𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Sunday, February 06, 2022
┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅
Generated Mon 7 Feb 02:41:14 GMT 2022
Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖)
Full hyperlinks for navigation omitted but are fully available in the originals
The corresponding HTML versions are at 𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈
Latest in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕 and older bulletins can be found at 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕-𝒂𝒓𝒄𝒉𝒊𝒗𝒆𝒔
Full IPFS index in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔 and as plain text in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔/𝒕𝒙𝒕
Gemini index for the day: gemini://gemini.techrights.org/2022/02/06/
╒═══════════════════ 𝐑𝐄𝐂𝐄𝐍𝐓 𝐁𝐔𝐋𝐋𝐄𝐓𝐈𝐍𝐒 ════════════════════════════════════╕
Previous bulletins in IPFS (past 21 days, in chronological order):
Qmehhm7o1VbxWg8uyeTcYkk6Hr1Cp4Ho21X2wCnesY9asd
Qmf3TSbMJS9koYs7ieZ1w3WBpaDp6x7rx5xnhC6B134fFL
QmbAVHY5Ges1nF9HNsiNn6FsQW8UdTFHURKDG1QgSKpKw7
QmZnZkCBXLzZg5rkewh3peFLzQ5xAZRm6HpjAvmtf39ELR
QmZeHUaFKnCwMohgf9hT7KAvQEFvHbBZ8MUZTtceSkoLZc
QmQLbqvdSXzQ59gWzwwt9RARegF8vZB68qihXTbNcDNoxy
QmXRhRDa28yw47e5ym8hgWTNSCTtmH5t22GCpvFvaGYDwN
QmNrH8cLM4mYaiBXzhdkhAQm8XM54JzRQa3Z1Ng4a41kcV
QmZjLA2jtgeEhSJihNxjJW3q7KaEU6iyCKve9pmkci3m61
QmTWgjCkngZ2r4jN8fZGmd7bpEdJL3pBfU6vKWFNxPmkYf
QmUa6NW563bcVpbJi9K42Aap4iTTXYmJcu5bTsjAcRc9yG
QmPENr81muU2jHsHXxDP2oXCR4itHu2Pb54BpV4z2a6v8g
QmT1WmWT8oyJF7h6FDnkDWXE6tEV7sUdo6MyboEn1kLiFx
Qmd7o1W8PgtXmeAFmAGFoVreMpLA1AVtvVjUMvVr7zc1YQ
Qma88nEdV64rLJsqR8uVd62B8zwrDvuX6Etg42wsovLPUQ
QmWMn5rx4mwf86jmAsH6KUasKtr2WVybRVa9b2sJECtwpz
QmS1wrYoYvTPNPTvZYppVeYPXTR8rHjtMkwCEYGCEaEWUU
QmTLUpA1Pbmatf5PSQgBbMk1Hj8eJFQAcNy7ahAe769Anx
QmbQWJTJVwCBMn6Bc7J9W2fhZtZYwQh4SrKoy4dF1Rj3Pm
QmZ3Z9HPLFuFUYdDqN8YY1cZW5M8k9MCEyfwYQiJSBdgg9
Qme1XwuhK1F1t6m8AJGPXQ8U9wCeB9UCDmmkPBEmWLharx
╒═══════════════════ 𝐈𝐍𝐃𝐄𝐗 ═══════════════════════════════════════════════════╕
⦿ An Implementation of a Gemini-to-HTTP/S Proxy/Gateway in Perl | Techrights
⦿ The EPO’s Overseer/Overseen Collusion — Part XXXXIII: A Legal No-Man’s Land | Techrights
⦿ IRC Proceedings: Saturday, February 05, 2022 | Techrights
⦿ [Meme] Almost a Decade for EPO Justice (Delayed, Hence Denied) | Techrights
⦿ Europe Has a Severe Corruption Crisis | Techrights
䷼ Bulletin articles (as HTML) to comment on (requires login):
http://techrights.org/2022/02/06/an-implementation-of-a-gemini-to-https-proxygateway-in-perl/#comments
http://techrights.org/2022/02/06/immunity-help-from-the-epo-ac/#comments
http://techrights.org/2022/02/06/irc-log-050222/#comments
http://techrights.org/2022/02/06/meme-almost-a-decade-for-epo-justice-delayed-hence-denied/#comments
http://techrights.org/2022/02/06/video-about-the-42th-part/#comments
䷞ Followed by Daily Links (assorted news picks curated and categorised):
http://techrights.org/2022/02/06/gnu-guile-sdl-0-6-0/#comments
http://techrights.org/2022/02/06/libredwg-0-12-5/#comments
http://techrights.org/2022/02/06/linux-on-ibm-palmtop/#comments
䷩ 𝚕𝚒𝚗𝚎 61
╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕
(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/06/an-implementation-of-a-gemini-to-https-proxygateway-in-perl/#comments
Gemini version at gemini://gemini.techrights.org/2022/02/06/an-implementation-of-a-gemini-to-https-proxygateway-in-perl/
⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.06.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧
Gemini_version_available_♊︎
✐ An_Implementation_of_a_Gemini-to-HTTP/S_Proxy/Gateway_in_Perl⠀✐
Posted in Free/Libre_Software, Site_News at 5:59 am by Dr. Roy Schestowitz
Video_download_link | md5sum c26ad6ca3ceadcbf142ba5c07550adf4
Perl-Powered Gemini-to-HTTPS Proxy
Creative Commons Attribution-No Derivative Works 4.0
http://techrights.org/videos/gemini-proxy-perl.webm
Summary: A mini-project that lets us self-host the Gemini proxy/gateway is
underway; it is custom-made for the needs of Techrights but generalised enough
to be used by other sites/capsules, too
THE VIDEO above is the first video of several. It explains how a project works
— a project that does not yet have a name (just generic “geminiproxy” or
gemini-proxy.pl). It does not yet go into the technical details and any finer
bits, as it’s just a high-level, over-encompassing introduction to what we try
to achieve, why it is important (privacy, self-determination etc.) as it is
still work in progress and work which we shall revisit later. The code is in
Git already (so far there have been bug fixes aplenty), so technically it is
publicly available.
“The code is in Git already (so far there have been bug fixes aplenty), so
technically it is publicly available.”As it stands, at the moment the site has
two HTTP and HTTPS (both are fully supported) access points. One is powered by
Gemini (static) and another by a database (dynamic). For the former, direct
access over gemini:// is possible and very much encouraged. The “master copy”,
however, is the latter, as it contains all the images, videos etc. We’ll carry
on tinkering for a while and then make follow-up videos/texts with more
concrete examples and use cases.
Stay tuned… █
䷩ 𝚕𝚒𝚗𝚎 117
╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕
(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/06/immunity-help-from-the-epo-ac/#comments
Gemini version at gemini://gemini.techrights.org/2022/02/06/immunity-help-from-the-epo-ac/
⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.06.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧
Gemini_version_available_♊︎
✐ The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXXIII:_A_Legal_No-Man’s_Land⠀✐
Posted in Courtroom, Deception, Europe, Law, Patents at 3:49 pm by Dr. Roy
Schestowitz
Series parts:
1. The_EPO’s_Overseer/Overseen_Collusion_—_Part_I:_Let_the_Sunshine_In!
2. The_EPO’s_Overseer/Overseen_Collusion_—_Part_II:_A_“Unanimous”
Endorsement?
3. The_EPO’s_Overseer/Overseen_Collusion_—_Part_III:_Three_Missing_Votes
4. The_EPO’s_Overseer/Overseen_Collusion_—_Part_IV:_The_Founding_States
5. The_EPO’s_Overseer/Overseen_Collusion_—_Part_V:_Germany_Says_“Ja”
6. The_EPO’s_Overseer/Overseen_Collusion_—_Part_VI:_A_Distinct_Lack_of_Dutch
Courage
7. The_EPO’s_Overseer/Overseen_Collusion_—_Part_VII:_Luxembourgish_Laxity
8. The_EPO’s_Overseer/Overseen_Collusion_—_Part_VIII:_Perfidious_Albion_and
Pusillanimous_Hibernia
9. The_EPO’s_Overseer/Overseen_Collusion_—_Part_IX:_More_Holes_Than_Swiss
Cheese
10. The_EPO’s_Overseer/Overseen_Collusion_—_Part_X:_Introducing_the
Controversial_Christian_Bock
11. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XI:_“General_Bock”_–
Battistelli’s_Swiss_Apprentice?
12. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XII:_The_French_Connection
13. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XIII:_Battistelli’s_Iberian
Facilitators_–_Spain
14. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XIV:_Battistelli’s_Iberian
Facilitators_–_Portugal
15. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XV:_Et_Tu_Felix_Austria…
16. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XVI:_The_Demise_of_the
Austrian_Double-Dipper
17. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XVII:_The_Non-Monolithic
Nordic_Bloc
18. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XVIII:_Helsinki’s_Accord
19. The_EPO’s_Overseer/Overseen_Collusion_—_Part_IXX:_The_Baltic_States
20. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XX:_The_Visegrád_Group
21. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXI:_The_Balkan_League_–_The
Doyen_and_His_“Protégée”
22. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXII:_The_Balkan_League_–
North_Macedonia_and_Albania
23. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXIII:_The_Balkan_League_–
Bulgaria
24. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXIV:_The_Balkan_League_–
Romania
25. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXV:_The_Balkan_League_–
Fresh_Blood_or_Same_Old,_Same_Old?
26. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXVI:_A_Trojan_Horse_on_the
Budget_and_Finance_Committee
27. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXVII:_Cypriot_Complicity
28. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXVIII:_Benoît_and_António’s
Loyal_“Habibi”
29. The_EPO’s_Overseer/Overseen_Collusion_—_Part_IXXX:_The_EPOnian_Micro-
States_–_Monaco_and_Malta
30. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXX:_San_Marino_and_the
Perfidious_Betrayal_of_Liberty
31. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXI:_The_Abstentionists
32. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXII:_“Plucky_Little
Belgium”?
33. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXIII:_Swedish_Scepticism
34. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXIV:_An_“Extremely
Dubious”_Proposal
35. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXV:_Slovakian_Scruples
36. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXVI:_Serbian_Sour_Grapes
37. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXVII:_Stubbornly
Independent_Slovenia
38. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXVIII:_Ensnared_in_the
Tentacles_of_the_SAZAS_Octopus
39. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXIX:_On_the_Slippery_Slope
to_Capture
40. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXX:_The_Idiosyncratic
Italians
41. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXXI:_Public_Service_or
Self-Service?
42. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXXII:_A_Parcel_of_Rogues?
43. YOU ARE HERE ☞ A Legal No-Man’s Land
“Of course, one consequence of the ability of the EPO’s management to act with
impunity is that there will never be any access to TRUE justice for those whose
human rights have been violated.”
–Anonymous,_a_few_days_ago
🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Staff of international organisations like the EPO⦈
Staff of international organisations like the EPO inhabit a legal no-man’s
land.
Summary: The EPO‘s immunity has been exploited by Benoît_Battistelli and
António_Campinos, albeit not without much help from the EPO’s Administrative
Council
As a general rule, EPO Administrative Council delegates who become implicated
in serious “irregularities” in their home countries can expect to face
consequences of some kind – even if the “sanction” may ultimately be nothing
worse than a small fine or being forced into early retirement.
“For all practical intents and purposes, international organisations conduct
their affairs in a legal no-man’s land where there are a number of factors
tending to facilitate and even encourage maladministration and abuse of
power.”This is because when operating on their home pitches these officials
must comply with the codes of conduct governing the activities of national
civil servants and, in this regard, they are subject to a certain degree of
public scrutiny.
But – most important of all – in their day-jobs as national civil servants they
do not enjoy the privilege of “immunity”.
On the contrary, they are subject to the jurisdiction of national
administrative and judicial authorities which operate under the framework of
domestic law and are subject to parliamentary oversight and some minimum level
of accountability.
“The low level of internal and external oversight combine with a remarkable
absence of public scrutiny to create an environment in which there is a
pervasive lack of transparency and accountability.”However, the rules of the
game change significantly different when we shift to the supranational arena in
which international organisations like the EPO operate.
For all practical intents and purposes, international organisations conduct
their affairs in a legal no-man’s land where there are a number of factors
tending to facilitate and even encourage maladministration and abuse of power.
The low level of internal and external oversight combine with a remarkable
absence of public scrutiny to create an environment in which there is a
pervasive lack of transparency and accountability.
“Question: how many fundamental rights enshrined in the ECHR can the EPO
violate without consequence for the individuals responsible?”
–Anonymous,_a_few_days_ago
This often results in the system being skewed by “perverse incentives” because
those who become implicated in serious maladministration or other wrong-doings
seldom – if ever – get called to account or suffer any prejudice to their
“career”.
In the case of the EPO, more often than not, such individuals end up being
rewarded for their misdeeds. Indeed, they often manage to land lucrative post-
retirement sinecures thanks to the EPO’s notorious_revolving_door and the_pan-
European_"good_brother"_crony_network.
🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Christoph Ernst from Germany⦈
Some Council delegates like Christoph Ernst from Germany have managed to land
lucrative post-retirement sinecures via the EPO’s notorious revolving door.
🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Martti Enäjärvi and EUIPO⦈
Despite his criminal conviction for credit card fraud in Finland, Martti
Enäjärvi enjoyed an impressive post-retirement career as a “Special Advisor” to
EUIPO director António Campinos.
In the next part we will consider how the rank-and-file staff of international
organisations like the EPO are exposed to the abuses of managers and senior
executives for whom “immunity” all too often translates into “impunity”. █
“So why do the Member States not only tolerate this situation, but also
participate (eg by way of CA/D 2/14) in enabling the abuses of human rights at
the EPO? Have they no shame?”
–Anonymous,_a_few_days_ago
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠋⠉⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⡿⡿⠿⢿⠿⡿⡿⠿⠿⢿⡿⡿⢿⠿⡿⠿⢿⠿⠿⣿⣿⡿⢿⠿⠿⠿⢿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠈⢿⣿⣿⣿⡿⣿⠟⡿⢾⡿⢿⢿⠻⢿⢿⡿⠿⢿⢿⢻⠿⣻⠿⡟⠿⣿⣟⠟⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣸⣿⣿⣿⣿⣛⣟⣛⣻⣟⣻⣛⣛⣿⣛⣻⣛⣻⣿⣻⣻⣟⣟⣻⣛⣛⣛⣛⣻⣛⣟⣻⣻⣛⣟⣻⣛⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠐⣀⠎⠒⠀⢾⣷⣖⠤⣀⠀⢀⠠⢤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠿
⣿⣿⣿⠿⠉⠀⠙⠓⣑⡆⠠⣸⡆⡁⠐⠍⢅⠓⠶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣤⠂⣶⡰⢎⡿⢛⠛⠃⠀⡔⠄⠀⠉⠉⠁⠀⠀⠀
⠟⠉⠉⠀⠀⠀⠀⠀⠈⠻⣮⡁⡇⣧⢳⡅⣉⢵⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡉⠡⣩⣶⡿⠟⢕⡭⠀⠐⠁⡈⣷⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠈⢮⣿⣿⡜⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣾⣿⣿⣯⣽⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠠⣖⠒⠒⠚⠩⠃⠀⡀⣰⡇⠛⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢟⡭⣉⣩⣶⣶⣝⢾⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠛⠟⠛⠿⠛⠛⠛⠁⠀⠀⠀⠀⢤⡤⠤⠄⠀⠀⠠⠻⠷⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⣿⣿⠿⢿⡇⣿⡿⢙⣽⣿⣷⣭⢭⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠬⠛⠃⢈⣊⣴⣦⡙⠿⠿⠟⠼⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢐⠣⠜⡲⢭⢉⢙⣱⡜⢿⡿⢙⣛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣦⡊⡠⠐⢄⢼⣆⠙⢟⣢⣶⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣶⣶⣶⣿⣷⣶⣶⣤⣤⣄⣀⣀⠀⢸⡿⣿⡿⣶⣦⣤⡶⣖⣿⣿⣿⣿⣫⡟⠁⠀⠀⠀⢀⣀⣠⣤⣶⣶⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣻⣿⣿⡻⣯⡿⣿⢟⣷⣿⣿⣿⠀⢈⣷⡶⣷⣶⣾⣿⡿⡿⣿⣻⠿⠋⣠⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣟⣯⠿⢾⠉⠁⠉⠁⠁⠉⠑⠚⠩⣼⣿⠋⢀⣿⠯⣽⣿⣿⣟⠳⣛⠤⠉⠁⠀⡮⡛⠛⢅⣹⣿⣿⠿⢿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⡄⠀⠂⢀⠀⠀⠀⠀⠀⠀⠨⣧⣀⣼⠿⣿⣿⡟⠏⠁⠀⠂⠀⠀⠈⠉⠀⣀⢼⡽⡏⢛⣿⣷⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣼⣶⠀⠀⠀⠀⠀⠀⠀⠈⠻⡯⠀⢠⠿⠀⠀⠀⠀⠀⠀⠁⠀⠀⡁⢩⠁⣡⣴⣿⣿⡿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣦⡀⢀⡀⠀⠀⠀⠀
⠀⢀⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡥⠀⠀⠀⠀⣀⣤⣴⣿⠃⠀⡃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠂⣀⣉⣿⣶⣿⣿⡿⠿⢟⢿⠻⣽⡛⣭⡛⣭⢯⢣⠀⠀⠀⠀
⣶⣿⣿⣻⣟⣟⣿⣻⣛⡟⡿⣭⡻⣛⠻⣿⢻⡿⠿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣶⣤⣤⣿⣿⣿⣿⣤⣼⣶⣷⣷⣶⣤⣦⣤⡄⠀⠀⠀⠄⣸⣸⣯⡩⣖⠱⢗⠋⣯⠸⠿⠼⠏⠿⠁⠿⠚⠿⠛⠾⠻⠤⠀⠀
⢶⡆⣶⢭⢸⡻⡚⢯⢻⡟⣾⡯⠆⠟⠎⠏⠸⠳⠈⠘⠎⠁⠃⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠟⠛⠛⣿⣿⣿⣿⡯⠅⠂⠈⣋⡘⣩⣭⣬⣴⣆⣶⣶⣿⢼⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿
⡘⣃⣫⣤⡌⣴⣶⣶⢰⣶⣶⡇⣿⣿⢸⣿⣿⣿⣇⣿⢸⢿⢰⡀⠀⠉⠉⠉⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⢉⠘⢸⣲⡆⡖⡺⠕⣳⠐⢃⣢⡏⣽⢹⣟⠃⣻⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿
⡇⣿⣿⣿⡇⣿⠟⠍⢸⢫⡬⡇⣿⣿⢸⣿⡿⠛⠋⣈⣈⣬⣦⣶⣶⠶⠴⢶⠶⠶⢶⣶⠶⢶⣶⣤⣴⠶⠶⣶⠤⠤⠤⣤⡤⢤⣤⡤⠤⠤⠤⠤⠬⠍⠃⠻⢻⣿⣿⡇⣶⣾⣬⣄⣚⡛⠀⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿
⡯⣿⣿⣿⡇⢃⣤⡀⢸⣶⡖⠇⠿⢟⣀⣥⣤⣤⣤⡶⠿⣿⣿⣿⡇⣔⢲⡟⠰⠂⡸⣙⣶⠀⣿⣿⡇⢐⢶⣿⡆⢱⣾⡟⣨⣺⣶⠀⠶⣒⢃⠶⠶⠾⣿⣛⣗⣊⣉⡀⠟⠸⣿⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿
⡇⣿⣿⡿⡇⣿⣿⠹⠘⣋⣥⣦⣤⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣿⠠⠛⣻⠁⣾⣿⣧⡘⣁⣼⣿⣏⡙⢃⣹⣿⠁⣿⠏⣨⣤⢛⡏⣱⣶⡟⢰⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣦⣜⡛⠋⢻⡇⣿⢿⣿⡇⣿⣿⣿⣿⣿⡇⣿
⡇⣿⣿⡁⡇⠇⣛⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣅⠙⢸⣿⡇⣿⣿⣿⣿⣿⡇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⡛⣋⢭⣭⣭⣴⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⡖⡖⡆⡄⠌⢩⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣛⣛⠋⠁⠂⢸⠀⡇⣿⢸⣿⣿⣿⣿⣿⣿⣿⢿⡷⠿⠿⠿⠿⠿⠿⠿⢿⣇⣧⡇⡇⣸⢸⠀⠀⠀⠀⠀⠈⣭⣭⡍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠸⠼⠓⠛⠛⠉⠉⠉⠀⠀⠀⠀⢰⢀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⢠⣤⣉⠤⢀⣤⣴⣬⢌⣶⣮⣿⡿⣍⢸⢸⣧⡄⡆⢍⣭⣭⣭⣫⡫⣽⣿⣿⣿⣿⡯⢋⣙⣫⣽⠀⣿⣿⣇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⢸⣿⣿⢽⢨⣿⣿⣯⣿⣿⣿⣟⢽⣪⢸⢸⣿⡇⡇⣵⣿⡿⡵⣵⣽⣿⣿⣿⣿⣕⡅⣾⣿⣿⣿⠀⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⢸⢿⡺⣳⢸⡿⣵⣷⣿⣿⢯⣪⣳⣿⢸⢸⣿⡇⡇⣿⢙⣟⣟⣾⢿⣿⣿⣿⠮⣲⡇⣿⣿⣿⡿⠀⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⡹⢹⢸⣿⣿⡇⡰⣝⣽⣿⢘⠿⠞⠛⠙⣯⣷⣿⣿⣿⢸⢸⣿⡅⡇⣯⢾⣾⣟⣋⣋⣽⡿⠻⣿⣿⡇⣿⢟⣿⡽⠀⣿⣿⣷⠀⢅⠌⠹⢿⣟⢿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡣⢁⠄⢨⢸⣿⣿⡇⢭⣾⣿⣫⠈⠀⣰⣶⣴⣾⣿⣷⣿⢟⢸⢸⣿⡇⡆⣯⢾⠉⠻⢿⢿⣿⣿⣥⣼⣿⡇⣻⢯⢾⣾⢀⣿⣿⣿⠈⢂⠂⠅⠍⠂⠢⡑⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠿⡯⡃⢞⠭⡒⠘⠀⠀⠀⢸⣿⣿⡇⣿⡿⡳⣵⣼⡇⠙⣻⣿⣿⣿⣿⣿⣵⢸⢸⣿⡇⠇⣳⣼⣷⣦⣮⣄⡉⣻⣿⣿⢟⡇⣷⣻⣿⣿⠐⣿⣿⣿⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⠹⠿⠿⠿⠿⢿⣿⣿
⣿⡗⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠁⢸⣿⣿⡇⣿⢝⣾⣿⡏⠁⠀⢉⠉⢿⣉⣽⡟⣾⢸⢸⣿⡇⢡⣿⡧⠉⠉⠁⠨⠵⠟⠛⠋⢸⡇⣿⣿⣿⣿⢀⣿⣿⡟⠀⢰⣿⢿⡿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡇⣿⣿
⣿⡏⣷⣽⣭⣯⣭⣴⣭⣭⣥⣥⣭⣭⣼⣽⠂⢸⣿⣿⡇⣫⣿⣿⣟⢜⠸⠘⠟⠑⢘⡯⢻⢹⢸⢸⢸⣿⠇⢸⣿⣣⣄⠀⠀⢀⠀⠀⠀⣠⣼⡇⠛⣯⣿⣟⠀⣿⣿⡇⠀⢸⣿⣦⣮⣿⣴⣴⣦⣦⣴⣧⣶⣶⣿⡟⢽⣿
⣿⡇⣿⣿⣿⣿⣿⢻⠻⢻⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⡇⣿⣿⢟⠎⡢⠊⠀⠃⢀⣘⣿⡾⣐⠀⢸⢸⣿⠇⡎⢿⢿⡿⠼⠼⠿⠿⠷⠤⠿⣿⡇⣛⣿⣾⣪⠀⣿⣿⡇⠀⢸⣿⣿⣿⡟⡟⡟⡟⣿⢻⣿⣿⣿⣿⡇⣨⣿
⣿⡇⣿⣿⣿⣿⣿⣾⣾⣾⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⡇⣿⠯⣃⠀⠀⠀⠀⢀⡠⠉⠍⠀⢑⠸⢸⢸⣿⡇⡁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠿⡉⠁⠘⠀⣿⣿⡇⠀⢸⣿⣿⣿⣷⣶⣷⣶⣿⣾⣿⣿⣿⣿⡇⢸⣿
⣿⣗⣛⡛⣛⠛⠛⠛⡛⢛⠙⠛⠛⠛⠙⠛⠀⢸⣿⣿⡇⢟⢭⡆⠀⠀⠀⠠⠐⢵⠀⡆⢄⠂⠀⢸⢸⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡿⣿
⣿⣿⣿⡧⣅⡁⠠⢀⠂⢀⠀⠄⠀⠀⠀⠀⠀⢸⣿⣿⡇⣫⣿⠀⠀⠀⡀⠍⠀⠀⠂⢀⠂⠀⠌⢸⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠨⣢⣿
⣿⣿⣿⣿⣬⠊⣔⠢⠈⠀⠀⠐⠀⠀⠀⠀⠀⢹⣿⣿⡇⣿⣿⡀⠀⢀⠂⠀⠀⢀⠂⠂⢀⠈⠀⢸⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⠤⡀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⢮⣿⣿
⣿⣿⣿⣿⣯⢉⢶⢁⠄⣈⠀⠀⢂⠠⠀⠀⠀⢸⣿⣿⡇⣿⣿⡧⠀⠢⠀⠀⠠⠂⠀⠀⠂⠀⠀⢸⢸⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣓⣽⣾⢸⣿⣿⡇⠀⠀⠀⠁⠠⠀⠀⠄⠀⠀⠀⠀⠀⢀⡊⣰⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡱⡂⢁⠁⠁⠀⠠⠀⠀⢸⣿⣿⡇⣿⣟⢭⠠⠁⠀⠠⠡⠀⠠⠀⠀⠀⠀⢸⢸⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⢸⣿⣿⡇⠀⠠⠀⠠⠀⠠⠀⠀⠀⠀⢀⠀⠄⢠⣽⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡷⡿⡀⡀⡀⡐⠀⠀⠀⠀⢸⣿⣿⡇⢿⣪⣣⠠⡠⠐⡑⠀⠀⠁⠀⠀⠀⠀⢸⢹⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⢸⣿⣿⡇⠀⡐⠂⠅⢀⠠⠀⠀⠠⠀⡡⣒⣕⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⢷⣬⣀⡤⡀⠰⠡⠀⠠⢸⣿⣿⡇⡳⣷⡏⡶⡓⡐⠀⠐⠀⠀⠄⠀⠀⠀⢸⢹⣿⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣟⢕⢸⣿⣿⡇⠈⠍⠀⡎⡡⢐⡀⡑⠨⡫⣗⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣯⣿⣴⡯⣆⢰⡘⢸⣿⣿⡇⣽⡏⡅⡍⣝⠁⡵⢷⠀⠂⠀⠀⣄⠀⢸⣸⣷⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣫⣻⡇⢸⣿⣿⡇⣘⣰⡪⣢⣵⣿⣷⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢸⣿⣿⡇⣿⠇⣾⣿⣷⣼⣶⡆⡂⠀⠀⠀⣵⡆⢸⣹⣿⣿⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡵⣽⣵⡇⢸⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⣯⠧⣏⣿⢻⢿⡿⠕⣨⣠⠀⠀⢻⢮⣸⣿⣿⢿⢸⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⢸⣾⣿⣿⡇⢸⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⡇⣳⣇⢿⣿⣿⣾⣯⢀⣨⡁⠂⠠⢸⣿⢻⣿⣿⢺⢸⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⢸⣿⣿⡿⡅⢸⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣿⣿⡇⣿⣳⡝⡻⢿⣿⡇⠀⢌⡆⠀⡐⢸⣟⢸⣿⣿⢻⢠⠀⠀⠀⠀⣾⢿⡇⠀⠀⠀⠀⣸⣿⢟⢾⡆⢸⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⣽⣿⢇⠒⡰⣏⢃⢪⣿⠇⠀⠀⠈⡳⢿⣿⣿⣾⢰⠀⠀⠀⢰⡳⣵⡃⠀⠀⠀⠀⢸⣫⣳⣿⡇⢸⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⣿⣯⣫⡇⣿⢾⢮⣿⡳⣅⠀⠐⠀⣿⣿⢻⣿⣿⢸⠀⠀⠀⢸⣾⣿⣷⠀⠀⠀⠰⢐⣽⣿⣿⡇⢸⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⡳⠳⣛⣣⢯⣻⣿⣳⡝⣁⡀⢀⢈⣿⢿⢿⣿⣽⠀⠀⠀⠀⢸⣿⣿⣯⠀⠀⠀⠨⣸⣿⡿⣓⡅⢸⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣟⣿⠿⠛⠸⠿⠿⠇⣓⣉⣉⣭⣥⣭⣥⢭⣬⡭⠤⠥⠿⠿⢹⣿⣿⠼⠀⠀⠀⢀⣾⣛⣛⣻⠀⢀⣀⣐⣛⣓⣂⣼⡇⢸⣿⣿⡇⠿⠿⠿⠿⠿⠿⠿⠿⠯⠽⠿⠯⠿⠯⠽⠿⠿⠿
⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⠣⣰⣾⣿⣿⣿⣿⣷⣶⣶⣾⣶⣶⣶⣶⣶⣶⣾⣧⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠣⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢈⢸⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣼⢯⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣾⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣟⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣾⡟⠉⢻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣼⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⣿⠇⡀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿
⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⢾⣤⠈⢻⠏⠙⠻⢿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠈⢿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⠁⠰⡏⠀⠀⠀⠀⠈⠹⣿⣿⡇⣾⣼⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣭⣷⣶⣼⣿⣮⣾⣿⣹⣿⣿⣿⡿⠛⣡⣌⡾⣿⡇⢀⣴⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹⣿⣇⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⡆⠀⠘⣽⠟⠈⠻⢿⣿⣿⣥⣸⣿⣿⠁⠀⣿⣿⣶⣿⠇⢰⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⣿⡇⢾⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿
⠟⠋⠀⠉⠉⠛⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⡘⡟⠀⠀⠀⠀⣿⠧⠈⢹⣿⡇⠀⠀⠘⠯⣿⠛⢳⣜⠽⣴⣿⣿⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡇⠈⠁⠀⠉⠿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿
⠄⠀⠀⠀⠀⠀⢺⣆⠀⠀⠀⠀⠀⠀⠀⢠⢯⣿⡆⢻⡟⠛⠃⠀⢰⠀⠀⠀⠀⣸⡽⠀⠀⠀⠱⠁⠀⠀⠐⠸⠁⠉⠓⣿⣜⣓⠩⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠁⠀⠀⠀⠄⠐⠋⢿⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠠⠤⠤⠴⠄⢸⣿⣿⣿⣿⣿⣾⣿⣃⣀⣶⣰⣦⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠈⠻⢍⠐⠀⠀⣰⣽⡟⠁⠀⠀⠀⠀⠀⣀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢰⠟⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣟⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠹⣟⠃⠀⠘⣦⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⡁⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣶⡆⠈⠀⠀⠀⠀⠀⠀⣀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠿⣷⣆⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿
⠄⠀⠀⠀⠀⢽⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢸⠙⠟⠿⣿⣿⣿⣿⣿⣿⣯⣛⠛⢿⣿⣿⣿⣿⡿⠶⠀⣴⣿⣴⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿
⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢸⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣀⣀⡀⣠⢲⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭⠿⠷⠾⢿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⡀⠀⢹⢀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
䷩ 𝚕𝚒𝚗𝚎 395
╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕
(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/06/irc-log-050222/#comments
Gemini version at gemini://gemini.techrights.org/2022/02/06/irc-log-050222/
⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.06.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧
Gemini_version_available_♊︎
✐ IRC_Proceedings:_Saturday,_February_05,_2022⠀✐
Posted in IRC_Logs at 2:35 am by Needs Sunlight
Also available via the Gemini protocol at:
* gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-050222.gmi
* gemini://gemini.techrights.org/irc-gmi/irc-log-050222.gmi
* gemini://gemini.techrights.org/irc-gmi/irc-log-social-050222.gmi
* gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-050222.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
QmdvcqqnycofXgt2uj14phWYFQsnR7Xa3uAkAHso5sdCz3 #boycottnovell 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
(full IRC log
as HTML)
IRC log for
#boycottnovell
QmRCRNijXKRaTJaaZXRvxXNvHmeNiHTqFSJ2Xx4T3qtoM9 (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
as plain/ASCII
text)
IRC log for
#boycottnovell-
QmdkAqiY4NedmisZP4DPAVB24ijXyNoJFNkKzz9ES433tX social 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
(full IRC log
as HTML)
IRC log for
#boycottnovell-
QmanE82TbFGqaAfEGTj39XhQJFrPnxmtL93fjKvH1nT84M social 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
(full IRC log
as plain/ASCII
text)
IRC log for
QmQGp7LJnPQXCj6RGvE7LrL9rJjr5YZULZSDk4i1aWEX7w #techbytes 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
(full IRC log
as HTML)
IRC log for
#techbytes
QmXVKGmMdtoKznoPKQNwe6bx7ZL1G1FjP1XFCGRUNurhd1 (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
as plain/ASCII
text)
IRC log for
QmQEKi4gSso13UWh2g9q7tMUCrMjiFM63gbhi7q2axzBSc #techrights 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
(full IRC log
as HTML)
IRC log for
#techrights
QmRzbkgMzMVwWHDqcFHSdQGauigWDANyZGHdK2LvsDfXnM (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
as plain/ASCII
text)
🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈
§ Bulletin for Yesterday⠀➾
Local_copy | CID (IPFS): Qme1XwuhK1F1t6m8AJGPXQ8U9wCeB9UCDmmkPBEmWLharx
䷩ 𝚕𝚒𝚗𝚎 522
╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕
(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/06/meme-almost-a-decade-for-epo-justice-delayed-hence-denied/#comments
Gemini version at gemini://gemini.techrights.org/2022/02/06/meme-almost-a-decade-for-epo-justice-delayed-hence-denied/
⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.06.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧
Gemini_version_available_♊︎
✐ [Meme]_Almost_a_Decade_for_EPO_Justice_(Delayed,_Hence_Denied)⠀✐
Posted in Europe, Law, Patents at 4:04 pm by Dr. Roy Schestowitz
🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇PO_2013,_2018,_2021,_2022_(ILO)⦈_
Summary: ILOAT has been far too slow in curtailing/stopping Benoît
Battistelli‘s EPO_abuses and nobody is being held accountable, either
⣿⣿⣿⣷⣿⣿⣿⣯⣿⡸⣼⣙⡜⡇⣗⠈⣯⡵⠽⡚⢑⠱⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡭⣩⡿⣍⣳⣉⠷⡬⠩⡍⠠⢡⠊⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡀⠀⠀⠐⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣯⣿⣿⣷⡽⢻⢯⠻⡿⣿⣿⣿⡿⣿⣟⡺⠏⣦⢡⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠛⣿⣿⣤⣄⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢿⣿⣾⣿⣿⣞⣿⣿⢯⣛⡺⣿⣝⢺⣛⣦⢉⢺⢒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⢸⠏⠀⠀⠀⢿⣿⠟⠛⢻⣿⣿⣿⡏⠁⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢻⣿⣿⣟⣿⡝⠝⠝⠝⡕⣟⢓⣕⠓⠂⠕⠍⠤⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⢸⠀⠀⠀⠀⠘⠻⠆⠀⠀⠉⣿⣿⣿⣤⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⠀⢸⣿⣏⠋⠁⠉⠑⢄⢸⡷⢍⡲⠠⠀⠀⠉⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⡇⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣀⢤⢀⣀⠚⠁⠀⠣⠣⠁⠂⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢬⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡀⠀⠀⠀⠀⠀⠀⠰⢹⡿⢿⣿⠟⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⠻⢿⣯⡉⠀⣾⠠⠓⠘⠀⢆⠃⢠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠸⣿⣿⣿⡟⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⢀⣼⣯⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠁⣁⠉⠔⠗⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡤⢀⣀⣤⣥⠀⠀⠀⠘⠿⣿⣧⣄⣀⣠⣀⣽⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⢻⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢂⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⢀⠀⣀⣀⣤⣄⣙⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⡇⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠂⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠃⠀⠈⠛⠿⠿⣿⣿⣿⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣤⡀⠀⣆⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠀⠀⢠⢰⣾⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠻⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⣿⣿⣦⡴⠙⠈⣀⣉⢾⣯⣭⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣬⡙⠇⣠⣤⣤⣄⠀⠀⢀⣤⡄⢀⣤⣤⣤⣍⠻⣿⡍⠙⣿⣿⣿⣿⣿⣿⡿⠀⠙⠯⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣌⡃⠛⠿⢇⣐⢺⢻⢿⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢉⣿⣿⢸⣿⡏⢹⣿⡇⠾⢿⣿⡇⠸⠿⠏⢹⣿⡇⣼⢧⣼⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⢹⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠙⠀⠚⠂⠁⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠇⢸⣿⡇⢸⣿⡇⢰⢸⣿⡇⠐⠀⠿⣿⣯⡄⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣀⣀⠀⢸⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠃⠀⢸⣿⡇⢸⣿⡇⠀⢸⣿⡇⢸⣿⡇⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢿⣿⣷⣬⣇⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣷⡄⠿⠿⠿⠿⠿⠈⠻⠿⠾⠟⠁⠀⠸⠿⠇⠘⠿⠷⠿⠟⠁⢸⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠈⠉⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡐⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣷⣦⣝⣻⣿⣦⣄⣀⡀⠀⠀⢀⣸⣿⣏⣻⣿⣿⡿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢺⢽⡇⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣶⣶⣴⣶⣤⣤⣄⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⠚⡿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⣧⠀⠀⠀⠀⠀⠀⢠⣴⣶⣦⢹⣿⣿⣿⣿⣿⣿⣿
⠈⠙⢋⡛⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⠡⠂⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣧⢨⣿⠐⣾⠀⠀⠀⠀⠀⠀⠘⢺⡟⠁⠈⣿⣿⣿⣿⣿⣿⣿
⠐⢈⠔⠛⠛⠿⢿⡟⣫⣿⣿⣶⣤⣤⣤⣄⠒⠠⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠎⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣲⣴⣾⣖⠶⠶⣍⣻⣿⡙⢻⣿⣛⠻⡿⠛⠑⢾⣞⣻⡻⠿⢿⣿⣿⣿⣿⣿⣷⣘⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣽⣿⣿⣿⣿⣿⠿⣿⣏⣿⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠸⣿⢿⢿⣹⣿⣿
⣿⣿⣮⡍⠀⢠⣿⣿⣏⢿⣿⣿⣿⣷⡄⠀⠀⠘⣿⠛⠿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠑⠋⣾⣿⣷⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠼⠿⠿
⣏⠉⠁⠀⠀⠈⠛⠻⡣⣈⠙⣿⣿⠿⣴⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⠟⠉⠛⠛⠋⠉⠉⠙⠛⣿⣾⡿⠟⢿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣏⣿⣷⣿⣯⣿⣿⣷⠀⠽⠿⠿⣿⣿⡿⠿⠀⠀⣼⣧⣤⣀⣀⠀⣠⣤⣤⣤⣄⠀
⢻⡇⠈⠀⠀⢸⣿⠀⠁⠘⠊⠿⡟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣯⣤⣤⣾⣥⣄⣈⣀⡀⠀⠈⢻⣿⣿⣿⣿⣷⣶⣶⣦⣶⣦⠄⢀⣠⣷⣶⣶⣶⣶⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣇⣀
⠀⠁⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣿⣿⢿⠿⠛⠛⠻⠿⠟⢡⣶⣿⣿⣿⠟⡍⢉⠭⠍⢩⢩⠭⠍⣛⠻⣿⣿⡿⣿⢿
⠀⠆⠲⣶⠊⠶⠄⠰⠴⠶⠆⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⠉⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠤⣷⣿⣿⣿⣧⡒⠗⡘⠄⠰⠸⠸⠩⡆⠐⠄⠂⠀⠀⠀⠀
[29A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢼⣓⢑⠝⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢮⠉⠢⢡⡈⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⢿⠏⣧⠅⠩⠣⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠟⢻⣿⣯⣤⣄⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢿⣿⣾⣿⣿⣿⣯⣟⢿⣿⣿⣿⣯⢞⢏⡟⢹⢞⠖⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⢸⣿⠁⠀⠀⠸⣿⡿⠛⠛⣿⣿⣿⣿⠋⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢻⣿⣟⣿⠏⠋⠎⡻⡫⣹⠓⠩⠣⣉⡿⠥⠍⠡⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢸⡇⠀⠀⠀⠀⠙⣷⠀⠀⠈⢹⣿⣿⣇⣠⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⠀⢸⣿⡿⣣⠸⡀⣰⣭⠿⣳⡢⡷⠡⠨⣞⠑⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢶⠨⢐⣣⣒⡅⡈⠄⠪⠉⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡅⠀⠁⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠚⣿⠿⣿⡿⠋⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⠻⢿⣯⣝⢈⢵⢇⠅⠭⠂⠀⡀⢠⠊⠊⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠂⠀⠀⣽⣿⣿⣿⣿⠷⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣿⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⢏⠠⠚⡖⠑⠀⠀⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠲⢆⡀⠀⠛⣿⣿⣿⠀⠀⠀⡈⠻⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠈⣧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡃⠀⠀⠈⠐⠀⡄⠀⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⣿⣿⣿⡏⠀⠀⠀⠈⠙⠻⣿⣶⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢹⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠡⠀⢀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠹⣿⣿⣿⠷⠀⣤⣶⣶⣶⣦⣼⡹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣠⣄⠀⢠⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⠀⠀⠀⢠⣰⣾⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣿⠉⠀⠀⠈⠉⠙⠛⠿⣿⡇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣦⣼⠙⠀⣀⣙⢿⣯⣭⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡈⠛⣩⣤⣤⣄⠀⠀⢀⣤⡄⢀⣤⣤⣤⣌⠻⣿⣿⠛⢻⣿⣿⣿⣿⣿⣿⡇⠈⠧⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣌⡐⠛⠿⢃⣖⣛⡻⢿⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢉⣿⣿⢸⣿⡏⢹⣿⡇⠾⢿⣿⡇⠸⠿⠏⢹⣿⡇⡉⣿⣇⣼⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢸⡇⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠙⠓⠚⠛⠁⠁⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠇⢸⣿⡇⢸⣿⡇⢀⢸⣿⡇⠰⠂⠿⣿⣯⡄⣿⣿⣾⣿⣿⣿⣿⡀⠀⠀⠀⣀⣀⠀⠈⡇⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠃⠀⢸⣿⡇⢸⣿⡇⠈⢸⣿⡇⢸⣿⡇⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢼⣿⣿⣄⣷⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣆⠿⠿⠿⠿⠿⠈⠻⠿⠾⠟⠃⠀⠸⠿⠇⠘⠿⠷⠿⠟⠁⢸⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠈⠉⠉⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠘⣿⣿⡿⠁⠈⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡙⠳⣶⣤⣄⡀⠀⠀⠀⠀⢀⣿⣤⣙⣿⣿⡟⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢱⢟⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣶⣶⣶⣦⣤⣤⣤⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣽⣿⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢨⠟⠿⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⡯⣿⠀⠀⠀⠀⠀⠀⠀⣤⣤⣴⠹⣿⣿⣿⣿⣿⣿⣿
⠉⠙⠛⠛⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠵⠣⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣇⣼⣿⣽⣿⡀⠀⠀⠀⠀⠀⠠⠺⡿⠋⠀⣿⣿⣿⣿⣿⣿⣿
⠐⠼⠵⠛⠿⠿⢿⠟⢿⣿⣿⣯⣬⣤⣀⡀⠒⠂⠠⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢹⣿⣿⣿⣿⣿⣿
⢤⣴⣶⣶⣶⣶⡞⢾⣿⡿⢿⣿⡿⠻⡿⠋⠑⢮⣜⣫⠹⠿⢿⣿⣿⣿⣿⣿⣿⣦⠻⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠸⣿⡽⣿⣹⣿⣿
⣿⣿⣿⡋⠀⢈⣿⣾⣟⢿⣿⣿⣿⣷⡈⠀⠀⠀⡿⠿⢿⠶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠼⠿⠿
⡏⠛⠉⠁⠀⠈⠻⠿⣃⢈⠙⣻⣿⠫⣴⣾⣿⣿⣿⣶⣤⣴⣿⣿⣿⠿⠛⠛⠛⠛⠛⠛⠛⠓⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣇⠀⠈⠉⠈⣿⣯⢻⣿⡿⣿⣿⣿⣿⠿⠀⢀⣾⣇⣀⡀⣀⡀⣠⣤⣤⣤⣄⠀
⢻⡇⠀⠀⠀⢺⣧⠀⠀⠐⠛⢿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⡀⠀⢹⣿⣿⣧⣀⣠⣼⣉⣉⣉⣉⠀⠀⠈⢿⣿⣿⣿⣿⣷⣶⣶⣤⣶⣤⠀⢀⣨⣷⣦⣤⣤⣴⣶⣶⣶⣾⣿⣷⣿⣿⣿⣿⣇⣀
⠈⠃⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⣀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣽⣿⣿⠿⠻⠛⢻⠿⡟⢁⣴⣿⣿⣿⢟⡍⢛⠭⠝⢩⢩⠭⠍⣛⠻⣿⣿⡿⣿⢿
⠀⠖⠲⣶⠎⢶⠄⠰⠰⠶⠖⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠋⠙⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠄⢿⣿⣿⣿⣧⣖⠗⡘⠄⠰⠸⠸⢩⡆⠐⠄⠂⠀⠀⠀⠠
[29A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣗⡽⡫⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⣀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣷⢷⡿⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠸⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣯⣯⣫⣿⢷⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣶⣶⣶⣶⣶⣤⣄⠀⠀⠀⠀⢸⣿⣿⣿⠿⢻⣿⣯⣀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⢿⡟⣿⣻⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⢸⣿⠋⠀⠀⠸⣿⣿⠿⠻⣿⣿⣿⣿⠛⠁⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡯⠥⣿⡼⡞⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢻⣷⠀⠀⠈⠹⣿⣿⣧⣠⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⠯⣚⣓⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠉⢀⠀⠀⢰⣿⣿⣿⣿⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣅⣈⠰⡅⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡅⡉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠁⠾⣿⣿⣿⣿⠏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠽⣟⣽⣫⣟⢼⣉⡩⣵⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠱⡆⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠁⢀⣿⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣱⢿⢿⢿⢿⢿⠏⡽⣿⡞⠹⡽⠯⣀⡻⢁⡴⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠶⣄⠀⠀⠿⣿⣿⣟⠀⠀⢀⠈⠻⣿⣿⣿⣿⣶⠀⠀⠀⠀⠰⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣯⡹⢍⡓⢨⠜⠠⣵⢻⠤⣼⡅⡈⣻⠣⣓⣄⣅⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣷⣿⣾⣿⡿⠁⠀⠀⠘⠻⠿⣿⣶⣾⣷⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢻⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡻⣪⣃⣴⢾⣿⠃⠦⠀⢷⣿⣖⣆⢖⣃⠸⡒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢽⣿⣿⣿⠧⡄⣤⣤⣴⣶⣤⣽⡽⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣄⠀⢨⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣄⡀⠀⠀⢠⣠⣿⣿⣿⣿⣷⣕⡧⢉⣃⣻⠒⡄⡘⡌⠂⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⠋⠀⠀⠉⠛⠛⠻⢿⣿⡇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣼⠛⢋⣉⣉⠿⣿⣿⡗⢻⠘⣟⡍⢅⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⣠⣤⣤⣄⠀⠀⢀⣤⡄⢀⣤⣤⣤⣄⠸⣿⣿⣿⡟⠙⣿⣿⣿⣿⣿⡇⠈⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣙⠛⠿⣧⣳⣿⣿⣿⠷⠀⠀⣰⢠⣝⡣⠔⠄⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢉⣿⣿⢸⣿⡏⢹⣿⡇⠾⢿⣿⡇⠸⠿⠏⢹⣿⡇⢹⣿⣿⡟⣼⣿⣿⠉⠁⠀⠀⠀⠀⠀⠸⡏⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠙⠛⢿⠿⠉⠁⠀⠁⠀⠀⠀⠁⣉⢝⠬⡉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠇⢸⣿⡇⢸⣿⡇⠀⢸⣿⡇⠰⠂⠿⣿⣯⡄⢻⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀⢀⣀⠀⠀⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠂⠃⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣿⡿⠃⠀⢸⣿⡇⢸⣿⡇⠀⢸⣿⡇⢸⣿⡇⢸⣿⡇⢰⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣆⣿⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⡇⠿⠿⠿⠿⠿⠈⠻⠿⠾⠿⠃⠀⠸⠿⠇⠘⠿⠷⠿⠟⠁⢸⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠈⠙⠉⢭⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠶⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣾⣻⣿⠁⠈⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⣉⡻⢿⣶⣤⣀⣀⠀⠀⣀⣸⣿⣶⣬⣿⣿⣾⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢸⣯⣿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡟⠟⢻⣿⣿⣻⣿⣿⠀⠀⠀⠀⠀⢠⡯⢿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⡟⠀⠁⠀⠈⠉⠈⠜⠛⣻⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡘⣿⣿⣿⣿⣿⣿⣿
⠈⠉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠧⠫⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣧⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠠⠟⣿⠟⠁⣿⣿⣿⣿⣿⣿⣿
⠐⢻⡿⠿⠿⡿⢿⣿⢿⣿⣿⣿⣽⣿⣭⡂⠒⠒⢢⡵⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣤⣼⣶⣶⣶⣶⣾⣿⣿⡿⢿⣿⡿⠿⡿⡛⠑⢤⣺⣟⠀⠿⢿⣿⣿⣿⣿⣿⣿⣿⣶⡹⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⡇⣿⣯⣻⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠸⢿⡟⡻⣿⣿⣿
⣿⣿⣿⡋⠉⢉⣿⣿⣿⢿⣿⣿⣿⣷⡄⠁⠰⠄⢿⠿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠠⢂⣀⢀⠀⠄⠠⠄⠞⠿⠿
⣟⠛⠉⠁⠀⠈⢿⠿⣋⢈⡝⣻⣿⠿⣼⣶⣿⣿⣿⣶⣦⣤⣿⣿⣿⡿⠟⠛⠿⠻⠛⠛⠛⠛⢇⣾⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠩⠂⢀⣴⣿⣽⡋⢀⡀⣠⣤⣤⣤⣤⠀
⢿⡇⠀⠀⠠⢺⣿⠀⠁⠙⠟⠻⣿⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢀⡀⠀⢺⣿⣿⣿⣀⣀⣽⣋⣉⣉⣉⠉⠁⠈⢻⣿⣿⣿⣿⣷⣶⣤⣤⣴⣤⠀⠀⢀⣶⣤⣤⣤⣤⣾⣾⣿⣷⣿⣷⣿⣿⣿⣿⣿⣄
⠈⠛⠀⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠠⠀⢄⣀⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣽⣿⣿⡿⠿⠟⢻⡿⣿⢿⣶⣿⣿⣿⢟⡍⢟⠭⠍⢩⢩⠭⠍⣛⡻⣿⣿⡿⣿⣿
⠀⠖⠲⣶⠋⢶⠄⠰⠴⠶⠖⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠴⣿⣿⣿⣿⣧⣗⠗⡘⠄⠰⠸⠸⢩⡇⠔⠄⠂⠀⠀⠀⠠
