steam is a video game cross-platform that Valve
                       created. It was launched as a standalone software
                       client in September 2003 as a way for Valve to
                       provide automatic updates for their games and
                       expanded to include games from third-party
                       publishers and now boasts a library filled with
                       thousands if not tens of thousands of games across
                       all gaming consoles.


                       In the following tutorial, you will learn how to
                       install Steam on your Debian 11 Bullseye desktop.


                # ⚓ What_Does_chmod_777_Mean⠀⇛


                       Linux operating systems, like most others, offer
                       multiple users to use the same system. This
                       requires implementing different permissions for
                       different files and folders to ensure the privacy
                       of operation.


                       The chmod command is used for changing these
                       permissions for the files and folders.


                       Chmod stands for change mode, and “mode” means
                       permissions in Linux terminologies.


                       In this tutorial, we’ll cover what chmod 777 means
                       and what the command does.


                # ⚓ How_to_Install_and_Use_Zsh_Shell_in_Ubuntu_and_Other
                  Linux⠀⇛


                       Oh my Zsh! Give your Linux Terminal a makeover
                       using this guide. Here, we explain how to install,
                       use and configure several themes in Zsh.


                # ⚓ How_to_install_tmux_on_Linux_–_Unixcop⠀⇛


                       tmux is an open-source terminal multiplexer for
                       Unix-like operating systems. It allows multiple
                       terminal sessions to be accessed simultaneously in
                       a single window.


                       Tmux is useful for running more than one command-
                       line program at the same time. It can also be used
                       to detach processes from their controlling
                       terminals, allowing remote sessions to remain
                       active without being visible.


                # ⚓ How_to_launch_Steam_games_using_Rofi_|_Hund⠀⇛


                       I recently figured out how to launch my Steam games
                       from the shell today. This means that I can now
                       start my games via my application launcher Rofi.


                # ⚓ How_to_install_the_Nessus_vulnerability_scanner_on_Rocky
                  Linux_–_TechRepublic⠀⇛


                       Nessus is a very popular vulnerability scanner used
                       by tens of thousands of organizations across the
                       globe. And although Nessus doesn’t prevent attacks,
                       it does a fantastic job of checking for
                       vulnerabilities and loopholes in your company’s
                       infrastructure.


                # ⚓ How_to_install_DeSmuME_on_a_Chromebook⠀⇛


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


                       If you have any questions, please contact us via a
                       YouTube comment and we would be happy to assist
                       you!


                       Most ROMs work, they must be extracted and in your
                       Linux Files in your file manager.


                # ⚓ How_to_Install_Overlord_on_Linux_–_Unixcop⠀⇛


                       Overlord provides a python-based console CLI which
                       used to build Red Teaming infrastructure in an
                       automated way. The user has to provide inputs by
                       using the tool’s modules such as C2, Email Server,
                       HTTP web delivery server, and the modules and
                       scripts will be generated on a cloud provider of
                       choice.


                       Overlord is still under development and it inspired
                       and uses the Red-Baron Terraform found on Github.


                       The tool supports AWS and Digital Ocean.


                # ⚓ How_To_Install_Hugo_on_Ubuntu_20.04_LTS_–_idroot⠀⇛


                       In this tutorial, we will show you how to install
                       Hugo on Ubuntu 20.04 LTS. For those of you who
                       didn’t know, Hugo is an open-source static website
                       generator designed for small projects and
                       informative sites. It is written in the Go
                       language, making it very secure and extremely fast.
                       Hugo provides a great writing experience and is
                       optimized for website viewing. Hugo supports
                       unlimited content types, taxonomies, menus, dynamic
                       API-driven content, and more, all without plugins.
                       Additionally, you can output your content in
                       multiple formats, including JSON or AMP


                       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 Hugo static website engine on
                       Ubuntu 20.04 (Focal Fossa). You can follow the same
                       instructions for Ubuntu 18.04, 16.04, and any other
                       Debian-based distribution like Linux Mint.


                # ⚓ How_To_Install_FFmpeg_on_Debian_11_–_idroot⠀⇛


                       In this tutorial, we will show you how to install
                       FFmpeg on Debian 11. For those of you who didn’t
                       know, FFmpeg is one of the best multimedia
                       frameworks that can be used to encode, decode,
                       transcode, and play nearly all multimedia files
                       that have been created on any platform. FFmpeg
                       compiles and runs on Linux, Mac OS, Microsoft
                       Windows, BSD systems, and many more.


                       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 through the step-by-
                       step installation of the FFmpeg on a Debian 11
                       (Bullseye).


                # ⚓ Figuring_out_Intel’s_WiFi_glitches_on_the_AX210_chipset._/
                  Debian_GNU/Linux_tells_you_it’s_glitching._Windows_somewhat
                  obscures_the_glitches._/_More_T-Mobile_Nokia_Trash_Can_lulz.
                  –_BaronHK’s_Rants⠀⇛


                       I finally figured out what will make the Intel
                       AX210 WiFi Chipset stay connected to my router and
                       stable, without complaining about expecting
                       hardware encrypted frames, and “software error
                       detected in firmware” and deauthenticating for
                       “reason 3”, among other problems.


          o § Games⠀➾


                # ⚓ Valve’s_Steam_Deck_dev_kit_got_the_early_benchmark
                  treatment_|_GamingOnLinux⠀⇛


                       Shared on a Chinese news website, one lucky
                       recipient of the Steam Deck developer kit decided
                       to show off some benchmarks although they probably
                       weren’t supposed to.


                       We already knew that the Steam Deck had some pretty
                       impressive internals, and that Valve had said it’s
                       “the most powerful gaming handheld in the world” in
                       their YouTube advert. However, we’ve not really
                       seen any good numbers until now.


                       Something to remember is that this is a dev kit,
                       and so tweaks are likely to be made before the
                       consumer units go out. Not only that but plenty of
                       developers will no doubt be tweaking their games
                       ahead of time. There will also be multiple updates
                       to the Steam Play Proton compatibility layer before
                       release too for running Windows games on it.


                # ⚓ Third_in_the_To_The_Moon_series,_time-loop_adventure
                  Impostor_Factory_is_out_|_GamingOnLinux⠀⇛


                       Ready for more adventuring that might make you need
                       a tissue to dry your eyes? Freebird Games are back
                       for the third game in the To The Moon series with
                       Impostor Factory.


                       Described as a “bonkers time-loop tragicomedy
                       murder mystery thriller featuring multiple
                       casualties and a suspicious cat” I still don’t
                       quite get if it’s a sequel, a prequel or what. The
                       good thing is you don’t need to know either, as
                       it’s playable completely standalone to their
                       previous games. This time the story is focused on a
                       character named Quincy, who was invited to some
                       sort of party at a suspicious secluded mansion that
                       has a time machine in the bathroom and somewhere
                       along the way people start dying.


          o § Desktop Environments/WMs⠀➾


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


                      # ⚓ A_future_pentablet_review⠀⇛


                             Hey, look what I just received! A tablet from
                             GAOMON for a video review oriented GNU/Linux
                             and Krita (soon).


                # § GNOME Desktop/GTK⠀➾


                      # ⚓ If_you_use_DuckDuckGo,_you_probably_aren’t_reading
                        this.⠀⇛


                             DuckDuckGo doesn’t put any of my posts on the
                             front page of its results even when you
                             specifically search for them.


                             According to Wikipedia, DuckDuckGo has an
                             “anti-content farm” policy that was created
                             by CEO Gabriel Weinberg, and it was designed
                             to filter out “sources of low quality
                             articles”.


                             While there’s nothing wrong with this in
                             theory, in fact, I am quite angry that they
                             don’t think that what I have to say should be
                             in their results at all, even if you search
                             specifically for me.


                             Techrights has a page about DuckDuckGo’s
                             shifty practices. Also, another one updated
                             with more nasty things they do in 2021.


                             GNOME Web defaults to DuckDuckGo as a way to
                             earn search royalties, and some others do
                             too. They pay very little, but more than
                             Google will to some smaller projects, and so
                             unfortunately Tor also uses it and this after
                             the pittance of something like $40,000 in a
                             one off donation, if memory serves correctly.


                             Interestingly, GNOME Web has been making the
                             Google experience better lately. In addition
                             to lying to it with UA hacks to make it think
                             you use Chrome and to silence the Get Chrome
                             spam, they’ve added a YouTube ad blocker in
                             the version “41” release and also, the option
                             (disabled by default) in the privacy settings
                             to get instant search results if you use
                             Google.


          o § Distributions⠀➾


                # ⚓ Nitrux_1.6.1_Is_Here_as_One_of_the_First_Distros_to_Ship
                  with_Linux_5.14_as_Default_Kernel⠀⇛


                       The new release, Nitrux 1.6.1, is here with Linux
                       kernel 5.14.8 as default kernel, alongside Linux
                       kernel 5.10.69 LTS and Linux kernel 5.4.149 LTS for
                       users who want to use a long-term supported kernel,
                       as well as the KDE Plasma 5.22.5 desktop
                       environment, KDE Gear 21.08.1 and KDE Frameworks
                       5.86 software suites.


                       On top of that, it includes the recently released
                       Inkscape 1.1.1 scalable vector graphics editor and
                       Mozilla Firefox 92 as default web browser, which is
                       available as a sandboxed AppImage by default.


                # ⚓ How_To_Pick_a_Linux_Distribution⠀⇛


                       I have suffered from distrohopping. Now that I have
                       settled for the last two years, here are some tips
                       to save your time.


                # § BSD⠀➾


                      # ⚓ GhostBSD_21.09.29_ISO_Now_Available⠀⇛


                             This new ISO contains installer fixes, GPU
                             auto-configuration improvement, software
                             updates.


                # § Screenshots/Screencasts⠀➾


                      # ⚓ Fedora_35_Beta_Run_Through_–_Invidious⠀⇛


                             In this video, we are looking at Fedora 35
                             Beta.


                      # ⚓ Fedora_35_Beta⠀⇛


                             Today we are looking at Fedora 35 Beta. It
                             comes with Gnome 41rc, Linux kernel 5.14, and
                             uses about 1.5-1.8GB of ram when idling.


                # § IBM/Red Hat/Fedora⠀➾


                      # ⚓ Advance_your_Red_Hat_OpenShift_skills_to_run
                        Kubernetes_at_enterprise_scale⠀⇛


                             As organizations expand their footprint
                             within cloud-native architectures, Red Hat
                             OpenShift and Red Hat products that extend
                             its functionality become key to scaling
                             infrastructure to manage more workloads and
                             applications. Red Hat now offers an extensive
                             portfolio of training and certifications to
                             teach the skills required for these advanced
                             Red Hat OpenShift capabilities.


                             We have recently launched advanced training
                             courses to help teams and individuals looking
                             to increase self-sufficiency in Red Hat
                             OpenShift administration. And we have even
                             more that are currently in development. We’ll
                             provide some course highlights in this post.


                      # ⚓ Red_Hat_Ansible_Automation_Platform_2_Drives_Cloud-
                        Native_Automation_and_Helps_Developers_Become
                        Automators⠀⇛


                             Red Hat, Inc., the world’s leading provider
                             of open source solutions, today announced Red
                             Hat Ansible Automation Platform 2 as the
                             company’s new standard for hybrid cloud
                             automation. Refined for the evolving
                             realities of computing at hybrid cloud scale,
                             the latest version of the platform adds self-
                             contained automation capabilities while
                             shifting automation more deeply into the
                             application development lifecycle.


                      # ⚓ Red_Hat_Ansible_Automation_Platform_2_Now_Fully
                        Restructured_For_A_Hybrid_Cloud-Native_World⠀⇛


                             Red Hat has announced Red Hat Ansible
                             Automation Platform 2 as the company’s new
                             standard for hybrid cloud automation. Refined
                             for the evolving realities of computing at
                             hybrid cloud scale, the latest version of the
                             platform adds self-contained automation
                             capabilities while shifting automation more
                             deeply into the application development
                             lifecycle.


          o § Devices/Embedded⠀➾


                # § Open Hardware/Modding⠀➾


                      # ⚓ Super_8_Camera_Brought_Back_To_Life⠀⇛


                             The Super 8 camera, while a groundbreaking
                             video recorder in its time, is borderline
                             unusable now. Even if you can get film for it
                             (and afford its often enormous price), it
                             still only records on 8mm film which isn’t
                             exactly the best quality of film around, not
                             to mention that a good percentage of these
                             cameras couldn’t even record audio. They were
                             largely made obsolete by camcorders in the
                             late ’80s and early ’90s, although some are
                             still used for niche artistic purposes. If
                             you’d rather not foot the bill for the film,
                             though, you can still put one of these to
                             work with the help of a Raspberry Pi.


                      # ⚓ Powercoders_and_Arduino_#Include_Promote_Equal
                        Opportunities⠀⇛


                             The Arduino #include program was first
                             announced as part of 2021’s Arduino Day.
                             Since then we’ve been working with
                             Powercoders, which runs a bootcamp to promote
                             equality in the IT industry.


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


                # ⚓ Open_Source_is_a_Relay_Race:_Reflections_from_our_Outgoing
                  Interim_General_Manager⠀⇛


                       I’ve been an individual member and occasional
                       volunteer of the OSI for a long time, but signing
                       on in August 2020 as Interim General Manager was a
                       jump into the deep end. Much of OSI’s past work was
                       informed by the connections and conversations held
                       with members and stakeholders in person, so we had
                       to chart a different path while still grounded by
                       the COVID-19 pandemic.


                       My challenge was to look for ways to continue our
                       work during lockdown, keep the organization moving
                       forward through a transitional year and support the
                       board on its journey towards a visioning body that
                       works with a staff-driven organization. Now it’s
                       time to hand things over to our new Executive
                       Director, Stefano Maffulli but first I’d like to
                       recap my time spent in navigating these waters.


                       [...]


                       I’m leaving OSI but will still be active in the
                       free and open source software community. I’m
                       looking forward to seeing all of you at in-person
                       events again (eventually) and at many online events
                       like SeaGL and the CROSS Research Symposium or on
                       upcoming video calls where we’re collaborating to
                       build a robust, diverse, welcoming and sustainable
                       future for open source practitioners and advocates.


                       As I step down from my year as the Interim General
                       Manager, I’m proud to remain a friend and
                       individual supporting member of the OSI.


                # § Events⠀➾


                      # ⚓ Linux_Plumbers_Conference_Matrix_and_BBB
                        integration⠀⇛


                             The recently completed Linux Plumbers
                             Conference (LPC) 2021 used the Big Blue
                             Button (BBB) project again as its audio/video
                             online conferencing platform and Matrix for
                             IM and chat. Why we chose BBB has been
                             discussed previously. However this year we
                             replaced RocketChat with Matrix to achieve
                             federation, allowing non-registered
                             conference attendees to join the chat. Also,
                             based on feedback from our attendees, we
                             endeavored to replace the BBB chat window
                             with a Matrix one so anyone could see and
                             participate in one contemporaneous chat
                             stream within BBB and beyond. This enabled
                             chat to be available before, during and after
                             each session.


                             One thing that emerged from our initial
                             disaster with Matrix on the first day is that
                             we failed to learn from the experiences of
                             other open source conferences (i.e. FOSDEM,
                             which used Matrix and ran into the same
                             problems). So, an object of this post is to
                             document for posterity what we did and how to
                             repeat it.


                      # ⚓ Bottomley:_Linux_Plumbers_Conference_Matrix_and_BBB
                        integration_[LWN.net]⠀⇛


                             James Bottomley explains how the integration
                             of Matrix and BigBlueButton was done for the
                             just-concluded Linux Plumbers Conference.


