𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Friday, August 05, 2022
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Generated Sat 6 Aug 02:40:22 BST 2022
Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖)
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Gemini index for the day: gemini://gemini.techrights.org/2022/08/05/


╒═══════════════════ 𝐑𝐄𝐂𝐄𝐍𝐓 𝐁𝐔𝐋𝐋𝐄𝐓𝐈𝐍𝐒 ════════════════════════════════════╕
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╒═══════════════════ 𝐈𝐍𝐃𝐄𝐗 ═══════════════════════════════════════════════════╕

⦿ António Campinos Once Again Failing to Obey Court Orders, Making Up Ludicrous Excuses for Non-Compliance | Techrights

⦿ Tux Machines is Now on Gemini and Techrights’ Gemini Capsule Restored After Outage That Killed the Whole System (Again) | Techrights

⦿ IRC Proceedings: Thursday, August 04, 2022 | Techrights

⦿ Asia Has Already Left Windows Behind | Techrights

⦿ LinuxToday (or Linux Today) Shows Signs of Agony | Techrights

⦿ [Meme] Dignity of Criminals | Techrights

⦿ Recruitment Potential at the EPO Has Never Been Worse | Techrights

⦿ [Meme] Criminals Have Feelings Too... | Techrights

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
		http://techrights.org/2022/08/05/epo-cant-obey-court-orders/#comments
		http://techrights.org/2022/08/05/gemini-capsule-restored/#comments
		http://techrights.org/2022/08/05/irc-log-040822/#comments
		http://techrights.org/2022/08/05/leaving-windows-behind/#comments
		http://techrights.org/2022/08/05/linuxtoday-sells-webspam/#comments
		http://techrights.org/2022/08/05/privacy-for-criminals/#comments
		http://techrights.org/2022/08/05/recruitment-epo-catastrophe/#comments
		http://techrights.org/2022/08/05/the-dignity-of-criminals/#comments

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
		http://techrights.org/2022/08/05/gnu-binutils-2-39/#comments
		http://techrights.org/2022/08/05/kio-admin/#comments
		http://techrights.org/2022/08/05/mageia-9-wants-artwork/#comments

                    ䷩ 𝚕𝚒𝚗𝚎 70

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/08/05/epo-cant-obey-court-orders/#comments
    Gemini version at gemini://gemini.techrights.org/2022/08/05/epo-cant-obey-court-orders/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 08.05.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ António_Campinos_Once_Again_Failing_to_Obey_Court_Orders,_Making_Up_Ludicrous
Excuses_for_Non-Compliance⠀✐


Posted in Europe, Patents at 10:38 am by Dr. Roy Schestowitz


Video_download_link | md5sum af31b6449352c52b10e23b8797df9886
ILOAT Judgments Ignored by EPO
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/epo-not-obeying-courts-again.webm


Summary: The absurdity of this situation is bare and completely naked for all
to see, as once again the EPO refuses to obey very explicit, unequivocal court
orders, which are nearly a decade overdue. Today’s EPO seems to have been taken
over by crime lords, or an embodiment of nepotism brought to us by the
Frenchman Campinos and his enablers from Alicante.


THE EPO‘s dictator António_Campinos (his father would hate him with a passion
if he was still alive) is once again proving to be no better — perhaps even
worse — than Benoît_Battistelli.


How predictable this was!


“So the EPO’s management, which shamelessly violates the privacy of workers and
applicants, now uses “privacy” as an excuse to not obey to law and to impede
freedom of expression!”Last month we repeatedly said that complying with
Judgment_No._4551 (ILOAT) should take no longer than a few minutes! Almost a
month has passed and guess what… no action taken!


What is Campinos waiting for? Well, he wants to go on holiday and merely
“discuss” the matter after frying himself in the Mediterranean for a few weeks
(no, not Portugal; he might as well vacation in his_true_homeland,_France).


The EPO has said nothing about ILO or ILOAT rulings against the EPO. Not a
word. No statement at all in over a week already, just this_site_update
(warning: epo.org link) which states: “Central Fee Payment will be fully
deployed and Online Fee Payment decommissioned on 10 September 2022.”


The Central Staff Committee (CSC) has meanwhile revealed a very belated message
(it took him over a fortnight to respond!) from “the f***ing president” (this
is how Campinos refers to himself in official meetings). To quote the
ridiculous excuses (using “privacy”, which Campinos_grossly_violates, as a
straw man):


     European Patent Office | 80298 MUNICH | GERMANY
     Chair of the Central Staff Committee


     Via mail only to: centralstcom@epo.org


     [...]


     president@epo.org
     Date: 22.07.2022


     Implementation of J. No. 4551


     Dear Mr Chair,


     Reference is made to your letter of 7 July concerning Judgment No.
     4551 delivered by the Tribunal in its 134th session concerning the
     use of mass e-mails within the Office as it resulted from the
     Communiqué of 31 May 2013.


     As expressed in my letter of 22 April 2020 and in discussions in
     different fora, in particular the WG on Resources & Communication,
     the Office has meanwhile strived to facilitate open communication,
     including through mass e-mails, between staff and their
     representatives. To this end, in addition to the pilot allowing
     invitations to general assemblies, a number of mass e-mails has also
     been allowed for specific purposes and an expanded right to mass e-
     mails was contemplated in the draft agreement on means of
     communication shared with you.


     The aforementioned Judgment No. 4551 now broadens the possibility to
     send mass e-mails. While the Office is committed to implementing the
     Tribunal’s orders in full, it also needs to ensure compliance with
     the new Data Protection Rules in force since 1 January 2022.


     At the moment, the Office is clarifying technical aspects with BIT
     and discussing data protection related aspects with the Data
     Protection Office and the Data Protection Board. These notably
     include the need for a further data protection statement and the
     possibility for staff to unsubscribe from the mailing list as well as
     the setting up of an ethics board comprising members appointed by the
     staff representation and the Office.


     We will keep you updated on the developments and set up a meeting
     after the upcoming summer break.


     Yours sincerely,
     António Campinos


     cc:
     LSC Berlin (via mail only to: lscbe@epo.org)
     LSC Munich (via mail only to: msc@epo.org)
     LSC The Hague (via mail only to: dhstcom@epo.org)
     LSC Vienna (via mail only to: pvwien@epo.org)


So the EPO’s management, which shamelessly violates the privacy of workers and
applicants, now uses “privacy” as an excuse to not obey to law and to impede
freedom of expression! incredible! Welcome to Lukashenko's_second_home…


In an open letter the CSC responded firmly (within limits given the
authoritarian nature of Team Campinos). “ILOAT Judgment 4551 on mass emails –
We demand its immediate execution,” said the title, informing colleagues that “
[i]n Judgment_No._4551 the Tribunal has, as of 6 July 2022, set aside in part
the Communiqué of 31 May 2013 and reinstated the former rules on mass emails as
published in Communiqué No. 10 and in the announcement of 28 December 2011.
Therefore, the limitation to 50 addressees has been set aside and Staff
Committee members have the possibility of addressing all staff in the context
of their statutory and official activities. In a reply letter of 22 July 2022,
the President of the Office states that time is needed to clarify technical
aspects and proposes that a meeting be scheduled after the summer break. As
explained in this open letter, we see no legal or technical requirements
preventing the immediate execution of the judgment. Therefore, we demand its
immediate execution.”


Here’s the response dated a week ago and discussed a little further in the
video above:


     European Patent Office | 80298 MUNICH | GERMANY


     Mr António Campinos
     President of the EPO


     By email


     OPEN LETTER


     [...]


     centralSTCOM@epo.org
     Reference: sc22109cl
     Date: 28/07/2022


     Execution of ILOAT Judgment No. 4551 (mass emails)


     Dear Mr President,


     In Judgment No. 4551 the Tribunal has, as of 6 July 2022, set aside
     in part the Communiqué of 31 May 2013 and reinstated the former rules
     on mass emails as published in Communiqué No. 10 and in the
     announcement of 28 December 2011. Therefore, the limitation to 50
     addressees has been set aside and CSC members have the possibility of
     addressing staff Office-wide in the context of their statutory and
     official activities. Similarly, LSC members have the possibility of
     addressing staff in their respective site by mass emails.


     We note that Staff Committees and their members still cannot
     technically send an email to more than 50 addresses and are not
     authorised to use the mailing lists DDL-ALL-STAFF(-XX) which already
     exist. Granting authorisation is technically a matter of seconds for
     BIT. It is also a necessity for any Staff Committee (member) “for the
     execution of [their] official business”, as recited in Article 2 of
     Communiqué No. 10.


     In your letter of 22 July 2022, you state that the Office is
     clarifying technical aspects which notably include “the possibility
     for staff to unsubscribe from the mailing list” and “the need for a
     further data protection statement”.


     Firstly, in considerations 10 and 11, the Tribunal held that emails
     fulfilling the criteria of Communiqué No. 10 and the announcement of
     28 December 2011 “shall be considered lawful” and ensure a reasonable
     balance between the interests of the organisation and the fundamental
     rights to free communication, information, and speech. Therefore,
     executing the judgment “as ruled” means restoring the status quo ante
     prior to 31 May 2013, at which time there was no need for a Staff
     Committee to ensure that staff can unsubscribe from the official
     mailing list. In consideration 10, the Tribunal further recalled that
     freedom of communication implies the right to freely choose the means
     by which the communications are sent. Imposing additional constraints
     (such as a possibility to unsubscribe) upon Staff Committees and
     their members would go against the ruling of the Tribunal, in
     particular the necessity for a body representing the staff to be able
     to circulate emails to all staff members, as recalled in
     consideration 12.


     Secondly, the judgment restored access to the EPO’s electronic
     (email) communications systems, whereby a Staff Committee does not
     need (or intend) to collect, store or process any personal data.
     Therefore, we do not see the need for any data protection statement.


     Finally, in consideration 11, the Tribunal considered that the mass
     emails sent by the staff representation and provided by the parties
     in the present case “did not exceed the limits to freedom of opinion
     and speech, and therefore did not justify a mechanism of a prior
     authorisation”. In this respect, there is no justification derivable
     from Judgment 4551 for the setting up of an Ethics Board prior to the
     execution of the judgment.


     In your letter you explain that time is needed and that a meeting
     will be scheduled after the upcoming summer break. As explained
     above, we see no legal or technical requirements preventing the
     immediate execution of the judgment.


     Consequently, we demand the immediate execution of the judgment.


     Yours sincerely,
     Alain Dumont
     Chairman of the Central Staff Committee


It has been rather telling. This past month Campinos carried with on the
tradition of obstructing justice and finding excuse to not obey ruling, or
barely obeying them (usually optics and PR, not real actions). Later they
wonder why people no_longer_want_to_work_for_the_EPO… █



                    ䷩ 𝚕𝚒𝚗𝚎 336

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/08/05/gemini-capsule-restored/#comments
    Gemini version at gemini://gemini.techrights.org/2022/08/05/gemini-capsule-restored/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 08.05.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Tux_Machines_is_Now_on_Gemini_and_Techrights’_Gemini_Capsule_Restored_After
Outage_That_Killed_the_Whole_System_(Again)⠀✐


Posted in Site_News at 7:00 am by Dr. Roy Schestowitz


Video_download_link | md5sum 3edc7e8034ec8a96a4be17156946a27e
More Migrations and Upgrades
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/power-outage-and-migrations.webm


Summary: We’re moving to lighter and simpler systems that are easier to
maintain (Alpine, Gemini, static pages); we’ve meanwhile faced a major obstacle
due to the whole neighbourhood here losing power


THE past week has been tough due to a couple of incidents, which are likely
related to one another, as explained in the video above. The lesson of the
story is, do not use (micro)SD cards for storage of servers, especially not for
something like a full base system (like a whole operating system).


“Moving from database-driven page delivery to static site generators seems to
be all the rage these days and we’re crafting our own.”For the Gemini capsule
of this site, we’re starting the system afresh on new storage for the third
time in less than 2 years! We rebuild everything for the second time this year
and it’s only August.


The other part of the video shows that the new CMS is coming along nicely. It’s
already used on a test site of Tux Machines and after further maturity (it’s
considered alpha quality for now) we’ll deploy the same sort of thing or
something very similar in Techrights. Moving from database-driven page delivery
to static site generators seems to be all the rage these days and we’re
crafting our own. Our webhost has just moved_from_WordPress_to_Hugo (hours
ago). █



                    ䷩ 𝚕𝚒𝚗𝚎 392

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/08/05/irc-log-040822/#comments
    Gemini version at gemini://gemini.techrights.org/2022/08/05/irc-log-040822/

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Gemini_version_available_♊︎


✐ IRC_Proceedings:_Thursday,_August_04,_2022⠀✐


Posted in IRC_Logs at 2:54 am by Needs Sunlight


Also available via the Gemini protocol at:


    * gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-040822.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-040822.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-social-040822.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-040822.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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈


§ Bulletin for Yesterday⠀➾


Local_copy | CID (IPFS):



                    ䷩ 𝚕𝚒𝚗𝚎 465

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/08/05/leaving-windows-behind/#comments
    Gemini version at gemini://gemini.techrights.org/2022/08/05/leaving-windows-behind/

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Gemini_version_available_♊︎


✐ Asia_Has_Already_Left_Windows_Behind⠀✐


Posted in GNU/Linux, Google, Microsoft, Windows at 5:00 am by Dr. Roy
Schestowitz


  🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Android_passes_Windows_6.5_years_ago;_Android_share_2.5
                                times_bigger⦈_
                              Source: StatCounter


Summary: Android (Linux-powered) is leaving Windows in the gutter; it’s hardly
shocking that the_criminals_who_run_Microsoft_try_to_prevent_Linux_from_even
booting_on_new_laptops


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡇⠀⠀⠴⠀⠀⠂⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠒⠀⠀⠤⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠶⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠆⠀⠠⠒⠖
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡇⠀⠀⣀⡀⠀⠀⡘⠀⠀⠁⠈⠂⠆⠁⢐⡀⠀⠀⠀⠀⠀⠀⠀⠁⢈⠀⠀⠈⠀⠀⠠⡁⡀⠀⠈⠀⢰⠈⠀⡂⠀⠀⢸⠀⠐⠀⠀⠈⢀⠁⠀⠀⠁⡨⠀⢌⢀⠀⡃⡁⢄⡀⠀⠀⠀⠀⠁⠱⠀⠀⠊⡀⠂⠈
⠀⠀⠀⡇⠀⢀⣀⡸⠀⠰⠀⠀⠀⣀⣀⠆⠈⠅⠀⡸⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⣀⡀⠀⠨⡀⡸⠀⠀⠀⠀⠡⠀⣀⠇⠀⢸⠀⠀⠀⠀⢀⢀⠀⢀⠀⡀⡈⠀⢅⢀⠇⠈⠌⢀⡐⠀⠀⠀⢀⣔⣀⠀⠀⢆⣀⠄⣠
⠀⠀⠀⡇⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⡀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠀⠘⠀⠐⠀⠃⠈⠁⠠⠈⠀⠆⠐⠃⠈⠃⠘⠀⠐⠀⠐⠃⠛⠀⠘⠀⠑⠃⠀⠃⠐⠀⠘⠃⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣏⡟⣻⢿⣿⣻⣟⣿⣻⢿⣻⣿⣟⣟⡿⣟⣿⣿⡿⣿⢿⢿⣻⣻⣻⢟⡿⡟⣟⣻⣻⣿⣏⣿⢯⣿⣟⣿⣿⣿⢟⣟⣟⡏⣿⣿⡹⣿⣟⣟⣿⣟⣿⣿⣟⣟⣿⣿⣫⢿⢻⣻⢻⣻⣻⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣧⡇⣟⣼⣝⣻⣿⣯⣻⣼⣝⣿⣿⣿⣟⣶⢻⣿⣛⣿⣞⣿⣓⣽⣿⣾⣻⣧⣿⣿⣿⣿⣿⣮⣿⣯⣻⣿⣿⣷⣮⣿⣻⣧⣻⣿⣟⣧⣿⣿⣧⣻⣿⣿⣿⣻⣿⣯⣿⣾⣟⣾⣼⣞⣽⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢿⣻⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣿⣽⣿⣿⣽⣾⣿⣧⣿⣯⣾⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣯⣭⣭⣽⣟⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣝⣛⣛⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣽⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⣛⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/08/05/linuxtoday-sells-webspam/#comments
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Gemini_version_available_♊︎


✐ LinuxToday_(or_Linux_Today)_Shows_Signs_of_Agony⠀✐


Posted in GNU/Linux, Marketing at 7:11 pm by Dr. Roy Schestowitz


Video_download_link | md5sum d80a09b7cf13e087fc328f2095e8c689
Trouble in LinuxToday?
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/linux-today-spam.webm


Summary: The Web site LinuxToday.com is pushing webspam instead of news picks;
it also sells data about visitors (the typical “We value your privacy” lie), so
it seems like “monetisation” tactics have taken precedence/priority over
readers (or what’s left of them anyway; the webspam inevitably drives more of
them away)


THE WEB site ‘Linux Today’ has been around for several decades. It’s one of the
first of its kind and lately it has been pushing_webspam instead of actual
stories. This is a familiar pattern, reminiscent of an “exit strategy” or an
attempt to “monetise” remaining readers on one’s way out.


“The World Wide Web is in a bad state, but Web sites resorting to webspam,
misinformation, and pure marketing would only accelerate the Web’s doom rather
than salvage it with some alternative “business models”…”The video above goes
through some of the latest “news” picks and shows that ZDNet‘s sister sites, as
well as ZDNet, probably face an existential crisis themselves. ZDNet, for
instance, used to cover “Linux” (usually anti-Linux pieces) about 3 times per
day and now it’s like 0.5 per day.


The World Wide Web is in a bad state, but Web sites resorting to webspam,
misinformation, and pure marketing would only accelerate the Web’s doom rather
than salvage it with some alternative “business models”… █


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


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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢋⠙⢙⡟⠽⠽⠭⢽⢽⡯⠿⠽⠽⣯⣿⠽⢽⠿⠽⠽⠽⠯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣧⣌⣉⣏⣩⣁⣟⣍⣹⣩⣙⣟⣯⣻⣟⣏⣯⣉⣉⣏⣩⣁⣜⣹⣉⣩⣋⣍⣉⣏⣁⣫⣿⣏⣉⣝⣉⣟⣭⣏⣻⣫⣉⣍⣋⣿⣙⣫⣣⣿⣉⣻⣋⣙⣍⣈⣍⣏⣹⣁⣏⣽⣫⣋⣍⣹⣙⣉⣍⣍⣉⣉⣏⣈⣛⣙⣿
⣿⡟⠻⡻⠙⡟⠛⡿⣻⠛⠻⡛⣟⠟⠛⠻⠙⢛⡛⡟⢻⠋⡟⠛⠛⠻⠟⠛⢹⠛⠙⣻⣟⠛⢛⠛⢻⠛⠛⢻⠙⢛⡟⡟⠙⡛⠻⠛⣏⠟⡟⠛⣻⠛⢛⠛⠙⠛⠛⣿⠛⠙⡟⠛⠻⡟⠿⣻⠛⢻⡻⡟⠻⡿⠛⠻⣿⣿
⣿⡿⠿⢿⠿⠿⣿⠿⠿⡿⠿⡿⠿⠿⠿⡿⢿⡿⠿⠟⡿⠿⠟⠿⠿⠿⢿⢿⠿⢿⠿⠿⣿⠿⢿⠿⠿⢻⡿⢿⡿⢿⠿⠿⠿⠿⠿⢿⠿⠿⢻⠿⠿⠿⡿⠿⡿⠿⠿⡿⡿⠿⢿⡿⠟⠟⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣶⣿⣶⣾⣿⣶⣶⣷⣶⣶⣷⣶⢶⣿⣶⣷⣾⣶⣷⣶⣶⣷⣶⣾⣾⣾⣷⣶⣾⣶⣿⣶⣾⣿⣷⣾⣶⣶⣷⣾⣶⣾⢷⣷⣶⣾⣶⢶⣾⣶⣶⡿⣾⣷⣷⣶⣶⣾⣶⣶⣶⣷⣿⢶⣾⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣧⣤⣶⣿⣤⣥⣤⣴⣧⣤⣼⣬⣧⣼⣵⣥⣧⣤⣼⣤⣤⣦⣧⣤⣴⣼⣵⣤⣼⣥⣦⣤⣤⣼⣦⣤⣴⣤⣬⣤⣬⣴⣧⣤⣬⣼⣬⣦⣼⣦⣤⣦⣤⣬⣤⣴⣤⣼⣼⣤⣤⣬⣶⣧⣤⣦⣬⣤⣧⣤⣬⣦⣤⣧⣬⣿⣿
⣿⣿⣍⣙⣏⣉⣉⣻⣙⣉⣉⣏⣻⣉⣩⣍⣉⣭⣹⣙⣏⣙⣩⣏⣉⣁⣏⣉⣽⣉⣉⣉⣉⣽⣹⣏⣩⣉⣉⣉⣉⣉⢹⣏⣙⣏⣉⣩⣉⣉⣍⣁⣏⣉⣉⣋⣙⣯⣻⣉⣉⣉⣉⣩⣁⣹⣭⣩⣻⣉⣉⣍⣏⣋⣉⣉⣉⣿
⣿⡟⠛⢛⡟⡟⠛⡻⠛⠛⠋⡟⡛⠛⣛⡻⠛⡟⠛⡟⢟⠋⡟⢛⠛⣻⠛⢻⠟⠛⢛⡟⠛⠋⢛⡛⢛⠛⠛⢻⠛⠋⠛⡛⡟⠛⢛⠛⠛⡛⢛⠛⡟⢛⡟⢻⠛⣛⠟⠛⡟⠛⣛⠛⢻⡛⢛⡟⣿⢛⠛⠟⠻⢻⠛⢛⡟⣿
⣿⡿⠿⢿⡿⠿⡿⠿⢿⠿⠿⠿⠿⠿⠿⠿⡿⠿⣿⠿⠿⢿⠿⠿⢿⠿⠾⢿⠿⠿⡿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⠿⡿⠿⢿⢿⠿⠿⠿⡿⠿⢷⡿⠿⢿⡿⢿⢿⠿⠿⠿⡿⢿⠿⠿⢿⠿⢷⢿⠿⠿⠿⡿⢿⠿⡿⠿⢿
⣿⣷⣶⣶⣷⣶⣿⣶⣾⣶⣶⣶⣶⣶⣶⣦⣷⣶⣷⣶⣶⣿⣶⣶⣶⣶⣶⣾⣶⣶⣶⣷⣶⣾⣾⣷⣶⣿⣾⣶⣶⣷⣯⣷⣶⣾⣶⣶⣶⣶⣶⣾⣷⣶⣾⣶⣶⣾⣷⣶⣷⣷⣾⣷⣴⣾⣷⣾⣶⣦⣾⣶⣷⣾⣶⣶⣶⣾
⣿⣇⣤⣤⣤⣤⣥⣴⣅⣿⣶⣦⣤⣇⣴⣤⣤⣤⣶⣥⣴⣼⣬⣤⣧⣤⣤⣌⣧⣤⣷⣦⣼⣦⣦⣤⣬⣤⣼⣦⣤⣽⣷⣧⣤⣧⣥⣤⣧⣤⣬⣦⣠⣾⣥⣬⣿⣤⣤⣤⣤⣥⣤⣤⣤⣯⣤⣧⣵⣢⣧⣤⣤⣧⣄⣾⣿⣿
⣿⣏⣉⣉⣩⣍⣉⢽⣉⣹⣭⣉⣯⣉⣋⣏⣩⣟⣉⣉⣯⣙⣹⢉⣭⣉⣫⢩⣯⣉⣙⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 630

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/08/05/privacy-for-criminals/#comments
    Gemini version at gemini://gemini.techrights.org/2022/08/05/privacy-for-criminals/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 08.05.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_Dignity_of_Criminals⠀✐


Posted in Europe, Patents at 11:04 am by Dr. Roy Schestowitz


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Repeat after me:  talking about our crimes is privacy
                                  violation⦈
            This is the EPO when instructed_to_stop_gagging_people


Summary: Benoît_Battistelli and António_Campinos have turned the EPO into s**t;
two men, one crêpe


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠛⠛⠛⠛⣴⣿⣿⣿⠿⠛⠋⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠐⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⠶⠒⠊⠡⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⢀⡀⡀⢀⣄⣸⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣠⣾⣿⣿⠆⡰⠀⠸⠸⡄⠄⠃⠘⠆⢶⠯⡨⢿⢱⢾⠶⠇⠂⠽⠿⢈⠡⠀⠀⠯⣿⣿⣦⡀⠀⠀⠀⠈⠁⠹⣿⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠁⠀⠀⠀⠀⢀⢀⡀⢔⣠⠶⠲
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⣿⢿⡿⢿⢿⢿⢿⢿⢿⡿⣿⠿⡿⡿⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣶⣴⣤⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⣠⣴⣴⣶⣶⣶⣶⣶⣦⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣚⣈⣈⣋⣱⣙⣘⣦⣤⣃⣞⣄⣁⣢⣜⣵⣘⣜⣸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀⣀⣠⣤⣴⣶⣶⣾⣿⣯⠭⢙⠛⣩⠽⣋⣽⠉⣿⡍⣋⠭⣭⡭⢛⣛⡻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⢏⢹⢻⠙⣽⢹⠝⡊⢏⢏⠋⡍⡫⠝⣽⢻⡙⣽⣿⣿⣿⣿⣿⣿⣿⡿⠁⣰⣿⣿⣿⣿⠿⢟⣛⣭⣵⣶⣶⣭⢑⣀⠜⠻⡜⠸⠈⠞⢛⣉⣢⣬⣛⠿⣿⣿⣷⣶⣾⣭⣽⣛⣻⠿⠿⣿⣿⣿
⠈⢿⣿⣿⣿⣿⢛⢛⠛⡟⡛⢟⠟⡿⣛⠻⣻⢛⢛⠻⣛⡟⣻⠟⣟⠛⢚⢟⢻⠻⢻⣿⣿⣿⠟⠁⠴⢟⣛⣭⣵⣶⣿⣿⣿⣿⣿⣿⢟⣵⣿⣿⣿⣷⣦⢀⣶⢻⣿⣿⣿⣿⣿⣿⣶⣯⣟⡿⢿⣿⣿⣿⣿⣿⣿⣷⣾⣿
⣧⡀⠙⠿⣿⣿⣴⣧⣦⣥⣧⣮⣦⣧⣽⣥⣿⣧⣧⣧⣵⣥⣭⣦⣯⣼⣼⣬⣦⣧⣾⣿⠟⠁⣀⢈⠩⠿⠻⡿⢿⣿⣿⣿⣿⣿⢟⣵⣿⣿⣿⣿⣿⣿⣿⢸⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣽⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣄⡈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣤⣾⣿⣿⣺⣷⣷⣾⣿⣿⣿⣯⣟⣷⣻⠟⢿⣿⣿⠿⠿⠿⠿⠸⢻⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠷⠆⢠⣄⡈⠉⠙⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⢿⣿⣿⣿⣿⡄⠘⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣦⣜⡧⣾⣿⣿⣶⣶⣿⣷⢠⢸⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠻⢿⠀⢐⡀⢀⠉⠙⠹⠙⠲⣖⡄⠀⠀⠀⠠⠀⠀⠀⢤⣤⣠⣶⣀⡀⠀⠈⠙⠿⣿⣷⡀⠘⡿⣿⣿⣿⣿⣽⣿⣿⣿⢿⣿⣿⣿⠓⠘⣿⣿⣿⣿⣿⣿⠸⢹⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠈⠉⠙⠿⢿⣿⣿⣿⣿⣿
⠀⠚⠈⠀⠑⠁⠀⡐⢲⣒⡠⣥⡤⠀⠀⠐⠄⠀⠀⠀⠸⣿⠶⢼⠟⠷⡦⠄⠄⢄⡀⠙⠳⠀⠹⣿⣿⣿⣿⠋⣷⡿⠛⢺⡧⡄⢀⠀⢠⣛⣟⠏⠉⠉⠉⠀⠈⠉⠉⠉⠉⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠽⣿⡿
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                    ䷩ 𝚕𝚒𝚗𝚎 687

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/08/05/recruitment-epo-catastrophe/#comments
    Gemini version at gemini://gemini.techrights.org/2022/08/05/recruitment-epo-catastrophe/

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Gemini_version_available_♊︎


✐ Recruitment_Potential_at_the_EPO_Has_Never_Been_Worse⠀✐


Posted in Europe, Patents at 9:42 am by Dr. Roy Schestowitz


Video_download_link | md5sum e2ffabfabd4df1ef1e24d53d93f177e4
EPO HR Failed and Recruitment is Defunct
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/epo-drain-of-talent.webm


Summary: The tyrants who have taken the reins at the EPO want obedient robots,
not human beings who are inclined to obey the law. Therefore, there seems to be
an effort underway to drive out well-educated, highly-qualified, conscientious,
experienced and charismatic workers who can stand in the way of profoundly
unlawful_strategies.


IT is undeniable that the EPO has a retention and recruitment crisis. People
don't_wish_to_work_for_tyrants and they can properly research matters online,
only to realise that Benoît_Battistelli and António_Campinos have turned a
once-reputable institution into a tyranny, compelling examiners to grant
illegal patents, such as European_software_patents.


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇EPO at Glassdoor⦈ Over the years we’ve amassed evidence of
the brain drain, the EPO’s low-ranked status as an employer, and bad reviews in
Glassdoor (see screenshot on the right).


Today’s EPO has resorted to very obscenely low qualification levels, even for
key positions such as “patent examiner”. The standards have fallen so sharply
that the place isn’t recognisable anymore. The above video speaks of a new
publication regarding Job_Groups_5_and_6 and here’s the content of the message.
“The team manager appointed in April retired in July and no replacement is
foreseen,” it says.


     Zentraler Personalausschuss
     Central Staff Committee
     Le Comité Central du Personnel


     Munich,28/07/2022
     sc22108cp


     § Paratechnicals: Highly skilled colleagues without a future?⠀➾


     When the “Paratechnicals and Paralegals” pilot project was launched
     in 2012, it was seen as the future of formalities work: “This project
     is all about offering a new and attractive professional home in which
     staff can reach their full potential.”1 Unfortunately, management
     changed its vision over the years, and with it the investment in the
     paratechnicals, who now find themselves in the position of “laissés
     pour compte”.


     Dear Colleagues,


     Your Staff representation continues its tour to the teams in Job
     group 5 and 6 and recently met with the team of paratechnicals. The
     dispirited colleagues shared many issues with us. We foremost noted
     they feel left behind.


     ⚓  1. Restructuration⠀⇛


     In 2017, the team of paratechnicals (PTs) was shrunk and split into 8
     teams. 6 in the different OCFD Directorates and 2 in the
     Classification and Documentation Department. This resulted in
     abruptly disrupting the cooperation between colleagues in the OCFDs.
     The latest reorganisation in April 2022 saw the PT being merged again
     into 3 teams in the Classification and File Management Directorate.


     This directorate has become very large, yet the feeling of
     togetherness is gone and replaced by a growing uncertainty about the
     future. Some colleagues from Classification and File Management do
     not feel they should belong to the PT team as the nature of their
     work is different.


     The team manager appointed in April retired in July and no
     replacement is foreseen. This reinforces the feeling that no one
     cares about the situation in the team. The absence of a TM also makes
     the rewarding exercise even more unpredictable.


     Each time teams are split and later merged again, work is negatively
     affected, and staff suffer. It particularly harms cooperation and
     long-established workflow. Stability and predictability play an
     important role in wellbeing at work. We observe that the current
     management model instead produces uncertainty and disengagement.


     _____
     1 See Gazette November 2012, pages.12 and 13: “A new way of working
     designed for the future”.


     =====================================================================
     ⚓  2. Massive backlog and understaffing⠀⇛


     PTs report that the backlog is considerable and automatic pre-
     classification fails more often than not. They would either need more
     staff or less manual re-distribution. Understaffing is the word that
     keeps popping up throughout the workday.


     Management has not yet offered a solution to the persistently high
     workload. “Fire brigading” across technical fields cannot be done ad
     hoc as each field has its specificities.


     Understaffing naturally poses a problem of flexibility too, it
     renders holiday coverage problematic, and leave requests have to be
     adjusted accordingly. Our colleagues like their jobs, they care about
     delivering the best possible quality, they wish the Office would give
     them the working conditions to achieve this goal.


     We cannot help but notice that management is unaware of the depth of
     the colleagues’ knowledge, and the time they have invested in
     learning. We are very concerned that the understaffing observed with
     PTs and generally in all JG 5&6 teams will lead to burn-outs and
     early retirement.


     ⚓  3. No future?⠀⇛


     The expectations that management places in artificial intelligence
     (AI) have not yet materialized but succession planning is not on the
     agenda.


     The colleagues foresee that in 5 to 10 years PT work will be
     automated and they fear that in the meantime their wellbeing and job
     satisfaction will continue to deteriorate.


     The whole situation leaves them to believe there is no future for
     them.


     ⚓  4. Inefficient IT tool⠀⇛


     Ansera is supposed to become the IT tool for PTs in the future but it
     does not meet the requirements of the work. Work efficiency is
     foreseen to be massively disrupted by the use of Ansera.


     PT colleagues would like to be involved in the development of their
     tools and have their feedback taken into account when implementing
     new functionalities or making corrections. They regret a stop in
     investment while intellectual (manual) classification still remains
     the norm.


     As can be seen in all areas at the EPO but especially for PTs,
     management’s expectations about AI influence staffing levels.
     Although AI has long been announced but has not yet materialized, the
     number of staff members is already shrinking continuously. The
     remaining colleagues are faced with an ever-growing workload.


     ⚓  5. Job Group mismatch⠀⇛


     The work requires in-depth knowledge of technical fields and is
     therefore very specialised. It also partly involves performing work
     for the divisions which should qualify the PTs as experts.


     =====================================================================
     While procedure experts are in JG 5 grade, PTs are still graded JG 6.


     We will convey to management all the issues identified, among which
     understaffing certainly is the most burning one.


     ⚓  6. In conclusion,⠀⇛


     After an already too long period of neglect, the Office urgently
     needs to take action to improve the working conditions of our PT
     colleagues.


     We would like to take this opportunity to thank our PT colleagues for
     a very informative meeting and for the trust they placed in us.


     The Central Staff Committee


Job Groups 5 & 6 seem to be facing the fate of some mangers who opposed
Battistelli or former colleagues of the fraudster Željko_Topić. They’re being
reassigned tasks or given unrealistic work expectations which render them
obsolete or simply scuttle the whole team. The Central Staff Committee is
informing other colleagues that this is happening. After Job Groups 5 & 6 it
can be many of the examiners, who are not_so_easy_to_manipulate. The tyrants
want obedient robots, not human beings who are inclined to obey the law. █


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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⠿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⠿
⣿⣿⣿⣿⣿⣿⣿⣏⠆⠰⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠡⠌⡇⠌⢹⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣃⡂⡳⠋⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣾⠏⣼⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⠪
⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣷⣾⢷⣶⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣷⡷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⢾⣿⣾⢿⣿⣿⣿⣿⣿⣿⢸⣿⡿⣿⣿⢿⣿⣶
⣿⣿⣿⣿⢠⡌⠹⠙⣙⢉⡙⠁⠋⣉⠋⠋⣿⣿⣿⣿⣿⣿⢀⠘⠉⡍⢹⠈⠉⠉⠉⠉⢹⣿⣿⡇⣿⣿⣿⣿⣿⡿⢈⠩⠁⠍⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠊⢹⠈⠉⢩⢘⠉⠉⢹⣿⣿⣿⢸⣿⡇⢩⢹⠸⠉⠉
⣿⣿⣿⣿⣶⣾⣷⣷⣶⣾⣷⣷⣷⣾⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠼⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠿⠿⡿⠿⢿⠿⠿⣿⡿⠿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠀⠭⡇⣋⣈⠺⠷⢸⡇⡉⢼⠁⢀⠙⣨⠘⠀⢡⠉⠘⡈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣷⣿⣿⣷⣶⣿⣷⣿⣾⣷⣾⣷⣿⣾⣶⣾⣾⣷⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⢩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭
⣿⣿⢸⣿⢋⣭⣍⢻⣿⣿⠿⢿⣿⣿⣿⣿⣿⢿⣿⢿⣿⡿⣿⡿⡿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⢸⣿⣜⠿⢟⠼⣿⣿⣂⣁⣸⣀⣁⣆⣒⣰⣿⢀⣂⣇⣊⣇⣂⣀⣂⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⢸⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⢿⡿⢿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡐⠛⢈⠀⡑⢈⣴⡇⣂⠃⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⢀⡊⠍⠻⠉⡍⠉⢽⡧⠀⠥⢸⡏⡍⠉⠙⡅⠉⢉⠋⠋⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⣿⣿⠟⣻⣿⣿⠀⠀⠀⡀⠀⠀⡇⠀⠀⢀⠀⠀⢸⠀⠀⠀⡀⠀⠀⡇⠀⠀⣀⠀⠀⢸⠀⠀⢠⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠞⣡⡿⡇⢤⠉⣿⣿⠀⠀⣺⣷⠂⠀⡇⠀⢐⣿⡖⠀⢸⠀⠀⣾⣿⠋⠀⡇⠈⢻⣿⡟⠁⢸⠀⠙⣿⣿⠋⢸⣿⣿⣿⣿⣒⣒⣚⣻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⡀⠀⠀⠀⠀⢀⣇⠀⠀⠀⠀⠀⣸⡀⠀⠀⢈⣀⣀⣇⣀⣈⣀⣁⣀⣸⣀⣀⣁⣈⣀⣸⣿⣿⣿⣿⣶⣶⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣀⣤⣤⣀⡀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⢀⣠⣤⣄⣀⡀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣠⣿⣿⣿⣿⣿⣿⣦⡀⠈⢿⣿⣿⢛⠻⠿⠿⠿⠿⠿⠿⡿⠿⠿⠿⠿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣴⣿⣿⣿⣿⣿⣿⣦⠀⠙⣿⣿⣿⠛⡿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⣿⣿⡔⣱⠖⡜⢿⣿⣷⠀⢸⣿⣿⣰⣠⣀⣌⣁⣁⣸⣸⣀⣷⣠⣀⣼⣧⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣧⠂⠿⢿⣿⣿⡇⠀⣿⣿⣇⣤⡁⣡⢈⣄⣧⣀⣄⣤⣀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠘⣿⣯⣤⣼⣼⣯⣦⣿⡟⠀⢸⣿⣿⢙⢛⢻⠛⢻⠩⠝⣛⠙⠛⢛⠛⡋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠸⣿⣿⣧⣤⣷⣼⣿⣿⠇⠀⣿⣿⡟⡛⢉⡏⣭⡍⠭⢫⣭⢻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠈⠻⣿⣿⣿⣿⡿⠟⠀⣠⣿⣿⣿⣶⣶⣾⣶⣾⣾⣷⣿⣶⣶⣾⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠙⢿⣿⣿⣿⣿⡿⠋⠀⣼⣿⠿⠷⠶⠾⠷⠶⠶⠶⠶⠶⠿⠿⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⡀⠉⠉⠁⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠉⠉⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

                    ䷩ 𝚕𝚒𝚗𝚎 969

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/08/05/the-dignity-of-criminals/#comments
    Gemini version at gemini://gemini.techrights.org/2022/08/05/the-dignity-of-criminals/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 08.05.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_Criminals_Have_Feelings_Too…⠀✐


Posted in Europe, Patents at 11:39 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇But_Data_Protection_Rules;_But_Data_Protection_Office;_Data
                             Protection_Board???⦈_


Summary: We’ve learned today that speaking to colleagues about the EPO‘s
corruption is regarded as a privacy problem by those who engage in this
corruption


