𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Friday, July 15, 2022
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Generated Sat 16 Jul 02:39:57 BST 2022
Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖)
Full hyperlinks for navigation omitted but are fully available in the originals
The corresponding HTML versions are at 𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈
Latest in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕 and older bulletins can be found at 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕-𝒂𝒓𝒄𝒉𝒊𝒗𝒆𝒔
Full IPFS index in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔 and as plain text in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔/𝒕𝒙𝒕
Gemini index for the day: gemini://gemini.techrights.org/2022/07/15/


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

QmaWVVRETtCzr9u3pkbf9NmBNErxp6EwwuuRbbGaNBDbxs
QmRnbEP8kvfDSZqPYikywBMxdJ2dsMPv4ujj2tKn8HPofU
QmRdcPDNXG7La9xrpj9Te3TGetenUACvpQoAsNtm1XNbZY
QmWvpCp84jsz33ggJ9VGNJLVVweLbvAgZC4QSMMpMtjws4
QmTanxCbrRzbMhGwCHPd6tznN3vqohgB6ksoqtyCiMnDFL
QmSGNyqayw9Kb8GtH2D4DicRMEG9NuJ9kQEJo4KgFc1NeH
QmcVu8iJ8yJqBwWTWX3TYY3ChamvbJm15Ne1VJxfTjdLY6
QmSDCize8znng3qFHzA4NgsDaeV7fzdXZrj1CKRp5JBbgK
QmW2xppCHSDJtWfjB5RvaKrsEtS7w97YEMS3ePee6oW9Mp
QmSGhRVAV44sV2y4ZAiDWo9kvmhjvgBBfpAKFP6AdRx6Pc
Qmf7RX5zTm8khR5YEXJ6a48wsPiHG9zDm63S7nvMHXK1PE
QmZQcpV8gJiG7uwAzM2U75TrNyBfZY4RZNaGfhLLDxdSqB
QmajcAdRfWtgWFRoBM7yDJL3X8EJ5w8Wxf6CNnraP2EQo6
QmateHRg7s96CyDx4BcnezZSfn66P9YWrKiMv5VvFfNyEU
QmehYSPymw58ozer2trPYvEomCKmEguPNgE3qdCbXcmNW9
QmP3Nw5usXTHPhcMx8yZ9TYsWzwSKRw9BNnbjhkoJ88gpe
QmNt7g1pzLJJDE5MHZ21wEEuyos1W3DFP2LTSjB2FLPJPi
QmXniW6uykwhxPzQFCih3ywbRTbNtozdD9MTkKJWNUUis7
Qmba4Ap4JVU96TSWT1jJZfQAasTyweA1EFu92C6ULqfYVF
QmQDNYLCxwvKJsAAbaMfkydsH6iMivVs54xVt3e1WhRa4V
QmZrgDSeEPr5Tk1kd6ixcTH5gK8gVF6UWZ8USDWkwExtL2


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

⦿ Clickfraud Spamnil | Techrights

⦿ The EPO Bubble — Part III — Dividing Up the Spoils... | Techrights

⦿ This is How to Kill a Reputable Patent Office in Only a Few Years | Techrights

⦿ IRC Proceedings: Thursday, July 14, 2022 | Techrights

⦿ Reporting Progress on Our New CMS Developmemt | Techrights

⦿ [Meme] Give Us More Money by Selling Monopolies to Foreign Corporations in Violation of the European Patent Convention                | Techrights

⦿ [Meme] Plot Twist | Techrights

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
		http://techrights.org/2022/07/15/clickfraud-spamnil/#comments
		http://techrights.org/2022/07/15/dividing-up-cooperation-slush-fund/#comments
		http://techrights.org/2022/07/15/dooming-the-epo/#comments
		http://techrights.org/2022/07/15/irc-log-140722/#comments
		http://techrights.org/2022/07/15/new-cms-developmemt/#comments
		http://techrights.org/2022/07/15/selling-monopolies/#comments
		http://techrights.org/2022/07/15/the-epo-plot-twist/#comments

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
		http://techrights.org/2022/07/15/bmw-joins-yocto-project/#comments
		http://techrights.org/2022/07/15/oem-and-flex/#comments
		http://techrights.org/2022/07/15/tor-browser-11-5/#comments

                    ䷩ 𝚕𝚒𝚗𝚎 67

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/07/15/clickfraud-spamnil/#comments
    Gemini version at gemini://gemini.techrights.org/2022/07/15/clickfraud-spamnil/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.15.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Clickfraud_Spamnil⠀✐


Posted in Deception at 3:13 am by Dr. Roy Schestowitz


Scamnil?


                    🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Clickfraud Spamnil⦈
  This has gone on for months and the whole channel can be banned when Google
                                 detects this


Summary: The ones shown above (in blue) are clickfraud, which SPAMnil has done
for a few months already (we’ve shown evidence extensively in the past) in
order to hide how poorly his videos are performing; to make matters worse, the
Linux_Foundation is financially_backing_this_clickfraud and it’s not helping
“Linux”, it’s tarnishing the brand (these videos are made with proprietary
software by the way)


⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿
⣿⡇⠀⠒⠂⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠐⠐⠂⠀⠀⠀⣠⠲⣿⣶⣄⢸⠀⠐⠒⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠂⠒⠀⠀⠀⢀⡔⣤⣶⣦⡀⠀⠀⠂⠐⠀⠀⠀⣠⢶⣭⣶⣦⢸⠀⠐⠐⠂⠀⠀⠀⠠⢂⣉⠲⠄⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⡀⠌⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣒⢺⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⠂⠀⠀⠀⠀⠀⠀⠀⠀⢺⣷⢂⡾⢿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠰⠀⢲⡇⠀⠀⢸
⣿⡇⠀⠐⠐⠒⠀⠀⠀⠀⠤⠃⢉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠚⠋⢸⠐⠀⠀⠀⠒⠀⠀⠀⠼⠞⠀⠀⠀⠐⠂⠐⠒⠂⠀⠀⠀⠦⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠣⠤⠈⠋⢸⠐⠒⠐⠀⠐⠀⠀⠀⠘⠓⠀⠀⢸
⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾
⣿⣿⣽⣿⣿⣿⣭⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣯⣿⣿⣯⣯⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣯⣿⣿⣽⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠤⠄⠀⠀⠀⠀⠀⢀⡀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⠠⠠⠀⠀⠀⠀⣀⢄⡠⣄⡀⠁⠠⠄⠠⠀⠀⠀⠀⣠⠤⢤⣄⠀⠃⠄⠤⠄⠀⠀⠀⠀⢀⣤⡀⠀⢸⠀⠠⠠⠄⠀⠀⠀⢀⠤⠀⢤⡀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠳⡆⣿⣿⣿⣿⡟⣷⡆⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⡟⣿⣿⠘⣷⠀⠀⠀⠀⠀⠀⠀⢸⡇⡺⣦⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠭⡅⠀⢸⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠈⣿⢸
⣿⡇⣀⢀⣚⡀⡀⠀⠈⠀⢄⠀⠀⠁⠓⠊⠉⠉⢙⣽⣷⣚⢿⣿⠟⠋⢹⢀⡀⠀⡀⣀⣀⡈⠃⠘⠿⠀⠏⠀⢀⡀⣀⢀⡀⠀⠘⠧⣀⡂⠿⠃⠀⢂⣀⣂⡒⣀⣀⠀⠀⢁⠀⠀⢸⢀⠀⠀⡀⡀⣀⡀⠻⠃⡀⠘⠛⢸
⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣭⣤⣤⣤⣤⣼⣤⠤⠤⣄⣀⡠⠤⢤⣤⣤⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼
⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣻⣿⣿⣿⣿⣿⣾⣿⣿⣶⣿⣫⣶⣞⣾⣻⣿⣿⣿⣗⣪⡙⣿⣿⢟⣋⣭⣠⣲⣶⣦⣭⣙⡻⠿⣫⣭⣶⣶⣲⣿⣶⣶⣲⣦⣭⡻⣿⣿⣿⠾⢟⣛⣛⣚⣓⣛⣛⡻⠿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣗⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣼⣟⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣹⣿

                    ䷩ 𝚕𝚒𝚗𝚎 116

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/07/15/dividing-up-cooperation-slush-fund/#comments
    Gemini version at gemini://gemini.techrights.org/2022/07/15/dividing-up-cooperation-slush-fund/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.15.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ The_EPO_Bubble_—_Part_III_—_Dividing_Up_the_Spoils…⠀✐


Posted in Europe, Patents at 1:26 am by Dr. Roy Schestowitz


Overview: [Teaser]_The_EPO’s_Deflating_Patent_Bubble_and_Pursuit_of_Illegal
Software_Patents_(With_Kangaroo_Courts,_UPC,_and_Bullied_Examiners)


Series parts:


   1. The_EPO_Bubble_—_Part_I_—_An_“Unprecedented_Surge”
   2. The_EPO_Bubble_—_Part_II_—_Signs_of_a_Deflating_Bubble?
   3. YOU ARE HERE ☞ Dividing Up the Spoils…
                 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Battistelli_and_the_pigs⦈_
The higher the volume of granted patents, the larger cash pool available to be
            divvied up between the EPO and its contracting states.


Summary: The corrupt presidency of António_Campinos sees a sharp decline in the
number of patent grants; as a result, it bullies_honest_examiners and seeks to
illegally expand patent scope (read: European_software_patents and other
unlawful monopolies) with help from the Administrative Council, motivated by
self-serving overzealous greed; there’s a lot of money at stake!


In the preceding parts we looked at the EPO’s “grant bubble” which commenced
with Benoît_Battistelli’s “unprecedented surge” of 2016 and we saw how this
“bubble” has started to deflate over the course of the last two years.


To the outside observer this development probably looks like the natural and
healthy “correction” of an undesirable and unsustainable state of affairs.


However, the senior management of the EPO and their “friends” on the
Organisation’s governing body – the Administrative Council – are likely to see
matters differently.


“The essential point to be grasped here is that every granted European patent
application generates “national renewal fees” (NRFs) in all of the designated
EPO contracting states during the time that it is maintained in force by its
proprietor.”Those who are inside EPOnia’s “golden circle” have a “vested
interest” in propping up the bubble in order to safeguard the lucrative cash
flow from the legendary “Dukatenesel”.


The essential point to be grasped here is that every granted European patent
application generates “national renewal fees” (NRFs) in all of the designated
EPO contracting states during the time that it is maintained in force by its
proprietor.


The NRFs generated by these patents are shared between the contracting states
and the EPO in accordance with Article_39_EPC (warning: epo.org link). The
current split is takes place on 50-50 basis.


Article 39 EPC foresees that the EPO could be awarded as much as 75% of the
overall NRF revenue – subject to the Administrative Council agreeing to a
change in the distribution ratio.


“In any event, the bottom line here is clear: the higher the volume of granted
patents, the larger the cash pool available to be divvied up between the EPO
and its contracting states.”However, in practice, an increase of the EPO’s NRF
dividend is unlikely to be approved by the Administrative Council because the
contracting states jealously guard their own share of the loot. If anything,
they would prefer to increase this and reduce the EPO’s slice of the cake if
only they could find a plausible pretext for doing so.


In any event, the bottom line here is clear: the higher the volume of granted
patents, the larger the cash pool available to be divvied up between the EPO
and its contracting states.


An increased grant rate at the EPO boosts the revenue of the national patent
offices of the contracting states. All of these national offices are financed
predominantly by NRFs from granted European Patents.


As an illustrative example, let us briefly consider what this implies in the
case of one of the EPO’s most significant contracting states, Germany.


“All of these national offices are financed predominantly by NRFs from granted
European Patents.”Back in 2014, Germany’s estimated NRF revenue share was € 149
million.


By 2021 this amount had risen to € 211 million, an increase of around 40%
compared to 2014.


To put these figures into perspective, in 2021 the total expenditure of the
German Patent and Trademark Office (DPMA) was € 248,5 million and it recorded
an operating profit of € 214,7 million which was transferred to the federal
treasury.


In other words, the revenue accruing to the DPMA from granted European patents
in 2021 (€ 211 million) was sufficient to cover about 85% of its expenditure.


This portion of the DPMA’s revenue was also more or less equivalent to its
reported operating profit (€ 214,7 million) which was transferred to the
federal treasury.


“In other words, the revenue accruing to the DPMA from granted European patents
in 2021 (€ 211 million) was sufficient to cover about 85% of its
expenditure.”No wonder that the German delegation on the EPO Administrative
Council was such an enthusiatic_supporter_and_"enabler" of Battistelli’s
“reforms” at the EPO!


The EPO for its part receives a 50% share of the total NRF revenue generated in
its contracting states.


This means that an increased grant rate also bolsters the EPO’s own internal
“slush fund” for keeping delegates from the_smaller_contracting_states “onside”
by means of EPO-financed_co-operation_projects.


In view of these circumstances it should come as no surprise that the ongoing
deflation of Battistelli’s “grant bubble” is a cause for concern in some
quarters. We shall look into this in more detail in the next part. █


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


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

                    ䷩ 𝚕𝚒𝚗𝚎 344

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/07/15/dooming-the-epo/#comments
    Gemini version at gemini://gemini.techrights.org/2022/07/15/dooming-the-epo/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.15.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ This_is_How_to_Kill_a_Reputable_Patent_Office_in_Only_a_Few_Years⠀✐


Posted in Europe, Patents at 4:08 am by Dr. Roy Schestowitz


Video_download_link | md5sum 28995d63e899a05cb2a50755a92c87ab
EPO Run Like a Bank
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/unsustainable-epo.webm


Summary: EPO administrators who lack an understanding of the scientific process
and patent law have turned the organisation upside down and doomed its actual
mission


THE video above concerns the second_part_of_the_current_EPO_series and António
Campinos running the EPO as if it was a bank.


Like Benoît_Battistelli before him, he has very poor grasp of patents and of
science. Maybe it’s not surprising that Battistelli chose him as his successor
and rigged the process, ensuring a reckless bankster keeps checks and balances
in the dark, in effect covering up a decade or so of EPO corruption.


It’s a safe prediction that there’s trouble ahead for the EPO; it’s a
reasonable forecast in light of the current implosion of a bubble, which ruins
Europe’s largest patent office; instead of relying on a steady flow of high-
quality patents from highly-specialised examiners we now have a mill_of_sorts.


The Office may have gone past “the_point_of_no_return”; a suitably_qualified
staff_pool_isn't_coming_back. █



                    ䷩ 𝚕𝚒𝚗𝚎 397

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/07/15/irc-log-140722/#comments
    Gemini version at gemini://gemini.techrights.org/2022/07/15/irc-log-140722/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.15.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ IRC_Proceedings:_Thursday,_July_14,_2022⠀✐


Posted in IRC_Logs at 2:59 am by Needs Sunlight


Also available via the Gemini protocol at:


    * gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-140722.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-140722.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-social-140722.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-140722.gmi
Over HTTP:


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


                                         #techrights_log_as_HTML5                                                                                  #boycottnovell_log_as_HTML5


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


                                    #boycottnovell-social_log_as_HTML5                                                                               #techbytes_log_as_HTML5


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


                                          #techrights_log_as_text                                                                                   #boycottnovell_log_as_text


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


                                     #boycottnovell-social_log_as_text                                                                                #techbytes_log_as_text


                          Enter_the_IRC_channels_now


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


CID                                              Description     Object type


                                                 IRC log for
 QmQL4tGfFpd6ratCo9Rr82Uyh59DtaepKhhgLiX21sqgcu #boycottnovell  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell
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                                                 as plain/ASCII
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                                                 IRC log for
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                                                 (full IRC log
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                                                 IRC log for
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 QmTi28yaVBnjm3A2cHAJmNMi4Fi9z36PKrhqmJ1vyjMz4t social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 (full IRC log
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                                                 IRC log for
 QmSUTdBWNyEY95HbDCZniKgMMqcvsVPVftVFotPAYu9JiF #techbytes      🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
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                                                 IRC log for
                                                 #techbytes
 QmYNizwbmW8hwZzcVJYPRu2jhy2FtPk9QuiSatPs6uxyvG (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
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                                                 IRC log for
 QmepvSYxJC8mK5dKKqUkSaLJbRhKAYydZBbp1bo9Bvnmfk #techrights     🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
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                                                 IRC log for
                                                 #techrights
 QmYizotshLiXq7rfysVonsrzTmTA5WSpdRGX7YHpK7PSym (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
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🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈


§ Bulletin for Yesterday⠀➾


Local_copy | CID (IPFS): QmZrgDSeEPr5Tk1kd6ixcTH5gK8gVF6UWZ8USDWkwExtL2



                    ䷩ 𝚕𝚒𝚗𝚎 524

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(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/07/15/new-cms-developmemt/#comments
    Gemini version at gemini://gemini.techrights.org/2022/07/15/new-cms-developmemt/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.15.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Reporting_Progress_on_Our_New_CMS_Developmemt⠀✐


Posted in Site_News at 8:12 pm by Dr. Roy Schestowitz


Video_download_link | md5sum 54e8bd754e6fa939cc26281e3d0230c6
Mockups and Prototype of New CMS
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/tuxmachines-mockups.webm


Summary: We’ve been developing software for lightweight site management that’s
more robust to downtime and is easier to maintain as sites grow very large
(tuxmachines.org is nearly 170,000 Drupal pages already; Techrights is over
34,000_WordPress_pages)


THE Content Management System (or software, CMS for short) conundrum is
unsolved. We’ve already explained the pervasive bloat problem, the growing
chains of dependency, the security risks, and — overall — the technical debt.
I’ve been dealing with Web sites creation for 25 years and with various CMS
packages for over 20 years. WordPress is a monster, Drupal is not easy to
manage (especially for administrators) and a lot of old systems are no longer
maintained/developed.


“Unlike caching, there’s no need for hash tables and re-computation of
pages.”So a couple of weeks ago we decided to develop our own with the
intention of keeping it super-simple and light. The chain of dependencies is
minimal and we’ll probably run it on Alpine, without Microsoft systemd.


The video above is a quick tour through the latest slate/state of things. It
looks something like this:


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


Given a week or two we’ll hopefully have a publicly-accessible beta of some
kind, not yet a migrated site. This can lessen complexity and server load.


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


Yes, this shows tuxmachines.org, not Techrights, but if the former site’s
migration goes well, we shall consider doing the same with Techrights, for
reasons that are explained in the video (faster workflow, more resource
efficiencies, more extensibility).


This post isn’t about any issues but about platforms that cover the issues.
Having said that, it helps explain what’s wrong with the Web and how it can be
tamed. Static pages are the only pages to be served with the new CMS, but
there’s a database of all the pages, from which we plan to generate GemText
files as well. The static pages are in effect exported from it. Unlike caching,
there’s no need for hash tables and re-computation of pages. █


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⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣦⣤⣤⣶⣦⣤⣤⣶⣶⣴⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀

                    ䷩ 𝚕𝚒𝚗𝚎 654

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/07/15/selling-monopolies/#comments
    Gemini version at gemini://gemini.techrights.org/2022/07/15/selling-monopolies/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.15.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_Give_Us_More_Money_by_Selling_Monopolies_to_Foreign_Corporations_in
Violation_of_the_European_Patent_Convention⠀✐


Posted in Europe, Patents at 4:13 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Heads of states + National delegates: More patents, please⦈
           Will you please check what the patent systems exist for?


Summary: When patents_get_treated_like_nothing_but_monetary_asset it’s hardly
surprising that the EPO sees them as something that needs to be granted in the
highest possible volume, as_fast_as_possible


⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠛⠻⢿⣿⣿⠿⠿⢿⠿⠿⣿⠿⢿⡿⠏⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣠⣄⣤⣤⣤⣤⣤⣤⣄⣸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣨⣿⢿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣼⣿⣿⣿⣿⡿⣿⣿⡏⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣯⣏⣿⠹⣿⡏⣿⢹⡏⣿⣿⡇⢻⣿⡯⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢹⣿⣿⣿⢿⣷⣿⢿⣇⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⠀⣿⡃⣿⣸⠇⣿⢹⡇⣾⡿⣿⢸⣟⠀⠀⠀⣀⣀⣀⣀⡀⠀
⠀⢀⣠⣴⣆⣀⣀⣀⠀⠀⠀⠀⢸⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢠⣶⣿⡇⠀
⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⣶⢻⣿⣶⣶⣿⣿⡟⣎⣶⣶⣦⣶⣾⣷⢲⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢀⣿⣿⣿⡟⣧⠀⡶⣆⠰⣶⠶⢰⡶⢠⡖⢶⠀⠀⠁⠈⠉⠉⠁⠀
⢀⢠⠀⢰⣤⡄⠀⢠⡄⠀⠀⣿⢸⡿⣿⣿⣿⣿⣽⣿⣿⣿⣏⡯⣿⣾⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⡞⣿⣶⢿⡟⣶⢰⣇⣿⠀⣿⠀⢸⡗⢀⡙⢷⡄⠀⣷⣾⣿⣿⣿⣿
⢸⢸⠀⣿⣿⣷⠀⢸⡇⠀⠀⠈⠉⢱⣽⣿⣿⣿⣿⣷⣿⣯⣭⣵⣯⣿⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡓⠘⠛⣂⠛⣲⣿⣓⠛⠘⠋⠛⠀⠛⠀⠘⠓⠂⠓⠚⠁⢠⣿⣿⣿⣿⣿⣿
⢸⠘⡀⣿⣿⣷⢠⢸⡇⠀⠀⠀⠀⠀⢹⣿⣿⠉⠛⢻⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿
⠸⠀⡇⢿⣿⣿⢨⠸⡇⠀⠀⠀⠀⠀⢸⠭⠛⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⠿⠋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠉⠁⠀⠀⠁⠀⠀⠀⠀⠀⢰⡋⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠹⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢠⠀⡆⠀⣶⠀⡆⢀⣀⢠⠀⠀⠀⠀⢼⡇⠀⢸⣿⣿⣿⣭⣵⣾⣿⣿⠟⣿⣷⣾⠈⠋⢍⣽⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⠀⠀⠉⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠂⠃⢻
⢸⠀⡇⠀⣿⠀⡇⠘⠛⠀⡇⠀⠀⠀⣿⣧⠀⠘⠉⠁⠈⢫⡛⠛⠋⠁⢴⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣽⣿⣷⣶⠄⠀⠠⣷⣶⣴⣶⣦⠀⠀⠀⠀⠀⠀⢰⢖⣭⢽⣶⣷⣶⠀⠀⢸
⢸⠀⡇⠀⣿⠀⡇⠀⠀⠀⡇⢀⠤⠜⠋⠁⠀⠀⠀⠀⠀⠘⣿⠆⢀⠐⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⣴⢅⢸⡟⣿⣿⣿⣿⠇⣤⣶⣿⣿⣷⡔⢽⣿⡵⠝⣡⣶⡄⠀⢸
⠘⠀⠃⠀⠈⠀⠃⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⠆⢀⣴⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⢿⣿⣟⣵⠶⡿⠹⠟⠀⣹⣿⣽⠿⠃⠉⠉⣉⣹⣿⣿⣿⣶⣁⠉⣾⣿⣿⣇⠀⠸
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣯⣤⣬⣿⣿⣿⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⢿⣾⣿⣿⣿⣿⣷⣼⣷⣶⠋⢀⣿⣦⣀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠛⢿⣿⣿⣿⣦⣤
⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣯⣿⣽⣟⣻⣿⣷⢶⣦⣴⣾⣿⣿⣿⣿⣿⣿⢸⣿⢿⠿⠿⢿⣿⣿⡿⣿⣷⣿⣿⣯⡰⢞⣿⢃⡈⠙⣋⢙⣛⠟⠀⢸⣿⣿⣿⣿⣿
⣿⠀⠀⠛⢛⣛⣻⡿⠛⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⡷⣿⢸⣿⣿⣏⡿⣿⣿⢯⣿⣿⣿⣿⣿⠋⠸⡿⠀⡏⠰⣶⣮⠿⠃⠰⠀⠈⠙⠉⠭⣍⢺⡿⠁⢈⣍⣻⡁⠠⠆⠀⠀⠸⣿⣿⣿⣿⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢿⣾⣯⣿⢻⣿⣿⡏⣽⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⢩⣾⡿⠀⠀⠀⠀⣀⣸⣿⢉⣙⠋⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠻⠩⠟⠯⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢷⣾⣿⣿⣿⣿⣿⣿⣻⣿⡿⢿⣿⣷⣾⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠸⡿⠁⠀⠀⠀⣰⣿⣿⣟⠀⠁⠀⠀⢀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⡏⢽⣿⡟⣷⡾⣿⣯⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠇⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⢼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠐⠂⠐⠂⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣟⣿⣿⣿⣿⣿⣿⣿⣯⢽⣿⣿⣧⣿⣿⣾⡿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⡤⠀⠀⣫⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣿⣭⣿⣼⣿⣛⣻⣸⢿⡇⣿⣼⣟⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⢨⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⢳⣿⣏⣫⣿⣿⣟⣛⣿⡿⠿⣷⣾⣯⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⢹⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣟⡿⣿⣿⣿⣼⣛⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠠⠄⠀⠀⠸⣿⣿⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣛⣿⣿⢿⢿⣷⣆⣿⢪⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠰⢿⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡃⠀⠀⠀⢀⣀⠀⠀⠀⠀⠛⠛⠀⠐⠂⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣯⣽⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⠂⠐⠓⢀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠿⠛⠇⣽⠉⠸⡯⠢⠪⠸⠕⠿⠱⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠛⠻⢿⣿⣿⠿⠿⢿⠿⠿⣿⠿⢿⣿⠏⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣠⣄⣤⣤⣤⣤⣤⣤⣄⣸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣨⣿⢿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣯⣏⣿⠹⣿⡟⣿⢹⡏⣿⣿⡇⢻⣿⡯⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢹⣿⣿⣿⢿⣿⣿⢿⣇⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⠀⣿⠁⣿⣸⠇⣿⢹⡇⣾⡿⣿⢸⣟⠀⠀⠀⢀⣀⣀⣀⡀⠀
⠀⢀⣤⣴⣂⣀⣀⣀⠀⠀⠀⠀⢸⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⣶⣿⡇⠀
⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⣶⢻⣿⣶⣶⣿⣿⡟⣎⣶⣶⣦⣶⣶⣷⢲⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢠⣿⣿⣿⡟⣧⠀⡶⡆⠰⣶⠶⢰⡶⢠⡖⢶⠀⠀⠁⠈⠙⠉⠁⠀
⢀⢠⠀⢰⣤⡄⠀⢠⡄⠀⠀⣿⢸⡟⣿⣿⣿⣿⣽⣿⣿⣿⣇⡯⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⡞⣿⣶⣿⡟⣶⢰⣇⣿⠀⣿⠀⢸⡗⠀⡙⢷⡄⠀⣷⣾⣿⣾⣿⣿
⢸⢸⠀⣿⣿⣷⠀⢸⡇⠀⠀⠈⠉⢱⣽⣿⣿⣿⣿⣷⣿⣯⣭⣵⣯⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡓⠘⠛⣂⡛⣲⣿⣓⠛⠘⠋⠛⠀⠛⠀⠘⠓⠂⠓⠚⠁⢠⣿⣿⣿⣿⣿⣿
⢸⠈⡄⣿⣿⣿⢀⢸⡇⠀⠀⠀⠀⠀⠹⣿⣿⠉⠛⢻⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿
⠸⠀⡇⢿⣿⣿⢰⠸⡇⠀⠀⠀⠀⠀⢈⢟⠛⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⠿⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠉⠁⠀⠀⠁⠀⠀⠀⠀⠀⣸⣄⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠹⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢠⠀⡆⠀⣦⠀⡆⢀⣀⢠⠀⠀⠀⠀⠸⡇⠀⢹⣿⣿⣿⣭⣿⣾⣿⣿⠿⢿⣿⣾⠈⠛⢍⣝⣝⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠀⠀⠉⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠒⠃⢻
⢸⠀⡇⠀⣿⠀⡇⠘⠛⠀⡇⠀⠀⠀⣾⣷⠀⠘⠉⠁⠈⢩⡛⠛⠋⠁⢴⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣽⣿⣷⣶⠄⡀⢠⣷⣶⣤⣶⡶⠀⠀⠀⠀⠀⠀⢰⢶⣭⢽⢶⣷⣾⠀⠀⢸
⢸⠀⡇⠀⣿⠀⡇⠀⠀⠀⡇⢀⠤⠜⠋⠁⠀⠀⠀⠀⠀⠘⣿⠆⢀⠐⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⣴⢅⢸⡟⣿⣿⣿⣿⠇⣤⣶⣿⢾⣷⡔⢽⢿⡵⠟⣡⣶⡀⠀⢸
⠘⠀⠃⠀⠈⠀⠃⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⡆⢀⣴⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⢿⣿⣟⣵⠶⡿⠹⠗⠀⣹⣿⣽⠿⠋⠉⠉⣉⣩⣿⣿⣿⣶⡁⠉⣾⣿⣿⣇⠀⠸
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣯⣤⣬⣿⣿⣿⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⢿⣾⢿⣿⣿⣿⣷⣼⣷⣶⠋⢀⣿⣦⣀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠙⢿⣿⣿⣿⣦⣤
⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣫⣿⣽⣟⣻⣿⣷⢶⣦⣴⣾⣿⣿⣿⣿⣿⣿⢸⣿⢻⠿⠿⠿⣿⣿⡿⣿⣷⣿⣿⣯⡰⢞⣿⢃⡉⠙⣋⢙⣛⠟⠀⢸⣿⣿⣿⣿⣿
⣿⠀⠀⠛⣛⣛⣻⡿⠛⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⢸⣿⣿⣏⡿⣿⣿⢯⣿⣿⣿⣿⣿⠋⠸⡿⠀⡏⠰⣶⣮⠿⠁⠰⠀⠈⠙⠉⠭⣭⣾⡿⠃⢨⣍⣻⠁⠠⠆⠀⠀⠸⣿⣿⣿⣿⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢿⣾⣧⣿⢻⣿⣿⡏⣽⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⢩⣿⣿⠀⠀⠀⠀⣀⣸⣿⢉⣉⠋⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠻⠉⠛⠯⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢷⣾⣿⣿⣿⣿⣿⣛⣻⣿⡿⢿⣿⣷⣾⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠘⡿⠁⠀⠀⠀⣰⣿⣿⣟⠀⠁⠀⠀⢀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⡏⢽⣿⡟⣷⡾⣿⣯⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠇⠀⠀⠀⠀⣨⣿⣿⡏⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠐⠂⠐⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣯⢽⡿⣿⣧⣿⣿⣼⡿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⠀⡤⠀⠀⣺⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣿⣭⣿⣼⣷⣛⣻⣸⢟⡇⣿⣼⣟⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⢀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⢻⣿⣏⣫⣿⣿⣟⣛⣿⡿⠿⣷⣾⣯⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⠀⠀⠀⠀⠈⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣟⡿⣿⣿⣿⣜⣛⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠠⠄⠀⠀⠸⣿⡿⠛⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣛⣿⣿⢿⢿⣷⣆⣿⢢⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠰⢿⡀⠀⠀⠀⠀⠀⠀⠈⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀
⠐⡃⠀⠀⠀⢀⢀⠀⠀⠀⠀⠛⠛⠀⠐⠂⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣯⣽⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⠃⠀⠋⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠿⠛⠇⣽⠉⠸⡯⠢⠪⠰⠕⠿⠱⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⣿⠿⠿⢿⠿⠿⣿⠿⢿⡿⠇⢠⣤⣤⣤⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣼⣿⣿⣿⣿⣿⣿⣿⡿⣇⣺⣿⢿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣼⣿⣿⣿⣿⡿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣯⣿⣿⠻⣿⠇⣿⢹⡇⣿⣿⡇⢸⣿⡯⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⢹⣿⣿⣿⢿⣿⣿⢿⣇⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣿⠀⣿⠅⣿⣸⠇⣿⢹⡇⣾⡿⣷⢸⣇⠀⠀⠀⣀⣀⣀⣀⡀⠀
⠀⢠⣤⣶⣀⣄⣠⡄⠀⠀⠀⠀⢸⣿⣿⣶⣺⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣴⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⣾⣿⡇⠀
⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⣶⢻⣿⣶⣶⣿⣿⡟⣎⣶⣶⣮⣶⣶⣷⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣸⣿⣿⣿⣟⣧⠀⡶⡆⠰⣶⠶⢰⡶⢠⡖⢶⠀⠀⠁⠉⠉⠉⠁⠀
⡄⢠⠀⣶⣶⡄⡆⢠⠀⠀⠀⣿⢸⡿⣿⣿⣿⣿⣽⣿⣿⣿⣏⡯⣿⣾⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⠃⣿⢲⢹⡏⣷⢰⣇⣿⠀⣿⠀⢸⡗⢀⡙⢷⡄⠀⣠⣿⣿⣿⣿⣿
⣧⢸⢰⣿⣿⡇⡇⢸⠀⠀⠀⠈⠉⠱⣽⣿⣿⣿⣿⣷⣿⣯⣯⣵⣯⣿⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠘⠛⣦⣿⣶⣿⣓⣛⠘⠋⠛⠀⠛⠀⠘⠓⠂⠓⠚⠁⢠⣿⣿⣿⣿⣿⣿
⢸⢸⢸⣿⣾⡇⠀⢸⡆⠀⠀⠀⠀⠀⢹⣿⣟⠙⠛⢿⣿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢛⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠸⠸⠈⢿⣿⡇⠀⢸⡇⠀⠀⠀⠀⠀⢠⠘⠻⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠘⣿⣽⣿⣭⣥⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣶⡁⠀⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠘⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀
⣄⢰⡄⠀⡇⢰⡆⢀⡀⢰⠀⠀⠀⠀⢿⡅⠀⣿⣿⣿⣿⣩⣽⣾⣿⡿⠿⣿⣷⣷⠈⠋⢿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⠀⠀⠀⠈⣄⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠓⠃⢿
⣯⢸⡇⠀⡇⢸⡇⠘⠋⢸⠀⠀⠀⢀⣾⣧⠀⠛⠉⠁⠈⣝⠛⠛⠋⠁⣴⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣾⣿⣿⣶⡶⠀⡄⠀⢿⣿⣿⣿⣿⡀⠀⠀⢀⣀⡀⠰⠶⣿⣝⣿⣷⣧⠀⠀⣸
⢹⢸⡇⠀⡇⠸⡇⠀⠀⢸⠀⢀⠤⠞⠉⠁⠀⠀⠀⠀⠀⢹⣷⠄⢀⠚⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣡⣾⡧⡸⡎⣿⣿⣿⡿⠛⣲⣾⣿⣿⣷⣧⡹⣿⡳⡿⢁⣴⡆⠀⢸
⠈⠈⠁⠀⠁⠀⠁⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣖⠅⢠⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⢿⣻⣵⣶⣿⠿⠉⡋⢀⣙⡿⣿⠿⠋⠀⠀⣠⣩⣿⣿⣿⣿⣦⡈⣰⣿⣿⣿⠀⠸
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣥⣤⣼⣿⣿⣿⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⡿⢧⣿⢻⣿⣿⣿⣷⣾⣷⣷⡋⣀⣶⣶⣠⣴⣿⣿⣿⣿⣿⣿⣿⡟⠉⢻⣿⣿⣿⣧⣴
⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣫⣿⣽⣟⣻⣿⣷⣶⣦⣴⣾⣿⣿⣿⣿⣿⡇⢸⡿⠸⠿⠿⠿⢿⠿⠿⢿⣿⣿⣿⣿⣰⣟⣿⢡⣀⣩⣍⠈⠏⠟⠀⢘⣿⣿⣿⣿⣿
⡿⠀⠘⠛⣛⣛⣻⠟⠛⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⡗⣿⢸⣿⣿⣏⡿⣿⣿⢯⣿⣿⣿⣿⣿⠋⠻⡟⠘⠁⢸⣷⡿⣿⡃⠀⠃⢸⠉⠉⠱⣾⣺⣿⠃⠀⣬⣽⡂⠀⠛⠀⠀⠐⣿⣿⣿⣿⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣇⢿⣾⣧⣿⢹⣿⣿⡏⣽⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⢰⣿⡿⠀⠀⠀⠈⢀⣬⣿⠉⣭⡁⠀⠐⣿⣿⣷⡀⠀⠀⠀⠀⠛⠻⠯⠫⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣟⣻⣿⡿⣿⣿⣷⣾⣿⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢸⡿⠁⠀⠀⠀⢠⣿⣿⣿⠀⠀⠀⠀⢀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣷⣿⢿⣿⣿⣿⣿⣿⣿⡏⣽⣿⡟⣷⡾⣿⣯⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣆⠀⠈⡇⠀⠀⠀⠀⣆⣿⣿⣿⠀⠀⠀⠀⠰⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢽⡿⣿⣧⣿⣿⣾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠶⠀⠀⠐⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣿⣭⣿⣼⣿⣛⣻⣸⢿⣇⣿⣼⣟⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠀⠀⠀⠀⠐⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣏⣫⣿⣿⣟⣛⣿⠿⠿⣷⣶⣯⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⡀⠛⢿⠀⠀⠀⠀⠀⠘⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣸⣿⣷⣟⡿⣿⣿⣿⣼⣛⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⡇⠠⠄⠀⠀⠀⢻⣿⣛⠆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣛⣿⣿⣿⢿⣷⣆⣿⢮⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⡇⠀⠀⠀⠀⠀⠀⠈⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠐⡃⠀⠀⠀⢀⢀⠀⠀⠀⠀⠛⠛⠀⠐⠂⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣯⣽⣿⣿⣿⣿⣿⣿⡿⠿⠋⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡇⠀⠙⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠿⠛⠇⣽⠉⠹⡯⠢⠪⠘⠕⠿⠱⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⡀⠈⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⣿⠿⠿⢿⠿⠿⣿⠿⢿⡿⠇⢠⣤⣤⣄⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣿⣿⣿⣿⣿⠿⣿⢿⡻⢇⣻⣿⢿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣼⣿⣿⣿⣿⡿⣿⣿⡏⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣧⡿⣿⠛⣿⠀⣿⢸⡇⣿⣾⡇⢸⢿⡏⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢹⣿⣿⣿⢿⣷⣿⢿⣇⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣤⣿⣄⣿⣸⠇⣿⢹⡇⣾⡾⣧⢸⣇⠀⠀⠀⣀⣀⣀⣀⠀⠀
⠀⢠⣤⣶⣄⣀⣠⡀⠀⠀⠀⠀⢿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⢰⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢰⣾⣿⠀⠀
⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⣶⢻⣿⣶⣶⣿⣿⡟⣎⣶⣶⣮⣶⣶⣷⢲⣶⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡮⣿⣿⢿⡟⣯⠀⡶⡆⠰⣶⠶⢰⡶⢀⡖⢶⠀⠈⠀⠉⠉⠉⠀⠀
⡄⡄⠀⣶⣶⡄⠀⣤⠀⠀⠀⣿⢸⡿⣿⣿⣿⣿⣽⣿⣿⣿⣇⡯⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣄⣿⣶⢸⣇⣶⢰⣇⣿⠀⣿⠀⢸⡗⠀⡙⢷⡄⠀⢠⣿⣿⣿⣿⣿
⡇⠀⢰⣿⣿⡇⡇⣿⠀⠀⠀⠈⠉⢱⣿⣿⣿⣿⣿⣷⣿⣿⣯⣥⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⠛⣦⣿⣒⣿⣷⣟⠚⠋⠛⠀⠛⠀⠘⠓⠂⠓⠚⠁⠠⣾⣿⣿⣿⣿⣿
⣧⢠⢸⣿⣿⡇⡇⢸⠀⠀⠀⠀⠀⠀⣻⣿⡏⠛⠻⢿⣯⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢹⡟⢙⠛⣻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿
⠹⠸⠘⣿⣿⡇⡁⢸⠀⠀⠀⠀⠀⠀⢄⠿⠻⣶⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠈⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡁⠀⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀
⡄⢰⠀⢰⡆⢸⠀⣀⡀⢰⠀⠀⠀⠀⣽⠇⠀⣿⣿⣿⣝⣩⣭⣾⣿⡟⠃⣸⣾⡇⠉⠹⢻⣿⠟⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣶⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⢀⠀⠀⠛⠘⣿
⡇⢸⠀⠸⡇⢸⠀⠛⠃⢸⠀⠀⠀⢰⣿⡦⠀⠛⠉⠀⠙⡝⠻⠛⠋⠠⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣾⣿⣿⣿⠍⣠⡆⢠⢻⣿⣿⣿⣿⣦⣤⢠⣴⣤⡄⠐⢚⣷⡾⢿⣿⠧⠀⠀⣿
⠁⢸⡀⠀⡇⢸⠀⠀⠀⢸⠀⣀⠤⠚⠉⠀⠀⠀⠀⠀⠀⢻⡦⠀⡀⠺⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣿⣿⣿⣿⡿⠿⣛⣡⣴⠿⣕⠜⣿⣿⣿⣿⣿⣋⣿⣿⣿⣿⣿⣧⡙⢷⣑⠟⣡⣼⡆⠀⣿
⠀⠈⠁⠀⠁⠈⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡮⠀⣰⣶⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⡇⣰⣿⣿⣭⡉⢀⡅⠐⣼⠿⣾⠛⠁⠀⣀⣤⣼⣿⣿⣿⣿⣦⡈⣰⣿⣿⣿⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣟⣥⣤⣽⣿⣿⣧⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⣿⡿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣿⣿⠤⢾⣿⣿⣿⣿⣿⣿⣿⣟⠉⢻⣿⣿⣿⣆⣲
⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⣫⣿⣽⣟⣻⣿⣷⢶⣦⣴⣾⣿⣿⣿⣿⣿⣇⣾⠁⢉⢉⣉⣉⡛⠛⡛⢻⣿⣿⣿⣿⣸⣫⡽⡡⣀⣉⣍⠈⠭⠟⠀⢸⣿⣿⣿⣿⣿
⠄⠀⠘⠛⣛⣛⡿⠟⠛⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⡗⣿⢸⣿⣿⣇⡿⣿⣿⢯⣿⣿⣿⣿⣿⠋⠻⡿⠁⠀⠸⢿⣟⣿⠀⠀⠃⠈⠉⠁⡲⡶⣼⣿⠃⠀⣬⣝⡆⠀⠛⠀⠀⠀⣿⣿⣿⣿⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣇⣿⣇⣿⣾⣧⣿⢻⣿⣿⡏⢽⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⢠⣼⣿⠉⣩⡋⠀⠈⣿⣿⣷⡀⠀⠀⠀⠀⠙⠈⡫⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢷⣾⣿⡻⣿⣿⣿⣛⣻⣿⡿⢿⣿⣷⣾⣿⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢹⡏⠀⠀⠀⠀⢠⣿⣿⠿⠀⠉⠀⠀⠀⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⡏⢭⣿⡟⣷⡾⣿⣯⣟⣟⣻⣿⣿⣿⣿⣿⣿⣿⣆⠀⠘⡇⠀⠀⠀⠀⢴⣾⣇⣾⠀⠀⠀⠀⢘⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣏⣿⣿⣿⣯⢽⡿⣿⣧⣿⣿⣼⡻⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⢤⠄⠀⠘⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣭⣿⣼⣷⣛⣻⣸⢿⡇⣿⣼⣟⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡀⠀⠀⠀⠀⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⢳⣿⣏⣫⣽⣿⣟⣛⡿⠿⠿⣷⣾⣯⣽⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡇⠀⠀⠀⠀⠘⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣟⡿⣿⣿⣿⣜⡛⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠄⠀⠀⠀⠿⣿⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣛⣿⣿⠟⢿⣷⣆⣿⢢⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠿⢺⠀⠀⠀⠀⠀⠀⠀⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠘⡃⠀⠀⠀⢀⣀⠀⠀⠀⠀⠛⠛⠀⠐⠂⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣯⣽⣿⣿⣿⣿⣿⣿⣿⠿⣋⣠⣤⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⠀⠘⠃⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠿⠛⠇⣭⠉⠸⡭⠢⠪⠘⠕⠿⠱⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⢠⣴⣿⣿⣿⣷⣤⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠁⠁⠉⠙⠛⠿⣿⣿⣿⠿⠿⢿⠿⠿⣿⠿⢿⡿⠋⢀⣀⣀⣀⣀⣉⣉⣉⣉⣉⣩⣥⣤⣀⣀⣤⣤⣤⣤⣀⣀⣀⣀⣀⣤⣤⣤⣤⣄⣸⣿⣿⣿⣿⣿⠿⣿⢿⡟⢘⣻⣿⢿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣼⣿⣿⣿⣿⡿⣿⣿⡏⣿⡿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣧⡏⣿⢉⣿⣀⣿⢸⡇⣿⣮⡇⢸⣿⡏⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢹⣿⣿⣿⢿⣷⣿⢿⣇⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣸⠇⣿⢹⡇⣾⡾⣧⢸⣇⠀⠀⢀⣀⣀⣀⡀⠀⠀
⠀⢀⣤⣶⣀⣀⣀⡀⠀⠀⠀⠀⢿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡇⠀⠀
⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⣶⢻⣿⣶⣶⣿⣿⡟⣎⣶⣶⣮⣶⣶⣷⢲⣶⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣷⡋⣿⣿⢿⡟⣧⠀⡶⣆⠰⣶⠶⢰⡶⢀⡖⢶⠀⠀⠘⠛⠛⠁⠀⠀
⡀⠀⠀⣶⣤⡄⡄⢠⠀⠀⠀⣿⢸⡿⣿⣿⣿⣿⣽⣿⣿⣿⣏⡯⣿⣾⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣸⣿⣿⣿⣶⢸⣗⣶⢰⣇⣿⠀⣿⠀⢸⡗⠀⡙⢷⡄⠀⢀⣶⣶⣾⣿⣿
⣇⠀⢰⣿⣿⡇⡇⢸⠀⠀⠀⠈⠉⠱⣽⣿⣿⣿⣿⣷⣿⣿⣯⣵⣯⣿⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠚⠛⡆⠛⠒⣿⣷⣟⡚⠋⠛⠀⠛⠀⠘⠓⠂⠓⠚⠁⠀⣿⣿⣿⣿⣿⣿
⢹⢸⢸⣿⢸⡇⡃⢸⠀⠀⠀⠀⠀⠀⢾⣿⣟⠙⠛⢿⣿⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠂⣿⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿
⠸⠸⠈⣿⣽⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠸⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡃⠀⣿⣿⠿⡿⢿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⡄⢰⡄⠀⡆⢸⠀⣀⡀⢰⠀⠀⠀⠀⣿⠄⠀⣿⣿⣿⣟⣩⣭⣿⣿⠟⢿⣿⣾⡄⠙⠳⣿⣑⣊⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⡀⠀⠀⢸⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⠀⠀⠘⠃⢻⣿
⡃⢸⡇⠀⡇⢸⠂⠛⠃⢸⠀⠀⠀⢠⣿⡆⠀⠛⠉⠀⠙⡙⠛⠛⠋⢠⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣟⣿⣿⡷⢠⣶⠀⣼⣿⣿⣿⣿⣾⣾⣷⣾⣷⣤⠀⠖⢾⣶⣿⣿⣷⠄⠀⢸⣿
⠀⢸⡇⠀⡇⢸⡂⠀⠀⢸⠀⡀⠤⠚⠉⠀⠀⠀⠀⠀⠀⢿⡦⠀⡀⠻⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⠿⠛⣛⣩⣴⣿⢿⡽⠈⣿⣿⣿⣿⢿⣻⣿⣿⣿⣿⣿⡈⠹⣟⢜⠏⣠⣷⠀⢸⣿
⠈⠈⠁⠀⠁⠈⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⡪⠀⣰⣶⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⠀⣷⣿⣷⣿⡁⢰⣀⡀⡿⢻⡟⠋⠀⠀⣠⣌⣽⣿⣿⣿⣶⣉⠁⣾⣿⣿⡇⠸⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣯⣤⣤⣿⣿⣿⣧⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⣿⡿⠁⠀⣿⣿⣿⣿⣿⣾⣿⣯⣇⣴⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣿⣿⣿⣷⣒⣖
⡤⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⣫⣿⣽⣟⣻⣿⣷⢶⣦⣴⣾⣿⣿⣿⣿⡟⠀⠀⠀⣀⣀⡤⠭⡝⠙⣛⢻⣿⣿⣿⣅⡾⣿⣿⢁⠉⠙⣉⢙⡛⠃⠀⣹⣿⣿⣿⣿⣿
⠁⠀⠈⠋⢙⢛⠿⠟⠛⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡗⣿⢸⣿⣿⣇⡿⣻⣿⢯⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠙⣛⣷⣭⠀⠀⠁⠀⠉⠉⢶⣭⣾⡿⠃⠈⣝⢫⠀⠰⠂⠀⠀⢹⣿⣿⣿⡏⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣇⣿⣇⢿⣾⣧⣿⢹⣿⣿⡏⣽⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣿⣿⠏⠀⠀⠀⠀⢀⣴⣿⠘⣛⠿⠀⢨⣿⣿⣇⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢷⣾⣿⣻⣿⣿⣿⣛⣻⣿⡿⢿⣿⣷⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠻⠇⠀⠀⠀⠀⢰⣿⡿⠛⠀⠛⠀⠀⠀⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⡏⢽⣿⡏⣷⠾⣿⣯⣟⣟⣻⣿⣿⣿⣿⣿⣿⣿⣆⠐⠇⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⠀⠀⠀⢸⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⡿⣿⣏⣿⣿⣿⣯⢽⡿⣿⣧⣿⣿⣼⡿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⢀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣭⣿⣼⣯⣛⣻⣸⠟⡇⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⠀⠀⠀⠀⠐⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⣿⣏⣫⣽⣿⣛⣛⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇⠀⠀⠀⠀⠈⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣷⣟⡿⣿⣿⣿⣜⡛⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⣀⠀⠀⠀⠚⠿⡚⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⡆⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣛⣿⣿⠟⢿⣷⣆⣿⢢⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⡁⠀⠀⠀⢀⣀⠀⠀⠀⠀⠛⠛⠀⠐⠂⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣯⣽⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠿⠙⠇⣭⠉⠹⡭⠢⠪⠸⠕⠿⠱⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⢰⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠻⢿⣿⣿⣿⠿⠿⢿⠿⠿⣿⠿⢿⡿⠟⢛⡛⢛⠛⠛⠛⠛⢛⣛⣛⣛⣋⣉⣁⣀⣀⣀⣀⣈⣛⣛⣛⣛⣛⣙⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⢿⣿⣿⡏⣿⣿⣿⢿⡟⠋⠉⠉⠉⠉⠉⠉⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣼⣿⣿⣿⣿⡿⣷⣿⡏⣿⡿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣧⡏⣿⢛⣿⣁⣿⢸⡇⣿⣯⡇⢸⡿⡏⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢹⣿⣿⣿⢻⣷⣿⢿⣇⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣸⠇⣿⢹⡇⣾⡾⣇⢸⣇⠀⠀⠀⢀⡀⠀⠀⠀⠀
⠀⢀⣀⣤⣀⣀⣀⣀⠀⠀⠀⠀⢸⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣩⣽⣿⠀⠀⠀
⠀⠈⠉⠙⠛⠛⠛⠋⠀⠀⠀⣴⢻⣿⣶⣖⣼⣿⡟⣏⣶⣶⣶⣶⣶⣷⢲⣾⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣷⣋⣿⣿⢯⡗⣦⠀⡶⣆⠰⣶⠶⢰⡶⢠⡖⢶⠀⠐⠛⠛⠛⠀⠀⠀
⢀⢠⠀⢰⣤⡄⠀⢀⡀⠀⠀⣿⢸⡿⣿⣿⣿⣿⣽⣿⣿⣿⣏⡯⣿⣿⢸⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣯⣿⣶⢿⣟⣷⢸⣇⣿⠀⣿⠀⢸⡗⠀⡙⢷⡄⠀⠀⣶⣶⣶⣶⣶
⢸⠸⠀⣾⣿⣇⠀⢸⡇⠀⠀⠈⠉⠱⣭⣽⣿⣿⣭⣷⣿⣿⣯⣵⣯⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠘⢻⡂⣛⣒⣿⣷⣟⡘⠋⠛⠀⠛⠀⠘⠓⠂⠓⠚⠁⠀⣾⣿⣿⣿⣿⣿
⢸⠀⡄⣿⣿⣿⠀⢸⡇⠀⠀⠀⠀⠀⠨⣹⣿⡍⠙⠻⣿⣍⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢹⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿
⠸⠆⡇⢻⣿⣿⢀⢸⡇⠀⠀⠀⠀⠀⢐⠃⠉⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠎⠀⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠉⠁⠀⠀⠁⠀⠀⠀⠀⠀⢸⠗⠀⣿⣿⣟⣿⣻⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⢠⣦⣴⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⢠⠀⡆⠀⣦⠀⡆⢀⣀⢰⠀⠀⠀⠀⢼⡄⠀⣿⣿⣿⣭⣭⣭⣾⣿⡿⠻⣾⣾⠈⠉⠹⣻⣿⣏⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⠀⠀⠈⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠙⠘⣿⣿
⢸⠀⡇⠀⣿⠀⡇⠘⠛⢸⠀⠀⠀⠀⣿⣇⠀⠛⠉⠁⠉⡝⠛⠛⠋⢀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣻⣿⣿⡎⣴⣇⢠⣿⣿⣿⣿⣿⣿⣿⣷⣶⡄⠀⢠⡤⣎⣿⡶⣶⣄⠀⠀⣿⣿
⠐⠀⡇⠀⢻⠀⡇⠀⠀⠀⡇⢀⠤⠞⠋⠁⠀⠀⠀⠀⠀⢿⡶⠀⡀⠻⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⡟⠻⠛⣛⣩⣴⡿⢟⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢜⣾⢏⣝⠏⣵⡄⠀⣿⣿
⠈⠀⠁⠀⠈⠀⠁⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⡪⠀⣰⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣟⣁⠘⣹⣿⣯⣍⠁⢨⠀⢨⡿⣯⠻⠇⠉⠉⠙⠿⣿⣿⣿⣆⡙⠳⢀⣾⣿⡇⠀⠿⠿
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣋⣤⣤⣿⣿⣿⣧⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⡿⠁⠀⣿⣿⣿⣿⣦⢾⣿⡇⡀⣴⣶⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⠦⢾⣿⣿⣷⣒⣲⣶
⣤⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⣫⣿⣽⣟⣻⣿⣷⢶⣦⣴⣾⣿⣿⣿⣿⡟⠀⠀⠀⣀⡁⠈⣩⡛⠹⠿⢿⣿⣿⣿⠀⣬⣿⣿⠿⠿⠿⠻⣿⣷⠀⠈⣿⣿⣿⣿⣿⣿
⠍⠀⠀⠉⠉⠛⠿⠟⠙⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡗⣿⢸⣿⣿⣇⡿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠹⢟⣛⣻⠁⠘⠃⠨⠛⠛⣝⠓⢹⣿⠫⠰⠤⣚⠀⢨⠀⠀⠀⣿⣿⣿⡏⠉⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣇⣿⣇⢿⣾⣧⣿⢹⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣿⣿⠟⠀⠀⠀⠀⠀⣀⣴⠀⣠⡯⠀⠰⣷⣶⡀⠀⠀⠀⠀⠙⠿⢿⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢷⣾⣿⣻⣿⣿⣿⣛⣻⡿⡿⢿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢀⠻⠇⠀⠀⠀⠀⢠⣾⣿⠿⠀⠶⠀⠀⠐⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⡏⢽⣿⡏⣷⠾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠟⠂⠀⠀⠀⠀⠀⠈⢸⠃⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣏⣿⣿⣿⣯⢵⡿⣿⣧⢿⣿⣾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠘⢸⣄⣶⡀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣭⣿⣼⣧⣛⣻⣸⠟⡇⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⠈⣿⡇⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⢳⣿⣏⣫⣽⣿⣛⣛⡿⠿⠿⢷⣾⣯⣽⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠐⠳⡙⠁⠀⠀⠀⠀⠰⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣏⡿⣿⣟⣿⣜⣛⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠿⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣛⣿⣾⠟⢿⣷⣆⣿⢢⣿⠩⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⡀⠀⠀⢀⢀⠀⠀⠀⠀⠛⠛⠀⠐⠂⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣭⣽⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠿⠩⠇⣭⠉⡘⡯⠢⠪⠸⠕⠿⠱⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠐⠉⠛⠛⠛⠛⠛⠻⠿⣿⣿⣿⠿⠿⢿⠿⠿⣿⠿⢿⡿⠟⢛⡛⣛⠛⠛⠛⢛⢛⣛⣛⣛⣛⣉⣉⣀⣀⣀⣀⣘⣛⣛⣙⣛⣛⣙⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⢿⣿⣿⡏⢿⣿⣿⢿⡟⠋⠉⠉⠉⠉⠉⠉⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣼⣿⣿⣿⣿⡿⣿⣿⡏⣿⡿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣧⡏⣿⢛⣿⣁⣿⢸⡇⣿⣿⡇⢸⣿⡏⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢹⣿⣿⣿⢻⣷⣿⢻⣇⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣸⠇⣿⢹⡇⣾⡿⣧⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣀⣴⣀⣀⣀⣀⠀⠀⠀⠀⢸⣿⣿⣶⣸⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣩⣽⣿⠀⠀⠀
⠀⠈⠉⠉⠛⠛⠛⠛⠀⠀⠀⣴⢻⣿⣶⣶⣼⣿⡟⣏⣶⣶⣶⣶⣶⣷⢲⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣷⣋⣿⣿⢿⡗⣦⠀⡶⣆⠰⣶⠶⢰⡶⢠⡖⢶⠀⠀⠛⠛⠛⠀⠀⠀
⢀⢠⠀⢰⣤⡄⠀⢀⡀⠀⠀⣿⢸⡿⣿⣿⣿⣿⣽⣿⣿⣿⣇⡯⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣯⣿⣶⢻⣟⣷⢸⣇⣿⠀⣿⠀⢸⡗⠀⡙⢷⡄⠀⠀⣶⣶⣶⣶⣶
⢸⢸⠀⣾⣿⣗⠀⢸⡇⠀⠀⠈⠉⠱⡭⣽⣿⣿⣽⣷⣿⣿⢯⣵⣯⣽⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠘⢻⡂⣛⣒⣿⣷⣟⡚⠋⠛⠀⠛⠀⠘⠓⠂⠓⠚⠁⠀⣼⣿⣿⣿⣿⣿
⢸⠀⡄⣿⣿⣯⠀⢸⡇⠀⠀⠀⠀⠀⢈⡹⣿⡍⠙⠻⣿⣍⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢹⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿
⠸⠆⡇⢻⣿⣿⢀⢸⡇⠀⠀⠀⠀⠀⢀⠡⠉⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠎⠀⠙⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠉⠁⠀⠀⠁⠀⠀⠀⠀⠀⡐⠄⠀⣿⣿⣿⣿⣫⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠆⠀⠀⢰⣤⣴⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⢠⠀⡆⠀⣦⠀⡆⢀⣀⢰⠀⠀⠀⠀⢿⠀⠀⣿⣿⣿⣭⣭⣭⣾⣿⡟⠻⢸⣾⠈⠙⠟⣿⣫⣙⣹⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⠀⠀⠨⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠙⠘⣿⣿
⢸⠀⡇⠀⣿⠀⡇⠘⠛⢸⠀⠀⠀⠀⣿⣥⠀⠛⠉⠁⠙⡝⠛⠛⠉⢠⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣻⣿⣿⡎⣴⣇⢠⣿⣿⣿⣿⣿⣿⣿⣷⣶⡀⠀⢠⡴⣎⣽⡶⣶⣄⠀⠀⣿⣿
⢸⠀⡇⠀⢿⠀⡇⠀⠀⠀⡇⢀⠤⠞⠋⠁⠀⠀⠀⠀⠀⢿⡦⠀⡀⠻⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⡟⠻⠛⣛⣩⣴⡿⢟⣧⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⡄⢼⣾⢏⣝⠏⣵⡄⠀⣿⣿
⠈⠀⠁⠀⠈⠀⠁⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⡪⠀⣰⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣟⣁⠸⣻⣿⣯⣍⠁⢨⠀⢨⡿⣯⠻⠇⠁⠉⠙⠿⣿⣿⣿⣆⡙⠳⢂⣾⣿⡇⠀⠿⠿
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣏⣤⣤⣿⣿⣿⣧⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⡿⠁⠀⣿⣿⣿⣿⣦⢿⣿⡏⣀⣴⣶⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⠶⢾⣿⣿⣷⣖⣒⣶
⣷⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⣯⣿⣽⣟⣻⣿⣷⢶⣦⣴⣾⣿⣿⣿⣿⡟⠀⠀⠀⣀⡈⠈⣩⡿⢹⡿⢿⣿⣿⣿⠀⣬⣿⣿⡿⠿⠿⠻⣿⣿⠀⠘⣿⣿⣿⣿⣿⣿
⠿⠀⠀⠉⠙⠹⠿⠟⠛⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡗⣿⢸⣿⣿⣇⡿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠻⢿⣛⣿⠑⠘⠃⢸⠛⠛⣝⠓⢹⣾⠻⠱⠤⣚⠀⢠⠀⠀⠀⣿⣿⣿⡏⠉⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣧⢿⣾⣧⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣿⣿⠏⠀⠀⠀⠀⠀⡄⣴⠂⣠⡏⠀⠰⣷⣶⡀⠀⠀⠀⠀⠍⠿⠹⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿⣿⣻⣿⣿⣿⣟⣻⣿⡿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢀⠹⠇⠀⠀⠀⠀⢸⣾⣿⡿⠀⠶⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⡏⢽⣿⡟⣷⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠟⠀⠀⠀⠀⠀⠀⠈⣟⠁⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣏⣿⣿⣿⣯⢽⡿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠘⣿⡀⣴⡀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣭⣿⣼⣧⣛⣻⡸⢟⡇⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⠀⣿⡇⠀⠀⠀⠀⢼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⢻⣿⣏⣫⣿⣿⣛⣛⡿⠿⠿⣷⣾⣯⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠐⠳⡉⠁⠀⠀⠀⠀⠈⣿⠿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣟⡿⣿⣗⣿⣜⣛⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠿⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣛⣿⣾⠟⢿⣷⣆⣿⢢⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⡀⠀⠀⢀⢀⠀⠀⠀⠀⠛⠛⠀⠐⠂⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣯⣽⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠿⠩⠇⣽⠉⠘⡯⠢⠪⠸⠕⠿⠱⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠒⠒⠛⠛⠛⠛⠛⠿⢿⣿⣿⣿⠿⠿⢿⠿⠿⣿⠿⢿⡿⠟⠛⠛⢛⠛⠛⠛⠛⠛⠛⢛⣛⣛⣋⣉⣉⣉⣉⣉⣙⠛⠛⠛⣛⡛⣛⢛⣛⣛⣛⣿⣿⣿⣿⣿⣿⢿⣿⣿⡇⣿⣿⣿⢿⡟⠛⠛⠛⠛⠋⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣼⣿⣿⣿⣿⡿⣿⣿⡏⣿⡿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣯⡎⣿⠿⣿⣁⣿⢹⡏⣿⣿⡇⢸⣿⡿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢹⣿⣿⣿⢿⣷⣿⢿⣇⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣾⣿⣿⣿⣸⠇⣿⢹⡇⣾⡿⣧⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⣠⡄⠀⠀⢀⠀⠀⠀⠀⢸⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣴⣿⣿⣿⣯⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣭⣿⡇⠀⠀⠀
⠀⠈⠉⠛⠛⠛⠛⠛⠀⠀⠀⣴⢻⣿⣶⣶⣼⣿⡟⣏⣶⣶⣶⣶⣶⣷⢲⣶⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣷⣋⣿⣿⢿⡟⣧⡀⡶⣆⠰⣶⠶⢰⡶⢀⡖⢶⠀⠐⠛⠛⠃⠀⠀⠀
⢀⠀⡀⢠⣤⣄⠀⠀⡀⠀⠀⣿⢸⡿⣿⣿⣿⣿⣽⣿⣿⣿⣏⡯⣿⣿⢸⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡗⢸⣿⡿⣿⣶⣿⣟⣿⢹⣇⣿⠀⣿⠀⢸⡗⠀⡙⢷⡄⠀⠀⣴⣶⣶⣶⣶
⢸⠀⡇⣼⣿⣿⠠⠀⡇⠀⠀⠈⠉⠱⣭⣽⣿⣿⣭⣷⣿⣿⣿⣵⣯⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓⠘⢻⣂⣛⣒⣿⣷⣟⣚⠋⠛⠀⠛⠀⠘⠓⠂⠓⠚⠁⠀⢰⣿⣿⣿⣿⣿
⡆⡇⡇⣿⣿⣿⢸⠀⡇⠀⠀⠀⠀⠀⠁⣯⢿⣷⢀⡍⣿⣯⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿
⡇⡇⠇⠛⣿⣿⢈⠀⡇⠀⠀⠀⠀⠀⢈⡯⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠛⡛⠛⠛⠋⠉⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠁⠉⠀⠀⠁⠀⠀⠀⠀⠀⠼⡋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣶⠀⠀⠀⣶⣴⣾⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⢠⠀⡄⠀⣴⠀⡆⢀⣀⠠⡀⠀⠀⠀⢺⡇⠀⣿⣿⣿⣯⣴⣿⣿⣿⠏⠻⣿⣾⠈⠙⢿⣻⣫⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠁⠀⠀⠀⢻⣿⣿⣿⣷⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢻⣿⣿
⠸⠀⢹⠀⢸⠀⡇⠘⠛⠀⡇⠀⠀⠀⣿⣧⠀⠙⠉⠁⠘⣝⠛⠛⠉⢠⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣧⠇⣴⡄⣸⣿⣿⣿⣿⣷⣶⣶⣠⡄⠀⠀⠀⢨⠻⣦⣤⢀⠀⠀⢸⣿⣿
⠀⠀⢸⠀⢸⠀⡇⠀⠀⠀⡇⢀⠤⠞⠋⠀⠀⠀⠀⠀⠀⢿⡷⠀⡀⠻⢿⣿⣿⠀⠀⠀⠀⢠⣤⡀⠀⣄⠀⠀⠉⠙⣿⣿⣿⣿⣿⡟⠿⠛⢛⣩⣼⣿⣗⡛⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣀⠸⣓⣳⠟⣵⠟⣃⠀⢸⣿⣿
⠀⠀⠈⠀⠈⠀⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⡪⠀⣰⣾⣿⡏⠀⠀⠀⠀⠸⣿⣿⣿⣿⠃⠀⠀⠀⠻⠿⣿⣿⢋⣀⠨⣹⣿⣛⡛⠁⣉⠁⠹⣿⣿⣿⣯⠹⠿⣿⣿⣿⣿⣧⡩⠽⣙⠍⣰⣿⡆⠸⠿⠿
⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣋⣤⣤⣿⣿⣿⣧⣤⣤⣤⣄⣀⣉⠉⠛⠻⠷⠄⠀⠀⣀⣴⣿⣿⡿⠁⠀⣿⣿⣿⣷⡄⢿⣷⡆⡀⣻⣈⠀⢀⣴⣦⣶⣿⣿⣿⣿⣦⣈⣼⣿⣿⣷⣒⣒⣒
⣞⠄⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡟⣫⣿⣽⣿⣿⣿⣿⣶⣦⣴⣾⣿⣿⣿⣿⡟⠀⠀⠀⠉⠉⣙⣛⣿⠾⣿⣿⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⢙⣿⣿⠁⠉⣿⣿⣿⣿⣿⣿
⠬⠀⠀⠉⠋⠻⠿⠟⠙⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡗⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠻⠿⣶⣶⡣⠀⠇⠀⡿⢿⢿⣄⣿⣿⠿⢁⣉⣡⠀⠍⠝⠀⢀⣿⣿⣿⡏⠉⠩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣃⣿⣧⢿⣾⣧⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⡈⢷⠄⠘⠧⠀⠈⣉⠃⠀⠘⠀⠀⠀⠹⣿⢿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣿⡻⣿⣿⣿⣛⣻⣿⡿⢿⣿⣷⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⢀⠘⠿⠁⠀⠀⠀⠀⡀⡇⣾⠀⠐⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⡏⢽⣿⡟⣿⡿⣿⣯⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⡆⡏⠙⠀⠉⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣟⣿⣿⣿⣏⣿⣿⣿⣯⢽⡿⣿⣇⣿⣿⣾⡿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠂⣇⠀⠀⠀⠀⠀⠀⢸⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣭⣿⣼⣷⣛⣻⡸⠏⡇⣿⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠿⠣⠀⠀⠀⠀⠀⢨⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⢳⣿⣏⣫⣽⣿⣛⣛⡿⠿⠿⣷⣶⣯⣽⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣸⣿⣷⣏⡿⣿⣟⣿⣜⣛⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆⠙⠻⢿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣇⣛⣿⣾⠟⢿⣷⣆⣿⢢⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⣀⠀⠀⢀⢀⠀⠀⠀⠀⠛⠛⠀⠐⠂⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣯⣽⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⠿⠩⠇⣭⠉⡌⡯⠢⠪⠸⠕⠿⠱⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⠚⠛⠛⠛⠛⠛⠛⠿⢿⣿⣿⣿⠿⠿⢿⠿⠿⣿⠿⢿⡿⠟⠛⠛⢛⠛⠛⠛⠛⠛⠛⠛⢛⣛⡛⢛⠋⣉⣉⣉⠛⠛⠛⠛⢛⡛⣛⢛⣛⡛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⢿⡟⠛⠛⠛⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣼⣿⣿⣿⣿⡿⣿⣿⡏⣿⡽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣯⠈⣿⣿⣿⠟⣿⢹⡟⣿⣿⡇⢸⣿⡟⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢹⣿⣿⣿⢿⣷⣿⣿⣇⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣵⣿⣶⣿⣸⠇⣿⢹⡇⣾⡿⣷⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣀⡄⠀⠀⢀⠀⠀⠀⠀⢸⣿⣿⣶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣰⣿⣿⣿⣟⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣩⣿⡇⠀⠀⠀
⠀⠀⠙⠛⠛⠛⠛⠛⠀⠀⠀⣶⢻⣿⣶⣶⣼⣿⡟⣏⣶⣶⣶⣶⣶⣵⢲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢟⣿⣿⢿⡟⣧⠀⡶⣆⠰⣶⠶⢰⡶⢠⡖⢶⠀⠘⠛⠛⠃⠀⠀⠀
⡀⠀⡀⠀⣄⣄⢠⠀⡀⠀⠀⣿⢸⡿⣿⣯⣿⣿⣽⣿⣿⣿⣏⡯⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⣿⣏⣿⣶⢸⣟⣿⢹⣇⣿⠀⣿⠀⢸⡗⠀⡙⢷⡄⠰⢴⣶⣶⣶⣶⣶
⡇⡇⠃⣤⣟⣿⢘⠀⡇⠀⠀⠈⠉⠱⣭⣽⣿⣿⡭⣷⣿⣿⣿⣁⣯⣽⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠓⠘⣻⠂⢛⣲⣿⣓⣟⡚⠋⠛⠀⠛⠀⠘⠓⠂⠓⠚⠁⠀⢈⣿⣿⣿⣿⣿
⡇⡇⠀⣷⣿⣿⠨⠀⡇⠀⠀⠀⠀⠀⠘⣡⠈⣿⣷⣆⣹⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿
⡇⡇⢠⠸⣿⣿⠀⠀⡇⠀⠀⠀⠀⠀⢀⡎⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡦⠀⠘⣟⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠉⠀⠀⠁⠀⠀⠀⠀⠀⢘⠇⠀⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠛⠁⣤⣴⣿⣦⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⡄⢠⠀⢰⠀⣆⠀⣀⠀⡆⠀⠀⠀⢀⡇⠀⣿⣿⣿⢷⣶⣶⣾⣿⠏⢻⣸⣾⠈⠉⠬⣩⣉⣉⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠛⣿⣿⣿
⠀⡇⢸⠀⢸⠀⣿⠀⠛⠀⡇⠀⠀⠀⣾⣷⠀⠘⠉⠁⠘⣮⠉⠉⠁⢀⣽⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣤⣤⣤⣤⣤⣤⣤⣾⡟⣿⣿⣦⠀⣤⠀⢹⣿⣿⣿⣿⣇⣀⡄⠀⠀⠀⠀⠀⠰⣦⣄⠀⠀⠀⠀⢹⣿⣿
⠀⡇⢸⠀⢸⠀⣿⠀⠀⠀⡇⢀⠤⠚⠋⠀⠀⠀⠀⠀⠀⢻⡷⠀⡐⠻⢿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⡿⠿⠛⠟⣋⣼⣿⡶⠷⣿⣿⣿⣿⣿⣿⣷⣶⠀⠀⠀⢠⢮⢬⣿⣫⡶⠄⠀⣼⣿⣿
⠀⠁⠈⠀⠈⠀⠉⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠚⠀⣴⣿⣿⡟⠩⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⡿⢋⣀⠐⣰⣿⡿⠿⠁⡞⠓⢿⣿⣿⣿⡿⠻⣿⣿⣿⣽⣿⡀⠺⢿⢧⠿⢀⣷⠀⠹⠿⠿
⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣋⣤⣤⣿⣿⣿⣧⣤⣤⣤⣄⣈⣉⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣾⡟⠁⠀⣿⣿⣿⣧⡄⢿⣶⡆⠉⠹⠙⠋⠉⢉⣉⣛⣾⣿⢿⣦⣜⠑⢡⣿⣿⣖⣒⣒⣒
⣿⡆⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡟⣿⣿⣿⣿⣿⣿⣿⢶⣦⣴⣾⣿⣿⣿⣿⡟⠀⠀⠀⠈⠛⠉⠹⠿⡎⣿⣷⣶⣶⡇⠀⢘⣿⣿⣿⣿⣏⠻⣿⣿⠟⠿⣿⣿⣿⣿⣿⣿
⠿⠅⠀⠉⠉⠭⠿⠟⠉⠁⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⡗⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢸⣷⣞⠻⠟⠀⠲⠀⠸⣿⣿⠀⣼⣿⣿⠟⠛⢛⠀⠺⠿⠀⠀⣿⣿⣿⡍⠭⠭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣗⣿⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠠⣿⣿⠃⠀⠀⠀⠀⠹⣘⠁⠸⠟⠈⠀⠶⡎⠀⢀⠀⠀⠀⠙⣿⢿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢷⣾⣿⡿⣿⣿⣿⣟⣻⣿⡿⢿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⣘⠀⡿⠃⠀⠀⠀⠀⠀⡇⣠⠀⠀⠀⠀⠀⢶⣾⡄⠀⠀⠀⠀⠀⠀⠃⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣷⣿⢿⣿⣿⣿⣿⣿⣿⡏⢽⣿⡟⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠇⠾⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣟⣿⣿⣿⣏⣿⣿⣿⣯⢽⡿⣿⣧⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣿⣭⣿⣼⣷⣛⣻⡸⢟⣇⣿⣽⣟⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣷⣧⠄⠀⠀⠀⠀⠀⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⢳⣿⣏⣫⣽⣿⣛⣛⡿⠿⠿⣷⣶⣯⣽⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠁⠹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠂⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣸⣿⣷⣟⡿⣿⣿⣿⣼⣛⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆⠙⠻⢿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣇⣛⣿⣾⢟⢿⣷⣆⣿⢢⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠄⠀⠀⢀⢀⠀⠀⠀⠀⠛⠛⠀⠐⠂⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣯⣽⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠿⠹⠇⣽⠉⠥⡭⠢⠪⠸⠕⠿⠱⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⢠⣿⣇⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⠛⠛⠛⠟⠿⠿⠿⣿⣿⣿⣿⠿⠿⢿⠿⠿⣿⠿⢿⡿⠿⠛⠛⢛⠛⠛⠛⠛⠿⠿⠟⠻⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⡛⣛⠛⣛⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣿⢿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣼⣿⣿⣿⣿⡿⣿⣿⡏⣿⡿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣯⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢹⣿⣿⣿⢿⣷⣿⣿⣇⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠿⣿⠋⣿⣹⠟⣿⢻⡇⣾⣿⣷⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣶⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣽⡧⠀⠀⠀⠀
⠀⠀⠈⠛⠛⠚⠓⠓⠂⠀⠀⣶⢳⣿⣶⣶⣼⣿⡿⣟⣷⣶⣶⣶⣶⣷⢲⣶⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡮⣿⣿⢿⡟⣯⠀⡶⣆⠰⣶⠶⢰⡶⢠⡖⢶⠀⠿⠿⠇⠀⠀⠀⠀
⡀⡀⠀⠀⣤⣤⠀⠀⣀⠀⠀⣿⢸⡟⣿⣯⣿⣿⣽⣿⣿⣿⣟⡯⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣶⢸⡏⣶⢸⣇⣿⠀⣿⠀⢸⡗⠀⡙⢷⣤⣦⣦⣶⣶⣶⣶⣶
⡇⡇⢀⢠⣿⣿⠀⠀⣿⠀⠀⠈⠉⠑⣭⣽⡏⣿⣯⡗⢿⣿⣿⣷⣋⣹⣬⣽⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠓⢸⣿⣦⣿⣶⣿⣳⣿⣞⡋⠛⠀⠛⠀⠘⠓⠂⠓⠚⠙⠻⣿⣿⣿⣿⣿⣿
⣧⢣⢸⢸⣿⣿⡇⠀⣿⠀⠀⠀⠀⠀⠈⢽⠂⣿⣿⣿⣦⣼⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣽⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⢸⠸⠘⢿⣿⡇⡀⣿⠀⠀⠀⠀⠀⢀⠘⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠉⠁⠀⠉⠀⠀⠀⠀⠀⠐⠄⠀⢸⣿⣿⣿⣿⣶⣿⢿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⠁⠀⣽⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⡄⢠⠀⢰⡄⢰⠀⣀⡀⡆⠀⠀⠀⠀⡆⠀⢸⣿⡿⢿⣿⣿⣿⣿⠟⠁⢰⣾⠀⠑⠏⣙⣭⣫⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠉⠀⢰⣤⣶⣾⣦⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠘⣿⣿⣿
⠀⡇⢸⠀⢸⡇⢸⠀⠛⠃⡇⠀⠀⠀⣼⡷⠀⠈⠉⠀⠈⣷⡍⠉⠀⢠⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⣤⣤⣴⣾⣿⣤⠀⠀⠀⠀⢸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠰⠀⠘⡇⢸⠀⠀⠀⢇⠀⠔⠚⠉⠀⠀⠀⠀⠀⠀⢻⡿⡆⠀⠛⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⡽⢳⣷⡄⣤⣄⡀⢿⣿⣿⣿⣿⠀⣀⡀⠀⠀⠀⠀⠀⢘⢦⣤⡀⠀⠀⠀⣿⣿⣿
⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠖⠅⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⣿⣿⢏⣘⠉⣉⣁⣴⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢰⢎⢦⣿⣳⡷⠀⠀⠻⠿⠛
⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣋⣤⣤⣽⣿⣿⣥⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⡿⠁⢰⣿⣿⣭⡉⠸⣎⣁⡙⣿⣿⣿⣟⢙⣿⣷⣾⣿⣿⡆⠺⢟⠧⠿⢁⣷⣒⣒⣒⣒
⣿⡗⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡟⣫⣿⣽⣟⣻⣿⡷⢶⣦⣴⣾⣿⣿⣿⣿⡟⠀⠀⠀⢿⣿⣿⣿⣦⢹⣿⣟⠀⠸⠎⠋⠀⢈⣉⣙⣿⣿⣿⣷⣀⠉⢂⣿⣿⣿⣿⣿⣿
⠙⠁⠀⠈⠉⠭⠭⠿⠉⠁⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣏⡿⣿⣿⢯⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢀⣌⡠⠭⢽⠃⠛⠟⠿⡆⠀⠀⠈⣿⣿⣿⣿⣿⠘⣿⣿⡗⠺⢿⣿⣿⠩⠭⠭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣯⣿⣿⣧⣿⣹⣿⣿⡏⣽⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⡈⠉⢆⣞⡏⠂⠸⠀⠀⢠⡴⠀⣴⣿⣿⣿⠛⢏⡀⠻⠿⠇⠀⢸⣿⣿⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢷⣾⣿⣿⣿⣿⣿⣻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⣷⠀⢹⣿⠃⠀⠀⠀⠀⠈⢁⡛⠈⠿⠇⠈⠲⠶⠀⠀⠄⠀⠀⠀⠻⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⢿⣟⣿⣿⣿⣿⣿⡿⣿⣿⡿⣷⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⣷⣇⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⡿⣿⣏⣿⣿⣿⣿⢽⡿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣿⣭⣿⣼⣧⣛⣻⡸⢿⡇⣿⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⣿⣿⢳⣿⣏⣫⣽⡿⣛⣛⡿⡿⠿⣷⣶⣯⣽⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠄⠀⠀⠀⠀⠈⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣸⣿⣷⣏⡿⣿⣷⣿⣜⣛⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣛⣿⣾⠟⢿⣷⣆⣿⢢⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡁⣱⡄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀
⠀⡀⠠⠄⠀⢀⠀⠀⠀⠀⠀⠛⠛⠀⠐⠂⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣯⣽⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⠿⠹⠇⣭⠉⠶⡭⠢⠪⠘⠕⠿⠱⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠂⠛⠛⠛⠛⠛⠻⠿⠿⣿⣿⣿⣿⠿⠿⢿⠿⠿⣿⠿⢿⡿⠿⠛⠻⢛⠛⠛⠛⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⡛⣛⠛⣛⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⣿⣿⢿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣼⣿⣿⣿⣿⡿⣿⣿⡏⣿⡿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣯⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢹⣿⣿⣿⢿⣷⣿⣿⣇⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠿⣿⠋⣿⣹⠟⣿⢻⡇⣾⣿⣷⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣶⣿⣿⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣩⣿⡧⠀⠀⠀⠀
⠀⠀⠈⠛⠛⠛⠒⠛⠃⠀⠀⣶⢳⣿⣶⣶⣼⣿⡿⣟⣷⣶⣶⣶⣶⣷⢲⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡮⣿⣿⢿⡟⣯⠀⡶⣆⠰⣶⠶⢰⡶⢠⡖⢶⠀⠿⠿⠃⠀⠀⠀⠀
⡀⡀⠀⠀⣤⣤⠀⠀⣀⠀⠀⣿⢸⡟⣿⣯⣿⣿⣽⣿⣿⣿⣟⡯⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣶⢸⡟⣶⢸⣇⣿⠀⣿⠀⢸⡗⢀⡙⢷⣤⣶⣶⣶⣶⣶⣶⣶
⡇⡇⠀⢠⣿⣿⡄⠀⣿⠀⠀⠈⠉⠁⣭⣽⡏⣿⣯⡷⢿⣿⣿⣷⣋⣽⣬⣽⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠓⢸⣿⣦⣿⣶⣿⣷⣿⣺⡋⠛⠀⠛⠀⠘⠓⠂⠓⠚⠙⠿⣿⣿⣿⣿⣿⣿
⣧⢳⢸⢸⣿⣿⡇⠀⣿⠀⠀⠀⠀⠀⠀⢨⠁⣿⣿⣿⣶⣼⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣽⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⢸⠸⠘⣿⣿⡇⡀⣿⠀⠀⠀⠀⠀⠀⡘⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠉⠁⠀⠉⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⣿⣿⣿⣶⣿⢿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⠁⠀⣽⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⡄⢠⠀⢰⡆⢰⠀⣀⡀⡆⠀⠀⠀⠨⡀⠀⢸⣿⡿⢿⣿⣿⣿⣿⠟⠉⢰⣿⠈⠙⠏⣍⣟⣝⣻⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠉⠀⢰⣦⣾⣿⣦⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠘⣿⣿⣿
⠀⡇⢸⠀⢸⡇⢸⠀⠛⠃⡇⠀⠀⠀⣾⡷⠀⠈⠉⠀⠈⣷⡍⠉⠁⢠⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣿⣤⠀⠈⠀⠀⢸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠁⢨⠀⠘⡇⢸⠀⠀⠀⢇⠀⠔⠚⠉⠀⠀⠀⠀⠀⠀⢻⡿⡆⠀⠛⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⡽⢳⣷⡄⣤⣄⡈⢿⣿⣿⣿⣿⡀⣀⡀⠀⠀⠀⠀⠀⢘⢦⣤⡀⠀⠀⠀⣿⣿⣿
⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠗⠅⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢿⣿⣿⢏⣘⠉⣉⣁⣶⣿⠿⢿⡿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢰⢎⢦⣿⣳⡷⠀⠀⠻⠿⠛
⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣋⣤⣤⣽⣿⣿⣥⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⡿⠁⢰⣿⣿⣭⡉⠸⣏⣁⡙⣿⣿⣿⣿⢙⣿⣷⣾⣿⣿⣆⠺⢟⠧⠿⢁⣷⣒⣒⣒⣒
⣿⡷⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣟⣫⣿⣽⣟⣻⣿⡷⢶⣦⣴⣾⣿⣿⣿⣿⡟⠀⠀⠀⢿⣿⣿⣿⣦⢹⣿⣇⠀⠸⠎⠋⠁⢈⣉⣙⣿⣿⣿⣷⣀⠉⢆⣿⣿⣿⣿⣿⣿
⠿⠁⠀⠈⠉⠭⠭⠿⠋⠁⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣼⣿⣿⣏⡿⣿⣿⢯⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢀⣌⡡⠭⣽⠃⠛⠟⢾⡦⠀⠀⠈⣿⣿⣿⣿⣿⠝⣿⣿⡗⠚⢿⣿⣿⠩⠭⠭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣷⣿⣿⣿⣿⣧⣿⣻⣿⣿⡏⣽⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⡈⠉⢒⣞⣫⠀⠘⠀⠀⢠⡴⠀⣰⣿⡿⡿⠛⢏⡀⠻⠿⠇⠀⢸⣿⣿⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⣷⠀⣸⡿⠋⠀⠀⠀⠀⠈⢁⡛⠈⠿⠇⠉⠲⠶⡀⠀⠄⠀⠀⠀⠻⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣷⣿⢿⣟⣿⣿⣿⣿⣿⡿⣿⣿⡿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠂⠀⠈⣶⣇⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣏⣿⣿⣿⣿⢽⡿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁⠀⠀⠀⠀⠀⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣭⣿⣼⣷⣛⣻⡸⢟⣇⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⣿⣿⢻⣿⣏⣫⣿⣿⣛⣛⡿⠿⠿⣷⣶⣯⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⡆⠀⠀⠀⠀⠈⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣟⡿⣿⣗⣿⣜⣛⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣛⣿⣾⢿⢿⣷⣆⣿⢢⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡁⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠠⠄⠀⢀⠀⠀⠀⠀⠀⠛⠛⠀⠐⠂⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣯⣽⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⠿⠹⠅⣽⠉⠶⡭⠢⠪⠰⠕⠿⠱⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠙⠛⠛⠛⠿⠻⠿⠿⠿⠿⣿⣿⣿⣿⠿⠿⢿⠿⠿⣿⠿⢿⣿⠿⠟⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠻⠛⠟⠻⢻⡛⣛⠟⣟⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣿⣿⣿⢿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣼⣿⣿⣿⣿⡿⣿⣿⡏⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣯⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢹⣿⣿⣿⢿⣷⣿⢿⣇⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣻⡇⣿⣿⣷⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣠⠀⠀⠀⡀⠀⠀⠀⠀⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡿⠿⠛⠛⠛⠛⠻⠿⠗⠶⠶⣾⡆⠀⠀⠀⠉⣩⣿⡇⠀⠀⠀⠀
⠀⠀⠈⠛⠛⠛⠛⠛⠃⠀⠀⣶⢻⣾⣶⣶⣝⣿⣿⣿⣿⣿⣿⣶⣶⣴⢲⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣪⣷⣶⣶⡖⣦⠀⡶⣆⠰⣶⠶⢸⡷⢢⡖⢶⠤⠿⠿⠇⠀⠀⠀⠀
⣀⠀⢀⠀⣠⣤⡀⠀⢀⠀⠀⣿⢸⡟⣿⣯⡟⣿⣿⣿⣿⣿⣟⡿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢹⡟⣶⢰⣇⣿⠀⣿⠀⢸⡗⢀⡙⢷⣴⣶⣶⣶⣶⣶⣶⣶
⣿⢸⠸⢠⣿⣿⡇⡆⣺⠀⠀⠈⠉⠁⢭⣽⡇⣿⣿⣷⠿⣿⣿⣷⣿⠿⣬⣽⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠚⢛⣶⣿⣖⠛⠓⣛⠘⠋⠛⠀⠛⠀⠘⠓⠊⠓⢚⣿⣿⣿⣿⣿⣿⣿⣿
⢻⢸⠀⢈⣿⣿⡇⡇⢸⠀⠀⠀⠀⠀⠈⣹⡃⢹⣿⣿⣿⣮⣿⣯⣵⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿
⢸⢸⠀⡀⢿⣿⡇⠃⢸⠀⠀⠀⠀⠀⢀⣿⠅⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣿⠛⢻⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠉⠁⠀⠈⠀⠀⠀⠀⠀⢨⢟⠀⢸⣿⣿⣿⣿⣯⣵⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⡀⣤⠀⡄⠀⡆⢰⠀⣀⡀⢆⠀⠀⠀⢸⣰⠀⢸⣿⡿⢿⣷⣶⣶⣶⡿⠏⢀⣿⠀⠛⢯⣻⣻⣯⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠐⠃⢙⡿⠛⠛⠛⠛⠛⠋⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠃⢻⣿⣿⣿
⡇⢹⠀⡇⠀⡇⢸⠀⠙⠃⢠⠀⠀⠀⣾⡿⠂⠈⠉⠀⠈⣿⡍⠉⠁⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⣤⣤⣤⣤⣤⣤⣶⣾⣧⡆⠀⠈⠃⢰⣤⣤⣶⣶⣆⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢸⣿⣿⣿
⡇⢸⠀⡇⠀⡇⢸⠀⠀⠀⢸⠠⠔⠊⠁⠀⠀⠀⠀⠀⠀⢹⡿⡆⠀⠛⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⡿⠏⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⡄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠃⠈⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡗⠅⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⣿⣿⣉⣁⠀⣰⣦⢀⣴⡄⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣠⡀⠀⠀⠘⠻⠟⠛
⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣋⣤⣤⣽⣿⣿⣧⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⡿⢙⣚⣩⣥⣼⣿⠿⣷⣹⣿⣿⣿⣷⣾⣷⡆⠀⠀⠀⠀⢠⢮⣬⣿⣱⡗⣐⣒⣲⣲⣶
⣿⣿⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡟⣯⣿⣽⣟⣻⣿⡷⢶⣦⣴⣾⣿⣿⣿⣿⡟⠀⠈⢿⣿⣿⣍⡁⢰⡉⠉⠻⣿⣿⣿⡏⠿⣿⣷⣶⣾⣷⡌⠾⣾⣅⣷⢡⣿⣿⣿⣿⣿
⠛⠛⠀⠀⠉⠉⠩⠿⠋⠁⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⡗⣿⢸⣿⣿⣏⡿⣿⣿⢯⣿⣿⣿⣿⣿⡏⠀⠀⠀⠈⣿⣿⣿⣿⣎⢻⣿⣧⠉⠽⠘⠟⠈⠛⠛⢿⣿⣿⣿⣤⡙⠒⢇⣿⣿⠯⠭⠭⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣓⣿⣧⢿⣾⣧⣿⣻⣿⣿⡏⣽⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⠉⢉⣉⣿⠉⠿⠿⣿⡆⠀⠀⠐⣿⣿⣿⣿⡏⠸⣿⣿⣶⠾⣿⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣟⣻⣿⡿⣿⣿⣿⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣷⣄⢀⡌⠁⢨⣿⣏⠀⠸⡃⠈⢡⣴⡀⢈⣿⣿⣿⡿⣇⠀⢿⢿⠇⠀⢽⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢽⣿⡿⣷⡾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁⠀⢺⣿⠃⠀⠀⠀⠀⠈⠁⠷⠈⢿⠫⠟⢦⣾⠀⠈⡀⠀⠀⠀⢹⣿⠆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠈⡑⠀⠀⠀⠀⠠⣴⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⢻⣿⣿⣿⣿⣿⣟⣻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣟⡿⣿⣿⣿⣿⡛⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣛⣿⣿⢟⢿⣷⣆⣿⢢⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠐⠠⠀⢀⠀⠀⠀⠀⠀⠛⠛⠀⠐⠂⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣯⣽⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠿⠹⠇⣽⠉⠶⡯⠢⠪⠐⠕⠿⠱⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⢠⣿⣵⠄⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠙⠛⠛⠟⠿⠿⠻⠿⠿⢿⣿⣿⣿⠿⠿⢿⠿⠿⣿⠿⢿⡿⠿⠟⠻⢿⠛⠛⠛⠻⠿⠿⠟⠛⠻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⡛⣛⠛⣛⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣿⢿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣼⣿⣿⣿⣿⡿⣿⣿⡏⣿⡿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣯⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢹⣿⣿⣿⢿⣿⣿⢿⣇⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣻⡇⣾⣿⣷⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣶⣶⡆⠀⠀⠀⠉⣉⣽⡇⠀⠀⠀⠀
⠀⠀⠈⠛⠛⠚⠛⠛⠃⠀⠀⣴⢻⣾⣶⣶⡆⣿⣿⣿⣿⣿⣿⣶⣶⣴⢲⣖⢶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘⣿⣿⢠⡖⣦⠉⡿⣏⠱⣾⠿⢹⡷⢢⡖⢶⠄⠿⠿⠇⠀⠀⠀⠀
⣀⢀⢀⠀⢠⣠⡀⡄⢀⠀⠀⣿⢸⡏⣿⣯⡇⣿⣿⣿⣿⣿⣏⡯⣿⣿⢸⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣶⢻⣗⣶⢰⣇⣿⠀⣿⠀⢸⡗⢀⡙⣷⣴⣶⣶⣶⣶⣶⣶⣶
⢻⢸⠈⠀⢼⣿⡇⡇⢸⠀⠀⠈⠉⠁⢭⣽⡇⣿⣿⣷⡿⢿⣿⣷⣿⣿⣬⣽⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣦⣿⣶⣾⣓⠛⠘⠋⠛⠀⠛⠀⠘⠓⠊⠓⢻⣿⣿⣿⣿⣿⣿⣿⣿
⢸⢸⠀⠀⣿⣻⡇⡇⢸⠀⠀⠀⠀⠀⠀⣈⠀⢸⣿⣿⣿⣆⣽⣿⣍⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣬⣽⣿⣿⣿⣭⣭⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿
⢸⠸⠆⠀⢿⣿⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠑⠀⢸⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⣧⣠⣽⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⡆⢠⠀⡆⠀⡇⢸⠀⢀⡀⢠⠀⠀⠀⢀⢔⠀⢸⣿⡿⢻⣿⣿⣷⣶⡾⠟⣁⣿⠀⠘⢠⣝⡉⢉⣸⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠠⠀⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠃⢻⣿⣿⣿
⡇⢸⠀⡇⠀⡇⢸⠀⠘⠃⢸⠀⠀⠀⣾⡟⠀⠈⠁⠀⠀⣿⣏⠋⠁⠀⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣤⠀⠀⠨⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢸⣿⣿⣿
⡇⢸⠀⡇⠀⡷⢸⡇⠀⠀⠸⠠⠒⠋⠁⠀⠀⠀⠀⠀⠀⢹⡿⠂⠀⠚⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⠇⠃⠀⠀⠀⢸⣦⣶⣾⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠃⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠅⣴⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⡟⢿⣁⠀⡀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠈⠛⠛⠛
⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣋⣤⣤⣽⣿⣿⣧⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⡿⢁⣸⠷⠂⣰⣾⣦⠜⢿⣿⣿⡿⠀⣀⣀⠀⠀⠀⠀⠀⡀⡜⢻⣧⢢⣄⣰⣶⣶⣶⣶
⣿⣿⠀⠀⣀⣀⣀⣠⣄⡀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡟⣯⣿⣽⣟⣻⣿⡷⠶⣦⣴⣾⣿⣿⣿⣿⡟⠀⢰⣶⣾⣿⡿⠏⡁⢶⠌⣿⣿⣿⣿⣿⡿⣆⠀⠀⢀⠀⠺⠜⣾⠿⣗⢡⣿⣿⣿⣿⣿
⠛⠛⠀⠀⠈⠈⠉⠛⠋⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⡗⣿⢸⣿⣿⣏⡿⣿⣿⢯⣿⣿⣿⣿⣿⡏⠀⠀⠀⠹⣿⣿⣷⣆⠱⣦⣤⠈⠿⠿⢻⡷⠱⣿⣿⣿⣿⣿⣄⠱⠻⡚⡇⣼⡷⠀⠀⠬⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣇⣿⣧⣿⣾⣧⣿⣻⣿⣿⡏⣽⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠿⠿⠟⢿⣷⢹⣿⣆⣀⠉⠈⠁⠀⣀⣀⣽⣿⠇⢸⣷⣎⡈⣸⣿⣿⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣿⡿⣿⣿⣿⣿⣻⣿⡿⣿⣿⣿⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠠⠄⠀⢲⡾⠀⠉⠉⠚⠀⠀⠀⠀⣼⣿⣿⢿⠄⠈⣻⣟⠉⠈⠹⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣷⣿⣿⣟⣿⣿⣿⣿⣿⡏⢭⣿⡟⣷⡾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⣰⣶⠂⠀⠀⠀⠀⢲⠂⡀⠲⠿⠹⠇⠀⠀⠀⠉⠘⠀⠀⠀⢻⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣯⢵⡿⣿⣧⣿⣿⣾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠰⠉⠀⠀⠀⠀⠛⢣⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠠⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡆⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣛⣿⣿⣿⢿⣷⣶⣿⢻⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠐⠂⠀⢀⠀⠀⠀⠀⠀⠛⠛⠀⠐⠂⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣯⣽⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠿⠹⠇⣽⠉⠿⡯⠢⠪⠰⠕⠿⠱⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⢠⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠐⠀⠀⠚⠛⠛⠛⠛⠛⠻⠿⣿⣿⣿⠿⠿⢿⠿⠿⣿⠿⢿⡿⠿⠛⠛⢛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⠛⠛⢛⣉⣉⠛⠛⠛⠛⢛⡛⣛⠛⣛⡛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣿⢿⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣼⣿⣿⣿⣿⡿⣿⣿⡏⣿⡿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣯⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⡏⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢹⣿⣿⣿⢿⣷⣿⢿⣇⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣻⡇⣾⣿⣷⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣠⠀⣀⢀⡀⠀⠀⠀⠀⣿⣿⣷⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷⢰⣶⣶⡆⠀⠀⠀⠉⢩⣽⣷⠀⠀⠀⠀
⠀⠀⠀⠙⠙⠛⠛⠛⠃⠀⠀⣶⢳⣾⣶⣶⡇⣿⣿⣿⣿⣿⣿⣶⣶⣴⢲⣖⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⠿⢻⡟⣿⠛⡿⣿⠻⣾⠿⣹⡷⢠⡖⢶⠀⠛⠛⠋⠀⠀⠀⠀
⢠⢀⠀⠀⢰⣤⡄⠄⢀⠀⠀⣿⢸⡇⣿⣯⣟⢿⣿⣿⣿⣿⣟⡯⣿⣿⢸⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣶⢸⡇⣶⢰⣇⣿⠀⣿⠀⢸⡗⢀⡙⣷⣴⣶⣶⣶⣶⣶⣶⣶
⢸⢸⠀⠀⣼⣿⡇⠀⢸⠀⠀⠈⠉⠁⢩⣽⣧⢾⣿⣷⡿⢿⣿⣷⣿⣿⣬⣽⣭⣭⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢘⣛⣦⣿⣒⣿⣓⠛⠘⠋⠛⠀⠛⠀⠘⠓⠂⠓⣻⣿⣿⣿⣿⣿⣿⣿⣿
⢸⢸⡆⡀⣿⣿⡇⠀⢸⠀⠀⠀⠀⠀⠀⢘⡁⢸⣿⣿⣿⣶⣽⣿⣍⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⢿⣿⣿⡿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⠸⠞⠇⠇⢻⣿⡇⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢠⣷⣿⣿⣿⣿⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣥⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⢸⡟⠛⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤
⡇⢠⠀⡆⠀⣧⠀⡆⢠⡄⢰⠀⠀⠀⢀⡄⠀⢸⣿⡿⠻⣿⣷⣶⣶⡾⠋⢀⣼⠆⠐⠢⠦⠤⠦⠤⣿⣿⡿⠿⢿⣿⣿⣿⠿⠿⠿⠋⠁⠀⢰⣷⣶⣾⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠈⠘⣿⣿⣿
⡇⢸⠀⡇⠀⣿⠀⡇⠈⠁⢸⠀⠀⠀⣼⠟⠀⠀⠀⠀⠀⣿⣯⠉⠉⠀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣶⣶⣶⣶⣶⣶⣶⣶⣆⢠⠀⠈⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣿⣿⣿
⡇⢸⠀⣧⠀⢿⠀⡇⠀⠀⠸⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⢸⡿⢃⠀⠙⠻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⠾⠀⠀⠀⠀⢀⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⣴⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛
⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣋⣤⣤⣼⣿⣿⣧⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⡿⠁⣰⣇⡀⢀⣤⡀⢻⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣶⣤⢄⡀⢠⣶⣶⣶⣷
⣿⣿⠀⠀⣀⣀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⣫⣿⣽⣟⣻⣿⣷⢶⣦⣴⣾⣿⣿⣿⣿⡟⠀⢚⣈⣡⣴⣿⡿⠏⣀⠉⣯⣿⣧⣶⣶⣶⠀⠀⠀⠀⠀⣱⠡⡸⡟⣮⠇⣾⣿⣿⣿⣿
⠚⠙⠀⠀⠀⠐⠛⠛⠃⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⡗⣿⢸⣿⣿⣏⡿⣿⣿⢯⣿⣿⣿⣿⣿⡏⠁⠂⠘⣿⣿⣯⣭⡀⢦⡉⠀⠻⣻⣿⣿⡝⢩⣦⣤⣤⣶⣤⠀⣷⠻⣰⡗⣼⡇⠒⠀⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣇⣿⣇⣿⣾⣧⣿⣻⣿⣿⡏⣽⣿⣿⣿⣿⣿⣿⣆⠀⠀⠘⣿⣿⣿⣷⡌⢿⣿⠀⠠⠇⠸⠇⠉⠙⠻⢿⣿⡟⢷⣈⠀⠶⢱⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢷⣾⣿⡻⣿⣿⣿⣛⣻⣿⡿⣿⣿⣿⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠉⠉⠀⠼⡟⠘⠿⠿⠷⠀⠀⠀⠀⢶⣾⣿⣿⠀⢘⣿⣷⠆⠿⢿⣿⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣷⣿⣿⣟⣿⣿⣿⣿⣿⡟⢭⣿⡟⣷⡾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢀⣼⠇⠀⠀⠀⠀⢀⠀⠀⣀⣿⣿⡟⠻⡀⠀⠿⢏⠀⠀⠈⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣏⣿⣿⣿⣯⢽⡿⣿⣧⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢸⡟⠀⠀⠀⠀⠀⠉⢀⠆⠀⠈⠘⠑⢤⡆⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣽⣿⣽⣧⣛⣻⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠁⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡆⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣛⣿⣿⣿⢿⣿⣇⣿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠒⠀⢀⠀⠀⠀⠀⠀⠛⠛⠀⠐⠂⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣽⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠿⠹⠇⣽⠉⠿⡯⠢⠪⠘⠕⠿⠱⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⢠⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠿⢿⣿⣿⠿⠿⢿⡿⠿⣿⠿⢿⡿⠿⠛⡛⣛⠛⠛⠛⠛⠛⠛⢛⣛⣛⣛⣉⣉⣉⣉⣉⣙⣛⣛⠛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡺⣿⣿⣿⢿⡛⠛⠛⠛⠛⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣼⣿⣿⣿⣿⡿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣯⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡏⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢹⣿⣿⣿⢿⣿⣿⢿⣇⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣷⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣠⣆⣀⣀⣀⠀⠀⠀⠀⢸⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣶⣶⡆⠀⠀⠀⠀⢩⣽⣿⠀⠀⠀⠀
⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⣴⢳⣾⣶⣶⣿⢽⣿⣿⣿⣿⣿⣶⣶⣶⢲⣶⣰⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠿⢿⡿⣿⠿⡿⣿⠿⣾⢿⣹⡷⢢⡖⢶⠐⠚⠛⠛⠀⠀⠀⠀
⢠⢀⡀⡄⢰⣦⣤⢠⢠⡀⠀⣿⢸⡇⣿⣿⣿⢽⣿⣿⣿⣿⣟⡯⣿⣿⢸⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣿⣲⢸⡇⣶⢸⣇⣿⠀⣿⠈⢻⡗⢀⡙⣷⣶⣶⣶⣶⣶⣶⣶⣾
⢸⣺⡇⡇⣿⣿⣿⢸⢸⡇⠀⠈⠉⠁⢩⣽⣿⢺⣿⣷⣿⠻⣿⣷⣿⡿⢮⣽⣭⣭⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢘⣿⣮⣿⣶⣿⡓⠛⠘⠋⠛⠀⠛⠀⠘⠓⠊⠓⣻⣿⣿⣿⣿⣿⣿⣿⣿
⢸⡇⡇⡇⣿⣿⣿⢸⢸⡇⠀⠀⠀⠀⠈⣽⡟⢸⣿⣿⣿⣯⣼⣿⣧⣔⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠘⠇⠇⠡⢙⣿⣿⠸⢸⡇⠀⠀⠀⠀⠀⣴⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢁⣭⣿⣿⣿⣍⣉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠿⣿⣿⢿⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⢸⣿⣿⣿⣿⣿⣷⡾⢿⣿⡟⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣤⣤⣤
⡇⢰⡄⣶⠀⣿⠀⡇⢠⣤⢸⡀⠀⠀⠀⣺⠄⢸⣿⠿⠛⣿⣿⣿⣾⡿⠛⢤⣼⡇⠁⠻⠯⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠃⠀⢸⣅⣬⣽⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠉⠘⣿⣿⣿
⡷⠸⡇⢿⠀⣿⠀⡇⠈⠉⢸⡇⠀⢀⣼⠟⠁⠀⠀⠀⠀⢻⣯⡉⠁⢀⣴⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠐⠒⢶⣶⣶⣶⣶⣶⣶⣶⡄⢀⠀⠸⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⣿⣿⣿
⣿⠀⡇⢻⠀⢸⠀⡇⠀⠀⠘⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⡳⢠⠉⠻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣷⠼⠀⠀⠈⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⠀⢼⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠟⣿⣿⣿⣅⠀⠀⠀⠀⠀⢸⣆⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⣤⣤⣬⣿⣿⣧⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⡿⠁⢀⡦⡀⠀⣀⠘⣿⣿⡿⣥⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⢄⡀⠀⢭⣭⣭⣭⣭
⣿⣿⡇⠀⣠⣴⣤⣴⣴⡆⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⣫⣿⣽⣟⣻⣿⣿⢶⣦⣴⣾⣿⣿⣿⣿⡿⠀⣾⠿⠏⡁⣿⣿⡶⠈⢿⣟⣿⠃⢀⣄⣀⠀⠀⠀⠀⠀⢀⢃⢸⡟⣞⠗⣾⣿⣿⣿⣿
⠛⠛⠁⠀⠀⠐⠒⠛⠋⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⡗⣿⢸⣿⣿⣇⡿⣿⣿⢯⣿⣿⣿⣿⣿⡿⠃⠂⢲⣿⣿⣿⠛⠋⡜⠶⠨⣿⣿⣿⣿⢻⠛⡀⠀⢀⣤⡀⠉⡦⢷⢡⠯⣸⡗⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣃⣿⣧⣿⣾⣧⣿⣻⣿⣿⡏⣽⣿⣿⣿⣿⣿⣿⣆⠀⠀⢹⣿⣿⣿⣦⡹⣶⣶⠈⢚⡋⣽⡃⠾⠿⣿⣶⣽⡿⣄⠈⡂⣁⢧⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢷⣾⣿⣻⣿⣿⣿⣻⣻⣿⡿⢿⣿⣿⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠛⠛⠋⠻⠷⢹⣿⣦⣬⠁⠀⠀⠀⣠⣤⣾⡿⠀⠨⣷⣦⠀⠼⢿⣷⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣷⣿⢿⣟⣿⣿⣿⣿⣿⡏⢽⣿⡟⣷⡾⣿⣯⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠈⣹⡇⠀⠈⠀⠀⠀⠀⠀⠀⣿⣿⡿⢿⠀⠀⣗⡪⠀⠀⠘⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣏⣿⣿⣿⣯⢽⣿⣿⣧⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢰⡖⠀⠀⠀⠀⠀⠺⠡⡄⠙⠟⠹⢃⣀⡅⠀⠀⠈⠀⠀⠀⠹⡷⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣿⣭⣿⣼⣷⣛⣻⣸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣯⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠃⠀⠀⠀⠀⠀⢹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠘⠀⠀⠀⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠙⠀⢀⡀⠀⠀⠀⠀⠛⠛⠀⠐⠂⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠿⠹⠇⣽⠉⠿⡯⠢⠪⠸⠕⠿⠱⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⢀⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⠿⠿⢿⡿⠿⣿⠿⢿⡿⠿⠇⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⣿⢿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣼⣿⣿⣿⣿⡿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣧⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢹⣿⣿⣿⢿⣿⣿⣿⣿⣿⣾⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⢸⣇⠀⢀⢤⣤⣤⡄⠀⠀⠀
⡀⠀⠀⠠⠶⢿⢤⣤⣤⠄⠀⠀⠀⢀⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣶⣾⣶⡆⠀⠀⢸⢀⣶⣿⡇⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢳⡆⣶⣶⣿⣷⣿⣿⣿⣶⣾⣶⣶⣷⢲⣶⣴⡶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⡿⡿⣿⣿⣷⢿⣹⣿⣣⡖⢶⠈⠉⠉⠉⠁⣀⣀⣀
⡄⡆⢠⢰⢠⣿⣿⡀⠀⣶⠀⣿⢸⡇⣿⣯⣿⢭⣿⣿⣿⣿⣟⡯⣿⣿⢸⣿⣿⣯⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⠒⢸⡇⣶⢰⣇⣿⠈⣿⠸⣿⣗⢀⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠃⣧⢸⢸⢸⣿⣿⡇⡇⣿⠀⠈⠉⠁⠉⠹⡿⡎⣿⣷⣿⡉⠛⣷⡯⢉⣈⢽⣭⣭⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢘⣿⣦⣿⣶⣜⠓⠛⠘⠋⠛⠀⠛⠀⠙⠓⠊⠓⢺⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⢸⠘⢸⣿⣿⡇⡇⣿⠀⠀⠀⠀⠀⠤⢽⠂⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⠘⠀⠀⠿⠿⠇⠃⠿⠀⠀⠀⠀⠀⣤⡾⠀⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠸⠿⣿⣿⡿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛
⢠⠀⠀⠀⠀⠀⡄⢠⠀⠀⠀⡄⠀⠀⠀⠤⡇⠀⣿⣿⣿⣿⣿⣿⣭⣭⣿⡏⢀⣿⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⣾⣾⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣶⣶⣶
⢸⠀⢱⠘⡇⠈⡇⢸⠀⣶⡆⡇⠀⠀⠀⣋⡇⠀⠿⠛⠉⢹⣿⠿⠿⠛⠉⣠⣿⡿⠀⠈⠑⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⣿⠿⢷⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⠀⠀⢸⣿⣿
⢸⡆⢈⠀⡇⠀⡇⢸⠀⠀⠀⢧⢀⠤⠒⠉⠀⠀⠀⠀⠀⠘⣿⣷⠀⠠⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⡿⠀⠀⠂⣷⣴⣲⣾⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢸⣿⣿
⢸⠇⠸⠀⠇⠀⠃⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣥⠇⠄⣨⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡄⠆⠀⠙⠿⠿⠿⠟⠻⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠹⣿⣏⣀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⢠⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣼⣿⣯⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⡿⠁⠀⠀⠀⠀⠀⢹⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠐⢶⣶⣶⣶⣶
⢘⣿⣿⠀⠐⠾⠿⢿⣿⠟⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⣫⣿⣽⣟⣻⣿⣿⢶⣦⣴⣾⣿⣿⣿⣿⡟⠀⡜⠤⡢⠂⢀⣀⡀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢙⠿⡸⡧⠻⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⡗⣿⢸⣿⣿⣏⡿⣿⣿⢯⣿⣿⣿⣿⣿⡿⠀⡈⣬⣥⣶⣤⣿⠟⢣⣀⠀⠀⢀⣠⣴⠳⠀⠀⠀⠀⠀⠐⠚⢔⣎⠣⡪⣰⡀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣫⣿⣧⢿⣾⣇⣿⣿⣿⣿⡏⣽⣿⣿⣿⣿⣿⣿⣆⠀⠈⢿⣿⣷⣦⠀⢀⣉⡀⠺⢹⡏⢿⠂⣀⣤⣄⠀⢱⣇⡀⠑⠀⠎⡂⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢷⣾⣿⣿⣿⣿⣿⣛⣻⣿⡿⢿⣿⣷⣾⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣷⡀⠈⣿⣿⠿⢷⣌⢿⣿⡀⠐⠂⠙⠁⠀⠉⠉⣓⣟⠀⠙⢦⣁⠭⡸⢿⣷⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⡟⢽⣿⡿⣷⡾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠐⠶⡄⠈⠻⠁⠇⠀⠀⠀⠀⣰⣿⡿⢿⠀⠀⠈⠉⠀⠀⠘⣿⣇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣿⣿⣿⣏⣿⣿⣿⣯⢽⣿⣿⣧⣿⣿⣼⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⡈⠁⠀⠀⠀⠀⢠⠀⡀⠐⠻⠻⠇⠀⠀⠀⠁⠀⠀⠀⠀⠹⠿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣿⣭⣿⣼⣷⣛⣻⡸⢿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⠁⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠻⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣯⣫⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⢰⣶⡆⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡠⡄⠀⠀⢀⣀⢀⠀⠀⠀⠛⠛⠀⠐⠂⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠿⠹⠇⣽⠉⠿⡯⠢⠪⠸⠕⠿⢱⣀⣀⡀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⣿⣆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⠿⠿⠿⠿⠿⣿⠿⢿⣿⠿⠇⢰⣶⣤⣤⣤⣤⣤⣤⣤⣴⣶⣿⣶⣶⣶⣾⣿⣷⣶⣦⣤⣤⣶⣶⣶⣶⣶⣶⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣼⣿⣿⣿⣿⡿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣧⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢹⣿⣿⣿⢿⣷⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⢸⣇⠀⠀⠤⠤⣤⣤⠀⠀⠀