[29A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣗⣽⠭⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣻⣯⡕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣻⣷⡖⢅⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣾⣿⣿⣶⣶⣦⣤⣀⠀⢸⣿⣿⣿⡿⠟⢿⣿⣇⣀⡀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠳⠁⠤⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⢾⣿⡿⠿⢿⣿⣿⣿⡿⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⠽⡿⣷⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠘⣿⡗⠀⠀⠙⢿⣿⣿⣆⣀⢜⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⢿⣯⢙⠂⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⣿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠃⡀⠀⠀⣼⣿⣿⣿⡿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⡫⣿⣿⣻⣿⢳⣅⣈⣾⠷⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣤⢤⡀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣿⡿⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣟⢾⣝⢾⣟⠉⣍⢑⠳⢬⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡀⠀⢸⣿⣿⣿⡿⠿⠿⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠈⠁⢸⣟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣵⢟⡿⠿⠿⠿⡯⠮⣞⡿⢷⢼⣾⢗⠿⣟⡻⠌⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣀⣀⣚⣷⣤⠄⠚⢻⣿⣿⣀⠀⠐⡄⠘⣿⣿⣷⣆⠀⠀⠀⠀⣴⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣯⡿⠉⡑⡊⢬⡳⣼⣿⡩⠤⢸⣟⣬⢼⣳⠨⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⣿⣿⣿⣿⣿⠃⠀⠈⠀⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠘⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢽⣟⣭⣤⣴⣢⢕⢴⣇⣊⠽⠀⠪⠟⠋⠉⠈⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⣿⡟⢳⢰⣾⣾⣿⣷⣶⣯⢻⣿⣿⣿⣿⣿⣿⣇⣀⣀⡀⠀⣄⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣄⣀⡀⠰⣾⣿⣿⣿⣿⣿⣶⣅⢻⠟⣻⠻⡿⠫⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⡏⠀⠀⠀⠈⠉⠙⠛⢿⣿⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣾⡟⢉⣩⣨⡹⠿⣿⣷⢲⣵⣧⡅⢡⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⣠⣤⣤⣌⠻⠇⢀⣤⡄⢀⣤⣤⣤⣄⠁⠀⢰⣿⣿⣿⡟⠉⣿⣿⣿⣿⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠶⣬⣙⣛⣟⣫⣿⣻⡿⡿⠂⠀⠰⣽⡂⠅⠄⠘⠡⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢉⣿⣿⢸⣿⡏⢹⣿⡇⠾⢿⣿⡇⠸⠿⠏⢹⣿⡇⠀⢺⣿⣿⣿⢏⣴⣟⠉⠉⠉⠀⠀⠀⠈⣿⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⠙⠛⠛⠁⠉⠀⠀⠀⠀⠀⠀⠿⣣⢉⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠇⢸⣿⡇⢸⣿⡇⠀⢸⣿⡇⠰⠄⠿⣿⣯⡄⢳⡫⣿⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠠⠀⠼⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠃⠀⢸⣿⡇⢸⣿⡇⠀⢸⣿⡇⢸⣿⡇⢸⣿⡇⠀⢀⣼⣿⣿⣿⣿⣿⠀⠀⠀⢈⣿⣿⣦⣸⡇⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣶⡆⠿⠿⠿⠿⠿⠈⠻⠿⠾⠿⠃⠀⠸⠿⠇⠘⠿⠷⠿⠟⠁⢠⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠛⠛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠠⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣢⢷⣿⡟⠉⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣉⡻⢿⣶⣤⣀⣀⠀⢀⣀⣼⣷⣦⢼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⣿⣻⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠃⠀⠹⠿⠿⣿⡿⠀⠀⠀⠀⠀⠀⣻⢿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⡇⠀⠀⠀⠀⠀⠀⠉⠠⡀⠀⠀⠀⠀⠈⠁⢀⣠⣠⣔⢿⣿⣿⣿⣿⣿⣿
⠀⠉⠋⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⡿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠴⠷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⠿⠋⢸⣿⣿⣿⣿⣿⣿
⠀⠚⣿⠟⠻⠿⠿⣿⣿⣿⣿⣿⣯⣷⣯⣛⠋⠙⠛⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢓⣿⣿⣦⣿⣿⣿⣿⣿⣿⡟⢻⣿⣯⣅⠀⣙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⣿⣿⣿⣿⣿⣿
⣤⣶⢷⣶⣶⣶⣾⣻⣿⣿⡿⣿⣿⠿⢿⡿⠛⠦⣰⣿⠇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣤⡙⣿⣿⣿⡿⣰⣿⣿⢸⣿⣿⣿⣿⣿⣿⣇⢸⣿⠛⣿⣌⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠻⣟⠻⡏⣿⣿
⣿⣿⣿⣟⠉⢀⣹⣿⣿⡻⣿⣿⣿⣿⣆⠁⠀⠂⢽⠿⢿⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣿⣿⡇⠛⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⣴⡄⠠⠠⠤⠦⠿⠿
⣿⡙⠏⢀⠀⠈⢻⠿⣿⣁⡙⢻⣿⡿⣧⣾⣿⣿⣿⣷⣦⣄⣾⣿⣿⣿⠟⠛⠿⠿⠿⠿⠿⠿⢿⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⣠⣶⣾⣋⠙⠁⢀⣤⣤⣤⣤⠀
⠟⣧⠀⠁⠠⠲⣿⡄⠉⠀⠟⠻⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣀⠀⠐⣾⣿⣿⣇⣀⣸⣏⣉⡉⠋⠉⠉⠉⠻⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣄⡀⢀⣰⣤⣤⣤⣤⣭⣽⣿⣷⣾⣷⣿⣿⣿⣿⣿⡂
⠀⠙⠁⠀⠀⠀⠙⠟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠄⢀⣀⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣼⣿⣿⣿⠿⠿⠿⣿⣿⣿⣷⣿⣿⣿⢟⡍⢟⠭⠝⢩⢩⠭⠍⣛⡻⣿⣿⣿⣿⣿
⠀⠖⠲⣶⠚⠶⠄⠰⠲⠶⠖⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠘⠛⠛⠻⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁⠀⠀⠀⠁⢀⣿⣿⣿⣿⣧⡗⠗⡜⠄⠱⠸⠸⢩⡇⠔⠄⠂⠀⠀⠀⠠
[29A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣳⢨⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⢀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⠣⠌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⡫⢿⣕⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣿⣿⣿⣿⣶⣶⣦⣤⣼⣿⣿⣿⣿⠿⢻⣿⣿⣀⣀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⢇⡴⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠸⣿⣿⠿⠿⣿⣿⣿⣿⠟⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣭⠜⣯⡷⠄⠇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢻⣿⠀⠀⠉⢻⣿⣿⣧⣀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⣝⣿⢪⠦⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠈⠙⣀⠀⠀⢰⣿⣿⣿⣿⠂⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢝⣯⡵⣺⣿⠧⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⢾⢿⡅⠀⠉⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠁⣶⣿⣿⣿⣿⠟⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⡚⠫⡉⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠆⠀⢸⣿⣿⣿⣿⡿⠿⢿⣦⡀⠀⠀⠀⠀⠀⠀⠉⢀⣿⣃⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣵⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⡿⣽⣿⣷⢽⣿⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣄⣠⣼⣿⣤⠄⠚⣿⣿⣿⣁⠀⠐⡄⠙⣿⣦⠀⠀⠀⠀⢸⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣯⣻⣽⣭⣯⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢹⣿⣿⣿⣿⣿⡇⠀⠉⠁⠈⡉⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢹⢿⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⡻⠿⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⡿⢛⢷⣾⣿⣿⣿⣶⣿⢿⣿⣿⣿⣿⣇⣀⣀⡀⠀⢩⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣄⣀⡀⠠⣾⣿⣿⣿⣿⣿⣾⣽⠻⣿⣿⣟⢿⣿⡗⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⠀⠀⠀⠈⠉⠉⠛⠿⣿⠀⢻⣿⣿⣿⣿⣿⣿⣷⠀⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣾⡟⢋⣩⣭⣽⠿⣿⣿⢹⢿⣿⡇⣿⡎⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⣠⣤⣤⣄⠈⠿⢛⣥⡄⢀⣤⣤⣤⣄⠀⠀⠉⠀⢸⣿⣿⣿⡟⢻⣿⣿⡀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠶⣬⣙⣛⠟⣻⣿⣿⡿⣿⢧⢄⢠⣭⣭⣿⣽⣗⠴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢉⣿⣿⢸⣿⡏⢹⣿⡇⠾⢿⣿⡇⠸⠿⠏⢹⣿⡇⣶⣦⠀⢻⣿⣿⣿⣇⠈⠉⠉⠁⠀⠀⠀⢹⠋⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⠟⠛⠛⠋⠉⠉⠈⠀⠉⠉⠭⣷⡻⢟⢈⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠇⢸⣿⡇⢸⣿⡇⠀⢸⣿⡇⠰⠀⠿⣿⣯⡄⣿⣿⡗⢋⢛⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠡⠀⣛⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠃⠀⢸⣿⡇⢸⣿⡇⠀⢸⣿⡇⢸⣿⡇⢸⣿⡇⠹⠛⠁⢀⣤⣾⣿⣿⡀⠀⠀⠀⣿⣿⣦⣈⡇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠙⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠿⠿⠿⠿⠿⡈⠻⠿⠿⠿⠃⠀⠸⠿⠇⠘⠿⠷⠿⠟⠁⠀⠀⣰⣿⣿⣿⣿⣿⣇⠀⠀⠀⠛⠛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣐⠢⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠛⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣲⣿⣿⡟⠉⠸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣍⣙⠿⣷⣦⣄⣀⠀⠀⣀⣠⡿⠀⠈⠹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣈⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠈⠟⠛⣛⡀⠀⠀⠀⠀⠀⣹⡽⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣶⡆⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⣁⣀⣤⢿⣿⣿⣿⣿⣿⣿
⠀⠉⢋⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢼⣿⣿⣿⣿⡿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣿⠏⢸⣿⣿⣿⣿⣿⣿
⠐⠛⣿⠿⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣯⣛⠋⠙⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣧⣿⣿⣿⣿⣿⣿⡟⣿⣿⣆⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⣿⣿⣿⣿⣿⣿
⣤⣴⣿⣶⣶⣶⣾⣻⣿⣿⡿⣿⣿⠿⢿⣿⠛⠢⣀⣿⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣤⡙⢿⣿⣿⣿⡿⣸⣿⣿⢹⣿⣿⣿⣿⣿⣿⠂⣿⡿⢿⣟⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢿⣟⢿⣿⣿⣿
⣿⣿⣿⣟⠋⢉⣹⣿⣿⣿⣿⣿⣿⣿⣦⠉⠀⠤⢽⠿⢿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⣿⣿⣿⠁⠿⣿⡿⣸⣿⣿⣿⣿⣿⣿⡇⣿⣷⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⣤⣤⠠⠤⠤⠄⠿⠿
⣿⡛⠋⡁⢀⠈⠻⠿⣿⣁⢙⢻⣿⡿⣧⣶⣿⣿⣿⣷⣦⣄⣾⣿⣿⣿⠟⠻⠿⠿⠿⠿⠿⠿⢿⣷⣀⣼⣿⣟⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⢠⣶⣾⣟⡙⠋⢀⣤⣬⣤⣬⠁
⠟⣯⠀⠁⠰⠺⣿⡄⠉⠈⠿⠻⣿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣠⠂⠐⣾⣿⣿⣇⣀⣨⣟⣉⡉⠛⠉⠉⠉⠻⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣄⡀⠀⣰⣤⣤⣤⣤⣭⣽⣿⣷⣾⣿⣿⣿⣿⣿⣿⣇
⠀⠛⠁⠀⠀⠀⠙⠟⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠄⠀⢠⣀⣠⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣽⣿⣿⣿⠿⠿⠿⣿⣿⢿⣿⣿⣿⣿⢟⡝⢟⠭⠝⢩⢩⠭⠍⣛⡻⣿⣿⣿⣿⣿
⠀⠖⠲⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠁⢰⣽⣿⣿⣿⣧⣗⠗⡜⠄⠰⠸⠸⢹⡇⠕⠄⠊⠀⠀⠀⠰
[29A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⢿⢋⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠉⠁⠀⠀⢀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡊⡆⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣚⡊⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⠿⢿⣿⣆⣀⡀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣟⣘⡵⣊⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢸⣿⡿⠿⠿⣿⣿⣿⣿⠟⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⠫⣝⢁⣍⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⣿⣷⠀⠀⠙⢿⣿⣿⡆⣀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⠿⢯⣯⣬⠢⠇⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠉⠇⠀⠀⠀⣸⣿⣿⣿⣿⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣏⠿⢮⡗⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⠻⣇⠀⠈⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠂⣾⣿⣿⣿⣿⠏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⠻⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣨⣒⣽⣡⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣝⣀⡐⣿⣿⣿⡿⠉⠋⡉⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⡟⣣⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣵⣿⣿⢿⢿⢿⡯⢿⣿⣿⣿⡿⣟⣿⣗⣥⠽⠇⠅⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢿⣷⣷⣶⣾⣿⠟⠀⠊⠙⠻⠿⣶⣤⣾⣤⣵⣦⠀⠀⠀⠀⢸⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣷⣞⣵⣯⣼⠮⡿⣽⢷⣿⣿⣷⣿⣛⣿⣿⣫⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⠤⣤⣴⣶⣶⣦⣸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠘⣷⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢛⣿⣷⣿⣿⣿⢿⡿⣿⣿⣿⣻⣾⣺⢭⣿⠝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠁⠉⠉⠛⠛⠻⢿⣿⣷⠙⣿⣿⣿⡇⢀⣀⡀⠀⢈⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣦⣤⣀⠰⣿⣿⡿⣿⣿⣿⣷⣷⡿⣺⣢⠷⢺⣹⠉⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⣽⣿⣿⣿⣿⣿⣧⠀⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⣿⣿⣿⣿⣟⣉⣤⣤⣜⠻⠿⠿⢿⠾⢻⡝⠛⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⣠⣤⣤⣄⠀⠈⢋⣭⡄⢀⣤⣤⣤⣄⠀⣀⣤⡄⠐⣾⣿⣿⣿⢀⣿⣿⡀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⣶⣬⣙⣏⣽⣿⢿⣿⠿⢷⠤⢤⣅⡂⣩⣘⡲⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢉⣿⣿⢸⣿⡏⢹⣿⡇⠾⢿⣿⡇⠸⠿⠏⢹⣿⡇⣿⣿⣿⡠⣿⣿⣿⣟⠈⠉⠉⠁⠀⠀⠀⢹⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠛⠋⠋⠃⠀⠀⠀⠀⠈⠁⠙⡀⠰⠂⠍⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠇⢸⣿⡇⢸⣿⡇⠀⢸⣿⡇⠐⠀⠿⣿⣯⡄⣿⣿⡿⠃⠉⠛⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⣂⡲⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠃⠤⢸⣿⡇⢸⣿⡇⠀⢸⣿⡇⢸⣿⡇⢸⣿⡇⠈⠀⠀⢀⣴⣿⣿⣿⡀⠀⠀⠀⣿⣿⣦⣈⡇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⠿⠿⠿⠿⠿⣈⠻⠿⠿⠿⠃⠀⠸⠿⠇⠘⠿⠷⠿⠟⠁⠀⠀⠠⠿⣿⣿⣿⣿⡇⠀⠀⠀⠛⠛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣙⠲⢶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡲⣿⣿⡿⠉⠹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣭⣿⣿⣿⣶⣤⣀⣀⣄⠀⠀⠀⠀⠘⠙⢋⣵⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣠⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⣽⡽⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢀⣁⣀⣤⢿⣿⣿⣿⣿⣿⣿
⠀⠀⢉⣉⣹⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠓⠲⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢿⡿⠟⢸⣿⣿⣿⣿⣿⣿
⠀⠉⣿⠞⠛⢿⢿⣿⣿⣿⣿⣿⣿⣿⣭⣝⡉⠉⠉⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠝⠿⣿⣿⣿⣿⣿⡇⣾⣿⣆⣿⣿⣿⣿⣿⣿⢹⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣖⣲⣿⣷⣶⡶⣿⣿⣿⣟⡿⣿⣿⡿⢿⣿⠛⠲⡄⢠⡏⡨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡙⣿⣿⣿⣿⣱⣿⣿⢸⣿⣿⣿⣿⣿⣟⢸⣿⠛⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⢿⢿⣿⣿
⣿⣿⣿⣯⠉⠉⣽⣿⣿⣿⣿⣿⣿⣿⣧⠁⠀⠂⠸⡿⢿⣷⣴⣾⣿⣭⣭⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⠃⠛⣿⡿⣸⣿⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢀⣠⣴⠤⠤⠤⠄⠿⠿
⣿⣛⠉⠀⠀⠀⢹⠿⣿⣁⣸⢛⣿⡿⢯⣶⣿⣿⣿⣿⣶⣤⣾⣿⣿⣿⠟⠻⠿⠿⠿⠿⠿⠿⢿⣿⣿⣸⣼⣿⣧⣿⣿⣿⣿⣿⣿⡏⣸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣶⣿⠋⠋⢀⣠⣨⣁⣤⡁
⡿⣿⠀⠁⠐⠚⣿⣇⠈⠈⠿⠙⢿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣠⠂⠐⣾⣿⣿⣇⣀⣩⣟⣉⣉⠛⠉⠉⠉⠳⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣄⡀⠀⣰⣦⣄⣀⣈⣭⣽⣿⣿⣴⣿⣮⣿⣿⣿⣿⡇
⠀⠙⠁⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠄⢠⣀⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣌⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⢟⡝⢟⠭⠝⢩⢩⠭⠍⣛⡻⣿⣿⣿⣿⣿
⠀⠖⠲⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠘⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠁⠈⣾⣿⣿⣿⣧⣗⠗⡘⠄⠰⠸⠸⢹⡇⠕⠄⠂⠀⠁⠀⠰
[29A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠠⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣣⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣰⣶⣾⣿⣿⣿⣿⣷⣶⣦⣤⣼⣿⣿⣿⣿⠿⠛⣿⣿⣅⣀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⢿⣿⡿⠿⢿⣿⣿⣿⡟⠋⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⡇⠀⠈⠛⣿⣿⣷⣀⡠⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢿⣻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠹⣄⠀⠀⢀⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⠛⠛⢿⡄⠀⢻⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠓⢶⣿⣿⣿⣿⡿⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣮⣻⣀⠼⢿⣿⣿⡟⠛⢉⠛⢿⡄⠀⠀⠀⠀⠀⠀⠈⠁⣸⣛⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⠃⠐⠋⠙⠿⠷⣶⣶⣷⣼⣿⣷⡄⠀⠀⠀⠀⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣷⣦⣴⣷⣶⣷⣤⣿⣿⣿⣿⣿⣿⣷⠀⠀⠁⠀⠻⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠉⠁⠙⠙⠛⠻⢿⣿⡏⢻⣿⣿⣿⣿⣀⣀⣄⠀⢨⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣤⣠⣀⠰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⡅⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠙⠁⢠⣿⣿⣿⣿⣿⣿⣿⠀⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣩⣤⣦⣽⡻⠿⣿⣿⣿⣿⣿⣿⣿⠶⠂⢺⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣷⡀⠀⣠⣀⣀⣄⣤⣤⡀⢻⣿⣿⣿⡇⢹⣿⣿⡇⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣶⣭⣻⣿⣿⣿⣿⣿⣿⣷⣤⣤⣿⣯⣻⣯⣿⣿⣦⢆⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠻⣷⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⠉⠉⠉⠉⠀⠀⠀⢹⡏⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⠛⠛⠟⠋⠈⠀⠁⠀⠉⠘⢛⡻⡸⠿⣿⡟⢯⠛⠉⠬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⠾⠡⢽⣿⣿⡀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢷⢫⢵⡽⠁⠊⠂⠐⠌⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⢀⣠⣾⣿⣿⣿⡇⠀⠀⠀⣻⣿⣷⣄⣧⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠈⠩⠒⠀⢀⠀⠁⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣷⣤⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣇⠀⠀⠀⠘⠛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⡛⠿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠀⠀⠀⠀⠀⢘⣾⣿⡿⠋⠹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣤⣴⣆⠀⠀⠀⠈⠉⠈⠀⠉⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⡀⣀⣦⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠙⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⡿⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿
⢀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠰⠷⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢀⣁⣠⣤⢿⣿⣿⣿⣿⣿⣿
⠀⠀⣋⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⢏⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣸⢿⣿⠟⢸⣿⣿⣿⣿⣿⣿
⠀⠛⣿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣭⣛⠉⠉⠛⢛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠹⣿⣿⣿⣷⣿⢰⣿⡟⢸⣿⣿⣿⣿⣿⠇⣿⣿⣷⣦⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣶⣶⣿⣾⣾⡶⣿⣿⣿⣿⡿⣿⣿⡿⢿⣿⠉⠢⡀⣸⡇⢹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣸⣿⣿⣿⠿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣧⣿⣯⣽⣿⣿⡇⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣯⠉⠉⣽⣿⣿⡿⣿⣿⣿⣿⣦⠁⠐⠢⢽⡿⢿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢤⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢀⣤⣦⠤⠤⠤⠞⢿⠿
⣿⣙⠋⣠⠀⠀⢹⠿⣿⣅⣪⢻⣿⡿⣧⣶⣿⣿⣿⣷⣶⣤⣿⣿⣿⣿⠟⠻⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣶⣟⠉⠁⢀⣤⣭⣡⣬⡁
⡿⣿⠈⠁⠀⠟⢿⣇⠈⠈⠿⠹⢿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠂⠀⠀⣠⠂⠐⣿⣿⣿⣇⣀⣸⣟⣉⡉⠛⠉⠉⠉⠻⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣄⡀⠀⣰⣤⣤⣀⣈⣭⣽⣿⣿⣾⣷⣾⣿⣿⣿⣿⣯
⠀⠙⠁⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠⢠⢤⣠⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣝⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⢟⡝⢟⢭⠝⢩⢩⠭⠍⣛⡻⣿⣿⣿⣿⣿
⠀⠖⠲⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠙⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠁⢸⣿⣿⣿⣿⣧⣗⢗⣜⠄⠰⠸⠸⢹⡇⠕⠄⠆⠀⠀⠈⠰
[29A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠏⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⣀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢗⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠠⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣞⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣶⣶⣶⣤⣤⣄⣀⣾⣿⣿⣿⡿⠟⢿⣿⣇⣀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣕⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⢻⣿⡿⠿⢿⣿⣿⣿⡟⠋⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⣿⡗⠀⠈⠙⣿⣿⣿⣄⣀⢽⡿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣦⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠋⢇⡀⠀⠀⣾⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⡿⣿⡿⣿⣿⣿⢿⣿⢖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⢿⣇⠀⢻⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠋⢲⣿⣿⣿⣿⡿⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡽⡬⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣻⣄⡰⣿⣿⣿⣿⠿⠛⠻⣆⠀⠀⠀⠀⠀⠀⠈⠁⣸⣏⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠽⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣿⣿⣿⣿⠏⠠⠊⠙⠻⠷⣦⣤⣷⣨⣷⣆⠀⠀⠀⠀⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡓⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣦⣤⣶⣶⣶⣦⣽⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⠑⠁⠛⠛⠛⠛⢿⣿⣧⠹⣿⣿⣿⣄⣀⣤⠀⠈⡅⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣀⣀⣀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⣿⣿⣿⣿⣿⣿⡇⢠⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣾⣟⢫⣥⣬⣹⢿⣿⣿⣿⣿⣿⣿⣿⣿⠩⠍⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡀⠀⣠⣄⣀⣀⣠⣤⡀⢰⣿⣿⣿⡟⢻⣿⣷⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣬⣙⣛⣻⣿⣿⣿⣿⣿⢧⣠⣠⣹⢿⣟⣻⢾⡴⡗⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠻⣿⣶⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡇⠈⠁⠀⠀⠀⠀⠀⣿⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠙⠿⠟⠟⠛⠉⠉⠉⠈⠛⠙⢹⣯⣿⡇⣿⣿⠃⠋⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⡿⡧⡿⢿⣿⣇⠀⠀⠀⠀⣀⠀⠀⢻⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⣷⣿⣿⠖⢃⡉⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⣤⣤⣄⣼⣾⣿⣿⠀⠀⠀⢨⣿⣿⣦⣸⡄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠈⠊⠷⠁⠀⠠⣐⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠠⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠈⢙⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠃⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣦⣉⡛⢿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠛⠿⠿⠻⠿⠿⡿⠀⠀⠀⠀⠀⢺⣿⣿⠏⠉⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣶⣶⣶⣶⣤⣤⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⢿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿
⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠹⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠁⣀⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠉⣋⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠻⣿⣿⣿⣿⡿⣿⡧⣾⣿⢨⣿⣿⣿⣿⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠣⡇⠀⠀⠀⠀⠀⠀⡟⣿⡿⠃⢹⣿⣿⣿⣿⣿⣿
⠀⠻⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣭⣛⡉⠉⠛⢛⠍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⢻⣿⣿⣿⣿⣱⣿⡟⢨⣿⣿⣿⣿⡇⣿⣿⣿⣷⣲⡄⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⣿⣿⣿⣿⣿⣿
⣶⣾⣿⣷⣶⣶⣿⣿⣿⣿⢿⣿⣿⡻⢿⡿⠙⠣⡀⣼⡽⠿⢭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣏⡟⢿⣿⢿⣿⣿⣿⣿⣷⣿⣿⣽⣿⣿⡏⡀⠀⠀⠀⠐⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢿⣿⣻⣿⣿⣿
⣿⣿⣿⣏⠉⢩⣽⣿⣿⡿⣿⣿⣿⣿⣦⠁⠐⠂⢿⠿⢿⣶⣶⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣱⣿⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⣀⣶⡤⠤⠤⠄⠶⢿⠿
⣿⣝⠋⣠⠀⠀⢻⠿⣿⣄⣝⣫⣿⣿⣵⣾⣿⣿⣿⣿⣶⣤⣿⣿⣿⡿⠟⠛⠻⠿⠟⠛⠻⠿⢿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣛⣛⣀⣠⣤⣤⣤⣄⠁
⡿⣧⠈⠀⠔⠟⣿⡆⠈⠈⠟⠻⣿⠁⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠁⠀⢀⣄⠀⢰⣿⣿⣿⣗⣀⣽⣏⣉⣉⣉⠉⠉⠉⠻⣿⣿⣿⣿⣷⣶⣤⣤⣶⣦⡄⢀⣀⣶⣦⣤⣤⣤⣿⣿⣿⣶⣿⣷⣾⣿⣿⣿⣿⣁
⠀⠙⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠄⠀⢀⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣽⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⢟⡝⢟⢭⠝⢩⢩⠭⠍⣛⡻⣿⣿⣿⣿⣿
⠀⠖⠲⣶⠏⢶⠄⠰⠴⠶⠖⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠙⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠈⠁⣱⣿⣿⣿⣿⣧⣗⢗⡜⠅⠱⠸⠸⢹⡇⠕⠄⠎⠀⠁⠀⠰
[29A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⣀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣽⡯⡁⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠼⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣽⠣⡁⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣀⣀⡀⠀⣸⣿⣿⣿⠿⢿⣿⣿⣀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢜⡏⠘⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠸⣿⣿⠿⠿⣿⣿⣿⣿⠛⠉⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⢻⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡊⢷⣏⣅⠊⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢻⣿⠂⠀⠉⠻⣿⣿⣷⣀⣠⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣻⣿⣾⣮⢺⣗⡤⢬⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⠙⣀⠀⠀⢰⣿⣿⣿⣿⡃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣏⣾⣭⣿⣻⣏⢿⣿⣿⣟⣿⣟⢪⣿⡉⡤⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⣿⡟⠙⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠑⢾⣿⣿⣿⣿⠟⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⠻⢿⣿⣿⣿⣿⣿⢯⢿⣿⣻⡿⢿⣿⣾⣿⣼⣜⣗⣪⠡⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣞⣻⣀⣿⢿⣿⣿⡿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠈⢀⣾⣋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣽⣿⣟⣝⣩⡿⣽⣿⣳⣷⣿⣿⠿⡽⣼⢷⣿⢍⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⠃⠘⠉⠙⠛⠷⣤⣴⣌⣲⡄⠀⠀⠀⠀⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣟⠻⣻⠏⣹⡯⣭⣝⢻⣟⡲⣺⣳⣯⢫⢞⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⣿⣿⣿⣿⣿⢶⣶⣷⣶⣷⣤⣿⢿⣿⣿⣷⠀⠀⠀⠀⢻⡉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡿⣏⣫⣿⣿⣾⣯⠳⣯⣹⣝⢯⣿⣟⢧⠤⠷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⡏⠀⠁⠉⠉⠉⠛⢿⣿⡏⢿⣿⣿⣀⣀⣄⠀⠨⡅⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣄⣀⡀⠠⣷⣿⣿⣿⣿⣿⣿⣽⣾⢿⣶⣟⢿⢰⡼⡢⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠘⠁⣸⣿⣿⣿⣿⣿⡄⢸⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣿⢋⣭⣬⣝⠿⣿⣿⣯⣿⣿⡟⠍⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⠀⡲⣠⣤⣤⣤⣤⣤⠀⣿⣿⣿⣿⣿⣿⣇⠀⠻⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣮⣛⣛⣿⣿⣿⣿⣿⣿⠷⣠⣤⡚⠬⠀⢅⣶⡪⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠟⠻⣿⣾⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⡇⠈⠁⠀⠀⠀⠀⠈⡏⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⠹⠿⠿⡿⠟⠉⠈⠁⠀⠚⠉⠋⡓⣆⠀⠀⠘⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⡿⠿⠿⡿⡿⠿⡻⢿⣿⡇⠀⠀⠀⢀⣀⡀⠀⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡬⣕⣳⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢰⣾⣶⣶⣼⣿⣿⣷⠀⠀⠀⢻⣿⣿⣦⣸⡀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⣿⣿⡄⠀⠀⠘⠛⠛⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣩⣿⣿⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠛⠀⠀⠀⠀⠀⢸⣿⣿⠏⠁⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣾⣿⣿⣿⣷⣶⣶⣶⣤⣤⣤⣤⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠈⠳⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⡿⢿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿
⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠠⠤⠾⢳⡄⠀⠀⠀⠀⠈⠁⣠⣤⣤⣞⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣉⠛⣿⣿⣿⣿⣿⢱⣿⣿⢸⣿⣿⣿⣿⢿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠟⢿⠿⠃⢸⣿⣿⣿⣿⣿⣿
⠀⠙⣿⠞⠛⠿⢿⣿⣻⣿⣿⣿⣿⣿⣯⣝⡋⠉⠛⠛⢻⣷⣼⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣧⡈⣿⣿⣿⣿⣼⣿⣇⣾⣿⣿⣿⣯⢸⣿⢿⣿⣯⣷⠀⠀⠀⠀⣠⢐⠀⢇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⣿⣿⣿⣿⣿⣿
⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢿⢿⠛⠲⡄⢀⣼⡿⠯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣉⣿⡟⢻⣿⣿⣿⣿⣿⣿⣾⣿⣿⠏⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣯⠍⠀⣼⣿⣿⡿⢿⣿⣿⣿⣧⠁⢀⡂⢸⡟⠻⠷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣀⣶⡤⠤⠠⠄⠴⢿⠿
⣿⣍⠁⠀⠀⠀⣹⠻⣿⢅⣬⣻⣿⡿⣷⣷⣿⣿⣿⣿⣷⣶⣿⣿⣿⡿⠛⠙⠛⠛⠛⠛⠛⠛⢿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⣰⣶⣿⣿⣋⣀⣀⣤⣤⣤⣌⡀
⠻⣿⠀⠀⠀⠚⣿⣆⠈⠀⠟⠙⢿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⡀⠀⢉⣿⣿⣿⣧⣠⣼⣏⣉⣈⣉⡉⠉⠉⠹⣿⣿⣿⣿⣿⣶⣶⣤⣴⣦⣤⢀⣀⣰⣦⣤⣤⣶⣾⣿⣿⣷⣾⣿⣾⣿⣿⣿⣿⣇
⠀⠉⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣿⣿⣿⠿⠿⠿⡿⣿⣿⣿⣿⣿⣿⢟⡍⢟⢭⠽⢩⢩⠭⠍⣛⡻⣿⣿⣿⣿⣿
⠀⠖⠲⣶⠎⠶⠄⠰⠶⠶⠖⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠈⠀⠸⣿⣿⣿⣿⣧⣖⠗⡜⠄⠱⠸⠸⢹⡇⠔⠄⠂⠀⠀⠀⠰
[29A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⠳⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⣀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡵⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠰⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⡶⡺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠟⠛⣿⣿⣤⣀⣀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⢎⢉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠋⠀⠀⠘⣿⣿⠿⠛⣿⣿⣿⣿⠟⠁⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣹⣷⢐⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢹⣿⠂⠀⠈⠹⣿⣿⣷⣀⡰⣿⢿⣿⣿⣿⣿⣿⣿⣿
⣧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣿⣀⢑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠙⢀⠀⠀⢠⣿⣿⣿⣿⡃⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⠕⡊⠺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⡿⠿⢿⣿⡟⠛⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠑⢾⢿⡿⣿⣿⠟⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡳⣾⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⢧⢀⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠉⢀⣿⣣⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣎⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣷⣶⣶⣿⣿⡿⠃⠴⠛⠿⣿⣍⡉⢄⠛⢷⡀⠀⠀⠀⢸⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡝⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣻⣿⣿⣿⣿⣷⣤⣶⣦⣤⣤⣘⣿⣿⣷⣿⡇⠀⠀⠀⠀⣻⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣯⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⠿⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⠏⠙⠙⠛⠛⠻⢿⣿⣿⢻⣿⣿⣇⣀⣠⡄⠀⢩⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣄⣀⡀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⠛⠟⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠈⠿⠀⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣟⣻⣩⣭⣹⠿⣿⣿⣿⣿⡿⢿⡟⢯⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⡵⡄⣤⣄⣀⣀⣀⣀⡀⢸⣿⣿⣿⣿⣿⣿⡆⠈⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣟⣻⣿⣿⣿⣿⣿⣿⣷⣀⣤⢲⠭⠴⣛⢺⡧⠕⠰⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠉⠉⠀⠀⠀⠀⠀⢹⡍⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿
⠙⠽⡿⣿⣿⠛⠍⠉⠉⠁⠘⠛⠛⣞⡕⢦⠘⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⣀⠀⢸⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡌⠮⣵⡷⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣾⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣿⣿⣷⣄⣇⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠈⠱⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡤⢤⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠈⠻⠻⣿⢿⣿⣿⣿⣇⠀⠀⠀⠙⢛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣩⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢹⠀⠀⠀⠀⠀⢐⣿⣿⡟⠉⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⣽⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣤⣤⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣤⣤⣤⣄⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⡄⠀⠀⠀⠙⠂⠀⠀⠀⣀⣼⡇⠀⠀⠀⠀⢀⢽⠿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⣀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⡇⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠞⠛⠛⢼⡇⠀⠀⠀⠀⠈⠁⢀⣤⣤⣴⢻⣿⣿⣿⣿⣿⣿
⠀⠀⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⡙⢿⣿⣿⣿⣿⡟⣿⣿⠦⣿⣿⣿⣿⣿⢿⣿⣷⣄⣀⣀⠀⠀⠀⠀⠀⠀⣗⣧⠀⠀⠀⠀⠀⠀⡾⢿⠿⠋⢸⣿⣿⣿⣿⣿⣿
⠀⠛⣿⠟⠛⠿⢿⣿⣿⣿⣿⣿⣾⣿⣯⣝⡋⠙⠛⠛⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣻⣿⣿⣿⣳⣿⣿⣰⣿⣿⣿⣿⣷⣼⣿⣻⣿⣿⣿⠀⠀⠀⠠⠾⠏⣙⠋⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⣿⣿⣿⣿⣿⣿
⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢻⠟⠋⠲⡄⣰⣯⠛⠷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣹⣟⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠃⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣯⠍⠁⣼⣿⣿⡟⢿⣿⣿⣿⣧⠁⡀⠂⣸⡛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣀⣶⣤⠤⠤⠤⠴⢿⠿
⣿⣍⠡⡠⠀⠀⣹⠻⣿⣅⣨⣫⣿⡿⣷⣾⣿⣿⣿⣿⣷⣶⣿⣿⣿⡿⠛⠙⠛⠛⠛⠛⠛⠛⣻⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⣴⣶⣾⣿⣋⣀⣀⣤⣤⣤⣄⡈
⠻⣿⡀⠀⠀⠛⣿⣆⠈⠀⠛⠙⢿⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠁⠀⠀⠤⠉⢉⣿⣿⣿⣧⣠⣼⣏⣁⣈⣁⡉⠀⠈⠻⣿⣿⣿⣿⣿⣶⣶⣤⣴⣦⣤⣀⣀⣰⣦⣤⣤⣾⣿⣿⣿⣷⣾⣿⣾⣿⣿⣿⣿⣃
⠀⠈⠁⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢰⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣼⣿⣿⣿⠿⠿⠿⡿⠿⣿⣿⣿⣿⣿⢟⡝⢟⢭⠝⢩⢩⠭⠍⣛⡻⣿⣿⣿⣿⣿
⠀⠖⠲⣶⠎⢶⠄⠰⠶⠶⠖⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠸⣿⣿⣿⣿⣧⣗⢗⡜⠄⠱⠸⠸⢹⡇⠕⠄⠊⠀⠀⠀⠰
[29A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⣀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⠂⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣿⣯⣿⣿⣾⠷⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠟⢻⣿⣯⣄⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣾⠽⡩⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡿⠁⠀⠀⠸⣿⡿⠿⠻⣿⣿⣿⣿⠛⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣾⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⡟⠀⠀⠉⢻⣿⣿⣇⣀⣠⡿⣻⣿⣿⣿⣿⣿⣿⣿
⣧⠀⢸⣿⣿⣿⣿⣿⣿⣷⢿⣿⠟⠿⡽⣿⢿⣯⣿⣟⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠁⡀⠀⠀⣸⣿⣿⣿⣿⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣾⡻⣲⢝⣿⢯⣶⣞⢾⣱⠛⡛⢹⡄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡷⠿⢿⣿⠏⢻⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠈⠐⠿⣿⣿⣿⡿⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⠻⢿⣿⣿⣿⣿⡇⣁⣀⡲⠋⡭⣿⣽⡠⢠⠃⡫⢂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡻⡆⠀⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠁⣰⣟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣸⣿⣿⢧⢷⠓⢝⢬⣼⡾⢽⢥⢢⠉⠠⣃⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣶⣶⣶⣿⣿⡿⠡⠐⠛⢿⣿⣉⠁⡉⠻⣦⠀⠀⠀⠀⢸⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣯⣿⡌⢓⣩⠁⢴⡐⢙⢗⡸⡻⣛⣆⠐⠠⠡⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣧⣤⣶⣤⣤⣄⣹⣿⣿⣶⣿⡆⠀⠀⠀⠘⣇⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡝⠾⣨⣅⣁⡉⣀⡮⡀⡑⢈⢭⣠⠿⠱⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⡿⠉⠉⠛⠛⠛⠻⢿⣿⣏⢿⣿⣿⣇⣀⣤⡀⠀⣅⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣀⣀⠀⠠⣷⣾⣿⣿⣿⣿⣦⣄⠇⠔⢃⢰⡅⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠹⠇⢨⣿⣿⣿⣿⣿⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣟⢉⣡⣭⣹⠿⣿⣿⢅⡀⡴⠟⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⢿⣷⡄⣰⣾⡿⣿⣦⢀⣠⣴⣿⡇⣴⣿⡿⣿⣦⠀⣀⣀⣀⣀⣀⠀⣼⣿⣿⣿⣿⣿⣿⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣽⣛⣿⣿⣿⣿⣿⣿⣿⣦⣀⣌⠂⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⣼⣿⠇⣿⣿⡇⣿⣿⠈⠉⣿⣿⡇⢻⣿⣧⣿⡿⢀⣿⣿⣿⣿⣿⣷⣿⣿⣿⡏⠉⠉⠀⠀⠀⠀⠀⣿⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠋⠿⢿⢟⢋⠙⠋⠁⠀⠑⠛⠉⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⠀⣿⣿⡇⣿⣿⠀⠀⣿⣿⡇⣾⣿⠛⣿⣷⠈⠿⡿⢿⣿⡿⡿⣟⢿⣿⡇⠀⠀⠀⠀⣀⠀⠀⢹⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣧⣤⡄⢿⣿⣇⣿⣿⠀⠀⣿⣿⡇⢿⣿⣄⣿⣿⠀⠀⠀⠰⣾⣷⣾⣮⣿⣿⣷⠀⠀⠀⠠⣿⣿⣦⣸⡄⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣬⣩⣭⣭⣩⣵⣦⣝⣛⣫⣥⣆⠠⣉⣉⣡⣈⡙⠛⠋⠁⠀⠀⠀⠀⠘⠟⠿⡿⣿⡿⢿⡄⠀⠀⠈⠙⠛⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣦⣍⣽⣿⣿⣷⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⠀⠀⠀⠀⠀⢽⣿⣿⠏⠉⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠲⣄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠙⣷⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣷⣶⣶⣶⣶⣶⣦⣤⣤⣤⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠄⠀⠀⠀⠈⠃⠀⠀⠀⣀⣴⠀⠀⠀⠀⠀⠀⣿⢿⠆⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣿⡧⢹⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠒⠚⠋⠰⡄⠀⠀⠀⠀⠀⠀⢀⣤⣠⣜⣿⣿⣿⣿⣿⣿⣿
⠀⠈⣋⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠙⢿⣿⣿⣿⣿⡏⣿⣿⡇⣿⣿⣿⣿⣿⡿⢿⣿⣷⣤⣀⣀⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⠀⠀⠀⠀⠞⣿⠿⠃⢻⣿⣿⣿⣿⣿⣿
⠀⠻⠿⠞⠛⠿⠿⣿⣿⣿⣿⣿⣾⣾⣭⣙⠉⠛⠛⢷⢐⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣷⡌⣿⣿⣿⣿⣷⣿⣿⣤⣿⣿⣿⣿⣿⣧⣼⣿⣻⣿⣿⣿⠀⠀⠀⠀⠴⠜⠉⠁⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣶⣾⢷⣶⣶⠶⣿⣿⣿⣿⢿⣿⣟⡛⢿⠟⠈⢢⣀⣶⣔⠩⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣹⣿⠹⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⢻⣿⢿⣿⣿⣿
⣿⣿⣿⣯⠉⢨⣽⣿⣾⡿⣿⣿⣿⣿⡦⠀⠐⠂⢻⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣽⣿⣿⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣶⠠⠤⠤⠄⣌⡿⢿
⣯⡉⠉⠀⠀⠈⠻⠿⣿⠀⡜⣫⣿⠿⣴⣾⣿⣿⣿⣿⣶⣴⣿⣿⣿⠟⠋⠙⠛⠛⠛⠛⠛⠛⣻⣿⣿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣷⣂⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣲⣷⣿⣿⣋⡀⣀⣤⣬⣤⣀⠀
⠽⣇⠀⠀⠐⠙⣿⡄⠀⠘⠟⠻⢿⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⠀⠈⢹⣿⣿⣿⣄⣠⣼⣋⣀⣈⣁⠁⠀⠈⠻⣿⣿⣿⣿⣿⣶⣦⣤⣴⣦⣄⡀⠀⣻⣤⣤⣤⣴⣿⣿⣿⣶⣾⣷⣾⣿⣿⣿⣿⣀
⠀⠉⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠄⠀⢀⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣽⣿⣿⡿⠿⠿⢿⠿⡿⢟⣷⣿⣿⣿⠟⡍⢏⠭⠝⢡⢩⠭⠍⣛⡻⣿⣿⣿⣿⣿
⠀⠖⠲⣶⠏⢶⠄⠰⠴⠶⠆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠉⠋⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⡗⠗⡘⠄⠰⠸⠸⢩⡇⠐⠄⠂⠀⠀⠀⠠
[29A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡏⠉⠀⠀⠀⢀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣿⣿⣿⣷⡾⡆⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣽⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠮⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⢸⣿⣿⣿⠿⢿⣿⣏⣀⡀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡛⣿⣿⣟⣿⣳⡓⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠋⠀⠀⠸⣿⣿⠿⠿⣿⣿⣿⣿⠛⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡿⠶⠟⢽⣿⡿⢫⣀⣤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢻⣿⠀⠀⠉⠻⣿⣿⣇⣀⠘⡻⢟⣿⣿⣿⣿⣿⣿⣿⣿
⣧⠀⢸⣿⣿⣿⣩⣿⣿⣶⢁⠀⢣⣝⣩⡘⢀⣼⣥⡀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠈⠁⠀⠀⠀⢰⣿⣿⣿⣿⠂⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡯⣮⢯⠄⠁⠀⠀⡊⡷⠀⠐⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⠿⠿⢿⣿⠋⢻⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠐⠾⣿⣿⣿⣿⠟⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⠻⢿⣿⣿⡛⣿⣿⠴⠠⠀⠀⠸⠏⠮⢼⠧⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡻⡇⠀⢿⣿⣿⣿⣿⡿⠦⠀⠀⠀⠀⠀⠀⠀⠈⢀⣿⣃⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣉⣻⠯⡩⠀⠀⠀⡁⢈⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣷⣶⣶⣶⣿⣿⠟⠁⠐⠛⠻⠿⣄⡀⢦⠈⢢⡀⠀⠀⠀⠀⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣏⠷⠐⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡻⣿⣿⣿⣿⣖⣤⣶⣶⣶⣆⣸⣿⣿⣿⣿⣧⠀⠀⠀⠀⢻⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡉⢲⣀⣀⣔⣔⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠏⠁⠉⠉⠉⠛⠻⣿⣿⣽⣿⣿⣿⣀⣀⣀⠀⢨⡠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣄⣀⡀⠀⣵⣾⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠈⠏⢸⣿⣿⣿⣿⣿⣿⡀⢸⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣟⢛⣥⣭⣙⠿⢿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⢿⣷⡄⣰⣾⡿⣿⣦⢀⣠⣴⣿⡇⣴⣿⡿⣿⣦⠀⣀⣄⣀⣠⡀⣸⣿⣿⣿⣿⣿⣿⣇⠈⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣮⣛⣻⣿⣯⣿⡻⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⣼⣿⠇⣿⣿⡇⣿⣿⠈⠉⣿⣿⡇⢻⣿⣇⣿⡿⢠⣿⣿⣿⣿⣿⢿⣿⣿⣿⡁⠉⠁⠀⠀⠀⠀⠈⡏⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⠙⠿⠛⢋⠁⠀⠁⠐⠁⠑⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⠀⣿⣿⡇⣿⣿⠀⠀⣿⣿⡇⣾⣿⠛⣿⣷⠈⣿⣿⠿⠿⣿⣞⡿⢿⣿⡅⠀⠀⠀⠀⢀⠀⠀⣧⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣧⣤⡄⢿⣿⣇⣿⣿⠀⠀⣿⣿⡇⢿⣿⣄⣿⣿⠀⠀⠀⠀⠘⢿⠿⠷⣿⣿⡇⠀⠀⠀⢨⣿⣿⣆⣹⡀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣌⣉⣭⣍⣩⣥⣦⣝⣛⣋⣥⡀⠤⣉⣉⣡⣈⡙⠛⠋⠁⠀⠀⠀⠀⠀⠈⠛⠛⠿⠻⡫⠀⠀⠀⠀⠛⡛⣛⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣍⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠋⠉⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣷⣷⣶⣶⣶⣶⣶⣤⣤⣤⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠉⠁⠀⠀⢀⣠⠀⠀⠀⠀⠀⠐⡷⢿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⣯⢹⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠐⠉⠉⠱⡄⠀⠀⠀⠀⠀⠁⣈⣤⣠⡜⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⢿⣿⣿⣿⣽⡿⢺⣿⡿⢸⣿⣿⣿⣿⣿⢹⣿⣿⣦⣤⣤⡄⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠟⣿⠿⠃⢹⣿⣿⣿⣿⣿⣿
⠀⠋⠿⠾⠛⠿⠿⣿⣻⣷⣿⣿⣾⣾⣭⣙⠋⠙⠛⠛⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢹⣿⣿⣿⢷⣾⣿⣇⣿⣿⣿⣿⣿⣯⣸⣿⣟⣿⣿⣿⠇⠀⠀⠀⠠⠅⠈⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⣿⣿⣿⣿⣿⣿
⣶⣶⣷⣷⣶⠶⣞⣿⣿⣿⡿⣿⣟⡛⢿⠟⠈⠳⣀⣸⣠⠨⠭⣶⣯⣾⣷⣶⣿⣿⣿⣿⣿⣾⣿⣿⣿⣭⣩⣿⡗⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢿⣿⣿⡟⣿⣿
⣿⣿⣿⣯⠉⢁⣽⣿⣷⡿⢿⣿⣿⣿⣦⠀⠐⠂⢸⡛⠻⠷⣶⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⣵⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⣶⡆⠤⠠⠄⣬⣿⠿
⣿⡍⠁⠀⠀⠀⢹⠿⣿⡅⣌⣫⣿⡟⢵⣶⣿⣿⣿⣿⣶⣤⣿⣿⣿⡿⠛⠙⠛⠛⠛⠛⠛⠛⢻⣿⣿⡿⠿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⡛⠁⢀⣠⣤⣄⡀⠁
⠿⣧⠀⠀⠀⠊⣿⡆⠀⠀⠛⠙⢿⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⣿⣄⣀⣼⣋⣉⣈⣉⠉⠁⠀⠻⣿⣿⣿⣿⣿⣷⣦⣤⣴⣦⡄⠀⠀⣸⣤⣤⣤⣤⣼⣿⣿⣷⣿⣷⣾⣿⣿⣿⣿⡃
⠀⠈⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣼⣿⣿⣿⠿⠿⠿⡿⡿⢟⣿⣾⣿⣿⢟⡍⢋⠭⠝⢩⢩⠭⠍⣛⡻⣿⣿⣿⣿⣿
⠀⠆⠲⣶⠎⢶⠄⠰⠶⠶⠖⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠙⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠠⣿⣿⣿⣿⣧⡒⠗⡘⠄⠰⠸⠸⢩⡆⠔⠄⠂⠀⠀⠀⠠
[29A⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⢀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣌⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠼⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣯⣯⣿⣿⣿⢿⣿⣿⣿⢿⣿⣿⠿⡟⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⣀⣀⠀⠀⢸⣿⣿⣿⡿⠟⢻⣿⣯⣀⡀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⣿⣿⣿⣿⣟⣝⣯⡯⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⢾⣾⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡿⠉⠀⠀⠸⣿⡿⠿⠿⣿⣿⣿⣿⠛⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣝⣹⣿⣿⣿⡟⣹⣟⣿⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⡷⠀⠀⠉⢻⣿⣿⣆⣀⢠⡿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⠀⢸⣿⣿⣿⣿⣿⣿⡏⠸⢷⣿⣿⡿⣽⡗⢛⢅⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠈⠁⡀⠀⠀⣸⣿⣿⣿⣿⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣷⡣⣷⡇⠂⠐⣌⠁⡀⣠⠈⣏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠿⢿⣿⠎⢻⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠒⡮⣿⣿⣿⣿⠏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⠻⢿⣿⣿⣿⣿⡿⢍⢴⣈⠛⡲⠺⠤⠘⠰⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡛⢇⢀⣿⣿⣿⣿⣿⠿⠿⢿⣦⡀⠀⠀⠀⠀⠀⠀⠉⢠⣟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣯⢟⠭⠓⠉⠛⠁⠈⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⡶⣶⣤⣤⣿⣿⡟⠉⠚⠛⠿⠿⣤⣀⢱⡄⢙⣿⣦⠀⠀⠀⠀⢸⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣟⣵⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⣿⣿⣿⣿⡆⠄⣶⣦⣶⣤⣸⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢟⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡵⠺⣆⣔⣒⡂⡄⠠⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣟⠁⠀⠉⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣇⣀⣠⡀⠀⣤⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣀⣀⡀⠀⣵⣾⣿⣿⣿⣷⣮⣇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⡿⠃⠀⠀⠀⠀⠀⠀⠹⣏⣽⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⠿⣫⣥⣭⣿⠿⣿⣿⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⢿⣷⡄⣰⣾⡿⣿⣦⢀⣠⣴⣿⡇⣴⣿⡿⣿⣦⠀⣀⣀⣀⡀⣿⣿⣿⣿⣿⡿⢿⣿⣿⡀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣮⣛⣻⣿⣿⢿⢿⡿⣿⣦⣀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⣼⣿⠇⣿⣿⡇⣿⣿⠈⠉⣿⣿⡇⢻⣿⣧⣿⡿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠈⠉⠁⠀⠀⠀⠀⢹⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⠛⠿⢛⠭⠉⠈⠁⠃⠁⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⠀⣿⣿⡇⣿⣿⠀⠀⣿⣿⡇⣾⣿⠛⣿⣷⠈⣿⣿⠿⢿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣧⣤⡄⢿⣿⣇⣿⣿⠀⠀⣿⣿⡇⢿⣿⣄⣿⣿⠀⠀⠀⠀⠘⠻⢟⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣦⣸⡇⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣬⣩⣭⣩⣩⣥⣦⣽⣛⣋⡁⠠⣀⣉⣉⣁⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠈⠙⠛⠿⠻⠿⠀⠀⠀⠀⠛⡛⡛⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣙⣛⣻⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣿⡟⠉⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣀⡀⠀⠀⠺⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⡅⠀⠸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣾⣷⣶⣶⣶⣶⣶⣦⣤⣤⣤⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠈⠉⠀⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⣿⠻⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⣀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠲⠚⠛⠑⡄⠀⠀⠀⠀⠀⠁⣀⣠⣠⡔⢿⣿⣿⣿⣿⣿⣿
⠀⠈⢋⢙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⢶⣿⣿⢼⣿⣿⣿⣿⣿⡟⣿⣿⣧⣄⣀⣠⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠘⣿⠿⠏⢸⣿⣿⣿⣿⣿⣿
⠀⠹⡷⠞⠟⠿⠿⣟⣻⣿⣿⣿⣷⣿⣭⡛⠉⠙⠛⡛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣌⢿⣿⣿⣿⣿⣼⣿⣏⢸⣿⣿⣿⣿⣿⡅⣿⣿⢿⣿⣿⣿⠀⠀⠀⠀⠴⠐⠉⠃⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⣿⣿⣿⣿⣿⣿
⣶⣾⣿⣶⣶⣶⣟⣟⣿⣿⣿⣿⣿⡿⢿⠿⠀⢢⣀⣦⣐⠉⢩⣹⣛⣻⣻⣿⣿⣿⣿⣿⣼⣿⣿⣿⣎⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢻⣿⢿⣟⣿⣿
⣿⣿⣿⣯⠉⢀⣽⣿⣶⡿⣿⣿⣿⣿⣆⠀⠐⠂⢿⠛⠿⠷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠞⣿⣿⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⣶⡄⠤⠤⠄⣬⡿⠿
