𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Thursday, November 25, 2021
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Generated Fri 26 Nov 02:40:26 GMT 2021
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/2021/11/25/


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

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QmeDHFuwxMuWGXnXY8ELJ4X5fk6wWvRiyFNXRQ9noLwTQw
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╒═══════════════════ 𝐈𝐍𝐃𝐄𝐗 ═══════════════════════════════════════════════════╕

⦿ IBM as Master of Hypocrisy | Techrights

⦿ Windows Vista Service Pack 11 (Vista 11) Has Failed to Curb the Growth of GNU/Linux | Techrights

⦿ [Meme] So Desperate That Edge Cannot Even Exceed 4% That They Block Rival Web Browsers | Techrights

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
		http://techrights.org/2021/11/25/ibm-and-the-hypocrisy/#comments
		http://techrights.org/2021/11/25/vista-11-failing/#comments
		http://techrights.org/2021/11/25/web-browsers-share/#comments

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
		http://techrights.org/2021/11/25/linux-5-15-5/#comments
		http://techrights.org/2021/11/25/mesa-21-2-6-released/#comments
		http://techrights.org/2021/11/25/proton-6-3-8/#comments

                    ䷩ 𝚕𝚒𝚗𝚎 55

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/11/25/ibm-and-the-hypocrisy/#comments
    Gemini version at gemini://gemini.techrights.org/2021/11/25/ibm-and-the-hypocrisy/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.25.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ IBM_as_Master_of_Hypocrisy⠀✐


Posted in Deception, IBM, Red_Hat at 3:58 pm by Dr. Roy Schestowitz


Video_download_link | md5sum 35757dd960a6311347374b1624b38f5f


http://techrights.org/videos/ibm-and-the-hypocrisy.webm


Summary: Free software projects and Free software developers have long been
humiliated_by_corporations_of_Western_misogynists, falsely claiming that the
Free software community isn’t inclusive enough (these are shameless projection
tactics; as a matter of public record, the_exact_opposite_is_true) and even the
eradication of supposedly offensive language isn’t something IBM takes
seriously


IBM’s attempt to distract from its_own_racism may be backfiring; as we_noted
yesterday (last night), IBM does not follow its very own advice. It has added
about 2 dozen projects to Microsoft’s GitHub (proprietary) under the Fedora
account over the past 17 months and IBM's_racism_culminates_in_highly_racist
culling_of_developers, just because they’re Persian (nationalism and racism are
the same in the context of some nations which are largely monocultural). Under
this Fedora account, which feeds Microsoft’s monopoly, half the projects use
“master” as their base branch. At least 65 projects!


In the video above, which took quite a while to record (it ended up being a lot
longer than planned), I speak about my history talking to IBM’s spinners and
liars. They’re destroying the credibility of Red Hat and they’ve already
decimated almost all the community component of Fedora. Instead it became just
a sandbox for IBM employees and maybe a shared_pool_for_Amazon/AWS, which key
operations_of_Fedora_have_been_outsourced_to. █



                    ䷩ 𝚕𝚒𝚗𝚎 107

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/11/25/vista-11-failing/#comments
    Gemini version at gemini://gemini.techrights.org/2021/11/25/vista-11-failing/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.25.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Windows_Vista_Service_Pack_11_(Vista_11)_Has_Failed_to_Curb_the_Growth_of
GNU/Linux⠀✐


Posted in GNU/Linux, Microsoft, Vista_10, Windows at 7:49 am by Dr. Roy
Schestowitz


Video_download_link | md5sum 4b8ca03aa2452f4b586ecf1a548a0c61


http://techrights.org/videos/windows-decline-unstoppable.webm


Summary: Windows market share continues to decrease in spite of billions of
dollars spent bribing the media for fake hype, especially in light of a new
Windows Service Pack (SP), Vista SP 11


THE video above is sort of a culmination of many thoughts and some discussions
we had this morning in IRC. The graph_on_the_right tells a story. Not only did
the release of Vista 11 fail to have an impact; Windows market share continues
to decrease both before and after the release.


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇The Windows market⦈ GNU/Linux is the fastest-growing
platform (not Apple operating systems), but it’s usually called neither “GNU”
nor “Linux”, so the media will pretend that “Linux” is failing and the Linux
Foundation will intentionally ignore the desktop market (while taking money
from Microsoft, which tries to protect Windows).


I’m personally very thankful to the many thousands of developers who have
worked on GNU/Linux since the 1980s (back when I was a kid). Their work is
paying off and bearing fruit, emancipating a lot of computer users even if the
corporate media refuses to acknowledge that. █


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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠉⠉⡍⠉⠉⠹⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣤⣶⣤⣦⣶⣴⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠶⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⣩⡙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠒⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡟⠉⠝⠉⠉⠉⠽⣿⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣬⣴⣦⣮⣤⣤⣿⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠆⠐⠒⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣠⣤⡄⠀⠀⠀⢸⡟⠛⠋⠙⡛⠛⠋⠙⠟⠛⠟⠛⠛⠻⠛⠛⠛⠋⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠻⠿⠃⠀⠀⣀⣼⣏⣀⣤⣈⣄⣀⣀⣈⣄⣉⣄⣁⣤⣀⣀⣀⣄⣇⣉⣄⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠋⠉⠉⠉⠉⠹⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣦⣤⣥⣮⣤⣤⣿⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠉⢉⠉⠉⠉⠹⣿⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣯⣭⣤⣤⣭⣤⣤⣿⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡛⡟⠛⠛⠛⢻⡟⣀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣃⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣥⣥⣀⣄⣤⣠⣧⠉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡉⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⣃⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡏⢐⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⡛⠛⠛⢻⣇⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⣀⠀⣀⠉⠁⠀⢀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⡀⠀⠀⠉⡀⠀⢀⠀⠀⠀⣀⠀⢀⠀⠀⢀⠀⠀⠀⢀⠀⠉⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣁⣄⣤⣠⣿⣄⣠⣦⣄⣠⣤⣄⣀⣤⣄⣀⣤⣦⣀⣤⣦⣀⣴⣤⣀⣤⣤⣀⣠⣤⣀⣠⣶⣄⣠⣦⣄⣠⣦⣄⣀⣤⣄⣀⣤⣤⣀⣤⣦⣀⣴⣤⣀⣠⣤⣀⣠⣤⣄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⡆⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣆⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⣆⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⡓⠈⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⡑⠆⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⡑⠆⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢶⣧⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢷⣷⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣷⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⠈⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⡤⢭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⠁⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠠⢁⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢴⡄⢲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠉⠨⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢊⡀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣌⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣶⡆⢛⣿⡈⢀⠁⡄⠉⡍⠋⡅⠈⣍⠉⠋⠋⡉⠭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣿⣿⣧⣼⣴⣧⣤⣧⣦⣥⣤⣤⣦⣼⣴⣬⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⡿⠿⢿⠿⠿⡿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠿⠆⣉⣿⠀⣿⢈⣈⠛⣿⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣷⣤⣶⣤⣶⣷⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 234

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/11/25/web-browsers-share/#comments
    Gemini version at gemini://gemini.techrights.org/2021/11/25/web-browsers-share/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.25.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_So_Desperate_That_Edge_Cannot_Even_Exceed_4%_That_They_Block_Rival_Web
Browsers⠀✐


Posted in Deception, GNU/Linux, Microsoft at 10:04 am by Dr. Roy Schestowitz


Fuelled by the growth of Linux, Android, Free Software, and GNU (Apple has
based its Web browser on a lot of Free software and Edge is a “me too” with
anticompetitive_edge/slant), in many respects Free software is becoming the
‘norm’, even if all those malicious browsers — Firefox_included — spy a lot and
leverage openwashing for the mere perception of ethics


          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Linux, Android, Free Software, and GNU⦈
                                 Graph_source


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇windows-meme⦈_


Summary: Linux/Android/Free Software/GNU (they go by very many names/brands)
may continue_to_grow to the point where Windows is as irrelevant as Blackberry;
this means that Microsoft’s grip on the Web too has slipped — to the point
where Microsoft frantically uses 'bailout'_money to hijack LinkedIn, GitHub,
etc. (it also rebrands_almost_everything_as_"Azure"_or_clown_to_fake_a
perception_of_growth)