                      # ⚓ Debian_Reunion_Hamburg_2021_is_almost_over…⠀⇛


                             The Debian Reunion Hamburg 2021 is almost
                             over now, half the attendees have already
                             left for Regensburg, while five remaining
                             people are still busy here, though tonight
                             there will be two concerts at the venue, plus
                             some lovely food and more. Together with the
                             day trip tomorrow (involving lots of water
                             but hopefully not from above…) I don’t expect
                             much more work to be done, so that I feel
                             comfortable publishing the following
                             statistics now, even though I expect some
                             more work will be done while travelling back
                             or due to renewed energy from the event! So I
                             might update these numbers later


                # § Web Browsers⠀➾


                      # § Mozilla⠀➾


                            # ⚓ This_Week_in_Glean:_Announcement:_Glean.js
                              v0.19.0_supports_Node.js⠀⇛


                                   From the start, the Glean JavaScript
                                   SDK (Glean.js) was conceptualized as a
                                   JavaScript telemetry library for
                                   diverse JavaScript environments. When
                                   we built the proof-of-concept, we
                                   tested that idea out and created a
                                   library that worked in Qt/QML apps,
                                   websites, web extensions, Node.js
                                   servers and CLIs, and Electron apps.


                                   However, the stakes are completely
                                   different when implementing a proof-of-
                                   concept library and a library to be
                                   used in production environments.
                                   Whereas for the proof-of-concept we
                                   wanted to try out as many platforms as
                                   possible, for the actual Glean.js
                                   library we want to minimize unnecessary
                                   work and focus on perfecting the
                                   features our users will actively
                                   benefit from. That meant, up until a
                                   few weeks ago, Glean.js supported
                                   browser extensions and Qt/QML apps.
                                   Today, that means it also supports
                                   Node.js environments.


                            # ⚓ These_Weeks_in_Firefox:_Issue_101⠀⇛


                            # ⚓ Dyn_async_traits,_part_1⠀⇛


                                   Over the last few weeks, Tyler Mandry
                                   and I have been digging hard into what
                                   it will take to implement async fn in
                                   traits. Per the new lang team
                                   initiative process, we are collecting
                                   our design thoughts in an ever-evolving
                                   website, the async fundamentals
                                   initiative. If you’re interested in the
                                   area, you should definitely poke
                                   around; you may be interested to read
                                   about the MVP that we hope to stabilize
                                   first, or the (very much WIP)
                                   evaluation doc which covers some of the
                                   challenges we are still working out. I
                                   am going to be writing a series of blog
                                   posts focusing on one particular thing
                                   that we have been talking through: the
                                   problem of dyn and async fn. This first
                                   post introduces the problem and the
                                   general goal that we are shooting for
                                   (but don’t yet know the best way to
                                   reach).


                            # ⚓ Firefox_Add-on_Reviews:_Top_anti-tracking
                              extensions⠀⇛


                                   The truth of modern tracking is that it
                                   happens in so many different and
                                   complex ways it’s practically
                                   impossible to ensure absolute tracking
                                   protection. But that doesn’t mean we’re
                                   powerless against personal data
                                   harvesters attempting to trace our
                                   every online move. There are a bunch of
                                   browser extensions that can give you
                                   tremendous anti-tracking advantages…


                # § FSF⠀➾


                      # ⚓ FSF_announces_JShelter_browser_add-on_to_combat
                        threats_from_nonfree_JavaScript⠀⇛


                             The Free Software Foundation (FSF) today
                             announced the JShelter project, an anti-
                             malware Web browser extension to mitigate
                             potential threats from JavaScript, including
                             fingerprinting, tracking, and data
                             collection. The project is supported by NLnet
                             Foundation’s Next Generation Internet (NGI)
                             Zero Privacy & Trust Enhancing Technologies
                             fund. Collaborators include Libor Polčák and
                             Bednář Martin (Brno University of
                             Technology), Giorgio Maone (NoScript), and
                             Ana Isabel Carvalho and Ricardo Lafuente
                             (Manufactura Independente). The JShelter
                             browser add-on is in development and the
                             first release is available.


                             Most modern Web sites contain a growing
                             number of programs that the user’s Web
                             browser downloads and runs automatically as
                             pages are loaded. While these JavaScript
                             programs can provide functionality to a site
                             in conjunction with native browser features,
                             they are also a significant liability both
                             from security and privacy perspectives.
                             Moreover, the software is typically licensed
                             under unethical terms by the FSF’s standards,
                             disempowering users and hampering learning
                             and security. With a thirty-six year history
                             of defending software ethics, The FSF
                             recognizes the importance and urgency of both
                             aspects of the problem and its role in
                             solving this significant challenge. In
                             response, the FSF has been working on an
                             ambitious new initiative, the JShelter
                             browser extension. This browser add-on will
                             limit the potential for JavaScript programs
                             to do harmful actions by restricting default
                             behavior and adding a layer of control.
                             JShelter is a significant next step in the
                             FSF’s “Free JavaScript Campaign,” providing a
                             new tool that can be used in conjunction with
                             another related extension, GNU LibreJS, which
                             allows the user to identify and run only
                             freely licensed scripts.


                      # ⚓ Keeping_your_freedom_intact_when_registering_or
                        renewing_as_a_DMCA_agent⠀⇛


                             DMCA agent registration only lasts three
                             years before it must be renewed. Use these
                             add-ons to register and renew without the use
                             of nonfree JavaScript.
                             Users shouldn’t be forced to use nonfree
                             software when interacting with their own
                             government. Every user has the right to
                             control their own computing, and the
                             government shouldn’t be forcing you to
                             download and install proprietary software
                             just to take advantage of its services. But
                             when it comes to registering and renewing the
                             status as an agent under the Digital
                             Millennium Copyright Act (DMCA) in the United
                             States, that’s exactly what the government
                             expects you to do.


                             The U.S. Copyright Office requires a
                             registered agent to renew their status every
                             three years to help ensure that the agent
                             directory stays up to date. However, the
                             renewal can only be done online, and you are
                             required to use nonfree software. We find
                             this unacceptable. Fortunately, three years
                             ago we devised a way to complete an agent’s
                             registration circumventing the use of nonfree
                             Javascript. Today, we confirm the process
                             still works and it can be applied to renewal
                             as well. We encourage everyone to learn more
                             about these tools to access your government
                             services in software freedom.


                # § Programming/Development⠀➾


                      # ⚓ A_tale_of_two_toolchains_and_glibc⠀⇛


                             Over the past few years, the LLVM toolchain
                             has seen increasing development and adoption
                             alongside the older, more established GNU
                             toolchain. The emergence of this new two
                             major toolchain world is bringing challenges
                             and questions for projects that need to
                             support both, in particular the GNU C library
                             (glibc), which only supports GCC.


                             Is it worth it to fix glibc (and other
                             projects which support only GCC) to build
                             with LLVM? Is it better to just replace them
                             with alternatives already supporting LLVM? Is
                             it best to use both GCC and LLVM, each for
                             their respective supported projects?


                             This post is an exploration starting from
                             these questions but does not attempt to give
                             any definite answers. The intent here is to
                             not be divisive and controversial, but to
                             raise awareness by describing parts of the
                             current status-quo and to encourage
                             collaboration. The obvious elephant in the
                             room, licensing, is left out despite being a
                             very important topic.


                      # ⚓ Ratiu:_A_tale_of_two_toolchains_and_glibc⠀⇛


                      # ⚓ 7_Open-source_solutions_to_build_eCommerce_system
                        with_Vue⠀⇛


                             Vue is a popular JavaScript framework for
                             building frontend web apps. It is proven to
                             be a reliable, production-ready, and
                             development environment for enterprises.


                             Vue framework community enriches it every day
                             with reusable open-source components for
                             almost everything.


                             In this article, we explore the open-source
                             options to build an eCommerce personalize
                             shopping experience with Vue.


                      # § Perl/Raku⠀➾


                            # ⚓ My_Favorite_Warnings:_exiting⠀⇛


                                   Perl has various ways to transfer
                                   control out of the normal flow: die(),
                                   goto(), return(), next, last, and redo
                                   are among the sorts of things I mean.
                                   Not all of these are suitable for all
                                   circumstances, and Perl issues an
                                   exiting warning for unsuitable cases.


    * § Leftovers⠀➾


          o ⚓ The_Power_and_Danger_of_Groupthink⠀⇛


                 Unfortunately, modern technology has brought us a new era
                 of Groupthinkers. I have been dealing with it for years.
                 This mind numb phenomenon is also called, The Echo
                 Chamber. The high tech internet based tech firms are full
                 of it. They see this as a good thing. Evan as a virtue.
                 How dare anyone stand up to the vast majority of our high
                 tech monopoly!


                 The most obvious reason for me to oppose them is that
                 simply put, I don’t fit in with them. I never have, nor
                 will I ever. As a child of God, I was made to be an
                 original.


                 I used to refer to myself as an idea man. I had a lot of
                 great ideas. I still do. There are of course many
                 challenges to being that way. One is, how does one
                 implement this into something real? Second is, how do I
                 present this to others in order to gain interest?


          o § Science⠀➾


                # ⚓ The_Challenge_and_Promise_of_Quantum_Computing⠀⇛


                       Quantum computing is still very much in the
                       experimental stages, but it’s starting to look like
                       it could eventually be feasible and practical.


                       “After decades of experimental and theoretical
                       efforts, we are now seeing the first examples of
                       quantum computational advantage in the areas of
                       quantum computing and quantum simulation,” said
                       Narang. “The opportunity now exists to build and
                       use the most powerful quantum computers and quantum
                       simulators to enable new applications and new
                       science, made accessible and jointly developed by
                       the community.”


                       There are a variety of applications for quantum
                       computing if the science becomes mainstream; some
                       already known, others still to be discovered.


                       Weidt pointed out that “the usefulness of the
                       applications of quantum computing scales somewhat
                       with the number of high-quality qubits.”


                       “As we scale up, quantum computing is poised to
                       radically change the way we approach problems in
                       fields like chemistry. The vast processing power of
                       quantum computers means we can, for example,
                       simulate complex chemical compounds. This has
                       implications for improved drug discovery, better
                       batteries and cleaner fertilizers, he detailed.


          o § Hardware⠀➾


                # ⚓ The_Coming_Copper_Shortage:_Aluminium_Or_Carbon_Nanotubes
                  To_The_Rescue?_|_Hackaday⠀⇛


                       The use of aluminium in wiring is unlikely to bring
                       a smile to the face of anyone who has had to deal
                       with it in a 1960s, or early 1970s-era house. The
                       causes behind the fires and other accidents were
                       myriad, including failure to deal with the higher
                       thermal expansion of aluminium, the electrically
                       insulating nature of aluminium oxide, and the
                       general brittleness of aluminium when twisted.


                       [...]


                       As the world moves to massively expand the use of
                       electrical cars and installation of wind turbines,
                       copper demand is predicted to outstrip current
                       copper supply. With aluminium likely to make a big
                       return as a result, it’s worth taking a look at
                       modern-day aluminium-based wiring, including
                       copper-clad aluminium and the use of carbon-based
                       replacements.


          o § Health/Nutrition⠀➾


                # ⚓ Cocaine,_ecstasy_found_in_river_at_Glastonbury_Festival⠀⇛


                       A river that runs through the Glastonbury Festival,
                       the largest greenfield music festival in the world,
                       is contaminated with illicit drugs such as cocaine
                       and ecstasy because stoned revellers often urinate
                       on the ground, scientists said.


                       Researchers from Bangor University found that
                       concentrations of MDMA, known as ecstasy,
                       quadrupled downstream in the Whitelake River in the
                       week after the Glastonbury Festival when it was
                       last held in 2019.


          o § Integrity/Availability⠀➾


                # § Proprietary⠀➾


                      # § Security⠀➾


                            # ⚓ Security_updates_for_Thursday⠀⇛


                                   Security updates have been issued by
                                   Debian (libxstream-java, uwsgi, and
                                   weechat), Fedora (libspf2, libvirt,
                                   mingw-python3, mono-tools, python-
                                   flask-restx, and sharpziplib), Mageia
                                   (gstreamer, libgcrypt, libgd,
                                   mosquitto, php, python-pillow,
                                   qtwebengine5, and webkit2), openSUSE
                                   (postgresql12 and postgresql13), SUSE
                                   (haproxy, postgresql12, postgresql13,
                                   and rabbitmq-server), and Ubuntu
                                   (commons-io and linux-oem-5.13).


          o § Environment⠀➾


                # § Energy⠀➾


                      # ⚓ New_study_shows_that_drought_could_shut_down_the
                        biggest_US_Hydro_Plants_in_the_next_few_years⠀⇛


                             According to newly-released projections from
                             the US Bureau of Reclamations, there’s a
                             significant chance that both Lake Powell and
                             Lake Mead — the largest hydroelectric power
                             sources in the country — will stop working in
                             the next few years.


                             Lake Powell had already dropped to about 33%
                             of its capacity in July 2021. According to
                             the Bureau’s new calculations, there’s a 34%
                             chance of reaching “critically low reservoir
                             elevations” by 2023. There’s a 25% chance
                             it’ll happen by 2024.


                             Lake Powell isn’t quite as dire, with only a
                             12% chance of dropping to critically low
                             capacity by 2024. That likelihood goes up by
                             another 10% in 2025, and will likely keep
                             going up. from there.



                    ䷩ 𝚕𝚒𝚗𝚎 5298

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 10.01.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_1/10/2021:_LLVM_13.0.0_Release_and_Linux_Mint_Plans⠀✐


Posted in News_Roundup at 4:48 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o § Desktop/Laptop⠀➾


                # ⚓ System76_readies_high-end_Oryx_Pro_Linux_laptops_with_Tiger
                  Lake-H_processor_and_Nvidia_RTX_dGPU_options⠀⇛


                       System76 is introducing its first high-end Linux-
                       based customizable laptop dubbed the Oryx Pro. This
                       model packs powerful components in a relatively
                       slim case (238-265 mm profile) and offers the
                       signature open source firmware with GPLv3 license
                       code that grants users total control over the iGPU,
                       GPU, keyboard, cooling system and battery.


                       The Oryx Pro is powered by the Intel Core i7-11800H
                       8-core / 16-thread processor with integrated 32 EU
                       UHD Xe graphics, which can be coupled with up to 64
                       GB of DDR4-3200 RAM plus up to 4 TB of NVMe PCIe
                       4.0 SSD storage via two M.2 slots. Users can opt
                       for a15.6-inch or 17.3-inch display with FHD
                       resolution, 144 Hz refresh rate and matte coating.
                       There is also a choice between the Nvidia RTX 3070
                       and 3080 dGPUs. System76 mentions that these are
                       the Max-Q versions, but does not specify the exact
                       wattage, unfortunately. Nevertheless, there is a
                       MUX switch, so the dGPU can be exploited to its
                       full capacity. As far as the operating system is
                       concerned, users can choose among the proprietary
                       Pop!_OS 21.04 or 20.04 versions and the Ubuntu
                       20.04 LTS. Accessories include an external DVD-RW
                       drive, mechanical switches for the keyboard
                       (shipping in November), plus carrying bags for each
                       size.


                # ⚓ Red_Hat_/_Fedora_To_Focus_On_Driving_New_Linux_Video
                  Improvements_Around_PipeWire⠀⇛


                       PipeWire from the start was designed around
                       handling the needs of both audio and video streams
                       on Linux. While PipeWire is already in use for
                       screencasting/recording under Wayland and working
                       with Flatpak’ed applications, recently much of
                       PipeWire’s focus has been on addressing the use-
                       cases of JACK and PulseAudio on the sound side. Now
                       that the audio support is in quite good shape, Red
                       Hat engineers are back to focusing on improvements
                       to the video support.


                       As part of bolstering the Linux multimedia stack,
                       Red Hat is going to be working on a fresh round of
                       video feature work to PipeWire led by its founder
                       Wim Taymans. In particular, the area they will be
                       focusing on is improving the video capture support
                       on Linux.


