𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Thursday, January 27, 2022
┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅
Generated Fri 28 Jan 02:43:01 GMT 2022
Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖)
Full hyperlinks for navigation omitted but are fully available in the originals
The corresponding HTML versions are at 𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈
Latest in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕 and older bulletins can be found at 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕-𝒂𝒓𝒄𝒉𝒊𝒗𝒆𝒔
Full IPFS index in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔 and as plain text in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔/𝒕𝒙𝒕
Gemini index for the day: gemini://gemini.techrights.org/2022/01/27/


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

QmfKHqGowjRxdQqskGCLaTJvfCGFi19QHkyd8kwa9PMJ21
QmP9Us6BzAW1DtJJVXeJt8AyhFyfNcNAfWtLTvSMzp6Ltp
QmRocUr84sVRrmmhApYkrairZ9gM3urZnz5pkw4h6pxA9b
QmQ1r9n2zgVqwtQ4bsQLNP2kbfnhn22xRMWVDD5qUuwkKF
QmU5vYfwSWKbwcf52ai4QQxmeVvq2qk4Rno1afMvVcdEUm
QmSRxd1L1Tjg5YFR28UqaVozsZZh3xMVhvDKvnfHxuctNe
QmUYb6AJaHEaYvQGdw1Z8bffPkohvdveAhmoUhNFHe4PB6
QmRXpMsysY15jnTdXabNj8RQWyYQoA287zCaWvJJjNWzB2
QmaSCmshgLNtetvtehrJTkVzA4UKVtdrEf2DcHz8b5gBoV
QmZWJhSMSsSbuTS3JfxxEo3tfs2QfTCENeVipKSaQVU5b2
Qmehhm7o1VbxWg8uyeTcYkk6Hr1Cp4Ho21X2wCnesY9asd
Qmf3TSbMJS9koYs7ieZ1w3WBpaDp6x7rx5xnhC6B134fFL
QmbAVHY5Ges1nF9HNsiNn6FsQW8UdTFHURKDG1QgSKpKw7
QmZnZkCBXLzZg5rkewh3peFLzQ5xAZRm6HpjAvmtf39ELR
QmZeHUaFKnCwMohgf9hT7KAvQEFvHbBZ8MUZTtceSkoLZc
QmQLbqvdSXzQ59gWzwwt9RARegF8vZB68qihXTbNcDNoxy
QmXRhRDa28yw47e5ym8hgWTNSCTtmH5t22GCpvFvaGYDwN
QmNrH8cLM4mYaiBXzhdkhAQm8XM54JzRQa3Z1Ng4a41kcV
QmZjLA2jtgeEhSJihNxjJW3q7KaEU6iyCKve9pmkci3m61
QmTWgjCkngZ2r4jN8fZGmd7bpEdJL3pBfU6vKWFNxPmkYf
QmUa6NW563bcVpbJi9K42Aap4iTTXYmJcu5bTsjAcRc9yG


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

⦿ On the Internet, Trust Should Not Become Centralised | Techrights

⦿ IRC Proceedings: Wednesday, January 26, 2022 | Techrights

⦿ [Meme] EPO: Pursuing an Eastern and Western District of Europe (for Patent Trolls and Software Patents) | Techrights

⦿ Microsoft-Connected Publishers Suffer and Perish With Microsoft (While Peddling ’Fake News’ for Their Beloved Sponsor) | Techrights

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
		http://techrights.org/2022/01/27/centralising-trust-is-bad/#comments
		http://techrights.org/2022/01/27/irc-log-260122/#comments
		http://techrights.org/2022/01/27/meme-epo-pursuing-an-eastern-and-western-district-of-europe-for-patent-trolls-and-software-patents/#comments
		http://techrights.org/2022/01/27/perishing-with-microsoft/#comments

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
		http://techrights.org/2022/01/27/archinstall-2-3-1/#comments
		http://techrights.org/2022/01/27/opnsense-22-1-released/#comments
		http://techrights.org/2022/01/27/pipewire-0-3-44/#comments

                    ䷩ 𝚕𝚒𝚗𝚎 58

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/01/27/centralising-trust-is-bad/#comments
    Gemini version at gemini://gemini.techrights.org/2022/01/27/centralising-trust-is-bad/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.27.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ On_the_Internet,_Trust_Should_Not_Become_Centralised⠀✐


Posted in Deception, Google, Microsoft, Security at 11:38 am by Dr. Roy
Schestowitz


Video_download_link | md5sum 58023098d2c54163340ddba23fed9bf5
Sites and Capsules Can Trust Themselves
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/self-signed-trust.webm


Summary: “Trust” is a word that lost its meaning in the era of “TPM” and
fancier_names_for_'Palladium'; we need to reject this idea that computers need
to check_with_Microsoft_if_the_operating_system_is_trusted (not just Windows!),
check with Gulag/Chrome if a Web site is trusted, and whether it's_OK_to_run
some_application/s_on_one's_own_computer (as if Jim Zemlin et al get to decide
what is trusted)


LAST night we_wrote about the growing popularity of self-signing Gemini
capsules. Over time more and more of them reject the CA model, which was mostly
reinforced by monopolistic corporations and their ‘pyramid scheme’, grabbing
“trust” off Web sites while selling those sites abundant (but suddenly
artificially scarce or expensive) “certificates” several times per year. Of
course Mozilla (with Firefox) helped those monopolistic corporations — with
them_being_financial_masters_of_Mozilla — just like it had embraced DRM (EME),
in effect participating in the attack on the open Web and harming disabled
(e.g. blind) people in the process. So much for Inclusion and/or Diversity…


“Apparently the ‘disease’ of CA conglemerates has already spread to GNU (wget)
and Curl (Microsoft GitHub; it really ought not be there).”The above video
explains that many people are installing and setting up Gemini servers this
month*, based on yesterday’s_statistics, and certificates (for TLS) remain one
of the technical barriers. Having privacy through TSL/SSL is excellent, but
outsourcing this whole system to nasty corporations (using Linux_Foundation as
their front) is not OK. This paves the way for censorship of sites (at browser
level), censorship of operating systems (at boot time), and censorship of
software (in_vivo).


Apparently the ‘disease’ of CA conglemerates has already spread to GNU (wget)
and Curl (Microsoft GitHub; it_really_ought_not_be_there). “It would be worth
checking the various TLS libraries and modules to see if they accept self-
signed certificates,” an associate told me this morning, as “wget and curl
don’t, at least by default. “If I recall correctly wget does not accept them at
all, the only choice with them is to ignore them if wget has to be used.” Quick
checks can confirm**. YMMV (e.g. derivative distributions). █
____
* As I point out in the video, loads of people seems to be installing Gemini
this month and here’s the latest bump:


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Geminispace_ay_2007⦈_


** Recent versions:


curl: (60) SSL certificate problem: unable to get local issuer certificate
wget: ERROR: The certificate of example.ddns.net is not trusted.
ERROR: The certificate of example.ddns.net doesn't have a known issuer.
⢀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 152

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/01/27/irc-log-260122/#comments
    Gemini version at gemini://gemini.techrights.org/2022/01/27/irc-log-260122/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.27.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ IRC_Proceedings:_Wednesday,_January_26,_2022⠀✐


Posted in IRC_Logs at 2:04 am by Needs Sunlight


Also available via the Gemini protocol at:


    * gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-260122.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-260122.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-social-260122.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-260122.gmi
Over HTTP:


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


                                         #techrights_log_as_HTML5                                                                                  #boycottnovell_log_as_HTML5


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


                                    #boycottnovell-social_log_as_HTML5                                                                               #techbytes_log_as_HTML5


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


                                          #techrights_log_as_text                                                                                   #boycottnovell_log_as_text


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


                                     #boycottnovell-social_log_as_text                                                                                #techbytes_log_as_text


                          Enter_the_IRC_channels_now


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


CID                                              Description     Object type


                                                 IRC log for
 QmWDbDMLPtcEhn1o2ooHr8NehuQJRKfd6NG7yp49Gtpzis #boycottnovell  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell
 QmaDcZ44otP8DqHbAxL2F3ZpQWP5jSZHygCdmDbQFj5t28 (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
                                                 #boycottnovell-
 QmaXy4757AqkXC57ok2qDg1VT5GyaFM4jmHnXEdLq3LzZE social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell-
 QmS4hadVWRJ5PtMJ4KTS4nxkTqWkWjrYNev1iHNj835FW3 social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 (full IRC log
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 QmcYmVHvpLkjAzU35Yw6rU8vSbV4yRuWRxtT8txY9TgJaW #techbytes      🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techbytes
 QmVACpag761AK6oQk5uVFWUEpJAxW1M9yqLMz2N9Afs3LX (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 QmeZcRZjRuCu9PxBTxUBYK6r1ziw6RAWD4dwWXuze99v3s #techrights     🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techrights
 Qmen3Ftha9f66UtLmAAzWDWje1CoWw8RJskLvRSXfk9X3N (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈


§ Bulletin for Yesterday⠀➾


Local_copy | CID (IPFS): QmUa6NW563bcVpbJi9K42Aap4iTTXYmJcu5bTsjAcRc9yG



                    ䷩ 𝚕𝚒𝚗𝚎 279

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/01/27/meme-epo-pursuing-an-eastern-and-western-district-of-europe-for-patent-trolls-and-software-patents/#comments
    Gemini version at gemini://gemini.techrights.org/2022/01/27/meme-epo-pursuing-an-eastern-and-western-district-of-europe-for-patent-trolls-and-software-patents/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.27.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_EPO:_Pursuing_an_Eastern_and_Western_District_of_Europe_(for_Patent
Trolls_and_Software_Patents)⠀✐


Posted in Europe, Patents at 12:19 am by Dr. Roy Schestowitz


                       🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇EPC? No, UPC⦈
  EPC has been ignored for ages (and_violated_routinely), so why not violate
                        national constitutions as well?


Summary: With the EPO so flagrantly lying_and_paying_for_misinformation maybe
we should expect Benoît_Battistelli and António_Campinos to have delusions of
grandeur… such as presiding over the Eastern and Western District of Europe,
just like Mr. Gilstrap and Mr. Albright (political appointment by Donald Trump,
ushering in “the_swamp”)


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


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

                    ䷩ 𝚕𝚒𝚗𝚎 775

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/01/27/perishing-with-microsoft/#comments
    Gemini version at gemini://gemini.techrights.org/2022/01/27/perishing-with-microsoft/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.27.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Microsoft-Connected_Publishers_Suffer_and_Perish_With_Microsoft_(While
Peddling_‘Fake_News’_for_Their_Beloved_Sponsor)⠀✐


Posted in Deception, Microsoft, Vista_10, Windows at 10:57 am by Dr. Roy
Schestowitz


Video_download_link | md5sum 4c9abb62b7da7b1c35b74bf0bb179ee1
Microsoft Success is Fake News
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/faking-vista11-success.webm


Summary: IDG and other fake news outlets/networks/sites (selling to companies
flattering articles about themselves or renting out ‘news space’ to them, not
just ad space) want us to think Microsoft is doing very well, but it’s just
that same old Ponzi_scheme


LAST night we published “Microsoft_'Delighted'_by_Windows_11_(Vista_11)_Usage,
Which_is_Only_1%_Three_Months_After_Official_Launch_and_Six_Months_After
Release_Online,” in effect twisting the_headline from PCWorld’s (IDG) Microsoft
henchman, who has promoted Microsoft there for many years (no pretence about
it).


And meanwhile, Microsoft_Bogdan is trying_to_substitute failure_in_the_market
with some vague and shallow perception of “happiness”.


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Ballmer: We've migrated 2% of Vista 10 users to Vista 11⦈
The actual numbers (or simple facts) don’t favour Microsoft. One version of
Windows cannibalises another while overall the market share of Windows
continues to fall. MinceR remarked on last night’s post, saying “I’d replace
“the failure Vista 11 has been” with “the failure that is Vista 11″, as it
remains a failure…”


XFaCE said “it is a “has been” OS to be fair”…


“Trying to claim that it’s too new to be judged would be a face-saving lie.”The
video above looks at the scarce coverage of the fake “delight” of Microsoft. I
try to explain why they’re lying and remind people who does the lying. This is
just another example of media capture by Microsoft, wherein the goal is to send
“positive messaging” about a failing_product (more like rebranding).


Remember that in one form or another (like a fake “leak”) Vista 11 has already
been “out there” for over 6 months. Yes, more than half a year. Trying to claim
that it’s too new to be judged would be a face-saving lie. █


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

                    ䷩ 𝚕𝚒𝚗𝚎 1445

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.27.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_27/1/2022:_Archinstall_2.3.1_and_Nix_2.6.0⠀✐


Posted in News_Roundup at 2:48 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o ⚓ Meet_The_Incredible_$15_Linux_Computer⠀⇛


                 Brian Benchoff is an embedded engineer who has graced us
                 with unique, whimsical devices like the RGB Gaming
                 Coaster and the Zip Drive Tower. Now he’s back with a
                 decidedly more practical design: a fully-functional Linux
                 computer — screen and keyboard included — that costs a
                 mere $15.


                 Well, sort of. . .


                 The self-described “Linux Swiss Army Knife” PC packs a
                 surprising amount of functionality. With its 2.5-inch IPS
                 display and 47-key silicone membrane keyboard (which
                 feels like an older TV remote control), you can bust it
                 out and run scripts, compile code, or even transform it
                 into a crypto wallet.


          o § Desktop/Laptop⠀➾


                # ⚓ Mars_15_Laptop_Full_Specification_–_Linux_Powered_Laptop⠀⇛


                       Mars 15 is the latest Linux-powered laptop from
                       Juno Computers. Featuring AMD Ryzen 5000X series of
                       processors, a 15.6-inch Full HD (1920x1080p) matte
                       display with 240Hz refresh rate, the Mars 15
                       notebook is powered by the Ubuntu operating system.
                       Mars 15 can be ordered right now from Juno
                       Computers’ website.


          o § Audiocasts/Shows⠀➾


                # ⚓ Linux_Action_News_225⠀⇛


                       The big disruption that looks like a bust, a
                       security issue you need to pay attention to, and
                       some great news for the Steam Deck.


                # ⚓ The_Linux_Link_Tech_Show_Episode_940⠀⇛


                       Joel and his raccoon buddies eat walleye.


                # ⚓ BSDNow_439:_Browser_Tab_Unix⠀⇛


                       ACM: It takes a community, Don’t use discord for
                       OSS projects, Unix in a browser tab, OpenIndiana
                       Hipster 2021.10 available, Omni OS CE v11 is out,
                       and more.


          o § Kernel Space⠀➾


                # ⚓ PipeWire_0.3.44_Released_With_Latency_Improvements,_Minimal
                  PW_Server_Support_–_Phoronix⠀⇛


                       This will hopefully be the year that PipeWire
                       becomes commonplace on the Linux desktop across all
                       major distributions for audio/video stream
                       management. But for as good as PipeWire is already,
                       frequent point releases continue evolving the
                       functionality and ironing out compatibility
                       improvements for existing JACK and PulseAudio
                       integration. PipeWire 0.3.44 is out today as
                       another step in the right direction.


                # ⚓ Linux_5.16.3⠀⇛


                       I'm announcing the release of the 5.16.3 kernel.

                       All users of the 5.16 kernel series must upgrade.

                       The updated 5.16.y git tree can be found at:
                       	git://git.kernel.org/pub/scm/linux/kernel/git/
                       stable/linux-stable.git linux-5.16.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_5.15.17⠀⇛


                # ⚓ Linux_5.10.94⠀⇛


                # ⚓ Linux_5.4.174⠀⇛


                # ⚓ Linux_4.19.226⠀⇛


                # ⚓ Linux_4.14.263⠀⇛


                # ⚓ Linux_4.9.298⠀⇛


                # ⚓ Linux_4.4.300⠀⇛


                # ⚓ The_Freezing_of_tasks_in_the_Linux_kernel_and_how_it’s_used
                  by_Ksplice⠀⇛


                # § Graphics Stack⠀➾


                      # ⚓ DirectFB2_Aims_To_Resurrect_DirectFB_For_Embedded
                        Systems⠀⇛


                             The DirectFB library had been a popular
                             option for embedded systems in running off
                             the Linux frame-buffer to avoid the full
                             overhead of an X11 server. But a number of
                             years ago DirectFB disappeared and ultimately
                             stopped being maintained. Meanwhile Wayland
                             has been making lots of inroads into mobile/
                             embedded and areas once popular for DirectFB
                             use. But now it turns out DirectFB2 is in
                             development as a fork of the original
                             DirectFB.


                             [...]


                             Some of the early changes made to DirectFB2
                             has been making use of the Meson build
                             system, limiting DirectFB2 to being a pure C
                             implementation, and modularizing the existing
                             source code. DirectFB2 also supports
                             interfacing with DRM/KMS directly rather than
                             just frame-buffer devices.


                             Not only is OpenGL working with DirectFB2,
                             but Vulkan is also possible per the FOSDEM
                             abstract though seemingly limited to CPU-
                             based acceleration using SwiftShader.


          o § Intel⠀➾


                # ⚓ Intel_Core_i9_12900K_P-State_Governor_Performance_On_Linux
                  Review⠀⇛


                       Since Intel’s Alder Lake launch one of the test
                       requests to come in a few times has been about the
                       Intel P-State CPU frequency scaling driver and how
                       its performance differs with the various governor
                       choices available for altering the CPU frequency
                       scaling behavior. Now that Linux 5.16 stable is out
                       and running in good shape on Alder Lake, here are
                       some Core i9 12900K benchmarks looking at various
                       CPU frequency scaling choices and their impact on
                       raw performance as well as CPU thermals and power
                       consumption.


                       With Alder Lake having seen fixes in Linux 5.16 as
                       well as ADL-S graphics being enabled by default on
                       this new kernel, it’s a good target for carrying
                       out the P-State testing. The main reader inquiry
                       has obviously been about how how well these new
                       Intel hybrid processors perform if moving from P-
                       State “powersave” as is often the default governor
                       on most distributions to instead using the
                       “performance” governor that tends to keep the CPU
                       in its higher performance states more aggressively
                       than powersave.


                # ⚓ Alder_Lake_system_features_DDR5,_six_GbE_ports,_and_20Gbps
                  USB_3.2_Gen2X2⠀⇛


                       Neousys unveiled two embedded PCs based on Intel’s
                       12th Gen S-series with up to 64GB DDR5-4800: The
                       “Nuvo-9000” has up to 6x GbE with optional PoE+, 5x
                       USB 3.2 Gen2 (including a 2×2 port), M.2 with PCIe
                       Gen4, and up to 2x PCIe x16. There is also a
                       smaller, fanless “Nuvo-9531.”


                       Neousys has announced two of the first embedded
                       computers based on Intel’s 7nm 12th Gen Alder Lake
                       processors. Both the PCIe x16 equipped Nuvo-9000
                       and more compact Nuvo-9531 use the high-end Alder
                       Lake S-series processors.


                # ⚓ Intel_Alder_Lake_N_Support_Introduced_For_Mesa_22.0_–
                  Phoronix⠀⇛


                       In addition to this week seeing Raptor Lake S
                       support added for Mesa 22.0, the Alder Lake N
                       additions have also been merged for this quarter’s
                       Mesa update.


                       Given the insignificant changes from the driver
                       perspective for the existing Alder Lake (S)
                       support, the Alder Lake N support is namely just
                       adding new PCI IDs and identifying them as Alder
                       Lake family while having “Display13″ for the
                       display capabilities.


                # ⚓ Intel_releases_patch_for_Alder_Lake’s_Thread_Director_Linux
                  support_to_increase_performance_and_energy_efficiency⠀⇛


                       With the release of Intel’s 12th Gen Core Alder
                       Lake series of CPUs, it was discovered that
                       performance for the new CPUs was more efficient in
                       Microsoft Windows 11 than in the Linux operating
                       system. This is due to Linux not having adequate
                       support for Intel’s Thread Director technology that
                       allows for the operating system to access high-
                       performing Golden Cove cores and the energy-
                       efficient Gracemont cores properly. Intel’s Thread
                       Director is created from the Enhanced Hardware
                       Feedback Interface or HFI.


          o § Applications⠀➾


                # ⚓ 6_Best_Free_and_Open_Source_Stock_Market_Investment_Tools⠀⇛


                       We have all read stories about people who have
                       experimented living without spending any money
                       whatsoever. By growing their own food, washing in
                       the river, using a solar panel to provide
                       electricity, and bartering for certain goods and
                       services, these adventures have met with limited
                       success. However, for us mere mortals the simple
                       fact is that we need money. Money to buy food, to
                       purchase clothes, to pay our bills, as well as
                       indulging in our other infinite wants and desires.


                       While it can be a struggle to make ends meet, it is
                       possible to make life easier through better money
                       management. Financial management is about planning
                       income and expenditure and making informed
                       decisions that enable you to survive financially.


                # ⚓ Why_universities_choose_open_source_collaboration
                  software⠀⇛


                       Higher education institutions are actively looking
                       for ways to adapt to rapidly improving technology
                       and enable students to use advances in computing to
                       study, collaborate, and learn in new ways. Many
                       institutions have been using open source software
                       to exchange knowledge more easily, ensure a better
                       learning experience, and handle administration with
                       fewer worries.


                       Demand for open source software in higher education
                       is drastically increasing especially as the need
                       for remote learning grows.
                       Universities usually have complex and unique
                       systems. From a technological point of view, this
                       makes it harder for universities to adopt
                       technologies not built with their specific
                       requirements in mind.


                # ⚓ 5_Best_Linux_Programs_for_Students_and_Teachers⠀⇛


                       Linux should be the first choice for students and
                       teachers as a free alternative to the
                       commercialised Operating Systems. But, useful
                       programs that are widely available on Mac and
                       Windows often isn’t to be found on Linux.


                       We have addressed 5 such software that are already
                       replacing your favourite program on Linux, and
                       which is replacing traditional homework.


          o § Instructionals/Technical⠀➾


                # ⚓ How_to_install_Docker_Engine_on_CentOS⠀⇛


                       Docker Engine is an open containerization program
                       for Linux and other platforms. Docker Engine
                       manages self-contained “containers” that operate
                       similar to virtual machines. In this guide, we’ll
                       go over how to install Docker Engine on CentOS.


                       Docker Engine only supports CentOS 7 and 8.
                       Therefore, if you are using an older release of the
                       operating system, you must upgrade before
                       attempting to install Docker on your CentOS system.


                # ⚓ How_to_Use_the_Terraform_Command_Line_Interface_(CLI)_on
                  Ubuntu⠀⇛


                       Terraform is a framework for building and
                       configuring infrastructure as code, with a command-
                       line interface and DSL language. Terraform can
                       manage existing and popular service providers as
                       well as custom in-house solutions to build and
                       configure complete distributed data centers.


                       The Terraform Command Line Interface (CLI) lets you
                       use Terraform without having to write any code or
                       configuration files. It’s an ideal way to prototype
                       infrastructure changes with your team before
                       writing code, deploying configurations locally on
                       your machine, or pushing them into production. The
                       CLI builds off of the terraformspec file format
                       that was created for this purpose by third parties
                       such as HashiCorp Nomad CLI Toolkit.


                       The CLI toolkit implements a JavaScript DSL to
                       define the infrastructure and uses the same
                       configuration format in both Terraform and the CLI.
                       The CLI toolkit also provides commands to generate
                       infrastructure templates, compose infrastructure
                       components into complete solutions, and manage
                       changes. The entire Terraform workflow is driven by
                       stateless functions that are defined in code and
                       executed by Terraform every time you make a change.
                       This allows you to think about your infrastructure
                       as a single design that can be easily modified at
                       runtime without reloading your configuration or
                       modifying your codebase.


                       A number of IT professionals and companies use the
                       Terraform command-line interface to manage and even
                       create new infrastructure or new cloud
                       infrastructures. The terraform command-line
                       interface can provide a more robust method for
                       automating changes that would take too long to
                       perform by hand. It is a powerful tool for managing
                       infrastructure.


                # ⚓ How_to_bring_all_your_chats_into_one_with_Ferdi⠀⇛


                       Are you tired of installing Slack, Discord, and
                       many other productivity tools on your Linux system?
                       Do you wish they could all be combined into one
                       easy-to-use program? If so, you must check out
                       Ferdi.


                       Ferdi is a helpful tool for Linux, Mac OS, and
                       Windows. It consolidates programs like Slack,
                       Discord, Twitter, Google Calendar, and many other
                       apps. Here’s how to get Ferdi working on Linux.


                # ⚓ Let’s_Manage_Remote_Machine_With_NoMachine⠀⇛


                       Here we go again! Today we will see how to install
                       Nomachine to manage remote machines.


                       With the help of NX Technology, the remote service
                       enables fast remote access. The service gives an
                       experience which you have never had before. Admins
                       can connect any OS-based remote machine fast, and
                       highest quality speed with no lagging. Specifically
                       during this pandemic situation where IT Admins are
                       supposed to provide support for end-users as well
                       to manager servers. Sometimes users are not having
                       a good internet speed, in such cased lightweight
                       remote access utility can help a lot. Above all The
                       utility is not only your own server but ensures
                       secure remote access too. And Yes! that utility is
                       totally free.


                # ⚓ Find_Related_Domains_and_Subdomains_with_assetfinder_–
                  blackMORE_Ops⠀⇛


                       assetfinder is a Go-based tool to find related
                       domains and subdomains that are potentially related
                       to a given domain from a variety of sources
                       including Facebook, ThreatCrowd, Virustotal and
                       more.


                # ⚓ Getting_Started_With_Docker_Containers:_Beginners_Guide_–
                  Front_Page_Linux⠀⇛


                       Container technology is not exactly new, but it is
                       a big topic in IT. Many enterprise Linux
                       distributions do their best to let you know that
                       they also have all the tools for you to be
                       successful with container technology. If you want
                       official description and documentation, please see
                       the Reference Articles at the end of this tutorial.
                       I will use my own words to give you a brief
                       description of Docker containers. Also, I will be
                       focusing on the basics of Docker and Docker-Compose
                       here, not going into the more enterprise tools such
                       as Kubernetes.


                       [...]


                       Now that we had a quick look at the PROs and CONs,
                       it is time to move on and see what the common
                       questions about Docker might be. I had a few when I
                       started, so I took down some notes and I am going
                       to go through the very same questions, hoping that
                       by now I have found a decent answer to those.


                # ⚓ Safety_RAM:_Protecting_memory_section_with_checksum_|_SUSE
                  Communities⠀⇛


                       This particular blog post is not going to be about
                       Linux memory managements and its safety or how to
                       write a safety critical software but will touch on
                       the topic that all safety critical software must
                       address properly. This topic is Freedom From
                       Interference (FFI).


                # ⚓ How_to_Install_and_Uninstall_.deb_Files_on_Ubuntu_22.04⠀⇛


                       All Debian-based distributions. like Debian, Ubuntu
                       and Linux-Mint utilize the Deb installation package
                       format.


                       Thousands of deb packages are available in the
                       Ubuntu repository, that can be installed via Ubuntu
                       Software Center or the apt and apt-get programs
                       from the command line.


                       Unfortunately, not all applications are available
                       through Ubuntu or third-party repositories. Those
                       applications must be manually downloaded and
                       installed from the developer’s websites. You should
                       especially be cautious when installing deb packages
                       from unauthorized sources to avoid cyber threats.


                       In this article, you will learn all the different
                       ways you can install the deb packages on your
                       Ubuntu system.


                # ⚓ How_To_Install_Terraform_On_Ubuntu_/_Rocky_Linux_&_Fedora_|
                  Tips_On_UNIX⠀⇛


                       Terraform is an open-source Infrastructure as a
                       code software tool developed by HashiCorp.it allows
                       you to manage your infrastructure by Codifying APIs
                       into declarative configuration files.


                       This tutorial will be helpful for beginners to
                       download terraform and install Terraform on Ubuntu
                       20.04 LTS, Ubuntu 18.04, Debian 10, Fedora 35, and
                       Rocky Linux 8.


                # ⚓ How_to_Install_Gitlab_on_Ubuntu_20.04_LTS_Focal_fossa_Linux
                  2022_Tip_–_Bollyinside⠀⇛


                       This tutorial is about the How to Install Gitlab on
                       Ubuntu 20.04 LTS Focal fossa Linux. We will try our
                       best so that you understand this guide. I hope you
                       like this blog How to Install Gitlab on Ubuntu
                       20.04 LTS Focal fossa Linux. If your answer is yes
                       then please do share after reading this.


                # ⚓ Transfer_Files_Between_Dropbox_And_Google_Drive_With_Rclone
                  –_OSTechNix⠀⇛


                       Rclone has a wealth of features. Generally, Rclone
                       is used to copy files from the local drive to a
                       cloud storage provider like Dropbox or Google Drive
                       and vice versa. How about copying files between two
                       different cloud providers? Yes, It is also
                       possible! In this brief guide, we will see how to
                       transfer files between Dropbox and Google Drive
                       with Rclone in Linux.


                       As you may already aware, Rclone doesn’t use the
                       local drive while synchronizing files between two
                       different cloud providers. Rclone employs server-
                       side transfers to minimize the local bandwidth use
                       and transfers the data from one provider to another
                       without using local disk. Hence, it reduces disk
                       writes and local network bandwidth significantly.


                # ⚓ How_To_Install_Putty_SSH_Client_on_Debian_11_–_idroot⠀⇛


                       In this tutorial, we will show you how to install
                       Putty SSH Client on Debian 11. For those of you who
                       didn’t know, PuTTY is an open-source, lightweight,
                       and free (MIT license) terminal emulator, serial
                       console, and network file transfer application. It
                       supports various protocols including SSH, telnet,
                       SCP, rlogin, etc.