⠀⡀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠤⢀⠊⠀⢠⠅⡀⢀⠃⠇⣐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠁⠀⡆⢱⠀⠠⠈⠁⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢅⠀⠈⢰⠈⠈⠰⢀⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠂⠀⠀⠀⠀⠐⠁⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠁⠀⠑⠂⠀⠂⠀⠁⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠐⠈⠀⠊⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠰⡤⢤⠦⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢄⠤⠤⡄⡀⠠⡄⠀⠠⡠⣤⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⢀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⠀⠀⣀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⡀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠨⠀⢸⠒⠰⠐⡄⢜⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠆⠆⠀⠀⠠⡓⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢨⢨⠒⠘⠤⡔⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠁⠈⠀⠉⠀⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠉⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠁⠀⠉⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠋⠓⠘⠊⠈⠀⠑⠓⠁⠁⠂⠁⠃⠀⠚⠃⠁⠃⠁⠘⠑⠈⠛⠘⠋⠑⠊⠈⠓⠁⠀⠘⠘⠈⠈⠋⠈⠛⠁⠁⠀⠀⠑⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡆⢰⣴⠠⡒⣦⣀⠠⠀⢰⡂⣠⡆⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣽⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣯⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣽⣭⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣷⣦⣬⣭⡭⣭⣋⢉⣙⣛⣛⣋⣋⣭⢝⣿⡿⠯⣿⣭⣯⣭⣭⣽⣿⣛⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠛⢿⣿⣿⡿⠛⠉⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣄⠀⠀⠀⠀⠀⠠⢛⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡆⠀⠀⠀⠀⢠⣿⣿⣷⠀⠀⠀⣀⡀⠀⠀⢸⣿⣿⣿⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⢘⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⡇⠀⠀⠀⣠⣿⣿⣿⣿⣧⠀⠀⠛⠋⠀⠀⣼⣿⣿⣿⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠈⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⣾⣿⣿⣿⣿⡇⠀⠀⢠⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⣀⣼⣿⣿⣿⣿⣜⣛⣛⣛⣛⣛⠙⠃⠙⠛⠋⠛⠃⠛⠸⠃⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣶⣤⡀⠙⠻⠿⠋⡄⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡟⣥⣬⡍⣭⣩⣭⢠⣤⣤⢠⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣄⠙⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⢀⣀⣤⣄⡈⠛⠛⠿⠟⠉⠀⠀⣠⣤⣾⠃⢸⣿⢿⣿⣿⣿⣿⣿⡟⣿⣼⣿⣿⣿⠁⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⣵⣾⣿⣿⣿⣿⣿⡅⠂⠀⠀⠀⠀⣼⣿⡿⠁⠀⠘⣿⣾⣿⣿⣿⣿⣿⠃⣸⣿⣿⣿⣿⢰⠿⠻⠧⠿⠹⠿⠸⠷⠿⠻⠿⠿⠇⢿⣼⠟⠿⠇⠿⠿⠿⣶⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣠⣾⣿⣿⣧⠀⠀⢀⣾⣿⣿⣿⣿⣿⠃⣼⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣖⣒⣂⣐⣂⡂⢀⣀⡀⣀⣀⠀⢤⣤⣤⣤⣡⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⣸⣿⣿⣿⣿⠀⢀⣾⣿⣿⣿⣿⣿⠏⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⠀⠨⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣠⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⡟⣠⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⡀⠀⠀⠨⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⣿⣿⣿⣿⡿⢋⣡⣴⣶⣯⣭⠽⠽⠟⠋⠀⣸⣿⣿⣿⣿⡟⠀⠁⢀⡸⣿⣿⣿⣿⡿⠿⣿⡿⠿⢿⡿⠈⠉⠀⠉⠁⠉⠈⠉⠁⠉⠉⠁⠀⠀⠀⠘⠛⠛⠿⣿
⢰⡀⠀⠀⠠⣔⣹⣿⣴⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠹⣿⡿⠋⠀⠛⠿⠿⠿⠿⠃⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡄⠀⠈⣷⣹⣿⢿⢣⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡄⠀⢹⣿⣿⣿⢀⣛⢷⡆⣿⣿⣿⢸⡿⠃⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⣿⣿⣿⣌⠻⠾⢃⡛⠿⠋⠚⠃⠀⠛⠃⠀⠛⠃⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⠻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠙⣿⣿⡟⠁⣿⡟⣥⣤⠉⣤⢠⣤⣤⣤⣄⠐⢀⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⠿⡿⠿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⢿⠇⠀⠿⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠉⠙⢻⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠛⢿⣿⣿⡿⠛⠉⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣄⠀⠀⠀⠀⠀⠠⢛⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⣿⡆⠀⠀⠀⠀⢠⣿⣿⣷⠀⠀⠀⣀⡀⠀⠀⢸⣿⣿⣟⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⢨⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡇⠀⠀⠀⣠⣿⣿⣿⣿⣇⠀⠀⠛⠋⠀⠀⣼⣿⣿⣿⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠈⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⣾⣿⣿⣿⣿⡇⠀⠀⢠⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⣀⣼⣿⣿⣿⣿⣜⣛⣛⣛⣛⣛⠙⠃⠙⠛⠋⠛⠃⠛⠸⠃⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣶⣤⠈⠙⠻⠿⠋⡄⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡟⣥⣤⡍⣭⣩⣭⢡⣤⣤⢠⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣄⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⢀⣠⣤⣄⡈⠛⠛⠿⠟⠁⠀⠀⣠⣤⣾⠃⢸⣿⢿⣿⣿⣿⣿⣿⡟⣿⣼⣿⣿⣿⠁⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⣵⣾⣿⣿⣿⣿⣿⡅⠂⠀⠀⠀⠀⣼⣿⡿⠁⠀⠘⣿⣼⣿⣿⣿⣿⣿⠃⣸⣿⣿⣿⣿⢰⠿⠻⠧⠿⠹⠿⠸⠷⠿⠻⠿⠿⠇⢿⣼⠟⠿⠇⠿⠿⠿⣶⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣠⣾⣿⣿⣧⠀⠀⢀⣾⣿⣿⣿⣿⣿⠃⣼⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣒⣂⣐⣀⡂⢀⣀⡀⣀⣀⠀⢤⣤⣤⣤⣥⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⣸⣿⣿⣿⣿⠀⢀⣾⣿⣿⣿⣿⣿⠏⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⠀⠈⡻⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣠⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⡟⣠⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⡀⠀⠀⠱⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⢿⣿⣿⣿⣿⡿⢋⣡⣶⣶⣯⣭⠿⠽⠿⠋⠀⣸⣿⣿⣿⣿⡟⠀⠁⢀⡸⣿⣿⣿⣿⡿⠿⣿⡿⠿⢿⡿⠈⠉⠀⠉⠁⠉⠈⠉⠁⠉⠉⠁⠀⠀⠀⠈⠋⠛⠿⣿
⢰⡀⠀⠀⠠⣔⣹⣿⣴⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠹⣿⡿⠋⠀⠛⠿⠿⠿⠿⠃⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡄⠀⠈⣧⣹⣿⢿⢣⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡄⠀⢹⣿⣿⣿⢀⣛⢷⡆⣿⣿⣿⢸⡿⠃⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⣿⣿⣿⣌⠻⠾⢃⡛⠿⠋⠚⠃⠀⠛⠃⠀⠛⠃⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⠻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠙⣿⣿⡟⠁⣿⡟⣥⣤⠉⣤⢠⣤⣤⣤⣄⠐⢀⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠿⠿⠿⢿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⢿⠇⠀⠿⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⣿⣿⡿⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣦⡀⠀⠀⠀⠀⠀⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⠀⠀⠀⠀⠀⣸⣿⣿⣧⠀⠀⢀⡀⠀⠀⢹⣿⣿⣿⡟⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⢈⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⣿⣿⣿⣿⠀⠀⠀⠀⣴⣿⣿⣿⣿⡆⠀⠻⠏⠀⠀⢸⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠈⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣽⣿⣿⣿⣿⣿⡀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣦⡀⠀⢀⣴⣿⣿⣿⣿⣿⣜⣛⣛⣛⡛⠛⠙⠃⠙⠛⠋⠛⠃⠛⠸⠃⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣶⣶⣄⠈⠛⠿⠛⢃⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⡟⣥⣤⡍⣭⣩⣬⢠⣤⣤⢠⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣄⠙⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⣀⣤⣤⣄⣙⠛⠛⠿⠛⠁⠀⢀⣤⣴⡟⠀⣿⡿⢿⣿⣿⣿⣿⣿⡻⣇⣿⣿⣿⣿⠃⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⣶⣿⣿⣿⣿⣿⣷⡑⠀⠀⠀⠀⢠⣿⣿⡏⠀⠀⠹⣷⣼⣿⣿⣿⣿⡿⢁⣽⣿⣿⣿⣿⣰⠿⠻⠧⠿⠹⠿⠸⠷⠿⠻⠿⠿⠇⢿⣼⠟⠿⠇⠿⠿⠿⣶⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣴⣿⣿⣿⡇⠀⠀⣠⣾⣿⣿⣿⣿⣿⢠⣾⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣖⣒⣂⣀⣀⡀⢀⣀⡀⣀⣀⠀⢤⣤⣤⣤⣥⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⣿⣿⣿⣿⡇⠀⢰⣿⣿⣿⣿⣿⣿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⠀⠘⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⢀⣼⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⠃⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⠀⠀⠈⠸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣿⣿⣿⣿⣿⠟⢋⣤⣶⣾⣿⡭⠻⠿⠟⠃⠀⣿⣿⣿⣿⣿⠇⠠⠀⢹⣿⣿⣿⣿⣿⡿⠿⣿⡿⠿⢿⠷⠈⠉⠀⠉⠁⠉⠈⠉⠁⠉⠉⠁⠀⠀⠀⠙⠛⠛⠻⣿
⣆⠀⠀⠀⢠⣊⣿⣷⣆⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠏⣿⣿⡟⠁⠐⠻⠿⠿⠿⠿⠁⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀⢿⣿⣿⣿⢣⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣧⡀⠀⣿⣿⣿⣿⢆⣛⢷⡆⣿⣿⣿⢸⡿⠃⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠄⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢸⣿⣿⣿⣌⠻⠾⢃⠛⠿⠋⠺⠃⠀⠛⠃⠀⠛⠃⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⠻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠄⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠻⣿⣿⠛⢿⣿⡟⣥⣤⠉⣥⢠⣤⣤⣤⣄⠀⢀⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⠀⠐
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠺⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠘⢿⠀⠘⣿⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠘⢿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠉⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⣿⣿⡿⠟⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣦⡀⠀⠀⠀⠀⠀⠄⣀⣄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⠀⠀⠀⠀⠀⣼⣿⣿⣇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⢨⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡗⠀⠀⠀⢀⣼⣿⣿⣿⣿⡄⠸⠿⠃⠀⠀⣿⣿⣿⣿⣷⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠈⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣽⣿⣿⣿⣿⣧⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣦⠀⠀⢀⣼⣿⣿⣿⣿⣿⣜⣛⢛⡛⠛⠛⠙⠃⠙⠛⠋⠛⠃⠛⠸⠃⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣶⣦⡄⠈⠛⠿⠛⣡⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⡟⣥⣬⡍⣭⣡⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣄⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⢀⣠⣤⣦⣄⡛⠛⠛⠿⠋⠀⠀⢠⣤⣴⠟⠀⣿⡿⣿⣿⣿⣿⣿⣿⠻⣷⣿⣿⣿⣿⠃⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣵⣾⣿⣿⣿⣿⣿⣯⠒⠀⠀⠀⠀⢰⣿⣿⠏⠀⠀⠻⣷⣿⣿⣿⣿⣿⡟⢁⣾⣿⣿⣿⣿⠰⠿⠻⠧⢿⠹⠿⠸⠷⠿⠻⠿⠿⠇⢿⣼⠟⠿⠇⠿⠿⠿⣶⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢀⣶⣿⣿⣿⡄⠀⠀⣴⣿⣿⣿⣿⣿⡟⢠⣿⣿⣿⣿⣿⣿⣿⣶⣷⣶⣶⣶⣖⣒⣒⣂⣀⡀⢀⣀⡀⣀⣀⠀⢤⣤⣤⣤⣥⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢈⣿⣿⣿⣿⡇⠀⣸⣿⣿⣿⣿⣿⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⠀⠸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢠⣼⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⡿⠁⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⡀⠀⠈⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡿⠟⣉⣴⣶⣾⣿⡯⠿⠿⠟⠁⠀⣿⣿⣿⣿⣿⠁⢠⠸⣿⣿⣿⣿⣿⣿⡿⠿⣿⡿⠿⢿⠏⠈⠉⠀⠉⠁⠉⠈⠉⠁⠉⠉⠁⠀⠀⠈⠘⠙⠛⠿⣿
⡄⠀⠀⠀⣤⣜⣿⣿⡞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⣿⣿⠟⠁⠚⠻⠿⠿⠿⠟⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣧⠈⠀⠹⣿⣿⣿⣿⢣⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣧⠀⠀⢹⣿⣿⣿⢆⣛⢷⡆⣿⣿⣿⢸⡿⠃⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠄⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢸⣿⣿⣿⣌⠻⠾⢃⠻⠿⠋⠺⠃⠀⠛⠃⠀⠛⠃⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⠻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠜⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠻⣿⡿⢿⣿⣿⡟⣥⣤⠉⣥⢠⣤⣤⣤⣄⠀⢀⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⠀⠐
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠙⠇⠀⢻⣿⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠈⠛⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢻⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣤⡀⠀⠀⠀⠀⠀⠀⣀⢄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⠀⠀⠀⠀⢀⣾⣿⣿⡆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⡇⠀⠀⠀⢀⣼⣿⣿⣿⣿⡄⠶⡿⠂⠀⠈⣿⣿⣿⣿⣇⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠈⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣧⠀⠀⠀⡼⣿⣿⣿⣿⣿⣿⣦⠀⠀⢀⣼⣿⣿⣿⣿⣿⣜⣛⢛⠛⠛⠛⠙⠃⠙⠛⠋⠛⠃⠛⠸⠃⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣷⣶⣦⡄⠘⠻⠿⠟⣀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⡟⣥⣤⡍⣭⣩⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣄⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢀⣠⣤⣦⣈⡟⠛⠻⠿⠋⠀⠀⣀⣤⣴⠟⠀⣿⡿⣿⣿⣿⣿⣿⣿⢿⣷⣿⣿⣿⣿⠃⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣵⣾⣿⣿⣿⣿⣿⣯⠂⠀⠀⠀⠀⢰⣿⣿⠋⠀⠀⠻⣷⣿⣿⣿⣿⣿⡟⢠⣿⣿⣿⣿⣿⠰⠿⠻⠧⠿⠹⠿⠸⠷⠿⠻⠿⠿⠇⢿⣼⠟⠿⠇⠿⠿⠿⣶⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢀⣶⣿⣿⣿⠀⠀⠀⣴⣿⣿⣿⣿⣿⡟⣠⣿⣿⣿⣿⣿⣿⣿⣶⣷⣶⣶⣶⣖⣒⣒⣂⣀⡀⢀⣀⡀⣀⣀⠀⣤⣤⣤⣤⣥⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢨⣿⣿⣿⣿⡇⠀⣼⣿⣿⣿⣿⣿⡿⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⠀⠸⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢀⣾⣿⣿⣿⣿⠇⠀⣿⣿⣿⣿⣿⡿⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⡀⠐⠿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡿⠟⣉⣴⣶⣾⣯⡍⠭⠿⠟⠀⠀⣿⣿⣿⣿⣿⠁⣠⢸⣿⣿⣿⣿⣿⣿⡿⠿⣿⡿⠿⠿⠏⠈⠉⠀⠉⠁⠉⠈⠉⠁⠉⠉⠁⠀⠀⠓⠚⠛⠛⢿⣿
⠀⠀⠀⠀⣔⣼⣿⣿⣜⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠏⣿⣿⠟⠀⠚⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣦⠙⠋⢻⣿⣿⣿⣿⢣⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡰⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣧⠀⠀⢻⣿⣿⣿⢆⣛⢷⡆⣿⣿⣿⢸⡿⠃⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢀⠄⠁⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢸⣿⣿⣿⣎⠻⠾⢃⡛⠿⠋⠺⠇⠀⠛⠃⠀⠛⠃⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⠻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠞⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠻⠟⢿⣿⣿⣿⡟⣥⣤⠉⣥⢠⣤⣤⣤⣄⠀⢀⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⠀⠰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠰⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠻⣿⣿⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠁⠀⠂⠉⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠹⠿⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣄⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣇⠀⠀⠀⠀⢀⣿⣿⣿⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⢨⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡏⠀⠀⠀⢠⣼⣟⣿⣿⣷⡀⢴⣶⠀⠀⠈⣿⣿⣿⣿⣏⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠈⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⡇⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⣰⣿⣿⣿⣿⣿⣜⣛⢛⡛⠛⠛⠙⠃⠙⠛⠋⠛⠃⠛⠸⠃⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣦⣤⡉⠙⠿⠿⠟⡀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣾⣿⣿⡟⣥⣤⡍⣭⣡⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣄⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⣀⣤⣄⣈⠟⠛⠿⠿⠋⠁⠀⣀⣀⣴⠇⢰⣿⡿⣿⣿⣿⣿⣿⣿⢻⣼⣿⣿⣿⣿⠃⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣥⣶⣿⣿⣿⣿⣿⣍⠂⠀⠀⠀⠀⣰⣿⣿⠋⠀⠈⢿⣧⣿⣿⣿⣿⣿⡟⣨⣿⣿⣿⣿⣿⠰⠿⠻⠧⠿⠹⠿⠸⠷⠿⠻⠿⠿⠇⢿⣼⠟⠿⠇⠿⠿⠿⣶⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⣀⣴⣿⣿⣿⠀⠀⠀⣴⣿⣿⣿⣿⣿⡏⣰⣿⣿⣿⣿⣿⣿⣿⣶⣷⣶⣶⣶⣖⣒⣒⣂⣀⡀⢀⣀⡀⣀⣀⠀⢤⣤⣤⣤⣥⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⢸⣿⣿⣿⣿⠀⠀⣼⣿⣿⣿⣿⣿⡿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⣾⣿⣿⣿⣿⠀⢰⣿⣿⣿⣿⣿⡿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⡀⠀⠪⠻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⣿⣿⣿⣿⡿⠟⣋⣤⣶⣿⣿⠍⠽⠿⠟⠀⢸⣿⣿⣿⣿⣿⠀⣤⠀⣿⣿⣿⣿⣿⣿⡿⠿⣿⡿⠿⠿⠟⠈⠉⠀⠉⠁⠉⠈⠉⠁⠉⠉⠁⠀⠀⠈⠛⠛⠛⠿⣿
⠀⠀⠀⢠⣴⣹⣿⣴⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠛⣿⣿⠟⠀⠺⠿⠿⢿⠿⠏⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣆⠻⠃⢻⣿⣿⣿⣿⢣⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡔⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢻⣿⣿⣿⢆⣛⢷⡆⣿⣿⣿⢸⡿⠃⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢠⠔⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢸⣿⣿⣿⣎⠻⠾⠃⠛⠿⠋⠺⠇⠀⠛⠃⠀⠛⠃⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⡻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⠞⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠛⠻⣿⣿⣿⣿⡟⣥⣤⠉⣥⢠⣤⣤⣤⣄⠀⢀⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⠀⣔
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣿⣿⢿⣿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠙⢿⣿⣿⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠂⠹⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠈⢿⡿⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠟⠋⠁⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡀⠀⠀⠀⠀⠀⠠⢂⣀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡆⠀⠀⠀⠀⢠⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⣿⣿⣿⠇⠀⠀⠀⣠⣿⣿⣿⣿⣇⠀⢠⣶⡆⠀⠀⣿⣿⣿⣿⣗⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠈⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣺⣿⣿⣿⣿⡄⠀⠀⢠⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣜⣛⠛⠛⠛⠛⠙⠃⠙⠛⠋⠛⠃⠛⠸⠃⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣮⣭⣍⠉⠻⢿⡿⠇⡀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣄⣠⣴⣿⣿⡟⣥⣤⡍⣭⣡⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣄⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣠⣄⠈⠻⠿⠿⡿⠋⠀⠀⢀⣀⣼⠇⢸⣿⢿⣿⣿⣿⣿⣿⡟⣿⣾⣿⣿⣿⣿⠇⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣩⣴⣾⣿⣿⣿⣷⡑⠄⠀⠀⠀⠀⣸⣿⡿⠃⠀⠘⣿⣾⣿⣿⣿⣿⣿⠇⣸⣿⣿⣿⣿⣿⢰⠿⠻⠧⢿⠹⠿⠸⠷⠿⠻⠿⠿⠇⢿⣼⠟⠿⠇⠿⠿⠿⣶⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢀⣴⣿⣿⣇⠀⠀⢀⣴⣿⣿⣿⣿⣿⠇⣼⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣖⣒⣒⣒⣀⡀⢀⣀⡀⣀⣀⠀⢤⣤⣤⣤⣥⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⢹⣿⣿⣿⣿⠀⢀⣾⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣠⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⡟⢠⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⠀⠈⡹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠟⣋⣤⣶⣿⣿⠿⠿⠿⠇⠀⢸⣿⣿⣿⣿⡿⠀⣿⡀⢹⣿⣿⣿⣿⣿⡿⠿⣿⡿⠿⠿⠿⠈⠉⠀⠉⠁⠉⠈⠉⠁⠉⠉⠁⠀⠀⠛⠛⠛⠛⢿⣿
⠀⠀⠀⣤⣆⣿⣿⣦⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⢻⣿⣿⠏⠀⠾⠿⢿⣿⡿⠋⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡌⠿⠗⠘⣿⣿⣿⣿⢣⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠸⣿⣿⣿⢆⣛⢷⡆⣿⣿⣿⢸⡿⠃⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠠⠈⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢠⣿⣿⣿⣎⡻⠾⢃⠛⠿⠋⠺⠇⠀⠛⠃⠀⠛⠃⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⡻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠⠇⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠈⠛⢿⣿⣿⣿⣿⡟⣥⣤⠈⣥⢠⣤⣤⣤⣄⠀⢀⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⢀⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠹⣿⣿⣿⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠑
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠀⠘⠈⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠙⢿⡟⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡿⠋⠁⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⢀⠞⠛⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣆⠀⠀⠀⠀⠀⣾⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡟⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣆⠀⠀⢶⣶⠀⠀⢸⣿⣿⣇⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠈⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣾⣿⣿⣿⣇⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢀⣼⣿⣿⣿⣜⣛⣛⣛⡛⠛⠙⠃⠙⠛⠋⠛⠃⠛⠸⠃⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣭⣍⡉⠛⢿⣿⠿⢀⠀⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣴⣾⡟⣥⣤⡍⣭⣩⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣄⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠺⠿⢿⣿⠟⠁⠀⠀⣀⣠⡟⢠⣿⣿⣿⣿⣿⣿⣿⣿⢿⣽⣿⣿⣿⣿⣿⠇⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣡⣴⣾⣿⣿⣿⣗⠄⠀⠀⠀⠀⢠⣿⣿⠟⠀⠈⢿⣧⣿⣿⣿⣿⣿⡟⢠⣿⣿⣿⣿⣿⣿⢰⠿⠻⠧⢿⠹⡿⠸⠷⠿⠻⠿⠿⠇⢿⣼⠟⠿⠇⠿⠿⠿⣶⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢀⣠⣾⣿⣿⠀⠀⠀⣴⣿⣿⣿⣿⣿⡏⠀⢹⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣷⢖⣒⣐⣒⣓⡂⢀⣀⡀⣀⣀⠀⢤⣤⣤⣤⣥⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠘⣿⣿⣿⣿⡆⠀⣼⣿⣿⣿⣿⣿⡿⣱⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⠀⢸⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣼⣿⣿⣿⣿⠇⠀⣿⣿⣿⣿⣿⡿⢱⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⡀⠀⠹⣟⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿⠟⣡⣤⣼⣿⡛⡿⠿⠿⠀⢰⣿⣿⣿⣿⣿⠁⣾⣿⣷⠀⣿⣿⣿⣿⣿⡿⠿⣿⡿⠿⢿⡿⠌⠉⠀⠉⠁⠉⠈⠉⠁⠉⠉⠁⠀⠐⠋⠛⠛⠛⢿⣿
⠀⠀⢀⣠⣰⣾⣷⡰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⣿⣿⡿⠋⠰⠾⣿⣿⣿⡿⠁⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣆⠈⠉⠀⠀⠘⣿⣿⣿⢣⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⡀⢸⣿⣿⢆⣛⢷⡆⣿⣿⣿⢸⡿⠇⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢷⣾⣿⣿⣎⡻⠾⢃⠛⠿⠋⠺⢇⣀⠛⠃⠀⠛⠃⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⡻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠌⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠈⢻⣿⣿⣿⣿⣿⡟⣥⣤⠉⣤⢩⣥⣤⣤⣄⠀⢀⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⠀⠲
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠻⡇⠻⣿⣿⣿⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠈⠐
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠁⠈⠊⠙⠘⠐⠻⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠈⠉⠁⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠼⢛⣻⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠁⠀⠀⠀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠺⠿⠁⠀⠀⣿⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠘⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣼⣿⣿⣿⣿⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣸⣿⣜⣛⣛⣛⣛⣛⣙⣃⠙⠛⠋⠛⠃⠛⠸⠃⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣬⣭⣈⠙⠻⠿⠿⢇⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⡄⣤⣤⡍⣭⣩⣭⢠⣤⣬⢡⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣄⠙⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⡀⠘⠿⠿⠿⠿⠋⠀⠀⣀⣠⡾⠁⣾⣿⢿⣿⣿⣿⣿⣿⡻⡧⠟⣿⣿⣿⣿⣿⠃⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣃⣴⣾⣿⣿⣿⣷⠢⠀⠀⠀⠀⠀⣾⣿⡟⠁⠀⠹⣿⣼⣿⣿⣿⣿⡿⢁⣴⢀⣿⣿⣿⣿⣿⠰⠿⠻⠧⠿⠹⠿⠸⠷⠿⠻⠿⠿⡇⢿⣼⠟⠿⠇⠿⠿⠿⣶⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣠⣾⣿⣿⡇⠀⠀⣠⣾⣿⣿⣿⣿⣿⢡⣾⡇⢸⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣖⣒⣂⣀⣒⡒⢒⣂⡀⣀⣀⠀⢤⣤⣤⣤⣥⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣻⣿⣿⣿⣇⠀⢰⣿⣿⣿⣿⣿⣿⢣⣿⣿⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⠀⠀⠻⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣰⣿⣿⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⠃⠛⠛⢿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⠀⠀⠀⠺⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡿⠟⢉⣤⣦⣿⣿⠻⠿⠿⠃⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⣷⠈⣿⣿⣿⣿⡿⠿⣿⡿⠿⠿⠿⠮⠍⠀⠉⠁⠉⠈⠉⠁⠉⠉⠁⠀⠀⠀⠀⠛⠛⠿⣿
⠀⠀⣀⡔⣶⣷⣆⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠞⢻⣿⣿⠋⠠⠾⠿⣿⣿⡿⠃⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢻⣷⣿⣿⣿⢣⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⢿⣿⣿⣿⢆⣛⢷⡆⣿⣿⣿⢸⡿⠇⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠈⢿⣿⣿⣎⠻⠾⢃⠛⠿⠋⠺⢇⣀⠛⠃⠀⠛⠃⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⠻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠈⣿⡿⣿⣿⣿⡟⣥⣤⠉⣥⢩⣥⣤⣤⣄⠀⢀⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⢀⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠈⠁⠘⢿⠿⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠋⠉⠛⠋⠝⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣾⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠞⣉⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠻⠿⠿⠿⠿⠿⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⣀⣀⠀⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠙⠛⠀⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠘⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣼⣺⣿⣿⣿⣷⠀⠀⠀⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⢘⣛⣛⣛⣛⣛⣙⣃⣙⡛⠋⠛⠃⠛⠸⠃⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣭⣭⣉⠙⠻⠿⠟⢀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⡟⣥⣤⡄⣤⣠⣬⢠⣤⣬⢩⣤⣤⡍⣤⣶⣄⣤⡄⣤⣤⣄⠙⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣀⡀⠘⠿⠿⠿⠟⠁⠀⢀⣀⣠⡟⠀⣿⡿⣿⣿⣿⣿⣿⣿⢻⣷⣿⣿⡿⠀⣿⣿⠁⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⣥⣶⣿⣿⣿⣿⣏⠢⠀⠀⠀⠀⢠⣿⣿⠟⠀⠀⠻⣷⣿⣿⣿⣿⣿⡟⣠⣿⣿⣿⠁⠀⣿⣿⣰⠿⠻⠧⠿⠹⠿⠸⠷⠿⠻⠿⠿⡇⢿⣼⠟⠿⠇⠿⠿⠿⣶⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢀⣠⣿⣿⣿⡀⠀⠀⣴⣿⣿⣿⣿⣿⡏⣰⣿⣿⣿⡇⠀⢸⣿⣿⣿⣶⣶⣶⣶⣶⢖⣂⣀⣒⣓⡒⢒⣒⡒⣀⣀⠀⠀⢠⣤⣤⣡⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠈⣿⣿⣿⣿⡇⠀⣼⣿⣿⣿⣿⣿⡿⠀⠈⠉⠙⣿⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⠀⠀⠈⠩⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⢀⣼⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⢠⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⠀⠀⠀⠀⠠⡽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡿⠛⣡⣴⣾⣿⡿⠻⠿⠿⠁⠀⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠘⠿⠀⣾⣿⣿⡿⠿⣿⡿⠿⣿⡿⠮⠉⠤⠍⠁⠉⠈⠉⠁⠉⠉⠁⠀⠀⠀⠀⠀⠙⠻⣿
⠀⢠⣴⣸⣿⣷⡔⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠟⢿⣿⡿⠁⠐⠿⠿⢿⣿⠿⠁⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣿⣿⢡⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣿⣿⢀⣛⢷⡆⣿⣿⣿⢸⡿⠇⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠘⣿⡈⠻⠾⢃⡻⠿⠋⠺⠇⣀⠻⠃⠀⠛⠃⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⡺⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠈⠃⠀⠸⠟⣭⣤⠉⣭⢡⣭⣤⣤⣄⠀⢀⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⠀⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠴⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠁⠉⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣴
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⠀⠀⠀⠀⠀⠠⢋⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠟⠛⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠘⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡹⣿⣿⣿⣿⣇⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣘⠛⠛⢛⣛⣛⣙⣃⣙⣛⣋⡛⡃⠛⠸⠃⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣭⣍⡉⠛⠿⡿⠟⡀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣥⣤⡍⣭⣩⣤⢠⣤⣬⢩⣤⣬⡍⣥⣶⣄⣤⡄⣤⣤⣄⠙⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⣀⠀⠿⠿⠿⠿⠋⠁⠀⢀⣀⣰⡟⢰⣿⡿⣿⣿⣿⣿⣿⣿⢿⣾⣿⣿⣿⣿⣿⣿⠀⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣋⣥⣶⣿⣿⣿⣿⣅⠄⠀⠀⠀⠀⣰⣿⣿⠋⠀⠈⢻⣧⣿⣿⣿⣿⣿⠏⣰⣿⣿⣿⣿⣿⣿⡏⠰⠿⠻⠧⠿⠹⠿⠸⠷⠿⠻⠿⠿⡇⢿⣼⠟⠿⠇⠿⠿⠿⣶⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢀⣴⣿⣿⣿⠀⠀⢀⣴⣿⣿⣿⣿⣿⡏⣼⣿⣿⣿⣿⣿⣿⡟⠁⠀⣴⣶⣶⣶⣶⢖⣒⣀⣀⣂⡒⢒⣛⡀⣀⣐⢲⣆⠀⠤⠀⢁⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢸⣿⣿⣿⣿⠀⢀⣾⣿⣿⣿⣿⣿⡟⠀⠀⠉⠛⠿⠿⣿⣿⠁⠀⣸⣿⣿⣿⣿⣿⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⢸⣿⡇⠀⠨⢿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢀⣾⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⡟⢰⠀⠀⠀⠀⠀⠀⣼⣿⠀⣰⣿⣿⣿⣿⣿⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⠘⠛⠃⠀⠀⠐⢇⣿⣿
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠿⢋⣤⣶⣿⣿⡟⠿⠿⠟⠀⢸⣿⣿⣿⣿⣿⠀⣿⠀⠀⠀⠀⠀⣤⣿⡟⢠⠿⠿⢿⡿⠿⢿⣿⠮⠭⠤⠍⠁⠭⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠘⣹
⠀⢤⣦⣿⣿⣴⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⠛⣿⣿⠟⠁⠺⠿⠿⣿⣿⠟⠀⠀⠀⠀⠰⣾⣿⣿⣿⣿⣿⡆⢻⡀⠀⠀⠀⠀⠙⠿⠁⢠⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⣩
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠄⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣆⠁⠀⠀⠀⠀⠀⠀⢰⢀⣛⢷⡆⣿⣿⣿⢸⡿⠇⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⣈⠻⠾⠃⠻⠿⢋⠺⢇⣀⠻⢇⠀⠛⠃⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⠻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⣥⣬⠉⣭⢩⣭⣤⣤⣄⠀⢀⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠉⠀⠀⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠙⠛⠙⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡀⠀⠀⠀⠀⠀⠠⠛⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⠿⠛⠿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠘⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢰⣿⣿⣿⣿⡇⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⡛⠛⠛⢛⣛⣙⣃⣙⣛⣋⡛⣃⠛⠸⠃⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣮⣭⣍⠙⠻⢿⡿⠗⡀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣥⣤⡍⣭⣩⣤⢠⣤⣬⢩⣤⣬⡍⣥⣶⣌⣤⡄⣤⣤⣄⠙⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⣀⠨⠻⠿⠿⡿⠋⠀⠀⣀⣀⣼⠇⢸⣿⢿⣿⣿⣿⣿⣿⡿⢿⣾⣿⣿⣿⣿⣿⣿⠀⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣫⣴⣾⣿⣿⣿⣿⡑⠄⠀⠀⠀⠀⣴⣿⣿⠋⠀⠘⢿⣾⣿⣿⣿⣿⣿⠏⣸⣿⣿⣿⣿⣿⣿⣿⠰⠿⠻⠧⠿⠹⠿⠸⠷⠿⠻⠿⠿⡇⢿⣼⠟⠿⠇⠿⠿⠿⣶⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣠⣾⣿⣿⡇⠀⠀⢀⣶⣿⣿⣿⣿⣿⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢰⣶⣶⣶⢖⣂⣀⣂⣀⡒⢒⣚⡓⣀⣐⢲⣶⠄⠀⢀⣁⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⣻⣿⣿⣿⣿⠀⢠⣿⣿⣿⣿⣿⣿⠟⣼⠟⠿⢿⣿⣿⣿⣿⣿⡟⠀⠀⣿⣿⣿⣿⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⢸⣿⣦⠀⠀⡎⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⣠⣿⣿⣿⣿⡿⠀⢸⣿⣿⣿⣿⣿⡟⣸⣿⠀⠀⠀⠀⠉⠉⣿⣿⡇⠀⣸⣿⣿⣿⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⡸⣿⠿⠀⠀⠀⠘⣻⣿
⠀⠀⠀⠀⡀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⡿⠟⣋⣤⣶⣿⣿⠿⠿⠿⠇⠀⢸⣿⣿⣿⣿⡿⠀⣿⣿⠀⠀⠀⠀⠀⢀⣿⣿⠃⠰⣿⠿⠿⢿⡿⠮⠭⠤⠭⠁⠉⠌⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⣿
⠀⢤⣦⣿⣿⣧⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠎⠻⣿⣿⠋⠀⠺⠿⢿⣿⡿⠋⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡄⢿⣿⠀⠀⠀⠀⠀⢿⣿⢡⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⣸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⡌⢻⡄⠀⠀⠀⠀⠘⠃⢀⣛⢷⡆⣿⣿⣿⢸⡿⠇⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠈⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠑⠀⠀⠀⠀⠀⠀⡈⠻⠾⠃⠛⠿⠋⠺⢇⣄⠻⠇⡀⠛⠃⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⠻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣤⣤⠉⣭⢩⣭⣤⣤⣅⠀⢀⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠙⠋⠀⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠈⠉⠙⠻⠛⠙⢿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡀⠀⠀⠀⠀⠀⢀⠜⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠛⠟⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡆⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡇⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠘⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡅⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⡛⠛⠛⠛⠛⠙⣃⣙⢛⣋⠛⠃⠛⠸⠃⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣭⣍⠙⠻⢿⡿⠇⡀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣥⣤⡍⣭⣩⣤⢠⣤⣤⢡⣤⣤⡍⣥⣶⣄⣤⡄⣤⣤⣄⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢀⣀⣤⣀⡸⠻⠿⠿⠟⠋⠀⠀⣀⣀⣼⠇⢸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣹⣿⣿⣿⣿⣿⣿⠁⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⣴⣾⣿⣿⣿⣿⣿⠲⠀⠀⠀⠀⠀⣾⣿⡿⠋⠀⠘⣿⣮⣿⣿⣿⣿⣿⡏⢨⣿⣿⣿⣿⣿⣿⣿⠰⠿⠻⠧⠿⠹⠿⠸⠷⠿⠻⠿⠿⠇⢿⣼⠟⠿⠇⠿⠿⠿⣶⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣠⣾⣿⣿⡇⠀⠀⢀⣴⣿⣿⣿⣿⣿⡏⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⣶⣶⣶⢖⣂⣀⣀⣐⡒⢒⣀⡀⣀⣚⢳⣶⣶⡄⠀⢁⣰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣿⣿⣿⣿⣷⠀⢀⣾⣿⣿⣿⣿⣿⡟⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⢸⣿⣿⡀⠀⠀⠹⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣰⣿⣿⣿⣿⡟⠀⢸⣿⣿⣿⣿⣿⡿⢰⣿⣿⡿⠛⠿⢿⣿⣿⣿⣿⡏⠀⠀⣿⣿⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⣸⣿⣿⣿⠀⠀⠀⠐⠟
⠀⠀⠀⣀⡀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣿⣿⣿⣿⣿⠿⢛⣡⣶⣾⣿⣿⢻⠿⠿⠇⠀⢸⣿⣿⣿⣿⡟⠀⣾⣿⣿⡏⠀⠀⠀⠀⠀⠸⠿⠷⠀⠀⠻⠿⠿⠮⠭⠤⠭⠥⠭⠬⠉⠁⠉⠉⠙⠛⠋⠁⠀⠀⠀⠀⠀
⠀⠰⣤⣻⣷⣧⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⢿⣿⡟⠁⠐⠿⠿⢿⣿⡿⠃⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⡄⢿⣿⣿⣿⠀⠀⠀⠀⠀⢠⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⠐
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⡄⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣷⡈⢻⣿⡇⠀⠀⠀⠀⠐⢀⣛⢷⡆⣿⣿⣿⢸⡿⠇⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠈⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠹⣿⠀⠀⠀⠀⠀⠈⠻⠾⠃⠛⠿⠋⠺⢇⣄⡻⢇⣀⠛⠃⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⠻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⠀⠀⠀⠀⠀⠀⣴⣾⠟⣤⣤⠈⣭⢩⣭⣭⣭⣍⠙⢁⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠺⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠈⠻⠿⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠉⠉⠉⠙⠉⢿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣤⡀⠀⠀⠀⠀⠀⢀⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣷⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡟⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠘⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⣛⠛⠛⠛⠛⠙⣃⣙⣛⣋⣛⣃⠛⠸⠃⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣷⣮⣭⡉⠛⠿⠿⠟⣀⡀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣥⣤⡍⣭⣩⣥⢠⣤⣤⢠⣤⣤⡍⣥⣶⣌⣤⡄⣤⣤⣄⠙⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⢀⣀⣤⣴⣦⣽⠛⠿⠿⠿⠋⠁⠀⣀⣀⣴⡿⠁⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠁⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣾⣿⣿⣿⣿⣿⣿⡗⠄⠀⠀⠀⠀⣴⣿⣿⠏⠀⠀⢿⣧⣿⣿⣿⣿⣿⡿⠈⣽⣿⣿⣿⣿⣿⣿⠰⠿⠻⠧⠿⠹⠿⠸⠷⠿⠻⠿⠿⠇⢿⣼⠟⠿⠇⠿⠿⠿⣶⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣠⣾⣿⣿⣿⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⢁⣼⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣶⣶⣶⢖⣂⣀⣐⣐⡒⢒⣂⡀⣐⣚⢲⣶⣶⣶⠄⠁⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⣻⣿⣿⣿⣿⠀⠀⣼⣿⣿⣿⣿⣿⣿⢃⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣿⣿⣿⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⢸⣿⣿⣏⠀⠀⠙⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣰⣿⣿⣿⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⠃⣼⣿⡿⠀⠉⠛⠛⠻⣿⣿⡇⠀⢸⣿⣿⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⣸⣿⣿⣿⠀⠀⠀⠀⢬
⠀⠀⠀⢠⣄⡀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠿⢛⣡⣶⣾⣿⣿⠿⠿⠿⠏⠀⢸⣿⣿⣿⣿⣿⠃⢰⣿⣿⡇⠀⠀⠀⠀⢠⣿⠿⠷⠀⠘⠿⢿⡿⠮⠭⠤⠭⠥⠭⠬⠉⠁⠉⠉⠽⠟⠛⠉⠀⠀⠀⠀⠀
⠀⠀⠰⣜⣿⣿⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠫⢿⣿⡿⠁⠐⠿⠿⠿⣿⠿⠋⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣆⠸⣿⣿⡇⠀⠀⠀⠀⠚⢠⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣠⠂⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣄⠹⣿⣧⠀⠀⠀⠀⠀⢀⣛⢷⡆⣿⣿⣿⢸⡿⠇⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠔⠁⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⢿⡄⠀⠀⠀⠀⠈⠻⠾⠃⠛⠿⠋⠺⢇⣄⡻⢇⣀⠟⠃⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⠻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠳⠀⠀⠀⠀⠀⠀⢰⠏⣥⣤⠀⣭⢩⣭⣭⣭⣍⠻⢋⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠰⠿⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠙⠉⠉⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣦⣀⠀⠀⠀⠀⠀⠀⡰⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠛⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠘⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⢁⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⠛⠛⠛⠛⣛⣙⣃⣙⣛⣋⣛⣃⡛⠸⠃⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣶⣮⣍⠙⠻⠿⠿⢇⡀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣥⣤⡍⣭⣡⣤⢠⣤⣬⢡⣤⣬⡍⣥⣶⣌⣥⡄⣤⣤⣄⠙⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢀⣠⣤⣶⣶⣼⡟⠛⠿⠿⠟⠁⠀⢀⣀⣠⣿⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⠀⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣾⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⢰⣿⣿⡟⠁⠀⠹⣿⣼⣿⣿⣿⣿⣿⠇⢹⣿⣿⣿⣿⣿⣿⠰⠿⠻⠧⠿⠹⠿⠸⠷⠿⠻⠿⠿⡇⢿⣼⠟⠿⠇⠿⠿⠿⣶⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣀⣴⣿⣿⣿⡇⠀⠀⢠⣼⣿⣿⣿⣿⣿⠏⠰⣿⣿⣿⣿⣿⣿⡇⠀⣴⣶⣶⣶⣶⣖⣒⣐⣒⣒⡒⢒⣚⡓⣀⣐⢶⣶⣶⣤⣦⣁⣠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠌⢹⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⠉⠙⣿⣿⣿⠁⢀⣿⣿⣿⣿⣿⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⢸⣿⣿⣿⣿⡇⠘⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⣠⣾⣿⣿⣿⣿⠇⠀⣿⣿⣿⣿⣿⣿⡟⢰⠀⠀⠀⠀⠘⣿⣿⣿⣧⣸⣿⣿⣿⣿⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⠘⠟⠋⠉⠉⠀⠀⠈⡽
⠀⠀⠀⢠⣤⢀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⣿⣿⣿⣿⣿⡿⢛⣩⣶⣶⣿⣿⡿⡿⠿⠿⠀⠀⣿⣿⣿⣿⣿⡟⠀⣿⣇⠀⠀⠀⠀⢹⣿⣿⠿⠿⣿⠿⠿⢿⡿⠮⠭⠤⠭⠥⠭⠬⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⢮⢿⣾⣮⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣽⣿⣿⠋⠐⠛⠿⠿⣿⡿⠟⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣧⠘⣿⣿⡄⠀⠀⠀⠸⡟⢠⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⠆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣆⠘⢿⣿⣆⠀⠀⠀⠹⢀⣛⢷⡆⣿⣿⣿⢸⡿⠇⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡴⠋⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⠻⣿⣆⠀⠀⠀⠈⠻⠾⠃⠛⠿⠋⠺⢇⣄⡻⢇⣀⠟⠃⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⠻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠄⠙⣿⡆⠀⠀⠀⠀⠛⠋⣥⣤⠉⣭⢩⣭⣭⣭⣍⠁⢀⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠈⠀⠀⠀⠀⠀⠀⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠉⠛⠛⠛⠻⢻⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣝⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⡄⠀⠀⠀⠀⠀⠀⡸⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⡇⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠘⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡥⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡘⠛⠛⢛⣛⣛⣙⣃⣙⣛⣋⣛⣃⡛⠸⠃⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣭⣉⠛⢿⣿⣿⢇⢀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⣥⣬⡍⣥⣠⣤⢠⣤⣬⢩⣤⣬⡍⣥⣶⣌⣤⡄⣤⣤⣄⠙⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣀⣠⣤⣦⣬⡿⠿⠿⣿⡟⠉⠀⢀⣀⣠⣾⠟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⢀⠀⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣷⣿⣿⣿⣿⣿⣿⣿⠦⠀⠀⠀⠀⢠⣾⣿⡿⠁⠀⢻⣿⣼⣿⣿⣿⣿⣿⠇⢻⣿⣿⣿⠇⢸⣰⡿⠻⠧⠿⠹⠿⠸⠷⠿⠻⠿⠿⡇⢿⣼⠟⢿⠇⠿⠿⠿⣶⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣀⣴⣿⣿⣿⡃⠀⠀⣠⣽⣿⣿⣿⣿⣿⠋⠀⠉⠉⢸⣿⠀⢸⣿⣶⣶⣶⣶⣶⣖⣒⣐⣒⣓⡒⢒⣘⡓⣒⣚⢿⣾⠶⠦⢀⣁⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠾⢻⣿⣿⣿⣿⡇⠀⣰⣿⣿⣿⣿⣿⣿⠏⡀⠀⠀⠀⠘⣿⠀⣾⣿⣿⣿⣿⣿⣿⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⠀⠀⠀⠀⠀⠩⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠊⢠⣾⣿⣿⣿⣿⠇⠀⣿⣿⣿⣿⣿⣿⠏⣰⣇⠀⠀⠀⠀⣿⣇⣿⣿⣿⣿⣿⣿⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⠀⠀⠀⠀⠀⠀⠘⢻⣿
⠀⠀⠀⠀⢠⣤⣀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠟⣫⣴⣶⣿⣿⣿⣿⣿⡿⠀⠐⣿⣿⣿⣿⣿⠏⢠⣿⣿⡄⠀⠀⠠⣿⣿⠿⠿⢿⡿⠿⢿⡿⠮⠭⠤⠭⠅⠉⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⢿
⡄⠀⠀⠻⣮⣿⣿⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣽⣿⣿⠋⠐⠾⠿⢿⣿⣿⡟⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡆⠸⣿⣿⣿⠀⠀⠀⠛⢠⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣠⠆⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⡄⠹⣿⣿⣇⠀⠀⠀⢀⣛⢷⡆⣿⣿⣿⢸⡿⠇⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⡴⠃⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣆⠘⢿⣿⡄⠀⠀⠈⠻⠾⠃⠛⠿⢋⠺⢇⣄⠻⠇⠀⠛⠃⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⡻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠞⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠈⠻⣧⠀⠀⣀⣀⣀⠈⣤⣤⠉⣭⢩⣭⣤⣤⣄⠀⢀⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠉⠀⠀⠉⠙⠿⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⢀⠿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠟⠻⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠄⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠘⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣟⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣘⡛⢛⣛⣛⣛⣙⣃⣙⣛⣋⣛⣃⠛⠸⠃⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣯⣭⣉⠛⠻⣿⣿⣿⡀⡀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣹⡟⣭⣤⡍⣭⣠⣬⢡⣤⣬⢩⣤⣬⡍⣥⣶⣄⣤⡄⣤⣤⣄⠙⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⢀⣠⣤⣤⣹⠿⠿⣿⣿⠟⠉⠀⠀⢀⣰⡿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⢠⣿⠁⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣪⣷⣾⣿⣿⣿⣿⣿⡳⠀⠀⠀⠀⠀⣰⣿⣿⠟⠀⠘⣿⣧⣿⣿⣿⣿⣿⡿⠘⣿⣿⡟⢸⣿⣰⠿⠻⠧⠿⠹⠿⠸⠷⠿⠻⠿⠿⡇⢿⣼⠟⠿⠇⠿⠿⠿⣶⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣀⣴⣿⣿⣿⠀⠀⢀⣬⣿⣿⣿⣿⣿⡟⠁⠀⠉⠙⡇⢸⣿⣿⣶⣶⣶⣶⣶⣖⣒⣒⣒⣒⡒⢒⣛⡓⣒⣚⠷⠖⠂⠀⢀⣁⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⠸⣿⣿⣿⣿⣿⠀⢀⣾⣿⣿⣿⣿⣿⡿⢁⡆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⠀⠀⠀⠀⠈⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⣰⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⡿⢡⣿⣇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⠀⠀⠀⠀⠀⠈⢻⡿⣿
⠀⠀⠀⠀⠀⣤⣄⡀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⢛⣩⣴⣾⣿⣿⣿⣿⣿⠇⠀⣾⣿⣿⣿⣿⡿⠁⣼⣿⣿⠀⠀⠀⢰⣿⠿⠿⣿⡿⠿⣿⡿⠮⠭⠤⠭⠅⠍⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠐⠙⢿
⢤⠀⠀⠘⣷⣿⣿⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⣿⣿⡿⠁⠰⠿⣿⣿⣿⣿⠋⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣧⠀⢿⣿⣿⡇⠀⠀⠞⢠⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⠰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⡔⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣧⠈⢿⣿⣇⠀⠀⠀⢀⣛⢷⡆⣿⣿⣿⢸⡿⠇⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣠⠞⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢻⣿⡄⠀⠀⠈⠻⠾⠃⠛⠿⢋⠺⢇⣄⠻⠇⠀⠛⠃⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⡻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠰⠋⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠙⣷⠀⠀⢀⣀⣠⠏⣥⣬⠉⣭⢩⣭⣤⣤⣄⠀⢀⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠈⠛⠻⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⠛⠛⠻⠛⠿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣻⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⡼⠿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡄⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠠⣶⡆⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣇⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠘⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⢁⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣜⣛⣛⣛⣛⣛⣙⣃⣙⣛⣋⠛⠃⠛⠸⠃⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣯⣟⡛⠛⢿⣿⣿⡆⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣭⣬⡍⣭⣩⣭⢡⣤⣬⢩⣤⣬⡍⣥⣶⣄⣤⡄⣤⣤⣄⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⣀⣀⣀⡿⠿⣿⣿⡿⠋⠀⠀⠀⢀⣼⠟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⠁⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣫⣵⣾⣿⣿⣿⣿⣟⠄⠀⠀⠀⠀⢠⣾⣿⡿⠃⠀⢿⣿⣿⣿⣿⣿⣿⣿⠏⢛⠀⣿⣿⣿⣰⠿⠻⠧⠿⠹⡿⠸⠷⠿⠻⠿⠿⡇⢿⣼⠟⠿⠇⠿⠿⠿⣶⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣠⣾⣿⣿⠁⠀⠀⣠⣿⣿⣿⣿⣿⣿⠃⣴⣿⠀⣿⣿⣿⣿⣶⣶⣶⣶⣶⣖⣒⣒⣂⣒⡒⢒⣛⡓⣀⣐⠂⠀⡤⣤⣤⣡⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠄⢺⣿⣿⣿⣿⡄⠀⣼⣿⣿⣿⣿⣿⣿⢃⣼⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⠀⠀⠀⢏⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢀⣾⣿⣿⣿⣿⡅⢰⣿⣿⣿⣿⣿⣿⢃⣾⣿⣿⡿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⠀⠀⠀⠀⠹⢟⣿⣿⣿
⠀⠀⠀⠀⠀⢤⣤⣀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠟⢋⣥⣤⣿⣿⣿⣿⣿⡿⠀⢸⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⡇⠀⢸⡿⠿⠿⣿⡿⠿⢿⡿⠮⠭⠤⠭⠁⠉⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠊⠛⠻⣿
⢦⡀⠀⠈⢿⣞⣿⣿⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠻⣿⣿⠟⠡⠾⣿⣿⣿⣿⡟⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡀⢿⣿⣿⣿⡇⠀⠀⢠⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⢹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡔⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣷⡈⢻⣿⣿⡟⠀⠀⢀⣛⢷⡆⣿⣿⣿⢸⡿⠇⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⠔⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡀⠹⣿⡇⠀⠀⠈⠻⠾⠃⠻⠿⢋⠺⢇⣀⡻⢇⠀⠛⠃⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⡻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠⠏⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠘⠇⠀⠀⠀⠻⣴⡏⣥⣤⠉⣭⢩⣭⣥⣤⣄⠀⢀⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠻⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⠛⠟⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⢿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣽⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⢀⠞⠻⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠻⠿⠿⠿⠟⠛⠛⠛⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡆⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⢴⣶⠆⠀⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣇⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠘⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣶⣾⣿⣜⣛⣛⣛⣛⣛⣙⣃⠙⠛⠋⠛⠃⠛⠸⠃⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣯⣝⡛⠛⢿⣿⣿⡗⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣭⣤⡍⣭⣩⣭⢠⣤⣬⢡⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣄⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⣀⣀⣀⣼⠿⢿⣿⡿⠋⠁⠀⠀⢀⣼⠏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣟⣭⣶⣿⣿⣿⣿⣟⠦⠀⠀⠀⠀⢀⣾⣿⡿⠃⠀⢻⣿⣿⣿⣿⣿⣿⣿⠇⣻⣿⣿⣿⣿⣰⠿⠻⠧⠿⠹⠿⠸⠷⠿⠻⠿⠿⡇⢿⣼⠟⠿⠇⠿⠿⠿⣶⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⣠⣾⣿⣿⡁⠀⠀⣠⣿⣿⣿⣿⣿⣿⠃⡀⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣷⣖⣒⣐⣒⣓⡒⢒⣒⡀⣀⣀⠀⢤⣤⣤⣤⣥⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠺⣿⣿⣿⣿⡇⠀⣼⣿⣿⣿⣿⣿⣿⢇⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⠀⠈⡿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⢀⣼⣿⣿⣿⣿⡇⢀⣿⣿⣿⣿⣿⣿⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⠀⠀⠈⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⢤⣤⣄⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢿⣿⣿⣿⣿⣿⠿⢛⣡⣤⣿⣿⣿⣿⣿⡿⠀⢰⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⡿⠿⢿⡿⠮⠩⠤⠉⠁⠉⠈⠉⠁⠉⠉⠁⠀⠀⠀⠛⠛⠛⠻⣿
⠦⡀⠀⠘⢿⣾⣿⣿⣮⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠛⣿⣿⠟⠁⠶⢿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⡿⠿⢣⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⡄⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣷⡄⢻⣿⣿⣿⠁⠀⢀⣛⢷⡆⣿⣿⣿⢸⡿⠇⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠹⠿⠃⠀⠀⠈⠻⠾⢃⡻⠿⢋⠺⢇⣀⠻⠇⠀⠛⠃⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⡻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠⠋⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⢦⣠⣾⠟⣭⣭⠉⣭⢩⣭⣥⣤⣄⠀⢀⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠈⠿⣿⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⠛⠻⠻⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⢀⠛⢻⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣷⡄⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣷⡀⠀⣠⣤⡄⠀⠀⣿⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⣿⣿⡇⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠈⠋⠀⠀⣰⣿⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠘⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⠃⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣠⣴⣾⣿⣿⣜⣛⣛⣛⣛⣛⡙⠃⠙⠛⠋⠛⠃⠛⠸⠃⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣛⡛⠻⢿⣿⣿⡶⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣥⣤⡍⣭⣩⣭⢡⣤⣬⢡⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣄⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⣼⠿⣿⣿⡿⠛⠀⠀⠉⢁⣼⠎⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣩⣴⣾⣿⣿⣿⣗⢄⠀⠀⠁⠀⢀⣾⣿⡿⠃⠀⢿⣿⣺⣿⣿⣿⣿⣿⠋⣿⣿⣿⣿⣿⣰⠿⠻⠧⠿⠹⠿⠸⠷⠿⠻⠿⠿⠇⢿⣼⠟⠿⠇⠿⠿⠿⣶⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⣠⣾⣿⣿⠁⠀⠀⣠⣿⣿⣿⣿⣿⣿⠃⣼⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⢖⣒⣒⣒⣂⡀⢀⣀⡀⣀⣀⠀⢤⣤⣤⣤⣥⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠺⣿⣿⣿⣿⡇⠀⣼⣿⣿⣿⣿⣿⣿⢇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠀⣼⣿⣿⣿⣿⡇⠠⣿⣿⣿⣿⣿⣿⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⡀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⣠⡀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡿⠟⣋⣤⣼⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⠃⣸⣿⡿⠋⢹⣿⣿⣿⡿⠿⣿⡿⠿⢿⠿⠮⠉⠀⠉⠁⠉⠈⠉⠁⠉⠉⠁⠀⠈⠛⠛⠛⠛⢿⣿
⣄⠀⠀⠰⣾⣼⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⣿⣿⡿⠉⠴⣿⣿⣿⣿⡿⠁⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⡄⠛⠋⠀⠀⠀⢻⣿⢣⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⣠⣴⣾⣿⢆⣛⢷⡆⣿⣿⣿⢸⡿⠃⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠸⣿⣿⣿⠿⣌⠻⠾⢃⡻⠿⠋⠚⠃⠀⠛⠃⠀⠛⠃⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⡻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠⠋⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠘⠿⠏⢠⣌⣻⣿⡟⣭⣬⠁⣤⢠⣤⣤⣤⣄⠘⢋⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⢀⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠈⠻⣿⠟⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠉⠛⠛⠛⠛⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⣿⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⡀⠛⢻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⡀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣆⠀⠀⢀⣀⠀⠀⠀⣿⣿⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣼⣿⣿⣿⡇⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣇⠀⠙⠛⠀⠀⣰⣿⣿⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠈⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⠇⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⣠⣾⣿⣿⣿⣜⣛⣛⣛⣛⣛⡙⠃⠙⠛⠋⠛⠃⠛⠸⠃⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣞⣛⠛⠻⢿⣿⣿⡆⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣥⣬⡍⣭⣩⣭⢠⣤⣤⢠⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣄⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⣶⣿⣿⣿⡿⠛⠀⠀⠉⢁⣴⠊⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⠁⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⣉⣴⣶⣿⣿⣿⡗⢄⠀⠈⠁⠀⢠⣾⣿⡿⠃⠀⢿⣷⣾⣿⣿⣿⣿⣿⠃⣽⣿⣿⣿⣿⣰⠿⠻⠧⠿⠹⠿⠸⠷⠿⠻⠿⠿⠇⢿⣼⠟⠿⠇⠿⠿⠿⣶⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣠⣾⣿⣿⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⢃⣾⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣷⣖⣒⣒⣂⣐⡒⢂⣀⡀⣀⣀⠀⣤⣤⣤⣤⣥⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢸⣿⣿⣿⣿⡆⠀⣰⣿⣿⣿⣿⣿⣿⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⠀⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣼⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⠃⠚⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⡀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⣠⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡿⠟⣣⣤⣾⣿⣿⣿⣿⡿⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣿⣿⣿⣿⡿⠿⣿⡿⠿⢿⡿⠎⠉⠀⠉⠁⠉⠈⠉⠁⠉⠉⠁⠀⠛⠛⠛⠛⠛⢿⣿
⡀⠀⠀⢲⣷⣿⣿⣿⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⡻⣿⣿⡿⠁⢴⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣆⢀⣴⣶⣿⣿⣿⣿⢣⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣆⠻⣿⣿⣿⣿⣿⢆⣛⢷⡆⣿⣿⣿⢸⡿⠃⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠉⠉⠉⠙⠈⠻⠾⠃⠛⠿⠋⠚⠃⠀⠛⠇⡀⠛⠃⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⡻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⠏⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣀⠀⣤⣤⠀⣤⢠⣤⣤⣤⣌⠻⢋⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⠠⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠐⢶⠎⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠛⠛⠹⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠟⠁⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠁⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠈⣙⡃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣦⠀⠀⠀⠀⢀⣾⣿⣷⡀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠀⠀⠀⢀⣼⣿⣿⣿⣧⡀⠰⣶⡖⢠⣾⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠘⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣿⣿⣿⣿⡇⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣄⠀⠀⣾⣿⣿⣿⣿⣿⣿⣜⡛⠛⠛⠛⠛⠙⠃⠙⠛⠋⠛⠃⠛⠸⠃⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣊⣛⠛⠿⣿⣿⣿⠁⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣭⣬⡍⣭⣠⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣌⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢐⣾⣿⣿⣿⠟⠃⠀⠈⠉⢀⡦⠁⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠃⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢗⣠⣶⣾⣿⣿⣷⠢⡀⠀⠈⠀⠀⣰⣿⣿⠟⠀⠀⢻⣿⣼⣿⣿⣿⣿⣿⢃⣾⣿⣿⣿⣿⡰⠿⠻⠧⠿⠹⠿⠸⠷⠿⠻⠿⠿⠇⢿⣼⠟⠿⠇⠿⠿⠿⣶⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⢀⣴⣿⣿⣏⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⢡⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣆⠀⢀⣀⣀⣀⣀⡀⢀⣀⡀⣀⣀⠀⣤⣤⣤⣤⣥⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢿⣿⣿⣿⣿⠀⠀⣰⣿⣿⣿⣿⣿⣿⠏⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⠀⢼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⢠⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⠏⣀⣤⣿⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⡀⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣀⡀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⢛⣡⣤⣿⣿⣿⣿⣿⡏⠀⠀⣿⣿⣿⣿⣿⡟⢸⣿⣿⠿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠁⠉⠈⠉⠁⠉⠉⠁⠘⠛⠛⠛⠛⠻⢿⣿
⠀⠀⠐⣾⣮⣿⣿⣧⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠝⢿⣿⣿⠏⠠⢶⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡘⠋⠀⠀⠀⠀⠀⢠⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⢻⢀⣛⢷⡆⣿⣿⣿⢸⡿⠇⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡀⠈⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣼⣧⣸⣌⠻⠾⢃⠛⠿⠋⠺⢇⣀⡻⢇⣀⠟⠃⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⡻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣰⠏⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⢻⠿⠃⢙⣿⣿⡟⣥⣤⠉⣭⢩⣭⣭⣬⣍⠻⢋⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⢰⣤⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠹⣿⠉⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠈⠩⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠉⠛⠛⠻⠿⠿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠋⠉⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠻⠿⠿⠛⠛⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣧⠀⠀⠀⠀⠀⣰⣿⣷⡄⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠄⠀⠀⠀⢀⣽⣿⣿⣿⣶⡖⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠘⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣿⣿⣿⣿⣿⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣧⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⡛⠛⠛⠛⠛⠙⠃⠙⠛⠋⠛⠃⠛⠸⠃⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣏⣉⠛⠻⢿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣥⣤⡍⣭⣩⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣄⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⠟⠁⠀⠀⠁⢀⡄⠈⠀⣿⣿⠿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⠃⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣋⣤⣶⣿⣿⣿⣷⠢⡀⠀⠈⠀⠀⢠⣾⣿⠟⠁⠀⠀⢹⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡰⠿⠻⠧⠿⠹⠿⠸⠷⠿⠻⠿⠿⠇⢿⣼⠟⠿⠇⠿⠿⠿⣶⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⣠⣿⣿⣿⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⢀⣀⣀⣀⣀⡀⢀⣀⡀⣀⣀⠀⣤⣤⣤⣤⣥⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⢺⣿⣿⣿⣿⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⠀⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⢀⣾⣿⣿⣿⣿⠀⠀⠀⣾⣿⣿⣿⣿⣿⡟⡾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⠀⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⡀⡀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠿⠛⣡⣤⣿⣿⣿⣿⣿⡿⠀⠀⢀⣼⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠈⠉⠀⠉⠁⠉⠈⠉⠁⠉⠉⠁⠈⠙⠛⠛⠛⠻⢿⣿
⠀⠀⣶⣦⣿⣿⣦⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠝⢿⣿⣿⠟⠁⢶⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇⠀⣸⣿⣿⣿⠟⢡⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡄⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣦⣽⣿⣿⠁⠀⢀⣛⢷⡆⣿⣿⣿⢸⡿⠃⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⠀⠁⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⡟⠀⠀⠀⠻⠾⠃⠛⠿⢋⠚⢇⣀⠛⢇⣀⠛⠃⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⠻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⡿⠃⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠛⠀⢀⣀⣀⣴⠏⣤⣤⠉⣭⢩⣭⣥⣬⣍⠻⢋⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⣤⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠘⠻⠛⠿⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠈⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠈⠛⠋⠛⠙⠿⠋⠛⢿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠛⠿⠛⠛⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⣼⣿⣦⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡆⠀⠀⠀⠀⢀⣾⣿⣿⣿⠂⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠘⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⢾⣿⣿⣿⣿⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⠛⠛⠛⠛⠛⠙⠃⠙⠛⠋⠛⠃⠛⠸⠃⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⣛⠛⠛⠿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣥⣤⡍⣥⣠⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣌⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⡿⠃⠀⠈⠉⠀⡀⠀⠀⠀⢿⣿⠋⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠇⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣋⣤⣶⣾⣿⣿⣾⢆⠀⠉⠉⠀⠀⢠⣶⣾⡿⠃⠀⠀⠀⠘⠟⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡰⠿⠻⠧⠿⠹⠿⠸⠷⠿⠻⠿⠿⠇⢿⣼⠟⠿⠇⠿⠿⠿⣶⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣠⣿⣿⣿⠀⠀⠀⠀⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡷⠂⠀⠀⢀⣀⣀⣀⣀⡀⢀⣀⡀⣀⣀⠀⣤⣤⣤⣤⣥⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢾⣿⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢀⣼⣿⣿⣿⣿⠂⠀⠀⠀⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠟⣁⣀⣾⣿⣿⣿⣿⣿⠀⠀⠀⣠⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⡿⠿⠇⠀⠈⠉⠀⠉⠁⠉⠈⠉⠁⠉⠉⠁⠘⠛⠛⠻⠛⠛⢿⣿
⠀⢴⣄⣿⣷⣆⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⠻⣿⣿⣿⠟⢁⣴⣾⣿⣿⣿⡟⠉⠉⠉⠁⠀⢀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢀⣾⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢆⣛⢷⡆⣿⣿⣿⢸⡿⠃⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠈⣿⣿⣿⣎⠻⠾⠃⠛⠿⠋⠚⠃⣀⠛⢇⡀⠛⠃⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⠺⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠘⠿⠘⣿⣿⡿⠁⣤⣤⠀⣤⢨⣭⣥⣤⣍⠻⢃⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⢠⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠳⠾⣿⠁⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠙⠛⠋⠉⠙⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠁⠀⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠽⠟⠁⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣄⠀⠀⠀⠀⠀⠀⠀⠰⣦⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣸⡇⣿⣿⣿⢻⣷⡿⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⢀⣾⣿⡿⠿⠁⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠘⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠐⣩⣽⣿⣷⡄⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⡛⠛⠛⠛⠛⠙⠃⠙⠛⠋⠛⠃⠛⠸⠃⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠿⢿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡟⣥⣤⡍⣥⣠⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣌⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣶⡤⠈⠙⠛⠋⠀⠀⠀⠀⠀⣿⡏⣽⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠃⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢏⣠⣤⣶⣶⣶⣾⡉⠙⠛⠿⠁⠀⢀⣠⣤⣴⡖⠀⠀⠀⠀⠘⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠰⠿⠻⠧⠿⠹⠿⠸⠷⠿⠹⠿⠿⠇⢿⣼⠟⠿⠇⠿⠿⠿⣶⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣾⣿⣿⣿⣿⣿⣿⣷⡈⠀⠀⠀⠀⢀⣼⣿⣿⠏⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡶⠂⢀⣀⣀⣀⣀⡀⢀⣀⡀⣀⣀⠀⣤⣤⣤⣤⣥⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣴⣿⣿⣿⣿⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⠀⢾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣼⣿⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⠀⢘⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠂⢀⣼⣿⣿⣿⣿⣿⠀⠀⠀⢀⣿⣿⣿⣿⣿⣇⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⠿⣿⡿⠿⢿⠿⠎⠉⠀⠉⠁⠉⠈⠉⠁⠉⠉⠁⠀⠙⠛⠛⠛⠛⢿⣿
⠠⣦⢿⣿⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⢳⣽⢿⣿⣿⣿⠟⢋⣥⣶⣿⣿⣿⡿⠻⠛⠟⠃⠀⣰⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⣿⣿⣿⣿⢣⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣰⣿⣷⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⣿⢆⣛⢷⡆⣿⣿⣿⢸⡿⠃⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣠⣾⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⡀⠀⠘⣿⣿⣿⣎⠻⠾⢃⠛⠿⠋⠘⠇⠀⠛⠃⠀⠛⠃⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⠺⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣘⣿⣿⣿⣿⣿⡟⣥⣤⠉⣭⢡⣤⣤⣤⣄⠙⢀⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⢠⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠹⣿⣿⣿⣿⣿⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠈⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠁⠋⠉⠉⠉⠙⠉⠙⣿⣿⣿⣿⣿⣿⣿⣧⡀⠈⠉⠉⠻⠟⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⢿⡿⠋⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⢀⣀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⢠⣾⣇⠀⠛⠛⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣷⣿⣿⡇⣿⣿⣿⢸⣿⣧⠘⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣭⣿⣿⣷⡀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⣛⢛⠛⠛⠛⠙⠃⠙⠛⠋⠛⠃⠛⠸⠃⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡟⣥⣤⡍⣥⣠⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣄⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣦⣌⠉⠛⠿⠿⠟⠀⠀⠀⠀⠀⣿⢩⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⠃⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢂⣈⣤⣤⣶⣤⡟⠛⠿⠿⡟⠉⠀⠀⣀⣀⣠⡄⠀⠀⠀⠀⠉⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠰⠿⠻⠧⠿⠹⠿⠸⠷⠿⠹⠿⠿⠇⢿⣼⠟⠿⠇⠿⠿⠿⣶⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣾⣿⣿⣿⣿⣿⣿⡍⠂⠀⠀⠀⠀⢀⣾⣿⣿⠋⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⢖⣀⣀⣀⣀⡀⢀⣀⡀⣀⣀⠀⢤⣤⣤⣤⣥⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣀⣴⣿⣿⣿⡇⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢘⣿⣿⣿⣿⡇⠀⠀⠀⢀⣿⣿⣿⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⠀⠘⣿⣿⣿⣿⣿⣿⣿
⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣠⣾⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣸⣿⣿⠛⢿⣿⣿⣿⣿⣿⡿⠿⣿⡿⠿⢿⠿⠎⠉⠀⠉⠁⠉⠈⠉⠁⠉⠉⠁⠀⠚⠛⠛⠛⠛⢿⣿
⢠⡼⣷⣇⢑⠀⠀⠀⠀⠀⠀⠀⠀⠸⣝⣿⣿⣿⣿⣿⠟⢋⣡⣶⣶⣿⣿⡿⡿⣿⡿⠁⢀⣆⠀⣾⣿⣿⣿⣿⣿⣿⣿⠿⠷⠾⣿⣿⣿⣿⢣⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣠⣾⣿⣆⢻⣿⣿⣿⣿⣿⣿⣇⠀⠀⠘⢿⣿⣿⣿⢆⣛⢷⡆⣿⣿⣿⢸⡿⠃⣿⡇⢸⣿⣿⣷⣿⢸⣏⣿⣸⣿⣿⡅⣿⠿⠀⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣴⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣆⢀⣀⠈⢿⣿⣿⣎⠻⠾⢃⠛⠿⠋⠚⢃⣀⠛⠃⠀⠛⠃⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⠺⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠉⠐⢈⣿⣿⣿⣿⣿⡟⣥⣤⠉⣭⢩⣭⣤⣤⣄⠀⢀⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⠤⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠚⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢿⣿⣿⣿⣿⣿⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠘⡛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠉⠁⠋⠛⠈⠋⠁⢻⣿⣿⣿⣿⣿⣿⣿⣄⠀⠉⠁⠉⠉⠋⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠿⠿⠟⠿⠿⠿⠛⠛⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆⠀⢀⣀⡀⠀⠀⠀⢸⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣦⠈⠛⠁⠀⠀⣠⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠘⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣷⣄⣀⣠⣾⣿⣿⣿⣿⣿⣿⣜⣛⣛⣛⣛⣛⣙⣃⡙⠛⠋⠛⠃⠛⠸⠃⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣥⣤⡍⣭⣩⣬⢠⣤⣬⢡⣤⣤⡍⣥⣶⣄⣤⡄⣤⣤⣄⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠁⣻⣿⣿⣎⢻⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡆⠠⠀⠀⠀⢠⣶⣿⣿⣿⣿⣷⠄⠈⠛⠛⠋⠁⠀⠔⠀⠀⠀⢀⣻⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡰⠿⠻⠧⠿⠹⠿⠸⠷⠿⠻⠿⠿⠇⢿⣼⠟⠿⠇⠿⠿⠿⣶⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣯⣵⣶⣿⣿⣿⣿⣯⠉⠛⠟⠋⠀⠀⣠⣴⣶⣶⡟⠁⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⢖⣀⣀⣀⣀⡀⢀⣀⡀⣀⣀⠀⠀⠀⠀⣤⣥⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣯⠑⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⢀⣼⣿⣿⣿⣿⢿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⠀⠀⠀⠰⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣤⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⣾⣿⣿⣿⣿⠃⠘⠛⠛⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⠀⠀⠀⠐⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠟⠉⣽⣿⣿⣿⣿⡇⠀⠀⠀⠈⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⠿⣿⡿⠿⢿⡿⠮⠉⠤⠉⠁⠉⠈⠉⠁⠉⠉⠀⠀⠀⠘⠛⠛⠻⢿⣿
⣤⢷⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣁⣤⣾⣿⣿⣿⣿⣿⠃⠀⠀⠀⣠⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⣾⣷⣿⣿⣿⢣⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠋⠀⢠⣶⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⢆⣛⢷⡆⣿⣿⣿⢸⡿⠃⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣿⣿⣷⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠻⠾⢃⡛⠿⠋⠚⢇⣀⠻⠃⠀⠛⠃⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⠺⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣰⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣧⡻⣿⠏⠀⣿⡏⢿⣿⣿⣿⡟⣭⣤⠉⣭⢩⣭⣥⣤⣄⠀⢀⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⢠⣴⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠸⢿⣿⡜⢿⣿⣿⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠘⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠙⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠉⠁⠀⠈⠉⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⡿⠀⠀⠀⢟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⠿⠟⠿⠿⠿⠿⠿⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⣄⠻⠟⠀⠀⠀⢠⣿⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠈⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣠⣶⣿⣿⣜⣛⣛⣛⣛⣛⣙⣃⣙⠛⢋⠛⠃⠛⠸⠃⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⢠⣹⣿⣿⣿⣿⣿⣿⣿⠋⣿⣿⣿⣿⡟⣥⣤⡍⣭⣩⣭⢠⣤⣬⢡⣤⣤⡍⣤⣶⣄⣤⡄⣤⣤⣄⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠸⣿⣏⢿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⠁⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣛⠻⢿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⢼⣿⣿⣾⣿⣿⣿⣿⠁⢸⣿⣿⣿⣿⣰⠿⠻⠧⠿⠹⠿⠸⠷⠿⠻⠿⠿⠇⢿⣼⠟⠿⠇⠿⠿⠿⣶⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⣗⣉⣤⣤⣴⣾⣿⢿⣿⣿⣿⡿⠗⠂⠈⠉⠉⢁⣾⠾⠋⠀⠀⣴⣾⣿⡟⠻⠛⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⢖⣒⣀⣀⣀⡀⢀⣀⡀⣀⣀⠀⠀⠀⠀⠀⢡⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣄⠈⠛⠋⠀⠀⣤⣾⣿⣿⡿⠃⠀⠀⢀⣾⣿⣿⡟⠀⠀⠀⠻⠿⣿⡆⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⠀⠀⠀⠀⠀⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠁⠀⢀⣠⣼⣿⣿⣿⠏⠀⠀⠀⣠⣾⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠁⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢽⣿⣿⡏⢸⣶⣶⣆⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠿⣿⡿⠿⢿⡿⠮⠩⠤⠉⠁⠉⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠛⠻⢿⣿
⡀⢦⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣠⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣾⣿⣿⣷⣼⣿⣿⣿⣧⣄⣀⣀⣤⣦⢘⣷⢠⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠠⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⢀⣛⢷⡆⣿⣿⣿⢸⡿⠃⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢋⢀⣄⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠻⠾⢃⡻⠿⢋⠺⢇⣀⠻⢇⡀⠛⠃⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⡺⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢣⣾⣿⣆⡀⠈⣿⣿⣿⣿⣿⣿⣷⡽⣿⣿⣿⠟⣿⣿⣿⣿⠀⢻⣿⡟⣭⣬⠉⣭⢩⣭⣭⣭⣍⠁⢀⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⢰⣶⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿⣿⣿⣿⣷⣷⡹⣿⣿⣿⣿⣿⣿⣿⡌⠛⠋⠀⠛⠿⠿⡿⠀⠈⠛⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠙⠻⠿⠿⠿⠷⢻⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⡿⠀⠀⠹⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠿⠿⠿⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣀⠀⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠘⠟⠁⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠘⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣘⣛⣛⣛⣛⣛⣙⣃⣙⣛⣋⣛⣃⠛⠸⠃⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣤⣤⡌⣤⣠⣤⢠⣤⣬⢩⣤⣬⡍⣥⣶⣄⣤⡄⣤⣤⣄⠙⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⢠⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣼⣿⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠰⠿⠻⠧⠿⠹⠿⠸⠷⠿⠻⠿⠿⠇⢿⣼⠟⠿⠇⠿⠿⠿⣶⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⡇⠤⠀⠀⠀⣠⣴⣿⣿⣿⣷⣦⣈⠛⠻⠿⠟⢃⣄⣤⠆⠀⣀⣿⣿⠃⠀⠈⠛⢿⣿⣿⣿⣿⡿⠀⠀⣶⣶⣶⣶⣶⣶⢖⣒⣐⣒⣒⡒⢂⣀⡀⣀⣀⠂⠀⠀⠀⢀⣁⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⣽⣶⣾⣿⣿⣿⣿⡈⠙⢿⣿⠏⠀⠀⣀⣴⣤⣴⡿⠋⠁⠀⢀⣿⡿⠃⠀⠀⠀⠀⣾⣿⣿⣿⣿⡇⠀⢰⣿⣿⣿⣿⣿⣿⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⠀⠀⠀⠀⢐⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠆⠀⠀⠀⢀⣼⣿⣿⣿⠋⠀⠀⠀⣰⣿⡟⣡⡄⠀⠀⠀⠀⠈⢿⣿⣿⣿⡇⠀⣼⣿⣿⣿⣿⣿⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⠀⠀⠀⠀⠀⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣠⣴⣶⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⡏⢰⣿⣿⣦⡀⠀⠀⠀⠀⠙⠛⠿⠃⢰⠿⠟⢿⡿⠿⢿⡿⠮⠭⠤⠭⠁⠉⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠚⠻⣿
⠀⢠⣆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣻⣿⣿⣿⣿⣿⠀⠀⠀⢠⣿⣿⣄⢸⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⢠⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢸⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢀⣛⢷⡆⣿⣿⣿⢸⡿⠇⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⡀⠀⠻⣦⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠻⠾⠃⠛⠿⠋⠺⢇⣄⠻⠇⡀⠛⠃⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⡺⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣰⣿⣿⣦⠀⢿⣿⣿⣿⣿⣿⣧⡻⣿⣿⣿⣿⠿⣿⣧⠀⠀⠀⠀⠀⠀⣤⣤⠉⣭⢩⣭⣥⣤⣍⠁⢀⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⣤⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⣿⣿⣿⣿⣿⣿⣷⡌⠻⠟⠁⠀⠀⠉⠛⠷⠦⠀⠀⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠉⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠛⢿⣿⣿⡷⢹⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠋⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠘⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣄⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⣛⠛⠛⠛⠛⠙⢃⣙⠛⣋⡛⣃⠛⠸⠃⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣭⣤⡍⣤⣨⣥⢠⣤⣤⢠⣤⣤⡍⣥⣶⣌⣤⡄⣤⣤⣄⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣽⠀⠀⠀⠀⣼⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⡿⠻⠧⠿⠹⠿⠸⠷⠿⠻⠿⠿⡇⢿⣼⠟⠿⠇⠿⠿⠿⣶⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣶⣌⣉⠛⠿⠿⠛⢁⢤⡶⠀⢸⣿⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡆⠀⠠⢖⣂⣀⣀⣒⡒⢒⣐⡂⣀⣀⠐⣶⣤⠀⣄⣡⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠟⣂⣀⣠⣤⣆⠈⠉⠿⠟⠉⠉⠀⢀⣤⣤⣴⡟⠈⠀⠀⣴⣿⣿⣿⣿⣿⣿⡟⠙⠻⢿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣄⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⠀⣿⠇⠀⣽⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣟⠷⢄⠀⠀⠀⢀⣼⣿⣿⡿⠋⠀⠀⣠⡞⢡⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠈⠉⢻⣿⣿⣿⡆⠀⣠⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⠀⠀⠀⠀⠉⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⣀⣤⣶⣿⣿⣿⣿⠃⠀⠀⣀⡉⢠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⣾⠿⠿⠿⠁⠰⠿⠻⠮⠭⠴⠭⠥⠭⠬⠉⠁⠉⠉⠀⠀⠀⠀⠈⠛⠛⢿⣿
⢀⠀⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠿⢻⣿⣿⣿⣿⣿⠀⠀⢰⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⢠⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⢀⣛⢷⡆⣿⣿⣿⢸⡿⠇⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠃⠠⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠈⠻⠾⢃⠻⠿⠋⡺⢇⣀⡻⢇⣀⠟⠃⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⡻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣾⣷⡀⢻⣿⣿⣿⣿⣿⣷⡻⣿⣿⣿⣿⣏⠉⠛⠀⠀⠀⠀⠀⠾⠋⣥⣤⠉⣭⢩⣭⣭⣭⣍⠛⢃⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⢤⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⡀⢿⣿⣿⣿⣿⣿⣿⣌⠻⣿⡿⠋⠀⠀⠀⠓⠀⠀⠀⠀⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠈⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠻⢿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣆⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠉⠉⠁⠹⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠘⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣄⡀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⣛⣛⡛⠛⠛⠙⠃⠙⠛⣋⠛⣃⠛⠸⠃⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣥⣬⡍⣥⣤⣬⢡⣤⣤⢠⣤⣤⡌⣥⣶⣄⣤⡄⣤⣤⣌⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣿⠻⠧⠿⠹⠿⠸⠷⠿⠻⠿⠿⡇⢿⣾⠟⢿⡇⠿⠿⠿⣶⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣤⣉⠙⠛⠛⠛⢡⣧⡶⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⡶⢀⣀⣀⣂⣐⡒⢒⣐⡂⣀⣀⠲⣶⣦⢤⣄⣡⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢀⣾⣿⡦⠀⠀⣀⣀⠀⠈⠉⠋⠉⠉⠀⣀⣤⣦⣴⡟⠁⠀⢀⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⠀⣿⠏⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣽⣶⣿⣿⣿⣿⣷⢤⠀⠀⠀⢀⣼⣿⣿⣿⠋⠀⠀⢰⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⠿⣿⣿⣿⣿⣿⣿⠏⠀⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⡀⠟⠀⠀⢨⣽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⣠⣶⣿⣿⣿⣿⡇⠀⢀⣴⠆⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠉⢻⡿⠿⠂⠀⠈⠉⠤⠭⠥⠭⠬⠉⠁⠉⠉⠁⠀⠀⠀⠐⠛⠛⢿⣿
⠀⡀⣤⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣿⣿⣿⣿⣿⠇⠀⢸⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣛⢷⡆⣿⣿⣿⢸⡿⠇⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⢠⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠈⠻⠾⠃⠻⠿⠋⠺⢇⣄⡻⢇⣀⠿⠇⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⡻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⣾⣆⠀⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠛⠿⣿⡄⠀⠀⠀⠀⠈⣥⣤⠀⣬⣩⣭⣥⣬⣍⠻⢋⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⣴⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣦⠸⣿⣿⣿⣿⣿⣿⣷⡝⢿⣿⣿⠿⠀⠀⠀⠰⠄⠀⠀⠀⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠛⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠿⢿⣿⣷⢿⣿⣿⣿⣿⣿⣿⣿⣎⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠙⠛⠋⢿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠘⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣤⡀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⣛⣛⣛⠛⠛⠙⠃⠙⠛⠋⠛⣋⠛⠸⢃⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣥⣬⡍⣭⣭⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣌⣤⡄⣤⣤⣌⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡿⠃⢀⣀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣿⢻⡧⣿⠹⡿⠸⠷⠿⠻⠿⢿⡇⢿⣾⠟⠿⠇⠿⠿⠿⣶⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣤⣌⡙⠛⠛⠋⢡⡧⠟⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣾⣶⢆⣀⣀⣐⣒⡒⢒⣂⡀⣀⣀⢲⣶⣶⣶⣤⣥⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⣠⣴⣤⣄⠀⠀⢀⠀⠈⠉⠉⠉⠉⠀⢀⣴⣶⣶⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⢸⣿⣿⠛⣻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⣰⣿⣟⣯⣴⣶⣿⣿⣿⣄⡀⠀⠀⠀⣠⣿⣿⣿⠋⠀⠀⡐⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⡸⣿⠇⠀⣻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⣀⣴⣾⣿⣿⣿⣿⠀⠀⡄⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠉⠉⠛⠿⠿⠿⢿⠿⠈⠉⠀⠉⠁⠭⠬⠭⠥⠍⠉⠵⠋⠀⠐⠙⠛⠛⠿⣿
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⣿⣿⣿⣿⣿⣿⠀⢰⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣛⢷⡆⣿⣿⣿⢸⡿⠇⣿⡇⢸⣿⣿⣿⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⡃⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠈⠻⠾⠃⠻⠿⠋⠻⣇⡄⠻⢇⣀⠿⠇⠻⠟⠘⠋⠛⠛⠛⠛⠇⠛⠛⡻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⣤⣤⠈⣭⣩⣤⣭⣭⣍⠻⢋⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⣤⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣧⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⠻⠿⠀⠀⠀⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠻⣿⣆⢿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⡿⠏⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠙⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠘⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣶⣤⡀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⣛⣛⡛⠛⠛⠙⠃⠙⠛⠋⠛⣋⠛⠸⢃⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣿⣿⣿⣿⣷⡂⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣭⣬⡍⣯⣭⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣌⣤⡄⣤⣤⣌⠻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⠃⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠏⣄⣴⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣿⢻⡧⢿⠹⠿⠸⠷⠿⠻⠿⢿⡇⢿⣾⠟⠿⡇⡿⠿⠿⣶⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⣤⠉⠉⠉⠀⣸⠛⠁⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣶⣶⣶⢆⣀⣀⣒⣒⡒⢒⣀⡀⣀⣐⢲⣶⣶⣶⣶⣥⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⢀⣠⣀⡀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⣠⣴⣿⡿⠃⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⢸⣿⣿⣿⡿⣹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⢠⣿⣿⢿⣫⣤⣶⣿⣷⣄⡀⠀⠀⠀⣴⣿⣿⣿⠁⠀⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⠇⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⣸⣿⣿⣿⠇⢨⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⣀⣴⣾⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠰⠿⠿⣿⡿⠿⠟⠀⠈⠉⠀⠭⠥⠭⠬⠭⠥⠍⠩⠽⠟⠉⠉⠀⠛⠚⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢠⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⢀⣛⢷⡆⣿⣿⣿⢸⡿⠇⣿⡇⢸⣿⣿⣿⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠻⠾⠃⠻⠿⠋⠻⢇⡀⠻⢇⣀⠿⠇⠻⠟⠸⠏⠛⠛⠛⠛⠃⠛⠛⡻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠄⣤⣤⠀⣤⣩⣤⣬⣭⣍⠻⢋⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⠠⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠸⣿⣿⣿⣿⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠨⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠈⠉⠛⠟⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⣿⠀⠀⠀⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣌⡻⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠘⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣶⣀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⣛⣛⠛⠛⠛⠙⠃⠙⠛⠋⠛⣋⡛⠸⢃⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣿⣿⣿⣿⣷⠄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣭⣬⡍⣯⣭⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣌⣥⡄⣤⣤⣬⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣿⣿⣿⣿⣿⣿⠀⢀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⢿⣿⣿⡿⠿⢃⣧⡿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣿⢻⠧⢿⠹⠿⠸⠷⠿⠻⠿⢿⡇⢿⣾⠟⢿⡇⠿⠿⠿⣶⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⠦⠀⠀⣀⣀⡼⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⣶⣶⣶⣶⠂⢀⣀⣒⣒⣒⡒⢂⣈⡐⣀⣒⢶⣶⣶⣶⣶⣷⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⣠⣾⣿⡿⠁⠀⡀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠛⠿⢿⣿⣿⣿⣿⣿⠇⠀⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⣼⣿⡿⢟⣠⣤⣾⡿⠄⠀⠀⠀⠀⣰⣿⣿⣿⡇⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⡏⠀⢀⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⣸⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⣿⣿⣾⣿⣿⣿⣿⣿⣶⣀⣀⣴⣾⣿⣿⣿⣿⡇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠙⠿⠿⠇⠀⠸⠎⠉⠤⠭⠥⠭⠌⠉⠁⠍⠉⠽⠋⠈⠛⠿⠛⠛⠉⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⡇⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⢠⣾⢷⡆⣶⣿⣦⢶⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣛⢷⡆⣿⣿⣿⢸⡿⠇⣿⡇⢸⣿⣿⣿⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠉⠉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⠻⠾⢃⡻⠿⠋⠻⢇⣀⡻⢇⡀⠿⠇⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⡻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣥⣤⠈⣭⣩⣭⣭⣭⣍⠻⢂⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢿⣿⣿⣿⢁⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠐
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠈⠻⠿⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⢀⠸⣿⣿⡇⣿⢻⣿⢿⣧⣿⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣯⠻⢿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠶⢶⣶⣶⣶⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠘⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⣛⠛⠛⠛⠛⠙⠃⠙⠛⠋⠛⣋⡛⠸⠃⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣭⣤⡍⣭⣭⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣌⣥⡄⣤⣤⣄⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⠃⠀⣠⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠛⠋⢸⠺⠋⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣿⠻⠧⠿⠹⠿⠸⠷⠿⠻⠿⠿⡇⢿⣾⠟⢿⡇⡿⠿⠿⣶⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠖⠒⠀⢀⣤⣤⡇⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡆⠀⢖⣒⣒⣂⣐⡒⢒⣒⡂⣀⣘⢳⣶⣶⣶⣶⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡟⠀⠀⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⣿⣿⣿⣿⡟⠀⢠⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⣾⣿⡿⣋⣤⣶⣿⡷⠤⠀⠀⠀⢀⣼⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠉⠛⣿⣿⣿⡟⠀⢀⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⣴⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠻⠿⣿⠇⠀⢸⡿⠮⠭⠤⠭⠥⢭⠬⠭⠥⠭⠉⠽⠟⠻⢿⣿⡿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣸⣿⣿⣿⣿⣿⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⢠⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⢿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢀⣛⢷⡆⣿⣿⣿⢸⡿⠇⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⠻⠾⠃⠛⠿⠋⠺⢇⣄⡻⢇⣀⠿⠇⠻⠟⠸⠋⠛⠛⠛⠛⠃⠛⠛⠻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⣤⣤⠀⣤⣨⣭⣥⣬⣍⠻⢋⣥⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢹⣿⣿⣿⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠈⠛⠿⡏⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠻⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣾⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠘⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⡛⠛⠛⠛⠛⠙⠃⠙⠛⠋⠛⠃⠛⠸⠃⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣟⣧⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣥⣤⡍⣧⣨⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣌⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⢃⣄⣴⠆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠿⠛⠋⠁⢸⠍⠁⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣿⠻⠧⠿⠹⠿⠸⠷⠿⠻⠿⢿⡇⢿⣾⠟⢿⡇⡿⠿⠿⣶⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⠛⠋⠀⢀⣴⣶⡞⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⠀⢰⣖⣂⣀⣐⣒⡒⢂⣀⡂⣀⣚⢿⣿⣶⣶⣶⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠀⠀⢠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣿⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⣋⣤⣶⣿⣟⠆⠀⠀⠀⢀⣰⣿⣿⣿⣿⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠹⣿⣿⣿⣿⣿⡟⠀⢰⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⣴⣿⣿⣿⣿⣿⣿⡇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠈⠉⠛⠿⠿⠁⠀⢾⡿⠯⠭⠴⠭⠥⢭⠬⠭⠥⠭⠭⢽⡿⠿⢿⣿⡿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⣿⣿⣿⣿⣿⡇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢀⣛⢷⡆⣿⣿⣿⢸⡿⠇⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⠻⠾⢃⡻⠿⠋⠺⢇⣄⡻⢇⣀⠿⠇⠻⠟⠸⠏⠛⠛⠛⠛⠃⠛⠛⠻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠛⣭⣤⠉⣤⣩⣭⣭⣬⣍⠻⢋⣥⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢹⣶⡄⠀⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠘⠻⠇⠀⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠻⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣶⣶⣄⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠘⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡕⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⠛⠛⠛⠛⠛⠙⠃⠙⠛⠋⠛⠃⠛⠸⠃⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠂⠀⣠⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣤⣤⡄⣤⣤⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣌⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠿⠋⢸⠾⠋⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣉⡉⠉⠀⢀⣀⡏⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣿⠻⠧⢿⠹⡿⠸⠷⠿⠻⡿⢿⡇⢿⣾⠟⢿⡇⠿⠿⠿⣶⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠟⠋⠁⠀⢀⣴⣿⣿⠁⠀⠀⣘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡖⠀⣶⢖⣀⣀⣀⣀⡒⢒⣛⡓⣒⣚⢷⣶⣶⣶⣶⣷⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⡄⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣿⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣯⣶⣿⣿⣿⣿⣥⠀⠀⠀⣠⣾⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢸⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⣸⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⡿⢻⣿⣿⣿⣿⣧⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠁⠀⠿⡿⠯⠭⠴⠭⠥⢭⠬⠭⠥⢭⠭⢽⣿⠿⢿⣿⡿⠿⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠋⢠⣿⣿⣿⣿⣿⡿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⢡⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⢀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣛⢷⡆⣿⣿⣿⢸⡿⠇⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠸⠇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠻⠾⢃⠛⠿⠋⠺⢇⣀⡻⢇⣀⠟⠇⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⠻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢸⡟⣥⣤⠉⣤⣨⣭⣭⣬⣍⠻⢋⣥⣬⡁⣤⣠⣤⣤⡄⣤⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠈⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡻⠿⡿⢿⣿⣿⣿⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠁⠀⠈⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⠀⣻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠀⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⠛⠛⠛⠛⠛⠙⠃⠙⠛⠋⠛⠃⠛⠸⠃⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⡏⣄⣴⡿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣤⣤⡄⣤⣠⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣌⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⠿⠿⠿⠟⠉⠀⡏⠈⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⠖⠂⠀⢀⣤⣶⠇⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⡿⠻⠧⢿⠹⠿⠸⠷⠿⠻⠿⢿⡇⢿⣼⠟⢿⠇⠿⠿⠿⣶⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠉⠀⠀⠀⢠⣿⣿⣿⠀⠀⢀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⡶⢶⢖⣒⣒⣚⣛⡒⢒⣛⡓⣒⣚⢷⣶⣶⣶⣶⣷⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣦⠄⣀⣤⣶⣤⡀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡆⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣸⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣵⣾⣿⣿⣿⣿⣦⣄⠀⢀⣴⣿⣿⣿⣿⣿⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⣸⣿⣿⣿⣿⣿⣿⡿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢩⣿⣿⣿⣿⣿⡄⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡿⠿⢿⠟⠀⠀⠿⠮⠭⠤⠭⠥⠭⠬⠭⠥⣭⠭⢽⣿⠿⢿⣿⠿⠿⠇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⢀⣿⣿⣿⠿⠿⠟⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠙⢡⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⢀⣛⢷⡆⣿⣿⣿⢸⡿⠇⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠈⠻⠾⠃⠛⠿⠋⠚⠃⠀⠛⠃⠀⠛⠃⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⡻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣴⣤⣤⣴⡆⣤⣤⠀⣤⢠⣤⣤⣤⣄⠀⢀⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠰⣿⣿⣿⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠿⣿⣿⣿⣿⣿⣿⡿⡿⠛⠁⠀⠀⠀⠉⠙⠿⢦⣴⣶⠆⠀⣴⣶⣦⣤⣶⣾⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⣶⣄⡀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⠀⢹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠀⠸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡷⡀⣀⣤⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠛⢿⣜⠛⠛⠛⠛⠛⠙⠃⠙⠛⠋⠛⠃⠛⠸⢃⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡿⠃⡿⠿⠋⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣤⣤⡄⣤⣤⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣌⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠟⠛⠛⠛⠉⠁⠀⣀⡇⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⠿⠋⠁⠀⣠⣿⣿⠃⠀⠀⣘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠰⠿⠻⠧⠿⠹⠿⠸⠷⠿⠻⠿⠿⠇⢿⣾⠟⢿⡇⠿⠿⠿⣶⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢰⣿⣿⣿⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⠉⢡⣿⣿⣿⣷⣶⡄⠀⠀⠀⢀⣒⣐⣒⣓⡒⢒⣒⡒⣒⣚⢷⣶⣶⣶⣶⣧⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⡶⣃⣤⣶⣿⣷⣦⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣫⣾⣿⣿⣿⣿⣿⣿⣿⣆⣠⣾⣿⣿⣿⣿⣿⣿⡇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⣿⣿⣿⣿⣿⡿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣈⣿⣿⡿⠿⠿⢿⠟⠀⠀⠠⠈⠉⠀⠉⠁⠉⠈⠉⠁⠉⠩⢽⣿⠿⠿⠿⠟⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠎⣠⣾⣿⣿⡏⠉⠉⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣶⣿⣿⣿⣿⢠⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣛⢷⡆⣿⣿⣿⢸⡿⠇⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠻⠾⢃⠻⠿⠋⠺⢇⣄⡻⢇⣀⠟⠃⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⡻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣥⣤⠉⣤⣨⣭⣭⣭⣍⠻⢀⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢁⣿⣿⣿⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⢀⠸⣿⣿⡇⣿⢻⣿⢿⣧⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠙⠛⠿⢆⣤⣶⣶⠀⣴⣶⣶⣶⣶⣿⣶⣤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣶⣶⣦⣄⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⠀⢹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⢂⢀⣴⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠘⠛⠛⠛⠛⠛⠙⠃⠙⠛⠋⠛⠃⠛⠸⠃⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠿⠟⢸⠟⠋⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠟⣫⡄⣤⣤⡄⣤⣠⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣌⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣛⣉⣉⠉⠁⠀⢀⣼⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⢀⣴⣿⣿⠀⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠿⠋⠁⠀⢀⣼⣿⣿⠀⠀⠀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⢀⣴⣿⣿⣿⣿⣰⣿⠻⠧⠿⠹⠿⠸⠷⠿⠻⠿⠿⠇⢿⣾⠟⢿⠇⠿⠿⠿⣶⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡆⠀⢀⣀⣀⣐⣒⡒⢒⣒⡒⣒⣚⢶⣶⣶⣶⣶⣥⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣾⢟⣠⣴⣿⣿⣿⡦⠀⠀⠀⢀⣴⣿⣿⣿⣿⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⣿⠿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣀⣀⣠⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢠⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⣸⣿⣿⣿⣿⣿⡿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢠⣿⣿⣿⣿⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⠿⠀⠀⠿⠮⠉⠀⠉⠁⠉⠈⠉⠁⠉⠉⠁⠻⠿⠿⠛⠋⠀⠙⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣴⣿⣿⣿⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⠨
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣛⢷⡆⣿⣿⣿⢸⡿⠇⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠻⠾⢃⠻⠿⠋⠺⢇⣤⡻⣇⣀⠟⠃⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⡻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣥⣤⠉⣤⣩⣭⣭⣭⣍⠻⢋⣥⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣿⣿⣿⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⣿⣻⣿⣻⡿⣿⢿⣿⣿⢿⡿⠟⠁⠀⠀⠛⠻⢿⢆⣤⣶⣦⠀⣴⣶⣶⣶⣶⣾⣶⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠻⠿⠋⠉⠀⠀⠀⠀⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠿⡿⠿⠟⠃⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⠀⢹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⡆⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀⠀⢀⣠⣶⣿⣿⡇⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡏⣄⣴⡿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣧⠘⠛⠛⠛⠛⠛⠙⠃⠙⠛⠋⠛⠃⠛⠸⠃⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠿⠛⠀⣟⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡟⣤⣤⡄⣤⣤⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣄⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣉⣭⣥⠤⠀⠀⢀⣤⡞⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠇⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⠿⠿⠛⠁⠀⠀⣰⣿⣿⡇⠀⠀⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⡀⠀⠀⣿⣿⣿⣿⣿⣰⣿⠻⠧⠿⠹⠿⠸⠷⠿⠻⠿⠿⠇⢿⣼⠟⢿⠇⠿⠿⠿⣶⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⡆⢀⣀⣀⣀⣀⡀⢀⣀⡀⣀⣐⢶⣶⣶⣶⣶⣥⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢟⣡⣶⣿⣿⣿⣿⣀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⠀⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢞⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⡿⢛⣿⣿⣿⣿⣿⡄⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⠀⠀⢻⣿⣿⣿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠁⢸⣿⣿⢿⣿⠿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⠋⠀⠸⠿⠮⠭⠤⠭⠥⠍⠈⠉⠁⠉⠉⠀⠀⠘⠛⠋⠈⠀⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢠⣾⣿⣿⣿⡀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣛⢷⡆⣿⣿⣿⢸⡿⠇⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠻⠾⠃⠻⠿⠋⠺⢇⣤⣻⣇⣀⠟⠇⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⡻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣥⣤⠀⣭⢩⣭⣭⣭⣍⠻⢋⣤⣤⡁⣤⣠⣤⣤⡄⣤⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⡟⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⣿⠀⠀⠀⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⣿⣿⣿⣿⡿⢿⢿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠉⠻⣿⣶⣶⠀⠀⣴⣶⣶⣤⣤⣴⣾⣷⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠀⣀⡄⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⢀⣴⣶⣶⣾⣿⠟⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⣠⣶⣿⣿⣿⣿⡟⠋⠀⠀⠀⠺⠛⠉⠉⠉⠉⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣶⣤⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⠀⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⡇⣤⣴⡿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⡘⠛⠛⠛⠛⠛⠙⠃⠙⠛⠋⠛⠃⠛⠸⠃⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⠿⠛⠀⡟⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⢸⣿⣿⣿⡟⣥⣤⡍⣤⣤⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣄⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣚⣉⣭⣥⠤⠀⠀⢀⣴⡇⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⢸⣿⣿⣿⠇⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠛⠁⠀⠀⣰⣿⣿⡇⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣰⣿⢻⠧⠿⠹⠿⠸⠷⠿⠻⠿⠿⠇⢿⣾⠟⠿⡇⠿⠿⠿⣶⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣶⣶⣶⢀⣀⣀⣀⣀⡀⢀⣀⡀⣀⣀⠐⢶⣶⣶⣶⣥⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢞⣤⣶⣿⣿⣿⣿⣂⠀⠀⠀⣠⣿⣿⣿⣿⣿⣇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⠀⠀⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⡿⢛⣿⣿⣿⣿⣿⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢰⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⠀⠀⢸⣿⣿⣿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠁⣼⣿⣿⢿⣿⠿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⠏⠀⠀⠿⠮⠭⠤⠭⠥⠭⠬⠩⠥⠉⠉⠀⠀⠛⠛⠋⠀⠀⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢠⣾⣿⣿⣿⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⠨
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣛⢷⡆⣿⣿⣿⢸⡿⠇⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠻⠾⠃⠻⠿⢋⡺⣇⣤⡻⢇⣀⠿⠃⠻⠟⠸⠏⠛⠛⠛⠛⠃⠛⠛⡻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⣥⣤⠈⣭⣩⣭⣭⣬⣍⠻⢋⣥⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⠀⡠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⢰⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣀⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⣿⠀⠀⢨⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⢿⣿⣷⣦⠀⠠⣶⣶⣶⣦⣴⣶⣿⣶⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣰⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠿⠟⠛⠉⠉⠉⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣶⣶⣦⣀⡀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⠀⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠀⠀⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡗⣄⣠⣶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣘⠛⠛⠛⠛⠛⠙⠃⠙⠛⠋⠛⠃⠛⠸⠃⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠟⠃⣿⠛⠉⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢸⣿⣿⡟⣭⣬⡍⣥⣤⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣌⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢛⣛⣋⣉⠉⠀⠀⣀⡿⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣸⣿⣿⠃⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠿⠋⠀⠀⢠⣾⣿⡇⠀⠀⢠⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣿⢻⠧⢿⠹⡿⠸⠷⠿⠻⠿⠿⠇⢿⣾⠟⢿⠇⠿⠿⠿⣶⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠁⠁⠀⠀⠀⠀⢀⣿⣿⣿⣷⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⢂⣀⣀⣂⣀⡀⢀⣀⡀⣀⣀⠀⠲⣶⣶⣶⣥⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡷⣁⣴⣾⣿⣿⣷⡤⠀⠀⠀⣠⣾⣿⣿⣿⣿⣇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⠀⠀⠈⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣾⣿⠿⣿⣿⣿⣿⣿⡄⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⠀⠀⠀⣸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣸⣿⣿⣿⣿⣿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡟⠁⠀⠰⠬⠭⠴⠭⠥⠭⠬⠭⠥⠍⠉⠀⠀⠐⠛⠛⠁⠙⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⢁⣴⣿⣿⣷⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⣆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣛⢷⡆⣿⣿⣿⢸⡿⠇⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⠻⠾⠃⠻⠿⠋⠻⣇⣤⡻⢇⣀⠿⠇⠻⠟⠸⠏⠛⠛⠛⠛⠃⠛⠛⡻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣤⣤⠀⣭⢩⣭⣭⣤⣍⠻⢋⣥⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⠀⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⢐⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠀⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⢀⠸⣿⣿⡇⣿⢻⣿⢿⣧⣿⠀⠀⣨⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⢿⣿⣶⣶⠀⠀⣴⣶⣶⣶⣶⣶⣿⣶⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠿⠟⠛⠋⠉⠉⠉⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣤⣤⣄⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⠀⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠀⠀⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣷⠀⠀⣠⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣜⠛⠛⠛⠛⠛⠙⠃⠙⠛⠋⠛⠋⠛⠸⠃⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠇⢸⣿⠟⠃⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢸⣿⡟⣭⣬⡍⣧⣤⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣄⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⠿⠿⠛⠛⠋⠁⠀⣸⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⠇⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⠟⠋⠀⠀⣴⣿⡿⠀⠀⢀⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⢻⠧⢿⠹⡿⠸⠷⠿⠻⠿⠿⠇⢿⣾⠟⢿⠇⠿⠿⠿⣶⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠁⠀⠀⠀⣼⣿⣿⣷⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣷⢆⣀⣀⣐⣀⡀⢀⣀⡀⣀⣀⠐⢶⣶⣶⣶⣥⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⢎⣠⣴⣾⣿⣦⣄⠀⠀⠀⠀⣰⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⠀⠀⠉⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣦⣠⣴⣾⣿⣿⣿⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢰⣿⣿⣿⣿⣿⢇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡿⠁⠀⠠⠬⠭⠤⠭⠥⠭⠬⠍⠥⠍⠉⠁⠀⠀⠚⠛⠃⠚⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠃⣠⣿⣿⣿⠉⠋⢉⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⣆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⢽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣛⢷⡆⣿⣿⣿⢸⡿⠇⣿⡇⢸⣿⣿⣿⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⠻⠾⠃⠻⠿⠋⠺⣇⣤⡻⣇⣀⠿⠇⠻⠟⠸⠏⠛⠛⠛⠛⠃⠟⠛⡻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣤⣤⠀⣭⣩⣭⣭⣭⣍⠻⢋⣥⣤⡈⣤⣠⣤⣤⡄⣤⠀⠀⠀⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⢐⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣤⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⢀⠸⣿⣿⡇⣿⢻⣿⢿⣧⣿⠀⠀⢻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠈⢿⣿⣷⣶⠄⠀⣴⣶⣶⣶⣶⣶⣿⣷⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠿⠿⠛⠋⠉⠉⠉⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⠀⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠀⠀⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡄⠀⢀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣜⠛⠛⠛⠛⠛⠙⠃⠙⠛⠋⠛⠋⠛⠸⠃⣸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⡿⢸⣶⡿⠃⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⣿⣿⡟⣭⣬⡍⣧⣤⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣄⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⠿⠿⠿⠛⠉⠀⢸⡇⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⠇⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣯⣶⣶⡶⠖⠀⠀⣠⣶⣿⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣿⢻⠧⢿⠹⠿⠸⠷⠿⠻⠿⠿⠇⢿⣾⠟⢿⠇⠿⠿⠿⣶⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠛⠛⠉⠀⠀⠀⢰⣿⣿⣿⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⢆⣀⣀⣂⣀⡀⢀⣀⡀⣀⣀⠐⢶⣶⣶⣶⣥⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣵⡴⣀⣤⣶⣶⣦⣀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⠀⠀⠙⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣟⣿⣾⣿⣿⣿⣿⣿⣿⣦⣀⣠⣶⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢁⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡿⠁⠀⠠⠬⠭⠴⠭⠥⠭⠬⠉⠥⠉⠉⠁⠀⠀⠘⠛⠁⠛⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠏⣠⣾⣿⣿⠛⠛⠛⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⣆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⢽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣛⢷⡆⣿⣿⣿⢸⡿⠇⣿⡇⢸⣿⣿⣿⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⠻⠾⠃⠻⠿⠋⠻⢇⣤⡻⣇⣀⠿⠇⠻⠟⠸⠏⠛⠛⠛⠛⠇⠛⠛⡻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣤⣤⠀⣬⣩⣭⣭⣭⣍⠻⢋⣥⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⢠⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⢌⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⢀⠸⣿⣿⡇⣿⢻⣿⢿⣧⣿⠀⠀⢼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠏⠀⠀⠈⢿⣿⣷⣶⠄⠀⣶⣶⣶⣶⣶⣶⣿⣷⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠸⠿⠟⠛⠋⠉⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⠈⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⣤⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣜⠛⠛⠛⠛⠛⠙⠃⠙⠛⠋⠛⠋⠛⠸⠃⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⢸⣤⣾⠧⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⣿⣿⡟⣭⣬⡍⣥⣤⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣌⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⡿⠿⠛⠉⠈⡇⠁⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⠇⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣭⣵⣶⡶⠂⠀⢀⣴⣾⠃⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣿⢻⠧⢿⠹⡿⠸⠷⠿⠻⠿⠿⠇⢿⣾⠟⢿⠇⠿⠿⠿⣶⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠟⠛⠁⠀⠀⢠⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⢂⣀⣀⣒⣀⡀⢀⣀⡀⣀⣀⠐⠶⣶⣶⣶⣥⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣪⡠⠀⣀⣤⣦⣤⡀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⠀⠀⠈⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣵⣾⣿⣿⣿⣿⣿⣧⡀⢀⣴⣿⣿⣿⣿⣿⣿⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⠀⠀⠀⢈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⠟⠁⠀⠠⠬⠭⠴⠭⠥⠭⠬⠉⠥⠍⠉⠁⠀⠀⠘⠋⠁⠚⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⣼⣿⣿⠿⠿⠟⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣾⢷⡆⣶⣿⣦⢶⡶⠶⣶⡶⢶⣆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⢹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣛⢷⡆⣿⣿⣿⢸⡿⠇⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⡻⠾⠃⠛⠿⠋⠺⢇⣤⣻⣇⣀⠿⠇⠻⠟⠸⠏⠛⠛⠛⠻⠃⠟⠛⡻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣤⣬⠁⣤⣩⣭⣭⣭⣍⠻⢋⣭⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⣠⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⢀⠸⣿⣿⡇⣿⢻⣿⢿⣧⣿⠀⠀⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠈⢿⣿⣷⣶⡆⠀⣴⣶⣦⣴⣶⣶⣿⣧⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠨⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣸⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠁⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠻⠿⠟⠋⠉⠉⠉⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⠀⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣜⠛⠛⠛⠛⠛⠙⠃⠙⠛⠋⠛⠋⠛⠸⠃⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⠏⣦⣾⠿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⢸⣿⣿⡟⣭⣬⡍⣧⣤⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣌⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⠿⠿⠿⠋⠁⠀⡏⠁⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣸⣿⣿⠇⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣽⣶⣶⠖⠂⠀⢀⣴⣾⠇⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣿⢻⠧⠿⠹⡿⠸⠷⠿⠻⠿⠿⠇⢿⣾⠟⢿⡇⡿⠿⠿⣶⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠛⠋⠁⠀⠀⢠⣿⣿⣿⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣶⣶⣶⢂⣀⣀⣀⣀⡀⢀⣀⡀⣀⣀⠐⢶⣶⣶⣶⣥⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⣦⢆⣠⣴⣶⣦⣄⠀⠀⠀⠀⢀⣾⣿⣿⣿⣧⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⠀⠀⠙⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣫⣷⣿⣿⣿⣿⣿⣿⣧⣀⣀⣴⣿⣿⣿⣿⣿⣿⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⠀⠀⠀⢸⣿⡿⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢨⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⠟⠁⠀⠰⠮⠭⠴⠭⠥⠭⠬⠩⠥⠉⠉⠁⠀⠀⠚⠁⠀⠉⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠝⢀⣼⣿⣿⠛⠛⠛⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⣆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣛⢷⡆⣿⣿⣿⢸⡿⠇⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⠻⠾⠃⠛⠿⠋⠻⢇⣤⣻⣇⣀⠿⠇⠻⠟⠸⠏⠛⠛⠛⠛⠃⠛⠛⡻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣤⣬⠁⣤⣩⣭⣭⣭⣍⠻⢋⣥⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⣠⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⢾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⢀⠸⣿⣿⡇⣿⢻⣿⢿⣧⣿⠀⠀⢻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⠀⠀⠀⠻⣿⣷⣶⠄⠀⣴⣶⣶⣤⣤⣶⣿⣷⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⣴⣿⣿⡀⠀⠘⢿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⢀⣾⣿⣿⣿⠇⠀⠀⠘⠿⠿⠛⠁⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⢀⣴⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⠀⠘⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⡂⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣇⠀⠀⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣷⡘⠛⠛⠛⠛⠛⠙⠃⠙⠛⠋⠛⠃⠛⠸⠃⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠃⡷⡿⠳⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⣥⣤⡍⣤⣤⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣌⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠿⠿⠿⠛⠛⠉⠀⢀⡇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠇⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣿⡿⠛⠁⠀⢠⣶⣿⠃⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⣹⣿⣿⣿⣰⣿⢻⠧⠿⠹⠿⠸⠷⠿⠻⠿⠿⠇⢿⣾⠟⢿⡇⠿⠿⠿⣶⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠉⠀⠀⠀⢰⣿⣿⣿⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⢀⣀⣀⣀⣀⡀⢀⣐⡒⣀⣚⢷⣶⣶⣶⣶⣧⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⡷⣁⣤⣾⣿⣷⣤⡀⠀⠀⠀⣠⣿⣿⣿⣿⣧⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⠘⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢟⣵⣿⣿⣿⣿⣿⣿⣿⣶⣄⣤⣾⡿⣿⣿⣿⣿⣿⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⠀⠀⠙⢿⣿⡿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⠏⠀⠀⠼⠮⠭⠴⠭⠥⠉⠈⠉⠁⠉⠉⠀⠀⠀⠘⠋⠀⠀⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣠⣾⣿⣿⠙⠛⠋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣛⢷⡆⣿⣿⣿⢸⡿⠇⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠻⠾⠃⠛⠿⠋⠻⢇⣤⡻⣇⣀⠿⠇⠻⠟⠸⠏⠛⠛⠛⠻⠃⠛⠛⡻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣤⣤⠉⣤⣩⣭⣭⣭⣍⠻⢋⣥⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⠀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⢼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣩⣿⣿⠁⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⢀⠸⣿⣿⡇⣿⢻⣿⢿⣧⣿⠀⠀⠀⠲
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⠿⣿⢿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠙⠿⣶⣶⠆⠀⣴⣶⣶⣤⣤⣶⣿⣧⡤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣦⣤⣄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⠀⠈⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡧⠀⢀⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠁⠀⠘⠛⠛⠛⠛⠛⠙⠃⠙⠛⠋⠛⠋⠛⠸⠃⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣾⣿⣿⣿⣿⣿⠿⠁⡷⠿⠛⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣤⣤⡄⣤⣤⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣌⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⡛⠛⠛⠉⠁⠀⣠⡇⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠉⠁⠙⢻⡿⠀⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⠋⠁⠀⣰⣿⣿⠃⠀⠀⣘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⢀⣠⣶⣿⣿⣰⣿⠻⠧⠿⠹⠿⠸⠷⠿⠻⡿⢿⡇⢿⣾⠟⢿⡇⠿⠿⠿⣶⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⡀⠀⢀⣀⠈⠉⠁⠀⠀⠀⠀⣰⣿⣿⣿⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣦⠀⠀⠀⢀⣀⣀⣀⣐⡒⢒⣛⡓⣒⣚⢷⣶⣶⣶⣶⣷⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣟⣤⣶⣿⣿⣿⣶⡄⠀⠀⠀⣴⣿⣿⣿⣿⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⣀⣀⣠⣤⣽⣿⣿⣿⣿⣿⣿⡧⠀⠀⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣿⡿⣿⣿⣿⣿⣿⡆⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢠⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠁⠀⠰⠦⠈⠉⠀⠉⠁⠉⠈⠉⠁⠉⠉⠽⠿⠿⠿⠿⠟⠃⠙⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⣴⣿⣿⣿⡉⠉⢉⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⠸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣛⢷⡆⣿⣿⣿⢸⡿⠇⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⠻⠾⠃⠛⠿⠋⠺⢇⣤⡻⢇⣀⠟⠃⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⡻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣤⣤⠉⣤⣩⣭⣭⣬⣍⠛⢂⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢉⣼⣿⣿⡇⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⢀⠸⣿⣿⡇⣿⢻⣿⢿⣧⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⠿⠿⢿⢿⣿⣿⣿⡿⠟⠛⠉⠀⠀⠉⠉⠉⠓⠶⠶⠂⠀⣤⣶⣶⣦⣴⣶⣿⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣥⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡧⡀⢀⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⠛⠛⠛⠛⠛⠙⠃⠙⠛⠋⠛⠋⠛⠸⠃⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠿⠑⡷⠿⠋⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣥⣤⡌⣤⣤⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣌⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⢟⣛⣛⡋⠉⠀⠀⣠⡇⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠟⠋⠀⠀⣰⣿⣿⠁⠀⠀⣘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠰⠿⠻⠧⠿⠹⠿⠸⠷⠿⠻⣿⢿⡇⢿⣾⠟⢿⡇⡿⠿⠿⣶⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣀⡀⠀⢀⣀⠈⠁⠀⠀⠀⠀⠀⣸⣿⣿⣿⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⢿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣐⣛⡒⢒⣛⡓⣒⣚⢷⣶⣶⣶⣶⣧⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⣏⣴⣾⣿⣿⣿⣶⡄⠀⠀⢀⣴⣿⣿⣿⣿⣧⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠙⠻⣿⡆⠀⠀⠀⠀⠀⣠⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣿⡿⣿⣿⣿⣿⣿⡆⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⡆⠀⠀⠀⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢰⣿⣿⣿⣿⣿⢇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⡿⠿⠿⠏⠀⠀⠀⠈⠈⠉⠤⠭⠥⠭⠬⠭⠥⣭⡭⣿⣿⠿⠿⠿⠿⠟⠙⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⣴⣿⣿⣿⡉⠉⢉⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣾⢷⡆⣶⣿⣦⢶⡶⠶⣶⡶⢶⣆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣛⢷⡆⣿⣿⣿⢸⡿⠇⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠻⠾⠃⠻⠿⠋⠻⢇⣀⠛⠃⠀⠛⠃⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⡻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣤⣬⠁⣤⣩⣭⣤⣤⣄⠀⢀⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢡⣾⣿⣿⠀⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⢀⠸⣿⣿⡇⣿⢻⣿⢿⣧⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⢿⢿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠉⠉⠉⠐⠶⠶⠂⠀⣠⣶⣶⣶⣴⣶⣿⣷⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⠀⠈⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠆⠀⣀⡄⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⠛⠛⠛⠛⠛⠙⠃⠙⠛⠋⠛⠃⠛⠸⠃⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⠟⠰⡗⠟⠁⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣥⣤⡄⣤⣠⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣌⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⣛⣛⣋⡉⠉⠀⠀⣀⡇⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠟⠁⠀⠀⣴⣿⣿⠀⠀⠀⣘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣿⠻⠧⢿⠹⡿⠸⠷⠿⠻⠿⠿⡇⢿⣼⠟⢿⠇⠿⠿⠿⣶⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⡀⠀⢀⡀⠈⠁⠀⠀⠀⠀⠀⣸⣿⣿⣿⡀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⠖⣶⢖⣒⣒⣒⣛⡒⢒⣚⡓⣂⣚⢷⣶⣶⣶⣦⣥⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡾⣏⣤⣶⣿⣿⣿⣶⠀⠀⠀⢀⣴⣿⣿⣿⣿⣇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⣰⣿⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣫⣾⣿⣿⣿⣿⣿⣿⣿⣷⣤⣰⣿⠟⣿⣿⣿⣿⣿⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⠁⢠⣿⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⣸⣿⣿⣿⣿⣿⣿⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣰⣿⣿⣿⣿⣿⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠈⠻⠿⠿⠟⠁⠀⠻⢿⡿⠮⠭⠴⠭⠥⠭⠬⠉⠥⠭⠭⢽⣿⠿⢿⣿⠿⠿⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⢁⣴⣾⣿⣿⠈⠉⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢠⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣛⢷⡆⣿⣿⣿⢸⡿⠇⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠈⠻⠾⠃⠛⠿⠋⠺⢇⣄⡻⢇⣀⠟⠃⠛⠛⠘⠏⠻⠛⠛⠻⠇⠛⠛⡻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⣤⢩⣭⣥⣬⣍⠛⢋⣥⣤⡀⣤⣠⣤⣭⡍⣥⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⢶⣶⣶⡀⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠠⣾⣿⣿⠇⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠻⠛⠿⠻⠿⠿⠿⠻⠛⠁⠀⠀⠀⠈⠉⠀⠀⠶⠶⠂⠀⣠⣶⣶⣦⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣦⣤⣄⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⠀⢹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⠄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠀⠘⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⢇⡀⣠⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⠛⠛⠛⠛⠛⠙⠃⠙⠛⠋⠛⠃⠛⠸⢃⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⡿⠟⢸⡿⠟⠁⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣥⣤⡄⣤⣠⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣌⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢛⣛⣋⣉⡉⠁⠀⢀⣸⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠟⠁⠀⢀⣼⣿⣿⠀⠀⢀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣿⠻⠧⢿⠹⡿⠸⠷⠿⠻⠿⠿⠇⢿⣾⠟⠿⠇⠿⠿⠿⣶⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡀⡀⠀⢀⣀⠈⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣶⣷⣖⣒⣒⣂⣀⡀⢀⣐⡒⣒⣚⢶⣶⣶⣤⣤⣥⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⣏⣴⣾⣿⣿⣿⣶⠀⠀⠀⢀⣼⣿⣿⣿⣿⣇⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢰⣿⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣻⣾⣿⣿⣿⣿⣿⣿⣿⣷⣤⣶⣿⠿⣿⣿⣿⣿⣿⡀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢠⣿⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠃⣸⣿⣿⣿⣿⣿⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⠀⠸⢿⡿⠮⠭⠤⠭⠥⠭⠬⠉⠁⠉⠩⢽⣿⠿⢿⣿⠿⠟⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⣴⣿⣿⣿⡈⠉⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢡⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢀⣛⢷⡆⣿⣿⣿⢸⡿⠇⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠈⠻⠾⠃⠻⠿⢋⡺⣇⣄⡻⢇⣀⠿⠇⠻⠟⠸⠏⠻⠛⠿⠻⠇⠛⠛⡻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⡏⣤⣤⠉⣭⣩⣭⣭⣭⣍⠻⢋⣤⣤⡈⣭⣩⣭⣭⡅⣤⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠸⡿⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⠿⢻⠿⡿⠿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠛⠉⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣤⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⠈⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠀⠹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣧⡿⢀⢀⣤⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⠛⠛⠛⠛⠛⠙⠃⠙⠛⠋⠛⠃⠛⠸⢃⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠟⠃⢸⠺⠋⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣤⣤⡄⣤⣠⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣌⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣛⣋⣉⣉⠁⠀⠀⣀⣼⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⠋⠀⠀⢠⣾⣿⡏⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣿⠻⠧⢿⠹⡿⠸⠷⠿⠻⠿⠿⠇⢿⣾⠟⠿⠇⠿⠿⠿⣶⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣖⣒⣂⣀⣀⡀⢀⣀⡒⣒⣒⢶⣶⣶⣤⣤⣥⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣫⣴⣾⣿⣿⣿⣆⠀⠀⠀⣠⣾⣿⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢫⣿⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣾⡿⢻⣿⣿⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣾⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠀⣼⣿⣿⣿⣿⡿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠀⠸⢿⡿⠮⠭⠤⠭⠥⠭⠈⠉⠁⠉⠩⢽⣿⠿⢿⣿⠿⠟⠘⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⣠⣶⣿⣿⣇⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⢡⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢀⣛⢷⡆⣿⣿⣿⢸⡿⠇⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠻⠾⠃⠛⠿⢋⡺⢇⣄⡻⢇⣀⠟⠃⠛⠛⠸⠏⠻⠛⠛⠛⠇⠛⠛⠻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣸⣿⡇⣤⣤⠉⣭⢩⣭⣭⣭⣍⠻⢋⣤⣤⡈⣭⣩⣭⣭⡍⣭⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⣿⡏⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠙⠙⠛⠛⠻⠟⠛⠛⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠛⠉⠁⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣶⣶⣦⡀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⠈⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠀⢹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣶⡏⣄⢀⣴⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⠛⠛⠛⠛⠛⠙⠃⠙⠛⠋⠛⠃⠛⠸⢃⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡿⠛⠁⢿⠙⠉⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣤⣤⡄⣤⣤⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣌⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣋⣭⣭⡭⠀⠀⢀⣠⡮⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠟⠉⠀⠀⢠⣿⣿⡇⠀⠀⢠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⡿⠻⠧⢿⠹⠿⠸⠷⠿⠻⠿⠿⠇⢿⣾⠟⠿⠇⠿⠿⠿⣶⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⡀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣧⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣖⣒⣂⣀⣀⡀⢀⣀⡒⣒⣒⢶⣶⣶⣤⣤⣥⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢟⣥⣶⣿⣿⣿⣿⣂⠀⠀⢀⣠⣾⣿⣿⣿⣿⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢫⣿⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢛⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⡟⢻⣿⣿⣿⣿⣷⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣾⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⣾⣿⣿⣿⣿⡿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠿⠿⠟⠀⠸⢿⡿⠮⠭⠤⠭⠥⠭⠌⠉⠥⠉⠩⢽⣿⠿⢿⣿⠿⠿⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣠⣾⣿⣿⡏⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠙⢡⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⠰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢀⣛⢷⡆⣿⣿⣿⢸⡿⠇⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠈⠻⠾⠃⠛⠿⢋⡺⢇⣤⡻⢇⣀⠟⠇⠛⠛⠸⠏⠛⠛⠛⠻⠇⠛⠛⠻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣸⣿⣿⡇⣤⣤⠉⣭⣩⣭⣭⣭⣍⠻⢋⣤⣤⡀⣭⣩⣭⣭⡍⣭⠙⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠉⠉⠋⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡍⠙⠛⠫⠯⠻⠿⠻⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣶⣶⣤⡀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⠈⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠀⢹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣾⠇⡀⣠⣦⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⠛⠛⠛⠛⠛⠙⠃⠙⠛⠋⠛⠃⠛⠸⢃⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠿⠋⠀⡟⠋⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣤⣤⡄⣤⣠⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣌⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣩⣭⡭⠤⠀⠀⢀⣤⡇⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⠿⠛⠀⠀⠀⣰⣿⣿⠃⠀⠀⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⡿⠻⠧⢿⠹⠿⠸⠷⠿⠻⠿⠿⠇⢿⣼⠟⠿⠇⠿⠿⠿⣶⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣁⡀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣖⣒⣒⣀⣀⡀⢀⣀⡒⣒⣚⢷⣶⣶⣶⣤⣥⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⣫⣴⣿⣿⣿⣿⣿⡄⠀⠀⢀⣴⣿⣿⣿⣿⣿⡀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⣿⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⠟⢻⣿⣿⣿⣿⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣼⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢠⣿⣿⣿⣿⣿⢇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠈⢿⣿⣿⠿⠿⠟⠁⠀⢿⡿⠮⠭⠤⠭⠥⠭⠬⠉⠁⢭⠭⢽⣿⠿⢿⣿⠿⠟⠀⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢁⣴⣿⣿⣿⢇⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠈⢠⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