                # ⚓ PipeWire_and_fixing_the_Linux_Video_Capture_stack⠀⇛


                       PipeWire has already made great strides forward in
                       terms of improving the audio handling situation on
                       Linux, but one of the original goals was to also
                       bring along the video side of the house. In fact in
                       the first few releases of Fedora Workstation where
                       we shipped PipeWire we solely enabled it as a tool
                       to handle screen sharing for Wayland and Flatpaks.
                       So with PipeWire having stabilized a lot for audio
                       now we feel the time has come to go back to the
                       video side of PipeWire and work to improve the
                       state-of-art for video capture handling under
                       Linux. Wim Taymans did a presentation to our team
                       inside Red Hat on the 30th of September talking
                       about the current state of the world and where we
                       need to go to move forward. I thought the
                       information and ideas in his presentation deserved
                       wider distribution so this blog post is building on
                       that presentation to share it more widely and also
                       hopefully rally the community to support us in this
                       endeavour.


          o § Audiocasts/Shows⠀➾


                # ⚓ A_First_Look_At_Q4OS_4.6_With_The_Plasma_Desktop_–
                  Invidious⠀⇛


                       In this video, I’m going to take a look at the
                       recently released Q4OS 4.6, codenamed “Gemini.”
                       Q4OS is a fast and friendly, desktop oriented
                       operating system based on Debian 11 Testing. Q4OS
                       now uses the Plasma desktop as its default.


                # ⚓ LHS_Episode_#432:_The_Weekender_LXXIX⠀⇛


                       It’s time once again for The Weekender. This is our
                       bi-weekly departure into the world of amateur radio
                       contests, open source conventions, special events,
                       listener challenges, hedonism and just plain fun.
                       Thanks for listening and, if you happen to get a
                       chance, feel free to call us or e-mail and send us
                       some feedback. Tell us how we’re doing. We’d love
                       to hear from you.


                # ⚓ Hackaday_Podcast_138:_Breakin’_Bluetooth,_Doritos_Rockets,
                  Wireless_Robots,_And_Autonomous_Trolling_|_Hackaday⠀⇛


                       Hackaday editors Elliot Williams and Mike Szczys
                       peruse the great hardware hacks of the past week.
                       There’s a robot walker platform that wirelessly
                       offloads motor control planning to a computer. We
                       take a look at automating your fishing boat with a
                       trolling motor upgrade, building the Hoover dam in
                       your back yard, and playing Holst’s Planets on an
                       army of Arduini. Make sure you stick around until
                       the end as we stroll through distant memories of
                       Gopher, and peek inside the parking garages of the
                       sea.


          o § Kernel Space⠀➾


                # ⚓ Rust_Concurrency_Philosophy:_A_Historical_Perspective⠀⇛


                       At first glance, Rust’s concurrency philosophy
                       resembles that of Sequent’s DYNIX and DYNIX/ptx in
                       the 1980s and early 1990s: “Lock data, not code”
                       (see Jack Inman’s classic USENIX’85 paper
                       “Implementing Loosely Coupled Functions on Tightly
                       Coupled Engines”, sadly invisible to search
                       engines). Of course, Sequent lacked Rust’s
                       automatic checking, and Sequent’s software
                       engineers made much less disciplined use of
                       ownership than Rust fans recommend. Nevertheless,
                       this resemblance has resulted in some comparisons
                       of Rust with the DEC Alpha, which had a similar
                       concurrency model.


                       Interestingly enough, DYNIX and early versions of
                       DYNIX/ptx used compile-time-allocated arrays for
                       almost all of its data structures. You want your
                       kernel to support up to N tasks? Very well, build
                       your kernel to have its array of N task structures.
                       This worked surprisingly well, perhaps because the
                       important concurrent applications of that time had
                       very predictable resource requirements, including
                       numbers of tasks. Nevertheless, as you might
                       expect, this did become quite the configuration
                       nightmare. So why were arrays used in the first
                       place?


                       To the best of my knowledge, the earliest published
                       complete articulation of the reason appeared in
                       Gamsa et al.’s landmark paper “Tornado: Maximizing
                       Locality and Concurrency in a Shared Memory
                       Multiprocessor Operating System”. The key point is
                       that you cannot protect a dynamically allocated
                       object with a lock located within that object. The
                       DYNIX arrays avoided deallocation (or,
                       alternatively, provided a straightforward
                       implementation of type-safe memory), thus allowing
                       these objects to be protected with internal locks.
                       Avoiding the need for global locks or reference
                       counters was an important key to the performance
                       and scalability prized by Sequent’s customers.


                # ⚓ Rusting_the_Linux_Kernel:_Atomics_and_Barriers_and_Locks,
                  Oh_My!⠀⇛


                       LKMM is not the most complex memory model out
                       there, but neither is it the simplest. In addition,
                       it is in some ways more strict than the C/C++
                       memory models, which means that strict adherence to
                       coding guidelines is required in order to prevent
                       compiler optimizations from breaking Linux-kernel
                       code. Many of these optimizations are not
                       localized, but are instead scattered hither and yon
                       throughout the compilers, including throughout the
                       compiler backends. The optimizations in the
                       backends are a special challenge to Rust, which
                       seems to take the approach of layering safety on
                       top of (or perhaps within) the compiler frontend.
                       Later posts in this series will look at several
                       pragmatic options available to Rust Linux-kernel
                       code.


                       There is one piece of good news: Compilers are
                       forbidden from introducing data races into code, at
                       least not into code that is free of undefined
                       behavior.


                       With all of that out of the way, let’s look at
                       Rust’s options for dealing with Linux-kernel
                       atomics and barriers and locks.


          o § Applications⠀➾


                # ⚓ Can_Linux_Run_Windows_EXE_Files?⠀⇛


                       Users who have recently migrated from Windows to
                       Linux often wonder if they can run Windows apps and
                       programs on their new system. The answer to this
                       affects a user’s perspective of Linux in general,
                       since operating systems should be easy to use and
                       at the same time, welcoming to the idea of running
                       different file formats.


                       A straightforward answer to the question is—Yes.
                       You can run EXE files and other Windows programs on
                       Linux, and it’s not as complicated as it sounds.


                       By the end, you’ll have a brief understanding of
                       executable files, along with different ways to run
                       said programs on Linux.


                # ⚓ The_best_VPN_for_Linux_for_2021 [Ed: How many of these
                  links are just sponsored?]⠀⇛


          o § Instructionals/Technical⠀➾


                # ⚓ How_To_Install_Apache_Maven_on_Debian_11_–_idroot⠀⇛


                       In this tutorial, we will show you how to install
                       Apache Maven on Debian 11. For those of you who
                       didn’t know, Apache Maven is a software project
                       management and comprehension tool. Based on the
                       concept of a project object model, Maven can manage
                       a project’s build, reporting, and documentation
                       from a central piece of information.


                       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 through the step-by-
                       step installation of the Apache Maven on a Debian
                       11 (Bullseye).


                # ⚓ How_To_Install_PIP_on_Debian_11_Linux_–_TecAdmin⠀⇛


                       Pip is a popular package management tool for
                       Python. It allows the Python developers to install
                       and manage additional Python libraries in their
                       applications. This is a similar application to nvm
                       for Node.js and composer for PHP. Pip stands for
                       Preferred Installer Program.


                       Rather than a package management utility, Pip can
                       create a completely isolated environment for the
                       Python application. In this tutorial, you will
                       learn about the installation of Pip on the Debian
                       11 Linux system.


                # ⚓ How_To_Install_Samba_File_Sharing_Server_on_Linux_System⠀⇛


                       The Samba file-sharing server of the SMB, in short,
                       is an open-source file-sharing server specially
                       designed for Linux systems. It allows sharing files
                       among client PCs from a hosted server. It’s not a
                       conventional FTP server type server, and it does
                       not require hosted files for the client users. You
                       can use the Samba file-sharing server on Linux to
                       access the Windows files over a network. Samba can
                       be used for both personal and business usage. In
                       Samba, users get both read and write permission for
                       file accessing. They can change, revise, edit files
                       over the server, and the changes go live
                       immediately. In a word, using the Samba for sharing
                       files with clients with access permission is
                       hassle-free and strong in Linux.


                # ⚓ How_To_Voice_Video_Calls_on_XMPP_and_Matrix_Made_Simple⠀⇛


                       This tutorial explains how to quickly voice and
                       video call with friends and family using XMPP and
                       Matrix telecommunication services. This tutorial’s
                       aimed for people who want easy calls without
                       technical knowledge especially school teachers and
                       computing beginners. Thus, we will use Movim and
                       Schildi via web browser so we can call everywhere
                       both on desktop and mobile. Let’s do it.


                # ⚓ How_to_Access_Clipboard_(Copy_&_Paste)_History_in_Ubuntu
                  via_GPaste_|_UbuntuHandbook⠀⇛


                       For those doing copy & paste actions frequently in
                       Ubuntu Linux, GPaste remembers the clipboard
                       history and allows to find them easily via few
                       click.


                       The clipboard is the place to store the text,
                       image, file path and all the stuff that you last
                       copied (or cut). The content in clipboard will be
                       overwritten once you do another copy & paste
                       action. So, when you trying to find out what you’ve
                       copied earlier, a clipboard manager will be
                       helpful.


                # ⚓ How_to_Install_and_Set_Up_PM2_on_Linux_Servers⠀⇛


                       Deployment is one of the most crucial and
                       conclusive stages of software development. A proper
                       deployment strategy is vital in delivering the best
                       experience to your users while utilizing your
                       services efficiently. However, this process also
                       brings its own set of challenges with it.


                       Node.js, the open-source JavaScript runtime, is a
                       popular choice for building the backend
                       infrastructure of your application by allowing you
                       to run JavaScript outside web browsers. But what if
                       your Node.js application crashes in production?
                       Find out how you can avoid such scenarios in this
                       article.


                # ⚓ How_to_enable_server-side_FastCGI_caching_with_Nginx_and
                  PHP_–_VITUX⠀⇛


                       Nginx is an open-source and high-performance web
                       server that can be used to speed up content and
                       application delivery. Nginx enhances security,
                       improves scalability, and also can be used as a
                       high availability load balancer. It can be used as
                       a reverse proxy and one of the most important uses
                       of Nginx is content caching. One of the best
                       approaches is to use Nginx as content caching. In
                       this article, we will discuss Nginx FastCGI content
                       caching for better performance of websites.


                # ⚓ 4_Ways_to_Hide_Desktop_Icons_in_Ubuntu_–_Make_Tech_Easier⠀⇛


                       If hiding the top bar and side panel isn’t enough,
                       and you want everything removed from your Ubuntu
                       desktop, then you’d probably also like to get rid
                       of those pesky icons on its surface. Read on to
                       learn how you can hide desktop icons in Ubuntu.


          o § Wine or Emulation⠀➾


                # ⚓ Wine,_Windows_programs,_and_gaming_on_Debian_GNU/Linux._The
                  XBOX_360_controller_is_“just_working”_now!⠀⇛


                       PC gaming, for me, is sort of a hit or miss thing.


                       Even though Wine (If you’re feeling cheeky, the
                       “Linux Subsystem for Windows”) and, for that
                       matter, Steam with Proton, a Wine fork optimized
                       for gaming, have advanced a lot.


                       I use laptops, and the only way to get a GPU
                       upgrade with a laptop is to buy a new laptop.


                       (Well, external GPUs are becoming more of a thing,
                       but I’m not really sure where the GNU/Linux support
                       stands on that, and if it would mean a proprietary
                       driver, no thanks anyway.)


                       Anyway, even up to a couple of years ago,
                       controllers under Wine were dicey and even getting
                       an XBOX 360 controller to be recognized involved
                       terrible hacks involving a userspace driver,
                       blacklisting a kernel module (xpad), and then
                       installing an XBOX 360 controller emulator program
                       for Windows in Wine so you could map the output of
                       the actual hardware to an emulated version of the
                       controller, which would send it along to video
                       games.


                       What a pain in the ass! I mean, not as much of one
                       as installing a GNU/Linux distribution in the 90s
                       with winmodems and having to tell X your modelines,
                       under pains and penalties of potentially frying
                       your computer monitor. (How uncivilized!). Modern
                       GNU/Linux should be no more difficult than a small
                       tweak here, a tweak there, and you’re done. At it’s
                       very worst, no problem is likely to come up that
                       would be worse than something that could come up
                       under Windows.


          o § Games⠀➾


                # ⚓ Maintenance_release:_Godot_3.3.4⠀⇛


                       While we’re busy working on both the upcoming Godot
                       4.0 and 3.4 releases (with a dev snapshot for 3.4
                       beta 5 available now), we still cherry-pick
                       important bug fixes to the 3.3 branch regularly for
                       maintenance releases (see our release policy).


                       Godot 3.3.3 was released a month ago, and a handful
                       of important fixes have been queued in the 3.3
                       branch since then. Most notably, users of the
                       GDScript LSP in Visual Studio Code have been
                       experiencing crashes in 3.3.3, which are fixed in
                       this new Godot 3.3.4.


                       Note: Version numbers can be confusing with three
                       branches worked on in parallel – this release is
                       3.3.4, i.e. a maintenance update to the 3.3 branch.
                       This is not the upcoming 3.4 feature release.


                       Godot 3.3.4, like all future 3.3.x releases,
                       focuses purely on bug fixes, and aims to preserve
                       compatibility. It is a recommended upgrade for all
                       Godot 3.3 users.


                # ⚓ Steam_Next_Fest_is_live_again_with_demos,_livestreams_and
                  more_|_GamingOnLinux⠀⇛


                       It’s that time again! From now until October 7 you
                       get to try out various new demos on Steam, watch
                       developer livestreams and much more.


                       This is another wonderful chance to test out
                       various games before they see a full release. For
                       the games included in the event, they are supposed
                       to be releasing somewhere between October 7, 2021
                       and May 1, 2022 so even if you find something you
                       like it might be a while before you get to see the
                       full complete thing.


          o § Distributions⠀➾


                # § Arch Family⠀➾


                      # ⚓ First_Arch_Linux_ISO_Powered_by_Linux_Kernel_5.14_Is
                        Now_Available_for_Download⠀⇛


                             That’s right Arch Linux fans, Arch Linux
                             2021.10.01 is up for grabs as I am writing
                             this and it comes with Linux kernel 5.14 by
                             default. The ISO image includes Linux 5.14.8
                             as default kernel since the recently released
                             Linux 5.14.9 kernel is still in the Testing
                             repos.


                             Linux kernel 5.14 is the latest kernel branch
                             available for GNU/Linux distributions,
                             bringing new features like a much-enhanced
                             AMDGPU graphics driver for AMD GPU users,
                             much-improved EXT4 and F2FS filesystems, the
                             core scheduling functionality to better
                             protect your computers against some of those
                             Spectre vulnerabilities, as well as some
                             goodies for ARM 64-bit (AArch64) and RISC-
                             V users.


                # § Debian Family⠀➾


                      # ⚓ Deepin_20.2.4_integrates_global_desktop_search⠀⇛


                             Barely a month and a half have passed since
                             its previous launch and is here Deepin 20.2.4
                             , a smaller version than the Chinese
                             distribution takes advantage of to introduce
                             a new feature, as well as a maintenance
                             update to use.


                             If you are already using Deepin 20 and keep
                             your system updated, you don’t have to do
                             anything else, because you are up to date,
                             but if you want to install the distribution
                             from scratch, Deepin 20.2.4 is the
                             recommended one at the moment. Although the
                             truth is that we would have to go back a
                             little earlier, to the launch of Deepin 20.2
                             , the latest regular version until what seems
                             like a conscious change in development and
                             releases.


                             In summary, Deepin 20.2 was followed by
                             Deepin 20.2.1 only with corrections, and
                             since then the versions that have followed
                             have been dedicated to applying patches, but
                             also new features of relative importance, but
                             one by one. Thus, Deepin 20.2.2 introduced a
                             new application store with support for
                             Android applications; Deepin 20.2.3 did the
                             same with integrating OCR support to extract
                             text from images …


                             … And Deepin 20.2.4 launches what its
                             developers have called an ” effective global
                             search “, a new search function with which
                             “quickly find the information you want”, they
                             have in the official announcement . And what
                             does this effective global search consist of?
                             In what you imagine.