⣿⡍⠁⠀⠀⠀⢻⠿⣿⠀⡈⣫⣿⡿⣵⣾⣿⣿⣿⣿⣶⣤⣿⣿⣿⡿⠛⠙⠛⠛⠛⠛⠛⠛⢿⣣⠾⡿⣿⢿⣿⣧⣽⣿⣿⣿⣿⣿⣿⣿⣿⣭⣣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣿⣿⢛⠀⢀⣠⣨⣤⡄⠉
⡟⣧⠀⠀⠀⠙⣿⡄⠀⠈⠟⠻⢿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⡀⠀⢹⣿⣿⣿⣀⣀⣼⣋⣁⣈⣉⠉⠉⠀⢿⣿⣿⣿⣿⣿⣤⣤⣤⣴⣤⣀⠀⠀⣾⣤⣤⣤⣤⣬⣽⣿⣷⣿⣷⣮⣿⣿⣿⣿⡃
⠀⠈⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢀⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣽⣿⣿⡿⠿⠿⠿⣿⡿⢿⣷⣿⣿⣿⢟⡍⢟⠭⠝⢩⢩⠭⠍⣛⡻⣿⣿⡿⣿⣿
⠀⠖⠲⣶⠏⢶⠄⠰⠰⠶⠖⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⠙⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁⠀⠀⠀⠀⢰⣿⣿⣿⣿⣧⣒⠗⡘⠄⠰⠸⠸⢹⡆⠐⠄⠂⠀⠀⠀⠠
[29A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⡇⢌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⢀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣕⣠⠊⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠼⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣯⣿⣿⢿⣽⢾⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣄⣀⣀⠀⠀⢸⣿⣿⣿⡿⠟⢻⣿⣯⣀⡀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢿⣿⣿⣿⣿⣿⣷⣟⣿⣿⣿⢿⣷⣿⣿⣿⣷⣻⣻⣾⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡿⠉⠀⠀⠸⣿⡿⠿⠿⣿⣿⣿⣿⠛⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣽⣿⡿⣻⣿⢻⣟⠣⣯⡝⠳⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⡷⠀⠀⠙⢻⣿⣿⣆⣀⢠⡿⢿⣿⣿⣿⣿⣿⣿⣿
⣧⠀⢸⣿⣿⣿⣿⣻⣿⠇⠺⢷⣿⢿⠿⡻⡷⠐⣄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠈⠁⡀⠀⠀⣸⣿⣿⣿⣿⢠⣷⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣝⣵⠕⡑⠟⣂⡳⠐⠬⠨⠉⢁⣑⣒⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠿⠿⣿⠙⠊⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⠏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⠻⢿⣯⣟⡷⣙⣟⠷⣍⢭⠊⠏⠑⠈⠀⠂⠶⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣝⠷⢀⡿⣿⣿⣿⣿⠿⠟⠿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠉⢀⣟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡐⣯⡵⠺⠻⡓⠑⡓⠚⠐⡀⠈⠃⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣤⣤⣼⣿⠖⠫⠐⠛⠿⠿⣦⣀⣈⣆⢈⣿⣿⣦⠀⠀⠀⠀⢸⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡷⣱⠡⣀⡀⠀⡠⠈⠀⠀⠐⢁⠈⡚⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣹⣿⣿⣿⣿⣤⢠⣶⣶⣶⣆⣸⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠈⣯⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡁⢂⣆⣀⣂⡀⡔⠐⠤⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠋⠁⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣠⡀⠀⣅⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣀⣀⡀⠀⣷⣾⣿⣿⣿⣷⣦⣈⡘⠀⢒⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⠏⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣿⣟⣥⣭⣿⠿⢿⣷⣀⠀⠌⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⢿⣷⡄⣰⣾⡿⣿⣦⢀⣠⣴⣿⡇⣴⣿⡿⣿⣦⠀⣀⣀⡈⢻⣿⣿⣿⣿⣿⡿⢿⣿⣿⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣮⣻⣻⣿⣾⢿⠿⡿⣿⣦⡀⢀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⣼⣿⠇⣿⣿⡇⣿⣿⠈⠉⣿⣿⡇⢻⣿⣧⣿⡿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⠉⠉⠀⠀⠀⠀⢻⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⠛⠻⠛⡛⠉⠈⠉⠊⠁⠘⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⠀⣿⣿⡇⣿⣿⠀⠀⣿⣿⡇⣾⣿⠛⣿⣷⠘⣿⣿⡿⠟⢛⣟⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣧⣤⡄⢿⣿⣇⣿⣿⠀⠀⣿⣿⡇⢿⣿⣄⣿⣿⠀⠀⠀⠀⠀⠘⢻⢛⣿⣿⢿⠀⠀⠀⠀⣿⣿⣦⣸⡇⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣬⣭⣭⣭⣭⣵⣦⣝⣛⣋⠁⠤⣀⣉⣉⡁⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⠐⡾⠛⢪⠄⠀⠀⠀⠛⢛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⣛⣛⡿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠉⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡄⠀⠀⢤⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣻⡅⠀⠸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣾⣾⣷⣶⣶⣶⣶⣶⣤⣤⣤⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠙⠛⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⣀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⡤⠴⠾⡇⠀⠀⠀⠀⠈⠁⣀⣠⣠⡔⣿⣿⣿⣿⣿⣿⣿
⠀⠉⠋⢙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡷⣾⣿⡇⣽⣿⣿⣿⣿⣿⡿⣿⣿⣅⣀⠀⣠⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⡜⣿⠿⠃⢸⣿⣿⣿⣿⣿⣿
⠀⠹⡿⠞⠿⠿⠿⣿⣻⣿⣿⣿⣾⣾⣍⡛⠉⠛⠛⡏⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡹⣿⣿⣿⣿⣧⣿⣿⡁⣿⣿⣿⣿⣿⣿⠁⣿⡿⣿⣿⣿⣿⠀⠀⠀⠀⣀⡄⠰⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⣿⣿⣿⣿⣿⣿
⣶⣾⣿⣶⡶⡶⣾⣿⣿⣿⡿⣿⣿⡟⢿⠿⠉⠢⣀⣦⣐⠙⠛⠻⣿⣛⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⡛⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⡆⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⣿⣿⣿⣿
⣿⣿⣿⣯⠉⢀⣽⣿⣶⡿⢿⣿⣿⣿⣦⠀⠀⠂⢹⠛⠿⠷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⣿⣿⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡆⠤⠤⠄⣌⡿⢿
⣿⡍⠉⠀⠀⠀⠻⠿⣿⣁⡈⣫⣿⡿⣵⣾⣿⣿⣿⣿⣶⣤⣿⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⣿⣡⢾⡿⣿⢿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣾⣿⠛⠁⢀⣠⣬⣤⡄⠉
⡟⣇⠀⠀⠀⠙⣿⡄⠈⠀⠟⠻⣿⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⡀⠀⢸⣿⣿⣿⣂⣀⣼⣋⣉⣈⣉⠉⠉⠉⢻⣿⣿⣿⣿⣿⣤⣤⣤⣴⣤⡀⠀⠀⣲⣤⣤⣤⣤⣬⣿⣿⣷⣿⣷⣾⣿⣿⣿⣿⣄
⠀⠈⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢀⣠⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣽⣿⣿⡿⠿⠿⠿⣿⣿⢟⣷⣿⣿⣿⢟⡍⢟⠭⠝⢩⢩⠭⠍⣛⡻⣿⣿⣿⣿⢿
⠀⠖⠲⣶⠋⢶⠄⠰⠴⠶⠖⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⠀⠀⠀⢀⣿⣿⣿⣿⣧⡖⢗⡘⠄⠰⠸⠸⢹⡆⠐⠄⠂⠀⠀⠀⠠
[29A⣹⣷⡶⣿⡾⢨⢍⡂⢯⠫⡗⡿⠓⡴⠄⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣛⣿⣟⣿⣾⣏⠎⢘⠅⠑⡌⠆⡄⠈⡄⠀⠈⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⡿⣿⣝⢏⣽⡔⡍⡍⠒⢅⡞⣅⠆⠐⡲⠒⠁⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⡿⣿⣷⣆⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢿⣿⣿⡮⣵⡆⠈⢐⠂⠀⠈⢐⣁⢈⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢾⣿⣿⠿⢿⣿⣿⣿⡿⠏⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⢻⣿⡇⡋⠃⠚⠂⠀⡐⠐⠀⢊⠁⡃⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠈⠿⡅⠀⠈⠛⢿⣿⣷⡄⡀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⠀⢸⣿⣇⠀⡀⠂⠠⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠉⠀⠀⠀⠀⣼⣿⣿⣿⡿⢨⣶⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣿⣿⣿⣿⡿⠿⠿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢒⣿⣿⣿⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠉⠻⢿⡇⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠈⠀⠘⣻⣿⣿⡇⠀⠀⢠⠈⢻⣷⣄⠀⠀⠀⠀⠀⠀⠈⠋⢨⡟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣶⣶⣶⣿⠁⠀⠀⠀⠉⠉⢻⣷⣶⣾⣷⣿⣿⣿⣦⡄⠀⠀⠀⠀⢲⡐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡶⠄⢴⣷⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⡇⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⠁⠀⠀⠀⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣀⡀⠀⡁⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣦⣀⣀⡀⠣⠾⠿⠿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠋⠀⠀⠀⠀⠀⠀⠈⠩⣿⣿⣿⣿⣿⣿⣿⡟⠛⣿⣿⡇⠀⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⣿⣿⣿⡶⠀⣤⣤⣬⠛⠿⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⢿⣷⡄⣰⣾⡿⣿⣦⢀⣠⣴⣿⡇⣰⣿⡿⣿⣦⠀⣄⠘⣿⣿⣿⣿⡟⣫⡇⣠⣿⣿⣿⠀⠙⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⣶⣤⣈⣛⠹⠞⠛⠛⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⣼⣿⠇⣿⣿⡇⣿⣿⠈⠉⣿⣿⡇⢻⣿⣇⣿⡿⢠⣿⠃⠉⠻⢛⡟⣿⣿⣿⣿⠋⠉⠉⠁⠀⠀⠈⢻⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⠛⠛⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⠀⣿⣿⡇⣿⣿⠀⠀⣿⣿⡇⣾⣿⠛⣿⣷⠈⠋⠀⠀⢸⣾⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣧⣬⡄⢿⣿⣇⣿⣿⠀⠀⣿⣿⡇⢿⣿⣄⣿⣿⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⣷⣦⢸⡇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣬⣉⣉⣉⣭⣵⣦⣍⣛⣋⠁⠠⢤⣍⣉⡁⠈⠙⠛⠋⠁⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠙⠛⠻⣟⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣶⣤⣽⣿⣿⣷⣦⣤⣀⣀⣠⣤⣤⣿⣿⣟⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⢶⣿⡿⠉⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢫⢻⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⡿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠉⠀⣀⣀⡀⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠉⠉⢛⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠛⢿⣿⣿⣿⣿⣿⣿⢺⣿⡷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠠⣿⡿⠟⢸⣿⣿⣿⣿⣿⣿
⠀⠈⠻⠔⠛⠚⠿⢹⣛⣷⣾⣿⣶⣶⣤⣌⣉⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⢹⣿⣿⣿⣿⢷⣿⣿⣀⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣖⣰⡾⣲⣶⠶⠖⠋⣻⣿⡛⢻⡿⡛⠛⠟⠉⠉⣀⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⣄⢩⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⢿⣿⣿
⣿⣿⣿⣯⡉⠀⣨⣿⣷⡼⢿⣿⣿⣿⣧⠀⠀⠀⠘⡙⠻⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢊⣽⣿⣣⣼⣿⠿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⢸⡻
⣼⣏⠉⠀⠀⠀⠈⡟⢛⡃⡀⢙⣽⡿⣧⣶⣿⣿⣿⣿⣷⣶⣿⣿⣿⠟⠉⠙⠛⠛⠙⠛⠁⠀⢛⣃⠾⠿⠿⢶⣿⣿⣿⣿⡛⣿⡏⠉⢹⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⢀⣤⣼⣏⠀⠀⠀⣀⣀⣀⣀⠀
⠸⢻⡀⠀⠀⠀⢻⣇⠀⠀⠐⠛⢿⡇⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣀⣀⣨⣚⣉⡈⠈⠁⠉⠁⠻⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣉⠀⠉⢩⣭⣁⣀⣀⣈⣭⣽⣭⣴⣷⣮⣿⣿⣿⣿⣇
⠀⠀⠁⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣼⣿⣿⣿⠿⠿⠿⡿⣿⠿⡓⣿⣶⣶⠒⡄⠀⠬⠍⢡⢠⠤⠄⣛⡻⣿⡟⠷⢿⢶
⠀⠆⠲⣶⠈⠶⠄⠰⠰⠶⠖⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠁⠀⠀⠀⠀⠀⢘⣿⣿⡿⣧⡒⠗⡘⠄⠰⠸⠸⢉⡄⠐⠄⠂⠀⠀⠀⠀
[29A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡮⠲⠉⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢯⣿⣿⣟⣟⣾⢫⣾⣿⣹⣿⣿⣞⡏⠾⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣴⣼⣿⣷⣿⣿⣿⣶⣶⣤⣀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠚⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣻⣿⣿⣾⣿⡽⣿⡿⣿⢿⣿⣿⣽⡷⣻⠇⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⡿⠟⠉⣿⣿⣤⣤⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢿⣿⣿⡛⣿⢟⡿⣯⣻⢶⣿⣺⣟⠑⠍⣒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⢻⣿⠛⠛⢻⣿⣿⣿⡟⠁⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⢻⣿⡟⢎⣾⣿⡻⠑⠁⠹⠉⠺⠏⢱⠦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⢙⠃⠀⠀⠉⣿⣿⣿⣠⡄⠸⢿⣿⣿⣿⣿⣿⣿⣿
⣧⠀⢸⣿⡧⣤⠁⡁⠙⠀⠀⠀⠀⠋⡪⡅⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡏⠈⠈⠙⢿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⡇⣶⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠌⠑⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡗⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠘⢿⡿⢿⣿⠟⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⠻⢿⣗⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢀⣼⣡⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠀⠀⠀⠈⠻⠿⣿⣿⣶⣤⣴⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⢨⣻⣷⡀⠀⠀⣀⣀⡀⢀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢰⣿⣿⣷⠀⠀⠀⠀⠸⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡅⠀⢀⣀⣄⣄⡀⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠞⢿⣿⣿⣤⣤⣄⠀⢰⡰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣤⣤⡀⠃⡶⢾⠿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠟⠁⠈⠙⠻⢿⣿⣿⣿⣿⡏⠉⣷⠀⣰⣿⣿⣿⣿⣿⡀⢸⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠿⠿⣿⣿⣷⠀⣠⣤⣄⡙⢻⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⢿⣷⡄⣰⣾⡿⣿⣦⢀⣠⣴⣿⡇⣴⣿⡿⣿⣦⠹⣿⣿⣿⣷⣴⣷⣼⣿⣿⣿⣿⣿⠿⠇⠈⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⢷⣦⣤⣬⠇⠻⠹⠛⠋⠃⠀⠻⣿⣿⣧⣠⣤⣤⣶⣶⣶⣿⣷⣄⠀⠀⠘⠛⠃⣼⣿⠇⣿⣿⡇⣿⣿⠈⠉⣿⣿⡇⢻⣿⣇⣿⡿⠀⢛⠉⢙⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢀⣾⣿⠏⠀⣿⣿⡇⣿⣿⠀⠀⣿⣿⡇⣾⣿⠛⣿⣷⠀⠍⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⣀⠀⠸⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣾⣿⣧⣤⡄⢿⣿⣇⣿⣿⠀⠀⣿⣿⡇⢿⣿⣄⣿⣿⢀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢻⣿⣿⣤⣧⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣭⣭⣍⣉⣥⣄⣉⠛⣋⣁⣄⣀⣉⣉⣡⣬⣙⣛⣋⣥⣾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠈⠉⠩⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠐⣾⣿⡏⠀⠘⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢽⢽⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠸⠛⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣠⣤⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽⣿⣿⣿⣿⣿⣿⡇⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀⣴⣤⡎⢻⣿⣿⣿⣿⣿⣿
⠀⢀⡀⢀⣭⣽⣴⢶⣖⣀⢀⡀⠄⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⢿⣿⣿⣿⣿⡏⠛⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠏⢿⠟⠁⢸⣿⣿⣿⣿⣿⣿
⠀⠀⣰⣉⣉⣉⣋⣠⣄⣿⣿⣿⣶⣾⣿⣶⣤⠀⠘⣿⣿⣿⡿⠛⠁⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣠⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿
⣿⣽⣯⣿⡿⠏⢡⣞⣛⢿⣭⣽⣯⣭⡙⠉⠁⠈⢆⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣯⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⣹⣿⣿⣿⣿⣿⡏⠀⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠿⣿⣿
⢿⡿⠿⠟⠂⠀⢾⣿⣿⡎⠻⣿⣿⣿⡟⢂⣀⣀⣨⣏⡉⢛⣶⣦⣄⡀⠀⠀⠀⠀⢸⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣷⣦⣤⡀⠀⠀⠀⣀⠀⠀⠀⠒⠂⠂⠠⠟⣻
⢺⣶⠀⠀⠀⠀⣠⡍⠱⠂⡆⣴⣿⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠈⠉⢙⢛⣿⣾⡟⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⢸⣿⠿⠿⢿⣿⠿⠿⠃⠀⢸⣿⣿⠅⣀⡠⣠⣤⣤⣤⣤⠀
⠈⠹⡆⠀⠀⠀⠹⣷⠀⠀⠈⠈⠙⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⠙⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣷⣦⣴⣾⣦⣤⣤⣤⣄⣀⡈⠹⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⡄⣠⣤⣿⣷⣶⣶⣶⣾⣿⣿⣾⣿⣿⣾⣿⣿⣿⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⠉⠹⠛⠿⢡⣿⣿⣿⣿⠗⡌⢁⠭⠌⢨⢩⠥⠍⣋⡻⢿⡿⡾⣿⢿
⠀⠆⠲⣶⠆⠶⠄⠰⠰⠶⠆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠉⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⡒⠗⡘⠄⠰⠸⠸⢉⡆⠐⠄⠀⠀⠀⠀⠀
[29A⣿⡏⡼⡿⢐⠀⠀⠈⠈⠁⡄⠓⠐⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠠⢴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠧⢡⣊⣪⠖⠃⠀⠈⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢤⣸⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⢸⣿⣿⣿⣿⣿⡀⠀⠀⠈⣛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣖⡲⡜⠐⡀⠀⠀⠀⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⢸⡿⠛⠉⢹⣿⣷⣶⣦⣾⣿⣿⣿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢿⣿⡭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⠁⠀⠀⠈⠙⢏⠉⠉⢿⣿⣿⣯⡀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢻⡯⠄⡁⣀⣤⣤⣔⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⠿⠛⠻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⢹⣿⣿⣧⣦⠀⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠈⠁⠀⢱⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠈⠟⠛⣿⠏⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⠀⠀⢀⣀⣠⣾⣿⣿⣿⣿⣿⢿⣄⡀⠀⠀⠀⠀⢠⠀⣴⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⢸⣿⣿⡆⠀⠀⠀⠸⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡷⠀⠀⠀⢀⣤⣤⣀⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠾⢿⣿⡇⠀⠀⠀⠀⠀⢀⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠚⠻⣿⡏⠘⠹⣿⣿⣿⣿⣿⣿⡿⠉⣶⠀⣸⣿⣷⣶⣶⡆⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠱⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⢝⣿⣿⣿⣿⣿⣷⣤⣿⣴⣿⣿⣿⣿⣿⣷⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠁⢿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢽⣿⣿⣿⠟⠿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠂⠀⠉⠛⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠈⣹⣿⠁⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠁⠀⠀⠀⢠⢭⡟⠀⠀⢀⣸⣿⣿⣿⣿⣿⠀⠀⠀⠀⣠⣤⡀⢸⡇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣦⣄⣀⣀⣀⣀⣀⣠⣶⣶⣾⣷⣶⣶⣿⣿⣿⣦⣽⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠻⠿⠿⠾⠷⠴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢀⣉⣿⡿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠈⠏⢿⡇⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⡇⠀⡟⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠸⢼⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠙⢿⡿⣿⡿⠿⣿⣿⣿⣿⣿⡇⢻⣻⣇⢀⣰⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣽⣿⣿⣿⡃⢈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣤⣤⣶⣶⣤⣄⡈⠀⠀⠀⠀⠼⣿⣿⣿⣿⠃⠈⣿⡍⠂⠈⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼⣿⣿⣿⣿⣿⣿⣏⠻⢿⣿⡿⣿⣯⣿⣧⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣿⣿⡗⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣩⡭⢯⣉⣉⣱⣲⣶⡄⠀⠀⢸⣿⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣇⣸⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡿⠋⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⡃⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣀⣉⣈⣉⡉⢛⣟⠛⢻⣿⣿⣟⣷⣦⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⢸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿
⣿⣝⠿⠙⠉⢀⣀⡙⢄⣤⣿⣵⣌⠁⠀⠀⠙⢄⢀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⡿⡿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠉⠀⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠁⣿⣿⣿
⠿⠿⠃⠀⠐⢿⣿⡿⠉⠻⡿⣿⣿⠃⣀⣤⣤⣼⣤⣀⣸⣿⣿⣶⠄⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣏⡂⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣉⣉⣙⣿⣿⣷⣦⠀⠀⢠⣠⠄⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉
⡄⠀⠀⠀⠀⣤⠀⠁⠀⡀⣾⣿⠃⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⡯⠉⠀⠀⠤⠀⠚⠛⠛⠛⠛⠯⣿⣿⣿⣿⣷⣄⣀⣀⣀⣛⡛⠉⠉⠛⣛⢋⠉⣀⠀⣚⣳⣆⣠⣶⣔⣾⣿⣿⣿⣧⠀⠀
⠱⠀⠀⠀⠀⠻⡆⠀⠀⠁⠈⠙⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⢀⣀⣀⣤⣾⣿⣿⣷⣶⣾⣷⣶⣶⣶⣶⣦⣤⣀⡘⢿⣿⣿⣿⠿⠿⣿⣿⣿⠟⢋⣶⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠁⠈⠀⢀⣽⣿⣿⣿⡶⠘⡄⠈⠤⠀⢠⢠⠬⠍⣛⠛⠽⠖⠿⠿⠶
⠀⠂⠲⣶⠂⠲⠄⠠⠰⠖⠆⠀⠀⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⠟⣁⡒⠗⠐⠄⠰⠸⠸⠉⠂⠐⠄⠀⠀⠀⠀⠀
[29A⣿⣿⣿⣿⣿⣧⣷⠮⡝⢎⠷⢃⡤⠲⣎⠟⢵⡁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣟⣿⠿⣿⣿⣷⣟⡷⣰⢵⢾⡌⠋⣕⣉⣀⠀⡤⠀⠀⠀⠀⠐⡦⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⣆⣾⣿⣿⣷⣿⣷⣶⣤⣀⡀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠘⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣻⣽⣾⢪⠞⡿⣻⣵⣇⠺⠩⠘⠈⠃⠉⠀⠉⠀⠀⠀⠀⠀⠸⣮⣏⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠜⠛⣿⣿⣤⣤⣤⣿⣿⣿⣿⠿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢿⣿⡿⡫⠒⡞⣧⡫⡎⡁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢼⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⢻⣿⠋⠉⠻⣿⣿⣿⣅⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢻⣿⡕⢰⣇⡟⣜⠑⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣹⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⠟⣿⣿⣿⡇⠀⠀⠀⠈⠡⠃⠀⠀⠈⢻⣿⣷⣶⣦⢐⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⠀⢸⣿⡟⣻⠹⡞⣝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡷⠀⠈⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡗⢹⢧⣧⣿⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠘⠂⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⣿⣿⣿⡅⠀⠀⠀⠉⠻⣆⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⣿⠏⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⠻⢿⣧⠀⢣⡙⡇⡷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢖⢡⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢿⣿⣿⣧⡀⣀⣱⣤⣴⣿⣷⣄⠀⠀⠀⠀⠀⢀⠀⣴⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⢿⡳⢷⡱⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣎⡜⢀⠘⠀⠀⠀⠀⠀⠀⣄⣶⣾⡄⠀⠀⠀⠀⠈⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠈⣧⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠄⢈⠀⠸⣶⠾⠷⠬⠢⣀⣀⣀⣀⣀⣀⣀⣴⠮⠾⠏⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡯⠀⠀⠘⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢄⠀⠀⠀⠀⠘⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠙⠿⢛⡉⢥⢞⠝⠉⠛⢟⢦⠍⠙⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⢿⢯⠙⢻⣿⣿⣿⣿⣿⣿⡿⠟⠠⣴⣶⡀⠀⡖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⠀⠀⠀⠀⢼⢿⣿⣿⣿⣦⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⠉⢹⠂⣼⣿⣿⣇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣦⡄⠀⣠⣠⡝⠿⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⢻⣿⣿⣿⣿⣷⣿⣷⣿⠿⠟⠛⠀⠈⠉⠛⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣌⠛⢛⠁⠸⠛⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⣶⣴⡞⠇⠀⠀⢿⣿⠏⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃⠀⠀⠈⣾⠁⠀⢸⣿⣿⣿⣿⡀⠀⠀⠀⣠⣤⡀⠸⡇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣶⣤⣤⣤⣤⣶⣶⣦⣤⣀⣀⣤⣇⣀⣀⣼⣿⣿⣿⣿⡇⠀⠀⠀⠻⢿⡿⠶⠿⠶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⡿⣩⣶⣶⣮⡙⢛⣥⣶⣶⣬⡻⢋⣴⣶⣦⣍⠛⢛⣥⣶⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣸⣿⣿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠿⠿⢨⣿⡿⢸⣿⡇⢸⣿⡇⠿⠿⢀⣿⣿⠘⠻⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢱⡟⣿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢠⣿⡿⠃⢸⣿⡇⢸⣿⡇⡶⢀⣾⣿⢏⣾⠀⣿⣿⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠅⣼⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣱⣿⣟⣁⡓⢸⣿⡇⢸⣿⡇⢠⣿⣿⣃⣚⢿⠀⣿⣿⢈⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡛⠛⠛⠛⢃⣌⠛⠿⠿⢛⣅⠛⠛⠛⠛⠛⣸⣄⠛⠛⢸⣿⣿⣾⣿⣿⣿⠋⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠄⢀⣭⣽⣿⣿⣿⣿⣿⣿⣿⢿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣽⣿⣿⣿⣿⣿⣴⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠁⢻⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣀⣉⡈⠙⠋⡙⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿
⣿⣹⣿⠻⠉⣈⣘⢻⣍⣭⣿⣭⣍⠉⠉⠈⠱⣮⢀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢼⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠋⠃⣿⣿⣿
⣿⡿⠆⠀⠰⣿⣿⣷⠙⢿⣿⣿⣿⠂⢀⣀⣀⣷⣄⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣤⣄⠀⠀⣠⣠⠀⠀⠀⠐⠀⠀⠀⠀⠛⠙⠛
⡀⠀⠀⠀⢀⣈⠉⠖⢀⢀⣾⣿⠹⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⡋⠀⠀⠀⠈⠉⠉⠉⠉⣽⡿⣯⠉⠙⠻⣻⠿⠛⠿⠿⠟⠛⢿⣿⣿⣿⣿⣿⣋⣑⣘⢛⡛⠛⠛⠛⢻⡟⠛⠋⠀⠀⣻⣿⣇⣠⣤⣠⣶⣷⣶⣶⣦⠀⠀
⢧⠀⠀⠀⠘⢿⡄⠀⠈⠀⠙⠏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⣿⣷⣶⣾⣶⣶⣶⣶⣤⣄⣀⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣳⣶⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠁⠀⠀⠉⠙⢉⣤⣾⣿⣿⣿⡷⠟⡍⢁⠭⠝⢡⢠⠬⠍⣛⡻⢻⡿⡿⠿⢿
⠀⠂⠲⣶⠈⠲⠄⠠⠴⠖⠆⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡨⣿⣿⣿⣿⠽⣥⡒⠗⡘⠄⠰⠸⠸⢉⡆⠐⠄⠂⠀⠀⠀⠀
[29A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣯⠆⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠀⢀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣿⠿⡺⡷⢅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣠⣤⣀⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢑⠈⠀⢹⣮⣟⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢿⣿⣷⡂⠀⠀⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢿⣿⣿⣿⣿⡟⣷⣫⣾⣿⣿⢏⡄⢶⣶⣶⠀⢶⣶⡶⠀⠀⠀⠀⢱⢾⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠐⣿⣿⣿⠿⣿⣿⣿⣿⡿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢻⣿⣿⣿⣇⣟⣼⣿⣿⢃⣾⣿⡌⢻⣿⠀⢺⡿⢀⡆⠔⡀⠆⠀⢡⣹⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠹⣿⠄⠀⠘⠻⣿⣿⣦⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣧⠀⢸⣿⣿⣿⠹⡞⣽⡿⠃⠾⠿⠿⠟⠎⠃⠀⠘⠠⠾⠵⠞⠠⠀⠁⢸⢱⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⢻⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠙⠀⠀⠀⠀⣿⣿⣿⣿⡗⣱⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢧⣧⣿⣿⣷⣤⣀⠀⣠⡴⠇⠀⠸⠄⠀⡀⠀⠀⠀⠀⣾⣾⡺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⠙⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⡿⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⠻⢿⣿⣭⣣⡙⡇⡿⣿⣽⣠⣤⡤⢤⣤⣤⣤⣀⠀⠀⢀⠀⢀⢾⢳⠊⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⢨⣿⣿⣿⡟⢁⠀⠉⠻⣿⣷⣀⠀⠀⠀⠀⠀⠈⠙⠉⢹⠟⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡘⣿⣿⡳⢿⡹⣿⡿⢛⣜⣛⢛⠓⠥⠄⡂⡃⣠⣴⣎⡾⢚⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⢤⢤⣄⣀⣠⣽⡇⠀⠙⣿⣿⣿⣇⠀⠈⣦⣀⣸⣿⣿⣧⡀⠀⠀⠀⠀⣦⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣇⢿⡻⡻⣶⠾⠿⠭⡿⣽⣫⣑⣒⣁⣁⣺⣵⠯⠾⠿⡺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⢾⣿⣿⣿⠁⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠹⠎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡟⠥⡆⣶⣑⣿⣿⣛⣉⣥⢞⡿⡫⠻⣟⢦⢍⣙⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠀⢰⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣀⠀⠀⡁⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣤⣤⣿⠚⣶⣿⣿⣿⣿⣿⣾⣭⣹⠧⡙⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⡆⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣯⣍⣤⣬⡻⠿⢿⡶⣭⠓⠯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠁⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣿⣿⣿⢿⡧⢠⣿⣿⣿⣷⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣷⣝⣻⣯⡿⣟⢿⣿⠷⠄⠀⠀⠀⣂⠓⠀⠀⢀⣄⣀⣀⣠⣤⣤⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠐⠀⣴⣄⠈⢿⣿⣿⣿⣿⣿⣽⣿⡟⠋⠉⠉⠁⠀⠈⠙⡟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣄⠈⠉⠛⠻⠟⠻⠋⠁⠁⠉⠀⠀⠀⠈⢁⠠⡤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢻⣿⣿⣷⣶⣿⣿⠀⡠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣤⡀⠀⢀⣀⠀⠀⠀⠀⠀⠈⠙⠛⣟⣯⠠⡟⠻⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢰⣶⣦⡀⢿⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣩⣶⣶⣮⡙⢟⣥⣶⣶⣬⡹⢫⣴⣶⣦⣄⠲⢂⣴⣶⢠⣭⣒⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠘⠻⠿⠿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠿⠿⢸⣿⡿⢸⣿⡇⢸⣿⡇⠿⠿⢀⣿⣿⢘⠻⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠈⢿⣿⣿⠛⠛⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢠⣿⡿⢃⢸⣿⡇⢸⣿⡇⡿⢃⣾⣿⢏⣾⡇⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠸⡟⣿⠀⠀⢹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣾⣿⣿⡿⠟⠿⠟⠻⠻⠏⠙⠿⡿⠟⠛⠿⠟⣰⣿⣟⣁⡛⢸⣿⡇⢸⣿⡇⢡⣿⣿⣃⣺⢿⡁⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢡⡇⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠴⢾⣿⣿⣿⣿⣿⣿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠛⠛⠛⠛⠃⣈⠛⠿⠿⢛⣅⡛⠛⠛⠛⢛⣸⣇⠛⠛⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠀⢀⣀⣀⢼⣿⣿⣿⣿⣿⣿
⠀⢀⣤⢤⣠⣼⣿⣿⣿⣿⣿⣥⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⢿⣿⡿⠈⣿⣿⣿⣿⣿⣿
⠀⠀⢈⣎⣉⣉⣙⣛⣿⣿⣿⣿⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢙⣿⣿⣿⣿⣽⣿⣯⣍⢛⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿
⠿⣿⣿⠿⠖⠀⢰⣿⣿⣿⠛⣿⣿⣿⣿⠆⢀⣈⣀⣀⠀⢠⣄⣀⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠿⡿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣿⣿⣿⣿⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⡛⠙⣹⣿
⣶⣿⡆⠀⠠⠀⣠⣽⠙⡷⣤⣤⣿⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠈⢉⣽⣿⣿⡟⠛⢿⣶⣿⢶⣾⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣿⣿⡿⢿⣿⣿⣿⣿⣷⠀⠀⣴⣶⡄⠀⠐⠈⣀⣀⣀⣀⠐
⠀⠹⢷⠀⠀⠀⠸⣿⡄⠀⠈⠁⠙⠏⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠐⠀⠀⢻⣿⣿⣅⣀⣰⣋⣀⣀⣀⣀⡀⠀⠙⢿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣄⠀⢀⣿⣯⣉⣁⣀⣨⣭⣽⣿⣵⣷⣿⣿⣿⣿⡿⢶
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣠⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣽⣿⣿⠿⠛⠛⡿⢿⣿⣟⣿⣿⣿⣿⢟⡝⢟⢭⠝⢡⢠⠤⠌⣛⡻⣿⣿⣿⣿⣿
⠀⠆⠲⣶⠊⢶⠄⠰⠲⠶⠖⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⠙⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢡⣿⣿⣿⣿⣧⣖⠗⡘⠄⠰⠸⠸⢹⡆⠐⠄⠂⠀⠀⠀⠀
[29A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⢀⢡⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣠⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠫⠗⠁⠀⠰⡦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣼⣿⣿⣿⣿⣿⣷⣶⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠐⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠠⠾⣮⣟⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⢙⣿⣿⣤⣄⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢿⣿⣿⣿⣿⡟⣧⣫⣾⣿⠟⠁⠀⢶⣶⣶⠀⣶⣶⣶⢢⡘⠇⠀⠱⢼⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠈⣿⡿⠛⠛⣿⣿⣿⣿⠛⠉⢻⣿⣿⣿⣿⣿⣿
⠀⠀⢻⣿⣟⣿⣇⣟⣼⣿⡏⠁⠀⠀⠀⠈⠙⠀⠛⠿⠡⢿⠗⠀⠀⠀⢡⣹⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠹⠏⠀⠀⠈⢻⣿⣿⣃⣀⠀⡻⣿⣿⣿⣿⣿
⣧⠀⢸⣿⣿⣿⠹⡞⣽⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⢸⢱⢆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠛⠉⠙⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠁⠀⠀⢀⣾⣿⣿⣿⣿⢠⣽⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣟⢻⢧⣧⣿⣿⣦⣀⣀⣀⣠⣴⡖⠀⢸⣷⣤⣀⠀⠀⠀⠀⣾⣾⡺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠁⠀⠀⠻⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣹⣿⢿⣿⡿⠃⣼⣿⣿⣿⣿⣿⣿
⠀⠙⠻⢿⣿⣀⢣⡙⡇⡷⡝⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⢀⢶⢣⣊⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠠⣿⣿⣿⣿⠀⠀⠐⡄⠈⣹⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢀⣸⣋⣴⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⠉⢿⡳⢿⡱⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡄⣵⣎⡾⢚⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⣤⣤⣶⠂⠀⠀⠻⣿⣿⣿⣷⣶⣶⣿⣾⣿⣿⣿⣿⣿⡟⡇⠀⠀⠀⠀⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡯⠀⠀⠘⢶⠾⠿⠼⡻⣿⣿⣿⣿⣿⣿⣿⣷⠯⠾⠿⡺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣿⣇⠀⠀⢀⣀⣠⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⡟⠀⠀⠀⠀⠻⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡕⠀⠀⠀⠀⠘⠿⢛⣉⣥⢞⣿⣿⣿⣟⣦⣍⣙⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠀⠀⠻⠿⢿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠫⣤⣴⡄⠀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣅⠂⠀⠀⠀⣰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠙⠟⠀⢸⣿⣿⣿⣿⣿⣿⠃⣿⡃⣰⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣻⢿⣿⡿⡇⠀⠀⠀⠁⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣶⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⢟⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠟⣿⣷⣾⣿⠟⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⣼⡇⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠈⡟⠙⠻⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠈⠉⠙⠈⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢻⣿⣿⣿⣿⣿⣿⣿⣄⣀⡀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⡷⡅⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣤⣴⣿⣿⣿⣶⣦⣬⣵⣽⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣼⣿⣷⣀⡇⠀⣸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠟⠉⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⡇⡟⣩⣶⣶⣮⡙⢋⣥⣶⣶⣭⡻⢫⣵⣶⣦⣍⠿⢛⣵⣶⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠘⠛⢛⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷⡀⠿⠿⢸⣿⡿⢸⣿⡇⢸⣿⡇⠿⠿⢀⣿⣿⠘⠻⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⢧⣿⠏⠉⢹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⡿⣿⣿⣿⣿⠖⢠⣿⡿⢃⢸⣿⡇⢸⣿⡇⣶⢂⣾⣿⢏⣾⡆⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⢫⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣀⣠⣴⣶⣶⣿⣿⣶⣄⡀⠀⠀⠀⠀⢀⣻⡟⠁⠜⠘⣿⣿⠏⣰⣿⣟⣁⡛⢸⣿⡇⢸⣿⡇⢡⣿⣿⣃⣺⢿⡇⣿⣿⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⣘⠻⠀⠀⠰⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠙⠀⠀⠈⠀⠙⣳⡀⠛⠛⠛⠛⠃⣈⡛⠿⠿⠛⣁⠛⠛⠛⠛⢛⣸⣆⠛⢛⣸⣿⣿⣻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⣀⣀⣀⡐⣿⣿⣿⣿⣿⣿
⠀⠠⠄⢐⣴⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠻⣽⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⣿⡇⠀⠀⠀⠀⠀⠀⣿⡿⠿⠁⣿⣿⣿⣿⣿⣿
⣀⣀⣠⣯⣀⣈⣉⢨⣴⣯⣽⣿⣿⣿⣿⣷⡶⢀⠀⠀⠀⠀⢀⠀⠀⠀⠸⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⠯⠽⣾⣿⣿⣿⣽⣿⣽⣍⠛⠁⠀⢢⠀⠀⠀⠁⠀⠀⠀⠀⠀⠹⣿⣿⣿⣇⠉⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⢿⣹⣿
⢻⡿⠿⠟⠂⠀⢺⣿⣿⡿⠹⢿⢿⣿⡿⠂⣀⣠⣤⣷⣲⡤⠑⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠓⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠙⠃⠀⠀⠀⠀⠀⠀⠤⢀⡀⠀⠀⢀⠀⠀⠀⠀⠠⠀⠄⠀⠠⡙
⢾⣷⠁⠀⠀⠀⣤⡏⠸⠇⢶⣤⣿⡿⢙⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⣤⣿⣿⠏⠁⠹⢿⠿⠟⠿⠿⠙⠛⢿⣿⣿⣿⣿⣿⣿⠟⠛⠛⢛⠂⠀⠀⠀⢀⣀⡀⣀⣀⣄⠨⠝⠀⢠⣶⣾⣄⣀⣄⣴⣦⣤⣤⡀⠀
⠘⠙⠧⠀⠀⠀⠘⣿⡀⠀⠈⠀⠙⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⢚⠿⠿⠀⣀⣀⣠⣄⣀⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣿⣿⣿⣿⣿⣷⣤⣤⣤⣶⣾⣿⣷⣾⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢀⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡟⠛⣿⣿⣿⣿⣿⢛⣿⣿⣿⣿⢟⡝⢟⠭⠝⢩⢩⠭⠍⣛⡻⣿⣿⡿⣿⢿
⠀⠖⠲⣶⠎⢶⠄⠰⠰⠶⠖⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠉⠙⠛⠛⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠉⠛⠋⢨⣿⣿⣿⣿⣧⡒⠗⡘⠄⠰⠸⠸⢩⡇⠐⠄⠆⠀⠀⠀⠀
[29A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⡙⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣷⢿⣿⡾⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣶⣾⣾⣿⣶⣶⣤⣮⣽⣿⣿⣿⣷⣀⠀⠀⠐⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠅⠳⢸⣮⣟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢻⣿⣧⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢿⣿⣿⣿⣿⡟⣷⣫⣾⣿⣿⢏⡄⢶⣶⣶⠀⣶⡶⡶⢂⠀⠈⠈⢱⢾⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠸⣿⡟⠛⠻⣿⣿⣿⣟⠁⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢻⣿⣿⣿⣇⣟⣼⣿⣿⢋⣾⣿⡌⢻⣿⠀⢹⡯⢡⢪⡆⠐⠠⠀⢡⣹⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠙⡇⠀⠀⠀⢻⣿⣿⣥⣦⠜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⠀⢸⣿⣿⣿⠹⡞⣽⣿⠃⠾⠿⠿⠿⠆⠋⠀⠘⠡⠷⠼⠗⠒⠀⠀⢰⢳⠇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠓⢧⠀⠀⠀⠀⠀⠂⠀⠀⢀⣼⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢧⣧⣿⣿⣷⣄⣀⣀⡠⡤⠇⠀⠸⢂⠀⠀⠀⠀⠀⠀⣾⣾⡺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⡿⠿⣿⡟⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⠻⢿⣿⣿⣧⡙⡇⡿⡯⢝⣤⣤⣤⣤⣤⢠⡤⠤⠄⡀⠀⠀⢄⢶⢳⢊⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⣿⣿⣿⣿⡀⠀⠀⢦⠀⣀⠀⠀⠀⠀⠀⢀⠀⣠⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢈⣝⢿⡳⢿⡹⣮⡿⡿⡿⢿⡃⢗⠝⣐⠜⠛⠘⣰⣎⡾⢚⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⣤⣴⣴⡖⠂⠀⠀⠙⠛⠻⢿⣿⣷⣶⣿⣿⣿⣷⡄⠀⠀⠀⠘⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣯⢎⠄⠹⣶⠾⠿⠬⡮⣔⣿⣳⣕⣗⣩⣳⣴⠮⠾⠿⡺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⠀⠀⣤⣤⣴⣦⣼⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠹⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣻⣵⣤⣴⣿⣿⣿⣛⣋⣥⢞⡿⠯⡻⣟⢦⢍⢙⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡏⠀⠀⠙⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣦⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣇⣿⣿⣿⣿⣿⣿⣿⢟⠚⠝⢓⢻⢯⡈⢩⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠙⣿⣿⣿⣿⣿⣿⣿⠙⣿⠀⢹⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⠻⠿⠿⠠⣾⡔⢬⣋⣤⣤⣤⣤⣄⡀⠀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⢹⣿⣿⣿⣿⣿⣿⣤⡿⠤⠄⠛⠻⢶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣶⣶⣶⣤⣾⣟⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠻⠃⠈⠛⠛⢻⣿⣿⣿⣿
⠀⠈⠈⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣾⣧⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⣉⣙⡛⠛⣿⢋⣡⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣀⡀⠀⣿⠀⢀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿
⠂⠀⠀⠠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣾⣿⣯⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣶⣿⣤⣾⡇⠀⠀⠀⠀⠀⡋⢻⣿⣿
⠀⠀⠀⠈⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡿⣫⣶⣶⣦⡙⢛⣥⣶⣶⣭⡛⢫⣵⣶⣦⣝⠿⢛⣽⣶⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠉⠀⣴⣿⣾⡾⠷⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⡁⠿⠿⢸⣿⡿⢸⣿⡇⢸⣿⡇⠿⠿⢀⣿⣿⠘⠻⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢹⣿⡖⢠⣿⡿⢃⢸⣿⡇⢸⣿⡇⣶⢂⣾⣿⢏⣾⡇⣿⣿⠘⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠋⣰⣿⣟⣑⡛⢸⣿⡇⢸⣿⡇⢡⣿⣿⣃⣺⢿⡇⣿⣿⠀⡿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢀⠞⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⣨⣼
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⢃⣬⡛⠿⠿⢛⣁⡛⠛⠛⠛⢛⣸⣇⠛⠛⣰⣿⣮⡛⣛⣛⣿⠉⢹⢿⣿⣗⡇⠀⠀⠀⠀⠀⠀⣶⣶⣾⡦⠀⠀⠀⠀⠀⢰⣿⣿
⠀⠠⢤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠿⠟⠋⠀⠀⠀⠀⠀⢀⢼⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡾⣽⣦⠽⠈⡁⠀⠀⠀⠀⠀⠀⠘⢻⠏⠀⠀⠀⠀⠀⢠⣿⣿⣿
⢀⣀⣋⣉⣉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⣶⣽⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣆⠁⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⡴⣿⣿⣿⣿
⣿⣿⣿⠿⠿⠿⣾⣿⣿⣿⣿⣿⣿⣍⠉⠁⢀⠰⡀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠘⠿⢻⣿⣿
⣿⡿⠟⠋⠀⠸⣿⣿⣿⠿⢿⢿⣿⡿⢃⣠⣤⣤⣿⣆⣀⠀⠀⠀⠈⠛⠟⣿⣿⣿⣧⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠉
⣿⡆⠀⠀⠠⣤⣟⠙⠟⢶⣦⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⢰⣾⣿⡿⠁⠈⡻⠟⠛⠛⠛⠋⠉⠛⣿⣿⣿⣿⣿⣿⣍⣉⣉⢩⣍⠉⠉⠀⢉⣿⣿⣿⣿⣿⣇⠠⠀⠀⠀⠀⢶⣿⣷⣄⣸⣿⣷⣶⣶⡦⠀⠀⠀
⠙⠷⠀⠀⠀⠘⣿⡄⠀⠀⠀⠉⠃⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠈⠹⠉⠁⠀⠀⢀⣠⣤⣤⣴⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣾⣿⣿⣿⣿⣿⣯⣽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢿⡿⣿⣿⣿⡿⢋⣿⣿⣿⣿⣷⢟⡝⢟⢥⠝⢩⢩⠭⠍⣛⡻⣿⣿⣿⣿⣿
⠀⠆⠲⣶⠎⠶⠄⠰⠰⠶⠆⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠉⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠁⠉⣩⣿⣿⣿⣿⣿⣧⡖⠗⡘⠄⠰⠸⠸⢩⡇⠔⠄⠆⠀⠀⠀⠀
[29A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡅⠠⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⢿⣿⣿⣿⣿⣿⣽⣟⣵⡟⠑⠀⠃⠰⡦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣤⣀⣀⣀⡸⢿⣿⣿⣿⣿⡀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣾⡿⣿⣵⣿⣿⣿⣿⣿⣿⣿⠽⢓⠿⠡⠀⠁⠀⠸⣮⣟⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠛⠛⣿⣿⣤⣤⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢿⣿⣿⣿⣿⡟⣧⣫⡾⣿⣍⠃⡄⢲⣶⣄⠀⢀⢄⠀⠀⠀⠀⠀⢱⢾⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣽⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢿⣿⠛⠛⢻⣿⣿⣿⡋⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢻⣿⣾⣾⣇⣟⣼⣿⣌⢀⡜⣦⠄⠡⡠⠀⢀⠐⠀⠀⠀⠀⠀⠀⢡⣹⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠱⠂⠀⠀⠈⣿⣿⣿⣤⡄⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⠀⢸⣿⣷⣿⠹⡞⣽⡝⠁⠦⠛⠫⠥⠄⠂⠀⠘⠀⠀⠀⠉⠀⠀⠀⢰⢱⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣾⢧⣧⣿⡧⡷⣄⠀⠀⠀⠠⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⣾⣾⡺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⢿⣿⠟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⠻⢿⣷⢯⢣⡙⡇⡷⡇⠕⢄⣤⣄⡀⠠⠀⠀⠀⠀⠀⠀⠀⢀⢶⢡⠊⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⣿⣿⣿⣯⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⠉⢿⡳⢿⡱⣤⡁⠘⠈⢁⠈⠁⠀⠀⠀⠂⠀⣰⣎⡼⢚⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢀⣀⣀⣤⠆⠀⠀⢻⣿⣿⣿⣄⣀⣈⣆⣰⣆⠀⠀⠀⠀⢸⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠊⠀⠀⠹⢶⠾⠿⠬⠢⣄⣀⣀⣈⣀⣀⣠⣴⠯⠾⠿⡺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣯⠀⠀⠀⠀⢀⠈⢻⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠈⠇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡇⢀⣠⣶⣦⣿⣿⣛⣋⢥⢞⠟⠋⠛⢟⢦⢍⡙⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠁⠀⢼⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣧⣀⡄⠀⠀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣤⣗⣾⣿⡿⣿⣿⣿⣿⡧⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠈⠻⡿⠙⣿⣿⣿⣿⣿⣿⣿⠿⠖⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣯⣵⣶⣿⣯⠛⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⠃⢼⠅⠠⠌⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠀⠉⣷⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠙⠿⠿⡧⠃⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣷⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠻⣿⣿⣿⢋⠀⠀⢜⣿⣿⣿⣿⡀⠀⠀⠀⣤⣤⡀⠈⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣄⣀⣀⣀⡀⠀⠀⢀⣀⣈⡉⠀⠀⠀⣴⢿⣿⣿⣿⣿⡇⠀⠀⠀⢹⣿⣿⣦⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⡟⣡⣶⣶⣮⡙⢋⣥⣶⣶⣬⡻⢫⣵⣶⣦⣍⠻⢛⣵⣶⠹⣿⣿⣿⣷⣶⣿⣿⣽⣿⣿⣧⡀⠀⠀⠀⠀⢠⣲⢶⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡅⠿⠿⢸⣿⡿⢸⣿⡇⢸⣿⡇⠿⠿⢀⣿⣿⠘⠻⣿⣿⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠘⢿⣾⡟⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⡛⠷⢠⣿⡿⠃⢸⣿⡇⢸⣿⡇⣶⢂⣾⣿⠏⣼⡀⣿⣿⢸⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣯⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣠⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣰⣿⣟⣁⡀⢸⣿⡇⢸⣿⡇⢡⣿⣿⣃⣚⢿⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠸⠋⠻⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠛⠛⠛⠛⢃⣌⡛⠿⠿⢛⣁⠛⠛⠛⠛⠛⣸⣆⠛⢛⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⠸⣿⣿⣿⣿⣿⣿⣿
⠀⠠⠔⣢⣶⣿⣽⣷⣿⣿⣯⣿⣟⣻⡿⠟⠿⠬⢫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⡻⢿⡿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠘⠹⡿⠃⠀⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣬⣤⣤⣭⡭⣽⣿⣿⣿⣿⣿⣿⣿⣿⠶⢤⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢹⣿⣟⣿⣿⣿⣿
⣾⣿⣿⡿⠟⠗⢴⣯⣿⣿⣾⣿⣷⣶⡄⠀⠀⠈⣷⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⢻⠗⣿⢿⣿⣿
⣿⠻⠟⠛⠁⠀⢿⣿⣿⠟⠻⠿⣿⣿⡋⣠⣤⣴⣼⣿⣤⠀⠑⠋⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠈⠀⠈⠙⠴⠆⠀⠀⠀⠀⣀⣥⣶⣿⠀⠀⠀⠀⢀⣉⠻
⡿⣷⠀⠀⠀⠠⣴⡌⠙⠛⣦⢾⣿⠇⢹⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⣤⣾⣿⠏⠉⢻⡿⠟⠛⠿⠟⠛⠛⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠻⠿⠿⠛⠛⣟⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⡀⣷⣴⣤⣤⣄⢀⠀⠀
⠁⠻⠆⠀⠀⠀⠹⡷⠀⠀⠀⠀⠙⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠙⠋⠉⠀⠀⠀⣀⣤⣤⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣤⣄⣠⣿⣿⣿⣿⣿⣗⣠⣶⢶⣶⣶⣶⣿⣿⣷⣿⣿⣿⣿⣿⣷⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⠟⣿⣾⣿⣿⣿⢟⡝⢛⠭⠍⢩⢩⠭⠍⣛⡻⣿⣿⡿⣿⢿
⠀⠆⠲⣶⠮⢶⠄⠰⠰⠶⠆⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠉⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠈⠁⣼⣿⣿⣿⣿⣧⡒⠗⡘⠄⠰⠸⠸⢩⡆⠐⠄⠂⠀⠀⠀⠀
[29A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠋⣷⡦⠨⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠸⡺⠿⢹⡮⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣀⣀⡘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣵⣿⣿⣽⣿⣿⣿⣿⠿⢷⣾⣝⠫⠀⠊⠸⣮⣟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣽⣿⣿⡿⠟⠛⢻⣿⣧⣤⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢿⣿⣿⣾⣷⡟⣧⡫⣾⣿⡯⠏⡄⢶⣶⣶⠀⣐⠶⡰⠀⠀⠀⠐⢱⢾⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢸⣿⡟⠛⠻⣿⣿⣿⡿⠛⢛⣿⣿⣿⣿⣿⣿⣿
⡀⠀⢻⣿⡿⣿⣇⣟⣼⣿⡟⢂⡮⡻⡀⢛⣟⠀⢸⡄⠀⢐⠢⠀⠀⠀⢡⣹⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⠇⠀⠀⠙⢿⣿⣿⣆⣀⢸⣿⣿⣿⣿⣿⣿
⣧⠀⢸⣿⣿⣹⠹⡞⡽⣽⠃⠶⠿⠿⠵⠄⠃⠀⠀⠀⠘⠰⠁⠀⠀⠀⢰⢹⢇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⣿⣿⣿⡿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡏⢠⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢧⣧⣿⢻⡶⣄⢀⠀⡀⠰⠆⠀⠘⠂⠀⠀⠀⠀⠀⠀⣾⣾⡺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠃⠈⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠒⣿⣿⣿⣿⡿⢃⣿⣿⣿⣿⣿⣿⣿
⠀⠙⠻⢿⣿⣽⢣⡙⡇⡷⣵⣚⣡⣄⣤⣄⡠⡀⠀⠀⣀⠀⠀⠀⢀⢾⢣⣊⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢸⣿⣿⣿⡓⠀⢀⠀⠙⢿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠈⢀⣾⣋⣴⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠉⡽⣿⡳⢿⡹⣦⣼⢾⠟⠗⢠⡄⢚⡇⠈⠀⠀⣴⣎⡾⢚⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠉⠀⠀⢸⣿⣿⣿⣇⡀⠀⣱⣀⣴⣿⣿⣿⣿⡀⠀⠀⠀⠰⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡏⣿⡷⡻⣶⠾⠿⠬⡯⣥⣒⣀⣀⣚⣓⣨⣼⠯⠾⠿⡺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣾⣾⣿⠁⠀⠀⠀⠉⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢛⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⠀⠀⠀⣧⢉⣬⣾⣾⣿⣿⣛⣋⢥⢞⣟⠏⠻⢟⢦⢍⡙⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⣿⣿⡆⠀⣠⣶⣾⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣤⣤⡄⠀⣬⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣿⣹⣿⣿⢿⢿⣿⣿⣿⠜⡁⢄⡩⢹⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡉⠀⠀⠈⠉⠉⢻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡛⠉⢻⡇⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠛⠛⠁⢍⢩⠭⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡇⢸⡏⣤⣿⣧⢀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠦⠀⠀⠐⠄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣄⠀⠻⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠈⡏⠙⠻⣿⣿⣿⣿⣿⣿⣿