⡄⠀⠀⠐⠲⠿⠶⠶⠶⠏⠀⠀⠀⠀⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣶⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⡷⢴⣶⣶⡆⠀⠀⠀⢀⣿⡿⠿⠀⠀⠀
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣴⢳⡆⣶⣶⣿⣷⣿⣟⣶⣶⣾⣶⣶⣷⢲⣶⣴⡶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣾⣿⣿⣿⣿⡿⡿⣿⣿⣷⢿⣹⣿⣣⡖⢶⣀⣀⣀⣀⣀⣀⣀⣀
⣦⣿⢰⠘⢠⣻⣿⡇⡇⣾⠀⣿⢸⡇⣿⣯⣿⢭⣽⣿⣿⣿⣟⡯⣿⣿⢸⣿⢾⣯⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⠛⢹⡇⣶⢸⣇⣿⠉⣿⢸⣿⣗⣀⡙⢷⣿⣿⣿⣿⣿⣿⣿⣿
⠉⢻⢸⠀⠘⣺⣿⡇⡇⢸⠀⠈⠉⠁⠉⣝⣿⡎⣽⣿⣿⣍⣉⣷⣏⡩⣬⣹⣭⣭⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢘⣿⣦⣿⣒⡜⠓⠛⠘⠋⠛⠀⠛⠈⠛⠓⠊⠓⢚⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⢸⠀⡇⣿⣿⡇⠁⢸⠀⠀⠀⠀⠀⢐⣾⠂⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢠⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⠀⠀⠁⠘⠛⠃⠀⠘⠀⠀⠀⠀⠀⢨⣟⠀⢸⣿⣿⣿⣿⣿⣭⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢼⢿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛
⢰⡄⢀⠀⡆⠀⡆⢰⠀⠀⠀⢠⠀⠀⠀⠡⡗⠀⢸⣿⣿⣿⣿⣾⣷⣶⣿⠏⢠⣿⠙⢟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢠⣶⣾⣿⣿⣷⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠰⢶⣿⣿
⢸⡇⢸⠀⡇⠀⡇⢸⡇⠿⠇⢸⠀⠀⠀⣴⡿⠀⠘⠋⠀⢸⣿⡛⠛⠉⠁⣰⣾⣿⠀⠀⠈⠉⠉⠉⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⣉⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⠀⠀⢸⣿⣿
⢸⡇⢸⠀⡇⠀⡇⢸⡇⠀⠀⢸⠠⠐⠊⠁⠀⠀⠀⠀⠀⠀⣿⡷⡆⠀⢾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⡏⠀⠠⠀⣧⣴⣶⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠘⠇⠘⠀⠃⠀⠁⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡇⠂⣠⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣷⠀⠆⠀⠻⣿⣿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿
⠐⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⠈⢿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣋⡀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣠⣤
⢠⣿⣧⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣿⣯⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⡟⠁⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠚⢻⣿⣿⣿⣿
⠀⢿⠿⠀⠈⠉⢙⣛⣿⠏⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣫⣿⣽⣟⣻⣿⣷⢶⣦⣴⣾⣿⣿⣿⣿⡟⠀⣘⡠⡢⠀⠀⠀⡈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢙⠞⣜⡇⠉⠉⢛⣛⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡗⣿⢸⣿⣿⣏⣿⣿⣿⢯⣿⣿⣿⣿⣿⡿⠀⠘⣃⣭⣤⣤⣾⠿⢃⡀⠀⠀⠀⣀⣴⠷⠀⠀⠀⠀⠀⠀⠎⢆⣌⢃⡺⣴⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣗⣿⣧⢿⣾⣧⣿⢿⣿⣿⡏⣽⣿⣿⣿⣿⣿⣿⣆⠀⠘⣿⣿⣷⣄⠀⢊⠁⠀⢋⢿⡟⢿⠀⣠⣄⣀⠐⢣⡆⠈⠱⠀⢎⡆⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢷⣾⣿⣿⣿⣿⣿⣛⣻⣿⡿⣿⣿⣷⣾⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣷⡀⠘⣿⣿⠿⣷⡌⢿⣟⡀⠐⠂⠛⠀⠉⠉⠙⣻⣿⠉⠱⠤⣁⠽⣸⣿⣷⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⡏⢭⣿⡟⣷⡾⣿⣯⣿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠤⠴⡇⠘⠿⠛⠇⠀⠀⠀⠀⢰⣿⣿⣷⠀⠀⠉⠛⠁⠀⠈⣿⣇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣟⣿⣿⣿⣟⣿⣿⣿⣯⢽⡿⣿⣧⣿⣿⣾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⡛⠁⠀⠀⠀⠀⢠⠀⠀⠠⠛⢻⠇⠀⠀⠀⠉⠀⠀⠀⠀⠘⢿⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣿⣭⣿⣼⣷⣛⣻⡸⢿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⠃⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠈⠺⢧⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀
⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⢻⣿⣏⣫⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⢰⣶⡆⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠦⠀⠀⢀⣀⠠⠀⠀⠀⠛⠛⠀⠐⠂⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠿⠹⠇⣽⠉⠿⡭⠢⠪⠸⠕⠿⣱⣤⣤⣄⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠿⠿⠿⠿⠿⣿⠿⢿⡿⠿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⢺⣿⣿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣼⣿⣿⣿⣿⡿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢹⣿⣿⣿⢿⣷⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⢸⣇⠀⠀⠒⠒⣲⣶⠀⠀⠀
⠆⠀⠀⠀⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⢿⣿⣷⣶⣿⣿⣿⣿⣿⣶⣶⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣰⣾⣶⡆⠀⠀⠀⠤⠽⠿⠿⠀⠀⠀
⠀⢀⠀⠀⠀⢠⣀⡀⡀⢀⠀⣴⢳⡆⣶⣶⣿⣷⣿⣟⣶⣶⣾⣶⣶⣷⢲⣶⣴⡶⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⣹⣿⣣⡖⢶⣤⣤⣤⣤⣤⣤⣤⣤
⢶⢸⢸⠀⡀⢸⣿⡇⠁⢸⠀⣿⢸⡇⣿⣯⣿⢭⣽⣿⣿⣿⣟⡯⣿⡿⢸⣿⣿⣯⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣿⠛⢹⡇⣶⢸⣇⣿⠉⣿⢸⣿⣗⣀⡙⢷⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⡼⠀⡇⣿⣿⡇⠀⢸⠀⠈⠉⠁⠉⢹⣿⡎⢹⣿⣿⣭⣬⣵⣭⣡⣬⣽⣭⣭⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣸⣿⣦⣿⣒⡘⠓⠛⠘⠋⠛⠀⠛⠘⠛⠓⠊⠓⠚⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⡇⡇⡇⢻⣿⣿⠀⢸⠀⠀⠀⠀⠀⠐⣽⠏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠀⠀⠀⠀⠀⢀⣿⠀⢸⣿⣿⣿⣿⣭⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣾⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉
⢰⡆⢠⠀⡆⠀⡆⠀⡆⢀⡀⢰⠀⠀⠀⠸⣽⠀⢸⣿⡿⢻⣿⣿⣶⣿⡿⠃⢰⣿⠈⠛⣿⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⢠⣶⣾⣿⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢸⣿⣿
⢸⡇⢸⠀⡇⠀⣯⠀⡇⠘⠃⢸⠀⠀⢀⣼⠟⠀⠈⠁⠀⠸⣿⡛⠋⠁⢀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠭⢭⣭⣭⣭⣭⣭⣭⣭⠀⠀⢸⣿⣿⣽⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠸⠸⠆⠀⢠⣿⣿
⠘⡇⠀⠀⡇⠀⣿⠀⡇⠀⠀⠸⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⣿⡟⠃⡀⠛⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⠏⠀⠠⢸⣧⣤⣬⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿
⠀⠃⠈⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡖⢄⣴⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⣿⣦⠠⠂⠘⢿⣿⣿⣿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿
⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢟⢀⠀⠻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢋⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣶⣶⣶⣶
⠀⣿⣿⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⣤⣤⣤⣽⣯⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⡟⠁⠀⠀⠀⠀⠀⣷⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠛⣿⣿⣿⣿⣿
⠀⠿⠊⠀⠀⠀⠩⠽⠿⠋⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⣫⣿⣽⣟⣻⣿⣷⢶⣦⣴⣾⣿⣿⣿⣿⡟⠀⢀⡂⡀⠀⠀⣄⠘⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⣙⠏⣎⠇⠉⠉⢉⣉⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⡗⣿⢸⣿⣿⣏⣿⣿⣿⢯⣿⣿⣿⣿⣿⡟⠀⠘⣃⣩⣤⣠⡾⠿⢁⡀⠀⠀⠀⣀⣴⠦⠄⠀⠀⠀⠀⠠⠆⠢⡌⢑⡈⣴⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣃⣿⣧⣿⣾⣧⣿⢿⣿⣿⡏⣽⣿⣿⣿⣿⣿⣿⣆⠀⠹⣿⣿⣯⡄⠀⡈⠁⠀⢌⢽⡿⢷⠀⣠⣀⣀⠄⣢⡆⠈⠨⡀⢏⢂⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢷⣾⣿⣿⣿⣿⣿⣟⣻⣿⡿⣿⣿⣷⣾⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣷⡀⠙⣿⣿⣿⣶⡘⣿⣇⡀⠰⠀⠛⠂⠉⠉⠛⣳⣿⠉⢓⠄⣘⠅⡼⣿⣷⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣷⣿⢿⣟⣿⣿⣿⣿⣿⡏⢽⣿⡟⣷⠾⣿⣯⣿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠁⠠⠬⡃⠸⠿⠓⠆⠀⠀⠀⠀⣴⣿⣿⣷⠀⠀⠋⠉⠀⠀⠘⣿⣇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣿⣿⣿⣏⣿⣿⣿⣯⢽⡿⣿⣧⣿⣿⣼⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢀⡛⠀⠀⠀⠀⠀⣠⠀⠀⠠⠻⢿⠇⠀⠀⠀⠉⠐⠀⠀⠀⠙⢿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣿⣭⣿⣼⣷⣛⣻⣸⢿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⠃⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠺⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⣿⣿⢻⣿⣯⣫⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⢰⣾⡆⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠛⠀⠀⢀⣀⠀⠀⠀⠀⠛⠛⠀⠐⠂⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠿⠹⠇⣽⠉⠻⠭⠢⠪⠸⠕⢿⣵⣶⣶⣦⡀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⠿⠿⢿⣿⢿⢿⣿⠿⡿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⡿⢈⣿⣿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⢸⡇⠀⠀⢀⣀⣀⣀⠀⠀⠀
⠀⠀⠀⠀⣠⣴⣆⣀⣠⣄⠀⠀⠀⠀⣿⣿⢹⣿⣿⣿⢿⣿⣿⢻⣟⣿⡻⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⢸⣇⠀⠀⡇⢩⣽⣿⠀⠀⠀
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣶⣿⣿⣿⣿⣿⣶⣶⣾⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⢴⣶⣶⡦⠀⠀⠀⠁⠈⠉⠉⠀⠀⠀
⢀⢰⢠⠀⡄⢰⣶⡆⠀⢠⠀⣶⢳⡆⣶⡶⣿⣷⣿⣟⣶⣶⣾⣶⣶⣷⢲⣶⣴⡖⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⡿⣿⣿⣿⢿⣹⣿⣧⡖⢶⣶⣶⣶⣶⣶⣶⣶⣶
⠘⢸⡜⡄⡇⣿⣿⣿⠀⢸⡇⣿⢸⡇⣿⡯⢿⢭⣽⣿⡟⣿⢟⡯⢿⡿⢸⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⠋⣿⠛⢹⡇⣶⢸⣇⣿⠛⣿⢸⣿⣗⣀⡙⢷⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⡇⡇⡇⣿⣿⣿⢠⢸⡇⠈⠉⠁⠉⢡⣭⡈⢩⣿⣷⣭⣮⣧⣬⣥⣬⣽⣭⣭⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣚⣿⡟⢓⣺⣿⣦⣛⣒⠘⠓⠛⠘⠋⠛⠀⠛⠸⠛⣓⡊⠓⠚⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠘⠃⠃⠃⠙⡿⡿⠸⠸⠇⠀⠀⠀⠀⢠⣿⠅⢸⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢿⣿⣿⣿⣿⣿⣿
⢀⡀⠀⠀⠀⠀⡀⠀⡀⠀⠀⢀⠀⠀⠀⢰⣿⠀⢸⣿⣿⣿⣿⡶⠿⣻⣿⡿⢙⣿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢸⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣠⣤
⠸⡇⢸⠀⡷⠀⣿⠀⡇⢰⣦⢸⠀⠀⠀⢐⣾⠀⠸⠟⠉⢸⣿⣿⣿⡿⠋⢠⣼⣿⠀⠀⠙⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⣴⣴⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⡌⠉⠈⣿⣿
⠀⡇⠀⠀⣷⠀⢻⠀⡇⠈⠁⢸⠀⣀⠤⠚⠉⠀⠀⠀⠀⠘⣿⣍⡁⢀⣴⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⣶⣶⣶⣶⣶⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⠘⠃⠀⠀⣿⣿
⠀⡇⠀⡆⢻⠀⠸⠀⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⡃⡂⢈⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠀⠀⠄⣿⣭⣽⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠐⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣷⠀⠀⠀⠹⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛
⠀⣸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡱⠐⠀⠹⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣭⣭⣭⣭⣭⣭
⠀⣿⣿⠁⠀⠶⠶⠶⢶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣽⣧⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⡿⠁⠀⠀⠀⠀⢹⣄⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠐⠻⣿⠿⣿⣿⣿
⠀⠉⠉⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⣫⣿⣽⣟⣻⣿⣷⢶⣦⣴⣾⣿⣿⣿⣿⡟⡀⢀⡀⠀⠀⢀⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢹⡻⢱⡤⠀⠀⠀⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡗⣿⢼⣿⣿⣯⣿⣿⣿⢯⣿⣿⣿⣿⣿⡏⠀⢞⣒⣡⣄⣴⡾⠎⠀⠀⠀⠀⢀⣠⠦⠀⠀⠀⠀⠀⠀⠴⠐⢔⡉⣂⢡⣆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣓⣿⣧⢿⣿⣧⣿⢻⣿⣿⡏⢽⣿⣿⣿⣿⣿⣿⣆⠈⢿⣿⣯⣍⠀⠀⠉⠀⠀⡩⣿⢿⡆⠀⣀⣀⠀⢠⣰⠀⠁⢕⠸⡰⣸⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢷⣾⣿⣿⣿⣿⣿⣻⣻⣿⡿⢿⣿⣶⣾⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣷⡀⠙⣿⣿⣷⣄⢻⣷⣀⠁⠶⠘⠓⠈⠉⠛⢛⢾⡏⠑⢦⡀⠫⠀⠿⣿⣆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⢿⣟⣿⣿⣿⣿⣿⡟⢽⣿⡟⣷⡾⣿⣯⣟⣟⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠀⠈⢍⠈⠿⠟⠳⠀⠀⠀⠀⠀⣸⣿⣿⡆⠀⠉⠁⠉⠀⠀⢹⣿⡆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣟⣿⣿⣿⣟⣿⣿⣿⣯⢽⡿⣿⣧⣿⣿⣾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢘⡛⠀⠀⠀⠀⠀⡄⠀⠀⠘⠟⣿⠁⠁⠀⠈⠁⠀⠀⠀⠀⠙⡷⠀⠀⠀
⠀⠀⠠⠄⠄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣿⣭⣿⣼⣷⣛⣻⣸⢟⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⢻⣿⣯⣫⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣷⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢤⠀⠀⠀⠀⠀⡀⠀⠀⢰⣾⡆⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠛⠛⠀⢐⣂⡀⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀
⠀⠿⠹⠅⣭⠉⠹⡭⠢⠪⠸⠕⣿⣿⣿⣿⣿⡆⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⠿⠿⠿⣿⠿⣿⣿⡿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡿⢸⡇⠀⠀⡠⢤⣤⣤⡀⠀⠀
⣀⠀⠀⠀⠴⣾⣧⣴⣶⡶⠀⠀⠀⠀⣿⣿⢹⣿⣿⣿⢿⣿⣿⢻⣏⣿⡻⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⢸⣇⠀⠀⡇⢰⣿⣿⠀⠀⠀
⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣿⣿⣿⣿⣿⣾⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣶⡶⠀⠀⣀⡉⠉⠉⠉⢀⠀⣀
⢤⢰⢠⠀⡆⣸⣿⣗⠀⢰⡆⣶⢳⡆⣶⡶⣿⢷⣿⣟⣶⣶⣾⣶⣶⣷⢲⣶⣴⡖⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⣹⣿⣫⡖⢶⣿⣿⣿⣿⣿⣿⣿⣿
⠈⢸⡎⡆⡇⣿⣿⣿⠀⢸⡇⣿⢸⡇⣿⣯⣿⢭⣝⣿⡛⣿⢟⡯⢿⣟⢸⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⢿⣿⠏⣿⠓⢹⡇⣶⢸⣇⣿⠻⣿⢸⣿⣗⣄⡙⢷⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⡇⡇⡇⣿⣿⣿⢸⢸⡇⠈⠉⠁⠉⣙⣿⡮⢩⣿⣿⣿⣾⣷⣮⣽⣬⣽⣭⣭⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠛⢓⣼⣿⣆⣛⡒⠘⠓⠛⠘⠋⠛⠀⠛⠸⢛⣓⡊⠓⠚⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⠁⠁⠁⠘⠟⠛⠘⠘⠃⠀⠀⠀⠀⢠⣿⡇⢸⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠛⠛⠛⠟⠿⠿⠿⠿
⢀⡄⢀⠀⡀⠀⣄⠀⡄⠀⠀⢠⠀⠀⠀⢨⣿⠀⢸⣿⣿⣿⣟⣛⣛⣿⣿⡟⢹⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⣤⣤
⠘⡇⢸⠀⣿⠀⣿⠀⡇⢸⡷⢸⠀⠀⠀⢸⣿⠀⠘⠋⠁⢸⣿⣿⣿⠟⠁⣸⣾⣿⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠀⠀⣧⣼⣿⣿⣧⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⣠⡄⠀⠈⣿⣿
⠀⡇⠀⠀⣿⠀⢻⠀⡇⠀⠀⢸⢀⠤⠒⠋⠁⠀⠀⠀⠀⠘⣿⣦⠀⠠⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⡄⠀⠸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠁⠀⠀⣿⣿
⠀⡇⠀⠃⠙⠀⠘⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣥⠄⠀⣠⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡟⠀⠀⠀⣿⣭⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠁⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣦⠀⠀⠀⠻⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⣀⣀⣉⣉
⠀⣼⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠀⠀⠘⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢼⣶⣷⣷⣿⣿⣷
⠀⣿⣿⠇⠀⠒⢛⣻⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣼⣧⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡿⠁⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠘⠻⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⣫⣿⣽⣟⣻⣿⣷⢶⣦⣴⣾⣿⣿⣿⣿⡟⠀⣀⢁⠀⠀⡀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢈⠟⡴⡆⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⡗⣿⣸⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⡏⠀⣑⣊⣥⣄⣴⠿⢇⠀⠀⠀⠀⢀⣴⠦⠀⠀⠀⠀⠀⠀⠬⠔⣄⠳⣊⢰⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣓⣿⣧⣿⣿⣯⣿⢻⣿⣿⡏⣽⣿⣿⣿⣿⣿⣿⣆⠈⢿⣿⣯⣍⠀⠀⠙⠀⠈⢩⣟⢿⠆⢀⣀⣀⢀⠀⣆⠈⠱⡀⢎⡂⣿⣧⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢷⣾⣿⣿⣿⣿⣿⣛⣻⣿⡿⣿⣿⣷⣾⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣷⡀⠙⣿⡿⣷⣌⢿⣗⡀⠁⠆⠛⠒⠉⠉⠛⢳⣾⠇⢱⣦⡑⠩⠰⠿⣿⡆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⡟⣽⣿⡟⣷⡾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠠⠌⠸⠿⠗⠂⠀⠀⠀⠀⢀⣾⣿⢿⡀⠀⠀⠁⠁⠀⠀⢽⣿⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣟⣿⣿⣿⣏⣿⣿⣿⣯⢽⡿⣿⣧⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢘⠃⠀⠀⠀⠀⢀⡀⠀⠀⠛⠻⡏⠀⠀⠀⠈⠀⠂⠀⠀⠈⠹⠗⠀⠀⠀
⠀⠀⠀⠂⠒⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣿⣽⣿⣼⣷⣛⣻⡸⢯⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠋⠀⠈⠀⠀⠺⠿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣯⣫⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡆⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠛⠛⢀⣐⣦⣀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠿⠹⠇⣭⠉⠿⡭⠢⠪⠸⠕⣿⣿⣿⣿⣿⣏⠀⠘⠉⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠘⣿⣷⣄⠀⠀⠀⠀⡰⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⣿⣿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡿⢸⡇⠀⠀⡤⠤⢤⣤⡄⠀⠀
⡄⠀⠀⠀⠲⠿⠷⠶⠾⠿⠀⠀⠀⠀⣿⣿⢹⣿⣿⣿⢿⣿⣿⢹⣇⣿⣹⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⢸⣇⠀⠀⣇⣰⣿⣿⠀⠀⠀
⠀⢀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣾⣿⣿⣿⣿⣾⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⡶⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀
⢰⢸⡰⠀⡇⣼⣿⣿⠀⢸⡆⣶⢳⡆⣶⡶⣿⣷⣟⣞⣶⣶⣾⣶⣶⣷⢲⣶⣴⡖⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⣹⣿⣫⡖⢶⣿⣿⣿⣿⣿⣿⣿⣿
⠈⢸⡇⡇⡇⣿⣿⣿⢰⢸⡇⣿⢸⡇⣿⣯⣿⢭⣝⣿⣉⣿⣟⡯⢿⡍⢸⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣧⣿⣿⢿⣿⠏⣿⠒⢸⡇⣶⢸⣇⣿⠻⣿⢸⣿⣗⣄⡙⢷⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⡇⡇⡇⣿⣿⣿⢸⢸⡇⠈⠉⠁⠉⠙⣿⡎⢩⣿⣿⣿⣿⣷⣿⣿⣮⣽⣭⣭⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠛⣓⣘⣛⣂⣛⠒⠘⠓⠛⠘⠋⠛⠀⠛⠸⢛⣓⡊⠓⠚⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠁⠀⠀⠀⠋⠛⠈⠈⠃⠀⠀⠀⠀⢘⣿⡁⢸⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢰⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛
⢠⡆⢀⠀⣄⠀⣤⠀⡆⠀⠀⢠⠀⠀⠀⢸⣿⠁⢨⣿⣿⣿⣭⣭⣭⣽⡿⠏⣸⣿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⣶⢰⣶⣶
⠀⡇⠸⠀⣹⠀⣿⠀⡇⠸⠿⢸⠀⠀⠀⣸⡟⠂⠈⠉⠀⢸⣿⠿⠟⠋⢀⣶⣿⡟⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⢉⢉⠉⢉⡉⠀⠀⢠⣤⣾⣿⣿⣍⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⢰⡆⠀⠀⣿⣿
⠀⡧⠀⡀⢸⠀⢸⠀⡇⠀⠀⠸⠤⠒⠊⠁⠀⠀⠀⠀⠀⠈⣿⡷⡀⠰⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠁⠀⠀⣿⣿
⠀⠟⠀⠃⠘⠀⠈⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⡑⢀⣴⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠏⠀⠀⢸⣏⣛⣻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠀⠜⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠘⢿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣄
⠀⣾⣿⡆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠈⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿
⠀⠿⠿⠃⠀⠉⠛⠻⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣽⣥⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⡿⠁⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣄⠀⠀⠙⠛⠛⣛⡛⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⣫⣿⣽⣟⣻⣿⡷⢶⣦⣴⣾⣿⣿⣿⣿⡟⠀⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠘⡛⠇⢮⠆⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡗⣿⢺⣿⣿⣿⡿⣿⣿⢯⣿⣿⣿⣿⣿⡏⠀⣒⣩⡤⣠⣶⠿⢅⠀⠀⠀⠀⢀⡴⠄⠀⠀⠀⠀⠀⠠⠥⢢⡙⠑⡈⣴⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣓⣿⣧⣿⣿⣧⣿⢻⣿⣿⡏⣽⣿⣿⣿⣿⣿⣿⣆⠈⢿⣿⣯⣅⠀⠈⠁⠀⠈⢽⡛⢷⠀⢀⣀⡀⠀⣀⡆⠨⠂⠐⢗⢠⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢷⣾⣿⣿⣿⣿⣿⣛⣻⣿⡿⣿⣿⣷⣾⣿⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣷⣀⢹⣿⡿⣶⡈⣿⣗⡀⠰⠆⠛⠂⠉⠉⠛⣓⣿⠁⢔⢤⢐⠅⠾⢿⣿⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⡟⢭⣿⡟⣷⡾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠠⠤⡌⠸⠿⠛⠆⠀⠀⠀⠀⢠⣿⣿⣷⠀⢈⠀⠈⠀⠀⠘⢿⣷⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣟⣿⣿⣿⣏⣿⣿⣿⣯⢽⣿⣿⣧⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⡚⠃⠀⠀⠀⠀⢠⠀⠀⠀⢛⢻⠇⠀⠀⠀⠁⠀⠀⠀⠀⠘⠛⠇⠀⠀⠀
⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣿⣭⣿⣼⣧⣛⣻⣸⢿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠻⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⢳⣿⣯⣫⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠒⠀⠀⠀⠀⠀⠄⠀⠀⢰⣾⡆⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠛⢛⣠⣽⣶⣄⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⢀⣧⡀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠿⠹⠇⣽⠉⠸⡯⠢⠪⠐⠕⢿⣿⣿⣿⣿⣿⡃⠸⠋⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠘⣿⣷⣄⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡄⠀⢀⣀⡀⠀⠀⠀⢸⣿⣼⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡿⢸⡇⠀⠀⡖⠒⣲⣶⡄⠀⠀
⠤⠀⠀⠀⠚⠛⠓⠚⠛⠟⠀⠀⠀⠀⢻⣿⢹⣿⣿⣿⢿⣿⣿⢸⣇⣿⣾⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⢸⣇⠀⠀⡇⣸⣿⣿⠀⠀⠀
⠀⢀⡀⠀⡀⢠⣄⣀⢀⠀⡀⠀⠀⠀⠸⣿⣿⣶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣶⡶⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤
⢰⢸⡇⡆⡇⣼⣿⣿⢨⠘⡇⣶⢳⡆⣶⡖⣿⣷⣟⣎⣶⣶⣾⣶⣶⣷⢲⣶⣶⡖⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⣹⣿⣫⡖⢶⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⡇⡇⠁⣿⣿⣿⢸⠀⡇⣿⢸⡇⣿⣯⣿⢭⣝⣿⣤⣿⣏⡯⣽⣤⢸⣿⣿⣏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣇⣿⡿⢿⣿⠏⣿⠒⢸⡇⣶⢹⣇⣿⢿⣿⢸⣿⣗⣄⡙⢷⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠘⡇⡇⢀⠻⣿⣿⢸⠀⡇⠈⠉⠁⠉⢹⣿⡮⠉⣿⣿⣿⣿⣵⣿⣿⣾⣽⣭⣭⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⠛⣓⣘⣛⣂⡛⠒⠘⠓⠛⠘⠋⠛⠈⠛⢸⣛⣓⡊⠓⠚⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠉⠉⠈⠀⠁⠀⠀⠀⠀⢸⣿⡇⠀⣿⣿⣿⣯⣽⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉
⠀⣆⠠⡀⢠⠀⢰⠀⡆⢀⣀⢰⠀⠀⠀⠸⣿⠂⢀⣿⠿⢿⣾⣿⣶⣾⠟⢁⣼⣿⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢠⣿⣿⣿⣿⣽⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠰⣾⣿
⠀⣿⠀⡇⢸⠀⢸⠀⡇⠘⠛⢸⠄⠀⠀⣸⠟⠁⠀⠀⠀⢸⣿⠛⠋⠁⢠⣿⣿⡟⠀⠀⠀⠀⠉⠉⠀⠉⠩⣭⣭⣭⣭⣭⣭⡍⠀⠀⢨⣭⣿⣿⣯⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⢴⡇⠀⠀⣿⣿
⠀⣿⠀⡇⢸⠀⢸⠀⡇⠀⠀⠘⠓⠊⠉⠀⠀⠀⠀⠀⠀⠈⣿⠗⢄⠐⠻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⣇⠀⠀⣿⣿⣟⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠛⠀⠁⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠎⢠⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠃⠀⠀⢸⡛⠛⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⢲⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠘⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⡤⠤⠤
⠀⣾⣿⡇⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿
⠀⠻⠻⠃⠀⠉⠩⠭⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣼⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣾⡿⠁⠀⠀⠀⠸⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠄⠀⠀⠉⢛⢛⣛⣛⣛⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡟⣯⣿⣿⣟⣻⣿⡿⢶⣦⣴⣾⣿⣿⣿⣿⡟⠀⡈⡠⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠃⡱⢣⡶⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⡟⣿⢸⣿⣿⣟⡿⣿⣿⢯⣿⣿⣿⣿⣿⡏⠀⣂⣩⣄⣠⡾⠿⠁⡀⠀⠀⢀⣀⡴⠄⠀⠀⠀⠀⠀⠠⠥⢪⡙⢖⢁⣧⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣓⣿⣧⣿⣿⣯⣿⢻⣿⣿⡏⣽⣿⣿⣿⣿⣿⣿⣆⠈⢿⣿⣭⡀⠀⠉⠁⠀⠉⣽⡻⡷⠀⣄⣀⣀⠈⢰⠀⠉⢆⠸⣑⣸⣿⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣟⣻⣿⡿⣿⣿⣷⣾⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣷⣌⢻⣿⡿⣦⡸⣿⣃⠈⠰⠘⠓⠈⠉⠙⢛⣳⡏⠈⣆⢌⠢⠅⠿⢿⣷⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣷⣿⣿⣿⣿⣿⣿⣿⣿⡟⣽⣿⡿⣷⡾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠠⠤⡅⠹⠿⠑⠆⠀⠀⠀⢀⣰⣿⣿⡇⠀⢀⠈⠀⠀⠀⠺⣿⡇⠀⠀⠀⠀
⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣯⢽⡿⣿⣧⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⡛⠀⠀⠀⠀⠀⣤⠀⠀⠐⡛⠿⠀⠀⠀⠀⠁⠀⠀⠀⠀⠙⠿⢆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣿⣯⣿⣼⣿⣛⣻⣸⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠟⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⢻⣿⣯⣫⣽⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣾⣿⣷⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠀⠀⠀⠀⠀⠂⠀⠀⢰⣾⡆⡙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠛⢛⣤⣿⣿⣧⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⢰⣧⡀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠿⠹⠇⣽⠉⠿⡯⠢⠪⠸⠕⢿⣿⣿⣿⣿⣿⡓⠸⠋⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠘⢿⣿⣄⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⣤⣀⣀⣀⡀⠀⠀⠀⢠⣿⣼⣿⣿⣿⣿⡿⣿⢻⡏⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⢸⡇⠀⠀⡎⢙⣻⣿⠀⠀⠀
⠶⠂⠀⠀⠈⠉⠋⠙⠛⠛⠃⠀⠀⠀⠀⣿⢹⣿⣿⣿⢻⣷⣿⢸⣇⣿⡿⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⢸⣇⠀⠀⠧⠼⠿⠿⠀⠀⠀
⠀⡀⣄⣀⢠⠀⣶⣤⡀⠀⣀⠀⠀⠀⠀⣾⣶⣶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣶⡆⠀⠀⣦⣦⣶⣶⣶⣶⣶⣶
⠀⠇⣿⢻⢸⢰⣿⣿⡇⠀⡏⣶⢳⡆⣶⡖⣽⢷⡟⣎⠶⣶⣾⣶⣶⠷⢲⣶⣴⡖⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⣹⣿⣣⡖⢶⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢿⢸⢸⢸⣿⣿⡇⡄⡧⣿⢸⡇⣿⠋⣘⢭⣝⣿⣶⣿⣗⡯⣿⣴⢸⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣇⣿⡿⢿⣿⡟⣿⠒⢹⡟⣿⢹⣇⣿⣿⣿⢸⣿⣗⣀⡙⢷⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠸⠸⠸⠈⣿⣿⡇⡇⣿⠈⠉⠁⠉⠀⣼⣮⠉⣷⣿⣿⣿⣥⣿⣿⣬⣽⣭⣭⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⢛⠓⢘⡛⠂⠛⠒⠘⠓⠛⠘⠋⠛⠻⢛⣸⣛⣓⠊⠓⢚⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡏⠀⣿⣿⣿⠷⠾⠛⢻⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⡆⢸⡄⣶⢰⡆⢸⡇⢸⠀⣤⡄⡇⠀⠀⠀⣹⡇⠀⠿⠛⢻⣿⣿⣿⡿⠋⣴⣿⣿⠈⠙⠻⠿⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⣿⣿⣿⣟⣻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⢀⢀⠘⠚⢺⣿⣿
⡇⢸⡇⢸⠈⡇⠘⡇⢸⠀⠉⠁⡇⢀⣠⠔⠋⠁⠀⠀⠀⠘⣿⣍⠁⠀⣼⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢶⣶⣶⣶⣶⠀⠀⠀⡋⣹⣿⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠸⠸⠃⠀⢸⣿⣿
⡇⢸⡇⢸⠀⡇⠀⠇⢸⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣋⡆⡈⢙⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡀⠀⢸⣿⣿⢿⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⡀⢈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠋⢰⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠛⠁⠀⢸⡿⠿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛
⠁⢈⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡫⠠⠀⠹⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣔⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣒⣶⣶⣶⣶⣶⣶
⠀⢸⣿⣿⠀⠠⣴⣶⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡪⡠⠀⠀⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠹⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿
⠀⠈⠉⠉⠀⠀⠀⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣬⣤⣤⣤⣼⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣾⡟⠁⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠨⠿⠭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡟⣫⣿⣽⣟⣻⣿⣷⠶⣦⣴⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⡘⠇⠷⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣗⣿⢸⣿⣿⣏⡿⣻⣿⢯⣿⣿⣿⣿⣿⡏⠀⣀⣡⠀⣠⡾⠇⢀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠠⠄⠢⡈⢘⡀⣾⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣓⣿⣧⢿⣾⣧⣿⢹⣿⣿⡏⣽⣿⣿⣿⣿⣿⣿⣆⠨⣿⣯⣍⠀⠘⠉⠀⠀⢩⣟⢷⠆⢠⣀⠀⠀⣁⡀⠈⢆⠲⢱⢰⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢷⣾⣿⣿⣿⣿⣿⣿⣻⣿⡿⢿⣿⣷⣾⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣷⣜⡛⣿⣷⣄⢻⣗⡀⠁⠆⠛⠂⠉⠙⠛⣻⡿⠁⢀⣌⠈⠅⠾⣿⣿⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⡟⢽⣿⡟⣷⡾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠤⢮⠈⠿⠏⠒⠀⠀⠀⠀⢀⣾⣿⣷⠀⠈⡊⠈⠀⠀⠸⣿⣷⠀⠀⠀⠀⠀
⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣿⣿⣿⣏⣿⣿⣿⣯⢽⡿⣿⣧⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠐⠃⠀⠀⠀⠀⢠⠀⠀⠐⢚⢸⠇⠀⡀⠀⠈⠐⠀⠀⠀⠘⠿⢷⡆⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣿⣭⣿⣼⣷⣛⣻⣸⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠇⠉⠀⠀⠀⠀⠛⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⢀⡀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⢳⣿⣏⣫⣽⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣽⣿⣷⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢠⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⢸⣧⡀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠿⠹⠇⣽⠉⠿⡯⠦⠮⠰⠕⠿⣿⣿⣿⣿⣿⣿⠹⠛⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠈⠻⠿⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⣤⣀⣀⣄⡀⠀⠀⠀⢀⣿⣼⣿⣿⣿⣿⡿⣿⢻⡏⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡿⢸⡇⠀⠀⡍⢛⣿⣿⠀⠀⠀
⠶⠂⠀⠀⠈⠉⠋⠛⠛⠛⠁⠀⠀⠀⠈⣿⢹⣿⣿⣿⢻⣷⣿⢸⣇⣿⣿⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⢸⣇⠀⠀⠧⠼⠿⠟⠀⠀⠀
⠀⡀⣄⣀⢠⠀⣶⣤⠀⠀⣄⠀⠀⠀⠀⣶⣶⣶⢾⣿⣾⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣾⣶⡆⠀⠀⣦⣦⣶⣶⣶⣶⣶⣶
⠀⠇⣿⢻⢸⢰⣿⣿⡆⠀⡏⣶⢳⡆⣶⡖⣿⣷⡟⣎⠶⣶⣾⣶⣶⠷⢲⣶⣴⡖⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⣹⣿⣣⡖⢶⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢿⢸⢸⢸⣿⣿⡇⠀⣇⣿⢸⡇⣿⠉⣠⢭⣝⣿⣶⣿⣗⡯⣿⣴⢸⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣇⣿⡿⢿⣿⡟⣿⠓⢹⡟⣿⢹⣇⣿⣿⣿⢸⣿⣗⣀⡙⢷⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠸⠸⠸⠈⣿⣿⡇⡇⣿⠈⠉⠁⠉⠀⢿⣮⠉⣿⣿⣿⣿⣥⣿⣿⣬⣽⣭⣭⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⠛⡓⢘⡛⠂⠛⠒⠘⠓⠛⠘⠋⠛⠻⢛⣸⣟⣓⠊⠓⢚⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⠀⣿⣿⣿⠷⠾⠟⣻⣿⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⡆⢸⡄⣶⢰⡆⢸⡇⢸⠀⣤⡄⡇⠀⠀⠀⢹⡇⠀⠿⠛⢻⣿⣿⣿⡿⠋⣴⣾⣿⠀⠉⠻⠿⢿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⣿⣿⣿⣟⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⢀⠘⠚⢺⣿⣿
⡇⢸⡇⢸⠈⡇⠸⡇⢸⠀⠉⠁⡇⢀⣠⠔⠋⠁⠀⠀⠀⠘⣿⣍⠁⠀⣼⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢶⣶⣶⣶⣶⠀⠀⠀⡋⣹⣿⣿⡛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠸⠸⠃⠀⢸⣿⣿
⡇⢸⡇⢸⠀⡇⠀⡇⢸⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣋⠆⡈⢙⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡀⠀⢸⣿⣿⢿⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⢈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠊⢰⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠛⠀⠀⠸⡿⠿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛
⠁⢈⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠫⠠⠀⠹⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣄⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⣒⣶⣶⣶⣶⣶⣶
⠀⢸⣿⣿⠀⠠⣴⣶⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡪⡠⠀⠀⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠙⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿
⠀⠈⠉⠉⠀⠀⠀⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣬⣤⣤⣤⣼⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣾⡟⠁⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠨⠽⠭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡟⣫⣿⣽⣟⣻⣿⣷⠶⣦⣴⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⡚⠇⠶⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡟⣿⢸⣿⣿⣏⡿⣻⣿⢯⣿⣿⣿⣿⣿⡏⠀⣀⣡⠀⣠⡾⠇⢀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠠⠄⠢⡈⢘⡀⣾⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣓⣿⣇⣿⣿⣯⣿⢻⣿⣿⡏⢽⣿⣿⣿⣿⣿⣿⣆⠨⣿⣯⣉⠀⠈⠋⠀⠀⢩⣟⢷⠄⢠⣀⡀⠀⣁⡀⠈⢆⠲⢱⢰⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢷⣾⣿⣿⣿⣿⣿⣟⣻⣿⡿⣿⣿⣷⣾⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣷⣔⡙⣿⣷⣄⢻⣗⡀⠁⠆⠛⠂⠉⠙⠛⣻⣿⠈⠐⣌⠈⠇⠾⣿⣿⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⡏⢽⣿⡏⣷⡾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠤⢮⠀⠿⠏⠲⠀⠀⠀⠀⢀⣾⣿⣷⠀⠀⠂⠈⠀⠀⠸⣿⣷⠀⠀⠀⠀⠀
⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣿⣿⣿⣏⣿⣿⣿⣯⢽⡿⣿⣇⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠐⠃⠀⠀⠀⠀⢠⠀⠀⠀⢚⢹⠇⠀⠀⠀⠈⠀⠀⠀⠀⠘⠻⣷⡆⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣿⣯⣿⣼⣷⣛⣻⣸⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⢀⡀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⢻⣿⣏⣫⣽⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣽⣿⣷⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡆⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢠⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⢸⣷⡀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠿⠹⠇⣽⠉⠿⡯⠦⠮⠨⠕⠿⣿⣿⣿⣿⣿⣿⠹⠋⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠈⠻⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣤⣄⣀⣠⣀⠀⠀⠀⠀⣿⣼⣿⣿⣿⣿⡿⣿⢻⡏⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⢸⡇⠀⢰⠉⣿⣿⡇⠀⠀⠀
⠒⠒⠀⠀⠀⠉⠉⠉⠋⠉⠉⠀⠀⠀⠀⣿⢹⣿⣿⣿⢻⣷⣿⢸⣇⣿⣿⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⢸⣇⠀⠘⠀⠟⠛⠃⠀⠀⠀
⡀⢀⢠⠀⡀⡄⢰⣶⡄⡆⢠⡀⠀⠀⠀⢸⣿⣿⢶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣶⡆⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶
⠇⠸⢸⡆⡇⡇⣾⣿⣇⡁⢸⣶⢳⡆⣶⡖⣽⢷⡟⣞⠶⣶⣾⣶⣶⠓⢲⣶⣴⡶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⣽⣿⢣⡖⢾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠸⡇⡇⡇⣿⣿⣿⢠⢸⣿⢸⡇⣿⠉⣽⢭⣝⣿⣷⣿⣟⡯⣿⣾⢸⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣷⣿⣿⣿⣿⡿⣿⠿⢻⡟⣿⢿⣇⣿⣿⣿⢸⣿⣗⢀⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠇⠇⠣⢸⣿⡿⠸⢸⡎⠉⠁⠉⠀⢻⣮⠉⢹⣿⣯⣿⢥⣯⣿⣬⣽⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⠛⠓⠚⠛⠂⠛⠒⠘⠓⠛⠘⠛⣛⣻⣛⣸⣛⣓⠊⠓⢺⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⡀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⢿⣿⠀⢸⣿⣿⡛⠛⢛⣻⣿⠟⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢠⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢻⣿⣿⠀⠀⠀⠀⠀⠀⡀⡀⣠⣤⣤
⢸⠀⣷⠠⡆⣷⠀⣿⠀⡇⢰⣦⢸⠀⠀⠀⣺⣿⠀⠼⠋⢹⣿⣿⣿⠿⠋⣴⣿⣿⠀⠉⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⢠⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⡀⣀⣄⠉⠃⣿⣿⣿
⢸⠀⣿⠀⡇⣿⠀⣿⠀⡇⠈⠁⢸⢀⡤⠖⠉⠀⠀⠀⠀⠈⣿⣦⡄⢀⣴⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⣶⣶⣶⣶⠒⠃⢾⣿⣿⣿⣷⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠃⠛⠛⠀⠀⣿⣿⣿
⠸⠀⣿⠀⡇⢻⠀⠹⠀⡇⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⣡⠂⢈⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢀⣶⣶⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⢠⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠑⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠘⣿⣿⣯⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⢐⢀⠘⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠭⠉⣹⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⣽⣿⣯⣽⣯⣿⣯
⠀⠀⢻⣿⡇⠀⠶⠶⠶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⢐⢄⢄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣷⣷⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⢿⡿⣿⣿⣿⣿
⠀⠀⠈⠉⠁⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣼⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣾⣾⡟⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡀⠀⠀⠀⠐⠒⠀⠒⠚⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡟⣫⣿⣽⣟⣿⣿⡷⠶⣦⣴⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠙⡏⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⢸⣿⣿⣏⡿⣻⣿⢿⣿⣿⣿⣿⣿⠋⠀⣂⠁⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢎⠂⠲⢪⠚⣴⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣗⣿⣧⣿⣾⣯⣿⢻⣿⣿⡏⢽⣿⣿⣿⣿⣿⣿⣆⢈⢿⣁⡁⠀⠿⠃⠀⠒⣰⢺⡄⠀⠀⠀⠀⠀⡄⠐⠌⠢⠲⢱⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡻⣿⣿⣿⣟⣻⣿⡿⢿⣿⣷⣾⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⣷⣤⡱⣶⡀⠐⠭⠸⠆⠈⠛⠛⠴⢿⠀⠀⠀⠨⠎⠾⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⡏⢽⣿⡏⣷⠾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠨⡁⠹⠿⠱⠀⠀⠀⠀⠀⣰⣿⣷⠀⠀⠀⠈⠁⠀⢸⣿⣷⠀⡀⠀⠀⠀⠀
⠀⠀⠀⠐⠂⠊⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣿⣿⣿⣏⣿⣿⣿⣯⢽⣿⣿⣧⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠘⠁⠀⠀⠀⠀⡄⠀⠀⠚⠹⠇⠀⠀⠀⠈⠂⠀⠀⠀⠙⠿⣿⠿⠂⠀⠀⠀
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣭⣿⣼⣷⣛⣻⣸⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠰⠌⠀⠀⠀⠀⠘⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣏⣫⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢰⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠛⠻⣿⣿⣿⣿⢛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⢹⣧⡀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⣀⣠⣤
⠀⠿⠿⠇⣽⠉⠿⡯⠲⠺⠴⠕⠿⠹⣿⣿⣿⣿⣾⡏⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠉⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠏⢿⣿⣿⣿⣿⣿⣿⣧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣠⣆⣀⣀⣄⡀⠀⠀⠀⣿⣼⣿⣿⣿⣿⡿⣿⢻⡏⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⢸⡇⠀⠘⢉⣿⣿⡇⠀⠀⠀
⠓⠒⠂⠀⠀⠉⠉⠉⠉⠉⠋⠀⠀⠀⠀⣿⢹⣿⣿⣿⢻⣷⣿⢸⣇⣿⣿⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⢸⣇⠀⠀⠘⠛⠛⠃⠀⠀⠀
⢀⢀⡀⡄⡄⠄⢀⣦⣦⢰⢠⡄⠀⠀⠀⠰⣷⣿⢶⣿⣾⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣖⣶⣾⣶⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶
⠸⠈⠇⣇⡇⠀⢸⣿⣿⢸⠈⣷⢳⡆⣶⠒⢹⢷⡟⣎⡶⣶⣾⣶⣶⠓⢲⣶⣴⡖⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⣽⡿⢢⡖⢾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⢹⢸⢸⣿⣿⠘⠀⣿⢸⡇⣿⠉⠀⢬⣝⣿⣿⣿⣗⡯⣿⣾⢸⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣇⣿⣿⣿⣿⣿⣿⢿⢿⡟⣿⢿⣇⣿⣿⣿⢸⣿⡗⢀⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠻⠘⠸⠈⣿⣿⠀⠀⡎⠉⠁⠉⠀⢀⣮⡍⢱⣿⣯⣿⠧⣿⣿⣬⣽⣭⣭⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠛⠓⡛⠛⠂⠛⠒⠘⠓⠛⠘⢻⣛⣿⣛⣸⣟⡓⠊⠓⢻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⣿⠀⢸⣿⣿⡛⠛⠛⣻⣿⡟⢹⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠙⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤
⠰⡆⢸⠀⡆⢸⡀⢸⡄⣿⢠⣶⢸⡄⠀⠀⢨⣿⠀⠘⠋⢹⣿⣿⣿⠿⠋⣷⣾⣿⠀⠈⠙⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠁⢰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⡄⡄⠉⠈⣿⣿⣿
⠀⡇⢸⠀⢀⠨⠇⢸⡇⣿⠀⠉⢸⣇⡤⠒⠉⠀⠀⠀⠀⠀⣿⣷⡄⢀⣴⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢶⣶⣶⣶⠖⠀⣿⣿⣿⣿⣭⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡇⠀⠀⠘⠁⠃⠃⠀⠀⣿⣿⣿
⠀⠇⢸⡇⠰⠠⠄⠘⠃⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣅⠆⢈⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⢠⣭⣽⣿⣿⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⡄⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠃⠁⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢻⣿⣿⣻⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⢀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⢐⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⠛⠛⣻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣽⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⠀⠰⠾⠷⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠈⠺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣶⣶⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⢿⡿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣬⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣾⡟⠁⠙⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠁⠁⠀⠉⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡟⣫⣿⣽⣟⣿⣿⡷⠶⣦⣴⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⢡⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡗⣿⢼⣿⣿⣏⡿⣻⣿⢯⣿⣿⣿⣿⣿⠏⠀⠂⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡡⠀⠒⡄⢣⣆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣓⣿⣧⣿⣿⣯⣿⢻⣿⣿⡏⢽⣿⣿⣿⣿⣿⣿⣆⠈⢖⣊⠁⠀⠆⠀⠀⠖⠶⣦⠀⠀⠀⠀⠀⠀⠀⡂⠩⠐⠌⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿⣿⣻⣿⣿⣿⣟⣻⣿⡿⢿⣿⣷⣾⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⣦⣄⢲⣶⠀⠈⠍⠶⠀⠒⠒⠲⠦⡆⠀⠈⠀⠕⠱⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣷⣿⢿⣿⣿⣿⣿⣿⣿⡏⢽⣿⡏⣷⡾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠈⠀⠿⠏⠰⠀⠀⠀⠀⠀⣶⡿⡂⠀⠀⠀⠉⠀⠘⢻⣿⣆⣀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣿⣿⣿⣏⣿⣿⣿⣯⢽⡿⣿⣧⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠐⠀⠀⠀⠀⠀⠀⠀⠀⢚⠸⠀⠀⠀⠀⠁⠀⠀⠀⠀⠹⢿⠿⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣿⣯⣿⣼⣷⣛⣻⣸⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⢳⣿⣏⣫⣽⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠃⠀⠀⠀⠀⠆⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣷⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠛⠛⢻⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠸⣷⣄⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡆⣀⣤⣤
⠀⠿⠿⠇⣽⠉⠿⡯⠪⠫⠽⠕⠿⠹⢿⣿⣿⣿⣶⣮⣽⡟⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⢀⠀⠀⠉⠁⠀⠀⠀⡜⢉⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣨⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣀⣴⣀⣄⣀⡀⠀⠀⠀⣿⣼⣿⣿⣿⣿⡿⣿⢿⡏⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡿⢸⡇⠀⠈⢹⣿⣿⠂⠀⠀⠀
⠶⠶⠆⠀⠀⠈⠉⠉⠙⠛⠛⠃⠀⠀⠀⣿⢹⣿⣿⣿⢻⣷⣿⢹⣇⣿⣿⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⢸⣇⠀⠂⠚⠛⠛⠀⠀⠀⠀
⢀⡀⢀⢠⢀⠠⠀⣶⣤⠀⠀⣄⠀⠀⠀⠀⣾⣿⠷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣶⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶
⠘⠇⠹⢸⢸⠀⢰⣿⣿⡇⡄⣷⢳⡆⣶⠒⠸⢷⡟⢏⡶⣶⣾⣶⣶⠓⢲⣶⣴⡶⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⣹⡿⢢⡖⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣼⠀⡜⣿⣻⡇⠇⣿⢸⡇⣿⠉⠠⢨⣝⡯⣿⣿⣖⡯⣿⣾⢸⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣗⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⢿⣇⣿⣿⣿⢸⣿⡗⢀⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠋⠃⠇⢻⣿⠇⠇⠾⠉⠁⠉⠀⠀⣮⡍⠱⣿⣯⣿⠧⣯⣿⣬⣽⣭⣭⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠂⠛⠒⠘⠓⠛⢚⣻⣛⣻⢛⣸⣟⡓⠊⠓⠻⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⢘⣿⠃⠠⣿⣿⣛⠛⢛⣻⣿⡟⢹⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⢺⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⢠⣤⣤⣤
⠀⡆⠸⡇⢰⠀⡇⠀⡇⢸⠀⣶⡄⡇⠀⠀⢰⣿⠥⠰⠛⠉⣿⣿⣿⠿⠋⢐⣾⣿⠀⠀⠉⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠁⣰⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢀⢀⣠⡄⠉⠘⣿⣿⣿
⠄⠃⠀⣇⠸⠀⡇⠀⡇⢸⠀⠀⠀⣇⡤⠐⠊⠀⠀⠀⠀⠀⢻⣷⡄⠀⣴⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢶⣶⣶⣾⡷⢀⣿⣿⣿⣿⣛⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡇⠀⠀⠘⠈⠉⠁⠀⠀⣿⣿⣿
⡇⠠⠀⣿⠀⠀⠇⠀⠇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⡜⠄⢀⣽⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⢈⣉⣽⣿⣟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿
⠀⢠⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⠃⠀⠀⠀⠀⠀⠀⠀⠉⢉⡉
⠀⠀⠀⣼⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠻⠛⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⠃⠀⠻⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠉⠍⠨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣥⣤⣥⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⡟⠉⠛⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣟⣶⡟⣫⣿⣽⣟⣿⣿⡷⠶⣦⣴⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⢓⡛⣱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⡗⣿⢼⣿⣿⣏⡿⣿⣿⢯⣿⣿⣿⣿⣿⠏⠀⠂⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠈⠢⠓⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣓⣿⣧⣿⣿⣧⣿⢹⣿⣾⡏⢽⣿⣿⣿⣿⣿⣷⣆⠀⠒⡚⠁⠐⠄⠀⠰⢆⠴⣄⠀⠀⠀⠀⠀⠀⢐⠀⠅⠎⢁⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢷⣾⣿⠻⣿⣿⣿⣛⣻⣿⡿⢿⣿⣷⣾⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⣦⡀⢶⡆⠀⠨⡅⠧⠀⠒⠒⠦⣶⠀⠀⠀⠣⡊⢸⣿⣿⡖⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⢺⣿⣿⣿⣿⣿⣿⡏⢽⣿⡏⣷⡾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠈⠈⢿⠇⠄⠀⠀⠀⢀⢀⣾⠗⠀⠀⠀⠀⠁⠀⢽⣿⣿⢀⣤⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣿⣿⣿⣏⣿⣿⣿⣯⢽⣿⣿⣇⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠐⠀⠀⠀⠀⢀⠀⠀⠀⠃⠇⠀⠀⠀⠀⠂⠀⠀⠀⠙⠛⠿⠛⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣿⣭⣿⣼⣷⣛⣻⣸⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠈⠁⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⢳⣿⣯⣫⣿⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣽⣿⣷⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢴⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⠀⢀⣀⠀⠀⣀⡀⠛⠛⠙⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠸⢿⣄⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣤⣔⣤⣤
⠀⠿⠿⠇⣽⠉⠿⡯⠪⠪⠽⠕⠿⠹⠻⢿⣿⣿⣶⣶⣾⡿⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣠⣦⣄⣀⣀⠀⠀⠀⣿⣼⣿⣿⣿⣿⣿⣿⢿⡟⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡿⢸⡇⠀⠊⢻⣿⣷⠀⠀⠀⠀
⠶⠶⠶⠀⠀⠀⠉⠛⠛⠛⠛⠋⠀⠀⠀⣿⢹⣿⣿⣿⢻⣷⣿⢸⣇⣿⣿⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣷⢸⣇⠀⠀⠺⠿⠟⠀⠀⠀⠀
⡀⡀⢀⠀⡄⡀⡄⢰⣦⣄⠀⢠⠀⠀⠀⠀⢸⣿⠿⣾⣾⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣶⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠇⠻⠘⠇⡇⡇⠁⣾⣿⣷⠀⣶⢳⡆⣶⠒⠸⢷⡟⣞⣶⣶⠾⣶⣶⠓⢲⣶⣴⡶⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⣹⡷⢢⡖⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⡇⣇⠀⢿⣿⣿⠀⣿⢸⡇⣿⠉⠀⢬⣝⣧⣿⣿⣖⡯⣿⣾⢸⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣇⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⢿⣇⣿⣿⣿⢸⣿⡗⢀⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠛⠛⠰⠈⡿⣿⠠⠸⠍⠁⠉⠀⠀⣮⣭⠁⣿⣿⣿⠧⣯⣿⣮⣽⣭⣭⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⠟⠛⠛⠊⠛⠒⠙⠛⠛⣚⣿⣿⣻⢛⣸⣛⡓⠊⠓⠻⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⢿⣯⠀⣿⣿⣟⠛⠛⣫⣿⡿⠙⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⢾⣿⣿⡇⠀⠀⠀⠀⠀⢀⢀⣠⣤⣤⣤
⠀⢰⡆⣿⠀⡆⢸⠀⢻⠀⡇⢰⡆⢸⠀⠀⠀⣿⠿⠠⠛⠉⣿⣿⣿⡿⠋⣰⣾⣿⠇⠀⠙⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠁⣰⣷⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⣿⣿⡇⠀⠀⢀⢠⢠⠈⠉⢹⣿⣿⣿
⠂⠀⠇⢸⠀⡇⢸⠀⢸⠀⡇⠀⠀⢸⡠⠔⠊⠁⠀⠀⠀⠀⠸⣷⣦⢀⢰⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢻⣿⣿⣿⡇⢀⣿⣿⣿⡿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠇⠀⠈⠘⠈⠘⠀⠀⢸⣿⣿⣿
⣸⠀⠆⢸⠆⠆⠸⠀⠘⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⠠⢀⣭⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠁⠀⢘⢛⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⡇⠀⠄⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠛⠃⠀⠀⠀⢀⡀⣀⣀⣉⣉⡁
⠃⠀⠀⢠⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠄⠹⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⠷⠿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⣿⣿⣿⣿⣿⣿⣿⡧
⠀⠀⠀⢰⢿⡇⠀⠙⢛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠅⠅⠌⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⣀⣰⣶⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⠿⠿⠿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⢀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⡟⠙⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠈⠉⠈⠈⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡟⣯⣿⣽⣟⣿⣿⡷⠶⣦⣴⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⡹⡂⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡗⣿⣸⣿⣿⣏⡿⢿⣿⢯⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⢀⢐⠐⡌⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣓⣿⣧⣿⣿⣯⣿⢻⣿⣿⡏⣽⣿⣿⣿⣿⣿⣷⣆⠀⠒⠊⠁⠠⠀⠀⠠⢀⢄⣀⠀⠀⠀⠀⠀⠀⠸⡀⢅⠇⢰⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠻⣿⣿⣿⣟⣻⣿⡿⣿⣿⣷⣾⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣷⣄⠑⣄⡀⣤⡄⠀⢨⠱⠧⠐⠒⠶⠤⣴⠀⠀⠘⢔⢁⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢺⣿⣿⣿⣿⣿⣿⡟⢽⣿⡟⣷⠾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠉⠸⢿⠖⠄⠀⠀⠀⠀⢀⣶⢎⠀⠀⠀⠀⠀⠀⢹⣿⣆⣠⣤⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣿⣿⣿⣟⣿⣿⣿⣯⢽⡿⣿⣧⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠛⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣿⣯⣿⣼⣿⣛⣻⣸⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⡀⠈⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⢷⣿⣯⣫⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣽⣿⣿⣿⣷⣟⡿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⠀⢀⣀⠀⠀⡀⠄⠛⠛⠀⢻⣿⣟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠘⠿⢤⡀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣦⣦⣷⣿
⠀⠿⠿⠇⣿⠉⠿⡯⠢⠪⠹⠕⠿⠱⠘⠛⣻⣿⣶⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⣀⡀⠀⠀⣿⣼⣿⣿⣏⣿⣿⣿⣿⡟⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⡏⢸⡇⠀⠒⣒⣶⡆⠀⠀⠀⠀
⠒⠶⠶⠶⠀⠀⠀⠛⠛⠛⠛⠛⠃⠀⠀⣿⢹⣿⣿⣟⢿⣿⣿⢹⣇⣿⣾⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣷⢸⣇⠀⠤⠿⠿⠇⠀⠀⠀⠀
⠀⡀⠀⠀⢀⡄⡀⡀⢰⣤⡄⡄⢀⠀⠀⠀⠀⣾⢿⣷⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⡆⠀⠠⣶⣶⣶⣶⣴⣶⣶⣶⣶
⠀⠇⠻⠈⠿⡇⡇⡇⣾⣿⡇⣷⢻⡆⣶⠒⠀⢵⡟⣎⢶⣶⠺⣶⣶⠓⢲⣖⣴⡶⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⣿⡷⢢⡖⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡇⡇⡇⣿⣿⡇⣿⢸⡇⣿⠉⠀⢨⣝⡯⠸⣿⣆⡯⣿⣶⢸⣿⣿⣯⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣇⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⢿⣇⣿⡟⣿⢸⣿⡗⢀⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠗⠃⠐⠹⡿⡇⠨⠩⠁⠉⠀⠀⢨⣭⡅⢨⣿⣯⣷⢯⣽⣮⣽⣭⣭⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠚⠛⠒⠻⠻⣟⣚⣿⣟⣇⢛⣸⣟⠓⠂⠓⠿⢿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⣿⣛⣛⣋⣽⣿⠋⣽⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠠⠄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⣀⡄⣤⣤⣤⣤
⠀⠀⠰⠀⣿⠀⡇⢾⠀⣿⢸⡇⣶⡆⡇⠀⠀⢀⣿⠇⠘⠋⠑⣿⣿⡿⠟⢡⣴⣿⡇⠀⠈⠛⠛⠿⠿⠻⠿⠿⠿⠿⠿⠿⠿⠟⠁⣠⣦⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⣺⣿⣿⠀⠀⠀⡀⣤⣤⠉⠁⢹⣿⣿⣿
⠀⡇⠀⠀⢸⠀⡇⢸⠀⣿⢸⡇⠀⠀⣧⠤⠒⠉⠀⠀⠀⠀⠀⢻⣷⡄⡠⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⣿⡇⢰⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠁⠉⠉⠀⠀⢸⣿⣿⣿
⣀⡧⠀⠀⢸⠀⠇⠸⠀⠛⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡆⡄⣠⣽⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠁⠾⠿⣿⣿⣷⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿
⣿⡁⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣾⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠛⠋⠁⠀⣀⣀⣀⣀⣀⣀⣀⣤⠀
⣿⠀⠀⠀⢰⣿⡆⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠨⠠⠈⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣯⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣷⣿⣿⣿⡆
⠿⡀⠀⠀⠸⠿⠇⠀⠉⠉⠙⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠐⠐⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣠⠀⣰⣬⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⡛⠛⡛⠛⣻⣟⣻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣴⣤⣤⣤⣤⣄⣀⣀⢀⡀⠀⠀⠀⠀⠀⣀⣤⣶⣾⡟⠻⣿⡿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣯⣿⣽⣟⣿⣿⡿⠶⣦⣴⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢮⣛⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⡗⣿⢺⣿⣿⣏⡿⣻⣿⢯⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⡀⠢⢡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣧⣿⣿⣯⣿⢹⣿⣿⡏⢽⣿⣿⣿⣿⣿⣷⣆⠀⠢⠋⠁⠀⠀⠀⠄⠠⣀⡀⠀⠀⠀⠀⠀⠠⢗⠀⡨⢂⣾⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠻⣿⣿⣿⣿⣻⣿⡿⣿⣿⣷⣾⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣷⣄⠁⣄⠀⣤⠀⠀⣌⠼⠄⠒⠒⠦⢤⡆⠀⠀⠣⠊⣸⢻⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠤⠰⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣷⣿⢺⣿⣿⣿⣿⣿⣿⡏⢽⣿⡟⣷⡾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠁⠹⠿⠐⠀⠀⠀⠀⠀⣴⡖⡀⠀⠀⠀⠀⠀⠀⣿⣿⣀⣶⣶⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣯⢽⣿⣿⣧⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠊⠠⠀⣀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣷⣿⣯⣿⣼⣿⣛⣻⣸⢿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡿⣿⣿⣿⣿⣯⣫⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣵⣿⣿⣿⣷⣟⡿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⢀⣀⣀⣀
⠀⡀⠀⠀⠀⢀⣀⠀⠀⠀⠒⠛⠛⠀⠘⢿⣿⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠙⠓⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣽⣿⣿
⠀⠿⠿⣇⣿⠏⠿⡯⠢⠪⠸⠕⠿⠱⠀⠀⢙⢷⡦⣤⣈⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠿⠿⢿⠿⣿⣿⣿⣿⣿⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⡀⠀⠀⣿⣼⣿⣿⣟⢸⣿⣿⣿⡟⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡏⢸⡇⠀⠒⣲⣶⡆⠀⠀⠀⠀
⠒⠴⠶⠦⠄⠀⠀⠘⠛⠛⠓⠛⠛⠀⠀⣿⢹⣿⣿⣟⢺⣿⣿⢹⣇⣿⣾⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣷⢸⣇⠠⠤⠿⠿⠇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣄⡀⠀⠀⣤⣄⠀⢀⡀⠀⠀⠀⢺⠿⣶⣾⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣷⣰⣶⣾⡆⠀⢰⣦⣴⣤⣤⣤⣤⣶⣶⣶
⠆⠿⠸⠆⠧⣿⢠⢸⢠⣿⣿⣴⢻⡆⣶⠒⠀⢰⡟⣎⣲⣶⠺⣶⣶⠓⢲⣖⣴⡖⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⡿⣿⡿⣾⢿⣿⡷⢢⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⢸⢸⢸⣿⣿⣿⢸⡇⣿⠉⠀⢨⡝⡧⠎⣿⣖⡿⣿⣶⢸⣿⣿⣯⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣇⣿⣿⣿⣿⣿⣿⣷⣿⣟⣿⢿⣇⣿⡏⣿⢸⣿⡗⢀⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠸⠘⠸⠈⣿⣿⠨⠩⠇⠉⠀⠀⠈⣭⣵⠀⣿⣯⣷⢯⣽⣮⣽⣭⣭⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠾⠛⠒⠿⣿⣟⣚⣻⣛⣣⢛⣸⣟⠓⠂⠓⠿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⢀⠀⠀⢀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⣿⣟⣛⣻⣿⣿⠏⢹⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠠⠌⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⢼⣿⣿⠀⠀⠀⠀⠀⠀⣄⣀⣤⣤⣤⣤
⠀⠀⠀⡇⢸⡆⠲⢸⠀⢸⠀⡇⢰⡆⢸⠀⠀⠀⣿⠧⠀⠋⠁⣿⡿⠿⠟⢓⣴⣿⡿⠀⠈⠛⠛⠿⠿⠻⠿⠿⠿⠿⠿⠿⠿⠟⠁⣠⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⣸⣿⣿⠀⠀⠀⡄⣄⣄⠉⠉⣿⣿⣿⣿
⡇⢸⠀⠃⢸⡇⢸⠸⠄⢸⠀⡇⠀⠀⢸⠤⠒⠈⠀⠀⠀⠀⠀⢹⣷⡄⡀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⡆⢰⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠁⠉⠉⠀⠀⣿⣿⣿⣿
⢇⣸⠄⠂⠸⠇⠰⠐⠆⠘⠁⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⡔⡀⣠⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠁⠾⢿⣿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣼⡇⠀⠢⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⢿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣾⣿⣿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠛⠉⠀⠀⣀⣀⣀⣀⣀⣠⣤⣤⠀
⣿⡇⠀⠀⠠⣿⣷⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢀⢈⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣷⣿⣿⣿⠀
⠿⠇⠀⠀⠰⠿⠿⠀⠈⠉⠉⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠒⢑⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣀⠀⣰⣭⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣛⡛⣛⣛⣻⣟⣛⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣦⣤⣤⣤⣤⣤⣄⣀⣀⢀⡀⠀⠀⠀⠀⠀⣀⣤⣶⣾⡟⠿⣿⡿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⣫⣿⣽⣟⣿⣿⡿⠶⣦⣴⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠠⡓⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⡗⣿⢸⣿⣿⣏⡿⣻⣿⢯⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⢄⠐⡉⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣾⣯⣿⢻⣿⣿⡏⢽⣿⣿⣿⣿⣿⣷⣆⠀⠢⠊⠀⠀⠀⠀⠄⠠⣀⡀⠀⠀⠀⠀⠀⠰⠐⢅⢎⢰⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣿⠻⣽⣿⣿⣟⣻⣿⡿⢿⣿⣷⣾⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣷⣄⠑⢄⠀⣤⠀⠀⡍⠾⠄⠒⠒⠆⢴⠀⠀⠀⠁⠊⣾⢻⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠴⠠⠇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣷⣿⢿⣿⣿⣿⣿⣿⣿⡏⢽⣿⡏⣷⠾⣿⣯⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠁⠹⠿⠠⠀⠀⠀⠀⠀⡾⠆⠀⠀⠀⠀⠀⠀⠴⠿⣷⣠⣾⣷⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣟⣿⣿⣿⣿⣿⣿⣿⣯⢽⡿⣿⣇⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣀⠀⠀⠀⠀⠀⠀⠁⠛⠛⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣷⣿⣭⣿⣼⣿⣛⣻⣸⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡿⣿⣿⢿⣿⣏⣫⣽⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣵⣿⣿⣿⣷⣟⡿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡆⡻⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣇⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢸⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡀⣀⣀⡀⣀⣀
⠀⡀⠀⠀⠀⢀⣀⠀⠀⠀⠜⠛⠛⠀⠐⠻⡿⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠈⠙⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣶⣿⣿⣿
⠀⠿⠿⢇⣿⠿⠿⡯⠢⠪⠸⠕⠿⠱⠀⠀⠈⠷⡆⢤⣈⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⠿⢹⢿⣿⣿⣿⣿⣿⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⣀⡀⠀⠀⣿⣼⣿⣿⣿⢸⣿⣿⣿⡟⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⡇⢸⡇⠐⠒⣶⣶⡆⠀⠀⠀⠀
⠂⣴⠶⠦⠤⠀⠀⠘⠛⠛⠒⠛⠛⠀⠀⣿⢹⣿⣿⣟⢺⣿⣿⢹⣇⣿⣾⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣷⢸⣇⠠⠤⠿⠿⠇⠀⠀⠀⠀
⡀⢀⠀⠀⠀⣠⢀⢀⠀⣦⣤⢠⢀⡀⠀⠀⠀⢸⢿⣿⣾⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⡆⠀⢰⣦⣤⣤⣤⣤⣦⣶⣶⣶
⠇⠸⠀⠇⠸⢸⢸⢸⢰⣿⣿⣶⢻⡆⣶⠒⠀⢰⡟⣎⡲⣶⠺⣶⣶⠓⢲⣖⣴⡖⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⣿⣿⡿⣿⢿⣻⡷⢢⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣸⠈⢸⣿⣿⣿⢸⡇⣿⠉⠀⢨⣝⣯⡇⣿⣖⡯⣿⣶⢸⣿⣿⣯⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣇⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⢿⣇⣿⡇⣿⢸⣿⡗⢀⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠘⠛⠀⠌⣿⣿⠈⠩⠇⠉⠀⠀⠈⣭⣵⠀⣽⣯⣵⣏⣽⣾⣽⣭⣭⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⠿⠾⠛⠒⠿⣿⣟⣚⣻⣛⣣⣛⣸⣟⠓⠊⠓⠿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⣻⣟⠀⣿⣿⣟⣛⣫⣽⣿⡏⢹⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠠⠌⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣺⣿⣿⠀⠀⠀⠀⠀⠀⣄⢠⣤⣤⣤⣤
⠀⠀⠀⢶⠘⡇⢸⠀⡇⢸⡆⢿⢰⣶⢸⠀⠀⠀⣾⠷⠀⠋⠁⣿⡿⠿⠟⢁⣴⣿⣿⠀⠈⠙⠛⠿⠿⠻⠿⠿⠿⠿⠿⠿⠿⠟⠁⣠⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⣿⣿⣿⠀⠀⠀⡄⣄⡄⠉⠈⣿⣿⣿⣿
⢰⠀⡇⢸⠀⡇⢸⠀⡇⠈⡇⢸⠀⠀⢸⡤⠒⠊⠀⠀⠀⠀⠀⢸⣷⡆⠀⢼⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⡆⣰⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠁⠁⠁⠀⠀⣿⣿⣿⣿
⢸⣀⡇⠘⠀⠿⠐⠀⠇⠀⠃⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡦⠀⣠⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠉⠁⠿⢿⣿⣿⣷⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿
⣸⣿⠀⠰⠀⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠃⠨⢻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣾⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠋⠉⠀⢀⣀⣠⣄⣤⣤⣤⣤⣤⠀
⣿⡟⠀⠀⠀⣾⣷⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⡀⢀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣭⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣾⣿⣿⣿⣿⣿⣿⣿⠀
⠿⢃⠀⠀⠀⠿⠿⠀⠈⠉⠉⠽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⡂⠐⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣠⠀⣰⣽⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣙⣋⣉⣙⣛⣛⣛⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⢀⣀⠀⠀⠀⠀⠀⣀⣤⣶⣾⡟⠿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⡟⣫⣿⣽⣟⣿⣿⡿⠶⣦⣴⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡐⡛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡟⣿⢸⣿⣿⣏⡿⣻⣿⢿⣿⣿⣿⣿⣿⡏⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⢐⠐⡌⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣇⣿⣿⣧⣿⢹⣿⣾⡏⢽⣿⣿⣿⣿⣿⣷⣆⠀⠒⠊⠀⠀⠀⠀⠆⠤⣄⠀⠀⠀⠀⠀⠀⠐⠀⢅⠆⢰⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢷⣾⣿⠻⣽⣿⣿⣿⣻⣿⡿⢿⣿⣶⣾⣿⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣷⣄⠑⣄⠰⣤⡀⠈⠍⠶⠀⠐⠒⠢⢴⠀⠀⠐⠠⠃⢿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠰⠂⠆⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⢿⣿⣿⣿⣿⣿⣿⡏⢽⣿⡟⣷⡾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠅⠹⠞⠰⠀⠀⠀⠀⢀⣿⠗⠀⠀⠀⠀⠀⠀⠸⣿⣧⣠⣾⣷⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣟⣿⣿⣿⣿⣿⣿⣿⣯⢽⡿⣿⣇⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠃⠗⢀⣀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣷⣿⣭⣿⣼⣧⣛⣻⣸⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡿⣿⣿⢿⣿⣏⣫⣿⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣵⣿⣿⣿⣷⣟⡿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡆⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠨⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⡀⣄⣠⣤
⠀⡀⠀⠀⠀⢀⣀⠀⠀⠀⠜⠛⠛⠀⠐⠻⡛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿
⠀⠿⠿⢇⣿⡿⠿⡯⠢⠪⠸⠕⠿⠱⠀⠀⠀⠰⠶⣠⣈⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⣀⢀⠀⠀⣿⣼⣿⣿⣿⢾⣿⣿⣿⡟⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡇⢸⡇⢰⠒⣲⣶⡆⠀⠀⠀⠀
⠂⢶⠶⠦⠤⠀⠀⠈⠛⠛⠒⠛⠛⠁⠀⣿⢹⣿⣿⣿⢺⣿⣿⢹⣇⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣷⢸⣇⠨⠤⠿⠿⠇⠀⠀⠀⠀
⡀⢀⠀⠀⠀⢠⢀⢀⠀⣤⣤⢠⠀⡀⠀⠀⠀⢸⢿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⡆⠀⢰⣦⣤⣤⣤⣴⣶⣶⣶⣶
⠇⠸⠄⠧⠸⢸⢸⠈⢸⣿⣿⣶⢻⡆⣶⡒⠀⢰⡟⣎⣲⣶⠚⣶⣶⠓⢲⣶⣴⡶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⣿⡷⢢⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⡿⠀⣼⣿⣿⣿⢸⡇⣿⠉⠀⢨⣝⣯⡏⣿⣖⡯⣿⣶⢸⣿⣿⣯⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⢿⣇⣿⡿⣿⢸⣿⡗⢀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠘⠇⠂⠇⢿⢿⠎⠉⡇⠉⠀⠀⠈⣭⣵⠁⣽⣯⣵⣏⣽⣾⣽⣭⣭⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⠛⠛⠛⠒⠿⢿⣟⣛⣻⣛⣧⣛⣸⣛⠓⠊⠳⠿⢿⣿⠿⣿⣿⣿⣿⠿
⠀⠀⠀⢀⠀⡀⠀⠀⡀⠀⡀⢀⠀⠀⢀⠀⠀⠀⣽⣿⠀⣿⣿⣿⣛⣫⣽⣿⡟⢻⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣄⣠⣤⣤⣤⣤
⠀⠀⠀⢸⠀⡇⢸⠀⡇⠸⡇⢸⢰⣶⢸⠀⠀⠀⣿⠿⠀⠋⠁⢿⡿⠿⠟⢋⣴⣿⣿⠀⠀⠙⠛⠿⠟⠟⠿⠿⠿⠿⠿⠿⠿⠟⠁⣴⣦⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⣿⣿⣿⠀⠀⠀⡄⡄⡄⠉⠈⣿⣿⣿⣿
⢸⠀⡇⢸⠀⣿⠸⠀⡇⠀⡇⢸⠀⠀⢸⡦⠒⠊⠀⠀⠀⠀⠀⢸⣿⣆⠠⢼⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⡆⣰⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠁⠁⠁⠀⠀⣿⣿⣿⣿
⢸⣀⡇⠘⠀⠿⠐⠀⠇⠀⠃⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⢊⣠⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠉⠀⠿⢿⣿⣿⣷⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿
⢸⣿⠀⠰⠀⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⠈⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠉⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⠀
⣿⡟⠀⠀⠀⣾⣿⠄⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⡁⣀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢿⠿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠿⠿⠀⠀⠀⠿⠿⠀⠈⠉⠩⠽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⡪⡂⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣠⠀⣲⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣉⣉⣉⣉⣻⣛⣛⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⢀⣄⠀⠀⠀⠀⠀⣠⣤⣶⣾⡟⠛⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⣿⣽⣿⣿⣿⡿⠶⣦⣴⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⡨⡈⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣾⣿⣿⣏⡿⣿⣿⢿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⢄⠑⡔⠂⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣯⣿⢻⣿⣿⡏⣽⣿⣿⣿⣿⣿⣿⣆⠀⢀⠁⠀⠀⠀⠀⠂⠶⣤⠀⠀⠀⠀⠀⠀⠀⢄⠠⠪⢸⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿⣿⡻⣽⣿⣿⣿⣿⣿⡿⣿⣿⣷⣾⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣷⣄⠑⢄⡐⣶⡀⠀⠆⠳⠀⠀⠒⠒⠼⠀⠀⠀⠣⠂⠿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠰⠆⠂⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢿⣿⣿⣿⣿⣿⣿⡟⣿⣿⡿⣷⡾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠆⠹⠏⠐⠀⠀⠀⠀⡔⣿⠑⠀⠀⠀⠀⠀⠀⢚⣿⣧⣰⣿⡿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⢽⣿⣿⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠓⢀⢤⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣯⣿⣽⣿⣛⣻⣸⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡿⣿⣿⣿⣿⣯⣻⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣽⣿⣿⣿⣷⣟⡿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡆⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠸⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣤⣴⣤⣤⣤
⠀⡀⠀⠀⠂⣀⣀⠀⠀⠀⠘⠛⠛⠀⠘⠚⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠈⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠤⠿⢿⢧⣿⣿⠿⡯⠢⠪⠸⠕⠿⠱⠀⠀⠀⠳⠦⢠⣈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⣀⡀⠀⣿⣼⣿⣿⣿⢶⣿⣿⣿⡟⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡏⢸⡇⠀⠀⣲⣷⡆⠀⠀⠀⠀
⠒⠲⠶⠶⠦⠀⠀⠀⠛⠛⠛⠛⠛⠃⠀⣿⢹⣿⣿⣿⢺⣿⣿⢻⣇⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣷⢸⣇⠀⠤⠿⠿⠃⠀⠀⠀⠀
