𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Monday, August 02, 2021
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Generated Tue 3 Aug 02:40:18 BST 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/2021/08/02/


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

⦿ It Almost Feels Like Battistelli Still Runs the EPO (by Extension/Proxy) | Techrights

⦿ Barrier and Synergy Can Work Together, Connecting Lots of Different Machines | Techrights

⦿ [Meme]  Vichyite Battistelli Committed Crimes and His Buddy António Snubs Courts That Confirm These Are Crimes | Techrights

⦿ Freenode is IRC... in Collapse | Techrights

⦿ IRC Proceedings: Sunday, August 01, 2021 | Techrights

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
		http://techrights.org/2021/08/02/a-mafia-run-office/#comments
		http://techrights.org/2021/08/02/barrier-and-synergy-setup/#comments
		http://techrights.org/2021/08/02/epo-crimes/#comments
		http://techrights.org/2021/08/02/freenode-is-irc/#comments
		http://techrights.org/2021/08/02/irc-log-010821/#comments

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
		http://techrights.org/2021/08/02/fwupd-1-6-2-released/#comments
		http://techrights.org/2021/08/02/linux-5-14-rc4/#comments
		http://techrights.org/2021/08/02/open-science-in-france/#comments

                    ䷩ 𝚕𝚒𝚗𝚎 61

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/08/02/a-mafia-run-office/#comments
    Gemini version at gemini://gemini.techrights.org/2021/08/02/a-mafia-run-office/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 08.02.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


✐ It_Almost_Feels_Like_Battistelli_Still_Runs_the_EPO_(by_Extension/Proxy)⠀✐


Posted in Deception, Europe, Patents at 8:49 am by Dr. Roy Schestowitz


Video_download_link | md5sum 1896f135f9b5c796cc52b36da723895a


http://techrights.org/videos/epo-media-absent.webm


Summary: The “Mafia” that destroyed the EPO is still being put in charge and is
using the EPO for shameless self-promotion; it is never being held accountable,
not even when courts demand remediatory action and staff_seeks_reparations


AN anonymous source told us and showed us that the EPO‘s staff union is
planning action to compel António_Campinos to obey courts and hold Benoît
Battistelli et al accountable for their abuses, which remain untackled. Can a
law school be managed by a criminal? Welcome to France, the true home of
Campinos! Endless harm continues to be caused by Battistelli’s associates and
right now the EPO’s Web site, in its latest “news” item, is boosting
Battistelli’s CEIPI (Campinos and Battistelli swapped seats) as if the EPO is
still being run for or by this guy from the shadows. Towards the end of the
video we also show the_overlapping_agenda.


The EPO cannot move on until it handles or repairs the past. Shutting tightly a
closet with skeletons (while occasionally adding yet more skeletons to it) is
assurance that when the bubble implodes it will be truly devastating. It’s like
a pressure cooker. Nothing at all has been resolved. Campinos has repeatedly
shown that he’s incapable of doing so and he’s still being sort of ‘bossed’ by
the_fits_of_Team_Battistelli. This is terrible, but what’s even more terrible
is the grotesque silence_in_the_media, in effect enabling_the_crimes_and
becoming_passively_complicit. █



                    ䷩ 𝚕𝚒𝚗𝚎 110

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/08/02/barrier-and-synergy-setup/#comments
    Gemini version at gemini://gemini.techrights.org/2021/08/02/barrier-and-synergy-setup/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 08.02.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


✐ Barrier_and_Synergy_Can_Work_Together,_Connecting_Lots_of_Different
Machines⠀✐


Posted in Free/Libre_Software, GNU/Linux at 11:28 am by Dr. Roy Schestowitz


Video_download_link | md5sum 504e3afe6abb01e0c9465ee2ce4eb1d2


http://techrights.org/videos/synergy-and-barrier.webm


Summary: Barrier and Synergy can be configured to work properly in conjunction,
though only provided different port numbers (non-default) are specified; in my
current setup I have two computers to my right, working over Barrier, and two
older ones on the left, working over Synergy; the video explains the setup and
the underlying concepts


SOFTWARE- or network-based KVM (not the kernel_“KVM”) is a wonderful thing with
a_rich_history* and present. For software KVM, in the Free software world there
are several options (outside the realm of it there are dozens!) and the most
famous one is explained in the above video as I’ve used it for over a decade on
many machines and became somewhat of a ‘guru’ at it (out of necessity, I’ve
even built things from source when I had difficulties).


In my current setup I get to control 5 low-cost computers (or 8 screens in
total) with just one keyboard and one mouse, using both barrier and synergy in
conjunction (they’re mostly based on the same code, but the latter, which is
the original, became “Open Core”, whereas the former is now the default in GNU/
Linux distributions because it is Free software).


Here’s Barrier on my main system (the “server” in the context of this setup):


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Barrier_settings⦈_


Here’s Synergy:


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇synergy-settings⦈_


In the video I also mention quicksynergy, but it may be mostly obsolete by now
though older distros still have it in their repository. It makes setup a lot
simpler and faster (hence “quick” in the name). It might be considered obsolete
by now, but it still works. With command line tools it’s also possible to
configure everything to work in the background since startup (no GUIs
required), but the learning curve is steeper. █
___
* According to Wikipedia: “Ibus, a now defunct computer company, secured patent
US5388032,[1] filed May 4, 1993, showing a KVM with a “discriminator” to
connect to multiple computers. The “discriminator” is now known as a KVM
switch.” That’s the source of the name. It is a concept that goes nearly 3
decades back. Many people still don’t know about it and never saw it in action.


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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠉⠙⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⠈⠉⠙⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠙⠛⠛⠟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣩⣉⣏⣀⣹⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⣋⣯⣉⣉⣋⣹⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣻⣻⣛⣛⣻⣿⣛⣛⣛⣿⣿⣿⣿⣿⣿⣟⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⡛⢟⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠿⠿⠿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣶⣶⣶⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⣿⣿⣿⢻⡿⢿⡿⣿⡿⡻⣿⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣷⣷⣿⣶⣾⣶⣷⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⣿⣿⣿⠻⠿⡟⡻⢻⠿⠿⡿⡿⠿⠛⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣵⣽⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⣿⢿⣿⣿⣿⣿⡿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣯⣦⣶⣦⣼⣶⣾⣶⣿⣿⣷⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣿⣿⣿⣭⣉⣿⣿⣬⣬⣿⣿⣿⣭⣽⣥⣭⣯⣮⣯⣭⣽⣿⣯⣿⣯⣻⣿⣿⣿⣮⣯⣭⣭⣭⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⡿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 235

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

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⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 08.02.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


✐ [Meme]_Vichyite_Battistelli_Committed_Crimes_and_His_Buddy_António_Snubs
Courts_That_Confirm_These_Are_Crimes⠀✐


Posted in Courtroom, Europe, Patents at 8:33 am by Dr. Roy Schestowitz


António_Campinos builds on top of Benoît_Battistelli‘s actions to euthanise the
EPO for a quick 'cash_grab'


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


Summary: Staff of the EPO is coming to realise (or reaching acceptance of the
fact) that the spirit_of_Battistelli — not just people_he_left_in_charge_of_the
EPO — dooms the Office and there’s no way out of this mess


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⢿⣿⠟⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⢻⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⠹⢃⡘⠏⣸⡇⣛⠻⡿⢛⡛⢛⠀⣿⣿⠟⣛⠛⣿⢛⡻⠛⠛⢿⣿⡇⢘⠀⣛⢻⡟⢛⠻⣿⣿⡿⢀⢻⠃⠸⣿⢛⡛⢻⠛⣛⡟⣿⢛⣛⢻⣿⣿⠀⡃⢼⡟⣛⡿⢛⡛⢿⠛⣻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣆⣼⣧⣰⣿⣇⣿⣀⣧⣙⣃⣸⣸⣿⣿⣄⣛⣁⣿⣸⣷⣐⣂⣾⣿⣇⣸⣀⣿⣸⣇⣒⣠⣿⣿⣇⣾⣆⣾⣆⣷⣘⣋⣸⣀⣿⣇⣷⣘⣛⣼⣿⣿⣀⣛⣸⣇⣿⣧⣙⣃⣼⣒⣸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⡟⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠟⣩⠉⡟⠩⠍⣯⠹⠋⠟⣩⡋⢽⣿⣿⠋⣭⡙⡏⢩⡍⣿⣿⣿⣿⢿⣿⡏⣀⣼⡿⠿⣿⢿⡿⣿⢿⡿⠿⣿⣽⢿⢻⡟⣦⣏⠡⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣤⣷⣬⣥⣿⣧⣾⣴⣿⣭⣤⣿⣿⣦⣍⣴⣧⣼⣧⣿⣿⣿⡏⢸⡿⠃⢻⣿⠟⢹⣿⠘⡇⢿⠀⡿⠖⠸⡟⠀⢸⠀⢀⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠀⠀⠀⠃⢀⠸⡟⡶⡃⠸⠀⠁⠘⣶⣶⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⠁⠀⠀⠀⠀⠀⢸⠀⠏⣠⠃⠀⠀⠀⠀⢻⣿⠀⠀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠈⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠯⠿⠾⠯⠿⣿⣿⣿
⠀⠀⠀⠀⠈⠇⢀⡚⠲⣰⡶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠙⠝
⢀⠀⠁⠰⠃⡾⣉⣋⢧⠘⡖⠻⡀⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡀⠀⢀⠀⢀⢀⠀⡄⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣀⠀⠐⣆⣶⣆
⠁⠀⠀⠀⢠⣉⣛⠛⠊⣰⠁⠀⠛⠀⠀⠀⠀⠰⠱⠋⠀⠉⠇⠁⠇⠅⠂⠀⠧⠪⠅⢰⠃⠥⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡇⣆⢶⢰⣷⣴⣠⢰⡤⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢾⣿⣿⣷⣦⡿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣷⣄⠀⠀⠀⠀⠀⢠⡄⠀⣀⢀⡀⣀⢀⡀⣀⠀⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣚⣿⣷⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠉⠈⠀⠀⢀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⡆⠀⠸⢹⣿⣷⡄⠀⠀⠀⢸⡇⠀⣿⣾⣇⡿⣼⢧⡿⢰⡿⠀⠀⠀⠀⠀⠀⣿⠀⢀⣀⣀⣀⣀⣀⣤⡏⡝⢫⡍⣭⣭⣭⢩⠉⣭⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⣾⣴
⡄⣠⠀⠀⠃⠾⣿⣿⣾⡿⠁⣿⢈⢹⣿⣿⡄⠀⠀⠀⠸⠇⡀⠿⠇⠿⠇⠿⠸⠧⢼⣧⡄⠀⠀⠀⠀⠀⣿⠀⢸⡿⠋⣻⣿⣿⣿⡇⣿⠀⣷⢿⣿⢹⢸⣇⣿⡸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⡆⠀⠀⠀⠀⢁⣸
⠀⠇⠀⠀⠀⠀⠀⠉⠉⢀⡴⢏⣻⢼⣿⣿⣴⠀⣴⢶⡀⣴⣦⢠⣤⢠⣤⢠⡄⣤⡄⣀⢀⣀⡀⠀⠀⠀⣿⠀⠈⠓⣾⣿⣿⠿⡿⠧⠭⠶⢍⣈⢉⣊⠞⣓⠶⣚⡛⣛⡻⣿⣿⡛⠻⠋⠀⠀⠀⠉⠛⠛⢃⡀⠀⠀⣝⣿
⠜⠀⠀⠀⠀⠀⠀⠀⠀⢺⣈⠛⢿⣾⣿⣿⡇⢠⣿⣬⢹⡇⣿⢸⣿⡾⡿⣾⢿⣿⡇⣿⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠉⣹⡇⣿⢸⣯⢹⣼⢿⡯⢸⢽⣰⣿⡞⡇⡅⣿⢮⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠘⠙⠁⡀⢸⣿⣿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣈⠓⠙⠚⠸⠄⠙⠋⠈⠛⠋⠘⠛⠃⠃⠛⠘⠹⠇⠿⠀⠿⠀⠀⠀⠀⣿⢀⣀⣠⡄⢋⣧⠿⠆⠓⣊⣛⣘⣓⣘⠛⠛⠋⣣⣿⣭⣭⣥⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠙⠁⣈⠂⢻⡟⢹⣇⣿⢸⡖⠀⢰⡖⣦⢰⣶⡄⣶⢠⣤⢠⣤⢠⣤⢠⣤⡄⣿⢸⣿⣿⣿⣾⣿⣿⣯⣭⣿⡇⣶⡆⣶⣷⣿⢻⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢁⢸⡇⢸⣯⣿⣸⣏⠀⢸⣇⡤⣿⢻⡇⣿⢸⣿⡟⡿⣼⠷⢘⢿⡅⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠗⠧⠏⠿⠻⠼⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣀⣼⣿⣷⣶⣄⠀⠁⠍⠭⠔⢈⢉⠁⠉⠈⠁⠛⠘⠛⠓⠃⠛⠓⠘⠾⠃⣿⢸⢛⣛⡛⣻⡛⣿⣫⢭⠍⣭⣭⠋⢭⠍⣭⣷⢰⠆⣶⣰⡎⡗⡆⡆⣶⣶⢻⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⢸⡏⡁⡇⣿⢻⣿⢸⣂⣿⢻⢸⢸⡆⣿⣿⢸⣅⣿⡟⡇⡅⢧⠗⠿⣱⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡟⠻⠟⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⠈⠉⢡⣭⣥⣮⣭⣮⣽⣿⣾⣾⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢻⣿⣦⣼⡄⠀⠀⠀⠐⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢤⡄⢸⣿⣿⡇⠀⠀⠀⠀⢈⠿⣷⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠇⣼⣿⣿⡇⠀⠀⢀⣀⣈⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣳⣤⣤⣽⣿⣿⣿⣤⢀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⠏⠁⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠰⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 299

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/08/02/freenode-is-irc/#comments
    Gemini version at gemini://gemini.techrights.org/2021/08/02/freenode-is-irc/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 08.02.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


✐ Freenode_is_IRC…_in_Collapse⠀✐


Posted in Free/Libre_Software at 12:23 pm by Dr. Roy Schestowitz


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


Summary: Freenode is now down to just 13,194 online users, which makes it the
6th biggest IRC network. Months ago it was #1 with almost 6 times as many users
as those below it. The graph above shows what the latest blunder has done
(another massive drop in less than a week, with a poem and the all-time chart
at the very bottom).


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Andrew-Lee⦈_


Freenode is FOSS
So said the BOSS
ROOT gave a TOSS
Wanted us to trust the ToS


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇l0de⦈_


Onboard came the edgy
It seemed kind of sketchy
Database down with the wedgie
IRC.com is fund-hedgy


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇bagira⦈_


No more anon access
Users and channels gettin’ nervous
A “RITUAL DEFAMATION” thesis
But self-harm being the Nemesis