⡆⠀⠈⠛⣿⠟⠶⠲⠃⠀⠉⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠿⢿⣷⣶⣾⠫⠀⢀⢻⣿⣿⣿⣮⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠁⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠡⣩⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⣿⣷⣄⣷⠀⣰⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⣤⣾⣿⣿⣿⣿⣿⡿⣩⣶⣶⣮⡙⢋⣥⣶⣶⣭⡻⢫⣴⣶⣦⣄⠒⢒⣵⣶⢹⣿⣷⣾⣾⣶⣾⣿⣭⣿⣿⣿⣿⣧⠀⠀⠀⠈⠛⢛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡇⠿⠿⢨⣿⡿⢸⣿⡇⢸⣿⡇⠿⠿⢀⣿⣿⢘⠻⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣺⣷⣿⡟⠉⢹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣿⡿⢃⢸⣿⡇⢸⣿⡇⣶⢂⣾⣿⠏⣾⠇⣿⣿⢠⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠐⣻⣿⠄⠀⠈⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣀⣀⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⣿⣿⡟⣱⣿⣟⣁⡛⢸⣿⡇⢸⣿⡇⢡⣿⣿⣃⣘⢿⡄⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣻⠽⠁⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠉⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣇⠛⠛⠛⠛⢃⣌⡛⠿⠿⢛⣅⡛⠛⠛⠛⢛⣸⣇⠛⠛⣸⣿⣿⣿⣷⣿⣛⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠁⣀⣀⣠⡔⣿⣿⣿⣿⣿⣿
⠀⠀⢤⣂⣾⣿⣾⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡻⢿⣿⡿⣿⣿⢿⣿⡿⣟⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⡿⠃⣿⣿⣿⣿⣿⣿
⡀⡀⣸⣋⣉⣙⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣿⣿⣿⣿⣰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢿⠿⠿⣾⣻⣿⣯⣿⣿⣭⡍⠙⠁⠈⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿
⢻⡿⠿⠟⠂⠀⢺⣿⣿⡿⠿⣿⢿⣿⡿⠀⣠⣤⣼⣿⣿⠿⠿⠿⠿⠿⠷⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠘⠛⠁⢹⡷⠀⠀⠀⠀⠀⠀⠠⣀⣠⣤⠀⠀⠀⢀⢉⣙
⢿⣿⠀⠀⠀⠠⣤⡏⠹⠦⣶⣴⣿⡿⠹⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠤⣤⣴⣾⡟⠛⢻⣿⡿⠿⡿⠿⠿⠿⣿⣿⣾⣿⣿⣿⡿⠿⠿⠿⠿⢿⢿⠿⠿⣿⠃⠀⠀⠀⠀⠀⢗⠀⠀⠉⠀⢠⣶⣾⣟⣻⣭⣤⣄⣀⣀⡀⠀
⠊⠹⠦⠀⠀⠀⠸⣿⠄⠀⠈⠀⠙⠇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢛⠟⠟⠀⠀⠉⠁⢀⣀⣠⣤⣤⣤⣼⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣦⣤⣀⣀⣿⣿⣿⣿⣿⣷⣀⣠⣴⣦⣤⣤⣴⣿⣿⣿⣾⣿⣿⣿⣿⣏⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢀⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⢟⡍⢛⠭⠝⢩⢩⠭⠍⣛⡻⣿⣿⡿⣿⢿
⠀⠆⠲⣶⠎⢶⠄⠰⠰⠶⠆⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⠉⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠛⠛⠻⠿⢱⣾⣿⣿⣿⣧⡖⠗⡘⠄⠰⠸⠸⢹⡆⠔⠄⠂⠀⠀⠀⠀
[29A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡟⠠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣽⣿⣿⣯⡷⠌⡀⠰⡦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣠⣄⣀⡀⡸⢿⣿⣿⣿⣿⣿⣿⣀⡀⠀⠘⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣻⣟⡷⣯⠅⠈⠀⠸⣮⣟⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⡿⠟⠛⠹⣿⣿⣤⣄⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢿⣿⣿⣾⣽⡟⣧⡫⣾⣿⣿⠎⡀⢶⢶⣶⠀⢐⠰⡢⠀⠀⠀⠀⠱⢾⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠘⣿⡿⠟⠛⣿⣿⣿⣿⡟⠋⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⢻⣿⣿⣼⣇⣟⣼⢻⡿⠃⣌⡿⡄⢳⡏⠀⠨⠖⢀⠀⠀⠀⠀⠀⢡⣹⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠘⡓⠀⠀⠈⠙⣿⣿⣗⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⠀⢸⣿⣿⣿⠹⡞⡽⡯⠀⠞⠯⠿⠻⠄⠃⠀⠘⠀⠄⠄⠀⠀⠀⠀⢠⢓⢆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡛⠿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢿⢧⣧⣿⠑⠷⢀⠀⠀⠀⠀⠄⠀⠘⠀⠀⠀⠀⠀⠀⠀⣾⣾⡺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣟⠁⠀⠸⢿⣄⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⡿⠟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⠻⢿⣿⣽⢣⡙⡇⡷⡌⠀⠀⣠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢶⢣⠊⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⣿⣿⣿⡇⠀⠀⢄⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠁⣀⣟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢟⢿⡳⢿⡱⣦⡐⠈⠁⠁⠀⠀⠀⠀⠀⠂⠀⣤⣎⡾⢚⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⠿⣿⣿⣷⣤⣄⣤⣧⣶⣿⣿⣷⠀⠀⠀⠀⠸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡄⠀⠀⠹⣶⠾⠿⠬⠢⣄⣀⣀⣀⣀⣀⣠⣴⠮⠾⠿⡺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⡅⠀⠀⢀⣀⣄⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡂⣀⣤⣶⣶⣿⣿⣛⣉⢥⢞⠟⠉⠻⢟⢦⠍⠙⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡿⠿⠀⠀⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣤⡄⠀⣄⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣶⣶⣤⣳⣿⡿⠿⢿⣿⣿⣿⡄⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠈⠛⠻⢙⣿⣿⣿⣿⣿⣿⣿⡟⢻⡉⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣏⠛⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠻⣿⣿⣿⣿⣿⣿⡅⣸⣣⣴⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣐⠆⠀⢫⣿⣿⣿⡿⣿⡇⠈⠀⠀⠀⠀⠀⠀⢻⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⠋⢿⡿⠍⠂⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⢷⠀⠀⣰⢿⣿⣿⣿⣾⣧⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣀⣀⣀⢀⣀⣀⠀⢀⣀⣀⣀⣀⣀⢰⠵⢶⣿⣿⣿⣿⣿⣿⠀⠀⠀⢐⣿⣿⣦⣸⡆⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⣿⣿⡟⣩⣶⣶⣮⡙⢋⣥⣶⣶⣭⡻⢫⣴⣶⣦⣍⠻⢛⣽⣶⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠛⠛⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡁⠿⠿⢸⣿⡿⢸⣿⡇⢸⣿⡇⠿⠿⢀⣿⣿⢘⠻⣿⣿⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣧⣿⠏⠉⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢠⣿⡿⠃⢸⣿⡇⢸⣿⡇⣶⢂⣾⣿⠏⣾⠃⣿⣿⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⡷⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡜⠟⣱⣿⣟⣁⡃⢸⣿⡇⢸⣿⡇⢡⣾⣿⣃⣚⢿⡇⣿⣿⢸⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢛⠻⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠙⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠛⠛⠛⠛⢃⣌⡛⠿⠿⢛⣅⡛⠛⠛⠛⢛⣸⣇⠛⠛⣸⣿⡿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⣤⣤⡔⣿⣿⣿⣿⣿⣿⣿
⠀⢠⢄⣠⣶⣷⣾⣿⣿⣯⣭⣭⣝⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢠⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⣛⣿⣛⣿⣏⣿⣿⠛⣧⡇⠀⠀⠀⠀⠀⠀⠼⣿⡿⠃⢸⣿⣿⣿⣿⣿⣿
⠀⠀⣔⣉⣉⣛⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠿⢯⣟⣿⣿⣭⣿⣯⣭⡙⡙⠁⠀⣆⣠⣿⣿⣻⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⢿⣿⣿⣿
⢿⣿⡿⠗⠂⠀⢾⣿⣿⠿⢿⣿⢿⣿⠗⢀⣀⣭⣽⣿⣿⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠙⠁⠈⢹⡟⠀⢀⡀⠀⠀⠀⠀⢀⣀⣶⡎⠀⠁⠀⠀⣩⠍
⣿⣶⠀⠀⠀⢀⣬⡉⠹⠂⣤⣼⣿⡏⢳⣿⣿⣿⣿⣿⣿⣦⣀⠀⠤⣤⣿⣿⠛⠛⣿⡿⠿⠿⠿⠿⠿⢿⣟⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⡿⠿⠿⣟⠁⠀⠀⠀⠀⠰⠇⠀⠀⠉⠃⠀⣰⣶⣿⣿⣷⣥⣤⣀⣄⡄⡀⠀
⠂⠿⠀⠀⠀⠀⢻⣧⠀⠀⠉⠈⠻⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡆⠈⡻⠛⠃⠀⠀⠁⠀⠀⢀⣀⣀⣠⣤⣽⣿⣿⣿⣿⣿⣷⣶⣶⣶⣷⣤⣤⣀⣰⣿⣿⣿⣿⣿⣷⣄⣀⣠⣦⣤⣤⣤⣽⣿⣿⣶⣿⣿⣿⣿⣏⠁⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢀⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⢟⡍⢝⠭⠝⢩⢩⠭⠍⣛⡻⣿⣿⡿⣿⢿
⠀⠆⠲⣶⠎⠶⠄⠰⠰⠶⠆⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠙⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠈⠛⠛⠿⢡⣿⣿⣿⣿⣧⣒⠗⡘⠄⠰⠸⠸⢩⡆⠐⠄⠂⠀⠀⠀⠀
[29A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡩⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠀⠀⠀⢀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣯⢿⠵⠀⠰⠆⠰⡦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠸⣿⣿⣿⣿⣇⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣟⣿⣿⡿⣿⣵⣿⣯⣿⣿⣻⡻⢿⣿⣻⠒⠋⠐⠀⠀⠸⣮⣟⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣿⣿⣿⣿⣿⣿⣷⣶⠽⠛⢻⣿⣧⣤⣄⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢿⣿⣿⣿⣿⡟⣧⣫⣾⣿⣏⠏⡀⢶⡆⣄⠀⠠⠀⠀⠀⠀⠀⠀⠱⢼⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠸⣿⣿⠛⠛⣿⣿⣿⣿⡉⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⢻⣿⣿⣿⣇⣟⣼⣿⣚⠁⠈⡡⠀⢀⠴⠀⢈⠀⠀⠀⠀⠀⠀⠀⢡⣹⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢹⣿⠀⠀⠈⠙⣿⣿⣧⣤⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⠀⢸⣿⣿⣽⠹⡞⣝⡖⠀⠾⠎⠷⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⢰⢱⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢝⣿⣿⣿⡇⠀⠀⠀⠀⠈⢐⠤⠀⠀⣰⣿⣿⣿⣿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣟⢻⢧⣧⣿⠡⢔⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⡚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠁⠛⣿⡿⢿⣿⢋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⠻⢿⣗⣶⣣⡙⡇⡷⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢶⢣⢊⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢰⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣼⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠘⡯⣿⡳⢿⡹⣤⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣤⣎⡼⢚⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣾⣿⣿⣿⡇⠀⠀⢢⠀⣠⡀⠀⠀⠀⠀⢿⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡎⠩⠙⠹⣶⠾⠿⠬⠢⣄⣀⣀⣈⣀⣀⣠⣴⠮⠾⠿⡺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣾⣾⠀⠀⠀⠈⠙⠛⢿⣿⣿⣶⣿⣿⣿⣷⠀⠀⠀⠀⠈⡇⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡃⢂⣴⣶⣤⣽⡿⣛⣉⢥⢞⠟⠋⠛⢟⢦⠍⠙⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⠀⠀⣠⣤⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣤⣤⡤⠀⠠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣦⣤⣤⡀⢷⣿⣿⣿⣿⣿⣿⣿⡇⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠈⠛⠛⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣭⣶⣶⣾⡛⠻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠹⣿⣿⣿⣿⣿⣿⡟⠐⠧⠀⠙⠛⠻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⡀⠀⠾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠉⠿⣿⣿⢙⡑⡅⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡲⣶⣶⣦⣞⡃⠀⠀⣹⣿⣿⣿⣇⠀⠀⠀⠀⣤⣤⡀⠘⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⣻⣿⣿⣿⣿⡀⠀⠀⠀⢿⣿⣿⣶⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡟⣡⣶⣶⣮⡙⢏⣥⣶⣶⣬⡻⢃⣴⣶⣦⣄⠲⢀⣴⣶⢰⣶⣤⣤⣤⣭⣿⣿⡟⣿⣿⣧⠀⠀⠀⠈⠀⠀⣶⣿⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡁⠿⠿⢸⣿⡿⢸⣿⡇⢸⣿⡇⠿⠿⢀⣿⣿⠘⠻⣿⣿⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠈⢿⢿⡏⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⡖⢠⣿⡿⢃⢸⣿⡇⢸⣿⡇⡶⢂⣾⣿⠏⣾⡇⣿⣿⢀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠹⣿⣇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣀⣀⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠛⣰⣿⣟⣁⡛⢸⣿⡇⢸⣿⡇⢠⣿⣿⣃⣘⢿⡄⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠸⠛⠻⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠙⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠛⠛⠛⠛⢃⣬⡛⠿⠿⢛⣅⡛⠛⠛⠛⠛⣸⣇⠛⠛⣸⣿⣿⣿⣽⣿⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣶⣶⣿⠻⣿⣿⣿⣿⣿⣿⣿
⠀⢠⣄⣠⣿⣿⣿⣿⣿⣿⣭⣿⣛⣛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⡿⣿⡿⢿⣿⡀⠀⠀⠀⠀⠀⠀⠻⡟⠋⠀⣿⣿⣿⣿⣿⣿⣿
⣀⣠⣭⣄⣌⣉⣡⣾⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣷⣿⣷⣿⣏⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠯⠝⢿⣿⣿⣿⣿⣿⣿⣦⡉⠋⠀⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠉⠀⡀⢈⢻⣗⡿⣛⣿⣿
⣿⠿⠟⠋⠀⠀⢿⣿⣿⠟⢻⠿⣿⣿⡋⢀⣤⣤⣽⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠛⠉⠙⣿⠗⠠⣤⣀⠀⠀⠀⡘⣤⣶⣿⠁⠀⠀⠀⠀⣉⣙
⢿⡗⠀⠀⠀⢠⣼⡀⠘⠲⣦⢾⣿⠗⢹⣿⣿⣿⣿⣿⣿⣷⣄⠀⢠⣴⣿⡿⠉⠙⣿⠿⠛⠿⠿⠿⠟⢛⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠻⠿⠟⠛⢻⣇⣀⣀⡀⠀⠀⠸⠀⠀⠈⠙⠀⠀⢼⣿⣿⢿⣦⣤⣤⣤⣤⣄⡀⠀
⠀⠻⠄⠀⠀⠀⢻⣧⠀⠀⠀⠀⠙⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣆⠘⠻⠟⠁⠀⠈⠀⠀⢀⣠⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣦⣤⣀⣼⣿⣿⣿⣿⣿⡖⣤⣠⣴⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⠟⢷⣿⣿⣿⣿⠟⡍⢋⠭⠍⢡⢩⠬⠍⣛⡻⣿⣿⡿⣿⢿
⠀⠆⠲⣶⠎⢶⠄⠰⠰⠶⠆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢙⠛⠁⣰⣿⣿⣿⣿⣧⡖⠗⡘⠄⠰⠸⠸⢩⡆⠐⠄⠂⠀⠀⠀⠠
[29A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣯⣿⣿⣿⢽⣾⠿⢆⢒⠦⠰⡦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⠐⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡻⣿⡿⣿⣵⣿⣿⣿⣿⣿⡻⣿⣿⡽⡹⠛⠸⠂⠀⠸⣮⣟⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣶⣾⣽⡿⠟⠋⠙⣿⣿⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢿⣿⣿⣿⣟⡟⣧⡫⣾⣳⣿⠋⡄⢶⠦⢶⠀⢤⢀⠀⠀⠀⠀⠀⠱⢼⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠈⣿⣿⠛⠛⢻⣿⣿⣿⡏⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⢻⣿⡿⣻⣇⣟⣼⣿⣝⢃⣼⣿⡄⢳⠉⠀⢘⠀⠀⢀⡄⠀⠀⠀⢡⣹⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠸⣿⠃⠀⠀⠙⣿⣿⣿⣤⣤⠻⣿⣿⣿⣿⣿⣿⣿
⣧⠀⢸⣿⣿⣿⠹⡞⣽⣟⠃⠼⠯⠏⠏⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⢨⢱⢆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠉⡢⡀⢀⣠⣿⣿⣿⣿⢳⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣻⢧⣧⣿⣘⣶⡄⡀⠀⣠⡄⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⡺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣿⡉⠀⠈⢿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠉⠻⣿⠿⢿⡿⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⠻⢿⣿⣍⢣⡙⡇⡷⡤⠀⠀⠀⡤⣤⡠⠀⠀⠠⠀⠀⠀⠀⢀⢾⢣⢊⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⡃⠀⠀⠀⠸⣿⣿⣷⣄⠀⠀⠀⠀⠀⢀⠀⣠⣿⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡘⡽⢿⡳⢿⡹⣦⡀⠙⠙⠛⠘⠖⠀⠀⠀⠀⠀⣴⣎⡼⢚⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⣸⣿⣿⣿⡆⠀⠀⢠⡀⠈⣿⣿⣿⣷⠀⠀⠀⠀⠸⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡗⠅⠀⡿⢶⠾⠿⠬⠢⣕⣁⣀⣩⣀⣈⣠⣴⠯⠾⠿⡺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣤⠀⠀⠀⠙⢿⣿⣿⣿⣦⣤⣾⣷⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢻⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠇⢇⣤⣦⣦⣽⣿⣛⣉⢥⢞⢟⠋⠛⢟⢦⠍⡙⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡀⠀⠀⣀⣀⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡄⣠⡄⠀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣤⣡⣿⣿⡿⠿⣿⣿⣿⣟⠈⠡⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠁⠀⠐⠿⢿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡛⠉⢃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣯⠛⠛⠛⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠋⠉⢿⣿⣿⣿⣿⣿⣿⡇⠈⣯⡤⠿⠈⠹⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢿⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠙⢻⣻⣟⢨⠩⠈⠁⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⡀⠆⠀⠀⢈⣻⣿⣿⣿⣿⣿⣇⠀⠀⠀⢀⣠⣄⡀⢸⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠟⠀⠀⠀⠐⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣾⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⡟⣡⣶⣶⣮⡙⢟⣥⣶⣶⣬⡲⢠⣴⣶⣦⣄⠀⢀⣤⣶⢠⣤⣤⣀⣬⣭⣭⣿⠿⣿⣿⣿⣿⡄⠀⠀⠀⠉⠉⢭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⣿⣿⣿⣿⡇⠿⠿⢸⣿⡿⢸⣿⡇⢸⣿⡇⠿⠿⢀⣿⣿⠘⠻⣿⣿⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢺⣾⣿⠋⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⡶⢠⣿⡿⠃⢸⣿⡇⢸⣿⡇⣿⢃⣾⣿⠏⣼⡇⣿⣿⠘⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⣟⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣀⣀⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣰⣿⣟⣑⡂⢸⣿⡇⢸⣿⡇⢡⣿⣿⣃⣚⢿⡅⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠐⡞⢻⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠛⠛⠛⠛⢃⣬⡛⠿⠿⢛⣅⡛⠛⠛⠛⠛⣸⣇⠛⠛⣸⣿⣿⣿⣟⣻⡿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⣴⣦⣶⡿⣿⣿⣿⣿⣿⣿
⠀⢠⣶⣲⣿⣿⣿⣿⣿⣿⣿⣽⣟⣛⡻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣾⣿⣿⣿⠿⢿⣿⡀⠀⠀⠀⠀⠀⠀⠹⡟⠛⠀⣿⣿⣿⣿⣿⣿
⣀⣅⣼⣥⣬⣭⣍⡽⣿⣿⣿⣿⣿⣿⣿⣿⡷⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣽⣿⣭⣿⣸⣿⣠⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⠯⠹⣾⣿⣿⣿⣿⣿⣷⣌⠉⠁⢈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⣿⣿⣿
⢻⡿⠿⠛⠁⠀⢸⣿⣿⡿⠛⡿⣿⣿⣟⠁⣠⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠴⠟⠿⢿⡿⠷⣶⣤⡀⠀⠀⠀⢈⣤⣼⠛⠁⠉⢀⠀⣉⣉
⢻⢿⠇⠀⠀⠀⢤⣆⠘⠛⢴⡴⣿⡟⠙⣿⣿⣿⣿⣿⣿⣿⣯⡉⠭⣉⣹⣿⠟⠛⢿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⢻⣿⠿⠿⣿⠀⠀⠀⠀⠀⠐⠇⠀⠀⠙⠆⠀⠠⣿⣿⡿⢿⣤⣄⣀⣀⣄⡀⠀
⠀⠘⠓⠀⠀⠀⠘⣿⠄⠀⠀⠀⠈⠃⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢻⡟⡋⠀⠀⠉⠀⠀⣀⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣦⣤⡀⢠⣿⣿⣿⣿⣿⣷⢄⣄⣤⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡍⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢀⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣿⣿⣿⠛⡝⢛⢭⠍⢩⢩⠭⠍⣛⡻⣿⣿⠿⣷⢾
⠀⠆⠲⣶⠮⢶⠄⠰⠰⠶⠖⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠈⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠈⠉⠛⠛⢡⣾⣿⣿⣿⣧⡖⠗⡘⠄⠰⠸⠸⢩⡆⠔⠄⠂⠀⠀⠀⠠
[29A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⡾⣮⢢⢪⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣽⣻⠯⣏⣉⡊⠱⠰⡦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀⣀⡀⠸⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣵⣿⣿⣿⣿⣿⣿⣽⣼⢳⡓⠏⠓⠂⠀⠸⣮⣟⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣦⣮⣽⣿⡿⠛⠛⣿⣿⣁⣀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢿⣿⣿⣿⣿⡟⣧⣫⣾⣿⣿⢋⡀⢶⡂⣆⠀⢶⢆⠐⢀⠀⠀⠀⢱⢾⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠘⣿⣿⠿⠿⢿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⢻⣿⣿⣿⣇⣟⣼⣽⡻⠃⢶⣯⡄⢻⡾⠀⠸⠀⠀⠀⡀⠀⠀⠀⢡⣹⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢹⣿⠄⠀⠘⠻⣿⣿⣷⠀⢘⢿⣿⣿⣿⣿⣿⣿⣿
⣧⠀⢸⣿⣿⣿⠹⡞⡝⢻⠁⠾⠿⠛⠏⠄⠓⠀⠈⠀⠀⠠⠀⠀⠀⠀⢰⢱⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣿⣿⣿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠛⣀⠀⠀⠀⣿⣿⣿⣿⢯⣬⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢧⣧⣿⠻⡶⠄⢀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⡺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠀⠀⠀⠻⢿⣿⡄⠀⠀⠀⠀⠈⠘⠂⣴⣿⣿⣿⣿⠟⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⠻⢿⣷⣟⣣⡙⡇⡿⣗⣂⠀⢀⠀⠠⡀⣀⠀⠀⠠⠀⠀⠀⢀⢾⢣⢊⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠀⠀⠀⠘⢿⣿⣆⠀⠀⠀⠀⠀⠀⠘⠋⠁⣿⣣⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣩⣏⢿⡳⢿⡹⣮⡬⠪⡥⠂⠕⡢⠪⠑⠐⠀⠀⣰⣎⡾⢚⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢿⣿⣿⣿⣇⠀⠀⢰⣀⣨⣿⣿⣷⣦⠀⠀⠀⠀⢸⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡌⠹⠑⣹⣶⠾⠿⠬⠦⣇⣄⣀⣀⣂⣈⣳⣴⠯⠾⠿⡺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⠀⠀⠀⠈⠙⠻⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠘⠀⠘⢿⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡏⣌⣶⣷⣾⣿⣿⣛⣉⢥⢞⠟⠋⢻⢟⢦⢍⠙⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄⠀⢀⣤⣴⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣠⠀⠀⣌⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣶⣶⣄⣶⣿⣿⠿⢿⣿⣿⣿⡇⡌⠋⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠈⠙⠛⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠋⠙⡃⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣟⠛⠛⠋⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⢿⣿⣿⣿⣿⣿⣿⠀⢸⠁⣴⣧⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠸⢿⣿⣿⣿⣿⣿⣷⡏⠉⠉⠙⠀⠀⠈⠉⡟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⠛⢿⢿⠏⢿⡅⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣶⣶⣬⠀⠀⠀⢸⣿⣿⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣷⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠊⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢰⣿⣷⣆⠸⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡟⣡⣶⣶⣮⡙⢟⣥⣶⣶⣤⡀⢠⣴⣶⣦⣄⠀⢀⣤⣶⢀⣀⣀⣐⣡⣤⣿⣿⠿⣿⣿⣿⣿⠀⠀⠀⠘⠿⠿⠿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣾⣿⣿⣿⡇⠿⠿⢸⣿⡿⢸⣿⡇⢸⣿⡇⠿⠿⢀⣿⣿⠘⠻⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣽⣿⣿⠟⠛⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⡶⢠⣿⡿⢃⢸⣿⡇⢸⣿⡇⣿⢃⣾⣿⠏⣼⡇⣿⣿⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠸⣿⡏⠀⠀⢹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣱⣿⣟⣑⡃⢸⣿⡇⢸⣿⡇⢡⣿⣿⣃⣚⢿⠇⣿⣿⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢀⢯⡷⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠛⠛⠛⠛⠃⣨⡛⠿⠿⢛⣁⡛⠛⠛⠛⠛⣸⣆⠛⠛⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠃⣀⣀⣀⢼⣿⣿⣿⣿⣿⣿
⠀⢀⣀⢴⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣏⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⠈⣿⣿⣿⣿⣿⣿
⠀⠾⣺⠚⠻⠿⠿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣄⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⠿⢿⡿⢿⣿⢻⡇⣰⣿⣿⡆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢿⣿⣿⣿⣿⣿
⣷⣿⣿⣿⣿⡶⢶⣿⣿⣿⣟⣿⣿⣛⠻⡿⠍⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⢿⣿⣿⣿
⣿⣿⣿⡿⠍⠈⣽⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣐⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢚⣿⣿⣿⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⢠⠀⠁⠉⢁⡀⣉⣙
⣾⣽⠁⠀⠀⠀⢘⡟⢻⡇⣼⣫⣿⣿⢳⣶⣿⣿⣿⣿⣿⣿⡟⠛⠛⠿⢿⣿⣿⢿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠁⠀⠈⢻⡅⠈⠛⢿⡁⠀⠀⣴⣶⣿⣟⠀⣀⣀⣀⡀⠈⠁
⠘⢿⡀⠀⠀⠈⢻⣧⠀⠀⠙⠉⠻⠇⢀⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⣿⣿⡟⠃⠀⠼⠋⠉⠉⠉⢉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣍⣉⣉⣭⣉⠉⠉⢉⣷⣤⣤⣴⣶⣄⠀⠀⣀⣤⣄⣀⣀⣨⣽⣿⣥⣿⣿⣿⣿⣿⡉⠙⠂
⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⠁⠀⣀⣠⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⡿⣧⣾⣿⣿⢟⡍⢛⠭⠝⢩⢩⠭⠅⣛⡻⣿⣿⠿⣶⣶
⠀⠆⠲⣶⠎⢶⠄⠰⠲⠶⠆⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⠋⠻⠿⠿⢋⣼⣿⣿⣿⣧⡖⠗⡘⠄⠰⠸⠸⢩⡇⠐⠄⠂⠀⠀⠀⠠
[29A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣿⣮⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⢿⣿⣿⣿⣽⣿⣿⣻⣿⠿⢅⡰⡍⠰⡦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣧⠀⡀⠀⠘⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣵⣿⣷⣿⣿⣿⣿⣿⣿⣬⡜⡁⠂⠀⠀⢸⣮⣟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣿⣿⣿⣿⣿⣷⣶⣼⠟⠛⠛⣿⣿⣤⣤⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢿⣿⣿⡿⢿⡟⣧⣫⣾⣿⣿⠇⠄⢶⢶⢶⠀⡖⠀⠀⠀⠀⠀⠀⢱⢾⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠈⢿⣿⠟⠛⢻⣿⣿⣿⡟⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⢻⣿⣿⣿⣇⣟⣼⣟⣿⢋⣾⣿⡄⢻⡿⠀⢹⠄⠀⠀⠀⠀⠀⠀⢡⣹⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠸⣿⡇⠀⠀⠉⣿⣿⣿⣠⡤⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿
⣧⠀⢸⣿⣿⣿⠹⡞⣽⣿⠃⠾⠼⠉⠍⠀⠃⠀⠐⠀⠀⠀⠀⠀⠀⠀⢰⢓⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⡿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠁⠙⢀⠀⠀⢀⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢧⣧⣿⠻⢒⡀⠀⠀⠠⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⡺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡟⠙⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠺⢿⡿⢿⣿⠟⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⠻⢿⣿⣌⢧⡙⡇⡷⡆⠀⣀⠠⡀⡀⠠⢄⠀⠀⠀⠀⠀⠀⢀⢾⢣⣊⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣧⠄⠀⠀⠉⢻⣷⣀⠀⠀⠀⠀⠀⠀⡉⢀⣼⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠠⡯⢿⡳⢿⡹⣦⡀⠈⠅⠤⡱⠔⠀⠀⠀⠀⠀⣠⣎⡾⢚⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣾⣿⣷⡀⠀⠀⠀⠈⢻⣿⣷⡄⠀⠀⠀⠀⢿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡗⠀⠀⡹⣶⠿⠿⠬⡦⣄⣀⣀⣈⣀⣀⣀⣴⠯⠾⠿⡺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣻⣿⣿⣿⣇⡀⠐⣸⣄⣤⣿⣿⡇⠀⠀⠁⠀⠘⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢇⣀⣤⣷⣭⣽⣿⣛⣋⢥⢞⡟⠋⠻⢟⢦⠍⠙⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⡟⠀⠀⠀⠉⠻⠿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣤⡤⠆⠀⢰⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣦⣤⣤⣀⢷⣿⣿⣿⢿⣿⣿⣿⡴⠌⠁⠀⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠄⠀⠀⣄⣤⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠶⠀⢸⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣩⣶⣶⣾⡟⠛⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠀⠀⠘⠓⠻⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⠏⢱⡇⣀⠈⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠉⠿⣟⣯⡿⣵⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣻⡇⠀⠀⠀⢀⣀⣀⠀⢳⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣧⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣄⡀⠀⠀⠀⠀⣭⠓⣿⣿⣿⣧⠀⠀⠀⢸⣿⣿⣧⣼⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡟⣡⣶⣶⣮⡙⢟⣤⣶⣶⣤⡀⢠⣴⣶⣦⣄⠀⢀⣴⣶⠀⠁⠀⠀⠀⠀⢿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠉⠉⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⡇⠿⠿⢸⣿⡿⢸⣿⡇⢸⣿⡇⠿⠿⢀⣿⣿⠘⠻⣿⣿⢰⣶⣶⣶⣶⣿⣿⣷⣦⣿⣿⣿⣷⠀⠀⠀⠀⠀⢸⣾⣿⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣄⣴⣿⣿⣿⣿⣿⣿⡖⢠⣿⡿⠃⢸⣿⡇⢸⣿⡇⣿⢃⣾⣿⢏⣼⡆⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⡿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣱⣿⣟⣑⡃⢸⣿⡇⢸⣿⡇⢡⣿⣿⣃⣚⢿⠇⣿⣿⢀⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠾⠻⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠛⠛⠛⠛⠃⣬⡛⠿⠿⢛⣅⡛⠛⠛⠛⠛⣸⣄⠛⠛⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢠⣶⣴⡎⣿⣿⣿⣿⣿⣿⣿
⠀⢠⢤⢰⣿⣾⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣼⣿⣛⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠺⣿⠛⠁⢹⣿⣿⣿⣿⣿⣿
⠀⢁⣽⣉⣙⣛⣋⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠻⣿⣿⣿⣿⡿⢿⠃⣹⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠯⠿⢿⣟⣿⣿⣿⣿⣿⣭⡙⠛⠁⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣗⣻⣷⣿⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢻⡿⢿⡋⣿⣿
⢿⢿⠿⠟⠀⠀⢾⣿⣿⡿⣿⡿⣿⣿⡟⢀⣠⣥⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣦⣤⣀⡀⠀⠀⡐⢃⣤⡿⠋⠉⠉⡀⠈⣉⣙
⣿⣾⠀⠀⠀⠠⣤⡍⠹⠲⣾⣼⣿⡏⢿⣿⣿⣿⣿⣿⣿⣿⣏⠉⢙⣛⣿⣿⠿⠿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠁⠹⠀⠈⠙⠏⠁⠀⣸⣿⣿⢿⣇⣤⣀⣀⣀⣀⡀⠀
⠀⠙⠆⠀⠀⠀⢹⣷⠀⠀⠈⠈⠙⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣆⠘⢿⡿⠏⠁⠐⠋⠁⠀⣀⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣶⣄⣁⠀⢰⣷⣶⣶⣿⣿⣦⣠⣀⣴⣶⣶⣶⣶⣶⣿⣿⣾⣿⣿⣿⣿⣮⡉⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢠⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣾⣿⣿⣿⢟⡝⢛⠭⠝⢩⢩⠭⠍⣛⡻⣿⣿⢿⣿⣿
⠀⠆⠲⣶⠎⠶⠄⠰⠰⠶⠆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠈⠻⠛⠋⢴⣿⣿⣿⣿⣧⡖⠗⡘⠄⠰⠸⠸⢩⡇⠐⠄⠂⠀⠀⠀⠠
[29A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣟⣷⠥⣝⡅⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠉⠁⠀⠀⢀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢿⣟⣿⣿⣽⣿⣿⣻⣸⠗⠁⠐⠀⠰⡦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣟⣟⡿⣿⣵⣿⣿⣽⣿⣿⣻⠞⠇⠉⢈⡂⠐⠀⠀⠸⣮⣟⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣾⣿⣶⣶⣾⣶⣾⣭⡿⠿⢻⣿⣶⣄⣀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢿⣿⣿⡿⣻⡟⣧⣫⡎⣽⣿⠋⠀⢲⠢⠄⠀⢠⠀⠠⠀⠀⠀⠀⢱⢼⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠐⣿⣿⠿⠿⢿⣿⣿⣿⡟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⢻⣿⣿⣿⣇⣟⣼⣯⠾⠁⠸⢍⡀⢋⠇⠀⠨⠀⠀⢀⠀⠀⠀⠀⢡⣹⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⢹⣿⠆⠀⠈⠙⣿⣿⣷⣀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⠀⢸⣿⣿⣻⠹⡞⣽⡵⠁⠠⠥⠐⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢱⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⢸⠚⣄⠀⠀⢀⣿⣿⣿⣿⢇⣶⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢧⣧⣿⠉⠂⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣾⡚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣻⠿⠋⠛⢿⣿⡀⠀⠀⠀⠀⠀⠁⠑⢾⣿⣿⣿⣿⠟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⠻⢿⣷⡥⢣⡙⡇⡷⡭⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢶⢣⠊⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣯⠄⠀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠀⠉⢀⣾⣣⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡨⡏⢿⡳⢿⡱⣦⡄⢀⠄⠀⠈⡀⢀⠀⠀⠀⠀⣰⣎⡾⢚⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣾⣿⣿⡆⠀⠀⢀⠀⠙⣿⣷⣦⠀⠀⠀⠀⠸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡇⠠⠀⠹⢶⠾⠿⠬⠢⣄⣀⣀⣰⣈⣀⣠⣴⠮⠾⠿⡺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⣿⣿⣿⣧⡄⠀⣀⣧⣤⣬⣿⣿⡆⠀⠀⠃⠀⢻⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡧⢠⣶⣶⣶⣿⡿⣛⡉⢥⢞⠟⠉⠛⢟⢦⠍⠙⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣿⣿⠁⠀⠀⠈⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠠⠀⠀⣬⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣤⣤⣄⢵⣿⣿⠿⢿⣿⣿⣿⣕⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠄⠀⠀⣤⣴⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⠆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣿⣿⣿⣩⣶⣶⣮⡝⠛⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢿⣿⡏⢿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣷⠀⣀⠸⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢹⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠉⠙⢛⡿⠍⡗⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠙⠏⣿⣿⣿⣹⣿⠀⠀⠀⠀⣀⣀⡀⢸⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣧⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠷⢶⠀⠀⠀⠀⠀⠀⠟⣿⣿⣿⣿⠀⠀⠀⠈⣿⣿⣿⣶⣇⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣇⠀⠀⠀⠙⠙⠛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣦⣤⣤⣴⣶⣿⣧⣤⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⣧⣿⡟⠁⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣄⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠹⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢘⠿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠈⠀⣤⣤⣶⢻⣿⣿⣿⣿⣿⣿
⠀⢀⣠⢤⣿⣾⣿⣿⣟⣿⣿⣿⠿⢿⣿⣿⣿⠿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣛⣿⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠸⢿⡟⠋⢸⣿⣿⣿⣿⣿⣿
⠀⠋⣹⠋⠛⠻⢛⣻⣿⣿⣿⣿⣷⣶⣶⣤⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣷⣿⣿⣿⠏⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠨⡇⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣟⡿⡿⣿⣿⣿⣿⣿⣏⠛⠿⠁⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⣟⣫⢿⣇⣶⣤⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢻⣿⢟⣿⣿⣿
⢿⣿⣿⠷⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡷⠀⢀⣁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣧⣤⡀⠀⠀⠀⠠⢝⣀⡐⠒⠁⠉⠀⠀⢉⣙
⣾⣦⠀⠀⠀⢀⣈⡛⢻⠄⣬⣱⣿⡏⢷⣾⣿⣿⣿⣿⣿⣿⡟⠛⠛⠻⢿⣿⠿⢷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⠉⠉⠙⠻⡉⠉⠹⠏⠁⠀⣠⣿⣾⣿⣇⣀⣀⣀⣀⣀⠈⠀
⠋⠻⠄⠀⠀⠀⢻⣧⠀⠀⠉⠉⠻⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣅⠐⣿⣿⢟⠀⠀⠛⠉⠁⠈⣉⣉⣉⣩⣿⣿⣿⣿⣿⣿⣭⣭⣍⣭⣭⣉⠉⠁⢨⣶⣶⣶⣶⣶⣄⢀⣀⣠⣤⣤⣤⣤⣴⣿⣿⣷⣿⣿⣿⣿⣏⡉⠛⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠉⠀⢀⣠⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⢏⡝⢃⠭⠍⢩⢩⠭⠍⣛⡻⢿⡿⠿⣷⢾
⠀⠆⠲⣶⠎⠶⠄⠰⠰⠶⠆⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠃⠋⠛⠿⠟⠁⣼⣿⣿⣿⣧⡖⠗⡘⠄⠰⠸⠸⢩⡆⠐⠄⠂⠀⠀⠀⠀
[29A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣽⣟⣵⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣏⡚⠵⡦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣧⢀⡀⠀⠚⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢿⣿⡿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣯⡫⠭⠍⠯⠅⠁⠸⣮⣟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣴⣿⣿⣿⣿⣷⣿⣾⣾⣽⠿⠛⠉⢻⣿⣯⣤⣀⣀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢿⣿⣿⣿⣽⡟⣧⣫⣾⣿⣿⢏⠄⢲⣶⣶⠀⠦⠀⡀⢀⠀⠀⠀⢱⢾⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠸⣿⣿⠿⠿⣿⣿⣿⣿⡟⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⢻⣿⣷⣿⣇⣟⣼⣟⣿⢃⣾⡟⠈⢙⣿⠀⠙⠀⢠⢈⡀⠀⠀⠀⢡⣹⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⠈⠻⣿⣿⡇⢀⣺⣿⣿⣿⣿⣿⣿⣿⣿
⣧⠀⢸⣿⣿⣿⠹⡞⡽⡿⠡⠾⠾⠵⠿⠄⠈⠀⠈⠀⠀⠁⠄⠀⠀⠀⢰⢱⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠈⠑⠫⣀⠀⠀⢰⣿⣿⣿⣿⢱⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣟⢿⢧⣧⣿⡛⣂⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⡺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⡿⠟⠙⠻⣿⣷⡀⠀⠀⠀⠀⠈⠉⠲⣾⣿⣿⣿⡿⢏⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⠻⢿⣿⢭⢣⡙⡇⡿⡝⠺⠤⡀⣠⣀⣠⠀⠀⠀⠀⠀⠀⠀⢀⢾⢣⣊⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⡥⠀⠀⠀⠈⣻⣿⣄⠀⠀⠀⠀⠀⠀⠉⠉⢀⣟⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡨⢏⢿⡳⢿⡹⣦⡍⠊⡘⡩⣫⣌⠏⠁⡀⠀⠀⣴⣎⡼⢚⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣼⣿⣿⣧⠀⠀⠀⡀⠈⢻⣿⣿⡆⠀⠀⢀⠀⢾⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡏⠣⣓⡹⣶⠾⠿⠬⡢⣄⣂⣀⣠⣌⣥⣲⣴⠯⠾⠿⡺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⣿⣿⣿⣄⠀⣀⣷⣤⣴⣿⣿⣿⠀⠀⠘⠀⠘⣏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡗⣚⣤⣷⣶⣿⣿⣛⣉⢥⢞⠟⠋⠛⢟⢦⢍⣙⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⡁⠀⠀⠀⠘⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠠⢠⠀⢠⡭⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣶⣶⣤⣷⣿⣿⠿⢿⣿⣿⣿⣤⠌⠁⡤⠀⠄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠷⠀⠀⣠⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠾⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣟⣿⣿⣿⣿⣿⣮⣶⣾⣶⣝⠛⠿⠧⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⠉⣷⢀⡀⠈⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⠀⠉⠉⠉⠁⠀⠀⠈⡟⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠉⠚⢟⣻⣯⢻⣞⠈⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠉⠳⡿⣿⣿⣛⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⡿⠿⢿⣿⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠻⠿⠷⠀⠀⠀⠀⠀⡿⣻⣿⣿⣿⡇⠀⠀⠀⢻⣿⣿⣦⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠏⣴⡾⢿⣶⡙⣴⣾⢿⣶⡄⣠⣾⠿⣶⡄⣠⣾⠿⣶⣄⠀⠀⠀⠀⢂⣷⣿⣿⣿⣿⣷⠀⠀⠀⠘⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⡄⢛⠃⣼⣿⠃⣿⣿⢸⣿⡇⣛⠛⣰⣿⡏⣛⡛⣰⣿⡟⣤⣴⣶⣶⣿⣿⣤⣽⣿⣿⣿⡇⠀⠀⠀⠀⠀⢷⣼⣿⠋⠉⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣄⣠⣾⣿⣿⣿⣿⣿⣿⡿⢃⣾⣿⢋⠀⣿⣿⢸⣿⡇⠟⣰⣿⠟⣰⡟⣰⣿⠟⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠸⢼⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣾⣿⣥⣤⠀⢿⣿⣼⣿⠇⣼⣿⣯⣤⡄⣼⣿⣯⣤⡌⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣩⠗⠀⠀⢹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⣤⣤⣤⣾⣷⣬⣭⣴⣶⣦⣤⣤⣤⣴⣦⣤⣴⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠁⢀⣀⣤⢺⣿⣿⣿⣿⣿⣿
⠀⢀⣤⢰⣻⣾⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠘⣿⣿⣿⣿⣿⣿
⠀⡌⣭⠛⠛⠻⠛⣻⣿⣿⣿⣿⣿⣷⣾⣦⣤⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⡿⢹⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡙⠿⠋⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⣭⡽⣿⣴⣧⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⢿⣿⣿⣿
⢿⣿⣿⠿⠆⠀⢴⣿⣿⣿⣿⣿⣿⣿⡿⠀⢀⣀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣧⣤⡀⠀⠀⠀⠀⠠⣀⣠⠒⠉⠉⠁⠈⠉⣙
⣾⣿⠀⠀⠀⠀⣈⡟⢻⡧⣼⣩⣾⡿⣳⣾⣿⣿⣿⣿⣿⣿⣟⠛⠛⠻⢿⣿⡿⢿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠉⠁⠉⠻⡉⠉⠛⡟⠉⠀⢀⣾⣾⣿⣟⣀⣀⣀⣀⣀⠉⠁
⠘⠻⡄⠀⠀⠈⠻⣷⠀⠀⠘⠉⠻⠇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣿⠁⠀⠜⠋⠁⠀⣉⣉⣉⣉⣽⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣍⡉⠉⠀⣷⣶⣶⣶⣶⣦⠀⡀⣠⣤⣤⣤⣤⣼⣿⣿⣿⣾⣿⣿⣿⣿⣉⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠘⠁⠀⣠⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣧⣿⣿⣿⢟⡍⢛⠭⠝⢩⢩⠭⠍⣛⠻⣿⣿⡿⣿⣿
⠀⠖⠲⣶⠎⠶⠄⠰⠲⠶⠆⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠉⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠙⠛⠻⠟⠉⣼⣿⣿⣿⣧⡖⠗⡘⠄⠰⠸⠸⢹⡇⠐⠄⠂⠀⠀⠀⠀
[29A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣽⣿⣿⣿⣿⣞⢥⢉⡈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⢀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣿⣿⣿⣯⢿⡿⣿⢿⣿⣯⣾⣽⣿⣿⣿⣟⡿⢡⠠⠄⠰⡦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠰⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣵⣿⣾⣿⣿⣿⡿⣬⣿⣦⢁⠗⣠⠆⠀⠸⣮⣟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣤⣤⣶⣿⣿⣦⣬⣶⣬⣍⣿⡿⠟⠛⣿⣿⣅⣀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢿⣿⣿⣾⣿⡞⣧⣫⣾⢿⣿⠃⡀⢶⢶⡦⠀⣄⠄⠀⠀⠀⠀⠀⢱⢾⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⣿⣿⡿⠿⢿⣿⣿⣿⡟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⢻⣿⣿⣷⣇⣟⣜⣫⡹⢃⣾⢾⠄⢑⡌⠀⢸⠈⢀⠀⡀⠀⠀⠀⢡⣹⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠸⣿⡇⠀⠈⠙⣿⣿⣿⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⠀⢸⣿⣿⣿⠹⡞⡿⡿⠀⠞⠽⠬⠶⠀⠀⠀⠈⠀⠀⠈⠀⠁⠀⠀⢰⢳⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠈⢙⢇⡀⠀⢀⣿⣿⣿⣿⡇⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢻⢧⣧⣿⢗⠢⣄⣀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⠿⠛⣿⣿⣄⠀⠀⠀⠀⠀⠉⠗⢶⣿⣿⣿⣿⠟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⠻⢿⣿⣼⢣⡙⡇⡿⡿⢺⢇⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⢀⢶⢣⢊⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⢹⣻⣦⡀⠀⠀⠀⠀⠀⠀⠉⠁⣸⣫⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⡭⢿⡳⢿⡹⣶⡉⢛⡋⡙⠀⠑⣠⠀⠄⠀⠀⣠⣎⡾⢚⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢰⣿⣿⣿⡀⠀⠄⡀⠉⢿⣷⣦⠀⠀⠀⡀⠐⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡅⠰⠣⠸⣶⠾⠿⠬⠣⣌⣠⣀⣈⣀⣃⣤⣴⠯⠾⠿⡺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣦⠀⠐⣹⣄⣤⣿⣿⡇⠀⠀⠃⠀⢻⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡇⣎⣤⣦⣤⣽⣿⣛⣋⣥⢞⠟⣋⠛⢟⢦⠍⠙⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣏⠀⠀⠀⠀⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⠄⠀⢈⢱⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣶⣤⣤⣄⢷⣿⣿⣿⢿⣿⣿⣿⡅⠊⠅⠄⠑⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⠆⠀⢠⡔⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣶⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣿⣿⣿⣭⣴⣾⣶⡝⠛⠿⠧⠀⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡧⠀⡀⣘⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⣿⣿⣿⡿⣷⠀⠉⠁⠁⠀⠀⠀⢸⡉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠉⠹⣿⠿⠙⢭⠏⠘⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⢻⣿⠀⠀⠀⠀⣀⣀⡀⠀⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⡿⠿⠿⣿⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠷⠂⠀⠀⠀⠠⠜⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣶⣇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠋⣴⡾⢿⣶⡙⣴⣾⢿⣶⡄⣰⣾⠿⣶⡄⣠⣾⠿⣶⣄⠀⠀⠀⠀⠂⣩⣿⣿⣿⣿⣇⠀⠀⠀⠘⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣴⣿⣿⣿⣿⣿⣄⢛⠃⣼⣿⠃⣿⣿⢸⣿⡇⣛⠛⣰⣿⡏⣛⡛⣰⣿⡟⣤⣤⣴⣶⣿⣯⣤⣿⣿⣿⣿⡄⠀⠀⠀⠀⢀⣿⣿⣿⠋⠘⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣾⣿⣿⣿⣿⣿⣿⡿⢃⣾⣿⢋⠀⣿⣿⢸⣿⡇⠟⣰⣿⠟⣰⡟⣰⣿⠟⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠙⣽⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣾⣿⣥⣤⠀⢿⣿⣼⣿⠇⣼⣿⣯⣤⡄⣼⣿⣯⣤⡌⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⡿⡿⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡰⣶⣤⣴⣤⣾⣷⣬⣭⣴⣶⣤⣤⣤⣤⣴⣦⣴⣶⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠁⣠⣤⣤⢻⣿⣿⣿⣿⣿⣿
⠀⢀⣠⣀⣽⣼⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠠⢺⣿⠿⠘⣿⣿⣿⣿⣿⣿
⠀⠊⣽⠛⠙⠛⠛⣻⣿⣿⣿⣿⣿⣷⣷⣦⣤⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣾⣿⣿⡟⢻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡙⠛⠋⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣭⣭⣽⢿⣴⣧⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢾⣿⣿⡿⣿⣿
⢿⣿⣿⠿⠆⠀⢴⣿⣿⣿⣿⣿⣿⣿⡿⠂⢀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣧⣤⣀⠀⠀⠀⠀⠷⣂⣰⠂⠉⠉⣀⠀⢉⣛
⣸⣷⠂⠀⠀⠀⣈⡛⢻⠧⣨⣩⣾⡿⢳⣾⣿⣿⣿⣿⣿⣿⣟⠛⠛⠻⢿⣿⡿⢿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠉⠁⠉⠻⡉⠙⠻⡏⠉⠀⠀⣶⣾⣿⣇⣀⣀⣀⣀⣀⠈⠀
⠘⠻⢄⠀⠀⠀⢻⣧⠀⠀⠘⠉⠻⠇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣿⠃⠀⠜⠋⠉⠈⣉⣉⣉⣭⣽⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣉⣉⠉⠈⣷⣶⣶⣶⣶⣦⠀⠀⢠⣦⣤⣤⣤⣴⣿⣿⣷⣿⣿⣿⣿⣿⡉⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠉⠁⠀⣠⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣵⣿⣿⣿⢟⡍⢟⠭⠝⢩⢩⠭⠍⣛⠻⣿⣿⠿⣿⢿
⠀⠖⠲⣶⠎⠶⠄⠰⠶⠶⠆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠈⠉⠙⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠚⠙⠙⢿⠿⠁⣽⣿⣿⣿⣧⡖⠗⡘⠄⠰⠸⠸⢩⡆⠐⠄⠂⠀⠀⠀⠠
[29A⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⢿⡟⣏⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠉⠁⠀⠀⢀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⢷⣿⣽⣿⣿⣿⣿⣿⣿⣿⢣⠃⠁⠰⡦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠴⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣵⣟⣿⣿⣿⣿⡿⡿⣿⣏⠍⠁⠠⠀⠀⠸⣮⣟⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣠⣴⣽⣷⣴⣤⣦⣭⣟⣿⡿⠟⠻⣿⣿⣅⣀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢿⣿⣿⣿⣿⡟⣧⡫⣾⣿⡿⠏⡄⢶⡦⢂⠀⡐⠂⠀⠀⠀⠀⠀⢱⢾⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠘⣿⣿⠿⠟⢿⣿⣿⣿⡟⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⢻⣿⣿⣿⣇⣟⣼⢻⡯⠃⣸⣃⡈⢻⠎⠀⢐⠀⠀⢀⠀⠀⠀⠀⢡⣹⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢹⣿⠆⠀⠈⠙⣿⣿⣷⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⠀⢸⣿⣿⣽⠹⡞⡽⣿⠁⠼⠵⠫⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢱⢆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢛⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠚⣄⡀⠀⢀⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢧⣧⣿⡱⣒⠄⡀⣀⠀⠀⠂⠀⠠⠀⠄⠀⠀⠀⠀⠀⣾⣾⡺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠛⣿⣿⡀⠀⠀⠀⠀⠀⠙⠓⣾⣿⣿⣿⣿⠟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⠻⢿⣿⣟⣣⡙⡇⡷⡼⣻⢤⡤⠠⡄⠠⠠⠀⠀⠀⠀⠀⠀⢀⢶⢣⠊⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡯⠀⠀⠀⢩⢿⣦⠀⠀⠀⠀⠀⠀⠈⠉⢀⣞⣣⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣯⢿⡳⢿⡹⣦⡠⠊⠩⠡⠙⠀⠀⠀⡀⠀⠀⣰⣎⡼⢚⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢰⣿⣿⣿⡀⠀⢄⡀⠉⢿⣷⣦⠀⠀⠀⡀⠸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡎⢩⠀⠻⣶⠾⠿⠬⡣⣄⣀⣀⣀⣀⣀⣠⣴⠯⠾⠿⡺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣦⡀⣀⣹⣤⣴⣿⣿⡆⠀⠈⠇⠈⢻⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣇⢨⣴⣷⣤⣽⣿⣛⣋⢥⢞⠟⠋⠛⢟⢦⠍⡙⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣏⠀⠀⠀⠀⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣠⠀⠀⣌⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣦⣤⣤⣀⣷⣿⣿⣿⣿⣿⣿⣷⡅⠈⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⠆⠀⣰⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣠⣆⠀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣈⣶⣶⣮⡛⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠹⡅⠀⣀⡻⠯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣾⣿⣽⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠘⢻⣿⣿⣿⣿⣿⡇⠀⠉⠁⠁⠀⠀⠀⢹⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠉⠻⡟⢿⡿⡻⢿⠉⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠈⣿⢽⣿⣿⢻⣿⠀⠀⠀⠀⣀⣀⡀⢸⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⡿⠿⢿⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠗⠀⠀⠀⠀⢀⢞⣳⣿⣷⣿⡄⠀⠀⠈⣿⣿⣿⣾⣇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⠏⣴⡾⢿⣶⡙⣴⣾⢿⣶⡄⣠⣾⠿⣶⡄⣠⣾⠿⣶⡄⠀⠀⠀⠀⠸⣽⣿⣿⣿⣿⣇⠀⠀⠀⠙⠛⢻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⣴⣿⣿⣿⣿⣿⡄⢛⠃⣼⣿⠃⣿⣿⢸⣿⡇⢛⠛⣰⣿⡏⣛⡛⣰⣿⡟⣤⣤⣴⣶⣾⣯⣤⣿⣿⣿⣿⡀⠀⠀⠀⠀⢰⣿⣿⡿⠃⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣾⣿⣿⣿⣿⣿⣿⡟⢃⣾⣿⢋⡀⣿⣿⢸⣿⡇⠟⣰⣿⠟⣰⡟⣰⣿⠟⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠈⢛⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣾⣿⣥⣤⠀⢿⣿⣼⣿⠇⣼⣿⣯⣤⡄⣼⣿⣯⣤⡌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢸⡿⡗⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠐⠲⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡰⣶⣤⣤⣴⣾⣷⣬⣭⣴⣶⣤⣤⣤⣤⣴⣦⣤⣶⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠉⠀⣡⣤⣄⢻⣿⣿⣿⣿⣿⣿
⠀⢀⣠⣀⣯⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣸⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣟⣿⡿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣿⡿⠟⠸⣿⣿⣿⣿⣿⣿
⠀⠎⣠⠛⠛⠛⢟⣿⣿⣿⣿⣿⣷⣶⣶⣦⣄⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣷⣿⣿⣿⡟⢻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⡻⠁⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣭⣭⡽⢿⣸⣥⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢿⣿⣿⡿⣿⣿
⢿⣿⣿⠿⠄⠀⣾⣿⣿⣿⣿⣿⣿⣿⡷⠀⢀⣁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣧⣤⣀⠀⠀⠀⠀⠗⣂⡐⠂⠉⠉⠀⠈⢉⡙
⣾⣴⠀⠀⠀⢀⣨⡋⢹⠥⣼⣩⣿⡟⢷⣾⣿⣿⣿⣿⣿⣿⣟⠛⠛⠿⢿⣿⡿⢿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠉⠙⢫⠉⠙⠻⡟⠉⠀⠀⣾⣾⣿⣇⣀⣀⣀⣀⣀⠈⠀
⠈⠻⠄⠀⠀⠀⢻⣧⠀⠀⠘⠉⠻⠇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣿⠂⠀⠘⠋⠉⠈⣉⣉⣉⣩⣿⣿⣿⣿⣿⣿⣯⣭⣭⣩⣭⣉⣉⠉⢈⣷⣶⣶⣶⣶⣦⢀⡀⢠⣦⣤⣤⣤⣴⣿⣿⣷⣿⣿⣿⣿⣿⡉⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠉⠁⢋⣠⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⢿⣴⣿⣿⣿⠟⡍⢏⠭⠍⢩⢩⠭⠍⣛⡻⣿⣿⠿⣿⢿
⠀⠆⠲⣶⠎⠶⠄⠰⠲⠶⠆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠈⠉⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠙⠻⠿⠏⠁⣸⣿⣿⣿⣧⡖⠗⡘⠄⠰⠸⠸⢩⡇⠐⠄⠂⠀⠀⠀⠠
