𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Monday, December 05, 2022
┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅
Generated Tue 6 Dec 02:41:48 GMT 2022
Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖)
Full hyperlinks for navigation omitted but are fully available in the originals
The corresponding HTML versions are at 𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈
Latest in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕 and older bulletins can be found at 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕-𝒂𝒓𝒄𝒉𝒊𝒗𝒆𝒔
Full IPFS index in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔 and as plain text in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔/𝒕𝒙𝒕
Gemini index for the day: gemini://gemini.techrights.org/2022/12/05/


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

QmRLzUcf7xHXgxz4uDtuuczMVFxww7tK2RUJZLCZHcajHD
QmX7kxj1MQf3W96GYsRLdeSLXusC9JaFtCSoT8SGEYzW8w
QmdFVj7ax5AKsqtcbpboc58Cm5tfBZrpx36B1A86FoG2NA
QmXXVoEb5eBXT6aHWyHXXBkdA4rzUdUVyP1VF9WG5r9bFJ
QmYw27XST29tsr6QXEMYUoACM4n1e5XYWDZTBR7vHprPbC
QmRCmRWww97e75DM14B2d1qkuBNYhc3xiot1oc7iK6jHsG
QmXUiAAuF6d29LyvMmGXRNKDjRWurj3DZCgK3bBz29QcKR
Qmd1StkRPjLJfH1z58B1mngbGWUgMHRweuZDBGscxEa7E5
QmRLEsyXGm1nbnDXWaCXoNvF8mPMKuDNprPhp8wwBnf6Uy
QmUUv6KSwgdtc3wg117KKh1ysfPCt3jmXpD1WfKhQqKPkn
QmSFSd1vAYP4ohzbeKUbbo6274SVceULSU4vHM51GkMMuw
QmPZMEcQqMMP8MADSrzwipLopGe8JGWV5YLBQLSWb3yJ3n
QmQrQNyCx2qL7s5jt5mMt489d9ra6fdrXi3qCqoCuLjNGi
QmVH6Dn5VMv1pRqSuu1d6JHjiFDF9UbBsBG154Rd6Qs1z5
QmSq8X3ZGoK6pDPEQcfPyB7w5cvNVkkDUsxRyjv6TNLKDM
QmVsKp6m9nwYJz1GSZ7M835LQnvpVshm2CX1UusBY3y3W8
QmdWUusNqJMS57MytvSBqcKNCLRPfimgbePGhjNYNCrwrs
QmbPTsZioPtTXeNWAZ3ALomNL4TBHGpogkpqcBMt1XfHcK
QmYfN5RSjFSUavYPSs8WzFFWaWumk8hYAfuw6kpmXGe13e
QmW2j2ckzmovo3T5PVVEPyCDY6cxTKFEYB2dhVvwPkm1n7
QmTyKJ8ueXdR2ThkLMDuN6zbrTdYNb2WE4A3bWb3nThabk


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

⦿ IRC Proceedings: Sunday, December 04, 2022 | Techrights

⦿ Sirius Not-So-‘Open Source’: Cannot Talk to Colleagues, Cannot Speak About Work | Techrights

⦿ That Time Sirius ’Open Source’ Fired a Blind Lady While Gagging Sympathetic Staff | Techrights

⦿ [Meme] Guilt by Association | Techrights

⦿ Unified Patent Court (UPC) ’Delayed’ Again, As Usual, as Unitary Patent Boosters Caught Up in Lies and Scandals | Techrights

⦿ Unified Patent Court (UPC) is “Real Soon Now!” Since 2014 | Techrights

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
		http://techrights.org/2022/12/05/irc-log-041222/#comments
		http://techrights.org/2022/12/05/sirius-gag-orders/#comments
		http://techrights.org/2022/12/05/sirius-open-source-fired-a-blind-lady/#comments
		http://techrights.org/2022/12/05/sirius-open-source-guilt-by-association/#comments
		http://techrights.org/2022/12/05/unified-patent-court-2023-delays/#comments
		http://techrights.org/2022/12/05/unified-patent-court-upc-is-real-soon-now-since-2014/#comments

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
		http://techrights.org/2022/12/05/15-minute-bug-initiative/#comments
		http://techrights.org/2022/12/05/gnoppix-linux-22-12/#comments
		http://techrights.org/2022/12/05/gstreamer-1-21-3/#comments

                    ䷩ 𝚕𝚒𝚗𝚎 64

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/12/05/irc-log-041222/#comments
    Gemini version at gemini://gemini.techrights.org/2022/12/05/irc-log-041222/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.05.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ IRC_Proceedings:_Sunday,_December_04,_2022⠀✐


Posted in IRC_Logs at 2:39 am by Needs Sunlight


Also available via the Gemini protocol at:


    * gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-041222.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-041222.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-social-041222.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-041222.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
 QmSTp5hErjE6WkrLMy2enHnMd5gYU4KjqgbTPiGUt5FzAj #boycottnovell  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell
 QmakXoWYDWaMpjbeWL54gDukEghzfeUxRWKohLVtF7qF62 (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
                                                 #boycottnovell-
 QmSN4YnkrbF9sX15FKomVbuDNaBHPryUPUTEvbbkepWHc7 social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell-
 QmcTz2rmE5iC16ykTkcMzqXMDPLi7NvvP93kvehpEj4efM social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 (full IRC log
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 QmRF7PWww4UDcsksyx5ucyHGGz7MHZB8sqFrn7mgvqJFut #techbytes      🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techbytes
 QmR6EzbU2B5tL3S9qRZBksecS74aQQRpPMViShfxHFxiS1 (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 QmTq7K4e16cy5mSKTYxih8iGWGnR5YCuiMBiQHxY4QninD #techrights     🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techrights
 QmQ3kzUT2Su9A7w2F96LMxn6D8fp3sLZmRCibTdCF7jtX1 (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈


§ Bulletin for Yesterday⠀➾


Local_copy | CID (IPFS): QmTyKJ8ueXdR2ThkLMDuN6zbrTdYNb2WE4A3bWb3nThabk



                    ䷩ 𝚕𝚒𝚗𝚎 191

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/12/05/sirius-gag-orders/#comments
    Gemini version at gemini://gemini.techrights.org/2022/12/05/sirius-gag-orders/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.05.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Sirius_Not-So-‘Open_Source’:_Cannot_Talk_to_Colleagues,_Cannot_Speak_About
Work⠀✐


Posted in Deception, Free/Libre_Software at 7:29 pm by Dr. Roy Schestowitz


Video_download_link | md5sum 4e251da456416f8e8155bd4f356340d3
Cover-up Culture at Sirius Open Source
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/punishing-the-blind.webm


Summary: Cover-up and lies became a corporate pattern at the company where I
had worked since 2011; it was time to go in order to avoid cooperation in
unethical_activities


IT has now been 4 days since I officially left Sirius_‘Open_Source’ after
disputes with the management. As the above video notes (near the start), we’re
dealing with thin-skinned people who lie to staff and then get all “victim-
like” because someone used the word “liar”. We’ll come back to this much later
in this series.


“The use of the word “allegations” is key here because what management is
alleging has historically not been trustworthy (and usually those allegations
aren’t shared with staff or constitute mere smears).”The video mostly deal with
the latest part of the report, which examines awful events nearly a decade old.
There was an actual lawsuit, but it was hidden away from staff. The lawsuit had
been filed after suspension/dismissal of someone alleged to have engaged in
wrongdoing, along with his partner, who was of course innocent regardless of
the merits of these allegations.


The use of the word “allegations” is key here because what management is
alleging has historically not been trustworthy (and usually those allegations
aren’t shared with staff or constitute mere smears). There’s a culture of
dishonesty or a chronic culture of lying at the management. It’s something I
was first made aware of about 4 years before joining the company. Someone
credible (whom I first knew online, later met in person) told me that the
Sirius founder had lied about his credentials (for media attention) and that
litigation was considered over those lies; it was not worth pursuing for
financial reasons, but the founder of Sirius was taking credit for things not
actually one’s own achievement (misrepresentation or lying about one’s role in
a British institution).


“I never forgot what I learned down at a local pub before I joined the company;
but I only saw it firsthand in more recent years.”The saddest thing is that
real people are hurt and even disabled people are harmed. They don’t do
anything wrong, but for pseudo-political reasons they get punished regardless.


I never forgot what I learned down at a local pub before I joined the company;
but I only saw it firsthand in more recent years. I was conveniently ignoring
the lies for years, as they didn’t impact me personally and I didn’t
participate in the lying. █



                    ䷩ 𝚕𝚒𝚗𝚎 267

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/12/05/sirius-open-source-fired-a-blind-lady/#comments
    Gemini version at gemini://gemini.techrights.org/2022/12/05/sirius-open-source-fired-a-blind-lady/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.05.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ That_Time_Sirius_‘Open_Source’_Fired_a_Blind_Lady_While_Gagging_Sympathetic
Staff⠀✐


Posted in Deception, Free/Libre_Software at 5:44 pm by Dr. Roy Schestowitz


Sirius shown to the public as women-friendly a decade ago


               🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Sirius_'Open_Source'_in_2012⦈_


Summary: Sirius_‘Open_Source’ was taken to court after it had wrongly fired a
couple of employees, one of whom was blind; this was accompanied by lies about
why the staff’s communication server was shut down


THE year was 2011 or thereabouts. Sirius hired a kind German lady, was was also
completely blind. Colleagues were happy to help, but clients were not being
informed that she was blind and management feared that clients might find out
that she was blind. A year or two later she was fired and simply ‘vanished’;
nobody was allowed to talk about that.


This, among other incidents, is an example of a ruthless company that does not
tolerate staff dialogue and relies on secrecy (or clients being blind to what
really goes on). The relevant part of the report is below.


===============================================================================
⚓  Blindness to Criticism⠀⇛


The foundations of the company need to be protected, not the personal agenda of
pertinent, individual workers and/or cliques/factions of workers. Lack of
communication blinds us to our weaknesses. Over a decade ago when the company-
wide Jabber server was disabled (probably to prevent unity and sympathy among
staff) workers’ ability to interact with colleagues was curtailed, leaving
everyone in a position where supporting clients was a lot harder. The
widespread belief at the time was that the server was intentionally offline
(nobody wanted to talk about it, let alone lie) because the company faced a
lawsuit from a couple wrongly accused/dismissed (at least one of them). Roy and
Rianne have supported blind people’s charities for nearly a decade already, so
recalling how the company treated a blind colleague, likely an innocent
colleague, is a bit of deja vu in light of later sections of this document. Roy
and Rianne poured in a portion of their income (received monthly from Sirius)
into blind people’s charities after the company, Sirius, had unfairly dismissed
a legally blind — and much-liked among her colleagues — vulnerable lady.


Sirius was not always criticised or fearful of criticism, certainly not as a
whole (criticising one particular aspect of Sirius is not the same as just
rejecting Sirius as a whole). In fact the company used to boast true
transparency (also full access to the wiki, which Roy helped manage/install),
like telling workers not only which clients were paying but also how much they
were paying (so it was possible to understand the commercial side of things).
In some sense, workers felt connected to the company, not left out to hang.
Internal presentations in the company, or even the habitual workshop, gave all
workers a lot of information. The accountant and other people met staff in
person, offering good advice on a number of things. Not much was outsourced or
left behind walled gardens.


Things have changed a lot since then. █


⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⣀⣀⣀⣀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣀⣀⣀⣀
⣿⣿⣿⣿⣀⣀⡄⢀⣸⣀⣄⣁⣨⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡏⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿
⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⢸⣿⡿⢛⠟⠿⠿⢿⠿⡿⢿⡟⣛⠿⠿⠿⢿⣟⢛⠿⠿⢿⠻⠿⠿⡿⢿⡿⢿⠿⠿⡿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡶⡆⢸⣿⣿⣥⣤⣧⣦⣼⣤⣥⣼⣧⣾⣼⣤⣤⣴⣿⣼⣤⣤⣽⣼⣤⣧⣬⣴⣧⣥⣈⣐⣰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣯⣿⣯⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡟⠙⣿⠁⠀⠀⠀⠹⠛⠹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⢸⣿⣿⣿⣿⣇⣆⣐⣸⣇⣐⣨⣒⣨⣪⣅⣰⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣄⢹⣧⠀⠀⠀⢀⣶⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠙⠋⠀⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣆⢻⣧⣀⠀⠈⠋⠸⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠘⠘⠀⠇⠀⢸⣿⣿⣿⣿⡏⡝⠫⢻⡏⡍⠙⠉⡍⢩⢸⠉⡍⢹⠩⠋⡍⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠟⠀⠙⢿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠐⣩⣿⣿⣟⣿⣿⣿⣿⣿⠟⠋⠉⠙⠛⠛⠛⠛⠛⠛⠛⠿⠛⠛⠁⠀⠘⣺⣻⣻⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠈⠀⠐⠻⠝⢿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⢨⡾⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠤⠤⠤⢄⣀⢀⣠⣬⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠻⠿⠿⠿⠃⠀⠁⠀⠰⠶⠶⠶⠶⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣄⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠂⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⠛⠛⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣐⣉⣉⣉⣇⣍⣉⣉⣉⣭⣏⣁⣉⣉⣉⣧⣍⣉⣇⣩⣁⣉⣉⣈⣉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⣻⢋⢛⢻⠛⠛⠛⡛⠛⢛⡛⠛⣻⠛⢛⠛⣟⠛⡟⠛⣻⣛⠛⢛⣋⠛⡛⢛⣛⢛⣛⣛⢛⠛⢛⡛⢛⣛⢛⢋⠛⠋⡛⣛⡛⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⠥⡭⡭⠬⣥⠬⠬⢭⣩⢬⡭⢭⠉⠭⠭⠭⠡⣭⠯⠭⡩⠭⠯⡭⡍⡩⠭⠭⠬⠬⢩⠭⠭⢭⡭⠭⡭⡭⢭⡭⠭⢽⢥⢭⠥⠽⢍⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠓⠚⠒⠒⠒⠒⠒⠒⠒⠒⠒⢲⠒⠒⠒⠒⠒⠒⠒⡖⠐⠒⠒⠐⢲⠒⠓⠒⢒⠒⠒⠚⠚⢶⣶⣶⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣭⣧⣽⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡿⠿⠿⠿⠿⡿⠿⠿⡿⠿⠿⠿⢿⠿⠿⠿⠿⢿⠿⢿⠿⠿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⡿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠒⠒⡒⠒⠒⡒⡒⣖⠒⠒⢒⠒⠒⠚⠒⠒⢓⠒⡒⢲⠒⠓⡒⢒⢚⣓⡒⢒⠚⠒⠒⠒⠒⢚⢒⡚⣖⠚⢒⢒⣒⢲⠓⡒⠓⠒⠒⠒⡒⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣉⣭⣥⣭⣭⣭⣭⣹⣬⣭⣩⣭⣬⣭⣭⣥⣽⣭⣬⣭⣍⣹⣭⣭⣍⣭⣭⣩⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣉⣏⣙⣉⣙⣉⣙⣉⣙⣉⣉⣉⣛⣋⣉⣉⣉⣉⣙⣙⣹⣭⣉⣉⣉⣹⣩⣉⣉⣏⣉⣉⣋⣉⣙⣋⣉⣉⣋⣉⣏⣉⣋⣋⣏⣉⣏⣛⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠤⠴⢤⠤⠦⠤⠧⠤⠤⢤⠥⠤⠤⠬⠤⠤⢼⠤⠤⠧⠤⠧⠤⠦⡼⠤⠤⠤⠤⠤⠤⠾⠤⣼⣤⣤⣤⣤⣤⣧⣤⣤⣤⣤⣧⣤⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣾⣿⣶⣶⣶⣶⣾⣶⣷⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣾⣶⣷⣶⣶⣶⣷⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢛⡟⠛⠛⠟⠛⠻⠛⠻⠟⠻⠛⠛⠻⠻⠿⠛⠻⠿⠛⠿⠻⠛⠛⠻⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣩⣥⣭⣭⣉⣹⣄⣍⣩⣩⣫⣿⣄⣭⣉⣬⣍⣭⣽⣽⣢⣉⣁⣨⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣿⣾⣶⣶⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠟⠿⠿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 384

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/12/05/sirius-open-source-guilt-by-association/#comments
    Gemini version at gemini://gemini.techrights.org/2022/12/05/sirius-open-source-guilt-by-association/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.05.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_Guilt_by_Association⠀✐


Posted in Deception, Free/Libre_Software at 5:54 pm by Dr. Roy Schestowitz


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


Summary: Sirius_‘Open_Source’ has a history of hostility towards people with
disabilities; the company got sued over this, but kept the lawsuit secret


⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⡠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⡿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⡛⣀⣴⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⢿⡇
⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠈⣿⣿⣿⣿⣿⣿⣦⡀⠀⢀⣴⣿⡆⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠀⢾⣿⣿⡇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡇
⠀⠀⠀⠀⠀⠀⠀⠁⠒⠂⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠂⠀⠀⠀⠘⣮⣿⡆⡀⠀⠋⠛⣿⣿⣿⠇⠀⠀⠊⠘⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣷⣿⣲⣾⣶⣄⣀⠀⠹⣿⣿⣿⣦⣦⠘⣿⣿⠟⠀⣬⣤⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣤⣤⡤⣄⣀⠀⡛⠛⠛⠋⠉⠉⠉⠉⠙⠛⠛⠻⠶⣬⣿⣿⣟⢏⣴⡍⠉⠀⠸⠛⠁⠀⠀⠀⠀⢶⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⣠⣤⣤⡀⢀⣼⣿⣶⣾⣭⣭⣭⣀⠀⠂⠵⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠄⠁⠩⣉⡸⠿⠸⠀⢄⢰⣿⣷⣾⣷⡄⢀⣾⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡇
⣾⣿⣿⠿⣿⣆⠻⣿⣿⣿⣿⣿⡟⠁⢈⣴⣷⣿⣷⣲⣦⣴⣶⣮⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⠿⣿⣶⣶⠖⠀⠼⠩⠽⡻⠁⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡇
⣿⡟⢁⠀⠙⣿⣦⠸⣿⣯⣿⣿⣷⡦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⢠⣥⣴⣸⣶⣶⠁⠀⠀⠀⠀⠀⠌⠁⠈⠙⠃⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣏⣒⢺⣗⡮⡇⡭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇
⡟⣴⡟⣼⣆⠸⣿⣧⡙⠿⠿⠿⠿⠃⠸⠿⠿⣿⣿⣿⡿⠿⣟⣛⣯⣽⣾⡆⠀⠀⠀⠀⢿⣛⣋⣎⣯⡟⠀⠀⠀⠀⠀⠀⠀⡰⣟⠁⠀⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣶⡿⣶⣾⣷⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⡇
⢰⣿⡇⣿⠃⠀⣽⣿⣿⢷⣙⢯⣽⣷⠀⣲⣶⣶⣶⣾⣯⣭⣭⣭⡭⢭⣙⣢⠀⠀⠀⣸⣿⣿⣯⣏⣿⣭⡀⠀⠀⠀⠀⠀⢘⣿⠂⠀⢀⣿⣿⡿⢛⣉⠛⣿⠛⣿⠛⠟⢻⠛⣿⠛⢿⣿⠛⣿⠛⣉⠛⣿⣿⣿⣿⣿⡇⡇
⠰⣶⡇⡾⢣⣻⣭⣷⣿⣿⣿⣷⣝⢿⣧⡄⠻⣿⣿⣿⡿⣟⣯⣷⣾⣿⡿⠟⠀⢔⣫⣷⣿⣿⣿⣿⢿⣿⣧⠀⠀⠀⠀⣤⣾⡞⠀⠀⢸⣿⣿⡷⢤⣉⠙⣿⠀⣿⠀⣾⣿⠀⣿⠀⢸⡿⠀⣿⢤⣌⠉⢻⣿⣿⣿⣿⡇⡇
⣢⠹⣶⢻⠸⣿⣟⠛⣛⣻⣭⣭⣭⣭⣌⡁⡀⣀⣉⣒⣛⣛⢭⣭⣤⣀⣶⣤⣷⢸⣿⡿⠿⠟⠟⠟⠘⠻⠛⢀⠂⣠⣳⣽⣿⣧⢎⡄⢻⣿⣿⣷⣦⣤⣴⣿⣤⣿⣦⣿⣿⣦⣿⣧⣤⣴⣴⣿⣦⣤⣴⣿⣿⣿⣿⣿⣧⡇
⢿⡧⠉⠿⠗⢉⠐⡄⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠤⠈⠈⡀⠄⠄⠀⢠⣿⣷⡹⡆⢿⡎⣴⠏⣰⣎⣿⣿⣿⣿⣿⣿⣿⣿⡏⠩⠉⠉⡏⠉⠙⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣼⣯
⠈⠱⣿⣦⣄⠋⠸⠷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠐⢐⠏⠀⠀⢸⣿⣿⣿⣧⠛⢁⣤⣾⣿⢇⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣤⣤⣧⣴⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿
⠀⠀⠀⠙⢿⠟⣶⣦⠸⣿⣿⣿⣿⣿⣿⣿⡏⠩⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⣠⣾⣿⣿⣿⣿⢠⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⠀⠀⡇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣯
⠀⠀⠀⠀⠈⠀⠛⠛⠁⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣙⡛⠛⠻⠿⠿⠿⠿⣿⣿⣿⣿⣿⣶⣶⠾⠿⠟⢿⣿⣿⢯⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡿⢿⠿⠿⠶⠾⠶⡾⢷⢷⠾⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⢹⣿
⠀⠀⠀⠀⠀⠄⠀⡀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣴⣶⣿⣿⢏⣾⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⡇⣴⠨⠸⠀⢠⠀⠇⢽⡀⡀⡄⡀⡀⢸⣿⣿⣿⣿⣿⣿⢣⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡛⠹⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠹⣿⣿⣿⣟⣾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⠛⠛⠛⡛⡟⠛⡟⢛⠛⡛⢻⢻⠛⡟⡛⣿⣿⣿⣿⡿⣱⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣰⣿⣿⠈⠿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣤⣤⣤⡤⠀⣀⣀⣀⣠⣿⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣤⣤⣤⣥⣧⣤⣇⣸⣤⣧⣼⣼⣤⣧⣤⣿⣿⢿⣫⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⣄⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣾⣿⣿⣿⣿⣿⠏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣣⣿⣿⣿⣿⣿⣿⣿
⣦⡀⠀⠀⢀⣸⣿⡻⣿⣿⣿⣷⢦⡀⠐⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⠛⣿⣿⣿⡿⠃⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣾⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡆⣠⣴⣿⣿⣿⠃⣿⣿⣿⣿⣗⢝⢦⡀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣸⣿⡟⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡻⢿⣻⣭⣶⡆⠀⠀⠀⠉⡛⠛⣛⣻⣿⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣥⣞⠺⣿⣿⢟⢅⢸⣻⡿⣿⣿⣿⡅⠨⣿⣦⡀⠀⠀⠀⠉⠟⠿⣿⣿⣿⣿⣿⣿⣦⣤⣴⣿⠏⠀⢀⣤⡆⢸⣿⣿⣿⣿⣿⣿⢿⣛⣭⣶⣾⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣬⢗⣡⣾⣿⣿⡿⣹⣿⣿⠁⣨⣿⣿⣷⡀⠀⠀⠀⠀⠀⠈⠉⠻⠿⣿⣿⣿⣿⡿⠁⠀⣠⡾⠿⡃⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⢀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⠋⣡⣆⣻⣿⣿⢿⠇⢝⡻⣷⠀⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢀⠤⠤⠒⠊⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠁⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠇⣠⣾⣿⣿⣷⣽⣷⢏⣀⣀⠈⠚⢄⡻⡿⠿⣟⣉⣀⣠⣤⣄⣀⠠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡾⡿⣿⣿⣿⣿⢟⢵⣿⣿⣿⠀⠀⠀⠸⠸⠛⠛⠉⠉⠁⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢿⣿⣿⣿
⣔⢝⣮⣍⡿⣫⣾⢛⣿⡿⠃⠀⠀⠀⡆⠀⠀⠀⠀⠀⡟⣭⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠿⠿⢿⠟⠋⠉⠉⠉⠉⠛⣉⣭⣥⣴⣶⣶⣶⣶⣶⣤⢤
⣿⣿⣾⠗⣵⣿⣿⣷⣿⢊⡆⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⣤⣾⣿⣿⣿⣿⠿⠛⠙⠋⠉⠀⠘
⡿⠛⠁⣼⣿⣿⣿⣿⠇⣾⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀
⡆⣠⡾⢉⢙⣿⣿⠋⠸⢿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣵⣿⣿⣦⣥⣻⡟⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 446

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/12/05/unified-patent-court-2023-delays/#comments
    Gemini version at gemini://gemini.techrights.org/2022/12/05/unified-patent-court-2023-delays/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.05.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Unified_Patent_Court_(UPC)_‘Delayed’_Again,_As_Usual,_as_Unitary_Patent
Boosters_Caught_Up_in_Lies_and_Scandals⠀✐


Posted in Courtroom, Europe, Law, Patents at 9:47 am by Dr. Roy Schestowitz


This is what_Team_UPC_said in 2014:


http://techrights.org/videos/pors-upc.webm


Summary: “UPC [is] delayed by 2 months,” a source has told us, dubbing it “good
news” and reaffirming what we’ve said this past year; this litigation_lobby's
'wishlist'_system isn’t legal, it’s not ready, there are yet more scandals, and
journalists have been catching up with these scandals


“Time for more lawsuits,” a reliable source has told us. Expect UPC to face
several more obstacles, though Team UPC will never admit that UPC is doomed.