                       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 Putty SSH Client on a
                       Debian 11 (Bullseye).


                # ⚓ 3_Ways_to_Install_Discord_Messenger_App_on_Ubuntu_–_VITUX⠀⇛


                       Discord is a well-known communication (messenger)
                       program. Discord can be used to communicate via
                       text, images, video, and audio.


                       It was created with gamers in mind, but the service
                       has grown in popularity among non-gamers to the
                       point where it is now regarded as a Slack
                       alternative for team and community collaboration.
                       Chat rooms and voice chat platforms make servers in
                       Discord.
                       Various open-source projects use Discord to
                       communicate with users and project members.


                       Discord runs on a variety of platforms, including
                       desktop Linux. This tutorial shows three different
                       ways to install Discord on Ubuntu 20.04 and newer:
                       Discord Installation on the command-line, Discord
                       Installation via Ubuntu Desktop GUI, and finally
                       Discord Installation via SNAP package manager.


                # ⚓ Grafana_Weather_Dashboard_using_InfluxDB_and_an_ESP32_–_In-
                  Depth_Tutorial_–_The_DIY_Life⠀⇛


                       Following one of my previous projects where I built
                       a weather station dashboard using InfluxDB and
                       Grafana on the reTerminal, I had quite a few
                       requests to do a more in-depth tutorial on how to
                       get each part set up and running. So in this
                       tutorial, I’m going to be going through each part
                       of the process, step-by-step, so that you can get a
                       similar setup running on your Raspberry Pi.


                       In this example, we’re going to use an ESP32 as our
                       data collection node to collect temperature,
                       humidity and pressure readings from some attached
                       sensors. It’ll then post these readings to an
                       InfluxDB database and we’ll then use Grafana to
                       visualise the data. Don’t worry if you don’t
                       understand what these are or how they work together
                       just yet, I’ll explain them each in more detail as
                       we work through them.


                # ⚓ Slackware_Cloud_Server_Series,_Episode_2:_Identity_and
                  Access_Management_(IAM)⠀⇛


                       This is the second episode in a series of articles
                       I am writing about using Slackware as your private/
                       personal ‘cloud server’ while we are waiting for
                       the release of Slackware 15.0.
                       Below is a list of past, present and future
                       episodes in the series. If the article has already
                       been written you’ll be able to access it by
                       clicking on its subject.
                       The first episode also contains an introduction
                       with some more detail about what you can expect
                       from these articles.


                # ⚓ Using_PIV_Smartcard_in_FreeIPA⠀⇛


                       Personal Identity Verification (PIV) is a standard
                       proposed by the US government for identification
                       and now is supported by various smart cards and USB
                       secure tokens. FreeIPA have supported
                       authenticating with PIV certificate but is not
                       enabled by default. In this article, I’ll cover how
                       to use PIV authenticate from user perspective with
                       an existing FreeIPA that enabled the corresponding
                       support.


                       In this article, I’m using a CanoKey Pigeon with
                       the ykman command from Yubico. It should work
                       exactly the same with Yubikey (just omit the -
                       r canokeys from all my following commands). If you
                       use other secure token for storing your
                       certificate, you should consult your token
                       provider.


                # ⚓ User_interfaces_with_dialog._Bash_scripting(IV)_–_Unix_/
                  Linux_the_admins_Tutorials⠀⇛


                       This is the last article of a series focused in Gnu
                       Bash scripting. On the first article we’ve just
                       created a simple script with commands, one after
                       another. We also saw some variables use.


                       The second article covered some bash control
                       structures. The third one covered redirections,
                       pipes, and command substitution.
                       On this last (for now) one, I will show how to
                       create user interfaces with dialog in our scripts.


          o § Games⠀➾


                # ⚓ Pocket-Sized_Doom_Is_Actually_Playable_|_Hackaday⠀⇛


                       It used to be that you needed a well-equipped
                       expensive new beige-box PC if you wanted to play
                       Doom at all. Now, you can do so in a form factor
                       with a footprint smaller than a credit card, as
                       demonstrated by this nifty little build from
                       Adafruit.


                       The build relies on the Retro-Go firmware for ESP32
                       devices, which can emulate a range of machines,
                       from the Nintendo NES and Game Boy to the NEC PC
                       Engine, Atari Lynx, and, yes, Doom itself. It can
                       even run Doom mods, via the WAD architecture used
                       by the game.


                # ⚓ Valve_Confirms_Steam_Deck_Will_Launch_Feb_25th_2022_–
                  Boiling_Steam⠀⇛


                       So Valve has decided to break the silence and has
                       announced that the Steam Deck will officially
                       release on Feb 25th for consumers. On that day, if
                       you were one of the first pre-orders, you will
                       receive an email from Valve to complete your
                       payment and you will have three days to act on it.
                       If you complete your order, the first unit will
                       ship on the 28th and be a few days later in the
                       hands of the first happy gamer.


                # ⚓ X4:_Foundations_5.00_gets_a_Beta_with_AMD_FidelityFX_Super
                  Resolution_(FSR)_|_GamingOnLinux⠀⇛


                       Egosoft continue upgrading their space sim X4:
                       Foundations with the big 5.00 version now in Beta,
                       readying up for the new X4: Tides of Avarice
                       expansion. This free update should release in full
                       with the expansion, and further advances their game
                       engine to provide a better space travel experience.


                       For some of what to expect in the free update you
                       will see a series of new big capital ships,
                       improved ship models and the big one for fans of
                       performance is the introduction of AMD FidelityFX
                       Super Resolution (FSR). New game mechanics will
                       also come along including ship salvaging and
                       recycling, plus an overhaul to your headquarters.
                       That’s just a small slice of what to expect
                       (there’s plenty more). Want to test it early? You
                       can! Find out how on their official forum.


                # ⚓ The_great_cartoony_adventure_Zniw_Adventure_is_now_on_GOG_|
                  GamingOnLinux⠀⇛


                       For those of you who stick to GOG.com, you can now
                       grab another quality cartoony point and click
                       adventure game with Zniw Adventure now available. A
                       good excuse to remind you of this absolute little
                       gem.


                       Inspired by adventure games and edutainment titles
                       from the 90′s, Zniw Adventure is a 2D point and
                       click title full of cartoon dinosaurs. It features
                       a comic book-esque art style, frame-by-frame
                       animation, and unlockable goodies like concept art
                       and minigames. The in-game encyclopedia fills as
                       you encounter prehistoric creatures allowing you to
                       read more about them. Enjoy the prehistoric world
                       in an unique cartoony style.


                # ⚓ SDL_2.0.22_will_default_to_Wayland_on_Linux_|
                  GamingOnLinux⠀⇛


                       Simple DirectMedia Layer (SDL) is one of the most
                       important pieces of open source for Linux gamers,
                       as it’s the tech used by various game engines and
                       games. It’s also about to continue changing the
                       game for the Linux desktop in the upcoming version.


                       What does it actually do? It’s a cross-platform
                       development library designed to provide low level
                       access to audio, keyboard, mouse, joystick, and
                       graphics hardware.


                # ⚓ A_look_at_Steam’s_top_releases_of_December_2021_on_Linux
                  and_Steam_Deck_|_GamingOnLinux⠀⇛


                       The latest report is out from Valve on what was
                       popular and sold well during December 2021. Let’s
                       take a look at what to expect from the list in
                       terms of basic compatibility on Linux and the Steam
                       Deck.


                       Each month Valve goes over the previous month to
                       show off games doing well, with it including titles
                       across different genres and both Early Access
                       titles and full releases. As usual, it’s a mix
                       between native Linux games and those that require
                       running the Windows version through Steam Play
                       Proton.


                # ⚓ Free_Software_game_“0_A.D.:Empires_Ascendant”_with
                  Stanislas_Dolcini⠀⇛


                       The upcoming “I Love Free Software Day” will focus
                       on Free Software Games. One of the most famous Free
                       Software Games is “0 A.D.: Empires Ascendant”. In
                       this Episode Bonnie Mehring talks with Stanislas
                       Dolcini, the project leader of 0 A.D. about the
                       game itself, the project, as well has how the game
                       became Free Software.


                       This podcast episode takes you on a journey through
                       the games development and it’s history of becoming
                       one of the most famous Free Software games. You can
                       also learn about how to participate and contribute
                       to 0 A.D. Discover together with Stanislas and
                       Bonnie how the community behind one of the best
                       known Free Software games works, where support is
                       needed, and the different types of developers and
                       contributors. Bonnie and Stanislas also tell the
                       success story of releasing 0 A.D. under a Free
                       Software licensed and talk about the positive side
                       of developing a Free Software game.


          o § Desktop Environments/WMs⠀➾


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


                      # ⚓ Release_Manager_Gives_Community_Update_On_Desktop
                        Environment⠀⇛


                             The openSUSE community received cheerful news
                             today after Leap release manager Luboš Kocman
                             updated the community on the desktop
                             environment expected for the next minor
                             release.


                             Leap 15.4, which is in the alpha phase of the
                             software release cycle, is planned to have
                             updated desktop environments.


                             Kocman’s email “KDE Plasma 5.24 LTS will be
                             in Leap 15.4” informed contributors on the
                             Project’s Factory mailing list that all the
                             “dependencies are already submitted” to SUSE
                             Linux Enterprise. Leap is built with the same
                             source code and exact same binary packages as
                             SLE.


                # § GNOME Desktop/GTK⠀➾


                      # ⚓ GNOME_Shell_is_Getting_Redesigned_Volume/Brightness
                        Pop_Ups⠀⇛


                             Right now, OSD bubbles in GNOME Shell look a
                             lot like this…


                             Although macOS uses big boxy pop-ups when a
                             user bashes the volume, brightness, etc key
                             both Windows 11 and ChromeOS use modestly
                             sized on-screen indicators, as do most mobile
                             OSes. Those are just as useful as GNOME’s
                             current toasts but don’t obscure as much of
                             the screen.


                             With some mockups in hand, GNOME devs got to
                             work on creating a set of subtler OSDs. Now a
                             merge request opened by Florian Müllner that
                             contributes the code needed to implement
                             them. He shares a screenshot of design
                             changes in his merge request, which you can
                             see below…


          o § Distributions⠀➾


                # ⚓ 8_Best_Rolling_Release_Linux_Distros_to_try_in_2022⠀⇛


                       Well, before hopping into the list of Linux
                       distros, let’s first understand what exactly is the
                       rolling-release distribution.


                       It is a distribution that releases the updates of
                       each of the programs that it includes at the moment
                       that it is proven that the program is in a stable
                       version. To clear it, let’s take the example of
                       Arch and Ubuntu. Arch is a rolling release Linux
                       distro because its developers offer the latest
                       upgrade & updates of kernel and software as soon as
                       their least stable versions are available.


                # § New Releases⠀➾


                      # ⚓ Nix_2.6.0_released⠀⇛


                             Nix 2.6.0 has been released!


                             Nix is a tool that takes a unique approach to
                             package management and system configuration.
                             Learn how to make reproducible, declarative
                             and reliable systems.


                # § SUSE/OpenSUSE⠀➾


                      # ⚓ IDG_study_“Cloud_Native_2022”:_Where_do_European
                        companies_stand_in_their_digital_transformation? [Ed:
                        IDG as corporate propaganda platform, hardly even
                        hiding it anymore]⠀⇛


                             The modernisation of IT infrastructure is
                             picking up speed, but most companies still
                             see a lot of room for improvement in their
                             digital transformation. This is the
                             conclusion of a recent study conducted by IDG
                             Research Services in collaboration with SUSE.
                             Even if in some cases the extent of
                             implementation differs significantly, the
                             companies surveyed from Germany, France and
                             the UK agree on one point: the time to deploy
                             cloud-native technologies is now.


                      # ⚓ openSUSE_Conference_Design_Contest_Begins_–_openSUSE
                        News⠀⇛


                             openSUSE begins an image design contest for
                             the openSUSE Conference 2022 today. The
                             design will be used for the conference poster
                             and t-shirt.


                             Submitted images must meet certain
                             requirements listed below and on the contest
                             wiki page. Designers are encouraged to use
                             open-source graphic editing software like
                             Inkscape, Gimp or Krita.


                             Submitted designs should be licensed under
                             CC-BY-SA 4.0 and allow everyone to use it
                             without attribution. Designs submitted must
                             be original and should not include any third
                             party materials conflicting with CC-BY-SA
                             4.0.


                      # ⚓ The_Evolution_of_Linux:_a_success_story_from_Fujitsu
                        and_SUSE_|_SUSE_Communities [Ed: Revisionism that omits
                        GNU]⠀⇛


                             Technological innovations are often
                             considered to be ideas and solutions that
                             take off immediately. But the evolution of
                             Linux tells a different story: From humble
                             beginnings in the 1990s, Linux has grown
                             slowly and steadily to become a leading
                             operating system in the business world, and
                             now a business-critical operating system to
                             run SAP. During this time, Fujitsu and SUSE
                             have continued to innovate together, helping
                             businesses everywhere to realize the benefits
                             of Linux by running their SAP applications on
                             it. I caught up with Jürgen Ellwanger and
                             Martin Werner at the Global Fujitsu SAP
                             Competence Centre to find out more about how
                             Fujitsu and SUSE supported the evolution of
                             Linux through a partnership of collaboration
                             and innovation.


                # § Arch Family⠀➾


                      # ⚓ Archinstall_2.3.1_Released_With_PipeWire_App_Profile
                        Added,_Btrfs_Install_Improvements_–_Phoronix⠀⇛


                             Archinstall as the quick and easy-to-use
                             installer for the Arch Linux distribution is
                             out with a new point release delivering a few
                             worthwhile enhancements to the text-based OS
                             installer.


                             Over the past year Archinstall has evolved
                             into a great option found on the Arch Linux
                             install media for providing a timely and
                             somewhat default configuration (at least
                             easily reproducible) of an Arch Linux
                             installation. Archinstall is great for
                             quickly deploying an Arch Linux install
                             without the hassles or without resorting to
                             the various desktop-focused Arch downstreams
                             like Manjaro and EndeavourOS.


                      # ⚓ Arch_Linux’s_Guided_Installer_Archinstall_2.3.1_Comes
                        With_Improved_BTRFS_and_Pipewire_Support_–_It’s_FOSS
                        News⠀⇛


                             In April last year, Arch Linux started
                             including a command line based guided
                             installer called Archinstall.


                             If you think that’s not much when compared to
                             the graphical installer of Ubuntu, Manjaro or
                             other distributions, you are right. But you
                             should also know that something is better
                             than nothing. Before the inclusion of
                             Archinstall, you were totally on your own for
                             installing Arch Linux and that’s not pretty
                             if you don’t refer to a guide.


                             Archinstall makes things a bit easier by
                             suggesting the installation steps even though
                             it is completely command line based. It’s
                             just a script after all.


                # § IBM/Red Hat/Fedora⠀➾


                      # ⚓ DevSecOps:_Why_you_should_care_and_how_to_get_started
                        |_Red_Hat_Developer⠀⇛


                             The increasing popularity of DevOps software
                             development methodologies has led to shorter
                             and more agile life cycles, in which software
                             is released and deployed in minutes or hours
                             rather than the days, weeks, or even months
                             required under traditional practices.
                             However, many development teams still
                             experience delays in getting releases into
                             production due to the security considerations
                             that are traditionally brought to bear at the
                             end of the life cycle. To address this,
                             organizations are more and more frequently
                             adopting a DevSecOps approach.


                      # ⚓ Let’s_try_to_do_marketing_as_a_team_again!⠀⇛


                             I’ve announced in the Mindshare, Design and
                             Ambassadors mailing lists that I will try to
                             revive the Marketing team.


                             Previously the marketing team was in charge
                             of several tasks related to how the Fedora
                             Project displays information to the public,
                             working closely with Design, that produces
                             assets, and Ambassadors, who attend events
                             promoting Fedora Linux and the Fedora
                             Project. The work of the team mostly focused
                             on communicating the changes and new features
                             in each release as bullet points that
                             Ambassadors could use in their events.


                      # ⚓ Discover_and_remediate_security_vulnerabilities
                        faster_with_Red_Hat_Insights⠀⇛


                             I woke up this morning and heard about the
                             latest vulnerability in my news feed. Today
                             it was polkit/pwnkit, a couple weeks ago it
                             was something else. (And another will be
                             along shortly, no doubt.) When these come out
                             the impact on IT teams are huge and for
                             anyone responsible for managing systems, one
                             of your first thoughts is “am I exposed and
                             to what extent?”


                             If you are using Red Hat Enterprise Linux
                             (RHEL), you can use Red Hat Insights to find
                             out what systems are exposed, and to what
                             extent.


                      # ⚓ What’s_new_for_developers_in_Java_18⠀⇛


                             In exciting news for Java developers, Java 18
                             forked off from the main line at the end of
                             last year and has entered Rampdown Phase Two.
                             This article highlights some of the features
                             that developers can look for in the upcoming
                             Java 18 release, including the new simple web
                             server module, a more sophisticated way to
                             annotate your Javadocs, and the
                             –finalization=disabled option, which lets you
                             test how a Java application will behave when
                             finalization is removed in a future release.
                             See the end of the article for where to
                             download Java 18 in early access builds.


                      # ⚓ IT_leadership:_3_practices_to_let_go_of_in_2022⠀⇛


                             While many organizations’ IT teams have
                             toiled away in obscurity for years, the last
                             two decades have increasingly shined a
                             spotlight on the critical role they play. IT
                             has become a zeitgeist in the business world,
                             especially since the pandemic.


                             An increase in remote workers over the last
                             two decades and the pandemic have accelerated
                             greater demand for faster, better, more
                             secure IT practices and infrastructure.
                             Today, employers and employees alike have
                             lofty and varied expectations for their
                             organizations’ technology.


          o § Devices/Embedded⠀➾


                # ⚓ BTT_SKR_Pico_–_A_Raspberry_Pi_RP2040_based_3D_printer
                  control_board⠀⇛


                       BigTreeTech BTT SKR Pico V1.0 is a 3D printer
                       controller board based on Raspberry Pi RP2040 MCU,
                       compatible with Raspberry Pi Linux SBC’s, and
                       specially designed for the compact Voron 0 3D
                       printer, but also working with other models.


                       The board comes with four TMC2209 motor drivers
                       covered by a heatsink for cooling, as well as
                       interfaces for temperature sensors, and a USB Type-
                       C port to connect to the host computer, usually a
                       Raspberry Pi board running Linux.


                # ⚓ Vu_Premium_TV_32-inch_with_Bezel-Less_Design,_Linux_OS
                  Launched_in_India:_Price,_Specifications_–_MySmartPrice⠀⇛


                       Vu, India’s popular online smart TV brand has
                       announced a new TV under the Premium series. The
                       company has unveiled the Vu Premium TV 32-inch in
                       India today. Previously, the company had announced
                       Vu QLED Premium TV in India with Android 11, Dolby
                       Vision, and 40W speakers. The newly launched
                       Premium TV 32-inch comes with features like a
                       premium bezel-less design, Linux OS, and more for
                       under Rs 15,000.


                # § Open Hardware/Modding⠀➾


                      # ⚓ PIR_Motion_Sensor_with_Arduino_Uno:_hc-sr501_Wiring,
                        Setup,_and_Coding_–_peppe8o⠀⇛


                             Detecting motion inside a monitoring area,
                             such as security area or home restricted
                             place, requires monitoring all the object
                             moves within thas perimeter. The PIR sensor
                             (HC-SR501) with Arduino is a good and cheap
                             option, as it has ability to measure up to 7
                             meters


                      # ⚓ This_dad_converted_a_Power_Wheels_into_a_DIY_fire
                        truck_toy,_complete_with_a_siren_and_lights_|_Arduino
                        Blog⠀⇛


                             After searching everywhere for an affordable
                             ride-on fire truck toy for his daughter this
                             past Christmas season YouTuber Jason Altice
                             (AKA CodeMakesItGo) had nearly given up, but
                             luckily enough was able to locate a free
                             Grave Digger Power Wheels that he could
                             modify into one. In its current condition,
                             the vehicle was in bad shape so it had to
                             first be almost completely disassembled,
                             which led to the discovery of a bad switch
                             that was causing the troubles.


                             Upon removing each panel and meticulously
                             painting it with coats of primer and bright
                             red paint, Altice moved onto the next step of
                             including a loud siren and some lights for
                             additional realism. He took an Arduino Nano,
                             loaded some sounds in the form of tone
                             melodies, and then ran the outputted signal
                             from the digital pin to an amplifier and
                             onwards to the horn.


                      # ⚓ This_Arduino_monitor_helps_prevent_bedridden_patients
                        from_getting_pressure_sores_and_more_|_Arduino_Blog⠀⇛


                             For people who are recovering from a major
                             surgery or those who have a disability,
                             ensuring proper posture while lying down for
                             extended periods of time is vital for
                             reducing joint pain and other ailments that
                             come about from a lack of movement, including
                             pressure sores. Rodrigo Mejiasz’s project
                             aims to solve the issue by using a small
                             device that monitors how long a patient has
                             been lying down in one position and alerts a
                             caregiver when it’s time to adjust them.


                      # ⚓ Monitor_For_Bedridden_Patients_Aims_To_Improve_Care_|
                        Hackaday⠀⇛


                             One of the joys of being a Maker and Hacker
                             is solving problems and filling needs. When
                             you can do both, well, that’s something
                             special. [rodrigo.mejiasz]’s project surely
                             fits into that special category of solving a
                             problem and filling a dire need with his
                             Bedridden Patient Monitor.


                             While [Rodrigo]’s project page does not
                             specify his motivation for creating this
                             project, one only needs to look as far as
                             their local hospital ward or senior care
                             facility to understand why this device is so
                             wonderful. Healthcare workers and caregivers
                             are stretched paper thin, and their attention
                             is being constantly interrupted.


                # § Mobile Systems/Mobile Applications⠀➾


                      # ⚓ Android_updates:_Features_aren’t_the_problem,
                        security_is_–_9to5Google⠀⇛


                      # ⚓ Widespread_FluBot_and_TeaBot_Malware_Campaigns
                        Targeting_Android_Devices⠀⇛


                      # ⚓ Samsung:_Android_updates_even_faster_in_the_future?_|
                        NextPit⠀⇛


                      # ⚓ Full_Android_on_a_smartwatch:_ridiculous_or_awesome?
                        –_PhoneArena⠀⇛


                      # ⚓ 8_of_the_best_Android_Auto_apps_available_in_2022⠀⇛


                      # ⚓ Realme_Pad_will_get_Android_12_&_3_years_of_security
                        updates_–_9to5Google⠀⇛


                      # ⚓ Shield_TV_will_get_Android_11_bug_fixes_soon_–
                        9to5Google⠀⇛


                      # ⚓ How_to_enable,_disable,_and_schedule_dark_mode_on
                        Android_–_Phandroid⠀⇛


                      # ⚓ No,_our_Android_app_doesn’t_contain_a_virus._It’s_a
                        false_positive_from_AVG._–_GSMArena.com_news⠀⇛


                      # ⚓ Why_Is_Android_Named_“Android?”⠀⇛


                      # ⚓ Sigfox_is_in_financial_trouble_–_CNX_Software⠀⇛


                      # ⚓ Samsung_Galaxy_A52s_5G_Getting_One_UI_4.0_Update
                        Based_on_Android_12_in_India_and_Europe:_Report_|
                        Technology_News⠀⇛


                      # ⚓ Magisk_v24.0_adds_Android_12_support,_debuts_Zygisk,
                        plus_more_–_9to5Google⠀⇛


                      # ⚓ Latest_Tap,_Tap_update_brings_Android_12_‘Columbus’
                        gesture_code_implementation,_Material_You_theming,_and
                        more⠀⇛


                      # ⚓ Xiaomi_Redmi_Note_11:_Budget_smartphone_announced
                        globally_for_US$179_with_a_Snapdragon_680_SoC,_Android
                        11_and_MIUI_13_–_NotebookCheck.net_News⠀⇛


                      # ⚓ OnePlus_9_gets_LineageOS_18.1_based_on_Android_11_–
                        Gizchina.com⠀⇛


                      # ⚓ Tecno_Pop_5X_debuts_with_Android_10_Go,_Unisoc
                        chipset_–_GSMArena.com_news⠀⇛


                      # ⚓ Samsung_may_speed_up_its_Android_updates_in_Europe_–
                        GSMArena.com_news⠀⇛


                      # ⚓ Huawei_is_back!_Exciting_new_phones_launching_soon
                        but_Android_fans_will_be_disappointed_|_Express.co.uk⠀⇛


                      # ⚓ Micromax_In_Note_2_Review:_Cleanest_Android
                        Experience_‘In’_This_Segment⠀⇛


                      # ⚓ Watch_The_Super_Bowl_On_The_65-inch_Sony_X85J_Android
                        TV_For_Only_$798⠀⇛


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


                # § Events⠀➾


                      # ⚓ The_FSFE_at_FOSDEM_2022_–_FSFE⠀⇛


                             This year’s edition will be kicked off by a
                             talk of Masafumi Ohta, teaching on Free
                             Software license and compliances at the
                             University of Electro-Communications in Japan
                             at 13:00 CET. In his talk, Ohta addresses the
                             issue on “How to teach OSS licenses and
                             compliances at a university”.


                             At 13:30 CET, Italo Vignoli, a well-known
                             Free Software advocate and a marketing and
                             public relations consultant, gives a
                             presentation on “Why the pandemic could help
                             FOSS, but was a win for proprietary
                             software”.


                      # ⚓ FOSDEM_2022_schedule_with_embedded_Linux,_IoT,
                        automotive…_sessions_–_CNX_Software⠀⇛


                             While typically taking place in Brussels,
                             Belgium, FOSDEM 2022 will take place online
                             just like FOSDEM 2021 due to COVID-19
                             restrictions. The good news is that it means
                             anybody can attend it live from anywhere in
                             the world, and makes it more like “FOSDIM”,
                             replacing European with International, in
                             “Free and Open Source Developers’ European
                             Meeting”.


                             FOSDEM 2022 will take place on February 5-
                             6 with 637 speakers, 718 events, and 103
                             tracks. I’ve made my own little virtual
                             schedule below mostly with sessions from the
                             Embedded, Mobile and Automotive devroom, but
                             also other devrooms including “Computer Aided
                             Modeling and Design”, “FOSS on Mobile
                             Devices”, “Libre-Open VLSI and FPGA”, and
                             others.


                      # ⚓ Talking_digital_with_Brian_Kernighan_|
                        Opensource.com⠀⇛


                             Brian Kernighan has written many popular
                             books about programming, computers, and
                             technology. My own bookshelf includes several
                             books authored or co-authored by Kernighan,
                             including The C Programming Language, Unix: A
                             History and A Memoir, The AWK Programming
                             Language, and others. I just added another
                             book by Kernighan, Understanding the Digital
                             World: What You Need to Know about Computers,
                             the Internet, Privacy, and Security, Second
                             Edition, published in 2021 by Princeton
                             University Press.


                      # ⚓ Australia/NZ_Linux_Meetings_«_etbe_–_Russell_Coker⠀⇛


                             I am going to start a new Linux focused FOSS
                             online meeting for people in Australia and
                             nearby areas. People can join from anywhere
                             but the aim will be to support people in
                             nearby areas.


                             To cover the time zone range for Australia
                             this requires a meeting on a weekend, I’m
                             thinking of the first Saturday of the month
                             at 1PM Melbourne/Sydney time, that would be
                             10AM in WA and 3PM in NZ. We may have corner
                             cases of daylight savings starting and ending
                             on different days, but that shouldn’t be a
                             big deal as I think those times can vary by
                             an hour either way without being too
                             inconvenient for anyone.


                             Note that I describe the meeting as Linux
                             focused because my plans include having a
                             meeting dedicated to different versions of
                             BSD Unix and a meeting dedicated to the HURD.
                             But those meetings will be mainly for Linux
                             people to learn about other Unix-like OSs.


                # § Web Browsers⠀➾


                      # § Mozilla⠀➾


                            # ⚓ Thunderbird_–_Hotkeys_Shortcuts_Cheatsheet⠀⇛


                            # ⚓ Another_Step_in_Automating_the_Pageload
                              Recordings⠀⇛


                                   In a previous article, Kimberly
                                   Sereduck told us about Updates to Warm
                                   Page Load Tests and how we are
                                   continuously working to make our tests
                                   more representative of real user
                                   behavior. Besides that, we are working
                                   on automating the process of recording
                                   the website’s page load.


                            # ⚓ Practicing_lean_data_is_a_journey_that_can
                              start_anywhere_–_Open_Policy_&_Advocacy⠀⇛


                                   “It’s not about the destination, but
                                   about the journey.” I’m sure data and
                                   privacy are the furthest from your mind
                                   when you hear this popular saying.
                                   However, after a year of virtually
                                   sharing Mozilla’s Lean Data Practices
                                   (LDP), I’ve realized this quote
                                   perfectly describes privacy, LDP, and
                                   the process that stakeholders work
                                   through as they apply the principles to
                                   their projects, products, and policies.


                                   [...]


                                   There is an appetite to understand how
                                   we as consumers can hold companies
                                   accountable. One of the biggest
                                   surprises for me came when I would
                                   field questions at the end of a
                                   presentation, and people would ask
                                   about their rights as consumers and how
                                   they can hold companies accountable.
                                   For example, people wanted to
                                   understand their rights and recourse
                                   options if companies contacted them
                                   without permission, didn’t honor their
                                   unsubscribe requests, or did something
                                   else frustrating. I teach LDP for
                                   individuals to apply it in a business
                                   context, but we are all also consumers
                                   and customers. LDP can help us better
                                   understand how our own data should be
                                   handled and improve our understanding
                                   of what organizations are doing. We can
                                   then remember how we feel about certain
                                   situations and then ensure we are doing
                                   things in a more consumer-friendly way
                                   within our organizations.