[29A⡿⣿⣟⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡏⡕⣣⢥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣭⡿⡹⢀⠁⠴⡧⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠰⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣾⣿⡿⣿⣵⣿⣿⡽⣻⣯⣿⢯⣿⣾⢠⣄⢢⠢⠀⠸⣮⣟⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣦⣤⣀⣬⣽⣻⣿⠿⠟⠙⣿⣿⣅⣀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢿⣿⣿⣾⣟⡟⣧⣫⣾⣿⢽⠃⡄⢲⣴⣲⠀⣦⢦⡤⢀⠀⠀⠀⠱⢾⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠘⣿⣿⡿⠿⢿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⢻⣿⣻⣯⣇⣟⣼⣻⡾⠃⡞⡿⡀⢻⣶⠀⠘⠉⠀⠐⠀⠀⠀⠀⢡⣹⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⠈⠛⣿⣿⣿⣀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⠀⢸⣿⣿⣿⠹⡞⡽⢯⠃⠾⠴⠡⠎⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢰⢱⢇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠊⠻⣇⡀⠀⠀⣾⣿⣿⣿⡏⣶⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣼⢧⣧⣿⠟⢒⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣾⣾⡚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠿⠛⢿⣿⣄⠀⠀⠀⠀⠀⠉⠕⢶⣿⣿⣿⣿⡿⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⠻⢿⣷⣅⢣⡙⡇⡿⡄⠈⠀⠀⠄⠠⠀⠠⠄⠀⠀⠀⠀⠀⢀⢶⢣⢊⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡷⠄⠀⠀⢙⣿⣦⡀⠀⠀⠀⠀⠀⠈⠉⠁⣸⣫⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢰⣏⢿⡳⢷⡱⣶⡐⢀⠀⠀⢐⢈⠀⠈⠘⠀⠀⣴⣎⡾⢚⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢰⣿⣿⣿⡀⠀⢀⠀⠉⢿⣿⣦⡀⠀⠀⡀⠐⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡄⡾⠀⠻⣶⠾⠿⠬⠢⣤⣀⣈⣤⣀⣀⣠⣴⠮⠾⠿⡺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢺⣿⣿⣿⣇⠀⠀⣱⣀⣠⣿⣿⡇⠀⠀⠃⠀⢻⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡇⢢⣤⣷⣤⣝⣿⣛⣉⢥⢞⠟⠋⠛⢟⢦⢍⡙⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠀⠀⠀⠈⠙⠛⣿⣿⣷⣿⣿⣿⣿⣿⣿⣇⣀⣀⠄⠀⢨⢱⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣦⣤⣤⡀⣧⣿⣿⣿⣿⣿⣿⣷⡀⠈⠁⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠆⠀⢠⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣴⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣛⣽⣶⣮⡻⠿⠿⠆⠀⠀⠠⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⡋⠉⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⣿⣿⣿⣿⣿⣿⡇⠀⠙⠂⠉⠀⠀⠀⢹⡏⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠙⠻⡿⢿⠟⣻⠉⠙⠉⠙⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠘⢿⠿⣿⡿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⡿⠿⢿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠷⠦⠆⠀⠀⠀⠀⡩⢺⣿⣷⣿⡆⠀⠀⠀⣿⣿⣷⣤⡇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠏⣴⡾⢿⣶⡉⣴⣾⢿⣶⡄⣠⣾⠿⣶⡄⣠⣾⠿⣶⡄⠀⠀⠀⠀⠠⢰⣿⣿⣿⣿⣇⠀⠀⠀⠙⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣄⢛⠃⣼⣿⠃⣿⣿⢸⣿⡇⢛⠛⣰⣿⡏⣛⡛⣰⣿⡟⣀⣠⣤⣤⣾⣏⣉⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣹⣿⡿⠋⠙⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⡿⢃⣾⣿⢋⠀⣿⣿⢸⣿⡇⠟⣰⣿⠟⣰⡟⣰⣿⠟⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠺⢿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣥⣤⠀⢿⣿⣼⣿⠇⣼⣿⣯⣤⡄⣼⣿⣯⣤⡌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢠⢻⡷⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣱⣦⣤⣤⣴⣾⣷⣬⣭⣴⣶⣦⣤⣤⣤⣴⣶⣴⣶⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠁⣀⣀⣀⢿⣿⣿⣿⣿⣿⣿
⠀⢀⣀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣹⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢺⢿⠟⠘⣿⣿⣿⣿⣿⣿
⠀⠞⢡⠞⠛⠿⠟⣿⣿⣿⣿⣿⣷⣶⣿⣭⣁⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⣾⣿⣿⡿⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣖⣷⣿⣿⣿⠿⣿⡿⣿⣿⣿⣿⣿⣟⡻⡿⠏⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⣛⣛⣿⣿⣹⣧⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣷⣿⣿
⢿⣿⣿⡿⠄⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣧⣤⡀⠀⠀⠀⠀⠄⣀⡀⠔⠁⠋⣀⠀⢙⡛
⣾⣿⠁⠀⠀⢀⣈⡛⢹⡥⣸⣩⣾⣿⢳⣶⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠊⠛⠉⠉⢫⠉⠙⢻⡟⠛⠀⢀⣾⣾⣿⣇⣀⣀⣀⣀⣀⠈⠀
⠈⠻⠄⠀⠀⠀⢻⣧⠀⠀⠙⠉⠻⠇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣇⠠⣶⣿⣿⠃⠀⠝⠋⠉⠉⣉⣉⣉⣉⣿⣿⣿⣿⣿⣿⣟⣍⣉⣉⣭⣉⠋⠉⠉⣧⣤⣤⣶⣶⣄⢀⠀⣠⣤⣤⣤⣤⣬⣿⣿⣷⣿⣿⣿⣿⣿⡉⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠉⠃⠉⣀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣥⣿⣿⣿⠛⡍⢋⠭⠍⢩⢩⠭⠍⣛⡻⣿⣿⠿⣿⢿
⠀⠖⠲⣶⠎⠶⠄⠰⠲⠶⠆⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠈⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠛⠙⢿⠟⠃⢩⣿⣿⣿⣧⡖⠗⡘⠄⠰⠸⠸⢩⡆⠐⠄⠂⠀⠀⠀⠠
[29A⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣅⡝⠈⢀⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣿⣿⣿⣿⢍⣭⣥⣻⠋⠀⠰⡦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠠⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣻⣿⣿⡿⣿⣵⣿⣯⢿⢿⣻⣿⣿⣿⣻⣮⣏⠈⠀⠀⠸⣮⣟⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣦⣀⣀⣌⣙⡿⣿⣿⠿⠛⣿⣿⣏⣀⣀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢿⣿⣿⣿⣿⡟⣧⣫⣞⣿⣏⠎⡄⢲⢶⡶⠀⡶⣶⡦⠀⠀⠀⠀⢱⢾⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢿⣿⡿⠿⢿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⢻⣿⣿⣿⣇⣟⣼⣿⡟⢃⡪⣴⡌⢏⡼⠀⢸⠙⠁⠈⠀⠀⠀⠀⢡⣹⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠸⣿⡷⠀⠀⠙⢿⣿⣿⣀⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⠀⢸⣿⣿⣿⠹⡞⣽⠏⠁⠺⠮⠿⠛⠆⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢱⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠹⠿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠈⠋⣧⡀⠀⠀⣼⣿⣿⣿⡟⣵⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⣿⢧⣧⣿⠫⠶⠀⣀⠀⢠⡤⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⡾⣾⡚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⠿⣿⣿⣇⠀⠀⠀⠀⠀⠈⠛⢶⣿⣿⣿⣿⡿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠉⠻⢿⣿⢿⢧⡙⡇⡷⡔⠤⣀⣤⠤⠠⢤⠄⢀⠀⠀⠀⠀⠀⢀⢾⢣⡊⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣯⠀⠀⠘⠻⣿⣧⡀⠀⠀⠀⠀⠀⠈⠉⠁⣸⣋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣠⡯⢿⡳⢿⡱⣦⣀⡉⠁⡀⠒⠋⢁⠀⠀⠐⠂⣵⣎⡾⢚⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣴⣿⣿⣇⠀⠀⡀⠀⠻⣿⣿⣦⡀⠀⠀⡀⠀⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡏⣱⢀⠹⣶⠾⠿⠬⠪⣤⣈⣈⣌⣀⣈⣠⣴⠮⠾⠿⡺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⣿⣿⣿⣿⣀⠀⠈⣦⣀⣨⣿⣿⡇⠀⠀⠣⠀⠻⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡇⢼⣦⣧⣤⣝⣿⣛⣋⢥⢞⢟⠋⠛⢟⢦⠍⠙⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⡖⠀⠀⠀⠙⠻⢿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣀⣀⠄⠀⢨⢱⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣦⣀⣀⡀⣷⣿⣿⣿⣿⣿⣿⣾⡏⠈⠱⠈⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⠄⠀⣠⣤⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣴⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⣭⣶⣬⡻⠿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠙⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⡏⠉⢀⣘⠯⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢟⣿⣿⣿⣿⣿⣿⡇⠀⠉⠉⠉⠀⠀⠀⢸⡍⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠙⢻⣿⣿⠟⠟⠍⠻⠍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢛⡿⣿⣿⡿⢿⣿⠀⠀⠀⠀⢀⣀⡀⠀⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⡿⠿⠿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠷⠲⠀⠀⠀⠀⠀⣙⢷⣿⣶⣿⡆⠀⠀⠀⣿⣿⣿⣷⣇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠏⣴⡾⢿⣶⡉⣴⣾⢿⣶⡄⣠⣾⠿⣶⡄⣠⣾⠿⣶⡄⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣇⠀⠀⠀⠘⠉⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣄⣛⠃⣼⣿⠃⣿⣿⢸⣿⡇⢛⠛⣰⣿⡏⣛⡛⣰⣿⡟⣀⣀⣀⣤⣤⣎⣛⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣾⣽⣿⠋⠙⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⡿⢃⣾⣿⢋⠀⣿⣿⢸⣿⡇⠟⣰⣿⠟⣰⡟⣰⣿⠟⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠹⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣥⣤⠀⢿⣿⣼⣿⠇⣼⣿⣯⣤⡌⣼⣿⣯⣤⡌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢰⡿⡿⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣳⣦⣤⣦⣴⣾⣷⣬⣭⣴⣶⣦⣤⣤⣤⣴⣶⣶⣶⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠁⣠⣤⣄⢻⣿⣿⣿⣿⣿⣿
⠀⢀⣀⡠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⢿⣿⠟⠘⣿⣿⣿⣿⣿⣿
⠀⢘⢫⠞⠛⠻⠿⣿⣿⣿⣿⣿⣷⣶⣿⣭⣁⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⣿⣿⣿⡿⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⣿⣿⣿⣿⣿⣿
⣞⣿⣿⣿⣿⠿⣿⢿⣿⣿⣿⣿⣿⣟⡻⡿⠅⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣛⣛⣿⡿⣹⣡⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢻⣿⠿⢷⣿⣿
⣿⣿⣿⡿⠄⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⠀⢀⣐⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣧⣤⣀⠀⠀⠀⠀⠕⣂⡀⠖⠉⠃⢀⠀⠙⡛
⣾⣷⠁⠀⠀⢀⣈⡟⢻⡥⣸⣩⣾⣿⢳⣶⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠊⠋⠉⠙⢻⡉⠙⠻⡟⠙⠀⢀⣾⣾⣿⣇⣀⣀⣀⣀⣀⠈⠀
⠈⠿⡄⠀⠀⠀⠿⣧⠀⠀⠙⠙⠻⠇⢐⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣶⣾⣿⠃⠀⠝⠋⠉⠉⣉⣉⣉⣉⣿⣿⣿⣿⣿⣿⣏⣍⣉⣉⣭⣙⠉⠉⢉⣧⣤⣤⣶⣶⣆⢀⠀⣠⣤⣤⣤⣤⣾⣿⣿⣷⣿⣿⣿⣿⣿⡉⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠉⠃⢁⣠⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣥⣾⣿⣷⢛⡍⢋⠭⠍⢩⢩⠭⠌⣛⡻⢿⡿⠿⣿⢿
⠀⠆⠲⣶⠎⠶⠄⠰⠲⠶⠆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠈⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⠛⠛⠿⡟⠋⢸⣿⣿⣿⣧⡖⠗⡘⠄⠰⠸⠸⢩⡆⠐⠄⠂⠀⠀⠀⠠
[29A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣏⣯⠓⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⢀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣽⡿⣿⠯⡿⡿⡤⠅⠲⡦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠴⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣵⡿⣿⣿⣿⡿⣿⣿⣷⣷⠖⢋⠀⠀⠀⠸⣮⣟⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣤⣀⣀⣌⣛⢿⣿⣿⠿⢻⣿⣿⣁⣀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢿⣿⣿⣿⣿⡟⣧⣫⡾⡿⣣⢃⡄⢲⣶⣶⠀⣶⣂⠀⢀⠀⢂⠀⢱⢾⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠘⣿⣿⡿⠿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⢻⣿⣿⣻⣇⣟⣼⣟⡏⠃⣸⣹⠄⢫⡭⠀⠈⠁⠀⠈⠀⠀⠀⠀⢡⣹⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⢹⣿⠆⠀⠈⠛⣿⣿⣷⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⠀⢸⣿⣿⣿⠹⡞⡝⠯⠀⠾⠕⠯⠿⠂⠀⠀⠈⠀⠀⠀⠄⠀⠀⠀⢰⢱⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠚⣀⠀⠀⢀⣿⣿⣿⣿⢧⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢧⣧⣿⠉⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⡚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⠿⣿⣿⡀⠀⠀⠀⠀⠀⠑⠳⣶⣿⣿⣿⣿⠟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠉⠻⢿⣿⣭⣧⡙⡇⡷⡔⠀⠠⠀⠤⡤⠀⠠⠠⠀⠀⠀⠀⠀⢀⢾⢣⠊⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣧⠀⠀⠙⢻⣿⣄⠀⠀⠀⠀⠀⠀⠨⠉⢁⣾⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢰⢯⢿⡳⢿⡱⣦⡂⠀⠀⡀⢀⠄⠀⠀⠀⠈⠊⣼⣎⡼⢚⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣾⣿⣿⡇⠀⠀⠀⠈⢻⣿⣷⣦⠀⠀⢀⠀⢸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡬⠀⠀⠺⣶⠾⠿⠼⠢⣄⣀⣀⣀⣀⣀⣠⣴⠯⠾⠿⡺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢸⣿⣿⣿⣯⡀⠀⢘⣆⣠⣹⣿⣿⡆⠀⠈⠇⠈⢻⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡇⠀⣐⣶⣤⣝⣿⣛⣉⢥⢞⠟⠋⠻⢟⢦⢍⢙⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣴⣶⠂⠀⠀⠀⠙⠛⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣇⣀⣀⠀⠀⣬⢱⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣦⣀⣀⡀⣷⣾⣿⣿⣿⣿⣿⣶⡔⠈⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣧⠀⠀⣤⣦⣦⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣦⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⣭⣷⣬⡻⠿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⡋⠉⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⠈⠁⠉⠁⠀⠀⠀⢹⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠛⢻⡿⡿⡟⡉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⢿⢻⣿⣿⡿⢿⣷⠀⠀⠀⠀⢀⣀⠀⢸⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⠿⠿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠶⠤⠀⠀⠀⠀⠈⢻⣿⣿⣾⣿⡄⠀⠀⠈⣿⣿⣿⣾⣇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠏⣴⡾⢿⣦⡉⣴⣾⢿⣶⡄⣠⣾⠿⣶⡄⣠⣾⠿⣶⡄⠀⠀⠀⠀⠀⣪⣿⣿⣿⣿⣇⠀⠀⠀⠙⠛⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣄⣛⠃⣼⣿⠃⣿⣿⢸⣿⡇⢛⠛⣰⣿⡏⣛⡛⣰⣿⡟⣀⣀⣀⣤⣴⣏⠛⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣽⣿⡿⠋⠙⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⡿⢋⣾⣿⢋⠀⣿⣿⢸⣿⡇⠞⣰⣿⠟⣰⡟⣰⣿⠟⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠺⢿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⣾⣿⣥⣤⠀⢿⣿⣼⣿⠇⣼⣿⣯⣤⡌⣼⣿⣯⣤⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄⠀⠀⠀⠀⠀⢀⣾⡗⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⢷⣤⣤⣦⣴⣾⣶⣬⣭⣴⣶⣦⣤⣤⣤⣴⣶⣶⣶⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠁⠀⣠⣤⣄⢻⣿⣿⣿⣿⣿⣿
⠀⠀⣀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣿⡿⠟⠘⣿⣿⣿⣿⣿⣿
⠀⣞⢵⠛⠛⠿⠿⣿⣿⣿⣿⣿⣷⣶⣾⣭⣁⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣯⣿⣿⣿⡿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣖⣿⣿⣿⣿⠿⡿⠿⣿⣿⣿⣿⣿⣟⡻⡟⠍⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣛⣿⣟⣿⡿⣟⣠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠻⣿⢛⢷⣿⣿
⣿⣿⣿⡿⠄⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡀⠀⠀⠀⠀⠔⣀⡀⠔⠁⠋⢀⠁⠙⡛
⣾⣧⠁⠀⠀⠀⣈⡟⢻⡥⣸⣩⣿⡿⢳⣶⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠈⠋⠉⠙⢫⠉⠙⢿⠛⠙⠀⢀⣶⣾⣿⣇⣀⣀⣀⣀⢀⠈⠁
⠈⠻⡄⠀⠀⠊⢻⣧⠀⠀⠙⠉⠻⠇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣇⠠⣶⣿⣿⠃⠀⠼⠋⠉⠉⣉⣉⣉⣉⣿⣿⣿⣿⣿⣿⣯⣍⣉⣩⣭⣉⠉⠉⢉⣧⣤⣤⣶⣦⣄⠀⠀⣠⣤⣤⣤⣤⣬⣿⣿⣷⣿⣿⣿⣿⣿⡉⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠙⠁⠉⣠⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣥⣾⣿⡿⢟⡍⠛⠭⠍⢩⢩⠭⠍⣛⠻⢿⠿⠿⣿⢿
⠀⠖⠲⣶⠎⠶⠄⠰⠲⠶⠆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠈⠙⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠘⠙⠛⠿⡟⠃⣸⣿⣿⣿⣥⡖⠗⡘⠄⠰⠸⠸⢉⡇⠐⠄⠂⠀⠀⠀⠀
[29A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣝⡉⠉⣒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⡆⣀⠀⡂⠰⡦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠜⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣵⣿⣿⣿⣿⣿⡿⣿⣿⣿⡏⠜⠁⡀⠂⠸⣮⣟⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣤⣶⣂⣀⣀⣘⡻⣿⣿⠿⠛⢻⣿⣿⣤⣀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢿⣿⣿⣿⣯⡟⣧⣫⣾⣿⣾⢏⡄⢶⣶⡲⠀⣒⠂⠀⢀⡀⠀⠀⠱⢾⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠘⣿⣿⠿⠿⢿⣿⣿⣿⡟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⢻⣿⣿⣿⣇⣟⣼⣻⣭⢃⣼⣽⡌⠿⣭⠀⢸⠺⠀⠀⠀⠀⠀⠀⢡⣹⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢸⣿⠆⠀⠈⠛⣿⣿⣿⣀⣬⡿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⠀⢸⣿⣿⢿⠹⡞⡝⠽⠁⠶⠿⠹⠟⠄⠃⠀⠘⠀⠀⠂⠀⠀⠀⠀⢸⢳⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠛⣀⠀⠀⢀⣿⣿⣿⣿⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣽⢧⣧⣿⡹⠶⢄⢀⠀⠠⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⣾⣾⡺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⢻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠙⠳⢶⣿⣿⣿⣿⠟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠉⠻⢿⣿⢟⣧⡙⡇⡿⡭⠕⡠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢶⢣⢊⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣇⠀⠈⠙⣿⣿⣦⡀⠀⠀⠀⠀⠀⠈⠉⢁⣾⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢰⢫⣿⡳⢿⡹⣯⡉⢀⢀⠐⠀⠐⠀⠀⠀⠀⠀⣴⣎⡾⢚⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⣿⣿⣿⡂⠀⠀⠀⠙⢿⣿⣿⣦⠀⠀⠀⡀⠸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣦⠁⠀⠹⣶⠾⠿⠬⠢⣄⣀⣀⣁⣨⣁⣠⣴⠯⠾⠿⡺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⢸⣿⣿⣿⣇⡀⠀⢹⣄⣄⣽⣿⣿⡆⠀⠀⠃⠀⢻⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡆⢰⣢⣦⣤⣝⡿⣛⣋⢥⢞⠟⠋⠻⢟⢦⠍⠙⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣲⣶⣶⠂⠀⠀⠈⠛⠻⢿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣇⣀⡤⡀⠀⣤⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣦⣀⣀⣀⢷⣿⣿⣿⣿⣿⣷⣶⠀⠈⢙⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣄⠀⢀⣤⣤⣤⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣋⣽⣶⣜⠻⠿⠿⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠈⠙⠛⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⡟⢽⠉⠉⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢙⣿⣿⣿⣿⣿⣿⡀⠈⠁⠈⠁⠀⠀⠀⢹⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿
⠙⠛⢿⠿⡿⣟⡩⠉⠁⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠻⠿⡻⣿⣿⢿⣷⠀⠀⠀⠀⠀⠀⠀⠘⡃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⠿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠛⠿⠦⠆⠀⠀⠀⠈⠀⢿⣿⣿⣾⣿⡄⠀⠀⠈⣿⣿⣿⣦⡇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⠏⣴⡾⢿⣶⡉⣴⣾⢿⣶⡄⣠⣾⠿⣶⡄⣠⣾⠿⣶⡄⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣇⠀⠀⠀⠙⠛⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣄⣛⠃⣼⣿⠃⣿⣿⢸⣿⡇⢛⠛⣰⣿⡏⣛⡛⣰⣿⡟⣀⣀⣀⣤⣵⡟⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⣽⣿⡿⠋⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⡿⢋⣾⣿⢋⠀⣿⣿⢸⣿⡇⠜⣰⣿⠟⣰⡟⣰⣿⠟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣾⣿⣥⣤⠀⢿⣿⣼⣿⠇⣼⣿⣯⣤⡌⣼⣿⣯⣤⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡆⠀⠀⠀⠀⠀⢀⣹⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣷⣤⣴⣤⣴⣾⣶⣬⣭⣴⣶⣦⣤⣤⣤⣶⣶⣶⣶⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠉⠀⣠⣤⣔⣻⣿⣿⣿⣿⣿⣿
⠀⠀⣀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⢿⡿⠟⠸⣿⣿⣿⣿⣿⣿
⠀⣚⢽⠟⠛⠿⠿⣿⣿⣿⣿⣿⣷⣶⣿⣯⡁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣭⣿⣿⣿⡿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣶⣶⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣟⠻⠻⠁⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⣻⡿⢟⣿⡟⣟⣠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⡷⣿⣿
⣿⣿⣿⡿⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡷⠀⢀⣐⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡀⠀⠀⠀⠀⢆⣀⡀⠔⠁⠃⠀⠀⠙⡛
⣾⣵⠁⠀⠀⢀⣘⡛⢻⡍⣨⣻⣿⡟⣳⣶⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⠋⠉⠙⢫⠉⠙⢻⠛⠓⠀⢠⣶⣿⣿⣇⣀⣀⣀⡀⡀⠈⠁
⠈⢻⠄⠀⠀⠀⢻⣧⠀⠀⠙⠙⠿⠃⢰⣿⣿⣿⣿⣿⣿⣿⣿⣆⠠⣾⣿⣿⠃⠀⠜⠋⠉⠉⣉⣉⣉⣩⣿⣿⣿⣿⣿⣿⣏⣍⣉⣩⣭⣉⠉⠉⢈⣷⣶⣤⣶⣦⣆⡀⠀⢠⣤⣤⣤⣤⣾⣿⣿⣷⣿⣿⣿⣿⣿⡉⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠉⠃⠁⣠⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⢟⣥⣿⣿⣿⢟⡍⢟⠭⠝⢩⢩⠭⠍⣛⡻⣿⠿⡿⣿⢿
⠀⠖⠲⣶⠈⠶⠄⠰⠲⠶⠆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⠻⠻⡿⠏⠁⣼⣿⣿⣿⣧⡒⠗⠘⠄⠰⠸⠸⢹⡆⠐⠄⠂⠀⠀⠀⠠
[29A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢩⠺⢋⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⢀⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣍⠇⠅⠀⠀⠰⡦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠰⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣵⣿⣿⣿⣿⣟⣿⢿⣞⡿⠕⠟⡀⠀⠀⠸⣮⣟⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣠⣄⣀⣀⡘⠻⣿⣿⡿⠿⠻⣿⣿⣥⣄⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢿⣿⣿⣿⡿⡟⣧⣫⣾⣿⣿⠏⡄⢶⣶⣔⠀⣢⠂⠒⠀⠀⠀⠀⢱⢾⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠐⣿⣿⡿⠿⢿⣿⣿⣿⡟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⢻⣿⣽⣻⣇⣟⣼⣿⣿⢃⣾⣿⡄⢻⣿⠀⠒⠀⠠⠀⠀⠀⠀⠀⢡⣹⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⠈⠙⣿⣿⣿⣀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⠀⢸⣿⣿⣽⠹⡞⣽⣿⠂⠾⠿⠿⠿⠆⠁⠀⠘⠀⠈⠀⠀⠀⠀⠀⢰⢱⢇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠘⠛⣇⡀⠀⢀⣿⣿⣿⣿⡇⣶⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢧⣧⣿⣾⣔⣤⣀⠀⢠⠄⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⣾⣾⡺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⠿⢿⣿⣿⣄⠀⠀⠀⠀⠈⠁⠛⢶⣿⣿⣿⣿⠟⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⠻⢿⣿⣿⢧⡙⡇⡷⣽⡦⠀⠀⠤⠄⠤⠄⠀⠀⠠⠀⠀⠀⢀⢶⢣⢊⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣧⠀⠈⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠁⠉⢁⣼⣫⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠁⠑⣿⣿⡳⢿⡹⣿⡁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣴⣎⡼⢚⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣾⣿⣿⡇⠀⠀⠀⠘⢻⣿⣿⣦⠀⠀⠀⡀⠘⣷⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠥⢃⡈⠹⣶⠾⠿⠬⠢⣅⣁⣐⣀⣀⣀⣠⣴⠯⠾⠿⡺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢘⣿⣿⣿⣯⡀⠀⢘⣆⣀⣽⣿⣿⡇⠀⠀⠃⠀⢻⡍⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡄⡅⣴⣦⣤⣛⢿⣛⣉⢥⢞⠟⠋⠛⢟⢦⠍⠙⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⠂⠀⠀⠀⠙⠛⢿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣇⣀⡠⡄⠀⢠⢱⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣦⣀⣀⣀⣷⣾⣿⣿⣿⣿⣿⣾⡄⠉⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣧⠀⠀⣠⣦⣦⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣻⣷⣶⣼⡻⠿⢿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡋⠉⠀⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣟⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡀⠈⠀⠉⠁⠀⠀⠀⢸⡉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠛⠻⡿⠿⢿⣿⠉⠛⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⠛⢚⣿⣿⣿⣾⣷⠀⠀⠀⠀⢀⣀⡀⠘⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠻⠷⠆⠀⠀⠀⠀⠀⠽⣹⣿⣬⣿⡄⠀⠀⠈⣿⣿⣿⣶⣇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⠏⣴⡾⢿⣦⡉⣴⣾⢿⣶⡄⣠⣾⠿⣶⡄⣠⣾⠿⣶⡄⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣇⠀⠀⠀⠘⠛⢛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣀⣛⠃⣼⣿⠃⣿⣿⢸⣿⡇⢛⠛⣰⣿⡏⣛⡛⣰⣿⡏⣀⣀⣀⣠⣴⡟⠻⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣯⣿⡿⠋⠙⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⡿⢋⣾⣿⢋⠀⣿⣿⢸⣿⡇⠜⣰⣿⠟⣰⡟⣰⣿⠟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠈⢳⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⣾⣿⣥⣤⠀⢿⣿⣼⣿⠇⣼⣿⣯⣤⡌⣼⣿⣯⣤⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄⠀⠀⠀⠀⠀⣰⠽⡗⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢷⣤⣴⣦⣴⣾⣶⣬⣭⣴⣶⣦⣤⣤⣤⣶⣶⣶⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠈⠀⣡⣤⣔⢻⣿⣿⣿⣿⣿⣿
⠀⢀⣀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢿⡿⠟⠸⣿⣿⣿⣿⣿⣿
⠀⣞⣱⠛⠛⠿⠿⣿⣿⣿⣿⣿⣷⣶⣾⣯⡁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣭⣿⣿⣿⡿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣶⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣟⠻⠛⠁⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⣻⠿⠿⣿⡟⣛⢠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡏⣿⣿
⣿⣿⣿⡿⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡷⠀⢀⣁⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣧⣤⣀⠀⠀⠀⠀⢄⣀⡀⠖⠁⠁⠀⠈⠙⣛
⣾⣽⠁⡀⠀⠀⣘⡛⢻⡏⣸⣹⣿⡟⢳⣾⣿⣿⣿⣿⣿⣿⡟⠻⠿⠿⢿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠙⠋⠉⠙⢯⠉⠙⢻⠛⠋⠀⢠⣾⣾⣿⣃⣀⣀⣀⣀⣀⠈⠀
⠙⠻⡄⠀⠀⠀⢿⣧⠀⠀⠙⠉⠻⠇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⣿⣿⡿⠁⠀⠜⠋⠉⠈⣉⣉⣉⣩⣿⣿⣿⣿⣿⣿⣏⣉⣉⣩⣭⣉⠉⠉⢈⣷⣶⣶⣷⣶⣆⡀⣀⣠⣤⣤⣤⣤⣿⣿⣿⣷⣿⣿⣿⣿⣿⡉⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠉⠋⢈⣠⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣵⣿⣿⣿⢟⡝⠋⠭⠝⢩⢩⠭⠍⣛⡻⣿⣿⡿⣿⢿
⠀⠆⠲⣶⠈⠶⠄⠰⠰⠶⠆⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠙⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠙⠻⠿⠿⠁⣼⣿⣿⣿⣧⡖⠗⡘⠄⠰⠸⠸⢩⡆⠐⠄⠂⠀⠀⠀⠠
[29A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣟⡿⠻⢎⠖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣻⣿⣿⣿⣫⠏⠍⢲⠊⠰⡦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠴⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣵⣿⣿⣿⢿⣿⣿⣿⣿⡿⢭⣝⡒⡀⠀⠸⣮⣟⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣄⣀⣘⠛⣿⣿⠿⠟⠻⣿⣿⣤⣄⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢿⣿⣿⣿⣿⡟⣧⣫⣾⣿⣿⢏⡄⢶⣶⣶⠀⠶⣶⡦⠀⡀⠀⡀⢱⢾⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠈⣿⣿⠿⠟⢿⣿⣿⣿⡟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⢻⣿⣿⣿⣇⣟⣼⣻⣿⢃⣾⣷⡄⢛⣿⠀⠨⡿⢡⡚⠂⠀⠀⠀⢡⣹⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⡆⠀⠈⠙⣿⣿⣿⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⠀⢸⣿⡿⣿⠹⡞⣿⣽⠃⠾⠯⠿⠾⠆⠃⠀⠘⠁⠋⠀⠀⠀⠀⠀⢰⢱⢇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠐⠈⠙⣄⡀⠀⢀⣿⣿⣿⣿⡇⣶⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣻⢧⣧⣿⢿⢖⠀⡀⠀⢀⣀⠆⠀⠀⠀⠀⠀⠀⢀⠀⠀⣾⣾⡺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠈⠁⠳⢶⣿⣿⣿⣿⠟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⠻⢿⣿⣿⢧⡙⡇⡿⡕⡱⡥⢄⣤⠄⠠⢠⠠⠀⠀⠀⠀⠁⢀⢶⢣⠊⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡉⠈⠛⢿⣿⣦⡀⠀⠀⠀⠀⠀⠈⠉⢀⣼⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣯⣿⡳⢿⡱⣶⡑⡑⢤⢚⠄⠪⠈⠀⠀⠀⠀⣴⣎⡾⢚⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠀⠀⠀⠈⠻⣿⣿⣦⠀⠀⠀⡀⠘⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡜⣉⡃⢻⣶⠾⠿⠬⠪⣌⣦⣀⣀⣀⣠⣠⣴⠯⠾⠿⡺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⣿⣿⣿⣿⡂⠀⠀⢢⠀⣙⣿⣿⡆⠀⠀⠃⠀⢻⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡖⣡⣠⣮⣤⣿⣿⣛⣋⢥⢞⠟⠋⠻⢟⢦⢍⣙⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣶⠀⠀⠀⠙⠻⢿⣿⣿⣦⣶⣿⣿⣿⣿⣿⣇⣀⡤⠀⠀⢠⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣦⣄⣀⣀⣷⣾⣿⣿⣿⣿⣿⣿⠄⠉⠁⠀⠀⠢⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⣿⡄⠀⢀⣀⣠⣀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢁⣶⠀⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⡿⠿⢿⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠀⠘⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⡋⠉⠀⠘⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⡇⠈⠈⠉⠁⠀⠀⠀⢸⡉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠙⢻⡿⣿⠿⣗⠉⠛⠉⠁⠁⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢛⡯⢿⣿⣿⣿⣷⠀⠀⠀⠀⢀⣀⠀⠘⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠁⠁⠉⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⠿⠿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠶⠶⢤⠀⠀⠀⠀⠀⠫⣫⣿⣮⣿⡄⠀⠀⠈⣿⣿⣿⣦⣇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⠏⣴⡾⢿⣦⡉⣴⣾⢿⣶⡄⣠⣾⠿⣶⡄⣠⣾⠿⣶⡄⠀⠀⠀⠀⠀⣩⣾⣿⣿⣿⣇⠀⠀⠀⠙⠛⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣀⣛⠃⣼⣿⠃⣿⣿⢸⣿⡇⢛⠛⣰⣿⡏⣛⡛⣰⣿⡟⠀⠀⠀⣀⣠⡞⠻⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣷⣿⡿⠋⠹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⡿⢋⣾⣿⢋⠀⣿⣿⢸⣿⡇⠞⣰⣿⠟⣰⡟⣰⣿⠟⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⣾⣿⣥⣤⠀⢿⣿⣼⣿⠇⣼⣿⣯⣤⡌⣼⣿⣯⣤⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄⠀⠀⠀⠀⠀⢐⡿⡗⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢳⣦⣴⣦⣴⣾⣷⣬⣭⣴⣶⣤⣤⣤⣤⣴⣶⣶⣶⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠈⠁⣠⣄⣄⢻⣿⣿⣿⣿⣿⣿
⠀⢀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢿⡿⠏⠸⣿⣿⣿⣿⣿⣿
⠀⢾⣽⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣾⣯⡅⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⡿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣟⠻⠟⠁⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⣻⠿⠿⣿⣿⣛⢁⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⢿⠇⣿⣿
⣿⣿⣿⡿⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡷⠀⢀⣡⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣧⣤⣀⠀⠀⠀⠀⢄⣀⡀⠖⠁⠁⠀⠁⠙⡛
⣾⣧⠁⠀⠀⠀⣘⡛⢿⡅⣸⣩⣿⡟⢳⣾⣿⣿⣿⣿⣿⣿⡟⠛⠿⠿⢿⣿⣿⢿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⠋⠉⠙⢯⠉⠙⢻⠛⠛⠀⢀⣶⣾⣿⣃⣀⣀⣀⣀⣀⠈⠀
⠉⠻⡄⠀⠀⠀⢻⣧⠀⠀⠙⠉⠻⠇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⣿⣿⡿⠃⠀⠘⠋⠉⢈⣉⣉⣉⣩⣿⣿⣿⣿⣿⣿⣯⣭⣍⣩⣭⣉⡉⠉⢈⣷⣶⣶⣶⣶⣆⣠⣀⣠⣦⣤⣤⣴⣾⣿⣿⣷⣿⣿⣿⣿⣿⣉⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠉⠙⢃⣠⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣥⣿⣿⣿⢟⡍⢛⠭⠝⢩⢩⠭⠍⣛⡻⣿⣿⡿⣿⢿
⠀⠖⠲⣶⠎⠶⠄⠰⠲⠶⠆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠙⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⠙⠛⡿⠟⢁⣾⣿⣿⣿⣧⡗⠗⡘⠄⠰⠸⠸⢹⡆⠐⠄⠂⠀⠀⠀⠠
[29A⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣟⡿⢫⠢⢲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣻⣬⠇⠓⡉⢈⡱⡦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠠⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣵⣿⣿⣿⣿⣿⣟⣷⣿⣯⣎⣿⢁⠈⢉⡹⣮⣟⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣤⣤⣀⣈⡙⠻⢿⡿⠿⠛⣿⣿⣥⣀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢿⣿⣿⣿⣿⡟⣧⣫⣾⣿⣿⢏⡄⢲⣶⣶⠀⣶⣶⠶⠀⠐⢐⡀⢳⢾⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⢿⣿⡿⠿⢿⣿⣿⣿⡿⠛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⢻⣿⣿⣿⣇⣟⣼⣿⣿⠃⣾⣿⡄⠛⣿⠀⠒⠾⢡⡂⠂⠀⠀⠀⢡⣹⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠘⣿⡗⠀⠀⠙⢿⣿⣿⡀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⠀⢸⣿⣿⣿⠹⡞⣽⡿⠁⠶⠹⠽⠾⠄⠃⠀⠈⠀⠊⠄⠔⠅⠀⠀⢰⢱⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠘⠛⢣⡀⠀⠀⣼⣿⣿⣿⡏⣴⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣻⢧⣧⣿⠁⠔⣀⢀⢀⣠⢀⠂⠀⠐⠀⠀⠀⠀⠀⡀⠀⣾⣾⡺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡻⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠉⠙⠶⣿⣿⣿⣿⡿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⠻⢿⣿⢟⢣⡙⡇⡿⡵⠪⢤⢄⢤⡄⡠⠀⡀⠀⠀⠀⠀⠀⢀⢾⢣⢊⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡋⠈⠙⢻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠉⠁⣸⣋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠁⣙⣯⣿⡳⢿⡱⣶⡕⢵⣎⠤⠤⢀⠤⢀⠀⡀⠀⣴⣎⡾⢚⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠀⠀⠀⠀⠻⣿⣿⣶⡀⠀⠀⡀⠀⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡉⡓⡋⠻⣶⠾⠿⠬⡪⣆⣁⣚⣀⣃⣄⣠⣴⠯⠾⠿⡺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⣿⣿⣿⣿⡂⠀⠀⢦⠀⠘⣿⣿⡇⠀⠀⠃⠀⠻⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡇⣁⣤⣶⣬⣿⣿⣛⣋⢥⢞⠟⠋⠛⢟⢦⢍⡙⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠀⠀⠀⠻⢿⣿⣿⣿⣤⣶⣾⣿⣿⣿⣿⣇⣀⣤⠄⠀⢠⣱⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣦⣤⣤⣀⣷⣿⣿⣿⣿⣿⣿⣧⠠⠋⠁⡀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡀⠀⠀⣀⣀⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣾⠀⣸⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⣷⣶⣮⡻⠿⠿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠁⠀⠸⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⡋⠉⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⣻⣿⣿⣿⣿⣿⣿⡇⠈⠈⠉⠉⠀⠀⠀⢸⡋⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠙⠻⣿⡿⡿⠟⠙⠻⠋⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠐⠿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢀⠀⠀⠀⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⢶⣤⣄⠀⠀⠀⠀⠉⠹⣻⣿⣮⣿⡄⠀⠀⠈⣿⣿⣿⣦⣇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣇⠀⠀⠀⠙⠛⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣶⣦⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⣀⣠⡚⠹⣿⣿⣿⣿⡀⠀⠀⠀⠀⢐⣿⣿⡿⠋⠙⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⢱⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄⠀⠀⠀⠀⠀⢰⡿⡷⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠐⠶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠉⠁⣠⣤⣤⣻⣿⣿⣿⣿⣿⣿
⠀⢀⣀⣠⣬⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⢿⡿⠿⠘⣿⣿⣿⣿⣿⣿
⠀⢞⣽⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣷⣿⣯⣅⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⡿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣟⡻⡛⠁⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⣻⢿⡿⣿⣿⢻⢁⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢿⣟⣿⣿
⣿⣿⣿⡿⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡷⠀⣀⣁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣧⣤⣀⠀⠀⠀⠀⢤⣀⡠⠖⠉⠃⠀⠀⡙⣛
⣼⣥⠀⠀⠀⠀⣘⡛⢻⡧⣸⣻⣿⡿⢳⣾⣿⣿⣿⣿⣿⣿⡟⠛⠿⠿⢿⣿⣿⢿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⠋⠉⠙⢯⠉⠙⠻⠛⡓⠀⢀⣾⣾⣿⣇⣀⣀⣀⣀⣀⠉⠀
⠘⠻⡄⠀⠀⠈⢿⣧⠀⠀⠙⠉⠻⠇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣇⠨⣿⣿⡿⠁⠀⠘⠋⠉⠈⣉⣉⣉⣩⣿⣿⣿⣿⣿⣿⣯⣭⣭⣩⣭⣉⡉⠉⢈⣷⣶⣶⣶⣶⣆⡠⢀⣠⣦⣤⣤⣤⣾⣿⣿⣷⣿⣿⣿⣿⣿⡉⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠙⠙⢃⣠⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣿⣿⣿⢟⡝⢋⠭⠝⢩⢩⠭⠍⣛⡻⣿⣿⣿⣿⣿
⠀⠖⠲⣶⠊⠶⠄⠰⠲⠶⠆⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠈⠉⠙⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠻⢿⠟⠁⣾⣿⣿⣿⣧⡒⠗⡘⠄⠰⠸⠸⢩⡆⠐⠄⠂⠀⠀⠀⠠
[29A⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⠾⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣯⣃⣏⢁⢠⣰⡶⢎⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠴⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣿⡿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢌⠤⢘⠹⣮⣟⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⣶⣶⣶⣤⣀⣬⣙⣻⢿⠿⠟⠻⣿⣿⣥⣀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢿⣿⣿⣿⣿⡟⣧⣫⣾⣿⣿⠏⠄⢶⣶⣶⠀⢶⡶⠆⠀⠀⠐⠁⢱⢾⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠘⣿⣿⠿⠿⢿⣿⣿⣿⡟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⢻⣿⣿⣿⣇⣟⣼⣿⢿⠋⢾⡿⠄⢿⡿⠀⢈⡒⠡⠒⠱⠀⠄⠀⢡⣹⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢹⣿⠆⠀⠈⠙⣿⣿⣿⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⠀⢸⣿⣿⣿⠹⡞⣽⡿⠁⠼⠿⠽⠿⠂⠃⠀⠈⠁⠆⠀⠀⠀⠀⠀⢨⢱⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠉⠙⣄⡀⠀⢀⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣾⢧⣧⣿⠷⡶⣤⣀⠀⣠⠄⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⣾⣾⡺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠈⠙⠳⢶⣿⣿⣿⣿⠟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⠻⢿⣿⣽⣧⡙⡇⡿⡶⣮⣡⣄⠤⡄⠤⠀⡄⠀⠀⠀⠀⠀⢀⢾⢣⣊⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡋⠈⠛⢿⣿⣦⡀⠀⠀⠀⠀⠀⠉⠉⢁⣼⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠁⢹⣯⣿⡳⢿⡹⣮⡰⡺⠼⠃⠁⠈⠒⠀⠀⠀⠀⣴⣎⡼⢚⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠀⠀⠀⠘⢿⣿⣿⣦⠀⠀⠀⡀⠘⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢬⣳⠅⠹⢶⠾⠿⠬⡢⣅⣀⣤⣀⣀⣀⣠⣽⠯⠾⠿⡺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⠀⣿⣿⣿⣿⠀⠀⠀⢆⠀⠙⣿⣿⡆⠀⠀⠇⠀⢻⡍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡇⣳⣴⣶⣤⣿⣿⣛⣉⢥⢞⡟⠋⠛⢟⢦⢍⣙⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣦⠀⠀⠀⠻⣿⣿⣿⣷⣤⣤⣾⣾⣿⣿⣿⣇⣀⡤⠀⠀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣦⣤⣤⣀⢧⣿⣿⣿⣿⣿⣿⣾⠤⡈⠑⠈⠀⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⢀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢁⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣹⣵⣶⣮⡟⠿⠿⠗⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃⠀⠺⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⡋⠉⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠄⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠉⠉⠉⠀⠀⠀⢹⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠛⠻⠿⡟⣛⠟⠍⠉⠂⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠈⠛⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢀⠀⠀⠘⡂⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡤⣦⣤⣀⠀⠀⠀⠀⠀⢹⣿⣿⣾⣿⡄⠀⠀⠈⣿⣿⣿⣦⣇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠑⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣇⠀⠀⠀⠙⠛⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⣀⣠⡜⠙⣿⣿⣿⣿⡀⠀⠀⠀⠀⢠⣟⣿⡿⠉⠹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⢳⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡄⠀⠀⠀⠀⠀⠸⡿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠐⠶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠈⠀⣠⣤⣔⢻⣿⣿⣿⣿⣿⣿
⠀⢀⣀⣤⣼⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢻⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠠⢿⡿⠟⠸⣿⣿⣿⣿⣿⣿
⠀⣚⣽⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣶⣾⣭⣀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⡿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⣻⣻⣿⣿⣿⣿⣟⣏⡻⠿⠃⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⡻⠿⠿⣿⣿⢻⢁⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⢿⣿⣿⣿
⣿⣿⣿⡿⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡷⠀⣀⣁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣿⣿⣿⣿⣿⣧⣤⣀⠀⠀⠀⠠⠄⣀⡀⠖⠃⠁⠀⠈⢙⣛
⣾⣥⠀⠠⠀⢀⣘⡛⢻⡧⣸⣩⣿⡟⢳⣶⣿⣿⣿⣿⣿⣿⡟⠛⠿⠿⢿⣿⣿⢿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⠋⠉⠙⢭⠉⠙⢿⠛⠓⠀⢀⣶⣾⣿⣃⣀⣀⣀⣀⣀⡉⠀
⠙⢻⡄⠀⠀⠀⢻⣧⠀⠀⠙⠉⠻⠇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⣿⣿⡿⠁⠀⠜⠋⠉⠉⣉⣉⣉⣩⣿⣿⣿⣿⣿⣿⣏⣭⣭⣩⣭⣉⡉⠉⢈⣷⣶⣶⣶⣶⣆⣠⣀⣠⣦⣤⣤⣤⣾⣿⣿⣷⣿⣿⣿⣿⣿⣉⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠋⠉⢈⣠⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣿⣿⣿⠟⡍⢋⠭⠝⢩⢩⠭⠍⣛⡻⣿⡿⣿⣿⢿
⠀⠖⠲⣶⠎⠶⠄⠰⠲⠶⠆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠙⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠛⠛⠿⠟⠁⣼⣿⣿⣿⣧⣒⠗⡘⠄⠰⠸⠸⢹⡆⠐⠄⠂⠀⠀⠀⠀
[29A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠯⡃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣻⣿⣿⣿⣿⣻⣂⠂⠠⠱⡦⢅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠴⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣎⢯⡷⢽⡖⣻⢺⣮⣟⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣴⣴⣤⣀⣨⣙⣻⣿⠿⠟⠻⣿⣿⣥⣀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢿⣿⣿⣿⣿⡟⣧⣫⣾⣿⣿⢏⡄⠶⡶⣢⠀⠦⠒⠒⠀⠐⠄⡂⢱⢼⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠘⣿⣿⠿⠟⢿⣿⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⢻⣿⣿⣿⣇⣟⣼⢿⣿⢃⣾⢿⡌⢛⢞⠀⢨⡋⠁⠞⠷⠈⠂⠀⢡⣹⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⠈⠙⣿⣿⣿⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⠀⢸⣿⣿⣿⠹⡞⣽⡻⠡⠾⠿⠿⠯⠄⠉⠀⠀⠀⠐⠠⠁⠀⠀⠀⢰⢳⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⢿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠙⠛⣄⡀⠀⢀⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢿⢧⣧⣿⣿⣔⣄⡀⠀⠠⠰⠃⠀⠀⠂⠀⠀⠀⠀⠀⠀⣾⣾⡺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠈⠁⠓⣶⣿⣿⣿⣿⠟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⠻⢿⣿⣿⣧⡙⡇⡿⡿⠿⢥⡠⣤⣤⡤⣄⠤⠀⠀⠀⠀⠀⢀⢾⢣⣊⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡏⠀⠛⢻⣿⣦⡀⠀⠀⠀⠀⠀⠈⠉⢁⣼⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡘⡻⣿⡳⢿⡹⣯⣀⠱⠾⠢⠍⠡⠀⠐⠀⠀⠀⣴⣎⡾⢚⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠀⠀⠀⠀⠻⣿⣿⣦⠀⠀⠀⠀⠘⣷⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⠁⠇⠹⢶⠿⠿⠬⠢⣄⣀⣀⣀⣈⣀⣠⣴⠯⠾⠿⡺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⢿⣿⣿⣿⠀⠀⠀⢦⠀⠘⣿⣿⡇⠀⠀⠇⠀⢻⡍⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡇⣑⣴⣦⣤⣽⣿⣛⣉⢥⢞⠟⠋⠻⣟⢦⢍⣙⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣶⠀⠀⠀⠙⢿⣿⣿⣿⣤⣤⣿⣿⣿⣿⣿⣇⣀⡤⠀⠀⣤⣱⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣦⣤⣤⣀⣷⣿⣿⣿⣿⣿⣿⣶⠄⡈⠅⠐⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⡀⠀⢀⣀⣀⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣦⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣮⡻⠿⠿⢗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠁⠀⠚⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡋⠉⠀⢙⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⡇⠈⠈⠉⠁⠀⠀⠀⢸⡉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠙⠻⡿⡟⢿⠍⠍⠉⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠹⢿⣿⣿⡿⣿⣷⠀⠀⠀⠀⠀⢀⠀⠘⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢶⣦⡀⠀⠀⠀⠀⠀⠑⢯⣷⣾⣿⡄⠀⠀⠀⣿⣿⣿⣦⣇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣇⠀⠀⠀⠙⠛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⣀⣠⡘⠉⣿⣿⣿⣿⡀⠀⠀⠀⠀⠠⣿⣿⡿⠋⠙⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢣⣾⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄⠀⠀⠀⠀⠀⢘⡿⡗⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠐⠲⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠈⠀⣠⣤⣔⢻⣿⣿⣿⣿⣿⣿
⠀⢀⣀⢤⣾⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠠⢿⡿⠏⠸⣿⣿⣿⣿⣿⣿
⠀⣚⣿⠛⠛⠛⠿⣻⣿⣿⣿⣿⣿⣿⣾⣯⣄⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣏⣿⣿⣿⡿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣻⣿⣟⣏⡻⡛⠁⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⠿⣿⣿⣿⣿⠿⢁⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡿⢿⣟⣿⣿
⣿⣿⣿⡿⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⡷⠀⢀⣩⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣧⣤⣀⠀⠀⠀⠠⢄⣀⠠⠒⠁⠁⠀⠈⢉⣛
⣾⣥⠀⠀⠀⢀⣘⡛⢻⡇⣸⣹⣿⡿⢳⣾⣿⣿⣿⣿⣿⣿⡟⠛⠛⠿⢿⣿⡿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⠛⠉⠙⢯⠉⠙⠻⠛⠛⠀⠀⣶⣾⣿⣃⣀⣈⣀⣀⣀⠈⠀
⠙⠿⡄⠀⠀⠈⢻⣧⠀⠀⠙⠉⠻⠇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣇⠠⣿⣿⡿⠁⠀⠜⠋⠉⢈⣉⣉⣉⣩⣿⣿⣿⣿⣿⣿⣯⣭⣭⣩⣭⣉⣉⠉⢈⣷⣶⣶⣶⣶⣆⣠⢀⣠⣦⣤⣤⣤⣾⣿⣿⣷⣿⣿⣿⣿⣿⣉⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠉⠁⢀⣠⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣤⣿⣷⣿⢟⡍⢏⠭⠝⢩⢩⠭⠍⣛⡻⣿⣿⡿⣿⢿
⠀⠆⠲⣶⠎⠶⠄⠰⠲⠶⠆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠙⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠙⠛⢻⠟⠡⣾⣿⣿⣿⣧⡒⠗⡘⠄⠰⠸⠸⢩⡆⠐⠄⠂⠀⠀⠀⠠
[29A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢻⠾⢂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣱⣨⢎⠲⡧⢌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠰⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⢮⣏⣟⢛⣳⢗⠸⣮⣟⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣴⣶⣤⣀⣨⣙⣻⣿⠿⠟⠙⣿⣿⣤⣄⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢿⣿⣿⣿⣿⡟⣧⣫⣾⣿⣿⢍⡄⢶⡦⣰⠀⢶⣦⡖⢀⡀⠝⡀⢱⢾⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠈⣿⣿⠿⠛⢿⣿⣿⣿⡟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⢻⣿⣿⣿⣇⣟⣼⣿⣿⢃⣾⢿⡌⢓⡿⠀⢼⡻⠁⢅⠱⠈⠀⠀⢡⣹⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⠈⠙⣿⣿⣿⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⠀⢸⣿⣿⣿⠹⡞⡿⡯⠣⠾⠿⠿⠿⠆⠃⠀⠀⠁⠖⠀⠀⠁⠀⠀⢰⢱⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠈⠛⣧⡀⠀⢀⣿⣿⣿⣿⡇⣶⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣾⢧⣧⣿⡿⣰⢠⣀⠀⡀⢴⠆⠀⠐⠀⠀⠀⠀⠀⠀⠀⣾⣾⡺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠈⠁⠑⣶⣿⣿⣿⣿⠟⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⠻⢿⣿⢯⢧⡙⡇⡿⡽⠷⢤⢤⢄⡠⠀⠀⠀⠀⠀⠀⠀⠀⢀⢶⢣⣊⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡟⠉⠛⢿⣿⣦⡀⠀⠀⠀⠀⠀⠉⠉⢁⣼⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⡳⢿⡹⣯⡄⠒⠨⡇⠀⠐⢴⠀⠀⠂⠀⣴⣎⡾⢚⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡍⠀⠀⠀⠻⣿⣿⣦⠀⠀⠀⠀⠐⣷⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠘⡁⠓⠹⣶⠾⠿⠼⠢⣎⣀⣀⣀⣀⣠⣠⣼⠯⠾⠿⡺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⢸⣿⣿⣿⡇⠀⠀⢢⡀⠘⣿⣿⡇⠀⠀⠇⠀⢻⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡇⣑⣤⣴⣤⣽⣿⣛⣋⢥⢞⢟⠫⠻⢟⢦⢍⢙⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⠂⠀⠀⠘⠿⣿⣿⣿⣦⣴⣾⣿⣿⣿⣿⣧⣀⣤⠀⠀⢠⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣶⣤⣤⣀⢷⣿⣿⣿⣿⣿⣿⣿⣄⠈⠁⠈⠀⠈⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣄⠀⠀⣀⣀⡀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⣠⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣮⡛⠿⠿⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠘⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡟⠛⠀⢛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠉⠁⠀⠀⠀⢸⡉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠙⠛⡿⡿⣿⡿⠭⠉⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣟⣿⣿⣿⣿⣷⠀⠀⠀⠀⢀⣀⠀⠈⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⢶⣦⡄⠀⠀⠀⠀⠀⠘⣋⣧⣬⣿⡀⠀⠀⠈⣿⣿⣿⣦⣇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣇⠀⠀⠀⠙⠛⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⢀⣠⡘⠉⣿⣿⣿⣿⡀⠀⠀⠀⠀⠨⣶⣿⡿⠉⠙⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢻⣼⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄⠀⠀⠀⠀⠀⢘⡿⡗⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠐⠲⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠁⠀⣠⣤⣔⢻⣿⣿⣿⣿⣿⣿
⠀⢀⡀⢴⣴⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢿⡿⠟⠸⣿⣿⣿⣿⣿⣿
⠀⣟⣟⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣷⣮⣄⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣏⣿⣿⣿⡿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣟⡻⡛⠁⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⠿⣿⣿⣿⡿⡻⢁⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢿⡷⣿⣿
⣿⣿⣿⠿⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⡷⠀⣀⣨⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣵⣿⣿⣿⣿⣿⣧⣤⣀⠀⠀⠀⠠⢄⣀⡠⠒⠉⠃⢀⠀⢉⣙
⣾⣧⠀⠠⠀⢀⣸⡟⠻⡧⣼⣹⣿⡟⢳⣾⣿⣿⣿⣿⣿⣿⡟⠛⠛⠻⢿⣿⡿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠙⠋⠉⠉⢯⠉⠙⢻⠛⠫⠀⢠⣾⣾⣿⣃⣀⣈⣀⣀⣀⡈⠀
⠙⠿⠄⠀⠀⠈⢻⣧⠀⠀⠘⠈⠻⠇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣿⠁⠀⠜⠉⠁⢈⣉⣉⣉⣭⣿⣿⣿⣿⣿⣿⣯⣭⣭⣩⣭⣉⣉⠁⢈⣷⣶⣶⣿⣶⣆⠠⣀⣠⣧⣤⣤⣤⣾⣿⣿⣷⣿⣿⣿⣿⣿⣉⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠉⠉⢉⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣄⣿⣿⣿⢛⡍⠋⠭⠝⢩⢩⠭⠍⣛⡻⣿⡿⡿⣿⣿
⠀⠆⠲⣶⠎⠶⠄⠰⠲⠶⠆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠿⠟⠁⣺⣿⣿⣿⣧⣒⠗⡘⠄⠰⠸⠸⢹⡆⠐⠄⠂⠀⠀⠀⠠