⢀⣛⢷⡆⣿⣿⣿⢸⡿⠇⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⡀⠀⠀⠀⠀⠈⠻⠾⠃⠛⠿⠋⠚⠇⣀⠻⢇⣀⠟⠃⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⠻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣤⣤⣤⠀⣤⣤⠀⣤⢠⣤⣤⣤⣍⠙⢉⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢉⣼⣿⣿⡿⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡜⠉⠙⠙⠛⠻⠟⠛⠛⠏⠛⠉⠀⠀⠀⠉⠋⠉⠁⣴⣶⡄⠀⣴⣶⣶⣦⣶⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⠈⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠀⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠃⣄⣴⣶⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⢿⣿⣿⣿⣜⠛⠛⠛⠛⠛⠙⠃⠙⠛⠋⠛⠃⠛⠸⠃⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠟⠋⠀⡏⠋⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣤⣤⡄⣤⣠⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣌⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣩⣭⣭⡤⠄⠀⠀⣠⣴⡇⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⠀⠀⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠿⠿⠋⠀⠀⠀⣼⣿⣿⠀⠀⠀⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡆⠰⠿⠻⠧⢿⠹⡿⠸⠷⠿⠻⠿⠿⠇⢿⣼⠟⢿⡇⠿⠿⠿⣶⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣀⠄⢀⣠⣤⣄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠈⣽⣿⣿⣧⠀⠀⠀⠰⠶⠶⢖⣂⣐⣒⣒⡒⢒⣒⡓⣒⣚⢷⣶⣶⣶⣦⣥⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢟⣣⣶⣿⣿⣿⣿⣿⣂⠀⠀⣠⣼⣿⣿⣿⣿⣿⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⣾⣿⣿⣿⣿⣧⡀⠀⠀⠀⢰⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⠟⣿⣿⣿⣿⣿⣧⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡄⠀⠀⠉⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⣸⣿⣿⣿⣿⣿⡿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣰⣿⣿⣿⣿⠿⢯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢀⣠⣴⣾⣿⡿⠿⠿⠿⠀⠀⠀⠀⠈⠉⠀⠉⠁⠉⠈⠉⠥⣭⠭⢽⣿⠿⠿⠿⠟⠀⠙⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⣴⣿⣿⣿⣣⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⢠⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣛⢷⡆⣿⣿⣿⢸⡿⠃⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠻⠾⠃⠛⠿⠋⠺⢇⣀⠛⠃⠀⠛⠃⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⠻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣤⣤⠀⣭⣩⣭⣥⣤⣄⠀⢀⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣼⣿⣿⣿⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠛⠛⠿⠿⢿⢿⡿⠿⡿⠟⠋⠁⠀⠀⠈⠉⠉⠁⠴⣶⡦⠀⢰⣶⣶⣶⣶⣶⣾⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠀⠀⠛⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢋⣴⡇⠀⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⠈⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢿⡄⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⢛⣿⣷⣶⣿⣿⠁⠀⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠀⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠉⣄⣴⡷⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢀⣴⣿⣿⣿⣿⣿⡿⠀⠀⠘⠛⠛⠛⠛⠛⠙⠃⠙⠛⠋⠛⠃⠛⠸⠃⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⣿⣿⡿⠿⠛⠁⠀⡇⠁⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⡏⣤⣤⡄⣤⣠⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣄⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⣭⣶⡶⠂⠀⠀⣠⣶⡇⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⠃⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠛⠁⠀⠀⠀⣾⣿⣿⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣰⣿⠻⠧⠿⠹⠿⠸⠷⠿⠻⠿⠿⠇⢿⣼⠟⢿⡇⠿⠿⠿⣶⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⣄⡄⢀⣠⣤⣄⡀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⡀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣶⣶⣶⠀⠀⢀⣀⣀⣐⣒⡒⢒⣚⡒⣀⣚⢷⣶⣶⣶⣶⣥⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢟⣯⣶⣿⣿⣿⣿⣿⣦⡀⠀⣠⣾⣿⣿⣿⣿⣿⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣷⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢰⣷⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⡸⣿⣿⣿⣿⠏⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠋⣠⣿⣟⡿⠿⠿⢫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠁⠀⢿⡿⠮⠉⠀⠉⠁⠉⠈⠉⠁⠉⠉⠁⠿⠟⠋⠀⠀⠀⠻⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢡⣾⣿⣿⣿⡳⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣛⢷⡆⣿⣿⣿⢸⡿⠇⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠻⠾⠃⠻⠿⠋⠺⢇⣄⡻⢇⣀⠟⠇⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⠻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣤⣤⠀⣭⢩⣭⣭⣭⣍⠻⢋⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⠀⢠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⢂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⢰⣿⣿⣿⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠉⠙⠋⠉⠙⠛⠟⠛⠋⠛⠉⠀⠀⠀⠀⠈⠀⠁⠰⠶⠆⠀⣠⣶⣶⣦⣤⣴⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁⠀⡈⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⢠⣾⣿⣿⣿⡟⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⣰⣿⣿⣿⣿⣿⡇⠀⠀⠀⢘⣿⣿⣿⡿⠟⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣄⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⠈⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⡀⢀⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠀⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠃⣷⠾⠻⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣷⡀⠘⠛⠛⠛⠛⠛⠙⠃⠙⠛⠋⠛⠃⠛⠸⠃⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⠿⠛⠛⠛⠉⠀⠀⣯⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⣥⣤⡄⣤⣠⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣌⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣿⣿⠟⠉⠀⢀⣴⣿⡇⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⢸⣿⣿⣿⣿⠇⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠁⠀⠀⠀⣾⣿⣿⡇⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣰⣿⠻⠧⠿⠹⠿⠸⠷⠿⠻⠿⠿⠇⢿⣾⠟⢿⡇⠿⠿⠿⣶⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡔⣀⣴⣶⣶⣤⡀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⠀⢀⣀⣀⣀⣀⡀⢀⣀⡀⣀⣘⢲⣶⣶⣶⣶⣥⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣽⣿⣿⣿⣿⣿⣿⣿⣄⣀⣴⣾⣿⣿⣿⣿⣿⣷⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⣿⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣹⣿⣿⣿⣿⣿⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣾⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⠀⣿⣿⡿⠋⠉⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣠⣿⣿⣿⠟⠛⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠰⢿⡿⠮⠭⠤⠭⠅⠭⠌⠉⠁⠉⠉⠁⠛⠛⠀⠀⠀⠘⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⣼⣿⣿⣿⠿⠃⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⢽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣛⢷⡆⣿⣿⣿⢸⡿⠇⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠻⠾⠃⠻⠿⠋⠺⢇⣄⡻⣇⣀⠿⠇⠻⠛⠸⠋⠛⠛⠛⠛⠃⠛⠛⡻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣥⣤⠀⣭⢩⣭⣭⣭⣍⠻⢋⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⠤⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⡇⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⣵⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠘⠛⠻⡇⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⣿⠀⠀⠈⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⠉⠙⠋⠛⠋⠛⠹⠟⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣴⣶⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⢀⣾⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣼⣿⣿⣿⣿⡇⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢸⣿⣿⣿⠿⠛⠛⠉⠉⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠘⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⠈⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⡧⡀⢀⣤⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣧⠀⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠀⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠿⠃⣷⠾⠛⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣇⠘⠛⠛⠛⠛⠛⠙⠃⠙⠛⠋⠛⠃⠛⠸⠃⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣛⣛⣛⠉⠁⠀⠀⣿⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⣸⣿⣿⣿⡟⣭⣤⡅⣤⣤⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣄⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⡿⠋⠁⠀⢀⣾⣿⡇⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⠃⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠊⠉⠉⠀⠀⠀⠀⣾⣿⣿⣇⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣿⠻⠧⠿⠹⠿⠸⠷⠿⠻⠿⠿⠇⢿⣾⠟⠿⠇⠿⠿⠿⣶⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⠖⣠⣴⣿⣿⣦⣄⠀⠀⠀⢀⣼⣿⣿⣿⣿⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⢀⢀⣀⣀⣀⣀⡀⢀⣀⡀⣀⣀⠲⣶⣶⣶⣶⣥⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢟⣵⣿⣿⣿⣿⣿⣿⣿⣧⣀⣴⣿⣿⣿⣿⣿⣿⣷⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢡⣿⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⠀⣿⣿⣿⣿⡿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣹⣿⣿⣿⣿⣿⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣾⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⡀⣿⣿⠏⠁⠀⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣠⣿⣿⣷⡛⠉⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠇⠀⠸⢿⡿⠮⠭⠴⠭⠥⠭⠌⠉⠁⠉⠉⠡⠟⠋⠀⠀⠀⠘⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⣼⣿⣿⣿⠿⠃⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣛⢷⡆⣿⣿⣿⢸⡿⠇⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠻⠾⠃⠻⠿⠋⠺⢇⣤⡻⢇⣀⠿⠃⠻⠛⠸⠋⠛⠛⠛⠛⠃⠛⠛⡻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⣭⣤⠀⣭⢩⣭⣭⣭⣍⠻⢋⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⢀⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣻⣿⠀⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⢾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⠈⠉⠉⠆⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⣿⠀⠀⠀⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠉⠉⠉⠋⠙⠙⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣴⣴⣶⣶⣾⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢹⣿⣿⣿⡏⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠸⣿⣿⣿⡄⠀⠀⠀⠀⠸⣿⣿⣿⡿⠛⠉⠉⠁⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠙⣿⣿⣆⠀⠀⠀⠀⠻⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠈⣿⣿⣆⠀⠀⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⠈⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⡗⡀⣠⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⣼⣿⣿⣿⣷⡀⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠈⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠛⠀⡿⠟⠉⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢰⣿⣿⣿⣿⣿⣷⠘⠛⠛⠛⠛⠛⠙⠃⠙⠛⠋⠛⠃⠛⠸⠃⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⣛⣭⣭⡭⠀⠀⢀⣤⡇⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡟⣭⣤⡍⣤⣤⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣄⠙⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠟⠁⠀⠀⣠⣿⣿⡇⠀⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⡿⠻⠧⠿⠹⠿⠸⠷⠿⠻⠿⠿⠇⢿⣾⠟⢿⠇⠿⠿⠿⣶⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡷⣃⣴⣿⣿⣿⣶⣄⠀⠀⠀⣠⣾⣿⣿⣿⣿⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡶⢠⢄⣀⣀⣀⣀⡀⢀⣀⡀⣀⣀⠲⣶⣶⣶⣶⣥⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⣾⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣷⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢠⣿⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⠀⣿⣿⣿⡿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣼⣿⡿⣿⣿⣿⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢀⣾⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⡀⣿⣿⠏⠀⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⣴⣿⣿⣿⡏⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠀⠾⢿⡿⠮⠭⠴⠭⠥⠭⠌⠉⠁⠉⠉⠡⠟⠁⠀⠀⠀⠐⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠟⢡⣾⣿⣿⡿⠛⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⣆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⢹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣛⢷⡆⣿⣿⣿⢸⡿⠇⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠻⠾⠃⠻⠿⠋⡻⢇⣄⠻⢇⣀⠿⠇⠻⠟⠸⠋⠛⠛⠛⠛⠃⠛⠛⡻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⣭⣤⠈⣭⣩⣭⣤⣬⣍⠛⢃⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⢠⣠⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⡀⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠈⠇⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⣿⠀⠀⢺⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡉⠛⠙⠛⠟⠻⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⣶⣶⣶⣶⣾⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⡀⠀⠀⠈⠻⢿⢿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣿⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⢘⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⢱⣤⣾⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢀⣾⣿⣦⡀⠀⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠈⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⡿⠿⠿⠟⠋⠁⢸⡏⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣿⣿⣿⣿⣆⠘⠛⠛⠛⠛⠛⠙⠃⠙⠛⠋⠛⠃⠛⠸⠃⠿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⣶⠖⠂⠀⢀⣴⣾⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣭⣤⡍⣤⣤⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣄⠙⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣛⠁⠀⠀⢀⣾⣿⣿⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⡿⠻⠧⠿⠹⠿⠸⠷⠿⠻⠿⠿⠇⢿⣾⠟⢿⠇⠿⠿⠿⣶⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⣣⣶⣿⣿⣿⣿⣿⣦⡀⠀⣀⣴⣿⣿⣿⣿⣿⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⠆⢠⢄⣀⣀⣀⣀⡀⢀⣀⡀⣀⣀⠲⣶⣶⣶⣶⣅⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢀⣿⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⠀⢻⣿⣿⡿⠻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢁⣿⣿⣻⣿⠿⢟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣾⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⠀⢸⡿⠋⠀⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣠⣿⣿⣿⣿⡀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⡏⠀⠾⢿⡿⠮⠭⠴⠭⠁⠭⠌⠉⠁⠉⠉⠡⠞⠀⠀⠀⠀⠀⠺⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡿⠋⣴⣿⡿⠿⠛⠉⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⣆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣛⢷⡆⣿⣿⣿⢸⡿⠇⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⠻⠾⠃⠻⠿⠋⠺⢇⣀⠻⢇⣀⠿⠇⠻⠟⠸⠋⠛⠛⠛⠛⠃⠛⠛⡻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠎⣥⣤⠈⣭⢩⣭⣭⣭⣍⠛⢃⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⢤⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⢋⣼⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⣛⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠈⠋⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⣿⠀⠀⠀⠺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡈⠉⠉⠈⠉⠉⠉⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠶⢶⣶⡾⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡆⠄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡗⡀⢀⣤⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠟⠁⣿⠻⠙⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢠⣶⣆⡀⠀⠀⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠈⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣛⣩⣉⡉⠁⠀⠀⣀⣿⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣾⣿⣿⣿⣦⡀⠘⠛⠛⠛⠛⠛⠙⠃⠙⠛⠋⠛⠃⠛⠸⠃⠿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⣿⡿⠋⠀⠀⢀⣼⣿⡏⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣥⣤⡅⣤⣤⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣄⠙⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡷⢂⣤⣶⣿⣿⣶⣄⡀⠀⠀⠀⣰⣿⣿⣿⣿⣇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⡿⠻⠧⠿⠹⠿⠸⠷⠿⠻⠿⠿⠇⢿⣼⠟⢿⠇⠿⠿⠿⣶⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣿⣿⣿⣿⣿⣿⣿⣦⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡶⠀⢀⣀⣀⣀⣀⡀⢀⣀⡀⣀⣀⠲⣶⣶⣶⣦⣅⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⣿⣿⠿⣿⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⣸⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⠀⠸⣿⣿⠛⠉⢮⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⣼⣿⣷⡿⠋⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣴⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⠀⠀⠟⠁⠀⠀⠈⡽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⢡⣿⣿⣿⡿⠿⠂⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⡿⠀⠿⢿⡿⠮⠭⠤⠭⠁⠭⠈⠉⠁⠉⠉⠡⠞⠀⠀⠀⠀⠀⠀⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⠏⠀⠛⠛⠉⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⣆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣛⢷⡆⣿⣿⣿⢸⡿⠇⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠨
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⠻⠾⠃⠻⠿⠋⠺⢇⣀⡻⢇⣀⠟⠃⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⡻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣥⣤⠀⣭⢩⣭⣭⣭⣍⠛⢁⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⢀⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⢛⣴⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠸⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⠙⠛⢿⢿⠿⢿⣿⢿⣿⣿⠿⠟⠉⠁⠀⠀⠀⠀⠉⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠈⠙⠿⣿⠿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⡿⢤⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⢠⡄⣴⠇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠿⠿⠟⠋⠀⠀⡇⠁⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢠⣾⣦⡀⠀⠀⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠈⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⠖⠂⠀⠀⣠⣶⡇⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣾⣿⣿⣿⣷⣄⠘⠛⠛⠛⠛⠛⠙⠃⠙⠛⠋⠛⠃⠛⠸⠃⠿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⢛⡃⠀⠀⠀⣰⣿⣿⡇⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣥⣤⡅⣤⣤⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣄⠙⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢰⡿⣣⣶⣿⣿⣿⣿⣿⣶⡀⠀⢀⣠⣾⣿⣿⣿⣿⣧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠰⠿⠻⠧⠿⠹⠿⠸⠷⠿⠻⠿⠿⠇⢿⣼⠟⠿⠇⠿⠿⠿⣶⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠟⣿⣿⣿⣿⣿⡷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⠶⠀⢀⣀⣀⣀⣀⡀⢀⣀⡀⣀⣀⠀⢲⣦⣴⣦⠁⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢸⡿⢟⣻⡿⠿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⣼⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⠀⠀⢿⠟⠉⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣴⣿⣿⣿⣇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣴⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⠀⢀⠈⠀⠀⠀⠀⠀⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⡿⠁⣾⣿⡿⠿⠛⠉⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⡿⠀⠸⢿⡿⠮⠭⠤⠭⠁⠭⠌⠉⠁⠉⠉⠡⠟⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⡿⠀⠈⣉⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⣆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣛⢷⡆⣿⣿⣿⢸⡿⠇⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⠻⠾⠃⠛⠿⠋⠺⢇⣀⠻⢇⣀⠟⠃⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⠻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣤⣤⠀⣭⢩⣭⣥⣬⣍⠻⢋⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⠀⢠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠉⣷⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠉⠛⠛⠛⠟⠻⠿⠿⠟⠟⠟⠋⠁⠀⠀⠀⠀⠀⠁⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⠛⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣏⣠⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⡿⢸⡦⡾⠇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⠿⠛⠛⠁⠀⠈⡇⠁⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢰⣿⣷⣄⠀⠀⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠈⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⣾⡿⠛⠁⠀⠀⣴⣾⡇⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⣿⣿⣿⣿⣿⣆⠘⠛⠛⠛⠛⠛⠙⠃⠙⠛⠋⠛⠃⠛⠸⠃⠿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠛⠅⠀⠀⠀⣼⣿⣿⡅⠀⠀⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣥⣤⡅⣤⣤⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣄⠙⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡠⠀⢀⣤⣦⣤⡀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣟⣵⣾⣿⣿⣿⣿⣿⣷⡀⠀⢀⣴⣿⣿⣿⣿⣿⣧⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠰⠿⠻⠧⠿⠹⠿⠸⠷⠿⠻⠿⠿⠇⢿⣼⠟⠿⠇⠿⠿⠿⣶⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⢋⣿⣿⣿⣿⣿⡧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡶⠀⢀⣀⣀⣀⣀⡀⢀⣀⡀⣀⣀⠀⠲⣶⣴⣦⡁⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣸⣿⣋⣽⠿⠛⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⣰⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⠀⠀⢹⡏⠁⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⣼⣿⣿⣿⡣⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣴⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⠀⢀⠈⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡟⢡⣾⣿⠿⠛⠋⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⡿⠀⠘⠿⡿⠮⠭⠤⠭⠁⠭⠌⠉⠁⠉⠉⠡⠟⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⡟⠀⢀⣀⡀⠄⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⣆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣛⢷⡆⣿⣿⣿⢸⡿⠇⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠐
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⠻⠾⠃⠛⠿⠋⠺⢇⣀⠻⢇⣀⠟⠇⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⠻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣤⣤⠀⣭⢩⣭⣤⣬⣍⠻⢋⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠉⠉⠙⣷⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠐
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⠉⠉⠛⠛⠛⠛⠛⠟⠻⠛⠋⠉⠀⠀⠀⠀⠀⠀⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢀⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡻⠀⠀⠀⠙⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣇⣶⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠻⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⠏⢰⡄⡟⠃⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣧⠀⠀⠀⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠛⠛⠛⠉⠁⠀⢈⡅⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠈⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⢺⣿⡟⠋⠀⠀⢀⣶⣿⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠠⣿⣿⣿⣿⣿⣆⠀⠘⠛⠛⠛⠛⠛⠙⠃⠙⠛⠋⠛⠃⠛⠸⠃⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠭⠀⠀⠀⠀⣾⣿⣿⡀⠀⠀⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣿⣿⣿⡟⣥⣤⡄⣤⣠⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣄⠙⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣔⡄⢀⣠⣴⣶⣦⣀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣸⣯⣶⣿⣿⣿⣿⣿⣿⣷⣄⠀⣠⣾⣿⣿⣿⣿⣿⣧⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠰⠿⠻⠧⠿⠹⠿⠸⠷⠿⠻⠿⠿⠇⢿⣼⠟⠿⠇⠿⠿⠿⣶⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⠆⠀⢀⣀⣀⣀⣀⡀⢀⣀⡀⣀⣀⠐⣶⣶⣴⣦⡁⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣻⣟⣩⡿⠟⠋⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⣠⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⠀⠈⣿⣿⠉⠀⠀⠈⠿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⣾⣿⣿⣿⡅⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣸⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⠀⠀⠘⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠋⢠⡿⠿⠛⠋⠁⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⠀⠐⠿⠿⠮⠭⠤⠭⠁⠉⠈⠉⠁⠉⠉⠁⠞⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⠏⠀⣠⣤⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣛⢷⡆⣿⣿⣿⢸⡿⠃⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⠻⠾⠃⠛⠿⠋⠺⢇⣀⠻⢇⣀⠟⠃⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⠻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣤⣤⠀⣤⢩⣭⣤⣬⣍⠻⢋⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠉⠉⣷⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⠉⠙⠛⠛⠋⠛⠛⠛⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣶⣿⡿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣅⡆⠀⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⢹⣿⣿⣿⣿⣿⡞⠇⠀⠙⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠏⢰⡴⡟⠃⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⣰⣿⣿⣿⣿⣿⡙⠇⠀⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠛⠛⠛⠉⠀⠀⢸⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠈⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⢾⣿⠟⠉⠀⠀⢀⣶⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⡿⠀⠀⠘⠛⠛⠛⠛⠛⠙⠃⠙⠛⠋⠛⠃⠛⠸⠃⠿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠭⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⣤⣤⡄⣤⣤⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣄⠙⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣠⣆⠔⢀⣠⣶⣶⣦⣀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣧⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣀⣀⣀⡀⠘⣿⣿⣿⣿⠁⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡿⣧⣾⣿⣿⣿⣿⣿⣿⣦⡀⢀⣠⣾⣿⣿⣿⣿⣿⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠰⠿⠻⠧⠿⠹⠿⠸⠷⠿⠻⠿⠿⠇⢿⣼⠟⢿⠇⠿⠿⠿⣶⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡦⠀⠀⢀⣀⣀⣀⣀⡀⢀⣀⡒⣒⣚⢿⣶⣶⣶⣶⣥⠀⠺⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣻⣟⣯⡿⠛⠋⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⡀⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⠸⣿⣿⣿⣿⠟⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣠⣾⣿⣿⣿⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣾⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⠀⠈⢻⡿⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠃⢰⠿⠟⠛⠉⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⠀⠐⠿⠿⠮⠉⠀⠉⠁⠉⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⠏⠀⣠⣤⣔⠂⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣛⢷⡆⣿⣿⣿⢸⡿⠃⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠻⠾⠃⠛⠿⠋⠚⢇⣄⠻⢇⣀⠟⠃⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⠻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⡇⠀⣤⣬⠁⣤⢩⣭⣤⣬⣍⠻⢋⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠘⠛⠛⣧⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠁⠙⠙⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣇⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⠇⢰⢠⡿⠂⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⠿⠟⠛⠋⠁⠀⢸⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠘⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣶⣿⡟⠋⠁⠀⢠⣶⣾⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠘⡛⠛⣛⡛⠛⠙⠃⠙⠛⠋⠛⠃⠛⠸⠃⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣟⠀⠀⠀⢠⣿⣿⣿⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣤⣤⡄⣤⣤⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣄⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣠⣆⠄⢀⣠⣶⣶⣦⣀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣧⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⢹⣿⣿⣿⣿⠏⠀⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡿⣧⣾⣿⣿⣿⣿⣿⣿⣧⣀⠀⣠⣾⣿⣿⣿⣿⣿⣆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠈⠻⢿⣿⣏⠀⠰⠿⠻⠧⠿⠹⠿⠸⠷⠿⠻⠿⠿⠇⢿⣼⠟⢿⠇⠿⠿⠿⣶⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢹⣿⣿⣿⣿⣿⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⠀⣰⢖⣀⣀⣀⣀⡐⢒⣀⡀⣒⣚⢷⣶⣶⣶⣶⣷⣶⢿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢀⣻⣿⣿⡿⠟⠋⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⣴⣶⣿⣿⣿⣿⣿⣆⠀⠀⠀⠛⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⢸⣿⣿⣿⣿⣿⡏⠈⠹
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣠⣿⣿⣿⣯⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⣸⣿⣿⣿⣿⠛⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠁⢰⠿⠟⠛⠉⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠧⠀⠰⠄⠀⠈⠉⠀⠉⠁⠉⠈⠉⠁⠉⠉⠹⠿⠿⠿⠟⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⠏⠀⣤⣶⡶⠘⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣛⢷⡆⣿⣿⣿⢸⡿⠃⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠻⠾⠃⠛⠿⠋⠺⢇⣄⠻⢇⡀⠛⠃⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⠻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⡇⠀⣤⣤⠀⣤⢩⣭⣥⣬⣍⠓⢀⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⠺⠿⠿⠇⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⠙⠉⠛⠛⠛⠛⠛⠋⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡁⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠇⢰⠠⠞⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠿⠿⠟⠛⠁⠀⠘⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠘⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣶⡶⠂⠀⠀⢀⣤⣾⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⡛⢛⣛⡛⠛⠙⠃⠙⠛⠋⠛⠃⠛⠸⠃⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⠀⠀⠀⢠⣾⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣥⣤⡍⣥⣠⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣄⠙⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣠⢄⠄⢀⣠⣤⣶⣤⡀⠀⠈⠀⠀⠀⣸⣿⣿⣿⣆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣣⣾⣿⣿⣿⣿⣿⣿⣧⡀⠀⣠⣼⣿⣿⣿⣿⣿⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡏⠰⠿⠻⠧⠿⠹⠿⠸⠷⠿⠻⠿⠿⠇⢿⣼⠟⠿⠇⠿⠿⠿⣶⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠟⢹⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⢻⣿⣿⣿⠃⠀⠀⠀⠀⢀⣶⢖⣀⣀⣀⣐⡒⢂⣀⡐⣒⣚⢷⣶⣶⣶⣶⣷⣶⠾⣿
⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢀⣻⣿⣿⡿⠟⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢸⣿⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⢸⣿⣿⣿⣿⣿⡿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⣠⣿⣿⣿⣏⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⣸⣿⣿⣿⣿⣿⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⡿⠁⠰⠿⠟⠛⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠈⠉⠤⠍⠥⠭⠬⠉⠥⠭⠭⢽⣿⠿⠿⠟⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⣿⠇⢀⣠⣶⡤⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢠⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣛⢷⡆⣿⣿⣿⢸⡿⠃⣿⡇⢸⣿⣿⣷⣿⢸⣏⣿⣸⣿⣿⡅⣿⠿⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠻⠾⠃⠛⠿⠋⠚⢇⡀⠛⠃⠀⠛⠃⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⠻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⡿⠀⣤⣤⠀⣬⢩⣥⣤⣤⣄⠀⢀⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⠺⠿⢿⡷⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠈⠉⠉⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⠈⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⡄⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠃⢀⠠⠆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣸⡇⣿⣿⣿⢻⣷⡿⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠿⠟⠛⠋⠀⠀⠈⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣷⣿⣿⡇⣿⣿⣿⢸⣿⣧⠘⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢶⡾⠗⠉⠀⠀⢠⣤⡮⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⠛⠛⠛⠛⠛⠙⠃⠙⠛⠋⠛⠃⠛⠸⠃⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠀⠀⠀⠀⢠⣿⣿⣧⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣤⣤⡄⣤⣠⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣄⠙⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣠⢀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡄⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢟⣥⣾⣿⣿⣿⣿⣿⣿⣇⠀⠀⣠⣾⣿⣿⣿⣿⣿⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡰⠿⠻⠧⠿⠹⠿⠸⠷⠿⠹⠿⠿⠇⢿⣼⠟⠿⠇⠿⠿⠿⣶⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠋⣸⣿⣿⣿⣿⡇⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠀⣰⣶⢖⣀⣀⣀⣀⡒⢒⣚⡒⣂⣚⢶⣶⣶⣶⣶⣷⣦⠈⠻
⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⣿⣻⡿⠽⠛⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠃⠀⣿⣿⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⢸⣿⣿⣿⣿⣿⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠛⠿⠿⣿⠇⠀⢸⣿⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⣸⣿⣿⣿⣿⣿⡏⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⠏⠀⠼⠟⠛⠉⠁⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠋⠀⠀⠿⢿⡿⠮⠭⠤⠭⠥⠭⠌⠉⠁⠭⠭⢽⣿⠿⠿⡿⠟⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⡟⠀⢀⣴⡶⠄⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢀⣛⢷⡆⣿⣿⣿⢸⡿⠃⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠟⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠻⠾⠃⠛⠿⠋⠘⠃⠀⠛⠃⠀⠛⠃⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⠺⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⣀⣀⡀⠀⣤⣤⠀⣤⢠⣤⣤⣤⣄⠀⢀⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⠛⢿⣿⣿⡿⡿⢿⡿⠿⠋⠀⠸⣿⣿⣇⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠁⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠶⣤⣤⣴⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣠⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠟⠀⡆⠸⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣛⣉⡉⠉⠀⠀⠀⡁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠘⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣿⠟⠁⠀⠀⠀⣴⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⠛⠛⠛⠛⠛⠙⠃⠙⠛⠋⠛⠃⠛⠸⠃⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣤⣤⡄⣤⣠⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣄⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⣾⠖⣠⣤⣶⣾⣿⣷⣤⡀⠀⠀⠀⣰⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠸⣵⣾⣿⣿⣿⣿⣿⣿⣿⣇⣀⣠⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⠿⠻⠧⠿⠹⠿⠸⠷⠿⠻⠿⠿⡇⢿⣼⠟⠿⠇⠿⠿⠿⣶⠀⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢠⣿⣿⣿⣿⣿⠀⢀⡄⠀⠀⣴⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠆⣰⣶⢖⣀⣀⣒⣒⡒⢒⣚⡒⣂⣚⢶⣶⣶⣶⣶⣧⣤⠻⣿
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠃⢀⣼⣿⣯⠝⠛⠁⠠⠟⠀⠀⣸⣿⣿⣿⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢠⣿⣿⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⢸⣿⣿⣿⣿⣿⣿⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣰⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠻⣿⣿⣿⠏⠀⢸⣿⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⣸⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⠏⠀⠘⠛⢉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠛⠀⠀⠻⢿⡿⠮⠭⠤⠭⠡⠭⠌⠉⠁⠉⠩⢽⣿⠿⠿⡿⠟⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠟⠀⠀⣾⢟⣛⣁⠀⠀⢰⣷⣦⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢀⣛⢷⡆⣿⣿⣿⢸⡿⠃⣿⡇⢸⣿⣿⣷⣿⢸⣏⣿⣸⣿⣿⡅⣿⠿⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠻⠾⠃⠛⠿⠋⠚⢇⣄⡻⢇⣀⠛⠃⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⠻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠿⣿⡮⢻⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣤⣤⠀⣤⢨⣭⣥⣬⣍⠙⢉⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠙⠄⢻⣿⣿⣿⣿⣿⣿⣿⣷⡌⠻⣿⣿⢿⡿⠄⠀⠀⠀⠀⠀⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠁⠀⠀⠀⠀⠀⠘⠃⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣶⣦⣤⣤⣴⡾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠿⠟⠁⠀⠂⠊⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣸⡇⣿⣿⣿⢻⣷⡿⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣥⣤⠤⠄⠀⠀⢀⣀⠂⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠘⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⠟⠛⠁⠀⠀⠀⣠⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣤⣾⣿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⠛⠛⠛⠛⠛⠙⠃⠙⠛⠋⠛⠃⠛⠸⠃⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣠⠆⠄⢀⣀⣄⣀⣤⣀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣤⣽⡷⢂⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣤⣤⡀⣤⣠⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣄⠙⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢟⣴⣾⣿⣿⣿⣿⣿⣿⡛⠀⠀⠀⣠⣾⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢸⠟⠛⢻⣿⣿⣴⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣾⠟⢿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣼⠀⠀⣼⣿⣿⣿⣿⣿⡿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡰⠿⠻⠧⠿⠹⠿⠸⠷⠿⠹⠿⠿⠇⢿⣼⠟⠿⠇⠿⠿⠿⣶⠀⢻⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠁⠀⢸⣿⣿⣿⣿⣿⢋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠆⢠⣶⢆⣀⣀⣀⣐⡒⢒⣚⡒⣂⣚⢶⣶⣶⣶⣶⣧⡄⠑⠟
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣠⣶⣿⣷⡆⠋⠁⠀⠀⠀⠀⢀⡆⠀⠀⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⠟⠁⠹⣿⣿⣿⣿⣿⣿⡟⠀⣾⣿⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⢸⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⠋⠀⣼⣿⣿⠿⠟⠀⠀⠀⠀⠀⠀⣠⣿⣿⡆⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠈⠛⢿⣿⣿⡟⠀⢀⣿⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⣸⣿⣿⣿⣿⣿⠇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢻⣿⣿⠃⠀⣀⣠⣤⣤⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠉⠉⠛⠁⠀⠘⠿⠿⠮⠉⠤⠭⠁⠭⠌⠉⠡⠭⠭⢽⣿⠿⠿⠿⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣯⣿⣿⣧⣤⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⢠⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣆⠀⠀⠀⢀⣛⢷⡆⣿⣿⣿⢸⡿⠃⣿⡇⢸⣿⣿⣷⣿⢸⣏⣿⣸⣿⣿⡅⣿⠟⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠹⣿⣿⣿⣿⣶⣦⠀⠻⠾⠃⠛⠿⠋⠘⠃⠀⠛⠃⠀⠛⠃⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⠺⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡘⢿⣿⣿⣿⠿⢻⣿⣿⠏⣤⣤⠀⣤⢠⣤⣤⣤⣄⠀⢀⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠺⠝⠿⠟⠟⠘⣿⣿⣿⣿⣿⣿⣿⣷⠀⠙⠟⠁⠰⣿⣿⣿⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠉⠋⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⣤⣤⣶⡾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠉⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡶⠀⡀⢀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠛⠛⠛⠁⠀⠀⠅⠋⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⣸⡇⣿⣿⣿⢻⣷⡿⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣿⣿⠟⠋⠁⠀⠀⣤⣴⡇⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣷⣿⣿⡇⣿⣿⣿⢸⣿⣧⠘⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⠄⡀⠀⠀⠀⠈⠙⠋⠉⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣘⠛⠛⠛⠛⠛⠙⠃⠙⠛⠋⠛⠃⠛⠸⠃⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡾⣩⣴⣾⣿⣷⣶⣾⣶⣤⠀⠀⠀⠀⣰⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⠏⠘⠉⠉⠛⢿⠟⣥⣤⡍⣤⣠⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣄⠙⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⣀⣴⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣾⠆⠀⠀⠀⠀⠀⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠋⠈⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢰⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⡿⠁⣿⣿⣷⡄⠀⠀⠀⠰⠿⠻⠧⠿⠹⠿⠸⠷⠿⠹⠿⠿⠇⢿⣼⠟⠿⠇⠿⠿⠿⣶⠀⢿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠰⣿⠿⢿⣿⡿⠁⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠈⠉⠙⢁⣀⠀⠀⠀⠀⠀⠀⠀⣴⢂⣀⣀⣀⣀⡀⢀⣀⡒⣒⣚⢷⣶⣶⣶⣶⣥⠀⠁⢿
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣠⣾⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣇⠀⢀⣀⣤⣤⣾⣿⣷⣄⠀⠀⠀⠀⠘⡿⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⢸⣿⣿⣿⣿⡏⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⠃⠀⠚⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⣸⣿⣿⣏⠛⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠏⠀⢰⣶⣶⡷⠆⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⡿⠛⠛⠀⠀⠀⠀⠀⠈⠉⠀⠉⠁⠉⠈⠉⠁⠉⠉⠙⠿⠿⠟⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣷⠆⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢻⣿⣿⣿⡟⢠⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⢀⣛⢷⡆⣿⣿⣿⢸⡿⠃⣿⡇⢸⣿⣿⣷⣿⢸⣏⣿⣸⣿⣿⡅⣿⠟⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢻⣿⣿⡀⠻⠾⢃⠛⠿⠋⠘⢃⣀⠛⢇⡀⠛⠃⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⠺⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠹⠿⣻⣿⣿⡟⣥⣤⠀⣤⢩⣭⣥⣤⣍⠀⢀⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠐⠈⠉⠻⠉⠉⠉⠿⠟⠟⣿⣿⣿⣿⣿⣿⣿⣧⠀⠐⠿⣿⣿⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠟⠀⡄⢀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⣛⣉⠙⠉⠁⠀⠀⠇⠈⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠟⠁⠈⠻⣿⣿⢸⣿⠀⣿⣿⣿⣸⡇⣿⣿⣿⢻⣷⡿⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠟⠉⠀⠀⠀⣴⣶⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠋⢹⡿⢀⣿⣿⣿⡟⢿⣿⡆⠀⠀⠀⠘⡇⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠈⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⡆⠄⢀⣀⣄⠀⠀⠉⠀⠀⠀⠀⠀⠀⣼⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣿⣿⣿⣿⡿⢸⠋⣠⠀⠀⠀⠀⢰⡘⠛⠛⠛⠛⠛⠙⠃⠙⠛⠋⠛⠃⠛⠸⠃⠽⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢟⣴⣾⣿⣿⣿⣿⣿⣿⡶⠄⠀⠀⠀⣰⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣡⣿⣾⣿⡆⠀⣤⣤⡀⣤⣠⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣄⠙⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣇⠀⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⠿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⠏⠀⠻⣿⣿⣿⣿⣿⠰⠿⠻⠧⠿⠹⠿⠸⠷⠿⠹⠿⠿⠇⢿⣼⠟⠿⠇⠿⠿⠿⣶⠀⠹⢿
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⡰⠿⢿⣛⣿⠿⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢠⣤⣤⣽⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⢀⣀⣀⣀⣀⡀⢀⣀⡒⣒⣚⢶⣶⣶⣶⣶⡅⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡿⠋⢀⣴⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⢸⣿⣿⢿⡿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⡿⠁⠀⠉⠛⠋⠛⠉⠁⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢀⡀⠀⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⠸⣿⣿⠊⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠃⠀⢾⣿⣿⣟⡃⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢻⣿⣿⣿⣿⡿⠟⠻⠇⠀⠸⠿⠧⠈⠉⠀⠉⠁⠉⠈⠉⠁⠉⠉⠀⠙⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⠃⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⢠⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⢀⣛⢷⡆⣿⣿⣿⢸⡿⠃⣿⡇⢸⣿⣿⣷⣿⢸⣏⣿⣸⣿⣿⡅⣿⠟⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢻⣿⡀⠻⠾⠃⠛⠿⠋⠘⢃⣀⠛⢃⡀⠛⠃⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⠺⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠙⣫⣿⣿⡟⣥⣤⠀⣤⢩⣭⣥⣬⣍⠙⢃⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠉⠉⠑⠙⠉⠋⠙⠙⠹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠿⠿⡿⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⠿⠛⢿⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡿⠛⢛⣋⣠⣾⣿⣿⣿⠁⠀⠀⠀⣿⡟⠁⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣏⢀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⠟⣳⣿⣿⣿⣿⣿⣿⣆⣴⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠟⢀⡀⣀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣭⣭⣉⡉⠁⠀⠀⢸⠁⠁⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠿⢟⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⠀⣿⣿⣿⣸⡇⣿⣿⣿⢻⣷⡿⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⡿⠿⠟⠋⠀⠀⠀⢠⣶⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣶⣶⣦⣤⣿⣿⣿⣿⣅⣿⣿⣿⣿⣿⣿⡀⠀⠀⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠀⠛⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡾⢀⣀⣴⣶⣦⣀⠀⣀⠀⠀⠀⠀⠀⢰⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠘⠛⠛⠛⠛⠛⠙⠃⠙⠛⠋⠛⠃⠛⠸⠃⠼⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢐⣴⣿⣿⣿⣿⣿⣿⣷⣯⠙⠀⠀⠀⢠⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⣿⣿⣿⣿⣿⡟⣥⣤⡀⣤⣠⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣄⣤⡄⣤⣤⣄⠘⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠐⢿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣼⣿⣿⣿⣿⠃⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⢻⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿⢷⣿⣿⣿⣿⣿⣿⣿⠰⠿⠻⠧⠿⠹⠿⠸⠷⠿⠹⠿⠿⠇⢿⣼⠟⠿⠇⠿⠿⠿⣶⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⣀⣀⣿⣟⡛⡿⠿⠃⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⣷⣶⠆⠀⢠⡄⢀⣀⣀⣀⣀⡀⢀⣀⡀⣀⣐⢲⣦⣠⡤⠀⠁⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡿⠉⣠⣾⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢠⣿⣷⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⠀⡿⠏⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⠻⣿⣿⡿⠁⢀⣀⣈⣉⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⠀⡤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⣺⣿⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⡿⠿⠿⢿⠼⠿⠿⡿⠮⠭⠤⠍⠁⠉⠈⠉⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⣠⣾⣿⣿⣿⡿⠃⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⢠⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⢀⣛⢷⡆⣿⣿⣿⢸⡿⠃⣿⡇⢸⣿⣿⣷⣿⢸⣏⣿⣸⣿⣿⡅⣿⠟⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠘⣷⡀⠻⠾⠃⠛⠿⠋⠘⢃⣀⠛⠇⡀⠛⠃⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⠺⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠈⣱⣿⣿⠇⣤⣤⠀⣤⢩⣭⣥⣤⣍⠛⢃⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠀⠉⠀⠈⠙⠙⠉⠙⠉⣿⣿⣿⣿⣿⣿⣿⣷⠀⠉⠉⠙⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣵⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢻⣿⣿⣿⡿⠿⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢈⣋⣭⣶⣤⣾⣿⣿⣿⣇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣏⢀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠻⠿⢿⣿⣿⡀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⠟⢠⠀⡀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠛⠿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣨⣭⣭⣉⡉⠁⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡟⠙⢻⣿⣿⣿⣇⠀⠀⠀⠀⠈⣿⣿⣿⣿⣷⡄⠀⠀⢸⣿⠀⣿⣿⣿⣸⡇⣿⣿⣿⢻⣷⡿⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢿⡿⠿⠟⠋⠀⠀⠀⣰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣶⣶⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⠀⠀⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠀⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⡞⣀⣤⣴⣾⣦⣀⡠⣀⠀⠀⠀⠀⠀⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⣿⣿⣿⣿⣿⣿⣧⠀⠘⠛⠛⠛⠛⠛⠙⠃⠙⠛⢋⠛⠃⠛⠸⠃⠸⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢨⣾⣿⣿⣿⣿⣿⣿⣿⣮⠉⠀⠀⠀⣠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡟⣥⣤⡄⣤⣠⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣌⣤⡄⣤⣤⣄⠘⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠸⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣆⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠰⠿⠻⠧⠿⠹⠿⠸⠷⠿⠹⠿⠿⠇⢿⣼⠟⠿⠇⠿⠿⠿⣶⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⣀⣼⣿⣛⢻⠿⠟⠀⠀⠀⠀⠀⠀⣸⣿⣧⢹⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠀⠀⣴⣶⢆⣀⣀⣀⣀⡀⢀⣀⡀⣀⣀⠐⢦⣤⠀⠀⠁⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⠏⢀⣴⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣾⣿⣿⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⠀⣈⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠻⣿⣿⠏⠀⣀⣀⣉⣉⠉⠁⠀⠀⠀⡀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⡀⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢸⣿⣿⣿⣟⡀⠀⠀⢀⠄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢻⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⢿⡿⠮⠭⠤⠭⠥⠉⠈⠉⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⣀⣼⣿⣿⣿⣿⠛⠀⠀⠁⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢿⣿⣿⣿⣿⢠⣾⢷⡆⣶⣿⣦⢰⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⢀⣛⢷⡆⣿⣿⣿⢸⡿⠃⣿⡇⢸⣿⣿⣷⣿⢸⣏⣿⣸⣿⣿⡅⣿⠟⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢻⣿⣷⡀⠻⠾⠃⠛⠿⠋⠘⠃⣀⠛⠃⣀⠛⠃⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⠺⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠙⠛⠒⠛⢻⠋⣥⣤⠈⣥⢨⣭⣤⣤⣍⠛⢀⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠉⠩⠉⠉⠙⠋⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠈⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢻⠿⠛⠛⠿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡷⠀⠀⠀⠀⠀⠸⠿⣛⣛⠛⠿⢿⣿⣿⣻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡦⠀⠀⠀⠀⣶⣿⣿⣿⣶⣤⣼⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠒⠛⠛⠛⠛⠉⠀⢸⠀⠂⠀⠈⠉⣿⡟⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢰⣿⣿⣷⣦⠀⠀⢸⣿⠀⣿⣿⣿⣸⡇⣿⣿⣿⢻⣷⡿⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠋⠀⠀⢠⣤⡾⠀⠀⠀⠀⠀⠛⠁⠀⢸⣿⣿⣿⠇⢿⣿⣿⣿⣿⣿⣦⡀⠀⣾⣿⣿⣿⣿⣧⠀⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠀⠛⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⣀⣤⣴⣆⣀⢈⠉⠉⠁⠀⠀⠀⣴⣿⣿⠃⠀⠀⠀⠀⠀⠀⢀⣄⣿⣿⣿⣿⡆⣼⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡆⠘⠛⠛⠛⠛⠛⠙⠃⠙⠛⠋⠛⣃⡛⠸⠃⠸⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣴⣿⣿⣿⣿⣿⣿⣷⡍⠂⠀⠀⠀⣠⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣥⣤⡄⣤⣠⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣌⣤⡄⣤⣤⣄⠈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⢰⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠰⠿⠻⠧⠿⠹⠿⠸⠷⠿⠹⠿⠿⠇⢿⣼⠟⠿⠇⠿⠿⠿⣶⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣀⢾⡿⠿⣿⣿⠇⠀⠀⠀⠀⣦⡀⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠆⠀⣴⣶⢆⣀⣀⣀⣀⡀⢀⣀⡀⣀⣀⠀⡤⡤⠀⠀⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⣿⣿⣿⣿⡿⠋⣀⣴⣿⣿⣿⡿⠁⠉⠀⠀⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⣿⣿⣆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⣿⣿⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⠀⣼⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠝⢿⣿⡿⠁⢀⣈⠉⠍⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣿⣿⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⡀⠏⠀⠀⠀⠀⠀⠀⠀
⢄⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⡿⠿⢿⡿⠮⠉⠤⠍⠁⠉⠈⠉⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⢠⣼⣿⣿⣿⠟⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⢿⣿⣿⣿⣿⣿⣿⢠⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⢻⣿⣿⣿⣿⣿⢀⣛⢷⡆⣿⣿⣿⢸⡿⠃⣿⡇⢸⣿⣿⣷⣿⢸⣏⣿⣸⣿⣿⡅⣿⠟⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠻⣿⣿⣿⣿⡈⠻⠾⠃⠛⠿⠋⠘⠃⣀⠛⢇⡀⠛⠃⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⠺⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠙⢿⠟⠛⠋⠀⢰⠟⣤⣤⠀⣤⢠⣭⣤⣬⣍⠑⢀⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠉⠀⠙⠋⠙⠉⠻⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠈⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣤⠀⠀⠀⠀⠀⠀⢠⣄⣀⣬⣽⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⢶⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠙⠛⠗⠙⢻⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⢀⠀⠀⠀⣠⣤⣶⣷⣤⣄⣩⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⡿⠃⢠⠀⠀⠉⢻⣿⠻⢿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣤⠤⠀⠀⠀⠀⡌⠀⠀⠀⠸⠟⠀⢰⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣄⠀⢸⣿⣷⣶⣦⡀⠀⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠀⠛⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⢀⣀⡀⠙⠻⠿⠿⠏⠀⠀⠀⣠⣾⣿⠃⠀⠀⠀⠀⠀⠀⣾⣿⣿⣇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⡀⠘⠛⠛⠛⠛⠛⠙⠃⠙⠛⢋⢛⣃⡛⠸⠃⠸⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣫⣴⣾⣿⣿⣿⣷⣔⠢⠀⠀⠀⠀⢰⣿⣿⡏⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡟⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣥⣤⡄⣤⣠⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣌⣥⡄⣤⣤⣄⠈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣴⣿⣿⣿⣧⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣹⣿⣿⣿⣿⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠰⠿⠻⠧⠿⠹⠿⠸⠷⠿⠻⠿⠿⠇⢿⣼⠟⠿⠇⠿⠿⠿⣶⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢠⣿⣿⣿⣿⣿⠀⠀⢠⡀⢰⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠆⠀⣠⣶⢆⣀⣀⣀⣀⡀⢀⣀⡀⣀⣀⠀⠦⣤⠀⠀⠁⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⡿⠛⣁⣴⣶⣾⣿⡗⠚⠛⠋⠀⠀⣼⣷⣾⣿⣿⣿⣿⣿⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣰⣿⣿⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⠀⣴⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⠻⣿⣿⠟⠀⠘⠛⡛⠿⠿⠛⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⡀⠟⠀⠀⠀⠀⠀⠀⠀
⢦⡄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⢰⣿⣶⣶⠆⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⢿⡿⠮⠍⠤⠍⠁⠩⠌⠉⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⣘⣿⣿⣿⡷⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢻⣿⣿⣿⣿⣿⣿⣿⢀⣛⢷⡆⣿⣿⣿⢸⡿⠃⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠹⣿⣿⣿⣿⣿⣿⡈⠻⠾⠃⠛⠿⠋⠚⠇⣀⠻⢇⣀⠛⠃⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⠺⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠈⢿⣿⣿⡟⠋⠉⠀⢰⠟⣥⣤⠀⣤⢨⣭⣥⣬⣍⠛⢀⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠛⠋⠛⠋⠛⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠉⠁⠀⠀⠀⠀⠈⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⣀⠀⢈⣻⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⠀⢠⣭⣿⣿⣿⣿⣿⣿⣾⣿⣿⣄⠀⠀⠀⠀⠀⠙⢿⣿⡟⠻⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡇⠀⠀⠀⠀⣈⣩⣵⣄⡉⠛⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣿⣿⣿⣿⣷⠅⡀⠀⠘⠿⣿⠿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⣬⣬⣉⡉⠉⠉⠀⢀⠃⠀⠀⠸⡿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢰⣶⣦⣤⣀⠀⠀⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠀⠛⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⢀⠀⠻⠿⢿⠿⠋⠁⠀⠀⣠⣶⡿⠀⠀⠀⠀⠀⢀⣾⣿⣿⡏⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣧⠀⠘⠛⠛⠛⠛⠛⠙⠃⠙⠛⢋⡛⣃⡛⠸⠃⠸⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣣⣴⣶⣿⣿⣷⣄⠦⡀⠀⠀⠀⠀⣼⣿⣿⠁⠀⠀⠀⠀⠀⣸⣿⣿⣿⠇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣥⣤⡄⣤⣠⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣌⣤⡄⣤⣤⣄⠈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢀⣴⣿⣿⣿⠀⠀⠀⠀⠀⣰⣿⣿⣿⡟⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢸⣿⣿⣿⣿⡆⠀⠀⠀⣰⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠰⠿⠻⠧⠿⠹⠿⠸⠷⠿⠻⠿⠿⠇⢿⣼⠟⠿⠇⠿⠿⠿⣶⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⣸⣿⣿⣿⣿⡇⠀⡀⢰⣿⣿⣿⣿⣿⠇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠆⠀⢠⣶⢆⣀⣀⣀⣀⡀⢀⣀⡀⣀⣀⠀⢶⣤⠄⠀⠁⠀⠘⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠋⣠⣴⣮⣿⣭⠽⠿⠛⠁⢀⣧⣾⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣰⣿⣿⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⠀⣠⠇⠀⠀⠀⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⠛⣿⣿⡿⠃⠐⠺⠿⠿⠿⠿⠃⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣆⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⡀⡟⠀⠀⠀⠀⠀⠀⠀
⢷⣆⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⢠⣶⣶⣦⡤⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⡿⠾⠿⢿⡿⠮⠭⠠⠭⠁⠩⠈⠉⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⡀⠀⢀⣿⣿⣿⣷⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⢀⣛⢷⡆⣿⣿⣿⢸⡿⠃⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠹⣿⣿⣿⣿⣿⣿⣿⣌⠻⠾⠃⠛⠿⠋⠺⠇⣀⠻⢇⣀⠟⠃⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⠻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠘⢿⣿⣿⣿⡿⠛⠛⠁⢀⠟⣥⣤⠀⣤⢨⣭⣥⣬⣍⠛⢀⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠛⠟⠟⢻⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠙⠋⠉⠀⠀⠀⠀⠈⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣧⡀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣶⡀⠀⠀⠀⠀⠀⢦⣤⣦⣿⣿⣿⡿⣿⣿⡄⠀⠀⠀⠀⠀⠙⠿⠿⠟⠻⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡇⠀⠀⠀⠀⠹⠿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣧⠂⠀⠀⣴⣾⣿⣷⣦⣬⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠚⠻⠿⠿⠋⢰⠀⠀⠈⣿⠉⢻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⣸⣿⣶⣤⣄⠀⠀⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠀⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⠟⠃⠀⠀⣀⣤⡾⠀⠀⠀⠁⣠⣿⣿⣿⢸⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣷⠀⠘⠛⠛⠛⠛⠛⠙⠃⠙⠛⠋⠛⢃⠛⠸⠃⠸⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢀⣠⣤⣶⣦⡀⢀⠈⠁⠀⠀⠀⣴⣿⡿⠁⠀⠀⠀⢰⣿⣿⣿⡇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣥⣤⡄⣤⣠⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣌⣤⡄⣤⣤⣄⠈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⣿⡄⠁⠀⠀⢀⣼⣿⣿⡇⠀⠀⠀⢠⣿⣿⣿⡿⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⣿⣿⣿⣿⣷⠀⠀⣰⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠰⠿⠻⠧⠿⠹⠿⠸⠷⠿⠻⠿⠿⠇⢿⣼⠟⠿⠇⠿⠿⠿⣶⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣾⣿⣿⣿⣿⠀⢰⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡶⠀⠀⣴⢆⣀⣀⣀⣀⡀⢀⣀⡀⣀⣀⠀⣶⣦⠄⠀⠁⠠⢟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠋⣀⣤⣺⣟⣛⣻⣿⠟⢀⣾⣿⣿⣿⣿⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣼⣿⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⠀⣙⠏⠀⠀⠀⠀⠀⠈
⣀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢻⡝⢿⣿⣿⠟⠁⠴⢿⣿⣿⣿⡟⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⣿⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⡀⡟⠀⠀⠀⠀⠀⠀⠀
⠿⣶⡄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠋⠀⣤⣤⣄⢀⠀⠀⠀⠀⠀⠀⢰⣧⣿⣿⣿⣿⣿⣷⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⠾⠿⠿⡿⠮⠭⠤⠉⠁⠭⠬⠉⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠃⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢺⣿⣿⣧⡀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣛⢷⡆⣿⣿⣿⢸⡿⠃⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣈⠻⠾⠃⠛⠿⠋⠺⠇⣀⠻⢇⣀⠟⠃⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⡻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠻⣿⣿⣿⣿⣿⡿⠛⠛⠋⠀⠘⣥⣤⠀⣬⢩⣭⣤⣬⣍⠛⢁⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⠛⠻⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠘⠿⠿⠛⠉⠀⠀⠀⠀⠈⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣦⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡄⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⠀⠀⠀⠀⠹⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡄⠀⠀⠀⠀⢡⡀⠀⠀⠀⠉⠉⠙⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣄⠀⠀⠀⠀⠀⢠⡀⣘⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡿⣽⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣯⡠⠀⠀⢀⣠⣤⣶⡈⠻⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢠⣿⣷⣦⣄⠀⠀⢸⣿⠀⣿⣿⣿⣼⡇⣿⣿⣿⢻⣷⡿⠈⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⠿⠃⡄⠀⠙⠛⡿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⣿⣿⣿⣿⣿⣆⠀⢸⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣧⠀⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⠗⠀⠀⠀⣀⣰⠇⠀⠀⠀⢁⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣿⣿⣿⣿⣿⣿⣇⠘⠛⠛⠛⠛⠛⠙⠃⠙⠛⠋⠛⢃⠛⠸⠃⠸⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡖⢀⣠⣤⣤⡀⢉⠉⠉⠀⠀⠀⢠⣾⣿⠏⠀⠀⠀⣰⣿⣿⣿⠏⠟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣥⣤⡅⣤⣠⣤⢠⣤⣤⢠⣤⣤⡄⣤⣶⣌⣤⡄⣤⣤⣄⠙⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣫⣾⣿⣿⣿⣿⣿⣄⠁⠀⠀⠀⣠⣿⣿⣿⠀⠀⠀⣰⣿⣿⣿⡟⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⢻⡇⣿⣿⣿⢸⡇⣿⣿⣿⣿⡃⣿⢸⣿⣿⡇⣿⣿⣿⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⢺⣿⣿⣿⣿⠀⢀⣾⣿⣿⣿⡏⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠰⠿⠻⠧⠿⠹⠿⠸⠷⠿⠻⠿⠿⠇⢿⣼⠟⠿⠇⠿⠿⠿⣶⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣼⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⠃⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠀⠀⣴⢖⣀⣀⣀⣀⡀⢀⣀⡀⣀⣀⠀⢠⡄⠀⠀⠁⠀⡺⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠟⢁⣀⣰⣿⣿⣿⣿⡿⣠⣾⣿⣿⣿⡇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣸⣿⢸⣿⣉⣿⣏⣿⢸⣿⡁⣿⣏⠀⣨⠁⠀⠀⠀⠀⠈⠈
⣄⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠛⣿⣿⠟⠁⠰⣾⣿⣿⣿⡿⠁⠁⠀⢸⣿⣿⣿⣿⣿⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣸⣿⣿⢸⣿⠉⣿⡏⣿⢸⣿⡁⣿⣏⡀⠏⠀⠀⠀⠀⠀⠀⠀
⠻⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⣤⣤⣐⠀⠉⠉⠀⠀⠀⠀⡀⢿⣿⣿⣿⣿⣇⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⠧⠿⠿⡿⠮⠭⠤⠍⠡⠭⠬⠉⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣅⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣦⡀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣾⢷⡆⣶⣿⣦⢲⡶⠶⣶⡶⢶⡆⣶⡆⣶⢆⣶⣶⢰⣶⣶⡆⣶⠶⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣛⢷⡆⣿⣿⣿⢸⡿⠃⣿⡇⢸⣿⣿⣷⣿⢸⣟⣿⣸⣿⣿⡅⣿⠿⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⠻⠾⠃⠛⠿⠋⠺⢇⣀⠻⢇⣀⠟⠃⠛⠛⠘⠋⠛⠛⠛⠛⠃⠛⠛⡻⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠹⣿⣿⣿⣿⣿⣿⡿⠛⠛⠃⠀⠘⣥⣤⠀⣬⢩⣥⣤⣬⣍⠻⢃⣤⣤⡀⣤⣠⣤⣤⡄⣤⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠈⠻⡿⠿⠋⠉⠁⠀⠀⠀⠀⢀⣿⣿⡆⣿⣿⣿⣿⣿⣿⠀⢸⣿⣛⡃⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⣇⣿⢻⣿⣿⣿⣿⠀⠸⣿⣿⡇⣿⢻⣿⢿⣧⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 2089