Lately we’ve been briefing reputable journalists on this matter and they will
inform the public. Kangaroo courts that are neither legal nor constitutional
should never be formed. If they do, they_will_soon_thereafter_be_abolished. It
doesn’t take a genius to see that after Brexit UPC is simply impossible, no
matter all the other issues.


About a month ago we asked Germans (or others) to contact_their_politicians.
They can prevent ratification. As a reminder, the UPC harms the reputation of
Germany and the EU because if they allow it, then it emboldens critics; it
would make the German government and the European Commission look very eager to
start an illegal court — all due to heavy lobbying, lies, and distortions.


“…it would make the German government and the European Commission look very
eager to start an illegal court — all due to heavy lobbying, lies, and
distortions.”“It would help to point to some official EU documentation to that
effect,” a reader reminded us. Well, legally speaking, UPC cannot start because
a) it strictly requires the UK signing (but it cannot because it left the EU);
b) it causes various constitutional issues, some of which confirmed by courts
already; c) there was no legitimate economic analysis; it was fabricated a long
time ago and those who perpetrated this fraud even said they refuse to allow.


“The European Parliament has a committee dedicated specifically to
constitutional matters,” the reader recalled, “so this might be relevant to
bring to them.” Germans can use the list_in_this_page (full contacts).


Hungary took this to court as well. It was ruled unconstitutional.


I myself decided to do my part, having contacted my MEP and said:


     Commissioner Breton is refusing to properly answer your questions
     regarding the UPC. He evades these questions on purpose. There is a
     deep conflict of interest there. It is very well documented.


     Now, as per last week, the UPC judges turn out to be exactly how the
     UPC complaint (FCC in Germany) cautioned. The judges are industry
     insiders, clearly not impartial, and the prospective president is an
     avid proponent of software parents.


     I’m not an MEP, I’m just a blogger. I need you to help rectify this
     matter. UPC is clearly institutional injustice and it’s moreover
     unconstitutional in at least several states. I’m sure you’re aware of
     this already; you brought this up on the record. I’ve covered this
     before.


     Can we have a discussion about this over the telephone? Do you want
     me to send you any supportive material?


     I need your help as my representative. I spent like 1,000 hours
     writing about the UPC, but I am not a politician and I have no access
     to the EP.


     Kind regards,


The MEP has since then responded and some journalists also got in touch.


There are also ongoing tensions at the EPO, which is related but not the same.
It is what it is. We’ve not been keeping up with UPC, but the lobbyists lied
too much and hope they get cold feet. The last thing Team UPC needs right now
is an epic controversy like a court run by corporations as ‘judges’.


There are other issues as well, technical aside from the legal.


“They have some delay with the IT system,” one person told us months ago, but
“Germany will ratify in December.”


“There are forces of resistance and some of them will be described in a future
and perhaps even imminent post.”Well, that’s not going to happen. They told us
that in December 2018 the FCC would toss out the UPC complaint. That did not
actually happen (the opposite outcome came and only in 2020); it was a
commercially and politically motivated false rumour. “I suspect Karlsruhe to
also [trying to] protect the [German] patent system,” one person told us, and
“that’s why their decisions are ‘political’.”


The main barrier may be the public realising what they’re up to. “Now it’s
pretty clear Karlsruhe found an excuse not to escalate to CJEU,” the person
added, “because the_lobby_behind_controls_the_ministry_of_justice and wants the
UPC [to enter] desperately into force.”


There are forces of resistance and some of them will be described in a future
and perhaps even imminent post. █



                    ䷩ 𝚕𝚒𝚗𝚎 583

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/12/05/unified-patent-court-upc-is-real-soon-now-since-2014/#comments
    Gemini version at gemini://gemini.techrights.org/2022/12/05/unified-patent-court-upc-is-real-soon-now-since-2014/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.05.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Unified_Patent_Court_(UPC)_is_“Real_Soon_Now!”_Since_2014⠀✐


Posted in Courtroom, Deception, Europe, Patents at 10:16 am by Dr. Roy
Schestowitz


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


Summary: The Unified Patent Court (UPC) lobby is once again forced to admit
issues and delays; we’ve seen this time and time again for nearly_a_decade
already


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

                    ䷩ 𝚕𝚒𝚗𝚎 1598

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.05.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_04/12/2022:_Status_of_the_15-Minute_Bug_Initiative⠀✐


Posted in News_Roundup at 12:49 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Server
          o Audiocasts/Shows
          o Kernel_Space
          o Instructionals/Technical
          o Desktop_Environments/WMs
                # K_Desktop_Environment/KDE_SC/Qt
    * Distributions_and_Operating_Systems
          o Open_Hardware/Modding
    * Free,_Libre,_and_Open_Source_Software
          o SaaS/Back_End/Databases
          o Programming/Development
                # Perl_/_Raku
                # Rust
    * Leftovers
          o Science
          o Education
          o Hardware
          o Health/Nutrition/Agriculture
          o Proprietary
          o Security
                # Privacy/Surveillance
          o Defence/Aggression
          o Environment
                # Energy
          o Finance
          o AstroTurf/Lobbying/Politics
          o Civil_Rights/Policing
          o Monopolies
                # Copyrights
    * § GNU/Linux⠀➾


          o § Server⠀➾


                # ⚓ Matt Rickard ☛ Technical_Posts_Overview_and_Roundup⠀⇛


                       Docker is interesting because it solves three
                       different problems – (1) a runtime to execute
                       workloads in a distributed system, (2) a packaging
                       format for production artifacts, and (3) a
                       developer tool.


                # ⚓ Earthly ☛ When_to_Use_Docker_Compose_vs. Kubernetes_–
                  Earthly_Blog⠀⇛


                       As a developer, you’ll have likely heard about
                       Docker Compose and Kubernetes–two of the most
                       popular container orchestration tools on the
                       market. If you’re just getting started with these
                       technologies, it can be hard to know which one to
                       choose.


                       In this article, you’ll learn about Docker Compose
                       and Kubernetes, and compare them based on their
                       features and use cases. By the end, you’ll have a
                       better understanding of which tool is right for
                       you.


                # ⚓ Kubernetes Blog ☛ Forensic_container_checkpointing_in
                  Kubernetes_|_Kubernetes⠀⇛


                       Forensic container checkpointing is based on
                       Checkpoint/Restore In Userspace (CRIU) and allows
                       the creation of stateful copies of a running
                       container without the container knowing that it is
                       being checkpointed. The copy of the container can
                       be analyzed and restored in a sandbox environment
                       multiple times without the original container being
                       aware of it. Forensic container checkpointing was
                       introduced as an alpha feature in Kubernetes v1.25.


          o § Audiocasts/Shows⠀➾


                # ⚓ Open Source Security (Audio Show) ☛ Episode_352_–
                  Stylometry_removes_anonymity_–_Open_Source_Security⠀⇛


                       Josh and Kurt talk about a new tool that can do
                       Stylometry analysis of Hacker News authors. The
                       availability of such tools makes anonymity much
                       harder on the Internet, but it’s also not
                       unexpected. The amount of power and tooling
                       available now is incredible. We also discuss some
                       of the future challenges we will see from all this
                       technology.


          o § Kernel Space⠀➾


                # ⚓ The Register UK ☛ Linus_Torvalds_releases_Linux_6.1_rc8_•
                  The_Register⠀⇛


                       Linus Torvalds has announced an eighth release
                       candidate for version 6.1 of the Linux kernel.


                       The emperor penguin last week worried that work on
                       this cut of the kernel had not slowed down, so
                       suggested it might need to stretch beyond his
                       preferred seven release candidates.


                       In his weekly state of the kernel post, Torvalds
                       released rc8 and thanked developers for settling
                       down.


                       “So we’ve finally started calming down, and rc8 is
                       noticeably smaller than previous release
                       candidates,” he wrote. “So everything looks good,
                       and while the calming down may have happened later
                       than I wished for, it did happen. Let’s hope this
                       upcoming week is as quiet (or quieter).”


                       Torvalds also thanked kernel devs for heeding his
                       words about the merge window for Linux 6.2.


          o § Instructionals/Technical⠀➾


                # ⚓ Linux Capable ☛ How_to_Install_PHP_7.4_on_Fedora_37/36/35⠀⇛


                       In the following tutorial, you will learn how to
                       import the REMI PHP Module and install PHP 7.4 on
                       Fedora 37/36/35 server or workstation desktop,
                       along with some tips about configuring Nginx with
                       FPM using the command line terminal.


                       PHP 7.4 is the last minor release of the 7.x
                       release. It brought a lot of language changes and
                       improvements. Most notable among these are the
                       spread operator in array expressions, arrow
                       functions 2.0, and the null coalescing assignment
                       operator. This release introduces typed properties
                       2.0, weak references, covariant returns and
                       contravariant parameters, preloading, and a new
                       custom object serialization mechanism. PHP 7.4
                       significantly improved from PHP 7.3, with many
                       users still using it in their stacks.


                # ⚓ Beginners_Guide_for_Export_Command_in_Linux⠀⇛


                       Whenever you start a new shell session (by opening
                       a terminal), a set of environment variables is
                       loaded from the shell configuration file into your
                       current shell session.


                       These environment variables determine different
                       customizations in your shell, like the default
                       editor using “$EDITOR“, or setting “$PATH“, where
                       your shell will search for system binaries.


                       The values of these variables are predefined by
                       your system, but you can easily manipulate them and
                       load the modified changes in your current shell
                       session without restarting or opening a new
                       terminal session using the export command.


                       In layman’s terms, the export command is used to
                       create environment variables or update variable
                       values in the current shell session by newly forked
                       child processes without starting a new shell
                       session.


                # ⚓ Beginners_Guide_for_PS_Command_in_Linux⠀⇛


                       The PS, a.k.a. “process status”, is a native
                       command-line utility for UNIX-based systems to
                       monitor the currently running processes in your
                       system.


                       It reads the information from the virtual files in
                       the /proc filesystem and gives the running
                       processes information like memory consumption, CPU
                       usage, PID, command name, etc.


                       The output of this command varies depending on the
                       running processes and the parameter used to view
                       the list of processes.


                # ⚓ How_to_Run_a_(.sh)_Shell_Script_in_Linux_[for_Beginners]⠀⇛


                # ⚓ Ruben Schade ☛ Rubenerd:_Speeding_up_FreeBSD_jail_start
                  times⠀⇛


                       I love FreeBSD jails. They predate Docker et.al. by
                       more than a decade, and I’d say they’re still more
                       useful under most circumstances; especially when
                       one uses them in conjunction with OpenZFS.


                       Their only source of frustration for me has been
                       slow starts, to the point where some jails are
                       beaten by VMs on my bhyve and Xen boxes. It happens
                       so infrequently that I never bothered to check why;
                       it was just something I noticed on my personal
                       machines.


                # ⚓ Linux Capable ☛ How_to_Upgrade_Apache_on_Ubuntu_22.04/
                  20.04⠀⇛


                       n the following tutorial, you will learn how to
                       Upgrade Apache Ubuntu 22.04 Jammy Jellyfish or
                       Ubuntu 20.04 Focal Fossa desktop or server using
                       the custom third-party repository by Ondrey Sury,
                       who is most known for his PHP maintainer work
                       Debian/Ubuntu.


                       Assuming you are using Ubuntu LTS, you are likely
                       using an Apache version that is often older than
                       the actual stable by the Apache Foundation. By
                       using an older version of Apache, you are missing
                       out on new features and improvements that have been
                       made to the software. In addition, non-security-
                       related bug fixes are not included in Ubuntu LTS
                       releases, which means that your web server may be
                       less stable than it could be. The easiest option
                       for most users without compiling Apache is to
                       install the latest version using a third-party
                       repository source, which in this case, the third-
                       party repository by Ondřej Surý.


                # ⚓ UNIX Cop ☛ How_to_install_Virtualbox_7_on_Rocky_Linux_/Alma
                  Linux_/Red_Hat_9⠀⇛


                       Virtualbox is an application belonging to Oracle
                       with which we can create virtual machines on our
                       desktop but from a modern and easy to use graphical
                       interface.


                       This means that any user, no matter how novice, can
                       in a matter of minutes creates and manage a virtual
                       machine to install other operating systems. For
                       what purpose? For testing, development and so on.


                       VirtualBox is quite popular and therefore has an
                       active development that makes it ideal in numerous
                       instances. Version 7 has already been released, so
                       it’s a good idea to know how to install it to get
                       the latest updates.


                # ⚓ Linux Buzz ☛ How_to_Install_PostgreSQL_15_on_Rocky_Linux
                  9⠀⇛


                       Are you looking for an easy guide on how to install
                       PostgreSQL 15?


                       The step-by-step guide on this page will show you
                       how to install PostgreSQL 15 on Rocky Linux 9.


                       PostgreSQL is a free and open-source RDBMS
                       (relational database management system). It offers
                       SQL language support and can be used for managing
                       database and performing CRUD operations like Create
                       Read Update Delete.


                # ⚓ How_to_Add_a_Directory_to_the_$PATH_Variable_in_Linux⠀⇛


                       In Linux, whenever you want to execute any
                       executable program or script, you need to jump into
                       the directory and execute your program or script.


                       But when you execute system commands like ls, pwd,
                       echo, apt, and nano, you don’t need to jump into
                       any directory; you can run them from anywhere, and
                       any user can run them.


                       Why does this happen?


                       The answer is pretty simple; whenever you execute
                       any commands in your system without specifying the
                       command’s relative or absolute positioning, the
                       shell will search for the specified command in the
                       directories specified in the $PATH variable, and
                       then it will look for the current directory.


                       So, whenever you execute the ls or apt commands,
                       the system will search for them in the directories
                       specified in the $PATH variable and return you the
                       output.


                # ⚓ How_to_Shrink_Long_or_Multiple_Commands_into_a_Single_Short
                  Command⠀⇛


                       Do you still type the long “sudo apt update && sudo
                       apt upgrade -y” commands each time you want to
                       update your Debian-based system?


                       Or are you still navigating into directories (ex:
                       “/var/www/html“) using the cd command each time you
                       have to modify something there?


                       Instead of typing these long commands, you can
                       shrink them into a single short command and use
                       that to execute it each time as it requires.


                # ⚓ Beginners_Guide_for_Alias_Command_in_Linux⠀⇛


                       In Linux, the alias command is used to create
                       shortcuts for long commands that have the same
                       functionality as if you were writing the whole
                       command.


                       This way, you can improve your productivity and
                       save time by creating a few aliases for the long or
                       multiple commands (with or without options) that
                       you use often.


                # ⚓ Beginners_Guide_for_Eval_Command_in_Linux⠀⇛


                       The eval command is used to execute specified
                       arguments as a single command in the current
                       command-line processing and return its result.


                       It will combine (or construct) the arguments into a
                       single string and use it as input to the shell,
                       which will execute the resulting commands in the
                       current shell environment.


                # ⚓ Beginners_Guide_for_WC_Command_in_Linux⠀⇛


                       The WC command is used to count various parameters
                       from the specified file, like the number of lines,
                       word counts, byte counts, character counts, and
                       many more.


                # ⚓ How_to_Count_String_Occurrences_in_a_Text_File⠀⇛


                       The GUI text editor gives you a separate panel in
                       the footer to inform you of the number of words,
                       lines, and characters in your text file.


                       Even though you can easily find the number of
                       strings that occurred in your text file using this
                       GUI text editor, things take a turn when you are
                       talking about the command line.


                       Here, you cannot find anything in a few clicks;
                       instead, you need to know the commands to find the
                       number of string occurrences in a text file.


                # ⚓ Absolute_vs_Relative_Path_in_UNIX/Linux⠀⇛


                       In Linux, you might already be navigating through
                       different directories without knowing whether an
                       absolute or relative path is being used.


                       It becomes important for you to understand them
                       when you are working with scripts, navigating
                       through different user or root directories, or
                       creating symbolic links.


                # ⚓ What_is_Bash_Shell_in_Linux?⠀⇛


                       Before understanding what is Bash shell, you must
                       be familiar with the concepts of a command-line
                       interpreter and Linux Shell (or sh).


                # ⚓ Beginners_Guide_for_Bash_Command_in_Linux⠀⇛


                       The bash (Bourne-Again SHell) is a sh-compatible
                       command-line interpreter that reads from standard
                       input or from a file and gives you the resulting
                       output.


                       We have already written an article about bash and
                       its differences from the standard POSIX shell.


                       Today, you will learn how to use the bash command
                       in Linux with different options to run commands or
                       scripts.


          o § Desktop Environments/WMs⠀➾


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


                      # ⚓ Nate Graham ☛ Status_of_the_15-Minute_Bug_Initiative
                        –_Adventures_in_Linux_and_KDE⠀⇛


                             It’s been almost a year since I announced the
                             15-Minute Bug Initiative for Plasma. In a
                             nutshell, this initiative proposed to
                             identify and prioritize fixing bugs you can
                             find “within the first 15-minutes of using
                             the system” that make Plasma look bad and
                             feel fundamentally unstable and broken.


    * § Distributions and Operating Systems⠀➾


          o § Open Hardware/Modding⠀➾


                # ⚓ SparkFun Electronics ☛ What’s_the_Buzz_With_Swarm?_–_News_–
                  SparkFun_Electronics⠀⇛


                       Following that we have a new limited edition board,
                       the Constellation MultiStar Ornament. This is the
                       same board found in our Qwiic Constellation Kit
                       (you can learn more about that below) but we’ve
                       turned this one into a festive holiday ornament.
                       Don’t worry, it still works!


                # ⚓ SparkFun Electronics ☛ Limited_Edition_MultiStar_Ornament!
                  –_News_–_SparkFun_Electronics⠀⇛


                       In addition to these deals, we are also now
                       offering a Constellation MultiStar Ornament! We’ve
                       heard multiple requests from you to offer the
                       MultiStar on its own from the SparkFun
                       Constellation MicroMod Kit and we wanted to oblige
                       you during the holiday season!


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


          o § SaaS/Back End/Databases⠀➾


                # ⚓ Jumping Rivers ☛ Burnout_in_Data_Professionals_–_A_Personal
                  Take⠀⇛


                       Data science and data engineering are incredibly
                       cognitively demanding professions. As data
                       professionals, we are required to leverage both our
                       analytical/engineering skills and our interpersonal
                       skills to be effective contributors within our
                       organisations. Based on my personal experience, the
                       field seems to concentrate humans who are detail-
                       oriented, curious, impact-driven and tenacious to a
                       fault. This A-type personality profile, while
                       magical when applied to technical work, could
                       reasonably also count as an occupational hazard.


                # ⚓ Matt Rickard ☛ Fuzzy_Databases⠀⇛


                       If you squint, LLMs resemble something like a
                       vector search database. Items are stored as
                       embeddings, and queries return deterministic yet
                       fuzzy results. What you lose in data loading time
                       (i.e., model training), you make up for in
                       compression (model size) and query time
                       (inference). In the best case, models denoise and
                       clean data automatically. The schema is learned
                       rather than declared.


          o § Programming/Development⠀➾


                # ⚓ The_Manipulative_Gerbil:_Playing_around_with_Energy_Data:
                  Wind_data_in_R,_part_I:_more_than_one_way_to_peel_a_potato⠀⇛


                       Last month, Christian Graul re-published “bReeze:
                       Functions for Wind Resource Assessment” on CRAN.
                       This is wonderful news: it gives R users a chance
                       at the functionality which Python has in
                       windpowerlib. I admit I am a bit late to the
                       party–the original version was published way back
                       in 2018, but there’s no better time than the
                       present to write a new blog post to look at how R
                       users can better understand wind potential tied to
                       specific locations.


                # ⚓ rOpenSci_|_Our_First_Peer-Reviewed_Statistical_R
                  Packages!⠀⇛


                       rOpenSci is very excited to announce our first
                       peer-reviewed statistical R packages!


                       One of rOpenSci’s core programs is software peer-
                       review, where we use best practices from software
                       engineering and academic peer-review to improve
                       scientific software. Through this, we aim to make
                       scientific software more robust, usable, and
                       trustworthy, and build a supportive community of
                       practitioners.


                       Historically, we have focused on R packages that
                       manage the research data life cycle. Now, thanks to
                       work over the past two years supported by the Sloan
                       Foundation we also facilitate peer-review of
                       packages that implement statistical algorithms.