⡀⠀⡀⡀⢀⢠⣀⠀⠀⣴⣤⡄⠀⡀⠀⠀⠀⢸⢿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⡆⠀⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠿⠸⠇⠿⠸⢸⡟⠀⡰⣿⣿⣷⢳⡇⣶⡒⠀⢰⡟⣎⣖⣶⠚⣶⣶⠗⢲⡖⣴⡶⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⡿⣿⣿⣿⢿⣿⡷⢢⡖⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⡇⡇⡇⣿⣿⣿⢸⡇⣿⠉⠀⢨⣝⣧⡷⣿⣗⡯⣿⣾⢸⣿⣿⣯⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣏⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⢿⣇⣿⣿⣿⢸⣿⡗⢀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠃⠃⠃⢹⠿⠎⠍⠇⠉⠀⠀⠈⢩⣵⠋⣹⣿⣵⣏⣽⣾⣿⣯⣭⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠓⠛⠛⠂⠛⠒⠘⠛⠛⣻⣿⣟⣯⣛⣸⣟⠓⠊⠓⠻⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠠⠀⣄⠀⠀⡄⠀⡄⢠⠀⠀⠀⡀⠀⠀⢰⣿⠀⢻⣿⣯⣭⣭⣭⣿⡟⠁⣿⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⢽⣿⣿⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣶⣤
⠀⠀⠀⢸⠀⣿⠸⠀⡇⠀⡇⢸⠀⣶⠘⡇⠀⠀⣰⠿⠀⠊⠁⢹⣿⠿⠛⠃⢴⣿⣿⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡋⠀⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⡀⣤⣤⠁⠀⣿⣿⣿⣿
⢸⠀⡇⢘⠀⣿⠀⠄⡇⠀⡇⢸⠀⠀⠀⠧⠒⠉⠀⠀⠀⠀⠀⠈⣿⣶⠠⠰⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⠟⠃⣼⣿⣿⣿⣿⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⠀⠀⠀⠁⠉⠉⠀⠀⣿⣿⣿⣿
⡼⣄⡇⠘⠀⠿⠀⠂⠓⠀⠃⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⠜⢠⣴⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⠀⣦⣴⣿⣿⣏⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠿
⢡⣿⠁⠐⠂⢲⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠤⣤⣤⣤⣤⣤⣤⣤⠀
⢸⣿⠀⠀⠀⢾⣿⡆⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⡂⠘⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣽⠟⠛⣛⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣻⣿⣿⣿⣿⣿⣿⣿⡂
⡿⠿⠀⠀⠀⠻⠿⠃⠀⠉⠭⠽⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣷⣶⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⢉⣭⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣥⣤⣤⣄⣀⣀⢀⣠⡀⠀⠀⠀⠀⣀⣥⣴⣾⡟⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣯⣿⣽⣟⣻⣿⣿⠶⣦⣴⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢁⢃⡿⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣇⡿⣿⣿⢿⣿⣿⣿⣿⣿⠋⠀⣄⣀⠴⠂⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⢐⠑⡄⡨⢢⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣧⣿⣾⣯⣿⢻⣿⣿⡏⢽⣿⣿⣿⣿⣿⣿⣖⠊⢷⣦⠀⢀⣀⠀⠘⠖⣿⠀⠀⢠⣀⢀⠀⠀⠑⡨⡎⣾⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢷⣾⣿⠻⣭⣿⣿⣿⣿⣿⡿⢿⣿⣷⣾⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣷⡆⠉⠛⠂⢻⣶⣀⠁⠈⠀⠀⠀⣠⣽⠀⠀⠀⠨⠀⠛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠐⠂⠈⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣷⣿⢾⣟⣿⣿⣿⣿⣿⡏⢽⣿⡏⣷⡾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠟⣿⠊⠀⠀⠀⠀⠀⠀⢛⢿⣿⣴⣿⡿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣿⡿⣿⣿⣿⣿⣿⣿⢽⣿⣿⣇⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠐⠖⠀⠀⠀⠀⠀⠀⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣭⣿⣼⣷⣛⣻⣸⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡿⣿⣿⣿⣿⣯⣫⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣽⣿⣿⣿⣷⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣞⡆⡛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠈⢾⣄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣷⣴⣶⣵⣤⣶
⠀⣀⢀⠀⢸⣷⣀⠀⠀⠀⠐⠛⠛⠁⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⢀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿
⠻⠿⠿⢇⣿⣿⠿⡯⠢⠪⠸⠕⠿⠹⠀⠀⠀⢱⠶⣤⣼⢛⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⠿⠿⣿⢿⣿⣿⣿⣿⣿⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⣀⡀⠀⣿⣼⣿⣿⣿⢶⣿⣿⣿⡟⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡏⢸⡇⠀⠐⣲⣷⡆⠀⠀⠀⠀
⠒⠲⠶⠶⠦⠀⠀⠈⠛⠛⠛⠛⠛⠃⠀⣿⢹⣿⣿⣿⢺⣿⣿⢻⣇⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣷⢸⣇⠐⠤⠿⠿⠃⠀⠀⠀⠀
⡀⠀⡀⡀⢀⢠⣀⠀⠀⣴⣤⡄⠀⡀⠀⠀⠀⠸⠿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⡆⠀⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠿⠸⠇⠿⠸⢸⡿⠀⡰⣿⣿⣷⢳⡇⣶⡒⠀⢰⡟⣎⣲⣶⠚⣶⣶⠗⢲⡖⣴⡶⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⣿⡷⢢⡖⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⡇⡇⡇⣿⣿⣿⢸⡇⣿⠉⠀⢨⣝⣧⡿⣿⣗⡯⣿⣾⢸⣿⣿⣯⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣹⣏⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⢿⣇⣿⣿⣿⢸⣿⡗⢀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠃⠃⠃⢹⠿⠎⠍⠇⠉⠀⠀⠈⢩⣵⠃⣹⣿⣵⣏⣽⣾⣽⣯⣭⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠓⠛⠛⠂⠛⠒⠘⠛⠛⣻⣿⣟⣫⣛⣸⣟⡓⠊⠓⠻⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⣄⠀⠀⡄⠀⡄⢠⠀⠀⠀⡀⠀⠀⠰⣿⠀⢹⣿⣯⣭⣭⣭⣿⡟⠉⣿⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣻⣿⣿⠁⠀⠀⠀⠀⠀⣤⣤⣤⣴⣶⣤
⠀⠀⠀⢸⠀⣿⠸⠀⡇⠀⡇⢸⠀⣶⠸⡇⠀⠀⣨⠿⠀⠊⠁⢸⣿⠿⠛⠃⢰⣿⣿⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡋⠀⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⡀⣤⣤⠁⠈⣿⣿⣿⣿
⢸⠀⡇⢸⠀⣿⠀⠀⡇⠀⡇⢸⠀⠀⠠⠧⠒⠉⠀⠀⠀⠀⠀⠈⣿⣶⠠⠰⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⠛⠃⣼⣿⣿⣿⣿⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⠀⠀⠀⠁⠉⠉⠀⠀⣿⣿⣿⣿
⡼⣄⡇⠘⠀⠿⠀⠂⠓⠀⠃⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⠜⢠⣴⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⠀⣦⣴⣿⣿⣏⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠿
⢱⣿⠁⠐⠂⢲⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠤⣤⣤⣤⣤⣤⣤⣤⠀
⢸⣿⠀⠀⠀⣾⣿⡆⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡂⡘⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠟⠛⣛⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣻⣿⣿⣿⣿⣿⣿⣿⠂
⡿⠿⠀⠀⠀⠻⠿⠇⠀⠉⠭⠭⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⣶⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⢩⣩⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣥⣤⣤⣄⣀⣀⢀⣠⡀⠀⠀⠀⠀⣀⣥⣴⣾⡟⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢐⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⣿⣽⣟⣻⣿⣿⠶⣦⣴⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢁⢃⡿⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣸⣿⣿⣏⡿⣻⣿⢯⣿⣿⣿⣿⣿⠋⠀⣄⡀⠰⠃⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⢐⠑⡄⡨⢠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣧⣿⣾⣯⣿⢻⣿⣿⡏⣽⣿⣿⣿⣿⣿⣿⣔⠊⢷⣆⠀⠀⣀⠀⠐⠗⣿⠀⠀⢠⣀⢀⠀⠀⠑⡨⡎⣼⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢷⣾⣿⠻⣿⣿⣿⣿⣿⣿⡿⣿⣿⣷⣾⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣷⡆⠉⠙⠂⢻⣦⢌⠁⠈⠀⠀⠀⣠⣽⠀⠀⠀⠈⠀⠛⣻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠐⠂⠈⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣷⣿⢿⣟⣿⣿⣿⣿⣿⡏⢽⣿⡏⣷⠾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠄⠀⠀⠀⠀⠀⠀⢀⠿⣻⠊⠀⠀⠀⠀⠀⠀⠛⢿⣿⣴⣿⡿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣿⡿⣿⣿⣿⣿⣿⣯⢽⣿⣿⣇⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠐⠖⠀⠀⠀⠀⠀⠀⠉⠈⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣭⣿⣼⣷⣛⣻⣸⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡿⣿⣿⣿⣿⣯⣫⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣵⣿⣿⣿⣷⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡑⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣞⡆⡛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠈⢾⣄⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣶⣶⣵⣦⣶
⠀⡀⣀⠀⠰⣷⣀⠀⠀⠀⠐⠛⠛⠁⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⢀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿
⠋⠿⠿⠧⣿⣿⠿⡯⠢⠪⠸⠕⠿⠱⠀⠀⠀⢱⠶⢤⣾⢛⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⢀⡀⠀⣿⣼⣿⣿⣿⢶⣿⣿⣿⡟⣿⠻⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡏⢸⡇⠀⠉⣻⣿⡇⠀⠀⠀⠀
⠒⠲⠶⠶⠶⠀⠀⠀⠙⠛⠛⠛⠛⠃⠀⣿⢹⣿⣿⣿⢺⣿⣿⢻⣇⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣷⢸⣇⠀⠀⠛⠛⠃⠀⠀⠀⠀
⢀⠀⡀⢀⢀⠀⡄⠀⡄⢰⣤⡄⠄⣄⠀⠀⠀⠐⢿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⡆⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣾
⠸⠀⠇⠻⠸⠖⡇⡇⡇⣼⣿⣷⢳⡆⣶⠒⠀⢰⡟⣎⣲⣶⡚⣶⣶⠗⢲⡖⢰⡶⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⢿⣿⡷⢢⡖⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡇⡇⡇⣿⣿⣿⢻⡇⣿⠉⠀⢨⣝⣧⢿⣿⣟⡯⣿⣿⢸⣿⣿⣯⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⢹⡇⣿⡗⢸⣿⠀⣿⠒⢸⡇⣿⢻⣇⣿⣿⣿⢸⣿⡗⢀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠃⠃⠃⠻⠿⠎⠍⠱⠉⠀⠀⠈⠉⣵⠋⢹⣿⣵⣟⣽⣼⣿⣯⣭⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠚⣣⣿⣷⣞⡛⠂⠛⠒⠘⠓⠛⠘⠋⠛⣻⢛⣸⣟⡓⠊⠓⠻⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⡄⢠⠀⠀⠀⡄⠀⠀⠀⣿⠀⢸⣿⣧⣯⣭⣽⣾⠿⣩⣿⡟⠻⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⢠⡄⣴⣶⣶⣶
⠀⠀⠀⠐⡇⣿⠀⡇⣿⠀⡇⢸⠀⣶⡆⡇⠀⠀⢠⠿⠂⠊⠁⢸⣿⠟⠛⠁⢰⣿⣿⡇⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠀⠿⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⢠⣴⣰⠀⠀⢹⣿⣿⣿
⠸⡂⢸⠀⡇⣿⠀⡇⢽⠀⣷⢸⡇⠀⠀⠇⠒⠉⠀⠀⠀⠀⠀⠀⢿⡷⡄⠐⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⡇⠀⣼⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠈⠀⠀⠀⢸⣿⣿⣿
⠄⣧⡼⠀⠃⠹⠀⠃⠘⠀⠙⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⠃⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⢹⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⣀⡀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿
⢁⣿⡇⠀⠂⠰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠊⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠠⢤⡤⡤⠤⠤⡤⠶⠀
⢸⣿⠃⠀⠀⢰⣿⣶⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢐⠀⠈⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠹⠿⠿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⡾⠿⠄⠀⠀⠸⠿⠇⠀⠀⠩⠽⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣦⢄⡀⠀⠈⠉⠩⠭⠍⠩⠭⠭⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣬⣤⣤⣤⣤⣤⣄⣀⣀⠀⣠⡄⠀⠀⠀⢀⣇⣤⣶⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠈⢇⠿⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣽⣟⣻⣿⡿⠶⣦⣴⣾⣿⣿⣿⣿⡟⢀⣀⠼⠋⢀⠀⠀⣀⢀⣤⠀⠀⠀⠀⠀⠀⠀⢧⠁⢘⢆⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣏⡿⣿⣿⢯⣿⣿⣿⣿⣿⠋⠀⢾⣿⣷⣄⠀⣤⡄⠀⣛⢸⡅⠀⠠⠤⣀⡆⠀⠀⠓⡜⣼⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢿⣾⣯⣿⢻⣿⣿⡏⣽⣿⣿⣿⣿⣿⣿⣄⠈⠻⠋⠈⡓⠸⣿⠆⡅⠀⠀⠀⢀⣶⣿⠃⠀⠀⠀⠀⠙⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⠻⣭⣿⣿⣿⣿⣿⡿⢿⣿⣷⣾⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠚⢻⠁⠀⠀⠀⠀⠀⠀⠹⢿⣿⡀⠀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠐⠒⠈⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣷⣿⢿⡟⣿⣿⣿⣿⣿⡏⢽⣿⡟⣷⡾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠿⠃⠀⠀⠀⠀⠀⠺⠁⠓⣿⠿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣿⡿⣿⣯⣿⣿⣿⣯⢽⣿⣿⣧⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣭⣿⣼⣿⣛⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣯⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⠀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣞⡆⡙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠈⠾⣷⣄⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣷⣴⣶
⣀⡠⢀⠀⢰⣿⣀⠀⠀⠀⠀⠛⠛⠁⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠛⠿⠿⠧⣿⣿⡿⡯⠢⠪⠸⠕⠿⠹⠀⠀⠀⠱⠶⡤⣈⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠀⢀⣀⠀⣿⣼⣿⣿⣿⢶⣿⣿⣿⡟⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡏⢸⡇⠀⠋⣹⣿⡗⠀⠀⠀⠀
⠒⠒⠶⠶⠶⠀⠀⠀⠙⠛⠛⠛⠛⠃⠀⣿⢹⣿⣿⣿⢺⣿⣿⢻⣇⣿⣿⣮⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣷⢸⣇⠀⠂⠚⠛⠃⠀⠀⠀⠀
⢀⠀⡀⢀⠀⡀⡄⡀⡄⢰⣤⡄⠄⢀⠀⠀⠀⠀⠿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⡶⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣾
⠸⠀⠇⠸⠀⠇⡇⡇⡇⣾⣿⣷⢳⣎⣶⠖⠀⢰⡟⣎⣒⣶⡚⣶⣶⠗⢲⡖⢲⡶⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⢻⣿⠉⣶⠿⢩⡟⣿⠿⣿⣿⣿⣿⢿⣿⡿⢢⡖⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡇⡇⠇⣿⣿⣿⢸⡿⣿⠏⠀⢨⣝⣧⢿⣿⣟⡯⣿⣿⢸⣿⣿⣯⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣇⣿⣷⣼⣿⠀⣿⠒⢸⡇⣶⢸⣇⣿⣿⣿⢸⣿⡗⢀⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠃⠛⠀⠻⡿⠎⠉⠹⠉⠁⠀⠈⠉⣱⡊⢹⣿⣵⣟⣽⣼⣿⣯⣭⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⢚⣿⣿⣷⣿⣟⠂⠛⠒⠘⠓⠛⠘⠋⠛⠃⢛⣸⣛⡓⠊⠓⠛⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⡄⢠⠀⠀⠀⡄⠀⠀⠀⢸⠀⢸⣿⣷⣯⣭⣽⣿⡿⠉⣽⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠸⠿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡇⠀⠀⠀⠀⠀⢠⡄⣴⣶⣶⣶
⠀⠀⠀⠀⡇⣿⠀⡇⢸⠀⣿⢸⡇⢶⡆⡇⠀⠀⢀⠶⠂⠊⠁⠸⣿⠛⠛⠁⢰⣿⣿⡇⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⢀⣿⣾⣿⣿⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡇⠀⠀⢠⣰⢰⠀⠀⢸⣿⣿⣿
⠀⡇⢸⠀⡇⢸⠀⡇⢸⠀⣿⢸⡇⠀⠀⠇⠒⠉⠀⠀⠀⠀⠀⠀⢻⡿⡆⠐⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⠇⠀⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠈⠈⠀⠀⢸⣿⣿⣿
⠄⣧⡼⠀⠃⠸⠀⠃⠘⠀⠘⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠃⢂⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⢿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿
⠁⣿⡇⠀⠂⠐⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠄⠊⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠤⡤⡤⡤⠤⠴⠶⠄
⢸⣿⡇⠀⠀⢰⣿⣷⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢕⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⣆⡀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⡇
⡾⠟⠇⠀⠀⠸⠿⠟⠀⠀⠩⠽⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⠠⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠔⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⠩⡏⣾⢇⠀⠀⠉⠍⠩⠭⠩⠭⠭⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣬⣬⣤⣬⣤⣤⣄⣀⣀⠀⣠⣄⠀⠀⠀⣸⣿⣧⣴⣾⡿⠁⡠⠖⠀⠀⠀⢀⢀⣠⠞⠀⠀⠀⠀⠀⠈⠀⢧⢱⠏⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣽⣿⣿⣿⣿⢶⣦⣴⣾⣿⣿⣿⣿⡟⢀⣾⣷⣄⠀⣀⡀⠈⢻⢋⡇⠀⢠⣦⡀⡔⠀⠀⠀⢴⢰⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⡟⣿⣾⣿⣿⣯⡿⣿⣿⢿⣿⣿⣿⣿⣿⡏⠀⠈⠿⠿⠛⠳⠘⣷⡆⡍⠀⠁⠀⢀⣠⣾⡏⠀⠀⠀⠁⠛⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣧⣿⣿⣯⣿⣿⣿⣿⡏⣽⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠈⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣯⣿⣿⣿⣿⣿⡿⣿⣿⣷⣾⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠐⠂⠀⠀⠀⠀⠐⠠⠀⠀⠀⠃⠴⠆⠀⠀⠀⠀⠈⠽⠛⠣⠀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠒⠐⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢿⣟⣿⣿⣿⣿⣿⡟⣿⣿⡟⣷⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⡀⠀⠀⠀⠀⠀⠀⠀⢾⠿⠇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣞⡇⡛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠾⣿⣦⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣶⣴⣴⣶⣶
⠀⡀⣀⡀⠀⣰⣆⠀⠀⠀⠀⠛⠛⠁⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⡤⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿
⠛⠿⠿⠇⣿⣿⡿⡯⠢⠪⠸⠕⠿⠹⠀⠀⠀⠱⡶⡄⢈⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⡀⠀⣿⣼⣿⣿⣿⢶⣿⣿⣿⡿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡿⢸⡇⠀⠎⢩⣿⣷⠀⠀⠀⠀
⠀⣰⡶⠶⠤⠄⠀⠀⠙⠛⠛⠓⠛⠋⠀⣿⢹⣿⣿⣿⢺⣿⣿⢻⣇⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⢸⣇⠀⠂⠚⠛⠋⠀⠀⠀⠀
⢀⠀⠀⠀⠀⠀⡄⡀⡄⢠⣤⡄⠄⢀⠀⠀⠀⠀⠿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠁⠀⠈⠀⠈⠙⠻⣿⣿⣿⣶⣶⣿⡶⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠸⠀⠇⠸⠀⠇⡇⡇⡇⣾⣿⣷⢳⣾⣶⡖⠀⢰⡟⣎⣲⣶⡞⣶⣶⡗⢲⡖⢲⡶⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡏⣶⣶⣴⣶⡀⣶⠶⢠⡖⣦⠀⡾⣿⣿⣿⢿⣿⡷⢢⡖⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡇⣧⠀⣿⣿⣿⢸⣿⣿⡏⠀⢨⣝⡧⣿⣿⣗⡯⣿⣿⢸⣿⣿⣯⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⢸⡇⣿⣷⣿⣿⡇⣿⠒⢸⡇⣶⢰⣇⣿⠈⣿⢸⣿⡗⢀⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠳⠛⠸⠹⡿⡮⠉⠹⠉⠁⠀⠈⠉⢱⡏⢩⣿⣵⣿⣹⣼⣿⣯⣭⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⠚⠷⣻⣷⣿⣿⠂⠛⠒⠘⠓⠛⠘⠋⠛⠀⠛⢸⣟⡓⠊⠓⠻⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⢀⡀⠀⠀⡀⠀⠀⠀⢸⠁⢸⣿⣿⣭⣭⣽⣿⣿⠿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣼⣿⣿⣿⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⢠⡄⣤⣶⣶⣶
⠀⠀⠀⠀⡇⢻⠀⡇⢸⠀⣿⠀⡇⢴⡆⡇⠀⠀⢀⠾⠂⠚⠉⠙⣿⠿⠟⠋⢨⣿⣿⡇⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⢰⠈⠀⢹⣿⣿⣿
⠀⡇⢸⠀⡇⢸⡄⡇⢸⠀⢸⠀⡇⠀⠀⠧⠒⠊⠁⠀⠀⠀⠀⠀⢹⣷⡆⠄⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠀⠀⢸⣿⣿⣿
⡆⣇⣸⠀⠃⠸⠇⠒⠸⠀⠘⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡧⢃⣴⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠄⠄⠈⠿⣿⡿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿
⠁⣿⡇⠀⠂⠐⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠁⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠠⢤⣤⣤⡤⡤⠤⢤⠄
⢸⣿⡇⠀⠀⢰⣿⣷⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢔⢀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠇⡀⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢈⢾⣵⡟⣀⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠼⠿⠇⠀⠀⠸⠿⠿⠀⠈⠩⠭⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠋⢁⣀⠀⡰⠃⠀⠀⠀⠀⣀⡴⠇⠀⠀⠀⠀⠈⢹⣼⣆⡿⢸⣿⠉⠉⠉⠉⠉⠉⠉⠭⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣬⣤⣤⣄⣀⣀⠀⣠⡄⠀⠀⠐⢟⣋⣥⣶⣾⡿⢇⣰⣄⡀⢤⣤⠘⢹⡏⣷⠀⠀⣴⢀⣤⠀⠀⠐⢬⢣⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣽⣿⣿⣿⣿⢶⣦⣴⣾⣿⣿⣿⣿⡟⠀⢾⣿⠿⣷⡞⣿⣦⢘⠁⠀⠀⠀⣠⣾⣿⠀⢠⠢⠨⠘⢻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⡟⣿⣾⣿⣿⣯⡿⣿⣿⢿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣿⠇⠈⠁⠈⠀⠀⠀⣻⣿⡿⠓⠀⠈⠡⠀⠀⠘⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣧⣿⣿⣯⣿⢻⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⢀⡯⠀⠀⠀⠀⠰⠀⠀⠈⠁⠁⠠⣶⠀⠀⠀⠀⠀⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣯⣿⣿⣿⣿⣿⡿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠸⣀⠀⠀⠀⠀⠈⠀⠀⠀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠒⠐⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⢿⣟⣿⣿⣿⣿⣿⡟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⢸⡿⠇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣄⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣞⡇⡛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣛⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⢾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢳⣶⣶⣶⣶⣶
⠀⡀⠀⡀⠀⣀⣄⠀⠀⠀⠀⠛⠛⠁⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣶⣶⠆⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿
⠈⠿⠿⠇⣿⣿⡿⡯⠢⠪⠽⠕⠿⠱⠀⠀⠀⠰⡶⣤⣈⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⡿⠿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣿⣼⣿⣿⣿⢶⣿⣿⣿⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡿⢸⡇⠀⡖⢲⣷⣶⠀⠀⠀⠀
⣤⣤⣤⣤⣤⡄⠀⠀⠒⠻⠷⠶⠾⠟⠀⣿⢹⣿⣿⣿⢻⣿⣿⢿⣇⣿⣾⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠁⣿⠉⣿⠋⣿⣻⣿⣿⣿⡇⣾⣿⣿⢸⣇⠀⠧⠾⠿⠟⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡀⡀⡀⢠⣤⡄⠄⢀⠀⠀⠀⠀⢿⣿⣶⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢠⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣷⣶⣿⣶⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠸⠀⠶⢸⠄⡇⡇⣇⠃⣿⣿⣷⢳⣾⣶⡖⠀⢰⡟⣎⣶⣶⡾⣶⣶⡷⢳⡶⢴⡖⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣆⣾⣿⣿⣿⡟⣶⠶⢠⡖⣦⠀⡶⣦⠹⣿⢿⣿⣿⢢⡖⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⢻⢠⣿⣿⣿⢸⣿⣿⡏⠀⢨⣝⣯⣿⣿⣗⡿⣿⣿⢸⣿⣿⣯⣬⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⢸⡇⣿⣷⣿⣿⡇⣿⠒⢸⡇⣶⢰⣇⣿⠀⣿⢸⣿⡗⢀⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠻⠸⠸⠙⣿⣮⠉⢹⠉⠁⠀⠈⢩⣵⡯⢩⣿⣷⣿⣿⣼⣿⣯⣭⣵⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⢺⣧⣿⣷⣿⣛⡂⠛⠒⠘⠓⠛⠘⠋⠛⠀⠛⠈⠛⠓⠊⠓⠻⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠰⣿⡆⢸⣿⣯⣭⣯⣭⣽⣿⠏⣽⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣤⣴⣶⣦
⠀⠀⠀⠀⡇⢸⡆⣖⢸⠀⢸⠀⡇⢰⡆⢇⠀⠀⢠⡿⠇⠘⠉⠈⣿⠿⠿⠋⢠⣾⣿⡟⠀⠈⠙⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠈⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⢠⣤⠈⠁⢹⣿⣿⣿
⡆⡇⢸⠀⡇⢸⡇⢹⢸⠀⢸⠀⡇⠀⠀⣼⠔⠒⠉⠀⠀⠀⠀⠀⢹⣷⡆⡄⢾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣷⣤⠀⠸⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠀⠀⢸⣿⣿⣿
⣇⣇⣸⠀⠇⠸⡇⠸⠸⠀⠘⠃⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡴⡁⣠⣽⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿
⠁⣼⡏⠀⠆⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣶⡆⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡅⣸⣻⡿⡀⠠⣤⣤⣤⣤⣤⣤⣤⡄
⠀⣿⡇⠀⠀⢀⣿⣷⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢌⢀⢈⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣯⢻⣿⣯⠄⠚⠛⠀⠄⠀⠀⣀⣤⢴⠀⠀⠀⠀⣀⠁⣿⡏⣿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡿⠇⠀⠀⠀⠿⠿⠀⠉⠉⠹⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⢑⢐⢘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠉⠀⢉⣡⡀⣠⡀⢲⣦⡄⢀⡿⣿⠀⠰⠶⡦⣠⣿⠀⡀⠸⡏⣾⣿⣯⠉⠭⠍⠉⣉⣩⣭⡅
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⠀⢀⡀⠀⠀⠺⠋⣁⣤⣶⣾⡟⠁⠸⠟⢿⣷⢻⣷⣾⡟⠉⠀⢠⣤⣾⣿⡇⠘⣿⣿⠞⢻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⣿⣿⣿⣿⣿⣿⢷⣦⣴⣾⣿⣿⣿⣿⡟⠀⣀⠀⡐⣿⡗⠀⠋⠉⠀⠀⠀⢸⣿⣿⡿⠃⠀⠙⠏⠀⠰⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣾⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⡌⠚⠛⠀⢰⣿⡇⠀⠀⠀⠀⠆⢤⠘⠟⠈⠀⢰⡄⠀⠀⠀⠀⠘⢿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣭⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠴⠢⠃⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡥⠀⠀⠀⠀⠀⠀⠀⣿⠗⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡆⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣛⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠘⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⣴⣾⣿⣶⣶
⠀⡀⠀⠀⠀⣶⣄⠀⠀⠀⠀⠛⠛⠃⠛⠛⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣾⣿⡇⠀⠀⠀⠐⠀⣿⣿⣿⣿⣿
⠿⠿⢿⡇⣿⣿⡿⡯⠢⠪⠼⠕⠿⠹⠀⠀⠀⠐⡖⡄⢈⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⢿⢿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣛⣁⣉⣉⠉⢉⣛⠿⣿⣿⡿⣿⣿⣿⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣿⣼⣿⣿⣿⢶⡿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡿⣇⠉⣿⠉⣿⠀⣿⢸⡇⣿⣿⡇⢸⣿⣿⢸⡇⠀⠐⢒⣲⣶⠀⠀⠀⠀
⢀⣀⣀⣀⣀⡀⠀⠀⠰⠶⠯⡤⣤⡶⠀⣿⢹⣿⣿⣿⢺⣿⣿⢻⣇⣿⣾⣮⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣸⣿⣿⡆⣿⠀⣿⠂⣿⣸⠇⣿⢹⡇⣾⣿⣿⢸⣇⠀⠧⠼⠿⠿⠀⠀⠀⠀
⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠂⢸⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⠀⠀⢰⣤⣤⣤⣤⣤⣴⣶⣶
⢠⡆⢰⠠⡆⣦⣺⢶⢰⣴⣿⣷⢳⣾⣶⡖⠀⢰⡟⣎⣶⣾⣾⣶⣶⣷⢲⣶⣶⡶⢼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢲⡄⣾⣿⣿⣿⡏⣷⠶⢠⡖⣦⠀⡶⣆⠰⣶⠶⢸⡿⢢⡖⢾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠀⠁⠈⢸⢸⢸⢸⣿⣿⢸⣿⣿⡏⠀⢨⣝⡧⢽⣿⣇⡧⣿⣿⢸⣧⣾⣯⣬⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢸⡇⣿⣷⣿⣿⣷⣿⠒⢸⡇⣶⢰⣇⣿⠀⣿⠀⢸⡗⢀⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⢸⢸⠘⣿⣾⢩⢱⡍⠁⠀⠈⠉⢡⡌⢩⣿⣷⣿⡿⣾⣿⣿⣭⣵⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡛⠚⠃⣛⣓⣚⣛⣆⣛⠒⠘⠓⠛⠘⠋⠛⠀⠛⠀⠘⠓⠊⠓⢻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠨⠉⠈⣿⣿⣟⡛⣛⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢹⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢠⣤⣤⣤
⡄⠀⠀⠀⣤⢰⡇⢴⢸⡄⢸⡆⡇⢠⡄⢸⠀⠀⠀⢘⠇⠠⠛⠉⣿⡿⠿⠟⠉⣶⣾⣿⠀⠙⠺⠯⠽⠿⠭⠿⠿⠿⠿⠿⠿⠿⣿⣀⠀⠈⠉⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⢀⣄⡄⠉⠈⣿⣿⣿
⡇⡆⠀⡄⠸⠘⡇⢸⢸⡇⢸⡇⡇⠈⠁⢸⣠⠔⠒⠁⠀⠀⠀⠀⢹⣷⡄⡀⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢶⣶⣶⣿⣿⣿⡇⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⣷⢦⡄⠈⠈⠉⠁⠀⢀⣿⣿⣿
⡇⢱⠀⡇⢸⠀⡇⢸⠨⠇⠸⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⡝⠆⢈⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣟⢿⣿⣍⣰⣿⠋⠀⠀⠀⢀⣀⣄⡀⠀⠀⠀⠀⢀⠁⣷⣏⣾⢳⡆⠀⠀⠀⠀⢸⣿⣿⣿
⠈⢸⣿⠁⢠⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢀⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠋⠀⢻⣿⣿⣧⣌⣷⣶⡄⣸⣿⣿⠀⠐⠲⠶⣶⣿⣷⣤⡝⡟⣾⣿⣀⣀⣠⣤⣄⣤⣤⡄
⠀⣿⡿⠀⠀⠀⣽⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠠⠈⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠟⠃⠀⠀⠻⠛⠻⣿⡟⢿⣿⣾⣇⠉⠀⢠⣴⣾⣿⣿⢻⣿⣿⡷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⢠⣿⣇⠀⠀⠀⣿⣿⠀⠐⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠭⠨⠨⡇⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠏⠀⠀⠀⡀⠰⣶⣾⣿⡇⠘⡿⠿⣿⠀⠀⢸⣿⣿⣿⠇⠈⠻⠿⠀⢸⣿⣿⣛⣛⣛⣛⣛⣻⡏
⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣥⣤⣄⣀⣀⠀⢀⡴⠿⠿⠛⠉⣁⣤⣶⣾⡟⠁⠀⢸⣿⣿⠏⠀⠀⠀⠁⠗⡠⠛⢻⠛⠃⢨⠀⠀⠀⠀⠘⣿⣿⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣻⣿⣿⣶⣦⣶⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⣧⠀⠀⠀⠀⠘⠉⠂⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠾⠿⠃⠀⠈⠀⠀⠀⠀⠀⠻⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣿⠻⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣿⡷⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣛⣻⣺⣿⣷⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣾⣿⣷⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣞⡇⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣛⣿⣿⢿⢿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢩⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⢀⣀⠀⠀⠀⠀⠅⠀⣤⣤⣤⣤
⠀⡀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠻⠛⠃⠛⠛⠘⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠙⠛⠛⠦⠄⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣻⡂⠀⠀⠀⠀⠀⢿⣿⣿⣿
⠠⠿⣿⣿⣿⣿⣿⡯⠢⠪⠹⠕⠿⠹⠀⠀⠀⠐⡆⠄⠈⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡁⣀⣀⣀⣀⠀⢀⣀⠀⣈⢻⡿⣿⣿⣿⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣿⣼⣿⣿⣿⢶⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣧⡉⣿⠉⣿⠀⣿⢸⡇⣿⣿⡇⢸⣿⡿⢸⡇⠀⠠⢰⣶⣶⠀⠀⠀⠀
⣀⣀⣀⣀⣀⡀⠀⠀⠠⣴⣷⣤⣤⣶⠀⣿⢹⣿⣿⣿⢺⣿⣿⢿⣏⣿⣾⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣸⣿⣿⣧⣿⣆⣿⠀⣿⣸⠇⣿⢹⡇⣾⡿⣿⢸⣇⠀⠆⠸⣿⡿⠀⠀⠀⠀
⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠰⢶⣿⣿⣿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤
⠀⡄⢠⠀⡄⣤⢰⢰⢰⢠⣿⣷⢻⣶⣶⡖⠀⢴⡟⣎⣶⣾⣾⣶⣶⣷⢲⣶⣶⡖⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢲⡄⣾⣶⣾⣿⡏⣿⠶⢠⡖⣦⠀⡶⣦⠰⣶⠶⢰⡶⢢⡖⢾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠁⠈⠀⠁⠈⢸⢸⢸⢸⣿⣿⢸⡿⣿⡏⠀⢨⣝⣧⣿⣿⣇⡯⣽⣿⢸⣷⣼⣯⣬⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢸⡇⣿⣷⣿⣿⣿⣿⠒⢸⡇⣶⢰⣇⣿⠀⣿⠀⢸⡗⢀⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⢸⢸⠸⣿⣾⢩⢱⡍⠁⠀⠈⠉⢡⣏⠉⣿⣷⣿⡿⣾⣿⣿⣭⣵⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣻⡚⠃⠛⣷⣚⣛⣂⣛⡒⠘⠓⠛⠘⠋⠛⠀⠛⠀⠘⠓⠊⠓⣻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠁⠀⠀⠀⠀⢸⡇⠀⣿⣿⣿⠿⠟⣛⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠻⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣤⣤⣤
⡆⠀⠀⠀⢠⢠⡆⢰⢰⡄⢸⡆⣇⢀⡄⢰⠀⠀⠀⢼⣂⠀⠟⠛⣿⣿⣿⠟⠋⣡⣾⣿⠈⠙⠻⠿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣄⠀⠀⠀⠀⣄⡄⠉⠘⣿⣿⣿
⡇⢠⠀⡄⢸⠀⡇⢸⠘⡇⢸⡇⣧⠈⠉⢸⣠⡤⠒⠉⠀⠀⠀⠀⢹⣷⡄⠀⣴⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⣶⣾⣿⢿⣿⡿⠃⣿⡿⠂⣤⠤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⢢⣬⣷⣿⠘⠀⠋⠃⠀⠀⣿⣿⣿
⡇⢸⠀⡇⢸⠀⡇⢸⠀⡇⠸⡇⣿⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣕⠀⢈⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠊⢿⣿⣿⣟⠁⣦⣤⣄⢙⡿⣾⣁⡦⡤⢤⣤⣠⣶⣮⡻⢻⣇⣿⠄⠀⠀⠀⢀⣿⣿⣿
⠸⢸⣿⠁⢠⠀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢀⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡁⠀⠀⢹⣿⣿⣿⣿⢿⣿⣮⡇⠙⠃⠀⣠⣶⣾⣿⣿⣿⣿⣿⣼⣿⣇⣀⣀⣀⣀⣀⣀⡄
⠀⣾⣿⠀⠈⠀⣹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡂⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠇⠀⠀⠀⠠⡄⢠⣿⣿⠈⠿⡷⣿⡇⠀⠀⣾⣿⣿⡿⠏⠹⣿⡟⠙⣿⣿⣿⣶⣿⣿⣾⣶⣶
⢀⣿⣷⠀⠀⠀⣿⣿⡇⠐⠶⠶⢷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠍⠀⠈⡇⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⡧⠀⠀⢀⣀⠀⠐⣿⣿⣿⡄⠀⠀⠹⢿⠆⠄⠻⣿⠿⠁⠆⠀⠀⠀⠀⣿⣿⡟⠛⠟⠻⣿⣿⡟
⠘⠉⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣥⣤⣤⣧⣤⣄⣀⣀⠀⣰⡿⠿⠿⠛⠉⣁⣤⣶⣾⡿⠁⠀⠀⢿⣿⠋⠂⠀⠀⠀⠀⠈⣁⠀⠻⠀⠂⣶⡄⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣿⣿⣿⣿⣿⣿⣶⣦⣶⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠰⣶⢸⡏⠀⠀⠀⠀⢽⡇⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⠶⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⡄⠀⠀⠀⢼⡇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠻⢷⣿⠀⠀⠀⢸⣇⠀⠀⠀⠀⠈⢐⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡻⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣧⠀⠈⠀⠀⠀⠰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢂⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⣴⣶⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢠⡆⠘⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢉⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣺⢿⣧⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣯⣫⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢉⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡇⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣛⣿⣿⢿⢿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣹⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣦⣤⡀⠀⠀⠀⠀⠀⠂⣠⣄⣤
⠀⡀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢻⠟⠂⠛⠋⠘⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠘⠻⠿⠿⢤⣀⣀⣀⡀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⢹⣿⣿
⢶⣿⣿⡷⣿⣿⣿⡯⠢⠪⠽⠕⠿⠹⠀⠀⠀⠐⡆⠀⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠂⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⡀⣀⣀⣀⣀⠀⢀⣀⠀⣀⢘⡿⢻⣿⣿⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣿⣿⣿⢶⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣧⡉⣿⠉⣿⠀⣿⢸⡇⣿⣿⡇⢸⣿⡟⢸⡇⠀⠀⠤⣤⣤⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠀⠀⠀⢠⣤⣷⣆⣠⣤⠀⣿⢹⣿⣿⣿⢺⣿⣿⢿⣏⣿⣽⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢸⣿⣿⣷⣿⣷⣿⠀⣿⣸⠇⣿⢹⡇⣾⡿⣷⢸⣇⠀⢀⣰⣿⣿⠀⠀⠀⠀
⠐⠘⠛⠋⠉⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠰⢿⣿⣿⣟⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤
⠀⡄⢠⠀⡄⣤⢰⢠⢰⢠⣿⣶⢻⣦⣶⡖⠀⢰⡟⣎⣶⣾⣿⣶⣶⣷⢲⣶⣴⡖⢼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢲⡄⣶⣶⣴⣿⣏⣿⠷⢠⡖⣦⠀⡶⣦⠰⣶⠶⢰⡶⢢⡖⢾⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠁⠈⠀⠁⠈⢸⢸⢸⢸⣿⣿⢸⡿⣿⡏⠀⢨⣝⣧⣿⣿⣇⡯⣽⣿⢸⣗⣼⣯⣬⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⣿⣗⣿⣿⣿⣿⠒⢸⡇⣶⢰⣇⣿⠀⣿⠀⢸⡗⢀⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⢸⡸⠘⣿⣾⢩⢡⡍⠁⠀⠈⠉⠁⣫⠉⣿⣷⣿⣿⣾⣿⣿⣭⣵⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣻⣞⡇⠛⢳⣞⣛⣂⣛⣒⠘⠓⠛⠘⠋⠛⠀⠛⠀⠘⠓⠊⠓⣻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠈⠈⠁⠀⠀⠀⠀⠐⠇⠀⣿⣿⣿⣶⠿⢛⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠘⢿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⡄⠀⠀⠀⢠⠀⡆⢠⠀⡄⢰⡆⡆⢀⣀⢰⠀⠀⠀⠈⡄⠀⠿⠛⣿⣿⣿⡿⠋⣡⣾⣿⠈⠙⠩⢹⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⡀⠛⠘⣿⣿⣿
⡇⢠⠀⡄⢸⠀⡇⢸⠀⡇⢸⡇⡧⠘⠛⢸⢀⣠⠔⠋⠀⠀⠀⠀⢹⣦⡀⠀⣠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⣶⣾⣿⡟⣿⣿⣅⣼⡟⣁⠉⠁⠀⣠⡀⣀⢤⠀⠀⠀⠀⢀⡐⣶⡿⣿⡖⠃⠓⠃⠀⠀⣿⣿⣿
⡇⢸⠀⡇⢸⠀⡇⢸⠀⡇⠘⡇⣿⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠸⣟⣱⡀⠉⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠘⢿⣷⣾⣦⣜⣿⣿⣂⣾⠛⣁⠼⠒⠛⠳⢦⣾⣿⣮⣙⢿⣽⡄⠀⠀⠀⠀⣿⣿⣿
⢹⢸⣶⠃⢠⠀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡁⠀⠀⠌⠙⠛⣹⣿⡏⢻⣿⣿⣤⠁⠀⢐⣿⣿⣿⣿⣿⣿⣿⣷⣿⣧⠀⠀⠀⠀⠉⣉⡉
⠀⣼⣿⠀⠈⠀⣹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡃⢀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣟⣛⡋⠀⠀⠀⠀⠛⢻⣿⣿⡇⠈⠽⠙⣿⣄⠀⢰⣿⣿⡿⠛⠉⢻⡿⠗⢹⣿⣿⣿⣿⣿⣿⣿⣷
⠀⣿⣿⠀⠀⠀⣿⣿⡇⠠⠶⠶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡢⠂⠀⠈⡏⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⠟⠁⠀⢰⣄⠀⠐⣿⣿⣿⠗⠀⠀⠐⠉⠁⡼⠁⠹⡿⡡⢘⠃⠀⠖⠀⢸⣿⡿⠿⠿⠿⠿⠿⠿
⠘⠉⠉⠀⠀⠀⠉⠉⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣧⣤⣄⣀⣀⠀⣰⠿⠿⠿⠛⠉⣁⣤⣴⣾⡿⠁⠀⠀⠸⣿⠏⠀⠀⠀⠀⣀⠀⣴⡇⠀⠉⠀⠺⡇⠀⠀⠀⠘⢿⣏⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣫⣿⣽⣿⣿⣿⣿⣶⣦⣶⣾⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠫⠀⠀⠀⠀⠀⠙⠿⠟⣡⠀⠋⠀⢸⣿⠀⠀⠀⠀⠊⠈⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⠶⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⢐⣦⣤⣿⡄⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣻⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡏⠈⠙⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⡏⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣧⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠠⠀⠈⢹⠿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣟⣿⣸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣀⣀⠀⠀⠀⠀⠈⠀⠘⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣏⣫⣿⣿⣟⣛⣿⣿⢿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⡃⢙⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣽⣿⣾⣿⣿⣟⡿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡇⡛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣛⣿⣿⢿⢿⣷⣶⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣼⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢛⠿⠄⠙⠃⠉⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠘⢿⣿⣿⣟⠀⠀⠀⠀⠀⠀⢤⡀⠀⢤⣶⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿
⢠⣿⣿⡷⣿⣿⣿⡯⠢⠪⠸⠕⠿⠹⠀⠀⠀⠱⡂⡄⢈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠃⠂⠀⠠⠤⠾⢿⣿⣿⡿⠿⠿⠛⠀⠀⠀⠀⠀⠀⣀⣈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡃⣀⣀⣀⣀⠀⢀⣀⠀⣀⢘⡿⢿⣿⣿⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣿⣿⣿⢶⡿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡿⣧⡈⣿⠉⣿⠀⣿⢸⡇⣿⣿⡇⢸⣿⡟⢸⡇⠀⠀⠤⢤⣤⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣀⣠⣤⠀⣿⢹⣿⣿⣿⢺⣷⣿⢿⣟⣿⣹⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢸⣷⣿⣧⣿⣶⣿⠀⣿⣸⠇⣿⢹⡇⣾⡿⣷⢸⣇⠀⣄⢰⣿⣿⠀⠀⠀⠀
⠉⠉⠛⠛⠛⠃⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⢿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢰⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣠
⠀⡄⢠⠀⡄⣀⢰⢠⢰⢀⣷⣶⢳⣦⣶⡖⠀⢴⡟⣎⣶⣶⣾⣶⣶⣷⢲⣶⣶⡖⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⡆⣶⣶⣸⣿⣏⣿⠶⢠⡖⣦⠀⡶⣆⠰⣶⠶⢰⡶⢢⡖⢾⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠃⠘⠀⠃⠘⢸⢸⢸⢸⣿⣿⢸⡿⣿⡏⠀⢨⣝⣧⣿⣿⣏⡯⣽⣿⢸⣯⣽⣯⣬⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⣿⣗⣿⣿⡏⣿⣲⢸⡇⣶⢰⣇⣿⠀⣿⠀⢸⡗⢀⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⢸⡸⠘⣿⣾⢩⠱⡍⠁⠀⠈⠉⢁⡯⠉⣿⣷⣿⣿⣾⣿⣿⣯⣵⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⣚⣣⡛⢓⣞⣛⣂⣛⣒⠘⠓⠛⠘⠋⠛⠀⠛⠀⠘⠓⠊⠓⣻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠛⠛⠈⠀⠃⠀⠀⠀⠀⠰⡎⠀⣿⣿⣿⣷⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁⠀⢿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉
⡄⠀⠀⠀⢀⠀⡆⢠⠀⡀⢰⡄⡆⢀⡀⢠⠀⠀⠀⠰⠆⢀⡿⠟⣿⣶⣾⡿⠏⣫⣾⣿⠉⠛⠍⣫⣿⣛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢴⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⡀⠛⠘⣿⣿⣿
⡇⢀⠀⡄⢸⠀⡇⢸⠀⡇⢸⡇⡯⠘⠛⢸⠀⣀⡤⠋⠉⠀⠀⠀⢻⣯⠁⠀⢠⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣾⣿⣿⢭⣭⣯⣼⡿⢡⡈⠉⠀⢠⣄⢀⢀⠀⠀⠀⠀⠀⠀⣶⣾⢶⡖⠃⠛⠃⠀⠀⣿⣿⣿
⡇⢸⠀⡇⢸⠀⡇⢸⠀⡇⠘⡇⣿⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠸⣟⡳⠄⠙⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣟⠋⠀⠹⣿⣶⣶⣬⣿⣿⣶⣼⠟⣋⡸⠃⠒⠲⢶⣼⣿⣮⣻⣿⣿⡀⠀⠀⠀⠀⣿⣿⣿
⢱⢸⣶⠃⢈⠀⠋⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⠀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠏⠀⠀⠂⢉⡉⡩⣽⣿⠹⣿⣿⣥⡌⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⣾⣇⠀⠀⠀⠀⠉⠉⠉
⠀⣼⣿⠀⠈⠀⢹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠅⠈⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣍⠀⠀⠀⠀⠛⢻⣿⣿⣿⠀⢙⠉⢻⣧⡤⠀⣿⣿⣿⠟⠋⠻⣿⡿⢀⣿⣿⣿⣿⣽⣯⣿⣯
⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⣴⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠒⠀⢘⡏⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠟⠁⠀⢠⣀⠀⠀⢿⣿⣿⡏⠀⠀⠀⠊⠉⠰⠀⠀⠯⡓⢈⡁⠀⠰⠂⠀⣿⣿⠿⠿⠿⠿⠿⠿
⠨⠛⠙⠀⠀⠀⠉⠉⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣦⣤⣤⣧⣤⣄⣀⣀⠀⢠⡾⠿⠿⠛⠉⣁⣤⣶⣾⡿⠁⠀⠀⠈⢿⣿⠀⠀⢀⠀⢀⡀⣴⣆⠀⣀⡠⢸⣷⠀⠀⠀⠀⣹⡏⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⣿⣽⣿⣿⣿⣿⣶⣦⣶⣾⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠸⠏⠀⠀⠐⢂⠈⠻⠛⣽⡄⠉⠁⠠⣿⡀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠒⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠂⢸⣶⣶⣿⣷⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣗⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄⠰⠈⢽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⢿⡇⠀⠀⢸⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣷⣿⢻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣀⣁⣸⣿⣿⠏⠈⠁⠀⠀⠀⡧⠀⠀⠀⠀⠈⠀⢠⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⣿⣿⣾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠖⠋⠙⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣛⣻⣸⢿⣷⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡿⣿⣿⢳⣿⣏⣫⣿⣿⣟⣛⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣹⣿⣿⣟⡿⣿⣿⣿⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣼⡇⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣛⣿⣿⢿⢿⣷⣶⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣴⣶⣶⣦⡄⠀⠀⠀⠀⠀⠁⠀⣤
⠀⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠛⠯⠄⠙⠃⢙⡻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⢿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⣠⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢿
⢠⣿⣿⣇⣿⣿⣿⡯⠢⠪⠸⠝⠿⠹⠀⠀⠀⠱⡶⡄⢈⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠈⠙⠛⠿⠷⠤⣴⣶⣦⢄⣀⠉⢁⣀⣽⣿⣿⣿⣿⣿⣿⡿⠇⠀⢀⠀⠀⠀⠐⢰⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠿⠿⢿⣿⡿⣿⣿⣿⡇⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣀⣉⠛⢛⣛⠛⣿⣿⡿⣿⣿⣿⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣿⣿⣿⢶⡿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣧⠈⣿⠉⣿⠀⣿⢸⡇⣿⣿⡇⢸⣿⡿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢀⠀⣿⢹⣿⣿⣿⢺⣷⣿⣿⣿⣿⠻⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⡀⣿⠀⣿⠀⣿⣸⠇⣿⢹⡇⣾⡿⣿⢸⣇⠀⡌⢩⣿⣿⠀⠀⠀⠀
⠒⠒⠲⠶⠶⠦⠀⠀⠈⠛⠛⠛⠛⠛⠀⠀⠀⠀⢿⣿⣶⣾⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣸⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠛⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⢀⢀⠀⣄⣶⢳⣆⣶⡖⠀⢴⡟⣎⣶⣾⣾⣶⣶⣷⢲⣶⣴⡶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣶⡶⢻⣿⣿⣿⣿⢿⡖⣦⠀⡶⣆⠰⣶⠶⢰⡶⢢⡖⢶⣶⣶⣶⣶⣶⣾⣿⣿
⠀⠇⠸⠀⠇⠻⢸⢸⢸⢸⣿⣿⢸⡿⣿⡏⠀⢨⣝⡯⣿⣿⣟⡯⢿⣿⢸⣟⢻⣯⣬⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⣿⣷⣾⣿⣧⣿⣒⢸⡇⣶⢰⣇⣿⠀⣿⠀⢸⡗⢀⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⢸⢸⢸⣿⣾⢩⢱⡍⠁⠀⠈⠉⢱⣭⢭⣿⣷⣾⣿⣾⣷⣿⣭⣵⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣞⠃⠛⢓⣺⣿⢆⣿⣲⡞⠓⠛⠘⠋⠛⠀⠛⠀⠘⠓⠊⠓⣻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⠘⠈⠀⢿⢿⠸⠘⠇⠀⠀⠀⠀⢠⡯⠀⣿⣿⣿⣻⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⣿⣿⣭⣭⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛
⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡀⡄⠀⠀⢀⠀⠀⠀⢸⡏⠀⣿⡿⣯⣭⣭⣿⠿⠋⣸⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣄⣸⡿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢰⣶⣶⣶
⡇⠀⠀⠀⢸⠀⡇⢸⠘⡇⢸⡇⡇⢰⡇⢸⠀⠀⢀⡜⠓⠈⠁⠀⣿⡛⠛⠁⢀⣿⣿⡏⠀⠀⠈⠉⠛⠋⠉⠛⠛⠛⠛⠛⣻⣿⣿⣻⠿⡿⢿⣿⠟⠒⠒⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⠀⢠⢠⣷⡇⠀⢀⣿⣿⣿
⡇⢸⠀⡇⢸⠀⡇⢸⠀⡇⢸⡇⣷⠀⠀⠸⠐⠊⠁⠀⠀⠀⠀⠀⢸⡿⢆⠄⠾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⣿⣿⣿⠿⠈⠻⣿⣿⣋⣘⣷⣦⣤⢸⣿⠖⠀⡀⣀⣀⠀⠀⣈⠻⣿⣲⡆⠀⠀⠀⠀⢸⣿⣿⣿
⢣⢸⣤⡇⠘⠀⠇⠘⠀⠃⠀⠃⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡞⠆⣴⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠂⠀⢤⠙⠛⢛⣻⣿⠻⣿⣿⡇⢸⠟⠁⠉⣭⣽⣿⣿⣷⣮⢻⣧⠀⠀⠀⠀⠘⠟⠿⠟
⠈⣸⣿⠀⠰⠀⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣁⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣽⠍⠀⠀⠀⠐⠻⣿⣿⣿⠀⠙⠉⢻⣿⣀⠀⢻⣿⣿⣿⣿⣿⣿⣿⢿⣶⣖⣖⣒⣒⣶⣒⣂
⠀⣿⣟⠀⠀⠀⣾⣿⡆⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⢀⠀⢻⡏⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡿⠑⠀⢀⡀⠀⠐⣿⣿⣿⡟⠀⢀⠀⠜⠛⢉⡦⠀⣾⣿⠧⢤⠈⠭⠟⠀⣿⣿⣿⣿⣿⣿⣿⣿
⢰⠿⠣⠀⠀⠀⠛⠛⠃⠀⠉⠉⠙⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣧⣤⣄⣀⣀⠀⢀⡾⠿⠿⠛⠉⣁⣤⣶⣾⡿⠁⠀⠀⠘⣿⣿⠁⠀⢈⠄⠀⠀⢠⣤⠀⠉⠫⠤⣦⠀⠀⠁⠀⢸⡇⠀⠀⠀⠙⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣷⣦⣴⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢸⡟⠀⠀⠘⠅⠸⠿⠿⣿⡆⠸⠗⠀⢾⡀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢤⣀⣤⡄⠀⠀⠘⠁⠀⠀⠀⡐⢩⣤⣤⣿⣷⠀⠀⢸⣿⡇⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡏⣽⣿⣿⣿⣿⣿⣷⣇⠈⠉⠁⠘⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⡇⢀⣤⣿⡇⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣻⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡇⠈⠁⢹⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⡾⣿⣯⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣀⠏⣿⣿⣿⣿⢷⠀⠀⠨⡗⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠂⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡿⣿⣟⣿⣿⣿⣿⢽⡿⣿⣯⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠠⣴⠛⠛⣿⣿⣿⠏⠀⠀⢀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣭⣿⣼⣧⣛⣻⣸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡿⣿⣿⢻⣿⣯⣫⣽⣿⣟⣛⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⠄⠀⠀⠀⠙⠋⠉⠉⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣵⣿⣾⣿⣿⣟⡿⣿⣿⣿⣼⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡇⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⢿⣷⣶⣿⣾⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⣸⡂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠛⠛⠀⠘⠃⢿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⣸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣼⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢾
⠀⠿⠿⠇⣿⠿⠿⡯⠢⠪⠼⠕⠿⠹⠀⠀⠘⢻⠶⡀⢈⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠻⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⢠⣄⠀⠤⣤⣶⣿⣿⣿⣿⣿⣿⡿⠀⠠⡄⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠿⠿⢿⣿⡿⣿⣿⣿⡇⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣀⣙⠛⢛⣛⠛⣿⣿⡿⣿⣿⣿⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣿⣿⣿⢶⡿⣿⣿⣿⣿⣿⣿⣟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣧⠈⣿⠉⣿⠀⣿⢸⡇⣿⣿⡇⢸⣿⡿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢀⠀⣿⢹⣿⣿⣿⢺⣷⣿⣿⣿⣿⠻⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⡀⣿⠀⣿⠀⣿⣸⠇⣿⢹⡇⣾⡿⣿⢸⣇⠀⡌⢩⣿⣿⠀⠀⠀⠀
⠒⠒⠲⠶⠶⠦⠀⠀⠈⠛⠛⠛⠛⠛⠀⠀⠀⠀⢿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣸⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠛⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⢀⢀⠀⣄⣴⢳⣆⣶⡖⠀⢴⡟⣎⣶⣾⣾⣶⣾⣷⢲⣶⣶⡶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣶⡶⢻⣿⣿⣿⣿⢧⡖⣦⠀⡶⣆⠰⣶⠶⢰⡶⢢⡖⢶⣶⣶⣶⣶⣶⣾⣿⣿
⠀⠇⠸⠀⠇⠻⢸⢸⢸⢸⣿⣿⢸⡿⣿⡏⠀⢨⣝⣯⣿⣿⣟⡯⢿⣿⢸⣟⢻⣯⣬⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⣿⣷⣾⣿⣷⣿⣒⢸⡇⣶⢰⣇⣿⠀⣿⠀⢸⡗⢀⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⢸⢸⢸⣿⣾⢩⢱⡍⠁⠀⠈⠉⢡⣯⠩⣿⣷⣾⣿⣾⣷⣿⣭⣵⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣞⠃⠛⢓⣺⣿⣢⣿⣲⡞⠓⠛⠘⠋⠛⠀⠛⠀⠘⠓⠊⠓⣻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⠘⠊⠀⢿⢿⠸⠘⠇⠀⠀⠀⠀⠨⡏⠀⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⣿⣿⣿⣭⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛
⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡀⡄⠀⠀⢀⠀⠀⠀⢲⡃⠀⣿⡿⣯⣭⣭⣿⠟⠃⣸⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣄⣸⡿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢰⣶⣶⣶
⡇⠀⠀⠀⢸⠀⡇⢸⢘⡇⢸⡇⡗⢰⡇⢸⠀⠀⢀⡔⠓⠀⠁⠀⣿⡛⠛⠁⢀⣿⣿⡏⠀⠀⠈⠉⠛⠋⠉⠛⠛⠛⠛⠛⣻⣿⣿⣻⠿⡿⢿⣿⡟⠐⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⠀⢠⢠⣷⡇⠀⢀⣿⣿⣿
⡇⢸⠀⡇⢸⠀⡇⠸⠀⡇⢸⡇⣷⠀⠀⠸⠐⠊⠁⠀⠀⠀⠀⠀⢸⡿⠆⠄⠾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⣿⣿⣿⠿⠊⠻⣿⣿⣋⣘⣷⣶⣤⢸⣿⠶⠀⡀⢀⣀⡀⠀⣈⠻⣿⣲⡆⠀⠀⠀⠀⢸⣿⣿⣿
⢣⢸⣤⡇⠘⠀⠇⠈⠀⠃⠀⠃⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡞⠆⣴⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡟⠂⠀⢤⠙⠛⢛⣻⣿⠻⣿⣿⡇⢸⠟⠁⠉⣭⣽⣿⣿⣿⣮⢻⣧⠀⠀⠀⠀⠘⠛⠿⠟
⠈⣸⣿⠀⠰⠀⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣁⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣯⠉⠀⠀⠀⠐⠿⣿⣾⣿⠀⢙⠉⢻⣿⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢿⣶⣒⣒⣒⣒⣒⣒⣂
⠀⣿⣟⠀⠀⠀⣾⣿⠂⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⢀⠀⢻⡏⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡟⠑⠀⢀⡀⠀⠐⣿⣿⣿⡗⠀⢀⠀⠜⠛⢉⡦⠀⣿⣿⡧⢤⠈⠭⠝⠀⣿⣿⣿⣿⣿⣿⣿⣿
⢰⠿⠣⠀⠀⠀⠛⠛⠃⠀⠉⠉⠙⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣧⣤⣄⣀⣀⠀⢀⡾⠿⠿⠛⠉⣁⣤⣶⣾⡿⠁⠀⠀⠘⣿⣿⠃⠀⠈⠀⠀⠀⢠⣥⠀⠙⡥⠥⣦⠀⠀⠃⠀⢸⡇⠀⠀⠈⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣷⣦⣴⣾⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢸⡟⠀⠀⠸⠃⠸⠿⠿⣿⡆⠸⠗⠀⣻⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢤⣀⣤⡄⠀⡀⠈⠁⠀⠀⠀⡘⢡⣤⣤⣿⣿⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣽⣿⣿⣿⣿⣿⣷⣇⠈⠉⠁⠐⠀⠀⠀⠀⠀⠐⠀⢸⣿⣿⣿⣿⡇⢀⣬⢿⡇⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣻⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡇⠈⠁⢹⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⡾⣿⣯⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣈⠏⣿⣿⣿⣿⢷⠀⠀⠨⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠂⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢽⡿⣿⣧⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠠⣴⠛⠛⣿⣿⣿⠏⠀⠀⢁⠐⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣭⣿⣼⣧⣛⣻⣸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡿⣿⣿⣿⣿⣯⣫⣿⣿⣟⣛⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⠄⠀⠀⠀⠙⠋⠉⠁⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣟⡿⣿⣿⣿⣼⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡇⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⢿⣷⣶⣿⣾⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣾⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⢀⣸⡂⠀⠀⠀⠀⠀⠀⠀⢀
⠀⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠛⠛⠀⠘⠋⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⣸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣼⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢼
⠀⠿⡿⠇⣿⠿⡿⡯⠢⠪⠼⠕⠿⠹⠀⠀⠘⢿⠿⠀⢈⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠻⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⢤⡄⠀⠤⣬⣶⣿⣿⣿⣿⣿⣿⡿⠀⢠⡄⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠉⠛⠻⠿⠿⠿⠿⠿⢿⣿⡿⣿⣿⣿⡏⣥⣤⣤⣄⣀⣀⣡⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣿⣿⡿⣿⣿⢿⣿⣿⡗⣿⣿⣿⢟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣿⣿⣿⢶⡿⣿⣿⣿⣿⣿⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣧⠉⣿⠉⣿⠀⣿⢸⡇⣿⣿⡇⢸⣿⡿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣿⢹⣿⣿⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⠀⣿⠀⣿⠀⣿⣸⠇⣿⢹⡇⣾⣿⣿⢸⣇⠀⠄⢰⣶⡆⠀⠀⠀⠀
⠤⠤⣤⣤⣄⡀⠀⠀⠰⠾⠿⠶⠶⠶⠀⠀⠀⢰⣿⣿⣶⣾⣿⣿⣿⣾⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⢠⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠤⠿⠿⠇⠀⠀⠀⠀
⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⡀⣶⢳⡆⣶⡒⠀⢴⡟⣎⣶⣿⣾⣶⣶⣷⢲⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣶⡶⣾⣿⣿⣿⣿⢳⡖⣦⠀⡶⣆⠰⣶⠶⢰⡿⢠⡖⣶⣤⣤⣤⣤⣤⣤⣤⣤
⠰⡆⢰⠰⡆⣶⣷⢷⢀⣾⣟⣿⢸⣿⣿⡏⠀⢨⣝⣯⣿⣿⣟⡯⣿⣿⢸⡿⣿⣯⣦⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣗⣸⣿⣟⣿⠒⢸⡇⣶⢰⣇⣿⠀⣿⠀⢸⡗⢀⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠀⠁⠀⢽⢸⢸⢹⣿⣾⢉⢹⠉⠁⠀⠈⠉⣑⣯⢹⣯⣥⣽⣥⣬⣵⣬⣭⣵⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⠛⢓⣛⣿⣦⣿⣶⣼⠓⠛⠘⠋⠛⠀⠛⠀⠘⠓⠊⠓⣻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⢸⢸⠘⣿⣿⢨⢸⠀⠀⠀⠀⠀⢸⠟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⣿⣿⣿⣿⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠀⠀⠀⠀⠀⣸⠁⢸⣿⣟⣿⣿⣟⣻⣿⠏⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠀⢸⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⣤⣤⣤
⡀⠀⠀⠀⡇⢸⡆⣶⢸⠀⢸⠀⡇⢠⡄⢰⠀⠀⠀⣽⠅⠘⠋⢹⣿⣿⡿⠋⢨⣾⣿⡇⠀⠉⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⢿⣿⣿⣿⣿⡷⠤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⣠⠈⠁⢹⣿⣿⣿
⡇⡆⢰⠀⠇⢸⡇⢸⢸⠀⢸⡀⡇⠈⠁⢸⠠⠔⠂⠁⠀⠀⠀⠈⣿⣦⠀⣀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⢶⣶⣿⣿⠿⠝⢻⣶⣞⣛⣸⣦⣤⣄⢹⣷⡤⢀⠀⠀⠀⠀⠀⠡⣧⣤⣀⠘⠘⠙⠀⠀⢸⣿⣿⣿
⡇⡇⢸⡂⠢⠀⡇⢸⢸⠀⠸⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡇⠄⣨⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡏⠀⠀⣤⠛⠛⠛⣿⣿⢿⣿⣿⡃⢲⣾⠃⠙⠛⠳⣾⣿⣮⡻⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿
⠊⣹⡟⠀⠤⠀⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠁⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⡶⡀⠀⠀⠘⠛⢿⣿⣿⣃⠈⢿⠛⣶⣿⡁⠀⢺⣿⣿⣿⣿⣿⣿⣮⣧⣀⣀⣀⣀⣀⣤⣤⡄
⠀⣿⡇⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠋⠀⠀⠀⡀⠀⢰⣿⣿⣿⡇⠀⠀⢀⠿⠿⠋⣡⠀⣿⣿⡏⡙⠻⠿⢿⢽⣿⣿⣿⣿⣿⣿⣿⡇
⢰⣿⣇⠀⠀⠀⣿⢿⠀⠐⢛⣛⡿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣬⣤⣤⣽⣤⣤⣄⣀⣀⠀⣰⠿⠿⠿⠛⠉⣁⣤⣶⣾⡿⠁⠀⠀⢻⣿⡿⠀⠀⠠⠀⠀⢠⣬⣥⠀⠙⢫⠃⣌⠈⠩⠔⠈⣿⣛⢛⣛⣛⣛⣛⡇
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣟⣿⣿⣿⣾⣦⣴⣾⣿⣿⣿⣿⡟⠀⠀⠄⠀⠘⣿⠃⠀⠘⣗⠀⢿⢿⣿⣿⡆⢰⡶⠈⣾⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⡀⠀⡀⢘⣄⠈⠋⠀⠀⠀⠀⠘⣿⣠⣶⣿⣷⠀⠀⠰⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣎⠸⠋⠨⣦⣠⠀⠀⠀⠀⡁⢰⣿⣿⣿⣿⣿⡀⢀⡸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡻⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣽⣿⣿⣿⣿⣿⣿⣿⣷⣄⠈⠍⠀⠀⠀⠀⠀⠀⡘⢻⣿⣿⣿⣿⡇⠘⠁⢿⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢈⣾⡶⢹⣿⣿⣿⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢽⡿⣿⣷⣿⣿⣾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢠⡜⠛⢻⣷⣾⣿⣿⡟⠋⠁⠀⠄⢸⣿⠀⠀⠀⠀⠀⠺⠧⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣭⣿⣼⣿⣛⣻⣸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠁⠀⠬⢿⣿⣿⡿⠀⠀⠀⠁⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⣯⣫⣿⣿⣟⣛⣿⣿⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⠀⠀⠰⠿⠷⠛⠛⠇⠀⠀⠀⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣽⣿⣿⣿⣷⣟⡿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡇⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⢿⣷⣶⣿⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣣⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠛⠛⠀⠘⠣⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⣤⣤⣿⣷⠀⠀⠀⠀⠀⠀⢠⣤⣤
⠀⠿⠿⠇⣽⢿⡿⡯⠢⠪⠸⠕⠿⠱⠀⠀⢻⣿⣿⢥⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠸⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⢀⣀⡀⢀⣐⣒⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠻⠿⢿⠿⠿⠿⠿⢿⣿⠿⣿⣿⣿⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣋⣁⣀⣠⣄⣈⣉⣉⣉⣉⣉⣉⣉⣉⣉⣿⣿⡿⣿⣿⣿⣿⣿⡟⣿⣿⣿⢟⡋⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣿⣿⣿⢶⡿⣿⣿⣿⣿⣿⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣧⠋⣿⠉⣿⠀⣿⢸⡏⣿⣿⡇⢸⣿⡏⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⣿⣿⣿⢺⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⠀⣿⠀⣿⠀⣿⣸⠇⣿⢹⡇⣾⣿⣷⢸⣇⠀⠤⢤⣤⡄⠀⠀⠀⠀
⢀⣀⣀⣀⣀⡀⠀⠀⠤⣴⣧⣤⢶⡖⠀⠀⠀⢸⣿⣿⣶⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣶⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⣀⣿⣿⡇⠀⠀⠀⠀
⠀⠚⠛⠉⠉⠁⠀⠀⠀⠀⠀⣶⢳⡆⣶⠒⠀⢴⡟⣎⣶⣷⣾⣶⣶⣷⢲⣶⣶⣶⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡶⣾⣿⣿⣿⣿⢣⡖⣦⠀⡶⣆⠰⣶⠶⢰⡷⢢⡖⣶⣀⣀⣀⣀⣀⣤⣤⣤
⢰⡀⢠⢠⡄⡆⡇⡆⠂⣾⣿⣿⢸⣷⣿⡉⠀⢨⣝⣿⣿⣿⣟⡯⣿⣿⢸⣿⣿⣯⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡗⣸⣿⡟⣿⢒⢸⡇⣶⢰⣇⣿⠀⣿⠀⢸⡗⢀⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠁⠈⠈⠁⠁⣧⢿⢠⣿⣿⣮⠉⢹⠉⠀⠀⠈⢩⢱⣯⢹⣬⣥⣽⣭⣬⣩⣭⣽⣵⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⠃⠛⢓⣾⣿⣦⣿⣲⣼⠓⠛⠘⠋⠛⠀⠛⠀⠘⠓⠊⢓⣻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⢸⢸⢻⣿⣿⠀⢸⠀⠀⠀⠀⠀⢞⡋⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠋⠉⠀⠈⠀⠀⠀⠀⠀⢸⠄⢸⣿⣿⡿⠾⢿⣿⣿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⠀⠹⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢁⡉⣉⣉⣀⣀
⠀⠀⠀⠀⡆⢸⠀⡄⢰⠀⢶⠀⡇⢠⡄⡆⠀⠀⠀⡨⡀⡸⠛⢹⣿⣿⣿⠏⢩⣾⣿⠀⠈⠛⠯⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⢠⠈⠁⢻⣿⣿⣿
⡀⡄⢠⠀⡇⢸⡅⣇⢸⠀⢸⠀⡇⠘⠃⢃⡠⠤⠒⠉⠀⠀⠀⠸⣷⣄⠀⢀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢶⣶⣶⣿⣿⡿⠙⢷⣿⡾⠟⢱⣤⣀⡈⢿⣦⡀⠀⠀⠀⠀⠀⠀⢂⣦⣀⠀⠘⠚⠚⠀⠀⢸⣿⣿⣿
⡇⡇⢸⠀⡇⢸⡇⢸⢸⠀⢸⠀⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣭⢘⠈⢙⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠂⠀⣄⠛⠛⠻⣿⣿⣿⣷⣾⠋⢵⣴⠟⠒⠓⢶⣾⣶⣝⢿⣿⡆⠀⠀⠀⠀⢸⣿⣿⣿
⠏⣽⡞⠀⡀⢈⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⡶⠂⠀⠀⠀⠒⢲⣾⣿⡇⠘⠿⠛⣶⣾⡏⠀⢰⣾⣿⣿⣿⣿⣷⣝⣇⣀⣀⣀⣀⣈⣉⣉⡉
⢠⣿⡇⠀⠀⢀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠹⣿⡇⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡿⠋⠀⠀⠀⡀⠀⢰⣿⣿⣿⠇⠀⠀⢀⠿⠿⠟⢃⠀⢹⣿⡿⠿⢿⣿⣿⢹⣿⣷⣶⣶⣶⣶⣶⡆
⢸⣿⡇⠀⠀⠸⣿⣿⠀⠒⢶⣶⡖⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣿⣤⣤⣄⣀⣀⢀⡼⠻⠿⠿⠛⠉⣀⣤⣶⣾⡿⠁⠀⠀⢿⣿⡏⠀⠀⠀⠀⠀⢀⣈⣡⠀⠘⣧⡇⡑⠀⢂⡩⠘⣟⠛⠛⠛⢛⣿⣻⠃
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣽⣟⣿⣿⣿⣶⣦⣴⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⢸⡿⠁⠀⣰⣂⢀⣿⣿⣿⣿⡂⢠⣧⠀⣿⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡟⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠀⠀⠀⢡⡀⠘⠀⠀⠀⠀⠐⢺⣟⣸⣼⣿⣧⠀⠁⢠⣾⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣷⠼⠃⠈⠁⡀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠀⠀⢼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢷⣾⣿⠻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠁⠀⠀⠀⠀⣀⡟⢿⣿⣿⣿⣿⠀⠛⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣷⣿⢾⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⡾⣿⣯⣯⣿⣻⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⡸⢶⣶⢻⣿⣿⣿⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠐⣀⢀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⡿⡿⣿⣿⣿⣿⣿⣿⢽⡿⣿⣧⣿⣿⣼⡿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣤⠿⠿⣷⣶⣶⣾⣿⡿⠛⠀⢀⡀⢸⡇⠀⠀⠀⠀⠠⣶⡆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣭⣿⣼⣧⣛⣻⣸⢿⣇⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⢁⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡿⣿⣿⢿⣿⣏⣫⣽⣿⣟⣛⣿⡿⠿⣷⣾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣇⢠⡀⠐⠂⢶⠮⡽⠿⠿⠆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣽⣿⣾⣿⣷⣟⡿⣿⣿⣿⣼⣛⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡆⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣟⣿⣿⢟⢿⣷⣖⣿⢺⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢲⣺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠛⠛⠀⠘⢣⣾⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢋⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⣀⣠⣼⡇⠀⠀⠀⠀⠀⠀⣀⣄⣠
⠀⠿⠿⠇⣽⠿⠿⡯⠢⠪⠸⡵⠿⠱⠀⠈⣿⣿⣿⣤⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⣿⣶⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠉⠋⠙⠛⠛⠛⠻⠛⠿⠿⠿⢿⠿⠿⠿⠿⢿⣿⠿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⣛⣛⣛⣋⣉⣉⣉⣛⣛⣛⡛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢿⡛⠛⠛⠛⠛⠋⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣿⣿⣟⢶⡿⣿⣿⣿⣿⣿⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣯⠋⣿⠉⣿⠁⣿⢹⡏⣿⣿⡇⢸⣿⡏⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⣿⣿⣟⢺⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠀⣿⠀⣿⠀⣿⣸⠇⣿⢹⡇⣾⣿⣷⢸⣇⠀⣀⣀⣀⡀⠀⠀⠀⠀
⠀⠀⠀⡀⠀⠀⠀⠀⣠⣴⣆⣀⣠⡄⠀⠀⠀⢸⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢨⠀⣾⣿⡇⠀⠀⠀⠀
⠉⠉⠛⠛⠛⠀⠀⠀⠀⠉⠉⣷⢻⡆⣶⠒⠀⢴⡟⣎⣶⣿⣾⣶⣶⣷⢲⣶⣶⣶⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡶⣾⣿⣿⣿⣿⢠⡖⣦⠀⡶⣆⠰⣶⠶⢰⡷⢢⡖⣾⢉⣉⣉⣁⣀⣀⣀⣀
⢠⠀⡄⢠⠀⡄⡆⡄⡆⣸⣷⣿⢺⡷⣿⠉⠀⢨⣝⣯⣿⣿⣟⡯⣿⣿⢸⣿⣿⣯⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡗⢿⣿⡿⣿⠶⢸⡇⣶⢰⣇⣿⠀⣿⠀⢸⡗⢀⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠘⠀⠃⠘⠀⠃⡇⡇⠇⣿⣿⡏⡍⢱⠉⠀⠀⠈⠉⢵⣯⣿⣍⣁⣿⣍⣈⣩⣭⣭⣵⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡚⠃⠛⢓⣾⣿⣦⣟⣒⣘⠓⠛⠘⠋⠛⠀⠛⠀⠘⠓⠊⢓⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣧⣷⠀⣿⣿⡇⠃⢸⠀⠀⠀⠀⠀⣹⠯⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⣽⣿⡿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠉⠈⠈⠈⠛⠃⠀⠘⠀⠀⠀⠀⠀⣸⠄⢸⣿⣿⣯⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⢀⠸⣿⣿⣿⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⣉⠉
⠀⠀⠀⠀⡄⣶⠀⡄⢠⠀⣦⢰⡀⣀⠀⡆⠀⠀⠀⣟⠀⣸⠛⣿⣿⣾⣿⠟⢡⣶⣿⠈⠙⠿⣽⣽⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣯⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢻⣿⣿⣿
⠀⡄⢠⠀⡇⢿⠀⡇⢸⠀⣿⢸⡇⠛⠃⡇⣀⡠⠜⠉⠀⠀⠀⢸⣯⡉⠁⢀⣾⣿⣿⠀⠀⠀⠀⠀⠁⠀⠀⠀⠤⣤⣤⣭⣿⣿⡾⠙⢾⣯⡽⠿⢫⣄⡉⠀⢲⣄⡀⠀⠀⠀⠀⠀⠀⠄⣄⠀⠀⠆⠿⠿⠀⠀⢸⣿⣿⣿
⠀⡇⢸⠀⡇⢸⠀⡇⢸⠀⢹⠈⡇⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⡨⠉⠛⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡟⠀⠀⡌⠛⠻⢿⣿⣿⣿⣿⣼⠛⣥⣤⡷⠰⢶⣤⣴⣦⡹⣿⣶⡄⠀⠀⠀⠀⢸⣿⣿⣿
⠖⣷⡞⠀⡁⠘⡀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠐⢼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⡶⠅⠀⠀⠹⠒⢶⣶⣾⡏⠸⢿⠺⣤⣾⠟⠀⢠⣶⣾⣿⣿⣿⣮⡻⡇⠀⠀⠀⠀⠙⠛⠛⠉
⢰⣿⡇⠀⠁⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅⠄⠈⢿⣿⠇⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠉⠀⠀⠀⡀⠀⢰⣿⣿⣿⡯⠀⠑⠀⣿⣿⠷⠀⠀⢿⣿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡄
⢸⣿⠃⠀⠀⢸⣿⡟⠀⠤⠶⠶⡖⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣿⣤⣤⣄⣀⣀⣠⠞⠻⠿⠿⠛⠉⣀⣤⣴⣾⡿⠁⠀⠈⣿⣿⡟⠀⠀⠀⠀⠀⢀⣐⣊⠀⠹⡿⣇⠢⠈⠍⣛⢸⡿⠿⠿⠿⠿⠿⢿⠆
⠋⠉⠁⠀⠀⠀⠉⠁⠀⠀⠈⠉⠁⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⣿⣽⣿⣿⣿⣿⣶⣦⣴⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⢸⣿⠁⠀⢰⠀⢰⣶⣾⣿⣿⠀⢀⡂⢉⣷⠀⠈⠁⠀⡋⠉⠈⠉⠉⠉⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⡿⣿⢸⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⢤⠀⠚⠁⠀⠀⠈⠡⢼⡟⢹⣽⣿⡇⠈⠁⢨⣿⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣦⣰⠂⢀⠃⡀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡇⠀⠀⢼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣿⠻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣷⣄⠈⠘⠃⠀⠀⠐⠄⢠⡿⣿⣿⣿⣿⣷⠐⠶⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣷⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⡾⣿⣯⣯⣿⣻⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠠⠈⡋⣶⡎⢿⣿⣿⣷⠀⠀⠠⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣟⣿⡿⣿⣿⣿⣿⣿⣿⢽⡿⣿⣧⣿⣿⣼⡿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢀⡸⠷⢿⣤⣬⣷⣼⣿⡿⠻⠀⠀⠀⢹⡇⠀⠀⠀⠀⢡⣤⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣭⣿⣼⣧⣛⣻⣸⢿⣇⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠉⠀⣸⣿⣿⣿⣿⠟⠀⠀⠀⠈⠀⠸⠇⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡿⣿⣿⢻⣿⣏⣫⣿⣿⣟⣛⣿⡿⠿⣷⣾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣃⢀⠀⠲⢰⣾⣭⣹⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡀⠈⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣽⣿⣾⣿⣷⣟⡿⣿⣿⣿⣜⣻⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡆⠙⠻⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣧⣟⣿⣿⠟⢿⣷⣆⣿⢪⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢲⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠛⠛⠀⠘⢣⣴⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣽⣿⣿⣿⣿⣿⣿⡿⠿⢻⣿⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢂⢀⠀⣠⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠿⠿⠇⣽⠿⠿⡯⠢⠪⠸⡵⠿⠱⠀⠘⣿⣿⣶⣤⣈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⣾⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢴⣧⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢸⣿⣾⣿
⠀⠀⠀⠐⠠⠈⠹⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⢿⡿⠿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⣛⠛⠻⠛⢟⡛⣛⠛⣛⡛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⡨⣿⣿⣿⢿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣿⣿⣿⢶⡿⣿⣿⣿⣿⣿⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣯⠋⣿⠉⣿⠁⣿⢹⡟⣿⣿⡇⢸⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⣿⣿⣟⢺⣷⣿⢿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠀⣿⠀⣿⠀⣿⣸⠇⣿⢻⡇⣾⣿⣷⢸⣇⠀⣀⣀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣆⣀⢀⡄⠀⠀⠀⣾⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⢸⠀⣿⣿⠇⠀⠀⠀⠀
⠠⠶⠖⠓⠒⠀⠀⠀⠉⠉⠉⣷⢻⡆⣶⠒⠀⢴⡟⣎⣶⣿⣾⣶⣶⣷⢲⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⣾⣿⣿⣿⣶⢠⡖⣦⠀⡶⣆⠰⣶⠶⢰⡷⢢⡖⢾⠈⠉⠉⠀⠀⠀⠀⠀
⢠⠀⡄⢠⢀⡀⡆⡄⡄⢸⣶⣿⢸⡇⣿⡉⠀⢨⣝⣯⣿⣿⣟⡯⣿⣿⢸⣿⣿⣯⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡗⣿⣿⣿⣿⣶⢸⡇⣶⢰⣇⣿⠀⣿⠀⢸⡗⢀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠘⠀⠃⠘⠈⠃⡇⡇⡇⣾⣿⡎⡍⢷⠉⠁⠀⠈⠍⣵⡏⣿⣉⣑⣿⣉⡈⣙⣭⣭⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⠃⠛⠓⣞⣛⣦⣛⡒⠘⠓⠛⠘⠋⠛⠀⠛⠀⠘⠓⠊⢓⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡇⡇⠃⣿⣿⡇⡇⢿⠀⠀⠀⠀⠀⢬⠕⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣟⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠁⠁⠀⠙⠟⠇⠃⠛⠀⠀⠀⠀⠀⣸⠁⢸⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠘⢿⣯⣭⣥⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⡀⣶⠀⡀⣀⠀⡆⢰⠀⠀⠀⡆⠀⠀⠀⡳⠀⢸⠟⣿⣶⣶⣿⠟⢑⣼⣿⠉⠻⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣴⣾⡛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠲⣿⣿⣿⣿
⢀⠀⢀⠈⡇⣿⠀⡇⣻⠀⡇⢸⠀⠿⠀⡇⢀⡀⠔⠋⠁⠀⠀⢻⣟⠋⠁⢀⣿⣿⣿⠀⠀⠀⠈⠉⠉⠉⠉⠉⣭⣭⣭⣭⣿⣿⣿⠝⢾⣯⡥⣿⢟⣍⡀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠆⠷⠇⠀⠀⣿⣿⣿⣿
⠨⠀⢸⠀⡇⣿⠀⡇⢸⠀⣷⢸⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠸⣿⢋⠰⠙⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⣟⠁⠀⣄⠿⠿⢷⣾⣿⣿⣿⣴⡟⢣⡄⣿⢠⣶⣤⣶⣤⢻⣿⣦⡄⠀⠀⠀⠀⣿⣿⣿⣿
⠆⣷⡞⠀⠁⠘⠀⠁⠈⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠊⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣭⠉⠀⠀⠹⠒⣶⣶⣾⣿⠙⣿⡿⣥⣼⡟⠀⢀⣤⣭⣿⣿⣷⣯⢿⡇⠀⠀⠀⠀⠛⠛⠛⠛
⢰⣿⡇⠀⠁⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠘⢿⣿⠃⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡿⠋⠀⠀⠀⡀⠀⣰⣾⣿⣿⡏⠀⠈⠀⣿⣿⡷⠄⠀⢿⣿⣿⣿⣿⣿⣷⣾⣯⣤⣾⣭⣭⣭⣽⠀
⣸⣿⠀⠀⠀⣻⣿⡇⠀⠤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣥⣥⣤⣬⣿⣤⣤⣄⣀⣀⣀⡞⠻⠿⠿⠛⠉⣀⣤⣴⣾⡿⠁⠀⠸⣿⣿⡟⠁⠀⠀⠈⠀⠀⠐⣊⠀⠾⠿⡗⠬⠩⠿⠏⢸⡿⠿⠿⠿⣿⣿⣿⠀
⠍⠉⠂⠀⠀⠈⠉⠁⠀⠀⠈⠉⠁⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣽⣿⣿⣿⣿⣶⣦⣴⣾⣿⣿⣿⣿⡟⠀⢀⠀⠀⢸⣿⠇⠀⢰⡀⢰⣶⣾⣿⣿⠀⢐⡀⢩⣇⠀⠘⠃⠘⠃⠀⠀⠀⠀⠀⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣺⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠈⣦⡀⠸⠁⠀⠀⠈⠉⢼⡟⣻⣽⣿⡄⠙⠃⢨⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣠⠂⣿⣗⡃⠀⠀⠀⠐⠀⣾⣿⣿⣿⣿⡇⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⡿⠇⠀⠀⠘⠀⢠⡿⣿⣿⣿⣿⡇⠰⡦⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣷⡾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠟⣴⡌⣿⣿⣿⠇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⣿⣿⣿⣿⣿⣿⢽⡿⣿⣧⣿⣿⣾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢀⣰⡶⢶⣤⣭⣥⣼⣿⠿⠆⠀⠀⠘⣿⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣭⣿⣼⣧⣛⣿⣸⢿⣷⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⠃⢀⣸⣿⣿⣿⣿⠏⠀⠀⠀⠃⠈⢿⠀⠀⠀⠀⠀⠻⠛⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡿⣿⣿⢿⣿⣏⣫⣿⣿⣟⣛⣿⡿⢿⣿⣾⣯⣿⣿⣿⣿⣿⣿⣿⣿⡃⢀⠀⠆⢴⣮⣙⣿⣿⡇⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣽⣿⣿⣿⣷⣟⡿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢰⣾⡇⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣟⣿⣿⣿⢿⣷⣶⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢲⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠛⠛⠀⠘⢫⣴⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣯⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣷⣾⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⣠⡇⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀
⠀⠿⠽⠇⣽⡿⠿⡯⠢⠪⠸⡵⠿⠱⠀⢹⣿⣿⣶⣤⣈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣾⣤⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢿⣿⣾⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 1980

