𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Wednesday, November 24, 2021 ┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅ Generated Thu 25 Nov 02:40:23 GMT 2021 Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖) Full hyperlinks for navigation omitted but are fully available in the originals The corresponding HTML versions are at 𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈 Latest in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕 and older bulletins can be found at 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕-𝒂𝒓𝒄𝒉𝒊𝒗𝒆𝒔 Full IPFS index in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔 and as plain text in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔/𝒕𝒙𝒕 Gemini index for the day: gemini://gemini.techrights.org/2021/11/24/ ╒═══════════════════ 𝐑𝐄𝐂𝐄𝐍𝐓 𝐁𝐔𝐋𝐋𝐄𝐓𝐈𝐍𝐒 ════════════════════════════════════╕ Previous bulletins in IPFS (past 21 days, in chronological order): QmViJLHdiRf7wrstUaHcTaXuiWpGyTkptFkDjYAFoJBJoj QmVzPu6Qip7yK3FGSsrMzEt3zNmqWufLFF5CZNmsVbHZLd QmYTFyk7SSEVeJPYyyFr91pb7fbKnpS4kiFjty9U136upV QmYKBd728JBm11x2JbtET9sF2KJXtKjGPDD1jVnpt7fLqz QmQba8m7JeAYTn4JDwkhe5nDZfnw9TnSASsQqLF7LBYEg2 QmT9Hh5LgzS2eg26pkvFLpdGLNAEURRLod8DffDCczhxy1 QmdEutfCAc7HzKtnLt7k7b2dajGSqfBSGnEPAuD2bontJM QmSuWrcnwPk5e1gVWiJbTq7uxUkNn8DzRVm659JmGTFR5W QmRDvU3Bb1mJHK7qGvaLg5kKvJ9tXx4qDntaaZU2EPXgnr QmXnPPSuiAbypBs2W4Hu14xEgjjptzNmzCptadFdRv7xt5 Qmed7VnZALGrUYrCRnPW72Zg4XmWFjZQUFe7BHLQ4EWp12 Qmak6N1wRPKAPf9DxMtCC9P4rZVS2rKi58Zcinr7iLRtd5 QmYZPeUTA2uaPPdjbKd4Mhnwn8aLtQKzy7Ft175ssdW8PT QmcNLdXKwxdD6cLvdgRCUDzCTD4PfjtBzdq6btKA1VdHeD QmXkgs6nUp2YxKaphy2EXnEaHqcAAagQyA5Z44RUfN2uvD QmdGDdRX8ZuGj76UZ5fvhjBZ81N9v4RyisduQDvtX5i4bQ QmXUd8Sk2pSNG2yA8y1Ddfd7zDgDgQCfztF4s5mGnkZKin QmeDHFuwxMuWGXnXY8ELJ4X5fk6wWvRiyFNXRQ9noLwTQw Qma6fG1kUmKGPn5zAHpVWkUoTsUNdRgGNmFYPmFKcxGEHK QmcehsKRe5D9pD1MUq2cbSWmBriwyeQoqZP3fXiJWEjy4z QmSWwJ7eRdx1kz73nTFtXRp2vF9nhTnV7sYYZVwuM6t9c5 ╒═══════════════════ 𝐈𝐍𝐃𝐄𝐗 ═══════════════════════════════════════════════════╕ ⦿ 3.5 Years Later the ’Master’ of Fedora is Still Microsoft and IBM Cannot Be Bothered to Alter Git Branch Names (Refuting or Ignoring Its Very Own Directive About Supposedly Racially-Insensitive Terms) | Techrights ⦿ IRC Proceedings: Tuesday, November 23, 2021 | Techrights ⦿ [Meme] Jimmy Zemlin Loves Microsoft | Techrights ⦿ Changing the Arrangement While News is a Bit Slow(er) | Techrights ䷼ Bulletin articles (as HTML) to comment on (requires login): http://techrights.org/2021/11/24/fedora-slaves-at-microsoft/#comments http://techrights.org/2021/11/24/irc-log-231121/#comments http://techrights.org/2021/11/24/microsoft-loves-linux-meme/#comments http://techrights.org/2021/11/24/thanksgiving-downtime/#comments ䷞ Followed by Daily Links (assorted news picks curated and categorised): http://techrights.org/2021/11/24/endless-os-4-0-released/#comments http://techrights.org/2021/11/24/php-foundation/#comments ䷩ 𝚕𝚒𝚗𝚎 57 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2021/11/24/fedora-slaves-at-microsoft/#comments Gemini version at gemini://gemini.techrights.org/2021/11/24/fedora-slaves-at-microsoft/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.24.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ 3.5_Years_Later_the_‘Master’_of_Fedora_is_Still_Microsoft_and_IBM_Cannot_Be Bothered_to_Alter_Git_Branch_Names_(Refuting_or_Ignoring_Its_Very_Own_Directive About_Supposedly_Racially-Insensitive_Terms)⠀✐ Posted in Deception, GNU/Linux, IBM, Microsoft, Red_Hat at 7:56 pm by Dr. Roy Schestowitz Older: 2_Years_After_Microsoft_Hijacked_GitHub_for_Monopoly_Fedora_Still_Has Well_Over_100_Projects_in_Microsoft’s_GitHub_(Not_Even_Counting_Red_Hat’s_and Systemd) 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Fedora Infrastructure at GitHub⦈ Summary: Today we demonstrate the hypocrisy of IBM; years after telling us that we should shun the term “master” and repeatedly insisting it had a racist connotation at least 65 Fedora repositories, still controlled by Microsoft, still use “master” A YEAR and a half ago we published the post above along with the screenshot above. The point that we made back then was, IBM/Red Hat clearly didn’t mind proprietary software lock-in, even if it had become controlled by Microsoft, a sworn enemy of copyleft and of_the_law_in_general. Earlier this week I noticed that SUSE/OpenSUSE and many other high-profile companies/projects you’d expect to have moved away from “master” as a branch name (because they themselves insisted that it was racially insensitive) not doing so themselves, in effect shaming the community and exercising immense hypocrisy (or double standards). If a company with the manpower/resources of IBM cannot be bothered to change branch names (this may complicate or break many scripts, workflows etc.), then why should we? IBM along with Microsoft and Intel were probably were most vocal about this thing, creating endless commotion to distract from their_own_racism,_which_they_did_for_profit. Racism pays them! Being racist means profit to those companies! Today we took a quick look at all the repositories of Fedora. It’s the project that used to have a community but mostly has IBM staff left; the CentOS ‘dick moves’ drove away what was left of a non-IBM component in Fedora, not to mention IBM's_Trumpian_ban_of_Fedora_contributors_based_on_their_nationality, which is abundantly racist in its own right (they even did this for Biden, not Trump). Yes, those projects or repositories are still controlled by Microsoft and IBM couldn’t be bothered to change branch names to something like “main”. About half of all projects are still saying “master” and we’ve taken 65 screenshots (for separate projects) to prove it and document it. See below (all of them say “master”). █ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_1⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_2⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_3⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_4⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_5⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_6⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_7⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_8⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_9⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_10⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_11⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_12⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_13⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_14⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_15⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_16⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_17⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_18⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_19⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_20⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_21⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_22⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_23⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_24⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_25⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_26⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_27⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_28⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_29⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_30⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_31⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_32⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_33⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_34⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_35⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_36⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_37⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_38⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_39⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_40⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_41⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_42⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_43⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_44⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_45⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_46⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_47⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_48⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_49⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_50⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_51⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_52⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_53⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_54⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_55⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_56⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_57⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_58⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_59⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_60⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_61⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_62⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_63⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_64⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_master_in_Fedora,_example_number_65⦈_ Index page 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Fedora_at_Microsoft⦈_ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⡶⣶⠶⠶⡶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶ ⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⣿⣿⣿⣿⠑⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠁⠀⠀⠁⠀⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠊⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡷⡷⢶⠷⣶⡶⠶⠶⣶⣶⣷⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⡿⢿⠋⠉⠁⣉⠀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡃⠀⠀⠈⠀⠀⢀⣿⣿⣿⣿⠁⠊⠘⠃⠛⠋⠛⠈⠛⠛⠛⠛⠛⠛⠛⠛⠂⠉⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡛⠛⠛⠑⢈⠀⣤⣰⣤⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡟⠉⠁⠤⠤⠀⢀⠴⢶⠿⣿⣿⣿⣶⡶⡶⣶⣶⣶⣶⣶⣶⣶⢶⠶⣶⣶⣶⢶⣶⣶⣶⠶⢾⣿⣿⣿⣿⣿⠿⠿⢿⣿⠩⠉⠋⠉⠀⠀⠤⣶⣾⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⡀⠀⠀⠀⠀⠀⣀⠀⢸⢻⣿⠛⠈⠰⠂⠋⠀⠀⠑⠙⠃⠐⠀⠘⠛⠛⠉⠈⠊⠛⠀⢸⡟⠛⠻⠛⠟⠂⠀⢠⣀⣀⣄⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣷⣶⣶⣾⣶⣶⣶⣶⣶⣾⣶⣾⣿⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣎⠰⠀⠈⠁⠀⠀⢰⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠈⢳⡛⠛⠏⠀⢉⢀⣀⣔⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠉⢉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⠁⠀⠀⠀⠀⠀⣠⣦⣦⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⢸⣿⠩⠌⡞⠛⠛⠛⠛⠛⠛⠛⠓⠛⠻⠉⠉⠉⣿⣆⠀⠀⠀⠀⠀⠀⠀⠁⠛⠛⠛⢟⣿⣿⡇⠀⠠⠂⠀⠛⠂⠁⠁⠀⠀⢼⣿⣿⡏⠀⠁⠀⠑⠈⠛⠃⠉⠂⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠁⢸⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣿⣿⠂⢠⣴⣤⣬⣤⣤⣦⣤⣦⣤⣬⣿⣿⣷⣤⣦⣦⣦⣴⣶⣦⣴⣤⣴⣵⣿⣿⣧⣦⣴⣤⣤⣦⣴⣤⣴⣥⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶ ⣿⡟⠉⡉⡛⠛⠛⠋⠛⠛⠛⠛⠛⠈⠛⠋⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⢩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣿⢩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⣿⡏ ⣿⣿⢸⣿⡏⠉⣿⠻⠿⠟⠻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠩⢹⡟⠩⠟⠿⠿⠿⠽⠛⠿⠿⠿⠟⠫⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇ ⣿⣿⢸⣿⣧⣴⣾⣶⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣦⣾⣷⣶⣴⣶⣴⣦⣶⣶⣶⣶⣴⣤⣴⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇ ⣿⣿⢸⣿⣁⢉⣀⣈⣉⣉⣉⣉⣈⡉⣉⣉⣉⣉⣈⣉⣈⣁⣀⣉⣉⣉⣈⣹⢉⢉⡉⣉⣉⣁⣿⣿⣿⣿⣿⣿⢸⣽⣈⣀⣉⣉⢉⣈⣩⣉⣉⣁⠉⢙⡀⣁⠈⣨⣉⣉⣉⣉⢉⣉⣍⣉⣈⣁⣈⣀⣉⣿⣿⣿⣿⡇⣿⡇ ⣿⣿⢸⣿⢉⣁⣁⣁⣉⡉⢏⢁⢈⣉⡉⢈⣩⣉⡠⡁⣈⣉⢁⡉⣉⢉⢇⠁⣈⡉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⢸⣟⣉⣉⣉⣉⣉⣈⣡⢉⣈⣈⣁⣁⡁⣉⣉⡉⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇ ⣿⣿⢸⣿⣁⣉⣈⣉⣉⣈⣙⣾⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇ ⣿⣿⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇ ⣿⣿⢸⣿⣀⣠⡠⢁⣉⣉⣿⣿⣄⣀⣀⣈⣸⣿⣧⣠⣎⣁⣁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣗⣀⣀⡈⣀⣉⣹⣿⣧⡐⣨⢀⣸⣿⣧⣠⣇⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇ ⣿⣿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⣿⡇ ⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿ ⣿⣿⢸⣿⡿⠿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠿⢿⣿⣿⣿⣿⣿⢿⡿⡿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿ ⣿⣿⢸⣿⡇⢀⣻⣉⣉⠉⠉⣈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡈⣸⣇⣀⡉⣉⢉⠉⣈⠈⡉⣈⣉⣉⣁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿ ⣿⣿⢸⣿⠿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⢸⣿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⡇⣿⣿ ⣿⣿⢸⣿⠶⠶⠶⠶⠶⠰⢶⠶⠶⠶⠧⢶⣶⣶⣶⣾⣦⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⢸⣷⠶⠶⠶⠶⠦⠴⠶⠶⠲⠶⠶⣶⣶⣶⣶⣶⣾⣶⣦⣶⣶⣶⣶⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿ ⣿⣿⢸⣿⣶⣶⣲⣶⣶⣶⣾⣶⣦⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣦⣶⣶⣔⣖⣲⣶⣶⣶⣢⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿ ⣿⣿⢸⣿⠛⠻⠛⠿⠻⠿⣻⣿⠛⠛⠛⣿⣿⠛⢙⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠛⠛⠻⠟⠻⢿⣿⡟⢋⠻⠛⢻⣿⡏⠋⡟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿ ⣿⣿⢸⣿⣶⣾⣮⣴⣶⣆⣿⣿⣧⣶⣶⣿⣿⣷⣾⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣶⣖⣧⣶⣰⣾⣿⣿⣦⣼⣶⣿⣿⣿⣾⣷⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿ ⣿⣿⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣿⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿ ⣿⣿⢸⡏⡉⠛⢹⠛⠋⠛⠛⠛⠙⠛⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⣿⣘⣛⣛⣛⣛⣛⣛⣓⣛⣛⣘⣒⣒⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣃⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿ ⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡿⠓⠙⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⠶⢶⡶⣾⣿⠿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣋⣀⣡⣕⣻⣿ ⣿⣿⣦⣄⣤⣄⣤⣤⣤⣤⣤⣤⣄⣠⣄⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ 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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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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣁⣿⣿⣥⣤⣤⣤⣬⣇⣴⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢠⣿⢈⣏⣩⢉⣍⢉⣍⢉⣹⣿⣇⠠⣹⣁⡏⢉⠉⢙⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ 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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣥⣿⣿⣶⣶⣶⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⣶⣶⡶⠶⢶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡏⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡿⣧⣤⢤⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣰⣀⣐⣐⣀⣆⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣴⣴⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⡿⠿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣾⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣾⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿ ⢸⣧⣤⣧⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣧⣼⣧⣤⣤⣤⣦⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣧⣼⣧⣤⣤⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿ ⢸⣇⣩⣉⣈⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣗⣩⣉⣈⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣗⣩⣉⣈⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿ ⢸⣏⣉⣉⣏⣏⣉⣉⣋⣉⣉⣹⣉⣩⣉⣉⣉⣉⣉⣹⣿⣿⣿⣿⡇⣿⣿⣏⣋⣉⡉⣍⣹⣉⣉⣉⢙⣙⣉⣹⣉⣉⣉⢉⣩⣉⣹⣿⣿⣿⡇⣿⣿⣏⣋⣉⣉⣉⣉⣉⣉⣉⣏⣉⣉⣉⣹⣉⣉⣉⣏⣉⣉⣉⡉⣿⡇⣿ ⢸⡧⠤⠤⠤⠧⠧⠥⠤⠤⠄⠤⠤⢤⣤⣤⣦⣧⣤⣤⣬⣿⣿⣿⡇⣿⣿⣧⣤⣤⣧⣤⣤⣤⣧⣧⣤⣤⣼⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⡇⣿⣿⣧⣤⣬⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿ ⢸⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿ ⢸⣇⣸⣍⣉⣉⣿⣯⣨⣉⣉⣿⣧⣸⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣸⣍⣉⣉⣿⣯⣨⣉⣹⣿⣄⣏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣸⣍⣉⣉⣿⣯⣨⣉⣍⣿⣧⣸⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿ ⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿ ⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⣇⣀⣏⣍⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣸⣇⣭⣍⣉⣉⣭⣩⣉⣉⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⡏⣉⣛⣙⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡯⣉⣛⣙⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⡟⠛⠛⠛⠛⠛⠛⠛⡟⠛⠛⠛⡛⠛⠻⠛⠛⠛⣿⣿⣿⣿⣿⡇⣿⣿⡟⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡟⠛⢻⠛⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⣏⣉⣉⣉⣉⣉⣏⣉⣉⣏⣉⣉⣉⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣏⣉⣉⣉⣹⣉⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⡟⢻⠿⠿⣿⡿⠻⠿⣿⣿⠛⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡟⢻⠿⠿⠿⣿⡿⡻⠿⢿⣿⠛⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⣷⣾⣶⣶⣿⣷⣾⣷⣿⣿⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢿⣷⣾⣷⣶⣶⣿⣿⣾⣶⣿⣿⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡗⣸⣉⣉⣉⣉⣉⣩⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠟⠛⠛⠛⠛⠛⠛⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡿⠿⠿⠿⠿⠿⠿⣿ ⢸⣐⣃⣌⣁⣏⣏⣉⣉⣈⣩⣹⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿ ⢸⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⡛⠿⠟⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿ ⢸⡗⠲⠶⠶⡖⠳⠶⠶⠖⠶⡶⠶⠿⠿⠷⠾⠷⠿⠿⠿⠟⠿⡿⠿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿ ⢸⣷⣷⣶⣶⣶⣶⣶⣶⣶⣷⣷⣶⣶⣶⣶⣷⣶⣶⣾⣶⣶⣶⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣾⣶⣿⣾⣿⣿⣿⣿⡇⣿ ⢸⣏⣹⡙⣙⣛⣿⣏⣈⣏⣿⣏⢈⣟⣉⣿⣿⢩⣟⣿⣏⠈⣏⣹⣿⠉⣿⣙⣿⣟⢛⣙⣛⣉⣟⣛⣛⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿ ⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡃⣿ ⢸⡟⠛⠛⠛⣿⢫⠉⠉⢩⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿ ⢸⡟⠛⠛⢻⢻⢳⠒⠒⠖⠛⠛⠛⡟⠛⢻⠛⠛⠛⠛⢻⠛⢻⠛⠛⠛⠛⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡟⡟⠛⠛⠛⠟⠛⠛⢻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣉⣽⡇⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿ ⢸⣇⣸⣍⣉⣉⣿⣯⣪⣏⣉⣿⣯⣀⣏⣩⣋⣉⣿⣿⣠⣏⣋⣹⣿⣂⣸⣉⣹⣿⣗⣸⣹⣿⣟⣉⣉⣉⣏⣉⣉⣹⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿ ䷩ 𝚕𝚒𝚗𝚎 2079 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2021/11/24/irc-log-231121/#comments Gemini version at gemini://gemini.techrights.org/2021/11/24/irc-log-231121/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.24.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ IRC_Proceedings:_Tuesday,_November_23,_2021⠀✐ Posted in IRC_Logs at 2:28 am by Needs Sunlight Also available via the Gemini protocol at: * gemini://gemini.techrights.org/tr_text_version/irc-log-techrights- 231121.txt * gemini://gemini.techrights.org/tr_text_version/irc-log-231121.txt * gemini://gemini.techrights.org/tr_text_version/irc-log-social-231121.txt * gemini://gemini.techrights.org/tr_text_version/irc-log-techbytes- 231121.txt 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  QmYbL8AdiMk9yXwP8NqeCBcepy3zW75u9CDoTkbuQawJZQ #boycottnovell 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #boycottnovell  QmfBQEQ11YCZpWbf3W85ikY84fcmHz4cGDEvncNVxiJndG (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ as 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═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2021/11/24/microsoft-loves-linux-meme/#comments Gemini version at gemini://gemini.techrights.org/2021/11/24/microsoft-loves-linux-meme/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.24.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ [Meme]_Jimmy_Zemlin_Loves_Microsoft⠀✐ Posted in GNU/Linux, Kernel, Microsoft at 1:11 pm by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Laughter_video:_Zemlin_love/Microsoft_'loves'_Linux⦈_ http://techrights.org/wp-content/uploads/2019/07/Jim-Zemlin-Open-Source-Loves- Microsoft.webm Summary: It’s funny, isn’t it? Lying for a living and sucking up to the liars pays off; you get to plunder actual Linux users while leaving_Linux_morally_and financially_bankrupt ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⡀⣀⠀⠀⢀⣀⠀⢀⡀⠀⡀⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢹⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢺⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣏⡽⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣿⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣷⠀⣼⠀⠘⢿⠀⢸⠀⢠⠀⢸⡀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⠷⣶⠟⠷⣶⣾⣿⣶⠶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣿⣽⣶⣶⣾⣶⠞⠒⠚⠒⠚⠛⠶⠒⠛⠒⠛⠒⠊⠀ ⠀⣶⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡟⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⢛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⠏⣿⣿⣿⣿⡟⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣶⣿⣿⣿⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⠙⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⡼⠻⠹⠿⠿⣿⣿⣿⣿⣿⣿⣿⡧⠾⠿⣿⣿⣿⣿⡇⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢿⣿⣿⣿⠆⠀⢹⣟⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠧⣿⡚⣿⣿⣿⣿⣿⣿⣤⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣭⣽⣿⣿⣭⣶⠀⣾⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⣾⣿⣠⣠⣦⠉⣿⣿⣿⣿⣿⣟⡟⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣙⣫⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣜⣿⢿⣾⣾⢿⣷⠘⠛⠛⠉⠉⠁⠀⠀⠓⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢻⣰⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⢿⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠶⠧⢻⣷⣶⣶⣿⠏⠚⠛⠀⠉⠀⠓⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⠀⠀⠘⢿⣿⣿⣿⠟⠀⠀⠉⠉⠛⠿⣿⣿⡟⠛⢻⡿⠉⠈⠙⣿⣿⠀⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣉⣿⣯⢁⡄⠀⠀⠀⠁⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⣸⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⣀⠀⠀⠀⠀⠰⣶⠇⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⡏⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣭⣴⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⠟⠲⢺⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣤⣤⣼⣿⣿⣿⣿⣤⣶⣦⣮⣿⣽⣿⣯⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣈⠉⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠛⠛⠛⠛⣟⣿⣿⣿⣿⣿⣿⡿⠋⣤⣈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⡿⢿⣿⣿⣟⣻⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢾⣗⣷⡿⠏⠅⠈⠉⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠁⠈⠀⠙⣿⣿⣿⣻⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠸⠛⠇⠈⠙⠉⠘⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⠟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠠⠴⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠀⠀⢀⣀⠀⢀⡀⠀⡀⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢹⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢺⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣏⡽⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣿⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⠀⣼⠀⠘⢿⠀⢸⠀⢠⠀⢸⠀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠖⠷⣶⠿⢷⣶⣾⣿⣶⠶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣿⣿⣶⣶⣾⣶⠞⠒⠚⠒⠚⠛⠶⠒⠛⠒⠛⠒⠊⠀ ⠀⣴⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⢛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⣿⣿⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣶⣿⣿⣿⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣦⡀⠀⠙⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⡪⠻⠾⠿⠿⣿⣿⣿⣿⣿⣿⣿⡧⠿⠿⣿⣿⣿⣿⡆⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⠂⠀⢹⣟⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠷⣿⡚⣿⣿⣿⣿⣿⣿⣤⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⠀⣾⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢾⣿⣠⣠⣦⠉⣿⣿⣿⣿⣿⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢙⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡼⣿⣿⣾⣾⣻⣿⠐⠛⠛⠉⠉⠁⠀⠀⠓⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢹⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⢿⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠤⡧⢻⣷⣶⣶⣿⠏⠚⠛⠂⠈⠁⠓⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⠀⠀⠐⢿⣿⣿⣿⠿⠀⠀⠉⠉⠛⠿⣿⣿⡟⠛⢻⡿⠉⠈⠙⣿⣿⠀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣯⣁⠄⠀⠀⠀⠁⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⣰⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢀⣀⠀⠀⠀⠀⠰⣶⠇⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⡟⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣭⣴⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣶⣶⣿⣿⣿⠞⠶⢾⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣤⣤⣼⣿⣿⣿⣿⣤⣤⣦⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣀⠉⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠛⠛⠛⠛⡿⢻⣿⣿⣿⣿⣿⡿⠃⣤⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⣿⢿⣿⣿⣟⣻⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢾⣗⣷⡿⠏⠁⠈⠉⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠁⠈⠀⢙⣿⣿⣷⡏⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠁⠀⠀⠀⠀⠀⠻⠋⠃⠘⠙⠁⠘⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⠟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠠⠴⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⡀⣀⠀⠀⢀⣀⠀⢀⡀⠀⡀⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢹⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢺⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣏⡹⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣷⣻⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣷⢀⣼⠀⠘⢿⠀⢸⠀⢠⠀⢸⠀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠒⢷⣶⠿⠷⣶⣾⣿⣷⠶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣶⣿⣶⣶⣾⣶⠚⠒⠚⠒⠚⠛⠶⠒⠛⠒⠛⠒⠊⠀ ⠀⣶⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⡛⢛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⣿⣿⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣶⣿⣿⣿⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⡀⠀⠙⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⡮⠻⠼⠿⠿⣿⣿⣿⣿⣿⣿⣿⡇⠿⠿⣿⣿⣿⣿⡇⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣟⠂⠀⢹⣟⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠷⣿⡚⣿⣿⣿⣿⣿⣿⣤⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣶⣷⠀⣾⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⣾⣿⣠⣠⣦⠉⣿⣿⣿⣿⣿⣟⣟⣿⡿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣙⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡼⣿⣻⣷⣾⣻⣿⠐⠛⠛⠉⠉⠁⠀⠀⠓⠓⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢹⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⢿⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠒⠧⠹⣿⣶⣶⣿⠇⠚⠛⠀⠀⠁⠓⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⠀⠀⠘⣿⣿⣿⣿⡿⠀⠀⠉⠉⠛⠿⣿⣿⡟⠛⢻⡿⠉⠈⠙⣿⣿⠈⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⣿⣯⣠⠄⠀⠀⠀⠁⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⣰⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢀⣀⠀⠀⠀⠀⠰⣶⠇⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣭⣴⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢀⣶⣶⣿⣿⣿⠶⠶⢾⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣤⣤⣼⣿⣿⣿⣿⣤⣴⣶⣮⣿⣽⣭⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣭⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣉⠉⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠛⠛⠿⣟⣿⣿⣿⣿⣿⡿⠃⣤⣁⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⠿⢿⣿⣿⣟⡻⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⢾⣗⣷⡿⠋⠁⠈⠉⠉⠁⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠁⠈⠀⠹⣽⣿⣿⠏⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠁⠀⠀⠀⠀⠀⠙⠋⠛⠘⠙⠉⠘⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⢟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠠⠴⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⡀⣀⠀⠀⢀⣀⠀⢀⡀⠀⡀⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢹⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢺⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣏⡹⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣻⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣷⠀⣾⠀⠘⢿⠀⢸⠀⢠⠀⢸⠀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⠷⠶⠿⣷⣶⣾⣿⣶⠶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣷⣾⣶⣶⣾⣶⠚⠒⠚⠒⠚⠛⠶⠒⠛⠒⠛⠒⠊⠀ ⠀⣶⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⡛⢛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⣿⣿⣿⣿⡟⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣶⣿⣿⣿⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣄⠀⠙⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⡪⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡇⠿⠿⣿⣿⣿⣿⣇⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣟⠀⠀⢹⣟⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠷⣿⡚⣿⣿⣿⣿⣿⣿⣤⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣶⣶⠀⣾⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢾⣷⣠⣠⣦⠉⣿⣿⣿⣿⣿⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢙⣹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⣿⣻⣷⣾⢻⣿⠘⠛⠛⠉⠉⠁⠀⠀⠓⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢹⣼⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⢿⣿⣿⣷⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆⠶⠷⠻⣿⣷⣾⣿⠇⠚⠛⠀⠈⠀⠓⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⠀⠀⠘⣾⣿⣿⣿⠿⠀⠀⠉⠉⠛⠿⣿⣿⡟⠛⢻⡿⠉⠈⠙⣿⣿⠀⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⣿⣯⣠⠄⠀⠀⠀⠁⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⣸⡆⣿⠀ ⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢀⣀⠀⠀⠀⠀⠰⣶⠇⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣭⣴⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄⣿⠀ ⠀⢸⡏⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢀⣶⣶⣿⣿⣿⠶⠶⢾⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣤⣤⣼⣿⣿⣿⣿⣴⣤⣶⣮⣯⣿⣭⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣈⠉⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠛⠛⠛⠛⡿⢻⣿⣿⣿⣿⣿⡿⠃⣥⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⡿⢿⣿⣿⣟⣻⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢾⣗⣷⡿⠋⠅⠈⠉⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠁⠈⠀⠻⣽⣿⣿⡏⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠻⠋⠋⠈⠛⠙⠘⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⠟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡟⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⡀⣀⠀⠀⢀⣀⠀⢀⡀⠀⡀⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢹⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢺⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣯⡹⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣿⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣷⢀⣸⠀⠘⢿⠀⢸⠀⢠⠀⢸⠀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⢷⣶⠿⡷⣶⣾⣿⣷⠶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣷⣿⣶⣶⣾⡶⠚⠒⠚⠒⠚⠛⠶⠒⠛⠒⠛⠒⠊⠀ ⠀⣶⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⣛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⣿⣿⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⢠⣾⣿⣿⣿⣷⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣄⠀⠙⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⡪⠻⠽⠿⠿⣿⣿⣿⣿⣿⣿⣿⡇⡿⠿⢿⣿⣿⣿⣇⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣟⠂⠀⢹⣟⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠷⣿⡚⣿⣿⣿⣿⣿⣿⣤⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣶⣶⠀⣾⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢾⣿⣠⣠⣦⠉⣿⣿⣿⣿⣿⣟⣟⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢙⣹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡼⣿⣻⣷⣾⣻⣿⠘⠛⠛⠉⠉⠁⠀⠀⠓⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢹⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⢿⣿⣿⣷⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡦⠢⠧⠻⣿⣷⣾⣿⠇⠚⠛⠀⠀⠀⠒⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢼⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⠀⠀⠘⣾⣿⣿⣿⠿⠀⠀⠉⠉⠛⠿⣿⣿⡟⠛⢻⡿⠉⠈⠙⣿⣿⠀⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⣿⣯⣠⠄⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⣰⡆⣿⠀ ⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢀⣀⠀⠀⠀⠀⠰⣶⠇⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⡟⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣭⣴⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣿⠀ ⠀⢸⡏⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢠⣶⣶⣿⣿⣿⠶⠶⢾⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣤⣤⣼⣿⣿⣿⣿⣤⣴⣶⣮⣽⣽⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣿⣿⣿⣿⣧⣾⣯⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣉⠉⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠛⠛⠛⠛⡻⣻⣿⣿⣿⣿⣿⡿⠋⢤⣈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⣿⢿⣿⣿⣟⡻⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠾⣗⣷⡿⠿⠅⠈⠉⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠁⠈⠀⢛⣽⣿⣿⣟⢿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠘⠙⠃⠘⠛⠋⠘⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⠟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡟⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⡀⣀⠀⠀⢀⣀⠀⢀⡀⠀⡀⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢹⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢺⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣏⡹⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣿⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣷⠀⣼⠀⠘⢿⠀⢸⠀⢠⠀⢸⠀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⢷⣶⠟⣷⣶⣾⣿⣶⡶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣳⣼⣶⣶⣾⢶⠚⠒⠚⠒⠚⠛⠶⠖⠛⠒⠛⠒⠊⠀ ⠀⣶⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⣛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⣿⣿⣿⣿⡟⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢠⣾⣿⣿⣿⣿⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⡀⠀⠙⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⡪⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡇⡾⠿⢿⣿⣿⣿⣇⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠀⠀⢹⣟⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠷⣿⡚⣿⣿⣿⣿⣿⣿⣤⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⠀⣾⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⣾⣿⣠⣠⣦⠉⣿⣿⣿⣿⣿⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣙⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⡼⣿⣻⣾⣾⣿⣿⠘⠛⠛⠉⠉⠁⠀⠀⠓⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢹⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⢿⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⠆⠲⠧⢻⣿⣶⣶⣿⠇⠚⠛⠀⠈⠀⠓⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠀⠀⠘⣶⣿⣿⣿⠿⠀⠀⠈⠉⠛⠿⣿⣿⡟⠛⢻⡿⠉⠈⠙⣿⣿⠀⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⣿⣯⣠⠄⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⣰⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢀⣀⠀⠀⠀⠀⠰⣶⠇⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣭⣴⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢠⣶⣶⣿⣿⣿⠶⠶⢾⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣠⣤⣤⡬⣿⣿⣿⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣤⣤⣼⣿⣿⣿⣿⣤⣴⣶⣮⣽⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣶⣿⣿⣿⣿⣧⣾⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣉⠉⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⠋⠛⠛⠛⣿⣟⣿⣿⣿⣿⣿⡿⠃⠤⢈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⡿⢿⣿⣿⣟⣻⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⢾⣗⣷⡿⠏⠄⠈⠉⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠁⠀⠀⢹⣽⣿⣿⣏⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠈⠻⠏⠑⠈⠉⠉⠘⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⠟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠠⠴⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠀⠀⢀⣀⠀⢀⡀⠀⡀⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢹⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢺⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣏⠹⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣷⣿⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⠀⣼⠀⠘⢿⠀⢸⠀⢠⠀⢸⠀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⢷⣶⠿⠷⣶⣾⣿⣷⠶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣷⣼⣶⣶⣾⣶⠚⠒⠚⠒⠚⠛⠶⠒⠛⠒⠛⠒⠊⠀ ⠀⣶⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠛⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⢛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⣿⣿⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢠⣾⣿⣿⣿⣿⡄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⠙⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⣪⠻⠾⠿⠿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⡿⠀⠀⢹⣟⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠧⣿⡚⣿⣿⣿⣿⣿⣿⣥⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣭⣿⣿⣿⣯⡆⠀⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢾⣿⣠⣠⣦⠉⣿⣿⣿⣿⣿⣟⣿⣿⣿⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢼⣿⢿⣯⣾⣿⡇⠜⠛⠛⠉⠉⠁⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⣿⣿⣿⣿⢿⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠲⠇⢻⣶⣦⣶⣿⠃⠛⠛⠀⠀⠀⠓⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠀⠀⠸⣷⣾⣿⣿⠿⠀⠀⠈⠉⠛⠿⣿⣿⡟⠛⢹⡿⠉⠈⠙⣿⣿⠀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣙⣿⣋⣁⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⣰⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢀⣀⠀⠀⠀⠀⠰⣶⠇⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⡀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⡏⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣭⣴⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣿⠀ ⠀⢸⡏⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢠⣶⣶⣶⣷⣶⠶⠶⢾⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣰⣾⣿⣿⣿⣯⣿⣿⣿⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣤⣤⣼⣿⣿⣿⣿⣤⣴⣦⣮⣿⣭⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣉⠉⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠛⠛⠛⠻⡿⣻⣿⣿⣿⣿⣿⡿⠃⣥⣁⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⡿⢿⣿⣿⣟⣻⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢾⣗⣷⡿⠯⠄⠈⠉⠉⠁⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠁⠈⠀⠙⣿⣿⣿⢏⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠈⠛⠛⠁⠈⠉⠁⠘⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⢟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢓⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⡀⣀⠀⠀⢀⣀⠀⢀⡀⠀⡀⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢹⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢺⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣏⡙⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣿⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⠀⣼⠀⠘⢿⠀⢸⠀⢠⠀⢸⠀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠲⢷⣶⠿⠷⣶⣾⣿⣶⠶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣧⣼⣶⣶⣾⣶⠚⠒⠚⠒⠚⠛⠶⠖⠛⠒⠛⠒⠊⠀ ⠀⣶⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⠛⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⢛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⡀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⠋⣿⣿⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢀⣾⣿⣿⣿⣿⣆⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣦⡀⠀⠙⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⡨⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡆⢸⠿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⡿⠀⠀⣻⣟⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠧⢿⡚⣿⣿⣿⣿⣿⣿⣵⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣽⣿⣿⣿⣿⡆⢀⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢿⠀⢾⣿⣠⣠⣦⠉⣿⣿⣿⣿⣿⣟⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢙⣹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢸⣿⣻⣿⣾⣿⡇⠞⠛⠛⠉⠉⠁⠀⠀⠓⠓⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢹⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⣿⣿⣿⣿⢿⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠆⢿⣷⣶⣶⣿⠃⠛⠛⠀⠀⠀⠓⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠀⠀⠸⣷⣾⣿⣿⠿⠀⠀⠉⠉⠛⠿⣿⣿⡟⠛⢻⡿⠉⠈⠙⣿⣿⠀⣃⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠆⢠⣙⣿⣏⣡⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⣰⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢀⣀⠀⠀⠀⠀⠰⣶⠇⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⡀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣭⣴⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠄⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⠶⠶⢾⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⡯⠩⣿⣿⣿⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣤⣤⣼⣿⣿⣿⣿⣤⣴⣦⣮⣭⣿⣯⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⣶⣶⣿⣿⣿⣿⣧⣾⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣉⠉⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠛⠛⢛⠛⠛⢿⣿⣿⣿⣿⣿⡿⠃⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⠿⢿⣿⣿⣟⣻⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢾⣗⣷⡿⠏⠅⠈⠉⠉⠁⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠁⠈⠀⢙⣿⣿⣿⡿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠁⠀⠀⠀⠀⠈⠻⠋⠑⠈⠙⠋⠘⣿⣷⡼⣿⣿⣿⣿⣿⣿⣿⣿⠟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠀⠀⢀⣀⠀⢀⡀⠀⡀⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢹⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢺⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣯⡹⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣻⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣷⡀⣾⠀⠘⢿⠀⢸⠀⢠⠀⢸⠀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠲⢷⠶⠿⠷⣶⣾⣿⣶⠶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣻⣼⣶⣶⣾⡶⠚⠒⠚⠒⠚⠛⠶⠒⠛⠒⠛⠒⠊⠀ ⠀⣴⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⠛⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⢛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⡀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣿⣿⣿⣿⡟⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢠⣾⣿⣿⣿⣿⡆⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⡄⠀⠘⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⡪⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡇⢸⢿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣿⣿⣿⣟⠀⠀⣹⣟⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠧⣿⡚⣿⣿⣿⣿⣿⣿⣥⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⢿⣷⡇⢀⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢼⣿⣀⣠⣦⠉⣿⣿⣿⣿⣿⣟⣿⣿⣿⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢙⡫⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠾⣿⠿⠿⠿⣿⡇⠚⠛⠛⠉⠉⠁⠀⠀⠓⠓⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢹⣰⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⣿⣿⣿⣿⢿⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣿⣧⢹⣿⣿⣿⣿⠃⠙⠛⠂⠀⠁⠒⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠀⠀⠸⣷⣿⣿⣿⠿⠀⠀⠈⠉⠛⠿⣿⣿⡟⠛⢹⡿⠉⠈⠉⣿⣿⠀⣃⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣬⣿⣭⣤⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⣰⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢀⣀⠀⠀⠀⠀⠰⣶⠇⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⡀⠀⠀⢀⣴⣶⣾⣿⣿⣿⣿⣽⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⡏⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣭⣴⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⠶⠶⢾⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⣿⣿⣿⠋⠨⣿⣿⣿⣿⣷⣿⣿⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣤⣤⣼⣿⣿⣿⣿⣤⣴⣦⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣷⣶⣶⣿⣿⣿⣿⣧⣾⣭⣥⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣉⠉⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠛⠻⡿⣟⣿⣿⣿⣿⣿⡿⠃⠤⣈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⡿⢿⣿⣿⣟⣻⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢾⣗⣷⡿⠛⠁⠈⠉⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠁⠀⠀⠙⣿⣿⣿⡟⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠁⠀⠀⠀⠀⠈⠘⠋⠑⠈⠙⠋⠘⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⠟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠠⠴⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⡀⠀⠀⢀⣀⠀⢀⡀⠀⡀⠀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢹⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢺⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣏⠹⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣿⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⢀⣼⠀⠘⢿⠀⢸⠀⢠⠀⢸⠀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⢷⢶⡟⢷⣶⣾⣿⣶⠶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣷⣼⣶⣶⣾⡶⠚⠒⠚⠒⠚⠛⠲⠒⠛⠒⠛⠒⠊⠀ ⠀⣴⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠛⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⢛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⡀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣿⣿⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢠⣾⣿⣿⣿⣿⡆⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣷⣄⠀⠈⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⣪⠻⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⡇⣸⢿⣿⣿⣿⣿⣧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣯⡀⠀⢸⣟⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠶⣽⡚⣿⣿⣿⣿⣿⣿⣤⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⡿⣿⣿⡷⢀⣼⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢻⠀⢾⣿⣀⣠⣦⠉⣿⣿⣿⣿⣿⣟⣟⣿⣿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢙⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠆⣿⡽⠿⠿⣽⡿⠘⠛⠛⠉⠉⠁⠀⠀⠓⠓⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣰⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⣿⣿⣿⣿⢿⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⠼⣿⣿⣿⣿⠇⠘⠛⠀⠀⠁⠓⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠀⠀⠸⣷⣿⣿⣿⠟⠀⠀⠈⠉⠛⠻⣿⣿⡟⠛⢻⡿⠉⠈⠙⣿⣿⠀⣃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡍⢰⣤⣿⣯⣤⠆⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⣰⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢀⣀⠀⠀⠀⠀⠰⣶⠇⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⡀⠀⣠⣾⣿⣿⣿⠋⣁⣤⣶⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⡏⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣭⣴⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⠟⣸⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⠶⠶⢾⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⣿⠏⠀⠨⣿⣿⣿⣿⣷⣿⣿⡇⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣤⣤⣼⣿⣿⣿⣿⣤⣤⣶⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣭⣥⣥⣤⣬⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣈⠉⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠛⠛⠛⠛⡿⣿⣿⣿⣿⣿⣿⡿⠃⢤⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⢿⢿⣿⣿⣟⣻⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢾⣗⣷⡿⠏⠁⠈⠉⠉⠁⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡘⠁⠀⠀⠹⣿⣿⣿⣟⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠈⠙⠓⠃⠀⠉⠋⠘⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⠟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⠶⠄⠠⠴⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⡀⠀⠀⢀⣀⠀⢀⡀⠀⣀⠀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢹⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢺⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣏⡹⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣷⣿⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⣀⣼⠀⠘⢿⠀⢸⠀⢠⠀⢸⠀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⢷⢶⡿⠷⣶⣾⡿⣶⠶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣶⣽⣶⣶⣾⡶⠚⠒⠚⠒⠚⠛⠲⠒⠛⠒⠛⠒⠊⠀ ⠀⣴⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠛⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⡛⣛⣛⣛⣛⡛⢛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⡀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢻⣿⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢠⣾⣿⣿⣿⣿⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣷⡄⠀⢹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⣨⠻⠝⠿⠿⣿⣿⣿⣿⣿⣿⣿⡇⡼⢿⣿⣿⣿⣿⣧⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢭⣿⣿⣽⢅⠀⠀⣟⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠧⣽⡚⣿⣿⣿⣿⣿⣿⣤⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣴⣦⡀⠀⠀⠀⣿⣿⣿⣛⣿⣿⠃⣠⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢻⠀⢾⣿⣀⣠⣦⠉⣿⣿⣿⣿⣿⣟⣿⣿⣿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣻⣿⣿⠀⠀⠀⠀⠀⢠⣾⣿⠻⡿⠃⠀⠘⢹⣯⣛⣛⣻⣿⠃⠛⠛⠉⠉⠁⠀⠀⠓⠓⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣰⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡿⢿⢿⣿⣿⣿⣿⢿⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⡿⢿⡗⠀⠂⠀⠛⠃⠿⣿⣿⡿⠟⠈⠛⠂⠈⠁⠓⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠉⠀⠀⠹⣶⣿⣿⣿⠟⠀⠀⠈⠉⠙⠻⣿⣿⡟⠛⢻⡿⠉⠈⠙⣿⣿⠀⣂⠀⣠⣦⣸⣷⠀⠀⠀⠀⠀⠀⠀⣷⣾⣿⣤⡖⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⣰⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢀⣀⠀⠀⠀⠀⠐⣶⠇⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⣼⣿⣿⣿⣿⠆⠀⠀⣀⣤⣶⣼⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣭⣴⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⠃⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⠀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢰⣶⣶⣶⣾⣷⠶⠶⢺⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠙⠋⠁⠀⠀⠀⠨⣿⣿⣿⣿⣷⣿⣿⣿⣶⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣤⣤⣼⣿⣿⣿⣿⣤⣤⣶⣮⣿⣿⣽⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣭⣽⣭⣭⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣉⠉⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠛⠛⠙⠛⠿⣿⣿⣿⣿⣿⣿⡿⠃⢤⣈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⡿⢿⣿⣿⣟⡻⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠼⣗⣷⡿⠏⠀⠈⠉⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡘⠁⠈⠀⠙⣿⣿⣿⣏⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠘⠉⠁⠈⠉⠉⠘⣿⣷⡼⣿⣿⣿⣿⣿⣿⣿⣿⠟⣽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠠⠴⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢓⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⡀⣀⠀⠀⢀⣀⠀⢀⡀⠀⢀⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢹⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢺⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣏⡽⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢰⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣿⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣷⡀⣼⠀⠘⢿⠀⢸⠀⢠⠀⢸⠀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⢷⢶⠟⢷⣶⣾⣿⡶⠶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣶⣿⣶⣶⣾⡶⠚⠒⠚⠒⠚⠛⠶⠒⠛⠒⠛⠒⠊⠀ ⠀⣴⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠛⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⡛⣛⣛⣛⣛⡛⢛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⡀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠙⢿⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢠⣾⣿⣿⣿⣿⡄⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⣾⣿⣿⣦⠀⠀⢻⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⣨⠻⠼⠿⠿⣿⣿⣿⣿⣿⣿⣿⡇⡼⣿⣿⣿⣿⣿⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡄⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣀⠀⠈⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠧⣽⡚⣿⣿⣿⣿⣿⣿⣴⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠰⣶⣄⣼⡏⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣽⣽⣿⣟⢀⣸⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢻⠀⠼⣿⣄⣠⣆⠉⣿⣿⣿⣿⣿⣟⡟⣿⣿⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢙⣻⣿⣿⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠈⠀⠂⡋⣿⣎⣉⣉⣾⡟⠘⠛⠉⠉⠁⠀⠀⠓⠓⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣰⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⣿⣿⣿⣿⢿⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⡀⢻⣿⠟⠀⠀⠀⠀⠀⠂⠀⠘⠛⠘⢿⣿⣿⡿⠁⠘⠂⠈⠁⠒⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠉⠀⠀⠹⣶⣿⣿⣿⠟⠀⠀⠈⠉⠙⠻⣿⣿⡟⠛⢹⡿⠉⠈⠙⣿⣿⢸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣾⣿⣿⣶⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⣀⠀⠀⠀⠀⠰⣶⠇⠀⠸⡇⣴⣾⣿⣿⣿⢸⣿⣿⣿⠏⠀⠀⠀⠀⠀⣀⣤⣶⣤⣿⣿⣿⣿⡟⠀⣤⣶⣷⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⡗⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣭⣴⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠿⠿⠋⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠄⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢰⣶⣶⣿⣿⣿⠒⠶⢺⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣷⣿⣿⣿⠁⠀⠘⠿⢿⣿⡟⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣤⣤⣼⣿⣿⣿⣿⣤⣤⣴⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣭⣭⣦⣤⣤⣤⣬⣭⣤⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣈⠉⠈⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠛⠛⠛⠋⠻⣿⣿⣿⣿⣿⣿⡿⠃⠤⣈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⣿⢿⣿⣿⣟⡻⣿⣿⣿⣷⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠼⣗⣷⡿⠟⠀⠈⠉⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡘⠁⠈⠀⠙⣿⣿⣿⠿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠸⠛⠂⠈⠛⠋⠘⣿⣷⡼⣿⣿⣿⣿⣿⣿⣿⣿⠟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠠⠴⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡿⢓⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⡀⠀⠀⢀⣀⠀⢀⡀⠀⡀⠀⡀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢹⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢺⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣏⡽⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣷⣿⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⡀⣸⠀⠘⢿⠀⢸⠀⢠⠀⢸⠀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⢷⢶⡿⢷⣶⣾⣿⣶⠶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣲⣽⣶⣶⣾⡶⠚⠒⠚⠒⠚⠛⠲⠒⠛⠒⠛⠒⠊⠀ ⠀⣴⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠛⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⡛⣛⣛⣛⣛⣛⢛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⢀⡀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣾⣿⣿⣿⣿⡄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢰⣿⣿⣿⣆⠀⠈⢻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⣪⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣛⣻⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣲⣿⣿⣿⣯⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠧⣿⡚⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣽⣿⣿⠃⢀⣸⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣻⠀⢼⣿⣠⣠⣦⠉⣿⣿⣿⣿⣿⣟⣟⣿⣿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢙⣻⣿⣿⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣟⢹⣯⣭⣭⣵⣿⠁⠋⠋⠉⠁⠀⠀⠓⠓⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⢿⠿⣿⣿⣿⣿⠿⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣷⣆⠀⠀⠀⠀⠀⠀⠐⠂⠀⠛⠛⠓⠻⣿⣿⣿⠇⠀⠂⠈⢡⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠁⠀⠀⠹⣷⣿⣿⣿⠟⠀⠀⠈⠉⠙⠻⣿⣿⡟⠛⢹⡿⠉⠈⠙⣿⣿⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⡏⠀⠀⠀⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣰⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣀⠀⠀⠀⠀⠰⣶⠇⠀⠸⡇⣴⣾⣿⣿⣿⢸⡿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣄⣾⣿⣿⣿⣿⠃⠀⠀⠀⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣭⣴⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰⣿⠟⣁⠀⠀⠀⠀⠀⠀⠀⣾⠄⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⠛⠓⢺⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣤⣤⣼⣿⣿⣿⣿⣤⣴⣴⣬⣯⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣭⣭⣥⣤⣤⣤⣤⣬⣭⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⡤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣯⣉⠉⠈⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠛⠛⠛⠛⡻⣿⣿⣿⣿⣿⣿⡿⠃⣤⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⡿⢿⣿⣿⣟⡻⣿⣿⣿⣷⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠾⣗⣷⡿⠋⠀⠈⠉⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡘⠁⠈⠀⠙⣿⣿⣿⠯⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠁⠀⠀⠀⠀⠀⠘⠋⠃⠈⠉⠉⠘⣿⣷⡽⣿⣿⣿⣿⣿⣿⣿⣿⠟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠰⠰⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⡀⡀⠀⠀⢀⣀⠀⢀⡀⠀⣀⠀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢹⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢺⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣏⡙⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡗⠛⢺⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢰⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣷⣻⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⠀⣼⠀⠘⢿⠀⢸⠀⢠⠀⢸⠀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⢷⡶⠟⠷⣶⣾⣿⣶⡶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣣⣼⣶⣶⣾⡶⠚⠒⠚⠒⠚⠛⠲⠒⠛⠒⠛⠒⠊⠀ ⠀⣴⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠛⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⠛⣛⣛⣛⣛⣛⢛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⢀⣀⣀⡀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠹⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣿⣿⣿⣿⣿⡄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣶⡀⠀⣴⣿⣿⣷⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⣨⠻⠼⠿⠿⣿⣿⣿⣿⣿⣿⣿⡇⡼⣛⣻⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣾⣿⣿⣖⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠧⣽⡚⣿⣿⣿⣿⣿⣿⣼⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢷⣷⡿⣿⣏⠀⣀⣰⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢻⠀⠼⣿⣀⣠⣦⠉⣿⣿⣿⣿⣿⣟⡟⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢙⣹⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⣋⢿⣥⣭⣭⣿⡇⠘⠁⠉⠁⢸⣿⡗⠓⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⢰⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⠿⢿⠿⣿⣿⣿⣿⠿⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⢻⣿⣿⠟⠁⠀⠈⠉⣺⣾⣿⠁⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠁⠀⠀⠹⣷⣿⣿⣿⠟⠀⠀⠀⠉⠙⠻⣿⣿⡟⠛⢹⡿⠉⠈⠙⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠁⠀⠀⣰⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣸⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠰⣶⠇⠀⠸⡇⣴⣾⣿⣿⣿⢾⠿⠋⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣄⣠⣿⣿⣿⣿⡏⠀⠀⢀⣿⣟⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣭⣴⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⣾⠀⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠛⠛⢺⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣷⣿⣿⣿⡟⠀⠀⠀⠘⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣤⣤⣼⣿⣿⣿⣿⣤⣤⣤⣬⣽⣿⣭⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣭⣭⣥⣤⣤⣤⣤⣤⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣈⠁⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠛⠛⠛⠛⠟⣿⣿⣿⣿⣿⣿⡿⠃⠤⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⡿⢿⣿⣿⣟⣻⣿⣿⣿⣷⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠾⣗⣶⡿⠏⠀⠈⠉⠉⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡘⠁⠈⠀⠙⣿⣿⣿⡟⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠙⠋⠃⠈⠋⠉⠘⣿⣧⡼⣿⣿⣿⣿⣿⣿⣿⣿⠟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠰⠰⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢒⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⡀⣀⠀⠀⢀⣀⠀⢀⡀⠀⠀⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢹⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢺⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣏⡽⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢰⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣿⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⠀⣼⠀⠘⢿⠀⢸⠀⢠⠀⢸⠀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⢗⣶⡻⢷⣶⣾⣿⣶⠶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣦⣼⣶⣶⣾⡶⠚⠒⠚⠒⠚⠛⠲⠒⠛⠒⠛⠒⠊⠀ ⠀⣴⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⠛⠛⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⢛⣛⣛⣛⣛⢛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠙⣧⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⣀⣀⣀⡀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠻⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⣿⣿⣿⣿⣿⡆⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣶⣦⠀⠀⣼⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⡪⠻⠾⠿⠿⣿⣿⣿⣿⣿⣿⣿⡇⣾⡛⡻⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⢳⣿⣦⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠦⣽⡚⣿⣿⣿⣿⣿⣿⣼⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⢻⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣶⣾⣿⣿⣃⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢻⠀⢼⣿⣀⣠⣦⠉⣿⣿⣿⣿⣿⣟⡿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢙⣻⣿⣿⠀⠀⠀⠻⣿⣿⣿⠇⠀⠀⠈⠀⠈⣘⣧⣿⣧⣴⣴⣼⣿⣿⡿⠁⠁⠀⠀⠒⠓⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣸⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⠿⢿⠿⣿⣿⣿⣿⠿⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣀⣘⣿⣿⣀⠀⠀⠂⠀⠻⠿⠿⠿⠘⣿⣿⣿⣿⡟⠁⠀⠒⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠁⠀⠀⠹⣷⣿⣿⣿⠟⠀⠀⠀⠉⠙⠻⣿⣿⡟⠛⢻⡿⠉⠈⠙⣿⣿⠀⢃⠐⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣶⣆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠰⣶⠇⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⡀⢿⣿⣿⣿⡟⠀⠀⣀⣤⣶⣄⡀⢸⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⡯⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣭⣴⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠉⠛⠉⠀⠀⣸⣿⣿⣿⣿⣷⣾⣿⣿⣿⠸⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⠛⠶⢸⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣤⣤⣼⣿⣿⣿⣿⣤⣤⣴⣮⣽⣯⣿⣯⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣭⣭⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣁⠉⠈⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠋⠛⠛⠛⡟⣿⣿⣿⣿⣿⣿⡿⠃⠤⣈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⡿⢿⣿⣿⣟⡻⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠼⣗⣷⡿⠋⠁⠈⠉⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡘⠁⠀⠀⠹⣿⣿⣿⣏⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠚⠇⠃⠈⠉⠉⠘⣿⣷⡼⣿⣿⣿⣿⣿⣿⣿⣿⠟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠰⠰⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢓⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠀⠀⢀⣀⠀⠀⡀⠀⣀⠀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢹⡉⠉⢹⠉⢹⣿⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢺⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣯⡽⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣿⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⡀⣼⠀⠘⢿⠀⢸⠀⢠⠀⢸⠀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⠷⣶⡿⣷⣶⣾⣿⣶⡶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣷⣽⣶⣶⣾⣶⠚⠒⠚⠒⠚⠛⠶⠒⠛⠒⠛⠒⠊⠀ ⠀⣴⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⠛⠛⠛⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣻⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⢛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢀⣀⣀⣀⡀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠉⠁⠁⠈⠛⠟⠛⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⣿⣿⣿⣿⣿⡆⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⠀⠀⠀⣶⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⡪⠻⠼⠿⠿⣿⣿⣿⣿⣿⣿⣿⣆⣟⠻⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣴⣒⣠⡿⡿⣿⣿⣮⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠧⣽⡚⣿⣿⣿⣿⣿⣿⣽⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⣿⢱⢿⣿⣿⣿⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢿⠀⢼⣿⣠⣠⣦⠉⣿⣿⣿⣿⣿⣟⣟⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢙⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣿⡟⣷⣶⣶⣿⣿⡞⠛⠁⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⢿⠿⣿⣿⣿⣿⠿⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠶⠿⣿⣿⣿⣥⣿⣿⣿⢿⡟⠁⠀⠒⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠁⠀⠀⠻⣶⣿⣿⣿⠟⠀⠀⠀⠉⠙⠻⣿⣿⡟⠛⢻⡿⠉⠈⠙⣿⣿⠀⣂⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⣀⠀⠀⠀⠀⠰⣶⠇⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⡀⠀⠀⠀⠀⠀⠈⢀⣴⣿⣿⣾⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣭⣴⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⡜⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⠶⠶⢺⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣷⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣤⣤⣼⣿⣿⣿⣿⣤⣴⣦⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣽⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣈⠉⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⡿⠋⠤⣈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⡿⢿⣿⣿⣟⣻⣿⣿⣿⣷⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠾⣗⣷⡿⠏⠅⠈⠉⠉⠁⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠉⠈⠀⠙⣿⣿⣿⢿⣿⣿⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠈⠙⠫⠁⠘⠛⠉⠘⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⢟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡟⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠰⠰⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠀⠀⢀⣀⠀⢀⡀⠀⢀⠀⣀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢹⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢺⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣏⡹⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣾⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⣀⣾⠀⠘⢿⠀⢸⠀⢠⠀⢸⠀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⢷⣶⡻⠷⣶⣾⣿⣶⡶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣶⣼⣶⣶⣾⡶⠚⠒⠚⠒⠚⠛⠶⠒⠛⠒⠛⠒⠊⠀ ⠀⣴⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠛⠛⠛⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⢛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢀⣀⣀⣀⣀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠃⠉⠉⠉⠻⠟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⡆⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⠀⠀⡇⢀⣴⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⡮⠻⠺⠿⠿⣿⣿⣿⣿⣿⣿⣿⣆⣟⠻⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣀⣿⠷⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠧⣽⡚⣿⣿⣿⣿⣿⣿⣽⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣸⣿⣏⠾⢿⣿⣿⣟⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣻⠀⢼⣿⣠⣠⣆⠉⣿⣿⣿⣿⣿⣟⣟⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢙⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⡟⠛⠁⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣰⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⢻⠿⣿⣿⣿⣿⠿⢿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣧⢿⣿⣿⣿⡏⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠁⠀⠀⠻⣶⣿⣿⣿⠟⠀⠀⠀⠉⠙⠻⣿⣿⡟⠛⢹⡿⠉⠈⠉⣿⣿⠀⣀⠀⠀⠀⠀⠀⠀⠀⢚⡟⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⣿⠀ ⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⣀⠀⠀⠀⠀⠰⣶⠇⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⡀⠀⠀⠀⠀⠀⠈⠉⣀⣤⣶⣼⣿⣾⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⡏⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣭⣴⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⢿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⠶⠶⢺⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣷⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣤⣤⣼⣿⣿⣿⣿⣤⣴⣦⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣵⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣉⠉⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠛⠛⠛⠻⠿⢻⣿⣿⣿⣿⣿⡿⠃⡤⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⠿⢿⣿⣿⣟⡻⣿⣿⣿⣷⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠾⣗⣷⡿⠟⠁⠈⠉⠉⠁⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠁⠈⠀⠙⣿⣿⣿⣟⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠙⠋⠃⠘⠋⠉⠘⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⢟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠀⠀⢀⣀⠀⢀⡀⠀⢀⠀⣀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢹⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢺⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣏⡹⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣿⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⣀⣼⠀⠘⢿⠀⢸⠀⢠⠀⢸⠀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⣷⠶⡿⠷⣶⣾⣿⣶⡶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣾⣽⣶⣶⣾⡶⠚⠒⠚⠒⠚⠛⠶⠒⠛⠒⠛⠒⠊⠀ ⠀⣴⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⠛⠛⠛⠛⠛⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⢛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣀⣤⣤⣤⣄⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠿⠿⠟⠻⠟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣸⣿⣿⣿⣿⣿⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣦⠀⠀⣿⡇⢀⣠⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⣪⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣆⣟⠭⣽⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣿⣷⡾⣿⣷⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠧⣿⡚⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣀⢸⣿⣿⡟⠾⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢿⠀⢾⣿⣠⣠⣦⠉⣿⣿⣿⣿⣿⣟⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢙⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⡿⠿⠂⠐⠓⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⠿⣻⢿⣿⣿⣿⣿⠿⢿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣼⣿⣿⣿⣿⢻⣿⠘⣿⣿⣿⣿⣟⡴⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠀⠀⠀⠻⣶⣿⣿⣿⠟⠀⠀⠀⠉⠙⠻⣿⣿⡟⠛⢻⡿⠉⠈⠙⣿⣿⠀⣂⠀⠀⠀⠀⠀⠀⢀⣼⣿⡟⢁⣿⣿⣿⣿⣇⢰⣿⣿⣿⡿⠋⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣸⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢀⣀⠀⠀⠀⠀⠀⣶⠇⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⡀⠀⠀⠀⠀⠀⠈⠛⣋⣤⣾⣿⣙⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⡏⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣭⣴⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠄⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣰⣶⣶⣶⣶⣶⠶⠶⢾⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⣿⣿⣿⣷⣿⡛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣤⣤⣼⣿⣿⣿⣿⣤⣴⣦⣮⣭⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣧⣾⣭⣴⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣁⠉⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠛⠟⠻⣿⣿⣿⣿⣿⣿⡿⠃⢤⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⡿⢿⣿⣿⣟⣻⣿⣿⣿⣷⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠾⣗⣷⡿⠋⠀⠈⠉⠉⠁⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠁⠀⠀⠙⣿⣿⣿⠿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠹⠉⠃⠈⠙⠋⠘⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⠟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠂⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢓⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠀⠀⢀⣀⠀⢀⡀⠀⢀⠀⡀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢹⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢺⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣏⠙⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣿⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⡀⣼⠀⠘⢿⠀⢸⠀⢠⠀⢸⠀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⢷⣶⡿⢷⣶⣾⣿⣶⠶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣶⣽⣶⣶⣾⠶⠚⠒⠚⠒⠚⠛⠲⠒⠛⠒⠛⠒⠊⠀ ⠀⣴⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⠛⠛⠛⠛⠛⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⢛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣠⣤⣤⣤⣤⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⠿⠿⠛⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣾⣿⣿⣿⣿⣿⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⠀⠀⣿⣏⠛⢀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⡮⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣄⣟⡭⣽⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣿⣿⣨⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠧⣿⡚⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⣸⣿⣿⣿⢣⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢾⣿⣠⣠⣆⠉⣿⣿⣿⣿⣿⣟⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢙⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⢾⣷⣦⣼⣿⣿⣿⣿⠶⠀⠐⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢻⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⠿⣻⢿⣿⣿⣿⣿⠿⢿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣼⣿⣿⣿⣿⡿⣿⠈⢹⣿⣿⣿⣿⣫⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠀⠀⠀⠻⣶⣿⣿⣿⠿⠀⠀⠀⠉⠉⠛⢿⣿⡟⠛⢻⡿⠉⠈⠙⣿⣿⠀⣃⠀⠀⠀⠀⠀⠀⢀⣿⣷⣿⣿⡞⣿⣿⣧⣉⠀⣼⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢀⣀⠀⠀⠀⠀⠀⣶⠇⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⡀⠀⠀⠀⠀⠀⠈⠛⣛⣵⣿⣿⣟⣿⣿⣿⣾⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⡗⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣭⣴⣄⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣰⣶⣶⣶⣶⣶⠶⠶⣾⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣿⣿⣿⣷⣿⡻⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣤⣤⣼⣿⣿⣿⣿⣤⣤⣦⣮⣽⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣧⣾⣤⣴⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣀⠉⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⡿⠃⡤⣀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⡟⠀⠀⠀⠀⠀⠀⣴⠿⢿⣿⣿⣟⣻⣿⣿⣿⣷⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠾⣗⣶⡿⠯⠁⠈⠉⠉⠁⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠁⠀⠀⠙⣿⣿⣿⡿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠚⠛⠃⠈⠉⠉⠘⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⠟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢓⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠀⠀⢀⣀⠀⢀⡀⠀⢀⠀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣾⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢹⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢺⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣏⡹⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣿⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⢀⣸⠀⠘⢿⠀⢸⠀⢠⠀⢸⠀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠲⣷⡶⡟⠷⣶⣾⣿⣶⡶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣟⣳⣽⣶⣶⣾⡶⠚⠒⠚⠒⠚⠛⠶⠒⠛⠒⠛⠒⠊⠀ ⠀⣴⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⠛⠛⠛⠛⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⢛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⣠⣤⣤⣤⣤⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣾⣿⣿⣿⣿⣿⣷⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⠀⠀⣿⣧⢿⣿⡏⢁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⡪⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣄⣏⣭⣽⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣿⣿⣿⣿⣶⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠧⣿⡚⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⢿⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣻⠀⢺⣿⣠⣠⣆⠉⣿⣿⣿⣿⣿⣟⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢙⣹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⠿⢹⣦⣬⣽⣿⣿⣷⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⢴⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠿⣻⢿⣿⣿⣿⣟⠿⠿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣶⣿⣿⣿⣿⣿⣿⠘⠛⢿⣿⣿⣿⣿⣟⡭⠁⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠀⠀⠀⢿⣤⣿⣿⣿⡿⠀⠀⠀⠈⠉⠛⢿⣿⡟⠛⢻⡿⠉⠈⠙⣿⣿⠀⣀⠀⠀⠀⠀⠀⠀⢠⣭⣿⢛⡙⢿⣿⣿⣿⡍⠀⠀⢸⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⣸⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⢀⣀⠀⠀⠀⠀⠀⢶⠇⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⡀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣄⠙⢿⣿⣿⣷⣴⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⡟⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣭⣴⣄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⠟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠄⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠸⣿⡿⠫⣿⣿⣿⣿⣷⣷⡙⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣤⣤⣼⣿⣿⣿⣿⣤⣤⣶⣬⣭⣽⣯⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣵⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣀⠈⠁⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⡿⠃⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⡿⢿⣿⣿⣟⣻⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢾⣗⣶⡿⠋⠀⠈⠉⠉⠁⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡘⠁⠈⠀⢹⣿⣿⣿⡿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠺⠋⠉⠈⠛⠙⠘⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⠿⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⠶⠄⠠⠴⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢓⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠀⠀⢀⣀⠀⢀⠀⠀⢀⠀⣀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢹⡉⠉⢹⠉⢹⣿⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢺⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⡏⡹⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣗⣻⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⣀⣼⠀⠘⢿⠀⢸⠀⢠⠀⢸⠀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⢷⢶⡿⠷⣶⣾⡿⣶⡶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣗⣳⣽⣶⣶⣾⠶⠚⠒⠚⠒⠚⠛⠶⠒⠛⠒⠛⠒⠊⠀ ⠀⣴⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠛⠛⠛⠛⠛⠛⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⢛⠛⠛⠛⠋⠋⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢀⣤⣶⣶⣶⣶⡄⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣾⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⠀⠀⣿⣏⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⡪⠻⠽⠿⠿⣿⣿⣿⣿⣿⣿⣿⣠⣯⡭⣭⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣺⣿⣟⣥⣶⣟⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠧⣵⡚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡄⢠⣤⣤⣼⣿⣿⣿⣿⣿⡿⣯⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢻⠀⢼⣿⣠⣠⣆⠉⣿⣿⣿⣿⣿⣟⣟⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣡⣾⣿⣿⣿⣿⣿⠿⠙⠛⣿⣍⣻⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⢰⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⠿⣻⣿⣿⣿⣿⣿⠿⠿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⠛⠛⢿⣿⣿⣿⣿⡿⣟⠋⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢼⣾⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠀⠀⠀⢿⣤⣿⣿⣿⡿⠀⠀⠀⠈⠉⠛⢿⣿⡟⠛⢹⡿⠉⠈⠙⣿⣿⠀⣀⠀⠀⠀⢰⣶⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣄⠀⠀⢸⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⣰⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠉⠀⢀⣀⠀⠀⠀⠀⠀⢰⠇⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⡀⠀⠀⣸⣿⣿⣿⡟⣛⣿⣿⣍⠀⠙⣻⣿⣿⣷⣴⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⡏⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣭⣴⣄⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠻⠿⠟⠃⢸⣿⣿⣿⣿⣷⡸⣿⣿⣿⡿⠏⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣸⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣷⣷⣈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣤⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣤⣭⣽⣿⣿⣿⣿⣤⣤⣴⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣈⠉⠀⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠛⠛⠛⠛⠻⣟⣿⣿⣿⣿⣿⡿⠃⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⣿⢿⣿⣿⣟⣻⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠼⣗⣶⡿⠟⠁⠈⠉⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠁⠀⠀⠙⣿⣿⣿⣯⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠈⠸⠋⠁⠈⠉⠋⠘⣿⣷⡼⣿⣿⣿⣿⣿⣿⣿⣿⠟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⠶⠄⠠⠴⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⢀⣀⣀⠀⠀⢀⣀⠀⢀⡀⠀⡀⠀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢹⡉⠉⢹⠉⢹⣿⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢾⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣏⡹⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣿⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⢀⣼⠀⠘⢿⠀⢸⠀⢠⠀⢸⠀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⣷⣶⡿⢷⣶⣾⣿⣶⠶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣷⣽⣶⣶⣾⡶⠚⠒⠚⠒⠚⠛⠶⠒⠛⠒⠛⠒⠊⠀ ⠀⣶⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠛⠛⠛⠛⠛⠛⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⢛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢀⣴⣶⣶⣶⣶⣄⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⣿⡟⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⢐⣾⡇⠀⠀⠀⠀⣀⣶⣶⠀⠀⣿⣏⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⡮⠻⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣠⣏⡭⣽⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣾⣿⣿⣠⡧⠀⠀⠀⠀⠀⣴⣤⣿⣿⣿⣿⣟⣽⣇⣤⡶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠧⣽⡚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢻⠀⢼⣿⣠⣠⣆⠉⣿⣿⣿⣿⣿⣟⣟⣿⣿⣳⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢙⣹⣿⣿⠀⠀⠀⠀⠀⢹⣿⣿⡿⠁⠀⠀⠱⣿⣿⣿⣿⣿⣿⠛⠛⠛⣯⣍⣻⣿⣿⣯⣀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣰⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⡧⢤⣴⣶⣿⣿⣿⣿⣿⣿⣿⠚⠛⠚⣿⣿⣿⣿⣿⣿⡻⠟⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠀⠀⠀⢿⣌⣽⣿⣿⣿⠃⠀⠀⠈⠉⠛⠿⣿⡟⠛⢻⡿⠉⠈⠙⣿⣿⠀⣀⠀⠀⢸⣿⣿⣿⠇⣽⣿⣿⣿⣿⣿⠟⠻⣿⣿⣷⣆⠰⢸⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⣸⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁⢀⣀⠀⠀⠀⠀⠀⠰⠇⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⡀⠀⠈⠛⠛⠁⠀⠛⣛⣿⣿⣿⠁⠀⢠⣾⣿⣿⣿⣷⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⡏⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣭⣴⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⡀⠀⠙⣿⠿⠋⠁⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣷⣷⣀⣔⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣤⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣤⣤⣤⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣭⣭⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣈⠉⠁⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⡿⠋⡤⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⠿⢿⣿⣿⣟⡻⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠾⣗⣷⡿⠛⠅⠈⠉⠉⠁⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠁⠈⠀⠙⣿⣿⣿⡿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠸⠙⠋⠈⠉⠃⠘⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⠟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⣀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠀⠀⢀⣀⡀⠀⡀⠀⣀⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢻⡉⠉⢹⠉⢹⣿⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢾⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣯⡹⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣿⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⣀⣼⠀⠘⢿⠀⢸⠀⢠⠀⢸⠀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⣷⣶⡿⠷⣶⣾⣿⣷⠶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣷⣿⣶⣶⣾⣶⠚⠒⠚⠒⠚⠛⠶⠒⠛⠒⠛⠒⠊⠀ ⠀⣴⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⢛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣠⣴⣶⣷⣶⣶⣦⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⢀⣶⣆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣿⣿⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣧⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣷⣸⡆⠀⠀⠀⢀⣠⣶⣶⠀⠀⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⢀⣪⠻⠿⡿⠿⣿⣿⣿⣿⣿⣿⣷⣸⡏⠭⢭⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢂⣀⣿⣿⣿⣿⣟⣽⡇⢀⣀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠧⣿⡚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢿⠀⢾⣿⣤⣠⣦⠉⣿⣿⣿⣿⣿⣟⣿⣿⣿⢳⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⣿⣿⠀⠀⠀⠀⣶⣿⣿⣿⠀⠀⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠛⢻⣯⣝⣿⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣸⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⠂⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⢹⣿⣿⣿⣿⣿⣿⢿⠇⠀⠀⠀⢀⡀⣿⠀ ⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠀⠀⠀⣷⡉⢿⣿⣿⣿⠇⠀⠀⠈⠉⠛⠻⣿⡟⠛⢻⡿⠉⠈⠙⣿⣿⠈⣃⠀⠀⠈⠙⠉⠁⠐⣼⣷⣿⣿⣿⣿⡿⠟⠋⣩⣿⣿⣿⣆⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣰⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠛⠁⢀⣀⠀⠀⠀⠀⠀⠀⠇⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⡀⠀⠀⠀⠀⠀⠀⠙⣛⣿⣿⣿⡋⠁⠀⠀⢻⣿⣿⣿⠟⢿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⡏⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣭⣴⣄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⡀⠀⠀⠀⠋⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣷⣷⡀⣠⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣤⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣤⣴⣴⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣬⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣀⠉⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠛⢛⠿⣿⣿⣿⣿⣿⣿⡿⠃⣤⣀⡁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⡿⢿⣿⣿⣟⣻⣿⣿⣿⣷⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠾⣗⣷⡿⠛⠁⠈⠉⠉⠁⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠁⠈⠀⢹⣿⣿⣿⡿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠈⠻⠻⠃⠘⠙⠑⠘⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⢟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠠⠴⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠀⠀⢀⣀⠀⠀⡀⠀⣀⠀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢹⡉⠉⢹⠉⢹⣿⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢾⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣯⡹⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣿⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⣀⣼⠀⠘⢿⠀⢸⠀⢠⠀⢸⠀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⣷⣶⡻⠷⣶⣾⣿⣷⡶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣿⣽⣶⣶⣾⡶⠚⠒⠚⠒⠚⠛⠶⠒⠛⠒⠛⠒⠊⠀ ⠀⣴⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣻⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⢛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣠⣶⣿⣿⣿⣿⣷⡀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣶⣂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣿⣿⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢀⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠹⣿⣧⣹⣆⠀⠀⠀⠀⢀⣀⣶⣶⠀⠀⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⢀⣮⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣧⣸⡏⠭⢽⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠹⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⢐⣠⣿⣿⣾⣿⣿⣿⡧⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠧⣵⡚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢈⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢿⠀⣼⣿⣠⣰⣦⠉⣿⣿⣿⣿⣿⣟⣿⣿⣿⢯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣻⣿⣿⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠈⠀⡻⣿⣿⣿⣿⣿⢿⢹⣿⣿⡉⠸⣯⣻⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣼⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠸⠿⠿⠛⠀⣶⣦⣶⣿⣿⣿⣿⣿⣿⠘⠻⣿⣿⣦⠀⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⢀⡀⣿⠀ ⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠉⠀⠀⠀⡏⠛⣿⣿⣿⣿⡇⠀⠀⠈⠉⠛⠻⣿⡟⠛⢻⡿⠉⠈⠙⣿⣿⠀⣂⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⠿⠛⠐⣾⣿⣿⣿⣧⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣼⡆⣿⠀ ⠀⢸⡿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⠷⣾⠿⠿⠋⢀⣀⠀⠀⠀⠀⠀⠀⠇⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⡀⠀⠀⠀⠀⠀⠀⠘⣛⣿⣿⣿⡛⠋⠀⠀⠀⠹⠿⠟⠛⠉⢿⠟⠋⠉⠠⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣯⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣭⣴⣄⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠄⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣷⣷⡀⢠⣶⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣤⣤⣤⣦⣶⣮⣽⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣦⣯⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣈⠉⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⡿⠋⢤⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⡿⢿⣿⣿⣟⣻⣿⣿⣿⣷⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠾⣗⣷⡿⠫⠅⠈⠉⠉⠁⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠁⠈⠀⢙⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠁⠀⠀⠀⠀⠀⠸⠫⠁⠘⠛⠋⠘⣿⣷⡼⣿⣿⣿⣿⣿⣿⣿⣿⢟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠠⠴⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⡀⣀⠀⠀⢀⣀⡀⠀⡀⠀⣀⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢹⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢺⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣏⡙⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣿⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⣀⣸⠀⠘⢿⠀⢸⠀⢠⠀⢸⠀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⢷⣶⡿⠷⣶⣾⣿⣶⠶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣾⣼⣶⣶⣾⢶⠚⠒⠚⠒⠚⠛⠶⠒⠛⠒⠛⠒⠊⠀ ⠀⣴⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⢛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣴⣾⣿⣿⣿⣿⣷⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣿⣿⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠸⣿⣦⢰⣄⠀⠀⠀⠀⠀⣠⣶⣶⠀⠀⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⣪⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣇⣼⣋⠭⣟⣿⣿⡿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠙⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣺⣿⣿⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠧⣿⡚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠿⣟⣾⣯⣿⣷⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢿⠀⣼⣿⣠⣠⣆⠉⣿⣿⣿⣿⣿⣟⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢙⣹⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠩⣿⣏⣿⣿⣿⣿⠙⣿⣿⣿⠁⠈⢝⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⣿⠀ ⠀⢻⣸⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⠿⣷⣾⣿⣿⣿⣿⠿⢿⣿⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠿⠿⠿⠃⢰⣶⣶⣿⣿⣿⣿⣿⣿⠘⢛⣻⣿⣿⡆⠀⢸⣿⣿⣿⣿⣧⡄⠀⠀⢀⡀⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠉⠀⠀⠀⡟⢿⣿⣿⣿⣿⡇⠀⠀⠉⠙⠛⠿⣿⡟⠛⢻⡿⠉⠈⠙⣿⣿⠀⣃⠀⠀⠀⠀⠀⠀⠀⢐⣾⣿⣿⣿⣿⣿⣿⠿⠀⠹⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⠂⠀⠀⠀⣰⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠡⢤⣿⣿⣿⠟⢁⣀⠀⠀⠀⠀⠀⠀⠃⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⣛⣽⣿⣿⡛⠛⠀⠀⠀⠀⠛⠉⠉⠀⢸⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⡏⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢚⣭⣴⣄⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣷⣷⡀⢀⣴⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣤⣤⣴⣶⣶⣮⣯⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣦⣭⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣀⠉⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠛⠛⠛⠛⡿⢻⣿⣿⣿⣿⣿⡿⠃⡤⣀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⡿⢿⣿⣿⣟⡻⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠾⣗⣷⡿⠯⠁⠈⠉⠉⠁⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠁⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠁⠀⠀⠀⠀⠀⠛⠛⠃⠈⠉⠋⠘⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⢟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⠶⠄⠰⠰⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⡀⣀⠀⠀⢀⣀⠀⠀⡀⠀⡀⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢹⡉⠉⢹⠉⢹⣿⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢾⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣯⡹⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣿⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⣀⣸⠀⠘⢿⠀⢸⠀⢠⠀⢸⠀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⣷⢶⠿⡷⣶⣾⣿⣶⡶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣾⣿⣶⣶⣾⡶⠚⠒⠚⠒⠚⠛⠶⠒⠛⠒⠛⠒⠊⠀ ⠀⣴⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣻⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⢛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢀⣴⣿⣿⣿⣿⣿⣿⣆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⣿⣿⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣦⠀⣤⠀⠀⢀⣠⣶⣶⠀⠀⣿⣿⢿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⣪⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣀⣿⣛⣛⣛⣿⣿⣿⣿⣿⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢻⣿⣷⣿⡆⠀⠀⠀⠀⠀⢐⣀⣿⣿⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠧⣽⡚⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⣿⣿⡏⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡿⡇⣖⣶⣶⣿⣷⡄⠀⠀⠀⠀⠀⣿⠀ ⠀⢿⠀⢼⣿⣠⣠⣦⠉⣿⣿⣿⣿⣿⣟⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢙⣻⣿⣿⠀⠀⠀⠀⠀⠀⣤⣿⣿⣷⡄⠀⢩⣿⣿⣿⣿⣿⣻⢹⣿⣿⠇⠈⣹⣝⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⣿⠀ ⠀⢹⣰⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⡿⣿⣿⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⢻⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⠀⢠⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⡀⣿⠀ ⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠋⠉⠁⠀⠈⢿⣿⣿⣿⣿⣿⣷⠀⠈⠉⠛⠻⠿⣿⡟⠛⢻⡿⠉⠈⠙⣿⣿⠀⣃⠀⠀⠀⠀⠈⠛⠋⠉⢸⣿⣿⣿⣿⣿⣿⡿⠌⢿⣿⣿⡿⠷⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⣰⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠁⠉⢻⣿⣿⣿⢏⣀⠀⠀⠀⠀⠀⠀⠁⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⡛⠛⠋⠀⠀⠈⠀⠀⠀⠀⣿⠿⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⡿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⠁⢚⣭⣴⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣿⠀ ⠀⢸⡏⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣷⣷⡀⠀⣠⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣤⣴⣴⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣦⣮⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣀⠉⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⡿⠋⣤⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⡿⢿⣿⣿⣟⣻⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠾⣗⣶⡿⠏⠁⠈⠉⠉⠁⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡘⠁⠈⠀⠹⣿⣿⣿⡏⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠩⠝⠋⠈⠛⠙⠘⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⢟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠰⠰⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠀⠀⢀⣀⠀⠀⡀⠀⣀⠀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢹⡉⠉⢹⠉⢹⣿⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢺⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣯⡹⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣿⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢸⡇⠀⠿⡏⠉⠇⠀⣿⡀⣼⠀⠘⢿⠀⢸⠀⢠⠀⢸⠀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⣷⢶⡿⡷⣶⣾⣿⣶⡶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣷⣽⣶⣶⣾⡶⠚⠒⠚⠒⠚⠛⠶⠖⠛⠒⠛⠒⠊⠀ ⠀⣴⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⠛⠛⠛⢛⡛⠛⠛⠛⠛⠛⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⢛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢀⣶⣿⣿⣿⣿⣿⣿⣆⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠐⠀⠀⠀⠀⣿⡟⣿⣿⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣧⣄⣠⣄⣠⣶⣶⠀⠀⣿⣿⢻⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⣪⠻⠿⡿⠿⣿⣿⣿⣿⣿⣿⢀⡿⣛⣛⣻⣿⣿⣿⣿⣿⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⢐⣀⣿⣿⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠧⣽⡚⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡟⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⢿⣷⡇⢐⣦⣶⣶⣶⡆⠀⠀⠀⠀⠀⣿⠀ ⠀⢿⠀⢼⣿⣤⣠⣦⠉⣿⣿⣿⣿⣿⣟⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣙⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⡇⢽⣿⣿⣿⣿⣿⢿⣿⣿⠃⠉⠉⣽⣝⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣸⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⡈⢸⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⡀⣿⠀ ⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠋⠉⠉⠀⢘⣿⣿⣿⣿⣿⣿⣧⠀⠉⠙⠛⠻⠿⣿⡟⠛⢻⡿⠉⠈⠙⣿⣿⠀⣃⠀⠀⠀⠀⠀⠸⢿⣿⠿⢿⣿⣿⣿⣿⣿⣿⢿⣿⡿⠿⠷⢶⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⣰⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⢟⣀⠀⠀⠀⠀⠀⠀⠁⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⡛⠛⠋⠀⠀⠀⠀⠀⠀⢼⣿⠿⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⡟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠉⢚⣭⣴⣄⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣷⣷⡀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣤⣤⣶⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣿⣶⣤⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣈⠉⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⢛⠛⡿⣿⣿⣿⣿⣿⣿⡿⠋⣤⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⣿⢿⣿⣿⣟⡻⣿⣿⣿⣷⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠾⣗⣷⡿⠯⠅⠈⠉⠉⠁⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡘⠁⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠈⠛⠛⠃⠈⠙⠃⠘⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⠟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠀⠀⢀⣀⡀⠀⡀⠀⣀⠀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢹⡉⠉⢹⠉⢹⣿⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢺⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣯⡹⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣿⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⡀⣼⠀⠘⢿⠀⢸⠀⢠⠀⢸⠀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⢷⣶⡿⠷⣶⣾⣿⣷⠶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣾⣼⣶⣶⣾⣶⠚⠒⠚⠒⠚⠛⠲⠒⠛⠒⠛⠒⠊⠀ ⠀⣴⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⠛⠛⠛⠛⡛⠛⠛⠛⠛⠛⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⢛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢠⣶⣿⣿⣿⣿⣿⣿⣆⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⡏⣿⣿⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⢸⣿⣿⣯⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⣪⠻⠿⠿⠿⣿⣿⣿⣿⣿⣇⢸⡿⠿⠿⢿⣿⣿⣿⣿⣿⣇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣟⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠦⠧⣿⡚⣿⣿⣿⣿⣿⣾⣷⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⣿⣿⣿⣿⣷⡇⢐⣦⣴⣶⣶⡆⠀⠀⠀⠀⠀⣿⠀ ⠀⢿⠀⢼⣿⣠⣠⣦⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢙⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠜⣿⣿⣿⣿⣿⣀⠛⠛⠛⠉⢉⣽⣝⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⢸⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣶⣾⣿⣿⣿⣿⣿⣿⣟⠛⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⡀⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠋⠉⠉⢿⣷⣿⣿⣿⣿⣿⣿⠈⠙⠛⠻⠿⢿⣿⡟⠛⢻⡿⠉⠈⠙⣿⣿⠀⣁⠀⠀⠀⠀⠀⠀⠀⢾⡿⣾⣿⣿⣿⣿⣿⠿⠟⠛⠣⠴⠦⢀⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢰⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠁⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⡀⠀⠀⠀⠀⠀⠀⠛⣹⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⣠⣼⣿⠿⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⡿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⢻⡿⠟⢛⣭⣴⣄⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠈⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣷⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣤⣴⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣶⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣀⠉⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⠛⠛⢛⠛⡿⣿⣿⣿⣿⣿⣿⡿⠋⣥⣈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⣿⢿⣿⣿⣟⣻⣿⣿⣿⣷⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢾⣗⣶⡿⠏⠁⠈⠉⠉⠁⠀⠀⠀⠉⠑⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠁⠈⠀⠹⣿⣿⣿⢿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠁⠀⠀⠀⠀⠈⠻⠙⠃⠈⠉⠉⠘⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⢟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠰⠰⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠀⠀⢀⣀⠀⠀⡀⠀⢀⠀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢹⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢺⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣏⡝⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣿⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⡀⣼⠀⠘⢿⠀⢸⠀⢠⠀⢸⠀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⣷⣶⡿⠷⣶⣾⣿⣶⡶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣾⣽⣶⣶⣾⣶⠞⠒⠚⠒⠚⠛⠶⠖⠛⠒⠛⠒⠊⠀ ⠀⣴⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⢛⠛⠛⠛⠋⠋⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣠⣶⣾⣿⣿⣿⣿⣷⣄⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣇⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⡀⠀⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⣪⠻⠿⠿⠿⣿⣿⣿⣿⣿⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣿⣿⣿⣿⣟⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⡁⠤⠧⣿⡚⣿⣿⣿⣿⣧⣿⣴⣒⣒⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇⢐⣦⣴⣶⣶⡆⠀⠀⠀⠀⠀⣿⠀ ⠀⢿⠀⣾⣿⣀⣰⣦⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢙⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣩⣿⣿⣿⣿⣿⣿⣿⠛⠛⠉⢉⣽⣽⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⣿⠀ ⠀⢹⣼⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣴⣿⣿⣿⣿⣿⣿⣿⣟⠛⠀⠀⢹⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⡀⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⢿⣿⣜⣿⣿⣿⣿⣿⣿⠋⠛⠿⠿⢿⣿⣿⡟⠛⢻⡿⠉⠈⠙⣿⣿⠀⣀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢦⠴⠤⠸⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢠⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠃⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⡀⠀⠀⠀⠀⠀⠀⠛⣛⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⢀⣠⣾⣿⠟⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⡟⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⡿⢛⣭⣴⣄⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠸⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣷⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣤⣤⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣤⣤⣤⣤⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣉⠉⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠛⠛⢿⢿⣿⣿⣿⣿⣿⡿⠃⠥⣈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⡿⢿⣿⣿⣟⣻⣿⣿⣿⣷⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠾⣗⣷⡿⠿⠅⠈⠉⠉⠁⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠁⠀⠀⠙⣿⣿⣿⡿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠻⠉⠃⠈⠛⠙⠘⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⠿⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠠⠴⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠀⠀⢀⣀⠀⢀⡀⠀⡀⠀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢻⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢺⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣏⡹⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣿⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⡀⣼⠀⠘⢿⠀⢸⠀⢠⠀⢸⠀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⠷⡶⡿⣷⣶⣾⣿⣶⡶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣾⣽⣶⣶⣾⡶⠚⠒⠚⠒⠚⠛⠶⠒⠛⠒⠛⠒⠊⠀ ⠀⣶⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⢛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⣠⣴⣶⣾⣶⣶⣶⣶⣄⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⡟⣿⣿⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⡀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⠀⠠⣿⣿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⡪⠻⠿⠿⠿⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣤⣿⣿⣿⣿⣟⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠧⣿⡚⣿⣿⣿⣿⣤⣟⣩⣭⣭⣿⣿⣿⡿⢿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⡇⣖⣦⣶⣶⣶⡆⠀⠀⠀⠀⠀⣿⠀ ⠀⢿⠀⣼⣿⣀⣠⣦⠉⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢙⣫⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⢉⣽⣽⣿⣿⣿⡛⠁⠀⠀⠀⠀⠀⣿⠀ ⠀⢺⣼⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⢻⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⡀⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠻⣿⣟⢻⣾⣿⣿⣿⣿⣿⡟⠻⠿⠿⣿⣿⣿⡟⠛⢻⡿⠉⠈⠉⣿⣿⠀⣀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢧⠴⠤⢸⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢰⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠙⢿⣷⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠃⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⡀⠀⠀⠀⠀⠀⠀⠙⣛⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢀⣠⣼⣿⠟⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⡏⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⢛⣭⣴⣄⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡋⠁⠀⠂⠀⠀⠸⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠄⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠛⠛⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣷⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣤⣤⣴⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣉⠉⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠻⣛⣿⣿⣿⣿⣿⡿⠃⣥⣈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⡿⢿⣿⣿⣟⣻⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠾⣗⣶⡿⠏⠁⠈⠉⠉⠁⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠁⠈⠀⠙⣿⣿⣿⡯⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠙⠋⠃⠈⠉⠉⠘⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⢟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠰⠰⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢓⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠀⠀⢀⣀⠀⢀⡀⠀⡀⠀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢻⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢺⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣏⡹⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣿⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⣀⣼⠀⠘⢿⠀⢸⠀⢠⠀⢸⡀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⣷⣶⡿⢷⣶⣾⣿⣶⠶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣺⣽⣶⣶⣾⡶⠚⠒⠚⠒⠚⠛⠶⠒⠛⠒⠛⠒⠊⠀ ⠀⣴⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢀⣤⣴⣶⣶⣦⣤⣦⡀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⡇⣿⣿⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⠀⠀⣿⣧⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⡮⠻⠿⠿⠿⣿⣿⣿⣿⡆⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣟⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠧⣿⡚⣿⣿⣿⣧⢸⠟⢛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⡷⣲⣦⣶⣿⣿⡀⠀⠀⠀⠀⠀⣿⠀ ⠀⢿⠀⢼⣿⣄⣠⣦⠉⣿⣿⣿⣿⣿⣿⣭⣭⣽⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢙⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣿⣟⣿⣿⣿⣿⣿⣛⠛⠋⣉⣯⣻⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢹⣸⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡦⣢⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⢿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⡀⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣭⣽⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡟⠛⢻⣿⠉⠈⠙⣿⣿⠀⣀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢧⠴⠤⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠘⢿⣷⣘⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠒⠃⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⡀⠀⠀⠀⠀⠀⠀⠛⣋⣿⣿⣿⣿⣿⡏⠀⠀⠀⠈⢀⣠⣾⡿⠟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⡟⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⢛⣭⣴⣄⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⢹⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠿⡿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣷⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣤⣴⣶⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣯⣈⠉⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⡿⠋⣤⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⡿⢿⣿⣿⣟⣻⣿⣿⣿⣷⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠾⣗⣷⡿⠟⠁⠈⠉⠉⠁⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠃⠈⠀⠙⣿⣿⣿⣟⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠛⠛⠃⠈⠉⠃⠘⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⢿⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠂⠶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠀⠀⢀⣀⡀⢀⡀⠀⡀⠀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢻⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢺⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣯⡽⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣿⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⢀⣼⠀⠘⢿⠀⢸⠀⢠⠀⢸⠀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⢷⣶⡿⡷⣶⣾⣿⣶⠶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣿⣽⣶⣶⣾⡶⠚⠒⠚⠒⠚⠛⠶⠒⠛⠒⠛⠒⠊⠀ ⠀⣴⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣻⣻⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⢛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⡀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⡏⣿⣿⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⠀⠀⣿⣯⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⡪⠻⠻⠿⠿⣿⣿⣿⣷⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣀⣿⣿⣿⣿⣟⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⡁⠤⠷⣽⡚⣿⣿⣿⡇⣸⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⡷⣲⣶⣼⣿⣷⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢾⣿⣤⣠⣦⠉⣿⣿⣿⣿⣿⣖⣛⣛⣾⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢙⣹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⣩⣭⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣸⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣥⠟⠘⣿⣿⣿⣿⣿⣿⣿⡶⠀⠀⠀⠀⡀⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣟⡻⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡟⠛⢹⣿⠉⠈⠉⣿⣿⠀⣁⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⡶⠦⢻⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢰⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⢻⣿⡍⢿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠁⠒⠇⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⡀⠀⠀⠀⠀⠀⠈⠛⣋⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢁⣤⣾⡿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⡟⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⣿⣶⣿⣿⣿⣿⡿⢛⣭⣴⣄⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡋⠀⠀⠁⠀⠀⢻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣷⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣥⣼⣿⣿⣿⣿⣤⣴⣴⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣴⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣈⠉⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⡿⠃⠤⣈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⡿⢿⣿⣿⣟⡻⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠾⣗⣷⡿⠏⠁⠈⠉⠉⠁⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠁⠀⠀⠙⣿⣿⣿⡟⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠁⠀⠀⠀⠀⠀⠹⠉⠁⠈⠋⠁⠘⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⠟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠀⠀⢀⣀⠀⢀⡀⠀⡀⠀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢻⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢺⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣯⡽⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣻⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⣀⣼⠀⠘⢿⠀⢸⠀⢠⠀⢸⠀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠖⣷⣶⡿⢷⣶⣾⣿⣶⠶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣷⣾⣶⣶⣾⡶⠚⠒⠚⠒⠚⠛⠶⠒⠛⠒⠛⠒⠊⠀ ⠀⣴⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣟⣻⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⢛⠛⠛⠛⠋⠋⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢀⣀⣠⣤⣄⣀⣠⣄⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⡏⣿⣿⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⡃⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣷⠀⠀⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⣪⠻⠿⡿⠿⣿⣿⣿⣇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠧⣿⡺⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⣗⣶⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢿⠀⣾⣿⣀⣠⣦⠉⣿⣿⣿⣷⣯⠴⠶⣶⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢙⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣽⣝⣿⣿⣿⣏⠁⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣼⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣟⣡⢰⣿⣿⣿⣿⣿⣿⣷⠆⠀⠀⠀⠀⡀⣿⠀ ⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢻⡿⠉⠈⠙⣿⣿⠀⣃⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⡷⠤⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣰⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠘⣿⣟⠛⣾⣿⣿⣿⣿⣿⣿⣇⠀⠀⠈⠉⠑⠲⠇⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⡀⠀⠀⠀⠀⠀⠀⠛⣛⣿⣾⣿⣿⣿⡏⠀⠀⠀⠀⣃⣴⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⡟⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⢻⣷⣭⣽⣿⣿⣿⡿⢛⣭⣴⣄⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠸⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣷⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣭⣭⣽⣿⣿⣿⣿⣤⣴⣶⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣤⣤⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣵⣿⣿⣿⣿⣧⣈⠉⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠟⠛⢿⣿⣿⣿⣿⣿⣿⡿⠃⣤⣈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⠿⢿⣿⣿⣟⣻⣿⣿⣿⣷⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢾⣗⣷⡿⠏⠁⠈⠉⠉⠁⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠃⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠙⠋⠋⠘⠉⠉⠘⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⢟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠠⠴⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⠀⠀⣀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠀⠀⢀⣀⡀⢀⡀⠀⣀⠀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢹⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢺⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣯⡽⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣿⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⣀⣼⠀⠘⢿⠀⢸⠀⢠⠀⢸⡀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⢷⣶⡿⠷⣶⣾⣿⣶⠶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣾⣽⣶⣶⣾⣶⠚⠒⠚⠒⠚⠛⠶⠒⠛⠒⠛⠒⠊⠀ ⠀⣴⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⡏⣿⣿⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣷⠀⠀⣿⣯⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⡮⠻⠿⠿⠿⣿⣿⣿⡆⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣀⣿⣿⣿⣿⣟⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠧⣿⡚⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣟⣳⣶⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢿⠀⢼⣿⣠⣰⣦⠉⣿⣿⣿⣾⣥⠴⠤⢬⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢙⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣿⣿⣿⣿⣁⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣼⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⠋⣰⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢹⣿⠉⠈⠙⣿⣿⠀⣃⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⠿⢼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣰⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⠟⠋⠉⠉⠀⢻⣿⡟⢲⣾⣿⣿⣿⣿⣿⣿⣇⠀⠀⠈⠉⠑⠶⠇⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⡀⠀⠀⠀⠀⠀⠀⠛⣛⣿⣿⣿⣿⣿⡏⠀⠀⠀⠘⣢⣾⡿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⡟⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠙⣿⣮⣹⣿⣿⣿⣿⡿⢛⣭⣴⣄⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠄⣿⠀ ⠀⢸⡧⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣷⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣤⣤⣴⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣀⠉⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠟⠻⠿⣿⣿⣿⣿⣿⣿⡿⠃⢤⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⣿⢿⣿⣿⣟⣻⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠾⣗⣶⡿⠛⠁⠈⠉⠉⠁⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠁⠈⠀⠙⣿⣿⣿⣟⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠈⠸⠉⠁⠈⠛⠋⠘⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⢟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠰⠰⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢓⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠀⠀⢀⣀⠀⢀⡀⠀⣀⠀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢻⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢺⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣯⣙⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣿⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⣀⣼⠀⠘⢿⠀⢸⠀⢠⠀⢸⠀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⢷⣶⡿⡷⣶⣾⣿⣶⠶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣷⣽⣶⣶⣾⡶⠚⠒⠚⠒⠚⠛⠲⠒⠛⠒⠛⠒⠊⠀ ⠀⣴⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⢛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⣿⣿⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣴⣶⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⣪⠻⠿⠿⠿⣿⣿⣿⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣀⣿⣿⣿⣿⣟⣽⡇⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠧⣿⡚⣿⣿⣷⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⢟⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢿⠀⣾⣿⣀⣠⣦⠉⣿⣿⣿⣾⣁⠤⠤⢽⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢙⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣿⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣸⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣼⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢻⡿⠉⠈⠙⣿⣿⠀⣃⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠧⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣰⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⠟⠋⠉⠉⠀⢿⣿⡛⢶⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠈⠉⠑⠶⠇⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⡀⠀⠀⠀⠀⠀⠀⠛⣛⣿⣿⣿⣿⣿⡋⠀⠀⠀⢹⣤⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⡏⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠻⣷⣬⣽⣿⣿⣿⣿⡿⢛⣭⣴⣄⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣷⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣤⣴⣦⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣈⠉⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠟⠛⢿⣿⣿⣿⣿⣿⣿⡿⠃⢬⣁⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⡿⢿⣿⣿⣿⣻⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠾⣗⣷⡿⠟⠁⠈⠉⠉⠁⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠁⠈⠀⠙⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠹⠋⠑⠈⠛⠃⠘⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⢟⣽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠀⠀⢀⣀⠀⢀⡀⠀⡀⠀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢻⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢺⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣏⡹⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣿⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⠀⣼⠀⠘⢿⠀⢸⠀⢠⠀⢸⡀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠒⢷⡶⠟⣷⣶⣾⣿⡶⠶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣿⣿⣶⣶⣾⠶⠞⠒⠚⠒⠚⠛⠶⠖⠛⠒⠛⠒⠊⠀ ⠀⣶⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣻⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⢛⠛⠛⠛⠙⠉⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣀⣀⣀⣀⣀⣄⡀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⣿⣿⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⠀⠀⣿⣯⢻⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⣾⠻⠿⠿⠿⣿⣿⣿⡆⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣽⣿⣟⣽⡇⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠷⣿⡚⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢾⣿⣤⣠⣦⡉⣿⣿⣿⣾⡴⣲⣶⣿⣿⣿⣟⣛⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣥⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣼⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣴⣿⣿⣿⣿⣿⣿⣿⡿⠟⣹⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡟⠛⢻⡿⠉⠈⠙⣿⣿⠀⣃⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠧⢿⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⣰⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⠟⠛⠉⠉⠈⣿⣿⡛⣾⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠈⠉⠐⠲⠇⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⡀⠀⠀⠀⠀⠀⠈⠛⣛⣿⣿⣿⣿⡟⠉⠀⠈⠹⣠⣾⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠻⣿⣾⣿⣿⣿⣿⣿⡿⢛⣭⣴⣄⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄⣿⠀ ⠀⢸⡿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣷⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣤⣦⣤⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣉⠉⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⡿⠋⢥⣈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠴⣾⣷⡟⠀⠀⠀⠀⠀⠀⣴⣿⢿⣿⣿⣟⣻⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢾⣗⣶⡿⠛⠁⠈⠉⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠉⠈⠀⢙⣿⣿⣷⣟⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠁⠀⠀⠀⠀⠈⠸⠋⠃⠈⠋⠃⠘⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⠿⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠠⠴⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⡀⠀⠀⢀⣀⠀⢀⡀⠀⣀⠀⣀⣀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⠹⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢺⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣏⡝⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣿⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⠀⣼⠀⠘⢿⠀⢸⠀⢠⠀⢸⡀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠲⠷⡶⡟⡷⣶⣾⣿⣶⡶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣿⣿⣶⣶⣾⡶⠞⠒⠚⠒⠚⠛⠲⠖⠛⠒⠛⠒⠊⠀ ⠀⣶⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⡀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⡀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⠀⠀⣿⣿⣻⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⣮⠻⠿⠿⠿⣿⣿⣿⡇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣽⣿⣟⣽⣧⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠧⣿⡚⣿⣿⣿⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣯⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⣾⣿⣤⣠⣦⡉⣿⣿⣿⣿⣭⣽⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢙⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣼⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣦⣴⣿⣿⣿⣿⣿⣿⠿⠋⣼⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡿⣿⣿⣿⣿⡟⠛⢻⡿⠉⠈⠙⣿⣿⠀⣃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⠣⢿⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⣰⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⠟⠛⠉⠉⠘⢿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠁⠀⠒⠇⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⡀⠀⠀⠀⠀⠀⠀⠛⣻⣿⣿⣿⡿⠋⠉⠉⠱⣠⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡿⢛⣭⣴⣄⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⡀⠀⠀⠀⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄⣿⠀ ⠀⢸⡟⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣷⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣥⣤⣭⣼⣿⣿⣿⣿⣤⣴⣤⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣁⠉⠁⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⢛⠛⢻⣿⣿⣿⣿⣿⣿⡿⠋⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠴⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⡿⢿⣿⣿⣟⣻⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠾⣗⣶⡿⠯⠁⠈⠉⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠁⠈⠀⠙⣿⣿⣾⡿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠁⠀⠀⠀⠀⠈⠛⠙⠓⠈⠙⠉⠘⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⢿⣽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠠⠴⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⡀⠀⠀⢀⣀⠀⢀⡀⠀⣀⠀⣀⣀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢹⡉⠉⢹⠉⢹⣿⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢺⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⡯⡙⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣿⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⠀⣽⠀⠘⢿⠀⢸⠀⢠⠀⢸⡀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⣷⡶⠟⢷⣶⣾⣿⣷⠶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣿⣿⣶⣶⣾⡶⠞⠒⠚⠒⠚⠛⠶⠖⠛⠒⠛⠒⠊⠀ ⠀⣶⠛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣻⣿⣿⡿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⣛⠛⠛⠛⠙⠋⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣠⣴⣶⣶⣶⣶⣶⣦⡀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⣿⣿⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⣴⣿⣿⣿⣿⣿⣿⡇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⠀⠀⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⢀⣪⠻⠿⡿⠿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣾⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠷⣿⡚⣿⣿⣿⣬⠬⢭⣿⣿⣿⣿⢿⣿⣿⣿⣷⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣯⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⣾⣿⣤⣰⣦⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢙⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣼⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣶⣿⣿⣿⣿⣿⢟⢡⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠿⡿⣿⣿⣿⣿⡟⠛⢻⣿⠉⠈⠙⣿⣿⠀⣃⠀⠀⠀⠀⠀⠀⢰⣾⣷⣿⣿⣿⣿⣿⣧⠿⠘⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⠟⠋⠉⠁⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠒⠃⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⡀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⡛⠛⠛⠆⣰⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡿⢛⣭⣴⣄⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣷⡀⠀⠘⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢹⣍⠹⣿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣿⣿⣿⣿⣷⣷⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣤⣶⣴⣦⣶⣶⣶⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣯⣁⠉⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⡿⠃⢥⣁⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠴⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⣿⢿⣿⣿⣟⣻⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢾⣗⣶⡿⠯⠅⠈⠉⠉⠁⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠁⠀⠀⠙⣿⣿⣿⣻⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠁⠀⠀⠀⠀⠈⠙⠋⠋⠈⠉⠙⠘⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠠⠴⠶⠆⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⡀⠀⠀⢀⣀⠀⢀⡀⠀⣀⠀⣀⣀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⠹⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢺⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣏⡝⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡷⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣿⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⠀⣽⠀⠘⢿⠀⢸⠀⢠⠀⢸⡀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⠷⣶⡟⠷⣶⣾⣿⣷⡶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣿⣿⣶⣶⣾⡶⠞⠒⠚⠒⠚⠛⠲⠒⠛⠒⠛⠒⠊⠀ ⠀⣶⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⢛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣶⣿⣿⣿⣿⣿⣷⡄⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⠀⠀⣿⣯⠻⠿⢿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⣬⠻⠿⡿⠿⣿⣿⣿⣿⡇⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣿⣟⣿⣿⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠷⣿⡚⣿⣿⣿⣿⣯⣽⣿⣿⣿⣯⣽⣿⣿⣿⣷⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣯⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢻⠀⣾⣿⣤⣠⣦⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢙⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⡟⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣼⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣹⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢾⣿⣿⣿⣿⣿⠋⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⠻⠿⠿⣿⣿⣿⡟⠛⢻⡿⠉⠈⠙⣿⣿⠀⣃⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣿⣿⣿⠼⠿⠻⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠃⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⡀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠛⠳⣄⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠙⠛⠟⢿⣿⢿⣿⡿⢛⣭⣴⣄⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣷⡀⠸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄⣿⠀ ⠀⢸⡿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠘⠛⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⠻⠯⣿⣿⣿⣿⣷⣷⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣤⣴⣴⣦⣶⣶⣾⣽⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣦⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣁⠉⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠛⠛⢻⢿⣿⣿⣿⣿⣿⡿⠃⠤⣁⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠴⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⣿⢿⣿⣿⣿⣻⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢼⣗⣶⡿⢛⠁⠈⠉⠉⠁⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠁⠀⠀⠙⣿⣿⣿⣟⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠁⠀⠀⠀⠀⠈⠙⠛⠅⠈⠉⠑⠘⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⢟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠀⠀⢀⣀⠀⢀⡀⠀⣀⠀⣀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡟⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢻⡉⠉⢹⠉⢹⣿⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢺⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣯⡙⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡷⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣿⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⢀⣼⠀⠘⢿⠀⢸⠀⢠⠀⢸⡀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠲⣷⣶⠟⣷⣶⣾⣿⢷⡶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣶⣽⣶⣶⣾⣶⠞⠒⠚⠒⠚⠛⠶⠖⠛⠒⠛⠒⠊⠀ ⠀⣶⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠛⠛⠛⣛⣛⣛⣛⠛⠛⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣻⣿⣿⡿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⢛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣠⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⡏⣿⣿⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⣴⣿⣿⣿⣿⣿⣿⣿⣧⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣷⣶⠀⠀⠛⠋⢻⠟⠛⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⢀⣮⠻⠿⡿⠿⣿⣿⣿⣿⣿⣨⠭⣽⣿⣿⣿⢿⣿⣿⣿⣇⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠷⣿⡺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣞⣿⣿⣿⣿⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⣾⣿⣤⣠⣦⡉⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣟⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠛⠓⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢹⣼⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣇⣼⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠛⠻⠿⠿⣿⣿⡟⠛⢻⣿⠉⠈⠙⣿⣿⠀⣃⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡥⠿⠞⢿⣿⣿⡿⠋⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⣸⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠙⢿⢿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠁⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⡀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣷⣤⢀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⡿⢛⣭⣴⣄⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠸⣿⣿⡯⣿⣿⣿⣿⣷⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣤⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣉⠉⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⠛⢛⠛⣿⣿⣿⣿⣿⣿⣿⡿⠃⣬⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠴⣾⣷⡟⠀⠀⠀⠀⠀⠀⣴⣿⢿⣿⣿⣟⣻⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠍⣾⣗⣷⡿⠿⠅⠈⠉⠉⠁⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠉⠀⠀⠙⣿⣿⣿⣟⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠁⠀⠀⠀⠀⠈⠹⠋⠃⠈⠙⠃⠘⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⠟⣽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡟⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠀⠀⢀⣀⠀⠀⡀⠀⣀⠀⢀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡟⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⠻⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢺⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣯⡹⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡷⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣿⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⠀⣽⠀⠘⢿⠀⢸⠀⢠⠀⢸⡀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠲⢷⡶⠟⠷⣶⣾⣿⣷⡶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣿⣿⣶⣶⣾⣶⠞⠒⠚⠒⠚⠛⠶⠖⠛⠒⠛⠒⠊⠀ ⠀⣶⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⠛⠛⣛⣛⣛⣛⣛⡛⠛⠛⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣻⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⢛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢠⣾⣿⣿⣿⣿⣿⣿⣦⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⣿⣿⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⡇⡿⠿⣿⣿⣿⣿⣿⣿⣿⠄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡆⠀⠀⠛⠁⠉⠻⢿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⢀⣬⠻⠿⡿⠿⣿⣿⣿⣿⣿⣧⣂⣷⣿⣿⣿⣽⣿⣿⣿⣦⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣦⠀⠀⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠷⣿⡺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣔⢾⣿⣿⣿⣀⣤⣤⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢿⠀⣾⣿⣤⣠⣆⡉⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣛⣿⣿⣿⣿⣿⣯⠀⠀⠀⠈⠁⠀⠀⠓⠓⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣼⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠓⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠋⠹⣿⣿⣿⣿⣿⣿⣿⣦⠈⠉⠛⠛⠿⠿⢿⡟⠛⢻⡿⠉⠈⠙⣿⣿⠀⣃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡵⠮⠻⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⣰⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠸⠉⢿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠁⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⡀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣶⣄⣠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠻⠿⠋⢛⣭⣴⣄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢺⣿⣿⡿⠹⣿⣿⣿⣿⣷⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣤⣴⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣷⣶⣿⣿⣿⣿⣧⣾⣦⣤⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣉⠉⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⡿⠃⣬⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠴⣾⣷⡟⠀⠀⠀⠀⠀⠀⣴⡿⢿⣿⣿⣟⣻⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢾⣗⣶⡿⠟⠁⠈⠉⠉⠁⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠋⠀⠀⢙⣿⣿⣷⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠁⠀⠀⠀⠀⠈⠨⠯⠋⠘⠛⠋⠘⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⢟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠠⠴⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢓⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⡀⣀⠀⠀⢀⣀⠀⢀⠀⠀⣀⠀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⠻⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢺⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣯⡙⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡷⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣿⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⠀⣽⠀⠘⢿⠀⢸⠀⢠⠀⢸⡀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⣷⡶⠟⠷⣶⣾⣿⡷⡶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣷⣿⣶⣶⣾⢶⠚⠒⠚⠒⠚⠛⠶⠖⠛⠒⠛⠒⠊⠀ ⠀⣴⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠛⢛⣛⣛⣛⣛⣛⠛⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⢛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣼⣿⣿⣿⣿⣿⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣿⣟⣿⣿⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠟⢿⣿⣿⣿⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⣬⠻⠿⡿⠿⡿⣿⣿⣿⣿⣿⣾⣥⣿⣿⣿⣷⣿⣿⣿⣧⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣷⣦⠀⠀⠀⠀⠀⠙⣟⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠷⣿⡚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡤⣾⣿⣿⣿⣠⣤⣤⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢿⠀⣾⣿⣤⣠⣦⡉⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢙⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⡿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠘⠋⠉⠁⠀⠀⠓⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣼⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⡾⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠷⠀⠀⠀⠈⠀⠛⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠀⢙⡿⢿⣿⣿⣿⣿⣷⠀⠈⠉⠛⠛⠿⢿⡟⠛⢻⣿⠉⠈⠙⣿⣿⠀⣃⠀⠀⠀⢰⣿⣿⣿⣿⣟⠦⠝⢿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⣸⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠘⢷⣞⣿⣿⣿⣿⢏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⡀⠀⠀⢸⣿⣿⣿⣿⣧⣤⣶⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠉⠀⢚⣭⣴⣄⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄⣿⠀ ⠀⢸⡿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣼⣿⣿⣿⠁⠸⣿⣿⣿⣿⣷⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣤⣴⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣿⣷⣶⣶⣿⣿⣿⣿⣧⣾⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣉⠉⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⢛⠛⣻⣿⣿⣿⣿⣿⣿⡿⠋⢤⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠴⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⡿⢿⣿⣿⣟⣻⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢾⣗⣷⡿⠋⠁⠈⠉⠉⠁⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠁⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠁⠀⠀⠀⠀⠈⠛⠫⠁⠈⠉⠓⠘⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⢟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡟⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠠⠴⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⡀⣀⠀⠀⢀⣀⡀⢀⡀⠀⣀⠀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢻⡉⡉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢾⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣯⡝⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡷⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣿⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⢀⣽⠀⠘⢿⠀⢸⠀⢠⠀⢸⡀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⠷⣶⡿⠷⣶⣾⣿⣷⡶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣷⣿⣶⣶⣾⣶⠞⠒⠚⠒⠚⠛⠲⠖⠛⠒⠛⠒⠊⠀ ⠀⣴⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠛⣛⣛⣛⣛⣛⠛⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⢛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣾⣿⣿⣿⣿⣿⣷⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⣿⡟⣿⣿⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢚⣛⣻⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⢀⣪⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣶⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣤⣄⠀⠀⠀⠀⠀⠉⣹⣿⣟⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠷⣿⡺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣟⣠⣤⣦⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢿⠀⣾⣿⣤⣠⣦⡉⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢙⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣿⣶⡾⢿⣿⣿⣿⣿⣿⡄⠀⠀⠘⠛⠛⠉⠉⠁⠀⠀⠓⠓⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣼⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠘⠛⠀⠈⠀⠛⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠉⠁⠀⠀⣏⣹⣿⣿⣿⣿⣷⠀⠀⠈⠉⠛⠛⠿⡟⠛⢻⡿⠉⠈⠙⣿⣿⠀⣃⠀⠀⣾⣷⣿⣿⣿⣧⡙⠿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠠⡀⡀⠁⠂⠀⠀⠀⠀⠀⠀⠀⣸⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⢿⡿⠟⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⡀⠀⣿⣿⣿⣿⣷⡁⣀⣤⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣭⣴⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣠⣿⣿⣿⣿⠟⣻⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄⣿⠀ ⠀⢸⣟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⠁⠀⠨⣿⣿⣿⣿⣷⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣤⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣧⣾⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣴⣿⣿⣿⣿⣧⣉⠉⠉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⡛⠛⢛⠛⣻⢿⣿⣿⣿⣿⣿⡿⠋⢤⣉⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠴⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⠿⢿⣿⣿⣟⣻⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢿⣗⣷⡿⠿⠅⠈⠉⠉⠁⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠉⠈⠀⢹⣿⣿⣿⠿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠁⠀⠀⠀⠀⠈⠻⠛⠛⠈⠛⠑⠘⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⠟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡟⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⢀⣀⣀⣀⣀⠀⠀⢀⣀⡀⢀⡀⠀⣀⢀⣀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡟⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢻⡉⡉⢹⠉⢹⣿⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢾⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣯⡙⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡷⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣾⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⡀⣽⠀⠘⢿⠀⢸⠀⢠⠀⢸⡀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⢷⡶⢿⣷⣶⣾⣿⣷⠶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣷⣿⣶⣶⣾⡶⠚⠒⠚⠒⠚⠛⠲⠖⠛⠒⠛⠒⠊⠀ ⠀⣶⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⠛⣛⣛⣛⣛⣛⡛⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⢛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣾⣿⣿⣿⣿⣿⣿⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⣿⣿⣿⣿⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣛⣛⣿⣿⣿⣿⣿⡇⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⢀⣬⠻⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣾⣿⣿⣷⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀⠀⠀⠀⠀⠀⠙⢿⣾⣿⣟⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠷⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣇⣠⣤⣦⠀⠀⠀⢘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⣾⣿⣤⣠⣦⡉⣿⣿⣿⣿⣿⣟⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⣿⣿⠀⠀⠀⠀⠀⢀⣷⣭⣽⣿⣿⣿⣿⣿⣿⡄⠀⠀⠘⠙⠛⠛⠋⠉⠁⠀⠀⠓⠒⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣼⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⠀⠀⠀⣴⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⡟⠀⠀⠐⠛⠛⠁⠉⠁⠛⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠉⠀⠀⠀⣧⣭⣿⣿⣿⣿⡷⠀⠀⠈⠉⠙⠛⠿⡟⠛⢻⡿⠉⠈⠙⣿⣿⠀⣃⠀⣴⣧⣾⣿⣿⢏⡙⠿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠠⣤⣀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⣼⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠿⠛⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⡀⣿⣿⣿⣿⣿⡄⠀⣀⣼⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣭⣴⣄⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⡿⠟⣺⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⢺⣿⣿⣿⠏⠀⠀⠨⣿⣿⣿⣿⣷⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣤⣤⣼⣿⣿⣿⣿⣤⣦⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣦⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣯⣈⠉⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⠛⠻⠛⣻⣿⣿⣿⣿⣿⣿⡿⠋⣥⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠴⣾⣷⡟⠀⠀⠀⠀⠀⠀⣴⡿⢿⣿⣿⣟⣻⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⢾⣗⣷⡿⠏⠁⠈⠉⠉⠁⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠁⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠁⠀⠀⠀⠀⠈⠩⠯⠁⠘⠉⠙⠘⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⢟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡟⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠂⢶⠄⠠⠴⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠀⠀⢀⣀⡀⢀⡀⠀⣀⠀⣀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡟⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢻⡉⡉⢹⠉⢹⣿⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢾⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣏⡙⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡷⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣿⣻⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢸⡇⠀⠿⡏⠉⠇⠀⣿⢀⣼⠀⠘⢿⠀⢸⠀⢠⠀⢸⡀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⣷⡶⣿⠷⣶⣾⣿⣷⠶⣾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣷⣽⣶⣶⣾⡶⡚⠒⠚⠒⠚⠛⠲⠖⠛⠒⠛⠒⠊⠀ ⠀⣶⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠛⣛⣛⣛⣛⠛⠛⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣻⣿⣿⡿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⢛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢠⣾⣿⣿⣿⣿⣿⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣿⣿⣿⣿⡟⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣾⣛⣛⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢶⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⢀⣬⠻⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣾⣿⣿⣾⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣟⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠷⣿⡚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣀⣿⣿⣇⣀⣤⣤⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⣾⣿⣤⣠⣦⡉⣿⣿⣿⣿⣿⣟⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⣿⣿⠀⠀⠀⢀⡀⢚⢻⣿⣿⣿⣿⣿⣿⣆⠀⠀⢸⣿⣿⠙⠛⠛⠋⠉⠁⠀⠀⠓⠓⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢹⣼⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⡛⠻⢿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⣠⣾⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⠂⠀⠘⠛⠛⠛⠛⠉⠉⠀⠛⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⠀⠀⠀⢿⣶⣿⣿⣿⣿⠇⠀⠀⠀⠉⠉⠛⠻⡟⠛⢻⡿⠉⠈⠙⣿⣿⠀⢃⣿⣻⣿⣿⡿⠻⢿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢠⣴⣤⣀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⣼⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠁⢀⣀⠀⠀⠀⠀⠀⠀⠁⠀⠸⡇⣴⣾⣿⣿⣿⠀⣼⣿⣿⣿⣿⡃⠀⠀⢈⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣭⣴⣄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⡦⣄⣸⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⣿⣿⠟⠁⠀⠀⠨⣿⣿⣿⣿⣷⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣤⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣤⣶⣦⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣿⣴⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣧⣉⠉⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠛⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿⡿⠋⠭⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠴⣾⣷⡟⠀⠀⠀⠀⠀⠀⣴⡿⢿⣿⣿⣟⣻⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢾⣗⣷⡿⠯⠅⠈⠉⠉⠁⠀⠀⠀⠉⠑⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠁⠈⠀⠹⣿⣿⣿⣯⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠁⠀⠀⠀⠀⠘⠹⠯⠆⠈⠛⠛⠘⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⢟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡟⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠀⠀⢀⣀⠀⢀⡀⠀⣀⠀⣀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡟⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢻⡉⠉⢹⠉⢹⣿⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢺⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣯⡙⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡷⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣿⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⠀⣽⠀⠘⢿⠀⢸⠀⢠⠀⢸⡀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⠷⡶⣟⣷⣶⣾⣿⣷⠶⣾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣿⣿⣶⣶⣾⣶⡚⠒⠚⠒⠚⠛⠶⠖⠛⠒⠛⠒⠊⠀ ⠀⣶⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⠛⠛⣛⣛⠛⠛⠛⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣻⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⣛⠛⠛⠛⠙⠋⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣴⣿⣿⣿⣿⣿⡄⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣿⡟⣿⣿⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⢛⣛⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⠀⠀⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⢀⣮⠻⠻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣟⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠷⣿⡚⣿⣿⣿⣿⣿⣿⣬⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⡄⢀⣠⣄⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢾⣿⣤⣠⣦⡉⣿⣿⣿⣿⣿⣟⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣽⣿⣿⠀⠀⠀⣰⢶⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⣿⣿⣿⣿⠙⠛⠛⠉⠉⠁⠀⠀⠓⠓⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣼⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⠿⠟⢻⠿⣿⢿⣿⣿⡛⠻⠿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣤⣤⣤⡴⣻⣿⣿⣿⣿⣿⣿⠇⠀⠐⠛⠻⠿⠛⠛⠛⠁⠉⠀⠛⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠀⠀⠀⠻⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠉⠙⢻⡟⠛⢻⡿⠉⠈⠙⣿⣿⢸⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⣰⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⢀⣀⠀⠀⠀⠀⠀⠀⠃⠀⠸⡇⣴⣾⣿⣿⣿⢰⣼⣿⣿⡏⠀⠀⠉⢻⣿⣇⣤⣶⣄⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣭⣴⣄⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣷⣄⡀⠀⣸⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄⣿⠀ ⠀⢸⡏⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢠⣤⣶⣶⣶⣶⣦⣤⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡿⠋⠉⠃⢿⣯⣿⣿⣿⣿⣷⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣤⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣤⣤⣼⣿⣿⣿⣿⣤⣤⣴⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣧⣾⣤⣦⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣈⠉⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⡿⠃⣭⣁⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠴⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⠿⢿⣿⣿⣟⣻⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢾⣗⣷⡿⡯⠅⠈⠉⠉⠁⠀⠀⠀⠉⠑⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠁⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠈⠻⠋⠋⠈⠉⠙⠘⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⢟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡟⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠂⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠀⠀⢀⣀⡀⢀⡀⠀⣀⠀⣀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢻⡉⠉⢹⠉⢹⣿⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢾⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣯⡙⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣿⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⠀⣽⠀⠘⢿⠀⢸⠀⢠⠀⢸⡀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⡷⡶⣿⠷⣶⣾⣿⣷⠶⣾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣿⣿⣶⣶⣾⡶⠞⠒⠚⠒⠚⠛⠲⠖⠛⠒⠛⠒⠊⠀ ⠀⣶⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠛⠛⠛⠛⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣻⣻⣿⣿⡿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⢛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⣾⣿⣿⣿⣷⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣿⡿⣿⣿⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⡷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⣶⠀⠀⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⢀⣬⠻⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣷⣶⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣿⣿⣿⣿⣟⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠷⣿⡺⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠠⣶⣦⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢾⣿⣤⣠⣦⡉⣿⣿⣿⣿⣿⣟⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢙⣽⣿⣿⠀⢀⣤⣿⣿⣷⣾⣿⣿⡄⠀⠀⠀⢻⣿⣿⣿⣿⣿⠙⠛⠛⠋⠉⠁⠀⠀⠛⠓⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⢼⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⠿⠟⢻⣟⣛⣻⣿⣿⡛⠛⠿⢷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢐⠊⢉⣻⣿⣿⣿⣿⣿⣿⡶⠀⠀⠛⠛⠿⣿⣿⠛⠛⠛⠀⠈⠁⠛⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠘⠿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠈⠙⢿⡟⠛⢻⡿⠉⠈⠙⣿⣿⢸⣧⣌⢰⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠻⣤⣴⣦⣴⣤⡀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⣴⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠇⠀⠸⡇⣴⣾⣿⣿⣿⢸⣿⡿⠂⠉⠙⠻⣿⣿⠃⣀⣤⣶⣤⡀⠀⠀⠀⠙⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣭⣴⣄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡀⠀⠀⠀⣿⡏⣸⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄⣿⠀ ⠀⢸⡏⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⠟⠛⢻⣿⣿⣿⣿⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡦⢤⠀⣿⡇⠨⣿⣿⣿⣿⣷⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣤⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣤⣤⣼⣿⣿⣿⣿⣤⣶⣶⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣶⣶⣶⣿⣷⣶⣿⣿⣿⣿⣯⣾⣶⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣧⣉⠉⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⡿⠋⣥⣈⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠴⣾⣷⡟⠀⠀⠀⠀⠀⠀⣴⢿⢿⣿⣿⣿⣻⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢾⣗⣷⡿⠟⠁⠈⠉⠉⠁⠀⠀⠀⠈⠁⠄⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠁⠈⠀⢛⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠁⠀⠀⠀⠀⠈⠙⠛⠃⠘⠛⠋⠘⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⢟⣽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠄⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠀⠀⢀⣀⡀⢀⡀⠀⣀⠀⣀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢻⡉⠉⢹⠉⢹⣿⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢾⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣯⡹⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡷⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣿⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢸⡇⠀⠿⡏⠉⠇⠀⣿⠀⣿⠀⠘⢿⠀⢸⠀⢠⠀⢸⡀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⣷⣶⣿⠷⣶⣾⣿⣷⡶⣾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣿⣽⣶⣶⣾⡶⠾⠒⠚⠒⠚⠛⠶⠖⠛⠒⠛⠒⠊⠀ ⠀⣶⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⠛⠛⠛⠛⠛⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⢛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢀⣴⣶⣶⣶⣦⡀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⣿⣯⣿⣿⣿⣿⡟⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⡼⣿⣿⣿⣿⣿⡇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⢀⣾⠻⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⡿⣷⣿⣾⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣟⣽⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠧⣿⡚⣿⣿⣿⣿⣿⣿⣥⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢾⣿⣤⣠⣦⡉⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⣿⣿⠀⣿⣿⣇⣠⣾⣿⡄⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠙⠛⠛⠉⠉⠁⠀⠀⠓⠓⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣾⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⠿⠟⢻⣯⣿⣿⣿⣿⠛⠛⠿⠷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⢿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠐⠛⠻⠿⣿⣿⣿⠛⠛⠛⠁⠈⠉⠓⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠀⠀⠀⠈⠻⠿⠿⠿⠋⠀⠀⠀⠀⠀⠈⠙⣿⡟⠛⢻⡿⠉⠈⠙⣿⣿⠀⢚⣽⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⣤⣤⣴⣤⣀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⣸⡆⣿⠀ ⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠰⠇⠀⠸⣇⣴⣾⣿⣿⣿⢠⡀⠛⠻⠿⣿⣿⡿⠀⠀⣀⣤⣶⣤⡀⠀⠈⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⢚⣭⣴⣄⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⢸⡀⠀⠀⠀⠠⣿⡇⠀⣸⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄⣿⠀ ⠀⢸⣟⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠉⠉⢹⣿⣿⣿⣿⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣸⣷⣄⣀⠀⠀⣿⡇⠀⠨⣿⣿⣿⣿⣷⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣤⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣤⣤⣼⣿⣿⣿⣿⣴⣶⣶⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣷⣶⣶⣿⣿⣿⣿⣧⣾⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣧⣉⠉⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠛⠻⢛⠛⢿⣿⣿⣿⣿⣿⣿⡿⠃⢭⣉⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠴⣾⣷⡟⠀⠀⠀⠀⠀⠀⣴⣿⢿⣿⣿⣟⣻⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⢾⣗⣷⡿⠯⠁⠈⠉⠉⠁⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠁⠈⠀⢙⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠈⠹⠿⠋⠘⠛⠟⠘⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡟⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠀⠀⢀⣀⡀⢀⡀⠀⣀⢀⣀⣀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢻⡉⠉⢹⠉⢹⣿⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢾⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣏⡽⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡷⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣿⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢸⡇⠀⠿⡏⠉⠇⠀⣿⠀⣽⠀⠘⢿⠀⢸⠀⢠⠀⢸⡀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⣷⣶⡿⡷⣶⣾⣿⣷⡶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣿⣿⣶⣶⣾⣶⠞⠒⠚⠒⠚⠛⠶⠖⠛⠒⠛⠒⠊⠀ ⠀⣶⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠛⠛⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣻⣿⣿⡿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⢛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣠⣴⣶⣤⣄⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣿⣏⣿⣿⣿⣿⡟⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⠿⢿⣿⣿⣿⡇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⠀⠀⣿⣿⣻⣿⣿⣿⡅⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⢀⣮⠻⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⡿⣷⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣿⣿⣿⣿⣟⣽⡇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠧⣿⡚⣿⣿⣿⣿⣿⣿⣥⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢾⣿⣤⣠⣦⡉⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⣿⣿⢰⣆⠀⣤⣶⡀⠀⠀⠀⠀⠈⠁⠹⣿⣟⣿⣿⣿⣿⠙⠛⠛⠉⠉⠁⠀⠀⠓⠓⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣼⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⠿⠿⢻⣯⣽⣿⣿⣿⠛⠛⠿⠷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣦⣄⠀⠀⠔⠖⠿⣿⣿⣿⣿⣿⠛⠛⠛⠃⠈⠁⠛⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠈⠻⠿⠿⠟⠋⠀⠀⠀⠀⠀⠈⠻⣿⡟⠛⢻⡿⠉⠈⠙⣿⣿⠸⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣤⣤⣦⣴⣦⣀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⣼⡆⣿⠀ ⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢲⠇⠀⠸⡇⣴⣾⣿⣿⣿⢸⣿⣿⣿⣿⣿⡟⠀⠀⠀⣀⣤⣶⣄⡀⠈⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣄⡀⢚⣭⣴⣄⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⢹⣿⠃⠀⠀⣸⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄⣿⠀ ⠀⢸⣟⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠉⠉⢸⣿⣿⣿⣿⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠸⣿⡆⠀⠀⠨⣿⣿⣿⣿⣷⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣤⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣤⣤⣼⣿⣿⣿⣿⣴⣶⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣶⣶⣿⣷⣶⣶⣶⣿⣿⣿⣿⣧⣾⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣼⣿⣿⣿⣿⣧⣉⠉⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡛⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿⡿⠋⣭⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠴⣾⣷⡟⠀⠀⠀⠀⠀⠀⣴⡿⢿⣿⣿⣟⣻⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢾⣗⣷⡿⠏⠁⠈⠉⠉⠁⠀⠀⠀⠈⠑⠄⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠉⠈⠀⢙⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠁⠀⠀⠀⠀⠈⠻⠻⠏⠈⠛⠝⢘⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⢟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡟⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠀⠀⢀⣀⡀⢀⡀⠀⣀⢀⣀⣀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢻⡉⠉⢹⠉⢹⣿⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢺⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣯⡹⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣿⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢸⡇⠀⠿⡏⠉⠇⠀⣿⢀⣿⠀⠘⢿⠀⢸⠀⢠⠀⢸⡀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⢷⣶⣿⠷⣶⣾⣿⣷⡶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣿⣿⣶⣶⣾⡶⠚⠒⠚⠒⠚⠛⠶⠖⠛⠒⠛⠒⠊⠀ ⠀⣶⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⠛⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⢛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢀⣤⣤⣤⣀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⣿⣏⣿⣿⣿⣿⡟⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⡿⢿⣿⣿⣿⡆⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣴⣶⣾⠀⠀⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⢀⣬⠻⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡿⢷⣾⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣟⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠷⣿⡛⣿⣿⣿⣿⣿⣿⣥⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢿⠀⢾⣿⣤⣠⣦⡉⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⣿⣿⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠈⠀⢹⣿⣿⣿⣿⣿⣿⠙⠛⠛⠋⠉⠁⠀⠀⠓⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢹⣼⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⠿⢻⣿⣭⣿⣿⣿⠛⠻⠿⢷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣾⣿⣿⣦⣀⠀⠀⠀⠰⠤⠴⣿⣿⣿⣿⣿⣿⠛⠛⠛⠁⠈⠁⠛⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⠀⠀⠈⠛⠿⠛⠛⠁⠀⠀⠀⠀⠀⠙⢿⣿⡟⠛⢻⡿⠉⠈⠙⣿⣿⢸⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣤⣤⣤⣴⣤⣀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⣸⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣶⠇⠀⠸⡇⣴⣾⣿⣿⣿⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣤⣶⣄⠙⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣯⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⠀⢚⣭⣴⣄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠛⠛⢻⣿⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄⣿⠀ ⠀⢸⣟⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⡀⠀⠀⠀⠨⣿⣿⣿⣿⣷⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣷⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣶⣶⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣧⣉⠉⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠟⠛⣿⣿⣿⣿⣿⣿⣿⡿⠃⣬⣁⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠴⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⡿⢿⣿⣿⣟⣻⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢾⣗⣷⡿⢏⠁⠈⠉⠉⠁⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠁⠈⠀⢙⣿⣿⣿⡿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠁⠀⠀⠀⠀⠈⠹⠟⠛⠈⠛⠛⠘⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡟⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⡀⣀⠀⠀⢀⣀⠀⢀⡀⠀⣀⠀⣀⣀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢻⡉⡉⢹⠉⢹⣿⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢾⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣯⡙⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣿⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⠀⣽⠀⠘⢿⠀⢸⠀⢠⠀⢸⡀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⣷⣶⣟⣷⣶⣾⣿⣷⡶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣿⣿⣶⣶⣾⡶⠚⠒⠚⠒⠚⠛⠶⠖⠛⠒⠛⠒⠊⠀ ⠀⣶⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⣛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⣠⣤⣀⡈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣿⣟⣿⣿⣿⣿⡟⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢀⣿⣿⣿⣿⣿⡆⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣶⠀⠀⣿⣿⣻⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⢀⣬⠻⠻⡿⠿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣾⣯⣿⣿⣿⣿⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣟⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⡁⠤⠧⣿⡻⣿⣿⣿⣿⣿⣿⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⣾⣿⣠⣠⣦⡉⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⣿⣿⣿⣿⣿⣿⠙⠛⠛⠋⠉⠁⠀⠀⠓⠓⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣼⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠿⢻⣯⣽⣿⣿⡟⠿⠿⠿⢷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣦⡀⠀⠀⠀⠀⠀⠠⣤⢤⣿⣿⣿⣿⣿⣿⠛⠛⠛⠁⠈⠁⠛⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⠀⠀⠈⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠙⣿⣿⡟⠛⢻⡿⠉⠈⠙⣿⣿⢸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⣸⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠰⣶⠇⠀⠸⡇⣴⣾⣿⣿⣿⢸⣿⣿⣿⠇⠀⠀⠀⠀⠀⣀⣤⣶⣽⡛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣤⣤⣶⣶⣶⠶⠶⠀⢚⣭⣴⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠿⢿⣿⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄⣿⠀ ⠀⢸⡟⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡀⠀⣸⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣷⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣤⣶⣶⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣧⣉⠉⠉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⢛⠟⢻⣿⣿⣿⣿⣿⣿⡿⠋⣥⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠴⣾⣷⡟⠀⠀⠀⠀⠀⠀⣴⡿⢿⣿⣿⣿⣻⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢾⣗⣷⡿⡋⠁⠈⠉⠉⠁⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠁⠈⠀⢙⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠈⠹⠏⠍⠈⠙⠛⠘⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⢟⣽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡟⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⡀⣀⠀⠀⢀⣀⠀⢀⡀⠀⣀⠀⣀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢻⡉⡉⢹⠉⢹⣿⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢾⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣏⠝⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡷⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣿⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⠀⣽⠀⠘⢿⠀⢸⠀⢠⠀⢸⡀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⢷⣶⡿⠷⣶⣾⣿⣷⡶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣿⣿⣶⣶⣾⠶⠚⠒⠚⠒⠚⠛⠲⠖⠛⠒⠛⠒⠊⠀ ⠀⣶⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠛⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⢛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⣀⣀⣀⡈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣿⣟⣿⣿⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣾⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⠀⠀⣿⣿⣻⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⣼⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣼⣯⣿⣿⣿⣿⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣟⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠧⣿⡛⣿⣿⣿⣿⣿⣿⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢾⣿⣤⣠⣦⡉⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⣿⣟⣿⣿⣿⣿⠙⠛⠛⠉⠉⠁⠀⠀⠓⠓⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣼⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠿⢻⣯⣽⣿⣿⡟⠿⠿⠿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣦⡀⠀⠀⠀⠀⠀⠀⣠⣠⣠⣿⣿⣿⣿⣿⣿⠛⠛⠛⠁⠈⠁⠛⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⠀⠀⠈⠙⠛⠛⠋⠁⠀⠀⠀⠀⠈⠹⣿⣿⡟⠛⢻⡿⠉⠈⠙⣿⣿⢸⣿⣿⣷⠂⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣤⣤⣤⣴⣤⡀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⣰⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠰⣶⠇⠀⠸⡇⣴⣾⣿⣿⣿⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⣀⣤⣾⣽⡛⠛⠛⠛⠙⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣤⣴⣶⣶⣶⠶⠶⠀⢚⣭⣴⣄⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡇⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⣿⠀ ⠀⢸⡗⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣀⣀⣸⣿⣿⣿⣿⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣷⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣤⣤⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣿⣤⣶⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣉⠉⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿⡿⠃⣤⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠴⣾⣷⡟⠀⠀⠀⠀⠀⠀⣴⠿⢿⣿⣿⣿⡻⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠡⢾⣗⣷⡿⠛⠅⠈⠉⠉⠁⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠁⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠹⠋⠏⠘⠉⠙⠘⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⠿⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡟⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⡀⣀⠀⠀⢀⣀⠀⢀⡀⠀⣀⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⠻⡉⠉⢹⠉⢹⣿⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢾⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣯⡝⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣿⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⠀⣽⠀⠘⢿⠀⢸⠀⢠⠀⢸⡀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠲⣷⣶⣟⡷⣶⣾⣿⣷⡶⣾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣷⣿⣶⣶⣾⡶⠚⠒⠚⠒⠚⠛⠲⠖⠛⠒⠛⠒⠊⠀ ⠀⣶⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⠛⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⡛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣀⣀⡀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⣿⣟⣿⣿⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣾⣿⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⠀⠀⣿⣿⣽⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⢀⣬⠻⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣼⣮⣿⣿⣿⣿⣅⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣟⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠧⣿⡚⣿⣿⣿⣿⣿⣿⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢾⣿⣠⣠⣦⡉⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⣿⣟⣿⣿⣿⣿⠙⠛⠛⠉⠉⠁⠀⠀⠓⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢹⢼⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⠿⢻⣯⣭⣿⣿⡿⠿⠿⢿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣐⣿⣿⣿⣿⣿⣿⠛⠛⠛⠃⠈⠁⠛⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⠀⠀⠈⠙⠛⠛⠋⠀⠀⠀⠀⠀⠉⠻⣿⣿⡟⠛⢻⡿⠉⠈⠙⣿⣿⢸⣶⣤⠀⠀⠀⠀⠀⠀⠘⢷⣾⣿⣿⣿⣿⣿⣿⣤⣤⣤⣴⣤⡀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⣰⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢱⣶⠇⠀⠸⡇⣴⣾⣿⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⡛⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣶⣶⣶⣶⣶⠲⠒⠀⢚⣭⣴⣄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄⣿⠀ ⠀⢸⡯⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣀⣀⣼⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣽⡇⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣷⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣤⣦⣴⣭⣿⣯⣿⣿⣿⣿⣿⣿⣿⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣉⠉⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⡛⢛⠛⢿⣿⣿⣿⣿⣿⣿⡿⠋⣤⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠴⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⠿⢿⣿⣿⣟⣻⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠾⣗⣶⡿⠯⠅⠈⠉⠉⠁⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠁⠀⠀⢙⣿⣿⣿⢿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠈⠻⠟⠇⠙⠉⠋⠘⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⢿⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⡀⣀⠀⠀⢀⣀⡀⢀⡀⠀⣀⠀⣀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⠻⡉⠉⢹⠉⢹⣿⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢾⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣏⡙⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣾⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⠀⣽⠀⠘⢿⠀⢸⠀⢠⠀⢸⡀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⢷⣶⣟⢷⣶⣾⣿⣷⡶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣿⣿⣶⣶⣾⣶⠚⠒⠚⠒⠚⠛⠲⠖⠛⠒⠛⠒⠊⠀ ⠀⣶⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⢛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⡀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣿⣿⣿⣿⡟⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣾⣿⣿⣿⣷⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⠀⠀⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⢀⣪⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣼⣿⣿⣿⣻⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣿⣿⣿⣿⣟⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠧⣿⡺⣿⣿⣿⣿⣿⣿⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢾⣿⣠⣠⣦⠉⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢙⣹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢻⣿⣟⣿⣿⣿⣿⠙⠛⠛⠉⠉⠁⠀⠀⠓⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⠿⢻⣧⣿⣿⣿⡿⠿⠿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⢀⣿⣿⣿⣿⣿⣿⠛⠛⠛⠁⠈⠁⠓⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⠀⠀⠈⠙⠛⠛⠉⠀⠀⠀⠀⠀⠉⢿⣿⣿⡟⠛⢻⡿⠉⠈⠙⣿⣿⢀⣀⠀⠀⠀⠀⠀⠀⠠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣴⣤⣀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⣰⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢱⣶⠇⠀⠸⡇⣴⣾⣿⣿⣿⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⣙⣽⣿⣿⡛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣶⣾⣿⣿⡟⠛⠃⠀⢚⣭⣴⣄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄⣿⠀ ⠀⢸⣟⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢀⣰⣿⣿⣿⣿⣧⣤⣤⣼⣿⣿⣿⣿⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣷⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣤⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣷⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣈⠉⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⡛⠛⠛⣻⣿⣿⣿⣿⣿⣿⡿⠋⣤⣁⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠴⣾⣷⡟⠀⠀⠀⠀⠀⠀⣴⡿⢿⣿⣿⣟⣻⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠾⣗⣷⡿⡛⠁⠈⠉⠉⠁⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠉⠈⠀⠙⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠁⠀⠀⠀⠀⠈⠛⠛⠂⠘⠙⠉⠘⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⢟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡟⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠀⠀⢀⣀⡀⢀⡀⠀⣀⠀⣀⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢻⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢾⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣯⡙⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣾⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⠀⣽⠀⠘⢿⠀⢸⠀⢠⠀⢸⡀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⠷⣶⠿⣷⣶⣾⣿⣷⠶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣿⣽⣶⣶⣾⡶⠚⠒⠚⠒⠚⠛⠲⠖⠛⠒⠛⠒⠊⠀ ⠀⣴⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⢛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⡟⣿⣿⣿⣿⡟⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣴⣿⣿⣿⣦⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⣮⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣼⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣿⣿⣿⣿⣟⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠧⣿⡺⣿⣿⣿⣿⣿⣿⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢾⣿⣤⣠⣦⠉⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢙⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠹⣿⣿⣿⣿⣿⢿⠙⠛⠛⠉⠉⠁⠀⠀⠓⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⢴⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⠿⢻⣷⣿⣿⣿⡿⠿⠿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣴⣿⣿⣿⣿⣿⣿⠛⠛⠛⠀⠈⠁⠛⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠙⠛⠋⠉⠀⠀⠀⠀⠈⠙⢿⣿⣿⡟⠛⢹⡿⠉⠈⠙⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣴⣤⣀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⣰⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣹⣶⠇⠀⠸⡇⣴⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⣛⣿⣿⣿⡛⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣶⣿⣿⣿⡟⠛⠃⠀⢚⣭⣴⣄⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄⣿⠀ ⠀⢸⡏⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢠⣼⣿⣿⣿⣿⣷⣤⣶⣾⣿⣿⣿⣿⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣷⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣤⣦⣦⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣯⣉⠉⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢛⠛⡛⠛⣻⣿⣿⣿⣿⣿⣿⡿⠃⣤⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠴⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⢿⢿⣿⣿⣟⣻⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⢾⣗⣷⡿⠟⠁⠈⠉⠉⠁⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠉⠈⠀⢙⣿⣿⣿⡟⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠁⠀⠀⠀⠀⠈⠻⠻⠋⠈⠙⠋⠘⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⢿⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠀⠀⢀⣀⡀⢀⡀⠀⣀⢀⣀⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢻⡉⠉⢹⠉⢹⣿⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢾⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣯⡙⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣾⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⠀⣽⠀⠘⢿⠀⢸⠀⢠⠀⢸⡀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⣷⡶⣻⡷⣶⣾⣿⣷⠶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣻⣿⣶⣶⣾⣶⡚⠒⠚⠒⠚⠛⠲⠖⠛⠒⠛⠒⠊⠀ ⠀⣶⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⣛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⣯⣿⣿⣿⣿⡟⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣴⣿⣿⣶⡆⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⠀⠀⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⣮⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣼⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣟⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠧⣿⡚⣿⣿⣿⣿⣿⣿⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢿⠀⢾⣿⣤⣠⣦⡉⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⣿⣿⣿⣿⣿⢿⠙⠛⠛⠉⠉⠁⠀⠀⠓⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⢸⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⠿⢻⣷⣿⣿⣿⡿⠿⢿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣿⣿⣿⣿⣿⣿⠛⠛⠛⠁⠉⠉⠛⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠉⠋⠉⠉⠀⠀⠀⠀⠈⠙⢿⣿⣿⡟⠛⢻⡿⠉⠈⠙⣿⣿⠀⠁⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣴⣤⣀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⣰⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠈⣱⣶⠇⠀⠸⡇⣴⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣛⣿⣿⣿⡛⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⡟⠉⠁⠀⢚⣭⣴⣄⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⣼⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣷⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣬⣭⣭⣭⣭⣥⣤⣤⣼⣿⣿⣿⣿⣤⣤⣴⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣦⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣯⣉⠉⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⡛⠛⣻⣿⣿⣿⣿⣿⣿⡿⠃⣬⣁⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠴⣾⣷⡟⠀⠀⠀⠀⠀⠀⣴⠿⢿⣿⣿⣟⣻⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢾⣗⣶⡿⠟⠁⠈⠉⠉⠁⠀⠀⠀⠈⠑⠄⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠁⠈⠀⠛⣿⣿⣿⣟⣿⣿⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠈⠙⠟⠋⠈⠙⠉⠘⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⠿⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠠⠴⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⡀⣀⠀⠀⢀⣀⠀⢀⡀⠀⣀⠀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢹⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢾⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣯⡙⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠑⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣷⣾⣻⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⠀⣽⠀⠘⢿⠀⢸⠀⢠⠀⢸⡀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠲⠷⡶⣛⣷⣶⣾⣿⠶⡶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣷⣼⣶⣶⣾⡶⠚⠒⠚⠒⠚⠛⠲⠖⠛⠒⠛⠒⠊⠀ ⠀⣴⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⢛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣿⣿⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣴⣶⣶⣶⡄⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣷⣶⠀⠀⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⣮⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣼⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣿⣿⣿⣿⣟⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠧⣿⡺⣿⣿⣿⣿⣿⣿⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢼⣿⣤⣠⣦⠉⣿⣿⣿⣿⣿⣟⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢙⣹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⡟⣿⣿⣿⣿⠙⠛⠛⠉⠉⠁⠀⠀⠓⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣴⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡿⢻⣯⣿⣿⣿⠿⢿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢦⣔⣿⣿⣿⣿⣿⣿⠛⠛⠛⠀⠉⠁⠓⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠉⠻⣿⣿⣿⡟⠛⢹⡿⠉⠈⠉⣿⣿⠀⢁⠀⠀⠀⠀⠀⠀⠀⣾⣾⣿⣿⣿⣿⣿⣿⣿⣤⣴⣤⣴⣤⣀⡀⠁⠂⠀⠀⠀⠀⠀⠀⠀⣰⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⢀⣀⠀⠀⠀⠈⣱⣶⠇⠀⠸⡇⣴⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣛⣿⣿⣿⡛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣷⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⡏⠉⠁⠀⢚⣭⣴⣄⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠄⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢠⣾⣿⣿⣿⣿⣷⣶⡾⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣷⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣬⣭⣭⣭⣭⣥⣤⣤⣼⣿⣿⣿⣿⣤⣦⣮⣭⣯⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣯⣁⠉⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠛⠛⣻⣟⣿⣿⣿⣿⣿⡿⠃⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠴⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⠿⢿⣿⣿⣟⣻⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠾⣗⣷⡿⠿⠅⠈⠉⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠁⠀⠀⠙⣿⣿⣿⣟⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠙⠋⠃⠈⠙⠁⠘⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⢟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢓⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⡀⣀⠀⠀⢀⣀⠀⢀⡀⠀⣀⠀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢹⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢾⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣯⠹⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠑⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣿⣻⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⠀⣽⠀⠘⢿⠀⢸⠀⢠⠀⢸⡀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠲⠷⣶⣛⠷⣶⣾⣿⣶⠶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣾⣿⣶⣶⣾⡶⠚⠒⠚⠒⠚⠛⠲⠖⠛⠒⠛⠒⠊⠀ ⠀⣴⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⢛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣤⣶⣦⣤⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⠀⠀⣿⣿⣻⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⣪⠻⠻⡿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣸⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣟⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠷⣿⡺⣿⣿⣿⣿⣿⣿⣤⣤⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢾⣿⣠⣠⣆⠉⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢙⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⢿⣿⣿⣿⣿⣿⠙⠛⠛⠉⠉⠁⠀⠀⠓⠓⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⢸⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡿⢿⣯⣿⣿⣿⢿⣿⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦⣤⣿⣿⣿⣿⣿⣿⠛⠛⠛⠀⠉⠁⠛⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠉⠉⠻⣿⣿⣿⡟⠛⢻⡿⠉⠈⠙⣿⣿⠈⢁⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣴⣤⣀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⣰⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⢀⣀⠀⠀⠀⠉⣱⣶⠇⠀⠸⡇⣴⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣋⣿⣿⣿⡛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣷⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣿⣿⣿⣿⡏⠉⠁⠀⢚⣭⣴⣄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠄⣿⠀ ⠀⢸⡗⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠠⢾⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣷⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣭⣭⣭⣭⣥⣤⣤⣼⣿⣿⣿⣿⣤⣤⣮⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣤⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣉⠈⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⠛⠛⠛⠛⣻⢿⣿⣿⣿⣿⣿⡿⠃⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠴⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⠿⢿⣿⣿⣟⣻⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠾⣗⣶⡿⠋⠁⠈⠉⠉⠁⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠁⠀⠀⠹⣿⣿⣷⣟⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠈⠘⠋⠁⠈⠉⠙⠘⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⢟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠠⠴⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⡀⣀⠀⠀⢀⣀⠀⢀⡀⠀⣀⢀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⠹⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢾⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣏⡹⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠑⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣿⣻⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⠀⣼⠀⠘⢿⠀⢸⠀⢠⠀⢸⡀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠲⠷⣶⣿⢷⣶⣾⣿⣶⠶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣿⣿⣶⣶⣾⡶⠚⠒⠚⠒⠚⠛⠲⠖⠛⠒⠛⠒⠊⠀ ⠀⣴⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⣛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⡟⣿⣿⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⣠⣤⣤⣄⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⠀⠀⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⣪⠻⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠷⣸⣿⣿⣿⣿⡆⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣿⣿⣿⣿⣟⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠧⣿⡚⣿⣿⣿⣿⣿⣿⣤⣤⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⠼⣿⣠⣠⣆⠉⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢙⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣟⣿⣿⣿⣿⠙⠛⠛⠉⠉⠁⠀⠀⠓⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣸⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⣿⣿⣿⢿⣿⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣆⣤⣿⣿⣿⣿⣿⣿⠙⠛⠛⠀⠈⠁⠛⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠉⠉⠉⠉⠀⠀⠈⠉⠛⠿⣿⣿⣿⡟⠛⢻⡿⠉⠈⠙⣿⣿⠈⠁⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣴⣤⣀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⣰⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⢀⣀⠀⠀⠀⢉⣱⣶⠇⠀⠸⡇⣴⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣋⣿⣿⣿⡛⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣷⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⡀⢚⣭⣴⣄⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠄⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠾⣿⣿⣿⣿⣿⠿⠛⢻⣿⣿⣿⣿⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣷⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣤⣦⣼⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣴⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣈⠉⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⠛⠛⠛⠛⣻⣟⣿⣿⣿⣿⣿⡿⠃⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠴⣾⣷⡟⠀⠀⠀⠀⠀⠀⣴⠿⢿⣿⣿⣟⣻⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠾⣗⣷⡿⠋⠀⠈⠉⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠁⠀⠀⠙⣿⣿⣷⣟⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠈⠹⠛⠋⠈⠉⠉⠘⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⢿⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠀⠀⢀⣀⠀⢀⡀⠀⣀⢀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⠹⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢾⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣯⡙⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠑⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣿⣻⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⠀⣽⠀⠘⢿⠀⢸⠀⢠⠀⢸⡀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠲⠷⢶⠛⡷⣶⣾⣿⠶⠶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣿⣿⣶⣶⣾⡶⠚⠒⠚⠒⠚⠛⠲⠖⠛⠒⠛⠒⠊⠀ ⠀⣴⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⢛⠛⠛⠛⠋⠋⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡯⣿⣿⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣀⣤⣀⣈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣶⠀⠀⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⣮⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠷⢰⣿⣿⣿⣿⡄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣿⣿⣿⣿⣟⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠧⣿⡚⣿⣿⣿⣿⣿⣿⣤⣤⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢻⠀⠾⣿⣠⣠⣦⠉⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢙⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⣿⡟⣿⣿⣿⣿⠙⠛⠛⠉⠉⠁⠀⠀⠒⠓⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣰⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⢿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣖⢴⣿⣿⣿⣿⣿⣿⠛⠛⠛⠀⠈⠁⠓⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⠀⠀⠉⠉⠉⠉⠀⠀⠉⠉⠛⢿⣿⣿⣿⡟⠛⢻⡿⠉⠈⠉⣿⣿⠀⣁⠀⠀⠀⠀⠀⠀⠠⡾⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣤⣴⣤⣀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⣰⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⢀⣀⠀⠀⠀⢋⣱⣷⠇⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⠀⠀⠀⠀⠀⠀⠈⠛⣛⣿⣿⣿⡛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣾⣿⣿⣿⣿⢀⣀⡀⢛⣭⣴⣄⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠄⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠿⣿⣿⣿⣿⣿⠛⠛⢻⣿⣿⣿⣿⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣷⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣤⣤⣬⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣀⠁⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠙⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿⡿⠃⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠴⣾⣷⡟⠀⠀⠀⠀⠀⠀⣴⠿⢿⣿⣿⣟⣻⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠾⣗⣶⡿⠋⠀⠈⠉⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠁⠀⠀⠙⣿⣿⣿⠟⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠁⠀⠀⠀⠀⠀⠙⠛⠃⠈⠉⠉⠘⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⢿⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢓⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠀⠀⢀⣀⠀⢀⡀⠀⣀⠀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⠹⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢾⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣏⡹⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣿⣻⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⠀⣽⠀⠘⢿⠀⢸⠀⢠⠀⢸⠀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⠷⢶⡻⠷⣶⣾⣿⣶⠶⣾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣶⣿⣶⣶⣾⡶⡚⠒⠚⠒⠚⠛⠲⠖⠛⠒⠛⠒⠊⠀ ⠀⣴⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⣛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣿⡟⣿⣿⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢀⣀⣀⡉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⠀⠀⣿⣿⣻⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⣪⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠧⢰⣿⣿⣿⣿⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣿⣿⣽⣿⣟⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠧⣿⡺⣿⣿⣿⣿⣿⣿⣤⣤⣾⣿⣿⣿⣿⣷⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢿⠀⠼⣿⣠⣠⣦⡉⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢙⣹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⠙⠛⠛⠉⠉⠁⠀⠀⠓⠒⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢹⢴⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣤⣿⣿⣿⣿⣿⣿⠙⠛⠛⠀⠉⠀⠚⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠁⠀⠉⠋⠉⠉⠀⠈⠉⠙⠛⢿⣿⣿⣿⡟⠛⢻⡿⠉⠈⠉⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣴⣤⣀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⣰⡆⣿⠀ ⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⢀⣀⠀⠀⠀⢏⣱⣶⠇⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⡀⠀⠀⠀⠀⠀⠀⠛⣛⣿⣿⣿⡛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣏⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣾⣿⣿⣿⣿⣀⣀⡀⢛⣭⣴⣄⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠄⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠛⣿⣿⡿⣿⡿⠛⠛⢻⣿⣿⣿⣿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣷⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣤⣦⣬⣭⣯⣽⣿⣿⣿⣿⣿⣿⣿⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣉⠁⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿⡿⠃⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠴⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⠿⢿⣿⣿⣟⣻⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠾⣗⣶⡿⠛⠀⠈⠉⠉⠁⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠁⠀⠀⢙⣿⣿⣿⡿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠹⠙⠁⠈⠉⠁⠘⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⢟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡟⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⠶⠄⠠⠴⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⡀⣀⠀⠀⢀⣀⠀⢀⡀⠀⣀⠀⣀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢹⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢾⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣏⠙⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣿⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⠀⣼⠀⠘⢿⠀⢸⠀⢠⠀⢸⠀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⣷⣶⡻⡷⣶⣾⣿⣶⠶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣷⣾⣶⣶⣾⡶⡚⠒⠚⠒⠚⠛⠲⠖⠛⠒⠛⠒⠊⠀ ⠀⣴⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⡛⣛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣿⣿⣿⣿⡟⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⣀⣀⡉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⠀⠀⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⡬⠻⠾⡿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠯⢠⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣟⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠧⣿⡚⣿⣿⣿⣿⣿⣿⣥⣤⣾⣿⣿⣿⣿⣶⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢿⠀⠼⣿⣀⣠⣦⠉⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢙⣹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⠙⠛⠛⠉⠉⠁⠀⠀⠓⠓⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣸⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⣿⣿⣿⣿⣿⣿⠘⠛⠛⠁⠉⠀⠚⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠋⠉⠀⠉⠛⠉⠉⠀⠉⠉⠛⠻⢿⣿⣿⣿⡟⠛⢻⡿⠉⠈⠙⣿⣿⠀⣀⠀⠀⠀⠀⠀⠀⠠⣿⣻⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣴⣤⣀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⣸⡆⣿⠀ ⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢀⣀⣀⣀⣀⣠⡀⠀⢀⣀⠀⠀⠈⣏⣱⣶⠇⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⡀⠀⠀⠀⠀⠀⠀⠛⣛⣿⣿⣿⡛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⡏⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣼⣿⣿⣿⣿⣀⣀⡀⢛⣭⣴⣄⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠄⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠛⠿⠿⠿⠿⠿⠛⠉⢹⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣷⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣤⣤⣬⣭⣯⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣉⠈⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠛⠛⣻⢿⣿⣿⣿⣿⣿⡿⠃⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠴⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⠿⢿⣿⣿⣟⣻⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢾⣗⣶⡿⠛⠀⠈⠉⠉⠁⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠁⠀⠀⢙⣿⣿⣿⣟⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠛⠋⠃⠈⠋⠁⠘⣿⣷⡽⣿⣿⣿⣿⣿⣿⣿⣿⢟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠠⠴⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⡀⣀⠀⠀⢀⣀⠀⢀⡀⠀⣀⠀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⠹⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢾⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣏⡹⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣿⣻⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⠀⣽⠀⠘⢿⠀⢸⠀⢠⠀⢸⠀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⢷⣶⡛⠷⣶⣾⣿⣶⡶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣶⣽⣶⣶⣾⡶⠚⠒⠚⠒⠚⠛⠲⠖⠛⠒⠛⠒⠊⠀ ⠀⣴⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⣛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡯⣿⣿⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠁⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⠀⠀⣿⣿⣻⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⣪⠻⠾⠿⠿⢿⣿⣿⣿⣿⣿⣿⡿⠿⢠⣾⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣟⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠧⣿⡺⣿⣿⣿⣿⣿⣿⣤⣤⣾⣿⣿⣿⣿⣶⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢿⠀⢼⣿⣀⣠⣦⠉⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢙⣹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⠙⠛⠛⠉⠉⠁⠀⠀⠓⠂⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣰⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣴⣿⣿⣿⣿⣿⣿⠛⠛⠛⠁⠈⠁⠛⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠁⠉⠛⠛⠉⠈⠉⠙⠛⠿⣿⣿⣿⣿⡟⠛⢻⡿⠉⠈⠉⣿⣿⠀⣀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣴⣤⣀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⣸⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢀⣀⣀⣀⣀⣤⡄⠀⢀⣀⠀⠀⠈⣏⣱⣶⠇⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⡀⠀⠀⠀⠀⠀⠀⠛⣛⣿⣿⣿⡛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣇⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⣸⣿⣿⣿⣿⣀⣠⡄⢛⣭⣴⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠄⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠙⠿⠿⠿⠿⠿⠋⠉⢹⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣷⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣤⣤⣽⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣀⠈⠈⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿⡿⠃⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠴⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⠿⢿⣿⣿⣟⣻⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠾⣗⣶⡿⠏⠁⠈⠉⠉⠁⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠉⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠁⠀⠀⠀⠀⠀⠙⠋⠃⠈⠋⠉⠘⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⢿⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⡀⣀⠀⠀⢀⣀⠀⢀⡀⠀⣀⠀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⠹⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢾⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣏⠙⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣿⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⠀⣽⠀⠘⢿⠀⢸⠀⢠⠀⢸⠀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⢷⡶⠛⣷⣶⣾⣿⡶⠶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣶⣾⣶⣶⣾⠶⠚⠒⠚⠒⠚⠛⠲⠖⠛⠒⠛⠒⠊⠀ ⠀⣴⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⢛⠛⠛⠛⠋⠋⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣿⣿⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⠀⠀⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⡪⠻⠻⡿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢀⣶⣿⣿⣦⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣟⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠧⣿⡺⣿⣿⣿⣿⣿⣿⣥⣤⣼⣿⣿⣿⣿⣤⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢿⠀⢼⣿⣤⣠⣦⠉⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠙⠛⠛⠉⠉⠁⠀⠀⠓⠓⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣼⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣶⣿⣿⣿⣿⣿⣿⠛⠛⠛⠁⠈⠁⠛⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁⠉⠛⠛⠉⠈⠙⠛⠻⠿⣿⣿⣿⣿⡟⠛⢻⡿⠉⠈⠙⣿⣿⠀⣀⠀⠀⠀⠀⠀⠀⠀⣺⣷⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣴⣤⣀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⣰⡆⣿⠀ ⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢀⣀⣀⣀⣀⣤⡄⠀⢀⣀⠀⠀⠘⣏⣱⣶⠇⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⡀⠀⠀⠀⠀⠀⠀⠛⣛⣿⣿⣿⡛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣏⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢀⣸⣿⣿⣿⣿⣀⣤⡤⢛⣭⣴⣄⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⠻⠿⠿⠿⠿⠉⠉⢹⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣷⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣤⣤⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣦⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣧⣁⠉⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠛⠛⠛⠛⣻⢟⣿⣿⣿⣿⣿⡿⠃⠤⣈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠴⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⠿⢿⣿⣿⣟⣻⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠡⠾⣗⣶⡿⠏⠁⠈⠉⠉⠁⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠁⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠙⠫⠁⠈⠉⠁⠘⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⢟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢓⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⡀⣀⠀⠀⢀⣀⠀⢀⡀⠀⣀⠀⣀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢹⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢺⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣏⠙⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣿⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⠀⣽⠀⠘⢿⠀⢸⠀⢠⠀⢸⠀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⢷⡶⠛⡷⣶⣾⣿⣶⡶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣿⣽⣶⣶⣾⢶⡚⠒⠚⠒⠚⠛⠲⠖⠛⠒⠛⠒⠊⠀ ⠀⣴⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⣛⠛⠛⠛⠋⠋⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣿⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⠀⠀⣿⣿⣻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⡮⠻⠾⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠁⣴⣶⣶⣦⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣟⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠧⣿⡺⣿⣿⣿⣿⣿⣿⣤⣤⣼⣿⣿⣿⣿⣤⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢻⠀⢼⣿⣀⣠⣦⠉⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣙⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⠙⠛⠛⠉⠉⠁⠀⠀⠓⠂⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣼⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⢴⣿⣿⣿⣿⣿⣿⠚⠛⠛⠁⠈⠀⠓⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠙⠛⠛⠋⠉⠛⠛⠻⠿⣿⣿⣿⣿⡟⠛⢹⡿⠉⠈⠙⣿⣿⠀⣀⠀⠀⠀⠀⠀⠀⢀⣔⣾⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣴⣤⣀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⣰⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣀⣀⣀⣠⣤⡄⠀⢀⣀⠀⠀⠘⣏⣱⣶⠇⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠛⣛⣿⣿⣿⡛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢀⣸⣿⣿⣿⣿⣀⣤⡤⢛⣭⣴⣄⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄⣿⠀ ⠀⢸⡏⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠈⠙⠛⠛⠻⠟⠉⠉⢹⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣷⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣤⣴⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣈⠉⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿⡿⠃⢤⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠴⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⡿⢿⣿⣿⣟⣻⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢾⣗⣶⡿⠏⠁⠈⠉⠉⠁⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠁⠀⠀⢙⣿⣿⣿⣟⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠁⠀⠀⠀⠀⠀⠙⠫⠁⠈⠉⠁⠘⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⢟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⡀⣀⠀⠀⢀⣀⠀⢀⡀⠀⣀⠀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢹⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢺⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣏⡝⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣿⣻⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⠀⣽⠀⠘⢿⠀⢸⠀⢠⠀⢸⠀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⠷⡶⠛⡷⣶⣾⣿⠶⠶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣷⣼⣶⣶⣾⠶⠚⠒⠚⠒⠚⠛⠲⠖⠛⠒⠛⠒⠊⠀ ⠀⣴⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⣛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣿⣿⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⠀⠀⣿⣿⣻⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⡪⠻⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⣤⣶⣶⣆⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣟⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠧⣿⡚⣿⣿⣿⣿⣿⣿⣥⣤⣼⣿⣿⣿⣿⣤⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢿⠀⠼⣿⣀⣠⣆⠉⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠙⠛⠛⠉⠉⠁⠀⠀⠓⠓⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣼⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣿⣿⣿⣿⣿⣿⠛⠛⠛⠁⠈⠁⠚⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠙⠛⠛⠋⠙⠛⠛⠿⠿⣿⣿⣿⣿⡟⠛⢻⡿⠉⠈⠙⣿⣿⠀⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣤⣴⣤⣀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⣰⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣀⣀⣀⣠⣤⡄⠀⢀⣀⠀⠀⠘⣏⣱⣶⠇⠀⠸⡇⣴⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣛⣿⣿⣿⡛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢀⣰⣿⣿⣿⣿⣤⣤⡤⢛⣭⣴⣄⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠙⠛⠛⠛⠛⠉⠉⢹⣿⣿⣿⣿⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣿⣿⣿⣿⣷⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣤⣤⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣯⣁⠉⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠛⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿⡿⠃⠤⣈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠴⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⠿⢿⣿⣿⣟⣻⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠾⣗⣶⡿⠏⠅⠈⠉⠉⠁⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠉⠀⠀⠙⣿⣿⣿⣟⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠁⠀⠀⠀⠀⠈⠹⠋⠃⠈⠙⠁⠘⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⢟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⡀⣀⠀⠀⢀⣀⠀⢀⡀⠀⣀⢀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢹⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢺⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⡯⡽⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣿⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⢀⣽⠀⠘⢿⠀⢸⠀⢠⠀⢸⠀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⢷⣶⡿⡷⣶⣾⣿⢶⠶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣿⣿⣶⣶⣾⠶⠚⠒⠚⠒⠚⠛⠲⠒⠛⠒⠛⠒⠊⠀ ⠀⣴⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⢛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⣿⣿⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⠀⠀⣿⣿⣻⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⣪⠻⠾⡿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⣠⣤⣤⣄⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣟⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠧⣿⡚⣿⣿⣿⣿⣿⣿⣤⣤⣤⣿⣿⣿⣿⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢻⠀⠸⣿⣀⣠⣆⠉⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⠙⠛⠛⠉⠉⠁⠀⠀⠓⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢻⣴⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣿⣿⣿⣿⣿⣿⠛⠛⠛⠀⠉⠀⠚⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠙⠛⠛⠛⠙⠛⠻⠿⢿⣿⣿⣿⣿⡟⠛⢻⡿⠉⠈⠙⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣾⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣴⣤⣀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⣰⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣀⣀⣀⣀⣤⡄⠀⢀⣀⠀⠀⠸⣏⣱⣶⠇⠀⠸⡇⣴⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣛⣿⣿⣿⡛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢀⣠⣿⣿⣿⣿⣤⣤⡤⢛⣭⣴⣄⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠙⠛⠛⠛⠛⠉⠁⢸⣿⣿⣿⣿⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣷⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣤⣥⣽⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣈⠉⠁⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠛⠛⠛⢛⣻⢿⣿⣿⣿⣿⣿⡿⠃⠤⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠴⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⠿⢿⣿⣿⣟⣻⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠾⣗⣷⡿⠿⠄⠈⠉⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠁⠀⠀⢙⣿⣿⣿⣟⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠁⠀⠀⠀⠀⠀⠛⠙⠃⠈⠉⠉⠘⣿⣷⡼⣿⣿⣿⣿⣿⣿⣿⣿⠟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠰⠰⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠀⠀⢀⣀⠀⢀⡀⠀⣀⠀⡀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢹⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢺⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣏⡹⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣿⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⠀⣽⠀⠘⢿⠀⢸⠀⢠⠀⢸⠀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⠷⣶⡻⡷⣶⣾⣿⠶⡶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣿⣽⣶⣶⣾⡶⠚⠒⠚⠒⠚⠛⠲⠒⠛⠒⠛⠒⠊⠀ ⠀⣴⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⢛⠛⠛⠋⠉⠋⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⡟⣿⣿⣿⣿⡟⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⠀⠀⣿⣿⣻⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⡮⠻⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⢀⣤⣤⣄⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣀⣿⣿⣿⣿⣟⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠧⣿⡚⣿⣿⣿⣿⣿⣿⣥⣤⣄⣿⣿⣿⣿⣀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢿⠀⠼⣿⣄⣠⣆⠉⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢙⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⠙⠛⠛⠉⠉⠁⠀⠀⠓⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⣰⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⡄⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣿⣿⣿⣿⣿⣿⠚⠛⠛⠀⠉⠈⠛⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠙⠛⠛⠛⠙⠻⠿⠿⣿⣿⣿⣿⣿⡟⠛⢹⡿⠉⠈⠙⣿⣿⢸⣧⣤⠀⠀⠀⠀⠀⠀⠽⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣴⣤⣀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⣰⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣀⣀⣠⣄⣤⡄⠀⢀⣀⠀⠀⠹⣏⣱⣶⠇⠀⠸⡇⣴⣾⣿⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⣽⣿⣿⡛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣠⣿⣿⣿⣿⣤⣤⡤⢛⣭⣴⣄⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠉⠋⠙⠛⠛⠉⠀⢸⣿⣿⣿⣿⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⡇⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣷⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣬⣽⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣉⠉⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠛⠛⠛⢛⣻⣿⣿⣿⣿⣿⣿⡿⠃⠬⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠴⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⡿⢿⣿⣿⣟⣻⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠡⠾⣗⣷⡿⠟⠀⠈⠉⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠁⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠁⠀⠀⠀⠀⠀⠛⠋⠃⠈⠉⠁⠘⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⠟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⠶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠀⠀⢀⣀⠀⢀⡀⠀⣀⠀⡀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢹⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢺⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣏⡝⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣿⣿⣻⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⠀⣼⠀⠘⢿⠀⢸⠀⢠⠀⢸⠀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⠷⣶⡛⠷⣶⣾⣿⠶⠶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣟⣿⣿⣶⣶⣾⡶⠚⠒⠚⠒⠚⠛⠲⠖⠛⠒⠛⠒⠊⠀ ⠀⣴⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⢛⠛⠛⠋⠉⠋⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣿⣿⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⠀⠀⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⡮⠻⠾⡿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⢁⣤⣤⣌⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣟⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠧⣿⡺⣿⣿⣿⣿⣿⣿⣥⣤⡄⣿⣿⣿⣿⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢿⠀⠾⣿⣄⣠⣆⠉⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢙⣹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡟⣿⣿⣿⣿⠙⠛⠛⠉⠉⠁⠀⠀⠓⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢻⣰⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣿⠀⠀⠀⠀⠀⠀⠠⣤⣄⣿⣿⣿⣿⣿⣿⠙⠛⠛⠀⠈⠁⠛⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠙⠛⠛⠛⠙⠻⠿⢿⣿⣿⣿⣿⣿⡟⠛⢻⡿⠉⠈⠉⣿⣿⢸⣿⣯⣶⠀⠀⠀⠀⠀⠉⠛⠾⣿⣿⣿⣿⣿⣿⣤⣤⣤⣴⣤⣀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⣰⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣀⣀⣠⣀⣤⡄⠀⢀⣀⠀⠀⠹⣏⣱⣶⠇⠀⠸⡇⣴⣾⣿⣿⣿⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⡛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣠⣿⣿⣿⣿⣤⣤⡤⢛⣭⣴⣄⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⢻⣿⡏⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠉⠋⠉⠙⠛⠉⠀⢸⣿⣿⣿⣿⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠⣿⡷⠀⠀⠀⠀⠀⠩⣿⣿⣿⣿⣷⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣬⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣴⣾⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣀⠉⠈⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠛⠟⡿⢿⣿⣿⣿⣿⣿⡿⠃⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠴⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⡿⢿⣿⣿⣟⣻⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠾⣗⣷⡿⠏⠁⠈⠉⠉⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠁⠀⠀⠙⣿⣿⣿⣽⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠘⠋⠃⠈⠉⠁⠘⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⢟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢓⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⢀⡀⣀⠀⠀⢀⣀⠀⢀⡀⠀⣀⠀⡀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⢹⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢺⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣏⠽⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠙⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢸⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣷⣿⣻⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⠀⣼⠀⠘⢿⠀⢸⠀⢠⠀⢸⠀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⠷⢶⠟⠷⣶⣾⣿⢶⠶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣏⣿⣶⣶⣾⠶⠞⠒⠚⠒⠚⠛⠲⠖⠛⠒⠛⠒⠊⠀ ⠀⣴⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⢛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣿⣿⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣦⣶⠀⠀⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⡮⠻⠾⡿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⢉⣀⣀⣉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣟⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠧⣿⡺⣿⣿⣿⣿⣿⣿⣤⣤⡄⣾⣿⣿⣿⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢻⠀⠼⣿⣀⣠⣆⠉⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢙⣽⣿⣿⢸⣿⣷⡄⠀⣤⠀⠀⠀⠀⠀⠀⠩⣿⡯⣿⣿⣿⣿⠙⠛⠛⠉⠉⠁⠀⠀⠓⠂⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⢰⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⣼⡿⡀⠀⠀⠴⡤⠔⣿⣿⣿⣿⣿⣿⠘⠛⠛⠀⠈⠁⠚⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠙⠛⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠛⢹⡿⠉⠈⠙⣿⣿⢸⣿⢿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣤⣤⣤⣴⣤⣀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⣰⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⣀⣀⣠⣄⣤⡄⠀⢀⣀⠀⠀⢹⣏⣱⣶⠇⠀⠸⡇⣴⣾⣿⣿⣿⠈⢲⣿⡿⢟⣿⡇⠀⠀⠀⣀⣤⣶⣄⠀⠙⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣤⣿⣿⣿⣿⣤⣤⡤⢛⣭⣴⣄⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠀⠀⣿⣿⠀⠀⠀⣸⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠈⠉⠉⠉⠛⠉⠀⢸⣿⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⠀⠀⠀⠨⣿⣿⣿⣿⣷⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣭⣭⣽⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣶⣶⣾⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣀⠉⠀⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠛⠛⡿⣻⣿⣿⣿⣿⣿⡿⠃⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠴⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⡿⢿⣿⣿⣟⣻⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠾⣗⣷⡿⠟⠀⠈⠉⠉⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠁⠀⠀⠙⣿⣿⣿⣟⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠁⠀⠀⠀⠀⠀⠙⠉⠋⠈⠉⠉⠘⣿⣯⡼⣿⣿⣿⣿⣿⣿⣿⣿⠟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⠀⠀⢀⣀⠀⠀⢀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠀⠀⢀⣀⠀⢀⡀⠀⡀⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⠹⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢺⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣏⡙⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠑⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢰⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⣏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣷⣿⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⠀⣸⠀⠘⢿⠀⢸⠀⢠⠀⢸⠀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⢳⡶⡟⠷⣶⣾⣿⢶⠶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣟⣽⣶⣶⣾⠶⠚⠒⠚⠒⠚⠛⠲⠖⠛⠒⠛⠒⠊⠀ ⠀⣴⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⣛⠛⠛⠛⠙⠋⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⣿⣿⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠀⠀⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⡨⠻⠾⡿⠿⡿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⣀⣀⡉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣾⣿⣟⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠧⣿⡚⣿⣿⣿⣿⣿⣿⣤⣤⡄⣾⣿⣿⣿⣀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣴⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢿⠀⠼⣿⣀⣠⣆⠉⣿⣿⣿⣿⣿⣟⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢙⡩⣿⣿⠀⢛⣿⣿⣿⣿⣷⡀⣶⠀⠀⠀⠁⢻⡣⣿⣿⣿⣯⠙⠛⠛⠉⠉⠁⠀⠀⠓⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢹⢰⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⡿⠿⣿⡿⣿⣿⣁⡀⠐⠀⠿⣿⣿⣿⣿⣿⠛⠛⠛⠀⠀⠁⠒⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠙⠚⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠛⢻⡿⠉⠈⠙⣿⣿⠀⣀⢠⣜⣛⣽⣿⡿⣿⠇⠀⠀⠀⠀⠀⠈⠉⢻⣦⣤⣤⣴⣤⡀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⣰⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⣀⣀⣀⣀⣀⡀⠀⢀⣀⠀⠀⢸⣏⣱⣶⠇⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⠀⠉⠚⠛⢋⣴⡟⠀⣀⣤⣶⣄⡀⠀⠀⠀⠙⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⣠⣿⣿⣿⣿⣤⣤⡤⢋⣭⣴⣄⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠰⣶⣤⣀⠀⢠⣼⣿⡇⣸⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠄⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠉⠉⠉⠋⠉⠀⢸⣿⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣧⣾⣿⣿⠇⠨⣿⣿⣿⣿⣷⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣧⣾⣦⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣈⠈⠀⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠛⠛⠛⠛⣻⢿⣿⣿⣿⣿⣿⡿⠃⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⠿⢿⣿⣿⣟⣻⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠾⣗⣷⡿⠟⠀⠈⠉⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡘⠁⠀⠀⠙⣿⣿⣿⠟⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠋⠃⠈⠉⠉⠘⣿⣷⡼⣿⣿⣿⣿⣿⣿⣿⣿⠟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠰⠰⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⠀⠀⢀⣀⠀⠀⢀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠀⠀⢀⣀⠀⢀⡀⠀⡀⠀⡀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⠹⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢾⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣏⡙⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠑⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢰⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⡏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣷⣾⣻⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⠀⣼⠀⠘⢿⠀⢸⠀⢠⠀⢸⠀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⠳⡶⡛⡷⣶⣾⡿⠶⠶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣿⣽⣶⣶⣾⠶⠚⠒⠚⠒⠚⠛⠲⠖⠛⠒⠛⠒⠊⠀ ⠀⣴⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⡛⡛⠛⠛⠛⠙⠉⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⣿⣿⣿⣿⡟⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣲⣦⠀⠀⣿⣿⢽⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⡨⠹⠞⠿⠿⠿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⣀⣀⡉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣾⣿⣟⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠧⣿⡚⣿⣿⣿⣿⣿⣿⣤⣤⡄⣾⣿⣿⣿⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢻⠀⠸⣿⣀⣠⣆⠉⣿⣿⣿⣿⣿⣟⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣙⡹⣿⣿⠀⠀⠀⠀⢘⣻⣿⣷⣿⣿⣀⡿⠈⢻⡗⣿⣿⣿⢽⠙⠛⠛⠉⠉⠁⠀⠀⠓⠂⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢹⢰⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⠟⢩⣿⠯⣿⡏⡠⠛⠻⠿⠿⣿⣿⠈⠛⠛⠀⠀⠀⠒⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠻⠟⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⡟⠛⢹⡿⠉⠈⠉⣿⣿⠀⢀⠀⠀⠀⠙⠷⣶⣿⡿⢓⡏⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⣰⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⣀⣀⣀⣀⣀⡀⠀⢀⣀⠀⠀⢹⣏⣰⣶⠇⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⡀⠀⠀⣀⡀⠉⢁⣴⣿⣥⣶⣄⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⣠⣿⣿⣿⣿⣤⣤⡤⢛⣭⣴⣄⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣨⣭⣿⣿⣿⣿⣿⣿⣿⣿⡷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⢸⣿⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⠳⣶⣾⣿⣿⣯⣿⣿⣿⣿⣷⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣭⣭⣭⣭⣽⣿⣽⣿⣿⣿⣿⣿⣿⣴⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣴⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣀⠈⠈⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡋⠛⠋⠛⠛⡻⣿⣿⣿⣿⣿⣿⡿⠃⡤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⠿⢿⣿⣿⣟⡻⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠾⣗⣷⡿⠏⠀⠈⠉⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡸⠁⠀⠀⠙⣿⣿⣿⡏⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⠁⠂⠈⠉⠁⠘⣿⣷⡼⣿⣿⣿⣿⣿⣿⣿⣿⠟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠠⠴⠶⠆⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢙⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⠀⠀⢀⣀⠀⠀⢀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠀⠀⢀⣀⠀⢀⡀⠀⡀⠀⡀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⠹⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢾⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣏⠙⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠑⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢰⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⡏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣷⣾⣿⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⠀⢸⠀⠘⢿⠀⢸⠀⢠⠀⢸⠀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠲⠓⣶⡛⠷⣶⣾⡿⠶⠶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣟⣛⣽⣶⣶⣾⠶⠚⠒⠚⠒⠚⠛⠲⠒⠛⠒⠛⠒⠊⠀ ⠀⣴⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⡛⠛⠛⠛⠛⠙⠉⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⣿⡟⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⠀⠀⣿⣿⣻⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⡨⠻⠜⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⣀⣀⡉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣤⡀⠀⠀⠀⢀⣀⣿⣿⣾⣿⣟⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠧⣿⡚⣿⣿⣿⣿⣿⣿⣤⣤⣄⣼⣿⣿⣿⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⡆⠀⡀⣸⣿⣿⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢻⠀⠸⣿⣀⣠⣆⠉⣿⣿⣿⣿⣿⣟⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢙⡹⣿⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡸⢏⣿⣿⣿⢽⠙⠛⠛⠉⠉⠁⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢻⢰⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠙⣉⠼⠿⣳⣿⠀⠚⠻⠿⣿⠈⠛⠛⠀⠈⠀⠓⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠻⠟⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⡟⠛⢹⡿⠉⠈⠉⣿⣿⠀⢀⠀⠀⠀⠀⠀⠀⠹⠿⡿⠿⢋⣴⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⣰⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢀⣀⣀⣀⣀⡀⠀⢀⣀⠀⠀⢸⣏⣱⣶⠇⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⣤⣿⣿⣿⣿⣤⣤⡤⢛⣭⣴⣄⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⢸⣿⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠿⣯⣿⣿⣿⣿⣷⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣭⣭⣭⣭⣭⣿⣯⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣧⣾⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣀⠈⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠛⠛⠛⠛⡻⣿⣿⣿⣿⣿⣿⡿⠃⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⠿⢿⣿⣿⣟⣻⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠾⣗⣷⡿⠟⠀⠈⠉⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡘⠁⠀⠀⠙⣿⣿⣿⢿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠁⠘⣿⣷⡼⣿⣿⣿⣿⣿⣿⣿⣿⠟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⠶⠄⠠⠴⠶⠆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠀⠀⢀⣀⠀⢀⡀⠀⡀⠀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⠹⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢾⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣏⠙⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠑⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢰⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⡏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣷⣾⣻⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⠀⣼⠀⠘⢿⠀⢸⠀⢠⠀⢸⠀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⠷⡖⡟⡷⣶⣾⣿⠶⡶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣗⣿⣶⣶⣾⡶⠚⠒⠚⠒⠚⠛⠲⠖⠛⠒⠛⠒⠊⠀ ⠀⣴⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⡛⣛⡛⠛⠛⠛⠋⠛⠋⠉⠉⠉⠉⠉⠙⣧⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⣿⣿⣿⣿⡟⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⡨⠺⠞⠿⠿⢿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⣁⣀⡙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣷⣦⡀⠀⢀⣿⣿⣾⣿⣟⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠦⣿⡚⣿⣿⣿⣿⣿⣿⣥⣤⣄⣼⣿⣿⣿⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⣿⣗⣦⡀⢠⣿⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢿⠀⠼⣿⣀⣠⣆⠉⣿⣿⣿⣿⣿⣟⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢙⡹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡿⢿⣿⣿⣧⢻⣿⠿⠙⠛⠛⠉⠉⠁⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⢰⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣔⣛⣫⣿⡇⠸⠿⠘⠛⠛⠀⠈⠀⠒⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠻⠟⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⡟⠛⢹⡿⠉⠈⠙⣿⣿⠀⢁⠀⠀⠀⠀⠀⠀⠀⠘⠌⠛⠿⠿⣛⣱⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⣰⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⣀⣀⣀⣀⣀⡀⠀⢀⣀⠀⠀⢹⣏⣱⣶⠇⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⣤⣿⣿⣿⣿⣤⣤⡤⢛⣭⣴⣄⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⢸⣿⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣷⣿⣿⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣀⠈⠈⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠙⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⡿⠃⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⠿⢿⣿⣿⣟⣻⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠾⣗⣶⡿⠏⠁⠈⠉⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡘⠁⠀⠀⠙⣿⣿⣿⢟⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠁⠀⠈⠉⠁⠘⣿⣷⡼⣿⣿⣿⣿⣿⣿⣿⣿⠟⡽⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⡬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⠀⠀⢀⣀⠀⠀⢀⣀⣀⣀⣀⡀⠀⢀⣀⣀⣀⠀⠀⢀⣀⠀⠀⠀⠀⡀⠀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⠹⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢺⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣏⠹⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠑⢾⡗⠛⢺⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢰⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⡏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣷⣾⣻⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⠀⢹⠀⠘⢿⠀⢸⠀⢠⠀⢸⠀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⠷⡖⡟⠷⣶⣾⡿⠶⠶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣶⣽⣶⣶⣾⡶⠚⠒⠚⠒⠚⠛⠲⠒⠛⠒⠛⠒⠊⠀ ⠀⣴⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⡛⢛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠙⣧⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠋⣻⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⡨⠻⠾⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⣁⣈⡙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣷⡄⠀⠀⢹⣿⣟⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠦⣿⡺⣿⣿⣿⣿⣿⣿⣥⣤⡄⣼⣿⣿⣿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣿⣿⣟⣳⡆⠀⣸⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢿⠀⠼⣿⣀⣠⣆⠉⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢙⡻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣛⣿⣿⣇⠸⠙⠛⠛⠉⠉⠁⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⢰⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣾⣶⣟⣯⣽⣿⠐⠛⠛⠀⠈⠀⠒⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠻⠿⠟⠻⠿⢿⣿⣿⣿⣿⣿⣿⡟⠛⢹⡿⠉⠈⠉⣿⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠯⠿⠟⢻⣿⣛⣡⠆⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⣰⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⢀⣀⣀⣀⣀⡀⠀⢀⣀⠀⠀⢹⣏⣱⣶⠇⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣤⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⣤⣿⣿⣿⣿⣤⣤⡤⢛⣭⣴⣄⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⢸⣿⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣷⣿⣟⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣭⣭⣭⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣀⠀⠀⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⡿⠂⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⠿⢿⣿⣿⣟⣻⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠼⣗⣷⡿⠋⠀⠈⠉⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡘⠁⠀⠀⠙⣿⣿⣿⣟⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⠉⠃⠈⠉⠁⠘⣿⣷⡼⣿⣿⣿⣿⣿⣿⣿⣿⠟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⠀⠀⢀⣀⠀⠀⢀⣀⣀⣀⣀⡀⠀⢀⣀⣀⣀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⠹⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢺⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣏⠙⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠑⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢰⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⡏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣷⣾⣻⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⠀⣸⠀⠘⢿⠀⢸⠀⢠⠀⢸⠀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠲⠳⢶⠛⠷⣶⣾⡿⠶⠶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣟⣲⣼⣶⣶⣞⡶⠚⠒⠚⠒⠚⠛⠲⠒⠛⠒⠛⠒⠊⠀ ⠀⣴⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⡛⠛⠛⠛⠋⠋⠉⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠏⣿⣿⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⡨⠺⠞⠿⠿⡿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⢁⣈⡙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣷⣦⠀⠀⢙⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀ ⠀⣿⠀⢉⠁⠤⠦⣿⡚⣿⣿⣿⣿⣿⣿⣤⣤⡄⣼⣿⣿⣿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢿⣿⣿⣓⣤⠀⢸⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢿⠀⠸⣿⣀⣠⣆⠉⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢙⡩⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣛⣻⣿⣿⠀⠛⠉⠉⠁⠀⠀⠒⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⢰⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⣾⣿⣿⣶⣞⣫⣽⡿⠀⠀⠈⠀⠓⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠿⠿⠿⠻⠿⢿⣿⣿⣿⣿⣿⣿⡟⠛⢹⡿⠉⠈⠙⣿⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⣰⢶⣀⣿⣿⡿⠟⢻⣿⣛⣡⠆⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⣰⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢀⣀⣀⣀⣀⡀⠀⢀⣀⠀⠀⢹⣏⣰⣶⠇⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⡀⠀⠀⠀⠀⠀⠀⠋⣁⣤⣶⣄⠀⣴⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⣤⣿⣿⣿⣿⣤⣤⡤⢛⣭⣴⣄⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⢸⣿⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣷⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣀⠀⠈⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠋⠛⠛⠛⡿⣿⣿⣿⣿⣿⣿⡿⠃⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⠿⢿⣿⣿⣟⣻⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠼⣗⣶⡿⠋⠀⠈⠉⠉⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡘⠁⠀⠀⠙⢿⣿⣶⣚⢿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠁⠂⠈⠉⠁⠘⣿⣷⡼⣿⣿⣿⣿⣿⣿⣿⣿⠟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⠶⠄⠠⠴⠶⠆⠀⠀⠀⠀⠀⡬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢓⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⠀⠀⢀⣀⠀⠀⢀⣀⣀⣀⣀⡀⠀⣀⢀⣀⣀⠀⠀⢀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⠹⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢺⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣏⠹⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠑⢾⡗⠛⢺⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢰⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⡏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣷⣾⣻⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⠀⣸⠀⠘⢿⠀⢸⠀⢠⠀⢸⠀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠲⠷⢶⠛⠷⣶⣾⣿⠶⠶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣆⣼⣶⣶⢾⡶⠚⠒⠚⠒⠚⠛⠲⠒⠛⠒⠛⠒⠊⠀ ⠀⣴⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⡛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠙⣧⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⢿⣿⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀ ⠀⣿⠀⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⡨⠺⠚⠿⠿⢿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⢁⣈⡙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⣦⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠦⣿⡚⣿⣿⣿⣿⣿⣿⣥⣤⡄⣼⣿⣿⣿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽⣿⣿⣓⣀⠀⢸⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀ ⠀⢿⠀⠸⣿⣀⣠⣆⠉⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢙⡩⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⠀⣼⣿⣛⣻⣿⣿⠀⠋⠉⠁⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⢰⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⣾⣿⣿⣿⣦⣛⣻⣽⣿⠀⠈⠀⠒⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠿⠿⠿⠻⠿⢿⣿⣿⣿⣿⣿⣿⡟⠛⢹⡿⠉⠈⠉⣿⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⣰⣎⢤⣿⣿⣿⡿⠟⢿⣿⣛⣡⠄⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⣰⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢀⣀⣀⣀⣀⡀⠀⢀⣀⠀⠀⢹⣏⣰⣶⠇⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⡀⠀⠀⠀⠀⠀⠀⠚⣋⣥⣶⣄⠀⢀⣴⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⣤⣿⣿⣿⣿⣤⣤⡤⢛⣭⣴⣄⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡷⣾⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⢸⣿⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣷⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣭⣭⣭⣭⣽⣽⣽⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣽⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣀⠀⠀⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠙⠛⠛⠻⣟⣿⣿⣿⣿⣿⡿⠃⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⠿⢿⣿⣿⣟⡻⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠾⣗⣷⡿⠏⠀⠈⠉⠉⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⠘⠁⠀⠀⠙⢿⣿⣷⣎⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⠁⠂⠈⠉⠁⠘⣿⣧⡼⣿⣿⣿⣿⣿⣿⣿⣿⠟⡽⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠠⠴⠶⠆⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⠀⠀⢀⣀⠀⠀⢀⣀⣀⣀⣀⡀⠀⣀⢀⣀⣀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⠹⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢺⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣏⡹⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠑⢾⡗⠛⢺⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢰⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⡏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣷⣺⣻⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⠀⣸⠀⠘⢿⠀⢸⠀⢠⠀⢸⠀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠲⠷⡶⠛⠷⣶⣾⡿⠶⠶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣗⣿⣶⣶⣾⡶⠚⠒⠚⠒⠚⠛⠲⠒⠛⠒⠛⠒⠊⠀ ⠀⣴⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⡛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢿⣿⣿⣿⡟⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀ ⠀⣿⠈⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣦⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⡨⠻⠞⠿⠿⠿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⢁⣈⡛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣴⣾⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀ ⠀⣿⠀⢉⠁⠤⠦⣿⡚⣿⣿⣿⣿⣿⣿⣥⣤⡄⣼⣿⣿⣿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠨⣿⣿⣿⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢿⠀⠸⣿⣀⣠⣆⠉⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢙⡹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣁⣿⣧⣾⣟⣻⣿⣿⣇⠠⠆⠀⠀⠓⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⢰⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⣾⣿⣿⣿⣿⣿⣔⣛⣛⣾⡟⠀⠐⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠿⠿⠿⠻⠿⢿⣿⣿⣿⣿⣿⣿⡟⠛⢹⡿⠉⠈⠉⣿⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⢬⡦⣜⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣃⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⣰⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢀⣀⣀⣀⣀⡀⠀⢀⣀⠀⠀⢹⣏⣰⣶⠇⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⡀⠀⠀⠀⠀⠀⠀⠛⣛⣷⣿⣍⡉⠉⠀⢠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣤⣿⣿⣿⣿⣤⣤⡤⢛⣭⣴⣄⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡷⡀⣰⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⢸⣿⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣁⠀⠈⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠛⠛⠛⠛⡿⢿⣿⣿⣿⣿⣿⡿⠂⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⠿⢿⣿⣿⣟⣻⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠼⣗⣷⡿⠋⠀⠈⠉⠉⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡘⠁⠀⠀⠙⢿⣿⣷⣙⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠁⠂⠈⠉⠁⠘⣿⣷⡼⣿⣿⣿⣿⣿⣿⣿⣿⠋⣽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⠶⠄⠠⠴⠶⠆⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢓⣷⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⠀⠀⢀⣀⠀⠀⢀⣀⣀⣀⣀⡀⢀⣀⣀⡀⣀⠀⠀⢀⣀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⠹⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢺⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣏⡙⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠑⢾⡗⠛⢾⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢰⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⡏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣷⣾⣻⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⠀⣼⠀⠘⢿⠀⢸⠀⢠⠀⢸⠀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠲⢳⠶⠛⢷⣶⣾⡿⢶⠶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣿⣆⣼⣶⣶⣾⣶⠚⠒⠚⠒⠚⠛⠲⠒⠛⠒⠛⠒⠊⠀ ⠀⣴⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⡛⢛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠙⣷⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⣿⣿⣿⣿⡟⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀ ⠀⣿⠀⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⠀⠀⣿⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⡨⠻⠸⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⢁⣈⡛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⠀⢀⣶⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠦⣿⡚⣿⣿⣿⣿⣿⣿⣤⣤⡄⣼⣿⣿⣿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⢨⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢿⠀⠼⣿⣀⣠⣆⠉⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢙⡻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡃⣿⣿⣿⢷⣿⣿⣿⣿⣿⠃⢠⠀⠒⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⢰⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣀⣾⣿⣿⣿⣿⣿⠚⣷⣭⣭⣵⣿⡀⢉⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠿⠿⠿⠻⠿⢿⣿⣿⣿⣿⣿⣿⡟⠛⢹⡿⠉⠈⠉⣿⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⣼⣯⣼⣿⣿⣿⣿⣿⣿⣤⡝⣿⣿⣿⣿⡁⠀⠂⠀⠀⠀⠀⠀⠀⠀⣰⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢀⣀⣀⣀⣀⡀⠀⢀⣀⠀⠀⢹⣏⣱⣶⠇⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⡀⠀⠀⠀⠀⠀⠀⠚⣛⣽⣿⣯⡉⠉⠉⠉⢁⣼⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣤⣿⣿⣿⣿⣤⣤⡴⢛⣭⣴⣄⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡷⡀⠀⣠⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠄⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⢸⣿⣿⣿⣿⢀⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣷⣷⣰⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣭⣭⣭⣭⣽⣽⣯⣿⣿⣿⣿⣿⣿⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣀⠀⠈⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠋⠛⠛⣿⢿⣿⣿⣿⣿⣿⡿⠋⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⠿⢿⣿⣿⣟⡻⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠾⣗⣷⡿⠏⠀⠈⠉⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡘⠁⠀⠀⠙⣿⣿⣿⡟⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⠉⠃⠈⠙⠁⠘⣿⣷⡼⣿⣿⣿⣿⣿⣿⣿⣿⠟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⠶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⢓⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⠀⠀⢀⣀⠀⠀⢀⣀⣀⣀⣀⠀⠀⣀⣀⡀⣀⠀⠀⢀⣀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⠉⢿⠉⠉⡏⠉⡿⠋⡉⠙⡏⠉⡉⠙⡾⠋⡉⠙⡞⠉⡉⠹⡞⠉⡉⠻⡏⠉⣉⣉⠉⢉⣹⣿⠉⡏⢹⠉⢹⡾⠋⡉⠙⡏⠉⡏⠉⡏⠉⣉⡟⠉⡉⠹⡉⠉⢹⠉⢹⣾⠉⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⠻⠉⡇⠀ ⠀⢸⠀⠀⠈⠀⠀⡇⠀⡇⠀⣧⣤⡇⠀⠃⠠⡇⠀⡇⠀⣧⡀⠙⢲⡇⠀⡇⠀⡇⠀⠛⣿⠀⢸⣏⠙⠶⣷⣿⠀⢸⡇⠀⡇⠀⣧⠀⠇⠀⡇⠀⠛⣧⡀⠑⢾⡗⠛⢺⠀⢸⣿⠀⢸⠀⠀⠀⢸⠀⢸⠀⢸⠆⠀⢰⡇⠀ ⠀⢸⠀⢸⠀⡇⠀⡇⠀⣇⠀⠇⠀⡇⠀⡇⠀⣇⠀⠇⠀⡏⠉⠇⠀⡇⠀⠇⢀⡇⠀⣿⣿⠀⢸⣷⣾⣻⣿⣿⠀⠸⣇⠀⠇⠀⣿⠀⠀⢰⡇⠀⠿⡏⠉⠇⠀⣿⠀⢼⠀⠘⢿⠀⢸⠀⢠⠀⢸⠀⠸⠀⢸⠀⢠⠀⣧⠀ ⠀⠈⠒⠚⠒⠓⠒⠓⠒⠛⠳⠶⠞⠓⠶⠷⠶⠟⠷⣶⣾⡿⢶⠶⢾⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣶⣿⣶⣶⣾⣟⣗⣾⣶⣶⣾⢶⠚⠒⠚⠒⠚⠛⠲⠒⠛⠒⠛⠒⠊⠀ ⠀⣴⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⢛⠛⠛⠋⠋⠉⠉⠉⠉⠉⠉⠙⣧⠀ ⠀⣿⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⣿⡏⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀ ⠀⣿⠀⣷⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣲⣶⠀⠀⣿⣧⢹⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⡨⠚⠞⠿⠿⠿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⢁⣈⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣼⡀⢠⣶⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⢉⠁⠤⠦⣿⡚⣿⣿⣿⣿⣿⣿⣤⣤⡄⡼⣿⣿⣿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣧⣾⣿⣷⣾⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢻⠀⠸⣿⣀⣠⣆⠉⣿⣿⣿⣿⣿⣟⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢙⡸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡉⣿⣿⣿⢻⠙⣟⣲⣾⡿⣿⡇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⢰⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣷⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⠘⠛⢿⣶⣶⣾⣿⣁⠘⠁⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀ ⠀⢸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠿⠿⠿⠻⠿⢿⣿⡿⣿⣿⣿⣿⡟⠛⢹⡿⠉⠈⠉⣿⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⣰⣴⢿⣿⣿⣿⣿⣿⣿⣤⣤⣄⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢀⣀⣀⣀⣀⡀⠀⢀⣀⠀⠀⢸⣏⣰⣶⠇⠀⠸⡇⣴⣾⣿⣿⣿⠀⡀⡀⠀⠀⠀⠀⠀⠀⠛⣃⣵⣿⣭⠉⠉⠉⠉⠈⢀⣽⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣤⣿⣿⣿⣿⣤⣤⡶⢛⣭⣴⡄⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡷⡀⠀⠀⣠⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣿⠀ ⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⢸⣿⣿⣿⣿⣀⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣰⣿⣷⡶⠀⠀⠀⠀⠨⣿⣿⣿⣿⣷⣷⣀⣼⣿⣿⣿⣿⣇⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣭⣭⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣭⣭⣭⣯⣽⣽⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣾⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⣀⠀⠀⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠙⠙⠉⠛⣻⢿⣿⣿⣿⣿⣿⡿⠂⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⡏⠀⠀⠀⠀⠀⠀⣴⠿⢿⣿⣿⣟⡻⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠾⣗⣶⡿⠋⠀⠈⠉⠉⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⢰⣾⠄⡘⠁⠀⠀⠙⣿⣿⣧⠞⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠁⠁⠀⠉⠁⠘⣿⣧⡼⣿⣿⣿⣿⣿⣿⣿⣿⠟⡽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⠶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⡬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡿⢓⣷⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ䷩ 𝚕𝚒𝚗𝚎 4000 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2021/11/24/thanksgiving-downtime/#comments Gemini version at gemini://gemini.techrights.org/2021/11/24/thanksgiving-downtime/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.24.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Changing_the_Arrangement_While_News_is_a_Bit_Slow(er)⠀✐ Posted in Site_News at 6:53 pm by Dr. Roy Schestowitz Video_download_link | md5sum 94e8fbe5aa2f83a300a8e55632e41169 http://techrights.org/videos/thanksgiving-shuffle.webm Summary: I’ve made it easier for myself to keep abreast of things like IRC channels and networks (incidentally, a day ago Freenode reopened to anonymous logins) and I’ve improved monitoring of the Web sites, Gemini capsule etc. (this video is unplanned and improvised) TODAY we’ve hardly published anything, but that does not mean we weren’t busy (in Git and other things, such as arguing_over_the_telephone). We’ll come back to to the usual routines and get back to normal by the end of this week for sure. 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Raucous laughter: Black Friday⦈ We don’t have a holiday here, except the consumerism festival being imitated (“Black Friday”) and polluting_the_World_Wide_Web_a_great_deal. It has become painful to watch some so-called ‘Linux’ so-called ‘news’ sites pushing Windows in “Sponsored Posts” (we won’t name the culprits). The Web has become frustratingly bad. So today I decided to show some of the tasks that were shuffled around or moved between screens and computers. There’s still 5 of them in total connected_over Barrier_and_Synergy and there’s a Palm PDA that occasionally comes in handy. They’re all reasonably_cheap, some are very old, but they help get work done on a low budget. Remember that Friday is Buy_Nothing_Day. █ 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Buy Nothing Day⦈ This photo (C) Lars Aronsson – Own_work,_CC_SA_1.0 ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⡀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀ ⣿⠁⠀⠄⠃⠀⠀⠉⣽⡟⠶⢤⣤⣄⡉⠛⠻⢿⣿⣿⣿⣿⣿⠗⠚⠉⡟⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣻⣽⠾⢿⣿⡿⠇⠀⣀⣠⣴⣖⣺⣿ ⣿⣤⣤⣀⠀⠀⠀⠀⠈⡇⠀⠀⠈⠉⠛⣻⠶⣤⣈⡙⠛⢿⣥⣧⣼⣶⣿⣶⣷⣹⠞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣯⣿⣟⣿⣿⠿⣻⣽⣾⣿⣿⣿⣿⠿⣿⠿⢷⣦⣯⣿⢻⣷⣤⣶⠿⠿⠿⠛⠋ ⣟⡓⠒⠿⡄⠀⠈⣹⣦⢰⠀⣤⣄⠀⠀⣤⣤⣴⣮⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⣿⣿⣟⠛⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⠏⣾⣿⣿⡿⣿⣿⣿⣇⣠⣤⣾⡿⠿⢻⣿⣿⡏⠀⠀⠀⠀⠤⢈⣀ ⣿⣿⣿⣯⣴⣂⣾⣿⣿⣾⡜⠓⠚⠀⠀⣿⣿⡿⠩⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡿⣿⣿⡏⠉⡯⠉⠉⠀⠈⠀⠀⡀⡶⣿⣶⣿⣿⣿⣿⣿⡿⠿⣬⣽⣿⣿⡟⠉⠉⠀⠀⠀⠀⣿⣿⠀⠀⣶⠀⢸⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠄⠀⠀⠀⠀⠈⠁⠀⠹⣿⣟⣿⣿⡟⠿⣿⣿⠉⣥⣿⣿⡇⠀⡇⠀⠀⠀⠀⣿⣿⡆⠀⣿⠀⢸⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⢿⡻⢿⡟⠀⠀⠀⠒⢀⠀⠀⠘⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠈⢽⣀⣿⣩⣿⣇⠐⣿⣀⣀⣀⣲⣿⣿⡇⠀⢿⢄⡰⠿⠿⠿ ⣿⣿⣿⡟⠟⠋⡿⠻⡿⠛⣿⡟⠀⠀⠀⣿⣿⣟⣛⣛⣻⠁⣾⣧⡙⠿⢿⣿⡿⢙⢍⠀⢀⠀⠉⠉⡄⠀⢈⠀⠀⢀⡀⠰⠀⠄⢴⠎⠀⣸⣿⣿⡋⡠⣤⠀⠻⠟⠿⠻⣿⣿⠀⣀⠀⠀⠀⠀⣿⣿⡧⢀⣀⠀⠀⣀⣠⣤ ⣿⣿⠻⠀⠀⡂⣯⠀⣷⢀⣻⡇⠀⠀⢀⣿⣿⣷⠿⠋⠣⠲⣿⣿⣿⣿⣿⣿⣧⠀⠁⣦⣘⣯⡔⠀⠾⡈⣼⠳⠶⠿⠭⠭⣭⡤⠈⠀⢰⣿⣿⡿⡼⣾⣿⡇⠀⠀⠀⠀⢸⣿⠀⠸⠚⠃⠀⠀⣿⣿⡇⠀⠈⠈⠉⠏⠁⠈ ⣿⣿⠂⠀⠀⠁⣿⢸⣿⢸⡇⠃⠀⠀⠋⣽⣷⣶⣿⣇⠀⠉⠙⠉⠛⠻⣿⣿⣿⡇⣴⣿⡿⣿⣿⡍⠙⠇⠙⠀⠀⠀⠐⢾⣿⡇⠀⠀⢸⣿⣿⣿⢽⣿⣽⡇⠄⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⢻⠀⠀⠀⠃⣿⢸⣿⢸⡇⠘⠀⠀⠘⣿⣿⣿⣿⣿⣷⡠⣄⠀⠀⠀⣿⣿⠏⣡⣼⣿⣿⣾⣿⣷⠈⠀⠀⠀⠀⠀⢚⣺⣿⠀⠀⠀⣼⣿⣿⣿⠀⡇⣾⡗⠀⠀⠀⠈⢸⣿⣿⣷⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⣷⣌⠀⠐⠀⠀⣿⢸⣿⣸⣿⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣷⣿⣷⣀⠀⣿⣇⠀⣿⣿⣿⣿⣿⣿⣼⡀⠀⠀⠀⢤⣠⣤⣬⡭⠀⠀⠀⣿⣿⣸⣿⠀⠁⠀⠀⠀⠀⠀⠀⢘⣿⠈⢀⣆⣀⣀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⡧⠀⠀⢰⡄⢹⠀⣿⣿⣿⠀⠀⠀⠀⢀⡀⢍⣛⣿⣿⣿⣿⣿⣿⣶⣹⣷⡀⣿⣿⣯⣿⣿⣿⣿⡇⠀⠀⠀⠢⣤⣤⣤⣦⠀⠀⢰⣿⣿⣿⣿⠀⠘⠀⠀⠀⠀⠀⠰⠁⣿⢠⣮⣽⣾⡄⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠘⠃⠀⠀⢀⡇⢸⠀⣿⣿⠁⠀⠀⠀⠀⠈⠛⠮⠲⠿⠛⠻⢿⣿⣿⣿⣿⠿⠷⠸⣿⣿⡇⣙⢻⣿⡇⠀⠀⠀⠐⠿⠍⢹⠁⠀⠀⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢱⣿⣾⣿⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠘⠀⠀⠀⠘⠇⢸⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⢸⣿⣿⡿⢖⣳⣤⠄⢻⣿⡿⢿⡿⡟⢱⠀⠀⠀⠈⢸⣠⡆⠀⠀⠀⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠩⠟⢋⣰⣿⣿⠤⣤⠀⠀⠀⠀⠀⠀ ⠀⣤⠀⠀⠀⠀⠈⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⣜⣋⣭⣴⠀⠈⢿⣧⠸⣧⠁⠀⠀⠀⢠⣤⣾⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠄⠀⢰⡿⠋⠋⣤⣴⣷⣶⣄⡀⠀⠀⠀ ⠀⠿⠶⣶⠿⢷⠔⠰⠾⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣽⣯⠟⢉⣽⡇⠀⠀⢿⠀⠙⠀⠀⠀⠀⠀⠻⣸⣿⠇⠀⢀⣀⣽⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⢰⡏⠀⠃⢸⣿⣿⣿⣿⣿⠀⠈⠁⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⡀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀ ⣿⠁⠀⠄⠃⠀⠀⠉⣽⡟⠶⢤⣤⣄⡉⠛⠻⢿⣿⣿⣿⣿⣿⠗⠚⠉⡟⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣽⢾⣿⣿⡿⠇⠀⣀⣠⣴⣖⣾⣿ ⣿⣤⣠⣀⠀⠀⠀⠀⠈⡇⠀⠀⠈⠉⠛⣻⠶⣤⣈⡙⠛⢿⣥⣧⣼⣶⣿⣶⣷⣹⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣭⣿⣟⣿⣿⠿⣻⣽⣾⣿⣿⣿⡿⠿⣿⣿⢶⣦⣿⣿⢻⣷⣤⣶⣷⠿⠿⠛⠋ ⣟⠓⠺⠿⠄⠀⠈⣹⣤⢰⠀⣤⣄⠀⠀⣤⣤⣤⣯⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⣿⣿⣟⠛⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⠏⣾⣿⣿⡿⣿⣿⣿⣧⣠⣤⣶⡯⠿⢻⣿⣿⡏⠁⠀⠀⠀⠤⢈⣀ ⣿⣿⣿⣯⣴⣆⣾⣿⣿⣾⡜⠓⠚⠀⠀⣿⣿⡿⠨⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡿⣿⣿⡏⠉⠯⠉⠁⠀⠀⠀⠀⠀⡶⣿⣶⣿⣿⣿⣿⣿⡿⠿⣬⣽⣿⣿⡟⠉⠉⠀⠀⠀⠀⣿⣿⠀⠀⣖⠀⢸⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠄⠀⠀⠀⠀⠈⠁⠀⠹⣿⣛⣿⣿⡟⠿⣾⣿⠉⣤⣿⣿⡇⠀⣇⠀⠀⠀⠀⣿⣿⡆⠀⣿⠃⢸⣿⣿⣿ ⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣆⠀⠀⠀⣿⣿⣯⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⢿⡻⢿⡟⠀⠀⠀⠒⢀⠀⠀⠘⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠈⢽⣀⣿⣩⣿⣇⠐⣿⣀⣀⣀⣰⣿⣿⡇⠀⣿⣄⣰⠿⠿⠿ ⣿⣿⣿⡟⠛⠋⡿⠻⡿⠛⣿⡟⠀⠀⠀⣿⣿⣟⣛⣛⣻⠁⣾⣯⡙⠿⢿⣿⡿⢙⢍⠀⢀⠀⠉⠉⡄⠀⢈⠀⠀⢀⠀⠰⠀⠄⢴⠎⠀⣸⣿⣿⡋⡠⣤⠀⠻⠟⠿⠻⣿⣿⠀⣠⠀⠀⠀⠀⣿⣿⡧⢀⣀⠀⠀⣀⣠⣤ ⣿⣿⠹⠀⠀⡆⣯⠀⣷⢀⣻⡇⠀⠀⢀⣿⣷⣷⠿⡋⠡⠲⣿⣿⣿⣿⣿⣿⣧⠀⠁⣂⣘⣮⣔⠀⢾⡈⣼⠳⠶⠿⠭⠭⣭⡤⠈⠀⢰⣿⣿⡿⡼⣾⣿⡇⠀⠀⠀⠀⢸⣿⠀⠸⠂⠃⠀⠀⣿⣿⡇⠀⠀⠈⠉⠏⠉⠈ ⣿⣿⠀⠀⠀⠃⣿⢸⣿⢸⡇⠃⠀⠀⠋⣽⣶⣶⣿⣧⠀⠉⠙⠉⠛⠻⣿⣿⣿⡇⣴⣿⡿⣿⣿⡍⠙⠇⠙⠀⠀⠀⠀⡨⣿⡇⠀⠀⢸⣿⣿⣿⣝⣿⣽⡇⠄⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⢻⠀⠀⠀⠀⣿⢸⣿⢸⡇⠘⠀⠀⠘⣿⣿⣿⣿⣿⣷⡰⣄⠀⠀⠀⣿⣿⠏⣡⣼⣿⣿⣾⣿⢷⢈⠀⠀⠀⠀⠀⡔⣷⢿⠀⠄⠀⣼⣿⣿⣿⠀⡇⣾⡗⠀⠀⠀⠈⢸⣿⣿⣷⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⣧⡌⠀⠀⠀⠀⣿⢸⣿⣸⣿⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣷⣿⣷⣀⠀⣿⣇⠀⣿⣿⣿⣿⣿⣿⣼⡀⠀⠀⠀⢄⣠⣤⣭⡭⠀⠀⠀⣿⣿⣸⣿⠀⠁⠀⠀⠀⠀⠀⠀⢘⣿⠈⢀⣆⣀⣀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⢿⡷⠀⠀⢠⠄⢹⠀⣿⣿⡿⠀⠀⠀⠀⢠⡀⣉⣻⣿⣿⣿⣿⣿⣿⣶⣹⣿⡄⣿⣿⣧⣿⣿⣿⣿⡇⠀⠀⠀⢢⣤⣤⣤⣤⠀⠀⢰⣿⣿⣿⣿⠀⠘⠀⠀⠀⠀⠀⠰⠁⣿⣠⣮⣽⣾⡄⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠈⠁⠀⠀⢈⡇⢸⠀⣿⣿⠁⠀⠀⠀⠀⠈⠛⠮⠳⠟⠛⠻⢿⣿⣿⣿⣿⠿⠷⠼⣿⣿⣇⣙⢻⣿⡇⠀⠀⠀⠐⢏⢿⢩⠁⠀⠀⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢱⣿⣾⣿⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠇⢸⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⢸⣿⡿⣿⢖⣳⣦⠄⢻⣿⡧⢿⡿⡟⢹⠀⠀⠀⠈⢠⣄⡄⠀⠀⠀⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠹⠟⢋⣰⣿⣿⠤⣤⠀⠀⠀⠀⠀⠀ ⠀⣄⠀⠀⠀⠀⠈⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠠⡜⣋⣭⣴⠀⠈⢿⣯⠸⣧⠁⠀⠀⠀⢠⣤⣾⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠄⠀⢰⠿⠋⠋⣤⣴⣷⣶⣄⡀⠀⠀⠀ ⠀⠿⠶⣶⠿⢷⠔⠰⠾⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣭⣯⠝⢩⣽⡇⠀⠀⢿⡀⠙⠀⠀⠀⠀⠀⠳⣸⣿⠇⠀⢀⣀⣽⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⢰⡏⠀⠃⢸⣿⣿⣿⣿⣿⠀⠈⠁⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⡀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀ ⣿⠁⠀⠄⠃⠀⠈⠉⣽⡟⠶⢤⣄⣄⡉⠛⠻⢿⣿⣿⣿⣿⣿⡗⠚⠙⡛⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣻⣽⢾⣿⣿⡿⠇⠀⣀⣠⣴⣶⣿⣿ ⣿⣤⣠⣀⠀⠀⠀⠀⠈⡇⠀⠀⠈⠉⠛⣳⢶⣤⣈⡙⠻⢿⣥⣧⣬⣶⣿⣶⣷⣹⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣯⣿⣟⣿⣿⠿⣻⣵⣾⣿⣿⣿⣿⠿⣿⣿⢶⣦⣭⣿⢻⣷⣤⣴⣷⠿⠿⠛⠛ ⣟⡓⠺⠿⡄⠀⠈⣩⣦⢰⠀⣤⣄⠀⠀⣤⣤⣤⣯⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⣿⣿⣟⠻⢿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⠏⣾⣿⣿⡿⣿⣿⣿⣧⣠⣔⣲⡿⠿⢻⣿⣿⡏⠁⠀⠀⡀⠤⢈⣀ ⣿⣿⣿⣯⣴⣆⣾⣿⣿⣾⡜⢓⠚⠀⠀⣿⣿⡿⠩⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡿⣿⣿⡏⠉⠯⠉⠉⠀⠈⠁⠀⠀⡶⣿⣶⣿⣿⣿⣿⣿⡿⠿⣤⣽⣿⣿⡟⠉⠉⠀⠀⠀⠀⣿⣿⠀⠀⡴⠀⢸⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠄⠀⠀⠀⠀⠈⠁⠀⠹⣿⣛⣻⣿⡟⠿⣿⣿⠉⣥⣿⣿⡇⠀⡇⠀⠀⠀⠀⣿⣿⡆⠀⣿⠀⢸⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⣿⣿⣿⣿⣾⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⢿⡻⢿⡟⠀⠀⠀⠒⢀⠀⠀⠘⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠈⢽⣀⣿⣩⣿⣇⠐⣿⣀⣀⣀⣰⣿⣿⡇⠀⣿⢄⡰⠿⠿⠿ 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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 5035 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.24.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Links_24/11/2021:_Alpine_Linux_3.15_and_Endless_OS_4.0_Released⠀✐ Posted in News_Roundup at 4:59 pm by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈ § Contents⠀➾ * GNU/Linux o Distributions o Devices/Embedded * Free_Software/Open_Source * Leftovers * § GNU/Linux⠀➾ o § Audiocasts/Shows⠀➾ # ⚓ Arch_User_Reacts_To_Linus_Tech_Tips_Linux_Challenge_Pt_2_– Invidious⠀⇛ The second episode of the Linus Tech Tips linux challenge is out and this time we’re tackling game streaming under linux, this is something I am incredibly familiar with so I hope the commentary I add gives some extra context for why and how the issues occur # ⚓ Boosting_your_Linux_Server_Security_with_CrowdSec_– Invidious⠀⇛ CrowdSec is a cutting-edge security solution for your Linux servers. As an intrusion prevention system, its goal is to stop unauthorized access and prevent attacks. But unlike other IPS solutions, it does it a different way – by using knowledge as power. CrowdSec was covered on this channel before, but in this video, you’ll see an updated look complete with an overview of how to set up protection for WordPress as well. # ⚓ Linux_fanboy_reviews_Windows_11_–_Invidious⠀⇛ # ⚓ Floating_Panel_Devlog:_States,_Transitions,_Thickness…_I had_been_optimistic._–_Kockatoo_Tube⠀⇛ # ⚓ News_–_Watch_State_of_the_Word_at_a_Watch_Party_with_your WordPress_Friends_–_WordPress.org⠀⇛ State of the Word 2021 is just around the corner! Although attending State of the Word in person would be ideal, not all WordPress community members get to enjoy the experience of attending the speech live with friends. This year, as State of the Word is streamed live for the second time, we want to restore that in person camaraderie through State of the Word watch parties for WordPress Community members around the world. o § Kernel Space⠀➾ # ⚓ The_backbone_of_a_Linux_Industrial_I/O_driver⠀⇛ As part of recent projects, we had to dig into the Linux kernel Industrial I/O (IIO) subsystem with the goals of supporting a new ADC and adding new features to an existing driver. These tasks involved quite a few discussions between our engineering team and the IIO maintainers and reviewers. The aim of this blog post is to summarize the substance of these explanations to help others understand how an IIO kernel driver works and interacts with the core IIO subsystem. # ⚓ Intel_Posts_New_Iteration_Of_Key_Locker_Support_For_Linux_– Phoronix⠀⇛ With Intel Tiger Lake mobile processors introduced last year there has been good open-source support going back to launch, but a few of the more niche features have seen slower than normal handling for getting the features supported by the upstream Linux kernel. The latest patch series being revived now is for Intel Key Locker support. Just a few days ago I talked about Intel pursuing a new Indirect Branch Tracking (IBT) patch series as part of their Control-Flow Enforcement Technology (CET) introduced on Tiger Lake. After months of silence, another Tiger Lake feature is seeing revised kernel patches emerge this week and that is for Key Locker. # ⚓ EasyOS:_Kernel_5.10.81_compiled_with_improved_AMD_CPU support⠀⇛ I don’t have a PC with AMD CPU, so haven’t bothered much with configuring the kernel to work with them. However, some guys testing EasyOS are keen on them, so today have given it a closer look. o § Benchmarks⠀➾ # ⚓ AMD_P-State_v4_Linux_Testing_On_A_Ryzen_5_5500U⠀⇛ With AMD having published a new revision to their AMD P-State Linux CPU frequency scaling driver that they are working towards mainlining with a goal of better power efficiency on Linux, here are some initial benchmarks of that new patch series when using a Ryzen 5 5500U notebook. The amd-pstate driver was updated a fourth time this past week since its unveiling in September with a goal of delivering better performance / power efficiency over the generic ACPI CPUFreq driver used on Linux systems. AMD’s P-State driver makes use of ACPI CPPC that is supported on Zen 2 and newer processors for making more precise handling and better informed decisions around ramping up/down the performance state of the processor. o § Applications⠀➾ # ⚓ Where_in_the_Stack?