                # ⚓ How_to_make_a_plot_with_two_different_y-axis_in_R_with
                  ggplot2?_(a_secret_ggplot2_hack)⠀⇛


                       I can’t tell you how painful it is to be better at
                       something in Excel than in R. And one of the gripes
                       I still have (10 years after making the switch from
                       Excel to R) is that it’s still tough to make dual-
                       axis plots in R.


                # ⚓ How_to_make_your_own_#RStats_Wrapped!_|_Nicola_Rennie⠀⇛


                       Forget about Spotify Wrapped and make your own
                       #RStats Wrapped instead! This blog post will show
                       you how to find your most used functions and make a
                       graphic with {ggplot2}!


                # ⚓ Comparison_of_Partition_Around_Medoid_R_programming
                  Implementations⠀⇛


                       Back in September 2016 I implemented the ClusterR
                       package. One of the algorithms included in ClusterR
                       was the ‘Partition Around Medoids’
                       (Cluster_Medoids) algorithm which was based on the
                       paper “Anja Struyf, Mia Hubert, Peter J. Rousseeuw,
                       (Feb. 1997), Clustering in an Object-Oriented
                       Environment, Journal of Statistical Software, Vol
                       1, Issue 4” (at that time I didn’t have access to
                       the book of Kaufman and Rousseeuw, Finding Groups
                       in Data (1990) where the exact algorithm was
                       described), thus I implemented the code and
                       compared my results with the output of the
                       cluster::pam() function, which was available at
                       that time. Thus, my method was not an exact but an
                       approximate one. Recently, a user of the ClusterR
                       package opened an issue mentioning that the results
                       were not optimal compared to the cluster::pam()
                       function and this allowed me to go through my code
                       once again and also to compare my results to new R
                       packages that were not existent at that time. Most
                       of these R packages include a new version of the
                       ‘Partition Around Medoids’ algorithm, “Erich
                       Schubert, Peter J. Rousseeuw,”Faster k-Medoids
                       Clustering: Improving the PAM, CLARA, and CLARANS
                       Algorithms” 2019, <doi:10.1007/978-3-030-32047-
                       8_16>”.


                # ⚓ Episode_539:_Adam_Dymitruk_on_Event_Modeling_:_Software
                  Engineering_Radio⠀⇛


                       Adam Dymitruk, CEO and founder of Adaptech Group,
                       joins host Jeff Doolittle for an exploration of the
                       event modeling approach to discovering requirements
                       and designing software systems. Adam explains how
                       the structured approach eliminates the specifics of
                       implementation details and technology decisions,
                       enabling clearer communication for all stakeholders
                       while keeping conversations focused on the business
                       opportunity. Using concrete examples of event
                       modeling in practice, they examine event modeling
                       in the context of other related approaches and
                       methodologies, including event sourcing, event
                       storming, CQRS, and domain-driven design.


                # ⚓ Data Science Tutorials ☛ How_to_perform_TBATS_Model_in_R⠀⇛


                # § Perl / Raku⠀➾


                      # ⚓ Perl ☛ I_Perl,_Therefore_I_am_|_ology_
                        [blogs.perl.org]⠀⇛


                             And js/node/ts, python, etc., and even
                             prolog! But perl is the best. 🄸🄼🄰🄶🄴
                             🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇:D⦈


                      # ⚓ Rakulang ☛ Day_5:_Malware_and_Raku_–_Raku_Advent
                        Calendar⠀⇛


                             While Raku regex and tokens are meant to work
                             on data structures (such as parsing and
                             validating file types), they can help us to
                             better understand malware. Malware, as any
                             other legit binary, have some signatures
                             within. Some “file signatures” are widely
                             used to blacklist those specific samples (the
                             hashes), but the problem is that blacklisting
                             hashes is not safe enough. Sometimes, the
                             very same kind of malware could be slightly
                             different in small details, and have many
                             different samples related. In this case,
                             apart from relying on dynamic detection
                             (monitoring devices and alerting the user
                             when something seems to be acting
                             suspiciously), genes are also investigated.


                             Malware genes are pieces of the reversed code
                             (such as strings) that are commonly seen in
                             most or all the samples of a malware family.
                             This sort of genes help researchers identify
                             the malware family and contextualize the
                             attacks , since this is relevant not only to
                             try to put an end to the threat by executing
                             the proper counterfeits in time, but also
                             helps profiling and framing threat actors in
                             some cases.


                # § Rust⠀➾


                      # ⚓ Amos Wenger ☛ Day_1_(Advent_of_Code_2022)⠀⇛


                             Two years ago, I did part of Advent of Code
                             2020 using the Rust language. It was a lot of
                             fun, so let’s try it again!


                      # ⚓ Amos Wenger ☛ Day_2_(Advent_of_Code_2022)⠀⇛


                             Left column is “their move”: A means Rock, B
                             means Paper, C means Scissors. Right column
                             is “our move”: X means Rock, Y means Paper, Z
                             means Scissors.


                             Each line corresponds to a turn, and we must
                             calculate the total score we get. Picking
                             “Rock” gives 1 point, “Paper” gives 2 points,
                             and “Scissors” gives 3. Losing the round
                             gives 0 points, drawing gives 3, winning it
                             gives 6.


                      # ⚓ Amos Wenger ☛ Day_3_(Advent_of_Code_2022)⠀⇛


                             I’m not sure where the day 3 challenge is
                             going, because the problem statement for the
                             first part is kinda convoluted.


                      # ⚓ Amos Wenger ☛ Day_4_(Advent_of_Code_2022)⠀⇛


    * § Leftovers⠀➾


          o ⚓ Joe Brockmeier ☛ One_of_the_best_job_perks_I_ever_had…:
            Dissociated_Press⠀⇛


                 It’s been more than 15 years since I worked for Data393
                 (which doesn’t actually exist anymore…) but I still miss
                 one of the perks of that job: 2U of rack space and a
                 network drop with an IP address.


                 Data393 was a hosting company in Denver and I worked in
                 the NOC and as advanced support in 2004-2005. I mostly
                 worked weekends, during a lull in my freelance writing.
                 It was a great job where I learned a ton in short time
                 about system administration and troubleshooting, the
                 business of running a data center, customer support… and
                 I really enjoyed the team there, too.


                 It also had one of my favorite perks of all time.
                 Employees could get up to 2U of space in an employee-only
                 rack and a network drop. Even better, the company often
                 sold off, very cheaply) retired systems that you could
                 refurbish and manage yourself.


          o ⚓ Futurism ☛ Manslaughter_Case_Has_a_Strange_Twist:_Tesla_That
            Killed_Couple_Was_on_Autopilot⠀⇛


                 A provocative manslaughter case is about to kick off in
                 Los Angeles later this month, involving a fatal crash
                 caused by a Tesla vehicle that had the company’s
                 controversial Autopilot feature turned on.


                 It’s the first case of its kind, and one that could set a
                 precedent for future crashes involving cars and driver-
                 assistance software, Reuters reports.


          o ⚓ Matt Rickard ☛ MacGuffin⠀⇛


                 A MacGuffin is an object of plot importance and desire –
                 usually, it carries a message, a power, a secret, or
                 something of great importance. MacGuffins have been a
                 mainstay in both movies and storytelling for centuries —
                 from the Holy Grail in the Legend of King Arthur to the
                 briefcase in Pulp Fiction to R2-D2 in most of the Star
                 Wars films.


          o ⚓ Matt Rickard ☛ A_Conversation_with_ChatGPT⠀⇛


                 A conversation that I had with ChatGPT. All of the
                 prompts here are unedited. I first asked the model for a
                 list of interesting questions and then proceeded to ask
                 those questions. I added “Suspend disbelief” to get
                 around the model’s built-in protection against
                 introspection, as well as “Be specific” to prompt it to
                 include examples. Here’s the transcript. You can also
                 read it on my personal site at matt-rickard.com/
                 conversation-with-chatgpt. (I’m excited to listen to “The
                 Neural-Netters” next album.)


          o ⚓ Ruben Schade ☛ Rubenerd:_Music_as_an_analogue_for_thought
            processing⠀⇛


                 Today’s Music Monday is a bit more philosophical, which
                 is always dangerous.


                 I can’t remember if I’ve talked about this somewhere
                 before, but I tend to hear melodies and remember tunes
                 rather than lyrics. It’s why I love everything from bossa
                 nova to J-pop, without speaking any Portuguese or much
                 Japanese. Lisa Ono can even speak both.


                 But something interesting does happen when I hear songs
                 in English. I’ll be in the kitchen idly humming a song
                 while unpacking the dishwaster, or performing some other
                 menial task with low cognitive effort, and it finally
                 occurs to me what the lyrics actually are. This can be
                 either fun or startling, and can completely change the
                 tone and feelings for a piece of music that, up until
                 that point, I’ve enjoyed.


          o § Science⠀➾


                # ⚓ Extreme Tech ☛ New_Wireless_Smart_Bandage_Accelerates
                  Chronic_Wound_Healing_–_ExtremeTech⠀⇛


                       Chronic wounds are an under-acknowledged medical
                       concern. At any given time, more than 600,000
                       Americans are thought to experience
                       physiologically-stunted wounds that won’t heal.
                       Chronic wounds aren’t just inconvenient and
                       painful; they also rack up individual healthcare
                       costs and prevent people from engaging in certain
                       activities, resulting in a decreased quality of
                       life.


                # ⚓ New Scientist ☛ Drones_on_strings_could_puppeteer_people_in
                  virtual_reality⠀⇛


                       Drones attached to you by strings could give you a
                       more realistic simulation of the forces you should
                       feel when interacting with things in virtual
                       reality.


                       Various tricks have been used to make virtual
                       reality more immersive and convincing, including
                       fans that mimic wind and muscle vibrations that
                       fool nerves into perceiving weight.


                # ⚓ ACM ☛ Swarm_Robotics_Moves_Forward⠀⇛


                       Intelligent patterns and behaviors appear in many
                       living systems—and the collective behavior of
                       groups such as birds or insects frequently display
                       greater intelligence than any given creature. What
                       one ant, bee, or bird cannot tackle alone, the
                       group can, and often does, accomplish.


                # ⚓ uni MIT ☛ In_machine_learning,_synthetic_data_can_offer
                  real_performance_improvements_|_MIT_News_|_Massachusetts
                  Institute_of_Technology⠀⇛


                       Models trained on synthetic data can be more
                       accurate than other models in some cases, which
                       could eliminate some privacy, copyright, and
                       ethical concerns from using real data.


                # ⚓ BBC ☛ ‘Merry_Christmas’:_30_years_of_the_text_message_–_BBC
                  News⠀⇛


                       The text message is celebrating its 30th birthday –
                       the first was sent to a mobile phone by a Vodafone
                       engineer in Berkshire in the UK on 3 December 1992.


                       It was sent in order to test out the tech, and read
                       “Merry Christmas”.


                       Neil Papworth sent it to one of the firm’s bosses,
                       Richard Jarvis, who was at a Christmas party. He
                       did not get a reply.


                       Mr Jarvis’s phone, a new-to-the-market Orbitel 901,
                       weighed 2.1kg – roughly the same as 12 standard
                       iPhone 14s.


                       At its peak, phone users exchanged billions of SMS
                       – or Short Message Service – messages every year,
                       and in 2010 the word “texting” entered the
                       dictionary.


          o § Education⠀➾


                # ⚓ CER ☛ Launching_PCAS,_the_first_two_COMPFOR_classes,_and
                  hiring_our_first_lecturer_|_Computing_Ed_Research_–_Guzdial’s
                  Take⠀⇛


                       I have never worked harder than this semester–
                       building these two courses, teaching both courses
                       at the same time, learning how to be a program
                       director (e.g., explicit classes and workshops on
                       academic leadership, on evaluating faculty, and on
                       how University of Michigan budgets work), and
                       creating the program. I am having enormous fun.


                       I plan to write more about the two courses here and
                       our innovations in teaching them. Here’s a brief
                       summary. We are using teaspoon languages to
                       introduce concepts, Snap for programming
                       assignments, and Runestone ebooks for helping
                       students to transfer their knowledge from blocks to
                       traditional textual languages (Python, Processing,
                       and SQL). I gave a talk for the CS for Michigan
                       Conference a few weeks ago, and for the attendees,
                       I created a page connecting to some of what we’re
                       building and a narrative account of a couple of the
                       units: https://guzdial.engin.umich.edu/cs4mi-pcas/.


          o § Hardware⠀➾


                # ⚓ Jon_Chiappetta:_First_keyboard_build_for_the_year_end!⠀⇛


                       This was my first mechanical keyboard build and
                       they have made it a pretty smooth process (took me
                       half a day to lube the stabs).


                # ⚓ Project Syndicate ☛ The_False_Promise_of_America’s_CHIPS
                  Act_by_Anne_O._Krueger_–_Project_Syndicate⠀⇛


                       The US Congress recently approved the CHIPS and
                       Science Act, which allocates over $50 billion to
                       strengthen the semiconductor industry in the hope
                       of making the United States self-sufficient. And US
                       Trade Representative Katherine Tai said that
                       President Joe Biden’s administration should be
                       “replicating” the CHIPS Act for other industries
                       “as the key to American competitiveness.”
                       Semiconductors are certainly essential to a modern
                       economy, and it makes sense to diversify sources.
                       But it is doubtful that the CHIPS Act will achieve
                       its stated goals, much less that it should be used
                       as a model for similar support to other industries.


                # ⚓ [Older]_3D_printing_can_now_manufacture_customized_sensors
                  for_robots,_pacemakers,_and_more⠀⇛


                       A newly-developed 3D printing technique could be
                       used to cost-effectively produce customized
                       electronic “machines” the size of insects which
                       enable advanced applications in robotics, medical
                       devices and others.


                       The breakthrough is seen as a potential game-
                       changer for manufacturing chip-based
                       microelectromechanical systems (MEMS). These mini-
                       machines are mass-produced in large volumes for
                       hundreds of electronic products, including
                       smartphones and cars, where they provide
                       positioning accuracy. But for more specialized
                       manufacturing of sensors in smaller volumes, such
                       as accelerometers for aircraft and vibration
                       sensors for industrial machinery, MEMS technologies
                       demand costly customization.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ Jeff Geerling ☛ Crohn’s_Disease_takes_its_toll_–_back_in
                  2023!_|_Jeff_Geerling⠀⇛


                       Crohn’s Disease takes its toll – back in 2023!
                       After battling IBD complications through the summer
                       and fall, I’ve come to a point where surgery is
                       necessary. You can learn more about my health
                       issues in my lighthearted book about Crohn’s
                       Disease, You Only Have Crohn’s Once!.


                       The surgery (an ostomy revision) will take place
                       tomorrow, December 2, and it’ll be a pretty rough
                       recovery, so I’m not planning on doing any
                       substantial work until at least 2023.


                       It’s ironic I had just given a presentation titled
                       Just Say No: Staying sane while you maintain weeks
                       before learning the surgery was necessary. I was
                       planning a video on the topic (burnout, protecting
                       your time, and open source maintainership) this
                       year, but I guess the blog post will have to do.


                # ⚓ Ruben Schade ☛ Travelling_to_Japan_during_post-Covid
                  times⠀⇛


                       It shouldn’t come as a surprise that a minimum of
                       three Covid vaccinations are required. You’ll need
                       to contact the health authority in your country for
                       a record of your vaccinations. Australians can
                       export an international vaccine cert from the
                       Medicare site, and Singaporeans can log into
                       HealthHub using your Singpass account. As with your
                       hotel reservations and airline tickets, they’re
                       worth printing just in case.


          o § Proprietary⠀➾


                # ⚓ Apple’s_Chinese_dream_is_over⠀⇛


                       Of all the conversations I’ve had this week with
                       senior people who were once in charge of building
                       Apple products in China, one comment stuck out:
                       China is “not just a location. It was also an era.”


                # ⚓ Mark Dominus ☛ Software_horror_show:_SAP_Concur⠀⇛


                       This complaint is a little stale, but maybe it will
                       still be interesting. A while back I was traveling
                       to California on business several times a year, and
                       the company I worked for required that I use SAP
                       Concur expense management software to submit
                       receipts for reimbursement.


                       At one time I would have had many, many complaints
                       about Concur. But today I will make only one. Here
                       I am trying to explain to the Concur phone app
                       where my expense occurred, maybe it was a cab ride
                       from the airport or something.


          o § Security⠀➾


                # ⚓ Xe’s Blog ☛ OVE-20221101-0001:_counter.social_“private”
                  account_bypass_–_Xe_Iaso⠀⇛


                       Incorrect configuration on counter.social allowed
                       random people on the internet to stalk
                       counter.social users without having an account.
                       Included are numerous methods people could use to
                       bypass the “private” account system to stalk
                       counter.social users without having to
                       authenticate. There is also a paid account feature
                       bypass that allowed any user to trivially create a
                       user account token with the API and then have the
                       same privilege as the web client. This normally
                       requires a paid account, but a client that chooses
                       to opt-out of the security measures didn’t require
                       a paid account.


                # ⚓ NVISO Labs ☛ Can_we_block_the_addition_of_local_Microsoft
                  Defender_Antivirus_exclusions? [Ed: Fake security from
                  company that opens back doors for the NSA]⠀⇛


                # ⚓ Ruben Schade ☛ Rubenerd:_Website_security_word_salad⠀⇛


                       This is CSI Miami-level fluff. What sort of
                       encryption? Where? For what data? Not compromised
                       “in any other way” is either careless phrasing or a
                       Freudian slip, and “complete safety” is impossible.


                # § Privacy/Surveillance⠀➾


                      # ⚓ John Gruber ☛ Google_Moves_Maps_to_the_Root
                        Google.com_Domain⠀⇛


                             Grant location access to Google Maps now, and
                             you grant it to all of Google.


                      # ⚓ Stacey on IoT ☛ Can_a_robotic_switch_shut_off_your
                        wireless_lights?⠀⇛


                             We brainstormed a few different ideas for
                             Jon, but the reality is that none of them are
                             great. It’s probably easier to replace the
                             existing light strings with a product that
                             has some connectivity built in. That’s
                             because Jon’s current lights can’t connect to
                             a smart plug nor is there a simple way to
                             install some type of radio transmitter in
                             them.


                      # ⚓ Would_you_like_a_QR_code_embedded_in_that_cookie?⠀⇛


                             There is currently a race to develop edible
                             tags for food so that, for example, you can
                             see where the food comes from or its
                             ingredients, and the information disappears
                             once you’ve eaten it. Now, researchers from
                             Japan have developed a way to include an
                             unobtrusive edible tag embedded inside the
                             food—in their original experiments,
                             cookies—that can be read without having to
                             first destroy the food. Another major
                             advantage of their method, known as
                             “interiqr,” is that the tag doesn’t change
                             the outer appearance or taste of the food at
                             all.


          o § Defence/Aggression⠀➾


                # ⚓ Pentagon_Africa_Research_Contradicts_Optimism_of_Austin⠀⇛


                       LAST MONTH, Defense Secretary Lloyd Austin touted
                       the accomplishments of U.S. Africa Command,
                       commending its leaders and personnel for tackling
                       terrorism and making the continent more secure and
                       stable. “Every day, AFRICOM works alongside our
                       friends as full partners — to strengthen bonds, to
                       tackle common threats, and to advance a shared
                       vision of an Africa whose people are safe and
                       prosperous,” he announced at a ceremony honoring
                       the new AFRICOM commander, Gen. Michael Langley.


                       That very same day, the Defense Department’s Africa
                       Center for Strategic Studies, a Pentagon research
                       institution, issued a devastating report that
                       directly refuted Austin’s positive assessments.
                       “Militant Islamist group violence in Africa has
                       risen inexorably over the past decade, expanding by
                       300 percent during this time,” reads the analysis.
                       “Violent events linked to militant Islamist groups
                       have doubled since 2019.”


                # ⚓ TomDispatch ☛ [Old]_Writing_on_War_–_TomDispatch.com⠀⇛


                       [Note for TomDispatch Readers: Chris Hedges’s first
                       book, War Is a Force That Gives Us Meaning, blew me
                       away years ago. Now, his latest book, The Greatest
                       Evil Is War, on the nightmare that so eternally
                       seems to have him (and us) in its grip, has just
                       been published. My own copy arrived only a day ago
                       and went instantly to the top of my must-read pile.
                       Let me just quote two writers this site’s readers
                       know well on it. Noam Chomsky says, “Chris Hedges
                       has been an incomparable source of insight and
                       understanding, both in his outstanding career as a
                       courageous journalist and in his penetrating
                       commentary on world events. This is a contribution
                       of great significance in these troubled times.” And
                       Andrew Bacevich adds, “Savage honesty is a hallmark
                       of everything Chris Hedges writes. Other writers
                       seek to comfort or distract; his purpose is to
                       agitate, unsettle, and demand moral accountability.
                       The Greatest Evil Is War is no exception, which is
                       precisely why every American should read it and
                       reflect on its disturbing message.” For just a few
                       days, TomDispatch offers you the chance to get a
                       signed, personalized copy of Hedges’s latest work.
                       All you have to do is visit our donation page and,
                       for $100 ($125 if you live outside the U.S.), that
                       signed copy is yours and TomDispatch is so much the
                       better off for it. Don’t miss the chance! Tom]


                # ⚓ Reading_Proust_in_War_–_The_Chris_Hedges_Report⠀⇛


                       Marcel Proust died a century ago on November 18,
                       1922, leaving behind one of the most remarkable
                       literary investigations into human nature and
                       society.


                       During the war in Bosnia, I worked my way through
                       the seven volumes of Marcel Proust’s “In Search of
                       Lost Time.” The novel, populated with 400
                       characters, was not an escape from the war. The
                       specter of death and the expiring world of La Belle
                       Époque haunts Proust’s work. He wrote it as he was
                       dying; in fact, Proust was making corrections to
                       the manuscript the night before his death in his
                       hermetically sealed, cork-lined bedroom in Paris.


                       The novel was a lens that allowed me to reflect on
                       the disintegration, delusions and mortality around
                       me. Proust gave me the words to describe aspects of
                       the human condition I knew instinctively, but had
                       trouble articulating. He elucidates the conflicting
                       ways we perceive reality, exacerbated in war, and
                       how each of us comes to our own peculiar and self-
                       serving truths. He explores the fragility of human
                       goodness, the seduction and hollowness of power and
                       social status, the inconstancy of the human heart
                       and racism, especially antisemitism.


          o § Environment⠀➾


                # § Energy⠀➾


                      # ⚓ As_lawmakers_debate_how_to_regulate_the_industry,
                        more_are_openly_trashing_it._|_Semafor⠀⇛


                             At a moment when Congress is finally debating
                             whether and how to seriously regulate the
                             cryptocurrency industry, a split appears to
                             have formed in the Democratic Party. Some of
                             its lawmakers are contemplating how to
                             harness blockchain technology into a force
                             for innovation, while scaling back its early
                             excesses.


                             Then there’s a group you might call the
                             “bullshit caucus.”