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/07/15/the-epo-plot-twist/#comments
    Gemini version at gemini://gemini.techrights.org/2022/07/15/the-epo-plot-twist/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.15.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_Plot_Twist⠀✐


Posted in Europe, Patents at 1:47 am by Dr. Roy Schestowitz


Oliver_Twist reference


          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Meme: Please sir may I have some more?⦈
  Papa António, will you feed poor, orphaned states in exchange for votes in
                         favour of illegal proposals?


Summary: The current EPO does not and cannot operate properly anymore; the sole
goal is milking it to death by giving millions of illegal European Patents (in
violation_of_the_European_Patent_Convention)


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⣼⡏⠀⠀⠀⠀⠀⠀⠹⣿⣿⣇⠀⠀⠙⢟⡉⠈⣫⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⢀⣀⠀⠀⢀⠀⠀⠀⣼⣿⣿⡀⠀⠀⠀⢻⡟⠛⣷⡈⣿⠛⠀⠀⠘⣿⠛⠛⠇⠛⢠⣿⡆⠀⢠⡞⠉⢻⣸⣿⣿⣿⣿⡀⠈⠉⢀⣿⣿⣿⣿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⠇⠀⠀⠀⢸⣧⣤⠟⠀⣿⠀⠀⠀⠀⣿⠶⡿⠀⢀⣿⣀⣿⡀⠈⠛⠷⣤⣿⣿⣿⣿⣿⠇⢀⡀⣾⣿⣿⣿⡆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⢟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣍⡛⢿⣿⠉⠁⠀⠀⠀⠀⣼⣧⡄⠀⢀⣿⣤⣤⣾⢀⣿⣤⣤⣶⣼⣏⠉⣹⣧⡸⣧⣠⣼⣿⣿⣿⣿⣿⣦⣶⡎⢿⣿⣿⣿⣿⠀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣏⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠀⠀⠀⢰⣿⠏⠻⣿⣿⣿⣿⣿⣷⣦⣹⡏⢻⣿⡇⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢠⡿⣇⠀⠈⣿⣧⡀⠉⡏⣸⠉⣹⡏⢹⣇⣾⠋⠉⢷⡄⢹⣿⣟⠈⢹⠩⣽⣿⣿⣿⣿⣿⣿⣿⡎⢿⣇⣀⣤
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣾⣀⣻⡄⠀⣿⠈⢷⡄⡇⠀⠀⢸⣷⣶⢼⣇⠀⠀⢸⡇⢸⡇⠻⣧⣸⠀⢸⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠼⠧⠀⠨⠷⠤⠿⠄⠈⠻⠇⠀⠠⠼⠧⠄⠈⠻⣤⡤⠞⠁⠼⠧⠀⠘⠿⠀⠼⠿⠄⠹⢧⣽⡿⢿⣿⣿⣿⠟⠉
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠤⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣄⣀⣤⣤⣀⢀⣀⣤⣠⣤⣶⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠈⠀⠀⠀⠀⠀⠸⢿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠻⣿⣿⣿⣿⣿⣿⡿⠉⠈⠉⠛⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⢻⣿⣿⢿⣟⠁⠀⣀⣀⣀⣀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⡀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⢬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⢿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⠿⠞⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠩⠿⣿⢿⣿⠛⠏⠀⠂⠀⠀⠀⠀⣀⣴⠁⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣧⣤⣮⣿⡄⠀⠀⠁⢀⣀⣴⣇⣈⠁⠀⠀⠀⠀⠀⢸⣿⣿⡿⢿⣿⡟⢹⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⣶⠸⣿⣿⣿⣿⣧⣴⣶⣿⣿⣿⣿⡍⠙⢧⡀⣿⣿⣦⡀⠀⠀⠁⠀⠈⠉⠛⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣍⣉⣝⣻⠛⠓⠒⠒⠤⠄⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠸⣿⣿⣿⣿⣿⣟⣷⣀⠈⢿⣿⣿⣿⡄⠈⢻⣞⣿⣿⢀⠀⠀⠀⠀⠀⠀⢀⠀⠩⣿⡿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡇⠀⠀⣀⡴⠒⠋⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⡠⡛⢿⣿⠀⢠⣄⣉⣹⣷⣄⡙⣿⣿⣧⠀⠀⢻⣿⣿⣄⢂⣀⡀⠀⠀⠀⠈⠀⢀⡀⠀⢀⣠⣄⠈⠉⠙⠛⠛⠿⠿⠿⠿⠿⠿⠯⣭⣧⣴⠯⠥⠤⠶⠒⠫⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡟⢛⣤⣼⣸⡇⡀⠉⠻⣿⣿⣿⣷⡘⢿⣿⡆⠀⠀⢻⣿⣿⣿⣿⡧⠀⢀⡀⣰⣴⡞⠑⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣾⣿⣿⠁⠀⢀⡤⠒⠉⣩⣽⣿⣷⣜⢿⣧⠀⠀⠀⣻⣿⣿⣯⣿⣥⣾⣿⡿⠍⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⢆⠀⣨⡤⠔⠓⢒⣺⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣘⣿⣿⣿⣿⣿⡿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣤⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠈⠈⢁⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡏⣃⣠⣾⣿⣯⡿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⣁⣀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⣶⣦⡄⠋⢻⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠼⡀⠀⠀⠸⠛⣿⣿⣿⣿⣿⣿⡿⠛⠟⠛⠋⠁⠐⠙⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⣶⠀⠀⠸⠀⠀⠀⠈⢻⣿⠟⠀⠀⠀⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⡀⠐⠾⠆⠀⠀⠾⠅⠛⠃⠀⠀⠀⢸⠉⣿⢰⠇⣿⠀⠀⣾⣀⣿⡀⠀⠘⣧⠏⠀⠀⠀⢸⣿⠫⣻⣷⢸⡿⠶⠶⣿⠀⢠⣏⣺⣧⡀⠈⣿⡀⡾⠀⢸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣠⣤⣶⣦⣄⣰⡀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡄⠸⠟⢀⣼⣧⣼⣏⠉⢹⣧⡀⢠⣿⣤⠀⠀⠀⣼⣿⡀⠙⠉⣼⣧⠀⢠⣿⣤⣾⡍⠉⣽⣷⡆⣘⣿⠣⣄⣾⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠴⠏⠁⣿⣿⣿⠷⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢰⡏⠉⠿⢀⣾⠋⠉⢳⡄⢉⡿⣇⠀⣸⣿⠉⠈⣿⠉⠉⠇⠀⠀⠉⡿⣇⠁⣼⣿⠉⢠⡾⠉⠙⣷⡄⢹⡏⠉⣿⠄⢹⣯⣭⡽⠃⠀⢀⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⢸⡇⠀⠀⢸⡇⢸⡇⢻⣤⠇⢸⡆⠀⣿⠒⠿⠀⠀⠀⢸⡇⢻⣤⡏⢸⡇⢸⡇⠀⠀⣼⡇⢸⡗⢶⣏⠀⢸⡗⠒⠇⠀⠰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⡤⠟⠀⠻⢤⡤⠞⠡⠼⠤⠈⠿⠀⠼⠧⠤⠿⠤⠤⠾⠀⠠⠼⠥⠈⠿⠀⠼⠧⠌⠳⢤⡤⣿⡆⠼⠧⠄⠻⠦⠼⠧⠤⠴⠇⠰⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣀⣀⣠⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 2048

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.15.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_15/07/2022:_Inkscape_1.2.1_is_Out,_BMW_Joins_Yocto_Project⠀✐


Posted in News_Roundup at 5:40 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Desktop/Laptop
          o Audiocasts/Shows
          o Kernel_Space
          o Graphics_Stack
          o Applications
          o Instructionals/Technical
          o Games
          o Desktop_Environments/WMs
                # GNOME_Desktop/GTK
    * Distributions_and_Operating_Systems
          o SUSE/OpenSUSE
          o Fedora_Family_/_IBM
          o EasyOS
          o Debian_Family
          o Canonical/Ubuntu_Family
          o Open_Hardware/Modding
    * Free,_Libre,_and_Open_Source_Software
          o Content_Management_Systems_(CMS)
          o Programming/Development
                # Perl_/_Raku
    * Leftovers
          o Hardware
          o Proprietary
          o Pseudo-Open_Source
                # Openwashing
          o Security
                # Privacy/Surveillance
          o Environment
                # Energy
          o Civil_Rights/Policing
    * § GNU/Linux⠀➾


          o ⚓ MIT Technology Review ☛ The_Download:_open_source_insecurity,_and
            gene_editing_plants [Ed: DARPA/DoD taking CoC up a notch these
            days; they'll soon demand that only Pentagon-approved coders can
            develop Free software that the US adopts for use. Of course they
            conveniently overlook the simple fact that proprietary software,
            both domestic and foreign, tends to have back doors one cannot
            detect or remove.]⠀⇛


                 It’s not much of an exaggeration to say that the whole
                 world is built on top of the Linux kernel—although most
                 people have never heard of it.


                 It is one of the very first programs that load when most
                 computers power up. It enables the hardware running the
                 machine to interact with the software, governs its use of
                 resources, and acts as the foundation of the operating
                 system.


                 It is the core building block of nearly all cloud
                 computing, virtually every supercomputer, the entire
                 internet of things, billions of smartphones, and more.


                 But the kernel is also open source, meaning anyone can
                 write, read, and use its code. And that’s got
                 cybersecurity experts inside the US military seriously
                 worried. Its open-source nature means the Linux
                 kernel—along with a host of other pieces of critical
                 open-source software—is exposed to hostile manipulation
                 in ways that we still barely understand. Read the full
                 story.


          o § Desktop/Laptop⠀➾


                # ⚓ Tom’s Hardware ☛ Tuxedo_Launches_Liquid-Cooled_Linux_Laptop
                  |_Tom’s_Hardware⠀⇛


                       Tuxedo may not be a household name for many of us,
                       but it is one of the well-known suppliers of high-
                       performance Linux-based laptops from Germany.
                       Earlier this year, the company introduced its
                       Stellaris 15 Gen4 notebook aimed at performance-
                       demanding users with an optional external liquid-
                       cooling system. To great surprise, Tuxedo only
                       offered the machine with Windows, but this week the
                       company finally began to offer it with Linux,
                       reports Phoronix.


                       The Tuxedo Stellaris 15 Gen4 is a very powerful
                       desktop replacement gaming laptop designed by
                       Clevo. It comes packing up to Intel’s Intel Core
                       i9-12900H processor mated with two DDR5 memory
                       modules and two PCIe 4.0 x4 M.2 SSDs as well as
                       Nvidia’s GeForce RTX 3080 Ti graphics chip. The
                       machine uses a 15.6-inch display with a 2560×1440
                       resolution and 240Hz refresh rate to maximize the
                       gaming experience.


                # ⚓ Ghacks ☛ Google_releases_Chrome_OS_Flex_for_PCs_and_Macs_–
                  gHacks_Tech_News⠀⇛


                       Chrome OS Flex is a special version of Google’s
                       Chrome OS that is bringing the operating system to
                       Windows PCs and Apple Macs.


                # ⚓ Chrome Uboxed ☛ How_to_switch_your_ChromeOS_Linux_container
                  from_Debian_to_Ubuntu⠀⇛


                       Linux on ChromeOS, a.k.a. Crostini, has been out of
                       beta and available for quite some time. Users that
                       want to leverage the flexibility and power of a
                       Linux environment have access to a Linux terminal
                       that opens the door to a plethora of executable
                       packages that aren’t readily available on ChromeOS
                       proper. Whether you’re looking to install an
                       alternative browser or install powerful app
                       development software, Linux on ChromeOS makes that
                       chore a breeze.


                       By default, the Linux container on ChromeOS runs
                       the stable and secure distro known as Debian. More
                       specifically, Debian 11 or “Bullseye.” While Debian
                       offers many of the tools that Linux users are
                       looking for, other distros offer up more
                       flexibility and access to a wider range of packages
                       without the need to add extra repositories.


          o § Audiocasts/Shows⠀➾


                # ⚓ Linux in the Ham Shack ☛ LHS_Episode_#474:_Shocker_|_Linux
                  in_the_Ham_Shack⠀⇛


                       Hello and welcome to Episode 474 of Linux in the
                       Ham Shack. In this short-topics episode, the hosts
                       discuss the utility of electrostatic discharge
                       protection, the continued relevance of Field Day,
                       the next QSO Today Virtual Ham Expo, Microsoft and
                       its impact on Open Source, the Software Freedom
                       Conservancy, WSJT-X and much more. Thank you for
                       tuning in. We hope you have a great week.


                # ⚓ DragonFly BSD Digest ☛ BSD_Now_463:_The_1.0_Legend_–
                  DragonFly_BSD_Digest⠀⇛


                       This week’s BSD Now gets into some history, as you
                       can guess from the title.


                # ⚓ Video ☛ deepin_20.6_Quick_overview_#linux_#deepin_#Shorts_–
                  Invidious⠀⇛


                       A Quick overview of deepin 20.6


          o § Kernel Space⠀➾


                # ⚓ Tom’s Hardware ☛ Initial_Intel_Meteor_Lake_iGPU_Support
                  Queued_for_Linux_5.20_|_Tom’s_Hardware⠀⇛


                       Intel developers have submitted Meteor Lake
                       graphics patches that are ready to be merged into
                       the next version of the Linux Direct Rendering
                       Manager (DRM-Next). Once completed, Linux 5.20 will
                       offer initial Meteor Lake graphics support. This is
                       yet another development that points to Meteor Lake
                       being on track, despite some whispers from the
                       rumor mill that it might be delayed.


                       Linux-centric news site Phoronix observed Intel
                       posting Linux driver patches for Meteor Lake
                       support earlier this month. Now, these patches are
                       queued for addition to the i915 kernel graphics
                       driver.


          o § Graphics Stack⠀➾


                # ⚓ Modesetting:_A_Glamor-less_RPi_adventure_–_Just_another
                  Igalia_Blogs_site⠀⇛


                       Glamor is a GL-based rendering acceleration library
                       for the X server that can use OpenGL, EGL, or GBM.
                       It uses GL functions & shaders to complete 2D
                       graphics operations, and uses normal textures to
                       represent drawable pixmaps where possible. Glamor
                       calls GL functions to render to a texture directly
                       and is somehow hardware independent. If the GL
                       rendering cannot complete due to failure (or not
                       being supported), then Glamor will fallback to
                       software rendering (via llvmpipe) which uses
                       framebuffer functions.


                # ⚓ Mike_Blumenkrantz:_All_Text_No_Fun⠀⇛


                       You know what I’m about to talk about.


                       You knew it as soon as you opened up the page.


                       I’ve said I was done with it a number of times, but
                       deep down we all knew that was a lie.


                       Let’s talk about XFB.


          o § Applications⠀➾


                # ⚓ Important_Release_of_Inkscape_version_1.2.1_fixes_data_loss
                  and_crash_issues⠀⇛


                       We’ve just resolved some critical issues in
                       Inkscape 1.2 that were identified by our community.
                       If you’re currently using Inkscape 1.2 then this is
                       an important update to install on your device.


                # ⚓ Towards_pluggable_GSS-API_modules_–_Simon_Josefsson’s
                  blog⠀⇛


                       GSS-API is a standardized framework that is used by
                       applications to, primarily, support Kerberos V5
                       authentication. GSS-API is standardized by IETF and
                       supported by protocols like SSH, SMTP, IMAP and
                       HTTP, and implemented by software projects such as
                       OpenSSH, Exim, Dovecot and Apache httpd (via
                       mod_auth_gssapi). The implementations of Kerberos
                       V5 and GSS-API that are packaged for common GNU/
                       Linux distributions, such as Debian, include MIT
                       Kerberos, Heimdal and (less popular) GNU Shishi/
                       GSS.