[29A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠧⠕⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⡄⠵⠶⡦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠴⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠿⡖⢥⠦⢸⣮⣟⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣶⣶⣄⣀⣬⣙⣻⣿⠿⠟⠙⣿⣿⣤⣄⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢿⣿⣿⣿⣿⡟⣷⣫⣾⣿⣿⠏⡄⢶⣶⣶⠀⣶⢶⡶⢀⠘⣎⠄⢱⢾⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠈⣿⣿⠿⠛⢿⣿⣿⣿⡟⠋⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⢻⣿⣿⣿⣇⣟⣼⣿⣿⢃⣾⣻⡌⢓⣿⠀⠨⠉⠀⡊⠵⠈⠀⠀⢡⣹⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⠈⠙⣿⣿⣿⣀⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⠀⢸⣿⣿⣿⠹⡞⣽⢾⠢⠾⠽⠿⠿⠆⠋⠀⠀⠀⠀⠁⠀⠄⠀⠀⢸⢱⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⡿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠈⠛⣧⡀⠀⢀⣿⣿⣿⣿⡇⣶⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢧⣧⣿⢿⡃⣠⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⡺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠉⠙⢾⣿⣿⣿⣿⠟⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⠻⢿⣿⣿⢧⡙⡇⡷⡜⢞⢠⡤⢄⡤⢄⠄⠀⠀⠀⠀⠀⠀⢀⢶⢣⣊⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡏⠉⠛⢿⣿⣦⡀⠀⠀⠀⠀⠀⠁⠉⢀⣼⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⡳⢿⡹⣶⣑⣿⣽⡕⡚⣍⠂⠤⢀⢄⠀⣴⣎⡾⢚⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡏⠀⠀⠀⠻⣿⣿⣦⡀⠀⠀⡀⠐⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡞⡚⠟⠹⢶⠾⠿⠬⡪⣖⣧⣄⣈⣄⣀⣼⣵⠯⠾⠿⡺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⢸⣿⣿⣿⡇⠀⠀⢢⡀⠈⣿⣿⡇⠀⠀⠇⠀⢻⡍⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡅⢁⣤⣶⣤⣽⣿⣛⣉⢥⢞⢟⡫⡻⢟⢦⢍⡙⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⣶⡆⠀⠀⠘⢿⣿⣿⣿⣦⣤⣼⣷⣾⣿⣿⣧⣀⣤⠀⠀⣠⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣦⣤⣤⣀⢷⣿⣿⣿⣿⣿⣿⣿⡀⠉⢅⠂⠈⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡄⠀⠀⣀⣀⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⣠⠀⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣮⡟⠿⠿⠷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠃⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣟⠛⠀⠘⠯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣦⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠹⣿⣿⣿⣿⣿⣿⡏⠀⠈⠉⠁⠀⠀⠀⢸⡉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠙⠛⡿⡿⣿⡿⠅⠙⠉⠁⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠙⣛⣿⣿⣿⣿⣷⠀⠀⠀⠀⣀⣀⡀⠈⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⢴⣦⣀⠀⠀⠀⠀⠀⠘⣫⣧⣬⣿⡀⠀⠀⠈⣿⣿⣿⣦⣇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠀⠀⠀⠀⠀⢄⣼⣿⣿⣿⣇⠀⠀⠀⠙⠛⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⢀⣀⠈⠛⣿⣿⣿⣿⡀⠀⠀⠀⠀⢨⣿⣿⡿⠉⠙⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢡⣻⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄⠀⠀⠀⠀⠀⢘⡿⡗⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠐⠲⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠈⠀⢠⣄⣄⢻⣿⣿⣿⣿⣿⣿
⠀⢀⡀⢤⣶⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢿⡿⠟⠸⣿⣿⣿⣿⣿⣿
⢀⣝⣻⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣷⣯⣄⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢻⣫⣿⣿⣿⣿⣿⣭⡛⠛⠁⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣻⠿⠿⣿⣿⠻⢁⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⡿⣿⣿
⣿⣿⣿⠿⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⡷⠀⣀⣭⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣧⣤⣀⡀⠀⠀⠀⢄⣀⡰⠒⠁⠋⠀⡈⢉⡙
⣾⣦⠀⠀⠀⢀⣸⡟⠻⡧⣸⣱⣿⡿⢳⣾⣿⣿⣿⣿⣿⣿⣟⠛⠛⠻⢿⣿⡿⠿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠉⠉⢩⠉⠙⠿⠋⡙⠀⢀⣾⣾⣿⣃⣀⣈⣀⣀⣀⡉⠀
⠘⢻⢄⠀⠀⠈⢻⣷⠀⠀⠘⠈⠻⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣿⣿⣿⠁⠀⠘⠉⠀⢀⣉⣭⣭⣭⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣍⣉⠁⢀⣷⣶⣶⣶⣶⣦⡠⣀⣠⣦⣤⣤⣤⣾⣿⣿⣷⣿⣿⣿⣿⣿⣉⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠉⠉⢁⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⢟⡍⢏⠭⠝⢩⢩⠭⠍⣛⡻⢿⣿⡿⣿⢿
⠀⠆⠲⣶⠎⠶⠄⠰⠰⠶⠆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠈⠉⠉⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⠛⠛⠿⠟⠁⣾⣿⣿⣿⣧⡒⠗⡘⠄⠰⠸⠸⢹⡆⠐⠄⠂⠀⠀⠀⠠
[29A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣻⠇⠖⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⢀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣅⢀⠱⡦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠰⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣾⡵⢷⣏⠈⢕⠸⣮⣟⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⣶⣦⣠⣬⣙⣻⣿⠿⠟⠛⣿⣿⣤⣄⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢿⣿⣿⣿⣿⡟⣧⣫⣾⣿⣿⢇⡄⢶⡶⣶⠀⢖⣶⡦⠀⠀⠈⠀⢱⢾⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣿⣿⠿⠛⢿⣿⣿⣿⡟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⢻⣿⣿⣿⣇⣟⣼⣿⣿⢃⣾⢿⡌⢫⣝⠀⢹⡉⠁⢂⡂⠀⠈⠀⢡⣹⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠙⢿⣿⣿⣀⣌⡿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⠀⢸⣿⣿⣿⠹⡞⣽⢯⠣⠾⠿⠾⠿⠆⠋⠀⠀⠀⠀⠈⠀⠄⠀⠀⢰⢱⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠈⠛⣆⡀⠀⢀⣾⣿⣿⣿⡇⣶⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢧⣧⣿⡯⡃⢀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⡺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠈⠉⠙⢶⣿⣿⣿⣿⠟⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⠻⢿⣿⢿⣧⡙⡇⡿⣜⣈⠠⣄⢄⠤⣠⡀⠀⠀⠀⠀⠀⠀⢀⢶⢣⢊⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣏⠉⠛⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠉⢀⣼⣫⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠁⢹⡯⢿⡳⢿⡹⣾⡱⡱⠫⠔⠋⠀⠁⠠⠄⡀⠀⣴⣎⡾⢚⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡏⠀⠀⠈⠻⣿⣿⣦⡀⠀⠀⡀⠐⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠨⣡⠀⢻⢶⠾⠿⠼⡢⣍⣀⣀⣀⣀⣐⣰⣴⠯⠾⠿⡺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⢸⣿⣿⣿⡇⠀⠀⠠⡀⠈⣻⣿⡇⠀⠀⠃⠀⢹⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡆⣐⣴⣦⣤⣽⣿⣛⣉⢥⢞⢟⠋⠻⢟⢦⢍⣙⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣴⡖⠀⠀⠘⢿⣿⣿⣿⣦⣤⣼⣷⣾⣿⣿⣧⣀⣤⠀⠀⣠⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣶⣤⣤⣀⢷⣿⣿⣿⣿⣿⣿⣿⣔⠈⠁⠆⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⢀⣀⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢰⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣮⡟⠿⠿⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠀⠐⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠀⠘⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⡟⠈⠈⠉⠁⠀⠀⠀⢸⡉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⠛⡟⡿⣿⠋⠉⠉⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠙⡿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⣀⡀⠘⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⢶⣤⣀⠀⠀⠀⠀⠀⠈⢋⣵⣬⣿⡄⠀⠀⠈⣿⣿⣿⣦⣇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣯⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠠⣼⣿⣿⣿⣇⠀⠀⠀⠙⠛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⢀⣀⡈⠋⣿⣿⣿⣿⡀⠀⠀⠀⠀⠸⣽⣿⡿⠉⠙⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡅⠀⠀⠀⠀⠀⢰⡽⡗⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠉⠀⣠⣤⣄⢻⣿⣿⣿⣿⣿⣿
⠀⢀⣠⣤⣧⣽⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠠⢿⡿⠟⠸⣿⣿⣿⣿⣿⣿
⢀⢙⣿⠛⠙⠛⠛⣿⣿⣿⣿⣿⣿⣷⣷⣯⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⡿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣭⡛⠛⠃⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣝⡿⠿⣿⣿⢻⢃⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣿⣿
⢿⣿⣿⠿⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⡷⠀⣀⣬⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣧⣤⣀⠀⠀⠀⠀⢤⣀⡀⠖⠁⠉⠀⠈⣉⣙
⣾⣷⠀⠀⠀⢀⣨⡟⢻⠇⣸⣱⣿⡿⢳⣾⣿⣿⣿⣿⣿⣿⣟⠛⠛⠻⢿⣿⡿⠿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠉⠉⢯⠉⠙⢿⠋⡛⠀⢠⣾⣾⣿⣃⣀⣈⣀⣀⣀⡈⠀
⠘⠻⣄⠀⠀⠈⢻⣷⠀⠀⠘⠈⠻⠇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⡿⠁⠀⠘⠉⠀⢀⣉⣉⣩⣭⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣉⣉⠁⢀⣷⣶⣶⣶⣶⣆⣠⣀⣠⣦⣤⣤⣤⣾⣿⣿⣷⣿⣿⣿⣿⣿⣁⠋⠇
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠉⠈⠐⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣵⣿⣿⣿⢟⡍⠋⠭⠝⢩⢩⠭⠍⣛⡻⣿⣿⡿⣿⢿
⠀⠆⠲⣶⠎⠶⠄⠰⠰⠶⠆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠈⠉⠉⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⠛⠛⠻⠟⠡⣾⣿⣿⣿⣧⡒⠗⡘⠄⠰⠸⠸⢩⡆⠑⠄⠂⠀⠀⠀⠠
䷩ 𝚕𝚒𝚗𝚎 1825
╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕
(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/06/video-about-the-42th-part/#comments
Gemini version at gemini://gemini.techrights.org/2022/02/06/video-about-the-42th-part/
⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.06.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧
Gemini_version_available_♊︎
✐ Europe_Has_a_Severe_Corruption_Crisis⠀✐
Posted in Europe, Fraud, Patents at 9:52 am by Dr. Roy Schestowitz
Video_download_link | md5sum a0124575f46bf3da906f214b3726f0d2
EPO as Magnet of Corruption
Creative Commons Attribution-No Derivative Works 4.0
http://techrights.org/videos/epo-corruption-complex.webm
Summary: Whilst a lot of the so-called ‘media’ or so-called ‘news’ sites which
are focused on patent issues (also the press at large) choose to ignore EPO
corruption this growing epidemic spreads and is being ‘normalised’, not only in
Europe but internationally (it’s a pandemic of crime); this vacuum in reporting
and much-needed transparency is the rationale for this series, amongst others
Part XXXXII of the ongoing_series was released last night at around midnight,
as usual. With a projection of about 50 parts in total we’re already looking at
a series as long as a 200-page book and it tells the story of unprecedented
corruption in European patent offices; it concerns Europe’s largest ever-patent
office, the EPO.
“Are we being governed by criminals?”The EPO has had issues for a long time,
culminating in the occasional strike or protest. But during the Benoît
Battistelli years the level of criminality soared in the management tiers;
António_Campinos is more of the same, mostly plundering staff and even
pensioners. Set aside the effect/impact on ordinary Europeans and scientists
all across the world.
The video above goes through the latest part and instead of reading through it
I try to interject some of my personal thoughts or my personal interpretation
of this dire situation. When Europe’s second-largest institution acts in bad
faith and intentionally_breaks_laws it’s already bad. That Europe’s largest
institution (EU/EC/EP) lets that happen and even_covers_up_the_abuses is even
worse. Are we being governed by criminals?
“I feel that many of us,” said an EPO insider quite recently, “not just
employees of the EPO, need truth and transparency. I am very optimistic at one
thing: the public will be aware of the scandals in the EPO, many of my
colleagues have retired with a “big file” containing confidential documents, a
kind of insurance against bullying from the Office. At the end, truth will
emerge.” █
䷩ 𝚕𝚒𝚗𝚎 1891
╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕
⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.06.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧
Gemini_version_available_♊︎
✐ Links_6/2/2022:_Inkscape_1.1.2_and_GNU_Guile-SDL_0.6.0⠀✐
Posted in News_Roundup at 3:18 am by Dr. Roy Schestowitz
🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈
§ Contents⠀➾
* GNU/Linux
o Distributions
o Devices/Embedded
* Free_Software/Open_Source
* Leftovers
* § GNU/Linux⠀➾
o § Desktop/Laptop⠀➾
# ⚓ IDC:_tablet_and_Chromebook_shipments_grew_in_2021,_but
things_are_slowing_down_–_GSMArena.com_news [Ed: IDC is
Microsoft_mouthpiece]⠀⇛
2020 was a banner year for tablets with record
shipments in the fourth quarter. This was driven by
the surge of people who work or study at home due
to the pandemic. Now with the pandemic easing off,
shipments are slowing down as well, according to
data from the IDC.
2021 was still positive for manufacturers as total
shipments went up 3.2% for the full year, reaching
a total of 168.8 million. That’s the most slates
shipped since 2016. However, the final quarter of
the year made it clear that the demand is past its
peak.
In Q4 2021 tablet shipments were down to 46 million
units, the first decline since the pandemic began.
Also, almost all manufacturers in the Top 5 posted
negative year-over-year growth (all but Amazon,
which is essentially level with a 1.3% rise).
o § Applications⠀➾
# ⚓ Inkscape_1.1.2,_1.2_alpha_released,_About_Screen_Contest
and_Other_Exciting_News!⠀⇛
You’ll be pleased to hear that we are releasing a
bugfix version which solves nearly 60 issues and
improves translations for 15 languages!
This release includes many crash fixes and resolves
issues with a number of broken extensions. Download
Inkscape 1.1.2 now for a smoother experience.
# ⚓ Best_Whiteboard_Applications_for_Linux_Systems⠀⇛
We will show you a couple of whiteboard
applications for Linux systems. I am sure these are
going to be super beneficial for you. Read on.
o § Instructionals/Technical⠀➾
# ⚓ How_to_Install_Slack_on_Linux:_An_Easy-to-Follow_Guide⠀⇛
This guide will show you how to easily install the
Slack application on both Ubuntu and Debian, as
well as RedHat-based distributions such as
AlmaLinux, Rocky Linux, and Fedora.
# ⚓ How_to_Create_a_Network_Proxy_Using_Stream_Processor_Pipy⠀⇛
# ⚓ How_to_Install_ZoneMinder_on_Ubuntu_22.04_|_20.04_LTS⠀⇛
Zoneminder is a free and open-source surveillance
camera management software available for Linux
only. Here we will learn the steps to install
ZoneMinder on Ubuntu 20.04 Focal Fossa or Ubuntu
22.04 Jammy JellyFish.
# ⚓ How_to_install_Lightworks_Video_Editor_on_your_Chromebook⠀⇛
As crazy as it may sound, it has been more than
four years since we unearthed the container project
that would eventually be responsible for bringing
Linux to Chromebooks. It has also given us new
tools such as Windows on Chrome OS thanks to the
efforts of Parallels. When Google first announced
Linux on Chromebooks and the ability to leverage
the integrated GPUs on Chrome OS devices, my
thoughts immediately went to video editing.
# ⚓ How_to_install_GNOME_Desktop_Environment_on_Debian_11_|
FOSS_Linux⠀⇛
Debian 11 comes with loads of great features for
casual and advanced users. Some of these great
features that make Debian 11 so attractive are its
stability, security, support for many
architectures, a great deal of support from the
community, and support for multiple Desktop
Environments like GNOME, Cinnamon, Xfce, etcetera.
It is ideal for servers as well.
With that said, there is no denying that GNOME is
one of the most versatile desktop environments that
Debian supports. It is very stable and has tons of
customizability options so that you can tweak it to
your liking. But still, if you are over the fence
about whether you should try the GNOME desktop
environment (DE) or not, you can check out this
great article that explains in detail ten reasons
why the GNOME DE rocks.
o § Games⠀➾
# ⚓ Steam_Deck_already_has_more_than_100_verified_and_playable
games [Ed: Thousands of games would work OK, but just haven't
been officially verified yet]⠀⇛
Valve officially announced its first portable
gaming console, the Steam Deck in July, 2021. The
company promised that the console would be able to
run AAA titles, mainly games that are already
available to be played on PC. The company also
recently confirmed that devices would start
shipping out to customers by the end of February.
Valve also launched a Steam Deck Verified program
that aimed at testing already existing and future
games on the Steam Deck, to ensure that they are
playable. Each individually tested game receives a
score at the end, which will help gamers know
whether their favorite games are supported by
default, or if they’re unspotted for various
reasons.
# ⚓ Valve_has_over_100_playable_games_for_the_Steam_Deck⠀⇛
Valve has tested over 100 games that will work with
the upcoming Steam Deck. From the 106 total games
that will work, 60 are verified to the highest
compatibility – meaning the controller
configuration and glyphs will match, the interface
is legible and that performance is good.
There are further 41 games that are playable, which
means that depending on the game, some tweaking
will be needed to make the game work as intended.
5 games were deemed unsupported, but 4 of those are
VR games, which naturally won’t work on the Steam
Deck.
# ⚓ Valve_Just_Made_Steam_Deck’s_Secret_Weapon_Even_Better⠀⇛
Valve’s Steam Deck begins shipping out to early
adopters at the end of February. And some of you
lucky Deck owners might feel tempted to switch over
to Windows for 100% game compatibility. But Valve
has an awesome (and proven) secret weapon to keep
you on Deck’s default OS. The Arch Linux-based
SteamOS 3.0 now has AMD FSR built in. Here’s why
that’s a big deal.
# ⚓ New_York_Times_outlays_seven-figure_sum_for_1,900_lines_of
JavaScript_–_yes,_we_mean_Wordle⠀⇛
Viral online puzzle game Wordle has been acquired
by The New York Times Company (NYTCo), publisher of
The New York Times.
The game requires players to guess a five-letter
word within six turns – a task made easier by
Wordle offering clues that players have chosen
letters used in the word, and whether or not they
are in the right position. Gameplay is similar to
codebreaking pegboard game Mastermind, but with 26
different “pegs” – and of course the answer has to
be an English word. A single puzzle is offered
daily.
o § Distributions⠀➾
# § New Releases⠀➾
# ⚓ What’s_New_in_elementary_OS_6.1_and_Should_You
Switch?⠀⇛
The new elementary OS 6.1, codenamed “Jólnir”
comes packed with a bunch of new features and
updates. Here’s everything you need to know.
elementary OS is a modern-day Linux distro
with a slew of innovative features and a
gorgeous user interface. It targets users who
are coming from either macOS or Windows
background. But users of traditional Linux
systems will also find elementary OS
appealing, thanks to its redefined desktop
environment and sleek design language.
The developers have recently released
elementary OS 6.1, dubbed Jólnir. It’s the
first point release in the 6 series and
succeeds elementary OS 6, Odin.
# § IBM/Red Hat/Fedora⠀➾
# ⚓ Clemson_partners_with_IBM_and_AgStack_to_aid_global
food_access [Ed: Openwashing and greenwashing of IBM,
sponsored by IBM itself with help from LF, its front
group]⠀⇛
# ⚓ For_IBM,_AI_Inference_Is_The_Most_Important_HPC [Ed:
Timothy Prickett Morgan really is an IBM-sponsored PR
machine; and he's not disclosing the funding source of
the puff pieces]⠀⇛
All of the commercial platform creators in
the world, since the dawn of time, which
arguably started in the enterprise in April
1964 with the advent of the System/360
mainframe, wants the same things. They want
to create a flexible, integrated, and useful
system where data can be stored and
applications run against it or create the
starting data, and one that provides the
maximum value to customers while at the same
time allowing them to extract the maximum
value out of customers.
# ⚓ IBM_Preconfigures_Power_System_Racks_Running_Oracle
Database [Ed: Timothy Prickett Morgan still doing IBM
puff pieces without disclosing IBM pays him to do
this...]⠀⇛
# ⚓ A_Complete_Rethinking_Of_Server_Virtualization
Hypervisors⠀⇛
# § Debian Family⠀➾
# ⚓ Raspberry_Pi_OS_Is_Now_Available_In_Glorious_64-bit_–
Review_Geek⠀⇛
After a year of beta testing, a stable
version of the 64-bit version of Raspberry Pi
OS is finally available. This long-awaited
operating system increases software
compatibility for closed-sourced
applications, which are often exclusive to
ARM64. Additionally, 64-bit Pi OS should
improve benchmark performance (not
necessarily real-world performance) thanks to
its improved instruction set.
# ⚓ Raspberry_Pi_OS_now_available_in_64-bit,_improving
app_compatibility⠀⇛
The Raspberry Pi series of single-board
computers has been a runaway success over the
years, thanks to its fantastic versatility
and low cost. From powering DIY electronics
projects to functioning as cheap PCs for
learning programming, the Raspberry Pi series
can do it all, and now another significant
upgrade has arrived: a 64-bit version of the
default operating system.
There are a few different operating systems
available for Pi boards, including a few
attempts at Android, but the default
operating system that most people go with is
Raspberry Pi OS. Previously known as
Raspbian, it’s a Debian-based Linux desktop
specifically built for the Pi family. Even
though some newer Pi computers have 64-bit
ARM CPUs, Raspberry Pi OS has remained only
32-bit, except for beta builds.
Raspberry Pi said in a blog post (via Ars
Technica), “we have continued to build our
Raspberry Pi OS releases on the 32-bit
Raspbian platform, aiming to maximise
compatibility between devices and to avoid
customer confusion. […] But we’ve come to
realise that there are reasons to choose a
64-bit operating system over a 32-bit one.
Compatibility is a key concern: many closed-
source applications are only available for
arm64, and open-source ones aren’t fully
optimised for the armhf port. Beyond that
there are some performance benefits intrinsic
to the A64 instruction set: today, these are
most visible in benchmarks, but the
assumption is that these will feed through
into real-world application performance in
the future.”
# ⚓ Raspberry_Pi:_New_‘glorious’_64-bit_operating_system
is_available_to_install_|_ZDNet⠀⇛
“Over the past year, we’ve been trialling a
beta of Raspberry Pi OS in glorious 64-bit.
Now it’s time to open it up to a wider
audience,” said Raspberry Pi’s Gordon
Hollingworth.
He said application compatibility is a “key
concern” behind the decision to choose a 64-
bit OS over a 32-bit one.
“Many closed-source applications are only
available for arm64, and open-source ones
aren’t fully optimised for the armhf port,”
explains Hollingworth, referring to the
Debian/Raspbian armfh ports.
He adds that there are some performance
benefits “intrinsic” to the A64 Armv8
instruction set. Today, these gains can
mostly be seen in benchmarks, but
Hollingworth believes they will become real-
world application performance enhancements in
the future.
Another “theoretical concern” was that 32-bit
pointers only allow users to address 4GB of
memory, which wasn’t optimal given developers
could use up to 8GB of RAM on the Pi 4.
However, as Hollingworth notes, few use cases
today require all 8GB of addressable memory
from a single process.
o § Devices/Embedded⠀➾
# § Open Hardware/Modding⠀➾
# ⚓ Raspberry_Pi_vs._Arduino:_Which_is_best_for_you?_|
Android_Central⠀⇛
So you’ve decided to buy a small single-board
computer to use in your great idea. There are
plenty to choose from, but the two most
popular platforms are Raspberry Pi and
Arduino. There are plenty of reasons why they
are popular, but the two biggest are price
and ease of use. Both are cheap and have a
small learning curve, so you can spend time
designing the rest of your project instead of
learning how to use an SBC (single-board
computer). Each has a huge community of
helpful users if you get stuck, too.
You might be thinking that the two are
interchangeable and you can buy whichever you
want from Amazon, but that’s not the case at
all. While you can do some of the same things
with either board, they’re unique and have
plenty of differences. The one you need
really depends on what you want to do with
it.
# § Mobile Systems/Mobile Applications⠀➾
# ⚓ Test_15_different_PinePhone_operating_systems_with
Megi’s_latest_multi-distro_demo_image_–_Liliputing⠀⇛
Trying out different operating systems on the
PinePhone is as simple as flashing a bootable
disk image to a microSD card, inserting it in
the phone, and powering it on and the
instructions for installing an OS to built-in
storage are almost as simple.
Not sure which operating system you want to
install though? That’s where a tool like
Megi’s multi-distro demo image can come in
handy. Instead of flashing a single operating
system to a microSD card, this image lets you
flash a whole bunch and then choose which one
you want to run when you boot your phone. The
latest version was released a few days ago,
and it contains 15 different operating
systems including Arch, Fedora, Mobian,
Sailfish, Ubuntu Touch and several different
versions of postmarketOS and Manjaro with
different user interfaces.
o § Free, Libre, and Open Source Software⠀➾
# ⚓ TriggerMesh,_Case_Study_in_Open_Sourcing_Enterprise
Software [Ed: "TriggerMesh is a sponsor of The New Stack."
Read as: this is a paid-for puff piece disguised as
"journalism"...]⠀⇛
# ⚓ Snowflake,_AWS_Warm_Up_to_Apache_Iceberg⠀⇛
Apache Iceberg emerged as an open source project in
2018 to address longstanding concerns in Apache
Hive tables surrounding the correctness and
consistency of the data. Hive was originally built
as a distributed SQL store for Hadoop, but in many
cases, companies continue to use Hive as a
metastore, even though they have stopped using it
as a data warehouse.
# § Web Browsers⠀➾
# ⚓ The_inside_story_of_the_browser_wars,_told_by_a
veteran_|_TechRadar⠀⇛
The story of Brendan Eich is in many ways the
story of the evolution of the internet and
the technologies we use to access it. It is
also a story of battles won, lost and soon to
play out.
Eich is best known as the creator of
programming language JavaScript, which he
developed over a sleepless period of ten days
in 1995. At the time, he was working for
Netscape, whose web browser dominated the
market before Internet Explorer spoiled the
party.
Recognizing that Netscape had lost its way,
Eich spun out another project he had been
working on, leading to the formation of the
Mozilla Foundation. The organization went on
to pioneer the concept of browser extensions
with Firefox, which quickly became a
household name, before it was crushed under
the weight of Google Chrome.
# § FSF⠀➾
# § GNU Projects⠀➾
# ⚓ GNU_Guile-SDL_0.6.0_available⠀⇛
release notes:
Lots of love this time. Shout out to
all technical writers!
Please see also the (currently wip,
it may have finished by the time
you read this) "Hooray!" series:
.
README excerpt:
Guile-SDL is a set of modules that
provide bindings for various
Simple DirectMedia Layer (http://
www.libsdl.org) libraries.
Most of the SDL functions are
wrapped, with the exception of a
few functions that are too C-centric.
The SDL threads, audio
and network functions are not
included. However, there are
(optionally configured) bindings for
SDL_mixer and SDL_ttf.
Also included is SDL_gfx 2.0.26 (by
Andreas Schiffler) source
code (ZLIB license) and bindings for
it.
This is alpha code (pre 1.0 release),
tested with various,
but not all, versions of Guile and
SDL. It may have bugs,
and the interfaces may change from
version to version.
NEWS for 0.6.0 (2022-02-05):
- bugfix: avoid range error in image
filter procedures
Procedures ‘imfi-add-c’ and ‘imfi-
sub-c’ used to convert 3rd arg
‘c’ (constant) from Scheme to C
using a signed integer function
that would signal range error for
large values. This is now
fixed to use an unsigned integer
function to do the job.
- intermittent crash fix reverted
The fix in Guile-SDL 0.5.3 (2021-
12-11) was not The Right Thing.
It has been reverted and a better
solution put in place. We now
initialize the ‘event-thread’
subsystem in test/cursor.scm. AHA
moment: .
- embedded SDL_gfx upgraded to
version 2.0.26
This brings bugfixes and MMX
support for x86_64 (amd64),
primarily. Now, "cd test && make
check TESTS=gfx.scm" really
flies!
NB: The license for SDL_gfx is now
the zlib license. See
src/SDL_gfx/LICENSE in the
distribution for the new text.
- ‘(sdl gfx) fps-manager-delay!’ can
have meaningful rv
The embedded SDL_gfx is currently
at version 2.0.26, but the
previous version was 2.0.22, and
its function that underlies
‘fps-manager-delay!’ did not have a
meaningful return value.
Previously, if you configured w/ ‘-
-disable-embedded-gfx’ and
built w/ SDL_gfx 2.0.24 or later
(that DOES have a meaningful
rv), such ignorance was foisted
upon you. Now, you are free to
fully enjoy that sweet rv. :-D
- changes to to ‘(sdl gfx) blit-rgba’
- accepts ‘#f’ for 2nd, 4th arg
The 2nd and 4th args to ‘blit-
rgba’ indicate the source and
destination rectangles,
respectively. Previously, they were
required to be fully specified.
Now, you can use ‘#f’ there to
indicate the entire (source/
destination) surface.
- return value more informative
Previously, ‘blit-rgba’ returned
‘#f’ if there were problems and
‘#t’ if not. However, "no
problem" was narrowly interpreted and
missed a certain common case -
- upshot is that it incorrectly
returned ‘#f’ even in that case.
Now, if there were no problems,
it returns an integer: 1 if a
blit was performed, 0 otherwise.
(If there were problems, it
returns ‘#f’ as before -- use
‘get-error’ to get more info.)
- new proc: ‘(sdl misc-utils) exact-
floor’
Actually, this is an old proc that
was misguidedly deleted in
2011 to make room for ‘exact-
truncate’. Both are useful in
their own right, it is now evident.
Live and learn.
- new proc: ‘(sdl sdl) must-lock?’
This wraps the convenience C macro
‘SDL_MUSTLOCK’. Useful (in
conjunction w/ ‘lock-surface’ and
‘unlock-surface’) for avoiding
segfaults when examining pixel data
from RLE-enabled surfaces.
- new proc: ‘(sdl gfx) multiply-
pixel-alpha!’
This multiples the alpha channel in
a 32-bit surface by FACTOR
(actually, FACTOR/256). The
underlying function has been
available in SDL_gfx since version
2.0.21, so this is a bit of
a late bloomer. Still, more alpha
blending for everyone!
- new proc: ‘(sdl gfx) fps-manager-
count’
This returns the frame count (i.e.,
how many times
‘fps-manager-delay!’ was called)
for an FPS manager.
Another late bloomer (again, since
SDL_gfx 2.0.21).
- documentation improvements
- external representations
described
The manual now includes a
description of the external
representation of these object
types:
Pixel Format
Rectangle
Color
Surface
Joystick
CDROM Drive
FPS Manager
Types with a standard (non-
custom, Guile-generated) external
representation are not
documented.
By the way, the Surface external
representation now also
includes "L" to indicate that the
surface is locked.
- image filtering procedures
general behavior documented
The manual now sports three
paragraphs describing commonalities
of the ‘imfi-*’ procedures, as
well as the special processing
done by ‘imfi-add-c’, ‘imfi-sub-
c’, ‘imfi-lshr’, ‘imfi-lshl’.
- say "byte", not "nybble"
The documentation for ‘surface-
pixels’ was simply wrong (but it
sounded groovy for a while to
Some Fool, probably).
- bootstrap/maintenance tools
upgraded:
Guile-BAUX 20211208.0839.a5245e7
GNU gnulib 2022-01-27 07:00:41
as before:
GNU Libtool 2.4.6
GNU Autoconf 2.71
GNU Automake 1.16.5
GNU Texinfo 6.8
tarballs and detached signatures:
https://ftpmirror.gnu.org/guile-sdl/
guile-sdl-0.6.0.tar.lz
https://ftpmirror.gnu.org/guile-sdl/
guile-sdl-0.6.0.tar.lz.sig
source code:
https://git.savannah.gnu.org/cgit/
guile-sdl.git/?h=p
homepage:
https://www.gnu.org/software/guile-sdl/
* § Leftovers⠀➾
o ⚓ China_reveals_draft_deepfake_regulations_that_restrict_use_•_The
Register⠀⇛
The Chinese government has unveiled a draft law clamping
down on deepfakes – the practice of using AI to adapt
existing digital content into realistic simulations of
humans.
The draft emerged last Friday from the Cyberspace
Administration of China and frames the need for
regulation in the context of the government’s desire to
ensure the internet is a tool for good and not the
wretched hive of scum and villainy it has often become.
The explanatory memorandum for the policy suggests
criminals and fraudsters will be attracted to using
digitally created voice, video, chatbots, or manipulation
of faces or gestures. The draft therefore rules out the
use of such fakes for any application that could disrupt
social order, infringe individuals’ rights, deliver fake
news, or depict sexual activity. It also proposes
requiring a grant of permission for use of what China
calls “deep synthesis” before it can be employed for
legitimate uses.
o § Science⠀➾
# ⚓ Streptococcal_pyrogenic_exotoxin_B_cleaves_GSDMA_and
triggers_pyroptosis_|_Nature⠀⇛
Gasdermins, a family of five pore-forming proteins
(GSDMA–GSDME) in humans expressed predominantly in
the skin, mucosa and immune sentinel cells, are key
executioners of inflammatory cell death
(pyroptosis), which recruits immune cells to
infection sites and promotes protective immunity.
o § Hardware⠀➾
# ⚓ Chip_shortage_has_NXP_in_driver’s_seat_•_The_Register⠀⇛
Chip shortages are so bad that customers are
willing to sign multiyear non-cancellable, non-
returnable (NCNR) contracts to secure supplies,
according to semiconductor supplier NXP.
Buyers want to have clear visibility on their
component orders, and “want to have it longer,”
said NXP CEO Kurt Sievers during an earnings call
this week, adding customers “would love to have
NCNRs for two years out.”
This is a symptom of the across-the-board
electronics shortages in sectors including
industrial and automotive, which have “very sticky
products, very long life cycles, so it fits the
nature of those industries,” Sievers said.
NXP isn’t alone in this. Analyst house IC Insights
reported NCNR policies are increasingly becoming
popular for chip manufacturers for those worried
about losing supplies.
o § Health/Nutrition/Agriculture⠀➾
# ⚓ Academic_performance_and_attitudes_of_dental_students
impacted_by_COVID-19⠀⇛
Previous studies only focused on attitudes and
behaviors of US dental students without examining
direct effects of the COVID-19 pandemic on academic
performance. This study examined effects of COVID-
19 pandemic on dental students’ academic
performance, self-reported attitudes, behavior, and
service utilization. We hypothesized that the
pandemic provided more beneficial learning
environments.
# ⚓ Top_strategies_and_tools_to_prevent_employee_isolation⠀⇛
Feelings of isolation and loneliness are growing as
employees continue to work from home.
[...]
Loneliness directly impacts physical health and can
lead to issues such as high blood pressure and
obesity, which can in turn increase an
organization’s overall healthcare costs, said Darcy
Gruttadaro, director of the American Psychiatric
Association Foundation’s Center for Workplace
Mental Health, located in Washington, D.C. The
organization educates employers about how to
support their workers’ well-being.
# ⚓ Work_From_Home_Or_Anywhere:_Top_30_Companies_For_Remote
Jobs_In_2022⠀⇛
Even before the pandemic uprooted everything in
2020, more and more people had been ditching the 9-
5 to work remotely and travel the world. But in
2020, only 5% of remote jobs could be done from
anywhere. Fast forward to 2022 and it’s a whole new
world, where remote working is not only a dream,
it’s a reality.
# ⚓ HDD_Centrifuge_Puts_COVID-19_Testing_Lab_In_A_Backpack_|
Hackaday⠀⇛
Throughout this two-year global COVID-19 nightmare,
one thing that has been sorely lacking is access to
testing. “Flu-like symptoms” covers a lot of
ground, and knowing if a sore throat is just a sore
throat or something more is important enough that
we’ve collectively plowed billions into testing.
Unfortunately, the testing infrastructure remains
unevenly distributed, which is a problem this
backpack SARS-CoV-2 testing lab aims to address.
The portable lab, developed by [E. Emily Lin] and
colleagues at the Queen Mary University of London,
uses a technique called LAMP, for loop-mediated
isothermal amplification. LAMP probably deserves an
article of its own to explain the process, but
suffice it to say that like PCR, LAMP amplifies
nucleic acid sequences, but does so without the
need for expensive thermal cycling equipment. The
kit contains a microcentrifuge that’s fashioned
from an e-waste hard drive, a 3D printed rotor, and
an Arduino to drive the motor and control the
speed. The centrifuge is designed to run on any 12
VDC source, meaning the lab can be powered by a car
battery or solar panel if necessary. Readout relies
on the trusty Mark I eyeball and a pH-indicating
buffer that changes color depending on how much
SARS-CoV-2 virus was in the sample.
o § Integrity/Availability⠀➾
# § Proprietary⠀➾
# § Security⠀➾
# ⚓ Open-source_Kubernetes_tool_Argo_CD_has_high-
severity_flaw_•_The_Register⠀⇛
A zero-day vulnerability in open-source
Kubernetes development tool Argo lets
malicious people steal passwords from
git-crypt and other sensitive
information by simply uploading a
crafted Helm chart.
Charts are the actual packaging format
of ubiquitous tool-for-managing-
Kubernetes applications Helm.
The vuln, tracked as CVE-2022-24438,
exists in Argo CD, a widely used open-
source continuous delivery tool for
Kubernetes. Patched versions available
from the project’s maintainers are
2.19, 2.2.4 and 2.3.0.
“It is possible to craft special Helm
chart packages containing value files
that are actually symbolic links,
pointing to arbitrary files outside the
repository’s root directory,” said a
member of the Argo project in a
security advisory about the flaw.
# ⚓ 12_CISO_resolutions_for_2022⠀⇛
It’s still early days, but if this year
is anything like years past, it’s safe
to say CISOs will have a lot to contend
with, from a continuing labor shortage
to the increasing sophistication of
cyberattacks to an ongoing threat from
nation-state actors.
# ⚓ Critical_Samba_Remote_Code_Execution_Flaw
Fixed⠀⇛
Samba has patched a vulnerability that
could enable remote, unauthenticated
attackers to execute arbitrary code as
root on impacted installations.
Samba is an interoperability software
suite that implements the Server
Message Block (SMB) networking
protocol, which provides file and print
services. It allows network
administrators to configure and set up
equipment as a domain controller (DC)
or domain member, and to communicate
with Windows-based clients. Samba runs
on many Unix or Unix-like systems like
Linux, as well as macOS and other
operating systems that use the SMB
protocol.
# ⚓ EU_launches_bug_bounty_programs_for_five_open
source_solutions⠀⇛
This time around, the list of software
that should be probed for weaknesses
includes:
LibreOffice – a free office suite
Mastodon – free and open-source
software for running self-hosted social
networking services
Odoo – a suite of business management
software
Cryptpad – a browser-based encrypted
open-source collaboration platform that
allows people to work together online
on documents, spreadsheets, and other
types of documents
LEOS is a software tool for drafting
and editing legislation, which is used
by European Commission, Parliament,
Council and several member states
# ⚓ Crypto_outfit_Qubit_appeals_to_the_honour_of
thieves_who_lifted_$80M_of_its_digi-dollars⠀⇛
Another week, another crypto upstart
admitting its lax security has been
exploited and parties unknown have made
off with millions. But this time
there’s a twist: the crypto upstart has
appealed for the return of its assets
by appealing to the thieves’
consciences.