⠀⠀⠀⠀⣀⡀⠀⣤⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⡤⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠠⠡⡠⣰⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣷⣴⣶⣄⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⠀⠁⡘⡛⣟⣲⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠐⠀⠠⢴⣤⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠉⠉⠛⢿⣿⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠆⠒⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠀⠀⠀⠸⡙⠉⣟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡶⠾⠶⠶⠄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⠐⣦⣴⣷⣤⣿⡿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣷⣿⢋⣿⡇⢠⣾⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣇⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢽⡏⠩⡝⠉⣯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⡿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣼⣷⣾⣿⣶⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⠏⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⡇⠐⡼⠄⣷⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⡏⣴⣷⣶⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⢀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠥⠤⠸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡃⡿⢿⣿⠿⣿⣯⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⢠⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣭⣭⣭⣭⣭⣍⣉⣉⣀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠐⠀⠀⢈⣆⠀⣷⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣯⣀⠀⠈⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡂⠀⠀⢿⣿⣿⣿⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣭⣭⣭⣭⣭⠭⢉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⠘⠸⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡍⢁⡀⠀⠀⠀⠀⠀⢀⡴⠂⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣭⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠨⢃⢁⣿⣥⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠖⠀⠀⢠⣿⡇⡀⠀⠀⣠⣴⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠘⢻⡧⣷⣴⠾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢀⣿⣷⣿⣿⣶⣾⣽⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⢴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⢾⡶⠾⠿⠿⠿⢿⡿⠿⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠶⠶⠶⠶⡲⠶⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⡀⠀⣦⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡤⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡀⢡⠀⣸⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣷⣴⣶⣦⠤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠁⡘⡛⣟⣲⣶⣶⣶⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠐⠚⠠⢴⣥⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣷⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠆⠂⠂⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠀⠀⠈⢹⡙⠉⣟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡾⠿⠾⠷⠦⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⠐⣦⣴⣷⣤⣿⡿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⢻⣿⡏⢠⣾⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠐⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠦⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣷⣼⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⢾⡏⠩⡝⠉⣯⡽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⠿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣼⣷⣾⣿⣶⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⠛⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⣸⡇⠐⡼⠄⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⡃⠰⢶⣷⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡒⠚⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠸⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠃⠿⢿⣿⠿⣿⣯⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣭⣭⣭⣭⣭⣍⣉⣉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠐⠀⠀⢈⣆⠀⣷⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣥⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⡉⡁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡅⠀⠀⢿⣿⣿⣿⣯⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣭⣭⣭⣭⣭⣭⠭⢭⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⠐⢸⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠍⢉⡀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣭⣭⡠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⠀⠨⣃⣁⣿⣥⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠂⠀⠀⢠⣿⡟⣄⠀⠀⢀⣴⣿⣮⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⣿⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠈⢻⡷⣿⣦⠺⢿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠐⠀⠀⠛⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢀⣿⣷⣿⣿⣶⣶⣮⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⢴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⢾⡷⡿⠿⠿⠿⣿⡿⠇⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠶⠶⠶⠶⡲⠶⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠁⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⡀⢀⣶⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡤⢤⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡰⣳⡽⣻⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣷⣴⣶⣦⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⠈⠁⡘⡛⣟⣲⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣖⠄⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠐⡊⡠⢴⣥⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⠤⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠻⡖⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠆⠒⠢⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀
⢈⡕⠊⠉⠹⡙⠙⣟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡾⠾⠷⠶⠦⠖⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⠙⣦⣴⣷⣤⣿⡿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⡿⢀⣴⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢲⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠦⠶⠦⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠹⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⣸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠏⠙⠐⠂⠀⠀⠀⠀⠀⠀⠀
⠄⢄⣽⡏⠩⡝⠉⣯⡽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠉⠊⠂⠀⠀⠀⠀⠀⠀⠀
⣊⡁⣿⣷⣾⣿⣶⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠥⠬⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⠒⠛⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀
⠆⠈⣺⡇⠐⡼⠆⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⠁⠀⢰⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠓⠚⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠬⡌⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⡉⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣌⡋⡿⢿⣿⢿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣍⣩⣀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠢⡴⢃⠀⢈⣆⠀⣷⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣗⣒⡁⣿⣿⣿⣿⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⡀⠙⢻⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⢉⣁⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣭⣤⡤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠻⠀⠨⣇⣁⣿⣤⣤⣥⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠖⠀⠀⠀⢀⣾⡟⣦⠀⠀⢀⣠⣾⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠃⠓⠀⠹⣿⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠘⢙⡿⣼⣷⡖⠿⢿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠂⠐⠙⠛⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣿⣷⣿⣿⣷⣶⣦⣽⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠕⡀⢴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⢾⣿⡾⠿⠿⠿⣿⡿⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠶⠶⠶⠶⣲⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠏⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⣀⠀⣶⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⢤⣤⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣰⣿⣿⣿⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⢤⣖⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⠋⠓⡙⡛⣟⣲⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣖⡲⠶⡂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠰⣿⣠⣴⣥⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠦⠶⠦⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀
⢘⡍⢟⠉⢹⡙⠙⣟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠆⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⠿⠿⠷⠦⠶⠦⠖⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠧⢿⣦⣴⣷⣤⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⠀⣴⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀
⠐⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣸⣿⣿⣿⠀⣿⣿⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠓⠇⠀⠀⠀⠀⠀⠀⠀
⡈⣽⣿⡏⠩⡝⠉⣯⡽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠋⠂⠀⠀⠀⠀⠀⠀⠀
⣺⣿⣿⣷⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⠛⠛⠛⠋⠂⠀⠀⠀⠀⠀⠀⠀
⡥⠭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⠛⠛⠃⠘⠈⠀⠀⠀⠀⠀⠀⠀
⠖⡾⣺⡇⠐⡼⠆⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⠁⠀⠠⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠒⢛⡋⠉⠀⠀⠀⠀⠀⠀⠀⠀
⢭⣻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣛⣛⣉⣉⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀
⣛⣟⣿⡿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣍⣩⣉⡁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⣽⣗⠀⢈⣆⠀⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣯⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣉⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠨⣟⣶⣿⣿⣿⣿⣿⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢰⣳⡻⢺⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢉⣉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣭⣥⣥⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠻⢀⢨⣇⣁⣿⣥⣤⣥⣤⣾⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡖⠂⠀⠀⠀⢀⣾⣿⢷⡄⠀⠀⣀⣴⣶⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠛⣷⣷⣿⣿⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠘⢙⣿⢼⣷⣤⠚⠿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠛⠉⠉⠛⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣶⣆⣨⣟⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡔⡤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⠶⠶⢾⣿⡿⠿⠿⠿⣿⠇⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠷⠶⠶⠶⣲⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠁⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⣀⢀⣷⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣤⣤⢤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣰⣿⣹⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⠉⠑⡛⡛⣟⣲⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣖⡢⠴⡦⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢰⣿⣤⣴⣧⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⢮⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠢⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡗⡟⠉⢹⡙⠙⣟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⠿⠿⠷⠶⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀
⢘⠲⣿⣦⣴⣷⣤⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣰⣾⣿⠆⠀⠀⠀⠀⠀⠀⠀⠐⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀
⠰⢮⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣿⣿⣿⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠏⠛⠓⠇⠀⠀⠀⠀⠀⠀⠀
⣜⢁⣿⡏⠹⡝⠉⣯⡽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠋⠊⠀⠀⠀⠀⠀⠀⠀
⢽⢕⣿⣷⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠰⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⠛⠛⠛⠃⠂⠀⠀⠀⠀⠀⠀⠀
⢽⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⡃⠘⠈⠀⠀⠀⠀⠀⠀⠀
⢽⡻⣿⡇⠐⡼⠆⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⠁⠀⠀⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠚⠛⡋⠉⠀⠀⠀⠀⠀⠀⠀⠀
⣻⠺⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣛⣉⣉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀
⢽⠺⣿⡿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⣉⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠻⢝⡿⠀⢘⣆⠂⣷⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣭⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⣿⢿⡿⣿⣿⣿⣿⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣯⡺⢻⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⢛⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣯⣭⣭⣭⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠻⡀⢨⣇⣁⣿⣭⣤⣥⣤⣽⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠂⠀⠀⠀⠀⠀⣾⣿⢳⡄⠀⠀⠀⣠⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢃⠶⣟⣿⣿⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠘⠙⣿⣼⣿⣦⠴⠿⠿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠛⠛⠑⠛⣶⣶⣶⣶⣶⣶⣶⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣤⣦⢀⣼⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡒⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⢾⣿⡿⡿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⢶⠶⡶⠶⣶⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⣀⠀⣶⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣤⡤⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡠⡷⣻⣾⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⢤⣔⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⠈⠑⡙⡛⣟⣲⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣆⠠⢔⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠰⠺⡤⢴⣥⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠋⠉⠛⢿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢚⣒⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠦⠲⠢⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀
⢈⠅⢃⠈⢹⡙⠙⣟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡾⠿⠾⠷⠦⠖⠦⠖⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠣⡿⣦⣴⣷⣤⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠦⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀
⠀⢾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣏⣿⣿⣿⣿⠀⠸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠋⠒⠇⠀⠀⠀⠀⠀⠀⠀
⠄⣄⣿⡏⠩⡝⠉⣯⡽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠉⠋⠂⠀⠀⠀⠀⠀⠀⠀
⡊⣅⣿⣷⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠆⠪⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⠓⠛⠂⠘⠁⠀⠀⠀⠀⠀⠀⠀
⣋⡉⣺⡇⠐⡼⠆⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⠁⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠒⠚⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀
⢭⡊⡒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣉⣈⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀
⣲⢍⡧⡿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⢼⣉⠀⢈⣆⠀⣷⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣯⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣉⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡧⢂⣪⢿⣿⣿⣿⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢨⡮⡻⢻⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⢙⣟⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣭⣭⣭⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠻⠀⢨⣇⣁⣿⣥⣤⣥⣤⣾⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠖⠀⠀⠀⠀⠀⠀⣼⣿⢹⣦⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢡⣳⢢⡩⣿⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠐⠉⣿⣼⣿⣧⡤⠶⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠐⠙⠑⠙⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣾⣿⣿⣦⣤⠄⣀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣐⡀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⢾⣿⡿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠷⠶⡶⠶⡲⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⣀⢀⣦⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⢤⣤⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡠⣩⣰⣺⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣶⣦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⠈⠁⡙⡛⣟⣲⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣖⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠰⠲⠤⢴⣤⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠋⠉⠉⠉⠻⢿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠘⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠆⠒⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠨⠀⠉⠈⢹⡙⠙⣟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣾⡾⠷⠾⠷⠦⠦⠢⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⠰⣦⣴⣷⣤⣿⡿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠦⠴⠦⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠰⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣏⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠏⠉⠁⠂⠀⠀⠀⠀⠀⠀⠀
⢀⢀⣿⡏⠩⡝⠉⣯⡽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣼⣷⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀
⢂⠰⣽⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣀⣼⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⠒⠛⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀
⠰⡈⣸⡇⠐⡼⠄⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠒⠚⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⢈⠌⢰⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⢖⡣⡿⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣩⣉⡁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠔⠇⠀⢘⣆⠀⣷⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣭⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡉⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡎⠠⢈⣿⣿⣿⣿⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣭⣭⣭⣭⣭⣭⣭⣍⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⡀⡠⢸⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁⢈⣿⣛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣭⣥⣥⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠺⠀⠨⢇⣁⣿⣥⣤⣤⣤⣤⣴⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠖⠀⠀⠀⠀⠀⠀⠀⣼⣿⢹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠒⠖⠅⢙⣿⣶⣶⣶⣶⣶⣶⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠐⠉⣻⣬⣿⣷⣄⠴⠾⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠂⠀⠀⠛⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣾⣿⣿⣧⣤⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡐⠀⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⢾⣿⡿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣫⣾⣿⣧⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠶⠶⠶⠶⣲⠶⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣽⣽⣿⣿⢭⣥⡅⣤⣤⣤⣤⡄⣤⣤⣀⣤⣤⣤⡄⣤⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡈⡛⣟⣲⣶⣶⣶⣶⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣯⣿⣿⢸⣿⠀⣿⢸⣿⣿⡇⣿⢰⣿⣇⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣤⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠋⠉⠉⠉⠉⠻⣿⣿⣿⣿⣷⣶⣶⣼⢭⣭⠝⠋⠌⠉⠄⠉⠉⠉⠉⠁⠉⠈⠁⠉⠀⠀⠀⠀
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣷⣶⣿⣿⣾⣿⣶⣿⣷⢻⡟⣿⡛⣾⣿⢻⣿⣻⣷⣿⡇⣿⣿⠀⠀
⠀⠀⠀⠀⠸⡙⠉⣟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⣏⢸⡿⡟⢿⡿⢸⡇⠿⠧⢿⡿⠸⠿⠿⠿⣿⠇⠿⠿⠀⠀
⠀⠀⠀⣦⣴⣷⣤⣿⡿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⡶⠶⢶⣤⡄⣤⣤⣤⡄⣤⣄⣤⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡏⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠿⡿⠿⢸⣿⡇⣿⣿⣿⡇⣿⢎⣻⣯⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⡏⠩⡝⠉⣯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠿⠿⠿⠿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠾⠯⠧⠙⠋⠙⠋⠛⠋⠛⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣷⣾⣿⣶⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⡇⠐⡬⠄⣷⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣛⣋⣙⣋⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠿⢿⣿⠿⣿⣯⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣉⣉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣆⠀⣷⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣿⣭⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢿⣿⣿⣿⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣭⣭⣭⣭⣭⣍⢩⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠁⠀⢠⣿⣟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣽⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠃⢁⣿⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢉⣻⣮⣿⣿⣤⠄⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⡶⢶⠶⠶⠶⠶⠶⡶⠾⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡿⣫⣴⣾⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠶⠶⠶⠶⠲⠶⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣭⣭⡍⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡙⠛⢲⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣾⣿⣿⣿⢸⣿⣿⡇⣿⢸⣟⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣠⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣽⠍⠉⠉⠉⠉⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢾⣯⣽⣿⠶⠶⢶⣶⣾⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⢻⡟⣿⣛⣿⣿⣻⣿⣿⣿⣿⡟⣿⣿⣿⣿
⠀⠀⠀⠀⠠⡉⠉⣋⠹⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡄⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣼⣿⣟⣿⣿⣼⣇⣿⣧⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣾⣿
⠀⠀⠀⣤⣴⣧⣤⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣾⣿⣷⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⡿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⡇⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⣿⢞⣻⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⢸⠁⠈⡉⠉⣯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢇⣿⣷⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠉⠀
⠀⠀⢸⣶⣶⣶⣶⣿⣟⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠟⢉⣉⡉⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⢈⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠛⢉⣀⣒⣛⣛⣛⣛⣛⣛⣓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠁⠐⡤⠀⣧⣘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣚⣛⣛⣛⣛⣛⣛⠛⢛⣛⣋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣶⣾⣿⣾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣹⣍⣉⣉⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠻⠿⢿⠿⡿⣭⣭⣭⣭⣭⣭⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣭⣭⣭⣭⣭⣭⣭⣭⣍⣉⡉⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣆⠀⣵⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣯⣭⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣭⣭⣭⣭⣭⣭⣍⣉⣉⣉⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⣿⣿⣿⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⣭⣭⣭⣭⣭⣭⡍⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠿⠿⠿⢭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠉⠀⠀⢠⣿⣛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢧⣤⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣽⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢉⣻⣬⢿⣃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⠿⢿⢿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⣾⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡿⣣⣴⣾⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠲⣶⠏⢶⠴⠰⠶⠶⠶⠐⠶⠶⠶⠾⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⣉⣾⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣿⣭⣭⡍⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡙⠛⢲⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣾⣿⣿⣿⢸⣿⣿⡇⣿⢸⣟⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣠⣅⣿⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⡽⠍⠉⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣾⣿⣿⣿⠶⠶⢶⣶⣶⣶⣶⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⢀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⢻⡟⣿⣛⣿⣿⣻⣿⣿⣿⣿⡟⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠉⠉⣋⠹⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢀⡄⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣼⣿⣟⣿⣿⣼⣇⣿⣧⣿⣿⣻⣿⣿⣿⣿⣇⣿⣿⣼⣿
⠀⠀⠀⣤⣴⣧⣤⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣷⣿⣷⣾⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠆⢿⣿⣿⣿⠿⢡⣾⣷⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⡇⢀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⣿⢞⣻⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⢸⠃⠈⡉⠉⣯⠙⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠄⢸⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠁⠀
⠀⠀⠸⣶⣶⣷⣶⣿⣟⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⡛⠛⠻⡏⠛⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠟⢉⣉⡉⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢿⣟⢿⣿⣿⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣶⣤⢀⣴⣷⠀⠀⠀⠀⠀⠀⠀⣸⡿⠛⢉⣀⣒⣛⣛⣛⡛⢛⣛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠁⠐⡤⠀⣧⣘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣷⣿⣿⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠁⢀⣚⣛⣛⣛⣛⣛⡛⠛⢛⣛⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣶⣾⣿⣶⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣟⣩⣉⣉⣉⣉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠻⠿⠿⠿⡿⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⢠⣯⣭⣭⣭⣭⣭⣭⣭⣭⣉⣉⡁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣆⠀⣵⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⣶⣭⠉⠀⠀⠀⠀⠀⠀⠀⠈⠩⣭⣭⣭⣭⣭⣭⣍⣉⣉⣉⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⣿⣿⣯⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⢩⣿⣿⣿⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⣭⣭⣭⣭⣭⣭⡅⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠛⠿⠿⢭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠉⠀⠀⠀⠀⢀⣾⣿⣿⣟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢧⣤⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣼⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢳⢴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣷⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣉⡹⡾⢿⣃⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠴⢶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣾⣿⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⠿⢋⣤⣶⣦⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠏⢶⠴⠰⠶⠶⠶⠀⠰⠶⠲⠶⠾⠿⠿⠿⠿⠿⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠉⢰⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢠⢤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣶⢶⣶⣰⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⡍⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡙⠛⢰⣲⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣼⣿⣿⣿⢸⣿⣿⡇⣿⢸⣟⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⡁⣓⢲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⡭⠉⠉⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢞⣽⣌⢼⠶⠶⠶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣂⡀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⢻⡟⣿⣛⣿⣿⣻⣿⣿⣿⣿⡏⣿⣿⣻⣿
⠀⠀⠀⠀⠀⠉⠉⣋⠹⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣼⣿⣟⣿⣿⣼⣇⣿⣧⣿⣿⣻⣿⣿⣿⣿⣇⣿⣿⣽⣿
⠀⠀⠀⣤⡤⢅⣤⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣷⣿⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠂⠹⣿⣿⣿⣿⠛⠀⣸⣧⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢡⣷⣿⣹⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣿⣿⣿⡇⢀⣰⣿⡅⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⣿⢞⣻⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⢐⠁⠈⡉⠉⢯⠹⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣀⢸⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀
⠀⠀⠨⣴⣴⣴⣶⣿⣟⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⠉⠛⠛⡍⠘⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠟⠉⣉⡉⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠸⡟⢿⣿⣿⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣦⣤⢀⣴⣿⠀⠀⠀⠀⠀⠀⣸⡿⠛⢉⣀⣒⣛⣛⣛⡒⢛⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡤⠀⣥⣘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠁⣀⣚⣛⣛⣛⣛⣛⡛⠛⢛⣛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠠⠺⠶⡺⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⠃⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣟⣉⣉⣉⡈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠳⠡⠿⠿⡿⢭⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⢠⣭⣭⣭⣭⣭⣭⣭⣭⢭⣉⣉⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡆⠀⣵⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⣰⣶⣤⠀⠀⠀⠀⠀⠀⠀⠉⣭⣭⣭⣭⣭⣭⣭⣍⣉⢉⢉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⣍⣭⣯⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⣾⣿⣿⣿⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣯⣭⣭⣭⣭⣭⡁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠛⠻⠿⠭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠉⠀⠀⠀⠀⠀⣰⣿⢿⣿⣏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢥⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢌⡤⡤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡎⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠲⢔⣢⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⣉⢳⡼⢿⣁⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢶⣶⣶⣶⣶⣶⣶⣶⣾⣷⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣽⣶⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠤⠒⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠟⠋⣠⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠏⢶⠴⠰⠶⠶⠶⠀⠐⠶⠒⠶⠶⠾⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠃⠀⣾⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⢄⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣷⢶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣽⣭⣭⣭⣭⣭⡍⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡙⠓⢲⣲⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣾⣷⣿⣿⢸⣿⣿⡇⣿⢸⣟⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⣁⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡭⠍⠉⠉⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣬⣷⣷⢿⠷⠶⢶⣶⣶⣶⣶⣶⣶⣷⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣶⣴⢂⡀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⢻⡟⣿⣛⣿⣿⣻⣿⣿⣿⣿⡏⣿⣿⢿⣿
⠀⠀⠀⠀⠀⠉⠉⣉⠹⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣼⣿⣟⣿⣿⣼⣇⣿⣧⣿⣿⣻⣿⣿⣿⣿⣇⣿⣿⣾⣿
⠀⠀⠀⣤⡤⣇⣤⣾⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣶⣶⣶⣷⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠈⠘⢫⣿⣿⣿⡿⠋⠀⢠⡄⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⡿⣿⣻⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢸⣿⣿⣿⡁⠀⢀⡈⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⣿⢞⣻⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⢰⠁⠈⡉⠉⢯⠹⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢆⡀⢰⣿⣿⣿⣿⣿⣾⣿⣷⠄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠁⠀
⠀⠀⢠⣶⣴⣴⣶⣿⣟⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣾⣿⣿⣿⠏⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠟⠉⣉⡉⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠸⡟⢿⣿⣿⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣦⡄⣠⣴⣷⠀⠀⠀⠀⠀⣸⡿⠛⢉⣀⣒⣛⣛⣛⡛⢛⣛⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡤⠀⣥⣘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣷⣾⣿⣿⣿⣷⣾⣿⣿⡏⠀⠀⠀⠀⠀⢁⣀⣚⣛⣛⣛⣛⣛⣛⠛⢛⣛⣁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣴⣾⣶⣶⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣟⣏⣉⣉⣉⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠻⠫⠿⠿⡿⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣨⣭⣭⣭⣭⣭⣭⣭⣭⢭⣉⣉⡁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡆⠀⣱⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡭⣽⣿⣿⣇⣴⣶⡄⠀⠀⠀⠀⠀⠀⢭⣭⣭⣭⣭⣭⣭⣭⣍⣍⡉⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⣽⣻⣯⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⢸⣿⣿⣿⣿⣿⣯⣥⠀⠀⠀⠀⠀⠀⠀⠙⢯⣯⣭⣭⣭⣭⣭⡭⠍⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠋⠳⠿⠭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⢀⣿⣟⣿⣿⣎⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢥⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢬⣤⡤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢲⢴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣾⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠛⡉⢣⡽⢏⡀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠶⣶⡶⣶⣶⣶⣶⣶⣶⣿⣿⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣦⣳⣶⣾⣟⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠴⠲⠶⠶⠶⠶⠶⠶⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠟⠋⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠏⢶⠴⠰⠶⠶⠶⠀⠂⠶⠲⠶⠶⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠏⠀⢰⣿⣿⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣷⢶⣶⣴⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣭⣭⣯⣭⣭⡍⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡙⠓⢲⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣼⣿⣿⣿⢸⣿⣿⡇⣿⢸⣟⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣡⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠭⠉⠉⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣼⣧⣶⣿⠷⠶⢶⣶⣾⣶⣶⣶⣶⣷⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣄⣴⠆⢀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⢻⡟⣿⣛⣿⣿⣻⣿⣿⣿⣿⡟⣿⣿⢿⣿
⠀⠀⠀⠀⠀⠉⠉⣋⠹⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡃⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣼⣿⣟⣿⣿⣼⣇⣿⣧⣿⣿⣻⣿⣿⣿⣿⣇⣿⣿⣼⣿
⠀⠀⠀⣤⣴⢦⢤⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣷⣿⣾⣶⣾⣷⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠎⠈⠘⠟⣿⣿⣿⣿⡏⠁⠀⢀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣽⣼⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⣿⢞⣻⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⢸⠃⠈⡉⠉⢯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢇⣀⠀⢰⣿⣿⣿⣿⣿⣷⣶⣦⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠁⠀
⠀⠀⢸⣶⣶⣶⣶⣿⣟⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⡿⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠟⢉⣉⡉⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⢀⢿⣿⣻⣿⣿⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡾⢻⣿⣿⣿⣷⡄⠀⣠⣶⡇⠀⠀⠀⠀⣸⡿⠛⢉⣀⣒⣛⣛⣛⡛⢋⣙⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠁⠐⡤⠀⣧⣘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣷⣾⣿⣿⣿⣿⣶⣿⣿⣿⡇⠀⠀⠀⠀⢁⣀⣚⣛⣛⣛⣛⣛⡛⠛⠛⣛⣁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣶⣾⣶⣾⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠻⠁⠀⠀⠀⢰⣿⣿⣿⣿⣿⣻⣛⣉⣉⣉⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠻⠿⠿⠿⡿⢭⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣿⣿⣿⠀⠀⠀⠀⠀⣬⣯⣭⣭⣭⣭⣭⣭⣭⣭⣉⣉⡁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢆⠀⣱⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡭⣽⣿⣿⣿⣿⢀⣶⣦⠀⠀⠀⠀⠀⢨⣭⣭⣭⣭⣭⣭⣭⣭⣍⣍⣉⡉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⣷⣻⣯⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⢰⣿⣿⣿⣿⢿⣿⣿⣤⡄⠀⠀⠀⠀⠀⠙⠿⣿⣯⣭⣭⣭⣭⣭⡭⠍⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠛⠻⠿⢭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣆⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣤⣠⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢼⡤⡤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢲⢔⣲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠛⠛⢦⣿⣉⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠶⣶⣶⣶⣶⣶⣶⣶⣶⣷⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣌⢶⣤⣾⣞⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠶⠴⠖⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⠋⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠏⢶⠴⠰⠶⠶⠶⠐⠖⠶⠲⠶⠶⠾⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠀⠀⣾⣿⠇⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣭⣭⣯⣭⣭⡍⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡙⠛⢲⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣼⣿⣿⣿⢸⣿⣿⡇⣿⢸⣟⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣠⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢼⣿⣾⣿⠷⠶⢶⣶⣶⣶⣶⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣀⣠⡀⣠⠄⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⢻⡟⣿⣛⣿⣿⣻⣿⣿⣿⣿⡟⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡉⠉⣋⠹⠿⠿⠿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣷⢀⣿⡧⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣼⣿⣟⣿⣿⣼⣇⣿⣧⣿⣿⣻⣿⣿⣿⣿⣇⣿⣿⣾⣿
⠀⠀⠀⣤⣴⣧⣤⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣶⣿⣷⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⠞⠿⠛⠹⠛⡿⢻⣿⣿⣿⣿⠇⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣰⣿⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⣿⢞⣻⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⢸⠃⠈⡉⠉⣯⠹⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠁⠀
⠀⠀⢸⣶⣶⣷⣶⣿⣟⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⣶⣾⣿⣿⣿⣿⣿⠏⠀⠉⠁⠀⠀⠀⠀⠀⠁⣼⣿⣿⡿⠟⢉⣉⡉⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠠⣿⣿⢿⣿⣿⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢉⣿⠿⢿⣿⣿⣿⣷⣄⠀⠀⣀⣴⡄⠀⠀⠀⣼⡿⠛⢉⣀⣒⣛⣛⣛⣛⣛⣛⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⠁⠐⡤⠀⣧⣘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡻⣿⣿⣤⣼⣿⣿⣿⣟⣁⣤⣾⣿⣿⡇⠀⠀⠀⣁⣀⣚⣛⣛⣛⣛⣛⡛⢛⣛⣛⣋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣶⣾⣿⣾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣭⣿⣿⣿⣿⣿⣿⣿⢋⣽⡛⠛⠃⠀⢀⣾⣿⣿⣿⣿⣿⣿⣟⣉⣉⣉⣉⣉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠻⠿⠿⠿⡿⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠾⡿⠟⠀⠀⠀⢸⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣍⣉⣉⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣆⠀⣵⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠭⣿⣿⣿⣿⣿⣿⣿⠃⠀⡀⠀⠀⠀⠀⢀⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣍⣉⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⣿⣿⣿⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠁⢸⣿⣿⣿⣿⣿⡻⠿⢷⣿⣤⡄⠀⠀⠀⠸⢿⣿⣿⣿⣭⣭⣭⣭⣭⣭⡭⠍⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠿⠿⠿⢭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⣥⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣼⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⠶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣞⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢷⢴⣶⣶⣶⣶⣶⣶⣶⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⢮⣋⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠦⣶⣶⣶⣶⣶⣶⣶⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣤⣤⡀⠈⡉⣀⣴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣝⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠏⢶⠴⠰⠶⠶⠶⠀⠶⠲⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡏⠀⠀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣿⣭⣭⡍⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡙⠛⢲⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣼⣿⣿⣿⢸⣿⣿⡇⣿⢸⣟⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣠⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠉⠀⠀⠀⠀⠈⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣾⣿⣿⣿⠶⠶⢶⣶⣾⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣀⣀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⢻⡟⣿⣛⣿⣿⣻⣿⣿⣿⣿⡟⣿⣿⢿⣿
⠀⠀⠀⠀⠠⡉⠉⣋⠹⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⣾⣦⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣾⣿⣟⣿⣿⣼⣇⣿⣧⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣼⣿
⠀⠀⠀⣤⣴⣧⣤⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⠾⠟⠟⠉⠼⠻⡿⠋⣿⡿⣸⣿⡇⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣨⣼⣠⢻⣇⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⣿⢞⣻⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⢸⠃⠈⡉⠉⣯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⢰⣾⣾⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠸⠷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠉⠀
⠀⠀⢸⣶⣶⣷⣶⣿⣟⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣟⣷⣶⣶⣿⣿⣿⣿⣿⣿⡏⠁⠈⠁⠀⠀⠀⠀⢘⠁⣼⣿⣿⡿⠟⠉⣉⡉⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠈⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⠋⣽⣿⠿⣿⣿⣿⣿⣶⣄⠀⠀⢀⣠⡄⠀⠀⠃⣼⡿⠛⢉⣀⣒⣛⣛⣛⣛⣛⣛⡂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠁⠀⡤⠀⣧⣘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠻⣿⣿⣧⣠⣿⣿⣿⣿⠟⠁⣀⣴⣿⣿⣿⠀⠀⠀⣁⣀⣚⣛⣛⣛⣛⣛⣛⢛⢛⣛⣋⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣶⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⠋⣸⡛⠛⠋⠀⣤⣾⣿⣿⣿⣿⣿⣿⣟⣉⣉⣉⣉⣉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠻⠿⢿⠿⡿⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⡿⠃⠸⠿⠟⠀⠀⠀⣿⣿⣯⣯⣭⣭⣭⣭⣭⣭⣭⣭⣉⣉⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣆⠀⣵⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢭⣿⣿⣿⣿⣻⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣍⣉⣉⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⣿⣿⣿⣭⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⢸⣿⣿⣿⣿⣿⡟⠻⠿⢶⣶⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⡭⠍⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠿⠻⠿⢭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣿⣿⣯⣥⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣽⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⠶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣯⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣴⣶⣶⣶⣶⣶⣶⣶⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⡉⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣴⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢉⣀⡀⠈⠉⠁⠀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣄⠴⡚⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠲⣶⠏⢶⠴⠰⠶⠶⠶⠐⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⠃⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣭⣭⡍⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡙⠛⢲⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣾⣿⣿⣿⢸⣿⣿⡇⣿⢸⣟⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣠⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠁⠀⠀⠀⠈⠉⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣮⣿⣿⣿⠷⠶⢶⣾⣾⣶⣶⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⡀⠀⡀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⢻⡟⣿⣛⣿⣿⣻⣿⣿⣿⣿⡟⣿⣿⣿⣿
⠀⠀⠀⠀⠠⡉⠉⣋⠻⠿⠿⠿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⣾⡠⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣼⣿⣟⣿⣿⣼⣇⣿⣧⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣽⣿
⠀⠀⠀⣤⣴⣧⣤⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣶⣶⣶⣶⣶⡶⠹⠿⢿⠋⠁⠟⢻⡿⠋⣿⡟⢰⣿⠇⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠀⠀⠂⠀⠀⠀⠀⠀⠰⡄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⣿⢞⣻⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⢸⠃⠈⡉⠉⣯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⣴⣶⣾⣿⣿⣿⣶⣷⠀⠀⠀⠀⠀⠸⠿⠷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠁⠀
⠀⠀⢸⣶⣶⣷⣶⣿⣟⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⡞⣓⣶⣴⣾⣿⣿⣿⣿⡿⣟⠋⠁⠀⠀⠀⠀⠀⢀⣻⠁⣼⣿⣿⡿⠟⠉⣉⡉⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠨⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⠋⣩⣿⡿⠿⣿⣿⣿⣷⣶⡀⠀⠀⠀⢀⡀⠀⣾⠃⣼⡿⠛⢉⣀⣒⣛⣛⣛⣛⣛⣛⣒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠁⠐⡤⠀⣧⣘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡃⠙⢷⣿⣿⣀⣀⣿⣿⣿⠿⠋⠀⢀⣴⣾⣿⣧⢀⠃⠀⣁⣀⣚⣛⣛⣛⣛⣛⣛⡛⣛⣛⣋⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣶⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣿⣹⣿⣿⣿⣿⣇⣴⣶⡆⠀⣸⠛⠛⠋⢸⣤⣾⣿⣿⣿⣿⣿⣿⣟⣉⣉⣉⣉⣉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠻⠿⢿⠿⡿⣭⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠘⠿⠋⠀⠀⣼⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⣍⣉⣉⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣆⠀⣵⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡭⣽⣧⣿⣿⣿⡛⢿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢠⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣉⣉⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⣿⣿⣿⣭⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⢿⣿⣿⣿⣿⣿⣿⠛⠛⠓⠦⠄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⠭⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠿⠿⠿⢭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣥⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣽⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⡶⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣯⠻⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣴⣶⣶⣶⣶⣶⣶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⢖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡶⢶⣶⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠁⠈⠉⠀⠀⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣶⣦⣄⠀⠀⢿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠲⣶⠏⢶⠴⠰⠶⠶⠶⠐⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣄⡆⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣯⣭⡍⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡙⠛⣲⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣾⣿⣿⣿⢸⣿⣿⡇⣿⢸⣟⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣠⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠉⠉⠁⠀⠀⠀⠉⠉⠉⠅⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣾⣿⣿⣿⡷⠶⢶⣾⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡁⠀⠀⢀⢀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⢻⡟⣿⣛⣿⣿⣻⣿⣿⣿⣿⡟⣿⣿⣿⣿
⠀⠀⠀⠀⠠⡉⠉⣟⠹⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣾⣧⡀⢀⣇⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣾⣿⣟⣿⣿⣼⣇⣿⣧⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿
⠀⠀⠀⣤⣴⣧⣤⣿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⡞⢻⡿⢻⠟⠉⠿⠻⣿⠟⢹⢿⠃⡸⠿⠃⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⣿⢞⣻⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⢸⠏⠈⡉⠉⣯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⢀⣼⣶⣶⣿⣷⣧⣤⡀⠀⠀⠀⠀⠀⠿⠿⠷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠉⠀
⠀⠀⢸⣶⣶⣷⣶⣿⣟⣛⣛⣛⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡖⣓⢢⣤⣶⣾⣿⣿⣿⣿⠟⠛⠉⠀⠀⠀⠀⠀⠀⣹⣿⠁⣼⣿⣿⡿⠟⢉⣉⡉⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⢨⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⡟⢉⣿⣿⣿⢿⣿⣿⣿⣶⣆⠀⠀⠀⠀⠀⠀⣾⣿⠃⣼⡿⠛⢉⣀⣒⣛⣛⣛⣛⣛⣛⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⠁⠐⡤⠀⣧⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠀⠘⢷⣾⣿⣇⣀⢸⣿⣿⡿⠟⠉⠀⠀⢠⣴⣿⡆⣛⠃⠀⣁⣀⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣋⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣶⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣿⡉⣿⣿⣿⣿⣿⣀⣴⣶⠀⠀⣘⠛⠛⢁⣸⣤⣾⣿⣿⣿⣿⣿⣿⣟⣫⣍⣉⣉⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠻⠿⢿⠿⡿⣭⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠐⠀⠀⠀⣸⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣉⡉⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣆⠀⣵⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠍⣿⣧⣿⣿⣿⡟⠛⣿⣿⡿⠋⠀⠀⠀⠀⠀⢠⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣍⣉⣉⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⣿⣿⣿⣭⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⣿⣿⣿⣿⡿⣿⡦⠛⠋⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⡭⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠿⠿⠿⢭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⢹⣿⣿⣿⠆⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣥⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣾⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⠶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢷⢶⣶⣶⣶⣶⣶⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣶⠶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⢶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠋⠉⠈⠁⠀⠀⠠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠲⣶⠏⢶⠴⠰⠶⠶⠶⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣤⡀⢄⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⡏⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⡛⠛⣲⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣾⣿⣿⣿⢸⣿⣿⡇⣿⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣤⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠉⠉⠁⠀⠉⠉⠉⠉⢽⣯⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢠⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⣀⠀⠀⢀⣀⡀⢀⢀⠀⠀⢀⠀⠀⠀⢿⣇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⡟⣿⣛⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿
⠀⠀⠀⠀⠸⡙⠉⣟⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣆⠀⠀⠀⢿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣼⣧⣿⣯⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿
⠀⠀⠀⣤⣴⣷⣤⣿⡿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡾⠻⣿⣿⢿⣿⠋⠘⠟⠜⣿⠟⠹⠃⠀⠸⠙⠀⠀⠀⠐⣶⣄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠉⠁⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⡌⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⡇⣿⢞⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⢸⡏⠩⡍⠉⣯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⣴⣤⣄⡀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠷⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠉⠀
⠀⠀⢸⣶⣶⣿⣶⣿⣟⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⠴⠄⡀⣀⠀⣴⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⢀⣼⣿⣿⣿⠁⣾⣿⣿⡿⠟⢉⣉⣉⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣟⣛⣛⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣇⡾⠒⢋⣶⠇⢿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠃⣼⡿⠛⢉⣀⣒⣛⣛⣛⣛⣛⣛⣛⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⠃⠐⡤⠄⣧⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡀⠀⠘⣧⣤⣿⣿⡇⠀⢸⣿⣿⡿⠛⠁⠀⠀⠀⢀⣴⡌⣛⣛⠃⠀⣁⣀⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⢿⡟⢻⣿⣶⣾⣿⡿⠀⣀⡀⠀⠀⠘⠉⠉⣁⣼⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣉⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠿⢿⢿⠿⣿⣯⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠀⣿⣷⣼⣿⣿⣿⣿⣧⣰⣿⠃⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⣉⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣆⠀⣷⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢭⣾⣤⣿⣿⣿⡍⠉⠋⠑⠿⠁⠁⠀⠀⠀⠀⠀⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣉⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⡭⢉⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠿⠿⠿⢭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣬⣬⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠁⢀⣿⣤⣤⣤⣤⣤⣤⣴⣶⣶⡶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣦⣤⣤⣤⣤⣤⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢿⣶⣶⣶⣶⣶⡶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⢲⣶⡶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠟⠛⠉⠒⠂⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⠶⠶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢶⠶⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⡍⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⡛⠛⣲⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣾⣿⣿⣿⢸⣿⣿⡇⣿⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣤⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠉⠉⠁⠀⠉⠉⠉⠉⢽⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⣀⠀⠀⢀⢀⡀⢀⢀⡀⠀⢀⠀⠀⠀⢿⣇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⡟⣿⣛⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿
⠀⠀⠀⠀⠸⡙⠉⣟⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢸⣆⠀⠀⠀⢿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣼⣧⣿⣯⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿
⠀⠀⠀⣤⣴⣷⣤⣿⡿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡿⠻⣿⣿⢿⣿⠋⠘⠟⠼⡿⠟⠹⠃⠀⠸⠙⠀⠀⠀⠐⣶⣄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠉⠁⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⡌⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⡇⣿⢞⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⢸⡏⠩⡍⠉⣯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⣴⣤⣄⡀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠷⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠉⠀
⠀⠀⢸⣶⣶⣷⣶⣿⣟⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⠴⠄⡀⣀⡀⣴⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⢀⣼⣿⣿⣿⠁⣾⣿⣿⡿⠟⢉⣉⣉⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣟⣛⣛⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣇⡾⠒⢋⣾⠇⢿⢿⣿⣿⣷⣤⡄⠀⠀⠀⠀⠀⢻⣿⣿⣿⠃⣼⡿⠛⢉⣀⣒⣛⣛⣛⣛⣛⣛⣛⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⠃⠐⡤⠄⣧⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡀⠀⠘⣧⣤⣿⣿⡇⠀⢸⣿⣿⡿⠛⠁⠀⠀⠀⢀⣴⡌⣛⣛⠃⠀⣁⣀⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢿⡟⢻⣿⣶⣾⣿⡿⠀⢀⡀⠀⠀⠘⠉⠉⣁⣼⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⣋⣉⣉⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠿⢿⢿⠿⣿⣯⣭⣭⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⣿⣷⣼⣿⣿⣿⣿⣇⣰⣿⠃⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⣉⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣆⠀⣷⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢭⣾⣤⣿⣿⣿⡏⠙⠋⠑⠿⠁⠁⠀⠀⠀⠀⠀⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣩⣉⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⡭⢍⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠿⠿⠿⢭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣭⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠁⢀⣿⣤⣤⣤⣤⣤⣤⣴⣶⣶⡶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢿⣶⣶⣶⣶⣶⡶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⢲⣶⡶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠟⠛⠉⠒⠂⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⡶⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢶⠶⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⡛⠛⣲⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣾⣿⣿⣿⢸⣿⣿⡇⣿⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣤⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠉⠉⠙⠉⠍⢹⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⡀⣀⡀⠀⣀⠀⠀⡀⠙⠈⣿⣿⣿⣇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⡟⣿⣛⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿
⠀⠀⠀⠀⠰⡙⠉⣟⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣾⣿⣷⣷⣿⣿⣿⣿⡄⠀⣧⡀⠀⠀⢻⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣼⣇⣿⣯⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿
⠀⠀⠀⣤⣴⣷⣤⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⡿⣿⡿⠉⠹⠋⡿⡿⠛⠛⠀⠀⡟⠃⠀⠀⠀⣶⣶⣶⣄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠈⠛⠁⠙⠁⠀⠀⠀⠀⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⣿⣿⣿⣷⡌⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⡇⣿⢞⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⢸⡏⠩⡍⠉⣯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠷⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠉⠀
⠀⠀⢸⣶⣶⣿⣶⣿⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣴⣶⣾⣿⠿⠟⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠁⣾⣿⣿⡿⠟⢉⣉⣉⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣟⣛⣛⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢰⢁⡄⠠⠀⣀⠀⡾⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠃⣼⡿⠛⢉⣀⣒⣛⣛⣛⣛⣛⣛⣛⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⠃⠐⡬⠄⣧⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣃⠀⠀⠈⢾⡁⠀⣿⣿⠀⠀⠘⣿⣿⡿⠟⠂⠀⠀⠀⠀⢀⠘⣛⣛⣛⠃⠀⣁⣀⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠈⠻⡿⠿⢿⣤⣤⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⢁⣀⣽⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣋⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠿⢿⢿⠿⣿⣯⣭⣭⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢀⣿⡆⠘⣿⣿⣿⡟⠁⠀⠠⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣭⣭⣭⣭⣭⣭⣉⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣆⠀⣷⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡅⣴⡀⣸⣿⣿⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⡭⢍⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠿⠿⡿⢭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠈⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠁⢀⣿⣤⣤⣤⣤⣤⣤⣶⣶⣶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢿⣶⣶⣶⣶⣶⡶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⢲⣶⡶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠿⠂⠤⠄⢀⠤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣶⡶⠶⠶⠶⠶⠶⢶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⠶⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠲⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡛⠛⣲⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣾⣿⣿⣿⢸⣿⣿⡇⣿⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣤⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠉⠉⠉⠉⠉⠙⠍⢫⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⢀⣄⣀⣀⡀⢠⡀⠀⡆⠙⠊⢿⣿⣿⣿⣇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⡟⣿⣛⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿
⠀⠀⠀⠀⠸⡙⠉⣟⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡧⠀⢹⠀⠀⠀⠸⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣼⣧⣿⣯⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿
⠀⠀⠀⣤⣴⣷⣤⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⢿⣿⠇⠡⡟⠹⣿⠟⠛⠃⠀⢸⠘⠀⠀⠀⢶⣶⣶⣶⣄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠈⠋⠁⠀⠋⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠸⣿⣿⣿⣿⣷⡌⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⡇⣿⢞⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⢸⡏⠩⡝⠉⣯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠷⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠉⠀
⠀⠀⢸⣶⣶⣿⣶⣿⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⠗⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⠁⣾⣿⣿⡿⠟⢉⣉⣉⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣟⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡎⣉⠀⠀⠀⠀⢀⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠃⣼⡿⠛⢉⣀⣒⣛⣛⣛⣛⣛⣛⣛⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⡃⠐⡤⠄⣧⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣃⠀⠀⠀⢣⡏⠀⢰⣿⡆⠀⠀⢻⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⢛⣛⣛⣛⠃⠀⣁⣀⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠙⢿⣟⡻⣧⣀⣀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣋⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠿⢿⢿⠿⣿⣯⣭⣭⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⣼⣧⠀⢻⣿⣿⡇⠋⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⣉⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣆⠀⣷⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡅⢰⣄⢀⣿⣿⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⢍⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠿⠿⡿⢯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠁⢁⣿⣤⣤⣤⣤⣤⣤⣴⣶⡶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢿⣶⣶⣶⣶⣶⡶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⣲⣶⡶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠿⠗⠠⠤⠀⠠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⠶⠶⠶⢶⠶⢶⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢶⠶⠶⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⡛⠛⣲⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣾⣿⣿⣿⢸⣿⣿⡇⣿⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣤⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠉⠉⠉⠉⠍⠹⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⣤⣀⣄⣄⢀⣄⠀⢲⡈⠓⠻⣿⣿⣿⣿⣇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⡟⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠸⡙⠉⣟⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⡇⠀⠀⠘⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣼⣧⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣤⣴⣷⣤⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⢿⣿⠟⣿⡟⠈⠸⠉⠿⡟⠋⠛⠀⠀⡇⠁⠀⠀⠰⣶⣶⣶⣶⣄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠉⠉⠀⠘⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⡌⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⡇⣿⢞⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⢸⡏⠩⡍⠉⣯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠷⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠉⠀
⠀⠀⢸⣶⣶⣿⣶⣿⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⠿⠃⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠁⣾⣿⣿⡿⠟⢉⣉⣉⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣟⣛⣛⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⢰⢁⡀⠀⠀⠀⠀⠰⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠃⣼⡿⠛⢉⣀⣒⣛⣛⣛⣛⣛⣛⣛⣓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⡃⠐⡤⠄⣧⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠀⠀⠀⠘⣼⠀⠀⣾⣷⠀⠀⠈⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠘⣛⣛⣛⣛⠃⠀⣁⣀⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠈⠻⡿⡛⢿⣄⣀⡀⢸⠏⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣙⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠿⢿⢿⠿⣿⣯⣭⣭⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢠⣿⡄⠈⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣭⣭⣭⣭⣭⣭⣉⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣆⠀⣷⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡭⢠⣦⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣭⣭⣭⣭⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠈⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⡭⣍⠍⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠿⠿⠿⢯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣥⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠁⢀⣿⣤⣤⣤⣤⣤⣤⣶⣶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢿⣶⣶⣶⣶⣶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣷⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⢲⣶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⣶⡶⠶⠶⠶⣶⡶⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⡛⠛⣲⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣾⣿⣿⣿⢸⣿⣿⡇⣿⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣤⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠉⠉⠉⠉⠉⠉⠩⠙⢯⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢁⠀⠀⠀⢠⣤⣤⣠⣀⣠⡀⠈⣇⠉⠚⢿⣿⣿⣿⣿⣇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⡟⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠸⡙⠉⣟⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⢹⣀⠐⠀⢻⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣼⣧⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣤⣴⣷⣤⣿⡿⠿⠿⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⡿⢻⢻⠃⠀⠛⠘⢻⠋⠉⠁⠀⠈⠀⠀⠀⠀⢶⣶⣶⣶⣶⣄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠁⠁⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡌⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⡇⣿⢞⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⢸⡏⠩⡍⠉⣯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠿⠿⠿⠿⠿⠿⠷⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠉⠀
⠀⠀⢸⣶⣶⣿⣶⣿⣟⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⡾⠛⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠁⣾⣿⣿⡿⠟⢉⣉⣉⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣟⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡎⣀⠀⠀⠀⠀⠀⠼⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠃⣼⡿⠛⢉⣀⣒⣛⣛⣛⣛⣛⣛⣛⣓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⠃⠐⡤⠄⣧⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡀⠀⠀⠀⠡⡇⠀⢰⣿⣇⠀⠀⠈⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⢙⣛⣛⣛⣛⠃⠀⣁⣀⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠉⢻⠯⠃⣿⣤⣄⡀⠻⠁⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣋⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠿⢿⢿⠿⣿⣯⣭⣭⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⣼⣷⠀⠸⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣉⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣆⠀⣷⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠅⣴⣄⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣭⣭⣭⣭⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠹⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⡭⣍⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠿⠿⠿⢯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠁⢀⣿⣤⣤⣤⣤⣤⣤⣶⡶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢿⣶⣶⣶⣶⡶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⢲⣶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠿⠛⠁⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⣶⣶⡶⠶⠶⠶⢶⢶⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠖⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⠿⠿⠿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⡛⠟⣲⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣾⣿⣿⣿⢸⣿⣿⡇⣿⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣤⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠉⠉⠉⠉⠉⠩⢍⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⡀⡀⡀⡀⣶⣠⣤⣤⢰⣦⠀⢱⠈⠚⢿⣿⣿⣿⣿⣿⣇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⡟⣿⣛⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿
⠀⠀⠀⠀⠠⡙⠉⣟⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⠿⢻⡟⣿⣿⣿⣿⠀⠀⡇⠀⠀⠸⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿
⠀⠀⠀⣤⣴⣷⣤⣿⡿⠿⠿⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠿⣿⣿⠏⡏⡟⠀⠈⠁⠉⡏⠀⠈⠀⠀⠁⠀⠀⠀⢲⣶⣶⣶⣶⣶⣄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⡌⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⡇⣿⢞⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⢸⡏⠩⡝⠉⣯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠾⠿⠿⠿⠿⠿⠿⠿⠿⠷⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠉⠀
⠀⠀⢸⣶⣶⣿⣶⣿⣟⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣠⣤⣶⡿⠋⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⣾⣿⣿⡿⠟⢉⣉⣉⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣟⣛⣛⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⢠⠄⠀⢀⣀⠀⠀⠻⣿⣿⣷⣤⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠃⣼⡿⠛⢉⣀⣒⣛⣛⣛⣛⣛⣛⣛⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⠃⠐⡤⠄⣧⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡀⠀⠀⠀⠀⢾⡀⣀⣻⢿⡄⠀⠀⢸⡿⠋⠀⠀⠀⠀⠀⠀⠀⠈⣛⣛⣛⣛⣛⠃⠀⣁⣀⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢉⣟⠂⠸⣷⣤⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣋⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠿⢿⢿⠿⣿⣯⣭⣭⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⢸⣿⡇⠀⠙⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣉⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣆⠀⣷⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠁⣶⣄⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢼⣿⣿⣿⣭⣭⣭⣭⣯⣽⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠙⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⡭⣍⠍⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠿⠿⠿⢭⣽⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠘⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠁⢀⣿⣤⣤⣤⣤⣤⣤⡶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢿⣶⣶⣶⣶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⢲⣶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⣿⣿⣿⣶⢶⡶⠶⠶⡶⠶⠶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠴⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠖⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⡛⠟⣲⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣾⣿⣿⣿⢸⣿⣿⡇⣿⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣤⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⠿⠟⠉⠉⠉⠀⠉⠉⠉⠩⢝⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⢀⢀⡄⣀⣰⣲⢰⣤⣄⣰⡆⠀⢳⠈⠛⢿⣿⣿⣿⣿⣿⣇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⡟⣿⣛⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿
⠀⠀⠀⠀⠸⡙⠉⣟⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣿⠻⢻⠾⣿⣿⠿⡿⠀⠘⡆⠀⠀⢻⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣼⣧⣿⣯⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿
⠀⠀⠀⣤⣴⣷⣤⣿⡿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⢿⣿⡿⠃⢋⠏⠀⠈⠀⠀⠏⠀⠀⠀⠀⠃⠀⠀⠀⣶⣶⣶⣶⣶⣶⣄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣷⡌⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⡇⣿⢞⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⢸⡏⠩⡝⠉⣯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠐⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠉⠀
⠀⠀⢸⣷⣶⣿⣶⣿⣟⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⣴⣶⣾⡟⠁⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣾⣿⣿⡿⠟⢉⣉⣉⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣟⣛⣛⣻⣻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⢠⠀⠀⣀⣄⠀⠀⠙⢿⣿⣷⡦⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠃⣼⡿⠛⢉⣀⣒⣛⣛⣛⣛⣛⣛⣛⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⠃⠐⡬⠄⣧⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣃⠀⠀⠀⠀⠀⠾⣀⣀⣿⢿⠀⠀⠀⠸⡟⠁⠀⠀⠀⠀⠀⠀⠀⣘⣛⣛⣛⣛⣛⠃⠀⣁⣀⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢸⣝⠂⠸⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠿⢿⢿⠿⣿⣯⣭⣭⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⣼⣿⡄⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣆⠀⣷⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⢠⣶⣄⣠⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢼⣿⣿⣿⣭⣭⣭⣭⣯⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠻⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⡭⢍⠍⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠿⠿⠿⢯⣽⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠹⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣥⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠁⢀⣿⣤⣤⣤⣤⣤⣤⡶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢿⣶⣶⣶⣶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⢲⣶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠟⠋⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⢿⣿⣿⣿⢷⠶⠶⠶⠶⠶⠶⡖⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠂⠒⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢶⠖⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠟⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⡛⠛⣲⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣾⣿⣿⣿⢸⣿⣿⡇⣿⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣤⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⡿⠿⠋⠉⠉⠁⠀⠈⠉⠉⠩⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⢀⢀⡀⣠⣰⣢⢰⣶⣄⣼⡄⠀⢇⠈⠙⣿⣿⣿⣿⣿⣿⣇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⡟⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠸⡙⠉⣟⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⠛⢻⠺⣿⣿⠿⠇⠀⠘⠀⠀⠘⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣼⣇⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣤⣴⣧⣤⣿⡿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⢿⣿⡿⠉⢻⠇⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⣶⣶⣶⣄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⡌⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⡇⣿⢞⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⢸⡏⠩⡍⠉⣯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠉⠀
⠀⠀⢸⣷⣶⣿⣶⣿⣟⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⣶⣾⣿⡏⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣾⣿⣿⡿⠟⢉⣉⣉⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣟⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢸⢰⠀⠀⣤⣄⠀⠀⠘⢿⣿⡿⠆⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠃⣼⡿⠛⢉⣀⣒⣛⣛⣛⣛⣛⣛⣛⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⡃⠐⡤⠄⣧⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡃⠀⠀⠀⠀⠀⠺⢤⣤⠿⢻⡀⠀⠀⠸⡏⠀⠀⠀⠀⠀⠀⠀⢀⣘⣛⣛⣛⣛⣛⠃⠀⣁⣀⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢰⣯⠁⠸⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣙⣉⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠿⢿⢿⠿⣿⣯⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⣿⣿⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣩⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣆⠀⣷⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠅⢰⣦⣄⣼⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢼⣿⣿⣿⣭⣭⣭⣽⣭⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠻⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⡭⣍⠉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠿⠿⠿⢯⣽⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠹⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣥⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠁⢁⣿⣤⣤⣤⣤⣤⣤⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢿⣶⣶⣶⣶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⢲⣶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠶⠶⠶⠶⠶⠒⠲⠶⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠯⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⡛⠛⣲⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣾⣿⣿⣿⢸⣿⣿⡇⣿⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣤⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡿⠟⠋⠉⠉⠁⠀⠈⠉⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⢀⢀⣀⣠⣦⢶⣤⡀⣾⡀⠈⡇⠙⠻⣿⣿⣿⣿⣿⣿⣇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⡟⣿⣛⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿
⠀⠀⠀⠀⠸⡙⠉⣟⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⠛⢻⠸⢿⡿⠛⠇⠀⠸⠀⠀⠘⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿
⠀⠀⠀⣤⣴⣷⣤⣿⡿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠻⢿⣿⡿⠁⢹⠃⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⡌⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⡇⣿⢞⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⢸⡏⠩⡝⠉⣯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠄⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠉⠀
⠀⠀⢸⣷⣶⣿⣶⣿⣟⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⠒⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣾⣿⣿⡿⠟⢉⣉⣉⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣟⣛⣛⣻⣻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⢰⠀⠀⣤⣤⠀⠀⠈⢻⣿⠿⠃⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⠃⣼⡿⠛⢉⣀⣒⣛⣛⣛⣛⣛⣛⣛⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⡃⠐⡤⠄⣧⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡀⠀⠀⠀⠀⠀⠛⢤⣤⠿⢻⡀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⢀⣀⣛⣛⣛⣛⣛⣛⠃⠀⣁⣀⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣸⣦⠁⠘⣿⣷⡦⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣉⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠿⢿⢿⠿⣿⣯⣭⣭⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⢀⣿⣿⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣆⠀⣷⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠁⢼⣦⣀⣼⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣭⣭⣭⣭⣯⣽⣿⣿⣿⣿⣿⣿⡿⠁⠀⠈⠻⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⡭⣍⠍⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠿⠿⠿⢯⣽⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠙⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠁⢁⣿⣤⣤⣤⣤⣤⣤⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢿⣶⣶⣶⣶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⢶⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⢲⣶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠷⠶⠶⠶⠶⠶⠒⠒⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠙⠻⠛⠉⠯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣭⡏⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⡛⠟⣲⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣾⣿⣿⣿⢸⣿⣿⡇⣿⢸⣟⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣤⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⡿⠟⠋⠉⠉⠉⠉⠉⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⢠⢀⢀⠀⡆⣶⣄⡀⣦⠀⠘⡀⠙⢿⣿⣿⣿⣿⣿⣿⣇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⡟⣿⣛⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿
⠀⠀⠀⠀⠸⡙⠉⣟⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣶⣶⣾⣿⣿⣿⣾⡿⠉⠿⠸⢿⡗⠙⠃⠀⠱⠀⠀⢻⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣼⣇⣿⣯⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿
⠀⠀⠀⣤⣴⣷⣤⣿⡿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠿⢿⣿⡿⠘⢸⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠀⣶⣶⣶⣶⣶⣶⣶⣄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⡇⣿⢞⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⢸⡏⠩⡍⠉⣯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡶⠆⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠉⠀
⠀⠀⢸⣷⣶⣿⣶⣿⣟⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⣿⣿⣿⣅⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣾⣿⣿⡿⠟⢉⣉⣉⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣟⣛⣛⣻⣻⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠸⢸⠀⠀⣶⣶⠀⠀⠈⢹⣿⠟⠃⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠃⣼⡿⠛⢉⣀⣒⣛⣛⣛⣛⣛⣛⣛⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⡃⠐⡬⠄⣧⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠀⠀⠀⠀⠀⠀⠙⠲⢶⡛⢹⣄⡀⠀⠘⠃⠀⠀⠀⠀⠀⠀⣀⣐⣛⣛⣛⣛⣛⣛⠃⠀⣁⣀⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣸⣧⠀⠘⢿⣿⠧⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠿⢿⢿⠿⣿⣯⣭⣭⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣩⣉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣆⠀⣷⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠁⢾⣦⣠⣾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠈⠻⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⢍⠍⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠿⠿⠿⢯⣽⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠙⢿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠐⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣤⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠁⢀⣿⣤⣤⣤⣤⣤⣤⣴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠈⢳⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢿⣶⣶⣶⣶⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠖⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⢲⣶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠷⠶⠶⠶⠖⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠰⠲⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡛⢟⣲⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣾⣿⣿⣿⢸⣿⣿⡇⣿⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣤⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⡿⠟⠋⠉⠉⠉⠉⠉⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⢠⢀⣀⢀⡆⣶⣄⡀⣦⠀⠘⡀⠙⢿⣿⣿⣿⣿⣿⣿⣇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⡟⣿⣛⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿
⠀⠀⠀⠀⠸⡙⠉⣟⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣾⡿⠉⢿⠸⢿⡗⠙⠃⠀⢱⠀⠀⢻⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣼⣧⣿⣯⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿
⠀⠀⠀⣤⣴⣷⣤⣿⡿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⠿⠟⠿⢿⣿⡿⠈⢸⠃⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠠⠀⣶⣶⣶⣶⣶⣶⣶⣄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⡇⣿⢞⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⢸⠏⠩⡍⠉⣯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡶⠆⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠉⠀
⠀⠀⢸⣶⣶⣿⣶⣿⣟⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⣿⣿⣿⣅⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣾⣿⣿⡿⠟⢉⣉⣉⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣟⣛⣛⣻⣻⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠸⢸⠀⠀⣶⣶⠀⠀⠈⢹⣿⠟⠃⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠃⣼⡿⠛⢉⣀⣒⣛⣛⣛⣛⣛⣛⣛⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⡃⠐⡤⠄⣧⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠀⠀⠀⠀⠀⠀⠙⠲⢶⡛⢻⣄⡀⠀⠘⠃⠀⠀⠀⠀⠀⠀⣀⣐⣛⣛⣛⣛⣛⣛⠃⠀⣁⣀⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣼⣧⠀⠘⣿⣿⠧⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣋⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠿⢿⢿⠿⣿⣯⣭⣭⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⣩⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣆⠀⣷⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠀⢾⣦⣠⣾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣭⣭⣭⣭⣯⣽⣿⣿⣿⣿⣿⣿⡿⠁⠀⠈⠻⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⡭⣍⠍⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠿⠿⠿⢯⣽⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠙⢿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠐⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠁⢁⣿⣤⣤⣤⣤⣤⣤⣴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠈⢳⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢿⣶⣶⣶⣶⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠖⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⢲⣶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠷⠶⠶⠶⠲⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠖⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠰⠲⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⡏⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡛⠛⣲⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣾⣿⣿⣿⢸⣿⣿⡇⣿⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣤⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠉⠉⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⢀⠀⠀⡄⣤⡀⢰⣄⠀⢑⠈⠻⣿⣿⣿⣿⣿⣿⣿⣇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⡟⣿⣛⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠸⡙⠉⣟⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣤⣤⣶⣾⣷⢿⢾⡏⠃⠇⠹⢿⠂⠙⠀⠀⠃⠀⠘⣿⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣼⣧⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣤⣴⣷⣤⣿⡿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣷⡿⠟⠿⣿⣿⡟⠸⢸⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠆⢰⣶⣶⣶⣶⣶⣶⣶⣄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⡇⣿⢞⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⢸⡏⠩⡍⠉⣯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡾⠃⠀⠀⠀⠹⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠉⠀
⠀⠀⢸⣷⣶⣿⣶⣿⣟⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠐⢿⣿⣿⣄⡀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣾⣿⣿⡿⠟⢉⣉⣉⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣟⣛⣛⣻⣻⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠸⣸⠀⠀⣶⣷⠀⠀⠈⢻⡿⠋⠁⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠃⣼⡿⠛⢉⣠⣒⣛⣛⣛⣛⣛⣛⣛⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⡃⠐⡤⠄⣧⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠀⠀⠀⠀⠀⠀⠙⠲⢶⣛⢹⣤⣀⣀⠘⠃⠀⠀⠀⠀⠀⠀⣀⣚⣛⣛⣛⣛⣛⣛⠃⠀⣁⣀⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣼⣧⠀⠈⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣋⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠿⢿⢿⠿⣿⣯⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⣩⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣆⠀⣷⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠁⢾⣦⣤⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠹⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⡭⢍⠍⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠿⠿⠿⢯⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠈⢻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣥⣬⣥⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠁⢁⣿⣤⣤⣤⣤⣤⣤⣴⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠘⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣠⠤⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢿⣶⣶⣶⣶⣶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⠟⠂⠀⠀⠀⠀⠀⠀⢿⣿⣿⣾⣶⣶⣶⣶⣶⣶⠶⠖⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⢲⣶⢶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠾⠶⠶⠖⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠶⠶⠶⠶⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⣷⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡛⠛⣲⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣾⣿⣿⣿⢸⣿⣿⡇⣿⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣤⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠉⠉⠉⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⢀⢀⠀⠀⡄⣤⡀⢠⣄⠀⢁⠉⠻⣿⣿⣿⣿⣿⣿⣿⣇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⡟⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠰⡙⠉⣟⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣤⣤⣶⣾⣷⢿⢺⡇⠀⠇⠙⢿⠀⠙⠀⠀⠃⠀⠘⣿⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣤⣴⣷⣤⣿⡿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⡟⠸⢸⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠆⢰⣶⣶⣶⣶⣶⣶⣶⣄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢼⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⡇⣿⢞⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⢸⠏⠩⡝⠉⣯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⡿⠃⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠉⠀
⠀⠀⢸⣷⣶⣿⣶⣿⣟⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠐⢿⣿⣿⣦⡄⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣾⣿⣿⡿⠟⢉⣉⣉⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣟⣛⣛⣻⣻⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠘⣼⠁⠀⣾⣿⡄⠀⠀⢻⣿⠋⠁⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠃⣼⡿⠛⢉⣀⣒⣛⣛⣛⣛⣛⣛⣛⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⠃⠐⡤⠄⣧⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡀⠀⠀⠀⠀⠀⠈⢓⡶⠟⢸⣧⣤⣄⣸⡇⠀⠀⠀⠀⠀⠀⣒⣚⣛⣛⣛⣛⣛⣛⠃⠀⣁⣀⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣼⣷⠀⠀⢿⣿⠿⠛⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣋⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠿⢿⢿⠿⣿⣯⣭⣭⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣩⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣆⠀⣷⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠅⢸⣷⣤⣾⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠙⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⡭⢍⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠿⠿⠿⢭⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠹⣿⣿⣷⣄⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣬⣭⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠁⢁⣿⣤⣤⣤⣤⣤⣤⣴⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⠄⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢿⣶⣶⣶⣶⣶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⢿⣿⣷⣶⣶⣶⣶⡶⠶⠶⠖⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⢲⣶⢶⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠶⠶⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⡀⠀⠀⠀⠲⠶⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡆⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡛⠛⣲⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⣿⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣤⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠉⠉⠉⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⢀⠀⠀⡆⣦⡀⠠⣦⠀⠁⠈⠻⣿⣿⣿⣿⣿⣿⣿⣇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡟⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠸⡙⠉⣟⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣥⣴⣶⣶⣷⣷⣾⡇⠀⠗⠘⢻⠄⠈⠀⠀⠁⠀⠈⣿⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣤⣴⣷⣤⣿⡿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⡿⠀⠛⠇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠂⢰⣶⣶⣶⣶⣶⣶⣶⣄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⡇⣿⢞⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⢸⡏⠩⡍⠉⣯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣾⡟⠋⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠉⠀
⠀⠀⢸⣷⣶⣿⣶⣿⣟⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⠊⡀⠀⠀⡀⠀⠰⠻⣿⣿⣧⣄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣾⣿⣿⡿⠟⢉⣉⣉⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣟⣛⣛⣻⣻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⢶⡇⠀⢺⣿⡆⠀⠀⢹⣿⠏⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⠃⣼⡿⠛⢉⣀⣒⣛⣛⣛⣛⣛⣛⣛⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⠃⠐⡤⠄⣧⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡃⠀⠀⠀⠀⠀⠀⢹⡻⠯⠽⣷⣶⣤⣼⡿⠀⠀⠀⠀⠀⠀⣒⣛⣛⣛⣛⣛⣛⣛⠃⠀⣁⣀⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣸⣿⡆⠀⠹⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣉⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠿⢿⢿⠿⣿⣯⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣩⣍⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣆⠀⣷⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⠰⣿⣦⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠈⠻⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⡭⢍⠍⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠿⠿⠿⢯⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠘⢿⣿⣿⣦⡀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣥⣭⣬⠭⢥⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠁⢁⣿⣤⣤⣤⣤⣤⣤⣴⡶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣦⡀⠀⠀⠀⠀⠈⢳⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⢤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢿⣶⣶⣶⣶⣶⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⠟⠉⠀⠀⠀⠀⠀⠀⢻⣿⣷⣶⢶⠶⠶⠶⠖⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⢲⣶⣶⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠶⠶⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⡄⠀⠀⠀⠐⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢶⠶⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⡛⠛⣲⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣾⣿⣿⣿⢸⣿⣿⡇⣿⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣤⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠉⠉⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⡀⠀⢀⢠⢀⠀⢦⠀⠀⡀⠙⢿⣿⣿⣿⣿⣿⣿⣇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⡟⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠸⡙⠉⣟⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⣦⣴⣶⣾⡶⡇⣿⠁⠸⠘⢻⡇⠈⠃⠀⠰⠀⠀⢿⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣼⣧⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣤⣴⣷⣤⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⠃⠇⠇⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠠⠰⣶⣶⣶⣶⣶⣶⣶⣄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢡⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⡇⣿⢞⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⢸⡏⠩⡝⠉⣯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣴⣾⡿⠋⠀⠀⠀⠨⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠉⠀
⠀⠀⢸⣶⣶⣿⣶⣿⣟⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡎⣁⠀⠀⢀⡀⠀⠛⣿⣿⣷⣤⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣾⣿⣿⡿⠟⢉⣉⣉⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣟⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠱⣏⠀⢸⣿⣷⠀⠀⠸⣿⡏⠁⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠃⣼⡿⠛⢉⣀⣒⣛⣛⣛⣛⣛⣛⣛⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⡃⠐⡤⠄⣧⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣃⠀⠀⠀⠀⠀⠀⠩⣟⠻⠍⣿⣶⣶⣶⣿⠃⠀⠀⠀⠀⠀⢐⣛⣛⣛⣛⣛⣛⣛⠃⠀⣁⣀⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢰⣿⣇⠀⠘⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣋⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠿⢿⢿⠿⣿⣯⣭⣭⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣉⣉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣆⠀⣷⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡭⠁⢿⣶⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢼⣿⣿⣿⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠙⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⡭⢍⠭⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠿⠿⠿⢯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠈⠻⣿⣿⣧⣀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣥⣤⣤⡤⢥⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠁⢁⣿⣤⣤⣤⣤⣤⣤⣴⣶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣄⠀⠀⠀⠀⠈⠳⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⡤⡤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢿⣶⣶⣶⣶⣶⡶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⠟⠋⠀⠀⠀⠀⠀⠀⠸⣿⣷⡶⡶⠶⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⢲⣶⣶⣶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⢀⠀⠀⠀⠐⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⣿⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⡛⢟⣲⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣾⣿⣿⣿⢸⣿⣿⡇⣿⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣤⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠉⠉⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⢀⠀⠀⡄⢀⠀⠀⣆⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡟⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠸⡙⠉⣟⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣣⣤⣴⣶⣶⣶⣾⡏⠀⠅⠘⢻⠂⠈⠀⠀⠁⠀⠘⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣼⣧⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣤⣴⣷⣤⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⠁⠿⠇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠂⢰⣶⣶⣶⣶⣶⣶⣄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠁⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣷⡌⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⡇⣿⢞⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⢸⡏⠩⡝⠉⣯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣶⣾⣿⡟⠁⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠉⠀
⠀⠀⢸⣷⣾⣿⣶⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡎⣀⠀⠀⣠⡀⠘⠻⣿⣿⣷⡶⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⠁⣾⣿⣿⡿⠟⢉⣉⣉⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣟⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠳⣇⠀⢸⣿⡧⠀⠀⢹⣿⡏⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⠃⣼⡿⠛⢉⣠⣒⣛⣛⣛⣛⣛⣛⣛⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⡃⠐⡤⠄⣧⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣃⠀⠀⠀⠀⠀⠀⢹⣝⠛⠛⣿⣶⣶⣿⣿⡇⠀⠀⠀⠀⠀⢚⣛⣛⣛⣛⣛⣛⠃⠀⣁⣀⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣸⣿⣇⠀⠸⠿⠿⠿⠋⠉⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣋⣉⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠿⢿⢿⠿⣿⣯⣭⣭⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⢀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣩⣉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣆⠀⣷⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡭⠀⢿⣷⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢼⣿⣿⣿⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠙⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⡭⢍⢭⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠿⠿⡿⢯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠈⠻⣿⣿⣧⣀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⡤⢤⣤⡄⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠁⢁⣿⣤⣤⣤⣤⣤⣤⣶⣶⣶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣄⠀⠀⠀⠀⠱⣶⣶⣶⣶⣶⣶⣶⣶⣤⣄⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢿⣶⣶⣶⣶⣶⣶⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⠛⠉⠀⠀⠀⠀⠀⠀⢿⣷⣶⡶⠶⠖⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⢲⣶⣶⣶⡶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣭⡏⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡛⠛⣲⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣤⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠉⠉⠉⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⡙⠉⣟⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣠⣤⣶⣶⣶⢾⢿⠄⠀⠀⠓⡷⠀⠁⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣤⣴⣷⣤⣿⡿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣶⣾⣿⠿⣿⣿⣿⡏⠘⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣶⣶⣶⣶⣶⣶⣄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣷⡌⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⢸⡏⠩⡍⠉⣯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢰⣶⣿⣿⠋⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠉⠀
⠀⠀⢸⣷⣶⣿⣶⣿⣟⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⢸⢡⡀⠀⢀⣄⠀⠛⢿⣿⣿⣶⠄⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⠁⣾⣿⣿⡿⠟⢉⣉⣉⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣟⣛⣛⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⢾⡀⣀⣿⣿⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠃⣼⡿⠛⢉⣀⣒⣛⣛⣛⣛⣛⣛⣓⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⠃⠐⡤⠀⣧⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡀⠀⠀⠀⠀⠀⠀⣯⡟⠛⢻⣿⣷⣾⣿⡟⠀⠆⠀⠀⠀⠘⣛⣛⣛⣛⣛⣛⠃⠀⣁⣀⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣶⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢀⣿⣿⡀⠀⠻⠿⠿⠛⠁⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣉⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠿⢿⢿⠿⣿⣯⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⢀⡀⠀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣉⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣆⠀⣵⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠅⠺⣿⣾⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠈⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⢭⣩⢭⡭⢍⠭⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠿⠿⠿⢭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⡀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⢶⣦⣤⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠁⠀⣿⣤⣤⣤⣤⣤⣤⣴⣶⣶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣦⡀⠀⠀⠀⠐⢶⣶⣶⣶⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢿⣶⣶⣶⣶⣶⣶⣶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠟⠉⠀⠀⠀⠁⠀⠀⢳⣶⡶⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⢲⣶⣶⣶⣶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢶⠶⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣽⣿⣿⣯⡏⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⡛⠛⣲⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣤⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠉⠉⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⡀⠀⢀⠀⠀⠀⢆⠀⠀⠈⠹⣿⣿⣿⣿⣿⣇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠸⡙⠉⣟⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣤⣴⣶⣾⡖⡇⣿⠀⠐⠐⢻⡆⠈⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣤⣴⣷⣤⣿⡿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⠻⢿⣿⣿⠃⠃⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⢰⣶⣶⣶⣶⣶⣄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣷⡌⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⢸⡏⠩⡍⠉⣯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣶⣾⣿⡟⠁⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠷⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠉⠀
⠀⠀⢸⣶⣶⣿⣶⣿⣟⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡏⡤⠀⢀⣤⡀⠘⠙⣿⣿⣷⡦⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⠁⣾⣿⣿⡿⠟⢉⣉⣉⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣟⣛⣛⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠱⣇⣀⣸⣿⡇⠀⠀⢸⣿⡋⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠃⣼⡿⠛⢉⣀⣒⣛⣛⣛⣛⣛⣛⣛⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⠃⠐⡤⠀⣧⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣃⠀⠀⠀⠀⠀⠀⢰⣯⠓⠚⣿⣿⣿⣿⣿⠃⠠⠀⠀⠀⠀⢛⣛⣛⣛⣛⣛⠃⠀⣁⣀⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣶⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣼⣿⣧⠀⠘⠿⠿⠛⠋⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣏⣛⣉⣉⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠿⢿⢿⠿⣿⣯⣭⣭⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⣀⠀⣠⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣉⣉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣆⠀⣵⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⠘⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠙⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⠭⠭⠩⢭⡭⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠿⠿⠿⢭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⣄⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠁⢀⣿⣤⣤⣤⣤⣤⣤⣴⣶⣶⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣄⠀⠀⠀⠀⠲⣶⣶⣶⣶⣶⣶⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢿⣶⣶⣶⣶⣶⣶⣶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠋⠀⠀⠀⠀⠀⠀⠸⣷⡶⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⢲⣶⣶⣶⣶⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⣄⣠⣷⣦⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣰⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣬⠋⢻⡛⡛⣟⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⣤⣼⣧⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠉⠙⠛⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⡀⢠⢠⢀⣀⡄⣦⣀⣰⣄⠀⢣⡙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⠏⢹⡙⠙⣿⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⢿⣿⡏⠙⡧⠻⣿⠋⠿⠀⠀⡇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠷⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣦⣴⣿⣴⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⠸⣿⠃⠀⠀⢀⡟⠀⠀⠀⠀⠀⠐⡄⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⢶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣤⣄⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀
⣽⣿⣿⣏⠹⡝⠉⣯⡽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡿⢿⠁⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣴⣿⣿⣿⠋⠁⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠇⠀⢸⢡⠄⢰⣰⣼⠀⠟⢿⣿⣿⣶⡦⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⠛⠓⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⢿⣄⣈⣿⣿⠆⠀⠘⣿⣿⠁⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡉⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡇⠘⡾⠆⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡆⠀⠀⠀⠀⠀⠈⣿⣟⠚⢻⣿⣿⣿⣿⣿⣶⡶⠀⠀⠀⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣉⡁⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣆⠈⠿⣿⠿⠿⠿⠋⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣉⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⣠⡀⢀⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣽⣭⣭⣭⣭⣭⣭⣭⡉⢁⠀⡀⠀⠀⠀⠀⠀⠀⠀
⢿⣿⣿⡁⢘⣆⠂⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡭⠁⠻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣉⡉⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠸⣿⣿⣿⣿⣿⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠈⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠍⠀⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀
⠀⢹⣿⡿⢿⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⡀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣭⡤⡭⠥⢥⡤⢭⣭⠉⢁⠨⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⣀⣸⣇⣁⣿⣭⣭⣭⣥⣶⣿⣿⣿⣷⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣶⠄⠀⠀⡄⠱⣶⣶⣶⣶⣶⣶⣶⣦⡤⡤⢀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠈⠀⠀⠘⣿⣿⣶⣶⡶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⠛⠛⠛⠛⣶⣶⣶⣶⣶⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡷⣶⣶⣶⣶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠇⠀⠀⠀⠲⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠿⠷⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⣄⣠⣷⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣰⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣬⠋⢻⡛⡛⣟⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⣤⣼⣧⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠉⠙⠋⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⡀⠀⣀⢀⢐⡀⣄⡀⢰⡄⠈⢅⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⠏⢹⡙⠙⣿⠿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⠏⢻⡇⠿⣿⠘⢷⠀⠘⠂⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠷⠶⠾⠶⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣦⣼⣿⣴⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠸⡿⠀⠈⠀⠰⡇⠀⠀⠀⠀⠀⠰⠰⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⢶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⠈⠙⠉⠉⠀⠀⠀⠀⠀⠀⠁⠀⢀⣀⣀⡀⠀⠀⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀
⣽⣿⣿⣏⠹⡝⠉⣯⡽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠁⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣾⣿⣿⡿⠋⠁⠀⠀⠨⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⡏⣤⠀⢆⣤⡇⠸⠻⣿⣿⣷⣦⡀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣛⣛⣛⣛⣛⠛⠓⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠹⣯⣀⣸⣿⣷⠀⠀⢹⣿⡟⠁⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡉⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡇⠘⡾⠆⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡀⠀⠀⠀⠀⠀⢸⣿⡓⠛⣿⣿⣿⣿⣿⣧⣴⡄⠀⠀⠀⣒⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣉⠁⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣾⣿⣷⡄⠹⣿⣿⡿⠿⠿⠋⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣛⣛⣉⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢀⣄⡀⣠⣿⣿⣿⣧⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⡉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣿⣿⡁⢘⣆⠂⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⠈⠻⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⢀⣀⣠⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣉⣉⠉⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠸⣿⣿⣿⣿⣿⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠈⢿⣿⣿⣿⠅⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠍⠁⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀
⠀⢹⣿⡿⢿⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣾⣿⣿⣷⣤⣤⡤⡭⠥⠄⠀⠨⠭⠉⢁⡨⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⣀⣸⣇⣁⣿⣭⣭⣭⣥⣶⣿⣿⣷⣶⣶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⡤⠀⠀⢀⠈⢶⣶⣶⣶⣶⣶⣶⣦⡤⠤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠉⠀⠀⠀⠁⠀⠀⢻⣿⣶⣶⣶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⠛⠛⠛⠛⣶⣶⣶⣶⣶⣶⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡷⣶⣶⣶⣶⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠠⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠾⠷⠶⠶⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⣄⣠⣷⣦⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣰⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣬⠋⢻⡛⡛⣟⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⣤⣼⣧⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠉⠙⠋⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⡀⠀⣀⢀⢐⡀⣄⠀⢰⡄⠈⢅⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⠏⢹⡙⠙⣿⠿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⠏⢻⡇⢿⣿⠘⢷⠀⠘⠂⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠶⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣦⣴⣿⣴⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠸⡿⠀⠈⠀⢰⡇⠀⠀⠀⠀⠀⠰⠰⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⠈⠙⠉⠉⠀⠀⠀⠀⠀⠀⠁⠀⢀⣀⣀⡀⠀⠀⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀
⣽⣿⣿⣏⠹⡝⠉⣯⡽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠁⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣾⣿⣿⡿⠋⠁⠀⠀⠨⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⡏⣤⠀⣆⣤⡇⠸⠿⣿⣿⣷⣦⡀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣛⣛⣛⣛⡛⠛⠓⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠹⣯⣀⣸⣿⣷⠀⠀⢹⣿⡟⠁⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⡉⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡇⠘⡼⠆⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡀⠀⠀⠀⠀⠀⢹⣿⡓⠛⣿⣿⣿⣿⣿⣧⣤⡄⠀⠀⠀⣒⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣉⠁⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣾⣿⣿⡄⠹⢿⣿⡿⠿⠿⠋⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣉⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢀⣄⡀⣰⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣿⣿⡁⢘⣆⠂⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⠈⠻⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⢀⣀⣠⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣉⣉⠉⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠸⣿⣿⣿⣿⣿⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠈⢿⣿⣿⣿⠅⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠍⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⡿⢿⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣾⣷⣿⣧⣤⣤⡤⡬⠀⠠⠀⠨⠍⠉⢀⠩⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⣀⣸⣇⣁⣿⣭⣭⣭⣤⣶⣿⣿⣿⣶⣶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⡤⠀⠀⢀⠈⢶⣶⣶⣶⣶⣶⣶⣦⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠉⠀⠀⠀⠁⠀⠀⢻⣿⣶⣶⡶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⠛⠛⠛⠟⣶⣶⣶⣶⣶⣶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡷⣶⣶⣶⣶⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠰⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠾⠷⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⡀⠀⢠⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⡄⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠠⠠⡀⣰⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣵⣴⣦⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⠀⠁⡈⡛⣟⣲⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢐⣤⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠉⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠀⠀⠀⠸⡙⠉⣟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣤⣤⣶⣶⣶⣦⡇⠀⣬⠸⢶⠄⠸⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⡶⠶⠶⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⣦⣴⣷⣤⣿⡿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢿⠇⠀⠁⠀⠸⠀⠀⠀⠀⠀⠀⠄⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠃⠉⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠘⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢼⡏⠩⡝⠉⣯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠏⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⣶⣾⣿⡟⠋⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢼⣷⣾⣿⣶⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⢡⡄⠠⢠⣤⠀⠿⢿⣿⣿⣤⡄⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⢾⡀⢈⣿⣿⠄⠀⠘⣿⣿⠋⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⢒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠸⡇⠐⡼⠄⣷⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣃⠀⠀⠀⠀⠀⠈⣿⡟⠿⢿⣷⣶⣶⣿⣿⢀⡄⠀⠀⠀⢀⣒⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢰⣿⣿⡄⠘⣿⣿⣿⠿⠿⠇⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⡉⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠿⢿⣿⠿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⡀⢀⣼⣿⣿⣯⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣍⣍⣉⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠐⠀⠀⢈⣆⠀⣷⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠁⠹⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⡍⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⢿⣿⣿⣿⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠈⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣽⣭⣭⣭⣭⣭⣭⣭⣭⣭⠭⢭⠭⠉⠍⠍⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⠀⠘⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⡀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡶⣶⡦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠨⠁⣁⣿⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣦⡀⠀⠀⠀⢲⣶⣶⣶⣶⣶⣶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⡿⣷⢁⣿⣿⣾⣿⣿⣷⣿⣿⣶⡶⣿⢻⡆⣿⡟⣷⢰⡟⣿⡖⢻⡟⠃⣿⠛⢰⡟⣿⡟⢻⡟⠃⣿⢠⣿⢻⡾⣿⡆⣿⠐⢸⣿⣿⡆⣾⣿⣷⢰⣿⣷⢸⣿⢻⡆⣿⡟⣷⠰⠿⣿⡆⠾⢹⣆⠼⠟⣷⠀⠀⠀
⠀⠀⠀⣿⡗⣿⢸⣿⣿⣶⣾⣷⣾⣿⣿⡇⠀⣿⠛⠃⣿⡟⣿⢸⡇⣿⡇⢸⡇⠀⣿⠛⢸⡇⣤⡅⢸⡇⠀⣿⢸⣿⢸⡇⣿⢿⣿⠀⢸⣿⢻⡆⣿⣿⣿⢸⣇⣿⢸⣿⢻⡇⣿⡇⣿⢰⡶⠿⠃⣶⠾⠇⢶⠶⠿⠀⠀⠀
⠀⠀⠀⠛⠛⠛⠘⠋⠛⠃⠘⢳⢚⠋⠙⠃⠀⠛⠀⠀⠛⠃⠛⠈⠛⠛⠁⠘⠃⠀⠛⠛⠈⠓⠛⠁⠘⠃⠀⠛⠈⠛⠛⠁⠛⠘⠛⠀⠘⠛⠛⠃⠙⠛⠋⠚⠃⠛⠛⠛⠘⠃⠛⠛⠛⠘⠃⠀⠀⠛⠀⠀⠚⠃⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠲⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⢤⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⡄⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣰⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣯⣽⣿⣿⣿⣿⣷⣴⣦⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡈⡛⣟⣲⣶⣶⣶⣶⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢐⣤⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠉⠉⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⡙⠉⣟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣶⣶⡖⡆⣷⠀⠨⠀⢶⡆⠘⠆⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⡶⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣦⣴⣷⣤⣿⡿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠇⣟⡏⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⢂⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠘⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢼⡏⠩⡝⠉⣯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠏⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢠⣶⣾⣿⡿⠋⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣷⣾⣿⣶⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⣏⡄⠐⢀⣤⠀⠸⢿⣿⣿⣧⣄⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢻⡇⢀⣿⣿⡆⠀⠈⣿⣿⠋⠁⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⡇⠐⡼⠄⣷⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠀⠀⠀⠀⠀⠀⣿⣟⠻⢻⣷⣶⣶⣿⣿⠀⡄⠀⠀⠀⠀⣐⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢀⣿⣿⣆⠈⣿⣿⣿⠿⢿⠏⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣉⣛⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠿⢿⣿⠿⣿⣯⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢀⣀⢀⣼⣿⣿⣿⣤⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣍⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣆⠀⣷⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠁⠙⢿⣿⣿⣿⣿⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⡭⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢿⣿⣿⣿⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⡉⠩⠭⠥⠉⠉⠍⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⠀⠘⠿⠿⡿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷⣶⣶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢁⣁⣿⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣦⡀⠀⠀⠀⢲⣶⣶⣶⣶⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⡿⣷⢀⣿⣿⣾⣿⣿⣷⣿⣿⣶⡶⣿⢻⡆⣿⡟⣷⢰⡟⣿⡔⢻⡟⠃⣿⠛⢰⡟⣿⡟⢻⡟⠃⣿⢠⣿⢻⡶⣿⡆⣿⠀⢸⣿⢿⡆⣾⣿⣷⢰⣿⣷⢸⣿⢻⡆⣿⡟⣷⠰⠿⣿⡆⠾⢹⡆⠼⠟⣷⠀⠀⠀
⠀⠀⠀⣿⡗⣿⢸⣿⣿⣶⣾⣷⣾⣿⣿⡇⠀⣿⠛⠃⣿⡟⣿⢸⡇⣿⡇⢸⡇⠀⣿⠛⢸⡇⣤⡅⢸⡇⠀⣿⢸⣿⢸⡇⣿⢿⣿⠀⢸⣿⢻⡆⣿⣿⣿⢸⣇⣿⢸⣿⢻⡇⣿⡇⣿⢰⡶⠿⠃⣶⠾⠇⢶⠶⠿⠀⠀⠀
⠀⠀⠀⠛⠛⠛⠘⠋⠛⠃⠘⢳⡞⠋⠙⠃⠀⠛⠀⠀⠛⠃⠛⠈⠛⠛⠁⠘⠃⠀⠛⠛⠈⠓⠛⠁⠘⠃⠀⠛⠈⠛⠛⠁⠛⠘⠛⠀⠘⠛⠛⠃⠙⠛⠋⠚⠃⠛⠛⠛⠘⠃⠛⠛⠛⠘⠃⠀⠀⠛⠀⠀⠚⠃⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⢠⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⡄⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣰⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣽⣿⣿⣿⣿⣵⣴⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡈⡛⣟⣲⣶⣶⣶⣶⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣤⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⠉⠉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⡙⠉⣟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣤⣤⣴⣶⣶⣾⣾⠈⢠⡁⠷⡧⠀⠇⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡶⠾⠾⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣦⣴⣷⣤⣿⡿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⡿⠀⠈⠀⠈⠇⠀⠀⠀⠀⠀⠠⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⠀⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⡏⠩⡝⠉⣯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣶⣶⣿⡿⠛⠁⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣷⣾⣿⣶⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⡏⣤⠀⠄⣤⠆⠸⢿⣿⣿⣧⣄⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢱⣇⢀⣹⣿⡇⠀⠀⢿⣿⠏⠁⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⡇⠐⡼⠄⣯⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠀⠀⠀⠀⠀⠀⣻⣿⠛⢻⣿⣶⣶⣿⣿⠅⣀⠀⠀⠀⠀⣀⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣧⠀⢿⣿⣿⡿⢿⠏⠁⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠂⠿⢿⣿⠿⣿⣯⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⠀⣸⣿⣿⣿⣤⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣩⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢘⣆⠀⣷⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠍⠘⢿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢿⣿⣿⣿⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠙⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⢭⣭⣭⠉⢭⠍⠥⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷⣶⣶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⢁⣁⣿⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣦⡀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⡿⣷⢀⣿⣿⣾⣿⣿⣷⣿⣿⣶⡶⣿⢻⡆⣿⡟⣷⢰⡟⣿⡔⢻⡟⠃⣿⠛⢰⡟⣿⡟⢻⡟⠃⣿⢰⣿⢻⡾⣿⡆⣿⠀⢸⣿⣿⡆⣾⣿⣷⢰⣿⣷⢸⣿⢻⡆⣿⡟⣷⠰⠿⣿⡆⠾⢹⣆⠼⠟⣷⠀⠀⠀
⠀⠀⠀⣿⡗⣿⢸⣿⣿⣶⣾⣷⣾⣿⣿⡆⠀⣿⠛⠃⣿⡟⣿⢸⡇⣿⡇⢸⡇⠀⣿⠛⢸⡇⣤⡄⢸⡇⠀⣿⢸⣿⢸⡗⣿⢿⣿⠀⢸⣿⢻⡆⣿⣿⣿⢸⣇⣿⢸⣿⢻⡇⣿⡇⣿⢰⡶⠿⠃⣶⠾⠇⢶⠶⠿⠀⠀⠀
⠀⠀⠀⠛⠛⠛⠘⠋⠛⠃⠘⢳⡚⠋⠙⠃⠀⠛⠀⠀⠛⠃⠛⠈⠛⠛⠁⠘⠃⠀⠛⠛⠈⠓⠛⠁⠘⠃⠀⠛⠈⠛⠛⠁⠛⠘⠛⠀⠘⠛⠛⠃⠙⠛⠋⠚⠃⠛⠛⠛⠘⠃⠛⠛⠛⠘⠃⠀⠀⠛⠀⠀⠚⠃⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠲⠶⠶⠶⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡀⠀⢠⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⡄⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠠⡀⣰⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣵⣴⣦⡆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡈⡛⣟⣲⣶⣶⣶⣶⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠐⠀⠀⢐⣤⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠉⠉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠙⢿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠀⠀⠀⠹⡙⠉⣟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣥⣤⣴⣶⣶⢲⢸⡄⠀⡇⠶⣶⠀⠳⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡶⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣦⣴⣿⣤⣿⡿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡟⠸⣿⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠰⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢼⡏⠩⡝⠉⣯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣴⣶⣿⣿⠟⠁⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢼⣷⣾⣿⣶⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡎⣤⠀⡆⣤⡄⠨⠻⣿⣿⣷⣤⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠹⣧⣀⣹⣿⣷⠀⠀⢻⣿⡟⠁⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⡇⠐⡬⠄⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡀⠀⠀⠀⠀⠀⢹⣿⠻⠻⣿⣶⣶⣾⣿⡇⣠⠀⠀⠀⠀⣀⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣿⣿⣷⡀⢿⣿⣿⡿⢿⡿⠉⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣋⣛⣉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠿⢿⣿⠿⣿⣯⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⣀⠀⣰⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠐⠀⠀⢈⣆⠀⣷⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠍⠘⢿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⠍⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⢿⣿⣿⣿⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠙⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⡭⢭⠭⠥⠉⠉⠍⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠿⠿⡿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣦⡀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣷⣶⣶⢶⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⢁⣁⣿⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⡶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⡀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⡿⣷⢀⣿⣿⣾⣿⣿⣷⣿⣿⣶⡶⣿⢻⡆⣿⡟⣷⢰⡟⣿⡔⢻⡟⠃⣿⠛⢰⡟⣿⡟⢻⡟⠃⣿⢰⣿⢻⡾⣿⡖⣿⠒⢸⣿⣿⡆⣾⣿⣷⢰⣿⣷⢸⣿⢻⡆⣿⡟⣷⠰⠿⣿⡆⠾⢹⣆⠼⠟⣷⠀⠀⠀
⠀⠀⠀⣿⡗⣿⢸⣿⣿⣶⣾⣷⣾⣿⣿⡇⠀⣿⠛⠃⣿⡟⣿⢸⡇⣿⡇⢸⡇⠀⣿⠛⢸⡇⣤⡄⢸⡇⠀⣿⢸⣿⢸⡷⣿⢿⣿⠀⢸⣿⢻⡆⣿⣿⣿⢸⣇⣿⢸⣿⢻⡇⣿⡇⣿⢰⡶⠿⠃⣶⠾⠇⢶⠶⠿⠀⠀⠀
⠀⠀⠀⠛⠛⠛⠘⠋⠛⠃⠘⢓⣞⠛⠙⠃⠀⠛⠀⠀⠛⠃⠛⠈⠛⠛⠁⠘⠃⠀⠛⠛⠈⠓⠛⠁⠘⠃⠀⠛⠈⠛⠛⠁⠛⠘⠛⠀⠘⠛⠛⠃⠙⠛⠋⠚⠃⠛⠛⠛⠘⠃⠛⠛⠛⠘⠃⠀⠀⠛⠀⠀⠚⠃⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠲⠶⠶⠶⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⢤⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⡄⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣰⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣽⣿⣿⣿⣿⣵⣴⣦⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⠈⠀⡈⡛⣟⣲⣶⣶⣶⣶⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢔⣤⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠉⠉⠛⠋⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⡤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠙⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⡙⠉⣟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⣤⣤⣶⣴⣤⣷⡇⠀⠄⠸⣶⠄⠸⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡶⠶⠾⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣦⣴⣷⣤⣿⡿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠘⢿⠇⠀⠁⠀⠹⠀⠀⠀⠀⠀⠀⡄⢲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠃⠈⠋⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠉⠁⠐⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢼⡏⠩⡝⠉⣯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣠⣶⣾⣿⠟⠋⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣷⣾⣿⣶⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠃⠀⢸⢡⠀⠀⢠⡤⠀⠿⣿⣿⣿⣤⡀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⣾⡀⣨⣿⣿⠀⠀⢸⣿⡿⠉⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⡇⠐⡼⠄⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡃⠀⠀⠀⠀⠀⢸⣿⡟⠟⣿⣷⣶⣾⡿⠃⢀⡀⠀⠀⠀⢀⣐⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣸⣿⣿⣄⠸⣿⡿⠏⠀⣶⠏⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣋⣛⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠿⢿⣿⠿⣿⣯⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⠀⣠⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣆⠀⣷⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡭⠈⠻⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⠍⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢿⣿⣿⣿⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠈⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⢭⣭⣭⠉⠭⠍⠥⠉⠉⠍⠅⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⠀⠘⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⣄⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣶⣶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠁⣁⣿⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣷⣄⠀⠀⠀⠐⣶⣶⣶⣶⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⡿⣷⢀⣿⣿⣾⣿⣿⣷⣿⣿⣶⣶⣿⢻⡆⣿⡟⣷⢰⡟⣿⡔⢻⡟⠃⣿⠛⢰⡟⣿⡟⢻⡟⠃⣿⢰⣿⢻⡾⣿⡖⣿⠒⢸⣿⣿⡆⣾⣿⣷⢰⣿⣷⢸⣿⢻⡆⣿⡟⣷⠰⠿⣿⡆⠾⢻⡆⠼⠟⣷⠀⠀⠀
⠀⠀⠀⣿⡗⣿⢸⣿⣿⣶⣾⣷⣾⣿⣿⡗⠀⣿⠛⠃⣿⡟⣿⢸⡇⣿⡇⢸⡇⠀⣿⠛⢸⡇⣤⡄⢸⡇⠀⣿⢸⣿⢸⡗⣿⢿⣿⠀⢸⣿⢻⡆⣿⣿⣿⢸⣇⣿⢸⣿⢻⡇⣿⡇⣿⢰⡶⠿⠃⣶⠾⠇⢶⠶⠿⠀⠀⠀
⠀⠀⠀⠛⠛⠛⠘⠋⠛⠃⠘⢓⠚⠛⠙⠃⠀⠛⠀⠀⠛⠃⠛⠈⠛⠛⠁⠘⠃⠀⠛⠛⠈⠓⠛⠁⠘⠃⠀⠛⠈⠛⠛⠁⠛⠘⠛⠀⠘⠛⠛⠃⠙⠛⠋⠚⠃⠛⠛⠛⠘⠃⠛⠛⠛⠘⠃⠀⠀⠛⠀⠀⠚⠃⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⢠⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣰⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣭⣭⣭⣿⣿⣿⣿⣵⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡈⡛⣟⣲⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢔⣤⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠉⠉⠛⠋⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠉⠻⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⡙⠉⣟⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⣤⣤⣶⣴⡄⡇⡧⠀⢈⠰⢴⡆⠘⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡶⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣦⣴⣷⣤⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢿⠇⠀⠀⠀⣘⠀⠀⠀⠀⠀⠀⠄⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠃⠈⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⡏⠩⡝⠉⣯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡇⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⣶⣾⣿⡿⠋⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣷⣾⣿⣶⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢰⢡⡄⢠⢠⣴⠀⠿⣿⣿⣿⣤⡀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠈⢾⡀⣈⣿⣿⠀⠀⠘⣿⣿⠋⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⡇⠐⡬⠄⣧⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡃⠀⠀⠀⠀⠀⠈⣿⡟⠟⣿⣷⣶⣾⡿⠃⠀⡀⠀⠀⠀⢀⣐⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣄⠸⣿⡿⠏⠀⣴⠏⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣋⣉⣛⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠿⢿⣿⠿⣿⣯⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⡀⢀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣆⠀⣷⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡭⠁⠻⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢽⣿⣿⣿⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠈⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⢭⣭⡭⠉⠩⠍⠅⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠿⠿⡿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣶⣶⡶⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⢁⢁⣿⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣄⠀⠀⠀⠐⣶⣶⣶⣶⣶⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⡿⣷⢀⣿⣿⣾⣻⣿⣷⣿⣿⣶⣶⣿⢻⡆⣿⡟⣷⢰⡟⣿⡔⢻⡟⠃⣿⠛⢰⡟⣿⡿⢻⡟⠃⣿⢰⣿⢻⡾⣿⡖⣿⠶⢸⣿⣿⡆⣾⣿⣷⢰⣿⣷⢸⣿⢻⡆⣿⡟⣷⠰⠿⣿⡆⠾⢹⡆⠼⠟⣷⠀⠀⠀
⠀⠀⠀⣿⡗⣿⢸⣿⣿⣶⣾⣷⣾⣿⣿⡖⠀⣿⠛⠃⣿⡟⣿⢸⡇⣿⡇⢸⡇⠀⣿⠛⢸⡇⣤⡄⢸⡇⠀⣿⢸⣿⢸⡗⣿⢿⣿⠀⢸⣿⢻⡆⣿⣿⣿⢸⣇⣿⢸⣿⢻⡇⣿⡇⣿⢰⡶⠿⠃⣶⠾⠇⢶⠶⠿⠀⠀⠀
⠀⠀⠀⠛⠛⠛⠘⠋⠛⠃⠘⢓⠞⠛⠛⠃⠀⠛⠀⠀⠛⠃⠛⠈⠛⠛⠁⠘⠃⠀⠛⠛⠈⠓⠛⠁⠘⠃⠀⠛⠈⠛⠛⠁⠛⠘⠛⠀⠘⠛⠛⠃⠙⠛⠋⠚⠃⠛⠛⠛⠘⠃⠛⠛⠛⠘⠃⠀⠀⠛⠀⠀⠚⠃⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣭⣭⣿⣿⣿⣿⣵⣴⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡈⡛⣟⣲⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣤⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠉⠉⠛⠋⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⡀⠀⢀⠀⠀⠀⡀⠀⠈⠉⠻⣿⣿⣿⣿⣿⣿⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⡙⠉⣟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⣴⣤⣶⣴⡖⡆⣷⠀⢨⠠⢶⡆⠘⠆⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠶⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣦⣴⣷⣤⣿⡿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠃⢿⡏⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠂⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢼⡏⠩⡝⠉⣯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠏⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢠⣶⣶⣿⡿⠋⠀⠀⠀⠹⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣷⣾⣿⣶⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⢩⡄⢰⢀⣤⠀⠼⢿⣿⣿⣤⡀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⢿⡄⣀⣿⣿⡆⠀⠈⣿⣿⠋⠁⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⡇⠐⡬⠄⣧⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣃⠀⠀⠀⠀⠀⠀⣿⣟⠿⢿⣷⣶⣾⡿⠃⠀⡀⠀⠀⠀⢀⣀⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢰⣿⣿⣆⠸⣿⡿⠋⠀⣴⠞⠁⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠿⢿⣿⠿⣿⣯⣭⣭⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣠⡀⢀⣾⣿⣿⣿⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣍⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣆⠀⣷⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡭⠁⠻⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢿⣿⣿⣿⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠈⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⠭⣭⡭⠉⠩⠍⠅⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣶⣶⡶⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠁⢁⣿⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⣄⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⡿⣷⢀⣿⣿⣾⣿⣿⣷⣿⣿⣶⣶⣿⢻⡆⣿⡟⣷⢰⡟⣿⡔⢻⡟⠃⣿⠛⢰⡟⣿⡿⢻⡟⠃⣿⢰⣿⢻⡾⣿⡖⣿⠶⢺⣿⣿⡆⣾⣿⣷⢰⣿⣷⢸⣿⢻⡆⣿⡟⣷⠰⠿⣿⡆⠾⢹⡆⠼⠟⣷⠀⠀⠀
⠀⠀⠀⣿⡗⣿⢸⣿⣿⣶⣾⣷⣾⣿⣿⡗⠀⣿⠛⠃⣿⡟⣿⢸⡇⣿⡇⢸⡇⠀⣿⠛⢸⡇⣤⡄⢸⡇⠀⣿⢸⣿⢸⡗⣿⢿⣿⠀⢸⣿⢻⡆⣿⣿⣿⢸⣇⣿⢸⣿⢻⡇⣿⡇⣿⢰⡶⠿⠃⣶⠾⠇⢲⠶⠿⠀⠀⠀
⠀⠀⠀⠛⠛⠛⠘⠋⠛⠃⠘⢓⢞⠛⠛⠃⠀⠛⠀⠀⠛⠃⠛⠈⠛⠛⠁⠘⠃⠀⠛⠛⠈⠓⠛⠁⠘⠃⠀⠛⠈⠛⠛⠁⠛⠘⠛⠀⠘⠛⠛⠃⠙⠛⠋⠚⠃⠛⠛⠛⠘⠃⠛⠛⠛⠘⠃⠀⠀⠛⠀⠀⠚⠃⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⢠⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣰⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣭⣭⣿⣿⣿⣿⣵⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡈⡛⢟⣲⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢔⣤⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠉⠉⠙⠋⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⡙⠉⣟⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣤⣶⣴⡖⣶⣷⠀⠀⠀⢶⡆⠀⠆⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡶⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣦⣴⣷⣤⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠇⢯⡏⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠜⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⡏⠩⡝⠉⣯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡏⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⣴⣶⣾⡿⠛⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣷⣾⣿⣶⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⢋⡄⠀⢀⣤⠀⠸⢿⣿⣿⣧⡄⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢿⡇⢀⣿⣿⡆⠀⠈⣿⣿⠋⠁⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⡇⠐⡬⠄⣧⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣃⠀⠀⠀⠀⠀⠀⣿⣟⠿⢻⣷⣶⣶⡿⠋⠀⠀⠀⠀⠀⢀⣀⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢠⣿⣿⣆⠘⣿⡿⠟⠀⢰⡞⠁⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣋⣛⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠿⢿⣿⠿⣿⣯⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣠⡀⢀⣼⣿⣿⣿⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠐⠀⠀⢈⣆⠀⣷⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡭⠁⠹⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢼⣿⣿⣿⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠈⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⢭⣭⡭⠉⠭⠍⠡⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠿⠿⡿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣄⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣷⣶⡶⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⢁⣁⣿⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣄⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⡿⣷⢀⣿⣿⣾⣿⣿⣷⣿⣿⣶⣶⣿⢻⡆⣿⡟⣷⢰⡟⣿⡔⢻⡟⠃⣿⠛⢰⡟⣿⡿⢻⡟⠃⣿⢰⣿⢻⡾⣿⡗⣿⠶⢺⣿⣿⡆⣾⣿⣷⢰⣿⣷⢸⣿⢻⡆⣿⡟⣷⠰⠿⣿⡆⠾⢹⡆⠼⠟⣷⠀⠀⠀
⠀⠀⠀⣿⡗⣿⢸⣿⣿⣶⣾⣷⣾⣿⣿⡖⠂⣿⠛⠃⣿⡟⣿⢸⡇⣿⡇⢸⡇⠀⣿⠛⢸⡇⣤⡄⢸⡇⠀⣿⢸⣿⢸⡗⣿⢿⣿⠀⢸⣿⢻⡆⣿⣿⣿⢸⣇⣿⢸⣿⢻⡇⣿⡇⣿⢰⡶⠿⠃⣶⠾⠇⢲⠶⠿⠀⠀⠀
⠀⠀⠀⠛⠛⠛⠘⠋⠛⠃⠘⢓⢞⠛⠛⠃⠀⠛⠀⠀⠛⠃⠛⠈⠛⠛⠁⠘⠃⠀⠛⠛⠈⠓⠛⠁⠘⠃⠀⠛⠈⠛⠛⠁⠛⠘⠛⠀⠘⠛⠛⠃⠙⠛⠋⠚⠃⠛⠛⠛⠘⠃⠛⠛⠛⠘⠃⠀⠀⠛⠀⠀⠚⠃⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠲⠶⠶⠶⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⡀⠀⢠⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⡄⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠠⠠⠀⣰⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣯⣭⣿⣿⣿⣿⣵⣴⣦⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡈⡛⣟⣲⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠐⠀⠀⢐⣤⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠉⠙⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠉⠛⣿⣿⣿⣿⣿⣿⣷⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠀⠀⠀⠸⡙⠉⣟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣦⣶⣶⣶⣾⣿⠈⢠⠀⢶⣦⠈⠇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡶⠶⠶⠷⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣦⣴⣷⣤⣿⡿⢿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡇⢿⡿⠀⠈⠀⠘⠇⠀⠀⠀⠀⠀⢠⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠘⠈⠉⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢼⡏⠩⡝⠉⣯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣤⣴⣶⡿⠟⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢼⣷⣾⣿⣶⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⡋⡌⠀⠀⣄⠆⠸⢿⣿⣿⣧⡀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⠛⠛⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢿⡇⠀⣿⣿⡆⠀⠈⣿⣿⠏⠁⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⡇⠐⡼⠄⣿⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣃⠀⠀⠀⠀⠀⠀⣿⣿⠿⢻⣷⣶⣶⣿⠏⠀⠀⠀⠀⠀⠀⣀⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢠⣿⣿⣆⠘⣿⡿⠟⠁⢠⡾⠃⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣛⣋⣛⣉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⠿⢿⣿⠿⣿⣯⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣠⡀⢀⣼⣿⣿⣿⡅⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⣍⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠐⠀⠀⢈⣆⠀⣷⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡭⠁⠙⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢿⣿⣿⣿⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠈⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⡭⠍⠭⠍⠡⠉⠉⠉⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠐⠸⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣄⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⢁⣁⣿⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣄⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⡿⣷⢀⣿⣿⣾⣿⣿⣷⣿⣿⣶⣶⣿⢻⡆⣿⡟⣷⢰⡟⣿⡖⢻⡟⠃⣿⠛⢰⡟⣿⡿⢻⡟⠃⣿⢰⣿⢻⣾⣿⡗⣿⠶⢺⣿⣿⡆⣾⣿⣷⢰⣿⣷⢸⣿⢻⡆⣿⡟⣷⠰⠿⣿⡆⠾⢹⣆⠼⠟⣷⠀⠀⠀
⠀⠀⠀⣿⡗⣿⢸⣿⣿⣶⣾⣷⣾⣿⣿⡷⠂⣿⠛⠃⣿⡟⣿⢸⡇⣿⡇⢸⡇⠀⣿⠛⢸⡇⣤⡄⢸⡇⠀⣿⢸⣿⢸⡗⣿⢿⣿⠀⢸⣿⢿⡆⣿⣿⣿⢸⣇⣿⢸⣿⢻⡇⣿⡇⣿⢰⡶⠿⠃⣶⠾⠇⢶⠶⠿⠀⠀⠀
⠀⠀⠀⠛⠛⠛⠘⠋⠛⠃⠘⢳⣞⡛⠛⠃⠀⠛⠀⠀⠛⠃⠛⠈⠛⠛⠁⠘⠃⠀⠛⠛⠈⠓⠛⠁⠘⠃⠀⠛⠈⠛⠛⠁⠛⠘⠛⠀⠘⠛⠛⠃⠙⠛⠋⠚⠃⠛⠛⠛⠘⠃⠛⠛⠛⠘⠃⠀⠀⠛⠀⠀⠚⠃⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠲⠶⠶⠶⠀⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⡀⠀⢠⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⡄⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠠⠠⠀⣰⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣵⣴⣦⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡈⡛⣟⣲⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠐⠀⠀⢐⣤⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠉⠙⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠉⠛⣿⣿⣿⣿⣿⣿⣷⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠀⠀⠀⠸⡙⠉⣟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣶⣦⣶⣶⣶⣾⣿⠀⠠⡀⢶⡦⠈⠇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡶⠶⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣦⣴⣷⣤⣿⡿⢿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡇⢿⡿⠀⠈⠀⠸⠇⠀⠀⠀⠀⠀⢠⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠘⠈⠉⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢼⡏⠩⡝⠉⣯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡏⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣤⣶⣾⡿⠟⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢼⣷⣾⣿⣶⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⡏⡌⠀⠀⣤⠆⠸⢿⣿⣿⣧⡀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⠛⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢿⡇⠀⣿⣿⡆⠀⠈⣿⣿⠏⠁⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⡇⠐⡼⠄⣿⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣃⠀⠀⠀⠀⠀⠀⣿⣿⠯⢻⣷⣶⣶⣿⠏⠀⠀⠀⠀⠀⠀⣀⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢠⣿⣿⣆⠘⣿⡿⠟⠁⢠⡶⠁⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣋⣛⣉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⠿⢿⣿⠿⣿⣯⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣠⡀⢀⣼⣿⣿⣿⡅⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⣍⣉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠐⠀⠀⢈⣆⠀⣷⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡭⠁⠙⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⡍⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢿⣿⣿⣿⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠈⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⡭⠍⢭⠍⠡⠉⠉⠍⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠐⠸⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣄⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⢁⣁⣿⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣄⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⡿⣷⢀⣿⣿⣾⣿⣿⣷⣿⣿⣶⣶⣿⢻⡆⣿⡟⣷⢰⡟⣿⡖⢻⡟⠃⣿⠛⢰⡟⣿⡿⢻⡟⠃⣿⢰⣿⢻⣾⣿⡗⣿⠶⢺⣿⣿⡆⣾⣿⣷⢰⣿⣷⢸⣿⢻⡆⣿⡟⣷⠰⠿⣿⡆⠾⢹⣆⠼⠟⣷⠀⠀⠀
⠀⠀⠀⣿⡗⣿⢸⣿⣿⣶⣾⣷⣾⣿⣿⡷⠂⣿⠛⠃⣿⡟⣿⢸⡇⣿⡇⢸⡇⠀⣿⠛⢸⡇⣤⡄⢸⡇⠀⣿⢸⣿⢸⡗⣿⢿⣿⠀⢸⣿⢿⡆⣿⣿⣿⢸⣇⣿⢸⣿⢻⡇⣿⡇⣿⢰⡶⠿⠃⣶⠾⠇⢶⠶⠿⠀⠀⠀
⠀⠀⠀⠛⠛⠛⠘⠋⠛⠃⠘⢓⣞⡛⠛⠃⠀⠛⠀⠀⠛⠃⠛⠈⠛⠛⠁⠘⠃⠀⠛⠛⠈⠓⠛⠁⠘⠃⠀⠛⠈⠛⠛⠁⠛⠘⠛⠀⠘⠛⠛⠃⠙⠛⠋⠚⠃⠛⠛⠛⠘⠃⠛⠛⠛⠘⠃⠀⠀⠛⠀⠀⠚⠃⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠲⠶⠶⠶⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣷⣄⣼⣏⣨⣿⣦⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣤⣤⣴⣶⣶⣶⣯⣼⣭⣤⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠛⢻⡛⡛⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣿⣛⢛⢛⠛⣿⣿⣿
⣿⣿⣿⣤⣼⣧⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣧⣼⣤⣬⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠋⢽⡛⠙⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣣⡀⢀⠀⠀⠀⠀⠀⠀⢰⣤⣀⡆⣇⣸⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠿⠿⢿⠋⠹⠋⢻⣿⣿⣿