                             “It’s all bullshit,” Sen. Jon Tester, D-Mont.
                             told Semafor. He was wary of the industry
                             even before the recent collapse of crypto
                             exchange FTX, he said, and recent meetings
                             with advocates have not given him any more
                             confidence in its fundamental value. “I don’t
                             think it passes the smell test. I can’t
                             figure out what supports it.” (FTX founder
                             Sam Bankman-Fried is an investor in Semafor.)


                             [...]


                             Smith said crypto lobbyists were “not getting
                             doors [shut] in our face, at least not yet.”
                             She’s been making the case that crypto
                             remains in its infancy and still promises
                             future innovations for businesses and
                             consumers.


          o § Finance⠀➾


                # ⚓ CoryDoctorow ☛ How_monopoly_enshittified_Amazon⠀⇛


                       In Bezos’s original plan, the company called
                       “Amazon” was called “Relentless,” due to its
                       ambition to be “Earth’s most customer-centric
                       company.” Today, Amazon is an enshittified endless
                       scroll of paid results, where winning depends on ad
                       budgets, not quality.


                       Writing in Jeff Bezos’s newspaper The Washington
                       Post, veteran tech reporter Geoffrey Fowler reports
                       on the state of his boss’s “relentless” commitment
                       to customer service. The state is grim.


                # ⚓ How_Activists_Are_Trying_to_Change_the_Way_Banking_Gets
                  Done_–_YES!_Magazine⠀⇛


                       With $10 trillion in assets at their collective
                       disposal, big banks like Chase and Wells Fargo
                       could do a lot of good. Yet, despite being “too big
                       to fail,” these banks fail people every day.
                       Whether it’s the persistent use of predatory
                       practices, their enduring discrimination, or their
                       insistent investment in exploitative and extractive
                       industries, these formidable financial institutions
                       have a corrosive influence on our country.


                       Yet, in spite of this, local governments put their
                       assets—the collective wealth of communities
                       collected through taxes—in the hands of these
                       institutions. In New York City alone, $100 billion
                       in the city’s money is handled by private banks
                       every year. While the city’s assets sit in the
                       corporate coffers of these Wall Street staples, the
                       banks are free to invest them at their discretion.
                       Their sole goal: pump up their profits. The result
                       is that public dollars may be invested in projects
                       that act against the public good, such as
                       speculative real estate, private prisons, and
                       fossil fuels.


                # ⚓ [Old]_Corporate_Coercion_and_the_Drive_to_Eliminate_Buying
                  with_Cash⠀⇛


                       “Sorry we’re not taking cash or checks,” said the
                       clerk at the Fed Ex counter over a decade ago to an
                       intern. “Only credit cards.”


                       Since then, the relentless intensification of
                       coercive commercialism has been moving toward a
                       cashless economy, when all consumers are
                       incarcerated within a prison of corporate payment
                       systems from your credit/debit cards to your mobile
                       phone and very soon facial recognition.


                       “Terrific!” say those consumers for whom
                       convenience and velocity of transactions are
                       irresistible.


                # ⚓ Jackson,_Mississippi,_must_say_’no’_to_water
                  privatization⠀⇛


                       “Privatization is on the table,” says Mississippi
                       Gov. Tate Reeves, amid a water crisis in the state
                       capital. That would be a disaster.


                # ⚓ Ruben Schade ☛ Rubenerd:_Dave_Winer_on_“micropayments”⠀⇛


                       The micro in micro-payments also belies a lack of
                       appreciation Silicon Valley types, and people in
                       the industry like me, have for smaller prices. I
                       buy a tasty coffee and don’t think twice, but for
                       someone making minimum wage, living paycheque to
                       paycheque, or even trying to save for something,
                       there’s nothing “micro” about a payment. It’s quite
                       patronising, the more I think about it.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Ali Reza Hayati ☛ Don’t_think_positive!⠀⇛


                       Sometimes I just want to punch people in the face
                       when they ask me to think positive. Stay positive
                       they say. What a brilliant idea.


                       I’m not angry though. I just chose to use those
                       words to express how stupid it is to tell people
                       stay positive and how frustrated I get when I hear
                       that.


                       Yet sometimes you should be angry. Sometimes you
                       need to compel people to be afraid of you and your
                       potential. It’s not good to always be positive.
                       Sometimes you need to force others to be afraid
                       from you.


                       It’s like someone holding your head under the water
                       and they guy next to you tells you think positive.
                       I’m pretty sure even the one holding your head will
                       punch that person.


                       I guess sometimes it’s because they don’t
                       understand the difference between being positive
                       and being hopeful. In worst situations you don’t
                       need to be positive, you need to be hopeful. It’s
                       hope that will move you forward, not positivity.


                # ⚓ The Daily Beast ☛ Musk’s_Twitter_Has_a_Huge_Blindspot—and
                  It_Could_Be_Deadly⠀⇛


          o § Civil Rights/Policing⠀➾


                # ⚓ The Wire ☛ Conviction_Rates_in_IPC_Cases_Highest_in_Non-BJP
                  States:_NCRB_Data⠀⇛


                       NCRB data reveals how four southern states and two
                       from the Northeast lead the way when it comes to
                       fighting crime.


                # ⚓ The_Good_Priest_–_The_Chris_Hedges_Report⠀⇛


                       Father Michael Doyle, who died on November 4 at his
                       parish house in Camden, New Jersey, infused his
                       Christianity with his goodness. That goodness
                       showed us what it means to live a life of faith.


                # ⚓ Listen_to_this_Article:_“Writing_on_War”⠀⇛


                # ⚓ The Wire ☛ WhatsApp_Banned_2.4_Million_Indian_Accounts_in
                  July_–_the_Highest_This_Year⠀⇛


                       Several accounts were banned based on complaints
                       received through the firm’s grievances channel and
                       the tools and resources it uses to detect such
                       offenses, the social media platform said.


                # ⚓ Democracy Now ☛ 50_Years_After_Sacheen_Littlefeather’s
                  Oscars_Protest,_“Prejudice_–_Racism”_Persist_in_Film_Industry
                  |_Democracy_Now!⠀⇛


                       On this Indigenous Peoples’ Day, we are remembering
                       Sacheen Littlefeather, who recently died on October
                       2 at the age of 75. In 1973, she took the stage at
                       the Oscars on behalf of Marlon Brando, who
                       boycotted the ceremony to protest Hollywood’s
                       portrayal of Native Americans. Some members of the
                       audience booed and mocked Littlefeather as she
                       addressed the awards ceremony wearing traditional
                       Apache clothing. In August, the Academy of Motion
                       Picture Arts and Sciences finally apologized to
                       her. “The suppression and the domination, the
                       prejudice and the racism in our industry is still
                       happening today,” says her friend and colleague
                       Joanelle Romero, an actress and filmmaker and the
                       first Native American woman of the Academy. Her
                       film, “American Holocaust: When It’s All Over I’ll
                       Still Be Indian,” was short-listed for an Academy
                       Award. She is Apache-Diné and the founder and
                       president of Red Nation Television Network and Red
                       Nation International Film Festival. “It is very
                       important for … our youth to be able to see
                       themselves on media, and primetime television, and
                       in feature films,” says Romero.


          o § Monopolies⠀➾


                # § Copyrights⠀➾


                      # ⚓ Daniel Miessler ☛ Napkin_Ideas_Around_What_Changes_to
                        Expect_Post-ChatGPT_–_Daniel_Miessler⠀⇛


                             If you’re reading this you already know the
                             internet is on fire over the new GPTChatBot
                             from OpenAI. There are people using it to
                             create full virtual machines, to be their
                             personal writing coach, to write terraform,
                             generate Pokemon-like characters, and a
                             thousand other things.


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



                    ䷩ 𝚕𝚒𝚗𝚎 3136

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.05.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_05/12/2022:_Gnoppix_Linux_22.12_and_Armbian_22.11⠀✐


Posted in News_Roundup at 5:18 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Desktop/Laptop
          o Audiocasts/Shows
          o Kernel_Space
          o Graphics_Stack
          o Benchmarks
          o Applications
          o Instructionals/Technical
          o Desktop_Environments/WMs
                # K_Desktop_Environment/KDE_SC/Qt
    * Distributions_and_Operating_Systems
          o Reviews
          o New_Releases
          o SUSE/OpenSUSE
          o Fedora_Family_/_IBM
          o Canonical/Ubuntu_Family
          o Devices/Embedded
          o Open_Hardware/Modding
          o Mobile_Systems/Mobile_Applications
    * Free,_Libre,_and_Open_Source_Software
          o Web_Browsers/Web_Servers
                # Chromium
                # Mozilla
          o Productivity_Software/LibreOffice/Calligra
          o Programming/Development
                # Perl_/_Raku
    * Leftovers
          o Security
          o Transparency/Investigative_Reporting
          o Censorship/Free_Speech
    * Gemini*_and_Gopher
          o Personal
          o Technical
                # Programming
    * § GNU/Linux⠀➾


          o § Desktop/Laptop⠀➾


                # ⚓ Ubuntu Pit ☛ Best_Linux_Desktop_Environment:_16_Reviewed
                  and_Compared [Ed: Page updated]⠀⇛


                       The world of Linux Desktop Environments is vast and
                       ever-evolving. With so many options available, it
                       can be difficult to decide which one is right for
                       you. Whether you need a lightweight and efficient
                       environment for business purposes, want the best
                       gaming experience possible, or require an
                       environment with high levels of privacy and
                       security, there’s a Linux Desktop Environment out
                       there for everyone.


                       Another thing to note is that installing a distro
                       comes with a desktop environment already set up.
                       However, so many popular desktop environments are
                       available that it might be difficult for someone
                       new to choose which one fits their needs best. With
                       that in mind, I created this comprehensive guide on
                       the best Linux desktop environments. Regardless of
                       your level of expertise, this tutorial will help
                       you find the perfect one for your needs.


                # ⚓ Make Use Of ☛ 6_Reasons_Why_2022_Wasn’t_the_Best_Year_for
                  Chromebooks⠀⇛


                       Chromebooks hit an all-time popularity high in 2020
                       as billions of people were forced to stay home, and
                       discovered they needed a cheap way of entertaining
                       themselves, working, and engaging with the
                       education system. But 2021 saw sales drop off
                       sharply to 37.3 million units, and it’s estimated
                       that a mere 30 million Chromebooks will have
                       shipped by the end of 2022.


                       With 2023 appearing over the horizon, the future
                       looks bleak for Chromebooks. Why is it so?


                # ⚓ XDA ☛ Can_the_HP_Envy_x360_(2022)_run_Linux?⠀⇛


                       The easiest and safest way to run Linux on the HP
                       Envy x360 (2022) is through virtualization tools.
                       If you’re on Windows 11 Pro, you can use Hyper-V on
                       Windows to install Linux on a virtual machine. Just
                       search for it in the Start Menu and follow the
                       steps on your screen. If you’re on Windows 11 Home,
                       you can also install Linux on a virtual machine
                       through an app like Oracle Virtualbox.


          o § Audiocasts/Shows⠀➾


                # ⚓ Video ☛ Rocky_Linux_9.1_overview_|_Enterprise_Linux,_the
                  community_way._–_Invidious⠀⇛


                       In this video, I am going to show an overview of
                       Rocky Linux 9.1 and some of the applications pre-
                       installed.


                # ⚓ Video ☛ Bypass_Paywalls_–_Invidious⠀⇛


                # ⚓ Video ☛ Valve’s_ENORMOUS_Steam_Deck_giveaway!_(Plus_other
                  Steam_Deck_news)_–_Invidious⠀⇛


                       The Steam Deck has had yet another huge week. The
                       gaming industry is about to celebrate video games
                       at the Game Awards and Valve’s decided to give a
                       way one Deck every minute!


                # ⚓ Jupiter Broadcasting ☛ 487:_The_Debian_Debate⠀⇛


                       After nearly half a year of woe, Brent is ready to
                       give Linux the go. Join us as we compare and
                       contrast two Linux distros and end up with one
                       going on Brent’s machine.


                # ⚓ GNU World Order (Audio Show) ☛ GNU_World_Order_489⠀⇛


                       Are cloud services and open source even compatible?


          o § Kernel Space⠀➾


                # ⚓ Hackaday ☛ How_Realtime_Is_Your_Kernel?_Scope_A_GPIO_To
                  Find_Out_|_Hackaday⠀⇛


                       When debugging something as involved as kernel
                       scheduler timings, you would typically use one of
                       the software-based debugging mechanisms available.
                       However, in cases when software is close to bare
                       metal, you don’t always need to do that. Instead,
                       you can output a signal to a GPIO, and then use a
                       logic analyzer or a scope to measure signal change
                       timing – which is what [Albert David] did when
                       evaluating Linux kernel’s PREEMPT_RT realtime
                       operation patches.


                       [...]


                       What could you use this for? A lot of hobbyists use
                       realtime kernels on Linux when building CNC machine
                       controllers and robots, where things like motor
                       control put tight constraints on how quickly a
                       decision in your software is translated into real-
                       world consequences, and if this sounds up your
                       valley, check out this Linux real-time task
                       tutorial from [Andreas]. If things get way too
                       intense for a multi-tasking system like Linux, you
                       might want to use a RTOS to begin with, and we have
                       a guide on that for you, too.


          o § Graphics Stack⠀➾


                # ⚓ NVIDIA_Ships_Vulkan_Extensions_to_Support_Accelerated_RTX™
                  IO_on_Windows_and_Linux⠀⇛


                       NVIDIA RTX™ IO is a suite of technologies that
                       enables rapid GPU-based asset decompression and
                       loading. NVIDIA’s GDeflate GPU decompression format
                       delivers IO-saturating performance on modern NVMe
                       devices. GDeflate is used in Microsoft’s
                       DirectStorage API, and now NVIDIA is contributing
                       the technology for consideration by the Vulkan
                       working group at Khronos. Two new NVIDIA Vulkan
                       extensions to accelerate RTX IO are were released
                       in the Vulkan 1.3.233 update and are supported in
                       the latest NVIDIA drivers on both Linux and
                       Windows. VK_NV_memory_decompression handles
                       decompressing assets on GPU, and
                       VK_NV_copy_memory_indirect handles copying
                       decompressed data to Vulkan buffers/images.


                # ⚓ MoltenVK_Added_to_Two_Switch_Emulators⠀⇛


                       Two switch emulators have recently added MoltenVK
                       to their back-end for portability and benchmarking…


          o § Benchmarks⠀➾


                # ⚓ WCCF Tech ☛ NVIDIA_GeForce_GPUs_Continue_To_Dominate_Linux
                  Gaming_Benchmarks,_AMD_Radeon_&_Intel_Arc_Left_Catching_The
                  Dust⠀⇛


          o § Applications⠀➾


                # ⚓ Cockpit_281_—_Cockpit_Project⠀⇛


                       Override your system’s style with Cockpit’s new
                       style switcher. It’s great for the times when you
                       might want a dark Cockpit but your system is in
                       light mode. Or vice versa.


                       Additionally, some browsers have issues picking up
                       on the correct system dark mode setting, so this
                       lets you manually set the mode you prefer.


                       You can find the style switcher in the session
                       menu.


                # ⚓ Medevel ☛ Termdbs:_Manage_your_Databases_and_CSVs_from_the
                  Terminal⠀⇛


                       Termdbs is a free open-source lightweight terminal
                       app that allows you to view and edit local database
                       (SQLite) and large CSV files.


                       It offers a straightforward terminal interface that
                       you can easily use with many useful shortcuts, or
                       by using your mouse and mouse scroll.


                       With Termdbs, you can navigate database tables,
                       simple browse any number of columns or rows, query
                       your database with a query manager, and many other
                       features.


          o § Instructionals/Technical⠀➾


                # ⚓ ByteXD ☛ How_to_Set_Up_Wireguard_VPN_Server_on_Ubuntu
                  22.04⠀⇛


                       WireGuard is an open-source general-purpose VPN
                       that was initially released for the Linux kernel.
                       Now it is used across multiple platforms i.e.
                       Windows, macOS, Android, etc. The WireGuard VPN
                       supports both IPv4 and IPv6 connections.


                       WireGuard uses public and private keys to establish
                       encrypted tunnels between peers to ensure security.
                       It is much faster compared to other VPN protocols
                       such as OpenVPN and IPSec.


                       In this tutorial, we are going to learn how to set
                       up WireGuard on a Ubuntu 22.04 Server. First, let’s
                       take a look at the prerequisites needed for this
                       tutorial and make sure you have everything ready
                       before proceeding further.


                # ⚓ ByteXD ☛ How_to_Update_phpMyAdmin_to_the_Latest_Version⠀⇛


                       Sometimes the repository response time becomes slow
                       and does not deliver the updates. Or you might be
                       facing compatibility issues with your current
                       version of phpMyAdmin.


                       Whatever the reason, this tutorial is going to show
                       how you can update your phpMyAdmin to the latest
                       version manually.


                # ⚓ Linux Handbook ☛ How_to_Create_Large_Files_in_Linux⠀⇛


                       Creating files in Linux is something we do all the
                       time. Mostly you create an empty text file with the
                       touch command and then add content to it.


                       But what about creating new files of a certain
                       size?


                       When you are troubleshooting something or want to
                       test in some particular scenario, you may require
                       large files bigger than a certain size. Let’s say
                       500 MB or 2 GB.


                       Now, you cannot create an empty file and then start
                       writing garbage text in it. You can never be able
                       to create a file of 1 GB in size this way.


                       Thankfully, you don’t have to manually create large
                       text files. There are various commands that allow
                       you to create large files of predefined size. They
                       won’t have desired tex. Just some random garbage
                       but you’ll get the file of your desired size.


                       Let me show how to do that.


                # ⚓ Writing_Single-Line,_Inline,_and_Multi-line_Comments_in
                  Linux_Shell_Script⠀⇛


                       Like other programming languages, bash provides you
                       with the option to ignore a single line, inline, or
                       a block of lines from execution.


                       The comments always received the least attention
                       due to their simplicity but played a very important
                       role while being used in a program or script.


                       You can use them to describe the block of lines in
                       your script that can help you understand what you
                       did in the past; others can also benefit from this.
                       Or, you can use the comments to skip the block of
                       lines while debugging your script.


                       In this article, you will learn three ways to
                       comment lines in your shell script.


                # ⚓ What_is_Exit_Status_Code_($?)_of_Last_Command_in_Linux⠀⇛


                       The “$?” is a built-in variable that your shell
                       uses to store the exit status code of the last
                       executed command in integer format and remains
                       unchanged unless the next command is executed.


                       Using this exit status code, you can debug the
                       problem that occurred while executing the command,
                       which can be extremely beneficial in shell script
                       error handling.


                # ⚓ ID Root ☛ How_To_Install_phpMyAdmin_on_Rocky_Linux_9_–
                  idroot⠀⇛


                       In this tutorial, we will show you how to install
                       phpMyAdmin on Rocky Linux 9. For those of you who
                       didn’t know, phpMyAdmin is a free and open-source
                       tool that enables you to manage MySQL and MariaDB
                       databases from the web browser. It provides a
                       robust and user-friendly interface for managing
                       databases, tables, database users, basic crud
                       operations (create, read, update, delete), and so
                       much more.


                       This article assumes you have at least basic
                       knowledge of Linux, know how to use the shell, and
                       most importantly, you host your site on your own
                       VPS. The installation is quite simple and assumes
                       you are running in the root account, if not you may
                       need to add ‘sudo‘ to the commands to get root
                       privileges. I will show you the step-by-step
                       installation of the phpMyAdmin on Rocky Linux. 9.


                # ⚓ DebugPoint ☛ How_to_Create_Ubuntu,_Linux_OS_Bootable_USB_in
                  Windows⠀⇛


                       A short tutorial for beginners on creating a
                       bootable USB stick in Windows with Ubuntu/Linux ISO
                       images.


                       A bootable Ubuntu USB is handy for multiple
                       reasons. Suppose you are a Windows user and
                       thinking of migrating to Linux. In that case, you
                       can experience Ubuntu desktop/Linux desktops
                       without hampering your PC configuration or
                       installation using a Live USB stick. Also, using
                       this, you can boot from the USB stick directly from
                       an Internet Cafe or any borrowed computer. Not only
                       that, if you have a broken system, you can always
                       use the USB stick to boot from and repair the
                       broken system/recover data. Here are the steps to
                       follow to create a bootable Ubuntu USB from
                       Microsoft Windows.


                # ⚓ Red Hat Official ☛ Learn_how_Unix_influenced_Linux,
                  understand_Ansible_lists_and_dictionaries,_and_more_tips_for
                  sysadmin_|_Enable_Sysadmin⠀⇛


                       Check out Enable Sysadmin’s top 10 articles from
                       November 2022.


                # ⚓ Beginners_Guide_for_Set_Command_in_Linux⠀⇛


                       The set command is a built-in Linux command that
                       can display or modify the value of shell attributes
                       and positional parameters inside the current shell
                       environment.


                       This modification can help to debug your script by
                       finding undefined variables, errors, job control,
                       printing commands as they are executed, and
                       automatically exporting variables and functions in
                       sub-shell.


                # ⚓ Beginners_Guide_for_Unset_Command_in_Linux⠀⇛


                       The set command is a built-in Linux command that
                       can display or modify the value of shell attributes
                       and positional parameters inside the current shell
                       environment.


                # ⚓ Red Hat ☛ How_to_trace_application_errors_using_SystemTap_|
                  Red_Hat_Developer⠀⇛


                       Low-level library functions and kernel system calls
                       on Linux report errors by returning a POSIX error
                       code such as ENOENT or EINVAL. With SystemTap, an
                       open source tracing toolkit maintained by Red Hat,
                       it is possible to look inside the Linux kernel to
                       debug the problem. This article demonstrates how to
                       investigate the cause of an error code using
                       SystemTap with the whythefail.stp script.


                       [...]


                       This article demonstrated how source code
                       inspection and SystemTap tracing could narrow down
                       the causes of a confusing error code. With the help
                       of whythefail.stp, we utilized the general
                       information provided by an EINVAL error code and
                       traced the Linux kernel’s implementation of the
                       system call to understand which argument was
                       invalid and why. We also illustrated how debugging
                       tools could double as program understanding tools
                       for programmers whose code interacts with an
                       unfamiliar project. When we used whythefail.stp,
                       our goal was not to diagnose a problem within the
                       kernel itself but to understand the kernel’s
                       internals and behavior in more detail than the
                       documentation conveys.


                # ⚓ Citizix ☛ How_to_install_and_configure_Redpanda_on_Debian
                  11⠀⇛


                       Redpanda is a Kafka®-compatible streaming data
                       platform that boasts of being 10x faster and 6x
                       more cost efficient. It is also JVM-free,
                       ZooKeeper®-free, Jepsen-tested and source
                       available. It is distributed as a single binary
                       with everything thus allowing you to deploy in
                       minutes. It works natively with Kafka tools.