                # ⚓ Medevel ☛ Best_11_Open-source_CalDAV_Self-hosted_Servers⠀⇛


                       CalDAV is the web standard calendaring extension
                       for the WebDAV. It allows CalDAV clients to access,
                       manage, sync and schedule calendar events and
                       calendars on servers.


                       CalDAV synchronizes calendar data across different
                       devices.


                       In this list, we preview some of self-hosted CalDAV
                       servers and clients that anyone can download, setup
                       and use on their local machines or servers.


                # ⚓ Medevel ☛ CardDavMATE_Is_an_Open-source_Self-hosted_CardDAV
                  Client⠀⇛


                       The CardDAV is an extension for the WebDAV which
                       allows users to sync and backup their contact from
                       CardDAV server to several clients and multiple
                       devices.


                # ⚓ Medevel ☛ Cabal_is_a_Promising_P2P_Secure_Chat_and
                  Messaging_Platform [Ed: Well, sadly uses some of Microsoft
                  GitHub and no licence information available]⠀⇛


                       Cabal is a fairly new experimental p2p protocol and
                       messaging apps that allow user to exchange messages
                       and files.


                       It does not require any central server, or even
                       create one, all is needed is the Cabal address
                       which is a secret key that can be shared among
                       friends, teams, and groups.


                       Cabal works on the internet, but it works as well
                       on your local network as you can chat directly with
                       the users connected on the same network without the
                       need to any internet access.


                # ⚓ Simon_Ser:_Status_update,_July_2022_·_emersion⠀⇛


                       I’ve continued working on my IRC suite this month.
                       Two of our extensions have been accepted in IRCv3:
                       read-marker synchronizes read markers between
                       multiple devices belonging to the same user, and
                       channel-context adds a machine-readable tag to
                       indicate the context of a message. Some other
                       server and client developers have already
                       implemented them!


                       soju has gained a few quality-of-life features.
                       Thanks to gildarts, there is a new channel update -
                       detached flag to attach or detach a channel, a new
                       contrib/migrate-db script to migrate the database
                       between backends, users can now delete their own
                       account, and the user password hashes are upgraded
                       when logging in. Additionally, read markers are
                       broadcast using Web Push (to dismiss notifications
                       when a message is read on another client), users
                       can now set a default nickname to use for all
                       networks, and the logic to regain the configured
                       nick should work on servers missing MONITOR support
                       (so I should no longer be stuck with “emersion_” on
                       OFTC).


                       Goguma now supports irc:// URLs, so it should be
                       easier to click on these links in various project
                       pages. If the user hasn’t joined the target channel
                       or network yet, a confirmation dialog will be
                       displayed. In the network settings page, a new
                       button opens a UI to authenticate on the IRC
                       network. A ton of other minor fixes and
                       improvements have been pushed as well.


                # ⚓ SUSE’s Corporate Blog ☛ ‘Contain’_your_excitement:_The_s3gw
                  is_in_town [Ed: Even AWS utilities get outsourced to a
                  Microsoft's proprietary prison]⠀⇛


          o § Instructionals/Technical⠀➾


                # ⚓ HowTo Forge ☛ How_to_Install_Standard_Notes_Server_on
                  Ubuntu_22.04⠀⇛


                       Standard Notes is an open-source encrypted notes
                       app. In this tutorial, you will learn how to self-
                       host your standard notes server on a Ubuntu 22.04
                       machine.


                # ⚓ ID Root ☛ How_To_Enable_EPEL_Repository_on_Rocky_Linux_9_–
                  idroot⠀⇛


                       In this tutorial, we will show you how to enable
                       the EPEL repository on Rocky Linux 9. For those of
                       you who didn’t know, Extra Packages for Enterprise
                       Linux (or EPEL) is a package repository that
                       provides additional packages that are not included
                       in standard Rocky Linux, AlmaLinux OS, CentOS,
                       Oracle Linux, and Scientific Linux. EPEL uses much
                       of the same infrastructure as Fedora, including
                       buildsystem, Bugzilla instance, updates manager,
                       mirror manager and more.


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


                # ⚓ MakeTech Easier ☛ How_to_Use_Emacs_to_Play_Music_with_EMMS
                  –_Make_Tech_Easier⠀⇛


                       Emacs is a brilliant program that can do many
                       things including handling files. With the Emacs
                       Multimedia System (EMMS) package, you can also
                       handle your music in Emacs. You can easily browse
                       music directories, create song playlists and even
                       display lyrics. Here we will show you how to play
                       music in Emacs.


                # ⚓ OMG Ubuntu ☛ How_to_Install_Linux_Mint’s_Apps_on_Ubuntu_–
                  OMG!_Ubuntu!⠀⇛


                       Linux Mint is far more than just the Cinnamon
                       desktop with a bit of green sprinkled on top. It
                       also includes a number of homegrown apps crafted by
                       Mint developers to enhance the overall experience.


                       Nemo file manager is probably the best known tool
                       in Mint’s software stable (as it’s available to
                       install from the Ubuntu archives). But other useful
                       tools include Bulky, Warpinator, and Hypnotix.
                       These are well-designed, user-friendly apps ably
                       tailored to their respective tasks but are not
                       available in the regular Ubuntu repos.


                       The good news is that you don’t have to switch to
                       Linux Mint to use some or even all of these apps.
                       The beauty of open-source software (especially
                       Mint’s, which is engineered to be distro-agnostic)
                       is that you can install (almost) anything wherever
                       you like.


                # ⚓ openqa:_asset_download_request_but_no_domains_passlisted⠀⇛


                # ⚓ Playing_with_NitroKey_3_—_PC_runner_using_USBIP_–_Patryk’s
                  blog⠀⇛


                       I’ve been wanting to use my brand new NitroKey 3,
                       but TOTP is not supported yet. So, I’m looking to
                       implement it myself, since firmware and tooling are
                       open-source.


                       NitroKey 3’s firmware is based on Trussed
                       framework. In essence, it’s been designed so that
                       anyone can implement an independent Trussed
                       application. Each such application is like a module
                       that can be added to Trussed-based product. So if I
                       write a Trussed app, I’d be able to add it to NK3’s
                       firmware.


                # ⚓ Linux Made Simple ☛ How_to_install_Project_Slippi_on_a
                  Chromebook⠀⇛


                       Today we are looking at how to install Project
                       Slippi 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_and_consoles,_all_you
                  need_to_know⠀⇛


                       While platforms like Steam are very easy to publish
                       for, the reality is that most of the revenue from
                       independent developers generally comes from
                       consoles (this, of course, speaking of devs not
                       focusing on mobile).


                       Consoles are cheap, easy to get access to, and have
                       a wide catalog of first and third party titles,
                       making them ideal devices for players wanting to
                       spend their time and money on games.


          o § Desktop Environments/WMs⠀➾


                # § GNOME Desktop/GTK⠀➾


                      # ⚓ This Week in GNOME ☛ #52_Happy_Birthday!_·_This_Week
                        in_GNOME⠀⇛


                             I am pleased to announce that TWIG is having
                             its first anniversary! 52 weeks ago, 52 TWIG
                             issues later, or to put it simply – one year
                             ago I launched TWIG!


                             The first issue was published on July 16,
                             2021, and was named “#1 Scrolling in the
                             Dark”. After discussing the concept with some
                             other GNOME contributors, we had to search
                             for “news” in order to have enough material
                             for the first issue.


                             Now, one year later, it gives me great
                             pleasure to announce that we have set a new
                             record for news on the anniversary. There has
                             never been that many news as this week in the
                             whole year! I am cautiously optimistic, and
                             claim the concept has now become established
                             in the GNOME community, and is being used by
                             more and more projects to quickly and easily
                             announce news.


                             What do you think about TWIG? Do you have any
                             suggestions for improvements? Criticism?
                             Compliments? Let us know! You can contact us
                             in our Matrix #thisweek:gnome.org room
                             anytime!


                             But now to the actual news – Next year is
                             sure to be at least as exciting!


    * § Distributions and Operating Systems⠀➾


          o § SUSE/OpenSUSE⠀➾


                # ⚓ openSUSE_Tumbleweed_–_Review_of_the_week_2022/28_–
                  Dominique_a.k.a._DimStar_(Dim*)⠀⇛


                       Dear Tumbleweed users and hackers,


                       During this week we managed to release a snapshot
                       every day. Granted, some were relatively small, but
                       overall, there were some nice updates in the 7
                       snapshots published (0708…0714).


                # ⚓ SUSE’s Corporate Blog ☛ SUSE_Linux_Enterprise_Server_(SLES)
                  Recognized_by_G2_as_the_‘Leader’_in_Server_Virtualization
                  Software_&_‘High_Performer’_in_Infrastructure-as-a-Service_|
                  SUSE_Communities [Ed: Fake awards as marketing stunts]⠀⇛


                       I’m excited to share that SLES was recognized by
                       G2, the world’s largest and most trusted tech
                       marketplace, as the Leader in its Server
                       Virtualization Software category and the High
                       Performer in the Infrastructure-as-a-Service
                       category.


          o § Fedora Family / IBM⠀➾


                # ⚓ Silicon Angle ☛ Red_Hat_announces_Matt_Hicks_as_its_new_CEO
                  –_SiliconANGLE [Ed: This publication is funded by Red Hat for
                  such puff pieces]⠀⇛


                       Red Hat Inc. sprang a surprise today as it
                       announced that Matt Hicks has been promoted to be
                       its new president and chief executive officer,
                       effective immediately.


                       Hicks (pictured) takes the reins from current
                       president and CEO Paul Cormier, who has moved
                       upstairs to become the open-source software
                       provider’s new chairman.


                       Red Hat is a subsidiary of IBM Corp. and seen as
                       one of the pioneers of open-source software. Its
                       flagship product is the Red Hat Enterprise Linux
                       operating system, which is widely used to power
                       thousands of enterprise data centers around the
                       world. The company also sells tools around
                       virtualization, software containers, middleware and
                       various other applications. It was acquired by IBM
                       in 2019 for $34 billion.


                       IBM CEO Arvind Krishna said Red Hat serves as the
                       foundation of thousands of enterprises’ technology
                       strategies thanks to its open-source, hybrid cloud
                       capabilities. “Matt’s deep experience and technical
                       knowledge of Red Hat’s entire portfolio makes him
                       the ideal leader as Red Hat continues to grow and
                       develop innovative, industry-leading software,” he
                       said.


                # ⚓ IT Pro Today ☛ Rocky_Linux_Releases_Its_RHEL_9_Clone_and_a
                  Build_Platform⠀⇛


                       The Rocky Enterprise Software Foundation has
                       released Rocky Linux 9 and the Peridot build
                       platform. Learn more.


                # ⚓ Ubuntu Pit ☛ 8_YUM_ThirdParty_Repositories_for_CentOS_and
                  RHEL⠀⇛


                       Repositories are like huge servers where the
                       developers store the application files. In Linux,
                       the repositories play a vital role in app
                       performance and installation. From my previous
                       experiences, I’ve faced issues while installing
                       applications due to a bad or broken repository.
                       Most major Linux distributions have their own
                       dedicated official Linux repository. Despite having
                       their own dedicated repository for Fedora, CentOS,
                       or Red Hat Linux, we might need to rely on some
                       thirdparty YUM repositories for package
                       installation via YUM commands.


          o § EasyOS⠀➾


                # ⚓ Barry Kauler ☛ Hardware_clock_set_to_local-time_or_UTC_now
                  hardware-profiled⠀⇛


                       An important feature of EasyOS is “hardware
                       profiling”, so that when on a USB-stick that is
                       booted on different computers, different video,
                       audio, etc hardware is detected and remembered.


                # ⚓ Barry Kauler ☛ Limine_3.12_compiled_in_OE⠀⇛


                       In response to issue #196, mintsuki has created a
                       new executable, ‘limine-version’, that just returns
                       the version of Limine.
                       In response to #197, mintsuki has added “–undeploy”
                       commandline option to the ‘limine-deploy’
                       executable. This will remove Limine from the mbr to
                       which it was installed, and restore the mbr to how
                       it was prior. With some caveats.
                       Both of these are great new features, and will be
                       incorporated into the “Limine Installer”.


          o § Debian Family⠀➾


                # ⚓ gotop_–_SparkyLinux⠀⇛


                       Another terminal based graphical activity monitor,
                       inspired by gtop and vtop, written in Go.


          o § Canonical/Ubuntu Family⠀➾


                # ⚓ AddictiveTips ☛ How_to_try_out_the_Linux_Mint_21_Beta⠀⇛


                       Linux Mint 21 codename “Vanessa” has its first Beta
                       out. Mint 21 has a lot of new and exciting things
                       to offer, such as a new version of the Linux
                       kernel, updated drivers, an updated Cinnamon
                       desktop, and more.


                       In this guide, we’ll show you how you can try out
                       the Linux Mint 21 beta. However, be warned that
                       this software is still developing, and you will run
                       into issues. Be sure to report these issues so Mint
                       developers can improve the OS for the final
                       release.


          o § Open Hardware/Modding⠀➾


                # ⚓ Arduino ☛ Driving_a_robot_car_with_nothing_but_your_voice_|
                  Arduino_Blog⠀⇛


                       Traditional control of RC cars and other small
                       vehicles has typically relied on some kind of
                       joystick-based solution, often with one for
                       adjusting direction and the other for speed. But
                       YouTuber James Bruton wanted to do something
                       different: make a rideable go-kart that is entirely
                       driven with one’s voice.


                       His solution is based around Deepgram’s speech
                       recognition service, which enables users to send
                       small snippets of audio samples up to its cloud via
                       an API and receive replies with a transcript of
                       what was said. As for the kart itself, its chassis
                       was created by first welding together several steel
                       tubes and attaching a based of thick plywood on
                       top. The front cutout allows for a large caster
                       wheel to spin left or right with the aid of a chain
                       driven by a repurposed windshield wiper motor
                       assembly. Absolute positioning of this wheel was
                       achieved by measuring the voltage of a
                       potentiometer that spins along with the chain. And
                       finally, a pair of hub motor wheels, akin to the
                       ones found on hoverboards and scooters, were placed
                       at the rear for propulsion. Each motor was
                       connected to its specific driver, and in turn, were
                       connected to an Arduino Uno.


                # ⚓ Tom’s Hardware ☛ Raspberry_Pi_Peers_into_Deep_Space_with
                  James_Webb_Space_Telescope_Digital_Frame_|_Tom’s_Hardware⠀⇛


                       The James Webb Space Telescope (JWST) is one of the
                       greatest tools we have for capturing deep space
                       images with extreme accuracy—capable of detecting
                       radiation from the cosmic microwave background.
                       Early images have made their way back to Earth and
                       the maker behind Cellar Nerd is displaying these
                       wonderous images on a custom, Raspberry Pi-powered
                       JWST-themed digital picture frame designed to
                       resemble the hexagonal golden mirror array found on
                       the telescope.


                # ⚓ Arduino ☛ A_flurry_of_Arduino_Cloud_updates_spell_sunshine
                  for_makers_|_Arduino_Blog⠀⇛


                       Arduino Cloud updates are like buses! They all come
                       along at once. But that just makes it all the more
                       exciting when we get to tell you about the new
                       things happening in Arduino’s awesome SaaS system.
                       So let’s jump right in there and take a look at
                       tags, filters, blinks and galleries.


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


          o § Content Management Systems (CMS)⠀➾


                # ⚓ Linux Links ☛ 3_Best_Free_and_Open_Source_Awk_Static_Site
                  Generators_–_LinuxLinks⠀⇛


                       LinuxLinks, like most modern websites, is dynamic
                       in that content is stored in a database and
                       converted into presentation-ready HTML when readers
                       access the site.


                       While we employ built-in server caching which
                       creates static versions of the site, we don’t
                       generate a full, static HTML website based on raw
                       data and a set of templates. However, sometimes a
                       full, static HTML website is desirable. Because
                       HTML pages are all prebuilt, they load extremely
                       quickly in web browsers.


                       There are lots of other advantages of running a
                       full, static HTML website.


          o § Programming/Development⠀➾


                # ⚓ Peter_Czanik:_The_syslog-ng_Insider_2022-06:_RHEL_9;_disk-
                  buffer;_Microsoft_Linux; [Ed: Quit saying "Microsoft Linux";
                  it's not called that and attributing Linux to Microsoft is
                  helping Microsoft attack the brand even further]⠀⇛


                       This is the 103rd issue of syslog-ng Insider, a
                       monthly newsletter that brings you syslog-ng-
                       related news.


                # ⚓ Best_Practices_for_Build_Options_–_Michael_Catanzaro’s
                  Blog⠀⇛


                       Occasionally I see upstream developers complain
                       that a downstream operating system has built their
                       software “incorrectly,” generally because some
                       important dependency or feature has been disabled.
                       Sometimes downstreams really do mess up, but more
                       often poor upstream defaults are to blame.
                       Upstreams must set good defaults because upstream
                       software developers know far more about their
                       projects than downstream packagers do. Upstreams
                       generally have a good idea of how they expect
                       software to be built by downstreams, whereas
                       downstreams generally do not. Accordingly, do the
                       thinking upstream whenever possible. When you set
                       good defaults, it becomes easier for downstreams to
                       build your software the way you expect, because
                       active effort is required for downstreams to mess
                       things up.


                # ⚓ WATCH_Blind_Learners_in_SA_Learn_Coding_with_Game_Using
                  Braille_–_SAPeople_–_Worldwide_South_African_News⠀⇛


                       On their partnership with the Bona Ubuntu Program
                       Prof Greyling says: “This must be one of the most
                       special moments in the five years of our project.”
                       Special thanks, he says, go to Leva Foundation’s
                       Operations Manager Jackson Tshabalala for arranging
                       it.


                       In a very early prototype the challenge on the
                       screen is simulated by a physical grid, while
                       “braille tags” are added to the tokens.


                # ⚓ Qt ☛ Qt_Quick_3D_Physics_in_Qt_6.4⠀⇛


                       Qt 6.4 includes the new module Qt Quick 3D Physics
                       as tech preview. As the name implies, this is a
                       module that adds physical simulation capabilities
                       on top of Qt Quick 3D. In particular, it enables
                       rigid body simulation using simple primitives
                       (spheres, boxes, planes and capsules) as well as
                       convex- and triangle meshes and heightmaps.
                       Physical properties such as mass, density, gravity
                       and friction are customizable. This makes it
                       possible to create physically correct behavior in
                       3D scenes without having to handcraft animations.


                # § Perl / Raku⠀➾


                      # ⚓ Perl ☛ Perl_Weekly_Challenge_173:_Sylvester’s
                        Sequence_in_dc⠀⇛


                      # ⚓ (Unofficial)_Debian_Perl_Sprint_2022_–_Bits_from
                        Debian⠀⇛


                             Three members of the Debian Perl Group met in
                             Hamburg between May 23 and May 30 2022 as
                             part of the Debian Reunion Hamburg to
                             continue perl development work for Bookworm
                             and to work on QA tasks across our 3800+
                             packages.


    * § Leftovers⠀➾


          o ⚓ SparkFun Electronics ☛ The_970-HA-JOKES_Payphone_Project_–_News_–
            SparkFun_Electronics⠀⇛


                 Have a listen to this classic hold music on infinite loop
                 and be taken back to a time when pay phones ruled the
                 street corner and peppered the mall food court.


          o § Hardware⠀➾


                # ⚓ The Next Platform ☛ Google_Follows_Suit_With_Microsoft_On
                  Ampere_Arm_Instances⠀⇛


                       A long time ago, when we first started The Next
                       Platform, Urs Hölzle, then senior vice president of
                       the Technical Infrastructure team at Google, told
                       us that to gain a 20 percent improvement in price/
                       performance it would absolutely change from the X86
                       architecture to Power architecture – or indeed any
                       other architecture – and even for one generation of
                       machines.


          o § Proprietary⠀➾


                # ⚓ IGEL_Optimises_Linux_Endpoints_for_Microsoft_Teams [Ed:
                  IGEL helps Microsoft tarnish the "Linux" brand]⠀⇛


          o § Pseudo-Open Source⠀➾


                # § Openwashing⠀➾


                      # ⚓ The Register UK ☛ CP/M’s_open-source_status_clarified
                        after_21_years_•_The_Register [Ed: GitHub is
                        proprietary. It's where code gets imprisoned, not
                        liberated. It moreover encourages licence
                        violations.]⠀⇛


                             The company that still owns Digital
                             Research’s CP/M operating system has granted
                             a new, more permissive license for the eight-
                             bit OS, making it free for anyone to modify
                             or redistribute.


                             It’s not often that we update a news story
                             from 21 years ago. Bryan Sparks, then CEO of
                             Caldera spin-off Lineo, gave Tim Olstead
                             permission to redistribute the OS, both as
                             source and binaries. Sadly, Mr. Olstead
                             passed away from cancer aged just 51. Back
                             then, we wrote that the Unofficial CP/M Web
                             Site was back, as Mr. Sparks changed the
                             permissions from the former owner himself to
                             the site as a whole.


                             For clarity, that’s a very good thing – Lineo
                             was under no obligation to do this – but
                             restricting redistribution to one person or
                             one site was limiting.


                             Lineo in turn spun off DRDOS, Inc., which
                             ended up owning the Digital Research
                             intellectual property. That company is still
                             around, and Mr Sparks is its president. This
                             month, retired programmer Scott Chapman
                             managed to contact Sparks and request
                             clarification of whether anyone else was
                             allowed to redistribute CP/M, and Sparks has
                             granted free rein.


                      # ⚓ TechRepublic ☛ What_are_OpenProject_Work_Packages,
                        and_how_do_you_create_one? [Ed: Well, the dash in
                        "open-source" tells you it is proprietary with
                        openwashing stunts]⠀⇛


                             penProject is a powerful, open-source…


                      # ⚓ TechRepublic ☛ New_open_source_solutions_library_from
                        Shoreline.io_aims_to_deliver_self-healing
                        infrastructure_|_TechRepublic [Ed: More openwashing
                        from the same site on the same day]⠀⇛


                             Incident automation company Shoreline.io has
                             unveiled its open source solutions library, a
                             collection of op packs designed to make it
                             easier to diagnose and repair the most common
                             infrastructure incidents in production cloud
                             environments.


                             The solutions library focuses on addressing
                             issues including JVM memory leaks, filling
                             disks, rogue processes and stuck Kubernetes
                             pods. It is launching with over 35 op packs
                             that are available for free to the Shoreline
                             community.


                      # ⚓ PR Newswire ☛ BMW_Group_Joins_the_Linux_Foundation’s
                        Yocto_Project⠀⇛


                             The Linux Foundation, the nonprofit
                             organization enabling mass innovation through
                             open source, today announced that BMW Group
                             is joining the Yocto Project as a member.


                      # ⚓ Yahoo News ☛ BMW_Group_Joins_the_Linux_Foundation’s
                        Yocto_Project⠀⇛


          o § Security⠀➾


                # ⚓ Geeks For Geeks ☛ Top_50_Penetration_Testing_Interview
                  Questions_and_Answers⠀⇛


                       Penetration testing stands for a process where the
                       security of a computer system is tested by trying
                       to gain access to its internal systems. In order to
                       carry out penetration testing, an attacker must
                       first identify which ports are open on the target
                       machine and then use those ports in order to
                       exploit security vulnerabilities. Once these
                       vulnerabilities are exploited, the attacker can
                       break into the target computer and try different
                       passwords or commands in an attempt to find
                       sensitive information that may be stored there.


                # ⚓ IPFire Official Blog ☛ blog.ipfire.org_–_OpenVPN_OTP/2FA⠀⇛


                       With the latest update of IPFire, a new feature is
                       available which helps to make OpenVPN connections
                       more secure: OpenVPN Two-Factor Authentication
                       (2FA). This post explains what Two-Factor
                       Authentication is, what it is good for, and how to
                       use it with IPFire and OpenVPN.


                # ⚓ Stacy on IoT ☛ 3_ways_to_fortify_your_smart_home_network
                  setup⠀⇛


                       It’s 2022 and you have a smart home. Given all of
                       the stories about IoT devices getting hacked or
                       hijacked with malware, are your router and home
                       network prepared to protect your home? If you have
                       an older router or don’t use advanced features of a
                       more modern one, maybe not. With that in mind, here
                       are some different ways to bolster your smart home
                       device security — assuming your router has the
                       right features.


                       To be clear, the primary goal here is to keep any
                       network intrusions limited solely to infected
                       devices. You don’t want some malicious actor
                       entering your home network through an IoT device
                       and gaining access to your other devices or your
                       network data.


                # ⚓ Ruben Schade ☛ Rubenerd:_Education_cuts_are_a_national
                  security_threat⠀⇛


                       I’m an egalitarian. I worked hard to be where I am,
                       but I also want to give people the same
                       opportunities I had. Free, universal education is
                       one of the hallmarks of a compassionate, civilised
                       society; one in which your character, skills, and
                       interests are all that matter in the pursuit of
                       knowledge and improvement of lives.


                # § Privacy/Surveillance⠀➾


                      # ⚓ Stacy on IoT ☛ Podcast:_Here’s_what_we_think_with
                        Wink_on_the_blink⠀⇛


                             This week’s show comes to y’all from Paris
                             and the English seaside, with Kevin and I
                             wondering exactly what happened to Wink. We
                             also offer options for the few remaining
                             holdouts on the platform. We then discuss
                             Hive’s decision to pull back on smart home
                             devices and its new smart thermostat (Hive
                             plans to continue making smart energy
                             devices). Then we focus on surveillance news
                             starting with San Francisco’s Rule’s
                             Committee broadening support for law
                             enforcement agencies to access Ring camera
                             data. Then we share how often police got
                             access to Ring device footage without the
                             owner’s permission. The Federal Trade
                             Commission has a warning for companies that
                             say they anonymize their data when in fact,
                             they do not, and Home Assistant now has a
                             program for formal integrations. We also
                             share our perspectives on BMW charging a
                             monthly fee for access to heated seats. We
                             end by answering a listener question about
                             network extenders.


          o § Environment⠀➾


                # § Energy⠀➾


                      # ⚓ uni Cornell ☛ Smart_thermostats_inadvertently_strain
                        electric_power_grids_|_Cornell_Chronicle⠀⇛


          o § Civil Rights/Policing⠀➾


                # ⚓ Daily Maverick ☛ We_can_still_turn_South_Africa_into_the
                  great_country_of_our_dreams⠀⇛


                       Democracies are challenged all over the world
                       because of the growing inequalities between
                       citizens. Political freedom without socioeconomic
                       justice that enables every citizen to feel
                       respected and heard, is unsustainable. Our country
                       is reaping the bitter fruits of neglecting
                       socioeconomic transformation to make freedom a
                       lived reality for all citizens.


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



                    ䷩ 𝚕𝚒𝚗𝚎 3201

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.15.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_15/07/2022:_Many_More_Laptops_With_GNU/Linux_(OEMs_and_Flex)⠀✐


Posted in News_Roundup at 6:50 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Desktop/Laptop
          o Kernel_Space
          o Instructionals/Technical
          o Games
    * Distributions_and_Operating_Systems
          o Arch_Family
          o Canonical/Ubuntu_Family
          o Devices/Embedded
          o Open_Hardware/Modding
          o Mobile_Systems/Mobile_Applications
    * Free,_Libre,_and_Open_Source_Software
          o Programming/Development
                # Java
    * Leftovers
          o Hardware
          o Health/Nutrition/Agriculture
          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 Freedom_of_Information_/_Freedom_of_the_Press
          o Civil_Rights/Policing
    * Gemini*_and_Gopher
          o Personal
          o Technical
                # Internet/Gemini
    * § GNU/Linux⠀➾


          o ⚓ Hackaday ☛ A_Linux_Business_Card_You_Can_Build_|_Hackaday⠀⇛


                 It is a sign of the times that one of [Dmitry’s] design
                 criteria for his new Linux on a business card is to use
                 parts you can actually find during the current component
                 shortage. The resulting board uses a ATSAMD21 chip and
                 emulates a MIPS machine in order to boot Linux.


                 We like that in addition to the build details, [Dmitry]
                 outlines a lot of the reasons for his decisions. There’s
                 also a a fair amount of detail about how the whole system
                 actually works. For example, by using a 0.8 mm PCB, the
                 board can accept a USB-C cable with no additional
                 connector. There is also a great explanation of the MIPS
                 MMU and don’t forget that MIPS begat RISC-V, so many of
                 the MIPS core details will apply to RISC-V as well (but
                 not the MMU). You’ll also find some critiques of the
                 ATSAMD21’s DMA system. It seems to save chip real estate,
                 the DMA system stores configuration data in user memory
                 which it has to load and unload every time you switch
                 channels.


          o § Desktop/Laptop⠀➾


                # ⚓ 9to5Linux ☛ TUXEDO_Aquaris_Announced_as_First_Water_Cooling
                  System_for_Linux_Laptops⠀⇛


                       Earlier this year, when TUXEDO Computers unveiled
                       the TUXEDO Stellaris 15 Gen4 Linux laptop, the
                       hardware vendor also introduced the TUXEDO Aquaris
                       external water cooling system, but at that time it
                       was only supported on TUXEDO Computers’ laptops
                       shipping with the Windows operating system pre-
                       installed.


                       Of course, TUXEDO Computers promised that they will
                       offer Linux support, and today the hardware vendor
                       announced in-house developed Linux drivers for the
                       TUXEDO Aquaris external water cooling system.


                # ⚓ GamingOnLinux ☛ Slimbook_recently_refreshed_a_bunch_of
                  their_Linux_laptops⠀⇛


                       Summer is getting hot and perhaps you want a new
                       laptop to take somewhere cooler to do a little work
                       and light gaming? Slimbook recently upgraded a
                       bunch of their machines. This is all in addition to
                       the recently announced KDE Slimbook 4 laptop.


                # ⚓ The Register UK ☛ Weird_Flex,_but_OK:_Now_you_can
                  officially_turn_these_PCs,_Macs_into_Chromebooks⠀⇛


                       Google on Thursday officially released Chrome OS
                       Flex, which aims to bring the web giant’s mega-
                       browser operating system to a wider range of
                       systems.


                       Flex was unveiled in February as a version of
                       Chrome OS that could run on any modern-ish Intel or
                       AMD (sorry, not Arm) processor. Since that debut,
                       the number of devices certified to run Chrome OS
                       Flex has almost doubled, from some 250 to more than
                       400, according to Google.


                       Among certified models are several MacBook Air
                       devices, Microsoft Surface, ASUS, Acer, and Lenovo
                       machines along with a laundry list of Dell
                       machines. Google plans to continually certify older
                       devices for Flex.


                       To get the Chrome OS experience – which, as the
                       name suggests, involves doing pretty much
                       everything on your desktop through the Chrome
                       browser – you would need to buy a Chromebook with
                       it installed, or go through a bit of a convoluted
                       process to put the OS on a system. Chrome OS Flex
                       is supposed to make that easy, and work on a range
                       of non-Chromebooks.


                # ⚓ Chromecast_Connect⠀⇛


                       It has been a while studying and working with the
                       Chromecast Protocol. This protocol is proprietary,
                       and officially only the Chrome browser, Android,
                       and iOS platforms support casting to a Chromecast-
                       enabled device.
                       Now, Chromium is open source, and so is Android,
                       but we would not want anything to do with Android
                       for obvious reasons, not to mention this feature
                       may be tucked away in Google Play Services.
                       So we settle with Chromium which is written in C++.
                       Thankfully almost all of the hard work was done by
                       many other open source projects, notably Node
                       CastV2. Not only this project provides a simple
                       implementation for the Chromecast protocol but also
                       a written explanation of the underlying stuff and
                       how things actually work.
                       All I need to figure out is how to implement that
                       is C.


          o § Kernel Space⠀➾


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


                       The kernel has thousands of configuration options,
                       many of which can change the kernel’s behavior in
                       subtle or surprising ways. Among those options is
                       CONFIG_ANDROID, which one might expect to be
                       relatively straightforward; its description reads,
                       in its entirety: “Enable support for various
                       drivers needed on the Android platform”. It turns
                       out that this option does more than that, to the
                       surprise of some users. That has led to a plan to
                       remove this option, but that has brought a surprise
                       or two of its own — and some disagreement — as
                       well.


                       The discussion started when Alex Xu reported a
                       read-copy-update (RCU) error that was appearing on
                       his system after resuming from suspend. Shortly
                       thereafter, Xu realized that the problem was tied
                       to the fact that his kernel had been built with
                       CONFIG_ANDROID enabled; among other things, that
                       option significantly reduces the time that can
                       elapse before RCU starts putting out stall
                       warnings.


                # ⚓ LWN ☛ Removing_the_scheduler’s_energy-margin_heuristic_
                  [LWN.net]⠀⇛


                       The CPU scheduler’s job has never been easy; it
                       must find a way to allocate CPU time to all tasks
                       in the system that is fair, allows all tasks to
                       progress, and maximizes the throughput of the
                       system as a whole. More recently, it has been
                       called upon to satisfy another constraint:
                       minimizing the system’s energy consumption. There
                       is currently a patch set in circulation, posted by
                       Vincent Donnefort with work from Dietmar Eggemann
                       as well, that changes how this constraint is met.
                       The actual change is small, but it illustrates how
                       hard it can be to get the needed heuristics right.


                       Reduction of energy use is, of course, a worthy
                       goal; energy that is not wasted becomes available
                       for the mining of more cryptocurrency, after all.
                       There are some smaller considerations as well, such
                       as environmental benefits, that justify the effort,
                       but the proliferation of battery-powered devices
                       has added more urgency to the task. If batteries
                       can be made to last longer, doomscrolling
                       interruptions will be fewer and users will be
                       happier.


                       These pressures have led to the addition of energy-
                       aware scheduling to the kernel. When the scheduler
                       considers the placement of tasks in the system, it
                       will work to reduce the amount of energy consumed
                       overall; this work includes running the CPUs at the
                       power level that is the most efficient for the
                       current load and powering down processors entirely
                       when possible. For example, if a CPU that is
                       currently running at a given power level can accept
                       another task without having to move to a higher
                       power level, it may make sense to move a task there
                       from another CPU.


                # ⚓ LWN ☛ A_BPF-specific_memory_allocator_[LWN.net]⠀⇛


                       The kernel does not lack for memory allocators, so
                       one might well question the need for yet another
                       one. As this patch set from Alexei Starovoitov
                       makes clear, though, the BPF subsystem feels such a
                       need. The proposed new allocator is intended to
                       increase the reliability of allocations made within
                       BPF programs, which might be run in just about any
                       execution context.


                       Allocating memory in the kernel can be tricky in
                       the best of situations. Depending on the execution
                       context at the time, the memory-management
                       subsystem may or may not have various options
                       available to find memory if an allocation request
                       cannot be immediately satisfied. For example,
                       memory can be freed by pushing its contents out to
                       persistent storage, but if memory is requested from
                       within a filesystem, calling back into that
                       filesystem to write out data could cause deadlocks
                       and is thus not an option. In many kernel contexts,
                       it is not possible to sleep to wait for memory to
                       become free. If the kernel is currently handling a
                       non-maskable interrupt (NMI) from the CPU, the
                       options are even more limited.


                       Most kernel code is written to run within a
                       specific context and with an awareness of the
                       available memory-allocation options; that
                       information is passed to the memory-management
                       subsystem via the GFP flags supplied with
                       allocation requests. When a specific function can
                       be invoked in multiple contexts, it generally must
                       allocate memory as if it were always running in the
                       most restrictive possible context; this can be
                       inconvenient for developers.


                       Over the years, mechanisms like memory pools
                       (“mempools”), which pre-allocate a certain amount
                       of memory to ensure that it will be available when
                       it is needed, have been developed to make life
                       easier. Naturally, mempools quickly created a new
                       problem: kernel developers adopted mempools as a
                       way of insulating themselves from memory-allocation
                       failures. Before long, much of the kernel’s memory
                       was tied up in mempools and unavailable where it
                       was actually needed. Over the years, a balance has
                       mostly been found between overenthusiastic mempool
                       use and being unable to allocate memory in critical
                       situations.


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


                       Some system administrators running Ubuntu 20.04 had
                       a rough time on June 8, when Ubuntu published
                       kernel packages containing a particularly nasty bug
                       that was caused by an Ubuntu-specific patch to the
                       kernel. The bug led to a kernel panic whenever a
                       Docker container was started. Fixed packages were
                       made available on June 10, but there are questions
                       about what went wrong with handling the patch; in
                       particular, it is surprising that kernel 5.13,
                       which has been beyond its end-of-life for months,
                       made it onto machines running Ubuntu 20.04, which
                       is supposed to be a long-term support release.


                # ⚓ LWN ☛ The_2022_embedded_Linux_update_[LWN.net]⠀⇛


                       A regular feature of the Embedded Linux Conference
                       (ELC) has been an update on the state of embedded
                       Linux from conference organizer Tim Bird. It has
                       been quite a few years since I had the opportunity
                       to sit in on one, so I took one at the 2022 Open
                       Source Summit North America (OSSNA) in Austin,
                       Texas. OSSNA is an umbrella conference that
                       contains ELC and a whole lot more these days. Bird
                       gave a look at recent kernel features from an
                       embedded perspective, talked a bit about some
                       different technology areas and their impact on
                       embedded Linux, and also tried to answer a question
                       that Andrew Morton posed in a keynote at ELC in
                       2008.


                       Among his many hats, Bird was the program committee
                       chair for ELC and he is a principal software
                       engineer at Sony Electronics. He started by saying
                       that he was trying to squeeze a talk that he gives
                       fairly regularly at other events down from its
                       usual hour and a half—to 40 minutes. So he warned
                       attendees that he would be moving fast. His goals
                       with the talk were to introduce new technologies
                       that have been added to the Linux kernel, so that
                       attendees could perhaps incorporate them into their
                       products, but also to start a conversation in the
                       ecosystem about areas that need attention.


                # ⚓ Justine Tunney ☛ Justine_Tunney:_Porting_OpenBSD_pledge()
                  to_Linux⠀⇛


                       There’s been a few devs in the past who’ve tried
                       this. I’m not going to name names, because most of
                       these projects were never completed. When it comes
                       to SECCOMP, the online tutorials only explain how
                       to whitelist the system calls themselves, so most
                       people lose interest before figuring out how to
                       filter arguments. The projects that got further
                       along also had oversights like allowing the
                       changing of setuid/setgid/sticky bits. So none of
                       the current alternatives should be used. I believe
                       this effort gets us much closer to having pledge()
                       than ever before.


                # ⚓ LWN ☛ Tunney:_Porting_OpenBSD_pledge()_to_Linux⠀⇛


                       Justine Tunney has created an implementation of the
                       OpenBSD pledge() system call for Linux.


          o § Instructionals/Technical⠀➾


                # ⚓ TecMint ☛ IPTraf-ng_–_A_Console-Based_Network_Monitoring
                  Tool⠀⇛


                # ⚓ Linux Hint ☛ How_to_read_a_local_text_file_using
                  JavaScript?⠀⇛


                # ⚓ HowTo Geek ☛ How_to_Format_a_USB_Drive_on_Linux_That_Works
                  With_Windows⠀⇛


                # ⚓ Its FOSS ☛ The_Ultimate_Guide_to_Epic_Games_Store_on
                  Linux⠀⇛


                # ⚓ Trend Oceans ☛ [Solved]_Termux_Package_Management_Issue_–
                  TREND_OCEANS⠀⇛


                       Brief: Today you will learn the cause of the Termux
                       package management issue, how to solve it, and
                       other ways to solve it.


                       If you have installed the Termux app from the
                       Playstore, you might face the below error while
                       upgrading or installing the package on an Android
                       device.


                # ⚓ H2S Media ☛ 3_Ways_to_install_Flowblade_video_editor_on
                  Ubuntu_22.04⠀⇛


                       Get the steps to learn the ways to install
                       Flowblade Video Editor on Ubuntu 22.04 LTS Jammy
                       JellyFish Linux using the command terminal.


                       Flowblade Movie Editor is a free and open-source
                       video editing software for Linux, available easily
                       using the default system repository.


                       With the video editor Flowblade, you can edit
                       videos for free on Linux. The open-source software
                       uses FFmpeg and can handle the video codecs
                       supported by the library. It is a non-linear video
                       editor that can handle multiple tracks, so you can
                       use multiple tracks of video and audio to create a
                       movie. Of course, you have to observe the copyright
                       if the material is used by third parties, which was
                       downloaded from YouTube with YouTube DL, for
                       example.


                # ⚓ Linux Capable ☛ How_to_Install/Enable_Remi_RPM_Repository
                  on_Rocky_Linux_9⠀⇛


                # ⚓ Linux Capable ☛ How_to_Install_Microsoft_Teams_on_Rocky
                  Linux_9 [Ed: Microsoft's proprietary spyware and vendor lock-
                  in]⠀⇛


                # ⚓ Linux Capable ☛ How_to_Install_GIMP_on_Rocky_Linux_9⠀⇛


                # ⚓ Linux Capable ☛ How_to_Install_GIT_on_Rocky_Linux_9⠀⇛


                # ⚓ Linux Capable ☛ How_to_Increase_DNF_Download_Speed_on_Rocky
                  Linux_9⠀⇛


                # ⚓ Linux Capable ☛ How_to_Install/Enable_EPEL/EPEL_Next_on
                  Rocky_Linux_9⠀⇛


                # ⚓ OMG Ubuntu ☛ A_Faster_Way_to_Edit_Text_Files_as_Root_in
                  Ubuntu_–_OMG!_Ubuntu!⠀⇛


                       Here’s a little time-saver if you (like me) often
                       need to edit text files as root in a graphical app
                       on Ubuntu.


                # ⚓ Trend Oceans ☛ What_is_Termux_&_How_to_use_the_Linux
                  Command_on_Android_with_Termux?_–_TREND_OCEANS⠀⇛


                       Brief: Today you will learn what Termux is and its
                       features and limitations. And how to install,
                       uninstall and manage your packages in Termux. Then
                       learn how to enable storage access on Termux and
                       Enable Other Repositories on Termux.


                # ⚓ Linux Hint ☛ How_To_Set_Up_Nginx_Server_Blocks_on_Ubuntu
                  22.04⠀⇛


                       Nginx is an open-source, freely available HTTP
                       server software. Additionally, it operates as a
                       proxy server for email (SMTP, POP3, IMAP). Nginx
                       also acts as a load balancer and reverse proxy for
                       UDP, TCP, and HTTP servers. According to W3Tech,
                       NGINX is currently the most widely used web server
                       since it routinely outperforms Apache and other
                       servers in benchmark tests assessing web server
                       speed.


                       This blog will demonstrate the method to set up
                       Nginx server blocks on Ubuntu 22.04. Let’s get
                       started!


                # ⚓ Linux Hint ☛ How_to_Install_Odoo_15_on_Ubuntu_22.04⠀⇛


                       Odoo 15 is a web-based business application package
                       that can be operated from a single console.
                       Warehouse Management, Open Source CRM, Billing &
                       Accounting, eCommerce, Website Builder, Human
                       Resources, Project Management, Manufacturing,
                       Purchase Management, Point of Sale, and Marketing
                       are just a few of the business apps offered on Odoo
                       15.


                       This blog will demonstrate the procedure of
                       installing Odoo 15 on Ubuntu 22.04. Let’s get
                       started.


                # ⚓ Linux Hint ☛ How_to_Setup_a_Raspberry_Pi_Samba_Server⠀⇛


                       Samba is an open-source secure network file sharing
                       system that allows Raspberry Pi users to easily
                       share files between the Raspberry Pi and other
                       devices like laptops or PCs. It works on the
                       Network Attached Storage (NAS) protocol principle
                       and is one of the easiest and quickest solutions
                       for sharing files between multiple devices through
                       the Internet.


                       This tutorial presents a detailed guideline for
                       setting up a Raspberry Pi Samba server to allow
                       file sharing between your Raspberry Pi and other
                       devices.


                # ⚓ Linux Hint ☛ How_to_run_Linux_games_natively_on_Raspberry
                  Pi⠀⇛


                       Raspberry Pi is an amazing platform that allows
                       users to play many games easily. The device
                       processor has an excellent capability to handle
                       games that require fewer memory resources so that
                       you can smoothly run the game without reducing your
                       device performance. You can run several games on
                       your Raspberry Pi device, but those designed for a
                       Linux environment are the ones you should try to
                       play out on your device.


                # ⚓ Linux Hint ☛ How_to_Run_Xbox_Cloud_Games_on_Raspberry_Pi⠀⇛


                # ⚓ Ubuntu ☛ Raspberry_Pi_HAT_tutorials_part_2_–_Blinkenlights
                  and_micro-Pong!_|_Ubuntu⠀⇛


                       Welcome to part 2 of our Raspberry Pi HAT tutorial
                       series written by our resident Pi developers, Dave
                       ‘waveform’ Jones and William ‘jawn-smith’ Wilson.


                       In this post, they teach us how to build a handheld
                       micro-Pong device with the Unicorn HAT Mini and
                       follow it up with a system monitor on the Unicorn
                       HAT HD.


                       Check out part 1, where William got us started with
                       the Unicorn pHAT and Dave shared his piwheels
                       project dashboard!


                       This is a guest post from William’s own blog, which
                       he’s kindly allowed us to share here. Check out his
                       site for more great Pi tutorials as well as some
                       equally colorful 3D printing projects.


                       That’s enough from me, over to William and Dave.


                # ⚓ [From_Arch]:_wxgtk2_may_require_manual_intervention⠀⇛


                       if pacman gives an error message like:


                            error: failed to prepare transaction
                            (could not satisfy dependencies) ::
                            removing wxgtk-common breaks dependency
                            ‘wxgtk-common’ required by wxgtk2


                       you will need to uninstall ‘wxgtk2′ and it’s
                       dependents first (the only such parabola packages
                       are ‘freefilesync’ and ‘odamex’)


                # ⚓ LinuxOpSys ☛ How_to_Check_Ports_in_Use_in_Linux_(Listening
                  Ports)⠀⇛


                       A listening port is a network port on which an
                       application or process waiting for a connection or
                       has established a connection. This helps the kernel
                       to act when receiving packets with this specific
                       port number.


                       The listening port could be closed, listening, or
                       in established states. Once service is started and
                       listening to a port no other applications or
                       services can use that port.


                       In this guide, we learn how to check ports in use
                       in Linux (Listening Ports). You can do this using
                       ss, netstat, and lsof.


                # ⚓ Linux Made Simple ☛ How_to_install_Deltatraveler_on_a
                  Chromebook⠀⇛


                       Today we are looking at how to install
                       Deltatraveler 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.


                # ⚓ Linux Shell Tips ☛ Difference_Between_a_Terminal,_Shell,
                  TTY,_and_Console⠀⇛


                       Terminal, Shell, TTY, and Console are terminologies
                       that are often confusing and loosely used to mean
                       the same thing. But it’s hardly the case. There are
                       nuanced differences that exist between each of
                       these components.


                       In this guide, we flesh out the differences between
                       these terminologies as they are used in UNIX/Linux
                       systems.


                # ⚓ Linux Shell Tips ☛ Difference_Between_SFTP,_SCP,_and_FISH
                  Protocols⠀⇛


                       Data transfer is one of the most common operations
                       carried out by users over the internet. When
                       transmitting data, caution needs to be taken to
                       ensure that data is transferred securely and not
                       compromised.


                       In this guide, we look at some of the secure data
                       transfer protocols and explore the differences that
                       exist between them.


                # ⚓ UNIX Cop ☛ How_to_install_Snap_on_CentOS_9_Stream⠀⇛


                       Hello, dear friends. Today, you will learn how to
                       install Snap on CentOS 9 Stream. With this, you
                       will be able to install many useful applications
                       using this technology from Canonical.


                       Snap is the self-sufficient package technology
                       developed by Canonical. As expected, it comes
                       integrated on Ubuntu, but it is also possible to
                       install it in other distributions like CentOS 9
                       Stream.


                       Flatpak is Snap’s natural competitor. Both offer
                       packages that can be run on any distribution that
                       supports them thanks to their box technology. That
                       is to say that in a single package are incorporated
                       all dependencies and libraries needed to run
                       without affecting the system.


                # ⚓ Linux Capable ☛ How_to_Install/Upgrade_Nginx_Mainline/
                  Stable_on_Rocky_Linux_9⠀⇛


                # ⚓ AddictiveTips ☛ How_to_encrypt_a_file_on_Linux_with_File
                  Lock_PEA⠀⇛


                       File Lock PEA is a java-based encryption tool. It
                       works excellent on Linux, especially if you’re not
                       a fan of tools like VeraCrypt, GnuPG, and others.
                       This guide will show you how to encrypt files on
                       Linux with File Lock PEA.


                # ⚓ dwaves.de ☛ MySQL_MariaDB_cheat_sheet⠀⇛


                # ⚓ AddictiveTips ☛ How_to_play_Hearts_of_Iron_IV_on_Linux⠀⇛


                       Hearts of Iron IV is a strategy game set during
                       World War II. In the game, players take control of
                       a nation during the war and fight to win. Here’s
                       how to play Hearts of Iron IV on Linux.


                # ⚓ AddictiveTips ☛ How_to_check_your_laptop_battery_from_the
                  Linux_command-line⠀⇛


                       Battery Top is an excellent application that Linux
                       users can install to monitor their laptop’s battery
                       status. In this guide, we’ll go over how to install
                       Battery Top on Linux and how to use it too.


                # ⚓ AddictiveTips ☛ Play_your_Epic_and_GOG_games_on_Linux_with
                  Heroic⠀⇛


                       The Heroic Game Launcher is an open-source tool for
                       Linux, Mac, and Windows. It allows users to
                       download, launch and play video games from the Epic
                       Games Store and GOG.com.


                       This guide will cover downloading and installing
                       the Heroic Games Launcher on Linux. We’ll also show
                       you how to use it to game on your Linux system.


          o § Games⠀➾


                # ⚓ GamingOnLinux ☛ Teenage_Mutant_Ninja_Turtles:_Shredder’s
                  Revenge_hit_a_million_sales_in_the_first_week⠀⇛


                       Not a big surprise but Teenage Mutant Ninja
                       Turtles: Shredder’s Revenge has managed to shift
                       over a million in the first week after release.
                       Developer Tribute Games confirmed the milestone
                       yesterday on the official Twitter.


                # ⚓ GamingOnLinux ☛ Yars:_Recharged_marks_a_return_of_the_1982
                  Atari_2600_classic⠀⇛


                       Atari continue to get their classics revamped and
                       remade for modern audiences, with the latest being
                       Yars: Recharged that’s a reimagining of the 1982
                       Atari 2600 classic and best-seller Yars’ Revenge in
                       partnership with Adamvision Studios and SneakyBox
                       the same teams behind Gravitar: Recharged and
                       Breakout: Recharged.


                # ⚓ GamingOnLinux ☛ Wine_manager_Bottles_default_runner_now
                  based_on_Valve’s_Wine_fork_and_Proton⠀⇛


                       Bottles is a thoroughly great application for
                       managing Windows applications and games on Linux.
                       It’s fast moving and a new release is out with
                       their new default runner called Soda, which is
                       based on Valve’s fork of Wine and Proton patches.


                # ⚓ GamingOnLinux ☛ Steam_Deck_Beta_update_and_a_Proton
                  Experimental_update_out_now⠀⇛


                       More extra fixes have come trickling down from
                       Valve with the Steam Deck Beta updated and a new
                       release of Proton Experimental too so here’s what’s
                       new.


                # ⚓ GamingOnLinux ☛ Armello_removes_advertising_Linux_and_macOS
                  support_due_to_their_party_system⠀⇛


                       Armello, a grim fairy-tale board game from League
                       of Geeks no longer advertises that it supports
                       Linux and macOS due to their new party system that
                       landed with the cross-play update.


                # ⚓ GamingOnLinux ☛ Focus_Entertainment:_Legends_and_Visions
                  bundle_has_some_good_stuff⠀⇛


                       Focus Entertainment: Legends and Visions from
                       Humble Bundle has some good looking games ready for
                       picking, so here’s a run over how they will work on
                       Linux desktop and Steam Deck. Using both the Deck
                       Verified rating and ProtonDB, here’s a list of
                       what’s available:


    * § Distributions and Operating Systems⠀➾


          o ⚓ Liam Proven ☛ Why_CP/M_didn’t_have_directory_separators,_and_what
            if_it_had_got_them?⠀⇛


                 CP/M did not support subdirectories, so it did not have a
                 directory separator.


          o § Arch Family⠀➾


                # ⚓ wxWidgets_3.2_update_may_need_manual_intervention⠀⇛


                       wxWidgets 3.2 provides a Qt frontend in addition to
                       the GTK3 one, so packages have been renamed from
                       wxgtk- to wxwidgets-. The GTK2 frontend is no
                       longer provided. If you have wxgtk2 installed, the
                       upgrade will fail with


          o § Canonical/Ubuntu Family⠀➾


                # ⚓ DebugPoint ☛ Linux_Mint_21_“Vanessa”_BETA_is_Now_Available
                  for_Testing⠀⇛


                       Linux Mint 21 “Vanessa” BETA release highlights
                       about new features, improvements and how you can
                       download and test.


          o § Devices/Embedded⠀➾


                # ⚓ CNX Software ☛ Orange_Pi_5_could_be_the_most_affordable
                  Rockchip_RK3588S_SBC⠀⇛


                       
                       Orange Pi 5 (LTS) is an upcoming single board
                       computer powered by Rockchip RK3588S cost-down
                       octa-core Cortex-A76/A55 processor that should
                       offer one of the best cost/performance ratios on
                       the market once it is launched.


                       The SBC is said to come with up to 32GB RAM, 32GB
                       eMMC flash, offers HDMI 2.1 and DisplayPort 1.4 8K
                       video outputs, up to two MIPI DSI display
                       interfaces, three camera interfaces, Gigabit
                       Ethernet, and WiFi 6 connectivity, and a few USB
                       ports plus a GPIO header.


          o § Open Hardware/Modding⠀➾


                # ⚓ Raspberry Pi ☛ How_do_I_start_my_child_coding?⠀⇛


                       You may have heard a lot about coding and how
                       important it is for children to start learning
                       about coding as early as possible. Computers have
                       become part of our lives, and we’re not just
                       talking about the laptop or desktop computer you
                       might have in your home or on your desk at work.
                       Your phone, your microwave, and your car are all
                       controlled by computers, and those computers need
                       instructions to tell them what to do. Coding, or
                       computer programming, involves writing those
                       instructions.


                # ⚓ Raspberry Pi ☛ Meet_Alex_Glow:_Lead_Hardware_Nerd⠀⇛


                       As the Lead Hardware Nerd at Hackster.io, Alex Glow
                       has an insider’s view of the technology that’s
                       coming down the rails at us in the near future.
                       Happily, she also makes it her business to share
                       that knowledge, supporting a community of almost
                       two million hardware tinkerers, inventors, and
                       improvers. She’s also the brains behind a good few
                       projects herself: she’s sent music into space, was
                       an early adopter of the companion robot, makes
                       projects with LEDs and PCBs, and… well, whatever
                       she feels like really.


                # ⚓ Linux Gizmos ☛ Kontron_3.5”_SBC_powered_by_Intel_Atom
                  X6000E_Series⠀⇛


                       Last month, Kontron unveiled their 3.5” Single
                       Board Computer powered by a variety of Intel
                       processors. The 3.5”- SBC-EKL can accommodate
                       processors from the Atom X6000E series, the Celeron
                       J6000/N6000 series and the Pentium J6000/N6000
                       series.


                       The 3.5”- SBC-EKL is capable of supporting the
                       following Intel processors…


          o § Mobile Systems/Mobile Applications⠀➾


                # ⚓ Express ☛ Android_warning_reveals_biggest_new_threat_to
                  your_Google_phone_|_Express.co.uk⠀⇛


                # ⚓ Gizmodo ☛ Nothing_Phone_(1)_Review:_A_Cool_Phone_for_Bored
                  Android_Users⠀⇛


                # ⚓ Google_Pixel_7_Pro_drama_as_leaked_Android_phone_gets
                  remote_wiped_|_T3⠀⇛


                # ⚓ 15_Best_Android_Widgets_for_Your_Android_Smartphone⠀⇛


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


          o ⚓ Linux Links ☛ Best_Free_and_Open_Source_Alternatives_to_Google
            Slides⠀⇛


                 
                 In this series we explore how you can migrate from Google
                 without missing out on anything. We recommend open source
                 solutions.


                 Google Slides lets you create pitch decks, project
                 presentations, training modules, and more. We recommend
                 the best free and open source alternatives.


          o ⚓ OpenSource.com ☛ 3_open_source_GUI_disk_usage_analyzers_for
            Linux⠀⇛


                 
                 Several great options for checking disk usage on your
                 Linux system have a graphical interface. Sometimes the
                 visual representation of disk utilization is easier or
                 newer users may not be as familiar with the various Linux
                 commands that display storage information. I am a person
                 who comprehends visual representations more easily than
                 the printout on the command line.


                 Here are several excellent GUI-based tools to help you
                 understand how your storage capacity is used.


          o § Programming/Development⠀➾


                # ⚓ Steve Kemp ☛ So_we_come_to_Lisp⠀⇛


                       Recently I’ve been working with simple/trivial
                       scripting languages, and I guess I finally reached
                       a point where I thought “Lisp? Why not”. One of the
                       reasons for recent experimentation was thinking
                       about the kind of minimalism that makes
                       implementing a language less work – being able to
                       actually use the language to write itself.


                       FORTH is my recurring example, because implementing
                       it mostly means writing a virtual machine which
                       consists of memory (“cells”) along with a pair of
                       stacks, and some primitives for operating upon
                       them. Once you have that groundwork in place you
                       can layer the higher-level constructs (such as
                       “for”, “if”, etc).


                       Lisp allows a similar approach, albeit with
                       slightly fewer low-level details required, and far
                       less tortuous thinking. Lisp always feels higher-
                       level to me anyway, given the explicit data-types
                       (“list”, “string”, “number”, etc).


                # § Java⠀➾


                      # ⚓ Linux Hint ☛ How_to_print_a_2d_array_in_java⠀⇛


                             In Java, arrays can be single-dimensional, 2-
                             dimensional, or multi-dimensional. Java’s
                             two-dimensional arrays are arrays within some
                             other arrays. The 2D arrays are also known as
                             matrices and they keep the data in the form
                             of a table i.e. columns and rows. A 2D array
                             can be created by specifying a data type
                             followed by an array name and two sets of
                             square brackets. In java, there are multiple
                             ways to print a 2D array such as using for-
                             each loop, for-loop, etc.


                      # ⚓ Linux Hint ☛ How_to_multiply_in_Java⠀⇛


                             The multiplication operator * and the
                             “multiplyExact()” method can be used to
                             multiply two values in java. The
                             multiplication operator performs
                             multiplication on any numeric value such as
                             int, float, or double. The multiplyExact()
                             method deals with only integer and double
                             type values. It takes two values, performs
                             multiplication on them, and returns the
                             resultant value. However, if the resultant
                             value exceeds the limit/range, it throws an
                             exception.