⣿⣿⣿⣧⣴⣿⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡇⢠⣴⣧⣼⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⢿⠾⠿⠻⢟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣏⠹⡝⠉⢯⡿⠿⠿⠿⠿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⡏⠘⠀⠀⠀⠀⢀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠿⡿⠿⠿⠿⠿⠿⠿⠿⢿⢉⠙⢉⢹⣿⣿⣿
⣿⣿⣿⣷⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⣼⡄⢂⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣶⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢿⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠚⡿⠆⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣟⣛⣛⣛⣟⠀⠀⠀⠀⢀⣷⣝⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⠁⠸⠄⢹⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⣸⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⢘⣆⠂⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠍⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣯⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⡀⢈⠰⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡿⣇⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿
⣿⣿⣿⣅⣸⣇⣁⣿⣭⣭⣭⣤⣤⣤⣶⣶⣶⣶⣶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣏⡾⣿⡆⠀⢠⣶⣶⣶⣶⣾⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⡭⢭⣭⣭⢽⣀⣈⠇⣼⣿⣿⣿
⣿⣿⣿⢰⠂⣦⠁⡶⢦⢆⢲⡖⡀⡶⢢⢸⡇⠖⠀⠀⢀⠀⡆⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⡆⠰⠀⢲⡖⡀⣶⠀⠀⢰⠐⢴⡀⡶⢸⡇⡖⢰⠜⢰⠀⣦⠃⡆⡆⡇⣶⢰⡜⣶⠐⣦⠁⠆⢰⠈⠴⢑⡎⠰⠀⣆⢹⣿⣿
⣿⣿⣿⠸⠀⡿⠀⣇⣸⢸⢸⡇⠇⣇⣸⠸⠃⠀⠀⠀⠘⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⡇⡇⣿⠀⠀⢸⠆⢸⠰⡷⢸⠇⡏⢰⡄⢸⠀⣯⢠⣇⣷⠀⣿⢠⠜⢾⠀⣿⠀⠆⠼⡀⠤⠰⠃⠠⠀⠟⣼⣿⡟
⣿⣿⣿⣀⣐⣃⣀⣃⣐⣀⣐⣂⣐⣂⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣃⣇⣛⣠⣁⠀⢰⣘⣀⣃⣴⣆⣓⣚⣴⣌⣒⣡⣘⣠⣐⣀⣂⣐⣠⣐⣒⣢⣆⣂⣶⣄⣀⣨⣇⣀⣠⣀⣿⡏⠀
⠀⣉⣉⠉⣀⡉⣻⣏⣀⣈⣩⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡄⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⠋⠀⠀
⣿⣿⣷⣄⣼⣏⣨⣿⣦⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣤⣤⣴⣶⣶⣶⣯⣼⣭⣤⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠛⢻⡛⡛⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣿⣛⢛⢛⠛⣿⣿⣿
⣿⣿⣿⣤⣼⣧⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣧⣼⣤⣬⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠋⢽⡛⠙⣟⠿⠿⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣢⡀⢀⠀⠀⠀⠀⠀⠀⢸⣤⣄⡆⣇⣸⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⠋⠹⠋⢻⣿⣿⣿
⣿⣿⣿⣧⣴⣿⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡇⢠⣴⣧⣼⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⢿⠾⠿⠻⢟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣏⠹⡝⠉⢯⡿⠿⠿⠿⠿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡏⠘⠀⠀⠀⠀⢀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠿⡿⠿⠿⠿⠿⠿⠿⠿⢿⢉⠙⢉⢹⣿⣿⣿
⣿⣿⣿⣷⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⣼⡀⢂⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣶⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢿⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠚⡿⠆⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣟⣛⣛⣛⣛⣿⣛⣟⠀⠀⠀⠀⢀⣷⣝⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⠁⠸⠄⢹⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⣸⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⢘⣆⠂⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠍⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣿⣭⣭⣿⣭⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⡀⢈⠰⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠂⠈⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡿⣇⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡿⠿⠿⢿⣿⣿⣿
⣿⣿⣿⣅⣸⣇⣁⣿⣭⣭⣭⣤⣤⣤⣶⣶⣶⣶⣶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣏⡾⣿⡆⠀⢤⣶⣶⣶⣶⣾⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⡭⢭⣭⣭⢽⣀⣈⠇⣼⣿⣿⣿
⣿⣿⣿⢰⠂⣦⠁⡆⢦⢆⢲⡖⡀⡶⢢⢸⡇⠖⠀⠀⢀⠀⡆⠀⡆⠠⠀⠀⠀⠀⠀⠀⠀⡆⠰⠀⢲⡖⡂⣶⠀⠀⢰⠐⢶⡀⡶⢸⡇⡖⢰⠜⢰⠀⣦⠃⡆⡆⡇⣶⢰⡜⣶⠐⣦⠁⠆⢰⠈⠴⢱⡎⠰⠀⣦⢹⣿⣿
⣿⣿⣿⠸⠀⡿⠀⣇⣸⢸⢸⡇⠇⣇⣸⢸⠃⠀⠀⠀⠘⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⡇⡇⣿⠀⠀⢸⠀⢾⠰⡷⢼⠇⡏⢰⡄⢸⠀⡷⢰⣇⣷⠀⡿⢠⡜⢾⠀⣿⠀⠄⠼⡀⠤⠰⠃⠠⠀⠟⣼⣿⡟
⣿⣿⣿⣀⣐⣃⣀⣃⣐⣀⣐⣂⣐⣂⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣃⣇⣛⣠⣁⠀⢰⣘⣀⣃⣴⣆⣓⣚⣴⣌⣒⣡⣘⣠⣐⣀⣂⣐⣠⣐⣒⣢⣆⣂⣶⣄⣀⣨⣇⣀⣀⣀⣿⠏⠀
⠀⣉⣉⠉⣀⡉⣻⣏⣀⣈⣩⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡄⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⠋⠀⠀
⣿⣿⣷⣄⣼⣍⣨⣿⣦⣦⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣤⣤⣴⣶⣶⣶⣯⣼⣭⣤⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠛⢻⡛⡛⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣛⢛⢛⠛⣿⣿⣿
⣿⣿⣿⣤⣼⣧⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣧⣼⣤⣬⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠋⢽⡛⠙⣟⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣢⡀⢀⠀⠀⠀⠀⠀⠀⢸⣤⣀⡆⣆⣸⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⠋⠹⠋⢻⣿⣿⣿
⣿⣿⣿⣧⣴⣿⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡇⢠⣴⣧⣼⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⢿⠾⠿⠻⢟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣏⠹⡝⠉⢯⡿⠿⠿⠿⠿⣿⣿⣿⢿⣿⢿⡿⠿⣿⣿⣿⣿⣿⡏⠘⠀⠀⠀⠀⢀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⠿⡿⠿⠿⠿⠿⠿⠿⠿⢿⢉⠙⢉⢹⣿⣿⣿
⣿⣿⣿⣷⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⣼⡄⢂⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣶⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢿⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠚⡿⠆⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣛⣛⣛⣻⣛⣛⣟⠀⠀⠀⠀⢀⣷⣝⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⠁⠸⠄⢹⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⣸⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⢘⣆⠂⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠍⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣿⣯⣭⣭⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⡀⢈⠰⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠂⠈⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡿⣇⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡿⠿⠿⢿⣿⣿⣿
⣿⣿⣿⣅⣸⣇⣁⣿⣭⣭⣭⣤⣤⣤⣶⣶⣶⣶⣶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣏⡾⣿⡆⠀⢤⣶⣶⣶⣶⣾⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⡭⢭⣭⣭⢽⣀⣈⠇⣼⣿⣿⣿
⣿⣿⣿⢰⠆⣦⠁⡶⢦⢆⢲⡖⡀⡶⢢⢸⡇⠖⠀⠀⢀⠀⡆⠀⡆⠠⠀⠀⠀⠀⠀⠀⠀⠆⠰⠀⢲⡖⡀⣶⠀⠀⢰⠐⢴⡀⡶⢸⡇⡆⢰⠜⢰⠀⣦⠃⡆⡆⡇⣶⢰⡜⣶⠐⣦⠡⠆⢰⠈⠴⢱⡎⠰⠀⣦⢻⣿⣿
⣿⣿⣿⠸⠀⡿⠀⣇⣸⢸⢸⡇⠇⣇⣸⢸⠃⠀⠀⠀⠘⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⡇⡇⣿⠀⠀⢸⠄⢾⠰⡷⢼⠇⡏⢰⡄⢸⠀⣷⢸⣇⣷⠀⡿⢠⡜⢼⠀⣿⠀⠄⠼⡀⠤⠰⠃⠠⠀⠟⣼⣿⡟
⣿⣿⣿⣀⣐⣃⣀⣃⣐⣀⣐⣂⣐⣂⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣃⣇⣛⣠⣁⠀⢰⣘⣀⣃⣼⣆⣓⣚⣴⣌⣒⣡⣘⣠⣐⣀⣂⣐⣠⣐⣒⣢⣆⣂⣶⣆⣀⣨⣇⣀⣀⣀⣿⠏⠀
⠀⣉⣉⠉⣀⡉⣻⣏⣀⣈⣩⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡄⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⠋⠀⠀
⠀⠀⠀⠀⠀⡀⠀⢠⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣥⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⢀⠀⣠⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣭⣭⣽⣭⣭⣥⣴⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠁⡒⡛⠟⣲⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣖⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⠀⠄⣤⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠉⠙⠩⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⡤⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠄⠐⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣷⣿⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠆⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⠉⢀⠈⠹⡙⠙⣟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣶⣷⣾⣶⣧⡇⠀⠘⠠⢴⠀⠰⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡶⠶⠶⠶⠤⠰⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠀⠘⣤⣴⣿⣤⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠀⣿⠇⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⠶⠶⠶⠶⠶⠶⠶⠦⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠈⠉⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣔⡏⠩⡝⠉⣯⡽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡶⠀⠀⠀⠰⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢻⣷⣾⣿⣶⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠠⠀⠀⡎⣀⠁⡀⣀⠀⠀⢾⣿⣿⣏⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⠓⠐⠀⠀⠀⠀⠀⠀⠀⠀
⠐⠀⢼⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢣⡇⠀⢸⣿⡇⠀⠀⢻⣿⡟⠃⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀
⠀⠈⢨⡇⠐⡼⠄⣷⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣃⠀⠀⠀⠀⠀⠀⣿⣿⠯⢻⣷⣦⣤⣸⡟⠀⠀⠀⠀⠀⠀⣀⣘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠰⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢠⣿⣿⣷⠈⣿⣿⢿⠋⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠂⠿⢿⢿⠿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⢀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣯⣽⣯⣿⣭⣭⣭⣭⣭⣭⣭⣭⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠀⢈⣆⠀⣷⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⠈⠻⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣉⠉⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠻⣿⣿⣿⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠘⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⠭⠭⡍⠉⠉⠁⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠂⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣧⡀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡶⣦⡄⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢁⣁⣿⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣦⡀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣷⢁⣿⣿⣾⣿⣿⣷⣿⣿⣶⣶⣿⢻⡆⣿⡟⣷⢰⡟⣿⡞⢻⡟⠃⣿⠛⢰⡟⣿⡿⢻⡟⠃⣿⢰⣿⢻⣾⣿⣷⣿⣶⣾⣿⣿⡆⣾⣿⣷⢰⣿⣷⢸⣿⢻⡆⣿⡿⣷⠰⠿⣿⡆⠾⢹⡆⠼⠟⣷⠀⠀⠀
⠀⠀⠀⣿⡇⣿⢸⣿⣿⣴⣾⣷⣾⣿⣿⡶⠂⣿⠛⠃⣿⡟⣿⢸⡇⣿⡇⢸⡇⠀⣿⠛⢸⡇⣤⡄⢸⡇⠀⣿⢸⣿⢸⡿⣿⢿⣿⠶⢺⣿⢿⡆⣿⣿⣿⢸⣇⣿⢸⣿⢻⡇⣿⡇⣿⢰⡶⠿⠃⣶⠾⠇⢰⠶⠿⠀⠀⠀
⠀⠀⠀⠛⠛⠛⠘⠋⠛⠃⠘⢳⣞⡻⠟⠃⠀⠛⠀⠀⠛⠃⠛⠈⠛⠛⠁⠘⠃⠀⠛⠛⠈⠓⠛⠁⠘⠃⠀⠛⠈⠛⠛⠑⠛⠘⠛⠀⠘⠛⠛⠃⠙⠛⠋⠚⠃⠛⠛⠛⠘⠃⠛⠛⠛⠘⠃⠀⠀⠛⠀⠀⠘⠃⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⢥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⢀⠁⣠⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣽⣭⣭⣤⣴⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠁⡒⡛⠟⣲⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⠀⠄⣤⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠉⠙⠩⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⠴⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠄⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠆⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⢀⠀⠈⠹⡙⠙⣟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣶⣶⣶⣷⣾⣶⣧⡇⠀⠈⠠⢴⠀⠰⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡶⠶⠶⠶⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠀⠛⢤⣴⣿⣤⣿⡿⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠀⣿⠇⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⠶⠶⠶⠶⠶⠶⠶⠦⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠈⠈⠉⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢔⡏⠉⡝⠉⣯⡽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡦⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢻⣷⣾⣿⣶⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠸⠀⠀⡎⣁⠁⠀⣀⠀⠀⢾⣿⣿⣏⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⠓⠐⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢣⡇⠀⢸⣿⡇⠀⠀⢻⣿⡟⠃⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢩⡇⠐⡬⠄⣷⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣃⠀⠀⠀⠀⠀⠀⣿⣿⠯⢻⣷⣤⣤⣸⡟⠀⠀⠀⠀⠀⠀⢀⣘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠰⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢠⣿⣿⣧⠈⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⢋⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠂⡿⢿⢿⠿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⡀⢀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣯⣿⣭⣯⣭⣭⣭⣭⣭⣭⣭⣭⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠀⢈⣆⠀⣷⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⠈⠻⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣉⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢻⣿⣿⣿⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠘⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⠭⠭⡍⠉⠉⠁⠬⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⠀⠂⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣧⡀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡶⡦⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢁⣁⣿⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣦⡀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⡿⣷⢁⣿⣿⣾⣿⣿⣷⣿⣿⣶⣶⣿⢻⡆⣿⡟⣷⢰⡟⣿⡞⢻⡟⠃⣿⠛⢰⡟⣿⡿⢻⡟⠃⣿⢰⣿⢻⣾⣿⣷⣿⣶⢾⣿⣿⡆⣾⣿⣷⢰⣿⣷⢸⣿⢻⡆⣿⡟⣷⠰⠿⣿⡆⠾⢹⡆⠼⠟⣷⠀⠀⠀
⠀⠀⠀⣿⡇⣿⢸⣿⣿⣴⣾⣷⣾⣿⣿⡶⠂⣿⠛⠃⣿⡟⣿⢸⡇⣿⡇⢸⡇⠀⣿⠛⢸⡇⣤⡄⢸⡇⠀⣿⢸⣿⢸⡿⣿⢿⣿⠾⢺⣿⢿⡆⣿⣿⣿⢸⣇⣿⢸⣿⢻⡇⣿⡇⣿⢰⡶⠿⠃⣶⠾⠇⢰⠶⠿⠀⠀⠀
⠀⠀⠀⠛⠛⠛⠘⠋⠛⠃⠘⢳⣞⣻⠛⠃⠀⠛⠀⠀⠛⠃⠛⠈⠛⠛⠁⠘⠃⠀⠛⠛⠈⠓⠛⠁⠘⠃⠀⠛⠈⠛⠛⠑⠛⠘⠛⠀⠘⠛⠛⠃⠙⠛⠋⠚⠃⠛⠛⠛⠘⠃⠛⠛⠛⠘⠃⠀⠀⠛⠀⠀⠘⠃⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⢀⠁⣀⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣭⣭⣽⣭⣭⣤⣴⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡒⡛⠟⣲⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠄⣤⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠉⠙⠩⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⠴⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠄⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠸⡙⠙⣟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣷⣾⣶⣧⡇⠀⠘⠠⢴⠀⠠⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡶⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⣠⣴⣿⣤⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠀⣿⠇⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠦⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠈⠈⠉⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⡏⠩⡝⠉⣯⡽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡦⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢻⣷⣾⣿⣶⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠰⠀⠀⡎⣁⠁⠀⣀⠀⠀⢾⣿⣿⣏⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⢸⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢣⡇⠀⢸⣿⡇⠀⠀⢻⣿⡟⠃⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢹⡃⠐⡬⠄⣷⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣃⠀⠀⠀⠀⠀⠀⣿⣿⠯⢻⣷⣤⣤⣸⡟⠀⠀⠀⠀⠀⠀⢀⣘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠓⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢠⣿⣿⣷⠈⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⠋⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠂⠿⢿⢿⠿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⢀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣭⣭⣭⣭⣭⣭⣭⣭⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣆⠀⣷⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⠈⠻⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢻⣿⣿⣿⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠘⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⠭⢭⠍⠉⠉⠉⠨⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣧⡀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢁⣁⣿⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣦⡀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣷⢁⣿⣿⣾⣿⣿⣷⣿⣿⣶⣶⣿⢻⡆⣿⡟⣷⢰⡟⣿⡞⢻⡟⠃⣿⠛⢰⡟⣿⡿⢿⡟⠃⣿⢰⣿⢻⣾⣿⣷⣿⣶⢾⣿⣿⡆⣾⣿⣷⢰⣿⣷⢸⣿⢻⡆⣿⡟⣷⠰⠿⣿⡆⠾⢹⡆⠼⠟⣷⠀⠀⠀
⠀⠀⠀⣿⡇⣿⢸⣿⣿⣴⣾⣷⣾⣿⣿⡶⠂⣿⠛⠃⣿⡟⣿⢸⡇⣿⡇⢸⡇⠀⣿⠛⢸⡇⣤⡄⢸⡇⠀⣿⢸⣿⢸⡿⣿⢿⣿⠞⢺⣿⢿⡆⣿⣿⣿⢸⣇⣿⢸⣿⢻⡇⣿⡇⣿⢰⡶⠿⠃⣶⠾⠇⢰⠶⠿⠀⠀⠀
⠀⠀⠀⠛⠛⠛⠘⠋⠛⠃⠘⢳⣞⡻⠛⠃⠀⠛⠀⠀⠛⠃⠛⠈⠛⠛⠁⠘⠃⠀⠛⠛⠈⠓⠛⠁⠘⠃⠀⠛⠈⠛⠛⠁⠛⠘⠛⠀⠘⠛⠛⠃⠙⠛⠋⠚⠃⠛⠛⠛⠘⠃⠛⠛⠛⠘⠃⠀⠀⠛⠀⠀⠘⠃⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⢀⠀⣠⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣭⣭⣽⣭⣭⣥⣴⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡒⡛⠟⣲⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣖⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⠀⠄⣤⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠉⠙⠩⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⡤⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⠀⠀⠀⠸⡙⠙⣟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣷⣾⣶⣧⡇⠀⠈⠠⢴⠀⠰⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡶⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⣠⣴⣿⣤⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠁⣿⠇⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠦⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠈⠁⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢄⡏⠩⡝⠉⣯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⡶⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢻⣷⣾⣿⣶⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠰⠀⠀⡎⣁⠀⡀⣀⠀⠀⢾⣿⣿⣏⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⢸⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢳⡇⠀⢸⣿⡇⠀⠀⢻⣿⡟⠃⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀
⠀⠀⢸⡃⠐⡬⠄⣷⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣃⠀⠀⠀⠀⠀⠀⣿⣿⠯⢻⣷⣤⣤⣸⡟⠀⠀⠀⠀⠀⠀⢀⣘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢠⣿⣿⣧⠈⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⠛⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠿⢿⣿⠿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⢀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣿⣭⣭⣭⣭⣭⣭⣭⣭⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣆⠂⣷⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⠈⠻⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣉⠉⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢻⣿⣿⣿⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠘⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⠭⠭⠍⠉⠉⠉⠤⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠊⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⡀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡶⡦⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢁⣁⣿⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣦⡀⠀⠀⠀⢐⣶⣶⣶⣶⣶⣶⣶⣶⣦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⡿⣷⢁⣿⣿⢾⣿⣿⣷⣿⣿⣶⣶⣿⢻⡆⣿⡟⣷⢰⡟⣿⡞⢻⡟⠃⣿⠛⢰⡟⣿⡿⢿⡟⠃⣿⢰⣿⢻⣾⣿⣷⣿⣶⣾⣿⣿⡆⣾⣿⣷⢰⣿⣷⢸⣿⢻⡆⣿⡿⣷⠰⠿⣿⡆⠾⢹⡆⠼⠟⣷⠀⠀⠀
⠀⠀⠀⣿⡇⣿⢸⣿⣿⣴⣾⣷⣾⣿⣿⡶⠂⣿⠛⠃⣿⡟⣿⢸⡇⣿⡇⢸⡇⠀⣿⠛⢸⡇⣤⡄⢸⡇⠀⣿⢸⣿⢸⡿⣿⢿⣿⠾⢺⣿⢿⡆⣿⣿⣿⢸⣇⣿⢸⣿⢻⡇⣿⡇⣿⢰⡶⠿⠃⣶⠾⠇⢰⠶⠿⠀⠀⠀
⠀⠀⠀⠛⠛⠛⠘⠋⠛⠃⠘⢳⣞⡻⠛⠃⠀⠛⠀⠀⠛⠃⠛⠈⠛⠛⠁⠘⠃⠀⠛⠛⠈⠓⠛⠁⠘⠃⠀⠛⠈⠛⠛⠁⠛⠘⠛⠀⠘⠛⠛⠃⠙⠛⠋⠚⠃⠛⠛⠛⠘⠃⠛⠛⠛⠘⠃⠀⠀⠛⠀⠀⠘⠃⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⢀⠀⣠⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣽⣭⣭⣥⣴⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠁⡒⡛⠟⣲⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣖⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⠀⠄⣤⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠉⠙⠩⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⡴⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠄⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠆⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⢠⢀⠈⠸⡙⠙⣟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣷⣾⣶⣧⡇⠀⠈⠠⢴⡀⠡⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡶⠶⠶⠶⠤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠘⣤⣴⣿⣤⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠁⣿⠇⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠁⠉⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⢴⡏⠩⡝⠉⣯⡽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⡶⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢻⣷⣾⣿⣶⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠸⠀⠀⡎⣀⠁⡀⣀⠀⠀⢾⣿⣿⣏⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⠓⠐⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢹⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢣⡇⠀⢺⣿⡇⠀⠀⢻⣿⡟⠃⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠀⠐⠐⠂⠀⠀⠀⠀⠀⠀
⠀⠘⢸⡇⠐⡼⠄⣷⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣃⠀⠀⠀⠀⠀⠀⣿⣿⠯⢻⣷⣤⣤⣸⡟⠀⠀⠀⠀⠀⠀⢀⣘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢠⣿⣿⣧⠈⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⢛⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠿⢿⣿⠿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⢀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣯⣯⣯⣿⣭⣭⣭⣭⣭⣭⣭⣭⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠂⠀⢈⣆⠀⣷⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⠈⠻⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣉⠉⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠐⠀⠀⠻⣿⣿⣿⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠘⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⠭⢭⠍⠉⠉⠁⠬⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡀⠂⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧⡀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡶⡦⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢁⣁⣿⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⡀⠀⠀⠀⠐⣶⣶⣶⣶⣶⣶⣶⣶⣦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣷⢁⣿⣿⣾⣿⣿⣷⣿⣿⣶⣶⣿⢻⡆⣿⡟⣷⢰⡟⣿⡞⢻⡟⠃⣿⠛⢰⡟⣿⡿⢿⡟⠃⣿⢰⣿⢻⣿⣿⣷⣿⣶⣾⣿⣿⡆⣾⣿⣷⢰⣿⣷⢸⣿⢻⡆⣿⡟⣷⠰⠿⣿⡆⠾⢹⡆⠼⠟⣷⠀⠀⠀
⠀⠀⠀⣿⡇⣿⢸⣿⣿⣴⣾⣷⣾⣿⣿⡶⠂⣿⠛⠃⣿⡟⣿⢸⡇⣿⡇⢸⡇⠀⣿⠛⢸⡇⣤⡄⢸⡇⠀⣿⢸⣿⢸⡿⣿⢿⣿⠶⢺⣿⢿⡆⣿⣿⣿⢸⣇⣿⢸⣿⢻⡇⣿⡇⣿⢰⡶⠿⠃⣶⠾⠇⢴⠶⠿⠀⠀⠀
⠀⠀⠀⠛⠛⠛⠘⠋⠛⠃⠘⢳⣞⠻⠛⠃⠀⠛⠀⠀⠛⠃⠛⠈⠛⠛⠁⠘⠃⠀⠛⠛⠈⠓⠛⠁⠘⠃⠀⠛⠈⠛⠛⠁⠛⠘⠛⠀⠘⠛⠛⠃⠙⠛⠋⠚⠃⠛⠛⠛⠘⠃⠛⠛⠛⠘⠃⠀⠀⠛⠀⠀⠘⠃⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣥⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⢀⢀⣠⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣽⣿⣭⣭⣽⣭⣭⣤⣴⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠁⡒⡛⠟⣲⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣖⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⠀⠄⣤⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠉⠙⠩⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⡴⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠄⢀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠆⠀⠠⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀
⢰⢠⠀⠈⠸⡙⠙⣟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣷⣾⢲⣷⡇⠀⠀⠰⢦⠀⠱⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡾⠶⠶⠶⠴⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠨⠚⢤⣴⣿⣤⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⢸⣻⠃⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠈⠈⠙⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⢴⡏⠩⡝⠉⣯⡽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⡶⠀⠀⠀⠠⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢹⣷⣾⣿⣶⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠀⢠⠋⡈⠀⠀⣀⠀⢠⢿⣿⣿⡏⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⠓⠐⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢘⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⢿⡁⠀⣾⣿⡄⠀⠈⣿⣿⠟⠃⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠂⠐⠘⠀⠀⠀⠀⠀⠀⠀
⠀⠘⢩⡇⠐⡼⠄⣷⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣃⠀⠀⠀⠀⠀⠈⣿⡿⠽⢿⣧⣤⣤⣿⡟⠀⠀⠀⠀⠀⠀⠀⣘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠓⠒⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢸⣿⣿⣆⠸⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⢋⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠀⠂⠿⢿⢿⠿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⠀⢀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣯⣯⣯⣿⣭⣭⣭⣭⣭⣭⣭⣭⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠀⢈⣆⠀⣷⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⠈⢻⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣉⠉⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⢻⣿⣿⣿⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠙⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⠭⠭⡍⠉⠉⠁⠭⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⠀⠂⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢁⣁⣿⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣦⡀⠀⠀⠀⠰⣶⣶⣶⣶⣶⣶⣶⣶⣦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣷⢁⣿⣿⣾⣿⣿⣷⣿⣿⣶⣶⣿⢻⡆⣿⡟⣷⢰⡟⣿⡞⢻⡟⠃⣿⠛⢰⡟⣿⡿⢻⡟⠃⣿⢰⣿⢻⣾⣿⣷⣿⣶⢾⣿⣿⡆⣾⣿⣷⢰⣿⣷⢸⣿⢻⡆⣿⡿⣷⠰⠿⣿⡆⠾⢹⡆⠼⠟⣷⠀⠀⠀
⠀⠀⠀⣿⡇⣿⢸⣿⣿⣴⣾⣷⣾⣿⣿⡖⠀⣿⠛⠃⣿⡟⣿⢸⡇⣿⡇⢸⡇⠀⣿⠛⢸⡇⣤⡄⢸⡇⠀⣿⢸⣿⢸⡿⣿⢿⣿⠶⢺⣿⢿⡆⣿⣿⣿⢸⣇⣿⢸⣿⢻⡇⣿⡇⣿⢰⡶⠿⠃⣶⠾⠇⢴⠶⠿⠀⠀⠀
⠀⠀⠀⠛⠛⠛⠘⠋⠛⠃⠘⢳⣞⡟⠛⠃⠀⠛⠀⠀⠛⠃⠛⠈⠛⠛⠁⠘⠃⠀⠛⠛⠈⠓⠛⠁⠘⠃⠀⠛⠈⠛⠛⠁⠛⠘⠛⠀⠘⠛⠛⠃⠙⠛⠋⠚⠃⠛⠛⠛⠘⠃⠛⠛⠛⠘⠃⠀⠀⠛⠀⠀⠘⠃⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⢀⢀⣠⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣽⣭⣭⣥⣴⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡐⡛⠟⣲⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢄⣤⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠉⠙⠩⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⡴⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠄⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣷⣾⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⠠⠀⠈⠸⡙⠙⣟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣷⣾⢲⣿⡇⠀⠀⠰⢦⡀⠱⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡶⠶⠶⠶⠤⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠀⠑⢠⣴⣿⣤⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⢸⣻⠁⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠈⠈⠙⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠍⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢤⡏⠩⡝⠉⣯⡽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⡶⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢻⣷⣾⣿⣶⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠀⢠⠋⡉⠀⠀⣀⠀⢠⢿⣿⣿⡏⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⠓⠐⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣸⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⢿⡁⠀⣾⣿⡄⠀⠈⣿⣿⠟⠃⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀
⠈⠐⢰⡇⠐⡬⠄⣷⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣃⠀⠀⠀⠀⠀⠈⣿⡿⠽⢿⣧⣤⣤⣿⡟⠀⠀⠀⠀⠀⠀⠀⣘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢰⣿⣿⣆⠸⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⢛⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠂⡿⢿⣿⠿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⠀⢀⣾⣿⣿⣿⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣯⣯⣯⣿⣭⣭⣭⣭⣭⣭⣭⣭⣈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣆⠀⣷⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⠈⢻⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣉⠉⠉⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢻⣿⣿⣿⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠙⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⠭⢭⠍⠉⠉⠁⠬⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠂⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡦⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢁⣀⣿⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣦⡀⠀⠀⠀⠰⣶⣶⣶⣶⣶⣶⣶⣶⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣷⢁⣿⣿⣾⣿⣿⣷⣿⣿⣶⣶⣿⢻⡆⣿⡟⣷⢰⡟⣿⡖⢻⡟⠃⣿⠛⢰⡟⣿⡿⢻⡟⠃⣿⢰⣿⢻⣿⣿⣷⣿⣶⢾⣿⣿⡆⣾⣿⣷⢰⣿⣷⢸⣿⢻⡆⣿⡿⣷⠰⠿⣿⡆⠾⢹⡆⠼⠟⣷⠀⠀⠀
⠀⠀⠀⣿⡇⣿⢸⣿⣿⣴⣾⣷⣾⣿⣿⡖⠀⣿⠛⠃⣿⡟⣿⢸⡇⣿⡇⢸⡇⠀⣿⠛⢸⡇⣤⡄⢸⡇⠀⣿⢸⣿⢸⡿⣿⢿⣿⠾⢺⣿⢿⡆⣿⣿⣿⢸⣇⣿⢸⣿⢻⡇⣿⡇⣿⢰⡶⠿⠃⣶⠾⠇⢴⠶⠿⠀⠀⠀
⠀⠀⠀⠛⠛⠛⠘⠋⠛⠃⢘⢳⣞⡛⠛⠃⠀⠛⠀⠀⠛⠃⠛⠈⠛⠛⠁⠘⠃⠀⠛⠛⠈⠓⠛⠁⠘⠃⠀⠛⠈⠛⠛⠁⠛⠘⠛⠀⠘⠛⠛⠃⠙⠛⠋⠚⠃⠛⠛⠛⠘⠃⠛⠛⠛⠘⠃⠀⠀⠛⠀⠀⠘⠃⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣾⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣭⣽⣯⣭⣤⣴⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡐⡛⢟⣲⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠄⣤⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠉⠙⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⠦⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠋⠛⢿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠸⡙⠙⣟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣷⣾⣼⠄⠀⡇⣴⣦⠈⡧⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡶⠶⠶⠶⠄⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⣠⣴⣿⣤⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡇⣿⡿⠀⠐⠁⠐⡏⠀⠈⠀⠀⠀⠀⠀⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠈⠈⠉⠋⠋⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢤⡏⠩⡝⠉⣯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣶⡶⠀⠀⠀⠰⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢻⣷⣾⣿⣶⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠅⠀⢰⢉⠉⠀⢀⣠⠀⣼⣿⣿⣿⡃⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⡛⠓⠐⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡸⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠸⣿⠀⢰⣿⣿⠀⠀⢹⣿⣿⠟⠃⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⡇⠐⡬⠄⣷⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡃⠀⠀⠀⠀⠀⢹⣿⡿⠿⣿⣤⣤⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⣙⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣸⣿⣿⡀⣿⣿⣿⣿⡟⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠂⠿⢿⢿⠿⣿⣯⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⠀⣠⣿⣿⣿⣿⡁⠉⠉⠀⠀⠁⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣯⣽⣭⣿⣭⣭⣭⣭⣭⣭⣭⣭⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣆⠀⣷⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠍⠘⢿⣷⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣉⠉⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠻⣿⣿⣿⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠻⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⢭⣭⠍⠉⠉⠁⠭⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡀⠀⠿⠿⡿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣄⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⡶⣦⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢁⣁⣿⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⡶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣄⠀⠀⠀⠀⠲⣶⣶⣶⣶⣶⣶⣶⣶⣦⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⡿⣷⢁⣿⣿⣾⣿⣿⣷⣿⣿⣶⡶⣿⢻⡆⣿⡟⣷⢰⡟⣿⡖⢻⡟⠃⣿⠛⢰⡟⣿⡿⢻⡟⠃⣿⢰⣿⢻⣿⣿⣷⣿⣶⣾⣿⣿⡆⣾⣿⣷⢰⣿⣷⢸⣿⢻⡆⣿⡟⣷⠰⠿⣿⡆⠾⢹⡆⠼⠟⣷⠀⠀⠀
⠀⠀⠀⣿⡇⣿⢸⣿⣿⣴⣾⣷⣾⣿⣿⡆⠀⣿⠛⠃⣿⡟⣿⢸⡇⣿⡇⢸⡇⠀⣿⠛⢸⡇⣬⡄⢸⡇⠀⣿⢸⣿⢸⡏⣿⢿⣿⠶⢺⣿⢿⡆⣿⣿⣿⢸⣇⣿⢸⣿⢻⡇⣿⡇⣿⢰⡶⠿⠃⣶⠾⠇⢰⠶⠿⠀⠀⠀
⠀⠀⠀⠛⠛⠛⠘⠋⠛⠃⠘⢳⡞⠋⠙⠃⠀⠛⠀⠀⠛⠃⠛⠈⠛⠛⠁⠘⠃⠀⠛⠛⠈⠓⠛⠁⠘⠃⠀⠛⠈⠛⠛⠁⠛⠼⠛⠄⠘⠛⠛⠃⠙⠛⠋⠚⠃⠛⠛⠛⠘⠃⠛⠛⠛⠘⠃⠀⠀⠛⠀⠀⠘⠃⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣾⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣯⣭⣽⣭⣭⣤⣴⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡐⡛⠟⣲⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣤⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠉⠙⠭⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠉⠻⣿⣿⣿⣿⣿⣿⣷⣿⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⡙⠉⣟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⡷⣾⣷⠀⠀⠀⣦⣆⠈⡆⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣶⣶⡶⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣴⣿⣤⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠇⣿⡏⠀⠈⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠈⠋⠛⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⡏⠩⡝⠉⣯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⡦⠀⠀⠀⠰⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣷⣶⣿⣶⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠁⠀⡜⣉⠁⡄⢠⡀⠀⣾⣿⣿⣿⠁⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢱⡏⠀⢰⣿⣧⠀⠀⢻⣿⣿⠟⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⡃⠐⡬⠄⣷⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡃⠀⠀⠀⠀⠀⢹⣿⠿⢿⣷⣤⣤⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣾⣿⣷⡈⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠿⢿⢿⠿⣿⣯⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⣰⣿⣿⣿⣿⠉⠉⠉⠀⠘⠃⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣿⣭⣭⣭⣭⣭⣭⣭⣭⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣆⠀⣷⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠍⠘⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢛⣿⣿⣿⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠈⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⠭⠭⠍⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣄⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢁⣁⣿⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣧⡀⠀⠀⠀⠀⠲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⡿⣷⢀⣿⣿⢾⣻⣿⣷⣿⣿⣶⠖⣿⢻⡆⣿⡟⣷⢰⡟⣿⡖⢻⡟⠃⣿⠛⢰⡿⣿⡿⢻⡟⠃⣿⢰⣿⢻⣾⣿⣷⣿⣶⣾⣿⣿⡆⣾⣿⣷⢰⣿⣷⢸⣿⢻⡆⣿⡟⣷⠰⠿⣿⡆⠾⢹⡆⠼⠟⣷⠀⠀⠀
⠀⠀⠀⣿⡇⣿⢸⣿⣿⣶⣾⣷⣾⣿⣿⡆⠀⣿⠛⠃⣿⡟⣿⢸⡇⣿⡇⢸⡇⠀⣿⠛⢸⡇⣬⡄⢸⡇⠀⣿⢸⣿⢸⡇⣿⢿⣿⠶⢺⣿⢿⡆⣿⣿⣿⢸⣇⣿⢸⣿⢻⡇⣿⡇⣿⢰⡶⠿⠃⣶⠾⠇⢴⠶⠿⠀⠀⠀
⠀⠀⠀⠛⠛⠛⠘⠋⠛⠃⠘⢳⡞⠋⠙⠃⠀⠛⠀⠀⠛⠃⠛⠈⠛⠛⠁⠘⠃⠀⠛⠛⠈⠓⠛⠁⠘⠃⠀⠛⠈⠛⠛⠁⠛⠼⠛⠀⠘⠛⠛⠃⠙⠛⠋⠚⠃⠛⠛⠛⠘⠃⠛⠛⠛⠘⠃⠀⠀⠛⠀⠀⠘⠃⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣭⣭⣭⣭⣯⣭⣤⣴⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡐⡛⢟⣲⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣤⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠉⠙⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠈⠉⠻⣿⣿⣿⣿⣿⣿⣷⣿⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⡙⠙⣟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣶⣧⣷⠀⣸⢠⣴⡄⠸⡆⠀⢀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡶⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣴⣿⣤⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢹⣿⠇⠀⠎⠀⢸⠃⠀⠀⠀⠘⠀⠀⠐⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠁⠉⠛⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⡏⠩⡝⠉⣯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣶⠦⠀⠀⠀⠰⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣷⣾⣿⣶⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡎⣉⠁⡄⣀⡄⢠⣿⣿⣿⣟⠁⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢷⡇⠀⣾⣿⡇⠀⠈⣿⣿⣿⠟⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢨⡃⠐⡬⠄⣧⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡂⠀⠀⠀⠀⠈⣿⣿⠿⢿⣧⣤⣤⣽⣿⠁⠀⠀⠀⠀⠀⠀⢀⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢀⣿⣿⣆⢸⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠿⢿⢿⠿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⢀⣼⣿⣿⣿⣿⠉⠉⠉⠉⠛⠁⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣯⣿⣭⣭⣭⣭⣭⣭⣭⣭⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣆⠀⣷⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠍⠻⣿⣾⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠹⣿⣿⣿⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠈⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⡭⠭⠍⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠻⣿⣿⣧⡀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡦⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢁⣁⣿⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣦⡀⠀⠀⠀⠀⠲⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⡿⣷⢀⣿⣿⢾⣿⣿⣷⣿⣿⣶⠖⣿⢻⡆⣿⡟⣷⢰⡟⣿⡖⢻⡟⠃⣿⠛⢸⣿⣿⡟⢻⡟⠃⣿⢰⣿⢻⣾⣿⣷⣿⣶⣾⣿⣿⡆⣾⣿⣷⢰⣿⣷⢸⣿⢻⡆⣿⡟⣷⠰⠿⣿⡆⠾⢹⡆⠼⠟⣷⠀⠀⠀
⠀⠀⠀⣿⡇⣿⢸⣿⣿⣴⣾⣷⣾⣿⣿⡄⠀⣿⠛⠃⣿⡟⣿⢸⡇⣿⡇⢸⡇⠀⣿⠛⢸⡇⣬⡄⢸⡇⠀⣿⢸⣿⢸⡇⣿⢿⣿⠶⢺⣿⢿⡆⣿⣿⣿⢸⣇⣿⢸⣿⢻⡇⣿⡇⣿⢰⡶⠿⠃⣶⠾⠇⢰⠶⠿⠀⠀⠀
⠀⠀⠀⠛⠛⠛⠘⠋⠛⠃⠘⢓⠞⠋⠙⠃⠀⠛⠀⠀⠛⠃⠛⠈⠛⠛⠁⠘⠃⠀⠛⠛⠈⠓⠛⠁⠘⠃⠀⠛⠈⠛⠛⠁⠛⠼⠛⠀⠘⠛⠛⠃⠙⠛⠋⠚⠃⠛⠛⠛⠘⠃⠛⠛⠛⠘⠃⠀⠀⠛⠀⠀⠘⠃⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⢀⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣥⣴⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡐⡛⠟⣲⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣖⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠄⣤⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠉⠙⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣷⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⡙⠙⣟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣶⣶⡇⠀⡸⢰⣴⡄⢱⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡶⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣴⣿⣤⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⢸⣿⠁⠀⠃⠀⠿⠁⠀⠀⠀⠀⠀⠀⠐⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠁⠙⠙⠛⠁⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⡏⠉⡝⠉⣯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣶⣶⠦⠀⠀⠀⠰⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢹⣷⣾⣿⣶⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠸⠀⢠⢋⡉⢠⠀⣀⠀⢸⣿⣿⣿⡏⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⣾⠁⠀⣾⣿⡀⠀⠸⣿⣿⡿⠗⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢰⡃⠐⡬⠄⣧⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡀⠀⠀⠀⠀⠈⣿⡿⡻⣿⣤⣤⣤⣿⣿⠀⠀⠀⠀⠀⠀⠂⢈⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢰⣿⣿⣄⣹⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠿⢿⢿⠿⣿⣯⣭⣭⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠀⢀⣼⣿⣿⣿⡏⠙⠛⠉⠉⠛⠁⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣿⣭⣭⣭⣭⣭⣭⣭⣭⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣆⠀⣷⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠁⢻⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠻⣿⣿⣿⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠙⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⡭⢭⠭⠍⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠿⠿⡿⢯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠈⢿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⡶⢀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢁⣁⣿⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣄⠀⠀⠀⠀⠀⠲⣶⣶⣶⣶⣶⣶⣶⣶⣦⡤⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⡟⣷⢀⣿⣿⢾⣿⣿⣷⣿⣿⡶⠂⣿⢻⡆⣿⡟⣷⢰⡟⣿⡖⢻⡟⠃⣿⠛⢸⣿⣿⡟⢻⡟⠃⣿⢰⣿⢻⣾⣿⣷⣿⣶⣾⣿⣿⡆⣾⣿⣷⢰⣿⣷⢸⣿⢻⡆⣿⡟⣷⠰⠿⣿⡆⠾⢹⡆⠼⠟⣷⠀⠀⠀
⠀⠀⠀⣿⡇⣿⢸⣿⣿⣴⣾⣷⣾⣿⣿⡄⠀⣿⠛⠃⣿⡟⣿⢸⡇⣿⡇⢸⡇⠀⣿⠛⢸⡇⣬⡄⢸⡇⠀⣿⢸⣿⢸⡇⣿⢿⣿⠷⢺⣿⢿⡆⣿⣿⣿⢸⣇⣿⢸⣿⢻⡇⣿⡇⣿⢰⡶⠿⠃⣶⠾⠇⢰⠶⠿⠀⠀⠀
⠀⠀⠀⠛⠛⠛⠘⠋⠛⠃⠘⠓⠚⠋⠙⠃⠀⠛⠀⠀⠛⠃⠛⠈⠛⠛⠁⠘⠃⠀⠛⠛⠈⠓⠛⠁⠘⠃⠀⠛⠈⠛⠛⠁⠛⠼⠛⠄⠘⠛⠛⠃⠙⠛⠋⠚⠃⠛⠛⠛⠘⠃⠛⠛⠛⠘⠃⠀⠀⠛⠀⠀⠘⠃⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣽⣿⣯⣭⣭⣭⣭⣤⣴⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡐⡛⢟⣲⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣥⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠉⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⡙⠉⣟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣷⣶⣾⠐⢰⢂⣶⣤⠸⡆⠀⢠⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣶⣶⡶⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣴⣿⣤⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠃⣿⡏⠀⠙⠀⢹⠇⠀⠁⠀⢰⠀⠀⠀⢲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⠈⠋⠛⠁⠀⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢐⡏⠉⡝⠉⣯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣶⣤⠀⠀⠀⠀⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣷⣶⣿⣶⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠇⠀⡖⣉⠁⡄⣐⡄⢠⣿⣿⣿⣿⠉⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢧⡏⠀⢷⣿⡇⠈⠘⣿⣿⣿⡷⠆⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⡃⠐⡬⠄⣷⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣓⠀⠀⠀⠀⠈⢳⣶⣟⣿⣧⣄⣀⣿⣿⠇⠀⠀⠀⠀⠠⠶⠂⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣾⣿⣆⢸⣿⣿⣿⣿⣿⣤⢀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠿⢿⢿⠿⣿⣯⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⢰⣿⣿⣿⣿⠛⠛⠛⠛⠿⠏⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣿⣭⣭⣭⣭⣭⣭⣭⣭⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣆⠀⣷⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡭⠹⣿⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⣿⣿⣿⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠈⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣍⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠿⠿⡿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠻⣿⣿⣿⡀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢁⣀⣿⣤⣤⣤⣤⣤⣴⣶⣶⣶⡶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣦⡀⠀⠀⠀⠀⠐⠲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⡿⣷⢀⣿⣿⢞⣿⣿⣷⣿⣿⠖⠀⣿⢻⡇⣿⡟⣷⢰⡟⣿⡔⢻⡟⠃⣿⠛⢿⣿⣿⡟⢻⡟⠃⣿⢰⣿⢻⣾⣿⣷⣿⣶⣾⣿⣿⡆⣾⣿⣷⢰⣿⣷⢸⣿⢻⡆⣿⡿⣷⠰⠿⣿⡆⠾⢹⡆⠼⠟⣷⠀⠀⠀
⠀⠀⠀⣿⡇⣿⢸⣿⣿⣴⣾⣷⢾⣿⣿⡆⠀⣿⠛⠃⣿⡟⣿⢸⡇⣿⡇⢸⡇⠀⣿⠛⢸⡇⣬⡄⢸⡇⠀⣿⢸⣿⢸⡇⣿⢿⣿⠿⢾⣿⢿⡆⣿⣿⣿⢸⣇⣿⢸⣿⢻⡇⣿⡇⣿⢰⡶⠿⠃⣶⠾⠇⢰⠶⠿⠀⠀⠀
⠀⠀⠀⠛⠛⠛⠘⠋⠛⠃⠘⠃⠘⠋⠙⠃⠀⠛⠀⠀⠛⠃⠛⠈⠛⠛⠁⠘⠃⠀⠛⠛⠈⠓⠛⠁⠘⠃⠀⠛⠈⠛⠛⠁⠻⠼⠛⠶⠞⠛⠛⠃⠙⠛⠋⠚⠃⠛⠛⠛⠘⠃⠛⠛⠛⠘⠃⠀⠀⠛⠀⠀⠘⠃⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⢀⣾⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣯⣭⣭⣭⣭⣥⣴⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡀⡛⢟⣲⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣖⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠄⣤⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠉⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣴⣶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⡙⠙⣟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣶⣷⡗⡄⣾⢰⣦⡄⢳⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡾⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣴⣿⣤⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⢹⣿⠃⠀⠋⠜⣿⠁⠈⠃⠀⠈⠀⠀⠀⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠉⠙⠛⠁⠘⠁⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡏⠉⡝⠉⣯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣶⣤⣤⠀⠀⠀⠀⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣷⣾⣿⣶⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢐⠀⢠⠞⡑⢠⠀⣲⠀⣼⣿⣿⣿⡟⠉⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⣼⠁⠈⣾⣿⡁⠉⢻⣿⣿⣿⡶⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⠃⠐⡬⠄⣷⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣃⠀⠀⠀⠀⠙⣶⣶⣿⣿⣄⣀⣨⣿⣿⠁⠀⠀⠀⠀⠤⠶⠈⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣿⣷⡀⢿⣿⣿⣿⣿⣿⣠⡀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠿⢿⢿⠿⣿⣯⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀⠀⣸⣿⣿⣿⡿⠿⠿⠿⢿⠿⠃⠁⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣯⣿⣭⣭⣭⣭⣭⣭⣭⣭⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣆⠀⣷⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⢹⣿⣾⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢹⣿⣿⣿⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠙⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣍⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠿⠿⡿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠈⢿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣾⡤⡀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢁⣁⣿⣤⣤⣤⣤⣤⣴⣶⣶⣶⡶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⡄⠀⠀⠀⠀⠀⠐⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡤⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣷⢀⣿⣿⢾⣿⣿⣷⣿⣿⠒⠀⣿⢻⡇⣿⡟⣷⢰⡟⣿⡔⢻⡟⠃⣿⠻⣿⣿⣿⡞⢻⡟⠃⣿⢰⣿⢻⣾⣿⣷⣿⣶⣾⣿⣿⡖⣾⣿⣷⢰⣿⣷⢸⣿⢻⡆⣿⣿⣷⠰⠿⣿⡆⠾⢹⡆⠼⠟⣷⠀⠀⠀
⠀⠀⠀⣿⡇⣿⢸⣿⣿⣴⣾⡷⢾⣿⣿⡆⠀⣿⠛⠃⣿⡟⣿⢸⡇⣿⡇⢸⡇⠀⣿⠛⢸⡇⣤⡄⢸⡇⠀⣿⢸⣿⢸⡇⣿⢿⣿⠿⢾⣿⢿⡆⣿⣿⣿⢸⣇⣿⢸⣿⢻⡇⣿⡇⣿⢰⡶⠿⠃⣶⠾⠇⢰⠶⠿⠀⠀⠀
⠀⠀⠀⠛⠛⠛⠘⠋⠛⠃⠘⠃⠘⠋⠙⠃⠀⠛⠀⠀⠛⠃⠛⠈⠛⠛⠁⠘⠃⠀⠛⠛⠈⠛⠛⠁⠘⠃⠀⠛⠈⠛⠛⠁⠻⠼⠛⠶⠞⠛⠛⠃⠙⠛⠋⠚⠃⠛⠛⠛⠘⠃⠛⠛⠛⠘⠃⠀⠀⠛⠀⠀⠘⠃⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠿⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣥⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⣶⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣭⣭⣽⣭⣭⣤⣴⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡐⡛⢟⣲⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣖⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣤⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠉⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⡙⠙⣟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣼⣦⢶⡇⣷⣶⣈⣧⠀⠀⡆⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣶⣶⡶⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣴⣿⣤⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡏⣿⡟⠀⠸⠃⢻⡟⠀⠙⠀⠀⠇⠀⠀⠐⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠙⠛⠋⠀⠙⠁⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡏⠉⡝⠉⣯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣷⣾⣿⣶⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡰⢒⠂⡄⢠⣦⢀⣾⣿⣿⣿⠟⠉⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠁⠀⢳⡾⠀⢠⣾⡏⠈⠙⣿⣿⣿⣷⡆⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⡃⠐⡬⠄⣷⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡂⠀⠀⠀⠈⢻⣶⣾⣿⣟⣀⣀⣹⣿⡟⠁⠀⠀⠀⢀⣤⠶⠘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢸⣿⣏⠙⣿⣿⣿⣿⣿⣇⣠⡀⠀⠀⠀⠀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠿⢿⢿⠿⣿⣯⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠀⠀⣾⣿⣿⣶⡿⠿⠿⠿⢿⡿⠙⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣿⣭⣭⣭⣭⣭⣭⣭⣭⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣆⠀⣷⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠍⢿⣷⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⣿⣿⣿⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠈⢻⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⡍⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠿⠿⡿⢯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠹⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢁⣀⣿⣤⣤⣤⣤⣤⣴⣶⣶⣶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠐⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⡿⣷⢀⣿⣿⢾⣿⣿⣷⣿⣿⠂⠀⣿⢻⡇⣿⡟⣷⢰⡟⣿⡖⢻⡟⠃⣿⢿⣿⣿⣿⡞⢻⡟⢃⣿⢰⣿⢻⣾⣿⣷⣿⣶⣾⣿⣿⡖⣾⣿⣷⢰⣿⣷⢸⣿⢻⡆⣿⣿⣷⠰⠿⣿⡆⠾⢹⡆⠼⠟⣷⠀⠀⠀
⠀⠀⠀⣿⡇⣿⢸⣿⣿⣴⣾⡷⢺⣿⣿⡆⠀⣿⠛⠃⣿⡟⣿⢸⡇⣿⡇⢸⡇⠀⣿⠛⢹⡇⣬⡄⢸⡇⠁⣿⢸⣿⢸⡇⣿⢿⣿⠿⢾⣿⢿⡆⣿⣿⣿⢸⣇⣿⢸⣿⢻⡇⣿⡇⣿⢰⡶⠿⠃⣶⠾⠇⢰⠶⠿⠀⠀⠀
⠀⠀⠀⠛⠛⠛⠘⠋⠛⠃⠘⠃⠘⠋⠙⠃⠀⠛⠀⠀⠛⠃⠛⠈⠛⠛⠁⠘⠃⠀⠛⠛⠈⠛⠛⠁⠘⠃⠀⠛⠈⠛⠛⠁⠻⠼⠛⠶⠞⠛⠛⠃⠙⠛⠋⠚⠃⠛⠛⠛⠘⠃⠛⠛⠛⠘⠓⠀⠀⠛⠀⠀⠘⠃⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣥⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⢀⣾⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣭⣽⣭⣭⣭⣭⣭⣥⣴⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡑⡛⢟⣲⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣖⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠠⠄⣤⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢻⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⡙⠙⣟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣷⣦⣶⣴⣼⢸⣶⣶⣺⡆⠀⢰⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡶⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣴⣿⣤⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢻⣿⠏⠁⡟⠘⣿⠏⠈⠃⠀⢸⠀⠀⠀⠰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠈⠛⠛⠃⠈⠋⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡏⠩⡝⠉⣯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠠⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣷⣾⣿⣶⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠆⠀⡴⠒⢀⠀⢤⡀⢰⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⣷⡇⠀⣥⣿⠃⠚⢻⣿⣿⣷⣦⡀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⡃⠐⡬⠄⣷⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡀⠀⠀⠀⠙⢧⣤⢿⣿⣇⠀⠈⣿⣿⠟⠁⠀⠀⠀⢀⣤⡆⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣼⣿⡉⢹⣿⣿⣿⣿⣿⣀⣀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠿⢿⢿⠿⣿⣯⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢀⣿⣿⣷⣾⡿⢿⣿⣿⣿⡟⠛⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣭⣿⣭⣭⣭⣭⣭⣭⣭⣭⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣆⠀⣷⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠍⣿⣦⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠻⣿⣿⣿⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠘⢿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡀⠀⠿⠿⡿⢯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠈⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣤⣀⡀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢁⣁⣿⣤⣤⣤⣤⣤⣴⣶⣶⡶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠲⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣴⣦⣤⡤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⡿⣷⢀⣿⣿⢾⣿⣿⣷⣿⣿⠀⠀⣿⢻⡇⣿⡟⣷⢰⡟⣿⡖⢻⡟⠃⣿⣿⣿⣿⣿⡞⢻⡟⢃⣿⢠⣿⢻⣾⣿⣷⣿⣶⣾⣿⣿⡶⣾⣿⣷⢲⣿⣷⢸⣿⢻⡆⣿⣿⣷⠰⠿⣿⡆⠾⢹⡆⠼⠟⣷⠀⠀⠀
⠀⠀⠀⣿⡇⣿⢸⣿⣿⣴⣾⡗⢺⣿⣿⡆⠀⣿⠛⠃⣿⡟⣿⢸⡇⣿⡇⢸⡇⠀⣿⠛⢹⡇⣬⡄⢸⡇⠁⣿⢸⣿⢸⡇⣿⢿⣿⠿⢾⣿⣿⡇⣿⣿⣿⢸⣇⣿⢸⣿⢻⡇⣿⡇⣿⢰⡶⠿⠃⣶⠾⠇⢴⠶⠿⠀⠀⠀
⠀⠀⠀⠛⠛⠛⠘⠋⠛⠃⠘⠃⠘⠋⠙⠃⠀⠛⠀⠀⠛⠃⠛⠈⠛⠛⠁⠘⠃⠀⠛⠛⠈⠛⠛⠁⠘⠃⠀⠛⠈⠛⠛⠁⠻⠾⠟⠶⠞⠛⠛⠃⠙⠛⠋⠚⠃⠛⠛⠛⠘⠃⠛⠛⠛⠘⠓⠀⠀⠛⠀⠀⠘⠃⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠿⠿⠭⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣥⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⢀⣾⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣽⣯⣭⣭⣭⣭⣭⣥⣴⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡐⡛⢟⣲⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣖⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠠⠄⣤⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⡙⠙⣟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣴⣦⣶⣇⣷⣶⣴⡆⠀⠐⡄⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣶⡶⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣴⣿⣤⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡟⣿⡿⠈⢿⢋⣿⡿⠋⠿⠀⠀⠇⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠙⠛⠛⠀⠙⠁⠀⠀⢀⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡏⠉⡝⠉⣯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣷⣾⣿⣶⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⠤⠄⠀⢀⡀⠀⣾⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡇⡶⠀⢃⣾⡧⠼⢿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⡃⠐⡬⠄⣧⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣃⠀⠀⠀⠸⣧⣀⣼⣿⡇⠀⠀⣿⣿⡿⠛⠁⠀⠀⠀⢀⣠⠙⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⡓⢻⣿⣷⣶⣿⣿⡇⢀⠀⠀⠀⠈⠉⢉⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠿⢿⢿⠿⣿⣯⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢸⣿⣷⣬⣿⣿⣿⣿⣿⣿⢿⠃⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣿⣭⣭⣭⣭⣭⣭⣭⣭⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣆⠀⣷⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡭⢹⣷⣰⣿⣿⣿⣿⡅⠈⠁⠉⠛⠁⠈⠀⠀⠀⠀⢠⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠛⣿⣿⣿⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠈⢻⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⡭⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠿⠿⡿⢯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⢻⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣧⣉⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢁⣁⣿⣤⣤⣤⣤⣤⣴⣶⣶⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⡄⠀⠀⠀⠀⠀⠈⠑⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⡤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣷⢀⣿⣿⢞⣿⣿⣷⣿⣿⠀⠀⣿⢻⡇⣿⡟⣷⢰⡟⣿⡞⢻⡟⠻⣿⣿⣿⣿⣿⡞⢻⡟⠃⣿⢠⣿⢻⣾⣿⣷⣿⣾⣾⣿⣿⡶⣾⣿⣷⢲⣿⣷⢸⣿⢻⡆⣿⣿⣷⠰⠿⣿⡆⠾⢹⣆⠼⠟⣷⠀⠀⠀
⠀⠀⠀⣿⡇⣿⢸⣿⣿⡴⢾⡇⢰⣿⣿⡆⠀⣿⠛⠃⣿⡟⣿⢸⡇⣿⡇⢸⡇⠀⣿⠛⢹⡇⣬⡅⢸⡏⠀⣿⢸⣿⢸⡏⣿⢿⣿⠿⢿⣿⣿⡇⣿⣿⣿⢸⣇⣿⢸⣿⢻⡇⣿⣗⣿⢰⡶⠿⠃⣶⠾⠇⢶⠶⠿⠀⠀⠀
⠀⠀⠀⠛⠛⠛⠘⠋⠛⠃⠘⠃⠘⠋⠙⠃⠀⠛⠀⠀⠛⠃⠛⠈⠛⠛⠁⠘⠃⠀⠛⠛⠘⠛⠛⠁⠘⠃⠀⠛⠈⠛⠛⠁⠻⠾⠿⠶⠞⠛⠛⠃⠙⠛⠋⠚⠃⠛⠛⠛⠘⠃⠛⠛⠛⠘⠓⠀⠀⠛⠀⠀⠘⠃⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠰⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠿⠿⠽⠫⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣥⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⢀⣾⣶⣶⣶⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣯⣽⣿⣭⣭⣽⣭⣭⣥⣴⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡐⡛⢟⣲⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣖⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠠⠄⣤⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠹⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⡙⠙⣟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣴⣦⣶⣇⣷⣶⣴⡇⠀⠐⡄⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠶⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣴⣿⣤⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡟⣿⡿⠈⢿⢫⣿⡿⠋⠿⠀⠀⠇⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠙⠛⠛⠀⠙⠀⠀⠀⢀⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡏⠉⡍⠉⣯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣷⣾⣿⣶⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⠤⠄⠀⢀⡀⢀⣶⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢘⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡇⡶⠀⢃⣾⡧⠼⢿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢨⡃⠐⡬⠄⣧⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣃⠀⠀⠀⠸⣧⣀⣼⣿⡇⠀⠀⣿⣿⡿⠛⠁⠀⠀⠀⢀⣠⠙⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⡓⢻⣿⣷⣶⣿⣿⡇⢀⠀⠀⠀⠈⠉⢉⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠻⢿⢿⠿⣿⣯⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢸⣿⣷⣬⣿⣿⣿⣿⣿⣿⢿⠃⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣿⣭⣭⣭⣭⣭⣭⣭⣭⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣆⠀⣷⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡭⢹⣷⣰⣿⣿⣿⣿⡅⠈⠁⠈⠛⠁⠈⠀⠀⠀⠀⢠⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠹⣿⣿⣿⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠈⢻⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⡭⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠿⠿⡿⢯⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⢻⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣉⣥⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢁⣁⣿⣤⣤⣤⣤⣤⣴⣶⣶⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⡄⠀⠀⠀⠀⠀⠈⠑⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⡤⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣷⢀⣿⣿⢞⣿⣿⣷⣿⣿⠀⠀⣿⢻⡇⣿⡟⣷⢰⡟⣿⡞⢻⡟⠻⣿⣿⣿⣿⣿⡞⢻⡟⠃⣿⢠⣿⢻⣾⣿⣷⣿⣾⣾⣿⣿⡶⣾⣿⣷⢲⣿⣷⢸⣿⢻⡆⣿⣿⣷⠰⠿⣿⡆⠾⢹⡆⠼⠟⣷⠀⠀⠀
⠀⠀⠀⣿⡇⣿⢸⣿⣿⡴⢾⡇⢰⣿⣿⡆⠀⣿⠛⠃⣿⡟⣿⢸⡇⣿⡇⢸⡇⠀⣿⠛⢹⡇⣬⡅⢸⡏⠀⣿⢸⣿⢸⡏⣿⢿⣿⠿⢿⣿⣿⡇⣿⣿⣿⢸⣇⣿⢸⣿⢻⡇⣿⣷⣿⢰⡶⠿⠃⣶⠾⠇⢲⠶⠿⠀⠀⠀
⠀⠀⠀⠛⠛⠛⠘⠋⠛⠃⠘⠃⠘⠋⠙⠃⠀⠛⠀⠀⠛⠃⠛⠈⠛⠛⠁⠘⠃⠀⠛⠛⠘⠛⠛⠁⠘⠃⠀⠛⠈⠛⠛⠁⠻⠾⠟⠶⠞⠛⠛⠃⠙⠛⠋⠚⠃⠛⠛⠛⠘⠃⠛⠛⠛⠘⠓⠀⠀⠛⠀⠀⠘⠃⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠰⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠿⠿⠽⠫⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣾⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣭⣿⣭⣭⣽⣯⣭⣤⣴⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡐⡛⠟⣲⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣖⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠄⣤⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠦⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⡙⠙⣟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣶⣤⣶⣶⣶⣤⣾⠀⠀⣇⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡶⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⢠⣴⣿⣤⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠛⢹⡏⣿⣿⠿⢿⠁⠀⡿⠆⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠈⠛⠿⠁⠹⠃⠀⠈⠀⡸⠋⠀⠀⠀⠀⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⡏⠉⡍⠉⣯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣷⣾⣿⣶⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣀⣀⠀⠀⠀⢀⣠⣿⣿⣿⣿⡿⠗⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢸⢰⠄⠐⢠⡷⢰⣿⣿⣿⣿⣃⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⡃⠐⡬⠄⣷⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡀⠀⠀⠘⣿⣀⣸⣿⣧⠀⠀⢿⣿⣿⡿⠓⠀⠀⠀⠀⢀⡘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠈⣿⡿⠿⣷⣦⣤⣼⣿⡏⠀⠀⠀⠀⠀⠒⠛⠃⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠿⢿⢿⠿⣿⣯⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣿⣿⡀⣿⣿⣿⣿⣿⣿⣾⡆⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣯⣿⣯⣭⣭⣭⣭⣭⣭⣭⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣆⠀⣷⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⣿⣄⣴⣿⣿⣿⡏⠉⠉⠋⠿⠟⠙⠁⠀⠀⠀⠀⣨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠙⣿⣿⣿⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠹⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⡭⢥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡀⠀⠿⠿⡿⢯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠹⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⣥⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢁⣁⣿⣤⣤⣤⣤⣤⣴⣶⣶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠈⠓⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⡿⣷⢀⣿⣿⢾⣿⣿⡷⣿⣿⠀⠀⣿⢻⡆⣿⡟⣷⢰⡟⣿⡞⢻⡿⣿⣿⣿⣶⡟⣿⡞⢻⣟⠃⣿⢠⣿⢻⣾⣿⣷⣿⣾⣾⣿⣿⣶⣾⣿⣷⢶⣿⣷⢺⣿⢻⡆⣿⣿⣷⠰⠿⣿⡆⠾⢻⣆⠼⠟⣷⠀⠀⠀
⠀⠀⠀⣿⡇⣿⢸⣿⣿⡔⢺⡇⢰⣿⣿⡆⠀⣿⠛⠃⣿⡟⣿⢸⡇⣿⡇⢸⡇⠘⣿⠛⢹⡇⣬⡄⢸⡏⠀⣿⢸⣿⢸⡇⣿⢿⣿⢿⢿⣿⣿⡗⣿⣿⣿⢸⣇⣿⢸⣿⢻⡇⣿⣷⣿⢰⡶⠿⠃⣶⠾⠇⢶⠶⠿⠀⠀⠀
⠀⠀⠀⠛⠛⠛⠘⠋⠛⠃⠘⠃⠘⠋⠙⠃⠀⠛⠀⠀⠛⠃⠛⠈⠛⠛⠁⠘⠃⠀⠛⠛⠘⠛⠛⠁⠘⠃⠀⠛⠈⠛⠛⠁⠻⠾⠿⠶⠞⠛⠛⠷⠙⠛⠋⠚⠃⠛⠛⠛⠘⠃⠛⠛⠛⠘⠓⠀⠀⠛⠀⠀⠘⠃⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠆⠠⠴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣾⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣯⣽⣯⣭⣭⣽⣭⣭⣤⣴⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡐⡛⢟⣲⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣖⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠄⣤⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⡙⠉⣟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣴⣶⣶⣧⣿⣶⣴⣧⠀⢸⡄⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡶⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣴⣿⣤⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢿⣿⣿⡿⣿⡿⠟⣿⢻⣿⡿⠿⡿⠀⢸⣷⠀⠀⠀⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠈⠛⠛⠁⠹⠁⠀⠁⠀⠿⠁⠀⠀⠀⠘⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⡏⠉⡝⠉⣯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣷⣾⣿⣶⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠆⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡏⣤⠀⠆⣬⡆⣸⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢰⡃⠐⡬⠄⣷⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡀⠀⠀⠱⣇⡀⣸⣿⡆⠀⠘⣿⣿⣿⠿⠃⠀⠀⠀⠀⢀⢙⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠙⣿⠿⢿⣧⣤⣤⣿⣿⠁⠀⠀⠀⠀⠠⠞⠛⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠿⢿⢿⠿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢠⣿⣧⠸⣿⣿⣿⣿⣿⣧⣶⠆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣭⣯⣿⣭⣭⣭⣭⣭⣭⣭⣭⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣆⠀⣷⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠍⣷⣄⣼⣿⣿⣿⠉⠉⠉⠻⠿⠋⠙⠀⠀⠀⠀⠀⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠛⣿⣿⣿⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢻⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⡭⠥⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡀⠀⠿⠿⡿⢯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⢻⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢁⣁⣿⣤⣤⣤⣤⣤⣴⣶⡶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠈⠑⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⡿⣷⢀⣿⣿⣾⣿⣿⠷⣿⣿⠀⠀⣿⢻⡆⣿⡟⣷⢰⡟⣿⡞⢻⣿⣿⣿⣿⣴⡟⣿⡞⢻⣟⠃⣿⢠⣿⢻⣾⣿⣷⣿⣾⣾⣿⣿⣶⣾⣿⣷⢶⣿⣷⣺⣿⢻⡆⣿⣿⣷⠰⠿⣿⡆⠾⢻⡆⠼⠟⣷⠀⠀⠀
⠀⠀⠀⣿⡇⣿⢸⣿⣿⡔⢸⡇⢰⣿⣿⡆⠀⣿⠛⠃⣿⡟⣿⢸⡇⣿⡇⢸⡇⠻⣿⠛⢹⡇⣤⡄⢸⡏⠀⣿⢸⣿⢸⡇⣿⢿⣿⠿⢿⣿⣿⡗⣿⣿⣿⢸⣇⣿⣸⣿⢻⡇⣿⣷⣿⢰⡶⠿⠃⣶⠾⠇⢶⠶⠿⠀⠀⠀
⠀⠀⠀⠛⠛⠛⠘⠋⠙⠃⠘⠃⠘⠋⠙⠃⠀⠛⠀⠀⠛⠃⠛⠈⠛⠛⠁⠘⠃⠀⠛⠛⠘⠛⠛⠁⠘⠃⠀⠛⠈⠛⠛⠁⠛⠾⠿⠶⠞⠛⠛⠷⠝⠛⠋⠚⠃⠛⠛⠛⠘⠃⠛⠛⠛⠘⠓⠀⠀⠛⠀⠀⠘⠃⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠆⠠⠴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡀⠀⢤⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⢤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠠⢑⣱⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣶⣶⣆⢠⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠊⡛⡛⣟⣲⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣖⣒⣄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡵⢠⣴⣥⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⡆⠄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠙⣿⢢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠀⠀⠀⠀⠀⠀⢀⠀⠉⣀⠻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠦⠀⠐⠆⠠⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣈⣉⠉⢹⡙⠙⣟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣶⣶⣾⣼⣿⣿⣾⡆⠀⣿⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡾⠿⠿⠷⠴⠲⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⢩⣿⣤⣴⣿⣤⣿⡿⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⢿⣿⠿⢻⡿⣿⣿⠿⢿⡧⠀⣿⡾⠀⠀⠰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠦⠦⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀
⢘⢃⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠘⠛⠋⠘⠏⠀⠘⠀⠹⠏⠀⠈⠀⠀⠃⠁⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠯⠽⠋⠇⠀⠀⠀⠀⠀⠀⠀
⢰⢬⣷⡏⠩⡝⠉⣯⡽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠊⠉⠀⠀⠀⠀⠀⠀⠀
⠈⢯⣻⣷⣾⣿⣶⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣀⣀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⠷⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⠓⠒⢢⠀⠀⠀⠀⠀⠀⠀
⠰⠾⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢰⣃⡄⠰⢂⣵⢢⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠓⠐⢚⠁⠀⠀⠀⠀⠀⠀
⢸⡽⢻⡇⠐⡼⠄⣷⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡀⠀⠀⢿⣅⢀⣿⣿⠈⠀⢻⣿⣿⣿⠿⠂⠀⠀⠀⢀⣀⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣚⣹⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⣿⠿⣿⣦⣤⣼⣿⣿⠁⠀⠀⠀⠀⠴⠿⠛⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⢛⠉⢈⢁⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠆⢯⡿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢸⣿⣆⢹⣿⣿⣿⣿⣿⣾⣷⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⣉⢈⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠐⢁⣿⠀⢈⣆⠂⣷⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠍⣷⣄⣼⣿⣿⣿⠋⠙⠻⠿⠿⠻⠟⠀⠀⠀⠀⢀⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠉⠉⠉⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢈⣧⢼⣿⣿⣿⣿⣯⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⢻⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⢭⣭⣭⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠭⡭⠫⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⢻⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣤⣤⡤⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠓⠀⢐⢅⣁⣿⣥⣤⣤⣤⣦⣶⣶⡶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⡤⠄⢤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⣗⡾⢟⣿⣶⣶⣶⣶⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣄⡀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⡖⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠈⠑⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠛⠉⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⠷⣷⠶⠶⠶⠖⠐⠂⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠆⠰⠴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡀⠀⢤⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⢤⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠠⢃⣱⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⢀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠊⡛⡛⢟⣲⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣖⣲⡐⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡔⣠⣴⣥⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠦⠄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠭⠄⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⡀⠀⠀⠀⡀⠀⢀⡀⢻⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠦⠀⠤⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣺⣏⠋⢹⡙⠙⣟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣶⣶⣷⣷⣿⣿⣿⣧⠄⢸⡆⠀⠁⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡾⠿⠿⠷⠴⠲⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠹⣛⣦⣴⣿⣤⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡿⣿⡿⠟⣿⢻⣿⡿⢿⡿⠆⢸⢿⠂⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠦⠦⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀
⠘⢢⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠙⠛⠀⠛⠁⠀⠁⠈⠟⠁⠀⠀⠀⠘⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠯⠭⠋⠅⠀⠀⠀⠀⠀⠀⠀
⠸⠽⣿⡏⠩⡝⠉⣯⡽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠓⠂⠉⠀⠀⠀⠀⠀⠀⠀
⢰⡪⣹⣷⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣀⡀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠗⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⠓⠒⢠⠀⠀⠀⠀⠀⠀⠀
⢰⢬⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⢡⡄⠶⣨⡖⣼⣿⣿⣿⣿⣁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⢃⡑⢘⠁⠀⠀⠀⠀⠀⠀
⢰⡛⢿⡇⠐⡼⠄⣷⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡀⠀⠘⣿⡀⣸⣿⡇⠁⠘⣿⣿⣿⡿⠗⠀⠀⠀⠀⣠⡘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⠒⢃⠁⠀⠀⠀⠀⠀⠀⠀
⢠⢬⣹⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠈⢻⡿⠿⣷⣤⣤⣿⣿⡏⠀⠀⠀⠀⠐⠞⠛⠛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⢛⠉⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣑⢇⡿⢿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢸⣿⡀⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⣉⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⢁⣛⠀⢈⣆⠀⣷⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⣿⣄⣾⣿⣿⣟⠉⠛⠟⡿⠟⠻⠋⠀⠀⠀⠀⢠⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠉⠉⡉⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢈⣒⣟⣿⣿⣿⣿⣯⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢹⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⠭⡉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠟⡌⠋⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⢻⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣤⡤⠤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠓⠀⣰⢅⣁⣿⣥⣤⣤⣤⣤⣶⣶⡶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⡤⠄⢤⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⣟⣞⢻⢿⣶⣶⣶⣶⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⡖⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠑⠉⠑⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠋⠉⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠿⢷⠶⠶⠶⠖⠂⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠆⠰⠴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡀⠀⢠⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⠤⢤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠠⢁⣱⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣭⣶⣶⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠊⡛⡛⢟⣲⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣖⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡐⠠⢤⣥⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠙⠙⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠖⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠙⠠⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⡀⢀⣀⠀⠀⣀⡀⠰⡝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀
⢸⢈⢈⠈⢹⡙⠙⣟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣿⣿⣿⣷⠀⣿⣶⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡾⠿⠿⠷⠴⠰⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠨⡚⣤⣴⣿⣤⣿⡿⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡿⠟⣿⢿⣿⣿⣿⣿⠀⣿⣿⠀⠀⠀⠰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠦⠤⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⠁⠛⠀⠀⠁⠁⠏⠀⠀⠀⠀⠃⠁⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠯⠥⠀⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠘⣵⡏⠩⡝⠉⣯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣄⣀⣀⡀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠂⠈⠀⠀⠀⠀⠀⠀⠀
⠈⠈⣸⣷⣾⣿⣶⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⠓⠒⢐⠀⠀⠀⠀⠀⠀⠀
⢘⢠⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡎⣬⡹⢦⡴⣻⣿⣿⣿⣿⣁⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠓⠐⢪⠀⠀⠀⠀⠀⠀⠀
⠀⠘⢻⡇⠐⡼⠆⣷⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣃⠀⢱⣇⢀⣿⣷⠈⠘⣿⣿⣿⣿⠿⠃⠀⠀⢠⣾⣧⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⢒⠁⠈⠀⠀⠀⠀⠀⠀⠀
⠀⣈⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠙⢿⣿⢿⣦⣤⣿⣿⣟⢀⣀⡀⠀⠐⠟⠛⠛⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⠛⢁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠰⠀⢣⠿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢸⣇⢸⣿⣿⣿⣿⣿⣿⣿⡇⣰⠾⡷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⣉⢈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣒⠀⢈⣆⠂⣷⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢭⣧⣸⣿⣿⣟⠛⠻⣿⣿⢿⡿⠁⠀⠀⠀⠀⢠⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢉⠉⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠣⡘⣻⣿⣿⣿⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⠭⡉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠉⡮⠋⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠠⢤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣥⣤⡤⡤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⠀⠐⢅⣁⣿⣥⣤⣤⣤⣦⣶⣶⣶⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⡤⠄⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⡳⣮⠙⢿⣶⣶⣶⣶⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣄⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⡖⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⠀⠓⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠋⠉⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣿⡿⠷⠶⠶⠶⠦⠖⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠆⠰⠴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⣄⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡀⡀⢠⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⠤⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠠⢁⣡⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣭⣭⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠉⡙⡛⣟⣲⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣖⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⢤⣥⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⠉⠽⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⢀⢀⣀⣀⠀⢀⡀⠀⢢⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠆⠀⠐⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠸⢂⠈⠹⡙⠙⣟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡶⢸⣿⡆⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡶⠾⠷⠷⠴⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢘⠨⠘⣦⣴⣿⣤⣿⡿⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⢻⡿⣿⣿⢿⣿⡇⣿⣿⠇⠀⠀⠀⢲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠁⠋⠀⠘⠈⠘⠁⠈⠉⠀⠟⠏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠯⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠰⣴⡏⠩⡝⠉⣯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣦⣤⣠⣆⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⣸⣷⣾⣿⣶⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⡀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⠓⠒⢀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡎⣭⣱⢦⣶⣿⣿⣿⣿⣏⣀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⠂⠐⠐⠁⠀⠀⠀⠀⠀⠀
⠀⠐⢻⡇⠐⡼⠄⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡀⢱⣇⢀⣿⡇⠉⢹⣿⣿⣿⣿⠟⠀⠀⢀⣴⣿⡆⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⡛⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠴⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠙⢿⣿⣷⣤⣼⣿⣿⣏⣀⣀⡀⠀⠸⠟⠛⠃⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⢋⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢂⡿⢿⢿⢿⣿⣯⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣇⢸⣿⣿⣿⣿⣿⣿⣿⠄⣴⣿⡷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣯⣭⣭⣭⣭⣭⣭⣭⡉⢀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠂⠀⢈⣆⠀⣷⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⣽⣤⣿⣿⣟⠛⠿⣿⡿⣿⠟⠈⠀⠀⠀⠀⢠⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣍⠉⠉⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⠄⠐⣻⣿⣿⣿⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢻⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⢭⡭⡥⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡀⠫⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠈⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣥⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠁⠀⠀⣅⣁⣿⣤⣤⣤⣤⣤⣶⣶⣶⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⡤⠄⢄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠐⢗⡌⠉⠿⣶⣶⣶⣶⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣦⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⠀⠑⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠋⠉⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⠷⠶⠶⠶⠶⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠖⠰⠴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣤⡀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡀⠀⢠⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣬⣥⠤⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠠⢁⣡⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣯⣭⣴⣶⣄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⡙⡛⣟⣲⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣖⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡐⠠⢤⣥⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠉⠉⠩⠽⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠢⠄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠈⢢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⣀⢀⣀⡀⠀⢀⡀⠀⢄⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠆⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀
⢰⢸⠀⠈⢹⡙⠙⣟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣷⣆⣿⣷⠀⠈⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡾⠿⠿⠷⠴⠐⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀
⢘⠠⣙⣤⣴⣿⣤⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⠿⣻⢿⣿⡿⣿⣿⢿⣿⡿⠁⠀⠀⠀⢲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⢀⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠀⠃⠀⠈⠀⠋⠀⠛⠃⠸⣿⠁⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠯⠅⠀⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢴⡏⠩⡝⠉⣯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣦⣤⣿⣆⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠓⠂⠁⠀⠀⠀⠀⠀⠀⠀
⠐⠨⣸⣷⣾⣿⣶⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⡀⠀⠀⠀⣼⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⠓⠐⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠎⣩⣹⢦⣼⣿⣿⣿⣿⣅⣀⠀⠀⠀⠀⢀⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠂⠒⢘⠁⠀⠀⠀⠀⠀⠀
⠀⠐⢹⡇⠐⡼⠄⣷⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣃⠸⣏⣀⣿⡏⠙⢿⣿⣿⣿⣿⠟⠀⢀⣴⣿⣿⡄⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⡛⠒⢂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠰⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠙⠿⣿⣷⣤⣼⣿⣿⣅⣠⣤⠖⠁⡿⠛⠛⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⠛⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢃⡿⢿⣿⢿⣿⣯⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢠⣸⣿⣿⣿⣿⣿⣿⣿⢠⣾⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⣈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢒⠀⢈⣆⠀⣷⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢩⣧⣼⣿⣟⠛⢿⣿⣿⣿⠇⠈⠀⠀⠀⠀⢠⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣩⠉⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⢀⠈⢻⣿⣿⣿⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠘⣿⣿⣿⣿⣦⠀⠈⠁⠁⠀⠀⠤⠄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⡭⢭⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡅⠛⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⢹⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠰⠶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣤⣠⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠂⠀⠐⢁⣁⣿⣤⣤⣤⣤⣤⣴⣶⣶⡶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⡤⠄⢄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠐⠗⡼⡋⠿⣶⣶⣶⣶⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⣄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⡖⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠑⡲⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠋⠉⠀⠀⠀⢀⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠷⠶⠶⠶⠶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠰⠴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣶⣄⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡀⠀⢠⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠠⠀⣡⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣯⣥⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠁⡙⡛⢟⣲⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣖⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⠠⢤⣥⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠉⠉⠍⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⡀⣀⣄⡀⢀⣀⠀⠀⡄⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠆⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠈⡀⠈⠸⡙⠙⣟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠐⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡶⠷⠿⠷⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⣤⣴⣿⣤⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠟⣿⢿⣿⢿⣿⣿⣿⣿⠟⠀⠀⠀⠀⢲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠀⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠁⠀⠉⠈⠁⠘⢻⠀⢿⡏⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠯⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠈⢦⡏⠩⡝⠉⣯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⢀⣀⣠⣾⣶⣾⣷⣄⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣷⣾⣿⣶⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣀⠀⠀⠀⣾⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⠓⠀⢀⠀⠀⠀⠀⠀⠀⠀
⠈⠀⢹⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢩⣽⢿⣼⣿⣿⣿⣿⣥⣀⠀⠀⠀⠀⣠⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠐⣹⡇⠐⡼⠄⣷⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣋⣿⣀⣾⡇⠋⣿⣿⣿⣿⡿⠋⢀⣠⣾⣿⣷⠀⣘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠱⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠻⢿⢷⣶⣾⣿⣿⣅⣴⣶⠏⢹⡟⠛⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⠙⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠂⠿⢿⢿⠿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⣼⣿⣿⣿⣿⣿⣿⡿⣼⣿⣿⡇⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠂⠀⢈⣆⠀⣷⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡭⣽⣶⣿⣿⠛⢿⣿⣿⣿⠃⠁⠀⠀⠀⠀⢀⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢻⣿⣿⣿⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢻⣿⣿⣿⣷⣄⠉⠉⠀⠀⠰⠶⠖⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⢭⠭⠄⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡀⠋⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠈⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠒⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣥⣠⡀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⢅⣁⣿⣤⣤⣤⣤⣤⣴⣶⣶⡶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⡤⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠐⠓⠈⠉⠿⣶⣶⣶⡶⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣦⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣶⣶⣶⣶⣶⣶⣶⣶⡖⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠃⡲⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁⠀⠀⠀⠀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡷⠶⠶⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⣀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠰⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⡄⣀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⢹⣇⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣧⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣭⣭⣭⣿⣯⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠀⣿⠿⠋⠉⠉⠉⠉⠉⠉⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣦⣶⣦⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢹⡇⣿⢽⣿⣿⣿⣯⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⣀⢀⣄⠄⢀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡿⠁⣼⣿⣿⣿⣿⣿⣿⣆⠀⠀⠈⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣶⣶⣿⣶⠶⠶⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢸⠿⡿⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⣿⠶⣿⢽⡧⣿⣿⡷⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠁⠈⠝⢸⣿⡏⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⡀⠾⠀⠀⠀⠀⢀⣤⣴⣷⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣄⣈⡉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⣉⣉⠙⠿⣿⣿⣿⣷⠈⢀⣀⣀⠀⣼⣿⣿⣿⡿⣿⠋⠉⠁⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣟⣛⣒⣒⣶⣿⣿⣿⣿⣿⣿⣷⣦⣈⠙⠻⣿⣧⠈⢰⠿⣇⣿⣿⣿⣿⣦⣤⣀⠀⠀⣠⣾⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⠃⠐⡬⠄⣧⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣒⣀⡙⠃⠈⣴⣿⠀⢻⣿⣿⣿⠿⢁⣠⣾⣿⣿⡇⠀⠀⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠹⠿⣿⣾⣿⣿⣶⣿⣿⢏⣼⣛⠛⠁⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣙⣋⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠻⠿⢿⠿⣿⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠇⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣯⣭⣭⣭⣭⣭⣍⣭⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣆⠀⣷⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡭⣽⣷⣿⣏⠻⣿⣿⡿⠀⢠⠀⠀⠀⠀⠀⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⣿⣿⣿⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢸⣿⣿⣿⣷⡄⠉⠁⠐⠿⠷⠖⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⡭⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠿⠿⡿⢭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⢿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢁⠀⣿⣤⣤⣤⣤⣤⣤⣶⣶⡶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⢶⣶⣶⣶⣶⣶⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠹⢶⣶⣶⡶⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⠦⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⣶⣶⣶⣶⣶⣶⢒⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣦⣤⣄⡀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠲⣶⠿⢶⠆⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢿⣿⣴⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⢹⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣿⣯⣭⣭⣯⣭⣭⣭⣭⣭⣭⣭⣤⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠀⣿⠿⠋⠉⠉⠉⠉⠉⠉⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣴⣦⣶⣤⣴⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢹⡇⣿⢽⣿⣿⣿⣯⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⣀⢀⣄⠄⢀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡿⠁⣼⣿⣿⣿⣿⣿⣿⡆⠀⠀⠈⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣶⣶⣿⣶⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢸⢿⡿⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⣿⠶⣿⢻⡧⣿⣿⡷⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠈⡝⢸⣿⡏⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⡀⠾⠀⠀⠀⠀⠀⣤⣴⣷⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣄⣈⡉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⣉⣉⠙⠿⣿⣿⣿⣷⠈⢀⣀⣀⠀⣼⣿⣿⣿⡿⣿⠋⠉⠁⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⡛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣟⣛⣒⣒⣶⣿⣿⣿⣿⣿⣿⣷⣦⣈⠙⠻⣿⣧⠈⢰⠿⣇⣿⣿⣿⣿⣦⣤⣀⠀⠀⣠⣾⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⠃⠐⡬⠄⣧⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣒⣀⡙⠃⠈⣴⣿⠀⢻⣿⣿⣿⠿⢁⣠⣾⣿⣿⡇⠀⠀⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠹⠿⣿⣾⣿⣿⣶⣿⣿⢏⣼⣛⠛⠁⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⣙⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠻⠿⢿⠿⣿⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠇⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣯⣭⣭⣭⣭⣭⣍⣩⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣆⠀⣷⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡭⣽⣷⣿⣏⠻⣿⣿⡿⠀⢠⠀⠀⠀⠀⠀⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣉⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⣿⣿⣿⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢸⣿⣿⣿⣷⡌⠉⠁⠐⠿⠷⠖⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⡭⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠻⠿⡿⢭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⢿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢁⠀⣿⣤⣤⣤⣤⣤⣤⣶⣶⡶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⢶⣶⣶⣶⣶⣶⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠹⢶⣶⣶⡶⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⠦⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⣶⣶⣶⣶⣶⣶⢶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣦⣤⣄⡀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠆⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢿⣿⣴⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⢹⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣽⣭⣭⣭⣭⣭⣭⣭⣤⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠿⠋⠉⠉⠉⠈⠉⠉⠩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣴⣦⣶⣦⣴⣤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢻⡇⣿⢽⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠐⣉⣄⣠⡤⢀⣀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡿⠁⣼⣿⣿⣿⣿⣿⣿⣿⠀⠸⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣶⣶⣶⣶⢶⠶⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠸⠸⢿⠟⣿⣿⣿⣿⠏⠀⠀⡤⠀⠀⠀⠰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⣿⠶⣿⢹⡧⣿⣿⡷⣿⣿⣿⣿⡿⠟⢁⡄⠀⠀⠀⠀⠀⣹⢽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⡀⠾⠿⠇⠀⠀⠀⣠⣶⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣄⣈⡉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⣉⣉⠙⠿⣿⣿⣿⣷⠈⢿⣧⡤⣄⠀⣿⣿⣿⣿⣿⠋⠈⠉⠀⢀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣟⣛⣒⣒⣶⣿⣿⣿⣿⣿⣿⣷⣦⣈⠙⠻⣿⣧⠈⣿⣼⠟⣧⣿⣿⣿⣿⣶⣤⡀⢀⣤⣿⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⠃⠐⡬⠀⣧⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣒⣀⡙⠃⠘⣿⣾⣯⡈⣿⣿⣿⣿⣃⣴⣿⣿⣿⡧⠀⠀⢀⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⡝⠛⣿⣿⣿⣿⣿⣿⣏⣼⣏⡉⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⣉⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠻⢿⢿⠿⣿⣭⣭⣭⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⣿⣿⣿⣿⣿⡿⡿⠿⠿⠧⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣭⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⡆⠀⣷⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡭⢹⣷⣿⣏⠻⣿⣿⠁⣰⡖⠀⠀⠀⠀⢠⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⣿⣿⣿⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠸⣿⣿⣿⣷⡌⠁⠘⠻⠿⠛⠁⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⡭⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠻⠿⡿⢭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⢿⣿⣿⡏⠛⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣤⣶⣶⣶⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⠲⢶⣶⣶⣶⣤⣤⣤⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠹⢶⣶⣶⣶⡶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠿⠓⠄⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣶⣶⣖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⠀⠀⠀⠀⠐⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣦⡀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠲⣶⠿⢷⠶⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢿⣿⣿⣶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⢹⣇⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣧⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣽⣿⣯⣭⣭⣿⣭⣭⣭⣭⣭⣭⣬⣤⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⡿⠏⠉⠉⠁⠈⠈⠉⠉⢭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣴⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢻⡇⣿⢽⣿⣿⣿⣷⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠰⣋⣡⢀⣤⠀⣀⡄⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡿⠁⣼⣿⣿⣿⣿⣿⣿⣿⡅⠀⠃⠁⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣶⣶⣾⣶⢶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠜⠃⠿⡿⣿⣿⣿⣿⡏⠀⠀⢴⠀⠀⠀⠀⢲⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⣿⠶⣿⢻⡧⣿⣿⡷⣿⣿⣿⣿⡿⠟⢁⣴⠃⠀⠀⠀⠀⢡⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⡀⠾⠿⠿⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣦⣶⠆⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣄⣈⡉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⣉⣉⠙⠿⣿⣿⣿⣷⠈⢿⣿⣦⢤⣄⣸⣿⣿⣿⡿⠏⠀⠉⠀⢀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣟⣛⣒⣒⣶⣿⣿⣿⣿⣿⣿⣷⣦⣈⠙⠻⣿⣧⠈⣿⣷⡟⢻⡿⣿⣿⣿⣶⣦⡄⢀⣤⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⠃⠐⡬⠄⣧⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣒⣀⡙⠃⠘⣻⣷⣿⣄⣻⣿⣿⣿⣿⣴⣿⣿⣿⡿⠀⠀⠀⣘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⡙⢻⣿⣿⣿⣿⣿⣿⣼⣯⡉⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣉⣉⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠻⠿⢿⠿⣿⣯⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⡿⠿⠿⠿⠗⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣭⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⠆⠀⣷⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠍⣿⣿⣿⣝⢿⣿⠃⣰⣞⠀⠀⠀⠀⠀⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⣿⣿⣿⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⢻⣿⣿⣿⣯⠉⠈⠛⠛⠛⠁⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⡭⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠻⠿⡿⢭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁⠀⠀⠀⠀⠘⣿⣿⣿⠹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣭⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣤⣤⣶⣶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢶⣶⣶⣤⣤⣤⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⢶⣶⣶⣶⣶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠿⠛⠂⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣶⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⠀⠀⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⣦⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⣿⣿⣿⡞⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⢹⣇⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣧⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣭⣽⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣥⣤⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣷⠀⣿⣿⣿⠟⠉⠉⠁⠀⠀⠈⠉⠩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣴⣤⣴⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢹⡇⣿⢽⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢰⣟⣩⣄⣴⢆⣄⣀⡀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⢶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡿⠁⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠇⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣶⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⡾⠻⠼⡿⢻⣿⣿⣿⡟⠁⠀⣼⠀⠀⠀⠀⠐⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⣿⠶⣿⢹⡧⣿⣿⡷⣿⣿⣿⣿⡿⠟⢁⣴⡿⠀⠀⠀⠀⢠⣿⣿⣿⡅⠀⣠⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⡀⠾⠿⠿⠇⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⠷⠀⠀⠀⠀⠀⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣄⣈⡉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⣉⣉⠙⠿⣿⣿⣿⣷⠈⢿⣿⣿⡦⣤⢠⣿⣿⣿⡿⠿⠀⠉⠁⢀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⡛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣟⣛⣒⣒⣶⣿⣿⣿⣿⣿⣿⣷⣦⣈⠙⠻⣿⣧⠈⣿⣿⣿⠛⣿⢿⣿⣿⣿⣷⡤⢀⣴⣾⣷⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⠃⠐⡬⠄⣧⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣒⣀⡙⠃⠘⣛⣻⣿⣧⣸⣿⣿⣿⣿⣶⣿⣿⣿⣿⠀⠀⠀⢐⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣯⠙⣿⣿⣿⣿⣿⣿⣽⣯⣍⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣙⣉⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠻⠿⢿⠿⣿⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠿⠿⠿⠛⠂⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⢆⠀⣷⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡭⢱⣿⣿⣯⣿⣿⡇⣸⣿⣋⡀⠀⠀⠀⣨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⣿⣿⣿⣭⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠘⣿⣿⣿⣿⡏⠈⠙⠛⠛⠁⠀⠀⠴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⡥⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠻⠿⡿⢭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣤⣶⣶⣶⡶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠒⢶⣦⣤⣤⣤⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠹⢶⣶⣶⣶⣶⡶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠿⠛⠓⠀⠀⠀⣀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡒⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⠀⠀⠀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠁⠀⢸⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⢹⣇⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣧⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣯⣿⣯⣭⣭⣭⣯⣭⣭⣭⣭⣭⣤⣤⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣷⠀⣿⣿⣿⡿⠋⠉⠉⠀⠀⠀⠉⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣴⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢹⡇⣿⢽⣿⣿⣿⣯⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢰⣿⣋⣥⣠⡖⢀⣀⡀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⡶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡿⠁⣾⣿⣿⣿⣿⣿⣿⣿⡧⠀⠇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣶⣶⣾⣶⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⣶⠛⠿⢿⢻⣿⣿⣿⡟⠁⠀⢸⠆⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⡶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⣿⠶⣿⢹⡇⣿⣿⡷⣿⣿⣿⣿⡿⠟⢁⣴⣿⠇⠀⠀⠀⠀⣼⣿⣿⡇⠀⣠⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⡀⠾⠿⠿⠿⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠰⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠟⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣄⣈⡉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⣉⣉⠙⠿⣿⣿⣿⣷⠈⢿⣿⣿⣷⢦⡄⣾⣿⣿⡿⠿⠀⠈⠁⢀⡄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣟⣛⣒⣒⣶⣿⣿⣿⣿⣿⣿⣷⣦⣈⠙⠻⣿⣧⠈⣿⣿⣿⡟⣻⢿⣿⣿⣿⣷⡤⢀⣴⣾⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⠃⠐⡬⠄⣧⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣒⣀⡉⠃⠘⣛⣛⣿⣿⣄⣿⣿⣿⣿⣷⣿⣿⣿⣿⠀⠀⠀⢀⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⣏⢻⣿⣿⣿⣿⣿⣿⣿⣭⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣉⣉⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠻⠿⢿⠿⣿⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⠻⠛⠟⠛⠒⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣭⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⢆⠀⣷⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠍⣾⣿⣿⣽⣿⣿⣸⣿⣋⣀⠀⠀⠀⢠⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⣿⣿⣿⣭⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⢸⣿⣿⣿⣯⡉⠙⠛⠛⠉⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⡥⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠻⠿⡿⢭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠈⣿⣿⣯⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣯⣯⣭⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣤⣦⣶⣶⡶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢦⣤⣤⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠹⢶⣶⣶⣶⣶⣶⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠿⠛⠉⠂⠀⠀⢀⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣶⣶⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣄⡀⠀⠀⣡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⡀⣸⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⡇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⢹⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣭⣯⣿⣭⣭⣭⣭⣭⣭⣭⣤⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⠿⠋⠉⠁⠀⠀⠈⠉⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣴⣦⣴⣶⣴⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢹⡇⣿⢽⣿⣿⣿⣷⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢰⣿⣿⣫⣅⡤⣠⣀⢀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡿⠁⣾⣿⣿⣿⣿⣿⣿⣿⣯⠂⠘⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣾⣶⣶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⣶⡾⠻⠻⡟⣿⣿⣿⡿⠁⠀⢼⠇⠀⠀⠀⠀⠀⢲⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⣿⠶⣿⢹⡇⣿⣿⡷⣿⣿⣿⣿⡿⠟⢁⣴⣿⣿⠇⠀⠀⠀⣼⣿⣿⣇⠀⣴⣿⡀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣷⣿⣿⣷⣿⣿⣿⣿⡀⠾⠿⠿⠿⠿⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠰⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣄⣈⡉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⣉⣉⠙⠿⣿⣿⣿⣷⠈⢿⣿⣿⣿⣷⢦⡄⣿⣿⣿⠿⠁⠈⠁⢀⣆⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣟⣛⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷⣦⣈⠙⠻⣿⣧⠈⣿⣿⣿⣿⡟⣻⢿⣿⣿⣿⣦⠄⣰⣾⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⠃⠐⡬⠄⣧⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣒⣀⡙⠃⠘⣛⣛⣛⣿⣧⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣭⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⣉⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠻⢿⢿⠿⣿⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠒⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣯⣭⣭⣭⣭⣭⣭⣭⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⢆⠀⣷⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠍⢸⣿⣿⣿⣿⣥⣿⣟⣀⡀⠀⠀⠀⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⣿⣿⣿⣭⣭⣭⣭⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⢸⣿⣿⣿⣏⠉⠛⠛⠋⠁⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⠭⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠿⠿⡿⢭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠘⣿⣿⣟⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣭⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⠶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣯⡁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠹⢶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠉⠉⠒⠀⠀⣠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣶⣶⣶⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣴⣤⡀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣶⣃⡍⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠀⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠁⠀⢸⡇⢠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⢹⣇⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣧⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣽⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⡿⠏⠉⠉⠁⠀⠀⠉⠉⣭⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣴⣦⣴⣦⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢹⡇⣿⢽⣿⣿⣿⡧⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢰⣿⣿⣿⣍⣤⢠⣀⢀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡿⠁⣾⣿⣿⣿⣿⣿⣿⣿⣯⠆⡸⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣶⣶⣶⢶⠶⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⣶⣷⠟⠹⡟⣿⣿⣿⡿⠃⠀⣿⠗⠀⠀⠀⠀⠀⠐⣶⣶⣶⣶⣶⣶⣶⡶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⣿⠶⣿⢹⡧⣿⣿⡷⣿⣿⣿⣿⡿⠟⢁⣴⣿⣿⡟⠀⠀⠀⣹⣿⣿⣇⠀⣴⣿⡄⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⡀⠾⠿⠿⠿⠿⠇⠀⠀⣰⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠠⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣄⣈⡉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⣉⣉⠙⠿⣿⣿⣿⣷⠈⢿⣿⣿⣿⣿⢦⡄⣿⣿⣿⠿⠁⠈⠉⢀⣆⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣟⣛⣒⣒⣶⣿⣿⣿⣿⣿⣿⣷⣦⣈⠙⠻⣿⣧⠈⣿⣿⣿⣿⣿⢻⢿⣿⣿⣿⣦⠄⣠⣾⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⠃⠐⡬⠀⣧⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣒⣀⡙⠃⠘⣛⣛⣛⣻⣿⣜⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⣘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⣙⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠻⠿⢿⠿⣿⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠒⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣭⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⢆⠀⣷⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡭⠉⣿⣿⣿⣿⣧⣿⣟⣁⡀⠀⠀⠀⣠⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⣿⣿⣿⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⣿⣿⣿⣿⡈⠛⠛⠋⠁⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⡭⠭⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠻⠿⡿⢭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⢻⣿⣿⣻⡷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣯⣭⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⡶⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠹⢶⣶⣶⣶⣶⣶⣶⣶⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠋⠉⠑⠂⠀⢀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣦⣄⠀⡀⣥⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⣝⣼⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠲⣶⠿⢷⠶⠰⠶⠶⠶⠀⠀⠖⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⢀⣿⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⢹⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣭⣭⣭⣯⣭⣭⣭⣭⣭⣭⣭⣤⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⠟⠉⠉⠉⠁⠀⠉⠉⣭⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢻⡇⣿⢽⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢰⣿⣿⣿⣯⣥⢆⢀⢀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡿⠁⣾⣿⣿⣿⣿⣿⣿⣿⣯⠆⣴⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣶⣶⣶⣶⢶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⣶⣶⡞⠏⡿⣿⣿⣿⡿⠃⠀⣿⠗⠀⠀⠀⠀⠀⠀⢶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⣿⠶⣿⢹⡇⣿⣿⡷⣿⣿⣿⣿⡿⠟⢁⣴⣿⣿⣿⠁⠀⠀⢹⣿⣿⣇⢀⣾⣿⡆⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⢿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣷⣿⣿⣷⣿⣿⣿⣿⡀⠾⠿⠿⠿⠿⠿⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠼⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠟⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣄⣈⡉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⣉⣉⠙⠿⣿⣿⣿⣷⠈⢿⣿⣿⣿⣿⡦⣤⢸⣿⣿⡿⠏⠉⠉⢁⣇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⡛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣟⣛⣒⣒⣶⣿⣿⣿⣿⣿⣿⣷⣦⣈⠙⠻⣿⣧⠈⣿⣿⣿⣿⣿⡟⡾⣿⣿⣿⣦⠤⣠⣾⣿⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⠃⠐⡬⠀⣧⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣒⣀⡙⠃⠘⣛⣛⣛⣻⣿⣄⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣉⣉⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠻⠿⢿⠿⣿⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠒⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣩⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⡆⠀⣷⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠍⢹⣿⣿⣿⣧⣿⣿⣁⣀⠀⠀⠀⢠⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣉⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⣿⣿⣿⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⢸⣿⣿⣿⡌⠛⠛⠋⠁⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⡭⠭⠥⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠻⠿⡿⢭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣬⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣎⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠹⢶⣶⣶⣶⣶⣶⣶⣶⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠋⠉⠱⠂⠀⢀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⣶⣶⣶⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣄⡠⣄⢤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣾⣯⠁⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠲⣶⠿⢷⠶⠰⠶⠶⠶⠀⠀⠖⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡏⠀⠀⣿⠇⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⢹⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣯⣿⣭⣭⣭⣭⣭⣭⣬⣬⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⡿⠋⠉⠉⠉⠁⠉⠉⢽⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣦⣦⣦⣴⣦⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢻⡇⣿⢽⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢰⣿⣿⣿⣿⣥⢄⢀⢀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡿⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⠆⣶⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⣿⣿⣷⣶⣶⣾⣶⣶⠶⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⣶⣶⡾⠟⡿⣿⣿⣿⡿⠃⢰⣿⠇⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⣿⠶⣿⢽⡧⣿⣿⡷⣿⣿⣿⣿⡿⠟⢁⣴⣿⣿⣿⡇⠀⠀⢹⣿⣿⣇⢀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⡀⠾⠿⠿⠿⠿⠿⠇⠀⢠⣾⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣄⣈⡉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⣉⣉⠙⠿⣿⣿⣿⣷⠈⢿⣿⣿⣿⣿⣷⢤⢸⣿⣿⡿⠏⠉⠉⢁⣇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⡛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣟⣛⣒⣒⣶⣿⣿⣿⣿⣿⣿⣷⣦⣈⡙⠻⣿⣧⠈⣿⣿⣿⣿⣿⣾⡾⣿⣿⣿⣦⡤⣠⣾⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⠃⠐⡬⠄⣧⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣒⣀⡙⠃⠘⣛⣛⣛⣛⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣋⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠻⠿⢿⠿⣿⣯⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠒⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣯⣯⣭⣭⣭⣯⣭⣭⣭⣭⣭⣍⣭⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣆⠀⣷⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡭⠉⣿⣿⣿⣯⣿⣿⣃⣀⠀⠀⠀⠀⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣉⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⣿⣿⣿⣭⣭⣭⣭⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⣿⣿⣿⣏⠙⠛⠋⠉⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⡉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠻⠿⡿⢭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣷⣶⣯⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⡶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣯⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠹⢶⣶⣶⣶⣶⣶⣶⣶⣶⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠋⠉⠉⠖⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⣶⣶⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣷⣦⡀⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠇⠀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠐⠖⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠀⠀⣿⡇⢰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⢹⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣽⣿⣯⣭⣭⣽⣭⣭⣭⣭⣭⣭⣬⣬⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠉⠉⠉⢩⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣴⣤⣤⣤⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢹⡇⣿⢽⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢰⣿⣿⣿⣿⣫⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡿⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⣆⢀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣶⣿⣷⣷⣶⣶⣶⣶⠶⠶⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⣶⣶⣶⠿⣿⢿⣿⣿⡟⠃⣼⣿⠎⠀⠀⠀⠀⠀⠀⠐⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⣿⠶⣿⢹⡧⣿⣿⡷⣿⣿⣿⣿⡿⠟⢁⣴⣿⣿⣿⣿⠀⠀⢹⣿⣿⡇⢰⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⡀⠾⠿⠿⠿⠿⠿⠿⠀⠀⣴⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣄⣈⡉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⣉⣉⠙⠿⣿⣿⣿⣷⠈⢿⣿⣿⣿⣿⣿⣦⡄⣿⣿⣿⠏⠙⠋⢹⡌⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣟⣛⣒⣒⣶⣿⣿⣿⣿⣿⣿⣷⣦⣈⠙⠻⣿⣧⠈⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣦⡤⣠⣾⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⠃⠐⡬⠀⣧⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣒⣀⡙⠃⠘⣛⣛⣛⣛⣻⣷⣸⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⣛⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠻⠿⢿⠿⣿⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠖⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣆⠀⣷⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡭⢱⣿⣿⣿⣿⣿⣃⣀⠀⠀⠀⠀⠨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣭⣉⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⣿⣿⣿⣭⣭⣭⣭⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⢸⣿⣿⣯⠙⠛⠛⠉⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣯⣭⣭⣭⢭⠭⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠻⠿⡿⢭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢶⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣴⣦⣶⣶⣶⣶⣶⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠹⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠉⠉⠖⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣄⢴⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⠶⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡏⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠀⠖⠶⠶⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠁⠀⣸⣿⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⢹⡇⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣧⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣯⣭⣯⣭⣭⣭⣭⣭⣭⣤⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠉⠉⠉⢩⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣴⣦⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢹⡇⣿⢽⣿⣿⣿⣷⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢰⣿⣿⣿⣿⣫⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡿⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⣆⢀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣶⢶⠶⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⣶⣶⣶⡾⡿⢿⣿⣿⡟⠃⣼⣿⠎⠀⠀⠀⠀⠀⠀⠐⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⣿⠶⣿⢹⡧⣿⣿⡷⣿⣿⣿⣿⡿⠟⢁⣴⣿⣿⣿⣿⠀⠀⢸⣿⣿⡇⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⡀⠾⠿⠿⠿⠿⠿⠿⠀⠀⣴⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣄⣈⡉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⣉⣉⠙⠿⣿⣿⣿⣷⠈⢿⣿⣿⣿⣿⣿⣦⡄⣿⣿⣿⠏⠙⠉⢹⡌⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⡛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣟⣛⣒⣒⣶⣿⣿⣿⣿⣿⣿⣷⣦⣈⠙⠻⣿⣧⠈⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣦⡤⣠⣾⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⠃⠐⡬⠄⣧⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣒⣀⡙⠃⠘⣛⣛⣛⣛⣻⣷⣸⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⣉⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠻⠿⢿⠿⣿⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠒⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣆⠀⣷⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡭⢱⣿⣿⣿⣿⣿⣃⣀⠀⠀⠀⠀⠨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣉⣉⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⣿⣿⣿⣭⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠉⠀⢸⣿⣿⣯⠙⠛⠛⠉⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣭⣭⣭⣭⠭⠭⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠿⠿⡿⢭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠹⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠉⠉⠶⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣄⢴⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠶⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡏⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠲⣶⠿⢷⠖⠰⠶⠶⠶⠀⠰⠶⠶⠾⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠁⠀⣸⣿⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⢹⣇⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣧⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣭⣭⣭⣽⣭⣭⣭⣭⣭⣭⣭⣤⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠉⠉⠉⢩⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣦⣤⣤⣴⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢹⡇⣿⢹⣿⣿⣿⣯⣿⣻⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢰⣿⣿⣿⣿⣿⡥⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡿⠁⣾⣿⣿⣿⣿⣿⣿⣿⣧⢠⣆⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣶⣿⣿⣷⣶⣶⣿⣶⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⣶⣶⣶⡶⢿⢿⣿⣿⡿⢣⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⢲⣶⣶⣶⣶⣶⡶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⣿⠶⣿⢸⡧⣿⣿⡷⣿⣿⣿⣿⡿⠟⢁⣴⣿⣿⣿⣿⠇⠀⠸⢿⣿⠁⢸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⡀⠾⠿⠿⠿⠿⠿⠿⠇⠀⢠⣿⣿⣷⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣄⣈⡉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⣉⣉⠙⠿⣿⣿⣿⣷⠈⢿⣿⣿⣿⣿⣿⣷⣄⢸⣿⣿⠋⠛⠛⢹⡈⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣟⣛⣒⣒⣶⣿⣿⣿⣿⣿⣿⣷⣦⣈⠙⠻⣿⣧⠈⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⣦⡤⣠⣾⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⠃⠐⡬⠄⣧⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣒⣀⡙⠃⠘⣛⣛⣛⣛⣛⣿⣜⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣉⣉⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠻⠿⢿⠿⣿⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠖⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣯⣭⣭⣭⣯⣭⣭⣭⣭⣭⣭⣭⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⡆⠀⣷⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⢹⣿⣿⣾⣿⣃⣀⠀⠀⠀⠀⠀⠩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣉⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⣿⣿⣿⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠁⠀⣿⣿⣿⡙⠟⠛⠉⠁⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣯⣭⣭⣭⡭⠭⠭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠻⠿⡿⢭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⡶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠹⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⢋⠉⠱⠂⠀⢀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⣶⣶⣶⣶⣶⣶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣤⣲⣶⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠶⠶⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠁⢀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠲⣶⠿⢶⠶⠰⠶⠶⠶⠀⠰⠶⠶⠾⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠃⠀⢸⣿⠇⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⢹⣇⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣧⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣯⣭⣭⣭⣭⣭⣭⣭⣭⣥⣤⣬⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣴⣤⣤⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢹⡇⣿⢹⣿⣿⣿⣯⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢰⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡿⠁⣾⣿⣿⣿⣿⣿⣿⣿⣧⢠⡆⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣾⣿⣷⣷⣶⣶⣿⣶⢶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⣶⣶⣶⣶⢿⢿⣿⣿⡿⢣⣿⣷⠂⠀⠀⠀⠀⠀⠀⠀⢲⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⣿⠶⣿⢹⡇⣿⣿⡷⣿⣿⣿⣿⡿⠟⢁⣴⣿⣿⣿⣿⡇⠀⠸⢿⣿⠀⣸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣷⣿⣿⣷⣿⣿⣿⣿⡀⠾⠿⠿⠿⠿⠿⠿⠇⠀⢠⣿⣿⣷⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣄⣈⡉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⣉⣉⠙⠿⣿⣿⣿⣷⠈⢿⣿⣿⣿⣿⣿⣿⣄⢸⣿⣿⠋⠛⠛⢻⡈⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣟⣛⣒⣒⣶⣿⣿⣿⣿⣿⣿⣷⣦⣈⠙⠻⣿⣧⠈⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣦⡤⣠⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⠃⠐⡬⠄⣧⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣒⣀⡙⠃⠘⣛⣛⣛⣛⣛⣻⣌⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣉⣉⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠻⠿⢿⠿⣿⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠖⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⠆⠀⣷⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡭⢱⣿⣿⣾⣿⣃⣀⠀⠀⠀⠀⠀⠩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣉⣉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⣿⣿⣿⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⢸⣿⣿⡝⠻⠛⠉⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣯⣭⣭⣭⡭⠭⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠻⠿⡿⢭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⡶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣮⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢋⠉⠱⠂⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣶⣶⣶⣶⣶⣶⣶⣶⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣦⣺⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡿⠁⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠖⠰⠶⠶⠶⠀⠰⠶⠶⠾⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠃⠀⢸⣿⡇⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⢹⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣿⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣴⣦⣴⣶⣴⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢻⡇⣿⢽⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢰⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡿⠁⣾⣿⣿⣿⣿⣿⣿⣾⣷⢠⡄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣶⢶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⣶⣶⣶⣶⢿⣿⣿⣿⡿⢣⣿⣷⠃⠀⠀⠀⠀⠀⠀⠀⢲⣶⣶⣶⣶⣶⣶⡶⢶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⣿⠶⣿⢻⡧⣿⣿⡷⣿⣿⣿⣿⡿⠟⢁⣴⣿⣿⣿⣿⡇⠀⠹⣿⣿⠀⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣷⣿⣿⣷⣿⣿⣿⣿⡀⠾⠿⠿⠿⠿⠿⠿⠇⠀⢠⣿⣿⣷⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣄⣈⡉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⣉⣉⠙⠿⣿⣿⣿⣷⠈⢿⣿⣿⣿⣿⣿⣿⣄⢸⣿⣿⠛⠛⠛⣿⠉⠁⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣟⣛⣒⣒⣶⣿⣿⣿⣿⣿⣿⣷⣦⣈⡙⠻⣿⣧⠈⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣦⡤⣠⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⠃⠐⡬⠄⣧⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣒⣀⡙⠃⠘⣛⣛⣛⣛⣛⣻⣏⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⠁⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣙⣋⣙⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠻⠿⢿⠿⣿⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠖⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣭⣭⣭⣭⣯⣭⣭⣭⣭⣭⣍⣭⣭⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣆⠀⣷⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡭⢉⣿⣿⣾⣿⣋⣀⠀⠀⠀⠀⠀⠉⢭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣩⣭⣍⣉⣉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⣿⣿⣿⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⢸⣿⣿⣝⠟⠛⠉⠁⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣯⣭⣭⣭⠍⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠻⠿⡿⢭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠹⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣋⠉⠱⠖⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣦⣻⣷⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠁⠀⣶⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠲⣶⠿⢷⠶⠰⠶⠶⠶⠀⠰⠶⠶⠶⠾⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠃⠀⢸⣿⡇⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⢹⣇⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣧⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣽⣭⣭⣭⣭⣭⣭⣬⣤⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠉⠉⠉⢽⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣴⣦⣤⣦⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢻⡇⣿⢽⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢰⣿⣿⣿⣿⣿⣏⠂⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡿⠁⣾⣿⣿⣿⣿⣿⣷⣷⡆⣴⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣶⢶⠶⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⣶⣶⣶⣶⢿⣿⣿⣿⠟⣽⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⣿⠶⣿⢹⡧⣿⣿⡷⣿⣿⣿⣿⡿⠟⢁⣴⣿⣿⣿⣿⡇⠀⠿⣿⣏⢀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⡀⠾⠿⠿⠿⠿⠿⠿⠇⠀⢨⣿⣿⣾⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣄⣈⡉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⣉⣉⠙⠿⣿⣿⣿⣷⠈⢿⣿⣿⣿⣿⣿⣿⣄⢸⣿⣿⠛⠛⠛⣏⠉⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣟⣛⣒⣒⣶⣿⣿⣿⣿⣿⣿⣷⣦⣈⠙⠻⣿⣧⠈⣿⣿⣿⣿⣿⣿⣷⣾⣿⣶⣦⣄⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⠃⠐⡬⠄⣧⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣒⣀⡙⠃⠘⣛⣛⣛⣛⣛⣻⣟⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡍⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣉⣉⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠻⠿⢿⠿⣿⣯⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠗⠂⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣯⣭⣭⣭⣭⣯⣭⣭⣭⣭⣭⣍⣭⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣆⠀⣷⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠍⣿⣿⣿⣿⣁⣀⠀⠀⠀⠀⠀⠉⢭⣭⣭⣭⣭⣭⣭⣭⣭⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⣿⣿⣿⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁⢸⣿⣿⡟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣭⣭⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠿⠿⡿⢭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣎⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⣉⡉⠱⠒⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣮⣿⣿⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠶⠶⠶⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡏⠀⢰⣿⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠰⠖⠶⠶⠾⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡿⠀⢀⣿⣿⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⢹⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣿⣭⣭⣭⣭⣭⣭⣬⣤⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣴⣦⣶⣦⣴⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢹⡇⣿⢽⣿⣿⣿⣷⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢰⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡿⠁⣾⣿⣿⣿⣿⣿⣷⣾⣆⣄⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣷⣿⣿⣷⣶⣶⣶⣶⢶⠶⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⣶⣶⣶⣶⢿⣿⣿⡿⢏⣾⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⣿⠶⣿⢻⡧⣿⣿⡷⣿⣿⣿⣿⡿⠟⢁⣴⣿⣿⣿⣿⡇⠁⣿⣿⡇⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⡀⠾⠿⠿⠿⠿⠿⠿⠇⠀⣸⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣄⣈⡉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⣉⣉⠙⠿⣿⣿⣿⣷⠈⢿⣿⣿⣿⣿⣿⣿⣀⣿⣿⡟⠙⠛⢻⣏⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣟⣛⣒⣒⣶⣿⣿⣿⣿⣿⣿⣷⣦⣈⠙⠻⣿⣧⠈⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣦⢤⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⠃⠐⡬⠀⣧⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣒⣀⡙⠃⠘⣛⣛⣛⣛⣛⣻⣸⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢀⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡁⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣉⣙⣉⣋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠻⢿⢿⠿⣿⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣟⠛⠂⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣭⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣆⠀⣷⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡭⢩⣿⣿⣿⣯⣤⣀⠀⠀⠀⠀⠀⠉⢭⣭⣭⣭⣭⣭⣭⣭⠭⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⣿⣿⣿⣭⣭⣭⣭⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⢸⣿⣿⡙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣭⣭⣍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠻⠿⡿⢭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⣼⣿⡿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣜⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠹⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢋⣁⠈⠷⠒⠀⡠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣯⣿⣿⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠶⠶⠶⠶⠶⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠏⠀⣼⣿⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠲⣶⠿⢷⠖⠰⠶⠶⠶⠀⠰⠖⠶⠾⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠀⢠⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⢹⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣿⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣴⣦⣦⣤⣴⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢹⡇⣿⢽⣿⣿⣿⣷⣿⣻⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢰⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡿⠁⣾⣿⣿⣿⣿⣿⣷⣾⣄⣄⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣶⣿⣿⣷⣶⣶⣿⣶⢶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⣶⣶⣶⣶⢿⣿⣿⡿⢏⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⣿⠶⣿⢹⡧⣿⣿⡷⣿⣿⣿⣿⡿⠟⢁⣴⣿⣿⣿⣿⡇⠁⣿⣿⡇⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⡀⠾⠿⠿⠿⠿⠿⠿⠇⠀⣸⣿⣿⣾⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣄⣈⡉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⣉⣉⠙⠿⣿⣿⣿⣷⠈⢿⣿⣿⣿⣿⣿⣿⣀⣿⣿⡏⠛⠛⢻⣏⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣟⣛⣒⣒⣶⣿⣿⣿⣿⣿⣿⣷⣦⣈⠙⠻⣿⣧⠈⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣦⣤⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⠃⠐⡬⠀⣧⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣒⣀⡙⠃⠘⣛⣛⣛⣛⣛⣻⣸⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢀⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡁⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣉⣙⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠻⠿⢿⠿⣿⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣟⠛⠂⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣭⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣆⠀⣷⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡭⢩⣿⣿⣿⣯⣤⣀⠀⠀⠀⠀⠀⠉⢭⣭⣭⣭⣭⣭⣭⣭⠭⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⣿⣿⣿⣭⣭⣭⣭⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⢸⣿⣿⡙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣭⣭⣍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠻⠿⡿⢭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⣼⣿⡿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠀⣿⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣜⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠹⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢋⣁⠈⠷⠒⠀⡠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣯⣿⣿⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⠶⠶⠶⠶⠶⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠏⠀⣼⣿⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠲⣶⠿⢷⠖⠰⠶⠶⠶⠀⠰⠖⠶⠾⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠀⢠⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⢹⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣯⣿⣯⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠉⠉⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣴⣦⣦⣤⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢹⡇⣿⢽⣿⣿⣿⣷⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢰⣿⣿⣿⣿⣟⠂⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡿⠁⣾⣿⣿⣿⣿⣿⣷⡇⣴⡀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣶⣾⣶⢶⠶⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⣶⣶⣶⣾⣿⣿⣿⠛⣽⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣶⣶⣶⣶⣶⡶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⣿⠶⣿⢹⡧⣿⣿⡷⣿⣿⣿⣿⡿⠟⢁⣴⣿⣿⣿⣿⠀⢻⣿⣿⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⡀⠾⠿⠿⠿⠿⠿⠿⠀⢠⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠠⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣄⣈⡉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⣉⣉⠙⠿⣿⣿⣿⣷⠈⢿⣿⣿⣿⣿⣿⣆⢸⣿⡿⠉⠉⠉⣷⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣟⣛⣒⣒⣶⣿⣿⣿⣿⣿⣿⣷⣦⣈⡙⠻⣿⣧⠈⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣶⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⠃⠐⡬⠄⣧⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣒⣀⡙⠃⠘⣛⣛⣛⣛⣛⣇⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⣘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣉⣉⣉⣋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠻⢿⢿⠿⣿⣭⣭⣭⣽⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⡛⠁⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⡭⠭⢭⣍⣭⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⢆⠀⣷⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠍⣽⣿⣿⣿⣤⣤⡀⠀⠀⠀⠀⠈⢩⣭⣭⣭⣭⣭⣭⣭⠍⠉⠉⠉⠉⠉⠀⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⣿⣿⣿⣭⣭⣭⣭⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⢠⣿⣿⣏⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣭⣭⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠿⠿⡿⢭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⡖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣮⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠹⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢋⣡⡀⢻⣓⣢⣠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⣶⣶⣶⣶⣶⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡶⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠶⠶⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡏⠀⣸⣿⡇⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠲⣶⠿⢷⠖⠰⠶⠶⠶⠀⠰⠖⠶⠶⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⠀⣠⣿⣿⢳⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⢹⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣯⣭⣭⣭⣭⣭⣭⣬⣤⣴⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠿⠋⠙⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣴⣦⣶⣶⣶⣶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢹⡇⣿⢿⣿⣿⣿⣯⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢰⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣷⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡿⠁⣾⣿⣿⣿⣿⣿⣗⣴⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡶⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⣶⣶⢿⣿⣿⣿⠟⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⣿⠶⣿⢽⡧⣿⣿⡷⣿⣿⣿⣿⡿⠟⢁⣴⣿⣿⣿⠈⠸⣿⣿⣀⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⡀⠾⠿⠿⠿⠿⠿⠀⢠⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠠⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣄⣈⡉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⣉⣉⠙⠿⣿⣿⣿⣷⠈⢿⣿⣿⣿⣿⣧⢸⣿⡿⠂⠉⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣟⣛⣶⣲⣶⣿⣿⣿⣿⣿⣿⣿⣦⣈⡙⠻⣿⣧⠈⣿⣿⣿⣿⣿⣾⣿⣿⣿⣶⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⠃⠐⡬⠄⣧⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣒⣀⡙⠃⠘⣛⣛⣛⣛⣧⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⢀⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣋⣛⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠿⢿⢿⠿⣿⣯⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⡍⠁⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣭⣯⣭⣭⣭⣭⣭⣭⣭⣭⡭⣭⣍⣭⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣆⠀⣷⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⣽⣿⣿⣿⣶⡶⠄⠀⠀⠀⠀⠈⢩⣭⣭⣭⣭⣭⣭⡭⠉⠉⠉⠉⠉⠉⠁⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⣿⣿⣿⣭⣭⣭⣭⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠉⢀⣿⣿⣮⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠯⣭⣍⡩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠿⠿⡿⢯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣿⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⡶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠹⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢉⣥⣀⢛⣁⣂⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⣶⣶⣶⣶⣶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡷⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠲⠶⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡏⠀⣼⣿⡇⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠰⠶⠶⠾⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⢀⣰⣿⣿⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⢹⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣯⣭⣭⣭⣭⣭⣭⣬⣤⣴⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠿⠋⠙⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣴⣦⣶⣦⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢻⡇⣿⢽⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢰⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡿⠁⣾⣿⣿⣿⣿⣿⣗⣴⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣶⣶⡶⠶⠷⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⣶⣶⢿⣿⣿⣿⠛⣾⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⣿⠶⣿⢻⡧⣿⣿⡷⣿⣿⣿⣿⡿⠟⢁⣴⣿⣿⣿⠀⢺⣿⣿⣀⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⡀⠾⠿⠿⠿⠿⠿⠀⢠⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠠⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣄⣈⡉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⣉⣉⠙⠿⣿⣿⣿⣷⠈⢿⣿⣿⣿⣿⣧⢸⣿⡿⠂⠉⠁⣿⡄⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣟⣛⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷⣦⣈⡙⠻⣿⣧⠈⣿⣿⣿⣿⣿⣾⣿⣿⣿⣶⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⠃⠐⡬⠄⣧⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣒⣀⡙⠃⠘⣛⣛⣛⣛⣧⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⢀⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣋⣉⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠻⢿⢿⠿⣿⣯⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣭⡭⠁⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣭⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣆⠀⣷⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⣽⣿⣿⣿⣶⡶⠄⠀⠀⠀⠀⠈⢩⣭⣭⣭⣭⣭⣭⡍⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠚⣿⣿⣿⣭⣭⣭⣭⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠉⢀⣿⣿⣮⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠯⢭⣍⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠿⠿⡿⢯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠁⣿⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⡶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠻⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢉⣥⣀⢛⣃⣂⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⣶⣶⣶⣶⣶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡷⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠶⠶⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡏⠀⣼⣿⡇⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠰⠖⠶⠾⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⢀⣰⣿⣿⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⢹⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣯⣿⣯⣭⣭⣭⣭⣭⣭⣭⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⡿⠋⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣴⣶⣶⣶⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢻⡇⣿⣽⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢰⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡿⠁⣾⣿⣿⣿⣿⣿⣰⣦⡀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣷⣶⣶⠶⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⣶⡾⣿⣿⣿⡟⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠐⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⣿⠶⣿⣿⡧⣿⣿⡷⣿⣿⣿⣿⡿⠟⢁⣴⣿⣿⠇⠙⣿⣿⣇⣸⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⡀⠾⠿⠿⠿⠿⡇⠀⣾⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⣄⣈⡉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⣉⣉⠙⠿⣿⣿⣿⣷⠈⢿⣿⣿⣿⣷⡀⣿⣿⡓⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⡛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣟⣛⣒⣲⣶⣿⣿⣿⣿⣿⣿⣷⣦⣈⡙⠻⣿⣧⠈⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⠃⠐⡬⠄⣧⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣒⣀⡙⠃⠘⣛⣛⣛⣻⣼⣿⣿⣿⣿⢿⠟⠀⠀⠀⠀⠀⠀⠀⣘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣙⣛⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠻⢿⢿⠿⣿⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⠉⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠭⢭⣭⣭⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣆⠀⣷⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢭⣿⣿⣿⣷⣶⠶⠀⠀⠀⠀⠀⠉⢭⣭⣭⣭⣭⣭⣭⣍⠉⠉⠉⠁⠉⠉⠁⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⣿⣿⣿⣭⣭⣭⣭⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⣸⣿⣷⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠯⣭⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠿⠿⡿⢭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣿⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣽⠇⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠹⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣡⣤⡘⣛⣁⣤⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⣶⣶⣶⣶⣾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠃⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⠶⠶⠶⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠁⢠⣿⣿⢠⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠲⣶⠿⢷⠶⠰⠶⠶⠶⠀⠰⠶⠾⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡇⢀⣾⣿⣿⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠎⠉⠉⠈⠉⠉⢉⠉⠉⠛⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⣿⣿⣦⡀⠉⢭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣤⣴⣤⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣆⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠄⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⣿⣿⣿⣿⣿⡆⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣶⣶⣶⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀
⡟⠉⠉⠉⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢻⣿⣿⡇⠀⣿⣿⣿⡿⠛⠛⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣧⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⣿⣿⣍⡀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣷⣿⣿⣿⣿⣿⡇⡆⠀⠀⠀⠀
⡇⠠⢀⠀⠄⠠⠀⠀⠀⠀⠄⠀⠀⠄⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠄⢸⣿⡟⠀⣼⣿⣿⣿⣿⣿⣆⡅⠀⠀⢀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⢿⠛⠉⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣾⣿⡗⠁⠈⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠹⣷⣿⣿⣿⣿⡿⠏⢀⣼⣿⣿⣿⡿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣾⣿⣿⣿⣿⣿⣶⣾⣶⣶⣶⣿⣿⣶⣿⣿⡿⠿⠿⠿⠿⠿⣿⣦⣴⡄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢘⣿⣿⣿⡿⠋⢀⣴⣿⡏⠹⣻⣿⣄⣿⣿⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
⠉⠛⠿⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⠀⢰⣿⣿⣿⡇⠀⣾⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⢉⠉⢁⢐⠀⠀⠀
⣿⣶⣤⣄⣀⡉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⡁⠙⠻⢿⣿⣿⣧⠀⢻⣿⣿⣧⣀⣿⣿⡛⠈⠀⣹⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣶⣾⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣦⣀⠉⠛⢿⣆⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⣿⣿⣿⡇⠚⡿⠆⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣦⣀⠈⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⢿⠟⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⠁⠨⠀⢹⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣷⡾⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⠍⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢇⠀⠀
⣿⣿⣿⡧⢙⣆⢆⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣾⠶⠀⠀⠀⠀⠀⠉⢭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⠀⠀⠐⠀⠈⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⢹⣿⣿⣉⠉⠀⠀⠀⠀⠀⠀⠀⣴⠀⠙⠻⠿⣿⣿⣿⣭⣭⣭⡭⠭⠭⠽⠯⣭⢭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣯⠉⠀⠀⠀⠀⠀
⣿⣿⣿⡿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁⠀⠀⠿⠁⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⣠⣿⠀⠀⠀⠀⠀⠈⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠭⠭⠭⠭⠉⠉⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣥⣸⣇⣁⣿⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⡿⠖⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣷⡤⡄⡀⠀⠀⠾⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⣩⣤⣼⣿⣿⣿⣷⡋⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⢻⣿⡿⢿⡿⠻⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⣠⣶⣇⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⣿⣄⣸⣇⣠⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⣰⡉⣻⣏⣀⣀⣰⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 3198