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


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⣶⢰⣶⢰⣶⢰⣶⢰⣶⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣶⡆⠀⠀
⠀⠀⠀⠀⠀⠀⣸⡛⣸⡛⣸⣿⣸⣿⣸⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⣬⣿⣬⣿⣈⡹⣽⠿⣽⣿⣽⣿⣿⠿⣽⠻⣽⢻⣽⣿⣽⣿⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣿⣯⣿⣯⣿⣯⣿⣯⣿⣯⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⣼⣿⣽⣿⣽⣷⣉⣷⠙⡛⠹⣛⢃⣧⣁⣷⡙⣧⠛⡙⡛⠻⣻⣿⣻⣿⡟⡛⡟⡻⡿⠻⡟⡻⡟⡻⣿⣿⣿⣿⡟⡙⡟⡙⡟⡛⡟⡻⡟⡻⣿⣿⣿⣿⡿⢛⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⢻⣿⢻⣿⢻⣿⢻⣿⢻⣿⢻⣿⣿⣿⣿⣿⣿⣿⣷⣿⣥⣷⣉⣭⣛⣩⣣⣷⣥⣷⣥⣷⣥⣷⣥⣷⣭⣭⣉⣭⣽⣿⣽⣷⣼⣷⣽⣷⣽⣷⣭⣤⣭⣭⣵⣇⣳⣧⢻⣯⣿⡟⣿⣿⣿⣿⣿⣟⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣸⣿⣸⣿⣸⣿⣸⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡙⠿⣿⣿⣷⣿⣷⣿⣯⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⣻⣿⣻⣿⣻⣿⣻⣿⣻⣿⣻⣿⣿⣿⣻⣿⣻⣿⣻⣿⣻⣿⣻⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣿⣟⣷⣛⡻⠟⣿⣟⣿⣟⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣭⣭⣭⡅⠀⠀
⠀⠀⠀⠀⠀⠀⠻⠿⠻⠿⠻⠿⠻⠿⠻⠿⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡄⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣹⡟⠋⠃⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⢿⡏⢛⢿⡿⣿⣿⣿
⢻⣿⣾⣿⣿⡿⠟⣿⣿⣻⣿⣿⣿⣿⣿⣿⣮⣃⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠐⢛⣧⣿⣿⢿
⣿⣿⣿⣿⣋⡑⢳⢟⢏⣘⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⠀⠀⢀⢻⣿⣿⠏⢱⣧⢘⣿⣿⣿⣿⣿⡿⣿⣟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣤⠀⢀⣠⣾⠿⣫⣅⡈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⢿⣿⠋⠉⠙⠻⣯⠁⠍⠋⠻⠟⠛⠛⠙⠻⣿⠛⢋⠈⠀⠀⣿⠠⣓⣾⣿⡷⠪⣾⣾⣿⣿⣿⣿⣿⣿⣛⠽⣿⠏⢈⣾⡿⠀⣹⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣷⠟⠋⠁⠀⠀
⣿⣿⣿⣿⠁⢈⣻⣿⣧⠛⠛⠀⠈⠀⠀⠀⠀⠉⡁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣠⣼⣿⣿⣿⣿⡿⠇⢠⠋⠙⣷⣿⣿⣿⣿⣿⣿⣰⠇⢀⠘⡋⠁⠺⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⠙⠃⠀⠀⠀⠀
⢻⣿⡿⡟⣧⣤⡨⣿⣿⣀⡀⠠⡌⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⣶⣸⡟⠋⣺⣧⣥⣤⣄⣀⡀⠀⢀⣴⣥⣾⣷⣿⣽⣿⣿⣟⢻⣀⠂⣨⣤⣦⣀⣀⠉⠉⠛⢻⣿⣿⣿⣿⣿⣿⣿⡆⡃⠀⠀⣴⣶⣦⡤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⡀⠐⢄⠁⠀⠀⠀⠀⠀⠀⠀⣜⠁⠀⠀⠀⢈⣼⡏⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡎⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣀⣴⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇⠉⢦⣼⡧⢠⣾⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⡶⠼⠀⢀⣶⡾⣿⣿⣿⡿⠇⠀⠀⠀⠉⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠷⢸⣿⣏⣿⣿⣿⣿⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠠⣿⣿⣿⣿⣿⣷⡀⢸⣿⣿⣿⣛⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⢉⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠁⣠⣶⠀⠀⠀⠀⠀⠀⠀⣯⣿⣿⣿⣟⡛⣿⣶⡆⣼⣿⣿⡝⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⢀⡿⠿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡋⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣾⣿⣿⣿⡯⡤⠀⣼⣿⣿⣿⣿⣿⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣾⣿⣾⡏⢻⣿⡇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠼⢿⣄⠙⢺⣿⣿⣷⡌⠹⣿⣿⠛⢋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣾⣿⣿⣿⣿⣿⢻⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡛⠛⠛⠀⠈⣿⡇⣼⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⡋⠿⠋⠀⠀⠘⢿⣿⣾⣿⣿⣿⣷⡀⣹⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠸⠛⢿⣿⣿⣿⡇⢸⣿⣿⢷⣤⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡧⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⠃⠀⠀⠀⠀⠀⣾⣿⣿⣿⣦⣿⣿⠟⠋⠋⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠒⠀⣾⣆⢻⣿⣿⣿⣶⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠷⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⢿⣿⣿⡟⢹⣏⠀⣤⣾⣿⡟⠀⠀⡀⠀⠀⠀⣿⣿⣿⠇⢘⣻⠏⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣉⣀⣀⡈⢻⣯⡄⢻⣿⡿⠋⠙⠟⢋⣉⣀⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠛⠛⠋⡋⣫⠛⠀⣸⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣿⠿⠿⠀⣿⡿⠀⠀⠀⢀⣤⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣇⠀⣤⣤⣤⣤⣄⠀⣤⣤⣼⣿⣿⢠⣤⣄⣤⢀⣤⣤⣤⣄⢠⣤⡄⢠⣤⡄⣤⣤⠀⠀⠂⠈⠈⠀⠀⠀⢸⣿⣿⣿⣿⡿⠃⠀⠀⢨⠀⠀⠐⠂⡀⣄⠀⣿⠁⠀⣠⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡏⣿⣿⠀⣿⣿⡇⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⠿⢸⣿⣇⣿⣿⡆⣿⣷⣼⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀⢀⢡⠸⣿⣿⣿⠟⠁⠀⡀⠀⠸⠀⠀⠀⢠⢠⠀⠀⢿⠀⣰⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣧⣿⣿⡄⣿⣿⡇⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⠀⢸⣿⡏⢩⣭⡅⢿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠈⢂⠂⡿⠋⠁⠀⠀⡰⠡⠁⠀⠀⠀⠀⠆⡌⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡏⢹⣿⡇⣿⣿⡇⣿⣿⠀⣿⣿⣼⣿⣿⢸⣿⣿⠀⠸⣿⣧⣾⡿⠃⢸⣿⣿⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢃⠂⠀⠀⠀⠀⠐⠸⠀⠀⠀⠈⠛⠙⠉⠁⠀⠀⠀
⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡤⢀⠀⠀⠀⠀⠀⠀⣤⡤⢤⣤⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⣤⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠌⠀⠀⠀⠀⠠⢠⠃⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠀
⢿⣿⣶⣿⣿⣿⡛⠉⠛⣿⣿⠋⣴⣿⣿⣿⡆⠴⠞⠀⠁⣦⣴⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠙⣿⣿⣿⣿⡄⠀⠀⠀⣱⣦⣄⠀⠀⠀⠀⡘⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀
⠈⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣰⣿⣿⣿⣿⣷⣦⡀⠀⠀⣿⣿⠀⠀⣴⣾⢿⣶⡄⢠⣶⡿⣷⣦⡀⠀⠀⠀⠀⠁⠀⠸⣿⣿⣿⡄⠀⠀⠀⠼⢿⣿⣶⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡂⣰⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⣿⣿⠀⠀⣿⣿⣼⣿⣿⢸⣿⣧⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣆⠀⠀⠀⠀⠻⢿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢻⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⣠⡄⠀⠀⣿⣿⣀⡀⣿⣿⢰⣶⣶⢸⣿⡇⢰⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣆⠀⠀⠀⠀⠀⠈⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠛⠀⢸⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠻⣿⡄⠀⠿⠿⠿⠇⠛⠿⠾⠿⠃⠈⠻⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡞
⠀⠀⠰⠀⣸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡄⠀⠀⠀⠀⣿⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣼⣿⣶⡄⠀⠀⣿⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⣽⣉⣻⣏⣉⣉⣉⣤⢀⣾⣿⣿⣿⡇⠀⠀⢿⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣽⣿⠋⢇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⡿⢿⣿⢿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠠⠚⢻⣀⣿⣿⣿
⣿⣿⣿⣿⣟⡟⣻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣟⣌⠀⢀⢻⣿⣯⠏⢱⣿⡻⣿⣿⣿⣟⣿⣿⣿⣟⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⣀⣀⣾⣿⣿⡏⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠙⢻⣯⠍⠩⠋⠻⡟⠛⠛⠛⠻⣿⠛⢋⠈⠀⠈⣿⠢⣓⣾⣿⡷⢩⣾⣾⣿⣿⣿⣿⣿⣿⣟⣿⣿⠃⢉⣾⣿⢀⣿⣿⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡿⠛⠉⠉
⣿⣿⣿⣿⠋⢸⣿⣿⣿⠿⠋⠀⠈⠀⠀⠀⠀⠉⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⣻⣤⣼⣿⣿⡿⠿⠿⠃⢰⠁⠙⣿⣿⣿⣿⣿⡿⣿⣱⠇⣀⠘⡛⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡏⠛⠛⠃⠀⠀
⣻⣿⣿⣿⣷⣦⣸⣿⣿⣄⣀⢰⡌⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠠⠄⢠⣼⣶⣿⣿⡿⣛⣁⣀⣀⣀⡀⠀⠀⣠⣼⣵⣿⣷⣿⣽⣿⣿⣿⣻⣀⡆⣰⣿⣿⣷⣤⣤⣈⠙⢿⣿⣿⣿⣾⣿⣿⣿⣿⢟⠿⠄⠀⢀⣴⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⢸⡸⠇⠀⠀⠀⠀⣀⠀⠀⢸⠀⠀⠀⠈⠉⣹⡿⢸⣼⣿⣿⣿⣿⣿⣿⣿⣷⡟⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠉⢿⣿⣿⣿⣿⣿⡇⠚⠀⠐⣠⣾⡥⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣶⣿⣾⣀⣐⣾⡾⠋⠉⠁⠀⠀⠀⠀⢀⠞⠻⠃⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⢹⣿⣏⣿⣿⣿⠟⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢠⣿⣿⣿⣿⣿⣷⠀⠀⠀⣻⣿⣿⣟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⣿⣿⣿⣿⡟⠃⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⢻⡷⣶⠤⠘⣿⣿⡹⢟⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⠐⠋⢿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢠⣾⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⠙⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⡿⣿⡿⠀⠀⣸⡟⢻⡿⣿⣷⡀⠀⣈⣿⣿⣟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⠀⣿⣿⣿⠿⣿⡄⠈⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡿⡿⠟⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡷⠘⠓⠀⠈⢻⣿⣄⡉⣿⣿⣧⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢀⣠⣤⣦⡀⠀⠀⠀⠀⢻⣿⣿⣿⣯⣃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡥⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢁⣠⣿⣿⠁⠾⠂⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡏⣴⣿⣿⣿⣿⡷⠀⠀⠀⠀⠈⣿⣿⣿⡿⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠿⠃⠀⠀⠀⠠⠸⣿⣿⣿⣿⣿⣿⣿⡿⠁⣸⣿⣷⣾⣿⣿⡇⠀⠀⢦⡄⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛
⣿⣿⡟⠉⢻⣿⣿⣿⣿⣿⣿⡟⣉⣉⣀⡉⠰⠂⢠⡀⠿⣿⣿⣿⡦⢀⣀⣀⠀⣤⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠂⠋⠉⠉⠍⠵⣿⠀⠀⣿⣿⣿⣿⣿⣿⠇⠀⠀⢸⠀⠐⢤⣿⣿⣿⣿⣿⣿⢿⡿⠉⠁⠀
⣿⣿⣇⠀⣼⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣇⠀⣤⣤⣤⣤⣄⠀⣤⣤⣼⣿⣿⢠⣤⣄⣤⢀⣤⣤⣤⣄⢠⣤⡄⢠⣤⡄⣤⣤⠀⠀⠈⠀⠀⠀⠀⠀⡀⢿⣿⣿⣿⣿⠏⠀⠀⠀⠈⠀⠀⠀⠉⠻⣿⣿⣿⠟⠁⠀⠀⠀⠀
⣷⡈⠋⣸⣿⣿⣿⣿⣿⣿⡏⢸⣿⡏⣿⣿⠀⣿⣿⡇⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⠿⢸⣿⣇⣿⣿⡆⣿⣷⣼⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠐⡐⢸⣿⣿⠛⠁⠀⠀⡆⡀⠀⠀⠀⠀⠐⠰⢿⣿⣧⡀⠀⠀⠀⠀⠀
⠛⢠⣾⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣧⣿⣿⡄⣿⣿⡇⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⠀⢸⣿⡏⢩⣭⡅⢿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⠌⠛⠁⠀⠀⠀⡜⡐⠀⠀⠀⠀⢀⢃⠇⢰⣿⣿⡇⠀⠀⠀⠀⠀
⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⡏⢹⣿⡇⣿⣿⡇⣿⣿⠀⣿⣿⣼⣿⣿⢸⣿⣿⠀⠸⣿⣧⣾⡿⠃⢸⣿⣿⠙⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⢀⠂⠀⠀⢰⢣⠃⠀⠀⠀⠀⡄⡜⠀⢸⣿⣿⡧⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣶⣦⣤⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣴⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠘⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣼⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⡃⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠁⣴⣾⢿⣶⡄⢠⣶⡿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢧⢁⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⣼⣿⣿⢸⣿⣧⣿⣿⡇⠀⠀⠀⠀⠀⠐⠀⠘⢿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣀⡀⣿⣿⢰⣶⣶⢸⣿⡇⢰⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⣿⣥⣤⣤⣀⣉⣙⣿⡷⠀⠀⠀⠀⠀⠀⢀⣾⣿⠀⠿⠿⠿⠇⠛⠿⠾⠿⠃⠈⠻⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣦⣀⣀⣴⣿⣿⣿⡿⢶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⣽⣋⣻⣏⣋⣉⣹⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿
⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⡏⠹⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣁⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠇⠁⠜⠻⣇⣸⣿⣿⡿
⣿⣿⣿⣿⣥⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣤⡀⠀⣚⣿⣿⡿⢩⣾⣷⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⢀⣀⣴⣿⣿⣿⡏⠁
⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⢿⡇⠀⠀⠉⢿⣐⠀⠛⠈⠋⠉⠉⠉⠉⢻⠏⢉⣀⠀⠀⢼⣿⢊⣴⣿⡿⠂⢶⡿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⠁⣴⣿⡎⡸⣿⣿⣿⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⣷⣧⣽⠗⠒
⣿⣿⣿⡇⡈⠞⣿⣿⡟⠛⠀⢀⣀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣻⣦⣿⣿⡿⠿⠿⠏⠐⡏⠀⢻⣿⣿⣿⣿⣿⣿⣿⡶⢃⣀⢛⠙⢼⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⠙⠛⠿⠛⠋⠀
⣿⣿⣿⣿⣿⣦⣿⣿⣷⣤⣾⡇⢘⠷⣤⠀⠀⠀⠂⠀⠀⠀⠀⢱⠀⠒⠰⣶⢿⣿⣿⣿⡿⣋⣀⣀⣀⣀⡀⠀⠀⣴⣵⣾⣿⣿⣮⣿⣿⣿⣿⣿⡶⠀⣀⣷⣿⣿⣍⣉⡙⠿⣿⣿⣿⣷⣿⣿⣿⣿⡿⠛⣷⡦⠄⠀⢀⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡐⣗⣻⡄⠀⠀⣄⡀⢀⣀⣠⣯⠀⠀⠀⠋⠈⣹⡟⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⡌⣿⣿⣿⣿⣿⡿⢿⣿⣿⣗⣀⣠⣿⣿⣿⣿⣿⣿⣻⣷⡈⠻⣿⣿⣿⣿⣿⣯⠙⢑⣠⣴⣾⣷⣾⣭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⢿⣿⣿⣷⣠⣀⣠⠾⠿⠁⢹⣿⣿⣿⣿⣿⣿⣿⡿⠿⠇⢸⣏⣽⣿⣿⠿⣋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢸⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠀⠀⢀⣀⣀⠀⠀⠀⠸⢿⣿⣿⡟⠁⠀⠀⠀⠀⣟⣿⣿⣿⣿⡛⣿⣶⣶⢤⠘⢿⡟⠛⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡘⢛⣛⡋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⢠⣾⣿⣿⣿⡗⠀⠀⠀⠀⠹⣿⣇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠙⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠚⣛⡁⢸⣿⣿⣿⣿⣿⡇⠈⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠃⢠⣿⣿⣿⣿⣿⡛⠋⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⠿⠟⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠋⡵⢀⡄⢠⣿⣿⣿⣿⣿⣿⠃⣴⡿⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠸⣿⣿⣷⣿⣿⠃⠀⠀⠀⠀⠀⠙⠻⠿⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡤⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠉⢹⣿⠃⠸⠿⠿⠁⠀⣽⣿⣿⣿⣿⣿⣾⡏⠀⠀
⣿⡇⠀⢻⣿⣿⣿⣿⣿⠀⣤⣄⠀⠀⢹⣿⣿⣿⡿⠧⠄⠀⠀⠀⠀⠀⡀⠀⠀⣶⠀⠀⠀⠀⠈⠻⣿⣿⡿⠃⠀⠀⠀⠀⠀⢀⣀⠀⠉⢻⣿⣿⣿⣾⡟⢻⣿⣿⣿⣿⣿⡏⠀⠀⢠⣼⠿⠃⣿⣿⣿⣿⣿⡟⢻⢣⠀⠀
⠻⡆⣠⣿⣿⣿⣿⣿⣿⣾⣿⡟⣀⣀⣈⡉⢿⣿⣷⣀⡠⠄⠀⠀⠀⢈⣀⣀⠀⣿⠀⠀⠀⠀⠀⣀⣈⠈⠀⠀⣄⠀⠀⠀⠀⠹⠏⠐⠐⡛⡩⢛⣿⡿⠃⣼⣿⣿⣿⣿⣿⡄⠀⠀⠈⠛⢦⣄⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀
⡆⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣧⠀⣤⣤⣤⣤⣄⠀⣤⣤⣼⣿⣿⢠⣤⣤⣤⢀⣤⣤⣬⣍⢩⣤⡌⢩⣤⡄⣤⣤⠀⠀⠀⠘⠀⠀⠀⠈⠀⡀⢹⣿⣿⣿⣿⠟⠁⠀⠀⡀⡀⠀⠉⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⡏⣿⣿⠀⣿⣿⡇⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⠿⢸⣿⣇⣿⣿⡆⣿⣷⣼⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⡘⢼⣿⣿⡿⠋⠀⠀⡰⠠⠀⠀⠀⠀⢼⣿⣿⣷⠀⠀⠀⠀⠀⠀
⣶⣿⣿⡟⠻⣿⣿⣿⣿⣿⡇⢸⣿⣧⣿⣿⡆⣿⣿⡇⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⠀⢸⣿⡏⢩⣭⡅⢿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣌⠿⠋⠀⠀⠀⢰⢃⠁⠀⠀⠀⠀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣩⣿⣿⠁⠀⣾⣿⣿⣿⣿⠁⣿⣿⡏⢹⣿⡇⣿⣿⡇⣿⣿⠀⣿⣿⣼⣿⣿⢸⣿⣿⠀⠸⣿⣧⣾⡿⠃⢸⣿⣿⠙⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠄⠀⠀⢀⠇⡎⠀⠀⠀⠀⠐⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀
⢹⣷⣾⣷⣾⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠰⣦⣤⣶⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠘⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀
⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣴⠀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠻⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠲⢶⣶⣤⡜⣿⣿⣿⣿⣧⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣴⣾⢿⣶⡄⢠⣶⡿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢼⣿⣿⠀⠙⣿⣿⣿⢻⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣇⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⣼⣿⣿⢸⣿⣧⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣋⣁⠀⠸⣿⡗⠃⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⡀⣿⣿⢰⣶⣶⢸⣿⡇⢰⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⣀⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡀⠿⠿⠿⠇⠻⠿⠾⠿⠃⠈⠻⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡟⢻
⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡄⢀⣀⣄⠀⠀⢀⣴⣿⣿⠟⠀⠀⢀⣶⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣆⣼⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⠃⠀⠀⠀⠘⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣏⠉⣿⣿⣿⣟⣉⣩⡙⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠃⠃⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠻⣿⣿⣿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡏⠉⢡⠿⣿⣹⣿⣿⣿⡿⠟
⣿⣿⣷⣷⣾⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣧⣤⠀⢰⣻⡿⣿⢋⣴⣿⣿⣿⣿⣿⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⢀⠀⢠⣿⣿⣿⣿⠓⠂⣠
⣿⣿⠟⣿⣿⣿⣿⣿⡟⠛⠿⠀⠁⢀⠰⠷⡆⠙⠁⠙⠏⠉⠉⠈⠙⠟⠉⣅⣀⠀⢠⣿⣎⣵⣶⣿⠗⢹⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢡⣾⡟⠀⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣧⡤⠼⣿
⣿⣷⣀⡓⣿⣿⡿⠉⠀⣀⢤⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣿⣷⣾⣿⣿⣿⠟⠟⠁⠚⠁⢘⣿⣿⣿⣿⣿⣿⣯⣷⠛⣀⡘⡋⢣⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠖⠀⢹
⣿⣿⣿⣿⣼⣿⣿⣦⣯⣿⢠⣹⢳⠄⠀⠀⠀⠀⠀⠀⠀⣼⠃⠙⠒⣶⣾⡿⣿⣿⣽⣿⣿⣁⣀⣀⣀⣀⣀⣀⠠⣶⣿⣿⣷⣿⣿⣯⣿⣿⣧⠄⣀⣬⣾⣿⣿⣿⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣠⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢋⢙⣆⠀⠀⣤⣠⣤⣤⣴⣿⣄⠈⠀⠈⠁⠈⢈⣽⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⢿⣿⣿⣿⣄⣀⣀⣮⣿⣿⣿⣿⣿⣿⣶⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣰⣟⣉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠷⠋⠀⠘⢿⣿⣶⣿⣿⣿⣿⣷⣦⣀⣀⣴⣿⡿⠈⣿⣿⣿⠿⣿⣿⣿⡿⠟⠻⠀⣹⣿⣿⠿⢋⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⡀⣿⣿⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠁⠀⢸⣿⣿⣿⣿⣛⣻⣿⣿⣳⣄⡉⠻⢫⣶⣿⣿⣿⣿⣿⣟⣟⠏⢸⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸⣿⢟⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢀⣤⣶⣦⣄⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⠈⣻⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠀⣴⣿⣿⣿⣿⣯⣀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠹⣿⣿⣿⣿⣯⣿⠟⠛⠁⠀⠀⠀⠉⠛⠛⠛⢿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡋⣿⣿⣿⣿⣿⣿⣿⣿⣀⣽⣿⣿
⢿⣿⣿⣿⣿⣿⣿⡅⢸⣿⣿⣿⣿⡿⠿⠋⢁⠀⠀⠀⠀⢿⣿⣿⠿⠿⠿⠿⠄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷⠂⠀⠀⠀⢀⣸⣯⣀⠀⠀⠀⢹⣿⣿⣿⣷⣾⣿⣿⠿⠛⠛⢩⡇⠘⣿⣿⢻⣿⣿⣿⡿⠿⣿⣿⣿⠋⠛⠃
⢀⣿⣿⣿⣿⣿⣿⡇⠘⣿⣿⣿⣿⡿⠻⣿⣿⠁⠀⠀⠀⣸⠋⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⠟⠀⠀⠀⠀⠘⠛⣿⣿⣄⠀⠀⠀⠁⢀⣙⣿⡿⣿⣿⣷⣶⣶⡿⠀⠀⠈⠀⠀⣿⣿⣿⣷⣄⢸⡟⣿⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⠀⢹⣿⡟⣉⣀⣀⡈⠀⠀⠀⠀⢠⣿⠀⣾⠟⢋⣀⣀⠀⠐⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⣄⠀⠀⠀⠀⠹⢿⡿⠿⡟⢟⡿⣻⣿⡿⢀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠤⣤⣿⣿⣿⣿⣿⣿⠇⠉⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣧⠀⣤⣤⣤⣤⣌⠁⣥⣤⣼⣿⣿⢠⣤⣤⣤⢀⣤⣤⣬⣍⢩⣭⡍⢩⣥⡄⣤⣤⠀⠀⠀⠀⠃⠀⠈⠙⠋⠁⢸⣿⣿⣿⣿⣿⠇⠀⠀⠀⡀⠈⣿⣿⣿⣿⠛⡁⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡏⣿⣿⠀⣿⣿⡇⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⠿⢸⣿⣇⣿⣿⡆⣿⣷⣼⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⡘⡌⣿⣿⣿⡿⠅⠀⢠⠀⠀⠀⢰⣿⣿⣿⣿⣈⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⣧⣿⣿⡆⣿⣿⡇⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⠀⢸⣿⡏⢩⣭⡅⢿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⡄⣿⠟⠉⠀⠀⢀⠆⠆⠀⠀⢸⣿⣿⣿⣿⣏⠁⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⣿⣿⡏⢹⣿⡇⣿⣿⡇⣿⣿⠀⣿⣿⣼⣿⣿⢸⣿⣿⠀⠸⣿⣧⣾⡿⠃⢸⣿⣿⠙⣿⣿⡇⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⡀⠀⠀⠀⡎⡜⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠠⠀⠀⠀⣶⣦⣴⣶⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⡇⠀⣿⣿⠀⠀⣴⣾⢿⣶⡄⢠⣶⡿⣷⣦⡀⠀⠀⠀⠀⠂⠀⠘⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⡇⠀⣿⣿⠀⢀⣿⣿⣼⣿⣿⢸⣿⣧⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠋⠀⠀⠀⠀⠠⠀⠀
⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡃⠀⣿⣿⣀⡀⣿⣿⢰⣶⣶⢸⣿⡇⢰⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠿⠟⠋⠉⠁⠀⠿⠿⠿⠇⠻⠿⠾⠿⠃⠈⠻⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀
⠀⢠⣴⣾⣀⣀⡀⣀⣠⣾⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀
⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⠙⣿⣿⣻⣟⣋⣉⡉⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⢿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡈⠂⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠩⠿⢿⣏⣿⣿⣿⣿⠿⠋⠻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡟⡟⠻⠿⣿⣛⠿⡿⢿⣿⣿⢿⠿⢿⣿⣿⣿⠟⠟⠻⢿⣾⣧⣀⣶⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢀⣀⣰⣿⣿⣿⣯⡅⠀⠀⣠⣴⣾
⣿⣿⣿⣿⡟⠻⠉⠉⠁⡀⠰⠎⠛⠛⠈⠁⠈⠏⠈⠄⠀⠀⠙⠁⠰⢦⣤⣠⣾⣿⣿⣿⣿⣯⠹⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⢿⡏⢀⣿⣿⣠⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣯⣶⣖⢺⣿⣿⣿
⣾⢿⣿⣿⡁⢠⣤⡞⢲⣧⠄⠀⣠⣦⠀⠀⠀⠀⢠⣀⢀⣀⢀⣰⣶⣾⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⠀⠻⠿⣿⣿⣿⣿⣿⣾⣟⣩⣦⣩⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠈⠿⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠏⢀⣀⣀⣀⠀⠀⠀⣾⡟⠈⠅⠹⣿⡻⣿⣿⣿⣽⣿⣿⣿⣶⣶⣶⣶⣤⣤⣤⠙⣿⣿⣿⣿⣿⣿⣿⡿⠿⠠⢾⣿⣿⣿⣿⣿⣿⣿⣿⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣤⣶⣒⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣴⣿⣿⣿⣿⣷⡄⢀⣿⣷⣦⠀⠀⠉⠀⠁⢃⣽⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢹⣿⣿⣛⣿⣿⣿⣷⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⠙⢿⡿⢻⣿⣿⣿⣿⣿⠇⠀⣰⣿⣬⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣶⣿⣿⣿⡿⢻⡇⠈⣿⣿⣿⣿⣿⣿⣿⣏⣉⡁⢸⣿⠟⣫⣼⣿⣿⣿⣿⣿⣿⠿⠛⢩⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣟⣾⣿⣿⣿⣿⡟⠀⠀⣿⣿⣿⣟⣿
⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠈⠉⠁⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠘⠃⠀⣿⣿⣿⣿⣷⣦⣿⣿⣿⣷⣤⠀⠛⠿⠿⣿⣿⣿⣿⣭⣹⣝⣧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢻⣿⣿⣿⣿⠋⠀⣀⠀⢿⣿⣿⣿⣿
⣿⣿⣿⣿⠁⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⢓⡀⠀⠈⠉⢻⣿⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣧⠀⣿⣿⣿⡿⢠⣾⣿⣿⣄⠹⣿⣿⣿
⣿⣿⣿⠏⠀⣠⣾⣿⣿⣿⣿⠆⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡋⠉⠉⠀⠀⠀⣼⣿⣗⡄⠀⠀⢿⢟⡛⠉⣙⢿⣿⣿⡿⠿⠿⠟⡋⠀⠀⠀⣿⣿⣿⣧⣾⣿⣿⣿⣿⣾⣿⠛⠛
⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⠿⠛⠓⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡏⠁⠀⠀⢀⣤⣿⣿⣿⣿⠀⠐⠈⢻⣿⣿⣿⣿⣿⣿⣷⣤⣤⣾⠃⠀⠀⢰⣿⣿⣿⣿⣿⣧⣼⣿⡟⠉⠛⠀⠀
⣿⣿⣇⠀⠀⣿⣿⣿⣿⣿⣿⣻⣥⣤⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣤⣦⣤⠀⠀⠀⠀⠀⠀⠈⠛⠻⠛⠁⠀⠀⠀⠈⠉⢹⣧⣿⣿⣿⣿⣶⣿⢿⣿⣿⢛⣿⣿⣿⣿⣿⡟⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⡿⢷⠀⠀⠀⠀
⣿⣿⣿⣄⠀⢸⣿⣿⣿⣟⣻⠁⣉⣁⣀⡀⢾⣿⣾⣿⢿⣿⣿⣿⡿⢉⣁⣀⠀⠀⠀⠀⢲⣦⣤⣤⣤⣤⣵⣤⡀⠀⠀⠀⠻⠋⠉⠀⡏⠈⠴⣹⠟⠁⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣧⠀⣤⣤⣤⣤⣄⠉⣤⣤⣼⣿⣿⢠⣤⣤⣤⢀⣬⣤⣬⣍⢩⣭⡍⢡⣤⡄⣤⣤⠀⠀⠠⠇⠀⠀⠁⠸⡸⡸⣿⣿⣿⣿⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡄⢸⣿⡏⣿⣿⠀⣿⣿⡇⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⠿⢸⣿⣇⣿⣿⡆⣿⣷⣼⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⠳⡘⣿⠿⠛⠁⠀⢀⠂⠄⣾⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠿⠛⠉⠁⠀⠀⠈⠁⢸⣿⣧⣿⣿⡄⣿⣿⡇⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⠀⢸⣿⡏⢩⣭⡅⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠘⠀⠑⠁⠀⠀⠀⢀⠏⠄⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⢹⣿⡇⣿⣿⡇⣿⣿⠀⣿⣿⣼⣿⣿⢸⣿⣿⠀⠸⣿⣧⣾⡿⠃⢸⣿⣿⠙⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡜⠘⠀⠀⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠁⡀⠀⠀⢠⣴⣶⣦⣴⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢻⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣴⣾⢿⣶⡄⢠⣶⡿⣷⣦⡀⠀⠀⠑⡀⠈⢿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢰⣿⣿⣼⣿⣿⢸⣿⣧⣿⣿⡇⠀⠀⠀⠀⢀⠈⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⡀⠀⠀⠀
⠀⠀⣠⣾⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⡘⣿⣿⢰⣶⣶⢸⣿⡇⢰⣶⡆⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⠗⠀⠀⠀
⣤⣶⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠇⠻⠿⠾⠿⠃⠈⠻⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢐⡦⠁⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⢫⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠍⠓⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⡄⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢉⣍⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣏⠀⠀⠀⠀⢼⡗⠀⠀⠁⠀⠘⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠻⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠏⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠉⡿⢿⣿⣿⣿⢿⣿⠿⠋⠙⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣷⣷⣀⣸⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡀⣀⣀⣾⣿⣿⣿⣤⡄⢀⣠⣾⣿⣿⣿⣿
⣿⡟⠻⡿⠛⠋⢁⠀⠾⣻⠿⢿⠻⠋⠿⠛⠟⠁⠀⠙⠟⠤⢤⣤⣄⣼⣿⣿⣿⣾⣿⠋⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣾⣿⢟⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿
⣿⡟⢀⣠⡴⢶⣾⡤⢠⠋⣀⣤⣶⣶⣦⠀⠀⢀⣀⠀⢀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣯⡾⠿⠃⠀⠛⢿⣿⣿⣿⣿⣿⣿⣛⣥⣽⡍⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⠿⣿⣯⡄⠀⢸⣿⣿⣿⣿⣿⠘⠉⠿⠿⠿⣿⡋⢉
⣿⣿⣿⣿⣿⣾⣿⣿⡏⣼⣿⣿⣿⣿⣿⣿⡀⣼⡟⠙⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣤⣌⠻⣿⣿⣿⣿⣿⣿⠿⠟⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡮⠩⠥⠄⣸⣿⣿⣿⣿⡿⠀⠀⠀⣀⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡄⠩⠁⠈⣻⠛⢛⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢻⡿⣿⣿⣿⣿⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢶⣿⣿⣿⣿⠟⠁⠀⠀⢰⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠿⠛⠟⠛⠙⢿⣿⣿⣅⣨⣿⣿⣿⣿⣶⣾⣿⣾⣿⣿⠿⢿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣏⣉⠃⠸⢟⣥⣿⣿⣿⣿⣿⣿⣿⣟⢸⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢾⣿⣿⣿⡏⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿
⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠸⡇⠠⣿⣿⣿⣿⣷⣾⣿⣿⣿⣷⡆⠻⠛⠻⢿⣿⣿⣟⣿⣿⡿⠙⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⠃⠀⠀⠀⠀⠻⣿⣿⣿⣿⣧
⣿⠏⠀⠀⠀⢀⣤⣤⣤⣄⠀⠀⠀⠈⣀⣼⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠈⣧⣀⠀⠁⠙⣿⣿⢧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠁⣿⣿⣿⣿⠀⠀⣶⣿⣿⣆⠈⣿⣿⣿⣿
⠏⠀⠀⢠⣾⣿⣿⣿⣿⣿⣃⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠋⠉⠃⠀⠀⠀⣿⣿⣷⡄⠀⠹⠻⠛⡋⣉⢋⣿⣿⣿⠛⠋⣉⣿⡄⠀⢸⣿⣿⣿⣿⢀⣴⣿⣿⣿⣿⣿⣿⠉⠹⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠂⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡛⠁⠀⠀⢀⡘⣿⢿⣿⣧⣤⣯⡾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇⠀⠀⣾⣿⣿⣿⡇⠘⣿⣿⢻⣿⠋⠙⠉⠀⠀⠙
⡀⠀⠀⠘⣿⣿⣿⣧⣾⣿⣿⠷⡄⢀⣼⣿⣷⣿⣾⣾⣿⣿⣿⣿⣦⣶⡄⠀⠀⠀⠀⠀⠙⠿⠿⠟⠀⠀⠀⠀⠘⠃⢳⣿⠛⠛⢻⠏⠛⡅⣿⠟⠋⣼⣿⣿⣿⣿⣿⡃⠀⣸⣿⣿⣿⣿⣷⡿⡿⠟⠀⠉⠀⠀⠀⠀⠀⠀
⣷⡄⠀⣾⣿⣿⣿⣿⣿⣯⣯⠀⣀⣀⣉⡙⢻⢿⣿⡿⠿⣿⣿⣿⡟⢉⣀⣀⠀⠀⠀⢤⣤⣤⣤⣤⣔⣦⣀⠀⠀⠀⠈⠂⠀⠀⣼⠀⠀⠘⠃⢢⢣⢸⣿⣿⣿⣿⠟⠀⢠⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣦⠛⣿⣿⣿⣿⣿⣿⠉⠀⣿⣿⣿⣧⠀⣤⣤⣤⣤⣤⠀⣤⣤⣼⣿⣿⢠⣤⣤⣤⢉⣭⣤⣬⣍⢩⣭⡄⢠⣤⡄⣤⣤⠀⠉⠀⠀⠀⠀⢉⢧⢺⣿⣿⠿⠋⠁⠀⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡿⠿⠻⣿⠙⠻⣿⣿⠀⢸⣿⡏⣿⣿⠀⣿⣿⡇⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⠿⢸⣿⣇⣿⣿⡆⣿⣷⣼⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀⡜⠈⠋⠉⠀⠀⠀⢀⡞⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠙⠆⣸⣿⣿⠇⢸⣿⣧⣿⣿⡆⣿⣿⡇⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⠀⢸⣿⡏⢩⣭⡅⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡼⢸⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⠀⣿⣿⡏⢹⣿⡇⣿⣿⡇⣿⣿⠀⣿⣿⣼⣿⣿⢸⣿⣿⠀⠸⣿⣧⣾⡿⠃⢸⣿⣿⠙⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠈⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⠄⠀⠁⠀⠀⠀⠀⠀⡀⢄⣄⡀⠈⡁⠀⠘⣶⣤⣴⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠻⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣴⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣶⣶⠀⠀⠀⠀⠂⠀⠀⠈⠘⠁⠀⠀⠙⢄⠀⠸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀
⠀⠀⢀⣴⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣴⣾⢿⣶⡄⢠⣶⡿⣷⣦⡀⠈⢆⠀⠹⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀
⢀⣤⣾⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⣿⠀⢰⣿⣿⣼⣿⣿⢸⣿⣧⣿⣿⡇⠀⠈⠂⠀⠹⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⡘⣿⣿⢰⣶⣶⢸⣿⡇⢰⣶⡆⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡇⠀⠀⠀⠀
⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠇⠻⠿⠾⠿⠃⠈⠻⠿⠿⠟⠁⠀⠀⠀⠀⠁⠀⢻⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡷⠉⠉⠁⠀⠀⠀⠀
⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣴⣆⠀⠀⠀⠀⠀⠀⠀⠠⣤⡖⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⣠⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠻⠟⠀⠀⠀⠀⠀⠀⠀⢀⣽⠃⠀⠀⠀⢀⠀⠐⡄⠀⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡇⠀⠀⠀⢸⣿⡆⠀⠐⠀⠈⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡛⢀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠘⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣉⡽⠿⣿⣿⣿⣿⡏⢀⣤⣶⣶⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡿⠿⠟⠿⣿⣿⣇⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣯⠀⣀⣀⣴⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠿⠏⡟⢠⠈⠿⠿⠛⣩⣿⣿⡿⠿⠻⠛⠀⠈⠛⠁⢴⣤⣤⣼⣿⣿⣿⣷⣿⠏⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣻⣿⡿⣹⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠟⢻⣿⣿⣿⣿⠟⢻⣿⣿
⣁⣠⣴⠷⣿⣷⡄⠀⢠⠏⢀⣤⣶⣷⣦⡀⠀⠀⢀⣸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣴⡿⠟⠃⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣽⣯⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠻⠿⣿⡿⠟⣿⣿⣿⣿⡷⠀⠈⠉⣹⣿⣷⣶⣶⣿⣿
⣿⣿⣿⣏⣿⣿⠇⣔⡘⣰⣿⣿⣿⣿⣿⣷⡄⢀⣿⣿⢿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⠻⣿⣿⣿⣿⣿⡿⠿⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠈⠀⢠⣿⣿⣿⣿⠃⠀⠀⠤⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣿⣿⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣬⡄⠢⠌⠏⣻⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢹⣿⣿⣿⣿⣦⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣼⣿⣿⣿⠇⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠟⠋⠉⠉⠉⠁⠹⣿⣿⣏⣈⣿⣿⣿⣾⣿⣿⣿⣿⡿⠟⢻⡇⠸⣿⣿⣿⣿⣿⣿⣿⣭⣭⡃⠘⣩⣼⣿⣿⣿⣿⣿⣿⣿⢭⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⠿⠿⢿⣉
⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⡇⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡎⠛⣿⣿⣿⣿⣿⣿⣿⣿⠟⡛⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠘⣿⣾⣶⣼⣿
⣿⠁⠀⠀⣀⣤⣶⣿⣷⣶⡀⠀⠀⠉⣩⣼⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠸⣿⣿⣿⣿⣿⣿⣷⣺⣿⣷⢿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿⣿⣿⣿⠁⠀⠀⢀⣤⢤⣴⡶⠛⠛⠛⠙⠋
⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣉⡉⠃⠀⠀⠀⠀⠈⠉⠻⣿⣿⠛⠁⣉⣛⣾⣿⣛⠛⠛⡟⣿⢯⣌⣿⣿⣿⣿⣿⠀⠀⠀⠹⠇⠀⠈⠁⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⡟⣿⣿⣿⠏⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡏⠀⠀⠀⢠⠼⣿⣶⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣽⣿⣿⣿⣿⣿⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡄⠀⢀⣸⣿⣿⣿⣿⣿⡿⡿⠐⠇⢀⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠙⠿⠟⠛⠀⠀⠀⠀⠙⠀⣿⣟⠋⢹⠏⢉⡵⣹⠟⠋⢸⣿⣿⣿⣿⣿⣏⣰⣿⣿⣿⣿⣿⣿⣆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡄⠸⣿⣿⣿⣿⣿⣿⣿⣧⠀⣀⣈⣉⡘⢿⢻⣿⡿⣿⣿⣿⡟⠛⢀⣀⣀⠀⠀⣤⣤⣤⣤⣤⣴⣦⣀⠀⠀⠀⠈⠁⠀⢸⡆⠀⠉⠙⢘⣼⡘⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣦⣬⣿⣿⣿⣿⣏⠀⠀⠀⣿⣿⣿⣧⠀⣤⣤⣤⣤⣤⠉⣤⣤⣼⣿⣿⢠⣤⣤⣽⢉⣭⣤⣬⣍⢩⣤⡄⢠⣤⡄⣤⣤⠀⠀⠀⠀⠃⠿⡜⣿⣿⠿⠛⠉⢰⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠛⠋⠁⣿⡇⢨⣿⣧⣴⡇⢸⣿⡏⣿⣿⠀⣿⣿⡇⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⠿⢸⣿⣇⣿⣿⡆⣿⣷⣼⣿⡇⣿⣿⠀⠀⠀⠀⢸⠀⠘⠉⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠳⣿⣿⣿⣿⠇⢸⣿⣧⣿⣿⡆⣿⣿⡇⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⠀⢸⣿⡏⢩⣭⡅⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⣿⣿⡏⢹⣿⡇⣿⣿⡇⣿⣿⠀⣿⣿⣼⣿⣿⢸⣿⣿⠀⠸⣿⣧⣾⡿⠃⢸⣿⣿⠙⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠘⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣴⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠀⠀⠀⠁⠀⠀⠀⠀⡀⣀⣄⠀⢠⠈⠁⠰⣿⣶⣦⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣠⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁⣶⣶⠀⠀⠘⠂⠀⠀⠑⠘⠛⠀⠀⠑⠄⠀⠸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣼⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⠃⠀⣿⣿⠀⠀⣴⣾⢿⣶⡄⢠⣶⡿⣷⣦⡀⠀⠀⢻⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀
⣴⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢢⡿⠀⣿⣿⠀⢰⣿⣿⣼⣿⣿⢸⣿⣧⣿⣿⡇⠈⢄⠀⢻⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⠀⣿⣿⣀⡘⣿⣿⢰⣶⣶⢸⣿⡇⢰⣶⡆⠀⠀⠇⠀⢹⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡻⣿⠀⠀⠀⠀⠀⠀
⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠿⠿⠿⠇⠻⠿⠾⠿⠃⠈⠻⠿⠿⠟⠁⠀⠀⠈⠂⠀⢿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠿⠟⠛⠀⠀⠀⠀⠀⠀
⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⢀⠀⠀⠄⢸⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⢘⠀⠀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡇⠀⠀⠀⢀⣸⡄⠀⠒⠀⠘⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠘⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣻⣿⣿⣿⣷⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠁⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠘⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠿⠏⠉⢸⣼⠿⠀⠀⠉⢻⣿⡿⠿⠛⠛⠻⡿⠛⡉⢈⠀⣹⣿⣿⣷⣸⣿⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣯⣿⡿⢿⣿⣿⣿⡟⢙⣿⣿⣿⣿⣿⣿⣿⣧⢠⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠫⢿⣿⣿⣿⣿
⠁⢠⡀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡹⣿⣿⣿⣿⣿⣿⣿⠇⣸⣿⠶⠾⠿⠿⣿⣿⣿⣿⣿⣿⡷⠾⣿⢿⣲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢋⣽⣿⣿⣷⣾⣾⣿⣿⣿⣿
⣿⣧⠸⣯⣶⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⣶⠠⣶⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣀⡙⢿⣿⣿⣻⣿⣿⣿⠢⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⠉⠙⠻⢿⣿⣿⣿⣿⡿⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣻⣟⣃⡀⠀⣀⣰⡟⠛⢙⣋⣌⡁⠀⠈⠛⠈⡙⠿⣿⣿⣿⣾⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢻⣿⣿⣿⣟⠉⠈⣻⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣿⣿⣿⣿⠃⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣛⢚
⣿⣿⣿⣿⣿⣿⡶⠿⠿⠁⠴⣿⣿⣿⣿⣄⠀⢠⣾⣤⣾⣤⣿⡿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣛⡛⠇⢸⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠙⠿⠿⠿⣏⣉⣽⣶
⣿⣿⣟⡟⠋⠁⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣦⣾⣿⣿⣿⠋⠀⠀⠹⡇⢸⣿⣿⣿⣿⣯⣽⣿⣿⣿⣧⡰⢿⣿⣿⣿⣿⡿⣿⣿⣿⡿⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣿⣿⣿⣿⠁⠀⠀⠀⠄⠀⠀⠀⠶⠴⣿⣿⣿⡿
⣿⣿⠋⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠃⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢿⣿⣿⣿⡏⣿⣿⣿⣧⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠁
⣿⠟⠀⢀⣴⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠟⠻⠋⠁⠀⠘⣿⣿⡿⣽⣿⣿⣿⣟⢿⡾⣿⣿⣿⣿⣿⣿⣟⣅⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⢀⣠⣐⣀
⠏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡗⠊⠀⠀⠀⠀⠙⠉⠁⠳⡧⣿⣿⣿⣦⣿⣿⣭⡍⠉⢩⣿⡿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟
⡄⠀⠀⢹⣿⣿⣯⣿⣿⡙⠋⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣄⡄⠀⠀⠀⠀⠘⠻⢿⡿⠟⠃⠀⠀⠀⠬⠀⣀⣠⣤⣤⣿⣿⣿⢟⣿⣿⢹⣿⣿⣷⣾⣿⣽⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣄⠀⣿⣿⣿⣿⣿⣿⡿⢷⠋⣀⣀⣀⡘⢿⣿⣿⣿⣿⣿⣿⡿⠅⢀⣀⣀⠀⣀⣀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠫⠃⠁⢸⠃⢫⡖⣸⠏⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣯⣿⣿⣿⣿⣿⠿⢁⡏⠀⣿⣿⣿⣧⠈⣤⣤⣤⣤⣬⠁⣤⣤⣼⣿⣿⢠⣬⣭⣭⢉⣥⣤⣤⣄⢠⣤⡄⢠⣤⡄⣤⣤⠀⠀⠁⢳⡱⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⣿⣿⣴⣿⠁⢸⣿⡏⣿⣿⠀⣿⣿⡇⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⠿⢸⣿⣇⣿⣿⡆⣿⣷⣼⣿⡇⣿⣿⠀⠀⠀⠂⡷⡝⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⣿⣿⣿⣿⡟⡛⠿⠁⢸⣿⣧⣿⣿⡆⣿⣿⡇⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⠀⢸⣿⡏⢩⣭⡅⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⠁⠱⠙⠉⠀⠀⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⠁⠀⠀⣿⣿⡏⢹⣿⡇⣿⣿⡇⣿⣿⠀⣿⣿⣼⣿⣿⢸⣿⣿⠀⠸⣿⣧⣾⡿⠃⢸⣿⣿⠙⣿⣿⡇⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠻⠿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣠⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⠀⠀⠀⠀⠁⠀⠀⠀⢀⣀⡀⠐⡄⠀⠈⢡⣶⣿⣶⣤⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣴⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⣶⣶⠀⠰⠀⠀⠈⠃⠹⠿⠀⠈⠂⠀⠀⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠕⠻⡇⠀⣿⣿⠀⠀⣴⣾⢿⣶⡄⢠⣶⡿⣷⣦⡀⠈⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣰⣶⡇⠀⣿⣿⠀⢰⣿⣿⣼⣿⣿⢸⣿⣧⣿⣿⡇⠀⠈⢿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⣿⣿⣀⡘⣿⣿⢰⣶⣶⢸⣿⡇⢰⣶⡆⠀⡄⠈⢿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣱⣾⡂⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠿⠿⠿⠇⠻⠿⠾⠿⠃⠈⠻⠿⠿⠟⠁⠀⠐⠀⠈⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠱⢸⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢸⣿⣿⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⢠⡆⠀⣃⠀⠸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠇⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠿⣻⣿⣿⡟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣧⢀⣸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣹⣖⣻⣿⣿⣿⣿⣿⣿
⠯⠀⠀⠶⠛⠋⠋⠑⠸⢩⢿⣿⠉⠉⠙⠙⠋⠡⢡⣤⢠⣾⣿⣿⣧⣿⠏⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢩⣾⣿⠛⣿⣿⣿⣿⣅⣾⣿⣿⣿⣿⣿⣿⣿⣦⣺⣿⣿⣿⣿⠉⣭⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠦⣠⣂⠀⡀⠀⠀⠀⠀⠀⠠⠀⡀⡀⠀⢀⢠⣤⣼⣿⣿⣿⣿⣿⣿⣿⣴⣟⣋⣁⣀⠉⠙⠻⣿⣿⣿⣿⣷⣠⣸⠟⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠙⢻⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣿⣿⣿
⣢⣿⣾⠇⠀⠀⠀⠀⠀⠀⠐⢀⡦⢚⣗⣿⣿⣿⣿⣿⣿⣿⣟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⢻⣿⣿⣿⣿⣿⡇⢲⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⡇⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⢟⠃⢉⣿⣿
⣯⣿⣷⣦⠀⢠⣴⣦⣴⣦⣴⣿⣧⡄⠀⠀⠈⠀⠩⡛⠿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢿⣿⣿⣿⣇⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠙⢿⣿⠿⣿⣉⣿⣶⣿⡄⠻
⣿⣿⣿⣿⣿⡿⠛⠛⠻⠛⠛⠻⢿⣶⣶⣠⣶⣶⣿⣶⠜⠉⠀⣩⠀⢻⣿⣿⣿⣿⣿⢻⣷⣶⣾⡁⣋⣹⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⠏⠀⠀
⣧⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠠⠶⠾⢿⣿⣿⣿⣿⠿⠁⠀⠀⠀
⣿⣿⡿⠀⠀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠁⢙⣿⣧⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠈⢿⣿⣿⣿⢿⣿⣿⣿⣶⣶⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠑⠉⠛⢿⡦⠀⠀⠀⠀
⣿⠟⠀⢀⣾⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢰⣿⣿⣿⡅⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣯⣌⠛⠀⠀⠀⢸⡟⠛⠻⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠶⠖⠒
⣆⠀⠀⢸⣿⣿⣿⣿⡿⢻⣿⡶⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡷⠂⠀⠀⢀⡀⡀⠀⠀⠀⠈⠳⣾⣿⣿⣿⣿⣿⡿⣿⣷⣤⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡟⠀⢠⣼⣿⣿⣿⣿⣧⣿⠟⠀⣠⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁⠀⠀⠀⠈⠋⢻⣿⣦⡶⠛⠻⣿⢋⠟⡩⣿⠿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣧⣾⢸⣿⣿⣿⣿⣿⣿⣁⡴⠋⣀⣀⣀⡀⣿⣿⣿⣿⣿⠿⠷⠀⠀⢀⣀⣀⢤⣦⣤⣤⣶⣦⣄⠀⠀⠀⠀⢨⣿⠁⠀⠰⢇⠀⠘⠀⠉⡄⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣾⣿⣿⣿⣿⣏⠼⠟⠁⠀⣿⣿⣿⣧⠈⣭⣭⣥⣤⣤⠀⣤⣤⣼⣿⣿⢠⣭⣭⣽⢉⣭⣤⣤⣄⢠⣤⡄⢠⣤⡄⣤⣤⠀⠀⠀⠀⡻⡜⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⠀
⠛⠛⢻⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⡏⣿⣿⠀⣿⣿⡇⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⠿⢸⣿⣇⣿⣿⡆⣿⣷⣼⣿⡇⣿⣿⠀⠀⠀⠀⢀⠙⢾⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀
⠀⠀⢰⣿⣿⣿⣿⠏⠀⠀⠀⢸⣿⣧⣿⣿⡆⣿⣿⡇⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⠀⢸⣿⡏⢩⣭⡅⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠸⠀⠀⢻⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⣾⣿⣿⠟⠁⠀⠀⠀⠀⣿⣿⡏⢹⣿⡇⣿⣿⡇⣿⣿⠀⣿⣿⣼⣿⣿⢸⣿⣿⠀⠸⣿⣧⣾⡿⠃⢸⣿⣿⠙⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠁⠀⢀⣀⣀⣀⠀⢄⠀⠀⢨⣥⣶⣿⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠃⠀⣶⣶⠀⠀⠀⠈⠃⠛⠻⠂⠈⠓⠀⠀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⣿⣿⠀⠀⣴⣾⢿⣶⡄⢠⣶⡿⣷⣦⡀⢻⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡆⠀⣿⣿⠀⢰⣿⣿⣼⣿⣿⢸⣿⣧⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⣿⣿⣀⡘⣿⣿⢰⣶⣶⢸⣿⡇⢰⣶⡆⠀⠀⢻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠿⠿⠿⠇⠻⠿⠾⠿⠃⠈⠻⠿⠿⠟⠁⠀⠂⠀⢿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⢉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠚⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⡐⠀⢿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⢠⣂⠀⢳⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣫⠽⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⢿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠿⠟⠿⣿⣿⣄⣀⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣛⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⠀⠰⠟⠋⠈⠉⠱⠻⢽⣿⡯⠁⠉⠉⠛⠤⢄⣤⣄⣼⣿⣿⣿⣿⡟⣹⣿⠟⠻⠿⢿⣿⣿⣿⣿⣿⣿⣟⢉⣿⣿⢋⢿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠻⣿⣿⣿⣿⣿
⣴⡦⠄⠀⠀⠀⠀⠀⠀⠀⣤⣴⣂⡄⠀⣀⣶⣮⣿⣿⣿⣿⣿⣿⣿⣿⣭⣤⣤⣤⣤⣀⡈⠻⣿⣿⣿⣿⣦⣜⣿⠻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠹⣿⣿⣿⣿
⣮⣿⠏⠀⠀⠀⠀⠀⠀⠐⠙⣺⣷⣟⣟⣿⣿⣿⣿⣿⣿⣏⣿⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⣿⣿⣿⣿⣿⡿⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠈⠙⠿⣿⣿⣿⣿⡿⢿⣤⣠⡘⠙⣿⣿⣿
⣭⣿⣷⣂⣀⣶⣷⣮⣶⣷⣿⣿⣷⣤⣀⡔⢉⢻⡝⡹⠿⠛⡫⠀⢿⣿⣿⣿⣿⣿⣿⣿⠿⠟⡇⠹⣿⣿⣿⣇⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠈⠛⢋⣿⣶⣾⣿⣿⡇⠀⠈⢿⣿
⢿⣿⣿⣿⣿⣿⡿⠛⠙⠛⠉⠉⠙⢿⣿⣴⣿⣿⡟⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣍⣿⣿⣿⣧⢘⣹⣿⣿⣿⣿⣿⣿⡯⡩⣿⣿⠁⠀⢛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠾⠿⣿⣿⣿⣿⢏⠃⠀⠀⠀⢻
⣾⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠹⣿⣿⣿⣿⣟⡿⣶⠧⢼⡟⠃⠀⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⠀⠀⣠⣴⣾⣿⣶⣄⡀⠀⠘⠻⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⣿⠟⠀⠀⢹⡿⣿⣿⣿⣷⣿⣇⣾⣷⡀⠀⢘⣀⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣃⠀⠀⠀⠀⠉⠓⢀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡦⠉⠀⠀⠀⠤⠀⠀⠈⠉⠻⣿⣷⡘⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠇⠀⢀⣿⣿⣿⣿⣻⣿⠉⣡⠟⠁⠀⠀⠀⢠⣿⣿⡄⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠁⠀⠀⠀⣶⢶⣶⣦⣄⠀⠀⢹⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣿⣄⠀⢸⣿⣿⣿⣿⣿⣿⡾⠉⠀⠔⠀⠀⢀⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠆⠀⠀⠀⠀⠸⢻⣿⣿⣧⣴⣾⡿⠿⠛⠛⢛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣻⣿⡧⢠⣼⣿⣿⣿⣿⣿⣿⠁⣀⣀⣀⡀⠀⢻⣿⣿⡟⠛⠆⠀⠀⢀⣀⣐⢶⣶⣶⣶⣿⣶⣄⠀⠀⠀⠀⠟⠛⠷⡟⠛⠑⠀⡀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣦⣸⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣧⠀⣤⣤⣬⣤⣤⠀⣤⣤⣼⣿⣿⢠⣭⣭⣽⢉⣭⣥⣤⣄⢠⣤⡄⢠⣤⡄⣤⣤⠀⠁⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣷⠀⠀⠀⠀
⠿⠟⠃⠉⠉⢹⣿⣿⣿⡟⠀⢸⣿⡏⣿⣿⠀⣿⣿⡏⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⠿⢸⣿⣇⣿⣿⡇⣿⣷⣼⣿⡇⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣿⣿⣿⠏⠀⠀⢸⣿⣧⣿⣿⡆⣿⣿⡇⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⠀⢸⣿⡏⢩⣭⡅⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣾⣿⣿⡟⠀⠀⠀⣿⣿⡏⢹⣿⡇⣿⣿⡇⣿⣿⠀⣿⣿⣼⣿⣿⢸⣿⣿⠀⠸⣿⣧⣾⡿⠃⢸⣿⣿⠹⣿⣿⡇⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⢠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠁⠀⣀⢀⣀⡀⠠⡀⠀⠀⢬⣥⣶⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣾⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠂⠀⣶⣶⠀⠀⠀⠘⠉⠓⠆⠀⠈⠂⠀⠀⢿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡀⠀⠀⣿⣿⠀⠀⣴⣾⢿⣶⡄⢠⣶⡿⣷⣦⡈⢿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⠀⠀⣿⣿⠀⢰⣿⣿⣼⣿⣿⢸⣿⣧⣿⣿⡇⠈⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀⠀⣿⣿⣀⡸⣿⣿⢰⣶⣶⢸⣿⡇⢰⣶⡆⠀⠀⢻⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠿⠿⠿⠇⠻⠿⠾⠿⠃⠈⠻⠿⠿⠟⠁⠀⢀⠀⢿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣰⡆⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠅⠀⠀⠀⠀⠀⠀⡐⠀⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒⠀⠛⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⢠⠇⠀⢷⡀⠘⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢛⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠹⣮⠿⠟⠿⠿⣿⣿⣿⣿⡿⠻⢿⢿⡿⠛⠛⣉⣈⣽⣿⣿⣗⣾⡿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⠛⣹⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣽⡀⠁⠀⠀⠀⠀⠑⠿⣹⣿⣧⠀⠀⠀⢩⣭⢿⣿⣿⣿⣿⣿⣿⣿⣁⣻⣩⣀⣀⡉⠙⠻⣿⣿⣿⣿⣿⢗⣼⣿⣿⣿⢿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠙⢿⣿⣿⣿⣿⣿⣿⣿
⣟⣷⠆⠀⠀⠠⠀⢀⠰⣴⣶⣾⣿⣦⣾⣾⣿⣿⣿⣿⣿⣿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡍⢿⣿⣿⣿⣿⣾⡅⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡛⢿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠈⣿⣿⣿⣿⣿⣿⣿
⣿⣯⡄⠀⢠⣬⣀⣢⣄⣠⣿⣿⣻⢟⠻⣿⣿⣿⣿⣿⠿⠟⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢘⣿⣿⣿⣿⡟⠑⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣍⡻⢿⣿⣿⣟⣛⣷⣤⡤⠀⠀⢻⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣿⣿⣿⣿⣿⠿⠿⠟⠋⠉⠸⣿⣭⠗⠈⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⣿⣷⣶⣜⣀⡿⢿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣤⣿⣿⣿⣿⣿⣏⠀⠀⠀⠙⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⢰⣿⣿⣿⣿⣿⣿⡿⣧⣹⣿⣇⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠈⠛⠿⣿⣿⡟⠁⠀⠀⠀⠀⠘⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠃⠀⣠⣤⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢹⣿⣿⣿⣿⣷⡿⣿⢻⣿⡁⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⣿⣿⣿⣿⣿⠃⠀⣸⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣋⡸⠃⠀⠀⠈⠛⠛⠙⠛⠻⢿⣿⣞⣿⣿⠀⣤⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣼⡟⠃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡏⠀⠀⠀⣠⢺⠃⠀⠀⠀⠀⠀⢹⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⡟⠉⣀⠀⢠⣿⣿⣿⣿⣿⣿⣟⣠⠞⠁⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠟⠋⡀⠀⠀⠀⠉⢸⣿⣿⣶⣄⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⣿⣿⡇⣴⣿⣆⢺⣿⣿⣿⣿⣿⣿⣿⣇⠄⢀⢀⣀⣴⣿⡆⠄⠀⠀⠀⢤⣤⣤⣤⣤⣧⣤⡀⠀⠀⠀⢹⣿⣿⣿⣆⣴⣇⣹⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⣿⣿⣿⣎⣿⣿⣦⣾⣿⣿⣿⣿⣿⡿⠁⣰⣿⣿⢻⡇⠈⠁⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠉⠉⠃⠹⠛⠛⣯⠇⣾⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿
⣿⣿⠿⠿⠿⠿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⡇⠀⠀⠀⠀⠀⠀⢀⠀⠙⠿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠁⠀⠀⠀⠀⠀⠘⣿⣿⣿⡟⣿⣿⣿⣿⡆⠙⠳⡇⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠈⣿⣿⣿⣿⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠃⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣶⣶⡀⠡⡐⠀⠈⢻⣿⣿⣿⣧⣤⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠗⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⠛⢉⡀⠀⠱⡄⠀⠀⢻⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⠛
⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣷⠀⠀⠀⠠⣦⠀⠀⠘⣆⣷⣄⠀⠘⢆⠀⠀⢻⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣰⣿⣿⣿⡿⠁⠀⠀⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⢻⣇⠀⠀⡿⠝⠙⠃⠀⠀⠑⡄⠀⢻⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠈⠻⢿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣠⣾⣿⣿⣿⣿⠁⠀⠀⠀⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠻⡄⠘⣷⠀⠀⠀⠀⠀⠀⠘⢄⠀⢻⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡁⠀⠁⠀⠀⠀⠀⡄⠀⠀⠀⠠⠀⠹⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢻⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠣⠀⠹⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⣿⣿⣿⠝⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢨⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠏⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣶⡟⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⠅⠀⠀⠀⠀⠄⠀⢀⠀⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠟⠃⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⢀⡃⠰⣆⠀⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢸⠅⠀⢹⡀⠀⢻⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⢿⣿⣿⣿⣿⣷⣾⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠻⢟⣿⣿⣿⣹⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠻⣿⣿⣧⣀⣼⣿⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡔⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢠⠈⠿⠉⠃⠉⠹⢿⣿⠿⣿⡯⠀⠛⠙⠟⠀⣬⣦⣤⣿⣿⣿⣿⣿⣛⣛⣛⡛⠋⠙⠻⣿⣿⣿⣿⣿⣿⣟⢯⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠁
⣿⣆⠀⠀⠀⠀⠀⠈⠙⢠⡼⣟⣀⡀⣠⣘⣾⣼⠟⠟⣿⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⢿⣿⣿⣿⣿⣷⣻⠟⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⢿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀
⣿⡿⠃⠀⠀⢁⠀⢀⠐⠷⣿⣿⣿⣟⣿⣿⡿⢁⣴⣿⠿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⢆⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣉⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣧⡀⠀
⣿⣿⣇⣠⣸⣿⣶⣾⣶⣾⣿⣿⡿⠇⠸⠟⣱⡿⠋⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⡿⣿⣭⣄⢃⢹⣿⣿⣿⣿⣇⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣟⡛⢛⣿⣯⣾⣿⣶⡀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣷⣿⣿⣯⣿⠺⢋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⠿⠟⠻⢿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⣟⣯⣷⣼⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠉⠉⠛⠻⠿⠟⠁⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⣸⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠛⣿⠋⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⡀⢀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣛⠁⠀⠀⠀⠉⠉⠉⠙⠋⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿
⣿⣿⣿⠟⣿⣿⡀⠀⠀⣤⣼⣿⣿⣿⣿⣿⣋⣉⠭⣹⣆⠀⠀⠀⠀⠀⠈⠻⣿⠿⠋⠀⠀⠀⠀⠿⠿⢛⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿
⣿⣿⡟⣠⣿⣿⡄⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⣨⣥⣄⡀⠀⠀⠀⢀⣀⣀⡀⣀⣀⠀⠀⠀⠀⠘⠿⣶⣤⣄⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⣿⣿
⣿⣿⣿⣿⣿⣿⣷⡀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⢿⣿⠙⠃⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣦⠀⠀⠀⠈⠉⢽⣿⡿⠋⣸⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿
⣿⣻⣿⣿⣿⣿⣿⣷⡖⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠈⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠟⠋⠀⠙
⣿⡿⠟⠉⠁⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⡟⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠹⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣦⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀
⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⡄⠀⠁⠀⠀⠀⠀⠀⢀⢀⠀⠡⠠⡀⠘⢿⣿⣿⣿⡃⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠐⢿⠿⠂⠀⠱⡀⠀⠀⢻⣿⣿⣿⣿⣆⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣄⢊⠀⠀⠘⢆⠀⠀⢻⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠟⠋⠁⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⢱⣧⠀⠀⢸⡄⠓⠄⠀⠀⠑⡄⠀⢻⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠏⠀⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⢿⡀⠀⣾⠀⠀⠀⠀⠀⠀⠈⠄⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢴⣶⣶⣶⣿⣿⣿⣿⡟⠀⠀⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠸⡍⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠙⣿⣿⣿⡏⠻⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡃⠀⠀⠀⠐⠀⠘⣿⣿⣷⡀⠘⠻⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢹⣿⣿⣿⣿⡟⠁⠀⠀⠀⣿⣿⡟⠛⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠠⠑⠀⠘⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣴⣶⣿⣿⣿⡟⠁⠀⠀⠀⠀⣿⣿⣇⠀⠉⠙⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡃⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠸⠀⢤⠠⠀⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⢾⠀⠈⢧⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣦⣬⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣻⣿⣿⣿⣻⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⣿⣿⠿⣿⣿⣿⢿⡿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣾⣥⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠀⡀⠻⠋⠉⠉⠉⢿⣿⣿⣿⡗⠀⠹⡛⢿⡠⠤⢄⡴⢃⡄⢾⣽⣿⣶⣾⣷⣶⣶⣦⣬⣿⣿⣿⣿⣿⣿⡿⣯⣷⣿⣿⣿⣿⣿⣿⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠟⢋⡅⠀⣩⣿
⣿⣶⢦⡀⠀⠀⢀⠀⡢⣡⣥⣦⣰⣤⣤⢀⣌⣷⣿⠏⣴⣿⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡜⣿⣿⣽⣿⣹⣛⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠹⣿⣿⣿⣿⣿⣿⣿⣷⠋⠀⣾⠀⠀⣿⠃
⣶⣿⣿⠃⠀⠆⠬⡁⠼⢶⠗⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣛⡛⠇⣹⣿⣿⣿⣿⣿⡏⣹⣿⣿⣿⣿⣿⣿⡇⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣧⣼⠃⠀⣸⡇⠀
⣿⣿⣿⣗⣠⣸⣿⣷⣾⣿⣿⣿⣿⠿⠚⠘⠛⠿⠋⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⣭⣿⣿⣟⣿⣼⣿⣿⣿⣿⣇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣶⣎⡻⡿⣿⣿⣿⣿⣿⣻⣀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣄⠀⡿⠀⠀
⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠛⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⢻⣿⣧⣭⣿⣿⣯⣽⣿⡇⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣾⠃⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⢿⡟⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀
⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⢦⠟⠀⠀⠀⠀⠀⠀⢠⣵⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⣤
⣿⣿⣿⣿⡿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣀⣠⡀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⢱⠀⠀⠀⣰⠺⡟⠀⢘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢹⣿⣿⡄⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⢰⣾⣶⣻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣿⣃⣼⣿⣿⣧⠀⠀⠀⠀⢿⣿⣿⣿⣿⢟⣹⣿⡿⣯⡀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣧⣤⡀⠀⠀⠀⠉⣿⠛⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿
⣿⣾⣿⣯⠻⣿⣿⣿⣄⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⣿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣿⣿⣿⡿⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣆⠀⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠋⠉⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡉⠙⠳⡃⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠈⠻⣿⣿⣿⣿⣀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠋⠁⠀⢿⣿⣿⣿
⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠁⠀⠀⠀⠀⠀⣠⡀⠀⠈⡀⠀⠀⠹⣿⣿⣿⣯⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣦⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠈⢿⣿⣿
⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠘⢄⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⠀⠈⢿⣿
⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠁⠀⠀⠈⢆⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⣿⣿⣧⠀⠀⠈⢿
⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀
⠙⢿⣿⣧⠀⢀⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⠀⠀⢠⠀⠀⠀⠀⠀⠀⠈⢀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠁⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⠋⣿⣿⡟⠛⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⢿⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⠀⠀⠀⠉⠉⠀⠀⢻⣿⠃⠀⠈⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡗⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠋⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⠒⣒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣿⣿⣿⣟⣋⣉⣙⣛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣩⡔⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⢀⠈⢿⠟⠋⠉⠻⣿⣿⣿⣿⡃⠉⡛⢿⣏⢥⣈⣀⡰⠟⢑⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡿⢫⡿⠋⣿⣿⡿⠿⢿
⣴⣦⣼⡅⠀⠀⠀⠀⠀⢄⣹⣤⢲⣤⣀⡀⢀⣨⣾⣿⣿⣧⡎⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠸⠃⠀⡿⠁⠀⣽⡟⠁⠀⠀
⣿⣿⣯⣿⠀⠀⠀⠓⠢⣰⠸⠿⣿⣿⣿⡷⣿⣿⣿⠟⠃⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⢿⣿⣭⣬⣃⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠰⠁⠀⠀⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣧⣀⣡⣶⣾⣿⣷⠖⠉⠉⠀⠀⠈⠻⠉⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣤⣤⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⣿⣿⣿⣿⣿⣿⣿⠿⠿⣇⣽⠛⠿⣿⣿⣿⣿⢥⣤⡄⠀⠀⠋⢻⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣯⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⢟⠻⠋⢀⣠⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠉⢳⣶⣶⣿⣿⣠⣼⣿⡇⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠗⣈⣰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠉⠙⠿⣿⣿⡿⠿⠁⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣣⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣿⣷⣦⣦⡀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠷⣾⣿⡿⠻⢢⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀
⣿⣿⣿⠋⣿⣿⣦⠀⠀⠀⠀⠀⠀⣴⣽⣿⣿⣿⠟⠉⠉⣯⢁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣼⣿⣿⠖⣺⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀
⢿⣿⡏⣴⣿⣿⣿⡄⠀⠀⠀⠀⠀⢸⣿⣵⣿⡟⠀⢀⣼⣿⣦⠀⠀⠀⠀⠀⠰⣶⣤⣤⣤⣼⣿⡏⡀⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀
⣿⣿⣿⣌⢻⣿⣿⣷⣤⣄⡀⠀⢀⣽⣿⣿⣿⣠⣶⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣯⣿⢰⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⣿⣿⣿⣿⣾⣿⡿⠿⠛⠉⠁⠀⠀⠛⢿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⡇⡼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⠙⠻⢖⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠈⠛⠃⢀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡇⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠁⠀⠈⢂⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠿⠟⠛⠉⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠁⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣀⣠⣦⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⡏⠀⠀⠹⣿⣿⣿⣿⣿⣿
⠀⠈⠻⣿⣷⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⡀⠀⠠⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⡿⠟⠀⠀⠀⠹⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣶⣾⣿⡟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢹⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⠛⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⠀⠀⠈⠻⣿⣿⣿⣿⡿⠁⠀⠀⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠉⣠⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⣽⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠻⢿⣿⣟⠽⠙⢿⣿⣿⣿⣿⠿⠿⣻⣿⣿⠿⠟⠛⠹⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣤⣄⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡩⠭⣭⡽⠋⣹⠛⠛⣻⣿⣿⢿⣿⣿⣿⣿
⠀⢉⡁⢠⠀⠛⠉⠀⠀⠈⠻⡟⠋⠱⠀⠀⠈⠘⠓⣖⣶⣶⣾⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣰⠋⠀⢸⠁⠀⠀⣸⠟⠁⠈⠛⣿⣿⣿
⣾⣿⣷⡿⣆⠀⠀⠀⣀⡀⠚⢷⣴⣿⣿⣶⡄⣴⣼⣿⡿⠉⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠙⣿
⣿⣿⣿⣿⣟⡀⠀⠀⣼⣨⣰⣄⠸⠟⠛⠉⠉⢿⡏⠉⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⣄⣼⣿⡿⠟⠋⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⣴⣷⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⠻⠻⣿⣿⣿⣿⣿⡋⣀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣷⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢰⠀⣹⣟⡋⠀⣸⣿⡇⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡟⣡⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣄⣠⠀⠀⠀⠀⢀⣼⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠐⠻⣿⣿⣿⣿⡿⠃⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⢺⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣷⣿⡿⠋⠙⠃⠀⠀⢰⣿⣿⣿⠿⠁⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣿⠇⣸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣟⡟⣼⡟⠃⠀⣠⣴⠂⠀⢸⣿⣿⠁⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣞⢿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⣀⣴⣿⣿⠇⠀⢸⣿⣿⡆⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣦⣿⣿⣿⣿⣶⣶⡦⠀⠀⠀⢰⣿⣿⣿⣾⣿⣿⡟⠁⠀⠀⢸⣿⣿⣧⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⡟⠆⠀⠀⠀⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠐⢻⣿⣧⠈⠛⠇⠀⠀⠀⣿⣿⣿⡿⠆⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡆⠀⠀⠀⠀⠀⣿⡿⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀
⠹⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀
⠀⠀⠹⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇⠀⠀⠀⠀⠀⣻⠁⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡄⠀⠀⠀⠀⠀⠀⠀⠿⠛⠛⠉⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠻⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣴⠂⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⠇⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢻⠟⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠉⣠⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣻⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠻⢿⣿⣟⠽⠙⢿⣿⣿⣿⣿⠿⠿⣻⣿⣿⠿⠟⠛⠹⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣤⣄⣥⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡩⠭⣭⡽⠋⡹⠛⠻⣻⣿⣿⢿⣿⣿⣿⣿
⠀⢉⡁⠠⠀⠛⠉⠀⠀⠀⠻⡟⠛⠹⠀⠀⠀⠘⠓⣶⣶⣶⣾⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣰⠋⠀⢸⠁⠀⠀⣸⠟⠁⠈⠛⣿⣿⣿
⣾⣿⣿⡿⣆⠀⠀⠀⣀⡀⢘⢷⣼⣿⣿⣶⡄⣴⣼⣿⡿⠉⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠙⣿
⣿⣿⣿⣿⣟⡀⠀⠀⣼⣌⣰⣄⠸⠟⠋⠉⠉⢿⡟⠉⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⣤⣼⣿⡿⠟⠋⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⣴⣷⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠈⠛⠻⣿⣿⣿⣿⣿⡋⣀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣷⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢲⢀⣹⣟⡋⢀⣹⣿⡇⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡟⣡⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣄⣠⠀⠀⠀⠀⢀⣼⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠐⠻⣿⣿⣿⣿⡿⠃⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⢻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⠃⠙⠃⠀⠀⢰⣿⣿⣿⠿⠁⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣿⠇⣸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣻⡟⣸⡿⠃⠀⣠⣼⠂⠀⢸⣿⣿⠁⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡆⢿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⢀⣴⣿⣿⠇⠀⢸⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣦⣿⣿⣿⣿⣶⣶⡦⠀⠀⠀⢰⣿⣿⣿⣾⣿⣿⡟⠁⠀⠀⢸⣿⣿⣧⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⡟⠆⠀⠀⠀⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣿⣇⠈⠛⠇⠀⠀⠀⣿⣿⣿⡿⠆⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡆⠀⠀⠀⠀⠀⣿⡿⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀
⠹⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀
⠀⠀⠹⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇⠀⠀⠀⠀⠀⣻⠁⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡤⠀⠀⠀⠀⠀⠀⠀⠿⠛⠛⠉⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠻⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣴⠂⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡿⠆⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢻⠟⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⠁⠀⠴⢶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠿⠿⡿⠿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠛⣿⣿⡤⠋⠻⣿⣿⣿⣿⣿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣤⢄⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠋⠉⠉⠀⠀⠀⠀⠀⠀⠈⡶⠂⠀⠿⠛⣿⣿⣿⣿⣿⣿⣿
⠛⠃⣽⡰⡆⠉⠁⠀⠀⠀⠘⢿⠿⣋⡓⠁⠈⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣹⣿
⣿⣿⣯⣿⢳⡄⠀⠀⣤⠀⢤⡌⢷⣿⣿⣷⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠉⠁⠧⠭
