𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Sunday, September 25, 2022 ┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅ Generated Mon 26 Sep 02:43:21 BST 2022 Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖) Full hyperlinks for navigation omitted but are fully available in the originals The corresponding HTML versions are at 𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈 Latest in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕 and older bulletins can be found at 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕-𝒂𝒓𝒄𝒉𝒊𝒗𝒆𝒔 Full IPFS index in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔 and as plain text in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔/𝒕𝒙𝒕 Gemini index for the day: gemini://gemini.techrights.org/2022/09/25/ ╒═══════════════════ 𝐑𝐄𝐂𝐄𝐍𝐓 𝐁𝐔𝐋𝐋𝐄𝐓𝐈𝐍𝐒 ════════════════════════════════════╕ Previous bulletins in IPFS (past 21 days, in chronological order): QmdXKq8frFc6SxT7BErqJC3fnDsbXQfhNmEGEc1BVWprrQ QmWERMsn1DfZrtyJQLRpzrUSCM3So8WboRGV5qBDKU6pKo QmeWggouo6JzSCSNPBkF9EbHtca8pg2uefQDca6Z63NbCy QmPd8eLQ2K4AVwUwwDXWDzcs9Y6q6rEafAqGPGCsRaNu1n QmfCsH16QBNTRxCFWkRbN8iKEXme1kZFksZvXhwcAkGbv1 QmbPTxQodgGofF9SkH91qnwS4xfGFrHEdPESATQe3KmLup QmVuPxmX77pHLEiaxQUdUu9Hv2c5on5vmDiepeKvhokhrK QmSSVivjsb74DwAwvNFUWiXAExS8esEHiJBzykMK9Da4BW QmYr91F9jQ6C4UgdRQqHE5QbcXGHYUcZYCYnigDogJGkyy QmVMkxTFB9LnSNGEQQ9wHzrmgcc9R1GBBrkXQwesnZn9sF QmVp5xT7mzD29ygLxoepcfrYB5u4Vyc9cndBz66AV7cb69 QmYPR3iBujyTHUCpxPHwsMNXJiNSLgfQa4AuzchgiUJ3M8 QmWTRh2ZdgwUGq9b4v8Cnv5g51yvN18PNFNC89vkDa478d QmQCpGVvMV5EduUzKqAToqKEmsDN4YWubH4KwPsA11BkFL Qmac6ycg4HgCXK32zmYm12JDmDQfL8BtJPF89Q129UbkCn QmTscUZbUfSgcCFNAKKV4rEvAsHABZ2Ct9K7RCSGGzRRDT QmcB3PmzUDz4gMMbVfzAbgcnKwRGZjhaY7foe2B7ox9dZW QmPRWZzVkej6AaPT8ApKxMdBRNbW94Cun6NRXmgn86A4C6 Qmey3FmUxZfMChKk9iWk1mHUB4Ymv2HgjzsQvr46EWDcdK QmesUFpQsQz19kHzMA7tU1y4kQBAYsznybzsWwLBxiEGvf QmUNJbX6AjW7qRrRLEqvkvgYaXD8vF7JZ7MVUdUWWqFEWb ╒═══════════════════ 𝐈𝐍𝐃𝐄𝐗 ═══════════════════════════════════════════════════╕ ⦿ YouTube (Alphabet Gulag) Keeps Censoring Videos About Free Software and GNU/Linux | Techrights ⦿ IRC Proceedings: Saturday, September 24, 2022 | Techrights ⦿ Microsoft is Trying to Eliminate POP3 and IMAP for E-mail (Attack on Commodity or Standard Protocols) | Techrights ⦿ GNU is Not UNIX: GNU Project Turns 39 | Techrights ䷼ Bulletin articles (as HTML) to comment on (requires login): http://techrights.org/2022/09/25/google-censoring-linux/#comments http://techrights.org/2022/09/25/irc-log-240922/#comments http://techrights.org/2022/09/25/microsoft-vs-pop-and-imap/#comments http://techrights.org/2022/09/25/sept-27-gnu-at-39/#comments ䷞ Followed by Daily Links (assorted news picks curated and categorised): http://techrights.org/2022/09/25/easyos-4-4/#comments http://techrights.org/2022/09/25/linux-6-0-rc7/#comments ䷩ 𝚕𝚒𝚗𝚎 57 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/09/25/google-censoring-linux/#comments Gemini version at gemini://gemini.techrights.org/2022/09/25/google-censoring-linux/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.25.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ YouTube_(Alphabet_Gulag)_Keeps_Censoring_Videos_About_Free_Software_and_GNU/ Linux⠀✐ Posted in Free/Libre_Software, GNU/Linux, Google at 1:53 am by Dr. Roy Schestowitz Video_download_link | md5sum ba5ff97dd6a8061425c736b83fd775b8 Google Suffocates Free Speech Creative Commons Attribution-No Derivative Works 4.0 http://techrights.org/videos/youtube-censorship-worsens.webm Summary: YouTube (the Alphabet/Google Gulag) seems to be weeding out discussion of software freedom; it’s a longstanding issue reported by several GNU/Linux- centric channels over the years LAST NIGHT I noticed that YouTube had once again issued sanctions against a channel for mentioning some piece of Free software or GNU/Linux. It’s not the first time; I’ve lost count! Even the high-profile channels complain that this keeps happening to them. The trend is clear to see. This_is_the_latest_example (Odysee_link) with further explanation in the video above. But I spent more time going through this video_about_“Record_Excess Deaths_in_Europe” — a subject I had been writing about for years in my_personal blog. The latter shows that YouTube goes out of its way to censor anything that discredits government policy on COVID-19. Even if based on factual information, presented by a medical doctor, and calling for greater urgency on COVID-19 (accusing our regime of being too soft, using the regime’s own data). “It happens a lot to Linux-centric channels, reducing the incentive to produce any further videos on the subject.”But for Techrights the first example is a lot more relevant because it happens all the time. It keeps happening. From the summary: “So, today I received an email about a second community strike, but no action appears to have been taken. Am I being hunted by the dogs? Is my time almost up? I am not sure. As of now, I do not have any notice on the channel itself, but just an email so I thought I would get this message out. If I disappear from the YT kingdom, I will be covertly releasing videos here…” It happens a lot to Linux-centric channels, reducing the incentive to produce any further videos on the subject. In the words of our associate: “Remember that [Bryan] Lunduke and others have commented that putting the string “Linux” in the video title gets it demonetized, at least initially. The status can be restored after a small fight, but by then the peak has past and there will be only a trickle of views left for that video. Most videos get all their views at the beginning, so this tactic of Google is a way to eliminate production of “Linux” videos. There used to be other sites which were always fighting demonetization, though I cannot recall which companies. For example the original GNUheter site always had problem with its ad revenue and the ad vendor usually refused to pay and never paid what was owed, claiming false stats.” “So it’s not just against the channels but against all coverage of Linux or GNU anywhere.” █ ䷩ 𝚕𝚒𝚗𝚎 134 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/09/25/irc-log-240922/#comments Gemini version at gemini://gemini.techrights.org/2022/09/25/irc-log-240922/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.25.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ IRC_Proceedings:_Saturday,_September_24,_2022⠀✐ Posted in IRC_Logs at 2:10 am by Needs Sunlight Also available via the Gemini protocol at: * gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-240922.gmi * gemini://gemini.techrights.org/irc-gmi/irc-log-240922.gmi * gemini://gemini.techrights.org/irc-gmi/irc-log-social-240922.gmi * gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-240922.gmi Over HTTP: 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇HTML5_logs⦈_ #techrights_log_as_HTML5 #boycottnovell_log_as_HTML5 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇HTML5_logs⦈_ #boycottnovell-social_log_as_HTML5 #techbytes_log_as_HTML5 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇t 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇text_logs⦈_ #techrights_log_as_text #boycottnovell_log_as_text 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇t 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇text_logs⦈_ #boycottnovell-social_log_as_text #techbytes_log_as_text Enter_the_IRC_channels_now =============================================================================== § IPFS Mirrors⠀➾ CID Description Object type IRC log for  QmSsoJzUZ9V89NGqgk7vFzDoCyp9XjJpkv56C1GfxhVKa6 #boycottnovell 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #boycottnovell  QmbpjE1PDvY3NUb8SqcHULWpS9hVPeBWiQDev56xaTQRhV (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ as plain/ASCII text) IRC log for #boycottnovell-  QmVi7AYevXSXiCDXPF9fiv1AsTbjdv6CYmnC4KbiNYSoXk social 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #boycottnovell-  Qmah15CKZs8MYHsJvCEuVs8bFfqa7C57EwaB84HoFFuNgi social 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ (full IRC log as plain/ASCII text) IRC log for  QmQgkvaZuTcRF7sJQ3PyeY3foo1ygWyRqXwQGtT2zAmjMv #techbytes 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #techbytes  QmeQZNxsHDyHRwCpZuV5QRqBDxDtB8apA8YbWEeibz13iS (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ as plain/ASCII text) IRC log for  QmQLjWX2XYQYqbEi6Ct4inFwaYJRRBf7MJDABeR67n6L8j #techrights 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #techrights  QmWVgtxKar517PDYXX6xtbAw2qRLQmzFANhweKQ8iUxg6Y (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ as plain/ASCII text) 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈ § Bulletin for Yesterday⠀➾ Local_copy | CID (IPFS): QmUNJbX6AjW7qRrRLEqvkvgYaXD8vF7JZ7MVUdUWWqFEWb ䷩ 𝚕𝚒𝚗𝚎 261 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/09/25/microsoft-vs-pop-and-imap/#comments Gemini version at gemini://gemini.techrights.org/2022/09/25/microsoft-vs-pop-and-imap/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.25.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Microsoft_is_Trying_to_Eliminate_POP3_and_IMAP_for_E-mail_(Attack_on Commodity_or_Standard_Protocols)⠀✐ Posted in Free/Libre_Software, Google, Microsoft, Protocol at 2:40 am by Dr. Roy Schestowitz Video_download_link | md5sum 926a0af805babd5d56f2959044221e99 Standard E-mail Under Attack Creative Commons Attribution-No Derivative Works 4.0 http://techrights.org/videos/war-on-email-ongoing.webm Summary: Microsoft is trying to decommoditise (read: control) E-mail by shutting out people who use standard protocols; how long have we got before E- mail becomes a surveillance-intensive walled garden? THE war on POSIX (e.g. systemd) and various other things that are stable and have worked for decades (e.g. X Server) is troubling enough on its own; what happens when the network stack comes under attack (e.g. TCP/IP), impacting clients and servers irrespective of the underlying operating system? Enter E-mail. We previously mentioned how Thunderbird_was_being_ruined by Mozilla and Mozilla_played_along_(passively)_with_Google's_coup_against_E-mail. Now, as per this_post (Gemini_link), Microsoft does this too. We’ve discussed this in IRC (HTML, text, GemText, Gemini) and the video above shares some personal views. Here’s the raw but redacted evidence, which is dated 3 days ago: From Enterprise Services ██████████████████ To Conner, Sean ███████████ Date Thu, 22 Sep 2022 19:27:12 +0000 Subject Legacy Email Protocols to be Retired To All [The Enterprise] Staff, Please be aware that Microsoft is disabling the use of several legacy protocols related to old methods of retrieving and sending email in the coming weeks. What does this mean for you? If you are using Outlook as [The Enterprise] provisions it, you do not need to do anything. If you use an alternate email program that relies on POP3, IMAP or SMTP, like native mail programs in iOS and Android, expect your [The Enterprise] email connection for that app to stop functioning when Microsoft chooses to disable these protocols. What should you do? [The Enterprise] only supports the use of the approved email client Outlook, Outlook 365 available in our [The Enterprise] tenant, or Outlook for iOS and Android. If you are not using Outlook, please switch today. If you require assistance, please contact ██████████████████. Instructions for installing Outlook for mobile devices can be found here [Link to internal documentation removed. —Editor]. Thank You, Enterprise Services See more in So_when_did_POP_and_IMAP_become_a_“legacy_protocol?”_–_The_Boston Diaries_–_Captain_Napalm (published about 2 days ago). We’d like to place special emphasis on the phenomenon — or the term — “decommoditisation” specifically, for at some later stage we plan to link it to the topic of the Halloween Documents, which we’ve already reproduced in Gemini (OSI censored the online copy of these, which means there’s suppression of such information, erasure of the past on behalf of Microsoft_as_sponsor). To be clear, it’s not a problem that’s limited to Microsoft; it should also be noted that GMail 1) already comes very close to blocking Thunderbird, and other IMAPS clients; 2) it does not support standard IMAPS in any case. “GMail ignores_the_existence_of_Thunderbird,” an associate reminds us, “and mainly_only_works_with_OAuth-encumbered_software.” To quote_Mozilla: “As of May 30, 2022, Google no longer allows Less secure apps [sic] access for Gmail accounts, thus OAuth is required. If you are using Google supplied app passwords, Thunderbird version 91.8.0 and newer will make that conversion for you. Further, Gmail accounts do not work with Thunderbird 31 and older because they do not support Google’s OAuth (implemented in bug 849540).” Cui bono and who stands to lose the most? █ ䷩ 𝚕𝚒𝚗𝚎 379 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/09/25/sept-27-gnu-at-39/#comments Gemini version at gemini://gemini.techrights.org/2022/09/25/sept-27-gnu-at-39/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.25.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ GNU_is_Not_UNIX:_GNU_Project_Turns_39⠀✐ Posted in Free/Libre_Software, FSF, GNU/Linux at 4:52 pm by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇gnu-39⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇1983..._...2022._Still_going.⦈_ Summary: Tomorrow (Tuesday) is a special day; 39 years since the message (announcement) below, so next year it’s 40 (a major time leap in the context of software development; not much stuff lasts this long) From CSvax:pur-ee:inuxc!ixn5c!ihnp4!houxm!mhuxi!eagle!mit-vax!mit- eddie!RMS@MIT-OZ From: RMS%MIT-OZ@mit-eddie Newsgroups: net.unix-wizards,net.usoft Subject: new Unix implementation Date: Tue, 27-Sep-83 12:35:59 EST Organization: MIT AI Lab, Cambridge, MA Free Unix! Starting this Thanksgiving I am going to write a complete Unix-compatible software system called GNU (for Gnu's Not Unix), and give it away free(1) to everyone who can use it. Contributions of time, money, programs and equipment are greatly needed. To begin with, GNU will be a kernel plus all the utilities needed to write and run C programs: editor, shell, C compiler, linker, assembler, and a few other things. After this we will add a text formatter, a YACC, an Empire game, a spreadsheet, and hundreds of other things. We hope to supply, eventually, everything useful that normally comes with a Unix system, and anything else useful, including on-line and hardcopy documentation. GNU will be able to run Unix programs, but will not be identical to Unix. We will make all improvements that are convenient, based on our experience with other operating systems. In particular, we plan to have longer filenames, file version numbers, a crashproof file system, filename completion perhaps, terminal-independent display support, and eventually a Lisp-based window system through which several Lisp programs and ordinary Unix programs can share a screen. Both C and Lisp will be available as system programming languages. We will have network software based on MIT's chaosnet protocol, far superior to UUCP. We may also have something compatible with UUCP. Who Am I? I am Richard Stallman, inventor of the original much-imitated EMACS editor, now at the Artificial Intelligence Lab at MIT. I have worked extensively on compilers, editors, debuggers, command interpreters, the Incompatible Timesharing System and the Lisp Machine operating system. I pioneered terminal-independent display support in ITS. In addition I have implemented one crashproof file system and two window systems for Lisp machines. Why I Must Write GNU I consider that the golden rule requires that if I like a program I must share it with other people who like it. I cannot in good conscience sign a nondisclosure agreement or a software license agreement. So that I can continue to use computers without violating my principles, I have decided to put together a sufficient body of free software so that I will be able to get along without any software that is not free. How You Can Contribute I am asking computer manufacturers for donations of machines and money. I'm asking individuals for donations of programs and work. One computer manufacturer has already offered to provide a machine. But we could use more. One consequence you can expect if you donate machines is that GNU will run on them at an early date. The machine had better be able to operate in a residential area, and not require sophisticated cooling or power. Individual programmers can contribute by writing a compatible duplicate of some Unix utility and giving it to me. For most projects, such part-time distributed work would be very hard to coordinate; the independently-written parts would not work together. But for the particular task of replacing Unix, this problem is absent. Most interface specifications are fixed by Unix compatibility. If each contribution works with the rest of Unix, it will probably work with the rest of GNU. If I get donations of money, I may be able to hire a few people full or part time. The salary won't be high, but I'm looking for people for whom knowing they are helping humanity is as important as money. I view this as a way of enabling dedicated people to devote their full energies to working on GNU by sparing them the need to make a living in another way. For more information, contact me. Arpanet mail: RMS@MIT-MC.ARPA Usenet: ...!mit-eddie!RMS@OZ ...!mit-vax!RMS@OZ US Snail: Richard Stallman 166 Prospect St Cambridge, MA 02139 ⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠟⠛⠻⣿⣿⡿⠟⠛⠻⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢠⣶⡆⠈⣿⠁⢰⣶⡄⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠃⣰⣿⡄⢸⣿⡇⢠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⠀⢠⠒⢢⢠⠒⢢⢰⠒⣄⠔⠀⠀⠀⣀⣀⢀⣖⠀⢀⣆⣆⣀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⡄⠙⣿⣿⣶⣿⡆⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡀⣸⢸⡀⣸⠈⢉⠎⡎⡂⠀⠸⡀⢈⠇⡇⠀⠀⡇⡇⠀⡇⣗⢒⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⠛⠹⣿⠇⠀⣿⣿⣿⣿⠇⢈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠁⠀⠁⠀⠈⠁⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣄⣀⣠⣾⣿⣷⣄⣀⣠⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣤⠀⣄⡤⢤⣠⡤⢼⢠⠤⢼⠨⢣⠤⡄⠀⢼⠄⡠⠤⡄⡤⠤⡄⠀⢠⡫⣍⢰⠉⢱⢰⠉⢱⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠉⡾⠘⢄⡠⠻⠇⢸⠸⣀⢼⠀⠨⣉⠆⠀⠸⡀⢧⣀⠇⡧⣀⠏⠀⠰⣄⡸⠸⣄⡸⠸⣄⡸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢿⣿⣿⣿⣿⣿⣁⣧⣀⣀⣟⣆⣇⣐⣽⣾⣀⣦⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠴⠿⠿⠦⢼⣿⣿⢿⢿⢿⡿⣿⣽⣿⡿⡿⡿⡿⣿⣿⣿⡡⠾⠿⠿⠆⠀⠀⠀⠀⠀⠠⣖⡢⢰⠀⢰⢰⠒⢢⣰⣒⣆⡶⢢⠖⠲⢠⠒⢢⢰⠒⡶⠒⡆⡖⠒⡆⡆⠀⡖⡗⢠⣒⣢⢰⠒⣖⡲⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⢸⣭⣿⣿⣿⣿⣿⡇⡇⡗⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠝⠸⠤⠚⢸⠤⠞⠑⠤⠆⠇⠈⠦⠔⠘⠤⠜⠸⠀⠇⠀⠇⡷⠤⠃⠣⠴⠇⠣⠘⠤⠔⠘⠀⠦⠼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⣀⣀⣀⣀⣀⠀⢀⣀⣀⣀⣀⣀⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⣿⠀⣿⢸⡟⣿⠀⠀⣾⠙⣷⢸⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡀⠀⡿⣿⢿⡧⣺⠒⢠⣎⢇⣇⣎⣴⡁⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠙⠛⢛⣘⣁⡛⠀⠀⠙⣛⣋⡘⠀⠛⠀⠂⠒⠐⠐⠐⠂⠂⠂⠒⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠋⢩⣽⣦⣤⣾⣍⠙⣿⡆⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣶⢒⣦⣶⡴⡴⣠⣄⣤⣠⢤⡄⡤⣰⣦⠤⡤⣤⣤⣶⠀⣦⢤⡄⡤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣶⠋⠽⣯⠓⣿⡙⣷⣿⠇⢸⡇⠀⢸⡇⣶⢲⡆⣶⠀⣶⠲⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠁⠉⠁⠉⠁⢁⣉⣉⣉⣉⣈⠉⣉⢉⣉⠊⠁⠉⠋⠉⠉⠉⠈⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣇⢤⠃⡈⢵⡬⠳⠚⠁⠀⠸⠷⠶⠸⠇⠿⠸⠇⠻⠶⠿⠼⠛⠦⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⣿⢀⣃⣙⢛⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡘⢆⠈⢢⣄⡝⠀⠀⠀⠀⠀⠀⣤⣤⣤⡀⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣿⠀⡓⡑⠊⡃⢛⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢿⣤⣾⠀⠀⠀⠀⠀⠀⠀⣇⣀⣸⣇⣒⢔⢲⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠀⠙⠘⠚⠓⠃⠛⠛⠘⠘⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⣟⠀⠀⠀⣿⠋⣿⣿⣿⡇⢰⣿⣿⣿⣿⣿⣿⡧⡀⣿⣿⡏⠀⠀⣾⣿⣭⣿⣿⣿⣿⣿⣿⡏⢻⣿⣃⣂⠀⢸⣿⣿⣿⣿⣿⠃⠀⡇⠀⣿⡏⣁⠀⠀⠨⠀⠀⠀⢨⣿⠀⠀⠀⠀⠀⠀⠀⠁ ⠀⠀⡄⠀⠀⠀⠀⠸⠀⠀⣿⠀⠀⠀⣿⠀⣿⡿⣿⠀⢸⣿⣿⣿⣿⢟⣵⡖⠶⣿⣿⠁⢀⣵⣿⣿⣿⣿⣉⡿⢿⣿⣿⣄⡸⣗⣈⣏⠀⣾⣿⣿⣾⠛⣿⠀⠀⠅⠀⠘⠀⢻⣠⡀⢐⡆⠀⠀⢸⢻⡄⠀⠀⠀⠀⠀⢠⣶ ⠀⠠⠁⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠉⠀⣼⣷⣿⠀⢸⣿⡿⣿⣿⣿⣻⣇⣶⢿⡟⠀⣾⡿⡿⣫⣶⣿⣿⢿⣾⣿⣿⣿⣿⣿⡷⣧⢀⣿⣻⢿⣾⠜⡏⠀⢠⠇⠀⠀⠘⠁⠀⠁⠘⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⡇ ⠀⠀⠛⠓⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢒⣀⣼⣿⡇⢀⢿⣥⣿⢿⣿⣿⠉⠸⣿⡿⠃⠀⠈⠈⢱⣿⠿⠿⣿⡎⢯⣿⣿⣿⣿⣿⣇⠁⠸⠟⣿⢸⡟⠀⡇⠀⢀⠀⢀⠀⠀⠀⠀⠀⢠⡀⠀⢠⡆⣼⠀⠀⠀⠀⠀⠀⣼⡇ ⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢻⠻⣷⣋⣦⣽⣿⣭⣠⣧⣤⠃⣠⣀⣀⠠⠀⢨⣴⣿⣿⣿⣿⡟⢸⡏⠙⢿⣿⣿⣟⠀⠀⠀⠁⢸⣷⣼⡿⡚⠀⠀⢸⠀⠲⠀⠀⣴⣠⡇⠀⠸⠃⣿⠀⠀⠀⠀⠀⠀⣇⡂ ⡀⠀⠀⠀⠀⠈⠁⠀⠁⠁⠚⠋⠉⣸⣿⣿⠉⠉⠙⠛⢛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⠘⠛⢀⡙⠛⠁⠀⠈⢀⣠⣾⣿⣿⣿⣶⣾⣶⣾⣿⣿⣿⢛⣛⣻⣿⢿⣶⣶⡶⢻⣿⣼⣿⣛⣯⣿⣿⡒⠲⠤⠤⠤⣀⣿⡇ ⠃⠀⣠⣤⠀⣠⣴⣶⣦⡀⠀⣠⣴⣿⣿⢿⣾⣵⣶⣦⡾⣾⣿⣿⣿⣿⡯⠿⣿⣿⢿⡉⠉⠄⠀⠉⠉⠀⠀⢀⣤⠿⣿⣻⣿⣿⣟⣿⣯⣿⣿⣿⣿⣷⢿⣿⠿⣿⣿⠿⡿⠗⣿⣿⣿⠷⠂⣿⣻⡟⠃⠀⠀⠀⠀⠸⣿⠷ ⡴⠿⣿⣿⠤⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⢻⣿⡿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣶⣿⣾⣿⣶⡄⠀⠀⠀⣴⣶⣿⣿⣿⣿⣿⠛⢷⣿⣯⣤⣶⣿⣿⣿⣦⣦⣤⣶⣦⣤⣤⣿⣿⣿⣤⣄⣛⣿⣇⡀⠀⡀⠀⡀⠀⠈⡠ ⠀⠠⣿⣿⠀⢿⣿⣴⣿⣿⢻⣿⡿⢿⣿⣿⢿⣟⢻⣿⣦⣤⣄⣭⣭⣭⣹⣿⣿⣿⣛⣛⣿⣿⣯⢖⠅⢀⣼⣿⣿⣿⣿⣿⡻⣿⡀⠀⢻⣿⣿⣻⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣍⣍⣿⢉⣱⡆⠰⠆⠀⢠⣤⡗ ⠁⠀⣿⣿⠀⣤⣤⠀⣿⡿⠸⣿⡇⢸⣿⣿⣿⣿⠉⣿⣿⢛⣛⢙⣙⢛⣛⣛⣛⣋⣭⣭⡨⠋⣰⠋⠀⢊⣿⠟⠛⡿⢿⣿⣷⡈⢸⠦⠈⣍⣁⣀⣈⣻⣿⣿⡿⢿⠿⢿⣿⣿⢿⣿⣿⣿⡻⣿⣿⣶⣦⣄⣀⠀⠀⢼⣿⠁ ⠀⠀⠛⠛⠀⠈⠛⠛⠛⠁⢰⣿⡛⢛⣿⣿⠈⡟⣛⠛⠁⣸⣿⣼⣿⣼⣛⡆⠉⠉⣋⠉⠙⢺⡏⠀⠀⢡⣶⢿⣿⣟⣀⣄⠙⡟⠁⠨⠀⠙⠛⠛⣑⡛⣛⣻⣿⡿⠶⢺⣶⣤⣶⣦⣠⣄⣵⣝⠉⠋⠉⠛⠿⠏⣿⣿⡿⢷ ⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢸⣯⡇⠀⠛⠟⠀⡇⡟⠀⠰⣏⡙⠋⠻⣿⣿⣇⢀⣰⣿⡆⠀⠘⠃⠠⠀⣴⣶⣄⣟⣿⣿⢁⠀⠀⠀⠀⠀⠸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣶⣟⣻⣟⣟⡟⠓⠿⢳⣚⣀⠨⠃⢠⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⣧⡇⠀⠀⠁⠻⡿⢶⡰⢿⣿⣿⠈⠉⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⠇⢤⠀⠀⠀⠀⠀⣬⣝⣟⣋⡝⠛⠉⣩⣋⣽⣿⣽⣭⡍⠉⢩⡿⣭⣄⣴⠖⠀⠀⠀⠀⠀⠀⠘⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣱⣼⣦⡄⠈⠁⠀⠀⠀⢀⣀⡀⢻⣿⣿⡟⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠉⠋⠧⣀⠺⠟⠛⠿⠛⠠⠉⢰⣿⣱⣶⣽⣷⣶⣤⣤⣴⣿⣫⣥⡄⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⣿⣿⣿⣿⣿⣭⣿⣶⣶⣴⣿⢿⣿⣄⠈⠟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠁⡄⠀⣀⠀⠀⠀⠀⠠⣤⠀⠁⠀⠐⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠤ ⠀⠶⠶⣶⠏⢶⠿⠰⠶⠶⢾⡿⠀⠀⠀⠀⠀⢸⣿⠟⠀⠀⣾⣿⣛⠋⠛⣛⠛⠋⠛⠿⠇⠈⠉⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠆⠀⠀⣿⡅⠀⠄⠀⠴⠻⢗⠒⠒⠒⠒⠶⠛⠛⠛⠉⠁⠀⠀⠒⠒⢒⡒ ⠀⢀⠀⠀⠀⠀⠀⡤⠀⢘⡇⠀⠀⠘⣿⠙⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⠇⡈⣿⣿⡇⠀⠀⢻⣿⣭⣶⣿⣿⣿⣿⣿⡏⣹⡿⢫⣂⠀⢸⣿⣿⣯⣿⣿⡏⠀⡏⠀⢸⡏⢩⠀⠀⠈⠁⠀⠀⢨⣿⡆⠀⠀⠀⠀⠀⠀⠈ ⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⣿⢿⣿⠀⢸⣿⣿⣿⣿⢻⣵⡖⠢⣿⣿⠁⢈⣴⣿⣿⣿⣯⣉⡿⢿⣿⣿⣇⡸⣛⢨⣧⠀⣾⣿⣿⣷⠋⣿⠅⠀⡅⠀⠘⠀⢹⣤⡀⠀⡃⠀⠀⢸⢻⡇⠀⠀⠀⠀⠀⠀⣴ ⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣿⣾⡏⠀⣾⣿⢿⣿⣿⣿⣻⣇⣶⣿⡟⠀⣿⡿⡿⣫⣾⣿⣿⢿⣾⣿⣿⣿⣿⣿⡖⣧⠀⣿⢻⣿⣾⡎⣯⠀⠀⠇⠀⡀⠀⠃⠀⠁⠘⡁⠀⠀⠈⠘⡇⠀⠀⠀⠀⠀⢀⣼ ⠀⠈⠛⠂⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢒⣠⣿⣿⠇⡠⣿⣴⣿⢿⣿⡟⠉⢸⣿⡟⠁⠀⠈⠈⢱⡿⠿⠿⣿⡎⢯⣿⣿⣿⣿⣿⣧⠁⠘⡟⣿⢹⡟⠀⣇⠀⠀⠀⠀⡄⠀⠀⠀⠀⠠⢄⠀⠀⣴⢰⡇⠀⠀⠀⠀⠀⢠⡟ ⣄⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⣿⣿⣗⢻⠻⣞⣡⣮⣽⣿⣥⣀⣧⣤⠁⣦⣀⣀⠀⠀⢠⣴⣿⣿⣿⣿⡟⢸⡏⠙⢿⣿⣿⣟⠀⠀⠀⠁⢸⣿⣤⣿⢚⠀⠀⠀⠃⠲⠄⠀⣤⣀⣎⠀⠀⠇⢸⡇⠀⠀⠀⠀⠀⢸⣒ ⠀⠀⠀⠀⠀⠁⠀⠀⠉⠐⠛⠉⠉⣿⣿⡟⠉⠉⠙⠛⢛⣛⣿⣿⣿⣷⣿⣿⣿⣿⣷⣶⣶⠘⠋⢀⡙⠛⠁⠀⠈⢀⣠⣾⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⢛⣛⣻⣿⢻⣶⣶⡶⢻⣿⣷⣿⣟⣻⣿⣿⡗⠲⠦⠤⠤⢀⣼⣽ ⠁⠀⣦⣤⠠⣤⣴⣶⣦⡀⠀⣠⣴⣿⣿⢿⣾⣵⣶⣦⡿⣿⣿⣿⣿⣿⡿⢿⣿⣿⢟⡉⠙⠄⠀⠉⠉⠁⠀⢀⣤⠿⣿⣻⣿⣿⣿⢿⣯⣿⣿⣿⣿⣿⢾⣿⠿⡿⣿⡿⢿⡷⣻⣿⣿⣷⠆⣸⣿⡿⠋⠀⠀⠀⠀⠀⡿⡿ ⡴⠿⣿⣿⢤⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⡿⢻⣿⡿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣶⣿⣾⣿⣦⡄⠀⠀⠀⣬⣶⣿⣿⣿⣿⣿⠛⢷⣿⣿⣤⣴⣿⣿⣾⣦⣦⣤⣤⣦⣤⣤⣿⡿⣿⣤⣄⡛⢻⣧⣀⠀⠀⠀⢀⠀⠀⢁ ⠀⢀⣿⣿⠀⢿⣿⣽⣿⣿⢻⣿⡿⢿⣿⣿⢿⣟⢻⣿⣦⣤⣀⣩⣍⣉⣛⣛⣛⣻⣛⣛⣿⣿⣯⢖⠅⢀⣼⣿⣿⣿⣿⣿⠻⣿⡀⠀⢻⣿⣿⣻⣯⣿⣿⣿⣿⣿⣿⣻⣻⣿⣿⣷⣟⣿⣍⣉⣽⡏⣹⡆⠀⢔⡂⢀⣤⡸ ⠀⠀⣿⣿⠀⣤⣤⠀⣿⡿⠸⣿⡇⢸⣿⣿⣿⣿⠉⣿⣿⢛⣟⢋⣛⢛⣛⣛⣛⣛⣭⣉⡹⠋⣠⠋⠠⢊⣽⠟⠟⡿⣿⣿⣷⡌⢸⡦⠈⣉⣁⣀⣈⣻⣿⣿⡿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⣿⣿⣷⣦⣌⣀⠀⠀⢰⣿⡇ ⠀⠀⠛⠛⠀⠈⠛⠛⠛⠁⢰⣽⠛⢻⣿⡿⢨⡟⡛⠛⠁⢸⣿⣼⣿⣜⠛⡍⠉⠉⡛⠛⠓⢺⡏⠀⠀⢩⣶⣿⣿⣿⣀⣅⠹⡟⠃⠘⠀⠸⠛⠛⣁⡛⢻⣻⣿⡿⠶⢾⣶⣤⣴⣦⣀⣍⣹⣎⠉⠙⠙⠛⠿⢿⢻⣿⣿⠷ ⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣼⣿⠀⠘⠻⠏⢸⣿⡏⠀⠰⣍⡙⠙⢿⣿⣿⣇⢀⢸⣿⡀⠀⠈⠁⢀⠀⣨⣾⣄⣝⣿⣿⠁⠀⠀⠀⠀⠀⠘⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣾⣽⢿⡟⣿⡿⠷⠴⠷⣖⣃⡄⡛⠀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢹⣿⡀⠀⠀⠀⢸⣿⡇⠀⠀⠩⠷⠿⣦⡹⣿⣿⣿⠉⠉⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⠇⣄⠀⠀⠀⠀⠀⣈⣛⣛⣛⡻⠟⢛⣻⣛⣿⣟⣻⣿⡍⠉⢉⣿⣍⣍⣠⠴⠀⠀⠀⠀⠀⠀⠐⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠀⠀⠀⠀⢘⣿⠇⠀⠀⠀⠀⢳⣼⣤⡈⠉⠋⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⣿⡿⠋⠀⠈⠀⠀⠀⠀⠀⠙⠿⠿⠋⠛⢣⣀⠮⣿⠿⠿⠿⠯⠉⢁⣾⣇⣴⣭⣾⣤⣤⣤⣤⣿⣟⣶⣠⠀ ⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⣿⣷⣶⠂⠀⣿⣿⣿⣿⣿⣧⣶⣶⣶⣴⣿⣿⣿⡌⠉⠟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠓⡄⠀⢠⠈⠁⠀⠀⠀⣤⠀⠃⠀⠀⡿⠯⣿⣯⣽⣿⣿⣿⣿⣿⣿⣥⠠ ⠀⠶⠶⣶⠏⢷⠷⠰⠶⠶⢿⡿⠂⠀⠀⠀⠀⢻⣿⠏⠀⠀⣿⢿⠿⠛⣛⡛⠛⠛⡛⢿⠅⠚⠛⠊⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠄⠀⠀⣻⣂⠀⠀⠀⡠⠾⣷⠠⠶⠶⠶⠶⠶⠿⠿⠛⠉⠁⠀⠐⠒⠤⠂ ⠀⢀⠀⠀⠀⠀⠀⡄⠀⢸⡃⠀⠀⠸⡟⢹⣿⣿⣿⠀⢾⣿⣿⣿⣿⣿⣿⠏⠸⣿⣿⠇⠀⠀⣿⣿⣼⣶⣿⣿⣿⣿⣿⡏⢹⣿⢏⣂⠀⢸⣿⣿⣯⣿⣿⡏⠀⠈⠀⢸⡿⢩⡀⠀⠀⠅⠀⠀⠀⣽⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⠀⠀⠀⠁⠀⢸⡇⠀⠀⢐⡇⢸⣿⢿⡇⠀⣾⣿⣿⣿⡿⢻⣶⠖⢲⣿⣿⠀⢈⣴⣿⣿⣿⣯⣉⡾⢿⣿⣿⣇⡚⣛⣠⣧⠀⣼⣿⣿⣷⡛⣿⡇⠀⠀⠀⠈⠁⡈⣧⣄⠀⣓⠀⠀⠀⡟⣷⠀⠀⠀⠀⠀⠀⣠ ⠀⠃⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠘⠁⠠⣿⣾⡇⠀⣿⣿⢿⣿⣿⣿⣹⣇⣶⣿⡟⠀⣿⡿⡿⣭⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⡷⣠⠀⣿⢿⣟⣿⡇⢹⠀⠀⡇⠀⠀⠀⠃⠀⠁⠀⠃⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⣰ ⠀⠙⠓⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣃⣠⣿⣿⠁⡰⣯⣴⣿⢿⣿⡟⠉⢸⣿⡟⠀⠸⠈⠈⢱⡿⠿⠿⣿⡎⢯⣻⣿⣿⣿⣿⣧⠁⠐⡟⣾⠁⡟⠁⣫⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡄⠀⠀⣰⠀⣿⠀⠀⠀⠀⠀⢠⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⣿⡗⠿⠿⣞⣡⣬⣿⣯⣅⣸⣧⣄⠀⣄⣀⣀⣀⠀⣠⣴⣿⣿⣿⣿⡿⢸⡏⠙⢿⣿⣿⡟⠀⠀⠀⠀⢸⣷⣤⣿⢖⠀⠀⠀⡇⠒⠄⠀⢠⡄⣼⠀⠀⠿⢸⡏⠀⠀⠀⠀⠀⢸⣕ ⠀⠀⠀⠀⠈⠁⠀⠈⠁⠘⠛⠛⢁⣿⣿⡏⠉⠛⠛⠛⢛⢛⣿⣿⣿⣷⣿⣿⣽⣿⣷⣶⣦⠹⠋⠁⠛⠛⠉⠀⠈⠀⣠⣾⣿⣿⣿⣷⣶⣶⣾⣾⣿⣿⠛⣛⣻⣿⢻⣶⣶⡶⠞⣿⣇⣿⡿⢻⣿⣿⣗⠒⠦⠤⠤⠄⢸⢿ ⠀⠰⣠⣤⠠⣠⣴⣶⣤⡀⠀⣤⣾⣿⣿⣷⣮⣴⣶⣦⡿⣿⣿⣿⣿⣿⣭⢿⣛⡿⣟⠉⠙⠀⠀⠉⠙⠁⠀⠀⣠⠿⢿⣻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣾⣿⡿⢿⣿⣿⠿⣷⣿⣿⣿⡟⠔⣸⣟⣿⠛⠀⠀⠀⠀⠀⢸⢿ ⡴⢿⣿⣿⣤⣿⣿⣿⣿⣿⣾⣿⣧⣾⣿⣿⣿⡿⢻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣶⣿⣦⡀⠀⠀⠀⣬⣶⣿⣿⣿⣿⣿⠛⢧⣿⣿⣭⣴⣷⣿⣷⣧⣴⣤⣤⣤⣤⣤⣼⣿⣿⣇⣄⡘⢻⣿⣀⠀⠀⠀⠀⡀⠀⠀ ⠀⣀⣿⣿⠀⢿⣿⣭⣿⣿⢿⣿⡿⢿⣿⣿⢿⣟⢻⣿⣦⣄⣈⣉⣉⣛⣛⣛⣛⣿⣛⣻⣿⣿⣯⢖⠄⢀⣴⣿⣿⣿⣿⣿⢻⣿⡁⠀⢻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣟⣿⣏⣉⣹⣟⢙⣦⠀⢠⣂⠀⣀⣀ ⠀⠀⣿⣿⠀⣤⣤⠀⣿⡿⠸⣿⡇⢸⣿⡿⣿⣿⠉⣿⣿⢟⣛⢛⣛⢻⣛⣟⣛⣛⣯⣉⡹⠋⣠⠋⠠⢚⣿⡿⠟⡿⣿⣿⣷⡈⢹⡦⠀⢉⣉⠈⣈⣻⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣷⣬⣍⣁⠀⠀⠀⣿⣿ ⠀⠀⠛⠛⠀⠈⠛⠛⠛⠁⣶⣝⠛⣻⣿⡇⢨⢛⡛⠛⠁⢸⣿⣼⣿⣘⢛⠉⠉⠙⡛⠛⢳⢸⡏⠀⠀⢩⣴⣶⣿⣟⣀⡉⠹⡟⠃⠐⠀⠸⠛⠛⢋⠻⠿⠿⣿⣿⠷⡴⣦⣤⣤⣤⣀⣉⣩⣎⠋⠻⠛⠛⠿⢿⢛⣿⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣿⣼⠀⠘⠿⠇⢸⢸⡇⠀⠴⠉⠻⠛⣿⣿⣿⡇⢀⣸⣿⠀⠀⠸⠃⢀⠀⣨⣯⣨⡝⣿⣿⠃⠀⠀⠀⠀⠀⠘⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⣭⠿⣿⢿⢿⠷⠤⠾⣴⠒⠀⣚⠅⡀ ⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣿⣿⠀⠀⠀⠀⢸⣼⠁⠀⠘⠹⠷⣷⣤⢩⣿⣿⡟⠉⠛⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠏⣀⠀⠀⠀⠀⠀⢀⣛⣛⣛⣛⠿⠛⣛⣛⣛⣛⣛⣛⡋⠛⠙⣻⣏⣋⣉⡤⠄⠁⠀⠀⠀⠀⠀⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠈⢆⣴⣄⠈⠙⠃⠀⠀⠀⠀⠀⠀⢾⣿⣿⡿⣿⡟⠋⠀⠈⠀⠀⠀⠀⠀⠋⠿⢿⠏⠛⢧⣀⠬⣿⠿⠿⠿⠏⠙⠂⣴⡟⣤⣍⣾⣤⣤⣠⣀⣼⣒⣒⣂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⣿⣦⣶⠀⢐⣿⣿⣿⣿⣷⣲⣶⣤⣴⣄⣾⣿⣾⡉⠉⠟⠇⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠒⡀⠀⠀⠈⠁⠀⠀⠀⣤⡀⠒⠀⠈⢽⣿⣽⣯⣿⣿⣿⣿⣿⣿⣿⣯⣁ ⠀⠷⠶⣶⠞⢿⠶⠰⠶⠶⣿⡧⠀⠀⠀⠀⠀⣿⣿⠏⠀⢈⣿⣿⡿⠟⠿⠟⠛⠻⠛⢿⡋⠘⠛⠛⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⡄⠁⠀⣹⡆⠀⠀⠀⣀⣼⣧⠤⠤⠤⠤⢴⡶⠿⠿⠟⠛⠉⠉⠉⠭⠭⠄ ⠀⡄⠀⠀⠀⠀⢠⠀⠀⣽⠀⠀⠀⢹⠇⢻⣿⣿⡿⠀⣾⣿⣿⣿⣿⣿⡿⠧⠸⣿⣿⠇⠀⠀⣿⣿⣵⣿⣿⣿⣿⣿⣿⡏⢸⡿⢇⣠⡀⢠⣿⣿⣿⣽⣿⡏⠀⠘⠀⠀⣿⢨⡄⠀⠀⠍⠀⠀⠀⣭⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⡄⠀⠀⠀⠀⠈⠀⠀⢸⠀⠀⠀⢘⠀⢸⡿⢿⡇⠀⣿⣿⣿⣿⡿⢫⣶⠖⢲⣿⣿⠀⢈⣴⣿⣿⣿⣯⣉⡞⢿⣿⣿⡇⣈⣛⡡⣧⠀⢼⣿⣿⣷⡏⢿⡇⠀⢀⠀⠀⠃⡈⢧⣄⠀⢸⠀⠀⠀⡼⢻⠀⠀⠀⠀⠀⠀⠀ ⠘⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣷⣾⠃⠐⣿⡿⢿⣿⣿⣿⣿⣇⡶⣿⠟⠀⣿⣿⡿⣥⣾⣿⣿⢿⣾⣿⣿⣿⣿⣿⡷⣰⠀⣾⢿⡏⣾⡆⢻⠁⠀⡼⠀⢠⠀⠛⠀⠈⠀⢋⠀⠀⠀⠁⢻⠀⠀⠀⠀⠀⠀⢀ ⠀⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣂⣸⣿⡿⠀⡸⣯⣼⣿⣿⣿⡏⠁⢹⣿⡟⠀⠸⠈⠈⢱⡿⢿⢿⣿⡎⢯⣻⣿⣿⣿⣿⣷⠁⠀⡿⣿⠃⡿⠃⣸⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠤⡀⠀⢠⡆⣾⠀⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠿⠷⣞⣠⣭⣿⣯⣅⣜⣥⡄⠀⣄⣀⣀⡀⠀⣥⣴⣿⣿⣿⣿⡟⢸⣏⠙⢿⣿⣿⡟⠁⠀⠀⠈⠀⣧⣦⣿⢗⠂⠀⠀⡇⠐⠦⠀⢠⡄⣰⠁⠀⠸⠀⣿⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠉⠀⠀⠉⠀⠘⠛⠛⢹⣿⣿⡏⠙⠛⠛⠛⠛⢻⣿⣿⣽⣶⣿⣿⣽⣿⣶⣶⣦⠹⠋⠁⠙⠛⠉⠀⠈⠀⣀⣼⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⠿⣛⣻⣷⠷⣶⣶⣶⠖⣿⣧⣿⣿⢻⣿⣿⣿⠒⠦⢤⠤⠄⣀⡇ ⠀⢤⣠⣤⠠⣠⣴⣶⣤⡀⠀⣤⣾⣿⣿⣷⣦⣴⣶⣦⡿⣿⣿⣿⣿⣯⡿⢿⣿⣿⡛⢉⠙⠀⠀⠉⠙⠁⠀⠀⣠⠿⢿⣛⣿⣿⣿⢻⣟⣻⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣞⣿⣿⣿⡔⢀⣟⣿⡟⠂⠀⠀⠀⠀⠈⠏ ⠴⣿⣿⣿⣴⣿⣿⣷⣿⣿⣾⣿⣧⣼⣿⣿⣻⡿⣿⣿⡿⣿⣷⣿⣿⣽⣾⣿⣿⣷⣶⣿⣶⣿⣤⡀⠀⠀⠀⣭⣴⣿⣿⣿⣿⣿⠛⢧⣼⣿⣭⣤⣿⣿⣷⣧⣴⣤⣤⣤⣤⣥⣸⣿⣿⣧⣀⡘⠛⣿⣄⡀⠀⠀⠀⡀⠀⠀ ⣀⣀⣿⣿⠀⢿⣿⣭⣿⣿⢿⣿⡿⢿⣿⣿⢿⣛⠻⣿⣦⣉⣉⣉⣙⣛⣛⣻⣿⣿⣿⣿⣿⣿⣯⢖⠄⠀⣴⣿⣿⣿⣿⣿⢿⣿⡁⠀⢻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣼⣻⣿⢛⣉⣿⠙⣳⠄⠠⣀⠀⢀⢀ ⠀⠐⣿⣿⠀⣤⣤⠀⣿⣿⠸⣿⣇⢸⣿⡿⣿⣿⠋⣿⣿⢟⣛⢛⣛⢻⣿⢿⡟⢛⣛⣉⠹⠋⣠⠋⠀⢚⣻⡿⠟⠿⣿⣿⣷⡘⢘⡆⠀⢛⡋⠈⠉⢻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣍⡁⠀⠀⠀⢸⣿ ⠀⠀⠛⠛⠀⠈⠛⠛⠛⠡⣦⡝⠛⣿⣿⡆⣬⢛⡛⠛⠁⣼⣿⣼⣿⣘⢛⠉⠉⢻⠛⠛⢣⢼⡇⠀⠀⢨⣵⣶⣿⣿⡀⡉⠹⡷⠃⠱⠀⠸⠟⠿⠋⠻⠿⠿⢿⣶⣷⡤⣮⣅⣠⣤⣉⣉⣉⣯⠛⠛⠟⠛⠿⣿⡟⣷⣾⣿ ⠀⠀⠀⠀⠀⠀⠀⡄⠀⢐⣏⡇⠀⠻⢿⠁⣿⢸⠁⠀⣼⠋⠿⠻⣿⣿⣾⡆⣀⣸⣿⠀⠀⠘⠀⢀⠀⣨⣭⡨⡽⣿⣿⠋⠀⠁⠀⠀⠀⠐⣶⣶⣾⢿⣿⣿⣿⣿⣶⣶⣿⣿⠿⣯⣭⠿⣿⢿⡿⠶⠤⢶⢦⠖⠀⢘⠋⠁ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⣿⣇⠀⠀⠀⠀⣿⣼⠀⠀⠘⠹⣶⣦⣌⣽⣿⣷⡏⠛⠛⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡏⡀⠀⠀⠀⠀⠀⢘⣚⢷⠿⢒⠿⠟⠻⡿⢟⣿⣟⣟⣛⠙⠛⢻⣟⣋⡉⣥⡄⠀⠈⠉⠉⠀⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⠀⢽⣷⠀⡀⠀⠀⠘⣄⣫⣀⠈⠛⠃⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⡿⠏⠀⠘⠀⠀⠀⠀⠀⠚⢿⣿⡟⠻⢶⡀⠩⣿⡿⣿⣿⠟⡙⠂⣠⡿⠈⣍⣫⣥⣀⣀⣀⣠⣶⢶⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⣿⣤⣦⠀⢰⣾⣿⣿⣿⣶⣲⣤⣤⣄⣄⣶⣶⣶⡙⠛⡿⣇⠁⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠢⡀⠀⠀⡈⠃⠈⠀⠀⢀⡀⠐⠀⠉⢹⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁ ⠀⠷⠶⣶⠿⣿⠆⠰⠶⠾⣿⠄⠀⠀⠀⠀⢸⣿⣿⠃⠀⢈⣿⣿⣿⠿⠿⠿⠿⠿⠿⢿⡋⠹⠯⠗⠂⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣀⠈⠀⢘⡇⠀⠀⠀⢀⣸⣷⡄⣠⣤⣬⣤⣬⣭⣿⡿⠟⠛⠋⠉⠩⢉⠁ ⠠⠀⠀⠀⠀⠀⣤⠀⠈⣇⠀⠀⠀⠑⠀⢻⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⡿⠠⢸⣿⣿⠁⠀⠐⣿⣿⣴⣶⣿⣿⣿⣿⣿⡏⢸⡷⢀⣠⡀⢀⣿⣿⣿⣽⣿⡟⠀⠘⠀⠀⣿⠉⣄⠀⠀⠈⠀⠀⠀⢨⣿⠀⠀⠀⠀⠀⠀⠀ ⢠⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡿⣿⡁⠀⣿⣿⣿⣿⡿⣯⣶⠂⢺⣿⡿⠀⢈⣾⣿⣿⣿⣧⣉⡞⢿⣿⣿⣇⡟⣛⡠⣥⠀⢸⣿⣿⣿⡟⣻⡇⠀⢀⠀⠀⠁⢀⢻⣤⡀⢘⠂⠀⠀⢸⢹⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⠀⢸⣿⡿⣿⣿⣿⣿⣿⣂⡾⣿⠏⠀⣿⣿⡿⣥⣾⣿⣿⢿⣾⣿⣿⣽⣿⣿⣷⢺⠀⣾⣟⡿⣿⡇⢛⡁⠀⣼⠀⢀⠀⠘⠀⠈⠁⢘⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠘⠛⠂⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⢐⣀⣼⣿⡿⠀⢼⣯⣾⡿⣿⣿⡏⠁⠻⣿⠟⠀⠈⠊⠘⣰⡿⢿⢿⣿⡎⣯⣿⣿⣿⣿⣿⣿⠈⠀⡿⢹⠇⣿⠃⢸⡀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢠⠀⠀⠀⡆⢸⡇⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠺⠿⠷⣋⣤⣽⣿⣯⣀⣸⣤⠌⠀⣀⣀⣀⡀⠀⣥⣴⣿⣿⣿⣿⡟⢸⣏⠙⢿⣿⣿⡟⠁⠀⠀⠈⠀⣿⣆⣽⡗⠂⠀⠀⢸⠐⠦⠀⠀⣤⢠⡇⠀⠐⠇⣾⠃⠀⠀⠀⠀⠀⠐ ⠀⠀⠀⠈⠉⠀⠈⠁⠀⠛⠛⠛⣸⣿⣿⠉⠛⠛⠛⠛⠛⣻⣿⣿⣿⣦⣿⣯⣽⣿⣶⣶⣦⠹⠋⠉⠛⠛⠉⠀⠈⠀⣀⣼⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⡿⣛⡶⣷⠿⣶⣶⣶⠶⣺⣿⣼⣿⠟⣻⣷⣿⡒⠶⠤⡤⠄⠀⣴ ⠀⡄⣠⣤⠀⣠⣴⣶⣤⡀⠀⣠⣿⣿⣿⣶⣦⣴⣶⣮⡷⣿⣿⣿⣿⣯⡽⢿⣿⡿⠟⠉⠛⠀⠀⠉⠛⠀⠀⠀⣠⡾⢿⣟⣿⣿⣿⢻⣟⣿⣿⣿⣿⣿⣶⣿⣿⣿⣷⣿⡿⣿⡞⣿⣿⣿⠅⠂⣽⣻⡿⠃⠀⠀⠀⠀⠀⠹ ⣴⣿⣿⣿⣴⣿⣿⣶⣿⣿⣾⣿⣧⣼⣿⣿⣻⠿⣿⣿⡿⣿⣧⣿⣿⣵⣶⣾⣿⣷⣦⣷⣶⣿⣤⡀⠀⠀⠀⣨⣴⣾⣿⣿⣿⣿⠟⢧⣼⣿⣭⣥⣼⣿⣷⣧⣤⣤⣬⣤⣤⣥⣱⣿⣿⣿⣀⣀⠛⣿⣇⡀⠀⠀⠀⢀⠀⠀ ⣀⡈⣿⣿⠀⢿⣿⣭⣿⣿⢿⣿⡿⢿⣿⣿⢿⣛⠻⣿⣮⣉⣉⣙⣛⣛⣛⣿⣿⣿⠿⣿⣿⣿⣯⢖⡆⠀⣴⣿⣿⣿⣿⣿⢿⣿⡂⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣼⣻⣿⡛⣛⣿⡛⢳⡄⠀⣄⠀⠀⠀ ⠈⠥⣿⣿⠀⣤⣤⠀⣿⡿⠸⣿⣇⢸⣿⡿⣿⣿⠋⣿⣿⢟⣛⢛⣛⢿⣿⠿⠿⢛⣛⣋⠹⠋⣡⠎⠀⠞⣻⡿⠿⣿⣿⣿⣷⡘⠙⣆⠀⢛⠛⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣤⣭⡉⠀⠀⠀⢠⣏ ⠀⠀⠛⠛⠀⠈⠛⠛⠛⢱⣄⠙⢛⣿⣿⠀⡌⣛⠛⠛⠁⣼⣿⣼⣟⡘⢛⠛⠛⢻⠟⠻⠧⢼⡏⠀⠀⢚⣭⣶⣶⣷⠈⡉⠹⡷⠇⠡⠀⠸⠿⠿⠟⠽⠿⠿⣿⣶⣷⡤⣯⣍⣁⣬⣉⢉⡋⣣⡻⠛⠿⠛⠿⣿⣷⢲⣾⣿ ⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⣿⡇⠘⠿⣿⠀⡇⡿⠀⠀⣔⠛⠟⢿⣿⣿⣾⠀⠀⣸⣷⠀⠂⠸⠁⢀⠀⢸⣿⡉⡻⣿⣿⠏⠀⠁⠀⠀⠀⠐⣶⣶⣾⣷⣾⣿⣿⣿⣶⣶⣿⣿⠿⣿⣝⣿⣿⣿⣿⣶⣤⣠⣦⠤⠄⠈⠫⠉ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⡇⠀⠀⠀⠀⣧⡃⠀⠀⠚⣻⣴⣦⡙⣻⣿⣷⡟⠛⠟⠀⠀⠀⠀⠈⣰⣿⣿⣷⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⠶⣿⠿⠿⡿⠿⡿⠿⢿⣗⠛⠛⠓⣾⡓⠓⢁⣀⠀⠀⠉⠁⠁⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠁⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠱⡉⣇⡈⠛⠻⠃⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⡿⠏⠀⠙⠀⠀⠀⠀⠀⠸⣿⣿⡿⠻⢶⠀⢉⣻⣿⣿⣿⣿⡛⠖⢀⣾⢇⣉⢫⣏⣀⣀⣀⢀⣴⠤⠤⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⣿⣧⣤⡄⠀⢰⣶⣿⣿⣿⣤⣤⣤⣄⣠⣄⣶⣶⣴⠚⠟⡿⣅⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡁⠀⠀⠉⠒⠀⠁⠀⢀⡀⠠⠀⠈⢙⣾⣟⣻⣛⣻⣿⣿⣿⣿⣿⣿⡃ ⠀⠶⠶⣶⠿⣷⠆⠰⠶⢾⣷⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⢘⣿⣿⣿⣿⣿⣿⠿⢿⠿⣿⠋⠽⡟⠷⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⣀⠘⠀⠐⡦⠀⠀⠀⠀⢈⣷⣀⣀⣀⣀⣉⣩⣭⣿⣿⡿⠟⠛⠛⠛⣛⠉ ⠀⠀⠀⠀⠀⠠⡄⠀⢨⡅⠀⠀⠀⠀⠈⣿⣿⣿⡇⠰⣿⣿⣿⣿⣿⣿⡿⠠⢸⣿⣿⠁⠀⠐⣿⣿⣴⣶⣿⣿⣿⣿⣿⡏⢸⡶⠂⣠⡀⠀⣿⣿⣿⢹⣿⣿⠀⠀⠁⠀⣿⠇⢠⠀⠀⠀⠀⠀⠀⠈⣽⡇⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠃⠀⢸⡇⠀⠀⠀⠀⠀⣿⠿⣿⠀⢰⣿⣿⣿⣿⠟⣥⣶⠒⢺⣿⡿⠀⢠⣾⣿⣿⣿⣯⣉⡞⢿⣿⣿⣇⣊⣓⣀⣽⡀⢸⣿⣿⣿⡎⢹⡇⠀⠀⡀⠀⠈⢀⢹⣤⡀⠀⡃⠀⠀⢠⠟⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣿⠀⢺⣿⡿⣿⣿⣿⣟⣿⣰⡾⣿⠃⢀⣿⢿⡿⣥⣾⣿⣿⢿⣾⣿⣿⣿⣿⣿⣷⢼⠄⣾⡟⡿⣵⣦⢨⡇⠀⢰⠃⠀⠀⠈⠀⠀⠁⠘⡁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠙⠓⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢂⣀⣿⣿⡇⢀⢿⣥⣾⡿⣿⣿⠋⠁⠿⣿⠏⠀⠈⠈⠘⣸⡿⢿⣿⣿⡎⣯⣻⣿⣿⣿⣿⣿⡈⠀⠿⢹⡇⣿⠃⢘⡁⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⣄⠀⠀⣴⢠⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⣷⠿⠿⢶⣋⣬⣽⣿⣯⣠⣻⣤⡌⠀⣄⣀⣀⠀⠀⣥⣼⣿⣿⣿⣿⡟⢸⣏⠙⢿⣿⣿⡿⠇⠀⠀⠈⠀⣿⣤⣼⡷⠂⠀⠀⢸⠀⠢⠀⠀⣤⠀⡎⠀⠀⠟⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠁⠀⠉⠁⠐⠛⠛⠃⣿⣿⣿⠉⠛⠛⠛⠛⠛⣻⣿⣿⣿⣾⣿⣯⣽⣿⣶⣶⡆⠻⠋⠉⠛⠛⠉⠀⠈⠈⣀⣼⣿⣿⣷⣶⣶⣷⣶⣶⣿⣿⡿⢿⡷⣶⠶⣶⣶⣶⡶⢶⣿⣸⣿⡿⣛⣷⣾⡇⠶⠦⡤⠤⢀⢠ ⢠⠀⣠⣤⠀⣠⣴⣶⣤⡀⠀⣠⣿⣿⣿⣶⣠⣴⣶⣮⡽⣿⣿⣿⣿⣯⣿⣿⣿⣿⡟⠛⠣⠀⠀⠉⠛⠀⠀⠀⣠⡾⠿⣟⣿⣿⣿⢿⣿⣻⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⡧⣻⣿⣿⡯⠀⣸⣻⣿⠳⠀⠀⠀⠀⠀⢸ ⣼⣿⣿⣿⣴⣿⣿⣶⣿⣿⣼⣿⣧⣼⣿⣿⣻⣿⣿⣿⣿⣿⣭⣿⣿⣵⣶⣿⣿⣧⣤⣧⣴⣷⣄⡀⠀⠀⠀⣨⣵⣾⣿⣿⣿⣿⡟⢧⣼⣿⣣⣥⣼⣿⣿⣯⣤⣆⣤⣥⣄⣉⣀⣿⣿⣿⣄⣀⠻⢿⣿⠀⠀⠀⠀⠀⠀⠀ ⠈⡉⣿⣿⠀⢿⣿⣽⣿⣿⢿⣿⡿⢿⣿⣿⢿⣛⠻⣿⣮⡉⠉⣛⣛⡛⡿⣿⣿⡿⠿⢿⣿⣿⣏⡤⡂⠀⣰⣿⣿⣿⣿⣿⢿⣿⡃⠀⢻⣿⣿⡿⣿⣻⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣧⡿⣿⡟⠛⢻⡟⠛⣤⠀⠠⠀⠀⠀ ⠩⠄⣿⣿⠀⣤⣤⠀⣿⡿⠸⣿⣇⢸⣿⡿⣿⣿⠃⣿⣿⣟⣛⢛⣛⢿⣿⠿⠿⢟⣛⠛⠻⠏⣡⠞⢀⠾⣻⣿⡿⣿⣿⣿⣷⡜⠙⣆⠀⠛⠛⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣌⡉⠀⠀⠀⠀⣜ ⠀⠀⠛⠛⠀⠊⠛⠛⠛⣥⣀⠙⢻⣿⣯⢀⡈⣛⠛⠛⠡⣼⣿⣼⣛⡘⢛⠛⠛⠿⠿⠿⢧⣰⡏⠀⠀⢚⣭⣵⣶⡷⠉⡙⢻⣵⠗⠁⡀⠸⡿⠿⠿⠹⢿⣿⣿⣶⣿⣍⣭⣍⣉⣉⣉⢉⡛⢳⡙⠟⢻⠿⠿⣿⣷⠶⣶⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣹⠀⠸⢿⡟⢸⡇⡟⠀⢀⡞⠻⡟⢿⣿⣷⣿⠀⠀⣸⣦⠀⠀⢺⠀⠀⠀⢘⣿⠙⡻⣿⣿⠇⠀⠉⠀⠀⠁⠀⣶⣶⣶⣶⣶⣶⣾⣿⣷⣾⣾⣿⣿⣿⣟⣻⣿⣿⣿⣦⣦⣀⣴⣠⠤⠀⠹⠍ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⣿⣿⠀⠀⠀⠀⢨⡇⡅⠀⠀⠖⡶⣴⣌⡙⣻⣿⣦⡟⠻⠟⠀⠀⠀⠀⠈⣰⣿⣿⣷⣷⣿⡟⢀⠀⠀⠀⠀⠀⠀⠾⢿⣿⠷⢿⡿⠿⠿⡿⢿⡿⠿⠷⠾⠿⠳⣾⠷⠛⢒⣀⡐⠂⠉⠀⠈⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⣧⡇⠀⠀⠀⠈⢪⠉⣇⠉⠛⠿⠃⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⡿⡟⠁⠉⠀⠀⠀⠀⠀⠘⣿⣾⣶⠾⢤⠀⢐⣻⣾⣿⣿⣿⠛⠧⠀⣰⡏⣙⠻⣛⣁⠀⠀⠀⣠⣤⡤⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣿⣇⣠⡂⠀⣠⣴⣿⣿⣷⡤⣄⣀⣀⡀⡀⣤⣤⣤⠚⠿⡿⡇⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡁⠀⠀⠉⠒⠈⠃⠀⠉⠀⠈⠄⠘⠛⣷⡾⣿⣿⣿⣿⣿⣿⣿⣷⣾⡗ ⠀⠶⠶⣶⠿⢷⠆⠰⠶⣿⡶⠀⠀⠀⠀⠀⢻⣿⣿⠃⠀⢺⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠛⡿⣿⠧⠄⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠘⠀⠠⢦⠀⠀⠀⠀⠈⣿⡀⠀⠀⢀⣋⣉⣛⣻⣿⣿⠿⠿⠛⠛⠛⠛ ⠀⠀⠀⠀⠀⢠⠀⠀⢭⠀⠀⠀⠈⠇⢘⣿⣿⣿⠁⢸⣿⣿⣿⣿⣿⣿⠿⠫⢻⣿⣿⠁⠀⢘⣿⣿⣶⣿⣿⣿⣿⣿⣿⡏⢸⣿⢯⣴⡀⠀⣿⣿⣿⣿⣿⣿⠁⠀⠃⠀⢸⠇⢬⠀⠀⠀⠅⠀⠀⠀⣽⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠀⠀⢸⡆⠀⠀⢰⠀⠀⣿⢻⣯⠀⢸⣿⣿⣿⣿⠟⣵⣶⠨⢾⣿⡿⠀⣨⣿⣿⣿⣿⣯⣉⡞⢿⣿⣿⣧⡘⣓⣢⣽⡀⢰⣿⣿⣿⡞⢹⣿⠀⠀⡀⠀⠈⠀⡨⣦⣄⠀⡛⠀⠀⠀⡜⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣿⣾⡏⠀⢾⣿⡿⣿⣿⣿⣿⣿⣰⣾⣿⠃⢰⣿⢿⡿⣥⣾⣿⣿⢿⣾⣿⣿⣿⣿⣿⣷⢾⡆⢸⡟⣿⣽⣷⢙⡇⠀⢠⠇⠀⡀⠈⠃⠀⠉⠀⡃⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀ ⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⣀⣿⣿⠇⢀⣿⣵⣿⣿⣿⣿⠋⠉⣿⣿⠏⠀⠠⠉⠘⣼⡿⢿⣿⣿⡎⣯⣿⣿⣿⣿⣿⣿⡌⠀⣿⢻⡇⣸⠋⢈⡇⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⡄⠀⠀⢠⠄⣾⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⡟⠿⢿⣶⣃⣬⣽⣿⣽⣠⣯⣤⠈⠠⣀⣀⣀⡀⠀⣥⣼⣷⣾⣾⣿⡿⢸⣏⠙⢿⣿⣿⣿⡇⠀⠀⠈⠀⣿⣶⣸⡿⠒⠀⠀⠘⠁⠦⠄⠀⢠⡀⣸⠀⠀⠸⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠉⠀⠀⠉⠀⠘⠛⠛⢣⣿⣿⡏⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣾⣿⣯⣽⣿⣦⣴⡆⠻⠏⠉⠻⠛⠉⠁⠈⠉⢀⣼⣿⣿⣷⣶⣶⣷⣶⣶⣿⣿⡿⠿⡷⣶⡶⣶⣶⣶⡶⢶⣿⣧⣿⡷⢶⣶⣾⣿⠴⢦⣠⣄⠀⠀ ⡄⠀⣠⣤⠀⣠⣴⣶⣤⡀⠀⣬⣿⣿⣷⣶⣠⣴⣶⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠣⠀⠀⠉⠓⠀⠀⠀⣀⣾⠿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣇⢺⣿⣿⡿⡕⢹⡟⣿⡟⠂⠀⠀⠀⠀⠀ ⣝⣛⣿⣿⣴⣿⣿⣶⣿⣿⣼⣿⣧⣼⣿⣿⣻⣿⣿⣿⡿⣿⣽⣿⣿⣿⣶⣿⣿⣧⣽⣧⣼⣷⣄⠀⠀⠀⠀⣊⣭⣶⣿⣿⣿⣿⡟⢯⣽⣿⣏⣋⣽⣿⣿⣯⣅⣄⣡⣭⣍⣙⣉⣽⣿⣿⣇⡀⠸⠿⣿⡀⠀⠀⠀⠀⠀⠀ ⢉⠉⣿⣿⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣞⠻⣿⣮⠉⠛⡛⠛⠿⠿⠿⢿⣿⠿⣿⣿⣿⣏⡤⡂⠀⣰⣿⣿⣿⣿⣿⣿⣿⡃⠀⢻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣯⡿⣿⡟⠛⢒⣿⠛⢧⡀⠀⠀⠀⠀ ⢁⡀⣿⣿⠀⣤⣤⠀⣿⡿⠸⣿⣇⢸⣿⡿⣿⣿⡀⣿⣿⣟⣛⢛⣛⢻⣿⣿⠿⠿⡟⠛⣻⠟⢩⠎⢀⠾⣿⣿⣿⣿⣿⣿⣮⡝⠛⣄⠀⠛⠻⠉⠉⠻⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣀⣛⠃⠀⠉⠀⢸ ⠀⠀⠛⠛⠐⠌⠛⠛⠛⣅⡀⠙⣻⣿⡏⢠⠈⡛⠛⠛⢁⣿⣿⣘⣛⠘⠛⠛⠻⢿⠿⠿⢆⢴⡏⠀⠀⢚⣻⣥⣶⣶⠉⠛⢻⣷⠦⠃⡀⠘⣿⢶⡾⠲⣿⣿⣿⣦⣽⣍⣩⣛⡉⣉⣉⠛⠛⠛⡝⠿⠿⡿⠿⣿⣶⡶⣦⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣷⠀⢻⣿⡇⢸⢰⡇⠀⢀⡾⢿⡿⣿⣿⣧⣶⠀⠀⣰⡆⠀⠀⢸⠀⠀⠀⢸⣻⠙⣻⣿⣿⡗⠀⠓⠀⠀⠁⠀⣤⣤⣴⣶⣶⣶⣾⣿⣯⣭⣼⣿⣿⣿⣛⣻⣿⣿⣿⣦⣤⣀⣤⣄⡭⠁⠸⢟ ⠀⠀⠀⠀⠀⠀⠁⠀⠐⣿⣿⠀⠀⠈⠀⢸⡞⠂⠀⠈⠷⣦⣠⡈⠻⣿⣿⣦⡿⠿⠿⠀⠀⠈⠀⢈⣰⣿⣿⣷⣷⣿⡿⠀⠂⠀⠀⠀⠀⠀⢼⣿⣽⣯⣽⣿⣿⣿⣿⣿⣿⣿⣷⠾⠿⠷⢶⡿⠾⠛⠉⡉⠉⠙⠒⠐⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠀⠀⠀⠀⢸⣿⠄⠀⠀⠀⠉⢍⠻⡋⠙⠿⣿⠃⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠁⠚⠀⠀⠀⠀⠀⢸⣶⣖⣶⠶⣮⠄⠐⣺⣶⣿⣷⣾⡿⢧⠄⢠⣾⠙⠺⣶⡛⠁⠀⠀⠀⣄⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⣿⡁⡐⡄⠀⣠⣼⣾⣿⣦⣀⣀⣀⠀⡀⠀⣤⣤⣠⠽⡿⣿⡫⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡉⠀⠀⠓⠢⠍⠋⠉⠉⠉⠁⡀⠀⠻⢧⣿⢷⣿⣿⣿⣿⣷⣿⣷⣶⣶ ⠀⠖⠲⣶⡿⢷⠆⠰⠶⣷⡶⠀⠀⠀⠀⠈⣿⣿⡿⠀⠀⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠟⣿⡿⣦⡀⠑⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠘⠄⠠⣄⠀⠀⠀⠀⠀⢷⡄⠀⠀⠀⠙⠛⠛⣿⣿⣿⣿⣿⠿⠿⠿⠿ ⠀⠀⠀⠀⠀⢤⠀⠀⣭⠀⠀⠀⠸⠁⢹⣿⣿⣿⠀⢾⣿⣿⣿⣿⣿⣿⠿⠩⢿⣿⣿⠀⠀⢘⣿⣿⣶⣿⣿⣿⣿⣿⣿⡟⢸⣿⠟⣥⣄⠀⣾⣿⣿⡧⣿⣿⠁⠀⠁⠀⢸⡯⢠⡀⠀⠀⠀⠀⠀⠀⢨⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠰⠀⢸⣿⢿⡇⠀⢸⣿⣿⣿⣿⢟⣽⣶⠂⣾⣿⡇⠀⣡⣿⣿⣿⣿⣧⣨⡞⢿⣿⣿⣇⡘⣛⣃⣽⡄⠠⣿⣿⣿⣾⡹⣿⠀⠀⡀⠀⠀⠁⡈⣧⣄⠀⢘⠀⠀⠀⢠⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢸⣿⣾⡇⠀⣿⣿⢿⣿⣿⣿⣿⣿⣰⣾⣿⠃⢰⣿⢿⡿⣥⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⢾⡆⢸⡿⣿⢻⣶⠊⣿⠀⢠⡇⠀⠀⠀⠃⠀⠈⠀⢋⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀ ⠓⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣿⣿⠁⢠⣟⣵⣿⢿⣿⣿⠋⠈⣿⣿⠏⠀⠀⠁⠘⣸⡿⢿⣿⣿⡎⣯⣿⣿⣿⣿⣿⣿⡌⠀⢻⢿⡟⢸⡟⠀⡇⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⠀⠀⢀⡆⢰⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⡿⠿⠿⡞⣣⣬⣿⣿⣬⣄⣯⣤⠂⠰⣀⣀⣀⡄⠀⣥⣼⣷⣾⣾⣿⡿⢸⣏⠙⢿⣿⣿⣿⠇⠀⠀⠀⠁⢸⣷⣸⣿⢖⠀⠀⠀⡇⠲⠄⠀⢀⡄⢠⠅⠀⠰⠇⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⠈⠁⠀⠀⠁⠀⠚⠛⠚⢸⣿⣿⡏⠛⠚⠛⠛⠻⠻⣿⣿⣻⣿⣼⣿⣯⣿⣿⣶⣴⡄⢿⠏⠉⠛⠿⠉⠀⠈⠉⢀⣼⣿⣿⣿⣷⣴⣷⣶⣶⣿⣿⣿⠿⠷⢶⡶⢶⣶⣦⣶⠶⣾⣷⣽⣷⠶⣖⣶⣿⠠⠦⣄⣀⣀⠀ ⡀⠀⣠⣤⠀⣠⣴⣶⣤⡀⠀⣼⣿⣿⣧⣖⣠⣴⣶⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢇⠀⠐⠙⠓⠀⠀⠀⣀⣾⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣾⣿⣿⣷⣴⣿⣿⣿⡭⠍⣿⢿⡿⠧⠀⠀⠀⠀⠀ ⣑⣛⣿⣿⣴⣿⣿⣶⣿⣿⣴⣿⣇⣸⣿⣿⣻⣿⣷⣿⡿⣿⣽⣿⣿⣿⣶⣿⣿⣧⣽⣯⣴⣶⣀⠀⠀⠀⠀⣚⣭⣶⣾⣿⣿⣿⡿⢯⣭⣿⣟⣋⣽⣿⣿⣼⣍⣤⣉⣉⣁⣈⣋⢹⣿⣿⣯⡀⠀⠿⣿⡇⠀⠀⠀⠀⠀⠀ ⠉⠉⣿⣿⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣟⠻⣿⣮⠛⠛⠛⠿⠿⠿⣿⢿⣿⣿⣿⣿⣿⣟⡤⡀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡃⠀⢹⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢿⣿⠟⠒⣿⠟⢧⡄⠀⠀⠀⠀ ⣁⠀⣿⣿⠀⣤⣤⠀⣿⡿⠸⣿⣇⢸⣿⡿⣿⣿⠀⣿⣿⣜⣛⢛⣛⢻⣿⣿⡿⠿⠿⠛⢿⠟⢩⠞⢀⠼⢿⣿⣿⣿⣿⣿⣾⡝⠟⣄⠀⠻⠿⠋⠛⠻⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣚⠓⠀⠉⠀⠀ ⠀⠀⠛⠛⠠⠈⠛⠛⢻⣁⡀⠙⣿⣿⡏⣀⠈⠛⠛⠛⢑⣿⣟⣘⣛⠘⠛⠿⠶⢿⠿⠿⢄⢰⡏⠀⠀⠔⣛⣥⣤⣯⡙⠛⠻⣷⡦⠋⡅⠘⣷⢶⣶⠖⣿⣿⣿⣶⣽⣏⣩⣟⡛⢋⣙⠛⠛⠟⣎⢿⠿⢿⠿⢿⣶⣦⢤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⡇⠀⣿⣿⠇⣿⢸⡇⠀⢀⠼⢿⢿⣿⣿⣧⣦⠀⠀⣴⡄⠀⠀⣼⠁⠀⠀⢸⣿⠻⢻⣷⣶⡆⠀⠙⠀⠀⠃⠀⣥⣤⣤⣶⣤⣵⣾⣿⣯⣭⣭⣿⣿⣿⣟⠳⣿⣷⣿⣦⣤⣀⢀⣄⣉⡉⠀⢟ ⠀⠀⠀⠀⠀⠈⠀⠀⢸⣷⡇⠀⠀⠉⠀⣻⢸⠀⠀⠨⠷⣆⣄⠘⠿⣿⣿⣶⡦⢿⡿⠀⠀⠈⠀⠘⢠⣾⣿⣦⣧⣿⣿⠁⠂⠀⠀⠀⠀⠀⢼⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⡮⢿⡿⣯⣿⠭⠯⠏⠉⠩⠉⠓⠀⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠉⡟⢛⠊⠻⠿⣿⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⡿⠃⠒⠀⠀⠀⠀⠀⢰⢶⣖⣦⣶⣎⡁⠀⠶⣶⣶⣶⣶⡶⢶⡀⠀⣼⠟⠶⢶⡾⠋⠀⠀⠀⢀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢸⣿⠀⢠⠀⠀⣀⣼⣾⣷⣆⣀⡀⠀⠀⠀⢀⣠⣀⣈⠽⣿⣿⠛⠟⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠀⠀⠑⢤⠍⠻⠉⠛⠉⠁⢂⠀⠼⢿⣬⣷⣾⣿⣿⣶⣶⣶⣿⣮⣤ ⠀⠖⠲⣶⡿⢷⠄⠰⢾⣶⠶⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⣿⣿⣿⣿⣿⣷⣿⣯⣿⣷⣷⠿⣿⣿⣆⡀⢫⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⠄⠀⣠⠀⠀⠀⠀⠀⢲⡆⠀⠀⠀⠸⠛⠲⠿⣿⣿⣿⣿⣿⠿⠿⠿ ⠀⠀⠀⠀⠠⡄⠀⢨⡅⠀⠀⠀⠹⠀⢻⣿⣿⡿⠀⢾⣿⣿⣿⣿⣿⣿⠟⠉⢻⣿⡿⠀⠀⢸⣿⣿⣶⣿⣿⣿⣿⣿⣿⡟⢘⣿⠟⣨⣅⠀⣼⣿⣿⣇⣿⣿⡇⠀⠘⠀⠀⡿⠠⡄⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠃⠀⠀⡗⠀⠀⠀⡰⠀⢸⡿⣿⡇⠀⣿⣿⣿⣿⡿⢫⣽⡶⠒⣿⣿⡇⠀⣠⣾⣿⣿⣿⣧⣨⡞⢿⣿⣿⣇⣜⣛⣁⣽⡄⠠⣿⣿⣿⡿⢉⣿⡆⠀⢀⠀⠀⠁⢀⢥⣤⡀⢀⡃⠀⠀⢠⠎⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⣷⣿⠃⠐⣿⣿⢿⣿⣿⣿⣻⣿⣰⣿⣿⠃⢰⣿⢿⡟⣥⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⢶⡇⢸⣿⣿⢻⣷⠎⣿⠀⠀⡼⠀⢠⠀⠙⠀⠀⠁⠘⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⠒⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⡿⠀⣸⣯⣽⣿⢿⣿⡿⠉⠘⣿⣿⠃⠀⡇⠁⠈⣼⡿⢿⣿⣿⡎⣯⣿⣿⣿⣽⣿⣿⡎⠀⢸⠧⡿⢸⡟⠀⣿⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢠⠀⠀⠀⣴⢠⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⠻⠷⣷⡞⣡⣭⣿⣯⣤⣨⣧⣤⠂⠠⣀⣀⣀⡀⠀⣠⣼⣷⣾⣾⣿⡿⢸⣏⠙⢿⣿⣿⣿⠏⠀⠀⠀⠁⢸⣷⣀⣿⠖⠀⠀⠀⡇⠰⠤⠀⠀⣤⠀⡌⠀⠀⠇⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠉⠁⠀⠈⠀⠀⠟⠓⠒⣾⣿⣿⠘⠛⠚⠛⠻⠿⢿⣿⣿⣻⣷⣾⣿⣯⣿⣿⣤⣴⡄⢿⠏⠉⠻⠿⠉⠁⠈⠉⢀⣸⣿⣿⣿⣶⣤⣶⣶⣶⣾⣿⣿⠿⠿⢶⣶⢶⣧⣦⣴⠶⢾⣿⣸⣿⡶⢖⣶⣾⡧⠴⡄⣀⣀⠀ ⠀⠀⣠⣤⠀⣠⣴⣶⣤⡀⠀⣿⣿⣿⣤⣆⣠⣴⣶⣮⡿⣿⣿⣿⣿⣛⣿⣿⣿⣿⡟⠛⢃⠀⠐⠚⠳⠀⠀⠀⢀⣶⣿⠿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣷⣿⣿⣿⡰⣿⣿⣿⡯⠍⣹⢻⣿⠧⠀⠀⠀⠀⠀ ⣐⣛⣿⣿⣤⣿⣿⣦⣿⣿⣴⣿⣇⣸⣿⣿⣻⣿⣳⣿⡿⣿⣿⣿⣟⣭⣶⣿⣿⣭⣽⣦⣼⣦⣀⠀⠀⠀⠀⢒⣩⣴⣾⣿⣿⣿⡿⣶⣩⣿⣟⣋⣹⣿⣿⣽⣍⣩⣉⣉⣉⣉⣋⢀⣿⣿⣿⡀⠀⠿⢿⣟⠀⠀⠀⠀⠀⠀ ⠉⠉⣿⣿⢙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣟⠻⣿⣯⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣟⡤⡀⠀⣠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⠿⠶⢺⡿⠻⣄⠀⠀⠀⠀ ⡀⠀⣿⣿⠀⣤⣤⠀⣿⡿⠸⣿⣇⢸⣿⡿⣿⣿⡀⣿⣿⢘⣛⢛⣿⣻⣿⣿⣿⠷⠾⠟⣿⠟⢫⠞⢀⣼⢿⣿⡿⣿⣿⣿⣦⡙⠷⣄⠀⠻⠿⠟⠛⠻⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣇⡐⠛⠀⠈⠀⠀ ⠀⠀⠛⠛⠀⠈⠛⠛⢛⡁⠀⢹⣿⣿⠋⡀⠈⠛⠛⠛⣱⣿⣛⣘⡛⠘⠻⠶⠶⣿⣿⣷⣅⢰⡏⠀⠈⠴⣛⣁⣤⣯⡙⠻⠿⣿⣦⠋⡅⠀⣷⣶⣶⠖⣾⣿⣿⣯⣝⣟⣛⣟⠛⠛⠙⠛⠻⠿⢯⢻⠿⢿⣿⣿⣶⣦⣤⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣟⡀⢸⣿⣿⠀⡇⣴⠄⠀⢠⡾⣿⣿⣿⣿⣦⣇⠀⠀⣶⡄⠀⠀⣾⠀⠀⠐⢸⣿⠻⢿⣧⣶⡆⠈⠙⠀⠀⠂⠀⣥⣤⣤⣤⣬⣭⣭⣿⣿⣭⣯⣽⣿⣿⣿⠷⢶⣶⣾⣧⣄⣈⢀⣠⠉⣉⠃⢻ ⠀⠀⠀⠀⠀⠐⠀⠀⣿⣿⠁⠀⠈⠉⠀⣷⠸⠀⠀⢩⣤⣌⣀⠛⢿⣿⣿⣰⣴⣿⡗⠀⠀⠈⠀⠐⢠⣾⣿⣦⣮⣿⣿⠁⠂⠀⠀⠀⠀⠀⢸⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣭⢿⣿⣯⣽⣯⠿⠭⠉⠉⠋⠩⠀⠔⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠃⠀⠀⠀⠀⣿⡄⠀⠀⠀⠘⠻⡛⢷⠘⠻⣿⣿⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⡿⠇⡐⠀⠀⠀⠀⠀⢠⣦⣬⣯⣥⣔⣉⠁⠬⣮⣴⣿⣷⣾⣶⣀⠀⣠⡟⠶⢦⢴⠟⠁⠀⠀⠀⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢻⡟⠀⠀⠀⠀⣀⣱⣾⣶⡄⠀⠁⠀⠀⠀⠀⣀⣀⣈⣻⣿⣿⠟⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠉⠡⢤⡑⠻⠛⠛⠛⠛⢂⠀⠰⠿⣥⣶⣦⣿⣶⣶⣶⣤⣾⣯⣩ ⠀⠖⠲⣶⠟⢷⠄⠰⣾⡶⠶⠀⠀⠀⠀⢸⣿⡶⡗⠀⢨⣿⣿⣿⣿⣿⣧⣿⣿⣶⣷⣼⡿⣿⣿⡄⠁⠫⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠁⡀⠀⠀⠄⠀⠀⠀⠀⢰⣄⠈⠀⠀⠀⠿⠷⢾⣾⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢠⠀⠀⢨⡄⠀⠀⠀⠄⠀⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⡿⠏⠏⣿⣿⡿⠀⠀⢸⣿⣿⣶⣿⣿⣿⣿⣿⣿⡏⠨⣿⠃⣠⣄⠀⣼⣿⣿⡧⣿⣿⡏⠀⠈⠀⠀⣿⠁⣄⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⡟⣿⠀⠀⣿⣿⣿⣿⡿⢫⣾⡗⠉⣿⣿⡇⠀⣠⣾⣿⣿⣿⣧⣨⡞⢿⣿⣿⣇⡐⣛⣁⣼⡄⠀⣿⣿⣿⢷⠉⢿⡇⠀⢀⠀⠀⠀⢀⢸⣤⡀⠀⡃⠀⠀⠀⡆⣻⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣿⠀⢰⣿⡿⢿⣻⣿⣿⣻⣇⣐⢻⣿⠃⢸⣿⢿⢟⣥⣾⣿⣿⢿⣾⣿⣿⣽⣿⣿⣷⠶⡇⢰⣿⢻⢯⣷⡄⢉⠀⠀⣸⠀⢀⠀⠈⠀⠀⠁⠀⡁⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀ ⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⡟⠀⣼⣫⣾⣿⣿⣿⡟⠉⢸⣿⣿⠃⠀⠇⠁⠉⣼⡿⢿⣿⣿⡌⣯⣿⣿⣿⣽⣿⣿⡌⠀⢸⡏⣿⢨⡟⠁⣸⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⠀⣼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⠿⢿⣷⠛⣠⣝⣿⣧⣅⣸⣃⣤⠃⢠⠀⣀⣀⡀⠀⣠⣼⣷⣾⣾⣿⡷⢸⣇⠙⢟⣿⣿⣿⠇⠀⠀⠀⠁⢸⣧⣀⣿⡷⠂⠀⠀⢸⠐⠤⠀⠀⣀⠀⣬⠀⠀⠸⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠈⠀⠀⠁⠀⠰⠞⠒⠂⣿⣿⣿⠚⠒⠒⠻⠿⠾⢿⣿⣿⣻⣧⣿⣿⣿⣿⣿⣤⣤⡜⠿⠏⠉⠻⠿⠉⠁⠘⠉⠀⣰⣿⣿⣿⣦⣤⣤⣤⣶⣾⣿⣿⠿⠿⠶⣶⠶⣦⣴⣴⣤⢶⣿⣢⣿⡶⠶⣒⣶⣿⠠⢤⠀⣀⠀ ⠀⠀⣠⣤⠀⣠⣴⣶⣤⡀⠀⣿⣿⣿⣤⣂⣠⣴⣶⣮⡿⣿⣿⣿⣟⣛⣿⡿⠿⣿⠛⠻⢇⠀⠐⠚⠶⠀⠀⠀⢀⣴⣿⡿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣷⣿⣿⣿⡅⢾⣿⣿⣏⠁⢈⡟⣿⡿⠀⠀⠀⠀⠀ ⣀⣛⣿⣿⣤⣿⣿⣤⣿⣿⣴⣿⣇⣸⣿⣿⣻⣿⣲⣿⡿⣏⣿⣷⣻⣭⣴⣿⣿⣭⣥⣤⣴⣦⡀⠀⠀⠀⠀⢒⣫⣵⣾⣿⣿⣿⡿⣶⣉⣿⣟⣛⣉⣿⣿⣯⣏⣉⣉⣉⣉⣉⣈⠁⣿⣿⣿⡃⠀⠸⢿⣿⠀⠀⠀⠀⠀⠀ ⠉⠉⣿⣿⢛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⠻⣿⣮⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡠⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠇⠈⠹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⡿⠶⢶⣿⠷⣆⡀⠀⠀⠀ ⠀⠀⣿⣿⠀⣤⣤⠀⣿⡿⠸⣿⣇⢹⣿⣷⣿⣿⡀⣿⣿⢒⣟⢛⣶⢶⣶⣷⣾⡷⠶⠿⣿⠟⢫⠞⠀⣴⣿⣿⣿⣿⣿⣿⣮⡙⠗⣄⠀⠻⠿⠟⠚⠻⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⣷⣿⣷⣾⣾⣟⠀⠚⠃⠀⠁⠀ ⠀⠀⠛⠛⠀⠈⠛⠛⡛⠁⠀⢹⣿⣿⠋⡀⠈⠛⠛⠛⣱⣞⣛⣘⠻⠼⠿⠷⢶⣾⣷⣶⡁⢰⡏⠀⠈⠴⢛⣋⣥⣭⡛⠿⠿⣧⣠⠚⡁⠀⣶⣦⣤⡶⣼⣿⣽⣯⣝⣟⠛⣛⠟⠛⠛⠛⠻⠿⠷⡻⣿⣿⣿⣿⣶⣤⣤⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⢳⠀⢸⣿⣿⠀⡇⣶⠀⠀⢠⣿⣿⣿⣿⣷⣠⡄⠀⠀⣧⡄⠀⠀⣿⠀⠀⠀⢸⠿⠻⢿⣧⣤⡄⠀⠹⠁⠀⠀⠀⣉⣀⣁⣤⣬⣭⣭⣿⣿⣛⣛⣽⣿⣶⡿⠿⢶⣶⣴⣷⣄⣀⠁⠀⡈⢛⠃⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⠀⠈⠉⠃⠀⡇⠏⠀⠀⢳⣤⠉⡈⠻⣿⣿⣷⣠⣠⣿⡇⠀⠀⠀⠀⠠⢠⣾⣿⣦⣎⣿⣿⠁⠄⠀⠀⠀⠀⠀⢘⣿⣟⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣭⡹⣿⣮⣩⣿⣻⡻⠛⠛⠛⠻⠭⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⣧⠄⠀⠀⠀⠘⢟⠿⠶⠒⢿⣿⣿⠀⠈⠀⠀⠀⠀⠀⣈⣿⣿⣾⣿⣿⡿⠇⠠⠀⠀⠀⠀⠀⠀⣤⣭⢍⣭⣍⠛⠉⠭⣯⣭⣭⣭⣭⣧⡄⠀⢀⣾⠧⣤⢤⡶⠒⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⣿⡅⠀⠀⠀⠀⢀⣧⣼⣦⠀⠈⠃⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠟⡿⠯⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠃⠉⠑⢄⡐⠻⡛⠻⠟⠛⠠⠉⠀⣾⣇⣒⣦⣵⣶⣤⣤⣤⣤⣭⣉ ⠀⠖⠶⣶⠏⢶⠄⠰⣷⠶⠶⠀⠀⠀⠀⣿⣿⣴⡆⠀⢸⣿⣿⣿⣯⣽⣭⣶⣶⣶⣤⣸⣿⣿⣷⡀⠁⠋⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⠀⠠⣄⠀⠁⠀⠀⠿⠯⣭⣿⣽⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠄⠀⠀⣧⠀⠀⠀⠀⠀⠈⣿⣿⣿⠇⢸⣿⣿⣿⣿⣿⣿⡿⠃⠈⣿⣿⡏⠀⠀⢘⣿⣿⣶⣿⣿⣿⣿⣿⣿⡟⠀⡿⠏⣠⣤⠀⢸⣿⣿⡿⣾⣿⡏⠀⠀⠁⠀⢨⠃⢤⡀⠀⠀⠀⠀⠀⠀⢠⣿⡂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⢿⣿⠀⢰⣿⣿⣿⣿⡟⣫⣾⡇⠰⣿⣿⡇⠀⣠⣿⣿⣿⣿⣧⢨⡞⢿⣿⣿⣇⣈⢉⣁⣴⡄⠀⣾⣿⣿⣷⠉⣹⡇⠀⠀⠀⠀⠀⠀⡈⡧⣄⠀⢘⠀⠀⠀⢰⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⡟⠀⢸⣿⡿⣿⣽⣿⣿⣿⣇⣓⢿⡿⠁⢸⣿⣿⢟⣥⣾⣿⣿⢿⣾⣿⣿⣿⣿⣿⣿⡷⡇⢰⣿⢻⣯⣿⡆⢨⡁⠀⢰⠃⠀⡀⠈⠁⠀⠀⠀⢃⠀⠀⠀⠀⠘⡅⠀⠀⠀⠀ ⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⠇⢀⣿⣩⣾⡿⣿⣿⡟⠉⢹⣿⣿⠃⠀⠅⠁⠋⣼⡿⢿⣿⣿⡌⣯⣿⣿⣿⣿⣿⣿⣏⠀⢸⡟⣿⠀⡟⠃⢸⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡄⢰⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⡿⠿⢾⣴⢋⣬⣝⣿⣧⡁⣸⣁⡄⠁⢠⠀⣀⢀⠀⢀⣤⣼⣷⣾⣾⣿⡷⢸⣏⠙⢿⣿⣿⣿⠟⠀⠀⠀⠁⠐⣧⣄⣿⡧⠂⠀⠀⢸⠀⠤⠄⠀⢀⡀⢠⠁⠀⠰⠇⣾⠃⠀⠀⠀⠀ ⠀⠁⠀⠀⠀⠀⠀⠴⠖⠒⢺⣿⣿⡗⠓⠒⠚⠿⠿⠿⢿⣿⣿⣿⣧⣿⣷⣿⣿⣯⣤⣤⡘⣿⠏⠙⠿⠟⠋⠁⠘⠉⠀⣠⣿⣿⣿⣦⣤⣴⣦⣴⣾⣿⣿⠿⠿⠶⣶⣶⣮⣤⣤⣤⠴⣾⡇⣿⣷⠶⠖⣶⣿⠠⢤⣄⡀⢀ ⠀⠀⣠⣤⠀⣠⣴⣶⣤⡀⠸⣿⣿⣷⣤⠀⣠⣴⣶⣯⡿⣿⣿⣿⣿⣛⣿⡿⢿⡿⠟⠻⠇⠀⠐⠒⠶⠀⠀⠀⢀⣴⣿⡿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣤⣿⣷⣿⣷⣿⣿⣿⡇⢸⣿⣿⣿⠉⠀⣿⢻⣿⠀⠀⠀⠀⠀ ⣀⣛⣿⣿⣤⣿⣿⣄⣿⣿⣸⣿⣇⣸⣿⣿⣿⣿⣲⣿⡿⣟⣿⣷⣛⣭⣼⣿⣿⣭⣶⣦⣴⣆⡀⠀⠀⠀⠀⢐⣫⣥⣶⣿⣿⣿⣿⢶⣙⣿⣿⢛⣉⣿⣿⣯⣟⣉⣉⣉⣋⣉⠈⠉⣸⣿⣿⡏⠀⠰⣿⣾⡇⠀⠀⠀⠀⠀ ⠉⠙⣿⣿⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣛⠻⣿⣮⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⡿⠶⠦⣿⠿⢦⡀⠀⠀⠀ ⠀⠀⣿⣿⠈⣭⣤⠀⣿⡿⠹⣿⣏⢹⣿⣷⣿⣿⡀⣿⣿⢖⣞⢲⣶⢶⣶⣶⣾⣷⡶⠿⣿⠟⢋⡔⠀⣴⣿⣿⣟⣿⣿⣿⣧⡛⠗⣄⠀⠻⢿⡟⠚⠻⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣾⣿⣶⣶⣿⠀⠴⠧⠀⠀⠀ ⠀⠀⠛⠛⠀⠈⠛⢛⠛⠁⠀⣽⣿⡟⠋⠀⠈⠛⠛⠛⣵⣜⣛⠘⠻⠼⠿⠷⣤⣾⣶⣦⠁⣠⠏⠀⠈⡴⠿⣋⣁⣍⡻⠿⢿⣧⣠⠸⡁⠀⣶⣦⣤⡤⢴⣿⣿⣿⣙⣿⠛⢻⠿⠿⠛⠿⠿⠿⠿⡽⣿⣿⣿⣿⣶⣤⣄⣀ ⠀⠀⠀⠀⠀⠀⠀⢸⡗⠆⠀⣿⣿⡇⢸⢠⡦⠀⠀⢈⣿⣿⣿⣿⣦⣠⡄⠀⠀⣭⡀⠀⠉⣟⠀⠀⠀⢰⣿⢿⢿⣯⣥⡤⠀⠻⠁⠀⠠⠀⢈⣉⣉⣠⣌⣙⣋⣿⣿⣛⣻⣹⣿⣶⣾⣿⣦⣶⣤⣾⣌⣀⠈⠀⡉⠛⠛⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣧⡇⠀⠉⠙⠁⢸⡀⠅⠀⠐⣃⣈⢃⠉⢿⣿⣿⣇⢤⣰⣿⡇⠀⠀⠃⠀⠔⢀⣼⣷⣔⣌⣿⣿⠃⠄⠀⠀⠀⠀⠀⢈⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣷⣶⣛⣿⣛⣟⡟⠓⢚⠛⠎⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠁⠘⡻⠷⣆⠶⣿⣿⣻⠀⠉⠀⠀⠀⠀⠀⢐⣾⣿⣿⣿⣿⣿⠟⠠⠀⠀⠀⠀⠀⠀⣌⣉⢛⣋⡩⠛⠋⢉⣭⣋⣽⣿⣭⣭⡅⠈⠉⣹⡯⣭⣄⣴⠖⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠘⣆⣵⣄⠀⠉⠃⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⡿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠏⠙⠛⢀⠐⠼⡿⠿⠿⠿⠯⠉⠁⣴⣿⣠⣠⣱⣦⣤⣤⣄⣠⣴⡓ ⠀⠖⠶⣶⠏⢶⠄⢰⡶⠶⠶⠀⠀⠀⠘⣿⣦⢴⡆⠀⢰⣿⣿⣿⣿⣶⣐⣶⢦⣤⣢⣰⣿⣷⣆⠉⠋⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠄⠀⠀⠀⠉⠀⠀⠀⠀⣄⠀⠂⠀⠈⢹⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠠⠀⠀⢸⡅⠀⠀⠀⠠⠀⢸⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⠿⠃⠘⣿⣿⡇⠀⠀⢘⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠈⡿⠋⢠⣤⠀⢸⣿⣿⡿⢸⣿⣿⠀⠀⠀⠀⠠⠄⠀⡄⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⢸⡿⢿⡇⠀⢸⣿⣿⣿⣿⡟⣱⣿⠇⠠⣿⣿⠇⠀⣴⣟⣿⣿⣿⣧⢨⡞⢿⣿⣿⣧⡈⣉⣅⢤⡄⠀⣾⣿⣿⢽⡎⢹⡷⠀⠀⡀⠀⠀⠀⡀⠧⣤⠀⢈⠁⠀⠀⠀⠆⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣾⡇⠀⢺⣿⡿⣿⣿⣿⣿⣿⣇⣒⣿⡟⠀⣸⣿⣿⢟⣴⣾⣿⣿⣿⣾⣿⣿⣟⣿⣿⣿⡇⡧⢠⣿⢿⡏⣾⡆⢨⡅⠀⢠⠇⠀⡀⠀⠁⠀⠈⠀⢈⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀ ⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⠃⢀⣟⣥⣿⣿⣿⣿⡟⠉⣹⣿⡿⠃⠀⠕⠁⠋⣼⡿⢿⣿⣿⡌⣏⣿⣿⣿⣿⣿⣿⣏⠁⢸⡟⣿⠃⡿⠃⢘⡁⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⣤⢠⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⠻⠿⣿⡴⢃⣬⣻⣿⣃⡁⣼⣁⡄⠀⢄⠀⣀⢀⠀⢐⣠⣼⣷⣶⣾⣿⡷⢸⣇⠙⢿⣿⣿⣿⠟⠀⠀⠀⠉⠀⣿⣄⣸⡷⠖⠀⠀⠀⠇⠤⡄⠀⢀⡀⢠⡅⠀⠀⡆⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⠶⠶⠖⢸⣿⣿⠓⠲⠶⠾⠿⠿⠿⣿⣿⣿⣿⣥⣿⣷⣻⣿⣯⣤⣤⡘⣿⠛⠙⠿⠟⠛⠁⠘⠉⠀⣠⣿⣿⣿⣤⣤⣴⣤⣴⣴⣿⣿⡿⡷⣷⣶⣶⣶⣤⣤⣤⡴⣾⣷⣸⣷⡶⠶⠶⣾⡇⠤⣄⠀⢀ ⠀⠀⣠⣤⢀⣠⣴⣶⣤⡀⠿⣿⣿⣶⣤⠀⣠⣴⣶⣦⡿⣿⣿⣿⢿⣻⣿⣿⣿⡿⠿⠿⠇⠀⠐⠲⠶⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣧⣾⣷⣿⣷⣼⣿⣿⣧⠰⣿⡿⣿⡏⠀⠰⢿⣿⠇⠀⠀⠀⠀ ⠀⣛⣿⣿⣤⣿⣿⣀⣿⣿⣸⣿⣇⣸⣿⣿⣿⣿⣺⣿⡿⣛⣿⣿⣛⣭⣽⣿⣿⣉⣲⣄⣴⣄⠀⠀⠀⠀⠀⠔⣛⣥⣶⣿⣿⣿⣿⣧⣘⣻⣾⠛⢋⣻⣿⣯⣟⣋⡉⠋⣛⡉⠉⠉⢱⣿⣿⣿⠀⠀⣿⣾⡿⠀⠀⠀⠀⠀ ⠛⠛⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢿⣛⠻⣿⣮⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡿⠁⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣶⠦⢼⡿⢶⡀⠀⠀⠀ ⠀⠀⣿⣿⠈⣭⣭⠉⣿⡿⠹⣿⣏⢹⣿⣷⣿⣿⡀⣿⣿⢖⣶⢶⣶⢶⣶⣷⣿⣿⣿⠿⣿⠿⢛⡕⠁⣴⣿⣿⣿⣿⣿⣿⣭⡛⡗⣄⠀⢹⣿⡿⠾⠿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣾⣿⣦⣶⣾⡇⠠⠿⠀⠀⠀ ⠀⠀⠛⠛⠀⠈⠛⠛⠛⠁⢰⣽⣿⡛⠋⠀⠈⠛⠛⠛⣵⣜⠛⠘⠛⣽⣿⣭⣤⣶⣦⣄⠁⣠⡏⠀⠘⣠⠾⠏⣁⣛⠻⢿⣿⣧⣀⠸⠓⠀⣦⣤⣤⣤⢬⣿⣿⣿⣙⢿⠿⢿⠿⠿⠟⠿⠿⠿⣿⣟⣿⣿⣿⣿⣶⣤⣄⣀ ⠀⠀⠀⠀⠀⠀⠀⢸⢖⠀⢸⣿⣿⠁⣾⢠⡄⠀⠀⣸⣿⣿⣿⣷⣆⣰⠀⠀⠈⣍⠉⠉⠃⣿⠀⠀⠀⢰⣿⢿⣿⣯⣅⣀⠀⠻⠋⠀⠀⠀⢘⡉⣉⣁⣈⣛⣛⣻⣿⡟⠻⢘⣳⣶⣶⣶⣦⣤⣤⣼⣌⡀⠘⠉⠉⠙⠛⠋ ⠀⠀⠀⠀⠀⠀⠀⣿⣤⠀⠀⠛⠛⠀⣿⠸⠃⠀⠰⣏⡘⠋⠹⣿⣿⣿⡇⣀⢰⣿⡇⠀⠀⠂⠀⠀⢀⣴⣶⣔⡜⣿⣿⠇⡀⠀⠀⠀⠀⠀⠈⣿⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⣷⣖⡛⢻⡟⣿⢟⠳⠂⠺⢓⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠉⠿⢾⣦⡌⢽⣿⣿⡇⠉⠙⠁⠀⠀⠀⠀⠐⣾⣿⣽⣿⣻⣿⡿⢀⠀⠀⠀⠀⠀⠀⣈⣛⣛⣛⣛⠻⠛⢛⣻⣛⣛⣛⣛⣻⣋⠈⠉⢉⡿⣉⣁⣠⡤⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠱⣀⣦⡀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⡟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⢿⡟⠙⠲⠀⠀⢼⡿⠿⣿⠿⠏⠙⠂⢠⣿⠃⢬⣉⣭⣤⣀⣀⣀⣀⣒ ⠀⠖⠶⣶⠏⢶⠄⢴⠶⠶⠖⠀⠀⠀⢸⣷⣤⣤⠀⠀⢴⣾⣿⣿⣿⣖⣠⣤⢤⣠⣠⢰⣶⣶⡆⠋⠋⡟⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠈⠀⠀⣀⠀⠀⠀⠈⠉⣿⣟⣛⣟⣛⣻⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⣽⣿⣿⡟⠀⢸⣿⣿⣿⣿⣿⣿⠿⠂⠘⣿⣿⡇⠀⠀⣙⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⠀⣿⠋⢠⡤⠀⢰⣿⣿⡿⢰⣿⣿⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⡀⠀⠀⠀⢰⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⢻⡟⣿⡇⠀⢸⣿⣿⣿⣿⠛⣵⣿⠀⢸⣿⣿⠀⢀⣼⣟⣿⣿⣿⣧⣸⡾⢿⣿⣿⣿⣈⢫⣥⠤⡦⠀⢺⣿⣿⠿⠄⠙⣿⠀⠀⠀⠀⠀⠀⢀⠹⢤⡀⠀⡁⠀⠀⠀⠖⢹⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⠃⠀⣿⣿⠿⣯⣿⣿⣟⣿⣄⡚⣿⡟⠀⣾⡿⣿⢿⣤⣾⣿⣿⣿⣶⣿⣿⣷⣿⣿⣿⡏⢲⠀⣿⣏⡟⣵⣦⠀⡅⠀⠀⡆⠀⠀⠀⠉⠀⠀⠀⠈⡁⠀⠀⠀⠀⢨⠀⠀⠀⠀ ⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⡿⠀⣰⣏⣽⣿⣿⣿⣿⠋⠁⢿⣿⡟⠁⠠⠜⠁⠃⣾⡿⢿⣿⣿⡌⣯⢿⣿⣿⣽⣿⣿⣗⠁⠀⡿⢹⡇⣽⠋⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⠀⣼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⠻⢷⣧⡞⢣⣭⣻⣿⣈⣁⣿⣀⠔⠀⢄⠀⠀⢀⠀⢐⣤⣼⣷⣶⣾⣿⡷⢸⣇⠙⢿⣿⣿⣿⠿⠀⠀⠀⠈⠀⣿⣄⣸⣿⠖⠀⠀⠀⡇⠠⢤⠀⠀⣀⠀⡌⠀⠀⠰⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⠶⠲⠆⣿⣿⣿⠒⠲⠶⠾⠿⠿⠿⣿⣿⣟⣿⣵⣿⣾⣻⣿⣯⣭⣤⠘⡿⠋⠙⠿⠿⠉⠀⠘⠉⠀⣠⣿⣿⣿⣴⣤⣴⣤⣤⣴⣿⣿⣿⡷⢶⣶⣴⣦⣥⣤⣤⣤⢶⣿⢠⣿⡶⠶⠲⢶⣿⠠⢤⠀⠀ ⠀⠀⣠⣤⠀⣠⣴⣶⣤⡀⡿⣿⣿⣶⣤⠀⣠⣴⣶⣾⡿⣿⢿⣿⢟⣿⣿⡿⢿⣿⠿⠿⡆⠀⠐⠲⠶⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣧⣼⣷⣾⣷⣬⣿⣿⣿⠠⣾⣿⣿⡟⠑⠀⠿⣿⡯⠀⠀⠀⠀ ⢀⣛⣿⣿⣤⣿⣿⣀⣿⣿⣸⣿⣇⣺⣿⣿⣿⣿⣺⣿⡿⣻⣟⣿⣻⣭⣸⣿⣯⣁⣲⣀⣴⣄⠀⠀⠀⠀⠀⠴⣛⣭⣴⣿⣿⣿⣿⣦⣙⣻⣾⠿⠋⣻⣽⣿⣝⡋⡉⠛⠙⣋⠉⠋⠐⣿⣿⣿⠁⠀⢰⣷⣿⠃⠀⠀⠀⠀ ⠛⠛⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⢟⣛⠻⣿⣮⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⣀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡏⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣫⣿⣷⣶⡦⢤⣿⠷⣆⠀⠀⠀ ⠀⠀⣿⣿⠉⣭⣭⠉⣿⡿⠹⣿⣏⢹⣿⣷⣿⣿⡀⣿⣿⢖⣲⢶⣶⣶⣿⣿⣿⣭⣿⣿⣿⡿⢚⡕⠀⣰⣿⣿⣿⣿⣿⣿⣭⠛⣷⣄⠀⢹⣿⣿⠾⠿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣧⣿⣷⣴⣶⣿⠀⠼⠅⠀⠀ ⠀⠀⡛⠛⠀⠈⠛⠛⠛⠁⢰⣽⣿⠛⠋⠈⠈⠛⠛⠻⣵⣘⠛⠘⣛⣹⣿⣭⣥⣶⣤⣤⠉⣠⡏⠀⠈⣀⠾⠟⣋⣛⠻⢿⣿⣗⣀⠸⠃⠀⢤⣤⣄⣤⢌⣿⣟⣿⣛⢻⡿⠿⠿⠿⠿⠿⠿⢿⣿⣯⢿⣿⣿⣷⣶⣤⣄⣀ ⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢸⣿⣿⠀⡆⢠⡀⠀⠀⣰⣿⣿⣿⣷⡄⣠⠀⠀⠈⣉⠉⢉⠂⠿⠀⠀⠀⢰⣾⢿⣿⣏⣁⣀⠀⢹⡋⠁⠨⠀⠘⠋⠙⢉⣈⠛⣛⣛⣿⡿⠿⠖⣓⣦⣤⣶⣦⣤⣤⣠⣧⡉⠉⠋⠉⠙⠛⠛ ⠀⠀⠀⠀⠀⠀⢀⣷⣴⠀⠘⠻⠟⠀⡇⠸⠀⠀⠰⢍⡙⠉⢻⣿⣷⣿⡄⡀⢸⣿⡄⠀⠀⠃⠀⡀⢀⣴⣧⡠⠘⣽⣿⡏⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣦⡽⢿⡿⢿⢿⠿⠦⠴⠷⡒⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⠈⢷⣶⣦⡈⣽⣿⣿⡏⠉⠛⠁⠀⠀⠀⠀⠠⣼⣿⣽⣿⣻⣿⡿⢀⠀⠀⠀⠀⠀⠀⢈⢛⠛⠛⠛⠻⠟⠛⢛⡛⣛⣿⣟⣛⣛⠉⠉⠛⣿⣏⣋⢉⣤⠤⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢢⢘⣇⡀⠉⠻⠃⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⡿⠟⠀⠀⠁⠀⠀⠀⠀⠀⠛⢿⢿⡿⠛⠶⠀⠀⢍⣿⣿⣿⣿⣿⠛⠒⢀⣼⡏⡈⣙⣩⣁⣀⡀⠀⢀⣠ ⠀⠖⠶⣶⠏⢶⠴⠶⠶⠶⠖⠀⠀⠀⣿⣧⡀⡀⠀⠀⢴⣾⣿⣿⡷⣤⢠⣤⣀⣀⢄⢴⣶⣆⡆⠚⠛⡿⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠈⠀⠀⢀⠀⠀⠀⠈⠛⣷⣿⣻⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⠟⠀⠘⣿⣿⠇⠀⠀⣹⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⠀⣿⠃⢠⣤⠀⢠⣿⣿⣿⢲⣿⣿⠅⠀⠀⠀⠀⠈⠀⢠⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⣿⠟⣿⡀⠀⣿⣿⣿⣿⣿⢋⣷⣿⠂⢸⣿⣿⠀⢀⣽⣟⣿⣿⣿⣧⢸⡾⢿⣿⣿⣿⣜⣓⣥⠠⣧⠀⢸⣿⣿⡿⠟⠉⣿⠀⠀⢀⠀⠀⠀⢀⠸⠤⡄⠀⠈⠀⠀⠀⢰⠘⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣳⣿⠀⠐⣿⣿⢟⣻⣿⣿⣿⣿⣠⡜⣿⡟⠀⣾⣿⣿⢿⣴⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⣲⠀⣾⡟⡿⢰⣷⠀⣽⠀⠀⡾⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡁⠀⠀⠀ ⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⡟⠀⣸⣯⣽⣿⢿⣿⣿⠋⠉⣿⣿⡟⠀⠠⠜⠀⠋⣾⡿⢿⣿⣿⡌⣯⣿⣿⣿⣿⣿⣿⣇⠁⠀⣿⢻⡇⢸⠛⠀⡇⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡄⢠⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⡏⢿⢿⣧⠞⣠⣍⣿⣿⣌⣀⣏⣀⠔⠀⠄⠀⠀⢀⠀⢐⣤⣼⣷⣶⣾⣿⡷⢸⣇⠙⢿⣿⣿⣿⡿⠀⠀⠀⠘⠀⢿⣰⣰⣿⠴⠀⠀⠀⠘⠠⢤⠀⠀⢀⡀⢠⠁⠀⠠⠇⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠴⠶⠶⢲⣿⣿⡗⠒⠶⠶⠿⠿⠾⢿⣿⣿⢿⣯⣵⣷⣖⣻⣿⣯⣬⣄⠸⣿⠛⠻⠿⠿⠛⠁⠘⠙⠈⣠⣿⣿⣿⣷⣤⣤⣦⣤⣴⣾⣿⣿⣿⣶⣴⣤⣦⣤⣤⣤⣤⣴⣾⡇⣿⣶⡶⠄⡤⣾⠇⢤⡄⠀ ⠀⠀⣠⣤⠀⣠⣴⣶⣤⡸⡿⣿⣷⣶⣤⠀⣠⣴⣶⣾⡿⡿⣿⣿⣟⣿⣿⣿⣿⣿⠿⠿⡀⠀⠰⠲⠦⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣯⣴⣶⣾⣿⣦⣿⣿⣿⡇⣼⣿⣿⣿⡋⠀⠼⢿⣿⠅⠀⠀⠀ ⢀⣛⣿⣿⣀⣿⣿⣀⣿⣿⣹⣿⣇⣻⣿⣿⣿⣿⣛⣿⡿⢻⣿⡟⣛⣩⣿⣿⣗⣑⣢⣀⣤⡄⠀⠀⠀⠀⠀⠴⢛⣩⣵⣶⣿⣿⣿⣧⡄⣻⣿⠟⠟⣻⣿⣿⣹⡛⢙⠛⠛⠛⠉⠛⠁⣾⣿⣿⡇⠀⠀⣷⣾⡏⠀⠀⠀⠀ ⠛⠛⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⢟⣛⠻⣿⣮⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⣀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡟⣿⣷⣶⣦⣤⣽⡷⣦⠀⠀⠀ ⠀⠀⣿⣿⠈⣿⣭⠉⣿⣿⠻⣿⣏⢻⣿⣷⣿⣿⡀⣿⣿⢔⣶⢦⣤⣭⣽⣭⣿⣭⣭⣿⣿⡿⢞⡵⠀⣰⣿⣿⡿⣿⣿⣿⣏⠻⣷⢄⠀⠹⣿⣿⠯⠿⣿⣿⣿⣿⣿⣿⣿⣏⣯⣿⣿⣿⣿⣿⣽⣷⣤⣤⣾⠅⠠⠷⠀⠀ ⠀⠀⠛⠛⠀⠈⠛⠛⠛⠁⣷⣽⡟⠛⠋⠈⠈⠛⠛⢻⣥⡜⠛⢘⣛⣙⣛⣏⣩⣯⣤⡤⠋⢠⡟⠀⠈⣉⣿⠟⠋⣛⢿⣿⣿⣷⢀⢸⠇⠀⢠⣄⣀⣀⣈⣽⣿⣿⣟⠻⡿⠿⢿⣿⠿⠿⠿⣿⣿⣿⡻⣿⣿⣶⣶⣦⣀⣀ ⠀⠀⠀⠀⠀⠀⢰⡆⡀⠀⣿⣿⡇⢰⡄⢀⠀⠀⠐⣺⣿⣿⣷⣧⡀⣀⠀⠈⢙⡋⠙⠋⠂⡿⠀⠀⠀⢡⣶⣿⣿⡏⣁⣨⠈⠹⡟⠁⢘⠀⠸⠛⠛⠋⡐⠛⠿⠻⣿⣿⠷⠖⠷⣦⣤⣴⣦⣀⣤⣀⣕⡙⠉⠙⠉⠛⠻⠿ ⠀⠀⠀⠀⠀⠀⢸⣇⡄⠀⠛⠿⠇⢸⡇⡟⠀⠀⣼⠋⠻⠛⢿⣿⣿⣿⠀⠀⢸⣿⠀⠀⠀⠂⠀⠀⠀⣨⣯⣨⠹⣽⣿⡟⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣯⡭⠿⣿⠿⡿⡷⠦⠄⡾⠤⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠘⢛⣧⣶⣄⣙⣽⣿⣷⡏⠛⠛⠀⠀⠀⠀⠀⠠⣼⣿⣻⣿⢷⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀⠻⠿⠾⠷⢾⡿⠿⠿⡿⠿⡿⠿⢿⡟⠋⠛⠛⢳⣟⠓⠃⢁⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠋⠁⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⢏⠩⡅⠈⠛⠿⠃⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡿⡟⠁⠈⠁⠀⠀⠀⠀⠀⠘⣿⣯⣿⠿⠧⡄⠀⣉⣿⣿⣿⣿⣿⠟⠧⠀⢠⣿⠉⡙⠋⣛⡀⠀⠀⠀⠀ ⠀⠖⠶⣶⠎⢶⠴⠰⠶⠶⠖⠀⠀⠀⣿⣄⢀⡀⠀⢀⣤⣾⣿⣿⣧⡄⢀⣀⡀⢀⢀⢠⣤⡄⡄⠟⠿⣿⠉⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠄⠈⠁⠈⠉⠉⠈⠀⠀⠛⢳⣶⠾⠿⠿⠿⣿⣿⣿⣿ ⠀⠀⠠⠀⠀⢰⡆⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⣿⣿⣿⣿⣿⣿⡿⠟⠀⢹⣿⣿⠃⠀⠀⣹⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠀⣟⠋⠠⣶⠄⠀⣿⣿⣿⠇⣿⣿⡇⠀⠀⠀⠀⠠⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠼⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠘⣿⢻⣿⠀⠀⣿⣿⣿⣿⣿⢫⣿⣿⠀⢸⣿⣿⠀⢀⣽⣟⣿⣿⣿⣧⢸⡾⢿⣿⣿⣿⣀⣉⣥⠄⢦⠀⢸⣿⣿⡿⠶⠉⢿⡇⠀⠀⠀⠀⠀⠀⡀⠧⢤⠀⢈⠁⠀⠀⠀⠆⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣾⡟⠀⢸⣿⡿⢻⣹⣿⣿⣿⣿⣰⣸⣿⡏⠀⣿⡿⣿⢯⣴⣿⣿⣿⢿⣾⣿⣿⣿⣿⣿⣿⡿⢺⠀⣾⡟⣿⢳⣷⠀⣨⠀⠀⣰⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⢈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⠇⠀⣾⣫⣼⣿⣿⣿⣿⠋⠉⣿⣿⡟⠀⠰⠘⠀⢃⣾⡿⢿⣿⣿⡌⣯⢿⣿⣿⣿⣿⣿⣷⠃⠀⣿⢻⡟⢸⡟⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⠀⣼⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⡿⡿⣾⣤⠛⣬⣙⣿⣧⡈⢨⣇⣀⠄⠀⠀⠀⠀⠀⠀⢐⣠⣿⣶⣶⣾⣿⡷⢸⣧⠙⢿⣿⣿⣿⡿⠃⠀⠀⠈⠁⢸⣣⣀⣿⡦⠂⠀⠀⢸⠀⠤⡀⠀⢀⡀⢀⡀⠀⠀⠄⠀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠶⠶⠶⢸⣿⣿⡗⠲⠶⠾⠿⠿⠿⣿⣿⣿⣿⣯⣽⣶⣖⣻⣿⣭⣬⣄⢸⣿⠛⠻⠿⡿⠛⠁⠘⠙⠀⢀⣿⣿⣿⣧⣤⣤⣦⣤⣤⣾⣿⣿⣿⣶⣴⣤⣦⣬⣤⣤⣤⣤⣼⣧⣸⣷⣦⠤⠤⣼⡇⠠⣄⠀ ⠀⠀⣠⣤⠀⣠⣴⣶⣤⡼⣿⣿⣷⣶⣤⠀⣠⣴⣶⣾⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠿⢿⠀⠀⠠⠶⡦⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣠⣶⣷⣿⣦⣽⣿⣿⣇⢠⣿⣿⣿⠏⠂⠠⠿⣿⡇⠀⠀⠀ ⢐⣛⣿⣿⣀⣿⣿⣀⣿⣿⡻⣿⣇⣾⣿⣿⣿⣿⣛⣿⡿⢿⣿⡿⣟⣩⣽⣿⣟⣃⣤⣀⣤⡀⠀⠀⠀⠀⠀⠤⢞⣫⣽⣷⣿⣿⣿⣯⡔⣻⣷⡿⠟⢛⣿⣿⣛⡟⠛⠙⠛⠛⠉⠈⠂⢸⣿⣿⣿⠈⠀⣼⣦⣿⠀⠀⠀⠀ ⠿⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⢟⣛⠻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⢀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⢻⣿⣶⣦⣤⣸⣿⣦⡀⠀⠀ ⠀⠀⣿⣿⠘⣿⣿⠛⣿⣿⢻⣿⣟⢻⣿⣿⣿⣿⡀⣿⣿⣔⣤⢠⣬⣭⣭⣭⣿⣭⣽⣿⣿⡿⢞⡵⠀⣠⣾⣿⡿⣿⣿⣿⣏⠻⣿⡄⠀⠹⣿⣿⡯⣽⣿⣿⣿⣿⣿⣿⣿⣟⣻⣽⣿⣿⣿⣿⣽⣿⣆⣤⣼⡇⠀⣹⡂⠀ ⠀⠀⠛⠛⠀⠈⠛⠛⠛⠡⣶⣽⡟⠛⠋⠈⠈⠛⠛⣿⣥⡘⠛⢘⣛⣙⣛⣋⣩⣭⣄⡨⠋⢠⡞⠀⠐⢉⣽⠟⠟⠿⢿⣿⣿⣷⠀⢸⠦⠀⢩⣉⣀⣀⣈⣹⣿⣿⣿⠻⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⣿⣿⣷⣶⣦⣀⣀ ⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⣿⣿⡇⢠⠀⠀⠀⠀⠀⣼⣿⣷⣶⣄⠀⡉⠉⠉⢙⠛⠛⠛⠀⣾⠀⠀⠀⢩⣴⣶⣿⡟⠃⠈⠉⠳⡟⠃⠐⠀⠘⠟⠛⠛⠁⠻⠿⠿⢿⣷⡿⣦⠴⢦⣤⣤⣤⣄⣀⣉⣹⡘⠋⠋⠟⠛⠻⠿ ⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠿⣿⠁⢸⠀⡇⠀⠀⣜⠛⠿⠻⣿⣿⣷⣷⠀⠀⣸⣿⠀⠀⠀⠁⠀⠀⠀⣨⣭⢈⠹⣻⣿⡟⠁⠀⠁⠀⠀⠀⠐⢶⣶⣶⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⢿⣯⣉⣿⣿⡿⣿⣷⣶⣄⠠⣦⠄ ⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⢻⣤⣦⣈⢛⣻⣿⣦⡗⠻⠟⠀⠀⠀⠀⠀⠁⣸⣿⣿⣷⢷⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠺⠿⢿⠷⠾⣿⠿⠿⠿⠿⢿⣿⠿⠿⠖⠻⠛⠗⣾⠳⠚⠘⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠛⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠩⡉⢻⠊⠙⠿⢿⠇⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⠉⠈⠂⠀⠀⠀⠀⠀⠘⢶⣶⣶⡶⣦⡄⠀⢐⢻⣶⣿⣿⣿⡿⠧⠄⠀⣼⡏⠓⠛⠚⠋⠀⠀⠀⠀ ⠀⠖⠶⣶⠎⢶⠶⠰⠶⠶⠖⠀⠀⢸⣦⡀⠀⠀⠀⢀⣠⣽⣾⣿⣆⣀⡀⠀⠀⠀⠀⢠⣄⡀⡨⠿⣿⣿⠋⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠠⠬⠉⠉⠉⠉⠉⠁⠀⠀⠸⠿⣤⣾⣶⣿⣿⣿⣶⣶⣶ ⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⣿⡿⠟⠀⢹⣿⣿⠁⠀⠀⣹⣿⣷⣾⣿⣿⣿⣿⣿⣿⡿⠀⡿⠃⠀⣴⠄⠀⣾⣿⣿⠇⣺⡿⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠠⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⠂⠀⠀⠀⠀⠀⢸⡿⢻⣇⠀⢸⣿⣿⣿⣿⡿⢫⣾⡟⠀⢾⣿⣿⠀⢀⣼⣟⣿⣿⣿⣇⢸⡞⢿⣿⣿⣿⣀⢉⣡⠀⢴⠄⠰⣿⣿⡿⢷⠈⢸⡇⠀⠀⠀⠀⠀⠀⠀⠠⢤⡀⠀⡁⠀⠀⠀⠐⢸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣗⣾⡇⠀⢸⣿⡿⢻⣽⣿⣿⣻⣿⣐⣺⣿⠏⠀⣿⡿⣿⢯⣴⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⢐⠄⢸⣿⣿⢣⣶⡄⢨⡄⠀⢠⠂⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⢀⣿⣩⣾⣿⣿⣿⡟⠋⠉⣿⣿⡟⠀⠐⠘⠀⢃⣾⡿⢿⣿⣿⡌⣯⢿⣿⣿⣿⣿⣿⣷⠈⠀⣿⠯⣿⢸⡟⠁⢸⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡄⢰⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⢹⡿⣿⡴⠃⣌⣻⣿⣃⠉⣸⣇⣀⠀⠀⠁⠀⠀⠀⠀⢐⣤⣿⣶⣶⣾⣿⡷⢸⣧⠙⢿⣿⣿⣿⡿⠃⠀⠀⠀⠃⢸⣇⡀⣾⡧⠆⠀⠀⠀⡇⠤⡄⠀⠀⣀⠀⡌⠀⠀⠠⠀⣾⠃⠀⠀ ⠀⠀⠀⠀⠀⠰⠶⠶⠆⣿⣿⣿⠒⠶⠶⠶⠿⡿⢿⣿⣿⣿⢿⣯⣽⣶⣖⣻⣿⣭⣭⣄⢸⣿⠛⠻⢿⡿⠛⠁⠘⠙⠀⢀⣿⣿⣿⣧⣤⣤⣤⣤⣤⣼⣿⣿⣿⣷⣤⣤⣤⣤⣤⣄⣤⣤⣤⣿⢀⣿⣦⡤⠤⢤⣿⠀⢠⡀ ⠀⠀⣠⣤⠀⣠⣴⣶⣤⡿⡿⣿⣶⣶⣤⠀⣠⣴⣶⣿⡿⣿⣿⣿⢿⣿⣿⣿⣿⡿⠿⢿⠀⠁⠠⠶⡤⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣶⣶⣿⣧⣼⣿⣿⣿⠀⣾⣿⣿⡟⠁⠀⠴⢿⡿⠀⠀⠀ ⢐⣛⣿⣿⣀⣿⣿⠀⣿⣿⠻⣿⣇⣾⣿⣷⣻⣿⣋⣿⡿⣿⣿⠿⣛⣉⣿⣷⣏⠂⣤⢀⣥⡀⠀⠀⠀⠀⠀⡠⠶⣋⣭⣿⣾⣿⣿⣯⡄⢒⣷⡿⠿⠛⣟⣿⣟⡟⠛⠋⠛⠛⠛⠉⠉⠀⣿⣿⣿⠇⠀⢠⣦⣼⡇⠀⠀⠀ ⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢟⣟⠻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⡀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⠉⠻⣿⣿⣷⣶⣿⣿⣿⣿⣿⣷⣷⣾⣿⣿⣶⣶⣼⣿⢟⣿⣷⣤⣤⣁⣿⣧⡄⠀⠀ ⠀⠀⣿⣿⠚⣿⣿⠛⣿⡿⠻⣿⣟⢻⣿⣷⣿⣿⡀⣿⣿⣄⣈⢉⣉⣉⣛⣿⣿⣻⣿⣿⣿⣿⠾⡫⠀⢠⣾⣿⣿⣿⣿⣿⣟⠿⣷⡀⠀⠸⣿⣿⣿⣽⣿⣿⣿⣿⣿⣾⣿⣿⣻⣿⣿⣿⣿⣷⣏⣿⣯⣁⣠⣿⠀⢈⡆⠀ ⠀⠀⠛⠛⠀⠈⠛⠛⠛⢁⣶⣽⠛⠛⠋⠛⠈⠛⠛⣿⣁⠘⠛⠘⠛⣛⣛⣛⣫⣍⣉⡘⠋⢀⡞⠁⠐⠛⣿⡿⠟⠻⢿⣿⣿⣷⠀⠘⡦⠀⢉⣉⡁⢀⣀⢛⣿⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣦⣤⣄⡀ ⠀⠀⠀⠀⠀⠀⣆⠀⠀⢸⣿⣿⠀⣄⠀⠀⠀⠀⠀⣿⣿⣶⣴⣈⠉⠉⠉⠙⠛⠛⠛⠓⠔⣾⠀⠀⠀⢋⣥⣶⣷⡟⠆⠉⠉⠳⡷⠃⠁⠀⠈⡿⠛⠟⠋⠻⠿⠿⢿⣷⣾⣦⠴⣦⣅⣀⣤⣄⢈⡉⢉⡎⠛⠛⠻⠛⠻⠿ ⠀⠀⠀⠀⠀⠀⣏⠀⠀⠸⢿⣿⠀⣿⢰⠇⠀⢀⡖⡻⡟⠿⣿⣿⣶⣧⠀⠀⢸⣷⠀⠈⠀⠁⠀⠀⠀⢸⣟⢉⢹⣳⣿⡿⠁⠀⠁⠀⠀⠀⠀⢶⣶⣶⣾⣷⣶⣶⣿⣾⣷⣶⣶⣾⣿⣿⣿⣛⣻⣿⣿⣿⣷⣦⣄⡀⣤⣀ ⠀⠀⠀⠀⠀⠘⣷⡎⠀⠀⠀⠀⠀⢹⠀⠀⠀⠈⠶⢶⣀⣄⠙⠛⣿⣿⣦⠦⠿⠿⠀⠀⠀⠀⠀⠁⣰⣿⢿⣷⣦⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣿⣬⣿⣿⣿⣿⣿⢿⣿⡿⣿⠶⠛⠿⠷⢴⡿⠔⠃⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡿⠃⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠉⢹⠛⢛⠈⠛⠿⣯⠇⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣾⣿⠋⠐⠂⠀⠀⠀⠀⠀⠰⢦⣤⣢⣶⣖⡉⠀⠐⢲⣶⣾⣶⣶⣶⢶⣀⠀⢠⡿⠓⠶⠦⠞⠉⠀⠀⠀ ⠀⠖⠶⣶⠊⢶⠗⠰⠶⠶⠖⠀⠀⢸⡄⠀⠀⠀⠀⠀⣀⣷⣾⣶⡄⠀⠈⠀⠀⠀⠀⢀⣀⡀⡈⡿⣿⣿⠟⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠙⠁⠈⠈⠠⣈⠙⠛⠉⠛⠛⠃⠀⠀⠰⠿⣇⣤⣶⣶⣿⣶⣶⣶⣤ ⠀⠀⠀⠀⠐⡆⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⢸⣿⣿⣿⣿⣿⣿⠿⠃⠀⢻⣿⣿⠀⠀⠀⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠀⡻⠃⠀⣴⠄⠀⣼⣿⣿⡷⣸⣿⡿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠾⡇⠀⠀ ⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⣿⡟⣿⡇⠀⢸⣿⣿⣿⣿⡟⣡⣿⡟⠀⢿⣿⡿⠀⢀⣿⣿⣿⣿⣿⣧⢸⡞⢿⣿⣿⣿⣀⡈⣡⡀⢴⠄⠀⣿⣿⣿⢿⠈⠘⡷⠀⠀⠀⠀⠀⠀⢀⠸⠤⡄⠀⢈⠀⠀⠀⠀⠂⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣿⠃⠀⣾⣿⠟⣋⣵⣿⣿⣿⣯⣐⢺⣿⠋⠀⣿⡿⣿⢫⣴⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⢐⠄⢸⣿⢻⢏⣶⡄⢀⡅⠀⠀⡆⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⡿⠀⢀⣟⣥⣾⣿⣿⣿⡟⠋⠘⣿⣿⠟⠀⠀⠈⠐⢃⣿⣿⢿⣿⣿⡌⣯⢿⣿⣿⣯⣿⣿⣿⠀⠀⢺⡏⣿⠀⡟⠃⢘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡤⢀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⡏⢿⣿⣦⡴⢃⣙⣫⢿⣃⠉⣸⣁⡀⠀⠀⠉⠀⠀⠀⠀⢐⣈⣿⣦⣶⣾⣿⣷⢸⣧⠙⢿⣿⣿⣿⡿⠇⠀⠀⠀⠃⢸⣇⡀⣸⣧⠄⠀⠀⠀⡇⠠⣄⠀⠀⢀⠀⢠⠀⠀⠀⠅⢸⡇⠀⠀ ⠀⠀⠀⠀⠀⢠⠶⠤⠠⣿⣿⣿⠲⠶⠴⠶⣿⣿⣿⣿⣿⡿⣿⣍⣳⣶⣖⣻⣿⣅⣠⡄⢺⣿⠛⠻⣿⡿⠛⠁⠘⠙⠀⢀⣿⣿⣿⣧⣀⣀⣦⣤⣤⣴⣿⣿⣿⣷⣤⣤⣤⣤⣥⣄⣠⣀⣤⣾⡇⣾⣶⣤⠤⠤⣼⡇⠀⡀ ⠀⠀⣠⣤⠀⣠⣤⣶⣬⡿⡿⣯⣴⣶⣤⠀⣠⣴⣶⣾⡿⣿⣿⡿⢿⣿⣿⣿⣿⣿⠿⣿⠀⠁⠠⢤⡤⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣴⣶⣾⣷⣌⣿⣿⢿⡁⣼⣿⣷⣿⠋⠀⠀⠶⣿⠇⠀⠀ ⣐⣛⣿⣿⣀⣿⣿⠀⣿⣿⠿⣿⣇⣾⣿⣧⣻⣿⢋⣿⡿⣿⣿⠿⣛⡩⣿⣷⡏⠣⢤⢀⣀⡀⠀⠀⠀⠀⠀⣠⠶⣛⣩⣽⣾⣿⣿⣯⡁⠠⣦⣿⠿⠛⣿⣿⣟⡿⠟⠛⠛⠿⠛⠙⠙⠀⣼⣿⣿⡏⠀⠀⣼⣤⡿⠀⠀⠀ ⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣟⠻⣿⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⠉⠻⣿⣿⣷⣶⣾⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣦⣿⡿⣿⣷⣤⣤⣉⣸⣷⣤⠀⠀ ⠀⠐⣿⣿⠛⣿⣿⠛⣿⡿⠿⣿⣟⢻⣿⣧⣿⣿⡀⣿⣿⣌⣉⢉⣙⣛⣛⣻⣟⣛⣻⣿⣿⣿⡴⡫⠀⢠⣾⣿⣿⣿⣿⣿⣟⠿⣿⡀⠀⠘⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⢛⣟⣿⣿⣿⣷⣟⣻⣿⣉⣉⣽⡇⠈⣳⠀ ⠀⠀⠛⠛⠀⠈⠛⠛⠛⣵⣷⣽⠛⠛⠋⠛⠈⠛⢛⣿⡁⠙⠛⠼⠿⠿⠟⠛⣛⣋⣉⠹⠛⢁⡞⠁⠀⢛⣻⡿⠗⠿⣿⣿⣿⣷⠈⠘⡦⡀⢉⣉⠁⠀⠀⢛⣿⠿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣧⣤⣄⡀ ⠀⠀⠀⠀⠀⢠⡀⠀⠀⣿⣿⣿⠀⡀⠀⠀⠀⠀⢀⣿⣿⣦⣦⡉⠉⠛⠛⠛⠻⠟⠻⠧⠐⡿⠀⠀⠀⢊⣭⣴⣶⡷⠎⠙⠛⠻⡷⠇⠁⠀⠀⡿⠿⠿⠏⠹⣿⣿⣿⣶⣼⣧⡤⣯⣉⡁⣀⣉⠉⠉⠋⣣⠻⠛⢛⠟⠿⠿ ⠀⠀⠀⠀⠀⢸⡁⠀⠀⣿⣿⡏⠀⡇⢰⠂⠀⢀⠾⢿⡿⣿⣿⣿⣴⡇⠀⠀⣰⣦⠀⠀⠀⠃⠀⠀⠀⢘⣛⠙⢹⢷⣷⣶⠀⠀⠁⠀⠀⠁⠀⢶⣦⣤⣶⣶⣴⣶⣶⣿⣷⣬⣥⣶⣿⣿⣿⣛⠻⣿⣿⣿⣷⣤⣄⡀⢀⡄ ⠀⠀⠀⠀⠀⢸⣷⠆⠀⠀⠈⠁⠀⡇⠈⠀⠀⠈⡵⣦⣠⡈⠛⠿⣿⣷⣰⠠⢿⡿⠀⠀⠀⠀⠀⠂⢰⣿⣿⣦⣮⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⢬⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠜⢿⠶⢭⣿⠥⠯⠉⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⢸⠟⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠓⣛⠻⡷⠘⠻⢿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣼⡿⠋⠐⠀⠀⠀⠀⠀⠀⢠⣦⣤⢤⣥⣄⣈⠁⠀⠴⣦⣴⣯⣥⣶⣶⣆⠀⠀⣼⠟⠦⡦⠴⠛⠁⠀⠀ ⠀⠖⠶⣶⠊⢿⠆⠰⠶⠶⠖⠀⠀⣧⠀⠀⠀⠀⠀⠀⢈⣦⣿⣦⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠟⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠃⠈⠉⠀⣀⠒⠛⠛⠻⠛⠛⠀⠈⠀⣾⣟⣐⣰⣤⣶⣶⣤⣤⣤ ⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⣿⠿⠃⠀⢻⣿⣿⠀⠀⠀⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠀⠹⠃⠀⢴⠆⠀⣸⣿⣿⡿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠀⠀ ⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⣿⠻⣿⠀⠀⣾⣿⣿⣿⣿⡟⣵⣿⡇⠀⢿⣿⡇⠀⢠⣿⣻⣿⣿⣿⣇⢸⡾⢿⣿⣿⣿⡄⢈⣡⡀⢼⡄⠀⣿⣿⣿⠿⠄⠈⣿⠀⠀⢀⠀⠀⠀⠀⡀⠦⣤⠀⢈⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⠀⠀⣿⣿⠟⣫⣿⣿⣿⣿⣇⣀⢻⣿⠃⢀⣿⣿⣿⢫⣴⣾⣿⣿⣿⣾⣿⣿⣷⣻⣿⣿⣷⢑⡆⢰⣿⢻⡇⣾⣶⠀⡅⠀⠀⡼⠀⠀⠀⠈⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⢈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡏⠀⣸⣏⣭⣿⣿⣿⣿⡟⠉⢹⣿⣿⠏⠀⠀⠈⠈⢃⣿⣿⢿⣿⣿⡌⣯⢿⣿⣿⣿⣿⣿⣿⡈⠀⢸⡟⣿⠁⣿⠋⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⠀⣼⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⡏⣿⢼⣤⠖⢀⣛⢫⣿⣈⠁⣿⣁⡠⠀⠈⠁⠀⠀⠀⠀⢐⣈⣿⣦⣾⣾⣿⣷⢸⣷⠙⢿⣿⣿⣿⣿⠇⠀⠀⠀⠋⠀⣿⣀⣸⣿⠴⠀⠀⠀⠸⠠⢤⡀⠀⠀⡀⢀⡀⠀⠀⠬⠀⣿⠀⠀ ⠀⠀⠀⠀⢀⡤⠤⠤⢸⣿⣿⡇⠶⠦⠴⢶⣿⣽⣿⣿⣿⣿⣿⣍⣷⣶⣚⣻⣿⣃⣁⡀⢾⣿⠛⠻⣿⡿⠛⠃⠘⠙⠀⢀⣿⣿⣿⣧⣄⣀⣦⣤⣤⣤⣿⣿⣿⣷⣦⣤⣤⣤⣌⣄⣠⣄⣠⣼⡧⢸⣷⣤⡤⠤⣤⣿⠀⢀ ⠀⠀⣠⣤⠀⣠⣴⣶⣾⣿⡿⣧⣴⣶⣤⠀⣠⣴⣶⣿⡿⣿⣿⡿⠿⣿⣿⣿⣿⣿⢿⣿⠈⠁⠠⢤⡤⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣰⣶⣾⣿⣌⣿⣿⣿⡏⢠⣿⣷⣿⡟⠁⠀⡴⢾⡟⠀⠀ ⣀⣛⣿⣿⠀⣿⣿⠀⣿⣿⠿⣿⣇⣾⣿⣧⣻⡿⢋⣿⡿⣿⣿⠿⢛⣋⣷⣿⠛⠦⡄⢀⣀⠀⠀⠀⠀⠀⠀⣀⠴⢛⣫⣽⣿⣿⣿⣯⡅⠡⣤⣿⠿⠛⢿⣿⣿⢻⠟⠛⠻⠿⠟⠛⠉⠁⢸⣿⣿⣿⠀⠀⢰⣤⣽⠃⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⢿⣟⢻⣿⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⠉⠳⣿⣿⣿⣶⣶⣿⣿⣿⣿⣶⣾⣶⣶⣶⣶⣶⣦⣾⣿⢿⣿⣤⣤⣈⢙⣿⣄⡀⠀ ⠀⠹⣿⣿⠛⣿⣿⠟⣿⡿⠿⣿⣟⢻⣿⣇⣿⣿⡀⣿⣿⣉⣉⢉⣛⢛⣛⣻⣿⣛⣻⣿⣿⣿⡴⡪⠀⢀⣾⣿⣿⣿⣿⣿⡿⢻⣿⡀⠀⠘⣿⣿⣿⣻⣿⣽⣿⣿⣿⣿⣿⣿⡟⣟⣿⣿⣿⣿⣾⣻⣿⡍⢉⢩⣿⠁⠑⠄ ⠀⠀⠛⠛⠀⠈⠛⠛⠛⣥⣴⡝⠛⠛⠋⠛⠈⠛⣛⣛⡑⠙⠻⠼⠿⠿⠿⠟⢛⣛⠉⠹⠟⢁⡞⠁⠠⠛⣻⣿⡿⢿⣿⣿⣿⣧⠈⠘⣦⡀⠙⡛⠃⠈⠉⠛⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣯⣄⣀⡀ ⠀⠀⠀⠀⠀⣄⠀⠀⠀⣿⣿⡇⢀⠀⠀⠀⠀⠀⢘⣿⣦⣤⣄⠓⠛⠛⠛⠛⠿⠿⠿⢇⠀⡾⠀⠀⠀⢒⣩⣥⣦⡶⠌⠙⠛⢻⣧⠆⠁⠄⠀⣿⠿⠿⠟⠹⣿⣿⣿⣷⣬⣯⣉⣭⣉⠉⢁⣉⠉⠙⠛⢳⠙⠟⠟⡿⠿⠿ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⡇⢸⠀⡴⠀⠀⠀⠼⢿⣿⣿⣿⣷⣴⡄⠀⠀⣶⡆⠀⠌⠈⠃⠀⠀⠀⢸⡿⠛⢻⢧⣶⣶⠂⠀⠁⠀⠀⠀⠀⣤⣤⣤⣴⣶⣤⣴⣶⣿⣿⣭⣥⣴⣿⣿⣿⡟⠳⣾⣷⣾⣶⣤⣀⡀⢀⣀ ⠀⠀⠀⠀⠀⣿⣔⠀⠀⠀⠉⠀⢸⠅⠁⠀⠀⢈⣨⡌⢁⠘⠿⠿⣿⣧⣠⢤⣿⡿⠀⠀⠀⠀⠀⠂⢠⣿⣿⣦⣜⣾⣿⠇⠐⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣍⣻⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⢿⣿⣍⣹⣏⡹⠩⠉⠉⠀⠉ ⠀⠀⠀⠀⠀⣿⠟⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠫⡿⠷⡆⠺⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣾⡿⣽⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣤⣭⢩⣩⣭⠙⠋⠉⢭⣭⣥⣭⣭⣭⣭⡄⠀⠀⢠⡿⠦⣤⣠⡴⠒⠀⠀ ⠀⠖⠲⣶⠊⢿⠖⠰⠶⠶⠖⠀⢸⣇⠀⠀⠀⠀⠀⠀⠱⣤⣧⣄⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠻⠏⠈⠙⠀⠀⠂⢿⠿⠿⠿⠿⠇⠉⠁⢠⣿⠃⣀⣄⣤⣤⣤⣄⣀ ⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⣿⣿⡿⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⠁⠀⢤⡆⠀⢸⣿⣿⡿⠰⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⠀ ⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⢸⣿⢻⣿⠀⠀⣿⣿⣿⣿⣿⠋⣴⣿⠃⠀⣿⣿⡇⠀⢠⣾⣻⣿⣿⣿⣷⢸⡞⢿⣿⣿⣿⡀⠀⣉⡀⠠⠄⠀⣾⣿⣿⠻⠆⠈⢷⠀⠀⠀⠀⠀⠀⠀⡀⠠⢤⠀⠀⠁⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣼⡏⠀⢰⣿⣿⢟⣩⣾⣿⣟⣿⣇⣀⢿⣿⠃⢰⣿⣿⣿⢫⣴⣿⣿⣟⣿⣾⣿⣿⣿⢿⣿⣿⣿⠀⡀⢀⣿⢿⡏⣰⣦⠀⣠⠀⠀⠰⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠇⠀⣸⣏⣽⣿⣿⣿⣿⠛⠉⢹⣿⣿⠇⠀⠨⠊⠘⢁⣿⣿⣿⣿⣿⡌⣏⢿⣿⣿⣯⣿⣿⣿⡄⠀⢸⡿⣾⠇⣽⠛⠀⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡄⢠⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⣴⣿⢹⣿⣿⣤⠖⣈⡛⠿⣟⢈⠉⢟⣀⡀⠀⠀⠁⠀⠀⠀⠀⠀⣈⣿⣦⣯⣿⣿⣷⢸⣷⠝⢿⢿⣿⣿⣿⠇⠀⠀⠀⠉⠀⣿⢀⢐⣿⡤⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⣀⠀⠀⠀⠄⢸⡇⠀ ⠀⠀⠀⠀⢠⡤⠤⠄⣿⣿⣿⠦⠤⢤⡽⣶⣿⣽⣿⣿⣿⣾⣿⣉⣶⣴⣒⣳⣾⣉⣁⡀⢿⣿⠟⢻⣿⡿⠛⠃⠘⠛⠀⠀⣿⣿⣿⣯⣄⣀⣠⣀⣠⣠⣿⣾⣿⣿⣦⣤⣄⣤⣄⣀⣀⣀⣀⣤⣿⠀⣿⣤⣤⠤⠀⣼⡇⠀ ⠀⠀⣠⣤⠀⣠⣤⣶⣿⡿⣿⣤⣴⣶⣤⠀⣠⣴⣶⣿⡿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⠈⠁⣠⢤⡄⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣡⣴⣼⣿⣍⣹⣿⣿⡏⠁⣾⣿⣾⡿⠃⠀⢠⢴⣿⠀⠀ ⢀⣛⣿⣿⠀⣿⣿⠀⣿⣿⠿⣿⣇⣼⣿⣧⣻⡿⢉⣿⡿⡿⣿⠷⠛⢛⣿⣯⠛⠆⡀⢀⣀⠀⠀⠀⠀⠀⠀⢀⡴⢟⣛⣭⣽⣿⣿⣿⡉⠉⢉⣽⣿⠿⢿⢿⣿⠻⠿⠛⠻⠿⠿⠛⠋⠋⢀⣿⣿⣿⠇⠀⠀⣤⣨⡏⠀⠀ ⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣶⣾⣿⢿⣿⡿⢿⣟⣻⣿⣮⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⡋⠳⣶⣿⣿⣴⣶⣾⣿⣿⣿⣶⣶⣴⣶⣶⣶⣤⣤⣼⣿⡿⣿⣦⣄⣈⠉⢿⣧⣀⠀ ⠨⠭⣿⣿⠿⣿⣿⠿⣿⣿⠿⣿⣟⢻⣿⡇⣿⣿⡀⣿⣿⣉⣙⢛⣛⢛⣟⢿⡿⢿⣿⣿⣿⣟⡴⢢⠁⢀⣼⣿⣿⣿⣿⣿⡿⢿⣿⡁⠀⠘⣿⣿⣿⣻⣿⣿⣿⣻⣿⣿⣿⣿⡿⢿⢿⣿⣿⣿⣾⡟⣿⣟⠉⠉⣿⡋⠉⠢ ⠀⠀⠛⠛⠀⠈⠛⠛⠛⣥⣤⡝⠛⠛⠿⠞⠊⠟⣛⡛⠑⠙⢻⠼⠿⠿⠿⠿⢟⡛⠛⢻⠟⢉⡼⠁⠠⠺⣿⣿⡿⣿⣿⣿⣿⣦⡘⠙⣦⠀⠙⠛⠛⠉⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣄⣀⡈ ⠀⠀⠀⠀⢀⡀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣹⣿⣤⣀⡀⠒⠒⠛⠛⠶⠿⠿⠿⣆⠠⡾⠀⠀⠀⠞⣛⣥⣤⣶⡌⠛⠛⠿⣆⠦⠃⡄⠀⢿⡷⣶⡾⠒⣿⣷⣶⣷⣬⣿⣉⣩⣛⠋⠉⢉⠉⠛⠛⠛⠜⢿⠿⢿⠿⢿ ⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⣿⠀⣿⠀⡄⠀⠀⢠⣾⣿⣿⣿⣿⣆⢠⠀⠀⠀⣤⡄⠀⠀⠈⠃⠀⠀⠀⠸⠿⠛⢻⣯⣤⣦⠀⠀⠁⠀⠀⠀⠀⢨⣤⣀⣠⣤⣤⣭⣬⣽⣿⣉⣉⣨⣭⣿⣿⡿⠿⢶⣶⣶⣷⣤⣀⡀⠀⠀ ⠀⠀⠀⠀⢸⣇⡀⠀⠀⠉⠋⠀⢸⠀⠀⠀⠀⢓⣤⡈⡀⠙⢿⣷⣿⣇⢀⣀⣿⣗⠀⠀⠀⠀⠀⠄⢠⣾⣿⣌⣜⣼⣿⡏⠠⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⢿⣷⣎⣉⣿⣘⡏⠛⠛⠂⠈ ⠀⠀⠀⠀⠈⡿⠆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠨⠽⢾⣶⡄⠴⣿⢿⣿⠀⠈⠁⠀⠀⠀⠀⠀⢀⣾⣿⣽⣽⣻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣄⣉⠋⢛⣉⠙⠛⠉⣉⣭⣉⣽⣋⣉⣭⣭⠀⠁⠈⣼⢧⣁⡀⣠⠤⠀⠀ ⠀⠖⠲⣶⠾⢷⠆⠰⠶⠶⠖⠀⢸⠀⠀⠀⠀⠀⠀⠀⢣⢀⣦⡀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⡿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠶⡟⠉⠓⠀⠀⠠⢽⡿⢿⣿⣿⠏⠉⠃⠀⣼⡟⠀⢈⣀⣥⣄⣀⣀ ⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠀⠈⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⣿⣿⡟⠀⠀⠀⣽⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠁⢸⠟⠀⢰⡦⠀⢸⣿⣿⣿⠃⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀ ⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⢹⡟⢻⡇⠀⢰⣿⣿⣿⣿⣿⢋⣶⣿⠃⠀⣿⣿⡇⠀⢠⣿⣻⣿⣿⣿⣷⢸⡞⢿⣿⣿⣿⡀⡈⣩⡄⢰⡄⠀⢾⣿⣿⡟⡧⠀⢻⡆⠀⠀⠀⠀⠀⠀⢀⠰⠴⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣿⡇⠀⢸⣿⡿⢛⣽⣿⣿⣏⣿⣇⡐⢿⡿⠃⢰⣿⣿⣿⢫⣴⣿⣿⣟⣿⣾⣿⣿⣷⣿⣿⣿⣿⠀⡄⠀⣿⣏⡿⢰⣷⠀⢠⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠁⢀⣾⣩⣽⣿⣿⣿⣿⠛⠉⢻⣿⣿⠃⠀⠈⠋⠘⢁⣿⣿⣿⣿⣿⡌⣏⢿⣿⣿⣏⣿⣿⣿⡄⠀⠸⣿⢸⡇⢸⠟⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣼⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⢿⡧⣎⣴⠆⣘⡛⣿⡃⡈⠉⠟⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣈⣿⣤⣮⣿⣿⣷⢸⣷⠝⢿⣿⣿⣿⣿⠗⠀⠀⠁⠘⠀⢼⣀⠀⣿⣦⠄⠀⠀⠀⠇⠠⣀⠀⠀⠀⠀⢀⠂⠀⠀⠄⠀⣿⠀ ⠀⠀⠀⠀⣤⡤⣤⢠⣿⣿⣿⠠⢤⣤⣴⣶⣯⣿⣿⣿⣷⣾⣟⢩⢦⣤⢲⣶⣞⣀⣀⡀⣿⣿⠿⢻⣿⡿⠿⠃⠸⠛⠀⠀⣹⣿⣿⣿⣀⣀⣠⣀⣠⣀⣾⣿⣿⣿⣥⣤⣄⣠⣄⣀⣀⣀⣀⣠⣾⡆⣸⣦⣤⡄⠀⢠⡟⠀ ⠀⠀⣠⣤⠀⣠⣤⣾⣿⣿⡿⣠⣴⣶⣤⠀⣠⣴⣾⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠈⠁⣠⣤⣄⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢈⣬⣭⣿⣯⣙⣿⡿⢿⠉⣸⣿⣷⣿⠛⠀⠀⡠⣾⡇⠀ ⣀⠛⣿⣿⠀⣿⣿⠀⣿⣿⠿⣿⣇⣼⣿⣧⣻⡿⢉⣿⡿⣿⣿⡷⠟⢻⣯⣭⠟⢄⡀⠀⣀⠀⠀⠀⠁⠀⠀⢀⣴⠞⣛⣿⣽⣿⣿⣿⡋⠩⢭⣽⣿⠟⢻⣿⣿⠟⠿⠿⠛⠿⠿⠏⠋⠙⠀⣼⣿⣿⡟⠀⠀⣰⣀⣿⠀⠀ ⣿⣿⣿⣿⣶⣿⣿⣶⣿⣿⣾⣾⣿⢿⣿⡿⢿⣟⣻⣿⣮⣿⣧⣾⣿⣿⣿⣿⣶⣶⣷⣿⣿⣦⡄⠀⠀⠀⠀⣥⣶⣿⣿⣿⣿⣿⣿⡟⠻⣶⣾⣿⣤⣴⣾⣿⣿⣿⣶⣴⣤⣤⣶⣶⣤⣤⣤⣿⣿⢿⣧⣀⣀⠙⢹⣿⣀⠀ ⠩⣭⣿⣿⠿⣿⣿⢿⣿⣿⣿⣿⣟⢻⣿⡇⣿⣿⡀⣿⣿⢙⣛⢛⣛⢻⣿⢿⡿⠿⣿⣿⣿⣟⡵⢒⠁⢀⣴⣿⣿⣿⣿⣿⡿⢿⣿⡃⠀⠘⣿⣿⣿⡿⣿⣟⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣿⣧⣿⢿⣿⠛⠛⢹⡟⠉⠀ ⠀⠀⠛⠛⠀⠈⠛⠛⠛⣁⣤⠝⠛⠛⠿⠖⠪⢟⣛⠛⠑⢛⣻⣼⣿⣿⣿⠿⠿⠟⠛⢻⠟⢉⡴⠃⢀⠾⢿⣿⡯⢿⣿⣿⣿⣦⠙⠉⣦⠀⠘⠛⠟⠉⠉⠻⢿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣇⣀⡀ ⠀⠀⠀⠀⢀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠈⢻⣷⣄⢀⠀⠰⠶⠶⠶⠶⣿⣿⣷⡄⢀⡼⠁⠀⠁⠮⢛⣁⣤⣤⡝⠛⠿⢿⣢⣤⠋⡁⠀⢿⣶⣶⣶⠒⣾⣷⣼⣷⣬⣻⡉⢛⡛⠛⠋⠉⠛⠛⠛⠟⠎⢻⡿⡿⣿⣿ ⠀⠀⠀⠀⢸⠃⠀⠀⣾⣿⡟⠀⡇⢠⠀⠀⠀⢀⣿⣿⣿⣿⣶⣆⣠⠀⠀⠀⣤⡀⠀⠈⠰⠇⠀⠀⠀⢸⠿⠻⢿⣏⣤⣤⠀⠀⠉⠀⠀⠀⠀⢈⣁⣀⣀⣤⣌⣩⣭⣽⣿⣋⣛⣉⣩⣿⣶⣿⠿⢦⣶⣤⣾⣤⣀⠀⠁⠀ ⠀⠀⠀⠀⣸⠀⠀⠀⠈⠙⠃⠀⡇⠀⠀⠀⠀⠂⣂⠛⠈⠻⣿⣯⣿⡀⢀⢀⣿⡇⠀⠀⠀⠀⠀⠄⢀⣾⣷⣄⡸⣹⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⢿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢻⣷⣖⡛⢻⡏⣻⢙⠛⠒⠀ ⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠋⠹⣲⣷⣤⠈⣼⣿⣿⢯⠉⠙⠁⠀⠀⠀⠀⠀⢀⣾⣿⣽⣻⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⠛⠛⠛⠛⠛⠿⠛⠛⣛⡛⣙⣛⣛⣛⣋⡁⠉⠉⢩⣿⡉⣈⢀⣤⠄⠀ ⠀⠖⠲⣶⠿⢷⠖⠰⠶⠶⠆⠀⡇⠀⠀⠀⠀⠀⠀⠘⣆⢸⣅⠀⠉⠻⠎⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠋⢿⣶⣿⠛⠓⠆⠀⠈⣹⣿⣿⣿⣿⣿⠛⠓⠀⢠⣿⠁⠈⠉⢉⣁⠀⠀ ⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⠿⠛⠀⠈⣿⣿⡏⠀⠀⢀⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⠇⠘⡟⠀⠰⡶⠀⠀⣿⣿⣿⠇⢽⡿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇ ⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⣿⠟⣿⡄⠀⢸⣿⣿⣿⣿⡟⢡⣾⣿⠀⠸⣿⣿⡇⠀⣠⣿⣻⣿⣿⣿⣗⢸⡞⢿⣿⣿⣿⣦⡀⣨⡄⠐⠦⠀⢸⣿⣿⡟⠧⠀⢸⡗⠀⠀⠀⠀⠀⠀⢀⠀⠤⢤⠀⠀⠁⠀⠀⠀⠀⢀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣴⣿⠁⠀⣾⣿⡿⢛⣽⣿⣿⣿⣿⣀⡐⣿⡿⠁⢰⣿⣿⣿⣫⣴⣿⣿⣟⢿⣾⣿⣿⣿⣿⣿⣿⣿⡆⡠⠀⣿⡟⣿⢰⣶⡀⢀⡀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠀⢀⣿⣩⣽⣿⣿⣿⣿⠛⠉⣿⣿⣿⠃⠀⠂⠋⠘⢡⣿⣿⣿⣿⣿⡌⣏⢻⣿⣿⣯⣿⣿⣿⡇⠁⠀⣿⢻⡏⢸⡟⠁⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⡆ ⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⡏⣿⣿⣦⡴⢂⣙⠻⢿⠃⠉⠙⠏⠀⠄⠀⠉⠁⠀⠀⠀⠀⠄⣈⣿⣤⣯⣿⣿⣷⢸⣷⠝⢿⢿⣿⣿⣿⠗⠀⠀⠀⠘⠁⢸⣇⡀⣾⣦⠄⠀⠀⠀⠂⠠⣄⠀⠀⠀⠀⠀⡐⠀⠀⠠⠀⢸⡇ ⠀⠀⠀⢀⣤⣤⡤⢸⣿⣿⡇⠤⣤⣭⣶⣾⣯⣿⣿⣿⣶⣾⣟⣩⣶⡤⢶⣶⣟⣈⣀⠀⣿⡿⠿⢻⣿⡿⠿⠁⠸⠻⠀⠀⣹⣿⣿⣿⣀⣀⣠⣀⣀⣀⣼⣷⣿⣿⣧⣤⣄⣀⣄⣀⣀⣀⣀⣀⣸⡧⢰⣧⣤⣄⠀⢀⣼⠁ ⠀⠀⣠⣤⠀⣠⣤⣾⣿⣿⡇⣠⣴⣶⣤⠀⣠⣴⣾⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⠁⣀⣤⣀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⣥⣭⣽⣯⣉⣿⣿⣿⡍⢁⣿⡷⣾⡟⠁⠀⠀⢴⣿⠀ ⠐⠛⣿⣿⠀⣿⣿⠀⣿⣿⡿⣿⣇⣼⣿⣇⣻⡿⢉⣿⡿⣿⣭⡷⠟⢻⣭⡝⠛⢀⠀⠁⡀⠀⠀⠀⠁⠀⠀⢀⣤⠾⢛⣻⣽⣿⣿⣿⡋⠉⣥⣨⣿⡿⠿⡿⣿⡟⣿⠿⠟⠿⢿⠏⠋⠋⠁⢸⣿⣷⣿⠀⠀⢀⣀⣸⡇⠀ ⣿⣿⣿⣿⣶⣿⣿⣶⣿⣿⣾⣾⡿⢿⣿⣿⢿⣟⣻⣿⣮⣿⣧⣾⣿⣿⣿⣿⣶⣶⣷⣾⣿⣦⡄⠀⠀⠀⠀⣭⣶⣿⣿⣿⣿⣿⣿⡟⠻⣶⣾⣿⣥⣤⣶⣿⣿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣄⣼⣿⣿⣿⣀⣀⠘⠛⣿⣇⠀ ⣯⣽⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣟⢻⣿⡇⣿⣿⡀⣿⣿⢛⣛⢛⣿⢿⣿⢿⡿⠿⣿⣿⣿⣟⣡⢖⠁⠀⣴⣿⣿⣿⣿⣿⣿⢿⣿⡃⠀⠈⣿⣿⣿⡿⣿⣟⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣼⠿⣿⡛⠛⠓⣿⠋⠁ ⠀⠀⠛⠛⠀⠈⠛⠛⢛⣁⣤⠝⠛⠻⡯⠞⠮⣟⣛⠛⠕⢛⣻⣼⣿⣾⣿⠿⠿⠿⠛⢻⠟⠋⡵⠃⢀⡾⢿⣿⡭⣿⣿⣿⣿⣮⠙⠋⢆⠀⠘⠿⠿⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣿⣿⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⡇⠀⠀⠀⠀⠀⠀⠙⢿⣇⡀⠀⠠⠤⠶⠶⠶⢶⣿⣷⣶⡄⠀⡼⠁⠀⢁⠤⠟⣋⣅⣤⡙⠛⠿⢿⣣⣤⠚⠁⠀⢰⣶⣦⣤⡦⣴⣿⣭⣽⣍⣹⡟⠛⡛⠛⠛⠋⠛⠛⠻⠿⢧⠻⡿⣿⣿⣿ ⠀⠀⠀⠀⡷⠀⠀⠀⣿⣿⡇⢰⠀⠠⠀⠀⠀⣨⣿⣿⣿⣿⣶⡄⣄⠀⠀⠀⣄⡀⠀⠈⠰⠇⠀⠀⠀⢸⣿⠿⢿⣿⣡⣤⠀⠀⠙⠁⠀⠀⠀⠘⣉⠈⢁⣀⣉⣉⣉⣻⣿⡟⠛⠃⣙⣳⣶⣶⣿⣦⣴⣤⣴⣦⡀⠀⠈⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠋⠛⠁⠘⠀⠀⠀⠀⠰⢏⣈⠋⠙⢿⣿⣿⣿⡀⠀⢠⣿⡇⠀⠀⠀⠀⠀⡀⢀⣴⣶⡄⢨⣱⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⣷⣤⡘⢻⡿⠹⠻⠿⠶⠄ ⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠋⣛⢦⣶⣄⢉⣽⣿⣷⡏⠉⠛⠁⠀⠀⠀⠀⠀⢀⣼⣿⣽⣻⢿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⠚⠿⠻⠟⠛⠿⠟⠛⢛⠛⢛⠻⠟⠛⣛⠋⠉⠋⠛⣿⡟⠊⠁⢀⣀⠀ ⠀⠆⠲⣶⠿⢷⠆⠰⠶⠶⠖⢐⡃⠀⠀⠀⠀⠀⠀⠰⡉⢩⠀⠈⠛⠻⠃⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣯⣿⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣦⣷⠟⠷⠄⠀⠈⡙⣿⣿⣿⣿⣿⠟⠳⠄⠀⣼⡏⠈⠙⠁⠋⠀⠀ ⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⢹⣿⣿⣿⣿⣿⣿⠿⠋⠀⠈⣿⣿⡇⠀⠀⢀⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⠇⢘⡟⠀⠰⠶⠀⠀⣿⣿⣿⡇⢸⣯⠿⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇ ⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⢸⣿⢻⣿⠀⠀⢼⣿⣿⣿⣿⠟⣡⣾⡿⠀⠸⣿⣿⠇⠀⣠⣿⣻⣿⣿⣿⣗⢸⡎⢿⣿⣿⣿⣂⣈⢡⡤⠀⠧⠀⢸⣿⣿⡟⠧⠀⠘⡷⠀⠀⠀⠀⠀⠀⠀⡀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣼⣿⠀⠀⣿⣿⡿⣋⣿⣿⣿⣻⣿⣀⡘⣿⡟⠁⢰⣿⣿⣿⣫⣴⣿⣿⣟⣿⣾⣿⣿⣷⣻⣿⣿⣿⡆⠀⠀⣾⡟⣿⢁⣶⡄⠀⡁⠀⠀⡔⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⣰⣏⣩⣿⣿⣿⣿⡿⠛⠉⣿⣿⡿⠃⠀⠊⠋⠸⢡⣿⣿⣿⣿⣿⡌⣏⢿⣿⣿⣯⣽⣿⣿⡇⠁⠀⣿⢷⡿⢐⡿⠃⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣴ ⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⢿⣿⣵⣀⡶⢀⡛⢛⠿⠁⠉⢹⠇⠀⠀⠈⠉⠁⠀⠀⠀⠀⢄⣈⣿⣤⣯⣽⣿⣷⢸⣷⠝⢿⢻⣿⣿⣿⡿⠀⠀⠀⠀⠃⢸⡇⡀⢸⣷⡤⠀⠀⠀⠰⠀⣀⡀⠀⠀⠀⠀⢀⠀⠀⠀⡄⠠⡿ ⠀⠀⠀⢠⣤⣤⡄⣿⣿⣿⠦⣤⣬⣭⣴⣿⣭⣿⣿⣶⣶⣾⣛⣩⣤⡤⢶⣶⣟⣂⣀⠀⣿⡿⠿⢿⣿⣿⠿⠃⠸⠻⠀⠀⣹⣿⣿⣿⣀⢀⣀⣀⣀⣀⣸⣿⣷⣿⣯⣄⣀⣀⣀⣐⣀⣀⣁⣀⣠⣿⠀⣾⣤⣠⡀⠀⢰⡇ ⠀⠀⣠⣤⠀⣠⣴⣿⣿⣿⡀⣠⣴⣶⣤⠀⣠⣴⣿⣿⡵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⠁⣀⣀⣀⠁⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠍⣩⣭⣽⣯⣉⣻⣿⡿⡏⢉⣽⣿⣼⣿⠋⠀⠀⢀⣾⡇ ⠐⠛⣿⣿⠀⣿⣿⠉⣿⣿⣿⣿⣇⣸⣿⢏⣻⠿⢉⣿⡿⣟⣿⡶⠟⣻⣩⡝⠋⢁⡀⠁⠀⠀⠀⠈⠁⠀⠀⢀⣠⡾⠟⣛⣿⣿⣿⣿⡛⠛⢯⣈⣿⠿⠿⣿⣿⡿⢿⡿⠿⠻⢿⠿⠛⠓⠏⠀⣿⣿⣽⡇⠀⠀⣀⣀⣿⠀ ⣿⣿⣿⣿⣴⣿⣿⣤⣿⣿⣯⣾⡿⢿⣿⣿⢿⣟⣻⣿⣮⣿⣥⣶⣶⣿⣿⣷⣶⣾⣷⣾⣿⣦⡀⠀⠀⠀⠀⣩⣴⣾⣿⣿⣿⣿⣿⡟⠻⣤⣶⣿⣧⣤⣴⣾⣿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣄⣰⣿⣿⣿⣇⣀⠀⠛⢻⣯⠀ ⣛⣻⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡗⢺⣿⡇⣿⣿⠉⣿⣿⢛⣛⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⡟⣡⢔⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⣿⣿⣿⡿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡿⣿⣿⠟⠓⢺⡟⠋ ⠀⠀⠛⠛⠀⠈⠛⠛⠛⢁⣵⡝⠛⣿⡯⠺⣮⣟⣛⠛⠵⢿⣿⣼⣿⣾⣿⣿⠷⠿⠿⢿⡿⠛⡵⠃⢀⣼⣿⣿⣽⣿⣿⣿⣿⣮⡙⠗⣄⠀⠘⠿⠿⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣷⣾⣾⣿⣿⣿⣿⣷⣿⣿⣶⣶⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⠁⠀⠀⠀⠀⠀⠀⠛⣿⣄⠀⠀⠩⠭⢭⣥⣤⣴⣾⣶⣦⡀⠠⡼⠁⠀⠀⡴⠿⠋⣁⣨⡙⠿⡿⣿⢧⢀⠸⠁⠀⢰⣦⣤⣤⡤⢤⣿⣭⣽⣍⡛⡿⠛⢛⠿⠟⠛⠛⠻⠿⠿⠷⡝⣿⣿⣿⣿ ⠀⠀⠀⢸⠆⠀⠀⢸⣿⣿⠀⢰⠀⡀⠀⠀⠀⢰⣿⣿⣿⣿⣤⠀⡄⠀⠀⠈⣁⠀⠉⠁⢸⡇⠀⠀⠀⢰⣿⣿⣿⣿⣁⣀⡀⠀⠻⠉⠀⠨⠀⠈⠋⠉⠉⢁⣈⠛⣛⣛⣿⣿⠛⠷⠛⣳⣦⣴⣶⣦⣀⣤⣀⣦⣌⠀⠀⠁ ⠀⠀⠀⢸⠀⠀⠀⠘⠛⠿⠀⢸⠀⠁⠀⠀⠠⠍⠙⠏⠛⣿⣿⣾⣿⠀⠀⢰⣿⡆⠀⠀⠘⠀⠀⡀⢀⣴⣦⡀⠘⢹⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣤⠩⠿⣿⠟⠟⠿⠶⠄ ⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠐⠚⡧⣴⣄⡈⢛⣻⣿⣷⡏⠚⠻⠃⠀⠀⠀⠀⠀⢀⣼⣿⣻⢿⢷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠿⠶⢾⡿⠿⠿⠿⠟⠿⠿⠿⠿⠗⠙⠛⠛⢲⡿⠒⠉⠀⢀⡀ ⠀⠆⠲⣾⠿⢷⠄⠰⠶⠶⠖⢸⠀⠀⠀⠀⠀⠀⠈⢫⠉⢟⠀⠉⠻⢿⠇⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣏⣾⣿⠋⠀⠁⠀⠀⠀⠀⠀⠀⠘⢳⣦⣶⡶⢦⣄⠀⠀⠚⣷⣾⣿⣷⣾⡿⠿⡄⠀⢠⣾⠋⠐⠓⠒⠃⠀ ⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⢘⣿⣿⡇⠀⠀⢈⣿⣿⣿⣿⡿⡿⢿⣿⣿⣿⣿⡇⠈⡋⠀⠐⡾⠀⠀⣿⣿⣿⡟⠸⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻ ⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⢸⡟⢻⣧⠀⠀⣿⣿⣿⣿⣿⣟⣱⣾⡟⠀⢸⣿⣿⠀⠀⣠⣿⣻⣿⣿⣿⣗⢠⣏⢿⣿⣿⣿⣇⡀⢡⣤⠀⣦⠀⠰⣿⣿⡿⠳⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⢀⠐⠤⠄⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣾⡏⠀⢐⣿⣿⠟⣋⣿⣿⣿⣻⣿⣀⡸⣿⡟⠀⢸⣿⣿⣿⣫⣴⣿⣿⣿⣿⣾⣿⣿⣿⣻⣿⣿⣿⡆⠠⠀⣸⣿⣹⠇⣷⡤⠀⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠇⠀⣸⣏⣥⣿⣿⣿⣿⡟⠋⠙⣿⣿⡿⠁⠀⠂⠋⠸⢡⣿⣿⣿⣿⣿⡌⣏⢿⣿⣿⣯⣻⣿⣿⣇⠀⠀⣿⡯⣿⠀⣿⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠ ⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⢻⡏⣥⣠⠖⢈⠛⠿⣿⢀⠉⢹⠃⠀⠀⠉⠉⠁⠀⠀⠀⠀⢄⣉⣿⣤⣮⣽⣿⣷⢸⣷⠙⢿⣻⣿⣿⣿⣿⠀⠀⠈⠀⠋⠀⣟⡀⢰⣷⣠⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢼ ⠀⠀⠀⣤⣄⣠⢀⣿⣿⣿⠠⣤⣬⣭⣦⣿⣽⣿⣿⣷⣶⣾⣛⣡⣤⡤⢶⣶⣖⣀⣀⠀⣿⡿⠿⢿⣿⣿⠿⠋⠸⠿⠂⠀⢹⣿⣿⣿⣁⠀⣀⣀⣀⣀⣠⣿⣼⣿⣿⣄⣀⣀⣀⣀⢀⡀⣈⣀⣀⣼⡆⢸⣧⣀⣀⠀⠀⣾ ⠀⠀⣠⣤⠀⣠⣴⣿⣿⡿⠀⣠⣴⣶⣤⠀⣠⣼⣿⣯⡵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠙⠁⣀⣀⡀⠁⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢉⣭⣩⣿⣍⢹⣿⣿⣿⠉⢹⣿⣧⣿⠟⠉⠀⠀⣼⣿ ⠀⠛⣿⣿⠀⣿⣿⠉⣿⣿⣿⣿⣇⣸⣿⢏⣻⠿⢉⣿⡿⣟⣷⡴⠿⣿⣍⡛⠋⠁⠈⠁⠀⠀⠀⠈⠁⠀⠀⠀⣠⡾⠿⣟⣻⣿⣿⣿⡟⠛⣏⣘⣿⣿⠿⣿⣿⣷⢿⣿⠿⠿⠿⣿⠛⠛⠛⠀⢹⣿⣿⣿⠀⠀⠀⡀⢸⡇ ⣶⣶⣿⣿⣤⣿⣿⣤⣿⣿⣿⣿⡿⢿⣷⣿⢿⣟⣻⣿⣮⣿⣭⣶⣶⣿⣿⣶⣶⣾⣶⣾⣿⣤⡀⠀⠀⠀⠀⣨⣥⣶⣿⣿⣿⣿⣿⡿⠻⣦⣴⣿⣯⣤⣤⣶⣿⣿⣾⣤⣤⣤⣤⣤⣤⣄⣠⣀⣿⣿⣿⣧⠀⠀⠘⠛⣿⡁ ⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢺⣿⡏⢿⣿⠉⣿⣿⢿⣿⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⡟⣡⠄⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣸⢿⣿⠿⠗⠒⣿⠛ ⠀⠀⠛⠛⠀⠈⠛⠛⠛⠉⣹⡽⣻⣿⡯⢶⣮⣟⡛⠻⠵⣾⣿⣼⣿⣾⣿⣿⣶⠾⠿⣿⡿⠛⡱⠇⢀⣼⣿⣿⣻⣿⣷⣿⣿⣌⠙⠗⣄⠀⠘⠿⢿⠟⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣼⣶⣿⣿⣿⣿⣿⣾⣿⣷⣴⣾⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⢒⣿⣿⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠉⠉⣩⣭⣭⣥⣴⣶⣤⣤⠈⠀⣼⠁⠀⠊⣄⠾⠟⣁⣉⡛⠿⣿⣿⢧⢀⠸⠓⠀⢰⣤⣤⣤⣤⢤⣽⣟⣿⣏⡙⢿⠿⠿⠿⠿⠿⠛⠿⠿⢿⣿⣎⢿⣿⣿⣿ ⠀⠀⠀⣶⠀⠀⠀⣼⣿⣿⠀⡄⠀⠀⠀⠀⠀⢰⣿⣿⣶⣦⣄⠀⠀⠀⠀⠈⡉⠉⠉⠁⢹⡇⠀⠀⠀⢰⣶⣿⣿⣿⢉⣀⡀⠈⠻⠋⠁⠈⠀⠀⠟⠉⠉⢁⠈⠛⠛⠛⣿⣿⠿⠷⠚⠷⣦⣤⣴⣦⣀⣠⣀⣠⣀⠁⠉⠉ ⠀⠀⠀⣿⠀⠀⠀⠻⠿⠇⠀⡇⠈⠀⠀⠀⣨⠋⠻⠟⢻⣿⣿⣺⡇⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⡀⠀⣨⣍⠀⢸⢩⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣟⣿⠿⢿⣭⡉⠿⢿⡿⢿⠷⣶⣤ ⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠰⠐⢧⣠⣄⠉⢛⣫⣿⣦⡗⠚⠿⠃⠀⠀⠀⠀⠀⠁⣸⣿⢿⣷⣦⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠨⢿⣿⣿⠶⢿⣿⡿⢿⣿⡿⢿⣿⠿⠿⠷⠎⠻⠿⠶⣾⠧⠔⠂⠀⠀ ⠀⠆⠲⣿⠿⢷⠄⠰⠶⠶⠖⠧⠀⠀⠀⠀⠀⠈⠉⣝⠛⡛⠈⠛⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣞⣼⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠸⢶⣄⣢⣴⣶⣈⠁⠀⠐⢶⣶⣶⣶⣶⣶⡶⣄⠀⠀⣴⡟⠒⠶⠀⠞⠉ ⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠈⣿⣿⣿⣿⣿⣿⡿⢛⠁⠀⢸⣿⣿⡇⠀⠀⢀⣿⣿⣿⣿⡿⡿⢿⣿⣿⣿⣿⡇⠀⠋⠀⠀⠾⠆⠀⢸⣿⣿⣿⠀⢿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⣿⡟⣿⡇⠀⠠⣿⣿⣿⣿⣿⣋⣴⣿⡏⠀⢸⣿⣿⠀⠀⣨⣿⣻⣿⣿⣿⣗⢨⣏⢿⣿⣿⣿⣇⡌⢁⣤⠀⠶⠄⠀⣿⣿⣿⠐⠆⠀⢺⠆⠀⠀⠀⠀⠀⠀⢀⠀⠂⢦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⠇⠀⢸⣿⣿⢟⣩⣿⣿⣿⣿⣇⣀⠸⣿⡟⠀⣸⣿⣿⣿⣫⣴⣿⣿⣿⢿⣾⣿⣿⣿⣻⣿⣿⣿⡗⠀⠀⢸⣿⢻⡇⣰⣦⠀⣀⠀⠀⢠⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⣾⣉⣵⣿⣿⣿⣿⠟⠋⠹⣿⣿⡿⠀⠀⠁⠋⠸⢡⣿⣿⣿⣿⣿⡈⣯⢿⣿⣿⣿⣹⣿⣿⣇⠀⠀⢾⡟⣾⠁⣿⠛⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣤⣾⡟⣿⣯⣄⣠⠆⡙⠛⠻⠿⠘⠉⣿⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⢄⣉⣿⣥⣮⣽⣿⣷⠸⣷⠹⢿⣻⣿⣿⣿⣿⠄⠀⠈⠀⠋⠀⣿⢀⠀⣿⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⢀ ⠀⠀⢀⣀⣀⡀⢸⣿⣿⡇⢨⣄⣩⣥⣐⣟⣵⣿⣶⣶⣶⣿⣛⣠⣤⡤⣶⣶⡖⠂⢀⠀⣷⡿⠿⢿⣿⣿⡿⠋⠘⠿⠂⠀⢹⣿⣿⣿⣇⠀⠀⡀⠀⣀⣀⣿⣼⣾⣿⣥⣀⣀⣀⣀⠀⠀⢈⠀⢀⣠⣆⠀⣧⣀⣀⡀⠀⢰ ⠀⠀⣨⣤⠀⣠⣼⣿⣿⡇⠀⣠⣴⣶⣭⠉⣩⣽⣿⣯⡵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠙⠁⣀⣀⡉⠁⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⣩⣉⣿⣍⠙⣿⣿⣿⠋⢉⣿⣷⣸⡿⠋⠁⠀⢀⣿ ⠀⠛⣿⣿⠀⣿⣿⠉⣿⣿⣿⣿⣇⣸⣿⢯⣿⡿⢁⣿⡿⣿⣧⡼⠿⣟⣋⡻⠏⠉⠉⠁⠀⠀⠁⠈⠁⠀⠀⠀⣀⣼⠿⢿⣛⣿⣿⣿⡿⠛⢛⡉⣹⣿⠿⣿⣿⣷⢾⣿⡿⠿⣿⣿⠙⠛⠚⠁⢈⣿⣧⣿⠇⠀⠀⠀⠀⣿ ⣶⣶⣿⣿⣤⣿⣿⣤⣿⣿⣿⣿⡿⢿⣷⣿⢷⣟⢻⣿⣮⣿⣥⣶⣶⣿⣿⣷⣤⣽⣦⣾⣷⣄⠀⠀⠀⠀⠀⣈⣭⣶⣾⣿⣿⣿⣿⡿⠻⣦⣬⣿⣟⣀⣠⣬⣿⣿⣤⣥⣀⣀⣀⣀⣠⣀⣀⡀⣸⣿⣿⣿⡀⠀⠀⠿⢻⣏ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⡏⢿⣿⠙⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣁⡠⠂⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⢿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣱⣿⣿⡿⠷⠶⢾⡟ ⠉⠉⠛⠛⠈⠈⠛⠛⠛⢙⣿⣽⣿⣿⡏⣶⣬⡟⠛⣻⢷⣾⣿⣼⣿⣼⣿⣿⣶⣾⠿⣿⡿⠟⣩⠎⢀⣴⣿⣿⣻⣿⣷⣿⣿⣄⠛⠷⣄⠀⠈⣿⣿⡿⠶⠿⢿⣿⣿⣿⣿⣿⣿⣿⣤⣧⣿⣿⣿⣿⣿⣶⣿⣷⣤⣤⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⢠⣼⡇⠀⠀⠈⠁⠀⠀⠘⢿⣆⠀⠈⠉⣋⣉⣩⣭⣍⣥⣦⣤⣄⠊⠀⡴⠃⠀⠊⣉⣾⠟⠋⢙⠻⢿⣿⣿⣇⢀⢸⠓⠀⠠⣤⣄⣀⣀⣀⣽⣟⣛⣛⠛⢿⠿⠿⢿⣿⠿⠿⠿⠿⣿⣿⣮⠻⣿⣿⣷ ⠀⠀⢠⡄⠀⠀⠀⣿⣿⡇⢀⡀⠀⠀⠀⠀⠀⣼⣿⣷⣦⣦⡀⠀⠈⠉⠉⢉⠉⠙⠛⡂⢱⡃⠀⠀⠈⢡⣶⣧⣿⣿⠉⠀⠀⠈⢱⠚⠁⠈⠀⠀⠿⠛⠛⠋⠀⠻⠿⠿⢿⣿⡾⢶⡄⠶⢤⣄⣠⣤⣄⢀⡀⢈⡅⠙⠉⠉ ⠀⠀⢸⡇⠀⠀⠐⠿⣿⠇⠈⠃⠀⠀⠀⠀⣐⡛⢿⠻⢿⣿⣧⣾⡇⠀⠀⢸⣷⠀⠀⠀⠘⠀⠀⠀⠀⣈⣉⠉⢹⢋⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠶⣶⣶⣾⣿⣶⣾⣿⣿⣿⣷⣶⣶⣞⣿⣿⣿⣏⡙⢻⣿⣿⣿⡷⣦⣄ ⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠠⢶⣄⣠⡈⠛⠿⣿⣷⣤⡦⠾⢿⠂⠀⠀⠀⠀⠀⠀⣰⣿⢿⣷⣦⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣽⣧⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⠻⠿⠦⢤⡿⠀⠆⠀⠀ ⠀⠆⠲⣿⠿⢶⠄⠰⠶⠶⠶⡃⠀⠀⠀⠀⠀⠈⠚⡛⠿⠆⠙⠻⢿⣯⠆⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡾⣼⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢠⣦⣄⢀⣤⣤⡀⠉⠀⠠⢴⣤⣴⣤⣤⣴⣶⣄⠀⠀⢀⣾⠳⠤⠤⠤⠒ ⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⢸⣿⣿⠃⠀⠀⢠⣿⣿⣿⣿⠿⡿⢿⣿⣿⣿⣿⡇⠀⡀⠀⠐⠶⠆⠀⢸⣿⣿⣿⠃⢻⢽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠇⠀⠀⠀⠀⠀⠀⠈⣿⠛⣿⠀⠀⢸⣿⣿⣿⣿⣿⣋⣶⣿⡃⠀⢺⣿⣿⠀⠀⣼⣿⣿⣿⣿⣿⣷⢠⣏⢿⣿⣿⣿⣧⣄⢀⣤⠀⢠⠄⠀⣿⣿⣿⠇⠆⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣰⣿⠀⠀⣾⣿⡿⢛⣹⣿⣿⣿⣿⣇⣀⢺⣿⡟⠀⣼⣿⣿⡿⣫⣴⣿⣿⣿⢿⣾⣿⣿⣿⣟⣿⣿⣿⡿⠘⠄⢰⣿⢿⡏⢰⣦⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡏⠀⢀⣟⣩⣽⣿⣿⣿⣿⠟⠋⢹⣿⣿⡟⠀⠀⠡⠃⠚⢡⣿⣿⣿⣿⣿⡈⣧⢿⣿⣿⣿⣹⣿⣿⣧⠈⠀⢸⡿⣾⠇⢸⠟⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣤⣴⣾⠛⣿⣡⣀⡴⠀⡛⢛⠻⡏⠈⠉⡿⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠄⣙⣿⣥⣯⣽⣿⣷⠸⣷⠝⢿⡻⣿⣿⣿⣿⠆⠀⠀⠁⠙⠀⣿⣀⠀⣿⣆⡄⠀⠀⠀⢠⠀⣀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀ ⠀⠀⣀⣀⣀⠀⣿⣿⣿⠄⣭⣌⣩⣤⣚⣋⣶⣿⣶⣶⣶⣾⣂⣤⣤⠰⣦⣶⡖⠒⠀⢠⣷⡿⠿⢿⣿⣿⠿⠋⠘⠿⠇⠀⢱⣿⣿⣿⡇⠀⠀⢀⠀⢀⢀⣽⣾⣶⣿⣥⣀⣀⣀⣀⠀⠀⠈⠁⠀⣀⣶⠀⢸⣀⣀⡀⠀⠀ ⠀⠀⣠⣤⠀⣠⣽⣿⣿⡀⠀⣠⣴⣾⣭⢉⣩⣽⣿⣯⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠛⠁⢀⣈⡉⠁⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⣉⣉⣻⣏⠙⢿⣿⣿⡟⠋⣹⣿⣤⣿⠟⠉⠀⠀⣠ ⠀⠛⣿⣿⠀⣿⣿⠫⣿⣿⣾⣿⣇⣸⣿⢿⣻⡿⢁⣿⡿⣿⣯⡽⠿⣿⣋⡻⠋⠉⠉⠃⠀⠀⠉⠙⠃⠀⠀⠀⣀⣼⠿⢿⣛⣿⣿⣿⡿⠛⣛⡋⣻⣿⣿⣿⣿⣿⡾⣿⣿⠿⢿⣿⡍⠛⠒⠒⠀⣿⣿⣼⡏⠀⠀⠀⠀⢨ ⣶⣶⣿⣿⣤⣿⣿⣤⣿⣿⣿⣿⡿⣿⣷⣿⢷⣟⢻⣿⣮⣏⣥⣤⣴⣿⣿⣧⣤⣽⣤⣶⣷⣄⠀⠀⠀⠀⠀⢚⣩⣴⣾⣿⣿⣿⣿⣿⠿⣦⣤⣾⣿⣁⣀⣬⣵⣿⣧⣥⣀⣀⣀⣀⣀⣀⣀⣀⢰⣿⣿⣿⡇⠀⠀⠸⠟⣿ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢻⣿⡏⢿⣿⠙⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣁⡠⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡷⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣿⣿⣿⠷⠦⠤⣿ ⠉⠉⠛⠛⠉⠈⠛⠛⠛⣹⣿⣽⣿⣿⢫⣤⣬⣟⢛⣿⣵⣾⣿⣼⣿⣼⣿⣿⣿⣿⣿⣿⡿⠿⣫⠎⠀⣰⣿⣿⣻⣿⣿⣿⣿⣅⠻⢿⢄⠀⠈⢿⣿⣿⠶⠿⢿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣽⣿⣿⣿⣿⣷⣼⣿⣆⣤⣴⣟ ⠀⠀⠀⠀⠀⠀⠀⣠⣴⠀⠀⠀⠉⠁⠀⠈⠻⢿⣄⠀⠀⠛⠛⣛⣛⣛⣉⣩⣭⣄⣀⠋⠀⣰⠃⠀⠈⡉⣽⠿⠋⠹⠻⣿⡿⣿⣇⢀⢨⠇⠄⠀⣤⣀⣀⣀⣀⣹⣟⣻⣿⠛⢿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣷⡙⣿⣿⣿ ⠀⠀⢠⠀⠀⠀⢠⣿⣿⠀⢀⠀⠀⠀⠀⠀⠀⣾⣿⣶⣤⣄⠀⠉⠉⠉⠉⠛⠛⠛⠛⡂⢰⠇⠀⠀⠀⢩⣴⣖⣿⣿⠓⠀⠈⠉⠳⠝⠃⠀⠀⠀⠻⠟⠛⠛⠁⠻⠿⠿⢿⣿⣶⣷⡄⠶⣤⣀⢀⣤⣄⠀⠈⠉⣁⠈⠋⠉ ⠀⠀⣼⠀⠀⠀⠸⢿⣿⠀⢘⠀⠀⠀⠀⠀⡰⠻⣿⠿⣿⣿⣷⣴⡄⠀⠀⢰⣶⠀⠀⠀⠘⠀⠀⠀⠀⢘⣛⢉⠙⠟⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⢴⣶⣶⣴⣷⣶⣶⣶⣾⣿⣷⣤⣤⣶⢾⣿⣿⣟⡛⠛⣿⣿⡿⣿⣦⣄ ⠀⠀⣾⠀⠀⠀⠀⠀⠁⠀⢸⠀⠀⠀⠀⠈⣅⣤⡀⣀⠘⠻⠿⣿⣧⣀⠤⢼⣿⠀⠀⠀⠀⠀⠐⠀⢰⣿⣿⣶⣤⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣻⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠹⣿⣦⣍⣼⣇⠨⠀⠉ ⠀⠖⠾⣶⠏⢶⠄⠰⠶⠶⠾⠀⠀⠀⠀⠀⠀⠘⢽⠿⢷⡆⠺⢿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⣿⣿⣾⡽⣽⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣤⣈⠉⣉⣉⡉⠛⠉⠉⢩⣍⣡⣭⣭⣤⣥⣤⠀⠀⠀⣰⡿⢄⣤⣀⡀ ⠀⣻⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⣹⣿⣿⣿⣿⣿⣿⠟⣛⠀⠀⢹⣿⣿⠁⠀⠀⢨⣿⣿⣿⣿⠿⡿⢿⣿⣿⣿⣿⡇⠀⡂⡀⠀⠾⠆⠀⢸⣿⣿⣿⡃⡿⢯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⠀⠀⠀⠀⠀⠀⠀⢸⡟⢻⣿⠀⠀⣿⣿⣿⣿⣿⢟⣁⣾⣿⠃⠀⣿⣿⣿⠀⠀⣼⣟⣿⣿⣿⣿⣷⢠⣏⢿⣿⣿⣿⣧⣄⢀⣤⡀⠴⠆⠀⣻⣿⣿⡇⠖⠂⠘⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣾⡏⠀⠀⣿⣿⡿⢻⣹⣿⣿⣯⣿⣇⣀⢿⣿⠏⠀⣼⣿⣿⡿⣫⣴⣿⣿⣿⢿⣾⣿⣿⣿⣞⣿⣿⣿⣿⠀⠀⢀⣿⡏⣿⢰⣦⡀⢀⡁⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⠇⠀⢸⣏⣩⣾⣿⣿⣿⣿⠛⠉⢻⣿⣿⡟⠀⠠⠩⠃⠚⢡⣿⣿⣿⣿⣿⡍⣯⢻⣿⣿⣿⣹⣿⣿⣿⠀⠀⢸⣿⢸⡇⢸⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣄⣴⣾⢻⡟⣤⣀⡴⠈⠻⢛⠿⠇⠋⠹⡟⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠄⢹⣿⣥⣯⣽⣿⣷⠘⣷⠙⢿⡿⣿⣿⣿⣿⠆⠀⠀⠁⠘⠁⢸⡇⠀⣼⣆⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁ ⠀⠀⣀⣀⣀⢸⣿⣿⣿⢈⣁⣉⣩⣄⣾⣻⣶⣷⣷⣶⣶⣟⢂⣤⣀⢤⣦⣶⠖⠒⠀⢰⣷⣿⡿⢿⣿⣿⡿⠏⠀⡿⠇⠀⢱⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣸⣧⣷⣿⣯⣄⣀⡀⣀⠀⠀⠀⠉⠀⢀⣰⡆⢠⣇⣀⣀⠀⠀ ⠀⠈⣡⣤⠀⣸⣿⣿⣿⡀⠈⣩⣽⣿⣭⢉⣩⣽⣿⣯⡼⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡆⠛⠁⢀⣈⠉⠁⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢉⣙⣻⣟⠛⢻⣿⣿⣿⠛⢩⣿⣇⣼⡿⠋⠁⠀⠀ ⠀⠛⣿⣿⠀⣿⣿⠏⣿⣿⣾⣿⣇⣸⣿⣷⣿⡿⢀⣿⡿⣿⣫⣽⢿⣟⣻⠻⠋⠉⠙⠃⠀⠀⠉⠙⠋⠀⠀⠀⢀⣴⡿⠿⣟⣿⣿⣿⡿⠛⢛⡋⢻⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣟⠓⠒⠘⠀⢹⣿⣗⣿⠀⠀⠀⠀⠀ ⣤⣤⣿⣿⣠⣿⣿⣤⣿⣿⣿⣿⣿⣿⣷⣿⢿⣟⢻⣿⣮⣏⣩⣤⣼⣿⣿⣤⣤⣷⣤⣶⣦⡀⠀⠀⠀⠀⠀⢒⣩⣵⣶⣿⣿⣿⣿⣿⠿⣆⣈⣽⣿⣋⣀⣠⣭⣿⣧⣭⣁⣀⣀⣀⣁⣀⡀⠀⠀⣾⣿⣿⣿⠀⠀⠰⠿⢲ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⣿⡏⣿⣿⠛⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣁⡠⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣷⣶⣦⡤⢼ ⠉⠉⠛⠛⠙⠊⠛⠛⠛⣻⣷⣽⣿⣟⣫⣠⣬⣟⣛⣿⣥⣼⣿⣼⣿⣼⣿⣯⣭⣽⣿⣿⣿⠷⣫⠎⠀⣰⣿⣿⠿⢿⣿⣿⣿⣉⠻⢷⢄⠀⠀⢿⣿⣿⠯⠿⢿⣿⣿⣿⣿⣿⣿⣿⣟⣹⣽⣿⣿⣿⣿⣿⣬⣿⣧⣀⣄⣾ ⠀⠀⠀⠀⠀⠀⢀⣤⣄⠉⠉⠉⠉⠁⠈⠙⢿⣶⠈⠁⠘⠛⠛⢛⣛⣛⣛⣩⣍⣁⣀⠛⠁⣰⠃⠀⠜⠉⣽⡿⠛⠻⠻⣿⣿⣿⡧⠀⠈⡧⠀⠈⣉⣉⠀⢀⡀⢙⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣝⢿⣿⣿ ⠀⠀⡀⠀⠀⠀⣸⣿⣿⠀⡀⠀⠀⠀⠀⠀⠤⣿⣷⣦⣤⡈⠉⠉⠉⠉⠛⠛⠛⠻⠻⡄⢰⠇⠀⠀⠐⢋⣥⣆⣶⣿⠲⠀⠉⠉⢻⡜⠃⠁⠀⠀⢻⠿⠿⠿⠋⠿⣿⣿⣿⣿⣦⣿⣄⢰⣤⣁⠀⣀⣀⠈⠉⠉⠉⠈⠛⠛ ⠀⠀⡇⠀⠀⠀⣿⣿⡏⠀⠇⠀⠄⠀⠀⠀⠼⢿⡿⢿⣿⣿⡇⣴⠀⠀⠀⣰⣆⠀⠀⠀⠸⠀⠀⠀⠀⢘⡛⠉⠻⡟⣾⣷⡆⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣶⣦⣤⣶⣶⣾⣿⣤⣭⣤⣶⣿⣿⣿⠟⠷⢾⣷⣾⣷⣦⣄ ⠀⠠⡇⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠘⣥⣄⠁⡀⠛⢿⢿⢿⣤⢠⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣮⣤⣸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣻⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡹⣿⣧⣈⢩⣟⠈⡁⠉ ⠀⠶⠷⣶⠏⢶⠄⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠭⠿⣿⣦⠀⢾⣿⢿⣿⠀⠈⠁⠀⠀⠀⠀⠀⠀⢰⣿⣿⣼⣽⣹⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣄⣉⠙⢛⣋⡉⠛⠛⠉⢉⣍⢉⣉⣛⣉⣩⣍⡀⠀⠀⢀⣿⣇⢁⡀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟⣋⠀⠀⣻⣿⣿⠀⠀⠀⢠⣿⣿⣿⣿⠿⢿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠸⠆⠀⢰⣿⣿⣿⡟⠘⠯⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠏⠀⠀⠀⠀⠀⠀⠀⣿⡏⢻⡇⠀⠀⣿⣿⣿⣿⣿⢟⣱⣾⣿⠁⠀⣿⣿⡿⠀⢀⣼⣟⣿⣿⣿⣿⣷⢠⣏⢿⣿⣿⣿⣧⣀⠀⣤⡄⠰⠆⠀⢸⣿⣿⡇⠲⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣃⣿⡇⠀⢰⣿⣿⠟⣋⣿⣿⣿⣿⣿⣀⣀⢿⣿⠋⠀⣾⣿⣿⡿⣫⣴⣿⣿⣿⢿⣶⣿⣿⣿⣜⣿⣿⣿⣷⠐⠄⠀⣿⡟⣿⠀⣦⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⢿⠁⠀⣸⣋⣡⣿⣿⣿⣿⡿⠛⠉⢿⣿⣿⠏⠀⠠⠩⠃⠚⢱⣿⣿⣿⣿⣿⡍⣧⢻⣿⣿⣿⣻⣿⣿⣿⠈⠀⢸⣿⢹⡟⠀⡟⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣀⣶⡞⣿⡇⡄⣠⠄⠘⠛⢻⢿⠅⠋⢹⠇⠀⠀⠈⠉⠉⠀⠀⠀⠀⠠⠄⢹⣯⣥⣮⣽⣿⣿⠘⣷⠝⢿⣿⣿⣿⣿⣿⡆⠀⠀⠁⠘⠃⢸⡇⠀⢸⣷⡀⠀⠀⠀⠀⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⣀⡀⢹⣿⣿⡇⣈⣁⣉⣁⣀⣿⣳⣶⣿⣶⣦⣾⡗⢒⣄⣀⢴⣤⣶⠆⠒⠀⢰⣷⣿⡿⣿⣿⣿⣿⠟⠀⡿⡇⠀⠙⣿⣿⣿⡏⠁⠀⢀⠀⠀⠀⣸⣇⣵⣾⣟⣁⣀⠀⢀⠀⠀⠀⠈⠀⠀⢀⣦⠀⣴⢀⠀⠀⠀ ⠀⠈⣠⣤⠀⣻⣿⣿⣧⡀⠈⣩⣿⣿⣭⠉⣩⣿⣿⣯⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠛⠃⠀⣈⠉⠁⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢛⣛⣛⣿⡛⠻⣿⢿⣿⠛⠋⣿⣷⢰⣿⠟⠉⠀⠀ ⠀⠛⣿⣿⠀⣿⣿⡏⣿⣿⣼⣿⣇⣸⣿⣷⣿⡿⢀⣿⡿⣿⣭⡿⡿⢛⢛⢿⠋⠉⠙⠁⠀⠀⠉⠙⠃⠀⠀⠀⢀⣴⣿⠿⢿⣿⣿⣿⡿⠿⠛⣛⠹⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣶⠛⠞⠀⠀⠘⣿⣯⣿⡇⠀⠀⠀⠀ ⣤⣄⣿⣿⣀⣿⣿⣤⣿⣿⣿⣿⣿⢿⣷⣽⢿⣛⢻⣿⣮⣋⣭⣤⣼⣿⣿⣤⣤⣵⣤⣴⣦⡀⠀⠀⠀⠀⠀⠐⣋⣥⣶⣿⣿⣿⣿⣿⠿⣆⣀⣽⣿⠋⣉⣀⣿⣿⣯⣬⣉⢀⠀⢀⣁⣀⠀⠀⠀⢸⣿⣿⣿⡁⠀⠀⢾⠆ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⣿⡟⢿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⡀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠋⣿⣷⣶⣦⣤⡀ ⠛⠛⠛⠛⠙⠚⠛⠛⠛⣻⣯⣹⣻⣛⣫⣠⣬⣛⣛⣿⣥⣼⣿⣼⣿⣽⣿⣿⣭⣿⣿⣿⣿⠷⢋⠔⠀⣠⣿⣿⢿⣿⣿⣿⣿⣋⠿⣷⣄⠀⠀⢿⣿⣿⣯⣽⣷⣾⣿⣿⣿⣿⣿⣿⣿⣙⣏⣿⣿⣿⣿⣿⣏⣿⣿⣀⣀⣰ ⠀⠀⠀⠀⠀⠀⠀⣀⡀⠉⠉⠉⠛⠁⠈⠛⢿⣆⠈⠁⠙⠿⠟⠻⠿⠛⠛⣋⣍⡉⠈⠟⠁⣰⠋⠀⠜⠛⣽⡿⠟⠻⢿⣿⣿⣿⡦⠀⠈⡧⠀⠈⣉⡉⠀⠀⠀⠙⣻⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣿ ⠀⢀⠀⠀⠀⠀⣮⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣄⣀⠀⠈⠙⠛⠛⠛⠿⠿⠿⠿⡀⢠⠇⠀⠀⠐⢃⣩⡄⣶⣶⠶⠈⠐⠙⢯⡦⠆⠁⠄⠀⢹⡿⠿⠿⠏⠹⣿⣿⣿⣷⣦⣽⣄⢈⣍⡉⠁⠀⣀⠉⠉⠙⠉⠃⠙⠛ ⠀⢸⠀⠀⠀⢸⣿⣿⠇⠀⠂⠀⠀⠀⠀⠀⣴⢿⣿⣿⣿⣷⣄⣤⠀⠀⠀⣰⡄⠀⠀⠀⠘⠀⠀⠀⠀⠸⠿⠛⢻⡿⣴⣶⡆⠂⠀⠁⠀⠀⠀⠀⢠⣤⣤⣄⣴⣤⣤⣤⣤⣿⣿⣍⣉⣀⣤⣿⣿⣿⡿⠷⢶⣶⣶⣿⣦⣄ ⠀⢸⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢚⢀⡈⠁⠈⠿⣿⣿⣿⣀⢀⡀⣿⣿⠀⠀⠀⠀⠀⠠⠀⢠⣾⣿⣄⣀⢰⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣏⡙⣿⣶⣀⠛⣿⠃⢉⠉ ⠀⠿⠶⣶⠆⢶⠄⠰⠶⠶⠶⠀⠀⠀⠀⠈⠉⠗⣾⣷⣤⠠⣴⣿⣿⢿⠈⠉⠁⠀⠀⠀⠀⠀⠀⢠⣾⣿⣽⣻⢻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⠛⠛⠛⠛⠻⠟⠛⠛⣛⠛⢙⡛⠋⢙⣋⡉⠈⠉⠉⢹⣿⠁⠀⠀ ⢸⡀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⡇⠀⠈⣿⣿⣿⣿⣿⣿⡿⢛⡁⠀⠀⣿⣿⡿⠀⠀⠀⢠⣿⣿⣿⣿⠿⢿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠸⠗⠀⠀⣿⣿⣿⠏⠈⠗⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠃⠀⠀⠀⠀⠀⠀⠀⣿⠋⣿⡄⠀⠘⣿⣿⣿⣿⡷⣋⣰⣾⣿⠀⠀⣿⣿⡇⠀⢀⣼⣟⣿⣿⣿⣿⣷⢠⣏⠽⣿⣿⣿⣇⣀⠀⣤⡄⠰⠆⠀⢸⣿⣿⡇⠐⠀⠀⢹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣰⣿⠀⠀⢰⣿⣿⢛⣉⣿⣿⣿⣹⣿⣀⡀⢿⣿⠃⠀⣾⣿⣿⡿⣣⣴⣿⣿⣿⢿⣶⣿⣿⣿⣎⢛⣿⣿⣷⠀⠀⠀⣾⡿⣽⠇⣶⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡻⡿⠀⠀⣾⣉⣥⣿⣿⣿⣿⡿⠛⠉⣿⣿⣿⠇⠀⠰⠙⠁⠚⢡⣿⣿⣿⣿⣿⡏⢧⢻⣿⣿⣿⣙⣿⣿⣿⠀⠀⠀⣿⢧⣿⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣄⣰⣶⠛⣿⢡⣀⣠⠄⠙⠟⠻⡿⠈⠋⢹⠇⠀⠀⠈⠉⠉⠀⠀⠀⠀⠠⠄⢻⣯⣥⣮⣽⣿⣿⠘⣷⡙⣿⡿⣿⣿⣿⣿⡇⠀⠀⠈⠘⠃⠀⡯⠀⢀⣷⣀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⢀⠀⣿⣿⣿⡄⣉⣈⣙⣁⢐⣟⣰⣶⣶⣦⣤⣶⡖⢢⣀⡀⣤⣤⣴⠆⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⠟⠀⡿⡇⠀⠙⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⢀⣇⣰⣾⣿⣁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣴⡀⢰⡆⠀⠀⠀ ⠀⠉⣩⣥⢀⣿⣿⣿⣦⡈⠉⣩⣿⣿⣭⠉⣩⣿⣿⣯⡽⣿⣿⣿⣷⣶⣿⣿⣿⣿⣷⡈⠟⠃⠀⠉⠉⠃⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣛⡛⣿⡛⠛⢷⣿⣿⡟⠛⢹⣿⡄⣾⡿⠋⠁⠀ ⠀⠛⣿⣿⠀⣿⣿⡟⣿⣿⡸⣿⣇⣸⣿⣷⣻⡿⢀⣿⡿⣫⣉⡿⢿⠛⠻⣿⠋⠉⠛⠄⠀⠀⠉⠙⠃⠀⠀⠀⢀⣠⣿⣿⠿⣿⣿⣿⣿⠟⠿⠛⠙⣿⣿⣿⣿⣿⣧⡼⣿⣿⡿⣿⣶⠛⠿⠃⠀⠀⣻⣿⣸⣿⠀⠀⠀⠀ ⣤⣀⣿⣿⣀⣿⣿⣤⣿⣿⣿⣿⣿⢿⣷⣽⢟⣟⠻⣿⣮⢛⣩⣤⣼⣿⣿⣄⣀⣦⣤⣶⣦⠀⠀⠀⠀⠀⠀⠰⢛⣩⣴⣾⣿⣿⣿⣿⡿⣆⣀⣹⣿⡟⠋⢀⣹⣽⣿⣨⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⢰⡶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⢀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡟⢹⣿⣶⣶⣤⣀ ⠛⠛⠛⠛⠙⠚⠛⠛⠻⢿⣏⣙⣛⠛⡋⣀⣌⣛⣛⣿⣥⣜⣛⣜⣻⣝⣛⣟⣻⣿⣿⣿⣿⡵⢛⠕⠀⢠⣾⣿⣿⣿⣿⣿⣿⡛⠿⣷⣄⠀⠀⢻⣿⣿⣯⣽⣿⣾⣿⣿⣿⣿⣿⣿⣿⡟⣟⣻⣿⣿⣿⣷⣿⣹⣿⣅⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⠙⠛⠛⠁⠈⠻⣷⡄⠉⠉⠫⠿⠿⠿⠿⠿⠛⣛⡋⠉⠙⠟⠁⣰⠋⠀⠐⠛⣻⣿⠿⢺⢿⣿⣿⣿⣦⠀⠀⣧⣀⠈⠉⠛⠁⠀⠀⠙⢻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡻⣿⣿ ⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⣄⣀⠀⠐⠒⠛⠛⠛⠿⠿⠿⠿⢷⡀⢠⠏⠀⠀⠠⠓⣉⡅⣶⣶⢦⠉⠙⠛⢯⣆⠦⠁⠄⠀⠸⣿⢿⣿⠟⢲⣿⣷⣶⣶⣦⣼⣏⡉⣩⡉⠉⠁⠈⠉⠉⠙⠛⠓⠘⠟ ⠀⡇⠀⠀⠀⢸⣿⣿⠀⠰⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣶⠀⡀⠀⠀⠀⣤⡀⠀⠀⠀⠘⠀⠀⠀⠀⠸⠿⠓⠿⡿⣰⣤⡄⠀⠀⠁⠀⠀⠀⠀⠀⣁⣀⣀⣠⣤⣀⣩⣤⣭⣿⣋⣉⣃⣉⣽⣷⣾⢿⠿⢦⣶⣦⣴⣦⣄ ⠀⡇⠀⠀⠀⠈⠙⠋⠀⠈⠀⠀⠀⠀⠀⠖⣀⠙⠃⠙⢿⣿⣿⣧⡀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⣶⡷⣔⢀⢡⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣟⡛⢻⣶⡀⠘⢻⡟⠙⠉ ⠀⠷⠶⣶⠊⢶⠄⠰⠶⠶⠶⠀⠀⠀⠀⠀⢙⡳⣼⣦⣀⢡⣽⣿⣿⢟⠈⠙⠃⠀⠀⠀⠀⠀⠀⢠⣾⣿⣹⣻⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠛⠛⡿⠟⠛⠛⠿⠛⠛⠿⠛⠛⠛⠁⠉⠉⠓⣾⡗⠀⠀ ⣗⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⡟⢛⣁⠀⠀⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⣿⠿⢿⠿⣿⣿⣿⣿⡇⠀⠀⠁⠀⠐⠗⠀⠀⣿⣿⣿⠟⠀⠙⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠀⠀⠀⠀⠀⠀⠀⢸⡟⢹⣿⠀⠀⢸⣿⣿⣿⣿⡷⣋⣴⣿⡟⠀⠸⣿⣿⡇⠀⢀⣼⣟⣿⣿⣿⣿⣷⢠⣯⠿⣿⣿⣿⢗⣀⠀⣤⡄⠠⠦⠀⢘⣿⣿⣿⠘⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣼⡿⠀⠀⣸⣿⡟⢛⣩⣿⣿⣿⣽⣿⣀⡘⣿⣿⠃⠀⣿⣿⣿⡿⣣⣴⣿⣿⣿⢻⣶⣿⣿⣿⣆⢹⣿⣿⣿⠆⠀⠀⣸⣿⢹⡇⢰⣦⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⡇⠀⠀⣟⣉⣴⣿⣿⣿⣿⡿⠛⠉⣿⣿⣿⠃⠀⠰⠹⠁⠚⢡⣿⣿⣿⣿⣿⡏⢷⠻⣿⣿⣿⣟⣿⣿⣿⡄⠀⠀⣿⡇⣿⠁⣼⠟⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣴⣞⢻⡿⣤⢀⡤⠈⠻⠟⡿⡏⠘⠋⣿⠁⠀⠀⠉⠉⠁⠀⠀⠀⠀⠠⠀⢻⣯⣡⣮⣽⣿⣿⠘⣷⣙⢿⡿⣿⣿⣿⣿⣇⠀⠀⠈⠀⠋⠀⣿⠀⠀⣾⣄⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠀⠀⢸⣿⣿⣿⢈⣁⣉⣉⣄⢸⢓⣴⣶⣦⣤⣤⣾⠖⢢⣀⡀⣦⣤⡶⠂⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⠟⠀⡿⡇⠀⠙⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣿⣸⣶⣿⣋⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢰⡆⠀⣆⠀⠀⠀ ⠈⠉⣩⣤⢸⣿⣿⣿⣤⡉⠉⣩⣿⣿⣭⠉⣫⣿⣿⣯⡿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣷⠈⠟⠃⠀⠉⠉⠃⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⡛⢻⡟⠛⢿⡾⣷⡿⠛⢛⣿⣇⢰⣿⠟⠉⠀ ⠀⠛⣿⣿⠘⣿⣿⡿⣿⣿⡸⣿⣇⣸⣿⣿⣻⡿⢀⣿⡿⣍⣉⣿⣿⠟⠻⣿⠛⠉⠛⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⣠⣾⣿⡿⢿⣿⣿⣿⡿⠟⠻⠛⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣷⠞⠛⠅⠀⠀⢸⣿⣇⣿⡇⠀⠀⠀ ⣀⣀⣿⣿⢀⢿⣿⣤⣿⣿⣿⣿⣿⢿⣿⣭⢻⣛⠻⣿⣮⢛⣉⣠⣼⣿⣯⣁⣐⣦⣠⣴⣄⠀⠀⠀⠀⠀⠀⠠⢛⣫⣤⣶⣿⣿⣿⣿⡻⣦⠀⣸⣶⡿⠉⠁⣹⣿⣿⣅⣉⠉⠀⠈⠈⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⠀⠀⣴ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⢀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡿⢫⣿⣷⣶⣤⣀ ⠛⠿⠿⠛⠹⠿⠿⠿⠿⣿⣋⣙⣛⠛⡋⣀⣈⣛⣛⣛⣁⣙⣛⣘⣛⣙⣻⣟⣛⣻⣿⣿⣿⣥⢟⡕⠀⢀⣾⣿⣿⣿⣿⣻⣿⡟⠿⣿⣄⠀⠀⢻⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣛⣿⣿⣿⣷⣾⣋⣿⣯⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠛⠻⠛⠈⠛⢿⣭⠉⠛⠙⠿⡿⠿⠿⠿⠿⠟⢛⡛⠋⠙⠟⠉⢠⠏⠀⡰⠛⣻⣿⢾⠺⣿⣿⣿⣿⣦⠈⠐⢷⡀⠀⠛⠛⠃⠈⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢿⣾ ⠀⠀⠀⠀⠀⢠⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣀⡀⠀⠒⠒⠲⠶⠶⢾⣿⣿⣿⣦⠀⢠⠏⠀⠀⠠⠖⢛⡁⣤⣴⣤⠉⠋⠙⢿⡂⣦⠉⠀⠀⠸⣿⣶⣶⣶⠒⣾⣷⣶⣿⣦⣈⣟⡉⢉⡛⠛⠉⠉⠉⠙⠛⠛⠛⠌⠻ ⢸⠀⠀⠀⠀⣿⣿⡏⠀⠆⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣄⠀⡀⠀⠀⠀⣄⡀⠀⠀⠁⠸⠀⠀⠀⠀⢸⢿⠇⠿⣿⣠⣤⡄⠀⠀⠃⠀⠀⠀⠀⠀⣉⣀⣀⢀⣄⣈⣉⣉⣹⣿⣿⠛⠛⢈⣙⣷⣶⣾⣿⣦⣤⣤⣤⣦⣀ ⠸⠀⠀⠀⠀⠉⠻⠃⠀⠀⠀⠀⠀⠀⠠⠎⠉⠛⠉⢻⣿⣿⣼⣇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢀⠀⢀⣴⣶⡀⠀⢁⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⠟⠻⣦⡄⠨⠿⣿⠏⠋ ⠸⠶⠶⣶⠊⢶⠄⠰⠶⠶⠶⠀⠀⠀⠀⠓⢻⢤⣶⣄⠈⣉⣽⣿⣷⡎⠘⠛⠋⠀⠀⠀⠀⠀⠀⢀⣼⣿⣳⢿⠿⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⠿⠷⠶⣿⡿⠿⠿⠿⠿⠻⠿⠿⠿⠿⠂⠙⠛⠓⢲⡟⠂⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠀⠀⣽⣿⣿⣿⣿⣿⣿⠟⣋⡀⠀⢈⣿⣿⡏⠀⠀⠀⣼⣿⣿⣿⣿⡿⢿⠿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠈⠛⠀⠀⣾⣿⣿⡿⠁⠙⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⠀⠀⠀⠀⣿⠋⢻⡇⠀⠀⣻⣿⣿⣿⣿⣿⣁⣶⣿⡇⠀⢸⣿⣿⡇⠀⢀⣼⣟⣿⣿⣿⣿⣷⢠⣯⠹⣿⣿⣿⢟⣀⡀⣠⡄⠀⠦⠀⠀⣿⣿⣿⠂⠂⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣽⣇⣿⡇⠀⠀⣿⣿⠟⣋⣹⣿⣿⣯⣿⣇⣀⠸⣿⡿⠁⠀⣿⣿⣿⡿⣧⣴⣿⣿⣿⢻⣾⣿⣿⣿⣯⣺⣿⣿⣿⡆⠀⠀⢸⣿⢻⡗⢰⣦⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣽⡟⣿⠁⠀⢸⣏⣩⣾⣿⣿⣿⣿⠟⠋⠹⣿⣿⡿⠃⠀⠈⠘⠁⠚⢠⣿⣿⣿⣿⣿⡏⢷⡻⣿⣿⣿⣞⣿⣿⣿⡇⠀⠀⣾⡟⣾⠇⢸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣠⣶⡞⣿⡇⣁⢀⡤⠈⠿⠟⠿⠏⠙⠉⡿⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠠⠀⢻⣯⣡⣮⣽⣿⣿⠘⣷⡝⢿⡿⣿⣿⣿⣿⣧⠀⠀⠈⠀⠛⠀⣼⠀⠀⢸⣆⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⣿⣿⣿⡇⣉⣀⣉⣉⡀⡞⢃⣶⣶⣦⣤⣴⣶⠖⣀⣀⢀⣦⣤⡶⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⠟⠀⡿⡇⠀⠙⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣹⣀⣶⣿⣏⡁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣶⠀⢰⠀⠀⠀ ⠉⠉⣩⣤⢹⣿⣿⣷⣬⡉⠉⣩⣿⣿⣭⠉⣻⣿⣿⣯⡭⣿⣿⣿⣶⣶⣿⣿⣿⣿⣷⠈⠟⠃⠀⠉⠛⠋⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⢻⡟⠛⠻⣶⢿⣾⠛⠚⣻⣿⢀⣾⠾⠃⠁ ⠀⠛⣿⣿⠘⣿⣿⣇⣿⣿⠸⣿⣇⣸⣿⣿⣻⡿⢀⣿⡿⠛⣛⣿⡿⠛⢿⡿⠛⠛⠻⠀⠀⠐⠋⠛⠇⠀⠀⠀⠀⣠⣾⣿⡿⢿⣿⣿⣿⡿⠿⠟⠛⣿⣿⣿⣿⣿⣿⣤⢷⣽⣿⣿⣷⡔⠻⠯⠀⠀⠀⣿⣿⢸⡟⠀⠀⠀ ⡀⣀⣿⣿⢀⢿⣿⣭⣿⣿⣿⣾⡿⢿⣿⣍⢿⣛⠻⣿⣦⢛⣉⣀⣴⣿⣆⣀⣀⣄⣠⣦⣄⠀⠀⠀⠀⠀⠀⠠⠞⣋⣥⣶⣿⣿⣿⣿⡛⣦⠀⢘⣴⡿⠋⠁⢈⣫⣿⣏⣘⠋⠁⠈⠉⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇⠀⠀⢠ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠂⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡅⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣶⣶⣾⣿⠟⣿⣷⣤⣤⣀ ⠿⠿⠿⠛⠽⠿⠿⠿⢿⣟⣉⣹⡛⢛⢋⣀⡈⢛⣛⣛⣁⣙⣛⣙⣛⣙⣿⣟⣛⣿⣿⣿⣿⣧⢞⡅⠀⢀⣾⣿⣿⣿⣿⣿⣿⡟⢻⣿⣄⠀⠀⢹⣿⣿⣿⣛⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⠿⡟⣿⣿⣿⣿⣶⣟⢻⣿⡍⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠿⠃⠈⠻⣿⣍⠙⠛⠻⢻⣿⣿⣿⣿⠿⠿⠿⠛⠛⠻⠿⠋⢡⠞⠀⡠⠿⢻⣿⢾⢿⣿⣿⣿⣿⣦⠈⠉⢦⡀⠀⠛⠛⠋⠉⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣶ ⠀⠀⠀⠀⠀⡠⣾⡆⠀⠀⠀⠀⠀⠀⠀⠈⣻⣆⡀⠀⠀⠠⠴⠶⠶⠶⣶⣿⣷⣶⣄⠀⢠⠏⠀⠀⠀⠦⠛⡉⣤⣬⣭⠙⠫⠽⢟⡀⣦⠘⠈⠀⠐⣶⣶⣶⣶⠖⣴⣿⣮⣭⣥⣈⣻⠛⠛⡛⠛⠋⠉⠙⠛⠛⠛⠿⠆⠹ ⡆⠀⠀⠀⢰⣿⣿⠇⠠⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⣀⠀⠀⠈⠀⠸⠀⠀⠀⠀⢸⣿⠇⡿⣿⣈⣀⡀⠀⠀⠏⠀⠀⠀⠀⠀⠉⠁⠉⠀⣀⡈⠙⣋⣙⣿⣿⠟⠻⠂⢛⣳⣦⣴⣶⣦⣀⣤⣄⣠⣄ ⠅⠀⠀⠀⠘⠛⠿⠀⠀⠀⠀⠀⠀⠀⢠⡉⠙⠯⠙⢿⣿⣷⣺⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠃⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⠿⠳⢧⣄⠉⠻⢿⡿⠙ ⠀⠶⠶⣶⠊⢶⠄⠰⠶⠶⠶⠀⠀⠀⠀⠐⠷⣄⣦⡀⠉⠛⣿⣿⣦⡇⠘⠿⠃⠀⠀⠀⠀⠀⠈⢀⣼⣿⢻⢷⣶⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣾⣷⠶⣿⣿⣿⣿⣿⡿⠿⡿⠿⠿⠿⠶⠘⠿⠷⠦⣼⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⠛⣉⡀⠀⢸⣿⣿⡏⠀⠀⠀⣼⣿⣿⣿⣿⡿⢿⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠟⠂⠀⣸⣿⣿⡿⠃⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⠉⣿⡆⠀⠀⣿⣿⣿⣿⣿⢟⣁⣾⣿⡃⠀⢸⣿⣿⡇⠀⢠⣾⣿⣿⣿⣿⣿⣷⣄⣯⠹⣿⣿⣿⡟⣤⡀⣠⣄⠀⠴⠀⠀⣿⣿⣿⠃⠂⠀⠀⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣰⣿⠁⠀⢰⣿⣿⠛⣋⣽⣿⣿⣏⣿⣇⣀⠸⣿⡟⠁⢀⣿⣿⣿⡿⣥⣴⣿⣿⣿⢻⣷⣿⣿⣿⣏⣻⣿⣿⣿⡇⠀⠀⢰⣿⢏⣿⢐⣦⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⣼⢋⣡⣾⣿⣿⣿⣿⠟⠋⢹⣿⣿⡿⠁⠀⠘⠘⠀⠙⢰⣿⣿⣿⣿⣿⡇⢿⡹⣿⣿⣿⡟⣻⣿⣿⡇⠀⠀⢸⡿⣼⡇⢸⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣠⣶⢻⣿⢁⡀⣠⠄⠙⠿⢻⡿⠋⠋⠹⡟⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠠⠀⢻⣯⣡⣮⣽⣿⣿⠘⣷⣝⢿⣿⣿⣿⣿⣿⣷⠀⠀⠈⠁⠙⠁⢸⡇⠀⢰⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢘⣿⣿⣿⠀⢉⣈⠙⣁⠠⠟⢢⣶⣶⣤⣤⣴⡷⠒⢀⣀⢠⣤⣤⡶⠀⠂⠀⢰⣾⣿⣿⣿⣿⣿⣿⠟⠀⡿⡇⠀⠙⣾⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⣸⣇⣷⣾⣟⡁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢠⡄⠀⡆⠀⠀ ⠉⠉⣡⣬⢹⣿⣿⣶⣭⡉⠉⣭⣿⣿⣭⠛⣻⣿⣿⣯⡭⣿⣿⣿⣶⣶⣿⣿⣶⣾⣷⠘⠟⠂⠀⠉⠛⠋⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⣿⠛⠻⣷⣾⣶⡾⠒⢻⣿⡇⢰⡿⠟⠀ ⠀⠛⣿⣿⠘⣿⣿⣄⣿⣿⠸⣿⣇⣸⣿⣿⣻⡿⢀⣿⡿⠛⣛⣿⡿⠿⢿⡿⠛⠛⠻⠀⠀⠐⠛⠻⠇⠀⠀⠀⠀⢀⣾⣿⣿⢿⣿⣿⣿⡿⠿⠿⠛⢻⣿⣿⣿⣿⣿⣤⡼⣿⣿⣿⣷⡶⠿⠷⠁⠀⠀⢺⣿⡇⣿⠃⠀⠀ ⠀⠀⣿⣿⠀⢿⣿⣿⣿⣿⣿⣾⡿⢿⣷⣝⢟⣙⠻⣿⣮⢋⣉⣀⣾⣿⣖⣁⣀⣄⣀⣤⡄⠀⠀⠀⠀⠀⠀⠠⠞⣋⣭⣴⣾⣿⣿⣿⣿⣦⠀⠈⣷⣿⠏⠋⠉⢏⣽⣟⣀⠋⠉⠀⠉⠑⠁⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣻⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣶⣿⣿⣿⣾⣿⣿⣿⣿⡇⠈⠻⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣶⣶⣶⣴⣿⡿⢻⣿⣦⣤⣀ ⠿⠿⠿⠿⢽⡿⣿⡿⣿⠟⠃⣝⠛⠛⠋⣀⠈⢛⣛⣛⣉⣙⣛⣙⣛⡛⣿⣿⣿⣿⣿⣿⣿⣣⠖⡁⠀⢀⣼⣿⣿⣿⣿⣿⣿⡿⢻⣿⡅⠀⠀⠹⣿⣿⣿⣛⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⢿⣿⣿⣿⣧⣼⠛⣿⣏⠉ ⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠿⠿⠂⠑⢺⣿⡋⠛⠛⠛⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠻⡿⠋⢡⠞⠀⠠⠾⢿⣿⢿⢽⣿⣿⣿⣿⣦⠈⠋⢧⡀⠀⠻⠿⠟⠉⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣦ ⠀⠀⠀⠀⠀⣠⣷⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣀⠀⠀⠀⠤⠤⡶⣶⣶⣶⣿⣶⣶⡄⠀⢠⡏⠀⠀⢀⠤⠟⡋⣨⣨⣍⠛⠻⠿⣿⢀⣠⠘⢉⠀⠀⣶⣶⣤⣤⡤⢠⣾⣭⣭⣭⣈⢹⡟⠛⠛⠿⠟⠛⠛⠛⠻⠿⠿⠷⠈ ⠀⠀⠀⠀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣷⣆⡀⠀⠀⠀⠀⠀⡀⠀⠉⠉⠀⠟⠀⠀⠀⠀⢰⣿⡇⣿⣿⢋⣀⣀⠀⠀⡻⠉⠀⠀⠀⠀⠙⠉⠉⠉⢀⠈⠛⠛⠛⣻⣿⠟⠿⠆⠛⠳⣤⣤⣴⣶⣀⣀⣀⢀⣄ ⠀⠀⠀⠀⠙⢻⠏⠀⠀⠀⠀⠀⠀⠀⣨⠛⠻⠟⠻⣿⣿⣇⣾⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣬⢀⠀⠋⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣻⠿⠿⣯⣍⠉⢹⡿⣿⠛ ⠀⠶⠲⣶⠊⢶⠄⠰⠶⠶⠶⠀⠀⠀⢠⠴⣆⣠⣄⠈⠛⠻⣿⣷⣤⡖⠼⢿⠃⠀⠀⠀⠀⠀⠈⠀⣸⣿⢯⣿⣶⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣽⣿⣬⣽⣿⣿⣿⣿⣿⡿⣿⣿⣿⣷⣶⠜⠿⠶⠤⢠⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⠁⠀⢸⣿⣿⣿⣿⣿⣿⡿⢉⣉⡀⠀⢸⣿⣿⡇⠀⠀⠀⣼⣿⣿⣿⣿⡿⠿⠻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠛⠀⠀⢸⣿⣿⡿⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡏⢹⣿⠀⠀⢸⣿⣿⣿⣿⡿⣏⣠⣿⣿⠁⠀⢹⣿⣿⠁⠀⢠⣾⣻⣿⣿⣿⣿⣦⣤⡯⠹⣿⣿⣿⡿⣄⡀⣠⣤⠀⠲⠀⠀⣻⣿⣿⠇⠉⠀⠀⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣇⣼⡟⠀⠀⢸⣿⡿⠋⣉⣿⣿⣿⣯⣿⣅⣀⢻⣿⡟⠀⠀⣿⣿⣿⡿⣥⣶⣿⣿⣿⣻⣷⣿⢿⣿⣧⣙⣿⣿⣿⡇⠀⠀⠀⣿⡇⣿⠀⣷⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⠇⠀⠀⣿⣁⣴⣿⣿⣿⣿⡿⠛⠉⢹⣿⣿⡟⠀⠀⠈⠜⠀⠏⢰⣿⣿⣿⣿⣿⡇⢻⡹⣿⣿⣿⣇⣻⣿⣿⡇⠀⠀⢸⣿⢸⡟⠀⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⣴⡎⢻⡟⢀⢀⡤⠀⠻⠟⢻⡿⠉⠋⢹⠇⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠠⠀⢻⣯⣡⣮⣽⣿⣿⠘⣿⡏⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠁⠘⠁⢸⡇⠀⠀⣷⣀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⡇⠈⣁⡈⢋⣀⠰⠓⣢⣴⣶⣤⣤⣾⡶⠂⣀⣀⢰⣤⣤⡶⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⠟⠀⡿⣇⠀⠙⢾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢘⣇⣶⣾⣿⣉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⣤⠀⢰⠀⠀ ⠉⠉⣠⣼⢹⣿⣷⣶⣭⡉⠉⣭⣿⣿⣭⠛⣻⣿⣿⣯⡽⣾⣿⣿⣶⣾⣿⣷⣶⣿⣧⠘⠟⠂⠀⠉⠛⠋⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⢿⠟⠛⢷⡶⣶⡾⠒⠒⣿⣯⠀⣸⠶⠀ ⠀⠛⣿⣿⠘⣿⣿⣄⣿⣿⠰⣿⣇⣸⣿⢿⣻⡿⢀⣿⡿⢛⣻⣿⡿⠿⣿⡿⠛⠛⠿⠀⠀⠐⠛⠻⠇⠀⠀⠀⠀⢀⣾⣿⣿⢿⣿⣿⣿⣿⢿⡿⠟⢹⣿⣿⣿⣿⣿⣧⣴⣯⣿⣿⣿⣦⠘⠿⠍⠀⠀⠐⣿⣟⢼⡏⠀⠀ ⠀⠀⣿⣿⠀⢿⣿⣿⣿⣿⣿⣾⡿⢿⣷⡍⢗⣛⠻⣿⣮⢛⣉⣀⣶⣶⣀⠀⢀⣄⣀⣤⡄⠀⠀⠀⠀⠀⠀⠠⠾⢛⣩⣵⣶⣿⣿⣿⡿⣧⠀⠀⢤⣼⠟⠙⠉⢻⣻⣿⢁⠛⠋⠁⠉⠙⠂⠀⠀⠀⠀⢰⣿⣿⣾⡇⠀⠀ ⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⢻⣿⡇⢻⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠻⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣦⣾⣿⠟⣿⣧⣤⣀ ⠿⠿⠿⢿⣿⣿⣿⣿⡿⠛⢃⡝⠛⠛⠋⠀⠈⠛⣛⡛⠙⠛⠛⢿⣿⠿⢿⠿⢿⣿⣿⣿⣿⣣⠖⡀⠀⢀⣼⣿⣿⣿⣿⢿⣿⡿⢿⣿⡇⠀⠀⠹⣿⣿⡿⡟⣿⣿⣿⣿⣻⣻⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣤⡟⢿⣿⡛ ⠀⠀⠀⠀⠀⠀⠀⠐⠒⠿⢿⠿⠚⠷⢮⣉⠈⠛⠛⢛⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⢿⡿⠋⢡⠞⠀⠠⠾⢿⣿⢽⢽⣿⣿⣿⣿⣦⠈⠋⢤⡀⠀⠹⠿⠿⠉⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷ ⠀⠀⠀⠀⠀⣰⡆⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⠀⠀⠀⠉⢡⣬⣤⣶⣤⣴⣷⣶⣦⡄⠀⢠⠎⠀⠀⢀⡤⠿⠋⣈⣀⣉⠛⠿⣿⣿⢡⢠⠸⠋⠀⠀⣶⣦⣤⣤⣤⢠⣾⣯⣩⣭⣉⠙⡿⠛⠻⠿⠿⠛⠛⠛⠿⠿⠿⠿⡎ ⠀⠀⠀⢀⣼⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⣲⣿⣷⣶⣶⣀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⡟⠀⠀⠀⠀⢰⣾⡇⣿⣿⠍⠀⡀⠀⠈⠻⠋⠀⠀⠀⠀⠸⠋⠉⠉⠁⠈⠛⠻⠛⠿⣿⡿⠿⠶⠘⠷⣤⣀⣤⣤⣄⢀⣀⠀⢀ ⠀⠀⠀⠈⠿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣘⠛⢻⡛⠿⣿⣿⡰⡶⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣍⠀⠀⠏⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣶⣶⣾⣿⣶⣿⣿⣿⣿⣶⣶⣶⣶⡛⢿⣿⣯⣍⠉⠛⣻⢿⡟ ⠀⠖⠲⣶⠏⢷⠄⠰⠶⠶⠖⠀⠀⠀⡀⢶⣀⢀⡀⠙⠛⠻⣿⣦⣠⠠⠸⣿⠀⠀⠀⠀⠀⠀⠈⠀⣸⣿⢯⣿⣤⣰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣏⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠿⣷⣤⣀⣸⡇ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠀⠀⢸⣿⣿⣿⣿⡿⣿⠟⢉⣁⠀⠀⣸⣿⣿⠃⠀⠀⢀⣼⣿⣿⣿⣿⡿⠿⡻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠙⠃⠀⢀⣿⣿⣿⠏⠀⠁⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠁⢻⡇⠀⠀⢸⣿⣿⣿⣿⣿⣁⣼⣿⣿⠀⠀⣿⣿⣿⠀⠀⣠⣾⣻⣿⣿⣿⣿⣦⣤⣯⠹⣿⣿⣿⡿⣀⡀⢠⣤⠀⠸⠀⠀⣸⣿⣿⡏⠈⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣀⣿⡇⠀⠀⣾⣿⡟⢋⣩⣿⣿⣿⣽⣿⣀⣀⢻⣿⠏⠀⢠⣿⣿⣿⡿⣥⣴⣿⣿⣿⣹⣷⣿⢿⣿⣯⠹⢿⣿⣿⡷⠀⠀⠀⣿⡟⣽⠅⣴⣤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡏⣿⠁⠀⢠⢟⣡⣴⣿⣿⣿⣿⡿⠛⠉⢿⣿⣿⡟⠀⠀⠎⠜⠀⠏⢰⣿⣿⣿⣿⣿⡇⢻⡹⣿⣿⣿⣇⣻⣿⣿⣇⠀⠀⠸⣿⢳⣿⠀⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣠⣶⠛⣿⠇⠀⢀⡤⠈⠿⠟⣿⠏⠙⠉⢻⠇⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠐⢻⣏⣁⣎⣽⣿⣿⡈⣿⡟⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠁⠘⠃⠀⣏⠀⠀⣼⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⡄⢉⠀⠙⢋⠀⠼⠃⣤⣤⣤⣤⣤⣴⠶⠀⣀⡀⣠⣤⣤⡦⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⡟⠀⣿⣷⠀⠙⢾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣗⣰⣴⣿⣋⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣠⠀⠀⡆⠀ ⠉⠁⣠⣿⢹⣿⣵⣾⣯⡉⠉⣭⣿⣿⣽⢻⣿⣿⣿⣯⡴⣶⣿⣿⣴⣿⣿⣷⣶⣾⣦⠸⠟⠃⠀⠘⠛⠋⠈⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣷⣶⣶⣾⣶⣶⣿⣿⣿⣿⡿⠛⠛⠻⢿⡶⠻⠷⣶⢶⣶⠶⠖⢺⣿⡀⣀⡷⠂ ⠀⠛⣿⣿⠘⣿⣿⡀⣿⣿⠰⣿⣇⣸⣿⢿⣻⡿⢀⣿⡿⡛⣻⣿⠿⠿⣿⡿⠟⠻⠿⠀⠀⠐⠚⠿⠆⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⢿⠿⠟⠛⣿⣿⣿⣿⣿⣧⣠⣮⣿⣿⣿⣦⡄⠿⠈⠁⠀⠀⢾⣿⠡⣿⠁⠀ ⠀⠀⣿⣿⠀⢿⣿⣿⣿⣿⣦⣾⡿⢿⣷⡝⢛⣛⠻⣿⣮⠛⠁⢠⣶⣶⡈⠁⢠⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀⢠⠶⢟⣉⣭⣶⣮⣿⣿⡿⣧⡀⠀⢰⣴⡟⠛⠉⠻⢹⣿⠋⠘⠛⠉⠈⠉⠂⠀⠀⠀⠀⠀⣾⣿⣷⡟⠀⠀ ⣿⣿⣿⣿⣾⣶⣶⣶⣿⣿⠿⣿⡇⢻⣿⣷⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⡏⠈⠳⣾⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣦⣰⣿⡿⢻⣷⣄⣀ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢃⠙⠛⠛⠋⠀⠈⠛⠛⠛⠙⠻⠿⠿⡿⢿⣿⠿⣿⣿⣿⣿⣿⣣⡴⡊⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⢿⣿⡋⠀⠀⠘⣿⣿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⣿⣿⣿⣿⣧⣼⠿⣿⡟ ⠀⠀⠀⠀⠀⠀⠈⠰⠲⢶⣿⠆⠐⢴⣝⠳⠘⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⡿⠛⢩⡞⠁⢠⢾⢿⣿⣽⣿⣿⣿⣿⣷⣦⠘⠋⢦⡀⠀⠹⠿⠿⠟⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣾⣿⣿⣿⣿⣿⣷⣿⢿ ⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀⠀⠉⢉⣉⣉⣭⣭⣤⣴⣶⣤⣤⡈⠀⢠⡎⠀⠀⠀⣐⡾⠟⢈⢈⡉⠻⢿⣻⣿⢧⢀⠠⠟⠂⠀⢤⣤⣤⣀⣤⡄⣼⣏⣛⣛⡋⠛⣿⠿⠿⠿⠿⠿⠟⠻⠿⠿⣿⣿⠆ ⠀⠀⠀⢠⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣷⣦⣤⣄⠀⠀⠀⠀⠀⠉⠙⠉⠉⠛⠓⠀⡾⠀⠀⠀⠈⢠⣶⡇⣿⣿⡟⠀⠀⠀⠈⢵⠊⠁⠀⠀⠀⠸⠟⠛⠛⠋⠀⠻⠿⠿⠿⣿⣷⡿⣦⠀⠶⣤⣀⣀⣠⣄⠀⠀⠀⠀ ⠀⠀⠀⠸⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠲⠟⣿⠿⢿⣿⣿⣠⡦⠀⠀⠀⢰⣦⠀⠀⠀⠀⠁⠀⠀⠀⠀⢈⣙⠁⠉⠟⣹⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣦⣤⣴⣶⣶⣶⣶⣾⣿⣷⣤⣤⣤⡶⠾⣿⣿⣛⠛⠛⠻⡿⢲ ⠀⠆⠲⣶⠟⢷⠄⠰⠶⠶⠖⠀⠀⠈⡁⣤⠀⣀⠈⠻⣿⣷⣷⣤⢠⠀⢼⣿⠀⠀⠀⠀⠀⠀⠐⠀⢰⣿⣟⣾⣤⣠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣿⣋⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣦⣄⠹⣿⣄⡀⠁⣿ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⠀⠀⣿⣿⣿⣿⣿⢿⣿⠏⢩⣀⠀⠀⣽⣿⣿⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠿⡻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⠃⠀⢀⣿⣿⣿⠏⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡟⠈⣿⡄⠀⠀⢿⣿⣿⣿⣿⣿⣀⣾⣿⣟⠀⠀⣿⣿⣿⠀⠀⣠⣾⣿⣿⣿⣿⣿⣦⣤⣯⠙⣿⣿⣿⡿⢀⡀⢠⣤⠀⠘⠀⠀⢸⣿⣿⡏⠈⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣇⣰⣿⠁⠀⢀⣿⣿⠛⢉⣹⣿⣿⣿⣽⣿⣀⡀⢿⣿⠋⠀⢰⣿⣿⣿⠟⣥⣶⣿⣿⣿⣻⣗⣿⣿⣿⣯⢈⣿⣾⣿⣿⠀⠀⠀⣿⣿⣹⡇⢐⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⠹⡟⠀⠀⠸⣋⣠⣾⣿⣿⣿⣿⠿⠛⠉⣿⣿⣿⠟⠀⠀⠊⠞⠐⠏⢰⣿⣿⣿⣿⣿⡇⢻⡹⣿⣿⣿⣷⣻⣿⣿⣿⠀⠀⠀⣿⠇⣿⠁⣺⠟⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⣴⡖⢹⣿⠀⠀⣠⠄⠘⠿⠛⣿⠏⠙⠉⣿⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠐⢻⣏⣁⣎⣿⣿⣿⡈⣿⡎⢿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠉⠀⠋⠀⣿⠀⠀⢸⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣷⠈⢉⠈⠛⠁⠠⠿⢢⣤⣴⣤⣤⣤⣷⠶⠀⡀⠀⣠⣠⣤⠤⠀⠀⠀⣴⣽⣿⣿⣿⣿⣿⣿⡟⠁⣿⣷⠀⠘⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣐⣤⣿⣟⠁⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⢠⡄⠀⢠⠀ ⠈⠀⣸⣿⢹⣿⣴⣿⣯⡉⠙⣯⣿⣿⣽⢿⣿⣿⣿⣯⡤⣾⣿⣿⣼⣿⣿⣶⣶⣶⣆⠹⠟⠉⠀⠛⠛⠋⠈⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⠿⠿⠿⠿⣶⠾⠷⣶⡶⣶⡶⠶⠒⣿⣇⢀⡀⠆ ⠀⠛⣿⣿⠸⣿⣿⡀⣿⣿⠰⣿⣇⣸⣿⢿⡻⠿⢀⣿⡿⠛⣿⣿⠿⢿⣿⡿⠿⠿⠿⠀⠀⠐⠒⠷⠆⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⢿⡿⠿⠻⣿⣿⣿⣿⣿⣿⣀⣴⢹⣾⣿⣦⣀⢸⢄⠉⠁⠀⢸⣿⡏⣼⡏⠀ ⠀⠀⣿⣿⠀⢿⣿⣿⣿⣿⣦⣾⡿⢿⣷⡕⢛⣟⠻⣿⣮⠛⠉⣈⣶⣴⠈⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⢀⡴⠟⣋⣩⣷⣶⣿⣿⡿⣯⡀⠀⢀⣶⡿⠛⠉⠛⢛⣿⡏⠁⠛⠋⠉⠋⠁⠀⠀⠀⠀⠀⢸⣿⣿⣾⠃⠀ ⣿⣷⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣇⢻⣿⣷⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⣴⣶⣿⣿⣿⣿⣿⣿⣿⡟⠈⠳⣶⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣶⣶⣤⣶⣶⣶⣦⣤⣤⣄⣿⣷⡿⣿⣆⣀ ⣿⣿⣿⣿⣿⣿⣿⣿⠿⠕⡁⠙⠛⠛⠋⠈⠈⠛⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⡴⡂⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠀⠀⠘⣿⣿⣿⣿⢿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡿⣿⣿ ⠀⠀⠀⠉⠉⠉⠩⠅⢴⣶⣿⠀⠢⢠⡖⠰⠲⠾⠿⢿⣿⣿⣿⣿⣷⣾⣿⣿⡿⠿⣿⡿⠟⢋⡾⠁⢀⣼⣿⣿⣻⣻⣿⣿⣿⣷⣄⠙⠻⢢⡀⠀⠹⣿⣿⡟⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⣾⣿⣿⣿⣿⣿⣷⣾⡿ ⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⠀⠀⠀⠈⠉⣉⣉⣉⣍⣉⣴⣦⣤⡀⠈⠀⢠⡞⠀⠀⠀⣀⣾⠟⠉⠈⡛⠿⣿⢿⣿⣇⢀⠀⡟⠂⠀⢠⣤⣀⣀⣀⡀⢨⣟⣛⡛⡛⠛⢿⡿⠿⢿⣿⣿⠿⠿⠿⣿⣿⣿⣷ ⠀⠀⠀⣀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣧⣤⣤⣀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠛⠣⠀⡞⠀⠀⠀⠈⢡⣴⡆⣿⣿⡟⠀⠀⠁⠉⢷⠜⠃⠀⠃⠀⠘⠿⠛⠛⠛⠁⠻⠿⡿⢿⣿⣷⣾⣦⡄⢴⣤⣀⠀⣀⣀⡀⠀⠀⠀ ⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠼⢿⡿⢿⣿⣿⣆⢠⡄⠀⠀⠀⢰⡆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⠛⠁⠋⡟⢰⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣶⣦⣤⣴⣶⣶⣭⣥⣄⣀⣤⢤⣿⣿⡛⠟⠳⠶⣿⠆ ⠀⠆⠲⣶⠿⢷⠄⠰⠶⠶⠖⠀⠀⠘⢀⡀⠉⠀⠙⢿⣿⣾⣧⡀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣴⡀⢀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣈⠉⣷⣆⡀⠈⢀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠀⠀⢀⣿⣿⣿⣿⣿⣿⡿⠋⣩⡄⠀⠀⣿⣿⣿⠀⠀⠀⢀⣿⣿⣿⣿⣿⡛⠻⡛⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⠋⠀⠀⣿⣿⣿⠏⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡃⢸⣿⠀⠀⠐⣿⣿⣿⣿⡿⣫⣠⣿⣿⡇⠀⠀⣿⣿⣏⠀⠀⣠⣿⣯⣿⣿⡿⣿⣮⣤⣧⠘⣿⣿⣿⣟⣠⡀⢠⣤⡀⠈⠀⠀⢈⣿⣿⣿⠀⠁⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣅⣾⡏⠀⠀⢸⣿⡿⠋⣉⣽⣿⣿⣯⣿⣧⣀⡘⣿⣿⠃⠀⢸⣿⡿⣿⠟⣥⣶⣿⣿⣿⣹⣧⣿⣿⣿⣷⡀⣿⣾⣿⣿⠀⠀⠀⣸⣿⢹⡇⠀⣤⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⡏⢻⠇⠀⠀⡞⣁⣤⣿⣿⣿⣿⣿⠟⠋⠙⣿⣿⣿⠇⠀⠀⢀⠏⠐⠏⢸⣿⣿⣿⣿⣿⣇⢻⡹⣿⣿⣿⣯⣹⣿⣿⣿⠀⠀⠀⣿⡏⣾⠇⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣠⣴⡊⣿⡇⠀⠀⡤⠀⠻⠿⠛⡿⠉⠛⠹⡿⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⡀⠐⢻⣏⣁⣎⣿⣿⣿⡈⣿⡬⢻⣿⢿⣿⣿⣿⣿⠆⠀⠀⠈⠀⠋⠀⣸⡁⠀⢠⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⡇⠙⠁⠘⠛⡀⠐⠗⢠⣤⣴⣤⣤⣤⡴⠆⢀⠀⠀⣤⣀⣤⡄⠀⠀⠀⣶⣽⣿⣿⣿⣿⣿⣿⡟⠁⣿⣿⠀⠘⢿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣹⣃⣦⣾⣿⡉⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⣤⠀⠀⡆ ⠀⠀⣻⣿⢹⣧⣼⣿⣯⡙⠛⣯⣿⣿⣽⢿⣿⣿⣿⣯⡤⣽⣿⣧⣼⣾⣿⣶⣶⣶⣄⠹⠟⠉⠀⠚⠛⠋⠈⠀⠀⠈⠈⠀⢀⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⠿⠿⠿⠿⢷⠶⠿⢶⡶⣶⣶⠶⠖⢺⣯⠀⠀⠀ ⠀⠛⣿⣿⠻⣿⣿⠀⣿⣿⠰⣿⣇⣸⣿⢿⣻⠿⢀⣿⡿⢛⣿⣿⠿⢿⣿⡿⠿⠿⠇⠀⠀⠐⠒⠶⠆⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⣿⣿⣿⣿⣿⣆⣰⠘⣶⣿⣶⣤⡠⢧⡈⠁⠀⠀⣿⣿⢡⣿⠀ ⠀⠀⣿⣿⠀⢿⣿⣷⣿⣿⣤⣾⡿⢿⣷⡝⢻⣞⠻⣿⣦⠛⠉⢨⣴⣾⠉⠀⠄⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⢛⣩⣽⣶⣿⣿⣿⣯⡀⠀⢀⣤⣿⠛⠛⠙⠟⣿⡟⠉⠚⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⣿⣿⣾⡟⠀ ⣶⣶⣿⣿⣴⣶⣶⣎⣿⣿⣿⣿⣇⢻⣿⣷⣿⣿⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⠉⠱⣶⣾⣿⣧⣴⣶⣶⣾⣿⣿⣿⣶⣤⣤⣤⣶⣶⣦⣤⣤⣄⣸⣿⣾⢿⣧⣀ ⣿⣿⣿⣿⣿⣿⣿⣿⠿⠕⠁⠙⠛⠛⠋⠈⠉⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⡤⠂⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠀⠀⠘⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣸⢿⣿ ⠀⠀⠉⠉⠉⠉⠉⠡⣤⣾⣧⠀⠀⢀⠖⠀⠶⠶⣶⣶⣶⣶⣶⣾⣶⣾⣷⣶⣿⡿⣿⣿⠟⢋⡴⠁⢀⣴⣿⣿⣛⣛⣿⣿⣿⣿⣄⠙⠿⢢⡀⠀⠸⣿⣿⡾⠲⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣦⣿⣿⣿⣿⣿⣿⣤⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⢷⡄⠀⠀⠀⠘⠛⠛⣛⣛⣋⣉⣭⣅⣀⡀⠉⠁⢀⡎⠀⠀⠈⡠⣼⠿⠙⠉⠛⠿⣿⠿⣿⡇⠀⠀⡷⠠⠀⢠⣄⣀⣀⣀⡀⠉⣽⡛⠿⠟⠛⢿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿ ⠀⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣹⣤⣀⣀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠛⠿⠆⠀⡞⠀⠀⠀⠀⢉⣤⡆⣾⣾⡟⠀⠀⠉⠙⢲⡵⠓⠀⠀⠀⠈⡿⠿⠿⠿⠉⠸⣿⣿⣿⣿⣷⣤⣧⣄⢠⣤⣀⠀⠀⣀⡀⠀⠀⠁ ⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣿⣿⣿⣿⣷⡀⢀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⠻⠃⠋⡿⢣⣶⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⣀⣤⣤⣠⣤⣤⣴⣭⣍⣈⣉⣀⣠⣽⣿⡿⠿⠿⠦⢶⡦ ⠀⠆⠲⣶⠿⢶⠴⠰⠶⠶⠖⠀⠀⠓⣀⡈⠁⠈⠻⣿⣷⣾⣄⡀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠠⠀⢠⣾⣷⣴⠀⢀⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⢿⣿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⠙⢓⣦⡀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⠀⠀⢸⣿⣿⣿⣿⡿⣿⡿⢉⣥⡄⠀⢠⣿⣿⡿⠀⠀⠀⢠⣿⣿⣿⣿⣿⡛⠻⣛⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠉⠀⠀⣼⣿⣿⡟⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣧⣴⣿⣿⡇⠀⢸⣿⣿⡇⠀⠀⣰⣿⣯⣿⣿⡿⣿⣾⣄⣿⡘⣿⣿⣿⣟⠡⣀⢠⣴⡆⠀⠁⠀⢀⣿⣿⣿⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣟⣠⣿⠃⠀⠀⣾⣿⡟⢋⣩⣿⣿⣿⣯⣿⣇⣀⡘⣿⡿⠁⠀⢸⣿⣿⣿⠟⣥⣶⣿⣿⣿⣹⣷⣿⣿⣿⣿⡀⢻⣾⣿⣿⠀⠀⠀⢸⣿⠃⣿⠀⢰⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡛⡿⠀⠀⢐⣋⣀⣴⣿⣿⣿⣿⣿⠟⠋⠹⣿⣿⣿⠃⠀⠀⢁⠋⠐⠏⣸⣿⣿⣿⣿⣿⣇⢹⡜⣷⣿⣿⣷⢹⣿⣿⣿⡀⠀⠀⢾⡟⣸⡇⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡀⣠⣖⠙⣿⠁⠀⢀⡄⠈⠿⠿⣿⡟⠙⠋⢹⠏⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⡀⠐⢻⣏⣁⣎⣿⣿⣿⡌⢿⡮⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠁⠙⠁⢸⡇⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⠀⠋⠀⠛⠃⠀⡸⠂⣤⣤⣤⣤⣤⣤⡴⠆⢀⠀⠀⣀⣠⣤⠄⠀⠀⠀⣶⣽⣿⣿⣿⣿⣿⣿⡿⠃⢸⣿⠀⠈⢫⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢸⣇⣦⣴⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡄⠀⠀ ⠀⠸⣻⣿⣿⣠⣽⣿⣯⡛⠛⣯⣿⣿⣽⢿⣿⣿⣿⣧⡤⣯⣿⣤⣽⣿⣷⣶⣶⣶⡄⠻⠟⠉⠀⠛⠛⠏⠉⠀⠀⠈⠈⠀⢀⣼⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⡿⠿⠿⠿⢷⡶⠶⢶⣦⢶⣴⠶⠦⠲⣾⡁⠀⠀ ⠀⢛⣿⣿⠻⣿⣿⠀⣿⣿⠰⣿⣇⣸⣿⢿⡻⠿⢀⣿⡿⢻⣿⣿⠿⢿⣿⡿⠿⠿⡇⠀⠀⠠⠲⠶⠆⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣇⣠⠶⢷⣾⣷⣄⡀⠻⠈⠉⠀⠀⢸⣿⡅⣼⡆ ⠀⠀⣿⣿⠠⢿⣿⣶⣿⣿⣤⣾⡿⢿⣷⡕⢷⣘⠻⣿⣦⠛⠉⢡⣤⣄⠁⠀⠀⠀⢈⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⢛⣋⣭⣵⣿⣿⣿⣯⡁⠀⠀⣄⣾⡟⠟⠻⠟⢻⣿⠛⠒⠟⠋⠙⠉⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⠃ ⣶⣶⣿⣿⣴⣵⣶⢟⣿⣿⡿⣿⣇⢸⣿⣷⣿⣿⣤⣿⣿⣶⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣷⣄⠀⠀⠀⠀⠀⢈⣴⣾⣿⣿⣿⣿⣿⣿⣿⠋⠹⣶⣾⣿⣿⣤⣤⣶⣶⣿⣿⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣄⢀⣿⣷⡿⣿⣄ ⣿⣿⣿⣿⣿⣿⣿⣿⠿⠕⠀⠙⠛⠛⠋⠘⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⡠⠔⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⡿⣿ ⠀⠉⠉⠉⠙⠛⠋⢥⣤⣾⡄⠀⠀⠠⠆⠠⣶⣶⣶⣶⣶⣶⣶⣿⣦⣽⣿⣿⣿⣿⣿⣿⠿⢛⡵⠁⠀⣴⣿⣿⣟⣿⣿⣷⣿⣿⣄⠛⠿⠢⡀⠀⠘⣿⣿⣿⠷⠾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣨⣥⣽⣿⣿⣿⣿⣿⣧⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠹⣷⡀⠀⠀⠀⠛⠛⠛⠛⢛⡛⢉⣩⣉⣀⡀⠙⠁⢀⡞⠀⠀⠈⡉⣽⡿⠛⠉⠟⢿⣿⣿⣿⡇⠀⠀⣵⠄⠀⠈⣉⡁⠀⠀⠀⠈⢻⡿⠿⠿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⣀⣀⡀⠀⠀⠙⠛⠛⠛⠛⠿⠿⠿⠿⠄⠀⡾⠀⠀⠀⠐⢋⣥⡄⣶⣶⡷⠄⠈⠀⠙⢣⡇⠗⠀⠀⠀⠀⢿⡿⠿⠿⠏⠠⣿⣿⣿⣿⣶⣤⣽⣀⠀⣬⡉⠁⠀⠀⠀⠈⠉⠉ ⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣦⠀⢀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠸⠿⠇⠟⣿⢇⣤⣤⠄⠀⠀⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣄⣀⣀⣤⣬⣍⣛⠉⠙⠁⢈⣙⣷⣶⠾⡿⢦⣤⣤ ⠀⠖⠷⣿⠏⢶⠶⠰⠶⠶⠖⠀⠠⠎⠀⠙⠂⠉⢿⣿⣶⣾⡀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣷⣠⠀⠀⣸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣽⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣁⡉⠉⠲⢤⠀⠀⠉ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⣿⣿⣿⣿⣿⣻⣿⠟⢀⣤⡄⠀⢸⣿⣿⡟⠀⠀⠀⢰⣿⣿⣿⣿⣿⡛⠻⣛⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠉⠀⠀⣸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠈⣿⠀⠀⠀⢿⣿⣿⣿⣿⣿⣅⣴⣿⣿⡁⠀⢸⣿⣿⡇⠀⠀⣴⣿⣯⣿⣿⠿⣿⣿⣄⣿⡚⢿⣿⣿⣿⢁⣄⢠⣶⡆⠀⠁⠀⠀⣿⣿⣿⡏⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣇⣼⣿⠀⠀⠀⣾⣿⠛⣉⣤⣿⣿⣿⣿⣿⣇⣀⢸⣿⡿⠁⠀⢸⣿⣿⣿⠟⣥⣶⣿⣿⣿⣹⣷⣿⣿⣿⣿⣆⣸⣿⣿⣿⡇⠀⠀⢸⣿⡏⣾⠀⣰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⠹⠇⠀⠀⢸⣋⣠⣾⣿⣿⣿⣿⡿⠛⠉⢹⣿⣿⡿⠃⠀⠀⠀⠋⠘⠋⣼⣿⣿⣿⣿⣿⣇⢹⡜⣿⣿⣿⣿⣻⣿⣿⣿⡅⠀⠀⢸⣿⢰⡿⠀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⢀⣤⡄⢻⡟⠀⠀⢠⠀⠘⠿⠿⢿⠏⠙⠋⣿⠇⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⡀⠐⢻⣏⣁⣞⣻⣿⣿⡅⢿⡮⡻⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠁⠘⠃⠀⡇⠀⠀⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⡇⠘⠁⠀⠛⠀⠀⠶⢂⣤⣤⣤⣠⣤⣤⡤⠀⠀⠀⢀⣀⣄⣤⠄⠀⠀⠀⣶⣽⣿⣿⣿⣿⣿⣿⡿⠃⢸⣿⠀⠈⢣⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⡧⢀⣴⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀ ⠀⠿⣻⣿⠁⣠⣽⣷⣯⡛⠛⣦⣿⣿⣿⣿⣿⣿⣿⣧⡤⣼⣿⣤⣴⣿⣷⣶⣶⣶⡄⢻⠿⠉⠁⠛⠛⠟⠁⠀⠀⠈⠈⠀⢀⣴⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⠿⠿⠿⠿⣶⠶⠶⣦⣴⣦⡶⠶⠖⢾⣇⠀⠀ ⠐⢟⣿⣿⠀⣿⣿⠀⣿⣿⠐⣿⣇⣸⣿⢿⠻⠿⢀⣿⡿⢿⣿⣿⢿⣿⣿⡿⠿⢿⡇⠀⠀⠠⠶⢶⡆⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣯⣀⣴⢶⣶⣷⣄⡀⠸⠄⠉⠁⠀⠀⣿⡿⢠⣷ ⠀⠀⣿⣿⢰⢿⣿⣤⣿⣿⣠⣾⡿⢿⣷⡵⢷⣘⠻⣿⣦⠛⠉⣥⣤⡜⠁⠀⠀⠀⢈⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⣛⣭⣭⣿⣿⣿⣿⡃⠀⠠⣄⣸⡿⠿⠛⠿⢿⣿⠟⠛⠾⠛⠉⠋⠁⠀⠀⠀⠀⠀⢀⣿⣿⣦⡿ ⣶⣶⣿⣿⣴⣵⣷⢛⣿⣿⣿⣿⣇⢸⣿⣧⣿⣿⣀⣿⣿⣶⣶⣿⣿⣿⣶⣶⣶⣶⣿⣿⣦⣄⠀⠀⠀⠀⠀⢈⣴⣶⣿⣿⣿⣿⣿⣿⣿⠎⠛⣴⣶⣾⣿⣥⣤⣴⣶⣿⣿⣶⣶⣤⣤⣀⣤⣤⣤⣤⣄⣀⡀⣸⣿⣽⠿⣧ ⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠙⠛⠛⠋⠚⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣀⠔⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣰⣿ ⠉⠙⠛⠛⠛⠛⠋⢀⣤⣦⠀⠀⠀⠠⠀⢠⣤⣤⣤⣤⣤⣤⣾⣿⣭⣽⣭⣿⣿⣿⣿⣿⠿⠟⣵⠃⠀⣰⣿⣿⠿⠿⣿⣯⣟⣿⣅⠛⠿⠦⡀⠀⠈⣿⣿⣿⡧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣩⣭⣿⣿⣿⣿⣿⣿⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠙⢾⣤⠀⠀⠈⠉⠿⠿⠿⠿⠿⠛⠛⣉⠉⠁⠈⠛⠁⢀⡞⠁⠀⠈⢉⣽⣿⠻⠉⠻⢿⣿⣿⣿⣷⠀⠈⢹⠄⡀⠈⡉⠉⠀⠀⠀⠈⠻⡿⡿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣇⣀⢀⠀⠀⠒⠚⠛⠛⠛⠿⠿⠿⠿⠷⡄⢀⡜⠀⠀⠀⠐⠒⣉⡄⣴⣶⡶⠄⠉⠒⠛⢯⣇⠧⠈⠠⠀⠀⢿⣿⣿⣿⠿⠃⣾⣿⣶⣶⣶⣄⣸⣏⠀⢉⡉⠉⠀⠀⠈⠉⠉⠉ ⠀⢠⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠸⠿⠇⠟⢿⣇⣤⣄⠄⠀⠀⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⣀⡀⢉⣉⣉⣛⠟⠛⠙⠃⠈⠙⣳⣦⣶⣾⣷⣄⣀ ⠀⠞⠿⣿⠏⢶⠆⠰⠶⠶⠖⠀⠠⠉⠈⠻⠉⠻⣿⣿⣤⣇⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⢠⠀⠉⢸⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣉⡉⠉⠓⠄⠀⠀⠉ ⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠋⢠⣤⠀⠀⣸⣿⣿⡇⠀⠀⠀⢰⣿⣿⣿⣿⣿⡟⠛⣛⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠉⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠁⢸⡿⠀⠀⠀⣿⣿⣿⣿⣿⣻⣠⣾⣿⣿⠀⠀⣻⣿⣿⡇⠀⢀⣴⣿⣽⣿⣿⠿⣿⣿⣅⣿⡚⢿⣿⣿⣿⢣⡀⠀⣴⣆⠀⠁⠀⠀⣹⣿⣿⡿⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣠⣿⡇⠀⠀⢸⣿⡿⠋⣩⣼⣿⣿⣿⣼⣿⣄⣀⢻⣿⡟⠀⠀⣸⣿⣿⣿⠟⣥⣶⣿⣿⣿⡹⣷⣿⡿⣿⣿⣅⣻⣿⣿⣿⡇⠀⠀⢀⣿⡟⣸⠁⠈⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡏⢿⠁⠀⠀⣟⣁⣴⣿⣿⣿⣿⣿⡿⠛⠉⢻⣿⣿⡿⠁⠀⠀⠀⠋⠘⠋⣼⣿⣿⣿⣿⣿⣇⠹⡜⣿⣿⣿⣿⣸⣿⣿⣿⡇⠀⠀⢸⣿⢳⣿⠀⣴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⣠⣦⠘⣿⠇⠀⠀⡀⠀⠻⠿⠿⣿⠉⠛⠉⣿⠃⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⡀⠘⢻⣏⣁⣞⣻⣿⣿⡅⢿⣮⡻⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠉⠈⠋⠀⣿⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⡀⠙⠀⠐⠋⠀⠀⠖⢀⣤⣤⣄⣀⣀⣥⠄⠀⠀⠀⢀⣀⣠⣤⠄⠀⠀⠀⣶⣼⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⠀⠉⠳⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⡿⢀⣤⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⡀⠀ ⢸⠿⣻⣿⠀⣨⣽⣿⣯⡛⠒⣦⣿⣿⣽⣿⣿⣿⣿⣦⡤⣿⣿⣭⣿⣿⣷⣶⣶⣶⡄⢻⠿⠉⠉⠛⠻⠿⠉⠀⠀⠈⠈⠀⠀⣰⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⠿⠿⠿⠶⣶⡶⠶⣦⣤⣤⣴⡤⠤⠰⣾⠀⠀ ⢰⣛⣿⣿⠀⣿⣿⠀⣿⣿⠰⣿⣇⣸⣿⢿⠻⡿⢀⣿⡿⣿⣿⡿⠿⣿⣿⡿⠿⣿⡇⠀⠀⠠⠶⣶⡤⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⡀⣠⠶⣦⣾⣦⣀⠈⠇⠉⠉⠀⠀⢸⣿⡃⣼ ⠀⠈⣿⣿⢸⢿⣿⣤⣿⣿⣠⣾⡿⢿⣷⡴⢆⣚⠻⣿⣦⠛⠙⣡⣤⡽⠋⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⢛⣫⣭⣿⣿⣿⣿⡋⠀⠀⣠⣸⣿⠿⠿⠻⠟⣿⡿⠛⠳⠛⠋⠛⠉⠀⠀⠀⠀⠀⠀⢸⣿⣧⣽ ⣤⣤⣿⣿⣬⣽⣿⢿⣿⣿⣿⣿⣇⢸⣿⣧⣿⣿⣀⣿⣿⣴⣶⣿⣿⣷⣶⣶⣶⣶⣿⣿⣦⣀⠀⠀⠀⠀⠀⢈⣥⣶⣿⣟⣿⣿⣿⣿⣿⡎⠛⣦⣤⣾⣿⣥⣤⣤⣶⣾⣿⣷⣶⣤⣄⣄⣀⣤⣤⣤⣀⣀⡀⢀⣿⣿⣿⢿ ⣿⣿⣿⣿⣿⣿⣿⣿⠻⠁⠀⠙⠛⠛⠋⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣀⠄⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣮ ⠛⠛⠛⠛⠛⠛⠋⢀⣰⡄⠀⠀⢀⣤⠀⢀⣤⣤⣤⣤⣤⣭⣭⣯⣭⣿⣭⣭⣿⣿⣿⣿⡷⠞⣡⠂⠀⣠⣾⣿⡿⣿⣿⣯⣿⣿⣉⠙⢿⡦⡀⠀⠈⢿⣿⣯⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⣏⣿⣿⣿⣿⣿⣿⣅ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠈⠀⢤⡀⠀⠉⠉⠹⠿⠿⠿⠿⠿⠛⠛⡛⠉⠉⠉⠟⠃⠀⡾⠁⠀⠘⠉⣹⣿⠿⠟⠻⣿⣷⣿⣿⣧⠀⠀⢹⣄⠀⠈⠉⠉⠁⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⠀⠀⠀⠀⠐⠒⠶⠶⠶⢿⣿⣿⣿⣶⡀⢀⡼⠀⠀⠀⠠⠖⣊⣁⢠⣤⣦⡄⠉⠓⠻⠏⣂⣤⠘⠀⠀⠀⢹⣿⣶⣶⣶⠂⣰⣿⣦⣶⣶⣄⣈⣟⠉⠉⡙⠛⠉⠉⠉⠉⠙⠛ ⠀⢠⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⢸⣿⡇⠿⢿⡇⣀⣀⡀⠀⠀⠋⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⣀⠈⠉⠋⢉⣛⠿⠟⠛⠛⠀⠛⠳⣤⣤⣴⣶⣄⠀ ⠀⠿⠿⣷⠏⢶⠆⠰⠶⠶⠖⠀⢨⠋⠙⠿⠛⢿⣿⣧⡠⡆⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠘⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⡆⠈⠛⠓⠌⡉⠉⠉ ⠀⠀⠀⠀⢸⣿⣿⣿⠇⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⢋⣵⣤⠀⠀⣿⣿⣿⡇⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⠛⢟⣻⣿⣿⣿⣿⡇⠀⠨⠀⠀⠀⢉⠁⠀⢠⣿⣿⣿⡟⡀⠀⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡏⠀⣿⡇⠀⠀⣸⣿⣿⣿⣿⣿⣯⣤⣿⣿⣿⠀⠀⣿⣿⣿⡁⠀⢀⣴⣿⣽⣿⣿⠿⣿⣿⣇⣿⡖⢻⣿⣿⣿⣷⣴⣤⣶⣶⡀⠋⠀⠀⣸⣿⣿⣿⠁⠈⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣧⣼⣿⠁⠀⠀⣿⣿⡟⢋⣭⣿⣿⣿⣿⣿⣿⣀⣄⣻⣿⡟⠀⠀⣼⣿⣿⣿⢟⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣹⣿⣿⣿⡇⠀⠀⠀⣿⣿⣹⡟⢰⣷⡄⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⠹⡿⠀⠀⢰⣟⣠⣴⣿⣿⣿⣿⣿⠿⠋⠉⣿⣿⣿⡟⠁⠀⠐⠃⠋⠘⠏⣼⣿⣿⣿⣿⣿⣿⠹⣏⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠸⣿⠧⣿⠇⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⢀⣴⡔⢻⡿⠀⠀⢀⡄⠈⠿⠿⢿⡿⠙⠛⠹⡿⠀⠀⠀⠈⠛⠛⠀⠀⠀⠈⠀⠀⣀⠘⢻⣏⣁⣞⣻⣿⣿⡇⢻⣮⡻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⠈⠛⠀⣼⠂⠀⢠⣷⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣇⠈⠃⠀⠚⠃⠀⠴⠆⣠⣤⣧⣀⣠⣤⣷⠶⠀⠀⠀⢠⣀⣠⣤⠠⠤⠀⠀⣦⣼⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⡄⠍⠻⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⢹⣗⣦⣾⣿⠋⠁⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⣀⠀ ⣿⣿⣿⡇⠀⠛⠛⠛⠛⠛⠲⠾⠿⢿⣿⣿⡿⣻⣿⣤⣾⣿⣿⣼⣿⣿⣷⣶⣶⣶⡄⢿⡿⠉⠉⠛⠿⠿⠉⠁⠀⠈⠈⠁⠀⣠⣿⣿⣿⣿⣷⣶⣴⣶⣶⣶⣶⣶⣿⣿⣿⡿⠿⠿⠷⣶⣶⣶⣶⣦⣤⣤⣦⡤⠴⢶⡟⠀ ⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠠⣠⣾⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡇⠀⠀⠠⠴⣶⡤⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⢠⣶⣶⣾⣷⣄⣀⣹⡍⠛⠁⠀⠠⣿⡯⢀ ⠉⠻⠿⢿⣿⣷⣤⣤⣤⣀⣀⣿⣿⣿⣿⣿⡮⢿⣽⣶⡶⠛⢻⣥⣭⡿⠇⠀⠀⠀⢑⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠿⠛⣻⣯⣽⣿⣿⣿⡋⠉⣹⣥⣨⣿⣿⡿⠿⣿⣿⣿⠟⢿⡿⠛⠻⠿⠛⠉⠀⠀⠀⠀⢀⣿⣿⣤ ⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣥⣤⣿⣿⣬⣤⣶⣶⣿⣿⣿⣷⣶⣾⣷⣶⣿⣿⣦⣀⠀⠀⠀⠀⠀⢈⣩⣴⣾⣿⣿⣿⣿⣿⣿⡿⠻⣦⣤⣽⣿⣏⣀⣤⣤⣿⣿⣿⣶⣤⣄⣀⣀⣀⣄⣀⣀⣀⣀⠀⢸⣿⣽⣿ ⣿⣿⣿⣿⣿⣿⣿⣤⠟⠉⠉⠉⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣀⡠⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢰ ⠛⠻⠛⠻⠿⠟⡉⣀⣤⣀⢀⡀⣠⣄⢀⣠⣤⣤⣤⣤⣭⣭⣽⣿⣙⣿⣿⣿⣿⣿⣿⣿⣿⠾⣣⠊⠀⣠⣾⣿⡿⣿⣿⣿⣿⣿⣏⠹⢿⣦⡀⠀⠀⢿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣛⣛⣿⣿⣿⣿⣶⣯ ⠀⠀⠀⠀⠀⠉⠉⠛⠛⠉⠀⠙⢿⣧⠀⠉⠉⠹⢿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠉⠙⠿⠋⠀⡾⠉⠀⠔⠛⣻⣿⣿⡷⢿⣿⣿⣿⣿⣧⡀⠀⠺⣆⠀⠈⠛⠛⠃⠀⠈⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠠⠤⠶⠶⠷⣶⣾⣿⣿⣷⣦⠀⢀⣼⠁⠀⠀⠠⠾⠛⣋⣠⣤⣤⡌⠙⠯⠿⣿⡰⢠⡐⠃⡀⠀⢸⣷⣶⣶⣶⡶⢠⣾⣯⣬⣽⣄⡈⣻⠛⠛⠛⠛⠛⠋⠉⠙⠛⠛ ⠀⣲⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣿⣿⣷⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠸⠇⠀⠀⠀⠀⢰⣿⡟⣿⣿⡏⣁⣀⡀⠀⠀⡻⠁⠀⠀⠀⠀⠀⠋⠉⠉⠉⠀⠈⠛⠛⠛⠻⠿⣿⠟⠿⠆⠛⠳⣦⣄⣤⣴⣄⠀ ⠸⠿⠿⣶⠎⢷⠶⠰⠶⠶⠖⠀⡜⠛⢻⡟⠻⣿⣿⣇⣿⡆⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣭⠀⠀⠘⢹⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⣶⣶⣿⣿⣶⣿⣿⣿⣷⣶⣶⣦⣤⣶⠒⠻⠛⣯⠉⠉⠉ ⠀⠀⠀⠀⣿⡿⢿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟⢁⣴⣤⠀⠀⣿⣿⣿⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⠛⢟⣻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠁⠀⢀⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡁⢸⣿⠀⠀⠀⢸⣿⣿⣿⣿⣟⣥⣴⣿⣿⣇⠀⠀⣿⣿⣿⠀⠀⢀⣼⣿⣽⣿⣿⠿⣿⣿⣇⣿⡒⢻⣿⣿⣿⡅⠀⣀⣴⣶⠀⠀⠀⠀⢨⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⣾⡏⠀⠀⢀⣿⣿⠛⢉⣠⣿⣿⣿⣧⣿⣯⣀⡈⣿⣿⠏⠀⠀⣼⣿⣿⣿⠟⣧⣶⣿⣿⣿⡟⣿⣻⣿⣿⣿⣇⣉⣿⣿⣿⡗⠀⠀⠀⣾⣿⢱⡇⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⡇⠻⠇⠀⠀⢸⣃⣠⣾⣿⣿⣿⣿⣿⠟⠋⠙⣿⣿⣿⠟⠀⠀⠀⠡⠋⠘⠋⣼⣿⣿⣿⣿⣿⣯⠹⣏⢿⣾⣿⣿⡎⣿⣿⣿⣇⠀⠀⠀⣿⡏⣿⡇⢰⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣤⠀⣿⡇⠀⠀⣀⠀⠸⠿⠿⢿⡟⠙⠋⢹⡟⠀⠀⠀⠉⠉⠋⠀⠀⠀⠀⠀⠀⡀⠐⢻⣏⣁⣞⣻⣿⣿⡇⢻⣮⡻⣿⡿⣿⣿⣿⣿⣿⠀⠀⠀⠉⠀⠙⠀⢸⡇⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡀⠙⠁⠀⠒⠀⠀⠶⠀⣀⣠⣀⣀⣀⣀⣤⠄⠀⠀⠀⣀⣀⣠⡤⠀⠀⠀⠀⣦⣼⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⡎⠌⠻⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢸⡇⣀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⡀ ⣿⣿⣿⠁⠀⠛⠒⠚⠳⠶⠲⠾⠿⢿⣿⣿⠿⢻⣣⢄⣘⣷⣆⣸⣽⣿⣧⣤⣴⣦⡀⢿⡿⠉⠉⠻⠿⠿⠉⠁⠀⠈⠉⠁⠀⣠⣿⣿⣿⣿⣥⣤⣠⣤⣖⣤⣤⣖⢾⣿⣻⣿⣿⡻⢶⢖⣦⣤⣖⢦⣠⣤⣤⣤⠤⠠⣾⠀ ⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⢸⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡇⠀⠀⠠⠴⣦⡤⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⠙⣿⣿⣷⣿⣿⣿⣿⣏⢻⣿⡏⣽⣿⠀⣿⡟⢹⣿⡇⠅⠈⠋⠀⠀⢸⣿⠁ ⠈⠙⠛⣿⣿⣦⣤⣤⣀⡀⢠⣿⡿⣛⠻⣦⠘⠟⢡⣤⠶⠛⠋⣄⣩⡙⠁⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⣛⣫⢽⣿⣿⣿⣼⣿⠏⢹⣿⣿⣿⣿⡏⡷⠶⣷⣿⡟⡴⠖⢢⣾⡿⠃⠀⠀⠀⠀⠀⢸⣿⣦ ⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⣤⣥⣌⣀⣠⣤⣶⣾⣿⣿⣦⣤⣴⣦⣴⣿⣿⣄⡀⠀⠀⠀⠀⠀⠐⣉⣥⠶⠿⠿⢿⠿⢿⣟⣾⡿⣣⣤⣼⣿⣿⣸⣿⣇⣤⣼⣿⣯⣤⣀⣠⣿⣟⣁⣀⣀⡀⠀⠀⠀⣿⢏⣿ ⣿⣿⣿⣿⣿⣿⣦⣸⠟⠉⠉⠙⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⡀⠀⠀⠀⣿⣿⣿⣿⣇⣿⢗⢿⣟⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡏⠁ ⠿⠿⠿⠿⠿⠛⠉⢀⡀⠀⠀⠀⢀⠀⠀⣀⣀⣀⣈⣉⣉⣛⣿⣟⣛⣟⣛⣿⣿⣿⣿⣿⣯⡾⣫⠆⠀⢠⣾⣿⡿⣿⣿⣿⣿⢿⡟⠻⢿⣆⡀⠀⠀⢻⣿⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢛⣛⣿⣿⣿⣿⣷⣶ ⠀⠀⠀⠀⠀⠀⠘⠿⠟⠀⠀⠀⢮⡀⠀⠉⠉⠛⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠻⡿⠋⠀⡴⠃⠀⠰⠛⢻⣿⡷⡶⢾⣿⣿⣿⣿⣧⡀⠁⠲⣆⠀⠈⠛⠛⠋⠈⠉⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡄⠀⠀⠀⠀⠀⠠⡤⣴⣶⣴⣾⣷⣶⣦⣄⠀⠀⠼⠁⠀⠀⢀⠤⠟⠋⢀⣀⣤⡈⠛⠿⠿⣿⢡⢠⡀⠏⠁⠀⠰⣶⣦⣤⣤⡤⢀⣴⣯⣭⣭⣄⡈⠹⡟⠛⠛⠻⠿⠛⠛⠛⠛⠛ ⠀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣶⣦⣆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠰⠃⠀⠀⠀⠀⢰⣾⡇⣼⣿⡏⠁⠀⠀⠀⠀⠹⠊⠁⠀⠁⠀⠀⠛⠉⠙⠉⠁⠈⠛⠻⠟⠻⠿⣿⠿⠷⠆⠐⠷⣤⣀⢀⣠⣤⡀ ⠰⠿⠷⣶⠿⢷⠶⠰⠶⠶⠆⠀⠾⠛⣿⠿⢿⣿⣷⡀⠰⠀⠀⠀⠀⢸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡉⠁⠀⠹⢁⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣤⣾⣷⣶⣶⣶⣶⣷⣦⣤⣤⣠⣤⠄⠸⠿⢏⠙⠛⠛ ⠀⠀⠀⢸⣿⠾⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣻⡿⠋⢠⣤⡄⠀⢠⣿⣿⣿⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⠛⢟⣻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠁⠀⠀⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡏⠀⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣟⣤⣼⣿⣿⡇⠀⢈⣿⣿⣿⠀⠀⢀⣾⣿⣽⣿⡿⠿⣿⣿⣇⣾⡖⢻⣿⣿⣿⣧⣀⡀⣴⣶⡀⠈⠀⠀⢀⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣏⢠⣿⠃⠀⠀⢸⣿⡿⠋⣉⣴⣿⣿⣿⣯⣿⣧⣀⡘⣿⣿⠋⠀⠀⣾⣿⣿⣿⢟⣧⣾⣿⣿⣿⡟⣿⣻⣟⣿⣿⣧⢘⣿⣿⣿⣿⠀⠀⠀⣸⣿⢃⣿⠀⢐⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⠈⠿⠀⠀⠀⢟⣁⣤⣾⣿⣿⣿⣿⡿⠟⠉⠹⣿⣷⣿⠏⠀⠀⠐⡡⠃⠘⠋⣼⣿⣿⣿⣿⣿⣿⠘⣏⢿⣾⣿⣿⣟⣿⣿⣿⣿⠀⠀⠀⣿⡿⢼⡏⠀⣝⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣤⡄⢸⣿⠀⠀⠀⡀⠀⠻⠿⠿⣿⠋⠙⠋⣿⠇⠀⠀⠀⠉⠉⠃⠀⠀⠀⠀⠀⠀⣀⠘⢻⣏⣁⣟⣛⣿⣿⡇⢻⣦⡻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠁⠙⠁⠀⡇⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣇⠈⠋⠀⠐⠂⠀⠀⠶⢀⣀⣀⣀⣀⣀⣡⣤⠀⠀⠀⠀⣀⣀⣠⡄⠀⠀⠀⠀⣤⣴⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⡎⠈⠻⣽⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠘⡷⢀⣠⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡏⠀⠐⠒⠒⠒⠲⠆⠶⠾⠿⣿⣿⣿⠿⣿⣆⣀⣰⣶⣄⣿⣿⣿⣤⣤⣤⣦⡀⣿⡿⠉⠉⠻⠿⠿⠋⠉⠀⠈⠉⠁⠀⢀⣿⣿⣿⣿⣧⣤⣠⣤⣄⣤⣤⣔⢾⣿⣻⣿⣿⡻⢶⢖⣦⣤⣖⢤⣀⣤⣠⣤⣤⠀⣴⡆ ⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡗⣸⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠀⠠⣤⣤⡄⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⠟⣿⣿⣷⣿⣿⣿⣿⣿⢻⣿⣿⣽⣿⠀⣿⡟⢽⣿⡇⠃⠈⠙⠁⠀⢀⣿⡇ ⠈⠙⢻⣿⣦⣤⣄⣀⡀⠀⢰⣿⢿⡛⣽⣄⠸⠋⢥⣤⠜⠛⠉⣀⣙⠟⠉⠀⠀⠈⠃⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣤⡾⠿⢟⣛⣽⣿⣿⣿⣽⣿⠏⢹⣿⣿⣿⣿⡟⣷⠶⣳⣿⡟⣰⠶⢢⣾⡿⠃⠀⠀⠀⠀⠀⠀⣿⣧ ⣀⣀⣈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣴⣄⣀⣈⣤⣤⣤⣼⣿⣿⣤⣤⣴⣤⣴⣿⣷⣄⠀⠀⠀⠀⠀⠀⠐⣋⣭⠶⠾⢿⢿⠿⢿⣟⣾⡿⢃⣀⣼⣿⣿⢹⣿⣇⡄⣼⣿⣯⣤⣀⣠⣿⡟⣁⣀⣀⠀⠀⠀⠀⢸⡿⣻ ⣿⣿⣿⣿⣿⣿⣄⡽⠋⠙⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⡀⠀⠀⠀⣻⣿⣿⣿⣇⣿⢷⣿⣟⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣿⡔⠋ ⠿⠿⠿⠿⠿⠛⠉⢀⠀⠀⠀⠀⣀⠀⠀⣀⣈⣉⣉⣉⣛⣛⣿⣛⢿⣿⣛⣿⣿⣿⣿⣿⣯⡾⢋⠄⠀⢀⣼⣿⣿⣿⣿⣿⣻⣿⡟⢻⢿⣧⡀⠀⠀⢻⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠻⠿⢿⣿⣿⣿⣿⣤ ⠀⠀⠀⠀⠀⠀⠸⠿⠇⠀⠀⠀⡁⠀⠘⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠻⣿⠋⠉⡴⠃⠀⠠⠛⠛⣿⡷⡯⣿⣿⣽⣿⣿⣦⡀⠙⠱⣄⠀⠈⠿⠿⠟⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠉⢉⣉⣩⣥⣤⣤⣶⣶⣤⣄⡀⠀⠀⣸⠁⠀⠀⢀⡀⠾⠛⢀⣀⣈⡙⠻⢟⣻⣿⢧⢠⡀⠟⠁⠀⠀⣤⣤⣄⣤⣀⠀⣠⣿⣉⣛⣋⠉⠛⡿⠿⠿⠿⠿⠿⠛⠛⠻⠿ ⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⣤⣤⡀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠙⠛⠛⠀⠸⠃⠀⠀⠀⠀⢠⣴⡇⣸⣿⣿⠁⠀⠀⠀⠈⠱⠊⠁⠀⠀⠀⠀⠻⠛⠛⠛⠋⠀⠛⠿⠿⠿⢿⣿⣶⣿⣤⠀⠴⣄⡀⠀⠀⣀⡀ ⠰⣿⠶⣶⠿⢶⠦⠰⠶⠶⠖⠀⠾⢿⣿⢿⣿⣿⣇⠀⢄⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠉⢸⠁⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣴⣶⣤⣤⣴⣴⣶⣦⣅⣀⣀⢀⠀⠀⠹⡷⠛⠛⠛ ⠀⠀⠀⢸⡷⢿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣻⠿⠋⢠⣦⡄⠀⢰⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡯⠛⢍⣻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡁⢀⣿⠀⠀⠀⢘⣿⣿⣿⣿⣿⣋⣤⣾⣿⣿⡀⠀⢸⣿⣿⣏⠀⠀⢠⣾⣿⣽⣿⡿⠿⣿⣿⣇⣾⣖⠻⣿⣿⣿⣧⣠⡀⣴⣶⡀⠀⠁⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡁⣼⣿⠀⠀⠀⣼⣿⡟⠋⣁⣼⣿⣿⣿⣽⣿⣇⣀⠸⣿⣿⠃⠀⠀⣿⣿⢿⣿⠟⣧⣾⣿⣿⣿⡏⣿⣸⣿⣿⣿⣧⣈⣿⣿⣿⣿⠀⠀⠀⢸⣿⡇⣿⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠙⠏⠀⠀⠠⠟⣀⣴⣾⣿⣿⣿⣿⡿⠛⠉⢹⣿⣿⣿⠃⠀⠀⠀⠡⠃⠘⠋⣼⣿⣿⣿⣿⣿⣿⠘⣇⢿⣾⣿⣿⣏⣿⣿⣿⣿⠀⠀⠀⢾⣿⢸⣿⠀⡼⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣤⠀⢿⡇⠀⠀⢀⠀⠈⠿⠿⠿⣿⠉⠛⠉⣿⠀⠀⠀⠀⠉⠙⠁⠀⠀⠀⠀⠀⠀⣀⠘⢻⣏⣁⣟⣛⣿⣿⡇⢻⣦⡻⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠈⠁⠘⠃⠀⣟⠀⠀⢀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡀⠘⠁⠀⠐⠂⠀⠠⠄⢀⣀⣀⣀⣀⣀⣤⡤⠀⠀⠀⠀⣀⢀⣠⡀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⡎⠈⠻⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡇⠀⠒⠒⠒⠲⠦⠠⠴⠿⢿⣿⣿⡿⠿⣟⠀⣀⣺⣷⣀⣩⣿⣿⣤⣤⣤⣄⠘⣿⡿⠛⠉⠽⠿⢿⠋⠉⠀⠀⠋⠁⠀⢀⣽⣿⣿⣿⣧⣤⣠⣤⣄⣤⣤⣄⢶⣿⣻⣿⣿⡻⣶⢖⣦⣤⣄⢤⣀⣠⣀⣤⣄⠀⢠⣦ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡇⣾⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⡟⣿⣿⣷⣿⣿⣿⣿⣿⢻⣿⣿⣽⣿⠀⣿⡿⢿⣿⡇⢸⠀⠙⠃⠀⠀⢸⣿ ⠉⠙⣷⣶⣤⣀⣀⡀⠀⠀⣼⣿⣿⠟⣥⠀⠛⠋⣵⣤⡜⠛⢋⣈⡙⠛⠉⠀⠀⠉⢃⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⣠⣾⠿⠿⣛⣻⣿⣿⣿⣿⣿⠏⢹⣿⣿⣿⣿⡟⢿⠶⣲⣿⡟⢰⣶⢦⣾⡿⠃⠀⠀⠀⠀⠀⠀⢸⣿ ⣀⣀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⣀⣤⣠⣀⢈⣀⣤⣤⣿⣿⣶⣤⣤⣴⣤⣴⣾⣷⣀⠀⠀⠀⠀⠀⠀⠐⢛⣩⠴⠶⢿⢿⠿⢿⣟⣾⡿⢣⣀⣸⣿⣿⢹⣿⡇⡀⣼⣿⢯⣀⣀⣠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣿⠋ ⣿⣿⣿⣿⣿⣇⣉⡿⠛⠛⠛⠿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⣀⠀⠀⠀⣺⣿⣿⣿⣇⣿⣧⢿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣦⣼⣧⠘ ⣿⣿⣿⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠋⠛⢛⣻⣿⠿⢿⡿⢿⣿⣿⣿⣿⣿⣯⡴⢋⠕⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡟⢛⣿⣇⠀⠀⠀⢹⣿⣿⣿⣟⢻⣿⣯⣿⣿⣟⣻⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣦ ⠀⠀⠀⠀⠀⠀⠾⠿⠀⠀⠀⠈⠁⠀⠙⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢿⣿⠟⠉⣰⠃⠀⠠⠿⢿⣿⣯⡯⣿⣿⣿⣾⣷⣦⡀⠉⠡⣄⠀⠀⠿⠿⠿⠋⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡀⠀⠀⠀⠀⠉⠉⣉⣉⣉⣁⣀⣴⣦⣤⣄⡀⠀⠀⢰⠁⠀⠀⠀⣀⡺⠟⠁⠁⣀⠙⠻⠿⣿⣿⢇⠀⠀⠽⠂⠀⠀⣤⣄⣀⣀⣀⡀⢀⣹⡛⠛⠛⠉⠛⢿⠿⠿⠿⣿⣿⠿⠿⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣠⣀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠳⠀⠰⠃⠀⠀⠀⠈⢠⣴⡆⢸⣿⣿⠃⠀⠀⠀⠉⢲⠝⠃⠀⠐⠀⠀⠹⠿⠻⠿⠛⠀⠸⠿⣿⡿⢿⣷⣦⣼⣤⡀⢠⣄⡀⠀⠀⠀⠀ ⣴⡷⠲⣶⠏⢶⠆⠰⠶⠶⠖⢠⡿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠃⠙⢹⠇⣴⣶⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣄⣀⣤⣤⣤⣌⣉⡀⠈⠀⠀⠀⠹⣷⡖⠿⠿ ⠀⠀⠀⣿⠿⣿⡏⠀⠀⠀⣿⣿⣿⣿⣿⣟⣿⠟⠁⣴⣦⠀⠀⢸⣿⣿⡟⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡟⠙⢋⣻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡏⠀⢸⡇⠀⠀⠀⢹⣿⣿⣿⣿⣟⣣⣤⣿⣿⣿⠀⠀⢸⣿⣿⡇⠀⠀⣠⣾⣿⣽⣿⡿⠿⣿⣿⣆⣾⡖⠻⣿⣿⣿⡧⢀⡀⣠⣶⡄⠀⠁⠀⠀⣼⣿⣿⡟⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣏⢀⣿⡇⠀⠀⢠⣿⣿⠛⢉⣤⣿⣿⣿⣯⣽⣿⣀⣀⢹⣿⡿⠁⠀⠀⣿⣿⢿⣿⠏⣦⣶⣿⣿⣿⡏⣿⣸⣿⢿⣿⣷⣩⣿⣿⣿⣿⠀⠀⠀⢰⣿⡟⣸⡇⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠈⠿⠁⠀⠀⠸⢃⣠⣴⣿⣿⣿⣿⣿⠿⠛⠉⢿⣿⣾⣿⠃⠀⠀⠀⡸⠃⠸⠃⣼⣿⣿⣿⣿⣿⣿⠘⣇⢿⣾⣿⣿⣟⣻⣿⣿⣿⠀⠀⠀⢸⣿⢳⣿⠁⢸⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⡄⠐⣿⠀⠀⠀⢀⠀⠹⡿⠿⢿⡟⠙⠛⢻⡿⠀⠀⠀⠈⠉⠛⠁⠀⠀⠀⠀⠀⠀⣀⠘⣿⣏⣉⣟⣛⣿⣿⡇⢻⣦⡻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠈⠋⠀⣼⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣇⠀⠛⠀⠀⠆⠀⠀⠤⠀⣀⣀⣀⣀⣀⣀⣤⡄⠀⠀⠀⢀⣀⢀⣀⡀⠀⠀⠀⢠⣴⣶⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡎⠈⠻⣾⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢿⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠀⠐⠲⠂⠒⠤⠤⠤⠶⠿⣿⣿⣿⡿⢿⡋⢀⣐⣶⣦⣈⣭⣿⣿⣄⣤⣤⣄⠘⣿⡿⠛⠉⠿⠿⣿⠛⠋⠀⠀⠋⠃⠀⠀⣼⣿⣿⣿⣧⣤⡀⣤⣄⣤⣤⣄⢤⡾⣺⣿⣿⡻⣶⢖⣤⣤⣄⢤⣄⣀⣀⣀⣀⡀⠀⣤ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⢦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⡟⣿⣿⣷⣿⣿⣿⣿⣯⢿⣿⣿⣽⣿⠀⣿⡏⢿⣿⡇⠈⠃⠙⠛⠁⠀⠀⣿ ⠉⠹⣶⣦⣀⣀⡀⠀⠀⢀⣾⣿⠿⢯⣅⠀⠛⠋⢥⣤⠼⠛⠉⡙⠛⠛⠉⠀⠈⠙⠆⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣠⣼⡿⠿⣿⣛⣿⣿⣿⣿⣿⠏⢹⣿⣿⣾⣿⡟⣷⡷⣳⣿⡟⠀⢔⢦⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⢀⠙⣿⣿⣿⣿⣿⣶⣾⣿⣀⡀⠀⢉⣄⣀⠀⢋⣀⣠⣤⣿⣿⣦⣀⣀⣠⣀⣴⣾⣦⡀⠀⠀⠀⠀⠀⠀⠠⠚⣉⠥⠶⢿⢿⠿⢿⣟⣾⡿⣣⠀⣸⣿⣿⢻⣿⡇⡈⣼⣿⢯⣀⣀⣠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢸⡏ ⣿⣿⣿⣿⣿⡉⢻⠿⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⠀⠀⠀⣲⣿⣿⣿⣇⣿⣧⢿⣿⠿⠿⠿⠿⠷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣷⣶⣶⣄⣯⡀ ⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠿⢿⡿⠿⣿⣿⢿⣿⣿⣿⣿⣿⣏⣴⢞⠅⠀⢀⣴⣿⣿⣿⣿⣿⢿⣿⡿⠿⣿⣏⠀⠀⠀⠹⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⢿⡿⣿⣿⣿⣿⣧ ⠀⠀⠀⠀⠀⠠⣾⡇⠀⠀⠀⠀⠀⠀⠾⠿⠿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡿⠿⣿⣿⠟⠉⣱⠏⠀⠠⡾⠿⣿⣯⣯⣿⣿⣻⣻⣷⣦⠈⠛⠑⣄⠀⠀⢻⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣶⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠘⠛⠛⢛⣛⣋⣉⣁⣤⣄⣀⡀⠈⠁⠀⣰⠁⠀⠀⠀⠠⣾⠿⠁⠁⠉⠙⠿⡿⢿⣿⡇⠀⠀⣸⠃⠀⠀⣀⣀⣀⢀⣀⠀⠈⣙⡟⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⡿⠿⠿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⣄⡀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠻⠿⠿⠿⠧⠀⢰⠃⠀⠀⠀⠈⢉⣤⡖⢸⣿⣿⠓⠀⠈⠉⠙⢢⡅⠗⠀⠐⠀⠀⢸⡿⠿⠿⠿⠃⠸⣿⣿⣿⣿⣷⣦⣠⣇⡀⠀⣄⡀⠀⠀⠀⠀ ⣼⠗⠲⣶⠏⢶⠆⠰⠶⠶⠆⣠⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠛⢻⡏⣴⣦⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⣠⣀⣀⣀⣀⣠⣍⡙⠉⠉⠉⠀⠈⠙⣶⡤⠤⠾ ⠀⠀⢸⡿⠿⣿⠃⠀⠀⠠⣿⣿⣿⣿⣿⣟⡿⠏⢀⣶⣦⠀⠀⣸⣿⣿⡇⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡯⠙⢋⣹⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⣿⣿⣿⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡇⠀⣿⡇⠀⠀⠀⢿⣿⣿⣿⣿⣛⣤⣴⣿⣿⣇⠀⠀⣹⣿⣿⡇⠀⠀⣠⣾⣿⣿⣿⡿⠿⣿⣿⣆⣾⣆⠻⣿⣿⣿⡿⢄⡀⢠⣶⣆⠀⠀⠀⠀⣸⣿⣿⣿⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡃⢰⣿⠀⠀⠀⣸⣿⡿⠉⣉⣴⣿⣿⣿⣯⣿⣿⣀⣀⢻⣿⡟⠁⠀⢠⣿⣿⣿⣿⢏⣦⣶⣿⣿⣿⡏⣿⣸⣿⣿⣿⣿⣈⣿⣿⣿⣿⠇⠀⠀⠀⣿⡿⢸⡏⢀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣧⠘⠏⠀⠀⠀⠛⢁⣠⣾⣿⣿⣿⣿⣿⠿⠋⠉⣿⣿⣾⡿⠃⠀⠀⠎⠘⠁⠺⠃⣼⣿⣿⣿⣿⣿⣿⠘⣇⢿⣾⣿⣿⣿⣹⣿⣿⣿⡀⠀⠀⢸⣿⠇⣿⡇⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠀⢺⡏⠀⠀⢀⡀⠀⢿⣿⢿⣿⠏⠛⠛⢻⡇⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⢀⡀⠘⣿⡟⢉⣟⣻⣿⣿⡇⢻⣦⡻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠉⠀⠛⠀⢨⡇⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡀⠘⠃⠀⠠⠂⠀⠀⠄⠀⣀⣀⡀⠀⢀⣈⣤⠄⠀⠀⠀⢀⡀⢀⣀⠀⠀⠀⠀⢨⣔⣶⣿⣿⣿⣿⣿⣿⣿⡇⢠⣿⡎⠈⠻⣾⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠄⠤⠄⠤⠄⠤⠾⢿⣿⣿⣿⡿⠿⠃⠀⣠⣶⣄⣈⣻⣿⣯⣀⣠⣤⡄⠸⣿⣟⠛⠛⢿⣿⣿⠛⠋⠀⠀⠋⠃⠀⠀⣸⣿⣿⣿⣯⣤⡀⣀⣀⣤⣤⣄⢤⡶⣲⣾⣿⡻⣷⢆⣤⣤⣄⢤⣄⠀⣀⣀⣀⡀⠀⠀ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣯⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⠀⣀⣠⣄⣀⠀⠀⠀⠀⠀⠀⣀⣴⣼⣿⣿⣿⣿⡟⣿⣿⣷⣿⣿⣿⣿⣯⢻⣿⣿⣽⣿⠀⣿⡏⢹⣿⡇⠉⠋⠉⠛⠃⠀⠀⢸ ⠉⢥⣤⣄⣀⠀⠀⠀⠀⢠⣾⣿⠿⢋⡀⠸⠟⠋⣁⡠⠾⠟⠋⠋⠻⠛⠉⠉⠉⠙⠄⠀⠀⠁⠉⠙⠁⠀⠀⠀⠀⣀⣼⣿⡿⠿⢛⣿⣿⣿⣿⣿⠏⢻⣿⣿⢸⣿⡟⣷⡿⣳⣿⣟⠄⢠⢦⣾⡿⠓⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠘⣻⣿⣿⣿⣿⣶⣶⣿⣏⡁⠀⠈⢁⣀⡀⠈⠉⠀⣀⣠⣿⣿⣄⣀⣀⣀⣀⣴⣶⣦⠀⠀⠀⠀⠀⠀⠀⠠⠞⣋⠥⠴⢾⢿⠿⠿⣟⣾⡿⣣⠀⢸⣿⣿⣿⣿⡇⠀⣼⣿⣯⣄⠀⣡⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾ ⣿⣿⣿⣿⣟⠛⣿⠿⠿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣶⣿⣿⢿⣇⢿⣧⣿⣯⠿⠿⠿⠿⠷⣷⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣶⣶⣶⣄⣸⡃ ⣿⣿⣿⣿⠟⠓⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣴⠖⡁⠀⠀⣴⣿⣿⣿⣿⣿⢿⣿⣿⠿⣿⣏⠀⠀⠀⠹⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠉⠉⠉⠀⠀⢤⣶⠄⠀⠀⠀⠂⠀⠠⢶⢶⣶⣶⣶⣶⣿⣿⣷⣶⣾⣷⣿⣿⢿⣿⣿⠟⠋⣡⠎⠀⢀⣾⡿⣿⣯⣟⣿⣿⣻⣿⣷⣆⠉⠛⢓⡄⠀⠀⢻⣿⣿⡿⠲⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠹⠛⠛⠛⠛⠛⠋⢉⣩⣀⣀⠀⠘⠁⠀⣸⠁⠀⠀⠀⠀⣼⡿⠃⠃⠉⠻⢿⣿⢿⣿⡇⠀⠀⢹⠦⠀⠀⢀⣀⠀⠀⠀⠀⠈⠙⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣄⠀⠀⠀⠀⠀⠘⠛⠛⠛⠻⠿⠿⠿⠿⠷⣆⠀⣠⠃⠀⠀⠀⠘⠋⣠⡄⢰⣶⡿⠆⠀⠀⠋⠛⢤⡂⠷⠈⠠⠀⠀⠸⣿⣿⣿⡿⠟⠀⣾⣿⣶⣶⣶⣤⣀⣹⡀⠀⢈⠉⠁⠀⠀⠀ ⡤⠖⠲⣶⠏⢶⠄⠰⠶⠶⢆⣸⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢿⠇⠺⢻⡏⣤⣤⣄⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡀⠈⠉⠉⣉⣙⡛⠛⠋⠛⠂⠈⠙⠶⣄⠀⢀ ⠀⠀⣿⠛⢿⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣻⠟⠋⣠⣶⡦⠀⠀⣿⣿⣿⡇⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡏⠙⢉⣹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣟⠀⢸⡷⠀⠀⠀⠘⣿⣿⣿⣿⣿⣋⣤⣾⣿⣿⡇⠀⠀⣿⣿⣿⡇⠀⠀⣠⣿⣯⣿⣿⡿⠿⣿⣿⣆⣿⡆⠻⣿⣿⣿⣟⣤⣤⢰⣶⣆⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣞⠀⣾⡇⠀⠀⠀⣼⣿⠟⠉⣁⣽⣿⣿⣿⣽⣿⣧⣀⡈⣿⣿⡟⠀⠀⢰⣿⣿⣿⣿⢯⣦⣾⣿⣿⣿⡟⣿⣸⣿⢿⣿⣿⣘⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⢱⡇⠀⢀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⡄⠻⠃⠀⠀⠸⠋⣀⣴⣾⣿⣿⣿⣿⡿⠟⠋⠙⣿⣿⣿⡟⠀⠀⠀⠌⠜⠁⠳⠁⣼⣿⣿⣿⣿⣿⣿⠸⣇⢿⣿⣿⣿⣿⣻⣿⣿⣿⡇⠀⠀⠠⣿⡏⣾⡇⠀⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⣿⠁⠀⠀⢀⠀⠸⣿⡿⢿⡿⠋⠛⠛⣿⠇⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀⠀⢀⠀⠾⣿⡛⢉⡟⣻⣿⣿⡇⢻⣦⡻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠉⠀⠛⠀⢰⡇⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠛⠀⠀⠀⠀⠀⠠⠀⠀⠀⣁⠀⠀⠀⣈⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢨⣔⣶⣿⣿⣿⣿⣿⣿⣿⡇⢨⣿⡎⠈⠻⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⣀⣼⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⠀⠀⠀⠀⠠⠠⠤⠀⡤⢿⣿⣿⣿⣿⣿⢿⠁⢀⣰⣶⣄⣚⣻⣿⣏⣀⣀⣤⡀⢸⣿⡟⠛⠛⣿⣿⣿⠛⠋⠀⠈⠋⠃⠀⠀⣸⣿⣿⣿⣯⣤⡀⣀⣀⣤⣤⣄⢤⡴⣣⣬⣿⡻⣷⢆⣤⣤⣄⢠⣄⡀⠀⣀⣀⡀⠀⠀ ⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡇⣼⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⡿⣿⣿⣷⣿⣿⣿⣿⣏⢻⣿⣿⣿⣿⠀⣿⡏⢹⣿⡇⠈⠙⠋⠛⠟⠁⠀⠀ ⠉⣤⣄⡀⠀⠀⠀⠀⠀⣴⣾⣿⡿⣋⠀⢹⠛⠉⢁⣸⠿⠟⠋⠛⠿⠟⠉⠉⠙⠻⡀⠀⠀⠉⠉⠛⠃⠀⠀⠀⠀⢀⣴⣿⣿⠿⢿⣿⣿⣿⣿⣿⠏⢻⣿⣿⢸⣿⡿⣿⠾⣳⣿⣟⡔⢀⢤⣾⡿⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⣿⣿⣿⣿⣶⣶⣶⣿⡋⠀⠀⠉⢁⠀⠀⠘⠉⣁⣀⣰⣿⣧⣀⠀⠀⣄⢀⣤⣶⣄⠀⠀⠀⠀⠀⠀⠀⠠⠶⢛⠩⠤⢶⢿⠿⢿⢟⣾⡿⣣⠀⢸⣿⣿⣿⣿⡇⠀⣼⣿⣯⡏⠀⣠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⣿⣿⣿⣿⡛⠻⡿⠿⠿⠿⣿⣷⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⣴⣾⣿⠿⣇⢿⣇⣿⢯⠿⠿⠿⠿⠷⣷⣿⣿⣾⣿⣷⣾⣿⣿⣿⣿⣶⣿⣿⣿⣿⣷⣶⣶⣶⣶⣦⣤⣀⡎ ⣿⣿⣿⡿⠗⠊⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣤⠖⡀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣏⠁⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠉⠉⠁⠀⠀⣠⣆⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣿⣷⣾⣿⣷⣿⣿⣿⣿⣿⠿⠛⣡⠎⠀⢀⣾⣿⣿⣟⣟⣿⣿⣾⢽⣿⣄⠉⠻⠒⡄⠀⠀⢹⣿⣿⣿⠷⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣬⣤⣽⣿⣿⣷ ⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣄⠀⠀⠀⠀⠈⠿⠿⠿⠿⠿⠟⠛⠛⣋⠉⠀⠈⠙⠋⠀⣰⠃⠀⠀⠉⠀⣽⣿⠋⠋⠛⠻⣿⣿⣿⣿⡇⠀⠀⢹⡦⠀⠀⠉⠉⠁⠀⠀⠀⠈⠛⢿⢿⢿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⠾⠿⠶⢿⣿⣿⣿⣶⡄⠀⡤⠃⠀⠀⠀⠐⠚⣉⡤⢰⣦⣶⠄⠀⠁⠒⠻⢇⡃⣦⠈⠀⠀⠀⠸⣿⣿⣶⣶⡶⠀⣰⣿⣦⣤⣤⣄⡀⢸⠉⠉⠉⠙⠙⠁⠀⠀ ⠀⠆⠶⣶⠎⢶⠄⠰⠶⠶⠆⣼⣷⣵⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠾⢻⡟⡀⣀⣀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠈⠉⠋⠉⠙⠛⠛⠛⠛⠂⠀⠛⠦⣀⠀⠀ ⠀⢸⡗⠘⣿⠁⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⠛⠁⣰⣶⡆⠀⢠⣿⣿⣿⠁⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠍⠙⢩⣹⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣿⣿⣿⡿⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠃⠀⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣟⣡⣤⣿⣿⣿⡄⠀⢸⣿⣿⣿⠀⠀⠀⣴⣿⣯⣿⣿⡿⠿⣿⣿⣆⣿⡂⠻⣿⣿⣿⣏⣦⣄⢀⣶⣆⠀⠀⠀⠀⢠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠰⠀⢰⣿⠀⠀⠀⢀⣿⣿⠋⢉⣠⣾⣿⣿⣿⣽⣿⣇⣀⡘⣿⣿⠏⠀⠀⢸⣿⣿⣿⣿⢫⣤⣾⣿⣿⣿⡟⣿⣸⣯⢿⣿⣿⣩⣿⣾⣿⣿⡇⠀⠀⠀⣾⣿⠃⣿⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡇⠘⠟⠀⠀⠀⠸⢁⣠⣴⣿⣿⣿⣿⣿⡿⠟⠋⠹⣿⣿⣿⠟⠀⠀⠀⠍⠝⠀⠻⢁⣾⣿⣿⣿⣿⣿⣿⠘⣇⢿⣾⣿⣿⣧⣽⣿⣿⣿⡇⠀⠀⠀⣿⡿⢰⡟⠀⣸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡇⠀⠀⠀⠀⠀⢻⣿⡿⣿⡟⠙⠛⠛⣿⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⠛⢉⡟⣻⣿⣿⡇⢻⣦⡻⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠉⠁⠙⠃⠀⣿⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠃⠀⠀⠀⠁⠀⠄⠀⠀⡀⠁⠀⠀⠀⢁⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⢨⣄⣶⣿⣿⣿⣿⣿⣿⣿⡇⢨⣿⡎⠌⠻⡞⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⢀⣰⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠄⠄⠀⢀⣴⣿⣿⣿⣿⣿⣿⡟⡀⢀⣶⣆⡀⣹⣿⣿⣏⣀⣀⣀⠀⢾⣿⡿⠛⠛⣿⣿⡿⠻⠋⠀⠈⠟⠃⠀⠀⢸⣿⣿⣿⣿⣤⡀⣀⣀⣤⣤⣄⢀⡤⣣⣬⣿⡻⣿⢄⣤⣤⣄⢠⣤⣀⠀⠀⢀⡀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣥⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⠉⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣠⣸⣿⣿⣿⣿⡿⣿⣿⣷⣿⣿⣿⣿⣏⢻⣿⣿⣿⣿⠀⣿⡏⢹⣿⡇⠉⠉⡟⠹⠟⠉⠀⠀ ⢠⣤⡀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣛⠀⣿⠟⠉⢉⣿⣿⡟⠛⠿⢿⠟⠉⠉⠙⢻⡀⠀⠀⠉⠉⠛⠃⠀⠀⠀⠀⢀⣰⣿⣿⡿⠿⣿⣿⣿⣿⣿⠏⢻⣿⣿⢸⣿⡿⣿⡶⣳⣿⣟⣴⠂⢠⣾⡿⢃⠂⠀⠀⠀⠀⠀⠀⠀ ⠘⢿⣿⣿⣿⣶⣶⣤⣾⣿⠁⠀⠈⠛⠀⡀⠐⠛⠉⢀⣀⣴⣷⣦⡀⠀⠀⡀⢀⣠⣶⡀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠟⠋⠥⢴⢿⠿⢿⣟⣾⡿⣣⠀⢸⣿⣿⣾⣿⡇⠉⣽⣿⣯⣟⠁⣠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣾⣿⡟⠛⢿⣿⠿⠿⢿⣷⣶⣶⣾⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⣤⣶⣿⠿⢇⢿⣇⣿⣷⠿⠿⠿⠿⠷⣷⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣶⣿⣿⣿⣿⣧⣶⣶⣶⣤⣤⣤⡀⣠ ⣿⣿⣿⡿⠦⠃⠀⠀⠀⠀⠉⠉⠉⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣤⠴⡊⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⠛⠛⠉⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣶⣾⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⡿⠟⣡⠎⠀⠀⣴⣿⣿⣟⡿⣿⣿⢾⣿⣿⣄⠋⠿⠦⡀⠀⠀⢹⣿⣿⣿⠧⣼⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣏⣉⣉⣉⣿⣿⣷ ⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣿⡿⠿⡿⠿⠿⠟⠛⠛⠉⠉⠉⠻⠋⠀⡰⠋⠀⠠⠈⠉⣹⣿⠟⠏⠛⢿⣿⣿⣿⣿⣦⠀⠀⢹⣆⠀⠀⠉⠙⠋⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠶⠶⢶⣶⣿⣿⣷⣶⣤⡀⠀⣰⠃⠀⠀⠀⠰⠖⢋⡁⢠⣤⣶⠄⠈⠉⠍⠿⣏⠆⣦⠘⠁⡀⠀⠘⣷⣶⣦⣶⣶⠄⢠⣾⣤⣤⣤⣀⡀⠉⡏⠙⠙⠛⠛⠋⠉⠉ ⠀⠖⠶⣶⠎⢶⠄⠰⠶⠶⠶⣲⣶⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠉⠀⠀⠀⠀⠀⣲⣿⡇⣼⢿⡿⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠙⠉⠉⠉⠁⠀⠈⠛⠛⠛⠛⠻⠿⠾⠿⠦⠀⠐⠢⢀⠀⠀ ⠀⢿⠏⢻⡟⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠛⢀⣶⣶⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠍⠙⢭⣹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣼⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠀⢀⣿⠀⠀⠀⠀⣻⣿⣿⣿⣿⣟⣤⣴⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⠀⢀⣴⣿⣯⣾⣿⠿⠿⣿⣿⣆⣿⡆⠻⣿⣿⣿⡏⠤⣄⢀⣶⣧⠀⠀⠀⠀⢀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠀⣾⡇⠀⠀⠀⣰⣿⡟⠉⢁⣠⣿⣿⣿⣯⣿⣿⣄⣀⠘⣿⣿⠋⠀⠀⣸⣿⣿⣿⡿⢫⣴⣾⣿⣿⣿⡟⣿⣸⣿⢿⣿⣿⣉⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⡏⣸⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⡀⠹⠇⠀⠀⠀⠏⢀⣠⣾⣿⣿⣿⣿⣿⠿⠟⠉⢿⣿⣷⣿⠏⠀⠀⠠⢉⠟⠠⡛⢁⣾⣿⣿⣿⣿⣿⣿⠹⣇⢿⣿⣿⣿⣯⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⢰⣿⠀⢠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⠛⠛⢻⡟⠀⠀⠀⠈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠛⢉⠟⢿⣿⣿⡆⢿⣦⡻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠃⠘⠋⠀⢸⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⠀⠀⠀⠈⡁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⢨⣿⡎⠘⠻⡟⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⣠⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⠏⠀⠠⣤⣤⠀⢻⣿⣿⣅⣀⣀⣀⠀⢿⣿⡿⠟⢛⣿⣿⡿⠿⠟⠀⠈⠟⠇⠀⠀⢸⣿⣿⣿⣿⣤⡀⣀⣀⣤⣤⣄⢀⡠⣨⣤⣼⡻⣿⢇⣤⣤⣄⢀⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣯⢠⣼⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠋⠀⢀⣀⣀⠀⠁⠀⠀⠀⠀⠀⢀⣠⣰⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣯⢻⣿⣿⣿⣿⠀⣿⡏⢹⣿⡇⠉⠉⠛⠉⠿⠏⠁⠀ ⣀⣀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣟⠋⠀⡿⠻⠉⢉⣹⣿⠟⠛⠿⣿⠟⠉⠙⠛⢧⠀⠀⠀⠉⠙⠛⠃⠀⠀⠀⠀⠀⣰⣿⣿⣿⠿⣿⣿⣿⣿⣿⠏⢿⣿⣿⢸⣿⡿⣿⡷⣳⣿⣟⣤⡂⢠⣾⡿⢓⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣿⣿⣶⣶⣦⣤⣤⣿⡟⠉⠀⠉⠁⠀⠀⠀⠚⠛⠀⠀⣶⣶⣆⠀⠀⢀⡀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠋⠩⢵⢶⠿⠿⢟⣾⡿⣣⠀⢸⣿⣿⣼⣿⡇⠉⣽⣿⢯⣿⠉⣠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣾⣟⠿⠿⣿⣿⣿⠿⣷⣶⣶⣶⣾⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⣠⣶⣿⠿⠇⢿⣇⣿⢷⠿⠿⠿⠿⠷⣶⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣶⣿⣿⣿⠿⣧⣤⣤⣤⣤⣤⣤⡀⠀ ⣿⣿⣿⡷⠔⠁⠀⠀⠀⠈⠙⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣀⡤⠂⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾ ⠛⠛⠁⠀⢀⣄⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣬⣭⣭⣯⣍⣿⣿⣽⣿⣿⣿⣿⣿⣿⠾⢫⡞⠀⠀⣴⣿⣿⡿⡿⣿⣿⣽⣻⣿⡀⠛⢿⡦⡀⠀⠀⢹⣿⣿⣿⣯⣬⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⠉⢉⣉⣻⣿⣿ ⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢻⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠉⠙⠿⠋⠀⣰⠋⠀⠀⠈⠉⣹⣿⠟⠟⠻⢿⣾⣾⣿⣿⣦⠀⠀⠸⣄⠀⠀⠛⠛⠛⠁⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣤⣴⣾⣶⣶⣦⣀⠀⠀⣰⠃⠀⠀⠀⡠⠕⠛⡁⢠⣀⣤⡀⠙⠛⠭⢿⡟⠄⢠⡐⠃⠀⠀⠀⣶⣶⣤⣤⣤⡄⠀⣴⣆⣉⣉⣁⠀⠉⠻⠛⠛⠛⠻⠛⠉⠉ ⠀⠖⠲⣶⠎⢶⠄⠰⠶⠶⠶⣴⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠂⠀⠋⠀⠀⠀⠀⠀⣰⣿⡇⣾⣿⡿⠀⠀⠀⠀⠀⠈⠗⠉⠀⠀⠀⠀⠀⠹⠛⠛⠛⠉⠀⠀⠻⠿⠿⠿⠿⣿⣶⠾⣦⡀⠀⠦⣀⠀⠀ ⠀⠅⠀⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣙⠛⠋⢀⣶⣶⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠍⠙⢩⣹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⠘⣿⣿⣿⣿⡿⣫⣤⣴⣿⣿⣧⠀⠀⣹⣿⣿⣿⠀⠀⢀⣴⣿⣿⣿⣿⠿⠿⣿⣿⣆⣿⡆⠻⣿⣿⣿⡏⢀⡀⠀⣶⣦⠀⠀⠀⠀⠀⣿⣿⡟⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⢠⣿⠀⠀⠀⠀⣾⣿⠏⠁⣀⣴⣿⣿⣿⣧⣿⣿⣀⣀⢹⣿⣿⠃⠀⠀⣸⣿⣿⣿⡿⢫⣴⣾⣿⣿⣿⡟⣿⣸⣿⢿⣿⣷⣈⣿⣾⣿⣿⣿⠀⠀⠀⢸⣿⡟⢀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣇⠈⠿⠀⠀⠀⠘⠁⣀⣤⣾⣿⣿⣿⣿⣿⠿⠛⠉⣿⣿⣾⣿⠃⠀⠀⠠⢁⠟⠀⡟⢁⣿⣿⣿⣿⣿⣿⣿⠹⣇⢿⣾⣿⣿⣿⣝⣿⣿⣿⣿⠀⠀⠀⢼⣿⢣⣿⠁⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡏⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠛⠛⠛⣿⡇⠀⠀⠀⠈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠛⢉⠿⢿⣿⣿⡆⢿⣮⡻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠋⠘⠋⠀⢨⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣠⣼⣿⣿⣿⣿⣿⣿⣿⡇⢈⣿⡎⠈⠻⡏⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢀⣼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⣼⡇⠀⠀⠀⢠⡾⠿⠋⠀⣀⣾⣿⣿⣿⣽⣿⣧⣀⡀⢻⣿⡿⠁⠀⠀⣾⣿⣿⣿⡿⢫⣴⣾⣿⣿⣿⡟⣿⣼⣿⢿⣿⣿⡄⣿⣼⣿⣿⣿⠀⠀⠀⢠⣿⣿⢀⡋⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⠀⠙⠃⠀⠀⠀⠈⠀⣀⣴⣾⣿⣿⣿⣿⣿⠿⠋⠙⣿⣿⣿⡿⠃⠀⠀⠠⢁⠏⠐⠟⢠⣿⣿⣿⣿⣿⣿⣿⠹⣇⢿⣿⣿⣿⣿⠛⣿⣿⣿⣿⠀⠀⠀⢸⣿⡇⣼⠇⠀⡚⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⡿⠛⠛⠛⣿⠀⠀⠀⠀⠙⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⠛⢉⠿⢿⣿⣿⡆⢿⣦⡻⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠈⠛⠀⠛⠀⠀⡇⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⢤⣼⣿⣿⣿⣿⣿⣿⣿⡇⠈⣿⡏⠘⠻⣏⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣰⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣾⣿⣶⣶⣷⡷⠀⠀⢀⣄⠀⢐⣶⣿⣯⠀⠀⣀⡀⠀⣿⣿⠿⠿⢿⣿⣿⡿⠿⠟⠀⠀⠟⠿⠀⠀⢉⣿⣿⣿⣿⣧⡀⠀⣀⣤⣤⣄⢀⡀⣠⣤⣴⡻⣿⢟⣤⣤⣄⢀⠀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡋⣠⣧⣴⣶⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡆⠘⠋⠁⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⠀⣿⡏⢹⣿⡇⠁⠉⠙⠒⠀⠲⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡿⠛⠀⢽⡹⠛⠉⠙⣿⣿⠟⠿⢿⣿⠟⠛⠛⠿⡇⠀⠀⠐⠋⠻⠿⠃⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠯⢿⣿⣿⢹⣿⣿⣿⡿⣳⣿⣟⣄⣀⢠⣾⡿⡓⠂⠀⠀⠀⠀⠀⠀⠀ ⣿⣶⣶⣦⣤⣀⣀⣼⡟⠋⠉⠘⠁⠀⠀⠀⠐⠚⠀⠁⢠⣶⣦⡀⠁⠀⠀⠀⠀⣘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠟⠉⢩⠷⠶⠿⢟⣿⡿⣧⠀⢸⣿⣿⢸⣿⡏⠋⣽⣿⢏⣾⡟⣡⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣭⡛⠿⢿⣿⣿⣿⣿⣷⣦⣤⣤⣴⣷⣴⣤⣤⣶⣶⣶⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢈⣤⣶⠿⠇⠿⢇⠿⢇⠿⠿⠿⠿⠷⣤⣿⡿⡾⣿⣣⣸⣿⣿⣿⣿⣤⣿⣿⣿⠿⢇⣀⣠⣤⣄⣀⣀⣀⠀ ⣿⣿⣤⠀⠉⠁⠀⠀⠈⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣀⡀⠐⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠧⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣈⡉⢉⣙⣛⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣯⡾⢋⡔⠀⠀⣰⣿⣿⡿⣿⣿⣿⣹⡿⣿⠋⠹⣿⣆⡀⠀⠀⠘⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⡿⠛⠛⠛⢿⣿ ⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠿⣿⠟⠁⢠⠏⠀⢀⠐⠻⢋⣿⡷⡷⢿⣿⣽⣿⣿⣿⣆⠈⠀⠱⣄⠀⠀⠹⠿⠿⠟⠈⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢉⣉⣁⣀⣠⣤⣤⣄⣀⠀⠀⠀⢰⠃⠀⠀⠀⢀⣀⠿⠛⢀⠀⣀⠈⠻⠿⣻⢻⡿⠀⢀⠀⡟⠂⠀⠀⣤⣤⣀⣀⣀⡀⠀⠀⣉⠙⠛⠛⠉⠙⠻⠿⠿⠿⠿⣿⠿⠛ ⠀⠆⠲⣶⠆⢶⠄⠰⠶⠶⣶⡀⢀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠙⠛⠛⠛⠛⠛⠻⠄⢀⠃⠀⠀⠀⠀⠁⣠⣶⡆⣸⣿⣿⠁⠀⠀⠀⠈⠑⡮⠘⠃⠀⠀⠀⠀⠸⡿⠿⠿⠿⠋⠀⠸⠿⣿⡿⢿⣷⣦⣄⣤⡀⠀⠀⡀⠀⠀ ⠀⠀⠛⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣭⠙⠋⠀⣴⣶⠆⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⢏⠉⢫⣽⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠇⠀⠀⠀⠀⣹⣿⣿⣿⠿⠋⣤⣴⣿⢿⣿⡀⠀⠀⣿⣿⣿⡇⠀⠀⢠⣾⣿⣵⣿⣿⠿⠿⣿⣷⣆⣿⡖⠛⣿⣿⣿⣇⡀⣠⠀⣰⣶⡀⠀⠀⠀⠀⣸⣿⣿⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⠀⠀⠀⠀⢠⠿⠟⠁⠀⣠⣿⣿⣿⣯⣼⣿⣇⣀⡀⢿⣿⡟⠁⠀⠀⣿⣿⣿⣿⡿⣫⣴⣾⣿⣿⣿⡟⣿⣼⣿⢿⣿⣿⣄⣼⣼⣿⣿⣿⠀⠀⠀⠀⣿⣿⠁⡀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⠀⠛⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⡿⠟⠋⢹⣿⣷⣿⡿⠀⠀⠀⠈⠱⠋⠐⠟⢠⣿⣿⣿⣿⣿⣿⣿⠹⣇⢿⣿⣿⣿⣿⠙⣿⣿⣿⣿⠀⠀⠀⢰⣿⡏⣼⡇⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠐⣾⣿⣿⣿⠟⠛⠟⢻⣿⠀⠀⠀⠀⠙⠛⠛⠀⠀⠀⠀⠀⠁⠀⠀⠠⢿⣿⠟⢩⠿⢿⣿⣿⡆⢿⣮⡻⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠙⠁⠻⠁⠀⡺⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⢤⣼⣿⣿⣿⣿⣿⣿⣿⡇⠈⣿⡏⠈⠻⣏⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⣠⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⣶⣶⣶⣶⡖⠀⠀⢀⡀⠀⠲⢖⣾⡇⠀⠀⢀⡀⠀⣿⣿⠿⠿⢿⣿⣿⣿⠿⠟⠀⠀⡟⠿⠀⠀⠈⣿⣿⣿⣿⣧⡀⠀⣀⣤⣤⣄⢀⡀⣠⣤⣤⡺⣿⢟⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣟⠁⣠⣤⣤⣶⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡆⠙⠋⠁⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣯⢻⣿⣿⣿⣿⠀⣿⡟⢹⣿⡇⠃⠈⠁⠲⠀⠀⠔⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠿⠃⠀⠟⠿⠙⠉⢉⣿⡿⠛⠻⣿⡿⠟⠛⠿⠿⡇⠀⠀⠐⠛⠻⠷⠃⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠯⢿⣿⣿⢹⣿⣿⣿⡿⣳⣿⣟⣄⣀⢠⣾⡿⡳⠆⠀⠀⠀⠀⠀⠀⠀ ⣶⣤⣤⣤⣀⣀⣀⣾⠟⠋⠁⠘⠀⠀⠀⠀⠀⠂⠈⠁⠁⣤⣆⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠛⢉⠭⠵⠾⢟⣾⡿⣧⡀⢸⣿⣿⢸⣿⡏⠏⣼⣿⠏⣾⣿⣣⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡙⠻⠿⣿⣿⣿⣿⣿⣦⣤⣀⣀⣴⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⢈⣡⣴⠿⠇⠿⠇⠿⢇⠿⠿⠿⠿⠷⣤⣿⡿⡾⢿⣃⣸⣿⣿⣿⣿⣀⣿⣿⣿⠿⠇⣀⣀⣀⣀⣀⡀⠀⠀ ⣿⣦⡀⠈⠋⠉⠉⠀⠙⠿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⣀⠄⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣯⣼⠟⡡⠀⠀⣠⣾⣿⡿⣿⣿⣿⣻⣿⣿⠛⢹⣿⣄⠀⠀⠀⠘⣿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⠟⠉⢠⠞⠀⠀⠴⠿⢗⣿⣷⡯⣿⣿⣽⣿⣿⣿⣄⠈⠉⠡⣄⠀⠀⠹⢿⣿⡿⠉⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣶⣶⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠉⠉⣀⣤⣀⣀⠀⠀⠁⠀⢠⠃⠀⠀⠀⠀⢐⡿⠟⠁⠁⠀⠙⠻⠿⠻⢻⢿⢀⠀⠀⡾⠂⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⠟ ⠀⠆⠲⣶⠀⢶⠄⠰⠶⠶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠿⠿⠿⠿⠿⢶⠀⠀⠋⠀⠀⠀⠀⠉⣁⣤⡆⣸⣿⣿⠃⠀⠀⠉⠉⠓⣮⠘⠆⠀⠐⠀⠀⠘⣿⡿⠿⠿⠟⠀⠀⣾⣿⣶⣶⣶⣄⡀⡀⡀⠀⠀⠀⠀⠀ ⠀⠀⢿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣉⠛⠋⠀⣾⣾⠀⠀⢠⣿⣿⣿⡇⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⢏⡉⢪⢽⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⣡⣤⣴⣿⣿⣿⠀⠀⢠⣿⣿⣿⡇⠀⠀⣠⣾⣿⣵⣿⣿⠿⠿⣿⣷⣆⣿⣖⠙⣿⣿⣿⣯⡐⣶⠀⣤⣶⡀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⡇⠀⠀⠀⠀⣾⠿⠏⠁⢀⣼⣿⣿⣿⣯⣿⣿⣄⣀⠘⣿⣿⡟⠀⠀⢀⣿⣿⣿⣿⡿⣡⣴⣾⣿⣿⣿⡟⣿⣾⣿⢿⣿⣿⣅⣾⣾⣿⣿⣿⡆⠀⠀⠀⣾⣿⡇⣼⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠃⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⡿⠟⠋⢹⣿⣿⣿⡟⠀⠀⠀⠈⠱⠃⠐⠏⢠⣿⣿⣿⣿⣿⣿⣿⠸⣧⢿⣿⣿⣿⣷⡯⣿⣿⣿⣿⡇⠀⠀⠀⣿⡿⢠⡿⠀⢠⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠟⠿⠛⢻⡇⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⠛⢩⠿⢿⣿⣿⡆⢿⣦⡻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠉⠃⠸⠇⠀⢸⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣉⢤⣼⣿⣿⣿⣿⣿⣿⣿⡗⠈⣿⣏⠈⠻⣯⢿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⠄⠀⢀⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣶⣶⣶⣶⣶⣶⣿⠃⠀⠀⠀⠀⠀⠲⢲⣾⡇⠀⠀⢀⡀⢰⣿⣿⠿⠿⢿⣿⣿⣿⠿⠟⠁⠀⡟⠿⠀⠀⠈⣿⣿⣿⣿⣯⡀⠀⣀⣤⣤⣄⠀⠀⣠⣬⣤⡺⣿⢟⣧⣤⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⡏⡁⣤⣤⣤⣶⣾⣿⣷⣾⣿⣿⣿⣿⣿⣿⣷⡄⠻⠋⠀⠀⠈⠉⠉⠃⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠀⣿⡟⢹⣿⡇⠏⠈⠉⠓⠄⠀⠴⠂ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⠈⠿⡟⠛⠛⢻⣿⣿⠻⢿⣿⣿⠟⠻⠿⢿⡀⠀⠀⠐⠚⠻⠷⠂⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⢯⢿⣿⣿⢻⣿⡗⣿⣿⣳⣿⣟⣆⡀⢠⣾⡿⣳⠃⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣄⣀⡀⠀⢀⣿⠟⠉⠁⠂⠀⠀⠁⠀⠴⠈⠈⠈⢠⣤⡄⠉⠀⠀⠀⠀⠀⢐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠿⠛⢋⠭⠥⠾⢟⣿⡿⣧⡁⢸⣿⣿⢸⣿⡟⠟⣽⣿⠏⢸⣿⣯⣿⡟⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣤⣤⣀⣀⣠⣤⣶⣶⣾⣿⣷⣶⣶⣴⣧⣴⣾⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢈⣩⣤⠿⠇⠿⠇⠿⢧⠿⠿⠿⠿⠷⣤⣻⡿⡾⢿⣃⣸⣿⣿⣿⣿⣇⣿⣿⣿⠿⠇⠀⣀⣀⣀⡀⠀⠀⠀ ⣧⣄⠀⠙⠉⠉⠉⠉⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠻⢿⣿⠿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣯⣴⠟⡡⠀⠀⢠⣾⣿⣿⣿⣿⣿⣻⣿⣿⠛⢻⣿⣆⠀⠀⠀⠈⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿ ⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐⠶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⠟⠋⢡⠞⠀⠀⡴⢿⢟⣿⣧⣯⣽⣿⣹⣗⣿⣶⣄⠈⠙⠑⣄⠀⠀⠸⣿⣿⣿⠏⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣦⣬ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠋⠉⣉⣁⠀⠀⠀⠈⠁⠀⢠⠏⠀⠀⠀⠀⢠⣾⠿⠁⠁⠈⠙⢿⣿⠿⣿⣿⠆⠀⠀⣸⠢⠀⠀⢀⣀⡀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⠛⠻⢿⣿⣿⣿⣿⣿⡿ ⠀⠆⠲⣶⠂⢶⠄⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠐⠒⠚⠛⠻⠿⠿⣿⣿⣿⣷⣆⠀⠀⠃⠀⠀⠀⠀⠊⢉⣠⡄⢸⣶⣿⠒⠀⠀⠀⠉⠻⢼⡠⠦⠈⠠⠀⠀⠈⣿⣿⣷⣾⡶⠂⠀⣰⣷⣦⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⡽⠛⠁⢠⣶⡶⠀⠀⢸⣿⣿⣿⠄⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⢏⡉⢣⠽⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡇⠀⠀⠀⠀⢸⣿⣿⣿⡿⠟⣤⣤⣾⣿⣿⣇⠀⠀⢸⣿⣿⣿⠀⠀⠀⣠⣾⣿⣷⣿⣿⠿⠿⣿⣷⣆⣿⣖⠙⣿⣿⣿⣿⡇⣴⠀⣠⣶⣄⠀⠀⠀⠀⢀⣿⣿⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⡅⠀⠀⠀⢠⡿⠿⠉⠀⣀⣼⣿⣿⣿⣥⣿⣿⣀⡀⠘⣿⣿⠏⠀⠀⢠⣿⣿⣿⣿⡿⣱⣴⣾⣿⣿⣿⡟⣿⡾⣿⢿⣿⣿⣅⣴⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⡏⢈⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠀⠀⠀⠀⠈⠀⣀⣤⣾⣿⣿⣿⣿⣿⠿⠛⠉⢿⣿⣿⣿⠟⠀⠀⠀⠈⠹⠃⠐⠏⣠⣿⣿⣿⣿⣿⣿⣿⠸⣧⢻⣿⣿⣿⣿⡍⣻⣿⣿⣿⡇⠀⠀⠀⣿⣿⢡⣾⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⡿⠛⠟⠛⣿⠇⠀⠀⠀⠘⠛⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⠟⢻⠿⢿⣿⣿⡆⢻⣦⡻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠉⠋⠘⠟⠀⢠⠇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣉⢤⣼⣿⣶⣿⣾⣿⣿⣿⡷⠀⣿⣏⠈⠻⣯⢻⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⣰⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣶⣿⠃⠀⠀⡀⡀⠐⢲⣶⣿⡂⠀⠀⠀⠀⢸⣿⣿⣿⠿⢿⣿⣿⣿⠿⠟⠁⠀⡟⠿⠀⠀⠈⣾⣿⣿⣿⣿⡀⠀⣀⣤⣤⣄⠀⠀⣠⣤⣥⡰⣿⢟⣯⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⣿⣿⡏⠉⣷⣄⣤⣴⣿⣷⣾⣾⣿⣿⣿⣿⣿⣿⣷⠀⠻⠋⠀⠀⠈⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣧⢿⣿⣿⣿⣿⠀⣿⡟⢻⣿⡏⠿⠂⠉⠓⠆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠟⠁⢙⡿⠟⠛⠛⣿⣿⡿⢿⣿⣿⣿⠿⠿⢿⣿⠀⠀⠀⠰⠺⠿⢷⠂⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣿⣿⢻⣿⡏⣿⣾⣳⣿⣟⣦⡀⢠⣾⡿⢣⣿⡄⠀⠀⠀⠀⠀⠀ ⣄⣀⣀⡀⠀⠀⢸⣿⠟⠋⠐⠀⠀⠀⠀⠀⠶⠀⠉⠉⢀⣀⡀⠉⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠟⠛⠫⠭⠵⢟⣿⡿⣧⠉⢸⣿⣿⢸⣿⡗⠟⣽⣿⠏⠘⣿⣯⣿⡟⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⢿⣿⣿⣿⣿⣿⣇⡀⠀⢀⣀⣄⣀⣀⣀⣀⣤⣤⣴⣿⣿⣷⣤⣤⣴⣤⣴⣶⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠐⣉⣤⠿⠇⠿⢇⠿⢇⠿⠿⠿⠿⠷⣀⣻⡿⡾⢿⣃⡸⠿⣿⡿⢿⣟⠿⣿⡿⠿⠇⠀⠀⢀⣀⠀⠀⠀⠀ ⣄⠀⠈⠛⠉⠉⠉⠙⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⡀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣴⠞⡩⠀⠀⢀⣾⣿⣿⣿⣿⣿⢿⣿⣿⠟⢻⣿⣄⠀⠀⠀⠈⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢶⣶⣶⣶⣶⣶⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⠟⠛⢁⡾⠁⠀⠠⢿⡿⣿⣯⣏⣿⣿⣻⣷⣿⣶⣄⠈⠛⢑⡄⠀⠀⠸⣿⣿⣿⡏⠲⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⠛⠛⠛⢉⡉⠁⠀⠀⠙⠉⠀⢠⠋⠀⠀⠀⠀⠠⣼⡿⠉⠃⠈⠛⢿⣿⢿⣿⣿⡆⠀⠀⢸⠦⠀⠀⠉⠉⠉⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⠀⠆⠲⣶⠊⢶⠄⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠐⠲⠶⠶⣶⣿⣿⣿⣷⣦⣄⠀⠀⠋⠀⠀⠀⠀⠒⠊⢁⡄⢰⣦⣶⡆⠀⠀⠒⠊⠾⢈⠀⡦⠈⠀⠀⠀⠀⣿⣿⣶⣶⣶⠖⠀⢠⣶⣤⣤⣤⣄⠀⠀⠉⠉⠉⠉⠉⠁ ⠀⠈⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⠙⠋⠀⣰⣿⡇⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣏⡉⢢⠭⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣼⣿⣿⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⣸⣿⣿⣿⠿⢋⣤⣤⣾⣿⣿⡇⠀⠀⢸⣿⣿⣿⠀⠀⠀⣠⣿⣿⣶⣿⣿⠿⢿⣿⣿⣆⣿⣖⠙⣿⣿⣿⣿⡠⣴⡀⢰⣶⣆⡀⠀⠀⠀⠀⣿⣿⣗⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣆⠀⠀⠀⠀⠰⠿⠟⠁⠀⣠⣿⣿⣿⣿⣼⣿⣧⣀⠀⠹⣿⣿⠋⠀⠀⢰⣿⣿⣿⣿⡿⣡⣴⣾⣿⣿⣿⡟⣿⡾⣿⣿⣿⣿⣧⣿⣷⣿⣿⣿⡇⠀⠀⠀⢸⣿⡿⢠⡃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠃⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⠿⠛⠙⣿⣿⣿⣿⠇⠀⠀⠀⠈⡸⠃⠜⠏⢠⣿⣿⣿⣿⣿⣿⣿⠘⣧⢻⣷⣿⣿⣿⡎⣻⣿⣿⣿⡇⠀⠀⠀⢸⣿⠇⣾⡇⠀⡜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠰⣾⣿⣿⣿⠟⠛⠟⠻⣿⠀⠀⠀⠀⠙⠛⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⠟⢻⠿⢿⣿⣿⡆⢻⣦⡹⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠈⠋⠀⠟⠀⠀⡇⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣉⢠⣼⣿⣶⣿⣾⣿⣿⣿⡷⠀⣿⣏⠎⠿⣿⢻⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣶⡞⠁⠀⠀⣀⠀⠐⠶⣶⣶⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⢿⣿⣿⣿⣿⡿⠁⠀⡟⢿⠀⠀⠈⢿⣿⣿⣿⣿⡀⠀⣀⣤⣤⣄⠀⠀⣠⣤⣥⡠⣾⢟⣯⣥⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⣻⣿⣿⠋⢉⣁⣀⣤⣴⣿⣷⣶⣶⣿⣿⣿⣷⣿⣿⣷⠀⠿⠛⠀⠀⠈⠙⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣧⢿⣿⣿⣿⣿⠈⣿⡟⢹⣿⡇⠿⠆⠀⠐⠢⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⠀⠸⢿⠻⠛⠻⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⠀⠀⠀⠰⠲⢶⣶⠂⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⢯⣿⣿⣿⢻⣿⡇⣷⣶⣳⣿⣟⣶⡀⢠⣾⡿⠃⡒⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⡀⠀⠀⠀⣾⡿⠟⠋⠁⢀⠀⠀⠀⢠⠄⠐⠉⠉⣀⣀⠈⠉⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠿⠛⠛⠭⠽⢟⣿⡿⣷⠉⢸⣿⣿⢸⣿⡇⡟⣽⣿⠏⠘⣿⣯⣿⡟⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⣿⣿⣶⣾⣿⣄⠀⠀⠀⣀⣄⣀⠀⢀⣀⣀⣤⣴⣿⣿⣧⣤⣤⣤⣤⣴⣶⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠐⢋⣡⠿⠇⠿⣇⠿⢇⠿⠿⠿⠿⠷⣀⣻⠿⠾⢿⡃⠸⠿⠿⠿⠿⣶⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠈⠻⠛⠙⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⡀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣶⣶ ⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣰⡶⡪⠀⠀⢀⣴⣿⣿⣿⣿⣿⠿⣿⣿⠿⠿⣿⣍⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣴⣶⣶⣶⣶⣶⣶⣾⣶⣦⣾⣿⣾⣿⣿⣿⣿⣿⡿⠛⢉⡼⠁⠀⣠⣿⡿⣿⣏⣟⣻⣿⣻⡯⣿⣶⡌⠈⠛⠒⡄⠀⠀⠘⣿⣿⣿⡿⠲⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠿⠿⠿⠿⠿⠟⠛⠛⠋⠉⠁⠈⠻⠋⠀⢠⠋⠀⠀⠀⠀⢈⣼⡿⠋⠋⠙⠻⣿⣿⣿⣿⣿⡆⠀⠀⢸⣦⠀⠀⠉⠉⠉⠁⠀⠀⠀⠈⠛⠿⠿⢿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿ ⠀⠆⠲⣶⠊⢶⠄⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠤⠤⣶⣶⣶⣿⣿⣶⣶⣤⡀⠀⠀⠊⠀⠀⠀⠀⠶⠊⠉⡀⢠⣤⣶⡄⠀⠉⠡⠠⢯⡃⠄⣤⠘⠀⡀⠀⠀⢷⣶⣶⣤⣤⣤⠀⠀⣤⣄⣀⣀⣀⠀⠀⠉⠉⠉⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡌⠛⠋⠀⣴⣷⠆⠀⠀⢼⣿⣿⣿⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣏⡈⢣⡬⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⢁⣤⣴⣿⣿⣿⡀⠀⠀⣽⣿⣿⣿⠀⠀⠀⣠⣿⣿⣶⣿⣿⠿⢿⣿⣿⣆⣿⣷⠘⣿⣿⣿⣿⡂⢠⢀⢠⣶⣆⠀⠀⠀⠀⠀⣼⣿⣏⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣰⡀⠀⠀⠀⠀⠸⠿⠋⠀⢀⣰⣿⣿⣿⣿⣼⣿⣇⣀⡀⢻⣿⣿⠃⠀⠀⢰⣿⣿⣿⣿⡿⣱⣴⣾⣿⣿⣿⡏⣿⡿⣿⣿⣿⣿⣆⣨⣿⣿⣿⣿⡗⠀⠀⠀⢰⣿⣿⠀⡍⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠁⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⠿⠛⠙⣿⣿⣿⣿⠃⠀⠀⠀⠈⡸⠁⢜⠏⣠⣿⣿⣿⣿⣿⣿⣿⠘⣷⢻⣷⣿⣿⣿⡬⢹⣿⣿⣿⡇⠀⠀⠀⢸⣿⡇⣼⡇⠀⠂⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⠟⠻⠛⢻⡿⠀⠀⠀⠀⠙⠻⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡿⠟⢛⠿⢿⣿⣿⡆⢹⣧⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠛⠀⠻⠁⠀⡍⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣁⢠⣼⣿⣶⣾⣾⣿⣿⣿⣿⠀⣿⣯⠊⠿⣿⢻⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣰⣶⣴⣶⣤⣶⣶⠖⠀⠀⠀⠀⠀⠠⠦⣶⣶⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⢿⣿⣿⣿⣿⡿⠁⠀⣿⢿⠀⠀⠈⢺⣿⣿⣿⣿⡀⠀⣀⣤⣤⣄⠀⠀⣠⣤⣥⡀⣴⢟⣿⣥⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⣿⡟⠉⣉⣀⣀⣤⣴⣷⣶⣶⣿⣿⣿⣿⣶⣿⣿⣧⠈⠿⠛⠀⠀⠈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣧⢾⣿⣿⣿⣿⠈⣿⡟⢻⣿⡇⠿⠗⠀⠓⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡟⠁⠀⠿⠿⠟⠛⠻⣿⣿⠿⠿⣿⣿⡿⠿⠿⣿⣿⠀⠀⠀⠠⠶⢶⣶⠆⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⢯⣿⣿⣿⢿⣿⡏⣷⣶⣳⣿⣟⣶⡄⢠⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⢀⣾⡿⠛⠉⠀⠀⠀⠀⠀⠀⠄⠀⠈⠉⠀⠀⠈⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠿⠟⢛⠋⠽⢟⣿⡿⣷⠉⢸⣿⣿⢸⣿⡇⡿⣽⣿⠏⠊⣿⣯⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣶⣶⣾⣯⠀⠀⠀⠀⣀⣀⡀⠀⠀⢀⣀⣠⣤⣿⣿⣤⣤⣀⣠⣀⣠⣶⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠐⢋⣉⠿⠇⠿⣇⠿⢇⠿⠿⠿⠿⠷⣄⣻⠿⠾⢿⡃⠸⠿⠿⠿⠿⣐⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠟⠋⠙⠛⠛⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠁⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣷⣶⣶ ⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣰⡶⢊⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣏⠁⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣶⣶⣿⣿⣤⣽⣿⣿⣿⣿⣿⣿⣿⡿⠟⢋⡴⠁⠀⢠⣾⡿⢿⣟⣿⢿⣿⢷⣿⣿⣧⡀⠙⠿⠖⠄⠀⠀⠈⣿⣿⣿⣿⠢⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢁⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⠿⠿⠿⠛⠛⠉⠉⠙⠿⠋⠀⢀⠞⠀⠀⠀⠉⠈⣴⣿⠋⠏⠙⠻⣿⣿⣿⣿⣿⡆⠀⠀⠙⣄⡀⠀⠘⠛⠛⠉⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠆⠲⣶⠊⢶⠄⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣴⣾⣶⣶⣤⣀⠀⠀⠀⠎⠀⠀⠀⠀⠤⠔⠛⠁⢠⣤⣴⡄⠈⠉⠩⠍⢫⡃⠄⣄⠐⠁⠀⠀⠀⢲⣶⣦⣤⣤⣤⡀⠀⢠⣀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠙ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⡔⠙⠁⢀⣾⣿⠆⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣇⡈⢣⡬⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠏⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⠀⠀⠀⠀⢈⣿⣿⣿⡿⠟⢀⣤⣴⣿⣿⣿⡀⠀⠀⣿⣿⣿⡇⠀⠀⠀⣰⣿⣯⣶⣿⣿⠿⢿⣿⣿⣆⣾⣷⠘⣿⣿⣿⣿⠀⢄⠀⢠⣾⣦⠀⠀⠀⠀⠀⣸⣿⡿⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⠀⠀⠀⠀⠀⠼⠿⠁⠀⢀⣴⣿⣿⣿⣯⣿⣿⣇⡀⠀⢿⣿⡿⠁⠀⠀⢰⣿⣿⣿⣿⡿⣱⣴⣾⣿⣿⣿⡏⣿⡟⣿⣿⣿⣿⣦⢤⡥⣾⣿⣿⣷⠀⠀⠀⠀⣿⣿⠃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⡿⠟⠋⢹⣿⣷⣿⡿⠃⠀⠀⠀⠈⡸⠁⠌⠎⢠⣿⣿⣿⣿⣿⣿⣿⠘⣿⢹⣷⣿⣿⣿⣦⣻⣿⣿⣿⣷⠀⠀⠀⢰⣿⡟⣰⡟⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣶⣿⣿⣿⡿⠛⠻⠛⢿⡏⠀⠀⠀⠀⠙⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠟⢛⡿⣿⣿⣿⡦⢹⣧⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⠁⠘⠁⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⢠⣼⣿⣶⣾⣶⣾⣿⣿⣿⠀⣿⣯⠊⠿⣿⢻⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣄⣲⣦⣤⣶⣶⠂⠀⠀⠀⠀⠀⠰⠄⢶⡖⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⣿⢿⠀⠀⠈⢻⣿⣿⣿⣿⡃⠀⣀⣤⣤⣄⠀⠀⣠⣤⣬⡀⣠⢞⣿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠹⣿⣿⠟⠉⢉⠀⣀⣀⣤⣷⣤⣤⣶⣿⣿⣶⣶⣿⣿⣦⠈⠿⠓⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣦⣿⣿⣽⣿⣧⢾⣿⣿⣿⣿⠈⣿⡟⢻⣿⡇⠿⠷⠀⠐⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡛⠀⠀⠻⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⠀⠀⠀⠠⠶⣶⣦⠄⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⢯⣿⣿⣿⣿⣿⡏⣿⣶⣳⣿⣟⣶⡆⢠⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⠿⠛⠁⠀⠀⠀⠀⠀⢀⡀⠀⠈⠁⠀⠀⠉⠉⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠿⠟⠛⠫⢟⣿⡿⣷⠛⢸⣿⣿⢸⣿⡇⡿⣽⣿⠏⠚⢻⣫⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣶⣦⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⣿⣷⣄⣀⣀⣀⣀⣠⣴⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠠⠚⣉⠿⢇⠿⣇⠿⢇⠿⠿⠿⠿⠷⡄⠻⠿⠾⢿⡷⠸⠿⠿⠿⠿⣀⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠹⠟⠙⠛⠛⠻⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶ ⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣠⣴⢂⠁⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣭⣿⣍⣩⣯⣯⣿⣿⣿⣿⣿⣿⣿⠾⢋⣴⠃⠀⢀⣾⣿⣿⡟⠿⢿⣿⡶⣿⣻⣇⡀⠋⠿⠦⠀⠀⠀⠈⢿⣿⣿⣿⡧⢴⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠉⠙⠿⠛⠀⢀⠞⠁⠀⠀⠉⠙⣡⢾⠟⠟⠛⢿⣿⣷⣿⣿⣿⣄⠀⠀⠘⣆⠀⠀⠘⠛⠛⠛⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠆⠲⣶⠊⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⢀⣀⣄⣤⣄⣤⣶⣦⣤⣄⣀⠀⠀⠀⡌⠀⠀⠀⠀⣀⠤⠛⠉⢀⣀⣠⣀⠉⠛⢋⣉⣟⠃⡄⢀⠀⠏⠁⠀⠀⢠⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠛⠛⠛⠛⠉ ⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣧⡝⠋⠁⢠⣿⡶⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣆⡈⢱⡬⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⢿⡿⠃⣠⣤⣾⣿⣿⣧⠀⠀⢀⣿⣿⣿⡇⠀⠀⠀⣴⣿⣯⣶⣿⣿⠿⢿⣿⣿⣆⣾⣷⠚⢿⣿⣿⣿⡂⡠⡀⢀⣶⣷⡀⠀⠀⠀⠀⢰⣿⣿⢨⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠿⠟⠁⠀⣀⣼⣿⣿⣿⣧⣿⣿⣀⡀⠘⣿⣿⡟⠁⠀⠀⢰⣿⣿⣿⣿⡿⣱⣴⣾⣿⣿⣿⡏⣿⡟⣿⣿⣿⣿⣧⣰⣤⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡇⣈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⡿⠟⠋⢻⣿⣷⣿⡿⠁⠀⠀⠀⠈⡸⠁⠜⠏⢠⣿⣿⣿⣿⣿⣿⣿⠘⣿⠹⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⢠⡗⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣶⣿⣿⣿⡿⠛⠟⠛⣿⠁⠀⠀⠀⠘⠛⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠟⠛⡿⢿⣿⣿⡧⢸⣧⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⠃⠘⠃⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠁⠀⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⢠⣼⣿⣶⣾⣶⣿⣿⣿⣿⠀⣿⣯⠊⠻⣿⡻⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣤⣄⣤⣤⣤⣶⡶⠀⠀⠀⢀⡀⠀⢠⡄⣶⡆⠀⠀⠈⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣿⢿⡆⠀⠈⢣⣿⣿⣿⣿⡃⠀⣀⣤⣤⣄⠀⠀⣠⣤⣬⡀⣀⢖⣿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⠛⠋⠁⠀⣀⣀⣼⣶⣤⣤⣾⣿⣷⣶⣶⣾⣿⣦⠘⠿⠓⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣦⣿⣿⣽⣿⣧⢸⣿⣿⣿⣿⠀⣿⡟⢻⣿⡇⠿⢶⡂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠋⠀⠐⣿⠿⠿⠿⠿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠠⠶⣶⣦⠄⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⡟⣷⣿⣳⣿⣟⣶⣆⢠⣾⡿⠃⠀⠠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⣿⠟⠛⠁⠀⠀⠀⠀⠀⢀⠀⠀⠉⠁⠀⠈⠛⠉⠀⠀⠀⠈⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠿⠿⠛⠛⢟⣾⡿⣿⡟⢻⣿⣿⢸⣿⡇⡿⣽⣿⠏⠚⠻⣫⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣶⣦⣤⣴⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣷⣀⣀⣀⣀⣀⣠⣴⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠠⠞⢋⠿⢇⠿⣇⠿⢇⠿⠿⠿⠿⠷⡄⠻⠿⠾⢿⣷⠸⠿⠿⠿⠿⠀⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠻⠟⠛⠛⠛⢧⣴⣶⣶⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡆⠀⠘⢿⣿⣿⣿⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣶⣶⣶⣶⣤ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢡⣤⠔⠁⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣈⣭⣽⣿⣉⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⡾⠟⣡⠊⠀⠀⣴⣿⣿⡿⣿⠿⣿⣧⣿⣿⡇⡀⠛⢿⠦⡀⠀⠀⠀⢿⣿⣿⣿⡯⣩⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢿⢿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠛⠻⣿⠟⠁⠀⡼⠁⠀⠀⠘⠙⢡⣾⡟⡟⠺⢿⣷⣿⣿⣿⣿⣄⠀⠀⠘⣆⠀⠀⠘⠿⠿⠟⠃⠀⠉⠉⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶ ⠀⠆⠲⣶⠎⢶⠆⠰⠶⠶⠖⠀⠀⠀⠀⠈⠉⠉⢉⣁⣀⣀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠌⠀⠀⠀⠀⣀⡠⠟⠋⠀⡀⢀⡀⠉⠛⠉⠛⢻⡿⠀⢀⠀⠞⠁⠂⠀⢠⣤⣤⣀⣀⡀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠿⠿⠛⠛ ⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣤⠉⠋⠀⣰⣿⡷⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣆⡈⢱⡬⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⡿⣿⠿⢁⣤⣤⣾⣿⣿⣇⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⣴⣿⣯⣶⣿⣿⠿⢿⣿⣿⣆⣾⣷⠚⢿⣿⣿⣿⡂⠠⢠⠀⣶⣷⡀⠀⠀⠀⠀⢀⣿⣿⡋⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⠿⠋⠀⠀⢠⣾⣿⣿⣿⣤⣿⣿⣀⡀⠘⣿⣿⡟⠀⠀⠀⣸⣿⣿⣿⣿⡿⣱⣴⣾⣿⣿⣿⡏⣿⣇⣿⣿⣿⣿⣧⡰⣾⣼⣿⣿⣿⠀⠀⠀⠀⣾⣿⡟⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣿⣿⣿⣿⣿⡿⠟⠉⢿⣿⣷⣿⡿⠀⠀⠀⠀⠉⡾⠁⢌⠏⢠⣿⣿⣿⣿⣿⣿⣿⠘⣿⠹⣿⣿⣿⣿⣷⣹⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⠃⣺⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣶⣿⣿⣿⠟⠿⠟⠻⣿⠁⠀⠀⠀⠘⠻⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠟⢛⡿⣿⣿⣿⡦⢸⣧⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠙⠋⠀⠋⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⣀⣼⣿⣶⣾⣶⣾⣿⣿⣿⠀⣿⣿⠊⠻⣿⡻⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣤⣠⣤⣤⣤⣶⡆⠀⠀⠀⠀⠀⠀⢤⣠⣶⠆⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⢿⢿⡆⠀⠈⢣⣿⣿⣿⣿⡇⠀⣀⣤⣤⣄⠀⠀⣠⣤⣤⡂⣀⢔⣾⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠙⣿⣿⣿⠋⠉⠀⠀⣀⣠⣾⣯⣄⣴⣿⣿⣷⣶⣶⣶⣿⣄⠘⠿⠛⠁⠀⠘⠛⠛⠏⠀⠀⠀⠀⠈⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣦⣿⣿⣽⣿⣧⢼⣿⣿⣽⣿⠈⣿⡟⢻⣿⡇⠿⠷⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠅⠀⠸⠿⠿⠿⠿⢿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠠⢴⣶⣤⠄⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⡏⣿⣿⣳⣿⣟⣶⣶⢠⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⣿⠟⠛⠁⠀⠀⠀⠀⠀⢀⠀⠈⠻⠁⠈⠉⠛⠋⠀⠀⠀⠉⠉⠄⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢀⣤⣿⠿⠿⠟⠛⢿⣾⡿⣿⡟⢻⣿⣿⢸⣿⡇⡿⣽⣿⠏⠾⠿⣫⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣦⣤⣤⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣆⣀⡀⢀⡀⠀⢀⣤⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠛⠿⢇⠿⢇⠿⢇⠾⠿⠿⠿⠷⣄⠻⠿⠾⢿⣳⠸⠿⠿⠿⠿⠀⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠛⠛⠟⠿⣤⣤⣤⣴⣾⣷⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡦⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⡎⠀⠈⢾⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⣶⣶⣤⣤ ⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢁⣤⠔⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠓⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣈⣉⣙⣛⣿⣛⢻⣻⣻⣿⣿⣿⣿⣿⣿⣿⣶⠟⣡⠊⠀⠀⣴⣿⣿⡿⣿⣿⣿⣏⣿⢿⣏⠁⠟⢿⣦⡀⠀⠀⠀⢻⣿⣿⣟⣿⢉⣽⣿⣿⣿⣿⣯⣤⣴⣾⣿⣿⣿⣿⡟⠛⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠿⣿⠟⠁⠀⡼⠃⠀⠀⠚⠛⢃⣽⡷⡶⠾⣿⣧⣿⣽⣿⣿⣄⠀⠀⠈⣄⠀⠀⠈⠿⠿⠿⠇⠀⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤ ⠀⠆⠲⣶⠏⢷⠖⠰⠶⠶⠖⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⢀⣀⣤⣀⣀⠀⠀⠁⠀⠀⡘⠀⠀⠀⠀⠀⣐⠿⠟⠁⠁⢀⠀⠙⠿⠛⠛⢻⢿⠀⠀⠀⡸⠑⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠋⠉⠉⠻⠿⠿⠿⠛ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡄⠙⠉⠀⣼⣿⡇⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣆⡀⢱⡬⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⡿⠿⠟⢀⣤⣴⣿⣿⣿⡆⠀⠀⢸⣿⣿⣿⡇⠀⠀⢀⣴⣿⣯⣾⣿⣿⠿⢿⣿⣿⣦⣾⣷⠚⢿⣿⣿⣿⡏⠀⡆⠀⣴⣶⡀⠀⠀⠀⠀⢀⣿⣿⣇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⠿⠁⠀⠀⣠⣿⣿⣿⣯⣼⣿⣯⣀⡀⠸⣿⣿⡟⠀⠀⠀⣸⣿⣿⣿⣿⡿⣱⣴⣾⣿⣿⣿⡏⢿⣇⣿⣿⣿⣿⣧⣤⣸⣼⣿⣿⣿⠆⠀⠀⠀⢸⣿⣿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣠⣤⣾⣿⣿⣿⣿⣿⠿⠛⠙⣿⣿⣶⣿⠿⠀⠀⠀⠀⠉⡟⠉⢌⠏⢠⣿⣿⣿⣿⣿⣿⣿⠘⣿⠹⣿⣽⣿⣿⣯⣽⣿⣿⣿⣿⠀⠀⠀⠀⣾⣿⠇⡬⠇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣶⣾⣿⣿⣿⠿⠿⠿⢻⡟⠀⠀⠀⠀⠙⠿⠿⠋⠀⠀⠀⠀⠠⠀⠀⠀⠀⢠⣾⣿⠟⢛⡿⣿⣿⣿⡦⢸⣧⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠙⠛⠀⠛⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⣀⣿⣿⣶⣾⣶⣶⣿⣿⣿⠀⢻⣿⠊⠻⣿⡻⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣄⣠⣀⣤⣤⣤⡄⠀⠀⠀⠀⠀⢀⠤⢠⣴⠖⠀⠀⠈⠀⠀⢸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢿⢿⡇⠀⠈⠃⣿⣿⣿⣿⡟⠀⣀⣤⣤⣄⠀⠀⣠⣤⣤⡃⢀⢀⣼⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠛⣿⣿⡿⠛⠋⠀⠀⢀⣀⣷⣦⣄⣴⣾⣿⣷⣴⣶⣶⣶⣄⠸⣿⠟⠁⠀⠘⠛⠛⠏⠀⠀⠀⠀⠈⠀⠁⠀⢀⣼⣿⣿⣿⣿⣿⣦⣿⣿⣽⣿⣇⢸⣿⣿⣿⣿⠠⣿⡟⢻⣿⡇⠶⠶⡦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠀⠀⠰⠿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢠⣤⣦⣤⠄⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⡏⣿⡿⣳⣿⣟⣷⣶⢠⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣶⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠉⠛⠛⠀⠀⠈⠉⠻⡄⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢀⢠⣾⠿⠿⠿⠛⢏⣾⡿⣿⡟⢻⣿⣿⢹⣿⡇⡿⣽⣿⠯⠾⠻⣫⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣤⣀⣀⣸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣶⣄⡀⠀⢀⡀⠀⢀⣤⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠟⠿⢇⠿⢇⠿⠇⠾⠿⠿⠿⠷⣄⠻⠿⠾⢿⣳⠸⠿⠿⠿⠿⠀⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⡿⠛⠿⠿⢧⣤⣤⣤⣶⣶⣶⣶⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣯⣿⣿⣿⣿⣿⣿⡇⠀⠉⢶⣶⣿⣿⣿⣧⣶⣶⣶⣶⣾⣿⣿⣶⣿⣶⣤⣤⣠⣤⣤⣤⣤⣤ ⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⣀⡄⠂⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣙⣛⣻⣟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⠿⣫⠎⠀⠀⣠⣿⣿⣿⢿⣿⣿⣏⣿⢿⣟⠉⠽⢿⣦⡀⠀⠀⠀⢻⣿⣿⣿⣿⢋⣻⣿⣿⣿⣿⣯⣍⣭⣿⣿⣿⣿⣿⣿⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⡿⠉⠁⡰⠋⠀⠀⠼⠻⢟⣹⡷⡾⢼⣿⣯⣿⣽⣿⣷⣄⠀⠈⠨⣆⠀⠀⠈⢿⣿⣿⠟⠀⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀ ⠀⠆⠲⣶⠏⢷⠶⠰⠶⠶⠖⠀⠀⠀⠉⠙⠛⠛⠛⠉⠉⠉⣀⣀⡀⠀⠀⠀⠉⠀⠀⠘⠁⠀⠀⠁⠀⢀⣾⠿⠁⠁⠀⠈⠛⠿⠛⠿⠿⣿⠀⠀⠀⢸⠓⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋⠛⠻⢿⣿⡿⠿ ⠀⠀⠀⠀⠀⠙⣻⣿⣿⣿⣧⡈⠉⠉⢀⣾⣿⠆⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣖⡀⢱⡤⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢣⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⠿⠿⠋⢀⣤⣴⣿⣿⣿⡄⠀⠀⣸⣿⣿⣿⠄⠀⠀⠀⣴⣿⣯⣶⣿⣿⠿⠿⣿⣿⣦⣼⣷⠚⢿⣿⣿⣿⡇⢀⣀⠀⣴⣶⡄⠀⠀⠀⠀⠀⣼⣿⡟⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⠟⠁⠀⠀⣰⣿⣿⣿⣯⣽⣿⣇⣀⠀⢺⣿⣿⠏⠀⠀⠀⣸⣿⣿⣿⣿⡿⣣⣴⣾⣿⣿⣿⡏⢿⣧⣿⡿⣿⣿⣷⣈⣾⣼⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⠿⠛⠛⣿⣿⣾⣿⠟⠀⠀⠀⠀⠉⡞⠉⠏⠞⢠⣿⣿⣿⣿⣿⣿⣿⠘⣿⡸⣿⣽⣿⣿⣿⣹⣿⣿⣿⣿⡇⠀⠀⠀⢼⣿⡇⣀⡍⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣶⣾⣿⣿⣿⠿⠿⠟⢿⡏⠀⠀⠀⠀⠛⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⡿⠿⢛⣿⣿⣿⣿⡦⢸⣧⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠛⠀⠺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢂⣀⣿⣷⣶⣾⣶⣾⣿⣿⣿⠀⢻⣿⠪⠻⣿⡿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠀⠀⠀⢀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⠀⠀⠀⠀⠀⠀⠀⣄⢠⣴⠆⠀⠀⠀⠀⠀⣼⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢸⢿⡇⠀⠈⠳⣿⣿⣿⣿⡿⠀⣀⣤⣤⣄⠀⠀⣠⣤⣤⡘⠀⢀⣤⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⡟⠛⠃⠀⠀⢀⣠⣥⣄⣀⣰⣿⣿⣦⣤⣴⣶⣶⡀⠹⡿⠏⠉⠀⠘⠻⠻⠏⠀⠀⠀⠀⠈⠀⠁⠀⢀⣴⣿⣿⣿⣿⣿⣤⣿⣿⣽⣿⣇⢸⣿⣿⣽⣿⡠⣿⡟⢿⣿⡇⠶⢶⣦⠀⠀⠠⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣴⣿⠛⠀⠀⠶⣶⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⡿⣳⣿⣟⣿⣶⢠⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣾⡿⠿⠓⠀⠀⠀⠈⠀⠀⠀⠀⠙⠛⠁⠈⠙⠛⠋⠁⠀⠉⠙⠳⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢠⣾⠿⢿⠿⠿⢛⣿⡿⣿⡿⢿⣿⣿⢹⣿⡇⡘⣽⣿⠯⠾⠻⣫⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣀⡀⢀⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡄⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠿⠿⢇⠿⢇⠿⠇⠿⠿⠿⠿⠷⣄⠻⠿⠾⢿⣣⡸⠿⠿⠿⠿⠀⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⠟⠛⠿⠿⢄⣀⣀⣠⣴⣶⣶⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣯⣽⣿⣿⣿⣿⣿⡅⠀⠉⢶⣶⣶⣿⣿⣧⣤⣤⣴⣶⣶⣿⣿⣶⣶⣶⣤⣀⣀⣀⣤⣤⣤⣀ ⠀⠀⠀⠀⠀⠈⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⣀⡠⠂⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠯⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠿⢿⡿⠿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣥⡿⢋⠔⠀⠀⣠⣾⣿⣿⢿⣿⣿⣟⣻⣿⣿⠋⠹⢿⣦⡀⠀⠀⠀⢹⣿⣿⣿⣿⠛⢻⣿⣿⣿⣿⣯⣋⣉⣭⣿⣾⣿⣿⣿⠿⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠿⢷⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⠿⣿⣿⡿⠋⠁⣰⠋⠀⠀⠴⠿⠟⣻⡧⣼⣭⣿⣯⣿⣳⣿⣶⡄⠀⠉⠁⣂⠀⠀⠀⢿⣿⣿⡿⠀⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀ ⠀⠆⠲⣶⠏⢷⠖⠰⠶⠶⠖⠀⠀⠈⠉⠛⠛⠛⠛⠛⠋⠉⢉⠁⠀⠀⠀⠈⠋⠀⠀⡰⠁⠀⠀⠀⠀⠀⣾⡿⠁⠁⠀⠉⠻⢿⣿⠿⢿⣿⠀⠀⠀⢸⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠿⠟⠛⠻⢿⣿⣿⡿ ⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣤⠉⠉⠀⢀⣾⣿⠁⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣖⡀⢱⡤⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⡿⠿⠟⠃⢀⣤⣾⣿⣿⣿⠀⠀⠀⣾⣿⣿⣿⠀⠀⠀⢀⣴⣿⣯⣾⣿⣿⠿⠿⣿⣿⣶⣼⣷⠞⢻⣿⣿⣿⡟⠰⣆⠀⣴⣶⣆⠀⠀⠀⠀⠀⣸⣿⡿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⠋⠀⠀⢀⣼⣿⣿⣿⣧⣾⣿⣇⠀⠀⢿⣿⣿⠋⠀⠀⠀⣼⣿⣿⣿⣿⡿⣳⣴⣾⣿⣿⣿⡏⢿⣷⣿⣿⣿⣿⣷⡤⣶⣾⣿⣿⣿⡇⠀⠀⠀⢠⣿⣿⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣿⣿⣿⠿⠛⠻⣿⣿⣾⣿⠏⠀⠀⠀⠀⠋⡾⠋⠍⠟⢠⣿⣿⣿⣿⣿⣿⣿⠈⣿⡸⣿⣽⣿⣿⣿⣭⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⡿⢠⡐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣶⣿⣿⣿⡿⠿⠿⠿⣿⠏⠀⠀⠀⠀⠻⠿⠿⠃⠀⠀⠀⠀⠀⠈⠀⠀⠈⢠⣾⡿⡿⢛⣿⣿⣿⣿⣧⢸⣧⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠈⠛⠁⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢂⣀⣿⣷⣶⣾⣶⣾⣿⣿⣿⠀⢻⣿⠪⠻⣿⡿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣄⠀⠀⠀⠀⠀⠀⢠⠀⣠⣤⠀⠀⠀⠀⠀⠀⣼⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢸⢿⡇⠁⠈⠻⣿⣿⣿⣿⡿⠀⣀⣤⣤⣄⠀⠀⣠⣤⣤⡘⠀⢀⣤⣼⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⠿⠛⠃⠀⠀⣀⣠⣤⣀⣀⣶⣿⣿⣦⣤⣤⣶⣶⡀⠹⡿⠯⠉⠉⠘⠿⠿⠟⠁⠁⠀⠀⠘⠈⠁⠀⠀⣠⣿⣿⣿⣿⣿⣤⣿⣿⣽⣿⣇⢸⣿⣯⣽⣿⣠⣿⡟⢿⣿⡇⠶⢶⣤⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣼⡿⠋⠀⠀⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⣳⣿⣟⣿⣶⢦⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠐⠻⠏⠁⠉⠙⠿⠋⠁⠉⠉⠻⢷⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⣼⡿⢿⠿⠿⢟⣿⡿⣿⣿⢿⣿⣿⢹⣿⡇⠘⣽⣿⢯⣾⠿⣫⣿⣟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠀⠀⢀⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀⠀⠀⠀⠀⠀⠀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠿⠇⠿⢇⠿⠇⠿⠿⠿⠿⠷⣄⠻⠿⠾⠿⣣⠸⠿⠿⠿⠿⠀⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠃⠨⠿⠆⢀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣷⣾⣶⣾⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣟⣻⣿⣿⣿⣿⣿⡄⠀⠉⢦⣴⣶⣾⣿⣷⣤⣤⣤⣶⣦⣿⣿⣧⣴⣦⣤⣀⠀⢀⣀⣠⣄⣀ ⠀⠀⠀⠀⠀⠘⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⡀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠿⠿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⡾⢋⡔⠁⠀⢀⣾⣿⣿⣿⣿⣿⣟⣻⣿⣿⠛⢻⢿⣆⠀⠀⠀⠀⠹⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣟⡛⢛⣉⣽⣵⣿⣿⣿⡿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⣶⣶⣶⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⣰⠟⠀⠀⠠⠿⠟⠹⣯⣼⣹⣿⣟⣻⣲⣿⢴⡄⠀⠁⠁⠀⠀⠀⠀⢻⣿⣿⣿⠆⠘⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀ ⠀⠆⠲⣶⠟⢷⠆⠰⠶⠶⠖⠀⠀⠈⠙⠻⠿⠿⠿⠛⠛⠋⠉⠉⠁⠀⠀⠙⠋⠀⠀⠰⠃⠀⠀⠀⠀⠀⣼⣿⠇⠈⠀⠉⠻⣿⠿⢿⣿⣿⠆⠀⠀⠈⡦⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠛⠿⢿⣿⣿⣿ ⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣤⠉⠉⠀⢠⣿⡿⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣗⡀⢱⡤⢽⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⠿⠿⠟⠁⣠⣤⣾⣿⣿⣷⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⢀⣴⣿⣿⣾⣿⣿⠿⠿⣿⣿⣦⣼⣷⡜⢻⣿⣿⣿⡇⢀⣤⠀⣰⣶⣆⠀⠀⠀⠀⠀⣸⣿⡿⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠏⠁⠀⠀⢠⣾⣿⣿⣿⣧⣿⣿⣄⠀⠀⣿⣿⣿⠃⠀⠀⠀⣼⣿⣿⣿⣿⣿⣻⣴⣾⣿⣿⣿⡏⢿⣷⣿⣿⣿⣿⣿⡄⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣿⣿⣿⠿⠛⢻⣿⣷⣿⣿⠇⠀⠀⠀⠀⠉⡿⠋⠛⠟⢡⣿⣿⣿⣿⣿⣿⣿⠎⢿⡸⣿⡽⣿⣿⣿⣹⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⡿⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣶⣿⣿⣿⡿⠿⠿⠿⣿⠉⠀⠀⠀⠈⠻⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⡿⡿⢛⣿⣿⣿⣿⣧⢸⣷⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠛⠃⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢂⣀⣿⣷⣴⣾⣴⣾⣿⣿⣿⠀⢻⣿⠪⢻⣿⡟⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠁⠀⠀⣾⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢸⢿⡇⠀⠀⠻⣹⣿⣿⣿⡿⠁⣀⣤⣤⣄⠀⠀⣠⣤⣤⡀⠀⢀⣤⣬⣟⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠛⠛⣿⣿⡿⠟⠛⠁⠀⠀⠀⣀⣄⣀⣀⣠⣿⣿⣤⣤⣤⣦⣦⡀⢻⣿⠯⠉⠉⠘⠿⠿⠟⠉⠁⠀⠀⠘⠈⠁⠀⠀⣠⣾⣿⣿⣿⣿⣤⣿⣿⣸⣿⡇⢸⣿⣯⣽⣿⢠⣿⡟⢿⣿⡇⠶⠶⢦⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣼⡟⠃⠀⠠⣬⢾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⣳⣿⣟⣿⣦⢤⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⣾⡿⠿⠁⠀⠀⠈⠀⠀⠀⠀⠸⠻⠛⠁⠙⠛⠟⠛⠉⠉⠉⠛⢧⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⣼⡿⢿⠿⠿⢟⣿⡿⣿⣿⢿⣿⣿⢹⣿⡇⠈⣽⣿⢯⣾⡿⣫⣿⣟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠀⠀⠸⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠿⠇⠿⢇⠿⠇⠿⠿⠿⠿⠷⣄⠻⠿⠾⠿⣃⠸⠿⠿⠿⠿⠀⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠁⠐⠿⠀⠀⢀⢀⣀⣤⣤⣤⣄⣠⣤⣤⣶⣶⣿⣿⣿⣿⣷⣶⣾⣷⣶⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⢻⣿⣿⣿⣿⣿⣧⠀⠉⢠⣤⣤⣾⣿⣿⣤⣤⣤⣴⣤⣶⣿⣧⣤⣦⣤⣀⠀⠀⢀⣀⣀⣀ ⠀⠀⠀⠀⠀⠘⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⢀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣣⡾⠏⡀⠀⠀⢀⣼⣿⣿⢿⣿⣿⡿⢻⣿⣿⠟⢛⣿⣆⠀⠀⠀⠀⠹⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡟⠛⢛⣻⣯⣽⣿⣿⣿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣶⣶⣶⣶⣶⣾⣿⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⢠⠞⠀⠀⡀⢿⠿⢻⣏⣼⣙⣿⡟⣻⢮⣿⢰⡀⠈⠛⠑⠀⠀⠀⠀⢻⣿⣿⣿⡆⠐⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀ ⠀⠖⠲⣶⠟⢷⠆⠰⠶⠶⠖⠀⠈⠛⠻⠿⠿⠿⠿⠿⠛⠛⠛⠉⠉⠀⠈⠛⠋⠁⠀⠐⠁⠀⠀⠀⠀⠀⣴⣷⠇⠙⠈⠙⢿⣿⣿⣿⣿⣿⡆⠀⠀⠈⡦⡀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠙⠻⠿⠿⣿⣿⠿⠿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⡄⠉⠁⠀⢰⣿⡿⠀⠀⠀⣿⣿⣿⡿⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣗⡀⢙⡤⠽⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⣿⠿⠿⠋⠀⣠⣴⣾⣿⣿⣇⠀⠀⢀⣿⣿⣿⣿⠀⠀⠀⢀⣴⣿⣷⣾⣿⣿⠿⠿⣿⣿⣶⣼⣷⡄⢻⣿⣿⣿⣇⢀⣀⡀⣰⣴⣆⠀⠀⠀⠀⠀⢰⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠰⠋⠁⠀⠀⢠⣾⣿⣿⣿⣴⣿⣿⡀⠀⠘⣿⣿⣿⠃⠀⠀⠀⣼⣿⣿⣿⣿⣿⢿⣴⣾⣿⣿⣿⣏⢿⣷⣿⣿⣿⣿⣿⣄⢸⣶⣿⣿⣿⡷⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⡿⠟⠋⢻⣿⣷⣿⡿⠃⠀⠀⠀⠀⢁⡿⠋⠛⡟⢁⣿⣿⣿⣿⣿⣿⣿⡎⢿⡼⣿⡼⣿⣿⣿⣨⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⢁⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣤⣶⣿⣿⣿⠿⠿⠿⢿⣿⠉⠀⠀⠀⠘⠻⢿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⡿⠿⢛⣿⣿⣿⣿⣦⠸⣷⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⠋⠸⠏⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⣈⣿⣷⣤⣴⣥⣾⣿⣿⣿⡄⢹⣿⡪⠻⣿⡿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡄⠀⠀⠀⠀⠀⠀⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢸⣿⡇⠀⠈⠻⢼⣿⣿⣿⣿⠃⣀⣤⣤⣄⠀⠀⣠⣤⣤⡀⠁⢀⣤⣤⣟⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠛⠒⣾⣿⡿⠛⠛⠀⠀⠀⠀⣠⣄⡀⣀⣠⣿⣷⣤⣀⣤⣤⣤⡀⢻⣿⠯⠉⠉⠹⠿⠿⠟⠉⠉⠀⠀⠘⠈⠁⠀⠀⢀⣾⣿⣿⣿⣿⣤⣿⣿⣹⣿⡇⢸⣿⣯⣽⣿⢀⣿⡟⢿⣿⡇⠶⢤⣄⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣿⡟⠀⠀⠀⣤⣤⣶⣾⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⢀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⣳⣿⣟⣿⣧⢠⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⣿⡿⠟⠁⠀⠀⠀⠈⠀⠀⠀⠙⠿⠇⠁⠉⠻⠟⠛⠉⠉⠛⠻⣇⠀⠀⠀⠀⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⢰⣿⢿⣿⠿⢟⣿⣿⣿⣿⢿⣿⣿⢹⣿⡇⠀⣽⣿⢯⣾⡿⣫⣿⣟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡶⠿⠇⠿⢇⠿⠇⠿⠿⠿⠿⠷⣄⠻⠿⠾⠿⢃⠸⠿⠿⠿⠿⠀⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠟⠀⠲⠆⠀⠀⠀⠀⣀⣤⣤⣀⣀⣀⣠⣤⣴⣶⣿⣿⣿⣷⣶⣶⣶⣦⣴⣾⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⢡⣤⣶⣿⣿⢻⣿⣿⣿⣿⣿⣮⠀⠉⢣⣤⣤⣤⣿⣿⣀⣀⣀⣤⣤⣤⣿⣿⣤⣤⣤⡀⠀⠀⠀⢀⣀⣀ ⠀⠀⠀⠀⠀⠲⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⢀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣶⠟⡁⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⢿⣿⣿⠿⠿⣿⣄⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⡟⠛⠛⢛⣻⣩⣿⣿⣿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⣤⣤⣤⣴⣦⣶⣯⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⢡⠎⠀⠀⠀⢶⠿⢻⣟⣸⢛⣿⡿⢾⠯⣿⢦⡀⠈⠛⠓⠄⠀⠀⠀⢻⣿⣿⣿⡇⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀ ⠀⠖⠲⣶⠏⢷⠆⠰⠶⠶⠖⠀⠉⠛⠻⣿⣿⣿⣿⠿⠿⠿⠛⠛⠉⠉⠉⠻⠟⠁⠀⠰⠋⠀⠀⠀⠀⠀⣰⣷⡏⠙⠉⠛⢿⣿⣿⣿⣾⣷⡆⠀⠀⠀⢦⡀⠀⠀⠛⠛⠋⠁⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⡿⠿⣿⣿⣿⣶ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣧⠀⠉⠁⠀⣸⣿⡇⠀⠀⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣗⡀⠙⡦⠽⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⡿⠿⠿⠁⠀⣤⣴⣿⣿⣿⡆⠀⠀⢠⣿⣿⣿⡇⠀⠀⠀⢀⣾⣿⣷⣾⣿⣿⠿⠿⣿⣿⣶⣸⣷⡄⢻⣿⣿⣿⣧⢀⢠⠀⣀⣶⣦⠀⠀⠀⠀⠀⢀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠋⠀⠀⠀⣠⣿⣿⣿⣯⣼⣿⣷⡀⠀⠸⣿⣿⡿⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⢿⣴⣾⣿⣿⣿⣏⢻⣷⢿⣿⣿⣿⣷⣌⢿⣷⣿⣿⣿⣿⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣠⣤⣾⣿⣿⣿⣿⣿⡿⠟⠋⢿⣿⣶⣿⡿⠃⠀⠀⠀⠐⢁⡿⠋⠛⡟⢁⣿⣿⣿⣿⣿⣿⣿⡎⢿⡜⣿⣞⣿⣿⣿⡌⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⢇⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⣾⣿⣿⣿⠿⠿⠿⢿⡟⠁⠀⠀⠀⠘⠿⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⡿⠿⢛⣿⣿⣿⣿⣦⠸⣷⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⠛⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠛⠉⠉⠙⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⣈⣿⣷⣤⣴⣥⣾⣿⣿⣿⡄⢹⣿⡪⠻⣿⡿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡄⠀⠀⠀⠀⠀⠀⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢸⣿⡇⠀⠀⠻⢸⣿⣿⣿⣿⠇⣀⣤⣤⣄⠀⠀⣠⣤⣤⡀⠀⢀⣤⣤⣞⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⠒⢲⣿⣿⡿⠟⠛⠀⠀⠀⢀⣠⣀⣀⣀⣠⣿⣷⣤⣤⣤⣤⣄⠀⢻⣿⠯⠉⠉⠙⠿⠿⠟⠉⠉⠀⠀⠘⠈⠃⠀⠀⢀⣾⣿⣿⣿⣿⣦⣿⣿⣹⣿⡇⢸⣿⣯⣽⣿⢀⣿⡟⢿⣿⡇⠶⣤⣤⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⣿⠟⠀⠀⢠⣶⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⢀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣳⣿⣟⣿⣷⢤⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣴⣿⡿⠏⠀⠀⠀⠀⠈⠀⠀⠀⠹⡿⠃⠈⠛⠿⠿⠛⠉⠋⠛⠿⣇⠀⠀⠀⠀⠈⠉⠛⠀⠀⠀⠀⠀⠀⠀⢰⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢹⣿⡇⠀⣽⣿⢯⣾⡿⣫⣿⣟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠇⠿⢇⠿⠇⠾⠿⠿⠿⠷⣅⠻⠿⠾⠿⢃⠸⠿⠿⠿⠿⠀⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⠀⠤⠄⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣤⣤⣴⣿⣿⣷⣶⣶⣦⣦⣤⣴⣾⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⢉⣤⣶⣿⣿⢻⣿⣿⣿⣿⣿⡷⠀⠙⢣⣤⣤⣤⣾⣿⣁⣀⣀⣠⣤⣤⣾⣿⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠲⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⢀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣴⠞⡁⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⢿⣿⣿⠿⠿⣿⣆⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⠻⠛⠛⣛⣫⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣼⣧⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠛⢡⡞⠀⠀⠀⣾⣿⢻⡿⣹⠻⣿⣿⢾⣯⣿⣦⡀⠉⠻⠗⠄⠀⠀⠀⠹⣿⣿⣿⣗⠀⢼⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⡁ ⠀⠖⠲⣶⠟⢷⠆⠰⠶⠶⠶⠀⠉⠻⢿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠉⠙⢻⠟⠁⠀⢰⠋⠀⠀⠀⠀⠈⣠⣮⡟⠙⠉⠻⢿⣿⣷⣿⣿⣿⡄⠀⠀⠀⢢⡀⠀⠀⠛⠛⠛⠁⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⠀⠀⣰⣿⣿⣿⡄⠀⠉⠁⢀⣼⣿⠇⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣗⡀⠙⡦⠽⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣻⠿⠿⠏⠀⢀⣤⣶⣿⣿⣿⡄⠀⠀⢠⣿⣿⣿⡇⠀⠀⠀⢠⣾⣿⣷⣾⣿⣿⠿⠿⣿⣿⣶⣸⣷⡄⢻⣿⣿⣿⣿⠀⠀⠀⣠⣶⣦⠀⠀⠀⠀⠀⢀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠁⠀⠀⠀⣴⣿⣿⣿⣧⣼⣿⣧⠀⠀⠸⣿⣿⡟⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⢿⣴⣾⣿⣿⣿⣏⢻⣷⢻⣿⣿⣿⣿⣆⢪⣲⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⣤⣾⣿⣿⣿⣿⣿⡿⠟⠛⣿⣿⣾⣿⡿⠃⠀⠀⠀⠀⢁⡿⠋⠛⡿⢁⣿⣿⣿⣿⣿⣿⣿⡎⢿⡞⣿⣞⣿⣿⣿⡄⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⣿⡇⣀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣴⣾⣿⣿⡿⠿⠿⠿⣿⡟⠁⠀⠀⠀⠙⠿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⣿⡿⡿⢿⣿⣿⣿⣿⣧⠸⣷⡘⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⠛⠀⠟⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠛⠋⠉⠉⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢈⣿⣷⣤⣴⣥⣼⣿⣿⣿⡆⢹⣿⡪⡻⣿⡿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠂⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢸⣿⣧⠀⠀⠻⢸⣿⣿⣿⣿⡇⣀⣤⣤⣄⠀⠀⣠⣤⣤⡀⠈⢀⣤⣤⣜⢿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⠂⢶⣾⣾⠿⠛⠋⠀⠀⠀⠀⣀⣀⢀⣀⣬⣿⣦⣀⣀⣤⣤⣄⠀⢿⣿⠟⠛⠉⠹⠿⠿⠿⠉⠋⠀⠀⠘⠋⠃⠀⠀⢀⣾⣿⣿⣿⣿⣧⣿⣿⢹⣿⡇⢸⣿⣯⣽⣿⠀⣿⡿⢿⣿⡇⠦⠄⢀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣨⣿⠋⠀⠀⢀⣤⣤⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣳⣿⣟⣿⣿⢢⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣴⣿⠿⠉⠀⠀⠀⠀⠉⠉⠁⠀⢹⡿⠍⠙⠿⣿⡿⠟⠛⠛⠛⢿⡇⠀⠀⠀⠀⠈⠙⠛⠁⠀⠀⠀⠀⠀⠀⢰⣾⠿⠿⣿⣿⣿⡿⣿⣿⣿⣿⣿⢹⣿⡇⠉⣽⣿⢯⣾⣿⣫⣿⣟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠿⠇⠿⢇⠿⠇⠾⠿⠿⠿⠷⣇⠻⠿⠾⠿⠃⠸⠿⠿⠿⠿⠀⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢤⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⣀⣀⣠⣤⣶⣿⣿⣷⣶⣦⣤⣤⣤⣤⣾⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢉⣡⣴⣶⣿⢿⣿⣿⣿⣿⣿⣷⠀⠉⢣⣀⣠⣤⣾⣿⣇⣀⣀⣀⣀⣠⣼⣿⣃⣀⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠴⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣴⠖⠉⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣎⠁⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢻⣛⣻⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣬⣽⣯⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢁⡔⠁⠀⠀⣼⣿⢻⡿⠻⠿⢿⣿⢶⣟⣻⣆⡀⠁⠻⠳⠄⠀⠀⠀⠸⣿⣿⣿⣿⠀⢠⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⡋ ⠀⠖⠲⣶⠏⢶⠆⠰⠶⠶⠶⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠋⠻⢿⡟⠁⠀⢠⠟⠀⠀⠀⠉⠉⢡⣬⡾⠻⠛⠻⣿⣾⣷⣿⣿⣷⡄⠀⠀⠀⢦⡀⠀⠀⠛⠻⠿⠋⠀⠀⠉⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⠉⠀⠀⣾⣾⠁⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣗⡀⠉⡦⠽⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡛⠻⠟⠋⠀⢀⣤⣶⣿⣿⣷⡀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢠⣾⣿⣷⣾⣿⣿⠿⠿⣿⣿⣶⣸⣿⡄⢻⣿⣿⣿⣏⠀⠀⠀⢀⣶⣦⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣤⣿⣿⣇⠀⠀⢹⣿⣿⡟⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⢿⣴⣾⣿⣿⣿⣿⢻⣷⢺⣿⣿⣿⣿⣆⠀⢧⣽⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⣤⣾⣿⣿⣿⣿⣿⡿⠟⠙⣿⣷⣼⣿⠿⠀⠀⠀⠀⠀⢁⡿⠛⠛⡿⢁⣿⣿⣿⣿⣿⣿⣿⡎⢿⡟⣿⣞⣿⣿⣿⡆⣱⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⡏⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣴⣾⣿⣿⡿⠿⠿⠿⣿⠏⠁⠀⠀⠀⠛⠿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⣿⡿⡿⠻⣿⣿⣿⣿⣧⠘⣷⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⠛⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠛⠉⠉⠉⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢈⣿⣧⣤⣴⣥⣼⣿⣿⣿⡆⢹⣿⡪⡻⣿⣿⢿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂⠀⠀⣶⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢸⣿⣷⠀⠀⠻⢞⣿⣿⣿⣿⡇⣀⣤⣤⣄⠀⠀⣠⣤⣤⡀⠀⢀⣤⣤⣔⢿⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢶⣶⡶⠟⠟⠂⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣀⣀⣀⣤⣄⣄⠀⢿⣿⠟⠛⠉⠹⠿⠿⣿⠉⠋⠀⠀⠘⠋⠛⠀⠀⠀⣾⣿⣿⣿⣿⣧⣿⣿⢹⣿⡇⢸⣿⣏⣽⣿⠀⣿⡿⢿⣿⡇⠦⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣸⡿⠃⠀⠀⢀⣀⣤⣴⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠁⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⡿⣳⣿⣟⣿⣿⢦⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣴⣿⠟⠁⠀⠀⠀⠈⠉⠀⠁⠉⠻⡯⠉⠉⠻⢿⠿⠛⠋⠛⠻⠿⡇⠀⠀⠀⠉⠉⠙⠛⠁⠀⠀⠀⠀⠀⠀⢠⣾⡿⠿⣿⣿⣿⡿⣿⣿⣿⣿⣿⢹⣿⡇⠁⣼⣿⢯⣾⣿⣫⣿⣟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠠⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠇⠿⢇⠿⠇⠾⠿⠿⠿⠷⣇⠻⠿⠾⠿⠃⠸⠿⠿⠿⠿⠀⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⣀⣤⣴⣾⣿⣶⣤⣤⣤⣤⣄⣠⣴⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣁⣤⣶⣿⢿⣿⣿⣿⣿⣿⣷⠀⠉⠳⣀⣀⣀⣤⣿⡏⠀⠀⢀⣀⣀⣠⣿⡇⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⠴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣴⣶⣾⣿ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣤⡴⠊⠄⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣏⠁⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⠿⠿⡟⢋⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⣈⣉⣟⣉⣉⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠟⢋⡔⠁⠀⠀⣴⡿⠛⡿⠻⠿⣿⣿⣴⣟⣻⡇⡀⠋⠻⠣⠄⠀⠀⠀⠸⣿⣿⣿⣟⠉⢠⣿⣿⣿⣿⣿⣦⣤⣴⣾⣿⣿⣿⣿⡟ ⠀⠖⠲⣶⠏⢶⠄⠰⠶⠶⠶⠙⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠻⣿⡿⠋⠀⢠⡞⠀⠀⠀⠈⠉⢁⣌⡷⠻⠒⠿⣷⣶⣧⣿⣯⣷⣄⠀⠀⠀⢠⡀⠀⠀⠹⠿⠿⠟⠀⠀⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠈⠁⠀⢠⣿⡿⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣗⣀⠈⡦⠼⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡿⠿⠟⠁⠀⣠⣤⣶⣿⣿⣧⠀⠀⠀⣸⣿⣿⣿⡇⠀⠀⠀⣠⣾⣿⣷⣾⣿⣿⠿⠿⣿⣿⣶⣸⣿⡄⢻⣿⣿⣿⣿⠀⠀⡄⢠⣶⣶⡀⠀⠀⠀⠀⠀⣸⣿⡿⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣤⣿⣿⡀⠀⠀⢿⣿⣿⠟⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣴⣾⣿⣿⣿⣿⢻⣿⢰⣿⣿⣿⣿⣆⠩⢿⣾⣿⣿⣿⠄⠀⠀⠀⢠⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣿⣿⣿⠿⠛⢻⣿⣷⣾⣿⠟⠀⠀⠀⠀⠀⢡⠿⠛⢛⡟⢁⣿⣿⣿⣿⣿⣿⣿⡏⢿⡏⣿⣏⣿⣿⣿⡇⣼⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⡿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣤⣴⣿⣿⣿⠿⠿⠿⠿⣿⠋⠀⠀⠀⠈⠻⠿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⣿⡿⡿⢿⣿⣿⣿⣿⣧⠘⣷⡘⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠘⠻⠃⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⠋⠉⠙⠁⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠉⣿⣷⣤⣴⣥⣼⣿⣿⣿⡆⢹⣿⡮⡻⣿⣿⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢸⣿⣷⠀⠁⠹⢎⣿⣿⣿⣿⡟⣀⣤⣤⣄⠀⠀⣠⣤⣤⡀⠀⢀⣤⣤⣄⢾⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣦⣾⣾⠿⠿⠁⠀⠀⠀⠀⡄⠀⠀⣠⣼⣿⣄⣀⣀⣤⣄⡄⠀⣿⣿⠟⠛⠉⠹⠿⢿⣿⠋⠋⠁⠀⠈⠋⠛⠀⠀⠀⣾⣿⣿⣿⣿⣧⣿⣿⢸⣿⡇⢸⣿⣏⣽⣿⠀⣿⡿⢿⣿⡇⠧⡤⠀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣻⡿⠃⠀⠀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠈⠁⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⡿⣳⣿⣟⣿⣿⢯⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣶⣿⠏⠁⠀⠀⠀⠉⠉⠉⠉⠙⣿⣿⠟⠿⢿⣿⡿⠟⠛⠛⠿⣿⡄⠀⠀⠀⠉⠉⠙⠛⠁⠀⠀⠀⠀⠀⠀⢠⣾⡿⠿⢿⣿⣿⡿⣿⣿⣿⣿⣿⢻⣿⡇⠋⣽⣿⢯⣾⣿⣫⣿⡟⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠇⠿⠇⠿⠇⠾⠿⠿⠿⠷⣇⠻⠿⠾⠿⠃⠸⠿⠿⠿⠿⠀⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣿⣿⣦⣤⣤⣤⣤⣀⣠⣶⣾⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣉⣤⣴⣾⠿⣿⣿⣿⣿⣿⣷⠀⠉⠳⣀⣀⣀⣰⣿⡟⠀⠀⠀⣀⣀⣠⣾⡟⠀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⡆⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣴⣶⣶ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣠⡴⠊⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣏⠉⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⢻⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⣙⣟⠛⠛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣧⠾⢋⡴⠁⠀⠀⣴⣿⠿⣿⠻⣿⣿⣿⣬⣟⢿⡏⡀⠊⢻⡧⠀⠀⠀⠀⠘⣿⣿⣿⣟⠋⠁⣽⣿⣿⣿⣿⣦⣤⣤⣴⣿⣷⣿⣿⣿ ⠀⠖⠲⣶⠏⢶⠆⠰⠶⠶⠾⠻⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠿⣿⡿⠋⠀⢀⡞⠁⠀⠀⠂⠉⠉⣜⣷⠶⠶⢾⣿⣤⣯⣽⣏⣷⣄⠀⠀⠀⢠⠀⠀⠀⠹⠿⣿⠿⠁⠀⠉⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣸⣿⣿⣄⠀⠈⠀⠀⢰⣿⠟⠀⠀⠀⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣗⣀⠉⡦⠼⣿⣿⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⠿⠿⠏⠀⠀⣠⣴⣶⣿⣿⣇⠀⠀⠀⣼⣿⣿⣿⡀⠀⠀⠀⣠⣾⣿⣷⣾⣿⣿⠿⠿⣿⣿⣶⣸⣿⡄⢻⣿⣿⣿⣿⠀⠀⠀⢀⣶⣦⡀⠀⠀⠀⠀⠀⣸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣯⣼⣿⣷⡀⠀⠀⢿⣿⣿⠏⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣯⣴⣾⣿⣿⣿⣿⢻⣿⢰⣿⣿⣿⣿⣆⠙⣱⣿⣿⣿⣿⡆⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⠿⠋⢻⣿⣦⣾⣿⠏⠀⠀⠀⠀⠄⢡⠿⠻⢛⠟⢡⣿⣿⣿⣿⣿⣿⣿⡏⢿⡏⣿⣏⣿⣿⣿⡇⢻⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣤⣾⣿⣿⣿⠿⠿⠿⢿⡿⠉⠀⠀⠀⠈⠻⠿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⣿⡿⡿⠿⣿⣿⣿⣿⣧⡘⣷⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠛⠃⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠛⠋⠉⠉⠁⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠉⣿⣧⣤⣼⣥⣭⣿⣿⣿⡆⢹⣿⡪⡻⣿⣿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢸⣿⣷⠀⠉⠹⢎⣿⣿⣿⣿⣿⣀⣤⣤⣄⠀⠀⣠⣤⣤⡀⠀⢁⣤⣤⣄⢾⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣤⣶⣶⠾⠃⠀⠀⠀⠀⢀⡀⠀⠀⣀⣴⣿⣀⣀⣀⣀⣄⡄⠐⣿⣿⠟⠛⠛⠻⣿⣿⣿⠛⠛⠁⠀⠈⠏⠛⠀⠀⠀⣾⣿⣿⣿⣿⣧⣿⣿⢹⣿⡇⢸⣿⡏⣽⣿⠀⣿⡿⢿⣿⡏⠧⠄⠀⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣻⠟⠀⠀⠀⣀⢀⣤⣴⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⠁⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⣳⣿⣟⣾⣿⢯⣾⡿⠃⠀⠀⠀⠈⠁⠀⠀⠀ ⠀⠀⠀⣠⣶⣿⠏⠀⠀⠀⠀⠈⠉⠉⠉⢻⢿⠏⠙⠿⣿⣿⡿⠛⠛⠛⢿⣿⡀⠀⠀⠀⠉⠉⠛⠟⠁⠀⠀⠀⠀⠀⠀⠀⣶⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⡇⠛⣽⣿⢯⣾⣿⣫⣿⡟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢿⠇⠿⠇⠿⠏⠿⠿⠿⠿⠷⣇⠻⠿⠾⠿⠃⠸⠿⠿⠿⠿⠀⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣷⣤⣤⣀⣀⣀⣀⣀⣴⣶⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢋⣡⣤⣶⣿⣿⣿⣿⣿⣿⣷⠉⠙⢳⡀⠀⣀⣠⣶⣿⠁⠀⠀⠀⠀⢀⣼⡿⠀⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣶⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⡆⠀⠀⠹⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣴⣶ ⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣠⡤⠀⠁⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠃⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢻⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢛⠛⠛⠛⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣯⡾⠟⡠⠂⠀⠀⡠⣾⠿⣿⠿⣿⣿⣿⣍⣿⢿⡏⠁⠙⠿⡦⡀⠀⠀⠀⠘⣿⣿⣿⡿⠛⠉⣹⣿⣿⣿⣷⣦⣠⣀⣤⣶⣶⣾⣿⣿ ⠀⠖⠲⣶⠏⢶⠆⠰⠶⠶⠶⠒⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⠋⠁⠀⡼⠁⠀⠀⠐⠘⠁⡈⣯⢶⠦⣿⣿⣭⣯⣿⣇⣷⡄⠀⠀⠀⢀⠀⠀⠀⠹⣿⣿⣿⠇⠀⠙⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⠈⡦⠼⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠰⠚⠛⠋⠀⠀⣠⣴⣶⣿⣿⡄⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⣠⣾⣿⣵⣿⣿⣿⠿⠿⣿⣿⣶⣸⣿⡄⠻⣿⣿⣿⣿⠁⠀⠀⢀⣶⣶⡄⠀⠀⠀⠀⠀⣸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣥⣼⣿⣧⠀⠀⠀⢿⣿⣿⠋⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣯⣴⣾⣿⣿⣿⣿⢻⣿⢰⣿⣿⣿⣿⣆⠈⢨⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⣿⣿⠿⠋⢻⣿⣦⣾⣿⠇⠀⠀⠀⠀⠈⢱⠿⠻⢛⠟⢁⣿⣿⣿⣿⣿⣿⣿⡏⢿⡏⣿⣯⣿⣿⣿⡇⣸⣿⣿⣿⣿⡇⠀⠀⠀⢰⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣤⣾⣿⣿⡿⠿⠿⠿⢿⡟⠉⠀⠀⠀⠈⠻⢿⡿⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣠⣿⡿⡿⠿⣿⣿⣿⣿⣧⡈⣷⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠛⠋⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠛⠋⠉⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠉⣿⣧⣤⣼⣥⣭⣿⣿⣿⡆⢹⣿⡦⡻⢿⣿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣷⠀⠀⠹⢆⣿⣿⣿⣿⣿⣀⣤⣤⣄⠀⠀⣠⣤⣤⡀⠀⢀⣤⣤⣄⢴⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⣴⣶⠾⠂⠀⠀⠀⠀⢀⠀⠀⠀⢠⣴⣿⣀⡀⣀⣀⣀⡀⠐⣿⣿⡟⠛⠛⠻⢿⣿⡿⠛⠛⠁⠀⠀⠏⠛⠀⠀⠀⣾⣿⣿⣿⣿⣧⣿⣿⢹⣿⡇⢸⣿⣏⣽⣿⠀⣿⡿⢿⣿⡏⠯⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡿⠏⠀⠀⠀⣀⢀⣀⣴⣿⣷⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⠁⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⡶⣲⣿⣟⣾⣿⢯⣾⡿⠃⠀⠀⠀⠀⠁⠀⠀⠀ ⠀⠀⠀⣠⣾⡿⠃⠀⠀⠀⠀⠁⠉⠁⠉⠛⢿⠏⠉⠛⢿⣿⡿⠛⠻⠿⢿⣿⡀⠀⠀⠀⠉⠉⠛⠿⠁⠀⠀⠀⠀⠀⠀⠀⣶⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⡏⠛⣽⣿⢯⣾⣿⣫⣿⡟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢿⠇⠿⠇⠿⠏⠿⠿⠿⠿⠷⣇⠻⠿⠾⠿⠃⠸⠿⠿⠿⠿⠀⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣿⣦⣤⣄⣀⣀⣀⣀⣀⣴⣶⣾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⣉⣤⣶⣾⣿⣿⣷⣿⣾⣿⠉⠙⠳⡀⠀⠀⣀⣴⣿⠃⠀⠀⠀⠀⢀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⣶⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣯⣇⣿⣿⣿⣿⣿⣿⡆⠀⠀⠘⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣤⣤⣴ ⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣀⡠⠔⠀⠀⠀⢀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠓⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⣿⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡴⠟⡡⠂⠀⠀⣀⣾⡿⣿⠿⣿⣿⣿⣉⣿⢿⣏⠁⠹⠻⡦⡀⠀⠀⠀⠈⣿⣿⣿⡿⠟⠋⢙⣿⣿⣿⣿⣦⣀⣀⣠⣴⣶⣾⣿⣿ ⠀⠖⠲⣶⠏⢶⠆⠰⠶⠶⠶⠒⢶⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⠿⣿⣿⣿⠏⠈⠀⡼⠃⠀⠀⠐⠙⠋⡀⣯⢴⡧⣿⣿⢩⣿⣿⣷⣷⡄⠀⠁⠀⢀⠀⠀⠀⠘⣿⣿⣿⠇⠀⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢼⣿⣧⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠐⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢑⡦⠽⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠰⠛⠙⠁⠀⢀⣠⣴⣾⣿⣷⡀⠀⠀⢀⣿⣿⣿⣿⠀⠀⠀⠀⣠⣾⣿⣵⣾⣿⣿⡿⠿⣿⣿⣶⣸⣷⡤⢻⣿⣿⣿⣿⠄⠀⣀⢠⣶⣶⡄⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣥⣼⣿⣇⠀⠀⠘⣿⣿⣿⠋⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣏⣴⣾⣿⣿⣿⡟⢻⣷⢰⣿⣿⣿⣿⣦⠐⢛⣼⣿⣿⣿⡇⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⣿⣿⣿⡿⠟⠙⢿⣷⣶⣿⡿⠃⠀⠀⠀⠀⡈⢱⡿⠻⢿⡟⢡⣿⣿⣿⣿⣿⣿⣿⡎⢿⡏⣿⣎⣿⣿⣿⡇⣸⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣴⣿⣿⣿⡿⠿⠿⠿⣿⠟⠁⠀⠀⠀⠘⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⢀⣿⣿⡿⠿⣿⣿⣿⣿⣧⡘⣷⡘⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠙⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠋⠙⠉⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠛⣿⣇⣀⣼⣩⣽⣿⣿⣿⡆⢹⣿⡮⡻⣿⣿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣤⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣷⠀⠉⠹⢆⣿⣿⣿⣿⣿⣀⣤⣤⣄⠀⠀⣠⣤⣤⡀⠀⢀⣤⣤⣄⢰⣾⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣤⣶⡶⠞⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣀⠀⣀⣀⣀⡀⠸⣿⣿⡿⠿⠛⢻⣿⣿⣿⠛⠟⠁⠀⠀⠏⠻⠀⠀⠀⣾⣿⣿⣿⣿⣧⣿⣿⢹⣿⡇⢸⣿⡏⣽⣿⠀⣿⡟⢽⣿⡏⠿⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⠿⠃⠀⠀⠀⣀⣀⣠⣴⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣲⣿⣟⣾⣾⢿⣾⡿⠃⠀⠀⠀⠀⠁⠀⠀⠀ ⠀⠀⢀⣠⣾⡿⠀⠀⠀⠀⠀⠁⠊⠉⠉⢹⣿⠹⠛⠻⣿⣿⠿⠻⠻⠿⢿⣿⠀⠀⠀⠀⠀⠉⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⢴⣿⠿⢿⣿⣿⡿⣿⣿⣿⣿⣿⢻⣿⡇⠛⣽⣿⢯⣾⣿⣫⣿⡟⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⡇⠿⠇⠿⠏⠿⠿⠿⠿⠷⣧⠻⠿⠾⠿⠃⠸⠿⠿⠿⠿⠀⠿⠿⠿⠿⢇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣷⣦⣀⣀⣀⣀⣀⠀⣀⣤⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⣉⣥⣴⣶⣿⣿⣿⣦⣿⣷⠉⠙⠳⡄⠀⠀⢀⣴⣾⠋⠀⠀⠀⠀⠀⣠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣦⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣤⠀⠀⠘⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣷⣾⣿⣶⣤⣄⣀⣀⣤ ⠀⠀⠀⠀⠀⠈⠙⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⣀⠄⠀⠀⠀⠀⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣴⠟⢡⠂⠀⠀⢀⣺⣿⣿⡿⣿⣿⣿⡏⣿⣿⣏⠋⠹⢻⣦⡀⠀⠀⠀⠈⢿⣿⣿⣿⠿⠛⠛⣿⣿⣿⣿⣭⣉⠉⣀⣠⣤⣴⣿⣿ ⠀⠖⠲⣶⠎⢶⠦⠰⠶⠶⠶⢒⣴⣶⣶⣷⣷⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠈⠁⡴⠃⠀⠀⠀⠙⠋⠀⢫⣤⣍⣽⣿⣋⣿⣲⣿⣶⡄⠀⠉⠀⢀⠀⠀⠀⠘⣿⣿⣿⡗⠀⠘⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢰⣿⣿⣧⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢆⡈⢳⡤⢽⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⠟⠛⠛⠁⠀⣀⣤⣾⣿⣿⣿⡀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⣰⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣆⣼⣷⡜⢿⣿⣿⣿⣿⣿⠆⣠⣀⣶⣶⣆⡀⠀⠀⠀⠀⢠⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⠀⠀⠀⢀⣴⣿⣿⣿⣷⣿⣿⣇⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣏⣤⣾⣿⣿⣿⡟⣿⣷⣾⣿⣿⣿⣿⣶⠘⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⡿⠟⠛⣿⣿⣶⣿⣿⠇⠀⠀⠀⠀⠛⢹⡿⢿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣷⠸⣿⡼⣿⣟⣿⣿⣿⣿⣽⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⡇⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣴⣿⣿⣿⡿⠿⠿⠿⣿⠛⠁⠀⠀⠀⠻⠿⣿⡿⠃⠀⠀⠀⠀⠈⠀⠋⠀⠀⠊⢠⣿⣿⣿⣿⣿⣿⣿⣿⣅⠸⣧⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠛⠟⠀⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠛⠛⠛⠁⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⢻⣿⣏⠁⣸⣛⣻⣿⣿⣿⡅⢻⣷⡪⠻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⡀⠀⠀⠀⢠⠀⠀⢈⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⣧⠑⠉⢻⣎⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣰⣾⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣴⣶⣾⠿⠆⠀⠀⠀⢀⣠⡀⠈⣠⣿⣿⣧⣀⣀⣀⣠⣠⠀⢸⣿⣿⣿⣿⠿⢿⣿⣿⣿⠿⠿⠃⠀⠘⡟⠿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣶⣶⣿⣿⣿⣥⣀⣀⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⣹⡿⠉⠀⠀⠀⣄⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠻⠋⠁⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠀⠀⠉⠉⠂⠀⠀ ⠀⠀⢀⣴⣾⡧⠀⠀⠀⠀⠘⠛⠉⠛⠛⣿⣿⣿⢿⣿⣿⣿⣿⠿⡿⢿⣿⣿⠀⠀⠀⠀⠐⠒⣾⣶⠆⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠉⠉⠀⠀⠀⠀⠉⠛⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠿⠿⣛⣫⣽⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⢀⣿⣿⠿⠛⠋⠉⠙⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣶⣦⣀⣀⣀⣀⣀⣀⣠⣴⣾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⢋⣡⣴⣶⣿⣿⣿⣷⣿⣿⡟⠛⠷⡄⠀⠀⢀⣴⣿⡟⠁⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣷⡀⠀⠙⢿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣷⣾⣿⣶⣦⣄⣀⣀⣤ ⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⣀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠙⠛⠿⡿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣴⠟⢋⠔⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⠛⢛⢿⣷⡀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠛⠛⣿⣿⣿⣿⣯⣋⠉⢉⣀⣤⣤⣾⣿ ⠀⠖⠶⣶⠎⢶⠶⠰⠶⠶⢶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⣴⠃⠀⠀⠠⠿⡿⠉⣿⣥⣏⣽⣿⣟⣻⣺⣿⣴⡄⠀⠉⠈⠀⠀⠀⠀⠈⣿⣿⣿⣷⠀⠀⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⡴⣾⣿⣷⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠂⠉⢢⣬⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡠⠞⠛⠙⠀⠀⣀⣴⣾⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⡿⠀⠀⠀⠀⣴⣿⣟⣿⣿⣿⣿⣿⣿⣿⣯⣄⣿⣦⠜⣿⣿⣿⣿⣿⣿⡧⣆⣠⣶⣾⣆⡀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣤⣿⣿⡆⠀⠀⠸⣿⣿⡿⠃⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠏⣩⣿⣿⣿⣿⡿⣿⡇⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⡿⠟⢻⣿⣷⣼⣿⡿⠁⠀⠀⠀⠀⡿⣹⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣷⠹⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣾⣿⣿⣿⡿⢿⠿⢿⣿⠋⠁⠀⠀⠀⠻⠿⣿⠟⠁⠀⠀⠀⠀⠀⠠⠋⠁⠁⠛⢠⣿⣿⣿⣿⣿⣿⣿⣿⡀⢹⣧⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠛⠿⠁⢺⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠋⠛⠋⠁⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⡛⠉⣹⠛⣿⣿⣿⣿⠀⢻⣷⣜⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢄⠀⠀⢈⣉⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⣧⠡⠙⢻⣎⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⣠⣾⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⣤⣶⡿⠯⠀⠀⠀⠀⢀⣀⡀⢈⣀⣶⣿⣧⣄⣀⣀⣄⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠋⠀⠘⡟⠿⠀⠀⠀⢘⣿⣿⣿⣿⣿⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣤⣶⣾⣿⣿⣧⡀⡀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⡿⡿⠁⠀⠀⢀⣄⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠈⠿⠛⠋⠁⠀⠈⠛⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠁⠈⠁⠉⠉⠀⠀ ⠀⠀⣀⣴⣿⡎⠀⠀⠀⠀⠙⠙⠛⠛⠛⣿⣿⡟⠿⣿⣿⣿⣿⠿⠿⢿⣿⣿⠀⠀⠀⠀⠤⠶⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠈⠛⠋⠀⠀⠀⠀⠉⠹⠆⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣠⣴⡿⠿⠿⣛⣛⣹⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⢀⣾⣿⡿⠛⠛⠉⠙⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣶⣄⣀⣀⣀⣀⡀⣀⣠⣴⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠞⠛⣉⣤⣶⣾⣿⣿⣷⣿⣿⡟⠛⠷⡆⠀⠀⠀⣠⣾⡟⠋⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣴⣶⣶⣶⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⡆⠀⠈⢷⣿⣿⣿⣿⣷⣶⣶⣶⣿⣷⣿⣿⣷⣶⣿⣶⣦⣄⣀⣀⣀ ⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣀⡠⢀⠀⠀⠀⡠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠿⠿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣤⡿⢋⠔⠁⠀⢀⣴⣿⣿⣿⣿⣿⣿⣟⢻⣿⣿⠟⢛⣿⣷⡄⠀⠀⠀⠀⢻⣿⣿⣿⣿⠟⠛⣿⣿⣿⣿⣿⡋⠉⠉⢉⣥⣤⣤⣿ ⠀⠖⠶⣶⠎⢶⠦⠰⠶⠶⣶⣤⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⣰⠏⠀⠀⣠⠿⣿⠏⣿⣯⣏⣻⣿⡟⣻⣶⣿⣷⡄⠀⠙⠉⠀⠀⠀⠀⠈⢿⣿⣿⣿⠄⠀⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢨⣿⣿⡤⠀⠀⠀⠀⣸⣿⡿⠀⠀⠀⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠂⠉⣦⢬⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠰⠞⠛⠉⠀⠀⣠⣴⣿⣿⣿⣧⠀⠀⠀⣸⣿⣿⣿⡯⠀⠀⠀⠀⣴⣿⣟⣿⣿⣿⣿⣿⣿⣿⣯⣀⣿⣦⠜⣿⣿⣿⣿⣿⡿⠤⣦⣀⣾⣿⣶⡀⠀⠀⠀⠀⢀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣴⣿⣿⡄⡀⠀⢿⣿⣿⡿⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⢋⣹⣿⣿⣿⣿⡿⣿⡇⣿⣿⣿⣿⣿⣬⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⣿⣿⠿⠛⢻⣿⣷⣼⣿⡿⠁⠀⠀⠀⠰⠟⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣷⢹⣿⢹⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⣿⡟⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣤⣾⣿⣿⣿⠿⠿⠿⢿⡿⠋⠀⠀⠀⠀⠿⢿⣿⠟⠁⠀⠀⠀⠀⠁⠠⠋⠁⢁⠋⢠⣿⣿⣿⣿⣿⣿⣿⣿⡀⢻⣧⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⠿⠃⢚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠛⠛⠋⠉⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠰⢾⣿⠛⠉⣹⠛⣿⣿⣿⣿⠀⢿⣷⣜⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠄⠀⠀⢈⣩⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⣧⠡⠙⢻⣞⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣤⣤⣶⣿⡿⠃⠀⠀⠀⢀⣀⠀⠙⢴⣿⣿⣧⣀⣀⣀⣤⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠋⠀⠘⡟⠿⠀⠀⠀⢘⣿⣿⣿⣿⣿⣁⣀⠀⣀⣀⣀⡀⣀⣀⣀⡀⣰⣴⣴⣾⣿⣿⣧⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢐⣿⡟⠁⠀⢀⣀⣠⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠘⢿⠟⠉⠉⠀⠈⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠁⠁⠀⠀⠉⠉⠀⠀ ⠀⠀⣀⣴⣿⠂⠀⠀⠀⠐⠋⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠠⡤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⡀⠙⠛⠋⠀⠀⠀⠈⠘⠿⡆⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠿⢟⣛⣫⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⣼⣿⣿⠿⠻⠛⠛⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣷⣄⣀⣀⡀⣀⣀⣀⣠⣴⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠛⣉⣠⣴⣾⣿⣿⣶⣾⣿⡟⠛⢷⣦⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣴⣶⣶⣶⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⡄⠀⠉⢶⣶⣿⣿⣿⣷⣴⣶⣶⣾⣶⣾⣿⣿⣶⣶⣶⣦⣄⡀⠀⣀ ⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⡀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣤⡾⢋⡔⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⠛⠛⣿⣷⡀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠿⠟⢿⣿⣿⣿⣿⡟⠋⠉⠉⣩⣀⣤⣼ ⠀⠖⠶⣶⠎⢶⠶⠰⠶⢶⣶⣤⣤⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⣰⠟⠀⠀⢀⠾⣿⠟⢿⣏⣛⣻⣿⣿⢻⠯⣿⣧⡄⠀⠙⠛⠂⡀⠀⠀⠀⢿⣿⣿⣿⡆⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢘⣿⣿⠀⠀⠀⠀⠀⣸⣿⡿⠀⠀⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⢆⠈⢲⠤⢿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠁⠀⢀⣠⣴⣿⣿⣿⣇⠀⠀⠀⣼⣿⣿⣿⡇⠀⠀⠀⢀⣴⣿⣿⣽⣿⣿⣿⣿⣿⣿⣷⣆⣿⣧⠜⣿⣿⣿⣿⣿⣿⣇⣂⣀⣼⣷⣦⡀⠀⠀⠀⠀⠀⣼⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣾⣿⣿⡀⠀⠀⣿⣿⣿⡟⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⢋⣩⣿⣿⣿⣽⡟⣿⣇⣾⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⣤⣾⣿⣿⣿⣿⣿⣿⠿⠛⢽⣿⣷⣾⣿⡿⠀⠀⠀⠀⠐⡟⣽⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣷⠹⣿⡹⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⠀⠀⠀⠀⢼⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣰⣿⣿⣿⡿⠿⠿⠿⣿⡟⠉⠀⠀⠀⠈⠻⣿⡿⠟⠀⠀⠀⠀⠀⠀⠰⠋⠀⠁⠋⢰⣿⣿⣿⣿⣿⣿⣿⣿⡄⢹⣧⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠛⠛⠛⠉⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⣿⡛⠉⣻⠛⣻⣿⣿⣿⠄⢻⣷⣌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠇⠀⠀⢊⣉⢤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⣧⠑⡙⠻⣾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⣶⡾⠗⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣆⠀⢀⣀⣀⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠋⠀⠈⡟⠿⠀⠀⠀⢘⣿⣿⣿⣿⣿⣇⣀⡀⠀⢀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣶⣿⣿⣟⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⠛⠁⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠘⢿⠛⠋⠁⠀⠈⠛⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠀⠀⠀⠀⠁⠀⠀ ⠀⠀⣠⣶⡆⠀⠀⠀⠀⠈⠊⠛⠛⠟⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⠀⠀⠀⠀⠠⢤⣶⣴⠄⠀⠀⠀⠀⠀⠀⠠⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠘⠟⠁⠀⠀⠀⠈⠛⢻⣆⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠿⠟⣛⣫⣿⣿⣿⣿⡟⠙⠁⠀⠁⠀⠀⣸⣿⡿⠿⠻⠛⠛⢻⣿⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⣷⣀⣀⠀⠀⠀⢀⣀⣤⣴⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠛⢋⣡⣴⣶⣿⣿⣷⣿⣿⡿⠟⢷⣤⠀⠀⠀⢠⣴⣿⠏⠀⠀⠀⠀⠀⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⣦⣤⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣻⢹⣿⣿⣿⣿⣿⣿⡇⠁⠉⢶⣶⣾⣿⣿⣷⣤⣶⣶⣶⣶⣶⣿⣿⣶⣶⣶⣦⣄⡀⠀⠀ ⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⡀⠄⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣠⡾⠛⡥⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡿⠛⡿⣷⡀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⡟⠛⠉⠉⢉⣁⣀⣤ ⠀⠖⠶⣶⠎⢶⠶⠰⠶⠶⣶⢠⣤⣤⣤⣴⣦⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⣠⠎⠀⠀⢀⣾⣿⡏⢿⣏⣛⢛⣿⣿⢿⠯⣿⣧⡄⠁⠙⠓⠂⠀⠀⠀⠀⢻⣿⣿⣿⡆⠀⢾⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡷⣀⡀⢱⡤⠼⣿⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠘⡅⠀⠀⠀⠀⣴⣿⣿⣿⠀⠀⠀⠀⠀⣴⡿⣫⣴⣿⣿⣿⣿⣿⣿⣷⡂⣼⡅⠄⢻⣿⣿⣿⣷⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣐⣶⣷⣤⣤⣶⡄⠀⠀⠀⢹⣿⡿⠋⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣯⠃⣠⣾⣿⣿⣵⡏⢷⣷⢠⡿⣿⣿⣿⣆⠀⠀⠀⣾⣿⣿⣷⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⣠⣶⣿⣿⣿⣿⣿⠿⠛⠀⠀⢠⡄⢠⡿⠂⠀⠀⠀⠀⠀⠀⣼⠿⡻⢿⠞⢱⣻⣿⣿⣿⣿⣿⡇⠘⣿⡎⣿⣝⣿⣿⣿⡄⠀⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣾⣿⣿⠿⠿⠿⠛⠟⠋⠁⠀⠀⠀⠀⠈⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣄⠈⣧⡀⢻⣎⣿⣿⣧⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⣿⠁⠁⣰⢛⣛⣿⣿⣷⠀⢹⣷⡈⠻⣿⣿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣿⣷⠀⠀⠙⠆⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢀⣀⣀⣀⣀⢀⣀⣀⠀⣀⣸⣿⣿⣿⣿⠿⢿⣿⣿⡿⣛⣛⣁⠀⠀⡏⣛⣀⣀⠀⠀⣿⣿⣿⣿⣿⠀⣀⣀⠀⠀⣀⣀⣀⠀⠀⠀⠀⢀⣀⠀⢰⡿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠙⣿⣷⢘⣻⣿⣿⣛⣸⣿⣿⡇⣿⣿⠙⠁⣿⣿⠀⠀⠉⠉⣾⣿⠛⣿⣷⠀⣾⣿⠛⣿⣷⡄⣿⣿⣿⣿⣿⡼⣿⣿⡀⣾⣿⠙⣿⣷⣶⣦⣼⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣤⡀⠀⢸⣿⣿⠛⢻⣿⣿⠇⣿⣿⠀⠀⣿⣿⠐⠂⠴⠀⣿⣿⢀⣉⣉⠀⣿⣿⠀⣿⣿⡇⣿⣿⢿⣿⣿⣿⣿⣿⠀⣿⣿⢀⣉⣉⢰⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣬⠙⣿⣷⠀⢸⣿⣿⠀⠈⣿⣿⠀⣿⣿⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿⠈⣿⣿⠀⣿⣿⠀⣿⣿⠃⣿⣿⠘⣿⣿⢻⣿⣿⠀⣿⣿⠈⣿⣿⠘⠁⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣿⢟⣀⢸⣿⣿⠀⠀⣿⣿⠀⣿⣿⣶⡆⣿⣿⣶⡆⠀⠀⠻⣿⣶⢿⣿⠘⠻⣿⣶⣿⠟⠀⣿⣿⠀⣿⣿⠙⣿⣿⠀⠻⣿⣶⢿⣿⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣠⣤⣶⣶⣾⣿⣿⣿⣿⣶⣿⣶⣶⣶⣶⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡒⠀⢸⡟⣫⡴⣦⡔⠀⠀⠀⠀⢠⣶⣶⣶⣶⣧⣤⣤⣤⣴⣦⣤⣾⣷⣤⣤⣤⣤⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣿⣶⣾⣿⢿⣿⣿⡛⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠻⠿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⣿⣿⣿⠟⠻⡿⠷⠘⠙⠻⢄⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡿⠿⠻⣿⣛⣛⠛⠉⠉⠉⠉⠉⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠰⠶⠶⠶⠀⢀⣀⣀⣀⣀⣀⣀⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢠⠌⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⣠⡖⠸⠅⣩⡀⡀⠀⠈⠁⠀⠀⠀⠀⠀⢻⣿⣿⣤⡀⠀⠀⢿⣿⣿⣿⣷⣤⣤⣶⣾⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⢸⣿⣿⣏⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⢿⣃⠀⠈⡶⠰⢿⡿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢸⡄⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⠀⠀⠀⣴⣿⣫⣴⣿⣿⣿⠿⠿⣿⣿⣆⣸⣧⠄⠻⣷⣿⣿⣿⠀⠀⠀⠀⢀⣤⣤⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡘⣾⣧⣤⣴⣶⠀⠀⠀⠀⢻⣿⡿⠋⠀⠀⠀⠀⠘⡿⣿⣿⣿⣿⡫⡆⣠⣾⣿⣿⣧⣟⢻⣷⣰⣻⣿⣿⣿⣧⠀⠀⠀⣾⣿⣿⣷⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣀⣤⣾⣿⣿⣿⣿⣿⠿⠋⠀⠀⣤⣀⣠⡟⠀⠀⠀⠀⠀⠀⠀⣼⠟⠻⢿⠟⠠⣿⣿⣿⣿⣿⣿⣿⠆⢿⡇⢿⣟⢿⣿⣿⣇⠀⢠⣾⣿⣿⣿⠀⠀⠀⠀⠀⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⡿⠿⠟⠛⠛⠛⠉⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⣿⣿⣿⣿⣆⠀⢻⡄⠹⣧⣻⣿⣿⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠙⣿⡀⡀⣠⣋⣙⣿⣿⣿⡄⠘⣿⡄⠙⢿⣿⠻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⣐⣿⣥⣤⣴⣶⠀⠀⠀⠀⢿⣿⡿⠃⠀⠀⠀⠀⠘⡿⣿⣿⣿⣿⡯⡆⣠⣾⣿⣿⣷⣿⠸⣿⡆⣼⣿⣿⣿⣷⡀⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⡿⠟⠃⠀⠀⣤⣀⣴⠍⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⢻⠟⢀⣻⣿⣿⣿⣿⣿⣿⠀⠻⣧⢹⣿⡻⣿⣿⣧⠀⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⣿⡿⠿⠿⠛⠛⠛⠉⠀⠀⠀⠀⠀⠙⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠿⣿⣿⣿⣿⣧⡀⢹⣄⠘⣷⣹⣿⣿⣦⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⣿⣄⣀⣠⣋⣉⣿⣿⣿⡆⠘⣿⣆⠜⢿⣿⡾⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣐⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣿⣿⡄⠀⠈⠷⢸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢀⣀⣀⣀⣀⢀⣀⣀⠀⣀⣸⣿⡿⣿⣿⠿⠿⣿⣿⡿⣛⣙⣃⠀⠀⠻⣛⣃⣀⠀⠀⣸⣿⣿⣿⣿⡇⣀⣀⠀⠀⣀⣀⣀⠀⠀⠀⠀⢀⣀⡀⠀⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠙⣿⣧⠘⣻⣿⣿⣛⣸⣿⣿⡇⣿⣿⠈⠀⣿⣿⠀⠀⠀⠀⣾⣿⠛⣿⣷⠀⣾⣿⠛⣿⣷⡄⣿⣿⣿⣿⣿⡽⣿⣿⠀⣾⣿⠙⣿⣷⣶⣆⣴⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣤⡀⠀⢻⣿⣿⠛⢻⣿⣿⠇⣿⣿⠀⠀⣿⣿⠀⠀⠴⠂⣿⣿⢀⣉⣉⠀⣿⣿⠀⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⢀⣉⣉⠈⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣬⠙⣿⣷⠀⢸⣿⣿⠀⠀⣿⣿⠀⣿⣿⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿⠈⣿⣿⠀⣿⣿⠀⣿⣿⠇⣿⣿⠘⣿⣿⢻⣿⣿⠀⣿⣿⠈⣿⣿⠐⠋⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣿⢟⠀⢸⣿⣿⠀⠀⣿⣿⠀⣿⣿⣶⡆⣿⣿⣶⡆⠀⠀⠻⣿⣶⢿⣿⠘⠻⣿⣶⣿⠟⠀⣿⣿⠀⣿⣿⠛⣿⣿⠀⠻⣿⣶⢿⣿⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣴⣶⣶⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⣶⡶⠂⠘⡟⢿⣶⣦⡴⠄⠀⠀⠀⢠⣴⣶⣶⣶⣧⣀⣤⣤⣤⣤⣤⣤⣾⣥⣠⣤⣤⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣾⣿⡿⣿⣿⡻⠇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢟⣿⣿⣿⡿⠿⣿⡿⠽⠛⢻⢆⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠿⢿⣛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠰⠶⠶⠖⠀⠀⣀⣀⣀⣀⣀⣀⣈⣭⣽⣿⣿⣿⣿⣿⣿⣿⡟⠀⠂⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢡⣴⠰⣏⣉⡀⡀⠀⠈⠇⠀⠀⠀⠀⠀⠹⣿⣿⣭⡀⠀⠀⣾⣿⣿⣿⣷⣤⣤⣤⣴⣾⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣿⡿⢿⣿⣿⣿⣿⣿⣯⠤⠀⣸⠒⢻⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠣⠀⠀⠀⠀⠀⣾⣿⣿⡿⠀⠀⠀⠀⠀⣴⣿⣫⣴⣿⣿⣿⠿⠟⣿⣿⣯⢠⣿⡤⠈⢿⣿⣿⣿⡇⠀⠀⠀⢀⣤⣤⠀⠀⠀⠀⠀⠀⢀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣁⣿⣦⣤⣶⣶⠀⠀⠀⠀⢿⣿⠟⠁⠀⠀⠀⠀⠘⡯⣿⣿⣿⢿⡯⡆⣠⣾⣿⣿⣿⣿⠙⣿⡆⣾⣿⣿⣿⣿⡄⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⣠⣴⣾⣿⣿⣿⣿⡿⠟⠁⠀⢠⣤⣀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠸⠟⠙⢻⠏⢀⣿⣿⣿⣿⣿⣿⣿⡀⠹⣷⠹⣷⡻⣿⣿⣧⠀⢠⣾⣿⣿⣿⠀⠀⠀⠀⠀⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⣿⡿⠿⠿⠛⠛⠛⠁⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠿⢿⣿⣿⣿⣧⡀⢹⣆⠉⣿⡼⣿⣿⣧⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⣿⣄⣀⣠⣋⣩⣿⣿⣿⡇⠈⣿⣧⠈⢻⣿⡞⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣐⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣾⣿⡆⠀⠈⠳⢸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢀⣀⣀⣀⣀⢀⣀⣀⠀⣀⣸⣿⡿⣿⣿⠿⠿⣿⣿⡿⣛⣙⣋⠀⠀⠹⣙⣃⣀⠀⠀⣸⣿⣿⣿⣿⡇⣀⣀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⣀⡀⢐⣾⠿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠙⣿⣧⡘⣻⣿⣿⣛⣸⣿⣿⡇⣿⣿⠈⠀⣿⣿⠀⠀⠀⠀⣾⣿⠙⣿⣷⠀⣾⣿⠛⣿⣷⠄⣿⣿⣿⣿⣿⡽⣿⣿⡀⣾⣿⠙⣿⣷⣶⣆⣀⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣤⡀⠀⢿⣿⣿⠛⢻⣿⣿⠃⣿⣿⠀⠀⣿⣿⠀⠀⠴⠂⣿⣿⢀⣉⣉⠀⣿⣿⠀⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⢀⣉⣉⠈⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⢂⣧⣤⣴⣶⠆⠀⠀⠀⠈⢿⣿⠟⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⢿⡯⡂⣠⣾⣿⣿⣿⣿⠘⣿⡇⣾⣿⣿⣿⣿⡄⠀⠀⢸⣿⣿⣿⡆⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⣿⠿⠋⠀⠀⢠⣤⢀⡾⠂⠀⠀⠀⠀⠀⠀⠀⡼⠟⠙⢚⠏⢀⣹⣿⣿⣿⣿⣿⣿⡀⠹⣿⠸⣷⡹⣿⣿⣿⡀⢀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠐⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⣿⡿⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠙⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠿⢿⣿⣿⣿⣧⡀⢹⣆⠉⢿⣼⣿⣿⣧⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠙⣿⡄⡀⣠⣋⣉⣿⣿⣿⣇⠈⢿⣧⢈⠻⣿⡟⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢸⣿⡆⠀⠈⠻⡘⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢀⣀⣀⣀⣀⢀⣀⣀⠀⣀⣸⣿⡿⣿⣿⠿⠿⣿⣿⡿⣟⣛⣋⠀⠀⠸⣙⣃⣀⠀⠀⣰⣿⣿⣿⣿⣇⣀⣀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⢀⠀⠀⢰⡿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠙⣿⣧⠘⣻⣿⣿⣛⣸⣿⣿⡇⣿⣿⠉⠁⣿⣿⠀⠀⠉⠉⣾⣿⠛⣿⣷⠀⣾⣿⠛⣿⣷⠀⣿⣿⣿⣿⣿⡽⣿⣿⡀⣾⣿⠙⣿⣷⣶⣦⣀⣴⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣤⡀⠀⢿⣿⣿⠛⢻⣿⣿⠇⣿⣿⠀⠀⣿⣿⠀⠀⣤⠂⣿⣿⢀⣉⣉⠀⣿⣿⠀⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⢀⣉⣉⠈⢉⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣬⠙⣿⣷⠀⢸⣿⣿⠀⠈⣿⣿⠀⣿⣿⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿⠈⣿⣿⠀⣿⣿⠀⣿⣿⠅⣿⣿⠰⣿⣿⢿⣿⣿⠀⣿⣿⠈⣿⣿⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣿⠟⠀⢸⣿⣿⠀⠀⣿⣿⠀⣿⣿⣶⡆⣿⣿⣶⡆⠀⠀⠻⣿⣶⢿⣿⠰⠻⣿⣶⣿⠟⠀⣿⣿⠀⣿⣿⠛⣿⣿⠀⠻⣿⣶⢿⣿⠀⠀⠀⠀⠀⠀⠀⣸⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣾⣿⣿⣶⣶⣶⣶⣦⣤⣤⣶⣶⣶⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⣦⡖⠆⠀⡿⠶⢶⣦⣤⠀⠀⠀⠀⠀⣤⣤⣤⣶⣷⣀⣀⣀⣀⣤⣤⣀⣤⣦⣀⣀⣀⣀⠀⠀⠀ ⠀⠀⠀⠀⠰⢶⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣦⣤⣿⣿⣿⣿⡿⠆⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀ ⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⣿⣿⣿⡿⠿⣿⣿⠙⠟⢻⣆⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠿⢿⣿⠟⠛⠿⠛⠛⠛⠛⠛⠉⠀ ⠀⠄⠲⣶⠀⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠉⠉⠉⠉⣉⣩⣿⣿⣿⣿⣿⣿⣿⣿⡿⠠⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⢋⣠⠀⣟⠘⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠘⣿⣿⣿⡉⠁⠀⢀⣽⣿⣷⣶⣄⣀⣀⣀⣤⣴⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⣸⣿⠿⢿⣿⣿⣿⣿⣿⣯⠤⠀⣼⠒⢻⣿⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⢀⣼⣿⣥⣾⣿⣿⡿⠿⠛⣿⣿⣿⢰⣿⣔⠈⢻⣿⣿⣿⡇⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⣠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣤⣴⣶⠆⠀⠀⠀⠈⢿⡿⠋⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⢟⡯⡇⣤⣾⣿⣿⣿⣿⠘⣿⡇⣾⣿⣿⣿⣿⣆⠀⠀⢸⣿⣿⣿⡆⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣀⣤⣶⣿⣿⣿⣿⣿⠿⠋⠀⠀⠠⣄⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⡼⠛⠙⢻⠏⢀⣻⣿⣿⣿⣿⣿⣿⠀⠹⣿⠸⣷⡙⣿⣿⣿⡀⢠⣾⣿⣿⣿⡇⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⡿⠛⠻⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠘⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠿⢿⣿⣿⣿⣧⡀⢹⣆⠉⢿⣼⣿⢿⣷⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠙⣿⡄⡀⣠⣋⣉⣿⣿⣿⣇⠈⢿⣧⢈⠻⣿⡿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢸⣿⡆⠀⠈⠻⡌⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢀⣀⣀⣀⣀⢀⣀⣀⠀⣀⣸⣿⡿⣿⣿⠿⠿⣿⣿⡿⣟⣛⣋⠀⠀⠸⣙⣛⣀⠀⠀⣀⣿⣿⣿⣿⣇⣀⣀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⢀⡀⠀⢠⡿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠙⣿⣷⡘⣻⣿⣿⣛⣸⣿⣿⡇⣿⣿⠉⠁⣿⣿⠀⠀⠉⠁⣾⣿⠙⣿⣷⠀⣾⣿⠛⣿⣷⠀⣿⣿⣿⣿⣿⡿⣿⣿⡀⣾⣿⠙⣿⣷⣶⣶⣀⣴⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣤⡀⠀⢿⣿⣿⠛⢻⣿⣿⠇⣿⣿⠀⠀⣿⣿⠀⠀⢴⠀⣿⣿⢀⣉⣉⠀⣿⣿⠀⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⢀⣉⣉⠈⢣⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣬⠙⣿⣷⠀⢸⣿⣿⠀⠀⣿⣿⠀⣿⣿⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿⠈⣿⣿⠀⣿⣿⠀⣿⣿⠄⣿⣿⠠⣿⣿⢿⣿⣿⠀⣿⣿⠈⣿⣿⠀⠘⠉⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣿⠟⠀⢸⣿⣿⠀⠀⣿⣿⠀⣿⣿⣶⡆⣿⣿⣶⡆⠀⠀⠻⣿⣶⢿⣿⠰⠻⣿⣶⣿⢟⠀⣿⣿⠀⣿⣿⠛⣿⣿⠀⠻⣿⣶⢿⣿⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣾⣿⣶⣶⣶⣶⣶⣦⣤⣤⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡴⠆⠀⣿⠶⢶⣶⣤⣄⠀⠀⠀⠀⣤⣤⣤⣴⣶⣄⣀⣀⣀⣠⣤⣀⣠⣤⣀⣀⣀⣀⠀⠀⠀ ⠀⠀⠀⠀⠠⢶⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣦⣤⣿⣾⣿⣿⡿⠆⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀ ⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⣻⣿⣿⣿⢿⣿⣷⡙⠟⠻⣦⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠛⠛⠛⠋⠀ ⠀⠄⠲⣶⠀⢶⠄⠰⠶⠶⠖⠀⠀⠀⠉⠉⠉⠉⠉⢙⣛⣻⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠛⣡⠀⣟⠐⠀⠀⠀⠀⢓⠀⠀⠀⠀⠀⠈⣿⣿⣿⡉⠁⠀⠀⣾⣾⣶⣶⣄⡀⠀⢀⣠⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣸⣿⠿⣿⣿⣿⣿⣿⣿⣧⠄⠀⣼⠒⢻⣿⢿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠃⠀⠀⠀⠀⢀⣾⣿⣵⣾⣿⣿⠿⠟⠛⣿⣿⣯⢰⣿⣔⠈⢻⣿⣿⣿⣇⠀⠀⠀⠀⣰⣶⡀⠀⠀⠀⠀⠀⠀⣠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⣤⣶⣶⠀⠀⠀⠀⠸⣿⡿⠋⠀⠀⠀⠀⠀⠊⢿⣿⣿⣿⢟⡟⣇⣴⣾⣿⣿⣿⣿⠘⣿⡇⣾⡿⣿⣿⣿⣆⠀⠀⢰⣿⣿⣿⡆⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣀⣴⣶⣿⣿⣿⣿⡿⠟⠋⠀⠀⡀⡀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⡾⠛⠙⠻⠋⢀⣿⣿⣿⣿⣿⣿⣿⠐⠹⣿⠸⣷⣝⣿⣿⣿⡄⢀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⡟⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠿⢿⣿⣿⣿⣧⡀⢹⣆⠉⢻⣜⣿⢿⣷⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠙⣿⡄⣀⣠⣋⣉⣿⣿⣿⣇⠈⢿⣧⠈⠻⣿⣿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⣰⣤⣤⣶⡶⠀⠀⠀⠀⠸⣿⡿⠃⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⢿⠗⣇⣴⣾⣿⣿⣿⣿⠈⣿⣇⢦⡿⣿⣿⣿⣆⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⣠⣴⣾⣿⣿⣿⣿⡿⠟⠁⠀⠀⣠⡀⣰⡇⠁⠀⠀⠀⠀⠀⠀⠀⡾⠋⠙⠻⠋⢠⣽⣿⣿⣿⣿⣿⣿⡔⠘⣿⠘⣿⣟⢿⣿⣿⡄⢀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠈⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣿⣿⠟⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠿⢿⣿⣿⣿⣷⡄⢸⣧⠀⢻⣞⣿⣿⣷⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠙⣿⡄⣀⣨⣋⣩⣿⣿⣿⣇⠈⢿⣷⠈⠻⣿⣿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢸⣿⣇⠀⠈⠻⠆⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢀⣀⣀⣀⣀⢀⣀⣀⠀⣀⣸⣿⡿⣿⣿⠿⠿⣿⣿⡿⣟⣛⣋⠀⠀⠸⣙⣛⣀⠀⠀⣀⣿⣿⣿⣿⣿⣀⣀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠙⣿⣷⡘⣻⣿⣿⣛⣸⣿⣿⡇⣿⣿⠉⠁⣿⣿⠀⠀⠉⠁⣾⣿⠛⣿⣷⠀⣾⣿⠛⣿⣷⠀⣿⣿⣿⣿⣿⣽⣿⣿⡀⣾⣿⠙⣿⣷⣶⣶⡀⣠⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣤⡀⠢⢿⣿⣿⠻⢿⣿⣿⠇⣿⣿⠀⠀⣿⣿⠐⠀⣰⠆⣿⣿⢀⣉⣉⠀⣿⣿⠀⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⢀⣉⣉⠈⢙⣦⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣬⠙⣿⣷⠀⢸⣿⣿⠀⠘⣿⣿⠀⣿⣿⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿⠈⣿⣿⠀⣿⣿⠀⣿⣿⠅⣿⣿⠡⣿⣿⢿⣿⣿⠀⣿⣿⠈⣿⣿⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣿⠟⠀⢸⣿⣿⠀⠀⣿⣿⠀⣿⣿⣶⡆⣿⣿⣶⡆⠀⠀⠻⣿⣶⢿⣿⠰⠻⣿⣶⣿⢟⠀⣿⣿⠀⣿⣿⠛⣿⣿⠀⠻⣿⣶⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣿⣶⣶⣤⣤⣤⣤⣤⣤⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠆⠀⣿⢶⣖⣦⣠⣄⠀⠀⠀⠀⣀⣤⣤⣤⣶⣄⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⢰⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣷⣤⣄⣿⣶⣿⣿⡿⠇⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀ ⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠽⣽⣿⣿⣿⣿⣿⣷⡚⡿⢿⣦⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠛⠛⠁ ⠀⠀⠲⣶⠀⢶⠄⠰⠴⠶⠖⠀⠀⠉⠙⠙⠉⠙⠛⢛⣛⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠔⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠿⠟⣁⡀⡟⠻⠀⠀⠀⠁⢳⠀⠀⠀⠀⠀⠈⣿⣿⣿⠛⠋⠁⠀⢨⣷⣴⣦⣄⠀⠀⠀⠀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣼⣿⢟⣻⣿⣿⣿⣿⣿⣯⣖⠀⣸⠋⠛⣿⣻⣿⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⠀⠀⠀⠀⠀⢠⣾⣿⣷⣿⣿⣿⠿⠛⠛⣿⣿⣿⢤⣿⡖⡀⠹⣿⣿⣿⣷⠀⠀⠀⠀⣠⣦⣄⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣤⣤⣶⡆⠀⠀⠀⠀⠹⣿⡿⠃⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠗⣇⣴⣾⣿⣿⣿⣿⡁⢿⣷⢰⣟⣿⣿⣿⣧⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⡀⣴⣾⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⢰⠓⠀⠀⠀⠀⠀⠀⠀⠀⠞⠋⠉⠩⠋⢠⣿⣿⣿⣿⣿⣿⣿⡟⠘⣿⡈⣿⣌⢿⣿⣿⣇⢀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⠓⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⡿⠿⢿⣿⣿⣿⣷⡄⠸⣧⡀⢻⣮⢿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠘⣿⣄⣀⣠⣉⣩⣽⣿⣿⣧⠀⢻⣷⡠⠹⢿⣿⢻⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢸⣿⣧⠀⠀⠙⠆⢿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢀⣀⣀⣀⣀⢀⣀⣀⠀⣀⣸⣿⡿⣿⣿⠿⠻⣿⣿⡿⣟⣛⣋⠀⠀⠸⣟⣛⣀⠀⠀⣀⣿⣿⣿⣿⣿⣀⣀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠙⣿⣷⡘⣻⣿⣿⣛⣸⣿⣿⡇⣿⣿⠈⠀⣿⣿⠀⠀⠀⠀⣾⣿⠛⣿⣷⠀⣾⣿⠛⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⡀⣾⣿⠙⣿⣷⣶⣶⡄⣠⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣤⡀⠀⢿⣿⣿⠻⢿⣿⣿⠇⣿⣿⠀⠀⣿⣿⠀⠀⣴⠂⣿⣿⢀⣉⣉⠀⣿⣿⠀⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⢀⣉⣉⠈⠉⢨⣯⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣬⠙⣿⣷⠀⢸⣿⣿⠀⠈⣿⣿⠀⣿⣿⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿⠈⣿⣿⠀⣿⣿⠀⣿⣿⠅⣿⣿⠁⣿⣿⢿⣿⣿⠀⣿⣿⠈⣿⣿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣿⠟⠀⢸⣿⣿⠀⠀⣿⣿⠀⣿⣿⣶⡆⣿⣿⣶⡆⠀⠀⠻⣿⣶⢿⣿⠰⠻⣿⣶⣿⢟⠀⣿⣿⠀⣿⣿⠛⣿⣿⠀⠻⣿⣶⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣶⣤⣤⣤⣤⣤⣄⣤⣶⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠆⠀⣿⠶⡲⣦⣀⡀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⠀⠀⠀⣀⣀⣀⣀⣀⡁⠀⢀⡀⠀⠀⠀ ⠀⠀⠀⠀⢰⣶⣦⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣶⣤⣄⣾⣶⣾⣿⡿⠇⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄ ⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡽⣽⣿⣿⣿⡿⣿⣯⡚⡿⠿⣄⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠟⠛⠁ ⠀⠀⠰⣶⠀⢶⠄⠰⠴⠶⠖⠀⠈⠉⠛⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⠟⢉⡀⡽⠩⠀⠀⠀⠉⢷⠀⠀⠀⠀⠀⠈⢿⣿⣿⠟⠋⠉⠀⠀⣷⣤⣤⣄⠀⠀⠀⠀⢀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢸⣿⣿⣯⠀⠀⠀⠀⠀⠀⢀⣼⡿⢛⣻⣿⣿⣿⣿⣿⣿⣖⡀⣸⠏⠉⣿⣿⣿⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠀⠀⠀⠀⠀⢠⣾⣿⣷⣿⣿⣿⠿⠛⠋⣽⣿⣿⢦⣿⣞⡀⠙⣿⣿⣿⣿⠀⠀⠀⠀⣴⣶⣆⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣰⣤⣴⣾⡆⠀⠀⠀⠀⢻⣿⠟⠁⠀⠀⠀⠀⠀⠐⢻⣿⣿⣿⣻⠗⣇⣴⣿⣿⣿⣿⣿⡇⢿⣿⢰⣟⣿⣿⣿⣷⡀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⢾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣀⡠⣶⣾⣿⣿⣿⣿⠿⠛⠀⠀⢀⣤⣀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠞⠋⠈⠹⠋⢠⣽⣿⣿⣿⣿⣿⣿⡏⠈⢿⡎⣿⣬⢻⣿⣿⣇⢀⣴⣿⣿⣿⡏⠀⠀⠀⠀⠀⠽⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⡿⠓⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠿⠿⣿⣿⣿⣿⣿⣄⠘⣷⡈⢹⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⢈⣿⣄⣀⣤⣉⣬⣽⣿⣿⣷⠀⢻⣷⡠⠹⢿⣿⣻⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣿⡆⠀⠀⠀⠀⢻⣿⠟⠁⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣻⠗⣅⣴⣿⣿⣿⣿⣿⡇⢿⣿⢰⣿⣿⣿⣿⣷⡀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣀⣠⣶⣿⣿⣿⣿⣿⠿⠋⠀⠀⢀⡤⠀⢼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠞⠉⠈⠹⠋⢠⣿⣿⣿⣿⣿⣿⣿⡏⠈⢿⡆⢿⣎⢻⣿⣿⣇⢀⣴⣿⣿⣿⣿⠀⠀⠀⠀⠀⠸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⡟⠒⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠿⠿⣿⣿⣿⣿⣿⡄⠈⣷⡀⢹⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠉⣿⣆⣀⣤⣉⣭⣽⣿⣿⣧⠀⢹⣿⡠⠙⢿⣿⣻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢸⣿⣷⠀⠀⠙⠇⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢀⣀⣀⣀⣀⢀⣀⣀⠀⣀⣸⣿⡿⣿⣿⠟⠻⣿⣿⡿⣟⣙⣛⠀⠀⠸⣟⣛⣀⠀⠀⣀⣾⣿⣿⣿⣿⣀⣀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠙⣿⣷⡘⣻⣿⣿⣛⣸⣿⣿⡆⣿⣿⠈⠀⣿⣿⠀⠀⠀⠀⣾⣿⠛⣿⣷⠀⣾⣿⠛⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⡀⣾⣿⠙⣿⣷⣦⣤⡄⢀⣴⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣤⡒⢢⣿⣿⣿⠿⢿⣿⣿⠇⣿⣿⠀⠀⣿⣿⠀⠀⣴⠆⣿⣿⢀⣉⣉⠀⣿⣿⠀⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⢀⣉⣉⠉⠉⠉⣻⡯⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣬⠙⣿⣷⠀⢸⣿⣿⠀⠸⣿⣿⠀⣿⣿⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿⠈⣿⣿⠀⣿⣿⠀⣿⣿⠅⣿⣿⠉⣿⣿⢿⣿⣿⠀⣿⣿⠈⣿⣿⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣿⠟⠀⢸⣿⣿⠀⠠⣿⣿⠀⣿⣿⣶⡆⣿⣿⣶⡆⠀⠀⠻⣿⣶⢿⣿⢰⠿⣿⣶⣿⢟⠀⣿⣿⠀⣿⣿⠛⣿⣿⠀⠻⣿⣶⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣤⣤⣤⣤⣤⣀⣀⣀⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⢠⣰⡖⠀⣿⢤⣦⣤⣀⡀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣤⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣷⣤⣄⣼⣶⣾⣿⣿⡇⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄ ⠀⠀⠀⠀⠀⠙⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢻⣿⣿⣿⣿⣿⣿⡝⡿⣿⣆⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛ ⠀⠀⠲⣶⠀⢶⠄⠰⠶⠶⠖⠈⠉⠛⠛⠛⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠋⡁⣹⠍⡍⠀⠀⠉⠵⠄⠀⠀⠀⠀⠀⢿⣿⣿⡿⠟⠋⠉⠉⣡⣤⣤⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀⣼⡿⢛⣻⣿⣿⣿⣿⣿⣿⣖⡀⣸⠏⠉⣿⡿⣿⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⡏⠀⠀⠀⠀⠀⢠⣿⣿⣶⣿⣿⣿⠿⠛⠛⣿⣿⣿⢦⣿⡖⡀⠙⣿⣿⣿⣷⠀⠀⠀⠀⣠⣶⣦⠀⠀⠀⠀⠀⠀⠀⣰⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣾⠀⠀⠀⠀⠀⢿⣿⠟⠁⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣫⠗⣇⣴⣿⣿⣿⣿⣿⡇⢿⣿⢰⣟⣿⣿⣿⣷⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣀⢠⣶⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⡤⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⠊⡹⠃⢠⣿⣿⣿⣿⣿⣿⣿⡟⠘⢿⡎⢿⣬⢻⣿⣿⣇⢀⣴⣿⣿⣿⣿⠀⠀⠀⠀⠀⠸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠟⠚⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⡿⠿⢿⣿⣿⣿⣿⢄⠘⣷⡀⢹⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⢙⣿⡄⣀⣠⣋⣩⣿⣿⣿⣧⠀⢹⣷⡠⠙⢿⣿⣻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣒⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢸⣿⣧⠀⠀⠙⠇⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢀⣀⣀⣀⣀⢀⣀⣀⠀⣀⣾⣿⡿⣿⣿⠿⠿⣿⣿⡿⣟⣛⣛⠀⠀⠸⣟⣛⣀⠀⠀⣀⣼⣿⣿⣿⣿⣁⣀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠙⣿⣷⡘⣻⣿⣿⣛⣸⣿⣿⡆⣿⣿⠉⠁⣿⣿⠀⠀⠈⠉⣾⣿⠛⣿⣷⠀⣾⣿⠛⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⡀⣾⣿⠙⣿⣷⣤⣤⣄⠀⣠⣾⡷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣤⡐⢢⣿⣿⣿⠿⢿⣿⣿⠇⣿⣿⠀⠀⣿⣿⠐⠂⣤⠄⣿⣿⢀⣉⣉⠀⣿⣿⠀⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⢀⣉⣉⠘⠉⠉⢊⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣬⠙⣿⣷⠀⢸⣿⣿⠀⠸⣿⣿⠀⣿⣿⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿⠈⣿⣿⠀⣿⣿⠀⣿⣿⡁⣿⣿⠋⣿⣿⣿⣿⣿⠀⣿⣿⠈⣿⣿⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣿⠟⠀⢸⣿⣿⠀⠀⣿⣿⠀⣿⣿⣶⡆⣿⣿⣶⡆⠀⠀⠻⣿⣶⢿⣿⢠⡻⣿⣶⣿⢟⠀⣿⣿⠀⣿⣿⠛⣿⣿⠀⠻⣿⣶⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣦⣤⣤⣤⣤⣄⣀⣀⣀⣶⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⢠⣂⡶⠀⢿⣦⡤⢤⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣀⣀⣸⣦⣾⣿⣿⣇⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄ ⠀⠀⠀⠀⠈⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⡭⣿⣿⣆⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟ ⠀⠀⠲⣶⠀⢶⠄⠰⠶⠶⠖⠉⠛⠛⠛⠿⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⠿⠋⡁⢹⠟⡅⠈⠀⠙⠱⡄⠀⠀⠀⠀⠀⢻⣿⣿⣿⠿⠋⠉⠉⢉⣤⣤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣾⡿⢟⣻⣿⣿⣿⣿⣿⣭⣒⠀⣼⠉⢩⣿⣻⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⣠⣿⣿⣶⣿⣿⣿⠿⠛⢻⣿⣿⣷⢰⣿⣖⠀⠹⣿⣿⣿⣿⠀⠀⠀⠀⢠⣶⣤⡀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣷⠀⠀⠀⠀⠀⢿⣿⠛⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣻⠗⣅⣴⣿⣿⣿⣿⣿⠈⣿⣧⢳⡟⣿⣿⣿⣧⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣀⡀⢰⣶⣿⣿⣿⣿⡿⠟⠃⠀⠀⢀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠋⠛⡻⠃⢸⣾⣿⣿⣿⣿⣿⣿⡔⠘⣿⡘⣿⣬⢿⣿⣿⣇⠀⣴⣿⣿⣿⣿⠀⠀⠀⠀⠀⠐⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠀⠈⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠿⢿⣿⣿⣿⣷⣄⠸⣧⠀⠻⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⢸⣿⡀⠀⣠⣋⣉⣿⣿⣿⣧⠀⢻⣷⡀⠻⣿⣷⣻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢸⣿⣧⠀⠀⠙⠦⢻⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢀⣀⣀⣀⣀⢀⣀⣀⠀⣀⣿⣿⡿⣿⣿⠿⠿⣿⣿⡿⣟⣛⣛⠀⠀⠸⣟⣛⣀⠀⠀⣀⣼⣿⣿⣿⣿⣃⣀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠙⣿⣧⡘⣻⣿⣿⣛⣸⣿⣿⡆⣿⣿⠙⠁⣿⣿⠀⠀⠉⠉⣾⣿⠛⣿⣷⠀⣾⣿⠛⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⡀⣾⣿⠙⣿⣷⣤⣄⣄⠀⣠⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣤⡒⢢⣿⣿⣿⠿⢿⣿⣿⡇⣿⣿⠀⠀⣿⣿⠀⠐⣤⠄⣿⣿⢀⣉⣉⠀⣿⣿⠀⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⢀⣉⣉⠘⠉⠉⢀⣼⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣬⠙⣿⣷⠀⢸⣿⣿⠀⠸⣿⣿⠁⣿⣿⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿⠈⣿⣿⠀⣿⣿⠀⣿⣿⡁⣿⣿⠛⣿⣿⣿⣿⣿⠀⣿⣿⠈⣿⣿⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣿⠟⠀⢸⣿⣿⠀⠀⣿⣿⠀⣿⣿⣶⡆⣿⣿⣶⡆⠀⠀⠻⣿⣶⢿⣿⢠⡻⣿⣶⣿⢟⠀⣿⣿⠀⣿⣿⠛⣿⣿⠀⠻⣿⣶⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣤⣤⣤⣠⣀⣀⣀⣠⣶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⢠⣀⣶⠀⢿⣷⣤⢤⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣠⣄⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣤⣀⢸⣧⣬⣿⣿⣇⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣶⣄ ⠀⠀⠀⠀⠉⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡫⢿⣷⣆⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟ ⠀⠀⠲⣶⠀⢶⠄⠰⠶⠶⠞⠉⠛⠛⠿⠿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠟⠉⢻⡟⡃⠈⠀⠙⠱⡄⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠟⠉⠉⢙⣅⣄⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣾⡿⢟⣿⣿⣿⣿⣿⣿⣭⠂⠀⣿⠉⢹⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⣴⣿⣯⣶⣿⣿⣿⠿⠛⢛⣿⣿⣷⣸⣷⣖⠀⢻⣿⣿⣿⣿⠀⠀⠀⠀⣰⣶⣶⡀⠀⠀⠀⠀⠀⠀⣰⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⡷⠀⠀⠀⠀⠈⣿⡿⠋⠀⠀⠀⠀⠀⠀⠽⣿⣿⣿⡿⣻⢕⣁⣴⣾⣿⣿⣿⣿⠘⣿⣇⢷⡿⣿⣿⣿⣦⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣀⠀⣴⣾⣿⣿⣿⣿⡿⠟⠁⠀⠀⢀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⢠⠿⠋⠛⡻⠃⢸⣿⣿⣿⣿⣿⣿⣿⠀⠹⣿⠘⣿⣜⢿⣿⣿⡄⠀⣤⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡯⠀⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠿⣿⣿⣿⣿⣧⡀⢹⣧⠈⢻⣎⣿⣿⣿⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠘⢻⣿⡀⠀⣰⢋⣙⣿⣿⣿⣇⠀⢿⣷⠈⠻⣿⣷⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⢄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢸⣿⣧⠀⠈⠹⠆⢻⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢀⣀⣀⣀⣀⠀⣀⣀⠀⣀⣿⣿⡿⣿⣿⠿⢿⣿⣿⡿⣟⣛⣛⠀⠀⠸⣟⣛⣀⠀⠀⣀⣼⣿⣿⣿⣿⣃⣀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠙⣿⣷⡘⣻⣿⣿⣛⣸⣿⣿⡆⣿⣿⠙⠁⣿⣿⠀⠈⠉⠉⣾⣿⠛⣿⣷⠀⣾⣿⠛⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⡀⣾⣿⠙⣿⣷⣤⣤⣄⠀⢠⣶⣷⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣤⡒⢢⣿⣿⣿⠿⢿⣿⣿⡇⣿⣿⠀⠀⣿⣿⠀⠀⣠⡄⣿⣿⢀⣉⣉⠀⣿⣿⠀⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⢀⣉⣉⠘⠉⠉⠐⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣬⠙⣿⣷⠀⢸⣿⣿⠀⠘⣿⣿⠁⣿⣿⠀⠀⣿⣿⠀⠀⠉⠀⣿⣿⠈⣿⣿⠀⣿⣿⠀⣿⣿⡁⣿⣿⠛⣿⣿⣿⣿⣿⠀⣿⣿⠈⣿⣿⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣿⠟⠀⢸⣿⣿⠀⠀⣿⣿⠀⣿⣿⣶⡆⣿⣿⣶⡆⠀⠀⠻⣿⣶⢿⣿⢠⡻⣿⣶⣿⢟⡀⣿⣿⠁⣿⣿⠛⣿⣿⠀⠻⣿⣶⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣀⣀⣀⡀⢀⣠⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⢀⣀⣴⠀⢿⣧⡤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⣀⣀⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣾⣯⣀⣀⢸⣧⣬⣿⣿⡇⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣷⣶⣾⣶⣶⣄ ⠀⠀⠀⠀⠙⠻⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⡻⢿⣿⣆⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿ ⠀⠀⠲⣶⠈⢶⠄⠰⠶⠶⠟⠉⠛⠻⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⣿⡟⠉⢻⡟⡛⠈⠈⠙⢳⣄⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠟⠋⠉⠛⣍⣉⡁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣹⣿⣿⡄⠀⠀⠀⠀⠀⠀⢠⣿⡿⢟⣿⣿⣿⣿⣿⣿⣥⠂⠀⣿⠉⢹⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⣴⣿⣯⣾⣿⣿⡿⠿⠛⢻⣿⣿⣷⣸⣷⣒⠀⢻⣿⣿⣿⣷⠀⠀⠀⠀⢰⣤⣦⡀⠀⠀⠀⠀⠀⠀⣰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⡖⠀⠀⠀⠀⠸⣿⡿⠋⠀⠀⠀⠀⠀⠐⡿⣿⣿⣿⡿⣻⢗⣀⣴⣾⣿⣿⣿⣿⠘⣿⡇⢾⡿⣿⣿⣿⣧⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⣴⣾⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⠋⠛⡿⠁⣘⣿⣿⣿⣿⣿⣿⣿⠀⠹⣿⠘⣿⣜⢿⣿⣿⣆⢀⣠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡅⠀⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⣿⣿⣿⣿⣧⡀⠹⣧⠘⢻⣎⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⢻⣿⡀⠀⣰⢋⣙⣿⣿⣿⣇⠀⢻⣷⠈⠻⣿⣷⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢸⣿⣧⠀⠈⠹⠆⢻⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢀⣀⣀⣀⣀⢀⣀⣀⠀⣀⣿⣿⡿⣿⣿⠿⢿⣿⣿⡿⣟⣛⣛⠀⠀⠸⣟⣛⣀⠀⠀⣀⣼⣿⣿⣿⣿⣇⣀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠙⣿⣷⡘⣻⣿⣿⣛⣸⣿⣿⡆⣿⣿⠙⠁⣿⣿⠀⠀⠉⠉⣾⣿⠛⣿⣷⠀⣾⣿⠛⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⡀⣾⣿⠙⣿⣷⣤⣄⣄⠀⠀⣴⣶⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣤⡒⢢⣿⣿⣿⠿⢿⣿⣿⡇⣿⣿⠀⠀⣿⣿⠠⠀⣠⡄⣿⣿⢀⣉⣉⠀⣿⣿⠀⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⢀⣉⣉⠘⠙⠉⢀⠌⠝⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣬⠙⣿⣷⠀⢸⣿⣿⠀⠘⣿⣿⠂⣿⣿⠀⠀⣿⣿⠀⠀⠉⠀⣿⣿⠈⣿⣿⠀⣿⣿⠀⣿⣿⡁⣿⣿⠛⣿⣿⣿⣿⣿⠀⣿⣿⠈⣿⣿⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣿⠟⠀⢸⣿⣿⠀⠀⣿⣿⠀⣿⣿⣶⡆⣿⣿⣶⡆⠀⠀⠻⣿⣶⢿⣿⢠⡻⣿⣶⣿⢟⠁⣿⣿⠁⣿⣿⠛⣿⣿⠀⠻⣿⣶⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣄⣀⣀⣀⣀⡀⠀⣠⣴⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠀⣀⣴⠀⢻⣇⣤⣀⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣯⣅⡀⢸⣧⣭⣿⣿⣷⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣷⣶⣶⣶⣶⣄ ⠀⠀⠀⠀⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣌⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿ ⠀⠀⠲⣶⠊⢶⠄⠰⠶⠾⠟⠛⠻⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⣿⠟⠋⢹⡟⠛⠈⠈⠹⢳⣄⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠿⠛⠛⠛⣏⣉⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣠⣿⡿⢛⣿⣿⣿⣿⣿⣿⣵⣒⠀⣿⡉⢹⣿⣻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡃⠀⠀⠀⠀⠀⣴⣿⣿⣾⣿⣿⡿⡟⠛⢻⣿⣿⡷⣼⢷⣒⠀⠻⣿⣿⣿⣷⠀⠀⠀⠀⢠⣤⣶⡀⠀⠀⠀⠀⠀⠀⣠⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⡇⠀⠀⠀⠀⠸⠿⠿⠋⠀⠀⠀⠀⠀⠀⠯⣿⣿⣿⡿⣻⢟⣀⣴⣿⣿⣿⣿⣿⠘⣿⣇⢯⡿⣿⣿⣿⣧⠀⠀⠀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢴⣾⣾⣿⣿⣿⠿⠛⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠋⠛⡽⠁⢸⣾⣿⣿⣿⣿⣿⣿⠀⠹⣿⠘⣿⣍⢿⣿⣿⡇⠀⣠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠁⠀⠚⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠿⣿⣿⣿⣿⣧⡀⢹⣧⠀⢻⣆⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⢻⣯⠀⠀⣰⢋⣙⣿⣿⣿⣇⠀⢿⣷⠈⠻⣿⣷⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢔⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢸⣿⣧⠀⠈⠹⠆⢻⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢀⣀⣀⣀⣀⢀⣀⣀⠀⣀⣿⣿⡿⣿⣿⠿⣿⣿⣿⡿⣟⣛⣛⠀⠀⠸⣟⣛⣀⠀⠀⣀⣼⣿⣿⣿⣿⣇⣀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠙⣿⣧⡘⣻⣿⣿⣛⣸⣿⣿⡆⣿⣿⠛⠁⣿⣿⠀⠈⠉⠉⣾⣿⠛⣿⣷⠀⣾⣿⠛⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⠙⣿⣷⣤⣄⣄⠀⠀⣤⣶⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣤⡐⢢⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⠀⠀⣿⣿⠠⠀⣠⠄⣿⣿⢀⣉⣉⠀⣿⣿⠀⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⢀⣉⣉⠘⠛⠛⠁⣈⠝⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣬⠙⣿⣷⠈⢸⣿⣿⠀⠘⣿⣿⠃⣿⣿⠀⠀⣿⣿⠀⠀⠉⠀⣿⣿⠈⣿⣿⠀⣿⣿⠀⣿⣿⡁⣿⣿⠟⣿⣿⣿⣿⣿⠀⣿⣿⠈⣿⣿⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣿⠟⠀⢸⣿⣿⠀⠀⣿⣿⠀⣿⣿⣶⡆⣿⣿⣶⡆⠀⠀⠻⣿⣶⢿⣿⢠⡻⣿⣶⣿⢟⠁⣿⣿⠀⣿⣿⠟⣿⣿⠀⠻⣿⣶⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣀⣀⣀⣀⣀⠀⠀⣠⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⣁⠀⣴⠂⢻⣇⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⣽⣿⡀⠀⢸⣏⣡⣾⣿⣿⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣶⣶⣾⣷⣶⣶⣶⣦⣄ ⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣾⣿⣟⣿⣿⣅⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⠀⠀⠲⣶⠋⢷⠄⠰⠶⠿⠿⠛⠿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠋⠽⣿⣿⡿⠛⢻⡿⠗⠈⠉⠹⢳⡄⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡿⠟⠛⠛⢏⠉⠉⠉⠉⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣠⣿⠿⣛⣿⣿⣿⣿⣿⣿⣷⣒⠀⣼⠉⢉⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⠃⠀⠀⠀⠀⠀⣼⣿⣷⣾⣿⣿⡿⠛⠛⢋⣿⣿⣷⣰⣿⣞⡀⠹⣿⣿⣿⣿⠀⠀⠀⠀⢠⣴⣦⡀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⠆⠀⠀⠀⠀⠸⣿⡿⠋⠀⠀⠀⠀⠀⠀⠊⣿⣿⣿⣿⣿⢚⣠⣶⣿⣿⣿⣿⣿⠈⣿⣇⢳⣟⣿⣿⣿⣧⠀⠀⠀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⣾⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠉⠉⠝⠁⣸⣾⣿⣿⣿⣿⣿⣿⡔⠘⣿⡘⣿⣌⢿⣿⣿⣆⠀⣰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⡿⠿⣿⣿⣿⣿⣷⡄⢸⣧⠐⠻⣦⢿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⢻⣯⡀⢀⣸⣉⣉⣿⣿⣿⣇⠀⢻⣷⡠⠻⣿⣷⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣒⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢸⣿⣧⠀⠈⠹⠦⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢀⣀⣀⣀⣀⢀⣀⣀⠀⣀⣿⣿⡿⣿⣿⠿⢿⣿⣿⡿⣟⣛⣛⠀⠀⠸⣟⣛⣀⠀⠀⣀⣸⣿⣿⣿⣿⣇⣀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠙⣿⣧⡘⣻⣿⣿⣛⣸⣿⣿⡆⣿⣿⠉⠁⣿⣿⠀⠈⠉⠉⣾⣿⠛⣿⣷⠀⣾⣿⠛⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⠙⣿⣷⣀⣄⣀⠀⠀⣠⣴⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣤⡒⣢⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⠀⠀⣿⣿⠠⠄⣤⠄⣿⣿⢀⣉⣉⠀⣿⣿⠀⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⢀⣉⣉⠘⠛⠙⠃⠨⠹⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣬⠙⣿⣷⠀⢸⣿⣿⠀⠸⣿⣿⠃⣿⣿⠀⠀⣿⣿⠀⠀⠁⠀⣿⣿⠈⣿⣿⠀⣿⣿⠀⣿⣿⠃⣿⣿⠿⣿⣿⣿⣿⣿⠀⣿⣿⠈⣿⣿⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣿⠟⠀⢸⣿⣿⠀⠀⣿⣿⠀⣿⣿⣶⡆⣿⣿⣶⡆⠀⠀⠻⣿⣶⢿⣿⢠⡻⣿⣶⣿⠟⠁⣿⣿⠀⣿⣿⠟⣿⣿⠀⠻⣿⣶⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⣠⣤⣤⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⢁⠀⣤⠀⢻⡇⣀⣀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠀⠀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⣿⣁⠀⢸⣏⣁⣾⣿⡆⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣶⣶⣦⣄ ⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣷⣾⣿⢟⣿⣿⣅⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠲⣶⠋⢷⠄⠰⠶⠿⠿⠻⠿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠽⣿⣿⡿⠛⢻⡿⠷⠘⠉⠹⢢⡀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠟⠛⠛⠛⠉⠉⠉⠉⠉⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⣋⣿⣿⣿⣿⣿⣿⣶⣖⠀⣼⠏⠉⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⣼⣿⣷⣿⣿⣿⡿⡛⠉⢉⣿⣿⣿⣲⣿⡞⡁⠘⣿⣿⣿⣿⡄⠀⠀⠀⢠⣴⣶⡄⠀⠀⠀⠀⠀⠀⢀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⠆⠀⠀⠀⠀⠹⣿⠿⠋⠀⠀⠀⠀⠀⠀⠞⣿⣿⣿⣿⡽⢋⣦⣾⣿⣿⣿⣿⣿⡀⢿⣿⢰⣿⢿⣿⣿⣷⡄⠀⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⢀⣶⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⢠⠗⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠁⠉⠜⠁⢨⣿⣿⣿⣿⣿⣿⣿⡟⠈⣿⡆⢿⣮⢻⣿⣿⣧⠀⢰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠈⠻⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⡿⠿⣿⣿⣿⣿⣿⣄⠘⣷⡈⠽⣧⣻⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⢹⣿⣀⣀⣼⣉⣩⣿⣿⣿⣧⠀⢻⣷⡠⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢸⣿⣧⠀⠀⠙⢧⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢀⣀⣀⣀⣀⢀⣀⣀⠀⣀⣿⣿⡿⣿⣿⠿⢿⣿⣿⡿⣟⣛⣛⠀⠀⠸⣟⣛⣀⠀⠀⣀⣸⣿⣿⣿⣿⣏⣀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠙⣿⣷⡘⣻⣿⣿⣛⣸⣿⣿⡆⣿⣿⠉⠀⣿⣿⠀⠀⠉⠉⣾⣿⠛⣿⣷⠀⣾⣿⠛⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⠙⣿⣷⣠⣀⣀⡀⠀⣠⣴⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣤⡒⣢⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⠀⠀⣿⣿⠀⠲⣤⠄⣿⣿⢀⣉⣉⠀⣿⣿⠀⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⢀⣉⣉⠺⠛⠛⠑⠋⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣬⠙⣿⣷⠈⢸⣿⣿⠀⠹⣿⣿⠃⣿⣿⠀⠀⣿⣿⠀⠀⠉⠀⣿⣿⠈⣿⣿⠀⣿⣿⠀⣿⣿⡃⣿⣿⠿⣿⣿⣿⣿⣿⠀⣿⣿⠈⣿⣿⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣿⠟⠀⢸⣿⣿⠀⠀⣿⣿⠀⣿⣿⣶⡆⣿⣿⣶⡆⠀⠀⠻⣿⣶⢿⣿⢠⡻⣿⣶⣿⠟⠁⣿⣿⠀⣿⣿⠟⣿⣿⠀⠻⣿⣶⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⣀⣀⠀⢀⠀⠀⠀⣠⣤⣤⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠁⢀⣤⠀⢻⣇⣀⣀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣼⣿⡉⠀⢸⣏⣋⣾⣿⣾⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣷⣤⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣶⣤⣄ ⠀⠀⠀⠐⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣾⣿⣟⣿⣿⣍⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠲⣶⠋⢷⠆⠰⠾⠿⠿⠿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠽⣿⣿⡿⠟⢻⡿⠷⠘⠙⠹⢦⡀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡿⠿⠛⠟⠋⠉⠉⠉⠉⠉⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⣻⣿⣿⣿⣿⣿⣿⣷⣖⠀⣼⢏⠉⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⠀⠀⠀⠀⠀⠀⣼⣿⣷⣿⣿⣿⡿⡛⠉⢉⣿⣿⣿⣲⣿⣎⡁⠘⣿⣿⣿⣿⡄⠀⠀⠀⢠⣦⣶⡄⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⠀⠀⠀⠀⠀⢸⣿⠿⠃⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⡿⢊⣦⣾⣿⣿⣿⣿⣿⡀⢿⣿⢰⣿⢿⣿⣿⣷⡄⠀⠀⢾⣿⣿⣿⡇⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⢀⣶⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⡀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠁⠉⠞⠁⢨⣿⣿⣿⣿⣿⣿⣿⡟⠈⣿⡎⢿⣮⠻⣿⣿⣧⠀⣰⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠛⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣏⠀⠈⠟⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⡿⠿⣿⣿⣿⣿⣷⣄⠈⣷⡈⠽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⢹⣿⣀⣀⣼⣉⣩⣿⣿⣿⣧⠀⢻⣷⡠⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⠀⠀⠀⠀⠀⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠟⣿⣿⣿⣿⡿⢚⣤⣾⣿⣿⣿⣿⣿⠀⣿⣿⢰⣿⢿⣿⣿⣷⡀⠀⠀⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠠⣶⣾⣿⣿⣿⣿⠟⠃⠀⠀⠀⣀⠀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⡸⠛⠁⠉⠟⠁⣬⣿⣿⣿⣿⣿⣿⣿⡜⠘⣿⡎⢿⣮⢻⣿⣿⣧⠀⣰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⡿⠿⣿⣿⣿⣿⣷⣄⠘⣧⡈⠽⣧⣻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⢻⣯⢀⢀⣼⣉⣉⣿⣿⣿⣇⠀⢻⣷⡠⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢸⣿⣧⠀⠀⠙⢧⢹⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢀⣀⣀⣀⣀⢀⣀⣀⠀⣰⣿⣿⡿⣿⣿⠿⢿⣿⣿⡿⣟⣛⣛⠀⠀⠸⣟⣛⣀⠀⠀⣀⣸⣿⣿⣿⣿⣏⣀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠙⣿⣧⡘⣻⣿⣿⣛⣸⣿⣿⡄⣿⣿⠉⠁⣿⣿⠀⠈⠉⠁⣾⣿⠛⣿⣷⠀⣾⣿⠛⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⠙⣿⣷⣀⣄⣀⠀⠀⢀⣤⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣤⡒⣢⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⠀⠀⣿⣿⠠⢤⣠⠀⣿⣿⢀⣉⣉⠀⣿⣿⠀⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⢀⣉⣉⠘⠛⠙⠓⠐⢈⠛⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣬⠙⣿⣷⠀⢸⣿⣿⠀⠸⣿⣿⠃⣿⣿⠀⠀⣿⣿⠀⠈⠉⠀⣿⣿⠈⣿⣿⠀⣿⣿⠀⣿⣿⠂⣿⣿⠿⣿⣿⣿⣿⣿⠀⣿⣿⠈⣿⣿⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣿⠟⠀⢸⣿⣿⠀⠀⣿⣿⠀⣿⣿⣶⡆⣿⣿⣶⡆⠀⠀⠻⣿⣶⢿⣿⢀⡻⣿⣶⣿⠟⠁⣿⣿⠂⣿⣿⠿⣿⣿⠀⠻⣿⣶⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠋⠉⠀⣤⡄⢾⡇⣀⠂⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⡉⠀⢸⣏⣛⣿⣷⣞⠀⠀⠀⠀⠀⢲⣶⣶⣾⣿⣦⣤⣤⣤⣤⣶⣶⣦⣴⣶⣤⣤⣤⣤⣀ ⠀⠀⠀⠐⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣼⣿⡿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠂⠲⣶⠋⢷⠟⠹⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢹⣿⣿⣿⠿⢿⣿⡿⠘⠙⠻⣦⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠛⠛⠉⠉⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⣛⣿⣿⣿⣿⣿⣽⣷⣒⠀⡿⡉⢩⣿⣻⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣾⣿⣷⣿⣿⣿⡿⠟⠛⢻⣿⣿⡷⣼⢿⣪⠀⠹⣿⣿⣿⣿⡀⠀⠀⠀⢀⣴⣶⣄⠀⠀⠀⠀⠀⠀⠀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⡶⠀⠀⠀⠀⠀⢿⣿⡟⠁⠀⠀⠀⠀⠀⠈⢟⣿⣿⣿⣟⡿⢺⣠⣶⣿⣿⣿⣷⣿⠘⣿⣇⢳⡟⣿⣿⣿⣷⡀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⢰⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠠⣶⣾⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⡼⠛⠙⢛⠟⠀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠹⣿⠘⣿⣌⢿⣿⣿⣇⠀⣰⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠨⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡁⠀⠀⠟⠛⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠿⣿⣿⣿⣿⣧⡀⢸⣧⠐⠻⣧⢿⣿⣿⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠛⣿⣇⠀⠀⡘⢋⣛⣿⣿⣿⣇⠈⢿⣷⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢸⣿⣧⠁⠈⠻⣧⢹⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢀⣀⣀⣀⣀⢀⣀⣀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣛⣛⠀⠀⠸⣟⣟⣀⠀⠀⣀⣸⣿⣿⣿⣿⣟⣀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠙⣿⣷⡘⢻⣿⣿⣛⣸⣿⣿⡀⣿⣿⠙⠁⣿⣿⠀⠈⠛⠃⣾⣿⠛⣿⣷⠀⣾⣿⠛⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⠙⣿⣷⣀⣀⠀⠀⠀⢀⣴⣤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣤⡒⣢⢿⣿⣿⣿⣿⣿⣿⡇⣿⣿⠀⠀⣿⣿⠠⠤⣀⡀⣿⣿⢀⣉⣉⠀⣿⣿⠀⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⢀⣉⣉⠘⠛⠛⠂⠀⠈⠟⠋⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⡆⠀⠀⠀⠀⠀⢿⣿⠟⠁⠀⠀⠀⠀⠀⢻⢿⣿⣿⣿⢟⡯⡆⣠⣾⣿⣿⣿⣿⡇⢹⣿⡆⣾⡿⣿⣿⣿⣦⠀⠀⠀⢸⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢐⢶⣾⣾⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⡿⠟⠽⢻⠏⠀⣷⣿⣿⣿⣿⣿⣿⣇⠂⢻⣷⠹⣷⡙⣿⣿⣿⣅⠀⢠⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⠋⠁⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢻⣆⠛⣿⣌⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⣿⡏⠉⠀⡞⠛⢻⣿⣿⣿⡄⠘⣿⣦⢈⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠠⢤⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣆⠀⠈⠻⣏⢻⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢀⣀⣀⣀⣀⢀⣀⣀⠀⣸⣷⣾⣿⣿⣿⣿⣿⣿⣿⡿⣟⣛⣋⠀⠀⢸⣻⣛⣀⠀⠀⣀⣸⣿⣿⣿⣿⣿⣀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠙⣿⣷⠘⢻⣿⣿⣛⣸⣿⣿⠀⣿⣿⠛⠁⣿⣿⠀⠙⠛⠋⣾⣿⠛⣿⣷⠀⣾⣿⠛⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⠙⣿⣷⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣤⡒⣢⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⠀⠀⣿⣿⢀⡀⢀⠀⣿⣿⢀⣉⣉⠀⣿⣿⠀⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⢀⣉⣉⠺⠿⠛⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣬⠙⣿⣷⠁⢸⣿⣿⠈⠘⣿⣿⠇⣿⣿⠀⠀⣿⣿⠀⠘⠋⠀⣿⣿⠈⣿⣿⠀⣿⣿⠀⣿⣿⠀⣿⣿⡿⣿⣿⣿⣿⣿⠀⣿⣿⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣿⠟⠀⢸⣿⣿⠀⠀⣿⣿⠀⣿⣿⣶⡆⣿⣿⣶⡆⠀⠀⠻⣿⣶⢿⣿⢀⡻⣿⣶⣿⠟⠃⣿⣿⠐⣿⣿⡿⣿⣿⠀⠻⣿⣶⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠚⠋⡁⣠⠀⢾⡆⠀⠀⠀⠀⠀⠀⠈⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣷⠛⠀⢸⡟⠚⣽⣶⡄⠀⠀⠀⠀⠀⢰⣶⣶⣶⣾⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀ ⠀⠀⠀⠀⢤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢶⣿⣿⣷⣶⣼⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠂⠲⣶⠟⢿⠟⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣺⣿⣿⣿⡿⢿⣿⣯⠹⠻⢻⣄⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠛⠛⠛⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀⣼⡿⢟⣻⣿⣿⣿⣿⣿⣿⣖⡂⢠⡏⠉⢹⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⡏⠀⠀⠀⠀⠀⣰⣿⣿⣾⣿⣿⣿⠿⠛⠛⣿⣿⣿⣆⣾⣷⣃⠀⢻⣿⣿⣿⣿⠀⠀⠀⠀⢀⣤⣴⣆⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⡆⠀⠀⠀⠀⠀⢿⣿⠟⠁⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⢿⡷⡇⣴⣾⣿⣿⣿⣾⡇⢹⣿⡇⣾⡿⣿⣿⣿⣧⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⣶⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⢀⠿⠛⠙⢻⠏⢀⣿⣿⣿⣿⣿⣿⣿⣇⠂⢻⣷⠸⣷⡝⣿⣿⣿⣇⠀⢠⣼⣿⣿⣿⣇⠀⠀⠀⠀⠀⠐⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⠛⠋⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⢻⣆⠋⢿⣎⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⣿⡉⠈⢀⡞⠛⣻⣿⣿⣿⡆⠘⣿⣦⢈⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣆⠀⠈⠻⣎⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢀⣀⣀⣀⣀⢀⣀⣀⠀⣸⣷⣾⣿⣿⣿⣿⣿⣿⣿⡿⣟⣛⣋⠀⠀⢸⣻⣛⣀⠀⠀⣀⣸⣿⣿⣿⣿⣟⣀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠙⣿⣧⠘⢻⣿⣿⣛⣸⣿⣿⠀⣿⣿⠛⠁⣿⣿⠀⠙⠛⠋⣾⣿⠛⣿⣷⠀⣾⣿⠛⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⠙⣿⣷⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣴⡒⣢⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⠀⠀⣿⣿⢀⡀⢀⠀⣿⣿⢀⣉⣉⠀⣿⣿⠀⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⢀⣉⣉⠺⠿⠓⠁⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣬⠙⣿⣷⠀⢸⣿⣿⠈⢹⣿⣿⠇⣿⣿⠀⠀⣿⣿⠀⠘⠋⠀⣿⣿⠈⣿⣿⠀⣿⣿⠀⣿⣿⠀⣿⣿⡿⣿⣿⣿⣿⣿⠀⣿⣿⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣿⠟⠀⢸⣿⣿⠀⠈⣿⣿⠀⣿⣿⣶⡆⣿⣿⣶⡆⠀⠀⠻⣿⣶⢿⣿⢀⡻⣿⣶⣿⠟⠃⣿⣿⠐⣿⣿⡿⣿⣿⠀⠻⣿⣶⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠋⠁⢠⠀⢶⡆⠀⠀⠀⠀⠀⠀⠈⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡶⠛⠀⢸⡗⠹⣝⣦⡄⠀⠀⠀⠀⠀⢠⣶⣶⣶⣷⣶⣀⣀⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⡀ ⠀⠀⠀⠠⢤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣶⣶⣼⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠆⠲⣶⠟⢿⠟⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢺⣿⣿⣿⣿⢿⣿⣯⠹⠻⢷⣄⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠛⠛⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀⣾⡿⢛⣻⣿⣿⣿⣿⣯⣿⣖⡂⢠⡿⠉⢹⣿⣻⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⡇⠀⠀⠀⠀⠀⣰⣿⣿⣾⣿⣿⣿⠿⠛⠋⣻⣿⣿⣗⣾⣷⣉⠀⢹⣿⣿⣿⣿⠀⠀⠀⠀⢀⣤⣶⣦⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⠆⠀⠀⠀⠀⠀⢿⣿⠋⠀⠀⠀⠀⠀⠀⠹⢻⣿⣿⣿⣻⠗⡇⣴⣾⣿⣿⣿⣿⣇⠸⣿⡇⣿⡿⣿⣿⣿⣧⠀⠀⠀⢸⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣶⣾⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⣜⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠋⠛⠹⠃⢠⣿⣿⣿⣿⣿⣿⣿⣧⠃⢻⣿⠸⣿⣝⢿⣿⣿⣧⠀⢀⣼⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⠛⠛⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠿⢿⣿⣿⣿⣿⣦⡀⢻⣆⠉⢿⣎⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠛⣿⡅⠀⢀⡞⢉⣻⣿⣿⣿⡆⠘⣿⣦⢈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣆⠀⠈⠻⣆⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢀⣀⣀⣀⣀⢀⣀⣀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣛⣋⠀⠀⢸⣻⣛⣀⠀⠀⣀⣸⣿⣿⣿⣿⣿⣁⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠙⣿⣷⡘⢻⣿⣿⣛⣸⣿⣿⠀⣿⣿⠉⠁⣿⣿⠀⠙⠛⠉⣾⣿⠛⣿⣷⠀⣾⣿⠛⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⠙⣿⣷⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣤⡒⣢⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⠀⠀⣿⣿⠀⡀⣀⠀⣿⣿⢀⣉⣉⠀⣿⣿⠀⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠆⣿⣿⢀⣉⣉⠺⠿⠗⠃⠀⠀⠻⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣬⠙⣿⣷⠁⢸⣿⣿⠈⢹⣿⣿⠇⣿⣿⠀⠀⣿⣿⠀⠘⠋⠀⣿⣿⠈⣿⣿⠀⣿⣿⠀⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣿⠟⠀⢸⣿⣿⠀⠀⣿⣿⠀⣿⣿⣶⡆⣿⣿⣶⡆⠀⠀⠻⣿⣶⢿⣿⢀⡻⣿⣶⣿⠟⠃⣿⣿⠀⣿⣿⣿⣿⣿⠀⠻⣿⣶⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠛⠋⠁⢀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠈⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡴⠛⠀⢹⡗⢿⣲⣦⡤⠀⠀⠀⠀⠀⢠⣴⣶⣶⣶⣦⣀⣀⣀⣀⣤⣤⣤⣄⣠⣀⣀⣀⣀⡀ ⠀⠀⠀⠠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣶⣤⣼⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠖⠲⣶⠟⢿⠿⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢸⣿⣿⣿⣿⣿⣿⣷⠹⠻⢷⣄⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠟⠛⠛⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⢠⣾⡿⢛⣿⣿⣿⣿⣿⣿⣷⣶⡂⢠⡿⠉⢹⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⠀⠀⠀⠀⠀⣰⣿⣿⣾⣿⣿⣿⠿⠛⠉⣹⣿⣿⡗⣾⣿⣉⠀⠹⣿⣿⣿⣿⡀⠀⠀⠀⢀⣦⣴⣄⠀⠀⠀⠀⠀⠀⠀⣠⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⠆⠀⠀⠀⠀⠈⣿⣿⠋⠁⠀⠀⠀⠀⠀⠹⣻⣿⣿⣿⣫⠗⣇⣴⣿⣿⣿⣿⣿⣯⠸⣿⡇⢿⡟⣿⣿⣿⣷⡀⠀⠀⢸⣿⣿⣿⣷⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⣶⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠉⠊⡹⠃⢀⣿⣿⣿⣿⣿⣿⣿⣿⠃⠹⣿⠸⣿⣏⢿⣿⣿⣧⠀⢀⣾⣿⣿⣿⣇⠀⠀⠀⠀⠀⠈⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠒⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠿⢿⣿⣿⣿⣿⣦⡀⢹⣆⠉⢻⣆⢿⣿⣿⣶⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠙⣿⡅⠀⢀⡟⣉⣛⣿⣿⣿⡆⠘⣿⣧⢈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣇⠀⠈⠻⣇⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢀⣀⣀⣀⣀⢀⣀⣀⠀⣸⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⣟⣛⣋⠀⠀⢸⣻⣛⣀⠀⠀⣀⣸⣿⣿⣿⣿⣿⣀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠙⣿⣧⡘⢻⣿⣿⣛⣸⣿⣿⠀⣿⣿⠉⠁⣿⣿⠀⠙⠛⠉⣾⣿⠛⣿⣷⠀⣾⣿⠛⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⠙⣿⣷⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣴⡒⣢⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⠀⠀⣿⣿⠀⢄⣀⠀⣿⣿⢀⣉⣉⠀⣿⣿⠀⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⢀⣉⣉⠺⠿⠛⠃⠀⠀⠙⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣬⠙⣿⣷⠁⢸⣿⣿⠈⢹⣿⣿⠇⣿⣿⠀⠀⣿⣿⠀⠚⠃⠀⣿⣿⠈⣿⣿⠀⣿⣿⠀⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣿⠟⠀⢸⣿⣿⠀⠀⣿⣿⠀⣿⣿⣶⡆⣿⣿⣶⡆⠀⠀⠻⣿⣶⢿⣿⢀⡻⣿⣶⣿⠟⠃⣿⣿⠀⣿⣿⣿⣿⣿⠀⠻⣿⣶⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠋⠁⢀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠈⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡶⠋⠀⢹⠓⠿⣐⣦⡄⠀⠀⠀⠀⠀⢠⣴⣶⣶⣾⣦⣀⣀⣀⣀⣤⣤⣤⣤⣄⣀⣀⣀⣀⡀ ⠀⠀⠀⠠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣿⣶⣤⣼⣷⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠖⠲⣶⠟⢿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢹⣿⣿⣿⣿⣿⣿⣧⠹⠿⢷⣄⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠛⠛⠋ ䷩ 𝚕𝚒𝚗𝚎 2131 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.25.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Links_25/09/2022:_EasyOS_4.4,_KDE_Reviewed⠀✐ Posted in News_Roundup at 7:57 am by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈ § Contents⠀➾ * GNU/Linux o Instructionals/Technical o Games o Desktop_Environments/WMs # K_Desktop_Environment/KDE_SC/Qt * Distributions_and_Operating_Systems o New_Releases o BSD o Canonical/Ubuntu_Family o Devices/Embedded o Open_Hardware/Modding o Mobile_Systems/Mobile_Applications * Free,_Libre,_and_Open_Source_Software o Web_Browsers/Web_Servers # Mozilla o Programming/Development # Perl_/_Raku # Shell/Bash/Zsh/Ksh o Standards/Consortia * Leftovers o Science o Education o Hardware o Health/Nutrition/Agriculture o Proprietary o Pseudo-Open_Source # Openwashing o Security # Integrity/Availability/Authenticity # Privacy/Surveillance o Defence/Aggression o Environment # Energy # Wildlife/Nature o Finance o AstroTurf/Lobbying/Politics o Censorship/Free_Speech o Freedom_of_Information_/_Freedom_of_the_Press o Civil_Rights/Policing o Internet_Policy/Net_Neutrality o Monopolies # Software_Patents # Copyrights * Gemini*_and_Gopher o Personal o Technical # Internet/Gemini # Programming * § GNU/Linux⠀➾ o § Instructionals/Technical⠀➾ # ⚓ Linux Capable ☛ How_to_Install_FreeOffice_on_Linux_Mint_21 LTS⠀⇛ From the desktop of every computer user to businesses around the world, FreeOffice is a free and open-source office suite with a word processor, spreadsheet application & presentation program. Compatible w/ Microsoft Office, making it an ideal choice if you want an alternative without expensive proprietary software that offers all features mainstream suites provide, such as complex documents, support multimedia elements, etc., plus some unique ones too – like being able open password-protected files! In the following tutorial, you will learn how to install FreeOffice on Linux Mint 21 LTS desktop with the official SoftMaker APT repository using the command line terminal and instructions on how to update and remove the software in the future if required. # ⚓ Linux Hint ☛ How_to_Merge_PDF_Files_Using_the_Command_Line on_Ubuntu⠀⇛ “Did you happen to see a presentation? You would have seen the screen with graphs and text, right? That data is in the PDF or portable documents format is, perhaps, the most popular for the ease of sharing documents that can be viewed on almost any device. The data presented on them is the same as it means to be, there can be an occasion when you need to show a single file of PDF, but it is divided into multiple parts; then what are you going to do?” This article will go through the methods to help you merge different PDF files on your Linux-based system. # ⚓ ID Root ☛ How_To_Install_Foxit_PDF_Reader_on_Manjaro_21_– idroot⠀⇛ In this tutorial, we will show you how to install Foxit PDF Reader on Manjaro 21. For those of you who didn’t know, Foxit PDF Reader is a multilingual freemium tool that can create, view, edit, digitally sign, and print PDF files. It is extremely easy to use and light-weight on your system, compared to the resource-hungry Adobe PDF reader. Foxit Reader available for Linux, macOS, and Windows 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 Foxit PDF Reader on a Manjaro 21 (Ornara). # ⚓ markaicode by Mark ☛ Disable_Unnecessary_Services_in Debian/Ubuntu_|_Mark_Ai_Code⠀⇛ Although the default installation scripts included with most Linux distribution CDs make it simple to install Linux, they also add a slew of services to your system that, at best, you’ll never use, and at worst, leave ports exposed to external intruders. The more services that operate, the more ports are left accessible to invaders. To secure your system, you should disable any superfluous services. This article is designed for users who want both practical instructions for quick installation and a thorough grasp of service administration. All Linux users, regardless of their present knowledge level, must learn how to deactivate and manage services. # ⚓ OSTechNix ☛ How_To_Visualize_Disk_Usage_With_Filelight_In Linux⠀⇛ This brief guide explains what is Filelight, how to install Filelight in Linux, and then how to visualize disk usage with Filelight in Linux operating systems. # ⚓ Hacker Noon ☛ Top_35_Linux_Console_Tips_and_Tricks_From Practical_Experience_|_HackerNoon⠀⇛ This article will be beginner friendly, only this time in the Linux console. The material is presented, in my experience, from the most frequently used to the rarest. As in the previous article about Nginx tips and tricks, I lacked these hints and tricks at the beginning of my career. o § Games⠀➾ # ⚓ Digital Music News ☛ What_Is_Trombone_Champ?_Make_Good Music_Terrible_With_a_Trombone⠀⇛ Using your mouse to slide the trombone’s pitch up or down, you must precisely hit the pitch as the song plays to receive the best possible score. Because the slider moves in the opposite direction from how you move your mouse, this adds a layer of extra difficulty, especially on some faster-paced songs. o § Desktop Environments/WMs⠀➾ # § K Desktop Environment/KDE SC/Qt⠀➾ # ⚓ Naman Sood ☛ KDE_review⠀⇛ Note: This article was originally written from mathNEWS as part of my Operating System Review series, but I decided to publish it here instead because this is not an operating system, and mathNEWS may not be as conducive to longer articles as it used to be. I write this article from a copy of Fedora 36 KDE installed on my main laptop. It’s great, it’s super intuitive, it’s mostly seamless, I really like it. I’m going back to GNOME. * § Distributions and Operating Systems⠀➾ o § New Releases⠀➾ # ⚓ Barry Kauler ☛ EasyOS_version_4.4_released⠀⇛ Version 4.4, 64-bit Dunfell-series, brings lots of little fixes and enhancements. Plus, a big-ticket item; apps now able to run in containers as user “spot”, an extra security layer above “crippled root”. As this is the Dunfell-series, almost completely compiled from source in “meta-quirky” (OpenEmbedded), the package repository is small compared with mainstream Linux distributions; however, this situation is being greatly ameliorated by additional SFS mega-packages — with more to come. o § BSD⠀➾ # ⚓ Ruben Schade ☛ Cartron_asks_what_FreeBSD_machines_I_use⠀⇛ These are my FreeBSD machines at the time of writing: [...] o § Canonical/Ubuntu Family⠀➾ # ⚓ Stacey on IoT ☛ IoT_news_of_the_week_for_Sept._23,_2022⠀⇛ Canonical brings Matter to Ubuntu, joins the CSA: This week, the Connectivity Standards Alliance (CSA) gained a new member: Canonical, the company that offers Ubuntu Linux software and services. Canonical will include support for the Matter protocol in Ubuntu Core, a containerized version of the software platform meant for embedded devices. Although Matter is platform-agnostic, it’s quite common for an IoT device to run on some flavor of Linux. As an added benefit for device makers working on Matter products, Canonical’s Ubuntu Core handles two important elements that Matter currently doesn’t: over-the-air updates and security maintenance. With this development, product engineers don’t have to worry about either of those for their Matter devices since Canonical is doing most of that work for them o § Devices/Embedded⠀➾ # ⚓ Linux Gizmos ☛ Mini_PC_enabled_by_Pentium_N6415_processor, dual_GbE_ports_and_Wi-Fi_6E⠀⇛ The ZBOX edge CI342 is a fanless Mini PC built around the Pentium N6415 processor along with Intel UHD graphics. The Mini PC supports up to 32GB of RAM, one M.2 2242/2280 socket and Wi-Fi 6E/ Bluetooth 5.2 connectivity. o § Open Hardware/Modding⠀➾ # ⚓ CNX Software ☛ M5Stack_Thermal_Camera_2_Unit_combines_ESP32 WiSoC_with_MLX90640_thermal_camera_–_CNX_Software⠀⇛ We’ve already seen the ESP32 used with a thermal camera (Flir Lepton 3.5) in the tCam-Mini IR board, but M5Stack Thermal Camera 2 Unit offers a more affordable ESP32 thermal camera solution thanks to the MLX90640 IR array thermal camera with a 32×24 resolution. Based on the ESP32-PICO-D4 system-in-package (SiP) with a dual-core microcontroller offering WiFi and Bluetooth connectivity, the camera module offers a field of view of 110°x75°, and a temperature measurement range of -40°C to 300°C. # ⚓ Adafruit ☛ Raspberry_Pi_Spy_Reviews_the_CrowPi_L_Raspberry Pi_Laptop_and_Learning_Platform_#piday_#raspberrypi @Raspberry_Pi⠀⇛ # ⚓ Mike Dominick ☛ Thelio_2022_Redesign_Review⠀⇛ While Thelio has a Denver face, where it shines is its Port-Land booty. Proudly proclaiming “real computers have ports”, it comes with a variety of HDMI, Display Port (depending on your GPU) and UBS- C ports. Whether your a developer who needs to connect IOT devices for debugging or a content creator preaching the gospel of Objective Binks, you’ll have the ports you need for your audio devices and (in my case) your mute pedal. Keen observers will notice that the back panel is slightly less styled than previous model, but that hardly detracts from the overall aesthetic appeal. # ⚓ Ubuntu_Aims_To_Support_the_$16+_Sipeed_LicheeRV_and_Other RISC-V_Boards⠀⇛ o § Mobile Systems/Mobile Applications⠀➾ # ⚓ XDA ☛ How_to_set_up_your_Android_smartphone_using_Google Voice_Access⠀⇛ # ⚓ HowTo Geek ☛ How_to_Show_the_Battery_Percentage_on Android⠀⇛ # ⚓ How_to_change_the_vibration_strength_on_Android_– Phandroid⠀⇛ # ⚓ How_to_convert_a_video_to_a_GIF_on_Android_–_Phandroid⠀⇛ * § Free, Libre, and Open Source Software⠀➾ o ⚓ Lee Yingtong Li ☛ Custom_fonts_in_KaTeX⠀⇛ KaTeX is a web-based mathematics typesetting library, similar to the erstwhile untouchable MathJax. Unfortunately, out of the box, KaTeX only supports one font, its default Computer Modern-based font, and does not have built-in functionality for customising this. Thankfully, it is not difficult to achieve this. o ⚓ Kodi Foundation ☛ Kodi_“Nexus”_Alpha_3⠀⇛ Time for another Alpha release for the upcoming Version 20 “Nexus” release of Kodi. As always, thanks go out to all contributors for their work – not only those in Team Kodi, but also to all the third party users that choose to roll up their sleeves and fix an issue. Everyone appreciates you for making Kodi better! o § Web Browsers/Web Servers⠀➾ # ⚓ uni Toronto ☛ Browsers_and_them_‘supporting’_TLS certificate_transparency⠀⇛ Certificate Transparency involves all Certificate Authorities logging newly issued TLS certificates in various public ‘CT Logs’, and then generally adding some Signed Certificate Timestamps (SCTs) to the issued TLS certificate to demonstrate that they’ve done this. Interested parties can then watch the CT logs to look for bad or mis-issued TLS certificates, and TLS clients can take steps to check that TLS certificates are in the logs. Famously, Firefox currently does not ‘support’ Certificate Transparency. But what does this actually mean? # § Mozilla⠀➾ # ⚓ Tantek_Çelik:_W3C_TPAC_2022_Sustainability_Community Group_Meeting [Ed: The Web is sheer bloat. It's not sustainable. W3C promotes DRM, which is massive contributor to pollution and waste.]⠀⇛ The W3C convened an annual TPAC in-person meeting from 2001-2019. After a couple of virtual TPACs, last week we finally returned to an in-person TPAC, the first in three years. It was great to see people, have informal conversations in hallways and outside at lunch & coffee breaks. I took some notes during meetings & breakout sessions. The Sustainability CG meeting is the first I’ve chosen to write-up. This year’s W3C TPAC Plenary Day was a combination of the first ever AC open session in the early morning, and breakout sessions in the late morning and afternoon. Nick Doty proposed a breakout session for Sustainability for the Web and W3C which he & I volunteered to co-chair, as co-chairs of the Sustainability (s12y) CG which we created on Earth Day earlier this year. Nick & I met during a break on Wednesday afternoon and made plans for how we would run the session as a Sustainability CG meeting, which topics to introduce, how to deal with unproductive participation if any, and how to focus the latter part of the session into follow-up actions. o § Programming/Development⠀➾ # ⚓ Daniel Lemire ☛ Optimizing_compilers_deduplicate_strings and_arrays⠀⇛ When programming, it can be wasteful to store the same constant data again and again. You use more memory, you access more data. Thankfully, your optimizing compiler may help. # ⚓ Frederic Cambus ☛ Toolchains_adventures_–_Q3_2022⠀⇛ This is the sixth post in my toolchains adventures series. Please check the previous posts in the toolchains category for more context about this journey. # ⚓ Idiomdrottning ☛ Planned_vs_evolved_behavior⠀⇛ Time and time again we find ourselves with problems where we wonder to what extent is this a deliberately planned behavior and to what extent has it just evolved. Most behavior is on a gradient somewhere between the two. # ⚓ Bart Wronski ☛ Progressive_image_stippling_and_greedy_blue noise_importance_sampling⠀⇛ I recently read the “Gaussian Blue Noise” paper by Ahmed et al. and was very impressed by the quality of their results and the rigor of their method. They provide a theoretical framework to analyze the quality of blue noise from a frequency analysis perspective and propose an improved technique for generating blue noise patterns. This use of blue noise is very different from “blue noise masks” and regular dithering – about which I have a whole series of posts if you’re interested. # § Perl / Raku⠀➾ # ⚓ Perl ☛ Casting_Perls_before_Splines⠀⇛ Any way I took it myself to analyse the situation and have finally come to the conclusion that we may be looking at the “problem” the wrong way. Perhaps we are looking at the bigger picture when we should seeing the picture bigger. Maybe, just maybe, that picture of a camel doesn’t symbolise Perl, but in fact IS Perl…Perl code, that is. I know it is possible to make pictures that aren’t valid perl code. But perhaps over the decades of use we have come to accept an illusion as a reality. When one gives such an illusion a “True” value, one also blurs the distinction between the Virtual Image and a Real Image.. You see a Virtual Image is an image that APPEARS to represent something, but only a Real Image can be projected. # § Shell/Bash/Zsh/Ksh⠀➾ # ⚓ [Old] Sean Conner ☛ We_could_have_skipped_writing_a program⠀⇛ It was only after lunch did I realize that none of us had to write a program. No, all it would have taken was running: [...] o § Standards/Consortia⠀➾ # ⚓ Sean Conner ☛ So_when_did_POP_and_IMAP_become_a_“legacy protocol?”⠀⇛ But on another level, this is concerning. Even though Microsoft announced this three years ago, it comes across as locking email down into a more centalized, proprietary system. I do have to wonder how long until Google decides that only certain clients can connect with Gmail? You know, for “enhanced security” or a “better experience.” I don’t use Gmail, but I do have concerns about my ability to run my own email server and general interoperability with the large email providers like Google and Microsoft. # ⚓ [Old] Jes Olson ☛ there_is_beauty_in_the_minimalism_of email⠀⇛ keep your crusty gmail account around for spam and trials and signups and whatever else, and get yourself a fastmail.com account. or a migadu.com account if you’re a techie. first: set email type to plaintext-only. this email account will only ever send or receive text. * § Leftovers⠀➾ o ⚓ Hackaday ☛ Honor_Your_Hacker_Heroes⠀⇛ We recently ran an article on a sweet percussion device made by minimal-hardware-synth-madman [Gijs Gieskes]. Basically, it amplifies up an analog meter movement and plays it by slamming it into the end stops. Rhythmically, and in stereo. It’s got that lovely thud, plus the ringing of the springs. It takes what is normally a sign that something’s horribly wrong and makes a soundtrack out of it. I love it. o ⚓ Hackaday ☛ Chandelier_Mimics_The_Solar_Analemma⠀⇛ The solar analemma is the shape the sun traces out when photographed each day at the same time and same location for a whole year – but you probably knew that already. [makendo] decided to use this skewed figure-eight shape as the inspiration for a chandelier, and the results are stunning. o ⚓ Hackaday ☛ TRS-80_Gains_Multiple_Monitor_Support,_And_High- Resolution_Graphics⠀⇛ To call [Glen Kleinschmidt] a vintage computing enthusiast would be an understatement. Who else would add the ability to control and address multiple VGA monitors to a rack-mounted TRS-80 Model 1? Multiple 64-color 640×480 monitors might not be considered particularly amazing by today’s standards, but for 70s-era computing, it’s a different story. o § Science⠀➾ # ⚓ SusamPal ☛ MathB.in_Turns_10⠀⇛ Today, MathB.in is the oldest mathematics pastebin that is still alive and serving its community of users. It isn’t the first mathematics pastebin though. It’s the second. The first one was written by Mark A. Stratman and hosted at mathbin.net until 2020. It was very popular in the #math and #physics channels on IRC networks between 2006 and 2013. It did not have live preview but it used an actual LaTeX system in the backend for rendering mathematical formulas into images, so the output was of pretty good quality. It served IRC users very well for sharing problems and solutions quickly with each other on IRC channels. Since late-2014, Mark’s website began intermittently displaying a notice that the website was shutting down. The notice replaced the actual pastebin on some days, so users were forced to look for alternatives. MathB.in was already available on the web and popular among IRC users by then, so it turned out to be a good alternative. Mark’s website disappeared sometime in late-2020. # ⚓ Adafruit ☛ Astro_Pi_Mission_Zero_2022/23_is_Open_#piday #raspberrypi_@Raspberry_Pi⠀⇛ If you’ve been involved in Mission Zero before, you will notice lots of things have changed. This year’s Mission Zero participants will be the first to use our brand-new online code editor, a tool that makes it super easy to write their program using the Python language. # ⚓ Wired ☛ Philadelphia’s_Diatom_Archive_Is_a_Way,_Way, Wayback_Machine⠀⇛ This crystalized during a 1948 expedition to Pennsylvania’s Conestoga River—a body of water heavily polluted by sewage and industrial runoff. As her team collected samples from throughout the creek, she recognized patterns in the diatom composition. Some species’ densities exploded in areas contaminated with sewage, while others thrived in spots tainted with chemicals. Soon, Patrick became adept at using the existence of certain diatoms as a key for diagnosing pollution in lakes and rivers. This supported the idea that greater diatom diversity correlated with healthier freshwater ecosystems—an insight ecologists coined the Patrick principle. o § Education⠀➾ # ⚓ Sabine Hossenfelder ☛ What_is_“Nothing”?⠀⇛ First things first, what do we mean by “nothing”? A first attempt to define nothing is to look at how we use the word in everyday language. Suppose your birthday is coming up and you say “Oh, I want nothing.” So when I give you a box for your birthday, you expect it to be empty It’s nothing, in the sense that it doesn’t contain any objects. We will call this the level 1 nothing. It’s a pre- science nothing, the nothing you might refer to before you’ve ever heard of physics. o § Hardware⠀➾ # ⚓ Hackaday ☛ CMOS_Oscillator_Circuit_Gets_An_Eatable_Input⠀⇛ In interaction designer [Leonardo Amico]’s work Processing Decay, lettuce is used as an input to produce sound as an element within a CMOS circuit.  # ⚓ Hackaday ☛ Minimal_Tic_Tac_Toe_Business_Card⠀⇛ The PCB business card has long been a way for the aspiring electronics engineer to set themself apart from their peers. Handing out a card that is also a two player game is a great way to secure a couple minutes of a recruiter’s time, so [Ryan Chan] designed a business card that, in addition to his contact information, also has a complete Tic-Tac- Toe game built in. # ⚓ Hackaday ☛ Animated_LED_Arrows_Point_The_Way⠀⇛ Visitors at the Garden D’Lights in Bellevue, Washington had a problem. While touring the holiday lights show, they kept straying off the path. The event organizers tried some simple LED arrows, but they were just more points of light among a sea filled with them. This is when [Eric Gunnerson] was asked to help out. He’s apparently had some experience with LED animations, even cooking up a simple descriptor language for writing animations driven by an ESP32. To make the intended path obvious, he turned to a PVC board with 50 embedded WS2812 pixels –RGB controllable LEDs. The control box was a USB power adapter and an ESP8266, very carefully waterproofed and connected to the string of pixels. The backer board is painted black, to complete the hardware. Stick around after the inevitable break, to get a look at the final # ⚓ Hackaday ☛ This_Scratch-Built_X-Ray_Tube_Really_Shines⠀⇛ On no planet is making your own X-ray tube a good idea. But that doesn’t mean we’re not going to talk about it, because it’s pretty darn cool. o § Health/Nutrition/Agriculture⠀➾ # ⚓ Futurism ☛ Woman_Horrified_To_Discover_Her_Private_Medical Photos_Were_Being_Used_To_Train_AI⠀⇛ An AI artist going by the name Lapine says she discovered that private medical photos from nearly ten years ago were being used in an image set that trains AI, called LAION-5B. Lapine made this unnerving discovery by using Have I Been Trained, a site that lets artists to check if their work has been used in the image set. When Lapine performed a reverse image search of her face, two of her private medical photos unexpectedly cropped up. # ⚓ Common Dreams ☛ Opinion_|_Where_Is_the_Mass_Mobilized Movement_for_Medicare_for_All?⠀⇛ Long before the Covid pandemic, it was important to ask, where are the mass movements to enact in Congress majoritarian-supported changes and reforms? Another question: Whatever happened to the mass rallies that used to command the attention of our 535 members of Congress to whom we have given our sovereign power? # ⚓ Common Dreams ☛ Opinion_|_Direct_Cash_Transfers_Lifted_28 Million_Americans_Out_of_Poverty_During_Pandemic⠀⇛ The U.S. Census Bureau recently reported that poverty dropped notably in 2021. Amid a pandemic and widespread economic pain, this is a significant accomplishment. # ⚓ TruthOut ☛ Water_Access_Has_Returned_to_Jackson,_But_a Long-Term_Health_Crisis_Remains⠀⇛ o § Proprietary⠀➾ # ⚓ Port Swigger ☛ Uber_hack_linked_to_hardcoded_secrets spotted_in_PowerShell_script⠀⇛ Uber is purported to rely on multi-factor authentication (MFA). Third-party experts have commented that an attacker may have been able to circumvent these controls by establishing a fake domain and any relaying authentication codes submitted to the genuine domain using a manipulator-in-the-middle (MitM) attack. o § Pseudo-Open Source⠀➾ # § Openwashing⠀➾ # ⚓ Protocol ☛ Passing_the_PyTorch [Ed: Openwashing by tarnishing away the brand "Linux"]⠀⇛ Meta is handing the reins for PyTorch, its popular open-source AI framework, to the nonprofit open-source software consortium Linux Foundation. PyTorch was designed to optimize deep learning, and gets its name from the AI programming language Python and open-source machine-learning library Torch. o § Security⠀➾ # ⚓ 4_CTF_Cloud_and_Linux_Security_Challenges_Now_Open_– Pentesting_Cloud⠀⇛ PenTesting.Cloud, a free learning platform, has released their first 4 challenges. Utilize your Linux and Cloud Computing skills to exploit vulnerabilities in a lab environment. New challenges are released every two weeks. They are setup in a CTF style, where you can earn points and compete against other members. Most challenges require Linux and/or Python experience to solve, along with Cloud knowledge. If you don’t have access to a Linux box, you can use an EC2 instance. Users with strong Linux and shell scripting skills will be able to earn the most points. The site was launched to promote free learning in the realms of Linux and Cloud security. It focuses on using Linux skills to discover and remediate common misconfigurations in the Cloud. The website is totally free, however you may incur a small AWS charge for the labs which require you to run them in your personal AWS sandbox account. # ⚓ Help Net Security ☛ Revolut_data_breach:_50,000+_users affected_–_Help_Net_Security⠀⇛ Revolut customers began noticing something was wrong on September 11, when some of them reported receiving “inappropriate wording via chat.” # § Integrity/Availability/Authenticity⠀➾ # ⚓ Of0x ☛ Thoughts_on_the_use_of_noVNC_for_phishing campaigns⠀⇛ Dear Fellowlship, today’s homily is a rebuke to all those sinners who have decided to abandon the correct path of reverse proxies to bypass 2FA. Penitenziagite! # § Privacy/Surveillance⠀➾ # ⚓ Wired ☛ A_Danish_City_Built_Google_Into_Its Schools—Then_Banned_It⠀⇛ The main issue Graugaard has highlighted is that they don’t really understand what students’ Google data is used for or where it goes. “Google is always saying, we don’t use the data of pupils for targeted advertising. We do not sell the data to third parties,” says Jesper Lund, chair of digital rights group IT Pol Denmark. But there is concern that Google does use students’ data for other purposes, such as improving its services or training artificial intelligence, he adds. # ⚓ Sean Conner ☛ Just_how_much_telemetry_does_The Enterprise_need_from_my_work_laptop?⠀⇛ Today, I turn on Satan’s replacement, Belial, the annoying Mac Laptop. I’m not sure what The Enterprise is doing to it, because as soon as I turned on Belial, the network connection here at Chez Boca dropped to near zero. # ⚓ MIT Technology Review ☛ Hated_that_video?_YouTube’s algorithm_might_push_you_another_just_like_it.⠀⇛ That algorithm shapes the information billions of people consume, and YouTube has controls that purport to allow people to adjust what it shows them. But, a new study finds, those tools don’t do much. Instead, users have little power to keep unwanted videos—including compilations of car crashes, livestreams from war zones, and hate speech—out of their recommendations. # ⚓ New York Times ☛ LinkedIn_Ran_Social_Experiments_On 20_Million_Users_Over_Five_Years⠀⇛ In experiments conducted around the world from 2015 to 2019, Linkedin randomly varied the proportion of weak and strong contacts suggested by its “People You May Know” algorithm — the company’s automated system for recommending new connections to its users. The tests were detailed in a study published this month in the journal Science and co-authored by researchers at LinkedIn, M.I.T., Stanford and Harvard Business School. LinkedIn’s algorithmic experiments may come as a surprise to millions of people because the company did not inform users that the tests were underway. # ⚓ Futurism ☛ Churches_Using_“Shameware”_Apps_To_Make Sure_Members_Don’t_Watch_Porn⠀⇛ An evangelical Southern Baptist church known as Gracepoint was caught relying on a little more than God’s watchful gaze to keep an eye on members of its congregation. And if a church feels compelled to clarify that it’s not a cult, well… New members joining Gracepoint’s congregation are asked to install an app called Covenant Eyes, which is explicitly marketed as an “anti-pornography” app. And according to a must-read investigation by Wired, Covenant Eyes spies on members’ web traffic, takes a screenshot of their phone screens every single minute, and then sends all this information to an “accountability partner.” In reality, it’s more like spyware. # ⚓ Wired ☛ The_Ungodly_Surveillance_of_Anti-Porn ‘Shameware’_Apps⠀⇛ Covenant Eyes is part of a multimillion- dollar ecosystem of so-called accountability apps that are marketed to both churches and parents as tools to police online activity. For a monthly fee, some of these apps monitor everything their users see and do on their devices, even taking screenshots (at least one per minute, in the case of Covenant Eyes) and eavesdropping on web traffic, WIRED found. The apps then report a feed of all of the users’ online activity directly to a chaperone—an “accountability partner,” in the apps’ parlance. When WIRED presented its findings to Google, however, the company determined that two of the top accountability apps—Covenant Eyes and Accountable2You—violate its policies. # ⚓ Scheerpost ☛ Military_Whistleblower_Challenges Pentagon’s_Warrantless_Purchase_of_Internet_Data⠀⇛ America’s data is proving again to be a hot commodity for the government. o § Defence/Aggression⠀➾ # ⚓ Meduza ☛ Kremlin_thinks_about_mobilizing_residents_of Abkhazia_and_South_Ossetia_—_Meduza⠀⇛ The Kremlin is considering the possibility of mobilizing not only Russian citizens, but also citizens of the self-proclaimed republics of Abkhazia and South Ossetia for the war in Ukraine, a source close to the Russian president’s administration told Meduza. # ⚓ Meduza ☛ Russia_may_formally_annex_occupied_territories_on September_30_—_Meduza⠀⇛ President Vladimir Putin’s address to the Federal Assembly may take place on September 30, report RIA Novosti and Verstka, according to a source in parliament.  # ⚓ Meduza ☛ More_than_700_people_arrested_in_anti-war_actions —_Meduza⠀⇛ More than 700 people have been arrested in cities across Russia during protests against the war in Ukraine and the Russian mobilization, reports independent media project OVD Info. # ⚓ Meduza ☛ Anti-war_protests_resume_in_Russian_cities, protestors_arrested_—_Meduza⠀⇛ September 24 saw actions against the war in Ukraine and the forced Russian mobilization in cities across Russia. Participants in the actions are being arrested. # ⚓ Meduza ☛ Putin_signs_law_toughening_punishments_during mobilization_—_Meduza⠀⇛ Russian president Vladimir Putin signed a law toughening punishments for crimes against military service during the mobilization period. The law also introduces criminal penalties for voluntary surrender and looting. o § Environment⠀➾ # ⚓ Deutsche Welle ☛ Pope_Francis_calls_for_world_to_abandon fossil_fuels⠀⇛ “Now is the time for new courage in abandoning fossil fuels to accelerate the development of zero- or positive-impact sources of energy,” Francis said. # ⚓ Scheerpost ☛ The_Hidden_Downside_for_Democracy_in_the Patagonia_Sale⠀⇛ Mitchell Beer records experts responses to the recent sale of the outdoor retail giant. # § Energy⠀➾ # ⚓ Common Dreams ☛ Opinion_|_Joe_Manchin_Is_My_Senator, But_We_Need_Your_Help_to_Defeat_His_Dirty_Deal⠀⇛ In 2014 I was notified that a group of fossil fuel corporations wanted to build the 42-inch Mountain Valley Pipeline across my organic farm in rural, southern West Virginia. I had no idea the twist and turn my life would be thrust into. Over the last 8 years, I have witnessed both state and federal agencies try on numerous occasions to short circuit and pervert the very laws and policies that we all depend upon to protect our homes, farms, and communities from devastating environmental destruction. This is a story about social justice and community protection. # ⚓ Common Dreams ☛ Opinion_|_A_Fossil_Fuel_Non- Proliferation_Treaty_Will_Save_Lives⠀⇛ We can almost always tell how sick a patient may be before seeing them just by looking at their address. Every day we treat patients who are desperately ill with a number of medical conditions all with the same root cause: environmental racism. Historical discriminatory housing policies have trapped non-white and low income communities in overpolluted neighborhoods. Neighborhoods in previously redlined zones have nearly twice as many oil wells, breathe dirtier air and have much less green space. # ⚓ TruthOut ☛ Minneapolis_Energy_Bills_and_Taxes_Are Funding_Right-Wing_Candidate_in_Wisconsin⠀⇛ # § Wildlife/Nature⠀➾ # ⚓ Pro Publica ☛ The_Racism,_and_Resilience,_Behind Today’s_Salmon_Crisis⠀⇛ Perched on a plywood scaffold over roaring waters, a Wenatchi father and son fished using long nets made by hand and under the cover of darkness so it’s harder for salmon to spot them. o § Finance⠀➾ # ⚓ DaemonFC (Ryan Farmer) ☛ Consumer_products_makers_shift promotions_into_high_gear_to_retain_customers_and_change buying_patters._Many_exploit_‘Consumer_Illiteracy’._| BaronHK’s_Rants⠀⇛ Consumer products makers shift promotions into high gear to retain customers and change buying patters. Many exploit “Consumer Illiteracy”. Today I got a third “free” bottle of “Natean” toothpaste from iBotta. They keep putting it on iBotta to encourage people to take some, hopefully to permanently change their buying behavior. The problem (for them) is that toothpaste is basically toothpaste and I’m no idiot. As soon as the “free after rebate” or “half price” rebates on something end, I switch and stock up on the competitor’s product, if they have rebates. # ⚓ Common Dreams ☛ Opinion_|_​​College_Debt_is_the_Tip_of_the Iceberg⠀⇛ President Joe Biden recently instituted a program to forgive some of the student debt that plagues approximately 45 million Americans. That is all well and good, but why are so many people in debt up to their eyeballs for a vaporous commodity that, in so many cases, delivers nothing?  This isn’t bitter hyperbole, but tangible fact when you add up all the dropouts and the hybrid degrees in, say, comparative Latin poetry and transpersonal themes of 19th century German philosophy (the esoteric, combo degree is the product of university gaslighting. Schools aspire to fleece the quirkiest students despite an increasingly limited job market focused on technical skills). There is room, in the open-minded, expansive world of intellectual curiosity, for all seekers of wisdom who pony up. # ⚓ Common Dreams ☛ Opinion_|_It’s_Lower-Income_Families_Who Will_Be_Hit_Hardest_by_Fed_Rate_Hikes⠀⇛ # ⚓ Scheerpost ☛ Class_Warfare_Grinds_On⠀⇛ Eve Ottenberg examines how corporations continue to find ways to screw their workers. o § AstroTurf/Lobbying/Politics⠀➾ # ⚓ The Gray Zone ☛ How_an_obscure_intellligence-linked_party fixed_a_second_Brexit_referendum_and_torpedoed_Corbyn⠀⇛ # ⚓ TruthOut ☛ Chomsky:_The_US_and_Israel_Are_Standing_in_the Way_of_Iran_Nuclear_Agreement⠀⇛ # ⚓ TruthOut ☛ International_Interference_in_Haiti_Is_Crushing Its_Garment_Industry⠀⇛ # ⚓ Craig Murray ☛ I_Am_Puzzled⠀⇛ There has been an unprecedented rush of people canceling their subscriptions to this blog the last five days. Not one person has given any reason, and where there have been messages, they have been of this unfriendly but uninformative nature. # ⚓ TruthOut ☛ House_Democrats_Call_on_DOJ_to_Investigate DeSantis_for_“Cruel_Migrant_Flights”⠀⇛ # ⚓ Meduza ☛ Head_of_Yakutia_says_residents_called_up_‘by mistake’_should_be_returned_—_Meduza⠀⇛ Aisen Nikolayev, Head of Yakutia, announced that residents mobilized “by mistake” must be returned from the armed forces. # § Misinformation/Disinformation/Propaganda⠀➾ # ⚓ The Economist ☛ How_Russia_is_trying_to_win_over_the global_south⠀⇛ Russia’s propaganda is not monolithic. Instead, as it does in the West, it seeks to exploit existing divisions and tensions. To do so, it can draw on decades of experience, going back to the cold war, of running influence operations in the developing world. “Russia is very effective at building on sentiments that already exist,” argues Jessica Brandt of the Brookings Institution, an American think-tank. “It’s fertile ground and they’re well-practised.” In Africa, Russian propaganda networks have pushed the line that Western sanctions, rather than Russia’s blockade of the Black Sea, caused food prices to spike—part of a long pattern of Western disregard for the developing world. Russian outlets also highlighted reports of the mistreatment of African students trying to flee Ukraine immediately after the invasion. In Latin America, Russian media tap into existing anti-imperialist and anti-American sentiment. In the Middle East, America’s failed interventions in Iraq and Libya are held up as proof of Western hypocrisy. Europe’s warm welcome of Ukrainian refugees is contrasted with the frostier welcome given to Syrians. o § Censorship/Free Speech⠀➾ # ⚓ MIT Technology Review ☛ The_world_is_moving_closer_to_a_new cold_war_fought_with_authoritarian_tech⠀⇛ Late last week, Iran, Turkey, Myanmar, and a handful of other countries took steps toward becoming full members of the Shanghai Cooperation Organization (SCO), an economic and political alliance led by the authoritarian-regimes of China and Russia. The group, formed in 2001, has quickly become one of the most important forces in global politics and has indicated that technology is a big part of its strategic future. Although much of the SCO’s focus is on regional development, such as railways and trade agreements, it has been a key player in the proliferation of technologies designed for social control, which foreign policy experts call “digital authoritarianism.” # ⚓ MIT Technology Review ☛ There’s_no_Tiananmen_Square_in_the new_Chinese_image-making_AI⠀⇛ When a demo of the software was released in late August, users quickly found that certain words—both explicit mentions of political leaders’ names and words that are potentially controversial only in political contexts—were labeled as “sensitive” and blocked from generating any result. China’s sophisticated system of online censorship, it seems, has extended to the latest trend in AI. # ⚓ NPR ☛ How_independent_bookstores_help_in_the_fight_against book_banning_and_why_it_matters⠀⇛ Bolgla’s store, Atlanta Vintage Books, is one of hundreds of independent bookstores across the country that have celebrated the freedom to read this week at a time when schools, universities and public libraries face what experts say are unprecedented attempts to ban or restrict reading materials. # ⚓ Vice ☛ Russian_Influencer_Says_She_Faces_6_Years_in_Prison for_Using_Instagram⠀⇛ According to Russian digital rights NGO Roskomsvoboda, Veronika Loginova is the first individual to be prosecuted after a Russian court banned Instagram and Facebook for “extremist” activities in March in the aftermath of the invasion of Ukraine. o § Freedom of Information / Freedom of the Press⠀➾ # ⚓ Scoop Media ☛ Aucklander_Inspires_Demonstration_Around British_Parliament_To_Free_Julian_Assange,_October_8th⠀⇛ Aucklander Matt Ó Branáin has inspired a historic demonstration in London on October 8th, to free jailed Australian journalist Julian Assange. Matt’s proposal to #HugBelmarsh prison with a Human Chain of 1,100 people went viral. Due to some difficulties, it has turned into a #FreeAssangeHumanChain of 5,000 to surround British Parliament, where the decision to free Julian can be made. Matt has launched a campaign for kiwis to help him represent New Zealand there. He is asking for help with travel costs and he will add the names of all who donate to special flax ribbons he will weave and take to the event. # ⚓ Scheerpost ☛ The_Israel_Files:_WikiLeaks_Docs_Show_Top Hollywood_Producers_Working_With_Israel_To_Defend_Its_War Crimes⠀⇛ The Israel Files is a new MintPress series exploring and highlighting the many revelations about the Israeli occupation of Palestine that WikiLeaks documents disclosed. It hopes to shed light on ma… # ⚓ VOA News ☛ Journalists_Arrested_in_Iran,_Warned_About Protest_Coverage⠀⇛ Nearly a dozen journalists — at least three of them women — have been detained over coverage of the protests and the death in custody of Mahsa Amini, 22, who was arrested by Iran’s morality police. Additionally, authorities have cut internet access as protests continue, according to rights groups and an Iranian diaspora news website. # ⚓ Axios ☛ NARA_withholding_Mar-a-Lago_search_records_to protect_DOJ’s_“ongoing_work”⠀⇛ In Thursday’s letter, Wall didn’t rule out handing over records in the future. “To the extent that we are able to release any additional records responsive to your request in the future, we will make them available to you,” she said. # ⚓ CBC ☛ Conservative_MPs_call_for_freelance_journalist_to_be booted_from_press_gallery_after_tweet⠀⇛ The issue spilled out of a moment during question period on Wednesday when Conservative MP Garnett Genuis quoted the band Queen while asking a question about inflation. The Queen reference was a dig at Prime Minister Justin Trudeau, who was spotted singing Bohemian Rhapsody with members of the Canadian delegation last weekend ahead of Queen Elizabeth’s funeral. # ⚓ ANF News ☛ Prison_sentence_for_JinNews_reporter_for_“terror propaganda”⠀⇛ The background to the proceedings were Önver’s Twitter posts, the content of which dealt with crimes against Kurds. The specific accusation was “chain-like terror propaganda in media organs”. During an interrogation by the Turkish police’s counter-terrorism department regarding the investigation, Önver had previously been questioned about, among other things, tweets about the political triple-murder of the Kurdish revolutionaries Sakine Cansız, Fidan Doğan and Leyla Şaylemez in 2013 by an MIT killer in Paris. Posts about the Roboski massacre, in which a total of 34 civilians were killed by the Turkish air force at the end of 2011, as well as the murder of human rights lawyer Tahir Elçi in 2015 in the old city of Amed (Diyarbakır) were also classified as “criminal” by the police at the time. The authorities based their investigation on the fact that Önver had shared videos showing people wearing cloth scarves in the “forbidden colours” of green, red and yellow. Further questions, according to the journalist, revolved around the location of the posted tweets and “the goal behind them”. # ⚓ ANF News ☛ Journalist_arrested_in_Iran_after_reporting_on Amini’s_death⠀⇛ Journalist Nilufar Hamedi has been imprisoned in the Iranian capital, Tehran. She was the first to publicise the case of 22-year-old Jina Mahsa Amini, who died under the custody of so-called morality police. This led to protests against the regime of Iran’s President Ebrahim Raisi throughout the country. In Eastern Kurdistan (Rojhilat), almost every town is in resistance against the ruling clergy and the system. o § Civil Rights/Policing⠀➾ # ⚓ Scheerpost ☛ DOJ_Admits_It_Has_No_Idea_How_Many_People_Die in_Law_Enforcement_Custody⠀⇛ Thousands of deaths in jails, prisons, and police custody have gone uncounted in recent years. Now the DOJ is calling for changes to federal law. # ⚓ Deutsche Welle ☛ Opinion:_The_mullahs_are_afraid_of_women⠀⇛ Massive protests sparked by a young Iranian woman’s death are shaking the foundations of the Islamic Republic. Iranian women are taking a huge risk and need more than expressions of solidarity, says Yalda Zarbakhch. # ⚓ Common Dreams ☛ US_Progressives_Express_Solidarity_With Iranian_Protesters_After_Death_of_Mahsa_Amini⠀⇛ “The Iranian people, led by young women, are demonstrating for their freedom and for a better life.” # ⚓ NPR ☛ The_Cherokee_Nation_is_renewing_its_push_for_a nonvoting_delegate_in_Congress⠀⇛ In 1835, U.S government officials and members of the Cherokee Nation signed the Treaty of New Echota, which led to the expulsion of Cherokees from their territory east of the Mississippi River in a mass exodus known as the Trail of Tears. A lesser-known provision of the same treaty also granted the Cherokee Nation a delegate in the House of Representatives “whenever Congress shall make provision for the same.” Now, the tribal government is calling on congressional leadership to finally make good on the pledge of its predecessors. # ⚓ DaemonFC (Ryan Farmer) ☛ Crazy_Russian_charged_with obstruction._|_BaronHK’s_Rants⠀⇛ This truly is a first. This is the first time I’ve ever heard about the cops charging someone for obstructing them while they’re trying to go away. # ⚓ Common Dreams ☛ ‘Catastrophic’:_Arizona_Judge_Allows_1864 Abortion_Ban_to_Go_Into_Effect⠀⇛ Pima County Superior Court Judge Kellie Johnson said in her ruling that Roe v. Wade, the 1973 U.S. Supreme Court ruling which affirmed the constitutional right to abortion care, had been the basis for barring the 1864 law from being enforced. Since Roe was overturned in June, she said, the injunction should be annulled. # ⚓ TruthOut ☛ Arizona_Judge_Lifts_Injunction_Against_State’s 1864_Anti-Abortion_Law⠀⇛ # ⚓ Common Dreams ☛ Federal_Judge_Allows_‘Untenable’_Plan_to Send_Juvenile_Inmates_to_Angola_Prison⠀⇛ Chief U.S. District Judge Shelly Dick ruled that the Office of Juvenile Justice (OJJ) can send two dozen children under the age of 18 from Bridge City Center for Youth, located outside New Orleans, to the Louisiana State Penitentiary, denying a motion brought by several law firms and the ACLU to halt the plan. o § Internet Policy/Net Neutrality⠀➾ # ⚓ APNIC ☛ Interdomain_BGP_policies_—_where_traffic_should exit_a_network⠀⇛ In this series, I’m going to discuss different reasons for these kinds of policies, and different ways to implement them in interdomain BGP. I’ll refer to Figure 1’s reference network throughout this post. o § Monopolies⠀➾ # § Software Patents⠀➾ # ⚓ Digital Music News ☛ Meta_Ordered_to_Pay_$175MM_For Infringing_‘Walkie-Talkie’_Live-Streaming_Patents⠀⇛ Court documents further allege that Katis met with Facebook’s Senior Product manager for Facebook Live to discuss the issue. Meta declined to enter an agreement with Voxer regarding the use of its patented technology and then launched Instagram Live in 2016. Meta has refuted these claims and says it will appeal the $175M decision. # § Copyrights⠀➾ # ⚓ Torrent Freak ☛ “House_of_the_Dragon”_Crushes_“The Rings_of_Power”_on_Pirate_Sites⠀⇛ “House of the Dragon” and “The Lord of the Rings: The Rings of Power” are two completely different TV series. However, their near- simultaneous premieres have tempted people to draw comparisons. While we can’t say which series is better, the download numbers show that torrenting pirates clearly favor the Game of Thrones prequel. * § Gemini* and Gopher⠀➾ o § Personal⠀➾ # ⚓ You_move_sixteen_tons,_and_what_do_you_get?_Another_inch over_and_deeper_in_exhaustion⠀⇛ So for reasons, Bunny and I are moving items from one storage unit company to another, and as part of that move, we’re consolidating into a larger storage unit. We have a 10′×15′ storage unit (3m×5m for those who use sane units) with a garage type door. The shelving units we use are these plastic module units that are easy to knock down and put back up. We have one wall lined with shelves already. Yesterday, we moved three more shelves into the unit along the opposite wall. Bunny was concerned about having enough space to close the garage door, but I assured her we had plenty of room by laying down one yet-to-be-installed shelf on the floor and showing that it fit into the space and didn’t extend beyond the opening. # ⚓ Star_Log_2022-09-24_22:00_AKDT_(Fairbanks,_AK,_US)⠀⇛ Cloud conditions continue to cause great difficulty for star gazing, but tonight, God cleared away most of the clouds around sunset, and kept it clear until about 10:30pm. This gave me about 1.5 hours of pleasant star gazing. # ⚓ Identity⠀⇛ Hey ~bartender, it’s been a long night. I just need a water, please, nothing special. It’s been a long night. I’ve been thinking about my identity, who I am, and who I want to be. I’ve also had to face some things that made me uncomfortable, but I needed to face them. I was born a man. Recently, I’ve been considering, “maybe I’m a woman.” I don’t know if it’s because I truly feel that way, or because of internalized sexism and the want to be someone else. I’m just not sure. o § Technical⠀➾ # § Internet/Gemini⠀➾ # ⚓ Gemini_Radio:_Episode_45⠀⇛ # § Programming⠀➾ # ⚓ Assembling_some_notes_on_Assembly_Language⠀⇛ So, I saw a thing on the YT channel “The 8- bit Guy” some time ago about Assembly Language, and I think the video before that was “The Basics of BASIC”, and over a couple months, I kept going back and thinking again and again about AL. “Wow!”, I thought. “It would be like writing code **straight** to the damn hardware, itself!” Which, is kinda IS doing that. So I started to put together some notes from a Github hosted “e-book” called “Some Assembly Required” by the “Hack Club” (an “organization” of developers/programmers who are in high school – sort of a national organization type of a thing), and I am a fair bit into SAR, and got down to the some specific code examples (which were geared for x86 (64-bit)), and I was like “this (AL) is essentially all math-based, yea?”, and I kinda steered away from AL after that. =============================================================================== * Gemini_(Primer) links can be opened using Gemini_software. It’s like the World Wide Web but a lot lighter. ䷩ 𝚕𝚒𝚗𝚎 3851 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.25.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Links_25/09/2022:_Linux_6.0_RC7_and_PostgreSQL-Related_Releases⠀✐ Posted in News_Roundup at 4:47 pm by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈ § Contents⠀➾ * GNU/Linux o Desktop/Laptop o Server o Audiocasts/Shows o Kernel_Space o Applications o Instructionals/Technical o Games o Desktop_Environments/WMs # GNOME_Desktop/GTK * Distributions_and_Operating_Systems o Fedora_Family_/_IBM o Debian_Family o Mobile_Systems/Mobile_Applications * Free,_Libre,_and_Open_Source_Software o Web_Browsers/Web_Servers # Chromium o SaaS/Back_End/Databases o Productivity_Software/LibreOffice/Calligra o Programming/Development # Perl_/_Raku # Python # Java # Rust * Leftovers o Science o Health/Nutrition/Agriculture o Security # Privacy/Surveillance o Transparency/Investigative_Reporting o Environment # Energy o Finance o AstroTurf/Lobbying/Politics o Monopolies # Copyrights * Gemini*_and_Gopher o Personal o Technical # Announcements # Programming * § GNU/Linux⠀➾ o § Desktop/Laptop⠀➾ # ⚓ Linux Links ☛ Linux_Around_The_World:_USA_–_Wyoming_– LinuxLinks⠀⇛ We cover events and user groups that are running in the US state of Wyoming. This article forms part of our Linux Around The World series. o § Server⠀➾ # ⚓ Matt Rickard ☛ Google_Infra_For_Everyone_Else_in_2022⠀⇛ Kubernetes is complex but arguably a good way to do things – even if you aren’t using it directly, many popular services were enabled or inspired by its API and workflow. It should be noted that Kubernetes is inspired by, but not Borg, the internal workload (not Docker) scheduler used by Google. Very few services at Google run on Kubernetes. So in a way, it wasn’t really “the Google way of doing things.” o § Audiocasts/Shows⠀➾ # ⚓ The_Feeling_of_Fast_|_LINUX_Unplugged_477⠀⇛ We finally give Brent his new laptop and get his reaction. Plus our best pick for replacing stock Android with something private. # ⚓ E52:_Learnings_from_Chef_&_the_Future_of_Open_Source⠀⇛ Adam Jacob is the Cofounder & CTO of Chef, the infrastructure automation platform, and CEO of System Initiative. o § Kernel Space⠀➾ # ⚓ Linus_Torvalds:_Linux_6.0-rc7⠀⇛ So I was thinking rc7 might end up larger than usual due to travel hitting rc6, but it doesn't really seem to have happened. Yeah, maybe it's marginally bigger than the historical average for this time of the release cycle, but it definitely isn't some outlier, and it looks fairly normal. Which is all good, and makes me think that the final release will happen right on schedule next weekend, unless something unexpected happens. Knock wood. Incidentally, rc7 is also (I think) the first time we have a clean 'make allmodconfig' build with no warnings from clang, since the patches for frame size problems in the amd display code got merged. The stack frame size is still pretty big (and the code isn't exactly pretty), but now it's below the level we warn about. So that's nice to see. Anyway, full shortlog below - a lot of it is GPU and network drivers, but there's various random other fixes in there too. Let's give this one (hopefully) final week of testing, but it all looks pretty good. Linus o § Applications⠀➾ # ⚓ Ubuntu Handbook ☛ Audacity_3.2.0_Released_with_Realtime Effects_&_Apple_Silicon_Support_|_UbuntuHandbook⠀⇛ Audacity audio editor got a new major update few days ago, features real-time effects and VST3 support. In the new 3.2.0 release, there’s a new “Effects” button in the tracks menu, allowing to place realtime effects. However, it does not yet ship with any effect so far. User has to get effects via plugins, though only Audio Units (macOS only), VST3, LV2, and LADSPA formats are supported at the moment. # ⚓ OMG Ubuntu ☛ NewsFlash_RSS_Reader_Has_Been_Ported_to_GTK_4 –_OMG!_Ubuntu!⠀⇛ RSS fans rejoice for a brand-new version of NewsFlash, a GTK RSS reader for Linux desktops, is out! NewsFlash 2.0 is the biggest update to this nifty news reader for a while. It sees devs finish work on the much-anticipated GTK 4 & libadwaita port. As a result, NewsFlash looks sharper, more refined, and a lot more consistent within itself. The app now boasts an adaptive layout that responds to screen width, letting the app work on mobile. # ⚓ PowerDNS ☛ First_Alpha_Release_of_PowerDNS_Recursor_4.8.0_| PowerDNS_Blog⠀⇛ We are proud to announce the first alpha release of PowerDNS Recursor 4.8.0. o § Instructionals/Technical⠀➾ # ⚓ ID Root ☛ How_To_Install_KeePassXC_on_Ubuntu_22.04_LTS_– idroot⠀⇛ In this tutorial, we will show you how to install KeePassXC on Ubuntu 22.04 LTS. For those of you who didn’t know, KeePassXC is a free open-source password manager or safe which helps you to manage your passwords in a secure way. It is built using Qt5 libraries, making it a multi-platform application that can be run on Linux, Windows, and macOS. KeePassXC also offers many features, including creating multiple databases, encrypting databases with a master key, and generating strong passwords. In addition, KeePassXC provides support for plugin development, allowing users to extend the application’s functionality. 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 KeePassXC password manager on Ubuntu 22.04 (Jammy Jellyfish). You can follow the same instructions for Ubuntu 22.04 and any other Debian-based distribution like Linux Mint, Elementary OS, Pop!_OS, and more as well. # ⚓ Linux Hint ☛ How_to_Create_Macros_in_VIM_for_Repetitive Tasks⠀⇛ Macros are technically the execution sequence of some operations and are usually created to perform the frequently occurring tasks quickly. In Microsoft Windows, you can find the MS Word, which has the functionality to let you create macros. In the Linux-based systems, you will see the VIM Editor and you can, like in MS word, create macros in VIM. It can also be recorded, which can later be played in a file. It is also called the record and play feature of the VIM editor. # ⚓ Linux Hint ☛ How_to_Copy_from_Clipboard_to_Nano⠀⇛ While you are using the nano editor and copying text, it is saved in a buffer called the Cutbuffer, and it is not the same as the clipboard because Gnome maintains the clipboard. You cannot paste anything from the nano editor to the other applications. Nano is a command line text editor that comes pre-installed in almost all Linux-based systems. It has a good set of features that make it above the others. But, how can you copy from the clipboard to the nano editor in Linux? This article will go through how to copy the text from the Cutbuffer and clipboard (Gnome) to the nano editor. # ⚓ Linux Capable ☛ How_to_Install_Audacity_on_Fedora_36 Linux⠀⇛ Audacity is a free and open-source digital audio editor and recording application software available for Windows, macOS, Linux, and other Unix-like operating systems. # ⚓ AddictiveTips ☛ How_to_back_up_directly_to_Google_Drive_on Linux⠀⇛ Did you know that you can back up your Linux files directly to Google Drive? It’s true! The Duplicati application makes sending your important Linux files to Google Drive incredibly easy. Here’s how to do it on your Linux system. # ⚓ LinuxTechLab ☛ How_Linux_Users_Can_Speed_Up_Their_Software Distribution_–_LinuxTechLab⠀⇛ The development of software is a very common practice these days. Software is a requirement in almost all fields, be it a small-scale business or a large organization. Hence, in today’s fast-growing world, it is important to take into consideration the aspect of speed where software delivery and distribution are concerned. Several tools, such as the JFrog distribution, GitLab, AWS CodeDeploy, etc., can be installed on Linux to speed up software delivery. # ⚓ Data Swamp ☛ Using_Netdata_on_NixOS_and_connecting_to Netdata_cloud⠀⇛ I’m still playing with monitoring programs, and I’ve been remembered about Netdata. What an improvement over the last 8 years! This tutorial explains how to get Netdata installed on NixOS, and how to register your node in Netdata cloud. # ⚓ uni Toronto ☛ Grafana_Loki_doesn’t_duplicate_a_central syslog_server_(or_vice_versa)⠀⇛ We’ve had a central syslog server for a long time, and recently we’ve set up a Grafana Loki server as well, where we’re sending pretty much a duplicate of the logs that go to the syslog server. After using Loki for a while, I’ve come to the conclusion that the two serve different purposes and neither makes the other unnecessary. (Grafana Loki is concisely called “Prometheus for logs”, or to quote its website it’s ‘a log aggregation system designed to store and query logs from all your applications and infrastructure’. You can see how this might sound like it duplicates a central syslog server.) # ⚓ Linux Capable ☛ How_to_Install_VidCutter_on_Linux_Mint_21 LTS⠀⇛ VidCutter is a free, open-source application that can be used to cut video and audio files. It has tools for cutting all sorts of media, but it’s not a full-blown video editor; instead, its focus lies solely on slicing up videos into clips you could then upload onto your website (or send someone). VidCutter has features that make it easy to get the exact clip you want. It supports many video and audio formats, so you’re not limited to just mp4 files. You can also use it to extract audio from a video file if you want the audio track. Once you’ve imported your media file, you can use the built-in player to preview it and mark out your clip’s start and end points using the easy-to-use interface. When you’re happy with your selection, hit the “cut” button, and VidCutter will do the rest. The output file can be saved in any format you like, so you’re not stuck with whatever format your source file is in. Whether you need to trim down a long video or extract a short clip for use elsewhere, VidCutter is the perfect tool for the job. In the following tutorial, you will learn how to install VidCutter on Linux Mint 21 LTS release series using two different methods, PPA or the alternative third-party Flatpak package manager. # ⚓ Linux Hint ☛ How_to_Install_Stellarium_on_Ubuntu_22.04⠀⇛ Stellarium is an open-source planetarium app that you install on your Linux system to give you a realistic 3D view of the sky. It is similar to how you would view the sky using your eyes or telescope. With Stellarium, you will get a powerful close view of the sky and plenty of features are at your disposal to spice your view. This guide presents how to install Stellarium on Ubuntu 22.04. # ⚓ How_to_Resize_an_Online_Multipath_Device_on_Linux⠀⇛ Disk space on Linux can be expanded by adding a new LUN or resizing an existing LUN on the system. In most cases, the online resizing of the multipath device involves two things: resizing the the logical unit (LUN) size and reflecting the size on the corresponding multipath device. In this article, we will show you how to resize an online multipath device on Linux. o § Games⠀➾ # ⚓ Boiling Steam ☛ Best_Steam_Deck_Games_Released_in_the_Past Week_–_2022-09-26_Edition_–_Boiling_Steam⠀⇛ Between 2022-09-19 and 2022-09-26 there were 204 new games validated for the Steam Deck. We have developed a series of filters to help you find the Best Steam Deck Games in those, based on the available Steam Ratings, their respective popularity, and a few other criteria. We hope it can help you find games that you would have otherwise never known, so that you won’t be running out of games to play on your Steam Deck anytime soon! # ⚓ ScummVM ☛ ScummVM_::_Get_ready_for_a_pink_adventure⠀⇛ Are you ready to be sent to Camp ChillyWawa and Dr. Periowinkle’s mansion as an intelligence agent? Armed with a book of knowledge, or Pink Digital Assistant, your mission will be to save children from dangerous threats and undo a spell cast on a little girl who has been transformed into a wombat. To succeed you will need to visit several countries and even travel into the past. On your way you will encounter historical monuments and exhibits. o § Desktop Environments/WMs⠀➾ # § GNOME Desktop/GTK⠀➾ # ⚓ OMG Ubuntu ☛ Eager_to_Try_Pop!