                # § Canonical/Ubuntu Family⠀➾


                      # ⚓ Linux_Mint_20.3_is_named_‘Una’_and_Debian_Edition_
                        (LMDE)_5_is_called_‘Elsie’⠀⇛


                             Back in July, we shared with you that Linux
                             Mint 20.3 would be released around Christmas.
                             Unfortunately, that was pretty much all we
                             knew about the upcoming version of the
                             Ubuntu-based operating system. Thankfully,
                             today, the developers give us some more
                             details.


                             Not only do we now know the name of Linux
                             Mint 20.3, but the moniker of the upcoming
                             Linux Mint Debian Edition (LMDE) 5 too.
                             Following Mint’s tradition of only using
                             female names, the former will be named “Una,”
                             while the latter shall be called “Elsie.”


                      # ⚓ Linux_Mint_20.3_due_by_Christmas_and_project’s
                        website_receives_a_fresh_look⠀⇛


                             Clem Lefebvre, head of the Linux Mint
                             project, has announced that the next version
                             of Linux Mint, version 20.3, will be
                             available by Christmas in three flavours –
                             Cinnamon, MATE and Xfce. The new update is
                             codenamed Una which is just one letter away
                             from the codename of the current version,
                             Uma. Accompanying today’s news, the project
                             updated its website so that it looks modern
                             and is easier to use.


                             In its announcement, the Mint team said the
                             upcoming version will have improved themes,
                             for example, the titlebars of applications
                             will be made larger allowing for larger
                             buttons and making them easier to grab and
                             move around. Further, they have been given
                             rounder corners so they look more pleasant.


                      # ⚓ Monthly_News_–_September_2021⠀⇛


                             The new website is now fully ready and live
                             on https://www.linuxmint.com. It looks minty,
                             it works on all devices and it looks modern.
                             It also does a better job than before at
                             welcoming newcomers, explaining what Linux
                             Mint is, why people love it and how to
                             install it.


                             It took longer than expected but the job is
                             done and we’re glad we took the time to
                             finally do it. I’d like to thank all the
                             people who sent us feedback and who helped us
                             with it.


                             The website no longer shows ads and this blog
                             announcement is no longer showing the
                             community sponsors. These were tough
                             decisions to take because they immediately
                             reduce our income but they also make Linux
                             Mint look more serious and professional.
                             We’re hopeful they’ll help us grow in the
                             long term and we’ll generate enough to not
                             worry about it.


                             We received a lot of positive feedback since
                             the website went live so we know you really
                             like it! I know we can’t please everybody and
                             taste is subjective but for most people this
                             is a very welcome change. Personally I
                             remember how amazing the previous website
                             looked when it was made in 2009, but what
                             looked amazing then just simply looks
                             outdated now. Although I grew attached to it
                             since it represented part of our identity
                             during these many years, getting the
                             opportunity to redesign it during this
                             development cycle was a relief and I’m very
                             happy with the result. We are a modern
                             operating system. We use Linux because it’s
                             better, not because it’s free or because it’s
                             old or because it didn’t embrace
                             controversial design changes. We use it
                             because it’s fast, because it works, because
                             it does what we want. It was important for
                             our website to not only convey these ideas
                             but to look modern as well.


                      # ⚓ Chihuahua-sized_robot_dog_developed⠀⇛


                             The little quadruped was designed by MangDans
                             in collaboration with Stanford Pupper.


          o § Devices/Embedded⠀➾


                # ⚓ Pocket_P.C._developer_units_are_now_shipping_(handheld
                  Linux_PC)⠀⇛


                       The company says it’s still finalizing the Debian
                       10 GNU/Linux software that will be pre-installed on
                       the Pocket P.C., but that the work is “ongoing and
                       progressing rapidly.”


                       But part of the point of this handheld is to be an
                       open platform, so you may also be able to install
                       other operating systems – Popcorn Computer’s parent
                       company Source Parts recently announced it’s
                       working to port postmarketOS to work on the device
                       as well. The team also released the hardware design
                       files for the Pocket P.C last year, which means
                       that anyone who’d prefer to build their own device
                       (or customize the design) can do that rather than
                       buying one.


                # § Mobile Systems/Mobile Applications⠀➾


                      # ⚓ Oppo_may_launch_its_first_Android_tablet_next_year_–
                        Times_of_India⠀⇛


                      # ⚓ Firefox_on_Android_will_soon_autofill_logins_for_all
                        your_apps⠀⇛


                      # ⚓ Google_is_making_one_of_Android’s_best_features
                        easier_to_use_on_Chrome_and_iPhone⠀⇛


                      # ⚓ The_Best_Android_Games_on_Sale_This_Week_–_Agent_A,
                        Doctor_Who:_The_Lonely_Assassins_and_More_–_Droid
                        Gamers⠀⇛


                      # ⚓ Best_Android_app_deals_of_the_day:_Worms_2,_Escapists
                        2,_more_–_9to5Toys⠀⇛


                      # ⚓ Emergency_SOS_for_Pixel_phones_can_record_videos,
                        call_emergency_services_and_alert_your_contacts_–
                        Liliputing⠀⇛


                      # ⚓ T-Mobile_shares_its_own_list_of_devices_getting_the
                        Android_12_update⠀⇛


                      # ⚓ Firefox_on_Android_is_getting_a_super-useful_time
                        saver_update_|_TechRadar⠀⇛


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


                # § Web Browsers⠀➾


                      # § Mozilla⠀➾


                            # ⚓ Anti-cheat_works_on_Linux,_Firefox_stumbles
                              again,_and_HDR_support_–_Linux_news_–_September
                              2021_–_Invidious⠀⇛


                                   This time, we have Red Hat hiring for
                                   HDR support on Linux, Firefox making
                                   more controversial decisions, and
                                   support for Linux from the major anti
                                   cheat providers, among a LOT of other
                                   linux gaming news.


                            # ⚓ Addressing_gender-based_online_harms_in_the_DSA
                              [Ed: Mozilla spends money on politics and
                              lobbying while firing actual engineers]⠀⇛


                                   Last year the European Commission
                                   published the Digital Services Act
                                   (DSA) proposal, a draft law that seeks
                                   to set a new standard for platform
                                   accountability. We welcomed the draft
                                   law when it was published, and since
                                   then we have been working to ensure it
                                   is strengthened and elaborated as it
                                   proceeds through the mark-up stage.
                                   Today we’re confirming our support for
                                   a new initiative that focuses on
                                   improving the DSA with respect to
                                   gender-based online harm, an objective
                                   that aligns with our policy vision and
                                   the Mozilla Manifesto addendum.


                                   An overarching focus of our efforts to
                                   improve the DSA have focused on the
                                   draft law’s risk assessment and
                                   auditing provisions. In order to
                                   structurally improve the health of the
                                   internet ecosystem, we need laws that
                                   compel platforms to meaningfully assess
                                   and mitigate the systemic risks
                                   stemming from the design and operation
                                   of their services. While the draft DSA
                                   is a good start, it falls short when it
                                   comes to specifying the types of
                                   systemic risks that platforms need to
                                   address.


                            # ⚓ MDN_Web_Docs_at_Write_the_Docs_Prague_2021 [Ed:
                              Mozilla does not mention the awful tragedy of
                              outsourcing to to proprietary software of
                              Microsoft, an attack on the Web itself]⠀⇛


                                   The MDN Web Docs team is pleased to
                                   sponsor Write the Docs Prague 2021,
                                   which is being held remotely this year.
                                   We’re excited to join hundreds of
                                   documentarians to learn more about
                                   collaborating with writers, developers,
                                   and readers to make better
                                   documentation. We plan to take part in
                                   all that the conference has to offer,
                                   including the Writing Day, Job Fair,
                                   and the virtual hallway track.


                            # ⚓ Superhero_passwords_may_be_your_kryptonite
                              wherever_you_go_online [Ed: So Mozilla wants your
                              passwords. Should you trust it?]⠀⇛


                                   A password is like a key to your house.
                                   In the online world, your password
                                   keeps your house of personal
                                   information safe, so a super strong
                                   password is like having a superhero in
                                   a fight of good vs. evil. In
                                   recognition of Cybersecurity Awareness
                                   month, we revisited our “Princesses
                                   make terrible passwords for Disney+ and
                                   every other account,” and took a look
                                   to see how fortified superhero
                                   passwords are in the fight against
                                   hackers and breaches. According to
                                   haveibeenpwned.com, take a look at the
                                   how many times these superhero
                                   passwords have showed up in breached
                                   datasets….


                            # ⚓ How_to_delete_your_jQuery_Reject_Plugin_in_1
                              easy_step.⠀⇛


                                   In my last post on testing Chrome
                                   version 100, I encouraged everyone to
                                   flip on that flag and report bugs. It’s
                                   with a heavy heart that I announce that
                                   Ian Kilpatrick did so, and found a bug.


                                   [...]


                                   Also, if you happen to work on any of
                                   the following 1936 sites using this
                                   script, you know what to do (pick
                                   option Roman numeral 3, just to be
                                   super clear).


                            # ⚓ The_Mozilla_Blog:_Analysis_of_Google’s_Privacy
                              Budget_Proposal [Ed: The person who wrote it
                              receives his salary from Google via Mozilla]⠀⇛


                                   Fingerprinting is a major threat to
                                   user privacy on the Web. Fingerprinting
                                   uses existing properties of your
                                   browser like screen size, installed
                                   add-ons, etc. to create a unique or
                                   semi-unique identifier which it can use
                                   to track you around the Web. Even if
                                   individual values are not particularly
                                   unique, the combination of values can
                                   be unique (e.g., how many people are
                                   running Firefox Nightly, live in North
                                   Dakota, have an M1 Mac and a big
                                   monitor, etc.)


                                   This post discusses a proposal by
                                   Google to address fingerprinting called
                                   the Privacy Budget. The idea behind the
                                   Privacy Budget is to estimate the
                                   amount of information revealed by each
                                   piece of fingerprinting information
                                   (called a “fingerprinting surface”,
                                   e.g., screen resolution) and then limit
                                   the total amount of that information a
                                   site can obtain about you. Once the
                                   site reaches that limit (the “budget”),
                                   further attempts to learn more about
                                   you would fail, perhaps by reporting an
                                   error or returning a generic value.
                                   This idea has been getting a fair
                                   amount of attention and has been
                                   proposed as a potential privacy
                                   mitigation in some in-development W3C
                                   specifications.


                            # ⚓ Niko_Matsakis:_Dyn_async_traits,_part_2⠀⇛


                                   In the previous post, we uncovered a
                                   key challenge for dyn and async traits:
                                   the fact that, in Rust today, dyn types
                                   have to specify the values for all
                                   associated types. This post is going to
                                   dive into more background about how dyn
                                   traits work today, and in particular it
                                   will talk about where that limitation
                                   comes from.


                                   [...]


                                   Early on in Rust, we debated whether
                                   dyn DoTheThing ought to implement the
                                   trait DoTheThing or not. This was,
                                   indeed, the origin of the term “dyn
                                   safe” (then called “object safe”). At
                                   the time, I argued in favor of the
                                   current approach: that is, creating a
                                   binary property. Either the trait was
                                   dyn safe, in which case dyn DoTheThing
                                   implements DoTheThing, or it was not,
                                   in which case dyn DoTheThing is not a
                                   legal type. I am no longer sure that
                                   was the right call.


                # § SaaS/Back End/Databases⠀➾


                      # ⚓ PostgreSQL_14_Ships_with_Improved_Performance_for
                        Heavy_Workloads⠀⇛


                             The PostgreSQL team released the PostgreSQL
                             14 database, providing users of the widely
                             deployed relational database with new
                             features.


                             PostgreSQL, also known as “Postgres”, is an
                             open-source, object-relational database
                             management system. It has been around for
                             over 30 years and advertises itself as “the
                             most advanced open-source relational database
                             in the world”. It is developed by a worldwide
                             team of volunteers and it is quite popular
                             due to its stability and advanced features.


                             PostgreSQL is perceived as a go-to solution
                             for performing complicated, high-volume data
                             operations. That’s because PostgreSQL is
                             better at handling extraordinary database
                             situations. Additional points that set
                             PostgreSQL apart are the fact it is object-
                             relational, ACID-compliant, highly
                             concurrent, and offers NoSQL support. And the
                             latest PostgreSQL 14 makes things even
                             better.


                # § LibreOffice on Chromebooks and Apache/OpenOffice⠀➾


                      # ⚓ How_to_install_LibreOffice_7.2_on_a_Chromebook⠀⇛


                             Today we are looking at how to install
                             LibreOffice 7.2 on a Chromebook. Please
                             follow the video/audio guide as a tutorial
                             where we explain the process step by step and
                             use the commands below.


                             If you have any questions, please contact us
                             via a YouTube comment and we would be happy
                             to assist you!


                      # ⚓ Apache_Month_in_Review:_September_2021⠀⇛


                             Welcome to the latest monthly overview of
                             events from the Apache community. Here’s a
                             summary of what happened in September …


                      # ⚓ This_Week_In_Security:_OpenOffice_Vulnerable,_IOS
                        Vulnerable,_Outlook…_You_Get_The_Idea_|_Hackaday⠀⇛


                             We start this week with a good write-up by
                             [Eugene Lim] on getting started on
                             vulnerability hunting, and news of a problem
                             in OpenOffice’s handling of DBase files.
                             [Lim] decided to concentrate on a file
                             format, and picked the venerable dbase
                             format, .dbf. This database format was
                             eventually used all over the place, and is
                             still supported in Microsoft Office,
                             Libreoffice, and OpenOffice. He put together
                             a fuzzing approach using Peach Fuzzer, and
                             found a handful of possible vulnerabilities
                             in the file format, by testing a very simple
                             file viewer that supported the format. He
                             managed to achieve code execution in dbfview,
                             but that wasn’t enough.


                             Armed with a vulnerability in one
                             application, [Lim] turned his attention to
                             OpenOffice. He knew exactly what he was
                             looking for, and found vulnerable code right
                             away. A buffer is allocated based on the
                             specified data type, but data is copied into
                             this buffer with a different length, also
                             specified in the dbase file. Simple buffer
                             overflow. Turning this into an actual RCE
                             exploit took a bit of doing, but is possible.
                             The disclosure didn’t include a full PoC, but
                             will likely be reverse engineered shortly.


                             Normally we’d wrap by telling you to go get
                             the update, but OpenOffice doesn’t have a
                             stable release with this fix in it. There is
                             a release candidate that does contain the
                             fix, but every stable install of OpenOffice
                             in the world is currently vulnerable to this
                             RCE. The vulnerability report was sent way
                             back on May 4th, over 90 days before full
                             disclosure. And what about LibreOffice, the
                             fork of OpenOffice? Surely it is also
                             vulnerable? Nope. LibreOffice fixed this in
                             routine code maintenance back in 2014. The
                             truth of the matter is that when the two
                             projects forked, the programmers who really
                             understood the codebase went to LibreOffice,
                             and OpenOffice has had a severe programmer
                             shortage ever since. I’ve said it before: Use
                             LibreOffice, OpenOffice is known to be
                             unsafe.


                      # ⚓ All_Your_(d)Base_Are_Belong_To_Us,_Part_1:_Code
                        Execution_in_Apache_OpenOffice_(CVE-2021–33035) [Ed:
                        How many still use OpenOffice instead of LibreOffice]⠀⇛


                             Venturing out into the wilderness of
                             vulnerability research can be a daunting
                             task. Coming from a background in primarily
                             web and application security, I had to shift
                             my hacking mindset towards memory corruption
                             vulnerabilities and local attack vectors.
                             This two-part series will share how I got
                             started in vulnerability research by
                             discovering and exploiting code execution
                             zero-days in office applications used by
                             hundreds of millions of people. I will
                             outline my approach to getting started in
                             vulnerability research including dumb
                             fuzzing, coverage-guided fuzzing, reverse
                             engineering, and source code review. I will
                             also discuss some management aspects of
                             vulnerability research such as CVE assignment
                             and responsible disclosure.