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 08.05.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_05/08/2022:_GNUnet_0.17.3_and_GNU_Binutils_2.39⠀✐


Posted in News_Roundup at 5:00 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Server
          o Audiocasts/Shows
          o Benchmarks
          o Applications
          o Instructionals/Technical
          o Games
          o Desktop_Environments/WMs
                # GNOME_Desktop/GTK
    * Distributions_and_Operating_Systems
          o SUSE/OpenSUSE
          o Slackware_Family
          o Debian_Family
          o Canonical/Ubuntu_Family
          o Open_Hardware/Modding
          o Mobile_Systems/Mobile_Applications
    * Free,_Libre,_and_Open_Source_Software
          o Web_Browsers
                # Chromium
                # Mozilla
          o GNU_Projects
          o Programming/Development
                # Rust
    * Leftovers
          o Hardware
          o Health/Nutrition/Agriculture
          o Security
                # Privacy/Surveillance
          o Defence/Aggression
          o Environment
                # Energy
                # Wildlife/Nature
          o Finance
          o AstroTurf/Lobbying/Politics
          o Censorship/Free_Speech
          o Civil_Rights/Policing
          o Internet_Policy/Net_Neutrality
          o Monopolies
    * Gemini*_and_Gopher
          o Personal
          o Technical
                # Programming
    * § GNU/Linux⠀➾