_OS_22.10?_Well,_You Can’t…_–_OMG!_Ubuntu!⠀⇛ Don’t hate me but I’ve some bad (if not entirely unsurprising) news for the Pop!_OS fans who plan to pounce on the presumed-to-be upcoming 22.10 release: you can’t. Before anyone groan: no, I’m not about to deliver a trite “…cOz vAnILLa ‘bUnTu is beTtEr” punchline. Sadly, Pop!_OS 22.10 is not going to be released this autumn — heck, it’s not even in development. System76’s software engineers want to take the time and effort prepping the next release would take and instead plough it in constructing their home-grown, Rust-based COSMIC desktop environment. System76’s Micheal Murphy confirmed the news in a Reddit comment, explaining: “We are going to focus our development time onto the Rust implementation of COSMIC instead of 22.10.” * § Distributions and Operating Systems⠀➾ o § Fedora Family / IBM⠀➾ # ⚓ Liam Proven ☛ liam_on_linux_|_On_the_strange_joys_of mainframe_OSes_and_legacy_tech_that_has_survived_into_modern times⠀⇛ I read this wonderful article on mainframe OSes. I’ve been meaning to do something like it for years, but I may use this as a jumping off point. I think, for me, what I find intriguing about mainframe OSes in the 21st century is this: On the one hand, there have been so many great OSes and languages and interfaces and ideas in tech history, and most are forgotten. Mainframes were and are expensive. Very, very expensive. Minicomputers were cheaper – that’s why they thrived, briefly, and are now totally extinct – and microcomputers were very cheap. All modern computers are microcomputers. Maybe evolved to look like minis and mainframes, like ostriches and emus and cassowaries evolved to look a bit like theropod dinosaurs, but they aren’t. They’re still birds. No teeth, no claws on their arms/wings, no live young. Still birds. One of the defining characteristics of micros is that’s they are cheap, built down to a price, and there’s very little R&D money. But mainframes aren’t. They cost a lot, and rental and licensing costs a lot, and running them costs a lot… everything costs a lot. Meaning you don’t use them if you care about costs that much. You have other reasons. What those are doesn’t matter so much. o § Debian Family⠀➾ # ⚓ My_Debian_Activities_in_August_2022⠀⇛ This month I accepted 375 and rejected 25 packages. The overall number of packages that got accepted was 386. I also had a closer look at the RM-bugs. All in all I addressed about 90 of them and either simply removed the package or added a moreinfo tag. In total I spent 13 hours for this task. Anyway, if you want to have your RM-bug processed in a timely manner, please have a look at the removal page and check whether the created dak command is really what you wanted. It would also help if you check the reverse dependencies and write a comment whether they are important or can be ignored or also file a new bug for them. Each removal must have one bug! o § Mobile Systems/Mobile Applications⠀➾ # ⚓ Android_phone_users_just_got_a_cool_Google_Play_features upgrade_|_T3⠀⇛ # ⚓ Gizmo China ☛ Realme_GT_2,_GT_Neo_3_receiving_Realme_UI_3.0 based_Android_13_early_access_update⠀⇛ # ⚓ Android Police ☛ How_and_why_you_should_enable_SIM_lock_on your_Android⠀⇛ # ⚓ HowTo Geek ☛ How_to_Turn_On_the_Flashlight_on_Android⠀⇛ # ⚓ Android Police ☛ YouTube_Music_for_Android_is_getting updated_Material_You_buttons⠀⇛ * § Free, Libre, and Open Source Software⠀➾ o § Web Browsers/Web Servers⠀➾ # § Chromium⠀➾ # ⚓ Alexandru Nedelcu ☛ Impressions_on_Web_Browsers⠀⇛ I’ve stayed away from Chrome because, soon after its release, Firefox became the underdog, and it was still the more customizable browser. But even to this Firefox fan it became clear that Chrome was superior — for example, when the Flash plugin or some tab or extension crashed, it wouldn’t crash the whole browser. o § SaaS/Back End/Databases⠀➾ # ⚓ PostgreSQL ☛ pgexporter_0.3⠀⇛ The pgexporter community is happy to announce version 0.3.0. # ⚓ PostgreSQL ☛ pgmoneta_0.6⠀⇛ The pgmoneta community is happy to announce version 0.6.0. o § Productivity Software/LibreOffice/Calligra⠀➾ # ⚓ Ubuntubuzz ☛ LibreOffice_Writer:_Mail_Merge_Made_Easy⠀⇛ This tutorial will help you to create mail merge with LibreOffice explained step by step with pictures and examples. Mail merge is a method of making stuffs consisted of multiple personalized copies like official letters, invitations, envelops, identity cards, student score reports etc. using word processor, spreadsheet and database. Finally, in this exercise we will make school letters for students’ parents as an example so you can practice and then adapt it to your own needs. Let’s study now! # ⚓ Video ☛ Pay_For_LibreOffice?_–_Invidious⠀⇛ This week in the Business News, a popular browser extension is bought by Avast, CA power wall bursts into flames, and Google founding group to open source audio codecs. Also, Mac users may be charged for LibreOffice. o § Programming/Development⠀➾ # ⚓ Bryan Lunduke ☛ Why_Javascript_is_Retarded:_Part_1⠀⇛ # ⚓ Carl Svensson ☛ Durden_|_datagubbe.se⠀⇛ Durden is a program that identifies, counts and, optionally, marks and/or cuts out and saves unique tiles in a given image file. # ⚓ Matt Rickard ☛ It’s_Just_a_Tarball⠀⇛ Sometimes complex software is simple when you go a few layers down. For example, take the container image. There’s so much complexity around building, deploying, and managing containers at scale. Yet, container images are just tarballs. With a few metadata files, you could quickly build one without any special tooling. In an unprivileged environment, in code, or even by hand. Or git’s object model. Git is known for its terrible UX, so sometimes, we assume that everything under the porcelain is also complex. Yet Git’s object model is pretty simple – content- addressed blobs (file-like), trees (folder-like), and commits that get stored in a .git/objects folder. # ⚓ Matt Rickard ☛ Social_Coding⠀⇛ Fortunately, we have an interesting counterfactual – GitLab, which among other things, is GitHub but de-emphasizes the social features – it’s more likely to be deployed on-prem and overall has significantly fewer consumer public users and projects. GitLab’s current market cap is $8.5b (GitHub was acquired by Microsoft in 2019 for $7.5b). # ⚓ Phil Eaton ☛ A_minimal_distributed_key-value_database_with Hashicorp’s_Raft_library_|_notes.eatonphil.com⠀⇛ When I wrote the “build a distributed PostgreSQL proof of concept” post I first had to figure out how to use Hashicorp’s Raft implementation. There weren’t any examples I could find in the Hashicorp repo itself. And the only example I could find was Philip O’Toole’s hraftd. It’s great! However, I have a hard time following multi-file examples in general. So I built my own single-file example. It’s not perfect but it helped me get started and may help you too. We’ll walk through that code, ~260 lines of Go, in this post. # ⚓ Linux Hint ☛ View_and_Access_Threads_in_GDB⠀⇛ Another name for a debugger would be a debugging utility. By spotting the code problems at different phases of an operating system or an application creation, it is considered to be a computer program that may enhance the process of building a software. A trial run may be examined by certain debuggers to determine which sections of code were skipped. The GNU Debugger is one of the many debugging tools that is available for C programmers and is the greatest debugging tool. It offers some tools that let the user view and assess a program while it is being run. Another excellent debugging functionality is to support many programming languages including C, C++, Ada, Fortron, and Pascal # ⚓ Linux Hint ☛ POSIX_Open_Function_in_C⠀⇛ Although there are a lot of libraries in C, the POSIX library is very well-known among the developers due to its wide range of system call functions, especially the system function calls for “files”. POSIX library for Linux operating system provides you with a variety of functions. There is an open() function that is purposely used to open a specific file from a system in one of those POSIX calls. It utilizes many options to create, open, read, write, and do many things on the Linux files. # ⚓ API_as_a_package:_Logging⠀⇛ Part 1 of this series laid out some ideas for how one might structure a {plumber} application as an R package, inspired by solutions such as {golem} and {leprechaun} for {shiny}. In this installment of the series we look at adding some functions to our package that will take care of logging as our application runs. If you haven’t already, we recommend reading the first installment of this series as the example package created for that post will form the basis of the starting point for this one. # ⚓ Ollin Boer Bohan ☛ Game_Emulation_via_Neural_Network⠀⇛ Although this looks like a video game, I did not write any game code. # ⚓ Vermaden ☛ Valuable_News_–_2022/09/05⠀⇛ The Valuable News weekly series is dedicated to provide summary about news, articles and other interesting stuff mostly but not always related to the UNIX or BSD systems. Whenever I stumble upon something worth mentioning on the Internet I just put it here. Today the amount information that we get using various information streams is at massive overload. Thus one needs to focus only on what is important without the need to grep(1) the Internet everyday. Hence the idea of providing such information ‘bulk’ as I already do that grep(1). # ⚓ Matt Rickard ☛ When_To_Roll_Your_Own_X⠀⇛ When should you reuse code and modify it to your requirements? When should you roll your own? There’s no general answer to this question, but a few guidelines that I’ve picked up over the years. # ⚓ Drew Olson ☛ Hello_World_Haskell⠀⇛ Teacher: Hello class! Welcome to your first day of functional programming. Today, we’re going to be talking about how to write the classic “Hello, World!” program in Haskell. It’ll be slightly more involved as we’ll ask for the user’s name and then greet them. I’m sure many of you have heard scary things about Haskell, but I promise you it’ll be fun. Student: I heard we have to learn about IO. That sounds scary! Teacher: What? No, there’s no need to worry about IO. In Haskell, when we want to perform an effect, we simply define a GADT to represent the capabilities of the effect. # ⚓ Rlang ☛ Minimax_Estimation_and_Identity_Testing_of_Markov Chains_|_R-bloggers⠀⇛ We briefly review the two classical problems of distribution estimation and identity testing (in the context of property testing), then propose to extend them to a Markovian setting. We will see that the sample complexity depends not only on the number of states, but also on the stationary and mixing properties of the chains. # ⚓ Ubuntu Pit ☛ Top_10_Best_PhpStorm_Themes_and_Color_Schemes in_2022⠀⇛ There’s no doubt that Phpstorm is by far the best IDE for PHP language with framework support. However, IDEs can get rather dull to work with sometimes or may lack the necessary optimization. The solution for that is to browse through Phpstorm themes and activate the one you like best. IntelliJ, Phpstorm and Webstorm are all Jetbrains products. They are all integrated development environments compatible with different languages. However, having the same parent company, IntelliJ- based templates are usable as Phpstorm and Webstorm themes. That said, our focus remains on Phpstorm only today – so let’s explore the options it has in store. # § Perl / Raku⠀➾ # ⚓ Perl ☛ Perl_Weekly_Challenge_182:_Unique_Array_and Date_Difference⠀⇛ # ⚓ Perl ☛ course_change_for_Kephra_|_lichtkind_ [blogs.perl.org]⠀⇛ Kephra, an editor for programming (mostly Perl) written in WxPerl is my main project since I stumbled into the Perl community. Most people I know already heard of it – but I want to write about a new development that might be helpful for some, which might consider to use it even if it has a very limited feature set (forth rewrite baby!). It was silent for some time – because being my main project – I tried to cram all my other ideas, mainly KBOS into it which bogged progress down. Maybe there will be an Object System just for Kephra, solving some issues I saw nowhere else dressed. But for now I’m surprised how much progress is possible, If you just focus on churning out features. I took stage sed (which is the bare minimal editor I once wrote as proof of concept) and just started to adding features and fixing issues. Sed stands for Single document EDitor and that is all what next release will bring. Am I serious ? and why should you care? Well I’m German – we never joke and it has strengths in its editing capability which sound like – ‘duh its an editor – but if you see how many so called Editors and IDE neglect this area while focusing on the big guns like refactoring, debugging and git integration. # § Python⠀➾ # ⚓ Paolo Melchiorre ☛ DjangoCon_US_2022⠀⇛ DjangoCon US is a six-day international conference for the community by the community about the Django web framework, held each year in North America. # ⚓ Didier Stevens ☛ New_Tool:_split-overlap.py⠀⇛ split-overlap.py is a tool to split a binary file in parts of a given size. For example: split-overlap.py 1000 test.data When test.data is a binary file with size 2500 bytes, the above command will create 2 files of 1000 bytes and one file of 500 bytes. It’s also possible to split a file with some overlap. # § Java⠀➾ # ⚓ Alexandru Nedelcu ☛ Java_19⠀⇛ Java 19 is now released, and it’s a big deal, as it ships with Virtual Threads (JEP 425), among other goodies, like structured concurrency (JEP 428), or improvements to pattern matching (JEPs 405, 427). I haven’t been as excited about a Java release in a long time. # § Rust⠀➾ # ⚓ Barry Kauler ☛ Rust_Hello_World_reduced_to_31KB⠀⇛ A criticism that I have of Rust is that it creates very large binaries. Yes, there are websites that explain how to reduce the size, but have to go through a lot of steps. This evening I was looking at this site, and compiled the first example: # ⚓ Armin Ronacher ☛ You_Can’t_Do_That:_Abstracting_over Ownership_in_Rust_with_Higher-Rank_Type_Bounds._Or_Can You?⠀⇛ A few years ago I wrote about how to get better at Rust by knowing when what you want to do is impossible. Sadly in many ways I don’t learn from my own mistakes and I keep running into a particular issue over and over again: Rust’s restrictions about being able to abstract over the borrow status / ownership of a values in some hard to discover situations involving higher-kinded type bounds. A few days ago I wrote a (now unpublished) article about how you can’t express a certain problem I keep manuvering myself with Rust’s lifetimes. However that post set in motion a chain of events that lead to a solution that actually works. Yet at the same time even though I thought it was impossible I don’t think the solution is obvious, I could have found it myself and it does not even work reliably. But more about that later. Let’s set the stage first: The problem I’m talking about relates to abstracting over borrows and owned values when combined with functions or something that uses higher- kinded trait bounds. In other words: one wants to create an API where it’s possible to either borrow or clone out of some input value. Think of a generic function that can produce both a String and a &str. * § Leftovers⠀➾ o ⚓ Ruben Schade ☛ The_pushback_against_decluttering⠀⇛ Marie Kondo took a polite but well-orchestrated torch to people’s junk piles a few years ago, with a book and American TV series that challenged people to think about what they’re carrying around. I’d been an avid reader of The Minimalists at this time, and had read about people who’s lives were crippled by hoarding. Marie Kondo spoke to the middle, which is why I think so many took it personally. The Internet’s general reaction was telling, if not surprising. Most people memed and sarcastically summarised her view into “does this spark joy?” because it was easier than answering her pointed and difficult questions, some of which cut to the core of how we’re conditioned to live our lives. There are entire industries that are built on the backs of, as George Carlin put it, people spending money they don’t have, on stuff they don’t need, to impress people they don’t like. How much of our economy would collapse overnight if people didn’t overextend themselves? o ⚓ Parliament_Today:_3.92_Lakh_Indians_Gave_up_Citizenship_in_Past_3 Years,_Says_Govt_|_NewsClick⠀⇛ Over 3.92 lakh Indians gave up their citizenship in the last three years and 1.70 lakh of them, the highest, took up American citizenship, Lok Sabha was informed on Tuesday. Union Minister of State for Home Nityanand Rai said that according to details provided by the Ministry of External Affairs, individuals renounced Indian citizenship for reasons personal to them and took citizenship in over 120 countries. A total of 3,92,643 Indians gave up their citizenship in 2019, 2020 and 2021, he said in a written reply to a question. o ⚓ Neil Selwyn ☛ What’s_not_good_with_‘Tech_For_Good’?_(notes_on Radhakrishnan_and_Powell_et_al.)_–_Critical_Studies_of_EDUCATION_– TECHNOLOGY⠀⇛ Similarly, much of the 2000s’ discourse around social media and web 2.0 was also imbued with a dogged sense of hope and enthusiasm. [...] In one sense, the continued promotion of ‘Tech For Social Good’ reveals some fundamental flaws in how technology is conceived by ‘big tech’ actors and associated groups responsible for developing and installing IT across society. As Alison Powell (2022) and colleagues reason, these narrowly-framed ideas of ‘For Good’ are rooted in highly limited understandings of technology ethics, values and virtue. o § Science⠀➾ # ⚓ Allen_School_News_–_Allen_School_researchers_bring_first underwater_messaging_app_to_smartphones⠀⇛ For millions of people who participate in activities such as snorkeling and scuba diving each year, hand signals are the only option for communicating safety and directional information underwater. While recreational divers may employ around 20 signals, professional divers’ vocabulary can exceed 200 signals on topics ranging from oxygen level, to the proximity of aquatic species, to the performance of cooperative tasks. The visual nature of these hand signals limits their effectiveness at distance and in low visibility. Two-way text messaging is a potential alternative, but one that requires expensive custom hardware that is not widely available. Researchers at the University of Washington show how to achieve underwater messaging on billions of existing smartphones and smartwatches using only software. The team developed AquaApp, the first mobile app for acoustic-based communication and networking underwater that can be used with existing devices such as smartphones and smartwatches. # ⚓ Sabine Hossenfelder ☛ Sabine_Hossenfelder:_Backreaction: The_Multiverse:_Science,_Religion,_or_Pseudoscience?⠀⇛ Why do physicists believe there are universes besides our own? I get a lot of questions about the idea that we live in this “multiverse”. Is it science, religion, pseudoscience, or just wrong? That’s what we’ll talk about today. # ⚓ IEEE ☛ Disentangling_the_Facts_From_the_Hype_of_Quantum Computing⠀⇛ Over the past five years, there has been undeniable hype around quantum computing—hype around approaches, timelines, applications, and more. As far back as 2017, vendors were claiming the commercialization of the technology was just a couple of years away. There was even what I’d call antihype, with some questioning if quantum computers would materialize at all. I hope they end up being wrong. More recently, companies have shifted their timelines from a few years to a decade, but they continue to release road maps showing commercially viable systems as early as 2029. And these hype- fueled expectations are becoming institutionalized: The Department of Homeland Security even released a road map to protect against the threats of quantum computing, in an effort to help institutions transition to new security systems. This creates an “adopt or you’ll fall behind” mentality for both quantum-computing applications and postquantum cryptography security. # ⚓ New Scientist ☛ Earthquakes_seem_to_come_in_a_more predictable_pattern_than_we_thought⠀⇛ We might be able to predict big earthquakes in the near future better than we thought, according to research that used machine learning to analyse decades of past earthquakes in California. There have been many attempts to predict earthquakes using real-world signals, such as changing water levels, or data catalogues, such as the time intervals between earthquakes, but there has been no consistently reliable method. o § Health/Nutrition/Agriculture⠀➾ # ⚓ Ruben Schade ☛ Rubenerd:_How_minds_process_bad_news⠀⇛ I’ll spare the details, but as I eluded to on Wednesday, stuff is rubbish right now. It’s the most challenging time since my late mum passed away, for a host of complicated or unavoidable reasons. At any given moment I’m desperate, upset, blue, or frustrated. I don’t mean to worry anyone! Nor do I want to wallow in self pity, nor am I fishing for compliments or reassurance, it’s just life right now. Given how the world is, I suspect you might be in a similar boat, or far worse. What I do want to raise is something I’ve observed in my head, especially over the last week, which has weirdly helped. When you get a bit of bad news, it hits you. When you get two or three bits of bad news, it feels twice or three times as bad. But after the forth, and fifth, and twelfth, the trajectory of pain and frustration seems to level off. Each new item is merely relegated to the stack. At least, that’s how it’s shook out for me lately. o § Security⠀➾ # ⚓ Mandiant ☛ GRU:_Rise_of_the_(Telegram)_MinIOns_|_Mandiant⠀⇛ Mandiant is tracking multiple self-proclaimed hacktivist groups working in support of Russian interests. These groups have primarily conducted distributed denial-of-service (DDoS) attacks and leaked stolen data from victim organizations. Although some of these actors are almost certainly operating independently of the Russian state, we have identified multiple so-called hacktivist groups whose moderators we suspect are either a front for, or operating in coordination with, the Russian state. # ⚓ uni Toronto ☛ Authenticated_SMTP_and_IMAP_authentication attacks_and_attempts_we_see_here⠀⇛ A while back I wrote about how large scale SSH brute force attacks seem to have stopped here. SSH isn’t the only form of authentication that we have exposed to the Internet; we also have both an IMAP server and an authenticated SMTP server, and unsurprisingly they also seem activity. To my surprise, the activity patterns are quite different (which took some time to discover, since they both actually authenticate through Dovecot). Our authenticated SMTP server sees widespread and determined probes from a wide range of IP addresses that appear to be attempting to brute force email addresses here; basically the kind of activity that I expected to see for SSH. However, many of these brute force attacks have no chance of success because they’re being directed against either logins that no longer exist or email addresses that were never logins in the first place, and were only aliases or mailing lists. The obvious guess is that attackers targeting authenticated SMTP simply scrape every From: address from your domain that they can find and then set their hordes loose on brute force attacks. # § Privacy/Surveillance⠀➾ # ⚓ Michael West Media ☛ Telling_us_what_we_want_to_hear –_Big_Tech’s_privacy_lies⠀⇛ Every time an advertiser pays YouTube or Facebook or Twitter to place an ad in your feed, your data is the selling point. And if you pay a subscription fee to avoid the ads, your data is still being used. Big Tech wins either way, but it’s your data, writes cyber security expert Manal al-Sharif. When you use social media for free in exchange for allowing the networks to collect and share your personal information, you are handing the tech moguls your information for free, Meanwhile Big Tech tells you they don’t “sell” your data. # ⚓ Patrick Breyer ☛ Breyer_on_Europol_lawsuit:_Courts must_protect_us_where_politics_is_hostile_to fundamental_rights⠀⇛ The European Data Protection Supervisor (EDPS) is going to court over the EU’s attempt to retroactively legalise large amounts of data Europol illegally collected on unsuspected citizens, including mobile phone and air traveller data. The EDPS is reacting to the heavily criticised Europol reform, which has given the agency broad powers since June 2022. o § Transparency/Investigative Reporting⠀➾ # ⚓ Michael West Media ☛ Information_Commissioner_cuffed_for withholding_information_–_Michael_West⠀⇛ Federal Court Justice Wheelahan has given the Information Commissioner a wrap across the knuckles for delaying a trial into her FOI review delays. Just over 12 months ago the then Senator Patrick filed an application in the Federal Court asking the court to order the Information Commissioner to make a decision on 23 FOI reviews which she had unreasonably delayed. Some of them had not been concluded after two years. The Information Commissioner was supposed to, within 14 days of his application, file any concerns as to the ‘competency’ of then Senator Patrick’s application. She did not. o § Environment⠀➾ # § Energy⠀➾ # ⚓ When_Market_Fundamentalism_Overcomes_Common_Sense: Myth_of_Electricity_Markets_|_NewsClick⠀⇛ So-called electricity markets were created to help private capital, not people. It is time we wound up these bogus markets and returned public services to people, to run cooperatively for their benefit. # ⚓ ACM ☛ These_Are_Not_the_Apes_You_Are_Looking_For⠀⇛ Imagine you want to stream some music. On today’s Web, you would sign up for a service such as Spotify or Apple Music. These platforms have obtained copyright licenses from record companies and artists, and they offer you that music for a monthly subscription. The music streaming services are centralized intermediaries. They exist to connect musicians and fans, and in exchange they take a substantial cut of the money. But a growing number of technology enthusiasts have a different vision, which they call Web3. To them, it “represents the next phase of the Internet and, perhaps, of organizing society.’a One of the pillars of the Web3 vision is tokenization: using representing ownership of different assets using cryptographic tokens that can be exchanged on a blockchain or other decentralized system. Only the person who knows the private key associated with a token can use or transfer it. A token can be used to represent anything, from frequent-flyer miles to hotel reservations. By transferring a token from user to user, it can record who owns an associated asset. o § Finance⠀➾ # ⚓ Terence Eden ☛ I’m_only_vegan_for_the_money⠀⇛ The price of dairy milk is now at parity with oat- milk and soya-milk. Yes, I’m sure there are some things for which plant milk is unsuitable. Even if you ignore all the environmental benefits of switching from cow-milk to plant-milk, it’s hard to ignore the benefit to your bank balance. # ⚓ CoryDoctorow ☛ Moneylike⠀⇛ For years, economics textbooks have included a “money story”: once upon a time, we bartered, trading chickens for cows. This was hard. If the going rate is 8 chickens for a cow and you only need 6 chickens, how could the chicken farmer make change? The answer was gold, variously said to have been chosen for its rarity, or its divisibility, or its shininess, or the ease of working such a soft metal. Whatever the reason, these anonymous prehistoric traders all agreed that gold would be our medium of exchange, our store of value and our unit of account. This story was handed down to generations of economics students, despite the fact that there is no evidence for it. The basis for this story was pure reasoning: “What circumstances could have given us money?” # ⚓ Ruben Schade ☛ Rubenerd:_P.G._Morgan’s_insights_into_D.B. Cooper⠀⇛ For those who haven’t heard of him, D.B. Cooper, as the press dubbed him, successfully hijacked a Boeing 727 in 1971, and parachuted out the plane’s rear airstairs mid-flight with millions of dollars. The man, and most of the money, have never been found. # ⚓ Michael West Media ☛ Qantas_board_gets_priorities_straight –_its_own_pay_–_as_Alan_Joyce_edges_towards_$8.7m_package⠀⇛ The Qantas board has gifted themselves and chief executive Alan Joyce handsome pay rises despite trashing customers, staff and the reputation of the national carrier. Michael Sainsbury analyses Qantas’ bonus scheme. They socialised the losses – and now they are about to privatise the profits. The eight-member Qantas board has gifted itself a collective 5% pay rise of a collective $2.4 million, including two retiring members who are not being replaced. This has added insult to the injury of tens of thousands of its customers, many of whom have struggled in recent weeks to get back from Asia after being stranded by multiple Jetstar cancellations and to workers being offered a pay rise of 6% over five years (1.2% each year). The company’s chairman Richard Goyder last year earned $658,000 (including post employment benefits) for his part-time job. This is now more than his 2019 financial year earnings of $584,000. It also makes him the highest paid Qantas director ever, besting his predecessor Leigh Clifford’s $654,000 in his final full year as chairman in 2018-2019. Goyder also chairs energy giant Woodside, currently absorbing its purchase of BHP’s petroleum assets and the Australian Football League, which has just completed a $4.5 billion broadcast and digital rights deal and is searching for a new chief executive. o § AstroTurf/Lobbying/Politics⠀➾ # ⚓ AIM ☛ The_Backend_of_Indian_Elections⠀⇛ India is one of the largest democracies in the world, and Indian elections are a sight worthy of attention. The grand and vibrant elections, however, are not easy to win. Data analytics and AI are major factors in the back end of these elections. [...] Social media is undoubtedly one way to get information, but it also presents a significant obstacle. It is very challenging to determine whether the opinion and input of a given account are valid or useful due to the anonymity of the account, doubts about whether the account is owned by a real person or a bot… # ⚓ Michael West Media ☛ Angst_over_corruption_watchdog,_first Queen’s_death,_now_fear_of_Dutton_deal_–_Michael_West⠀⇛ Reports that Labor is in talks with Peter Dutton over the looming Federal Integrity Commission laws have spread alarm Anthony Albanese might walk back on his pledge for a credible anti-corruption body. Callum Foote reports on the timing, the critical detail, the delays and the latest scare. Call it what you like: a Federal ICAC, a Commonwealth Integrity Commission or Bloody Well About Time, the introduction of an anti-corruption body to root out the dodgy business which has plagued Australian federal politics for years, and increasingly so, was one of the major issues at the 2022 election. # ⚓ Michael West Media ☛ Queen_Elizabeth_and_King_Rupert:_seven decades_of_exercising_soft_power_and_hard⠀⇛ After both lost their fathers suddenly in 1952, Rupert Murdoch and Queen Elizabeth were thrust into unexpected positions of power. Seventy years later, that is just one of many similarities between the pair. # ⚓ Antipope ☛ Necroqueen!_–_Charlie’s_Diary⠀⇛ My brain is going offline until next Tuesday to show respect during the Necroqueen’s procession into the Western Lands. After a short mummification there will be an economic (but not metabolic) recovery. Meanwhile, I had a dream, and it went someething like this … # § Misinformation/Disinformation/Propaganda⠀➾ # ⚓ Michał Woźniak ☛ Fighting_Disinformation:_We’re Solving_The_Wrong_Problems⠀⇛ Tackling disinformation and misinformation is a problem that is important, timely, hard… and, in no way new. Throughout history, different forms of propaganda, manipulation, and biased reporting have been present and deployed — consciously or not; maliciously or not — to steer political discourse and to goad public outrage. The issue has admittedly become more urgent lately and we do need to do something about it. I believe, however, that so far we’ve been focusing on the wrong parts of it. Consider the term “fake news” itself. It feels like a new invention even though its literal use was first recorded in 1890. On its face it means “news that is untrue”, but of course, it has been twisted and abused to claim that certain factual reporting is false or manufactured — to a point where its very use might suggest that a person using it not being entirely forthright. That’s the crux of it; in a way, “fake” is in the eye of the beholder. o § Monopolies⠀➾ # § Copyrights⠀➾ # ⚓ Michael Geist ☛ Why_the_Online_News_Act_is_a_Bad Solution_to_a_Real_Problem,_Part_Four:_Undermining Canadian_Copyright_Law_and_International_Copyright Treaty_Obligations⠀⇛ The series on why Bill C-18, the Online News Act, is a bad solution in search of a real problem has thus far focused on three issues: the risk to the free flow of information stemming from mandatory compensation for linking, how the bill encourages clickbait and other low quality news given the absence of standards in the definition of “news content”, and the unprecedented government intervention in a sector where independence is essential. Today’s post raises an unlikely issue given that Bill C-18 is the responsibility of Canadian Heritage Minister Pablo Rodriguez, who also has part responsibility for copyright law in Canada. Buried within the bill is Section 24, a short provision with big copyright implications: For greater certainty, limitations and exceptions to copyright under the Copyright Act do not limit the scope of the bargaining process. What does this mean and why is it in the bill? Bill C-18 is designed to force Internet platforms (called “digital news intermediaries”) to negotiate agreements with news organizations making news available. However, one of the problems with this approach is that platforms don’t typically use the news in a manner that would be compensable. For example, the platforms may link to the news, feature a headline with the link or sometimes offer a one-or-two sentence summary or quote from the article. The reality is that these uses are generally permitted under Canada’s fair dealing copyright law rules and does not require a licence or compensation. This presents a quandary for the government, which wants to require payment but it knows that the platforms are permitted to make use of the works without payment. * § Gemini* and Gopher⠀➾ o § Personal⠀➾ # ⚓ SpellBinding:_GHIWNSK_Wordo:_CALLA⠀⇛ # ⚓ 2022-09-25_–_the_missing_round_tuits⠀⇛ I have an abundance of source material – photos, memories, thoughts swirling in my head – from the recent trip. What I’m lacking is the motivation to write about it. I’m confident that motivation arrive at some point. I just need to distract myself until it does, and stop letting myself feeling bad about it. In the meantime, I’ll continue to walk, and to try and find photos in amongst the now-familiar spaces I travel in. I’m fortunate to have the time, right? o § Technical⠀➾ # ⚓ How_to_trigger_services_restart_after_OpenBSD_update⠀⇛ # § Announcements⠀➾ # ⚓ RELEASE:_The_Yoyo_of_Zonk⠀⇛ Masséna and I are proud to presend The Yoyo of Zonk, a crazy asymetrical two-player zelda-like roguelite featuring a strong gen Z sense of humor. What the fuck does any of that mean? could you ask. Well, even I am not sure how to explain it clearly. I gotta say, I don’t know what gendra this game is supposed to be in, and I’m perfectly fine with that (I hate the concept of game gendra). I recon you should probably read the game booklet, it will give you a good idea of how fucked up this game is. Trust me on this one: it’s worth it. # § Programming⠀➾ # ⚓ Forth_Unorthodoxia⠀⇛ I’ve been really enjoying myself neck-deep in Forth. After implementing the basics of a i386 Forth, to the point of being able to define new words and load files, I started digging through my pre-covid notes from my last Forth bender, and uncovered a bunch of forgotten treasures… I do the round of languages with an orbital period of a few years. I’ll tinker with some Forth-like language for a bit. Then, depending on which direction I was pushing, I will spend some time with Lisp, or maybe Smalltalk… Lisp if I was frustrated with being unable to transform and reason about code; Smalltalk if I was getting into the token interpreter aspects of Forth… =============================================================================== * Gemini_(Primer) links can be opened using Gemini_software. It’s like the World Wide Web but a lot lighter. ╘══════════════════════════════════════════════════════════════════════════════╛ ¶ Lines in total: 5599 ➮ Generation completed at 02:44, i.e. 63 seconds to (re)generate ⟲