The crypto concern is Qubit Finance –
an outfit that offers decentralized
lending and borrowing and operates
under the motto “Lend to ascend –
Borrow for tomorrow.”
# ⚓ Targeted_ransomware_takes_aim_at_QNAP_NAS
drives,_warns_vendor:_Get_your_updates_done
pronto⠀⇛
QNAP has urged NAS users to act
“immediately” to install its latest
updates and enable security protections
after warning that product-specific
ransomware called Deadbolt is targeting
users’ boxen.
“DeadBolt has been widely targeting all
NAS exposed to the internet without any
protection and encrypting users’ data
for Bitcoin ransom,” warned the
Taiwanese company in a statement late
yesterday.
# ⚓ Alpha-Omega_Project_takes_a_human-centered
approach_to_open-source_software_security_|_CSO
Online⠀⇛
The Log4j vulnerability crisis that
erupted in late-2021 heightened the
security world’s awareness of supply
chain risks in free and universally
deployed open-source software.
Following an intense holiday season
push by admins and cybersecurity
professionals to track and remediate
the Log4j flaw, the White House held a
meeting of industry leaders to discuss
improving open source software
security.
# ⚓ SnapFuzz:_New_fuzzing_tool_speeds_up_testing_of
network_applications_|_The_Daily_Swig⠀⇛
An open source fuzzing tool developed
by researchers at the Software
Reliability Group of Imperial College
London aims to solve some of the thorny
problems of testing network
applications.
SnapFuzz uses a series of techniques to
speed up the testing of network
protocols and overcome the timin
constraints and other limitations that
make it difficult to fuzz networking
applications.
While SnapFuzz is still in its early
stages, it shows promising results and
its developers hope it will soon become
a mainstay in the toolbox for testing
networking applications.
# ⚓ The_Apache_Log4j_team_talks_about_the_Log4Shell
patching_process_–_The_Record_by_Recorded
Future⠀⇛
On December 9, 2021, the internet
learned of a major security bug in a
little-known Java library named Apache
Log4j. This little bug—codenamed
Log4Shell—had one of the most
significant impacts on the software
landscape and triggered one of the most
massive and well-coordinated patching
drives in the recent history of the
internet.
For the past month, government
agencies, security firms, and IT
experts alike have all worked together
to audit Java-based applications, find
which were vulnerable to Log4Shell
attacks, worked with vendors to deliver
patches, and then encouraged their
customers to apply them as soon as
possible.
# ⚓ Whistleblower_claims_NSO_offered_‘bags_of_cash’
for_access_to_US_phone_networks⠀⇛
A whistleblower’s allegations about
spyware maker NSO Group should be
investigated by American prosecutors,
US House Rep Ted Lieu (D-CA) has said.
The informant claimed senior NSO
executives offered “bags of cash” to
California-based telecoms security and
monitoring outfit Mobileum to assist in
its surveillance work, according to the
Washington Post on Tuesday.
Specifically, it’s alleged NSO wanted
to gain, with Mobileum’s help,
Signaling System 7-level access to US
cellular networks, a position that can
be abused to determine a cellphone’s
location, redirect and read its
incoming text messages, snoop on calls,
and more. SS7 is the glue between
telecommunications providers, and
subverting it opens up a wealth of
opportunities for spies and miscreants.
Gerry Miller, who spent over six years
at Mobileum and rose to veep of network
security and client solutions, claimed
that in August 2017, when asked how
Mobileum would get paid, NSO co-founder
Omri Lavie said: “We drop bags of cash
at your office.”
# ⚓ A_tale_of_command_line_booby_traps_and_bored
engineers_•_The_Register⠀⇛
Take a trip back to when mainframes and
terminals were all the rage and The
Cloud was the smoke produced by the
mainframe when a washing-machine-sized
disk was about to let go. Welcome to
another Who, Me? confession.
Today’s plea for forgiveness comes from
a reader Regomised as “Doug” and is a
warning to careless administrators.
“Back in the days when terminals were
still fairly common,” said Doug, “the
company I worked for provided ‘local’
data based on the result of a search
run on the client’s main dataset held
on their server.”
“We could telnet from these terminals
to our box – and frequently had to in
the early days,” he recalled. The
client itself was nationally known in
back then and had spanked millions
getting this remote site up and
running.
Things were going swimmingly. Right up
until a month after go-live when Doug
and a pal were stuck at the client site
on a Friday evening. The client’s own
engineer had long gone, and Doug was
finishing up the last checks to allow a
weekly backup to kick off.
He ambled up to a darkened terminal
near the server room and tapped the
return key to bring it to life. The
prompt was odd, something he’d not seen
before. Tappity tap: whoami
# § Privacy/Surveillance⠀➾
# ⚓ How_Covid_stole_our_privacy_–_UnHerd⠀⇛
As soon as I turn on my phone, it
becomes a node in a network,
giving me access to the entire
world. But it also gives Apple
access to information about me
and my behaviour; I become
another source in their vast
banks of data.
So, as Stephanie Hare rightly
points out in Technology Is Not
Neutral, it’s never just an
object. Technology is as much
social as scientific, as much
economics as engineering. There’s
little point in Silicon Valley
companies hiring an ethicist to
decide a product’s value — its
effects go far beyond the shiny
thing that comes out of the box.
# ⚓ Utopia_P2P:_Internet_with_Privacy_Upgrade
–_TheGWW.com⠀⇛
Privacy is the modern internet’s
foundational issue.
# ⚓ Doubts_over_Facebook’s_ability_to
innovate_as_it_sees_first-ever_fall_in_user
numbers⠀⇛
# ⚓ UK’s_new_Brexit_Freedom_Bill_promises
already-slated_GDPR_reform,_easier_gene
editing_rules⠀⇛
The UK government is having a
second pass at flogging the
benefits of Brexit, as much as
they exist, in a new bill that
promises to accelerate work on AI
and gene editing.
The so-called Brexit Freedoms
Bill — its actual title will be
decided by Parliamentary clerks —
will also offer a “more agile way
to regulate new digital markets
and AI and [create] a more
proportionate and less burdensome
data rights regime compared to
the EU’s General Data Protection
Directive.”
The bill promises to make it
easier to amend or remove
“retained EU law” which was left
in place following the UK’s
departure from the political and
trading bloc.
o § Defence/Aggression⠀➾
# ⚓ Opinion:_UCLA_must_investigate_holdings_for_ties_to_Uyghur
genocide_–_Daily_Bruin⠀⇛
As the Uyghur genocide continues to unfold, our
institutions don’t deserve the benefit of the
doubt.
The Uyghurs are a predominantly Muslim ethnic
minority that live in the autonomous region of
Xinjiang. The Chinese government, under the
semblance of counterterrorism, seeks to deprive
Uyghurs of their religious and cultural identities.
Many human rights organizations have documented the
mass internment, torture and religious persecution
of Uyghurs at the hands of the Chinese government.
Other allegations include forced labor,
sterilization and reeducation – all amounting to
the official label of genocide according to the
U.S. Department of State.
# ⚓ UK_to_splash_another_£1.4bn_on_protecting_non-existent
‘national_interests_in_space’⠀⇛
The UK government is to spend an extra £1.4bn on
space defence on top of the £5bn allocated to
upgrade the Skynet satellite communication system.
The Defence Space Strategy, intended to “bolster
our national interests in space,” according to the
UK’s Ministry of Defence, was accompanied by a
speech from Chief of the Air Staff Sir Mike Wigston
in which the usual bogeymen were trotted out.
“Russia and China have tested anti-satellite
weapons creating debris fields that will linger for
decades,” warned Wigston, adding: “Russian
satellites continually make close approaches to
other satellites, what we call rendezvous and
proximity operations, possibly an indication of
espionage activity, or possibly rehearsing
something much more sinister.”
o § Environment⠀➾
# § Energy⠀➾
# ⚓ UK_government_told_to_tighten_purse_strings_or_public
will_have_to_foot_the_bill_for_nuclear
decommissioning⠀⇛
The UK government is being warned that
taxpayers will have to make up a
multibillion-pound shortfall to decommission
nuclear power stations unless a history of
overspending is reversed.
French firm EDF Energy runs seven Advanced
Gas-cooled Reactor (AGR) stations in the UK,
part of eight second-generation reactors set
to be decommissioned which provide 16 per
cent of the nation’s electricity. The AGR
stations are scheduled to stop producing
electricity by 2028.
Last year the government injected £5.1bn into
the Nuclear Liabilities Fund – now valued a
£14.8bn – which it set up in 1996 to meet the
costs of decommissioning AGR and Pressurised
Water Reactor stations.
o § Finance⠀➾
# ⚓ No,_Linus_Torvalds_is_not_Bitcoin_Creator_Satoshi_Nakamoto
[Ed: Feeding clickbait with more clickbait]⠀⇛
# ⚓ India_to_adopt_digital_rupee_and_slap_a_30_per_cent_tax_on
cryptocurrency_income⠀⇛
India’s government has ordered its Reserve Bank to
have a digital rupee into circulation by next year,
and outlined plans to raise revenue with a 30 per
cent income tax on cryptocurrency and non-fungible
tokens.
The two plans were announced yesterday by finance
minister Nirmala Sitharaman as she revealed the
nation’s budget for 2022.
The crypto tax is the first item listed in a
section of the budget memo headed “Revenue
Mobilization”. The document [PDF] explains that
India wants to tax income from crypto-assets at a
30 per cent flat rate.
By comparison, India currently taxes short-term
capital gains made by selling shares at 15 per
cent. The budget memo also calls for a one per cent
tax on sales of cryptographic assets, payable by
parties to the transaction, to widen India’s tax
base.
o § AstroTurf/Lobbying/Politics⠀➾
# ⚓ Gaming_Twitter’s_Trending_Algorithm_To_Make_A_Point_|
Hackaday⠀⇛
If you have ever taken to Twitter to gauge the
zeitgeist, you’ll have noticed that among the
trending hashtags related to major events of the
day there are sometimes outliers of minority
interest associated with single-issue causes. When
a cause with a distasteful pedigree was cited one
as proof of widespread public support in a debate
in the UK’s House of Lords there were concerns
raised that a flaw in the ranking algorithm might
be responsible, and it was left to [Mallory Moore]
to prove the hypothesis by getting a
#ThisIsAnExploit hashtag trending without a
groundswell of popular support.
o § Censorship/Free Speech⠀➾
# ⚓ The_EARN_IT_Act_is_back_to_attack_Section_230_protections_•
The_Register⠀⇛
The EARN IT Act, a legislative bill intended “to
encourage the tech industry to take online child
sexual exploitation seriously” has been revived in
the US Senate after it died in committee back in
2020.
And advocacy groups have once again decried the
bill for threatening free speech and access to
encryption, and for imperiling the liability
protection that allows online service providers to
host third-party content. In other words, the
bill’s reception has been much the same as it was
two years ago.
US Senators Lindsey Graham (R-SC) and Richard
Blumenthal (D-CT) on Tuesday reintroduced the bill
[PDF] claiming that online service providers are
disinterested in keeping child sexual abuse
material (CSAM) off their platforms.
o § Internet Policy/Net Neutrality⠀➾
# ⚓ The_Internet_Is_Just_Investment_Banking_Now⠀⇛
The internet has always financialized our lives.
Web3 just makes that explicit.
Twitter has begun allowing its users to showcase
NFTs, or non-fungible tokens, as profile pictures
on their accounts. It’s the latest public victory
for this form of … and, you know, there’s the
problem. What the hell is an NFT anyway?
# ⚓ Web3_use_cases_for_storage_flimsy_for_now⠀⇛
o § Digital Restrictions (DRM)⠀➾
# ⚓ US_right_to_repair_bills_aim_to_make_ownership_great_again
•_The_Register⠀⇛
American farmers may soon be able to repair their
agricultural equipment without paying the maker of
their machinery for the privilege. And owners of
other products may also see fewer repair barriers,
depending upon how two new pieces of federal
legislation are received.
The Agriculture Right to Repair Act [PDF], a US
Senate bill introduced on Tuesday by Senator Jon
Tester (D-MT), aims to force farm equipment makers
to provide parts, documentation, software, and
tools for repairs to third parties on reasonable
terms.
The Freedom to Repair Act, introduced to the House
of Representatives on Wednesday by US
Representatives Mondaire Jones (D-NY) and Victoria
Spartz (R-IN), promises to “legalize repairing what
you own or taking it to the repair shop of your
choice” by revising copyright law.
# ⚓ Remote_code_execution_vulnerability_in_Samba_due_to_macOS
interop_module⠀⇛
An exploit in Samba 4 allowed remote code as root
due to a bug in its support for Mac clients. It’s
fixed in 4.13.17, 4.14.12 and 4.15.5, and in case
you can’t update, there are patches.
The vuln is being tracked as CVE-2021-44142 and
received a CVSS rating of 9.9.
[...]
Early versions of what was then called OS X used
Samba to do this, but after Samba switched to GPL3,
Apple dropped Samba in OS X 10.7, and switched to
its own implementation.
o § Monopolies⠀➾
# § Patents⠀➾
# ⚓ Purdue_University_lawsuit_says_Google_copied
smartphone_technology [Ed: Google is no good, but
universities funded by the public turning into
parasites isn't good either]⠀⇛
Purdue University’s Purdue Research
Foundation has sued Google LLC in Texas
federal court, alleging that Android software
for eliminating programming errors in
smartphones copies parts of its professors’
invention.
The foundation asked the U.S. District Court
for the Western District of Texas for
royalties and an undisclosed amount of money
damages on Tuesday based on Google’s alleged
willful patent infringement.
The complaint said two professors and two
students at the West Lafayette, Indiana
university invented the patented technology,
which detects software programming errors
that could affect a mobile device’s power
management.
Purdue said that after a Google engineer
posted an article about one of the professors
in an Android forum in 2012, another Google
engineer found and incorporated code
disclosed by the inventors into Android
software.
# ⚓ BlackBerry_offloads_its_‘legacy’_patents_–_some_of
the_stuff_that_made_its_phones_hum⠀⇛
# § Copyrights⠀➾
# ⚓ U2_Share_Acoustic_‘Sunday_Bloody_Sunday’_With_New
Lyrics⠀⇛
Bono and the Edge have released an acoustic
version of U2′s “Sunday Bloody Sunday,”
complete with updated lyrics in the final
verse, to coincide with the 50th anniversary
of the titular Bloody Sunday massacre. You
can watch the performance below.
The opening track on the band’s landmark 1983
album War was inspired by the Bogside
Massacre, which took place on Jan. 30, 1972,
when British soldiers shot 26 unarmed
civilians during a protest march in Derry,
Northern Ireland, ultimately killing 14
people. The black-and-white performance video
is intercut with footage from the massacre.
# ⚓ Sound_Library,_opens_use_of_Pokémon_Diamond_and_Pearl
soundtrack⠀⇛
While some game companies have been busy
purging their music libraries from content
creation platforms like YouTube, The Pokémon
Company has officially made some of the
iconic music from its franchise available for
anyone to use globally.
Starting today, if you weren’t part of the
system’s original launch in Japan in late
2021, anyone can access the new Pokémon DP
Sound Library, a digital resource where you
can listen to or download music from the
official Pokémon Diamond and Pearl soundtrack
for use in content creation and even some
performances.
# ⚓ Attack_on_Titan:_Japanese_Manga_publishers_sue
Cloudflare_•_The_Register⠀⇛
Four major Manga publishers are set to sue
internet-grooming firm Cloudflare, on grounds
its content delivery network facilitates
piracy of their wares.
The four companies – Kodansha, Shueisha,
Shogakukan and Kadokawa – together dominate
the market for Japanese comics and own many
iconic properties.
The publishers also believe they’re victims
of widespread piracy.
Japanese media report the companies are
therefore going to file a suit against
Cloudflare, which they feel facilitates
piracy by providing its services to sites
that share unlicensed Manga.
Cloudflare has seen this movie before: in
2017 Japanese publishers asked it to help
take down a pirate Manga site called
Mangamura. Cloudflare helped, and Mangamura
collapsed. Cloudflare later promised to stop
mirroring Japanese sites if it was satisfied
the content they host was pirated.
䷩ 𝚕𝚒𝚗𝚎 3597
╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕
⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.06.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧
Gemini_version_available_♊︎
✐ Links_6/2/2022:_LibreDWG_0.12.5_and_FOSDEM_2022⠀✐
Posted in News_Roundup at 6:29 pm by Dr. Roy Schestowitz
🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈
§ Contents⠀➾
* GNU/Linux
o Distributions
o Devices/Embedded
* Free_Software/Open_Source
* Leftovers
* § GNU/Linux⠀➾
o ⚓ Linux_Weekly_Roundup_#168⠀⇛
Welcome to this week’s Linux Weekly Roundup, we had a
full week in the world of Linux releases, but I and my
family are busy moving and my workstation is packed away,
so I couldn’t make any videos of these Linux releases,
and my computer is still packed away for a while.
So this week, Trisquel 10.0, Garuda Linux 220131, Bodhi
Linux 6.1.0 alpha, Nitrux Linux 2022.02.02, Peppermint OS
2022-02-02, Zorin OS 16 “Education”, and Slackware 15.0
was released.
o § Audiocasts/Shows⠀➾
# ⚓ Rootdo_Takes_Linux_Minimalism_Way_Too_Far_–_Invidious⠀⇛
Some times Linux people take software minimalism a
little bit too far and rootdo is one of those
cases, this is minimal replacement to doas which is
already excessively minimal.
o § Kernel Space⠀➾
# ⚓ Linux_5.17-rc3⠀⇛
Things look fairly normal so far, with a pretty
average number of
commits for an rc3 release.
The diffstat shows that we've had more filesystem
activity than is
perhaps usual, The filesystem activity is all over,
ranging from cifs
re-introducing fscache support after the rewrite,
to vfs-level error
handling fixes, to just regular filesystem-specific
fixes (btrfs,
ext4, xfs), to some unicode Kconfig cleanups. So
it's not one single
thing, it just happened that we had more filesystem
stuff than is
perhaps common at this point.
That said, driver fixes (networking, gpu, sound,
pin control, platform
drivers,scsi etc) still dominate. On the driver
side, some reverts to
re-enable hw-accelerated scrolling for legacy fbdev
devices perhaps
stand out.
Outside of that, it's a mixed bag of random stuff -
the usual arch
updates (kvm noise stands out), generic networking
and core kernel,
and tooling (selftests and perf). And some
documentation fixes.
Shortlog appended for more details, but I don't see
anything that
makes me worried for the 5.17 release. Knock wood.
Please go test,
Linus
# ⚓ Kernel_updates_available_for_PCLinuxOS_»_PCLinuxOS⠀⇛
Current kernels:
kernel-5.4.177-pclos1-1-1pclos2022.x86_64.rpm
kernel-5.10.98-pclos1-1-1pclos2022.x86_64.rpm
kernel-5.15.21-pclos1-1-1pclos2022.x86_64.rpm
kernel-5.16.7-pclos1-1-1pclos2022.x86_64.rpm
# ⚓ Linux_5.16.6⠀⇛
# ⚓ Linux_5.15.20⠀⇛
# ⚓ Linux_5.10.97⠀⇛
# ⚓ Linux_5.4.177⠀⇛
# ⚓ Linux_5.16.7⠀⇛
# ⚓ Linux_5.15.21⠀⇛
# ⚓ Linux_5.10.98⠀⇛
# § Graphics Stack⠀➾
# ⚓ 3dfx_Glide_Coming_to_Linux_with_Support_for_Modern
GPUs⠀⇛
A developer has implemented 3dfx’s Glide
application programming interface into Mesa’s
Gallium3D driver stack for modern GPUs. The
implementation allows users to play games
that rely on Glide under Linux to run on
modern hardware.
o § Applications⠀➾
# ⚓ 6_Best_Free_and_Open_Source_Robotic_Process_Automation
Tools⠀⇛
Robotic Process Automation (RPA) is a business
process automation technology that uses attended or
unattended software bots to automate repetitive,
tedious, and time-consuming back-end office tasks
while users concentrate on high-value tasks.
This type of software lets you create ‘bots’ to
complete a wide variety of tasks, as well as manage
and schedule the bots based on the nature of the
task.
# ⚓ 9_Practical_Examples_of_the_cut_Command_in_Linux [Ed: It’s
a GNU program, not “Linux” command; a_kernel_does_not_have
such_tools]⠀⇛
Linux-based operating systems offer many command-
line text processing utilities you can use in your
day-to-day routine. The cut command is one such
text manipulation utility that uses delimiters,
bytes, fields, and columns to fetch a required
string from a flat-file database or a line.
Since a flat-file database does not have a
structural relationship and the records are
separated with the help of delimiters, cut is an
ideal tool to extract characters or bytes of
information. This article discusses the cut command
in detail and demonstrates some practical examples
with different filter options to get you started
with the tool.
# ⚓ New_release_of_sbuild-qemu_Utilities_|_Christian_Kastner⠀⇛
I just released a new version of the sbuild-qemu
utilities as part of sbuild. Notable changes are
support for new architectures, and a new sbuild-
qemu-boot utility to start a VM and interact with
its console directly through the terminal.
As a reminder, these utilities leverage
functionality in vmdb2, autopkgtest, and sbuild to
use QEMU VM images for building and testing
packages in strongly isolated environments and/or
on foreign architectures and/or that might break
the system.
[...]
However, there’s an autopkgtest issue (#10031002)
with the host-guest communication bridge on armhf
and on multi-core arm64 (single-core seems to work
fine) that currently makes images unusable for
sbuild and autopkgtest. I haven’t yet figured out
what the problem seems to be, but for the time
being, the images can still be used with sbuild-
qemu-boot.
o § Instructionals/Technical⠀➾
# ⚓ 2_ways_to_Install_OpenRGB_on_Ubuntu_22.04_|_20.04_LTS_–
Linux_Shout⠀⇛
Learn the commands to install OpenRGB tools on
Ubuntu 22.04 LTS Jammy JellyFish or Ubuntu 20.04
LTS Focal Fossa Linux using the terminal to control
RGB lights.
OpenRGB earlier known as OpenAuraSDK is free,
multivendor software for controlling RGB lighting.
The project is focused to provide support for
multiple hardware manufacturers’ products to reduce
the programs load, which are limited to Windows,
superfluous.
# ⚓ How_To_Install_Memcached_on_Fedora_35_–_idroot⠀⇛
In this tutorial, we will show you how to install
Memcached on Fedora 35. For those of you who didn’t
know, Memcached is a high-performance distributed,
in-memory caching system. It primarily is used to
speed up sites that make heavy use of databases.
Memcached has an API with a very large hash table
distributed across multiple machines. when a table
is full, subsequent inserts cause older data to be
purged in the least recently used order.
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 Memcached on a Fedora 35.
# ⚓ Mastodon_Setup_with_Docker_and_nginx-proxy_|_~rriemann⠀⇛
I have been working on a setup with Mastodon that
is easy to repeat and share. A setup with very few
steps. Please consider that this setup is not
enough for a production environment. It requires
additional security measures. Please put your
recommendations in the comments! :grinning:
Our starting point is the docker-compose.yml
shipped with the Mastodon code. Why is it not
enough? It assumes you setup up proxy with HTTPS
endpoints yourself. So let’s integrate this as well
in Docker.
# ⚓ 3_Ways_To_Install_Skype_In_Ubuntu_22.04_LTS_|_Itsubuntu.com
[Ed: But it spyware and vastly better options exist in
2022]⠀⇛
Skype is a popular video-conferencing application.
It was bought by Microsoft and thus we started to
name it Microsoft skype. Microsoft skype has a
massive userbase. It is free to install and use.,
You can use it on any operating system like
Windows, Linux, macOS, and Android.
In this post, we will show you the multiple ways to
install Skype in Ubuntu 22.04 LTS.
# ⚓ Cloudlinux_command_to_install_ALT-PHP,_Nodejs,_Python_from
SSH_|_Elinux.co.in_|_Linux_Cpanel/_WHM_blog_|_Linux
Webhosting_Blog,_Linux_blogs⠀⇛
If you are in love with SSH or black screen and
want to install Cloudlinux ALT-PHP, Nodejs or
Python using SSH then you can use below command.
# ⚓ WHM_API_to_suspend/unsuspend_account_with_account_summary_|
Elinux.co.in_|_Linux_Cpanel/_WHM_blog_|_Linux_Webhosting
Blog,_Linux_blogs⠀⇛
If you want to suspend the account using WHM API
from SSH and mention the reason of suspension then
use below command.
# ⚓ WHM_API_to_change_the_main_account_domain_name_from_the_SSH
|_Elinux.co.in_|_Linux_Cpanel/_WHM_blog_|_Linux_Webhosting
Blog,_Linux_blogs⠀⇛
If you want to change the cpanel hosting account
domain name using SSH or whmapi then you can run
below command.
# ⚓ How_to_install_Ardour_on_a_Chromebook⠀⇛
Today we are looking at how to install Ardour 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.
# ⚓ Install_Build_Essential_Tools_On_Ubuntu_22.04_LTS_|
Itsubuntu.com⠀⇛
Tutorial To Install build essential tools on Ubuntu
22.04 LTS. You can also follow this tutorial to
install build essential tools on Ubuntu 20.04 LTS.
Build essential is not a software or application.
Build essential is a meta-package that is required
to compile the application on Linux. It includes
the GCC/g++ compilers and libraries required to
compile software written in C and C++. You need
build-essential tool in your Linux to compile the
program or source code.
# ⚓ Install_PHP_Mcrypt_Extension_On_Ubuntu_22.04/Debian_
[Updated]_|_Itsubuntu.com⠀⇛
Tutorial To Install PHP Mcrypt Extension On Ubuntu
22.04/Debian [Updated]
PHP developers have removed it from the PHP package
bundle because of no further development in Mcrypt.
Some of the alternatives to Php Mcrypt are Sodium
(available as of PHP 7.2.0) and OpenSSL.
But if you still want to use it then this tutorial
is for you where we are going to show you the
process to install PHP Mcrypt extensions on Ubuntu
22.04 LTS.
# ⚓ Install_Kubernetes_Cluster_on_Centos_8_With_Kubeadm_and
CRI-O⠀⇛
This guide will teach you how to deploy a
Kubernetes Cluster on CentOS 8 by using kubeadm and
with CRI-O Container runtime
# ⚓ How_to_install_Microsoft_Teams_on_Zorin_OS_16_–_Invidious
[Ed: This is spyware; better use something else]⠀⇛
# ⚓ vga=792_removed_from_legacy_boot_mode⠀⇛
When the Linux kernel is booted on a PC with
legacy-BIOS firmware, the screen starts up in a
text-mode. This is different from the graphics
modes — the former just renders text characters and
cannot display graphics.
However, if the kernel passes a “vga=” or “video=”
parameter, the video can be flipped into a graphics
mode. I introduced “vga=792″ a few years ago for
legacy-BIOS bootup, so as to display a logo and
also to be able to run GUI apps within the initrd.
I experimented with GUI apps to ask for keyboard
layout and password.
Windows computers manufactured from 2012 onwards
have UEFI firmware, and this does startup in a
graphics mode, so no parameter is required on the
kernel commandline.
# ⚓ How_to_fix_missing_Linux_header_error_for_VMware
Workstation_–_TREND_OCEANS⠀⇛
I tried to run VMware Workstation to install a
secondary operating system to test functionality,
but it flagged me an error: “VMware Kernel Module
Updater: Kernel header X.X.X-X-amd64 were not
found.”
Intentionally I ignored the message and clicked on
“Install” to proceed with the installation. As a
result, I got another error which stated, “C header
files matching your running kernel were not found”.
# ⚓ How_To_Set_Up_An_SFTP_Server_On_Rocky_Linux_8_|_LinuxTeck⠀⇛
SFTP (SSH File Transfer Protocol) is also called
Secure FTP. It is a method for uploading and
downloading files over an encrypted connection
between two computers. Unlike FTP and FTPS, it
works differently. Since SFTP is built upon the SSH
(Secure Shell) protocol, version 2.0, it supports
the full functionality of SSH, such as public-key
encryption, to provide strong user authentication
and secure encrypted communications over any
reliable data stream.
Although SSH is used in this context, it may also
be used to transfer management information over
VPNs and to secure file transfers using Transport
Layer Security (TLS). SSH is a client-server
protocol that allows for secure communication. The
Internet Engineering Task Force (IETF) developed
and adopted SFTP to replace insecure shell
protocols in 2006; it is an extension of SSH 2.
FTP is a tool used for transferring data between
computers. This service is no longer popular
because it lacks security since this protocol
reveals sensitive data and credentials in plain
text. Hackers can easily steal data by using this
protocol. Therefore, we recommend using SFTP in
place of FTP, as it is more secure than the simple
file transfer protocol (FTP and FTPS), and you can
also protect your data with encoding features,
cryptographic hashes, password sniffing, and
authentication on the server and the client.
# ⚓ How_To_Install_Laravel_on_CentOS_Stream_9_–_idroot⠀⇛
In this tutorial, we will show you how to install
Laravel on CentOS 9 Stream. For those of you who
didn’t know, Laravel is the most popular PHP
framework which is free and open source. Laravel
has been developed as a framework that is based on
PHP integrating open-source that has multiple tools
for creating web applications of all kinds of sizes
and complexity.
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 Laravel PHP framework on CentOS
9 Stream.
# ⚓ How_To_Install_Syncthing_on_Debian_11_–_idroot⠀⇛
In this tutorial, we will show you how to install
Syncthing on Debian 11. For those of you who didn’t
know, Syncthing is a free and open-source file
syncing application used to sync files between
multiple remote devices over the internet.
Syncthing does not upload your files to a central
server like Nextcloud but exchanges your data
directly between your devices. All your data is
encrypted with TLS when transmitting between your
devices. Syncthing is available for Linux, BSD,
macOS, Windows, Android, and Solaris.
This article assumes you have at least basic
knowledge of Linux, know how to use the shell, and
most importantly, you host your site on your own
VPS. The installation is quite simple and assumes
you are running in the root account, if not you may
need to add ‘sudo‘ to the commands to get root
privileges. I will show you through the step-by-
step installation of the Syncthing remote file
synchronization on a Debian 11 (Bullseye).
# ⚓ A_practical_solution_for_GNU/Hurd’s_lack_of_drivers:
NetBSD’s_rumpkernel_framework⠀⇛
GNU/Hurd is the original Free Software operating
system started in the 1980s. Its microkernel design
has been evolving over the years and the project
has not quite hit mainstream use. I believe this is
due to one main reason: the lack of drivers for
peripherals and hardware. In this talk, I explain
how NetBSD kernel drivers have been reused in a
microkernel setting and demonstrate their use to
boot up a GNU/Hurd system via a userspace rump disk
driver, with a driverless Hurd kernel, gnumach. The
ACPI management, PCI management, and actual driver
are in separate processes with RPC interfaces
between them, which separates out their debugging,
licencing concerns and execution. I believe this
aligns with the original vision for the operating
system, (as a Hurd of servers).
# ⚓ How_to_instal_Icinga2_on_Ubuntu_20.04_LTS_Focal_–_Linux
Shout⠀⇛
Learn the steps to install the Icinga monitoring
solution on Ubuntu 20.04 LTS Focal Fossa desktop or
server using the command terminal, in this
tutorial.
What is Icinga?
Icinga is an open-source monitoring software
platform available as a standalone solution that
was originally released as a variant of Nagios.
Unlike Nagios, Icinga has a modular architecture
and a multi-threaded design.
The web interface comes in different variants,
which makes Icinga particularly adaptable. Similar
to Nagios, the software can be expanded. However,
it differs in that the configuration takes place
via the web interface and not via configuration
files.
o § Games⠀➾
# ⚓ Best_Linux_Gaming_Distros_In_2022_For_Gamers⠀⇛
List Of Best Linux Gaming Distros In 2022 For
Gamers.
Gaming on Linux-based operating systems is a
different experience. These days Linux is providing
more support for various games. Game developers are
slowly turning their attention to the Linux distros
and they have started to develop games for the
Linux distros too.
You are at the right blog post if you are looking
for the best Linux gaming distros in 2022 for
gamers.
o § Desktop Environments/WMs⠀➾
# § K Desktop Environment/KDE SC/Qt⠀➾
# ⚓ Status_update:_Mass_packaging,_and_mass_learning_–
post_#2⠀⇛
As I had mentioned in my last post, I already
knew the basics of packaging. Flatpak is
certainly new for me though. I have used
Flatpaks, but never published them.
It was easy to learn packaging and writing
manifests. I submitted a couple of easy
applications to Flathub before the
contribution period started, so as to get a
good idea of what I’ll be doing during the
coming weeks.
o § Distributions⠀➾
# ⚓ Tails_vs._Linux_Kodachi:_Which_Privacy_Protection_Distro
Should_You_Choose?⠀⇛
When it comes to maintaining privacy on Linux, you
have two options: Tails and Linux Kodachi. But
which one should you go for? Let’s find out.
When it comes to privacy protection, you can’t beat
Linux. And for those who want the ultimate in
privacy and security, two Linux distributions are
leading the way: Tails and Linux Kodachi. Both
distributions are self-contained, portable, and use
the latest technologies to allow you to remain
anonymous online without leaving any trace of your
activity when you’re done.
But what are the differences? And which ultra-
private Linux distribution is right for you? We’re
going to answer these questions by taking a look at
the overall goals of these two specialized Linux
distributions, how they are alike, and what makes
them different.
# § Slackware Family⠀➾
# ⚓ Slackware_Cloud_Server_Series,_Episode_4:
Productivity_Platform⠀⇛
Welcome to the fourth episode in a series of
articles that I am writing about using
Slackware as your private/personal ‘cloud
server’.
Check out the list below which shows past,
present and future episodes in the series, if
the article has already been written you’ll
be able to click on the subject.
# § Debian Family⠀➾
# ⚓ Free_Software_Activities_for_2021⠀⇛
Most of my contributions to Free software
continue to happen within Debian.
As part of the Data Protection Team I
responded to various inbound queries to that
team. Some of this involved chasing up other
project teams who had been slow to respond –
folks, if you’re running a service that
stores personal data about people then you
need to be responsive to requests about it.
Some of this was dealing with what look like
automated scraping tools which send no
information about the person making the
request, and in all the cases we’ve seen so
far there’s been no indication of any data
about that person on any systems we have
access to. Further team time was wasted
dealing with the Princeton-Radboud Study on
Privacy Law Implementation (though Matthew
did the majority of the work on this).
The Debian Keyring was possibly my largest
single point of contribution. We’re in a
roughly 3 month rotation of who handles the
keyring updates, and I handled 2021.03.24,
2021.04.09, 2021.06.25, 2021.09.25 +
2021.12.24
For Debian New Members I’m mostly inactive as
an application manager – we generally seem to
have enough available recently. If that
changes I’ll look at stepping in to help, but
I don’t see that happening. I continue to be
involved in Front Desk, having various
conversations throughout the year with the
rest of the team, but there’s no doubt Mattia
and Pierre-Elliott are the real doers at
present. I did take part in an NM Committee
appeals process.
In terms of package uploads I continued to
work on gcc-xtensa-lx106, largely doing
uploads to deal with updates to the GCC
version or packaging (8 + 9). sigrok had a
few minor updates, libsigkrok 0.5.2-3,
pulseview 0.4.2-3 as well as a new upstream
release of sigrok CLI 0.7.2-1. There was a
last minute pre-release upload of
libserialport 0.1.1-4 thanks to a kernel
change in v5.10.37 which removed termiox
support.
# § Canonical/Ubuntu Family⠀➾
# ⚓ The_Edge_of_the_Cloud_is_Now_in_Space_–_Parabolic
Arc⠀⇛
The successful Lonestar demonstration mission
included pivotal contributions from the
digital artist Cecilie Waagner Falkenstrøm
and her software team at ARTificial Mind with
Niels Zibrandtsen of the Mind Future
Foundation, open source software leader
Canonical Ltd., and space commercialization
leader Redwire Space. ARTificial Mind
provided the digital content and blockchain
capabilities. Canonical provided a unique
“edge of network” kernel of Ubuntu Linux, the
leading operating system for container, Cloud
and hyperscale computing, to operate on the
constrained space hardware aboard the ISS.
Redwire Space leveraged their existing server
hardware on the ISS from their microgravity
3D printing capability. Lonestar brought the
concept and the team together in support of
its customers in its work to bring data to
the edge.
o § Devices/Embedded⠀➾
# § Open Hardware/Modding⠀➾
# ⚓ The_Q2,_A_PDP8-Like_Discrete_Transistor_Computer_|
Hackaday⠀⇛
[Joe Wingbermuehle] has an interest in
computers-of-old, and some past experience of
building computers on perfboard from discrete
transistors, so this next project, Q2, is a
complete implementation of a PDP8-like
microcomputer on a single PCB. Like the DEC
PDP-8, this is a 12-bit machine, but instead
of the diode-transistor logic of the DEC, the
substantially smaller Q2 uses a simple NMOS
approach. Also, the DEC has core memory, but
the Q2 resorts to a pair of SRAM ICs, simply
because who wants to make repetitive memory
structures with discrete 2N7002 transistors
anyway?
[...]
A 40-pin header was added, for programming
via a Raspberry Pi in case the front panel
programming switches are proving a bit
tedious and error prone.
# ⚓ How_to_Build_a_Morse_Code_Receiver_with_Raspberry_Pi
|_Tom’s_Hardware⠀⇛
This tutorial is the second in a two part
series for building a building-to-building
morse code communications system. In it,
we’ll explore how to create a morse code
receiver using a Raspberry Pi and a Wyze
camera. In a prior article, we explained how
to build a morse code transmitter light with
Raspberry Pi so this is for the receiving end
of the communication.
I recently moved into a new place, and
discovered that my friend and I live in
buildings that face each other. We’re about a
kilometre apart, but both our balconies have
line of sight to each other. I’ve always
wanted to build a communications network with
my friends since I was a kid, so I dusted off
an old book about Morse, one of my Raspberry
P’s and got to work. I’m a big fan of mixing
old and new technologies, so instead of using
something modern, I decided to use Morse
code.
This project is the second (and more
difficult) part – receiving and interpreting
morse code. Thankfully morse has constant
time values for each component of the
message, and we use that – with some error
bands – to make assumptions about which
letters are being transmitted based on the
length of the light pulses. Here’s how to do
it.
# ⚓ Designing_devices_for_long-term_care_and_reuse⠀⇛
I love charity shops (what are called thrift
shops in the US). In the UK they are so
popular they account for almost half of all
stores in some shopping streets. You can give
unwanted clothes, furnishings, kitchen items,
records, CDs, DVDs and books. Items are
checked, cleaned and resold for pennies. The
profits go to causes like health research,
foreign aid, hotlines for abuse, suicide or
drug problems, veterans help, animal welfare,
and children’s aid. You can pick up great
bargains like an expensive designer jacket or
a rare, collectable music album.
But mysteriously, a notable absence in many
charity shops is technology. That seems
strange because each year we throw away 50
million tons of phones, tablets, games
consoles, remotes, TV screens, headphones,
laptops, and digital cameras. Most end up
crushed and exported to low-wage recycling
facilities in countries with lax
environmental regulations.
[...]
If adults shared phones and computers the way
that children swap toys it would be much
harder to tie individuals to digital actions.
To this end there are two forms of propaganda
akin to the “war against public transport” in
the USA and elsewhere. One message suggests
that sharing is a low status behaviour. The
other spreads fear about “security and
safety”.
By pushing people to form psychological
attachments to devices and to identify with
their phone as a brand symbol and extension
of themselves, advertisers insinuate an unmet
need to carry a personal device. Just as open
WiFi sharing was besmirched by the spectre of
terrorists and child molesters using “your
internet”, portraying sharing as a dirty,
unhygienic affair like drug addicts sharing
needles, shuts down our openness and
willingness to efficiently use fewer devices.
This over-individuation has led people to
misuse smartphone technology, overloading one
specific device as a citadel of personal
data, identity, connection and access, and
creating a single point of catastrophic
failure or loss. Technically, this is an
awful design.
A better technical design to discourage waste
is if devices are designed to be shared. How
does this work? The personalised parts of a
phone or tablet are a separate module from
the “sharable” body. The body would contain
the radio components, battery and display,
while a small, easily swappable private part
(a users enclave) would contain storage,
contacts, call credits and private keys.
This was the original idea behind the
Subscriber Identity Module (SIM) which was
poorly implemented and has been mishandled,
or plainly resisted by manufacturers from the
get go. Similarly, modern computers have no
good reason to contain a hard disk. To
maximise reuse, all should boot only from
removable storage and explicitly retain no
state.
# ⚓ Open-Hardware_Dog_Treat_Dispenser_is_a_Stepping_Stone
For_Behavioral_Research⠀⇛
The principles of open-source hardware are
starting to make great strides in scientific
research fields. [Walker Arce] tells us about
his paper co-authored with [Jeffrey R.
Stevens], about a dog treat dispenser
designed with scientific researchers in mind
– indispensable for behavior research
purposes, and easily reproducible so that our
science can be, too. Use of Raspberry Pi,
NEMA steppers and a whole lot of 3D printed
parts make this build cheap (< $200 USD) and
easy to repeat for any experiments involving
dogs or other treat-loving animals.
Even if you’re not a scientist, you could
always build one for your own pet training
purposes – this design is that simple and
easy to reproduce! The majority of the parts
are hobbyist-grade, and chances are, you can
find most of the parts for this around your
workshop. Wondering how this dispenser works,
and most importantly, if the dogs are
satisfied with it? Check out a short
demonstration video after the break.
# § Mobile Systems/Mobile Applications⠀➾
# ⚓ The_15_Best_Ways_To_Recycle_Your_Phone_Safely⠀⇛
# ⚓ The_Best_Games_Like_Wordle_for_Android_–_Baikoh,
Letterpress,_Typeshift_and_More_–_Droid_Gamers⠀⇛
# ⚓ How_To_Get_Adobe_Photoshop_On_Android⠀⇛
# ⚓ How_to_speed_up_your_Android_smartphone_with_these_8
tips_–_Gizchina.com⠀⇛
# ⚓ Android_12′s_customization_shortcomings_drove_me_back
to_third-party_launchers_and_icon_packs⠀⇛
# ⚓ Motorola_MA1_Review:_Wireless_Android_Auto_for_the
rest_of_us⠀⇛
o § Free, Libre, and Open Source Software⠀➾
# ⚓ SearX,_an_Alternative_to_Google_Scholar⠀⇛
Do you want to search online for academic papers
and journals? Many people use Google Scholar for
that. For people who seek privacy, they might want
to use an alternative, and Searx Science is very
good for that. This article introduces you to use
Searx to search scientific publications with easy
examples and practices. Let’s start!
[...]
First look will give you a searX logo at the
center, a search box, and a tiny ‘Advanced
settings’ button. In general, all Searx instances
will look the same as this. Once you did a search,
the results would look like pictured below.
However, SearxNG, a modified version of of Searx,
has a slightly different look and feel.
# § Web Browsers⠀➾
# § Mozilla⠀➾
# ⚓ Jean-François_Fortin_Tam:_Year_MMXVIII
summarized_in_4_minutes⠀⇛
Was thrilled that Mozilla finally got
their sh!t together when it comes to
performance in Firefox, with the
initial release of Firefox Quantum in
late 2017. This was one of the first
times since 2010 where I had a somewhat
solid argument to convince Chrome users
to consider Firefox again. Personally
however, I was stuck on pre-quantum
Firefox up until 2019 due to my
reliance on Quicksaver’s “Tab Groups”
extension (the successor to the
Panorama feature), which eventually got
succeeded by Drive4ik’s “Simple Tab
Groups” extension, which is an absolute
must-have; if you’re a chaos warrior,
use it—you’ll thank me later.
# § Productivity Software/LibreOffice/Calligra⠀➾
# ⚓ LibreOffice_7.3.0_for_Slackware_15.0_(and_-current)⠀⇛
LibreOffice Community Edition 7.3.0 was
released last week… on the day we were
preparing the Slackware 15.0 release. You’ll
forgive me that my focus was elsewhere and
that it took until today to upload a new set
of packages for Slackware 15.0 and -current.
The main selling point of the 7.3 release
cycle is better interoperability with
Microsoft’s Office file formats. Note that
the Microsoft proprietary file formats are
still based on a deprecated standard (since
2008 actually), whereas LibreOffice uses the
ISO standard OpenDocument Format.
These improvements center on three areas
(text copied partly from the release notes)…
# ⚓ FOSDEM_2022_–_News_from_the_ODF_Toolkit_(with_Notes)
by_Svante_Schubert⠀⇛
You can access and download Svante Schubert’s
slides about “News from the ODF Toolkit”
which was supposed to be features during
FOSDEM 2022 but for some reason didn’t work
out.
# § FSF⠀➾
# § GNU Projects⠀➾
# ⚓ LibreDWG_–_News:_libredwg-0.12.5_released_
[Savannah]⠀⇛
Fixed many more minor fuzzing errors.
See https://www.gnu.org/software/
libredwg/ and NEWS
Here are the compressed sources:
https://ftp.gnu.org/gnu/libredwg/
libredwg-0.12.5.tar.gz (17.4MB)
https://ftp.gnu.org/gnu/libredwg/
libredwg-0.12.5.tar.xz (9MB)
Here are the GPG detached signatures
[*]:
https://ftp.gnu.org/gnu/libredwg/
libredwg-0.12.5.tar.gz.sig
https://ftp.gnu.org/gnu/libredwg/
libredwg-0.12.5.tar.xz.sig
Use a mirror for higher download
bandwidth:
https://www.gnu.org/order/ftp.html
Here are more binaries:
https://github.com/LibreDWG/libredwg/
releases/tag/0.12.5
Here are the SHA256 checksums:
4b5b38943e4a060bfee34a8542701b26102262610b1dd4dc58d76fadfb995106
libredwg-0.12.5.tar.gz
d3de19cde6adc27cb65cc353ae01a1e8aa15d1ab6ca4ce2563b76e73e8b2f1bd
libredwg-0.12.5.tar.xz
65f00b1d02012a40b09adae1e10956d17374de46d189b18236f824841e958111
libredwg-0.12.5-win32.zip
dfb609aa05883056effaaf51f0a95617803e06b1c4e4572cd3cee948087cbb35
libredwg-0.12.5-win64.zip
[*] Use a .sig file to verify that the
corresponding file (without the
.sig suffix) is intact. First, be sure
to download both the .sig file
and the corresponding tarball. Then,
run a command like this:
gpg --verify libredwg-0.12.5.tar.gz.sig
If that command fails because you don't
have the required public key,
then run this command to import it:
gpg --keyserver keys.gnupg.net --recv-
keys B4F63339E65D6414
and rerun the gpg --verify command.
# § Programming/Development⠀➾
# ⚓ No_ARM_Printer_Driver?_Just_Write_Your_Own_|
Hackaday⠀⇛
When you think of the small machines that
print the sticky labels on packages, you
might not expect to find a complex printer
with its own programming language (ZPL).
However, [Dan Pastusek] was looking around
online and found a small label printer on
everyone’s favorite online warehouse for a
great price that suggested it supported ZPL.
Unfortunately, [Dan] had big dreams for
creating a Raspberry Pi-based print station
and found the drivers packaged for this
particular printer were not ARM compatible.
Not quite content to leave it there, he began
to chip away at the layers until he had a
working driver.
ZPL, at its core, is just a language
describing ASCII commands transmitted over a
serial connection. So while the printer
showed up as an endpoint, it wasn’t working
as the filters (the part of the driver that
knows how to convert from a PNG to ZPL) was
x86 only. On Linux, printer drivers also have
a PPD file that describes what a printer can
handle in paper size and other settings. The
PPD file for the little printer gave the
first clue. In the ShortNickName field, it
identifies itself as HPRT N41, which is a
popular HP printer. So this little printer
must be a clone of a printer in that family.
Notably, they don’t support ZPL. Instead, the
HPRT series support TSPL, another printer
language developed by TSC.
* § Leftovers⠀➾
o § Hardware⠀➾
# ⚓ The_Coolest_Controller_Mod,_Hands_Down_|_Hackaday⠀⇛
Video games are a great way to relax, and sometimes
get your heart rate up at the same time. But unless
you’re playing something like Dance Dance
Revolution, the controls pretty much always require
the use of both hands. Even the old Atari
controller benefited from using the other hand for
support.
But what if you don’t have the use of both hands?
Or you have a repetitive stress injury? Or you just
want to eat cheese curls with chopsticks while you
play? [Akaki Kuumeri] has you covered with one of
the hands-down greatest uses for 3D printing we’ve
seen — a PlayStation DualShock 4 controller
modified for one-handed use. If this looks
familiar, it may be because [Akaki] made a PS5
controller version a while back, but who can get
one of those, anyway?
o § Integrity/Availability⠀➾
# § Proprietary⠀➾
# § Security⠀➾
# § Privacy/Surveillance⠀➾
# ⚓ Google_Warned_About_Passcode_Theft⠀⇛
Google told a U.S. lawmaker that
it received a warning last May
that a European technology
company was “siphoning” user
passcodes to aid surveillance
carried out by foreign
governments.
Google told Sen. Ron Wyden (D-
Ore.) that the company had been
tipped off that Mitto may have
been “siphoning off two-factor
text messages for surveillance
companies and their foreign
government clients,” according to
a Wyden aide.
It’s not clear who made the
allegation, which, if true, could
have allowed foreign governments
to access personal accounts.
Google said it looked into the
matter but “due to a lack of
visibility into
telecommunications…
o § Monopolies⠀➾
# ⚓ FOSS_Patents:_Ericsson_to_ITC:_Apple_mischaracterizes_our
position_on_patent_enforcement,_and_base_stations_are_way
harder_to_replace_than_smartphones,_especially_after_Huawei
ban⠀⇛
This week is “Public Interest Statement Week”
between Apple and Ericsson. Statements on the
public interest with respect to the effect of
import bans help the U.S. International Trade
Commission (USITC, or just ITC) as it determines
whether to institute investigations and can
delegate to the Administrative Law Judge (ALJ) in
charge of the investigation the analysis of
potential public-interest concerns.
# ⚓ No_IP,_no_right_to_information?_CJEU_to_clarify_scope_of
article_8_Enforcement_Directive [Ed: This is about trade
secrets, not IP, which is a fictional thing and misleading
misnomer; Jan Jacobi relies on propaganda terms here...]⠀⇛
Under article 8(1) of the Enforcement Directive
(Directive 2004/48/EC) a claimant in infringement
proceedings can request a court to order certain
parties to disclose information. This so-called
‘right to information’ includes information on the
origin of the infringement (e.g. who manufactured
the counterfeit goods) and its extent (the
quantities produced or the price under which a good
was sold). An action to obtain the information can
be directed at the infringing party as well as
third parties potentially involved in the
infringement (producers, distributors etc.).
# ⚓ FOSS_Patents:_Ericsson_and_Apple_may_soon_meet_in_Texas
court_over_dueling_FRAND_claims:_new_filing_calls_Apple_an
“unlicensed_[patent]_infringer”⠀⇛
Reading Ericsson’s late-Friday filings in the two
FRAND cases in the Eastern District of Texas
creates a bit of a High Noon feeling: a duel is in
the air. Just a courtroom duel, fortunately.
May I refer you to my Wednesday post on Apple’s
reply in support of its motion to dismiss
Ericsson’s (earlier-filed) case, which also
contains a table that juxtaposes the parties’
procedural preferences. It’s fascinating to see
this dispute unfold, with both parties playing the
game at the highest level, but with Ericsson
possibly having devised a strategy that Apple–no
matter how hard and smart it tries–may not be able
to thwart.
# § Patents⠀➾
# ⚓ The_Unified_Patent_Court_And_Unitary_Patent_–
Introduction [Ed: Herbert Smith Freehills intentionally
promoting fiction and fake_news in an effort to usher
in a totally illegal system they hope to profit from]⠀⇛
A new patent right and patent enforcement
system is coming for patent protection in the
Europe which is likely to commence at the end
of 2022 or early 2023 depending on when the
final preparations are in place.
# ⚓ UPC_Roadshow_February_2022 [Ed: Meissner Bolte is
promoting_a_crime]⠀⇛
The Unitary Patent and Unified Patent Court
(UPC) are coming – and Meissner Bolte is
hitting the (virtual) Road!