          o § Server⠀➾


                # ⚓ Electronics Weekly ☛ The_Lost_Opportunity⠀⇛


                       Back in 1999, Saski told me: “The Wintel world used
                       to be untouchable but now a new era is coming. The
                       opportunity for change is Linux.”
                       The argument went that, if the Linux operating
                       system became mainstream, “then the basis for
                       competition in the microprocessor market becomes
                       cost/performance not architecture,” said Saski.
                       Asked if NEC would take advantage of the
                       opportunity by seeking to establish its own
                       proprietary microprocessor architecture Sasaki
                       replied: “That would be difficult, but we have a
                       strong background in the MIPS architecture.”
                       Sasaki did not rule out NEC developing its own
                       microprocessor, he merely said that MIPS would be
                       the “first priority” if the opportunity arose.
                       Whether or not the opportunity is there “depends on
                       the applications software”, said Sasaki.
                       If this becomes available then PC makers may
                       support Linux just as IBM and HP have supported
                       Linux in servers.
                       “It all depends on our customers’ decision,” said
                       Sasaki, “up to now we have had no way to tell. But
                       now we have a chance.”


                # ⚓ Why_Kubernetes_is_the_‘Secret_Sauce’_for_Bank
                  Digitization⠀⇛


                       Google “banking” and “disruption,” and nearly 200
                       hits sprawl across more than 20 pages of search
                       results.


                       The high interest in banking disruption isn’t
                       surprising. Though disruption is a favorite
                       business buzzword that can easily lend itself to
                       hyperbole, it truly is accurate for the banking and
                       financial services industry.


          o § Audiocasts/Shows⠀➾


                # ⚓ Video ☛ KaOS_2022.06_Quick_overview_#linux_#kaos_–
                  Invidious⠀⇛


                       A Quick Overview of KaOS 2022.06


                # ⚓ Video ☛ Linux_User_Plays_Cruelest_Joke_EVER_on_Coworker_–
                  Invidious⠀⇛


          o § Benchmarks⠀➾


                # ⚓ Neowin ☛ Despite_Alder_Lake_optimization,_Windows_11
                  struggles_to_stay_ahead_of_Ubuntu_/_Linux_–_Neowin⠀⇛


                       Back at its Architecture Day 2021 event, when Intel
                       shared the core design details of its Alder Lake
                       CPU architecture, the firm stated that Windows 11
                       was optimized in a way to best take advantage of
                       the Alder Lake’s Performance Hybrid architecture
                       and the new Thread Director technology that helps
                       Windows 11 task scheduling.


                       A comparison test in November last year indeed
                       showed that the Intel 12th Gen chips were a bit
                       ahead of Ubuntu and the Linux 5.15 kernel. With the
                       succeeding Linux 5.16 too, the performance of Alder
                       Lake was not as consistent as on Windows 11.


          o § Applications⠀➾


                # ⚓ OMG Ubuntu ☛ A_Wild_Metadata_Cleaner_for_Linux_Appeared!⠀⇛


                       
                       The GTK-based Metadata Cleaner app on Flathub looks
                       ideal.


                       This Python-based GTK app lets you view and clean
                       metadata from a variety of file types. The app is
                       totally open source and leverages the mat2 library
                       for its file-washing abilities.


                       While most metadata routinely embedded in files is
                       innocuous or banal some may reveal more information
                       than you’d like.


                       For example, photos taken on most cameras and
                       smartphones embed a data about where a picture was
                       taken, the device it was taken on, and more as EXIF
                       (Exchangeable Image File Format). You don’t need to
                       be über-paranoid to want to remove location data
                       from photos you share with others!


                # ⚓ Make Use Of ☛ The_4_Best_Self-Hosted_Google_Photos
                  Alternatives⠀⇛


                       Smartphone users take hundreds, if not thousands of
                       photos every year, and many have relied on Google
                       Photos to automatically upload and store their
                       holiday snapshots for free. The service ceased to
                       offer unlimited storage in 2021, meaning that users
                       had to either fork over cash to Google or find
                       another solution—either by moving to another
                       provider or self-hosting.


                       Here are some of the best self-hosted Google Photos
                       alternatives to create your own media server on
                       Linux.


          o § Instructionals/Technical⠀➾


                # ⚓ Vitux ☛ How_to_Mount_NFS_on_Debian_11⠀⇛


                       With NFS (Network File System), you can share files
                       and folders with other systems in a network. NFS is
                       based on a client-server architecture that allows
                       users to remotely connect and access files through
                       the network. With NFS, users can access shared
                       files and folders as if they exist in their own
                       system.


                # ⚓ Unix Men ☛ How_to_Protect_Your_Linux_System_Against
                  Log4Shell⠀⇛


                       A serious flaw in the Log4j framework enables
                       cybercriminals to gain access to vulnerable systems
                       by injecting a single malicious code. This
                       vulnerability is known as Log4J, a free logging
                       library distributed by the Apache Software
                       Foundation.


                       Java is used in a vast array of contemporary
                       digital products, including web servers, cloud
                       solutions, and applications – making all of these
                       products vulnerable to hacking through the
                       Log4Shell vulnerability.


                # ⚓ MakeTech Easier ☛ How_to_Enable_Wake-on-LAN_in_Ubuntu_–
                  Make_Tech_Easier⠀⇛


                       We all feel the desire to automate everything. Our
                       cars, houses and especially our computers. Wake-on-
                       LAN is the perfect way to automate turning your PC
                       on.


                       While this guide will focus on how to enable Wake-
                       on-LAN in Ubuntu, you can apply it to Linux
                       distros, and you can even find the feature in
                       Windows.


                # ⚓ TechRepublic ☛ How_to_connect_to_Linux_Samba_shares_from
                  Windows_|_TechRepublic⠀⇛


                       When Windows 10 was released, it seemingly broke
                       the ability to easily connect to Linux Samba
                       shares. It appeared one could not write to Linux
                       share from Windows 10. Considering how many
                       businesses rely on Samba for the sharing of
                       folders, this was a bad move on the part of
                       Microsoft. Fortunately, the ability to connect to
                       Samba shares wasn’t actually removed from the
                       Windows platform, it was merely tucked a bit out of
                       sight.


                # ⚓ Use_GNOME_Keyring_with_Sway_::_Major_Hayden⠀⇛


                       SSH key authentication makes it easier to secure
                       SSH servers and it opens the door to automation
                       with projects such as Ansible. However, working
                       with encrypted SSH keys becomes tedious when you
                       have several of them for different services. This
                       is where an SSH agent can help!


                # ⚓ Ubuntu ☛ How_to_build_a_snap_using_ROS_2_Humble_|_Ubuntu⠀⇛


                       We’ve recently celebrated the release of ROS 2
                       Humble Hawksbill with a post detailing how to get
                       started developing for the new release in
                       containers. In addition, we shared an overview of
                       the new features included with this new release,
                       particularly its enhanced security features.


                       This week we are tackling the logical next step in
                       software development: packaging. Indeed, once we’re
                       done developing our super cool ROS 2 Humble
                       application, we still have to get it out into the
                       hands of our users.


                       In this post, we are going to see how to package a
                       ROS 2 Humble application as a snap with an ‘hello
                       world’-like example.


                # ⚓ AboutChromebooks ☛ Still_using_apt_for_Linux_on_a
                  Chromebook?_Try_Nala_instead⠀⇛


                       I noticed a fair number of commenters on my last
                       post, “Why I use a Chromebook”, use the Linux on a
                       Chromebook feature. More than expected, to be
                       honest. I’ll bet only a few, if any, of them have
                       stopped using apt, or the Advanced Package Tool,
                       command to install Linux apps. I have. I now use
                       Nala for Linux, which is a front-end for the apt
                       package manager command.


                # ⚓ Linux Made Simple ☛ How_to_install_FreeCAD_0.19.1_on_a
                  Chromebook⠀⇛


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


          o § Games⠀➾


                # ⚓ Godot Engine ☛ Godot_Engine_–_Godot_3.5:_Can’t_stop_won’t
                  stop⠀⇛


                       After 9 months of development, Godot 3.5 is out and
                       it comes fully packed with features and quality of
                       life improvements!


                       While most development focus is on our upcoming
                       Godot 4.0 release, many contributors and users want
                       a robust and mature 3.x branch to develop and
                       publish their games today, so it’s important for us
                       to keep giving Godot 3 users an improved gamedev
                       experience. Most of work was aimed at implementing
                       missing features or fixing bugs which are critical
                       for publishing 2D and 3D games with Godot 3.x, and
                       at making the existing features more optimized and
                       reliable.


                       Godot 3.5 is compatible with Godot 3.4.x projects
                       and is a recommended upgrade for all 3.4.x users.


          o § Desktop Environments/WMs⠀➾


                # § GNOME Desktop/GTK⠀➾


                      # ⚓ Fitting_Endless_OS_images_on_small_disks_–_Will
                        Thompson⠀⇛


                             People like to fixate on the disk space used
                             by installing a calculator app as a Flatpak
                             when you don’t have any other Flatpak apps
                             installed. For example, on my system GNOME
                             Calculator takes up 9.3 MB for itself, plus
                             803.1 MB for the GNOME 42 runtime it depends
                             on. Regular readers will not be surprised
                             when I say that that 803.1 MB figure looks
                             rather different when you realise that
                             Calculator is just one of 70 apps on my
                             system that use that runtime; 11.5 MB of
                             runtime per app feels a lot more reasonable.


                             But I do have one app installed which depends
                             on the GNOME 3.34 runtime, which has been
                             unsupported since August 2020, and the GNOME
                             3.34 runtime only shares 102 MB of its files
                             with the GNOME 42 runtime, leaving 769 MB
                             installed solely for this one 11 MB app.


    * § Distributions and Operating Systems⠀➾


          o § SUSE/OpenSUSE⠀➾


                # ⚓ openSUSE_Tumbleweed_–_Review_of_the_weeks_2022/29-31⠀⇛


                       Dear Tumbleweed users and hackers,


                       I was in the fortunate situation of enjoying two
                       weeks of offline time. Took a little bit of effort,
                       but I did manage to not start my computer a single
                       time (ok, I cheated, checked emails, and staging
                       progress on the phone browser). During this time,
                       Richard has been taking good care of Tumbleweed –
                       with the limitations that were put upon him, like
                       reduced OBS worker powers and the like. In any
                       case, I still do want to give you an overview of
                       what changed in Tumbleweed during those three
                       weeks. There was a total of 8 snapshots released
                       (0718, 0719, 0725, 0728, 0729, 0731, 0801, 0802). A
                       few of those snapshots have only been published,
                       but no announcement emails were sent out, as there
                       were also some mailman issues on the factory
                       mailing list.


          o § Slackware Family⠀➾


                # ⚓ The Register UK ☛ Fancy_a_freshened_up_SLAX_or_ChromeOS
                  replacement_Peppermint_OS?⠀⇛


                       Slax, one of the lightest-weight Linux distros
                       around, and Peppermint OS, a web-centric Debian
                       remix, both put out new versions this week.


                       Slax is a very lightweight live-medium distro from
                       Czech developer Tomáš Matějíček (Czech language).
                       As The Reg mentioned at the time, earlier this
                       year, Slax got its first update in a couple of
                       years. That update, version 11.2, was based on
                       Debian, as the last few Slax releases have been.


                       Slax goes back to its roots


                       Now, Slax 15 is out. After nine years, Slax is
                       returning to its Slackware roots. Slax 15 is based
                       on the recently-released Slackware 15 – which
                       itself is the first new Slackware release in six
                       years. (Slax’s version numbers denote the version
                       of the underlying OS.)


          o § Debian Family⠀➾


                # ⚓ Thorsten_Alteholz:_My_Debian_Activities_in_July_2022⠀⇛


                       This month I accepted 420 and rejected 44 packages.
                       The overall number of packages that got accepted
                       was 422.


                       I am sad to write the following lines, but
                       unfortunately there are people who rather take
                       advantage of others instead of doing a proper
                       maintenance of their packages.


                       So, in order to find time slots for as much
                       packages in NEW as possible, I no longer write a
                       debian/copyright for others. I know it is a boring
                       task to collect the copyright information, but our
                       policy still requires this. Of course nobody is
                       perfect and certainly one or the other license or
                       copyright holder can be overlooked. Luckily most of
                       the contributors maintain their debian/copyright
                       very thouroughly with a terrific result.


                       On the other hand some contributors upload only
                       some crap and demand that I exactly list what is
                       missing. I am no longer willing to do this. I am
                       going to stop processing after I found a few
                       missing things and reject the package. When I see
                       repeatedly uploads containing only improvements
                       with things I pointed out, I will process this
                       package only after all others from NEW are done.