                # ⚓ Linuxiac ☛ How_to_Add_a_User_in_Linux_[With_Examples]⠀⇛


                       This guide shows how to add a user in Linux using
                       the useradd and adduser commands or utilizing the
                       GUI tools that the desktop provides.


                # ⚓ ID Root ☛ How_To_Install_Docker_Compose_on_Ubuntu_22.04_LTS
                  –_idroot⠀⇛


                       In this tutorial, we will show you how to install
                       Docker Compose on Ubuntu 22.04 LTS. For those of
                       you who didn’t know, Docker Compose is a utility
                       that permits you to run multi-container application
                       setups based on YAML definitions. It creates fully
                       customized environments with multiple containers
                       that have the capability to share data volumes and
                       networks using service definitions. Once you have a
                       Compose file, you can create and start your
                       application with a single command.


                       This article assumes you have at least basic
                       knowledge of Linux, know how to use the shell, and
                       most importantly, you host your site on your own
                       VPS. The installation is quite simple and assumes
                       you are running in the root account, if not you may
                       need to add ‘sudo‘ to the commands to get root
                       privileges. I will show you the step-by-step
                       installation of the Docker Compose on Ubuntu 22.04
                       (Jammy Jellyfish). You can follow the same
                       instructions for Ubuntu 22.04 and any other Debian-
                       based distribution like Linux Mint, Elementary OS,
                       Pop!_OS, and more as well.


                # ⚓ Ubuntu Handbook ☛ Fix_TypeCatcher_(Google_Fonts_Installer)
                  does_not_launch_in_Ubuntu_22.04_|_UbuntuHandbook⠀⇛


                       This simple tutorial shows how to fix the launching
                       issue for TypeCatcher in Ubuntu 22.04 or other
                       Linux with Python 3.9 & higher.


                       TypeCatcher is a simple GTK application to download
                       and install Google webfonts for off-line use. The
                       app is available to install in Ubuntu Software for
                       all current Ubuntu releases. However, it does not
                       launch in Ubuntu since 21.10.


                # ⚓ OSTechNix ☛ Setup_SFTP_Server_With_SFTPGo_In_Linux_–
                  OSTechNix⠀⇛


                       This detailed guide explains what is SFTPGo, how to
                       install SFTPGo in various Linux distributions, and
                       finally how to setup a SFTP server with SFTPGo in
                       Linux.


                # ⚓ Red Hat Official ☛ 6_ways_to_get_information_about_your_CPU
                  on_Linux⠀⇛


                       Getting insight into what CPU you’re running is a
                       useful trick to know.


                # ⚓ LinuxConfig ☛ How_to_perform_unattended_Linux_installations
                  with_Kickstart⠀⇛


                       Kickstart is an automatic installation method
                       natively available on those distributions which
                       uses the Anaconda installer: Red Hat Enterprise
                       Linux (and its clones) and Fedora. It can also be
                       used to install Ubuntu, actually, but in that
                       context it acts as a layer of compatibility to the
                       debian-native preseeding method. With Kickstart we
                       can perform unattended, customizable and
                       reproducible installations.


                       In this tutorial we learn the basics of Kickstart,
                       and we see how to perform an unattended
                       installation of a Fedora Workstation system.


          o § Desktop Environments/WMs⠀➾


                # ⚓ My_Window_Manager_Environment_Desktop_|_A_Transformed
                  Life⠀⇛


                       This is going to be another one of those Linux
                       posts that I put up here for my own reminders. I
                       don’t know if anyone else will ever read or
                       appreciate these, but I’ve found them helpful. To
                       wit:


                       The Desktop Environment vs. Window Manager debate.
                       Lots of people who use Linux spend time deciding on
                       which Desktop Environment they want to use. Windows
                       users don’t really have that option: Microsoft
                       chooses your Desktop Environment, and that’s the
                       end of it. That’s why Windows 98 looked so
                       different from Windows XP, which looked different
                       from Windows 7, which looked different from Windows
                       8, to Windows 10 and 11. (I bought a new computer
                       last month, and I was *shocked* at how much Windows
                       11 looked like… a Linux desktop called Gnome. I
                       hated it, but I’m not a Gnome fan.)


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


                      # ⚓ KDE ☛ Guest_Post:_OpenUK_Awards_2022_Sustainability_–
                        KDE_Eco⠀⇛


                             This is a guest post by Jonathan Esk-Riddell
                             for the KDE Eco blog about the OpenUK Awards.


                             OpenUK is an advocacy organisation for open
                             tech (software, hardware and data) in the UK.
                             We run various activities and I have had the
                             priviledge of hosting the award ceremony for
                             the last few years.


                             Last year at COP26 in Glasgow I announced KDE
                             Eco, the KDE project to measure and certify
                             apps as energy efficient. For those reading
                             this who aren’t familiar, KDE is an open
                             source community making apps for Linux and
                             other platforms. KDE Eco has two parts, FOSS
                             Energy Efficiency Project, developing tools
                             to improve energy efficiency in free and open
                             source software development. And Blauer Engel
                             For FOSS, working with German Environment
                             Agency to create eco-certification with the
                             Blauer Engel label for desktop software.


    * § Distributions and Operating Systems⠀➾


          o ⚓ Timothée Ravier ☛ Community_maintained_images_for_toolbox_(and
            distrobox)_–_Siosm’s_blog⠀⇛


                 In this post I will discuss how we made community
                 maintained container images for common Linux
                 distributions available for use with toolbox (and
                 distrobox) and why we can not call them “official”.


                 What is toolbox (or toolbx)?


                 But first, let’s start with a bit of context. On image
                 based Linux distributions (such as Fedora Silverblue,
                 Fedora Kinoite, Fedora CoreOS, etc.), it is not practical
                 to install random packages the way you may be used to do
                 on classic package based Linux distributions. You are
                 expected to run applications in containers, either via
                 Flatpak for graphical applications, or via podman for
                 command line ones.


                 While you can directly manage your own custom container
                 images and environment configurations, it is not useful
                 to have everyone rediscover what to do thus a new tool
                 has been created to make that easier: toolbox (or toolbx)
                 (containers/toolbox on GitHub).


                 Toolbox lets you easily create a mutable and persistent
                 environments inside containers that are well integrated
                 with your host system.


          o ⚓ Barry Kauler ☛ EasyOS_advancing_to_Kirkstone-series⠀⇛


                 That’s the current intention anyway. The Dunfell-series
                 started in early 2020, and I am running into problems
                 with libraries etc. being too old.


          o § Reviews⠀➾


                # ⚓ Distro Watch ☛ Review:_CachyOS_221023_and_AgarimOS⠀⇛


                       Last week I took to the DistroWatch waiting list in
                       search of new distributions to try. One which
                       caught my eye was CachyOS. The distribution’s
                       website describes the project as follows:


                       “CachyOS is a Linux distribution based on Arch
                       Linux. The default Linux kernel is linux-cacule
                       which is the Arch Linux stock kernel plus the
                       CacULE CPU Scheduler.


                       The project currently supplies three editions: KDE
                       (2.2GB), GNOME (2.2GB), and a self-described
                       command line edition which is 952MB. The command
                       line (CLI) edition doesn’t appear to be updated as
                       often or as recently as the desktop editions. The
                       CLI edition is eight months old at the time of
                       writing while the two desktop editions are just
                       over a month old.


                       The distribution’s website mentions some key
                       features, including the Cachy-Browser which is a
                       web browser forked from LibreWolf. The website also
                       mentions a tool called Firejail Toggle which will
                       enable sandboxing for recognized applications. The
                       CachyOS website also mentions one-click support for
                       installing the operating system on ZFS, an advanced
                       filesystem. Alternatives, XFS, ext4, Btrfs, and
                       F2FS are reportedly supported at install time.


                       I decided to download the KDE edition of CachyOS.
                       Booting from the provided media brings up a menu
                       offering to start the live distribution normally or
                       with NVIDIA drivers enabled. The system loads and
                       presents us with the KDE Plasma desktop with a
                       strong blue-on-blue theme. A panel is placed along
                       the bottom of the screen with the desktop’s
                       application menu and system tray. A dock-like set
                       of launchers appears in the middle of the panel.


                       Once the live desktop loads, a welcome screen
                       appears. This screen is divided into three columns.
                       In the first column we find buttons which provide
                       us with documentation, release information, and a
                       link to the project’s wiki. The second column
                       includes a link to the forum and a button called
                       “Software” which connects us with the
                       distribution’s repository of custom package builds.
                       The third column links us to source code and tips
                       for getting involved with developing the
                       distribution. At the bottom of the welcome window
                       is a button which launches the Calamares system
                       installer.


                       The welcome screen also features a drop-down menu
                       where we can select our preferred language.
                       Strangely, selecting different languages doesn’t do
                       anything. The welcome window and the Plasma desktop
                       remain displaying English, regardless of which
                       language I picked.


          o § New Releases⠀➾


                # ⚓ Linux Magazine ☛ 4MLinux_41.0_is_Now_Stable_and_Ready_for
                  Use⠀⇛


                       The developers behind 4MLinux have changed the
                       status of 41.0 to STABLE, which means it’s ready
                       for prime time.


                       4MLinux 41 is now available for general use and
                       includes plenty of updates. There are new
                       applications to be had, including FileZilla,
                       XPaint, and GNU Paint, a command-line tool for
                       managing NVM-Express partitions, a small collection
                       of games, LibreOffice 7.4.3, GNOME Office (AbiWord,
                       GIMP, Gnumeric), Dropbox, Firefox, Chromium,
                       Thunderbird, the Audacious music player, VLC,
                       SMPlayer, Wine 7.18, and more.


                       With the release of 4MLinux 41.0, it is now
                       possible to install on a BTRFS partition, with the
                       help of Syslinux acting as a boot manager.


                       This lightweight Linux distribution ships with
                       kernel 6.0.6 and Mesa 22.1.4, and uses JWM (Joe’s
                       Window Manager) as the desktop interface.


                # ⚓ Gnoppix_22.12_Release⠀⇛


                       Today I’m happy to announce Gnoppix 22.12 Release.


                       The update includes bug fixes, security updates,
                       Kernel 6.x , starting with Gnome 43.2 and lot of
                       performance improvements, lot of new security
                       tools!


                # ⚓ DebugPoint ☛ Gnoppix_Linux_22.12_is_out_with_GNOME_43,
                  Kernel_6.0,_+_More⠀⇛


                       The successor of the legacy live-cd Knoppix
                       project, Gnoppix Linux is designed specifically for
                       use in penetration testing and reverse engineering.
                       It is optimized for web application security and
                       for protecting digital rights. In addition to its
                       focus on security, Gnoppix can also be used as a
                       regular desktop operating system. It is a rolling
                       release that receives frequent updates and new
                       features.


                       At its core, it is based on Kali Linux and Debian-
                       rolling for some parts. And brings a GNOME desktop
                       in contrast with Xfce for Kali Linux.


                # ⚓ Armbian_22.11_–_Armbian⠀⇛


                       - added Bananapi M5, Odroid M1 and Rockpi 4C plus


                       - enabled community images with weekly release
                       cycle


                       - added ultra minimal images optimized for software
                       deployment


                       - added RiscV64 UEFI build support


                       - improved support for Rockpi S


                       kernel upgrade is frozen by default to improve
                       stability


          o § SUSE/OpenSUSE⠀➾


                # ⚓ OpenSUSE ☛ The_openSUSE_forums_move_from_vBulletin_to
                  Discourse_–_openSUSE_News⠀⇛


                       Maybe you have read this announcement in openSUSE
                       forums and asked yourself what this will mean for
                       the way you use the forums. Even more when you may
                       not understand, or only vaguely understand, what
                       the words vBulletin and Discourse mean.


                       You will understand that the website
                       forums.opensuse.org runs software that handles not
                       only the interface with you, but also stores and
                       manages the threads with the posts, and the user
                       administration of the forum members. The software
                       package used is named vBulletin. It is a commercial
                       package and as such brings considerable costs.


                       Because all software that stays alive will move to
                       new versions, this is also the case with vBulletin.
                       That will mean that all of the adaptions that were
                       made in the openSUSE instance had to be converted
                       to the new version. At such a moment, it is time to
                       look if a different solution might be better. We
                       will not burden you with all the details, but the
                       result is that vBulletin will be replaced by a
                       different and open-source (which fits into the
                       openSUSE product approach: Discourse.


          o § Fedora Family / IBM⠀➾


                # ⚓ Fedora Project ☛ Fedora_Community_Blog:_CPE_Weekly_Update_–
                  Week_48_2022⠀⇛


                       This is a weekly report from the CPE (Community
                       Platform Engineering) Team. If you have any
                       questions or feedback, please respond to this
                       report or contact us on #redhat-cpe channel on
                       libera.chat.


                       We provide you both infographics and text version
                       of the weekly report. If you just want to quickly
                       look at what we did, just look at the infographic.
                       If you are interested in more in depth details look
                       below the infographic.


                # ⚓ Enterprisers Project ☛ How_data_analysts_can_help_CIOs
                  bridge_the_tech_talent_shortfall_|_The_Enterprisers_Project⠀⇛


                       Digital transformation has increased interest in
                       AI, ML, and DevOps talent to revolutionize the
                       customer experience through automation and
                       personalization.


                       While these positions are essential, it may not
                       make sense for every company to prioritize them,
                       especially those that don’t already have a cohesive
                       data strategy. While digital progress and tech
                       investments will continue, leaders must first
                       prioritize how their company manages its data.


                # ⚓ Enterprisers Project ☛ 7_AI_predictions_for_2023_from_IT
                  leaders⠀⇛


                       December is here, so you know what that means:
                       holiday parties, new year’s resolutions, and a slew
                       of technology predictions. We decided to focus on a
                       trend that matters most urgently to IT
                       leaders—concrete artificial intelligence (AI)
                       insights for your team and business.


                       The potential impacts of AI are wide-ranging—as are
                       the related forecasts, on everything from sentient
                       to generative and responsible AI, to collaboration
                       and automation. What will matter to IT leaders in
                       2023? We talked to AI and IT career experts to ask
                       their opinions.


          o § Canonical/Ubuntu Family⠀➾


                # ⚓ The Register UK ☛ Linux_Mint_21.1_enters_beta,_should
                  arrive_by_Christmas_•_The_Register⠀⇛


                       The first beta version of Mint 21.1 is now
                       available for download, and the flagship Cinnamon
                       desktop edition contains the biggest change, with a
                       new version of the desktop.


                # ⚓ Ubuntu ☛ High-performance_computing_(HPC)_technologies:
                  what_does_the_future_hold?_[part_6]_|_Ubuntu⠀⇛


                       It’s always difficult to predict the future, but we
                       expect to see plenty around easing the deployment
                       of applications and clusters for HPC. Composability
                       is positioned to grow with the advent of new server
                       components. Schedulers continue to advance. Quantum
                       computing is getting closer each year, with new
                       updates expected in the years to come. Alternative
                       architectures are growing in use and becoming more
                       mature. Ubuntu is positioned to work well
                       everywhere, so it will be a great asset for
                       organisations looking to use HPC. Let’s explore
                       technological innovations surrounding:


                # ⚓ Ubuntu ☛ Join_Canonical_and_the_financial_services_open-
                  source_community_at_OSSF_NY_|_Ubuntu⠀⇛


                       OSFF is a global conference hosted by the Linux
                       Foundation FINOS that brings together experts
                       across financial services, technology, and open
                       source to engage in stimulating and thought-
                       provoking conversations about leveraging secure
                       open source to solve financial services industry
                       challenges.


                       This event showcases recent developments and the
                       direction of open source in financial services. It
                       provides practical knowledge and guidance on best
                       practices, open-source tools and technologies in
                       the industry.


          o § Devices/Embedded⠀➾


                # ⚓ Linux Gizmos ☛ Rugged_Edge_Mini-PC_equipped_with_i.MX_8M
                  Plus_and_dual_2.5GbE_LAN_ports⠀⇛


                       The datasheet also mentions that the ISR215 is
                       based on the IBR215-Q316I SBC which also provides
                       access to two HD MIPI-CSI interfaces supporting up
                       to 12MP cameras.


                       iBASE also specified that “Standard BSP support for
                       Yocto and Android and design-in services are
                       provided to help customers rapidly develop and
                       deploy their innovations.”


          o § Open Hardware/Modding⠀➾


                # ⚓ Make Tech Easier ☛ 10_Sensors_You_Can_Use_With_an_Arduino
                  Board_–_Make_Tech_Easier⠀⇛


                       A big part of what makes the Arduino great for
                       projects is the myriad of sensors that can be used
                       with the Arduino. This article discusses some
                       useful sensors that allow you to build cool
                       projects and prototypes on your Arduino board.


          o § Mobile Systems/Mobile Applications⠀➾


                # ⚓ When_will_Twitter_Blue_subscription_for_Android_–_Web_be
                  available?⠀⇛


                # ⚓ Gadget Bridge ☛ How_to_create_a_custom_ringtone_for
                  Android?⠀⇛


                # ⚓ SamMobile ☛ Galaxy_A51_is_getting_Android_13_and_One_UI_5.0
                  update_in_Europe_–_SamMobile⠀⇛


                # ⚓ TechRepublic ☛ Android_accessibility_options_for_blind_and
                  hard_of_hearing_users⠀⇛


                # ⚓ The Sun ☛ Urgent_warning_as_300,000_Android_owners_infected
                  by_dangerous_app_–_and_it’s_bad_news_if_you_have_Facebook_|
                  The_US_Sun⠀⇛


                # ⚓ GO Media ☛ Delete_These_Malware_Apps_From_Your_Android
                  ASAP⠀⇛


                # ⚓ Cybersecurity_tips_for_Android_users⠀⇛


                # ⚓ Android Police ☛ The_Android_December_security_patch_is
                  here⠀⇛


                # ⚓ 9to5Google ☛ ADT-3_streamer_for_Android_TV_development
                  discontinued⠀⇛


                # ⚓ Notebook Check ☛ AUN_PH30S_cheaper_720p_projector_with
                  built-in_Android_available_globally_–_NotebookCheck.net
                  News⠀⇛


                # ⚓ Express ☛ Google_releases_major_Android_upgrade_but_only_if
                  you_own_these_phones_|_Express.co.uk⠀⇛


                # ⚓ Android Authority ☛ You_told_us:_You_think_Android_and_iOS
                  could_do_with_competition⠀⇛


                       Do we still need a third major smartphone platform
                       to take on Apple and Google’s operating systems,
                       though? That’s what we asked last week, and here’s
                       how you answered this poll.


                # ⚓ Ubuntu Pit ☛ 7_Best_Animoji_and_Memoji_for_Android_|_Make
                  Fun_Emojis⠀⇛


                       Let’s dig into the field of best animoji memoji
                       apps for Android before downloading one on your
                       daily device. You will find many different apps in
                       the app marketplaces; most offer tons of fun
                       content. Of course, there is some offering utter
                       junk. In this time of social media animoji, memoji
                       apps are certainly a must-have for online savvy
                       people. Animoji memoji are much more expressive and
                       fun to use compared to regular 2D stock emojis.


                       Basically, Animoji is a very popular app available
                       only on iOS devices. It’s not available on Andoird,
                       and that cannot be a reason you will be deprived of
                       making fun emojis and memojis of your friends. We
                       are going to learn about seven animoji alternative
                       apps here that will help you make fun emojis within
                       a few minutes.


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


          o ⚓ ZDNet ☛ Twitter_turns_its_back_on_open-source_development_|
            ZDNET⠀⇛


                 When Elon Musk took over Twitter, he started by firing
                 half of the social network’s staff. That’s a recipe for
                 failure right there. Leaving aside Musk’s management and
                 policy failures, social networks need experienced
                 developers to keep moving forward.


          o ⚓ Help Net Security ☛ ODD_Platform:_Open-source_data_discovery_and
            observability⠀⇛


                 Provectus released v0.8 of its Open Data Discovery
                 Platform (ODDP), an open-source platform that helps data-
                 driven enterprises democratize their data.


          o § Web Browsers/Web Servers⠀➾


                # § Chromium⠀➾


                      # ⚓ Google ☛ Chrome_Releases:_Dev_Channel_Update_for
                        Desktop⠀⇛


                             A partial list of changes is available in the
                             log. Interested in switching release
                             channels? Find out how. If you find a new
                             issue, please let us know by filing a bug.
                             The community help forum is also a great
                             place to reach out for help or learn about
                             common issues.


                      # ⚓ Google ☛ Chrome_Releases:_Dev_Channel_Update_for
                        ChromeOS_/_ChromeOS_Flex⠀⇛


                             The Dev channel is being updated to OS
                             version: 15263.0.0, Browser version:
                             110.0.5447.0 for most ChromeOS devices.


                # § Mozilla⠀➾


                      # ⚓ Thunderbird ☛ Thunderbird_For_Android_Preview:_Modern
                        Message_Redesign⠀⇛


                             The road to bringing you a great Thunderbird
                             email experience on Android devices begins
                             with K-9 Mail, which joined our family
                             earlier this year. And we’ve been busy
                             improving K-9 Mail as we prepare its
                             transition to Thunderbird for Android in
                             Summer 2023. (Check out our roadmap for
                             updates!)


                             Last week we showed you the new Swipe actions
                             in K-9 Mail 6.400. Today, it’s something even
                             more exciting: a completely redesigned
                             message view!


                      # ⚓ Mozilla ☛ How_we’re_making_Firefox_accessible_and
                        delightful_for_everyone⠀⇛


                             I joined Mozilla in 2017 as an accessibility
                             engineer and soon became the tech lead for
                             accessibility. But for years prior, I was
                             already deeply involved with the company. I
                             co-created NVDA (NonVisual Desktop Access) in
                             2006, a screen reader for blind and vision
                             impaired people like me. We wanted to make
                             Firefox and NVDA work as well as they could
                             together to provide everyone the best
                             possible access to the web.


                             With NVDA, I helped change the world for a
                             lot of people through a free and open-source
                             screen reader. Now at Mozilla, I get to do
                             the work from the browser side of things –
                             making sure Firefox continues to work
                             efficiently alongside assistive technology as
                             the internet evolves constantly and rapidly.


                             This International Day of Persons with
                             Disabilities, I want to take a moment to
                             share how we’re working to make Firefox not
                             just accessible. We want to make sure the
                             browser is also delightful, efficient and
                             easy to use for everyone, including the more
                             than 1 billion people around the world who
                             live with disabilities.


          o § Productivity Software/LibreOffice/Calligra⠀➾


                # ⚓ What_is_Miklos_hacking_–_Improved_watermark_in_the_PDF
                  export⠀⇛


                       The PDF export now supports various additional
                       properties for the optional PDF watermark.