⣿⣿⣿⣿⣿⣓⠀⠠⣾⣅⣠⣧⡄⠛⠛⠋⠉⢹⡟⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⠛⠁⠀⠀⠀⠀⠀⢸⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⢿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⢠⡟⡀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣧⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠛⠿⣿⣿⣿⡿⠿⠁⣤⣴⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠏⣡⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠂⣴⣶⣤⣤⣴⣿⣿⠈⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⡿⠋⠁⠈⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠛⠿⢿⢿⡿⠟⠋⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡃⢀⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⡿⠟⠁⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣧⡸⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣧⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣬⣿⣿⣿⣧⢀⣤⡄⠀⠀⠀⢀⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⠉⠉⠀⠀⠀⠀⠈⠻⢿⣿⣧⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡷⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠇⠘⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠁⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⣠⣤⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣴⣦⢂⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡅⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡿⠁⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠟⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⡉⠀⣠⠴⢶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡟⠋⣹⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⠿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣽⣿
⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣠⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣟⡿⢿⣿⣿⡟⠛⠉⠉⠉⠙⠛⠿⠿⠯⢭
⢉⣍⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠀⢶⣷⣶⣶⣶⡄⠀⠀⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣹⣿⣋⣉⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣶⣿⣦⣤⡆⠤
⣿⣿⣿⣏⣿⡿⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⣾⣿⣿⣿⣟⠀⠀
⣿⣿⡿⠛⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⢿⠀⣀
⣿⣿⠀⣾⣧⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⠛⣿⣿⣿⣿⣿⠟⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡟⠀⠀⠛
⣿⡇⠀⣿⣿⣆⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠉⣠⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⠀⠀⠀
⣿⡇⢰⣿⣿⣿⣶⣿⡿⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠹⠿⠿⣿⣯⣿⠗⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀
⣿⣿⣮⠻⣿⣿⣿⡿⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠃⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡟⣿⠁⠀⢀⣤⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠀⠈⠀⠶⡿⠏⠁⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⠀⠀⣤⣤⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⣿⣿⡏⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠗⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠟⠛⢋⣉⣈⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣵⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣴⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣧⣄⣀⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢉⠉⠛⠛⠿⡿⣿⣏⡛⠿⠿⢿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠉⠛⠛⠛⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣿⣿⣿⣿⠟⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠁⠀⠀⢨⣿⣿⣿⣿⣿⣿⣷⣤⡀⠙⢧⣠⣤⣤⣀⡀⠀⠀⠀⣀⣤⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠻⠿⣿⣿⠿⠆⠀⠀⢹⠜⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⣿⣷⣶⣻⣆⡔⡜⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⣿⣿⢿⣿⣿⣿⣷⣿⠋⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣶⣦⣤⣿⣿⡟⣻⣿⣿⣿⣿⣧⠀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣉⠛⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢻⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠟⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡏⠙⠿⢿⣿⣱⠟⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡏⠁⠀⠀⠀⣠⣤⣄⣀⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⣿⣴⣾⣾⣿⠏⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡄⠀⠀⠀⠹⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡏⠋⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣹⣧⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣼⡟⠘⠃⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⣿⣼⠂⠀
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠇⠀
⣿⣿⣏⡟⣿⣿⣻⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢫⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠀⠀⠀⠈⠉⢻⢻⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠻⠿⣧⣀⣀⣀⣀⠀⠀⠀⠀⢰⣰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠉⠙⠛⢿⣿⣟⣥⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠈⢿⣿⣿⣿⡿⢧⠀⠀⢼⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣩⣤⣤⣤⠶⠶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣲⣾⣿⣶⣶⣷⣠⣽⠧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠉⠀⠀⠀⠀⠟⠛⠛⠛⠿⠛⠁⢀⣼⣿⣿⡿⠃⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⡆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣰⣿⣿⠛⢻⣿⣿⣿⣿⣅
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⠋⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠯⠟⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠿⣿⣿⡗⠂⢾⣿⣿⣿⣿⠿⠃
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣾⢿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠈⣿⣿⣆⠀⡿⠿⢶⣿⣿⠛⠋⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠚⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡏⣼⣿⣿⣿⣿⣿⣿⣿⠀⢸⣷⣿⣿⣿⣶⠃⠀⣼⣿⠃⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢉⠀⣿⣿⣿⣿⣿⣿⣿⡟⠀⣼⢩⠇⢹⣿⣥⣀⣴⣿⠃⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣿⣿⣿⣿⣿⡿⠟⠀⣾⣿⣼⠀⠀⠈⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣟⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠋⠁⠀⡤⢀⠗⠿⠀⠀⠀⣹⢏⣿⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠍⠀⢠⢤⡞⡵⠃⠀⠀⠀⠀⣰⢫⡿⠁⠿⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢏⡜⠁⠀⠀⠀⠀⡴⣳⣿⡟⠂⣸⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⡎⠀⠀⠀⠀⠀⢼⡾⠁⠈⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠛⡅⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⢀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣱⠏⠀⠀⠀⡀⠀⠀⠸⣿⣿⣶⣶⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⡏⠁⠀⡀⣈⣥⣤⢀⡀⠉⠻⢿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⢀⠈⢙⣿
⠘⣩⣍⠛⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠻⠟⠹⠿⢿⣿⡿⠇⠈⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣉⣠⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡽⠿⢿⢿⣿⣿⣿⣿⣷⣯⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⠇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠉⠉⠻⢧⠀⣀⣀⣀⣀⣀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠛⠛⠛⠛⠋⠙⠟⠋⠀⠀⢀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⣰⣿⠿⠿⣿⠿⠿⡄⠀⠨
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠉⠛⠛⠛⣦⣀⣀⣀⠠⠁⠀⠀⠀⠀⠈⠃⠘⣿⣿⣿⣿⣿⣛⣹⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⢺⣿⣿⣿⣿⣶⣞⣿⣄⡀
⣿⣿⣿⢿⠋⠉⠈⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣯⣿⣿⣿⣿⣿⣿⠿⣿⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡀⣰⣿⣿⣿⣿⡋⣹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⠃⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢉⣻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⠈⠙⢿⣿⣏⠉⢻⣿⡀⠈⣨⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠙⠻⠁⠀⠈⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢶⣾⠏⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠈⢿⣿⣦⣸⠟⠛⣿⡿⠋⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠈⠘⣿⡟⠻⠟⡿⡫⢞⣵⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⠃⠀⣫⡦⣼⣿⣿⠟⠀⣰⣿⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⡀⠀⠀⠙⠀⠀⠘⠁⠀⠉⠘⠁⡀⢸⣿⣿⣿⣿⣿⣿⡟⠀⢰⢠⠇⠘⢿⣷⣶⣤⣿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⢿⣿⣷⡄⠀⠀⠀⠀⠰⠀⠀⠀⠀⢧⢣⢸⣿⣿⣿⣿⡿⠋⠀⠀⣿⢼⠀⠀⠀⠙⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⢰⠛⡜⣾⣿⡿⠟⠉⠀⠀⡴⣠⠉⠈⠀⠀⠀⣰⢣⡾⣆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡠⢀⠈⡄⠀⠘⣿⣿⣄⠀⠀⠀⠀⠀⠀⠈⡐⠹⠈⠋⡄⠀⠀⢀⡞⡰⠁⠀⠀⠀⠀⡴⣡⡟⠀⠋⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡀⠀⠘⢆⠀⠘⣿⣿⣧⠀⠈⢦⣄⠀⢀⠇⠀⠀⡌⠀⠀⣠⢟⡼⠁⠀⠀⠀⠀⡼⡵⠟⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣤⠀⠈⠣⡀⠘⣿⣿⡆⠀⠘⣿⣿⠀⠀⠀⠘⠀⠀⢠⢏⡞⠀⠀⠀⠀⠀⢺⡾⠁⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠘⣿⣇⠀⠀⠸⣿⡆⠀⠀⠀⠀⢠⢋⠞⠀⠀⠀⠀⣠⠀⠈⠴⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠙⣿⣧⠀⠀⢻⣿⣶⣄⠀⣠⠃⠂⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⣠⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡈⢿⣧⠀⠈⠿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡠⠋⠀⠀⠀⠀⠀⣴⣦⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⠠⡈⢿⣆⠀⠀⠀⠈⠻⣿⣷⣦⡄⠀⠀⠀⠀⠀⠠⢎⡼⠁⠀⠀⠀⠀⠀⠀⠙⠃⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠘⣿⣆⠀⠀⠀⠀⠈⠙⠿⠧⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⢸⣧⣤⣤⣄⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢸⣿⣿⣿⣿⣿⣤⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡄⠈⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣒⠂⠀⠂⠀⠀⠈⠛⠃⠙⠉⠙⠛⠛⠁
⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⢻⡿⢿⣯⣿⣿⣿
⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⠉⢺⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⢀⣀⣀⣼⣿⣿⡟⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠻⣿⣯⣭⣿⣿⣿⣿⠿⠛⠛⣿⣿⠛⠋⠉⠉⢻⣿⣿⣷⣾⣿⡿⢿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⢹⣿⣿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠿⠿⠟⠛⠛⠆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠉⠉⠀⡀⠐⠊⠍⡋⠋⠀⠉⠉⠁⠀⠀⠀⠁⡀⢛⣷⣤⣾⣿⣿⣿⣿⣿⡧⠘⠋⠻⣿⣿⣿⣿⣿⣿⣿⣯⡇⣀⡾⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠷⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣭⣴⣟⣿⣤⡀⠀⠀⠠⠀⠀⠀⠀⢶⣦⠤⠤⠤⠿⣿⣿⠏⢸⣿⣿⣿⣿⣶⣶⣤⣄⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣨⣯⣿⣿⣿⣿⣧⣄⡈⠉⠙⠻⣿⣿⣿⣿⣿⣿⠀⠀⣀⣤⣤⣤⣀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠃⠀⠂⠠⠄⣀⣠⣼⡞⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠈⢻⣿⣿⣿⣿⣄⣼⣟⠛⣻⡟⢉⣉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢉⣴⣶⣶⣶⡄⠀⠀⢸⣿⣿⣿⠃⣠⣶⠖⠁⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡿⠛⢻⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣆⣼⣿⣿⣿⡏⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⣿⣿⣯⣽⣿⣟⣾⣿⣿⡻⠿⣣⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢺⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⠁⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡗⣸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣾⡿⢿⣿⣿⣿⣿⣿⣿⣥⣀⡼⣻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣼⣿⣿⣿⣿⡟⠀⣿⣿⢧⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡟⠛⠁⢻⣿⣇⣾⣿⣿⣿⣿⣿⣿⣬⣭⣿⣿⣿⣿⣿⣿⣿⡿⠋⠛⣿⣧⡀⢹⣿⣿⣿⣿⣿⣡⣴⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠘⠻⣿⣿⣿⣿⣆⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠏⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠹⣿⣷⣾⡿⠛⢿⣿⣿⠿⠟⠋⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣿⣶⣜⣿⣿⣿⣿⣿⡟⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡿⠋⠀⠀⠀⢻⣿⠿⠟⣻⣿⣿⣿⣽⠏⣿⣏⣹⣿⣿⣿⣿⠃⠀⠀⠀⠀⢰⣿⣿⣟⠁⠀⢸⡟⠁⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⣰⡷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠸⡿⠰⠒⠉⢉⠝⣵⡟⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡞⢠⣼⣹⡿⣿⣶⣶⡞⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⡟⣟⣿⣿⠻⣇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣦⡀⠀⠀⠀⠀⠀⠠⠉⠁⠊⠛⠁⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⣄⠃⠀⠊⢹⣷⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀
⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡿⠋⠀⠀⠀⠀⠈⠉⢠⣾⣿⣿⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢿⣿⣿⣿⡿⠋⠀⠀⢸⢼⠀⠀⠀⢀⠝⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣁⣀⣀⣀⣤⣄⡀⠀⣴⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠱⣸⣿⡿⠋⠀⠀⢠⢂⠂⠀⠀⠀⠀⡎⡼⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⣄⣿⣿⣿⣿⠟⠉⣡⣾⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠹⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠘⠁⡀⠀⠀⢠⢃⠎⠀⠀⠀⠀⡘⡼⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠙⣿⣿⣿⣧⣴⣿⣿⣿⠟⠛⠻⠿⠿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠐⡄⠀⠹⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⢠⠇⠎⠀⠀⠀⠀⠀⡽⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠈⠹⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠹⣿⣿⣦⠀⠀⢱⣦⠀⠀⠀⠀⠀⠀⢀⡏⡜⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠻⣿⣿⠏⠀⠀⣀⣀⣠⠄⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠁⣠⣶⣿⣿⣿⣿⣿⡆⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠘⢿⣧⡀⠀⠘⣿⣷⣦⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠘⠙⢿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⢂⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡀⠀⠸⣿⣿⣽⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠈⢩⣷⣴⡄⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠃⠀⠀⣿⣿⠻⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡄⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⠆⢻⠏⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⣿⡍⠠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠀⠀⠀⠛⠀⣸⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡟⠋⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠁⠛⢻⣷⣿⣿⣿
⣿⣿⣿⣿⣻⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄⠀⢸⣿⣿⣿⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢤⣤⣾⣿⣿⣇⡬
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠙⠿⣿⣭⣽⠟⣻⡿⠟⠛⠛⠻⡿⠛⣋⠉⠀⢩⣿⣿⣷⣾⣿⡷⠻⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢀⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⠛⠉⠉⠈⠉
⣿⣿⣿⣿⠹⣿⣿⣿⣿⠿⠋⠉⠉⠀⠀⠈⠀⠉⠍⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠉⣿⣧⣼⣿⣿⣿⣿⣿⡇⠐⠏⠙⣷⣿⣿⣿⣿⡿⣿⣽⡄⣠⡘⠏⠣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠛⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣶⣧⣹⣿⣿⣦⣴⣴⡏⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⡄⢰⣾⣾⣿⠛⠈⣻⣿⣿⣶⣤⣤⣄⣀⢠⣼⣵⣾⣿⣿⣿⣿⣿⣿⣿⣦⠂⣰⣿⣿⣅⣉⠉⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣠⣶⣶⣷⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣇⠀⠀⠀⠀⣀⠀⣠⣦⡀⠀⠀⠈⣱⠿⠋⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠻⣿⣿⣿⣿⣿⣏⢧⣴⣿⢤⣴⣿⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⣉⣉⡀⠀⠀⠀⢰⡿⣿⣿⣿⣿⠇⢀⡠⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡿⠿⢻⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠟⣻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣴⣿⣿⣿⣿⣧⡀⢀⣿⣿⣿⣿⣿⣿⣾⡿⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣩⢹⣿⣖⣼⣿⣿⣟⠟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢸⡟⢻⡿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⡟⢰⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡆⠺⣷⣄⠙⣿⣿⣿⣿⡿⣿⣿⡟⠚⣡
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢹⣿⣿⣿⣿⣿⣿⡿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠟⠛⠁⢸⣿⣇⣼⣿⣿⣿⣿⣿⣏⣩⣽⣿⣿⣿⣿⣿⢿⣿⠟⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠏⠘⠻⣿⣿⣿⣿⣧⣿⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠇⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⣾⣿⣿⡿⠛⠉⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣓⣈⣿⣶⡜⣿⣿⣿⣿⣿⣿⣷⡦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡿⠿⠃⠀⠀⠀⠘⣿⣿⣿⣿⣿⠟⣻⣿⠙⣻⣛⢹⣿⣿⣿⡟⠀⠀⠀⠀⠀⣼⣿⣿⣿⢀⣙⣻⠏⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠛⠃⣀⢶⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠟⠛⠛⡚⡫⡿⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⠀⢤⡿⣿⣿⡇⢸⣿⡟⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣠⣶⡾⣿⠀⠁⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠂⠊⠚⠘⠁⠀⣿⣿⣿⣿⣿⡟⠀⠀⡀⡆⠀⠑⠩⡳⣿⡁⢸⡿⠁⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣯⣿⠿⠛⠿⢿⣟⣻⣿⣿⣿⠏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢿⣿⣿⣿⠋⠀⠀⠀⠇⠇⠀⠀⠀⡌⣻⡷⠘⡇⠀⠀⠀⠀⢀⣠⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣸⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠡⠱⢸⡿⠋⠁⠀⢀⠆⡄⠀⠀⠀⠀⡸⢰⠃⠀⡀⠀⠀⠀⠀⣰⣿⣿⣿
⠀⠸⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣥⣶⣦⣀⠀⠀⣰⣿⣻⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠈⢿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠈⠠⠀⠀⢀⡎⡜⠀⠀⠀⠀⢀⢣⠇⠀⠀⠁⠀⠀⠀⣼⣿⣿⣿⣿
⠀⠀⣷⣾⣿⣿⣿⣯⡉⠹⣿⣿⣿⣿⣿⣿⣿⠟⠀⢸⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⢀⠀⠈⢿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡼⡰⠀⠀⠀⠀⠀⢈⡏⠀⠀⠀⠀⠀⠀⠀⡛⠛⠛⠛⠛
⠀⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠈⢿⣿⣿⣷⠀⠀⠀⢳⠤⠀⠀⠀⠀⠀⢸⠁⠃⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠈⠙⠛⠉⠳⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⢿⣿⣿⡀⠀⠀⠸⣿⣦⣀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡿⢻⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢲⣦⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⢻⣿⣿⣄⠀⠀⠘⢿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠃⠀⠀⢀⣀⣴⣿⡿⠀⢸⣿⣿⠆⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡄⠀⠀⠀⠛⠛⠻⠷⣄⡀⠀⠀⠀⠀⠀⠀⢠⢂⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣸⣿⣿⣿⣿⡟⠀⠀⣰⣿⣿⣿⣿⡇⠀⠘⣿⡿⢴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣄⠀⠀⠀⠀⠀⠀⠈⠓⣷⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾
⠀⠀⠀⢾⣿⣿⣿⣿⣿⣥⣴⣾⣿⣿⣿⣿⣿⣷⠀⠀⣿⠏⢨⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠁
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣿⠁⢾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⣿⣿⣻⣟⣛⣩⣹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠛⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡄⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣹⡟⠋⠃⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⢿⡏⢛⢿⡿⣿⣿⣿
⢻⣿⣾⣿⣿⠿⠚⣿⣿⣻⣿⣿⣿⣿⣿⣿⣾⢃⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡟⠀⠀⠐⢛⣧⣿⢿⣿
⣿⣿⣿⣿⣋⡑⢳⣟⢃⣘⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⠀⠀⢀⢻⣿⣿⠇⢱⣧⢘⣿⣿⣿⣟⣿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣤⠀⢀⣀⣾⠿⣩⣄⡈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⣿⢿⣿⠋⠉⠙⠛⣧⠁⠍⠉⠻⠟⠛⠛⠙⠻⣿⠛⠋⠈⠀⠀⡿⠀⣓⣺⣿⡷⠫⣾⣾⣿⣿⣿⣿⣿⣿⣛⠭⣿⠋⢀⣾⣿⠀⣸⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⠟⠋⠁⠀⠀
⣿⣿⣿⣿⠁⢈⣻⣿⣯⠋⠉⠀⠈⠀⠀⠀⠀⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⣠⣼⣿⣾⣿⡿⡿⠇⢠⠋⠙⣧⣿⣿⡿⣿⣿⣿⣰⠇⢀⠘⠋⠁⠸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⠙⠃⠀⠀⠀⠀
⣻⣿⡿⠻⣯⣤⡠⣿⣿⣀⡀⠠⠌⠻⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⣦⣸⡟⠋⣺⣧⣬⣤⣄⣀⡀⠀⢀⣴⣥⣾⣷⣾⣽⣿⣿⣟⢻⣀⠄⣠⣤⣦⣀⣀⠉⠉⠛⢻⣿⣿⣿⣿⣿⣿⣿⡆⢁⠀⠀⣴⣶⣦⡤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠐⢀⠁⠀⠀⠀⠀⠀⠀⠀⣜⠀⠀⠀⠀⢈⣼⡏⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡎⢿⣿⣿⣿⣿⣿⡿⣿⣷⣿⣄⣼⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇⠈⢦⣼⡧⢠⣾⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣾⣿⣿⣿⡶⠘⠀⠀⣶⡾⣿⣿⣿⡿⠃⠀⠀⠀⠉⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠗⢸⣿⣏⣿⣿⣿⣿⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠠⣿⣿⣿⣿⣿⣧⡀⢸⣿⣿⣿⣛⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⣉⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠁⣠⣶⠀⠀⠀⠀⠀⠀⠀⣯⣿⣿⣿⣟⡛⣿⣶⠆⣸⣿⣿⡝⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⠿⣿⢿⣿⣿⡇⢸⣿⣿⣿⡋⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣾⣿⣿⣿⡧⡤⠀⣼⣿⣿⣿⣿⣿⣾⣻⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣾⡏⢻⣿⡇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠼⢷⣄⠉⢺⣿⣿⣷⡌⠹⣿⣿⠛⢋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣾⣿⣿⣿⣿⣿⢻⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡙⠛⠛⠀⠈⣿⡇⣼⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⡋⠿⠋⠀⠀⠈⢿⣿⣾⣿⣿⣿⣷⡀⣹⣿⣿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⡹⠛⢿⣿⣿⣿⡇⢸⣿⣿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡧⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⠃⠀⠀⠀⠀⠀⣾⣿⣿⣿⣦⣿⣿⠟⠛⠋⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠖⠀⣶⣆⢹⣿⣿⣿⣶⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠷⠀⠀⠀⠀⠀⣭⣤⣤⡉⣿⠿⠟⣋⣭⣤⣤⣀⠀⢿⣿⡏⠀⠀⣤⣤⣤⠀⣿⣿⣿⠃⢘⣻⠏⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⢀⣸⣿⣯⡄⢻⣿⡿⠋⠙⠿⣿⡟⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠉⠀⣼⣿⣿⠛⣿⣿⣧⠈⢉⣀⣄⡀⣿⣿⣿⠀⠛⣁⣀⣄⣈⡛⠀⠀⠀⢀⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣶⣆⣨⡴⣾⠈⠉⠀⠀⠀⠀⠀⠹⣿⣿⣶⣶⣤⠀⠀⠀⣿⣿⣿⡇⠀⠀⣿⣿⣿⠀⣿⣿⣿⠀⣾⣿⣿⠛⣿⣿⣿⠀⣾⣿⣿⠻⣿⣿⡆⢀⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣆⠀⠀⣿⣿⣿⡇⠀⠀⣿⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⣼⣿⣿⣷⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⠿⠋⠉⠉⠉⢩⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡇⠀⣿⣿⣿⡇⠀⠀⣿⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⠉⣭⣭⣭⠸⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⢠⣿⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⣿⣿⣿⣧⣤⠀⢿⣿⣿⣀⣿⣿⡿⠀⣿⣿⣿⣀⣿⣿⣿⠀⣿⣿⣿⣀⣿⣿⡏⠀⠁⠀⠀⠀
⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠘⣿⣿⣆⡛⠛⠛⠛⠛⠀⠈⠛⠿⠿⠿⠛⠁⠀⠘⠻⠿⠋⠛⠛⠛⢀⠈⠛⠻⠿⠟⠋⠀⠀⠀⠀⠀⠀
⢿⣿⣶⣿⣿⣿⡟⠉⠛⣿⣿⠋⣴⣿⣿⣿⡆⠴⠞⠨⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠙⣿⣿⣿⣷⡄⠀⠀⠀⢶⣦⣄⠀⠀⠀⠀⡘⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⣰⣿⣿⣿⣿⣿⣆⡀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⣿⣿⣿⡄⠀⠀⠀⢼⢿⣿⣶⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡀⣴⣿⣿⣿⣿⣿⠿⠛⠉⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣆⠀⠀⠀⠀⠻⢿⣿⣿⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢻⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⣠⡄⠀⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣆⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠛⠀⢸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠻⣿⡄⣿⠃⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡞
⠀⠀⠰⠀⣸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡄⠀⠀⠀⠀⣿⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣼⣿⣶⡄⠀⠀⣿⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⣼⣉⣻⣏⣋⣉⣉⣤⢀⣾⣿⣿⣿⡇⠀⠀⢿⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡄⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣹⡿⠋⠇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣯⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⡿⢿⣿⠿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠚⢻⣀⣿⢿⣿
⣿⣿⣿⣿⣋⡛⢻⣿⣗⣼⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣏⠀⠀⢀⢛⣿⣯⡏⢱⣯⡺⣿⣿⣿⣟⣿⡿⣿⣟⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣄⠀⣀⣀⣾⣿⣽⡌⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠉⠉⠉⠻⣭⠅⠩⠋⠻⡟⠛⠛⠛⠻⣿⠛⢋⠈⠀⠈⣿⠢⣓⣺⣿⡷⢩⣾⣾⣿⣿⣿⣿⣿⣿⣛⡿⣿⠃⢉⣾⣿⠀⣻⣿⣿⣟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡶⠋⠉⠉
⣿⣿⣿⣿⠋⢨⣿⣿⣿⠛⠋⠀⠈⠀⠀⠀⠀⠉⡁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⣻⣤⣼⣿⣿⡿⠿⠿⠃⢰⠁⠙⣿⣿⣿⣿⣿⡿⣿⣱⠇⢀⠘⡛⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡏⠛⠚⠃⠀⠀
⣻⣿⣿⣿⣶⣦⣸⣿⣿⣄⣀⢠⡌⢻⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠄⢠⣴⣶⣿⣿⡿⣛⣁⣀⣀⣀⡀⠀⠀⣠⣬⣥⣾⣷⣷⣽⣿⣿⣿⣿⣀⡆⣰⣿⣿⣷⣤⣤⣈⠙⢿⣿⣿⣿⣾⣿⣿⣿⣿⢛⠻⠀⠀⢀⣴⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠸⠸⠇⠀⠀⠀⠀⡀⠀⠀⢸⠁⠀⠀⠈⠉⣸⡿⢸⣼⣿⣿⣿⣿⣿⣿⣿⣷⡝⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣤⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⢿⣿⣿⣿⣿⣿⡅⠚⠀⠐⣠⣾⡥⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣶⣿⣾⣀⣀⣾⠿⠋⠀⠁⠀⠀⠀⠀⢀⠞⠻⠁⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⢹⣿⣏⣿⣿⣿⠟⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢠⣿⣿⣿⣿⣿⣷⠀⠀⠀⣻⣿⣿⣟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⢿⣿⣿⣿⡟⠁⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⢻⡷⣶⠄⠘⣿⣿⡹⠟⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⠐⠋⢿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⠁⢀⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣯⣿⣿⣾⡇⠙⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⠿⣿⡿⠀⠀⣸⡟⢻⡿⣿⣷⡀⠀⣈⣿⣿⣟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⠀⣿⣿⣷⠿⣿⡄⠈⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡻⠿⠟⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡆⠘⠓⠀⠈⢛⣿⣄⡁⣿⣿⣧⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢀⣠⣤⣤⡀⠀⠀⠀⠀⢻⣿⣿⣿⣯⡃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡅⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠉⢁⣠⣾⡿⠁⠾⠂⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡏⣴⣿⣿⣿⣿⡗⠀⠀⠀⠀⠈⣿⣿⣿⡿⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠿⠂⠀⠀⠀⠀⣬⣤⣤⡍⣿⣿⠟⣃⣤⣤⣤⣈⠁⢺⣿⣿⡇⠀⣤⣤⣤⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛
⣟⣿⡟⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣴⠂⢠⡀⢿⣿⣿⣿⣦⣄⠄⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⣼⣿⣿⠛⣿⣿⣧⠈⢉⣁⣄⡀⣿⣿⣿⠀⠀⣈⣠⣌⣉⡙⠻⢿⡿⠉⠀⠀
⣿⣿⡇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠈⠈⢁⣿⣷⣄⣤⡉⠉⠛⠇⣀⣤⠀⠛⠀⠀⠀⠀⠈⢻⣷⣶⣶⣾⣷⣆⠀⠀⣿⣿⣿⡇⠀⠀⣿⣿⣿⠀⣿⣿⣿⠀⣾⣿⣿⠛⣿⣿⣿⠀⣾⣿⣿⢻⣿⣿⡆⠀⠀⠀⠀⠀
⣧⡈⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠘⣽⣾⣿⠘⠷⢂⣤⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣆⠀⣿⣿⣿⡇⠀⠀⣿⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⣼⣿⣿⣷⠀⠀⠀⠀⠀
⠛⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⣠⣶⠿⠿⠿⠿⠀⣠⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠀⣿⣿⣿⡇⠀⠀⣿⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⠉⣭⣭⣭⠀⠀⠀⠀⠀
⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠁⠀⠀⠀⢰⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⣿⣿⣿⣧⣤⠀⢿⣿⣿⣀⣿⣿⡿⠀⣿⣿⣿⣀⣿⣿⣿⠀⣿⣿⣿⣀⣿⣿⡏⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠘⣿⣿⣆⡛⠛⠛⠛⠛⠀⠈⠛⠿⠿⠿⠛⠁⠀⠘⠻⠿⠋⠛⠛⠛⠀⠈⠛⠿⠿⠟⠋⢀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠘⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣼⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣧⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠁⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⢿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣋⣥⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⣿⣥⣤⣄⣀⣉⣙⣯⡷⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣋⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣦⣀⣀⣴⣿⣿⣿⡿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⣽⣋⣻⣏⣋⣉⣹⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿
⣆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⡏⠹⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣉⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠇⠁⡼⠻⣇⣸⣿⣿⡿
⣿⣿⣿⣿⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣤⡀⠀⣜⣿⣿⡿⢩⣾⣷⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⢀⣀⣴⣿⣿⣿⡇⠀
⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡿⠿⡇⠀⠀⠉⢿⣐⠈⠋⠈⠏⠉⠉⠉⠉⢻⠏⢉⣀⠀⠀⢬⣿⢊⣰⣿⡿⠂⠶⡿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⠁⣴⣿⡆⠸⣿⣿⣿⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⣷⣧⣽⠗⠒
⣿⣿⣿⡇⡘⠞⣿⣿⡟⠋⠀⢀⣀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣻⣤⣿⣿⡿⠿⠿⠏⠐⡏⠀⢻⣿⣿⣿⣿⣿⢿⣭⡶⠃⣀⠛⠙⢸⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⠙⠛⠿⠛⠋⠀
⣿⣿⣿⣿⣿⣦⣿⣿⣷⣤⣾⡇⢘⠻⣤⠀⠀⠀⠂⠀⠀⠀⠀⢱⠀⠒⠰⣶⢿⣿⣿⣿⡿⣋⣀⣀⣀⣀⡀⠀⠀⣴⣵⣾⣿⣿⣦⣿⣿⣿⣿⣿⡦⠀⣀⣷⣿⣿⣍⣉⡙⠿⣿⣿⣿⣷⣿⣿⣿⣿⡟⠛⣷⡦⠄⠀⢀⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡔⣗⣻⡄⠀⠀⠄⡀⠀⣀⣠⣯⠀⠀⠀⠉⠀⣹⡟⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⡌⣿⣿⣿⣿⣿⡿⢿⣟⣿⣷⣀⣠⣿⣿⣿⣿⣿⣿⣻⣷⡈⠻⣿⣿⣿⣿⣿⣯⠑⢁⣠⣴⣾⣷⣾⣭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⢿⣿⣿⣧⣄⣀⣠⠾⠿⠁⢸⣿⣿⣿⣿⣿⣿⣿⡿⠿⠧⢸⣏⣽⣿⣿⠿⣋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢸⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠀⠀⢀⣀⣀⠀⠀⠀⠸⢿⣿⣿⡟⠁⠀⠀⠀⠀⣟⣿⣿⣿⣿⡛⣿⣶⣶⢤⠘⢿⣟⠛⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡘⢛⣛⡋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⢠⣾⣿⣿⣿⡗⠀⠀⠀⠀⠹⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠙⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠚⣛⡁⢸⣿⣿⣿⣿⣿⡇⠈⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠁⢠⣿⣿⣿⣿⣿⠛⠋⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⠿⠛⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠋⣥⢀⡄⢠⣿⣿⣿⣿⣿⣿⠃⣴⡿⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠸⣿⣿⣷⣿⣿⠃⠀⠀⠀⠀⠀⠙⠻⠿⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡤⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠉⢹⣿⠃⠸⠿⠿⠁⠀⣽⣿⣿⣿⣿⣿⣾⡏⠀⠀
⣿⡇⠀⢹⣿⣿⣿⣿⣿⠀⣴⣄⠀⠀⢹⣿⣿⣿⡿⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠻⣿⣿⡿⠂⠀⠀⠀⠀⣤⣤⣤⡀⠉⠻⠟⣁⣤⣤⣬⣉⠛⢿⣿⣿⣿⠁⣤⣤⣤⠘⠿⠃⣿⣿⣿⣿⣿⡟⢻⢣⠀⠀
⠻⡆⣠⣿⣿⣿⣿⣿⣟⣾⣿⣿⣧⡄⠘⣿⣿⣿⣷⣀⣠⠄⠀⠀⠀⣸⡃⢀⢠⣿⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣄⠀⠀⠀⣿⣿⣿⡇⠐⠁⣾⣿⣿⠛⣿⣿⣧⠈⢋⣩⣄⡀⣿⣿⣿⠀⠂⣀⣩⣄⣉⡙⠛⠀⠀⠀⠀⠀
⡆⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⢹⠿⠿⠿⠋⠀⠀⠀⠀⠋⣉⣿⡏⠀⠃⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⡇⠀⠀⣿⣿⣿⠀⣿⣿⣿⠀⣾⣿⣿⠛⣿⣿⣿⠀⣾⣿⣿⢻⣿⣿⡆⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⢀⡈⠷⠀⠀⠀⠀⠀⢀⣴⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡀⣿⣿⣿⡇⠀⠀⣿⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⣼⣿⣿⣿⠀⠀⠀⠀⠀
⣶⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠉⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡁⣿⣿⣿⡇⠀⠀⣿⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⠉⣭⣭⣭⠀⠀⠀⠀⠀
⣩⣿⣿⠁⠀⣾⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢻⣿⣿⡇⣿⣿⣿⣧⣤⠀⢿⣿⣿⣀⣿⣿⡿⠀⣿⣿⣿⣀⣿⣿⣿⠀⣿⣿⣿⣀⣿⣿⡟⠀⠀⠀⠀⠀
⢹⣷⣾⣷⣾⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⢂⠀⠀⠹⣿⣇⡛⠛⠛⠛⠛⠀⠈⠛⠿⠿⠿⠛⠁⠀⠘⠻⠿⠋⠛⠛⠛⠀⠈⠛⠿⠿⠟⠋⣀⠀⠀⠀⠀⠀
⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠻⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠲⢶⣶⣤⡀⣶⣶⣿⣿⣷⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⣶⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢼⣿⣷⠀⠙⣿⣿⣿⢫⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣇⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣟⣉⣭⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠹⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣋⣀⠀⠘⣟⡧⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⢛⣋⣉⣠⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⣀⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠟⣟⣻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⢻
⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡄⢀⣀⣀⠀⠀⢀⣴⣿⣿⠟⠉⠁⢐⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣆⣼⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⠃⠀⠀⠀⠘⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣏⠉⣿⣿⣿⣟⣋⣩⣙⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠃⠆⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡏⠉⢁⠿⣿⣹⣿⣿⣿⡿⠟
⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣧⣤⠀⢰⣻⡿⣿⢋⣶⣿⣿⣿⣿⣿⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⢀⠀⢠⣿⣿⣿⣿⠛⠂⣠
⣿⣿⠟⣿⣿⣿⣿⣿⡟⠛⠿⠈⠁⢀⠰⠷⡆⠙⠃⢹⠏⠉⠉⠉⠙⠟⠉⣅⣀⠀⢠⣿⣯⣵⣿⣿⠗⢹⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢡⣾⡟⠑⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣧⡤⠼⣿
⣿⣿⣠⡓⣿⣿⡿⠉⠀⣀⢤⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣿⣷⣾⣿⣿⣿⠟⠟⠁⠊⠁⢘⣿⣿⣿⣿⣿⣿⣯⣷⠟⣀⡘⡋⢫⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠖⠀⢹
⣿⣿⣿⣿⣼⣿⣿⣷⣿⣿⣠⣽⣳⠄⠀⠀⠀⠀⠀⠀⠀⣼⡟⠙⠒⣿⡾⡿⣿⣿⣽⣿⣿⣁⣄⣄⣀⣀⣀⣀⠠⣶⣿⣿⣷⣿⣿⣯⣿⣿⣧⠄⣀⣬⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣠⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢛⢙⣆⠀⠀⣦⣠⣤⣤⣴⣿⣄⡈⠀⠘⠁⠈⢉⣽⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⢿⣿⣿⣿⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣶⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣰⣟⣉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠷⠏⠀⠘⢿⣿⣶⣿⣿⣿⣿⣷⣦⣀⣀⣴⣿⡿⠈⣿⣿⣿⠿⣿⣿⣿⡿⠟⠻⠀⣹⣿⣿⠿⢋⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⡘⣿⣿⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠃⠀⢸⣿⣿⣿⣿⣛⣻⣿⣿⣳⣄⡉⠻⢫⣶⣿⣿⣿⣿⣿⣟⣟⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸⣿⢟⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢀⣤⣶⣦⣄⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⠈⣻⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠀⣴⣿⣿⣿⣿⣯⣀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠉⠛⠛⠛⠿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣀⣽⣿⣿
⢿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⠿⠋⢁⠀⠀⠀⠀⢿⣿⣿⠿⠿⠿⠿⠄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷⠂⠀⠀⠀⢀⣸⣯⣀⠀⠀⠀⢹⣿⣿⢿⣷⣾⣿⣿⠿⠛⠛⢩⡅⠘⣿⣿⢻⣿⣿⣿⡿⠿⣿⣿⣿⠋⠛⠃
⢀⣿⣿⣿⣿⣿⣿⡇⠘⣿⣿⣿⣿⡿⠻⣿⣿⠁⠀⠀⠀⣸⠋⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⠟⠀⠀⠀⠀⠘⣥⣤⣤⡄⠀⠀⠀⣀⣤⣤⣤⣙⠛⣿⣷⣶⣶⠁⣤⣤⣤⠀⠀⣿⣿⣿⣷⣄⢸⡟⣿⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⠀⢹⣿⣿⣿⣷⡂⠉⠀⠀⠀⠀⣠⣿⡀⣾⡟⢻⠟⠀⠀⠐⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣄⠀⠀⠀⣿⣿⣿⡇⠸⠂⣾⣿⣿⠛⣿⣿⣧⠈⢃⣠⣄⡀⣿⣿⣿⠀⠀⣉⣩⣍⣈⡙⠻⠇⠉⠃⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣀⠀⠀⠀⠘⠿⣿⣷⣿⣶⣟⣷⡿⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⡄⠀⣿⣿⣿⡇⠀⠀⣿⣿⣿⠀⣿⣿⣿⠀⣾⣿⣿⠛⣿⣿⣿⠀⣾⣿⣿⢻⣿⣿⡆⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡇⠀⠀⣿⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⣼⣿⣿⣿⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⠀⣿⣿⣿⡇⠀⠀⣿⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⠉⣭⣭⣭⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠋⣽⣷⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢀⠀⠀⠙⣿⣿⣿⡇⣿⣿⣿⣧⣴⠀⢿⣿⣿⣀⣿⣿⡿⠀⣿⣿⣿⣀⣿⣿⣿⠀⣿⣿⣿⣀⣿⣿⡟⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠢⠀⠀⠘⣿⣿⣇⡛⠛⠛⠛⠛⠀⠈⠛⠿⠿⠿⠛⠁⠀⠘⠻⠿⠋⠛⠛⠛⠀⠈⠛⠿⠿⠟⠋⡀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠘⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠘⣿⣶⣶⣶⣿⡏⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣏⣉⣩⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠘⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣟⣛⣋⣉⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠋⠀⠀⠀⠀⠠⠀⠀
⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣋⣉⣙⠛⠛⠋⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠿⠟⠋⠉⠉⠉⠉⠉⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀
⠀⢠⣴⣾⣀⣀⡀⢀⣠⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀
⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⠙⣿⣿⣻⣟⣏⣉⡉⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⢿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡘⠃⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠈⠩⠿⢿⣯⣿⣿⣿⣿⠿⠋⠻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠛⢿⣿⣛⢿⣿⢿⣿⣿⢿⠿⢿⣿⣿⣿⠟⠟⠻⢿⣷⣧⣀⣷⣿⣿⣏⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢀⣀⣴⣿⣿⣿⣏⡅⠀⠀⣠⣴⣾
⣿⣿⣿⣿⣟⠻⠉⠉⠁⡀⠰⠎⠛⠛⠈⠁⠈⠟⠂⠀⠀⠀⠙⠁⠐⢦⣤⣠⣿⣿⣿⣿⣿⡏⢹⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⢿⡯⢀⣿⣿⣠⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣯⣶⣖⢺⣿⣿⣿
⣾⢿⣿⣿⡁⣠⣴⡟⢺⣧⠄⢠⣠⣶⠀⠀⠀⠀⢠⣀⣀⣀⢀⣰⣶⣾⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⠀⠻⠿⣿⣿⣿⣿⣿⣾⣟⣥⣮⣩⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠟⠉⠈⠿⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠟⢈⣀⣀⣀⠀⠀⠀⣾⡿⠈⠍⠹⣿⠻⡿⣿⣿⣽⣿⣿⣿⣶⣶⣶⣶⣤⣤⣤⠙⣿⣿⣿⣿⣿⣿⣿⡿⠿⠠⢾⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣤⣶⣒⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣼⣿⣿⣿⣿⣿⡄⢀⣿⣷⣦⠀⠀⠉⠀⢀⢃⣽⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣛⣿⣿⣿⣷⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⠙⢿⣿⢻⣿⣿⣿⣿⣿⡇⠀⣰⣿⣬⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣿⣿⣿⡿⢻⡇⠈⣿⣿⣿⣿⣿⣿⣿⣏⣉⡃⢸⣿⠟⣫⣼⣿⣿⣿⣿⣿⣿⠿⣛⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣟⣾⣿⣿⣿⣿⡟⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠈⠉⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠘⠃⠀⣿⣿⣿⣿⣷⣦⣿⣿⣿⣷⣤⠀⠛⠿⠿⣿⣿⣿⣿⣯⣽⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢻⣿⣿⣿⣿⠋⠀⣀⠀⢿⣿⣿⣿⣿
⣿⣿⣿⣿⠉⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⢓⡀⠀⠈⠉⢻⣿⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⠀⣿⣿⣿⡿⢠⣾⣿⣿⣄⠹⣿⣿⣿
⣿⣿⣿⠏⠀⣠⣾⣿⣿⣿⣿⠇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡏⠉⠉⠀⠀⠀⣼⣿⣗⣄⠀⠀⢿⣟⡛⠉⣙⢿⣿⣿⡿⠿⠿⠟⡏⠀⠀⠀⣿⣿⣿⣷⣾⣿⣿⣿⣿⣾⣿⠛⠛
⣿⣿⡟⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⠿⠛⠓⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡟⠁⠀⠀⢀⣤⣿⣿⣿⣿⠀⠐⠉⢻⣿⣿⣿⣿⣿⣿⣷⣤⣤⣾⠃⠀⠀⢰⣿⣿⣿⣿⣿⣧⣼⣿⡟⠉⠛⠀⠀
⣿⣿⣆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣥⣤⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⣤⣦⣤⠀⠀⠀⠀⠀⠀⠈⠻⠟⠛⠁⠀⠀⠀⠈⠉⠉⣤⣤⣤⡜⣿⡖⠛⣉⣭⣭⣤⣉⠛⣿⣿⣿⡟⠀⣤⣤⣬⢻⣿⣿⣿⣿⣿⣧⡿⢷⠀⠀⠀⠀
⣿⣿⣿⣄⠀⢸⣿⣿⣿⣟⣿⠋⠿⠟⠀⠀⣾⣿⣾⣿⣿⣿⣿⣿⣿⣛⡙⠦⠀⠀⠀⠀⢲⣦⣤⣤⣤⣤⣵⣤⡀⠀⠀⠀⣿⣿⣿⡇⠈⠀⣾⣿⣿⠛⣿⣿⣧⠘⢋⣩⣄⡀⣿⣿⣿⠀⠟⣉⣡⣭⣀⡀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠰⣿⣿⡿⡿⠈⠻⠿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣿⣿⣿⡇⠀⠀⣿⣿⣿⠀⣿⣿⣿⠀⣾⣿⣿⠛⣿⣿⣿⠀⣾⣿⣿⢻⣿⣿⡆⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣦⣴⣾⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣷⠀⠀⣿⣿⣿⡇⠀⠀⣿⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⣼⣿⣿⣿⠀⠀⠀⠀⠀
⣿⣿⣿⠟⠛⠉⠁⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠙⠇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⢿⣿⣿⣿⣿⡄⠀⣿⣿⣿⡇⠀⠀⣿⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⠉⣭⣭⣭⠀⠀⠀⠀⠀
⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠸⠻⣿⣧⠀⠀⠀⠀⠀⠀⢰⡦⠀⠀⠡⡀⠀⠈⢿⣿⣿⣿⣷⡀⣿⣿⣿⣧⣶⠀⢿⣿⣿⣀⣿⣿⡿⠀⣿⣿⣿⣀⣿⣿⣿⠀⣿⣿⣿⣀⣿⣿⡟⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠻⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠑⡄⠀⠈⢿⣿⣿⣿⣧⡛⠛⠛⠛⠛⠀⠈⠛⠿⠿⠿⠛⠁⠀⠘⠻⠿⠋⠛⠛⠛⣀⣈⠛⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠈⠢⡀⠀⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢺⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠑⡀⠈⢿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠈⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⡀⠀⠀⠀
⠀⠀⣠⣾⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⠷⠀⠀⠀
⣤⣾⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢰⡫⠉⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣸⣯⡆⠀⠀⠀⠀⠀⠀⠀⠀⠌⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⢻⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⣨⠋⠀⠀⠀⢀⡄⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣉⣭⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⠀⠀⠀⠀⣹⡗⠀⠀⠁⠀⠘⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠻⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠏⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠉⠿⢿⣿⣿⣿⢿⣿⠿⠋⠙⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣷⣷⣀⣸⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡀⣀⣀⣾⣿⣿⣷⣤⡄⢀⣠⣾⣿⣿⣿⣿
⣿⡟⠻⡿⠛⠋⠁⠀⠾⣻⠿⢿⠻⠋⠿⠛⠟⠀⠀⠙⠛⠤⢤⣤⣀⣼⣿⣿⣿⣾⣿⠋⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣾⣿⢛⣿⣿⣿⣿⣯⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿
⣿⡟⢀⣠⡴⢶⣾⡄⢠⠋⣀⣤⣶⣶⣦⠀⠀⢀⣀⠀⢀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣯⡾⠿⠃⠀⠛⢿⣿⣿⣿⣿⣿⣿⣛⣧⣽⣍⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⠿⣿⣯⡄⠀⢸⣿⣿⣿⣿⣿⠘⠉⠿⠿⠿⣿⡏⢉
⣿⣿⣿⣿⣿⣾⣿⣿⡏⣼⣿⣿⣿⣿⣿⣿⡀⣼⣟⠸⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣤⣌⠻⣿⣿⣿⣿⣿⣿⠿⠗⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡮⠩⠥⠄⣸⣿⣿⣿⣿⡿⠀⠀⠀⣀⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡄⠉⠁⠈⣻⡛⢙⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢻⡿⣿⣿⣿⣿⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢶⣿⣿⣿⣿⠟⠁⠀⠀⢰⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠿⠛⠟⠛⠛⢿⣿⣿⣅⣨⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⠿⢿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣏⣉⠃⠸⢟⣥⣽⣿⣿⣿⣿⣿⣿⣟⢹⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢼⣿⣿⣿⡏⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿
⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠸⡇⠠⣿⣿⣿⣿⣷⣾⣿⣿⣿⣷⡆⠻⠛⠻⢿⣿⣿⣏⣿⣿⡟⠙⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⠃⠀⠀⠀⠀⠻⣿⣿⣿⣿⣧
⣿⠏⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⠀⠁⣁⣼⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠈⣧⣀⠀⠁⠙⣿⣿⢧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠁⣿⣿⣿⣿⠀⠀⣶⣿⣷⣦⠈⣿⣿⣿⣿
⠋⠀⠀⢠⣾⣿⣿⣿⣿⣿⣃⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠋⠉⠃⠀⠀⠀⣿⣿⣷⡄⠀⠙⠻⠛⡉⣉⢋⣿⣿⣿⠛⠋⢉⣿⡄⠀⢸⣿⣿⣿⡿⢀⣴⣿⣿⣿⣿⣿⣿⠉⠹⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠂⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡋⠀⠀⠀⢀⡘⣿⢿⣿⣧⣤⣯⡾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇⠀⢀⣾⣿⣿⣿⡇⠸⣿⣿⢻⣿⠋⠙⠉⠀⠀⠙
⡀⠀⠀⠘⣿⣿⣿⣷⣾⣿⣿⠷⡄⢀⣼⣿⣿⣿⣾⣾⣿⣿⣿⣿⣦⣶⡄⠀⠀⠀⠀⠀⠙⠿⠿⠟⠀⠀⠀⠀⠘⠃⢳⠟⣭⣭⣭⡅⠛⡅⠛⣋⣥⣤⣤⣉⠻⣿⣿⡃⠀⠈⣭⣭⣭⠻⣷⡿⡿⠛⠀⠉⠀⠀⠀⠀⠀⠀
⣷⡄⠀⣾⣿⣿⣿⣿⣿⣯⣭⠀⠀⠈⣿⣿⣿⢿⣿⡿⠿⣿⣿⣿⣟⠉⢵⠂⠀⠀⠀⢤⣤⣤⣤⣤⣔⣦⣀⠀⠀⠀⠈⠀⣿⣿⣿⡇⠀⠀⣾⣿⣿⠛⣿⣿⣧⠘⢋⣠⣄⡀⣿⣿⣿⠀⠛⣀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀
⣿⣿⣦⠛⣿⣿⣿⣿⣿⣿⠉⠁⣀⡴⠏⣿⡟⢾⠙⠃⠀⢉⣩⣿⡿⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⣿⣿⣿⠀⣿⣿⣿⠀⣾⣿⣿⠛⣿⣿⣿⠀⣾⣿⣿⢻⣿⣿⡆⠀⠀⠀⠀⠀
⣿⣿⡿⠿⠻⣿⡙⠻⣿⣿⣠⣾⠟⢀⠘⠁⠀⠀⠄⢀⣴⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⠀⠘⠻⣿⣿⣿⣿⣿⡆⠀⠀⠀⣿⣿⣿⡇⠀⠀⣿⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⣼⣿⣿⣿⠀⠀⠀⠀⠀
⠉⠀⠀⠀⠀⠙⠆⣸⣿⣿⣿⣿⡿⠋⡠⠀⠀⠀⠀⣿⣿⣿⠛⠛⠇⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠙⣿⣿⣿⣿⣿⡀⠀⠀⣿⣿⣿⡇⠀⠀⣿⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⠉⣭⣭⣭⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣴⡷⠆⠀⢃⠀⠀⠘⣿⣿⣿⣿⣦⣤⠀⣿⣿⣿⣧⣶⠀⢿⣿⣿⣀⣿⣿⡿⠀⣿⣿⣿⣀⣿⣿⣿⠀⣿⣿⣿⣀⣿⣿⡟⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⡀⣄⢀⠀⠳⡀⠀⠘⣿⣿⣿⣿⣿⣆⠛⠛⠛⠛⠛⠀⠈⠛⠿⠿⠿⠛⠁⠀⠙⠻⠿⠋⠛⠛⠛⠀⠈⠛⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣴⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⡿⡄⠀⠀⠀⠤⠀⠀⢈⠘⢣⠄⠀⠙⢄⠀⠸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀
⠀⠀⢀⣴⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇⠀⠀⠀⠀⠘⠆⢰⣷⡇⠘⠱⠀⠀⠈⢆⠀⠹⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀
⢀⣤⣾⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣾⣿⣷⣶⡀⠀⠀⠀⠀⠂⠉⠁⠀⠀⠀⠀⠀⠈⠂⡀⠹⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣯⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡇⠀⠀⠀⠀
⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣿⠀⠀⠀⠀⠀⠁⠀⢻⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠷⠉⠉⠁⠀⠀⠀⠀
⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠰⣱⡏⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⣠⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠻⠛⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⢀⠀⠐⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡇⠀⠀⠀⢰⣿⡆⠀⠐⠀⠈⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⠻⠝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⣩⡿⢿⣿⣿⣿⢿⣿⡿⠋⠙⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣤⣠⣾⣿⣿⣿⣦⡄⢀⣠⣾⣿⣿⣿⣿
⣿⣿⡿⡿⠻⡟⢉⠻⠿⣻⠿⣿⠿⠛⠿⠛⠿⠀⠀⠛⠟⠤⣤⣤⣄⣾⣿⣿⣿⣿⣿⠋⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣾⣿⢿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿
⣿⣟⢉⣠⡼⣿⣿⡤⢰⠋⣠⣴⣶⣶⣦⠀⠀⢀⣁⠀⣀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣯⡾⠿⠃⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣯⣽⡍⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⠿⣿⣯⡄⠀⢸⣿⣿⣿⣿⣿⠙⠉⠿⠿⢿⣿⣟⢩
⣿⣿⣿⣿⣿⣾⣿⣿⡏⣼⣿⣿⣿⣿⣿⣿⣄⣼⣟⡻⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣤⣌⠻⣿⣿⣿⣿⣿⣿⠿⠿⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡾⠩⠷⠤⣸⣿⣿⣿⣿⣿⠀⠀⠀⣈⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡔⠽⡋⠸⣻⡻⢻⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢶⣿⣿⣿⣿⡟⠁⠂⠀⢴⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠿⠿⠟⠛⠛⢿⣿⣿⣇⣸⣿⣿⣿⣿⣶⣾⣿⣾⣿⣿⡿⢿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣏⣙⠇⠸⢟⣥⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢾⣿⣿⣿⡏⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿
⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠸⡇⠠⣿⣿⣿⣿⣷⣾⣿⣿⣿⣷⡆⠻⠛⠻⢿⣿⣿⣿⣿⣿⣿⠟⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⠃⠀⠀⠀⠀⠻⣿⣿⣿⣿⣯
⣿⠟⠀⠀⠀⣀⣤⣤⣤⣀⡀⠀⠀⠉⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⣧⣀⠀⠁⠙⣿⣿⢷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⢁⣿⣿⣿⣿⠀⠀⣶⣿⣿⣦⠈⣿⣿⣿⣿
⠟⠀⠀⢠⣾⣿⣿⣿⣿⣿⣃⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣛⣙⠏⠀⠀⠀⣿⣿⣷⡄⠀⢹⠿⠛⣛⣛⢛⣿⣿⣿⠛⣛⣉⣿⡄⠀⢸⣿⣿⣿⣿⢀⣴⣿⣿⣿⣿⣿⣿⠉⠹⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠂⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡟⠁⠀⠀⢀⡘⣿⢿⣿⣧⣤⣯⡿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡏⠀⢀⣾⣿⣿⣿⡇⠸⣿⣿⢻⣿⠋⠛⠉⠀⠀⠙
⡄⠀⠀⠸⣿⣿⣿⣷⣾⣿⣿⠷⡄⢀⣼⣿⣿⣿⣿⣾⣿⣿⣿⣿⣦⣶⡄⠀⠀⠀⠀⠀⠙⠿⠿⠿⠃⠀⠀⠀⠘⠃⢳⣿⠿⠛⢻⠏⢛⡕⣿⠟⠋⣼⣿⣿⣿⣿⣿⡗⠀⣸⣿⣿⣿⣿⣷⡿⡿⠟⠈⠉⠀⠀⠀⠀⠀⠀
⣷⡄⠀⣾⣿⣿⣿⣿⣿⣯⣯⠈⠀⠘⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡉⢽⠀⠀⠀⠀⢤⣤⣤⣤⣤⣔⣦⣀⠀⠀⠀⠈⠂⠀⠀⣽⠀⠀⠙⠃⢢⢣⢹⣿⣿⣿⣿⠟⠁⢠⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣦⠛⣿⣿⣿⣿⣿⣿⠙⠁⣀⡴⠏⣿⡿⣾⠹⠋⠀⢉⣩⣿⡿⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⢀⢹⢧⢺⣿⣿⠿⠛⠁⠀⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡿⠿⠻⣿⡛⠻⣿⣿⣠⣾⠟⢀⡘⠃⠀⠀⠄⢀⣴⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢄⠀⠘⠻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠈⠏⠉⠀⠀⠀⢀⡞⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠀⠀⠀⠀⠙⠆⣸⣿⣿⣿⣿⣿⢋⡠⠀⠀⠀⢠⣿⣿⣿⠛⠻⠇⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠙⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡼⢹⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣼⡿⠖⠀⢃⠀⠀⠘⣿⣿⣿⣿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠈⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣀⢤⣄⠀⠳⡀⠀⠘⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠻⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣼⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣧⡄⠀⠀⣦⠀⠀⢘⡘⣻⡄⠀⠙⢄⠀⠸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀
⠀⠀⢀⣴⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣧⠀⠀⠀⠀⠹⡆⢰⣿⡗⠘⠱⠀⠀⠈⢆⠀⠹⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀
⢀⣤⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣾⣿⣷⣶⡀⠀⠀⠀⠙⠚⠛⠉⠀⠀⠀⠀⠀⠈⠂⡀⠹⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡂⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣯⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠁⠀⠹⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡇⠀⠀⠀⠀
⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠁⠀⢻⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡿⠙⠉⠁⠀⠀⠀⠀
⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠰⣻⡿⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⣣⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢿⡿⠟⠀⠀⠀⠀⠀⠀⠀⢀⣽⠃⠀⠀⠀⣀⠀⠐⡄⠀⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⡗⠀⠀⠀⢸⣿⡆⠀⠚⠀⠈⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠘⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⡿⠿⣿⣿⣿⣿⡏⣠⣤⣶⣶⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣧⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣯⡀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⠿⣿⢠⠘⠿⠿⠟⣹⣿⣿⣿⠿⣿⠿⠮⠋⠛⡧⢴⣤⣴⣾⣿⣿⣿⣷⣿⡏⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣻⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠟⢻⣿⣿
⣯⣠⣶⣿⣿⣷⣆⡠⢠⡏⢠⣴⣾⣿⣦⡀⠈⠀⣀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡿⠿⠋⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣽⣯⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠻⢿⣿⡿⠟⣿⣿⣿⣿⣿⠀⠈⢉⣿⣿⣿⣶⣶⣿⣿
⣿⣿⣿⣿⣿⣿⡧⣼⡺⣰⣿⣿⣿⣿⣿⣷⡄⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⠻⣿⣿⣿⣿⣿⡿⠿⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⠈⠀⢠⣿⣿⣿⣿⠇⠀⠀⢤⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⣯⣟⣻⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢹⣿⣿⣿⣿⣧⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣾⣿⣿⣿⠇⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠿⠛⠉⠉⠉⠉⠻⣿⣿⣏⣈⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣭⣽⡃⠸⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢹⣿⡿⠿⢿⣏
⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠘⣇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡏⠛⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⠀⠀⠀⠀⠀⠙⣿⣿⣶⣾⣿
⣿⠉⠀⠀⣀⣴⣶⣿⣷⣶⡄⠀⠀⠉⣭⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠁⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⠃⠀⠀⢀⣤⣤⣶⡶⠛⠛⠛⠛⠋
⠋⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣫⣹⠃⠀⠀⠀⠀⠉⠉⠻⣿⣿⢛⡍⣙⣻⣿⣿⣿⠛⢻⣿⣿⣿⣬⣿⣿⣿⣿⣿⠀⠀⠀⠻⡇⠀⠈⠁⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⣟⣿⣿⣿⡟⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⠁⠀⠀⢠⡼⣿⣶⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣽⣿⣿⣿⣿⣿⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣄⠀⢀⣸⣿⣿⣿⣿⣿⡿⡿⢳⡇⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠙⠿⠿⠿⠃⠀⠀⠀⠙⠀⣿⣟⠋⣹⡏⢉⣵⣹⠟⠋⢸⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣮⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣷⠈⠀⢸⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⠻⣦⠀⠀⠀⠀⣤⣤⣤⣴⣶⣼⣦⣀⠀⠀⠀⠈⠁⠀⣼⡇⠀⠙⠛⢸⣼⣼⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣦⣼⣿⣿⣿⣿⣯⠀⢀⣀⣴⠿⢙⡿⠏⡟⣿⠉⣙⣿⣿⡏⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠃⡿⡝⣿⣿⠿⠛⠉⢰⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠛⠋⠁⣿⣇⢩⣿⣿⣴⣿⢛⣁⡔⠋⠀⢸⠇⣠⣾⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⡄⠀⠙⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠙⠋⠁⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠳⣿⣿⣿⣿⣿⡟⠁⠐⠀⠀⠀⢰⣿⣿⣿⠙⠻⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠹⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⢠⢿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⣿⡿⠇⠈⢆⠀⠀⠹⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠘⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢠⣤⣶⣦⡈⢣⡀⠀⠹⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣠⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣶⡀⠀⢹⣧⠀⢀⣿⡹⣿⣧⠀⠑⡄⠀⢸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣼⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠘⣋⣻⣧⠀⠀⠀⠀⢻⡆⢸⣿⣧⠻⣿⠀⠀⠘⡄⠀⢻⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠄⠀⠀⠀⠀⠀⠀
⣴⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣷⠀⠀⠀⠈⠿⡿⠿⠋⠁⠀⢀⠀⠀⠘⢆⠀⢻⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠀⠀⠀⠀⢇⠀⢻⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠈⠢⠈⢿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠿⠟⠛⠀⠀⠀⠀⠀⠀
⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠘⣿⡏⠀⠀⠀⢀⠀⠀⠄⢸⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿⠟⠀⠀⠀⠀⠠⠀⠀⢀⣿⠁⠀⠀⠀⢸⠄⠺⡤⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡅⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡇⠀⠀⠀⢠⣼⡇⠀⢷⠀⠘⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢪⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠘⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣻⣿⣿⣿⣷⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠳⠚⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠿⠟⠉⢿⣽⣿⠿⠳⢹⣿⣿⣿⡿⢟⠛⠿⣿⠛⡋⣈⣈⣹⣿⣿⣷⣾⣿⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣟⢙⣿⣿⣿⣿⣿⣿⣿⣧⢠⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠫⣿⣿⣿⣿⣿
⠁⢠⣄⣥⠀⠁⠀⠀⠀⠀⠠⠝⣒⡳⠂⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⠇⣸⣿⡷⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢛⣽⣿⣿⣷⣿⣿⣿⣿⣿⣿
⣿⣧⢽⣿⣷⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣷⡰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣀⡙⢿⣿⣿⣻⣿⣿⣿⡺⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⠉⠙⠻⢿⣿⣿⣿⣿⡿⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣻⣿⣣⡀⠀⣀⣴⡿⠛⢻⣋⣈⡁⠈⠉⠻⣭⡟⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢻⣿⣿⣿⣿⠉⢈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⣿⣿⣿⣿⠃⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣟⣛
⣿⣿⣿⣿⣿⣿⡿⠿⠿⠁⠼⣿⣿⣿⣿⣆⠀⢠⣿⣮⣾⣿⣿⡿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣛⣻⡇⢸⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠙⠿⠿⠿⣏⣉⣿⣿
⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣦⣾⣿⣿⣿⠟⠀⠀⢹⡇⢸⣿⣿⣿⣿⣿⣽⣿⣿⣿⣧⡴⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣿⣿⣿⣿⠃⠀⠀⠀⠤⠀⠀⠰⠶⠼⣿⣿⣿⡿
⣿⣿⠋⠀⠀⢀⣀⣠⣀⡀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠃⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢿⣿⣿⣿⡟⣿⣿⣿⣧⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣰⠀⠀⠀⠀⠀⠀⢀⠀⠈⠛⠟⠁
⣿⠟⠀⢀⣴⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠿⢿⡟⠁⠀⠸⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣿⣿⣿⣿⣿⡿⠀⠂⠀⠀⠀⠀⠀⠀⠈⠢⣀⣸⣒⣂
⠏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠙⠉⠉⢻⣯⣿⣿⣿⣶⣿⣿⣽⡍⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿
⣆⠀⠀⢹⣿⣿⣯⣿⣿⡹⡋⡁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣅⡄⠀⠀⠀⠀⠘⠿⣿⡿⠿⠋⠀⠀⠀⢬⠠⣀⣠⣤⣤⣿⣿⣿⢟⣿⣿⢹⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣄⢀⣿⣿⣿⣿⣿⣿⡿⣷⣿⡅⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣀⣀⣀⣠⣄⠀⠀⠀⠀⠀⠫⠋⠁⣸⠋⢫⡖⣸⠏⡁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠿⣅⣿⠏⢀⣴⣿⣿⣿⣿⡿⢿⣿⣿⡏⠈⠁⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠏⠆⠀⠀⠁⢳⣱⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⣿⣿⣶⣿⣁⡔⠻⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡷⡟⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⢏⡀⠀⠀⠀⠀⣽⣿⣿⡟⠿⣿⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠈⢻⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠱⠛⠉⠀⠀⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡀⠈⠀⠀⠀⠀⢀⣶⣶⡆⠸⡀⠀⠈⢿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠻⠿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣰⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠋⢉⣄⡀⠑⣄⠀⠀⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣴⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣷⣤⠀⠀⣶⡄⠀⠈⣗⢻⣿⡄⠈⢦⡀⠀⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠽⠿⣿⠉⠁⠀⠀⠘⣷⠀⢰⣿⡎⢿⣿⠀⠀⠱⡀⠈⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⣿⣧⡀⠀⠀⠀⠸⣦⠸⣿⠿⠈⠛⢀⠀⠀⠱⡀⠈⢿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠋⠀⠁⠀⠀⢀⣘⠀⠀⠀⠈⡄⠈⢿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣱⣿⡒⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⣼⣿⠀⠀⠀⠀⠐⠄⠈⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⢿⣸⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⢀⣼⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣹⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠠⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡟⠉⠉⠉⠀⠀⠀⠀⠀⠈⠀⠀⣸⡿⠀⠀⠀⠀⢰⡆⠀⣧⠀⠹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿
⠯⣀⡙⠿⠟⠟⠛⠳⠿⢽⣿⣿⡏⠉⠹⠹⡏⣭⣡⣤⣠⣿⣿⣿⣿⣿⠯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣥⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠉⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢦⣴⣦⣄⡀⠀⠀⠀⡠⢐⢧⡴⣿⣤⡄⢀⣠⣮⣼⣿⣿⣿⣿⣿⣿⣿⣴⣿⣋⣁⣀⠉⠙⠻⣿⣿⣿⣿⣿⣼⣻⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠙⢻⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣿⣿⠇⠁⠀⠆⠐⠆⠰⠿⣺⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⢻⣿⣿⣿⣿⣿⡏⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡏⠀⠘⠻⢿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿
⣯⣿⣿⣶⡀⢠⣴⣯⣴⣷⣼⣿⣿⣬⣽⣟⣻⣿⣿⡿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢿⣿⣿⣿⣇⣀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠈⠛⢿⣿⠿⣿⣉⣿⣿⣿⡏⠻
⣿⣿⣿⣿⣿⡿⠛⠛⠻⠟⠛⠻⢿⣿⣿⣿⣿⣿⣿⣷⠞⠉⠈⣯⠀⢻⣿⣿⣿⣿⣿⢿⣷⣶⣾⡅⣛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣀⣴⣴⣿⣿⣿⣿⣿⠇⠀
⣧⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢹⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢩⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣦⣦⠀⢠⡶⠿⢿⣿⣿⣿⣿⠿⠛⠂⠀⠀
⣿⣿⡿⠀⠀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠈⠉⢻⣿⣷⡄⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠂⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠓⠉⠛⣿⣦⠄⠀⠀⠀
⣿⠿⠁⢠⣾⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⢰⣿⣿⣿⣇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⢺⡟⠛⠿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠷⠖⠒
⣯⠀⠀⢸⣿⣿⣿⣿⡿⣿⣿⣶⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠋⠀⠀⢀⡀⡀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⡿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣟⠀⢠⣼⣿⣿⣿⣿⣷⣿⠟⣀⣠⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠙⠻⠛⠷⠀⠀⠀⠈⠋⢻⣿⣶⡶⢟⢻⣿⢏⠟⡩⣿⠿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⣿⢸⣿⣿⣿⣿⣿⣿⣃⣴⠟⢁⡀⠀⢠⣿⣿⣿⣿⣿⡿⢷⠒⠀⠀⠀⠰⣶⣶⣤⣼⣿⣦⣄⠀⠀⠀⠀⢩⣿⠁⠀⢱⣇⠂⠚⠀⠉⡔⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣾⣿⣿⣿⣿⣿⡿⠿⢡⠄⠈⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠉⠀⠀⠸⠚⠀⠀⠀⠀⡿⣜⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣶⠀
⠛⠛⢻⣿⣿⣿⣿⣿⠇⠀⠀⠀⠘⠓⢀⣼⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠠⡀⠈⠛⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀
⠀⠀⢸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡈⠛⠇⠀⠀⠀⠀⠈⣀⡀⠑⡄⠀⠀⢻⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢰⣿⡿⠂⠘⡄⠀⠀⢻⣿⣿⣿⣷⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡀⠀⠀⢀⡀⠀⠀⣠⣰⣦⣀⠘⢆⠀⠀⢹⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⢆⠀⠘⣿⡄⠀⢘⣯⣿⣿⣧⠈⠳⡀⠀⢹⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⠀⠀⠀⠀⠸⣷⠀⣾⣿⣅⢻⣿⠀⠀⠘⡄⠀⢻⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡷⠀⠀⠀⠀⢹⡷⡿⣿⠟⠀⠉⢀⠀⠀⠘⢄⠈⢻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⡆⠀⢻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠈⠂⠀⢿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢉⡿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣼⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⢿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠄⠠⡐⠀⢿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠤⠄⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⢠⣇⠀⢷⡀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣀⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣯⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣇⣴⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣁⡈⠹⠟⠛⠛⠛⠻⠿⣽⣿⣿⡋⠙⠟⠻⣭⣧⣤⣤⣼⣿⣿⣿⣿⡿⣹⣿⠿⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣟⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠻⣿⣿⣿⣿⣿
⣾⣶⣕⢀⠀⠀⠀⠈⠨⣶⣷⣾⣿⣆⢀⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣥⣴⣤⣤⣀⣈⠻⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠄⠹⣿⣿⣿⣿
⣿⣿⠟⠀⢢⠀⠇⡙⢶⣵⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣦⣠⣾⠛⣿⣿⣿
⣿⣿⣿⣆⣨⣶⣿⣿⣿⣷⣿⣿⣿⣯⣻⣿⣿⣿⡿⣻⡿⠿⡿⠀⢿⣿⣿⣿⣿⣿⣿⣿⠿⠿⡇⢹⣿⣿⣿⣟⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠙⠛⢛⣿⣷⣾⣿⣿⣯⠀⠘⢿⣿
⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠉⠉⠙⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣍⣿⣿⣿⣧⢘⣹⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⡁⠁⢛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠾⠿⣿⣿⣿⣿⣟⠃⠀⠀⠈⢻
⣾⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡇⠀⠀⠀⠈⠂⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠹⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠇⠀⠈⠳⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠁⠀⠀⠀⠀⠀
⣿⣿⣿⡿⠀⠀⣠⣴⣾⣿⣶⣦⡀⠀⠘⠻⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⣿⡟⠀⠀⢹⡿⣿⣿⣿⣿⣿⣷⣿⣿⡄⠀⢾⣀⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡿⠁⠀⣸⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠙⠛⢀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡶⠏⠀⠀⠀⠤⠀⠉⠈⠉⠻⣿⣷⡚⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⠋⣹⠟⠁⠀⠀⠀⢠⣿⣿⡆⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡏⠀⠀⠀⣶⢶⣶⣶⣄⠀⠀⢹⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣿⣇⠀⢹⣿⣿⣿⣿⣿⣿⡾⠋⣀⠔⠀⠀⢀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠋⠙⡇⠀⠀⠀⠀⠸⢻⣿⣿⣧⣴⣿⣿⡿⠟⠻⢻⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣧⢰⣼⣿⣿⣿⣿⣿⣿⡗⠂⠀⠀⠀⠐⢻⣿⣿⡟⠻⠇⠀⠀⠀⠀⢿⣶⣶⣶⣶⣿⣶⣄⠀⠀⠀⠈⠿⠛⠿⣿⠛⠛⠉⡇⠀⠈⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣦⣸⣿⣿⣿⣿⣿⡏⠀⠀⠀⣾⠃⣠⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡅⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣷⠀⠀⠀⠀