                # ⚓ Dirk Eddelbuettel ☛ Dirk_Eddelbuettel:_RcppXts_0.0.5_on
                  CRAN:_Routine_Refreshment⠀⇛


                       A full eight and half years (!!) since its 0.0.4
                       release, version 0.0.5 of RcppXts is now on CRAN.
                       The RcppXts package demonstrates how to access the
                       export C API of xts which we contributed a looong
                       time ago.


                       This release contains an accumulated small set of
                       updates made as the CRAN Policies evolved. We now
                       register and use the shared library routines
                       (updates in both src/init.c and NAMESPACE), turned
                       on continuous integration, switched it from the now
                       disgraces service to another, adopted our portable
                       r-ci along with r2, added badges to the README.md,
                       updated to https URLs, and made sure the methods
                       package (from base R) was actually imported
                       (something Rcpp has a need for at startup). That
                       latter part now triggered a recent email from the
                       CRAN maintainers which prompted this release.


                # ⚓ Sparky:_g4music⠀⇛


                       A fast, fluent, light weight music player written
                       in GTK4, with a beautiful, adaptive user interface,
                       so named G4Music. It is also focusing on high
                       performance, for those people who has huge number
                       of songs.


          o § Canonical/Ubuntu Family⠀➾


                # ⚓ 9to5Linux ☛ Linux_Mint_20.3_Users_Can_Now_Upgrade_to_Linux
                  Mint_21,_Here’s_How⠀⇛


                       
                       With Linux Mint 21 the upgrade process is done
                       through a new utility that the Linux Mint team
                       worked on during the development cycle of Linux
                       Mint 21. The utility is called mintupgrade (Upgrade
                       Tool) and while it launches from the command line
                       it provides users with a full graphical upgrade
                       process.


                       Upgrade Tool was first made available a few months
                       ago for Linux Mint Debian Edition 4, allowing users
                       to upgrade to Linux Mint Debian Edition 5. But, as
                       of today, August 5th, 2022, it’s also available for
                       Linux Mint 20.3 “Una” users who want to upgrade
                       their installations to Linux Mint 21 “Vanessa”.


          o § Open Hardware/Modding⠀➾


                # ⚓ Arduino ☛ This_high-precision_AC_meter_handles_inductive
                  loads_|_Arduino_Blog⠀⇛


                       AC (alternating current) meters are useful tools
                       for measuring power draw. One might use an AC meter
                       to monitor the power consumption of their devices
                       and appliances with the goal of lowering their
                       energy bill. Makers in particular can benefit from
                       AC meters to learn about the power consumption of
                       their own projects. Basic AC meters are cheap and
                       easy to find, but they don’t measure inductive
                       loads accurately. This DIY high-precision digital
                       AC meter can handle inductive loads.


                       An inductive load is any device or appliance that
                       utilizes electric coils, which are found in motors,
                       transformers, relays, and many other basic electric
                       parts. Those coils create both a standard resistive
                       load and an inductive load. The higher the
                       inductive load relative to the resistive load, the
                       less accurate typical AC meter readings become. An
                       air conditioning unit, for example, is a
                       substantial inductive load. Cheap AC meters measure
                       the peaks of the current’s sine wave, but inductive
                       loads alter the shape of the wave so that it is no
                       longer a sine wave and that makes the meter’s
                       calculations inaccurate.


          o § Mobile Systems/Mobile Applications⠀➾


                # ⚓ How_to_Unlock_Android_Phone_without_Password⠀⇛


                # ⚓ Pocket Lint ☛ How_to_turn_on_your_flashlight_or_torch_on
                  your_Android_phone⠀⇛


                # ⚓ Android Central ☛ How_we_test_and_review_smart_home_devices
                  at_Android_Central_|_Android_Central⠀⇛


                # ⚓ Business Insider ☛ How_to_Screen_Mirror_Your_Android_to_a
                  TV_or_Computer⠀⇛


                # ⚓ Android Police ☛ Descenders_brings_its_manic_downhill
                  freeriding_to_Android⠀⇛


                # ⚓ Indian Express ☛ Android_13_Early_Access_program_for_Realme
                  GT_2_Pro_starts:_Here’s_how_to_enroll_|_Technology_News,The
                  Indian_Express⠀⇛


                # ⚓ FOSSBytes ☛ List_Of_Xiaomi_Devices_That_Will_Get_Android_13
                  Update:_Did_Yours_Make_The_Cut?⠀⇛


                # ⚓ Make Use Of ☛ Samsung_Begins_Rolling_Out_the_One_UI_5_Beta
                  With_Android_13⠀⇛


                # ⚓ Android_13_Might_Fix_Your_Pixel_6_Fingerprint_Scanner_Woes
                  –_Review_Geek⠀⇛


                # ⚓ Notebook Check ☛ Retroid_Pocket_3_arrives_in_multiple
                  colours_with_Android_11_from_US$119_–_NotebookCheck.net
                  News⠀⇛


                # ⚓ GSM Arena ☛ YouTube_finally_lets_Android_users_zoom_in_on
                  videos_–_GSMArena.com_news⠀⇛


                # ⚓ PC Mag ☛ The_Best_Wireless_Adapters_for_CarPlay_and_Android
                  Auto_in_2022_|_PCMag⠀⇛


                # ⚓ Gizmodo ☛ We_Miss_These_Quirky_Android_Phone_Experiments⠀⇛


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


          o ⚓ OSI Blog ☛ Welcome_to_Deep_Dive_AI [Ed: Stefano Maffulli
            continues to make excuses for Microsoft GPL violations (Copilot)
            while Microsoft_pays_him_to_do_this, under the guise of “AI”.
            Today’s OSI is run by a group of openwashing phonies.]⠀⇛


          o ⚓ Apache Blog ☛ The_Apache_News_Round-up:_week_ending_5_August_2022
            :_The_Apache_Software_Foundation_Blog⠀⇛


                 Welcome, August –we’re opening the month with another
                 great week. Here’s what the Apache community has been up
                 to…


          o § Web Browsers⠀➾


                # § Chromium⠀➾


                      # ⚓ Google ☛ Chromium_Blog:_Chrome_105_Beta:_Custom
                        Highlighting,_Fetch_Upload_Streaming,_and_More⠀⇛


                             Unless otherwise noted, changes described
                             below apply to the newest Chrome beta channel
                             release for Android, Chrome OS, Linux, macOS,
                             and Windows. Learn more about the features
                             listed here through the provided links or
                             from the list on ChromeStatus.com. Chrome 105
                             is beta as of DATE. You can download the
                             latest on Google.com for desktop or on Google
                             Play Store on Android.


                # § Mozilla⠀➾


                      # ⚓ Jamie McClelland ☛ Jamie_McClelland_|_Fine_tuning
                        Thunderbird’s_end-to-end_encryption⠀⇛


                             I love that Thunderbird really tackled
                             OpenPGP head on and incorporated it directly
                             into the client. I know it’s been a bit rough
                             for some users, but I think it’s a good long
                             term investment.


                             And to demonstrate I’ll now complain about a
                             minor issue :).


                             I replied to an encrypted message but
                             couldn’t send the response using encryption.
                             I got an error message indicating that “End-
                             to-end encryption requires resolving
                             certificate issues for” … and it listed the
                             recipient email address.


          o § GNU Projects⠀➾


                # ⚓ GNUnet ☛ GNUnet_0.17.3⠀⇛


                       This is a bugfix release for gnunet 0.17.2. In
                       addition to the fixed in the source, the
                       documentation websites including the handbook have
                       been updated and consolidated: https://
                       docs.gnunet.org .


                # ⚓ GNU_Binutils_2.39_Released⠀⇛


                       This release contains numerous bug fixes, and also
                       the following new
                       features:

                         * The ELF linker will now generate a warning
                       message if the stack is made
                           executable.  Similarly it will warn if the
                       output binary contains a
                           segment with all three of the read, write and
                       execute permission
                           bits set.  These warnings are intended to help
                       developers identify
                           programs which might be vulnerable to attack
                       via these executable
                           memory regions.

                           The warnings are enabled by default but can be
                       disabled via a command
                           line option.  It is also possible to build a
                       linker with the warnings
                           disabled, should that be necessary.

                         * The ELF linker now supports a --package-
                       metadata option that allows
                           embedding a JSON payload in accordance to the
                       Package Metadata
                           specification.

                         * In linker scripts it is now possible to use
                       TYPE=<type> in an output
                           section description to set the section type
                       value.

                         * The objdump program now supports coloured/
                       colored syntax
                           highlighting of its disassembler output for
                       some architectures.
                           (Currently: AVR, RiscV, s390, x86, x86_64).

                         * The nm program now supports a --no-weak/-
                       W option to make it ignore
                           weak symbols.

                         * The readelf and objdump programs now support a
                       -wE option to prevent
                           them from attempting to access debuginfod
                       servers when following
                           links.

                         * The objcopy program's --weaken, --weaken-
                       symbol, and
                           --weaken-symbols options now works with unique
                       symbols as well.

                       Our thanks go out to all of the binutils
                       contributors, past and
                       present, for helping to make this release possible.
          o § Programming/Development⠀➾


                # ⚓ Medevel ☛ Mintable_is_the_Best_Open-source_Finance
                  Automation_for_Geeks⠀⇛


                       Mintable is an open-source project that is released
                       under the MIT License.


                # § Rust⠀➾


                      # ⚓ Rust Blog ☛ Non-lexical_lifetimes_(NLL)_fully_stable
                        |_Rust_Blog⠀⇛


                             As of Rust 1.63 (releasing next week), the
                             “non-lexical lifetimes” (NLL) work will be
                             enabled by default. NLL is the second
                             iteration of Rust’s borrow checker. The RFC
                             actually does quite a nice job of
                             highlighting some of the motivating examples.
                             “But,” I hear you saying, “wasn’t NLL
                             included in Rust 2018?” And yes, yes it was!
                             But at that time, NLL was only enabled for
                             Rust 2018 code, while Rust 2015 code ran in
                             “migration mode”. When in “migration mode,”
                             the compiler would run both the old and the
                             new borrow checker and compare the results.
                             This way, we could give warnings for older
                             code that should never have compiled in the
                             first place; we could also limit the impact
                             of any bugs in the new code. Over time, we
                             have limited migration mode to be closer and
                             closer to just running the new-style borrow
                             checker: in the next release, that process
                             completes, and all Rust code will be checked
                             with NLL.


    * § Leftovers⠀➾


          o ⚓ Counter Punch ☛ ‘We_Are_Limited_Only_By_Our_Imagination_and_Our
            Will_to_Act’:_Hopeful_Words_As_Liberal_Shibboleth⠀⇛


                 Based, presumably, in the God’s Eye view of our limited
                 earth home gained from his 2,842 orbits, Garan’s message
                 of hope simply amplifies the top-down liberal order with
                 its absolute faith in progress – especially technological
                 progress – which if we believe in sufficiently will make
                 limitations disappear. Although likely unintended, the
                 unspoken subtext is, don’t bother with the (messy,
                 dissatisfying), reality you’re in. But I must protest:
                 Limits are not just punishment for failure of
                 imagination! From “the bottom-up” view, from within the
                 entanglements of embodied earth-life, the message is
                 different: it’s by staying in the reality we are in, with
                 its troubles and uncertainties, now intensified by the
                 global contexts of pandemic and climate catastrophe, that
                 the imagination that serves the “All-one” of
                 interdependence and planetary health is engaged. Staying
                 in our places and relationships would not be impossibly
                 difficult – our ancestors did it! – except for its being
                 contrary to the most fundamental lessons we’ve been
                 taught and to which we are obedient: the work of
                 imaginations being not to serve the “All-one” or “All-in-
                 all” but to except us from the current troubles, to
                 escape, surmount, achieve, strive, succeed; never to stay
                 with limiting reality. Staying in is the stuff of
                 failure, and that we must fear as we’d fear the hellhound
                 on our trail.


          o ⚓ Counter Punch ☛ Remembering_Vin_Scully⠀⇛


                 For anyone who grew up a baseball fan, the voice of Vin
                 Scully was a much a part of the essence of the game as
                 the gloves, bats, balls, and the action on the field he
                 so deftly and at times eloquently chronicled. For a
                 staggering sixty-seven years he was the voice of the
                 Dodgers, first in Brooklyn and then in Los Angeles, but
                 listeners throughout the country were familiar with his
                 voice and effortlessly literate style from his long-time
                 stints on national broadcasts: World Series and All-Star
                 games on TV and radio, and NBC’s Saturday game of the
                 week, paired with Joe Garagiola.


                 Scully’s distinctively melodious, fluidly garrulous
                 baritone punctuated the decades for millions of Americans
                 who can still vividly recall his dramatic evocations of
                 some of baseball’s most memorable moments, many conveyed
                 with a near-preternatural verbal fluency and rhetorical
                 flair that gave his extemporaneous exclamations the feel
                 of polished literature: Don Larsen’s World Series perfect
                 game in 1956, Sandy Koufax’s perfect game in 1965, Hank
                 Aaron’s record-breaking 715th homerun in 1974 (“What a
                 great moment for the country and the world—a black man is
                 getting a standing ovation in the Deep South for breaking
                 the record of an all-time baseball idol”), Bill Buckner’s
                 infamously booted ball in the 1986 World Series, and the
                 hobbled Kirk Gibson’s miraculous homer in the 1988 World
                 Series.


          o ⚓ Hackaday ☛ Buzzword_Bingo_Bitcoin_Burial_Burrowing_Blueprint
            Balked_At_By_Bureaucracy⠀⇛


                 Many of you will at some time have heard the unfortunate
                 tale of [James Howells], a Welsh IT worker who threw away
                 a hard drive containing 8,000 Bitcoin back in 2013. Over
                 the years he’s hatched various schemes to persuade his
                 local council to let him dig up the landfill where it’s
                 reputed to be buried, and every time he’s been rebuffed.
                 Despite the fall in the price of cryptocurrencies he’s
                 back with another. With the added spice of AI and robot
                 dogs alongside the cryptocurrency angle, it reads like a
                 buzzword bingo card and adds a whole new meaning to
                 “Bitcoin mining”. Seemingly despite generous offers the
                 local council are still not keen on letting him dig for
                 the drive.


          o ⚓ Hackaday ☛ 30_Free_Circuit_Simulators_Lightly_Reviewed⠀⇛


                 We live in a time where great software is available with
                 the click of a mouse, often for free or — at least — low
                 cost. But there’s a problem: how do you select from so
                 many alternatives? We were interested in [Lee Teschler]’s
                 review earlier this year of 30 free circuit simulators.
                 If you are selecting one or don’t like the one you are
                 currently using, it is well worth the time to review.


          o ⚓ Counter Punch ☛ The_Tale_of_3M⠀⇛


                 So people were wearing all kinds of weird shit on their
                 faces. And then a few companies like 3M said, “We got it.
                 We’re national heroes. We’re like the dudes who landed on
                 the moon.” And I was like, “No you aren’t! You’re fuckin’
                 making a boatload of cash. You’re not sacrificing your
                 life, running into enemy fire with a knife between your
                 teeth. No, you saw that you could make a trillion dollars
                 by pumping out face masks. Stop acting like you cured
                 polio with a third grade chemistry set.


                 Anyway, 3M made a lot of the face masks. Not mine. Mine
                 were made by Frito-Lay so that I could wear it on the bus
                 but then, in a pinch, eat it. They were delicious. Do you
                 have any idea how much guac you can fit on one of those
                 things? It’s great. But a lot of people were wearing the
                 far less edible 3M masks.


          o ⚓ Counter Punch ☛ End-Times:_a_Visit_to_Isle_de_Jean_Charles,
            Louisiana⠀⇛


                 I left Thibodaux, Louisiana at 9 a.m. on July 27, 2022.
                 An hour later, I arrived at Isle de Jean Charles where I
                 had a vision of the world a hundred years in the future.


                 Thibodaux is a handsome town — a sort-of miniature New
                 Orleans, but without the music, art, architecture, or
                 sophistication of the city 60 miles to the east. What it
                 has is a tight grid of streets, canopied sidewalks, two
                 or three Creole restaurants, and a welcoming scale.
                 Parking is easy and a walk through downtown takes about
                 15 minutes.


          o ⚓ Counter Punch ☛ America’s_Biggest_Reservoirs_Hit_By_Dead_Pool
            Jitters⠀⇛


                 In a word, the implications are unspeakable.


                 America’s monuments, the Statue of Liberty, Mount
                 Rushmore, the Lincoln Memorial, and Hoover Dam are the
                 foundations of Americana, the essence of America, its
                 character, and its culture. Hoover Dam, one of the
                 greatest engineering feats of all time, 96 lives lost
                 during construction, defines America’s true grit during a
                 bygone era that had to overcome great challenges tagged
                 with the Great Depression, soup kitchens & breadlines
                 (NYC 82 breadlines by 1932), the Dust Bowl, incipient
                 fascism in Europe, and a brewing world war.


          o ⚓ Counter Punch ☛ We_Should_Aspire_to_be_Peasants⠀⇛


                 After all, who wouldn’t like to see some more cash?
                 Farmers, like everyone else, have been through a lot
                 lately. Years of stagnant or falling farm income in many
                 ways paralleled the stagnant wages of so many Americans.
                 The COVID-19 pandemic sent shockwaves through our supply
                 chain, crashing farm prices and disrupting markets.


                 But the story is not so simple.


          o ⚓ Counter Punch ☛ The_Fire_Inside_Mike_Davis⠀⇛


                 The occasion for such remarks, with their pugilistic
                 zest, was the thirtieth anniversary of the publication of
                 his path-breaking City of Quartz: Excavating the Future
                 in Los Angeles (1990), long regarded as both a classic
                 and an outlier, with its blend of noir-haunted conjuring
                 and granular, sociological exploration of L.A.’s myriad
                 political ecologies. “In Los Angeles there are too many
                 signs of approaching helter-skelter”, Davis writes near
                 the close: “cops are becoming more arrogant and trigger-
                 happy, and a whole generation is being shunted toward
                 some impossible Armageddon”. Within 18 months, the
                 reckoning he had intuited came to pass, when the city
                 erupted in a cataclysmic uprising, sparked by the
                 acquittal of four LAPD officers charged with the use of
                 excessive force during the arrest of Rodney King: a
                 typically brutal incident, but unusual in having been
                 captured on videotape by an onlooker. As chants of “no
                 justice, no peace” echoed through downtown L.A., swathes
                 of the city were reduced to rubble and ash – leading
                 President George H. W. Bush to declare a “federal
                 disaster area” – as protestors exposed and countered a
                 long-standing tradition of police violence with tactics
                 of civil disobedience, arson, and looting. Six weeks
                 after the conflagration, Daryl Gates, the notoriously
                 authoritarian and techno-militarist police chief (accused
                 of instituting a de facto racist law-enforcement regime),
                 resigned his post.


                 America’s intellectual establishment, meanwhile, shaken
                 from its foggily panoptic perch, began to pay attention
                 to Davis (once viewed as a fatalist, prone to hyperbole,
                 even by fellow radicals), deeming him worthy of a
                 MacArthur Foundation grant in 1998. For this self-
                 described “wild, extreme leftist”, however, such
                 plaudits, and the milieux they emanated from, have
                 generally been treated as distractions from the work, to
                 which he consistently brings a virtuosic analytical
                 rigour, as well as an omnivorous array of personal
                 passions. What other Marxist scholar has thought to
                 compile a history of the car-bomb, as Davis did in Buda’s
                 Wagon (2007), or invested time and energy in writing a
                 trilogy of science fiction novels for young adults, as
                 with his Islands Mysterious series (2003)? Wild
                 originality is one of his hallmarks.”


          o ⚓ Counter Punch ☛ Sympathy_For_The_Plethora_Of_Devils⠀⇛


                 I only write this as if any of it matters.


                 As Cassius said to Brutus in Shakespeare’s (1654 to 1616)
                 “Julius Caesar,” “the fault …is …that we are underlings”


          o § Hardware⠀➾


                # ⚓ Hackaday ☛ Stewart_Platform_Wields_Magic_Fingers_To_Massage
                  Your_Scalp⠀⇛


                       Attention Hackaday editors: We on the writing crew
                       hereby formally request budget allocation for
                       installing a Stewart platform head massager on the
                       chair of each workstation in the secret underground
                       writer’s bunker. We think the benefits that will
                       accrue thanks to reduced stress alone will more
                       than justify the modest upfront costs. Thank you
                       for your consideration.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ The Nation ☛ Monkeypox_Makes_It_3_Strikes,_and_Now_We’re
                  Out⠀⇛


                       I graduated from high school in 1981. My youth was
                       framed by the AIDS epidemic. I could ignore it for
                       several years while cloistered in college, but as
                       soon as I ventured out into the world, there it
                       was: the virus.


          o § Security⠀➾


                # ⚓ Help Net Security ☛ Phishing_campaign_targets_Coinbase
                  wallet_holders_to_steal_cryptocurrency_in_real-time_–_Help
                  Net_Security⠀⇛


                       In this video for Help Net Security, Nick Ascoli,
                       VP of Threat Research, PIXM, discusses a
                       multilayered phishing campaign targeting
                       cryptocurrency exchange Coinbase. Attackers are
                       sending out spoofed Coinbase emails to harvest
                       personal credentials and use them to log into
                       users’ legitimate accounts in real-time.


                # ⚓ InfoSecurity Magazine ☛ GwisinLocker_Ransomware_Targets
                  Linux_Systems_in_South_Korea_–_Infosecurity_Magazine [Ed: The
                  issue is not Linux itself. Microsoft-friendly media loves
                  blaming the victims of back doors in Windows, but when it
                  comes to Linux, if the victim uses an awful password, they'll
                  blame "Linux". Bribery leads to inherent biases.]⠀⇛


                # ⚓ Security Affairs ☛ New_Linux_botnet_RapperBot_brute-forces
                  SSH_servers [Ed: This is a password issue, not a "Linux"
                  issue]⠀⇛


                # § Privacy/Surveillance⠀➾


                      # ⚓ Counter Punch ☛ The_Officer_of_the_Future:_Facial
                        Recognition_and_the_Border-Industrial_Complex⠀⇛


                             Sounds like this has the potential to be
                             creepy, right? Well, to set the record
                             straight, House Homeland Security Committee
                             member Clay Higgins (R-LA) argued before
                             Congress in July that it’s just fine, just a
                             matter of convenience.


                             “The image that has been presented to the
                             citizens that we serve is that this is some
                             sort of nefarious technology and big brother
                             is watching you,” the congressman explained.
                             “But really it’s using photographic images
                             that travelers willingly have provided, or
                             are available on their passports or visas, or
                             driver’s licenses. We already have that
                             information.”


          o § Defence/Aggression⠀➾


                # ⚓ The Nation ☛ When_Did_Cars_Become_Weapons_of_the_Right?⠀⇛


                       In the United States during 16 months in 2020 and
                       2021, vehicles rammed into groups of protesters at
                       least 139 times, according to a Boston Globe
                       analysis. Three victims died and at least 100 were
                       injured. Consider that a new level of all-American
                       barbarity, thanks to the growing toxicity of right-
                       wing politics, empowered by its embrace of ever-
                       larger, more menacing vehicles being cranked out by
                       the auto industry.


                # ⚓ Common Dreams ☛ Opinion_|_Hiroshima_and_Ukraine—an
                  Existential_Teachable_Moment⠀⇛


                       77 years ago the U.S. nuclear bombing of Hiroshima,
                       Japan on August 6, 1945 and three days later,
                       Nagasaki, resulted in immediate deaths of
                       approximately 120,000 majority civilians and by
                       year’s end over 210,000. This legacy continues to
                       this day in large part through the voices of the
                       hibakusha, atomic blast survivors, and through
                       having planted the seeds of the first man-made
                       existential threat, nuclear war.


                # ⚓ Common Dreams ☛ ‘Alarming’:_Nearly_1/3_in_US_Worry_About
                  Violence,_Intimidation_at_Polls⠀⇛


                       “This is a shameful failure of our democracy.”


                       That’s what Heidi Beirich, co-founder of the Global
                       Project Against Hate and Extremism (GPAHE), said
                       Thursday in response to survey results that show
                       notable shares of U.S. voters are afraid of
                       encountering intimidation or violence at polling
                       stations.


                # ⚓ Democracy Now ☛ Greenpeace_Warns_of_Twin_Nuclear_Crises_in
                  Ukraine_from_Chernobyl_to_Russian_Military_Control_of
                  Zaporizhzhia_Plant⠀⇛


                       Safety conditions at Ukraine’s Russian-occupied
                       Zaporizhzhia nuclear plant are “completely out of
                       control,” according to the International Atomic
                       Energy Agency. This comes as the Russian military
                       has deployed heavy artillery batteries and laid
                       anti-personnel landmines at the site in recent
                       weeks. “Nuclear plants are extremely vulnerable to
                       external attack in the context of a war zone,” says
                       Shaun Burnie, senior nuclear specialist with
                       Greenpeace, who says something as simple as the
                       loss of power could unleash “massive releases of
                       radioactivity” at rates worse than the Cheronobyl
                       disaster of 1986.


                # ⚓ Democracy Now ☛ Warnings_Grow_over_Nuclear_Annihilation_as
                  Tensions_Escalate_Between_U.S.,_Russia_&_China⠀⇛


                       The U.N. warned this week that humanity is “one
                       miscalculation away from nuclear annihilation” as
                       tensions escalate globally. We speak with Ira
                       Helfand, former president of the International
                       Physicians for the Prevention of Nuclear War, who
                       says the U.N. Security Council permanent members,
                       comprising Russia, China, the U.S., the U.K. and
                       France, are pursuing nuclear policies that are
                       “going to lead to the end of the world that we
                       know.” We also speak with disarmament activist Zia
                       Mian, co-director of Princeton’s Program on Science
                       and Global Security, who says non-nuclear weapon
                       states must pressure other countries to sign onto
                       the 2017 Treaty on the Prohibition of Nuclear
                       Weapons.


                # ⚓ Counter Punch ☛ Summer_1914:_War_Enthusiasm,_Real_and
                  Imaginary⠀⇛


                       In view of this, the upper classes experienced the
                       outbreak of war in 1914 as a deliverance after
                       years of uncertainty, tension, and fear, and they
                       heaved a sigh of relief. The coming of the war,
                       writes Eric Hobsbawm,


                       When he learned the news, the famous Field Marshal
                       Lord Horatio Herbert Kitchener declared laconically
                       that “it is better to have an end of the
                       uncertainty.” And a young Briton “from a good
                       family,” Rupert Brooke, who would later be well
                       known as an antiwar poet, expressed his enthusiasm
                       in these verses:


                # ⚓ Counter Punch ☛ Roaming_Charges:_The_Mad-Eyed_Lady_of_Pac
                  Heights⠀⇛


                       Some may say that Pelosi, now  82, has entered her
                       second childhood. If so, it’s a delinquent one.
                       Certainly her political inhibitions have dissolved,
                       allowing her natural inclination to foment trouble
                       to run rampant. One looks in vain for a rational
                       motivation behind her ad hoc trip to Taiwan, an act
                       of belligerency that might have sparked a war with
                       another nuclear power. But to what end? China is
                       not going to relinquish its entirely legitimate
                       claims to Taiwan. Far from a model democracy,
                       Taiwan is a former gangster state, whose repressive
                       government was shaped by Chiang Kai-Shek, who
                       retreated there in 1949 with his battered gang of
                       CIA-financed KMT thugs, where he promptly
                       instituted a violent crackdown on leftists known as
                       the White Terror, a vicious form of martial law
                       that lasted for the next 45 years.


                       Sure Pelosi represents many rich Chinese exiles,
                       who have made fortunes in San Francisco and now
                       fantasize about sticking it to the CCP from the
                       safety of their Nob Hill mansions. But Pelosi
                       doesn’t need their money or support. She’s well
                       beyond that now. (Though her husband Paul is surely
                       watching with avaricious eyes the reaction of the
                       markets to this junket of the damned.) Pelosi’s
                       trip seems more personal, an almost pathological
                       assertion of her autonomy. It’s the act of a
                       playground bully and the Mad-Eyed Lady from Pac
                       Heights has come to see the world as her
                       playground–provocation for the sake of provocation.
                       Damn the consequences.


                # ⚓ Counter Punch ☛ Nancy_Pelosi’s_Taiwan_Trip:_A_Needless
                  Provocation⠀⇛


                       A Needless Provocation


                       Why did Pelosi go?  She insists she went to
                       demonstrate unwavering support of Taiwan’s
                       democracy and confront China’s imminent threat to
                       Taiwan’s security. “In the face of the Chinese
                       Communist Party’s (CCP) accelerating aggression,”
                       she wrote, “our congressional delegation’s visit
                       should be seen as an unequivocal statement that
                       America stands with Taiwan, our democratic partner,
                       as it defends itself and its freedom.”


                # ⚓ Counter Punch ☛ Beyond_the_Mulish,_Look_to_the_Stars⠀⇛


                       The New York Times columnist Tom Friedman even
                       suggested that her visit could touch off WW3. It’s
                       a measure of the strangeness of political “face”
                       (we denigrate the Chinese preoccupation with
                       “face,” as if our “credibility” did not amount to
                       exactly the same thing) when the diplomatic visit
                       of a lone government official can become the kind
                       of spark that the assassination of Archduke
                       Ferdinand played in setting off WW1. But almost any
                       inadvertency could start WW3, because deterrence,
                       to “work” (until it doesn’t “work” that is)
                       requires hair-trigger preparedness.


                       It’s an outrage, it’s evil, it’s incredibly stupid,
                       and it ought to be illegal under international law.
                       Oh, wait a minute, it is illegal under
                       international law. See the Kellogg-Briand pact
                       against war, in force since 1929; the treaty on
                       Nuclear Weapons Proliferation (NPT), in force since
                       1971; and also the United Nations Treaty on the
                       Prohibition of Nuclear Weapons (TPNW) in the
                       process of being ratified by a majority of the
                       world’s nations and having the force of
                       international law applicable to all since 22
                       January 2021.


                # ⚓ The Nation ☛ Why_Can’t_AIPAC_Defend_Israel?⠀⇛


                       The American Israel Public Affairs Committee
                       (AIPAC) is the most influential, if not the most
                       notorious, pro-Israel lobbying organization. So
                       when it decided last year to start a super PAC and
                       get directly involved in unlimited election
                       giving—something it had not done before—the
                       organization was clearly making a statement. This
                       year it has spent tens of millions on TV ads, but
                       what speaks the loudest is the one thing those ads
                       never mention: Israel.


                # ⚓ Counter Punch ☛ Why_Resistance_Matters:_Palestinians_are
                  Challenging_Israel’s_Unilateralism,_Dominance⠀⇛


                       Now that Israelis are embarking on their fifth
                       election in less than four years, it is important
                       to raise the question: “How do Palestine and the
                       Palestinians factor in Israeli politics?”


                       Israeli politicians and media, even those who are
                       decrying the failure of the ‘peace process’, agree
                       that peace with the Palestinians is no longer a
                       factor, and that Israeli politics almost entirely
                       revolves around Israel’s own socio-economic,
                       political and strategic priorities.


                # ⚓ Counter Punch ☛ Letter_From_Crimea:_Stalin,_Putin_and_the
                  Exile_Tartars⠀⇛


                # ⚓ Counter Punch ☛ Russia_and_the_European_Union_Continue
                  Transition_to_Wartime_Economies⠀⇛


                       With costs mounting, Putin has increasingly
                       promoted the need to fortify the Russian economy’s
                       immediate and long-term position. In April, the
                       head of Russia’s Central Bank, Elvira
                       Nabiullina, stated that the Russian economy would
                       see a “structural transformation” during the second
                       and third quarters this year to offset inflation,
                       supply chain issues, and reduced imports.


                       To alleviate domestic concerns related to the cost
                       of the war, the Kremlin increased the minimum wage
                       and pension payments by 10 percent in May. The
                       initiative also appeared to help muffle any
                       domestic opposition on June 30, when two bills were
                       submitted to the lower house of Russia’s
                       parliament, the Duma, to give the Russian
                       government greater control over the domestic
                       economy.


                # ⚓ Counter Punch ☛ Our_Dangerous_Ally_Could_Drag_us_into_War
                  With_China⠀⇛


                       Apart from brief isolationist periods, the US has
                       been almost perpetually at war.


                       The record is clear. Time and time again we have
                       allowed ourselves to be drawn into the imperial
                       wars of the UK and then the US. We have forfeited
                       our strategic autonomy.


                # ⚓ Counter Punch ☛ Diplomacy,_Not_Weapons,_Will_End_the_War⠀⇛


                       For the outside world, the risk of an expanded war,
                       one that could easily slip into a battle of nukes,
                       must not be discounted.  Putin has made clear that
                       he is ready to use chemical weapons or tactical
                       nukes if needed to avoid a battlefield defeat.


                       Thanks to the inspiring leadership of President
                       Volodymyr Zelensky, the incredible valor of
                       Ukrainian forces and citizen soldiers and timely
                       arms aid from the U.S. and its NATO allies, the
                       Ukrainians were able to repel Russian troops from
                       their February-March advance on Kyiv. President
                       Biden led a concerted NATO effort to contain the
                       Russians through weapons transfers and economic
                       sanctions.


                # ⚓ Counter Punch ☛ Why_January_6_Means_More_to_Washington_than
                  It_Does_to_America⠀⇛


                       Once again, they’re all just a bunch of lazy slack-
                       jawed hicks who can’t be coaxed off their tractors
                       to bother with the greatest threat to liberal
                       democracy since Hitler wore lederhosen. Just like
                       those lazy peasants who dare not vote, the rural
                       lumpenproletariat are just genetically pre-
                       dispositioned to be indifferent to what really
                       matters in this world and trust me when I tell you
                       that many of my neighbors are equally mystified and
                       annoyed by these condescending coastal elites who
                       keep trying to sell them tickets to Washington’s
                       biggest monster truck rally since Watergate.


                       As a genderqueer anarchist who has spent the better
                       part of her life being chased by irate farm folk
                       with rusty pitchforks and the other part trying to
                       convince these same people to turn their rage
                       against Washington instead from the comfort of my
                       flaming windmill, I feel that I am somewhat
                       absurdly equipped to explain both of these crowds
                       of assholes in this stand-off to each other, seeing
                       as I’m pretty much equally despised by both of
                       them.


          o § Environment⠀➾


                # ⚓ Common Dreams ☛ Green_Critics_Say_Manchin_Side_Deal_Equals
                  ‘Climate_Disaster’⠀⇛


                       The so-called “side deal” negotiated by Sen. Joe
                       Manchin and the Democratic leadership faced growing
                       backlash from climate organizations on Thursday
                       after a draft copy of the legislation confirmed
                       that the proposal would help accelerate approval of
                       fossil fuel projects, potentially including a
                       fracked gas pipeline running through West Virginia.


                       “This should no longer be considered a ‘side deal,’
                       it is the main event for fossil fuel polluters.”


                # § Energy⠀➾


                      # ⚓ Common Dreams ☛ Applause_as_Court_Rejects_Trump-Era
                        Coal_Plan_Defended_by_Biden_Administration⠀⇛


                             Environmentalists celebrated Thursday after a
                             federal court rejected a pair of U.S. Bureau
                             of Land Management coal mining plans that
                             were drawn up during the Trump presidency and
                             defended in legal proceedings by the Biden
                             administration.


                             “This ruling is a shameful confirmation that
                             the Biden administration has no real interest
                             in defending public lands or the climate,”
                             said Jeremy Nichols, Climate and Energy
                             Program director for WildEarth Guardians.
                             “Thankfully the courts are upholding law and
                             science, but it’s sad that President Biden is
                             allowing his administration to undermine his
                             promises to protect our health and our
                             climate.”


                      # ⚓ [Old] Renewables_are_not_THE_solution_|_Stop_at_Zona-
                        M⠀⇛


                             “Solar panels on every surface” seems like an
                             easy fix as long as you don’t look too
                             closely at the processes involved. Solar
                             electric panels are great at generating
                             electricity. That is not the issue though.
                             What [many places] need is heat. And solar
                             electric panels are just shy of useless in
                             heat generation.


                # § Wildlife/Nature⠀➾


                      # ⚓ Pro Publica ☛ How_a_Federal_Agency_Is_Contributing_to
                        Salmon’s_Decline_in_the_Northwest⠀⇛


                             Crystal Conant was camped for the night on a
                             bluff overlooking the upper Columbia River in
                             northeast Washington, beading necklaces by
                             the glow of a lantern.


                             The next morning, hundreds would gather at
                             Kettle Falls for the annual salmon ceremony,
                             held since time immemorial to celebrate the
                             year’s first fish returning from the ocean.
                             Conant and fellow organizers needed necklaces
                             for everyone who would come. Honoring the
                             gift of salmon, she said, requires giving
                             gifts in turn.


                      # ⚓ USF_professor_discovers_new_species_while_part_of
                        team_studying_impact_of_oil_spills_in_the_Gulf_of
                        Mexico⠀⇛


                             Even after teaching biology for nearly three
                             decades, Heather Judkins still gets excited
                             about conducting field research. An associate
                             professor of Integrative Biology on the USF
                             St. Petersburg campus, Judkins will continue
                             her studies of cephalopods, such as octopus
                             and squid, on July 26 as part of a team of
                             scientists aboard the R/V Point Sur for a 12-
                             day research cruise around the Gulf of
                             Mexico.
                             The goal of the cruise is to identify and
                             quantify long-term trends in fishes,
                             crustaceans and cephalopods in the midwaters
                             of the Gulf in response to the Deepwater
                             Horizon oil spill that occurred in 2010.
                             “We’re collecting specimens and looking at
                             the biodiversity in that area and how it
                             changes over time,” Judkins said. “We want to
                             know what we could see in the future, in the
                             unfortunate event of another oil spill.”


          o § Finance⠀➾


                # ⚓ Counter Punch ☛ The_Rise_of_Monster_Donor-Advised_Funds⠀⇛


                # ⚓ Counter Punch ☛ The_Proposed_Wealth_Tax_on_Colombia’s_4,700
                  Richest_People_Would_Raise_$1_Billion⠀⇛


                       It is an unprecedented sum of money for the
                       Colombian state, but the coalition that makes up
                       the Pacto Histórico considers it a necessary
                       measure to address both the fiscal deficit that
                       ballooned under former President Iván Duque and to
                       finance the proposed social programs designed to
                       alleviate poverty and reduce economic inequality.


                       While the bill is yet to be finalized, a
                       progressive wealth tax on the nation’s millionaires
                       and billionaires will be a core feature.


                # ⚓ [Old] On_the,_er…_limits_of_tiny_houses_|_Stop_at_Zona-M⠀⇛


                       Tiny houses and electric cars have been co-opted by
                       lifestyle salesmen, so save your money or put it
                       toward causes that can help instead, like
                       libraries, homeless shelters, and expanding mass
                       transit


                # ⚓ [Old] Your_cautionary_tale_before_purchasing_any_“smart
                  home”_stuff_|_Stop_at_Zona-M⠀⇛


                       This Christmas, give “smart home” gadgets as gift
                       only to people you do NOT care about, and only if
                       you really, really can’t find anything better (or
                       as a way to get rid of smart gadgets that someone
                       else dumped on you).


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ The Nation ☛ Hangers-On⠀⇛


                # ⚓ Counter Punch ☛ How_the_Elites_Use_Identity_Politics_to
                  Wage_Class_War⠀⇛


                       So everyone got riled up about identity politics,
                       while the one identity never mentioned, and
                       possibly the most important, though assiduously
                       elided in the public sphere, is class identity.
                       Both political parties ignored working people’s
                       economic concerns, to the delight of their mega-
                       corporate donors. The public’s desire for single-
                       payer health care, increased minimum wage,
                       affordable higher education, decent infrastructure,
                       an end to foreign military adventures and other
                       such social benefits couldn’t be ditched fast
                       enough by Dems and a GOP both utterly beholden to
                       Big Money.


                       The role of identity politics in any sane attempt
                       to fight back against the power of obscene wealth
                       is discussed in Elite Capture, a new book by
                       Olufemi Taiwo. It asks at the outset, what is
                       identity politics? It is, according to Dominic
                       Gustavo at the World Socialist Web Site and quoted
                       by Taiwo, “an essential tool utilized by the
                       bourgeoisie to maintain its class domination over
                       the working class by keeping workers divided along
                       racial and gender lines.” Hard to argue with that.
                       But then alternatively, Taiwo asks, is identity
                       politics “as embodied in critical race theory, a
                       dangerous ideology and threat to the established
                       order that the powers that be aim to stamp out?”


                # ⚓ Counter Punch ☛ How_Social_Media_Helped_Fuel_the_Rise_of
                  White_Nationalism⠀⇛


                       Evidence is mounting that white nationalist groups
                       who want to establish an all-white state played a
                       significant role in the violent attack on the U.S.
                       Capitol that left five dead and dozens wounded.


                       Thus far, the hearings “have documented how the
                       Proud Boys helped lead the insurrectionist mob into
                       the U.S. Capitol building in Washington, D.C,”
                       journalist James Risen wrote in the Intercept.


                # ⚓ Counter Punch ☛ Memo_to_Michigan_Governor_Gretchen
                  Whitmer⠀⇛


                       In mid- March 2020 when the big pro and college
                       basketball and hockey leagues canceled their
                       tournaments (essentially leaderless under Trump’s
                       reality TV misgovernment), Americans generally
                       started to physically or ‘socially’ distance,
                       shelter, and restrict contacts for public health
                       reasons.


                       State governments stepped into the leadership
                       vacuum left by federal covid dereliction.  The
                       ‘reopen’ backlash that the governor’s opponent now
                       says she will campaign on started immediately.


                # ⚓ The Nation ☛ The_Religious_Right-Wingers_Working_to_Run
                  Ohio⠀⇛


                       Over the past few months, Republicans in
                       statehouses across the country have been working
                       diligently to curtail their constituents’ civil
                       rights. After Florida’s infamous “Don’t Say Gay”
                       bill was signed by Governor Ron DeSantis in March,
                       public school teachers have been banned from
                       discussing sexual orientation and gender in the
                       classroom unless it is deemed “age appropriate or
                       developmentally appropriate.” One school district
                       reportedly warned teachers not to wear rainbow-
                       colored clothing.


                # ⚓ Common Dreams ☛ Opinion_|_Drunk_on_Power:_The_Neo-Liberal
                  Capture_of_the_South_African_Mediascape_by_the_US_State
                  Department⠀⇛


                       An old fish swims by a young fish, and in passing,
                       comments, “Good morning youngster. How’s the water
                       today?”


                # ⚓ Pro Publica ☛ The_Fed_Keeps_Getting_More_Powerful._Is_It
                  Bad_for_America?⠀⇛


                       Law professor Lev Menand has a new book out on that
                       strange institution, the Federal Reserve, what it
                       does and how its power and responsibility have
                       grown over time.


                       Menand is an associate professor at Columbia Law
                       School specializing in finance and regulation.
                       Before he joined the law school, he held various
                       roles at the Treasury Department during the Obama
                       administration and was an economist at the Federal
                       Reserve Bank of New York, helping to oversee large
                       lenders.


                # ⚓ Democracy Now ☛ Hungary_PM_Viktor_Orbán_Addresses_CPAC_as
                  American_Right_Embraces_His_Authoritarian_Rule⠀⇛


                       We speak with international affairs scholar Kim
                       Lane Scheppele on the rise and fall of Hungary’s
                       constitutional democracy and how Prime Minister
                       Viktor Orbán has gained popularity among the
                       American right ahead of his speech today at the
                       Conservative Political Action Conference. “Orbán
                       presents, especially for the American right, a kind
                       of irresistible combination of culture war issues,”
                       says Scheppele. “These culture war issues in
                       Hungary disguise the fact that underneath the
                       surface Orbán has been changing the laws of the
                       country so that gradually he has shut down all of
                       the independent institutions that might tell him
                       no.” She says U.S. Republicans are now engaging in
                       a very “Orbán-like” campaign to rig elections so
                       they win regardless of the popular vote.


                # ⚓ Counter Punch ☛ Elite_Lapdogs_Always_Welcome_in_the
                  Corporate_Media⠀⇛


                       Cuomo’s appearances – both of which were with close
                       friends, Maher and Abrams – were clearly an attempt
                       to rebrand himself from unethical propagandist to
                       fearless journalist. Cuomo explained that he was an
                       optimistic person who was not bitter about what had
                       happened at CNN. Looking back on his departure from
                       CNN he said “I feel like I lost a sense of purpose
                       for a while because of how things ended.” Cuomo’s
                       recollection concealed that he was clearly bitter,
                       so much so that he threatened a lawsuit against CNN
                       and demanded $125 million in restitution for the
                       damages to his reputation.


                       Nonetheless, Cuomo claimed that he wanted to serve
                       the American people with his podcast and broadcast
                       program by breaking the hyper-partisan frame used
                       in most reporting. This is rich coming from someone
                       whose success is owed to a CNN program that
                       preached to the Democratic Party choir by ritually
                       lampooning Trump.


                # ⚓ Meduza ☛ ‘Standing_up_for_the_oppressed’:_The_Kremlin’s
                  newest_propaganda_guide_suggests_likening_Russia’s_invasion
                  of_Ukraine_to_the_First_World_War_—_Meduza⠀⇛


                       Story by Andrey Pertsev. Translation by Sam
                       Breazeale.


          o § Censorship/Free Speech⠀➾


                # ⚓ Techdirt ☛ Nick_Sandmann,_Who_We_Were_Told_Would_Be_Rich
                  Beyond_Belief_From_All_The_Media_Companies_He_Sued,_Loses
                  Basically_All_Of_His_Cases⠀⇛


                       A while back, we noted that there was something of
                       a Rorschach test in how you viewed basically
                       everything about Nick Sandmann, the MAGA-hat
                       wearing high school student who became front page
                       news after a video of him standing in front of a
                       Native American demonstrator, Nathan Phillips, went
                       viral. Everyone had their own interpretations.
                       Context was often lacking. People’s personal
                       beliefs may have clouded their own interpretations
                       — across the board. But, as we noted, people’s own
                       interpretations of what they saw… just is not
                       defamatory. But Nick Sandmann sued anyway. He sued
                       a whole bunch of media companies. And his fans
                       (generally those in the Trump world), insisted he
                       was going to end up owning these companies.


                # ⚓ Techdirt ☛ Philippines_Legislator_Offers_Up_Bill_That_Would
                  Criminalize_‘Ghosting’⠀⇛


                       Real problems are what legislators are supposed to
                       be solving. The Philippines has plenty of those,
                       ranging from (government-endorsed) extrajudicial
                       killings of drug dealers and drug users to abuses
                       of state power to silence journalists to the actual
                       murders of human rights activists.


                # ⚓ Techdirt ☛ Please_Don’t_Normalize_Copyright_As_A_Tool_For
                  Censorship⠀⇛


                       Yes, yes, copyright is a tool for censorship.
                       Contrary to the claims of copyright system
                       supporters that copyright can’t be used for
                       censorship, the reality is that is basically the
                       only thing that copyright is good for. I mean, at
                       this point, you are either not paying attention, or
                       are just outright lying if you claim that copyright
                       isn’t regularly used to silence people. I could go
                       on linking to examples, but you get the point.


                # ⚓ Techdirt ☛ Thanks_To_Automated_Copyright_Claims_And_A
                  Troll,_Infamous_CounterStrike_Clip_Gets_A_DMCA_Takedown⠀⇛


                       At this point, every reader here should be aware
                       that YouTube has a copyright/DMCA problem it has
                       yet to solve. Going through the myriad of posts
                       we’ve done about DMCA and ContentID takedowns on
                       YouTube, the theme is abundantly clear: YouTube’s
                       automated systems are wide open for mistakes,
                       fraud, and abuse. If you don’t think that’s the
                       case, you aren’t paying attention. This is
                       especially illuminated when either very obviously
                       non-infringing clips get taken down via DMCA
                       notice, or when super famous clips that have been
                       around forever are suddenly hit with a DMCA notice
                       and get taken down.


                # ⚓ Meduza ☛ Blacklisted_Russia_has_declared_12_organizations
                  ‘undesirable’_so_far_this_year._Here’s_what_you_need_to_know
                  about_their_work._—_Meduza⠀⇛


                       Since January, the Russian Attorney General’s
                       Office has declared 12 organizations “undesirable,”
                       on the grounds that they pose a threat to national
                       security. The number of organizations that Russia
                       deems “undesirable” grows with each passing year
                       and at this rate 2022 is also poised to see a new
                       record. Meduza sums up what you need to know about
                       the organizations blacklisted so far this year. 


          o § Civil Rights/Policing⠀➾


                # ⚓ Counter Punch ☛ What_Does_It_Mean_to_Say_You’re_Sorry?_On
                  Pope_Francis’s_Visit_to_Canada⠀⇛


                       Seated in a wheelchair in a small town outside
                       Edmonton, Pope Francis explained the reasons for
                       his visit before directly apologizing for the
                       Church’s past sins: “I have come to your native
                       lands to tell you in person of my sorrow, to
                       implore God’s forgiveness, healing and
                       reconciliation, to express my closeness and to pray
                       with you and for you. I humbly beg forgiveness for
                       the evil committed by so many Christians against
                       the Indigenous peoples.” The words were deeply felt
                       by many. Several Indigenous Canadians were shown
                       wiping away tears while the Pontiff spoke.


                       In a similar moral situation, and after years of
                       hesitancy by the institution, the International
                       Committee of the Red Cross’s (ICRC) President,
                       Cornelio Sommaruga, expressed moral failure for his
                       humanitarian organization’s lack of action during
                       World War II. At the annual ICRC press conference
                       in 1995, referring to the 50th anniversary of the
                       end of World War II, he said: “But believe me,
                       every moment spent today on our humanitarian
                       responsibilities to assist the victims of war and
                       political violence reminds me of our institution’s
                       moral failure with regard to the Holocaust, since
                       it did not succeed in moving beyond the limited
                       legal framework established by the States. Today’s
                       ICRC can only regret the possible omissions and
                       errors of the past.” Sommaruga expressed similar
                       regret when he took part in the 1995 ceremony to
                       commemorate the liberation of the concentration
                       camp at Auschwitz.


                # ⚓ Counter Punch ☛ Kansas_Trusted_Women⠀⇛


                # ⚓ Counter Punch ☛ Let’s_Be_Frank_About_Kansas⠀⇛


                       Believe it or not this move was consistent with the
                       postmodern post-Marxist post-left turn by the very
                       intellectuals people see as elite. When it comes to
                       intellectuals I am hesitant to call them elite as
                       most trendy intellectuals like to do. If as Adorno
                       says the radical part of art is its uselessness the
                       same is true for ideas. If one can create ideas
                       rather than materials that seems to be a good thing
                       in a world where materials are destroying our
                       ability to subsist.


                       My turn against the so-called populist left has
                       earned me a lot of righteous finger wagging from
                       elitist anti-intellectuals but it is a popular idea
                       amongst people. The crude attempt to reclaim class-
                       first leftism from post-Marxist intellectuals has
                       only furthered the alienation most people feel from
                       the left.


                # ⚓ Counter Punch ☛ Anti-Abortion_and_the_Lives_of_Children:_A
                  Freudian’s_Perspective⠀⇛


                       The question here is whether there is something
                       unique about anti-abortionists as distinct from
                       people espousing other reactionary causes,
                       expressed in their preoccupation with the life of
                       the unborn and their disconnect or indifference to
                       the death of born children worldwide and to the
                       death of pregnant mothers. This dichotomy about
                       life and death in anti-abortionists’ behavior is
                       extremely stark as there is so much publicized
                       about the needless and preventable cruelty and
                       killing of children in the world today. I would
                       even argue that historically, the present so-called
                       liberal democracies are unprecedented in
                       sanctioning cruelty, killing, and psychological
                       unawareness of children.


                       Sibling rivalry is expressed in everyday life, in
                       the stories of Cain and Abel and Joseph and his
                       brothers, and in the clinical literature. Freud
                       interpreted Goethe’s one single memory from his
                       ‘earliest years of childhood’ as an expression of
                       sibling rivalry: Goethe remembered that he was
                       ‘overjoyed’ to hurl every little dish, cooking-pot
                       and pan out the window and smash them to bits after
                       the birth of a brother when he was not yet four.
                       Freud had a patient who brought out the proximity
                       in his life of the birth of a brother and the
                       memory of flinging objects out the window, and
                       other analysts relayed to Freud the same sequence,
                       of their patients’ throwing things out the window
                       right after the birth of a sibling. Freud commented
                       that “the new baby must be got rid of – through the
                       window, perhaps because he came in through the
                       window.” In everyday life, it is not uncommon for
                       parents to mitigate or try to eliminate any anger
                       and resentment by the pretense of providing the
                       older child with a gift supposedly from the newborn
                       infant as if to say that the new baby is not taking
                       anything away but giving a present. Parents’ own
                       ambivalent sibling feelings are apparent when they
                       do not see and do not protect the younger sibling
                       from many expressions of hostility. This is
                       painfully represented in contemporary novelist
                       Sally Rooney’s Normal People depicting a brother’s
                       murderous behavior towards his sister with the
                       collusion of their mother.


                # ⚓ Techdirt ☛ Federal_Judge_Places_County_Jail_Into
                  Receivership_After_County_Fails_To_Comply_With_Consent
                  Decree⠀⇛


                       In an extremely rare move, a federal court has
                       ordered a jail into receivership, placing it under
                       the direct control of a court-appointed third party
                       that will (hopefully) carry out the needed changes
                       Hinds County, Mississippi either can’t or won’t do.
                       (h/t Scott Greenfield)


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ Techdirt ☛ Tech_Giants_Urge_FCC_To_Raise_Pathetic_U.S.
                  Definition_Of_‘Broadband’_To_1_Gigabit⠀⇛


                       INCOMPAS, the DC trade policy and lobbying group
                       primarily steered by tech giants, is urging the FCC
                       to finally boost the U.S.’ pathetic definition of
                       broadband. The FCC’s current definition of
                       broadband, 25 Mbps down, 3 Mbps up, is looking a
                       bit pathetic, particularly on the upstream side.
                       And the lower standard helps the uncompetitive
                       telecom sector obscure its failure to broadly
                       deliver next-gen speeds.


                # ⚓ Techdirt ☛ Google_Fiber’s_2016_Expansion_Freeze_May_Be
                  Coming_To_An_End⠀⇛


                       When Google Fiber launched back in 2010, it was
                       heralded as a game changer for the broadband
                       industry. Google Fiber, we were told, would
                       revolutionize the industry by taking Silicon Valley
                       money and disrupting the viciously uncompetitive
                       and anti-competitive telecom sector.


          o § Monopolies⠀➾


                # ⚓ Krebs On Security ☛ Scammers_Sent_Uber_to_Take_Elderly_Lady
                  to_the_Bank⠀⇛


    * § Gemini* and Gopher⠀➾


          o § Personal⠀➾


                # ⚓ 🛌⠀⇛


                       When I have good dreams I wake disappointed that
                       they aren’t my reality.
                       When I have bad dreams I wake shaken from the night
                       of torment.


                # ⚓ Hell_Week⠀⇛


                       It was bound to happen sooner or later. But the
                       timing really does suck.


                       I started hearing a clanging noise from my truck a
                       couple of months ago, very intermittently.
                       Something like the sound of an exhaust pipe just
                       starting to drag on the ground. Sometimes followed
                       by other noises, which sounded like bearing noise
                       of some sort. I haven’t been able to track it down.


                       Money is, of course, a critical concern right now.
                       In our post-Covid economy, our once just adequate
                       incomes have turned into a slow backpedal and
                       decline. So taking it somewhere to have an expert
                       work on it was out of the question. It’s heart
                       wrenching seeing everything that you’ve worked for
                       slowly slip away.


                # ⚓ Rewards_in_a_small_world⠀⇛


                       I was picking up on the idea of a sort of exchange
                       taking place as I was considering what a
                       “contributive economy” might be in light of Marcia
                       B.’s criticism of the commercialisation of the
                       role-playing games hobby…


          o § Technical⠀➾


                # ⚓ Short_impressions_of_Lubuntu_and_Regolith_Linux⠀⇛


                       I have been using Ubuntu on my laptop for the past
                       4 years. At first for window managers I had Unity,
                       then Gnome 3. Later I became interested in a tiling
                       window manager. I tried a few out but settled on i3
                       after some time figuring out how to configure it
                       for Dvorak. Like someone’s Vim dotfiles, it’s easy
                       to get stuck in a continuous never-complete
                       reconfiguring of one’s setup. I added the ability
                       to change volume, change brightness, jump to
                       different workscreen setups, etc etc. But I always
                       had little bugs that would creep in. Probably a
                       result of my particular combo of fish shell,
                       Dvorak, i3, and my audio setups.


                       About 6 months ago I stumbled across RegolithOS,
                       which bills itself as Ubuntu with i3 preconfigured.
                       Surely I didn’t need that, I thought. But oh, what
                       the heck, it looks nice in screenshots. Should I
                       try it?


                       It’s an easy install on top of Ubuntu. And I wanted
                       to update my (for shame) old Ubuntu 18.04 LTS to
                       something more recent, to 20 or 22. So I backed up
                       my computer, then updated to 20, then to 22.04 and
                       then Regolith’s add-ons. Oh, what the heck, if it
                       brakes, it will brake fabulously I thought.


                # ⚓ Solving_a_bad_ARP_behavior_on_a_Linux_router⠀⇛


                       So, I recently switched my home router to Linux but
                       had a network issues for devices that would get/
                       renew their IP with DHCP. They were obtaining an
                       IP, but they couldn’t reach the router before a
                       while (between 5 seconds to a few minutes), which
                       was very annoying and unreliable.


                # ⚓ Fair_Internet_bandwidth_management_on_a_network_using
                  Linux⠀⇛


                       A while ago I wrote an OpenBSD guide to fairly
                       share the Internet bandwidth to the LAN network, it
                       was more or less working. Now I switched my router
                       to Linux, I wanted to achieve the same.
                       Unfortunately, it’s not really documented as well
                       as on OpenBSD.


                       The command needed for this job is “tc”, acronym
                       for Traffic Control, the Jack of all trades when it
                       comes to manipulate your network traffic. It can
                       add delays or packets lost (this is fun when you
                       want to simulate poor conditions), but also traffic
                       shaping and Quality of Service (QoS).


                # ⚓ Snow_Crash_–_Metaverses_and_Viral_Culture⠀⇛


                       Snow Crash – A book by Neal Stephenson, published
                       in 1992.


                       In 2021, the book came back into vogue following
                       Facebook’s announcement that they were changing
                       their name to Meta and aiming to develop a
                       metaverse. The concept of a metaverse first appears
                       in /Snow Crash/.


                       After actually reading the book, I find the link
                       between Facebook and Snow Crash even more ironic
                       than most journalists point out. Usually, it’s the
                       case that Zukerberg’s vision of a metaverse is
                       contrasted strongly with Stephenson’s.


                       However, the most relevant part of the book with
                       regard to Facebook, for me, is its theme of ‘viral
                       language’.