                # § FSF⠀➾


                      # ⚓ FSF_job_opportunity:_Outreach_and_communications
                        coordinator⠀⇛


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


                             Reporting to the executive director, the
                             outreach and communications coordinator works
                             closely with our campaigns, licensing,
                             technical, and operations teams to plan,
                             write, edit, publish, and promote high-
                             quality, effective materials, both digital
                             and printed. These materials are a critical
                             part of advancing the FSF’s work in support
                             of the GNU Project, free software adoption,
                             copyleft licensing, and freedom on the
                             Internet; and against Digital Restrictions
                             Management (DRM), software patents, and
                             proprietary software. Nearly every
                             publication from the FSF goes through this
                             public-facing position, tying together our
                             work across various constituencies.


                # § Programming/Development⠀➾


                      # ⚓ LLVM_14.0.0_Release_Notes¶⠀⇛


                             This document contains the release notes for
                             the LLVM Compiler Infrastructure, release
                             14.0.0. Here we describe the status of LLVM,
                             including major improvements from the
                             previous release, improvements in various
                             subprojects of LLVM, and some of the current
                             users of the code. All LLVM releases may be
                             downloaded from the LLVM releases web site.


                             For more information about LLVM, including
                             information about the latest release, please
                             check out the main LLVM web site. If you have
                             questions or comments, the LLVM Developer’s
                             Mailing List is a good place to send them.


                             Note that if you are reading this file from a
                             Git checkout or the main LLVM web page, this
                             document applies to the next release, not the
                             current one. To see the release notes for a
                             specific release, please see the releases
                             page.


                      # ⚓ LLVM_13.0_Released_With_Official_Flang_Binary
                        Packages,_Improved_OpenCL_Clang_Support_–_Phoronix⠀⇛


                             LLVM 13.0 was tagged overnight as the latest
                             half-year update to this widely-used, very
                             powerful open-source compiler stack.


                             LLVM 13.0 is now available with many features
                             that accumulated over the course of the
                             summer. Some of the LLVM 13 highlights
                             include:


                             - Flang as the Fortran front-end is now
                             included in the official LLVM binary
                             packages.


                      # ⚓ Giant_Working_NERF_Gun_Runs_On_Tiny_Arduino_|
                        Hackaday⠀⇛


                             Well, here it is: a shoe-in for the new
                             world’s largest NERF gun. (Video, embedded
                             below.) The Guinness people haven’t shown up
                             yet to award [Michael Pick], but at 12.5
                             feet, this baby is over twice as long as the
                             current record holder, which belongs to
                             former NASA mechanical engineer Mark Rober
                             and his now-puny six-foot six-shooter.


                             We have to wonder if it is technically bigger
                             than the six-shooter, because they seem to be
                             roughly the same scale, except that [Michael]
                             chose a much bigger model to start from. The
                             main body is made from wood, and there are a
                             ton of 3D-printed details that make it look
                             fantastically accurate. The whole thing
                             weighs over 200 pounds and takes at least two
                             people to move it around. We especially love
                             the DIY darts that [Michael] came up with,
                             which are made from a PVC tube inside a
                             section of pool noodle, topped off with a 3D
                             printed piece for that distinctive orange
                             cap.


                      # ⚓ Minimalist_Timer_Counts_Down_With_LED_Matrix_|
                        Hackaday⠀⇛


                             Looking for something with a bit more style
                             than the traditional kitchen timer, [Martin
                             Jonasson] decided to take the last couple of
                             months to design and build his own take on
                             the idea using a rotary encoder, 16×9 LED
                             matrix, and a Teensy 2.0 microcontroller.
                             Were there better things he could have spent
                             that time on? Possibly. But you probably
                             wouldn’t have been reading it about it here,
                             so we won’t trouble ourselves with such
                             thoughts.


                      # ⚓ Canonical:_What_is_an_IoT_marketplace?⠀⇛


                             The Internet of Things (IoT) ecosystem is
                             expanding at a rapid rate, with the number of
                             devices growing every year. The increase in
                             physical hardware being manufactured
                             multiplies the amount of software needed to
                             perform various functions on new platforms.
                             There are a range of IoT use cases, including
                             voice-controlling the lights in your home,
                             monitoring air pollution, or the parking
                             feature of a self-driving car. With various
                             entities publishing specialised software for
                             all these use cases (and many more), it can
                             often be time-consuming to compare possible
                             solutions. For somebody interested in working
                             on an IoT project but unsure where to start,
                             it can be difficult to discover the software
                             you need. An IoT marketplace, as a
                             centralised platform for IoT applications,
                             can help to solve these issues.


                             [...]


                             Often, using an IoT marketplace allows you to
                             easily choose and install the software you
                             want in one place. Thus, you don’t need to
                             research the software you want to install,
                             then navigate to the company page that owns
                             that software, to search for individual
                             download pages to then install the software
                             you want in a non-standard way. Was the
                             software pre-packaged and available for
                             click-to-install? Would you need to extract
                             the contents of the downloaded folder and run
                             the installer in the terminal? This time-
                             consuming process can all be optimised by
                             using an IoT marketplace like the Snap Store.


                      # ⚓ Read_and_write_XML_files_with_wxWidgets⠀⇛


                             XML files are a perfect choice for storing
                             the settings of your wxWidgets cross-platform
                             application. Confused about how to use the
                             wxWidgets classes to read and write XML
                             files? No worries. In this hands-on tutorial,
                             you’ll learn how to read and write XML files
                             with wxWidgets, using the classes
                             wxXmlDocument, wxXmlNode and wxXmlAttribute.
                             We’ll expand a previously presented wxWidgets
                             template application, such that it stores its
                             application window dimensions in an XML file.


                      # ⚓ QML_Runtime_features:_part_1⠀⇛


                             This post is a refresher about some features
                             of the qml binary that is installed along
                             with the Qt SDK, which should help to explain
                             why we now prefer to use it, rather than
                             older tools like qmlscene and qmlviewer.


                      # § Red Hat Pushing Microsoft Proprietary Software⠀➾


                            # ⚓ SQL_Server_on_Red_Hat_Enterprise_Linux_at_Data
                              Platform_Virtual_Summit_2021 [Ed: IBM only cares
                              about money]⠀⇛


                                   At this year’s Data Platform Virtual
                                   Summit (DPS) 2021, I was honored to
                                   present “Monitoring SQL Server on Linux
                                   performance with Performance Co-Pilot
                                   and Grafana.” In this post I’ll cover
                                   some of the topics I touched on during
                                   my talk and include some suggestions
                                   for DBAs who might be new to Linux.


                      # § Java⠀➾


                            # ⚓ New_Red_Hat_Developer_e-book:_Quarkus_for
                              Spring_Developers⠀⇛


                                   Red Hat Developer has published Quarkus
                                   for Spring Developers, a comprehensive,
                                   149-page e-book introducing Quarkus to
                                   Java developers, with a focus on
                                   helping people familiar with Spring
                                   make the transition. This includes the
                                   Spring Framework and Spring Boot, and
                                   any other modules within the Spring
                                   ecosystem.


                                   While Java continues to be one of the
                                   most widely used programming languages
                                   for building applications, Java
                                   developers often struggle to make their
                                   applications smaller and faster to meet
                                   modern computing requirements.


                                   Quarkus is designed to help.


    * § Leftovers⠀➾


          o ⚓ What_a_car’s_cabin_air_filter_looks_like_after_nobody_has_changed
            it_in_19_years._–_BaronHK’s_Rants⠀⇛


                 I got a 2003 Chevy Impala from mom a couple of years ago
                 for free because it needed all kinds of work.


                 One thing that every car owner should know how to do
                 themselves is change their engine and cabin air filters,
                 because it’s not that hard and over the years they will
                 plug up and could cause the systems they protect to
                 malfunction or work less than ideally.


                 But shops charge $70 and up for a cabin air filter job
                 sometimes and $40 and up for an engine air filter. Since
                 these should be replaced so often, the jobs can get
                 really expensive. Not changing the cabin air filter can
                 result in a dysfunctional HVAC system or damage to it’s
                 components, weird smells, restricted air flow, and has
                 some impact on gas mileage as the engine has to runthis
                 system. Then it’s even more expensive.


          o § Hardware⠀➾


                # ⚓ Pixel_Pump_Pick_&_Place_Positions_Parts_Precisely_|
                  Hackaday⠀⇛


                       You’ve finally decided to take the plunge and build
                       a board with surface-mount parts. After carefully
                       dispensing the solder paste with a syringe, it’s
                       time to place the parts. You take up your trusty
                       tweezers and reach to grab a SOIC-14 logic IC—only
                       there’s not a great way to grab it. The IC is too
                       long to grab one way and has leads obstructing the
                       other. You work around the leads, drop the IC into
                       place, and then pick up an 0402 resistor. You
                       gently set the resistor into your perfectly
                       dispensed solder paste, pull the tweezers away, and
                       the resistor has stuck to your slightly magnetic
                       tweezers. [Robin Reiter] realized that hobbyists
                       and small manufacturers needed a better way to
                       assemble their surface-mount designs, so he’s
                       building the Pixel Pump Pick & Place, an open-
                       source vacuum assembly tool.


          o § Integrity/Availability⠀➾


                # § Proprietary⠀➾


                      # § Security⠀➾


                            # ⚓ Security_updates_for_Friday⠀⇛


                                   Security updates have been issued by
                                   Debian (curl, krb5, openssl1.0, and
                                   taglib), Fedora (cifs-utils), SUSE
                                   (libqt5-qtbase and rubygem-
                                   activerecord-4_2), and Ubuntu (linux-
                                   raspi, linux-raspi-5.4 and linux-
                                   raspi2).


                            # ⚓ Baby’s_Death_Alleged_to_Be_Linked_to_Ransomware
                              [Ed: This happens_on_a_much_grander_scale_due_to
                              Microsoft]⠀⇛


                                   Access to heart monitors disabled by
                                   the attack allegedly kept staff from
                                   spotting blood & oxygen deprivation
                                   that led to the baby’s death.


                                   A U.S. hospital paralyzed by ransomware
                                   in 2019 will be defending itself in
                                   court in November over the death of a
                                   newborn, allegedly caused by the
                                   cyberattack.


                                   As the Wall Street Journal reported on
                                   Thursday, the baby’s mother, Teiranni
                                   Kidd, gave birth to her daughter, Nicko
                                   Silar, on July 16, 2019, without
                                   knowing that the hospital was entering
                                   its eighth day of clawing its way back
                                   from the attack.


                            # ⚓ A_Hospital_Hit_by_Hackers,_a_Baby_in_Distress:
                              The_Case_of_the_First_Alleged_Ransomware_Death⠀⇛


                                   When Teiranni Kidd walked into
                                   Springhill Medical Center on July 16,
                                   2019, to have her baby, she had no idea
                                   the Alabama hospital was deep in the
                                   midst of a ransomware attack.


                            # ⚓ A_Death_Due_to_Ransomware⠀⇛


                                   What will be interesting to see is
                                   whether the courts rule that the
                                   hospital was negligent in its security,
                                   contributing to the success of the
                                   ransomware and by extension the death
                                   of the infant.


                            # § Privacy/Surveillance⠀➾


                                  # ⚓ Locked_In_Your_Home⠀⇛


                                         What brand is your home? Do you
                                         live in a Google, Apple, or
                                         Amazon house? Because in a modern
                                         “smart home” you may choose only
                                         one, and that choice locks you
                                         into dependence on only that
                                         vendor and its approved partners
                                         for any future appliances and
                                         home gadgets. Your “AI” voice
                                         assistant may talk to you, but it
                                         won’t talk to its competitors.


                                         [...]


                                         With the current trajectory, the
                                         smart home will become much like
                                         your phone–under a single
                                         vendor’s control, not yours. They
                                         will get to choose which
                                         appliances integrate, which
                                         services they use for your voice
                                         queries, and what happens to your
                                         personal data. If they do
                                         something you don’t like, it will
                                         be even harder (and more
                                         expensive) to switch to a
                                         competitor than it already is
                                         with a phone or laptop.


                                         Fortunately it’s not too late to
                                         change the current situation. If
                                         there is any hope for a smart
                                         home where you hold the keys, it
                                         must start with open standards
                                         for how devices communicate. Only
                                         then is there a space where truly
                                         open alternatives to Big Tech
                                         smart home gadgets can exist for
                                         the average consumer outside of
                                         do-it-yourself electronics
                                         projects.


                                         There is an effort underway with
                                         the industry organization Matter
                                         to create such standards but like
                                         with other industry standards
                                         membership and compliance is
                                         voluntary. Consumers should
                                         pressure existing smart home
                                         companies to comply with open
                                         standards and vote with their
                                         wallet. For our part, we will
                                         continue our work to build
                                         alternatives that don’t lock you
                                         in, based on our Social Purpose
                                         commitment to protect people’s
                                         privacy, security and freedom.


                                  # ⚓ PhishLabs_spying_on_my_WordPress_blog?⠀⇛


                                         WordPress gives me a list of
                                         where people link to my blog
                                         from, and today I noticed some
                                         company called PhishLabs.
                                         Including directly through from
                                         their main site and from a
                                         “threatintel” subdomain.


                                         It appears to be owned by
                                         Gartner, and claims that they do
                                         “digital brand and reputation
                                         management”, but I’m unable to
                                         determine exactly what they mean
                                         by this.


                                         I’ve had a WordPress blog before
                                         and I know that as soon as you
                                         start criticizing big
                                         corporations, they have these
                                         firms they hire to monitor blogs,
                                         figure out if what you’re saying
                                         is a “threat” to their brand, and
                                         from there….I don’t know what
                                         they want exactly.


          o § Monopolies⠀➾


                # § Patents⠀➾


                      # ⚓ Not_a_class_ACT:_the_so-called_App_Association_is
                        simply_an_Apple_Association_and_does_NOT_represent_app
                        developers’_interests_in_fair_distribution_terms [Ed:
                        Microsoft_AstroTurfing_groups recycled]⠀⇛


                             Enough is enough. While I have previously
                             agreed, and may in the future agree, with ACT
                             | The App(le) Association on some patent
                             policy questions, its pro-Apple advocacy in
                             the App Store antitrust context–which I
                             already mentioned in May–gets worse by the
                             month. Judges, policy makers, and journalists
                             should see that lobbying scheme for what it
                             is.


                             Three months ago, New York-based attorney
                             David Cohen wrote a blog post entitled “On
                             Deceptive Apps and Practices: Unmasking the
                             ACT App(le) Association.” Mr. Cohen was
                             rightfully astonished when he saw ACT
                             claiming to speak on small businesses’ behalf
                             at a Federal Trade Commission (FTC) hearing.
                             I trust he will not attempt to assert any
                             copyright against me for borrowing the term
                             “App(le) Association” from him, and I
                             appreciate that he quoted me in the
                             aforementioned post.


                             [...]


                             In other words, Apple was using its
                             mouthpiece named ACT to tell the media that
                             Apple should continue with its stranglehold
                             on app developers large and small. In
                             reality, there’s not a single app developer
                             out there who truly thinks Apple’s death grip
                             is a good thing–and if any make public
                             declarations to the contrary (which are few
                             and far between), it’s because they expect
                             (which doesn’t necessarily mean they’ve been
                             promised) Apple to reciprocate that favor in
                             some form or another.


                             If ACT respected not only itself but also,
                             more generally, human intelligence, it would
                             have realized that when the New York Times
                             exposes an apparent lack of credibility and
                             legitimacy, it’s over. I mean, seriously, the
                             NYT paragraph I quoted above should have
                             given them and their other backers pause.
                             Apple stops at nothing to defend its iOS app
                             distribution monopoly, but other companies
                             should be profoundly concerned that this App
                             Store propaganda effort also discredits ACT’s
                             work on other issues, such as SEPs,
                             regardless of whether those positions may be
                             correct.