                                   Lean Data Practices is a journey. For
                                   many there won’t be an ultimate
                                   destination because it is an iterative
                                   process. If you try to apply all the
                                   principles across your entire
                                   organization at once, you will find
                                   yourself overwhelmed and likely
                                   unsuccessful. To maximize your chance
                                   of success, my advice — which is the
                                   same advice we give when we present —
                                   is to just start somewhere. Choose one
                                   aspect of your business and focus on
                                   that, one pillar at a time. Once you’ve
                                   successfully applied the principles, go
                                   to a different business unit and do the
                                   same. Remember to review and adapt as
                                   products and business needs (or data!)
                                   change as well. You may likely never
                                   reach your destination, but you will
                                   see your company improve in its
                                   practices along the way.


                            # ⚓ Tor_vs._VPN:_Is_One_Better_than_the_Other?⠀⇛


                                   Tor and VPN have unique ways to ensure
                                   user privacy on the Internet. They’re
                                   fundamentally very different yet have
                                   many similar aims. Due to the overlap
                                   in features, you may be weighing the
                                   pros and cons of using one over the
                                   other. Or maybe they can be treated
                                   equally but with separate purposes.
                                   This guide digs into everything you
                                   need to know about which software
                                   should be used for more Internet
                                   anonymity.


                            # ⚓ New_Alpha_Release:_Tor_Browser_11.5a2_(Windows,
                              macOS,_Linux)⠀⇛


                                   Tor Browser 11.5a2 is now available
                                   from the Tor Browser download page and
                                   also from our distribution directory.


                                   This version includes important
                                   security updates to Firefox.


                # § Content Management Systems (CMS)⠀➾


                      # ⚓ WordPress_5.9_Goes_Live_with_Full_Site_Editing_
                        (FSE)⠀⇛


                             WordPress 5.9 marks the introduction of the
                             next generation of themes that allows greater
                             customization and simpler building.


                             Every year, everyone is waiting to see what
                             the next version of the most popular CMS on
                             the planet is going to bring. WordPress 5.9
                             “Josephine” is the first WordPress release of
                             2022. It is named in honor of Josephine
                             Baker, an international jazz singer. The new
                             version brings improvements to WordPress that
                             will change the way many people build their
                             websites.


                # § Programming/Development⠀➾


                      # ⚓ A_deeper_look_into_the_Genesis_GV60_digital_cockpit⠀⇛


                             We announced in 2021 that Hyundai Motor
                             Company has selected Qt as their key HMI
                             technology partner for all Hyundai, Kia, and
                             Genesis brands. Since then, they have
                             released their new electric luxury SUV
                             Genesis GV60, and we love it!


                      # ⚓ Dirk_Eddelbuettel:_td_0.0.6_on_CRAN:_Minor_Bugfix⠀⇛


                             The td package for accessing the twelvedata
                             API for financial data has been updated once
                             more on CRAN and is now at version 0.0.6.


                             The release comes in response to an email
                             from CRAN who noticed (via r-devel) that I
                             was sloppy (in one spot, it turns out) with a
                             logical expression resulting in an expression
                             of length greather than one. Fixed by
                             wrapping an all() around it—and the package
                             was back at CRAN minutes later thanks to
                             automated processing over their end.


                      # ⚓ Dirk_Eddelbuettel:_RcppArmadillo_0.10.8.1.0_on_CRAN:
                        Upstream_Updates⠀⇛


                             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) 950 other packages
                             on CRAN, downloaded over 22.9 million times
                             (per the partial logs from the cloud mirrors
                             of CRAN), and the CSDA paper (preprint/
                             vignette) by Conrad and myself has been cited
                             451 times according to Google Scholar.


                             This release brings another upstream update
                             10.8.0, and first bug fix release 10.8.1. As
                             updates by Conrad can come a little quicker
                             than the desired monthly cadence CRAN aims
                             for, we skipped the 10.8.0 release for CRAN
                             only but of course generally provide them via
                             the Rcpp drat repo as well as via general
                             updates to the repo, and full reverse
                             dependency testing (for which results are
                             always logged here).


                      # § Rust⠀➾


                            # ⚓ This_Week_In_Rust:_This_Week_in_Rust_427⠀⇛


    * § Leftovers⠀➾


          o ⚓ An_Appreciation_of_a_Modern-Day_Troubadour⠀⇛


                 The stage name? Meat Loaf. For Crying Out Loud. OK. How’s
                 this for a pitch in 1977 to record companies for the
                 breakthrough hit, Bat Out Of Hell? It’s a song about a
                 guy on a motorbike crashing, dying, with his heart
                 leaving his body like a bat. That song will give the
                 album its title, then we’ll have a song about a guy
                 rejecting his girl by telling her there ain’t no way I’m
                 ever going to love you and another about a man who wants
                 to end the relationship and is praying for the end of
                 time so I can end my time with you. What record producer
                 in their right mind would consider such an outlandish
                 proposal? Remember, this was the late seventies. The
                 Carter presidency. Music was polarized. In the blue
                 corner, disco. In the red, punk. Bruce Springsteen and
                 Queen were fighting the good fight but the dross seemed
                 overwhelming.  Rudely flapping its wings along comes the
                 Bat Out of Hell album with its Wagnerian overtones and
                 sense of Gotterdammerung and an overweight singer named
                 after a dish not known for its gastronomic appeal. T-bone
                 steak, roast lamb, leg of pork, roast potatoes maybe, but
                 Meat Loaf?


                 After a slow burn, something happened, word of mouth and
                 radio play resurrected it and soon, say 1978, no high
                 school or college dance was complete without a track or
                 two, especially Two Out of Three Ain’t Bad. This was
                 before MTV. It’s still appealing to young and not-so-
                 young romantics with global sales in excess of 40 million
                 and the album sales hit 200,00 a year.


          o ⚓ A_Theory_About_Conspiracy_Theories⠀⇛


                 Move forward to the year 1920, and none other than
                 Winston Churchill gave us a more modern conspiracy theory
                 when saying, “the movement among the Jews … this
                 worldwide conspiracy [is] for the overthrow of
                 civilization [it] has been steadily growing.” During the
                 1930s, Churchill’s antisemitism was, of course, out-
                 gunned by German Nazism inventing the scientific
                 hallucination of a Jewish Race.It sought to legitimize
                 the Holocaust. In the 1950s, US Senator Joe McCarthy
                 believed, “this government [will] deliver us to disaster
                 … this must be a product of a great conspiracy.”


                 Conspiracy theories are more like fantasies. They are not
                 theories in our scientific understanding. In short, a
                 theory is an explanation of an aspect of the natural or
                 social world that has been repeatedly tested, and
                 verified in accordance with scientific methods relying on
                 accepted protocols of observations, measurement, and a
                 critical evaluation of the findings produced. None of
                 this is the case when it comes to conspiracy theories.


          o ⚓ Boxed_In⠀⇛


                 Shortly after the spectacular collapse of Lehman Brothers
                 in 2008 and the global recession that came tumbling after
                 it, an Italian playwright named Stefano Massini began
                 working on a fictionalized account of the men who’d
                 founded the eponymous firm a century and a half earlier.
                 I Capitoli del Crollo, or Chapters of the Fall, saw its
                 first productions in 2010 on Italian stages, followed by
                 performances on national radio. And then the play took
                 off in various translations across Europe, drawing
                 acclaim throughout the 2010s in France, Germany, Spain,
                 and elsewhere. Despite its title, the play is mostly
                 about the rise of Lehman Brothers; it follows three
                 generations of Lehman men to tell a giddy tale about the
                 growth of their bank and, by extension, rapacious
                 American capitalism. In 2016, Massini published a 760-
                 page expanded version, Qualcosa sui Lehman (Something
                 About the Lehmans), which was billed as a novel and, like
                 the playscript, was written in a sort of Homeric free
                 verse befitting the epic ambitions of the project.


                 No doubt, part of the appeal of Massini’s work for
                 directors was the open-ended nature of the play. Written
                 in the third person, with no lines assigned to particular
                 characters, it left theater artists free to shape their
                 productions as they wished, even as they hewed to
                 Massini’s script. Some European stagings used seven
                 actors to play the Lehman men across the 164-year saga,
                 as well as the dozens of other people they encountered;
                 others used four or as many as 12.


          o ⚓ The_Tonga_Volcanic_Eruption_was_So_Intense_It_Caused_the
            Atmosphere_to_Ring_Like_a_Bell⠀⇛


                 The atmospheric wave pattern close to the eruption was
                 quite complicated, but thousands of miles away it
                 appeared as an isolated wave front traveling horizontally
                 at over 650 miles an hour as it spread outward.


                 NASA’s James Garvin, chief scientist at the Goddard Space
                 Flight Center, told NPR the space agency estimated the
                 blast was around 10 megatons of TNT equivalent, about 500
                 times as powerful as the bomb dropped on Hiroshima,
                 Japan, during World Word II. From satellites watching
                 with infrared sensors above, the wave looked like a
                 ripple produced by dropping a stone in a pond.


          o § Science⠀➾


                # ⚓ SHERLOC_And_The_Search_For_Life_On_Mars_|_Hackaday⠀⇛


                       Humanity has been wondering about whether life
                       exists beyond our little backwater planet for so
                       long that we’ve developed a kind of cultural bias
                       as to how the answer to this central question will
                       be revealed. Most of us probably imagine that NASA
                       or some other space agency will schedule a press
                       conference, an assembled panel of scientific
                       luminaries will announce the findings, and
                       newspapers around the world will blare “WE ARE NOT
                       ALONE!” headlines. We’ve all seen that movie
                       before, so that’s the way it has to be, right?


                       Probably not. Short of an improbable event like an
                       alien spacecraft landing while a Google Street View
                       car was driving by or receiving an unambiguously
                       intelligent radio message from the stars, the
                       conclusion that life exists now or once did outside
                       our particular gravity well is likely to be reached
                       in a piecewise process, an accretion of evidence
                       built up over a long time until on balance, the
                       only reasonable conclusion is that we are not
                       alone. And that’s exactly what the announcement at
                       the end of last year that the Mars rover
                       Perseverance had discovered evidence of organic
                       molecules in the rocks of Jezero crater was —
                       another piece of the puzzle, and another step
                       toward answering the fundamental question of the
                       uniqueness of life.


          o § Health/Nutrition⠀➾


                # ⚓ From_Raincoats_to_Napkins,_Toxic_‘Forever_Chemicals’_Found
                  in_Everyday_Products⠀⇛


                       Despite the existence of safer alternatives, toxic
                       “forever chemicals” linked to a wide range of
                       health problems are found in most products labeled
                       stain- or water-resistant, from rain jackets and
                       hiking pants to mattress pads, comforters, napkins,
                       and tablecloths.


                       “We need urgent action at the state and federal
                       levels to solve the PFAS crisis, including by
                       quickly stopping its use in products we wear and
                       use in our homes.”


                # ⚓ Covidian_Musings⠀⇛


                       By the time he was assassinated, he (and the
                       movement) were calling for an end to the barbarous
                       war against the people of Vietnam, a universal
                       guaranteed annual income, with  public housing and
                       healthcare as an economic right for everybody. Feel
                       free to check. In 1967, a year before he was struck
                       down in Memphis supporting the striking “sanitation
                       workers” and organizing for the Poor People’s
                       Campaign, he gave a speech at New York’s Riverside
                       Church: “Beyond Vietnam: A Time to Break Silence.”


                       He announced, “I am convinced that if we are to get
                       on the right side of the world revolution, we as a
                       nation must undergo a radical revolution of values.
                       We must rapidly begin to shift from a ‘thing-
                       oriented’ society to a ‘people-oriented’ society.
                       When machines and computers, profit motives and
                       property rights are considered more important than
                       people, the giant triplets of racism, materialism,
                       and militarism are incapable of being conquered.”
                       He named the United States as “the greatest
                       purveyor of violence in the world today.”


                # ⚓ Opinion_|_Biden_Must_Take_on_Big_Pharma_Over_Cancer_Drug
                  That_Costs_$189,000_Per_Year⠀⇛


                       What if we told you American taxpayers funded the
                       invention of a highly successful prostate cancer
                       medication, but if they need it, American prostate
                       cancer patients are forced to pay far more than
                       people living in similar nations?


                # ⚓ Dems_Sound_Alarm_as_Key_US_Vaccine_Agency_‘Running_Out_of
                  Money’⠀⇛


                       As the House Democratic leadership prepared to
                       fast-track a vote to provide $500 million in
                       additional military aid to Ukraine, a small
                       contingent of congressional Democrats argued that
                       the federal government’s immediate attention should
                       be on the United States’ flagging pandemic
                       response—particularly on the global stage.


                       In a letter to President Joe Biden on Tuesday, nine
                       Democratic lawmakers warned that the United States
                       Agency for International Development (USAID) is “a
                       little over a month away from running out of money”
                       to finance its global vaccination efforts as
                       coronavirus cases, hospitalizations, and deaths
                       remain elevated worldwide.


                # ⚓ “Takeover”:_Young_Lords’_Juan_González_on_Hospital_Protest
                  Doc._Shortlisted_for_Academy_Award⠀⇛


                       The documentary “Takeover,” which chronicles the
                       radical actions of the Young Lords, was recently
                       shortlisted for an Academy Award. In 1970, the
                       Puerto Rican collective took over a condemned
                       hospital in the South Bronx to demand the
                       construction of a new hospital, free healthcare for
                       all, and more. “I’m still amazed there’s been so
                       much interest in what we did as youngsters more
                       than 50 years ago,” says Democracy Now! co-host and
                       Young Lords founding member Juan González. “I hope
                       that some of the lessons of what we did right and
                       what we did wrong will resonate with younger people
                       these days.”


                # ⚓ College_Students_Struggle_to_Address_a_Mental_Health
                  Crisis⠀⇛


                       Around 11:30 am on December 15, a Northeastern
                       University student was found unresponsive in Snell
                       Library, one of the main libraries on campus.
                       Boston Fire and EMS arrived on the scene. Just a
                       few hours later, the Northeastern University Police
                       Department gave the library an “all clear.” The
                       student was pronounced dead in an apparent suicide.
                       The university administration’s response? Sending
                       an e-mail to all students that read, “The
                       university is making counseling and other mental
                       health services available to everyone in the
                       university community who needs support.” Finals
                       week proceeded as normal, and students began
                       shuffling into the library again. This story was
                       produced for Student Nation, a program of the
                       Nation Fund for Independent Journalism, which is
                       dedicated to highlighting the best of student
                       journalism. For more Student Nation, check out our
                       archive or learn more about the program here.
                       StudentNation is made possible through generous
                       funding from The Puffin Foundation. If you’re a
                       student and you have an article idea, please send
                       pitches and questions to [email protected].


                # ⚓ Africa_CDC_Director:_Vaccine_Inequity_Prolongs_the
                  Pandemic._Global_Cooperation_Can_Stop_New_Variants.⠀⇛


                       As new cases of the highly infectious Omicron
                       variant continue to climb in undervaccinated parts
                       of the world, we speak to the head of the Africa
                       Centers for Disease Control and Prevention about
                       how vaccine inequity could lead to even more
                       variants of the coronavirus. Dr. John Nkengasong
                       says only 10% of the population is fully immunized
                       in Africa, a continent of 1.3 billion people, and
                       millions of vaccines donated by COVAX went unused
                       because of their short shelf life. Meanwhile,
                       several countries in Africa have begun
                       manufacturing their own vaccines. “We have to shift
                       our focus to vaccinating — that is, making sure
                       that vaccines that are arriving at the airport
                       actually get into the arm of the people,” says Dr.
                       Nkengasong.


          o § Integrity/Availability⠀➾


                # § Proprietary⠀➾


                      # § Security⠀➾


                            # ⚓ Easily_Exploitable_Linux_Flaw_Exposes_All
                              Distributions:_Qualys_|_eSecurityPlanet⠀⇛


                                   An easily exploited flaw in a program
                                   found in every major Linux distribution
                                   is the latest serious security issue
                                   that has arisen in the open-source
                                   space in recent weeks.


                                   Researchers at cybersecurity vendor
                                   Qualys this week disclosed the memory
                                   corruption vulnerability in polkit’s
                                   pkexec, which if exploited by a bad
                                   actor can enable an unprivileged user
                                   to gain full root privileges on a
                                   system, giving the unprivileged user
                                   administrative rights.


                                   The vulnerability, tracked as CVE-2021-
                                   4034, has “been hiding in plain sight”
                                   for more than 12 years and infects all
                                   versions of polkit’s pkexec since it
                                   was first developed in 2009, Bharat
                                   Jogi, director of vulnerability and
                                   threat research at Qualys, wrote in a
                                   blog post.


                                   Polkit’s (formerly PolicyKit) pkexec is
                                   a component used to control system-wide
                                   privileges in Unix-like operating
                                   systems, enabling non-privileged
                                   processes to communicate with
                                   privileged processes in an organized
                                   fashion. It also can be used to execute
                                   commands with elevated privileges using
                                   the command pkexec followed by the
                                   command intended to be executed with
                                   root permission.


                            # ⚓ Serious_PwnKit_flaw_in_default_Linux
                              installations_requires_urgent_patching [Ed: Local
                              privilege escalation in systemd spun as doom for
                              "Linux"]⠀⇛


                            # ⚓ PolKit_vulnerability_can_give_attackers_root_on
                              many_Linux_distros_(CVE-2021-4034)⠀⇛


                            # ⚓ Linux_Bug_in_All_Major_Distros:_‘An_Attacker’s
                              Dream_Come_True’⠀⇛


                            # ⚓ Local_privilege_escalation_vulnerability_found
                              on_‘polkit’_program_found_on_every_Linux
                              variant⠀⇛


                            # ⚓ Linux_version_of_LockBit_ransomware_targets
                              VMware_ESXi_servers
                               [Ed: Lawrence Abrams, a Microsoft booster,
                              framing a VMware issue as "Linux"]⠀⇛


                                   LockBit is the latest ransomware gang
                                   whose Linux encryptor has been
                                   discovered to be focusing on the
                                   encryption of VMware ESXi virtual
                                   machines.


                                   [...]


                                   While ESXi is not strictly Linux, it
                                   does share many of its characteristics,
                                   including the ability to run ELF64
                                   Linux executables.


                            # ⚓ Malware_Log_Analysis:_Don’t_Let_the_HTTP_Code
                              Fool_You_–_ISPProtect⠀⇛


                                   An essential component of the analysis
                                   and cleanup of websites infected with
                                   malware is viewing and evaluating the
                                   log files. However, even here there are
                                   things to consider that might seem odd
                                   at first glance.


                            # ⚓ Security_updates_for_Thursday_[LWN.net]⠀⇛


                                   Security updates have been issued by
                                   CentOS (polkit), Debian (uriparser),
                                   Fedora (cryptsetup, flatpak, flatpak-
                                   builder, and polkit), Gentoo (polkit),
                                   Mageia (virtualbox), Red Hat (httpd24-
                                   httpd, httpd:2.4, and parfait:0.5),
                                   SUSE (clamav, log4j, python-numpy, and
                                   strongswan), and Ubuntu (vim).


                            # ⚓ FBI_Releases_PIN_on_Iranian_Cyber_Group_Emennet
                              Pasargad⠀⇛


                                   The Federal Bureau of Investigation
                                   (FBI) has released a Private Industry
                                   Notification (PIN) that provides a
                                   historical overview of Iran-based cyber
                                   company Emennet Pasargad’s tactics,
                                   techniques, and procedures to enable
                                   readers to identify and defend against
                                   the group’s malicious cyber activities.


                            # ⚓ [Slackware]_Security_updates_for_glibc_and
                              chromium⠀⇛


                                   Two reminders about security related
                                   package updates in my repositories.


                            # ⚓ Enterprise_Linux_Security_Episode_16_–_Library
                              Poisoning_–_Invidious⠀⇛


                                   We’ve discussed supply-chain attacks in
                                   the past, and now it’s time to see an
                                   actual example that happened recently.
                                   However, this particular incident is
                                   especially unique as the libraries in
                                   question were allegedly poisoned by the
                                   actual developer. In this episode, Joao
                                   and Jay discuss the recent sabotage
                                   regarding two very popular NPM
                                   libraries.


                            # § Privacy/Surveillance⠀➾


                                  # ⚓ 9th_Circuit_to_review_secrecy_of_CRS-
                                    based_travel_surveillance⠀⇛


                                         May court records related to
                                         orders requiring a travel
                                         reservations company to provide
                                         real-time updates to the U.S.
                                         government whenever a “person of
                                         interest” makes reservations for
                                         flights or other travel  be kept
                                         secret from the public, the
                                         press, and other travel companies
                                         including the airlines on which
                                         the target plans to travel?


                                         That issue is now before the 9th
                                         Circuit Court of Appeals in the
                                         case of Forbes Media and Thomas
                                         Brewster vs. the United States
                                         (Court of Appeals Docket #21-
                                         35612).


                                         The legal question before the 9th
                                         Circuit is whether courts can
                                         keep their own actions secret.
                                         That’s important, but the the
                                         underlying facts raise other
                                         issues as well.


          o § Defence/Aggression⠀➾


                # ⚓ Democrats_Urge_Biden_to_Abandon_Dangerous_Trump_Policies_on
                  Nuclear_Weapons⠀⇛


                       Ahead of the release of a key document laying out
                       the administration’s nuclear doctrine, President
                       Joe Biden is facing a fresh call from Democrats in
                       Congress to firmly reject what they see as former
                       President Donald Trump’s misguided and dangerous
                       policies on atomic weapons.


                       “It is your best chance to take bold steps that
                       reduce our reliance on nuclear weapons, elevate
                       arms control, and, retire President Trump’s new,
                       unnecessary warfighting nuclear weapons.”


                # ⚓ ‘There_Is_No_Military_Solution’:_Jayapal,_Lee_Demand
                  Diplomacy_on_Ukraine⠀⇛


                       Democratic Reps. Pramila Jayapal and Barbara Lee,
                       two top members of the Congressional Progressive
                       Caucus, implored the Biden administration on
                       Wednesday to urgently pursue a diplomatic outcome
                       in Ukraine, warning that “there is no military
                       solution” to surging tensions with Russia.


                       “Diplomacy needs to be the focus,” Jayapal (D-
                       Wash.), the chair of the CPC, and Lee (D-Calif.),
                       the head of the caucus’ Peace and Security
                       Taskforce, said in a statement.


                # ⚓ Gun-Maker_Slammed_for_‘Children’s_Assault_Rifles’_Based_on
                  AR-15⠀⇛


                       Gun control advocates on Wednesday sharply
                       condemned an Illinois-based company for recently
                       unveiling the JR-15, a long rifle inspired by the
                       AR-15 but marketed for children.


                       “The marketing of children’s assault rifles… can
                       only increase the threat of gun death and injury to
                       children.”


                # ⚓ Dems_Demand_Biden_Stop_Maintaining_Saudi_Jets_Causing
                  ‘Untold_Suffering’_in_Yemen⠀⇛


                       A group of 12 House Democrats is urging President
                       Joe Biden to suspend a contract that keeps Saudi
                       warplanes maintained and able to cause “untold
                       suffering” on the people of Yemen.


                       The letter to Biden, led by Rep. Tom Malinowski (D-
                       N.J.), comes amid an escalation in the Saudi-led
                       coalition’s bombing of Yemen and on the same day
                       United Nations officials warned that the civilian
                       death toll from the bombing campaign could break
                       records this month.


                # ⚓ Despite_Rights_Abuses,_Biden_Approves_$2.5_Billion_Arms
                  Sale_to_Egypt⠀⇛


                       The U.S. State Department on Tuesday approved a
                       sprawling $2.5 billion arms sale to Egypt even as
                       the Biden administration continues to withhold a
                       far smaller sum of military aid—$130 million—over
                       expressed concerns about human rights abuses by the
                       government of President Abdel Fattah al-Sisi, a
                       disconnect that critics said makes a mockery of
                       U.S. leaders’ rhetoric.


                       Authorized on the 11th anniversary of the 2011
                       Egyptian revolution, the weapons sale includes 12
                       Super Hercules C-130 transport aircraft as well as
                       $355 million worth of air defense radar systems.


                # ⚓ Britain’s_Forces_Eye_Australia⠀⇛


                       With the AUKUS arrangements being firmed up, US and
                       UK sailors, personnel and miscellaneous staff are
                       being readied for more time Down Under, ensuring
                       that Australia becomes a staging ground for future
                       forward military operations.  Canberra has
                       relinquished much say in this; the song sheets and
                       blueprints are coming from elsewhere.


                       The UK, reprising its long history of using
                       Australia for its own military adventurism, is keen
                       to massage the recently minted AUKUS agreement. 
                       Last week, the UK Secretary of Defence Ben Wallace
                       and Foreign Secretary Liz Truss met Dutton and
                       Australian Foreign Affairs Minister Marise Payne in
                       Sydney for annual AUKMIN talks.  The meeting had a
                       distinctly nostalgic note to it: maternal
                       Britannia, dropping in to see its rather
                       (territorially) large offspring.


                # ⚓ Truckloads_of_Guns⠀⇛


                       Incredibly, even long before this most recent
                       tragedy, the majority of police surveyed were in
                       favor of people carrying guns legally (“Police Gun
                       Control Survey: Are legally-armed citizens the best
                       solution to gun violence?” Police1, April 8, 2013).
                       The line of reasoning in the arming of civilians is
                       that armed people will stop armed criminals, or act
                       as a deterrent to potentially armed wrongdoers.


                       This discussion will not review the number of
                       police shootings of mostly people of color in the
                       US that is a well-documented issue. The insanity of
                       guns in the US always returns to the Second
                       Amendment and its underpinnings in the wild west
                       and colonial history. The Second Amendment to the
                       Constitution gave citizens the right to bear arms
                       and the right to form militias and is about as
                       useful today as someone planning to travel across
                       the US by Conestoga wagon. Part of the Second
                       Amendment also became a means to enforce racism
                       throughout US history. Segregation and racism were
                       targeted through the barrel of a gun as civil
                       rights workers found out in Mississippi in 1964.
                       Black leaders such as Martin Luther King, Jr. and
                       Malcolm X were treated similarly. Medgar Evers was
                       summarily sentenced to death at the end of a rifle
                       for his work with the NAACP, and teenager Emmett
                       Till was tortured and gunned down before being cast
                       into a river. The list is endless!


                # ⚓ Ukraine_as_Game_Board⠀⇛


                       The world watches as the squabble between US and
                       Russia heats up.  Russia moves troops around its
                       territory. Washington insists Moscow has no right
                       to move those troops near Russia’s border with
                       Ukraine.  The Pentagon is moving some of its forces
                       closer to Russia’s borders: into Poland, Latvia,
                       Lithuania among others.  Meanwhile, Kyiv continues
                       to take its orders from Washington—which helped
                       create the current political reality there when it
                       openly intervened in the electoral process in 2014
                       as part of its expansion eastward via NATO after
                       the dissolution of the Soviet Union.  The US
                       conveniently insists that Cold War-style regions of
                       influence are a relic of the past and that
                       countries should be able to choose their own
                       alliances. In other words, the US should be able to
                       expand its empire wherever it wishes.  Moscow, for
                       obvious reasons, disagrees.  The current debate
                       over Ukraine is not about freedom for the Ukrainian
                       people, but also about Moscow expanding its
                       influence into Europe at Washington’s expense.  A
                       prime example of this struggle is the Nordeast 2
                       natural gas line that enables Russian energy firms
                       to transport and sell their resource to Germany and
                       other European nations at a much cheaper rate than
                       US energy firms can sell their product in the same
                       markets.


                       Then there’s NATO.  The fact of its continued
                       existence reveals much about its true intent. NATO
                       is a tool of US empire; a military means to keep
                       the nations in the alliance under D.C.’s dominion.
                        Like the Monroe Doctrine is unofficially to Latin
                       America, NATO is to Europe.  Masquerading as a
                       benevolent protector and equal alliance of nations,
                       its true purpose is to engage other capitalist
                       nations in Washington’s pursuit of hegemony.  While
                       Washington continues to pretend that NATO exists to
                       defend freedoms that only the United States can
                       dispense, NATO continues to be part of the US
                       empire’s armed wing.  This is truer now than at any
                       time since the 1980s, when the Reagan White House
                       moved nuclear missiles into Europe despite massive
                       protests.


                # ⚓ U.S/Russian_Negotiations_and_Getting_to_Yes⠀⇛


                       But isn’t presenting your position on what is non-
                       negotiable part of negotiations? Just as 100,000
                       Russian troops on the eastern border of Ukraine are
                       part of the negotiations, Blinken’s statement about
                       non-starters is part of the general negotiating
                       process.


                       The meeting in Geneva was part of a classic
                       negotiation at the highest levels with much at
                       stake. Ever since Roger Fisher, William Ury, and
                       Bruce Patton published Getting to Yes in 1981 after
                       establishing the Harvard Negotiating Project,
                       negotiating has become a big international
                       business. The book has been translated into 35
                       languages. Paul Meerts of the Clingendael Institute
                       and the Swiss Robert Weibel among others spent
                       years training diplomats in negotiation in the
                       newly independent countries following the fall of
                       the Berlin Wall. Negotiation simulations regularly
                       take place in the private sector as well.


                # ⚓ A_Very_Long_War⠀⇛


                       Granted, during the years of schooling that
                       preceded my deployment there, I had amassed all
                       sorts of facts, some of them at least marginally
                       relevant to the matter at hand. Yet despite the
                       earnest efforts of some excellent teachers, I had
                       managed to avoid acquiring anything that could be
                       dignified with the term education. Now, however
                       haltingly, that began to change. A year later, when
                       my tour of duty ended, I carried home from Vietnam
                       the barest inkling of a question: How had this
                       massive cockup occurred and what did it signify?