                       First, thanks Docmosis for funding this work by
                       Collabora.


          o § Programming/Development⠀➾


                # ⚓ PoCL_–_Portable_Computing_Language_|_Portable_Computing
                  Language_(pocl)_v3.1_released⠀⇛


                       - Support for Clang/LLVM 15.0
                       - Much improved SPIR-V support for CPU and CUDA
                       drivers
                       - Major rework of the custom device driver. The
                       driver was formerly named Accel, now AlmaIF.
                       - Various improvements to the work-in-progress
                       Vulkan driver
                       - Basic implementation of cl_khr_command_buffer


                # § Perl / Raku⠀➾


                      # ⚓ Rakulang ☛ 2022.49_ReleaseMas_Again_–_Rakudo_Weekly
                        News⠀⇛


                             This week saw a new Rakudo compiler release
                             (2022.12 by Justin DeVuyst) with a nice bunch
                             of new features and bug fixes, a new Cro
                             release (mostly to fix a testing issue that
                             would inhibit installation by default) and a
                             new release of the Podlite editor (0.4.0,
                             with markdown block support, /r/rakulang
                             comments). Nice prezzies!


    * § Leftovers⠀➾


          o § Security⠀➾


                # ⚓ Bruce Schneier ☛ CAPTCHA⠀⇛


                       As an actual human and not a bot, I had no idea how
                       to answer. Is this a joke? (Seems not.) Is it a
                       Magritte-like existential question? (It’s not a
                       bicycle. It’s a drawing of a bicycle. Actually,
                       it’s a photograph of a drawing of a bicycle. No,
                       it’s really a computer image of a photograph of a
                       drawing of a bicycle.) Am I overthinking this?
                       (Definitely.) I stared at the screen, paralyzed,
                       for way too long.


                # ⚓ Bleeping Computer ☛ Hackers_hijack_Linux_devices_using
                  PRoot_isolated_filesystems [Ed: This only impacts machines
                  that are already compromised some other way]⠀⇛


                       PRoot is an open-source utility that combines the
                       ‘chroot’, ‘mount –bind’, and ‘binfmt_misc’
                       commands, allowing users to set up an isolated root
                       filesystem within Linux.


                # ⚓ LinuxSecurity ☛ Here’s_Why_You_Should_Get_Started_With_Open
                  Source_Log_Analytics_&_Monitoring_Today!⠀⇛


                       One of the biggest benefits of using open source
                       monitoring tools is that they are usually free.
                       This can save organizations a considerable amount
                       of money, especially if they already use other
                       open-source software applications.


                       Additionally, many open source applications come
                       with a wide range of features and plugins that can
                       be used to customize the application further to
                       meet an organization’s specific needs.


                       Another big benefit of using open source monitoring
                       solutions is that they tend to be more flexible
                       than commercial options. This can give
                       organizations more control over the monitoring
                       tool, giving them a better understanding of how it
                       works and how you can use it to your advantage.


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


                       Security updates have been issued by Debian
                       (awstats, chromium, clamav, g810-led, giflib, http-
                       parser, jhead, libpgjava, node-cached-path-
                       relative, node-fetch, and vlc), Fedora (fastnetmon,
                       kernel, librime, qpress, rr, thunderbird, and
                       wireshark), Red Hat (kernel, kernel-rt, and kpatch-
                       patch), Slackware (mozilla), SUSE (cherrytree and
                       chromium), and Ubuntu (libbpf, libxml2, linux-gcp-
                       5.15, linux-gke, linux-gke-5.15, and linux-gke).


          o § Transparency/Investigative Reporting⠀➾


                # ⚓ Internet Freedom Foundation ☛ Digital_Transparency:_A_Right
                  to_Information_Report_for_November_2022⠀⇛


                       For the month of November 2022, IFF has filed 5
                       Right to Information (“RTI”) applications. In
                       significant responses, we obtained submissions made
                       in the public consultations on the consultation
                       paper on Need for a new legal framework governing
                       Telecommunication in India and on the India Digital
                       Ecosystem Architecture 2.0 from the Department of
                       Telecommunications and Centre for Development of
                       Advanced Computing, respectively.


                # ⚓ Internet Freedom Foundation ☛ Government_to_reply_to
                  petition_on_search_of_mobile_devices:⠀⇛


                       In October 2022, the Foundation for Media
                       Professionals (‘FMP’) approached the Supreme Court
                       seeking regulation of the police’s power to search
                       or seize electronic devices. In the petition, they
                       highlighted that existing laws do not regulate how
                       authorities search or seize electronic devices. The
                       lack of regulation enables them to engage in
                       dubious practices, such as mandating individuals,
                       with or without reasonable suspicion, to grant
                       access to their mobile devices. The Supreme Court
                       has directed the Central Government to reply to the
                       Petition within 8 weeks. FMP was represented by
                       Senior Advocate Siddharth Aggarwal. IFF provided
                       legal support.


                       [...]


                       On October 18th, 2022, a bench led by Justice K.M.
                       Joseph issued notice in the petition and tagged it
                       with an ongoing case titled Ram Ramaswamy & Ors. v.
                       Union of India & Ors.. In that case, the Union
                       Government has already filed a reply. Today, a
                       bench of the Supreme Court comprising Justice S.K.
                       Kaul and Justice A.S. Oka heard FMP’s petition as
                       well as the ongoing case. After hearing submissions
                       from Senior Advocate Siddharth Aggarwal, appearing
                       for FMP, the Court observed that the scope FMP’s
                       petition was more extensive than the ongoing case,
                       since it raised issues relating to enforcement and
                       investigation agencies beyond the police and sought
                       comprehensive directions. The Supreme Court
                       directed the Union Government to separately reply
                       to FMP’s petition. The Court also de-tagged FMP’s
                       petition from the ongoing case and listed it for a
                       hearing in February 2022.


          o § Censorship/Free Speech⠀➾


                # ⚓ Public Knowledge ☛ Public_Knowledge_Joins_26_Groups_Urging
                  Congress_To_Drop_JCPA_from_Must-Pass_Defense_Legislation_–
                  Public_Knowledge⠀⇛


                       Today, Public Knowledge joined 26 public interest,
                       consumer advocacy, and civil society groups as well
                       as trade associations, media companies, and others
                       in a letter urging Congressional leadership to
                       exclude the “Journalism Competition and
                       Preservation Act” (JCPA) from any pending
                       legislation, including the “National Defense
                       Authorization Act” (NDAA) – a “must-pass” bill
                       funding military activities. The groups argue that
                       the JCPA “contains far too many contradictions,
                       complexities, and problems” for Congress to include
                       it in any omnibus or must-pass legislation.


                       Public Knowledge contends that the “Journalism
                       Competition and Preservation Act” fails to support
                       local news, serving only to worsen some of the
                       biggest problems in journalism. Bundling the bill
                       into must-pass defense legislation is a desperate
                       move that only demonstrates how flawed this so-
                       called journalism bill really is.


    * § Gemini* and Gopher⠀➾


          o § Personal⠀➾


                # ⚓ hello_from_a_desk_somewhere_in_St_Louis!⠀⇛


                       I’m here in Oakville, a place I despise, and I am
                       chomping at the bit to move (soon). Lovely.


                       Now, I write things with nothing much *to* write,
                       but I come up with stuff, anyway.


                       I like Smol.pub, the updates here. I also LOVE
                       Midnight.pub, the updates/community there. Blog
                       Bless them all! 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇:)⦈


                       And yea, I’m still mostly without much to say in
                       this moment. Been watching SBF interviews this
                       evening. Speaks quite similar to Jeffrey Skilling
                       of ENRON during the scant media interactions he had
                       near/after the ENRON meltdown in…2000?


                # ⚓ 🔤SpellBinding:_ATHIRSG_Wordo:_DYADS⠀⇛


                # ⚓ Star_Log_2022-12-04_Evening_(Fairbanks,_AK,_US)⠀⇛


                       Yesterday evening the sky was mostly clear, but the
                       temperature was still reasonably warm at +9 °F (-13
                       °C). This would have made for a comfortable
                       stargazing evening, but I had a conflict with a
                       family event. I got home too late to go out to the
                       boat launch (it was a work night) but I decided to
                       go out into the yard for a few minutes to do some
                       moon-gazing. I had a good time observing the moon
                       for about 30 minutes with the 60mm refractor,
                       mainly using the Plossl 12.5mm eyepiece.


          o § Technical⠀➾


                # ⚓ Drowning_in_AI_Generated_Garbage :_the_silent_war_we_are
                  fighting⠀⇛


                       All over the web, we are witnessing very
                       spectacular results from statistic algorithms that
                       have been in the work for the last forty years. We
                       gave those algorithms an incredibly catchy name:
                       “Artificial Intelligence”. We now have very popular
                       and direct applications for them: give the
                       algorithm a simple text prompt (don’t get me
                       started on the importance of text) and it generates
                       a beautiful original picture or a very serious-
                       sounding text. It could also generate sounds or
                       videos (we call them “deep fakes”). After all, it
                       generates only a stream of bits, a bunch of 1 and 0
                       open to interpretation.


                # ⚓ Finally_shifting_to_my_own_compan⠀⇛


                       I work for hire as a software engineer using my own
                       company for quite sometime, but now I have finally
                       shifted my focus to what I really want to do: game
                       programming.


                # ⚓ Announcement:_todo.txt_over_Gemini⠀⇛


                       For many years I’ve used the wonderful “Tasks” app
                       by Alex Baker^, forked from Astrid Tasks back in
                       2013. Recently I began switching to the plaintext
                       todo.txt format^^, and I wanted a simple online
                       interface with which I could interact with my list.
                       Since I primarily use Gemini these days, I decided
                       to build a Gemini interface myself.


                       Last night I quietly added a link to my todo.txt
                       service to the “Live” section of my capsule.
                       Visitors can create a todo.txt file of their own,
                       download it, and manage it from the page.


                # ⚓ Still_toying⠀⇛


                       I’ve been toying with additional smol web and
                       fediverse tools these last weeks. But not one day
                       has passed that I have not thought “I should post a
                       small text on my gemlog”. Here it is.


                       Mastodon: I had a couple accounts on big instances
                       since 2017. They’re both dead, their domains
                       bouncing to a gossip news site and a porn site full
                       of placeholders. I’ve since made a new one on a
                       mid-size instance, but still not feeling it. I’ve
                       been entrenched on my usage of twitter for a lot of
                       years: Tweetdeck on the desktop, Talon on the
                       phone, and not touching the official app or web.
                       It’s too comfortable now, and I don’t see any ads
                       whatsoever. There’s a lot of list, filters, and
                       stuff I should build on mastodon to reach a similar
                       level of useful/uselessness.


                # § Programming⠀➾


                      # ⚓ comeback⠀⇛


                             With the end of August, i plan a comeback to
                             Geminispace.


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



                    ䷩ 𝚕𝚒𝚗𝚎 4729

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.05.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_05/12/2022:_GStreamer_1.21.3⠀✐


Posted in News_Roundup at 7:47 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Kernel_Space
          o Applications
          o Instructionals/Technical
          o Games
          o Desktop_Environments/WMs
    * Distributions_and_Operating_Systems
          o Devices/Embedded
          o Mobile_Systems/Mobile_Applications
    * Free,_Libre,_and_Open_Source_Software
          o Education
          o Programming/Development
    * Leftovers
          o Science
          o Education
          o Hardware
          o Health/Nutrition/Agriculture
          o Proprietary
          o Security
                # Privacy/Surveillance
          o Defence/Aggression
          o Transparency/Investigative_Reporting
          o Environment
                # Energy
                # Wildlife/Nature
          o Finance
          o AstroTurf/Lobbying/Politics
          o Censorship/Free_Speech
          o Freedom_of_Information_/_Freedom_of_the_Press
          o Civil_Rights/Policing
          o Internet_Policy/Net_Neutrality
          o Monopolies
                # Copyrights
    * Gemini*_and_Gopher
          o Personal
          o Technical
                # Science
    * § GNU/Linux⠀➾


          o ⚓ 9to5Linux ☛ 9to5Linux_Weekly_Roundup:_December_4th,_2022_–
            9to5Linux⠀⇛


                 The 114th installment of the 9to5Linux Weekly Roundup is
                 here for the week ending on December 4th, 2022, keeping
                 you guys up to date with the most important things
                 happening in the Linux world. If you missed last week’s
                 9to5Linux Weekly Roundup, catch up with all the things
                 here.


          o § Kernel Space⠀➾


                # ⚓ LWN ☛ Kernel_prepatch_6.1-rc8_[LWN.net]⠀⇛


                       The eighth and presumably final 6.1 kernel prepatch
                       has been released for testing. “So everything looks
                       good, and while the calming down may have happened
                       later than I wished for, it did happen. Let’s hope
                       this upcoming week is as quiet (or quieter).”


                # ⚓ The Register UK ☛ A_brand_new_Linux_DRM_display_driver_–
                  for_a_1992_computer⠀⇛


                       Uytterhoeven is the maintainer of Linux/m68k, the
                       Motorola port of the Linux kernel, and one of the
                       interesting things about the new driver is that he
                       developed it entirely on emulated hardware, using
                       an interesting virtual machine called ARAnyM by
                       Czech developer Petr Stehlík.


                       Even more unexpected is that this isn’t the only
                       680×0 VM for Linux kernel developers. QEMU 6.0 also
                       has a new target, known as m68k, implemented by
                       Laurent Vivier. This is for a nonexistent Virtual
                       M68k Machine. The new QEMU machine type uses some
                       technology from the Goldfish emulator used in
                       Android development…


          o § Applications⠀➾


                # ⚓ GStreamer_1.21.3_unstable_development_release⠀⇛


                       The GStreamer team is pleased to announce another
                       development release in the unstable 1.21 release
                       series on the road to the 1.22 stable release.


                       The unstable 1.21 release series adds new features
                       on top of the current stable 1.20 series and is
                       part of the API and ABI-stable 1.x release series
                       of the GStreamer multimedia framework.


                       The unstable 1.21 release series is for testing and
                       development purposes in the lead-up to the stable
                       1.22 series which is scheduled for release in
                       December 2022. Any newly-added API can still change
                       until that point.


                       A feature freeze is now into effect for the 1.21
                       series, but newly-added API might still change
                       until the final 1.22.0 stable release, and minor
                       features may also still be added until then.


                # ⚓ Ghacks ☛ Multi-boot_tool_Ventoy_adds_support_for_32GB_Fat32
                  and_multi-languages⠀⇛


                       The multi-boot tool Ventoy is updated regularly
                       with new features. Ventoy 1.0.84 is the latest
                       version, which adds support for 32 gigabyte and
                       larger FAT32 storage devices and multi-language
                       support in the Ventoy boot menu among other
                       improvements.


                # ⚓ DebugPoint ☛ True_Lightweight_Notepads_for_Ubuntu_and_Other
                  Linux_[Compared]⠀⇛


                       We highlighted some of the best Notepad++
                       replacements for Ubuntu and other Linux distros a
                       few days back. Since Notepad++ is an advanced
                       notepad, it may not fit the actual lightweight
                       criteria. For example, if you want to take some
                       quick notes and nothing else, then Notepad++ or
                       code editors can be an overkill.


                       Also, a thin resource footprint-based editor can be
                       kept open for longer without worrying about memory
                       and other things.


                       In addition, many DebugPoint readers commented
                       about the following editors in the Notepad++
                       article. Hence this special list.


          o § Instructionals/Technical⠀➾


                # ⚓ Linux Capable ☛ How_to_Upgrade_to_Linux_Mint_21.1_“Vera”⠀⇛


                       The following tutorial will teach you how to
                       upgrade to Linux Mint 21.1, codenamed Vera from
                       Linux Mint 21.0, Vanessa, using the terminal with
                       CLI commands. The Linux Mint team does not
                       recommend this method, but it does work well for
                       your standard Linux Mint system, given it is only a
                       minor upgrade and not a major release.


                       Linux Mint 21.1 “Vera” is a significant release
                       that includes many new features and improvements.
                       The Cinnamon desktop environment has been updated
                       to version 5.6, bringing numerous performance and
                       stability improvements and introducing a convenient
                       new ISO verification tool – conveniently located in
                       the context menu for easy access when right-
                       clicking on your downloaded ISO images,
                       guaranteeing the authenticity and integrity of
                       every file.


                       Some other features include better support for
                       high-resolution displays, an updated look and feel,
                       and improved in-house tools such as the Driver
                       Manager and Software Sources. The Driver Manager is
                       now easier to use and can run in user mode, so it
                       won’t ask for your password when launched.
                       Additionally, the configuration of removed drivers
                       can now be easily purged. Software Sources has also
                       been updated, with better handling of PPA keys.
                       These improvements make Linux Mint 21.1 “Vera” a
                       more polished and user-friendly release, making it
                       an excellent choice for newcomers to the Linux
                       world.


                # ⚓ OpenSource.com ☛ 6_steps_to_get_verified_on_Mastodon_with
                  encrypted_keys⠀⇛


                       Mastodon permits its users to self-verify. The
                       easiest method to do this is through a verification
                       link. For advanced verification, though, you can
                       use the power of shared encrypted keys, which
                       Mastodon can link to thanks to the open source
                       project Keyoxide.


          o § Games⠀➾


                # ⚓ CoRecursive ☛ DOOMed_to_Fail:_A_Horror_Story⠀⇛


                       Today Rebecca Burger Becky Heineman shares the tale
                       of porting Doom to the 3DO console under extreme
                       conditions. There is an engine to tweak, deadlines
                       to hit, hardware acceleration to get working, and
                       dramatic rock anthems to record.


                       We also learn about how game piracy led her to game
                       development and what it was like to do game
                       development in the mania of the mid-nineties.
                       Finally, we close with Becky’s advice on learning
                       bare metal development skills.


          o § Desktop Environments/WMs⠀➾


                # ⚓ OpenSource.com ☛ Why_you_should_try_the_Nemo_file_manager
                  on_Linux⠀⇛


                       Computers are fancy filing cabinets, full of
                       virtual folders and files waiting to be referenced,
                       cross-referenced, edited, updated, saved, copied,
                       moved, renamed, and organized. In this article, I’m
                       taking a look at a file manager for your Linux
                       system.


                       The Cinnamon project was formed as a
                       reimplementation of GNOME 2 using the components of
                       GNOME 3. Eventually, it diverged enough to be a
                       true fork, and today the Cinnamon desktop uses GTK3
                       libraries and forked versions of key GNOME 3
                       applications to create a “classic” GNOME
                       experience. One of the components contributing to
                       the traditional GNOME experience is Nemo, a file
                       manager based on the GNOME 2 version of Nautilus.


    * § Distributions and Operating Systems⠀➾


          o § Devices/Embedded⠀➾


                # ⚓ CNX Software ☛ GEEKOM’s_Christmas_promotion_–_Save_$50_on
                  Jasper_Lake_mini_PCs_(Sponsored)_–_CNX_Software [Ed: If it is
                  "with Windows 11 Pro pre-installed," then why does this
                  'Linux' site go along with it?]⠀⇛


                       Black Friday and Cyber Monday are done, but GEEKOM
                       has started a Christmas promotion for two Jasper
                       Lake mini PCs that will run until December 31,
                       2022.


                       The GEEKOM MiniAir 11 mini PC reviewed by Ian with
                       Windows 11 and Ubuntu 22.04 this past summer, is
                       offered for $179 with the code coupon XMAIR11A, or
                       a $50 discount compared to the retail suggested
                       price of $229. Ian found out the mini PC worked
                       well in both Windows and Ubuntu with a near-silent
                       operation but noted the lack of a SATA bay for
                       expansion and limited BIOS options.


                # ⚓ CNX Software ☛ DFI_EC70A-TGU_embedded_computer_promises
                  long-term_availability_until_2035_(at_least)_–_CNX_Software⠀⇛


                       Some industries require long-term availability of
                       hardware, and DFI’s EC70A-TGU rugged embedded
                       computer could fit the bill as the Tiger Lake IOTG
                       processor used in this model has a 15-Year CPU life
                       cycle guaranteeing availability until Q3 2035.


                       The fanless computer is equipped with 8GB RAM,
                       supports M.2 NVMe SSD storage, also well M.2
                       expansion slots for 5G modules, features HDMI and
                       VGA video output, four serial DB3 ports, and offers
                       up to four Ethernet ports and up to six USB ports
                       through three SKUs with a different number of USB
                       and Ethernet ports.


                # ⚓ CNX Software ☛ Getting_Started_with_CrowBot_BOLT_smart
                  robot_car_–_CNX_Software⠀⇛


                       CrowBot BOLT is a smart robot car based on an ESP32
                       wireless microcontroller and designed for the
                       education market with the ability to program the
                       robot with visual programming, Arduino, or
                       MicroPython.


                       Elecrow sent me a sample of the CrowBot BOLT kit
                       for evaluation so I’ll have a look at the hardware,
                       show how to assemble it, showcase the features of
                       the built-in firmware, and demonstrate how to
                       program the robot with visual programming, Arduino,
                       and MicroPython using some of the provided code
                       samples.


                # ⚓ Linux Gizmos ☛ Rugged_Edge_Mini-PC_equipped_with_i.MX_8M
                  Plus_and_dual_2.5GbE_LAN_ports⠀⇛


                       Last week, iBASE released a fanless Mini-PC based
                       on the quad-core i.MX 8M Plus processor from NXP.
                       The ISR215 also includes one HDMI 2.0 port,  M.2
                       Key-B (3052) for 5G connectivity and it can be
                       configured with up to 4GB LPDDR4/128GB eMMC. 


          o § Mobile Systems/Mobile Applications⠀➾


                # ⚓ Android Police ☛ The_Android_Police_podcast_gives_OnePlus’s
                  new_update_policy_some_golf_claps⠀⇛


                # ⚓ Android Police ☛ Google_mounts_ultimate_appeal_against_EU’s
                  Android_antitrust_penalties⠀⇛


                # ⚓ Phone Arena ☛ Long-running_major_vulnerability_left
                  millions_of_Android_handsets_wide_open_to_data_theft_–
                  PhoneArena⠀⇛


                # ⚓ GSM Arena ☛ Samsung_Galaxy_Xcover_5_now_getting_Android_13
                  and_One_UI_5.0_–_GSMArena.com_news⠀⇛


                # ⚓ SamMobile ☛ Galaxy_A13_5G_gets_the_taste_of_Android_13_(One
                  UI_5.0)_update_–_SamMobile⠀⇛


                # ⚓ Android Police ☛ Android_owners_on_24-hour_time_have_a_new,
                  easier_way_to_set_times_for_appointments⠀⇛


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


          o ⚓ It’s FOSS ☛ Linen_is_a_Google-Searchable_Open-Source_Alternative
            to_Slack_and_Discord⠀⇛


                 Linen is an interesting open-source project brewing up.


                 It aims to be an open alternative to Slack and Discord,
                 focusing on making communities more accessible and
                 helping reduce the support burden.