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.25.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_25/11/2021:_PHP_8.1.0_Released_and_Linux_5.15.5⠀✐


Posted in News_Roundup at 9:34 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o § Desktop/Laptop⠀➾


                # ⚓ Where_Can_You_Buy_a_Preinstalled_Linux_Laptop?⠀⇛


                       Linux has become a perfectly capable and easy-to-
                       use operating system, but where can you actually
                       buy a Linux laptop? You won’t find them in big box
                       stores, aside from Chromebooks. Fortunately, that’s
                       less of an issue as more of us do our shopping
                       online. Now it’s only a matter of knowing where to
                       look and what to look for.


                       Here is a list of large corporations, smaller
                       companies, and resellers that are happy to sell you
                       a laptop with Linux preinstalled.


          o § Server⠀➾


                # ⚓ Amazon_Linux_3_To_Be_Based_On_Fedora_Community_Linux⠀⇛


                       Amazon Web Services (AWS) released an early version
                       of its upcoming distro, Amazon Linux 3, which is
                       based on Red Hat’s Community Linux, Fedora.


                       With Fedora as upstream, the new Amazon distro,
                       AL2022 is extremely stable after extensive package
                       stability tests and contains all available security
                       updates. In addition, it is optimized for Amazon
                       EC2 and integrates seamlessly with the latest AWS
                       features and many AWS-specific tools.


                       The brand new Amazon Linux also includes frequent
                       and flexible quarterly updates, as each AL2022
                       update matches a specific version of the Amazon
                       Linux package archive. Updates are only required if
                       the user wants to make a move and not if a new
                       version is released.


                # ⚓ Amazon_Linux_2022_Was_Recently_Opened_to_Public_Preview⠀⇛


                       The cloud provider will let you run many Linux
                       distributions or their own homebrew Linux, Amazon
                       Linux 2022.


                       Amazon Linux 2022 (AL2022) is an Amazon’s new
                       general purpose Linux for AWS that is designed to
                       provide a secure, stable, and high-performance
                       execution environment to develop and run your cloud
                       applications. The distro has had two major releases
                       till now – the first (Amazon Linux) in 2010, and
                       the second (Amazon Linux 2) in 2017.


                       Amazon Linux is popular among AWS users for its
                       tight integration with AWS tools, and no license
                       costs. That combination is a clear pitch for the
                       AWS users to also use the upcoming AL2022 if they
                       want full AWS experience.


          o § Audiocasts/Shows⠀➾


                # ⚓ How_to_install_LeoCAD_on_Elementary_OS_6.0_–_Invidious⠀⇛


                       In this video, we are looking at how to install
                       LeoCAD on Elementary OS 6.0.


                # ⚓ Red_Hat_Enterprise_Linux_8.5_Quick_overview⠀⇛


                       A Quick overview of Red Hat Enterprise Linux 8.5


                # ⚓ How_Did_Linus_Torvalds_Commit_To_AmogOS?_–_Invidious⠀⇛


                       Git doesn’t have any form of user validation system
                       therefore you can do hilarious things like this and
                       there’s nothing built into it to stop you but
                       luckily there is a way to validate work.


                # ⚓ Distro:_Checking_Out_Ubuntu_Unity_For_The_Memes_–
                  Invidious⠀⇛


                       I recently heard about Ubuntu Unity and I was
                       curious how usable Unity 7 would be like in 2021,
                       if it’s exciting I might make a followup video
                       about my thoughts.


          o § Applications⠀➾


                # ⚓ A_shortcuts_editor_for_Xfce_and_a_couple_of_other_things⠀⇛


                         As you may know, I’m the maintainer of xfce4-
                       terminal and a developer for Thunar. It just so
                       happens that both of these programs have a ton of
                       shortcuts. Until now, there was no GUI for changing
                       shortcuts. Users had to manually edit the
                       `accels.scm` file which is doable yet cumbersome.


                         Additionally xfce4-terminal, being a terminal
                       emulator, has the problem of its shorcuts colliding
                       with the shorcuts of terminal applications,
                       rendering them unusable. To fix that issue users
                       needed to once again dive into the `accels.scm`
                       file and change the default shortcuts manually.


                         That is why I created a new widget called
                       XfceShortcutsEditor in libxfce4ui. Applications
                       that use XfceGtkActionEntries for their
                       accelerators can easily integrate that editor in
                       their UI and enjoy the benefits without any
                       additional complexity.


                # ⚓ BlueGriffon_compiled_but_is_broken⠀⇛


                       Oh wow, finally got the WYSIWYG HTML editor
                       BlueGriffon to compile, and run, here it is…


                # ⚓ Richard_Hughes:_New_LVFS_redirect_behavior⠀⇛


                       tl;dr: if you’re using libfwupd to download
                       firmware, nothing changes and everything continues
                       as before. If you’re using something like wget that
                       doesn’t follow redirects by default you might need
                       to add a command line argument to download firmware
                       from the LVFS.


                       Just a quick note to explain something that some
                       people might have noticed; if you’re using fwupd >=
                       1.6.1 or >= 1.5.10 when you connect to the LVFS to
                       download a firmware file you actually get
                       redirected to the same file on the CDN. e.g.
                       downloading https://fwupd/download/foo.cab gets a
                       redirect to https://cdn.fwupd/download/foo.cab
                       which is then streamed to the user. Why this
                       insanity?


          o § Instructionals/Technical⠀➾


                # ⚓ How_to_install_Aseprite_on_Linux⠀⇛


                       Aseprite is a pixel-art program that users can use
                       to create 2D animations for video games. It is paid
                       software, and users can purchase the product via
                       the official website. However, the source code is
                       also available for free. Here’s how to install
                       Aseprite on Linux.


                # ⚓ How_to_convert_images_on_Linux_with_XnConvert⠀⇛


                       Aseprite is a pixel-art program that users can use
                       to create 2D animations for video games. It is paid
                       software, and users can purchase the product via


                # ⚓ How_to_install_TWS_on_a_Chromebook⠀⇛


                       Today we are looking at how to install Interactive
                       Brokers TWS 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.


                # ⚓ How_to_Install_Python_3_or_Python_2_on_Ubuntu_20.04_–_Linux
                  Nightly⠀⇛


                       Ubuntu is a great distro for developers. Python
                       programmers will need to install Python on the
                       system before it’s possible to code programs and
                       run Python scripts on Ubuntu.


                       This tutorial will show you how to install Python 2
                       or Python 3 on Ubuntu 20.04.


                # ⚓ How_To_Install_VNC_Server_on_Debian_11_–_idroot⠀⇛


                       In this tutorial, we will show you how to install
                       VNC Server on Debian 11. For those of you who
                       didn’t know, VNC stands for Virtual Network
                       Computer. This is a graphical desktop sharing
                       system that uses the Remote Frame Buffer protocol
                       (RFB). Those who are not comfortable with the
                       command line, use VNC to let them use a keyboard
                       and mouse to interact with a graphical desktop
                       environment on a remote server.


                       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 VNC Server on a Debian 11
                       (Bullseye).


                # ⚓ Install_OBS_Studio_27.1.3_on_Fedora_35/34_[NVIDIA_NVENC
                  Xorg_(X11)_/_XWayland]_[stable_/_edge]_–_If_Not_True_Then
                  False⠀⇛


                       This is guide howto install OBS Studio 27.1.3
                       [stable / edge] on Fedora 35/34 [Xorg or Wayland
                       support]. OBS Studio is free and open source
                       software for video recording and live streaming. I
                       use here Snapcrafters (Snap) version of OBS Studio,
                       which is community-supported modified build of OBS
                       Studio. Screen capture in a Wayland session is at
                       least available edge channel, in video I test here
                       options to use NVIDIA NVENC with Xorg (X11) /
                       XWayland.


                # ⚓ How_to_install_and_configure_Wildfly_on_CentOS_8_–_Unixcop
                  the_Unix_/_Linux_the_admins_deams⠀⇛


                       WildFly (formerly known as JBoss) is an application
                       server written in Java and developed by Red Hat. It
                       is an open source application server for JEE
                       applications, it is fast and lightweight and
                       particularly efficient for web and business
                       applications.


                       The technology behind WildFly is also available in
                       JBoss Enterprise Application Platform 7.


                       JBoss EAP is a hardened enterprise subscription
                       with Red Hat’s world-class support, long multi-year
                       maintenance cycles, and exclusive content.


                # ⚓ How_to_run_Prometheus_with_Podman_–_NextGenTips⠀⇛


                       Prometheus is an open-source system monitoring and
                       alerting toolkit. Prometheus collects and stores
                       its metrics as time-series data. Metrics
                       information is stored with the timestamp at which
                       it was recorded, alongside optional key-value pairs
                       called labels.


                       In this tutorial we are going to learn how to run
                       Prometheus with Podman.


                # ⚓ How_to_Install_PuTTY_on_Ubuntu_22.04_|_20.04_LTS_–_Linux
                  Shout⠀⇛


                       Learn the steps and commands to install free PuTTY
                       on Ubuntu 22.04 LTS Jammy JellyFish and 20.04 Focal
                       fossa using Terminal to get a free SSH and telnet
                       client.


          o § Games⠀➾


                # ⚓ Steam_Adds_Linux_Support_for_DLSS,_24_More_Games_|_Tom’s
                  Hardware⠀⇛


                       Valve has updated its Proton solution – the piece
                       of software that’s meant to bridge the divide
                       between Windows and Linux gaming — to version 6.3-
                       8. Following the company’s announcement of the
                       Steam Deck handheld gaming device, Valve has been
                       doubling down on its Proton efforts, because the
                       Linux-powered gaming device is going to need a
                       robust game library to compete.


                       The new version of Proton brings Linux support to a
                       number of games that were previously locked out of
                       the Linux ecosystem. Crucially, some BattleEye-
                       infused games are now also supported — the gap
                       between Linux and Windows gaming environments seems
                       to be shrinking even in anti-cheat solutions, whose
                       support is crucial for a device that aims to enable
                       AAA and eSports gaming on the go. Games such as
                       Conan Exiles, DayZ, Planetside 2, and
                       PlayerUnknown’s Battlegrounds (and others) all
                       require BattleEye suppport.


                # ⚓ NVIDIA_DLSS_for_DX11_&_DX12_Games_Now_Available_on_Linux
                  via_Proton⠀⇛


                       As promised last month, following the initial
                       release of NVIDIA DLSS on Linux via Valve’s Proton
                       with compatibility for Vulkan games like DOOM
                       Eternal, Wolfenstein Youngblood, and No Man’s Sky,
                       the new version of Proton (6.3.8) released
                       yesterday added NVIDIA DLSS support for DirectX 11
                       and DirectX 12 games.


                       Needless to say, that’s by far the largest group of
                       games compatible with NVIDIA’s Deep Learning Super
                       Sampling technology out of the over 130 games and
                       apps that support it. For example, out of the most
                       recent DLSS additions, Deathloop, Back 4 Blood,
                       Battlefield 2042, Marvel’s Guardians of the Galaxy,
                       Grand Theft Auto: The Trilogy – The Definitive
                       Edition, Alan Wake Remastered, F.I.S.T.: Forged In
                       Shadow Torch, Bright Memory Infinite, Jurassic
                       World Evolution 2, Chivalry II, The Elder Scrolls
                       Online, Swords of Legends Online, Hot Wheels
                       Unleashed, and Assetto Corsa Competizione are all
                       DX11 and/or DX12 titles. Only Crysis Remastered
                       Trilogy, Rise of the Tomb Raider, Shadow of the
                       Tomb Raider, and Baldur’s Gate III support Vulkan.


                # ⚓ Linux_Gaming_with_Ubuntu_Desktop_Part_1:_Steam_&_Proton⠀⇛


                       The holidays are coming, and if you’re anything
                       like me that means only one thing: The Steam Autumn
                       Sale is live!


                       A few years before joining Canonical as the Ubuntu
                       Desktop Product Manager, I was a video game
                       producer (with at least one of my titles getting a
                       native Linux port you’ll be pleased to hear). So
                       improving the gaming experience on Ubuntu is high
                       on my to-do list. With the Linux user base on Steam
                       breaking the 1% ceiling earlier this year- which
                       may or may not be related to the upcoming Linux-
                       based Steam Deck– 2022 is shaping up to be a great
                       year for Linux gaming!


                       In the first of a mini-series of blogs, I wanted to
                       break down some of the easiest ways to get started
                       with gaming on Ubuntu. With part 1 we start with
                       the obvious; Steam (and Proton).


          o § Distributions⠀➾


                # § IBM/Red Hat/Fedora⠀➾


                      # ⚓ Red_Hat_Bolsters_Partner_Ecosystem_to_Accelerate_Data
                        Science_Pipelines_Across_the_Open_Hybrid_Cloud⠀⇛


                             Red Hat, Inc., the world’s leading provider
                             of open source solutions, today announced the
                             availability of Red Hat OpenShift Data
                             Science as a field trial, as well as an
                             expanded partner ecosystem focused on this
                             new cloud service offering. As leading
                             artificial intelligence and machine-learning
                             (AI/ML) partners support the service, Red Hat
                             customers are provided with a range of
                             solutions optimized for Red Hat OpenShift,
                             letting them select the technologies to best
                             meet their specific machine learning needs
                             across the open hybrid cloud and edge
                             computing environments.


                      # ⚓ Command_Line_Heroes:_Season_8:_Humans_as_Robot
                        Caretakers⠀⇛


                             People often distrust robots. But can robots
                             trust humans?


                      # ⚓ Diversity_in_the_Tech_Industry:_‘We_Have_a_Long_Way
                        to_Go’⠀⇛


                             This week, host Connor Craven interviews
                             Laurie Krebs, CFO and SVP at Red Hat, about
                             where the tech industry can be more diverse,
                             how it can improve its diversity, and what
                             the future holds for the movement.


                             Hello, and welcome to 7 Layers. Where every
                             episode we look at the different technologies
                             that connect our world. From literal wires in
                             the ground, to switches and routers, and all
                             the way up to the exploding amount of smart
                             devices around us.


                      # ⚓ The_Inside_Playbook⠀⇛


                             Edge computing and networking is not specific
                             to any industry; all of these scenarios span
                             many different types of organizations.
                             However, all edge scenarios have one common
                             factor: creating and consuming data resources
                             that are geographically distributed. As a
                             final objective we want to analyze, consume
                             or react to data to fulfill our customer and
                             business needs.


          o § Devices/Embedded⠀➾


                # § Open Hardware/Modding⠀➾


                      # ⚓ ESP32_Brings_Air_Purifier_Online_With_Home_Assistant
                        |_Hackaday⠀⇛


                             A lot of hackers are rightfully concerned
                             about the privacy issues that surround many
                             of today’s “smart” gadgets, but it’s hard to
                             argue that the ability to remotely control
                             devices around your home isn’t convenient.
                             Enter self-hosted, open source projects like
                             Home Assistant. This provides the framework
                             for building out a home automation system
                             without having your soul information sold,
                             but as you might expect, you’re going to have
                             to put some effort in to get the most of it.


                      # ⚓ N-Gage_Controller_Uses_All_The_Buttons_|_Hackaday⠀⇛


                             If there’s anything you can guarantee about a
                             video game system, it’s that in 20 years
                             after one suffers a commercial failure there
                             will be a tiny yet rabid group of enthusiasts
                             obsessed with that system. It’s true for the
                             Virtual Boy, the Atari Jaguar, and of course,
                             the Nokia N-Gage. For those not familiar,
                             this was a quirky competitor of the Game Boy
                             Advance that was also a cell phone. And for
                             that reason it had more buttons than a four-
                             player arcade cabinet, which has led to
                             things like this custom controller.


                             Most N-Gage gaming these days takes place on
                             emulators, this build is specifically built
                             for the emulator experience. The original
                             system had so many buttons that it’s
                             difficult to get even a standard 102-key
                             keyboard mapped comfortably to it, so
                             something custom is almost necessary.
                             [Lvaneede], the creator of this project, took
                             some parts from an existing arcade cabinet he
                             had and 3D printed the case in order to craft
                             this custom controller. The buttons he chose
                             are a little stiff for his liking, but it’s
                             much better than using a keyboard.


                      # ⚓ PicoMite_Gives_Your_Pico_A_Deluxe_BASIC_|_Hackaday⠀⇛


                             What makes developing a microcontroller
                             project quick and easy? Tops on our list are
                             an interactive shell and comprehensive
                             libraries that handle all the low-level
                             peripheral stuff. You think we’re talking
                             MicroPython? Not today! MMBasic has just been
                             ported to the Raspberry Pi Pico dev board,
                             and it has all the batteries included.


                             Just to give you a taste, it has built-in
                             support for SD cards, all sorts of displays,
                             touch screens, real-time clocks, IR remotes,
                             numerous sensors, and of course WS2812 LED
                             strips. And because all of this is baked into
                             the BASIC, writing code to use any of these
                             peripherals is straightforward.


                      # ⚓ Build_Your_Own_HP41C_|_Hackaday⠀⇛


                             There was a time when engineers carried slide
                             rules. Then there was a time when we all
                             carried calculators. Sure, calculators are
                             still around, but you are more likely to use
                             your phone. If you really need serious number
                             crunching, you’ll turn to a full computer.
                             But there was that awkward time when
                             calculators were very important and computers
                             were very expensive that calculators tried to
                             be what we needed from full-blown computers.
                             The HP41C was probably the pinnacle of that
                             trend. If you’ve ever had one, you know that
                             is a marvel of the day’s technology with
                             alphanumeric capabilities and four plug in
                             ports for more memory or ROMs. It really was
                             a little hand-held computer. Didn’t have one?
                             Don’t worry, you can now build your own. In
                             fact, the HP emulator will also act like an
                             HP15C or 16C, if you prefer.


                             You can see the device in action in the video
                             below. As you might expect, this version uses
                             a through-hole ATMEGA328 and even at 8 MHz,
                             the emulation is faster than the original
                             calculator. The machine also has over double
                             the memory the original calculator had along
                             with a real-time clock built-in. The display
                             is also backlit, something we all wanted in
                             the original.


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


                # § Web Browsers⠀➾


                      # § Mozilla⠀➾


                            # ⚓ Mozilla_Open_Policy_&_Advocacy_Blog:_Mozilla
                              reacts_to_new_EU_draft_law_on_political
                              advertising_online⠀⇛


                                   The European Commission has just
                                   published its draft regulation on the
                                   transparency of political advertising
                                   online. The draft law is an important
                                   step towards increasing the resilience
                                   of European democracies for the digital
                                   age. Below we give our preliminary
                                   reaction to the new rules.


                                   We’ve long championed a healthier
                                   ecosystem for political advertising
                                   around the world, whether its by
                                   pushing for stronger commitments in the
                                   EU Code of Practice on Disinformation;
                                   uncovering the risks associated with
                                   undisclosed political influencer
                                   advertising on TikTok; supporting
                                   efforts to limit political
                                   microtargeting; or pushing platforms to
                                   effectively implement their Terms of
                                   Service during electoral periods. We’re
                                   glad to see that in its draft law the
                                   European Commission has taken on board
                                   many of our insights and
                                   recommendations, and those of our
                                   allies in the policy community.


                # § Productivity Software/LibreOffice/Calligra⠀➾


                      # ⚓ CODE_21.11_delivers_key_features_for_secure,_easier
                        and_faster_online_document_collaboration⠀⇛


                             Collabora announces the availability of
                             Collabora Online Developer Edition CODE
                             21.11. This major new release targets the
                             three key areas: ease of use, performance and
                             interoperability. The release demonstrates
                             the company’s mission to the technology
                             leader in collaborative editing. Collabora
                             Online businesses the most effective and
                             secure document creation environment with
                             dedicated support and depth of development
                             horsepower.


                             CODE 21.11 is the herald of the next major
                             business supported Collabora Online release.
                             This free developer version includes all
                             features and enhancements that will be
                             available in our enterprise version, expected
                             early December. CODE releases allows everyone
                             to learn about new features early.


                # § Content Management Systems (CMS)⠀➾


                      # ⚓ CMSes_&_static_site_generators:_why_I_(still)_chose
                        WordPress_for_my_business_websites_–_The_Open
                        Sourcerer⠀⇛


                             Not everything is perfect of course. As of
                             2021, on the performance front, getting
                             consistent and reliable caching working with
                             SuperCache is a mindboggling experience, full
                             of “mandelbugs” (like this one); in my case,
                             each of my websites has at least some (or
                             all) of the caching behavior not working
                             (whether it is some pages never being able to
                             generate cache files, or the cached files not
                             being retained, no matter what you do and
                             what combination of voodoo incantation and
                             settings you use), but maybe someday someone
                             will complete a heavy round of refactoring to
                             improve the situation (maybe you can help
                             there?) and things will Just Work™. But for
                             now, I guess I’ll live with that.


                             All in all, it is only from 2019 onwards,
                             after much research (and much technological
                             progress in general), that I found myself
                             with enough tooling to make this work in a
                             way that would meet my expectations of design
                             & workflow flexibility, and therefore feel
                             confident enough that this will be my long-
                             term solution for a particular type/segment
                             of my websites. My personal website (of which
                             this blog is only a subset) still is hand-
                             coded, however, because it “does the job.”


                             Years ago, someone once told me that whenever
                             someone in your team decides to write your
                             company’s website from scratch (or using some
                             templating system), they “inevitably end up
                             reimplementing WordPress… poorly.”


                             So yeah. We’re using WordPress.


                # § Programming/Development⠀➾


                      # § PHP⠀➾


                            # ⚓ 25_Nov_2021:_PHP_8.1.0_Released⠀⇛


                                   The PHP development team announces the
                                   immediate availability of PHP 8.1.0.
                                   This release marks the latest minor
                                   release of the PHP language.


                            # ⚓ PHP_8.1_Released_With_Fibers,_Enumerations,
                              Read-Only_Properties_&_Much_More_–_Phoronix⠀⇛


                                   PHP 8.1.0 was just officially released
                                   as the latest annual feature update to
                                   this widely-used, server-side
                                   programming language.


                                   PHP 8.1 finally introduces the notion
                                   of “enums” or enumerations for a custom
                                   type that is a discrete number of
                                   possible values. PHP enums can be used
                                   anywhere an object can be used.


                            # ⚓ Remi_Collet:_PHP_version_8.1.0_is_released!⠀⇛


                                   RC5 was GOLD, so version 8.1.0 GA is
                                   just released, at planed date.


                                   A great thanks to all developers who
                                   have contributed to this new major and
                                   long awaiting version of PHP and thanks
                                   to all testers of the RC versions who
                                   have allowed us to deliver a good
                                   quality version.


                                   RPM are available in the remi-php81
                                   repository for Fedora ≥ 33 and
                                   Enterprise Linux ≥ 7 (RHEL, CentOS,
                                   Alma, Rocky…) and as Software
                                   Collection in the remi-safe repository.


    * § Leftovers⠀➾


          o ⚓ Surfboard_Gets_Jet_Upgrades_|_Hackaday⠀⇛


                 Surfing is a fun and exciting sport but a lot of
                 beginners can get discouraged with how little time is
                 spent actually riding waves while learning. Not only are
                 balance and wave selection critical skills that take time
                 to learn, but a majority of time in the water is spent
                 battling crashing waves to get out past the breakers.
                 Many people have attempted to solve this problem through
                 other means than willpower alone, and one of the latest
                 attempts is [Andrew W] with a completely DIY surfboard
                 with custom impeller jet drives.


                 The surfboard is hand-made by [Andrew W] himself using a
                 few blocks of styrofoam glued together and then cut into
                 a generic surfboard shape. After the rough shaping is
                 done, he cuts out a huge hole in the back of the board
                 for the jet drive. This drive is almost completely built
                 by [Andrew] as well including the impeller pumps
                 themselves which he designed and 3D printed. The pair of
                 impellers are driven by some beefy motors and a robust
                 speed controller that connects wirelessly to a handheld
                 waterproof throttle to hold while surfing. Once
                 everything was secured in the motor box the surfboard was
                 given a final shaping and then glassed. The final touch
                 was an emergency disconnect attached to a leash so that
                 if he falls off the board it doesn’t speed away without
                 him.


          o ⚓ Inverted_Pendulum_Balanced_On_A_Drone_|_Hackaday⠀⇛


                 [Nicholas Rehm] works during the day at the Applied
                 Physics Laboratory at John Hopkins, Maryland, so has
                 considerable experience with a variety of UAV
                 applications. The question arose about how the
                 perseverance mars rover landing worked, which prompted
                 [Nicholas] to hang a rock under his drone, attached via a
                 winch. This proved to be interesting. But what is more
                 interesting for us, is what happens when you try to
                 attach an inverted pendulum to the top of a drone in
                 flight? (video embedded, below)


                 This is a classic control theory problem, where you need
                 to measure the angle of the pendulum with respect to the
                 base, and close the loop by calculating the necessary
                 acceleration from the pendulum angle. Typically this is
                 demonstrated in one dimension only, but it is only a
                 little more complicated to balance a pendulum with two
                 degrees of freedom.


          o § Education⠀➾


                # ⚓ Surviving_the_Right-Wing_Assault_on_Education⠀⇛


                       Shedding Neutrality and Staying Online: How
                       Teachers Can Survive the Threat of Right-Wing
                       Nationalism in School – Guest Blog by Leah
                       Rosenzweig


                       A recent article by the editors of Rethinking
                       Schools recalls an 1867 Harper’s Weekly editorial
                       which invoked the phrase: “The alphabet is
                       abolitionist,” meaning during the denial of
                       literacy under the “slavocracy,” merely learning or
                       teaching others to read and write was in itself an
                       abolitionist act.


                       Educators have always been vulnerable to the threat
                       of white nationalism—what with their main duty
                       being the enhancement and diffusion of knowledge, a
                       great, if not the greatest, weapon of all (just
                       look at how fearful the idea of teaching formerly
                       enslaved people to read made white supremacists
                       during reconstruction).


                       Now — 150 years later — white supremacism has
                       evolved, not only as an intrusion to the way
                       teachers relay facts or clarify concepts or ideas,
                       but as a threat to the very stasis of the
                       classroom, as kids are becoming influenced by back-
                       alley online movements that promote nationalism,
                       anti-Semitism, and misogyny. And so, while teachers
                       don’t and shouldn’t create incognito accounts on
                       4chan, they should try to stay current with right-
                       wing Internet trends, so that they’re able to catch
                       things like hand symbols and disconcerting research
                       paper citations.


          o § Hardware⠀➾


                # ⚓ Find_Your_Way_In_The_Starry_Skies_With_DobsonianDSC_|
                  Hackaday⠀⇛


                       An obvious problem with the use of a telescope is
                       getting the former to point at the proper part of
                       the sky which you intend to observe, or vice versa
                       when you spot something interesting and wish to
                       record the exact location. While all of this can be
                       done manually with some trouble, there’s a lot to
                       be said for automating this process. Unfortunately
                       these Digital Setting Circles (DSC) features are
                       not cheap even as add-on, which is why [Vladimir
                       Atehortúa] created DobsonianDSC as a low-cost DIY
                       solution.


                       As the name suggests, this project is based around
                       a Dobsonian-style telescope: Newtonian tube with
                       simple altazimuth base. Aside from the mechanical
                       construction, this system uses an ESP32 as its
                       controller along with two rotary encoders, with the
                       simple circuit detailed in a build guide. The
                       firmware for the ESP32 is written in the Arduino C
                       dialect, and a guide for flashing the ESP32 with
                       the Arduino IDE and connecting it to the WLAN is
                       provided as well.


          o § Integrity/Availability⠀➾


                # § Proprietary⠀➾


                      # § Security⠀➾


                            # ⚓ Linux_5.15.5⠀⇛


                                   I’m announcing the release of the
                                   5.15.5 kernel.


                                   All users of the 5.15 kernel series
                                   must upgrade.


                                   The updated 5.15.y git tree can be
                                   found at:
                                   git://git.kernel.org/pub/scm/linux/
                                   kernel/git/stable/linux-stable.git
                                   linux-5.15.y
                                   and can be browsed at the normal
                                   kernel.org git web browser:


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


                                   thanks,


                                   greg k-h


                            # ⚓ What_does_the_Product_Security_and
                              Telecommunications_Infrastructure_bill_mean_for
                              me?⠀⇛


                                   The UK’s Department for Culture, Media
                                   and Sport (DCMS) introduced a bill to
                                   Parliament yesterday. But what does
                                   that mean for IoT manufacturers and
                                   consumers?