                       Since that question implied rendering judgment on a
                       war in which I had (however inconsequentially)
                       participated, it wasn’t one that I welcomed. Even
                       so, the question dogged me. During the ensuing
                       decades, while expending considerable effort
                       reflecting on America’s war in Vietnam, I never
                       quite arrived at a fully satisfactory answer. At
                       some level, the entire episode remained
                       incomprehensible to me.


                # ⚓ San_Jose_Passes_First-of-Its-Kind_Insurance_Requirement_for
                  Gun_Owners⠀⇛


                # ⚓ San_José_Set_to_Pass_First-in-Nation_Gun_Liability
                  Insurance_Law⠀⇛


                       In what one gun control advocate called “a victory
                       for gun safety,” the San José City Council voted
                       Tuesday to advance a measure that would make the
                       city the first in the nation to require firearm
                       owners to carry liability insurance and pay a
                       yearly fee.


                       “Whether you’re pro-guns or anti-guns, no one can
                       argue that we have substantial injury in our
                       community and substantial issues that need to be
                       addressed.”


                # ⚓ “Gangsters_of_Capitalism”:_Jonathan_Katz_on_the_Parallels
                  Between_Jan._6_and_1934_Anti-FDR_Coup_Plot⠀⇛


                       We speak to award-winning journalist Jonathan Katz
                       about his new book “Gangsters of Capitalism:
                       Smedley Butler, the Marines, and the Making and
                       Breaking of America’s Empire.” The book follows the
                       life of the Marines officer Smedley Butler and the
                       trail of U.S. imperialism from Cuba and the
                       Philippines to Haiti, the Dominican Republic,
                       Nicaragua and Panama. The book also describes an
                       effort by banking and business leaders to topple
                       Franklin D. Roosevelt’s government in 1934 in order
                       to establish a fascist dictatorship. The plot was
                       exposed by Butler, who famously declared, “War is a
                       racket.” The far-right conspiracy to overthrow
                       liberal democracy has historical parallels to the
                       recent January 6 insurrection, says Katz.


                # ⚓ Cuba:_60_Years_of_a_Brutal,_Vindictive,_and_Pointless
                  Embargo⠀⇛


                       In mid-December, some 114 members of Congress sent
                       a forceful letter to President Joe Biden calling
                       for “immediate humanitarian actions” to lift the
                       economic sanctions “that prevent food, medicine,
                       and other humanitarian assistance from reaching the
                       Cuban people.” With Cuba struggling to emerge from
                       a dire, Covid-generated economic crisis, the
                       congressional representatives are pushing the White
                       House to end the restrictions imposed by the Trump
                       administration on remittances and travel and
                       restore the Obama-era policy of engagement with the
                       island nation. “Engagement,” the members concluded,
                       “is more likely to enable the political, economic,
                       and social openings that Cubans may desire, and to
                       ease the hardships that Cubans face today.”1


          o § Environment⠀➾


                # § Energy⠀➾


                      # ⚓ ‘Monumental_Victory’_as_Biden_Cancels_Boundary_Waters
                        Mining_Leases⠀⇛


                             Environmentalists and progressives on
                             Wednesday cheered a decision by the Biden
                             administration to cancel a pair of mining
                             leases in northern Minnesota that critics
                             warned would threaten the pristine Boundary
                             Waters Canoe Area Wilderness. 


                             “Some places are simply too special to
                              mine.” 


                      # ⚓ New_Analysis_Exposes_‘Bogus’_Job-Creation_Claims_of
                        Fossil_Fuel_Industry⠀⇛


                             Although oil and gas production increased in
                             the United States from 2010 to 2020, new
                             research out Wednesday reveals that last
                             decade’s boom coincided with a decline in
                             drilling and fracking jobs—giving lie to the
                             fossil fuel industry’s claims about its
                             positive impact on employment.


                             “Outlandish jobs claims have one goal: to
                             hype the scope and impact of the oil and gas
                             industry.”


                # § Wildlife/Nature⠀➾


                      # ⚓ This_Unsung_Aquatic_Hero_Could_Get_a_Big_Boost_From
                        Dam_Removals⠀⇛


          o § Finance⠀➾


                # ⚓ Opinion_|_It’s_Time_for_a_Global_Billionaire_and
                  Millionaire_Wealth_Tax_to_Save_Our_Living_Planet⠀⇛


                       Our politicians, flush from millionaire/billionaire
                       campaign “contributions,” like to pretend that the
                       cost of dealing with the climate and biodiversity
                       crises is prohibitively expensive and pretend that
                       we should wait until the cost of solutions come
                       down before we act, but is this really true?


                # ⚓ 80+_Dems_Tell_Biden_to_Release_Secret_Memo_on_Student_Debt
                  Authority⠀⇛


                       With the federal moratorium on student loan
                       repayments set to end in less than 100 days, dozens
                       of Democratic members of Congress on Wednesday
                       implored President Joe Biden to use his executive
                       authority to cancel at least $50,000 in student
                       debt per borrower.


                       “We can and must provide this relief to millions of
                       borrowers and their families.”


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Opinion_|_No_More_Backroom_Deals—Let_the_American_People
                  See_Who_Is_Willing_to_Fight_for_Them⠀⇛


                       The following is based on an email sent to
                       supporters of Sen. Bernie Sanders (I-Vt.) on
                       Wednesday, January 26, 2022:


                # ⚓ Supreme_Court_Justice_Stephen_Breyer_Is_Retiring,_Opening
                  Seat_for_Biden_Nominee⠀⇛


                # ⚓ Biden_Urged_to_Nominate_Black_Woman_to_Supreme_Court_as
                  Breyer_Says_He’ll_Retire⠀⇛


                       Reports that U.S. Supreme Court Justice Stephen
                       Breyer plans to retire prompted progressives
                       Wednesday to urge President Joe Biden to fulfill a
                       campaign promise and nominate a progressive Black
                       woman who will counter the high court’s right-wing
                       supermajority and protect democracy, human rights,
                       and the climate. 


                       “The status quo is failing all of us, so Biden’s
                       choice is crucial.”


                # ⚓ Pelosi_Announces_Another_Run_for_Congress,_Doesn’t_Discuss
                  Speaker_Role⠀⇛


                # ⚓ Virginia’s_Republican_Governor_Youngkin:_Trump_in
                  Sheepskins⠀⇛


                       Moreover, he said hardly a word about his sketchy
                       corporate past, beyond declaring he had been a
                       “financier” or worked in “the financial sector”. Of
                       course these designations cover a myriad of
                       types—from jailed junk bond kings in the 1980s, to
                       creators of slash-and-burn “financial instruments”
                       behind the 2008 crash (who escaped jail, how times
                       change), to bankers who oversee the provision of
                       microcredit for the poor. Youngkin is definitely
                       not among the latter.


                       Youngkin took office as Virginia’s governor on 15
                       January. Two days later he gave his inauguration
                       speech. Here are some key points from Youngkin’s
                       address:


                # ⚓ Opinion_|_Fox_News’_Favorite_Economic_Pundit_Ain’t_Joe
                  Manchin._It’s_Somebody_Even_Worse⠀⇛


                       FOX News is exultant! Not only have they found a
                       new Senate hero in Joe Manchin—a Democrat no
                       less—but also in one of the Democratic party’s past
                       policy stalwarts, Harvard Professor Larry Summers.
                       In addition to having briefly served as President
                       of that supposed bastion of American liberal
                       thought, Summers has served as Secretary of The
                       Treasury under President Clinton, and as the Chief
                       Economist of the World Bank, which, for Trump
                       world, is an instrument for strengthening big
                       government globally and, God forbid,
                       multilateralism!


                # ⚓ Manchin_Internationally_Reviled_Over_Climate_Obstruction⠀⇛


                       The threat Sen. Joe Manchin poses to the planet by
                       refusing to back ambitious climate legislation has
                       not gone unnoticed by people in parts of the world
                       that are most at risk for destruction from global
                       heating, according to new reporting.


                       As The Guardian reported Wednesday, the right-wing
                       Democrat who represents West Virginia has gained
                       infamy in the Global South, including in the
                       Marshall Islands, where 96% of the capital city of
                       Majuro is at risk for frequent flooding due to
                       rising sea levels.


                # ⚓ Nina_Turner_Announces_Run_for_Congress_in_Likely_Rematch
                  Against_Shontel_Brown⠀⇛


                # ⚓ ‘On_the_Side_of_the_People’:_Nina_Turner_Launches_New
                  Congressional_Run_in_Ohio⠀⇛


                       Democrat Nina Turner announced Wednesday she’s
                       running again to represent Greater Cleveland in
                       U.S. Congress, bringing back an agenda of
                       priorities like Medicare for All, a living wage,
                       and recurring federal relief amid the ongoing
                       pandemic, and a fresh promise to be a fighter for
                       “a progressive future that works for all.”


                       “Greater Cleveland needs… a leader who knows
                       poverty is a policy choice.”


          o § Censorship/Free Speech⠀➾


                # ⚓ The_Project_Censored_Newsletter—January_2022_–_Censored
                  Notebook,_Newsletters⠀⇛


                       Project Censored has received a grant from the Free
                       Press to support our media literacy educational
                       programs. The grant will fund at least three new,
                       paid summer internships, enhancements to the weekly
                       radio show, and expansion of the Project’s Campus
                       Affiliates Program, which includes our critical
                       media literacy curriculum and educator development.
                       Stay tuned for more details as we put this welcome
                       support to work.


                # ⚓ Devin_Nunes,_CEO_Of_Trump’s_TRUTH_Social,_Confirms_That
                  ‘Free_Speech’_Social_Media_Will_Be_HEAVILY_Moderated⠀⇛


                       It’s never been a secret that for all of the public
                       claims about how Donald Trump’s upcoming social
                       network “TRUTH Social” will be for “free speech”
                       that this was never actually the plan. We noted
                       right up front that its terms of service appeared
                       to be way more restrictive than all the competitors
                       it was criticizing — and even said it would be a
                       violation of terms to “annoy” anyone working for
                       the site. When Rep. Devin Nunes — who has a long
                       history of suing people for criticizing and mocking
                       him (i.e., no friend of free speech) — announced he
                       was retiring from Congress to become CEO of Trump’s
                       social network, we noted that he’d be quick to ban
                       people on the site.


          o § Civil Rights/Policing⠀➾


                # ⚓ Rights_Groups_Demand_Hearings_on_the_‘Fourth_Amendment_Is
                  Not_For_Sale_Act’⠀⇛


                       More than four dozen consumer advocacy, media
                       justice, and privacy rights groups on Wednesday
                       urged the Senate and House Judiciary Committees to
                       hold hearings on the Fourth Amendment Is Not For
                       Sale Act—a bill meant to curb warrantless mass
                       surveillance—as soon as possible.


                       “This legislation would stop this flagrant abuse of
                       our privacy and shut down a clandestine business
                       sector that trades away our essential rights for
                       profit.”


                # ⚓ Republicans_Tripped_Up_by_Their_Anti-
                  Citizens Initiative Law⠀⇛


                       To make a long story much shorter, it’s no news to
                       anyone that Montana and national property values
                       have skyrocketed in the last few years. The median
                       price for a home in the U.S. right now is $375,000.
                       In Montana the median price is $359,678. The
                       incredible increase in the cost of owning a home is
                       great for the speculators, investors, and flippers
                       who just want to make a killing and pocket the
                       profits. But it’s not so great for those who are
                       facing property taxes based on the sky-high prices
                       — especially those who have been living in their
                       homes for a long time, are elderly, on fixed
                       incomes, and have no intention of selling them.


                       Comes now a replay of a successful citizen’s
                       initiative from the 1980s that capped property tax
                       increases — but was almost immediately overturned
                       by the Legislature. This time around, a group
                       called Cap Montana Property Taxes wants to gather
                       signatures for CI-121, a constitutional initiative
                       that would amend Montana’s constitution to revert
                       tax valuations back to 2019 levels, cap rates on
                       residences at 1% and limit increases in assessed
                       valuations to either 2% or the inflation rate,
                       whichever is lower. Being a constitutional
                       amendment, it couldn’t be overturned through
                       legislative action.


                # ⚓ Cops’_New_Favorite_Junk_Science_Is_Pretending_Being
                  Anywhere_Near_Fentanyl_Will_Literally_Cause_Them_To_Die⠀⇛


                       The longer we live, the more we become accustomed
                       to cop fiction.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ House_Introduces_‘Innovation’_Act_That_Will_Kill
                  Innovation⠀⇛


                       A few weeks ago, we warned that Congress should not
                       include the ridiculously dangerous SHOP SAFE bill
                       in the expected USICA bill. Unfortunately, Congress
                       did not listen.


                # ⚓ Winding_Down_Our_Latest_Greenhouse_Panel:_The_Lessons
                  Learned_From_SOPA/PIPA⠀⇛


                       Ten years ago a coalition of strange bedfellows
                       came together to thwart one of the most problematic
                       pieces of legislation in tech policy history. In
                       the process they made history, rekindled waning
                       optimism about the health of democratic process,
                       forged longstanding new alliances across activism,
                       politics, academia, and industry, and redefined
                       what’s possible in the tech policy arena and the
                       halls of Congress. Not bad for a day’s work.


                # ⚓ Kazakhstan_government,_telcos_must_put_an_end_to_internet
                  shutdowns_–_Access_Now⠀⇛


                       Access Now and the #KeepItOn coalition are appalled
                       by the internet shutdowns at the hands of
                       authorities and telecommunications providers in the
                       first weeks of January 2022. Through an open letter
                       to President Kassym-Jomart Tokayev, the coalition
                       is demanding action, and the assurance of open,
                       accessible internet for all across Kazakhstan.


                       “It was a disgraceful start to 2022 — shutting down
                       the internet when people needed it most,” said
                       Anastasiya Zhyrmont, Eastern Europe & Central Asia
                       Regional Outreach Coordinator at Access Now. “These
                       prolific attacks on freedom of speech and access to
                       information must not set a precedent for the year
                       ahead in Kazakhstan. The #KeepItOn coalition is
                       demanding the nation set a better standard.”


                # ⚓ Who_should_police_social_media?_|_Social_Media_News_|_Al
                  Jazeera⠀⇛


                       Twitter reports record number of government
                       requests to remove content.


                # ⚓ Analysis:_the_Myanmar_junta’s_Cybersecurity_Law_would_be_a
                  disaster_for_human_rights_–_Access_Now⠀⇛


                       As the one year anniversary of the military’s
                       illegal coup in Myanmar nears, the junta’s
                       methodical efforts to achieve ultimate control over
                       civic space are continuing. The recently revived
                       draft Cybersecurity Law will effectively extinguish
                       any remaining avenues for dissent and expression
                       against an increasingly violent regime, and must be
                       immediately withdrawn.


                       On January 13, leaked documents revealed the
                       military’s attempts to reintroduce a notorious and
                       oppressive law, previously shut down by Access Now
                       and other civil society and industry stakeholders.
                       The latest draft — an unofficial English version of
                       which was shared with Access Now through partners —
                       appears to resurrect all the major fears around
                       suppression of freedoms that were enshrined in the
                       original iteration. It is expected to pass as early
                       as next week after a two-week token consultation.


                       The latest draft confers overbroad powers to the
                       junta to censor expression online and undermine
                       data protection, with no prospect for independent
                       oversight or effective remedy. Military-controlled
                       ministries will be granted powers to implement the
                       law — including the Ministry of Defence (Ch. 1)
                       with its decades-long history of human rights
                       abuses, including serious international violations
                       amounting to crimes against humanity and genocide.


                       If passed, this bill will enshrine in law the death
                       of online civic space in Myanmar — throttling any
                       remaining rights of the people of Myanmar to
                       freedom of expression, association, information,
                       privacy, and security. The redrafted text is
                       designed to commandeer control of cybersecurity,
                       electronic communications, cybercrime, data
                       protection, and VPN services in not only an
                       illegitimate, but also practically impossible
                       manner.


          o § Monopolies⠀➾


                # § Copyrights⠀➾


                      # ⚓ The_Kept_and_the_Killed_–_The_Public_Domain_Review⠀⇛


                             Of the 270,000 photographs commissioned by
                             the US Farm Security Administration to
                             document the Great Depression, more than a
                             third were “killed”. Erica X Eisen examines
                             the history behind this hole-punched archive
                             and the unknowable void at its center.



                    ䷩ 𝚕𝚒𝚗𝚎 4383

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.27.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_28/1/2022:_GNU_Poke_2.0_and_OPNsense_22.1_Released⠀✐


Posted in News_Roundup at 9:38 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o § Audiocasts/Shows⠀➾


                # ⚓ Video_Editing_on_Linux_Featuring_Librem_14_–_Purism⠀⇛


                       Video editing is a complex topic with a wide-range
                       of software to choose from. In this series,
                       produced with Gardiner Bryant, we will cover some
                       of the common video editing suites available for
                       Linux. We will then jump into some of the other
                       software that you can choose when producing
                       multimedia content on Linux. Instead of just
                       telling you about how awesome Librem 14 actually
                       is, we thought it would be useful to show Librem 14
                       in action.


                # ⚓ Nuclear_Music_Streaming_App_For_Windows,_Mac,_Linux_–
                  Invidious⠀⇛


                       Say goodbye to proprietary music players filled
                       with ads, tracking, and profiling.


                # ⚓ How_to_install_OBS_Studio_on_Zorin_OS_16_–_Invidious⠀⇛


                       In this video, we are looking at how to install OBS
                       Studio on Zorin OS 16.


                # ⚓ Linux_Easy_Anti_Cheat_Can’t_Be_Easier_Than_THIS!!_–
                  Invidious⠀⇛


                       When Linux Eeasy Anti Cheat support was first
                       announcement it had some issues that made it much
                       harder to implement for many games that it needed
                       to be but now there’s absolutely no way to make the
                       EAC process


          o § Kernel Space⠀➾


                # ⚓ Script_SNAFU_means_Linux_notification_didn’t_reach_everyone
                  •_The_Register⠀⇛


                       A small SNAFU in Linux kernel land meant that a
                       notification regarding the stable review cycle for
                       the 5.16.3 release didn’t reach everyone it should
                       have.


                       For the first time in the 31-year history of the
                       Linux kernel, there were over 999 commits to a
                       stable version, which caused a very minor problem.


                       Greg Kroah-Hartman, lead maintainer of the -stable
                       branch, has a set of scripts which CC various
                       interested parties when there’s been a new release.


                       “Usually I split big ones out in two releases over
                       the week,” he told The Reg. “This time, I did it
                       all at once to see what it would stress. The ‘bug’
                       of not copying some people on an email is the only
                       thing that broke that I noticed, so we did pretty
                       well.”


                       He told the kernel development mailing list: “Found
                       the problem, this was the first set of -rc releases
                       that we have over 999 commits and the script was
                       adding the cc: to msg.000 not msg.0000. I’ll fix
                       this up.”


                # ⚓ Resurrecting_fbdev_[LWN.net]⠀⇛


                       The Linux framebuffer device (fbdev) subsystem has
                       long languished in something of a purgatory; it was
                       listed as “orphaned” in the MAINTAINERS file and
                       saw fairly minimal maintenance, mostly driven by
                       developers working elsewhere in the kernel graphics
                       stack. That all changed, in an eye-opening way, on
                       January 17, when Linus Torvalds merged a change to
                       make Helge Deller the new maintainer of the
                       subsystem. But it turns out that the problems in
                       fbdev run deep, at least according to much of the
                       rest of the kernel graphics community. By seeming
                       to take on the maintainer role in order to revert
                       the removal of some buggy features from fbdev,
                       Deller has created something of a controversy.


                       Part of the concern within the graphics community
                       is the accelerated timeline that these events
                       played out on. Deller posted his intention to take
                       over maintenance of the framebuffer on Friday,
                       January 14, which received an ack from Geert
                       Uytterhoeven later that day. Two days later, before
                       any other responses had come in, Deller sent a pull
                       request to Torvalds to add Deller as the fbdev
                       maintainer, which was promptly picked up. On
                       January 19, Deller posted reversions of two patch
                       sets that removed scrolling acceleration from
                       fbdev. In the meantime, those reversions had
                       already been made in Deller’s brand new fbdev Git
                       tree.


                # ⚓ The_first_half_of_the_5.17_merge_window_[LWN.net]⠀⇛


                       As of this writing, just short of 7,000 non-merge
                       commits have been pulled into the mainline kernel
                       repository for the 5.17 release. The changes pulled
                       thus far bring new features across the kernel; read
                       on for a summary of what has been merged during the
                       first half of the 5.17 merge window.


                # ⚓ Struct_slab_comes_to_5.17_[LWN.net]⠀⇛


                       The page structure is at the core of the memory-
                       management subsystem. One of these structures
                       exists for every page of physical memory in the
                       system; they are used to track the status of memory
                       as it is used (and reused) during the lifetime of
                       the system. Physical pages can adopt a number of
                       different identities over time; they can hold user-
                       space data, kernel data structures, DMA buffers,
                       and so on. Regardless of how a page is used, struct
                       page is the data structure that tracks its state.
                       These structures are stored in a discontiguous
                       array known as the system memory map.


                       There are a few problems that have arisen with this
                       arrangement. The page structure was significantly
                       reorganized for 4.18, but the definition of struct
                       page is still a complicated mess of #ifdefs and
                       unions with no mechanisms to ensure that the right
                       fields are used at any given time. The unlucky
                       developer who needs to find more space in this
                       structure will be hard put to understand which bits
                       might be safe to use. Subsystems are normally
                       designed to hide their internal data structures,
                       but struct page is heavily used throughout the
                       kernel, making any memory-management changes more
                       complicated. One possible change — reducing the
                       amount of memory consumed by page structures by
                       getting rid of the need for a structure for every
                       page — is just a distant dream under the current
                       organization.


                       So there are a lot of good reasons to remove
                       information from struct page and hide what remains
                       within the memory-management subsystem. One of the
                       outcomes from the folio discussions has been a
                       renewed desire to get a handle on struct page, but
                       that is not a job for the faint of heart — or for
                       the impatient. Many steps will be required to reach
                       that goal. The merging of the initial folio patches
                       for 5.16 was one such step; the advent of struct
                       slab in 5.17 is another.


                # § Graphics Stack⠀➾


                      # ⚓ Intel’s_Vulkan_1.3_Support_All_Ready_For_Mesa_22.0_–
                        Phoronix⠀⇛


                             As expected, Intel’s open-source “ANV” driver
                             is ready to go with Vulkan 1.3 for Mesa 22.0.


                             On Tuesday was The Khronos Group’s
                             announcement of the Vulkan 1.3 specification.
                             Both Intel and Radeon (RADV) had launch-day
                             driver patches ready with the merge requests
                             timed for the embargo lift. This was great
                             timing and showing the successes these days
                             of the open-source Linux GPU drivers compared
                             to the OpenGL API support delays experienced
                             years ago. RADV managed to mainline its
                             patches that same day while the Intel ANV
                             patches were pending a bit longer as they
                             were merging the Vulkan dynamic rendering
                             support as required by Vulkan 1.3.


                      # ⚓ Writing_an_open_source_GPU_driver_–_without_the
                        hardware⠀⇛


                             After six months of reverse-engineering, the
                             new Arm “Valhall” GPUs (Mali-G57, Mali-G78)
                             are getting free and open source Panfrost
                             drivers. With a new compiler, driver patches,
                             and some kernel hacking, these new GPUs are
                             almost ready for upstream.


                             In 2021, there were no Valhall devices
                             running mainline Linux. While a lack of
                             devices poses an obvious obstacle to device
                             driver development, there is no better time
                             to write drivers than before hardware reaches
                             end-users. Developing and distributing
                             production-quality drivers takes time, and we
                             don’t want users to be reliant on closed
                             source blobs. If development doesn’t start
                             until a device hits shelves, that device
                             could reach “end-of-life” by the time there
                             are mature open drivers. But with a head
                             start, we can have drivers ready by the time
                             devices reach end users.


                             Let’s see how.


                      # ⚓ Rosenzweig:_Writing_an_open_source_GPU_driver_–
                        without_the_hardware⠀⇛


                             Here’s a war story from Alyssa Rosenzweig on
                             the process of writing a free driver for
                             Arm’s “Valhall” GPUs without having the
                             hardware to test it on.


                      # ⚓ Graphics_Driver_Changes_Begin_Lining_Up_For_Linux
                        5.18⠀⇛


                             The first set of feature updates have been
                             submitted to DRM-Next for staging until the
                             Linux 5.18 kernel cycle begins around the end
                             of March.


                             It was less than one week ago Linux 5.17-rc1
                             released that marked the end of the merge
                             window for Linux 5.17. However, due to the
                             cut-off of new DRM-Next material happening
                             prior to the merge window, there is already a
                             lot of new code ready to get staged in DRM-
                             Next for the follow-on kernel cycle (5.18).


                             Sent out today were the first of several drm-
                             misc-next pull requests expected for Linux
                             5.18. The drm-misc-next area continues
                             collecting the Direct Rendering Manager
                             changes for the core subsystem code and
                             smaller drivers. Expect more drm-misc-next
                             pull requests along with the big Intel and
                             AMD driver feature pull requests to continue
                             coming over the next several weeks.


                      # ⚓ In_defense_of_NIR⠀⇛


                             Shortly after I joined the Mesa team at Intel
                             in the summer of 2014, I was sitting in the
                             cube area asking Ken questions, trying to
                             figure out how Mesa was put together, and I
                             asked, “Why don’t you use LLVM?” Suddenly,
                             all eyes turned towards Ken and myself and I
                             realized I’d poked a bear. Ken calmly
                             explained a bunch of the packaging/shipping
                             issues around having your compiler in a
                             different project as well as issues radeonsi
                             had run into with apps bundling their own
                             LLVM that didn’t work. But for the more
                             technical question of whether or not it was a
                             good idea, his answer was something about
                             trade-offs and how it’s really not clear if
                             LLVM would really gain them much.


                             That same summer, Connor Abbott showed up as
                             our intern and started developing NIR. By the
                             end of the summer, he had a bunch of data
                             structures a few mostly untested passes, and
                             a validator. He also had most of a GLSL IR to
                             NIR pass which mostly passed validation.
                             Later that year, after Connor had gone off to
                             school, I took over NIR, finished the Intel
                             scalar back-end NIR consumer, fixed piles of
                             bugs, and wrote out-of-SSA and a bunch of
                             optimization passes to get it to the point
                             where we could finally land it in the tree at
                             the end of 2014. Initially, it was only a few
                             Intel folks and Emma Anholt (Broadcom, at the
                             time) who were all that interested in NIR.
                             Today, it’s integral to the Mesa project and
                             at the core of every driver that’s still
                             seeing active development. Over the past
                             seven years, we (the Mesa community) have
                             poured thousands of man hours (probably
                             millions of engineering dollars) into NIR and
                             it’s gone from something only capable of
                             handling fragment shaders to supporting full
                             Vulkan 1.2 plus ray-tracing (task and mesh
                             are coming) along with OpenCL 1.2 compute.


                             Was it worth it? That’s the multi-million
                             dollar (literally) question. 2014 was a
                             simpler time. Compute shaders were still
                             newish and people didn’t use them for all
                             that much more than they would have used a
                             fancy fragment shader for a couple years
                             earlier. More advanced features like Vulkan’s
                             variable pointers weren’t even on the
                             horizon. Had I known at the time how much
                             work we’d have to put into NIR to keep up, I
                             may have said, “Nah, this is too much effort;
                             let’s just use LLVM.” If I had, I think it
                             would have made the wrong call.


          o § Applications⠀➾


                # ⚓ Here’s_Why_Ksnip_is_My_New_Favorite_Linux_Screenshot_Tool
                  in_2022_–_It’s_FOSS_News⠀⇛


                       So, I recently upgraded to a dual-monitor setup
                       (1080p + 1440p).


                       While I was excited about the productivity boost by
                       getting things done faster without the need to
                       manage/minimize active windows constantly, there
                       were a few nuances that I came across.


                       To my surprise, Flameshot refused to work. And, for
                       the tutorials or articles I write, a screenshot
                       tool that offers minor editing or annotation
                       capabilities comes in handy.


                       If you have a similar requirement and are confused,
                       the GNOME Screenshot tool is an option that works
                       with multiple screens flawlessly.


                       However, it does not offer annotations. So, I will
                       have to separately open the image using another
                       image editor or Ksnip to make things work.


          o § Instructionals/Technical⠀➾


                # ⚓ How_to_configure_Pure-FTPD_on_Ubuntu/Debian_with_Self
                  Signed_Certificate⠀⇛


                       In this post, you will learn how to configure Pure-
                       FTPD.


                       Pure-FTPD is a free FTP server which mainly focuses
                       on security. It can be setup really easily within
                       five minutes and it does not take much time or
                       effort to setup. Pure-FTPD offers many features
                       like limiting simultaneous users, Limiting
                       bandwidth on each user to avoid saturation of the
                       network speed, hiding files through permissions and
                       moderating new uploads and content. In this
                       tutorial we will see how to easily configure Pure-
                       FTPD server with Self Signed Certificate


                       File Transfer Protocol (FTP) is a way to receive or
                       transfer data from one server to another. It is a
                       standard communication protocol that enables the
                       transfer or receiving of data over network. For in
                       our case, We can use SFTP protocol for linux
                       servers to transfer files, but if we have to create
                       a FTP server we can use Pure-FTPD


                # ⚓ How_to_create_and_use_a_Red_Hat_Satellite_manifest⠀⇛


                       In this multi-part tutorial, we cover how to
                       provision RHEL VMs to a vSphere environment from
                       Red Hat Satellite. Learn how to prepare the
                       Satellite environment in this post.