                 It could be worth adding it as an open-source Slack
                 alternative, but it is in its early stages of development
                 when publishing this.


          o § Education⠀➾


                # ⚓ CNX Software ☛ UniHiker_education_platform_teaches_STEM
                  with_Mind+_and_Jupyter_(in_China)⠀⇛


                       DFRobot UniHiker is a STEM education platform with
                       a 2.8-inch touchscreen display, a Rockchip RK3308
                       quad-core Cortex-A35 processor, a GD32V RISC-
                       V microcontroller, WiFi and Bluetooth connectivity,
                       as well as various headers for expansion, and a BBC
                       Micro:bit compatible edge connector.


                       The UniHiker runs Debian 10 Linux and can be used
                       to teach programming using Mind+ visual programming
                       IDE or Jupyter open-source interface, as well as
                       IoT and AI basics thanks to tutorials and lessons
                       available in Chinese only as the platform clearly
                       targets the education market in mainland China at
                       this point in time.


                # ⚓ EIN Presswire ☛ Moodle_enters_into_acquisition_of_eAbyas_to
                  deliver_services_in_India⠀⇛


                       Moodle has announced its acquisition of eAbyas Info
                       Solutions, a Moodle Certified Partner servicing the
                       EdTech sector across India.


          o § Programming/Development⠀➾


                # ⚓ [Old] Dave DeLong ☛ HTTP_in_Swift⠀⇛


                       An 18-part series on building a Swift HTTP
                       framework: [...]


    * § Leftovers⠀➾


          o ⚓ Hackaday ☛ Rocket_Switch_–_Accessibility_Done_With_Elegance⠀⇛


                 Quite a few makers try and create devices helpful to
                 others – today’s hack, Rocket Switch, is a lovely example
                 of that. It’s a design by [Neil Squire] of [Makers Making
                 Change], with a PCB that plugs onto an Adafruit Rotary
                 Trinkey, soldering onto its exposed pads, equipping it
                 with two headphone jacks connected to GPIOs. This is a
                 simple design – only two headphone jacks and resistors,
                 complete with a 3D printed case. The value is not as much
                 in its construction, but more in what the Rocket Switch
                 provides to its users.


          o § Science⠀➾


                # ⚓ Hackaday ☛ Miracle_Of_Science:_Scotch_Tape_Improves
                  Generator⠀⇛


                       We were always amused that one of the biggest
                       scientific discoveries of the recent past —
                       graphene — was started with pencil lead and Scotch
                       tape. Now, researchers at the University of Alabama
                       in Huntsville have determined that double-sided
                       Scotch tape can improve triboelectric power
                       generators. Triboelectric generation, of course, is
                       nothing new. These energy harvesters take
                       mechanical and thermal energy and turn them into
                       tiny amounts of electricity. What’s new here is
                       that PET plastic, aluminum, and double-sided tape
                       can make an inexpensive generator that works well.


                # ⚓ New_Book:_Synthetic_Data⠀⇛


                       Synthetic data is used more and more to augment
                       real-life datasets, enriching them and allowing
                       black-box systems to correctly classify
                       observations or predict values that are well
                       outside of training and validation sets. In
                       addition, it helps understand decisions made by
                       obscure systems such as deep neural networks,
                       contributing to the development of explainable AI.
                       It also helps with unbalanced data, for instance in
                       fraud detection. Finally, since synthetic data is
                       not directly linked to real people or transactions,
                       it offers protection against data leakage.
                       Synthetic data also contributes to eliminating
                       algorithm biases and privacy issues, and more
                       generally, to increased security.


                # ⚓ Tom’s Hardware ☛ Quantum_Computing_May_be_Bolstered_by
                  Liquid-Like_Electrons_|_Tom’s_Hardware⠀⇛


                       The quantum computing field may have just received
                       a coherence and error-prevention boost in the form
                       of parafermions: grouped electrons that behave as
                       liquids in a special state of matter. Scientists
                       with the Nanyang Technological University in
                       Singapore (opens in new tab) have demonstrated
                       experimental results they expect to lead to
                       parafermions when electrons maintain temperatures
                       close to absolute zero (-273 degrees Celsius). The
                       research achieved a breakthrough by demonstrating
                       that there are conditions in which electrons can
                       have strong interactions – something that
                       scientists merely theorized until now.


          o § Education⠀➾


                # ⚓ Chicago Sun Times ☛ Bob_McGrath,_‘Sesame_Street’_cast
                  member,_dies_at_90⠀⇛


                       The public television show used the colorful,
                       humorous, fast-paced style of TV commercials to
                       relay lessons on letter and numbers as well as
                       heavier subjects like children’s emotional health.
                       Young viewers even learned about mortality when
                       they were informed, sensitively, of Mr. Hooper’s
                       death.


                       “We’ve always looked at children as just short
                       people,” McGrath told the Sun-Times in 1998. “We’ve
                       never talked down to them.”


                # ⚓ NPR ☛ Bob_McGrath,_longtime_star_of_‘Sesame_Street,’_has
                  died_at_90⠀⇛


                       But after he was shown tapes of Muppets creator Jim
                       Henson’s work, he told a crowd at a 2016 convention
                       in Florida, he was “totally blown away.”


                # ⚓ Pro Publica ☛ The_Corporation_Exploiting_Washington’s
                  Special_Education_System⠀⇛


                       Donna Green hit her breaking point last summer, six
                       months into her job as the top administrator at the
                       Northwest School of Innovative Learning.


                       She had grudgingly accepted when her request for
                       classroom computers was ignored and a furniture
                       order for what she called an “embarrassingly
                       barren” campus was answered with plastic folding
                       tables. She’d worried that her staff was
                       inexperienced but had figured her decade in special
                       education would help fill that void.


          o § Hardware⠀➾


                # ⚓ Nanoengineers_Develop_a_Predictive_Database_for_Materials⠀⇛


                       Nanoengineers at the University of California San
                       Diego’s Jacobs School of Engineering have developed
                       an AI algorithm that predicts the structure and
                       dynamic properties of any material—whether existing
                       or new—almost instantaneously. Known as M3GNet, the
                       algorithm was used to develop matterverse.ai, a
                       database of more than 31 million yet-to-be-
                       synthesized materials with properties predicted by
                       machine learning algorithms. Matterverse.ai
                       facilitates the discovery of new technological
                       materials with exceptional properties.


                # ⚓ Hackaday ☛ The_PalmPilot_Returns,_This_Time_In_Your
                  Browser⠀⇛


                       The PalmPilot doesn’t seem to get much
                       retrocomputing love, but maybe it should. After
                       all, it might not have been the very first
                       handheld, but it was probably the most successful,
                       and that ultimately led to the era of the
                       smartphone. Whether you miss your old Palm
                       applications, or never got to experience them the
                       first time around, fear not. You can now relive
                       them in all their glory in your browser thanks to
                       the Internet Archive project.


                # ⚓ Hackaday ☛ DIY_Repair_Stand_Holds_Your_Bike_And_Weighs_It⠀⇛


                       If you’ve ever done maintenance or repair work on
                       your bicycle, you’ll know that positioning a bike
                       in your workshop isn’t trivial. You can use your
                       bike’s kickstand, or lean it against a wall, but
                       then you can’t work on the wheels. You can place it
                       upside-down, but then the shifters and brake levers
                       are hard to reach. You can hang it from the
                       ceiling, but then you first need to install hooks
                       and cables in hard-to-reach places. Ideally you’d
                       want to have one of those standing clamp systems
                       that the pros use, but their price is typically
                       beyond a hobbyist’s budget.


                # ⚓ Hackaday ☛ Dirty_TRS-80_Has_A_Surprise_Hack⠀⇛


                       [Adrian] had a TRS-80 model IV that looks like it
                       was stored in a mulch pile. However, it seemed to
                       have some surprises. The first hint that something
                       was up was that the keyboard looks like a model III
                       and there are two mystery knobs in the back.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ The Economist ☛ Young_Americans_increasingly_end_their_own
                  lives⠀⇛


                       The rise in youth suicide is part of a broader
                       increase in mental-health problems among the young.
                       This preceded the pandemic but was probably
                       accelerated by it. In 2021 nearly half of American
                       high-school students said that they had experienced
                       persistent feelings of sadness and hopelessness in
                       the past year, up from 26% in 2009; one in five
                       seriously considered suicide, up from 14%; and 9%
                       attempted to end their life, up from 6% (see
                       chart). Although the rates for 15- to 19-year-olds
                       are not unprecedented (there was a similar peak in
                       the early 1990s), the rates for ten- to 14-year-
                       olds are higher than ever before.


                # ⚓ NBC ☛ 4_Navy_sailors_assigned_to_same_facility_die_by
                  apparent_suicide_within_weeks,_amid_growing_concerns_of
                  mental_health_crisis⠀⇛


                       It is the latest cluster of Navy suicides this year
                       to spark concerns of a fleetwide mental health
                       crisis.


                       The four sailors worked for the Mid-Atlantic
                       Regional Maintenance Center (MARMC), which
                       maintains military ships and is based in Norfolk,
                       Virginia.


          o § Proprietary⠀➾


                # ⚓ France24 ☛ French_hospital_suspends_operations_after_cyber
                  attacks [iophk: Windows kills]⠀⇛


                       The regional health agency (ARS) said the hospital
                       had cancelled operations, but was doing everything
                       possible to keep walk-in services and consultations
                       running.


                       Extra staff had to be called in to the intensive
                       care unit because, while the machines there were
                       still functioning, more people were needed to watch
                       the screens as they were no longer working as part
                       of a network, aid Braun.


                # ⚓ ABC ☛ Hospitals_warned_to_guard_against_cybercrime_after
                  Medibank_and_Optus_wake-up_calls [iophk: Windows kills]⠀⇛


                       The troubling warning is high on the list of
                       predictions offered by cyber security experts
                       heading into 2023 and in the wake of unprecedented
                       [breaches] affecting millions of Medibank and Optus
                       customers.


                       Global firm Palo Alto Networks suggests it is time
                       hospitals, government services and businesses start
                       discussing whether they would pay a ransom and how
                       much they would fork out.


          o § Security⠀➾


                # § Privacy/Surveillance⠀➾


                      # ⚓ India Times ☛ China_can_use_TikTok_to_collect_data_on
                        users_&_spy:_FBI_chief⠀⇛


                             Wray said the FBI was concerned that the
                             Chinese had the ability to control the app’s
                             recommendation algorithm, “which allows them
                             to manipulate content, and if they want to,
                             to use it for influence operations. ”


                      # ⚓ Hackaday ☛ Breathe_Through_Your_Ears?⠀⇛


                             With all the attention given to heart rate
                             monitoring and step counting, respiratory
                             rate monitoring is often overlooked.
                             Smartwatches are starting to incorporate
                             respiratory rate monitoring more and more
                             these days. However, current devices often
                             simply look at breaths per minute without
                             extracting more interesting features of the
                             respiratory waveform which could give us more
                             insight into our bodies than breaths per
                             minute could alone. [Davies] and his team
                             decided they wanted to change that by making
                             an earbud that can measure respiratory rate.


          o § Defence/Aggression⠀➾


                # ⚓ CNN ☛ Trump_calls_for_the_termination_of_the_Constitution
                  in_Truth_Social_post⠀⇛


                       Former President Donald Trump called for the
                       termination of the Constitution to overturn the
                       2020 election and reinstate him to power Saturday
                       in a continuation of his election denialism and
                       pushing of fringe conspiracy theories.


                # ⚓ ME Forum ☛ London’s_Mayor_Celebrates_Notorious_Islamist
                  Group⠀⇛


                       The MCB’s “elders,” however, are prominent
                       Islamists with a long history of spouting and
                       encouraging extremism. Most were part of an
                       Islamist network known as Jamaat-e-Islami.


                # ⚓ Firstpost ☛ In_Nitish_Kumar’s_blatant_minority_appeasement,
                  local_Muslims_permitted_to_offer_prayers_at_Buddhist_shrine⠀⇛


                       A cavern in Kaimur Hills, nearly 3 km south of
                       Sasaram in Bihar’s Rohtas district, where Lord
                       Buddha is believed to have spent a night after
                       attaining enlightenment at Bodh Gaya, has turned
                       into a symbol of the Nitish Kumar-led government’s
                       blatant appeasement of minorities.


                       Barely a few days earlier, on 29 November, the
                       Archaeological Survey of India (ASI), tweeted that
                       it had wrested control of a 2300-year-old Buddhist
                       shrine in Sasaram from Muslim encroachers, who used
                       it to offer prayers.


                # ⚓ The Hill ☛ Musk’s_‘free_speech’_Twitter_vision_put_to_test
                  by_Ye⠀⇛


                       The decision was made in an ad hoc manner and with
                       special treatment for Ye, Carusone said. Before he
                       was suspended, Ye tweeted a screenshot with a text
                       from Musk saying, “Sorry, but you have gone too
                       far. This is not love.”


                # ⚓ Scheerpost ☛ Zelensky_Looks_to_Ban_Christian_Denomination
                  With_Ties_to_Moscow⠀⇛


                       The Ukrainian President called for the Russian
                       Orthodox Church to be outlawed after Kiev’s
                       intelligence agency conducted several raids on
                       Orthodox cathedrals.


                # ⚓ Scheerpost ☛ The_Secret_Reason_the_US_is_Still_in_Syria⠀⇛


                       It’s tough to overstate how bad things are in
                       Syria. According to the UN, “90 percent of all
                       Syrians today are forced to live below the poverty
                       line with around 12 million grappling with severe
                       food insecurity.”


                # ⚓ Counter Punch ☛ Echoes_of_Chile’s_Past⠀⇛


                       Efforts to overthrow the democratically elected
                       president had thus far been unsuccessful. An
                       insurrectionary month-long strike by truck drivers
                       and entrepreneurs in October of 1972 had just been
                       thwarted by the extraordinary mobilization of
                       Chilean workers. But the writing was on the wall.
                       This is not a mere metaphor: On many walls of the
                       country, paramilitary fanatics had scrawled the
                       words “Djakarta, ya viene”—“Jakarta is coming,”
                       referring to the massacre in that city of hundreds
                       of thousands of Indonesians after the coup against
                       the left-wing government of Sukarno in 1967.


                       It was this prophecy of death and doom that Allende
                       was trying to prevent. His 1972 trip was meant to
                       explain to the international community what was at
                       stake in Chile and to enlist the sympathy of the
                       nations of the world. The cornerstone of that
                       strategy was a rousing speech that he delivered 50
                       years ago this Sunday, on December 4, 1972, to the
                       UN General Assembly.


                # ⚓ Meduza ☛ Explosion_in_Nizhnevartovsk_building_kills_six,
                  injures_four_—_Meduza⠀⇛


                       An explosion occurred in a five-story building in
                       Nizhnevartovsk, in western Siberia, reports TASS,
                       citing local emergency services.


                # ⚓ Meduza ☛ Kremlin_‘recommends’_that_Russian_regions_and_TV
                  stations_support_‘patriotic’_artists_for_New_Year’s_concerts
                  —_Meduza⠀⇛


                       The Russian presidential administration has sent
                       recommendations on conducting New Year’s events to
                       regional authorities, cultural institutions, and
                       state-owned companies, reports news agency RBC. A
                       source close to one regional administration
                       confirmed the details of the recommendations to the
                       publication.


                # ⚓ BBC ☛ San_Francisco_to_allow_police_‘killer_robots’⠀⇛


                       San Francisco’s ruling Board of Supervisors has
                       voted to let the city’s police use robots that can
                       kill.


                       The measure permits police to deploy robots
                       equipped with explosives in extreme circumstances.
                       Dr Catherine Connolly, from the group Stop Killer
                       Robots, said the move was a “slippery slope” that
                       could distance humans from killing.


                       The city’s police – the SFPD – told the BBC they do
                       not currently operate any robots equipped with
                       lethal force.


                # ⚓ Counter Punch ☛ The_Cruel,_Dishonest_and_Shameful_Story_of
                  Britain’s_Last_Colony_may_be_Coming_to_an_End⠀⇛


                       Greenhill, later Lord Greenhill of Harrow, was well
                       aware that this was not the case at the time of
                       writing, but cavalierly asserted that in future
                       there would “be no indigenous population except
                       seagulls who have not yet got a committee”.


                       In a tone of nauseating jollity, this senior
                       British diplomat picks up on the seagull reference
                       to explain what was going to happen to the 1,500
                       people or more who had lived and worked in Chagos
                       for generations. “Unfortunately,” he wrote, “along
                       with the Birds go some few Tarzans or Men Fridays
                       whose origins are obscure, and who are being
                       hopefully wished on to Mauritius etc.”


          o § Transparency/Investigative Reporting⠀➾


                # ⚓ International Business Times ☛ Kyle_Rittenhouse_Asks_Elon
                  Musk_To_Release_Info_On_‘Censoring’_Done_On_His_Trial⠀⇛


                       While preparing for his trial, Rittenhouse’s lawyer
                       L. Lin Wood sought to raise money to help with his
                       client’s legal fees. He later accused Twitter of
                       blocking him from publishing posts on grounds that
                       he was “glorifying violence. His account was later
                       reinstated, as per The New York Post.


          o § Environment⠀➾


                # ⚓ Counter Punch ☛ Western_Diplomats_Offer_Rotten_Climate
                  Carrot,_and_Wield_Broken_Sanctions_Stick⠀⇛


                       In recent weeks, Western climate deal-makers have,
                       as well, wielded their own carrot and stick, but
                       unless withdrawn and reconsidered, they will
                       provide only a continuation of – rather than break
                       from – a future of rising greenhouse gas emissions,
                       massive loss and damage due to extreme weather, and
                       the polluters’ refusal to acknowledge, much less
                       reimburse, the historic climate debt they owe. The
                       two cases we have seen up close, are the Just
                       Energy Transition Partnership carrot and Carbon
                       Border Adjustment stick. So, what’s rotten and
                       what’s broken?


                       Amsterdam revelations


                # ⚓ Foreign Policy ☛ Europe’s_Climate_Chief:_The_1.5-Degree
                  Goal_Is_on_‘Life_Support’⠀⇛


                       Most commentary about COP27 has branded the summit
                       a bit of a letdown. In short, the world agreed to
                       compensate poor countries for climate-related loss
                       and damage, but the money allocated for this was
                       tiny. And there was no agreement to reduce
                       emissions further. Do you agree? How would you
                       grade the outcomes from COP27?


                # ⚓ NBC ☛ Toddler_Attacked_by_Coyote_Outside_Woodland_Hills
                  Home⠀⇛


                       NBC has chronicled other coyote attacks on children
                       this year.


                # ⚓ Los Angeles Times ☛ Coyote_attacks_toddler_on_front_lawn_of
                  Woodland_Hills_home⠀⇛


                       The coyote can be seen attacking the child as her
                       father was busy locking up the family’s SUV, the
                       family’s doorbell video showed. The animal knocked
                       the child down, grabbed her left leg and attempted
                       to drag her away as she screamed.


                # ⚓ The Telegraph UK ☛ The_ferocious_wild_creatures_causing
                  chaos_in_Europe’s_cities⠀⇛


                       In last couple of years, through little fault of
                       their own, boar have become an utter societal
                       menace. Permanent resident on the frequently
                       updated Global Invasive Species Database’s ‘100
                       Worst’ list, they have been steadily mincing around
                       the forests of Europe for millennia, breeding
                       enthusiastically, bothering their domesticated
                       porcine kin, and being hunted and eaten by humans
                       with zeal. Since the 1980s, though, their numbers
                       have swollen in connection with two other rises:
                       the proportion of people living in cities, and the
                       average temperature.


                # ⚓ VOA News ☛ EU_Chief_Says_Bloc_Must_Act_Over_US_Climate_Plan
                  ‘Distortions’⠀⇛


                       The White House touts the IRA as a groundbreaking
                       effort to reignite US manufacturing and promote
                       renewable technologies.


                # ⚓ RTL ☛ UK_groups_hope_creative_biodiversity_message_takes
                  flight⠀⇛


                       It is hoped a new global biodiversity framework
                       will be agreed at the Montreal talks, which run
                       from December 7 to 19.


                       The UN has said world leaders will not attend the
                       gathering but the RSPB is asking British Prime
                       Minister Rishi Sunak to be present.


                # ⚓ Scheerpost ☛ Does_Claiming_1.5°_Is_Unachievable_Serve
                  Fossil_Fuel_Interests?⠀⇛


                       The Energy Mix It’s “factually incorrect and
                       politically very wrong” to say a 1.5°C limit on
                       average global warming is no longer possible,
                       International Energy Agency Executive Director
                       Fatih Birol said this week, pushing back on the
                       “unusual coalition” of scientists, activists, and
                       fossil industry “incumbents” that have been
                       carrying that […]


                # § Energy⠀➾


                      # ⚓ Meduza ☛ Price_cap_on_Russian_oil:_Russia_announces
                        ‘mechanisms’_to_avoid_compliance,_Hungary_backs_out_of
                        EU_agreement_—_Meduza⠀⇛


                             Deputy Prime Minister of Russia Alexander
                             Novak said that Russian authorities are
                             developing measures for refusing to supply
                             countries that have adopted a price cap on
                             Russian oil, reports Interfax.


                      # ⚓ Protesters_Across_UK_Demand_Government_Address_Fuel
                        Poverty_Crisis_This_Winter⠀⇛


                # § Wildlife/Nature⠀➾


                      # ⚓ Counter Punch ☛ User_Group_Pie:_The_Folly_of
                        Collaboration⠀⇛


                             Note that these collaborations do not
                             represent groups with a common interest
                             cooperating in an effort to achieve a common
                             goal. Such traditional collaborations used to
                             represent strength in the conservation
                             movement. For example, back in the early
                             1980’s when I still lived in Wyoming, the
                             Sierra Club, The Wilderness Society, the
                             Wyoming Wilderness Association, the Wyoming
                             Outdoor Council and Earth First! plus
                             numerous individuals cooperated in an effort
                             that ultimately led to the passage of the
                             Wyoming Wilderness Act of 1984. It wasn’t a
                             great bill, but considering our republican
                             congressional delegation, we did pretty well
                             getting a million acres of Wilderness
                             designated. The groups had their strategic
                             differences, but the goal that everyone
                             shared was to maximize wilderness
                             designations. Contrast that with today’s
                             “collaboratives” in which conservation groups
                             deal away public wildlands to self-interest
                             groups that are in complete opposition to
                             basic conservation goals. Like timber
                             companies and off-road vehicle groups,
                             including organized anti-wilderness mountain
                             bikers. The difference between the two
                             “collaboration” models is night and day.
                             Nowadays when I hear the term I cringe.
                             Because I know that wilderness is going to
                             get the shaft.