⠀⇛ For one of my projects – not KDE-related – I have a parser, written in YACC / bison. To build the project, the bison grammar needs to be compiled (by the bison command) to C, and then the C can be compiled to the final executable. On my workstation, the bison step would fail when the build was run one-process-at-a-time in KDE konsole. Workarounds were really weird: build with a -j flag to build with more processes at once, or pipe the build-output to cat, or run the build in xterm instead of konsole. So where is the bug? In konsole, in bison, or in something underneath? It’s definitely something to do with the terminal emulator: here’s a screenshot of bison compiling a sample file successfully in xterm, and crashing in konsole, roxterm and alacritty. It crashes in cool- retro-term as well, but leaves the terminal itself in a messed-up-state. It also crashes on the FreeBSD text console. # ⚓ Wireshark_3.6.0_Release_Notes⠀⇛ Wireshark is the world’s most popular network protocol analyzer. It is used for troubleshooting, analysis, development and education. # ⚓ Wireshark_3.6_Network_Analyzer_Release_–_itsfoss.net⠀⇛ After a year of development, a new stable branch of the Wireshark 3.6 network analyzer has been released. Recall that initially the project developed under the name Ethereal, but in 2006, due to a conflict with the owner of the Ethereal trademark, the developers were forced to rename the project to Wireshark. The project code is distributed under the GPLv2 license. o § Instructionals/Technical⠀➾ # ⚓ Running_Linux_on_the_GPD_Pocket_3_mini-laptop_– Liliputing⠀⇛ The GPD Pocket 3 is a tiny laptop computer with an 8 inch touchscreen display, a swivel-hinge that allows you to fold the screen over the keyboard for use in tablet mode, and a modular port system that allows you to customize the little computer’s capabilities. # ⚓ How_to_install_phpMyAdmin_on_Ubuntu_20.04_LTS_using repository⠀⇛ Well, we can install phpMyadmin by manually downloading and setting its files along with Apache on Ubuntu. However, it could be difficult for a few users to go through various steps to configure phpMyAdmin, instead of that we can automate its installation using the phpMyadmin repository on Ubuntu 20.04 LTS Focal Fossa. phpMyAdmin is an open-source web platform developed in PHP to manage MariaDB or MySQL database server via a graphical web interface. Most of the hosting platforms come with this database web-based management application, already, however, if you are using some private virtual server or cloud hosting then you may need to install it manually. And here in this article, we learn that. # ⚓ How_to_Install_Icinga_2_on_Ubuntu_20.04_|_RoseHosting⠀⇛ In this article, we are going to explain about installing Icinga 2 Monitoring Software on Ubuntu 20.04. Icinga is an open-source and cross-platform monitoring tool that monitors network resources, generates performance data, sends notifications about outages and etc. It is one of the most popular monitoring tools on the internet that provides high availability and distributed monitoring. Besides the installation, we will explain in more detail the configuration and accessing the Icinga through the web interface. Icinga 2 installation may take up to 40 minutes but don’t worry it is very easy and straightforward. Let’s Start # ⚓ How_to_listen_to_radio_on_the_Linux_desktop_with_ease⠀⇛ Want to listen to the radio on your Linux desktop but can’t find a radio app with a simple user interface? If so, Raddiola is for you. It’s a simple, easy-to-use radio program that you can use to listen to internet radio on the Linux desktop. # ⚓ How_to_play_Halo_Wars:_Definitive_Edition_on_Linux⠀⇛ Halo Wars: Definitive Edition is the PC release of Halo Wars. Halo Wars is a real-time strategy video game based inside of the Halo video game universe. Here’s how you can get the game working on Linux. # ⚓ FreeBSD_CPU_Information_Command_–_nixCraft⠀⇛ How do I get more information about CPU under FreeBSD operating systems such as CPU Speed and model using the command-line options? # ⚓ How_to_install_PHP_7.2/7.3/7.4_or_8.0_on_Amazon_Linux_2_– nixCraft⠀⇛ While working with an application, I needed PHP 7.4 and 8.0 on Amazon Linux 2 EC2 and Lightsail instance. Here is how to install PHP version 7.2/ 7.3/7.4 or 8.0 on Amazon Linux 2 using the yum command. The default PHP version is 5.4.16 on Amazon Linux version 2. However, for Lightsail or EC2 cloud server, I needed either PHP 7.4 or PHP 8.0 as my application works with both versions flawlessly. So, let us see how a developer can install PHP 7.4 or 8.0 on an Amazon Linux 2 virtual machine. # ⚓ How_to_set_up_the_Pretty_Hostname_–_Unixcop_the_Unix_/ Linux_the_admins_deams⠀⇛ A pretty hostname avoids most of the limitations of other hostname types, giving users more freedom when naming their systems. In this tutorial, we will show you how to set up a pretty hostname for a Linux system in two different methods. # ⚓ How_to_install_and_use_SAR_command_(to_Monitor_system Performance)_in_Linux_–_Unixcop_the_Unix_/_Linux_the_admins deams⠀⇛ System Activity Report (sar) is a Unix System V- derived system monitor command used to report on various system loads, including CPU activity, memory/paging, interrupts, device load, network and swap space utilization. Sar uses /proc filesystem for gathering information. In this tutorial, We will show you how to install and use SAR command in Linux. # ⚓ How_to_Ping_a_Port_Number_in_Linux_–_Unixcop_the_Unix_/ Linux_the_admins_deams⠀⇛ Ping is a computer network administration software utility used to test the reachability of a host on an Internet Protocol (IP) network. It is available for virtually all operating systems that have networking capability, including most embedded network administration software. Port numbers belong to transport layer protocols, such as TCP and UDP. Port numbers help identify where an Internet or other network message forwarded when it arrives. So Pinging ports is one of the most effective troubleshooting technique in order to see if a service is alive or not. In this tutorial, we will show you how to ping a port in Linux using three different tools. # ⚓ How_to_install_Apache_Cassandra_with_Podman_–_NextGenTips⠀⇛ Apache Cassandra is a free and open-source, distributed, wide-column store, NoSQL database management system designed to handle large amounts of data across many commodity servers, providing high availability with no single point of failure. Linear scalability and proven fault-tolerance on cloud infrastructure make it the perfect platform for mission-critical data. # ⚓ Force_SSH_Client_to_Use_IPv4_or_IPv6_–_Putorius⠀⇛ In this Linux quick tip we will discuss using command line options to force the SSH client to use IPv4 or IPv6 specifically. We will also show you how to set which IP protocol you would like to use in your SSH client configuration file. # ⚓ How_to_Install_Zoom_on_Linux_–_Make_Tech_Easier⠀⇛ “Can I install Zoom on Linux?” was the first question that came to mind when my bosses informed me that we would be working from home and using Zoom for remote meetings and one-on-one interactions with fellow employees and clients. The answer to that first question is yes, you can install Zoom on Linux. Let’s look at how to download and install the Zoom client on four different Linux distributions: Fedora, Manjaro (Arch), OpenSUSE, and Ubuntu/Debian. # ⚓ How_to_upgrade_from_Fedora_34_to_Fedora_35_|_FOSS_Linux⠀⇛ The official stable release of Fedora Workstation 35 was made available for download on November 2, 2021, after being pushed back to resolve some outstanding bugs. You can now install or upgrade to Fedora 35 Desktop, Fedora cloud, Fedora Servers, or any spin or labs that come with any new release cycle. If you prefer a fresh installation, you will have to download the latest ISO, create a bootable USB and perform a fresh install. I prefer an upgrade of the Fedora 34 system to Fedora 35. An upgrade will retain any existing files and all installed applications. The article is a step-by-step guide on how to upgrade to Fedora 35 via GUI (GNOME software) and the CLI method. # ⚓ »_Android_–_how_to:_wireless_access_device_(wifi_wlan)_via ftp_and_how_to:_save_apps_to_apk_and_send_via_bluetooth_or even_messenger_(whatsapp,_signal,_telegram)_|_dwaves.de⠀⇛ what is definately great and a big plus is the “openness” of the Android (a by Google heavily modified GNU-Linux) environment. o § Games⠀➾ # ⚓ Lands_Awakened_is_live_now_for_Albion_Online,_big_open- world_improvements_|_GamingOnLinux⠀⇛ Albion Online, the free to play MMO that has native Linux support, has been upgraded with some massive improvements landing in the Lands Awakened update. One of the big noticeable changes is the rework of the open-world areas. Expect to find improved visuals and layouts in all the biomes, better mobs that become stronger over time and give better rewards, a rework of dungeons and treasure sites that spawn randomly and more. You also get the War Gloves weapon, new Elite levels for weapons and armour, a rework of Guild Seasons and so on. # ⚓ Settlement-builder_King_under_the_Mountain_hits_Early Access_|_GamingOnLinux⠀⇛ King under the Mountain is a fresh take on building up a settlement, this time with a fantasy setting that looks a bit nordic. The visual style of it will be instantly familiar to anyone who has played the likes of Prison Architect and RimWorld, with the small floaty characters and colourful tile-based building. Currently in Early Access, for the second time, after initially being available on itch.io as an early Alpha. This version is much further along although still largely incomplete. # ⚓ Steam_Autumn_Sale_2021_is_live_now⠀⇛ It’s that time of the year again. It’s getting cold outside, dark and so you should keep warm with some new games. The Steam Autumn Sale 2021 is up. You know the drill, you probably have a Wishlist stocked full of interesting games but for those who don’t we have a couple of items you should take a look at including… # ⚓ Zid_Journey_is_another_colourful_and_inviting_prehistoric adventure_coming_up_|_GamingOnLinux⠀⇛ Developer Azure Mountain has announced the second game in the Zid and Zniw Chronicles series, with Zid Journey. The game will offer up a familiar look and feel, with its classic point and click adventure gameplay and cartoony visuals much like its predecessor Zniw Adventure. Set in the Cretaceous Period, it stars Zid, a young dinosaur who is searching for the lost parents of a tyrannosaur hatchling. # ⚓ Hanoi_Puzzles:_Flip_Match_is_a_nice_no-frills_experience based_on_the_Tower_of_Hanoi_|_GamingOnLinux⠀⇛ One for puzzle game fans after something to relax with and test the brain a little, Hanoi Puzzles: Flip Match released back in October from Hanoi Studios. The developer tells us it has a similar idea to the previous title Hanoi Puzzles: Solid Match, this time around it adjusts the gameplay with “a harder mechanic, enhanced graphics and colours, new original soundtrack and dozens of new challenges”. At its core the main mechanic is taken from the Tower of Hanoi, with you moving around differently sized discs to get them to fit together. # ⚓ Neverwinter_Nights:_Enhanced_Edition_gets_an_official_HD model_and_texture_pack_|_GamingOnLinux⠀⇛ Love the Neverwinter Nights: Enhanced Edition from Beamdog and want to make it look just that little bit more modern? Beamdog has your answer now. After years of work, Beamdog has now released a free HD Models & Textures Pack for Neverwinter Nights: Enhanced Edition that gives a visual boost to player character models and their equipment (including armour, weapons and shields). The newer models now support “normal and spec information”, plus they can be further modded by the community just the the base game. # ⚓ Capture_monsters_and_explore_dungeons_in_Siralim_Ultimate on_December_3_|_GamingOnLinux⠀⇛ Thylacine Studios have announced that their dungeon-crawling and monster-catching roguelike RPG, Siralim Ultimate, which leaves Early Access on December 3. A game that the developer says is a bit like “Pokemon meets Diablo, or more accurately, Dragon Warrior Monsters meets Path of Exile”. It might not be a looker but it has a huge amount of depth and replay value to it, and one that’s easy enough to really get stuck into. o § Desktop Environments/WMs⠀➾ # § K Desktop Environment/KDE SC/Qt⠀➾ # ⚓ Plasma_wonder_tools:_Digital_Clock⠀⇛ A bunch of months back down the trouser leg of time, I published my Plasma is awesome article. Indeed, it’s the most cohesive, consistent and convenient desktop environment in the Linux world, and beyond. You get a great experience, with big things as well as small ones. A good example is the Digital Clock widget, the topic of today’s piece. You may think, digital clock, who cares? Well, if you’ve used other operating systems and/or desktop environments, you would. Quite often, the clock tool is merely a simple placeholder for time and date, perhaps calendar, and … that’s about it. Also, you may say: wait, didn’t we talk about this already? Yes, we did talk about the Digital Clock in 2018, so it would be nice to see how things have changed and improved three years later. Now, let’s see how Plasma handles it, and why it does a better job than its rivals. After me. # § GNOME Desktop/GTK⠀➾ # ⚓ How_To_Survive_GNOME_With_GNOME_Extensions⠀⇛ When you start as a Linux User, you are very likely to fall in two camps. Either you are a GNOME user, or a KDE user, whether it was by choice or by default. So you already know you won’t be missing any fanboy-ism or any flamewar in the Linux community. Since a good chunk of Linux users are tinkerers, we end up with a lot of experiments: different distros, different desktops, different bootloaders, different everything. I personally think it’s very healthy, even if it goes against having a consistent experience across the board. This is what happens when users are able to modify and tweak every piece of the system. It’s an inherent property of its original design. Of course, you can avoid the GNOME vs KDE war by using something completely different altogether, like a tiler i3, awesomevm or other alternatives… or just use both GNOME and KDE and recognize that they both have some merits. These days I tend to find myself more at home in KDE than in GNOME, but I still use GNOME on one of my machines – it moved recently to GNOME 41. Out of the box I’m in the camp that GNOME defaults are not for me, making it barely usable. Thankfully there’s the wonderful world of GNOME Extensions to make it possible to live in GNOME, keeping the good bits and ironing out the bad ones with Extensions. I won’t go at length on how to install extensions, suffice to say that you simply need the above link and a browser plugin (available for Firefox and Chromium/ Chrome) if you like it the easy way. So, here is what I recommend if you feel a little lost by the lack of customization or options in Vanilla GNOME. I will split my recommended extensions into three parts: Essential, Important, and Nice to have. # ⚓ The_Top_8_Features_of_the_GNOME_Desktop_Environment⠀⇛ GNOME is one of the oldest and most popular interfaces for free and open-source operating systems like Linux. But modern GNOME looks nothing like its origins, and it has evolved into one of the best ways to use a computer. Whether you’re already using Linux or curious why you might want to make the switch, here are some of the best features of GNOME. [...] On GNOME, the panel at the top does not contain any app launchers. This panel is small and black, like on a phone or tablet, and is lately static. It contains the date and time, a few system indicators in the top right, an Activities button in the top left, and the name of the currently running app next to that. You click that Activities button when you want to do anything unrelated to the currently open app. Otherwise, there’s little on-screen to distract you from what you’re doing. o § Distributions⠀➾ # ⚓ Deepin_20.3_Released_with_Kernel_5.15,_Scrolling_Screenshot Support⠀⇛ The beautiful Debian based Linux distribution Deepin 20.3 was released. Features Kernel 5.15, new features and optimizations for its core apps. The stable Linux kernel has been updated to v5.15 with better support for Intel 12th Gen processors and NTFS file systems. Though the iso image by default boots with 5.10 LTS kernel, user have to select the new kernel to install from ‘Advanced’ menu in Grub boot-loader. The Deepin screen capture can now take scrolling screenshots via the ‘Scrollshot‘ option. After selecting an app window to capture, a ‘Scrollshot’ option is available in tool-bar. By clicking on it, you may scroll the page to take a continuous screenshot with real-time preview. Also OCR is supported in this mode to extract text from image. # ⚓ Distribution_kit_for_mobile_phones_NemoMobile_0.7 Released⠀⇛ After more than a year of development, an updated distribution kit for mobile phones NemoMobile 0.7 version was released, using the developments of the Mer project, but based on the ManjaroArm project. The system image size for Pine Phone is 740 MB. All applications and services are open under GPL and BSD licenses and are available on GitHub . NemoMobile was originally planned as an open replacement for Nokia’s Harmattan project and was developed in collaboration between the community and Jolla. However, over time, Jolla focused on the partially closed SailfishOS without paying due attention to the open part of the Mer – NemoMobile project. The last release of NemoMobile took place in April 2013 In 2019, a team of enthusiasts began the transfer of NemoMobile components from the Mer base to the Manjaro base. There have also been projects to port NemoMobile to other operating systems like Fedora and OpenEmbedend. The main reason for moving from the Mer base was obsolete components. In particular, Mer still uses version 5.6 of Qt due to licensing restrictions. # § New Releases⠀➾ # ⚓ Alpine_Linux_3.15_Released_with_Linux_5.15_LTS,_GNOME 41,_and_UEFI_Secure_Boot_Support⠀⇛ Alpine Linux 3.15 is here more than five months after Alpine Linux 3.14 to provide those who want to use this security-oriented distribution on their computers. As you can imagine, this is a major update and it’s the first release of Alpine Linux to be powered by the latest and greatest Linux 5.15 LTS kernel series. Highlights of this release include initial support for UEFI Secure Boot on the 64-bit (x86_64) architecture, support for disk encryption in the installer, support for out- of-tree kernel modules via AKMS (inspired by DKMS), gzip compressed kernel modules, and SimpleDRM as default in-kernel framebuffer driver for a flicker-free boot. # ⚓ Alpine_3.15.0_released⠀⇛ We are pleased to announce the release of Alpine Linux 3.15.0, the first in the v3.15 stable series. # ⚓ Alpine_Linux_3.15_Released_–_Builds_Off_Linux_5.15, Drops_MIPS64,_SimpleDRM_For_FB⠀⇛ Alpine Linux 3.15 is out today as the newest feature update to this lightweight/embedded/ containers focused Linux distribution known for its musl+Busybox usage along with OpenRC as the init system. Alpine Linux 3.15 ships with a wide variety of package updates including use of the Linux 5.15 LTS kernel, LLVM 12, PostgreSQL 14, Rust 1.56, OpenJDK Java 17, GNOME 41, X.Org Server 21.1, KDE Plasma 5.23, and many other updates. # ⚓ Endless_OS_4.0_Released_as_Long-Term_Supported Series,_Based_on_Debian_Bullseye⠀⇛ Endless OS 4.0 is a major release that introduces numerous new features and enhancements, starting with an improved app grid navigation with clickable arrows that allow users to more easily navigate between app pages, with dots that indicate the total number of pages and the page you’re currently on. This release also introduces fast user switching to allow you to easily switch to a different user while another user is still logged in. The new feature has been implementing in both the user menu and the lock screen. # § SUSE/OpenSUSE⠀➾ # ⚓ Digest_of_YaST_Development_Sprints_135_&_136⠀⇛ As already explained in this same blog quite some time ago the YaST Partitioner can be used to set up several kinds of encryption, but “Regular LUKS2” was not one of those. That was intentional because using LUKS2 comes with many challenges, as summarized in this Bugzilla comment. But now the time has come to start introducing experimental support for general LUKS2 encryption. Initially it will be available in openSUSE Tumbleweed and pre-releases of SLE-15-SP4 but only if the environment variable YAST_LUKS2_AVAILABLE is set. Check the description of this pull request for screenshots and more information. Support for LUKS2 in AutoYaST will have to wait a bit, until we have received some feedback from interactive installations and ironed out all the details. But AutoYaST users can meanwhile test and enjoy another new feature available also in Tumbleweed and 15.4 pre-releases – support for identifying EFI systems in dynamic profiles, which includes both rules and ERB templates. Learn more and see some examples in the description of the corresponding pull request. The last feature for Tumbleweed and the upcoming 15.4 that we want to highlight in this report is the brand new support for NTLM authentication in linuxrc. # § IBM/Red Hat/Fedora⠀➾ # ⚓ A_year_of_collaboration:_2020-2021_IBM_Developer partnership_program⠀⇛ In December 2020, the IBM Developer team decided to launch its first-ever Partner Developer Success Program. The idea for this program is simple: Collaborate with partners on co-hosted webinars to educate external developers about the values and benefits of IBM and partner technologies. The partners that we decided to collaborate with were either part of the Hybrid Cloud Build Team ecosystem, were global system integrators (GSIs), independent software vendors (ISVs), or part of Red Hat Marketplace. Overall, these are partners that are already deeply rooted in the IBM tech ecosystem, and the goal with this program is to highlight and share technology insights. Since the program’s conception, we have collaborated with more than 10 different partners on 30+ Crowdcast.io webinars, attracting an average of over 200 attendees worldwide. We have also started collaborating with partners in various geographic regions and languages, such as Latin America, Europe, and the Middle East. We have begun live- streaming our sessions across our YouTube, Twitter, and Twitch channels. # ⚓ Customizing_provisioning_templates_in_Red_Hat Satellite_using_snippets⠀⇛ Red Hat Satellite’s provisioning templates are very powerful, but also hard to customize and maintain. A recently introduced feature makes extending and customizing default templates much easier to accomplish and maintain. In this post, we’ll provide an overview of the Kickstart default provisioning template and how to create a custom provisioning template using snippets that better address your environment. # ⚓ Veeam_Ransomware_Protection_with_Red_Hat_Enterprise Linux_as_the_Immutable_Repository⠀⇛ Veeam Backup and Replication is a backup, recovery and data management platform that modernizes data protection for cloud, physical and virtual environments. In this post we’re going to look at using Veeam as part of a strategy to guard against ransomware attacks. Ransomware attacks continue to be damaging and costly events for all sizes of companies. Immutable backups are just one component in an overall business continuity strategy to protect against these types of revenue and reputation draining catastrophes. Linux is key to this strategy, and specifically Red Hat Enterprise Linux, can act as that immutable backup repository—whether on-premise, or in the cloud as part of your hybrid-cloud implementation. o § Devices/Embedded⠀➾ # ⚓ Sipeed_LicheeRV_–_A_$16.90_Allwinner_D1_Linux_RISC- V_board⠀⇛ Finally! There’s now a much more affordable Allwinner D1 RISC-V Linux board thanks to Sipeed LicheeRV Nezha CM SBC sold for $16.90 and up on Aliexpress, that’s much cheaper than the $100 asked for Nezha SBC, although still not incredibly cheap as we’ll see from the specifications below. Sipeed LicheeRV is actually both a board and a system-on-on-module with an edge connector, and is equipped with 512MB DDR3, a USB-C OTG port, a MicroSD card socket, and an SPI display interface. The dual M.2 edge connector can be plugged into a carrier board, and they will be a “86 Box” (86x86mm) for HMI display that can be used for home automation. # ⚓ $17_SBC_runs_Linux_on_Allwinner_D1_RISC-V_SoC⠀⇛ Sipeed has launched a tiny, SoM-like “LicheeRV” SBC that runs Linux on an Allwinner D1 RISC-V SoC. The board supports standalone use, but is primarily intended to plug into upcoming “Lichee RV-86” panel PC and future carriers. In Nov. 2020, Allwinner and Alibaba’s T-head subsidiary announced an Allwinner D1 SoC based on T-head’s RISC-V-based XuanTie C906 core. At the time, Sipeed said it would produce a $12.50 SBC based on the SoC that would arrive in early 2021. The SBC was delayed due to supply issues, and Sipeed instead went to Indiegogo in May to launch a more feature rich Nezha SBC based on the Allwinner D1 starting at $99. # § Open Hardware/Modding⠀➾ # ⚓ Oscilloscope_Probes_Itself_To_Add_Video_|_Hackaday⠀⇛ Modern oscilloscopes are often loaded with features, but every now and then you run into a feature that seems easy to implement yet isn’t available. [kgsws] wanted to use his Rigol DS1074 to show live measurements in his YouTube videos, but found out that this scope doesn’t support video output. Not to be deterred, [kgsws] decided to add this feature himself. In the video embedded below, he describes in detail the process of adding a USB Video Capture (UVC) interface to his oscilloscope. The basic idea was to find the signals going into the scope’s display and read them out using a Cypress EZ-USB board. This is a development board that can be used to design USB devices, and supports the UVC mode. However, with no documentation of any of the Rigol’s internal circuitry [kgsws] had to probe the display connector to find out which pin carried which signal. And since he had no other scope available than this Rigol, he hooked up the various bits of the disassembled instrument so that it could (awkwardly) probe its own internal signals. # ⚓ 7_Segment_Display_And_Raspberry_PI_Pico:_Wiring_and Setup_with_MicroPython⠀⇛ 7 segment display can be controlled with a few Micropython lines from Raspberry PI Pico. It is one of simplest projects and a funny way to start coding and cabling In this tutorial, I’m going t show you how to connect and configure a 7 segment display with a Raspberry PI Pico. If you are interested in how to get it working with Raspberry PI computer boards (like RPI Zero, RPI 4 model B, RPI 3 model A/B, and so on), please refer to my Control a 7 Segment Display from Raspberry PI with Python. o § Free, Libre, and Open Source Software⠀➾ # § Programming/Development⠀➾ # ⚓ Dependency_Derby_|_Coder_Radio_441⠀⇛ Are Linux devs getting upset with the Python community? We weigh in on a nuanced issue. Plus the mass-mod resignation over at Rust, and Mike’s thoughts on setting up a dev environment on Windows 11. # ⚓ Adobe_XD_Bridge_TP_for_Qt_Design_Studio_released!⠀⇛ Adobe XD Bridge TP for Qt Design Studio released! Qt Design Studio is a UI design and development tool that enables designers and developers to rapidly prototype and develop complex UIs. # § Python⠀➾ # ⚓ Python_virtualenv_and_venv_dos_and_don’ts⠀⇛ * § Leftovers⠀➾ o ⚓ Dead_on_Archival⠀⇛ Being a child of the 1980s is kind of strange nowadays. I don’t feel old but am often quick to make references that date me. Pop culture is obviously a rife minefield for this but I also run into this as a writer and journalist. In my younger days, I was a reporter at Forbes Magazine but was based in Austin, Texas. On occasion, I got to travel to New York and work out of the Forbes office on 5th Avenue. In the early aughts, it was a big time magazine and just felt cinematic. A bustling newsroom with reporters taking calls, editors demanding more info before deadline, and beleaguered copy editors wondering what happened to the American education system. When I got a tour on my first visit, I took a spiral staircase down to the Forbes archives. Though I expected a library like one Indiana Jones would have stumbled upon, instead it was rows of grey filing cabinets. Think of the ones that were behind the accounting department in the U.S. version of The Office. As the archivist explained a bit about how some 75 years of work was organized, I wondered what happens to all this when they digitize the files. Instead, I should have been wondering what happens when publications go bust. What happens to all this history? Today’s Tedium is looking at the archives of defunct publications and what, if any, second life they manage to get o § Science⠀➾ # ⚓ Why_Deep_Frying_Turkey_Can_Go_Very_Wrong_|_Hackaday⠀⇛ It all sounds fairly straight forward, but there are two ways that this often goes wrong, leading to leaping flames and calls to the fire department. The first of all is simple: overfilling. Lowering a turkey into oil will necessarily displace that oil. A pot filled to the brim will thus overflow the second the turkey enters the pot, with hot oil streaming down the sides of the cooking vessel directly towards the gas burner below. It’s a beginner’s mistake, but one that happens all too often. To avoid this, it’s important to account for the volume of the turkey before dropping it in the pot, to avoid starting a conflagration. The second major cause of turkey fires is from attempting to deep fry a frozen turkey. The ice on the frozen turkey quickly turns to steam when it comes into contact with the hot oil. The steam rapidly expands, creating bubbles and quickly throwing hot foaming oil all over the place. This can easily cause severe burns by itself, but the presence of a gas burner only increases the danger. The hot aerosolized oil typically catches fire, either from the burner itself or simply the hot surfaces in the vicinity, and quickly creates a huge fireball. o § Hardware⠀➾ # ⚓ A_Flip_Clock_That_Flips_Up,_Not_Down_|_Hackaday⠀⇛ The venerable flip clock has become an outsized part of timekeeping culture that belies the simplicity of its mechanism. People collect and restore the electromechanical timepieces with devotion, and even seek to build new kinds of clocks based on split-flap displays. Designs differ, but they all have something in common in their use of gravity to open the leaves and display their numbers. # ⚓ Cracking_Open_The_Prince_Floppy_After_The_Purple_Reign_| Hackaday⠀⇛ Readers of a certain vintage will no doubt remember the time when Prince eschewed his royal position and became an unpronounceable symbol. People had no choice but to refer to him as TAFKAP, The Artist Formerly Known As Prince, and members of the music press were sent a 3.5″ floppy disk with a font file containing a single character — that gender- transcending shape that would soon become another one of Prince’s guitars. But it’s 2021, and now you can get it from the Internet Archive. Fun fact: the file wasn’t ever locked down. In fact, the symbol was available on Prince’s Compuserve and fan club CD-ROM. While some people trawl auction sites for overalls and weird keyboards, others look for ridiculous items from the zeitgeist, like a copy of this floppy. Take [Anil Dash] for instance. [Anil] finally pulled the trigger after 15 years of debating this particular purchase. [Anil]’s interest was reignited after reading this analysis of whether the symbol could ever be put into Unicode. (Between being trademarked, a logo, and a personal character, it’s ineligible for inclusion.) # ⚓ You_Can’t_Upgrade_Soldered-On_Laptop_RAM?_Think_Again_| Hackaday⠀⇛ The write-up is a fascinating primer on how DRAM identification works, which for removable DIMMs is handled by an onboard FLASH chip containing the details of the chips on board. A soldered-on laptop has none of these, so instead it employs a series of resistors whose combination tells the BIOS what memory to expect. Some research revealed their configuration, at which point the correct chips were sourced. Surprisingly it’s not as easy as one might expect to buy small quantities of some RAM chips, but he was eventually able to find some via AliExpress. An aside is how he checked the chips he received for fakes, including the useful tip of hiring a dentist to take an x-ray. # ⚓ Mechanical_Musical_Sculpture_Recalls_The_Four_Muses_| Hackaday⠀⇛ Music was created by humans, but often we find ourselves creating performances with machines. [Alana Balagot] and [Federico Tobon] did just that, constructing the stunning 4 Muses musical sculpture with their combined talents. 4 Muses is made up of four individual instruments, under the command of a single keyboard controller. The keyboard can be used to play the instruments live, or alternatively, can learn from the player or be used as a sequencer. It can also act as a simple device to play back music using the four instruments. The pipe instrument uses servo-controlled valves, which allow air from a blower fan to reach several wood pipes. The xylophone instead uses solenoids to play its 13 tines. Percussion is provided by a mechanized cajón drum, using motors to actuate mallets that strike the various sections of the box. Meanwhile, hackers will be familiar with the concept of the motor-noise instrument, which drives stepper motors at different frequencies to generate tones. o § Integrity/Availability⠀➾ # § Proprietary⠀➾ # § Security⠀➾ # ⚓ CVE-2021-41816:_Buffer_Overrun_in CGI.escape_html⠀⇛ A buffer overrun vulnerability was discovered in CGI.escape_html. This vulnerability has been assigned the CVE identifier CVE-2021-41816. We strongly recommend upgrading Ruby. # ⚓ CVE-2021-41819:_Cookie_Prefix_Spoofing_in_CGI:: Cookie.parse⠀⇛ A cookie prefix spoofing vulnerability was discovered in CGI::Cookie.parse. This vulnerability has been assigned the CVE identifier CVE-2021-41819. We strongly recommend upgrading Ruby. # ⚓ Ruby_2.6.9_Released⠀⇛ This release includes security fixes. Please check the topics below for details. # ⚓ Ruby_2.7.5_Released⠀⇛ # ⚓ Ruby_3.0.3_Released⠀⇛ # ⚓ Security_updates_for_Wednesday⠀⇛ Security updates have been issued by Debian (openjdk-17), Fedora (libxls, roundcubemail, and vim), openSUSE (bind, java-1_8_0-openjdk, and redis), Red Hat (kernel, kernel-rt, kpatch- patch, krb5, mailman:2.1, openssh, and rpm), Scientific Linux (kernel, krb5, openssh, and rpm), SUSE (bind, java- 1_8_0-openjdk, redis, and webkit2gtk3), and Ubuntu (bluez). # ⚓ VMware_Releases_Security_Updates_|_CISA⠀⇛ VMware has released security updates to address multiple vulnerabilities in vCenter Server and Cloud Foundation. A remote attacker can exploit this vulnerability to obtain access to sensitive information. # ⚓ CISA_Releases_Capacity_Enhancement_Guides_to Enhance_Mobile_Device_Cybersecurity_for_Consumers and_Organizations_|_CISA⠀⇛ CISA has released actionable Capacity Enhancement Guides (CEGs) to help users and organizations improve mobile device cybersecurity. # ⚓ Malware_downloaded_from_PyPI_41,000_times_was surprisingly_stealthy⠀⇛ # ⚓ GoDaddy_Breach_Exposes_SSL_Keys_of_Managed WordPress_Hosting_Customers⠀⇛ A data breach at GoDaddy exposed SSL keys issued to an undisclosed — but likely large — number of active customers using its Managed WordPress website hosting service. The incident has sparked concerns about attackers hijacking domains for ransomware or spoofing them for credential theft and other malicious purposes. # § Privacy/Surveillance⠀➾ # ⚓ Apple_Sues_NSO_Group [Ed: Spying companies sue spying company; helps distract and deflect focus (off and away from themselves)]⠀⇛ NSO Group’s Pegasus spyware is favored by totalitarian governments around the world, who use it to hack Apple phones and computers. [...] This follows in the footsteps of Facebook, which is also suing NSO Group and demanding a similar prohibition. And while the idea of the intermediary suing the attacker, and not the victim, is somewhat novel, I think it makes a lot of sense. I have a law journal article about to be published with Jon Penney on the Facebook case. o § Environment⠀➾ # § Energy⠀➾ # ⚓ The_Corbett_Report_–_How_Green_Finance_is Monopolizing_the_Planet⠀⇛ Whitney Webb returns to the program to discuss her recent work on the “green” transformation of the global financial system. From NACs to GFANZ, Webb and Corbett break down the latest attempt to monopolize the world’s natural resources and how this financial scam represents the next step along the path to the Great Reset, Agenda 2030 and the 4th Industrial Revolution. o § Monopolies⠀➾ # § Copyrights⠀➾ # ⚓ William_Wells_Brown,_Wildcat_Banker_–_The_Public Domain_Review⠀⇛ A cottage industry, yes, but a barbershop bank? Ross Bullen plots how a story told by William Wells Brown — novelist, historian, playwright, physician, and escaped slave — circulated, first through his own works, and then abroad, as a parable of American banking gone bad. ䷩ 𝚕𝚒𝚗𝚎 6482 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.24.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Links_24/11/2021:_PHP_Foundation_and_Flatpak_Criticisms⠀✐ Posted in News_Roundup at 9:32 am by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈ § Contents⠀➾ * GNU/Linux o Distributions o Devices/Embedded * Free_Software/Open_Source * Leftovers * § GNU/Linux⠀➾ o § Server⠀➾ # ⚓ Kubernetes_1.23_rc_testing_with_MicroK8s⠀⇛ Today, Kubernetes 1.23 release candidate was made available upstream for testing and experimentation. General availability is planned for December 7th, so now is the time to report back any issues or bugs. Developers, DevOps and open source software enthusiasts can try out the latest features using MicroK8s. MicroK8s is a lightweight, CNCF-certified Kubernetes distribution with a streamlined UX. It can run from a local workstation to the cloud and is ideal to build edge clusters as it includes all Kubernetes services and useful addons in a single light package. MicroK8s tracks all upstream releases, and allows users to select between stable versions for production, beta, or release candidate versions for testing. o § Audiocasts/Shows⠀➾ # ⚓ Linus_is_having_a_real_rough_go_of_it,_isn’t_he?