                      # ⚓ [Older]_On_Deceptive_Apps_and_Practices:_Unmasking
                        the_ACT_App(le)_Association⠀⇛


                             The ACT App Association should really be
                             called the ACT Apple Association. It was
                             founded in 1998 by Microsoft as a lobbying
                             arm utilizing smaller player’ as a front to
                             support its defense against antitrust charges
                             on both sides of the Atlantic. Over the
                             years, it remained a vehicle for Big Tech
                             interests. Although hard to find (and
                             strategically placed off the members’ page),
                             if you scroll all the way down this page you
                             see the ACT App(le) association’s main
                             sponsors are Apple, Microsoft, Intel,
                             Verizon, and AT&T (other recent sponsors have
                             included Facebook, Oracle, and eBay).


                             I have written about this “hide behind a
                             supposed app association” charade last year.
                             Since then, we’ve seen real app developers
                             fight for their lives in the Epic Games vs.
                             Apple litigation. However, the ACT App
                             Association filed an amicus brief in support
                             of… Apple (!), and its blog similarly takes
                             Apple’s side. So why is an “app association”
                             opposed to app developers’ interests?


                             [...]


                             I hope the FTC understands why the
                             association’s small app developers supposedly
                             support Apple in the Epic v. Apple
                             litigation, why these app developers
                             supposedly care so strongly about standards
                             essential patents (although app developers
                             are never required to take SEP licenses), or
                             how these app developers have the resources
                             to support a 22-employee trade association.
                             The answer is easy. It’s because the ACT App
                             (le) Association represents Apple, Microsoft,
                             Intel, Verizon and AT&T – not app developers.


                             Also misleading is the Association’s claim at
                             last week’s hearing to represent “thousands
                             of small business software application
                             development companies…located across every
                             state in America.” The Association’s
                             membership page lists thirty entities. Ten of
                             these are European entities surprisingly
                             listed without websites. The remaining ones
                             include a venture capital company, a
                             marketing company, a design company, and at
                             least one entity that appears to be out of
                             business. It is unclear how the remaining
                             dozen or so entities amount to “thousands of
                             small [app developers] … located across every
                             state in America.”



                    ䷩ 𝚕𝚒𝚗𝚎 7012

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⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 10.01.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_1/10/2021:_KaiOS_3.0_and_Xfce_Update⠀✐


Posted in News_Roundup at 11:26 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o § Audiocasts/Shows⠀➾


                # ⚓ KDE_DEVLOG_–_Fixing_This_Weird_Bug_In_Desktop_Applets_–
                  Kockatoo_Tube⠀⇛


          o § Kernel Space⠀➾


                # ⚓ Another_system_update_adventure_with_RAUC,_Barebox_&_Yocto
                  Project_–_Bootlin’s_blog⠀⇛


                       After experiencing both SWupdate and Mender in the
                       past we recently got the opportunity to work with
                       another update framework for embedded systems
                       called RAUC.


                       This time the choice of RAUC as system upgrade
                       framework was mainly motivated by the Phytec IMX6
                       board ecosystem which is based on both Barebox and
                       Yocto Project.
                       Indeed RAUC and Barebox are both developed by
                       Pengutronix and both are designed to provide a
                       complete and homogeneous solution that will be
                       introduced in this post.


                # ⚓ Paul_E._Mc_Kenney:_So_You_Want_to_Rust_the_Linux_Kernel?⠀⇛


                       There has been much discussion of using the Rust
                       language in the Linux kernel (for example, here,
                       here, and here) and 2021 LInux Plumbers Conference
                       had a number of sessions on this topic, as did
                       Maintainers Summit. At least two of these sessions
                       mentioned the question of how Rust is to handle the
                       Linux-kernel memory model (LKMM), and I volunteered
                       to write this blog series on this topic.


                       This series focuses mostly on use cases and
                       opportunities, rather than on any non-trivial
                       solutions. Please note that I am not in any way
                       attempting to dictate or limit Rust’s level of
                       ambition. I am instead noting the memory-model
                       consequences of a few potential levels of ambition,
                       ranging from “portions of a few drivers”, “a few
                       drivers”, “some core code” and up to and including
                       “the entire kernel”. Greater levels of ambition
                       will require greater willingness to accommodate a
                       wider variety of LKMM requirements.


          o § Benchmarks⠀➾


                # ⚓ Fedora_Server_35_Performance_Looking_Good_–_Initial
                  Benchmarks_With_Intel_Xeon_Ice_Lake⠀⇛


                       Given this week’s release of Fedora 35 Beta I have
                       begun my benchmarking to look at how this next
                       installment of Fedora Linux is shaping up given
                       that it tends to be at the forefront of open-source
                       innovations given Red Hat’s investments. For our
                       initial F35 benchmarking is looking at the Fedora
                       Server 35 Beta performance compared to Fedora 35 on
                       a dual Intel Xeon Platinum 8380 server.


                       This initial testing is quite straight-forward and
                       from the same Intel Xeon Platinum 8380 “Ice Lake”
                       reference platform, Fedora 34, Fedora 34 with all
                       stable release updates, and Fedora 35 Beta were
                       carried out for seeing how this H2’2021 Linux
                       distribution release update is looking. The stable
                       release of Fedora 35 is currently expected for the
                       end of October.


          o § Applications⠀➾


                # ⚓ Video_Trimmer_–_quickly_trim_videos⠀⇛


                       Video editing is the process of editing motion
                       video footage. In the new age of personal video,
                       video editing is becoming a central function of the
                       desktop, with the popularity of video editing
                       software ever increasing.


                       Any self-respecting operating system that has
                       ambitions on becoming the dominant force on the
                       desktop therefore needs to have a good selection of
                       video editing software. Video sharing websites such
                       as YouTube are now enormously popular with hundreds
                       of thousands of new videos uploaded every day.


                # ⚓ MAKE_MORE_with_Inkscape_–_Stroke_Fonts⠀⇛


                       Inkscape, the most used and loved tool of Fedora’s
                       Design Team is not just a program for doing nice
                       vector graphics. With vector graphics (in our case
                       SVG) a lot more can be done. Many programs can
                       import this format. Also, Inkscape can do a lot
                       more than just graphics. The last article of this
                       series showed how to design embroidery with
                       Inkscape and the extension Ink/Stitch. This time,
                       several extensions for Inkscape will be examined.
                       All are helpful for working with so called Stroke
                       or Hershey Fonts.


                       Inkscape version 0.91+ includes an extension called
                       Hershey Text – Extensions > Text > Hershey Text.
                       This extension brings a small set of Stroke Fonts
                       or Hershey Fonts. If you try testing all of the
                       extensions Inkscape comes with, you might get to
                       this one and ask yourself, “What is it for? It just
                       renders text?”


          o § Instructionals/Technical⠀➾


                # ⚓ How_to_Install_GitLab_on_Debian_11⠀⇛


                       GitLab is a free and open-source DevOps platform
                       that allows teams to iterate faster and innovate
                       together. It is a web-based tool developed by
                       GitLab Inc. It is very similar to GitHub and
                       provides a Git repository manager providing wiki,
                       issue-tracking, and continuous integration and
                       deployment. GitLab community edition is available
                       absolutely free for development and production
                       environment.


                       In this tutorial, I will show you how to install
                       GitLab with Nginx and Let’s Encrypt SSL on Debian
                       11.


                # ⚓ How_to_Install_&_Create_a_VM_on_VirtualBox_with_Pop!_OS
                  20.04_–_LinuxCapable⠀⇛


                       VirtualBox is a free and open-source hypervisor for
                       x86 and x86-64 virtualization, which the Oracle
                       Corporation develops. The software targets users
                       wishing to create virtual environments for servers
                       and desktops that allow users and administrations
                       to run multiple guest operating systems on a single
                       computer for either testing methods or production
                       use. VirtualBox may be installed on Windows, macOS,
                       Linux, Solaris, and OpenSolaris.


                       In the following tutorial, you will learn how to
                       install VirtualBox on your Pop!_OS 20.04 desktop,
                       along with creating a new Virtual Machine from
                       scratch.


                # ⚓ How_to_Install_Tor_Browser_on_Pop!_OS_20.04_–
                  LinuxCapable⠀⇛


                       Tor, also known as The Onion Router, is open-
                       source, free software that enables anonymous
                       communication when using online services such as
                       web surfing. The Tor network directs the Internet
                       traffic through an accessible worldwide volunteer
                       overlay network with over six thousand relays and
                       continues to grow. Many users want to find more
                       ways to keep their information and activities
                       anonymous or at least as private as possible, which
                       has led to Tor Browser growing quite popular in
                       recent years as it conceals a user’s location and
                       usage from anyone conducting network surveillance
                       or traffic analysis.


                       The Tor network is intended to protect the personal
                       privacy of users and their freedom and ability from
                       conducting communication without having their
                       activities monitored, and data were taken without
                       their consent and used to sum it up.


                       In the following tutorial, you will learn how to
                       install the latest Tor Browser on Pop!_OS 20.04.


                # ⚓ How_to_Add_a_User_to_Sudoers_on_Linux_Mint_–_LinuxCapable⠀⇛


                       When installing Linux Mint, the user account that
                       was created during the initial setup has sudo
                       rights. However, there may be a need to add
                       additional sudo users or to remove the access. This
                       is a straightforward process with a few commands.


                       In the following tutorial, you will learn to add a
                       user to the sudoers group on any current Linux Mint
                       system.


                # ⚓ How_To_Install_Telnet_on_Ubuntu_20.04_LTS_–_idroot⠀⇛


                       In this tutorial, we will show you how to install
                       Telnet on Ubuntu 20.04 LTS. For those of you who
                       didn’t know, Telnet is a protocol that allows you
                       to connect to remote computers (called hosts) over
                       a TCP/IP network using a client-server protocol to
                       establish a connection. Telnet listens to all the
                       requests by the user usually on TCP port 23, but
                       you can change it accordingly.


                       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 Telnet on Ubuntu 20.04 (Focal
                       Fossa). You can follow the same instructions for
                       Ubuntu 18.04, 16.04, and any other Debian-based
                       distribution like Linux Mint.


                # ⚓ What_is_Shebang_in_Linux_Shell_Scripting?⠀⇛


                       The seemingly insignificant #! characters at the
                       beginning of a shell script has a major
                       significance on how your script will be executed.


                # ⚓ What_Nodes_are_broken?_|_Adam_Young’s_Web_Log⠀⇛


                       While I tend to think about the nodes in OpenStack
                       term, the people that physically move the servers
                       around are more familiar with their IPMI address.
                       We have several nodes that are not responding to
                       IPMI requests. Some have been put into the
                       manageable state, some are in error.


                # ⚓ Legible_Error_traces_from_openstack_server_show_|_Adam
                  Young’s_Web_Log⠀⇛


                       If an OpenStack server (Ironic or Nova) has an
                       error, it shows up in a nested field. That field is
                       hard to read in its normal layout, due to JSON
                       formatting. Using jq to strip the formatting helps
                       a bunch


                # ⚓ Debugging_a_Clean_Failure_in_Ironic_|_Adam_Young’s_Web
                  Log⠀⇛


                       My team is running a small OpenStack cluster with
                       reposnsibility for providing bare metal nodes via
                       Ironic. Currently, we have a handful of nodes that
                       are not usable. They show up as “Cleaning failed.”
                       I’m learning how to debug this process.


          o § Games⠀➾


                # ⚓ Cyberpunk_speedrunner_platformer_Aeon_Drive_is_out_now
                  starring_Kira_Buckland_|_GamingOnLinux⠀⇛


                       Developer 2Awesome Studio has released Aeon Drive,
                       a cyberpunk themed platformer with a speedrunning
                       theme.


                       Aeon Drive stars Jackelyne, a space ranger
                       desperate to get home. Voiced by actress Kira
                       Buckland, who is best known for the voice of 2B in
                       Nier: Automata, Reimi Sugimoto in JoJo’s Bizarre
                       Adventure: Diamond Is Unbreakable, Trucy Wright in
                       the Ace Attorney series, and Hiyoko Saionji in the
                       Danganronpa series (and a lot more). Armed with a
                       power sword and teleportation dagger, Jackelyne
                       must dash through the neon-infused metropolis of
                       Neo Barcelona, using time and space-bending
                       abilities to find all the drive cores to fix her
                       ship – and save the city from doom.


                # ⚓ Steam_is_doing_another_Tabletop_Fest_starting_October_21
                  all_about_RPGs_|_GamingOnLinux⠀⇛


                       While today will see the Steam Next Fest arrive,
                       Valve have more plans as the digital Tabletop Fest
                       returns to Steam between October 21 – 25 and this
                       time around it’s all about the RPGs.


                       Kicking off at 10 AM PST / 5 PM UTC it will see a
                       big sale with hundreds of titles discounted, so you
                       might want to start filling up your wishlist. There
                       will also be around 18 hours of streaming from
                       developers, which is being done in partnership with
                       Auroch Digital. Starting off with Robert Kurvitz,
                       lead writer and designer on Disco Elysium.


                # ⚓ The_State_of_Linux_Gaming_–_Invidious⠀⇛


                # ⚓ The_Ultimate_BRRRT_Simulator:_Fully_Featured_A-10_Warthog
                  Cockpit_|_Hackaday⠀⇛


                       The Arduinos take input from switches and control
                       knobs, but also run 7-segment displays and analog
                       dials driven by servos. The panels were all laser-
                       cut using MDF or perspex and backlit using LEDs.


                # ⚓ The_upcoming_No_VR_Mod_for_Half-Life:_Alyx_shows_off
                  amazing_progress_|_GamingOnLinux⠀⇛


                       I consider Half-Life: Alyx played in VR to be one
                       of the greatest gaming experiences I’ve ever had
                       but for a lot of people it’s just not possible and
                       so the No VR Mod is in progress.


                       For whatever reason some cannot use VR be it due to
                       price, physical ability and more. But if you still
                       want to be able to experience the story first-hand
                       you’re currently a bit stuck. There are a few hacky
                       mods floating around to enable mouse/keyboard
                       support but they’re all really quite rough. The No
                       VR Mod looks like a different breed though, with
                       smooth movement and it all just looks good.


                # ⚓ XIGNCODE3_anti-cheat_working_towards_Steam_Deck_support_by
                  launch_|_GamingOnLinux⠀⇛


                       XIGNCODE3 is another popular anti-cheat like Easy
                       Anti-Cheat and BattlEye that currently causes
                       issues for Linux and it’s going to hopefully see
                       support (thanks Reddit) for Linux and the Steam
                       Deck by launch.


                # ⚓ Proton_Experimental_Enables_NVIDIA_DLSS_For_D3D12_Games,
                  Proton_Now_Handles_More_Games⠀⇛


                       Valve published new versions of Proton and Proton
                       Experimental last night.


                       With the latest Proton Experimental update as of
                       yesterday, NVIDIA’s Deep Learning Super Sampling
                       (DLSS) is now working for Direct3D 12 games when
                       setting the “PROTON_ENABLE_NVAPI=1″ environment
                       variable and using a supported NVIDIA graphics card
                       on a new enough driver. Proton was previously
                       working for DLSS Vulkan titles while now DLSS for
                       D3D12 games should be working with the above met
                       conditions.


                # ⚓ Steam_Play_Proton_6.3-7_is_out_now,_Proton_Experimental
                  gets_DLSS_for_DX12_games_on_Linux⠀⇛


                       Two big bits of news for Steam Play Proton today
                       with two new versions getting released so let’s
                       take a look and see exactly what’s new for the
                       Windows compatibility layer.