                       The theme/theory is elaborated quite a bit in the
                       book, so I won’t try to cover it too much
                       (actually, much of the theory it is a tad facile. I
                       have to say I enjoyed /Cryptonomicon/ a lot more
                       than this book).


                # § Programming⠀➾


                      # ⚓ C++20_is_pretty_good⠀⇛


                             I’ve upgraded to gcc v12, which has the C++
                             standard in it, although it’s not fully
                             compliant. Too bad it doesn’t have “format
                             ()”, for example. There’s some nice stuff in
                             C++20, and I’ve barely scraped the surface of
                             what it can do. It is clear that some people
                             have a deep understanding of C++. Perhaps I’d
                             consider myself a journeyman in C++. I no
                             longer work in industry, but I guess I’m
                             around average in terms of knowledge. I think
                             most programmers are well below mastery
                             level, mostly banging out code that works.
                             And that suffices. Google and Facebook are
                             not going to be knocking on my door any day,
                             although curiously some time ago I did have
                             someone *claiming* to be from Google say they
                             were interested in interviewing me. I didn’t
                             take them up on their offer. I’m not
                             interested in joining the Cult Of Google, and
                             I’m confident that they wouldn’t have me as a
                             member, either. But I digress …


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



                    ䷩ 𝚕𝚒𝚗𝚎 5430

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 08.05.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_05/08/2022:_KIO_Admin,_GitLab’s_Betrayal⠀✐


Posted in News_Roundup at 2:31 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Audiocasts/Shows
          o Instructionals/Technical
          o Desktop_Environments/WMs
                # K_Desktop_Environment/KDE_SC/Qt
                # GNOME_Desktop/GTK
    * Distributions_and_Operating_Systems
          o PCLinuxOS/Mageia/Mandriva/OpenMandriva_Family
          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 Events
          o Programming/Development
                # Python
                # Java
    * Leftovers
          o Security
          o Finance
          o Censorship/Free_Speech
    * Gemini*_and_Gopher
          o Technical
                # Misc.
                # Programming
    * § GNU/Linux⠀➾


          o ⚓ Barry Kauler ☛ Problem_with_Limine_on_Fujitsu_laptop_may_be
            fixed⠀⇛


                 The laptop is a Fujitsu Futro MA574, and I read somewhere
                 that it has 32-bit Windows. From other reading, it seems
                 that 32-bit Windows must have 32-bit UEFI.


                 Unlike Linux, that can run 64-bit Linux on a 32-bit UEFI,
                 as long as the kernel has “CONFIG_EFI_MIXED” set.


          o § Audiocasts/Shows⠀➾


                # ⚓ Video ☛ How_to_install_Linux_Mint_21_Cinnamon_–_Invidious⠀⇛


                       In this video, I am going to show how to install
                       Linux Mint 21 Cinnamon.


                # ⚓ Video ☛ Google’s_Linux_distro,_Linux_on_M2_macs,_and
                  Material_You_for_GNOME_–_Linux_and_Open_Source_news_–
                  Invidious⠀⇛


                # ⚓ Linux Made Simple ☛ Peppermint_OS_08-02-2022⠀⇛


                       Today we are looking at Peppermint OS 08-02-2022.
                       It is based on Devuan 11, Linux Kernel 5.10, XFCE
                       4.16, and uses about 700MB of ram when idling.


                # ⚓ Video ☛ Peppermint_OS_08-02-2022_Run_Through_–_Invidious⠀⇛


                       In this video, we are looking at Peppermint OS 08-
                       02-2022.


                # ⚓ Video ☛ Fedora_No_Longer_Accepts_This_As_A_FOSS_Licence_–
                  Invidious⠀⇛


                       There has been debate about Creative Commons 0 for
                       quite a while on whether it’s actually good to use
                       as a software licence and recently Fedora made the
                       decision that it’s not but what do you think


          o § Instructionals/Technical⠀➾


                # ⚓ HowTo Forge ☛ Install_WildFly_with_Nginx_Reverse_Proxy_on
                  Rocky_Linux_8⠀⇛


                       WildFly is an open-source and cross-platform
                       application server developed by RedHat. Learn how
                       to install Wildfly with Nginx as a reverse proxy on
                       Rocky Linux 8.


                # ⚓ Linux Hint ☛ Share_Raspberry_Pi_Terminal_–_Install_GoTTY⠀⇛


                       GoTTY is a lightweight Go language-based command-
                       line application that enables Raspberry Pi users to
                       access and control the device terminal on their
                       browsers. It turns your CLI tools into a web
                       application, thus allowing you to see your
                       Raspberry Pi terminal using the IP address of your
                       device. It’s useful when someone wants to access
                       your device terminal to work on a project.


                # ⚓ Linux Hint ☛ How_to_Install_and_Use_the_bottom_Command_on
                  Raspberry_Pi_for_System_Monitoring⠀⇛


                       The bottom command is an open-source command-line
                       utility that enables Linux users to monitor the
                       performance of their systems, such as CPU
                       resources, system temperature, memory information,
                       network resources and much more. Since this tool
                       supports both Linux and ARM-based architecture,
                       thus you can install it on your Raspberry Pi to
                       monitor your device performance.


                       This article shows you the most straightforward
                       approach to install the bottom command on Raspberry
                       Pi to monitor your system performance.


                # ⚓ Linux Hint ☛ How_to_Test_Speed_of_Raspberry_Pi_SD_Card⠀⇛


                       The SD is the backbone of your Raspberry Pi device
                       because, without it, you won’t be able to use an
                       operating system on your device. The reason is that
                       most operating systems don’t support USB boot on
                       your Raspberry Pi device. Thus, having a good-speed
                       SD card is necessary for the users to enjoy a
                       smooth desktop environment. If you somehow purchase
                       an SD card for your Raspberry Pi device and you
                       don’t have information about whether the card is
                       good enough for a smooth desktop experience, you
                       should need to perform an SD card test.


                       This article provides a way to determine your
                       Raspberry Pi card speed, as this will help you
                       continue with the current SD card or purchase a new
                       one for your device.


                # ⚓ Barry Kauler ☛ More_tutorial_pages_updated⠀⇛


                # ⚓ Linux Hint ☛ Redis_ZREM⠀⇛


                       Redis sorted sets store unique elements in an
                       ordered manner. Hence, it can be used in low
                       latency applications such as priority queues, real-
                       time leaderboards, secondary indexing, etc. Each of
                       these set elements is assigned a rank and placed in
                       ascending order based on the score value. Several
                       commands are available to add, update, and remove
                       the sorted set members efficiently. The most
                       important thing about sorted sets is that after the
                       addition or removal of a set member, it still
                       manages to maintain the member ranks and order.


                # ⚓ Linux Hint ☛ Redis_BRPOP⠀⇛


                       The list is a popular Redis data type that stores a
                       sequence of strings based on the insertion order.
                       One list can hold more than 4 billion elements. The
                       unique fact about the Redis list is it maintains
                       the HEAD and TAIL properties where the elements can
                       be inserted from both sides. Usually, the LPUSH and
                       RPUSH commands are used to insert the elements into
                       a list. Meanwhile, the brand new list is created
                       with the specified key. All the list commands
                       behave the same way where a new list is created
                       when passed with a non-existing key.


                # ⚓ Analyze_PCAP_Files_using_Malcolm_Network_Traffic_Analysis
                  tool_–_kifarunix.com⠀⇛


                       In this tutorial, you will learn how to analyze
                       PCAP files using Malcolm network traffic analysis
                       tool. Malcolm can be used to analyze offline full
                       PCAP files or can be used to monitor and analyze
                       live network traffic. Malcolm is integrated with
                       Suricata and Zeek (formerly Bro). These two tools
                       can be used to analyze PCAP files.


                # ⚓ Make Use Of ☛ How_to_Install_the_Opera_Web_Browser_on
                  Linux⠀⇛


                       Opera is a renowned web browser used by millions of
                       users worldwide. Here’s how to install it on your
                       Linux machine.


                       While most Linux distributions come with Firefox,
                       every major web browser now has a Linux
                       version—even Microsoft’s own Edge. With Chromium-
                       based browsers becoming the web’s de facto default,
                       Linux users may need one to supplement Firefox.


                       Opera is a great Chromium-based alternative, and
                       it’s been around even longer than Firefox. It
                       includes modern staples like sync and ad-blocking,
                       plus VPN and a crypto wallet. The unique Workspaces
                       feature, which brings virtual desktop-like
                       organization to your web browser, is truly a
                       killer.


                # ⚓ Make Use Of ☛ How_to_Use_FFmpeg_Commands_for_Audio_and
                  Video_Processing_on_Linux⠀⇛


                       Almost anyone who deals with videos may have heard
                       of FFmpeg before. For those who are unfamiliar,
                       FFmpeg is a free and open-source program that can
                       convert any video format to another and alter its
                       codecs.


                       FFmpeg supports nearly all audio/video codecs
                       (H.264, H.265, VP8, VP9, AAC, OPUS, and more), file
                       formats (MP4, FLV, MKV, TS, WEBM, MP3, etc.), and
                       even streaming protocols (HTTP, RTMP, RTSP, HLS,
                       etc.).


                       Here’s how you can install and use FFmpeg to
                       process audio and video files on Linux.


                # ⚓ H2S Media ☛ Install_PostgreSQL_pgAdmin_4_on_Ubuntu_22.04
                  LTS_Jammy_Linux⠀⇛


                       Learn the commands to install – the PostgreSQL GUI
                       interface pgAdmin 4 tools on Ubuntu 22.04 LTS Jammy
                       JellyFish Linux to manage Databases using a web-
                       based graphical user interface.


                       Just like popular phpMyAdmin to graphically manage
                       MySQL or MariaDB databases, here we have pgAdmin.
                       It is also a free and open source software to
                       provide a graphical interface to develop and
                       administrators of PostgreSQL databases. The open
                       source license of pgAdmin is inherited from the
                       PostgreSQL project. pgAdmin runs on Windows, Linux,
                       macOS, and other Unix derivatives.


                       However, unlike Linux pgAdmin on Windows and macOS
                       can easily be installed to manage remote or local
                       running PostgreSQL.


                       Well, that pgAdmin offers two types of installation
                       one is Desktop Deployment and other Server
                       Deployment.


                # ⚓ UNIX Cop ☛ How_to_install_GLPI_on_Ubuntu_22.04⠀⇛


                       In this post, we will show you how to install GLPI
                       on Ubuntu 22.04.


                       GLPI is a web application that allows us to deploy
                       a fleet management system. It has also evolved and
                       with it, you can also manage hardware, software,
                       and data centers by linking the asset inventory to
                       the helpdesk.


                       Let’s get started.


                # ⚓ PC Linux ☛ Inkscape_Tutorial:_Create_A_Magnifying_Effect⠀⇛


                       Here’s a neat effect that I saw at goinkscape.com.
                       It uses clipart of a magnifying glass and an object
                       of your choice. I’m using a red crayon.


                # ⚓ PC Linux ☛ Watching_Live_OTA_TV_With_MPlayer⠀⇛


                       Last month, I took you through how to set up VLC to
                       watch live, OTA (over the air) broadcasts via a USB
                       TV tuner. This month, let’s take a look at how to
                       do the same with MPlayer.


                       MPlayer is one POWERFUL multimedia powerhouse
                       program. Did I mention that it was powerful? As
                       with anything that wields that much power, it can
                       sometimes present a level of complexity that is
                       daunting, as it strives to cover as many multimedia
                       bases as it can. In fact, MPlayer will often play
                       files that other multimedia programs simply shrug
                       at.


                       MPlayer is a multiplatform program, with versions
                       for Linux, MacOS, and Windows. MPlayer is also
                       “desktop agnostic” That means that it doesn’t use
                       either the Qt or GTK+ programming toolkits, opting
                       instead for good, sound code that runs equally well
                       regardless of which programming toolkit is
                       employed.


                # ⚓ HowTo Geek ☛ How_to_Use_Linux_Signals_in_Bash_Scripts⠀⇛


                       The Linux kernel sends signals to processes about
                       events they need to react to. Well-behaved scripts
                       handle signals elegantly and robustly and can clean
                       up behind themselves even if you hit Ctrl+C. Here’s
                       how.


                # ⚓ Ubuntubuzz ☛ How_To_Upgrade_LibreOffice_On_Ubuntu_20.04⠀⇛


                       This tutorial will explain the steps to upgrade
                       preinstalled LibreOffice 6.4 to latest version 7 or
                       later at Ubuntu Focal Fossa LTS 22.04. This will
                       give you many benefits come from newest version,
                       including, new Candy and Yellow Ideas templates in
                       Impress and better Tabbed / Ribbon user interface
                       in all.


                # ⚓ Its FOSS ☛ Install_Spotify_on_Manjaro_and_Other_Arch_Based
                  Distros⠀⇛


                       Spotify needs no introduction. It is the most
                       popular music streaming service.


                       You can play Spotify in a web browser, but using
                       the desktop application would be a better option if
                       you use it extensively.


                       Why? Because you can control the playback with the
                       media key, get notifications for the songs, and
                       don’t need to worry about accidentally closing the
                       browser tab or window. The desktop client gives a
                       wholesome experience.


                       Spotify provides a repository for Ubuntu and
                       Debian. But what about installing Spotify on Arch
                       Linux?


                # ⚓ ID Root ☛ How_To_Install_CMake_on_Rocky_Linux_9_–_idroot⠀⇛


                       In this tutorial, we will show you how to install
                       CMake on Rocky Linux 9. For those of you who didn’t
                       know, CMake is an extensible, open-source system
                       that manages the build process in an operating
                       system and in a compiler-independent manner. It
                       also is quite sophisticated to support complex
                       environments requiring system configuration,
                       preprocessor generation, code generation, and
                       template instantiation. Additionally, CMake can
                       generate wrappers and executables in any
                       combination, making it very versatile.


                       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 CMake on Rocky Linux. 9.


                # ⚓ Citizix ☛ How_to_install_and_configure_Squid_Proxy_on
                  Ubuntu_22.04⠀⇛


                       In this guide we will learn how to install and
                       configure Squid Proxy server on a Ubuntu 22.04
                       server.


                       Squid is a caching proxy for the Web supporting
                       HTTP, HTTPS, FTP, and more. It reduces bandwidth
                       and improves response times by caching and reusing
                       frequently-requested web pages. Squid has extensive
                       access controls and makes a great server
                       accelerator. It runs on most available operating
                       systems.


                       Squids reverse proxy is a service that sits between
                       the Internet and the webserver (usually within a
                       private network) that redirects inbound client
                       requests to a server where data is stored for
                       easier retrieval. If the caching server (proxy)
                       does not have the cached data, it then forwards the
                       request on to the web server where the data is
                       actually stored. This type of caching allows for
                       the collection of data and reproducing the original
                       data values stored in a different location to
                       provide for easier access.


                       A reverse proxy typically provides an additional
                       layer of control to smooth the flow of inbound
                       network traffic between your clients and the web
                       server.


                # ⚓ Linux Made Simple ☛ How_to_install_ClassiCube_on_a
                  Chromebook_in_2022⠀⇛


                       Today we are looking at how to install ClassiCube
                       on a Chromebook in 2022. Please follow the video/
                       audio guide as a tutorial where we explain the
                       process step by step and use the commands below.


                # ⚓ Linux Hint ☛ Configuring_SASL_on_Linux⠀⇛


                       “The two most significant challenges that server
                       administrators face when attempting the SASL
                       configuration on Linux or any other platform are
                       the installation channel and the choice of the
                       mechanisms you want to support with SASL.


                       You can install SASL using the tarball installation
                       method or the UNIX package installation methods.
                       Again, there is an array of mechanisms that SASL
                       can support.


                       You can choose to support plaintext mechanisms such
                       as LOGIN and PLAIN mechanisms. You can also opt for
                       any type of shared secret mechanism. Shared secret
                       mechanisms include CRAM-MD5, SCRAM, or DIGEST-MD5.
                       Finally, Kerberos authentication protocol users may
                       also choose GSSAPI for Kerberos 5 or KERBEROS_V4
                       for Kerberos version 4.


                       This article is specific and will discuss the SASL
                       installation using the shared secret mechanism
                       (CRAM-MD5). Again, this article will use the LDAP
                       protocol. Thus, only attempt going through this
                       guide once you have LDAP-SASL properly running in
                       your systems.”


          o § Desktop Environments/WMs⠀➾


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


                      # ⚓ PC Linux ☛ digiKam_7.7.0_Released⠀⇛


                             After three months of active maintenance and
                             another bug triage, the digiKam team is proud
                             to present version 7.7.0 of its open source
                             digital photo manager. See below the list of
                             most important features coming with this
                             release.


                             Bundles packaging improvements


                             Qt 5.15 LTS used in Windows and macOS bundle


                             With this release we take care about
                             upgrading the Qt framework with a LTS
                             version. Since Qt 5.15.2, the framework is
                             only published privately to the registered
                             clients from the Qt Company. By chance, the
                             KDE project deals with the Qt company to
                             provide a rolling release of the whole Qt
                             framework including all the most important
                             patches. This is the Qt collection patch used
                             from now by the digiKam AppImage bundle. This
                             allows digiKam to benefit from important
                             fixes as to support the most recent version
                             of Mysql and Mar iadb database in the QtSql
                             plugin. Even if Qt 5.15.5 is just released as
                             open-source, more than one year later 5.15.2,
                             we will continue to use the Qt Collecti on
                             Patch, as the last customer Qt5 release is
                             5.15.8. So there exists again a serious gap
                             between the open-source and the customer
                             versions of Qt.


                      # ⚓ KIO_Admin⠀⇛


                             I’ve gotten annoyed with the inability to
                             manage system files so I’ve made a KIO worker
                             that enables Dolphin to view and edit files
                             as root.


                             The way this works is actually fairly
                             exciting. It’s pulling off worker chaining:
                             The admin worker itself contains gloriously
                             little logic, all it does is translate all
                             worker calls to dbus calls, and those dbus
                             calls go out to a privileged polkit helper.
                             The polkit helper then translates the URIs
                             from admin:///foo to file:///foo and uses the
                             regular KIO API to recreate the request in
                             root-scope. KIO then, behind the scenes, acts
                             just like it would in dolphin proper, using
                             the existing file worker code to execute the
                             file operations.


                             The advantages are amazing! It’s fairly
                             little actual code (albeit a lot of
                             boilerplate). Since it’s an ordinary worker
                             on the Dolphin side we can expect all file
                             operations to just work™ because really
                             admin:// is just like trash:// or desktop://.
                             Because ultimately the file worker is
                             actually in charge of doing the work, all
                             things are generally expected to work (it’s
                             the same code that powers regular file
                             operations).


                # § GNOME Desktop/GTK⠀➾


                      # ⚓ Aarch64_for_GNOME_Nightly_apps⠀⇛


                             We had aarch64 builds of the runtime since
                             the very early days of Flatpak (long before
                             Flathub), and you could manually build your
                             applications for aarc64 natively or by using
                             qemu. Now you will also be able to download
                             aarc64 builds of GNOME applications straight
                             from the Nightly repository so all 3 of you
                             out there with such machines can finally
                             rejoice.


                             The person mostly responsible for this is my
                             good friend Julian Sparber who got around
                             shorting through all the infrastructure
                             needed and baited me into fixing the edge
                             cases. Special thanks also to Bart for taking
                             care of the GitLab Runners as usual.


                      # ⚓ Ubuntu Handbook ☛ This_Extension_Enables_Rounded
                        Window_Corners_in_Ubuntu_22.04/Fedora36_|
                        UbuntuHandbook⠀⇛


                             Gnome finally has an extension to enable
                             rounded corners for all app windows, and
                             customize the window borders!


                             Start in Gnome 40, more and more applications
                             use GTK4 toolkit for rendering their user
                             interface. So, you have modern apps with
                             rounded (bottom) corners and classic GTK3 and
                             Qt apps with sharp (bottom) corners.


                             To make your system apps look consistent,
                             this project is created and works on Ubuntu
                             22.04, Fedora 35/36, Arch Linux, Manjaro
                             Linux with GNOME.


    * § Distributions and Operating Systems⠀➾


          o § PCLinuxOS/Mageia/Mandriva/OpenMandriva Family⠀➾


                # ⚓ PC Linux ☛ Short_Topix:_Wolfenstein,_Doom_Designer_Making_A
                  New_Game⠀⇛


                       In case you haven’t heard, Microsoft OFFICIALLY
                       killed off Internet Explorer, otherwise known as
                       IE, in June of this year. The raucous cheering
                       noise echoed throughout the computer world, glad to
                       be finally done with this scourge upon web
                       browsers. IE 11, the latest and last version, was
                       officially released on October 17, 2013… nearly
                       NINE YEARS AGO… with the nearly as infamous release
                       of Windows 8.1.


                       To commemorate the milestone occasion, the Mozilla
                       team sent a cake to the folks at Microsoft. But
                       this might not be the end just yet. The IE core
                       engine is hanging around as “Internet Explorer
                       Mode” in the new Microsoft Edge browser, and it’s
                       looking like Microsoft plans to continue supporting
                       that until 2029 at the earliest. Once that happens,
                       maybe it’ll be an occasion for another cake… or
                       maybe a steak dinner?


                # ⚓ PC Linux ☛ Repo_Review:_AbiWord⠀⇛


                       AbiWord is a lightweight and powerful word
                       processor with many features. Started back in 1998
                       and continuing to this day, AbiWord is well known
                       in the open-source community, although development
                       seems to have slowed down somewhat in recent years.
                       In this article, I’ll take a quick look at this
                       small and efficient word processor.


                # ⚓ PC Linux ☛ From_The_Chief_Editor’s_Desk…⠀⇛


                       Linux is unbeatable when it comes to supporting
                       older hardware. Do you have a 10 year old laptop?
                       Sure, no problem. Linux will thrive on it. But, can
                       you really expect Linux to support old, obsolete
                       hardware F-O-R-E-V-E-R? It wasn’t all that long ago
                       when Linux support for floppy disk drives was going
                       to be dropped because the kernel modules were no
                       longer being maintained. I don’t know about you,
                       but I haven’t even seen floppy disks available for
                       purchase in over a decade, after seeing them
                       available just about everywhere for years. For what
                       it’s worth, I do still have two USB floppy disk
                       drives available for use (and I’ve used them only
                       once since I became a Linux user), but because they
                       use a USB interface, they don’t use the kernel’s
                       floppy disk drive driver. Instead, the Linux kernel
                       sees the USB floppy disk drive merely as another
                       USB storage device. If I recall correctly, someone
                       stepped up at the 11th hour with an offer to
                       support the antique barely-used driver, saving it
                       from being omitted from the Linux kernel.


                # ⚓ PC Linux ☛ Screenshot_Showcase⠀⇛


          o § SUSE/OpenSUSE⠀➾


                # ⚓ Xen,_QEMU_update_in_Tumbleweed⠀⇛


                       
                       The openSUSE Tumbleweed produced five snapshots
                       since last Thursday that have so far been released.


                       Among some of the packages updated this week
                       besides those listed above in the headline were
                       curl, ffmpeg, fetchmail, vim and more.


                       Snapshot 20220802 was released a couple hours ago
                       and updated just four packages. The update of
                       webkit2gtk3 2.36.5 fixed video playback for the
                       Yelp browser. It and webkit2gtk3-soup2 also fixed a
                       couple Common Vulnerabilities and Exposures. An
                       update of yast2-trans provided some Slovak
                       translations.


          o § Fedora Family / IBM⠀➾


                # ⚓ PC Linux ☛ The_Creature_Has_A_New_Master…⠀⇛


                       In the week of July 05, 2022, it became public that
                       Lennart Poettering was no longer working for Red
                       Hat, having been hired by Microsoft. Such an event
                       should have no repercussions whatsoever, were it
                       not for who Lennart Poettering is, were Microsoft
                       not the company it is, and were the future of GNU
                       Linux not at stake here.


                       [...]


                       We must not forget Steve Ballmer’s famous quote:
                       Linux is a cancer that attaches a sense of
                       intellectual property to everything it touches.


                       Now the question remains: Who is the cancer now?
                       Because Microsoft is sticking to everything related
                       to Linux, and like a parasite, will control its
                       host (The Last Of Us sends regards).


                       However, it has been some time since Microsoft gave
                       up fighting openly against Linux, and decided to
                       infect it from the inside in order to be better
                       able to erode it, with less resistance and more
                       ease.


                       As Brian Lunduke, in his article Microsoft’s
                       growing control of Linux, tells us: Microsoft
                       controls: The largest open source hosting on Earth,
                       a large portion of the Linux conferences, The Linux
                       Foundation, The Open Source Initiative, and
                       prominent Linux developers. (It’s not just Lennart
                       who has moved to Microsoft, many open source
                       developers are already working for it: Steve
                       French, Matteo Croce, Matthew Wilcox, Tyler Hicks,
                       Shyam Prasad N, Michael Kelley, Guido Van Rossum,
                       the father of the Python language).


                       [...]


                       Systemd is just software. It does no harm by
                       itself. The problem is the people (and the
                       corporations that control it).


                       Since its creation, from how it was conceived, in
                       2010, it has, in 12 years, achieved a position of
                       dominance in the Linux ecosystem, where other
                       solutions have taken decades, being improved upon.


                       But, the rush to make systemd a “standard,” was,
                       without soft words, a power struggle.


                       A power struggle between Red Hat and Canonical,
                       which also had a solution, Upstart, that competed
                       with systemd.


                       [...]


                       Not to mention Github, which, under Microsoft’s
                       direction, suffered a mass exodus to other
                       platforms (Gitea, Gitlab, SourceForge, etc…),
                       because Microsoft would abuse the code hosted there
                       (as it ended up abusing).


                       So, I leave the Ned Stark meme to you the reader,
                       and like him, I say: Prepare for impact!


                # ⚓ IT Pro Today ☛ IT_Modernization_Project_Taps_Red_Hat
                  Ansible,_Hashicorp⠀⇛


                       Asia Development Bank’s IT modernization project
                       was boosted by the adoption of Red Hat Ansible and
                       Hashicorp Terraform. Learn about the initiative.


                # ⚓ Red Hat Official ☛ Red_Hat_recognises_Australia_and_New
                  Zealand_partners_for_their_contribution_to_customer_success
                  through_open_innovation⠀⇛


                       The annual Red Hat Australia and New Zealand
                       Partner Awards recognise our dedicated partners in
                       the region for their ongoing commitment to
                       delivering end-to-end customer solutions and
                       expertise using Red Hat’s open source technology
                       portfolio.


                       At Red Hat, we believe that the future of IT is
                       driven and supported by an ecosystem of highly
                       skilled, aligned partners committed to working
                       hand-in-hand with Red Hat and each other.
                       Successful businesses depend on creative, nimble
                       and resilient ecosystems of partners, and we are
                       proud to have an ecosystem that empowers customer
                       success through sustained innovation in open source
                       technologies across industries to jointly deliver
                       results with greater confidence.


                # ⚓ Red Hat Official ☛ Transforming_into_next_generation
                  businesses:_lessons_from_APAC_service_providers⠀⇛


                       Internal and external pressures in the last decade
                       have pushed service providers to begin transforming
                       their processes and adopt technology company, or
                       “techco”, characteristics. Agile organizational
                       structures and processes that leverage software are
                       some initiatives companies have embarked on. Other
                       approaches include flexible workforce, and
                       ecosystem partnerships to create new and exciting
                       services for customers.


                       For example, the APAC region is very varied in both
                       the approach and progress of its service providers.
                       Some of the most advanced 5G networks in the world
                       can be found in China, Japan, and Korea, with
                       service providers looking to deploy 5G standalone
                       (SA), following the allocation of spectrum, whilst
                       others in South Asia and ASEAN (Association of
                       Southeast Asian Nations) remain focused on getting
                       adequate coverage of 4G while working to roll out
                       5G.


          o § Canonical/Ubuntu Family⠀➾


                # ⚓ Beta News ☛ New_Ubuntu_Linux_version_tragically_delayed_by
                  serious_bug⠀⇛


                       Canonical is usually quite dependable when it comes
                       to Ubuntu releases. When a new version of the
                       Linux-based operating system is expected, it
                       usually becomes available on time.


                       Sadly, Ubuntu 22.04.1 won’t become available today
                       as expected — a huge gut-punch to the Linux
                       community. Why is Canonical disappointing fans of
                       the operating system? Well, it seems a serious bug
                       has caused the tragic delay. This serious issue
                       causes snaps not to run on computers that use the
                       OEM install option.


                # ⚓ OMG Ubuntu ☛ Ubuntu_22.04.1_Point_Release_Delayed_Until_Aug
                  11⠀⇛


                       Canonical’s Lukasz Zemczak announced the new on the
                       Ubuntu developer mailing list earlier, noting that
                       an “unexpected issue” affecting OEM installs and
                       Snaps was discovered late in testing. Given the
                       relative severity of the issue with regards to the
                       Ubuntu desktop experience (see below for details)
                       the scheduled release has been punted/postponed/
                       put-off by a week.


                       So what’s literally the issue here?


                # ⚓ Make Use Of ☛ Major_Snap_Bug_Delays_Ubuntu_22.04_Point
                  Release⠀⇛


                       The issue affects installations that were done by
                       PC manufacturers offering Ubuntu preinstalled.
                       After the user accounts were set up, they would be
                       unable to use Snap, Ubuntu’s newer package
                       management system.


                # ⚓ The Register UK ☛ Ubuntu_Focal_user?_Expect_a_Jammy_upgrade
                  popup_soon_•_The_Register⠀⇛


                       Ubuntu 20.04 is nowhere near end of life, but 22.04
                       is starting to hit its stride.


                       As is fairly well understood now, the first release
                       of Ubuntu in each even-numbered year is a Long Term
                       Support (LTS) release. Ubuntu 20.04 “Focal Fossa”
                       gets support and updates until 2025 and won’t reach
                       its official end-of-life until 2030. “Jammy
                       Jellyfish” – the 22.04 release – is the replacement
                       LTS version, receiving mainstream support until
                       April 2027 and arriving at its end of life in April
                       2032.


                       However, users of the previous LTS release don’t
                       start to receive upgrade notifications until the
                       subsequent LTS gets its first point release. For
                       Jammy, if all goes well, that should be today:
                       August 11 is the planned release date for Ubuntu
                       22.04.1. Canonical has published a list of bug-
                       fixes on its Discourse, and you can also track its
                       status on Launchpad.


                       Among many others, 22.04.1 contains a fix for the
                       latest speculative-executation flaw, Retbleed. This
                       has led to speculation about a new law of computer
                       speed changes.


                # ⚓ UBR-1_on_ROS2_Humble⠀⇛


                       The latest ROS2 release came out just a few weeks
                       ago. ROS2 Humble targets Ubuntu 22.04 and is also a
                       long term support (LTS) release, meaning that both
                       the underlying Ubuntu operating system and the ROS2
                       release get a full 5 years of support.


                       Since installing operating systems on robots is
                       often a pain, I only use the LTS releases and so I
                       had to migrate from the previous LTS, ROS2 Foxy (on
                       Ubuntu 20.04). Overall, there aren’t many changes
                       to the low-level ROS2 APIs as things are getting
                       more stable and mature. For some higher level
                       packages, such as MoveIt2 and Navigation2, the
                       story is a bit different.


          o § Devices/Embedded⠀➾


                # ⚓ CNX Software ☛ 52Pi_CM4_Router_Board_also_features_HDMI,
                  40-pin_Raspberry_Pi_HAT_header,_and_OLED_display⠀⇛


                       
                       We’ve already seen compact Raspberry Pi CM4 based
                       router boards with two Ethernet ports from
                       DFRobots, Seeed Studio, and MCUZone. 52Pi CM4
                       Router Board expands on the same principle but also
                       offers HDMI output, a 40-pin GPIO header for
                       Raspberry Pi HAT expansion boards, and a small OLED
                       information display.


                       The board also includes two Gigabit Ethernet, plus
                       the WiFi and Bluetooth connectivity from the
                       Raspberry Pi CM4, and the extra features make the
                       board larger (146x50mm) than competitors. But that
                       makes the platform that much more flexibly, and can
                       be used as a gateways for all sorts of projects
                       thanks to the wide range of Raspberry Pi HAT
                       available in the market.


                # ⚓ Hackaday ☛ Converting_An_80s_Typewriter_Into_A_Linux
                  Terminal_|_Hackaday⠀⇛


                       Typewriters may be long past their heyday, but just
                       because PCs, word processor software, and cheap
                       printers have made them largely obsolete doesn’t
                       mean the world is better off without them. Using a
                       typewriter is a rich sensory experience, from the
                       feel of the keys under your fingers that even the
                       clickiest of PC keyboards can’t compare with, to
                       the weirdly universal sound of the type hitting
                       paper.


                       So if life hands you a typewriter, why not put it
                       back to work? That’s exactly what [Artillect] did
                       by converting an 80s typewriter into a Linux
                       terminal. The typewriter is a Brother AX-25, one of
                       those electronic typewriters that predated word
                       processing software and had a daisy wheel
                       printhead, a small LCD display, and a whopping 8k
                       of memory for editing documents. [Artillect]
                       started his build by figuring out which keys mapped
                       to which characters in the typewriter’s 8×11
                       matrix, and then turning an Arduino and two
                       multiplexers loose on the driving the print head.
                       The typewriter’s keyboard is yet used for input, as
                       the project is still very much in the prototyping
                       phase, so a Raspberry Pi acts as a serial monitor
                       between the typewriter and a laptop. The video
                       below has a good overview of the wiring and the
                       software, and shows the typewriter banging out
                       Linux command line output.


                # ⚓ Liliputing ☛ This_dirt_cheap_4G_LTE_modem_on_a_USB_stick
                  can_be_hacked_to_run_mainline_Linux_–_Liliputing⠀⇛


                       There are a number of cheap “4G LTE WiFi modems”
                       available from Chinese devices makers are basically
                       tiny computers/mobile routers powered by Qualcomm
                       Snapdragon 410 processors and Android-based
                       software.


                       But hackers have discovered that they can be
                       modified to run mainline Linux software like Debian
                       11.


          o § Open Hardware/Modding⠀➾


                # ⚓ Purism ☛ Librem_5_USA_At_Shipping_Parity:_New_Orders_Ship
                  Within_10_Business_Days_–_Purism⠀⇛


                       For anyone who is new to the product, the Librem 5
                       USA is our premium phone that shares the same
                       hardware design and features as our mass-produced
                       Librem 5, but with electronics we make in the USA
                       using a separate electronics supply chain that
                       sources from US suppliers whenever possible. This
                       results in a tighter, more secure supply chain for
                       the Librem 5 USA. The Librem 5 USA uses the same
                       PureOS as our other computers and so it runs the
                       same desktop Linux applications you might be used
                       to, just on a small screen. PureOS on the Librem 5
                       USA demonstrates real convergence, where the device
                       becomes more than just a phone, it becomes a full-
                       featured pocket-sized computer that can act like a
                       desktop when connected to a monitor, keyboard and
                       mouse, or even a laptop (or tablet!) when connected
                       to a laptop docking station. All of your files and
                       all of your software remains the same and follows
                       you where you go. Applications just morph from the
                       smaller screen to the larger screen when docked,
                       just like connecting a external monitor to a
                       laptop.


                # ⚓ Arduino ☛ LEGO-firing_turret_targets_tender_tootsies_|
                  Arduino_Blog⠀⇛


                       Stepping on LEGO bricks is a meme for a reason: it
                       really @#$%&! hurts. LEGO brick design is
                       ingenious, but the engineers did not consider the
                       ramifications of their minimalist construction
                       system. We’ve seen people do crazy things for
                       Internet points, such as walk across a bed of LEGO
                       like they’re hot coals — or in Adam Beedle’s case,
                       build a LEGO-firing turret specifically to shoot
                       plastic bricks under a person’s feet.


                       This project consists of two distinct sub-systems:
                       the mechanical turret that launches the LEGO bricks
                       and the targeting system that recognizes feet. For
                       the former, Beedle devised a clever rubber band-
                       based mechanism that cranks into position with a
                       rack and pinion. An Arduino Uno rotates the pinion
                       with a continuous-rotation servo motor. The pinion
                       gear has a few teeth missing, so it releases the
                       rubber bands and flings the loaded LEGO brick after
                       a few rotations. Another brick then drops down from
                       a hopper and the cycle repeats, resulting in
                       automatic firing.


                # ⚓ Arduino ☛ Reducing_automotive_fuel_consumption_with_an
                  Arduino_|_Arduino_Blog⠀⇛


                       Every car sold in the last few decades is equipped
                       with an engine control unit, or ECU for short. Its
                       job is to control nearly every aspect about the
                       vehicle’s performance by reading various sensors
                       and acting upon those inputs accordingly. However,
                       some older rides aren’t nearly as performant as
                       they could be, which is why YouTuber Robot Cantina
                       wanted to modify their 1997 Saturn coupe for better
                       fuel efficiency.


                       To accomplish this goal, Robot Cantina created a
                       lean burn system that works by making the ECU think
                       the engine is burning more fuel than the actual
                       amount, thus decreasing fuel consumption. They took
                       a cheap air/fuel mixture sensor and connected its
                       input to the engine’s manifold. Due to how it
                       outputs a wideband, linear voltage, the signal had
                       to be converted with an Arduino Uno into a narrow,
                       lower voltage range via a lookup table.


                # ⚓ Arduino ☛ Over-engineered_robotic_scalp_scratcher_knows_all
                  the_moves_|_Arduino_Blog⠀⇛


                       Those cheap wire-arm head massagers are great at
                       giving your scalp a nice, relaxing rub. But they’re
                       handheld implements that force the user to either
                       manipulate the massager themselves or talk a
                       partner into performing the task. David McDaid
                       decided that the experience would be much more
                       pleasant if a robot took care of the hard work, so
                       he built this Stewart platform head massager.


                       A Stewart platform is a dexterous manipulator often
                       used with robotic end effectors or for orienting
                       equipment. The standard setup requires six linear
                       actuators, each with universal joints on both ends.
                       The actuators mount between two plates in an
                       arrangement that gives the top plate six degrees of
                       freedom (DoF): pitch, roll, yaw, and linear
                       movement in each of the three spatial axes. A
                       Stewart platform is perfect for this application,
                       because it lets the robot move the head massager in
                       a variety of different ways that mimic manual
                       movement.


          o § Mobile Systems/Mobile Applications⠀➾


                # ⚓ Notebook Check ☛ Realme_announces_an_Android_13_closed_beta
                  program_for_the_GT_2_Pro_–_NotebookCheck.net_News⠀⇛


                # ⚓ Nokia_5.4_Receives_Android_12_Update_–_Phandroid⠀⇛


                # ⚓ Notebook Check ☛ Teclast_P30_Air_launches_with_Android_12,
                  a_metal_build_and_LTE_support_–_NotebookCheck.net_News⠀⇛


                # ⚓ Pocket Lint ☛ How_to_delete_and_uninstall_apps_from_your
                  Android_phone⠀⇛


                # ⚓ SlashGear ☛ Why_You_Need_To_Stop_Using_Instant_Apps_On_Your
                  Android_Phone⠀⇛


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


          o § Events⠀➾


                # ⚓ FSF ☛ Free_Software_Directory_meeting_on_IRC:_Friday,
                  August_5,_starting_at_12:00_EDT_(16:00_UTC)⠀⇛


                       Help improve the Free Software Directory (FSD) by
                       adding new entries and updating existing ones.
                       Every Friday we meet on IRC in the #fsf channel on
                       Libera.Chat.


                # ⚓ FSF ☛ Free_Software_Directory_meeting_on_IRC:_Friday,
                  August_12,_starting_at_12:00_EDT_(16:00_UTC)⠀⇛


                       Join the FSF and friends Friday, August 12, from
                       12:00 to 15:00 EDT (16:00 to 19:00 UTC) to help
                       improve the Free Software Directory.


                # ⚓ OSI Blog ☛ Reflecting_on_SCaLE_19x⠀⇛


                       We spent this past weekend in Los Angeles at the
                       SCaLE 19X conference and it was a great time. Three
                       of our board members were speakers at this year’s
                       conference. Aeva Black’s keynote presentation was
                       on Saturday, July 29th. They discussed what Open
                       Source maintainers can begin doing to prepare for
                       federal SBoM (software bill of materials)
                       requirements under discussion in Congress today.


                       New OSI board member’s Josh Berkus and Amanda Brock
                       also spoke at this year’s event. Berkus spoke about
                       voting software. He explored the Open Source
                       options available for voting software and spoke in-
                       depth into how Elekto works. Brock talked about the
                       state of Open Source in government. She discussed
                       how Open Source software got to this position,
                       challenges and risks faced, and the needs of
                       curation and stewardship to build critical
                       infrastructure in 2022 and beyond.


          o § Programming/Development⠀➾


                # ⚓ LWN ☛ GitLab_plans_to_delete_dormant_projects_in_free
                  accounts_(Register)⠀⇛


                       The Register reports that GitLab is planning to
                       start deleting repositories belonging to free
                       accounts if they have been inactive for at least a
                       year.


                # ⚓ Liliputing ☛ Lilbits:_GitLab_could_delete_inactive
                  projects,_Google’s_messed_up_messaging_strategy,_and_Purism’s
                  priciest_Librem_5_Linux_smartphone_now_ships_more_quickly_–
                  Liliputing⠀⇛


                       GitLab is a software development, hosting and
                       deployment company that’s proven popular with open
                       source software developers and which currently
                       hosts many popular projects. But according to a
                       report from The Register, some of those projects
                       could disappear soon.


                       That’s because GitLab is said to be planning to
                       start deleting inactive projects from users on
                       GitLab’s free service tier if they haven’t been
                       updated in the past 12 months. In order to stave
                       off deletion, developers just need to issue a
                       commit, open an issue, or otherwise show that the
                       project is active. But there’s a decent chance that
                       this policy could still lead to deletion of many
                       older software projects that haven’t been updated
                       in a long time, but which may still be in use or
                       which may be relied upon by other software
                       projects.


                # ⚓ Kubernetes Blog ☛ Kubernetes_Removals_and_Major_Changes_In
                  1.25_|_Kubernetes⠀⇛


                       As Kubernetes grows and matures, features may be
                       deprecated, removed, or replaced with improvements
                       for the health of the project. Kubernetes v1.25
                       includes several major changes and one major
                       removal.


                # ⚓ Linux Hint ☛ Setenv_C_Function⠀⇛


                       “The “setenv ()” function is used in C programming
                       for adding or updating a variable in the
                       environment which is in the calling process. This
                       “setenv ()” function contains three parameters. The
                       envname, envval, and the overwrite are the three
                       parameters of this “setenv ()” function in C. When
                       we want to update or add some new variable in the
                       environment, then, we utilize this “setenv ()”
                       function. It is not mandatory for setenv () to be
                       re-entrant. A function doesn’t need to be thread-
                       safe if re-entrant behavior is not necessary.


                       In this guide, we will explore this concept in deep
                       detail and will provide codes where we will utilize
                       the “setenv ()” function in C programming. We will
                       also discuss the syntax of this “setenv ()”
                       function here in detail in this guide and will show
                       you how to pass the parameters to this “setenv ()”
                       function in C programming.”


                # § Python⠀➾


                      # ⚓ Linux Hint ☛ Python_Setattr()_Function⠀⇛


                             We are all aware that an object function and
                             function constructor can be used to refer
                             specifically to a class variable. The setattr
                             () method is the only other alternative to
                             this one. In dynamic programming, where the
                             variable name is not static, the setattr()
                             method is helpful. The dot operator is
                             inapplicable in that situation. Using the
                             user input as an illustration, it sets the
                             value of an object attribute. A value is
                             assigned to an object’s attribute using the
                             setattr() function in Python. It accepts an
                             object, a string, and an unspecified value as
                             parameters but doesn’t provide any output.
                             When we wish to give an object a new
                             attribute and assign a value to it, it is
                             useful.


                             You will gain knowledge about the setattr()
                             method of Python in this article, while we
                             cover what it accomplishes, when to employ
                             it, and when it is unnecessary. Regardless of
                             whether the attribute is present or not, the
                             method is used to define an attribute’s value
                             for an object.


                      # ⚓ Linux Hint ☛ Python_Itertools_Combinations⠀⇛


                             We cover the combinations() function by
                             utilizing the Itertools. However, it is
                             crucial to comprehend its utilization before
                             delving further into the topic. Let’s first
                             have a look at it. We frequently experience
                             combinations or permutations when performing
                             different calculations. But even though we
                             may compute numbers, dealing with large
                             values would be challenging sometimes. Think
                             about what might occur if we had tools that
                             could make this determination for users.


                      # ⚓ Linux Hint ☛ Python_Itertools.Islice()_Function⠀⇛


                             In addition to the tools used to effectively
                             loop through data known as Itertools, Python
                             offers its users many important operations
                             and structures that facilitate a simpler
                             dealing with the data. A for-loop-steppable
                             data structure can be iterated over using the
                             Python library called Itertools. Iterator
                             algebra is created using this module as a
                             quick, memory-efficient technique, either
                             alone or in combination. This module includes
                             features that make the optimal use of
                             computing resources.


                             Additionally, using this module tends to make
                             the code easier to read and maintain.
                             Itertools is a built-in package in Python
                             that enables us to manage the iterators
                             effectively. They simplify the process of
                             iterating across iterables like lists and
                             strings. The Islice() is one such Itertools
                             feature. This section is devoted to the
                             islice approach in its entirety.


                # § Java⠀➾


                      # ⚓ TecAdmin ☛ Understanding_the_Access_Modifiers_in_Java
                        –_TecAdmin⠀⇛


                             An access modifier is a special kind of
                             variable declaration that controls how and
                             where other code can use the declared class,
                             variable, or method. This blog will explain
                             what access modifiers are and the three
                             different levels of visibility for classes,
                             methods, and variables with some practical
                             examples.


                             Understanding the scope of your code is
                             essential for writing readable and
                             maintainable programs. Access modifiers are
                             one way to achieve this goal. They tell other
                             users of your code how you want them to
                             interact with specific methods or variables.
                             If you’re new to Java programming, these
                             concepts may seem confusing at first glance;
                             however, once you learn about them once or
                             twice, they become much clearer. Keep reading
                             to learn more about access modifiers in Java.


    * § Leftovers⠀➾


          o ⚓ An_Update_–_blog.theuse.net⠀⇛


                 There have been a lot of changes going on for me in the
                 past few months. Without going onto a lot of details that
                 I would rather not share, I’ve changed a lot in my
                 personal and online life and I’ve taken on some new
                 interests and possible changes in my future.


                 This blog has been running in one form or another for
                 many years and I don’t want to get rid of it but it will
                 be mainly focused on things that interest in me in the
                 Usenet world.


          o § Security⠀➾


                # ⚓ GwisinLocker_ransomware targets_South_Korean_industrial_and
                  pharma_firms⠀⇛


                       GwisinLocker is a new ransomware family that
                       targets Linux in industrial and pharma companies
                       with sophisticated “double extortion” ransomware
                       campaigns. 


                # ⚓ USCERT ☛ CISA_and_ACSC_Release_Top_2021_Malware_Strains⠀⇛


                       CISA and the Australian Cyber Security Centre
                       (ACSC) have published a joint Cybersecurity
                       Advisory on the top malware strains observed in
                       2021. Malicious cyber actors often use malware to
                       covertly compromise and then gain access to a
                       computer or mobile device. As malicious cyber
                       actors have been using most of these top malware
                       strains for more than five years, organizations
                       have opportunities to better prepare, identify, and
                       mitigate attacks from these strains.


                # ⚓ CISA ☛ F5_Releases_Security_Updates_|_CISA⠀⇛


                       F5 has released security updates to address
                       vulnerabilities in multiple products. A privileged
                       attacker could exploit some of these
                       vulnerabilities to take control of an affected
                       system.


                # ⚓ USCERT ☛ Cisco_Releases_Security_Updates_for_RV_Series
                  Routers⠀⇛


                       Cisco has released security updates to address
                       vulnerabilities in Cisco Small Business RV160,
                       RV260, RV340, and RV345 Series Routers. A remote
                       attacker could exploit some of these
                       vulnerabilities to take control of an affected
                       system. For updates addressing lower severity
                       vulnerabilities, see the Cisco Security Advisories
                       page.


                # ⚓ USCERT ☛ CISA_Adds_One_Known_Exploited_Vulnerability_to
                  Catalog⠀⇛


                       CISA has added one new vulnerability to its Known
                       Exploited Vulnerabilities Catalog, based on
                       evidence of active exploitation. These types of
                       vulnerabilities are a frequent attack vector for
                       malicious cyber actors and pose significant risk to
                       the federal enterprise. Note: to view the newly
                       added vulnerabilities in the catalog, click on the
                       arrow in the “Date Added to Catalog” column, which
                       will sort by descending dates. 


                # ⚓ Mozilla ☛ A_back-to-school_checklist_for_online_safety⠀⇛


                       The first day of school is right around the corner.
                       Whether that brings some relief, gives you jitters
                       or both, we’re here to support families with one
                       major thing: internet safety.


                       For parents, thinking about the dangers of the web
                       can be scary. But it doesn’t have to be. While the
                       internet isn’t perfect, it’s also a wonderful place
                       for learning and connecting with others. Here’s
                       what families can do to make the best of it while
                       staying safe this school year.


                # ⚓ Reproducible_Builds_in_July_2022_—_reproducible-
                  builds.org⠀⇛


                       In our reports we attempt to outline the most
                       relevant things that have been going on in the past
                       month. As a brief introduction, the reproducible
                       builds effort is concerned with ensuring no flaws
                       have been introduced during this compilation
                       process by promising identical results are always
                       generated from a given source, thus allowing
                       multiple third-parties to come to a consensus on
                       whether a build was compromised. As ever, if you
                       are interested in contributing to the project,
                       please visit our Contribute page on our website.


          o § Finance⠀➾


                # ⚓ DaemonFC (Ryan Farmer) ☛ Walmart_fires_200_corporate
                  employees_in_the_“Don’t_Call_it_a_Recession”_Recession.
                  Bonus:_Celsius_“crypto”_investors_beg_bankruptcy_judge_for
                  help._–_BaronHK’s_Rants⠀⇛


                       Walmart has had a problem with too many managers
                       since at least when I worked there in the mid-
                       2000s.


                       Now Biden’s “Democrats have an election. Don’t say
                       recession.” has claimed more victims, and I doubt
                       they’ll be the last.


                       The corporate layoffs are a complete blood bath all
                       over America as companies tighten their wallets and
                       try to get spending under control so that they’ll
                       survive and can appease Wall Street with layoffs
                       during falling revenue.


                       It’s an old, old, trick.


                       I certainly have no love for Donald Trump. I didn’t
                       vote for him. But if Trump was in office, the media
                       would be wall-to-wall “recession” right now. You’d
                       be hearing it 24 hours a day. They’re holding off
                       because of Biden.


                       They want Biden. They want Democrats. That’s why
                       they’re not going to throw them any hard balls
                       about the economy, Monkeypox, mass layoffs,
                       hyperinflation, or any of the other messes we’re
                       in.


                       I can’t bring myself to vote for either party in
                       Illinois this year.


                       Pritzker is just Biden in miniature. He’s trying to
                       contain public anger until after the election.
                       Trying to buy my vote with $50 of the taxes the
                       state stole from me to begin with leading up to a
                       major gas tax hike that drains it all back out of
                       my wallet and then some. It’s an insult.


                       The other guy, the Republican, Darren Bailey, is a
                       straight up Nazi, and a dumbass.


          o § Censorship/Free Speech⠀➾


                # ⚓ New York Times ☛ In_Indonesia,_classic_internet
                  censorship⠀⇛


                       I want us to consider the implications of this new
                       reality: In three of the four most populous
                       countries in the world, governments have now given
                       themselves the power to order that the internet be
                       wiped of citizens’ posts that the authorities don’t
                       like.


                       Indonesia — the world’s fourth-most populous
                       country, and a democracy — is in the process of
                       implementing what civil rights organizations say
                       are overly broad regulations to demand removal of
                       online speech that officials consider a disturbance
                       to society or public order. Most major internet
                       companies, including Google, Meta, Netflix, TikTok,
                       Apple and Twitter have effectively agreed to go
                       along with the rules, for now.


                       Indonesia’s regulations are another sign that
                       strict online controls are no longer confined to
                       autocratic countries like China, Iran, North Korea
                       and Myanmar. They are also increasingly the realm
                       of democracies that want to use the law and the
                       internet to shape citizens’ discussions and
                       beliefs.


                       In free societies, there has long been a tug of war
                       over free speech and its limits. But one of the
                       enduring questions of the online era is what
                       governments, digital companies and citizens should
                       do now that the internet and social media make it
                       both easier for people to share their truth (or
                       their lies) with the world and more appealing for
                       national leaders to shut it all down.


    * § Gemini* and Gopher⠀➾


          o § Technical⠀➾


                # ⚓ Thinking_About_ARM_TrustZone⠀⇛


                       I’ve found I rarely have the motivation to write
                       really long and in-depth posts recently, and yet I
                       have a strong motivation to write medium-length
                       posts such as this one. This is my gemlog so I
                       don’t know why I keep holding myself to writing
                       standards instead of just writing what I feel like,
                       so I’m at least going to try writing more stuff
                       like this rather than just not writing anything as
                       I’ve been doing.


                # § Misc.⠀➾


                      # ⚓ Crumbling_clods_of_clay_and_earth.⠀⇛


                             I remember that time when I went to see Terry
                             at his house, which was a ways out south of
                             Rodiqum. It was still clear of the U34 out
                             there, back then. We ate some macaroni or
                             something, and set down there in the room.


                             And he had this whole rear axle hanging on
                             the wall, like someone would with a stag’s
                             head for a trophy. Rusty, with the housing
                             undone to show the gear. Probably like some
                             old gm 10-bolt 2:29 or something.


                      # ⚓ bandd-workmate-536-renovate_–_2022-08-05⠀⇛


                             whilst i consider this as a prototype
                             renovation i expect that i’ll be using the
                             workmate 536 for a few tasks to confirm that
                             they work.


                      # ⚓ Irish_Climate_Targets_July_2022⠀⇛


                             Last week (28 July), the Irish government
                             reached an agreement on targets for carbon
                             reduction across multiple sectors.


                             The background: legislation has already been
                             passed stating that Ireland must reduce its
                             carbon emissions by 51% by 2030. Think of the
                             passing of this legislation as phase 1.


                             Phase 2 involved negotiating how that number
                             would be reached, sector by sector (energy
                             sector, transport, agriculture, housing,
                             etc.).


                      # ⚓ ‘Splorin_Photos⠀⇛


                             Today I had a few different reasons for
                             venturing out. We only had enough food left
                             at the house for the kids to eat lunch so I
                             needed to pick something up for myself to eat
                             while we were out. That’s not entirely true
                             but we didn’t have anything else *easy* to
                             make and I didn’t feel like making something
                             that took much time or effort :-P. So I
                             picked up a pita to go and then we found a
                             nice shady spot under a tree to park and eat.
                             The kids entertained themselves running up
                             and down a hill and looking at wildlife in
                             the lake.


                # § Programming⠀➾


                      # ⚓ About_tables_in_gemtext_(yes_again_🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽
                        ⦇;)⦈_⠀⇛


                             I think that the human readable rendering of
                             a csv file in a gemini client is a good
                             feature as such. On the other hand, let’s not
                             forget why we use tables, we don’t make
                             databases. This approach forces you to
                             multiply as many files as you want to
                             integrate tables, which seems to me to be a
                             very cumbersome way of working.


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



                    ䷩ 𝚕𝚒𝚗𝚎 7197

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 08.05.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_05/08/2022:_Mageia_9_Wants_Artwork⠀✐


Posted in News_Roundup at 12:33 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Desktop/Laptop
          o Server
          o Audiocasts/Shows
          o Kernel_Space
          o Applications
          o Instructionals/Technical
          o Games
          o Desktop_Environments/WMs
                # GNOME_Desktop/GTK
    * Distributions_and_Operating_Systems
          o PCLinuxOS/Mageia/Mandriva/OpenMandriva_Family
          o Red_Hat_/_Fedora_Family_/_IBM
          o Debian_Family
          o Open_Hardware/Modding
          o Mobile_Systems/Mobile_Applications
    * Free,_Libre,_and_Open_Source_Software
          o Content_Management_Systems_(CMS)
          o Programming/Development
                # Java
          o Standards/Consortia
    * Leftovers
          o Hardware
          o Health/Nutrition/Agriculture
          o Proprietary
          o Security
                # Privacy/Surveillance
          o Defence/Aggression
          o Transparency/Investigative_Reporting
          o Environment
                # Energy
          o Finance
          o AstroTurf/Lobbying/Politics
          o Censorship/Free_Speech
          o Civil_Rights/Policing
          o Digital_Restrictions_(DRM)
          o Monopolies
                # Copyrights
    * Gemini*_and_Gopher
          o Personal
          o Technical
                # Science
    * § GNU/Linux⠀➾


          o § Desktop/Laptop⠀➾


                # ⚓ FOSSBytes ☛ Chrome_OS_Vs_Windows:_The_Ultimate_Comparison
                  [Ed: A false dichotomy, as usual]⠀⇛


                       Gone are the days when Windows was your only good
                       option when choosing an operating system. Thanks to
                       the open-source community at large, Desktop Linux
                       has witnessed steady growth in the past few years,
                       and so has Google’s OS for computers and Chrome OS.


                       Introduced in 2011, Chrome OS has grown immensely
                       over the last decade, especially with the COVID-19
                       pandemic taking the previous two years by storm and
                       work/study-from-home becoming the new norm. But the
                       real question is, has Chrome OS developed enough to
                       challenge Windows? Here’s the only ultimate Chrome
                       OS Vs Windows comparison you’ll ever need!


          o § Server⠀➾


                # ⚓ The New Stack ☛ Google_Puts_Open_Source_in_Chip_Design_and
                  Manufacturing_–_The_New_Stack⠀⇛


                       Chip manufacturers are on speed dial for cloud
                       giants like Google and Amazon when they need volume
                       production of internally designed chips. But a
                       program led by Google is trying to open source
                       silicon on the roadmap to combat that domination.


                       Google is leading a group of partners that provides
                       open source software tools for chip designers to
                       design, verify and test virtual versions of the
                       chips, and then get the physical parts manufactured
                       in factories for free. The goal is to help do-it-
                       yourselfers, universities and chip startups cut the
                       designs and production cost of chips.


                       [...]


                       The New Stack is a wholly owned subsidiary of
                       Insight Partners, an investor in the following
                       companies mentioned in this article: Unit, Bionic.


                # ⚓ Ubuntu ☛ Canonical_talks_cloud_native_and_career
                  development_at_community_meetup_in_Manila_|_Ubuntu⠀⇛


                       The Cloud Native Computing Foundation (CNCF)
                       defines Cloud Native as


                       A technology that empowers organisations to build
                       and run scalable applications in modern, dynamic
                       environments such as public, private, and hybrid
                       clouds. Containers, service meshes, microservices,
                       immutable infrastructure, and declarative APIs
                       exemplify this approach.