                      # ⚓ Linux Hint ☛ How_to_return_an_array_in_java⠀⇛


                             As we know that arrays are very important for
                             a programming language as they group the
                             values of same data type in one variable so
                             in Java array also play a vital role. When we
                             create functions or methods we usually pass
                             variables as arguments. But what if we want
                             to return a large amount of data having same
                             data type at once from a function or method?


                             We can do that by returning an array where we
                             want to use numerous values of the same data
                             type without occupying the large memory
                             space.


    * § Leftovers⠀➾


          o ⚓ Next_in_Nonprofits_171_–_Federated_communication_“Fediverse”_with
            Aral_Balkan⠀⇛


                 Aral joins host Steve Boland to discuss decentralized
                 social communication tools for nonprofit organizations
                 (and everyone else!). Aral talks about federated
                 communications tools (the Fediverse) like Mastodon
                 (microblogging like Twitter but without corporate
                 ownership), PixelFed (more image focused like Instagram)
                 and many other ideas. Aral discusses the problematic
                 relationship between charities seeking to have real
                 engagement with audiences and how corporate platforms
                 interfere at best, or undermine those efforts. Federate
                 tools for communication and the small web in general puts
                 more control in the hands of users and removes algorithms
                 from the communications outreach loop for charities.


          o § Hardware⠀➾


                # ⚓ Speculative_calculations_open_a_backdoor_to_information
                  theft⠀⇛


                       Sometimes a computer bleeds from its heart and
                       reveals droplets of private information. That’s the
                       case with the “Retbleed” hardware vulnerability
                       made public today: This vulnerability occurs in the
                       microprocessors that execute the instructions of a
                       computer program and perform the corresponding
                       calculations. In some cases, the processors –
                       namely the central processing units (CPU) – also
                       perform special calculations that shorten the
                       computing time and speed up the overall computing
                       process. In the process, they leave traces in the
                       memory that hackers could exploit to gain
                       unauthorized access to any information in the
                       system – for example, they could steal encryption
                       keys or security-relevant passwords. This is
                       especially risky in cloud environments where
                       multiple companies share computer systems. The
                       National Center for Cyber Security in Bern,
                       Switzerland considers the vulnerability serious
                       because the affected processors are in use
                       worldwide. However, the manufacturers have already
                       taken initial measures to close the vulnerability.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ duvaR ☛ Turkish_imam_dismissed_after_inciting_violence
                  against_doctors⠀⇛


                       During a Friday sermon on July 8, imam Ahmet Gür in
                       the Central Anatolian province of Konya called for
                       violence against doctors in the face of a
                       healthcare strike earlier in the week.


                       “They have turned the killing of doctor against the
                       state, nation. Yesterday, none of the hospitals
                       were on duty. For example, you went to the hospital
                       for your son to get an injection; otherwise, he
                       will die. But the doctor tells you to go away since
                       they are on a strike. Would you not kill him, beat
                       him, swear at him? Let’s not give an opportunity to
                       this. Let everyone be wise,” imam Gür said.


                       Shortly afterwards, the imam’s video appeared on
                       social media, stirring a huge reaction.


                # ⚓ Democracy Now ☛ “Reinfection_Wave”:_Ed_Yong_on_BA.5_Omicron
                  Variant_Spread_Amid_Mask_Mandate_Rollbacks,_Funding_Cuts⠀⇛


                       COVID-19 cases are rising as the BA.5 Omicron
                       variant puts more people in the hospital amid high
                       rates of reinfection, which is the focus of a new
                       piece by Pulitzer Prize-winning journalist Ed Yong
                       in The Atlantic that is headlined “Is BA.5 the
                       ‘Reinfection Wave’?” Yong warns the premature
                       rollback of protective policies, like mask mandates
                       and public health funding, has left people more
                       vulnerable to reinfection. Meanwhile, a concerning
                       number of Americans continue to distrust the
                       vaccine. Rather than focusing on community-based
                       measures that will protect the most vulnerable
                       first, “the Biden administration’s posture has been
                       moving toward an era of individual responsibility,”
                       says Yong.


          o § Security⠀➾


                # § Privacy/Surveillance⠀➾


                      # ⚓ New York Times ☛ China’s_Surveillance_State_Hits_Rare
                        Resistance_From_Its_Own_Subjects⠀⇛


                             Security researchers say the leaked database,
                             apparently used by the police in Shanghai,
                             had been left online and unsecured for
                             months. It was exposed after an anonymous
                             user posted in an online forum offering to
                             sell the vast trove of data for 10 Bitcoin,
                             or about $200,000. The New York Times
                             confirmed parts of a sample of the database
                             released by the anonymous user, who posted
                             under the name ChinaDan.


                             In addition to basic information like names,
                             addresses and ID numbers, the sample also
                             featured details that appeared to be drawn
                             from external databases, like instructions
                             for couriers on where to drop off deliveries,
                             raising questions about how much information
                             private companies share with the authorities.
                             And, of particular concern for many, it also
                             contained intensely personal information,
                             such as police reports that included the
                             names of people accused of rape and domestic
                             violence, as well as private information
                             about political dissidents.


                      # ⚓ Purism ☛ Privacy_in_Depth⠀⇛


                             In the security world there is a concept
                             called “Defense in Depth” that refers to
                             setting up layers of defense so that if an
                             attacker bypasses one layer there are other
                             layers they must contend with. In physical
                             security this might take the form of a lock
                             on the outside door of an office building, a
                             security guard inside the foyer who
                             identifies a visitor, access to different
                             floors in the building protected by keycards
                             in the elevator, additional locked rooms or
                             safes on a particular floor for particularly
                             sensitive property, and security guards
                             patrolling the building and reviewing
                             security camera footage. In the digital world
                             this might take the form of firewalls,
                             network segmentation, multi-factor
                             authentication, event log monitoring, and
                             malware scanners.


                             A similar approach, which I’ll call “Privacy
                             in Depth” applies the same principles to
                             privacy. When you have an attacker who is
                             attempting to violate your privacy, you can
                             assume that at some point they may be able to
                             bypass one layer of defense, and if they do,
                             you want to have additional layers available
                             to protect your personal data. Protecting our
                             customers’ privacy is a core tenet in our
                             Social Purpose and in this post I will
                             describe the layers of privacy defenses we
                             have built into the Librem 14, Librem Mini,
                             Librem 5 and Librem 5 USA product lines.


                      # ⚓ Techdirt ☛ NSO_Group_Hacking_Prompts_Apple_To_Add_A
                        ‘Lockdown_Mode’_To_Its_Devices⠀⇛


                             Israeli malware maker NSO Group’s frequent
                             targeting of iPhones has led to multiple
                             rounds of patches, a federal lawsuit, and
                             Apple instituting a notification program to
                             inform customers their devices have been
                             compromised.


          o § Defence/Aggression⠀➾


                # ⚓ Medforth ☛ FBI_busts_Islamist_bomb_maker_in_Austria⠀⇛


                       According to the “Salzburger Nachrichten”, the
                       investigators got on the boy’s trail thanks to tips
                       from the American FBI. The user from Austria
                       probably came to the attention of the US federal
                       police during a worldwide internet monitoring for
                       radical Islamist content. The student was placed in
                       custody by the regional court because of the risk
                       of escaping and the risk of committing the crime.
                       According to the court’s decision at the time, it
                       could not be replaced by less severe means as long
                       as the accused did not “reduce his extremist
                       views”.


                # ⚓ Democracy Now ☛ As_Biden_Visits_Israel,_Palestinians_Urge
                  U.S._Not_to_Build_Jerusalem_Embassy_on_“Stolen_Property”⠀⇛


                       President Biden is in Israel as part of a four-day
                       trip to the Middle East, where he reaffirmed his
                       support for Israel despite growing disapproval
                       among members of the Democratic Party over the
                       state’s brutal treatment of Palestinians. The Biden
                       administration faces criticism over plans to build
                       a U.S. embassy in Jerusalem on land that was
                       illegally confiscated by Israel from Palestinians
                       in 1948, as well as the State Department’s
                       whitewashed investigation of Shireen Abu Akleh’s
                       killing, which multiple other independent
                       investigations have determined was caused by an
                       Israeli bullet. “By not engaging in dismantling the
                       structures of discrimination and oppression … that
                       Israel maintains, the United States is in fact
                       supporting those structures,” says historian Rashid
                       Khalidi, whose family is among the Palestinians
                       whose seized lands are set to be used for the
                       embassy.


                # ⚓ Democracy Now ☛ Family_of_Slain_Palestinian_American
                  Journalist_Shireen_Abu_Akleh_to_Biden:_Hold_Israel
                  Accountable⠀⇛


                       President Biden will be visiting the Palestinian
                       territories and meeting President Mahmoud Abbas on
                       Friday. Ahead of Biden’s trip, the family of
                       Shireen Abu Akleh demanded Biden call out Israel
                       over her killing while covering a raid on the Jenin
                       refugee camp in the West Bank. On Wednesday, U.S.
                       Secretary of State Antony Blinken invited Shireen
                       Abu Akleh’s family to visit the United States. “We
                       will continue to call for justice, and we will
                       continue to call on the U.S to carry out a
                       transparent investigation by an independent body,”
                       says Shireen Abu Akleh’s niece, Lina Abu Akleh. “In
                       addition, we continue to call on the U.N. and the
                       ICC to carry out an investigation and hold Israel
                       accountable and put an end to this grotesque
                       impunity that Israel continues to enjoy.” We speak
                       with Rashid Khalidi, Palestinian American professor
                       of modern Arab studies at Columbia University.


                # ⚓ Democracy Now ☛ “Shameful”:_Biden’s_Trip_to_Saudi_Arabia
                  for_More_Oil_Ignores_Human_Rights_Abuses,_Khashoggi_Murder⠀⇛


                       President Biden is set to meet with Saudi Arabia’s
                       Crown Prince Mohammed bin Salman on Friday as part
                       of a four-day visit to restore key relationships
                       and build security cooperation in the Middle East.
                       Human rights activists are outraged that the U.S.
                       is willing to support a leader responsible for
                       human rights violations including in the brutal war
                       in Yemen, the state-sanctioned killing of
                       Washington Post columnist Jamal Khashoggi and more.
                       One of Biden’s aims is to convince Saudi Arabia to
                       increase oil production, an answer to pressures at
                       home over skyrocketing gas prices from the Russian
                       war in Ukraine. “If we’re willing to sacrifice for
                       oil prices, there are much less heinous sacrifices
                       to be making than to continue military support for
                       the governments of Saudi Arabia and the UAE,” says
                       Sarah Leah Whitson, executive director of Democracy
                       for the Arab World Now.


          o § Transparency/Investigative Reporting⠀➾


                # ⚓ IT Wire ☛ Former_CIA_engineer_convicted_of_espionage_in
                  Vault_7_case⠀⇛


                       A former CIA engineer has been convicted of
                       espionage for leaking documents to WikiLeaks that
                       exposed the agency as engaging in mass
                       surveillance.


                       The conviction of Joshua Schulte on eight spying
                       and obstruction charges was announced in a
                       Manhattan court on 13 June.


                       The Vault 7 exploits were released beginning in
                       March 2017 and continued until September that year.


          o § Environment⠀➾


                # § Energy⠀➾


                      # ⚓ DeSmog ☛ As_Alarm_Over_Plastic_Grows,_Saudis_Ramp_Up
                        Production_in_the_US⠀⇛


                             The flares started last December, an event
                             Errol Summerlin, a former legal-aid lawyer,
                             and his neighbors had been bracing for since
                             2017. After the flames, nipping at the night
                             sky like lashes from a heavenly monster, came
                             the odor, a gnarled concoction of steamed
                             laundry and burned tires.


                             Thus did the Saudi royal family mark the
                             expansion of its far-flung petrochemical
                             empire to San Patricio County, Texas, a once-
                             rural stretch of flatlands across Nueces Bay
                             from Corpus Christi. It arrived in the form
                             of Gulf Coast Growth Ventures (GCGV), a plant
                             that sprawls over 16 acres between the towns
                             of Portland and Gregory. The complex contains
                             a circuit board of pipes and steel tanks that
                             cough out steam, flames and toxic substances
                             as it creates the building blocks for plastic
                             from natural gas liquids.


          o § Finance⠀➾


                # ⚓ Techdirt ☛ North_Carolina_Republicans_Push_Bill_Forcing
                  Towns_To_Destroy_Electric_Car_Chargers⠀⇛


                       The core GOP belief in “small government” and “free
                       markets” and “no taxpayer waste” doesn’t hold up
                       quite as well as it used to to scrutiny, assuming
                       it ever did at all.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ ME Forum ☛ CAIR_Polls_Itself,_Revealing_Its_Failure_to
                  Unite_Muslims⠀⇛


                       Carried out between May and June 2022 “during the
                       2022 primary season of local and state elections,
                       and congressional midterm elections,” CAIR’s survey
                       collected 525 responses from voters who claimed to
                       be Muslim, answering questions about various
                       “social and policy issues” as well as political
                       party affiliations and opinions.


                       But the methodology was shoddy. Respondents were
                       found by CAIR entirely through its own email lists
                       and social media pages, with the resulting survey
                       then speciously presented as a proper exercise in
                       data analysis. This was not a survey of American
                       Muslims, but mostly of American Islamists; and only
                       those who subscribe to CAIR.


                # ⚓ Helsinki Times ☛ TikTok’s_global_takeover:_Coincidental_or
                  calculated?⠀⇛


                       One of the main factors that keeps a large audience
                       on the app is the ‘For You’ page, an endless cycle
                       of content, catered to the user and their
                       interests, based on a plethora of deciding
                       components. Firstly, the liking, commenting, and
                       sharing of the video, as well as the watch time,
                       and the number of times it has been rewatched.
                       Thus, the algorithm grapples with this information
                       and builds an idea of the content the user would
                       appreciate, using categories based on hashtags of
                       posts, the song utilized, and the actual account
                       itself. Broken down bluntly as the TikTok rabbit
                       hole by some, the app has become the perfect place
                       to search for and explore new interests regarding
                       content, regardless of how contrasting they are to
                       previous suggestions.


                # § Misinformation/Disinformation⠀➾


                      # ⚓ NPR ☛ A_rape,_an_abortion,_and_a_one-source_story:_a
                        child’s_ordeal_becomes_national_news⠀⇛


                             Later in the afternoon, he issued a further
                             public statement saying, “My heart aches for
                             the pain suffered by this young child” and
                             thanking law enforcement officers for getting
                             the accused rapist off the streets. Yost did
                             not offer any apology to the Indianapolis
                             newspaper or even a reference to the
                             vindication of The Star’s reporting.


                      # ⚓ Nieman Lab ☛ Unimaginable_abortion_stories_will
                        become_more_common._Is_American_journalism_ready?⠀⇛


                             In, say, a reported story about a child who
                             must travel out of state to receive an
                             abortion because abortion is illegal after
                             six weeks in the state where she lives, there
                             are other reasons a publication might leave
                             out identifying details.


          o § Censorship/Free Speech⠀➾


                # ⚓ YLE ☛ Green_Party_MP_sees_Tiktok_account_deleted_after
                  posting_abortion_rights_video⠀⇛


                       Virta announced the deletion of her account in a
                       tweet and also via a press release.


                # ⚓ AccessNow ☛ Indonesia:_Hold_public_consultations_on_the
                  revised_draft_of_the_Criminal_Code_and_repeal_restrictive
                  provisions⠀⇛


                       Note: Access Now and 23 other organizations call
                       for recent draft amendments to Indonesia’s Criminal
                       Code to be repealed. These amendments risk
                       curtailing civic freedoms – particularly the right
                       to freedom of expression and information online
                       through expanded defamation provisions. The
                       Indonesian government must also conduct public
                       consultations before adopting the draft amendments.


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


                # ⚓ The Dissenter ☛ Assange_Fights_Extradition_To_United_States
                  With_Two_Appeals⠀⇛


                       Assange faces 18 charges, 17 of which are charges
                       under the US Espionage Act. All of the allegations
                       against him stem from the publication of documents
                       that WikiLeaks obtained from US Army whistleblower
                       Chelsea Manning in 2010.He has been jailed at Her
                       Majesty’s Prison Belmarsh since April 11, 2019,
                       when the Ecuador government revoked his political
                       asylum and allowed the British police to enter
                       their London embassy and drag him to a police van.


          o § Civil Rights/Policing⠀➾


                # ⚓ New York Times ☛ For_Blind_Internet_Users,_the_Fix_Can_Be
                  Worse_Than_the_Flaws⠀⇛


                       “I’ve not yet found a single one that makes my life
                       better,” said Mr. Perdue, 38, who lives in Queens.
                       He added, “I spend more time working around these
                       overlays than I actually do navigating the
                       website.”


                       Last year, over 700 accessibility advocates and web
                       developers signed an open letter calling on
                       organizations to stop using these tools, writing
                       that the practical value of the new features was
                       “largely overstated” and that the “overlays
                       themselves may have accessibility problems.” The
                       letter also noted that, like Mr. Perdue, many blind
                       users already had screen readers or other software
                       to help them while online.


    * § Gemini* and Gopher⠀➾


          o § Personal⠀➾


                # ⚓ Incompatible_with_now⠀⇛


                       I'm on holidays in my country of origin with family
                       at the moment,
                       after a long absence. It's wonderful. That said, a
                       few nights ago
                       though we all settled in to watch a popular game of
                       local $sport on
                       TV, and although I'm glad I was there, I found
                       myself feeling
                       completely alienated by almost everything I saw.

                       Although I have a TV in my country of residence, I
                       only use it for
                       streaming and playing games - there's no over-the-
                       air TV, and we
                       prefer to read news online.  This has been our
                       situation for at least
                       a decade.  Thus, being subjected to the fire hose
                       of prime-time mental
                       malware (sorry, "advertising") was a genuine shock.
                # ⚓ Moving_North⠀⇛


                       We’re moving to the Pacific Northwest on Saturday.
                       We’ve signed the lease and paid first month’s rent
                       on the new apartment already. I will not miss the
                       Central California heat one bit. I’m honestly so
                       excited to get out of here.


          o § Technical⠀➾


                # ⚓ The_Old_Computer_Challenge_V2:_day_5⠀⇛


                       Some quick news for the Old Computer Challenge!


                       As it’s too tedious to monitor the time spent on
                       the Internet, I’m now using a chronometer for the
                       day… and stopped using Internet in small bursts.
                       It’s also currently super hot where I live right
                       now, so I don’t want to do much stuff with the
                       computer…


                       I can handle most of my computer needs offline.
                       When I use Internet, it’s now for a solid 15
                       minutes, except when I connect from my phone for
                       checking something quickly without starting my
                       computer, I rarely need to connect it more than a
                       minute.


                # § Internet/Gemini⠀➾


                      # ⚓ Torifying_Lagrange⠀⇛


                             A great thing about gemini is that gemtext
                             documents tend to be very lightweight, and so
                             it usually does not take very long to load
                             them over Tor. So, assuming Tor does a
                             reasonably good job at hiding your IP
                             address, and throwing in all the built-in
                             privacy benefits of Gemini, one can enjoy a
                             comfortable feeling of privacy while browsing
                             Gemini capsules. It is easy to torify
                             Lagrange with torsocks, by simply running
                             “torsocks lagrange”.


                             I ran into a serious problem, however, in
                             using a torified lagrange: for some unknown
                             reason, the background task which handles
                             refreshing your feeds will (apparently)
                             lockup, causing the feeds never to finish
                             refreshing, and driving one of your CPU cores
                             to switch to space-heater mode (100% usage
                             forever). This only happens once every few
                             times you refresh your feeds, but since
                             lagrange (1.13.6) is hardcoded to refresh
                             your feeds every 16 minutes, then inevitably
                             you will switch back to Lagrange to find that
                             the feed refresher has gotten stuck in this
                             infinite-loop-like behavior.


                      # ⚓ Bob’s_New_Not-So-Secret_Online_Journal:_–_Guess_what
                        happens_when_you_accidentally_do_a_shutdown_instead_of
                        a_reboot…?⠀⇛


                      # ⚓ Deplatforming_sex⠀⇛


                             i subscribe to the academic journal “Porn
                             Studies”. Volume 8 Issue 4 was dedicated to
                             the topic of “Deplatforming sex”.


                      # ⚓ Gemini_Radio:_Episode_42⠀⇛


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



                    ䷩ 𝚕𝚒𝚗𝚎 4883

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.15.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_15/07/2022:_Tor_Browser_11.5_and_Krita_5.1_Beta_2⠀✐


Posted in News_Roundup, Site_News at 4:13 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Desktop/Laptop
          o Audiocasts/Shows
          o Kernel_Space
          o Instructionals/Technical
          o Games
          o Desktop_Environments/WMs
                # K_Desktop_Environment/KDE_SC/Qt
    * Distributions_and_Operating_Systems
          o Fedora_Family_/_IBM
          o Canonical/Ubuntu_Family
          o Devices/Embedded
          o Open_Hardware/Modding
    * Free,_Libre,_and_Open_Source_Software
          o Web_Browsers
                # Mozilla
          o Productivity_Software/LibreOffice/Calligra
    * Leftovers
          o Hardware
          o Health/Nutrition/Agriculture
          o Security
                # Privacy/Surveillance
          o Defence/Aggression
          o Transparency/Investigative_Reporting
          o Environment
                # Energy
                # Wildlife/Nature
                # Overpopulation
          o Finance
          o AstroTurf/Lobbying/Politics
          o Censorship/Free_Speech
          o Freedom_of_Information_/_Freedom_of_the_Press
          o Civil_Rights/Policing
          o Digital_Restrictions_(DRM)
          o Monopolies
                # Copyrights
    * Gemini*_and_Gopher
    * Finance
    * Technical
          o Internet/Gemini
          o Programming
    * § GNU/Linux⠀➾


          o § Desktop/Laptop⠀➾


                # ⚓ A_tale_of_too_many_macs_–_Fading_Memories⠀⇛


                       It’s missing so many keys. I know, that’s par for
                       course with Apple, but when using Krita, a missing
                       Insert key means no easy way to create layers. And
                       there’s a lot of inconsistency between
                       applications. In Terminal, you switch tabs with
                       Control-Tab, in Firefox with Option-Command-Left/
                       Right, in Qt Creator with Option-Tab. I haven’t
                       figured out what it is in Kate. Navigating around
                       text is also inconsistent between applications. And
                       that means that I just never get any finger memory
                       down: especially since I also use all other
                       operating systems…


                       The window manager is also pretty primitive and
                       needs help from an external utility called
                       Rectangle.


                       And the permissions stuff is crazy. The wacom
                       tablet driver needs permissions to use
                       Accessibility — as does, for some reason Dropbox.


                       The hardware for the rest is fine… The screen is
                       good, I don’t mind the notch since I run pretty
                       much everything full-screen, all the time. Battery
                       life is good, but not as good as the 13″‘ battery
                       life was.


                       As for the rest of the hardware, the screen is
                       fine, I don’t mind the notch, because I pretty much
                       always use all applications full-screen, because of
                       how bad window management is compared to KWin, even
                       with Rectangle.


          o § Audiocasts/Shows⠀➾


                # ⚓ Video ☛ The_Best_Gaming_Linux_Distro_–_Invidious⠀⇛


                       What is the best Linux distro for gaming?


                # ⚓ Video ☛ Microsoft’s_black_box_certificate_guidelines_are
                  yet_another_attack_on_the_Linux_Desktop_–_Invidious⠀⇛


                       Spoiler alert: Microsoft’s still the enemy.


                # ⚓ Video ☛ Peppermint_OS_2022_Review_–_Lightweight_Linux_ep._1
                  –_Invidious⠀⇛


                       What other distros should be in this series? Let me
                       know below! We’re taking a look at Peppermint OS
                       since they have made the move from Ubuntu LTS to
                       Debian Bullseye.


          o § Kernel Space⠀➾


                # ⚓ LWN ☛ Linux_5.18.12⠀⇛


                       I'm announcing the release of the 5.18.12 kernel.

                       This, and the 5.15.55, 5.10.131, and 5.4.206
                       releases are only for those users
                       of the drivers/mtd/nand/raw/gpmi-nand/gpmi-nand.c
                       driver, to prevent known data
                       loss issues with that codebase.  If you don't use
                       this driver, no need to
                       upgrade.

                       The updated 5.18.y git tree can be found at:
                       	git://git.kernel.org/pub/scm/linux/kernel/git/
                       stable/linux-stable.git linux-5.18.y
                       and can be browsed at the normal kernel.org git web
                       browser:

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

                       thanks,

                       greg k-h
                # ⚓ LWN ☛ Linux_5.15.55⠀⇛


                # ⚓ LWN ☛ Linux_5.10.131⠀⇛


                # ⚓ LWN ☛ Linux_5.4.206⠀⇛


                # ⚓ LWN ☛ Stable_kernel_updates_delayed⠀⇛


                       The stable kernel updates that were due on July 14
                       have been delayed for several days, according to
                       Greg Kroah-Hartman, due to problems that have come
                       up with the Retbleed mitigation patches.


          o § Instructionals/Technical⠀➾


                # ⚓ OSNote ☛ How_to_Install_the_Latest_Python_Version_on_Debian
                  11_–_OSNote⠀⇛


                       Python is an interpreted, interactive, object-
                       oriented programming language. It was created by
                       Guido van Rossum in 1991.


                       Python runs on Windows, Linux/Unix, Mac OS. Python
                       can be used to develop desktop GUI applications and
                       CGI scripts for the web. Also, it’s used for
                       server-side scripting for Apache HTTP Server sites.
                       Python is most popular for its elegance and
                       simplicity.


                # ⚓ ID Root ☛ How_To_Install_R_Programming_Language_on_Fedora
                  36_–_idroot⠀⇛


                       In this tutorial, we will show you how to install R
                       Programming Language on Fedora 36. For those of you
                       who didn’t know, R is an open-source programming
                       language and free software environment for
                       statistical computing and graphical representation
                       created and supported by the R Core Team and the R
                       Foundation. Developed by Robert Gentleman and Ross
                       Ihaka in 1993, R is a free and open-source
                       programming language that is mostly used in
                       statistical computing, modeling, data analytics,
                       and scientific research.


                       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 R programming language on a
                       Fedora 36.


                # ⚓ Install_Devolution_Remote_Desktop_Manager_on_Ubuntu/Debian
                  –_kifarunix.com⠀⇛


                       In this tutorial, you will learn how to install
                       Devolution remote desktop manager on Ubuntu/Debian
                       desktop systems. According to Devolution’s page,
                       Remote Desktop Manager allows you to centralize and
                       secure access to all your remote connections,
                       manage privileged credentials, configure your
                       network for remote access, and restrict permissions
                       to specific users. IT teams can use the integrated
                       credential management features to store and manage
                       account passwords, in addition to integrating
                       existing password manager solutions directly into
                       Remote Desktop Manager. User privileges and
                       permissions can be easily managed using our role-
                       based access controls, which can work with your
                       active directory groups to help admins create a
                       granular protection system. All of these systems
                       can help enforce your least-privilege principles
                       and protect sensitive data so you can comply with
                       data security regulations.


                # ⚓ Packit_–_how_to_create_pull-request_for_Fedora_from
                  upstream_|_Miroslav_Suchý⠀⇛


                       I am a contributor to fedora-license-data upstream,
                       and I investigated what will be the easiest way to
                       build a new version of the Fedora package. I ended
                       up using Packit for that. With just one command, it
                       creates a pull request in src.fedoraproject.org.


                # ⚓ TecAdmin ☛ S3_&_Cloudfront:_404_Error_on_Page_Reload_
                  (Resolved)⠀⇛


                       I have recently deployed a published Node.js
                       application via Amazon S3 static website hosting.
                       After deployment, I noticed that we get the 404
                       error message while refreshing the pages. After a
                       few searching, I got the reason behind it. I found
                       that the application required a special
                       configuration for routing like .htaccess in Apache
                       servers. But here is the issue, we can’t use the
                       .htaccess file with S3 static website hosting.


                       In this tutorial, we will discuss solving this
                       issue with the options provides under the S3
                       configuration. Also, provide you with instructions
                       to fix this issue for the users using the
                       Cloudfront.


          o § Games⠀➾


                # ⚓ Hackaday ☛ Homebrew_Stream_Deck_Pedal_Emulates_The_Real
                  Thing⠀⇛


                       Pedals are a great way to control functions on your
                       computer. You’re rarely using your feet for
                       anything else, so they can handle some tasks,
                       freeing up your hands. This Elgato Stream Deck
                       controller from [DDRBoxman] does just that.


          o § Desktop Environments/WMs⠀➾


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


                      # ⚓ Krita ☛ Krita_5.1_Beta_2⠀⇛


                             Today we’re releasing the second beta for
                             Krita 5.1!


                             For the full list, check out the work-in-
                             progress full release notes!


                             Or check out Wojtek Trybus release video!


    * § Distributions and Operating Systems⠀➾


          o § Fedora Family / IBM⠀➾


                # ⚓ Linux Shell Tips ☛ What_are_CentOS_and_CentOS_Stream_and
                  History⠀⇛


                       CentOS (Community ENTerprise Operating System) also
                       widely referred to as CentOS Linux, is a free and
                       open-source community-developed Linux distribution
                       that was based on RHEL. It is a no-cost RHEL build
                       that was popular for handling production workloads
                       and also as a desktop distribution.


                       For a long time, CentOS enjoyed a good run winning
                       the adulation of thousands of Linux users until its
                       sudden demise on December 31, 2021. CentOS 8 was
                       unilaterally discontinued by RedHat in favor of
                       CentOS Stream which is the upstream and current
                       development branch of RHEL, thus marking the end of
                       support for the CentOS Project.


                # ⚓ Linux Shell Tips ☛ The_History_of_AlmaLinux_(Enterprise)
                  Distribution⠀⇛


                       AlmaLinux is a stable, robust, and community-driven
                       Linux distribution that was originally created by
                       CloudLinux as a successor to CentOS which turned
                       End-Of-Life at the end of December 2021.


                       AlmaLinux is completely free and open source and
                       places an emphasis on long-term stability and
                       providing an enterprise-ready environment for
                       handling production workloads. It is 1:1 binary
                       compatible with RHEL and is a perfect solution for
                       users who cannot afford to pay for an RHEL
                       subscription.


                # ⚓ Red Hat Official ☛ Modernization:_Why_is_it_hard? [Ed:
                  Buzzword that IBM uses to sell more complexity and bloat
                  (selling more contracts for managing this new complexity)]⠀⇛


                       Modernizing a portfolio of legacy applications
                       presents some unique challenges in enterprise
                       environments. In my first blog in this series,
                       Modernization: Why is it important?, I recommended
                       considering these two points when deciding whether
                       to embark on a modernization project:


                # ⚓ Red Hat Official ☛ ABB_and_Red_Hat_partner_to_deliver
                  further_scalable_digital_solutions_across_industrial_edge_and
                  hybrid_cloud⠀⇛


                       ABB and Red Hat today announced a global
                       partnership to enable industries using ABB’s
                       process automation and industrial software to scale
                       rapidly and flexibly leveraging Red Hat’s industry
                       leading enterprise platforms and application
                       services built on Red Hat Enterprise Linux.


                # ⚓ Venture Beat ☛ Red_Hat’s_new_CEO_to_focus_on_Linux_growth
                  in_the_hybrid_cloud,_AI_and_the_edge_|_VentureBeat⠀⇛


                       When IBM acquired Linux vendor Red Hat for $34
                       billion in 2019, Paul Cormier took the reins as Red
                       Hat CEO. After three years, Cormier is now handing
                       those reins over to a new leader.


                       Yesterday, Red Hat announced that long-time
                       engineering leader at the company, Matt Hicks, will
                       now be the company’s president and CEO. Cormier
                       will move to the chairman role, where he will
                       continue to be an active participant in the
                       company’s activities.


                # ⚓ SDx Central ☛ Ericsson_Cloud-Native_5G_Core_Rides_Red_Hat
                  OpenShift_–_SDxCentral⠀⇛


                       Ericsson and Red Hat are working to validate the
                       former’s cloud-native 5G core to work across the
                       latter’s OpenShift software platform in a move
                       similar to one struck by Ericsson earlier this year
                       with Red Hat rival VMware.


                       Honoré LaBourdette, global VP at Red Hat, explained
                       that the two vendors have validated services that
                       support virtual evolved packet core (vEPC), 5G
                       core, IP multimedia subsystem (IMS), operating
                       support systems (OSS), and business support systems
                       (BSS). The vendors noted that proof of concepts
                       (PoCs) have been running with service providers.


                       The new agreement is billed as an expansion of
                       ongoing work between Ericsson and Red Hat targeting
                       the telecommunications space. It’s focused on
                       making sure Ericsson’s services running as cloud-
                       native functions (CNFs) can operate at scale for
                       telecom operators using Red Hat’s OpenShift and
                       OpenStack platforms to support their 5G network
                       deployments.


                # ⚓ Red Hat ☛ New_HTTP_clients,_a_Java_generator,_and_more_in
                  Fabric8_6.0.0_|_Red_Hat_Developer⠀⇛


                       The Fabric8 Kubernetes client has been simplifying
                       Java developers’ use of Kubernetes for several
                       years. The 6.0.0 release represents a major body of
                       work spanning about five months of effort in both
                       the core of the project and in related utilities.


                # ⚓ Enterprisers Project ☛ 4_reasons_to_invest_in_leadership
                  training_for_everyone_|_The_Enterprisers_Project [Ed: “The
                  Great Resignation” lie/myth once again pushed by IBM, which
                  is lying off its own staff]⠀⇛


                       As a leadership and change consultant, I believe
                       “The Great Resignation” is shorthand for the
                       collective sigh (or perhaps scream) that’s emanated
                       from management and HR offices across the country
                       as they watch key employees leave the fold.


                       As study after study attempts to answer the “why,”
                       leaders are thinking more immediately about their
                       approach to talent management and developing
                       strategies to retain their top talent.


                       Another idea is surfacing, too: Individuals that
                       have always been considered top talent may in fact
                       be standing in the way of new talent, quirky
                       talent, creative talent, quiet talent, or diverse
                       talent. Firms that overhaul their talent-management
                       strategy to better understand the traits, skills,
                       and capabilities required to drive business
                       objectives are often better able to identify
                       individuals who meet key criteria and prioritize
                       them for development opportunities.


                # ⚓ Red Hat Official ☛ Introducing_VDUSE:_a_software-defined
                  datapath_for_virtio⠀⇛


                       vDPA device in userspace (VDUSE) is an emerging
                       approach for providing software-defined storage and
                       networking services to virtual machine (VM) and
                       container workloads. The vDPA (virtio data path
                       acceleration) kernel subsystem is the engine behind
                       VDUSE. If you’re not familiar with the vDPA kernel
                       framework, please refer to our Introduction to vDPA
                       kernel framework and vDPA bus drivers for kernel
                       subsystem interactions blogs to become familiar
                       with concepts such as vDPA bus, vDPA bus driver,
                       and vDPA devices, as we assume readers are familiar
                       with those topics in this blog.


          o § Canonical/Ubuntu Family⠀➾


                # ⚓ Ubuntubuzz ☛ Ubuntu_22.04_Review,_A_Future_of_FOSS
                  Computing⠀⇛


                       We think Ubuntu Jammy is a future of Free and Open
                       Source Software computing. With the default
                       technology it implements –including GNOME, Pipewire
                       and Snap– and the OEMs availability quickly growing
                       around, Ubuntu is one among few which sets the
                       standard for FOSS computings and the others will
                       surely follow. We recommend Jammy for any new user
                       especially those with mid-high specifications and
                       they can start the journey with Live USB first. The
                       drawbacks are real, and there are few of them, but
                       this release can be considered the greatest LTS
                       ever. Kudos to Canonical and all Ubuntu developers!
                       Congratulations to the community!


                # ⚓ Linuxiac ☛ Linux_Mint_21_Has_Released_Betas_of_Its
                  Cinnamon,_Xfce,_and_Mate_Editions⠀⇛


                       Linux Mint 21 “Vanessa“ is close to its final
                       version with the release of beta versions of its
                       spins. So here’s what’s new!


                       Linux Mint has proven itself as perhaps the best
                       Ubuntu derivative throughout the years, and the
                       distro has established a large user base.


                       As a result, it is increasingly the preferred
                       choice for a desktop system among Linux users at
                       the expense of Ubuntu, which has implemented
                       controversial solutions in its latest releases.


                       That’s why each new version of Linux Mint is widely
                       anticipated, and the upcoming 21 release is no
                       exception.


          o § Devices/Embedded⠀➾


                # ⚓ CNX Software ☛ ASRock_Industrial_iEPF-9010S/iEP-9010E_Edge
                  AIoT_platforms_feature_Alder_lake_S_CPU,_up_to_128GB_RAM_–
                  CNX_Software⠀⇛


                       ASRock Industrial has released the iEPF-9010S and
                       iEP-9010E high-end, rugged Edge AIoT platforms
                       powered by 12th Gen Intel Alder Lake S processors,
                       equipped with up to 128GB RAM, 4G LTE, 5G, Wi-Fi
                       6E, Bluetooth 5.2 connectivity, and real-time TSN/
                       TCC networking.


                       The I/O rich embedded computers are designed for
                       highly demanding workloads and mission-critical
                       industrial applications such as factory automation,
                       machine automation, robotic control, AI-enabled AOI
                       (automated optical inspection), autonomous
                       vehicles, smart cities, and more.


                # ⚓ Linux Hint ☛ What_are_the_different_versions_of_Raspberry
                  Pi?⠀⇛


                       Raspberry Pi’s are the single-board computers that
                       are just like the desktop computers and laptops in
                       working but they are the palm-size in physical
                       appearance. Initially, it was released for teaching
                       the usage of Desktop computers in educational
                       institutions but later on, on the basis of its size
                       and usage, it was being used in different projects
                       of Electronics and IoT as a microcontroller.


                       To date, the Raspberry Pi foundation has released a
                       number of models of Raspberry Pi, among which the
                       top Raspberry models are being discussed in the
                       guide.


          o § Open Hardware/Modding⠀➾


                # ⚓ Linux Hint ☛ How_To_Remove_The_Arduino_Library?⠀⇛


                       To interface different sensors or devices with
                       Arduino boards there are libraries used in the
                       Arduino code that helps the microcontroller to
                       recognize the devices attached with it. Moreover,
                       libraries enhance the functionality of the Arduino
                       boards in such a way that some extra functions can
                       be performed through the microcontroller.
                       Sometimes installing a library for any specific
                       device might not work, or you need to install an
                       updated version of that particular library. So, if
                       you’re looking for a way to uninstall the library
                       from the Arduino then read this guide as I have
                       explained the process of uninstalling an Arduino
                       library.


                # ⚓ Arduino ☛ This_device_detects_different_household_sounds
                  through_tinyML_|_Arduino_Blog⠀⇛


                       For people who suffer from hearing loss or other
                       auditory issues, maintaining situational awareness
                       can be vital for keeping safe and autonomous. This
                       problem is what inspired the team of Lucia Camacho
                       Tiemblo, Spiros Kotsikos, and Maria Alifieri to
                       create a small device that can alert users to
                       certain household sounds on their phone.


                       The team decided to incorporate embedded machine
                       learning in order to recognize ambient sounds, so
                       they opted for an Arduino Nano 33 BLE Sense. After
                       recording many samples of various events, such as a
                       conversation, knocking on the door, the TV, a
                       doorbell, and silence, they fed them into a tinyML
                       model with the help of Edge Impulse’s Studio. The
                       resulting model was able to successfully
                       differentiate between events around 90% of the
                       time.


                # ⚓ Arduino ☛ A_temperature-sensing_Pac-Man/Ghost_LED_matrix
                  for_retro_gamers_|_Arduino_Blog⠀⇛


                       Instructables users Monserrath Velasco and Santiago
                       Guerra have created an LED matrix that not only
                       features classic Pac-Man characters, but also shows
                       the current ambient temperature by coding it as the
                       Ghost’s color which ranges from blue (cold) to red
                       (hot).


                       The matrix itself was fashioned out of several
                       WS2812B LED strips, which contain a total of 71
                       individually-addressable LEDs. After soldering them
                       together using some wire and gluing them to a
                       cardboard backing, the team connected the strip to
                       an Arduino Uno along with a BME280 environmental
                       sensing module. The final component was a single
                       momentary pushbutton switch that gives users the
                       option to change between the Ghost and Pac-Man
                       figures.


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


          o § Web Browsers⠀➾


                # ⚓ DaemonFC (Ryan Farmer) ☛ Lynx:_For_a_Matthew_Garrett-free
                  Web_browsing_experience._Bonus:_Which_news_sites_are_worth
                  reading?_(Not_the_Bill_Gates_ones.)_–_BaronHK’s_Rants⠀⇛


                       The modern Web is crap, because it’s unusable if
                       you value your sanity. Mr. Garrett claims he’s a
                       Open Source developer, but at the same time uses
                       platforms that don’t even allow you to read his
                       blog without proprietary software (JavaScript
                       programs are usually proprietary software), images
                       (bandwidth hog), and other nasties.


                       [...]


                       Much of “the news” is credibility zero these days,
                       especially the ones you don’t pay for. I’ve noticed
                       the ones that have their hands out and paywalls
                       actually have better stories that usually have some
                       point to them once I get past the paywall. NPR
                       takes so much money from people like Bill Gates,
                       and outfits like Microsoft, Amazon, Walmart, Koch
                       Industries, Exxon, and more and gives them shout
                       outs while you’re in the car using them for
                       background music.


                       “This article about Amazon workers trying to
                       organize brought to you by the company that is
                       threatening them for organizing. Amazon…..When you
                       need a tuba, some blu ray discs, and three packages
                       of chocolate covered cherries at 4 AM….Amazon.”


                       I’m very concerned with what’s happening to “the
                       news”, at least as much as “the Web”. They’re in a
                       state of terminal rot and corruption to the point
                       where it’s almost a gift that you can’t read some
                       of this bullshit in a way that preserves some of
                       your sanity.


                       For example, many are reporting that Senator Joe
                       Manchin of Virginia is blocking a new spending deal
                       because he’s “worried about inflation”.


                       What they’re not reporting on is that taxing the
                       rich to reduce the federal deficit would LOWER, not
                       increase, inflation. By refusing to tax the rich,
                       the Senator from West Virginia is forcing the
                       federal government to create and borrow money,
                       INCREASING the inflation he is complaining about,
                       to spare unproductive billionaires like Elon Musk
                       and Bill Gates and Warren Buffett from having to
                       pay taxes.


                       More alarming, however, is the fact that there’s
                       more “Billshit” than ever in the news this week.


                       A total “Billshit” overload.


                # § Mozilla⠀➾


                      # ⚓ Tor ☛ New_Release:_Tor_Browser_11.5⠀⇛


                             Tor Browser 11.5 is now available from the
                             Tor Browser download page and also from our
                             distribution directory. This new release
                             builds upon features introduced in Tor
                             Browser 10.5 to transform the user experience
                             of connecting to Tor from heavily censored
                             regions.


                             We began reshaping the experience of
                             connecting to Tor with the release of Tor
                             Browser 10.5 last year, including the
                             retirement of the Tor Launcher and the
                             integration of the connection flow into the
                             browser window. However, circumventing
                             censorship of the Tor Network itself remained
                             a manual and confusing process – requiring
                             users to dive into Tor Network settings and
                             figure out for themselves how to apply a
                             bridge to unblock Tor. What’s more,
                             censorship of Tor isn’t uniform – and while a
                             certain pluggable transport or bridge
                             configuration may work in one country, that
                             doesn’t mean it’ll work elsewhere.


                      # ⚓ Mozilla ☛ Bridget_Todd,_IRL_Podcast_New_Host
                        Interview⠀⇛


                             I always have too many tabs open — at any
                             given time I have like 40 open. It’s the kind
                             of thing, where you know when you have so
                             many open that you can’t even see them. So,
                             whenever, I accidentally close a tab, I tell
                             myself, you know, maybe you weren’t going to
                             read that long article in The Atlantic,
                             anyway, or like maybe you weren’t actually
                             going to apply for that fellowship and it’s
                             good that the link is no longer just up
                             there. Every time I accidentally close the
                             tab I feel like it’s the universe telling me
                             that it wasn’t meant to be and you’re free
                             now.


          o § Productivity Software/LibreOffice/Calligra⠀➾


                # ⚓ Vote_on_the_LibreOffice_branding_icons_–_LibreOffice_Design
                  Team⠀⇛


                       LibreOffice application icons are undoubtedly
                       awesome. But over the years they have become a bit
                       dated and do not fit well into the zeitgeisty icon
                       design. Plus, the set has no good main icon, which
                       is in particular an issue on macOS where this icon
                       is shown on the launcher bar.


                       Many proposals have been submitted and finally the
                       TDF members elected one concept in a first poll.
                       Now we like to involve the larger community into
                       the design work. The question is whether icons
                       should be flat or have some gradient. Please use
                       the following link to vote.


                # ⚓ Making_unsorted_lookups_in_Calc_fast⠀⇛


                       The VLOOKUP spreadsheet function by default
                       requires the searched data to be sorted, and in
                       that case it performs a fast binary search. If the
                       data is not sorted (for example if it would be
                       impractical to have the data that way), it is
                       possible to explicitly tell VLOOKUP that the data
                       is not sorted, in which case Calc did a linear one-
                       by-one lookup. And there are other functions such
                       as COUNTIF or SUMIF that essentially do a lookup
                       too, and those cannot even be told that the data is
                       sorted and so they processed the data linearly.
                       With large spreadsheets this can actually take a
                       noticeably long time. Bugreports such as
                       tdf#139444, tdf#144777 or tdf#146546 say operations
                       in such spreadsheets take minutes to complete, or
                       even “freeze”.


    * § Leftovers⠀➾


          o ⚓ The Nation ☛ The_Literary_Games_of_Fernando_Pessoa⠀⇛


                 If ever a writer was fated to bear a particular name, it
                 was Fernando Pessoa. In Portuguese the word pessoa means
                 “person”; in Latin it means “mask” or “character.” Pessoa
                 spent his life adopting personas, masks, and characters
                 from almost the moment he began his writing career. These
                 alternative personalities were still Pessoa, even when he
                 signed his works under a pseudonym. Many of his alter
                 egos were poets like himself, although only a few were
                 Portuguese. One was an anti-Fascist Italian critic,
                 another a psychiatrist, a third studied engineering; the
                 others included monks, an assistant bookkeeper, a 19-
                 year-old hunchbacked girl who suffered from tuberculosis,
                 a translator of Portuguese literature into English, an
                 inventor and solver of riddles, a French satirist, a
                 toga-wearing lunatic obsessed with Greece who lived in an
                 asylum, and even a Voodooist. As Pessoa explained in
                 1928, “Pseudonymous works are by the author in his own
                 person, except in the name he signs.” His works were what
                 he called “heteronymous”; they were “by the author” but
                 “outside of his own person. They proceed from a full-
                 fledged individual created by him, like the lines spoken
                 by a character in a drama he might write.” Pessoa’s
                 heteronyms were people with birthdays and deathdays; they
                 had the whole gestalt—passions, fears, dreams, and
                 clearly traced literary paths. As for him, he was a
                 fingidor: a feigner, a pretender, an impostor who
                 believed he could do “more in dreams than Napoleon.”


          o ⚓ Common Dreams ☛ Opinion_|_This_Is_My_Song_for_a_Suffering,
            Imperfect_Nation_I_Still_Love⠀⇛


                 It’s hot and hazy as July rolls around. Growing up in the
                 Baltimore swamplands, we used to say, “It’s not the heat,
                 it’s the humidity.” Meaning that the humidity was harder
                 to deal with than the feverish temperatures. At some
                 point in my family, the phrase morphed into: “It’s not
                 the heat, it’s the stupidity.” At the time, we meant the
                 antics of people when it gets hot, including public
                 drunkenness, mishaps with fireworks, and fights over
                 slights. (These days, sadly enough, you’d have to add to
                 that list slaughtering people at a July 4th celebration
                 with an AR-15-style rifle.)


          o ⚓ Shadowproof ☛ Protest_Song_Of_The_Week:_‘FITS/My_Love_Can’t_Be’
            By_Katie_Alice_Greer⠀⇛


          o § Hardware⠀➾


                # ⚓ Hackaday ☛ Building_A_Better_3D_Scanner_With_An_IPhone,_And
                  Making_Art⠀⇛


                       Apple’s FaceID system uses infrared depth-sensing
                       technology to authenticate people via their faces.
                       It can also be used for simple 3D scanning, and
                       [Scott Yu-Jan] found a better way to do that.


                # ⚓ Hackaday ☛ This_Jet_Engine_Will_See_You_Through⠀⇛


                       Have you ever wished you could peer inside a
                       complex machine while it was still running? We sort
                       of can with simulations and the CAD tools we have
                       today, but it isn’t the same as doing IRL. [Warped
                       Perception] made a see-thru jet engine to
                       experience the feeling. The effect, we dare say, is
                       better than any simulation.


                # ⚓ Hackaday ☛ Visual_Cryptography_For_Physical_Keyrings⠀⇛


                       Visual cryptography is one of those unusual cases
                       that kind of looks like a good idea, but it turns
                       out is fraught with problems. The idea is
                       straightforward enough — an image to encrypt is
                       sampled and a series of sub-pixel patterns are
                       produced which are distributed to multiple separate
                       images. When individual images are printed to
                       transparent film, and all films in the set are
                       brought into alignment, an image appears out of the
                       randomness. Without at least a minimum number of
                       such images, the original image cannot be resolved.
                       Well, sort of. [anfractuosity] wanted to play with
                       the concept of visual cryptography in a slightly
                       different medium, that of a set of metal plates,
                       shaped as a set of keyrings.


                # ⚓ Hackaday ☛ Embedded_Dashboard_Definitely_Displays_Data⠀⇛


                       Oftentimes, we’ll find ourselves using an PC
                       attached to a project for serial debugging. Other
                       times, we’ll be squinting at a status LED trying to
                       remember the flash code we invented. This embedded
                       dashboard from [hgrodriguez] aims to land somewhere
                       in the middle.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ TruthOut ☛ Poll:_Nearly_6_in_10_Americans_Want_Marijuana
                  Legalized⠀⇛


                # ⚓ Pro Publica ☛ Pharma_Companies_Sue_for_the_Right_to_Buy
                  Blood_From_Mexicans_Along_Border⠀⇛


                       In the year since the United States blocked
                       Mexicans from entering the country to sell their
                       blood, the two global pharmaceutical companies that
                       operate the largest number of plasma clinics along
                       the border say they have seen a sharp drop in
                       supply.


                       In a suit challenging the ban, the companies
                       acknowledged for the first time the extent to which
                       Mexicans visiting the U.S. on short-term visas
                       contribute to the world’s supply of blood plasma.
                       In court filings, the companies revealed that up to
                       10% of the blood plasma collected in the U.S. —
                       millions of liters a year — came from Mexicans who
                       crossed the border with visas that allow brief
                       visits for business and tourism.


                # ⚓ Counter Punch ☛ Monkeypox_and_Bio-Engineered_Plagues⠀⇛


                       Predictably the U.S. health bureaucracy is slow out
                       of the gate. Of the two monkeypox vaccines, the
                       better one is in short supply. That’s the two-dose
                       Jynneos vaccine, which the department of Health and
                       Human Services is releasing, but so far less than a
                       million shots. Meanwhile, states can request doses
                       of an older smallpox vaccine, ACAM2000, from the
                       national stockpile, which contains roughly 100
                       million doses. This vaccine features some lousy
                       side effects, and those with heart disease or the
                       immunocompromised should avoid it.


                       Plans to produce more Jynneos should have ramped up
                       a month or two ago. They did not. They are only
                       doing so now. Naturally demand outstrips supply, as
                       monkeypox cases multiply, possibly exponentially.
                       So far, the CDC reports a mere 600 plus cases in
                       the U.S. with over 6000 worldwide. But unreported
                       cases could be exploding. If this sounds like
                       you’ve been here before, you’re correct. Think
                       February 2020, as covid just got rolling, then
                       rolling…then snowballing. Have federal agencies
                       like the CDC, FDA and HHS learned from that
                       miserable experience? So far prognostications don’t
                       look good.


          o § Security⠀➾


                # ⚓ EFB_ePIL._Pinching_passenger_PII_from_pilots_|_Pen_Test
                  Partners⠀⇛


                       The Passenger Information List (PIL) or Passenger
                       Manifest is a document which is provided to the
                       crew prior to each flight. In its most basic form
                       it will include passenger names and their seat
                       numbers.


                       Various applications have now been developed which
                       digitalise the PIL, hence it is often called the
                       Electronic Passenger Information List (ePIL). These
                       applications remove the need for a printed PIL, can
                       be updated frequently and provide several functions
                       to the crew which were unavailable using a paper
                       PIL. Whilst an ePIL is more frequently used by the
                       cabin crew than the pilots, it is common for them
                       to be installed on EFB’s for pilots to use.


                # ⚓ Diffoscope ☛ diffoscope_219_released⠀⇛


                       The diffoscope maintainers are pleased to announce
                       the release of diffoscope version 219. This version
                       includes the following changes:


                       * Don't traceback if we encounter an invalid
                       Unicode character in Haskell
                         versioning headers. (Closes: reproducible-builds/
                       diffoscope#307)
                       * Update various copyright years.
⚓ LWN ☛ Security_updates_for_Friday⠀⇛


     Security updates have been issued by Debian (webkit2gtk and
     wpewebkit), Fedora (curl, kernel, openssl1.1, php, subversion, xorg-
     x11-server, and xorg-x11-server-Xwayland), Oracle (grub2), SUSE
     (gnutls, kernel, logrotate, oracleasm, p11-kit, and python-PyJWT),
     and Ubuntu (libhttp-daemon-perl and python2.7, python3.10, python3.4,
     python3.5, python3.6, python3.8, python3.9).


⚓ Video ☛ Enterprise_Linux_Security_–_Episode_36_–_Invidious⠀⇛


     In episode 36 of the Enterprise Linux Security podcast, Jay and Joao
     record an episode live for the first time.


    * § Privacy/Surveillance⠀➾


          o ⚓ Hackaday ☛ Apple_AirTags_Hacked_And_Cloned_With_Voltage
            Glitching⠀⇛


                 Apple AirTags are useful little devices. They essentially
                 use iPhones in the wild as a mesh network to tell the
                 owner where the AirTag is. Now, researchers have shown
                 that it’s possible to clone these devices, as reported by
                 Hackster.io.


          o ⚓ EFF ☛ EFF_and_ACLU_File_Amicus_Brief_Objecting_to_Warrantless,
            Suspicionless_Electronic_Device_Searches_at_the_Border⠀⇛


                 That is exactly what happened in the case of Haitao
                 Xiang. Mr. Xiang was under investigation by the FBI and
                 Monsanto while he was living in St. Louis. But, instead
                 of applying for a warrant, government officials waited
                 until he was traveling internationally to seize his
                 electronic devices in order to search them
                 warrantlessly.  


                 EFF and the ACLU have filed an amicus brief in the case
                 arguing against warrantless, suspicionless border
                 searches of electronic devices like Mr. Xiang’s. As the
                 brief states:


                 And it is exactly for this reason that border protection
                 officers and customs officials must have a higher
                 standard when they want to search an electronic device.
                 EFF will continue to fight for the belief that digital
                 rights do not end simply because a person approaches the
                 border.


          o ⚓ AccessNow ☛ Telegram_vs_Russia:_Access_Now_tells_the_European
            Court_of_Human_Rights_why_encryption_must_be_protected_–_Access
            Now⠀⇛


                 For millions of people in Russia, Telegram’s encryption
                 makes it the last remaining avenue to communicate
                 securely and access information freely — governmental
                 attempts to seize platform data must be rejected.


                 Telegram is challenging the Russian government’s order to
                 block and fine the messaging app for failing to provide
                 information that would enable authorities to decode
                 encrypted messages of six crime suspects. The company
                 argues that, in effect, this means creating a backdoor
                 mechanism for decoding all Telegram communications and
                 threatening privacy and freedom of expression rights of
                 all users. On June 10, 2022, Access Now, ARTICLE 19,
                 Electronic Frontier Foundation, Human Rights Watch,
                 Privacy International, and Reporters Without Borders,
                 filed a joint submission to the European Court of Human
                 Rights.


                 “Journalists and activists in Ukraine and Russia are
                 fighting to end this war. Platforms like Telegram are
                 often their main source of communication, and they bear
                 disproportionate risks if their identities and messages
                 are revealed to Russian authorities,” said Natalia
                 Krapiva, Tech Legal Counsel at Access Now. “Encryption is
                 the last protective wall standing between at-risk
                 advocates and the security forces seeking to silence
                 them.”


          o ⚓ The Register UK ☛ San_Francisco_cops_want_real-time_access_to
            private_security_cameras_for_surveillance⠀⇛


                 The new proposal—championed by Mayor London Breed after
                 November’s wild weekend of orchestrated burglaries and
                 theft in the San Francisco Bay Area—would authorize the
                 police department to use non-city-owned security cameras
                 and camera networks to live monitor “significant events
                 with public safety concerns” and ongoing felony or
                 misdemeanor violations.


                 Currently, the police can only request historical footage
                 from private cameras related to specific times and
                 locations, rather than blanket monitoring. Mayor Breed
                 also complained the police can only use real-time feeds
                 in emergencies involving “imminent danger of death or
                 serious physical injury.”


                 [...]


                 Cagle said San Francisco Supervisors have received
                 “hundreds and hundreds and hundred of messages in just
                 the last few days” from residents who oppose the
                 proposal. And he pointed to a survey [PDF] of 372 likely
                 voters, commissioned by the ACLU, that found 60 percent
                 of San Franciscans oppose letting the police use private
                 cameras to monitor people.


                 In a joint letter [PDF], 17 organizations including the
                 ACLU of Northern California, EFF, social justice center
                 GLIDE, and the San Francisco Public Defender’s Office,
                 urged the Board of Supervisors to oppose or
                 “significantly amend” the policy, which they say will
                 “allow the SFPD to engage in unprecedented live
                 surveillance” via thousands of private cameras.


          o ⚓ AccessNow ☛ About_time!_Congress_makes_it_harder_for_U.S.
            companies_to_buy_blocklisted_spyware_firms_like_NSO_–_Access_Now⠀⇛


                 Access Now applauds the U.S. House of Representatives in
                 passing U.S. Representative Tom Malinowski’s amendment to
                 the National Defense Authorization Act (NDAA) that will
                 make it difficult for a U.S. company to buy a firm
                 blocklisted on the U.S. Entity List. The decision came
                 yesterday in response to U.S. defense contractor L3Harris
                 Tech’s attempt to acquire sanctioned spyware maker NSO
                 Group, which ultimately failed thanks to White House
                 opposition.


                 “Spyware is used to invade the personal lives of people
                 across the globe, eroding privacy, and risking lives,”
                 said Jennifer Brody, U.S. Policy and Advocacy Manager at
                 Access Now. “This amendment sends a clear message from
                 the U.S. government: surveillance tech’s unchecked rule
                 is coming to an end.”