                       Firstly, NVIDIA announced back in August that DLSS
                       would come to Proton in September for DirectX 11 /
                       12. Well, their date was a bit off there it seems
                       but Valve / CodeWeavers managed to pull in DLSS
                       support for at least DirectX 12 in Proton
                       Experimental as of September 30. To enable it you
                       need to set PROTON_ENABLE_NVAPI=1 as a launch
                       option for games. Additionally this release also
                       fixes crashes in Project Wingman, Satisfactory and
                       other Unreal Engine 4 games using the Vulkan
                       renderer.


          o § Desktop Environments/WMs⠀➾


                # ⚓ Xfce’s_Apps_Update_for_September_2021:_New_Releases_of
                  Thunar,_Mousepad,_Whisker_Menu⠀⇛


                       While we skipped August because of the summer
                       holidays, the month of September 2021 brought some
                       great releases, starting with the awesome Thunar
                       file manager, which received not one but two
                       maintenance updates, up to version 4.16.10.


                       While Thunar 4.16.9 introduced support for using
                       the move action when dragging files of different
                       users, the ability to open the correct folder when
                       middle-clicking in tree-view, fixes a issue where a
                       folder was missing in history when it was opened in
                       a new tab, and disabled automatic queueing of file
                       transfers, Thunar 4.16.10 only addressed a
                       regression that could crash the file manager when
                       using the clipboard.


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


                      # ⚓ Calamares_and_Hacktoberfest_2021⠀⇛


                             Calamares is an independent Linux-distro-
                             installer. It was recently added to FreeBSD
                             ports as well, although you won’t be able to
                             use it as an installer yet. The Calamares
                             project is KDE-adjacent – but independent –
                             so it participates ins some things that KDE
                             projects do not. One of those things is
                             Hacktoberfest.


                      # ⚓ August/September_in_KDE_Itinerary⠀⇛


                             Travel is slowly returning, and that shows in
                             many improvements of KDE Itinerary being
                             driven by real-world testing and feedback
                             again in the past two month since the last
                             summary.


          o § Distributions⠀➾


                # ⚓ Download_Linux_–_Linux_Nightly⠀⇛


                       Linux refers to the kernel on which distributions
                       are built. You can think of it as the core to all
                       systems that are running on Linux.


                       Linux distributions are the download links featured
                       above – such as Ubuntu, Fedora, Manjaro, etc. These
                       are collections of software and configurations that
                       have been packaged with the Linux kernel. A team of
                       developers is responsible for each distro, and
                       attaches their own branding or moniker (i.e. “Linux
                       Mint) to it. Typically, the devs will release free
                       updates and support for the distro they’ve created.


                       Another term you’ll hear often is GNU, or GNU/
                       Linux. The GNU project is responsible for a massive
                       amount of the free software you’ll find availalble
                       across all Linux distributions.


                       While the Linux kernel provides an operating system
                       with its core functionality, the GNU software, as
                       well as software from other developers, allows us
                       to interact with the operating system and do
                       things. Since GNU and Linux are both so integral to
                       Linux distributions, the term GNU/Linux is
                       exceedingly common.


                       Both the Linux kernel and GNU software are free.
                       That’s why so many Linux distributions exist in the
                       first place. Anyone is free to take these
                       components, bundle them together, add their own
                       spin to the package, and then release the finished
                       product as a separate operating system (Linux
                       distro). This is very different than systems like
                       Microsoft Windows, where the code for the OS and
                       its applications are locked tightly behind a closed
                       source and copyright laws.


                # § SUSE/OpenSUSE⠀➾


                      # ⚓ GNOME,_Plasma_Releases_Make_Progress_While_Tumbleweed
                        Rolls⠀⇛


                             GNOME 41 has reached openSUSE Factory staging
                             and KDE’s Plasma 5.23 is nearing a release in
                             an openSUSE Tumbleweed snapshot as it
                             progresses through staging.


                             openSUSE’s rolling release turned out four
                             snapshots this week and updated software
                             packages like Mesa, curl, catfish, PipeWire,
                             Perl and more.


                             The 20210928 snapshot improved the
                             transferring of data via an update of curl
                             7.79.1, which made it work with OpenSSH 8.7;
                             the command line tool and library also
                             adjusted a setup to not change connection
                             data upon repeat invokes. An update of
                             inkscape 1.1.1 fixed a crash and improved the
                             startup time of the graphics editor
                             application. Two other packages updated in
                             the snapshot were yast2-network 4.4.26 and
                             yast2-nfs-client 4.4.1; the latter had an
                             update that supports systemd mount options in
                             fstab.


                      # ⚓ openSUSE_Tumbleweed_–_Review_of_the_weeks_2021/39_–
                        Dominique_a.k.a._DimStar_(Dim*)⠀⇛


                             Dear Tumbleweed users and hackers,


                             After the massive update in the last week due
                             to a full rebuild caused by glibc 2.34, this
                             week seems ‘somewhat’ quieter. Or at least
                             from a Release manager PoV less involvement
                             hungry. Yet, we managed to release 5
                             snapshots during this week (0923, 0924, 0926,
                             0927, and 0928).


                # § IBM/Red Hat/Fedora⠀➾


                      # ⚓ Junichi_Uekawa:_Garbage_collecting_with_podman_system
                        prune.⠀⇛


                             Garbage collecting with podman system prune.
                             Tells me it freed 20GB when it seems to have
                             freed 4GB. Wondering where that discrepancy
                             comes from.


                      # ⚓ Use_this_tool_to_build_an_API_without_code_|_Enable
                        Sysadmin⠀⇛


                             Application programming interfaces (APIs) are
                             like fuel for digital transformation,
                             enabling companies to develop applications
                             and microservices quickly. DataTrucker.IO is
                             a new, free and open source (Apache 2.0) no-
                             code/less-code API backend that decreases the
                             time required to build APIs.


                      # ⚓ New_application_samples_in_Red_Hat_OpenShift_4.8_|
                        Red_Hat_Developer⠀⇛


                             As Red Hat OpenShift continues to evolve and
                             improve, our efforts to promote developer
                             success ramp up as well. The OpenShift
                             developer dashboard provides sample
                             applications that are just a few clicks away
                             from deployment. These samples are spread
                             across a wide range of software development
                             interests and stacks, so you’ll probably find
                             one of interest to you.


                             For OpenShift 4.8, four new samples have been
                             added, while four others have been updated. A
                             total of 14 samples are at hand for the new
                             or curious developer. We’ll review all the
                             samples in this article.


                      # ⚓ 5_ways_leaders_can_boost_psychological_safety_on
                        teams⠀⇛


                             “Welcome to the family.” That’s how it should
                             feel right from the start when new people
                             join the team at any company.


                             Of course, relating a workplace to a home is
                             an ambitious promise. To live up to it, you
                             need to ensure that your people experience a
                             safe place where they can be who they are
                             with no fear of being punished or humiliated
                             for sharing their ideas, raising concerns, or
                             making mistakes.


                      # ⚓ Contribute_to_Call_for_Code_projects_as_part_of
                        Hacktoberfest⠀⇛


                             We’re excited that Call for Code will be
                             participating in Hacktoberfest again this
                             year. Now in its eighth year, Hacktoberfest
                             is a global online festival meant to drive
                             contribution to and involvement in open
                             source projects.


                             Both Call for Code and Hacktoberfest
                             encourage contributions from people of all
                             backgrounds and skill levels. Call for Code
                             is of course a great opportunity for
                             experienced open source contributors to get
                             involved in projects that address social and
                             humanitarian issues, but if you’re brand new
                             to open source projects, we’ve got you
                             covered there as well. Our “Call for Code:
                             Introduction to Open Source” online course is
                             available at no cost and introduces you to
                             key concepts, tools, and processes that you
                             need to start contributing to any open source
                             project. Start learning, and earn a badge by
                             completing this course.


                # § Canonical/Ubuntu Family⠀➾


                      # ⚓ Linux_Mint_20.3_“Una”_Arrives_This_Christmas_with
                        Dark_Apps_and_Other_Visual_Changes⠀⇛


                             Linux Mint 20.3 will be dubbed “Una” and will
                             be the third major update to the Linux Mint
                             20 series based on the Ubuntu 20.04 LTS
                             (Focal Fossa) operating system series, which,
                             of course, will be supported with software
                             updates and security patches until 2025.


                             Most probably, Linux Mint 20.3 “Una” will be
                             derived from the recently launched Ubuntu
                             20.04.3 LTS point release, but, like with
                             Linux Mint 20.2 “Uma”, Linux Mint 20.1
                             “Ulyssa”, and Linux Mint 20 “Ulyana”, it will
                             stick to the long-term supported Linux 5.4
                             LTS kernel series rather than using the newer
                             Linux kernel 5.`11.


                      # ⚓ Meet_Mini_Pupper:_the_Robot_Dog_That_Is_Just_as_Smart
                        as_a_Border_Collie⠀⇛


                             Powered by a Raspberry Pi 4B microprocessor,
                             Mini Pupper uses Ubuntu and ROS to run its
                             FSN (Full Self-Navigation) System. It also
                             supports SLAM (Simultaneous Localization and
                             Mapping), which allows it to map its
                             surroundings and learn in real-time from
                             objects around it using Lidar or a camera
                             sensor.


          o § Devices/Embedded⠀➾


                # ⚓ Pocket_P.C._devkits_ship,_U-blox_GNSS_module_replaced_by
                  SIMCom_SIM33ELA_due_to_import_ban⠀⇛


                       The Pocket P.C. (aka Popcorn Computer) is a
                       handheld Linux computer based on Allwinner A64 with
                       2GB RAM, 32GB storage, a 4.95-inch Full HD display,
                       and a QWERTY keyboard that was introduced in 2019,
                       and reminds me of PocketCHIP from a few years also
                       with an Allwinner processor, a display, a keyboard,
                       and a battery.


                       The initial plan was to start shipping the device
                       by May 2020, and there are been delays for reasons
                       we’ll explain below, but the good news is that
                       Source Parts has just announced the developer units
                       had been shipped.


                # § Open Hardware/Modding⠀➾


                      # ⚓ UDOO_KEY_ESP32_&_RP2040_board_to_launch_for_$4_–_CNX
                        Software⠀⇛


                             UDOO is known for its x86 boards that embed
                             an Arduino compatible MCU, but the UDOO KEY
                             is different, as it does without an Intel or
                             AMD processor, and instead, combines
                             Raspberry Pi RP2040 microcontroller with
                             Espressif ESP32 WiFi & Bluetooth WiSoC.


                             As we noted in the past combining Raspberry
                             Pi Pico/RP2040 with ESP32 does not make a lot
                             of sense in most cases, but here’s the UDOO
                             KEY will be offered for just $4 for the first
                             units, so they’ll basically throw the ESP32,
                             an IMU sensor, and a microphone for free
                             since it’s the same price as one Raspberry Pi
                             Pico, before eventually selling the device
                             for $20.


                      # ⚓ Eolim_STEAMMIANS_Kit_helps_teach_young_kids_about
                        electronics_through_interactive_stories_|_Arduino
                        Blog⠀⇛


                             Teaching children concepts in science,
                             technology, engineering, and mathematics is
                             extremely important as the world is becoming
                             even more dependent on people with those
                             skills. To help achieve this goal, Leyla
                             Tawfik, Serena Cangiano and the Ethafa team
                             came up with a series of interactive learning
                             solutions that they call “STEAMMIANS.” Each
                             one targets a particular subset within the
                             field of electronics and their first,
                             “Eolim,” is focused on guiding kids ages 9-11
                             on how to use certain kinds of sensors to
                             perform various actions.


                # § Mobile Systems/Mobile Applications⠀➾


                      # ⚓ Google_Play_Warning:_200_Evil_Android_Apps_Stole_From
                        10_Million_Phones⠀⇛


                      # ⚓ Epson_debuts_a_fairly_affordable_new_Android_TV
                        projector_–_9to5Google⠀⇛


                      # ⚓ How_to_pair_your_Android_TV_with_the_new_Google_TV
                        remote⠀⇛


                      # ⚓ How_to_scan_a_QR_code_with_an_Android_phone_–_CNET⠀⇛


                      # ⚓ How_to_turn_your_Android_into_a_mobile_hotspot⠀⇛


                      # ⚓ How_to_Access_Google_“My_Activity”_on_Android⠀⇛


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


                      # ⚓ How_to_change_your_lock_screen_shortcuts_on_Android
                        12_on_a_Pixel_|_Android_Central⠀⇛


                      # ⚓ How_to_Set_Up_a_Conference_Call_on_Android_–
                        businessnewsdaily.com⠀⇛


                      # ⚓ Samsung_Galaxy_A02′s_Android_11_update_is_rolling_out
                        –_GSMArena.com_news⠀⇛


                      # ⚓ Do_you_really_have_or_use_an_Android_this_old?_–
                        SlashGear⠀⇛


                      # ⚓ Best_Android_app_deals_of_the_day:_Double_Dragon
                        Trilogy,_The_Last_Express,_Agent_A,_more_–_9to5Toys⠀⇛


                      # ⚓ Top_10_Best_Hunting_Android_Games_–_2021⠀⇛


                      # ⚓ Google_Meet_finally_adds_background_videos_for
                        Android⠀⇛


                      # ⚓ Google_Assistant_Reminders_on_Android_gets_dark_theme
                        –_9to5Google⠀⇛


                      # ⚓ Android_Auto_now_works_in_Tesla_vehicles_through_the
                        browser_–_Electrek⠀⇛


                      # ⚓ Android,_iOS_apps_bad_for_privacy,_study_finds_•_The
                        Register⠀⇛


                      # ⚓ Motorola’s_first_Android_tablet_in_years_is_the_Moto
                        Tab_G20⠀⇛


                      # ⚓ 3_Ways_to_Copy_&_Paste_Text_from_Android_to_PC_or
                        Vice_Versa⠀⇛


                      # ⚓ Fairphone_4_supported_by_postmarketOS⠀⇛


                             The Fairphone 4 from the Dutch manufacturer
                             Fairphone BV was officially presented
                             yesterday. Like its predecessors, it is a
                             mid-range device whose concept is
                             characterized by fair conditions in
                             production and the use of raw materials that
                             are as clean as possible. The modular
                             structure stands for longevity and easy
                             repairability. For the first time, the
                             manufacturer is offering a generous guarantee
                             period of five years, which is unusual in the
                             industry.


                      # ⚓ /e/_cloud_is_a_deGoogled_Alternative_to_Google
                        Drive⠀⇛


                             Google Drive is a popular cloud storage
                             service that works great for the most part.


                             However, it may not be the most private
                             option out there. So, to take total control
                             of your data, the best way is to spin up a
                             Nextcloud instance and store your essential
                             data while getting access to other
                             collaboration tools.


                             While that sounds good to hear, not everyone
                             can put the effort to create and maintain
                             their instance. This is where ecloud comes
                             in—built by the same team behind /e/ OS, the
                             de-googled Android operating system.


                      # ⚓ Cross_Compile_to_PinePhone_Part_Four⠀⇛


                             Now we’ve got ourselve a handy script for
                             cross compiling, I think it’s time to
                             introduce other means of cross compiliing and
                             why I not using existing methods.


                             Pmbootstrap is a script to build packages for
                             postmarketOS. It supports cross compiling and
                             various other options, it also handles
                             dependencies for you. And you can use apline
                             ports build files directly without hacking it
                             as we did on part two for ArchLinux. Most
                             important, it’s available as pip package.
                             Meaning you can use it to build packages for
                             postmarketOS even if you’re not on Apline
                             Linux! PinePhone is well supported by
                             PostmarketOS and Plasma Mobile developers
                             also work closely with PostmarketOS
                             developers. If you have postmarketOS
                             installed on your pinephone or any Android
                             phones postmarketOS supports (there are over
                             1000 devices postmarketOS supports), do try
                             pmbootstrap.


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


                # § Web Browsers⠀➾


                      # § Mozilla⠀➾


                            # ⚓ KaiOS_3.0_with_the_current_Gecko_84.0_is
                              distributed⠀⇛


                                   KaiOS is based on the code of Mozilla’s
                                   Firefox OS and the third major version
                                   has just been released. The success of
                                   KaiOS shows how much Mozilla had backed
                                   the wrong horse with Firefox OS. Kai OS
                                   Technologies from Hong Kong did not
                                   concentrate the development of the
                                   operating system on smartphones or TV
                                   sets, but on the promising category of
                                   feature phones.