                # ⚓ How_to_install_Redmine_on_Ubuntu_20.04_–_NextGenTips⠀⇛


                       In this tutorial, we are going to learn how to
                       install Redmine on Ubuntu 20.04.


                       Redmine is a free and open-source, web-based
                       project management and issue tracking tool. It
                       allows users to manage multiple projects and
                       associated subprojects. It has project wikis and
                       forums, time tracking, and role-based project
                       controls.


                # ⚓ How_to_Install_Grafana_on_Rocky_Linux⠀⇛


                       Grafana is free and open-source analytics and
                       visualization tool. It’s a multi-platform web-based
                       application that provides customizable charts,
                       graphs, and alerts for supported data sources.


                       By default, Grafana supports multiple data sources
                       like Prometheus, Graphite, InfluxDB, Elasticsearc,
                       MySQL, PostgreSQL, Zabbix, etc. It allows you to
                       create an interactive and beautiful dashboard for
                       your application monitoring system.


                       This tutorial will show you how to install Grafana
                       with Nginx as a Reverse Proxy on the Rocky Linux
                       system.


                # ⚓ How_to_Install_Lighttpd_Web_server_on_CentOS_8⠀⇛


                       In this post, you will learn how to Install
                       Lighttpd on CentOS 8


                       Lighttpd is an open-source, secure, fast, flexible,
                       and more optimized web server designed for speed-
                       critical environments with less memory utilization
                       as compared to other web servers. It can handle up
                       to 10,000 parallel connections in one server with
                       effective CPU-load management. Also, It comes with
                       an advanced feature set such as FastCGI, SCGI,
                       Auth, Output-Compression, URL-Rewriting and many
                       more. Lighttpd is an excellent solution for every
                       Linux server, due to its high-speed io-
                       infrastructure that allows us to scale several
                       times better performance with the same hardware
                       than with other alternative web-servers.


                       In this article we will learn how to Install
                       Lighttpd Web server on CentOS 8.


                # ⚓ How_to_install_flameshot_on_RHEL/CentOS_using_Snapcraft⠀⇛


                       In this post, you will learn how to install
                       Flameshot on RHEL / CentOS


                       Flameshot is a powerful open source screenshot and
                       annotation tool for Linux, Flameshot has a varied
                       set of markup tools available, which include
                       Freehand drawing, Lines, Arrows, Boxes, Circles,
                       Highlighting, Blur. Additionally, you can customize
                       the color, size and/or thickness of many of these
                       image annotation tools.


                       Snap is a software packaging and deployment system
                       developed by Canonical for operating systems that
                       use the Linux kernel. The packages, called snaps,
                       and the tool for using them, snapd, work across a
                       range of Linux distributions and allow upstream
                       software developers to distribute their
                       applications directly to users. Snaps are self-
                       contained applications running in a sandbox with
                       mediated access to the host system.


                # ⚓ How_to_Convert_Ubuntu_20.04_In_Zentyal_Firewall⠀⇛


                       Greeting for the day! We are going to convert
                       Ubuntu 20.04 in Zentyal today. The Server is a very
                       popular OS among Linux admins across the planet.
                       Though Zentyal community edition comes as dedicated
                       os too, I was just testing what if we convert
                       running Ubuntu Machine to the server? The verdict
                       was clear that Servers get ready much quicker in
                       comparison to installing dedicated OS instead.
                       Thought to create a write-up for the same. We have
                       categorized the article into three parts. First, a
                       brief introduction of the server and its features.
                       Second, how to convert Ubuntu into the Server. The
                       third part will be having a conclusion and other
                       views regarding the scenario.


                # ⚓ 5_ways_to_make_your_Ansible_modules_work_faster_|_Enable
                  Sysadmin⠀⇛


                       Ansible is a powerful open source tool that helps
                       you automate many of your IT infrastructure
                       operations, from the smallest of tasks to the
                       largest. Ansible has hundreds of modules to help
                       you accomplish your configuration needs, both
                       official and community-developed. When it comes to
                       complex and lengthy workflows, though, you need to
                       consider how to optimize the way you use these
                       modules so you can speed up your playbooks.


                       Previously, I wrote about making your Ansible
                       playbooks run faster. Here are five ways I make my
                       Ansible modules work faster for me.


                # ⚓ 1_DNS_server_container_Podman_dirty_easy⠀⇛


                       Linux distributions. So, what is a DNS? A DNS
                       server is a service that helps resolve a fully
                       qualified domain name (FQDN) into an IP address and
                       performs a reverse translation of an IP address to
                       a user-friendly domain name.


                       Why is name resolution important? Computers locate
                       services on servers using IP. However, IPs are not
                       as user-friendly as domain names. It would be a big
                       headache to remember each IP address associated
                       with every domain name. So instead, a DNS server
                       steps in and helps resolve these domain names to
                       computer IP addresses.


                       The DNS system is a hierarchy of replicated
                       database servers worldwide that begin with the
                       “root servers” for the top-level domains (.com,
                       .net, .org, etc.). The root servers point to the
                       “authoritative” servers located in ISPs and large
                       companies that turn the names into IP addresses.
                       The process is known as “name resolution.” Using
                       our www.business.com example, COM is the domain
                       name, and WWW is the hostname. The domain name is
                       the organization’s identity on the Web, and the
                       hostname is the name of the Web server within that
                       domain. Debian DNS server setup can be found the
                       link.


                # ⚓ Deploy_a_Kubernetes_Cluster_based_on_Calico_and_openSUSE
                  Kubic_–_Hollow_Man’s_Blog⠀⇛


                       openSUSE Kubic is a certified Kubernetes
                       Distribution based on openSUSE MicroOS. Calico is
                       an open-source project that can be used by
                       Kubernetes to deploy a pod network to the cluster.
                       In this blog, I will show you how to deploy a
                       Kubernetes Cluster based on Calico and openSUSE
                       Kubic by a Virtual Machine. We are going to deploy
                       a cluster that has a master and a worker.


                       I was intended to use Oracle VM VirtualBox.
                       However, it turned out that on my machine, when I
                       tried to run kubeadm at openSUSE Kubic in
                       VirtualBox, it always stuck at watchdog: BUG: soft
                       lockup – CPU#? stuck for xxs! with CPU usage around
                       100%. As a result, I switched to VMware Workstation
                       Pro and the issue got solved. Guess it’s caused by
                       some bugs of VirtualBox.


                # ⚓ Qemu_backup_on_Debian_Bullseye_–_Michael_Ablassmeier_–_..⠀⇛


                       In my last article i showed how to use the new
                       features included in Debian Bullseye to easily
                       create backups of your libvirt managed domains.


                       A few years ago as this topic came to my interest,
                       i also implemented a rather small utility (POC) to
                       create full and incremental backups from standalone
                       qemu processes: qmpbackup


                       The workflow for this is a little bit different
                       from the approach i have taken with virtnbdbackup.


                       While with libvirt managed virtual machines, the
                       libvirt API provides all necessary API calls to
                       create backups, a running qemu process only
                       provides the QMP protocol socket to get things
                       going.


          o § Games⠀➾


                # ⚓ Steam’s_latest_crazy_indie_hit_Vampire_Survivors_is_coming
                  to_Linux_|_GamingOnLinux⠀⇛


                       The developer of Vampire Survivors, an absolute
                       smash-hit on Steam has confirmed that a Linux
                       version is in the works. Their latest update post
                       mentioned it might be available by the end of the
                       month, if all goes well.


                       Developed by poncle, it arrived on Steam in Early
                       Access for Windows on December 17 – 2021 and
                       suddenly on January 6 – 2022 it starting gathering
                       thousands of players. More arrived each day, and
                       this game of complete chaos suddenly managed to be
                       a total hit with an all-time peak player count of
                       37,075 and that was only hit yesterday so it’s
                       continuing to grow all the time. On Steam, it’s
                       managed to hit an Overwhelmingly Positive rating
                       too.


                # ⚓ Prison_Architect:_Perfect_Storm_DLC_and_The_Tower_update
                  get_a_surprise_release_|_GamingOnLinux⠀⇛


                       Today Paradox Interactive and Double Eleven have
                       done a surprise launch of the Prison Architect:
                       Perfect Storm expansion. Plus, as always for
                       Paradox, there’s a free update out now too called
                       The Tower. So not only do you have to worry about
                       what the inmates have smuggled around but you now
                       also need to look to the skies. No one wants to sit
                       in a freezing cold cell, or have wild rats running
                       across their feet.


                # ⚓ Steam_Lunar_New_Year_Sale_2022_is_now_live_|
                  GamingOnLinux⠀⇛


                       Do you feel the need for some new games? Perhaps to
                       continue building up a collection for the upcoming
                       Steam Deck? Now is yet another chance for you with
                       the Steam Lunar New Year Sale 2022. Not only is
                       there a big sale but if you head over to the Points
                       Shop, you’ll also get a new sticker each day too.


                # ⚓ Gaming_Chromebooks_Running_Steam_Are_Reportedly_On_the
                  Way⠀⇛


                       Don’t worry, gamers, there will be plenty of RGB
                       lighting.


                # ⚓ Open_3D_Game_Engine_2111.2_Released_–_Phoronix⠀⇛


                       In addition to closing in on the Godot 4.0 release,
                       another equally exciting effort in the open-source
                       game engine space is the Open 3D Engine originally
                       from the Amazon Lumberyard code and backed by the
                       Linux Foundation and other organizations. Open 3D
                       Engine 2111.2 is out today as the newest stable
                       point release for this less than one year old open-
                       source game engine effort.


                       Back in December saw the release of O3DE 21.11 as
                       the first major release of this open-source game
                       engine under the Apache 2.0 license. O3DE 2111.2 is
                       the latest in that stable lineage for this game
                       engine. a


                # ⚓ Release_Notes_for_Open_3D_Engine_2111.2_–_Open_3D_Engine⠀⇛


                       Open 3D Engine release 2111.2 is a maintenance and
                       quality of life improvement release based on
                       2111.1. This release is bugfix-only and contains no
                       new features.


                # ⚓ An_Up-To-Date_Development_Environment_For_The_Nokia_N-Gage
                  |_Hackaday⠀⇛


                       One of the brave but unsuccessful plays from Nokia
                       during their glory years was the N-Gage, an attempt
                       to merge a Symbian smartphone and a handheld game
                       console. It may not have managed to dethrone the
                       Game Boy Advance but it still has a band of
                       enthusiasts, and among them is [Michael Fitzmayer]
                       who has produced a CMake-based toolchain for the
                       original Symbian SDK. This is intended to ease
                       development on the devices by making them more
                       accessible to the tools of the 2020s, and may serve
                       to bring a new generation of applications to those
                       old Nokias still lying forgotten in dusty drawers.


          o § Desktop Environments/WMs⠀➾


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


                      # ⚓ Beginning_with_Season_of_KDE_2022_–_post_#1⠀⇛


                             I usually learn something between semesters
                             when I have holidays. During September –
                             October 2021, I tried learning some Qt and
                             looking around codebase for KDE apps. But
                             something just didn’t work out. I suspect my
                             leaning style wasn’t correct.


                      # ⚓ KDE_Gear_22.04_release_schedule_finalized⠀⇛


                             It is available at the usual place https://
                             community.kde.org/Schedules/
                             KDE_Gear_22.04_Schedule


                             Dependency freeze is in six weeks (March 10)
                             and Feature Freeze a week after that, make
                             sure you start finishing your stuff!


                # § GNOME Desktop/GTK⠀➾


                      # ⚓ ‘Burn_My_Windows’_Added_Some_More_Cool_Animations_on
                        App_Close⠀⇛


                             Want some cool desktop animations? the ‘Burn
                             My Windows’ extension added some more
                             animation effects for Ubuntu 20.04+, Fedora
                             workstation, and other Linux with GNOME
                             3.36+.


                             Previously when user clicks to close an app
                             window, the extension applies a burning
                             window down effect.


                             [...]


                             See the short videos for new effects when
                             closing app windows:


                             energizea energizeb Matrix T-Rex-Attack tv-
                             close wisps
                             There’s also new “Broken Glass” effect in
                             upcoming release to shatter your windows into
                             a shower sharp shards!


                             For each animation, there’s a setting page to
                             change the animation speed, scale, color,
                             etc.


          o § Distributions⠀➾


                # ⚓ PETget_now_PKGget⠀⇛


                       The traditional package manager in Puppy Linux is
                       the “Puppy Package Manager”, often just known as
                       the “PPM”.


                       EasyOS has a derivative of the PPM, named “PETget”.
                       However, I have never been entirely happy with that
                       name, as the package manager can install virtually
                       any type of package — .deb, .rpm. .tgz, .tar.zst,
                       .tar.xz, etc., as well as .pet packages.


                # ⚓ What_to_expect_in_the_next_release_of_EasyOS⠀⇛


                       I am posting these thoughts while filling in time.


                       Right now, my main desktop PC is doing a complete
                       recompile in OpenEmbedded. This is now “revision
                       7″, and the binary packages created will have “-r7″
                       in their names.


                # § BSD⠀➾


                      # ⚓ OPNsense_22.1_released⠀⇛


                             For more than 7 years now, OPNsense is
                             driving innovation through
                             modularising and hardening the open source
                             firewall, with simple
                             and reliable firmware upgrades, multi-
                             language support, fast adoption
                             of upstream software updates as well as clear
                             and stable 2-Clause BSD
                             licensing.

                             22.1, nicknamed "Observant Owl", features the
                             upgrade to FreeBSD 13,
                             switch to logging supporting RFC 5424 with
                             severity filtering, improved
                             tunable sysctl value integration, faster boot
                             sequence and interface
                             initiation and dynamic IPv6 host alias
                             support amongst others.

                             On the flip side major operating system
                             changes bear risk for regression
                             and feature removal, e.g. no longer
                             supporting insecure cryptography in
                             the kernel for IPsec and switching the
                             Realtek vendor driver back to its
                             FreeBSD counterpart which does not yet
                             support the newer 2.5G models.
                             Circular logging support has also been
                             removed.  Make sure to read the
                             known issues and limitations below before
                             attempting to upgrade.

                             Download links, an installation guide[1] and
                             the checksums for the images
                             can be found below as well.
                      # ⚓ OPNsense_22.1_Released_With_This_Open-Source_Firewall
                        Now_Powered_By_FreeBSD_13⠀⇛


                             OPNsense, the FreeBSD-based firewall/router
                             software stack forked from pfSense, is out
                             with its first major release of 2022.


                             OPNsense has now been going on seven years
                             strong and with OPNsense 22.1 is another big
                             step forward for the BSD router/firewall OS
                             project. OPNsense 22.1 shifts the base
                             package set to the excellent FreeBSD 13.


                             OPNsense 22.1 also features logging
                             improvements, better sysctl tuning
                             integration, faster booting/start-up, and a
                             range of other enhancements.


                # § IBM/Red Hat/Fedora⠀➾


                      # ⚓ IBM_Sales_Surge._The_Company’s_Turnaround_May_Be
                        Taking_Hold. [Ed: This is a lie. IBM is collapsing and
                        it offloaded some units to fake growth while laying_off
                        staff. This writer (Eric J. Savitz) has lied for
                        Microsoft too for over a decade [1, 2]. IBM gets fake
                        news published, then links_to_it.]⠀⇛


                             IBM posted strong results Monday for its
                             fourth quarter, with its best sales growth in
                             more than a decade. The results suggest that
                             CEO Arvind Krishna’s strategy for returning
                             the legacy tech giant to growth is beginning
                             to pay off.


                      # ⚓ When_to_Use_API_Management_and_Service_Mesh_Together
                        –_DevOps.com⠀⇛


                             I recently chatted with Mark Cheshire,
                             director of product, Red Hat, to discuss the
                             nuances between API management and service
                             mesh. According to Cheshire, API management
                             and service mesh can work quite well side-by-
                             side for particular use cases. For example, a
                             large organization using service mesh could
                             benefit from applying API management that
                             wraps microservices in a usable contract for
                             internal departments. Or, API management
                             could help a company expose specific APIs
                             from the mesh to outside partners.


                      # ⚓ Adopting_open-source_platforms_to_modernize_citizen
                        services_–_StateScoop⠀⇛


                             States like Tennessee are modernizing their
                             legacy, siloed and on-premises systems to a
                             more integrated and agile infrastructure to
                             keep pace with the digital demands of
                             customers.


                             In an exclusive StateScoop interview, KPMG
                             managing director, advisory Mark Calem, Red
                             Hat chief technologist, North America public
                             sector David Egts and Tennessee Department of
                             Human Services chief information officer
                             Wayne Glaus discuss how states can use open-
                             source platforms to engage with constituents
                             more fully and to improve the digital
                             services they deliver.


                      # ⚓ BU_and_Red_Hat_Announce_First_Research_Incubation
                        Awards_|_BU_Today_|_Boston_University⠀⇛


                             For almost five years, Boston University and
                             Red Hat, a leading provider of open-source
                             computer software solutions, have
                             collaborated to drive innovative research and
                             education in open-source technology. Now that
                             partnership has announced the first
                             recipients of the Red Hat Collaboratory
                             Research Incubation Awards. (Open source
                             means that the original source code is made
                             available for use or modification by users
                             and developers.)


                             The awards are administered through BU’s Red
                             Hat Collaboratory, housed within the Rafik B.
                             Hariri Institute for Computing and
                             Computational Science & Engineering, and Red
                             Hat Research. “This collaborative model gives
                             us the opportunity to increase the diversity
                             and richness of open engineering and
                             operations projects we undertake together,
                             and also allows us to pursue fundamental
                             research under one umbrella,” says Heidi
                             Picher Dempsey, Red Hat research director,
                             Northeast United States.


                      # ⚓ What_a_C++,_C,_Go_or_Rust_developer_should_know_about
                        RHEL_9⠀⇛


                             The purpose of this blog is to explain to
                             system developers some of the new C++, C, Go
                             or Rust features in Red Hat Enterprise Linux
                             (RHEL) 9.


                      # ⚓ How_open_managers_can_talk_to_neurodivergent
                        teammates_about_performance⠀⇛


                             I’ve had many conversations recently that
                             have me looking at a crucial question that
                             impacts neurodivergent corporate employees
                             and their managers: how do we understand,
                             encourage, measure, nurture, and assess the
                             career development of neurodivergent people?
                             Development opportunities, and how managers
                             assess performance, are critical aspects of
                             career growth, financial compensation,
                             morale, feelings of self worth, happiness,
                             employee retention, and the ability of
                             individuals and companies to achieve their
                             goals. And yet, I believe it is something
                             that can be subjective, underappreciated, and
                             under-invested in. As a late-diagnosed
                             autistic person who has had significant
                             anxiety, social phobia, and other mental
                             health conditions for my entire career, and
                             as someone who has been in senior leadership
                             roles, leading hundreds of employees, I’ve
                             thought about this quite a bit.


                # § Debian Family⠀➾


                      # ⚓ Gunnar_Wolf•_Progvis_—_Now_in_Debian_proper!_
                        (unstable)⠀⇛


                             Progvis finally made it into Debian! What is
                             it, you ask? It is a great tool to teach
                             about memory management and concurrency.


                # § Canonical/Ubuntu Family⠀➾


                      # ⚓ Telco_workloads_orchestration_in_multi-clouds
                        environments_–_focus_for_Open_Source_MANO_release
                        ELEVEN_|_Ubuntu⠀⇛


                             Open source MANO release ELEVEN is here with
                             another set of exciting features for the
                             telco world!!


                      # ⚓ Vanilla’s_accessibility_documentation_process_|
                        Ubuntu⠀⇛


                             Following on from our previous post about
                             accessibility by design, we’d like to share
                             our accessibility documentation process here
                             in the Web & Design team. In the Vanilla
                             squad, we work hard to make sure the Vanilla
                             framework is as accessible as possible. We
                             don’t claim to be perfect, but accessibility
                             is a real priority to us and we’re
                             continuously trying to improve. We’ve
                             recently started writing some accessibility
                             docs to go alongside our components. They
                             outline how the components work, and any
                             important accessibility considerations to
                             note in implementation.


                      # ⚓ SD_Times_news_digest:_Canonical_announces_Charmed
                        Kubeflow_updates;_CodeLogic_unveils_new_plugin_for
                        JetBrains’_IntelliJ_IDEA;_First_preview_of_.NET
                        Community_Toolkit_v8.0.0_–_SD_Times⠀⇛


                             The team at Canonical, the provider of
                             Ubuntu, today announced the release of the
                             MLOps platform, Charmed Kubeflow 1.4. With
                             this, data science teams are empowered to
                             collaborate on AI/ML innovation from concept
                             to production on any cloud.


                             The solution is free to use and can be
                             deployed in any environment without
                             constraints, paywall, or restrictive
                             features. This release brings users a
                             centralized, browser-based MLOps platform
                             that runs effectively on any conformant
                             Kubernetes.


          o § Devices/Embedded⠀➾


                # ⚓ Allwinner_F1C100s_handheld_computer_should_cost_$15_to
                  manufacture⠀⇛


                       Brian Benchoff’s “minimum viable computer’” is a
                       Linux handheld computer powered by an Allwinner
                       F1C100s ARM9 processor that could fit into your
                       pocket and should cost about $15 (BoM cost) to
                       manufacture in quantity.


                       The open-source hardware Linux “computer” comes
                       with 32MB or 64MB RAM, a 2.3-inch color display, a
                       48-key keyboard, a USB port, and is powered by two
                       AAA batteries. Don’t expect a desktop environment,
                       but it can run a terminal to execute scripts, or
                       even run Doom.


                # ⚓ India’s_government_may_foster_home-grown_mobile_OS_•_The
                  Register⠀⇛


                       India’s minister of state for Electronics and IT
                       Rajeev Chandrasekhar has revealed the nation’s
                       government intends to develop a policy that will
                       encourage development of an “indigenous mobile
                       operating system”.


                       Speaking at the launch of a policy vision for
                       Indian tech manufacturing, Chandrasekhar said
                       India’s Ministry of Electronics and Information
                       Technology believes the market could benefit from
                       an alternative to Android and iOS and could “even
                       create a new handset operating system” to improve
                       competition, according to the Press Trust of India.


                       “We are talking to people. We are looking at a
                       policy for that,” Chandrasekhar told local media,
                       adding that start-ups and academia are being
                       considered as likely sources of talent and
                       expertise to build the OS.


                       “If there is some real capability then we will be
                       very much interested in developing that area
                       because that will create an alternative to iOS and
                       Android which then an Indian brand can grow,” he
                       added.


                       The minister offered no timeframe for a decision on
                       whether to proceed with the policy, nor the level
                       of assistance India’s government might provide.


                       Nor did he say much to suggest he knows that past
                       attempts to create alternative mobile operating
                       systems, or national operating systems, have
                       cratered.


                       Even Microsoft, famously, failed to make an impact
                       with Windows Phone despite throwing billions at the
                       OS and acquiring Nokia to ensure supply of handsets
                       to run it. Mozilla’s Firefox OS was discontinued
                       after efforts to crack India’s mobile market with
                       low-cost devices failed. The Linux Foundation’s
                       Tizen hasn’t found a lot of love.


                # ⚓ Reverse_engineering_an_’80s_NeXT_keyboard_|_Arduino_Blog⠀⇛


                       Working with vintage computer technology can feel a
                       bit like the digital equivalent of archeology.
                       Documentation is often limited or altogether absent
                       today — if it was ever even public in the first
                       place. So you end up reverse engineering a device’s
                       functionality through meticulous inspection and
                       analysis. Spencer Nelson has a vintage NeXT
                       keyboard from the ’80s and wanted to get it working
                       with modern computers via USB. To make that happen,
                       he reverse engineered the protocol and used an
                       Arduino as an adapter.


                       NeXT was a computer company founded by Steve Jobs
                       in the ’80s, in the period after he left Apple. A
                       little over ten years later, Apple bought NeXT and
                       Jobs rejoined the company. NeXT only released a few
                       computers, but they are noteworthy and desirable to
                       collectors. This particular keyboard is from 1988
                       and worked with the first generation NeXT Computer.
                       Unlike modern keyboards that share the USB
                       protocol, keyboards from this era utilized
                       proprietary protocols. This particular model had an
                       enigmatic protocol that Nelson became obsessed with
                       deciphering.


                # ⚓ Reverse_Engineering_The_NeXT_Computer_Keyboard_Protocol_|
                  Hackaday⠀⇛


                       The NeXT computer was introduced in 1988, with the
                       high-end machine finding favor with universities
                       and financial institutions during its short time in
                       the marketplace. [Spencer Nelson] came across a
                       keyboard from one of these machines, and with
                       little experience, set about figuring out how it
                       worked.


                       The keyboard features a type of DIN connector and
                       speaks a non-ADB protocol to the machine, but
                       [Spencer] wanted to get it speaking USB for use
                       with modern computers. First attempts at using pre-
                       baked software found online to get the keyboard
                       working proved to be unreliable. [Spencer]
                       suspected that the code, designed to read 50
                       microsecond pulses from the keyboard, was
                       miscalibrated.


                # ⚓ [Older]_Device_neutrality_coming_to_Europe?_|_Stop_at_Zona-
                  M⠀⇛


                       The EU Parliament, says FSFE, missed the chance to
                       introduce strong requirements for interoperability
                       based on Open Standards: “This is a lost chance to
                       leverage competition with accessible and non-
                       discriminatory technical specifications [that would
                       allow] market actors to innovate on top of
                       technical specification standards and build their
                       own services”.


                       However, things look better than they did before
                       for digital and consumer rights in EU, and let’s
                       hope, as FSFE puts it, that getting Device
                       Neutrality in european legislations does become the
                       first step towards real digital interoperability of
                       digital products and services. I mean, we have
                       already endured too much idiocy likke this around
                       non-interoperable electronic components like,
                       haven’t we?


                # ⚓ The_SHA2017_Badge_Just_Keeps_On_Giving,_This_Time_It’s_A
                  Solar_Monitor_|_Hackaday⠀⇛


                       The SHA badge used an ESP32 as its processor, and
                       paired it with a touch keypad and an e-ink screen.
                       Its then novel approach of having a firmware that
                       could load MicroPython apps laid the groundwork for
                       the successful open source badge.team firmware
                       project, meaning that it remains versatile and
                       useful to this day.


                # ⚓ Recreating_MS_Paint_For_The_ESP32⠀⇛


                       Microsoft Paint was one of the first creative
                       outlets for many children when they first laid
                       hands on a computer in the 1990s. Now, [Volos
                       Projects] has brought the joy of this simple
                       application to a more compact format on the ESP32!


                # ⚓ Apollo_Lake_edge_AI_mini-PCIe_offers_up_to_two_Myriad_X
                  VPUs⠀⇛


                       Nexcom’s Linux-ready “AIEdge-X 100-VPU” edge AI
                       mini-PC combines an Apollo Lake SoC with up to 2x
                       Myriad X VPUs. Key specs include 2x GbE, 2x HDMI
                       2.0, 2x USB 3.0, and an M.2 M-key slot.


                       The fanless, 179.5 x 106 x 37mm AIEdge-X 100-VPU,
                       which follows other AIEdge-X systems such as
                       Nexcom’s larger, 9th Gen Coffee Lake powered
                       AIEdge-X 300, is primarily designed for smart
                       retail applications such as smart signage,
                       automated checkout machines, QSRs (Quick Service
                       Restaurants), drive-thru kiosks, and endless
                       aisles, which refers to online shopping from a
                       brick-and-mortar store. Other applications include
                       license plate recognition, body temperature
                       checking, transit kiosks, and other smart city and
                       edge AI tasks.


                # ⚓ Coreboot_Merges_Support_For_Intel’s_Arm-Based_PSE_Offload
                  Engine_–_Phoronix⠀⇛


                       As of yesterday Intel’s contributed Programmable
                       Services Engine “PSE” support has been merged into
                       mainline Coreboot for supporting this Arm-based
                       dedicated offload engine found within select Intel
                       processors.


                # ⚓ Turn_On_Sarcasm_With_the_Flip_Of_a_Switch⠀⇛


                       Sarcasm is notoriously difficult to distinguish in
                       online communities. So much, in fact, that a famous
                       internet rule called Poe’s Law is named after the
                       phenomenon. To adapt, users have adopted several
                       methods for indicating implied sarcasm such as the
                       /s tag, but more recently a more obvious sarcasm
                       indicator has appeared that involves random
                       capitalization througout the sarcastic phrase.
                       While this looks much more satisfying than other
                       methods, it is a little cumbersome to type unless
                       you have this sarcasm converter for your keyboard.


                       The device, built by [Ben S], is based around two
                       Raspberry Pi Pico development boards and sits
                       between a computer and any standard USB keyboard.
                       The first Pi accepts the USB connection from the
                       keyboard and reads all of the inputs before sending
                       what it reads to the second Pi over UART. If the
                       “SaRcAsM” button is pressed, the input text stream
                       is converted to sarcasm by toggling the caps lock
                       key after every keystroke.


                # ⚓ Reject_Modernity;_Return_To_Tamagotchi_|_Hackaday⠀⇛


                       Browsing through the recent projects on
                       Hackaday.io, we’ve found this entry by
                       [NanoCodeBug]: a single-PCB low-power trinket
                       reviving the “pocket pet” concept while having some
                       fun in the process! Some serious thought was put
                       into making this device be as low-power as possible
                       – with a gorgeous Sharp memory LCD and a low-power-
                       friendly SAMD21, it can run for two weeks on a pair
                       of mere AAA batteries, and possibly more given a
                       sufficiently polished firmware. The hardware has
                       some serious potential, with the gadget’s platform
                       lending itself equally well to Arduino or
                       CircuitPython environments, the LCD being
                       overclock-able to 30 FPS, mass storage support to
                       enable pet transfer and other PC integrations, a
                       buzzer for all of your sound needs, and an
                       assortment of buttons to help you create mini-games
                       never seen before. [NanoCodeBug] has been working
                       on the hardware diligently for the past month,
                       having gone through a fair few revisions – this is
                       shaping up to be a very polished gadget!