§ Defence/Aggression⠀➾


    * ⚓ Counter Punch ☛ Highland_Park,_Buffalo,_and_Fascism_Denial_in_U.S.
      Media_Culture⠀⇛


           It’s not a pretty story.


           The F-Word Taboo


    * ⚓ Counter Punch ☛ Roaming_Charges:_The_Screams_of_the_Children_Have_Been
      Edited_Out⠀⇛


           After firing several blasts of shots toward the school, the
           Uvalde shooter enters the building. It’s now 11:33 in  the
           morning. By this time, several more 9/11 calls have alerted the
           police to a shooting incident at the school. A school security
           camera records the shooter as he saunters down the hallway,
           pauses briefly to peer around a corner, runs a hand through his
           hair, then continues down the hall toward classrooms 111 and
           112.


           At this point, a young boy wearing glasses comes out of the
           bathroom on the left side of the hall, freezes when he sees the
           shooter open fire, then runs back into the bathroom.


    * ⚓ Common Dreams ☛ ‘Danger_to_Democracy’:_Lawsuit_Aims_to_Keep_Jan._6
      Insurrectionist_Off_Michigan_Ballot⠀⇛


           A lawsuit filed Thursday with a Michigan appellate court aims
           to preemptively block Republican gubernatorial candidate Ryan
           Kelley from appearing on the state’s general election ballot,
           citing his embrace of and active participation in the January
           6, 2021 attack on the U.S. Capitol.


           The lawsuit, submitted by retired attorney and registered voter
           Lee Estes, argues that Kelley should be barred from the general
           election ballot “because he has ‘engaged in insurrection’ in
           violation of the Fourteenth Amendment and therefore is
           ineligible to serve as a candidate for governor for the state
           of Michigan.”


    * ⚓ Common Dreams ☛ Leaked_Bannon_Clip_Confirms_Trump’s_False_Victory_Claim
      on_Election_Night_Was_Planned⠀⇛


           Leaked audio of Steve Bannon published earlier this week by
           Mother Jones confirms that days before the 2020 presidential
           election, Republican incumbent Donald Trump planned to
           prematurely declare victory on the night of November 3
           regardless of whether it was true.


           “What Trump’s gonna do is just declare victory. Right? He’s
           gonna declare victory. But that doesn’t mean he’s a winner,” a
           chuckling Bannon told a group of associates on October 31,
           2020. “He’s just gonna say he’s a winner.”


    * ⚓ Common Dreams ☛ House_Votes_Down_Amendments_to_Cut_‘Outrageous’
      Military_Budget⠀⇛


           Progressive campaigners rebuked members of Congress who on
           Wednesday night voted down a pair of amendments to the latest
           National Defense Authorization Act that would have
           significantly limited the U.S. military budget.


           “Despite the outcome of today’s vote, it’s never too late for
           members of Congress to come to their senses and budget for our
           actual needs over weapons-makers’ wants.”


    * ⚓ Common Dreams ☛ Sanders_Unveils_Resolution_to_End_US_Support_for
      ‘Catastrophic’_Saudi-Led_War_in_Yemen⠀⇛


           As U.S. President Joe Biden visits the Middle East this week,
           three senators introduced a joint resolution to end the United
           States’ involvement in the Saudi-led war on Yemen.


           “This war has created the world’s worst humanitarian crisis
           today and it is past time to end U.S. complicity in those
           horrors.”


    * ⚓ Counter Punch ☛ Vicarious_Zeal:_Fighting_to_the_Last_Ukrainian⠀⇛


           With such language crowning the efforts of the Allies, the Axis
           powers – certainly Germany and Japan – could continue fighting
           the war of extermination, aware that no terms they could submit
           would be taken seriously.  There would be no compromise in this
           existential confrontation.  It made the Allied advance in
           Western Europe slower and enabled the Soviet Union to expel
           German forces and duly occupy most of Eastern Europe.  It made
           negotiations about whether Japan would retain its emperor on
           surrendering nigh impossible, leaving the route open for the
           use of atomic weapons against Hiroshima and Nagasaki.


           The supply of weapons to Ukraine in its efforts against Russia
           has become a zealous mission that will supposedly achieve
           victory. Messianic impulses tingle and move through the
           Washington and London establishment, with some echo in Warsaw
           and the capitals of the Baltic states.  An air of unreality –
           be it in terms of negotiating the future of Ukrainian territory
           under Russian occupation – fills such corridors of power.


    * ⚓ Counter Punch ☛ Riflelandia:_On_the_Massacre_in_Uvalde,_Texas⠀⇛


           Rifles for colonizing. They were the preferred weapons of the
           westward expansion of the white Anglo-Saxon Protestants
           (WASPs). The Conquest of the West was no simple advance through
           wild, unpopulated territory. It required the dispossession,
           mainly by rifleshot, of dozens of indigenous nations over
           millions of square kilometers of land. 


           Rifles for decimation. Once conquered, the native people tended
           to rebel, from the Powhatans on the East Coast as early as the
           17th century, to the various Plains Indians, such as the
           Cheyenne and the Sioux, as well as the Apaches and Comanches in
           the Southwest. They ended up decimated, virtually annihilated.
           The 1890 massacre of the Sioux at Wounded Knee is still
           solemnly commemorated today.


    * ⚓ Common Dreams ☛ Not_One_Single_Republican_Votes_for_Probe_of_Neo-Nazis
      in_US_Military_and_Police⠀⇛


           Zero House Republicans on Wednesday supported a measure
           requiring the Pentagon and federal law enforcement agencies to
           publish a report on countering white supremacist and neo-Nazi
           activity in their ranks.


           Rep. Brad Schneider’s (D-Ill.) amendment to the National
           Defense Authorization Act (NDAA) for fiscal year 2023 directing
           the FBI, Department of Homeland Security, and Department of
           Defense “to publish a report that analyzes and sets out
           strategies to combat white supremacist and neo-Nazi activity in
           the uniformed services and federal law enforcement
           agencies” passed in a party-line 218-208 vote.


    * ⚓ Common Dreams ☛ Omar_Slams_NDAA_Provision_Blocking_US_Aid_to_Afghans
      Amid_‘Horrific’_Crisis⠀⇛


           Rep. Ilhan Omar warned Wednesday that a provision buried in the
           sprawling National Defense Authorization Act would bar the
           Pentagon from distributing aid to the people of Afghanistan
           even as they’re engulfed in a massive humanitarian emergency
           following two decades of deadly U.S. occupation.


           “Afghanistan is facing one of the most horrific humanitarian
           crises on the planet,” Omar (D-Minn.), a member of the House
           Foreign Affairs Committee, wrote on Twitter. “We should be
           doing everything in our power to deliver humanitarian
           assistance to the Afghan people, not needlessly limiting the
           aid we can supply.”


    * ⚓ Counter Punch ☛ The_Death_Penalty_is_Back_With_a_Vengeance⠀⇛


           A Google search discloses that 108 countries have abolished the
           death penalty for all crimes and another 144 have outlawed it
           in law or in practice.  Fifty five countries still use it to
           discipline those who have committed certain offenses. We are
           among the fifty five. Although we executed 11 people in 2021,
           we try to be reasonable in its application.   Proof of that  is
           shown by two cases that have gone through the courts in the
           last two years.  Both of them arrived in the court system
           because of what has proved to be a very tricky problem. In 2021
           the problems involved Richard Moore in South Carolina and
           Michael Mance in Georgia.  Both concerned the proper way to
           execute someone sentenced to death.


           At the time of his conviction South Carolina generously
           permitted someone in Mr. Moore’s position to choose which of
           the two state authorized methods of execution he would like to
           have applied to the  event.  The choices were between (a) the
           electric chair or (b) lethal injection.  In the case of a
           prospective decedent who declined to choose, the default was
           (b).  Mr. Moore declined to choose and his failure to choose
           meant the default would apply and he would be put to death  by
           lethal injection.  There were, as it turned out,  no drugs
           available for lethal injection so the state was unable to
           execute Mr. Moore who had, as it were, the last laugh.  His
           laughter was, however, cut short by the South Carolina
           legislature. It promptly added the firing squad as the default
           execution method instead of lethal injection and said that
           newly enacted method applied to Mr. Moore.  Some may think it
           strange that a state can effect a change in how the death
           penalty is applied after the date it has been imposed but that
           is, apparently, not an issue.  Thanks to some additional
           appeals Mr. Moore has now filed, how he will be executed is, as
           of this writing unknown.  The issue is now before the South
           Carolina Supreme Court.


    * ⚓ Counter Punch ☛ How_To_Get_the_War_Out_of_America⠀⇛


           The Senator’s aide obliged me. The chances of any bill passing
           both chambers of Congress that would trim the Pentagon budget
           by 10%, according to the aide, were zero. When I asked if this
           was because the public perception was that we needed this
           amount to defend the country, the aide responded that it was
           not only the public perception but the reality. The Senator was
           convinced, as were most in Congress, that the Pentagon’s threat
           assessments were accurate and reliable (this despite the
           Pentagon’s history of failed forecasting).


           As described to me, the military assesses threats across the
           globe including such countries as China and Russia, then
           designs a military strategy to counter those threats, works
           with weapons manufacturers to design weapons to integrate into
           that strategy, then produces a budget based on that strategy.
           Congress, Democrats and Republicans alike, overwhelmingly
           approve the budget. After all, it’s the military. They clearly
           know the business of war.


    * ⚓ Counter Punch ☛ Sins_of_the_Father⠀⇛


           Like thousands of others in the military and elsewhere
           throughout the US bureaucracy of war, our fathers were family
           men. Each engaged in their way with their children, their wives
           and their lives at home. They enjoyed vacations with us, they
           scolded us when we didn’t measure up and they supported our
           childhood interests. Meanwhile, they went to work and figured
           out ways to kill people. All in the name of an ideology sold as
           democracy but actually just twentieth century imperialism.
           Craig McNamara’s response to his father’s work expanding and
           defending the war was similar to mine. We both became fervent
           opponents to it. Like me, the younger McNamara expressed his
           opposition to the war at first through symbolic protest—hanging
           antiwar posters on his wall, reading pacifist literature and
           attending protests. Ultimately, his antiwar activities and
           understanding turned radical, as did mine. Violent protests and
           an anti-imperialist analysis replaced peace signs and black
           armbands. Like millions of others, we realized the war on the
           Vietnamese was not a mistake, but a matter of policy; a policy
           founded in a lust for empire.


           When the politics of revolution became too much, Craig McNamara
           left for Latin America. By then his father was no longer part
           of the government. Instead, he was on the board of the World
           Bank devising development plans for the Global South. Of
           course, these plans were designed to benefit Washington and
           Wall Street, not the people of the nations the World Bank
           claimed to be developing. Indeed, while the younger McNamara
           was living in Santiago, Chile during the heady days of the
           socialist Allende government, his father was working with some
           of the very people who were organizing Allende’s bloody
           downfall. Craig describes reading the newspaper and finding out
           his father (who was unaware of his son’s presence in the city)
           was meeting with various officials, capitalists and others in
           another part of the city. He weighed contacting his father, but
           decided against it. After all, what would he have to say?


    * ⚓ TruthOut ☛ Biden_Says_He’d_Use_Military_Force_on_Iran_as_“Last_Resort”
      to_Prevent_Nukes⠀⇛


    * ⚓ Common Dreams ☛ Biden_Says_He_Would_Go_to_War_With_Iran_as_‘Last
      Resort’⠀⇛


           U.S. President Joe Biden said in an interview aired Wednesday
           that he would be willing to go to war with Iran to prevent the
           country from obtaining a nuclear weapon, a position that drew
           condemnation from advocacy groups and foreign policy analysts
           who questioned the moral, strategic, and legal bases for such a
           stance.


           “It makes absolutely zero sense that he won’t delist the IRGC
           to prevent an Iranian nuke but would launch a war to prevent an
           Iranian nuke.”


    * ⚓ Counter Punch ☛ The_Real_Shinzo_Abe:_He_Was_No_Peacemaker⠀⇛


           Shinzo Abe, the former prime minister of Japan, was shot in the
           back. Murdered in cold blood. It was an act of depravity
           carried out in broad daylight on July 8 at a campaign rally in
           the ancient city of Nara, Japan’s first established capital.
           Gun deaths in Japan are incredibly rare. In all off 2021 there
           was just one. Gun ownership in the country, per head of
           population, is the lowest of members of the G7, at just 0.3 per
           100 people.


           Handguns are banned but weapons can be purchased, under strict
           guidelines, for hunting.


    * ⚓ The Nation ☛ The_Misremembering_of_Shinzo_Abe⠀⇛


           Tokyo, Japan—In the days following the assassination of Shinzo
           Abe on July 8, heartfelt tributes to the late former prime
           minister filled television screens, showing fellow party
           members speaking tearfully in front of reporters and his
           supporters laying flowers at the site where he was shot. Even
           the mainstream newspapers, which had been more critical of Abe
           prior to his death, remembered him as a leader who, despite
           being controversial, was fiercely determined.


    * ⚓ Techdirt ☛ Court_Denies_Immunity_To_Child_Protection_Workers_Who
      Allowed_An_NYPD_Officer_To_Abuse_His_Son_To_Death⠀⇛


           The public expects cops to be better people than they are.
           Maybe they have the same weaknesses but having the training and
           experience to overcome them. But when you’re a cop, you’re
           encouraged to turn interactions into altercations and solve
           most problems with violence. And when all else fails, you can
           always just lock someone up. Is it any wonder law enforcement
           is home to an alarming number of domestic abusers?


    * ⚓ The Nation ☛ Resurrecting_the_American_Century_Is_a_Huge_Mistake⠀⇛


           “The American Century Is Over.” So claims the July 2022 cover
           of Harper’s Magazine, adding an all-too-pertinent question:
           “What’s Next?”


    * ⚓ Scheerpost ☛ Ignoring_How_Militarism_Fuels_Climate_Change_Will_Be_the
      Death_of_Us⠀⇛


           Sue Ann Martinson explores the many ways that the U.S. military
           contributes to the existential threat of climate change.


    * ⚓ Meduza ☛ A_mercenaries’_war_How_Russia’s_invasion_of_Ukraine_led_to_a
      ‘secret_mobilization’_that_allowed_oligarch_Evgeny_Prigozhin_to_win_back
      Putin’s_favor_—_Meduza⠀⇛


           Political squabbles and personal conflicts nearly cost Evgeny
           Prigozhin his prized position in Vladimir Putin’s circle of
           trust. Over the course of the war in Ukraine, Russia’s Defense
           Ministry has gradually erased the boundaries between
           mercenaries and the military. The armed forces essentially
           commandeered the recruiting network built by the Wagner Group
           (the private military company that Prigozhin finances) and
           largely excluded the organization itself from the initial
           invasion of Ukraine in February 2022. The Russian army and
           other mercenary groups performed so poorly on the battlefield,
           however, that Moscow eventually called on Wagner’s regulars,
           restoring Prigozhin to the president’s good graces.


    * ⚓ Meduza ☛ A_history_of_forced_conscription_Russia’s_first_military_draft
      of_2022_ends_soon._That_could_spell_danger_for_recent_college_graduates.
      —_Meduza⠀⇛


           Russia’s first military draft of 2022 will end on July 15.
           Since it began on April 1, enlistment offices have largely
           avoided using Chechen War-era methods of rounding up draftees,
           but that doesn’t mean they haven’t broken laws. Protecting
           young people from forced recruitment is becoming increasingly
           difficult; if an enlistment office is given instructions to
           send a specific person to the army, there’s effectively no way
           to prevent the person from having to serve. Meduza looks at how
           Russia’s most recent conscription has played out.


    * ⚓ Meduza ☛ Russian_missile_strike_on_Vinnytsia_kills_more_than_20,
      injures_dozens_The_victims_include_three_children_—_Meduza⠀⇛


           A Russian missile strike in the central Ukrainian city of
           Vinnytsia killed at least 21 people, including three children,
           and injured dozens more, according to Ukraine’s State Emergency
           Service. At least 42 people are still missing, 91 people have
           sought medical treatment, and 52 have been hospitalized — 34 of
           them in critical condition. 55 buildings and 40 vehicles were
           damaged.


    * ⚓ TruthOut ☛ DOJ_Requests_Fake_Electors_Scheme_Info_From_Jan._6
      Committee⠀⇛


    * ⚓ TruthOut ☛ During_Biden’s_Israel_Visit,_Palestinians_Urge_US_to_Reverse
      Embassy_Plans⠀⇛


    * ⚓ Counter Punch ☛ Letter_From_Crimea:_Victims_of_Yalta_in_Today’s
      Ukraine⠀⇛


           While biking around Novocherkassk, it’s near Rostov and was
           once the capital of the Don Cossacks, I thought about the
           destiny of many Cossacks at the end of World War II.


           I first became aware of their fate in the 1970s. In those years
           my father made business trips to London, and often he would
           bring back books that were not published in the United States.


    * ⚓ Counter Punch ☛ Canons_of_the_Cold_War:_The_Weaponization_of
      Literature⠀⇛


           These operations initially began during the de-Nazification of
           post-war Germany but, as the Soviet Union began to pose a
           serious threat to America’s European influence, shifted to
           anti-communism under the pretense of creating a space in which
           artistic-intellectual activity could exist free from
           authoritarian interference. During this time, the American
           State organized and funded conferences, literary magazines,
           libraries, publishers, writers, and translation programs. It
           also ran parallel operations targeting art, theatre, cinema,
           science, and journalism.


           The culmination of America’s Cold War cultural operations was
           the Congress for Cultural Freedom, which has been described as
           both the cultural counterpart to the Marshall Plan and as a
           cultural NATO. The CCF organized, funded, and directed cultural
           activities and publications in an attempt to establish a global
           network of sympathetic artists. Whereas the Marshall Plan
           focused upon economic liberalisation, the CCF focused upon
           intellectual liberalisation, establishing what was purported to
           be an ideology-free zone in which artistic freedom was able to
           exist. In reality, it was a space in which American State
           ideology was continuously reproduced, serving to bolster and
           secure American hegemony.


    * ⚓ Counter Punch ☛ $2_Trillion_for_War_Versus_$100_Billion_to_Save_the
      Planet⠀⇛


           Saleemul Haq, the director of the International Center of
           Climate Change and Development, is from Bangladesh. He is a
           veteran of the UN climate change negotiations. When Haq read a
           tweet by Marianne Karlsen, the co-chair of the UN’s Adaptation
           Committee, which said that “[m]ore time is needed to reach an
           agreement,” while referring to the negotiations on loss and
           damage finance, he tweeted: “The one thing we have run out of
           is Time! Climate change impacts are already happening, and poor
           people are suffering losses and damages due to the emissions of
           the rich. Talk is no longer an acceptable substitute for action
           (money!)” Karlsen’s comment came in light of the treacle-slow
           process of agreement on the “loss and damage” agenda for the
           27th Conference of Parties or COP27 meeting to be held in Sharm
           el-Sheikh, Egypt, in November 2022.


           In 2009, at COP15, developed countries of the world had agreed
           to a $100 billion annual adaptation assistance fund, which was
           supposed to be paid by 2020. This fund was intended to assist
           countries of the Global South to shift their reliance on carbon
           to renewable sources of energy and adapting to the realities of
           the climate catastrophe. At the time of the Glasgow COP26
           meeting in November 2021, however, developed countries were
           unable to meet this commitment. The $100 billion may seem like
           a modest fund, but is far less than the “Trillion Dollar
           Climate Finance Challenge,” that will be required to ensure
           comprehensive climate action.


    * ⚓ Common Dreams ☛ Opinion_|_Just_How_Much_Bigger_Is_the_US-NATO_Military
      Force_Than_Russia’s?⠀⇛


§ Transparency/Investigative Reporting⠀➾


    * ⚓ Shadowproof ☛ Jury_Finds_Former_CIA_Programmer_Guilty_Of_Leaking_CIA
      Hacking_Materials_To_WikiLeaks⠀⇛


           The jury deliberated for nearly three days before announcing a
           verdict. Judge Jesse M. Furman in the Southern District of New
           York did not schedule a sentencing date because there are other
           charges pending against Schulte.


§ Environment⠀➾


    * ⚓ TruthOut ☛ Montana_Kids_Are_Suing_Their_State_for_Violating_Right_to_a
      Clean_Environment⠀⇛


    * ⚓ TruthOut ☛ US_Is_on_Track_to_Fall_Far_Short_of_Emissions_Reduction
      Goals,_Report_Finds⠀⇛


    * § Energy⠀➾


          o ⚓ TruthOut ☛ 70,000_Acres_of_Federal_Land_Were_Just_Handed_to_the
            Fossil_Fuel_Sector⠀⇛


          o ⚓ Common Dreams ☛ Biden_Urged_to_Reject_‘Preemptive_Giveaway’_to
            Manchin_on_Destructive_Oil_Projects⠀⇛


                 Environmentalists implored President Joe Biden on
                 Thursday not to go through with a reported ploy to
                 approve climate-damaging fossil fuel projects in a bid to
                 secure Democratic Sen. Joe Manchin’s support for limited
                 renewable energy funding, warning that such a deal would
                 be a net negative for the planet.


                 Mitch Jones, managing director of policy at Food & Water
                 Watch, said that “there is abundant evidence that
                 incentivizing cleaner energy technology while also
                 advancing new dirty energy projects does not reduce
                 climate pollution.”


    * § Wildlife/Nature⠀➾


          o ⚓ Counter Punch ☛ Will_Egypt_Drain_the_World’s_Second_Largest
            Wetlands?⠀⇛


                 Sudd is Africa’s largest freshwater wetland at roughly
                 3,500 square miles in an otherwise dry region of South
                 Sudan. It’s under threat by a megaproject named Jonglei
                 Canal that has the potential to devastate this ecological
                 gem.


                 According to conservationists: “Even a partial loss of
                 the Sudd would be an ecological disaster, desiccating the
                 world’s second largest swamp and ending seasonal flooding
                 of the surrounding grasslands, which comprise Africa’s
                 largest intact area of savannah.” (Source: Will Nile
                 Canal Project Dry Up Africa’s Largest Wetland? Grist,
                 July 8, 2022)


          o ⚓ Counter Punch ☛ Drought_in_the_Horn_of_Africa:_Worst_in_40
            Years⠀⇛


                 Desperately needed support from UN agencies (World Food
                 Programme (WFP), UNHCR and UNICEF) is limited due to lack
                 of donations from member states. WFP have been forced to
                 halve food rations due to the “lowest levels of funding
                 on record”. Leading to what UNICEF describe as a
                 “humanitarian catastrophe……. Urgent aid is needed to
                 prevent parts of the region sliding into famine.” The
                 disruption caused to supply chains and food production by
                 the war in Ukraine is adding to the crisis, dramatically
                 increasing food prices and limiting availability.


                 The region’s agriculture has been decimated by year on
                 year rising temperatures and decreasing rainfall. Food
                 insecurity, in a region with some of the poorest people
                 in the world, is intensifying with the threat of famine
                 looming, and food prices have sky rocketed. Livestock has
                 perished – in Ethiopia alone 2.1 million livestock have
                 died and 22 million are at risk, emancipated with little
                 or no milk production – the primary source of nutrition
                 for young children.


    * § Overpopulation⠀➾


          o ⚓ Counter Punch ☛ Water,_Water,_No_Longer_Everywhere⠀⇛


                 “Water, water everywhere, nor any drop to drink.”
                 Coleridge’s “Rime of the Ancient Mariner” is only halfway
                 descriptive of the planet’s current water situation.
                 Water is drying up everywhere; oceans and rivers are
                 becoming more polluted and poisoned; watersheds are being
                 drained at a phenomenal rate to meet the needs of
                 industry, sports, and agriculture. Quality drinking
                 water, especially in developing countries, is becoming a
                 major challenge. And everywhere, good water, access to
                 which should be a human right, is becoming expensive and
                 privately owned.


                 First, the basic facts on the global water crisis, as
                 provided by UNICEF…


§ Finance⠀➾


    * ⚓ Counter Punch ☛ The_Worst_is_Yet_to_Come:_When_the_Center_Does_Not
      Hold⠀⇛


           This is especially true here in the United States, as it was in
           post-World War I Germany’s nurturing the rise of Naziism and
           its demonic voice, Adolph Hitler, the consummate outsider who
           managed to crawl up the mountain to ascend its peak. The core
           disabling affliction of the United States in the 21st Century
           is an energized and armed extreme right-wing and a listless,
           passive center, a development lamented by liberals who would
           sell their souls long before parting with their stocks and
           bonds, all for a non-voting seat at various illiberal tables of
           power. This lack of humane passion at the political center
           serves as a reinforcing complement to the violent forces of
           alienation waiting around the country for their marching
           orders, as the January 6th insurrectionary foray foretells.
           Together these contrasting modes of ‘citizenship’ signal the
           death of constitutional democracy as it has functioned, with
           ups and downs, flawed by slavery, genocide, and patriarchy at
           birth, indeed ever since the republic was established in 1787
           as ‘a more perfect union.’ In 2022 a fascist alternative is
           assuming institutional, ideological, and populist prominence
           with active support of many American oligarchs who fund by
           night what they disavow when the sun shines (again recalling
           the behavior of German industrialists who thought of Hitler as
           their vehicle, whereas it turned out the other war around).


           This contemporary political ordeal is systemic, and not only
           the sad tale of American moral, economic, and political
           decline, temporarily hidden from public awareness by an orgy of
           excess military spending that has lasted for decades, a
           corporatized, compliant media, diversionary exploits abroad,
           and a greedy private sector that grows bloated by arms sales
           and a regressive tax structure, Pentagon plunder, and its
           profit-driven regimen. What may be most negatively revealing is
           the failure to take account of geopolitical failure or
           sanctified domestic outrages (mass shootings in schools and
           elsewhere with legally acquired weapons suitable only for
           organized military combat). It is time to link the inability to
           mount any serious challenge to the tyranny of the Second
           Amendment as interpreted by the IRA in cahoots with Congress
           and the Supreme Court, cowing much of the public to sullen
           sense of silent hopelessness. Even before these hallowed
           institutions acquired their Trumpist edge, they shied away from
           constructing rights as if they were aware of the violent
           societal and ecological fissures tearing up the roots of
           bipartisan civility. The moral rot is less the work of the
           sociopaths among us than it the outcome of a two-party
           plutocratic dynamic that is controlled by infidels and their
           bureaucratic minions who either actually like the way things
           are working out or feel impotent to mount a challenge with any
           chance of enacting benevolent change.


    * ⚓ Common Dreams ☛ Opinion_|_Marco_Rubio’s_“Pro-Life”_Family_Leave_Death
      Tax_Is_an_Open_Assault_on_Social_Security⠀⇛


           A 25-year-old college graduate is struggling to pay back his
           student loans. He gets a call from his sister breaking the news
           that their mother was just killed by a drunk driver. Before
           they can lay her to rest, they receive a bill from the
           government, demanding thousands of dollars. What for? To cover
           the cost of the parental leave benefits their mom took during
           their first few months of life.


    * ⚓ Common Dreams ☛ Poll_Shows_Majority_of_US_Voters_Oppose_Triggering
      Recession_to_Battle_Inflation⠀⇛


           Amid fears by progressive economists that the U.S. Federal
           Reserve will move the country closer to a recession by raising
           interest rates, a new poll published Thursday revealed that
           American voters overwhelmingly oppose a call by former Treasury
           Secretary Larry Summers to tackle inflation by effectively
           taking jobs from millions of people.


           “Larry Summers’ cure for fighting inflation is worse than the
           disease itself.”


    * ⚓ Common Dreams ☛ ‘It’s_Only_Getting_Worse’:_IMF_Chief_Says_Global
      Recession_Risk_Rising⠀⇛


           The global economic outlook has “darkened significantly,” with
           the world facing an elevated risk of a recession within the
           next year, the head of the International Monetary Fund warned
           Wednesday.


           “Multiple crises facing the world have intensified.”


    * ⚓ Insight Hungary ☛ New_tax_law_sparks_protests_in_Budapest⠀⇛


           Thousands of Hungarian workers are protesting against
           legislation that would increase the tax rate for small
           businesses, passed earlier this week by the ruling Fidesz
           party. Around half a million individuals used the popular
           simplified tax regime, KATA. According to new rules, workers
           paying KATA will have to look for other solutions from
           September 1 since the legislation tightens the eligibility for
           the simplified tax regime.


           Protesters have blocked traffic in the heart of Budapest, on
           the Erzsebet Bridge that connects the Buda and Pest on Tuesday,
           Wednesday, and Thursday.


    * ⚓ TruthOut ☛ Sanders_Rebukes_Senate_for_Crafting_$50_Billion_“Handout”_to
      Microchip_Industry⠀⇛


    * ⚓ Common Dreams ☛ Sanders_Warns_Congress_Is_Working_‘Behind_Closed_Doors’
      on_$50_Billion_in_Corporate_Welfare⠀⇛


           Sen. Bernie Sanders took to the Senate floor Wednesday to
           criticize fellow members of Congress for working to approve
           billions of dollars in handouts to major corporations as the
           country is embroiled in a worsening cost-of-living crisis, a
           deadly pandemic, and an intensifying climate emergency.


           “This may be a radical idea in the halls of Congress, but no, I
           do not believe that this legislation should approve a $10
           billion bailout for Jeff Bezos.”


    * ⚓ TruthOut ☛ Nearly_Half_of_GOP_Congressional_PACs’_2022_Funding_Comes
      From_27_Billionaires⠀⇛


    * ⚓ Counter Punch ☛ Homelessness_is_a_Policy_Choice_and_We_Can_Choose
      Differently⠀⇛


           I’ve lived on the streets, been in Hollywood films, owned my
           own footwear service, rubbed elbows with a Saudi Prince, and
           even sung for Donald Trump at Mar-a-Lago — while in and out of
           homelessness. I’ve also been to federal prison and battled
           substance abuse.


           In some ways, I’ve lived an unusual life. But with 140 million
           Americans poor or low-income, there’s nothing unusual about
           growing up in a broken home, enduring homelessness, or ending
           up in the criminal justice system.


    * ⚓ Common Dreams ☛ Opinion_|_Biden_Trip_to_Saudi_Arabia_Is_a_Signal_to_All
      Brutal_Dictators_of_the_World⠀⇛


           President Biden has set out on his travels to Saudi Arabia. The
           implications of the trip for the intertwined issues of human
           rights and energy policy are dire.


§ AstroTurf/Lobbying/Politics⠀➾


    * ⚓ Counter Punch ☛ The_European_Union:_Myth_and_Reality⠀⇛


           The strict European hierarchy


           The European Union is run on a day-to-day basis by Germany for
           German interests. Except when it’s kowtowing to American
           interests. An academic literature (played up by The Economist
           in 2013) has Germany as ‘reluctant hegemon’ – just so much
           palaver. Yet for this crucial issue of Ukraine, German leaders
           have failed to look not only after the interests of Europe over
           which it exercises tutelage but those of Germany itself.


    * ⚓ Counter Punch ☛ The_Democrats’_Third-Party_Massacres⠀⇛


    * ⚓ Counter Punch ☛ Pennsylvania_is_Being_Poached_by_Populist_Frauds⠀⇛


           This is a country where you’re never more than 15 minutes from
           both an Amish farm and an abandoned factory. This is a country
           where people hunt to put food on the table and not to prove how
           big their dick is. This is a country where diversity means that
           every skinny Black dude on the wrong side of town has a fat
           hillbilly baby-mama with a couple of beautiful caramel children
           in tow. This is a country of doublewides with rainbow flags and
           ranch homes with Blue Lives Matter signs. This is a complicated
           and often contradictory state but it’s also a state with a lot
           more heart than brains and it’s a state that has been
           repeatedly raped by Washington for that honorable flaw. A place
           where all the factory workers now cut their paychecks at
           growing prisons filled with their opioid-addicted children who
           sought to erase themselves after coming home from the latest
           bipartisan forever war.


           This is how Pennsylvania became Trump Country and this is what
           the smug wonks on CNN will never grasp about the MAGA sickness.
           Once again, I’ve never been to Alabama, but the people who live
           between Pittsburgh and Philadelphia didn’t vote for Trump
           because they’re racist or sexist even if he clearly is. They
           only got on board with that orange motherfucker when they saw
           how uncomfortable he made elitist little shits like James
           Carville. The people I know who voted for Trump knew full well
           that they were casting a ballot for a lecherous cretin they
           wouldn’t let within fifteen feet of their daughters but as far
           as they were concerned, they weren’t just voting for a man who
           macks on his own offspring, they were voting to throw a
           screaming orange brick through the White House window. MAGA was
           their revenge against a bipartisan political machine that fed
           our state to NAFTA and the Iraq War.


    * ⚓ Telex (Hungary) ☛ Orbán:_This_is_a_new_era_of_European_history⠀⇛


           On most Fridays, Hungary’s Prime Minister gives an interview on
           one of the state-owned radio stations. Since the independent
           media has not had a chance to interview him for many years,
           these weekly radio interviews are the only opportunity to find
           out what the leader of the country thinks about current events,
           how he sees his opponents and any issues at hand.


    * ⚓ Telex (Hungary) ☛ Hungary_to_help_get_Ukraine’s_grain_out⠀⇛


    * ⚓ The Nation ☛ The_Democratic_Party_Is_No_Match_for_a_Nation_on_Fire⠀⇛


    * ⚓ Common Dreams ☛ Opinion_|_The_Nation_Needs_You,_Mr._President,_So
      Please_Don’t_Run_in_2024⠀⇛


           Pundits are focused on Joe Biden’s tanking poll numbers, while
           progressives continue to be alarmed by his dismal job
           performance. Under the apt headline “President Biden Is Not
           Cutting the Mustard,” last week The American Prospect summed
           up: “Young people are abandoning him in droves because he won’t
           fight for their rights and freedom.” Ryan Cooper wrote that “at
           a time when Democrats are desperate for leadership—especially
           some kind of strategy to deal with a lawless and extreme
           Supreme Cour—he is missing in action.”


    * ⚓ Counter Punch ☛ Why_Grassroots_Democrats_Have_Turned_Against_Biden⠀⇛


           Yes, Senators Joe Manchin and Kyrsten Sinema team up with
           Republicans to stymie vital measures. But the president’s
           refusal to issue executive orders that could enact such popular
           measures as canceling student debt and many other policies has
           been part of a derelict approach as national crises deepen.
           Recent events have dramatized the downward Biden spiral.


           Biden’s slow and anemic response to the Supreme Court’s long-
           expected Dobbs decision overturning Roe v. Wade spotlighted the
           magnitude of the stakes and the failure. The grim outlook has
           been underscored by arrogance toward progressive activists.
           Consider this statement from White House communications
           director Kate Bedingfield last weekend as she reacted to wide
           criticism: “Joe Biden’s goal in responding to Dobbs is not to
           satisfy some activists who have been consistently out of step
           with the mainstream of the Democratic Party. It’s to deliver
           help to women who are in danger and assemble a broad-based
           coalition to defend a woman’s right to choose now, just as he
           assembled such a coalition to win during the 2020 campaign.”


    * ⚓ Counter Punch ☛ How_to_Prevent_an_American_Theocracy⠀⇛


           Just weeks ago, states could implement at least some common-
           sense limits on carrying guns. Public school employees couldn’t
           impose their religious practices on students. And the EPA could
           hold back our climate disaster by regulating planet-heating
           carbon emissions from coal plants.


           Thanks to an appalling power grab by the Supreme Court’s
           conservatives, all that’s been demolished too. And they’ve
           hinted that the right to take contraception, marry someone
           regardless of your sexual orientation, and even to choose your
           own elected representatives could be next.


    * ⚓ Counter Punch ☛ Worsening_Chaos:_Israel’s_Political_Instability_is_Now
      the_Norm⠀⇛


           Bennett’s coalition government consisted of eight parties,
           welding together arguably one of the oddest coalitions in the
           tumultuous history of Israeli politics. The mishmash cabinet
           included far right and right groups like Yamina, Yisrael
           Beiteinu and New Hope, along with centrist Yesh Atid and Blue
           and White, leftist Meretz and even an Arab party, the United
           Arab List (Ra’am). The coalition also had representatives from
           the Labor Party, once the dominant Israeli political camp, now
           almost completely irrelevant.


           When the coalition was formed in June 2021, Bennett was
           celebrated as some kind of a political messiah, who was ready
           to deliver Israel from the grip of the obstinate, self-serving
           and corrupt Netanyahu.


    * ⚓ Counter Punch ☛ The_“New”_Middle_East_Resembles_The_Old_Middle_East⠀⇛


           Biden argued that “fundamental freedoms are always on the
           agenda when I travel abroad, as they will be during this trip,
           just as they will be in Israel and the West Bank.”  But Biden’s
           endorsement of Israeli national security policy in the wake of
           Israeli responsibility for the killing of Palestinian-American
           journalist Shireen Abu Akleh is particularly ill-timed. 
           Similarly, Biden is ignoring his intelligence community in
           going hat-in-hand to Saudi Crown Prince Mohammed bin Salman for
           increased oil production in view of MBS’s responsibility for
           the sadistic killing of Saudi dissident journalist Jamal
           Khashogghi.  The Biden-MBS photo op will be particularly
           disheartening.


           U.S. handling of Israel resembles Trump’s handling.  There has
           been no challenge to Naftali Bennett’s aggressive settlements
           program on the West Bank, and no restoration of the modest
           relations that once existed between the United States and the
           Palestinians.  The Trump administration bestowed legitimacy on
           the settlements, and his policy is still in place.  Biden
           indicated he would reopen the U.S. consulate to the
           Palestinians in Jerusalem, but Israeli pressure blocked that
           move.  Similarly, the Palestinian mission in the United States
           closed by Trump remains unopened by Biden.  Biden’s essay
           falsely claimed that he “rebuilt U.S. ties with the
           Palestinians.”


    * § Misinformation/Disinformation⠀➾


          o ⚓ Scheerpost ☛ Patrick_Lawrence:_This_Week_in_Fake_News_/_Artless
            Dodgers⠀⇛


                 It absolutely galls me that we must read The Times and
                 the other major dailies in this manner. You can wring the
                 truth out of them with effort, though often this is
                 impossible. And the truth here is they are not telling us
                 the truth as they purport to report Ukraine.


§ Censorship/Free Speech⠀➾


    * ⚓ Techdirt ☛ The_Public_Hates_The_Idea,_Pushed_By_GOP_Political_Spammers,
      That_Google_Will_Let_Political_Spam_Bypass_Spam_Filters⠀⇛


           For a few months now, we’ve been following this nonsense story,
           driven almost entirely by executives at the GOP’s favorite
           digital marketing (read: spamming) operation, that Google is
           censoring political spam from Republicans. This was all based
           on either an incompetent, or deliberate, misreading of a study,
           which did find that an untouched Gmail account sent more GOP
           political spam to the spam folder than Democratic spam.


    * ⚓ Techdirt ☛ Paperwork_Suggests_Donald_Trump_Has_Left_The_Board_Of_His
      ‘Tech’_Company;_But_Truth_Social_Says_He’s_Still_There⠀⇛


           It’s no secret that Donald Trump’s Trump Media and Technology
           Group — which was launched with big plans, but so far only has
           a total flop of a barely used social media app, Truth Social,
           to show for it — was struggling. But then came the news that
           the ponzi-scheme-esque reverse merger deal was actually leading
           to serious legal investigations, and it appears that Trump and
           some of his friends may have decided it was perhaps better to
           take a more “hands off” approach.


    * ⚓ Meduza ☛ Vladimir_Putin_enacted_more_than_100_new_laws_today._Here_are
      the_ones_you_need_to_know._—_Meduza⠀⇛


           The Russian authorities can now designate anyone they consider
           under “foreign influence” a “foreign agent” — even without
           evidence of the receipt of foreign funding. In addition, those
           blacklisted as “foreign agents” are now banned from teaching at
           state and municipal schools, receiving government financial
           support for creative projects, and selling goods and services
           to the state. What constitutes “foreign influence” remains
           unclear. 


    * ⚓ Internet Freedom Foundation ☛ Meta’s_1st_Annual_Human_Rights_Report
      Wrongs_Humans_of_India⠀⇛


           Following growing criticism against Meta’s efforts to contain
           the spread of hate speech and incitement to violence, it
           released its first annual Human Rights Report, which includes a
           brief section reporting on the Meta commissioned independent
           human rights impact assessment (HRIA) for India. In a stark
           contrast to the reporting on country specific HRIAs released so
           far, the reporting on India seems perfunctory and non-
           reflective of the inputs provided by several civil society
           organisations who participated in the assessment. Furthermore,
           Meta fails to publish the full report of the HRIA which leads
           to concerns around transparency and accountability.


§ Freedom of Information / Freedom of the Press⠀➾


    * ⚓ Techdirt ☛ The_Journalism_Competition_Preservation_Act_Is_Lose-Lose
      Legislation⠀⇛


           How many times have you shared a link today? How many times
           have you used a search engine to look for information? We use
           links and snippets to gain and share information so often that
           we don’t even think about it. It’s an essential component of
           the internet, so intrinsic that an internet without links
           simply doesn’t work. For this reason, it’s alarming that
           certain members of Congress are pushing “link tax” proposals,
           like the Journalism Competition Preservation Act (JCPA), that
           will monetize links in a way that changes how this essential
           internet infrastructure works.


§ Civil Rights/Policing⠀➾


    * ⚓ Counter Punch ☛ Trial_by_Committee⠀⇛


           Rep. Bennie Thompson, the Mississippi Democrat who heads the
           nine-member panel, came close to blaming the former president
           for staging the violent attack with help from the far-right
           Proud Boys and Oath Keepers gangs.


           “Donald Trump summoned a mob to Washington, D.C., and
           ultimately spurred that mob to stage a violent attack on our
           democracy,” he said.


    * ⚓ EFF ☛ Impact_Litigation_in_Action:_Building_the_Caselaw_Behind_a_Win
      for_Free_Speech⠀⇛


           The win is not only good for those who would speak up against
           the powerful, it’s also a great example of how EFF’s patient
           work in the courts over many years can pay off. In fact, we
           were pleasantly surprised by the number of cases that EFF has
           been involved in that were relied upon by the Court.


           By our count, the order cites eight cases that EFF participated
           in, either as counsel or as amicus curiae—and quite a few where
           we filed multiple briefs, participating at multiple levels of
           the judicial system. Not bad for an opinion that runs barely 15
           pages long. The cases stretch across the issues, with several
           on copyright-specific John Doe cases (In re Verizon; In re DMCA
           Section 512(h) Subpoena to Reddit), a couple on copyright
           itself (Google v. Oracle; Kelly v. Arriba Soft), and some
           focusing on fair use (Lenz v. Universal; Dr. Seuss v.
           ComicMix). There are also a couple where we helped behind the
           scenes but ultimately did not file a brief. 


           All in all, the case cites over 17 years’ of work by EFF
           lawyers who helped to carefully build the legal foundations
           that the Court relied upon. The earliest cases cited here by
           the Court were decided in 2003, and the latest were in 2021. We
           weren’t alone in this—our friends at Public Citizen had a huge
           role in developing this caselaw, as did the ACLU, EPIC, and
           many private attorneys over the years. But EFF’s mark is
           unmistakable.


    * ⚓ Counter Punch ☛ Putin_and_Biden:_Free_Brittney_Griner_Now!⠀⇛


           It is outrageous that you have imprisoned WNBA basketball
           player, Black woman, U.S citizen, and player for your Russian
           teams, Brittney Griner on trumped up charges of possession of
           marijuana and held her in prison since February 17, 2022. This
           is a clear violation of her civil and human rights, as well as
           a moral, tactical, and strategic catastrophe for you. Admit
           your mistake and free her now. We call on the U.S. and Russia
           to not negotiate an exchange of prisoners because Ms. Griner is
           not a spy but a friend of Russia who you have cruelly
           terrified, imprisoned, and persecuted. Free Brittney Griner
           now.


           Why was Ms. Griner in Russia? Because she is a women’s
           basketball superstar so underpaid in the U.S. that she—like
           others—must also play in Russia to supplement her income. Ms.
           Griner has played in Russia for the last seven years, “earning
           over $1 million per season—more than quadruple her WNBA
           salary.” At a time when Russia is treating professional women’s
           basketball players better financially than they are treated in
           the US, and in turn they are choosing to play in your country,
           it is outrageous that you would persecute her. Free Britney
           Griner now.


    * ⚓ Common Dreams ☛ Opinion_|_The_GOP’s_Army_of_Christian_Nationalists_and
      White_Supremacists_Poses_a_Danger_Greater_Than_You_Know⠀⇛


           The Supreme Court’s disastrous rulings on prayer on public
           school property and abortion rights have finally focused proper
           attention on the role of religious extremism in undermining
           democratic self-rule. For decades, not only has it been
           underestimated, most of the media has misunderstood Christian
           fundamentalism’s goals.


    * ⚓ TruthOut ☛ The_US_Is_Descending_Into_a_Crisis_of_Overt_Fascism._There’s
      Still_a_Way_Out.⠀⇛


    * ⚓ Pro Publica ☛ In_Arizona,_an_Ex-Husband_Sues_Abortion_Clinic_on_Behalf
      of_Embryo⠀⇛


           Nearly four years after a woman ended an unwanted pregnancy
           with abortion pills obtained at a Phoenix clinic, she finds
           herself mired in an ongoing lawsuit over that decision.


           A judge allowed the woman’s ex-husband to establish an estate
           for the embryo, which had been aborted in its seventh week of
           development. The ex-husband filed a wrongful death lawsuit
           against the clinic and its doctors in 2020, alleging that
           physicians failed to obtain proper informed consent from the
           woman as required by Arizona law.


    * ⚓ Common Dreams ☛ ‘They_Want_to_Hold_Women_Captive’:_GOP_Blocks_Bill
      Protecting_Right_to_Travel_for_Abortion⠀⇛


           This is a breaking story… Please check back for possible
           updates…


           Democratic leaders and reproductive rights advocates swiftly
           blasted anti-choice Republican lawmakers on Thursday after U.S.
           Sen. James Lankford blocked a bill intended to protect the
           right of pregnant people across the country to travel for
           abortion services.


    * ⚓ Common Dreams ☛ ‘This_Is_Sick’:_Indiana_Doctor_Investigated_Over
      Abortion_Care_for_Child_Rape_Victim⠀⇛


           Indiana’s Republican attorney general sparked widespread
           outrage on Wednesday night by launching an investigation into a
           doctor in his state who recently provided legal abortion care
           to a child rape victim from Ohio.


           “They’re either actively trying to get her killed, or just
           don’t give a damn that they’re putting her in danger.”


    * ⚓ Common Dreams ☛ Legal_Experts_Warn_Dobbs_Ruling_Puts_Nation_on
      ‘Dangerous_Backward_Path’⠀⇛


           A nonpartisan group of legal experts warned Thursday that the
           “logic” of the U.S. Supreme Court’s 6-3 ruling in Dobbs v.
           Jackson Women’s Health Organization—which stated that the right
           to abortion cannot be protected under the 14th Amendment
           because it is “not deeply rooted in the nation’s history and
           tradition”—puts the country on a “dangerous backward path.”


           “The requirement that rights be ‘deeply rooted’ is a sleight of
           hand that, if adopted more broadly, would sabotage the
           developing body of civil rights.”


    * ⚓ Counter Punch ☛ Did_Dobbs_Help_the_Left_Rediscover_How_Political_Change
      is_Made?⠀⇛


           On July 8, President Joe Biden signed an executive order that
           directed the Department of Health and Human Services (HHS) to
           take steps to protect and expand access to medical abortion and
           contraception while ensuring that patients are eligible to
           obtain emergency care. In addition, the order seeks to push
           back against threats posed by surveillance in states outlawing
           abortion by directing federal agencies to take additional
           actions to protect patient privacy. The order was in response
           to a two-week pressure campaign by leftists who were frustrated
           by the Democratic Party’s tepid response the Supreme Court’s
           decision in Dobbs v. Jackson Women’s Health Organization, which
           overturned the 1973 Roe V. Wade ruling protecting abortion
           rights for women. Many threatened that they would not fund or
           vote for the Democratic Party unless leaders took action.


           The ways in which this pressure moved Biden from inaction to an
           executive order illustrates what activist scholars such as
           historian Howard Zinn long argued: one can’t be neutral on a
           moving train and change only occurs through sustained protest
           and agitation from the citizenry. Indeed, Lawrence O‘Donnell
           explained that when he worked for the Democratic Party, they
           ignored the demands from the left because many were never
           willing to actually withhold their votes on election day–
           ultimately succumbing to the fear tactics of the party’s
           ongoing “vote blue no matter who” propaganda campaign. As
           Biden’s recent executive order illustrates, those seeking to
           codify abortion rights need to agitate and annoy Democratic
           leadership to take aggressive action.


    * ⚓ Counter Punch ☛ Will_Abortion_Bans_Overtake_Inflation_as_the_Key_Issue
      in_the_Midterms?⠀⇛


           The Republicans are focused on anger with high inflation. Non-
           Trumpian conservative adjunct lecturer at Hillsdale College,
           Henry Olsen, wrote in his Washington Post column that inflation
           is even worse than the official numbers suggest. Citing
           statistics from an American Farm Bureau Federation survey, he
           sees prices for goods people regularly purchase rising much
           faster than for things they don’t. For instance, food used at
           home rose by almost 12 percent over the past year; eggs in
           particular cost more than 32 percent. These numbers are real
           and alarming.


           Democrats, on the other hand, are highlighting the large
           demonstrations resulting from SCOTUS overturning Roe v. Wade.
           Pro-choice organizers said there were more than 380 protest
           events in cities including Washington DC, New York City, Los
           Angeles, and Chicago against the decision to eliminate a
           woman’s constitutional right to determine if she wants to be
           pregnant.


    * ⚓ The Nation ☛ 30_Years_Ago_and_Today:_History_Repeats_Itself.⠀⇛


    * ⚓ Common Dreams ☛ Opinion_|_Right-Wing_Zealots_on_the_Supreme_Court
      Threaten_to_Make_American_Theocracy_a_Reality⠀⇛


           Barely a month ago we lived in a world where all Americans had
           the right to decide for themselves whether to continue a
           pregnancy. For much of the country, that’s now history.


    * ⚓ FAIR ☛ ‘Whether_You’re_on_the_Supreme_Court_Shouldn’t_Depend_on_How
      Many_People_You_Give_Your_Phone_Number_to’⠀⇛


           Janine Jackson: “The Lonely Chief: How John Roberts Lost
           Control of the Court.” That was the plaintive headline of
           Politico’s June 25 report explaining that Roberts, along with
           his “middle of the road” approach on abortion, would likely be
           a casualty of the court’s Dobbs v. Jackson Women’s Health
           ruling.


    * ⚓ Counter Punch ☛ The_Pink_Tide_Surges_in_Latin_America⠀⇛


           Ebb and flow of the class struggle in Latin America


           The tidal metaphor describes the shifting constellations of
           governments in what Washington long considered its exclusive
           domain ever since the 1823 Monroe Doctrine. The Pink Tide is a
           reaction to and a struggle against neoliberalism, which is the
           contemporary form of capitalism. The Pink Tide first entered
           its flow phase in 1998 with the election of Hugo Chávez as
           president of Venezuela. What followed was truly a sea change
           with a developing expression of sovereignty and independence.
           An alphabet soup of regionally integrated entities arose: ALBA,
           UNASUR, MERCOSUR, Petrocaribe, CELAC, etc.


    * ⚓ Counter Punch ☛ “No_One_Is_Paying_Attention_to_Your_Protests”⠀⇛


           This pointed insult was shouted without a trace of irony
           through a chain-link fence toward a group of nuclear weapons
           opponents last Tuesday by a military guard equipped with
           binoculars and wearing a camera strapped around his neck.


           The protest group was at the perimeter of Büchel Air Force Base
           in west-central Germany on July 12, the 205th anniversary of
           the birth of Henry David Thoreau — the naturalist and theorist
           of conscientious defiance of illegitimate authority.


§ Digital Restrictions (DRM)⠀➾


    * ⚓ Techdirt ☛ Ubisoft_Teaches_Customers_They_Don’t_Own_All_That_DLC_They
      ‘Bought’⠀⇛


           While we were just discussing how everyone occasionally gets
           reminded that for many digital goods these days you simply
           don’t actually own what you’ve bought, all thanks to Sony
           disappearing a bunch of purchased movies and shows from its
           PlayStation platform, this conversation has been going on for a
           long, long time. Whereas the expectation by many people is that
           buying a digital good carries similar ownership rights as it
           would a physical good, instead there are discussions of
           “licensing” buried in the Ts and Cs that almost nobody reads.
           The end result is a massive disconnect between what people
           think they’re paying for and what they actually are paying for.


    * ⚓ DaemonFC (Ryan Farmer) ☛ Netflix_thinks_that_the_solution_to_its
      financial_woes_is_a_deal_with_Microsoft_to_put_ads_into_your_TV_shows._–
      BaronHK’s_Rants⠀⇛


           Netflix thinks that the solution to its financial woes is a
           deal with Microsoft to put ads into your TV shows.


           Netflix is in major financial crisis. They’re doing huge
           layoffs. They’ve spent years mismanaging the platform and have
           only themselves to blame.


           Even though the DRM is malicious, and encourages people to be
           jerks who can’t share with their friends, it’s not the cause of
           their financial problems.


           Back when it wasn’t so expensive and had shows that people
           wanted to watch, people would pay the money to subscribe and
           then keep paying, usually even if there wasn’t anything on that
           they wanted to watch that month.


           However, with the state of the economy being pretty lousy, and
           hyperinflation causing people to struggle to put food on the
           table, and gas in the gas tank, Netflix seems to have figured
           out what the solution is to losing a million subscribers per
           annum.


           No, the solution is not canceling all the good shows, it’s not
           raising the price another $3-4 a month every year; it couldn’t
           possibly be paying $50 million for a documentary about Michelle
           Obama that nobody wants to see. But they’ve done all of this.


§ Monopolies⠀➾


    * § Copyrights⠀➾


          o ⚓ Torrent Freak ☛ Manga_Piracy:_Operator_of_MangaBank_Sentenced_By
            Chinese_Authorities⠀⇛


                 Following a complaint from Japanese publishers and a
                 criminal process in China, a man in his thirties has been
                 sentenced for operating MangaBank, a massive manga piracy
                 site that shut down in 2021. Local authorities found no
                 copyright infringement in China but accepted that the
                 man’s behavior ran contrary to the right of communication
                 to the public.


          o ⚓ Torrent Freak ☛ RIAA_Takes_Down_‘Infringing’_.ETH_Domain_Auctions
            from_OpenSea⠀⇛


                 The RIAA is no stranger to sending takedown requests. In
                 most cases, these notices target pirated content but more
                 recently the group has been defending its members against
                 “infringing” Ethereum Name Service (ENS) domain name
                 sales on OpenSea. The NFT marketplace complied with the
                 request and pulled the auctions, including that of
                 RIAA.eth.


§ Gemini* and Gopher⠀➾


    * § Personal⠀➾


          o ⚓ Clarity⠀⇛


                 Now mind you, I don’t mean the kinda clarity like a
                 “moment of clarity” in the vain an alcoholic would (which
                 I am btw I’m 5 years clean off drink (still smoke up 420
                 tho)), but instead is a sort of renewed outlook on what
                 it is exactly I should be focusing on and how I should
                 take action in one area or the other. I’ve, maybe, not
                 been the most personable friend right now. Went through a
                 bit of a breakdown among a circle of people i’m close
                 with, over things we wouldn’t have known of the other or
                 have even talked about , yet at the same time maybe
                 should’ve at more appropriate times much earlier smfh.


          o ⚓ Terraforming⠀⇛


                 At the library today I came across a picture book about
                 terraforming. The subtitle of the book was something
                 along the lines of “let’s make a new Earth!” The book
                 explains how we could terraform Mars to replace the
                 planet we are destroying. It begins by showing Earth in
                 the year 2070, and how by then it is already barely
                 inhabitable because of our highly pollutant ways of life.
                 But, rather than changing our ways of life, heck, LETS
                 TERRAFORM ANOTHER PLANET!


          o ⚓ don’t_get_me_*not*_going⠀⇛


                 A road trip marred by stultifying standstill delays
                 provided most of yesterday’s sensory bang for the buck.


                 Sitting there with the guitar (I was a passenger the
                 first half), I remembered past thoughts on automobile
                 brake lights as another key intelligence indicator for me
                 – specifically, more brake usage suggesting lesser
                 grokking prowess with respect to the likes distance,
                 velocity, and mass in a time(ing) context.


          o ⚓ SpellBinding:_CEGIPNK_Wordo:_REPAY⠀⇛


          o ⚓ Old_Friends⠀⇛


                 School is a funny environment. You are forced into it;
                 you are surrounded by other kids who just happen to be
                 there. Later, college is not that different. From this
                 limited pool, you pick some friends, and you make some
                 enemies. You are stuck together, and you see each other
                 every day.


                 As you get older, some of your old friends remain close.
                 You still spend free days and weekends together. Maybe
                 even find ways to work together. And thank god you no
                 longer have to deal with the jerks.


                 [...]


                 Maybe you check in on facebook or whatever, every so
                 often, and smile when you see them doing something fun.
                 Maybe they hate social media, or maybe you do. Maybe you
                 exchange a few words, but somehow that just does not do
                 the trick. You promise to get together soon, and then
                 there is more stuff to take care of, and more time
                 passes.


    * ⚓ TecMint ☛ MySQL_Backup_and_Restore_Commands_for_Database
      Administration⠀⇛


           This article shows you several practical examples on how to
           perform various backup operations of MySQL/MariaDB databases
           using the mysqldump command and also we will see how to restore
           them with the help of mysql and mysqlimport command in Linux.


           mysqldump is a command-line client program, it is used to dump
           local or remote MySQL databases or collections of databases for
           backup into a single flat file.


§ Finance⠀➾


    * ⚓ Re:_The_Cheapest_Cup_of_Tea_in_Town⠀⇛


           When I started drinking tea a couple of years ago, I remember
           having read somewhere that you can get hot water for tea just
           about everywhere in asian countries like Japan or China. The
           people there use to prepare their thermos flask with a first
           infusion of Sencha or Gunpowder in the morning, and then simply
           refill the flask with hot water over the course of the day. The
           tea leaves obviously remain in the flask all day. Getting
           several infusions out of good quality tea leaves is not a
           problem at all.


§ Technical⠀➾


    * § Internet/Gemini⠀➾


          o ⚓ i_love_my_puter_all_my_friends_are_inside_it⠀⇛


                 this was prompted by a particular gemlog, but being in
                 these… idk, modern tech / web critical circles i’ve seen
                 this type of thing a lot, and have always had rather
                 strong feelings about it, so may as well just write
                 something now.


    * § Programming⠀➾


          o ⚓ Storing_information_on_paper_using_the_Pen_To_Paper_protocol⠀⇛


                 Here is a draft for a protocol named PTPDT, an acronym
                 standing for Pen To Paper Data Transfer. It comes with
                 its companion specification Paper To Brain.


                 The protocol describes how a pen can be used to write
                 data on a sheet of paper. Maybe it would be better named
                 as Brain To Paper Protocol.


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


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