                       These techniques enable loosely coupled systems
                       that are resilient, manageable, and observable.
                       Combined with robust automation, they allow
                       engineers to make high-impact changes frequently
                       and predictably with minimal toil.


                       Cloud native is about speed and agility.


          o § Audiocasts/Shows⠀➾


                # ⚓ Video ☛ Enterprise_Linux_Security_Episode_38_–_De-
                  anonymizing_Ransomware_Domains_–_Invidious⠀⇛


                       When Ransomware attacks begin spreading, how would
                       officials go about finding the source? Most of the
                       time, finding the culprit(s) behind cyber-attacks
                       is a very challenging task. In this episode of
                       Enterprise Linux Security, Joao and Jay discuss
                       some methods that were recently used to de-
                       anonymize ransomware domains.


                # ⚓ Video ☛ Save_Hours_of_Work_with_RegEx_–_Invidious⠀⇛


                       RegEx is a formidable tool that many just don’t
                       understand, but can save literally thousands of
                       hours of work.


                # ⚓ Video ☛ Linux_Mint_21_Released!_10_Exciting_Reasons_You
                  Should_Check_It_Out_–_Invidious⠀⇛


                       The all-new Linux mint 21 “Vanessa” is now OUT with
                       some major improvements and changes throughout the
                       system. A new base bringing the latest software
                       versions, a set of improved Linux Mint apps, and a
                       number of well picked big and small advancements
                       throughout the system make this release a huge
                       update to Linux Mint.


                # ⚓ Video ☛ Four_days_at_SCaLE19x_in_five_minutes!_–
                  Invidious⠀⇛


          o § Kernel Space⠀➾


                # ⚓ Make Use Of ☛ Linux_Kernel_5.19_Released_With_7_New
                  Features⠀⇛


                       A new version of the Linux kernel has arrived. Like
                       most updates, version 5.19 doesn’t contain one
                       headline-grabbing feature. Instead, it’s filled
                       with various odds-and-ends improvements that make
                       Linux more performant across hardware both new and
                       old.


                       Maybe 5.19 will be a release that surprises you.
                       But if you don’t want to be surprised, here’s some
                       of what to expect.


          o § Applications⠀➾


                # ⚓ Linux Links ☛ Streaming_with_Linux:_Amazon_Music_Unlimited
                  –_LinuxLinks⠀⇛


                       This is a new series that surveys popular streaming
                       services from a Linux perspective. I am not
                       reviewing any of the streaming services themselves
                       although I may make comments from a personal
                       perspective along the way.


                       To start the series, I’m looking at Amazon Music
                       Unlimited. This is a music subscription service
                       with a catalogue of around 90 million songs. It
                       costs $8.99/£8.99 per month to Prime members
                       ($9.99/£9.99 for non-Prime members). I took
                       advantage of the recent Amazon Prime Day deal
                       offering a 4 month free trial. At the time of
                       writing, there’s still a 1 month free trial
                       available. Up to 10 devices can be authorized to a
                       music library account.


                       The service offers a wide-ranging song catalogue
                       and bundles in lossless and hi-res tracks in the
                       standard subscription fee. If you’re a follower of
                       my music software reviews, you’ll know I’m a huge
                       fan of music encoded with FLAC (Free Lossless Audio
                       Codec).


          o § Instructionals/Technical⠀➾


                # ⚓ H2S Media ☛ How_to_Install_exa_on_Ubuntu_20.04/22.04-_ls
                  command_alternative⠀⇛


                       Here in this tutorial, we will find out how to
                       install and use Exa on Ubuntu 20.04 or 22.04 linux.
                       The commands given here can be used on other Debian
                       or Ubuntu-based systems as well.


                       exa is a modern alternative to the ls command. exa
                       is a revised terminal command (with more features)
                       for listing files or folders. Colors are used for a
                       clearer presentation by distinguishing file types
                       and metadata. Symlinks, Git, and other attributes
                       are also taken into account. It’s small, fast, and
                       just one single binary.


                # ⚓ Red Hat Official ☛ Linux_tool_alternatives,_configuring
                  firewalls,_and_more_sysadmin_tips_|_Enable_Sysadmin⠀⇛


                       July 2022 was another excellent month for Enable
                       Sysadmin. During the month, we published 24 new
                       articles and received more than 770,000 reads from
                       over 520,000 readers across the site.


                # ⚓ ByteXD ☛ How_to_Set_and_Unset_Environment_Variables_in
                  Linux_–_ByteXD⠀⇛


                       In this tutorial, you will be acquainted with
                       multiple methods to manage environment variables by
                       checking all available variables (local and
                       global), along with common ways to set/unset
                       system-wide and remote login session accessible
                       variables.


                # ⚓ ID Root ☛ How_To_Install_VSCodium_on_Linux_Mint_21_–
                  idroot⠀⇛


                       In this tutorial, we will show you how to install
                       VSCodium on Linux Mint 21. For those of you who
                       didn’t know, VSCodium is an open source, free to
                       use, and community-driven binary distribution of
                       Microsoft’s editor VSCode. The source code for this
                       product can be found on GitHub, which is licensed
                       under the MIT license and will always remain free
                       as long as you don’t mind installing extra features
                       via plugins or extensions from third parties like
                       Telemetry.


                       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 a VSCodium on Linux Mint 21
                       (Vanessa).


                # ⚓ ID Root ☛ How_To_Install_ClamAV_on_Ubuntu_22.04_LTS_–
                  idroot⠀⇛


                       In this tutorial, we will show you how to install
                       ClamAV on Ubuntu 22.04 LTS. For those of you who
                       didn’t know, ClamAV is an open-source antivirus
                       engine for detecting trojans, viruses, malware, and
                       other malicious threats. It supports multiple file
                       formats (documents, executables, or archives),
                       utilizes multi-thread scanner features, and
                       receives updates for its signature database at
                       least 2-4 times a day.


                       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 ClamAV 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.


                # ⚓ TecMint ☛ 10_Things_to_Do_After_Installing_Linux_Mint_21⠀⇛


                       This guide explains 10 things that you should do
                       after installing Linux Mint 21, Vanessa. This
                       focuses on the Cinnamon edition but should work for
                       those who have installed the Mate and XFCE editions
                       as well.


                # ⚓ Linux Shell Tips ☛ How_to_Install_Let’s_Encrypt_SSL
                  Certificate_on_Domain⠀⇛


                       Consider this scenario, you have a website project
                       that is up and running but you need some security
                       surety to maintain the integral identity of your
                       website project.


                       Website security provides the certainty that
                       potential and growing internet traffic is never
                       diverted from a web platform since users can trust
                       their access to it. The Let’s Encrypt SSL
                       certificate is a digital certificate responsible
                       for authenticating a web app’s identity via an
                       activated encrypted connection.


                       For Linux users running and managing web apps via
                       various Linux server distribution systems (either
                       for personal or commercial reasons), the Let’s
                       Encrypt SSL certificate is good at not only keeping
                       customer information private and secure but also
                       encapsulating their online transactions from prying
                       eyes.


                       This article will walk us through the installation
                       and activation of the Let’s Encrypt SSL
                       certificates on an active domain name.


                # ⚓ Linux Shell Tips ☛ How_to_Check_Let’s_Encrypt_SSL
                  Certificate_Expiration_Date⠀⇛


                       Consider this scenario, you have a web app or
                       website up and running and secured by a Let’s
                       Encrypt certificate. The latter statement has no
                       problem until you start wondering when you
                       installed the Let’s Encrypt SSL certificate
                       associated with your domain name and how many days
                       you have towards its expiration.


                       This article will walk us through a valid solution
                       and also provide an alternate permanent solution so
                       that we do not ever have to worry about the Let’s
                       Encrypt SSL certificate’s expiration dates.


                # ⚓ OpenSource.com ☛ Delete_the_local_reference_to_a_remote
                  branch_in_Git_|_Opensource.com⠀⇛


                       After you merge a GitLab or GitHub pull request,
                       you usually delete the topic branch in the remote
                       repository to maintain repository hygiene. However,
                       this action deletes the topic branch only in the
                       remote repository. Your local Git repository also
                       benefits from routine cleanup.


                       To synchronize the information in your local
                       repository with the remote repository, you can
                       execute the git prune command to delete the local
                       reference to a remote branch in your local
                       repository.


                # ⚓ Citizix ☛ How_to_Setup_Prometheus_Monitoring_On_Kubernetes
                  Cluster⠀⇛


                       In this guide, we will learn how to set up
                       Prometheus for monitoring on a Kubernetes cluster.
                       This setup collects node, pods, and services
                       metrics automatically using Prometheus service
                       discovery configurations.


                # ⚓ Trend Oceans ☛ How_to_Enable_PipeWire_and_Disable
                  PulseAudio_in_Ubuntu_22.04_–_TREND_OCEANS⠀⇛


                       There are lists of applications that I can’t afford
                       to miss after setting up newly installed
                       distributions, and one of them is EasyEffects,
                       which enhances the audio quality to the next level.
                       Without it, I don’t get the real vibe from the
                       music.


                       If you have ever used the EasyEffects, you will
                       know it requires a PipeWire audio server, and it
                       won’t work if you are using PulseAudio as an audio
                       server, so I do have two options.


                       One option is that I could install PulseEffects, or
                       else I could enable PipeWire, which is bundled with
                       Ubuntu 22.04, and as you know, PulseAudio doesn’t
                       support the latest Bluetooth earphones, so it’s
                       better for me to enable Pipewire.
                       After making the changes, EasyEffects started
                       working, so if you are having a similar kind of
                       problem, then this article will be useful for you
                       and you can even follow the below steps if your
                       Bluetooth headset is not working in Ubuntu 22.04.


                # ⚓ markaicode by Mark ☛ How_to_Update_from_Rocky_Linux_8_to
                  Rocky_Linux_9_|_Mark_Ai_Code⠀⇛


                       Gregory Kurtzer, the original CentOS creator,
                       founded the Rocky Project. This came after Redhat
                       announced the demise of CentOS Linux. This Linux
                       distribution created to meet CentOS’s initial aims
                       was first published on April 30, 2021, with the
                       public availability version following on June 21,
                       2021.


                       The most astonishing thing about Rocky Linux is
                       that it is a free and open-source system that is
                       bug-for-bug compatible with Red Hat Enterprise
                       Linux. Rocky Linux 9 is the most recent release
                       version of this Linux distribution.


          o § Games⠀➾


                # ⚓ GamingOnLinux ☛ Steam_adds_support_for_Nintendo_Joy-Con
                  controllers_in_Beta⠀⇛


                       Steam is ever-improving and constantly expanding
                       what is supported by Steam Input. Just recently
                       they added a new Steam Client Beta with support for
                       the Nintendo Joy-Con controllers.


                # ⚓ GamingOnLinux ☛ Crypt_of_the_Necrodancer:_SYNCHRONY_DLC
                  released_into_Early_Access⠀⇛


                       A pleasant surprise for Crypt of the Necrodancer
                       fans! SYNCHRONY, a new DLC for Necrodancer,
                       released today into early access. This surprise
                       content for the pioneering 2015 rythm-roguelike is
                       itself an act of necromancy, as until recently the
                       game had not seen new content since the Amplified
                       DLC in 2017. Today’s release of Synchrony into EA
                       follows a July update to the base game aimed at
                       making Necrodancer compatible with Steam Deck.


                # ⚓ GamingOnLinux ☛ Claim_the_fun_and_challenging_Frick,_Inc.
                  from_Kenney_FREE_for_24_hours⠀⇛


                       Frick, Inc. is an amusing game with a name that’s
                       slightly silly because it’s fricking frustrating
                       too. The developer, Kenney, has made it free to
                       grab on itch.io for 24 hours.


                # ⚓ GamingOnLinux ☛ Nara:_Facing_Fire_inspired_by_Hollow_Knight
                  is_live_on_Kickstarter_with_Linux_support⠀⇛


                       Ready for another beautiful and engaging looking
                       metroidvania? Loved Hollow Knight? You should keep
                       an eye on Nara: Facing Fire that’s live on
                       Kickstarter. A game I briefly covered last month,
                       the developer plans to offer full Native Linux
                       support.


                # ⚓ GamingOnLinux ☛ Last_Call_BBS,_the_final_game_from
                  Zachtronics_has_left_Early_Access⠀⇛


                       Last Call BBS, the final game from the clever
                       people at Zachtronics has left Early Access and is
                       out now along with Native Linux support. Such a
                       shame to see such a great developer move on.
                       They’ve had some really amazing games over the
                       years with my personal favourite being Opus Magnum
                       from 2017.


                # ⚓ GamingOnLinux ☛ Fantasy_city-builder_Songs_of_Syx_adds
                  diseases,_makes_you_care_for_the_elderly⠀⇛


                       Songs of Syx is a fantasy city-builder that made a
                       bit of a splash at release selling a few thousand
                       copies pretty quickly, but as always many more
                       games appear and some fall off the radar but Songs
                       of Syx continues expanding.


                # ⚓ GamingOnLinux ☛ No_more_DLC_for_Oxygen_Not_Included,_devs
                  decide_to_do_free_updates_instead⠀⇛


                       Oxygen Not Included is not getting any more DLC,
                       Klei Entertainment has announced. Instead, they’re
                       going to keep pumping out free updates for all
                       players. What is it? ONI is a space colony building
                       game where you have to manage a growing group of
                       people in a hostile environment.


          o § Desktop Environments/WMs⠀➾


                # § GNOME Desktop/GTK⠀➾


                      # ⚓ Mini-GUADEC_2022_Berlin:_retrospective_|_Philip
                        Withnall⠀⇛


                             I’m really pleased with how the mini-GUADEC
                             in Berlin turned out. We had a really
                             productive conference, with various
                             collaborations speeding up progress on Files,
                             display colour handling, Shell, adaptive
                             apps, and a host of other things. We watched
                             and gave talks, and that seemed to work
                             really well. The conference ran from 15:00 to
                             22:00 in Berlin time, and breaks in the
                             schedule matched when people got hungry in
                             Berlin, so I’d say the timings worked nicely.
                             It helped to be in a city where things are
                             open late.


                             c-base provided us with a cool inside space,
                             a nice outdoor seating area next to the
                             river, reliable internet, quality A/
                             V equipment and support for using it, and a
                             big beamer for watching talks. They also had
                             a bar open later in the day, and there were
                             several food options nearby.


                             At least from our end, GUADEC 2022 managed to
                             be an effective hybrid conference. Hopefully
                             people in Guadalajara had a similarly good
                             experience?


    * § Distributions and Operating Systems⠀➾


          o § PCLinuxOS/Mageia/Mandriva/OpenMandriva Family⠀➾


                # ⚓ Time_to_Make_Mageia_9_Beautiful_–_The_Artwork_Drop_is_Open
                  |_Mageia_Blog_(English)⠀⇛


                       As with every release, the artwork for Mageia 9
                       will come from you, the great community that
                       supports and makes Mageia possible. The Development
                       of Mageia 9 is progressing quickly, with many major
                       updates and key features getting ready for testing
                       and release. With this progress, it’s time to get
                       the artwork ready for release. As in previous
                       years, we’re looking for your contributions and
                       ideas, but not just images and photos – if you have
                       icons and logos, or ideas on how login screens or
                       animations should look, then it’s time to discuss
                       or show them off.


          o § Red Hat / Fedora Family / IBM⠀➾


                # ⚓ IBM Old Timer ☛ IBM_emeritus_Irving_Wladawsky-Berger:
                  Disruptive_Forces_Necessitate_Bold_Decisions⠀⇛


                       In January of 2021 I attended Predictions 21, an
                       online event organized by Forrester Research.
                       “Faced with the pandemic, firms did things that
                       once seemed impossible – sometimes overnight,” said
                       Forrester last year, adding that “2021 will be the
                       year that every company – not just the 15% of firms
                       that were already digitally savvy – doubles down on
                       technology-fueled experiences, operations,
                       products, and ecosystems.”


                       Earlier this year I attended Predictions 22, and
                       was particularly curious to see how things had
                       changed in the intervening year. “Disruptive Forces
                       Necessitate Bold Decisions,” was the overriding
                       message in this year’s event guide. “The old ways
                       of working no longer work. The future is up for
                       grabs. Leading firms will use the crucibles of 2020
                       and 2021 to forge a path to an agile, creative, and
                       resilient tomorrow.”


                # ⚓ Fedora Project ☛ Fedora_Community_Blog:_CPE_Weekly_Update_–
                  Week_31_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 (https://libera.chat/).


                # ⚓ ZDNet ☛ From_software_developer_to_CEO:_Red_Hat’s_Matt
                  Hicks_on_his_journey_to_the_top [Ed: On the WWW, thought I'm
                  not sure about paper form, like 90% of "news" is already
                  paid-for webspam, sponsored by the companies the 'articles'
                  are about. This means that nowadays being a "professional
                  journalist" means being compromised, becoming a corporate
                  parrot.]⠀⇛


                # ⚓ Slashdot ☛ From_Software_Developer_To_CEO:_Red_Hat’s_Matt
                  Hicks_On_His_Journey_To_the_Top [Ed: IBM paying "news" sites
                  to do Red Hat churnalism/stenography, pretending all is
                  well]⠀⇛


                # ⚓ Enterprisers Project ☛ 4_tips_to_help_retain_IT_talent⠀⇛


                       Over the past two years, IT leaders have been
                       tasked with juggling innovation to keep business
                       operations running efficiently – all at breakneck
                       speed while collaborating with external partners.
                       CIOs must also collaborate with internal
                       stakeholders to manage the risks.


                       As business models and customer interactions have
                       shifted to digital platforms, technology management
                       has also changed to allow employees to remain
                       productive in this new environment.


                       Organizations today have a diverse and truly
                       globalized workforce and must consider different
                       cultures, time zones, and currencies. Many
                       employees also struggle with challenges such as
                       balancing the demands of work and family, dealing
                       with a more solitary work environment, and more –
                       all of which affect mental health and work
                       performance.


                # ⚓ Enterprisers Project ☛ Developer_burnout:_3_ways_to_avoid
                  it_on_your_IT_team⠀⇛


                       Software development is continuous and constantly
                       changing. As a result, modern developers may feel
                       “always on,” with little downtime to recharge. A
                       study from Haystack found that 83 percent of
                       software developers suffer from workplace burnout.


                       It’s no secret that the pandemic increased feelings
                       of burnout, but other variables exacerbate these
                       feelings as well. The top reasons developers cited
                       in the study for burnout included high workload (47
                       percent), inefficient processes (31 percent), and
                       unclear goals or targets (29 percent).


                       Developer experience (DevEx) refers to the overall
                       interactions and feelings that a developer
                       experiences when working toward a goal. It can play
                       a critical role in curating positive experiences
                       for both developers and end users. A frictionless
                       developer experience that uncomplicates processes
                       and helps prevent developer burnout is vital.


          o § Debian Family⠀➾


                # ⚓ CNX Software ☛ Inexpensive,_Snapdragon_410-based_“4G_LTE
                  WiFi_Modem”_made_to_run_Debian_11⠀⇛


                       Some ultra-compact 4G LTE wireless routers housed
                       in what looks like a largish USB dongle are based
                       on Qualcomm Snapdragon 401 (MSM8916) quad-core
                       Cortex-A53 processor and have been hacked to run
                       Debian 11 with Linux 5.15 instead of the pre-loaded
                       Android OS.


                       Soon after Extrowerk had purchased a ~$20 “4G LTE
                       WiFi modem” USB dongle, he noticed it would show as
                       “Android” when connected to his PC. It also turned
                       out that Chinese hacker HandsomeYingYan had already
                       done some work on the device modding the lk2nd
                       bootloader and the Linux kernel for the OpenStick
                       project for “mainline Linux on msm8916-based 4G USB
                       modem”, and documented his work (in Chinese) to run
                       Debian 11 on the “4G USB WiFi Modem” pictured
                       below.


          o § Open Hardware/Modding⠀➾


                # ⚓ Medevel ☛ 16_Open-source_Projects_to_Build_a_CCTV_System
                  With_Raspberry_Pi⠀⇛


                       Raspberry Pi is still the most popular affordable
                       SBC (Single Board Computer). It is used as the core
                       in many of projects for education, healthcare,
                       security, and IoT.


                # ⚓ Geeky Gadgets ☛ MangoPi_MQ_Pro_with_64-bit_RISC-
                  V_processor⠀⇛


                       
                       MangoPi has officially launched their second RISC-
                       V mini PC after unveiling it earlier this year. The
                       MangoPi MQ Pro measures just 65 x 30mm and is
                       available with either 512MB or 1GB of DDR3L memory
                       and is equipped with 2 x USB Type-C ports, 1 x mini
                       HDMI 1.4 port, 1 x microSD card reader plus a 40-
                       pin GPIO header compatible with Raspberry Pi
                       boards. The mini PC also supports Bluetooth 4.2 and
                       Wi-Fi 4 connectivity.


                       The MangoPi MQ Pro is the company second mini PC
                       powered by a RISC-V processor and follows on from
                       the tiny MangoPi MQ powered by a Allwinner D1s
                       processor supported by 64MB of RAM and featuring 2
                       x USB-C ports, 1 x microSD card reader, WiFi and
                       Bluetooth.


          o § Mobile Systems/Mobile Applications⠀➾


                # ⚓ Phone Arena ☛ T-Mobile_brings_(theoretically)_stable
                  Android_12_goodies_to_its_OnePlus_8_and_8T_variants_–
                  PhoneArena⠀⇛


                # ⚓ SlashGear ☛ How_To_Tell_If_Your_Android_Phone_Is
                  Overheating⠀⇛


                # ⚓ SlashGear ☛ Why_You_Probably_Need_To_Change_Your_Android
                  Phone’s_Equalizer_Settings⠀⇛


                # ⚓ Android Headlines ☛ Can_You_Control_Smart_Blinds_Using_Your
                  Android_Phone?⠀⇛


                # ⚓ India Times ☛ Google_Meet_may_soon_add_these_‘non-work’
                  features_for_Android_users_–_Times_of_India⠀⇛


                # ⚓ Hindustan Times ☛ This_Asus_ROG_Phone_6_is_now_the_MOST
                  powerful_Android_phone_in_the_world!_|_Mobile_News⠀⇛


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


          o ⚓ OpenSource.com ☛ Scalable_storage_for_the_masses_to_debut_in
            ownCloud_Infinite_Scale_|_Opensource.com⠀⇛


                 So far, ownCloud users have only had the opportunity to
                 choose between simple local file storage based on a
                 POSIX-compatible file system or EOS Open Storage (EOS).
                 The latter causes massive complexity during setup. More
                 recent versions of ownCloud feature a functionality
                 called Decomposed FS. This file system is supposed to
                 bring oCIS to arbitrary storage backends and even
                 scalable ones.


                 During the rewrite of ownCloud from PHP to Go, the
                 company behind the private cloud solution is introducing
                 massive changes to the backend of the software. This
                 time, the developers do away with a tedious requirement
                 of the first versions of ownCloud Infinite Scale (oCIS).
                 By implementing a file system abstraction layer, oCIS can
                 use arbitrary backend-storages (and even such storage
                 mechanisms that can seamlessly scale out). This article
                 explains the reasons behind ownCloud’s decision, the
                 details behind the Decomposed FS component, and what it
                 means for ownCloud users and future deployments.


                 To understand the struggle that oCIS faces, it’s
                 important to have a quick look back at the genesis of
                 ownCloud Infinite Scale. What started as an attempt to
                 gain more performance resulted in a complete rewrite of
                 the tool in a programming language that was different
                 from the previous one. ownCloud did, however, partner
                 with several companies and institutions when rewriting
                 its core product. Amongst the organizations that ownCloud
                 partnered with was a university in Australia. Said
                 university used EOS, a storage technology developed by
                 CERN, the European physics research institute notorious
                 for running projects like the Large Hadron Collider
                 (LHC). For the partnership between ownCloud and the
                 Australian University to make any sense, oCIS needed to
                 be tied to the existing on-premises storage solution of
                 the institute.


          o § Content Management Systems (CMS)⠀➾


                # ⚓ Ariadne Conill ☛ Migrating_away_from_WordPress⠀⇛


                       Astute followers of this blog might have noticed
                       that the layout has dramatically changed. This is
                       because I migrated away from WordPress last
                       weekend, switching back to Hugo after a few years.
                       This time around, the blog is fully self-hosted,
                       rather than depending on GitHub pages, and the
                       deployment pipeline is reasonably secure. Perhaps
                       we can call it a “secure blog factory” with some
                       further work, even.


                # ⚓ The_Month_in_WordPress_–_July_2022⠀⇛


                       July 2022 brought a lot of exciting announcements
                       and proposals for the WordPress project, from an
                       updated timeline for the WordPress 6.1 release, to
                       design updates on WordPress.org. Read on to learn
                       more about the latest news from the community.


                # ⚓ Medevel ☛ Rasa_is_a_Machine_Learning_Framework_For_Building
                  Text_and_Voice_Intelligent_Conversations⠀⇛


                       Rasa is a free and open-source community-powered
                       machine learning framework to automate text- and
                       voice-based conversations.


                       [...]


                       Rasa is licensed under the Apache-2.0 License.


                # ⚓ Medevel ☛ 15_Open-source_Free_Live-chat_Widget_Solutions_To
                  Boost_Your_Customer_Engagement⠀⇛


                       In this article we created you a list of the best
                       open-source chat widget solutions, which vary in
                       features, and options. We recommend going through
                       the list and look through all of their features
                       before making a final decision.


          o § Programming/Development⠀➾


                # § Java⠀➾


                      # ⚓ Ubuntu Pit ☛ Top_15_Best_Netbeans_Themes_for_Free_in
                        2022⠀⇛


                             Netbeans is an open-source IDE known for its
                             easy usage, intuitive interface, and Java
                             implementation. However, users sometimes have
                             their own preferences for which they might
                             wish to use one of the other NetBeans themes.
                             And there are plenty of options to choose
                             from!


                             That said, themes aren’t just used to make
                             the software look pretty. They have a lot
                             more to them and actually contribute much to
                             the user experience besides the UI. Different
                             themes in IDEs work to keep the codes
                             organized and enhance their readability,
                             among other benefits.


          o § Standards/Consortia⠀➾


                # ⚓ Chromecast_Protocol⠀⇛


                       After almost a month of reconnaissance through the
                       study of Chromium’s code, VLC’s code and other
                       people’s attempts, we finally have figured out the
                       Chromecast protocol, and it works flawlessly and
                       reliably!


    * § Leftovers⠀➾


          o ⚓ [Old] Where_I_hope_to_go_(just_NOT_with_SubStack)_|_Stop_at_Zona-
            M⠀⇛


                 A couple of months ago, NiemanLab republished what Casey
                 Newton learned from a year on Substack, that is plenty of
                 details and tips about leaving a media company and start
                 your own publication.


          o ⚓ TruthOut ☛ Feel_Like_Everything_Is_Crumbling?_This_Oral_History
            of_the_Future_Offers_Hope.⠀⇛


          o ⚓ The Nation ☛ Juan_Emar’s_Forgotten_Vanguard⠀⇛


                 The Chilean writer known as Juan Emar chose that name
                 amid a lifetime of dissatisfaction. Born Álvaro Yáñez
                 Bianchi in 1893 in Santiago, he was the son of a
                 prominent Chilean lawyer and newspaper magnate, and
                 adopted his nom de plume around 1924 to express his
                 disdain for the country’s intellectual landscape and his
                 place in it. Contemporary Chilean literature’s staid
                 criollismo movement was looking to the countryside for
                 naturalist visions of rural life—imagine Little House on
                 the Pampas—but Bianchi was more interested in European
                 experimentalism. “Juan Emar” was meant to sound like
                 “J’en ai marre,” French for “I’m fed up.”


          o ⚓ Hackaday ☛ The_FishFeeder_Keeps_Your_Fish_Fed_While_You’re_Away⠀⇛


                 With summer in full swing in the Northern Hemisphere,
                 millions of people are out on vacation leaving millions
                 of homes empty. Thanks to modern technology it’s easier
                 than ever to keep an eye on those empty homes: internet-
                 connected cameras report suspicious activity, and smart-
                 home devices like curtains and light bulbs can be
                 operated from your holiday home. If you’ve got an
                 aquarium and want to keep your fish well-fed during your
                 vacation, then [FoxIS]’s internet-connected automated
                 fish feeder might come in handy too.


          o ⚓ Common Dreams ☛ Opinion_|_Remembering_the_Life_and_Work_of_David
            Moberg_(1943-2022)⠀⇛


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


          o § Hardware⠀➾


                # ⚓ CNX Software ☛ Renesas_RZ/A3UL_Cortex-A55_CPU_runs_RTOS_for
                  HMI_with_quick_startup_times_–_CNX_Software⠀⇛


                       Renesas RZ/A3UL is a single-core Cortex-A55
                       processor clocked at up to 1 GHz designed to run
                       FreeRTOS or Azure RTOS on high-definition
                       (1280×800) HMI solutions requiring quick startup
                       times such as industrial equipment, home
                       appliances, office automation equipment, audio
                       equipment, and POS terminals.


                # ⚓ CNX Software ☛ Sonoff_ZBDongle-E_Zigbee_3.0_USB_dongle
                  features_EFR32MG21_MCU_with_+20dBm_radio_–_CNX_Software⠀⇛


                       ITEAD has just released a new “ZBDongle-E” Zigbee
                       3.0 USB adapter with Silicon Labs Mighty Gecko
                       EFR32MG21 Arm Cortex-M33 microcontroller with a
                       +20dBm radio for extended range.


                       The new dongle is an alternative to the popular
                       Texas Instruments CC2652P-based Sonoff Zigbee 3.0
                       USB Dongle Plus, also known as “ZBDongle-P”, with a
                       more compact design, and many of the same features.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ TruthOut ☛ Defeat_of_Anti-Abortion_Amendment_in_Kansas
                  Shows_Voters_Favor_Bodily_Autonomy⠀⇛


                # ⚓ TruthOut ☛ Biden_Signs_Executive_Order_Directing_Medicaid
                  to_Pay_Abortion_Travel_Expenses⠀⇛


                # ⚓ Common Dreams ☛ Opinion_|_Anti-Abortion_Extremism_Is
                  Scaring_Voters—Even_the_Conservative_Ones⠀⇛


                       Our country may be divided on the issue of
                       abortion. But when it comes down to it, most
                       Americans believe that it’s a pregnant person’s
                       right to decide for themselves whether to continue
                       a pregnancy.


                # ⚓ Common Dreams ☛ In_‘Critical_Step_to_Fight_Monkeypox,’
                  Biden_Administration_Declares_Emergency⠀⇛


                       Following growing activist pressure and criticism,
                       the Biden administration on Thursday declared
                       monkeypox a national public health emergency, a
                       move that empowers federal agencies to better
                       direct resources toward combating an outbreak
                       that’s infected thousands of Americans.


                       “When you have an outbreak, the most important
                       thing is you have to act fast, you have to
                       mobilize.”


          o § Proprietary⠀➾


                # ⚓ NBC ☛ Taiwanese_websites_hit_with_DDoS_attacks_as_Pelosi
                  begins_visit⠀⇛


                       The attacks hit at least four websites — those of
                       President Tsai Ing-wen, the National Defense
                       Ministry, the Foreign Affairs Ministry and the
                       country’s largest airport, Taiwan Taoyuan
                       International.


                       It wasn’t clear where the cyberattacks came from.
                       Their timing added to concerns over China’s
                       vehement opposition to the visit by Pelosi, D-
                       Calif.


          o § Security⠀➾


                # ⚓ Bleeping Computer ☛ New_Linux_malware_brute-forces_SSH
                  servers_to_breach_networks [Ed: Now the Microsofters are
                  trying to blame "Linux" for weak passwords, which are brute-
                  forced. This is getting utterly ridiculous given that Windows
                  has actual back doors.]⠀⇛


                       A new botnet called ‘RapperBot’ is being used in
                       attacks since mid-June 2022, focusing on brute-
                       forcing its way into Linux SSH servers to establish
                       a foothold on the device.


                # ⚓ Maritime_regulation._All_Hands-on_Deck!_|_Pen_Test
                  Partners⠀⇛


                       Since January 1st 2021 the International Maritime
                       Organization (IMO) has been enforcing Resolution
                       MSC. 428(98) of the International Safety Management
                       (ISM) Code.


                       This resolution encourages Vessel Owners to ensure
                       that cyber risks are appropriately addressed in
                       existing safety management systems (SMS) by no
                       later than the first annual verification of the
                       company’s Document of Compliance (DOC) after
                       January 1, 2021.


                # ⚓ eSecurity Planet ☛ Cobalt_Strike_Inspires_Next-generation
                  Crimeware_|_eSecurityPlanet⠀⇛


                       Cobalt Strike is a legitimate vulnerability
                       scanning and pentesting tool that has long been a
                       favorite tool of hackers, and it’s even been
                       adapted by hackers for Linux environments.


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


                       Security updates have been issued by CentOS
                       (firefox, thunderbird, and xorg-x11-server), Debian
                       (xorg-server), Gentoo (Babel, go, icingaweb2,
                       lib3mf, and libmcpp), Oracle (389-ds:1.4, go-
                       toolset:ol8, httpd, mariadb:10.5, microcode_ctl,
                       and ruby:2.5), Red Hat (xorg-x11-server),
                       Scientific Linux (xorg-x11-server), SUSE (buildah,
                       go1.17, go1.18, harfbuzz, python-ujson, qpdf, u-
                       boot, and wavpack), and Ubuntu (gnutls28, libxml2,
                       mod-wsgi, openjdk-8, openjdk-8, openjdk-lts,
                       openjdk-17, openjdk-18, and python-django).


                # § Privacy/Surveillance⠀➾


                      # ⚓ [Old] NEVER_mix_your_employer_and_your_smartphone⠀⇛


                             Rachel By The Bay recently shared that she
                             bought a second phone just because she wanted
                             THAT other phone, and that only, to “take the
                             burden of all of the crap her new employer
                             was about to throw at her”.


          o § Defence/Aggression⠀➾


                # ⚓ NBC ☛ After_Alex_Jones’_lawyers_accidentally_leak_years_of
                  emails,_Infowars_financial_documents_are_revealed_in_court⠀⇛


                       Lawyers for Alex Jones appeared to have
                       accidentally sent over the entire contents of the
                       Infowars founder’s phone to the lawyers for the
                       plaintiffs in his defamation trial, according to
                       court proceedings Wednesday.


                       Mark Bankston, a lawyer for the parents of one of
                       the children killed in the 2012 Sandy Hook
                       Elementary School massacre and who are now suing
                       Jones, said during the proceedings that “12 days
                       ago, his [Jones’] attorneys messed up and sent me a
                       digital copy of every text” and email from Jones’
                       phone.


                # ⚓ Foreign Policy ☛ Taliban_Killings_Skyrocket_in_Forgotten
                  Afghanistan⠀⇛


                       This is not the first warning that Taliban killings
                       are on the rise. In January, the United Nations
                       reported that more than 100 former Afghan officials
                       had likely been killed since the Taliban seized
                       Kabul in August 2021, most of those killings
                       conducted by the militant group. But former Afghan
                       officials believe that the numbers are continuing
                       to rise as Afghanistan has receded from the
                       spotlight with Russia’s full-scale invasion of
                       Ukraine and few consequences from U.S. officials.


                # ⚓ The Hill ☛ Alex_Jones’s_attorney_‘messed_up’_and_sent_two
                  years_of_texts_to_Sandy_Hook_parents’_lawyers⠀⇛


                       The legal team for far-right conspiracy theorist
                       Alex Jones accidentally sent two years of his phone
                       records to the attorneys for parents of a Sandy
                       Hook school shooting victim, cross-examination
                       revealed Wednesday during his defamation trial.


                # ⚓ TruthOut ☛ Jan._6_Committee_Has_Requested_Alex_Jones_Texts,
                  Sandy_Hook_Parents’_Lawyer_Says⠀⇛


                # ⚓ NPR ☛ A_judge_unleashed_a_tirade_on_a_prominent_Jan._6
                  defendant_for_his_post-plea_comments⠀⇛


                       But Friedrich, who was nominated to the federal
                       bench by former President Trump, grew audibly
                       frustrated when she turned to Straka’s recent
                       public comments about both his cooperation and his
                       plea deal.


                # ⚓ Telex (Hungary) ☛ The_captured_American_spy_plane_that
                  crashed_during_a_Hungarian_pleasure_flight⠀⇛


                       Sixty-one years ago, on 6 August 1961, the accident
                       known as the Lumumba Street tragedy occurred when a
                       Malév plane – a passenger plane converted from an
                       American “spy plane” – crashed into a high-rise
                       building in Zugló during a sightseeing flight in
                       Budapest. Even though thirty people died in the
                       disaster, it was not reported in the newspapers
                       until days later.


                # ⚓ TruthOut ☛ 21st-Century_US_Foreign_Policy_Is_Shaped_by
                  Fears_of_China’s_Rise,_Chomsky_Says⠀⇛


                # ⚓ Scheerpost ☛ Patrick_Lawrence:_Language_and_Its_Enemies⠀⇛


                       Media critic Patrick Lawrence lays out how the
                       aftermath and potential consequences of Pelosi’s
                       Taiwan visit are made obscure by certain media
                       outlets.


                # ⚓ TruthOut ☛ Warnings_Grow_over_Nuclear_War_as_Tensions
                  Escalate_Between_US,_Russia_and_China⠀⇛


                # ⚓ Counter Punch ☛ As_the_War_in_Ukraine_Devastates_the
                  Nation’s_Ecosystems,_the_World_Reaches_Record-High_Military
                  Spending⠀⇛


                       While ignoring the climate disaster, the U.S. is
                       not only spending to boast its own military powers
                       but also providing Ukraine with weapons and other
                       aid in its ongoing conflict with Russia.


                       With the war in Ukraine raging on, the U.S. Senate
                       voted 86 to 11 in May and gave its approval to
                       President Joe Biden’s massive additional aid
                       package of $40 billion to help Ukraine on top of
                       the nearly $14 billionauthorized just two months
                       prior. This total financial aid package for Ukraine
                       of around $54 billion is now almost as large or
                       larger than the entire 2021 defense budgets of
                       several countries: France’s military budget was
                       $56.6 billion in 2021, Germany’s was $56 billion,
                       Japan’s was $54.1 billion and Australia’s military
                       spending stood at $31.8 billion. In contrast, there
                       are also other ongoing struggles and attempts by
                       some countries to achieve independence worldwide.
                       They grab little attention and receive no
                       substantial financial support.


                # ⚓ Common Dreams ☛ Opinion_|_Reflections_on_Russia’s_Antiwar
                  Protests_and_Ours⠀⇛


                       Simultaneously, we find ourselves witnessing the
                       playing out of the repression of dissent against
                       the illegal and hugely unpopular 2022 Russian
                       invasion of Ukraine, along with the repression of
                       dissent against the illegal and hugely unpopular
                       2003 American invasion of Iraq. The arena for the
                       latter has been the ongoing extradition campaign
                       against Julian Assange for the 2010 Wikileaks
                       release of “Collateral murder” a video of a 2007
                       U.S. helicopter attack killing several Iraqi
                       civilians, including two journalists. The most
                       noteworthy recent Russian event—in real time—came
                       with a court sentencing Moscow district councilor
                       Aleksei Gorinov to seven years in prison for
                       breaking a recently adopted law against spreading
                       “false information.” Gorinov’s crime was calling
                       the Ukraine invasion a “war” and not a “special
                       military operation.” A good moment, perhaps, to
                       consider the respective fates of the two antiwar
                       efforts—dramatically different in one aspect and
                       depressingly similar in another.


                # ⚓ The Nation ☛ How_the_“Brooks_Brothers_Riot”_Set_the_Stage
                  for_Insurrection⠀⇛


                       In the wake of a bitterly disputed presidential
                       election, a central hub of government operations
                       was suddenly under siege. A group of aggrieved
                       right-wing protesters defied security and flooded
                       into the now-chaotic center of activity. Government
                       officials were harassed and feared for their
                       safety, as charges of fraud and betrayal of the
                       people’s will rose up from the angry mob.


          o § Transparency/Investigative Reporting⠀➾


                # ⚓ The Dissenter ☛ Justice_Department:_NSA_Whistleblower
                  Reality_Winner_Must_Wait_To_Apply_For_Pardon⠀⇛


                       Winner’s attorney Alison Grinter sent a letter to
                       the Justice Department’s Office of the Pardon
                       Attorney on June 29 and singled out Trump’s
                       actions.“We are asking that the waiting period be
                       waived on this application for pardon because as
                       the former President has been shown to have had no
                       respect for our democratic institutions and norms
                       and has shown a willingness to subvert, manipulate,
                       and hide the truth, now is the right time to
                       forgive those who brought us the truth when we
                       needed to know it,” Grinter argued. Grinter further
                       maintained that it was necessary to stand up to
                       “political retaliation and scapegoat scare tactics”
                       and pardoning Winner would help bring about healing
                       and reconciliation. She also contended, as the US
                       government is focused on fighting Russia in
                       Ukraine, it is wrong for the Justice Department to
                       continue to punish Winner.On August 3, four days
                       after National Whistleblower Appreciation Day, the
                       Office of the Pardon Attorney replied, “We have
                       concluded that it would not be appropriate to grant
                       a waiver of the waiting period in her case to
                       permit her to apply for a pardon at this time.” The
                       response mostly quoted the guideline that the
                       Justice Department often follows, but it also was
                       insulting to Winner.


          o § Environment⠀➾


                # ⚓ The Nation ☛ In_the_Era_of_Climate_Migration,_What_Will
                  “Home”_Mean?⠀⇛


                       In modern American parlance, the meaning of “home”
                       is entangled in real estate. In young adulthood, I
                       learned that to be a “grown-up” was to buy your own
                       house, even if it left you with a crippling
                       mortgage that would devour most of your earnings.
                       The idea lies at the core of the American Dream,
                       that postwar fantasy that exerts a stubborn
                       influence on our culture no matter how outdated it
                       becomes. This article is an excerpt from Madeline
                       Ostrander’s new book At Home on an Unruly Planet:
                       Finding Refuge on a Changed Earth, published by
                       Henry Holt.


                # ⚓ Hackaday ☛ Reduced_Sulfur_Emissions_Could_Cause_Climate
                  Shock⠀⇛


                       When we talk about emissions these days, we
                       typically talk about cutting them back for the good
                       of the environment. However, the climate system is
                       a complex beast, and one we’re still learning to
                       understand.


                # ⚓ Pro Publica ☛ The_EPA_Has_Identified_23_U.S._Facilities
                  Whose_Toxic_Air_Pollution_Puts_People_at_Risk⠀⇛


                       The U.S. Environmental Protection Agency on
                       Wednesday announced plans to “engage and inform”
                       nearly two dozen communities across the country
                       where air pollution from commercial sterilizer
                       plants has significantly increased lifetime cancer
                       risks for nearby residents. The facilities use a
                       toxic gas called ethylene oxide to sanitize medical
                       and dental equipment and fumigate certain food
                       products. The announcement comes after the EPA’s
                       inspector general and news publications including
                       ProPublica and The Texas Tribune highlighted the
                       agency’s yearslong failure to inform communities of
                       their risks.


                       The EPA said that its analysis of the industry’s
                       self-reported emissions data showed that about a
                       quarter of the nearly 100 commercial sterilizers
                       the agency regulates are exposing nearby residents
                       to unacceptable cancer risks from ethylene oxide.
                       It posted risk maps and other information online
                       for each of the high-risk facilities and announced
                       dates for national and community-specific webinars
                       and in-person meetings in the coming weeks.


                # ⚓ Common Dreams ☛ First-of-Its-Kind_Greenwashing_Lawsuit
                  Targets_Gas_Giant_for_Methane_Lies⠀⇛


                       Warning that a Washington, D.C. utility has run
                       afoul of the U.S. capital’s consumer protection
                       law, three public interest groups on Thursday
                       announced a first-of-its-kind lawsuit against
                       Washington Gas Light Company over what they called
                       the “greenwashing” of its use of highly pollutive
                       methane gas.


                       U.S. PIRG Education Fund, Environment America
                       Research and Policy Center, and ClientEarth filed
                       their lawsuit in the District of Columbia Superior
                       Court, saying Washington Gas is consistently
                       misleading more than one million customers by
                       advertising its use of natural gas as a “smart
                       choice for the environment.”


                # § Energy⠀➾


                      # ⚓ The Verge ☛ Spain_bans_setting_the_AC_below_27
                        degrees_Celsius⠀⇛


                             A decree published on Tuesday morning in the
                             official state gazette and scheduled to go
                             into effect next week mandates that air
                             conditioning in public places be set at or
                             above 27 degrees Celsius (about 80 degrees
                             Fahrenheit) and that doors of those buildings
                             remain closed to save energy.


                             Those public places include offices, shops,
                             bars, theaters, airports, and train stations.
                             The decree is being extended as a
                             recommendation to all Spanish households. The
                             rules include maintaining heating at or below
                             19 degrees Celsius (about 66 degrees
                             Fahrenheit) in the winter and will remain in
                             place at least through November 2023.


                      # ⚓ Pro Publica ☛ Manchin_Trades_Climate_Support_for
                        Massive_WV_Pipeline⠀⇛


                             From his Summers County, West Virginia,
                             farmhouse, Mark Jarrell can see the
                             Greenbrier River and, beyond it, the ridge
                             that marks the Virginia border. Jarrell moved
                             here nearly 20 years ago for peace and quiet.
                             But the last few years have been anything but
                             serene, as he and his neighbors have fought
                             against the construction of a huge natural
                             gas pipeline.


                             Jarrell and many others along the path of the
                             partially finished Mountain Valley Pipeline
                             through West Virginia and Virginia fear that
                             it may contaminate rural streams and cause
                             erosion or even landslides. By filing
                             lawsuits over the potential impacts on water,
                             endangered species and public forests, they
                             have exposed flaws in the project’s permit
                             applications and pushed its completion well
                             beyond the original target of 2018. The
                             delays have helped balloon the pipeline’s
                             cost from the original estimate of $3.5
                             billion to $6.6 billion.


          o § Finance⠀➾


                # ⚓ The Dissenter ☛ Equifax_Whistleblower_Says_He_Was_Fired
                  After_Exposing_Fraud_Related_To_Consumer_Complaints⠀⇛


                       Stephen Leary, a whistleblower for the US credit
                       reporting agency known as Equifax, says he was
                       fired after he refused to submit fraudulent data
                       about customer complaints to a US government
                       agency.He filed a lawsuit in a federal court in
                       Atlanta, Georgia, where Equifax is headquartered.
                       It alleges that Equifax violated a section of the
                       Consumer Financial Protection Act, which protects
                       employees of “consumer reporting agencies” from
                       this type of retaliation.“This case is about a
                       company punishing a dedicated employee for refusing
                       to ‘play ball’ when it tried to cover up its
                       regulatory violations that placed the financial
                       security of everyday Americans in jeopardy,” the
                       complaint declares.


                       Equifax garnered a notorious reputation in 2017
                       after a massive data breach compromised the
                       personal data of more than 145 million Americans,
                       as well as thousands of Canadians and nearly a
                       million citizens in the United Kingdom. The
                       company’s outreach to the public was viewed as
                       “haphazard,” “ill-conceived,” and a “dumpster
                       fire.”


                # ⚓ TruthOut ☛ Sinema_Wants_to_Prevent_Closure_of_Tax_Loophole
                  for_Rich_in_Reconciliation_Bill⠀⇛


                # ⚓ Common Dreams ☛ After_Shielding_Tax_Loophole_for_Private
                  Equity,_Sinema_Backs_Senate_Bill⠀⇛


                       Sen. Kyrsten Sinema announced late Thursday that
                       she has agreed to back Democrats’ new
                       reconciliation bill, but only after securing
                       changes to a proposed levy on major corporations
                       and forcing the removal of a provision targeting a
                       notorious tax loophole exploited by rich investors.


                       In a statement, Sinema (D-Ariz.) said that she and
                       the Democratic leadership agreed to strip out “the
                       carried interest tax provision, protect advanced
                       manufacturing, and boost our clean energy economy
                       in the Senate’s budget reconciliation legislation.”


                # ⚓ Common Dreams ☛ Siding_With_‘Private_Equity_Buddies,’
                  Sinema_Targets_Corporate_Tax_Provisions⠀⇛


                       As Senate Democrats work to finalize their new
                       reconciliation package, corporate-friendly Sen.
                       Kyrsten Sinema is reportedly demanding the removal
                       of language taking aim at a notorious tax loophole
                       that primarily benefits rich private equity
                       investors and billionaire hedge fund managers.


                       Politico reported Wednesday that the Arizona
                       Democrat—a major recipient of private equity
                       campaign cash—”wants to nix language narrowing the
                       so-called carried interest loophole,” which allows
                       some ultra-wealthy executives to pay a lower tax
                       rate than ordinary employees.


                # ⚓ TruthOut ☛ Sanders_Takes_Aim_at_Big_Oil,_Big_Pharma
                  Concessions_in_Inflation_Reduction_Act⠀⇛


                # ⚓ Common Dreams ☛ Sanders_Announces_Amendment_to_Strip_All
                  Fossil_Fuel_Handouts_From_Manchin_Deal⠀⇛


                       Sen. Bernie Sanders announced Wednesday that he
                       will be filing amendments to remove fossil fuel
                       industry giveaways from Democrats’ new
                       reconciliation bill and strengthen the
                       legislation’s drug price provisions, which the
                       Vermont senator has characterized as unacceptably
                       weak.


                       In a speech on the Senate floor, Sanders reiterated
                       the message he delivered in Tuesday remarks
                       outlining what he sees as the deep flaws of the
                       reconciliation package, the product of months of
                       negotiations primarily between fossil fuel industry
                       ally Sen. Joe Manchin (D-W.Va.) and Senate Majority
                       Leader Chuck Schumer (D-N.Y.).


                # ⚓ Common Dreams ☛ Bowman_Introduces_Bill_to_Help_People
                  ‘Crushed_by_the_Burden_of_High_Prices’⠀⇛


                       Stressing the need for a “new economic playbook”
                       that prioritizes human needs over corporate greed,
                       U.S. Rep. Jamaal Bowman on Thursday introduced
                       proposed legislation that would tackle excessive
                       profiteering with targeted price controls.


                       “In my district and across the country, people
                       simply cannot afford to live.”


                # ⚓ Common Dreams ☛ Opinion_|_How_to_Stop_the_GOP_From_Killing
                  Medicare,_Social_Security,_and_Us⠀⇛


                       It’s The Ronald Reagan Memorial Competition: which
                       Republican can make the rich richer and the poor
                       poorer the fastest?


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Scheerpost ☛ Elite_Lapdogs_Always_Welcome_in_Corporate
                  Media⠀⇛


                       Chris Cuomo’s return is a reminder that corporate
                       media personalities are not accountable to the
                       public, they are accountable to the elites they
                       serve.


                # ⚓ Insight Hungary ☛ CPAC_embraces_Viktor_Orban_despite_his
                  previous_remarks_on_‘mixed-race’_society⠀⇛


                       Viktor Orban, Hungary’s nationalist Prime Minister,
                       has traveled to Dallas to give an opening speech at
                       CPAC Texas on Thursday. The Conservative Political
                       Action Conference featured Orban after he sparked
                       outrage with his comments against Europe becoming a
                       ‘mixed-race’ society. After his controversial
                       remarks, one of his closest advisors stated it was
                       a ‘pure Nazi’ speech and resigned.


                       In his CPAC address, the Hungarian PM attacked the
                       media, saying their coverage of him is ‘fake news’
                       due to the country’s ‘zero tolerance policies ‘ for
                       racism and anti-Semitism. He also stated that a
                       ‘Christian politician cannot be racist’, and that
                       those who accuse him or his government of racism
                       and anti-Semitism are “idiots”.


          o § Censorship/Free Speech⠀➾


                # ⚓ Common Dreams ☛ ‘Catastrophic’:_Michigan_Town_Votes_to
                  Defund_Library_Over_LGBTQ+_Material⠀⇛


                       A library in western Michigan is at risk of closing
                       in the next year after town residents voted against
                       a tax that would have funded 84% of the facility’s
                       budget, following a fight over a book with LGBTQ+
                       themes on the library’s shelves.


                       On Tuesday, people in Jamestown Township voted 62%
                       to 37% against approving a millage that would have
                       been applied to residents’ property taxes in order
                       to fund Patmos Library.


          o § Civil Rights/Policing⠀➾


                # ⚓ Associated Press ☛ Suit:_Police_chasing_white_suspect
                  wrongly_arrest_Black_man⠀⇛


                       A suburban Boston police officer who was pursuing a
                       white suspect pinned a 20-year-old Black man to the
                       ground as he was walking home and placed a knee on
                       the man’s neck despite having no evidence that he
                       was involved in any crime, according to a federal
                       civil rights lawsuit filed Wednesday.


                # ⚓ NPR ☛ Undercover_journalist_in_Afghanistan_finds_Taliban
                  are_abducting,_imprisoning_women⠀⇛


                       Navai chronicles the Taliban’s treatment of women
                       in the new PBS Frontline documentary, Afghanistan
                       Undercover, which she started researching in early
                       2020.


                       “I started looking at the land [the Taliban] were
                       taking and what was happening to women in the
                       territory they were taking over. And it was
                       frightening,” Navai says. “I wanted to make a
                       documentary almost as a warning: Listen, everybody,
                       this is what’s happening.”


                # ⚓ TruthOut ☛ Anti-Abortionists_Deny_Importance_of_Kansas
                  Vote,_But_It’s_Massively_Significant⠀⇛


                # ⚓ Scheerpost ☛ Right-Wing_Extremists_Are_Making_Fiction_Come
                  True⠀⇛


                       Nina Burleigh looks into the political implications
                       of the overturning of Roe v. Wade.


                # ⚓ Common Dreams ☛ Opinion_|_The_Very_Good_People_of_Kansas⠀⇛


                       I want to talk about Kansas. Not about its corn as
                       high as an elephant’s eye, nor about Dorothy and
                       Toto trying to find their way home, but about
                       Kansas as the geographic and Republican center of
                       America, Kansas as the vintage Norman Rockwell core
                       of America, Kansas as what the Republican Party was
                       before being hijacked by Newt Gingrich and then
                       mugged by a New York real estate con artist.   


                # ⚓ Common Dreams ☛ ‘It’s_About_Damn_Time’:_4_Louisville_Cops
                  Charged_in_Killing_of_Breonna_Taylor⠀⇛


                       Following two years of racial justice activism, the
                       U.S. government on Thursday charged four current
                       and former Louisville, Kentucky officers for
                       alleged federal crimes related to the March 2020
                       killing of Breonna Taylor, a 26-year-old unarmed
                       Black woman who was shot dead in her own home
                       during a botched police raid.


                       “Justice delayed is justice denied. But it’s never
                       too late to do the right thing.”


                # ⚓ Common Dreams ☛ Russian_Court_Sentences_Brittney_Griner_to
                  9_Years_in_Penal_Colony_on_Drug_Charges⠀⇛


                       Following a Russian court’s announcement of a
                       guilty verdict in the case of U.S. basketball star
                       Brittney Griner on Thursday, calls mounted for
                       President Joe Biden to take any necessary steps to
                       help free the Women’s National Basketball
                       Association player.


                       Griner’s attorneys said they would “certainly file
                       an appeal” of the “unreasonable” verdict, which
                       came five months after Griner was arrested for
                       carrying two vape cartridges containing less than a
                       gram of hashish oil in her luggage at a Moscow
                       airport.


          o § Digital Restrictions (DRM)⠀➾


                # ⚓ Hollywood Reporter ☛ Roku’s_Decline:_Wall_Street_Sees_Rocky
                  Road_Ahead⠀⇛


                       Nathanson fears that Roku’s numbers, like other
                       companies’, had been elevated by consumer demand
                       for streaming video during the pandemic and
                       propped-up higher advertising spend in 2021. But,
                       as the second quarter showed, Roku’s advertising,
                       which is easy to turn off and on, appears more
                       susceptible to a recession than traditional TV
                       advertisers. At the same time, the company is
                       facing competition on three sides, Nathanson
                       writes.


                # ⚓ The Verge ☛ One_of_the_most_enduring_shows_on_TV_is_getting
                  put_behind_a_Peacock_paywall⠀⇛


                       NBC’s long-running soap opera Days of Our Lives
                       will be leaving broadcast television after 57 years
                       on to stream exclusively on Peacock, the network
                       announced on Wednesday. The change means that fans
                       who previously have been able to watch the show for
                       free on broadcast will now have to pay for a
                       streaming service to learn what happens next in the
                       show’s fictional town of Salem. New episodes of
                       Days of Our Lives will debut beginning September
                       12th.


          o § Monopolies⠀➾


                # § Copyrights⠀➾


                      # ⚓ Torrent Freak ☛ LaLiga_&_Movistar_Will_Block_IPTV
                        Pirates,_No_Court_Process_Needed⠀⇛


                             Top-tier football league LaLiga and
                             subscription TV platform Movistar Plus+ have
                             won a joint lawsuit in Spain that allows them
                             to block IPTV services until 2025 without
                             needing permission from the courts. A second
                             lawsuit won by Movistar Plus+ allows the TV
                             platform to advise local ISPs of piracy-
                             facilitating sites on a weekly basis and have
                             them blocked within three hours.


                      # ⚓ Torrent Freak ☛ CloudStream-3_Piracy_App_Taken_Down
                        By_Sky_UK_DMCA_Notice⠀⇛


                             Popular open source Android app Cloudstream-
                             3 allows people to watch movies and TV shows
                             by aggregating content from dozens of major
                             streaming sites. Following a DMCA takedown
                             notice sent to Github on behalf of Sky UK,
                             which complains about the availability of a
                             single TV episode, Cloudstream-3′s main
                             development repo has been consigned to
                             history.


    * § Gemini* and Gopher⠀➾


          o § Personal⠀➾


                # ⚓ Manhattan⠀⇛


                       I was schlepping down to the decent bagel shop two
                       blocks away. The one on my block is awful, and the
                       really good one is twenty blocks away. Well worth
                       the mile walk, but lately there’s been a line of
                       thirty-somethings around the block. So, the decent
                       bagel is good enough.


                # ⚓ SpellBinding:_EYKLNUI_Wordo:_SAVOR⠀⇛


                # ⚓ I_broke⠀⇛


                       I don’t know what else to call it, I guess since I
                       still have my wits about me I’m not broken per say
                       but I decided to drive out into the woods to get
                       away from my life for a while. Or not a while, just
                       tonight.


          o § Technical⠀➾


                # § Science⠀➾


                      # ⚓ The_Joule_Thief⠀⇛


                             The “Joule Thief” is a simple voltage booster
                             circuit that allows batteries that would
                             otherwise be considered “dead” (with voltages
                             as low as ~0.3 V) to power LEDs.


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


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