                            # ⚓ Firefox_Wayland_development_in_2021⠀⇛


                                   It’s been long time from my last update
                                   about Firefox news on Linux and I’ve
                                   finally got some time to sum up what
                                   we’ve been working on for last year and
                                   what’s coming. There haven’t been
                                   introduced any new exciting features
                                   (from Linux perspective) for the last
                                   year but rather a hidden but important
                                   changes.


                                   From Linux desktop developers
                                   perspective 2021 is a year of Wayland.
                                   KDE has been shipping decent Wayland
                                   compositor which becomes default for
                                   Fedora 34. It’s actually pretty fast
                                   and gives you smooth feeling of “good
                                   old times” with X11/Gtk2/name-your-
                                   favorite environment where any graphics
                                   change was just instant without lags or
                                   slow transitions. I must mention Robert
                                   Mader who created a new Firefox Wayland
                                   SW backend for the KDE.


                # § Productivity Software/LibreOffice/Calligra⠀➾


                      # ⚓ Fixing_a_LibreOffice_bug_in_less_than_eight_hours!⠀⇛


                             LibreOffice’s QA community works on
                             identifying, testing and fixing bug reports
                             from users around the world. Gabriele Ponzo,
                             a long-time LibreOffice contributors and part
                             of The Document Foundation’s Membership
                             Committee, tells us about how a bug was
                             recently fixed in just under eight hours…


                # § CMS⠀➾


                      # ⚓ Diamantedesk:_Open-source_Ticketing_System_for
                        business⠀⇛


                             Diamantedesk is an open source web-based
                             Ticketing, help-desk solution aims to allow
                             you to customize for business needs.


                             Diamantedesk offers reliability, flexibility,
                             scalability, and extensibility for many
                             enterprise sectors like IT support, shipping,
                             customer services, healthcare and more.


                             It is built to improve customer service and
                             convert feedback into valuable experience


                             The system comes with a rich set of features
                             and fancy look with informative dashboard
                             filled with graphs, charts, and logs.


                             [...]


                             It is published under the Open Software
                             License (OSL 3.0).


                # § Programming/Development⠀➾


                      # ⚓ Qt_6.2_LTS_adds_a_large_number_of_modules_and_support
                        for_Apple_Silicon_and_Windows_11_–_itsfoss.net⠀⇛


                             Qt 6.2 LTS is now available not only to be
                             the first release with long-term support of
                             the sixth major version of the framework ,
                             but also to start laying the foundations that
                             will allow developers to truly transition
                             from Qt 5 by having almost achieved the
                             parity with version 5.15, which has become
                             the penultimate LTS.


                             Qt 6.2 LTS comes with many interesting news
                             that should give it a strong boost and open
                             the door to many projects to start the
                             migration to the current major version of the
                             framework . Of course, before starting to
                             explain the news, those responsible recalled
                             the main aspects of Qt 6, which already we
                             summarized at the time .


                             What stands out the most about Qt 6.2 LTS is
                             the inclusion of a large number of new
                             modules to approach parity with version 5.15,
                             which are the following: Qt Bluetooth, Qt
                             Multimedia, Qt NFC, Qt Positioning, Qt Quick
                             Dialogs, Qt RemoteObjects, Qt Sensors, Qt
                             SerialBus, Qt SerialPort, Qt WebChannel, Qt
                             WebEngine, Qt WebSockets, and Qt WebView . On
                             this aspect, the company has said that “the
                             API for these modules is mostly compatible
                             with previous versions of Qt 5 and will only
                             require minor adjustments of the user code
                             when it is transferred to Qt 6” .’


                      # ⚓ Qt_Creator_5.0.2_released⠀⇛


                      # ⚓ Dirk_Eddelbuettel:_RcppArmadillo_0.10.7.0.0_on_CRAN:
                        New_Upstream⠀⇛


                             Armadillo is a powerful and expressive C++
                             template library for linear algebra aiming
                             towards a good balance between speed and ease
                             of use with a syntax deliberately close to a
                             Matlab. RcppArmadillo integrates this library
                             with the R environment and language–and is
                             widely used by (currently) 912 other packages
                             on CRAN.


                             This new release brings us Armadillo 10.7.0
                             released this morning by Conrad. Leading up
                             to this were three runs of reverse
                             dependencies the first of which uncovered the
                             need for a small PR for subview_cols support
                             which Conrad kindly supplied.


                      # ⚓ PoCL_1.8_OpenCL_Implementation_Coming_With_LLVM_13
                        Support,_Better_SPIR-V_On_CUDA⠀⇛


                             PoCL is the open-source project implementing
                             OpenCL for CPU-based execution as well as
                             multi-device support by getting its Portable
                             Computing Language implementation working
                             atop NVIDIA GPUs via CUDA, AMD GPUs via HSA,
                             and other experimental implementations
                             through leveraging LLVM/Clang.


                      # ⚓ Arm_Begins_Adding_Armv9_Support_To_The_GNU_Compiler
                        Toolchain⠀⇛


                             Arm engineers have begun landing their Armv9
                             enablement work in the GNU compiler
                             toolchain.


                             Yesterday brought the initial Armv9 commits
                             to GNU Binutils. This included adding armv9-
                             a to -march for the GNU Assembler as well as
                             for GAS adding the Cortex-X2, Cotex-A510, and
                             Cortex-A710.


                      # § Python⠀➾


                            # ⚓ Awesome_Python_Video_Tutorials_Keep_You
                              Motivated_|_Hackaday⠀⇛


                                   Programming languages are one of those
                                   topics that we geeks have some very
                                   strong and often rather polarised
                                   opinions about. As new concepts in
                                   computing are dreamt up, older
                                   languages may grow new features, if
                                   viable, or get left behind when new
                                   upstarts come along and shake things up
                                   a bit. This scribe can remember his
                                   early days programming embedded
                                   systems, and the arguments that ensued
                                   when someone came along with a project
                                   that required embedded C++ or worse,
                                   Java, when we were mostly diehard C
                                   programmers. Fast forward a decade or
                                   two, and things are way more
                                   complicated. So much choice, so much
                                   opinion.


                      # § Java⠀➾


                            # ⚓ 8_reasons_why_I_learned_Core_Java_|
                              Opensource.com⠀⇛


                                   Computer programming, also known as
                                   coding for short, is not about which
                                   language you use. It’s about developing
                                   programming logic and learning to think
                                   like a programmer. The language you
                                   start with should be the one that helps
                                   you the most in this endeavor. So you
                                   have to ask yourself the question:
                                   “What do you want to do as a
                                   programmer?”


                                   For example, if you want to work on
                                   Android app development, video game
                                   development, desktop GUI applications,
                                   or just general software development, I
                                   think learning Java is an excellent
                                   option. It’s the language I chose, and
                                   it has made a whole world of
                                   programming available to me. In India,
                                   where I live, the average salary of a
                                   Java programmer is around 5.9 Lakhs per
                                   Annum (LPA) (it can be as high as 10
                                   LPA, depending on your experience.)


                                   Java is a vast language, though, with
                                   lots of frameworks and variants to
                                   choose from. Core Java is the term the
                                   tech industry has developed to refer to
                                   the central components of the Java
                                   language—the thing that people use to
                                   write the frameworks and has developed
                                   the cottage industry around Java. I
                                   believe that Core Java is one of the
                                   most powerful skills you can acquire
                                   because understanding the basics of
                                   Java gives you a significant advantage
                                   when learning all of the related tools
                                   built on top of it.


    * § Leftovers⠀➾


          o § Integrity/Availability⠀➾


                # § Proprietary⠀➾


                      # § Security⠀➾


                            # ⚓ Reproducible_Builds_(diffoscope):_diffoscope
                              186_released⠀⇛


                                   The diffoscope maintainers are pleased
                                   to announce the release of diffoscope
                                   version 186. This version includes the
                                   following changes:


                                   [ Chris Lamb ]
                                   * Don't call close_archive when
                                   garbage-collecting Archive instances
                                   unless
                                     open_archive returned successfully.
                                   This prevents, amongst others, an
                                     AttributeError traceback due to
                                   PGPContainer's cleanup routines
                                   assuming
                                     that its temporary directory had been
                                   created.
                                     (Closes: reproducible-builds/
                                   diffoscope#276)
                                   * Ensure that the string "RPM archives"
                                   exists in the package description,
                                     regardless of whether python3-rpm is
                                   installed or not at build time.

                                   [ Jean-Romain Garnier ]
                                   * Fix the LVM Macho comparator for non-
                                   x86-64 architectures.
⚓ Crashes_in_OpenBSD,_DragonFly_BSD_and_Electron_due_to_deprecation_of_the
IdenTrust_root_certificate⠀⇛


     The termination of the IdenTrust root certificate (DST Root CA X3)
     used to cross-sign the Let’s Encrypt CA root certificate resulted in
     problems with Let’s Encrypt certificate validation in projects using
     older versions of OpenSSL and GnuTLS. Problems also affected the
     LibreSSL library, the developers of which did not take into account
     past experience related to failures that occurred after the AddTrust
     root certificate of the Sectigo (Comodo) certification authority
     expired.


     Recall that in releases of OpenSSL up to and including the 1.0.2
     branch and in GnuTLS before release 3.6.14 , there was an error that
     did not allow the correct processing of cross-signed certificates, if
     one of the root certificates used for signing expired, even if other
     valid ones were saved. chains of trust (in the case of Let’s Encrypt,
     the aging of the IdenTrust root certificate does not allow
     verification, even if the system supports its own Let’s Encrypt root
     certificate valid until 2030). The essence of the error is that older
     versions of OpenSSL and GnuTLS parsed the certificate as a linear
     chain, while according to RFC 4158, a certificate can represent a
     directed distributed circular graph with several trust anchors that
     need to be considered.


⚓ BloodHound_–_Hacking_Active_Directory_Trust_Relationships⠀⇛


     Attackers can use BloodHound to easily identify highly complex attack
     paths that would otherwise be impossible to quickly identify.
     Defenders can use it to identify and eliminate those same attack
     paths. Both blue and red teams can use BloodHound to easily gain a
     deeper understanding of privilege relationships in an Active
     Directory environment.


     It is a single page JavaScript web application, built on top of
     Linkurious, compiled with Electron, with a Neo4j database fed by a
     PowerShell ingestor.


⚓ Getting_Started_With_Kali⠀⇛


     Kali is a Debian based distribution aimed at penetration testing. I
     haven’t felt a need to use it in the past because Debian has packages
     for all the scanning tools I regularly use, and all the rest are free
     software that can be obtained separately. But I recently decided to
     try it.


     Here’s the URL to get Kali [1]. For a VM you can get VMWare or
     VirtualBox images, I chose VMWare as it’s the most popular image
     format and also a much smaller download (2.7G vs 4G). For unknown
     reasons the torrent for it didn’t work (might be a problem with my
     torrent client). The download link for it was extremely slow in
     Australia, so I downloaded it to a system in Germany and then copied
     it from there.


     [...]


     Installing VMs for both these distributions was quite easy. Most of
     my time was spent downloading from a slow server, trying to get SCSI
     emulation working, working out how to convert image files, and
     testing different compression options. The time spent doing stuff
     once I knew what to do was very small.


§ Privacy/Surveillance⠀➾


    * ⚓ Coalition_Letter_to_the_48th_U.N._Human_Rights_Council_(HRC)_on_Pegasus
      –_Access_Now⠀⇛


           We, the undersigned civil society organizations and independent
           experts, call on Member States of the U.N. Human Rights Council
           (HRC) to take urgent action at the ongoing 48th regular session
           of the HRC to denounce the unfolding and unprecedented scale of
           human rights violations by States facilitated by the use of the
           NSO Group’s Pegasus spyware and provide immediate, robust
           support for impartial and transparent inquiries into the
           abuses.


           We are deeply alarmed by the Pegasus Project revelations, a
           major investigation conducted by Forbidden Stories, and a
           consortium of 16 media organizations, alongside Amnesty
           International who was a technical partner in the
           investigations. The investigation was based on a leak of 50,000
           phone numbers of potential targets of NSO Group surveillance
           technology, a list which includes journalists, activists, human
           rights defenders, lawyers, world leaders, and civil society
           actors. So far, at least 180 journalists in 20 countries were
           identified as potential targets of Pegasus spyware between 2016
           to June 2021.


           Adding to the revelations, further cases of targeted
           surveillance continue to unfold. The most recent victim
           targeted by Pegasus spyware is the Budapest-based
           photojournalist Dániel Németh. According to an investigation by
           media organization Direkt36 and forensic analysis by Citizen
           Lab, independently validated by Amnesty International, two of
           Németh’s phones were hacked by a government client of the NSO
           in early July 2021. Németh is not the only Hungarian journalist
           to be hacked using Pegasus, Amnesty International’s forensic
           checks confirmed that two of Direkt36 investigative
           journalists, András Szabó and Szabolcs Panyi, and another
           investigative reporter, Brigitta Csikász, were also hacked in
           2019.


    * ⚓ Act_now_against_spyware,_coalition_tells_UN_Human_Rights_Council_–
      Access_Now⠀⇛


           As the U.N. Human Rights Council (HRC) convenes at the ongoing
           48th regular session, Access Now joins 94 civil society
           organizations and independent experts in urging member states
           to denounce abuses facilitated by spyware technologies.


           The Pegasus Project revealed a long list of journalists,
           activists, human rights defenders, lawyers, world leaders, and
           civil society actors that were a target of NSO Group’s Pegasus
           Spyware. The U.N. HRC should mandate comprehensive measures to
           investigate and prevent further violations linked to the sale,
           export, and use of Pegasus spyware and cases of targeted
           surveillance.


           “Member States must urgently act to address the perpetual human
           rights abuses by States facilitated by NSO Group’s Pegasus
           spyware,” said Laura O’Brien, UN Advocacy Officer at Access
           Now. “The clandestine surveillance industry must be held
           accountable.”


           The recent revelations showcased the unprecedented scale of
           human rights violations by States facilitated by the use of
           Pegasus with Budapest-based photojournalist Dániel Németh being
           the latest victim targeted by the spyware.


§ Freedom of Information/Freedom of the Press⠀➾


    * ⚓ Russian_journalist_acknowledges_emigration,_denounces_new_felony
      charges_as_effort_to_silence_his_investigative_reporting⠀⇛


           Roman Dobrokhotov, the editor-in-chief of The Insider, has
           responded to new criminal charges that he allegedly crossed the
           Russian border illegally. The criminal case “was conjured out
           of thin air,” he argued in an editorial published by The
           Insider, asserting that he was within his rights when he left
           the country in August, weeks after federal agents raided his
           home and interrogated his parents. Russian officials seized his
           international passport at the time, but Dobrokhotov says he
           maintains his general civil passport.


§ Civil Rights/Policing⠀➾


    * ⚓ Why_the_cybersecurity_industry_should_treat_civil_society_as_critical
      infrastructure_–_The_Record_by_Recorded_Future⠀⇛


           Cybersecurity risks now affect everyone, but those risks aren’t
           the same everywhere. The Record spoke with Access Now’s Asia
           Policy Director and Senior International Counsel Raman Jit
           Singh Chima about how the human rights organization helps
           secure activists and journalists around the world. Chima, who
           also serves as the organization’s global security lead, shared
           details about risks facing human rights defenders in the Asia-
           Pacific region—from spyware and social media monitoring to
           disrupting access to certain apps or the entire Internet.


           Protecting civil society from these threats must be a key part
           of cybersecurity policy discussions, Chima told The Record,
           much like we think about how we need to protect power grids and
           other utilities that keep society functioning.


           “Understand that people who protect civil liberties, rights,
           and democracy are critical infrastructure and need to be talked
           about as such when you engage in cybersecurity conversations
           with national governments in this region,” he explained.


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