⠿⠟⠋⠉⠉⣹⣿⣿⣿⡿⠁⠀⠀⢀⣽⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢆⠀⠈⠻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣿⣿⣿⠏⠀⠀⠀⠀⢸⣿⣿⣿⣆⠈⠻⠀⠀⠀⠀⠀⢀⣀⠀⠢⠀⠀⠘⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣾⣿⣿⣟⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠀⢣⡁⠀⠈⢿⣿⣿⣿⣷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣾⣿⣿⣿⠏⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡅⠀⠀⠀⢀⠀⠀⠀⣀⢶⣦⡄⠱⡄⠀⠈⢿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⣾⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢿⠃⠀⠀⠸⣧⠀⠀⢸⡿⣿⣯⡀⠈⢢⠀⠀⢿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢻⡆⠀⣾⡇⠈⢻⡅⠀⠀⢣⠀⠈⢿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠘⢿⠤⠿⠇⠀⠈⠁⡀⠀⠀⠑⡄⠈⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠈⡆⠀⢻⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠠⡈⢂⠀⢿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣩⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣼⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⠻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⡄⢠⡐⠀⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒⠀⠛⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⢰⣇⠀⢿⡄⠘⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢛⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠹⣮⠿⠟⠿⠿⣿⣿⣿⣿⡿⠻⢿⢿⡿⠛⠛⣉⣈⣽⣿⣿⣗⣾⡿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⠛⣹⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣽⡀⠁⠀⠀⠀⠀⠑⠿⣹⣿⣧⠀⠀⠀⢩⣭⢿⣿⣿⣿⣿⣿⣿⣿⣁⣻⣩⣀⣀⡉⠙⠻⣿⣿⣿⣿⣿⢗⣼⣿⣿⣿⢿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠙⢿⣿⣿⣿⣿⣿⣿⣿
⣟⣷⠆⠀⠀⠠⠀⢀⠰⣴⣶⣾⣿⣦⣾⣾⣿⣿⣿⣿⣿⣿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡍⢿⣿⣿⣿⣿⣾⡅⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡛⢿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠈⣿⣿⣿⣿⣿⣿⣿
⣿⣯⡄⠀⢠⣬⣀⣢⣄⣠⣿⣿⣻⢟⠻⣿⣿⣿⣿⣿⠿⠟⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢘⣿⣿⣿⣿⡟⠑⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣍⡻⢿⣿⣿⣟⣛⣷⣤⡤⠀⠀⢻⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣿⣿⣿⣿⣿⠿⠿⠟⠋⠉⠸⣿⣭⠗⠈⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⣿⣷⣶⣜⣀⡿⢿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣤⣿⣿⣿⣿⣿⣏⠀⠀⠀⠙⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⢰⣿⣿⣿⣿⣿⣿⡿⣧⣹⣿⣇⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠈⠛⠿⣿⣿⡟⠁⠀⠀⠀⠀⠘⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠃⠀⣠⣤⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢹⣿⣿⣿⣿⣷⡿⣿⢻⣿⡁⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⣿⣿⣿⣿⣿⠃⠀⣸⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣋⡸⠃⠀⠀⠈⠛⠛⠙⠛⠻⢿⣿⣞⣿⣿⠀⣤⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣼⡟⠃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡏⠀⠀⠀⣠⢺⠃⠀⠀⠀⠀⠀⢹⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⡟⠉⣀⠀⢠⣿⣿⣿⣿⣿⣿⣟⣠⠞⠁⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠟⠋⡀⠀⠀⠀⠉⢸⣿⣿⣶⣄⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⣿⣿⡇⣴⣿⣆⢺⣿⣿⣿⣿⣿⣿⣿⣇⠄⢀⢀⣀⣴⣿⡆⠄⠀⠀⠀⢤⣤⣤⣤⣤⣧⣤⡀⠀⠀⠀⢹⣿⣿⣿⣆⣴⣇⣹⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⣿⣿⣿⣎⣿⣿⣦⣾⣿⣿⣿⣿⣿⡿⠁⣰⣿⣿⢻⡇⠈⠁⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠉⠉⠃⠹⠛⠛⣯⠇⣾⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿
⣿⣿⠿⠿⠿⠿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⡇⠀⠀⠀⠀⠀⠀⢀⠀⠙⠿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠁⠀⠀⠀⠀⠀⠘⣿⣿⣿⡟⣿⣿⣿⣿⡆⠙⠳⡇⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠈⣿⣿⣿⣿⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠃⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢀⣶⣶⡀⠡⡐⠀⠈⢻⣿⣿⣿⣧⣤⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠗⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⠛⢉⡀⠀⠱⡄⠀⠀⢻⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⠛
⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣷⠀⠀⠀⠠⣦⠀⠀⠘⣆⣷⣄⠀⠘⢆⠀⠀⢻⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣰⣿⣿⣿⡿⠁⠀⠀⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⢻⣇⠀⠀⡿⠝⠙⠃⠀⠀⠑⡄⠀⢻⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠈⠻⢿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣠⣾⣿⣿⣿⣿⠁⠀⠀⠀⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠻⡄⠘⣷⠀⠀⠀⠀⠀⠀⠘⢄⠀⢻⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡁⠀⠁⠀⠀⠀⠀⡄⠀⠀⠀⠠⠀⠹⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢻⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠣⠀⠹⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⣿⣿⣿⠝⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢨⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠏⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣶⡟⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⠅⠀⠀⠀⠀⠄⠀⢀⠀⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠟⠃⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⢀⡃⠰⣆⠀⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢸⠅⠀⢹⡀⠀⢻⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⢿⣿⣿⣿⣿⣷⣾⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠻⢟⣿⣿⣿⣹⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠻⣿⣿⣧⣀⣼⣿⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡔⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢠⠈⠿⠉⠃⠉⠹⢿⣿⠿⣿⡯⠀⠛⠙⠟⠀⣬⣦⣤⣿⣿⣿⣿⣿⣛⣛⣛⡛⠋⠙⠻⣿⣿⣿⣿⣿⣿⣟⢿⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠁
⣿⣆⠀⠀⠀⠀⠀⠀⠙⢠⡼⣗⣠⡀⣠⣘⣾⣼⠟⠟⣿⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⢿⣿⣿⣿⣿⣷⣻⠟⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⢿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀
⣿⡿⠃⠀⠀⢁⠀⢀⠐⠷⣿⣿⣿⣟⣿⣿⡿⢁⣴⣿⠿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⢆⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣉⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣷⡀⠀
⣿⣿⣇⣠⣸⣿⣶⣾⣶⣾⣿⣿⡿⠇⠸⠟⣱⡿⠋⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⡿⣿⣭⣄⢃⢹⣿⣿⣿⣿⣇⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣟⡛⢛⣿⣯⣾⣿⣶⡀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣷⣿⣿⣯⣾⠺⢛⣽⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⠿⠟⠻⢿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⣟⣯⣷⣬⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠉⠉⠛⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⣼⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠛⣻⠋⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⡀⢀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⢙⠁⠀⠀⠀⠉⠉⠉⠙⠋⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿
⣿⣿⣿⠟⣿⣿⠀⠀⠀⣤⣼⣿⣿⣿⣿⣿⣏⣩⠍⣻⣆⠀⠀⠀⠀⠀⠈⠻⣿⠿⠋⠀⠀⠀⠀⠿⠿⢛⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿
⣿⣿⡟⣠⣿⣿⡄⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⣨⣥⣄⡀⠀⠀⠀⢀⣀⣀⡀⣀⣀⠀⠀⠀⠀⠘⠿⣶⣤⣄⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⣿⣿
⣿⣿⣿⣿⣿⣿⣷⡀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⢿⣿⠙⠃⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣦⠀⠀⠀⠈⠉⠽⣿⡿⠋⣹⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿
⣿⣻⣿⣿⣿⣿⣿⣷⡖⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠉⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠟⠋⠀⠙
⣿⡿⠟⠉⠁⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⡟⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠹⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣦⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀
⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⡄⠀⠁⠀⠀⠀⠀⠀⢀⢀⠀⠡⠀⡀⠘⢿⣿⣿⣿⡃⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠐⢿⠿⠂⠀⠱⡀⠀⠀⢻⣿⣿⣿⣿⣆⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢄⢊⠀⠀⠘⢆⠀⠀⢻⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠟⠋⠁⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⢹⣧⠀⠀⠸⠄⠓⠄⠀⠀⠱⡄⠀⢻⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠏⠁⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⢿⡀⠀⣾⠀⠀⠀⠀⠀⠀⠈⠄⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢴⣶⣶⣶⣿⣿⣿⣿⡏⠀⠀⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠘⡟⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠙⣿⣿⣿⡏⠻⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡃⠀⠀⠀⠐⠀⠘⣿⣿⣷⡀⠘⠿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢹⣿⣿⣿⣿⡟⠁⠀⠀⠀⣿⣿⡟⠙⣿⣵⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠠⠑⠀⠘⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣴⣶⣿⣿⣿⡿⠁⠀⠀⠀⠀⣿⣿⣇⠀⠉⠹⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⢀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡃⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⠀⢻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⠀⢤⠠⠀⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⢾⠀⠈⢧⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣦⣬⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣻⢿⣿⣿⣻⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⠿⣿⣿⣿⡿⡿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣾⣥⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠀⡀⠻⠏⠉⠉⠙⢿⣿⣿⣿⡗⠀⠙⠛⢿⡠⠤⢀⡴⢃⡄⢾⣿⣿⣷⣾⣷⣶⣶⣦⣬⣿⣿⣿⣿⣿⣿⡿⣯⣷⣿⣿⣿⣿⣿⣿⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠟⢋⡅⠀⣩⣿
⣿⣶⢦⡀⠀⠀⢀⣀⡢⣡⣤⣦⣰⣤⣤⢀⣌⣷⣿⠏⣴⣿⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⣿⣽⣿⣹⣛⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠹⣿⣿⣿⣿⣿⣿⣿⣷⠋⠀⣾⠀⠀⣿⠃
⣶⣿⣿⠃⠀⠂⠨⡁⠼⣾⠟⣿⣿⡿⣿⣿⣿⣿⣿⡿⠋⠉⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣛⡛⠇⣹⣿⣿⣿⣿⣿⡏⣹⣿⣿⣿⣿⣿⣿⡇⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣧⣼⠃⠀⣸⡇⠀
⣿⣿⣿⣗⣠⣸⣿⣷⣾⣿⣿⣿⣿⠿⠘⠐⠛⠿⠉⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⣭⣿⣿⣟⣿⣼⣿⣿⣿⣿⣇⣀⣴⣿⣿⣿⣿⣿⣿⣿⣶⣌⡛⣿⣿⣿⣿⣿⣿⣻⣀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣄⠀⡿⠀⠀
⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠛⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠻⣿⣧⣭⣿⣿⣿⣽⣿⡇⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣾⠃⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡿⢿⡟⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠈⠹⠿⢿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀
⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣠⠟⠀⠀⠀⠀⠀⠀⢠⣵⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣤
⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟⣀⣠⡀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⢓⠀⠀⠀⣰⠺⠟⠀⢘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢹⣿⣿⡄⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⢰⣾⣷⣺⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣣⣼⣿⣿⣧⠀⠀⠀⠀⢿⣿⣿⣿⣿⢟⣹⣿⡿⣯⡀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣥⣤⡀⠀⠀⠀⠉⣿⠟⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿
⣿⣾⣿⣯⠻⣿⣿⣿⣄⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⣽⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣿⣿⣿⡿⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣆⠀⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠋⠉⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡉⠙⠳⡇⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠈⠻⣿⣿⣿⣿⣀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠛⠁⠀⢿⣿⣿⣿
⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠁⠀⠀⠀⠀⠀⣠⡀⠀⠈⡀⠀⠀⠻⣿⣿⣿⣯⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠈⢿⣿⣿
⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠘⢄⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⠀⠈⢿⣿
⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠁⠀⠀⠈⢆⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⣿⣿⣇⠀⠀⠈⢿
⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀
⠙⢿⣿⣧⠀⢀⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠀⠀⢠⠀⠀⠀⠀⠀⠀⠈⢀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠁⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⠋⣿⣿⡟⠛⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⢿⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⠀⠀⠀⠉⠉⠀⠀⢻⣿⠃⠀⠉⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠋⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⠒⣒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣿⣿⣿⣟⣋⣉⣙⣛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣩⡔⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⢀⠈⢿⠟⠉⠉⠻⣿⣿⡿⣟⡀⠉⠛⢻⡏⢥⣌⣀⡰⠟⢑⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡿⢫⣿⠋⣿⣿⡿⠿⢿
⣴⣦⣼⡅⠀⠀⠀⠀⠀⢄⢩⣄⢲⣤⣀⡀⢀⣨⣾⣿⣿⣧⡎⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠼⠃⠀⡿⠁⠀⣽⡟⠁⠀⠀
⣿⣿⣯⣿⠀⠀⠀⠓⠠⣰⢘⠿⣿⣿⣿⠷⣿⣿⣿⠿⠃⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⢿⣿⣥⣬⣃⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠰⠁⠀⠀⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣧⣀⣠⣶⣾⣿⣷⠖⠉⠁⠀⠀⠉⠻⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣥⣤⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⣿⣿⣿⣿⣿⣿⣿⠿⠿⣆⣽⠛⠿⣿⣿⣿⣿⢥⣤⡄⠀⠀⠋⢻⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣯⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠟⣻⠋⢀⣠⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠉⢳⣶⣶⣿⣿⣀⣼⣿⡇⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠟⣁⣰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠉⠙⠿⣿⣿⡿⠿⠁⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣣⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣿⣷⣦⣦⡀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠿⣾⣿⡿⠻⢢⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀
⣿⣿⣿⠋⣿⣿⣦⠀⠀⠀⠀⠀⠀⣴⣽⣿⣿⣿⠟⠋⢉⡯⢁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣿⣿⣿⠞⣸⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀
⢿⣿⡏⣴⣿⣿⣿⡄⠀⠀⠀⠀⠀⢸⣿⣵⣿⠟⠀⢀⣼⣿⣦⠀⠀⠀⠀⠀⠰⣶⣦⣤⣤⣼⣿⣏⡀⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀
⣿⣿⣿⣌⢻⣿⣿⣷⣤⣄⡀⠀⢀⣾⣿⣿⣿⣠⣶⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣯⣿⢰⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⣿⣿⣿⣿⣾⣿⡿⠿⠛⠉⠁⠀⠀⠛⢿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⡇⡽⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣟⠙⠻⢖⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠈⠛⠃⢀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡇⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠁⠀⠈⢂⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠿⠟⠛⠉⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠁⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣀⣠⣦⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠠⢂⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⡏⠀⠀⠹⣿⣿⣿⣿⣿⣿
⠀⠈⠻⣿⣷⡄⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢙⡀⠀⠠⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⡿⠟⠀⠀⠀⠹⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣶⣶⣿⡗⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⠛⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⠀⠀⠈⠻⣿⣿⣿⣿⡿⠁⠀⠀⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠉⣠⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣹⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣟⠻⢿⣿⣟⡽⠛⢿⣿⣿⣿⣿⠿⠿⣻⣿⣿⠿⠟⠛⠹⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣤⣄⣥⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡩⢭⣭⡽⠋⡹⠛⠻⣻⣿⣿⢿⣿⣿⣿⣿
⠀⢉⡡⣠⠀⠛⠉⠀⠀⠀⠻⡹⠛⠉⠀⠀⠈⠘⠒⣖⣶⣶⣾⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣰⠋⠀⢸⠁⠀⠀⣸⠟⠁⠈⠛⢿⣿⣿
⣾⣿⣷⡿⣆⠀⠀⠀⣀⡀⢒⢷⣬⣿⣿⣶⡄⣴⣼⣿⡿⠉⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠙⣿
⣿⣿⣿⣿⣟⡀⠀⠠⣼⣨⣴⣄⠸⠟⠛⠉⠉⢿⡏⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⠟⠃⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⣴⣷⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠈⠻⠻⣿⣿⣿⣿⣿⡋⣀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣷⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢰⠀⣹⣟⡋⢀⣸⣿⡇⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡟⣡⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣄⣠⠀⠀⠀⠀⢀⣼⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⡿⠃⠙⠃⠀⠀⢰⣿⣿⣿⠿⠁⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣿⠇⣸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣻⡟⣸⡟⠃⠀⣠⣴⠂⠀⣸⣿⣿⠁⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣖⢿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⣀⣴⣿⣿⠇⠀⢸⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣦⣿⣿⣿⣿⣶⣶⡦⠀⠀⠀⢰⣿⣿⣿⣾⣿⣿⡟⠁⠀⠀⢸⣿⣿⣧⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⡟⠆⠀⠀⠀⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣿⣧⠈⠛⠇⠀⠀⠀⣿⣿⣿⡿⠆⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡆⠀⠀⠀⠀⠀⣿⡿⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀
⠹⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀
⠀⠀⠹⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⠁⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡤⠀⠀⠀⠀⠀⠀⠀⠿⠛⠛⠉⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠻⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣴⠂⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⠇⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢻⠟⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠉⣠⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣻⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣟⠻⢿⣿⣟⡽⠙⢿⣿⣿⣿⣿⡿⠟⣻⣿⡿⠿⠟⠛⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣤⣄⣥⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡩⠭⣭⡽⠋⡹⠛⠻⣿⣿⣿⢿⣿⣿⣿⣿
⠀⢉⡡⠠⠀⠛⠉⠀⠀⠁⠻⡿⠟⠩⠀⠀⠈⠘⠓⣶⣶⣶⣾⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣰⠋⠀⢸⠁⠀⠀⣸⠟⠁⠈⠛⣿⣿⣿
⣾⣿⣷⡿⣆⠀⠀⠀⣀⡀⠘⢷⣼⣿⣿⣶⡄⣴⣼⣿⡿⠋⠉⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠉⣿
⣿⣿⣿⣿⣟⡀⠀⠀⣼⣩⣱⣈⠹⠟⠉⠉⠉⢿⡏⠉⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⣤⣼⣿⡿⠟⠋⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⣴⣷⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠈⠛⠻⣿⣿⣿⣿⣿⠋⣀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣷⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢲⠀⣹⣟⡋⢀⣸⣿⡇⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡟⣡⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣄⣠⠀⠀⠀⠀⢀⣼⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⠃⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⢺⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⠃⠙⠃⠀⠀⢸⣿⣿⣿⠿⠁⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣿⠇⣸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣛⡟⣼⡿⠃⠀⣠⣼⠂⠀⣸⣿⣿⠁⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡖⢿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⢀⣴⣿⣿⠇⠀⢸⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣯⣦⣿⣿⣿⣿⣶⣶⡦⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⢸⣿⣿⣧⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⡟⠆⠀⠀⠀⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣿⣇⠈⠛⠇⠀⠀⠀⣿⣿⣿⡿⠆⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡆⠀⠀⠀⠀⠀⣿⡟⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀
⠹⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀
⠀⠀⠹⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⠁⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡤⠀⠀⠀⠀⠀⠀⠀⠿⠛⠛⠉⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠻⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣴⠂⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⠃⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢻⠟⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⠁⠀⠴⢶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠿⠿⡿⠿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠛⣿⣿⡤⠋⠻⣿⣿⣿⣿⣿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣴⢄⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠋⠉⠉⠀⠀⠀⠀⠀⠀⠈⡴⠒⠀⠿⠛⣿⣿⣿⣿⣿⣿⣿
⠛⠃⣽⡰⡆⠉⠁⠀⠀⠀⠘⢿⠿⣋⡓⠁⠈⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣹⣿
⣿⣿⣯⣿⢳⡄⠀⠀⣤⠀⢬⡌⢷⣿⣿⣷⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠉⠁⠧⠭
⣿⣿⣿⣿⣿⣓⠀⠠⣾⣅⣠⣧⡄⠛⠛⠋⠉⢹⡟⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⠛⠁⠀⠀⠀⠀⠀⢸⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⢿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⢠⡿⡀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣧⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠛⠿⣿⣿⣿⡿⠿⠁⣤⣴⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠏⣡⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠂⣴⣷⣤⣤⣴⣿⣿⠈⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⡿⠋⠁⠈⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠛⠿⢿⣿⡿⠟⠋⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡃⢀⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⡿⠟⠁⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣧⡸⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣧⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣬⣿⣿⣿⣧⢀⣤⡄⠀⠀⠀⢀⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⠉⠉⠀⠀⠀⠀⠈⠻⢿⣿⣧⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡷⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡦⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠇⠘⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠁⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⣤⣠⣤⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣴⣦⢀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡅⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡿⠁⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠟⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄
⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⡉⠀⣠⠴⢶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡟⠋⣹⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⠿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣽⣿
⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣠⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣟⡿⢿⣿⣿⡟⠛⠉⠉⠉⠙⠛⠿⠿⠯⢭
⢉⣍⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠀⢶⣷⣶⣶⣶⡄⠀⠀⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣹⣿⣋⣉⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣶⣿⣦⣤⡆⠤
⣿⣿⣿⣏⣿⡿⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⣾⣿⣿⣿⣟⠀⠀
⣿⣿⡿⠛⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⢿⠀⣀
⣿⣿⠀⣾⣧⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⠛⣿⣿⣿⣿⣿⠟⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡟⠀⠀⠛
⣿⡇⠀⣿⣿⣆⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠉⣠⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⠀⠀⠀
⣿⡇⢰⣿⣿⣿⣶⣿⡿⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠹⠿⠿⣿⣯⣿⠗⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀
⣿⣿⣮⠻⣿⣿⣿⡿⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠃⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡟⣿⠁⠀⢀⣤⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠀⠈⠀⠶⡿⠏⠁⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⠀⠀⣤⣤⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⣿⣿⡏⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠗⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠟⠛⢋⣉⣈⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣵⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣧⣴⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣧⣄⣀⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢉⠋⠛⠛⠿⡿⣿⣏⡛⠿⠿⢿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠉⠛⠛⠛⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣿⣿⣿⣿⠟⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠁⠀⠀⢨⣿⣿⣿⣿⣿⣿⣷⣄⡀⠙⢧⣠⣤⣤⣀⡀⠀⠀⠀⣀⣤⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠻⠿⣿⣿⠿⠆⠀⠀⢹⠜⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⣿⣷⣶⣻⣆⡔⢟⠂⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⣿⣿⢿⣿⣿⣿⣷⡿⠊⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣶⣶⣤⣿⣿⡟⣫⣿⣿⣿⣿⣧⠀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣏⠛⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢻⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠟⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠈⠈⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡏⠙⠿⢿⣿⣱⠟⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡋⠁⠀⠀⠀⣠⣤⣄⣀⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⣿⣴⣾⣾⣿⠏⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡄⠀⠀⠀⠹⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡏⠋⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣹⣧⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣼⡟⠘⠃⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⡖⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣼⣿⣼⠂⠀
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠇⠀
⣿⣿⣯⡿⣿⣿⣻⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢫⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⡹⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠀⠀⠀⠈⠉⢻⢿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠻⠿⣧⣀⣀⣀⣀⠀⠀⠀⠀⢸⣰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠉⠙⠛⢿⣿⣟⣥⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠈⢿⣿⣿⣿⡿⢧⠀⠀⢽⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣩⣤⣤⣤⡶⡶⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣲⣾⣿⣶⣶⣷⣰⡟⠇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠉⠀⠀⠀⠀⠝⠛⠛⠻⠿⠛⠁⢀⣾⣿⣿⡿⠃⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣾⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣰⣿⣿⠛⢻⣿⣿⣿⣿⣅
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⠋⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠯⠟⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠿⢿⣿⡗⠀⢾⣿⣿⣿⣿⠿⠃
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣾⢿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠈⣿⣿⣆⠀⡿⠿⢶⣿⣿⠟⠋⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠚⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡏⣼⣿⣿⣿⣿⣿⣿⣿⠀⢸⣷⣿⣿⣿⣶⠁⠀⣼⣿⠃⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢉⠀⣿⣿⣿⣿⣿⣿⣿⡟⠀⢸⢩⠇⢹⣿⣥⣀⣴⣿⠃⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⣿⣿⣿⣿⣿⡿⠟⠠⣞⣿⣼⠀⠀⠈⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣟⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠋⠁⠀⡤⢀⠗⠿⠀⠀⠀⣹⢏⣿⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠅⠀⢠⢠⡞⡵⠃⠀⠀⠀⠀⣰⢫⡿⠁⠿⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢏⡞⠁⠀⠀⠀⠀⡴⣱⣿⡟⠂⣸⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠎⠀⠀⠀⠀⠀⢼⡾⠁⠈⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠛⡇⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⢀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣱⠏⠀⠀⠀⡀⠀⠀⠸⣿⣿⣶⣶⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⡯⠀⠀⠀⣈⣥⣤⢀⡀⠉⠻⢿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⢀⠀⢹⣿
⠘⣩⣍⠛⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠿⠟⠹⠿⢿⣿⡿⠃⠈⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣉⣠⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡽⠿⢿⢿⣿⣿⣿⣿⣷⣯⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⠇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠉⠉⠻⢧⠀⣀⣀⣀⣀⣀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠛⠛⠛⠛⠋⠙⠟⠋⠀⠀⢀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⣰⣿⠿⠿⣿⠿⠿⡄⠀⠨
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠉⠛⠛⠛⣦⣀⣀⣀⠠⠃⠀⠀⠀⠀⠈⠁⠘⣿⣿⣿⣿⣿⣛⣹⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⢺⣿⣿⣿⣿⣶⣞⣿⣄⠀
⣿⣿⣿⢿⠋⠉⠈⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣯⣿⣿⣿⣿⣿⣿⠿⣿⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡀⣰⣿⣿⣿⣿⡋⣹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⠃⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢉⣻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⠈⠙⢿⣿⣏⠉⢻⣿⡌⠈⣠⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠙⠻⠁⠀⠈⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢶⣾⠏⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⢿⣿⣦⣸⠟⠛⣿⡿⠋⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠈⠘⣿⡟⠻⠟⡿⡫⢞⣵⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⠃⠀⣨⡦⣼⣿⣿⠟⠀⣰⣿⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⡀⠀⠀⠙⠀⠀⠘⠁⠀⠉⠸⠁⡀⢸⣿⣿⣿⣿⣿⣿⡏⠀⢰⢠⠇⠘⢿⣷⣶⣤⣿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⢿⣿⣷⡄⠀⠀⠀⠀⠰⠀⠀⠀⠀⢧⢣⢸⣿⣿⣿⣿⡿⠋⠀⠀⣿⢸⠀⠀⠀⠙⢿⣿⠿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠹⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⢠⠛⡜⣾⣿⡿⠟⠉⠀⠀⡴⣠⠉⠈⠀⠀⠀⣰⢣⡾⣆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡠⢀⠈⡄⠀⠘⣿⣿⣄⠀⠀⠀⠀⠀⠀⠈⡘⠹⠈⠋⡄⠀⠀⢀⡞⡰⠁⠀⠀⠀⠀⡴⣡⡟⠀⠋⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡀⠀⠘⢆⠀⠘⣿⣿⣧⠀⠈⢦⣄⠀⢀⠃⠀⠀⡌⠀⠀⣠⢟⡼⠁⠀⠀⠀⠀⡼⡵⠛⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣠⠀⠈⠣⡀⠘⣿⣿⡇⠀⠘⣿⣿⠀⠀⠀⠘⠀⠀⢠⢏⠞⠀⠀⠀⠀⠀⢸⡾⠁⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠘⣿⣇⠀⠀⠸⣿⡆⠀⠀⠀⠀⢠⢋⠞⠀⠀⠀⠀⣠⠀⠈⠰⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠙⣿⣧⠀⠀⢻⣿⣶⣄⠀⢠⠃⠂⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⣠⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡈⢿⣧⠀⠘⠿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡠⠋⠀⠀⠀⠀⠀⣴⣦⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⠠⡈⢿⣆⠀⠀⠀⠈⠛⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⢎⡼⠁⠀⠀⠀⠀⠀⠀⠙⠁⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠘⣿⣦⠀⠀⠀⠀⠈⠹⠿⠧⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⢸⣧⣤⣤⣄⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣤⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡄⠈⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣒⠂⠀⠂⠀⠀⠈⠛⠃⠙⠉⠙⠛⠛⠁
⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⢻⡿⢿⣯⣿⣿⣿
⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⠉⢺⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⢀⣀⣀⣼⣿⣿⡟⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠻⣿⣯⣭⣿⣿⣿⣿⠿⠛⠛⣿⣿⠛⠋⠉⠉⢻⣿⣿⣷⣾⣿⡿⢿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⢹⣿⣿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠿⠿⠟⠛⠛⠆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠉⠉⠀⡀⠐⠊⠍⡋⠋⠀⠉⠉⠁⠀⠀⠀⠁⡀⢛⣷⣤⣾⣿⣿⣿⣿⣿⡧⠘⠋⠻⣿⣿⣿⣿⣿⣿⣿⣯⡇⣀⡾⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠷⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣭⣴⣟⣿⣤⡀⠀⠀⠠⠀⠀⠀⠀⢶⣦⠤⠤⠤⠿⣿⣿⠏⢸⣿⣿⣿⣿⣶⣶⣤⣄⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣨⣯⣿⣿⣿⣿⣧⣄⡈⠉⠙⠻⣿⣿⣿⣿⣿⣿⠀⠀⣀⣤⣤⣤⣀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠃⠀⠂⠠⠄⣀⣠⣼⡞⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠈⢻⣿⣿⣿⣿⣄⣼⣟⠛⣻⡟⢉⣉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢉⣴⣶⣶⣶⡄⠀⠀⢸⣿⣿⣿⠃⣠⣶⠖⠁⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡿⠛⢻⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣆⣼⣿⣿⣿⡏⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⣿⣿⣯⣽⣿⣟⣾⣿⣿⡻⠿⣣⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢺⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⠁⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡗⣸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣾⡿⢿⣿⣿⣿⣿⣿⣿⣥⣀⡼⣻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣼⣿⣿⣿⣿⡟⠀⣿⣿⢧⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡟⠛⠁⢻⣿⣇⣾⣿⣿⣿⣿⣿⣿⣬⣭⣿⣿⣿⣿⣿⣿⣿⡿⠋⠛⣿⣧⡀⢹⣿⣿⣿⣿⣿⣡⣴⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠘⠻⣿⣿⣿⣿⣆⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠏⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠹⣿⣷⣾⡿⠛⢿⣿⣿⠿⠟⠋⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣿⣶⣜⣿⣿⣿⣿⣿⡟⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡿⠋⠀⠀⠀⢻⣿⠿⠟⣻⣿⣿⣿⣽⠏⣿⣏⣹⣿⣿⣿⣿⠃⠀⠀⠀⠀⢰⣿⣿⣟⠁⠀⢸⡟⠁⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⣰⡷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠸⡿⠰⠒⠉⢉⠝⣵⡟⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡞⢠⣼⣹⡿⣿⣶⣶⡞⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⡟⣟⣿⣿⠻⣇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣦⡀⠀⠀⠀⠀⠀⠠⠉⠁⠊⠛⠁⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⣄⠃⠀⠊⢹⣷⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀
⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡿⠋⠀⠀⠀⠀⠈⠉⢠⣾⣿⣿⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢿⣿⣿⣿⡿⠋⠀⠀⢸⢼⠀⠀⠀⢀⠝⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣁⣀⣀⣀⣤⣄⡀⠀⣴⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠱⣸⣿⡿⠋⠀⠀⢠⢂⠂⠀⠀⠀⠀⡎⡼⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⣄⣿⣿⣿⣿⠟⠉⣡⣾⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠹⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠘⠁⡀⠀⠀⢠⢃⠎⠀⠀⠀⠀⡘⡼⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠙⣿⣿⣿⣧⣴⣿⣿⣿⠟⠛⠻⠿⠿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠐⡄⠀⠹⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⢠⠇⠎⠀⠀⠀⠀⠀⡽⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠈⠹⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠹⣿⣿⣦⠀⠀⢱⣦⠀⠀⠀⠀⠀⠀⢀⡏⡜⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠻⣿⣿⠏⠀⠀⣀⣀⣠⠄⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠁⣠⣶⣿⣿⣿⣿⣿⡆⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠘⢿⣧⡀⠀⠘⣿⣷⣦⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠘⠙⢿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⢂⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡀⠀⠸⣿⣿⣽⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠈⢩⣷⣴⡄⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠃⠀⠀⣿⣿⠻⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡄⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⠆⢻⠏⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⣿⡍⠠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠀⠀⠀⠛⠀⣸⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡟⠋⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠁⠛⢻⣷⣿⣿⣿
⣿⣿⣿⣿⣻⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄⠀⢸⣿⣿⣿⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢤⣤⣾⣿⣿⣇⡬
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠙⠿⣿⣭⣽⠟⣻⡿⠟⠛⠛⠻⡿⠛⣋⠉⠀⢩⣿⣿⣷⣾⣿⡷⠻⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢀⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⠛⠉⠉⠈⠉
⣿⣿⣿⣿⠹⣿⣿⣿⣿⠿⠋⠉⠉⠀⠀⠈⠀⠉⠍⠀⠀⠁⠁⠀⠀⠀⠀⠀⡀⠉⣿⣧⣼⣿⣿⣿⣿⣿⡇⠐⠏⠙⣷⣿⣿⣿⣿⡿⣿⣽⡆⣠⡘⠏⠣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠛⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣶⣧⣹⣿⣿⣦⣴⣴⡏⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⡄⢰⣾⣾⣿⠟⠈⣻⣿⣿⣶⣤⣤⣄⣀⢠⣼⣵⣾⣿⣿⣿⣿⣿⣿⣿⣦⠂⣰⣿⣿⣅⣉⠉⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣠⣶⣶⣷⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣇⠀⠀⠀⠀⣀⠀⣠⣦⡀⠀⠀⠈⣱⠿⠋⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣦⠀⠀⠈⠻⣿⣿⣿⣿⣿⣏⢧⣴⣿⢤⣴⣿⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⣉⣉⡀⠀⠀⠀⢰⡿⣿⣿⣿⣿⠇⢀⡠⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡿⠿⢻⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠟⣻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣴⣿⣿⣿⣿⣧⡀⢀⣿⣿⣿⣿⣿⣿⣾⡿⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣩⢹⣷⣖⣼⣿⣿⣟⠟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢸⡟⢻⡿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⡟⢰⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡆⠺⣷⣄⠙⣿⣿⣿⣿⡿⣿⣿⡟⠛⣡
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢻⣿⣿⣿⣿⣿⣿⡿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠟⠛⠁⢸⣿⣇⣼⣿⣿⣿⣿⣿⣏⣩⣽⣿⣿⣿⣿⣿⢿⣿⠟⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠏⠘⠻⣿⣿⣿⣿⣧⣿⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠇⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⣾⣿⣿⡿⠟⠉⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣓⣈⣿⣶⡜⣿⣿⣿⣿⣿⣿⣷⡦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡿⠿⠃⠀⠀⠀⠘⣿⣿⣿⣿⣿⠿⣿⣿⠙⣻⣛⢩⣿⣿⣿⡟⠀⠀⠀⠀⠀⣼⣿⣿⣿⢀⣙⣻⠏⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠛⠃⣀⢶⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠟⠛⠛⡚⡻⡿⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠸⠀⢤⡿⣿⣿⡇⢸⣿⡟⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣠⣶⡾⣿⠀⠁⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠂⠊⠚⠘⠁⠀⣿⣿⣿⣿⣿⡿⠀⠀⡀⡆⠀⠑⠘⡳⣿⡁⢸⡿⠁⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣯⣿⠿⠛⠿⢿⣟⣻⣿⣿⣿⠟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢿⣿⣿⣿⠋⠀⠀⠀⠇⠇⠀⠀⠀⡌⣻⡷⠘⡇⠀⠀⠀⠀⠀⣠⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠡⠱⢸⡿⠋⠁⠀⢀⠆⡄⠀⠀⠀⠀⡸⢰⠃⠀⡀⠀⠀⠀⠀⣰⣿⣿⣿
⠀⠸⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣥⣶⣦⣀⠀⠀⣰⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠈⢿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠠⠀⠀⢀⡎⡜⠀⠀⠀⠀⢀⢣⠇⠀⠀⠁⠀⠀⠀⣼⣿⣿⣿⣿
⠀⠀⣷⣿⣿⣿⣿⣯⡉⠛⣿⣿⣿⣿⣿⣿⣿⠟⠀⢸⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⢀⠀⠈⢿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡼⡰⠀⠀⠀⠀⠀⢈⡏⠀⠀⠀⠀⠀⠀⠀⡙⠛⠛⠛⠛
⠀⠀⣸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠈⢿⣿⣿⣷⠀⠀⠀⢳⠤⠀⠀⠀⠀⠀⢸⠁⠃⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠈⠙⠛⠉⠳⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⢿⣿⣿⡀⠀⠀⠸⣿⣧⡀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡿⢻⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢶⣦⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⢻⣿⣿⣄⠀⠀⠘⢿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠃⠀⠀⢀⣀⣴⣿⣿⠀⢸⣿⣿⠆⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡄⠀⠀⠀⠛⠛⠿⠷⣄⠀⠀⠀⠀⠀⠀⠀⢠⢂⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣸⣿⣿⣿⣿⡏⠀⠀⣰⣿⣿⣿⣿⡇⠀⠘⣿⡿⢴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣄⠀⠀⠀⠀⠀⠀⠐⢙⣷⣀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾
⠀⠀⠀⢾⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣷⠀⠀⣿⠟⣨⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠁
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣿⠀⢺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⣿⣿⣻⣟⣛⣩⣹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠛⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣅⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣻⣿⠋⢏⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⢻⣿⡿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⠚⢻⣷⣿⣿⣿
⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⠀⢀⢻⣿⣿⣏⢳⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⣄⣠⣾⣿⣿⣟⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠍⠙⠻⣯⠍⠽⠋⠻⡿⠛⠛⠛⠻⣿⠛⣋⠉⠀⠈⣿⠿⣗⣾⣿⡿⢿⣾⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⠏⢈⣾⣿⢀⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⠟⠛⠁⠀⠀
⣿⣿⣿⣿⣫⣿⣿⣿⣿⢿⠟⠈⠈⠀⠀⠀⠀⠉⡁⠀⠈⠉⠀⠀⠀⠀⠀⠁⠀⠉⣻⣦⣼⣿⣿⣿⣿⡿⠇⢸⡏⠙⣷⣿⣿⣿⣿⣿⣿⣹⡗⣠⡘⡛⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠃⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣦⣸⣿⣿⣆⣠⣴⡎⢻⣦⡀⠀⠀⠠⠀⠀⢀⠀⢰⡆⠠⠄⠴⣾⣾⣿⡟⠻⣻⣯⣭⣥⣄⣀⣀⠀⢀⣴⣵⣿⣿⣿⣿⣿⣿⣿⣿⣇⡆⣸⣭⣧⣀⣀⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣴⣶⣶⡦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠺⣤⢇⠀⠀⠀⠀⢀⠀⡀⣼⡃⠀⠀⠀⣫⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣎⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣶⠀⠀⠙⢿⣿⣿⣿⣿⣿⡧⠙⢦⣼⣧⣤⣿⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣄⣀⣾⣿⣿⣿⣿⡿⠟⠁⢀⠀⠉⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠿⢸⣿⣏⣿⣿⣿⣿⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠠⣿⣿⣿⣿⣿⣷⡀⢸⣿⣿⣿⣟⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⣉⣈⡀⠀⠀⢺⣿⣿⣿⣿⣿⡁⣠⣶⠂⠀⠀⠀⠀⠀⠀⣯⣿⣿⣿⣟⣛⣿⣶⡆⣼⣿⣿⡝⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣿⢿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡋⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣾⣿⣿⣿⡯⣤⡀⣾⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠼⢿⣄⠙⢺⣿⣿⣷⡌⠻⣿⣿⠛⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⠿⠿⠀⠈⣿⣇⣼⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⡟⠿⠋⠀⠀⠙⢿⣿⣾⣿⣿⣿⣷⡄⣹⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣿⠟⢿⣿⣿⣿⡇⢸⣿⣿⢿⣤⡀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡧⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠇⠀⠀⠀⠀⠀⣾⣿⣿⣿⣶⣿⣿⠟⠛⠋⠁⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠁⣾⣆⢻⣿⣿⣿⣶⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠿⠂⠀⠀⠀⠈⣿⣿⣿⣿⣿⢿⣿⣿⡟⢹⣯⠀⣶⣿⣿⣟⠀⠀⡄⠀⠀⠀⣿⣿⣿⠇⣘⣻⡏⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣂⣸⣿⣯⡄⢻⣿⡿⠛⠛⠿⣿⡟⠁⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠛⠛⠛⡛⣫⡟⠀⣸⣿⣿⣿⣿⣿⡏⠀⠀⢁⠀⢀⢠⣿⠿⡿⠀⣿⡿⠁⠀⠀⣀⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣶⣦⣨⣴⣾⠈⠉⠀⠀⠀⠀⠀⠹⣿⣿⣷⣷⣤⠀⠀⠀⠀⠀⠀⠂⠈⠈⠙⠀⠀⢸⣿⣿⣿⣿⣿⠃⠀⠀⢸⠀⠀⠘⠣⡃⣄⠀⣿⠁⠀⣠⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⢡⠸⣿⣿⣿⠟⠁⠀⡀⠀⠸⠀⠀⠀⢠⢠⠈⠀⢿⠀⣸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⠿⠋⠉⠉⠉⢩⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡈⢆⠂⡿⠋⠁⠀⠀⡰⠱⠁⠀⠀⠀⠀⠆⡎⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢃⠆⠀⠀⠀⠀⡘⣸⠀⠀⠀⠈⢿⡟⠙⠉⠀⠀⠀
⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⡀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⡀⠀⠘⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡏⡌⠀⠀⠀⠀⠠⢠⠇⠀⠀⠀⠀⢠⣾⡷⠀⠀⠀⠀
⢿⣿⣾⣿⣿⣿⡟⠉⠻⣿⣿⠏⣵⣿⣿⣿⡆⠴⠟⠸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠙⣿⣿⣿⣿⡄⠀⠀⠀⣿⣦⣄⠀⠀⠀⠀⡜⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⠀⠀⠀⠀
⠘⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⣰⣿⣿⣿⣿⣿⣧⡀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠹⣿⣿⣿⡄⠀⠀⠀⣿⣿⣿⣶⡀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⠿⠟⠉⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣆⠀⠀⠀⠛⠿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢻⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⣠⡄⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣆⠀⠀⠀⠀⠀⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠛⠃⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠻⣿⡄⣿⣏⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡞
⠀⠀⠰⠀⣸⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣆⠀⠀⠀⠀⣿⡰⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣼⣿⣷⡄⠀⠀⣿⡅⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⣿⣟⣻⣟⣏⣉⣩⣤⣠⣾⣿⣿⣿⡇⠀⠀⢿⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⠋⢏⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⡿⢿⣿⢿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠠⠚⢻⣠⣿⣿⣿
⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⠀⢀⢻⣿⣿⡟⢳⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⣀⣠⣾⣿⣿⣏⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠍⠙⢻⣯⡍⠽⡋⢿⡿⠛⠛⠛⠻⣿⠛⣋⠉⠀⠈⣿⠯⣗⣾⣿⡷⢹⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢉⣾⣿⢀⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡿⠛⠋⠉
⣿⣿⣿⣿⠫⢺⣿⣿⣿⠿⠏⠈⠉⠀⠀⠀⠀⠉⡩⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⣻⣤⣼⣿⣿⣿⠿⠿⠇⢰⠉⠙⣿⣿⣿⣿⣿⣿⣿⣽⠇⣀⡘⡛⠓⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠃⠀⠀
⣿⣿⣿⣿⣿⣦⣼⣿⣿⣤⣤⣴⡎⢻⣦⡀⠀⠀⠤⠄⠀⢠⠀⢰⠆⠰⠄⢴⣾⣷⣿⣿⡿⣛⣁⣀⣀⣀⣀⠀⠀⣠⣾⣵⣿⣿⣿⣿⣿⣿⣿⣿⣇⡆⣰⣿⣿⣷⣤⣤⣈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⡄⠀⢀⣴⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢾⡸⡇⠀⠀⠀⢀⣀⠀⣀⢸⠁⠀⠀⠸⠛⣹⡿⢸⣼⣿⣿⣿⣿⣿⣿⣿⣷⡟⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠉⢿⣿⣿⣿⣿⣿⡏⠛⠋⠐⣤⣾⡥⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣾⣄⣐⣿⡿⠋⠉⠁⠀⠀⠀⠀⣠⠞⠻⠃⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⢹⣿⣏⣿⣿⣿⡟⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢠⣿⣿⣿⣿⣿⣷⠀⠀⠀⣻⣿⣿⣟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⡟⠃⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⢻⡷⣶⠤⡘⣿⣿⡽⢟⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠘⠋⢿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢠⣾⣿⣿⣿⡟⢁⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠙⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣼⡟⢻⣿⣿⣷⡀⠀⣈⣿⣿⣟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⠀⣿⣿⣿⢿⣿⡄⠈⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠘⠓⠀⠈⢻⣿⣦⡉⣿⣿⣷⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢀⣤⣴⣦⡀⠀⠀⠀⠀⢿⣿⣿⣿⣯⣃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡧⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⣩⣬⣿⣿⠃⠾⠂⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡏⣴⣿⣿⣿⣿⡷⡀⠀⠀⠀⢈⣿⣿⣿⣿⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⠃⠀⠀⠀⠰⠸⣿⣿⣿⣿⣿⣿⣿⡿⠃⣺⣿⣷⣿⣿⣿⡇⠀⠀⢦⡄⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛
⣿⣿⣟⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣾⠇⢢⡀⣿⣿⣿⣿⣦⣤⡆⠀⠀⣤⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠂⠋⠉⠉⠍⡵⣿⠆⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⠀⠐⣤⣿⣿⣿⣿⣿⣿⣿⡿⠉⠁⠀
⣿⣿⣏⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡃⣀⠈⠨⢡⣿⣷⣄⣼⡉⠉⠛⠇⣀⣤⠀⠛⠀⠀⠀⠀⠈⢻⣿⣶⣶⣾⣷⣆⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⢿⣿⣿⣿⣿⠟⠀⠀⠠⠘⠀⠀⠀⠉⠻⣿⣿⣿⡿⠁⠀⠀⠀⠀
⣷⡈⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠠⣜⣿⣿⣿⠙⠿⢂⣤⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡐⢸⣿⣿⠟⠁⠀⢀⡆⡄⠀⠀⠀⠀⠘⠰⢿⣿⣷⡀⠀⠀⠀⠀⠀
⠛⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣤⣶⠿⠿⠿⠿⠀⣠⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠌⠛⠁⠀⠀⠀⡜⡐⠀⠀⠀⠀⢀⢃⠇⢰⣿⣿⡇⠀⠀⠀⠀⠀
⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠁⠀⠀⠀⢰⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠂⠀⠀⢰⢣⠃⠀⠀⠀⠀⡄⡜⠀⢸⣿⣿⡯⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠛⠂⠀⠀⠠⠀⠀⠘⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠌⠀⠀⠀⠀⠐⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠘⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣼⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣧⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⢿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀
⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣋⣥⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⣿⣥⣤⣤⣀⣉⣙⣿⡷⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣦⣄⣀⣴⣿⣿⣿⡿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⣿⣏⣻⣟⣟⣩⣹⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿
⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡿⠹⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⡾⠻⣧⣸⣿⣿⡿
⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡄⠀⣞⣿⣿⡿⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⣀⣀⣴⣿⣿⣿⡿⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡇⠑⠀⡉⢿⣖⠈⠛⠙⠟⠙⠉⠉⠉⢿⠏⢉⣀⡀⠀⣼⣿⣫⣷⣿⡿⠒⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⣼⣿⣏⣸⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣽⠟⠚
⣿⣿⣿⡇⣺⣟⣿⣿⡿⠛⠀⢀⣀⡀⠀⠁⠐⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣀⢸⣿⣶⣿⣿⡿⠿⠿⠟⠐⡏⠀⣻⣿⣿⣿⣿⣿⣿⣿⣶⢃⣄⢛⠙⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠛⠟⠿⠛⠋⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⣏⣙⡿⣥⠀⠀⠀⠦⠄⠀⠀⢠⣿⠖⠓⢲⣶⢿⣿⣿⣿⣿⣋⣀⣀⣀⣀⡀⠀⠀⣴⣷⣾⣿⣿⣾⣿⣿⣿⣿⣿⡾⠀⣯⣿⣿⣿⣍⣉⣛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⡶⠄⠀⢀⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣻⡄⠀⠀⣦⡀⣀⣄⣸⣿⡁⠀⠀⠛⠉⣹⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣀⣠⣿⣿⣿⣿⣿⣿⣿⣷⡜⠻⣿⣿⣿⣿⣿⣿⠙⢓⣤⣵⣾⣿⣾⣯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠁⠀⠀⢿⣿⣿⣷⣤⣀⣠⣾⡿⠃⢹⣿⣿⣿⣿⣿⣿⣿⡿⠿⠧⢸⣏⣽⣿⣿⠿⣋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢼⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⢀⣀⣀⠀⠀⠀⠸⢿⣿⣿⡟⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⣿⣶⣶⣦⠘⢿⣟⠟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡘⢛⣛⡋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⣠⣾⣿⣿⣿⡟⠀⠀⠀⠀⠻⣿⣇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠹⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠚⣛⡁⢸⣿⣿⣿⣿⣿⡇⠈⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢰⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠿⠿⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⣿⢡⡅⢠⣿⣿⣿⣿⣿⣿⠇⣴⡿⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠸⣿⣿⣿⣿⣿⠃⠀⠆⠀⠀⠀⠙⠻⠿⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡥⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠉⣽⣿⠃⢸⣿⡿⠁⠀⣿⣿⣿⣿⣿⣿⣾⡏⠀⠀
⣿⡇⠈⢻⣿⣿⣿⣿⣿⢀⣴⣤⡀⠀⢹⣿⣿⣿⡿⠿⠄⠀⠀⠀⠀⢀⡀⠀⠀⣶⡀⠀⠀⠀⠈⠻⣿⣿⡿⠃⠀⠀⠀⠀⠀⣀⣀⠀⠉⢻⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⡏⠀⠀⢡⣼⠿⠣⣿⣿⣿⣿⣿⡿⢻⢧⠀⠀
⠻⡶⣲⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⡄⠘⣿⣿⣿⣷⣀⣠⡄⠀⠀⠀⣾⡇⢠⢠⣿⠀⠀⠀⠀⢀⣀⣈⠉⠀⠀⣄⠀⠀⠀⠀⠹⠏⠔⠰⡛⡩⢛⣿⣿⠃⣼⣿⣿⣿⣿⣿⡇⠀⠀⠈⠛⢦⣤⣿⣿⣿⣿⠟⠁⠀⠈⠀⠀
⣆⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢀⠉⢹⡿⠿⠿⠏⠀⠀⠀⠈⠋⣉⣿⡏⠀⠃⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠀⡄⢹⣿⣿⣿⣿⡿⠁⠀⠀⡀⡀⠀⠉⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠞⢀⡜⢷⠄⠀⠀⠀⠀⢀⣴⣾⣿⡿⡅⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡜⣼⣿⣿⡿⠋⠀⠀⡰⡠⠀⠀⠀⠀⣼⣿⣿⣷⠀⠀⠀⠀⠀⠀
⣶⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⡿⠃⠈⠛⠁⠀⠀⠀⠀⠀⣰⣿⣿⡏⠉⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠙⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⣌⠿⠋⠀⠀⠀⢰⢣⠁⠀⠀⠀⠀⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀
⣩⣿⣿⠁⠀⣾⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⠦⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢻⣿⣿⣏⣜⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠄⠀⠀⢀⡇⡎⠀⠀⠀⠀⠐⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⢹⣷⣾⣷⣾⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⢂⠀⠀⠹⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡼⠘⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠑⠄⠀⠻⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠲⣶⣶⣦⡞⣿⣿⣿⣿⣷⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⣷⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣼⣿⣿⡁⢻⣿⣿⣿⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣇⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣟⣋⣭⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠹⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣋⣥⠀⢽⣿⡿⠃⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⢛⣋⣉⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⠀⠀⣀⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⣿⣿⣿⣿⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢨⡟⢻
⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡆⢀⣠⣄⠀⠀⢀⣴⣿⣿⠟⠋⠁⢐⣿⣿⣿⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣆⣼⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⠟⠀⠀⠀⠘⣿⣿⡟⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣏⡉⣿⣿⣿⣟⣋⣩⣙⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠋⠿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⢹⠿⣿⣹⣿⣿⣿⣿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡀⢰⣻⣿⣿⢏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⢀⡀⣠⣿⣿⣿⣿⣟⢂⣤
⣿⣿⠿⣿⣿⣿⣿⣿⡟⠿⠿⠈⠁⣨⠻⢿⡆⠛⠋⢹⡏⠋⠉⠉⠙⠟⢉⣥⣀⠀⢸⣿⣯⣿⣿⣿⠗⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢩⣾⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣽⣿⣿⣿⣿⣿⣿⡵⠼⣿
⣿⣿⣠⡟⣿⣿⣿⠋⠀⣤⢤⣴⡀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣤⣬⣿⣷⣾⣿⣿⣿⠿⠟⠁⠚⠁⢸⣿⣿⣿⣿⣿⣿⣿⣷⠟⣤⣛⡛⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠖⠀⢹
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣤⣿⣳⡄⠀⠀⠀⠀⠀⠀⢀⣿⣟⡛⠲⣿⣿⣿⣿⣿⣿⣿⣿⣃⣤⣄⣀⣀⣀⣀⡰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⠅⣰⣼⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣠⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣟⣻⣧⠀⢀⣦⣠⣤⣤⣼⣿⣌⡉⠀⠘⠅⠭⢋⣽⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⢿⣿⣿⣿⣄⣀⣠⣿⣿⣿⣿⣿⣿⣿⣶⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣰⣿⣉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠀⠙⢿⣿⣾⣿⣿⣿⣿⣿⣦⣄⣀⣴⣿⣿⠈⣿⣿⣿⠿⣿⣿⣿⡿⠟⠻⠀⣹⣿⣿⠿⢋⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣘⣿⣿⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠃⠀⢸⣿⣿⣿⣿⣛⣻⣿⣿⣳⣄⡉⠻⣫⣶⣿⣿⣿⣿⣿⣿⣟⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸⣿⢿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢀⣤⣶⣦⣤⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠈⣻⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⣴⣿⣿⣿⣿⣯⣄⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠿⠿⠃⠀⠀⠀⠉⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣡⣽⣿⣿
⢿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣋⣁⡀⠀⠀⠀⢿⣿⣿⠿⠿⠿⠿⠄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠆⠀⠀⠀⢀⣸⣿⣀⡀⠀⠀⢹⣿⣿⣿⣷⣿⣿⣿⠿⠟⠛⢻⡏⠘⣿⣿⢿⣿⣿⣿⣿⠿⣿⣿⣿⠋⠛⠃
⢨⣿⣿⣿⣿⣿⣿⡇⠘⣿⣿⣿⣿⡿⢻⣿⣿⠁⠀⠀⠀⣸⠋⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠟⠃⠀⠀⠀⠘⠛⣿⣿⣧⠀⠀⠀⠁⢈⣙⣿⡿⣿⣿⣷⣶⣾⣿⠀⠀⠉⠀⠀⣿⣿⣿⣷⣄⢸⡟⣿⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡀⢹⣿⣿⣿⣷⣊⠉⠁⠀⠀⠀⣠⣿⣀⣾⡟⢻⡟⠀⠀⡐⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣄⡀⠀⠀⠀⠹⣿⡿⢿⣟⢟⡿⣻⣿⡿⢀⣿⣿⣿⣿⣿⡯⠀⠀⠀⠤⣤⣿⣿⣿⣿⣿⣿⠗⠉⠃⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣠⡄⠀⠀⠘⠿⣿⣿⣿⣷⣟⣷⡿⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠇⠀⠈⠙⠋⠁⢸⣿⣿⣿⣿⣿⠇⠀⠀⡀⡄⢸⣿⣿⣿⣿⠛⡋⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠁⣠⣴⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡜⡌⣿⣿⣿⡿⠅⠀⢠⢀⠁⠀⢰⣿⣿⣿⣿⣈⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡝⡌⣿⠟⠋⠀⠀⢠⠆⠎⠀⠀⢸⣿⣿⣿⣿⣏⠁⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠋⣽⣿⠉⠀⠀⠀⠀⠀⣠⡄⠀⠀⢂⠀⠀⠙⣿⣿⣿⣧⣯⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠀⡀⠀⠀⢀⡞⡜⠀⠀⠀⢸⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⠀⠀⠀⠀⠀⠈⠁⢀⠀⠈⠢⡀⠀⠘⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠑⢄⠀⠘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣏⣉⣩⣿⡁⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠘⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣻⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀
⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣟⣛⣋⣉⣉⢱⣆⡀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠠⠀⠘⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠋⠀⠀⠀⠀⠠⠀⠀
⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣋⣉⣛⠛⠛⠋⢉⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠈⢿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⠿⠟⠋⠉⠉⠉⠉⠉⣁⢀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡘⠃⠀⠀⠀⠀⠀
⠀⢠⣴⣾⣀⣀⡀⣀⣠⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀
⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠜⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⠙⣿⣿⣿⣟⣏⣉⡉⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠀⠀⠀⠀⠀⢰⠀⠀⠄⠀⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡙⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠍⠩⠿⢿⣯⣿⣿⣿⣿⠿⠋⠻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡟⡟⡻⣿⣿⣛⢿⡿⢿⣿⣿⢿⠿⢿⣿⣿⣿⠟⠟⠻⣿⣿⣧⣀⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢀⣀⣰⣿⣿⣿⣯⡥⠀⠀⣠⣶⣾
⣿⣿⣿⣿⣟⣿⠉⠉⠃⡀⠰⠎⠛⠛⠈⠛⠈⠟⠎⡄⠀⠀⠙⠁⠴⣦⣤⣠⣿⣿⣿⣿⣿⣿⢹⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣁⣿⣿⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⣶⢺⣿⣿⣿
⣾⢿⣿⣿⡅⣠⣴⡟⢾⣯⠄⢠⣠⣶⠀⠀⠀⠀⢠⣄⣀⣀⢀⣰⣶⣾⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⠀⠻⠿⣿⣿⣿⣿⣿⣿⣟⣯⣮⣭⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠈⢿⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣬⣁⣀⣀⠀⠀⠀⣾⡿⠈⠍⠻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣤⣤⠙⣿⣿⣿⣿⣿⣿⣿⡿⠿⠠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣤⣶⣒⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣼⣿⣿⣿⣿⣿⡄⢀⣿⣿⣶⡀⠀⣉⠁⢙⢃⣽⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣛⣿⣿⣿⣷⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢿⣿⢻⣿⣿⣿⣿⣿⡇⠀⣰⣿⣽⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣾⣿⣿⣿⡿⢿⡇⠈⣿⣿⣿⣿⣿⣿⣿⣏⣉⡃⢸⣿⢟⣫⣼⣿⣿⣿⣿⣿⣿⠿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣟⣾⣿⣿⣿⣿⡟⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠈⠉⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠘⠇⠀⣿⣿⣿⣿⣿⣦⣿⣿⣿⣷⣦⠀⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⢻⣿⣿⣿⣿⠋⠀⣀⠀⢿⣿⣿⣿⣿
⣿⣿⣿⣿⠋⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⢳⡀⠀⠈⠉⢻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⢠⣾⣿⣿⣄⠹⣿⣿⣿
⣿⣿⣿⠏⠀⣠⣾⣿⣿⣿⣿⠇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡟⠉⠉⠀⠀⠀⣽⣿⣷⣄⠀⠀⣿⣿⡛⢉⣙⣿⣿⣿⣿⠿⠿⢟⡟⠀⠀⠀⣿⣿⣿⣷⣾⣿⣿⣿⣿⣾⣿⠛⠛
⣿⣿⡟⠀⠠⣿⣿⣿⣿⣿⣿⣿⣷⠆⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⠿⠛⠛⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡟⠁⠀⠀⢀⣤⣿⣿⣿⣿⠀⡒⠙⢻⣿⣿⣿⣿⣿⣿⣷⣴⣶⣾⠇⠀⠀⢰⣿⣿⣿⣿⣿⣷⣼⣿⡿⠉⠛⠀⠀
⣿⣿⣇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣥⣤⠀⠀⠀⢹⣿⣿⣿⣿⣿⣷⣤⣶⣦⠀⠀⠀⠀⠀⠀⠘⠻⠿⠛⠁⠀⠀⠀⠈⠉⢹⣯⣿⣿⣿⣿⣶⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣟⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⡿⢷⠀⠀⠀⠀
⣿⣿⣿⣄⠀⢸⣿⣿⣿⣟⣿⠋⠿⠟⠀⠀⣾⣿⣾⣿⣿⣿⣿⣿⣿⣛⡛⢦⡀⠀⠀⠀⢶⣦⣤⣤⣤⣤⣵⣤⡀⠀⠀⠀⠻⠏⠉⠈⡏⠈⠴⣹⠟⡁⢸⣿⣿⣿⣿⣿⡇⠀⠀⢀⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⢸⣿⣿⣿⡿⠈⠿⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠠⠇⠀⠀⠁⢸⡸⣸⣿⣿⣿⣿⡏⠀⢀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣾⠂⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠳⡘⣿⠿⠛⠁⠀⢀⠂⠄⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠿⠛⠉⠁⠀⠀⠘⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠹⠇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⢿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠑⠁⠀⠀⠀⢀⠏⠄⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠸⢿⣿⣷⠀⠀⠀⠀⠀⠀⢰⣶⠆⠀⠡⡀⠀⠈⢿⣿⣿⣿⣷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡞⠘⠀⠀⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠑⡄⠀⠈⢿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢨⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣤⡀⠈⠢⡀⠀⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢻⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⢀⠀⢂⡤⠀⠘⠄⠀⠀⠑⡀⠈⢿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣗⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠐⢀⠈⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⡀⠀⠀⠀
⠀⠀⣠⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢮⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢴⡿⠿⠷⠀⠀⠀
⣤⣾⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡔⠀⠀⠀⠀⠈⠀⠈⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢰⣯⠉⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢎⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣻⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⣀⡄⠀⠀⡀⠈⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣉⣍⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠀⠀⠀⠀⣿⣷⠀⠀⠁⠀⠘⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠻⠝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⣩⡿⢿⣿⣿⣿⢿⣿⡿⠋⠙⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣤⣠⣾⣿⣿⣿⣦⡄⢀⣠⣾⣿⣿⣿⣿
⣿⣿⡿⣿⠻⡟⢉⠻⠿⣻⡿⣿⠿⠻⢿⠿⠿⡉⠙⠻⠟⠬⣶⣤⣄⣿⣿⣿⣿⣿⣿⠋⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣾⣿⢿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿
⣿⣟⢉⣠⣼⣿⣿⡤⢰⠏⣠⣴⣶⣶⣦⠀⠀⢀⣁⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡾⠿⠋⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣍⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⠿⣿⣯⡅⠀⢸⣿⣿⣿⣿⣿⠙⠉⠿⠿⢿⣿⣟⢩
⣿⣿⣿⣿⣿⣾⣿⣿⡏⣼⣿⣿⣿⣿⣿⣿⣄⣼⣟⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣤⣌⢻⣿⣿⣿⣿⣿⣿⡿⠿⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡾⠩⠷⠤⣸⣿⣿⣿⣿⣿⠀⠀⠀⣈⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣵⡔⡿⣿⠿⣿⡿⢻⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢶⣿⣿⣿⣿⡟⠁⠂⠀⢼⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠿⠿⠟⠛⠛⢿⣿⣿⣇⣸⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⢿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣏⣙⠇⡸⢟⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢾⣿⣿⣿⡏⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿
⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠸⡇⠨⣿⣿⣿⣿⣷⣾⣿⣿⣿⣷⡆⠻⠛⠻⢿⣿⣿⣿⣿⣿⡿⠟⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⠃⠀⠀⠀⠀⠻⣿⣿⣿⣿⣯
⣿⡟⠁⠀⠀⣀⣤⣤⣤⣄⡀⠀⠀⠉⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⣧⣀⠀⠁⠙⣿⣿⢷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⢁⣿⣿⣿⣿⠀⠀⣶⣿⣿⣦⠘⣿⣿⣿⣿
⠟⠀⠀⢠⣾⣿⣿⣿⣿⣿⣋⡀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣟⣙⠇⠀⠀⠀⣿⣿⣷⡄⠀⢹⢿⠛⣛⣛⣛⣿⣿⣿⠛⣛⣩⣿⡄⠀⢸⣿⣿⣿⣿⢀⣼⣿⣿⣿⣿⣿⣿⠉⠹⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠂⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡿⠁⠀⠀⢀⡘⣿⢿⣿⣧⣬⣯⡿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡏⠀⢀⣾⣿⣿⣿⡇⠸⣿⣿⢻⣿⠋⠛⠉⠀⠀⠙
⡄⠀⠀⠸⣿⣿⣿⣷⣾⣿⣿⠿⡄⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⡆⠀⠀⠀⠀⠀⠙⠿⠿⠟⠃⠀⠀⠀⠘⠃⢻⣿⠿⠛⢻⠏⢛⡝⣿⠿⠋⣾⣿⣿⣿⣿⣿⡗⠀⣸⣿⣿⣿⣿⣷⡿⣿⠟⠈⠉⠀⠀⠀⠀⠀⠀
⣷⡄⠀⣾⣿⣿⣿⣿⣿⣯⣯⠌⠀⠘⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡉⢽⠂⠀⠀⠀⢤⣤⣤⣤⣤⣶⣦⣀⠀⠀⠀⠈⠃⠀⠀⣾⠀⠀⠙⠃⢣⢣⢹⣿⣿⣿⣿⠟⠁⢠⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣦⠛⣿⣿⣿⣿⣿⣿⠙⠁⣀⡴⠟⣿⡿⣾⠹⠛⠀⢛⣫⣿⡿⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⢀⢻⢧⢻⣿⣿⠿⠛⠁⠀⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡿⠿⠻⣿⡛⠻⣿⣿⣠⣾⠟⢀⡘⠃⠀⠈⠄⢀⣴⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢄⠀⠘⠻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠈⠏⠉⠀⠀⠀⢀⡞⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠀⠀⠀⠀⠙⠦⣸⣿⣿⣿⣿⣿⢋⡠⠀⠀⠀⢠⣿⣿⣿⠛⠻⡇⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠙⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡼⢹⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣼⡿⡶⠀⢃⠀⠀⠘⣿⣿⣿⣿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠉⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠳⡀⠀⠘⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠻⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣼⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣧⡄⠀⠀⣶⠀⠀⢹⡘⣿⣤⡀⠙⢄⠀⠸⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀
⠀⠀⢀⣴⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣧⠀⠀⠀⠀⠹⡇⢸⣿⣗⠘⢳⠀⠀⠈⢆⠀⠹⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀
⢀⣤⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣾⣿⣷⣶⡀⠀⠀⠀⠙⠾⠛⠉⠀⠀⠀⠀⠀⠈⢂⡀⠹⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡂⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣯⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠁⠀⠹⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡇⠀⠀⠀⠀
⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠑⠀⢻⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠙⠉⠁⠀⠀⠀⠀
⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⣣⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢿⡿⠟⠀⠀⠀⠀⠀⡄⠀⢀⣽⠃⠀⠀⠀⣈⠀⠘⣄⠀⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⡟⠀⠀⠀⢸⣿⡇⠀⠚⠀⠈⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⢞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠘⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⡿⠿⣿⣿⣿⣿⡏⣀⣤⣶⣶⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣇⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣯⡀⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⠟⣿⢀⠘⠿⠿⠟⣹⣿⣿⡿⠿⣿⠟⠮⠋⠛⠧⢴⣤⣴⣾⣿⣿⣿⣷⣿⡏⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣻⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠟⢻⣿⣿
⣯⣠⣴⣷⣿⣷⣄⠠⢠⡏⢠⣤⣾⣿⣦⡀⠈⠀⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡿⠿⠋⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣽⣯⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠻⢿⣿⡿⠟⣿⣿⣿⣿⣿⠀⠈⢉⣿⣿⣿⣶⣶⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣼⡺⣰⣿⣿⣿⣿⣿⣷⡄⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⠻⣿⣿⣿⣿⣿⡿⠿⠽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⠈⠀⢠⣿⣿⣿⣿⠇⠀⠀⢤⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⣯⣟⣻⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢹⣿⣿⣿⣿⣧⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣼⣿⣿⣿⠇⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠿⠛⠉⠉⠉⠉⠻⣿⣿⣏⣈⣿⣿⣿⣾⣿⣿⣿⣿⡿⠟⢿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣭⣽⡃⠸⣫⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢹⣿⡿⠿⢿⣍
⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠘⡇⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡏⠛⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⠀⠀⠀⠀⠀⠙⣿⣿⣶⣾⣿
⣿⠉⠀⠀⣀⣤⣶⣿⣷⣶⡄⠀⠀⠉⣩⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠁⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⠃⠀⠀⢀⣤⢤⣶⡶⠛⠛⠛⠛⠋
⠋⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣫⣹⠃⠀⠀⠀⠀⠉⠉⠻⣿⣿⢛⡍⣙⣻⣿⣿⣿⠛⢛⣿⣿⣿⣌⣿⣿⣿⣿⣿⠀⠀⠀⠻⡇⠀⠈⠁⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⣟⣿⣿⣿⡟⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡿⠁⠀⠀⢠⡼⣿⣶⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⣽⣿⣿⣿⣿⣿⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣄⠀⢀⣸⣿⣿⣿⣿⣿⡿⡿⢳⡇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠙⠿⠿⠻⠂⠀⠀⠀⠙⠀⣿⣟⠋⢹⡏⢉⣵⣹⠟⠋⢸⣿⣿⣿⣿⣿⣟⣸⣿⣿⣿⣿⣿⣿⣎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡄⠸⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢸⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⠻⡧⠀⠀⠀⠀⣤⣤⣤⣴⣴⣴⣦⣀⠀⠀⠀⠈⠁⠀⣼⡇⠀⠉⠛⢸⣼⣼⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣦⣼⣿⣿⣿⣿⣯⠀⢀⣀⣴⠿⢉⡟⠏⡟⣿⠋⣙⣿⣿⡏⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠃⡿⡜⣿⣿⠿⠛⠉⢰⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠛⠋⠁⣿⡧⢹⣿⣿⣴⣿⢛⣁⡔⠋⠀⢸⠇⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⡄⠀⠙⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠙⠋⠁⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠳⣿⣿⣿⣿⣿⡟⠁⠐⠀⠀⠀⢰⣿⣿⣿⠙⠻⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠹⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⡿⠇⠈⢆⠀⠀⠹⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠘⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣼⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢠⣄⣶⣦⡌⢣⠀⠀⠹⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣠⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣷⡀⠀⢹⣇⠀⢀⣿⡹⣿⣧⠀⠑⡄⠀⢸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣼⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡘⣋⣻⣧⠀⠀⠀⠀⢻⡄⢸⣿⣇⠻⣿⠀⠀⠘⡄⠀⢻⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠄⠀⠀⠀⠀⠀⠀
⣴⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⣧⠀⠀⠀⠈⠳⠿⠿⠋⠁⠀⢀⠀⠀⠈⢆⠀⢻⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠀⠀⠀⠀⢇⠀⢻⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠂⠈⢿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠿⠟⠛⠀⠀⠀⠀⠀⠀
⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠘⣿⡏⠀⠀⠀⢀⠀⠀⠄⢸⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⢸⠀⠲⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡅⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡇⠀⠀⠀⢠⣼⡆⠀⠷⠀⠘⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠊⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠘⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣻⣿⣿⣿⣿⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠋⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠳⠘⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⠟⠉⢻⣼⢿⠰⠓⢩⢿⣿⣿⠿⠟⠛⠿⡿⠛⡋⢈⡀⣹⣿⣿⣷⣾⣿⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢿⣿⣿⣿⣟⢙⣿⣿⣿⣿⣿⣿⣿⣧⢰⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠫⣿⣿⣿⣿⣿
⠁⢠⣀⣥⡀⠁⠀⠀⠀⠀⠠⢉⠒⠃⠂⠀⠀⠀⣀⣽⣿⣿⣿⣿⣿⣿⣿⠇⣸⣿⡷⠾⠿⠿⣿⣿⣿⣿⣿⣿⡷⠿⣿⢿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢋⣽⣿⣿⣷⣿⣿⣿⣿⣿⣿
⣿⣯⢹⣿⣶⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣶⠠⣶⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣀⡙⢿⣿⣿⣻⣿⣿⣿⡺⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⠉⠙⠻⢿⣿⣿⣿⣿⡿⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣻⣿⣣⡀⠀⣀⣰⡿⠛⢛⣋⣌⡁⠀⠉⠛⣭⡟⠿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢻⣿⣿⣿⣿⠉⢈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⣿⣿⣿⣿⠃⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣟⣛
⣿⣿⣿⣿⣿⣿⡷⠿⠿⠁⠼⣿⣿⣿⣿⣆⠀⢠⣿⣯⣿⣾⣿⡿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣛⣻⡇⢸⠟⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠙⠿⠿⠿⣏⣉⣽⣿
⣿⣿⣟⡿⠋⠁⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣦⣾⣿⣿⣿⠏⠀⠀⢹⡇⢸⣿⣿⣿⣿⣿⣽⣿⣿⣿⣧⡴⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣿⣿⣿⣿⠁⠀⠀⠀⠄⠀⠀⠐⠶⠼⣿⣿⣿⡿
⣿⣿⠋⠀⠀⢀⣀⣠⣀⡀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠃⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢿⣿⣿⣿⡟⣿⣿⣿⣧⣵⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢂⣠⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⠏⠁
⣿⡟⠀⢀⣶⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡟⢻⠟⠁⠀⠘⣿⣿⡿⣽⣿⣿⣿⣟⢿⣾⣿⣿⣿⣿⣿⣿⣟⣥⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⣨⣐⣀
⠏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡗⠂⠀⠀⠀⠀⠙⠉⠉⢳⣯⣿⣿⣿⣶⣿⣿⣽⡍⠉⢹⣿⣿⣿⣿⣿⣿⡿⠿⠇⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿
⡄⠀⠀⢹⣿⣿⣯⣿⣿⡹⠋⡁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣅⡄⠀⠀⠀⠀⠘⠿⣿⡿⠿⠃⠀⠀⠀⢬⠠⣄⣠⣤⣴⣿⣿⣿⢟⣿⣿⢹⡿⠛⠑⠚⠋⣁⣩⡍⣥⣶⣶⣶⡄⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣄⢀⣿⣿⣿⣿⣿⣿⡿⣷⣿⡅⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⣀⣀⣀⣀⣠⣄⠀⠀⠀⠀⠀⠫⠃⠁⠘⠋⠋⢀⣤⣥⣄⠈⣴⣿⢿⣿⣆⢸⣿⡇⢻⣿⣇⣿⡿⠀⣿⣿⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠿⢅⣿⠏⢀⣴⣿⣿⣿⣿⡿⢿⣿⣿⡏⠈⠁⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠰⣶⣿⢿⣿⡆⢸⣿⣿⣿⡄⢻⣿⡇⣛⣋⡘⣿⣿⠸⣿⣿⢻⣿⡆⣿⣿⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⣿⣿⣴⣿⣁⡄⠛⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣧⠀⠀⠀⣿⣿⣼⣿⣃⢸⣿⡏⣿⣷⠸⣿⣧⢻⣿⡇⢿⣿⡆⣿⣿⡘⣿⣧⣿⠿⠇⠻⠛⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⣿⣿⣿⣿⣟⣿⡿⢋⡀⠀⠀⠀⠀⣽⣿⣿⡟⠿⢿⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠈⢻⣿⣿⣿⣿⣇⠀⠀⢸⣿⣏⢻⣿⡆⣿⣿⢿⣿⣇⢿⣿⣾⠿⠿⠸⠛⢃⡈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡀⠈⠀⠀⠀⠀⢀⣶⣶⡆⠘⡀⠀⠈⢿⣿⣿⣿⣿⣄⡀⠈⣿⣿⣾⠿⠃⠟⠛⠀⠋⠉⠀⠀⠀⠰⠾⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣰⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠈⠉⢉⣀⡀⠑⡄⠀⠀⢻⣿⣿⣿⣿⣿⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣴⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣷⣤⠀⠀⢶⡄⠀⠈⡇⢻⣿⡄⠈⢦⠀⠀⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠵⠻⣿⠉⠁⠀⠀⠘⣧⠀⢰⣿⡎⢿⣿⠀⠀⠱⡀⠈⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣲⣿⣿⣧⡀⠀⠀⠀⠸⣦⠸⣿⠟⠈⠛⢀⠀⠀⠱⡀⠈⢿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⣸⠀⠀⠀⠈⡄⠈⢿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣱⣿⡒⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠐⠄⠈⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⡻⣺⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⢀⣸⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣹⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠠⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⢰⡇⠀⣃⠀⠹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣷⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣹⣶⣻⣿⣿⣿⣿⣿⣿
⠯⢀⠉⠷⠛⠋⠋⠓⠺⢽⣿⣿⠉⠉⠙⠙⠋⣭⣡⣤⢠⣾⣿⣿⣧⣿⠏⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣾⣿⢻⣿⣿⣿⣿⣅⣾⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⠉⣭⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠦⣤⣆⢀⡀⠀⠀⠀⠀⠀⢦⡠⡟⣄⡀⢀⢠⣦⣼⣿⣿⣿⣿⣿⣿⣿⣴⣿⣋⣁⣀⠉⠙⠻⣿⣿⣿⣿⣿⣨⣻⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠙⢻⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⣿⣿⠇⠁⠀⠀⠀⠀⠐⠻⢰⡶⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⢻⣿⣿⣿⣿⣿⡏⣳⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡇⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣿⣿
⣯⣿⣿⣶⡀⢠⣴⣮⣴⣦⣼⣿⣿⣬⡭⡉⡘⠻⣿⡿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢿⣿⣿⣿⣇⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠙⢿⣿⠿⣿⣉⣿⣿⣿⡆⠻
⣿⣿⣿⣿⣿⡿⠛⠛⠻⠛⠛⠻⢿⣶⣾⣿⣿⣾⣿⣶⠜⠉⠈⣫⠀⢻⣿⣿⣿⣿⣿⢿⣷⣶⣾⡁⣋⣹⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣀⣰⣴⣿⣿⣿⣿⣯⠃⠀
⣧⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢹⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠙⢿⣿⣿⣿⣟⣿⣿⣿⣿⡿⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡀⡂⠀⠠⠶⠾⢿⣿⣿⣿⣿⠿⠙⠀⠀⠀
⣿⣿⡿⠀⠀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠈⠉⢙⣿⣷⡀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠂⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠑⠉⠛⢿⡦⠄⠀⠀⠀
⣿⠿⠀⢀⣾⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣯⣭⠟⠀⠀⠀⢺⡟⠛⠻⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⡿⢿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠶⠖⠒
⣇⠀⠀⢸⣿⣿⣿⣿⡿⢿⣿⣶⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠃⠀⠀⢀⡀⡀⠀⠀⠀⠈⢳⣾⣿⣿⣿⣿⣿⡿⣿⣷⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡟⠀⢠⣼⣿⣿⣿⣿⣷⣿⠟⢀⣠⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠙⠛⠛⠇⠀⠀⠀⠈⠋⢻⣿⣦⡶⠛⠻⣿⢏⠟⡩⣿⠿⠃⠿⠟⠻⠿⠿⣋⣩⡉⣤⣶⣶⣶⡄⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⣿⢸⣿⣿⣿⣿⣿⣿⣁⣴⠛⠁⡀⠀⢠⣿⣿⣿⣿⣿⡿⢷⠐⠀⠀⠀⠰⣶⣦⣤⣴⣶⣦⣄⠀⠀⠀⠀⢩⡿⠁⠀⠀⠃⠀⢈⣤⣤⣄⠀⣴⣿⢿⣿⣆⢸⣿⡇⢻⣿⣇⣿⡿⠀⣿⣿⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣾⣿⣿⣿⣿⣯⡿⠿⠁⠄⠈⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠰⣶⣿⢿⣿⡆⢸⣿⣿⣿⡄⢻⣿⡇⣛⣋⡘⣿⣿⠸⣿⣿⢻⣿⡆⣿⣿⣾⣿⣧⠀⠀⠀⠀⠀⢶⣶⠀
⠛⠛⢻⣿⣿⣿⣿⣿⠁⠀⠀⠀⠘⠓⠀⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠠⠀⠀⠛⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣿⣿⣼⣿⣃⢸⣿⡏⣿⣷⠸⣿⣧⢻⣿⡇⢿⣿⡆⣿⣿⡘⣿⣧⣿⠿⠇⠻⠛⠂⠀⠀⠀⠀⠈⠁⠀
⠀⠀⢰⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡈⠛⠇⠀⠀⠀⠀⠀⡀⡀⠐⡄⡀⠀⢻⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣏⢿⣿⡆⣿⣿⢿⣿⣇⢿⣿⣾⠿⠿⠸⠛⠃⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢰⣿⡿⠀⠘⡄⠀⠀⢻⣿⣿⣿⣷⣴⡄⠀⠈⣿⣿⣾⠿⠃⠟⠛⠀⠋⠉⠀⢤⣴⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣠⣦⣀⠘⢆⠀⠀⢹⣿⣿⣿⣿⣿⡆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠻⠆⠀⠈⣷⡄⠀⢘⣧⢻⣿⣧⠈⠳⡀⠀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⠀⠀⠀⠀⠘⣷⠀⣼⣟⡀⠻⣿⠀⠀⠐⡄⠀⢻⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡶⠀⠀⠀⠀⠹⠶⠽⠿⠓⠀⠉⠀⠀⠀⠘⢄⠈⢻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⠆⠀⢻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠀⠀⠀⠀⠈⠂⠀⢿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢉⡽⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠸⣼⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠟⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⢿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⡄⠠⡐⠀⢿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠠⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡯⠀⠀⠀⠀⢠⣇⠀⢷⡀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣫⡽⢿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣇⣀⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⡀⠹⠟⠋⠉⠙⠻⠿⣽⣿⡿⠁⠉⠋⠻⣥⢥⣤⣤⣼⣿⣿⣿⣿⡟⣹⣿⠟⠻⠿⢿⣿⣿⣿⣿⣿⣿⣟⣭⣿⣿⢛⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠻⣿⣿⣿⣿⣿
⣼⣶⠄⠀⠀⠀⠀⠀⠠⣴⣤⣴⣛⣄⠀⣀⣾⣦⣿⣿⣿⣿⣿⣿⣿⣿⣭⣤⣴⣤⣤⣀⣈⠻⣿⣿⣿⣿⣮⣞⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠹⣿⣿⣿⣿
⣾⣿⠏⠀⠀⠀⠀⠐⠀⠔⠻⣳⣶⣟⣿⣿⣿⣿⣿⣿⣿⣟⣿⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⣿⣿⣿⣿⣿⡿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠈⠹⠿⣿⣿⣿⣿⡿⣿⣄⣠⣜⠛⣿⣿⣿
⣿⣿⣿⣂⣠⣶⣷⣾⣾⣷⣿⣿⣷⣮⣟⡵⣯⣻⡟⣻⡿⠻⡿⠀⢿⣿⣿⣿⣿⣿⣿⣿⠿⠟⡇⠹⣿⣿⣿⣇⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠈⠛⢋⣿⣶⣾⣿⣿⣏⠀⠈⢿⣿
⣿⣿⣿⣿⣿⣿⡿⠛⠙⠛⠉⠉⠙⢿⣿⣷⣿⣿⡿⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣍⣿⣿⣿⣧⢘⣹⣿⣿⣿⣿⣿⣿⣯⣩⣿⣿⠁⠁⢛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠾⠿⣿⣿⣿⣿⣟⠃⠀⠀⠀⢻
⣾⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡇⠀⠀⠀⠀⠂⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠹⣿⣿⣿⣿⣿⡿⣶⡯⢿⡿⠃⠀⠈⠑⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀
⣿⣿⣿⡿⠀⠀⣠⣴⣾⣿⣶⣤⡀⠀⠘⠻⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⣿⡟⠀⠀⢹⡿⣿⣿⣿⣷⣿⣷⣿⣷⡀⠀⢸⣀⣿⣿⣿⣿⣿⣿⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣃⠀⠀⠀⠀⠙⠛⢀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡶⠉⠀⠀⠀⠤⠀⠁⠈⠉⠻⣿⣷⡚⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠇⠀⢀⣿⣿⣿⣿⣿⣿⠋⣩⠟⠁⠀⠀⠀⢠⣿⣿⡄⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠃⠀⠀⠀⣶⢶⣶⣦⣄⠀⠀⢹⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣿⣅⠀⢹⣿⣿⣿⣿⣿⣿⡾⠉⠀⠔⠀⠀⢀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠆⠀⠀⠀⠀⠸⢻⣿⣿⣧⣴⣾⣿⠿⠛⠛⠛⠻⣿⣿⠿⠟⠻⠟⣋⣩⡀⣤⣶⣶⣶⡄⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣻⣿⣧⢰⣼⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⢻⣿⣿⡟⠛⠆⠀⠀⠀⠀⢿⣶⣶⣶⣶⣿⣶⣄⠀⠀⠀⠈⠟⠛⠛⠛⠛⠙⠀⢀⣤⣤⣄⠛⣵⣿⢿⣿⣆⢸⣿⡇⢻⣿⣇⣿⡿⠀⣿⣿⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣦⣸⣿⣿⣿⣿⣿⡏⠀⠀⠀⣼⠃⣠⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠰⣶⣿⢿⣿⡆⢸⣿⣿⣿⡄⢻⣿⡇⣛⣋⡘⣿⣿⠸⣿⣿⢻⣿⡆⣿⣿⣾⣿⣧⠀⠀⢾⣷⠀⠀⠀⠀
⠿⠟⠃⠉⠉⣹⣿⣿⣿⡿⠀⠀⠀⢀⣽⣿⣿⡿⣿⣹⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⠻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣿⣿⣼⣿⣃⢸⣿⡏⣿⣷⠸⣿⣧⢻⣿⡇⢿⣿⡆⣿⣿⡘⣿⣷⣿⠿⠇⠻⠛⠂⠀⠈⠁⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣿⣿⣿⠏⠀⠀⠀⠀⢸⣿⣿⣿⡆⠈⠻⠀⠀⠀⠀⠀⢀⣀⠀⠢⠀⠀⠘⢿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣏⢻⣿⡆⣿⣿⢿⣿⣇⢿⣿⣾⠿⠿⠸⠛⠃⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣾⣿⣿⣟⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣶⣿⡗⠀⠣⠀⠀⠈⢿⣿⣿⣿⣷⣶⡀⠀⠈⣿⣿⣾⠿⠃⠟⠛⠀⣋⣩⣤⣤⣤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⡀⠀⠀⠀⢀⠀⠀⠀⣀⢴⣆⡀⠱⡀⠀⠈⢿⣿⣿⣿⣿⣷⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⣾⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠂⠀⠀⠸⢧⠀⠀⢸⡿⣿⣇⠀⠈⢢⠀⠀⢿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠻⡆⠀⣼⡁⠈⢻⠄⠀⠀⠣⠀⠈⢿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠘⢷⡤⠻⠇⠀⠀⠀⠀⠀⠀⠑⠀⠈⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢠⣮⠀⠀⠀⠈⡆⠀⢻⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠀⠀⠀⠀⠀⢀⠀⢿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣉⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣼⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠙⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⢀⡐⠀⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒⠀⠛⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⢠⣇⠀⢿⡀⠘⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠁⢸⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢛⣿⣿⣿⣿⣿⣿⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠁⣬⠿⠗⠞⠿⣿⣟⣿⣿⡿⠋⠛⢿⡟⠛⠋⠉⠈⢹⣿⣿⣆⣾⡿⣫⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣻⣿⣿⣿⣿⣿⣿⠛⣹⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣰⠀⠁⠀⠀⠀⠀⠀⠙⢉⡝⣅⠀⠀⠀⠁⣀⢹⣿⣿⣿⣿⣿⣿⣿⣀⣙⣀⣀⣀⡈⠙⠻⣿⣿⣿⣿⣿⠅⣼⣿⣿⣍⢿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠈⢿⣿⣿⣿⣿⣿⣿⣿
⣏⣷⠀⠀⠀⠀⠀⠀⠰⢔⣦⣘⣶⣦⣼⣶⣿⣿⣿⡿⣿⣿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡉⢿⣿⣿⣿⣿⣺⡅⡝⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡛⢿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠈⣻⣿⣿⣿⣿⣿⣿
⣿⣯⡄⠀⢀⣤⣀⣠⣄⣠⣿⣿⣫⢎⠻⣛⣿⣿⣿⣿⠟⠋⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⢘⣿⣿⣿⣿⠛⠁⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣍⡻⠿⣿⣿⣟⣋⣤⣤⡄⠀⠀⠻⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣿⣿⣿⣿⣿⠿⠿⠛⠋⠀⠐⣪⣍⠓⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⡿⣿⣷⣶⢌⣀⡿⢿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⣤⣿⣿⣿⣿⣿⡇⠀⠀⠀⠙⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⡇⠰⣿⣿⣿⣿⣿⣿⡟⣇⢹⣿⡅⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠈⠛⠿⣿⣿⠧⠀⠀⠀⠀⠀⠘⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠃⠀⣠⣤⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢹⣿⣿⣿⣿⣷⡿⣾⢹⣿⡁⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⣿⣿⣿⣿⣿⠃⠀⣸⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣁⠠⠃⠀⠀⠈⠙⠛⠙⠛⠚⢿⣿⢞⣿⣷⠀⣠⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣼⡟⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡏⠀⠀⠀⣠⢺⠃⠀⠀⠀⠀⠀⢹⣄⣼⣿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣯⡟⠉⣀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣠⠞⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠉⢸⣿⣿⣦⣄⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⣿⣿⡇⢴⣿⣆⢺⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⠀⣀⣴⣿⡆⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⢙⣿⣿⣿⣆⣴⣇⣹⡿⢟⣿⣿⣿⣿⡿⠿⠛⠛⠀⣀⣠⡀⣤⣶⣶⣶⡄⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢀⣿⣿
⣿⣿⣿⣆⣻⣿⣦⣾⣿⣿⣿⣿⣿⡿⠀⣰⣿⣿⢻⡇⠈⠁⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠁⠈⠃⠉⠋⠉⠋⠃⢈⣭⣭⣍⠋⣴⣿⢿⣿⣆⢸⣿⡇⢻⣿⣇⣿⡿⠀⣿⣿⢿⣷⡀⠀⠀⠀⠀⠀⣼⣿⠿
⣿⣿⠿⠿⠿⠿⢿⢹⣿⣿⣿⣿⣿⣷⣾⣿⣿⣯⡛⡇⠀⠀⠀⠀⠀⠀⢀⠀⠙⠻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠰⣶⣿⢿⣿⡆⢸⣿⣿⣿⡄⢻⣿⡇⣛⣋⡘⣿⣿⠸⣿⣿⢻⣿⡆⣿⣿⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠁⠀⠀⠀⠀⠀⠈⣻⣿⣿⡟⣿⣿⣿⣿⡆⠙⠳⡇⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠈⣿⣿⣿⣿⣯⡄⠀⠀⠀⠀⣿⣿⣼⣿⣃⢸⣿⡏⣿⣷⠸⣿⣧⢻⣿⡇⢿⣿⡆⣿⣿⡘⣿⣷⣿⠿⠇⠻⠛⠂⠀⠀⠀⠀⢀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠀⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢀⣶⣶⠀⠡⠀⠀⠈⢻⣿⣿⣿⣧⣤⡀⠀⠀⢸⣿⣏⢿⣿⡆⣿⣿⢿⣿⣇⢿⣿⣾⠿⠿⠸⠛⠃⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠇⠿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠈⠋⠉⡀⠀⠱⡀⠀⠀⢻⣿⣿⣿⣿⣷⡀⠀⠈⣿⣿⣾⠿⠃⠟⢛⣀⣋⣩⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⠛
⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣠⠀⠀⠀⡂⢧⣄⠀⠘⢄⠀⠀⢻⣿⣿⣿⣿⣇⠀⠀⠁⠀⠀⠀⢾⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣰⣿⣿⣿⡟⠁⠀⠀⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⢛⣇⠀⠀⡿⠉⠙⠂⠀⠀⠑⡀⠀⢻⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠻⢿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⣠⣾⣿⣿⣿⡿⠁⠀⠀⠀⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠻⡄⠘⣧⠀⠀⠀⠀⠀⠀⠐⢄⠀⠻⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠠⠀⠹⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢻⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠂⠀⠹⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⠍⣻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠏⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣶⡟⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠟⠃⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠂⠀⣆⠀⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢸⠀⠀⠹⠀⠀⢻⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢻⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣶⣾⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠻⠟⣻⣿⣯⣹⣿⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠿⠿⠻⣿⣿⣧⡀⣸⣿⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⠀⠻⠉⠁⠉⠉⠓⣿⠿⣿⡏⠀⠛⠙⠏⠀⢠⣤⣠⣿⣿⣽⣿⣟⣛⣋⣋⡛⠉⠙⠻⣿⣿⣿⣿⣿⣿⣟⢩⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠁
⣿⢄⠀⠀⠀⠀⠀⠀⠀⢀⡘⡇⣀⡀⢠⣀⣶⣼⠟⠛⣿⡏⠉⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⢿⣿⣿⣿⣿⣵⡙⠟⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠈⢿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀
⣷⡿⠁⠀⠀⠀⠀⠀⠐⠄⣶⣿⣯⡗⢿⣿⡿⢁⣴⣿⠟⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⠄⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣉⠻⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣧⡀⠀
⣿⣿⣇⣀⣰⣾⣦⣶⣶⣾⣿⣿⡿⠁⠘⠟⣱⡿⠋⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⠿⣿⣭⣄⢃⢹⣿⣿⣿⣿⣁⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣍⠛⢛⣿⣧⣶⣿⣦⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⣿⣯⣯⣾⠺⢋⣽⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⠹⠿⠛⠛⢿⣷⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⣛⣯⣧⣨⡟⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠈⠉⠛⠻⠟⠛⠃⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⣰⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠋⢹⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢿⣿⣿⣿⣿⣻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠙⠁⠀⠀⠀⠉⠉⠉⠙⠋⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿
⣿⣿⣿⠟⣿⣿⠀⠀⠀⣤⣼⣿⣿⣿⣿⣿⣋⣉⠉⢹⡆⠀⠀⠀⠀⠀⠈⠻⢿⠿⠋⠀⠀⠀⠀⠿⠺⠓⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿
⣿⣿⡟⣠⣿⣿⡄⠀⠸⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⣠⣥⠄⡀⠀⠀⠀⢀⣀⣀⠀⢀⣀⠀⠀⠀⠀⠈⠿⠶⣤⣄⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣿
⣿⣿⣿⣿⣿⣿⣷⡀⠀⢸⣿⣿⣿⣿⣿⣯⣷⣾⢿⣿⠙⠃⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣦⠀⠀⠀⠈⠁⠽⣿⡾⠋⣸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⣠⡀⣤⣶⣶⣶⡄⠀⣿⣿⣿⡄⠀⠀⢠⣿⣿⣿⣿⣿⣿
⣿⣻⣿⣿⣿⣿⣿⣷⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⢋⣭⣤⣌⠉⣴⣿⢿⣿⣆⢸⣿⡇⢻⣿⣇⣿⡿⠀⣿⣿⢿⣷⡀⠀⣿⣿⡿⠟⠋⠀⠙
⣿⡿⠏⠉⠁⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⡏⠹⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠹⣿⣿⣿⣿⡧⠀⠀⠀⠀⠰⣶⣿⢿⣿⡆⢸⣿⣿⣿⡄⢻⣿⡇⣛⣋⡘⣿⣿⠸⣿⣿⢻⣿⡆⣿⣿⣾⣿⣧⠀⠉⠁⠀⠀⠀⠀⠀
⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⡄⠀⠁⠀⠀⠀⠀⠀⢀⢀⠀⠁⠀⡀⠘⢿⣿⣿⣿⡃⠀⠀⠀⠀⣿⣿⣼⣿⣃⢸⣿⡏⣿⣷⠸⣿⣧⢻⣿⡇⢿⣿⡆⣿⣿⡘⣿⣧⣿⠿⠇⠻⠛⠂⠀⠀⢀⣀⣤⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠐⠿⠛⠂⠀⠡⡀⠀⠀⢻⣿⣿⣿⣿⣆⠀⠀⢸⣿⣏⢻⣿⡆⣿⣿⢿⣿⣇⢿⣿⣾⠿⠿⠸⠛⠃⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢄⢈⠀⠀⠘⢄⠀⠀⢻⣿⣿⣿⣿⡆⢠⡈⣿⣿⣾⠿⠃⠟⠛⣀⣋⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠟⠋⠁⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⢡⣇⠀⠀⠨⠄⠂⠄⠀⠀⠑⡄⠀⢻⣿⣿⣿⣷⣼⣷⣥⣤⣶⣶⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠏⠀⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢿⡀⠀⢞⠀⠀⠀⠀⠀⠀⠈⠄⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢴⣶⣶⣶⣿⣿⣿⣿⡏⠀⠀⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠙⣿⣿⣿⡇⠹⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠐⠀⠘⣿⣿⣧⠀⠈⠻⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢹⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⡟⠙⣛⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣴⣶⣿⣿⣿⡟⠀⠀⠀⠀⠀⢿⣿⣇⠀⠈⠙⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡁⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠸⠀⢠⠠⠀⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠘⠀⠈⠧⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⢛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣷⣦⣬⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣻⠟⣿⣿⣻⣩⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⣿⣿⠿⣿⢻⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣖⣥⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠀⡀⠻⠋⠁⠁⠉⠿⣿⢟⡻⠂⠀⠙⠉⢿⠠⠤⢀⡴⢃⡀⢴⣽⣿⣶⣾⣶⣶⣶⣦⣬⣻⣿⣿⣿⣿⣿⡿⣯⣷⣿⣿⣿⣿⣿⣿⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠟⢋⡁⠀⣩⣿
⣧⣴⢆⡀⠀⠀⢀⠀⠀⣀⡠⣄⠀⣠⣄⢀⣄⣶⣿⠏⣴⣿⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⣽⣿⣹⣛⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠙⢿⣿⣿⣿⣿⣿⣿⣷⠋⠀⣾⠀⠀⣿⠃
⣶⣿⣿⠃⠀⠀⠈⠁⠨⢄⢆⣾⣿⡟⣿⣿⣿⠾⣿⡾⠋⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣛⡛⠇⣹⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⡇⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣧⣼⠃⠀⣸⡇⠀
⣿⣿⣿⣇⣀⣠⣾⣷⣾⣿⣾⣿⣿⠿⠈⠀⠉⠿⠉⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⣍⣿⣿⣟⣷⢼⣿⣿⣿⣿⣇⣀⣬⣿⣿⣿⣿⣿⣿⣿⣶⣌⡛⠿⣿⣿⣿⣿⣿⣋⣀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣄⠀⡿⠀⠀
⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠛⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⣯⣤⣬⣿⣿⣯⣽⣿⡇⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣾⠃⠀⠀
⣷⣿⣿⣿⣿⣿⣿⣿⡟⠉⠁⠀⠀⠀⠀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡿⢿⠛⠀⠀⢻⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠈⠹⠿⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀
⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⣾⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⢠⠟⠀⠀⠀⠀⠀⠀⢠⣵⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⣤
⣿⣿⣿⣿⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟⢀⣠⡀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠿⢑⠀⠀⠀⢰⠺⠛⠀⠈⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢿⢸⣿⣿⡄⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⢰⣾⣶⣸⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣿⣃⣼⣿⣿⣧⠀⠀⠀⠀⢿⣿⣿⣿⣿⢋⣹⣿⡿⣯⡀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣥⣤⡀⠀⠀⠀⠉⣿⠛⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿
⣿⣼⣿⣯⠻⣿⣿⣿⣄⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⣹⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡀⣤⣶⣶⣶⡄⠀⣿⣿⣿⡄⢀⣀⣠⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣿⣿⣿⡿⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣆⠀⠀⠈⢸⠿⠿⠛⠿⠿⢋⣥⣤⣄⠀⣴⣿⢿⣿⣆⢸⣿⡇⢻⣿⣇⣿⡿⠀⣿⣿⢿⣷⡘⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠋⠉⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡁⠙⠳⡃⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠈⠻⣿⣿⣿⣿⣀⠀⠀⠰⣶⣿⢿⣿⡆⢸⣿⣿⣿⡄⢻⣿⡇⣛⣋⡘⣿⣿⠸⣿⣿⢻⣿⡆⣿⣿⣾⣿⣧⠹⠋⠁⠀⢻⣿⣿⣿
⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⡀⠀⠀⠹⣿⣿⣿⣯⢀⣼⡄⣿⣿⣼⣿⣃⢸⣿⡇⣿⣷⠸⣿⣧⢻⣿⡇⢿⣿⡆⣿⣿⡘⣿⣷⣿⠿⠇⠻⠛⠂⠀⠀⠀⠈⢿⣿⣿
⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁⠀⠘⢄⠀⠀⠸⣿⣿⣿⣿⣿⣇⢸⣿⣏⢻⣿⡆⣿⣿⢿⣿⣇⢿⣿⣾⠿⠿⠸⠛⠃⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⠀⠈⢿⣿
⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠁⠀⠀⠈⢆⠀⠀⠙⢿⣿⣿⣿⣿⠈⣿⣿⣾⠿⠃⠟⠛⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⣿⣿⣇⠀⠀⠈⢻
⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠸⣿⣿⣿⣿⣷⣥⣤⣴⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀
⠙⢿⣿⣧⠀⢀⣠⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⢀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠁⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⠋⣿⣿⡟⠛⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢻⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⠀⠀⠀⠉⠉⠀⠀⢹⣿⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡗⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠟⠋⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⠒⣒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣿⢿⣿⣿⣿⣛⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣟⣋⣉⣙⣛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣉⡄⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⢀⠈⢿⠟⠉⠉⠋⣿⣿⡿⢛⡀⠈⠛⢻⡏⢥⣀⣀⡰⠏⢁⣱⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡿⢫⡿⠋⣿⣿⡿⠿⢿
⣴⢤⣼⡄⠀⠀⠀⠀⠀⠀⢠⣄⢰⣤⣀⡀⢀⣨⣾⣿⣿⣧⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠰⠃⠀⡿⠁⠀⣽⡟⠁⠀⠀
⣿⣿⣯⣿⠀⠀⠀⠐⠀⢰⠘⠿⣿⣿⣿⠧⢿⣿⣿⠟⠁⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⢿⣿⣥⣬⡁⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠈⢻⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠠⠁⠀⠀⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣇⣀⣠⣶⣾⣷⣶⠆⠉⠁⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣾⣾⣿⣤⣤⣿⠾⣿⣿⣿⣿⣿⣿⣿⣿⣄⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠁⣿⣿⣿⣿⣿⣿⣿⠿⠿⢆⣹⠛⠿⣿⣿⣿⣿⠥⣤⡀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣯⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⣦⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠛⠛⠋⢀⣠⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⢳⣶⣶⣾⣵⣀⣼⣿⡇⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⢿⠟⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠉⠙⠿⣿⣿⡿⠿⠁⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣣⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣿⣷⣦⣦⡀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠷⣾⣿⡟⠛⢢⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀
⣿⣿⣿⠃⣿⣿⣦⠀⠀⠀⠀⠀⠀⣰⣽⣿⣿⣿⠟⠁⠉⡯⢁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢼⣿⣿⠒⣸⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀
⠿⣿⡇⣴⣿⣿⣿⡄⠀⠀⠀⠀⠀⢸⣿⣷⣿⠟⠀⢀⣼⣿⣦⠀⠀⠀⠀⠀⠰⣶⣤⣤⣤⣼⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣛⣙⢻⣿⣿⣿⣿⣿⣧⡀⠀⠀
⣿⡯⣷⣌⢻⣿⣿⣷⣤⣄⡀⠀⢀⣼⣿⣿⣿⣠⣶⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣯⣿⢰⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡀⣤⣶⣶⣶⡄⠀⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣆⡀
⣿⣿⣿⣿⣾⣿⡿⠿⠛⠉⠁⠀⠀⠛⢿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⡇⡼⣾⣿⣿⣿⣿⠿⠟⠛⠀⠀⢀⣤⣤⣄⠀⣴⣿⢿⣿⣆⢸⣿⡇⢻⣿⣇⣿⡿⠀⣿⣿⢿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⠙⠛⢖⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠈⠛⠃⢀⣿⣿⣿⣿⠰⣶⣿⢿⣿⡆⢸⣿⣿⣿⡄⢻⣿⡇⣛⣋⡘⣿⣿⠸⣿⣿⢻⣿⡆⣿⣿⣾⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠄⠀⠀⠀⣸⣿⣿⣿⣿⡄⣿⣿⣼⣿⣃⢸⣿⡏⣿⣷⠸⣿⣧⢻⣿⡇⢿⣿⡆⣿⣿⡘⣿⣷⣿⡿⠇⠻⠛⣢⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠁⠀⠀⢂⠀⢀⣿⣿⣿⣿⣿⡇⢸⣿⣏⢿⣿⡆⣿⣿⢿⣿⣇⢿⣿⣾⠿⠿⠸⠛⠃⠈⠉⠁⠵⠖⠂⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠁⠀⢀⣀⣶⣾⣿⣿⣿⣿⣿⣿⠈⣿⣿⣾⠿⠃⠟⠛⠀⠋⠉⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣀⣠⣦⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣥⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⡏⠀⠀⠹⣿⣿⣿⣿⣿⣿
⠀⠈⠻⣿⣷⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⡀⠀⠀⠀⠀⢹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⡿⠟⠀⠀⠀⠹⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣶⣾⣿⡗⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⠛⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⠀⠈⠻⣿⣿⣿⣿⡿⠁⠀⠀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠉⣀⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⢹⣿⣿⣿⣿⣷⣴⣶⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡟⠻⠿⣿⣟⠉⠉⢽⣿⢿⣿⣿⠛⠟⣻⣿⡿⠿⠟⠛⠙⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⡤⢀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⠭⣭⡽⠋⡹⠛⠛⣻⣿⣿⢿⣿⣿⣿⣿
⠀⢁⠁⠠⠀⠛⠉⠀⠀⠀⠻⠘⠋⠀⠀⠀⠀⠘⠂⣐⣶⣶⣼⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡰⠋⠀⢸⠁⠀⠀⣸⠟⠀⠈⠛⢿⣿⣿
⣾⣿⣷⡟⣆⠀⠀⠀⡀⠀⠀⠡⣤⣞⣿⣶⡄⣴⣜⣿⡿⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠉⢿
⣿⣷⣿⣿⣟⡀⠀⠀⣌⡀⠠⡀⠘⠉⠈⠉⠈⢻⡏⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⣀⣼⣿⡿⠟⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⣤⣦⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠈⠛⠻⣿⣿⣿⣿⣿⠋⣀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣷⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⠀⢹⣟⡉⠀⣸⣿⡇⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡟⣡⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣄⣀⠀⠀⠀⠀⢀⣼⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⢲⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⣿⡿⠃⠙⠁⠀⠀⢰⣿⣿⣿⠿⠁⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⢿⠇⣸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣓⠛⡰⠿⠃⠀⣠⣤⠂⠀⢸⣿⣿⠁⠀⠀⠐⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠿⠿⣿⠟⠋⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡆⢿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠁⢀⣴⣿⣿⠃⠀⢸⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡀⣤⣶⣶⣶⡄⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣦⣿⣿⣿⣿⣶⣶⡤⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⢸⣿⣿⣧⡀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⣴⣿⢿⣿⣆⢸⣿⡇⢻⣿⣇⣿⡿⠀⣿⣿⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⡟⠆⠀⠀⠀⢿⣿⣿⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⡇⠰⣶⣿⢿⣿⡆⢸⣿⣿⣿⡄⢻⣿⡇⣛⣋⡘⣿⣿⠸⣿⣿⢻⣿⡆⣿⣿⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣿⣧⠈⠛⠇⠀⠀⠀⣿⣿⣿⡿⠂⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣼⣿⣃⢸⣿⡏⣿⣷⠸⣿⣧⢻⣿⡇⢿⣿⡆⣿⣿⡘⣿⣷⣿⠿⠇⠻⠛⢂⣾⣆⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡆⠀⠀⠀⠀⠀⣿⡟⠃⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣏⢿⣿⡆⣿⣿⢿⣿⣇⢿⣿⣾⠿⠿⠸⠛⣃⣈⣩⣥⣥⣤⣶⣶⣾⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀
⠹⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠈⣿⣿⣾⠿⠃⠟⠛⠀⠋⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀
⠀⠀⠹⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇⠀⠀⠀⠀⠀⣻⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠁⠀⠀⠀⠀⠀⢠⣦⡤⠀⠀⠀⠀⠀⠀⠀⠿⠛⠛⠉⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⠂⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠂⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢻⠟⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠉⣠⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⢹⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡟⠻⠿⣿⣟⠹⠙⢽⣿⢿⣿⣿⠛⠟⢻⣿⣿⠿⠟⠛⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣤⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⡩⠭⣭⡽⠋⡹⠛⠛⣻⣿⣿⢿⣿⣿⣿⣿
⠀⢉⠁⠠⠀⠛⠉⠀⠀⠀⠛⠘⠑⠀⠀⠀⠀⠈⠁⣐⣶⣶⣼⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢰⠋⠀⢸⠁⠀⠀⣸⠟⠁⠈⠛⢿⣿⣿
⣶⣿⣷⡿⣆⠀⠀⠀⡀⠀⠀⠠⣤⣞⣿⣶⡄⣤⣔⣿⡿⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠉⢿
⣿⣷⣿⣿⣟⡀⠀⠀⣬⡀⢀⡀⠘⠉⠉⠉⠈⢻⡏⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣾⣷⣄⣼⣿⡿⠟⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⣤⣦⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠈⠛⠻⣿⣿⣿⣿⣿⠋⣀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣷⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢀⠀⣹⣟⡉⠀⣸⣿⡇⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡟⣡⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣄⣀⠀⠀⠀⠀⢀⣼⣿⣿⡿⠟⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷⣿⡿⠃⠙⠁⠀⠀⢰⣿⣿⣿⠿⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⢿⠇⣸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣓⡓⣸⠿⠃⠀⣠⣤⠂⠀⢸⣿⣿⠁⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠿⠿⣿⠟⢋⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡆⢿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⠀⢀⣴⣿⣿⠇⠀⢸⣿⣿⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡀⣤⣶⣶⣶⡄⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣯⣦⣿⣿⣿⣿⣶⣶⡤⠀⠀⠀⢰⣿⣿⣿⣾⣿⣿⡟⠁⠀⠀⢸⣿⣿⣧⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⣴⣿⢿⣿⣆⢸⣿⡇⢻⣿⣇⣿⡿⠀⣿⣿⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⡟⠆⠀⠀⠀⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇⠰⣶⣿⢿⣿⡆⢸⣿⣿⣿⡄⢻⣿⡇⣛⣋⡘⣿⣿⠸⣿⣿⢻⣿⡆⣿⣿⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣿⣧⠈⠛⠇⠀⠀⠀⣿⣿⣿⡿⠂⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣼⣿⣃⢸⣿⡏⣿⣷⠸⣿⣧⢻⣿⡇⢿⣿⡆⣿⣿⡘⣿⣷⣿⠿⠇⠻⠛⢂⣿⣆⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡆⠀⠀⠀⠀⠀⣿⡟⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣏⢿⣿⡆⣿⣿⢿⣿⣇⢿⣿⣾⠿⠿⠸⠛⣃⣈⣩⣥⣥⣤⣶⣶⣾⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀
⠹⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠈⣿⣿⣾⠿⠃⠟⠛⠀⠋⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀
⠀⠀⠹⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇⠀⠀⠀⠀⠀⣻⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠁⠀⠀⠀⠀⠀⢠⣦⡤⠀⠀⠀⠀⠀⠀⠀⠿⠛⠛⠉⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⠂⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠺⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠂⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢻⠟⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡉⠁⠀⠴⢶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠿⠿⡿⠻⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠋⠛⣿⣿⡄⠉⠘⢿⣟⣿⣿⡿⠛⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣤⢄⣡⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠿⠛⣿⣿⣿⣿⣿⣿⣿
⠒⠂⣅⠰⡆⠉⠁⠀⠀⠀⠈⠻⠛⠁⠓⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣹⣿
⣿⣿⣯⣾⢳⡄⠀⠀⣀⠀⠠⠀⢠⣼⣻⣶⣦⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠉⠑⠂⠭
⣿⣿⣿⣿⣿⣃⠀⠀⣼⣄⢠⡠⠄⠛⠉⠁⠁⢹⡟⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⠛⠁⠀⠀⠀⠀⠀⢐⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡿⢿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⢠⡞⡀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡾⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣧⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠙⠻⣿⣿⣿⡿⠿⠁⣤⣄⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠏⣡⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣸⣶⣤⣤⣴⣿⡏⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡟⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⡿⠃⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⠻⢿⢿⡿⠟⠁⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠃⢀⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⡿⠛⠁⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠟⠛⠛⠛⣉⣠⡀⣤⣶⣶⣶⡄⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣧⡸⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡧⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠉⣴⣿⢿⣿⣆⢸⣿⡇⢻⣿⣇⣿⡿⠀⣿⣿⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣬⣿⣿⣿⣧⠀⣤⡄⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⢿⣿⡆⢸⣿⣿⣿⡄⢻⣿⡇⣛⣋⡘⣿⣿⠸⣿⣿⢻⣿⡆⣿⣿⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠀⠀⠀⠀⠈⠻⢿⣿⣧⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣼⣿⣃⢸⣿⡏⣿⣷⠸⣿⣧⢻⣿⡇⢿⣿⡆⣿⣿⡘⣿⣷⣿⠿⠇⠻⠛⠂⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡷⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⢿⣿⡆⣿⣿⢿⣿⣇⢿⣿⣾⠿⠿⠸⠛⢃⣈⣉⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣾⠿⠃⠟⠛⠀⠋⠉⠀⠀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠇⠘⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠆⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠁⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⣄⣠⣤⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣴⣦⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡿⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⡉⠀⣠⠴⢶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡟⠋⣹⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⠿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣽⣿
⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣠⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣟⡿⢿⣿⣿⡟⠛⠉⠉⠉⠙⠛⠿⠿⠯⢭
⢉⣍⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠀⢶⣷⣶⣶⣶⡄⠀⠀⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣹⣿⣋⣉⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣶⣿⣦⣤⡆⠤
⣿⣿⣿⣏⣿⡿⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⣾⣿⣿⣿⣟⠀⠀
⣿⣿⡿⠛⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⢿⠀⣀
⣿⣿⠀⣾⣧⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⠛⣿⣿⣿⣿⣿⠟⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡟⠀⠀⠛
⣿⡇⠀⣿⣿⣆⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠉⣠⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⠀⠀⠀
⣿⡇⢰⣿⣿⣿⣶⣿⡿⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠹⠿⠿⣿⣯⣿⠗⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀
⣿⣿⣮⠻⣿⣿⣿⡿⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠃⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡟⣿⠁⠀⢀⣤⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠀⠈⠀⠶⡿⠏⠁⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⠀⠀⣤⣤⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⣿⣿⡏⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠗⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠟⠛⢋⣉⣈⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣵⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣧⣴⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣧⣄⣀⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢉⠋⠛⠛⠿⡿⣿⣏⡛⠿⠿⢿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠉⠛⠛⠛⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣿⣿⣿⣿⠟⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠁⠀⠀⢨⣿⣿⣿⣿⣿⣿⣷⣄⡀⠙⢧⣠⣤⣤⣀⡀⠀⠀⠀⣀⣤⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠻⠿⣿⣿⠿⠆⠀⠀⢹⠜⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⣿⣷⣶⣻⣆⡔⢟⠂⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⣿⣿⢿⣿⣿⣿⣷⡿⠊⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣶⣶⣤⣿⣿⡟⣫⣿⣿⣿⣿⣧⠀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣏⠛⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢻⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠟⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠈⠈⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡏⠙⠿⢿⣿⣱⠟⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡋⠁⠀⠀⠀⣠⣤⣄⣀⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⣿⣴⣾⣾⣿⠏⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡄⠀⠀⠀⠹⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡏⠋⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣹⣧⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣼⡟⠘⠃⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⡖⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣼⣿⣼⠂⠀
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠇⠀
⣿⣿⣏⡟⣿⣿⣻⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢫⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⡹⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠀⠀⠀⠈⠉⢻⢿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠻⠿⣧⣀⣀⣀⣀⠀⠀⠀⠀⢰⣰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠋⠙⠛⢿⣿⣟⣥⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠿⠛⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠈⢿⣿⣿⣿⡿⢧⠀⠀⢼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣩⣤⣤⣤⠶⠶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣲⣾⣿⣶⣶⣷⣰⣞⠵
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠉⠀⠀⠀⠀⠟⠛⠛⠛⡿⠛⠁⢀⣼⣿⣿⡿⠃⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⡆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣰⣿⣿⠛⢻⣿⣿⣿⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣟⠉⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠯⠟⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠿⢿⣿⡗⠀⢾⣿⣿⣿⣿⠿⠃
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣾⢿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠈⣿⣿⣆⠀⡿⠿⢶⣿⣿⠟⠋⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠚⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡏⣼⣿⣿⣿⣿⣿⣿⣿⠀⢸⣷⣿⣿⣿⣶⠁⠀⣼⣿⠃⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢉⠀⣿⣿⣿⣿⣿⣿⣿⡟⠀⣸⢻⠇⢹⣿⣥⣀⣴⣿⠃⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣿⣿⣿⣿⣿⡿⠟⠀⣾⣿⣼⠀⠀⠈⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠋⠁⠀⡤⢀⠗⠿⠀⠀⠀⣹⢏⣿⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠅⠀⢠⣤⡞⡵⠃⠀⠀⠀⠀⣰⢫⡿⠉⠟⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢏⡞⠁⠀⠀⠀⠀⡴⣱⣿⡿⠂⣸⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠎⠀⠀⠀⠀⠀⢼⡾⠁⠈⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠋⡇⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⢀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣱⠏⠀⠀⠀⡀⠀⠀⠸⣿⣿⣶⣶⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⠯⠀⠀⡀⣈⣥⣤⢀⡀⠉⠻⢿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⢀⠈⢙⣿
⠘⣩⣍⠛⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠿⠟⠹⠿⢿⣿⡿⠇⠈⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣉⣠⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡽⠿⢿⢿⣿⣿⣿⣿⣷⣯⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⠇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠉⠉⠻⢧⠀⣀⣀⣀⣀⣀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠛⠛⠛⠛⠋⠙⠟⠋⠀⠀⢀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⣰⣿⠿⠿⣿⠿⠿⡄⠀⠨
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠉⠛⠛⠛⣦⣀⣀⣀⠠⠁⠀⠀⠀⠀⠈⠃⠘⣿⣿⣿⣿⣿⣛⣹⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⢺⣿⣿⣿⣿⣶⣞⣿⣄⡀
⣿⣿⣿⢿⠋⠉⠈⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣯⣿⣿⣿⣿⣿⣿⠿⣿⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡀⣰⣿⣿⣿⣿⡋⣹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⠃⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢉⣻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⠈⠙⢿⣿⣏⠉⢻⣿⡀⠈⣨⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠙⠻⠁⠀⠈⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢶⣾⠏⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠈⢿⣿⣦⣸⠟⠛⣿⡿⠋⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠈⠘⣿⡟⠻⠟⡿⡫⢞⣵⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⠃⠀⣫⡦⣼⣿⣿⠟⠀⣰⣿⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⡀⠀⠀⠙⠀⠀⠘⠁⠀⠉⠘⠁⡀⢸⣿⣿⣿⣿⣿⣿⡟⠀⢰⢠⠇⠘⢿⣷⣶⣤⣿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⢿⣿⣷⡄⠀⠀⠀⠀⠰⠀⠀⠀⠀⢧⢣⢸⣿⣿⣿⣿⡿⠋⠀⠀⣿⢼⠀⠀⠀⠙⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⢰⠛⡜⣾⣿⡿⠟⠉⠀⠀⡴⣠⠉⠈⠀⠀⠀⣰⢣⡾⣆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡠⢀⠈⡄⠀⠘⣿⣿⣄⠀⠀⠀⠀⠀⠀⠈⡐⠹⠈⠋⡄⠀⠀⢀⡞⡰⠁⠀⠀⠀⠀⡴⣡⡟⠀⠋⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡀⠀⠘⢆⠀⠘⣿⣿⣧⠀⠈⢦⣄⠀⢀⠇⠀⠀⡌⠀⠀⣠⢟⡼⠁⠀⠀⠀⠀⡼⡵⠟⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣤⠀⠈⠣⡀⠘⣿⣿⡆⠀⠘⣿⣿⠀⠀⠀⠘⠀⠀⢠⢏⡞⠀⠀⠀⠀⠀⢺⡾⠁⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠘⣿⣇⠀⠀⠸⣿⡆⠀⠀⠀⠀⢠⢋⠞⠀⠀⠀⠀⣠⠀⠈⠴⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠙⣿⣧⠀⠀⢻⣿⣶⣄⠀⣠⠃⠂⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⣠⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡈⢿⣧⠀⠈⠿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡠⠋⠀⠀⠀⠀⠀⣴⣦⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⠠⡈⢿⣆⠀⠀⠀⠈⠻⣿⣷⣦⡄⠀⠀⠀⠀⠀⠠⢎⡼⠁⠀⠀⠀⠀⠀⠀⠙⠃⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠘⣿⣆⠀⠀⠀⠀⠈⠙⠿⠧⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⢸⣧⣤⣤⣄⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢸⣿⣿⣿⣿⣿⣤⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡄⠈⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣒⠂⠀⠂⠀⠀⠈⠛⠃⠙⠉⠙⠛⠛⠁
⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⢻⡿⢿⣯⣿⣿⣿
⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⠉⢺⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⢀⣀⣀⣼⣿⣿⡟⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠻⣿⣯⣭⣿⣿⣿⣿⠿⠛⠛⣿⣿⠛⠋⠉⠉⢻⣿⣿⣷⣾⣿⡿⢿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⢹⣿⣿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠿⠿⠟⠛⠛⠆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠉⠉⠀⡀⠐⠊⠍⡋⠋⠀⠉⠉⠁⠀⠀⠀⠁⡀⢛⣷⣤⣾⣿⣿⣿⣿⣿⡧⠘⠋⠻⣿⣿⣿⣿⣿⣿⣿⣯⡇⣀⡾⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠷⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣭⣴⣟⣿⣤⡀⠀⠀⠠⠀⠀⠀⠀⢶⣦⠤⠤⠤⠿⣿⣿⠏⢸⣿⣿⣿⣿⣶⣶⣤⣄⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣨⣯⣿⣿⣿⣿⣧⣄⡈⠉⠙⠻⣿⣿⣿⣿⣿⣿⠀⠀⣀⣤⣤⣤⣀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠃⠀⠂⠠⠄⣀⣠⣼⡞⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠈⢻⣿⣿⣿⣿⣄⣼⣟⠛⣻⡟⢉⣉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢉⣴⣶⣶⣶⡄⠀⠀⢸⣿⣿⣿⠃⣠⣶⠖⠁⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡿⠛⢻⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣆⣼⣿⣿⣿⡏⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⣿⣿⣯⣽⣿⣟⣾⣿⣿⡻⠿⣣⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢺⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⠁⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡗⣸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣾⡿⢿⣿⣿⣿⣿⣿⣿⣥⣀⡼⣻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣼⣿⣿⣿⣿⡟⠀⣿⣿⢧⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡟⠛⠁⢻⣿⣇⣾⣿⣿⣿⣿⣿⣿⣬⣭⣿⣿⣿⣿⣿⣿⣿⡿⠋⠛⣿⣧⡀⢹⣿⣿⣿⣿⣿⣡⣴⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠘⠻⣿⣿⣿⣿⣆⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠏⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠹⣿⣷⣾⡿⠛⢿⣿⣿⠿⠟⠋⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣿⣶⣜⣿⣿⣿⣿⣿⡟⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡿⠋⠀⠀⠀⢻⣿⠿⠟⣻⣿⣿⣿⣽⠏⣿⣏⣹⣿⣿⣿⣿⠃⠀⠀⠀⠀⢰⣿⣿⣟⠁⠀⢸⡟⠁⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⣰⡷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠸⡿⠰⠒⠉⢉⠝⣵⡟⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡞⢠⣼⣹⡿⣿⣶⣶⡞⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⡟⣟⣿⣿⠻⣇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣦⡀⠀⠀⠀⠀⠀⠠⠉⠁⠊⠛⠁⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⣄⠃⠀⠊⢹⣷⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀
⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡿⠋⠀⠀⠀⠀⠈⠉⢠⣾⣿⣿⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢿⣿⣿⣿⡿⠋⠀⠀⢸⢼⠀⠀⠀⢀⠝⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣁⣀⣀⣀⣤⣄⡀⠀⣴⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠱⣸⣿⡿⠋⠀⠀⢠⢂⠂⠀⠀⠀⠀⡎⡼⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⣄⣿⣿⣿⣿⠟⠉⣡⣾⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠹⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠘⠁⡀⠀⠀⢠⢃⠎⠀⠀⠀⠀⡘⡼⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠙⣿⣿⣿⣧⣴⣿⣿⣿⠟⠛⠻⠿⠿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠐⡄⠀⠹⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⢠⠇⠎⠀⠀⠀⠀⠀⡽⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠈⠹⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠹⣿⣿⣦⠀⠀⢱⣦⠀⠀⠀⠀⠀⠀⢀⡏⡜⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠻⣿⣿⠏⠀⠀⣀⣀⣠⠄⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠁⣠⣶⣿⣿⣿⣿⣿⡆⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠘⢿⣧⡀⠀⠘⣿⣷⣦⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠘⠙⢿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⢂⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡀⠀⠸⣿⣿⣽⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠈⢩⣷⣴⡄⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠃⠀⠀⣿⣿⠻⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡄⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⠆⢻⠏⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⣿⡍⠠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠀⠀⠀⠛⠀⣸⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡟⠋⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠁⠛⢻⣷⣿⣿⣿
⣿⣿⣿⣿⣻⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄⠀⢸⣿⣿⣿⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢤⣤⣾⣿⣿⣇⡬
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠙⠿⣿⣭⣽⠟⣻⡿⠟⠛⠛⠻⡿⠛⣋⠉⠀⢩⣿⣿⣷⣾⣿⡷⠻⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢀⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⠛⠉⠉⠈⠉
⣿⣿⣿⣿⠹⣿⣿⣿⣿⠿⠋⠉⠉⠀⠀⠈⠀⠉⠍⠀⠀⠁⠁⠀⠀⠀⠀⠀⡀⠉⣿⣧⣼⣿⣿⣿⣿⣿⡇⠐⠏⠙⣷⣿⣿⣿⣿⡿⣿⣽⡆⣠⡘⠏⠣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠛⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣶⣧⣹⣿⣿⣦⣴⣴⡏⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⡄⢰⣾⣾⣿⠟⠈⣻⣿⣿⣶⣤⣤⣄⣀⢠⣼⣵⣾⣿⣿⣿⣿⣿⣿⣿⣦⠂⣰⣿⣿⣅⣉⠉⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣠⣶⣶⣷⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣇⠀⠀⠀⠀⣀⠀⣠⣦⡀⠀⠀⠈⣱⠿⠋⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠻⣿⣿⣿⣿⣿⣏⢧⣴⣿⢤⣴⣿⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⣉⣉⡀⠀⠀⠀⢰⡿⣿⣿⣿⣿⠇⢀⡠⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡿⠿⢻⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠟⣻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣴⣿⣿⣿⣿⣧⡀⢀⣿⣿⣿⣿⣿⣿⣾⡿⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣩⢹⣿⣖⣼⣿⣿⣟⠛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢸⡟⢻⡿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⡟⢰⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡆⠺⣷⣄⠙⣿⣿⣿⣿⡿⣿⣿⡟⠚⣡
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢹⣿⣿⣿⣿⣿⣿⡿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠟⠛⠁⢸⣿⣇⣼⣿⣿⣿⣿⣿⣏⣩⣽⣿⣿⣿⣿⣿⢿⣿⠟⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠏⠘⠻⣿⣿⣿⣿⣧⣿⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠆⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⣾⣿⣿⡿⠛⠉⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣓⣈⣿⣶⡜⣿⣿⣿⣿⣿⣿⣷⡦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡿⠿⠃⠀⠀⠀⠘⣿⣿⣿⣿⣿⠿⣿⣿⠉⣿⣛⢩⣿⣿⣿⡟⠀⠀⠀⠀⠀⣼⣿⣿⣿⢀⣙⣻⠏⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠛⠃⣀⢶⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠟⠛⠛⡚⡫⡿⠀⣿⣿⣾⣿⣿⣿⡇⠀⠀⠘⠀⢤⡿⣿⣿⡇⢸⣿⡟⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣠⣶⡾⣿⠀⠁⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠂⠊⠚⠘⠁⠀⣿⣿⣿⣿⣿⡿⠀⠀⡀⡆⠀⠑⠘⡳⣿⡁⢸⡿⠁⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠿⠛⠿⢿⣟⣻⣿⣿⣿⠏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢿⣿⣿⣿⠋⠀⠀⠀⠇⠇⠀⠀⠀⡌⣻⡷⠘⡇⠀⠀⠀⠀⢀⣠⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣼⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠱⢸⡿⠋⠁⠀⢀⠆⡄⠀⠀⠀⠀⡸⢰⠃⠀⡀⠀⠀⠀⠀⣰⣿⣿⣿
⠀⠸⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣭⣶⣦⣀⠀⠀⣰⣿⣻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠈⢿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠈⠠⠀⠀⢀⡎⡜⠀⠀⠀⠀⢀⢣⠇⠀⠀⠁⠀⠀⠀⣼⣿⣿⣿⣿
⠀⠀⣷⣾⣿⣿⣿⣯⡉⠙⣿⣿⣿⣿⣿⣿⣿⠟⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⢀⠀⠈⢿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡼⡰⠀⠀⠀⠀⠀⢈⡏⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛
⠀⠀⣸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠈⢿⣿⣿⣷⠀⠀⠀⢳⠦⠀⠀⠀⠀⠀⢸⠁⠃⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠙⠛⠉⠳⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡀⠀⠀⠸⣿⣦⣀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡿⢻⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢶⣦⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⢻⣿⣿⣄⠀⠀⠘⢿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠃⠀⠀⢀⣀⣴⣿⡿⠁⢸⣿⣿⡆⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡄⠀⠀⠀⠛⠛⠿⡷⣄⠀⠀⠀⠀⠀⠀⠀⢠⢂⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣸⣿⣿⣿⣿⡏⠀⠀⣰⣿⣿⣿⣿⡇⠀⠘⣿⡿⢴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣄⠀⠀⠀⠀⠀⠀⠘⢹⣶⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾
⠀⠀⠀⢾⣿⣿⣿⣿⣿⣧⣴⣾⣿⣿⣿⣿⣿⣷⠀⠀⣿⠏⢨⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠁
⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣿⠁⢺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⣿⣟⣻⣟⣛⣩⣹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠛⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⢶⡖⡶⠖⠶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟⣿⣿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠿⣋⣰⣶⣶⣾⣶⣸⣷⣦⣬⣄⣟⣿⡛⠿⠛⢓⣣⣎⡙⣉⣀⣠⣉⡸⠛⠛⣉⠙⠚⠻⠗⠿⠛⠺⢿⡗⢻⣿⡂⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⣺⣿⣗⣿⣿⣺⣿⣿⣿⣿⣺⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⡛⢙⣩⢰⣶⣷⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣾⣖⣿⣿⣲⣿⣗⣿⣿⣲⣿⣗⣿⣿⣺⣾⣆⣦⣶⣢⣦⢁⣎⢻⡂⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣷⣺⣿⣗⣿⣿⣺⣿⣷⣿⣷⣺⣿⣿⡿⠟⣿⣩⣥⣴⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣾⣿⣗⣿⣿⣺⣿⣗⣿⣿⣺⣿⣖⣿⣿⣺⣿⣗⣿⣿⣺⣿⣖⣿⢸⡂⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠾⠿⠿⢃⣋⣩⣤⣥⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⣿⣿⣿⣿⣗⣿⣿⣾⣿⣷⣿⣿⣺⣿⣷⣿⣿⣾⣿⣗⣿⣾⡆⠀⠀
⠀⠀⠀⠀⠀⠀⣿⡿⠟⡛⠛⣩⡥⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⢽⣿⡏⣿⣿⢽⣿⡯⣿⣿⢹⣿⡯⣿⣿⢽⣿⡯⣿⡯⠇⠀⠀
⠀⠀⠀⠀⠀⠀⣥⣤⢼⣿⡯⣿⣿⢽⣿⣿⣿⣿⣽⣿⡿⣿⣿⣿⣯⣽⣿⣿⣯⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⡯⣿⣿⢽⣿⡯⣿⣿⢽⣿⡯⣿⣿⢽⣿⡯⣿⣿⢼⣿⡧⣿⡯⠅⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣯⢽⣿⡯⣿⡿⢽⣿⣏⡿⠿⢩⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣽⣿⡯⣿⣿⢽⣿⡯⣿⣿⢽⣿⡭⣿⣿⢽⣿⡯⣿⣿⢽⣿⡯⣿⡏⠅⠀⠀
⠀⠀⠀⠀⠀⠀⠿⠿⠹⠿⠧⠿⠿⠼⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠯⠿⠿⠽⠿⠯⠿⠿⠽⠿⠯⠿⠿⠽⠿⠯⠿⠿⠽⠿⠯⠿⠿⠄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 2410