                # ⚓ Remoticon_2021_//_Voja_Antonic_Makes_You_A_Digital_Designer
                  |_Hackaday⠀⇛


                       [Voja Antonic] has been building digital computers
                       since before many of us were born. He designed with
                       the Z80 when it was new, and has decades of
                       freelance embedded experience, so when he takes the
                       time to present a talk for us, it’s worth paying
                       attention.


                       For his Remoticon 2022 presentation, he will
                       attempt to teach us how to become a hardware expert
                       in under forty minutes. Well, mostly the digital
                       stuff, but that’s enough for one session if you ask
                       us. [Voja] takes us from the very basics of logic
                       gates, through combinatorial circuits, sequential
                       circuits, finally culminating in the description of
                       a general-purpose microprocessor.


                # ⚓ Robotic_Xylophone_Makes_Music_with_MIDI_Magic⠀⇛


                       The MIDI format has long been used to create some
                       banging electronic music, so it’s refreshing to see
                       how [John P. Miller] applied the standard in his
                       decidedly analog self-playing robotic xylophone.


                       Framed inside a fetching Red Oak enclosure, the 25-
                       key instrument uses individual solenoids for each
                       key, meaning that it has no problem striking
                       multiple bars simultaneously. This extra fidelity
                       really helps in reproducing the familiar melodies
                       via the MIDI format. The tracks themselves can be
                       loaded onto the device via SD card, and selected
                       for playback with character LCD and rotary knob.


                       The software transposes the full MIDI music
                       spectrum of a particular track into a 25-note
                       version compatible with the xylophone. Considering
                       that a piano typically has 88 keys, some musical
                       concessions are needed to produce a recognizable
                       playback, but overall it’s an enjoyable musical
                       experience.


                # ⚓ The_Eclipse_Oniro_Project_aims_to_deliver_consumer_&_IoT
                  software_that_works_across_multiple_operating_systems_–_CNX
                  Software⠀⇛


                       So basically I understand Oniro aims to provide a
                       vendor-agnostic platform to develop software that
                       runs on various operating systems and hardware in
                       order to reduce fragmentation in the consumer and
                       IoT device industry. I will not insert an xkcd meme
                       here, but you know what I mean. Right now, Oniro
                       relies on the Poky/Yocto Project build system and
                       supports three operating systems with Linux,
                       ZephyrOS, and FreeRTOS allowing it to be used in
                       application processors and microcontrollers.


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


                # ⚓ Libre_Arts_–_Weekly-ish_recap_—_26_January_2021⠀⇛


                       Highlights: new releases of Scribus, Flameshot,
                       Surge, ZynAddSubFX, Zrythm, Giada; Audacity
                       resurrects real-time effects, Ardour gets cue
                       markers.


                # § Events⠀➾


                      # ⚓ Brian_Kernighan_on_the_origins_of_Unix⠀⇛


                             Once again, the COVID pandemic has forced
                             linux.conf.au to go virtual, thus depriving
                             your editor of a couple of 24-hour, economy-
                             class, middle-seat experiences. This
                             naturally leads to a set of mixed feelings.
                             LCA has always put a priority on interesting
                             keynote talks, and that has carried over into
                             the online event; the opening keynote for LCA
                             2022 was given by Brian Kernighan. Despite
                             being seen as a founder of our community,
                             Kernighan is rarely seen at Linux events; he
                             used his LCA keynote to reminisce for a while
                             on where Unix came from and what its legacy
                             is.


                             He began by introducing Bell Labs, which was
                             formed by US telecommunications giant AT&T to
                             carry out research on how to improve
                             telephone services. A lot of inventions came
                             out of Bell Labs, including the transistor,
                             the laser, and fiber optics. Such was the
                             concentration of talent there that, at one
                             point, Claude Shannon and Richard Hamming
                             shared an office. Kernighan joined Bell Labs
                             in 1967, when there were about 25 people
                             engaged in computer-science research.


                             Early on, Bell Labs joined up with MIT and
                             General Electric to work on a time-sharing
                             operating system known as Multics. As one
                             might have predicted, the attempted
                             collaboration between a research lab, a
                             university, and a profit-making company did
                             not work all that well; Multics slipped later
                             and later, and Bell Labs eventually pulled
                             out of the project. That left two researchers
                             who had been working on Multics — Ken
                             Thompson and Dennis Ritchie — without a
                             project to work on.


                             After searching for a machine to work on,
                             Thompson eventually found an old PDP-7, which
                             was already obsolete at that time, to do some
                             work on filesystem design. The first Unix-
                             like system was, in essence, a test harness
                             to measure filesystem throughput. But he and
                             Ritchie later concluded that it was something
                             close to the sort of timesharing system they
                             had been trying to build before. This system
                             helped them to convince the lab to buy them a
                             PDP-11/20 for further development. [Brian
                             Kernighan] The initial plan was to create a
                             system for document processing, with an
                             initial focus of, inevitably, preparing
                             patent applications. The result was
                             “recognizably Unix” and was used to get real
                             work done.


                # § SaaS/Back End/Databases⠀➾


                      # ⚓ Top_10_features_of_MongoDB_Atlas_|_FOSS_Linux⠀⇛


                             MongoDB is a NoSQL general-purpose document-
                             oriented database that is free to use. It is
                             a scalable, versatile NoSQL document database
                             platform built to overcome the constraints of
                             previous NoSQL solutions and the approach of
                             relational databases. It helps the user store
                             and deals with an enormous amount of data.


                             MongoDB’s horizontal scaling and load
                             balancing capabilities have given application
                             developers unprecedented flexibility and
                             scalability. There are different MongoDB
                             editions; however, we will focus on MongoDB
                             Atlas in this article.


                             MongoDB Atlas is a multi-cloud database
                             service created by the MongoDB team. Atlas
                             makes it easy to deploy and manage databases
                             while also giving users the flexibility they
                             need to develop scalable, high-performance
                             global applications on the cloud providers of
                             their choice.


                             It is the world’s most popular cloud database
                             for modern applications. Developers can use
                             Atlas to deploy fully managed cloud databases
                             on AWS, Azure, or Google Cloud. Developers
                             can relax easily knowing that they have rapid
                             access to the availability, scalability, and
                             compliance they need for enterprise-level
                             application development.


                      # ⚓ Node-firebird-driver-native_version_2.4.0_has_been
                        released_with_a_few_features_added.⠀⇛


                             Node-firebird-driver-native version 2.4.0 has
                             been released with a few features added.


                      # ⚓ Rqlite_7.0_Released_For_Distributed_Relational
                        Database_Built_Atop_SQLite_–_Phoronix⠀⇛


                             Rqlite 7.0 is now available as a lightweight,
                             distributed relational database. This open-
                             source database system for cluster setups is
                             built atop SQLite while aiming to be easy-to-
                             use and fault-tolerant.


                      # ⚓ PostgreSQL:_Announcing_the_release_of_AgensGraph
                        2.5⠀⇛


                             The AgensGraph Development Team are pleased
                             to announce the release of AgensGraph v2.5.


                             AgensGraph is a new generation multi-model
                             graph database for the modern complex data
                             environment. AgensGraph is a multi-model
                             database, which supports the relational and
                             graph data model at the same time that
                             enables developers to integrate the legacy
                             relational data model and the flexible graph
                             data model in one database. AgensGraph
                             supports ANSI-SQL and openCypher (http://
                             www.opencypher.org). SQL queries and Cypher
                             queries can be integrated into a single query
                             in AgensGraph.


                             AgensGraph is based on the powerful
                             PostgreSQL RDBMS, and is very robust, fully-
                             featured and ready for enterprise use.
                             AgensGraph is optimized for handling complex
                             connected graph data and provides plenty of
                             powerful database features essential to the
                             enterprise database environment including
                             ACID transactions, multi-version concurrency
                             control, stored procedure, triggers,
                             constraints, sophisticated monitoring and a
                             flexible data model (JSON). Moreover,
                             AgensGraph leverages the rich eco-systems of
                             PostgreSQL and can be extended with many
                             outstanding external modules, like PostGIS.


                             For more details please see the release
                             notes.


                      # ⚓ PostgreSQL:_Announcing_the_release_of_Apache_AGE
                        (incubating)_0.6.0⠀⇛


                             Apache AGE(incubating) is a PostgreSQL
                             extension that provides graph database
                             functionality.


                             AGE is an acronym for A Graph Extension, and
                             is inspired by Bitnine’s fork of PostgreSQL
                             10, AgensGraph, which is a multi-model
                             database. The goal of the project is to
                             create single storage that can handle both
                             relational and graph model data so that users
                             can use standard ANSI SQL along with
                             openCypher, the Graph query language.


                      # ⚓ Apache_Kafka_3.1_opens_up_data_streaming_for
                        analytics⠀⇛


                             Apache Kafka is continuing to build out its
                             event data streaming technology platform as
                             the open source project moves forward.


                             Apache Kafka 3.1 became generally available
                             on Jan. 24, providing users of the open
                             source event streaming technology with a
                             series of new features.


                             Organizations use Kafka to enable real-time
                             data streams that can be used for operations,
                             business intelligence and data analytics.


                             Kafka is a developed by an open source
                             community of developers that includes
                             Confluent, an event streaming vendor that
                             provides a commercial platform for Kafka, as
                             well as Red Hat, which has a managed Kafka
                             service.


                             Gartner analyst Merv Adrian said he looks at
                             Kafka as a data source that feeds a database.


                             “More uses and users are moving upstream to
                             engage with data in motion, before it comes
                             to rest, and Kafka and its adjacent
                             technologies are moving to capture share of
                             that business,” Adrian said.


                # § Productivity Software/LibreOffice/Calligra⠀➾


                      # ⚓ Nibble_Stew:_Building_a_part_of_LibreOffice_on
                        Windows_using_only_Meson_and_WrapDB⠀⇛


                             In earlier posts (starting from this one) I
                             ported LibreOffice’s build system to Meson.
                             The aim has not been to be complete, but to
                             compile and link the main executables. On
                             Linux this is fairly easy as you can use the
                             package manager to install all dependencies
                             (and there are quite a few of them).


                             [...]


                             It does on my machine. It probably won’t do
                             so on yours. Some of the deps I used could
                             not be added to WrapDB yet or are missing
                             review. If you want to try, the code is here.


                             The problematic (from a build system point of
                             view) part of compiling an executable and
                             then running it to generate source code for a
                             different target works without problems. In
                             theory you should be able to generate VS
                             project files and build it with those, but I
                             only used Ninja because it is much faster.


                      # ⚓ Regression_fix:_Missing_lines_in_docx⠀⇛


                             Interoperability is a very important aspect
                             of the LibreOffice. Today, LibreOffice can
                             load and save various file formats from many
                             different office applications from different
                             companies across the world. But bugs
                             (specially regression bugs) are inevitable
                             parts of every software. There are situations
                             where the application does not behave as it
                             should, and a developer should take action
                             and fix it, so that it will behave according
                             to the expectation of the user.


                             What if you encounter a bug in LibreOffice,
                             and how does a developer fix the problem?
                             Here we discuss the steps needed to fix a
                             bug. In the end, we provide a test and make
                             sure that the same problem does not happen in
                             the future.


                             [...]


                             The bug reporter should carefully describe
                             the “actual results” and why it is different
                             from the “expected results”. This is also
                             important because the desired software’s
                             behavior is not always as obvious as it seems
                             to be for the bug reporter.


                             Let’s talk about a recently fixed regression
                             bug: The “NISZ LibreOffice Team” reported
                             this bug. The National Infocommunications
                             Service Company Ltd. (NISZ) has an active
                             team in LibreOffice development and QA.


                # § FSF⠀➾


                      # ⚓ Chile_citizens:_Support_these_constitutional
                        proposals_for_free_software_and_user_privacy_by_Feb_1⠀⇛


                             Chile is in the midst of governmental
                             changes, and with these changes comes the
                             opportunity for the people of Chile to make
                             their voices heard for long-term benefits to
                             their digital rights and freedoms. Chilean
                             activists have submitted three constitutional
                             proposals relating to free software and user
                             freedom, but they need signatures in order to
                             have these proposals submitted to the
                             constitutional debate.


                             We encourage free software community members
                             in Chile to have a look at these proposals,
                             and sign those that uphold digital freedom
                             and autonomy. The deadline for collecting
                             signatures is February 1st.


                             Some further explanation and other
                             information gathered by one of our community
                             members, Felix Freeman, is included below.
                             The English version of Felix’s message is
                             provided below.


                      # § GNU Projects⠀➾


                            # ⚓ GNU_poke_2.0_released⠀⇛


                                   I am happy to announce a new major
                                   release of GNU poke, version 2.0.


                                   This release is the result of a full
                                   year of development. A lot of things
                                   have changed and improved with respect
                                   to the 1.x series; we have fixed many
                                   bugs and added quite a lot of new
                                   exciting and useful features.


                                   See the complete release notes at
                                   https://jemarch.net/poke-2.0-
                                   relnotes.html for a detailed
                                   description of what is new in this
                                   release.


                                   We have had lots of fun and learned
                                   quite a lot in the process; we really
                                   wish you will have at least half of
                                   that fun using this tool!


                # § Programming/Development⠀➾


                      # ⚓ Python_sets,_frozensets,_and_literals⠀⇛


                             A Python “frozenset” is simply a set object
                             that is immutable—the objects it contains are
                             determined at initialization time and cannot
                             be changed thereafter. Like sets, frozensets
                             are built into the language, but unlike most
                             of the other standard Python types, there is
                             no way to create a literal frozenset object.
                             Changing that, by providing a mechanism to do
                             so, was the topic of a recent discussion on
                             the python-ideas mailing list.


                             [...]


                             In the end, this “feature” would not be a big
                             change, either in CPython, itself, or for the
                             Python ecosystem, but it would remove a small
                             wart that might be worth addressing.
                             Consistency and avoiding needless work when
                             creating a literal frozenset both seem like
                             good reasons to consider making the change.
                             Whether a Python Enhancement Proposal (PEP)
                             emerges remains to be seen. If it does, no
                             major opposition arises, and the inevitable
                             bikeshed-o-rama over its spelling ever
                             converges, it just might appear in an
                             upcoming Python—perhaps even Python 3.11 in
                             October.


                      # ⚓ Terraform_For_Each_Loop_Examples_–_buildVirtual⠀⇛


                             The Teraform for each meta argument allows
                             you to use a map or a set of strings to
                             deploy multiple similar objects (such as
                             virtual machines) without having to define a
                             separate resource block for each one. This is
                             great for making our Terraform plans more
                             efficient!


                             Note: for_each was added in Terraform 0.12.6,
                             and support for using it with Terraform
                             modules was added in 0.13. Let’s go straight
                             into looking at some examples of how to use
                             Terraform for each loops.


                      # ⚓ Strange_Computer_Languages:_A_Hacker’s_Field_Guide_|
                        Hackaday⠀⇛


                             Why do we build radios or clocks when you can
                             buy them? Why do we make LEDs blink for no
                             apparent purpose? Why do we try to squeeze
                             one extra frame out of our video cards? We
                             don’t know why, but we do. That might be the
                             same attitude most people would have when
                             learning about esolangs — esoteric
                             programming languages — we don’t know why
                             people create them or use them, but they do.


                             We aren’t talking about mainstream languages
                             that annoy people like Lisp, Forth, or VBA.
                             We aren’t talking about older languages that
                             seem cryptic today like APL or Prolog. We are
                             talking about languages that are made to be…
                             well… strange.


                      # § Perl/Raku⠀➾


                            # ⚓ Perl_Weekly_Challenge_149:_Fibonacci_Digit_Sum
                              and_Largest_Square⠀⇛


                            # ⚓ My_Favorite_Warnings:_precedence_|_Tom_Wyant_
                              [blogs.perl.org]⠀⇛


                                   Perl possesses a rich and expressive
                                   set of operators. So rich, in fact,
                                   that other adjectives can come to mind,
                                   such as prolix, or even Byzantine.


                                   Requests for help navigating Perl’s
                                   operator space appear repeatedly on
                                   outlets such as PerlMonks. These seem
                                   to me to involve two sorts of
                                   confusion: precedence (discussed here)
                                   and functionality (string versus
                                   numeric — maybe another blog post).


                                   The precedence warnings category has
                                   some help here, though as of Perl 5.34
                                   there are only two diagnostics under
                                   it:


                      # § Rust⠀➾


                            # ⚓ Niko_Matsakis:_Panics_vs_cancellation,_part_1⠀⇛


                                   One of the things people often complain
                                   about when doing Async Rust is
                                   cancellation. This has always been a
                                   bit confusing to me, because it seems
                                   to me that async cancellation should
                                   feel a lot like panics in practice, and
                                   people don’t complain about panics very
                                   often (though they do sometimes). This
                                   post is the start of a short series
                                   comparing panics and cancellation,
                                   seeking after the answer to the
                                   question “Why is async cancellation a
                                   pain point and what should we do about
                                   it?” This post focuses on explaining
                                   Rust’s panic philosophy and explaining
                                   why I see panics and cancellation as
                                   being quite analogous to one another.


    * § Leftovers⠀➾


          o ⚓ Building_Switching_Points_For_A_Backyard_Railway_|_Hackaday⠀⇛


                 A home-built railway is one of the greatest things you
                 could possibly use to shift loads around your farm. [Tim]
                 and [Sandra] of YouTube channel [Way Out West] have just
                 such a setup, but they needed some switching points to
                 help direct carriages from one set of rails to another.
                 Fabrication ensued!


          o § Science⠀➾


                # ⚓ Study_gives_more_evidence_that_certain_high-tech_utopias
                  are_utopias_|_Stop_at_Zona-M⠀⇛


                       In standardized accountings of trade, money and
                       materials flow in opposite directions. But when
                       embodied resources are considered, net flows of
                       money and resources goes in the same direction.


                       The overall result is that “Rich nations accomplish
                       a net appropriation of materials, energy, land, and
                       labor”.


                       And what is really interesting (not because it is
                       new, but because how it is backed and quantified by
                       data) is the final implication:


                       [Regardless of moral and ethics issues] “we cannot
                       all grow. Since this growth-based model of
                       development requires the appropriation of resources
                       from poorer regions, it seems illusory for all
                       poorer nations to be able to catch-up”, and if
                       those countries must develop, the richer ones have
                       to give up something.


                # ⚓ Jukebox_Electromechanical_Automation_Explained_|_Hackaday⠀⇛


                       If you ever been curious how old-school jukeboxes
                       work, it’s all electromechanical and no computers.
                       In a pair of videos, [Technology Connections] takes
                       us through a detailed dive into the operation of a
                       1970 Wurlitzer Statesman model 3400 that he bought
                       with his allowance when he was in middle school.
                       This box can play records at either 33-1/3 or 45
                       RPM from a carousel of 100 discs, therefore having
                       a selection of 200 songs. This would have been one
                       of the later models, as Wurlitzer’s jukebox
                       business was in decline and they sold the business
                       in 1973.


                       [...]


                       External appearances aside, it’s the innards of
                       this mechanical wonder that steal the show. The
                       mechanism is known as the Wurlamatic, invented by
                       Frank B. Lumney and Ronald P. Eberhardt in 1967.
                       Check out the patent US3690680A document for some
                       wonderful diagrams and schematics that are artwork
                       unto themselves.


          o § Hardware⠀➾


                # ⚓ Upgrading_A_Soviet_Calculator_With_A_Modern_CPU_|
                  Hackaday⠀⇛


                       Today’s supply chain issues can make it hard to buy
                       microcontrollers, or really any kind of
                       semiconductor. But for those keeping retrocomputers
                       alive, this problem has always existed: ancient
                       components might have been out of production for
                       decades, with a dwindling supply of second-hand
                       parts or “new old stock” as the only option. If a
                       rare CPU breaks, you might have no option but to
                       replace the entire computer.


                       [Piotr Patek] ran into this issue when he obtained
                       an Elektronika MK-85 programmable calculator with a
                       broken CPU. Unable to find a replacement, he
                       decided instead to build a pin-compatible CPU unit
                       based on an STM32 microcontroller. Of course no
                       modern CPU is pin-compatible with a Soviet design
                       from the 1980s, so [Piotr] had to design a small
                       interposer PCB to match the original pinout. This
                       also gave him enough space to add an efficient DC/
                       DC converter chip that generates the 2.5 V supply
                       for the STM32.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ Better_Farming_Through_Electricity_|_Hackaday⠀⇛


                       Chinese researchers are reporting that applying an
                       electric field to pea plants increased yields. This
                       process — known as electroculture — has been tested
                       multiple times, but in each case there are
                       irregularities in the scientific process, so there
                       is still an opportunity for controlled research to
                       produce meaningful data.


                       This recent research used two plots of peas planted
                       from the same pods. The plants were tended
                       identically except one plot was stimulated by an
                       electric field. The yield on the stimulated plot
                       was about 20% more than the control plot.


          o § Integrity/Availability⠀➾


                # § Proprietary⠀➾


                      # § Pseudo-Open Source⠀➾


                            # § Privatisation/Privateering⠀➾


                                  # § Linux Foundation and OSI⠀➾


                                        # ⚓ Why_you_want_labels_for_software,
                                          just_like_for_food⠀⇛


                                               Here is my own synthesis,
                                               as simple as possible, of a
                                               much geekier post about a
                                               very geeky concept that, in
                                               an age where so much
                                               depends on how software is
                                               used AROUND you, becomes
                                               every year more important
                                               for everybody.


                                               A Software Bill of
                                               Materials (SBOM) is
                                               becoming an increasingly
                                               expected requirement from
                                               software releases. Reading
                                               through blog posts and
                                               social media, there still
                                               seems that some confusion
                                               persists about what an SBOM
                                               can/could do for your
                                               project.


                                        # ⚓ The_Linux_Foundation_makes_record
                                          progress_in_addressing_talent
                                          shortages⠀⇛


                                               The Linux Foundation
                                               summarises the progress
                                               made in 2021 towards its
                                               goal of ensuring anyone can
                                               start an open-source
                                               technology career.


                                        # ⚓ EV_charging_software_goes_open
                                          source_with_Project_Everest [Ed:
                                          There is no such this as "the Linux
                                          open-source foundation"; this is
                                          greenwashing and openwashing all-in-
                                          one]⠀⇛


                                               The development and
                                               expansion of the EV
                                               charging software ecosystem
                                               is a critical component to
                                               the mainstream adoption of
                                               electric vehicles. However,
                                               the industry has become
                                               complex and fragmented,
                                               with multiple isolated
                                               solutions and inconsistent
                                               technology standards. This
                                               slows and threatens the
                                               adoption of EVs.


                                               In response, PIONIX has
                                               developed a project called
                                               EVerest, an open-source
                                               software stack designed to
                                               establish a common base
                                               layer for a unified EV
                                               charging ecosystem.


                                               EVerest has gained some
                                               serious cred in the
                                               developer world, with its
                                               biggest support LF Energy
                                               (the Linux open-source
                                               foundation for the power
                                               systems sector). I spoke to
                                               the project’s brainchild,
                                               Dr. Marco Möller, managing
                                               director of PIONIX, to find
                                               out more.


                                        # ⚓ Spotlight_on_Libre_Space
                                          Foundation,_OSI_Associate_Member⠀⇛


                                               Did you know that one of
                                               OSI’s members is leading
                                               the effort to take open
                                               source to infinity and
                                               beyond?! Libre Space
                                               Foundation (LSF) is a non-
                                               profit foundation
                                               registered in Greece whose
                                               vision is “an Open and
                                               Accessible Outer Space for
                                               all.” The organization
                                               works to promote, advance
                                               and develop free and open
                                               source technologies and
                                               knowledge for space.


                                               Recently, Libre Space
                                               Foundation, on behalf of
                                               the OpenSatCom.org activity
                                               of the European Space
                                               Agency, partnered with
                                               Inno3 to investigate open
                                               source development models
                                               in the satellite
                                               communications industry and
                                               share their findings in a
                                               report. As the authors
                                               explain, “..the SATCOM
                                               industry has been
                                               traditionally multiple
                                               vertical ecosystems and
                                               moved towards some
                                               standardization (through
                                               efforts like CCSDS, ECSS,
                                               DVB, etc.) on various of
                                               its parts. Yet it is far
                                               from an Open Ecosystem and
                                               specific actions should be
                                               taken to explore this
                                               direction for the benefit
                                               of the SATCOM industry.”


                      # § Security⠀➾


                            # ⚓ Apple_Releases_Security_Updates_for_Multiple
                              Products⠀⇛


                                   An attacker could exploit some of these
                                   vulnerabilities to take control of an
                                   affected system.


                            # ⚓ Why_Security_in_Kubernetes_Isn’t_the_Same_as_in
                              Linux:_Part_1_|_MarketScreener⠀⇛


                                   The risks of a Kubernetes (K8s)
                                   deployment are actually the same as in
                                   traditional Linux servers.


                            # ⚓ Do_you_need_pkexec_and_polkit_on_a_WM?_NO!_CVE-
                              2021-4034⠀⇛


                                   Thanks to Somewhat Reticent for being
                                   always on alert and contributing:


                                   Do you need pkexec and polkit on a WM?
                                   NO! CVE-2021-4034


                                   Not unless you want some automated menu
                                   and icons to click on and use various
                                   user/root rights to execute a gui!
                                   Otherwise you are “safe“.


                                   Don’t think because RH is reporting
                                   this the only affected parties are RHEL
                                   users, anyone who uses their systemd
                                   elogind and polkit derivatives are
                                   equally affected.


                                   But gksu/gksudo was insecure and had to
                                   be erased from nearly every distro that
                                   is an IBM “client”.


                            # ⚓ Bug_bounties:_finding_and_fixing_security_holes
                              with_European_Commission_funds_–_The_Document
                              Foundation_Blog⠀⇛


                                   Free and open source software (FOSS) is
                                   about much more than driving costs
                                   down, in some cases even down to zero –
                                   it’s about giving control back to
                                   users, developers and even nations.
                                   With FOSS, everyone gains the freedom
                                   to study, improve and share the
                                   software – and to use it whenever and
                                   wherever they want, without being
                                   restricted by vendor lock-in
                                   strategies.


                                   FOSS has been widely used amongst
                                   government bodies and public services,
                                   so thanks to the coordination of their
                                   recently formed Open Source Programme
                                   Office (OSPO), the European Commission
                                   has started a series of hackathon and
                                   “bug bounty” programmes to help
                                   selected projects find (and potentially
                                   fix) security issues.


                            # ⚓ CVE-2021-4034_–_Ariadne’s_Space⠀⇛


                                   Before we get into this, I have seen a
                                   lot of people on Twitter blaming
                                   systemd for this vulnerability. It
                                   should be clarified that systemd has
                                   basically nothing to do with polkit,
                                   and has nothing at all to do with this
                                   vulnerability, systemd and polkit are
                                   separate projects largely maintained by
                                   different people.


                                   We should try to be empathetic toward
                                   software maintainers, including those
                                   from systemd and polkit, so writing
                                   inflammatory posts blaming systemd or
                                   its maintainers for polkit does not
                                   really help to fix the problems that
                                   made this a useful security
                                   vulnerability.


                            # ⚓ Windows_ransomware_LockBit_makes_the_jump_to
                              Linux [Ed: Pro-Windows site. Misses the point
                              that over_90%_of_ransomware_is_a_Windows
                              problem.]⠀⇛


                                   First, they came for Windows. Then, for
                                   Tux. As cool as Linux is, it’s
                                   increasingly becoming a target for
                                   ransomware-friendly cyber criminals
                                   intent on ruining people’s days.


                            # ⚓ These_critical_security_bugs_put_Linux_servers
                              at_risk_of_attack [Ed: Attack from the inside
                              maybe; you need to actually have an account on
                              such machines to begin with... compare to Windows
                              with remotely-exploitable full compromise bugs/
                              back doors]⠀⇛


                            # ⚓ Patch_Now:_A_newly_discovered_critical_Linux
                              vulnerability_probably_affects_your_systems⠀⇛


                            # ⚓ Experts_Urge_Firms_to_Patch_Trivial-to-Exploit
                              Flaw_in_Linux_PolicyKit⠀⇛


                            # ⚓ IoT_security_certification_group_gains_steam
                              [Ed: Another fake security consortium? Their
                              shoddy products might be best off avoided
                              altogether, as there's rarely a practical need
                              for such gimmicks.]⠀⇛


                                   The ioXT Alliance, which offers a
                                   certification program for IoT security,
                                   announced it has certified 195 products
                                   and grown to 580 members. Meanwhile,
                                   Timesys is seeking participants for a
                                   survey on IoT security.


                            # § Privacy/Surveillance⠀➾


                                  # ⚓ The_best_and_the_worst_in_2022:_data
                                    protection_laws_across_the_world⠀⇛


                                         Don’t look up. From catastrophic
                                         data breaches, to spyware attacks
                                         that haunt people with the
                                         specter of their own private
                                         communications, to the routine
                                         exploitation of our personal data
                                         for profit and political
                                         manipulation, privacy violations
                                         have become daily news. None of
                                         this will stop until we do
                                         something about it.


                                         On Data Protection Day 2022, we
                                         are urging governments around the
                                         world to take action to prevent
                                         rampant data violations. To do
                                         so, they must enact and strongly
                                         enforce data protection laws.