                                   First, this bill has been a long time
                                   coming. Many people have been lobbying
                                   and working hard to create it. Industry
                                   and others with vested interests had to
                                   be consulted, draft guidance had to be
                                   produced and then acceptable wording
                                   had to be agreed.


                                   Numerous researchers including us have
                                   been exposing and drawing attention to
                                   poor smart product security too.


                                   I’ve expressed concern along the way at
                                   attempts from industry to water it
                                   down, but the bill as it stands is a
                                   good first step towards enforcing IoT
                                   security.


                                   [...]


                                   Banning default passwords will help
                                   mitigate issues such as the problem
                                   with Sky routers we exposed recently.


                            # ⚓ Book_Review:_Designing_Secure_Software⠀⇛


                                   Designing Secure Software (Amazon, No
                                   Starch Press) by Loren Kohnfelder is
                                   one of the latest entries in No Starch
                                   Press’s line of security books. This
                                   book stands out to me for two big
                                   reasons. First, this is one of the most
                                   mindset-centric books I’ve seen (which
                                   means it is likely to age better than a
                                   lot of more technically-specific
                                   books). Second, this book caters to
                                   developers more than security
                                   professionals (but don’t take this to
                                   mean it’s only for developers), which
                                   is definitely a distinguishing feature
                                   from so many other security books.


                            # ⚓ 4_Certificate_Authorities_to_use_with_Let’s
                              Encrypt_SSL_certificates⠀⇛


                                   It’s obvious from the foregoing that
                                   I’m not in favor of the switch to the
                                   ZeroSSL CA as the default, so which of
                                   the other three would I recommend? I
                                   still use the Let’s Encrypt CA, but
                                   Buypass’s certificates have a longer
                                   lifetime – 180 days, compared to 90
                                   days for the other CAs. When next I
                                   have to issue a new certificate or
                                   renew an existing one, I wouldn’t mind
                                   specifying Buypass as the CA.



                    ䷩ 𝚕𝚒𝚗𝚎 3111

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.25.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_25/11/2021:_LibreOffice_7.2.3_and_Mesa_21.2.6_Released⠀✐


Posted in News_Roundup at 1:54 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o § Audiocasts/Shows⠀➾


                # ⚓ KDE_Floating_Panels:_PULL_REQUEST_DONE!_And_Next_Projects!
                  –_Kockatoo_Tube⠀⇛


                # ⚓ Bad_Voltage_3×40:_The_House_on_the_Hill⠀⇛


                       Stuart Langridge, Jono Bacon, and Jeremy Garcia
                       hold these rights to be self-evident…


          o § Kernel Space⠀➾


                # § Graphics Stack⠀➾


                      # ⚓ mesa_21.2.6⠀⇛


                             Hi List,

                             It's a bit late, but here is mesa 21.2.6.
                             Since 21.3.0 is now available,
                             I think this will be the last 21.2 release
                             (there should be 21.3.1 next
                             week), barring any serious regressions in
                             21.2.6.

                             Being that it's the night before a holiday
                             here in the States, I'll let
                             the press delve into all of the gory details
                             of what's in here :) I'll
                             see you all again as release manager next
                             year for 22.0.

                             Cheers,
                             Dylan
                      # ⚓ Mesa_21.2.6_Released_As_Likely_The_Last_Of_The_Series
                        –_Phoronix⠀⇛


                             With Mesa 21.3 having released last week and
                             its first point release due next week, Mesa
                             21.2.6 has been published as likely the last
                             update to that N-1 series for these open-
                             source OpenGL/Vulkan drivers.


                             Mesa 21.2.6 ships with various Intel OpenGL/
                             Vulkan driver fixes, a few RadeonSI fixes,
                             continued compatibility improvements for the
                             Zink OpenGL-on-Vulkan, a few ACO compiler
                             back-end fixes, and other minor fixes
                             throughout. The Zink changes are perhaps most
                             significant and then mostly the other usual
                             AMD and Intel fixing churn.


          o § Applications⠀➾


                # ⚓ Wireshark_3.6_Released_With_Support_For_World_of_Warcraft
                  “WOWW”_Protocol,_Many_Others⠀⇛


                       Wireshark as the very useful and powerful open-
                       source packet analyzer for networking and other
                       communication protocols is out with a shiny new
                       release.


                       Wireshark 3.6 adds support for importing captures
                       from text files based on regular expressions, much
                       improved RTP player support, adding of USB Link
                       Layer reassembly, improvements to the user’s guide
                       and documentation, support for decoding the Vector
                       Informatik Binary Log File (BLF) file format, many
                       protocol updates, and a lot of new protocols are
                       now supported by Wireshark.


          o § Instructionals/Technical⠀➾


                # ⚓ Touching_Firefox_on_Linux_|_sunweaver’s_NET⠀⇛


                       More as a reminder to myself, but possibly also
                       helpful to other people who want to use Firefox on
                       a tablet running Debian…


                       Without the below adjustment, finger gestures in
                       Firefox running on a tablet result in image moving,
                       text highlighting, etc. (operations related to
                       copy+paste). Not the intuitively expected
                       behaviour…


                # ⚓ How_to_Install_and_Use_Tmux_(Terminal_Multiplexer)_in_Linux
                  System⠀⇛


                       Tmux is one of the most used and useful terminal
                       tools for Linux and Unix-like operating systems.
                       Mostly system admins, server admins, and power
                       Linux users use this wonderful terminal tool for
                       more productivity and efficiency. The term Tmux is
                       the shortened form of Terminal multiplexer that can
                       handle multiple terminal tabs and windows
                       simultaneously on the Linux system. The inbuilt
                       system generates a serial number to monitor and
                       look up each active Tmux window on the system.
                       Though this fascinating tool was first released in
                       2007, from then the demand for this tool is now
                       high. Installing and using the Tmux terminal tool
                       is easy for both Linux server and desktop
                       distributions.


                # ⚓ Install_WPS_Office_on_Ubuntu_20.04/Debian_11_–
                  kifarunix.com⠀⇛


                       In this tutorial, you will learn how to install WPS
                       Office on Ubuntu 20.04/Debian 11 desktop systems.
                       WPS Office is a lightweight, feature-rich
                       comprehensive office suite with high compatibility.
                       Capable of handling texts in Writer, Presentation,
                       Spreadsheet and PDF files. It serves as a handy and
                       professional consultant to help you improve work
                       efficiently.


                       WPS can be used on Linux as perfect replace of
                       LibreOffice and more so, saves the Linux
                       enthusiasts of having to rely on running external
                       Windows machines just for the purposes of working
                       with documents only.


                # ⚓ FreeAptitude_–_Be_more_productive_with_Bash_aliases⠀⇛


                       Aliases are one of the most interesting features
                       provided by a Bash shell, and probably the last to
                       be regularly adopted. Usually, they are intended as
                       a way to create shortcuts to execute the most used
                       commands followed by the options that are not
                       assumed by default from the command itself.
                       However, there is a more appealing way to write
                       them that boost our productivity when executing
                       either frequent or infrequent tasks.


                # ⚓ Upgrade_Ubuntu_20.04_To_22.04_LTS_Jammy_using_Command_or
                  GUI⠀⇛


                       Learn the commands that will fully Upgrade your
                       Ubuntu 20.04 LTS Desktop or Server to Ubuntu 22.04
                       LTS set to launch in April 2022. However, even
                       before that if anybody would like to upgrade to
                       test the same, here are the steps to follow.


                       Here in this tutorial, we will learn the simple
                       command line and Graphical steps on how to upgrade
                       to Ubuntu 22.04 from the previous LTS 20.04
                       version.


                # ⚓ Install_Kubernetes_Using_Minikube_In_CentOS_Linux_–
                  OSTechNix⠀⇛


                       Kubernetes can be installed and configured in a
                       variety of ways, including on personal computers,
                       physical servers, virtual machines, and as a cloud
                       service. We will learn how to install a single node
                       Kubernetes cluster using Minikube in CentOS Linux.


                       For the purpose of this guide, we will install
                       Minikube on CentOS 7 natively running on top of the
                       virtual machine layer. Before installing
                       Kubernetes, you need to have a basic understanding
                       of Kubernetes and its architecture and containers.
                       Please refer to our previous article attached below
                       to know about the concepts.


                # ⚓ How_To_Install_Eclipse_IDE_on_Debian_11_–_idroot⠀⇛


                       In this tutorial, we will show you how to install
                       Eclipse IDE on Debian 11. For those of you who
                       didn’t know, Eclipse is an open-source integrated
                       development environment (IDE) that helps
                       programmers develop software applications and
                       software components by providing developers with
                       tools to compile code, and many more. It supports
                       many plugins to enhance the capabilities to use for
                       other programming languages development
                       environments such as PHP, C++, and JavaScript.


                       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 Eclipse on a Debian 11
                       (Bullseye).


                # ⚓ How_to_install_KVM_server_on_Debian_9/10_Headless_Server_–
                  nixCraft⠀⇛


                       Kernel-based Virtual Machine (KVM) is a
                       virtualization module for the Linux kernel that
                       turns it into a hypervisor. How can I install KVM
                       with bridged networking, setup guest operating
                       system as the back-end virtualization technology
                       for non-graphic Debain Linux 9.x/10.x server?


                       You can use KVM to run multiple operating systems
                       such as Windows, *BSD, Linux distribution using
                       virtual machines. Each virtual machine has its
                       private disk, graphics card, a network card and
                       more.


                # ⚓ How_to_install_RVM-_Ruby_Version_Manager_on_Ubuntu_20.04
                  LTS⠀⇛


                       RVM- Ruby Version Manager is a tool meant to use
                       the command line for installing and managing the
                       various ruby versions easily. Here we see the
                       commands for installation of RVM on Ubuntu 20.04
                       LTS Focal fossa.


                # ⚓ How_to_stop_Firefox_from_auto_updating_in_Linux⠀⇛


                       In Linux, Firefox has this bad habit of wanting to
                       update itself when you’re not ready to perform that
                       task. And it will not let you open a new tab or
                       window until you allow it to apply the update. I
                       find it very annoying. There are any number of
                       knobs you can tune to disable this feature in
                       about:config, but there’s no guarantee that they’ll
                       work as expected. And if you use more than one
                       Firefox profile, as most power users do, you’ll
                       have to tune about:config for each profile. In this
                       post, I’ll show you how to do it system-wide, and
                       it’s guaranteed to work.


                       With the default setting, Firefox will download and
                       install the update in the background, and then
                       throw up the prompt shown here when you want to
                       open a new tab or window. That means you won’t be
                       able to open that new tab or window until you agree
                       to restart Firefox. And that almost always happens
                       when I’m in the middle of doing something very
                       important and not ready to restart Firefox.


                # ⚓ How_to_Use_lshw_in_Linux_(With_a_Practical_Example)_–
                  CloudSavvy_IT⠀⇛


                       What if there was a command which would let you, in
                       an easy-to-read format, view all of the hardware in
                       your Linux system? Welcome to lshw, the great tool
                       often overlooked even by seasoned Linux
                       professionals.


                # ⚓ How_to_Set_Hostname_in_Docker_Compose⠀⇛


                       Wondering how to set hostname in Docker Compose?
                       I’ll show you that.


                # ⚓ How_to_Index_Your_Docker_Image’s_Dependencies_With_Syft_–
                  CloudSavvy_IT⠀⇛


                       Syft is a CLI utility that generates a Software
                       Bill of Materials (SBOM) for container images. An
                       SBOM is a catalogue of dependencies used by your
                       image. It gives you visibility into the “materials”
                       that form your image’s filesystem.


                       Producing an SBOM can help you identify overly
                       complex package supply chains that put you at risk
                       of dependency confusion attacks. Distributing an
                       SBOM alongside your image informs users of what
                       lies below the surface. This provides a useful
                       starting point when tightening supply chain
                       security.


                       Syft is developed by Anchore which also offers a
                       complete container scanning engine. The Syft CLI is
                       capable of extracting package lists from images
                       using popular operating systems and programming
                       languages. Both Docker and OCI images are
                       supported.


                # ⚓ How_to_Mount_or_Symlink_a_Single_File_in_a_Docker_Container
                  –_CloudSavvy_IT⠀⇛


                       Docker volume and bind mounts are used to bind
                       directories on the host OS to locations in the
                       container’s file system. While they’re commonly
                       used to mount entire directories, you can also use
                       them to symlink individual files.


                # ⚓ How_(and_Why)_to_Run_Docker_Inside_Docker_–_CloudSavvy_IT⠀⇛


                       Running Docker inside Docker lets you build images
                       and start containers within an already
                       containerized environment. There are two possible
                       approaches to achieve this depending on whether you
                       want to start child or sibling containers.


                       Access to Docker from inside a Docker container is
                       most often desirable in the context of CI and CD
                       systems. It’s common to host the agents that run
                       your pipeline inside a Docker container. You’ll end
                       up using a Docker-in-Docker strategy if one of your
                       pipeline stages then builds an image or interacts
                       with containers.


          o § Games⠀➾


                # ⚓ Real-time_explosive_tower_defense_arrives_in_Sky_Fleet_on
                  December_17_|_GamingOnLinux⠀⇛


                       Build up an army and speed around the skies in your
                       air ship in Sky Fleet, the action-based tower
                       defense game arriving on Steam on December 17.


                       You build up your squad, place down various
                       defences and engage in fast-paced real-time shoot-
                       outs, while speeding around various floating
                       islands. At the same time you need to deal with
                       resources, so it plays out quite like an RTS, as
                       you and enemies compete for them to try and assault
                       their stronghold.


                # ⚓ Nina_Aquila:_Legal_Eagle_adds_Linux_support_in_the_new
                  update_|_GamingOnLinux⠀⇛


                       Along with a major upgrade to the base game, Nina
                       Aquila: Legal Eagle, Season One now has native
                       Linux support. This game was originally available
                       via itch.io and Newgrounds, where it was quite
                       popular, with the Steam version bundling all
                       content together.


                       Update version 5 added Linux support, new
                       animations, Steam Cloud support, improved
                       performance for low-spec machines and various other
                       improvements.


                # ⚓ Valheim_gets_a_new_patch,_plus_teasers_for_Mistlands_and
                  Caves_|_GamingOnLinux⠀⇛


                       Iron Gate are showing off more of what’s to come
                       with the next major upgrade for Valheim, along with
                       a small content patch. First up we have patch
                       0.205.5 which is out now and it includes a new
                       armour set, along with something stirring in the
                       swamps – oh no, it’s scary enough.


                # ⚓ Godot_Engine_gets_AMD_FidelityFX_Super_Resolution_|
                  GamingOnLinux⠀⇛


                       The free and open source Godot Engine recently had
                       support for AMD FidelityFX Super Resolution merged
                       into the code, ready for the next big release. A
                       wonderful case of open source tech meeting
                       together.


                       What is FidelityFX Super Resolution (FSR)? Put
                       simply: a fancy upscaler. FSR allows you to bring
                       down the rendering resolution and have FSR boost it
                       up to a higher resolution, giving you a clear
                       picture. The result is that you should see better
                       performance than simply using the native resolution
                       – something 4K users seem quite happy about.


                # ⚓ Humble_puts_up_the_Best_of_Sandbox_bundle_with_some_good
                  picks_|_GamingOnLinux⠀⇛


                       They might not actually be the “best” but still
                       pretty good. The Humble Best of Sandbox Bundle is
                       live now. This time around is a pretty interesting
                       mix, both with games that have Linux native builds
                       and others that work just fine with the Steam Play
                       Proton compatibility layer.


                # ⚓ Steam_Play_Proton_6.3-8_out_with_initial_BattlEye_support,
                  CEG_DRM_and_more_games_|_GamingOnLinux⠀⇛


                       Probably one of the more exciting releases of
                       Proton lately, with lots of what was previously in
                       Proton Experimental now in the main release with
                       Proton 6.3-8 out now. Be sure to check out our full
                       Steam Play guide if you need more info.


                       A big addition is the start of support for BattlEye
                       games. Before getting overly excited though, this
                       is just the start of it with only Mount & Blade II:
                       Bannerlord and ARK: Survival Evolved confirmed to
                       be supported by Valve. This is what was previously
                       announced, with developers only needing to get in
                       touch with BattlEye to have it turned on.


                       We also have the older CEG DRM now hooked up and
                       working, bringing with it more classics working
                       that relied on it.


                       On top of that there’s even support for NVIDIA DLSS
                       for games that use DirectX 11 and 12, although it
                       still needs you to make some manual adjustments to
                       turn it on for now which includes using this launch
                       option PROTON_ENABLE_NVAPI=1 %command% and also
                       setting dxgi.nvapiHack = False in a DXVK
                       configuration file.


          o § Desktop Environments/WMs⠀➾


                # § GNOME Desktop/GTK⠀➾


                      # ⚓ This_GTK_App_Checks_Contrast_Ratio_Between_2_Colors
                        in_Ubuntu_Linux⠀⇛


                             Designers and website developers may
                             sometimes need to check WCAG color contrast
                             to make web content more accessible to people
                             with disabilities.


                             Without using an online website each time,
                             Linux has a stylish GTK4 app “Contrast” which
                             allows to check whether the contrast between
                             two colors meet the WCAG requirements.


                             The app has a simple user interface that
                             displays one color as background and another
                             as font color of the text. By clicking on the
                             double arrow icon between two color codes, it
                             reverses background color as text font and
                             font color as background.


          o § Distributions⠀➾


                # ⚓ Alpine_Linux_3.15_bids_a_fond_farewell_to_MIPS64_support⠀⇛


                       The compact Linux distribution Alpine has gained
                       the latest LTS Linux kernel with the update to
                       version 3.15, but fans must say goodbye to support
                       for the MIPS64 architecture.


                       The release is the first in the 3.15 stable series
                       and, as well as the 5.15 LTS Linux kernel, received
                       a raft of updated tools and components, including
                       the 16.13 LTS version of Node.js (version 17 is
                       also included) and GNOME 41.


                       There is also some initial support for UEFI secure
                       boot on x86_64, but the time has come to say
                       goodbye to the MIPS64 port.


                       “The architecture is EOL,” notes the release blog.
                       “The mips64 builder is gone. There is no way we can
                       build any packages anymore, we can no longer fix
                       any security issues, so it’s prudent to officially
                       decommission mips64.”


                # § New Releases⠀➾


                      # ⚓ MX_Linux_has_Released_a_New_Edition_for_Newer
                        Hardware_–_It’s_FOSS_News⠀⇛


                             MX Linux 21 was officially unveiled last
                             month while introducing a new Fluxbox
                             edition. However, the Advanced Hardware
                             Support (AHS) ISO was not a part of it.


                             Recently, MX Linux announced the availability
                             of MX Linux 21 AHS and a new AHS repo for
                             existing MX Linux 21 users.


                             In this article, let us explore more about
                             it.


                      # ⚓ Endless_OS_4.0_is_a_Long-Term_Support_Version_with
                        Usability_Improvements_–_It’s_FOSS_News⠀⇛


                             Endless OS is a Debian-based Linux distro
                             that focuses on bundling several important
                             applications and resources to help make the
                             most out of your computer without needing an
                             internet connection.


                             It is primarily tailored for education and
                             for users who do not have constant access to
                             the internet. And, if you are connected to
                             the internet, there are tools to help you
                             browse the web and stay in touch with
                             friends/family.


                             And, their latest release, Endless OS 4.0, is
                             a Long-Term Support version that comes with
                             several improvements. Let us take a brief
                             look at it.


                      # ⚓ Endless_OS_4.0_is_Out_as_a_Long-Term_Supported
                        Release⠀⇛


                             Rebuilt on the base of Debian 11 Bullseye,
                             Endless OS 4.0 is here with improved app grid
                             navigation, fast user switching, and many
                             other improvements.


                             The developers of Endless OS have just
                             announced the release of Endless OS 4.0. It’s
                             a major update and it focuses mainly on
                             helping users to take advantage of their
                             internet connection when they suppose to have
                             it.


                      # ⚓ Endless_OS_4.0.0_Release_Notes_|_Endless_OS_Support
                        Site⠀⇛


                             What’s new in this major release of Endless
                             OS?


                # § Arch Family⠀➾


                      # ⚓ Archinstall_2.3_Released_For_Easily_Installing_Arch
                        Linux_–_Phoronix⠀⇛


                             Added to the Arch Linux install media back in
                             April was Archinstall for easy and quick
                             installations. It’s worked very well for
                             basic Arch Linux installs in a matter of
                             minutes while with Archinstall 2.3 now
                             available it has even more features.


                # § IBM/Red Hat/Fedora⠀➾


                      # ⚓ Five_data_centers,_150TB_images_downloaded_weekly,
                        1m+_cores_–_Now,_that’s_a_storage_challenge [Ed:
                        "Sponsored by Red Hat" it says at the bottom. The
                        Register has become a total joke, running ads as though
                        they're articles. This is not journalism but
                        churnalism.]⠀⇛


                             For the last eight years, Red Hat Ceph has
                             been at the heart of Workday’s storage
                             strategy, in a collaboration that has spawned
                             upstream contributions from the Workday and
                             Red Hat engineering teams that the entire
                             community benefit from.


                      # ⚓ How_we_implemented_an_authorization_cache_for_Envoy
                        proxy⠀⇛


                             This is the second article in a two-part
                             series about an authorization cache we
                             developed for the Envoy open source proxy as
                             a part of Google Summer of Code 2021. The
                             first article in the series showed the design
                             of our cache, based on Proxy-Wasm and
                             integrated with Red Hat 3scale API
                             Management. In this part, we focus on the
                             implementation aspect of the design described
                             in the previous article (check it out if you
                             haven’t already).


                      # ⚓ Build_and_extend_containerized_applications_with
                        Project_Thoth⠀⇛


                             Container technologies have created a de
                             facto industry standard for developing,
                             deploying, and shipping applications.
                             Containers make it possible to provide more
                             maintainable and self-sustaining runnable
                             units that can be directly managed using
                             cluster orchestrators such as Kubernetes and
                             Red Hat OpenShift.


                             This article is for developers interested in
                             using intelligent package management to
                             control the quality of container images and
                             provide more robust containerized runtime
                             environments. Our discussion is based on
                             Project Thoth for Python, one of the world’s
                             most popular programming languages. The ideas
                             we present can be generalized to other
                             language ecosystems.


                      # ⚓ 9_ways_to_show_gratitude_to_your_team⠀⇛


                             Your company can have the most innovative
                             tech on the block, but it won’t amount to
                             much if you don’t have a solid team behind
                             you that feels supported. The Great
                             Resignation is at least somewhat reflective
                             of people finally realizing their worth and
                             proves how important it is for leaders to
                             show employees how much they are appreciated.


                             Showing gratitude is especially pertinent
                             this year as many employees work from home
                             and don’t get to experience the camaraderie
                             of in-office relationships and support they
                             may have previously enjoyed. Sharing your
                             thanks with employees helps to boost morale.
                             And gratified employees will take more pride
                             in their work.


                      # ⚓ 5_automation_and_RPA_must-reads⠀⇛


                             When you say “automation,” some IT people
                             picture job-stealing robots. IT leaders will
                             need to know how to allay that worry in the
                             months and years to come. But here’s a piece
                             of good news: Some forward-looking IT leaders
                             are finding automation actually has talent
                             retention benefits, as David Egts, chief
                             technologist, North America Public Sector,
                             Red Hat, recently wrote.


                             “Automation is an effective way to help
                             businesses become more resilient, but it also
                             helps retain the key talent you have and
                             attract new talent to up-level your team,”
                             Egts notes. How? Teams that have made
                             progress on the automation journey are seeing
                             benefits including an increased sense of
                             belonging, for example:


                             “Many organizations have gone from siloed
                             automation to automation communities of
                             practice that span these silos. Instead of
                             tasks being manually executed or even
                             automated in isolated pockets of an
                             organization, an automation community of
                             practice lets everyone share their best ideas
                             and build on each other’s work.


                             So rather than belonging to the employee, the
                             processes belong to the community of practice
                             with authorship attribution back to the
                             author. Plus, the community contributors
                             identify with the community because their
                             contributions and spans of influence visibly
                             and positively impact the entire organization
                             in ways they couldn’t do as individuals,”
                             said Egts.


                      # ⚓ Top_15_articles_sysadmins_are_thankful_for_|_Enable
                        Sysadmin⠀⇛


                             Enable Sysadmin has published hundreds of
                             articles; these are the favorites sysadmins
                             turn to month after month.


                      # ⚓ What_are_you_thankful_for_at_work?⠀⇛


                      # ⚓ Tomasz_Torcz:_ACME_&_FreeIPA_–_super_easy⠀⇛


                             This post will be short. Recent FreeIPA
                             versions contain ACME server implementation,
                             which makes TLS certificate issuance a
                             breeze.


                      # ⚓ Mark_J._Wielaard_»_Blog_Archive_»_Valgrind_3.18.1⠀⇛


                             3.18.1 fixes a number of bugs and adds
                             support for glibc-2.34, and for new platforms
                             x86/FreeBSD and amd64/FreeBSD. Debuginfo
                             reading is faster, and Rust demangling has
                             been improved. For PPC64, ISA 3.1 support has
                             been completed, and some newer ARM64 and S390
                             instructions are also supported. See the
                             release notes for details of changes. Note,
                             3.18.0 had no formal release — it was pulled
                             at the last minute due to a packaging
                             problem.


                      # ⚓ CPE_Weekly_Update_–_Week_of_November_22nd_–_26th_–
                        Fedora_Community_Blog⠀⇛


                             Purpose of this team is to take care of day
                             to day business regarding CentOS and Fedora
                             Infrastructure and Fedora release engineering
                             work. It’s responsible for services running
                             in Fedora and CentOS infrastructure and
                             preparing things for the new Fedora release
                             (mirrors, mass branching, new namespaces
                             etc.). The ARC (which is a subset of the
                             team) investigates possible initiatives that
                             CPE might take on.


          o § Devices/Embedded⠀➾


                # § Open Hardware/Modding⠀➾


                      # ⚓ Arduino_UNO_Mini_Limited_Edition_launched_to
                        celebrate_10_million_Arduino_UNO_milestone_–_CNX
                        Software⠀⇛


                             Ten million Arduino UNO boards have been
                             shipped since its launch in 2010, and the
                             Arduino team has designed the Arduino UNO
                             Mini Limited Edition to celebrate the
                             impressive milestone.


                             The Arduino UNO Mini has basically all the
                             same features as the original Arduino UNO but
                             uses a quarter of the area, and features a
                             USB Type-C port for programming the board
                             with the Arduino IDE.


                      # ⚓ 3D_printer_controller_combines_ESP32-S3_&_Microchip
                        SAME51_microcontrollers_(Crowdfunding)_–_CNX_Software⠀⇛


                             Here’s another ESP32 3D printer controller
                             board with the Phi MainBoard 5LC powered by
                             both an ESP32-S3-WROOM module and a Microchip
                             SAME51 Cortex-M4F microcontroller, and
                             providing Ethernet and WiFi connectivity.


                             Designed by Likha Labs from the Philippines,
                             Phi MainBoard 5LC is pre-loaded with
                             RepRapFirmware firmware running the Duet Web
                             Control interface that allows users to upload
                             G-code files, configure settings, start jobs,
                             control the device, and monitor prints.
                             Besides 3D printers, the developers explain
                             the board can also be used to drive other
                             digital-fabrication equipment, such as CNC
                             machines.


                      # ⚓ Seaberry_Mini-ITX_carrier_board_for_Raspberry_Pi_CM4
                        exposes_11_PCIe_slots_and_sockets⠀⇛


                             The Raspberry Pi CM4 may only have a one PCIe
                             x1 Gen 2 interface, but this has not stopped
                             ALFTEL from designing Seaberry, a mini-ITX
                             carrier board for the Raspberry Pi Compute
                             Module 4 with eleven slots and sockets making
                             use of the single 5 Gbps PCIe Gen 2
                             interface.


                             The board also offers two SATA ports, one
                             Gigabit Ethernet port, one RJ45 console port,
                             two HDMI ports, a micro SD card slot, two USB
                             2.0 ports, as well as the usual 40-pin GPIO
                             expansion header, besides the PCIe x16 slot,
                             a PCIe x1 side slot, and M.2 and mPCIe
                             sockets.


                      # ⚓ Codasip_Adopts_Imperas_for_RISC-V_Processor
                        Verification⠀⇛


                             Imperas Software Ltd., the leader in
                             verification solutions for RISC-V, and
                             Codasip, the leader in customizable RISC-
                             V processor IP, today announced that Codasip
                             has adopted Imperas reference designs and the
                             Imperas DV solution for Codasip IP. Codasip
                             has invested heavily into processor
                             verification to deliver the industry’s
                             highest quality RISC-V processors.


                             Codasip has included Imperas golden reference
                             models in its DV testbenches to ensure an
                             efficient verification flow that accommodates
                             a wide range of flexible features and options
                             while scaling across the entire roadmap of
                             future cores to enable rigorous confirmation
                             of functional quality.


                # § Mobile Systems/Mobile Applications⠀➾


                      # ⚓ Glodroid_brings_Android_12_to_the_PinePhone_(sort_of)
                        –_Liliputing⠀⇛


                      # ⚓ android:_Asus_ROG_Phone_2_finally_starts_receiving
                        Android_11_update_in_select_regions_–_Times_of_India⠀⇛


                      # ⚓ How_to_Change_the_Default_Web_Browser_on_Android⠀⇛


                      # ⚓ Android_12L_Will_Fix_Wallpaper_Bug_That_Crashes
                        Games⠀⇛


                      # ⚓ How_to_use_Android_12’s_call_screening_features_–_The
                        Verge⠀⇛


                      # ⚓ How_to fix_your_Android_12_power_button_so_it_turns
                        off_your_phone_–_The_Verge⠀⇛


                      # ⚓ One_UI_4.0_hands-on:_Android_12_for_Samsung_devices_–
                        9to5Google⠀⇛


                      # ⚓ Oppo_Android_12_(ColorOS_12)_update_tracker:_Eligible
                        devices,_release…⠀⇛


                      # ⚓ Asus_manages_to_bring_Android_11_to_the_ROG_Phone_2…
                        only_a_full_year_late⠀⇛


                      # ⚓ How_to_Reinstall_Previously_Used_App_on_Your_Android
                        Easily⠀⇛


                      # ⚓ Here’s_how_to_sign_documents_on_Android_|_Tom’s
                        Guide⠀⇛


                      # ⚓ Here’s_how_to_print_from_an_Android_phone_or_tablet_|
                        Tom’s_Guide⠀⇛


                      # ⚓ A_New_Android_Tablet_With_5G_Connection⠀⇛


                      # ⚓ Samsung_One_UI_4_review:_It’s_the_(very)_little
                        things⠀⇛


                      # ⚓ Fairphone_beats_the_entire_Android_ecosystem_with_six
                        years_of_support_|_Ars_Technica⠀⇛


                      # ⚓ The_best_Black_Friday_Android_phone_deals⠀⇛


                      # ⚓ The_7_Best_Web_Browsers_for_Android⠀⇛


                      # ⚓ New_Android_TVs_get_6_free_months_of_Peacock_Premium
                        –_9to5Google⠀⇛


                      # ⚓ Black_Friday_deals_on_Android_apps_and_games_–_Times
                        of_India⠀⇛


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


                # § Productivity Software/LibreOffice/Calligra⠀➾


                      # ⚓ LibreOffice_7.2.3_Released_with_More_Than_100_Bug
                        Fixes,_Download_and_Update_Now⠀⇛


                             Released in mid-August 2021, the LibreOffice
                             7.2 office suite series comes with many new
                             features and improvements, such as native
                             support for Apple M1 machines, improved
                             interoperability with the MS Office document
                             formats, and dozens of UI enhancements for a
                             better user experience.


                             LibreOffice 7.2.3 is here today one and a
                             half months after the LibreOffice 7.2.2 point
                             release to fix even more bugs and security
                             issues. A total of 112 bug fixes and
                             improvements to document compatibility are
                             included in this update.


                      # ⚓ The_Document_Foundation_announces_LibreOffice_7.2.3
                        Community⠀⇛


                             The Document Foundation announces LibreOffice
                             7.2.3 Community, the second minor release of
                             the LibreOffice 7.2 family targeted at
                             technology enthusiasts and power users, which
                             is available for download from https://
                             www.libreoffice.org/download/. This version
                             includes 112 bug fixes and improvements to
                             document compatibility.


                             LibreOffice 7.2.3 Community is also available
                             for Apple Silicon from this link: https://
                             download.documentfoundation.org/libreoffice/
                             stable/7.2.3/mac/aarch64/.


                             For enterprise-class deployments, TDF
                             strongly recommends the LibreOffice
                             Enterprise family of applications from
                             ecosystem partners, with long-term support
                             options, professional assistance, custom
                             features and Service Level Agreements: https:
                             //www.libreoffice.org/download/libreoffice-
                             in-business/.


                             LibreOffice Community and the LibreOffice
                             Enterprise family of products are based on
                             the LibreOffice Technology platform, the
                             result of years of development efforts with
                             the objective of providing a state of the art
                             office suite not only for the desktop but
                             also for mobile and the cloud.


                      # ⚓ Czech_translation_of_the_LibreOffice_Draw_Guide_7.1⠀⇛


                             Our team has finished translating the
                             LibreOffice Draw Guide 7.1. As usual, it was
                             a team effort, namely: translations by Petr
                             Kuběj, Zdeněk Crhonek, Radomír Strnad,
                             Ludmila Chládková; text corrections by
                             Marcela Tomešová, Martin Kasper, Eva
                             Kmochová, Věra Dvořáková; localized pictures
                             by Roman Toman; and technical support from
                             Miloš Šrámek. Thanks to all of the team for
                             their work!


                # § Education⠀➾


                      # ⚓ 10_Best_Free_and_Open_Source_Linux_Educational
                        Games⠀⇛


                             Educational games are games designed to teach
                             people, typically children, about a certain
                             subject or help them learn a skill as they
                             play. Sometimes this type of software is
                             known as games edutainment because they
                             combine education and entertainment.


                             This type of software aids the ‘normal’
                             learning process, either by helping the
                             individual to absorb new information, or as a
                             support for recalling information already
                             learned. Educational programs, especially
                             those for the youngest students, are often
                             designed with the idea of ‘learn through
                             play’. Many children are easily bored, and
                             they are much more likely to be attentive if
                             they find the activity or task to be
                             enjoyable.


                # § FSFE⠀➾


                      # ⚓ Upcycling_Android:_Keep_using_your_phone_with_Free
                        Software⠀⇛


                             It is the European Week for Waste Reduction,
                             a week that is dedicated to promoting the
                             reuse of products and materials and to
                             helping save resources and reduce waste in
                             everyday life. The FSFE joins in with the new
                             initiative “Upcycling Android” – an
                             initiative to help saving resources by
                             reusing one of our most valuable devices of
                             our daily life, our phones.


                             Every year, manufacturers produce 1.5 billion
                             phones worldwide – and unfortunately,
                             probably almost as many are thrown away after
                             what is usually a far too short hardware
                             lifespan. The short lifespan of these phones
                             often stems from so-called “software
                             obsolescence”, the situation in which users
                             are faced with the dilemma of either buying
                             new hardware or living with outdated
                             software. The environmental consequences of
                             these short hardware lifespans can be dire.
                             To help users in overcoming this problem,
                             with Upcycling Android we enable people to
                             upcycle Android phones with Free Software.
                             Every time we keep using our current phone
                             instead of buying a new one we help avoid the
                             production of new phones and the growing
                             disposal of e-waste.


                # § Public Services/Government⠀➾


                      # ⚓ Schleswig-Holstein_dumps_Vole_in_favour_of_open
                        source⠀⇛


                             The north-German state of Schleswig-Holstein
                             plans to switch to open-source software,
                             reports Mike Saunders from LibreOffice.


                             By the end of 2026, Microsoft Office is to be
                             replaced by LibreOffice on all 25,000
                             computers used by civil servants and
                             employees (including teachers), and the
                             Windows operating system is to be replaced by
                             GNU/Linux.


                             Apparently it is a done deal and already
                             codified by the Schleswig-Holstein state
                             parliament.


                             The state’s digital minister Jan Philipp
                             Albrecht said that part of the transition to
                             open source is already in the works, and
                             pointed out that 90 percent of state
                             administration conferencing is conducted
                             using the open source video conferencing
                             platform Jitsi.


                      # ⚓ 25,000_German_state_computers_will_bid_goodbye_to
                        Windows_and_say_Hello_to_Linux⠀⇛


                             The German state of Schleswig-Holstein has
                             decided that it’s done with closed,
                             proprietary Windows and is moving to open-
                             source Linux/GNU by the end of the year 2026.


                             The first step will be in the form of
                             migrating around 25,000 computers to The
                             Document Foundation’s LibreOffice from
                             Microsoft’s Office suite of applications and
                             then eventually moving all these devices over
                             to Linux by dumping Windows entirely. These
                             25,000 computers are going to be “used by
                             civil servants and employees (including
                             teachers)” essentially implying that a large
                             part of the state-run administration and the
                             education sector will be embracing the open-
                             source way.


                # § Programming/Development⠀➾


                      # ⚓ NVIDIA’s_Open-Source_Image_Scaling_SDK_1.0_Released_–
                        Phoronix⠀⇛


                             Last week NVIDIA announced the Image Scaling
                             SDK as an open-source, cross-platform GPU
                             image upscaling implementation that with
                             their own hardware makes use of DLSS.
                             Following the brief exposure over the past
                             week, NVIDIA Image Scaling SDK 1.0 has been
                             formally christened.


                             The NVIDIA Image Scaling SDK can work on the
                             likes of Intel and AMD Radeon hardware via
                             the SDK’s generic compute shaders that are
                             MIT licensed. Integrating the NVIDIA Image
                             Scaling SDK does require integration on part
                             of the game/engine developer.


                      # ⚓ Tips_for_formatting_when_printing_to_console_from_C++
                        |_Opensource.com⠀⇛


                             When I started writing, I did it primarily
                             for the purpose of documenting for myself.
                             When it comes to programming, I’m incredibly
                             forgetful, so I began to write down useful
                             code snippets, special characteristics, and
                             common mistakes in the programming languages
                             I use. This article perfectly fits the
                             original idea as it covers common use cases
                             of formatting when printing to console from
                             C++.


                      # § Rust⠀➾


                            # ⚓ In_response_to_the_moderation_team_resignation
                              [Ed: Rust project doing massive damage control
                              campaign now, just as those_who_resigned_had
                              predicted. Rust lacks legitimacy. GAFAM prisoner.
                              Microsoft controlled.]⠀⇛


                                   As top-level team leads, project
                                   directors to the Foundation, and core
                                   team members, we are actively
                                   collaborating to establish next steps
                                   after the statement from the Rust
                                   moderation team.


                            # ⚓ This_Week_In_Rust:_This_Week_in_Rust_418⠀⇛


    * § Leftovers⠀➾


          o § Integrity/Availability⠀➾


                # § Proprietary⠀➾


                      # ⚓ When_the_IoT_vendor_goes_bust⠀⇛


                             Over recent years, legislation has started to
                             emerge to protect consumers from unethical
                             behaviour from IoT vendors. Far too many
                             smart devices didn’t charge for a
                             subscription to the online platform that made
                             the device ‘smart’. As a result,
                             manufacturers had a perverse incentive to
                             end-of-life product in order to sell you
                             their next great smart thing.


                             A good example of this was the Revolv home
                             hub: Google’s Nest division acquired the firm
                             behind the $300 hub. Two years later, they
                             shut the platform down, leaving consumers
                             with a pile of useless electronics, orphaned
                             from the platform. Uproar ensued, resulting
                             in the US FTC investigating. Fortunately for
                             Revolv owners, the FTC ruled in their favour
                             and made Google compensate hub owners.


                             Sonos owners will recall a similar kerfuffle
                             around their ‘recycle mode’ that killed the
                             device when one traded up for a newer
                             product, among many negative press stories
                             around the length of product support.


                             Existing and planned regulation for IoT is
                             increasingly having manufacturers state up
                             front how long they will support the product
                             for. Whilst some legislation is focussed on
                             the longevity of product security updates,
                             others focus on length of platform support.


                             This is good: it will allow consumers to make
                             informed decisions about the smart products
                             they buy. I, for one, don’t expect to be
                             replacing a smart door lock after a couple of
                             years simply because the manufacturer wanted
                             to sell me a newer version.


                      # § Security⠀➾


                            # ⚓ Researchers_Detail_Privilege_Escalation_Bugs
                              Reported_in_Oracle_VirtualBox⠀⇛


                                   A now-patched vulnerability affecting
                                   Oracle VM VirtualBox could be
                                   potentially exploited by an adversary
                                   to compromise the hypervisor and cause
                                   a denial-of-service (DoS) condition.


                                   “Easily exploitable vulnerability
                                   allows high privileged attacker with
                                   logon to the infrastructure where
                                   Oracle VM VirtualBox executes to
                                   compromise Oracle VM VirtualBox,” the
                                   advisory reads. “Successful attacks of
                                   this vulnerability can result in
                                   unauthorized ability to cause a hang or
                                   frequently repeatable crash (complete
                                   DoS) of Oracle VM VirtualBox”


                            # ⚓ How_the_SAML_Standard_Provides_Single_Sign-On
                              Services_–_CloudSavvy_IT⠀⇛


                                   Single Sign-On and zero trust networks
                                   depend on securely passing
                                   identification details back and forth
                                   between users, identity providers, and
                                   service providers. SAML is the glue
                                   that lets that happen.


                            # ⚓ Security_updates_for_Thursday⠀⇛


                                   Security updates have been issued by
                                   Fedora (busybox, getdata, and php),
                                   Mageia (couchdb, freerdp, openexr,
                                   postgresql, python-reportlab, and rsh),
                                   openSUSE (bind, java-1_8_0-openjdk, and
                                   kernel), SUSE (java-1_7_0-openjdk), and
                                   Ubuntu (icu).


                            # ⚓ What_is_the_OSI_Model_–_7_Layers_of_OSI_Model
                              Explained⠀⇛


                                   International Organization for
                                   Standardization (ISO) developed the OSI
                                   model in 1984.


                                   OSI model is an acronym for Open System
                                   Interconnect.


                                   The OSI model is a model that allows us
                                   to categorize network communications
                                   and divide different activities of the
                                   network in seven conceptual layers.
                                   This model tries to explain how the
                                   data of an application passes through
                                   the device and out in the physical
                                   network using the seven conceptual
                                   steps or layers.


                                   In simpler words, it explains how one
                                   application performs different steps to
                                   communicate its data to another
                                   application running on a different
                                   device.


                                   The OSI model was created for creating
                                   a common industry standard, which could
                                   have helped inter-operability between
                                   different vendors.


                                   However, this model did not gain a lot
                                   of popularity. So it is used as a
                                   reference or a teaching tool today. The
                                   OSI model does not directly match the
                                   networking systems we use in reality,
                                   but it is still useful because it
                                   describes the several processes used in
                                   electronic communication.


                            # § Fear, Uncertainty, Doubt/Fear-mongering/
                              Dramatisation⠀➾


                                  # ⚓ New_Linux_malware_hides_in_cron_jobs_with
                                    invalid_dates [Ed: This is not a "Linux"
                                    issue; it's about applications that run
                                    over the Web and have holes in them, maybe
                                    because admins do not patch them]⠀⇛


                                         Security researchers have
                                         discovered a new remote access
                                         trojan (RAT) for Linux that keeps
                                         an almost invisible profile by
                                         hiding in tasks scheduled for
                                         execution on a non-existent day,
                                         February 31st.


                                         Dubbed CronRAT, the malware is
                                         currently targeting web stores
                                         and enables attackers to steal
                                         credit card data by deploying
                                         online payment skimmers on Linux
                                         servers.


                            # § Privacy/Surveillance⠀➾


                                  # ⚓ SUCCESS!_New_German_government_calls_for
                                    European_ban_on_biometric_mass_surveillance
                                    –_Reclaim_Your_Face⠀⇛


                                         The newly-agreed German
                                         government coalition has called
                                         for a Europe-wide ban on public
                                         facial recognition and other
                                         biometric surveillance. This
                                         echoes the core demands of the
                                         Reclaim Your Face campaign which
                                         EDRi has co-led since 2020,
                                         through which over 65 civil
                                         society groups ask the EU and
                                         their national governments to
                                         outlaw biometric data mass
                                         surveillance.