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/08/02/irc-log-010821/#comments
    Gemini version at gemini://gemini.techrights.org/2021/08/02/irc-log-010821/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 08.02.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


✐ IRC_Proceedings:_Sunday,_August_01,_2021⠀✐


Posted in IRC_Logs at 2:22 am by Needs Sunlight


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


                                         #techrights_log_as_HTML5                                                                                  #boycottnovell_log_as_HTML5


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


                                    #boycottnovell-social_log_as_HTML5                                                                               #techbytes_log_as_HTML5


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


                                          #techrights_log_as_text                                                                                   #boycottnovell_log_as_text


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


                                     #boycottnovell-social_log_as_text                                                                                #techbytes_log_as_text


                          Enter_the_IRC_channels_now


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


CID                                              Description     Object type


                                                 IRC log for
 Qmf7EdNR6atgxcvaMzLDZxrcTiShqRFGRt9o35X3ApjnRr #boycottnovell  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell
 QmbSsPFrE8PWXLi764LzB4Fx3BFJPPQ7fmHmarJV9NfkRc (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
                                                 #boycottnovell-
 QmQp65EpABo9769MNfD98HyK2zPD1yfmY4pk5ozx7bhC9X social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell-
 QmUD67eyWqUZrPe95Lju6bskyBBHk6koJyv1F25oreJ3Y6 social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 (full IRC log
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 QmWL4DUwtNDwuqYKGxUmC86PsvLz4aodMkgCivxXTC4fSE #techbytes      🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techbytes
 QmZ9eeWtKRwQo5MaS5VnAPUpmdqWPLaKxKbknKQBRR98C6 (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 Qmd4NxeW5CmDmyxBqsKGUs3KSRrwVeYPhQDi9MSuPZKUpP #techrights     🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techrights
 QmNrk5ioLkwvLDrzk54bFeGF9NwEirtZETS7kVXPfMLH1A (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈


§ Bulletin for Yesterday⠀➾


Local_copy | CID (IPFS): QmNSNxDGf8uW24qwfnLjXrvXVvHmUMuSgb1HJu756yHhud



                    ䷩ 𝚕𝚒𝚗𝚎 2524

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 08.02.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


✐ Links_2/8/2021:_XEyes_1.2_and_Fwupd_1.6.2_Released⠀✐


Posted in News_Roundup at 2:47 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⠀➾


                # ⚓ Kubuntu_Focus_Team_Announces_High-Performance_Focus_XE⠀⇛


                       From the makers of the Focus M2 (one of the hottest
                       KDE-specific laptops on the market), comes the new
                       Focus XE. And although it’s focused on those
                       looking for something small in form factor, it’s
                       certainly big in performance.


                       Sporting 11th generation CPUs and high-speed audio/
                       data ports, this machine isn’t an entry-level,
                       budget-friendly laptop. The specs of the XE include
                       a 4-core processor (Intel Core i7), up to 64GB of
                       3200 MHz RAM, up to 2TB NVMe storage, and Intel
                       IRIS Xe Graphics. Other features include dual-band
                       5 GHz wireless, RJ-45 Gigabit Ethernet, Bluetooth
                       dual version 5.2, and Thunderbolt v4. You’ll also
                       find two USB-A 3.2 GEN1 ports, and one USB-C 3.2
                       GEN2 port. An illuminated keyboard with 4mm of
                       travel, a generous trackpad, a 1.0 MP HD webcam,
                       and a 49 Whr Li-ION battery with FlexiCharge
                       Battery Optimization (available in the BIOS), are
                       all housed in a composite aluminum and plastic
                       chassis.


          o § Linux Magazine⠀➾


                # ⚓ A_Bash_web_server⠀⇛


                # ⚓ Anatomy_of_a_kernel_attack⠀⇛


                # ⚓ Control_USB-powered_devices_with_a_Raspberry_Pi⠀⇛


                # ⚓ Linux_Mint_20.2_Now_Available_and_Better_Than_Ever⠀⇛


                # ⚓ Better_security_auditing_with_Auditd_and_the_Integrity
                  Measurement_Architecture⠀⇛


                # ⚓ Creating_custom_Ubuntu_images⠀⇛


                # ⚓ How_to_compile_your_own_kernel⠀⇛


                # ⚓ The_sys_admin’s_daily_grind⠀⇛


                # ⚓ FOSSPicks⠀⇛


                # ⚓ This_month_we_celebrate_the_steady_and_powerful_Linux
                  kernel⠀⇛


                # ⚓ AlmaLinux_Minimal_8.4_and_SystemRescueCD_8.03⠀⇛


                # ⚓ This_month_in_Linux_Voice.⠀⇛


                # ⚓ Using_a_static_website_generator⠀⇛


                # ⚓ Three_decades_of_Linux⠀⇛


                # ⚓ A_command-line_file_manager⠀⇛


                # ⚓ Getting_started_with_kernel_development⠀⇛


                # ⚓ Golang:_Harder_than_scripting,_but_easier_than_programming
                  in_C⠀⇛


                # ⚓ Optimizing_the_Linux_Kernel⠀⇛


                # ⚓ A_VPS_from_start_to_finish⠀⇛


                # ⚓ Zack’s_Kernel_News⠀⇛


                # ⚓ Non-Fungible_Fun⠀⇛


                # ⚓ A_one-to-one_drop-in_replacement_for_CentOS⠀⇛


                # ⚓ Sniffing_WiFi_with_an_ESP8266_microcontroller⠀⇛


                # ⚓ A_modern_compression_tool⠀⇛


          o § Kernel Space⠀➾


                # ⚓ Work_Is_Back_Underway_On_A_Task_Isolation_Interface_For_The
                  Linux_Kernel_–_Phoronix⠀⇛


                       Red Hat’s Marcelo Tosatti has submitted his latest
                       patches implementing a basic task isolation
                       interface for the Linux kernel that would be
                       particularly useful for real-time workloads and
                       high-bandwidth networking applications making use
                       of user-space drivers.


                       In an effort to eliminate or at least lower
                       operating system noise for relevant user-space
                       applications, this task isolation interface could
                       be used for letting the kernel know that latency-
                       sensitive code is being executed. Applications
                       would notify the kernel via new prctl() options
                       “PR_ISOL_*”.


                # ⚓ Linux_5.13.7⠀⇛


                       I'm announcing the release of the 5.13.7 kernel.

                       All users of the 5.13 kernel series must upgrade.

                       The updated 5.13.y git tree can be found at:
                       	git://git.kernel.org/pub/scm/linux/kernel/git/
                       stable/linux-stable.git linux-5.13.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
                # ⚓ Linux_5.10.55⠀⇛


                # ⚓ Linux_5.4.137⠀⇛


                # ⚓ Linux_4.19.200⠀⇛


                # ⚓ Kernel_prepatch_5.14-rc4⠀⇛


                       The 5.14-rc4 kernel prepatch is out for testing.
                       “Nothing to see here, entirely normal rc4″.


                # § Graphics Stack⠀➾


                      # ⚓ xeyes_1.2.0⠀⇛


                             This release of xeyes adds support for using
                             the Present and Xinput2
                             extensions so that your X server is even
                             smoother when making eyes at you.

                             Alan Coopersmith (4):
                                   Update README for gitlab migration
                                   Update configure.ac bug URL for gitlab
                             migration
                                   Remove redundant declaration of hypot()
                             for SVR4 systems
                                   xeyes 1.2.0

                             Keith Packard (3):
                                   Add support for the 'Present'
                             extension. [v3]
                                   Use XI2 raw events to notice when mouse
                             moves [v2]
                                   Clean up compiler warnings

                             git tag: xeyes-1.2.0

                             https://xorg.freedesktop.org/archive/
                             individual/app/xeyes-1.2.0.tar.bz2

                             SHA256:
                             f8a17e23146bef1ab345a1e303c6749e42aaa7bcf4f25428afad41770721b6db
                             xeyes-1.2.0.tar.bz2
                             SHA512:
                             2d1614614b3ba3d1ebaa0e9801a2e159389b94aaacafb962d326b7e6dc712c1eb2c12a50ceb10b3135cf0eee6ae86bbf84e73098deb08e73792f14a60616b4d8
                             xeyes-1.2.0.tar.bz2
                             PGP:  https://xorg.freedesktop.org/archive/
                             individual/app/xeyes-1.2.0.tar.bz2.sig

                             https://xorg.freedesktop.org/archive/
                             individual/app/xeyes-1.2.0.tar.gz

                             SHA256:
                             727e651fd4597f6aa131b67474372a081dccd28ea2cdd364f21dae6e59003ee8
                             xeyes-1.2.0.tar.gz
                             SHA512:
                             95461702cf27615bb7d4eb09b84f9589b810fa905a913b11050b32ce4004a4926e1521b3506a1bf378cb42b0bd6d8735871b6be2382824e2706f4ca24356db45
                             xeyes-1.2.0.tar.gz
                             PGP:  https://xorg.freedesktop.org/archive/
                             individual/app/xeyes-1.2.0.tar.gz.sig
                      # ⚓ X.Org’s_XEyes_1.2_Released,_Other_Updated_X11
                        Components_Too_–_Phoronix⠀⇛


                             Several X.Org/X11 components saw new releases
                             on Sunday for kicking off August, including
                             the xeyes program seeing its first non-point
                             release in eleven years.


                             The fun XEyes demo program that’s long been
                             around to demonstrate an application
                             following the mouse and rendered using X
                             SHAPE is out with a new release. It’s been 11
                             years since xeyes 1.1 was released while
                             Sunday brought xeyes 1.2.


          o § Applications⠀➾


                # ⚓ Best_Educational_Applications_for_Linux⠀⇛


                       Searching for the best Linux educational Software
                       to help with studies? You have come to the right
                       place. Teachers, students, and school
                       administrators have to get creative when it comes
                       to finding quality software that can be free of
                       cost, or at affordable rates.


                       Quality educational apps are hard to find,
                       particularly on a student budget. Therefore, it
                       makes sense that schools and students turn to open-
                       source software to save up money. Many people don’t
                       have an idea about the various outstanding
                       educational applications that are present for a
                       Linux OS.


                # ⚓ Fwupd_1.6.2_Adds_a_Plugin_to_Check_Lenovo_Firmware
                  Settings,_Support_for_New_Hardware⠀⇛


                       Fwupd 1.6.2 is a massive update and introduces a
                       new plugin for checking Lenovo firmware settings,
                       support for installing UEFI updates from GRUB,
                       initial support for the powerd daemon, support for
                       CapsuleOnDisk, as well as support for soft-
                       requirements that can be ignored with the –force
                       parameter.


                       In addition, this release adds the ability for
                       devices to only accept version upgrades, allows the
                       discovery of Redfish BMCs specified by MAC or VID-
                       PID and introduces the ability to automatically
                       connect the BMC network interface at startup, and
                       allows fwupd to request interactive action from the
                       end user.


          o § Instructionals/Technical⠀➾


                # ⚓ How_to_Install_Thinkorswim_Trading_Platformon_Ubuntu
                  20.04⠀⇛


                       ThinkorSwim is a web-based trading platform
                       developed by TD Ameritrade. It allows users to
                       trade in various stock, options, futures, and
                       equities from the web-based interface. It has also
                       a desktop application available for Windows, macOS,
                       and Linux operating systems. However, it is very
                       complex and designed for advanced users.


                       In this post, we will show you how to install
                       Thinkorswim on Ubuntu 20.04 desktop.


                # ⚓ How_to_Install_BoltWire_CMS_with_Nginx_on_Ubuntu_20.04
                  LTS⠀⇛


                       Bolt is a lightweight content management system
                       (CMS) built on the popular PHP framework. Bolt is
                       perfect for a small business that wants to maintain
                       its own website without worrying about having to
                       learn HTML and other programming languages. Bolt
                       features advanced features such as robust wiki
                       markups, e-commerce, a photo gallery and album
                       builder, audio gallery and player, and guestbooks.


                       Boltwire stands out for being completely free of
                       charge for individuals and groups of all sizes who
                       have a need for a CMS. Joe Casabona is the creator
                       of Boltwire and he shares his passion by helping
                       others get the most out of his open-source project.
                       Bolt is used in over 200 countries to manage over
                       500,000 websites. Its developers are volunteers and
                       expect that all users take part in the project by
                       offering feedback and contributing to its
                       development.


                # ⚓ How_to_Install_Google_Chrome_on_Linux_Mint_h⠀⇛


                       This should be a really simple topic but I am
                       writing this because I see so many websites
                       recommending strange command line steps for
                       installing Google Chrome on Linux Mint. That would
                       work but that’s unnecessarily complicated,
                       specially for beginners not familiar with the
                       command line.


                       In reality, you don’t need to go terminal way at
                       all. All you have to do is to go to Google Chrome’s
                       website and download the installer file for Ubuntu
                       and install it.


                # ⚓ How_To_Backup_And_Restore_Linux_System_With_Timeshift_–
                  OSTechNix⠀⇛


                       There are plethora of Linux Backup applications
                       exists. But deciding which one is best for your
                       requirement is not so easy. In this guide, I am
                       going to explain what is Timeshift, and its
                       benefits and how to backup and restore Linux system
                       with Timeshift.


                # ⚓ How_To_Install_Apache_Solr_on_Debian_10_–_idroot⠀⇛


                       In this tutorial, we will show you how to install
                       Apache Solr on Debian 10. For those of you who
                       didn’t know, Apache Solr is an open-source search
                       platform written in Java. Solr aims at providing
                       distributed indexing, replication, and load-
                       balanced querying with automated failover and
                       recovery.


                       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 Apache Solr on a Debian 10
                       (Buster).


                # ⚓ How_to_Create_Users_using_adduser_Command_in_Linux_guide
                  2021⠀⇛


                       In terms of user management, adduser Command in
                       Linux operating system is an important command,
                       which is being used for all administration like
                       work with the system. Actually, either “adduser” or
                       “useradd”, both the commands are functioning in
                       similar ways. Basically, UNIX is a very large
                       operating system which is mainly used as Server as
                       well as Network administrative role. For this, a
                       number of normal users are required to be created
                       in this operating system by the administrator
                       (root) to assign specific tasks and roles to
                       specific users. Hence, creating and managing users
                       is a very sensitive task for administrator (root)
                       of the system.


                # ⚓ How_to_Enable_Caps_Lock_Key_Indicator_in_Ubuntu_–_Make_Tech
                  Easier⠀⇛


                       I am sure most of us have been through situations
                       where we enter a password, but the system rejects
                       it, repeatedly. Then we realize it’s our fault, as
                       we didn’t notice that the Caps Lock key was on.


                       Is there a way to avoid such situations? For
                       Ubuntu/Linux, you can use a key lock indicator to
                       display your key lock status on screen. Here we
                       show you two such tools: Lock-Keys and Keyboard
                       Modifiers Status extensions.


                # ⚓ How_to_Install_AWS_CLI_Version_1_on_Ubuntu⠀⇛


                       The AWS CLI is a command-line tool to control and
                       manage your AWS services. There are multiple ways
                       of installing AWS CLI on Linux. You can install it
                       using its bundled installer, irrespective of
                       whether you have superuser permissions on your
                       system.


                # ⚓ How_to_become_a_Linux_Samurai⠀⇛


                       The beauty of Linux is that it is made by
                       programmers, for programmers. It can run on almost
                       any hardware and there is an endless variety of
                       distributions for almost every use case. It is
                       preferred by programmers for its versatility,
                       scalability, container portability, security, and
                       many other features.
                       By Nuno Martins, senior channel solutions rchitect
                       at Red Hat
                       Most importantly, it’s free and open source, which
                       means that it is built and supported by a community
                       of developers who are always at the forefront of
                       innovation and are willing to help each other out.
                       Knowing a few useful command line tricks can save
                       you a lot of time and frustration. Some you may
                       already know, and others may prove to be a hidden
                       gem you weren’t aware of before. Either way, here
                       are some of the essential command line tips and
                       tricks that I think could save you a couple of
                       keystrokes.


                # ⚓ How_to_get_system-related_information_on_the_Linux_command
                  line_with_Neofetch⠀⇛


                       Want to share the specifics of your Linux system
                       with someone else via the internet but don’t want
                       to go through the trouble of searching for and
                       typing in each detail one by one? Don’t worry;
                       there’s a command-line program called Neofetch that
                       will display all of the information you need right
                       on the terminal.


                       In this lesson, we’ll go through the fundamentals
                       of installing and using Neofetch. But, before we go
                       any further, please in mind that this tutorial’s
                       instructions and commands were tested on Ubuntu
                       20.04 LTS.


                # ⚓ How_to_install_CentOS_8_on_VirtualBox_in_Windows_10
                  Complete_Guide_2021⠀⇛


                       Are you a new user of Linux? Are you looking to
                       start using Linux? Are you want to switch from
                       Windows to Linux?


                       It totally depends on you, what propose to attract
                       you to have look at this post?


                       But I assured you, you will get all the information
                       related CentOS including How to install CentOS 8 on
                       VirtualBox and on Computer/Desktop. CentOS/RHEL 8
                       are similar operating system is working and
                       configuring. RHEL 8 is the most used operating
                       system worldwide in the form of Servers.


                # ⚓ How_to_install_Linux_apps_on_your_Chromebook⠀⇛


                       Chrome OS has become one of the most popular
                       desktop operating systems thanks in large part to
                       its availability on a wide range of devices at
                       different price points, ease of use, integration
                       with Google services and strong security. In the
                       past, it’s been widely considered a functional, but
                       ultimately limited environment.


                       However, Google has done much to change this over
                       the years by adding offline capabilities to many of
                       its services and support for Android applications.
                       One of the most recent and exciting features added
                       to ChromeOS is the ability to run Linux apps. In
                       this guide, we’ll help you get started on
                       installing Linux apps on your Chromebook.


                       First things first, make sure your device is
                       running at least ChromeOS 69 or later. Make sure
                       you have the most recent version of the OS. You can
                       update Chrome OS by going to Settings > About
                       Chrome OS > Check for updates. Once you’re updated,
                       head over to the Chrome OS Settings again. This
                       time, we’re going to Advanced > Developers and
                       click “Turn On” next to Linux Development
                       Environment.


                # ⚓ How_to_install_gtop_(System_Monitoring_Dashboard)_on_Linux
                  –_Unixcop⠀⇛


                       gtop is a tool which reads information about
                       processes and the state of the system in dynamic
                       mode. As its name, we can think that it is a
                       graphic top command. It contains some views to
                       monitor your cpu, memory, swap, disk and network
                       usage with a percentage and graphical
                       representation. It also shows you the path of the
                       commands in progress.


                       Gtop is one of the nifty tool that is capable to
                       display system processes dynamically in graphic
                       mode on your Linux terminal.


                       As the name implies, Gtop stands for graphic top
                       command which reads system process, memory, CPU,
                       network and disk usage information and populate the
                       results in graphic mode with a percentage.


                # ⚓ How_to_use_Certbot,_create_a_certificate_for_domain_and
                  submain_–_Unixcop⠀⇛


                       Let’s Encrypt is a non-profit certificate authority
                       run by (ISRG) that provides (TLS) encryption
                       certificates at no charge. Certbot identifies the
                       server administrator by a public key. The first
                       time the agent software interacts with certbot
                       generates a new key pair and proves to the Let’s
                       Encrypt CA that the server controls one or more
                       domains. It is similar to the traditional CA
                       process of creating an account and adding fields to
                       that account.


                       In this tutorial, you will use Certbot to obtain a
                       free SSL certificate for Nginx on Ubuntu and set up
                       your certificate to renew automatically. We will be
                       using the default Nginx configuration file of a
                       server vhosts. We is likely recommend to creating
                       new Nginx server vhosts files for each domain, it
                       helps avoid mistakes. Maintains the default files
                       as a backup configuration as intended if your set
                       up SSL using server is not working.


                # ⚓ Install_Oracle_19c_on_Rockylinux_Almalinux_Centos8⠀⇛


                # ⚓ Set_up_an_SSH_tarpit_in_Ubuntu_Server_20.04:_Here’s_how_–
                  TechRepublic⠀⇛


                # ⚓ How_to_Install_Webmin_on_Rocky_Linux_8⠀⇛


                       Webmin is a web-based control panel for system
                       administration. It is mainly designed for Linux/
                       Unix-like system administrations. Webmin is written
                       in Perl language.


                       Webmin web interface is used to set up user and
                       disk management, Apache, DNS, PHP, MySQL, check CPU
                       usage, system info, network config, and more.


                # ⚓ OpenSSH_Change_a_Passphrase_With_ssh-keygen_command [Ed:
                  Just updated]⠀⇛


                # ⚓ How_to_Import_Export_Database_in_MYSQL_MariaDB⠀⇛


                       Import or Export database from MySQL or MariaDB
                       database from MySQL shell or command line. This is
                       the easiest method to export database or particular
                       table from a database.


                       If you have a huge database which is more than
                       500Mb, it will be very hard to export which takes
                       more time to import or export the entire database
                       which may result in timeout error.


                       In this guide you are going to learn how to import
                       or export database using command line from MySQL
                       shell. You will also learn some fixes to the
                       problems where you cannot export your database.


                # ⚓ How_To_Install_MongoDB_Compass_on_Ubuntu_20.04_LTS_–
                  idroot⠀⇛


                       In this tutorial, we will show you how to install
                       MongoDB Compass on Ubuntu 20.04 LTS. For those of
                       you who didn’t know, Mongo DB Compass is a GUI for
                       Mongo Database software. It’s helpful software for
                       those that want a better GUI way of managing their
                       Mongo DB setups. MongoDB compass allows you to view
                       the real-time performance for DB server metrics.


                       This article assumes you have at least basic
                       knowledge of Linux, know how to use the shell, and
                       most importantly, you host your site on your own
                       VPS. The installation is quite simple and assumes
                       you are running in the root account, if not you may
                       need to add ‘sudo‘ to the commands to get root
                       privileges. I will show you the step-by-step
                       installation of the MongoDB Compass GUI on Ubuntu
                       20.04 (Focal Fossa). You can follow the same
                       instructions for Ubuntu 18.04, 16.04, and any other
                       Debian-based distribution like Linux Mint.


                # ⚓ How_To_Set_Up_SSH_Tunneling_–_TecAdmin⠀⇛


                       If you are connecting with a different Linux device
                       on a different network then you would have to
                       expose it to the public internet and that may put
                       your system and files at the risk. Therefore, SSH
                       Tunneling is used to transmit data in a fast and
                       secured manner from source to client machine and
                       vice versa.


                       SSH Tunneling is a practice of creating a secured
                       and encrypted SSH connection between a server
                       machine and a client machine through which data can
                       be transferred and service can be relayed. In our
                       today’s article, we will see how to set up SSH
                       Tunneling and route your traffic securely via SSH
                       tunnels.


                # ⚓ Using_Checkmk_for_Monitoring_Your_Linux_Server
                  Infrastructure⠀⇛


                       There are tons of tools available for monitoring
                       your IT infrastructure. This includes monitoring
                       the Linux servers, containers, databases,
                       applications and more.


                       Services like BetterUptime are convenient and we
                       use it for downtime monitoring.


                       However, for more granular control, I prefer
                       deploying tools like Prometheus with the beautiful
                       Grafana dashboard.


                       Recently, I came across a project that gives a
                       complete view of your IT infrastructure within a
                       very short span of time.


          o § Games⠀➾


                # ⚓ Valve_fires_back_in_the_lawsuit_from_Wolfire_Games_|
                  GamingOnLinux⠀⇛


                       We’ve been waiting to hear how the lawsuit from
                       Wolfire Games (and others) would progress against
                       Valve, and now we at least have word from Valve on
                       what they think. Naturally, Valve are trying to get
                       the whole thing dismissed. What a shocker, as if we
                       didn’t all expect Valve to fire back and try to
                       shut it all down. What company wouldn’t?


                       As a quick reminder: the original lawsuit alleges
                       that Valve’s 30% cut is abuse of their market
                       position, and it complains about how Valve handles
                       Steam keys too. David Rosen of Wolfire also tried
                       to clarify some details in a later blog post which
                       claimed that Valve would remove their game
                       Overgrowth if they sold it cheaper elsewhere.


                       In the new motion filed on July 26, Valve were
                       quite blunt with their reasoning for wanting it all
                       thrown out. The point about Steam keys is an
                       interesting one, as the motion states “Plaintiffs’
                       allegations that Valve’s Steam Key rules amount to
                       an unlawful PMFN* fail for the straightforward
                       reason that Valve, which created and owns Steam,
                       has no duty under the antitrust laws to create a
                       method (here, Steam Keys) for game developers to
                       sell Steam-enabled games in stores that compete
                       with Steam.”.


                # ⚓ Typing_adventure_RPG_‘Nanotale_–_Typing_Chronicles’_out_now
                  for_Linux_|_GamingOnLinux⠀⇛


                       This was a surprise to see. Nanotale – Typing
                       Chronicles from Fishing Cactus, PID Games, 2PGames
                       recently published an official native Linux build.
                       Coming from the same developer who created Epistory
                       – Typing Chronicles, you don’t need to have played
                       their first game as this is a full standalone
                       experience and it looks absolutely gorgeous.


                       “Nanotale – Typing Chronicles is an atmospheric
                       typing adventure RPG set in a colorful vibrant
                       world. Follow Rosalind, a novice Archivist, as she
                       journeys out to explore a distant world. On her
                       quest to gather knowledge, she collects samples of
                       mystic natural beauties. Everything is peaceful.
                       War is a thing of the distant past.


                       In the shadows, a tale of dissonant magic is
                       spreading, instilling corruption into broken
                       hearts.”


                # ⚓ AMD_+_Valve_Working_On_New_Linux_CPU_Performance_Scaling
                  Design_–_Phoronix⠀⇛


                       Along with other optimizations to benefit the Steam
                       Deck, AMD and Valve have been jointly working on
                       CPU frequency/power scaling improvements to enhance
                       the Steam Play gaming experience on modern AMD
                       platforms running Linux.


                       It’s no secret that the ACPI CPUFreq driver code
                       has at times been less than ideal on recent AMD
                       processors with delivering less than expected
                       performance/behavior with being slow to ramp up to
                       a higher performance state or otherwise coming up
                       short of disabling the power management
                       functionality outright. AMD hasn’t traditionally
                       worked on the Linux CPU frequency scaling code as
                       much as Intel does to their P-State scaling driver
                       and other areas of power management at large.


                # ⚓ AMD_and_Valve_working_towards_a_new_CPU_performance_scaling
                  design_for_AMD_CPUs_|_GamingOnLinux⠀⇛


                       With the X.Org Developers Conference 2021 coming
                       up, they’ve now announced that the initial program
                       schedule is up and there’s a fun sounding talk from
                       AMD developer Ray Huang on working with Valve on
                       new performance scaling design for AMD CPUs.


                       It’s not a big surprise to see work being done in
                       this area, considering that the upcoming Steam Deck
                       will be based on a custom AMD Zen 2 design with 8
                       RDNA 2 CUs for the graphics. Performance on such a
                       device is going to make or break it and so Valve
                       appearing to be pushing many different areas to get
                       it sorted and this is just one of them.


          o § Desktop Environments/WMs⠀➾


                # ⚓ UnityX_10_Desktop_Environment_Makes_Great_Progress,_Now
                  Features_New_Panel_and_Sidebar_Designs⠀⇛


                       Announced in early May, UnityX is the successor to
                       Unity7, and, the next major release, UnityX 10, is
                       planned for later this year as part of the upcoming
                       Ubuntu Unity Remix 21.10 distribution, which, of
                       course, will be based on the forthcoming Ubuntu
                       21.10 (Impish Indri) operating system release.


                       UnityX 10 promises great new features compared to
                       Unity7, including a new sidebar design for the
                       application launcher and the opened apps view, a
                       new panel with system tray icons, including for
                       standalone Wi-Fi, Bluetooth and PulseAudio icons, a
                       Logout shortcut, as well as an pplication launcher
                       and an “opened apps” shortcuts.


          o § Distributions⠀➾


                # § Debian Family⠀➾


                      # ⚓ Debian_Improves_Docs_To_Inform_Users_Their_Systems
                        Might_Not_Work_Without_Non-Free_Firmware⠀⇛


                             Debian 11 “Bullseye” is set to be released
                             mid-August while out this morning is the
                             third release candidate of the Debian
                             Bullseye installer. With this installer
                             update is more documentation for users
                             letting them know the risks of modern
                             graphics cards and the like that are often
                             inoperable unless loading firmware that isn’t
                             considered free software.


                             With many modern graphics processors
                             including those from AMD and even the Nouveau
                             driver with recent generations of NVIDIA
                             GPUs, there is often a situation of not only
                             having 3D hardware acceleration not working
                             but even display mode-setting can fail that
                             leads to a blank screen or driving the
                             unaccelerated display at a sub-optimal
                             resolution. Especially for newer GPUs and
                             modern displays, these open-source drivers
                             are useless without the firmware files that
                             are publicly redistributable but binary-only
                             and thus not considered free software.
                             There’s similar situations of network
                             adapters and other components not working
                             without loading the Linux firmware files, but
                             in the case of GPUs it’s rather a blocker if
                             you don’t even have a working display for
                             your desktop.


          o § Devices/Embedded⠀➾


                # ⚓ Teensy_SBC_runs_Linux_or_NuttX_on_SAMA5D⠀⇛


                       Starcat is crowdfunding an open spec, Teensy form-
                       factor “Jupiter Nano” SBC that runs Linux or NuttX
                       on a Cortex-A5 based Microchip SAMA5D. The $65-and-
                       up board offers 128MB RAM, a microSD slot, dual
                       micro-USB ports and 41 I/O pins.


                       Seattle based Starcat, which has previously
                       launched a HackEEG Arduino shield, has returned to
                       Crowd Supply with an Arduino-like SBC. Although the
                       63.5 x 28.6mm Jupiter Nano has a quasi Teensy 4.1
                       form factor, it runs Linux, as well as the open
                       source NuttX RTOS, on Microchip’s SAMA5D27C. The
                       power-sipping SoC has appeared on Microchip’s 40 x
                       38mm SAMA5D27 SOM and Groboards’ 51 x 23mm, Feather
                       form-factor Giant Board.


                # § Mobile Systems/Mobile Applications⠀➾


                      # ⚓ Realme_UI_2.0_(Android_11)_update_tracker:_These
                        phones_received_so_far⠀⇛


                      # ⚓ Jetpack_Compose_for_Android_turns_general
                        availability_–_Channel_Asia⠀⇛


                      # ⚓ How_To_Connect_Xbox_Controller_To_Android_Phone⠀⇛


                      # ⚓ ‘Android_for_Feature_Phones’_shows_up_in_details
                        hands-on_–_9to5Google⠀⇛


                      # ⚓ Android_STB_and_TV_Market_to_Register_a_CAGR_of
                        14.11%_by_2025_–_Report_by_Market_Research_Future_
                        (MRFR)⠀⇛


                      # ⚓ Material_You_is_the_one_Android_12_feature_Apple_iOS
                        won’t_copy_|_Android_Central⠀⇛


                      # ⚓ Gboard_Material_You_redesign_rolling_out_on_Android
                        12_–_9to5Google⠀⇛


                      # ⚓ Galaxy_A20_now_getting_Android_11_in_the_U.S._–
                        SamMobile_–_SamMobile⠀⇛


                      # ⚓ JioPages_Brings_Study_Mode_for_Android_TV_and_STB
                        Users⠀⇛


                      # ⚓ How_To_Block_Texts_on_an_Android_Device⠀⇛


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


                # § FSF⠀➾


                      # § GNU Projects⠀➾


                            # ⚓ GNU_C_Library_2.34_Released_With_More
                              Functionality_Squeezed_Into_libc⠀⇛


                                   Version 2.34 of the GNU C Library
                                   (glibc) is now available with a wide
                                   variety of changes that accumulated
                                   over the past six months.


                                   Glibc 2.34 is now available and ready
                                   to begin appearing with forthcoming
                                   Linux distribution updates. Among the
                                   many changes to find with GNU C Library
                                   2.34 are:


                                   - All functionality formerly
                                   implemented in libpthread, libdl,
                                   libutil, and libanl has been integrated
                                   into the libc library itself. Empty
                                   static archives of these former
                                   libraries are still provided so as to
                                   not be too disruptive of a change with
                                   applications moving forward only
                                   needing to link against libc.


                            # ⚓ GNU_C_Library_2.34_released⠀⇛


                                   Version 2.34 of the GNU C library has
                                   been released. Significant changes
                                   include the folding of libpthread,
                                   libdl, libutil, and libanl into the
                                   main library, support for 64-bit (year-
                                   2038 safe) times on 32-bit systems,
                                   support for the close_range() system
                                   call, a handful of security fixes, and
                                   many other changes.


    * § Leftovers⠀➾


          o § Civil Rights/Policing⠀➾


                # ⚓ Will_This_Court_Case_End_the_Mining_Industry’s_150-Year
                  Dominance_of_the_West?_–_Mother_Jones⠀⇛


                       Early one May morning, I escaped Tucson’s
                       unrelenting grid and drove south through Pima
                       County on Arizona’s state Route 83, into the heart
                       of the Madrean Sky Islands, an almost mythical
                       landscape of shadowy, isolated peaks where several
                       biological zones overlap. The blue-gray Whetstone
                       Mountains marked the distant eastern horizon, the
                       Patagonias loomed to the south, and to the
                       immediate west rose the camelback ridgeline of the
                       Santa Ritas. There, oaks and junipers stippled
                       upper elevations, and rolling swells of grass
                       blanketed low slopes. A haven for wildlife and a
                       balm for those seeking respite in nature, this
                       region contains some of the rarest intact
                       ecosystems and the highest-quality streams among
                       the deserts of the Southwest, providing habitat for
                       ocelots, jaguars, and a dozen other endangered
                       species.


          o § Monopolies⠀➾


                # ⚓ Next_Generation_IP [Ed: Next-generation buzzword/BC. What
                  drugs are those people doing?]⠀⇛


                # ⚓ FOSS_Patents:_Patent_injunction_‘reform’_bill_expected_to
                  be_signed_into_law_next_week_by_Germany’s_Federal_President⠀⇛


                       In late June, the Federal Council of Germany
                       decided not to veto a patent “reform” bill that the
                       country’s Federal Parliament had adopted two weeks
                       earlier. I have previously voiced my opinion that
                       the practical impact is going to amount to a cost
                       increase (particularly affecting defendants)
                       without moving the goalposts unless a plaintiff
                       makes an inexcusable mistake. In particular,
                       patentees should give serious consideration to
                       making a formal licensing offer so as to counter
                       any claims of irreparable harm to a defendant and/
                       or any third parties.


                       The measure is designed to take immediate effect,
                       but in order to do so, it needs to be signed into
                       law by Federal President Frank-Walter Steinmeier
                       and, finally, published in Germany’s Federal Law
                       Gazette. The Federal President’s Office informed me
                       today that the bill is presently undergoing a
                       routine check and slated to be signed into law next
                       week (i.e., the week of August 9).


                # § Patents⠀➾


                      # ⚓ 2020_China_Top_10_IP_Cases:_Winners’_Sun_is_truly_a
                        Winner:_A_Simple_Selfie-Stick_Utility_Model_Patent
                        Crushes_Infringers_in_China⠀⇛


                             Each year The Intellectual Property Tribunal
                             of the Supreme People’s Court releases a list
                             of top 10 technical intellectual property
                             rights court case decisions. The 2020 list
                             came out a few months ago, and we have been
                             highlighting some of these cases.


                             Today, we will cover a utility model patent
                             infringement case. As one of the three types
                             of patents one can obtain in China (the other
                             two being invention patents and design
                             patents), utility models are popular due to
                             their reduced costs and relative ease of
                             prosecution (no substantive examination).
                             Some might argue that a utility model patent
                             has limited value, having restricted subject
                             matter eligibility, a shorter term, and lower
                             patentability requirements. Because they are
                             not substantively examined, many “garbage
                             patents” are granted, and then often
                             subsequently invalidated once they are
                             challenged.


                      # ⚓ Innovations_in_digital_healthcare_–_navigating_patent
                        challenges [Ed: Notice how they only ever give a
                        platform and voice to patent litigation fanatics and
                        aggressive law firms, not anybody who represent the
                        public interest in this patent battlezone]⠀⇛


                             Technologies such as Artificial Intelligence
                             (AI), Augmented Reality (AR), Robotics and
                             Machine Learning (ML), are increasingly being
                             leveraged across society to enhance the way
                             people live their everyday lives. In recent
                             years, healthcare has become an area of
                             particular focus, with innovative
                             technologies being adopted to monitor health,
                             assist in diagnosis, and manage and treat
                             disease.


                             From the perspective of European patent law,
                             these new digital health technologies present
                             no new patentability challenges in themselves
                             compared to traditional medical device
                             technology or software in general. However,
                             the coming together of medical device
                             technology and software combines two
                             traditionally separate areas of patent
                             practice which have their own separate
                             issues. On the one hand, under European law,
                             additional hurdles are placed in the way of
                             obtaining patents for software. On the other
                             hand, inventions relating to healthcare
                             technology, pharmaceuticals and medical
                             devices must navigate various medical
                             exclusions. The combination of these two
                             traditionally separate areas of technology
                             means that applicants are often presented
                             with a unique set of challenges. That said,
                             with the right team of experienced patent
                             attorneys working collaboratively, many of
                             these challenges can be overcome at an early
                             stage by the careful drafting of patent
                             applications.


                      # ⚓ “Shall_be_the_Property”_is_not_an_Assignment_of
                        Patent_Rights[Ed: Patents are not rights, Dennis
                        Crouch, so quit promoting this propaganda. You're a law
                        lecturer, so surely you know this, but your blog is
                        funded by patent litigation fanatics and profiteers who
                        make a living from misleading judges, legislators
                        etc.]⠀⇛


                             Dr. Islam is a professor at Michigan (UM).
                             Back in 2012 though he took an unpaid leave-
                             of-absence to start a LASER company. During
                             that time he filed a number of patent
                             applications that came from his time on-leave
                             and that he assigned to Omni. However, UM
                             argued that it owned the patents based upon
                             his employment agreement; that it had
                             expended some ongoing funds; and that Islam
                             had bounced ideas off of some of the faculty
                             members. This argument between Islam and UM
                             was internal. UM did not file any paperwork
                             with the PTO attempting to claim ownership
                             and UM is not a party to the present
                             litigation.


                             Omni later sued Apple for infringement, but
                             the iPhone giant argued that Omni lacked
                             standing since UM was the real patent owner.
                             The district court sided with Omni — finding
                             that Omni had received rights from the
                             inventor, and that Islam had not assigned his
                             rights to UM. On appeal, the Federal Circuit
                             has affirmed.


                             [...]


                             Judge Newman wrote in dissent and argued that
                             “these patents are the property of the
                             University.”


                             Although both the majority and dissent
                             conclude that the issue is a matter of
                             contract law, neither cite to the governing
                             law of contracts for this case–the law of
                             Michigan.


                      # ⚓ Patent_case:_Oticon_A/S_and_GN_Resound_A/S_vs.
                        Sivantos_GmbH,_EPO⠀⇛


                             Although the grounds of the decision under R.
                             111(2) EPC do not have to deal in detail with
                             all the arguments of the parties, at least
                             the key points of discussion must be
                             addressed. The grounds must respond to the
                             relevant facts, evidence and arguments and
                             contain the logical chain that led to the
                             formation of the final judgment.


                             Proceedings before the EPO are governed by
                             the principle of uniformity of the language
                             of the proceedings. For the written copy of
                             the decision, only the language of the
                             proceedings shall be used. Only the decision
                             in a single language of the proceedings meets
                             the requirements of R. 111(2) EPC on the
                             grounds of the decision.


                      # ⚓ CommWorks_Solutions_patent_challenged⠀⇛


                             On July 30, 2021, Unified filed a petition
                             for inter partes review (IPR) against U.S.
                             Patent 8,923,846, owned by CommWorks
                             Solutions, LLC, an NPE and subsidiary of IP
                             Investments Group LLC. The ‘846 patent
                             relates to the recovery of information in a
                             mobile communications network. It has been
                             asserted against Comcast Cable
                             Communications.


                      # ⚓ Beware_misleading_mails_from_scammers [Ed: Total
                        scammers_run_the_EPO; have these scammers got the
                        audacity to post this with a straight face?]⠀⇛


                             The EPO has become aware that malicious
                             emails have been sent to European patent
                             attorneys purporting to be from the EPO,
                             containing unsolicited attachments or
                             including links to third party domains. The
                             EPO does not send out such emails. The latest
                             known phishing attempt alleges that the
                             recipient’s Smart Card to access EPO services
                             has expired, but future phishing attempts
                             could be made in relation to other EPO
                             services or e.g. fees.


                      # ⚓ Another_Transfer_from_TX_to_CA:_Looking_at_the
                        Particulars_of_the_Case_(But_not_Too_Closely) [Ed:
                        United States shot itself in the foot and discredited
                        the whole patent system by letting courts become like
                        companies that cheat to attract "clients" (lawsuits).
                        By an author funded by litigation fanatics.]⠀⇛


                             Sito Mobile (SITO) sued Hulu in the Western
                             District of Texas (Waco), alleging
                             infringement of seven of its patents. U.S.
                             Patent Nos. 8,825,887; 9,026,673; 9,135,635;
                             9,135,636; 9,591,360; 10,009,637; and
                             10,171,846. Both SITO and Hulu are Delaware
                             companies with Hulu headquartered Santa
                             Monica and SITO in New Jersey (although SITO
                             is currently going through Chapter 11
                             reorganization bankruptcy).


                             Although venue was “proper,” Hulu argued that
                             the case should be transferred to the Central
                             District of California for convenience. 28
                             U.S.C. § 1404(a). Judge Albright refused, but
                             the Federal Circuit has now granted Hulu’s
                             petition for mandamus and ordered the case
                             transferred.


                      # § Software Patents⠀➾


                            # ⚓ AI_Can_Invent_–_Australia_Is_First_to_Recognise
                              Non-Human_Inventorship [Ed: Patent law is
                              becoming ever more deadly (see COVID blunders)
                              and farcical, as it's clear it's anything but
                              beneficial to society and innovation has nothing
                              whatsoever to do with it (a system gamed by
                              bots)]⠀⇛


                                   The Australian Federal Court recently
                                   handed down its first-instance
                                   judgement in Thaler v Commissioner of
                                   Patents [2021] FCA 879 where the
                                   central issue considered was whether an
                                   artificial intelligence (AI) system
                                   could be an ‘inventor’ for the purposes
                                   of the Australian Patents Act 1990
                                   (Act) and its corresponding
                                   regulations. The Court found that an AI
                                   system can be an inventor – where
                                   ‘inventor’ may be construed broadly to
                                   include a ‘person or thing that
                                   invents’1. This decision puts Australia
                                   in the spotlight as a favourable
                                   country to patent AI-created inventions
                                   – for now. Given the subject-matter and
                                   controversy generated by this decision,
                                   an appeal to the Full Federal Court is
                                   almost certain.


                                   This Federal Court decision is an
                                   appeal from a Patent Office hearing
                                   where the Office rejected Australian
                                   patent application no. 2019363177 in
                                   the name of Stephen L. Thaler (the
                                   creator of the AI system) on the ground
                                   that the AI system (Device for the
                                   Autonomous Bootstrapping of Unified
                                   Sentience (DABUS)) could not be
                                   considered as an inventor in the
                                   context of the Patent Regulations 1991.