_|_Reacting to_Linux_Daily_Driver_Challenge_pt._2_–_Invidious⠀⇛ Linux can be weird, Linux can be broken. And LinusTechTips’ latest Linux Daily Driver Challenge (part 2) video has really shown there are still glaring issues with using a Linux-based OS as your daily OS. # ⚓ Podcast_Episode:_The_Revolution_Will_Be_Open_Source⠀⇛ # ⚓ The_Lessons_of_Jellyfin_|_LINUX_Unplugged_433⠀⇛ We revisit some old assumptions about the open- source Plex-alternative, Jellyfin. We each try it out, and along the way, gain a few insights about open source. o § Kernel Space⠀➾ # ⚓ Google_Pixel_6_and_Pixel_6_Pro_are_seeing_work_for_mainline Linux_kernel_support⠀⇛ The Google Pixel 6 and the Pixel 6 Pro are the first smartphones powered by the company’s in-house Tensor SoC. They also shipped with Android 12 out- of-the-box, and if you take a look at the kernel sources, you can find Linux kernel 5.10 under the hood. If you’ve already bought either device for the sake of aftermarket development, then you’ll be happy to know that Google has recently started populating a mainline Linux kernel 5.15 branch for the Pixel 6 family. What’s more interesting is that XDA Recognized Developer Freak07 has already managed to compile and boot the mainline kernel release for the device duo. # ⚓ Xen_pvUSB_Linux_Driver_Patches_Updated,_More_Than_10_Years In_The_Making_–_Phoronix⠀⇛ An effort recently restarted that originally dates back many years is the “pvUSB” front-end driver for Linux to allow physical USB devices to be used within Xen domains. Juergen Gross of SUSE has recently been working on this driver that dates back to the original pvUSB implementation for the Linux 2.6 kernel in 2008 by Fujitsu engineers. This year he has taken to getting that code cleaned up and working against the latest upstream state of the kernel and other basic changes. While Xen is not as popular as it once was, there still are users interested in seeing this USB device support for Xen para-virtualized use-cases. # ⚓ Linux_Driver_For_Arm_China’s_Zhouyi_AI_Accelerator Proposed,_But_Lacks_Open_User-Space_–_Phoronix⠀⇛ The Zhouyi AI accelerator was developed by Arm China and is found in some SoCs so far. An open- source Linux kernel driver is being worked on for it but unfortunately for now at least any mainline ambitions are immediately stalled over the lack of an open-source user-space/client. A Baidu engineer posted a set of patches implementing the Zhouyi AI accelerator support in a new “zynpu” driver for the kernel. The more than five thousand lines of code provide this initial support. The Zhouyi AI accelerator is found in some Arm SoCs like the Allwinner R329. # § Graphics Stack⠀➾ # ⚓ Dave_Airlie:_video_decode:_crossing_the_streams⠀⇛ I was interested in how much work a vaapi on top of vulkan video proof of concept would be. My main reason for being interested is actually video encoding, there is no good vulkan video encoding demo yet, and I’m not experienced enough in the area to write one, but I can hack stuff. I think it is probably easier to hack a vaapi encode to vulkan video encode than write a demo app myself. With that in mind I decided to see what decode would look like first. I talked to Mike B (most famous zink author) before he left for holidays, then I ignored everything he told me and wrote a super hack. # ⚓ Airlie_Exploring_Possibility_Of_VA-API_On_Top_Of Vulkan_Video_–_Phoronix⠀⇛ Well known open-source Linux graphics expert David Airlie of Red Hat has recently been working on early Vulkan Video support for Mesa’s Radeon “RADV” and Intel “ANV” drivers. As part of that effort and in part due to lack of software making use of Vulkan Video extensions right now, he has started exploring the feasibility of implementing the Video Acceleration API (VA-API) atop Vulkan Video. Airlie explained today that he has been investigating the possibility of VA-API on top of Vulkan Video, namely on the video encode side for not having any good software out there at the moment exercising the Vulkan Video encode extensions. o § Benchmarks⠀➾ # ⚓ Blender_3.0′s_Cycles_X_Rendering_Performance_Is_Looking Great⠀⇛ A status update on Blender’s “Cycles X” project was published today ahead of the upcoming Blender 3.0 release and with already some feature additions planned for Blender 3.1. As we have come to expect, Cycles X with Blender 3.0 will yield big performance improvements over Blender 2.93 when running on NVIDIA GPUs with their proprietary stack. NVIDIA GPU support with Blender remains the best option for the moment and is enjoying significant uplift with the Blender 3.0 code. o § Applications⠀➾ # ⚓ Best_Free_and_Open_Source_Alternatives_to_Adobe_XD⠀⇛ We are long-standing admirers of Adobe’s products. They develop many high quality proprietary programs. It’s true there are security and privacy concerns in relation to some of their products. And there’s considerable criticism attached to their pricing practices. But the real issue is Adobe Creative Cloud does not support Linux. And there’s no prospect of support forthcoming. What if you are looking to move away from Adobe and embark on a new world of online freedom, where you are not tracked, monetised and attached to Adobe’s ecosystem. We only recommend free and open source alternatives. Our recommended software don’t necessarily replicate every feature of their Adobe counterparts but they offer sufficient functionality for many tasks. # ⚓ 5_open_source_alternatives_to_Microsoft_Exchange⠀⇛ For decades, Microsoft Exchange has ruled the market for email and groupware services. This top dog dominates the corporate world, and the omnipresent Outlook mail client has become the de facto standard for groupware. Since Exchange is closely integrated with Microsoft’s Office products, users have access to a wide variety of productivity software and features, whether they’re using a desktop or a mobile client. However, many companies have concerns about storing their data in the Microsoft cloud. In this article, I look at some open source alternatives and their advantages. It’s not just about becoming vendor- independent and reducing costs; it’s about using software with open standards and a different level of security—for the groupware server itself and the operating system behind it. o § Instructionals/Technical⠀➾ # ⚓ How_To_Install_Xrdp_Server_on_Debian_11_–_idroot⠀⇛ In this tutorial, we will show you how to install Xrdp Server on Debian 11. For those of you who didn’t know, Xrdp is an open-source implementation of the Microsoft Remote Desktop Protocol (RDP) that allows you to control a remote system graphically. Using Xrdp, you can log in to a remote machine same as Microsoft Remote Desktop Protocol (RDP). This article assumes you have at least basic knowledge of Linux, know how to use the shell, and most importantly, you host your site on your own VPS. The installation is quite simple and assumes you are running in the root account, if not you may need to add ‘sudo‘ to the commands to get root privileges. I will show you through the step-by- step installation of the Xrdp server on a Debian 11 (Bullseye). # ⚓ How_To_Install_and_Use_Pigz_To_Compress_Files_Faster_in Linux⠀⇛ Using a compression tool is not a new thing to talk about. Since you’re using a Linux distribution, you probably already know a lot of kinds of stuff about compressing files. Mostly, in server-level works, you might need to make files smaller or change the file type. On that occasion, using a compression tool might really help to save time. In the world of compression, the Pigz tool is a handy and easy- to-use compression tool for Linux. It’s easy to install and use the Pigz tool in all major Linux distributions. # ⚓ Failed_to_open_directory_on_Kali_Linux_Virtualbox_– blackMORE_Ops⠀⇛ I added E:\Kali_Shared to my Kali Linux Virtualbox image and then tried to open it within Kali Linux. Received an Failed to open directory error. This seems to be a common problem with different versions of Linux running in Virtualbox where you get Virtualbox shared folder permissions denied error message. # ⚓ How_To_Run_A_Command_After_The_Previous_One_Has_Finished_On Linux_–_Linux_Uprising_Blog⠀⇛ This article explains how to run a command after the previous command has finished running. Using this, you can run not just 2 commands, but any number of commands, after the previous one has finished. This will work with Sh, Bash, Zsh and other shells. You can run a command after the previous one has finished, depending on the previous command’s exit status (if it failed or not) or regardless of this. # ⚓ How_to_Install_and_Use_acme.sh_script_to_get_free_SSL Certificates_on_Linux_–_VITUX⠀⇛ There are some popular methods of generating SSL and TLS certificates in Linux. One of the most popular methods of issuing SSL certificates is Let’s encrypt which is a certificate authority that offers free SSL certificates. There is an even easier way to issue the certificate which does not require any dependencies and requirements. The acme.sh script written in Shell makes it easy to generate and install SSL certificates in Linux systems. In this article, we will learn how to install the acme.sh script in the Linux system and how to use it to generate and install SSL certificates. # ⚓ How_to_unhide_menu_bar_in_Virtualbox_–_blackMORE_Ops⠀⇛ So I went in and hid the top menu bar and bottom status bar in Virtualbox. After they disappeared, now I cannot find out how to unhide those. Took me a little bit time to figure out, hence this post so that I don’t forget it and someone else having the same to unhide menu bar in Virtualbox can find this. # ⚓ How_to_apply_a_chroma_key_using_ImageMagick⠀⇛ Yesterday, I wrote a short post on the fediverse with an overview of how to take a screenshot of an app with a context menu showing in elementary OS, while keeping its alpha channel and drop shadow using Krita. # ⚓ Useful_Tmux_Configuration_Examples⠀⇛ This article is part 2 of my tmux series. In the previous article, you learned how to use tmux: what tmux is, how to manage multiple terminals, and how to use tmux’s powerful features. However, in that article, I didn’t cover much how to customize tmux. This is what this article is for. Here you’ll learn some configurations that I use. My hope is that by exposing a list of my personal tmux configurations and my reasoning behind them, you will see a general pattern and understand it enough to make tmux your own. # ⚓ Beginners⠀⇛ Here’s the final recap. In this guide, we learned about tmux session, window, pane, and server. We learned about their relationships with each other. We also learned a little about configuring tmux. In the next article, you will learn more about configuring tmux in detail. I will update this guide with the link to the next article when it is ready. # ⚓ Install_Zentyal_and_Add_Windows_to_Primary_Domain Controller⠀⇛ This series will be titled Preparation for the setting up and managing Zentyal as PDC (Primary Domain Controller) through Parts 1-14 and covers the following topics. # ⚓ How_to_Access_Command_History_on_Linux⠀⇛ With a large and mature feature set, it’s easy to see why Bash is the default shell on many Linux distributions. It faces competition for power users, however, from alternatives such as Zsh. # ⚓ Setting_up_an_NFS_Server_and_Client_on_Debian_9_(Stretch)⠀⇛ This guide explains how to set up an NFS server and an NFS client on Debian 9. NFS stands for Network File System; through NFS, a client can access (read, write) a remote share on an NFS server as if it was on the local hard disk. In this Tutorial, I will show you two different NFS exports, the export of a client directory that stores files as user nobody/nogroup without preserving filesystem permissions and a export of the /var/www directory which preserves permissions and ownership of files, as required on a hosting server setup. # ⚓ How_to_Install_balenaEtcher_on_Debian_11_Bullseye_– LinuxCapable⠀⇛ balenaEtcher is a free and open-source flashing utility tool famous for writing image files such as .iso and .img files and zipped folders onto storage media to create live SD cards and USB flash drives. balenaEtcher has cross-platform support on Linux, BSD, macOS, and Windows and is developed by balena and licensed under Apache License 2.0. In the following tutorial, you will learn how to install baelnaEtcher on Debian 11 Bullseye and how to create a Linux distribution boot disk. # ⚓ How_to_create_an_EC2_Instance_using_Python_Boto3⠀⇛ In this article we will see how we can create an EC2 instance using Python Boto3. We will use the “create_instances” method to create an instance. There are many more methods that come under EC2 instance service, to know about them visit the official page of Boto3 here. All these different methods help create different resources which come under EC2 Service of AWS. # ⚓ How_to_install_Mysql_Server_8_on_Debian_11_–_Citizix⠀⇛ MySQL is an open-source relational database management system. Its one of the popular relational management system. Mysql is commonly installed as part of the popular LAMP or LEMP (Linux, Apache/Nginx, MySQL/MariaDB, PHP/Python/Perl) stack. It implements the relational model and Structured Query Language (SQL) to manage and query data. In this guide we are going to install mysql 8 on Debian 11. # ⚓ How_to_install_Toontown_Rewritten_1.3.0_on_a_Chromebook⠀⇛ Today we are looking at how to install Toontown Rewritten on a Chromebook. Please follow the video/ audio guide as a tutorial where we explain the process step by step and use the commands below. # ⚓ How_to_install_and_set_up_Jenkins_in_Debian_11⠀⇛ In this Guide we are going to learn how to install and configure Jenkins in a Debian 11 Server. Jenkins is a popular opensource automation tool to perform continuous integration and build automation. Jenkins allows to execute a predefined list of steps, e.g. to compile golang source code to build build binary file. The trigger for this execution can be time or event based. # ⚓ How_to_play_Roblox_on_Linux⠀⇛ Roblox is officially supported on a wide range of platforms, but Linux is missing from that list. Though it doesn’t have official support, you can still play Roblox on Linux. It takes effort to get Roblox running on Linux. But it isn’t impossible. The trick is to use the Wine compatibility layer. This will allow Windows programs to run on Linux like Roblox Player and Studio. # ⚓ Analyzing_Webserver_logs_with_Logstalgia_–_LinuxTechLab⠀⇛ There are many tools available to analyze the web server logs but none is as interesting as logstalgia. Logstalgia is a real-time website visualization tool that analyzes the web server logs & presents them in a manner that server logs appear like they are playing ping-pong. Requests appear as colored balls (the same color as the host) which travel across the screen to arrive at the requested location. Successful requests a # ⚓ dust_command_in_Linux_–_Unixcop_the_Unix_/_Linux_the_admins deams⠀⇛ Hello, friends. In this post, we will help you with another great little utility for our terminal. Today you will learn how to use the dust command in Linux. This command allows us to have a more advanced view of the disk size of system directories. # ⚓ Merge_changes_with_git_diff_and_patch_|_Enable_Sysadmin⠀⇛ Sysadmins modify lots of files. Sometimes they’re code. Other times they’re configuration files, YAML playbooks, XML, policy documents, kickstart files, and probably a few takeaway lunch orders, too. It’s important to track what you’ve changed and share your changes with others who may need to adjust their local copies of files. o § Games⠀➾ # ⚓ VR-exclusive_Warhammer_Age_of_Sigmar:_Tempestfall_is_out, works_on_Linux_with_Proton_|_GamingOnLinux⠀⇛ Ready to sweat a little? Jump into the bleak fantasy world of the VR-exclusive Warhammer Age of Sigmar: Tempestfall. Note: key provided for us. A new release from Carbon Studio, in Warhammer Age of Sigmar: Tempestfall you carry the mighty powers of a Lord-Arcanum to deliver justice through the Realm of Death. Defy the odds in challenging battles, outsmart the dark forces, and grow your power by upgrading your magical weapons to gain an edge in combat. Played on Linux with the Steam Play Proton compatibility layer, it’s mostly smooth Warhammer melee action. Currently with Proton Experimental (Proton GE did not work at all) the main issue is small videos not loading, like the tutorial videos but it doesn’t really detract from the overall experience, thankfully as the developer also explains with text below each video. As with any newer game running through Proton, there was some stuttering while building up a shader cache too, hopefully as more people play it this will be less of an issue for Linux VR gamers since there will be shaders to download from Steam. # ⚓ The_Imperium_Is_Driven_by_Hate._Warhammer_Is_Not.⠀⇛ There are no goodies in the Warhammer 40,000 universe. None. Especially not the Imperium of Man. # ⚓ Diving_Into_China’s_Draconian_Video_Game_Regulations⠀⇛ Even if you’re against these particular regulations (what are you, in favor of fun, you monster?), there are plenty of times when China’s gaming laws make more sense than ours. For instance, banning games that are entirely about simulated sexual assault, or calling out tech and gaming companies for infringing on users’ rights and preventing them from building monopolies. o § Distributions⠀➾ # ⚓ Deepin_20.3_Brings_in_Linux_Kernel_5.15_LTS_With_a_New Screen_Capture_Mode⠀⇛ Deepin is one of the most beautiful Linux distributions out there. It may not be a popular choice for regular users considering it a resource- intensive distribution, but it offers a good user experience. With the latest Deepin 20.3 release, they have added the latest Linux Kernel 5.15 LTS as an upgrade option and some improvements. [...] In addition to that, you get some progress in it for Apple M1 and Intel’s upcoming discrete graphics. You can explore more about the changes/ improvements that come with Linux Kernel 5.15 LTS in our original coverage. It is worth noting that the default remains Linux Kernel 5.10 LTS. So, you will have to explicitly select the latest kernel while installing Deepin Linux. # § SUSE/OpenSUSE⠀➾ # ⚓ MicroOS_Expands_Security_With_Keylime⠀⇛ Recently MicroOS gained some new options in relation with security. The distribution has now integrated Keylime, an open source project for doing remote attestation with TPMs. If you follow the news about Windows 11, you are aware of what is a TPM. The Trusted Platform Module (TPM) is a cryptoprocessor, described by the Trusted Computing Group (TCG) in a specification that has been standardized in a ISO/IEC document. You can find the TPM already soldered in the mainboard of your computer, but they can also be found as a service in the firmware, or inside your CPU. This co-processor can be used for many tasks related with security. For example, we can use it to generate symmetric and asymmetric keys, encrypt some memory blocks (not too big, as they are a bit slow), or to as storage for keys that can be used only for us (or applications that have permissions). # § IBM/Red Hat/Fedora⠀➾ # ⚓ IT_hiring:_5_ways_to_attract_talent_amidst_the_Great Resignation⠀⇛ With IT job opportunities so competitive right now, professionals are leaving their roles more quickly than recent grads are able to fill them. But even on small teams, it is possible to compete with big players and attract and hire top talent. These days, employees are prioritizing flexibility. Having proven that they are just as productive (if not more) working from home, many folks are unwilling to go back to in-person full-time. Building out flexible work policies, focusing on upskilling, and offering competitive benefits should be a part of your plan to create a work environment tailored to the 2021 employee. But how do you get the right candidates in the door? Here are five ways to attract top talent that might also land your organization on the Best Places to Work list! # ⚓ Normalize_web_services_with_Camel_K_and_AtlasMap, Part_1⠀⇛ This two-part series walks through a simple way to normalize and connect services through Camel K, a part of the Apache Camel project. The scenario in this article addresses a common problem today: Organizations find themselves with a menagerie of different services using different APIs, perhaps because of partnerships or acquisitions. Apache Camel makes it easy to harmonize and normalize the APIs, and its Camel K extension brings Apache Camel’s operations to Kubernetes, allowing containers to expose these endpoints. In this article, we will focus on the benefits of choosing this framework and provide an overview of our base integration flow using Camel K to normalize a backend API. Part 2 will show you how to implement the integration flow step-by-step. We’ll also cover how to simplify data mapping with AtlasMap. # ⚓ Change_deployments_on_the_fly_in_OpenShift_4.8_|_Red Hat_Developer⠀⇛ Red Hat OpenShift 4.8 introduces a very valuable—and possibly very dangerous—new feature: The ability to use a form-based editor to edit deployments. In earlier versions of OpenShift, you could edit the YAML for a Deployment object. In OpenShift 4.8, you can now do the same thing with a fill-in-the-blanks form, so you don’t need to know the proper YAML formatting for values, lists, and dictionaries. The form can also prompt you with existing values where appropriate. Keep reading to learn why the new form-based editor is both an exciting feature and a double-edged sword. # ⚓ Amazon_Linux_2022_Launched,_Completely_Re-based_with Fedora⠀⇛ Amazon Linux 2022 to be based upon Fedora Linux and available via AWS AMIs. We wrap up the announcement and express our views about this change in terms of FOSS ecosystem. # ⚓ Amazon’s_Own_Linux_Distribution_is_Now_Completely Based_on_Fedora⠀⇛ In case you did not know already, Amazon has its own general purpose Linux distribution, unsurprisingly called Amazon Linux. It is intended to be used on AWS servers. When you are deploying a server, you have the choice to use Amazon Linux along with other popular choices of Ubuntu, Debian etc. Since it is from Amazon, there is no licensing fee and Amazon controls on repositories and packages. You can expect a tight integration with AWS tools and access to new AWS innovations with Amazon Linux. Amazon Linux 2022 (AL2022) in the next release in the line of Amazon Linux 1 and 2 and it will be released in 2022 (you can guess that from the version number). # ⚓ Helvum_and_EasyEffects:_Two_great_applications_for PipeWire_users⠀⇛ For a piece of software infrastructure, nothing is more important than good applications to showcase it’s features and demonstrate the possibilities it enables. Fortunately there is a very large body of existing applications because PipeWire implemented the PulseAudio and Jack APIs. This article highlights some of the great efforts undertaken in the community around creating interesting applications for PipeWire in an interview with the maintainers of two of the most popular applications built with PipeWire. They are Wellington Wallace, maintainer of EasyEffects for PipeWire and Tom Wagner, maintainer of the Helvum patchbay application for PipeWire. # ⚓ Rebasing_Fedora_Silverblue_to_Kinoite⠀⇛ Some time ago I was thinking if it’s possible to rebase my ostree system from one to another and how difficult this is. After some thinking I decided to try it by rebasing Fedora 35 Silverblue on my gaming machine to Fedora 35 Kinoite. In this post I will write what I did and what difficulties I had along the road. # ⚓ Will_Thompson:_On_Flatpak_disk_usage_and deduplication⠀⇛ There is a blog post doing the rounds asserting that Flatpak Is Not The Future. The post is really long, and it seems unlikely that I and the author will ever agree on this topic, so I’m only going to talk about a couple of paragraphs about disk usage and sharing of runtimes between apps which caught my eye. This is highly relevant to my day job because all apps on Endless OS are Flatpaks—for example, the English downloadable version has 58 Flatpak apps pre- installed, and 13 runtimes—and I’ve had and answered some of the same questions discussed in the post. # ⚓ Flatpak_Is_Not_the_Future⠀⇛ Flatpak calls itself “the future of application distribution”. I am not a fan. I’m going to outline here some of the technical, security and usability problems with Flatpak and others. I’ll try to avoid addressing “fixable” problems (like theming) and instead focus on fundamental problems inherent in their design. I aim to convince you that these are not the future of desktop Linux apps. o § Devices/Embedded⠀➾ # ⚓ Fairphone:_Pioneering_the_path_to_circularity⠀⇛ The “circular economy”, a concept that is becoming more and more prominent in the current Zeitgeist. In short, it’s an economic system aimed at eliminating waste and facilitating the continual use of resources. A world in which we are genuinely circular is one where materials can be used, recycled and reused to their fullest extent. There’s a catch, of course: for most materials, it’s quite unlikely that recycling alone will be able to meet humanity’s growing demands for them, at least in the coming decades. In addition, recycling also causes waste and we lose a notable amount of materials during the process. While globally we are recycling more, there are barriers. On the journey towards a circular economy, it is critical to assess opportunities and acknowledge the limitations. Developing a mutual understanding of the needs and requirements will ultimately drive the preservation of resources and promote longevity. This is where the KPN-led initiative of the product circularity report comes in. [...] Now that the Fairphone 3 has been analyzed and the insights discussed, the parties involved are looking back to evaluate the lessons learned and share insights from diving into product circularity. # ⚓ What_is_embedded_Linux?_Part_I⠀⇛ The above is an excerpt from Linus Torvalds’ original announcement of what came to be known worldwide as the Linux operating system (OS), dated August 1991. In hindsight, it is inconceivably modest now that we are in a much better position to appreciate the full revolutionary extent of his post. Today, more than 96.4% of the top 1 million server applications run on Linux [2]. Across public clouds, 90% of the workloads use Linux as their OS, with Ubuntu being the most popular Linux distro [3], [4]. Despite debuting as a general-purpose operating system (GPOS) for x86-based hardware, Linux moved beyond web servers and has seen widespread adoption for embedded systems ever since. This two-part blog series aims to provide the reader with a broad overview of topics spanning the world of Linux, embedded systems and the Internet of Things (IoT) in general. In part I of this blog series, we’ll start by taking a look at the embedded ecosystem, followed by an explanation of Linux’s role in it, and will conclude by explaining the rationale behind the OS growing popularity in embedded systems. In part II, we’ll focus on the most pressing challenges facing enterprises today within the embedded space. Let’s get started. # ⚓ A_100_Mhz_6502_CPU_|_Blathering_–_CubicleNate’s_Techpad⠀⇛ I am not an expert in… well… anything, but I am I am continually impressed by the work done by so many in the world, especially in the “retro tech” world. I read this post by Jürgen Müller on his personal site concerning his project of an FPGA based 100 Mhz 6502 CPU. Just reading the title, my thoughts went in numerous directions about the amazing possibilities Using FPGA to emulate vintage computer hardware, let along the 6502 CPU is not new but packaging it on a small board the size of a 40-pin dual inline package hasn’t been done before. The work of Jürgen Müller is an extension on the work of others. This project is packaged on a Spartan-6 FPGA with 64 Kbyte on-chip RAM, mounted on a small circuit board and coined the 65F02. It has the ability to access the external bus on the host system with the correct timing. The FPGA CPU core runs at 100 MHZ where the idea is to make this a “universal” accelerator for 6502 and 65C02 based computers that only requires plugging it into the CPU socket. This won’t work with all computers based on this architecture and there are some limitations. More complex systems like the Commodore 64 with bank switching also provide some challenges as the extended memory cannot be run at the accelerated rate. The expansion boards and bank switching need to be known and emulated by the 65F02. While it makes an effort to detect and access the time- critical peripheral devices there are likely to be incompatible software and and-on hardware. Also, not all software should be accelerated, like video games as they are tied closely to the original systems timings. # ⚓ OWC_launches_Mercury_Elite_Pro_mini_USB-C_storage_drive_for Mac,_Windows,_and_Linux [Ed: There’s NO_connection_to_“LINUX” (as_usual) and I’m guessing that it’s a sponsored ‘article’ that Brian Fagioli is being compelled to make, discrediting BetaNews and himself ahead of Black_Friday_SPAM_festival. Meanwhile, CNX is selling out again, shilling Microsoft malware as as “Sponsored Post”. Not the first time; even worse sellout than previous similar examples from the same site…]⠀⇛ Today, OWC launches its latest portable storage drive. Called “Mercury Elite Pro mini,” this elegant storage solution has a USB-C port and ships with both a USB-C cable and USB-A adapter. In other words, it can be used with any modern computer — whether it has a USB Type-C port or not. In fact, the company says the drive is compatible with Mac, Windows, and Linux-based operating systems, including Android and Chrome OS. # ⚓ AMD_Ryzen_V1000/R1000_Mini-ITX_board_is_made_for_game arcades,_slot_machines_–_CNX_Software⠀⇛ Axiomtek GMB140 is a compact Mini-ITX motherboard powered by AMD Ryzen Embedded V1000/R1000 processor and mostly designed for gaming applications, as well as medical imaging, interactive kiosks, control rooms, and video surveillance. But when we’re not talking about your kids playing games at home here, but instead slot machines, arcade systems, and electronic gaming machines (EGM) powered by the GMB140 board with a PCIe interface for gaming I/O modules, and optional support for a 9-bit serial port for the SAS 6.02 protocol. # § Open Hardware/Modding⠀➾ # ⚓ Introducing_the_Arduino_UNO_Mini_Limited_Edition: Pre-orders_now_open⠀⇛ The iconic Arduino board is back, in the shape of the UNO Mini Limited Edition. Pre- orders have just gone live, so don’t dawdle if you want to get your hands on this stunning piece of Arduino history. # ⚓ Arrow_launches_PSA_Certified_PSoC_64_IoT_Security Workshop_Development_Kit_–_CNX_Software⠀⇛ In 2019, we wrote that Cypress PSoC 64 microcontrollers for Secure IoT applications was one of the first microcontrollers compliant with Arm’s Platform Security Architecture (PSA) designed to secure the Internet of Things. Arrow has now launched the PSoC 64 IoT Security Workshop Development Kit, its first PSA Certified platform, which happens to be based on Cypress PSoC 64, and developed in collaboration with Infineon who purchased Cypress Semiconductor last year. # ⚓ Live_Jam_Kit_Helps_Electronic_Musicians_Stay_In_Sync |_Hackaday⠀⇛ Jamming live with synths and drum machines can be fun, but for [Christian], there was a little something missing. He was looking for a way to keep everyone in the group on the beat and rocking out, and decided to build something to help. The ethos of the build was to put one person ultimately in charge of the mix using Ableton. This stops the volume race, as each musician turns their own volume up and the jam devolves into a noisy mess. Each musician also gets a sync button they can hit if their instrument has drifted out of time. Everyone in the jam also gets their own monitor signal in their headphones, as well as a looper as well. # ⚓ Young_people_can_name_a_piece_of_space_history_with Astro_Pi_Mission_Zero⠀⇛ # § Mobile Systems/Mobile Applications⠀➾ # ⚓ The_10_most_powerful_Android_phones_in_the_world today_according_to_AnTuTu_–_Market_Research_Telecast⠀⇛ # ⚓ MediaTek_Chip_Could_Have_Allowed_Eavesdropping_on Android_|_Digital_Trends⠀⇛ # ⚓ You_can_change_the_Android_12_square_clock_on_Google Pixel_lock_screen⠀⇛ # ⚓ What_to_Do_If_Apps_Keep_Crashing_on_an_Android Device⠀⇛ # ⚓ How_to_Get_Chrome_Extensions_on_Android_–_gHacks_Tech News⠀⇛ # ⚓ How_To_Enable_.docx_in_Google_Docs_App_on_Your Android⠀⇛ # ⚓ Get_the_best_Android_TV_box_at_its_lowest_price_ever |_Android_Central⠀⇛ # ⚓ Android_12_update_for_the_US_Galaxy_S21_models_brings refresh_rate_bug,_Samsung_working_on_a_fix_– PhoneArena⠀⇛ # ⚓ Samsung_One_UI_4_vs._Android_12:_Which_Software_Is Best?_|_Digital_Trends⠀⇛ # ⚓ Android_11_adoption_reaches_24.2%,_still_behind Android_10_–_comments⠀⇛ # ⚓ Bag_a_basic_Android_phone_for_less_than_$100_for Black_Friday_|_Android_Central⠀⇛ # ⚓ These_are_the_best_Android_phones_in_late_2021_– 9to5Google⠀⇛ o § Free, Libre, and Open Source Software⠀➾ # ⚓ The_syslog-ng_Insider_2021-11:_3.35;_SSB;_MacOS;_mqtt() destination_updates; ⠀⇛ This is the 96th issue of syslog-ng Insider, a monthly newsletter that brings you syslog-ng- related news. [...] § Syslog-ng 3.34: MQTT destination with TLS and WebSocket support Version 3.33 of syslog-ng arrived with basic MQTT support. Version 3.34 has added many important features to it: user authentication, TLS support and WebSocket support. These features give you both security and flexibility while sending log messages to an MQTT broker. This blog helps you to make your first steps securing your MQTT connection. # ⚓ My_philosophy_for_productive_instant_messaging⠀⇛ We use Internet Relay Chat (IRC) extensively at sourcehut for real-time group chats and one-on-one messaging. The IRC protocol is quite familiar to hackers, who have been using it since the late 80’s. As chat rooms have become more and more popular among teams of both hackers and non-hackers in recent years, I would like to offer a few bites of greybeard wisdom to those trying to figure out how to effectively use instant messaging for their own work. For me, IRC is a vital communication tool, but many users of 1 find it frustrating, often to the point of resenting the fact that they have to use it at all. Endlessly catching up on discussions they missed, having their workflow interrupted by unexpected messages, searching for important information sequestered away in a discussion which happened weeks ago… it can be overwhelming and ultimately reduce your productivity and well-being. Why does it work for me, but not for them? To find out, let me explain how I think about and use IRC. The most important trait to consider when using IM software is that it is ephemeral, and must be treated as such. You should not “catch up” on discussions that you missed, and should not expect others to do so, either. Any important information from a chat room discussion must be moved to a more permanent medium, such as an email to a mailing list,2 a ticket filed in a bug tracker, or a page updated on a wiki. One very productive use of IRC for me is holding a discussion to hash out the details of an issue, then writing up a summary up for a mailing list thread where the matter is discussed in more depth. I don’t treat discussions on IRC as actionable until they are shifted to another mode of discussion. On many occasions, I have discussed an issue with someone on IRC, and once the unknowns are narrowed down and confirmed to be actionable, ask them to follow-up with an email or a bug report. If the task never leaves IRC, it also never gets done. Many invalid or duplicate tasks are filtered out by this approach, and those which do get mode-shifted often have more detail than they otherwise might, which improves the signal-to-noise ratio on my bug trackers and mailing lists. # § Web Browsers⠀➾ # § Mozilla⠀➾ # ⚓ 4_ways_Mozilla_could_fix_its_Firefox_problem⠀⇛ The open-source app is one of the better browsers on the market but has been hemorrhaging market share for years. As of today, Firefox only has 3.66% of the web browser market share. If I were to guess, the majority of those users are on Linux. That figure alone should tell you how much trouble Firefox is in. We’re talking “Danger, Will Robinson”-level trouble. A 3% market share is hard to bounce back from. So with Firefox so dangerously close to complete irrelevancy, what can Mozilla do to recover? I have a few suggestions. Four, to be exact. # § FSFE⠀➾ # ⚓ Public_Money?_Public_Code!_Spanish_Brochure⠀⇛ Thanks to the support and hard work of our volunteers, our Public Money? Public Code! brochure is now available in Spanish. In this event we will explore the already implemented good practices, but also the challenges that lie ahead to modernise the public digital infrastructure with public code in Spain. The event will be held in Spanish. In the framework of our Public Money? Public Code! initiative we demand that software developed by the public sector with publicly funded money should be available to the public under a Free Software license. To support these demands, we provide an exhaustive brochure which is dedicated to public bodies and serves as an instrument to address decision-makers to inform them about the advantages of Free Software. Thanks to that it has become easier to convince them of modernising public digital infrastructure with public code. # § Programming/Development⠀➾ # ⚓ PHP_Foundation_formed_to_fund_core_developers,_vows to_pay_‘market_salaries’⠀⇛ The trigger for this initiative appears to be the decision of Nikita Popov, a significant PHP contributor, to focus mainly on LLVM in future. Popov, currently a software developer at JetBrains working on the PhpStorm IDE, will be leaving the company from 1 December, according to a post by product marketing manager Roman Pronskiy, which also introduces the new foundation. # ⚓ The_New_Life_of_PHP_–_The_PHP_Foundation⠀⇛ During PHP’s 26-year history, the language has been actively developed by a huge number of people, such as Rasmus Lerdorf, Zeev Suraski, Andi Gutmans, Nikita Popov, and many, many others. In 2021, PHP is in for another round of evolution. [...] The PHP Foundation will be a non-profit organization whose mission is to ensure the long life and prosperity of the PHP language. # ⚓ [Old] Avoiding_Busses⠀⇛ It’s always been the case that there are certain parts of PHP source code that only a few people understand. The Karma system used to help us determine where a contributor could commit code in the source tree; If you had /Zend karma, you had a clue about Zend. Among those people with /Zend karma, some people understood more than others. This was a perfectly sustainable way of developing the language, because while /Zend is complicated, it’s written in a language that everybody working on a C project understands. In principle, we can take people who know a little C and turn them into a / Zend karma worthy workhorse for PHP, able to produce patches, and fixes, and features. Indeed, we have done, and are still doing that in the incubator that is Stackoverflow chat. Many moons have passed … What do you think the bus factor of PHP is today ? # ⚓ Why_Now_Is_the_Time_to_Get_a_Job_in_Tech⠀⇛ Now is a great time to get started with a career in tech. The recent Great Resignation and corresponding churn in the job market means many organizations are looking to hire workers immediately. According to the recent Job Openings and Labor Turnover (JOLTS) report, 4.4 million Americans left their jobs in September, and there are now 10.4 million job openings, which passes pre-pandemic levels. # § Python⠀➾ # ⚓ Dynatrace_:_OneAgent_release_notes_version 1.229⠀⇛ Starting with Dynatrace version 1.231, the Extension Framework (also referred to as the plugins framework) will start using Python 3.8. The Python 3.6 component will be replaced by Python 3.8. * § Leftovers⠀➾ o ⚓ The_Radical_World_of_Chicago’s_Black_Comic_Artists⠀⇛ It’s Life as I See It, a recent anthology of work by Chicago-based Black comic artists from 1940 to 1980, takes its name from a cartoon by Charles Johnson, which shows a Black artist standing with an older white man in front of a large canvas. The canvas is painted black and surrounded by a thick white border. In the caption, the artist informs the other man that the painting is life as he sees it. o ⚓ Ridley_Scott_Blames_His_Latest_Movie_Bombing_At_The_Box_Office_On Facebook_And_Millennials,_Rather_Than_Pandemic_And_Poor_Marketing⠀⇛ I will admit that, until this morning, I had never heard of Ridley Scott’s movie The Last Duel. It was released this fall in theaters only, which is a bold move while we’re still dealing with a raging pandemic in which most people still don’t want to go sit in a movie theater. And so, the box office results for the movie were somewhat weak. Indeed, it’s now Scott’s worst performing movie at the box office. o ⚓ In_the_Interest_of_Mezcal⠀⇛ Some old mezcaleros can still harvest a big agave, or maguey in a matter of minutes. They have such strength. They’re the voice of the earth when they speak, nature itself when they see you, and when they say nothing they’re the silence of the fields. o ⚓ A_Final_Word_or_Two_From_the_Wise_Old_Philosopher⠀⇛ A professor of history and faculty affiliate in the philosophy department at Harvard University, Peter Gordon is dazzled by Jurgen Habermas’s “brilliant and highly illuminating history of philosophy that spans the millennia, Achsenzeit to the modern era.” Famous philosophers like to toss in some German words: achsenzeit means Axial Age (think Axial Age, think Karl Jaspers). The first big insight Gordon offers us is that the famous philosopher aims to “self-consciously vindicate postmetaphysical thinking as the telos of our spiritual history.” Postmetaphysical thinking has to do with moving beyond “absolute knowing” onto a horizontal plane of partiality and fragmented forms of knowing. Basically, during the Axial Age (800-300 BCE) some break- through thinkers (like Isaiah or Buddha) oriented us toward a “new, transcendent principle (God, Logos, Nirvana) that was the telos of human life. We might say, then, that they all had in common a certain affirmation of metaphysics.” The idea of history having (or carrying an inherent purpose (or direction) is immensely controversial in theological and philosophical thought. For strong-minded secularists, teleological thinking reeks of Christian ideas of a providential God working out his purposes in history behind our backs. Secularists do not like the idea of providence; and they sense that a philosopher like Kant sneaks a “weak form of providence” into his writings. o § Science⠀➾ # ⚓ A_Giant_Hole_In_The_Sun_Is_Throwing_Out_Charged_Particles Towards_Earth⠀⇛ According to SpaceWeather.com, this could cause some minor geomagnetic unrest in the planet’s magnetosphere. To the uninitiated, the plasma that it spews consists of free-flowing electrons and protons. They originate from the Sun’s outermost layer, that’s capable of reaching temperatures up to 1.1 million degrees celsius. While the geomagnetic unrest won’t really cause massive solar storms that could knock out our electronics, it is expected to put on a show for people residing at the poles, resulting in beautiful auroras. o § Education⠀➾ # ⚓ School_Sued_for_Denying_Equal_Education_to_Students_with Disabilities_–_Validated_Independent_News⠀⇛ “Pittsburg Unified has a separate, unequal and illegal system of education for students of color and those with disabilities,” said Linnea Nelson, senior staff attorney for the ACLU of Northern California, quoted in Ed Source. The lawsuit is based on the 2018-19 California Department of Education’s district report on Pittsburg Unified showing that students with disabilities in the district are five times as likely to be suspended for disrupting school activities as disabled students from other schools throughout the state. They are also more likely to be chronically absent, with a 22% absentee rate compared to 19.5% nationally. Superintendent of the district Janet Schultze claimed that the lawsuit overlooks the progress that has been made in the district over the years in closing achievement gaps, but the ACLU lawsuit claims that the district has not yet adopted a sufficient number of initiatives to combat achievement gaps. # ⚓ Nikole_Hannah-Jones:_Anti-History_Laws_Are_Right’s_Attempt to_Control_Our_Memory⠀⇛ # ⚓ COVID-19’s_Negative_Impact_on_Higher_Education_Institutions and_Faculty_Salaries_–_Validated_Independent_News⠀⇛ Even though COVID-19 brought about billions of dollars in relief funding, according to the American Association of University Professors (AAUP), “cuts are looming large because state revenues are projected to fall by as much as $200 billion by the end of the 2020-21 fiscal year, according to projections by the Urban Institute.” # ⚓ Colleges_are_walking_away_from_remote_education_–_and that’s_a_good_thing⠀⇛ Indeed, research on human learning consistently finds that the social context of learning is critical, and the emotions involved in effective human relations play an essential role in learning. Think of a teacher who had a great impact on you – the one who made you excited, interested, intrigued, and motivated to learn. Was this teacher a calm and cool transmitter of facts, or a person who was passionate about the subject and excited to talk about it? And how did this teacher relate to you? Were you an empty container into which information was poured, or a person whose thinking and enthusiastic responses were valued and important? o § Hardware⠀➾ # ⚓ Observing_A_Plant’s_Vascular_System_With_X-Ray_Video_| Hackaday⠀⇛ [Ben Krasnow] has a knack for showing us what’s inside of things while they’re moving. This week’s Applied Science experiment has him making time- lapse X-ray videos of things. This plant’s vascular system is just one of a few examples, the others being a dial clock and the zoom lens on a DSLR. o § Health/Nutrition/Agriculture⠀➾ # ⚓ Opinion_|_It’s_International_Food_Workers_Week—Support Organizing_That_Centers_Those_Who_Feed_Us⠀⇛ Every year, the Food Chain Workers Alliance marks International Food Workers Week in November. As peoples’ thoughts turn to holiday feasts, it’s a time to recognize the labor that people working from field to factory contribute to feeding the world. What started as an awareness campaign in 2012 by organized food and farmworkers leveraging end-of-year holidays around the need to raise the minimum wage and improve working conditions from farm to table, the campaign has become more relevant than ever in 2021. # ⚓ Homeless_Students_Uniquely_Challenged_by_COVID-19_Pandemic –_Validated_Independent_News⠀⇛ According to a November 2020 report produced by Poverty Solutions, based at the University of Michigan, and SchoolHouse Connection, a Washington, D.C. homeless advocacy organization, estimates that 423,164 students who were identified as homeless in 2019 “may not be in school at all, or receiving basic needs and educational supports.” While the identification and enrollment of homeless students is down, in fact the number of children and youth experiencing homelessness has likely increased due to the economic crisis, according to the report. # ⚓ COVID-19_Risks_Heightened_by_Rundown_Facilities_at Disadvantaged_Schools_–_Validated_Independent_News⠀⇛ As Becky Pringle, the president of the National Education Association (NEA), told Truthout,  “The pandemic has caused America to see what educators have seen forever.” The lack of funding for school  infrastructure disproportionately impacts students of color. # ⚓ As_Poll_Finds_Most_US_Voters_Support_Insulin_Price_Cap, Senators_Push_Inclusion_in_Build_Back_Better_Act⠀⇛ As a new survey published Tuesday showed overwhelming support among American voters for capping the cost of insulin at $35 per month, progressive U.S. lawmakers underscored what they insisted is the Senate’s imperative to include a provision allowing Medicare to negotiate lower drug prices in its version of the Build Back Better budget reconciliation bill. The Data for Progress poll found that 87% of all respondents—including 94% of self-described Democrats, 84% of Independents, and 82% of Republicans—”strongly” or “somewhat” favor the insulin price cap. # ⚓ WHO_Covid-19_Test_Deal_With_Spain_Shows_‘Path_to_a_Better World’_With_Vaccine-Sharing⠀⇛ Public health experts and justice campaigners worldwide celebrated after a United Nations agency revealed Tuesday that a Spanish research institution struck a deal on “the first transparent, global, nonexclusive licence for a Covid-19 technology,” a model that could be replicated for various tests, treatments, and vaccines to help end the pandemic. “This licence is a testament to what we can achieve when putting people at the center of our global and multilateral efforts.” # ⚓ Why_Moderna_Refuses_to_Share_Rights_to_the_COVID-19_Vaccine With_the_Government_That_Paid_for_Its_Development⠀⇛ I teach drug regulation and patent law at Saint Louis University’s Center for Health Law Studies. Moderna recently offered to share ownership of its main patent with the government to resolve the dispute. Whether or not this is enough to satisfy the government’s claims, I believe the dispute points to serious problems in the ways U.S. companies bring drugs and vaccines to market. # ⚓ DOJ_Files_Emergency_Brief_Asking_Court_to_Unblock_COVID Vaccine_Work_Rules⠀⇛ # ⚓ ‘Stop_the_Carnage’:_Biden_Urged_to_Fight_Big_Pharma’s Vaccine_Greed_at_Key_WTO_Meeting⠀⇛ A coalition of civil society organizations and progressive U.S. lawmakers gathered Tuesday to send President Joe Biden an urgent message ahead of the World Trade Organization’s Ministerial Conference next week: Ensure adoption of a patent waiver for Covid-19 vaccines or risk prolonging the global pandemic indefinitely. “Presence of the virus anywhere is a threat to people everywhere.” # ⚓ ‘Once_We’re_Gone,_We’re_Not_Coming_Back’⠀⇛ “There’s enough labor for four people but not enough income for one,” his father, Jeff, said. Like most farmers, Jeff sells his cattle, corn and soybeans at prices set by a global commodities market, but only large farms can absorb the narrow profit margins. Though the family’s small farm is valuable — its 880 acres are assessed at $1.3 million — property taxes eat up most of the money it does make. # ⚓ Expanded_benefits_for_vets_exposed_to_burn_pits_coming,_but for_some_it’s_too_late⠀⇛ “I knew that deploying could cost me my life,” Thomas, now 41, told ABC News. “I didn’t think it would be like this.” o § Integrity/Availability⠀➾ # § Proprietary⠀➾ # ⚓ MediaTek_to_make_chips_for_ARM-based_Windows_PCs: Report⠀⇛ For those unaware, MediaTek already has a presence in the segment of computers. It offers low-end and entry-level chips for Chromebooks “Apple has shown the world that it can be done. The Wintel partnership that’s gone on for so long has to be under some pressure, and when there’s pressure, there’s an opportunity for companies like ours,” XDADevelopers quoted Eric Fisher, Vice President of Corporate Sales and Business development as saying. # § Security⠀➾ # § Privacy/Surveillance⠀➾ # ⚓ NSO_Made_Millions_Selling_Phone_Hacking Tools_To_The_Princes_And_Kings_Of_The United_Arab_Emirates⠀⇛ NSO Group can’t get a break. Too bad. It really doesn’t deserve one. The inability of the Israeli exploit purveyor to escape this endlessly negative news cycle is entirely its own fault. And each passing day seems to uncover something new and nasty about the tech company, which has built its business by seemingly selling to whoever wants to buy, no matter how morally repugnant. # ⚓ Apple_Sues_Israel’s_NSO_Group_in_Effort to_Protect_iPhone_Users_From_Pegasus Spyware⠀⇛ Apple on Tuesday sued NSO Group, accusing the Israeli company—widely criticized for selling surveillance technology to repressive governments around the globe—of infecting targeted iPhones with Pegasus spyware, which has been used to crack down on dissidents and journalists. In its lawsuit, the U.S. tech giant accused the Israeli surveillance company of violating its terms and conditions as well as U.S. federal and state laws. # ⚓ South_Korean_Gov’t_Gave_Millions_Of Facial_Photos_Collected_At_Airports_To Private_Companies⠀⇛ Facial recognition systems are becoming an expected feature in airports. Often installed under the assumption that collecting the biometric data of millions of non-terrorist travelers will prevent more terrorism, the systems are just becoming another bullet point on the list of travel inconveniences. # ⚓ Apple_Sues_Israeli_Spyware_Maker,_Seeking to_Block_Its_Access_to_iPhones⠀⇛ The lawsuit is the second of its kind — Facebook sued the NSO Group in 2019 for targeting its WhatsApp users — and represents another consequential move by a private company to curb invasive spyware by governments and the companies that provide their spy tools. Apple, for the first time, seeks to hold NSO accountable for what it says was the surveillance and targeting of Apple users. Apple also wants to permanently prevent NSO from using any Apple software, services or devices, a move that could render the company’s Pegasus spyware product worthless, given that its core business is to give NSO’s government clients full access to a target’s iPhone or Android smartphone. # ⚓ Moscow_tells_13_mostly_U.S._tech_firms they_must_set_up_in_Russia_by_2022⠀⇛ The demand, from state communications regulator Roskomnadzor late on Monday, gave few details of what exactly the companies were required to do and targeted some firms that already have Russian offices. # ⚓ #PrivacyofThePeople:_Society_and community_management_apps⠀⇛ In the latest post in our #PrivacyOfThePeople series, we look at the privacy implications of the society and community management applications that resident associations are increasingly adopting in Tier 1 and Tier 2 cities across India. We analyse the user rights from harm and consent-based frameworks, and how the upcoming data protection law may protect users. # § Confidentiality⠀➾ # ⚓ [Old] The_Joy_of_Cryptography⠀⇛ This book assumes knowledge of basic discrete math concepts; a quick review of these topics is provided in Chapter 0. Readers may also benefit from some familiarity with data structures, algorithms, and theoretical computer science. Sorry, there are no solutions available for the exercises. All the sensible textbook titles were already taken. Actual joy not guaranteed. This book is licensed under Creative Commons BY-NC-SA 4.0. You must give attribution to the author, must not use this book for commercial purposes, and must distribute derivative works under the same license. # ⚓ [Old] A_Cryptographic_Compendium⠀⇛ This site contains a brief outline of the various types of cipher systems that have been used historically, and tries to relate them to each other while avoiding a lot of mathematics. o § Defence/Aggression⠀➾ # ⚓ Opinion_|_Go_Ahead,_Take_Their_Guns._The_US_Would_Be_a_Less Dangerous_Place⠀⇛ Expect the gun control debate in America to really get hot over the next 12 months as Beto O’Rourke runs for governor of Texas. O’Rourke said, when running for president in 2019, “Hell yes, we’re going to take your AR-15, your AK-47!” # ⚓ Empire_Can’t_be_Fixed,_It_Must_be_Dismantled⠀⇛ “Some people feel that ending the war in Vietnam and driving Nixon from office created a momentum for change.”  