                                         Today, 24 November 2021, the new
                                         German government announced their
                                         highly-anticipated coalition
                                         deal, including the strongest
                                         commitments seen so far in Europe
                                         to “rule … out” “biometric
                                         recognition in public”. They
                                         further called to “reject
                                         comprehensive video surveillance
                                         and the use of biometric
                                         recording for surveillance
                                         purposes”.


                                         The center-left Social Democrats
                                         (SPD), the environmentalist
                                         Greens and the business-focused
                                         Free Democrats (FDP) jointly
                                         emphasised the vital importance
                                         of anonymity in public as well as
                                         online. Their statement echoes
                                         the demands of over 65 groups in
                                         the Reclaim Your Face campaign,
                                         co-led by EDRi.


          o § Censorship/Free Speech⠀➾


                # ⚓ Dead_and_Alive:_Affidavits_filed_by_States_and_High_Courts
                  reveal_470_pending_cases_under_the_struck_down_S.66A⠀⇛


                       The People’s Union of Civil Liberties (PUCL), with
                       IFF’s legal assistance, had filed an application in
                       the Supreme Court (SC) seeking directions to ensure
                       that authorities do not prosecute individuals under
                       S.66A of the Information Technology Act, 2000 (IT
                       Act, 2000), which the SC had struck down in Shreya
                       Singhal vs Union of India (2015). On Aug 8th, 2021,
                       SC issued notice to all States/UTs and High Courts.
                       8 HCs and 6 States have replied to the application
                       and they demonstrate the widespread non-compliance
                       with the decision in Shreya Singhal. We await
                       responses from other States/UTs and High Courts.


                       [...]


                       In March 2015, S.66A was declared unconstitutional
                       by the Hon’ble Supreme Court in Shreya Singhal v.
                       Union Of India as it violated the right to freedom
                       of expression guaranteed under Article 19(1)(a) of
                       the Constitution of India. The Court found that S.
                       66A was vague and could be arbitrarily interpreted
                       to penalize even innocent speech. Significantly,
                       the Court found that the provision was not
                       ‘severable’ i.e., no part of the section could be
                       saved and the provision as a whole was declared
                       unconstitutional. This means that the provision was
                       void ab initio i.e was deemed to never have existed
                       on the statute books. The effect should have been
                       that Courts ought to have dismissed all pending
                       cases under S.66A, and authorities ought not to
                       have instituted fresh cases under S. 66A.


                       However, the story did not end there. In 2018, a
                       study by Apar Gupta and Abhinav Sekhri highlighted
                       that authorities continued to prosecute individuals
                       under S.66A even after Shreya Singhal.
                       Subsequently, in 2019, PUCL, one of the original
                       petitioners in Shreya Singhal, approached the
                       Supreme Court seeking directions to ensure the
                       implementation of Shreya Singhal. In February 2019,
                       the Supreme Court directed the Union of India to
                       ensure compliance with its decision by making
                       available copies of the judgment to Chief
                       Secretaries of States/UTs across the country. The
                       Chief Secretaries, in turn, were directed to
                       sensitise police departments across the country.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ Burkina_Faso_must_immediately_end_its_internet_shutdown⠀⇛


                       ccess Now and the #KeepItOn coalition are demanding
                       that the government of Burkina Faso reinstate
                       internet access for all, and without exception.


                       It has now been five days since authorities shut
                       down the internet on November 20, citing vague
                       “public safety” and “national defence” reasons.
                       Today, the Kaboré government has extended the
                       blackout until November 27.


                       “The #KeepItOn coalition is outraged that the
                       government of Burkina Faso shut down the internet,”
                       said Felicia Anthonio, Campaigner and #KeepItOn
                       Lead at Access Now. “Authorities made a bad
                       decision earlier this week when they disconnected
                       millions, but today’s 96-hour extension truly
                       reflects their blatant contempt for human rights.”



                    ䷩ 𝚕𝚒𝚗𝚎 4696

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.25.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_25/11/2021:_Proton_6.3-8_and_Linux_Mint_Compared_to_Ubuntu⠀✐


Posted in News_Roundup at 7:28 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_#237⠀⇛


                       AlmaLinux 8.5 is available:


                       https://almalinux.org/blog/almalinux-os-85-stable-
                       now-available/


                       Release of Lakka 3.6:


                       https://www.lakka.tv/articles/2021/11/14/lakka-3.6/


                       LF Decentralized Storage Migrated to Open License:


                       https://github.com/zerotier/lf/releases/tag/1.1.0.0


                       SeaMonkey 2.53.10 Released:


                       https://www.seamonkey-project.org/news#2021-11-16


                       Fedora Linux 37 intends to end support for 32-bit
                       ARM architecture:


                       https://www.mail-archive.com/devel-
                       announce@lists.fedoraproject.org/msg02684.html


                       Release of Proxmox VE 7.1:


                       https://forum.proxmox.com/threads/proxmox-ve-7-1-
                       released.99846/


                       Oracle Linux 8.5 Released:


                       https://blogs.oracle.com/linux/post/announcing-the-
                       release-of-oracle-linux-8-update-5


                       Cinnamon 5.2 desktop environment released:


                       https://github.com/linuxmint/Cinnamon/releases/tag/
                       5.2.0


                       Ubuntu Touch 20th Firmware Update:


                       https://ubports.com/blog/ubports-news-1/post/
                       ubuntu-touch-ota-20-release-3790


                # ⚓ The_Planck_EZ_Keyboard._47_Keys_Are_All_You_Need!_–
                  Invidious [Ed: Possibly paid-for spam, but it's hard to be
                  entirely sure]⠀⇛


                       I love the two previous keyboards that purchased
                       from ZSA, which were the ErgoDox EZ and the
                       Moonlander. But I noticed that ZSA has another
                       keyboard called the Planck EZ, which a tiny
                       keyboard with just 47 keys. Is such a keyboard even
                       usable? YES!


                # ⚓ FLOSS_Weekly_657:_Web_3.0_and_Beyond_–_WordPress_Breach,
                  SCO_vs_IBM_lawsuit⠀⇛


                       What never stops and what’s barely started are the
                       topics debated by our panel of co-hosts: Doc
                       Searls, Katherine Druckman, Aaron Newcomb and Simon
                       Phipps. We start with the SCO vs. IBM (and before
                       that, many others) lawsuit, which was reportedly
                       settled. What really happened with the GoDaddy and
                       WordPress breach? It’s been 25 years of PHP and
                       then look forward to the time when we’re all in Web
                       4.0 talking about what failed in Web 3.0.


          o § Instructionals/Technical⠀➾


                # ⚓ The_magic_one-line_ImageMagick_7_AppImage_installer⠀⇛


                       To install ImageMagick 7 on any distribution that
                       supports AppImage, copy and paste this one-line
                       script into your favourite shell:


                # ⚓ PAM_SSH_agent_authentication_(with_Ansible)⠀⇛


                       Specifically for use with Ansible, I’m known to
                       recommend adding NOPASSWD: ALL to the sudoers entry
                       and be done with it. No mucking about with sudo
                       passwords (in essence users’ login passwords), no -
                       K option, no passwords in clear-text files because
                       people are unwilling to use Ansible vault, etc. It
                       makes lives easier all around, and yes, I am aware
                       that there are people who get the screaming heebie-
                       jeebies when I say NOPASSWD:. So be it.


                       There is an alternative to authenticating use of
                       sudo using SSH agent forwarding instead of login
                       passwords. If you’re new to agent forwarding, I
                       recommend you read the Illustrated Guide to SSH
                       Agent Forwarding, which explains the concept and
                       its pitfalls very well.


                # ⚓ Jenkins⠀⇛


                       In this article, you will learn more about how
                       Jenkins’s deployment stages and pipeline tools can
                       be used to help automate software development. You
                       will learn how to leverage Jenkins’s deployment
                       phases and Pipeline features to help automate your
                       software development. You’ll leave with a better
                       grasp on what a Jenkins Pipeline is and you’ll know
                       how to set up Jenkins and the Pipeline plug-in.


                # ⚓ So_long_and_thanks_for_all_the_disks!⠀⇛


                       Free (as in libre) was a tradition that would
                       continue until the very end of the disk series: one
                       of the last floppies compiled contained a version
                       of the touch command. Fish helped bring about wider
                       knowledge of open source, GNU, Unix and its related
                       command line tools to the Amiga user base,
                       preparing a generation of young computer
                       enthusiasts not only for the systems they might
                       encounter at universities and workplaces but also
                       for the coming of Linux. Thus, he contributed to
                       building a foundation for the continued use and
                       growth of free software after both the demise of
                       his disk series and the Amiga platform, a legacy of
                       which the effects are still highly tangible.


                       Fish would go on to release a thousand disks before
                       switching to distribution on CD-ROMs in 1994.
                       However, the then imminent arrival of dial-up
                       Internet (giving us commoners access to Aminet)
                       meant that only a few of these CD:s were made.
                       Though he and his disk series will live on in
                       memory for as long as there are Amiga users, his
                       real achievement was bringing the joy and
                       philosophy of free software to a world-wide user
                       base outside academia, long before free software
                       itself helped build the Internet that made his
                       disks obsolete.


                       Here’s to you, Fred, 35 years later. So long and
                       thanks for all the disks!


                # ⚓ I_wish_systemd_logged_information_about_the_source_of
                  “transactions”⠀⇛


                       Modern Linux doesn’t work this way, especially with
                       systemd involved. Systemd has a D-Bus interface
                       that people can use, there’s hardware events that
                       may trigger a reboot, there are various programs
                       that may decide to ask systemd to reboot the
                       system, and under some circumstances systemd itself
                       can decide that a particular, harmless looking
                       process failure or ‘systemctl’ transaction actually
                       will trigger a reboot through some weird chain of
                       dependencies and systemd unit settings. These days,
                       it’s entirely possible to have a system go through
                       an orderly shutdown and reboot with no clues in the
                       logs as to what actually did it or why it happened.


                       However, systemd also has all of the information it
                       needs to log a summary of this. Every time systemd
                       starts a “transaction” (a set of changes to units),
                       it knows what the starting request is and generally
                       who asked for it (and how). It could routinely log
                       this, which would make it much easier to trace back
                       mysterious events later.


                # ⚓ How_to_Recover_Deleted_Files_in_Linux⠀⇛


                       Losing data is one of the most unsettling and
                       harrowing experiences that any user can go through.
                       The prospect of not ever finding precious data once
                       it is deleted or lost is what usually inspires
                       anxiety and leaves users helpless. Thankfully,
                       there are a couple of tools that you can use to
                       recover deleted files on your Linux machines. We
                       have tried out a few data recovery tools that can
                       help you get back your deleted files and one that
                       stood out among the rest. This is the TestDisk data
                       recovery tool.


                       TestDisk is an opensource and powerful data
                       recovery tool that, apart from recovering your
                       data, rebuilds and recovers boot partitions and
                       fixes partition tables. It recovers deleted files
                       from filesystems such as FAT, exFAT ext3, ext4, and
                       NTFS to mention just a few, and copies them to
                       another location. TestDisk is a command-line data
                       recovery tool, and this is one of the attributes
                       that sets it apart from other data recovery tools.


                       In this guide, we will demonstrate how you can
                       recover deleted files in Linux using the Test disk
                       utility tool. We will demonstrate how TestDisk can
                       recover deleted data from a removable USB drive in
                       Ubuntu 20.04.


                # ⚓ How_to_Install_Gtop_System_Monitoring_Tool_in_Linux⠀⇛


                       System monitoring is an important aspect of Linux
                       administration as it helps a Linux user or
                       administrator identify and later investigate the
                       performance statuses of various operating system
                       software and hardware elements related to the
                       system’s disk usage, CPU utilization, and main
                       memory consumption.


                       Gtop is an ideal candidate for Linux system
                       monitoring due to its rich and graphical monitoring
                       dashboard/interface. Its graphical display accounts
                       for the operating system’s disk usage, CPU, and
                       main memory info. Gtop’s visual layout also
                       projects running processes statistics like how much
                       resource is being utilized or overused.


                # ⚓ How_to_install_Python_3.10_on_Debian_11?_–_Unixcop_the_Unix
                  /_Linux_the_admins_deams⠀⇛


                       Hello friends. In this rather short post, we will
                       help you to install Python 3.10 on Debian 11.


                       Debian 11 has Python, do I have to upgrade?


                       The answer to this question depends on the needs of
                       each user. Some users are developers in this
                       language and therefore need to take advantage of
                       the latest features of this; On the other hand,
                       there are also the testers who with their expertise
                       help the growth of the language and the
                       applications that use it.


                       There is also a third group more focused on server
                       administration. These are more careful at the
                       moment of making any new installation, but they can
                       also be forced to instate it in favor of some
                       scripts, libraries, or programs that require it.


                       On the opposite side are the desktop users who are
                       not forced to do this. If you are an occasional
                       system user or do not belong to any of this group
                       then it is not strictly necessary leaving the
                       decision up to you,


                       So, let’s go for it. The process is fast and
                       secure.


                # ⚓ How_To_Install_RPM_Fusion_on_AlmaLinux_8_–_idroot⠀⇛


                       In this tutorial, we will show you how to install
                       RPM Fusion on AlmaLinux 8. For those of you who
                       didn’t know, RPMFusion is a massive third-party
                       software source for Fedora Linux. RPM Fusion is not
                       a standalone repository but an extension of
                       Fedora’s default packages that could not be
                       included due to Fedora being bound by the same
                       legal restrictions as Red Hat. The RPM Fusion
                       repository comes in two flavors, Free and Non-Free.
                       The free repository contains a free version of the
                       software that is open source and non-free, which
                       have mostly almost all free software but are closed
                       source and mainly proprietary.


                       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 RPM Fusion on an AlmaLinux 8.
                       You can follow the same instructions for Fedora,
                       RHEL, CentOS, and Rocky Linux distributions.


                # ⚓ How_to_install_Funkin’_Post-Mortem_Mixup_(Vs._King)_on_a
                  Chromebook⠀⇛


                       Today we are looking at how to install Funkin’
                       Post-Mortem Mixup (Vs. King) 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.


                # ⚓ How_to_install_Viber_on_Elementary_OS_6.0⠀⇛


                       Firstly we run an optional command, this command is
                       only needed if you cant launch Flatpak applications
                       like your default browser on your system. For some
                       reason, we couldn’t, so if you can, you can skip
                       the first command.


                # ⚓ How_to_Install_VirtualBox_Guest_Additions_on_Kali_Linux_–
                  Linux_Nightly⠀⇛


                       VirtualBox Guest Additions will help you get the
                       most out of your Kali Linux virtual machine. It
                       gives you automatic resolution scaling, a shared
                       clipboard between the host and VM, and drag and
                       drop ability. The step by step instructions below
                       will explain how to install VirtualBox Guest
                       Additions on Kali Linux.


                       Kali Linux will ordinarily install the Guest
                       Additions software automatically, as long as it
                       successfully detects that the operating system is
                       installed inside VirtualBox. If you want to
                       reinstall Guest Additions because it’s not working,
                       or just upgrade to the latest version, the
                       instructions below will also help you.


                # ⚓ How_to_get_the_active_title_of_an_X_program_|_Definite’s
                  Extractor⠀⇛


                       I have scripts that will utilise the SFDC case
                       number, but why type it manually when the computer
                       can do it?


                       Firstly, you need to have xdotool installed, for
                       RHEL or CentOS Stream, it is in EPEL. I have tried
                       xprop and xwininfo, but they do not accept search
                       with WM_Class


                       Secondly, get the WM_Class of the X program,
                       usually it is just the program name. If you are
                       unsure, open that X program, then run xprog and
                       click at the X program, then search WM_CLASS
                       amongst the output.


          o § Games⠀➾


                # ⚓ Proton_6.3-8_Is_Here!_Many_More_Games_Work_–_Boiling
                  Steam⠀⇛


                       The state of Linux gaming through Proton is only
                       getting better as time goes by. Just a few months
                       ago Valve released Proton 6.3-7, and with it came a
                       few more playable titles and bug fixes. Today,
                       Valve has officially rolled out the Proton 6.3-
                       8 release, and it’s even juicier, jam-packed than
                       before.


                # ⚓ Proton_6.3-8_Brings_Support_for_Marvel’s_Guardians_of_the
                  Galaxy,_Mass_Effect_Legendary_Edition⠀⇛


                       Proton 6.3-8 is a massive update that brings
                       support for numerous Windows games, which you can
                       now play on your Linux box. Among these, there’s
                       Age of Empires 4, Assassin’s Creed, Breath of Death
                       VI, Call of Duty: Black Ops II singleplayer,
                       DEATHLOOP, FIA European Truck Racing Championship,
                       Fly’N, Game Dev Tycoon, Ghostbusters: The Video
                       Game Remastered, GreedFall, Mafia II (Classic), and
                       Magicka.


                # ⚓ Proton_6.3-8_Released_With_More_Windows_Games_Playable,
                  Support_For_Some_BattlEye_Games⠀⇛


                       It’s been almost two months since Proton 6.3-
                       7 released and two weeks since 6.3-8 RC while this
                       evening that Proton 6.3-8 stable release is out for
                       empowering Valve’s Steam Play in running Windows
                       games on Linux.


          o § Distributions⠀➾


                # § IBM/Red Hat/Fedora⠀➾


                      # ⚓ AWS_embraces_Fedora_Linux_for_its_cloud-based_Amazon
                        Linux_|_ZDNet⠀⇛


                             By and large, the public cloud runs on Linux.
                             Most users, even Microsoft Azure customers,
                             run Linux on the cloud.


                             In the case of market giant Amazon Web
                             Services (AWS), the cloud provider will let
                             you run many Linux distros or their own
                             homebrew Linux, Amazon Linux. Now, AWS has
                             released an early version of its next distro,
                             Amazon Linux 3, which is based on Red Hat’s
                             community Linux, Fedora.


                # § Canonical/Ubuntu Family⠀➾


                      # ⚓ Linux_Mint_vs_Ubuntu_In_Less_Than_10_Minutes⠀⇛


                             Who wins a battle between Linux Mint vs
                             Ubuntu? Which one is better?


                             Ubuntu is the most famous Linux distribution
                             in the world. Its development started back in
                             2004. It is based on Debian distribution,
                             which is why Ubuntu also uses the dpkg
                             packaging system (And .deb package format)
                             along with the apt packager manager.


                             Linux Mint, on the other hand, is based on
                             Ubuntu. Its development started in 2008.
                             Hence, Mint by extension is also based on
                             Debian, and uses the same package manager and
                             packaging system.


                             There are many key and minor differences
                             between Linux Mint and Ubuntu. But often, the
                             question comes to: Which Linux distribution
                             should a new Linux user use on daily basis?
                             Ubuntu or Linux Mint?


                             To answer that, we will be comparing both
                             distributions by many different criteria in
                             this article.


          o § Devices/Embedded⠀➾


                # § Open Hardware/Modding⠀➾


                      # ⚓ Controlling_PWM_fans_with_the_Raspberry_Pi_CM4_IO
                        Board’s_EMC2301⠀⇛


                             The better option is to use the built-in PWM
                             fan controller on the IO Board (pictured
                             above). And to do that, we’re going to need
                             to use the Raspberry Pi’s I2C bus!


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


                # § Education⠀➾


                      # ⚓ Email_Netiquette⠀⇛


                             We needed email but people got stressed out
                             and they started flocking to these silo sites
                             like Facebook and Twitter which have a more
                             codified interaction pattern that enforces or
                             rewards brevity, picture tagging, and event
                             scheduling.


                             If we wanna get people back into email then
                             we can’t be all shamey and gatekeepy about
                             it.


                # § Programming/Development⠀➾


                      # ⚓ Using_AWK_with_CSV_Files⠀⇛


                             Unfortunately, things get more complex from
                             there.


                             CSV files can contain commas, line-breaks,
                             and delimited quotes within the quoted
                             values, which is great for storing data in a
                             CSV file, but is something that AWK is just
                             not well suited to handle: [...]


                      # ⚓ Dirk_Eddelbuettel:_nanotime_0.3.4_on_CRAN:
                        Maintenance_Update⠀⇛


                             Another (minor) nanotime release, now at
                             version 0.3.4, arrived at CRAN overnight. It
                             exports some nanoperiod functionality via a
                             C++ header, and Leonardo and I will use this
                             in an upcoming package that we hope to talk
                             about a little more in a few days. It also
                             adds a few as.character.*() methods that had
                             not been included before.


                             nanotime relies on the RcppCCTZ package for
                             (efficient) high(er) resolution time parsing
                             and formatting up to nanosecond resolution,
                             and the bit64 package for the actual
                             integer64 arithmetic. Initially implemented
                             using the S3 system, it has benefitted
                             greatly from a rigorous refactoring by
                             Leonardo who not only rejigged nanotime
                             internals in S4 but also added new S4 types
                             for periods, intervals and durations.


                      # ⚓ Dirk_Eddelbuettel:_RcppArmadillo_0.10.7.3.0_on_CRAN:
                        Bugfix,_New_Features⠀⇛


                             Armadillo is a powerful and expressive C++
                             template library for linear algebra aiming
                             towards a good balance between speed and ease
                             of use with a syntax deliberately close to a
                             Matlab. RcppArmadillo integrates this library
                             with the R environment and language–and is
                             widely used by (currently) 928 other packages
                             on CRAN.


                             I somehow missed to blog and tweet about the
                             recent release based on the Armadillo 10.7.3
                             upstream release. Conrad is in “long-term
                             support mode”, and 10.7.* is meant to provide
                             fixes and stability relative to the most
                             recent release which we did on September 30.
                             We did actually find a regression when
                             checking reverse-dependencies requiring an
                             upstream move to 10.7.3. At the same time, we
                             folded pull request #352 in. It addresses an
                             old bug of ours where Armadillo fields types
                             were not converted correctly in all
                             dimensions.


                      # ⚓ PHP_Established_New_Non-Commercial_Organization_PHP
                        Foundation⠀⇛


                             The reasons behind the establishment of the
                             PHP Foundation is that one of the key
                             contributors, Nikita Popov, has decided to
                             switch his focus away from PHP to LLVM.


                             You might think that large open source
                             projects are well-funded, but this is not
                             true. In fact many of them rely on a small
                             group of maintainers, as is exactly the case
                             with PHP.


                             Despite being used by 78% of the web, PHP
                             only has a few full-time contributors.


                             Nikita Popov, a well-known long-time PHP
                             ecosystem contributor, is the author of
                             generators, variadic functions and argument
                             unpacking, engine exceptions, uniform
                             variable syntax, and many other PHP
                             contributions. He is also known for PHP
                             Parser which laid the groundwork for many
                             other tools.


                             Popov started working on PHP in 2011 and
                             worked on PHP at JetBrains with the PhpStorm
                             team, making significant contributions to
                             three major releases there – PHP 7.4, PHP
                             8.0, and PHP 8.1.


    * § Leftovers⠀➾


          o ⚓ Toward_an_Undiscovered_Country⠀⇛


                 Hamlet, himself, was uneasy. After all, his dead father’s
                 ghost told him he was murdered by his brother, Hamlet’s
                 uncle Claudius. What was Hamlet to make of this
                 accusation? And what was he to make of this apparition?
                 Was it a ghost, a demon of some kind, or some other
                 manifestation? Of course, the story does not end well for
                 Hamlet or his royal family, but the quote is powerful
                 because, like all good quotes, it stands alone. It has a
                 presence that transcends context and the literary work
                 itself. Indeed, this one has endured centuries, if only
                 now relegated mostly to the province of memes.


                 I have been thinking a lot about that quote lately. If
                 one is being honest, to take even a minute to try and
                 comprehend the scale and complexity of this universe is
                 overwhelming. Certainly, it cannot be done in this unit
                 of time we call a minute. It cannot be done in any
                 measure of human time or with the mere five senses we are
                 told we are limited to. But there is a space that is
                 beyond this one that our corporeal selves inhabit. I can
                 sense it. Many can.


          o ⚓ Who_Killed_Thomas_Sankara?⠀⇛


                 Ouagadougou, Burkina Faso—Yamba Elysée Ilboudo, a 62-
                 year-old former driver and presidential bodyguard, sat
                 behind a wooden dock that framed his small form. An
                 illiterate soldier who started and ended his military
                 career as a private, Ilboudo is among 14 men accused of
                 participating in the assassination of President Thomas
                 Sankara—a celebrated pan-Africanist and Marxist political
                 leader—and 12 other men more than 34 years ago. Reporting
                 for this story was supported by the Fund for
                 Investigative Journalism.


          o ⚓ The_North_is_No_Yellow_Rose_of_Texas,_However…⠀⇛


          o ⚓ Diane_di_Prima_and_the_Dream_of_the_East_Village_Avant-Garde⠀⇛


                 Freddie was running late. He was supposed to be in the
                 East Village at the Poets Theatre, where his closest
                 friend, the poet Diane di Prima, was hosting a night of
                 dance performances. Recently, the friends had lost one of
                 their number, to drugs or suicide, they weren’t sure
                 which. Freddie was going to dance in their memory. As the
                 audience waited, di Prima paced the lobby, worried that
                 something similarly awful had happened to Freddie; she
                 could tell amphetamines were starting to unravel him. But
                 then he appeared, in black tights, a black leotard, toe
                 shoes, and a mask painted on his face. “Kill all the
                 lights,” he told di Prima. It was the spring of 1964, and
                 the dance, For Sergio, had begun.


          o ⚓ Linus_Tech_Tips,_The_Time_Has_Come_To_Say_Sayonara⠀⇛


                 Now as for the video it’s an even bigger cluster fuck
                 than the last one. I’m not going to go through everything
                 I hated about it, because I just don’t have that kind of
                 time. However the general theme of the video seems to be
                 that everything that doesn’t work in Linux must be the
                 fault of Linux. For example, at some point Linus blames
                 Linux because downloading a script from Github was hard.
                 Github has fuck all to do with Linux and is a proprietary
                 Microsoft product. He also blames Linux because Discord
                 screen sharing doesn’t work in Linux and the proprietary
                 Nvidia drivers suck on Linux and the manufacturer of his
                 exotic streaming equipment, like his GoXLR, doesn’t
                 support Linux at all.


                 I’m tired of this riff. I realize LTT makes their nut on
                 views so I understand that generating this kind of drama
                 is going to create more views which in turn puts more
                 money into Linus’ pocket. That’s fine. I’m a realist and
                 realize that we live in a world where ultimately greed
                 reigns supreme.


                 However, let’s not pretend for a second that this is a
                 fair view of whether or not Linux can work for a gamer.
                 Let’s also not pretend that the fact it requires actual
                 effort, makes it an invalid choice. Lots of things in
                 life require an effort but are not automatically
                 invalidated. For example, driving a car.


          o § Science⠀➾


                # ⚓ This_Thanksgiving,_I’m_Grateful_for_a_President_Who
                  Believes_in_Science⠀⇛


                       I’ve been pretty critical of the Biden
                       administration—as I promised I would be on
                       Inauguration Day. I believe that my job is to tell
                       the truth, even to my own “team.” Maybe especially
                       to my own team. But even if I didn’t believe that,
                       I’ve largely resigned myself to dying a bitter old
                       man who was never once satisfied by the pace of
                       progress. Dub me unforgiven.


                # ⚓ Consecutive_squareful_numbers⠀⇛


                       On Saturday I was thinking about how each of !!48,
                       49, 50!! is a multiple of a square number, and
                       similarly !!98, 99, 100!!. No such sequence of four
                       numbers came immediately to mind. The smallest
                       example turns out to be !!242, 243, 244, 245!!.


                       Let’s say a number is “squareful” if it has the
                       form $$a\cdot b^2$$ for !!b>1!!. The opposite,
                       “squarefree”, is a standard term, but “non-
                       squarefree” sounds even worse than “squareful”. Do
                       ten consecutive squareful numbers exist, and if so,
                       how can we find them?


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ Did_Big_Pharma_Buy_Senator_Sinema_a_Fluff_Piece_in_the
                  Washington_Post?⠀⇛


                # ⚓ Whatever_Passes_for_“Normal”_Amid_COVID_Is_About_to_Take
                  Yet_Another_Hard_Turn⠀⇛


                # ⚓ Health_Sector_Has_Outspent_All_Others_on_Lobbying_for
                  Nearly_3_Years_in_a_Row⠀⇛


                # ⚓ Protect_Yourself_From_Salmonella_This_Thanksgiving⠀⇛


                       Thanksgiving is just a few days away, and I regret
                       to inform you that there’s a multidrug-resistant
                       salmonella outbreak running rampant in the nation’s
                       poultry industry.


                       I know that’s daunting, but something to be
                       thankful for this year is the ProPublica reporters
                       who spent the past several months uncovering that
                       the outbreak never abated and looking into how
                       fragmented food safety rules left the U.S.
                       Department of Agriculture, the Centers for Disease
                       Control and Prevention and the Food and Drug
                       Administration ill-equipped to stop it. I know I
                       am.


                # ⚓ Cuba’s_Homegrown_Covid-19_Vaccines_Poised_to_Protect
                  Millions_in_Poor_Nations⠀⇛


                       Despite the added challenges created by a six
                       decade-long U.S. blockade, Cuba’s public biotech
                       sector has developed two highly effective vaccines
                       and its universal healthcare system has inoculated
                       four-fifths of its population.


                       Additionally, the island has begun exporting its
                       homegrown doses and is on the verge of sharing its
                       recipes with impoverished nations abandoned by Big
                       Pharma and wealthy countries.


                # ⚓ How_antivaxxers_weaponized_an_abstract_by_a_Goop_doctor
                  against_COVID-19_vaccines⠀⇛


                       As the pandemic has progressed since the
                       introduction of safe and effective vaccines against
                       COVID-19 nearly a year ago, we’ve seen antivaxxers
                       resurrect old tactics and trope over and over
                       again. Public health officials, scientists,
                       doctors, and the media seemed rather surprised at
                       these ideas and have struggled to deal with them,
                       not so much because they are that hard to refute
                       but because they had never seen them before. After
                       all, before the pandemic, most scientists and
                       doctors were “shruggies” about medical
                       pseudoscience and antivaccine conspiracy theories,
                       not really thinking or caring much about quackery
                       and the harm it caused. Some were even openly
                       dismissive and contemptuous, thinking such
                       misinformation too obviously wrong to be worth
                       their spending any intellectual firepower
                       addressing. So, although skeptics were not
                       surprised at how rapidly antivaxxers weaponized the
                       VAERS database to portray COVID-19 vaccines as
                       deadly (a tactic that even doctors who should know
                       better have fallen for), claimed they are full or
                       toxins or “permanently alter you DNA,” or render
                       women infertile, all while donning the mantle of
                       “health freedom” and claiming that “natural herd
                       immunity” is the way to end the pandemic, the rest
                       of the world sure did seem surprised and
                       unprepared. So it is with another favorite tactic
                       of antivaxxers, the weaponization of bad studies
                       and scientific abstracts.


                # ⚓ What’s_One_of_the_Most_Dangerous_Toys_for_Kids?_The
                  Internet.⠀⇛


                       We all know how difficult it can be to close our
                       social media apps and walk away from our devices.
                       Just one more scroll, we tell ourselves. Just one
                       more peek at a link. And then, suddenly, we’re deep
                       down the rabbit hole of yet another feed.


                       These apps are addictive by design. We know this.
                       And we know full well who’s making a bundle off our
                       weaknesses. (Howdy, Mark Zuckerberg!) But we still
                       can’t help ourselves.


                       So, if we adults are seemingly powerless in the
                       face of such digital temptation, where does that
                       leave our kids?


                # ⚓ Why_Lush_Cosmetics_is_exiting_the_‘dark_and_dangerous
                  alleyway’_of_social_media⠀⇛


                       Lush Cosmetics will deactivate its social media
                       accounts later this week in a bid to get tech
                       companies to make online platforms safer.


                       The U.K. retailer, which sells bath and body
                       products and has a large footprint in Canada,
                       announced its plan Monday to cease posting on
                       Instagram, Facebook, TikTok and Snapchat accounts
                       by Friday.


                       The company, which likened social media to “a dark
                       and dangerous alleyway,” said the deactivation
                       decision is meant to address consumers’ mental
                       health challenges and will not be reversed unless
                       the platforms are made safer.


                # ⚓ Study_Finds_Link_Between_Far_Right_and_High_Corona_Rates_in
                  Germany⠀⇛


                       An interdisciplinary team at the Research Institute
                       for Social Cohesion and a researcher from Munich
                       systematically investigated the connection between
                       the election results and the spread of the
                       pathogen. The experts’ findings are clear: The
                       higher the number of votes the AfD got in a region
                       in the 2017 election, the faster the coronavirus
                       spread there in 2020.


                       The researchers say there is no other party
                       represented in the German parliament whose election
                       results correlate so strongly and systematically
                       with coronavirus infection rates.


                       The researchers’ calculations are so precise that
                       they can quantify the correlation to within a
                       single decimal place. “If the AfD gained one
                       percentage point more in a district, then the
                       incidence there was higher there by an average of
                       2.2 percentage points in the phase of the first
                       wave when numbers rose,” says Christoph Richter, a
                       sociologist who studies right-wing extremism at the
                       Jena Institute for Democracy and Civil Society.
                       Mathematically, that means: If the party received
                       one in 10 votes in one district and twice as many
                       in another, the level of infection in the two
                       regions differed on average by a healthy 22
                       percent.


          o § Integrity/Availability⠀➾


                # ⚓ Why_it_matters_to_us_if_exploits_are_available_for_security
                  issues⠀⇛


                       In general, the more that plug and play exploits
                       exist for something, the more chances are that low-
                       skill people can use the exploit against you
                       casually. They might be running an exploit they
                       found on the web, or it might be part of a broadly
                       available canned toolkit they’re using. But either
                       way, the easier it is to get the exploit in some
                       usable form, the more you’re exposed to casual
                       people who would never write their own exploit but
                       who are perfectly happy to run someone else’s to
                       break into your system (or just to break it).


                # § Proprietary⠀➾


                      # ⚓ WhatsApp_users_beware;_do_not_answer_video_calls_from
                        unknown_callers_[here's_why]⠀⇛


                             “It was around 2 a.m. when I received a call
                             from an unknown person on Facebook Messenger.
                             When I received the call, I saw a nude girl
                             on the other end. I disconnected the call
                             immediately. However, before I could figure
                             out what exactly happened, I received a few
                             screenshots of my video call on Messenger,” a
                             shaken professor told IANS on the condition
                             of anonymity.


                             Starting to panic, he immediately blocked the
                             user. After an hour, the professor got an
                             audio call where another man asked him to pay
                             Rs 20,000 via a digital payment app within
                             five minutes, else he would post these
                             screenshots on Facebook for his friends and
                             family community to see.


                      # ⚓ Apple_suing_‘hacker-for-hire’_firm_NSO_that_Canadian
                        cyber_watchdog_Citizen_Lab_warned_them_about⠀⇛


                             The move by Apple comes after cybersecurity
                             watchdog group Citizen Lab, at the University
                             of Toronto, warned Apple of a vulnerability
                             in its software that could allow a type of
                             spyware called Pegasus to infect Apple
                             devices without the user doing anything or
                             knowing about it.


                      # ⚓ Apple_sues_NSO_Group_to_curb_the_abuse_of_state-
                        sponsored_spyware⠀⇛


                             Apple’s legal complaint provides new
                             information on NSO Group’s FORCEDENTRY, an
                             exploit for a now-patched vulnerability
                             previously used to break into a victim’s
                             Apple device and install the latest version
                             of NSO Group’s spyware product, Pegasus. The
                             exploit was originally identified by the
                             Citizen Lab, a research group at the
                             University of Toronto.


                      # § Security⠀➾


                            # § Privacy/Surveillance⠀➾


                                  # ⚓ Helicopter_Footage_Obtained_By_The_ACLU
                                    Shows_Pervasive_Surveillance_Of_Peaceful
                                    Anti-Police_Violence_Protests⠀⇛


                                         Thanks to a trove of public
                                         records, the ACLU can provide
                                         some insight on how the
                                         California Highway Patrol engaged
                                         in surveillance of anti-police
                                         brutality protests. While one
                                         would expect police helicopters
                                         to fly over protests to keep an
                                         eye out for any illegal activity,
                                         it appears the officers manning
                                         the surveillance cameras were
                                         more interested in trying to
                                         identify protesters who weren’t
                                         breaking any laws.


                                  # ⚓ Why_We_Should_Reject_Mark_Zuckerberg’s
                                    Dehumanizing_Vision_of_a_“Metaverse”⠀⇛


                                         We’ll all be hearing a lot about
                                         the metaverse in the guises of
                                         cleverly crafted tech language
                                         over the months and years ahead.
                                         Technical descriptions such as
                                         the one found in Wikipedia can be
                                         confusing and lacking in “big
                                         picture” implications. It’s
                                         useful to note that this is a
                                         seismic shift, comparable to the
                                         Internet in scope and scale, and
                                         it’s planned to become the
                                         dominant paradigm for human
                                         communications, transitioning our
                                         business, social, and cultural
                                         life from physical to online
                                         environments.


                                         But I want to be careful not to
                                         mince words in describing what
                                         this technology coup is really
                                         all about: nothing less than an
                                         attempt to fabricate an alternate
                                         “reality” other than the physical
                                         one we now inhabit. This new
                                         reality can be accessed, of
                                         course, only by paying customers
                                         and those in a position to afford
                                         and understand it. It is a
                                         technology designed by elites and
                                         for elites and implicitly leaves
                                         behind much of humanity in its
                                         wake.


                                  # ⚓ Amazon_has_Been_Lobbying_Hard_Against
                                    Privacy_Protections_–_Mostly_with_Success;
                                    Who’s_Smiling_Now?⠀⇛


                                         The Amazon department tasked with
                                         spreading that fear grew from two
                                         dozen employees in 2015 to around
                                         250 today. As well as wielding
                                         sticks, Amazon offers carrots.
                                         For example, to encourage
                                         politicians to support an Amazon-
                                         drafted privacy bill in Virginia,
                                         the company increased its
                                         political donations from $27,750
                                         in 2016 to $277,500 last year.
                                         According to the new report,
                                         consumer advocates were not
                                         consulted, and only found out
                                         about the bill shortly before it
                                         was passed. In addition, Amazon
                                         has registered at least 180
                                         lobbyists in 44 US states.


                                  # ⚓ HS:_Finland’s_[SUPO]_calls_for_greater
                                    intelligence_powers⠀⇛


                                         Statements submitted to the
                                         Ministry of the Interior, which
                                         is preparing a report on the
                                         functioning of the intelligence
                                         laws adopted in 2018 to the
                                         Finnish Parliament, reveal that
                                         the concerns are related to the
                                         vague nature of the existing laws
                                         and the lack of statistical data
                                         on violations of the secrecy of
                                         communications of citizens.


                                         The Parliament has obligated
                                         intelligence authorities to keep
                                         record of any communications
                                         intercepted and opened
                                         accidentally.


                                         [SUPO] in 2018 was granted
                                         basically all of the clandestine
                                         intelligence gathering powers it
                                         requested. The powers can be
                                         wielded without concrete
                                         suspicions of criminal activity
                                         if national security is deemed to
                                         be under threat.


                                  # ⚓ Irish_DPC_demanded_noyb_to_sign_a_“non-
                                    disclosure_agreement”_or_remove_noyb_from
                                    Facebook_procedure._noyb_files_criminal
                                    report_against_DPC.⠀⇛


                                         The Irish Data Protection
                                         Commission (DPC) has taken the
                                         unheard-of move, to demand noyb
                                         to draft and sign a “non-
                                         disclosure agreement” (NDA)
                                         within one working day. In
                                         absence of such an NDA for the
                                         benefit of the DPC and Facebook,
                                         the DPC would not comply with the
                                         duty to hear the complainant
                                         anymore. Schrems: “The DPC
                                         engaged in procedural blackmail.
                                         Only if we shut up, the DPC would
                                         ‘grant’ us our legal right to be
                                         heard. We have reported the
                                         incident to the Austrian Office
                                         for the Prosecution of
                                         Corruption. This is a regulator
                                         clearly asking for a ‘quid pro
                                         quo’ to do its job, which likely
                                         constitutes bribery in Austria.”


                                         Facebook would especially benefit
                                         from the NDA, as new documents
                                         indicate that EU regulators may
                                         find Facebook’s “GDPR bypass”
                                         illegal — possibly declaring
                                         Facebook’s use of personal data
                                         since 2018 unlawful, with major
                                         implications for Facebook’s
                                         business model in Europe.


                                  # ⚓ Do_no_harm?_How_the_case_of_Afghanistan
                                    sheds_light_on_the_dark_practice_of
                                    biometric_intervention⠀⇛


                                         In August 2021, as US military
                                         forces exited Afghanistan, the
                                         Taliban seized facial recognition
                                         systems, highlighting just how a
                                         failure to protect people’s
                                         privacy can tangibly threaten
                                         their physical safety and human
                                         rights. Far from being good tools
                                         which fell into the wrong hands,
                                         the very existence of these
                                         systems is part of broader
                                         structures of data extraction and
                                         exploitation spanning continents
                                         and centuries, with a history
                                         wrapped up in imperialism,
                                         colonialism and control.


                                  # ⚓ Big_brother_at_the_Prague_airport._The
                                    state_refuses_to_explain_how_the_biometric
                                    camera_system_works⠀⇛


                                         When Václav Mach, collaborator of
                                         the Czech digital-legal
                                         organization, an EDRi member,
                                         Iuridicum Remedium (IuRe) and law
                                         student at the University of
                                         Olomouc, asked the state for more
                                         detailed information on the use
                                         of smart biometric cameras at
                                         Prague’s Václav Havel Airport, he
                                         obtained just general phrases.
                                         “They kept secret what they
                                         could. Their non-transparency
                                         doesn’t add to their
                                         credibility,“ he says in an
                                         interview with HlídacíPes.org.
                                         The article below is a summary of
                                         the more extensive interview,
                                         translated from Czech into
                                         English by EDRi member IuRe.


                                  # ⚓ Why_chat_control_is_so_dangerous⠀⇛


                                         According to a legal opinion by
                                         Prof. Dr. Ninon Colneric (PDF)
                                         automated scanning could indeed
                                         be illegal. Surveillance without
                                         a specific reason or reasonable
                                         suspicion is prohibited in the EU
                                         due to the fact of its violation
                                         of fundamental rights. The
                                         European Court of Justice has
                                         repeatedly confirmed this view
                                         and, for example, reproved the
                                         retention of data on a number of
                                         occasions.


                                         Nevertheless, attempts to revive
                                         the data retention zombie with
                                         legal tricks have not died down.
                                         The demand can be found regularly
                                         in council papers of various EU
                                         countries. Thus, this type of
                                         mass surveillance is still part
                                         of the German Telecommunications
                                         Act („Telekommunikationsgesetz“),
                                         although being currently
                                         suspended.


          o § Defence/Aggression⠀➾


                # ⚓ Undoing_Cricket_Imperialism⠀⇛


                       The cricket geophenomenon, much more captivating
                       than the cricket game, fuels complex enchantment
                       globally, most notably in South Asia. The
                       phenomenon wrestles with cricket formats, racism
                       bouts, and fights over advertisement revenues. Yet,
                       international cricket generates white, black, and
                       brown megastars to everyone’s delight amidst match
                       boycotts, match-fixing, and national rivalries. In
                       numbers of the global audience, cricket is second
                       only to football (soccer) and gaining ground. The
                       2019 Men’s Cricket World Cup attracted a cumulative
                       average of 1.6 billion viewers. In 1900, cricket
                       debuted as an Olympic sport with only two teams
                       competing, England and France (which knew nothing
                       about cricket). In 2028, after 128 years, cricket
                       will return as an Olympic sport with a wide-
                       reaching competition.


                       21st-century cricket transcends far beyond England,
                       its weather, culture, intentions, language, and
                       rules, though the England cricket team remains a
                       formidable international competitor. However, the
                       game’s format, dynamics, epicenter, money, power,
                       indeed everything about cricket is changing. For
                       centuries, cricket was a single-nation sport, male
                       by gender and white by race, played leisurely,
                       primarily in the summer months. Cricket is now a
                       global phenomenon, electrifying as heck, running
                       nonstop all year round, empowered by male and
                       female teams of variant colors and races,
                       generating millions of dollars in advertisement
                       revenues. Running commentary is no longer just in
                       English, and unofficial Hindi commentary draws
                       millions of more listeners. The ICC hosts several
                       multilateral cricket competition series of “great
                       pitch and moment” — far beyond Shakespeare’s
                       oration, who probably knew cricket more as a
                       grasshopper.