                            # ⚓ Australian_court_decision_to_recognise_non-
                              humans_as_inventors_is_brave,_verging_on
                              foolhardy [Ed: How the propaganda mill of EPO
                              fraudsters (Joff Wild and his groupies) responded
                              to the shocking news that two countries now give
                              patents to bots]⠀⇛


                                   The decision taken by an Australian
                                   court to recognise that non-humans can
                                   be inventors is a courageous one,
                                   writes Mark Summerfield. Whether it is
                                   the right one, though, is a completely
                                   different issue


                # § Copyrights⠀➾


                      # ⚓ AG_Øe_advises_that_partial_designs_may_be_protected
                        as_unregistered_designs⠀⇛


                             Just before closing down for summer vacation,
                             Advocate General (AG) Saugmandsgaard Øe
                             issued his Opinion in Case C-123/20
                             concerning the protectability of ‘partial
                             designs’ (design rights for part of a
                             product) as an unregistered Community design
                             right.


                             The request for preliminary ruling by the
                             Court of Justice of the European Union (CJEU)
                             originates from the German Federal Court of
                             Justice (Bundesgerichtshof). The German court
                             is currently hearing a dispute between the
                             Italian racing car manufacturer Ferrari and
                             Mansory Design, a car modification company
                             located in Germany [the summary below is
                             based is on the submission by the
                             Bundesgerichtshof to the CJEU, available in
                             German here and in English here].



                    ䷩ 𝚕𝚒𝚗𝚎 3909

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 08.02.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


✐ Links_2/8/2021:_Linux_5.14_RC4_and_20%_Growth_in_Steam⠀✐


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o ⚓ 9to5Linux_Weekly_Roundup:_August_1st,_2021⠀⇛


                 It’s August already, and this means that we’re getting
                 new releases of Ubuntu and Debian GNU/Linux. But, until
                 then, this past week brought us new releases of the
                 PulseAudio sound server, KDE Plasma 5.22 desktop
                 environment, as well as the Arch Linux and 4MLinux
                 distributions.


                 On top of that, I published another awesome monthly
                 roundup of Xfce app updates, and, if you have the time,
                 you can test drive the upcoming releases of MX Linux 21
                 and Linux Lite 5.6 distributions. You can enjoy these and
                 much more in 9to5Linux’s Linux weekly roundup for August
                 1st, 2021, below!


          o ⚓ Linux_Weekly_Roundup_#141⠀⇛


                 Welcome to this week’s roundup of Linux Releases.


                 In this week, Amarok Linux 3.1.1, Artix Linux 20210726,
                 Linux Lite 5.6 RC, MX Linux 21 Beta 1, Absolute Linux
                 20210730, and Freespire 7.7 have been released.


                 May you have a wonderful week and enjoy your summer!


          o § Desktop/Laptop⠀➾


                # ⚓ AWS_adds_browser_access_to_its_cloudy_WorkSpaces_desktops_–
                  but_not_for_Linux_•_The_Register⠀⇛


                       Amazon Web Services has stolen a march on
                       Microsoft’s cloud desktop plans by adding browser
                       access to its WorkSpaces desktop-as-a-service
                       offering.


                       Browser access will only work for WorkSpaces
                       running Windows. Linux users are out in the cold
                       and AWS hasn’t said when or if penguin-powered
                       desktops will get to play. The service uses
                       Amazon’s WorkSpaces Streaming Protocol (WSP), which
                       doesn’t allow use of graphics-intensive instance
                       types. AWS customers that run WorkSpaces from the
                       Asia Pacific (Mumbai) and GovCloud (US-West)
                       Regions also need not apply.


                       For the rest of us, the service means browsers are
                       now approved clients for an AWS WorkSpace – but not
                       without complications. WorkSpaces set up to stream
                       over the PCoIP protocol will work in Chrome or
                       Firefox. WSP WorkSpaces can use any Chromium-based
                       browser.


          o § Audiocasts/Shows⠀➾


                # ⚓ Linux_Action_News_200 [Ed: Linux Action News once again
                  engaging in Microsoft apologism and boosting, perhaps_as_the
                  owners_of_the_show_would_demand]⠀⇛


                       Microsoft’s next kernel patch fixes a long-standing
                       Linux issue, we’ll share the details. Plus
                       ChromeOS’s next power user feature you haven’t
                       heard of, and Valve’s broader plans that came into
                       focus this week.


                # ⚓ Josh_Bressers:_Episode_282_–_The_security_of_Rust:_who_left
                  all_this_awesome_in_here? [Ed: Since when does Microsoft get
                  to tell_us_anything_about_security (while shilling projects
                  it controls in GitHub)?]⠀⇛


                       Josh and Kurt talk about a story from Microsoft
                       declaring Rust the future of safe programming,
                       replacing C and C++. We discuss how tooling affects
                       progress and why this isn’t always obvious when
                       you’re in the middle of progress.


                # ⚓ 162:_Framework_Laptop,_Pop!_OS_Rolling_Release,_Linux_Mint,
                  WayDroid_|_This_Week_in_Linux⠀⇛


                       On this episode of This Week in Linux, we’ll cover
                       the modular laptop that respects your Right to
                       Repair called the Framework laptop. In the Distro
                       News, we’ve got updates from Linux Mint and a very
                       interesting potential plan for a Rolling Release
                       edition of Pop!_OS from System76. We’re going to
                       jump into an enterprise grade tool with Apache
                       Cassandra 4.0. Then in the Linux Mobile News, we’ve
                       got an interview with Rudi Timmermans of the
                       WayDroid project which is looking to make it
                       possible to run Android Apps on Linux Phones like
                       Ubuntu Touch. We’ve also got news from NVIDIA,
                       they’ve released new Drivers with a lot of great
                       features and they’ve even Open Sourced some
                       content. All that and so much more on episode 162
                       of This Week in Linux, recorded live on July 31,
                       2021. Your Weekly Source for Linux GNews!


          o § Kernel Space⠀➾


                # ⚓ Linux_5.14-rc4⠀⇛


                       Nothing to see here, entirely normal rc4.  It's
                       mostly a very nice and
                       flat diffstat - so small spread out changes - with
                       the exception of a
                       couple of blips in selftests and the xfs fixes.

                       Mostly drivers, some arch updates, networking, plus
                       tooling and
                       selftests. Nothing odd stands out.

                       Shortlog appended for people who want to scan the
                       details,

                                        Linus
                # ⚓ Linux_5.14-rc4_Released_With_Change_Following_Some_Broken
                  Android_Apps,_Other_Fixes_–_Phoronix⠀⇛


                       Linux 5.14-rc4 is available today as a rather
                       smooth update with nothing too worrisome but just a
                       decent amount of fixes and nothing that is causing
                       Linux creator Linus Torvalds to be frustrated.


                       Linus briefly summed it up in the 5.14-rc4
                       announcement, “Nothing to see here, entirely normal
                       rc4. It’s mostly a very nice and flat diffstat – so
                       small spread out changes – with the exception of a
                       couple of blips in selftests and the xfs fixes.
                       Mostly drivers, some arch updates, networking, plus
                       tooling and selftests. Nothing odd stands out.”


          o § Instructionals/Technical⠀➾


                # ⚓ Linux_for_Starters:_Your_Guide_to_Linux_–_Understanding_the
                  File_System_–_Part_12_–_LinuxLinks⠀⇛


                       This is a series that offers a gentle introduction
                       to Linux for newcomers.


                       Ubuntu has a very different file system compared to
                       Windows. It’s organized in a completely different
                       way designed to offer more security, but it’ll feel
                       very unfamiliar if you’ve come exclusively from a
                       Windows background.


                       It’s therefore worth devoting time to learning
                       about the file system in Ubuntu.


                # ⚓ Mount_Microsoft_OneDrive_in_Linux_With_OneDriver_GUI_Tool
                  [Ed: Giving Microsoft control over files is not a wise
                  idea]⠀⇛


                       On Windows, Microsoft provides a free cloud storage
                       service in the form of OneDrive. It comes
                       integrated with Windows and you get 5 GB of free
                       storage with your Microsoft account.


                       This works great on Windows but like Google,
                       Microsoft also does not provide a native client for
                       OneDrive on Linux desktop.


                       You can access your OneDrive data through browser,
                       of course. In addition to that, there are some
                       other ways to access OneDrive on Linux.


                # ⚓ How_to_Migrate_From_CentOS_8_to_Rocky_Linux_8/Alma_Linux_8
                  –_LinuxBabe⠀⇛


                       As you may already know, Red Hat decided to abandon
                       the vanilla CentOS 8 project, which will reach end-
                       of-life on December 31, 2021, and shift its focus
                       to CentOS Stream. This tutorial is going to show
                       you how to migrate from CentOS 8 to Rocky Linux 8/
                       Alma Linux 8.


                # ⚓ How_to_Install_Latest_qBittorrent_on_Ubuntu_20.04_Desktop
                  and_Server_–_LinuxCapable⠀⇛


                       qBittorrent is a cross-platform free and open-
                       source BitTorrent client. qBittorrent is a native
                       application written in C++ which uses Boost, Qt 5
                       toolkit, and libtorrent-rasterbar library and is
                       extremely lightweight and fast. qBittorrent is very
                       popular amongst torrent users as the main
                       alternative to UTorrent.


                # ⚓ How_to_Install_MariaDB_on_Rocky_Linux_and_AlmaLinux⠀⇛


                       MariaDB is a free and community-developed
                       relational database system that is a compatible
                       drop-in replacement for the hugely popular MySQL
                       database management system.


                       It was forked from MySQL after the original
                       developers of MySQL expressed their misgivings with
                       the acquisition of MySQL by Oracle. Since then,
                       MariaDB is guaranteed to remain free and open
                       source under the GNU license.


                # ⚓ How_to_Create_Backup_with_tar_Command_in_Linux⠀⇛


                       Hello Linux Geeks, if you are looking for free
                       command line backup tools on Linux systems then tar
                       command is the solution for you. Tar command can
                       create backup of your application, configurations
                       files and folders of the system.


                       Tar stands for ‘tape archive’ and can archive
                       multiple files and directories into a tar file.
                       This tar can also be compressed using gzip and
                       bzip2 compression utility. Once we have a tar
                       backup ready then we can easily transfer it to
                       remote backup server using scp or rsync commands.


                       In this post, we will demonstrate how to create
                       backup with tar command in Linux.


                # ⚓ How_To_Get_KDE_Plasma_5.22_for_Your_Computer⠀⇛


                       KDE Plasma 5.22 with its tagline Stability,
                       Usability, Flexibility released last June is the
                       latest desktop technology of KDE and Free Software
                       Community. It features new looks to the desktop,
                       System Settings and many other improvements. Want
                       it? If you would love to try it or further install
                       it for daily use, here’s how to.


                # ⚓ Time-stretch_in_Kodi⠀⇛


                       VLC has a really neat feature which consists of
                       time-stretching audio to allow users to speed up or
                       slow video playback with the [ and ] keys without
                       affecting the pitch of the sound. I recently
                       switched to Kodi as my video player of choice and I
                       was looking for the equivalent feature.


                # ⚓ Kubermatic_on_Hetzner⠀⇛


                       Hello and welcome to another article about
                       Kubernetes. In this article we will go through the
                       Kubermatic installation on Hetzner Cloud. But first
                       of all let us go through a few questions:


                # ⚓ Genius_Level_Support_Engineer_Interview⠀⇛


                # ⚓ How_to_Install_Damn_Vulnerable_Web_Application_on_Rock
                  Linux_8_–_LinuxCapable⠀⇛


                       Damn Vulnerable Web Application (DVWA) is a PHP and
                       MySQL web application that is a free and open-
                       source vulnerable web application. Its main goal is
                       to aid security professionals in testing their
                       skills and tools with various levels of difficulty
                       to help web developers better understand the
                       processes of securing web applications.


                # ⚓ How_to_Show_Disk_Usage_in_Linux_With_the_du_Command⠀⇛


                       If your PC is running slow or you’re having issues
                       installing updates and software, there’s a high
                       chance you might be running out of disk space. The
                       handy du command makes it convenient for Linux
                       users to stay aware of their disk consumption and
                       make an upgrade if required.


                       But how exactly do you issue this command on Linux?
                       Let us find out.


                # ⚓ How_to_install_MX_Linux_with_disk_encryption_|_FOSS_Linux⠀⇛


                       MX Linux is an operating system based on the Debian
                       stable. The system is generated from a cooperative
                       venture between the AntiX and former MEPIS
                       communities. This is a mid-weight Linux distro
                       designed with a nice look, an efficient desktop
                       with simple configuration, and greater solid
                       performance.


                       It also has basic tools like a graphic installer
                       that generally handles the computer’s UEFI, a GUI-
                       based method to change a Linux kernel, and other
                       core programs.


                       After that brief introduction of MX Linux, let us
                       go through the system’s installation process on our
                       VMware workstation. We will channel our
                       concentration from the normal setup to installing
                       the OS with the disk encryption option.


                       Note: You can diversify your MX Linux knowledge on
                       its features since we also have another article
                       that has covered all the MX Linux features. The
                       latter will take you through a video guide of its
                       features.


                # ⚓ How_to_install_the_WaterFox_Browser_on_a_Chromebook_in
                  2021⠀⇛


                       Today we are looking at how to install the WaterFox
                       Browser 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.


                       If you have any questions, please contact us via a
                       YouTube comment and we would be happy to assist
                       you!


                       This tutorial will only work on Chromebooks with an
                       Intel or AMD CPU (with Linux Apps Support) and not
                       those with an ARM64 architecture CPU.


                # ⚓ How_to_update_Kali_Linux_repository_|_FOSS_Linux⠀⇛


                       This article will cover the steps needed for you to
                       update your Kali Linux system repo. The Kali Linux
                       Operating system is Debian-Linux-based. The
                       distribution comes with several advanced tools
                       meant for streamlined utilities, accuracy boosting,
                       quick and easy execution of pen-testing, and social
                       engineering tools.


                       Like any other Linux distro, Kali supports audio
                       play files, office, web browsers, programming
                       software, and other software supported by either
                       major OSs (Windows and macOS). Additionally, the OS
                       comes with a Kali NetHunter App Store used in
                       easing browsing, installation, and keeping your
                       apps up to date.


                       Kali Linux comes with a large set of tested and
                       pre-installed applications, making it simpler for
                       use than other systems. The system was officially
                       released into the market in 2013 as a complete re-
                       branding of Backtrack Linux with a GNOME UI. Their
                       developers ripped all the unwanted stuff off
                       Backtrack by getting rid of junky utilities and
                       updating the useful ones in the white-hat
                       community.


                       To add on, the OS includes slightly over 600
                       completely free tools. It also has an open-source
                       Git tree that is publicly available. It is a well-
                       known OS among Cybersecurity professionals.


                # ⚓ Install_and_use_Fish_shell_in_Linux_–_Unixcop⠀⇛


                       Fish Shell stands for friendly interactive shell
                       which is fully-equipped, smart and user-friendly
                       command-line shell that supports a lot of handy
                       features unlike any other shell.


                       Features are Autosuggestion, Sane Scripting, Man
                       Page Completions, Web-Based configuration and
                       Glorious VGA Color.


                       Fish shell makes your command line more productive,
                       useful & fun without remembering a bunch of Linux
                       commands because of their handy features.


                       let’s go ahead and install it by following the
                       below steps.


                # ⚓ Ubuntu_package_management_with_apt_|_FOSS_Linux⠀⇛


                       Ubuntu-based distros feature several package
                       management systems for installing, upgrading,
                       managing dependencies, and removing software.
                       Advanced Packaging Tool (APT) is the default
                       package manager for distros like Ubuntu, Debian,
                       Linux Mint, and POP!_OS.


                       APT works with the apt command in Ubuntu to provide
                       access to over 60,000 software packages,
                       dependencies, metadata, and instructions to install
                       software applications in your system.


                       This article guides users on working with APT
                       through the apt command, searching, installing,
                       updating packages, upgrading a system, and adding
                       extra repositories for additional software. It will
                       also introduce other package managers like aptitude
                       and dpkg.


                # ⚓ MySQL_user_management_|_FOSS_Linux⠀⇛


                       ySQL is among the most popular database managers in
                       the world. It contains many features that make it
                       reliable, efficient, and robust. Its maximum
                       reliability is achieved if it is rightly used.
                       Creating users with limited permissions on the
                       database is one of the easiest and reliable ways to
                       increase MySQL security.


                # ⚓ Docker_Logs:_What_They_Are_and_How_to_Use_Them_(with
                  Examples)⠀⇛


                       In this article, we are going to show you
                       everything you need to know about Docker logs and
                       how to work with them.


                       Life would be much simpler if applications running
                       inside Docker containers always behaved correctly.
                       When things inevitably start going wrong you need
                       diagnostic information to figure out how and why.


                       If you are a system administrator and responsible
                       for building and managing containerized
                       applications, docker logging is one of the most
                       important for you. Dealing with the logs are one of
                       the best ways to help reveal errors, aid in
                       debugging, and optimize your application’s
                       performance.


          o § Games⠀➾


                # ⚓ Steam_Survey_Shows_Linux_Marketshare_Hitting_1.0%⠀⇛


                       Not only did Valve announce Steam Deck in July but
                       the overall Linux gaming marketshare according to
                       the Steam Survey also hit a multi-year high.


                       According to the Steam Survey numbers out today for
                       July 2021, Steam on Linux hit a 1.0% marketshare,
                       or a +0.14% increase over the month prior.


          o § Desktop Environments/WMs⠀➾


                # ⚓ Xfce:_Search_improvements⠀⇛


                       Welcome back. This is my last (or second to last)
                       blog post for this year’s Google Summer of Code
                       with Xfce and Thunar. Unlike previous weeks this
                       time I have only one new thing to talk to you
                       about. Searching in Thunar.


                        Most of you might have noticed that Thunar has had
                       a significnt deficiency for a while. Thunar has
                       been missing a decent solution for searching for
                       files in the filesystem. Users could search for
                       files in the selected directory, but even that was
                       a pretty mediocre experience, because results
                       weren’t being filtered while searching. Fortunately
                       there is another program under the Xfce umbrella
                       that makes searching for files a breeze. That
                       program is, of course, Catfish. Unfortunately this
                       status quo requires users to juggle between Thunar
                       and Catfish even when searching for simple things.


                        In the past two weeks I’ve been working on two
                       things. First, making Catfish easier to use through
                       Thunar. Second improving Thunar’s built-in search
                       features to make routine and/or simple searches
                       possible without leaving Thunar. The first
                       improvement is pretty straightforward. A new button
                       has been added that allows the user to open catfish
                       with the specified search query from inside Thunar.
                       As far as the improving the built-in search
                       features goes, I’ve implemented a basic depth-
                       limited recursive search in Thunar that is accessed
                       from the location bar, which can now be used as
                       both a location bar and a search bar. As the user
                       types his/her search query the view is updated with
                       the results. For convenience in addition to the
                       current directory and its subdirectories, Thunar
                       searches the GTK-Recent database for eligible
                       entries.


                # § GNOME Desktop/GTK⠀➾


                      # ⚓ Emmanuele_Bassi:_Documenting_GNOME_for_developers⠀⇛


                             You may have just now noticed that the GNOME
                             developers documentation website has changed
                             after 15 years. You may also have noticed
                             that it contains drastically less content
                             than it used to. Before you pick up torches
                             and pitchforks, let me give you a short tl;dr
                             of the changes:


                             Yes, this is entirely intentional
                             Yes, I know that stuff has been moved
                             Yes, I know that old URLs don’t work
                             Yes, some redirections will be put in place
                             No, we can’t go back


                      # ⚓ Nishit_Patel:_GSoC_Project_update_part_II⠀⇛


                             While reading the documentation, I came
                             across a bug that was leading to broken
                             links. After some debugging and testing, I
                             was able to fix the bug. It was due to a
                             missing configuration in the documentation
                             engine.


          o § Distributions⠀➾


                # § Reviews⠀➾


                      # ⚓ Review:_Pacstall_–_AUR_for_Ubuntu⠀⇛


                             Back in May I briefly talked about Arch
                             Linux’s User Repository (also known as the
                             AUR). Arch Linux itself has a relatively
                             small collection of official software
                             packages and so many members of the Arch
                             community (and those who use its derivative
                             distributions) run packages from the AUR. The
                             AUR contains scripts provided by third-
                             parties which enable software to be installed
                             using scripts. While installing software this
                             way manually can be tedious, there are any
                             number of helper programs which assist Arch
                             users in building and installing software
                             from the AUR scripts.


                             As a result, Arch Linux, which has a
                             relatively small number of official packages
                             (11,945 at the time of writing) can offer an
                             additional 70,500 through the AUR collection.
                             This puts the combined collection of Arch
                             software in a similar range as Debian and
                             Ubuntu. In the article from May we touched on
                             a number of methods other distributions use
                             to augment their official repositories with
                             third-party software. These methods included
                             Nix, Copr, Slackbuilds, and personal package
                             archives (PPA).


                             One project which has come along since then
                             is called Pacstall. The Pacstall project aims
                             to provide Ubuntu users with a third-party
                             repository similar in style to Arch’s, along
                             with a convenient command line tool to
                             automate most of the work. “Pacstall will
                             attempt to become the AUR Ubuntu wishes it
                             had. It takes the AUR and puts a spin on it,
                             making it easier to install programs without
                             scouring GitHub repos and the likes.”


                             Pacstall can be set up using a Deb package or
                             a single-line shell command. I decided to
                             take Pacstall for a spin on Ubuntu MATE 21.04
                             to see how it would perform. Reading the
                             description of the project I was uncertain of
                             where third-party software scripts would be
                             coming from. For instance, I was unclear as
                             to whether Pacstall would use (and possibly
                             translate) existing AUR scripts or if it
                             would be duplicating the work of the AUR in a
                             new approach. I was unable to find
                             documentation which explained where these
                             scripts came from and how many there were.


                             With a little looking around I discovered
                             Pacstall learns how to install packages from
                             another repository specific to this program.
                             Which means it is not connected to or
                             learning from the AUR, simply providing a
                             similar service. At the time of writing there
                             are about five dozen recipes for building
                             third-party software in the Pacstall
                             repository. So how well does it work?


                # § Arch Family⠀➾


                      # ⚓ Arch_Reproducible_Progress_July_2021⠀⇛


                             At the end of July, I had some days off and
                             some more time to focus on some
                             unreproducible packages in Arch Linux and get
                             some of the issues resolved. This post goes
                             through the resolved issues by category.


                # § IBM/Red Hat/Fedora⠀➾


                      # ⚓ Digital_transformation_strategy:_6_factors_to_rethink
                        post-pandemic_|_The_Enterprisers_Project⠀⇛


                             After a pedal-to-the-metal year of digital
                             transformation, it may be tempting for
                             leaders to ease up on the gas. However, it is
                             only a matter of time before “life happens”
                             and we experience the next major
                             interruption, says Greg Bentham, vice
                             president, cloud infrastructure services at
                             Capgemini Americas. “Now that we are emerging
                             out of the pandemic in many parts of the
                             world, the biggest lesson learned is that
                             companies that had a clear digital strategy
                             have emerged even stronger than ever.”


                             “Companies that had a clear digital strategy
                             have emerged even stronger than ever.”
                             COVID-19 also taught us that in expecting the
                             unexpected, a solid technology strategy goes
                             a long way. “Across our industries and
                             through our boards, we’ve seen those
                             advantages realized through both commercial
                             productivity and an internal ease with
                             business and employee retention,” says Jay
                             Upchurch, CIO at SAS. “This puts more
                             pressure on CIOs to drive digital
                             transformation faster.”


                      # ⚓ How_to_open_and_close_directories_in_the_Linux
                        terminal_|_Opensource.com⠀⇛


                             To open a directory on a computer with a
                             graphical interface, you double-click on a
                             folder. It opens, and you are now “in” that
                             folder.


                             To open a directory in a terminal, you use
                             the cd command to change your current
                             directory. This essentially opens that folder
                             and places you in it.


                      # ⚓ What’s_new_in_the_Red_Hat_OpenShift_4.8_console⠀⇛


                             Red Hat OpenShift 4.8 brings many exciting
                             new capabilities for developers. This article
                             focuses on what’s new in the OpenShift
                             console, including devfiles and certified
                             Helm charts in the developer catalog, the
                             ability to drag and drop Spring or Quarkus
                             JARs directly from your desktop, a
                             streamlined developer experience for
                             building, deploying, and scaling cloud-native
                             applications in hybrid-cloud environments,
                             and much more. Developers will also find
                             enhanced features for Red Hat OpenShift
                             Serverless, Red Hat OpenShift Pipelines, Red
                             Hat OpenShift GitOps, and more.


                # § Debian Family⠀➾


                      # ⚓ First_test_EasyOS_Bullseye_series⠀⇛


                             Debian 11 “Bullseye” is due to be released in
                             about a week, so I thought, why not, update
                             EasyOS from the Buster-series to the
                             Bullseye-series.
                             Built it, booted, and got a working desktop.
                             Some issues though…
                             NetworkManager isn’t working, so used SNS to
                             connect to the Internet.
                             Bluealsad reports a failure due to problem
                             with dbus.
                             Some packages are missing, for example
                             required by libreoffice.


          o § Devices/Embedded⠀➾


                # ⚓ Raspberry_Pi_Compute_Module_4_mini_router_keeps_cool_with
                  aluminum_alloy_cover⠀⇛


                       There are many hardware platforms based on
                       Raspberry Pi CM4 system-on-module, but in most
                       instances, only the baseboard is provided, and you
                       have to handle mounting and/or make an enclosure by
                       yourself.


                       One of those boards was Seeed Studio’s “Dual
                       Gigabit Ethernet Carrier Board for Raspberry Pi
                       Compute Module 4”, which as the name implies,
                       offers two Gigabit Ethernet ports, as well as two
                       USB 3.0 ports, and a micro HDMI port for video
                       output. I say “was” because the company has now
                       designed a PC/ABS case with an aluminum alloy cover
                       acting as a heatsink to keep the RPi CM4 module
                       cool.


                # § Open Hardware/Modding⠀➾


                      # ⚓ This_magnetically_levitated_globe_is_an_attractive
                        piece_of_home_decor_|_Arduino_Blog⠀⇛


                             While trying to think of his next project,
                             Herwig Taveirne came up with the idea to
                             craft some kind of levitating display that
                             can showcase certain objects. Some of the
                             criteria included completely magnetic
                             levitation, stable floating, and overall
                             safety since magnets can get quite hot when
                             in use.


                             The floating globe case was constructed with
                             a wooden lantern as its base, which helps
                             everything look cleaner. The top of the
                             lantern houses a large electromagnet that
                             faces towards the bottom, along with a Hall-
                             effect sensor that dangles below it to
                             measure the distance between the globe and
                             the magnet. An Arduino Nano is responsible
                             for controlling the lifting magnet based on
                             what the sensor reads in order to keep a
                             stable position. There is also a set of six
                             other coils at the base that get activated
                             depending on the current rotation of the
                             globe, and these provide small boosts to one
                             side of the globe to keep it spinning
                             smoothly.


                      # ⚓ A_flask_of_goo_that_moves_to_the_groove_|_Arduino
                        Blog⠀⇛


                             Ferrofluid is an interesting substance that
                             is attracted to a magnetic field. While
                             manually playing with a flask of such goo is
                             interesting for a few minutes, GreatScott!
                             had other ideas. His 3D-printed rig arranges
                             a half-dozen custom electromagnets on the
                             side of the flask. This allows an Arduino
                             Nano to control the magnetic field
                             arrangement, and thus fluid movement, with
                             the help of six MOSFETs.


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


                # ⚓ dav1d_0.9.1_Released_With_More_Optimizations_–_Particularly
                  For_Older_CPUs⠀⇛


                       Dav1d 0.9.1 was released on Sunday as the newest
                       feature update to this leading open-source CPU-
                       based AV1 video decoder.


                       Dav1d 0.9.1 principally benefits those on older
                       CPUs such as processors supporting SSE2 and SSE4
                       but not the newer AVX-era Intel/AMD CPUs. There are
                       10-bit optimizations for SSE4, 10 and 12-bit SSSE3
                       optimizations, and a variety of other improvements
                       to Dav1d’s SSE2/SSE4 Assembly. There is also film
                       grain Arm NEON support and other fixes.


                # § SaaS/Back End/Databases⠀➾


                      # ⚓ PostgreSQL_Weekly_News_–_August_1,_2021⠀⇛


                             PostgreSQL Weekly News is brought to you this
                             week by David Fetter


                # § FSF⠀➾


                      # § GNU Projects⠀➾


                            # ⚓ diffutils-3.8_released_[stable]⠀⇛


                                   This is to announce diffutils-3.8, a
                                   stable release.


                                   There have been 47 commits by 5 people
                                   in the 2.6 years since 3.7.


                                   See the NEWS below for a brief summary.


                                   Thanks to everyone who has contributed!
                                   The following people contributed
                                   changes to this release:


                                   Bruno Haible (2)
                                   Dave Odell (1)
                                   Jim Meyering (23)
                                   KO Myung-Hun (1)
                                   Paul Eggert (20)


                                   Jim [on behalf of the diffutils
                                   maintainers]


                            # ⚓ The_GNU_C_Library_version_2.34_is_now
                              available⠀⇛


                                   The GNU C Library version 2.34 is now
                                   available.
                                   The GNU C Library is used as the C
                                   library in the GNU system and
                                   in GNU/Linux systems, as well as many
                                   other systems that use Linux
                                   as the kernel.
                                   The GNU C Library is primarily designed
                                   to be a portable
                                   and high performance C library. It
                                   follows all relevant
                                   standards including ISO C11 and
                                   POSIX.1-2017. It is also
                                   internationalized and has one of the
                                   most complete
                                   internationalization interfaces known.


    * § Leftovers⠀➾


          o § Health/Nutrition⠀➾


                # ⚓ Medicines_Directive_interpreted_by_the_CJEU_in_an
                  interesting_new_ruling_C-178/20⠀⇛


                       Marketing authorisations (MA) and their legal
                       status have become increasingly interesting for
                       anyone working in the medicinal products area. The
                       recent CJEU ruling on July 8th in the case C-178/20
                       Pharma Expressz (find here), is especially so.
                       There, the CJEU brings further clarification to the
                       provisions of the Medicines Directive 2001/83/EC
                       (find here) in the context of MA.


                       A medicinal product not subject to medical
                       prescription in one Member State may not be placed
                       on the market in another Member State unless that
                       Member State, too, has granted its marketing
                       authorisation. In the absence of such an
                       authorisation, it still may be possible to supply
                       that medicinal product where its use meets special
                       medical needs in accordance with EU law.


                       Pharma Expressz, a Hungarian company, attempted to
                       place its medicinal products on the market in
                       Hungary without complying with the requirements
                       stipulated by Hungarian law, i.e. had not applied
                       for an MA. Consequently, the Hungarian authorities
                       ordered the company to stop its importation of the
                       products.


                       Under Hungarian law, medicinal products without an
                       MA, issued either by the Hungarian authorities or
                       the European Commission, may be placed on the
                       market only where their use for medical purposes is
                       notified to those authorities by a medical
                       practitioner prescribing medicinal products. In
                       order to comply with the requirements, the
                       medicinal practitioner needs to obtain from the
                       competent governmental authorities a declaration
                       concerning the specific use. This procedure was not
                       followed in the case by Pharma Expressz since the
                       medicinal products at hand were sold without
                       prescription.


                       Pharma Expressz appealed the decision, refusing
                       marketing authorisation, to the Fővárosi
                       Törvényszék (Budapest High Court, Hungary). On
                       appeal, Pharma Expressz claimed that the specific
                       requirement of compliance with Hungarian law
                       regulations was contrary to EU law because the
                       medicinal products in question had previously been
                       granted marketing authorisation in another Member
                       State and the products were available without
                       medical prescription.


                       In its ruling, the Court stated that the Medicines
                       Directive (Articles 70-73) requires that an MA is
                       granted by the competent authorities of that Member
                       State, or under the centralized procedure
                       established by the Commission, in order for a
                       pharmaceutical product to be placed on the
                       Hungarian market. Thus, a medicinal product placed
                       on the Hungarian market needs either an MA by the
                       Hungarian authorities, or an MA authorization
                       through the centralized procedure of the European
                       Medicines Agency. This requirement applies whether
                       the medicinal product is sold under prescription or
                       not.


                       The alternative procedure, namely that of mutual
                       recognition, requires the application of strict
                       conditions, such as the MA application for a given
                       medicinal product in one Member State with the
                       objective to recognize that specific MA in yet
                       other Member States. The factual situation in the
                       case at hand does not meet these requirements.


                # ⚓ Supermarket_With_Hudson_Valley,_New_York_Stores_Recalls_15
                  Items⠀⇛


                       . The recall is being issued due to the potential
                       presence of small plastic pieces in the product,
                       officials say.


          o § Integrity/Availability⠀➾


                # § Proprietary⠀➾


                      # § Security⠀➾


                            # § Privacy/Surveillance⠀➾


                                  # ⚓ New_Apple_Patent_Reveals_The_Ultimate
                                    iPhone_Upgrade [Ed: Framing mass
                                    surveillance and abuses of human rights as
                                    “innovation”]⠀⇛


                                         The patent explains how the
                                         technology will work, saying, “An
                                         optical imaging array is aligned
                                         with the aperture. Above the
                                         aperture, the display is arranged
                                         and/or configured for increased
                                         optical transmittance. For
                                         example, a region of the display
                                         above, or adjacent to, the
                                         imaging aperture can be formed
                                         with a lower pixel density than
                                         other regions of the display,
                                         thereby increasing inter-pixel
                                         distance (e.g., pitch) and
                                         increasing an area through which
                                         light can traverse the display to
                                         reach the optical imaging array.”


          o § Finance⠀➾


                # ⚓ Wolf_Richter:_After_Slashing_33%_of_Workers_in_6_Years,
                  Railroads_Complain_about_Labor_Shortages,_amid_Uproar_over
                  Slow_Shipments_|_naked_capitalism⠀⇛


                       Railroads are finding it difficult to hire workers
                       and their labor shortfall has prevented them from
                       meeting transportation demand.


                # ⚓ Pfizer_Court_Fight_Could_Legalize_Medicare_Copays_and
                  Unleash_‘Gold_Rush’_in_Sales⠀⇛


          o § Monopolies⠀➾


                # ⚓ India_counsel_call_for_design_system_overhaul [Ed: By
                  "Sources" they mean sponsors and they moan for "interested
                  parties during litigation" i.e. international law firms
                  rather than people of India. This is a propaganda mill for
                  colonialism through unjust laws, imposed by blackmailing
                  officials]⠀⇛


                       Sources criticise the current examination process
                       in India and how it holds back interested parties
                       during litigation and elsewhere


                # ⚓ Why_might_an_Australian_Applicant_consider_nominating_the
                  Korean_International_Search_Authority_(KR-ISA)?⠀⇛


                       The Patent Cooperation Treaty (PCT) is an
                       international agreement that is administered by the
                       World Intellectual Property Office (WIPO) with the
                       aim of streamlining the securing of patents in
                       multiple jurisdictions. The patent offices of
                       approximately 150 countries and multi-country
                       regions, participate in the running of the PCT,
                       including the Australian Patent Office (IP
                       Australia) the European Patent Office, the US
                       Patent and Trademark Office, The Chinese
                       Intellectual Property Office, and the Japanese and
                       Korean Patent Offices.


                       One of the features of the PCT is that after
                       lodging an international patent application with
                       the Applicant’s “Receiving Office” (usually the
                       Patent Office in which the Applicant resides) the
                       Applicant then receives an international search
                       report (ISR), and written opinion on patentability
                       (WO). Most commonly the Receiving Office (RO), the
                       International Search Authority (ISA) and the
                       International Preliminary Examining Authority
                       (IPEA) are a department (or departments) of the
                       Applicant’s local Patent Office and so the ISR and
                       WO issue from the same Patent Office. However,
                       depending on the Receiving Office that the
                       international application is filed with, it may be
                       possible for the Applicant to choose between a
                       number of ISA’s. Some example RO’s and their
                       competent ISAs and IPEAs are set out in the table
                       below:


                # ⚓ Counsel_weigh_up_options_as_EU_eyes_enhanced_GI
                  protection⠀⇛


                       Locally sourced items such as cutlery, marble and
                       tweed could soon be given the same protection as
                       cheese and wine, but could it work in practice?


                # ⚓ The_economic_value_of_designs [Ed: They mean monopolies on
                  designs. Yes, monopoly is good for monopoly "owner"...]⠀⇛


                       In a 2016 study, 75% of German consumers said that
                       design was more important to them than it had been
                       five years earlier (study by Adobe, “State of
                       Create”, 2016, p. 22). Nearly half of the consumers
                       were willing to spend more money for a product with
                       good design. In a time where the products with
                       which we surround ourselves define who we are,
                       product design is essential to our purchasing
                       decisions. This also applies to fast-moving
                       consumer goods. For that reason, product design has
                       developed into one of the most important marketing
                       tools and decisive competitive factors. Today, a
                       successful brand is defined not only via the
                       trademarks used, but also by unique and memorable
                       designs.


                # ⚓ ANDA_cases_will_hit_decade_low,_suggests_H1_2021_data⠀⇛


                       Pfizer challenged the most ANDAs, Aurobindo filed
                       the majority of applications and Williams &
                       Connolly managed the most cases, according to new
                       data


                # ⚓ Counsel:_EU_IP_support_schemes_for_SMEs_lack_‘winning
                  formula’ [Ed: EU promoting monopolies and propping up
                  misleading propaganda terms, then wonders why there’s
                  resistance to it (it also_covers_up_EPO_crimes)]⠀⇛


                       Seven months after the EU announced measures to
                       raise IP awareness among SMEs, sources discuss
                       their potential and where the bloc should focus
                       next


                # § Patents⠀➾


                      # ⚓ [Older]_Overview_Of_The_Costs_Of_Patent_Infringement
                        And_Patent_Nullity_Proceedings_In_Germany [Ed: The
                        financial burden should always be on monopolists, not
                        the accused parties they bully, but Germany is 'sold'
                        to the highest bidder already (and their lawyers)]⠀⇛


                             Since the beginning of 2021, a new cost
                             regime regarding the legal fees for lawyers
                             and courts applies in Germany. Roughly
                             estimated, this will lead to a fee increase
                             of 10 %. This article provides an overview.


                             Cost issues in patent infringement and patent
                             nullity proceedings


                             Unlike many other foreign legal systems,
                             Germany has a costs regime that is guided by
                             the principle that the losing party in a
                             legal dispute should bear the costs of the
                             legal dispute. As a consequence, the losing
                             party must pay both court costs and opposing
                             attorneys’ fees. There is a legal framework
                             for this with tables that show how much these
                             costs to be paid by the losing party are in
                             detail. If the party has not reached a
                             different agreement with its own attorney
                             and/or patent attorney, these statutory rules
                             may also determine which fee is to be paid to
                             these own attorneys / patent attorneys –
                             irrespective of the outcome of the
                             proceedings.


                      # ⚓ Revealing_Private_Information_in_a_Patent_Race [Ed:
                        The monopoly gold rush is good for nobody]⠀⇛


                             In this paper I investigate the role of
                             private information in a patent race. Since
                             firms often do their research in secrecy, the
                             common assumption in patent race literature
                             that firms know each other’s position in the
                             race is questionable. I analyze how the
                             dynamics of the game changes when a firm’s
                             progress is its private information, and I
                             address the question whether revealing it
                             might be to a firm’s advantage. I find that a
                             firm has an incentive to reveal its
                             breakthrough only if its rival has not done
                             so, and only if the research is costly.


                      # ⚓ IP_Waiver_for_COVID-19_Vaccines:_What_the_United
                        States’_Support_Means_in_Practice [Ed: All those patent
                        lawyers that lobby to kill millions of people just to
                        keep prices artificially high with patents dig their
                        own grave; the public opinion on the patent system is
                        rapidly shifting]⠀⇛


                             On May 5, 2021, the Biden Administration
                             announced its support for waiving
                             intellectual property protections for COVID-
                             19 vaccines. Understandably, the news made
                             headlines and stirred passionate reactions
                             from the medical community and IP holders
                             alike. But actually bringing about that
                             waiver will be a complicated process, and one
                             that depends on many countries and parties
                             besides the United States.


                             The text of the Administration’s announcement
                             shows that waiving international IP
                             protections will be easier said than done:


                             The Administration believes strongly in
                             intellectual property protections, but in
                             service of ending this pandemic, supports the
                             waiver of those protections for COVID-19
                             vaccines. We will actively participate in
                             text-based negotiations at the World Trade
                             Organization (WTO) needed to make that
                             happen. Those negotiations will take time
                             given the consensus-based nature of the
                             institution and the complexity of the issues
                             involved.


                             In other words, it is the WTO as a whole that
                             must effectuate an IP waiver. And given that
                             WTO decisions are made by unanimous agreement
                             of its 164-country membership without any
                             formal vote, that process will require far
                             more than support from the United States, as
                             dissent from any one country on the terms of
                             a waiver would block the initiative.


                      # ⚓ China’s_Supreme_People’s_Court_Rules_Utility_Model
                        Patent_Unenforceable_if_Corresponding_Invention_Patent
                        Application_Fails_to_Grants⠀⇛


                             In a decision released by the Intellectual
                             Tribunal of China’s Supreme People’s Court
                             (SPC) on July 23, 2021, the SPC explained
                             that a granted utility model patent may be
                             unenforceable when a corresponding invention
                             patent application was rejected during
                             substantive examination. The plaintiff had
                             filed both utility model and invention patent
                             applications on the same day for the same
                             invention. While the utility model granted,
                             the invention patent application was rejected
                             in substantive examination for lacking
                             novelty and inventiveness.


                      # ⚓ Tesla_discloses_Cybertruck_design_influences_in
                        fascinating_new_patent_–_Electrek⠀⇛


                             Tesla has obtained today a design patent for
                             the Cybertruck, and the patent application
                             references several interesting prior designs
                             that could have influenced Tesla’s unique
                             design.


                             Today, Tesla was granted three design patents
                             for the Model Y, Roadster, and the
                             Cybertruck.


                             The latter is interesting because it features
                             a radical design that has been controversial.


                             Some praise it, while others think it looks
                             like garbage.


                      # ⚓ Apple_hit_with_patent_infringement_lawsuit_for
                        selling_a_smart_water_bottle⠀⇛


                             An Ohio-based company is suing Apple for
                             selling smart water bottles that connect to
                             smartwatches like an Apple Watch, allegedly
                             infringing on two patents covering similar
                             technology.


                             The plaintiff in the case is non-practicing
                             entity Xennial IP LLC, which owns U.S. Patent
                             No. 7,792,409 and U.S. Patent No 10,664,571.
                             Both properties cover a “communicative sports
                             water bottle” that can connect to a smart
                             device and track health metrics like water
                             intake.


                      # ⚓ Low_level_of_judicial_activity_during_the_2021_Mobile
                        World_Congress [Ed: When tech events get hijacked by
                        patent aggressors looking for a buck by terrifying
                        people or stealing inventories]⠀⇛


                             As readers familiar with the telecoms sector
                             will be well aware, Barcelona hosts every
                             February the Mobile World Congress (“MWC”),
                             the most important international trade fair
                             in this field. Due to the pandemic, last year
                             the organizers decided to cancel the show
                             scheduled for February 2020. This year, a
                             downsized version of the MWC was held between
                             28 June and 1 July 2021.


                             To help resolve in an expeditious way
                             intellectual property disputes that may arise
                             during the MWC, 7 years ago, the Commercial
                             Judges of Barcelona decided to approve a
                             Protocol that seeks to guarantee that cases
                             are resolved within extremely short time
                             frames. This year, on 5 May 2021, the
                             Commercial Judges of Barcelona held a meeting
                             with the Commercial Judges of Alicante, who
                             have competence to hear cases dealing with EU
                             trademarks and designs, and agreed the
                             following measures: a) to give priority
                             handling of intellectual property and unfair
                             competition cases relating to products to be
                             exhibited at the fair; b) to resolve
                             preliminary injunction applications conducted
                             “ex parte” within 48 hours and those
                             conducted “inter partes” within 10 days,
                             provided that a protective letter had been
                             filed; c) to decide on the admissibility of
                             protective letters within 24 hours; d) to
                             hold hearings via remote connection; and e)
                             that the Barcelona Commercial Courts would
                             immediately enforce any preliminary
                             injunctions and/or other urgent measures
                             approved by the Alicante Commercial Courts in
                             cases involving EU trademarks and/or designs.


                      # ⚓ Promptu_Systems_Corporation_V_Sky_UK_Limited_And
                        Others,_19_July_2021,_Case_No._[2021]_EWHC_2021_(Pat)⠀⇛


                             In this decision of the Patents Court, Meade
                             J dismissed an infringement claim brought by
                             Promptu against Sky, on grounds that
                             Promptu’s patent lacked inventive step. The
                             decision is interesting as it grapples with
                             issues of infringement where some steps of a
                             claimed method are performed outside the UK.
                             The decision also provides helpful guidance
                             on the instruction of experts in cases
                             involving lengthy prior art documents.


                      # ⚓ D3O:_Making_an_Impact_in_Personal_Protective
                        Equipment [Ed: Two people were exploited by criminals
                        who engage in corruption at the EPO as a reputation-
                        laundering distraction]⠀⇛


                             D30 is an orange goo that you can wrap around
                             your hands and then, if you whack with a
                             mallet, you will notice that nothing happens
                             to your hand. The first D3O material was
                             developed by Philip Green and Richard Palmer,
                             two inventors who were finalists of the
                             European Inventor Award 2019, organized by
                             the European Patent Office (EPO).


                      # ⚓ Dusseldorf_appeals_court_narrowly_avoids_divergent
                        outcomes_in_Via_v._TCL_patent_cases_concerning_Sisvel
                        v._Haier_FRAND_defense,_deems_TCL_unwilling_either
                        way⠀⇛


                             There are two key reasons for which cases
                             with overlapping issues get consolidated in
                             the U.S. (if necessary, this may even involve
                             a venue transfer). The first one is that
                             divergent decisions are highly undesirable.
                             The second is efficiency (for the court and
                             the parties). Not so in Germany, where each
                             patent is litigated separately unless two or
                             more patents are from the same patent family.
                             Inconsistent rulings by German courts are
                             possible for another reason: judges aren’t
                             bound by precedent (no stare decisis etc.).


                             With respect to standard-essential patents
                             (SEPs), there was a period of a few months
                             during which one patent litigation division
                             of the Mannheim Regional Court–the Second
                             Civil Chamber under Presiding Judge Dr.
                             Holger Kircher–applied EU case law (Huawei v.
                             ZTE) differently from the other–the Seventh
                             Civil Chamber under Presiding Judge Dr. Peter
                             Tochtermann. I declared myself in agreement
                             with the latter, but then came the first of
                             two Sisvel v. Haier decisions by the Federal
                             Court of Justice, and Judge Kircher as well
                             as his colleagues in Munich “won.”


                      # ⚓ Webinar_Materials_–_Truly_Inventive:_Improving_the
                        Quality_of_Issued_Patents [Ed: Joe Matal moved from
                        USPTO leadership (interim) to the private sector,
                        highlighting sever issues like revolving doors]⠀⇛


                             In our latest webinar, Unified’s Chief IP
                             Counsel, Jonathan Stroud, was joined by
                             Joseph Matal, Partner at Haynes and Boone,
                             LLP, to discuss reform proposals for
                             improving the quality of issued U.S. patents.


                      # ⚓ Deadlines:_Thoughts_for_Good_and_Bad_Practices?⠀⇛


                             Over the decades (sigh) I’ve been involved in
                             various capacities in cases where
                             practitioners have missed deadlines.
                             Sometimes, the client’s partly to blame. For
                             example, imagine a client at the last minute
                             dumping a lot of information they expect to
                             be included in an application or any claim is
                             barred (say by a prior publication). At other
                             times, the lawyer misses the date. For
                             example, imagine key docketing personnel
                             leave and that leaves a knowledge gap, or an
                             unanswered email box, allowing a deadline to
                             pass by.


                             Obviously, having dual docketing systems is
                             important. Ensuring dates are entered
                             correctly is important. Ensuring that there
                             is a person responsible for the deadline,
                             likewise important. And, of course, much of
                             this is now automated.


                      # ⚓ The_benefits_of_outsourcing_patent_activities_for
                        life_science_companies_in_a_changing_IP_landscape [Ed:
                        The term "life science" is a misnomer, just like "IP";
                        the patent cartel leverages these propaganda term to
                        further an unlawful agenda]⠀⇛


                             Intellectual property is a corner stone in
                             the long-term strategy of many companies,
                             this is especially true for those in the life
                             sciences space. Covid-19 was a hammer blow to
                             the global economy and many life sciences
                             firms were forced to reconsider their
                             strategies, including with regard to
                             acquisitions, research and development, and
                             intellectual property. In 2019, biotechnology
                             and pharmaceutical companies spent $306
                             billion on IP-related activities, compared to
                             only $140 billion in 2020, a 54% decrease
                             (Lexology). Although this slump might be
                             alarming to some, with last year’s losses
                             creating over $1.4 trillion in excess funds,
                             2021 is set to be a memorable year for
                             intellectual property as the life sciences
                             sector recovers.


                      # ⚓ The_impact_of_AI_on_life_sciences_for_in-house_IP
                        teams
                         [Ed: “HEY HI” and “HI PEE”; more useless buzzwords
                        along with “life sciences” (to pretend_nature_and_life
                        are_somehow_“inventions”]⠀⇛


                             Life sciences have been tremendously impacted
                             by artificial intelligence; it could be
                             argued that life sciences companies are
                             slowly transitioning into biotech firms. As
                             the implementation of AI on inventions,
                             intellectual property teams are at crossroads
                             in terms of how to protect their inventions,
                             which range from biopharma to intelligent
                             treatments, and image recognition for
                             diagnosis just to name a few. In the
                             meantime, in-house intellectual property
                             teams can resort to either patents or trade
                             secrets.


                      # ⚓ Universities_seek_to_ease_the_technology_licensing
                        process [Ed: If taxpayers and tuition fees funded it,
                        they ought not pursue patents in the first place, let
                        alone pass these to trolls]⠀⇛


                             Fifteen prestigious universities have agreed
                             to jointly license the patents they own in
                             three physical sciences fields, aiming to
                             become a one-stop shop where large tech
                             companies can negotiate agreements to use
                             their intellectual property.


                             The University Technology Licensing Program
                             (UTLP) began operations in September 2020,
                             when the University of California’s Los
                             Angeles and Berkeley campuses signed on. They
                             were joined by Caltech and Brown, Columbia,
                             Cornell, Harvard, Northwestern, Princeton,
                             and Yale Universities along with SUNY
                             Binghamton and the Universities of Illinois,
                             Michigan, Pennsylvania, and Southern
                             California.


                      # ⚓ Kane_Biotech_Receives_Decisions_to_Grant_for_Two
                        European_Patents_Providing_Broad_Protection_of
                        coactiv+™_Technology_for_Wound_Care,_Skin_Infections
                        and_Personal_Care_Formulations [Ed: Given the awful
                        quality_of_today’s_European_Patents, this does not
                        deserve a press release]⠀⇛


                      # ⚓ Opposition_–_an_underestimated_weapon [Ed: Opposing
                        unjust monopolies isn't a weapon and justice is not a
                        war. This is a gross reversal of narratives to make
                        victims seem like aggressors.]⠀⇛


                             In the context of protecting trademark
                             rights, an opposition is an underestimated
                             tool to stop infringing activities from the
                             beginning – even before infringing products
                             and services appear on the market. The
                             negotiation leverage for an amicable solution
                             is much higher than in trademark litigation
                             and the cost risk for the trademark owner is
                             significantly lower.


                             Significant differences are seen in
                             opposition systems around the globe. This
                             chapter looks at the German, European and US
                             systems with regard to formalities,
                             proceedings, remedies, costs and recommend
                             appropriate strategies from the opponent’s
                             perspective. A good strategy and necessary
                             preparations are key to success.


                      # ⚓ How_to_manage_your_patent_portfolio [Ed: No, there is
                        no such thing as "intellectual property rights"
                        ()several different lies in that term) and monopolies
                        are not a "portfolio"; it's rather revealing who these
                        people front for...]⠀⇛


                      # ⚓ Patents_and_Drug_Availability⠀⇛


                             Amarin Pharma, Inc. v. Hikma Pharmaceuticals
                             USA Inc., Docket No. 21-02024 (Fed. Cir.
                             2021) is up on appeal again. The district
                             court found Amarin’s asserted patent claims
                             obvious and the Federal Circuit affirmed that
                             holding in a R.36 affirmance without opinion.


                             Following the Federal Circuit’s decision, an
                             ad-hoc group of doctors, patients, and Amarin
                             stock holders (collectively known as EPA Drug
                             Initiative II) moved to intervene in the
                             lawsuit and asked the court to vacate its
                             judgment based upon “multiple fatal
                             statistical errors in analyzing and
                             interpreting the prior art.”


                             [...]


                             One reason that I expect EPADI to lose is
                             that it had requested permission to file an
                             amicus brief in the original appeal as had
                             the Biotechnology Innovation Organization
                             (BIO). The Federal Circuit denied EPADI’s
                             request but permitted BIO’s.


                      # ⚓ Congratulations_Judge_O’Malley [Ed: Better than
                        Dennis Crouch's race-baiting against CAFC judges whose
                        decisions he did not like]⠀⇛


                             I’m writing about Judge O’Malley because she
                             has announced her plans to retire on March
                             11, 2022. These future-retirement
                             announcements are designed to provide
                             President Biden time to name a successor.
                             Barring other changes, this will be Biden’s
                             second nominee following Judge Cunningham’s
                             recent Senate confirmation.


                      # ⚓ Supreme_Court_Called_Again_to_Review_IPR_Appeal:_This
                        time_on_Discretionary_Denials [Ed: The war on PTAB goes
                        on, boosted by people who favour fake patents and
                        frivolous litigation]⠀⇛


                             IPR proceedings have two major decision
                             points. Institution: After IPR petition is
                             filed, the PTO Director determines whether or
                             not to institute the IPR. The statute
                             provides the director with discretionary
                             authority on whether or not to institute the
                             IPR, but does create a threshold — requiring
                             that the petition show at least “a reasonable
                             likelihood that the petitioner would
                             prevail.” 35 U.S.C. 314. Also, the PTO
                             Director has delegated their institution
                             authority to the PTAB, and so a PTAB panel
                             actually makes the decision. Final Decision:
                             If the IPR is instituted then the PTAB is
                             charged with holding a trial and reaching a
                             final decision “with respect to the
                             patentability of any patent claim
                             challenged.” On the other hand, if
                             institution is denied, the case is over and
                             no appeal is permitted. “The determination by
                             the Director whether to institute an inter
                             partes review under this section shall be
                             final and nonappealable.” 35 U.S.C. 314(d).
                             Note here that “nonappealable” has been
                             generally interpreted as ordinarily not
                             appealable. See Cuozzo Speed Technologies,
                             LLC v. Lee, 136 S. Ct. 2131 (2016) and Thryv,
                             Inc. v. Click-To-Call
                             Technologies, LP, 140 S. Ct. 1367 (2020).


                             With NHK-Fintiv, PTAB panels are able to use
                             their discretionary authority to deny
                             institution in situations involving parallel
                             litigation guided by a six-factor test that
                             generally dance around the overarching
                             question of whether “instituting a trial
                             would be an inefficient use of Board
                             resources.”


                      # ⚓ Three_recent_Utility_Decisions_at_the_PTAB [Ed:
                        Dennis Crouch is still concern-trolling_PTAB, in
                        pursuit of patent maximalist agenda (maximising
                        lawsuits). He’s sponsored by a litigation giant.]⠀⇛


                             Utility Doctrine does not get much use in
                             patent prosecution. Still, examiners do
                             reject claims on utility grounds. The
                             following are three recent PTAB decisions
                             that all reverse examiner utility rejections.
                             In Horne, focus is whether a partially-built
                             tool has any utility; In Zauderer, the
                             question is whether a theoretical rocket ship
                             design has any credible utility; and in
                             Grajcar the question focuses on whether data
                             was provided to support a sex-selection
                             method.