                                         Data protection laws are a
                                         critical tool to ensure minimum
                                         rules are in place to safeguard
                                         our personal information online
                                         and offline. The European Union
                                         was one of the first movers,
                                         establishing a data protection
                                         framework in the ‘90s, and
                                         working continuously to improve
                                         it. Other countries followed
                                         suit. Brazil and Ecuador are
                                         among the latest to pass strong,
                                         modern data protection laws.


                                         Other countries are lagging
                                         behind, and despite constant
                                         privacy scandals, some have no
                                         comprehensive data protection
                                         laws at all. Others have passed
                                         promising laws, but ignore them.
                                         Even where strong laws exist,
                                         enforcing them is proving harder
                                         than expected. Here’s a look at
                                         countries with some of the best
                                         and worst data protection laws in
                                         2022.


                                  # ⚓ Reclaim_your_face!_Now_|_Stop_at_Zona-M⠀⇛


                                         If you don’t, it will be used
                                         against you. Maybe already it is.


                                         There is evidence that biometric
                                         mass surveillance in EU Member
                                         States and by EU agencies has
                                         already resulted in violations of
                                         EU data protection law, and
                                         unduly restricted people’s rights
                                         including their privacy, right to
                                         free speech, right to protest and
                                         not to be discriminated against.
                                         That is why you must “reclaim
                                         your face”!


          o § Environment⠀➾


                # ⚓ The_unsustainable_dumbness_of_“smart”_recycling_|_Stop_at
                  Zona-M⠀⇛


                       Because innovation, of course.


                       According to the Washington Post and to this
                       summary there is a startup throwing money and human
                       ingenuity to tackle “a flaw in our waste management
                       systems that many people probably aren’t aware of.”


                       Lasso Loop, the story says, is developing “a hefty
                       home appliance machine that automatically sorts and
                       breaks down the recyclables you toss inside it”.


                # § Energy⠀➾


                      # ⚓ There_is_only_one_problem_with_these_electrification
                        strategies_|_Stop_at_Zona-M⠀⇛


                             … it’s their “Business as Usual” foundation.


                             [...]


                             If none of those issues existed, it would
                             indeed become physically and geopolitically
                             feasible to replace all the ” fossil fuel-
                             burning machines [i.e. ALL] Power plants,
                             cars, and trucks, HVAC systems, stoves,
                             roofs, etc [of TODAY]” with the same number
                             of the same things, just electric.


                             If none of those issues existed, every owner
                             of a car or a single-family home with
                             disposable income left could follow advice
                             like “make your next car electric, turn your
                             home into a big battery”.


                             As reality stands today, instead… first, most
                             people who don’t fit that profile today may
                             never become part of the mass market that
                             certain strategies would need to function IF
                             they were feasible.


                             Second, I have a strong feeling that in the
                             next years a non-negligible number of people
                             who do fit that profile today will find
                             advice like “move to an apartment building
                             properly served by public transit” much more
                             interesting, if not the only alternative
                             still affordable, than “keep owning a car and
                             a single-family home”. What will happen of
                             certain strategies then?


          o § Finance⠀➾


                # ⚓ Digital_Services_and_Tools_Fuel_Fastest_GDP_Growth_Since
                  1984 [Ed: Fake economy and "growth" delusion? What grew? Wall
                  Street?]⠀⇛


                       Today’s GDP report showed that the U.S. economy
                       grew by 5.7% in 2021, the most robust economic
                       growth since 1984.


                       The crucial role of digital technology in this
                       rebound is not doubted. Digital services and tools
                       empowered the recovery by giving Americans more
                       choices than ever before to more safely get back to
                       work, school, shopping, and leisure. New digital-
                       enabled options like remote work, remote classes,
                       and contactless shopping options like buy online,
                       pickup in-store/curbside and home delivery sparked
                       this positive growth, despite ongoing pandemic
                       challenges.


                       Digital services and tools have been essential to
                       carry small and medium-sized businesses (SMBs)
                       through the pandemic, helping them connect with
                       both workers and customers alike. By utilizing both
                       new and existing digital tools, businesses were
                       able to rapidly expand contactless shopping,
                       dining, and entertainment options. For example,
                       retailers rapidly expanded omnichannel offerings,
                       allowing consumers to safely shop from home and
                       choose whether to pick up their orders curbside in
                       front of physical stores or have their orders
                       delivered to their homes.



                    ䷩ 𝚕𝚒𝚗𝚎 6958

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.27.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_27/1/2022:_Mabox_Linux_21.11_Herbolth_and_PipeWire_0.3.44⠀✐


Posted in News_Roundup at 6:30 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o ⚓ The_sorry,_sorry_state_of_Linux_packaging_|_Stop_at_Zona-M⠀⇛


                 On one hand yeah, sure: today there are many more
                 programs “packaged” for Linux than twenty years ago. On
                 the other, I feel myself longing every year more for the
                 good old days when lots of developers limited themselves
                 to, you know, “we don’t release Linux binary packages of
                 our software, because Linux distros are too fragmented
                 and we don’t know for WHICH one we should build
                 packages.”


                 Today, if you need ten programs not present in the
                 default repositories of your Linux distribution, you may
                 likely need to run almost as many separate software
                 distribution systems, all deliberately created to
                 simplify your life of course, all blissfully unaware of
                 each other.


                 Forget compiling from sources: it would just move the
                 problem to installing the same number of separate,
                 possibly uncompatible toolchains, most of which are much
                 more complex to set up and use that the good old “./
                 configure make && make install” of yore.


                 Oh, and of course you should be prepared to re-run all
                 those systems every time you upgrade your Linux
                 distribution. Not manually, of course! Without doubts,
                 the Right Thing To Do ™ would be to handle everything
                 with some custom-made Ansible playbooks, or some other CM
                 system, right? To add, that is, another level of
                 embarrassing complexity to a problem that should not
                 exist in the first place.


          o § Kernel Space⠀➾


                # ⚓ PipeWire_0.3.44⠀⇛


                       This is a bugfix release that is API and ABI
                       compatible with previous 0.3.x releases.


          o § Graphics⠀➾


                # ⚓ A_$1.25_Billion_Hit:_NVIDIA_Is_Apparently_Throwing_in_the
                  Towel_When_It_Comes_to_Its_Planned_Acquisition_of_Arm
                  Holdings⠀⇛


                       NVIDIA (NASDAQ:NVDA) has apparently found it
                       impossible to surmount an ever-increasing pile of
                       obstacles that now litter the path toward its
                       acquisition of Arm Holdings.


                # ⚓ DirectFB2_project_brings_back_DirectFB_graphics_library_for
                  Linux_embedded_systems_–_CNX_Software⠀⇛


                       DirectFB2 is a new open-source project that brings
                       back DirectFB, a graphics library optimized for
                       Linux-based embedded systems that was popular
                       several years ago for 2D user interfaces but has
                       since mostly faded away. DirectFB2 attempts to
                       preserve the original DirectFB backend while adding
                       new features such as modern 3D APIs like Vulkan and
                       OpenGL ES.


                       I personally used it in 2008-2009 while working
                       with Sigma Designs media processors that relied on
                       the DirectFB library to render the user interfaces
                       for IPTV boxes, karaoke machines, and so on. I
                       remember this forced me to switch from a
                       MicroWindows + Framebuffer solution, but the
                       DirectFB API was easy enough to use and allowed us
                       to develop a nicer user interface.


                # ⚓ Intel’s_Vulkan_Linux_Driver_Lands_Dynamic_Rendering_Support
                  –_Phoronix⠀⇛


                       As part of pushing it across the Vulkan 1.3
                       milestone, Intel’s open-source graphics driver
                       developers have merged their
                       VK_KHR_dynamic_rendering support to mainline.


                       Vulkan dynamic rendering for the Intel “ANV” Vulkan
                       driver was pending on the mailing list for the past
                       month while on Vulkan 1.3 day it was successfully
                       merged, with this extension being part of the core
                       specification now. The Khronos documentation on
                       dynamic rendering explains, “If you’re not using
                       multiple subpasses or input attachments though, go
                       ahead, rip those render pass objects right out!
                       Dynamic rendering offers similar rendering
                       performance to a single pass render pass object but
                       with a much simpler interface on all
                       implementations. Hopefully this extension will make
                       writing future Vulkan renderers just a bit more
                       enjoyable.”


                # ⚓ Intel’s_Linux_Graphics_Driver_Patched_For_New_Security
                  Issue_But_Can_Impact_Performance_–_Phoronix⠀⇛


                       Intel’s “i915″ kernel graphics driver has been
                       patched for a software issue that could lead to
                       malicious user-space trigger DMAR read/write faults
                       or worse is the possibility of user-space gaining
                       access to random memory pages. Unfortunately, the
                       security fix comes with performance implications.


                       If not running with an IOMMU active, CVE-2022-0330
                       could lead to user-space gaining access to random
                       memory pages. This could mean either data leaks
                       and/or random memory corruption. The issue with the
                       Intel graphics driver stems from a missing TLB
                       flush when releasing memory that was backing a GPU
                       buffer object to the system memory.


                # ⚓ AMDVLK_2022.Q1.2_Released_With_Vulkan_1.3_Support⠀⇛


                       AMDVLK as AMD’s official open-source Vulkan Linux
                       driver derived from their Radeon Software driver
                       sources but using the LLVM shader compiler back-end
                       is out with a new release. AMD is ready with day-
                       after support for the newly-launched Vulkan 1.3
                       specification for AMDVLK.


                       The AMDVLK 2022.Q1.2 driver enables Vulkan 1.3
                       support as well as enabling SPIRV 1.6 support. The
                       VK_EXT_provoking_vertex and
                       VK_EXT_depth_clip_control extensions are enabled
                       too with today’s release.


          o § Instructionals/Technical⠀➾


                # ⚓ Gemini_Is_A_Little_Gem⠀⇛


                       In this brief blog post, I’ll talk about Gemini
                       from a different point of view. Not attacking these
                       arguments individually, but trying to talk a bit
                       about what attracts me to the protocol and how I
                       see it. I hope that by the end of this post, you’ll
                       have a different approach to reasoning about
                       Gemini. And, if you decide to write criticism about
                       it, that you’ll take what is written here into
                       account.


                # ⚓ Annotating_my_website_page_structure⠀⇛


                       While I was trying to figure out how to link a
                       manifest.json file to my feed reader, I found
                       myself looking at the source code behind Jeremy
                       Keith’s website home page. The fact that you can
                       see the source code behind how a page loads is an
                       amazing feature behind the web. You can see the
                       code that tells a browser how a web page loads.
                       Sometimes the source code behind a site is almost
                       or completely illegible but there are plenty of
                       sites out there whose code you can peruse.


                # ⚓ CSS_Specificity_Demo⠀⇛


                       I built an interactive demo to illustrate how
                       specificity in CSS works.


                # ⚓ Hashing_out_the_hash_command_on_Linux_|_Network_World⠀⇛


                       When you type “hash” on a Linux system, you could
                       get one of two very different responses depending
                       on the shell you are using.


                       If you are using bash or a related shell such as
                       ksh, you should see a list of the commands that you
                       have used since your terminal session began,
                       sometimes with a count of how many times each
                       command was used. This can be more useful than
                       using the history command if you just want to see
                       your very recent command activity, but the hash
                       command is not a single executable. Instead, it
                       relies on your shell.


                # ⚓ Learn_About_Blender_and_Maybe_Get_a_Free_Book_–_What’s_Not
                  to_Like?⠀⇛


                       The event is Blender 101, an online event from the
                       All Things Open folks, which will feature Jason van
                       Gumster, author of Blender for Dummies, which is
                       popular enough to now be in its fourth edition.
                       Better yet, some copies of the book will be given
                       away “to randomly chosen attendees.”


                # ⚓ Why_must_you_use_./_to_run_your_Ubuntu_scripts?_The_meaning
                  of_Linux’s_dot_slash_explained._–_Coffee_Talk:_Java,_News,
                  Stories_and_Opinions⠀⇛


                       When you run your own executable command or shell
                       script on Linux, you must prepend ./ to the Unix
                       command. But why?


                       Why must you use a dot slash to run commands in
                       Unix? You don’t have to do that in Windows with a
                       batch file.


                # ⚓ What_Is_Doas_and_How_to_Install_It⠀⇛


                       Doas is a privilege escalation program similar to
                       sudo. It is designed to be as lightweight and
                       simple as possible. It is the default privilege
                       escalation program for OpenBSD but also available
                       for other UNIX-like operating systems through the
                       OpenDoas program.


                # ⚓ Shell_Aliases_Every_Linux_User_Needs_–_Invidious⠀⇛


                       One of the most common questions I get from new-to-
                       Linux users is, “How can I become a power user?”
                       Well, learning the terminal and the terminal
                       commands is the best thing you can do. And big part
                       of becoming more proficient at the command line is
                       creating your own Bash aliases. So today, I’m
                       taking a fresh install of Ubuntu and adding aliases
                       to it’s bashrc. These are aliases that I think
                       most, if not all, Ubuntu users would find helpful.


          o § Games⠀➾


                # ⚓ Steam_Deck_Launching_February_25th⠀⇛


                       Hello, the day is almost here! On February 25th, we
                       will be sending out the first batch of order emails
                       to reservation holders. Customers will have 3 days
                       (72 hours) from receipt of their order email to
                       make their purchase, before their reservation is
                       released to the next person in the queue. The first
                       units will be on their way to customers starting
                       the 28th, and we plan to release new order email
                       batches on a weekly cadence.


                       In addition, we’re sending out press units for full
                       review shortly. Press review embargo on Steam Deck
                       coverage will lift on February 25th, but keep an
                       eye out for some preview coverage and impressions
                       before that. In the meantime we’re working to tie
                       up the last few loose ends and polish some rough
                       edges, and are excited to get these out to you at
                       the end of next month!


                # ⚓ Steam_Deck_launches_February_25,_weekly_purchase_invites
                  planned_|_GamingOnLinux⠀⇛


                       The date a great many have no doubt be waiting for,
                       Valve has today officially announced their Steam
                       Deck handheld will launch officially on February
                       25.


                       It will go by the date each user put in their
                       reservation of course, starting off with the first
                       lucky few who managed to dodge Valve’s server
                       issues at the time. The first batch of order
                       invitation emails go out on February 25, and each
                       person has just 72 hours to make the actual
                       purchase before it moves onto the next person in
                       the queue.


                # ⚓ Valve_To_Formally_Launch_Steam_Deck_On_25_February,
                  Shipping_Begins_28_February_–_Phoronix⠀⇛


                       After slipping from the original shipping target of
                       Q4 due to component shortages, Valve is making good
                       on their Q1’2022 shipping plans for the Steam Deck.


                       Valve just announced the Steam Deck will indeed
                       begin shipping by the end of February. 25 February
                       is when they will ship the first batch of order
                       emails to reservation holders and they will have
                       three days to complete their orders. Steam Deck
                       units are expected to begin shipping to customers
                       on 28 February.


                       Valve also confirmed that new order emails will be
                       sent out on a weekly basis to reservation holders.
                       Valve will send out the order emails in the same
                       order as reservations that began last year. Valve
                       has not confirmed the planned weekly batch sizes or
                       how many units will be ready to ship on 28
                       February.


                # ⚓ Godot_Engine_–_Godot_OpenXR_1.1.1_Plugin_Release⠀⇛


                       The Godot XR contributors are delighted to release
                       our latest version of the Godot OpenXR plugin!


                       This release contains several updates to provide
                       Godot XR developers access to the latest and
                       greatest XR APIs and features.


                # ⚓ SDL2_On_Linux_Now_Prefers_Wayland_Over_X11_–_Phoronix⠀⇛


                       With today’s SDL2 Git, Wayland is now preferred
                       over X.Org/X11 by default without having to set the
                       SDL video driver environment variable.


                       As of today’s Git development code for the Simple
                       DirectMedia Layer and what will be the behavior in
                       the upcoming SDL 2.0.22, Wayland is now preferred
                       when present. While SDL2 has offered Wayland
                       support for some time now, SDL2 would out-of-the-
                       box prefer X11 (and XWayland in turn) support. The
                       SDL_VIDEODRIVER=wayland environment variable can be
                       used for forcing the Wayland code path while now
                       it’s the preferred route.


                # ⚓ Valve_Working_On_Radeon_Dynamic_VRS_For_The_Steam_Deck_To
                  Increase_Power_Savings_–_Phoronix⠀⇛


                       Yet another open-source Radeon Vulkan “RADV” driver
                       improvement being worked on by Valve’s engineers is
                       around better controlling variable rate shading
                       “VRS” behavior with a focus on improving power
                       savings for the Steam Deck.


                       Vulkan has the VK_KHR_fragment_shading_rate
                       extension for being able to control the shading
                       rate depending upon the frame region being shaded.
                       The shading at a lower resolution for less
                       important areas of the screen can help with
                       increasing performance as well as power-savings.
                       One of the frequently cited examples around
                       variable rate shading is often for the landscape
                       within racing games.


          o § Desktop Environments/WMs⠀➾


                # ⚓ Sway_1.7_improves_screen_capture_and_virtual_reality_in
                  Wayland_–_itsfoss.net⠀⇛


                       sway 1.7 is available to continue the evolution of
                       this Wayland composer and window manager based on
                       or inspired by the popular i3.


                       Despite being “just” a window manager, Sway is one
                       of the most interesting developments when it comes
                       to Wayland composers, and not only that, but is
                       considered by many to be the best implementation of
                       the protocol out there, even by comparison. on top
                       of the GNOME Mutter.


                       On the other hand, it has been one of the brave few
                       to openly say “no” to NVIDIA and EGLStreams in
                       order to narrowly defend the standards agreed upon
                       by almost everyone around Wayland and GBM. You
                       know, the word “standard” gives NVIDIA hives, and
                       the exact reasons are known only to the
                       corporation’s executives.


                       The first notable new feature of Sway 1.7 is the
                       remove option –my-next-gpu-wont-be-nvidia, so the
                       ones that users will have to use from now on
                       –unsupported-gpu instead. It’s important to note
                       that, at least officially, the official NVIDIA
                       driver is still not supported (Nouveau should be
                       fine), but we assume that this is a first step
                       towards integrating the particular GBM
                       implementation powered by the GPU manufacturer.


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


                      # ⚓ Season_of_KDE_Kicks_Off⠀⇛


                      # ⚓ Season_of_KDE_2022⠀⇛


                             I am Ayush Singh, a second-year student of
                             the Indian Institute of Technology, Dhanbad,
                             India. My application has been accepted in
                             the Season of KDE 2022. I will be working on
                             writing a Rust wrapper for KConfig KDE
                             Framework. This post describes my journey
                             with KDE and why I submitted this Project for
                             the Season of KDE.


                      # ⚓ Creating_Rust/QML_Project⠀⇛


                             For the last few months, I have been pushing
                             Rust/QT development along. I am the author of
                             ki18n crate and am currently in the middle of
                             creating kconfig crate as a part of Season of
                             KDE 2022.


                             In this post, I will walk you through
                             creating a new Rust/QML project using cargo-
                             generate templates. I made these templates to
                             encourage more people to test out Qt
                             development with Rust.


          o § Distributions⠀➾


                # § New Releases⠀➾


                      # ⚓ Mabox_Linux_21.11_Herbolth_released⠀⇛


                             After almost half year of development, the
                             next major Mabox Linux 21.11 release codename
                             Herbolth is ready for download.


                # § BSD⠀➾


                      # ⚓ Playing_with_CD-RWs_on_FreeBSD⠀⇛


                             It’s worth mentioning as well that CD-RWs do
                             typically take longer to burn that a CD-R,
                             even discounting the time taken to blank
                             them. It’s more than an acceptable compromise
                             for me, but don’t be surprised if the drive
                             reports 4 for the drive speed. I did briefly
                             have a CD burner and CD-RW media as a kid
                             that worked at 8×, but both those are long
                             gone.


                             This was a fun experiment! Now I have a
                             reliable way to generate these disc images
                             with a few CD-RWs.


                      # ⚓ A_proof_of_concept:_running_OpenBSD_on_the
                        PinePhone⠀⇛


                             As mentioned in the piece, this comes with a
                             bit of a warning: [...]


                # § Canonical/Ubuntu Family⠀➾


                      # ⚓ Canonical_releases_Charmed_Kubeflow_1.4_to_simplify
                        enterprise_AI_projects⠀⇛


                             Canonical Ltd. on Tuesday released Charmed
                             Kubeflow 1.4, the newest version of its
                             platform for simplifying enterprise
                             artificial intelligence projects.


                             U.K.-based Canonical is the maker of Ubuntu,
                             one of the most widely used versions of the
                             Linux operating system. Ubuntu is especially
                             popular in the enterprise, where it’s
                             commonly used to power public cloud
                             environments. The operating system is
                             frequently deployed together with Kubernetes.


                             A growing number of enterprises are running
                             AI models in their Kubernetes environments to
                             support machine learning initiatives. In
                             2018, Google LLC released an open-source tool
                             called Kubeflow to simplify the task of
                             running AI software on Kubernetes.
                             Canonical’s newly updated AI platform,
                             Charmed Kubeflow, is a customized version of
                             Google’s Kubeflow designed to be easier to
                             use.


                             Canonical provides the software under an
                             open-source license. In addition to
                             Kubeflow’s core features, Charmed Kubeflow
                             includes automation code that the company
                             says simplifies a number of day-to-day
                             management tasks. The software can be
                             deployed in the public cloud, as well as on-
                             premises.


          o § Devices/Embedded⠀➾


                # § Open Hardware/Modding⠀➾


                      # ⚓ Simulating_the_IBM_360/50_mainframe_from_its
                        microcode⠀⇛


                             The IBM System/360 was a groundbreaking
                             family of mainframe computers announced on
                             April 7, 1964. System/360 was an extremely
                             risky “bet-the-company” project for IBM,
                             costing over $5 billion, but the System/360
                             ended up as a huge success, setting the
                             direction of the computer industry for
                             decades. The S/360 architecture was so
                             successful that it is still supported by
                             IBM’s latest mainframes, almost 60 years
                             later. I’m developing a microcode-level
                             simulator1 for the IBM System/360 Model 50
                             (link to the simulator); this blog post
                             provides background to understand the Model
                             50 and the simulator.


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


                # § FSF⠀➾


                      # § GNU Projects⠀➾


                            # ⚓ Internet_Hall_of_Famer_Dr._Richard_Stallman_to
                              give_presentation_to_the_Jeff.pro_GNU+Linux_User
                              Group⠀⇛


                # § Programming/Development⠀➾


                      # ⚓ Part_1:_The_life_of_an_optimization_barrier⠀⇛


                             Many engineers choose Rust as their language
                             of choice for implementing cryptographic
                             protocols because of its robust security
                             guarantees. Although Rust makes safe
                             cryptographic engineering easier, there are
                             still some challenges to be aware of. Among
                             them is the need to preserve constant-time
                             properties, which ensure that, regardless of
                             the input, code will always take the same
                             amount of time to run. These properties are
                             important in preventing timing attacks, but
                             they can be compromised by compiler
                             optimizations.


                      # ⚓ The_Qt_Company_launches_digital_advertising
                        solution⠀⇛


                             The Qt Company, the leading global provider
                             of software technology, today announces the
                             launch of Qt Digital Advertising to help Qt
                             users monetize UI/UX screens built with Qt.
                             The new solution, which will significantly
                             streamline and enhance revenue generation
                             opportunities for mobile, desktop and
                             embedded applications and devices, was
                             designed to focus on monetization,
                             productivity and disruption.


                             For the first time ever, mobile, desktop and
                             embedded developers can generate revenue by
                             leveraging digital advertising directly
                             within the Qt development framework. Users
                             will no longer be required to implement
                             cumbersome, costly, inefficient monetization
                             platforms, that are not fully integrated, to
                             generate revenue. Instead, and with the help
                             of Qt, organizations can instantly build and
                             monetize the right digital advertising
                             business case for their cross-platform
                             scenarios, from prototype to final product.
                             The solution will also create new business
                             cases for advertisers to run efficient
                             marketing campaigns on embedded device UIs,
                             capitalizing on opportunities presented by
                             the rapidly growing IoT and connected devices
                             industry, in addition to being a new business
                             model for The Qt Company and its customers.


                      # ⚓ NodeKit_Update⠀⇛


                             Since the initial demo of NodeKit at last
                             week’s Small Is Beautiful, we now actually
                             have a nodekit command, the server now does
                             naïve restarts on route changes, and routes
                             are now lazily loaded the first time they’re
                             hit.


    * § Leftovers⠀➾


          o § Science⠀➾


                # ⚓ James_Webb_Space_Telescope:_When_to_expect_the_first_images
                  from_the_state-of-the-art_observatory⠀⇛


                       The observatory’s permanent home is a stable point
                       in space known as Lagrange Point 2, also referred
                       to as L2. L2 is also a point in space where
                       gravitational forces of the Earth and Sun are in
                       equilibrium, allowing JWST to stay aligned with
                       Earth. L2 will also allow JWST to have a wide,
                       unobstructed view of the universe at any given
                       moment, unlike telescopes closer to Earth (like
                       Hubble) whose point of view is often obscured by
                       the Earth itself.


                       JWST is a once-in-a-generation space observatory
                       poised to usher in a new chapter for astronomy by
                       peering into distant corners of the universe,
                       surveying the atmospheres of Earth-like exoplanets,
                       and observing more distant stars and galaxies than
                       its predecessors. As the Hubble Space Telescope’s
                       successor, it is also one of the most expensive
                       space missions (roughly $9.7 billion) in history.
                       In other words, a lot is at stake.


          o § Education⠀➾


                # ⚓ GOP_Is_Increasingly_Bent_on_Controlling_Schools._Glenn
                  Youngkin_Is_a_Case_Study.⠀⇛


                # ⚓ Higher_education_must_stop_covering_up_misconduct⠀⇛


                       Some universities even require a pre-emptive NDA to
                       initiate a complaints process, and they commonly
                       negotiate deals directly with perpetrators without
                       involving the victims at all. In many university
                       processes, complainants are not permitted to see
                       the final decision – or they are asked to sign an
                       NDA before they can access it. Where the
                       complainant is a party, they are told that they
                       “must” sign an NDA to “protect themselves”. This is
                       neither true nor accurate – a complainant does need
                       a one-sided confidentiality clause, but it should
                       not come at the price of protecting the person who
                       harmed them.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ Only_10_Percent_of_Africa’s_Population_Is_Fully
                  Vaccinated⠀⇛


                # ⚓ Sanders_Demands_End_to_Medicare_Premium_Hike_From
                  Alzheimer’s_Drug⠀⇛


                       Building on his recent letter to U.S. President Joe
                       Biden, Sen. Bernie Sanders on Tuesday wrote to a
                       key government analyst to push for a swiftly ending
                       a Medicare premium hike tied to Biogen’s pricey and
                       potentially ineffective Alzheimer’s drug.


                       “Alzheimer’s is a horrible disease and we must do
                       everything possible to find a cure for the millions
                       of seniors who suffer from it, but we cannot allow
                       pharmaceutical companies to rip off seniors.”


                # ⚓ Anne_Frank:_RFK_Jr._now_versus_RFK_Jr._in_2015⠀⇛


                       Since writing my “preview” last Friday of the
                       antivaccine “Defeat the Mandates” rally held on
                       Sunday, I have been debating whether or not to
                       write a followup post. The reason was that I just
                       didn’t know if there was anything much to say,
                       given that the rally went pretty much as I had
                       predicted, with a stacked bill of antivaccine
                       cranks old (e.g., Robert F. Kennedy, Jr. and Del
                       Bigtree) and new (e.g., Dr. Robert Malone, Dr.
                       Peter McCullough, and Steve Kirsch), antimaskers,
                       and COVID-19 minimizers spewing a litany of common
                       anti-“lockdown,” antimask, and antivaccine
                       propaganda, all couched in rhetoric of “freedom”
                       and “resistance to tyranny,” just as expected and
                       the same as it ever was for antivaxxers. I was
                       originally not going to write further about this,
                       but leave it to RFK Jr. to give me a reason when he
                       sullied the memory of Anne Frank:


                # ⚓ St._Petersburg_announces_new_restrictions_for_minors
                  following_spike_in_coronavirus_hospitalizations⠀⇛


                       After noting a marked increase in the number of
                       local children hospitalized with COVID-19, the St.
                       Petersburg authorities have announced additional
                       public health restrictions for minors. With the
                       Omicron strain running rampant, Russia has recorded
                       record-breaking daily increases in coronavirus
                       cases over the past few days. In St. Petersburg, an
                       increasing number of classes have been forced to
                       switch to distance learning in order to quarantine
                       schoolchildren with COVID-19 and other respiratory
                       infections. The additional restrictions for minors
                       will enter force on January 28 and remain in place
                       until February 13.


                # ⚓ EPA_Takes_Action_to_Combat_Industrial_Air_Pollution⠀⇛


                       The Environmental Protection Agency launched
                       sweeping changes this week to address long-standing
                       problems brought to light by ProPublica’s reporting
                       on industrial air pollution. Shortly after the
                       November publication of our investigation,
                       administrator Michael S. Regan toured some of the
                       largest toxic hot spots identified by our analysis
                       and said the agency was consulting ProPublica’s
                       work as it considered reforms. On Wednesday, Regan
                       announced the EPA’s next steps, which include a
                       significant expansion of air monitoring in some of
                       the most polluted neighborhoods in the country and
                       a new wave of unannounced inspections of polluters.


                       “We are going to keep these facilities on their
                       toes so that they’re doing their due diligence all
                       the time and not just when there’s a planned
                       inspection,” he said. “Being on the ground, seeing
                       the situation for myself, and talking directly with
                       community members, it is startling that we got to
                       this point.”