                # ⚓ The_Costs_of_War_(to_You)⠀⇛


                       Recently, my husband, a naval officer currently
                       serving with the Department of Energy, spent a week
                       with colleagues touring a former nuclear testing
                       site about 65 miles north of Las Vegas. Between
                       1951 and 1957, the U.S. conducted more than 1,000
                       nuclear tests in those 680 square miles of desert
                       and only stopped when scientists began urging that
                       the tests be halted because of soaring cancer rates
                       among the downwind residents of Arizona, Nevada,
                       and Utah.


                       My spouse’s trip was a kind of ritual Department of
                       Energy personnel undertake to learn about nuclear
                       weapons as they maintain our country’s vast and
                       still wildly expanding arsenal.


                # ⚓ The_High_Stakes_of_the_U.S.-Russia_Confrontation_over
                  Ukraine⠀⇛


                       The People’s Republics of  Donetsk (DPR) and
                       Luhansk (LPR), which declared independence in
                       response to the U.S.-backed coup in Ukraine in
                       2014, have once again become flashpoints in the
                       intensifying Cold War between the United States and
                       Russia. The U.S. and NATO appear to be fully
                       supporting a new government offensive against these
                       Russian-backed enclaves, which could quickly
                       escalate into a full-blown international military
                       conflict.


                       The last time this area became an international
                       tinderbox was in April, when the anti-Russian
                       government of Ukraine threatened an offensive
                       against Donetsk and Luhansk, and Russia assembled
                       thousands of troops along Ukraine’s eastern border.


                # ⚓ Our_Blind_Faith_in_the_Military_Will_Destroy_Us⠀⇛


                       Who is America’s god? The Christian god of the
                       beatitudes, the one who healed the sick, helped the
                       poor, and preached love of neighbor? Not in these
                       (dis)United States. In the Pledge of Allegiance, we
                       speak proudly of One Nation under God, but in the
                       aggregate, this country doesn’t serve or worship
                       Jesus Christ, or Allah, or any other god of justice
                       and mercy. In truth, the deity America believes in
                       is the five-sided one headquartered in Arlington,
                       Virginia.


                # ⚓ Yemen’s_Houthi_Rebels_Respond_to_US_Secretary_of_Defense
                  Lloyd_Austin⠀⇛


                       In 2015, Saudi Arabia and the UAE, along with other
                       Arab states, attacked Yemen with the objective of
                       restoring the government of Yemeni President
                       Abdrabbuh Mansur Hadi, who the Houthis had
                       overthrown the year before.


                       The remarks from Houthi spokesman Mohammad Ali al-
                       Houthi came in response to comments made by US
                       Defense Secretary Lloyd Austin on November 20. 
                       Speaking at the annual Manama Dialogue security
                       conference in Bahrain, Secretary Austin reiterated
                       the US commitment to Saudi Arabia’s defense.  The
                       US, Austin said, was “significantly enhancing Saudi
                       Arabia’s ability to defend itself.  * * * America’s
                       commitment to helping our friends defend their
                       sovereign space is unwavering.”


                # ⚓ Vigilantes_on_Parade:_Rightwing_Extremism_and_the_Threat_of
                  National_Implosion⠀⇛


                       A dangerous precedent has been set in this ruling,
                       empowering vigilantes who believe they are
                       deputized to enforce “the law” against perceived
                       political enemies. Rittenhouse traveled to a city
                       that he didn’t live in, to a state in which he is
                       not a resident, while illegally possessing an
                       assault rifle he had no right to wield, in the name
                       of “protecting” property he didn’t own, in the
                       process killing two men in violent altercations
                       that would have been avoided entirely if Kenosha
                       police had done their job, corralling vigilantes
                       who looked to commit violence, and separating them
                       from those engaged in protests or destruction of
                       property. Even for those who are fixated on the
                       property damage question, it’s difficult to defend
                       Rittenhouse’s actions when he engaged in vigilante
                       violence, with no training in dealing with conflict
                       situations, and when responsibility for enforcing
                       the law clearly falls on the police.


                       The Rittenhouse case shouldn’t be interpreted in a
                       vacuum, as it occurred within a larger political
                       environment in which other rightwing vigilantes
                       seek to justify violence, and even murder, under
                       the guise of “self-defense.” Consider, for example,
                       the Ahmaud Arbery case in Georgia, where three
                       white vigilantes stalked, cornered, and shot a
                       black man who was jogging through a neighborhood –
                       and away from them – under the false premise that
                       he may have been responsible for a local burglary.
                       There is no plausible scenario in which these three
                       men can reasonably claim self-defense, when the
                       altercation was entirely of their own initiation,
                       when the man murdered was unarmed, and when he had
                       nothing to do with the crime in question. And of
                       course, there is the issue of implicit or explicit
                       racial bias related to the defendants, which is
                       also difficult to ignore in a country where
                       research shows that assumptions of guilt related to
                       violent crime are consistently racialized, with
                       black men assumed to be the prime perpetrators in
                       violent and other criminal acts. If the Arbery
                       defendants successfully justify their actions as
                       “self-defense,” then the courts will have
                       effectively criminalized being black in America. An
                       acquittal sends a message that white vigilantes can
                       commit violence and murder at will against people
                       of color who have the nerve to venture out into
                       public, and with black men’s mere existence
                       constituting a “threat” from which white people
                       need “protection.”


                # ⚓ Dems_and_GOP_Fight_About_Domestic_Spending_—_But_Not_About
                  Huge_Military_Budgets⠀⇛


                # ⚓ “The_War_Party”:_Jeremy_Scahill_on_How_U.S._Militarism
                  Unifies_Democrats_&_Republicans⠀⇛


                       As Democrats in Congress struggle to pass the $1.75
                       trillion Build Back Better Act, there is large
                       bipartisan consensus in the U.S. Congress to spend
                       over $7 trillion over the next 10 years in military
                       spending. The United States spends more each year
                       on defense than China, Russia, India, the U.K.,
                       Germany, France, Japan, South Korea, and Australia
                       combined. “Democrats have to engage in theater
                       about human rights and international law and due
                       process, but they ultimately, at the end of the
                       day, are just as aggressive as Republicans,” says
                       investigative journalist Jeremy Scahill of the
                       Intercept. His most recent piece is titled, “The
                       War Party: From Bush to Obama, and Trump to Biden,
                       U.S. Militarism Is the Great Unifier.” We also
                       speak with Scahill about the Biden administration’s
                       ongoing persecution of military whistleblowers,
                       including Daniel Hale.


                # ⚓ Can_You_Bankrupt_White_Supremacy?_Jury_Holds
                  Charlottesville_Organizers_Liable_for_$26M_in_Damages⠀⇛


                       A federal jury has ordered a group of white
                       supremacists to pay over $26 million in damages for
                       their role in organizing the deadly 2017 “Unite the
                       Right” rally in Charlottesville, Virginia. “Is
                       bankrupting these organizations, is bankrupting
                       these individuals enough to actually stop the
                       growing threat … of white supremacy and Nazism in
                       the United States?” asks Slate senior editor Nicole
                       Lewis. “I don’t think so.” Lewis also discusses the
                       Ahmaud Arbery murder case and why claims of self-
                       defense from armed white people serve as a “racist
                       dog whistle.” She says it’s inevitably a one-sided
                       trial when “the McMichaels are the only ones
                       [surviving] that get to claim they’re scared.”


                # ⚓ Dems_“Need_to_Get_Thicker_Skin,”_GOP_Lawmaker_Whines_Week
                  After_Gosar_Censure⠀⇛


                # ⚓ Defense_Minister_Says_Russia_to_Boost_Military_Over
                  ‘Increased_NATO_Activity’_Near_Border⠀⇛


                       After weeks of rising tensions between Russia and
                       Ukraine, along with its Western allies, Russian
                       Defense Minister Sergei Shoigu said Wednesday that
                       his country is boosting combat readiness due to
                       NATO activity near its borders.


                       “The tense military and political situation in the
                       world and NATO’s increased activity near the
                       Russian borders prompt the need to further develop
                       the armed forces qualitatively,” Shoigu said,
                       referring to the North Atlantic Treaty Organization
                       made up of 30 member nations including the United
                       States.


                # ⚓ Rally_Organizers_Used_Burner_Phones_to_Talk_With_Trump
                  Officials_on_January_6⠀⇛


                # ⚓ “Why_Are_Ahmaud_Arbery’s_Killers_So_Scared?”:_Self-Defense
                  Claims_by_White_Attackers_Seen_As_Racist⠀⇛


                       Update on Nov. 24: Jurors on Wednesday afternoon
                       returned guilty verdicts against all three of the
                       white men charged with killing 25-year-old Ahmaud
                       Arbery in February 2020. Travis McMichael fired the
                       fatal shots and was convicted on all counts,
                       including the charge of malice murder. His father
                       Gregory McMichael, a former police officer, and
                       neighbor William “Roddie” Bryan were convicted of
                       felony murder and other charges.


                # ⚓ All_Three_Men_Charged_in_Ahmaud_Arbery’s_Killing_Found
                  Guilty_of_Murder⠀⇛


                # ⚓ Guilty._Guilty._Guilty:_Jury_Convicts_All_3_Assailants_for
                  Ahmaud_Arbery_Murder⠀⇛


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


                       A Georgia jury on Wednesday found three men guilty
                       as charged for the 2020 murder of unarmed Black
                       jogger Ahmaud Arbery.


                # ⚓ Opinion_|_The_Exoneration_Club_of_America_Welcomes_Kyle
                  Rittenhouse⠀⇛


                # ⚓ The_Disinformation_that_Got_Told:_Michael_Cohen_Was,_in
                  Fact,_Hiding_Secret_Communications_with_the_Kremlin⠀⇛


                       The details of any disinformation in the dossier —
                       the possibility that Russian intelligence
                       deliberately planted false stories about secret
                       communications Michael Cohen had with the Kremlin —
                       are important because they may have served the
                       overall Russian operation. In some cases, such as
                       the claim that Carter Page was Paul Manafort’s
                       purported go-between with Russian rather than
                       Konstantin Kilimnik, might have provided cover. The
                       claims that Russia had years old FSB intercepts of
                       Hillary they planned to release as kompromat,
                       rather than recently stolen emails from John
                       Podesta, would similarly provide cover. In others,
                       disinformation might have worked in the same way
                       Oleg Deripaska’s double game did, increasing the
                       vulnerability of Trump’s people even while making
                       it more likely they’d do what Russia wanted.


                       I have argued in the past that the Trump Tower deal
                       wasn’t important because it showed that Trump was
                       pursuing a real estate deal while running for
                       President. Rather, it was important to the success
                       of the Russian operation because it gave Russia
                       proof, before any hint of the Russian operation
                       became public, that Donald Trump would be willing
                       to work, in secret, with sanctioned banks and a GRU
                       officer to make an impossibly lucrative real estate
                       deal happen.


                # ⚓ European_commission_vows_to_create_tools_to_combat_use_of
                  people_for_political_purposes⠀⇛


                       The proposals include the restriction of
                       activities, suspension of licenses, suspension of
                       permits for refueling, maintenance, stops, transit
                       and overflight over the EU territory. Specific
                       measures will be proportionate and will be
                       determined on a case-by-case basis, the commission
                       said.


                # ⚓ XTRA_GUAC:_Here’s_Everything_Enbridge_Is_Buying_Cops_to
                  Fight_Protesters⠀⇛


                       Hundreds of invoices reveal how Enbridge spent $3
                       million in reimbursements on Minnesota police to
                       surveil Line 3 protestors.


          o § Transparency/Investigative Reporting⠀➾


                # ⚓ Why_There_Are_So_Few_Whistleblowers⠀⇛


                       The fact that there are so few whistleblowers
                       points to the failure of the system, particularly
                       the failure of the oversight system.  The press
                       certainly hasn’t been helpful.  Chelsea Manning,
                       who provided video evidence of war crimes, was
                       dismissed by Washington Post oped writer Ruth
                       Marcus as a “cross-dressing Little Red Riding
                       Hood.”  Edward Snowden, who provided fulsome
                       evidence of illegal massive surveillance, was
                       dismissed by Post senior writer David Ignatius as
                       an “intelligence defector,” not a “whistleblower.” 
                       NBC’s David Gregory accused then Guardian reporter
                       Glenn Greenwald of “aiding” and “abetting” Snowden,
                       and suggested he could be charged with a crime.  So
                       whistleblowers cannot count on support from the
                       mainstream media.


                       Nor can congressional committees expect military
                       and intelligence officers to “self-report”
                       transgressions, let alone crimes.  We’ve recently
                       learned that senior military officers and civilian
                       officials have been covering up a war crime that
                       took place in Syria two years ago, taking the lives
                       of dozens of women and children.  According to
                       the New York Times, the military command in Iraq
                       and the Central Command headquarters in Florida
                       participated in the cover-up.  Even the Department
                       of Defense’s independent Inspector General omitted
                       any reference in his report to the Air Force F-15
                       attack fighters that dropped three 500-pound
                       bombs.  The IG was relying on an assessment of the
                       strike that was prepared by the secret unit that
                       carried out the strike.


          o § Environment⠀➾


                # ⚓ 33_Ways_to_Celebrate_Buy_Nothing_Day⠀⇛


                       Black Friday, the day after American Thanksgiving,
                       is typically the busiest shopping day of the year
                       in the US. It’s also Buy Nothing Day in North
                       America, a day of protest against consumerism. On
                       November 26 this year, why not skip the online
                       bargain hunting and instead do something good for
                       the planet that’s also good for your soul?


                # ⚓ Opinion_|_After_COP26_Failures,_Major_Challenges_and
                  Immense_Opportunities_Ahead⠀⇛


                       What is next on the global climate agenda? This
                       year’s United Nations Climate Change Conference
                       (COP26) in Glasgow certainly did not fail, but nor
                       was it much of a success. While world leaders
                       entered into some promising new agreements on
                       targets, global greenhouse-gas emissions so far are
                       not being reduced at the pace we need. And while
                       some countries’ climate pledges have been
                       strengthened, the lack of concrete measures for
                       achieving them is a real worry. We still see a
                       yawning policy gap.


                # ⚓ Opinion_|_How_Europe_and_the_US_Wasted_the_Opportunity
                  Presented_by_the_Covid_and_Climate_Crises⠀⇛


                       The silver lining in the gloomy cloud of the
                       pandemic was the opportunity it gave the West to
                       mend its ways. During 2020, rays of light shone
                       through. The European Union was forced to
                       contemplate a fiscal union. Then, it helped remove
                       Donald Trump from the White House. And a global
                       Green New Deal suddenly appeared less far-fetched.
                       Then 2021 came along and drew the blackout
                       curtains.


                # ⚓ ‘Unsettling’:_New_Study_Reveals_Arctic_Ocean_Warming_for
                  Over_a_Century⠀⇛


                       New research published Wednesday revealed the
                       Arctic Ocean has been warming for decades longer
                       than scientists previously understood, raising
                       fresh concerns as the polar region faces the
                       growing threat of a total loss of the seasonal ice
                       that is crucial to the survival of the imperiled
                       marine ecosystem.


                       “We’re talking about the early 1900s, and by then
                       we’ve already been supercharging the atmosphere
                       with carbon dioxide.”


                # § Energy⠀➾


                      # ⚓ Texas_Gas_Companies_Hit_Texas_Consumers_With_‘Whoops
                        You_Froze_To_Death’_Surcharge⠀⇛


                             If you hadn’t noticed, the United States
                             isn’t really prepared for climate change. In
                             part because corporations and disinformation
                             mills have convinced countless Americans a
                             destabilizing climate isn’t actually
                             happening. But also because we were already
                             perpetually underinvesting in our core
                             infrastructure before the symptoms of an
                             unstable climate began to manifest. It’s a
                             massive problem that, as John Oliver
                             highlighted six years ago, doesn’t get the
                             same attention as other pressing issues of
                             the day. You know, like the latest influencer
                             drama or the mortal threat posed by TikTok.


                      # ⚓ The_EPA_Administrator_Visited_Cancer-Causing_Air
                        Pollution_Hot_Spots_Highlighted_by_ProPublica_and
                        Promised_Reforms⠀⇛


                             Two days after ProPublica published a first-
                             of-its-kind analysis of industrial air
                             pollution, the Environmental Protection
                             Agency announced that its administrator,
                             Michael S. Regan, would visit the communities
                             featured in our reporting. During last week’s
                             “Journey to Justice” trip across the South,
                             Regan toured the Houston ship channel, the
                             Louisiana community of Mossville and a
                             stretch of land along the Mississippi River
                             known as Cancer Alley — places that we
                             identified as among the largest hot spots of
                             toxic air pollution in the country.
                             Environmental advocates who hosted several
                             different parts of the tour told ProPublica
                             that they first received calls about the
                             visit in late October, two weeks after we
                             sent the EPA questions about their areas’
                             elevated cancer risk. Longtime residents
                             believed it was the first time that the
                             nation’s top environmental regulator visited
                             Mossville and Cancer Alley.


                             Our investigation exposed significant flaws
                             in how the EPA protects vulnerable
                             neighborhoods from hazardous air pollution.
                             We identified more than a thousand hot spots
                             of cancer-causing air across the country and
                             found that, on average, census tracts where
                             the majority of residents are Black
                             experience more than double the level of
                             cancer risk from toxic air pollution as
                             majority-white tracts.


                      # ⚓ KXL_Pipeline_Company_Exploits_NAFTA_Provision_to_File
                        $15_Billion_Claim_Against_US⠀⇛


                             The Canadian company behind the canceled
                             Keystone XL pipeline filed a formal request
                             for arbitration this week under the North
                             American Free Trade Agreement to seek over
                             $15 billion in economic damages over the
                             Biden administration’s revocation of the
                             cross-border oil project’s permit.


                             In its Monday filing, TC Energy criticizes
                             the permit’s cancellation as “unfair and
                             inequitable” and argues the U.S. government
                             should pay damages for the “regulatory roller
                             coaster” the company endured while seeking to
                             build the pipeline.


                      # ⚓ U.S._to_release_50_million_barrels_of_oil_from
                        reserve_in_move_to_bring_down_prices⠀⇛


                             The U.S. strategic petroleum reserve
                             currently holds more than 600 million barrels
                             of crude in stockpile to ensure supply during
                             unexpected natural disasters or other
                             national security events.


                             The reserves are stored in caverns created in
                             salt domes along the Texas and Louisiana Gulf
                             Coasts.


                             More than 32 million barrels will be released
                             in the next few months, while the other 18
                             million will be an acceleration of the
                             release of barrels that had already been
                             planned beyond that.


                      # ⚓ Hamilton_youth_charged_after_$46M_in_cryptocurrency
                        stolen_from_U.S._resident⠀⇛


                             A Hamilton youth has been charged in the
                             theft of $46 million in cryptocurrency after
                             investigators learned some of it was put
                             toward buying a gaming username.


                             Local police worked with the FBI and U.S.
                             Secret Service to investigate millions in
                             missing currency stolen via what’s known as a
                             SIM swap attack, said Det.-Const. Kenneth
                             Kirkpatrick from Hamilton Police Service’s
                             cybercrimes unit.


                             The three agencies started working together
                             in March 2020 after an American reported the
                             loss.


                # § Wildlife/Nature⠀➾


                      # ⚓ Species_Spotlight:_To_Save_the_Narrow_Sawfish,_First
                        We_Must_Find_Them⠀⇛


          o § Finance⠀➾


                # ⚓ Disaster_Capitalism_‘Hits_New_Heights’_as_Wall_Street
                  Profiteers_Cash_In_on_Recovery_Loans⠀⇛


                       Critics of post-crisis profiteering responded with
                       disgust to new reporting that private financial
                       institutions in the U.S. are taking advantage of
                       the federal government’s failure to respond swiftly
                       to disasters by providing loans—to be repaid, with
                       interest, by taxpayers—to landlords affected by
                       floods, wildfires, and other catastrophes that are
                       growing in frequency and intensity due to the
                       fossil fuel-driven climate emergency.


                       “A few profit and the rest of us pay.”


                # ⚓ CEOs_Are_Blaming_Inflation_for_Price_Hikes_While_Earning
                  Record_Compensation⠀⇛


                # ⚓ Brexit,_Encouraging_European_Companies_to_Move_to_the_UK?⠀⇛


                       As early as the time when BoJo was a Brussels-based
                       journalist covering the EU he started to lie about
                       it, saying the eurocrats wanted to ban “curvy
                       bananas”, and that their compensation was generous
                       enough for them to live in luxury chateaus in the
                       countryside around Brussels.


                       Some of his former colleagues suggest that BoJo was
                       a Remainer until he realized this was not the Tory
                       route leading to the prime ministership, and
                       switched his position accordingly. Some of BoJo’s
                       journalism confirms this impression, but it’s also
                       possible that the opportunistic BoJo was merely
                       hedging his bets.


                # ⚓ Dollar_Tree_CEO—Who_Made_Over_$10_Million_Last_Year—Blames
                  Inflation_for_Price_Hike_to_$1.25⠀⇛


                       Dollar Tree CEO Michael Witynski—who raked in
                       around $11 million in total compensation last
                       year—announced Tuesday that his company is raising
                       prices to $1.25 at stores across the United States,
                       pointing to the current “inflationary environment.”


                       “Corporations are using the excuse of inflation to
                       raise prices and make fatter profits.”


                # ⚓ Jorge_Arreaza_on_Venezuela_Recovering_from_Sanctions_In_New
                  Post-Petro_Economic_Plan⠀⇛


                # ⚓ GOP_Offers_Taste_of_2022_Attack_Ads_If_Democrats_Approve
                  Tax_Cut_for_Millionaires⠀⇛


                       The top Republican on the House Budget Committee
                       offered an early look this week at the kind of
                       attack ad that Democrats are sure to face ahead of
                       the crucial midterm elections if they ignore
                       progressives’ warnings and keep a large tax cut for
                       wealthy households in their Build Back Better
                       package.


                       “At a time of massive income inequality, we must
                       increase taxes on the 1%, not give them huge tax
                       breaks.”


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ How_to_Take_Over_a_Country⠀⇛


                       The country is sinking into political quicksand,
                       living in two worlds: the fantasyland of Donald
                       Trump, who insists he won reelection, enveloped in
                       the Big Lie by his loyalists who have set his fable
                       in concrete, and the reality in which President Joe
                       Biden and his Democrats have passed trillions of
                       dollars in legislation intended to help all
                       Americans live better lives.


                       Extracting the country from the insidious menace of
                       an all-encompassing far-right packaging of lies and
                       manufactured cultural bull will be difficult, if
                       not impossible, unless Republicans wake up and
                       sideline Trump. The Republican strategy seems
                       intended to stir anger, resentment and bitterness
                       against Biden and “radical liberals” to attract
                       voters to their base in order to retake power.


                # ⚓ Democrats:_Giving_Up_on_the_White_Working_Class_Would_be
                  Disastrous⠀⇛


                       For some Democratic pundits—notably Thomas Frank
                       and James Carville—winning over these voters is the
                       party’s best chance at future electoral successes.
                       Frank, best known as the author of Listen, Liberal
                       and What’s the Matter with Kansas?, believes there
                       are two impulses at war in “Leftland.” One is that
                       Democrats need to build a broad coalition of
                       working class people. (The other impulse, he says,
                       is “I’m better than you.”)


                       For others—Steve Phillips and Sally Kohn among
                       them—appealing to white working class voters is a
                       waste of time and would be akin to making a deal
                       with the devil.


                # ⚓ Jury_Finds_“Unite_the_Right”_Organizers_Liable_for_$25.3
                  Million_in_Damages⠀⇛


                # ⚓ UN_Human_Rights_Envoy_Slams_Racist_Voter_Suppression_in
                  US⠀⇛


                # ⚓ Opinion_|_Unaccountable_Institutions_Are_Ruining
                  Democracy—and_Your_Life⠀⇛


                       Three centers of power increasingly dominate our
                       lives, but are less and less accountable: The
                       Supreme Court, the Federal Reserve, and Big Tech. 


                # ⚓ US_Legal_Observers_Report_‘Balanced_and_Transparent’
                  Election_Process_in_Venezuela⠀⇛


                       A delegation of observers from a New York City-
                       based progressive legal group on Wednesday pushed
                       back against the Biden administration’s claims
                       about Venezuela’s recent regional elections in
                       which allies of President Nicolás Maduro’s
                       socialist party were largely victorious.


                       “We observed a balanced and transparent voting
                       process which voters expressed confidence in.”


                # ⚓ The_Secret_Speech_of_Jen_Psaki⠀⇛


                       White House Press Secretary Jen Psaki reaffirmed
                       Joe Biden’s stance that he was not an “old friend”
                       of Xi Jinping before the summit between the two
                       leaders last week.  This was big news. And the
                       media play it received was quite disturbing to
                       Psaki, as it turns out.


                       Seeking to clarify matters, she wrote a statement
                       to read to the press corps explaining her stance on
                       China-US relations.  She planned to read it to the
                       press during Thanksgiving week. Presidential
                       advisors, however, put the kabosh on the statement
                       – and reportedly tried to put the kabosh on Psaki
                       herself after they saw her draft.  From reliable
                       sources, who asked to remain anonymous because of
                       the sensitivity of the situation, we have obtained
                       portions of the statement which has come to be
                       known among Washington insiders as the PPP, Psaki’s
                       Psecret Pspeech. 


                # ⚓ Opinion_|_How_Deep_Canvassing_by_Progressives_Can_Change
                  Rural_Politics_in_the_US⠀⇛


                       It’s Nov. 1, and Precious Cogwell is canvassing in
                       Alamance County, North Carolina, encouraging people
                       to go to the polls the next day. No one answers
                       Cogwell’s knock at the front door of a brick ranch
                       house, but she spies a man around back and walks
                       over, a stack of voter guides in her arms.


                # ⚓ Opinion_|_We_Do_Exist:_Why_the_Palestinian_Voice_Should
                  Take_Center_Stage⠀⇛


                       At a recent New York event, the President of the
                       Foreign Press Association Ian Williams declared,
                       before an approving audience, that it is time “to
                       reclaim the narrative on Palestine”.


                # ⚓ Raids,_Arrests_and_Death_Threats:_Israel’s_Strategy_of
                  Silencing_Human_Rights_Defenders⠀⇛


                       The Palestinian organizations included in the
                       Israeli order are Addameer Prisoner Support and
                       Human Rights, Al-Haq, the Bisan Center for Research
                       and Development, Defense for Children Palestine,
                       Union of Agricultural Work Committees (UAWC) and
                       the Union of Palestinian Women’s Committees.


                       Considering the significance of these organizations
                       in Palestine and their global networks among like-
                       minded civil society organizations, the Israeli
                       decision provoked a public outcry. One of the many
                       statements of condemnation was a joint statement by
                       rights groups, Amnesty International (AI) and Human
                       Rights Watch (HRW), in which they called Gantz’s
                       move an “appalling and unjust decision”, which
                       represents “an attack by the Israeli government on
                       the international human rights movement.”


                # ⚓ Noam_Chomsky_Warns_of_‘Very_Dangerous’_US_Antagonism_of
                  China⠀⇛


                       Linguist and dissident Noam Chomsky this week
                       condemned the Biden administration’s aggressive
                       anti-China foreign policy, while dismissing the
                       imperialist notion that Beijing poses a threat to
                       the United States and urging a departure from the
                       “provocation” that for decades has characterized
                       the U.S. stance toward the rising giant.


                       “There is constant talk about what is called the
                       China threat… What exactly is the China threat?”


                # ⚓ An_activist_radio_host_has_put_his_life_on_the_line_for
                  voting_rights._Biden,_it’s_your_move⠀⇛


                       Legendary Black radio host Joe Madison is two weeks
                       into a hunger strike that could become a risk to
                       his health. Madison, 72, is doing it for one
                       reason: To pressure President Joe Biden and
                       Democrats in Congress to pass voting rights
                       legislation as the GOP actively works to restrict
                       ballot access.


                       As Madison told CNN’s Don Lemon on Friday, “Just as
                       food is essential for the existence of life, voting
                       is essential for the existence of democracy.”


          o § Censorship/Free Speech⠀➾


                # ⚓ Content_Moderation_Case_Studies:_Facebook_Suspends_Account
                  For_Showing_Topless_Aboriginal_Women_(2016)⠀⇛


                       Summary: Facebook’s challenges of dealing with
                       content moderation around “nudity” have
                       been covered many times, but part of the reason the
                       discussion comes up so often is that there are so
                       many scenarios to consider that it is difficult to
                       create policies that cover them all.


                # ⚓ Mobile_internet_disrupted_in_Burkina_Faso_after_shooting_of
                  protesters⠀⇛


                       Network data from NetBlocks confirm a significant
                       disruption to mobile internet connectivity in
                       Burkina Faso from around 10:30 p.m. UTC Saturday 20
                       November 2021 affecting cellular service. The
                       incident comes amid political unrest and the
                       shooting of protesters by a French military convoy
                       on Saturday.


                       Metrics corroborate user reports of mobile data
                       disruptions on providers including Orange
                       (AS37577). The data blackout is ongoing as of
                       Monday and is likely to limit the free flow of
                       information online and suppress news coverage of
                       events on the ground.


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


                # ⚓ Legal_Wrangle_Between_NYT_and_O’Keefe_Puts_Press_Freedom_at
                  Risk⠀⇛


                       Yet Sobchak’s absolutism was overstated. The line
                       is a reference to the famous Pentagon Papers case
                       of 1971, in which the Supreme Court ruled that the
                       federal government could not restrain the New York
                       Times and the Washington Post ahead of time from
                       publishing classified documents pertaining to the
                       Vietnam War.


                # ⚓ Lawmakers_Ask_French_Government_To_Grant_Asylum_To
                  Assange⠀⇛


                       Assange’s father, John Shipton, acknowledged this
                       support, recalling that WikiLeaks also published
                       the U.S. National Security Agency (NSA) and Central
                       Intelligence Agency (CIA) spying on French
                       Presidents Jacques Chirac (1995-2007), Nicolas
                       Sarkozy (2007-2012), and François Hollande (2012-
                       2017).


                # ⚓ Rwandan_online_video_reporter_given_“absurd”_seven-year-
                  jail_sentence⠀⇛


                       Also known as Cyuma Hassan, Niyonsenga had enjoyed
                       eight months of freedom after his initial acquittal
                       before being returned to prison following the high
                       court’s decision on 11 November to convict him on
                       charges of assault, obstructing police officers and
                       practicing journalism without a press card.


                       Niyonsenga’s problems date back to 15 April 2020,
                       when he was arrested while on his way to cover the
                       impact of the government’s coronavirus lockdown,
                       and was charged with contravening the lockdown and
                       showing false press cards to the police.


                # ⚓ Norwegian_TV_journalists_arrested_in_Qatar⠀⇛


                       He confirms that NRK is still waiting for an
                       explaination on why the two journalists got
                       arrested.


                # ⚓ Norway_criticises_Qatar_over_arrest_of_Norwegian
                  journalists⠀⇛


                       Ekeland and Ghorbani were released on Tuesday and
                       left the country shortly after, NRK said. Their
                       equipment had been confiscated however, the
                       broadcaster added. The reporters arrived in Oslo
                       earlier on Wednesday.


                # ⚓ Khashoggi_Fiancé_Urges_Justin_Bieber_to_Cancel_Saudi_Arabia
                  Concert⠀⇛


                       Hatice Cengiz published her opinion piece in The
                       Washington Post, for whom Jamal Khashoggi was a
                       contributing columnist. Khashoggi was brutally
                       murdered at a Saudi consulate in Istanbul, by men
                       acting on the orders of Crown Prince Mohammed bin
                       Salman.


                       “Cancel your December 5 performance in Saudi
                       Arabia,” Cengiz writes. “This is a unique
                       opportunity to send a powerful message to the world
                       that your name and talent will not be used to
                       restore the reputation of a regime that kills its
                       critics.”


                       “Please know that your invitation to participate in
                       a concert in Jiddah comes directly from MBS, as the
                       crown prince is known. Nothing of significance
                       happens in Saudi Arabia without his consent, and
                       certainly not an event as important and flashy as
                       this. Your face is even featured on the event’s
                       website with his – the executioner of my fiance,
                       Jamal.”


          o § Civil Rights/Policing⠀➾


                # ⚓ Our_Inflexible,_Outdated_Constitution⠀⇛


                       From the electoral college to gun rights to the
                       hilariously archaic right to refuse to quarter
                       troops in your home and the $20 threshold for a
                       civil jury trial, the U.S. Constitution contains
                       many head-scratching relics of an America we
                       wouldn’t recognize. Living in the age of the
                       musket, James Madison might not be so quick to
                       argue for legalizing the AR-15, assuming that a
                       well-regulated state militia was still a thing.


                       A work of genius the U.S. Constitution is not. It
                       is almost impossible to amend—it is in fact the
                       hardest to amend in the world. The immutability of
                       the document is highlighted by the inability of the
                       world’s most powerful democracy to enshrine a right
                       as basic as gender equality, a principle that the
                       vast majority of other countries, even
                       dictatorships and authoritarian regimes, have
                       managed to include (at least in theory) in their
                       founding charters.


                # ⚓ Those_Whiny_Nazis_Are_Now_Broke_Nazis,_Too⠀⇛


                       It took three days of deliberation, on top of four
                       weeks of ugly, sometimes racist arguments, for a
                       federal jury in Charlottesville, Va., to find that
                       the loathsome white supremacists who organized the
                       2017 Unite the Right rally were indeed loathsome
                       and would have to pay more than $26 million in
                       damages to nine plaintiffs because of their
                       conspiracy to commit violence. The jury deadlocked
                       on two counts of violating federal civil rights
                       law, and instead used a Virginia state law to reach
                       their verdict, but the plaintiffs’ attorneys were
                       jubilant nonetheless. “It’s a resounding victory
                       for our plaintiffs,” Amy Spitalnick, the executive
                       director of Integrity First for America, told me,
                       sitting in the Charlottesville airport on her way
                       home for what should be a happy Thanksgiving.


                # ⚓ No_Immunity_For_Cops_Who_Used_A_Field_Drug_Test_To_Turn
                  Stress_Ball_Sand_Into_Cocaine⠀⇛


                       Getting probable cause is easy, especially when you
                       have accomplices. Law enforcement loves drug dogs,
                       which give them the permission they need to engage
                       in warrantless searches. All a dog has to do is
                       “alert”… or almost “alert”… or be presented in
                       sworn testimony as feeling ways about an odor.
                       Permission obtained. Searches permitted.


                # ⚓ Most_Americans_Look_Favorably_on_Global_Governance⠀⇛


                       This approval of global governance is especially
                       striking in the case of the United Nations. A
                       February 2020 Gallup poll reported that 64 percent
                       of U.S. respondents wanted the UN to play a leading
                       or a major role in world affairs. Similarly, a Pew
                       Research Center poll that summer found that 62
                       percent of Americans had a positive view of the
                       world organization, compared to 31 percent with a
                       negative one. Respondents gave the UN particularly
                       high ratings for promoting peace (72 percent) and
                       promoting human rights (70 percent), while also
                       according it positive ratings for promoting
                       economic development, taking action on climate
                       change and infectious diseases, and caring about
                       the needs of ordinary people.


                       The strong support for the United Nations has
                       continued during 2021. A survey done in early
                       September by Public Opinion Strategies and Hart
                       Research Associates found that 84 percent of U.S.
                       respondents believed it important for the United
                       States to maintain an active role in the UN, that
                       69 percent viewed the UN as a relevant organization
                       needed in the world today, and that 63 percent
                       favored resuming payment of U.S. dues to the UN
                       (which the Trump administration had halted).
                       Although the favorable rating of the UN dropped
                       somewhat (to 56 percent) from the poll’s finding
                       the preceding year, the unfavorable rating also
                       dropped (to 26 percent), leaving the global body
                       with an approval ratio among Americans of more than
                       two to one.


                # ⚓ Uninformed_Juries_Produce_Incorrect_Outcomes⠀⇛


                       I was in my early thirties when I reflected upon
                       this wisdom when performing part of his eulogy. It
                       was horrible legal advice, but I know it saved my
                       soul.


                       The mistakes I made as a teenager have informed my
                       whole life’s purpose. My doctoral dissertation, on
                       forgiveness, would not have been written if I had
                       not accounted for my own moral failings.


                # ⚓ Dramatic_Video_Shows_Militarized_Canadian_Police_Raid
                  Wet’suwet’en_Land_Defenders_&_Journalists⠀⇛


                       We feature dramatic video footage just released
                       that shows a violent raid Friday by Canadian
                       federal police on one of the camps set up to keep
                       Coastal GasLink out of sovereign Indigenous
                       territory. Fifteen people in total were arrested,
                       including two journalists. Wet’suwet’en land
                       defender Sleydo’, also known as Molly Wickham, has
                       now been released. The new footage was filmed by
                       documentary filmmaker Michael Toledano, who was
                       also just released. The raid ended a 56-day
                       blockade of the drilling site. The 400-mile
                       pipeline within Wet’suwet’en land violates both
                       Indigenous and Canadian laws.


                # ⚓ “Furious_and_Disgusted”:_Teen_Survivor_Speaks_Out_After
                  Wealthy_White_Serial_Rapist_Gets_Probation⠀⇛


                       The survivor of a serial rapist who received
                       probation joins us to speak out after a New York
                       judge sparked international outrage when he ruled
                       it is inappropriate to jail the man who attacked
                       her. Christopher Belter pleaded guilty to raping
                       and sexually assaulting her along with three other
                       teenage girls age 15 and 16, but he will avoid
                       serving time in prison, and instead receive 8 years
                       of probation. Belter is white, and from a prominent
                       family who lives in a wealthy neighborhood near
                       Niagara Falls. “This sentencing is telling rapists
                       it’s OK to rape and telling victims that there’s no
                       point in coming forward,” says Mara. Her lawyer
                       Steven Cohen of the HoganWillig law firm notes a
                       non-white defendant who pleaded guilty to these
                       crimes would “absolutely and appropriately be in
                       prison.”


                # ⚓ Protest_Song_Of_The_Week:_‘Colonizer’_By_Tanya_Tagaq⠀⇛


                       The following article was originally published at
                       Ongoing History Of Protest Music.The latest single
                       from Canadian indigenous throat singer Tanya
                       Tagaq’s forthcoming album, “Tongues,” is about
                       accountability. “Oh, you’re guilty,” she sings.
                       “It’s not a question,” a press release from her
                       states.“Tongues” will be released on March 11,
                       2022, and it “speaks not to horrors and crisis, as
                       previous Tanya Tagaq albums wordlessly, powerfully
                       encircled, but directly of these things.” She says
                       the album is Tagaq at “her most explicit and
                       specific.” The music is a balance of “industrial,
                       electronic sounds with poetic passages from Tagaq’s
                       bestselling mytho-biography, Split
                       Tooth.”“Colonizer” comes from Tagaq’s improvised
                       live show with Nanook of the North in
                       Manchester,which overlooks New York City’s Columbus
                       Circle. The tune serves as a response to Tagaq’s
                       performing inboth visible and symbolic colonial
                       spaces.Tagaq also released a second version,
                       “Colonizer (Tundra Mix),” which will appear on the
                       album.This mix is a collaboration with producers
                       Saul Williams and Gonjasufi. It is starker andslow-
                       building yet well suited to the song’s theme.“These
                       two mixes of ‘Colonizer’ are so different, but we
                       liked them both equally,” Tagaq wrote
                       onTwitter, describing both versions as “a
                       reflection on accountability and action.”Tagaq’s
                       album is an invitation to listeners to “join her in
                       a personal victory over colonization, over those
                       who take without consent.”Listen to both versions
                       of “Colonizer”:


                # ⚓ Opinion_|_Democrats_May_Deliver_Some_Temporary_Relief_for
                  Immigrants—But_Fight_Must_Continue⠀⇛


                       Following months of sustained protests by immigrant
                       rights advocates, the House of Representatives has
                       finally passed its version of the Build Back Better
                       Act, and with it, a mixed bag of relief provisions
                       for millions of undocumented immigrants.


                # ⚓ Black_Women_Matter⠀⇛


                # ⚓ South_Dakota_Supreme_Court_Kills_Recreational_Marijuana_Law
                  Approved_by_Voters⠀⇛


                       The South Dakota Supreme Court on Wednesday upheld
                       a lower court’s ruling in striking down a voter-
                       approved measure that would have legalized
                       recreational marijuana.


                       “Legalization opponents… are now petitioning the
                       courts to overturn the will of the people.”


                # ⚓ Does_Biden’s_Lower_Approval_Rating_Mean_Democrats_Should
                  ‘Move_to_the_Center’?⠀⇛


                       Recent polls show that President Joe Biden’s
                       approval rating has declined significantly since he
                       took office.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ Company_Promises_‘Seamless_Parking_Experience’_In_Exchange
                  For_The_Permission_To_Track_App_Users_All_Over_The_Internet⠀⇛


                       Paying for parking should be simple. A driver
                       exchanges money for space and time. End of
                       discussion.


                # ⚓ Biden_FCC_Green_Lights_Yet_More_Telecom_Consolidation_With
                  Verizon_Tracfone_Merger⠀⇛


                       For literally 30 years telecom regulators have,
                       with the occasional rare exception, rubber stamped
                       a steady parade of mergers, resulting in a
                       consolidated, less competitive overall market. The
                       end result of these decisions are everywhere, from
                       terrible customer service and high prices, to
                       routine apathy to consumer privacy and spotty
                       overall telecom coverage. And while regulators
                       occasionally affix merger conditions designed to
                       limit these harms, these conditions are usually
                       either pathetic (often because they’re volunteered
                       by the companies themselves) or they’re just not
                       enforced in any meaningful capacity (outside of the
                       rare and laughable fine).


          o § Digital Restrictions (DRM)⠀➾


                # ⚓ The_Next_‘Elder_Scrolls’_Game_Will_Be_A_PC,_Xbox
                  Exclusive⠀⇛


                       Almost exactly a year ago, Microsoft acquired
                       Zenimax Media, a parent company for several video
                       game publishers, including Bethesda. When that
                       occurred, some sizable percentage of the gaming
                       community asked the immediate and obvious question:
                       does this mean games from Bethesda and others would
                       be Microsoft exclusives? Xbox chief Phil Spencer
                       was the first to weigh in on the question by giving
                       a total non-answer.


          o § Monopolies⠀➾


                # § Patents⠀➾


                      # ⚓ Why_Are_Drug_Prices_So_High?_Because_Asshole_McKinsey
                        Consultants_Figure_Out_Ways_To_Re-Patent_The_Same_Drugs
                        Over_And_Over⠀⇛


                             The House Oversight Committee recently
                             launched an investigation into the giant
                             consulting firm McKinsey, and its role in
                             inflating drug prices as well as pushing
                             opioids at every opportunity.


                      # ⚓ Eyes_on_Trade:_Rethinking_Trade_–_Season_1_Episode
                        42:_MC12,_Part_1:_Danger_and_Opportunity_at_the_12th
                        WTO_Ministerial⠀⇛


                             LINKS: MC12 Global Call to Action 3 Million
                             TRIPS Petitions Delivered to President Biden
                             Senators Sanders, Warren, Baldwin and Brown
                             call on Biden to Push for TRIPS Waiver at
                             MC12 Reuters: Activists Urge Biden to Push
                             for Intellectual Property Waiver…


                # § Copyrights⠀➾


                      # ⚓ FitGirl_Game_Repacker_May_Be_The_Most_Productive
                        Pirate_Online_Today⠀⇛


                             FitGirl is best known online for “repack”
                             releases that allow people to download
                             pirated videogames using minimal bandwidth.
                             Aside from the massive popularity of the
                             repacker’s website is the sheer volume of
                             output from what is believed to be a one-
                             person team. In October, FitGirl repacked 157
                             games, around five videogames every single
                             day.


                      # ⚓ Stream-Ripping_Site_Yout.com_Blocked_in_Brazil
                        Following_Criminal_Complaint⠀⇛


                             Popular stream-ripping site Yout.com is being
                             targeted in a criminal complaint in Brazil.
                             As part of the proceeding, local ISPs have
                             blocked access to the site, which hasn’t yet
                             had a chance to defend itself in court. Under
                             Brazilian law, Yout’s operator Johnathan
                             Nader risks a multi-year prison sentence but
                             both sides could work out a deal as well.


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