                             Ex parte Horne, APPEAL 2020-004000, 2021 WL
                             2788193 (2021)


                             Applicant claimed a saw blade blank without
                             cutting teeth and the examiner rejected the
                             claims as lacking utility since it was just a
                             work-in-process. On appeal, the PTAB reversed
                             — finding that creation of the blank is a
                             useful step in the blade manufacture process.
                             “Contrary to the Examiner’s suggestion, the
                             utility requirement of § 101 does not require
                             an invention to be a ‘final product’ made to
                             sell to end users.”


                             [...]


                             Grajcar’s application claims a method of sex-
                             selection of tilapia using 440-460 nm
                             wavelength light (this is blue/violet). The
                             examiner rejected the inventio as lacking
                             utility since the patentee provided no
                             experimental data proving that it actually
                             works. On appeal, the PTAB reversed — finding
                             that the specification did include a sample
                             of 12 larvae treated with 450 nm light and
                             resulted in 9 males, 1 intersex, and 2
                             female. The particular claim is directed to
                             “selecting sex”, which is seemingly more
                             general than selecting males in particular.
                             In the appeal the PTAB interpreted the claim
                             as selecting males, thus resolving the
                             dispute.


                      # ⚓ Adequate_Notice_and_the_Administrative_Procedures_Act
                        [Ed: Crouch still trying to create a rift between CAFC
                        and PTAB]⠀⇛


                             Here, the CAFC has vacated a PTAB IPR
                             decision based upon a sua sponte claim
                             construction. The court found that the agency
                             did not provide the notice and opportunity to
                             respond required by the Administrative
                             Procedures Act (APA).


                      # ⚓ Roche_Diabetes_and_WilmerHale_rebut_insulin_pump
                        infringement_claim_in_London⠀⇛


                             The UK High Court has held that an insulin
                             pump product owned by Roche Diabetes Care
                             does not infringe a patent of US medical
                             device company Insulet (case no: HP-2020-
                             000026). It also found the patent invalid for
                             added matter, obviousness and novelty.
                             Insulet launched proceedings against
                             competitor Roche in 2018, seeking an
                             injunction after the latter launched its own
                             insulin pump product.


                             An insulin pump targets type one diabetics,
                             who are typically unable to produce insulin
                             from the pancreas following a rise in blood
                             glucose concentration. Left untreated, high
                             glucose levels can lead to hyperglycaemia,
                             which can have toxic effects. Insulin pumps
                             are a relatively recent invention, with the
                             majority of diabetics using self-
                             administration injector pens at regular
                             intervals throughout the day.


                             However, the pump offers a continuous insulin
                             delivery to the patient, as well as
                             moderating insulin flows if necessary. They
                             are gaining in popularity in the UK,
                             especially among children and those with more
                             limited physical capacity.


                      # ⚓ Daimler_reloaded:_another_automotive_company_takes
                        patent_license_from_Nokia,_which_consistently_insists
                        on_end-product-level_licensing⠀⇛


                             There’s a big “See I told ya so” waiting for
                             you toward the end of this post as far as
                             patent licensing to car makers is concerned,
                             but let’s look at this news in a logical
                             sequence of steps:


                             Nokia just sent out its earnings release for
                             the second quarter (and the first half) of
                             2021. Irrespectively of how strongly I’ve
                             sometimes disagreed with their positions in
                             litigation, I always read their statements
                             and have an active subscription to their news
                             releases.


                             [...]


                             It’s not just highly unlikely but even
                             unthinkable that Nokia, despite getting its
                             way in the largest-scale and highest-profile
                             automotive SEP dispute ever, would have
                             changed course and granted an exhaustive and
                             otherwise unrestricted license to an
                             automotive supplier. The most plausible
                             scenario is that after Daimler’s defeat
                             someone else decided that hold-out was just
                             going to cost a ton of legal fees, for
                             nothing.


                             You can’t argue with success. Or, as
                             investors often say, the trend is your
                             friend.


                             If it were up to me, I’d prefer Avanci and
                             all of its members (as some do) to offer an
                             exhaustive component-level license at the
                             chipset, network access device (NAD), and
                             telecommunications control unit (TCU) level.
                             But I don’t get to decide. Marconi, the
                             company behind Avanci, can do only what its
                             members are able to agree upon. Apart from a
                             few hold-outs, car-level patent licensing is
                             now uncontroversial. It’s a fact of life.


                      # ⚓ July_2021_Developer_Updates [Ed: Squashing bogus
                        patents has become a business]⠀⇛


                             Unified’s Portal now includes Ex Parte Re-
                             examinations. Users now can find up-to-date
                             information on any given case, and search by
                             case by number, patent number, or by party.


                      # § Software Patents⠀➾


                            # ⚓ WSOU_’213_reexamination_request_granted⠀⇛


                                   On July 27, 2021, just three weeks
                                   after Unified filed an ex parte
                                   reexamination, the USPTO granted
                                   Unified’s request, finding substantial
                                   new questions of patentability on the
                                   challenged claims of U.S. Patent
                                   8,103,213. Formerly owned by the Nokia
                                   Corporation, the ‘213 patent is
                                   currently owned by WSOU Investments,
                                   LLC and has been asserted against NEC
                                   in the Western District of Texas.


                            # ⚓ Officials_Approve_World’s_First_Patent_to
                              Credit_an_AI_as_Inventor [Ed: The "hey hi" hype
                              and other nonsense as justification for patent
                              maximalists, irrespective of any actual benefits
                              to society]⠀⇛


                                   Intellectual property (IP) officials in
                                   South Africa have made history in a
                                   landmark decision to award a patent
                                   that names an artificial intelligence
                                   (AI) as the inventor.


                                   The patent—which was filed by an
                                   international team of lawyers and
                                   researchers led by the University of
                                   Surrey’s, Professor of Law and Health
                                   Sciences, Ryan Abbott —is for a food
                                   container based on fractal geometry.
                                   This container was designed and created
                                   by an AI called DABUS (“device for the
                                   autonomous bootstrapping of unified
                                   sentience”).


                                   Historically, an “inventor” of a patent
                                   had to be a human being, although the
                                   ownership of that patent is commonly
                                   given to the company that employs the
                                   inventor. While patent law in many
                                   jurisdictions is very specific in how
                                   it defines an inventor, the DABUS team
                                   is arguing that the status quo is not
                                   fit for purpose in the Fourth
                                   Industrial Revolution.


                            # ⚓ AI_Invention_Gets_Patent_In_a_World_First;_Sets
                              Precedent_for_IP_Laws_Everywhere [Ed: No, it does
                              not “Set Precedent for IP [sic] Laws Everywhere”
                              because that’s just the nature of different
                              places having different laws; and patent
                              maximalists are jubilant about another blow to
                              the credibility of a crooked system]⠀⇛


                                   In the world’s first intellectual
                                   property (IP), officials in South
                                   Africa awarded a patent to an invention
                                   made by an artificial intelligence (AI)
                                   system – creating a landmark decision
                                   that could steer the course of IP laws
                                   everywhere.


                                   The AI system did not file the
                                   groundbreaking patent, but by an
                                   international team of lawyers and
                                   researchers led by Ryan Abbott,
                                   Professor of Law and Health Sciences at
                                   the University of Surrey in England.
                                   South African IP officers awarded the
                                   patent for a food container design
                                   based on fractal geometry, the design
                                   of which was designed and developed by
                                   an AI system called DABUS, or “Device
                                   for the Autonomous Bootstrapping of
                                   Unified Sentience).


                            # ⚓ South_Africa_Issues_World’s_First_Patent_With
                              AI_Inventor [Ed: Very slippery slope in South
                              Africa]⠀⇛


                                   The patent office in South Africa on
                                   Wednesday issued the world’s first
                                   patent for an invention created by
                                   artificial intelligence, furthering a
                                   fight over recognition for such patents
                                   in other countries.


                                   The Companies and Intellectual Property
                                   Commission, an agency under the
                                   country’s Department of Trade, Industry
                                   and Competition, issued the patent to
                                   Stephen Thaler, who runs a company
                                   called Imagination Engines in Missouri
                                   and who is behind another invention,
                                   called a device for the autonomous
                                   bootstrapping of unified sentience, or
                                   DABUS.


                            # ⚓ South_Africa_issues_world’s_first_patent_naming
                              AI_as_inventor [Ed: It's not an inventor at all,
                              that's just patent maximalism at work, trying to
                              make conflicts and legal wars because they profit
                              from chaos]⠀⇛


                                   In this article written by Intellectual
                                   Property Magazine, Mathys & Squire
                                   partner Jeremy Smith provides his
                                   commentary in response to the recent
                                   news that the South African patent
                                   office (Companies and Intellectual
                                   Property Commission Department of Trade
                                   and Industry (CIPC)) has issued the
                                   world’s first patent for an invention
                                   that lists an artificial intelligence
                                   (AI) as the inventor and the AI’s owner
                                   as the owner of the patent.


                            # ⚓ Australian_Court_Rules_That_AI_Can_Be_an
                              Inventor [Ed: Even the corrupt EPO opposed
                              this]⠀⇛


                                   The overturned ruling bucks the trend
                                   we’ve previously seen in the US and UK.


                            # ⚓ Artificial_intelligence_can_now_be_recognised
                              as_an_inventor_after_historic_Australian_court
                              decision [Ed: The patent system and patent law
                              hijacked for an entirely different agenda that
                              does not reward science and innovation at all]⠀⇛


                                   In a landmark decision, an Australian
                                   court has set a groundbreaking
                                   precedent, deciding artificial
                                   intelligence (AI) systems can be
                                   legally recognised as an inventor in
                                   patent applications.


                                   That might not sound like a big deal,
                                   but it challenges a fundamental
                                   assumption in the law: that only human
                                   beings can be inventors.


                                   The AI machine called DABUS is an
                                   “artificial neural system” and its
                                   designs have set off a string of
                                   debates and court battles across the
                                   globe.


                            # ⚓ World’s_first_patent_for_AI-generated_invention
                              could_have_repercussions_on_intellectual_property
                              law [Ed: Patent law bordering on the laughable
                              now. It has nothing whatsoever to do with the
                              original purpose of the law.]⠀⇛


                                   The patent—which was filed by an
                                   international team of lawyers and
                                   researchers led by the University of
                                   Surrey’s, Professor of Law and Health
                                   Sciences, Ryan Abbott —is for a food
                                   container based on fractal geometry.
                                   This container was designed and created
                                   by an AI called DABUS (“device for the
                                   autonomous bootstrapping of unified
                                   sentience”).


                                   Historically, an “inventor” of a patent
                                   had to be a human being, although the
                                   ownership of that patent is commonly
                                   given to the company that employs the
                                   inventor. While patent law in many
                                   jurisdictions is very specific in how
                                   it defines an inventor, the DABUS team
                                   is arguing that the status quo is not
                                   fit for purpose in the Fourth
                                   Industrial Revolution.


                # § Trademarks⠀➾


                      # ⚓ Trademark_on_Product_Design:_Are_these_biscuit_sticks
                        functional⠀⇛


                             A potentially important product design
                             trademark case is pending before the U.S.
                             Supreme Court involving those chocolate
                             covered bready-sticks. Ezaki Glico Kabushiki
                             Kaisha v. Lotte International America Corp.,
                             Docket No. 20-1817 (Supreme Court 2021).


                             Glico’s Pocky product has been sold since
                             1966 and are apparently popular. Lotte’s
                             Pepero’s are a knock-off version. Glico sued
                             for trademark infringement, asserting Glico’s
                             trademark rights in the product design of
                             chocolate-covered elongated rod biscuits.
                             Glico registered this particular mark back in
                             1989. Reg. No. 1,527,208.


                      # ⚓ Trademarks_“Eco-friendly”_What’s_New_in_Poland?⠀⇛


                             Recent research indicates that the eco-
                             cosmetics segment in Poland grew by 39%
                             between July 2019 and June 2020 while the
                             product range of this product group grew by
                             almost 50% over the year. Despite the
                             pandemic, the market for organic food also
                             grew by about 20%, i.e. 3.5 times more than
                             the average for the entire food basket. The
                             media and the advertising industry have to
                             keep up with the change in consumer
                             behaviour. Eco-campaigns, apart from the
                             products themselves, additionally refer to
                             values such as care for the environment,
                             ecology or healthy lifestyle. The opposite of
                             natural media is the so-called
                             “greenwashing”, which is unjustified building
                             of an ecological image and misleading
                             consumers about the origin or characteristics
                             of products.


                             [...]


                             On January 1st, 2022, the new Regulation
                             2018/848 of the European Parliament and of
                             the Council will come into force, which will
                             apply in the European Union, including
                             Poland. It will also affect the amendment of
                             the Polish Organic Farming Act. The
                             regulation defines the rules regarding
                             organic production and the related
                             certification, the use of labels referring to
                             organic production such as BIO (biological)
                             and EKO (ecological) in labelling and
                             advertising materials.


                      # ⚓ Sky_v_SkyKick:_door_open_for_broad_brands,_but
                        caution_remains [Ed: Lawyers or litigation people won't
                        mind if you claim to "own" the Sky, too]⠀⇛


                             Counsel say broad trademark specifications
                             are back on the cards but that brands should
                             still be cautious


                      # ⚓ This_week_in_IP:_SkyKick_opens_door_for_brands,_IP
                        ‘heart’_of_UK_innovation,_InterDigital_beats_Lenovo⠀⇛


                             In-house and private practice sources say the
                             latest ruling in Sky v SkyKick, which limits
                             the ability to invalidate broad trademarks
                             based on bad faith, accounts for the
                             difficulty brands face when trying to predict
                             future product launches.


                             In a decision handed down on Monday, July 26,
                             the England and Wales Court of Appeal
                             reversed a High Court decision that had said
                             some trademark specifications of media
                             company Sky were too broad and had been filed
                             in bad faith.


                             However, the finding that cloud management
                             company SkyKick infringed Sky’s trademarks
                             still stands, as does the High Court’s
                             rejection of Sky’s passing off claims.


                      # ⚓ Trademark_surge_at_USPTO_stifles_Madrid_and_pharma
                        filers [Ed: China turning a broken system against
                        itself, first in patents and now in trademarks. Get
                        popcorn.]⠀⇛


                             The 63% increase in filings, largely being
                             driven by Chinese applicants, has forced
                             brand owners to double down on organisation
                             and due diligence


                      # ⚓ Around_the_IP_Blogs⠀⇛


                             The Fashion Law Blog published a follow-up
                             concerning the Puma vs Nike battle over
                             Nike’s trade mark application for ‘footware’.
                             After having opposed the Nike’s application
                             in the US for being generic and descriptive,
                             Puma has now withdrawn its opposition. Nike’s
                             application for registration is also pending
                             in several other countries, including Canada,
                             Australia, and India.


                             [...]


                             The recent decision of the German
                             Constitutional Court concerning the
                             constitutionality of the UPC has attracted
                             wide commentary in the the patent blogosphere
                             [see, e.g., IPKat posts here and earlier
                             here]. Juve Patent has now featured an
                             opinion piece concerning the (uncertain)
                             future of the UPC.


                      # ⚓ Puma_Has_Withdrawn_its_Opposition_in_U.S._Fight_Over
                        Nike’s_“Footware”_Trademark⠀⇛


                             Puma and Nike appear as though they may have
                             come to a resolution in their battle over
                             “footware,” the trademark that Nike has been
                             angling to register in the U.S. and beyond.
                             On the heels of a win for Nike in May when a
                             court in the United Kingdom dismissed Puma’s
                             appeal (after a UK Intellectual Property
                             Office hearing officer rejected its bid to
                             block the registration of Nike’s mark),
                             thereby, paving the way for Nike’s
                             application for the “footware” mark to
                             proceed in the registration process, counsel
                             for Puma alerted a domestic trademark body
                             that it was withdrawing its challenge against
                             Nike’s “footware” mark in the U.S.


                             [...]


                             In addition to its genericness claim, Puma
                             argued that Nike’s mark is also ineligible
                             for registration because the Nike is far from
                             the only party in the business of selling
                             products that “combine footwear, hardware
                             and/or software technologies.” In fact, Puma
                             claims that it started “manufacturing and
                             selling footwear incorporating computer
                             technology at least as early as 1986,” while
                             other companies, such as Under Armour, Altra,
                             and Samsung, are similarly offering up tech-
                             centric footwear products.


                      # ⚓ OK._Everyone_knows_MESSI._But_Miley_Cyrus?⠀⇛


                             The CJEU’s conclusion may or may not be
                             factually (and legally) correct, but given
                             the worldwide attention to soccer and soccer
                             players perhaps it may be a plausible
                             “inference” and justifies a finding that
                             MESSI and MASSI are not confusingly similar.
                             Yet, it really seemed an exceptional
                             decision, quite unlikely to be extended or
                             applied to other cases, especially for
                             identical names.


                             Well, we were all wrong. Because, of course,
                             with the decision T‑368/20 of 16 June 2021,
                             the General Court set the same standard for
                             Ronaldo’s own trademark.


                             NOT!!!!!!!!!!!!!


                             Case T‑368/20 did not deal with Ronaldo, but
                             rather with Ms Miley Cyrus, who may perhaps
                             be a talented musician, but certainly is
                             neither Messi, nor Ronaldo.


                             In short, MILEY CYRUS was filed for various
                             goods and services in classes lasses 9, 16,
                             28 and 41 and got an opposition based on a
                             stylized mark CYRUS in classes 20 and 41.


                             [...]


                             As also (and regrettably in vain) argued by
                             EUIPO, since neither ‘miley’ nor ‘cyrus’ is a
                             common first name or surname, this implies
                             that the relevant public who will identify
                             the mark applied for, MILEY CYRUS, as
                             referring to a famous singer, is also likely
                             to perceive the surname alone as the short
                             version of the full name, thus identifying
                             the same person, i.e. a classic case of
                             reverse confusion.


                             The refence to the earlier BARBARA BECKER
                             judgment (C-51/09 P) in para. 33 of the MILEY
                             CIRUS judgment is unconvincing, precisely
                             because “Becker” is an extremely common last
                             name, while “Cyrus” clearly isn’t.


                # § Copyrights⠀➾


                      # ⚓ Austrian_Supreme_Court_refers_further_questions_for_a
                        preliminary_ruling_on_the_InfoSoc_Directive⠀⇛


                             The first case (4 Ob 40/21t – in German)
                             relates to the operation of an online video
                             recording device. The defendant was offering
                             an internet protocol television (“IPTV”)
                             service to business clients (e.g., network
                             operators, hotels and stadiums). The IPTV
                             service included two relevant features: (1)
                             an online videorecorder allowing the clients’
                             customers to record individual programs; and
                             (2) a replay function allowing the customers
                             to watch television programs for up to seven
                             days on demand, if they chose to activate
                             this function for an individual television
                             channel. The IPTV service included TV
                             programs created and broadcasted by the
                             Claimant.


                             [...]


                             The first question seeks to distinguish this
                             case from C-265/16 VCAST/RTI (Katpost here)
                             and the second question from C-527/15
                             Stichting Brein (Filmspeler) (Katpost here).
                             After legal analysis, the referring court
                             indicated that it is inclined to find in
                             favor of the copyright holder on both
                             questions (ie, that the operation of the
                             online video recorder constitutes a
                             communication to the public and thus
                             copyright infringement under the InfoSoc
                             Directive). However, the court was of the
                             view that the case law lacks sufficient
                             clarity to enable it to answer the questions
                             without referral to the CJEU.


                             The second case (4 Ob 44/21f – in German)
                             relates to an online streaming platform aimed
                             at émigrés from the territory of former
                             Yugoslavia. The defendant operated the
                             platform based on license agreements with TV
                             channel operators. Under these agreements,
                             the defendant was obliged to block the
                             streaming signal for certain shows in certain
                             territories. The claimant is the owner of the
                             copyright in several TV shows broadcast on
                             the relevant TV channels. It claims that
                             circumventing the defendant’s geo-blocking
                             measures is relatively easy, the defendant is
                             aware of customers using its service outside
                             the licensed territory, and it fails to
                             prevent such illicit use.



                    ䷩ 𝚕𝚒𝚗𝚎 6341

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✐ Links_2/8/2021:_Open_Science_in_France_and_Zoom_Pays_to_Settle_Privacy
Violations⠀✐


Posted in News_Roundup at 9:04 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o § Games⠀➾


                # ⚓ Orbiter_Space_Flight_Simulator_goes_open_source_|
                  GamingOnLinux⠀⇛


                       Orbiter Space Flight Simulator is a classic
                       comprehensive 3D space flight simulator and the
                       developer has recently made it open source as
                       they’ve haven’t had enough time for it.


                       Worth noting that currently it only supports
                       Windows, and it’s a little on the older side with
                       it using DirectX 7. However, since it’s now open
                       source under the MIT license, this gives it a much
                       better chance of seeing more developers come along
                       to potential upgrade it and bring it to more
                       platforms like we’ve seen happen to other projects.
                       There’s already some options being talked about to
                       make it more cross-platform friendly.


                # ⚓ Iron_Gate_tease_more_of_what’s_coming_to_Valheim_in_Hearth
                  &_Home_|_GamingOnLinux⠀⇛


                       Sounds like development on the co-op survival game
                       Valheim is progressing well, with the first major
                       upgrade Hearth & Home currently on schedule for
                       release this quarter. Hopefully then we will see
                       Hearth & Home before the end of September, if all
                       continues going well.


                       [...]


                       This is in addition to what they already announced
                       previously including: darkwood roofs and window
                       hatches; new cooking station extensions like a
                       spice rack, butcher table, pots and pans; tweaks to
                       how stamina and health affect combat to allow for
                       more playstyles; a bunch of new foods like
                       Eyescream, Shocklate smoothie, various wolf meats,
                       and more plus onions you can plant.


                # ⚓ Top_16_Best_Android_Games_Under_20_MB_For_2021_(Download)⠀⇛


                       Many games are available on the Google Playstore
                       but finding the perfect small size game with good
                       graphics and best stress reliever is not that easy
                       as it seems oh and action genre too! Follow through
                       as we have listed 16 best Android games under 20 MB
                       that you can download and play.


                # ⚓ Space_sandbox_game_Avorion_has_a_huge_2.0_Beta_available
                  now⠀⇛


                       Avorion is a single-player or online co-op space
                       survival sandbox game, one where you construct your
                       ships with individual blocks and go explore the
                       galaxy. It’s fantastic and is rated highly by users
                       too and now they’re getting close to a big free
                       update with the 2.0 Beta.


                       The list of what’s new and improved is a long one.
                       There’s a whole new progression system, which they
                       say is designed to challenge you. “The new
                       progression is meant to challenge you on your way
                       to the center of the galaxy. Players will be
                       required to prove themselves in a new area before
                       they can get their hands on the new building
                       knowledge. But if you don’t like that, you can just
                       go for Avorion Classic!”.


                # ⚓ Valve_talk_about_learning_from_mistakes_with_the_upcoming
                  Steam_Deck_|_GamingOnLinux⠀⇛


                       As we all know the Steam Machines didn’t go
                       anywhere and Valve have clearly learned a lot from
                       it, as they spoke about in a recent video from IGN
                       (as IGN continue to have the exclusives on this).


                       Valve are no stranger to hardware at this point of
                       course. They didn’t just do the failed Steam
                       Machines but also produced the Steam Link, Steam
                       Controller, worked with HTC for the original Vive
                       and they also have their Valve Index VR headset
                       too. By now, they have hopefully enough experience
                       to know exactly what they need to make a success
                       out of the Steam Deck and so far everything is
                       looking rather positive on that.


                       Designer Greg Coomer actually mentioned how “we
                       actually did start out by working with other
                       companies and seeing what we could make happen with
                       partnerships, but it became clear we started
                       prototyping and more and more we just started
                       creating devices to solve problems for customers
                       ourselves and really the Steam Deck feels like the
                       culmination of a lot of that earlier work”. Coomer
                       goes on to directly mention their earlier stuff
                       like the Steam Machines, Steam Link and also the
                       Steam Controller.


                # ⚓ Steam_Survey:_Linux_Gaming_Market_Share_Climbs_to_1%_For
                  First_Time_in_Years⠀⇛


                       Valve has today published its monthly update for
                       Steam Hardware Survey, with an update for July.
                       Besides the regular fluctuations in the market
                       share of CPU and GPU vendors, there is another
                       interesting change slowly happening. According to
                       the newest data from the survey, gaming on Linux
                       has climbed to 1.0% for the first time in years.


                       Back in 2018, Valve introduced Proton, a technology
                       that translates Windows-specific API calls to Linux
                       equivalents, enabling thousands of Linux gamers to
                       play the games that they wanted to, but were unable
                       because they weren’t using Windows OS.


                       At the same time, many Linux gamers were trying out
                       the Proton software and the market share of Linux
                       gamers managed to climb to around 2% of a much
                       smaller Steam customer base. However, after this
                       testing period ended, only 0.8-0.9% of gamers were
                       still using Linux distros, and the percentages
                       stayed within that range for some time.


                # ⚓ Lutris_game_manager_0.5.9-beta1_is_out_adding_Epic_Games
                  Store_support⠀⇛


                       It’s been a while since we had a new major release
                       of Lutris, the free and open source game manager
                       that allows you to bundle together all of your
                       games in a single application.


                       Now available as a Beta, Lutris 0.5.9 is the
                       biggest release for some time and adds in initial
                       support for downloading and running games from the
                       Epic Games Store. Much like the Heroic Games
                       Launcher, since Epic don’t support Linux all
                       downloads will be Windows versions you need to then
                       run through a compatibility layer (but Lutris sorts
                       that for you).


                # ⚓ Linux_has_finally_hit_that_almost_mythical_1%_user_share_on
                  Steam_again⠀⇛


                       The day I’m sure many have been waiting for, and
                       just as many probably thought it wouldn’t happen.
                       Linux has finally hit 1% again on the Steam
                       Hardware Survey.


                       Not the first time, in fact years ago when Steam
                       for Linux was pretty fresh we actually saw it
                       remain over 1% for a while. That didn’t last long
                       though, and it’s been bouncing around at sub 1% for
                       multiple years now as we’ve been showing on our
                       dedicated Steam Tracker.


          o § Distributions⠀➾


                # § IBM/Red Hat/Fedora⠀➾


                      # ⚓ Next_Open_NeuroFedora_meeting:_02_August_1300_UTC⠀⇛


                             Please join us at the next regular Open
                             NeuroFedora team meeting on Monday 02 August
                             at 1300UTC in #fedora-neuro on IRC
                             (Libera.chat). The meeting is a public
                             meeting, and open for everyone to attend. You
                             can join us over…


                      # ⚓ Use_OpenCV_on_Fedora_Linux_‒_part_1⠀⇛


                             The technology world changes daily and the
                             demands for computer vision, artificial
                             intelligence, and machine learning are
                             increasing. The technology that allows
                             computers and mobile phones to see their
                             surroundings is called computer vision. Work
                             on re-creating a human eye started in the
                             50s. Since then, computer vision technology
                             has come a long way. Computer vision has
                             already made its way to our mobile phones via
                             different applications. This article will
                             introduce OpenCV on Fedora Linux.


                      # ⚓ How_to_Set_Up_Postfix_SMTP_Relay_on_CentOS/Rocky
                        Linux_with_Sendinblue⠀⇛


                             This tutorial is going to show you how to set
                             up Postfix SMTP relay with Sendinblue on
                             CentOS/Rocky Linux. Postfix is a popular
                             open-source SMTP server. Previously I wrote
                             an article on how to easily set up a full-
                             blown email server on CentOS/Rocky Linux with
                             iRedMail, which helped a lot of readers run
                             their own email servers.


                             However, some readers told me that port 25 is
                             blocked by hosting provider/ISP as a way to
                             control email spam, so they couldn’t send
                             emails. Vultr would unblock port 25 if you
                             ask them to, and ScalaHosting doesn’t block
                             port 25 at all, so I recommend using
                             ScalaHosting VPS. Some other hosting
                             providers/ISPs like DigitalOcean would refuse
                             to unblock port 25.


                      # ⚓ In_The_API_World,_Nobody_Knows_You_Are_An_IBM_i_–_IT
                        Jungle⠀⇛


                             One of the earliest memes of the early years
                             of the commercial Internet was captured in a
                             famous cartoon in The New Yorker magazine
                             penned by Peter Steiner and showing a dog at
                             a computer, which quipped: “On the Internet,
                             nobody knows you’re a dog.”


                             Somewhere back in the archive – it was in
                             September 1997, which is not online because
                             we were a paper, subscription publication for
                             the first seven years of The Four Hundred –
                             we did a riff on this meme with a lead essay
                             called, On The Net, No One Knows You Are An
                             AS/400. This was when IBM has doing its big
                             e-commerce push and the WebSphere variant of
                             the Apache Web server was not yet dominant
                             and Netscape Communications, the big dog in
                             Internet infrastructure servers, was getting
                             ready to port its codes from Unix to OS/400.
                             Netscape came and went, as did I/NET and a
                             few other providers, and WebSphere came to
                             dominate, as often happens when a vendor
                             sells an integrated stack of technology.


                             Fast forward to 2021, and the world has
                             learned from the hyperscalers such as Google
                             and Facebook and Microsoft and Amazon to
                             think not in terms of Internet protocols and
                             services, but rather at an abstraction layer
                             one notch higher but still below the
                             applications themselves, called appropriately
                             enough the application programming interface,
                             or API, layer. Now, APIs are how programs are
                             stitched together and how infrastructure
                             itself is controlled. So, as we say in the
                             title of this essay, nearly three decades
                             after that meme in the The New Yorker: In a
                             world dominated by APIs, no one knows – or
                             cares or needs to care – if you are an IBM i
                             platform.


                      # ⚓ No_More_Shouting_The_Name_“Power”_(Well,_Except_In
                        Our_Title_Here)_–_IT_Jungle⠀⇛


                             The marketing people at IBM have been at work
                             again, apparently, and it looks like there
                             will be some subtle branding changes coming
                             with the launch of Power10-based servers
                             later this year, very likely by September or
                             maybe October.


                             One of my pet peeves about the IT industry is
                             that vendors sometimes feel compelled to
                             shout their company names or product brands
                             when it is completely unnecessary. They seem
                             to choose a brand and then work backwards to
                             come up with some abbreviation that they
                             think is clever. It’s when they overreach
                             that it gets annoying, and language is my
                             thing so I get to have this pet peeve.


                             The Stanford University Network Microsystems
                             company, for instance, was SUN Microsystems,
                             and its Scalable Processor Architecture was
                             shouted out at SPARC. These are not
                             particularly useful acronyms, and thank
                             heavens SUN didn’t call its Unix operating
                             system SOLARIS, with some preposterous
                             meaning backcast on it like SUN Operating
                             Linux Ain’t Real In Systems or even though of
                             yet, since Linux Torvalds had only just
                             started quietly working on it in 1991 for his
                             PC and Solaris came out in 1992, seven years
                             after SUN had started off in the workstation
                             business using its own SunOS and then merged
                             it with the AT&T System V Unix, both of which
                             were variants of the open source Berkeley
                             Software Distribution, or BSD, of Unix. Why
                             shout some things and not the other?


                             Why shout at all? Hewlett Packard (Enterprise
                             was not yet its core and sole focus) didn’t
                             shout for the sake of shouting, but it had a
                             real acronym that meant something when it
                             launched its Precision Architecture Reduced
                             Instruction Set Computing (PA-RISC)
                             processors for minicomputers running its HP-
                             UX Unix variant and then eventually the HP-
                             3000, which competed with System/3X and then
                             AS/400 iron, had its Multi-Programming
                             Executive, or MPE, operating system ported to
                             these machines. (It never did make the jump
                             to Itanium, as HP’s HP-UX, OpenVMS, and
                             NonStop platforms did. Also, they have all
                             stopped years ago.)


          o § Devices/Embedded⠀➾


                # ⚓ Jupiter_Nano_ARM_based_mini_PC_can_run_NuttX_RTOS_or
                  Linux⠀⇛


                       If you have been patiently waiting for the
                       previously announced Jupiter Nano mini PC and
                       development board capable of running NuttX RTOS or
                       Linux to launch. You will be pleased to know it is
                       now available via the Crowd Supply website offering
                       a high performance ARM based mini computer
                       measuring just 2.86 x 6.35 cm in size. prices start
                       from $65 and worldwide shipping is expected take
                       place sometime during December 2021. Free shipping
                       is provided throughout the United States and
                       worldwide shipping is available for $10.


                # ⚓ Seeed_Dual_Gigabit_Ethernet_Carrier_Board_for_Raspberry_Pi
                  Compute_Module_4_Review:_Serving_Your_Needs⠀⇛


                       When the Raspberry Pi Compute Module 4 was released
                       in late 2020, we knew that it was destined for
                       embedded server projects. The official Compute
                       Module IO board has all of the connections, but the
                       awkward form factor shows that it was never meant
                       to be used in a project. For project use, we need
                       bespoke carrier boards which break out the required
                       connections.


                       Seeed’s Dual Gigabit Ethernet Carrier Board is
                       compatible with all Raspberry Pi Compute Module 4
                       boards and is designed to create network devices,
                       file server and software router applications. The
                       inclusion of USB 3.0 is a sweetener for those of us
                       eager to create low power, large storage devices
                       based on the Raspberry Pi.


                # ⚓ Fenix_Linux_Streams_YouTube_Fullscreen_on_Raspberry_Pi_4⠀⇛


                       The Raspberry Pi 4 is an excellent little computer,
                       but even its biggest fan would have to admit that
                       it’s not very good at streaming fullscreen videos
                       from YouTube. There are some things you can do to
                       improve its performance, but Fenix Pi Mk1 Plasma, a
                       lighter Linux distribution based on the Raspberry
                       Pi OS and running KDE, aims to fix it for good.


                       The Spanish creator behind Fenix is so into Linux
                       that Chrome’s mouse pointer gains a little Tux
                       penguin when you access the website. As seen in the
                       video from leepspvideo embedded above, it’s able to
                       play a fullscreen 1080p video from YouTube with
                       very few dropped frames on an 8GB Raspberry Pi 4
                       that hasn’t been overclocked. Looking at the video
                       we can see that Fenix Pi is based upon Raspberry Pi
                       OS, which means that installing software and using
                       the GPIO, camera, etc should be a piece of cake, or
                       is that Pi? The OS is also installable to a USB SSD
                       / flash drive making it a good all purpose Pi
                       distro.


                # § Mobile Systems/Mobile Applications⠀➾


                      # ⚓ Google_Play_puts_Android_apps_on_notice:_No_naughty
                        JavaScript,_Python,_Lua_•_The_Register⠀⇛


                      # ⚓ Check_Which_Apps_on_Android_Have_your_Google_Account
                        access_–_H2S_Media⠀⇛


                      # ⚓ google:_Google_won’t_let_users_sign_in_on_old_Android
                        devices_from_Sep_27,_IT_News,_ET_CIO⠀⇛


                      # ⚓ iTWire_–_Google_Play_Protect_detects_only_31%_of
                        Android_stalkerware⠀⇛


                      # ⚓ A_new_Android_app_might_tempt_iPhone_users_to_switch
                        |_Express.co.uk⠀⇛


                      # ⚓ Africa:_Key_African_Broadcasters_Increase_Their
                        YouTube_Footprint_but_Android_App_Numbers_Drop_Away_–
                        Individual_Talent_Develops_Own_Channels_–
                        allAfrica.com⠀⇛


                      # ⚓ Samsung_Galaxy_A11_review:_A_solid_starter_smartphone
                        –_Android_Authority⠀⇛


                      # ⚓ Realme_MagDart_may_bring_66W_magnetic_charging_to
                        Android,_much_higher_than_Apple’s_15W_MagSafe_–
                        Technology_News⠀⇛


                      # ⚓ Monday:_TSMC_contamination,_password_grab,_Android
                        Trojans_&_home_office_rules_–_Market_Research
                        Telecast⠀⇛


                      # ⚓ A_new_banking_virus_has_infected_thousands_of_Android
                        smartphones_and_steals_money⠀⇛


                      # ⚓ [Update:_Aug._02]_Xiaomi_Android_11_update_bugs_&
                        issues_tracker:_Here’s_the_current_status⠀⇛


                      # ⚓ Xiaomi_Android_11_update_tracker:_Mi_&_Redmi_devices
                        received_beta/stable⠀⇛


                      # ⚓ Xbox_Game_Pass_Update_Suggests_It_Might_Be_Heading_to
                        Android_TV_Soon_–_MySmartPrice⠀⇛


                      # ⚓ Snapchat_Dark_mode_for_Android_phones:_Here’s_how_to
                        get_the_feature⠀⇛


                      # ⚓ Bush_/_Alba_/_Argos_10Nou_10″_Android_Tablet
                        replacement_battery_–_Android_OS⠀⇛


                      # ⚓ Best_Android_Emulator_to_play_Ragnarok_X_on_PC_|
                        TechBullion⠀⇛


                      # ⚓ Turkish_taxis_drivers_get_contactless_payments
                        acceptance_on_NFC_Android_phones_•_NFCW⠀⇛


                      # ⚓ Poll:_Do_you_use_custom_ROMs_on_your_Android
                        devices?⠀⇛


                      # ⚓ Android-powered_Nokia_400_feature_phone_reappears
                        online⠀⇛


                      # ⚓ Infinix_Smart_5A_With_Dual_Rear_Cameras,_Android_11_
                        (Go_Edition)_Launched_in_India:_Price,_Specifications_|
                        Technology_News⠀⇛


                      # ⚓ Steps_to_change_Android_interface_color_12⠀⇛


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


                # § Programming/Development⠀➾


                      # ⚓ Fortran_newsletter:_August_2021⠀⇛


                             Welcome to the August 2021 edition of the
                             monthly Fortran newsletter. The newsletter
                             comes out at the beginning of every month and
                             details Fortran news from the previous month.


    * § Leftovers⠀➾


          o ⚓ Rebirth_of_a_Nation:_US_History_According_to_DW_Griffith⠀⇛


          o § Science⠀➾


                # ⚓ France_recognises_open_source_in_its_National_Plan_for_Open
                  Science_2021-2024_Permalink⠀⇛


                       The French Ministry of Research shared its Second
                       National Plan for Open Science for the years 2021-
                       2024 on 6 July. The Plan foresees several
                       initiatives aimed at increasing the reach of open
                       science principles, and, for the first time,
                       includes open source as a critical component of
                       scientific research that needs to be recognised and
                       supported.


                # ⚓ Second_National_Plan_for_Open_Science:_Generalising_open
                  science_in_France:_2021-2024⠀⇛


                       This second National Plan extends the scope to
                       include source code from research, structures
                       actions promoting data sharing and openness through
                       the creation of the Recherche Data Gouv (Gov Data
                       Research) platform, increases the number of
                       transformative levers available to generalise the
                       practice of open science and is divided up into
                       different disciplines and themes. It is firmly
                       attached to a European-wide vision and, in the
                       context of the French presidency of the European
                       Union, proposes to act in favour of open science
                       being effectively taken into account in both
                       individual and collective assessments for research.
                       This involves initiating a process of sustainable
                       transformation in order to ensure that open science
                       becomes a common and shared practice, encouraged by
                       the whole international ecosystem of higher
                       education, research and innovation.


          o § Hardware⠀➾


                # ⚓ Will_Nvidia’s_huge_bet_on_artificial-intelligence_chips_pay
                  off?⠀⇛


                       Now Mr Huang wants to make it broader and deeper
                       still. In September Nvidia confirmed rumours that
                       it was buying Arm, a Britain-based firm that
                       designs zippy and energy-efficient chips for most
                       of the world’s smartphones, for $40bn. The idea is
                       to use Arm’s design prowess to engineer central
                       processing units (CPUs) for data centres and AI
                       uses that would complement Nvidia’s existing
                       strength in specialised chips known as graphics-
                       processing units (GPUs). Given the global reach of
                       Arm and Nvidia, regulators in America, Britain,
                       China and the European Union must all approve the
                       deal. If they do—a considerable “if”, given both
                       firms’ market power in their respective
                       domains—Nvidia’s position in one of computing’s
                       hottest fields would look near-unassailable.


          o § Integrity/Availability⠀➾


                # § Proprietary⠀➾


                      # ⚓ Ransomware_attacks_hit_record_300_mn_in_1st_half_of
                        2021:_Report [iophk: Windows TCO]⠀⇛


                             Ransomware attacks globally surged in the
                             first half of 2021, with 304.7 million,
                             surpassing 2020′s full-year total (304.6
                             million), says a new report.


                             After posting record highs in both April and
                             May, cybersecurity firm SonicWall recorded
                             another new high of 78.4 million ransomware
                             attacks in June 2021 alone.


                             The ransomware showed massive year-to-date
                             spikes in the US (185 per cent) and the UK
                             (144 per cent).


                      # § Security⠀➾


                            # § Privacy/Surveillance⠀➾


                                  # ⚓ Elite_students_are_debating_hot-button
                                    issues_on_an_invite-only_TikTok_clone⠀⇛


                                         This is Polemix, a new, exclusive
                                         app aimed at promoting free
                                         discourse among young people. As
                                         the world’s biggest social
                                         networks continuously battle
                                         misinformation and draw
                                         controversial lines between
                                         dangerous and appropriate speech,
                                         the founders of Polemix believe
                                         they’ve found a better solution:
                                         a free market of ideas, with
                                         selective admission. So far, the
                                         app has attracted a young
                                         community that’s eloquent,
                                         outspoken, and passionate about
                                         the app’s stated philosophy. But
                                         it has also served as a
                                         microcosmic experiment with
                                         online debate culture in
                                         concentrated form, and a real-
                                         world demonstration of the
                                         caveats required to bring such a
                                         lofty ideal to life.


                                  # ⚓ FB_developing_AI,_new_ways_to_detect
                                    users_under_age_13⠀⇛


                                         Admitting that it is not easy to
                                         detect and remove accounts
                                         belonging to people under the age
                                         of 13, Facebook has said that it
                                         is looking at ways to convince
                                         people under age 13 to not lie
                                         about their age, including using
                                         the artificial intelligence (AI)
                                         technology.


                                  # ⚓ Zoom_settles_user_privacy_case_for_$85M⠀⇛


                                         The case alleges that the
                                         teleconferencing software program
                                         was sharing personal data with
                                         various social media platforms,
                                         including Facebook and LinkedIn,
                                         and was allowing “Zoombombing,”
                                         where hackers would disrupt
                                         meetings by sharing pornographic
                                         images and racial slurs.


                                         A preliminary settlement, which
                                         still requires approval from a
                                         judge, was filed on Saturday.


                                  # ⚓ Zoom_reaches_$85_mln_settlement_over_user
                                    privacy,_‘Zoombombing’⠀⇛


                                         Subscribers in the proposed class
                                         action would be eligible for 15%
                                         refunds on their core
                                         subscriptions or $25, whichever
                                         is larger, while others could
                                         receive up to $15.


                                         Zoom agreed to security measures
                                         including alerting users when
                                         meeting hosts or other
                                         participants use third-party apps
                                         in meetings, and to provide
                                         specialized training to employees
                                         on privacy and data handling.


                                         The San Jose-based company denied
                                         wrongdoing in agreeing to settle.


                                  # ⚓ Zoom_Settles_Consumer_Claims_Over_Privacy
                                    for_$85_Million⠀⇛


                                  # ⚓ AI_Log_Analytics_Startup_Coralogix_Closes
                                    $55M_Funding_Round⠀⇛


                                         Israeli startup Coralogix, a
                                         company that develops advanced
                                         machine learning log analytics,
                                         announced on Thursday that it
                                         raised $55 million in a Series C
                                         funding round led by Israeli VC
                                         firm Greenfield Partners, with
                                         participation from Red Dot
                                         Capital Partners, StageOne
                                         Ventures, Eyal Ofer’s O.G. Tech,
                                         Janvest Capital Partners, Maor
                                         Investments, and 2B Angels.


                                         The investment brings the
                                         company’s total amount raised to
                                         $96 million.


                                         Founded in 2015, Coralogix built
                                         a platform, Streama, that helps
                                         engineering teams manage their
                                         log data and provides them with
                                         automatic insights while reducing
                                         cost. The solution processes
                                         millions of log file records and
                                         gives monitoring, visualization,
                                         and alerting capabilities with no
                                         reliance on storage or indexing,
                                         solving the challenge of data
                                         growth in large-scale systems.


          o § Defence/Aggression⠀➾


                # ⚓ Opinion_|_George_W._Bush_Should_Shut_Up_and_Go_Away⠀⇛


                       By now, George W Bush should have completed volumes
                       one and two of his prison letters.


                # ⚓ We_Don’t_Need_to_Wait_for_Centuries_to_Build_a_Better
                  World⠀⇛


                       If the above were true, then there would have been
                       no revolutions in history. That is quite obviously
                       not the case. Consciousness can change rapidly. It
                       does so exceptionally and under rare circumstances
                       during periods of social upheaval. Yes, not
                       everyday occurrences. But they do happen. “There
                       are decades where nothing happens, and there are
                       weeks where decades happen,” Lenin famously said.
                       To read this article, log in or or Subscribe. In
                       order to read CP+ articles, your web browser must
                       be set to accept cookies.


                # ⚓ Burkina_Faso_sees_more_child_soldiers_as_jihadi_attacks
                  rise⠀⇛


                       She and her family are among the lucky ones who
                       survived the June attack, in which about 160 people
                       were killed — the deadliest such assault since the
                       once-peaceful West African nation was overrun by
                       fighters linked to al-Qaida and the Islamic State
                       about five years ago. As that violence increases,
                       so too does the recruitment of child soldiers.


                       The number of children recruited by armed groups in
                       Burkina Faso rose at least five-fold so far this
                       year, up from four documented cases in all of last
                       year, according to information seen by the AP in an
                       unpublished report by international aid and
                       conflict experts.


          o § Environment⠀➾


                # § Energy⠀➾


                      # ⚓ Forgotten_oil_and_gas_wells_linger,_leaking_toxic
                        chemicals⠀⇛


                             The crisis unfolding on Watt’s 75,000-acre
                             ranch offers a window on a growing problem
                             for the oil industry and the communities and
                             governments that are often left to clean up
                             the mess. According to the Environmental
                             Protection Agency, 3.2 million abandoned oil
                             and gas wells exist in the United States.
                             About a third of them were plugged with
                             cement, which is considered the proper way to
                             prevent harmful chemical leaks. But most
                             haven’t been plugged at all.


                             Many of the wells are releasing methane, a
                             greenhouse gas containing about 86 times the
                             climate-warming power of carbon dioxide over
                             two decades. Some are leaking chemicals such
                             as benzene, a known carcinogen, into fields
                             and groundwater.


          o § Finance⠀➾


                # ⚓ Opinion_|_We_Need_Radical_Economic_Change—Not_Biden’s
                  Corporate_Capitalism⠀⇛


                       President Joe Biden’s stimulus packages do not
                       fulfill his promise to “build back better.” We must
                       demand more.


                # ⚓ ‘A_Devastating_Failure’:_Eviction_Ban_Expires_as_House_Goes
                  on_Vacation_and_Biden_Refuses_to_Act⠀⇛


                       A nationwide eviction moratorium officially expired
                       Saturday after the Biden administration refused to
                       extend it unilaterally and Congress failed to act
                       in time, putting millions of people across the U.S.
                       at risk of losing their homes in the near future as
                       the highly virulent Delta strain tears through the
                       country.


                       “We cannot be abandoning the up to 11 million
                       Americans that are in need, particularly when
                       emergency rental assistance—the $46 billion that we
                       authorized—has not gotten out.”—Rep. Alexandria
                       Ocasio-Cortez


                # ⚓ Trump_Loyalists_Are_Behind_Lawsuits_Excluding_Farmers_of
                  Color_From_Debt_Relief⠀⇛


                # ⚓ Foreigners_file_slew_of_lawsuits_against_alleged_Israeli
                  investment_scammers⠀⇛


                # ⚓ Legal_tender_in_El_Salvador:_First_the_U.S._dollar,_and_now
                  Bitcoin⠀⇛


                       On June 8, 2021, the Legislative Assembly of El
                       Salvador adopted the Bitcoin Law, which will enter
                       into force on September 9, 2021. The law aims to
                       promote economic growth for the country and to
                       facilitate greater financial inclusion of its
                       population, 70% of which does not have access to
                       traditional financial services.


                       The Bitcoin Law seeks to create basic rules for the
                       use of Bitcoin and consists of 16 articles, which
                       can be summarized as follows:


                       1. Bitcoin is established as legal tender, adding
                       it to the United States dollar, which was adopted
                       in 2001 (the Salvadoran Colón is a legal tender in
                       El Salvador, pursuant to the Monetary Integration
                       Law, but in practice it is not in current use).


                       2. All prices can be established in Bitcoin. This
                       is optional and it is left to the discretion of
                       economic agents whether to continue to price in
                       dollars, or to establish some type of price in
                       Bitcoin.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Bernie_Sanders_Headlines_Rally_for_Nina_Turner_Ahead_of
                  Primary_Election_in_Ohio⠀⇛


                # ⚓ AOC_Slams_Conservative_Dems_Who_Would_Rather_Skip_Town_Than
                  Vote_to_Extend_Eviction_Ban⠀⇛


                       Congresswoman Alexandria Ocasio-Cortez on Sunday
                       skewered conservative members of the House
                       Democratic caucus who left town for vacation
                       instead of backing an effort to extend the
                       nationwide eviction moratorium that officially
                       expired this weekend, leaving millions of people at
                       imminent risk of being forced out of their homes.


                       “The House should reconvene and call this vote and
                       extend the moratorium. There’s about 11 million
                       people that are behind on their rent, at risk of
                       eviction.”—Rep. Alexandria Ocasio-Cortez


                # ⚓ Trial_By_Fire:_Too_Hot_to_Handle?⠀⇛


                # ⚓ Opinion_|_Biden_Isn’t_Withdrawing_Troops_From_Iraq,_He’s
                  Relabeling_Their_Mission⠀⇛


                       Iraqi Prime Minister Mustafa al-Kadhimi and
                       President Biden announced last week that Washington
                       will end its combat mission in Iraq by the end of
                       the year. However, these long-serving U.S. soldiers
                       are not coming home: many of the 2,500 American
                       service members are expected to remain in the
                       country for “training and advisory” purposes.


                # ⚓ Opinion_|_There’s_No_‘Vaccine_Mandate’—But_That_Doesn’t
                  Stop_WaPo_From_Asking_People_How_They_Feel_About_It⠀⇛


                       The Washington Post (7/29/21) let the opposition
                       rather than the facts frame its latest story on the
                       new federal directive on testing, masks and
                       vaccination. The headline read:


                # ⚓ Election_Officials_Are_Facing_Unprecedented_Threats_to
                  Independence_and_Safety⠀⇛


                # ⚓ Opinion_|_Congress_Must_Act_to_Protect_Election_Officials⠀⇛


                       The following is adapted from oral testimony given
                       Wednesday before the House Administration Committee
                       about efforts to subvert the election process. The
                       written testimony is here.


                # ⚓ Opinion_|_How_Women_of_Color_in_Congress_Are_Pushing_a
                  Grassroots_Agenda⠀⇛


                       If Donald Trump’s 2016 presidential election
                       victory was a political earthquake that shattered
                       norms and expectations, the 2018 midterm wins by
                       four women of color ought to be seen as a similarly
                       earth-shattering occurrence. Alexandria Ocasio-
                       Cortez of New York, Ayanna Pressley of
                       Massachusetts, Rashida Tlaib of Michigan and Ilhan
                       Omar of Minnesota won seats as Democrats in the
                       House of Representatives, bringing with them a
                       political sensibility that had traditionally been
                       dismissed as too radical. Ocasio-
                       Cortez and Pressley, in particular, beat incumbents
                       who were establishment favorites within the
                       Democratic Party, turning their lack of federal
                       political experience from a liability into an
                       asset.


                # ⚓ Manchin_Donated_to_Defense_Fund_of_Republican_Investigated
                  for_Insider_Trading⠀⇛


          o § Censorship/Free Speech⠀➾


                # ⚓ Pitchers’_Star_Naveen_Kasturia_On_Censorship:_It_Is_Like
                  Judging_Your_Own_People’s_Maturity⠀⇛


                       Censorship in OTT is among the hot topics which pop
                       out every now and then, what are your views on it?


                       To me censorship is not a good idea, either for OTT
                       or films, people can’t be forced to watch or
                       restrained from watching certain things. And by the
                       end people will watch what they want to, as
                       everything’s available on the internet. Makers too
                       have to self censor themselves and good stories
                       getting suffered from censorship shouldn’t happen.
                       There could be a certification for the content but
                       censorship is like judging your own people’s
                       maturity. I’m against it.


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


                # ⚓ Body_of_Reuters_Photographer_Was_Mutilated_in_Taliban
                  Custody,_Officials_Say⠀⇛


                       “Danish always chose to be on the front lines so
                       that abuses and atrocities could not remain
                       hidden,” said Meenakshi Ganguly, the South Asia
                       director for Human Rights Watch. “The brutality
                       with which Taliban fighters punished Danish proves
                       the abuses that he was documenting.”


                       Human Rights Watch and other watchdog groups say
                       the Taliban have carried out a series of revenge
                       killings in Kandahar Province, where some of the
                       most brutal episodes in Afghanistan’s last four
                       war-torn decades have occurred.


          o § Civil Rights/Policing⠀➾


                # ⚓ Labor_Unions_Must_Start_Building_Toward_Bigger_and_Longer
                  Strikes⠀⇛


                # ⚓ Incarcerated_Organizers_Call_for_Mass_Actions_in_August_to
                  Abolish_Prisons⠀⇛


                # ⚓ Turkish Demonstrators_Protest_Brutal_Slaying_of_Kurdish
                  Family⠀⇛


                       VOA Kurdish Service’s Van, Turkey-based stringer
                       Arif Aslan said after Saturday’s protest, police
                       began attacking demonstrators.


                       Aslan told VOA that police attacked him and
                       prevented him from taking any footage of the
                       clashes. The police, Aslan said, told him that his
                       VOA credentials were not acceptable, and Van’s
                       public prosecutor wanted Aslan arrested.


          o § Monopolies⠀➾


                # § Patents⠀➾


                      # ⚓ What_US_in-house_want_from_China_counsel [Ed: This
                        propaganda mill continues to be just an amplifier of
                        parasitic lawyers' agenda (because they pay for it)]⠀⇛


                             Sources from four US companies, including
                             Teleflex and USG, say they want regular
                             updates and insight on CNIPA from outside
                             lawyers


                      # § Software Patents/Hey Hi⠀➾


                            # ⚓ Australian_court_rules_an_AI_can_be_considered
                              an_inventor_on_patent_filings [Ed: Two more
                              patent offices have gone completely bonkers. It's
                              time to consider if this sort of moment is a
                              suggestion we need to scrap the patent system and
                              start it over again. It's rigged and unhelpful to
                              actual innovation. In COVID's case, it is killing
                              millions of people unnecessarily. For profit.]⠀⇛


                                   An Australian Court has decided that an
                                   artificial intelligence can be
                                   recognised as an inventor in a patent
                                   submission.


                                   In a case brought by Stephen Thaler,
                                   who has filed and lost similar cases in
                                   other jurisdictions, Australia’s
                                   Federal Court last month heard and
                                   decided that the nation’s Commissioner
                                   of Patents erred when deciding that an
                                   AI can’t be considered an inventor.


                                   Justice Beach reached that conclusion
                                   because nothing in Australia law says
                                   the applicant for a patent must be
                                   human.


                                   As Beach’s judgement puts it: “… in my
                                   view an artificial intelligence system
                                   can be an inventor for the purposes of
                                   the Act.


                # § Copyrights⠀➾


                      # ⚓ U.S._Govt:_Persistent_‘Copyright_Troll’_Lawyer_Should
                        Serve_Full_Prison_Sentence⠀⇛


                             The U.S. Government is opposing a request
                             from copyright troll lawyer Paul Hansmeier,
                             who asked the court for a reduced prison
                             sentence due to the hardships he endured
                             under coronavirus restrictions. The U.S.
                             attorney notes that these conditions were the
                             same for everyone, and highlights that the
                             lawyer continues to make new victims from his
                             prison cell.


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