                # ⚓ Spotify_sides_with_Joe_Rogan_after_Neil_Young_ultimatum⠀⇛


                       Earlier this month, an open letter signed by 270
                       health care professionals urged Spotify to take
                       action against COVID-19 vaccine misinformation that
                       it said was spread on Rogan’s show, which boasts a
                       wide reach, with an estimated 11 million listeners
                       per episode.


                # ⚓ Spotify_picks_Joe_Rogan_over_Neil_Young⠀⇛


                       Spotify and Warner Records didn’t immediately reply
                       to a request for comment from The Verge. In a post
                       on his website, Young thanked his label for its
                       support and said that Spotify has “become the home
                       of life threatening COVID misinformation.”


                # ⚓ Neil_Young_Removes_Music_From_Spotify_in_Protest_of_Joe
                  Rogan’s_Podcast⠀⇛


                       Spotify will remove Neil Young’s music from its
                       platform, per his request, following his objections
                       to Joe Rogan’s statements about the Covid-19
                       vaccine on his Spotify-hosted show. The music is
                       expected to be removed later Wednesday.


                       A rep for Spotify said in a statement to Variety:
                       “We want all the world’s music and audio content to
                       be available to Spotify users. With that comes
                       great responsibility in balancing both safety for
                       listeners and freedom for creators. We have
                       detailed content policies in place and we’ve
                       removed over 20,000 podcast episodes related to
                       COVID since the start of the pandemic. We regret
                       Neil’s decision to remove his music from Spotify,
                       but hope to welcome him back soon.”


                # ⚓ Neil_Young_Pulls_Music_from_Spotify,_Blasts_It_as_the_‘Home
                  of_Life-Threatening’_Covid_Lies⠀⇛


                       On Monday, Young posted a since-deleted letter on
                       his website addressed to his management and record
                       label demanding his music be removed from Spotify,
                       noting that the company can have “Rogan or Young.
                       Not both.” The Wall Street Journal first reported
                       the news that Spotify will take down Young’s
                       catalog. Spotify begun to remove Neil Young’s
                       catalog Wednesday evening.


                       In Young’s new letter, he blasts Spotify as “a very
                       damaging force via its public misinformation and
                       lies about Covid.” He thanked his label Warner
                       Records for standing by his decision and noted that
                       a majority of his streaming revenue comes from
                       Spotify.


          o § Integrity/Availability⠀➾


                # § Proprietary⠀➾


                      # ⚓ Dropbox,_Microsoft_OneDrive_send_out_warnings_to
                        macOS_users⠀⇛


                             They warn that some users may have problems
                             when attempting to open files stored in
                             either service using another Mac application.
                             They urge customers to update their apps once
                             macOS 12.3 is installed.


                      # § Security⠀➾


                            # ⚓ Security_updates_for_Wednesday⠀⇛


                                   Security updates have been issued by
                                   CentOS (httpd), Debian (libxfont,
                                   lrzsz, nss, openjdk-17, policykit-1,
                                   webkit2gtk, and wpewebkit), Mageia
                                   (polkit), openSUSE (expat, json-c,
                                   kernel, polkit, qemu, rust1.55,
                                   rust1.57, thunderbird, unbound, and
                                   webkit2gtk3), Oracle (httpd:2.4, java-
                                   11-openjdk, and polkit), Red Hat
                                   (httpd:2.4, OpenShift Container
                                   Platform 3.11.570, polkit, and Red Hat
                                   OpenStack Platform 16.1 (etcd)),
                                   Scientific Linux (polkit), Slackware
                                   (polkit), SUSE (aide, expat, firefox,
                                   json-c, kernel, polkit, qemu, rust,
                                   rust1.55, rust1.57, thunderbird,
                                   unbound, and webkit2gtk3), and Ubuntu
                                   (policykit-1 and xorg-server).


                            # ⚓ Qualys_Research_Team_Warns_of_Significant
                              polkit_Vulnerability_Affecting_All_Linux_Users
                              [Ed: This headline is false. It affects systemd
                              users. And systemd isn't Linux, it's IBM vendor
                              lock-in which isn't even compliant with UNIX
                              philosophy.]⠀⇛


                            # ⚓ Jan_26,_2022_Serious_Privilege_Escalation_Flaw
                              in_Linux_Component_Patched_By_Dennis_Fisher⠀⇛


                                   The bug is the result of Pkexec not
                                   validating the number of arguments
                                   passed to it. Rob Joyce, director of
                                   cybersecurity at the NSA, said on
                                   Twitter Wednesday that he’s concerned
                                   with the ease of exploitation for this
                                   vulnerability.


                            # ⚓ 12-year-old_vulnerability_in_Linux_gives
                              attackers_root_privileges_–_SiliconANGLE [Ed:
                              Systemd is not Linux]⠀⇛


                            # ⚓ Major_Linux_PolicyKit_Security_Vulnerability
                              Uncovered:_Pwnkit_–_SoylentNews⠀⇛


                            # ⚓ New_DeadBolt_ransomware_targets_QNAP_devices,
                              asks_50_BTC_for_master_key [Ed: Why would anyone
                              even connect a storage device to the open
                              Internet in the fist place? "Smart" hype?]⠀⇛


                                   A new DeadBolt ransomware group is
                                   encrypting QNAP NAS devices worldwide
                                   using what they claim is a zero-day
                                   vulnerability in the device’s software.


                            # ⚓ New_DeadBolt_Ransomware_Targets_NAT_Devices⠀⇛


                            # § Privacy/Surveillance⠀➾


                                  # ⚓ Data_privacy_laws_will_increasingly
                                    dominate_business_worldwide⠀⇛


                                         Data privacy will continue to
                                         become a more significant
                                         consideration and it’s going to
                                         be exceedingly difficult to do
                                         business anywhere in the world
                                         without encountering data privacy
                                         laws, according to Richard Marr,
                                         General Manager, APAC, Auth0, a
                                         product unit of Okta.


                                  # ⚓ What_went_down_at_#PrivacyCamp22?⠀⇛


                                         In this special anniversary
                                         edition of Privacy Camp 2022, we
                                         reflected on a decade of digital
                                         activism and thought together
                                         about the best ways to advance
                                         human rights in the digital age.
                                         #PrivacyCamp22 brought together
                                         close to 300 academics, activists
                                         and privacy experts who built on
                                         the lessons of the past and
                                         collectively articulated
                                         strategic ways forward for the
                                         promotion of everyone’s digital
                                         rights.


                                  # ⚓ Paying_with_cash,_old_school⠀⇛


                                         There’s a coffee shop down the
                                         street that has a big outdoor
                                         seating area, so I feel safe
                                         sitting there for a morning brew
                                         and to prepare for WFH that day.
                                         This morning I overheard the
                                         owner shout out “old school”! in
                                         response to a customer paying
                                         with cash which made me smile.


                                  # ⚓ Google_kills_FLoC,_unveils_new_plan_to
                                    replace_tracking_cookies_—_here’s_how_it
                                    works⠀⇛


                                         Google has ditched its planned
                                         user-profiling system, FLoC, and
                                         is instead developing a new
                                         system called Topics, the company
                                         announced today (January. 25).


                                         Topics, described by Google
                                         Senior Director of Product Ben
                                         Galbraith as “one of the most
                                         ambitious efforts we’ve ever
                                         undertaken” during a conference
                                         call with reporters, is meant to
                                         replace third-party advertising
                                         cookies in Chrome by the end of
                                         next year.


                                         But you won’t be able to use or
                                         try Topics just yet. Developer
                                         trials begin in a couple of
                                         months, and user trials are still
                                         a long way off.


                                  # ⚓ A_guide_to_getting_your_data_from
                                    WhatsApp⠀⇛


                                         It’s important to understand how
                                         much of your data is stored in
                                         the cloud. Why? Because our
                                         research exposes that law
                                         enforcement can use cloud
                                         extraction techniques to obtain
                                         vast quantities of your data.
                                         These techniques means law
                                         enforcement can circumvent asking
                                         companies like WhatsApp for your
                                         data and avoid getting a warrant.
                                         So the use of this technology
                                         means there is no limit on what
                                         they can obtain, no transparency
                                         and no clear, accessible or
                                         effective legal safeguards to
                                         protect your data from risk of
                                         abuse and misuse.


                                  # ⚓ Proposal_for_a_European_Interoperability
                                    Framework_for_Smart_Cities_and_Communities_
                                    (EIF4SCC)⠀⇛


                                         The proposed Framework is
                                         initiated to support EIF at local
                                         and Regional level and was
                                         jointly managed by DG DIGIT as
                                         part of the ISA² Programme (2016-
                                         2020), and by DG CONNECT in the
                                         framework of the Living-in.eu
                                         movement. A co-creation process
                                         with city/community
                                         administrators in the European
                                         Union was created and together
                                         with Deloitte and KU Leuven e a
                                         proposal for the European
                                         Interoperability Framework for
                                         Smart Cities/Communities
                                         (EIF4SCC) was developed.


          o § Defence/Aggression⠀➾


                # ⚓ US’s_Support_for_Invasions_Should_Disqualify_It_From
                  Leading_on_Russia-Ukraine⠀⇛


                # ⚓ Biden_Claims_He_Wants_to_End_the_Yemen_War._His_Actions
                  Suggest_Otherwise.⠀⇛


                # ⚓ Biden_OK’s_$2.5_Billion_Arms_Sale_to_Egypt,_Disregarding
                  Government_Oppression⠀⇛


                # ⚓ United_Russia_asks_Putin_to_start_supplying_military_aid_to
                  Donetsk_and_Luhansk_‘people’s_republics’⠀⇛


                       Russia’s ruling party has initiated an appeal
                       asking the country’s leadership to start supplying
                       military assistance to the self-proclaimed
                       “people’s republics” in eastern Ukraine, Interfax
                       reported on Wednesday, January 26. 


                # ⚓ Lock_Him_Up:_Oath_Keeper_Leader_Denied_Bail_in_Jan._6
                  ‘Seditious_Conspiracy’_Case⠀⇛


                       On Wednesday afternoon, a federal judge in Plano,
                       Texas, ruled that Rhodes, the founder of the right-
                       wing Oath Keepers militia, should be denied bail.
                       Magistrate Judge Kimberly Priest Johnson announced
                       her decision in a 17 page decision (embedded
                       below). Johnson wrote that Rhodes’ “authoritative
                       role in the conspiracy, access to substantial
                       weaponry, and ability to finance any future
                       insurrection, combined with his continued advocacy
                       for violence against the federal government, gives
                       rise to a credible threat that Defendant’s release
                       might endanger others.”


                # ⚓ Chinese_APT_27_hackers_targeting_companies,_says_Germany
                  [iophk: Windows TCO]⠀⇛


                       Germany’s domestic intelligence agency, the Federal
                       Office for the Protection of the Constitution
                       (BfV), said APT 27 had used a malware variant to
                       target commercial companies.


                       The BfV said the attackers had been exploiting
                       vulnerabilities in commonly used software since
                       March 2021 as a gateway for the attacks.


                # ⚓ Leading_Turkish_women_targeted_by_Islamists_and
                  government⠀⇛


                       The jailing of prominent journalist Sedef Kabas and
                       threats against famous pop diva Sezen Aksu are
                       stirring controversy in Erdogan’s Turkey. It’s part
                       of a trend that brings Islamists and government
                       supporters together.


          o § Transparency/Investigative Reporting⠀➾


                # ⚓ Automotive_Lobbying_Group_Abandons_the_Term_“Self-
                  Driving”⠀⇛


                       While the group didn’t directly mention Tesla in
                       its announcement, the move is likely a response to
                       the Elon Musk-led company’s efforts to market its
                       “Full Self-Driving” feature, a highly controversial
                       driver assist feature that has landed the company
                       in hot water with lawmakers on a number of
                       occasions.


          o § Environment⠀➾


                # ⚓ Nations_Join_Forces_To_Fight_Illegal_Fishing_In_Gulf_Of
                  Guinea⠀⇛


                       Besides at-sea patrols, the countries will share
                       information from the Regional Monitoring, Control
                       and Surveillance Centre in Ghana, which was formed
                       by the Fisheries Committee for the West Central
                       Gulf of Guinea (FCWC) in 2021.


                       Other partners include the Regional Maritime
                       Security Centre for West Africa in Côte d’Ivoire;
                       European Fisheries Control Agency; Multinational
                       Maritime Coordination Centre; and Trygg Mat
                       Tracking, a fisheries intelligence analysis
                       company. Additional funding is supplied by the
                       Norwegian Agency for Development Cooperation,
                       according to SeafoodSource.


                # ⚓ The_Supreme_Court_vs._the_Earth⠀⇛


                       What’s particularly shocking about this case is
                       that the EPA does not currently have any such rules
                       in place. The agency tried to regulate greenhouse
                       emissions under President Barack Obama’s Clean
                       Power Plan, but conservative justices (of course)
                       blocked that plan from taking effect. Then, the
                       Trump administration came in and shoved the CPP off
                       the edge of their flat Earth. Arguably, the D.C.
                       Circuit has since reopened the possibility of a
                       revised CPP, but the Biden administration has said
                       that it will not try to reinstate the plan.
                       Instead, it has instructed the EPA to come up with
                       a completely different rule, a process that is
                       underway at the agency right now.


                # § Energy⠀➾


                      # ⚓ Elon_Musk,_Threat_or_Menace_Part_2⠀⇛


                             Last April I wrote Elon Musk: Threat or
                             Menace? flagging three of his externalities;
                             the carbon footprint of his infatuation with
                             cryptocurrencies, the environmental impact
                             and cost of his infatuation with colonizing
                             Mars, and the threat his infatuation with
                             camera-only autonomy for Teslas posed to
                             innocent bystanders. Last August I followed
                             up with Autonowashing, detailing the
                             incredible “depths of irresponsibility
                             involved in Tesla’s marketing”.


                      # ⚓ How_will_Europe_cope_if_Russia_cuts_off_its_gas?⠀⇛


                             But a shutdown is no longer unthinkable. Mr
                             Gustafson now says: “I don’t think it is
                             unlikely at all that Putin would actually
                             reach for the gas tap over Ukraine.” Unlike
                             his Soviet predecessors, the Russian
                             president can afford the cost of a brief
                             energy shock. Jaime Concha of Energy
                             Intelligence, an industry publisher, has
                             crunched the numbers. Not counting any
                             penalties (for breach of contract, say) and
                             assuming the average daily price seen in the
                             fourth quarter of 2021, he reckons a complete
                             cut-off of piped gas to Europe would cost
                             Gazprom between $203m and $228m a day in lost
                             revenues. So if such an embargo lasted three
                             months (Mr Putin’s leverage fades in spring,
                             when gas demand drops to just 60% of that in
                             January), lost sales would add up to about
                             $20bn.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Healing⠀⇛


                # ⚓ Taking_on_Your_Tweets⠀⇛


                # ⚓ Can_Congress_Really_Use_Insider_Information_to_Trade
                  Stocks?⠀⇛


                       Banning members of Congress from trading individual
                       stocks is a no-brainer. Let’s get it done.


                # ⚓ Vague_Social_Media_Laws_Create_Fear_in_the_Middle_East._Can
                  Encryption_Tools_Help?⠀⇛


                       Far from being the savior of democracy in the
                       Middle East, four experts said Monday that social
                       media, and government regulation of it, is
                       beginning to hurt civil rights activists.


                       The world is witnessing an increase in laws
                       restricting social media access and hence
                       regulating freedom of speech, especially in the
                       Middle East, agreed the panelists, speaking at a
                       Brookings Institution event.


          o § Misinformation/Disinformation⠀➾


                # ⚓ YouTube_permanently_bans_Dan_Bongino⠀⇛


                       YouTube on Wednesday permanently banned
                       conservative commentator Dan Bongino from the
                       platform, saying he attempted to evade a previous
                       suspension.


                       The Fox host uploaded a video to his main channel
                       while his secondary channel, which primarily hosted
                       short clips from his digital radio show, was
                       actively suspended for violating YouTube’s COVID-19
                       misinformation policy.


          o § Censorship/Free Speech⠀➾


                # ⚓ EU_wants_to_build_its_own_DNS_infrastructure_with_built-in
                  filtering_capabilities⠀⇛


                       The European Union is interested in building its
                       own recursive DNS service that will be made
                       available to EU institutions and the general public
                       for free.


                       The proposed service, named DNS4EU, is currently in
                       a project planning phase, and the EU is looking for
                       partners to help build a sprawling infrastructure
                       to serve all its current 27 member states.


                       EU officials said they started looking into an EU-
                       based centrally-managed DNS service after observing
                       consolidation in the DNS market around a small
                       handful of non-EU operators.


                       “The deployment of DNS4EU aims to address such
                       consolidation of DNS resolution in the hands of few
                       companies, which renders the resolution process
                       itself vulnerable in case of significant events
                       affecting one major provider,” officials said in
                       the DNS4EU infrastructure project revealed last
                       week.


                       But EU officials said that other factors also
                       played a role in their decision to build DNS4EU,
                       including cybersecurity and data privacy.


                # ⚓ Censoring_Joe_Rogan_Is_No_Solution_to_Vaccine
                  Misinformation⠀⇛


                       There’s a campaign underway to kick podcast host
                       Joe Rogan off Spotify for spreading COVID
                       misinformation. But Rogan at his worst couldn’t do
                       as much damage to public trust in science as the
                       political and scientific establishment has during
                       the pandemic.


                # ⚓ China_censors_re-write_‘Fight_Club’_ending,_say_authorities
                  triumphed⠀⇛


                       The renowned classic film “Fight Club” appears to
                       have been censored on popular Chinese entertainment
                       platform Tencent Video – though rather than merely
                       cutting scenes from the film, government censors
                       created a new ending altogether in place of the
                       cult movie’s iconic conclusion.


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


                # ⚓ El_Salvador_must_investigate_use_of_Pegasus_to_spy_on
                  dozens_of_journalists⠀⇛


                       Reporters Without Borders (RSF) calls on El
                       Salvador’s public prosecutor to open an
                       investigation into the use of the Pegasus spyware
                       to hack into the phones of at least 35 Salvadorean
                       journalists. RSF is also providing recommendations
                       to journalists whose phones may have been infected.


                # ⚓ Three_Iranian_journalists_transferred_to_prisons_notorious
                  for_mistreating_detainees⠀⇛


                       Reporters Without Borders (RSF) is alarmed by the
                       transfers of three Iranian journalists to prisons
                       notorious for cruel, inhuman and degrading
                       treatment, in a practice often used to deliberately
                       break the resistance of prisoners of conscience.
                       These transfers come just days after another
                       journalist, Baktash Abtin, died as a result of not
                       being treated when he caught Covid-19 in Tehran’s
                       Evin prison.


          o § Civil Rights/Policing⠀➾


                # ⚓ Investigation_Shows_Faulty_Drug_Tests_Resulted_In_Hundreds
                  Of_New_York_Prisoners_Being_Wrongly_Punished⠀⇛


                       The justice system may say lofty things about debts
                       to society or rehabilitation, but when it all comes
                       down to it, a person in jail is just something to
                       be processed. Whatever happens to them is
                       supposedly well-deserved. If you can’t do the time,
                       don’t do the crime. This catchy phrase also refers
                       to pretrial detainees who haven’t been convicted of
                       any crimes but who simply don’t have the means (or
                       the judicial permission) to spend their pre-trial
                       days out in the open.


                # ⚓ When_Whiteness_Starts_Seeing_Itself⠀⇛


                       By 2044, the United States’ white population will
                       dwindle from a majority to a plurality, according
                       to the Census Bureau. White Americans—though they
                       will still outnumber every other racial group in
                       the country—have not taken this news well.


                # ⚓ Protest_Song_Of_The_Week:_‘Landlord_Of_The_Gentriflies’_By
                  Calm._(Featuring_Lee_Reed_and_Buddha)⠀⇛


                       Calm is a hip-hop duo featuring rapper Time and
                       producer Awareness. Time has also done engineering
                       work for Common and is a journalist who has worked
                       with Noam Chomsky.


                       They recently released the concept album
                       “Conversations with A Willow Tree.” The album is an
                       ode to a willow tree set in a dystopian world where
                       plants are the heroes that fight colonialism and
                       environmental collapse.“Landlord of the
                       Gentriflies,” which appears on the album, is a
                       scathing critique of gentrification. The opening
                       verse from Time features the hard-hitting rebuke:
                       “Since that eviction letter, this ain’t really been
                       home”.It continues, “Landlord didn’t discover this,
                       that’s Chris Columbus syndrome. We’re just trying
                       to raise the roof, they just wanna raise the rent.
                       I’ve been working 3 jobs, I gave that cracker every
                       cent. Landlord of the flies, dollar signs in his
                       eyes. Let’s stop working for the rich, so we can
                       live our fucking lives.”The second verse is from
                       Canadian rapper Lee Reed, known for his political
                       lyrics and socialactivism. His verse further
                       explores the ill effects of capitalist-fueled
                       gentrification. “Half a million evicted they still
                       insisting the system work. Assisted living let you
                       live in thirst. This government place people
                       second, business first. They gentrified our
                       existence, but we been dispersed,” Reed
                       raps.Renter’s rights is a subject close to Reed’s
                       heart. He recently released “Drop The Charges,”
                       acharitable single whose proceeds support the
                       Hamilton Encampment Support Network (HESN).HESN is
                       an organization that supports homeless residents of
                       Hamilton, Ontario, Canada. Just like several major
                       cities throughout the world, the housing crisis is
                       forcing more people onto the streets.Listen to
                       “Landlord of the Gentriflies”:


                # ⚓ CIA_Funded_Experiments_On_Danish_Orphans_For_Decades⠀⇛


                       This article was funded by paid subscribers of The
                       Dissenter Newsletter. Become a monthly subscriber
                       to help us continue our independent journalism. An
                       extraordinary Danish Radio report exposed how
                       scores of children in Denmark, many of them
                       orphans, were subject to CIA-funded experiments for
                       at least two decades.


                       The purpose of these activities remains unknown, as
                       authorities continue to actively suppress the truth
                       of what happened in the 1960s and early 1970s.


                # ⚓ Navalny’s_brother_is_added_to_federal_wanted_list_in
                  Russia⠀⇛


                       Police in Russia have added Oleg Navalny, the
                       brother of jailed opposition leader Alexey Navalny,
                       to a federal wanted list, the nation’s Interior
                       Ministry reported on Tuesday. The announcement does
                       not list the charges.


                # ⚓ Redwood_Forest_in_California_Is_Returned_to_Native_Tribes⠀⇛


                       The group, the Save the Redwoods League, which was
                       able to purchase the forest with corporate
                       donations in 2020, said it was transferring
                       ownership of the 523-acre property to the
                       Intertribal Sinkyone Wilderness Council, a group of
                       10 native tribes whose ancestors were “forcibly
                       removed” from the land by European American
                       settlers, according to a statement from the league.


                       The tribes will serve as guardians of the land in
                       partnership with the Save the Redwoods League,
                       which has been protecting and restoring redwood
                       forests since 1918.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ Fresh_Off_Its_Merger_Failure(s),_AT&T_Gets_Back_To
                  Promising_Big_Fiber_Investments_That_May_Or_May_Not_Happen⠀⇛


                       We’ve noted for years how AT&T has this pattern in
                       which they’ll promise a massive wave of new fiber
                       investment and jobs if they get “x” (X=merger
                       approvals, deregulation, tax breaks, a bunch of new
                       subsidies, whatever). Then, a few years later,
                       somebody will realize they failed utterly to meet
                       those obligations. This happens over and over and
                       over and over again, and not only does AT&T never
                       see much in the way of accountability, nobody in
                       state or federal leadership seems to learn much of
                       anything from the process (usually because they’re,
                       well, corrupt).


                # ⚓ From_The_Revolt_Against_SOPA_To_The_EU’s_Upload_Filters⠀⇛


                # ⚓ Enough_Is_Enough:_The_Senate_Should_Stop_Playing_Games_And
                  Confirm_Gigi_Sohn⠀⇛


                       Joe Biden entered office a year ago with a mandate
                       to end corporate control of our government by
                       establishing programs to benefit working families
                       and by appointing qualified public servants to
                       execute and oversee those programs.


                # ⚓ GOMIX_brings_faster,_cheaper_Internet_to_millions_in
                  eastern_DRC⠀⇛


                       GOMIX, the Democratic Republic of Congo’s third
                       Internet Exchange Point, launched in Goma, the main
                       capital of the North Kivu province in the east of
                       the DRC, in September 2021.


                       Initiated by the Internet Service Provider
                       Association (ISPA-DRC) in partnership with the
                       Internet Society, GOMIX will improve Internet
                       access for nearly 4 million urban residents. It
                       will also facilitate creating local content,
                       hosting services at a local and national level, and
                       promoting interconnection between local Internet
                       Service Providers (ISPs).


          o § Digital Restrictions (DRM)⠀➾


                # ⚓ Spotify_Stock_(SPOT)_Has_Lost_Nearly_25%_of_Its_Value_In
                  2022_and_45%_Over_the_Past_Year_—_What’s_Going_On?⠀⇛


                       Meanwhile, some are speculating that Spotify could
                       follow Netflix in raising its prices – a
                       significant possibility because music streaming
                       services feature similar song libraries and mainly
                       cost the same in the States. Plus, Spotify’s long-
                       awaited HiFi support doesn’t yet have a release
                       date, company officials announced two weeks ago,
                       despite the fact that Apple Music and Amazon Music
                       unveiled the feature at no added cost last summer.


                # ⚓ Will_Hollywood’s_Streaming_Ambition_Lead_to_Big_Gaming
                  Buys?⠀⇛


                       Most Hollywood giants have similarly retreated from
                       video game ambitions. NBCUniversal shut down its
                       game studio in 2019, before its current CEO, Jeff
                       Shell, took over. And Discovery chief David Zaslav
                       hasn’t detailed plans for Warner Bros. Interactive
                       Entertainment once the company closes its mega-
                       merger with WarnerMedia, currently led by CEO Jason
                       Kilar, beyond saying it won’t require any asset
                       sales to hit its debt-reduction targets. Some say
                       it will take a bigger gaming footprint. Warners’
                       “Mortal Kombat is great IP, which has good value;
                       the rest of what makes money is licensed product,”
                       MKM Partners analyst Eric Handler says, adding that
                       the gaming unit will be “a sub-scale business as
                       part of Discovery/Warner.”


          o § Monopolies⠀➾


                # ⚓ EU_court_sides_with_Intel_in_appeal_of_$1.2B_antitrust
                  fine⠀⇛


                       A European court announced Wednesday that it
                       overturned a $1.2 billion fine on Intel, which the
                       European Union had imposed on the semiconductor
                       chip manufacturer in 2009 over alleged violations
                       of antitrust laws.


                       The European Commission, the executive branch of
                       the EU, accused Intel of abusing its position as a
                       global leader for x86 computer microprocessors and
                       excluding competitors from the market, stretching
                       from October 2002 to December 2007.


                       The EU alleged that Intel granted rebates to four
                       equipment manufacturers, including Dell and Lenovo,
                       which were conditional on the companies purchasing
                       microprocessors from Intel.


                # § Copyrights⠀➾


                      # ⚓ YouTube_Wants_‘Fraudulent”_Copyright_Claimant_Kept_in
                        Class_Action_Lawsuit⠀⇛


                             When musician Maria Schneider launched a
                             class action lawsuit against YouTube
                             demanding access to Content ID, she did so
                             with ‘Pirate Monitor’. Due to this company’s
                             allegedly fraudulent actions, YouTube filed a
                             counterclaim that the plaintiffs now want
                             severed from the case. According to them,
                             YouTube wants a “guilt-by-association weapon”
                             to sully the class.


                      # ⚓ Rojadirecta_Operator_Faces_Multi-Year_Prison_Sentence
                        in_Upcoming_Trial⠀⇛


                             Popular sports streaming site Rojadirecta
                             finds itself at the center of a criminal
                             lawsuit in Spain. The prosecution seeks a
                             four-year prison sentence for the operator
                             and up to two years for five accomplices.
                             Spanish football league LaLiga and Mediapro
                             demand even higher sentences and also want
                             six million euros in damages.


                      # ⚓ Google_Drive’s_Autodetector_For_Copyright
                        Infringement_Is_Locking_Up_Nearly_Empty_Files⠀⇛


                             We’ve talked at length about the issues
                             surrounding automated copyright infringement
                             “bots” and how often those bots get the
                             primary question they’re tagged with wrong.
                             Examples of this are legion: Viacom’s bot
                             takes down a Star Trek panel discussion, all
                             kinds of bots disrupted the DNC’s livestream
                             of its convention, and one music
                             distributor’s bot firing off DMCA notices to,
                             well, everyone. Google itself has reported
                             that nearly 100% of the DMCA notices it gets
                             are just bot-generated buckshot.


                      # ⚓ Wherein_The_Copia_Institute_Tells_The_Copyright
                        Office_That_Link_Taxes_Are_A_Good_Idea_Only_If_You_Want
                        To_Kill_Off_Journalism⠀⇛


                             It’s hard to believe that even after the huge
                             disaster “link taxes” have been in Europe and
                             Australia that people would push to have them
                             in the United States, and yet here we are.
                             This brewing bad idea has some foolish
                             friends in Congress, who tasked the Copyright
                             Office with doing a study on the viability of
                             importing this nonsense into American law,
                             and via our already over-encumbered copyright
                             law. The Copia Institute filed a public
                             comment as part of this study and provided
                             testimony at a hearing in December. In both,
                             we pointed out that a site like Techdirt is
                             exactly the sort of small, independent media
                             outlet such a scheme is supposed to help yet
                             is instead exactly the sort of small,
                             independent media outlet such a scheme most
                             definitely would hurt.


╘══════════════════════════════════════════════════════════════════════════════╛
                       ¶ Lines in total: 8719
    ➮ Generation completed at 02:43, i.e. 46 seconds to (re)generate ⟲