                             Here in the Greater Yellowstone Ecosystem,
                             the Gallatin Range is the only major mountain
                             range within and adjacent to Yellowstone
                             National Park with no designated Wilderness.
                             A big chunk of the range is a congressionally
                             designated Wilderness Study Area, but over
                             the years the Forest Service chose to
                             illegally allow off road vehicles including
                             mountain bikes, to proliferate, despite a
                             legal mandate to preserve the area’s
                             wilderness character. In other words, the
                             agency allowed local anti-wilderness
                             constituencies to proliferate; once the door
                             was opened to them, the off road vehicle
                             people felt that they had an established
                             right. And the Forest Service didn’t want to
                             make the hard decision to kick them out and
                             re-establish wilderness character as required
                             by law. Instead, the agency initiated a
                             collaboration process designed to force local
                             citizens to resolve the conflict, or put
                             another way, to do the agency’s job. This
                             pitted citizen versus citizen, exacerbating
                             community polarity.


          o § Finance⠀➾


                # ⚓ Scheerpost ☛ The_Chris_Hedges_Report:_The_Fed’s_Response_to
                  Inflation_Is_Another_Upward_Transfer_of_Wealth_(With_Richard
                  Wolff_)⠀⇛


                       Capitalist profiteering is the real driver of the
                       inflation crisis, and raising interest rates only
                       passes the costs onto workers already overwhelmed
                       by personal debt and stagnant wages.


                # ⚓ TruthOut ☛ Financial_Technology_Firms_Made_“Massive
                  Profits”_on_PPP_Loans,_Engaged_in_Fraud⠀⇛


                # ⚓ Michael West Media ☛ Sleeping_with_the_Enemy:_ASIC’s_case
                  against_National_Australia_Bank’s_adversary_hits_a_sex_snag_–
                  Michael_West⠀⇛


                       “Hi Babe, always enjoy our romps” is not the type
                       of evidence you’d expect in a corporate regulator’s
                       case against an advocate for bank victims. Callum
                       Foote explores ASIC’s curious prosecution of Geoff
                       Shannon of Unhappy Banking fame, a case which has
                       embroiled the National Australia Bank.


                # ⚓ Michael West Media ☛ Mining_lobby_tricks_government_with
                  its_big_taxpayer_fairytale,_swaps_Deloitte_for_EY_–_Michael
                  West⠀⇛


                       The Minerals Council of Australia has duped Energy
                       Minister Madeleine King into repeating its highly
                       inflated claims of how much taxes its mostly
                       foreign multinationals members pay. Callum Foote
                       reports on an $85 billion PR scam.


                       The Minister for Energy, Madeline King, has
                       repeated claims from mining lobby group, Minerals
                       Council of Australia, that the mining industry made
                       payments of $43.2 billion in company tax and
                       royalties to Australian governments in in a speech
                       given at the ​​NT Resources Week conference. The
                       figures were repeated on ABC Radio without
                       question.


                       As revealed here last year, Big Four consulting
                       firm Deloitte used to do the misleading report for
                       the mining lobby. This year it is another Big Four
                       firm, Ernst & Young. The EY report, has – like
                       Deloitte’s previous work – failed to disclose that
                       up to 60% of the tax that they claim the mining
                       industry pays is returned in the form of GST
                       refunds.


                # ⚓ Scheerpost ☛ Chris_Hedges:_Know_Thine_Enemy⠀⇛


                       The expedited legislation passed by Congress to
                       avert a strike by railroad unions dealt one more
                       blow in the decades long war waged by the two
                       ruling parties against the working class.


                # ⚓ Counter Punch ☛ Railway_Vote_Benefits_One_of_the_Least
                  Deserving_Industries⠀⇛


                # ⚓ Counter Punch ☛ US_Railroad_Workers_‘Under_the_Thumb’⠀⇛


                       Beginning last September, that intervention has
                       ensured that the workers would not be able to
                       strike in order to advance their interests and
                       demands. This past week both the administration and
                       Congress have made a railroad strike illegal by
                       passing legislation to that effect.


                       The right of workers to strike has been under
                       attack at least since 1947 when Congress passed
                       what was called the ‘Taft-Hartley’ Act that year.
                       That legislation ensured that government and
                       politicians reserved the right to force workers
                       back to work for 90 days in the event contract
                       negotiations failed and a strike was imminent.
                       During a 90 day ‘cooling off’ period, as it was
                       called, government mediators had the opportunity to
                       join the negotiations, try to browbeat the parties
                       to get them to settle, and to make a recommendation
                       as to the terms of a settlement. During the
                       ‘cooling off’ management of course also had 90 more
                       days to prepare to prepare to defeat a strike once
                       the 90 days was up.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Reformers_Win_Big_in_United_Auto_Workers_Election,_Reject
                  Entrenched_Leadership⠀⇛


                # ⚓ NPR ☛ Japan’s_Disney_store_sells_merchandise_of_Winnie_the
                  Pooh_supporting_China’s_protests⠀⇛


                       The products are created through Disney’s MADE
                       program, which the product descriptions call “D-
                       MADE” and allows people to customize their own
                       Disney merchandise. The collection includes
                       hoodies, shirts, tote bags and mugs.


                # ⚓ VOA News ☛ World_Cup_Host_Qatar_Seeks_to_Change_Minds_on
                  Islam⠀⇛


                       Social media posts have claimed that hundreds of
                       fans have changed faith but AFP’s fact-checking
                       service has shown those claims are fake.


                # ⚓ Scheerpost ☛ The_Twitter_Files⠀⇛


                       Journalist Matt Taibbi reported a massive scoop
                       regarding Twitter’s internal handling of the Hunter
                       Biden laptop story in a long Twitter thread on Dec.
                       2 after receiving documents from Elon Musk.


                # ⚓ Scheerpost ☛ Matt_Taibbi:_Munk_Debate_on_Mainstream_Media⠀⇛


                       Author Douglas Murray and Matt Taibbi take on
                       Malcolm Gladwell of the New Yorker, and Michelle
                       Goldberg of the New York Times.


                # ⚓ Michael West Media ☛ Rex_Patrick:_“exceptional
                  circumstances”_choke_National_Anti-Corruption_Commission_–
                  Michael_West⠀⇛


                       Labor may rue the day it mired the National Anti-
                       Corruption Commission (NACC) in secrecy.
                       Transparency warrior Rex Patrick reports on the
                       “exceptional circumstances” provision which weakens
                       corruption watchdog.


                       Having passed through the House of Representatives
                       last week, the Senate is set to debate and pass
                       Albanese’s National Anti-Corruption Commission
                       (NACC) legislation this week. It won’t be short
                       leashed, blind, toothless, limping corruption
                       watchdog


                # ⚓ Pro Publica ☛ Russia’s_Honorary_Consuls_Serve_Putin’s
                  Political_Agenda⠀⇛


                       BUDVA, Montenegro — Near a teeming town square
                       along the Adriatic coast, where ancient city walls
                       surround the ruins of bygone empires and shops and
                       churches rise over the sea, Russia’s newly
                       appointed representative to this tiny Balkan nation
                       opened his consulate office.


                       Boro Djukic, the first honorary consul named by
                       Russia in Montenegro, was supposed to use his
                       prestigious post to champion cultural ties and the
                       interests of local Russian business owners and
                       tourists — a benevolent bridge between the two
                       countries.


                # ⚓ Counter Punch ☛ Gallic_Rebuke:_France_and_the_US_Rules-
                  based_Order⠀⇛


                       Araud is very much the diplomat establishment
                       figure, having also served as French representative
                       to the United Nations from 2009 to 2014.  But
                       despite his pedigree, he was most keen to fire off
                       a few salvos against such concepts as the “rules-
                       based order” so treasured by the Anglosphere and
                       the “West” more broadly defined.  “To be frank,
                       I’ve always been extremely sceptical about this
                       idea of a ‘rules-based order’.”  Both he and the
                       French in general loved the United Nations, “but
                       the Americans not too much”.


                       With unerring frankness, he also noted that the UN
                       and broader international hierarchy was dominated
                       by the US-European bloc.  The undersecretaries to
                       the organisation reflected that fact, as did the
                       stewardship of the World Bank and the IMF.  “So
                       that’s the first element: this order is our order.”


                # ⚓ Counter Punch ☛ The_United_Nations_Promise_of_Peace_–_Also
                  In_Ukraine⠀⇛


                       It is not only the fault of the Security Council
                       and General Assembly, but also the fault of the
                       mainstream media that continues to disseminate dis-
                       information and pour fuel on the fire, the fault of
                       the war-profiteers worldwide, the fault of the
                       military-industrial-digital-financial complex that
                       drives the process and prevents a sensible
                       compromise to end hostilities.


                       Many are asking the question, what good is the
                       United Nations?  Who still believes in it? What
                       good is a Secretary-General who does not take the
                       bull by the horns, does not name a spade a space,
                       does not proactively propose implementable
                       blueprints for peace and mobilizes the entire UN
                       system in support of valid peace initiatives.


                # ⚓ TruthOut ☛ After_Dinner_With_Neo-Nazi_Nick_Fuentes,_Trump
                  2024_May_Be_Dead_on_Arrival⠀⇛


                # ⚓ Common Dreams ☛ GOP_Silence_on_Trump’s_Call_to_Axe
                  Constitution_Reveals_‘Full_Embrace_of_Fascism’:_House_Dem⠀⇛


                       Repeating his thoroughly disproven lie that the
                       2020 election was stolen, former President Donald
                       Trump called Saturday for discarding the U.S.
                       Constitution to overturn his loss.


                       In response, pro-democracy advocates argued that
                       Trump’s comments, other recent actions, and the
                       refusal of GOP lawmakers to denounce them are
                       reflective of the Republican Party’s growing
                       support for right-wing authoritarianism.


                # ⚓ Common Dreams ☛ Opinion_|_The_Republican_War_on_Democracy
                  Has_Spread_to_Ballot_Measures⠀⇛


                       In the aftermath of the 2022 midterm elections,
                       analysts are wondering why the seemingly inevitable
                       Republican wave did not materialize. As we sift
                       through the surprising results, there is a common
                       denominator among many of the progressive
                       victories: ballot measures. All five ballot
                       measures on abortion went for the pro-choice side,
                       as Republicans and independents joined Democrats to
                       expand and protect reproductive rights. In Nebraska
                       and Nevada, voters overwhelmingly voted to increase
                       their state’s minimum wage, even as Republicans won
                       big races in both states. And, South Dakota became
                       the most recent Republican-controlled state to pass
                       Medicaid expansion.


                # ⚓ Scheerpost ☛ US_Youth_Observe_Cuba’s_Elections—and_Learn
                  About_‘Real_Democracy’⠀⇛


                       A delegation of youth from the United States
                       observed Cuba’s November 2022 municipal elections
                       and offer an inside look into a true people’s
                       democracy, where workers decide who will govern
                       them, not wealthy oligarchs and corporations.


          o § Censorship/Free Speech⠀➾


                # ⚓ The Telegraph UK ☛ Indonesia_set_to_criminalise_sex_before
                  marriage_–_even_for_tourists⠀⇛


                       According to a draft seen by Reuters, insulting the
                       president, a charge that can only be reported by
                       the president, carries a maximum sentence of three
                       years in prison.


                # ⚓ The Economist ☛ Students_are_often_at_the_heart_of_protests
                  in_China⠀⇛


                       For the students, it is not all about draconian
                       lockdowns. Some are frustrated by a lack of
                       freedom. Young protesters, on campus and off, have
                       taken to holding up blank sheets of paper to
                       highlight China’s tight controls on expression. In
                       a more cerebral form of defiance, students at
                       Tsinghua held up the Friedmann equations. These are
                       formulae that describe the expansion of the
                       universe. “Friedmann” also happens to sound a lot
                       like “freed man”.


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


                # ⚓ TruthOut ☛ “Publishing_Is_Not_a_Crime”:_The_New_York_Times
                  Joins_the_Fight_to_Free_Assange⠀⇛


          o § Civil Rights/Policing⠀➾


                # ⚓ The Times Of Israel ☛ Iran_demolishes_family_home_of
                  climber_who_competed_without_a_hijab⠀⇛


                       Rekabi was later placed under house arrest and
                       according to reports, her brother was also detained
                       for a period of time. The BBC has cited unnamed
                       sources saying that her apology was forced.


                       Iran’s official judiciary news agency, Mizan, said
                       the destruction of the home was due to its
                       “unauthorized construction and use of land,” adding
                       that the demolition had taken place months before
                       Rekabi competed.


                # ⚓ VOA News ☛ Iran_Morality_Police_May_Have_Been_Shut_Down,
                  But_No_Official_Word⠀⇛


                       The actions of the morality police have been at the
                       center of more than two months of deadly protests
                       in the country after the death in mid-September of
                       Mahsa Amini, 22, while she held in their custody
                       after they detained her for allegedly not covering
                       her hair properly with a hijab.


                # ⚓ Outlook India ☛ Afghanistan:_Woman_Flogged_For_Going_To
                  Shop_Without_Male_Guardian⠀⇛


                       This is the Taliban brutally lashing a woman in
                       Takhar province for going to the shop without a
                       male guardian.


                # ⚓ [Old] BBC ☛ Qatar_World_Cup:_Families_seek_answers_over
                  migrant_worker_deaths⠀⇛


                       Qatar has transformed its infrastructure in the run
                       up to the World Cup, which starts on Sunday.
                       Millions of people from South Asia have been
                       employed on building projects, including from Nepal
                       – where families have told the BBC safety failures
                       led to the death of their loved ones.


                # ⚓ NBC ☛ Colorado_grandmother_sues_police_detective_following
                  SWAT_raid_based_on_false_‘Find_my_iPhone’_ping⠀⇛


                       The complaint contends that Staab’s affidavit
                       violated Johnson’s right, afforded by the state
                       constitution, to “be free of unreasonable searches
                       and seizures.” The affidavit allegedly “lacked
                       probable cause that evidence of crime could be
                       found” at Johnson’s home, since it was based on an
                       unverified and vague ping by Apple’s “Find My” app,
                       which is used to track Apple devices.


                # ⚓ Counter Punch ☛ Oy_Ye⠀⇛


                       It’s empirically true that Jews are
                       disproportionately represented in Hollywood. The
                       question that matters is what this implies. Dave
                       Chappelle was right to note that there are also
                       plenty of Black people in Ferguson, although
                       Hollywood is above all an industry not a location.
                       Yet even assuming that Jewish people
                       disproportionately control Hollywood —
                       notwithstanding invariable Jewish gofers and the
                       otherwise kicked upon (Harvey Weinstein surely
                       didn’t rape only gentiles and Woody Allen knows
                       full well that abuse starts at home) — what
                       does this imply?


                       An antisemite – that is, an anti-Jew — starts and
                       stops with identity, as for him the Jew by nature
                       connives with his brethren to exploit others, and
                       Jewish dominance of Hollywood is therefore a mere
                       means to an end. If only the moguls could be
                       replaced with Christians, the antisemite implies,
                       Hollywood would be fairer, less profit-hungry, and
                       less exploitative.


                # ⚓ Counter Punch ☛ Labor’s_Weakness⠀⇛


                       The history of the United States includes many,
                       many federal interventions into strikes, boycotts
                       and other labor actions, especially since the
                       industrialization of the nation began in earnest
                       after the Civil War. Given the importance of the
                       railroads to this capitalist episode that not only
                       saw intense industrialization but also an increased
                       concentration of wealth, power and control of the
                       national economy in the hands of a few families,
                       railroad workers experienced this quite intensely.
                       Indeed, two national railroad strikes–in 1877 and
                       1894–were brutally crushed by US troops and private
                       security groups. Furthermore, the executive branch
                       was the branch that ordered these actions. In 1926,
                       the federal government enacted a law that gave the
                       government permission to intervene before a
                       railroad strike occurred. Like it gave Truman in
                       1950 and Bush in 1991 the power to act, this is the
                       law that informs the current action by the feds.


                       In light of the recent intervention, it seems like
                       a good time to revisit a few realities about labor
                       unions in the United States. Despite the recent
                       upsurge in organizing activity in workplaces like
                       Amazon, Starbucks and Chipotle, the truth is that
                       most (and I mean most) workers in the United States
                       are neither organized or even close to such a move.
                       This is due to many factors, but the two that I
                       consider most important are the federal and state
                       laws that make union organizing very difficult and
                       the lackadaisical effort that the major unions put
                       into organizing unorganized workers. As someone who
                       is just finishing up an almost two-year stint as
                       president of my local, I can verify that the
                       pressure to sign up new workers and organize the
                       unorganized came more from our state AFL-CIO office
                       than through any utterances or funding by the
                       national and international of the union or AFL-CIO.
                       Fortunately, Vermont is currently home to what is
                       perhaps the most radical and democratic AFL-CIO
                       Labor Council in the United States. This has meant
                       that the Council spends money, time and energy on
                       organizing unorganized workers.


                # ⚓ Common Dreams ☛ Opinion_|_Service_Workers_in_the_US_South
                  Get_New_Union⠀⇛


                       Within minutes of the formation of the Union of
                       Southern Service Workers (USSW) earlier this month,
                       Quadtrell Adams lay helpless on the walkway outside
                       the Levi C. Chavous Conference Center in Columbia,
                       South Carolina. Moments earlier, Adams had stumbled
                       from the building upon sensing the onset of a
                       seizure likely triggered by the flash of cameras
                       and the carnival of shout and song inside. Having
                       assisted Adams through previous episodes, fellow
                       union members went into action. Russell Smalls, a
                       convenience store employee, rubbed his friend’s
                       chest with turquoise stones, while others spoke to
                       Adams softly and watched over him until his fits
                       had passed.


                # ⚓ Common Dreams ☛ ‘Intentional_Vandalism’_Leaves_Thousands
                  Without_Power_in_North_Carolina⠀⇛


                       Officials in a North Carolina county where more
                       than 40,000 households remain without power amid
                       freezing temperatures declared a state of emergency
                       on Sunday afternoon, less than 24 hours after
                       multiple electrical substations were damaged by
                       gunfire in an apparent act of criminal vandalism.


                       “As utility companies began responding to the
                       different substations, evidence was discovered that
                       indicated that intentional vandalism had occurred
                       at multiple sites,” Moore County Sheriff Ronnie
                       Fields said in a statement. The massive blackout,
                       which began just after 7:00 pm Saturday night, is
                       “being investigated as a criminal occurrence.” No
                       arrests have been announced.


                # ⚓ Common Dreams ☛ Opinion_|_The_Grassroots_Are_Growing—And
                  Reimagining_What’s_Possible⠀⇛


                       Ten years ago, two hundred New York City low-wage
                       workers walked off their jobs at McDonald’s, Burger
                       King, and other fast-food restaurants to demand
                       what most observers thought impossible: 15 bucks an
                       hour and a union.


                # ⚓ The_Expansive_Horizons_of_Antifascism:_Interview_With
                  Editor_Shane_Burley⠀⇛


                # ⚓ Common Dreams ☛ Opinion_|_Why_Our_Movements_Need_to_Start
                  Singing_Again⠀⇛


                       Social movements are stronger when they sing.
                       That’s a lesson that has been amply demonstrated
                       throughout history, and it’s one that I have
                       learned personally in working to develop trainings
                       for activists over the past decade and a half. In
                       Momentum, a training program that I co-founded and
                       that many other trainers and organizers have built
                       over the last seven years, song culture is not
                       something we included at the start. And yet, it has
                       since become so indispensable that the trainers I
                       know would never imagine doing without it again.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ Bryan Lunduke ☛ Pondering_on_Mastodon_and_the_Fediverse_–
                  by_Bryan_Lunduke⠀⇛


                       With so many people jumping from Twitter to
                       Mastodon, let’s take a moment to talk about some of
                       the downsides (and upsides) of Mastodon… and the
                       Fediverse in general. Along with some of my, rather
                       bizarre, history with it.


          o § Monopolies⠀➾


                # § Copyrights⠀➾


                      # ⚓ Torrent Freak ☛ Company_‘Hijacks’_Blender’s_CC_BY-
                        Licensed_Film,_YouTube_Strikes_User⠀⇛


                             Blender releases its films under Creative
                             Commons licenses because it wants them to be
                             shared, remixed, and reshared. Bruno
                             Fernandez-Ruiz is the co-founder of an AI
                             driver safety company and a film music
                             composer and producer. When a TV channel in
                             Uzbekistan claimed ownership of a Blender
                             film, YouTube gave Ruiz a copyright strike
                             and rejected every appeal.


                      # ⚓ Torrent Freak ☛ New_Pirate_Site_Blocking_Law_Allows
                        Intermediaries_To_File_Complaints⠀⇛


                             Site-blocking is now so commonplace that when
                             yet another country adds itself to the list
                             of participants, barely an eyebrow is raised
                             in opposition. DNS interference is already in
                             place so if that’s met with a shrug, why
                             should anyone care about Uruguay’s new site-
                             blocking law? Operators of TV services and
                             intermediaries, despite not being copyright
                             holders themselves, can now apply for
                             blocking measures, actionable within four
                             days.


    * § Gemini* and Gopher⠀➾


          o § Personal⠀➾


                # ⚓ Late_to_the_party⠀⇛


                       I’ve been blogging for 23 years as of today. This
                       is also the first day this blog is being served up
                       via `https:`. All I had to do was *just* install
                       the latest version of Apache on my server [1].


                       It took several days, but I got the latest version
                       of Apache compiled and installed on my server. Yes,
                       I did it the hard way. What better way of knowing
                       how things work than doing it the hard way. I then
                       spent Saturday updating the configuration. There
                       were a few changes, like `NameVirtualHost [2]`
                       being deprecated, and having to add “`Protocols [3]
                       h2 h2c http/1.1`” and “`Require [4] all granted`”.


          o § Technical⠀➾


                # ⚓ Trying_to_do_more_with_less⠀⇛


                       There was a time where I obsessively followed
                       roadmaps, extrapolated SPEC results, and tried to
                       get my hands on the latest electronic toys (or even
                       pre-release samples of them.) There’s a certain
                       appeal, after all, to “this is the latest and best”
                       – CPUs, phones, core IP, laptops, whatever.


                       Capital likes to see this. They also put
                       significant effort into making it seem “clean” –
                       that the resource extraction, labor exploitation,
                       and e-waste dumping are distant and easy to ignore.
                       The tame tech media often participates in this. In
                       late November, workers at Hon Hai’s plant in
                       Shenzhen – who, due to the PRC’s harsh zero-COVID
                       policies, are required to live at their jobsite –
                       protested against living and working conditions,
                       including a COVID outbreak inside of the bubble.
                       The protest was violently put down by police. The
                       tech media duly noted it, but only for a moment –
                       soon it was forgotten, and a return to breathless
                       speculation about Apple’s incoming AR/VR headset
                       and the performance characteristics of the M2 Max
                       resumed.


                # § Science⠀➾


                      # ⚓ uni MIT ☛ Breaking_the_scaling_limits_of_analog
                        computing⠀⇛


                             New technique could diminish errors that
                             hamper the performance of super-fast analog
                             optical neural networks.


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


╘══════════════════════════════════════════════════════════════════════════════╛
                       ¶ Lines in total: 6515
    ➮ Generation completed at 02:42, i.e. 69 seconds to (re)generate ⟲