# ⚓ Opinion:_QCs_must_shun_limelight_if_juniors_are_to
thrive [Ed: When litigation firms bribe the media
(including this writer) and hire lobbyists to write/
change the law it's hardly surprising we end up with
more lawsuits, i.e. the public pays extortionate fees
to people who produce nothing at all]⠀⇛
A senior judge, who predicts a spike in IP
cases, says QCs’ tendency to dominate
litigation is reducing juniors to mere “tiles
on a screen”
# ⚓ Vorwerk_wins_against_Lidl_in_dispute_over_kitchen
appliance [Ed: This is framed as marketing/promotion
for patent litigation firms (the real clients of JUVE)
instead of news/reporting, i.e. the usual from JUVE]⠀⇛
Lidl may no longer sell its Monsieur Cuisine
kitchen machine. Düsseldorf Higher Regional
Court issued the ruling in the second
instance in a dispute with household
electronics manufacturer Vorwerk. The court
found that Lidl infringed a patent held by
the German company for its Thermomix kitchen
machine.
Technically, the patent DE10226940 is for a
heating technology used to cook food in the
mixing bowl.
[...]
The dispute concerned German companies only,
with Vorwerk not filing actions against the
Chinese manufacturers.
# ⚓ Dutch_courts_could_have_international_jurisdiction_to
hear_FRAND_claims [Ed: Dutch courts have openly_enabled
(with_help_from_the_government)_criminals_from_the_EPO
get_away_with_crimes; do we want to rely on them for
patent disputes?]⠀⇛
The District Court of The Hague has declared
both international and territorial
jurisdiction to decide on a FRAND case
brought against patent pool Access Advance by
Turkish television manufacturer Vestel.
Access Advance had challenged this assertion
based on three of four of its members not
being domiciled in the Netherlands.
However, the court decided that the parties’
connection to Netherlands-based Philips was
strong enough to warrant the setting of a
FRAND rate to cover the whole patent pool. As
such, Vestel’s proceedings against the pool
members on the merits of a FRAND licence will
continue.
This case is unusual in that implementer
Vestel commenced proceedings, rather than the
patent holder. Overall, the decision could
have implications for other patent pools in
the Netherlands, especially if the licensor
is based in the Netherlands. The outcome of
the next set of proceedings could open the
door for the Dutch courts to decide FRAND
determination.
# ⚓ Exclusive:_Nordic_IP_chief_quit_FSA_board_before
Nokia_licensing_deal [Ed: This is clearly limited to
patents; the term “IP” is nonsense, but those who call
their own site after this propaganda term will never
wish to admit it (they’re paid to relay the false
narratives)]⠀⇛
Nordic Semiconductor’s legal head told
Managing IP it was time to change tack on the
end device v component level licensing debate
# ⚓ UK_IPO_launches_call_for_views_on_the_Designs_System
[Ed: UK-IPO pretends to care what the British public
thinks while actually adopting the proposals of foreign
lobbyists]⠀⇛
The designs system enables rights holders to
protect designs and enforce their rights. We
are seeking views and evidence from users of
the system so that we can ensure the UK’s
designs framework works for the businesses,
consumers and designers that use it.
This will help us better understand how we
can make the most of new opportunities and
flexibilities now that we have left the EU,
and how new and emerging technologies may
impact the design system.
# ⚓ Kilburn_&_Strode_hires_Hoffmann_Eitle_director_in
Amsterdam [Ed: The salaried spammer Amy Sandys, who
intentionally publishes fake news to advance illegal
agenda, is once again doing spammy JUVE_ads_as_‘news’;
hiring one person isn’t new, but this is marketing, not
reporting]⠀⇛
Ferro is now bringing his prior experience in
the technology and semiconductor sector to
expand Kilburn & Strode’s European practice.
# ⚓ USPTO_Third_Party_Submissions [Ed: This means that
many fake patents are being allowed with any real fact-
checking or scrutiny; this system has gone defunct,
made to benefit mass litigation firms and
monopolies.]⠀⇛
Out of every 1,000 issued patents, only about
14 include prior art submissions from third
parties.
[...]
The following are some recently issued
patents that include third party submissions
if you want to look through the file
histories: 11,228,023; 11,225,200;
11,224,546; 11,224,456; 11,228,055;
11,221,486; 11,220,614; 11,219,722;
11,219,166.
# ⚓ FDA_Approves_Generic_Restasis [Ed: The lack of
generics up until now, due solely to patents, made the
lives of many people a lot worse]⠀⇛
On Wednesday, the U.S. Food and Drug
Administration announced approval to Mylan
Pharmaceuticals for a generic form of
Allergan’s RESTASIS® (Cyclosporine Ophthalmic
Emulsion 0.05%) product for treatment of
chronic dry eye. RESTASIS® is “a calcineurin
inhibitor immunosuppressant indicated to
increase tear production in patients whose
tear production is presumed to be suppressed
due to ocular inflammation associated with
keratoconjunctivitis sicca.”
# ⚓ Public_consultation_opens_on_latest_EPC_and_PCT-EPO
Guidelines [Ed: Criminals who took over the EPO pretend
to care about the general public while breaking the law
in every aspect]⠀⇛
The latest version of the EPC and PCT-EPO
Guidelines will come into force on 1 March,
and a preview version has been published
today. In parallel the EPO has opened its
public user consultation on these latest
Guidelines. Users are invited to submit their
comments in any one of the EPO’s three
official languages via an online form. The
deadline for contributions is 15 April 2022.
[...]
We encourage all patent professionals and
interested stakeholders to take this
opportunity to comment on the EPC and PCT-EPO
Guidelines.
The anonymised comments will be discussed
with the members of the SACEPO Working Party
on Guidelines in a meeting scheduled for May
2022.
# ⚓ Top_4_changes_to_the_2022_EPO_Guidelines_for
Examination [Ed: Constant and chronic liars, who
endlessly lie about UPC (Simmons & Simmons LLP), which
is illegal, rooting for corrupt_EPO_management instead
of condemning it; the unlawful guidelines do not comply
with EPC; of course Simmons & Simmons LLP is happy to
use the EPO’s words to promote software patents,
disregarding common sense and so_much_more]⠀⇛
The European Patent Office has today
published an advance preview of its annual
update to the Guidelines for Examination
which will come into force on 1 March 2022.
[...]
Following G 1/19, which maintained the status
quo by applying COMVIK to assess computer-
implemented simulations, G-II, 3.3.2 has been
updated to make it clearer how to approach
establishing whether or not there is a
technical effect when the claimed subject
matter involves a simulation. The new
discussion delineates different situations
where simulations are involved, covering the
gamut from purely numerical simulations with
no direct link with physical reality, to
simulations which interact with the outside
world.
Important concepts that were reinforced in G
1/19 are now emphasised in the Guidelines. In
particular, that output data of a simulation
may have a ‘potential technical effect’ – a
technical effect that would be produced when
the data is used according to an intended
technical use.
Correspondingly, G-VII, 5.4.1 has been
updated to refer to G-II, 3.3.2 when
formulating the objective technical problem
for mixed technical and non-technical claims.
# ⚓ Proven_Networks_proven_to_be_PAE_in_public_interest
statements_—_Unified_Patents⠀⇛
On January 27, 2022, Unified Patents filed a
public interest statement in the ITC on the
Proven Networks v. NetApp (inter alia)
investigation. Unified focused on Proven
Networks’ status as a litigation funded,
investment-driven NPE run and controlled by
the Russ, August, and Kabat firm. Read the
public statement below and also find comments
from a member of Congress, NetApp, and
others.
# § Software Patents⠀➾
# ⚓ Velos_’086_patent_successfully_challenged_—
Unified_Patents⠀⇛
On January 27, 2022, less than a year
after Unified filed its request for ex
parte reexamination, the USPTO issued a
final office action rejecting all
challenged claims of U.S. Patent
9,743,086, owned by Velos Media. Velos
Media had designated the ’086 patent as
essential to the HEVC standard. During
reexamination, to overcome the
rejections, Velos was forced to greatly
amend the claims of the ’086 patent
such that they are no longer essential.
# ⚓ MBHB_Webinar_on_Patent-Eligibility_and_the
Expanding_Notion_of_Abstraction [Ed: Patent
litigation profiteer Michael Borella has taken
his dishonest lobbying from blog_as_a_platform to
“webinar” (ads)]⠀⇛
McDonnell Boehnen Hulbert & Berghoff
LLP will be offering a live webinar
entitled “The Expanding Reach of the
Abstract Idea — What Is and Is Not
Patentable Eight Years After Alice” on
February 16, 2022 from 10:00 am to 11:
15 am (CT). In this presentation, MBHB
attorney and Patent Docs author Michael
Borella will review the current state
of patent eligibility and how the
exclusionary principle is licking its
lips. But in addition to sounding the
alarm, he will offer attendees an
unconventional take on what courts are
actually looking for in order for
claims to be found eligible — valuable
information that might just save your
inventions from judicial doom.
# § Trademarks⠀➾
# ⚓ The_TTABlog®:_CAFC_Affirms_TTAB:_“.SUCKS”_(Stylized)
Fails_to_Function_as_a_Source_Indicator_for_Domain
Registry_Operator_Services⠀⇛
In October 2020, the TTAB upheld failure-to-
function refusals of the term .SUCKS in
standard character and in stylized form
(shown below), for domain registry services
related to the gTLD in the proposed mark.
[TTABlogged here]. Applicant Vox Populi
appealed only the refusal of the stylized
version of the mark, arguing that the
stylization makes the proposed mark
registrable. The court, however, found no
error in the Board’s conclusion that the
stylized form of .SUCKS fails to create a
commercial impression separate from the
unregistrable term .SUCKS. In re Vox Populi
Registry Ltd., Appeal No. 2021-1496 (Fed.
Cir. February 2, 2022) [precedential (Opinion
by Judge Timothy B. Dyk).
[...]
The question, then, was whether the
stylization of the stylized form rendered
that mark registrable.The court observed that
this issue requires a subjective
determination “based on a viewer’s first
impression.” The court cited several well
known TTAB decisions as examples (stylized
versions of CONSTRUCT-A-CLOSET (registrable),
JACKSON HOLE (registrable), BUNDT
(unregistrable), and SADORU (unregistrable),
and then concluded that the Board did not err
in ruling that the stylized form of .SUCKS
fails to create a separate commercial
impression.
# ⚓ TTABlog_Test:_How_Did_These_Four_Section_2(d)_Appeals
Turn_Out?⠀⇛
In January 2022, the Board decided twenty-two
(22) appeals from Section 2(d) refusals. It
affirmed them all. Here are the first four
Section 2(d) decisions of this month. Has the
streak been broken? How do you think they
turned out? [Answers in first comment].
In re Charlie’s Chalk Dust, LLC, Serial No.
88417905 (February 1, 2022) [not
precedential] (Opinion by Judge Elizabeth A.
Dunn). [Section 2(d) refusal of PACHAMAMA
for, inter alia, "herbal tinctures" and
"essential oils; non-medicated topical skin
care preparations" all "containing naturally
occurring trace amounts of CBD derived from
hemp and less than .3% THC," in view of the
registered mark PACHAMAMA PEOPLE for “Dietary
and nutritional supplements made of herbs;
Herbal tinctures for use as nutritional
supplements; Herbal tinctures for use in
healing.”]
䷩ 𝚕𝚒𝚗𝚎 5325
╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕
⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.06.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧
Gemini_version_available_♊︎
✐ Links_6/2/2022:_Absolute_GNU/Linux_15.0_and_Linux_on_IBM_PalmTop⠀✐
Posted in News_Roundup at 11:31 am by Dr. Roy Schestowitz
🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈
§ Contents⠀➾
* GNU/Linux
o Distributions
o Devices/Embedded
* Free_Software/Open_Source
* Leftovers
* § GNU/Linux⠀➾
o § Audiocasts/Shows⠀➾
# ⚓ Full_Circle_Weekly_News_#247⠀⇛
# ⚓ GNU_World_Order_446⠀⇛
Slackware 15 has been released. In the second half
of the show, packages **attica** , **audiocd-kio**
, **baloo** , and **baloo-widgets**.
# ⚓ 184:_Slackware_15,_ProtonDB,_Peppermint_OS,_Raspberry_Pi,
Tiny_Core,_Trisquel_|_This_Week_in_Linux_–_TuxDigital⠀⇛
On this episode of This Week in Linux, Slackware
15.0, Tiny Core Linux 13.0, Trisquel 10.0,
Peppermint OS, 64-bit Raspberry Pi OS, System76:
Kudu Laptop & Scheduler, LibreOffice 7.3, KDE
Falkon 3.2, GStreamer 1.20, Steam Deck Verified &
Anti-Cheat Update, Statistics Changes On ProtonDB
and Aurin: AUR Install Via Browser. All that and
much more on Your Weekly Source for Linux GNews!
o § Applications⠀➾
# ⚓ Inkscape_1.1.2_Delivers_More_Bug_Fixes,_Inkscape_1.2
Promises_Major_UX_Changes⠀⇛
Coming more than four months after Inkscape 1.1.1,
Inkscape 1.1.2 delivers more bug fixes for users of
the Inkscape 1.1 series. These bug fixes improve
various components to work as expected, such as
Toolbar fields, which again use the units selected
by the user as display units in Document
preferences.
Also improved in Inkscape 1.1.2 is support for
graphic tablet pens that have a built-in eraser tip
as they now again automatically switch to the
correct tool. Moreover, improves repeated copy/
paste of an object into a new document with a Live
Path Effect to also paste the current object rather
than an outdated one.
# ⚓ Best_Free_and_Open_Source_Alternatives_to_Cisco_Secure
IDS⠀⇛
Cisco Systems, Inc. is an American multinational
technology corporation that focuses on networking
hardware and software. It has over 75,000 employees
with its headquarters in San Jose, California.
Cisco has been participating in open source
development for almost 30 years including founding
projects like OpenDaylight, FD.io, VPP, PNDA, SNAS,
and OpenH264, and contributing to projects like
OPNFV, Kubernetes, OpenStack, Ansible, Chef,
Puppet, Maven, and many others.
Cisco has also been a key contributor to the Linux
kernel over the years, accounting for about 0.5% of
total kernel commits, and is a Platinum Member of
the Linux Foundation and Premium Sponsor of the
Open Source Initiative.
o § Distributions⠀➾
# § New Releases⠀➾
# ⚓ Educational_Distro_Escuelas_Linux_7.3_Is_Here_with
Linux_5.15_LTS,_LibreOffice_7.3,_and_More⠀⇛
Coming more than three months after Escuelas
Linux 7.2, the Escuelas Linux 7.3 release is
here to bump the kernel version to the latest
long-term supported series, Linux 5.15 LTS,
which brings support for newer hardware, as
well as better support for existing devices.
Escuelas Linux is based on Bodhi Linux, which
is derived from Ubuntu, and uses the Moksha
desktop environment (an Enlightenment fork).
The new release ships with Moksha 0.3.4-10, a
release that comes with a lot of goodies,
including the ability to drag a window to the
left or right side of the screen to maximize
it on half of the screen.
# § Slackware Family⠀➾
# ⚓ Absolute-15.0_released⠀⇛
Six years from 14.2, version 15 of Slackware
arrived a couple days ago. Still rock-solid.
Still without systemd. Still crazy after all
these years…. ?
I’m giddy.
I still love the approach Slackware takes
toward a solid, bare-bones system. I like to
dress it up just enough to make it quickly
productive and up- to-date for myself. I will
keep the “rolling update” going with the
roughly monthly snapshots… the next release
of Slackware might be a while 🄸🄼🄰🄶🄴
🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇:-)⦈
o § Devices/Embedded⠀➾
# ⚓ IBM_PalmTop_Running_Modern_(Modified)_Linux_|_Hackaday⠀⇛
The handheld computing market might seem dominated
by smartphones today, but before their mass
adoption there were other offerings for those who
needed some computing power on-the-go. If a 90s
laptop was too bulky, there was always the IBM
PalmTop which packed punch for its size-to-weight
ratio, and for the era it was created in. [Mingcong
Bai] still has one of these antiques and decided to
see if it was still usable by loading a customized
Linux distribution on it.
The PalmTop sported modest hardware even for its
time with an Intel 486SL running at 33 MHz with 20
MiB of RAM. This one also makes use of a 1 GB
CompactFlash card for storage and while [Mingcong
Bai] notes that it is possible to run Windows 95 on
it, it’s not a particularly great user experience.
A Linux distribution customized for antique
hardware, AOSC/Retro, helps solve some of these
usability issues. With this it’s possible to boot
into a command line and even do some limited text-
based web browsing as long as the Ethernet adapter
is included.
# § Open Hardware/Modding⠀➾
# ⚓ OpenBikeSensor_Measures_Close_Calls_|_Hackaday⠀⇛
Cycling is fun, healthy, and good for the
environment. But unfortunately it’s not
always the safest of activities, as
inconsiderate drivers can be a significant
hazard to cyclists. Several countries,
including Germany, France, and Belgium have
introduced legislation mandating a minimum
passing distance of at least 1.5 meters
between cars and bikes. Enforcing such a rule
is tricky however, and without accurate data
on average passing distances it’s hard to
know how many drivers are following it.
Enter OpenBikeSensor, an open-source hardware
and community science project designed to
gather exactly this information. Currently in
its prototype phase, it aims to make a simple
bike-mounted sensor that measures the lateral
distance to any passing vehicles. The
resulting data is collected online to
generate maps highlighting danger zones,
which can ultimately be used by city planners
to improve cycling infrastructure.
# § Mobile Systems/Mobile Applications⠀➾
# ⚓ The_best_habit_tracker_apps_for_Android_–_Android
Authority⠀⇛
# ⚓ Android_users_warned_over_Google_Play_Store_password
security_app_that_can_steal_your_money_–_delete_it
NOW⠀⇛
# ⚓ Renders_of_Android-powered_Pixel_tablet_surface;
images_are_based_on_Google_patent_–_PhoneArena⠀⇛
# ⚓ Android_Phone_Going_Straight_To_Voicemail?_Try_This_|
Screen_Rant⠀⇛
# ⚓ This_Samsung_Galaxy_S22_news_will_have_all_Android
rivals_worried_|_Express.co.uk⠀⇛
o § Free, Libre, and Open Source Software⠀➾
# § Programming/Development⠀➾
# ⚓ Twist_Promises_Easier_Quantum_Programming_|
Hackaday⠀⇛
We keep trying to learn more about quantum
computers. But the truth is, the way we
program quantum computers — or their
simulators — today will probably not have
much in common with how we program them in
the future. Think about it. Programming your
PC is nothing like programming the ENIAC. So
we expect we’ll see more and more
abstractions over the “bare metal” quantum
computer. The latest of these is Twist, from
MIT.
According to the paper (and the video,
below), Twist expresses entangled data and
processes in a way that traditional
programmers can understand. The key concept
is known as “purity” of expressions which
helps the compiler determine if data is
actually entangled with another piece of data
or if any potential entanglement is
extraneous. A pure expression only depends on
qubits it owns, while a mixed expression may
use qubits owned by other expressions.
# ⚓ Write_code_inspired_by_Shakespeare_with_esolang_|
Opensource.com⠀⇛
Maybe you’ve heard that playwright William
Shakespeare contributed 1,700 new words to
the English language. But did you know that
he has an entire programming language as
well?
SPL (Shakespeare programming language) was
created to make source code resemble
Shakespeare plays. It is an esoteric
language, also known as an esolang. An
esolang is a computer programming language
designed to experiment with weird ideas,
create a challenge for programmers, or simply
serve as a source of amusement, rather than
for practical use.
* § Leftovers⠀➾
o ⚓ Hendrix_in_Our_Time⠀⇛
Three completed studio albums: Are You Experienced?
(1967), Axis: Bold as Love(1968), Electric Ladyland
(1969). That’s all we have from Jimi Hendrix. Each
distinctive. Each meticulously crafted. Each musically
innovative and thematically coherent. There’s nothing
else like them in the canon of rock music. And then he
was gone. Dead in a London flat at the age of 27 and, as
a consequence, forever linked to the ghosts of two
infinitely lesser talents: the Texas screecher Janis
Joplin and the messianic drug-fiend Jim Morrison.
To read this article, log in here or subscribe here. In
order to read CP+ articles, your web browser must be set
to accept cookies.
o ⚓ New_Frontex_command_structures:_Vice_directors_begin_their_work⠀⇛
Since 2016, the EU border agency has been given
considerably more power. A new management post is now
responsible for the currently established armed border
force, a deportation unit and data retention.
o ⚓ Camping_For_$25:_Thrift_Store_Hacks_To_Keep_Cozy_|_Hackaday⠀⇛
A hacker is somebody who’s always thinking creatively to
solve problems, usually using what they have on hand.
Sometimes that means using a 555 to build a CPU, and
other times it means using a dead flashlight to start a
fire. In the video below the break, [Kelly] shows us a
series of hacks you can use while camping in the woods
for a night to keep you warm, dry, and well fed!
o § Health/Nutrition/Agriculture⠀➾
# ⚓ Opinion_|_Farms_at_the_Breaking_Point_Worldwide⠀⇛
o § Integrity/Availability⠀➾
# § Proprietary⠀➾
# § Security⠀➾
# § Privacy/Surveillance⠀➾
# ⚓ Biometric_mass_surveillance:_New_study
warns_of_Chinese_surveillance_methods_in
Europe⠀⇛
Also on Friday, 4 February, the
Winter Olympics will open in
Beijing, China, against a
backdrop of serious human rights
concerns. However, in the run-up
to the upcoming 2024 Olympics in
Paris, organisers in Europe are
also looking into the possibility
of increasing biometric mass
surveillance at sporting events.
In doing so, politicians would
deliberately accept the loss of
privacy, limitation on freedom of
expression, and the division of
society and discrimination.
o § Defence/Aggression⠀➾
# ⚓ Opinion_|_Tone-Deaf_Navy_Lawsuit_Wrongfully_Calls_State_of
Hawaii_Shut_Down_of_Leaking_Jet_Fuel_Tanks_‘Erroneous’⠀⇛
Two lawsuits filed on February 2, 2022 by the U.S.
Department of Justice on behalf of the Department
of Defense and the Department of Navy challenge the
State of Hawaii’s emergency order to shut down and
defuel the leaking 80-year-old jet fuel tanks.
These lawsuits have created another public
relations nightmare for the U.S. Navy and the
Department of Defense as residents of O’ahu have
expressed their dismay and outrage to the
continuing threat of jet fuel to their drinking
water aquifer. In November 2021, the Red Hill tank
system leaked jet fuel into the drinking water of
93,000 residents in military housing around Pearl
Harbor Navy Base and Hickam Air Force base.
# ⚓ Opinion_|_Is_Congress_Willing_to_Fix_Biden’s_Failed_Yemen
Policy?⠀⇛
# ⚓ Police_in_Hesse_expand_use_of_„Super_Recognisers“⠀⇛
In Frankfurt, two full-time officers are now
working for the humanoid facial recognition. Every
day, they compare current wanted persons with
existing pictures in police databases. The
procedure is also supposed to work with concealed
faces.
# ⚓ Death_Surrounds_Us_—_We_Cannot_Ignore_Its_Reality,_or_Its
Mystery⠀⇛
# ⚓ A_‘Welcome_Move’:_Biden_Restores_Sanctions_Waiver_Targeting
Iran⠀⇛
Supporters of the Iran nuclear deal welcomed news
Friday that the Biden administration restored
sanctions waivers seen as key to a mutual return to
the agreement.
“Trump never should have revoked these waivers in
the first place, which are in the U.S. interest and
benefit nonproliferation efforts.”
# ⚓ Russia,_Ukraine,_and_The_New_York_Times⠀⇛
Ukraine shares a border with Russia the way Mexico
and Canada do with the United States. Since 1823,
we have claimed the right to defend our hemisphere
in accordance with the Monroe Doctrine, and now
Russia is putting into practice a similar policy
against a militarized Ukraine. The parallels are
close; the reasons for a defensive posture,
obvious. Yet Secretary of State Antony Blinken has
said the US no longer believes that there are
spheres of influence.
Or rather, there is just one sphere: the ever-
expanding terrain of legitimate Western democracies
approved by NATO. This worldview—an immediate,
unexamined consequence of the fall of Soviet
communism in 1991—cut a clear path through the
Clinton, George W. Bush, Obama, and (for all the
fuss) Trump administrations. But there were two
bumps that might have served as a warning. In 2008,
Georgia’s attack on Russian troops in South Ossetia
was answered with decisive and crushing force, and
in 2014, Russia responded to the US-backed coup in
Ukraine by annexing Crimea. Vladimir Putin
explained that when he next visited Sevastopol, he
would prefer not to be greeted by NATO sailors on
the Black Sea.
# ⚓ The_Politics_of_the_Capitol_Insurrection_Are_Spreading
Across_the_Country⠀⇛
There was a sense, on the afternoon of the Capitol
insurrection, that violent white American Trumpism
had reached its apex. But by the next morning, as
Republican politicians and right-wing media figures
began rewriting history in real time—claiming
antifa actually did it, pretending the
insurrectionists merely went on self-guided tours
of the building and “took selfies,” portraying the
white mobs as victims—it became clear that the
previous day’s act of sedition hadn’t been the
final spasm of white supremacist anti-democracy but
the harbinger of white supremacist anti-democracy
to come. And those who support and excuse it are
attempting to give the anti-democratic violence of
the insurrection a veneer of respectability by
dressing it up in the language of election
integrity.
o § Finance⠀➾
# ⚓ Opinion_|_The_Federal_Reserve_Is_About_to_Give_US_Workers
the_Shaft⠀⇛
o § AstroTurf/Lobbying/Politics⠀➾
# ⚓ House_Dems’_New_Anti-Progressive_PAC_Is_Funded_by_Corporate
Lobbyists_and_PACs⠀⇛
# ⚓ Forced_Sterilizations_Are_Still_Legal_in_31_States,_New
Report_Shows⠀⇛
# ⚓ South_Dakota_Governor_Signs_“Cruel_and_Dangerous”
Transgender_Athletes_Ban⠀⇛
# ⚓ Stop_the_Saber-Rattling!_Greens_Call_for_Immediate
Diplomacy_to_Resolve_Ukraine_Crisis⠀⇛
Green Party leaders called on the Biden
administration to immediately cease escalating
military tensions and pursue a diplomatic solution
to the Ukraine crisis.
In response to fear of Russian military incursion
into Ukraine, this week U.S. troops from a number
of bases across the country have been put on high
alert for possible deployment to Europe, and the
U.S. has sent a second batch of weapons to Ukraine.
Paramilitaries trained by the CIA in the U.S. are
reportedly advising counterparts in eastern
Ukraine, even while Democrats in Congress are fast-
tracking for passage this week a bill for $500
million more in weapons for Ukraine.
The Biden administration’s threats of military
buildup and sanctions against Russia are escalating
this crisis to an increasingly dangerous level. The
one-upmanship and nuclear and military rhetoric
must cease immediately. The only gains in a
military clash are for military contractors.
“The risk of this conflict erupting into a
disastrous large-scale war is too great to ignore
in order to please arms makers and bellicose
politicians,” said Madelyn Hoffman, 2020 Green
Party candidate for U.S. Senate from New Jersey and
a member of the Green Party Peace Action Committee
(GPAX). “Specifically, in the matter of Ukraine,
the U.S. should negotiate a reduction of military
forces in the conflict zone. We call on the Biden
administration to pursue a diplomatic solution. We
urge the Biden administration to heed European
Union allies France and Germany calling for
diplomacy, to acknowledge that Ukraine leaders
believe Russian invasion is not imminent, and to
pursue possible grounds for talks on secondary
issues. The United States must also respect
Ukraine’s right to self-determination.”
o § Freedom of Information/Freedom of the Press⠀➾
# ⚓ Arrests_Aim_to_Silence_Kashmiri_Journalists_and_Human
Rights_Defenders_–_Censored_Notebook⠀⇛
India, the world’s largest democracy, continues to
use draconian laws to silence and incarcerate
journalists and human rights defenders in Kashmir.
On February 4, Fahad Shah, founder and editor of
the Kashmir Walla was arrested by local police for
“uploading anti-national content…to create fear
among the public.” On January 6, Kashmiri
journalist Sajad Gul was arrested and later booked
under the Public Safety Act, which allows for the
detention of civilians for up to two years. One of
the most prominent arrests is that of human rights
activist Khurram Parvez on November 22, 2021.
# ⚓ Chris_Hedges:_Mass_politics_must_be_rooted_in_class
struggle⠀⇛
o § Civil Rights/Policing⠀➾
# ⚓ Biden_Should_Replace_Breyer_With_a_True_Progressive⠀⇛
# ⚓ Disabled_Activist_Speaks_Out_Against_Ableism_During
Pandemic⠀⇛
# ⚓ Referral_Unit_at_Europol:_German_police_had_thousands_of
internet_contents_removed_last_year⠀⇛
Currently, hosting providers can decide whether to
voluntarily comply with removal requests in the
area of „Islamist terrorism“ from Europol. From 7
June, these will become removal orders, which can
be sent directly to companies by national
authorities via a new platform.
# ⚓ Paid_Leave_for_All:_Worker_Advocates_Demand_Expanded
Protections⠀⇛
Economic justice advocates and Democratic lawmakers
on Saturday issued fresh demands for comprehensive
paid leave for the nation’s workers, saying such
protections would address crucial gaps in labor law
that the ongoing pandemic has underscored.
The calls came on the 29th anniversary of the
Family and Medical Leave Act (FMLA), which provides
eligible employees with up to 12 weeks of job-
protected leave to care for a new child or take
care of one’s own or family member’s illness. But,
worker advocates say, the groundbreaking law is
sorely insufficient, because the leave is unpaid
and FMLA doesn’t cover all workers.
o § Monopolies⠀➾
# § Patents⠀➾
# ⚓ Counsel_call_for_transparency_in_China’s_bad-faith
screening
[Ed: When Sukanya Sarkar says "sources" she means
sponsors (for whom she amplifies something for lobbying
purposes)]⠀⇛
Sources say China’s measures to tackle bad-
faith patent filings have delivered mixed
results, and genuine applicants are suffering
because of its lack of transparency
# ⚓ Counsel_laud_India_SC’s_rare_TM_decision,_but_want
more ][Ed: This is about trademarks, but same author.
Notice how they always tell what "Counsel" have to say
but nobody else; bought 'journalism'.]⠀⇛
The Supreme Court of India’s recent trademark
infringement ruling on identical marks is
welcome, but counsel hope that the forum
settles more key issues soon
# ⚓ Counsel_at_odds_over_UK_designs_overhaul [Ed: Max
Walters still a faithful mouthpiece of lawsuits-happy
sponsors of his journalism (lobbying). what do people
who cannot profit from litigation have to say, Max?]⠀⇛
Counsel say the UKIPO’s call for views on
post-Brexit design laws provides a chance to
explore new opportunities, but note that red
flags have been raised
# ⚓ Continental_Europe’s_patent_firms_slow_to_increase
hourly_rates [Ed: The aggressive litigation firms that
pay_this_writer for propaganda charge ‘only’ half a
grand an hour?]⠀⇛
€700 is substantial in terms of hourly rates,
even for a European partner specialising in
patent litigation. This is what a partner at
a leading German patent litigation firm
charges on average per hour in a normal
infringement case.
“In litigation for US clients, I can charge
up to €1,250 per hour,” reveals the partner
of a leading German patent litigation firm.
In large global patent battles, one patent
attorney reports that the wallets of US
clients are particularly loose. They can also
charge up to €1,200 per hour for such
proceedings.
In contrast, in 2021, partners in law and
patent attorney firms across Europe charged
an average of €460 per hour for patent
litigation. This is one result of a current
survey by JUVE Patent among European patent
firms.
# ⚓ A_remote_village,_a_world-changing_invention_and_the
epic_legal_fight_that_followed [Ed: Instead of feeding
people Ocado is just suing people with junk patents
that courts already frown upon; of course the EPO
played a role]⠀⇛
If your groceries are supplied by Ocado in
the U.K. (or Kroger in Cincinnati and
Atlanta, or Casino in Paris, for which Ocado
supplies technology), you have experienced
his legacy. The retail industry increasingly
relies on automated warehouses, and the
approach that Hognaland pioneered and that
Ocado built on, is even more advanced than
Amazon’s. AutoStore systems are being used in
more than 40 countries, with 29,000 robots on
wheels.
It would be an inspiring story of inventive
genius in logistics, except for one problem:
Hognaland’s idea turned out to be so valuable
that Ocado adapted it without permission.
That set off an ongoing global patent battle
between the two companies, with billions at
stake. When Ocado won one stage of a U.S.
legal case in December, its value rose by
more than £1 billion that day, while
AutoStore’s dropped.
On one side is a quiet, determined
Scandinavian company that spent a quarter of
a century diligently making its robots work,
one step at a time. On the other, an
aggressive British disrupter that seized on
the idea to turn itself into a juggernaut.
And beneath it all, a classic question: does
a revolutionary innovation belong to the
person who had the idea, or should it belong
to the world?
# ⚓ American_Manganese_poised_to_add_China_to_its_global
patent_portfolio [Ed: US has fallen so far behind that
now there’s an effort to secure patents in China rather
than the other way around; Chinese_patent_quality_is
regarded_as_a_joke]⠀⇛
The Chinese patent office has issued the
company with a ‘Notice of Allowance’ for the
company’s National Phase Patent Application
for its technology RecycLiCo.
# ⚓ An_End_To_Adapting_The_Description_To_Allowed_Claims
At_The_EPO? [Ed: This board, like all the other boards,
isn’t compliant with the EPC; it’s basically a kangaroo
court_controlled_by_the_EPO’s_corrupt_and_truly
illegitimate_regime]⠀⇛
According to EPO Examining Division practice,
once claims are found to be allowable, the
description must be “adapted to the claims to
avoid inconsistencies between the claims and
the description” (The Guidelines for
Examination in the European Patent Office,
Part F, Chapter IV, section 4.3, paragraph
iii1). In a recent decision (T1989/182) an
EPO Technical Board of Appeal considered the
legal basis for this requirement.
# ⚓ Implementing_Regulations_Confirm_The_GCC_Patent
Office’s_New_Working_Model
[Ed: Overzealous litigation giant Gowling WLG, which
spreads fake news for financial gain, is trying to
extend its 'patent hegemony' regime to the Gulf]⠀⇛
In January 2021, the Patent Office of the
Gulf Cooperation Council (GCC patent office)
stopped accepting new GCC patent applications
following a meeting of the GCC Supreme
Council. This meeting resulted in an amended
GCC Patent Regulation being issued in May
2021 and more recently the Implementing
Regulations in November 2021. Below we take
you through the key takeaways for the new
Regulations.
A review of the Regulations confirm the
position set out in the amended GCC Patent
Regulation, that the GCC Patent Office will
resume handling patent applications, their
examination and grant, as well as annuities.
However, the significant change from pre-
January 2021 applications, is that the GCC
Patent Office will only do so upon request
from a national patent office in the GCC.
Rather than file directly with the GCC Patent
Office, applicants will have to file for a
GCC patent through a national office.
# ⚓ Nokia_4G_patent_upheld_by_European_Patent_Office,
stronger_than_ever_thanks_to_Daimler’s_wasteful
litigation_effort [Ed: Nokia leverages patents from the
EPO to tax everything, and to nobody’s actual
advantage]⠀⇛
The dispute with Daimler is the gift that
keeps on giving to Nokia. The case settled
seven months ago, but yesterday Nokia’s
EP2550762 on “signalling of channel
information” got upheld by an opposition
panel of the European Patent Office with only
a minor amendment, which still allows Nokia
to claim that it is essential to the 4G/LTE
standard. The patent relates to carrier
aggregation (aggregating bandwidth from
different parts of the spectrum).
Nokia didn’t assert that standard-essential
patent (SEP) against Daimler, but it was on a
list accompanying Nokia’s infringement
notice, so Daimler and its supplier TomTom
challenged it, possibly also hoping to drive
up Nokia’s litigation costs. Daimler wasn’t
actually listed as a party, but their lawyers
(Quinn Emanuel) obviously weren’t opposing
the patent pro bono.
[...]
Daimler’s litigation department managed that
litigation a bit like people who order
whatever item on the restaurant menu is
priciest. You could take a burger straight
out of McDonald’s, put it on the menu, charge
$350, and those types of people would order
it even if they could get a filet mignon from
wagyu beef at half the price at what would
still be an upscale restaurant on the other
side of the street. There came a point when
others in the organization were no longer
prepared to support that wasteful spending.
Now they just have to realize at Daimler that
it’s a mistake in German patent litigation
not to hire interdisciplinary teams
consisting of attorneys at law and patent
attorneys. Patent attorneys won this one for
Nokia.
Nokia definitely got a lot of value out of
the Daimler dispute. But again, sophisticated
tech companies, above all smartphone makers,
are the real challenge, provided that can
come up with a new challenge to EP’762 as
merely rehashing Daimler’s unavailing
arguments won’t help.
# ⚓ Relief_Announces_That_Collaboration_Partner,_Acer
Therapeutics,_was_Issued_U.S._Patent_11,202,767
Covering_ACER-001_Methods_of_Use_for_Treatment_of_Urea
Cycle_Disorders_and_Maple_Syrup_Urine_Disease⠀⇛
# ⚓ Worldwide:_For_The_First_Time_In_History_–_Australian
Court_Rules_That_Artificial_Intelligence_Can_Be
Registered_As_An_Inventor_In_A_Patent [Ed: This has
been mostly a source of shame and disgrace to
Australia, which got conned_by_buzzwords, lies, and
lawyers]⠀⇛
In the last month, the Australian court has
set a global legal precedent, according to
which an artificial intelligence system can
be registered as an inventor under a patent.
Although the decision is not a formal legal
precedent, it may be the first far-reaching
change in the realm of intellectual property,
science, technology and business.
# ⚓ UK_Court_Rules_Apple_Must_Unconditionally_Commit_To_A
FRAND_License_To_Avoid_An_Injunction [Ed: Blackmail
(embargo) by patents benefits nobody, even if in this
particular case it hurts a nasty company like Apple]⠀⇛
In a recent judgment (Optis Cellular
Technology LLC & Ors v Apple Retail UK Ltd &
Ors [2021] EWHC 2564 (Pat), 27 September
2021), Meade J, sitting in the England and
Wales High Court, gave a decision in a series
of trials relating to eight of Optis’s
patents in the field of telecommunications.
Each of these patents is asserted to be a
standard-essential patent (SEP) and was
declared to the European Telecommunications
Standard Institute (ETSI).
# ⚓ T_1989/18:_adaptation_of_the_description_of_a
European_patent_application [Ed: Suffice to say, these
EPO_tribunals_are_patently_rigged; a dog wagged by its
own tail]⠀⇛
Prior to grant of a European patent
application, examiners often request the
description to be adapted for consistency
with the subject matter of the allowable set
of claims. This became a more onerous
exercise following an update to the EPO
Guidelines for Examination in March 2021,
which set out a significantly greater range
of circumstances in which the description
should be adapted. A recent decision from an
EPO Board of Appeal considered whether there
was legal basis for refusing an application
if the description was not adapted to the
subject matter of the claims.
# ⚓ Progress_for_the_realisation_of_the_Unified_Patent
Court [Ed: No, UPC is illegal; as such, it_will_be
stopped, just like before…]⠀⇛
The Unified Patent Court (UPC) is a proposed
common patent court open for EU member states
hearing cases regarding infringement and
revocation of European patents (including the
new Unitary Patent). If carried through, the
Unitary Patent and the UPC represents
significant changes to European patent law.
In essence, it will create a single approach
to patent protection and litigation across
the participating EU member states.
# ⚓ [Older]Current_Patenting_Issues_In_Europe_Facing_Life
Sciences/Biotech_Innovators_And_Effective_Claim
Drafting_Strategies_To_Avoid_Pitfalls [Ed: Notice the
total disregard for the law; they look at the law as an
obstacle to overcome, not obey, in the name of
aggression/litigation]⠀⇛
This paper is in two sections. The first
relates to current topics, issues and
developments in European patent practice in
that may be relevant for innovators in the
life sciences. As far as possible, this first
part tracks the issues discussed from a US
perspective in the paper submitted by my co-
panellist Courtenay Brinckerhoff of Foley &
Lardner LLP, in the hope that US-based
readers can better compare the situation in
the US with that in Europe. The second part,
focussing on differences between US and
European practice and how to avoid these
differences becoming pitfalls for US
applicants, is more timeless – as in general
these issues change relatively little over
time, and yet they remain problems if they
remain unfamiliar. For completeness, both
sections include some information on issues
that are general to all applicants but
equally or especially relevant to those in
the life sciences.
# ⚓ [Older]_Judge_Albright_Issues_Updated_Standing_Order
for_Patent_Cases [Ed: The patent_trolls’_kangaroo
court]⠀⇛
The Eastern District of Texas manages more
patent cases than any other district court in
the United States.
# ⚓ Imugene_welcomes_new_chief_medical_officer_and_talks
significant_new_patents [Ed: Too much emphasis on
patents instead of products; in this case, patents from
EPO whose own examiners complain_about_invalid
grants]⠀⇛
Imugene’s Leslie Chong discusses with
Proactive’s Andrew Scott the appointment of
Dr Steven Cha as Chief Medical Officer and a
member of the company’s executive management
team. IMU has recently received a notice of
grant from the Japanese Patent Office which
protects its oncolytic virotherapy CF33,
including VAXINIA (CF33-hNIS) and CHECKVacc
(CF33-hNIS-antiPDL1). The company has also
opened the doors to a large and lucrative
market for immuno-oncology by securing a
Notice of Grant from the European Patent
Office for its HER-Vaxx immunotherapy.
# ⚓ [Older]_An_Absolute_Novelty_Design_Patent_Trap_for
the_Unwary [Ed: Design_patents are a sham]⠀⇛
Global design patent strategies are
increasingly being relied upon by retail and
consumer products companies as a cost-
effective way to protect key product lines.
However, it is important to understand the
various nuances of global design patent
strategies since there are traps for the
unwary, most notably in Australia and China.
# ⚓ EPO_to_Allow_Applicants_to_File_Early_Requests_to
Obtain_a_Unitary_Patent [Ed: EPO knowingly_breaking_the
law_yet_again; and since nobody ever holds the EPO
accountable for its many crimes even the so-called law
firms are boosting these illegal acts for personal
(financial) gain)]⠀⇛
The EPO has issued a notice explaining that,
in the lead up to the entry into force of the
Unified Patent Court (UPC) Agreement, which
will make “Unitary” Patents available based
on a granted European patent, it will be
possible for applicants to file early
requests for a European patent to take
unitary effect after grant.
# ⚓ The_Fundamentals_of_the_Unified_Patent_Court_System
and_the_New_Unitary_Patent [Ed: Orrick, Herrington &
Sutcliffe LLP cannot help itself; it knowingly_misleads
clients_and_lobbies_for_illegal_agenda_using_fake_news
strategies]⠀⇛
To understand the impact of the Unitary
Patent and the Unified Patent Court, it is
helpful to consider the status quo of
European patent law.
Each European country has its own patent
laws, and patents are generally granted with
national effect only.
# ⚓ The_UPC_Opt-out_for_European_Patents_–_Should_I_Stay
or_Should_I_Go? [Ed: For the second time in one week
this so-called 'law' firm produced misleading
headlines, in order to promote this idea that an
illegal system is already here and in force]⠀⇛
For further insights related to the Unitary
Patent and the Unified Patent Court click
here.
Proprietors of European Patents will have the
opportunity to avoid jurisdiction of the
Unified Patent Court by filing so-called opt-
out applications during an initial
Transitional Period of at least seven years.
An opt-out will remove the jurisdiction of
the UPC for the opted-out European Patent and
effectively maintain the judicial status quo:
Opted-out European Patents can only be
enforced or invalidated by national courts in
the same way they can now.
However, a European Patent can only be opted
out so long as it has not yet been the
subject of UPC proceedings. For example, once
a revocation action has been filed against a
European Patent with the UPC, opting out will
be impossible. Accordingly, the decision of
whether or not to opt-out can be time
critical.
# ⚓ Germany:_UPC_–_Progress_Towards_The_Start_Of_The
Unitary_Patent_System [Ed: Keltie, which has_long
promoted_illegal_agenda (breaking of the law does not
bother so-called ‘law’ firms), is once again pushing
fake news and utterly illegal agenda]⠀⇛
Following delays from Brexit and a
constitutional challenge in Germany, the
deposit of Austria’s instrument of
ratification on the Protocol on Provisional
Application to the Agreement on a Unified
Patent Court (UPC) in mid January 2022 has
started the provisional application period
which allows final preparations for the UPC
to be made.
# ⚓ Unitary_Patent_court:_where_we_are_and_where_we’re
going [Ed: Bugnion SpA, with an utter conflict of
interest, also maliciously spreads false_“news” in an
effort to enforce an illegal and unconstitutional
agenda]⠀⇛
# ⚓ EPO_Issues_Guidance_On_Achieving_Unitary_Patent
Status_From_Day_1_Of_The_UPC/UP_System_For_European
Patent_Applications_Coming_Up_To_Grant [Ed: EPO is
(once again) intentionally breaking the law and Herbert
Smith Freehills, profiteers of patent trolls, cheer for
the criminals]⠀⇛
# ⚓ The_Unitary_Patent_and_the_Unified_Patent_Court_Are
Expected_to_Go_Live_in_Less_than_a_Year [Ed: More fake
news, as usual, from people with a clear conflict of
interest]⠀⇛
The Unitary Patents system – providing for
the new Unitary Patent and Unified Patent
Court (UPC) – will have a profound impact on
patent protection, patent enforcement and
patent revocation proceedings in Europe.
# ⚓ Unified_Patent_Court_starts_final_preparations [Ed:
And yet another large so-called ‘law’ firm is promoting
a_crime, based on fake news that it helped promote with
other such firms]⠀⇛
Austria deposited its ratification of the
Protocol on Provisional Application of the
Agreement on a Unified Patent Court as the
thirteenth signatory state with the European
Council on 18 January 2022. As a result, the
phase of provisional applicability of the
Agreement on a Unified Patent Court (UPCA)
will enter into force. This phase includes
the final organisational preparations for the
launch of the UPC. The Chairman of the
Preparatory Committee, Alexander Ramsay,
expects that the UPC could start its work
after a preparatory phase of about eight
months. Subsequently, Germany as “gatekeeper”
is to deposit its instrument of ratification
of the UPCA, so that the UPCA will enter into
full force four more months later.
# ⚓ ILOAT:_Former_EPO_president_Battistelli_violated
staff’s_right_of_free_association [Ed: And see_the
pattern]⠀⇛
The EPO violated the fundamental right of
free association of its staff in 2014 by
giving (former) president Benoit Battistelli
the power to determine the detailed
conditions relating to the staff committee
elections. The Administrative Tribunal of the
International Labour Organization (ILOAT) has
ruled this in its judgment 4482, which was
published after its 133d session late
January. The decision, together with two
other ILOAT judgments in which high moral
damages were awarded, is yet again a display
of the lack of legal protection and democracy
at the EPO in the Battistelli era.
Last year, the ILOAT had already ruled that
Battistelli abused his power in July 2013 by
restricting the rights of staff members to
strike (case 4430), see also this blogpost.
At the time the ILOAT ruled that Circular No.
347, regulating the restrictions, was
unlawful. This time Circular No. 355 was
quashed by the ILOAT, which contained
implementing rules for a “social democracy”
reform introduced by the Administrative
Council in decision CA/D 2/14 on 28 March
2014.
# § Software Patents⠀➾
# ⚓ $12,000_for_Atlantic_IP_Services_sub,_Speir
Technologies,_prior_art⠀⇛
On January 28, 2022, Unified added 6
new PATROLL contests, with a $2,000
cash prize for each, seeking prior art
on the list below. The patents are
owned by Speir Technologies, an
Atlantic IP Services subsidiary. The
contests will all end on May 31, 2022.
Please visit PATROLL for more
information or click on each link
below.
We also have third-party prior art
providers giving our researchers a head
start in the hunt! Click on each of the
contests to find more from Traindex.io,
Techson IP, IPscreener, Ambercite, and
Google Patent Analytics.
# ⚓ $2,000_for_eSignature_prior_art⠀⇛
On January 26, 2022, Unified Patents
added a new PATROLL contest, with a
$2,000 cash prize, seeking prior art on
at least claim 1 of U.S. Patent
8,065,527. The patent is owned by
eSignature, LLC, an NPE. The ’527
generally relates to a system and
method for embedding a written
signature into a secure electronic
document. It is currently being
asserted against Adobe.
# ⚓ $18,000_for_Dominion_Harbor_sub,_Redwood
Technologies,_prior_art [Ed: Microsoft-connected
(via IV) patent troll Dominion_Harbor]⠀⇛
On January 28, 2022, Unified added 9
new PATROLL contests, with a $2,000
cash prize for each, seeking prior art
on the list below. The patents are
owned by Redwood Technologies, LLC, an
NPE and entity of the Dominion Harbor
Group. The contests will all end on May
31, 2022. Please visit PATROLL for more
information or click on each link
below.
# § Trademarks⠀➾
# ⚓ TTAB_Affirms_“Unlawful_Use”_Refusal_of_HARBOR_HEMP
COMPANY_for_Supplements_“Containing_Legally_Produced
Industrial_Hemp_Extract”⠀⇛
Applicant Harbor Hemp applied to register the
mark HARBOR HEMP COMPANY in standard
character and design form (below), for non-
medicated skin preparations (Class 3),
dietary and nutritional supplements (Class
5), and electronic cigarettes (Class 34), all
“containing legally produced industrial hemp
extract.” USPTO refused registration as to
the Class 5 goods on the ground that the
goods are “per se unlawful under the FDCA and
therefore Applicant does not have a bona fide
intent to use the mark in lawful commerce
under Sections 1 and 45 of the Trademark
Act.” The Board affirmed that refusal. It
also affirmed refusals of the entire
applications based on the applicant’s failure
to disclaim “HEMP COMPANY” and its failure to
amend the description of the mark to conform
to the application drawing and the color
claim of record.. In re Harbor Hemp Company
LLC, Serial Nos. 88377702 and 88377730
(January 27, 2002) [not precedential]
(Opinion by Judge Thomas Shaw).
[...]
Applicant did not submit evidence of FDCA
approval, and so it was unlawful for
applicant to introduce its goods into the
marketplace at the time of its application
filing date. [I believe that the drug
Epidiolex is the only drug derived from
marijuana that has been approved by the FDCA
- ed. (FDA announcement here)].
Nevertheless, applicant argued that, at least
for intent-to-use applications, registration
should be allowed where use in any one state
is illegal, since the trademark owner can
avoid selling in states where it is illegal.
The Board disagreed.
# ⚓ Design_Systems_in_China_and_the_European_Union [Ed:
Which institution is more corrupt? EUIPO or its Chinese
counterpart?]⠀⇛
The design of a product can be protected by
an intellectual property right through a
registration before an intellectual property
office. In this article, it will be compared
the design systems of China and European
Union.
In general terms, the scope of protection of
a design encompasses the appearance of the
whole or a part of a product resulting from
the features of, in particular, the lines,
contours, colors, shape, pattern, texture
and/or materials of the product itself and/or
its ornamentation.
[...]
A Chinese patent design is valid for a
maximum of 15 years from the filing date
subject to the payment of annuity fees. The
new Patent Law increases the term of design
patents from 10 years to 15 years, which is a
reflection of the preparation of China’s
accession to the Hague Agreement, since the
minimum protection period for designs is 15
years among the contracting states of the
Hague Agreement.
In the EU, a RCD is initially valid for 5
years from the filing date and can be renewed
for 5‑year periods, up to a maximum of 25
years. However, the protection of an
unregistered design only lasts 3 years from
the date of its first public disclosure
within the EU territory.
# § Copyrights⠀➾
# ⚓ BREIN_Chases_Largest_Dutch_Pirate_IPTV_Supplier
Around_The_World⠀⇛
Dutch anti-piracy group BREIN is leaving no
stone unturned to hold the one-time largest
pirate IPTV trader in the Netherlands to
account. After investigations in the UK and
Portugal, BREIN says it has now tracked the
man to Brazil, where it intends to enforce
civil proceedings and report the man to the
authorities, while seizing domains.
╘══════════════════════════════════════════════════════════════════════════════╛
¶ Lines in total: 6729
➮ Generation completed at 02:42, i.e. 58 seconds to (re)generate ⟲