But these were only “marginal victories. The structural determinants of another imperial war, and for another effort to consolidate total power, remain essentially as strong as ever. A massive and centralized empire absorbs such setbacks . . . as a sponge absorbs water.”[1] Indeed, Reagan’s covert 1980s Central America wars came just a few years later.  Then Iraq, Kosovo, Afghanistan, back to Iraq. Along with many smaller engagements and a spread of special operations and drone warfare across a vast swathe of the globe. Meanwhile, the 9-11 attacks, blowback from Middle Eastern wars, have built up a foreign and domestic surveillance state Nixon only imagined. (He did, in the form of the Huston Plan, which played into his impeachment.) # ⚓ Opinion_|_Jogging_in_Broad_Daylight_Should_Not_Be_a_Death Sentence⠀⇛ On Monday, closing arguments began in the trial of the three white Georgia men who shot down Ahmaud Arbery, a 25-year-old Black man for the apparent crime of jogging while Black. # ⚓ Ahmaud_Arbery is_Responsible_for_His_Own_Death⠀⇛ Ahmaud Arbery is an African American resident of the extended neighborhood, and he likes to run. The father son McMichael team  are a former cop and former coast guard ensign; they are white, they carry guns, spend much time viewing security recordings, and consider themselves to be the neighborhood’s armed guardians. # ⚓ Subpoenas_for_Roger_Stone,_Alex_Jones_Expose_Bizarre Underbelly_of_Jan._6_Attack⠀⇛ # ⚓ Is_China_Really_a_Threat?_Noam_Chomsky_Slams_Biden_For Increasingly_Provocative_Actions_in_Region⠀⇛ We feature an excerpt from our recent interview with world-renowned scholar and political dissident Noam Chomsky about how the Biden administration is continuing a reckless foreign policy, despite taking a softer tone than the Trump administration. “The trajectory is not optimistic,” Chomsky says. “The worst case is the increasing provocative actions towards China. That’s very dangerous.” Chomsky will join us on our 25th anniversary online celebration on the evening of December 7. # ⚓ Octogenarian_Egyptian_thinker_jailed_for_saying_Islam spread_by_conquest⠀⇛ Maher claimed in many of his speeches, writings, and TV appearances, that the early Islamic conquests were “military invasions”, and called on Egypt’s top Islamic institution – Al-Azhar – to apologise on behalf of the Prophet Muhammad’s companions who led the raids. According to Maher, those “invasions aimed to enslave women rather than spread Islam” around the world. # ⚓ ISIS_using_TikTok_to_recruit_young_suicide_bombers_in_bid to_carry_out_Christmas_attacks⠀⇛ The account used to spread the ISIS videos has been operating for 18 months which has been watched thousands of times. # ⚓ Liverpool_bomber_‘reverted_to_Islam’_in_months_before attack⠀⇛ Associates are believed to have told detectives that Al Swealmeen, 32, an Iraqi asylum seeker, had since returned to Islam, although sources said that was “not a motive for an attack”. Counterterrorism police are yet to find evidence of an ideology that motivated him. # ⚓ Jan._6_Organizers_Used_Anonymous_‘Burner_Phones’_to Communicate_with_White_House_and_Trump_Family,_Sources_Say⠀⇛ The three sources said Kylie Kremer took one of the phones and used it to communicate with top White House and Trump campaign officials, including Eric Trump, the president’s second-oldest son, who leads the family’s real-estate business; Lara Trump, Eric’s wife and a former senior Trump campaign consultant; Mark Meadows, the former White House chief of staff; and Katrina Pierson, a Trump surrogate and campaign consultant. # ⚓ [ISIS]_is_stealing_thousands_of_sheep_in_Syria_to_finance terror_cells⠀⇛ The jihadi group is engaged in an ‘easy and lucrative’ smuggling operation as it looks to other sources of finance beyond the oil that once funded its self-proclaimed caliphate. Cells in Hama and areas bordering Raqqa and Aleppo are said to be carrying out widespread black market operations after Isis lost its territorial stranglehold in 2019. Sheep stolen from locals are being sold at live cattle markets by fighters posing as shepherds, either in northern regions controlled by the Kurdish-led Syrian Democratic Forces (SDF), which is backed by the US, further south in regime-held Syria or across the border in Iraq. # ⚓ In_Ethiopia,_Facebook_allowed_posts_inciting_violence_to_go viral_for_years._The_company’s_response_is_both_dismissive and_ineffective._|_Media_Matters_for_America⠀⇛ Facebook’s lax approach to content moderation has resulted in the incitement of violence and the spread of hate speech in Ethiopia — despite the company designating the nation “at risk” and repeatedly proposing to create resources for proper content moderation. Now, the company continues to placate its users by having high-level officials give vague statements and make empty promises while demonstrating minimal actual progress. Ethiopia — with approximately 110 million people and over 11 million Facebook users — has been in a state of civil unrest for almost a year. In 2018, Prime Minister Abiy Ahmed came to power and was initially praised for promoting civil liberties, including releasing political prisoners and lifting restrictions on media. However, long-simmering political tensions quickly returned between government forces and the Tigray People’s Liberation Front, which was in power prior to Ahmed’s election, eventually leading to violence. The fighting since then has displaced over 1.7 million people in the Tigray region, and the United Nations aid chief warned in October that hundreds of thousands there now face famine. Though human rights groups have found both sides to be responsible for atrocities, the United Nations refugee agency, UNHCR, reported that government forces have committed massacres of ethnic Tigrayans and weaponized sexual assault against thousands of women. Now, the United States government is reportedly considering labeling the actions by Ahmed’s government as a genocide. o § Transparency/Investigative Reporting⠀➾ # ⚓ Lots_Of_Big_Media_Companies_Had_Access_To_The_Facebook Files;_Only_Gizmodo_Decided_To_Put_In_The_Work_To_Make_Them Public⠀⇛ Over the last month or so, you’ve probably heard a lot about the Facebook Files or the Facebook Papers, which are the documents shared by former Facebook employee and whistleblower Frances Haugen with the media, starting with the Wall Street Journal, and then a rather reluctant “consortium” of seventeen big name US-based news organizations. The reluctance was apparent in the name of the Slack group created for all of the reporters working on the project: “Apparently We’re A Consortium Now.” o § Environment⠀➾ # ⚓ Before_the_Storm:_How_Do_You_Know_When_to_Go?⠀⇛ # ⚓ Chamber_of_Commerce_Lobbying_on_Climate_Investing_‘At_Odds’ With_Member_Stances,_Says_Report⠀⇛ As the impacts of a changing climate rapidly intensify worldwide, the climate crisis is also hitting businesses and the financial sector where it hurts: the wallet. That’s part of the reason that so-called ESG funds, which promise to emphasize environmental, social, and governance issues in making investment decisions, have become one of the fastest growing sectors in the financial world. By some estimates, nearly a third of the world’s assets under management could be held in ESG investments within a few years. # ⚓ Gerrymandering_is_a_climate_problem⠀⇛ “Redistricting happens every 10 years, following the decennial census,” said Adam Podowitz-Thomas, senior legal strategist at the Princeton Gerrymandering Project. The goal is straightforward: As populations rise and fall over time in different parts of the country, political boundaries need to shift as well to ensure roughly equal representation per number of residents. But too often, the process devolves into a partisan power grab, with Democrats and Republicans both engaging in gerrymandering. The term gerrymandering dates from 1812, when then- Massachusetts governor Elbridge Gerry signed a bill approving wildly distorted maps drawn to benefit his party. One of the new districts was said to resemble a salamander – or, as one contemporary wit described it, a “Gerry-mander.” # ⚓ Schools’_Infrastructure_in_Crisis_as_Climate_Changes_– Validated_Independent_News⠀⇛ The Hechinger Report delves into several Alaskan school districts where failing school infrastructure prevents community members from being safe in an extreme weather event. According to data from a March 2021 produced by the University of Alaska Anchorage’s Institute of Social and Economic Research, Alaska spends roughly a third of the recommended amounts to properly maintain and expand its school facilities. Kachemak Selo, a village on the Kenai Peninsula closed its high school for several weeks in December 2020, “because it was raining in the building”(Kevin Lyon, Kenai Peninsula Borough School District director). About 170 miles from Kachemak Selo on the Kenai Peninsula rests the town of Seward. Seward is a beautiful, rural town that is ribboned by the Kenai Fjords, glacier flows from the Kenai mountains. The constant glacial outpours make Seward a “pretty hazardous place to live” according to Stephanie Presley, program lead for the Seward- Bear Creek Flood Service Area. These dangers extend to Seward’s public schools. Recent Seward High School graduate Selma Casagranda said of Seward’s schools “There’s just a lot of stuff that goes unfixed, and if something were to happen, I don’t know what we would do.” Alaska is not the only state in America that needs substantial infrastructure funding. # § Energy⠀➾ # ⚓ Hoping_to_Lower_Pain_at_the_Pump,_White_House_Says It’s_Opening_Oil_Reserves⠀⇛ # ⚓ Right-Wing_Group_Uses_‘B.S.’_Environmental_Justice Argument_in_Effort_to_Keep_an_Oil_Pipeline_Alive⠀⇛ A right-wing group that has a history of receiving funding from conservative foundations and ExxonMobil is trying to frame the state of Michigan’s attempts to shut down the aging Line 5 oil pipeline as an assault on the Black community.  That industry-backed spin has not gone down well with Michigan activists. “I think that’s B.S. I think it’s phoney baloney,” Theresa Landrum, a community activist in Detroit, told DeSmog. “The Black community is not benefiting. We have been suffering all along.” # ⚓ The_World_Bank_Can’t_be_Trusted_to_Stand_Up_to_Big Fossil_Fuel_Companies⠀⇛ # ⚓ Explained:_What_is_El_Salvador’s_Bitcoin_city?⠀⇛ Bukele’s administration is counting on Bitcoin to spur the country’s economic growth, and investment, assuming that Bitcoin price remains on an overall upward trajectory. Here we explain Bukele’s plan for a Bitcoin city. # ⚓ Govt_plans_bill_to_ban_private_cryptocurrency,_allow RBI_digital_coin⠀⇛ The government will move a bill to frame rules for cryptocurrencies aimed at prohibiting private coin while providing a framework for the creation of an official digital currency to be issued by the Reserve Bank of India (RBI). The bill is listed among 26 items of legislation for consideration in the winter session of parliament, according to a bulletin issued by the Lok Sabha on Tuesday. The crypto industry is hopeful there won’t be a complete ban on cryptocurrencies. # ⚓ India_announces_bill_to_ban_cryptocurrencies⠀⇛ Between 15 and 100 million people in Asia’s third-largest economy are estimated to own cryptocurrencies, with total holdings in the billions of dollars. Their investments will now face an uncertain future. India’s central bank announced in June that it is working to introduce its own digital currency by the end of the year, while warning it has “serious concerns” about private cryptocurrencies like Bitcoin, Ethereum and others. # ⚓ Harvard_and_Yale_Should_Do_More_Than_Just_Divest⠀⇛ But our work at Harvard and Yale, and across higher education, is far from over. As world leaders fail repeatedly to deliver necessary climate action, the importance of divestment and strategies that center direct action over conventional bureaucratic politics has never been greater. Yet our universities’ responsibility doesn’t end with their hard- won promises to make their endowments fossil- free. We need meaningful follow-through on their commitments, on a timeline that reflects the urgency climate science and justice demand. And we need our universities to sever their toxic ties to the fossil fuel industry in research and programming, as well as use their outsize endowments to accelerate a just fossil-free economy that invests in frontline communities for generations to come. # § Wildlife/Nature⠀➾ # ⚓ The_Dreaded_Rainforest_Shift⠀⇛ Studies of the Amazon Rainforest over the past decade have shown telltale signals of an impending shift from a carbon sink of heat- trapping gases to a source of greenhouse gases. It’s a dangerous shift that will destabilize the atmosphere of the entire planet. Alas, the dreaded shift has been confirmed via a laborious ten-year airborne detailed study. The study shows the eastern Amazon rainforest has become a significant source of carbon emissions, competing with cars, trains, planes, and power plants. This travesty is officially confirmed via hundreds of aircraft vertical profiling measurements of the air above the rainforest over a period of nearly one decade. (Source: Amazonia As A Carbon Source Linked to Deforestation and Climate Change, Nature, July 14, 2021) o § Finance⠀➾ # ⚓ Warren,_Sanders_Request_8_Million_Student_Loan_Borrowers_Be Moved_Out_of_Default⠀⇛ # ⚓ Warren,_Sanders,_and_Baldwin:_Investors_‘Made_Off_Like Bandits’_at_Expense_of_Striking_Alabama_Miners⠀⇛ As Alabama miners continue their seven-month strike against Warrior Met Coal, a trio of U.S. senators on Tuesday sent letters of inquiry to the private equity firms the lawmakers say “made off like bandits” after taking over the company while workers “endured severe cuts to pay and benefits” in order to ensure its success. “We have long been concerned that some private equity firms pursue strategies that extract value from portfolio companies at the expense of workers and communities.” # ⚓ “Skimpflation”:_the_Latest_Attempt_to_Hype_Inflation Fears⠀⇛ I had mixed feelings on hearing this report. On the positive side, I had made arguments like this a quarter century ago, when the party line (the views of the elites in both political parties) was that that the official CPI overstated inflation. The issue then was that there was a concerted effort to cut Social Security benefits. There is an annual cost-of-living adjustment (COLA) for Social Security that is tied to the CPI. The goal at the time was to reduce this COLA so that the government paid out less in Social Security. # ⚓ The_Real_Cost_of_a_Hamburger⠀⇛ Unfortunately, assessing the real price of a hamburger is difficult because much of the overhead is hidden from view or simply ignored. Most people do not see the pain of the animals as they are branded, castrated, and slaughtered. Nor are most people fully aware of the multiple hormones and chemicals dumped into feed or directly injected into the animals. Nor have they considered how these high rates of hormone and chemical use may pose risks for humans through the creation of resistant germs and bacteria. While there is a growing awareness of the health costs – including high rates of heart attack, colon cancer, and high blood pressure, resulting from a heavy meat diet – even the best assessments of the health risks are far from complete. But these costs, while real and significant, pale by comparison to the ecological cost of livestock production. There is no other single human activity that has degraded and destroyed more of the American landscape and perhaps the global landscape as well as our love affair with the cow and the meat-dominated diet. # ⚓ The_Establishment_Panic_at_Cryptocurrency⠀⇛ Leaving aside matters of inspiration, much the same can be said of Hillary Clinton, failed US presidential candidate, tenured alarmist grump, ever worried about inroads being made into establishment power by rogue elements keen to snatch the crown of power.  One of them, in her mind, is the threat posed by cryptocurrency. During a panel discussion at the Bloomberg New Economy Forum in Singapore, she made the following commentworth quoting in full: “One more area I hope nation-states start paying greater attention to is the rise of cryptocurrency because what looks like a very interesting and somewhat exotic effort to literally mine new coins in order to trade with them has the potential for undermining currencies, for undermining the role of the dollar as the reserve currency, for destabilising nations, perhaps starting with small ones but going much larger.” # ⚓ What_China_Learned_From_U.S._Capitalism’s_Development⠀⇛ Chinese leaders have learned, implicitly or explicitly, from how U.S. capitalism lost those capacities. Thus, China organized both its employer-employee relationships and its international linkages differently. By doing so, the Chinese economy is ascending while that of the United States is descending. The process is, of course, uneven; the differences between the United States and China vary. But the general pattern and direction remain the same: China up and the United States down. From 1820 to the 1970s, U.S. capitalism employed a fast-growing number of workers and paid them a real wage that grew every decade until the 1970s. That remarkable performance enabled, validated, and combined with a culture that emphasized consumption (the positive) as the compensation for labor (the negative). The combination blunted the appeals of dissidents, radicals, socialists, and other critics of capitalism until the 1930s. Productivity grew across the 150 years even faster than real wages and boosted profits rapidly. The United States outperformed other capitalisms in both the profits accruing to the employer class and the real wages flowing to the employee class. # ⚓ Five_Crises_of_Capitalism:_The_Challenges_Facing_the_Left Today⠀⇛ There are several interacting crises in this new epoch. The Bible had only four horsemen of the apocalypse—Pestilence, War, Famine, and Death. Today, we have five. The first is the global economic crisis. The Great Recession of 2008 ended the long neoliberal boom, which began in the early 1980s, triggering what David McNally calls a “global slump” and Michael Roberts calls a “long depression.” # ⚓ Voters_From_Both_Parties_Overwhelmingly_Want_Biden_to_Crack Down_on_Corporate_Crime⠀⇛ Although President Joe Biden’s domestic agenda has been hobbled to some degree by unified Republican obstruction as well as opposition from several right-wing Democrats, he still has the executive authority to challenge corporate abuses—and new survey data released Tuesday shows that an overwhelming majority of U.S. voters, regardless of political affiliation, want his administration to do just that by aggressively enforcing existing laws. “A Biden administration that pursues crooked CEOs and brings down abusive corporate titans will find a willing audience in the American public.” # ⚓ ‘Now,_Let’s_Take_This_Nationwide’:_Biden_Raises_Minimum Wage_for_All_Federal_Contract_Workers_to_$15⠀⇛ Chair of the Congressional Progressive Caucus Pramila Jayapal celebrated Monday’s announcement from the U.S. Labor Department that all federal contract workers will be paid at least $15 per hour starting in January, but also took the opportunity to argue that should be the wage floor should for all U.S. workers. “Great news,” tweeted Jayapal in response to the news. “Now, let’s take this nationwide and give over 30 million workers a much-needed and well- deserved raise.” o § AstroTurf/Lobbying/Politics⠀➾ # ⚓ Trump-Allied_Lawyers_Ordered_to_Pay_$187,000_in_Fees_for Their_Election_Lawsuit⠀⇛ # ⚓ Amid_GOP_Attacks,_UN_Expert_Warns_of_Near_‘Tyranny’_Against Voting_Rights_of_US_Minorities⠀⇛ After completing an extended visit to explore the current state of U.S. society and democracy, a United Nations expert on Monday blasted near “tyranny” against the voting rights of minorities nationwide. “The patchwork of constitutional and civil rights in the country are not sufficiently protecting those most in need of protection.” # ⚓ Ocasio-Cortez_Leads_Campaign_to_Add_Immigration_Reform_Back Into_Reconciliation⠀⇛ # ⚓ California_Progressives_to_Feinstein:_Support_Nixing Filibuster_for_Voting_Rights—or_Resign⠀⇛ Dozens of grassroots advocacy groups representing more than 150,000 Californians demanded Tuesday that Sen. Dianne Feinstein step down if she’s unwilling to support—at the very least—a voting rights carve-out for the filibuster, an archaic Senate rule that Republicans have used to tank several pro-democracy bills in recent weeks. In a letter to Feinstein, more than 65 progressive organizations including Indivisible East Bay and the Poor People’s Campaign warned that the GOP’s aggressive voter suppression efforts and redistricting schemes nationwide mean that “we are headed toward permanent minority rule over much of the country and therefore over Congress and the presidency—a minority rule which will make a mockery of the idea that citizens have the right to determine how they are governed.” # ⚓ The_Excommunication_of_Liz_Cheney⠀⇛ When neoconservatism was still the favored faith of elites in the Republican Party, Liz Cheney was a high priestess. She worshiped at the altar of defense budgets and surveillance schemes. She preached a gospel of tax cuts for the rich, giveaways for corporations, and austerity for the masses. Intensely ambitious and always on message, she rose rapidly in the ranks of the party that extended from her father’s reign as the initiator of forever wars. # ⚓ Socialists_Secure_Massive_Victory_in_Venezuelan_Elections⠀⇛ # ⚓ Venezuela’s_socialists_win_elections_in_landslide_–_so_US tries_to_discredit_them⠀⇛ # ⚓ Opinion_|_Inflated_Excuses:_Centrists_Continue_to_Find Excuses_to_Stall_Progress⠀⇛ The potential landmark progressive legislation Build Back Better Bill came one step closer to becoming a reality last week. The House passed the close to $2 trillion compromise version of the bill which still includes sweeping initiatives to combat climate change and strengthen the nation’s economic and social safety net. Hailing its passage, President Biden declared that the bill was “fiscally responsible” and “Above all, it puts us back on the path to build our economy back better than before by rebuilding the backbone of America: working people and the middle class.” # ⚓ Breaking_News:_AOC’s_District_Has_Opinions⠀⇛ The residents of New York Rep. Alexandria Ocasio- Cortez’s district, like all New Yorkers, love to argue. No one can agree which Colombian bakery has the best empanadas. Given that the district is in both the Bronx and Queens, it is home to both Mets and Yankees fans.The state’s 14th congressional district is well-known for its diversity. It’s the type of place where you might find a Bangladeshi woman in full body covering selling Korans next to a sex worker. Everyone has their differences, but for the most part people get along. # ⚓ Corporate_Media’s_Portrayal_of_Generational_Divide_Is_So Cheugy⠀⇛ Millennials, you’re not young and cool anymore. Gen Z thinks your skinny jeans are basic, your side- parted hair is dorky and your choice of the laughing/crying emoji is embarrassing. Moreover, they’ll take sick days for period cramps, ask higher-ups to take on projects and ask if your organization celebrates Juneteenth. # ⚓ ‘What_Hypocrisy’:_Right-Wing_Dems_Quiet_as_Military_Budget Far_Exceeds_Cost_of_Biden’s_Agenda⠀⇛ Right-wing Democrats who have spent the past several months griping about the cost of the Build Back Better Act—and lopping roughly $2 trillion off the bill’s top line—are facing growing pushback from progressive lawmakers and analysts as Congress gets ready to approve a military budget that’s far more expensive on an annual basis. Stephen Semler, co-founder of the Security Policy Reform Institute, estimated Monday that projected U.S military budgets over the next decade will cost roughly $8.31 trillion—double the combined price tag of the Biden administration’s big-ticket agenda items, which include the $1.9 trillion American Rescue Plan, the $550 billion bipartisan infrastructure law, and the $1.75 trillion reconciliation package. # ⚓ Opinion_|_Pramila_Jayapal_Wins_Down_Payment_on_Social Progress⠀⇛ Rep. Pramila Jayapal has never made any bones about the fact that her vision for economic transformation goes far beyond President Biden’s. As the chair of the Congressional Progressive Caucus, she’s been a leading champion of Medicare for All, a pathway to citizenship for undocumented immigrants, a wealth tax, living wages and union rights for all workers, student debt cancellation, and many other policies left out of the president’s Build Back Better plan. # ⚓ Uncertain_future_for_Bissen_data_centre_as_Google_increases investments_in_Belgium⠀⇛ While Google’s data centre in Bissen seems to have stalled, a fourth centre has just been completed in Belgium, where a fifth is also planned and another plot of land has just been purchased. In recent years, major industrial projects have been the subject of intense discussion in Luxembourg. The possible construction of a Google data centre in Bissen was no exception. But does the American [Internet] giant still want to establish itself in Luxembourg? The question has been raised once more after Google announced major investments in Wallonia. # ⚓ Democracy_slipping_away_at_record_rate,_warns_IDEA⠀⇛ A greater number of countries are sliding towards authoritarianism, while the number of established democracies under threat has never been so high, the International Institute for Democracy and Electoral Assistance (IDEA) said on Monday. # ⚓ As_Gerrymanders_Get_Worse,_Legal_Options_to_Overturn_Them Dwindle⠀⇛ Voting-rights advocates are in a North Carolina state court in Raleigh this month, arguing in three lawsuits that Republican gerrymanders of the State Legislature and the state’s 14 seats in the House of Representatives are so extreme that they violate the state Constitution. Only two years ago, some of the same lawyers were arguing that remarkably similar Republican gerrymanders of the same legislature, drawn a decade ago, violated the same clauses of the constitution. That trial ended with a resounding verdict in their favor, but only after the gerrymandered maps were used for almost a decade. Winning those kinds of cases, however belatedly, now appears much more of a long shot. Experts say that even as gerrymanders become ever more egregious, the legal avenues to overturn them are becoming narrower. # ⚓ Gerrymandering:_How_it’s_being_exposed_and_how_it_affects your_state⠀⇛ The gaming happens by drawing congressional and state legislative maps to politicians’ advantage. Republicans have benefited more in recent elections, and they’re off to a solid start this year as states draw new congressional district boundaries to account for the 2020 Census. # ⚓ Bannon’s_Plea⠀⇛ # ⚓ Five_Reasons_the_Left_Won_in_Venezuela⠀⇛ For the first time in four years, every major opposition party in Venezuela participated in elections. For the fifth time in four years, the left won in a landslide. Voters elected 23 governors, 335 mayors, 253 state legislators, and 2,471 municipal councilors. The governing United Socialist Party of Venezuela (PSUV) won at least 19 of 23 governorships (one race remains too close to call) and the Caracas mayoralty in the November 21 “mega-elections.” Of the 335 mayoral races, the vote count has been completed in 322 of them, with PSUV and its coalition taking 205, opposition coalitions 96, and other parties 21. Over 70,000 candidates ran for these 3,082 offices, and 90% of the vote was counted and verified within hours of polls closing. Turnout was 42.2%, eleven points higher than last year’s parliamentary elections. o § Misinformation/Disinformation⠀➾ # ⚓ Twitter_verified_a_fake_account_in_the_Norwegian government,_but_it’s_not_Twitter’s_fault⠀⇛ Norway’s Minister of Finance, Trygve Slagsvold Vedum, has never had a Twitter account. The report states that several fake accounts impersonating Vedum cropped up since he was elected into office this September, so much so that the Ministry of Finance sent out a tweet last month warning that the Minister of Finance doesn’t actually have an account. The translated tweet reads, “We want to inform that Minister of Finance Trygve Slagsvold Vedum does not have private Twitter. Accounts that appear in his name are therefore fake and will be reported.” # ⚓ How_Fake_News_on_Facebook_Helped_Fuel_a_Border_Crisis_in Europe⠀⇛ But social media, particularly Facebook, also have given Mr. Lukashenko a vital assist, as an unpredictable accelerant to the hopes and illusions of people who have fallen prey to the empty promises of profiteers and charlatans on the [Internet]. Some were in it for money, promising to smuggle migrants across borders for hefty fees; some appeared to bask in the attention they received as online “influencers” for sharing information; others seemed motivated by a genuine desire to help people suffering. There has been no evidence to suggest a coordinated campaign by Mr. Lukashenko to target migrants with fake information online. # ⚓ Farm_laws:_Fake_social_media_profiles_targeting_Sikhs exposed⠀⇛ A new report shared exclusively with the BBC ahead of its publication on Wednesday identified 80 accounts in the network, which have now been suspended because they were fake. The influence operation used accounts across Twitter, Facebook and Instagram to promote Hindu nationalism and pro-Indian government narratives. o § Censorship/Free Speech⠀➾ # ⚓ UN_Human_Rights_Committee_Criticizes_Germany’s_NetzDG_for Letting_Social_Media_Platforms_Police_Online_Speech⠀⇛ # ⚓ Civil_Rights_Groups_Denounce_‘Unlawful’_Book-Banning_Effort by_Texas_GOP⠀⇛ Two prominent national civil rights groups on Tuesday blasted efforts by Texas Gov. Greg Abbott and state Rep. Matt Krause—both Republicans—to compel school districts to censor hundreds of books, including many popular LGBTQ+, reproductive rights, and racial justice titles, following the passage of laws prohibiting the teaching of the racist history of the United States and banning transgender athletes from interscholastic athletics. “Students need materials and information created with them in mind, in which they can see their own identities and experiences reflected.” # ⚓ How_are_the_Authorities_in_Central_Asia_Trying_to_Control the_Internet?⠀⇛ Recently, the authorities of the Central Asian countries have been actively regulating online activities, adopting various laws that help them control the internet. How are things going with the freedom of the [Internet], with internet censorship in these countries? # ⚓ From_Myanmar_to_Sudan,_autocratic_regimes_have_weaponised_ [Internet]_shutdowns._Time_to_fight_back.⠀⇛ Internet censorship is nearly as old as the internet itself. While much of the theorizing about the early internet viewed it as a free and open space for the exchange of new ideas, a number of governments had different ideas about its potential. While China is well-known for its sophisticated internet censorship apparatus, several governments across the Middle East and North Africa — including Tunisia, Saudi Arabia, and Syria—were early adopters of certain censorship tactics such as keyword filtering and DNS tampering. Similar to China, these countries targeted a range of content, including sites that offered information about human rights violations, sex, and certain religions, as well as those that encouraged political opposition. But in recent years, governments have taken the more decidedly extreme tactic of cutting off internet access entirely, depriving their citizens of a lifeline to the world…and each other, a tactic that Human Rights Watch has rightly called “collective punishment.” # ⚓ Experts_Warn_Against_Total_Repeal_of_Section_230⠀⇛ Communications experts say action by Congress to essentially gut Section 230 would not truly solve any problems with social media. Experts emphasized that it is not possible for platforms to remove from their site all content that people may believe to be dangerous. They argue that Section 230 of the Communications Decency Act, which shields platforms from legal liability with respect to what their users post, is necessary in at least some capacity. # ⚓ How_China’s_Huawei_technology_is_being_used_to_censor_news halfway_across_the_world⠀⇛ Such intrusions are hard to detect, but the 18 countries in the report acknowledge blocking – notifying users via their browsers that the content they are trying to access is restricted – making censorship a starting point for researchers to assess whether countries are using middleboxes to undermine human rights, according to Weber and Ververis. Glenn Schloss and Rob Manfredo of Huawei’s U.S. corporate communications team acknowledged CPJ’s request for an interview when the report was initially published, but did not subsequently respond to emailed questions. The interview with Weber and Ververis has been edited for length and clarity. # ⚓ Olympolitik:_Fake_Peng_Shuai_Scandal_Fuels_US_Effort_to Boycott_Beijing_Olympics⠀⇛ The New York Times reported on November 3 that Chinese tennis star Peng Shuai had published allegations of sexual assault against former Vice Premier of the People’s Republic of China Zhang Gaoli on the social media platform Weibo. Peng’s post was deleted within 24 hours. This led to a firestorm of speculation in U.S. corporate media about Shuai’s “safety” and whether the tennis star had gone missing. The hashtag #WhereisPengShuai went viral 10 days later after the CEO of the World Tennis Association (WTA), Steve Simon, called on Chinese authorities to investigate the situation. Prominent celebrities and tennis players such as Serena Williams also went public with their concern for Peng. # ⚓ China_Says_Tennis_Star_Peng_Shuai’s_Case_“Maliciously_Hyped Up”⠀⇛ Evidence of her claims have also been scrubbed from China’s highly censored [Internet]. # ⚓ China_urges_‘certain_people’_to_stop_‘malicious_hyping’_of tennis_star_Peng_Shuai⠀⇛ Amnesty International’s China researcher Alkan Akad also told Reuters the video call did little to ease fears over Peng’s wellbeing and that the IOC was entering “dangerous waters”. # ⚓ Hollywood_Warms_to_Saudi_Arabia’s_Money_Again⠀⇛ The major indicator of a change in temperature, however, is that Hollywood is now actively courting Saudi money once more. Both Desert Warrior and Kandahar are being financed and produced by MBC Studios, the production arm of regional broadcast giant MBC, which — following a major land grab of assets by Salman in 2018 — is now majority-owned by the Saudi government. Dollar figures weren’t revealed, but MBC Studios managing director Peter Smith told THR at the time that it was making a “substantial investment” in Kandahar. # ⚓ Historic_Bail_for_Nurses_Charged_with_Blasphemy,_Lawyer Says⠀⇛ Usually those charged under Pakistan’s widely condemned blasphemy laws even with little or no evidence languish in jail for years until verdicts and appeals are exhausted. Nurse Mariam Lal and student nurse Nawish Arooj, arrested on April 9, received bail from a sessions court on Sept. 23, attorney Atif Jamil Paggan said. # ⚓ Christian_Sentenced_to_Death_for_‘Blasphemy’_Acquitted⠀⇛ The life prison sentence of Sajjad Masih Gill, 37, had been converted to the death penalty on March 10 under Islamist pressure. His attorney, Javed Sahotra, said that a two-judge division bench of the Lahore High Court on Oct. 26 acquitted Gill on grounds of insufficient evidence and ordered his release. o § Freedom of Information/Freedom of the Press⠀➾ # ⚓ Al-Shabaab_Kill_Somali_Journalist_Who_Criticised_Them_on Radio⠀⇛ This is the second death of a journalist in 2021, directly linked to Al-Shabaab. In March, the National Union of Somali Journalists (NUSOJ) said another reporter Jamal Farah Adan, a freelance Journalist whose radio programmes were also critical of Al-Shabaab and its operations was shot dead in Galmudug State, reports Aggrey Mutambo for The Nation. o § Civil Rights/Policing⠀➾ # ⚓ Baltimore_Police_Department_Sued_For_Seizing_Phones,_Cash, And_Jewelry_From_Crime_Victims_Recovering_From_Shootings⠀⇛ It’s not enough that law enforcement can seize property if it pretends it must be linked to some criminal endeavor, even if the cops can’t be bothered to actually find any direct evidence of said criminal endeavor… or even bring charges against forfeiture victims. It’s not enough that almost anything can be seized when accompanied by criminal charges, which can lead to officers stripmining someone’s residence while serving warrants. # ⚓ Georgia_GOP_Redraws_Political_Map_as_Senate_Democrats_Do Nothing⠀⇛ # ⚓ Opinion_|_It_Turns_Out_We_Are_the_Martians_Sent_to_Destroy Earth_With_a_Powerful_and_Deadly_‘Heat-Ray’⠀⇛ Who knew that Martians, inside monstrous tripodal machines taller than many buildings, actually ululated, that they made eerily haunting “ulla, ulla, ulla, ulla” sounds? Well, let me tell you that they do—or rather did when they were devastating London. # ⚓ Algorithmic_Bias_in_Online_Test-Monitoring_Programs_– Validated_Independent_News⠀⇛ Proctorio operates as a browser plug-in that can detect whether a student’s gaze is directed at the camera, how often they look away from the screen, how much they type, as well as how often the student moves their mouse in comparison to the rate of activity to a class average. On the basis of these measures, the software calculates a “suspicion score” for each student, flagging students who deviate too much from the norms for possible acts of cheating. # ⚓ The_Acquittal_of_Kyle_Rittenhouse:_A_Judicial_Travesty⠀⇛ On Friday, after four days of deliberations, a Kenosha jury returned a verdict of “not guilty on all counts” against Kyle Rittenhouse. Rittenhouse had been charged with wrongfully killing two people, wounding a third, and nearly striking a fourth with an AR-15 rifle during protests against police brutality in Kenosha, Wisconsin, on August 25 last year. # ⚓ Kyle_Rittenhouse_Is_Not_the_Enemy._He’s_the_Latest_Product of_the_Outrage_Industry⠀⇛ The Kyle Rittenhouse furor is a fascinating illustration of how US politics has become mired in self-consuming tribalism. It shows how non- conversations, non-thinking now posture as serious political and social engagement. And it demonstrates once again the success of a practice beloved of elites the world over: offer bread and circuses to keep the masses from seeing the big picture and rising up. # ⚓ The_Counterrevolution_of_Kyle_Rittenhouse⠀⇛ Therefore the so-called populists are erasing the elimination of hierarchy by claiming we are all already equal. Such is the mentality of American institutions today which have systematically been taken over by the right. The fact that people advocate for equity rather than equality goes to show how far we’ve fallen. The Democrats remain willfully asleep at the wheel while Republicans obstruct democracy at every turn and as a result we are in the midst of a fifty-year counterrevolution according to Pascal Robert. The MAGA judge in the Rittenhouse case is one of many examples and we have to recognize the system is rigged and not worth saving. The judge said the victims of Rittenhouse couldn’t be called victims but only rioters or looters. In the postmodern world of Trumpism, a member of the jury is eliminated for expressing racial equality by saying “Black Lives Matter” while a white supremacist is allowed who says “All Lives Matter” because this is viewed as a racially neutral statement. I don’t care for Orwell’s anti-communism but this is the definition of Orwellian doublespeak. A similar standard is applied to teaching “both sides” of the Holocaust in schools. Indeed Donald Trump normalized the “good people on both sides” narrative. # ⚓ How_Unaccountable_Institutions_are_Shaping_Your_Life⠀⇛ Our only option is to turn up the pressure and keep fighting for our democracy. # ⚓ Blockade_on_Critical_Race_Theory_in_Texas_Public_Schools_– Validated_Independent_News⠀⇛ As Bendery noted, the Texas law “goes a bit further than those of other states” by preventing students from participating in public policy advocacy as part of a civics or social studies class. The law’s language is written so broadly, Bendery reported, that it applies to students “engaging in the most basic of civic activities, such as communicating with their own elected officials about a particular topic.” # ⚓ Nikole_Hannah-Jones_on_“The_1619_Project,”_Teaching Critical_Race_Theory_&_White_Supremacy_on_Trial⠀⇛ Amid a right-wing attack on teaching critical race theory, we speak in-depth with Pulitzer Prize–winning journalist Nikole Hannah-Jones, creator of the New York Times Magazine’s 1619 Project, which reframes U.S. history by marking the year when the first enslaved Africans arrived on Virginia soil as the foundational date for the United States. The project launched in 2019, and has been expanded into an anthology of 18 essays along with poems and short stories, even as several states have attempted to ban it from school curriculums. “We should all as Americans be deeply, deeply concerned about these anti-history laws because what they’re really trying to do is control our memory and to control our understanding of our country,” says Hannah-Jones. Hannah-Jones’s new book that she co-edited is out this month, titled “The 1619 Project: A New Origin Story,” along with an adaptation of the 1619 Project for children, “Born On The Water.” Hannah-Jones describes the role of her own teachers in opening her eyes beyond the usual curriculum that excluded the history she has now uplifted. She also discusses the trial of the murderers of Ahmaud Arbery, and how she felt when she won the Pulitzer Prize on the same day as one of her heroines, the formerly enslaved pioneering anti-lynching journalist, Ida B. Wells. # ⚓ Judge_Says_NYPD_Illegally_Withheld_Footage_in_Police Shootings⠀⇛ A New York state judge ruled last week that the New York City Police Department illegally withheld body-worn footage in two police shootings, including the killing of Kawaski Trawick. The judge said at an October hearing in the case that the NYPD had been operating in “bad faith.” # ⚓ A_Patient_in_a_Psychiatric_Ward_Was_Seen_on_Video_Possibly Being_Sexually_Assaulted._No_One_Reported_It.⠀⇛ A Chicago hospital with a history of patient-care violations didn’t tell police that a patient in its psychiatric unit may have been sexually assaulted by another patient, even though the incident was caught on surveillance video. Nor did the facility, Roseland Community Hospital on the far South Side, closely monitor the alleged attacker — identified in records as a 49-year-old man with a history of sexual violence and aggression — as it was supposed to do. # ⚓ Opinion_|_Rittenhouse’s_Acquittal_Is_an_Endorsement_of Critical_Race_Theory⠀⇛ The acquittal of Kyle Rittenhouse is a powerful endorsement of critical race theory. We all know that no one is teaching critical race theory in the K-12 system. The current discussions of Critical Race Theory (CRT) are the result of a tried-and- true right-wing strategy to create weird forms of cathexis where they link the name of something obscure with things that bother people at their core, to create lightning rods by which to channel toxic energy through the bodies of their followers, in ways that bond people to their to their death cult. # ⚓ Kevin_Strickland_exonerated_after_42_years_in_Missouri prison⠀⇛ A Missouri man wrongfully convicted of a triple murder in 1978 and imprisoned for more than 42 years has been exonerated and released. Kevin Strickland, 62, has maintained his innocence since his arrest at age 18. He was sentenced in June 1979. # ⚓ Is_the_Four-Day_Workweek_Finally_Within_Our_Grasp?⠀⇛ Proponents of four-day weeks say the key is to rein in meetings. “You have better discipline around meetings. You’re a lot more thoughtful in how you use technology,” said Alex Soojung-Kim Pang, author of “Shorter,” a book about the four-day workweek. He also said that a shorter week requires workers to set aside time for focused work and refrain from email or other communications during that time. “To paraphrase William Gibson, the four-day week is already here for most companies,” said Mr. Pang, an organizational strategy consultant in Menlo Park, Calif. “It’s buried under a whole bunch of rubble of outmoded practices and bad meetings. Once you clear that stuff away, then it turns out the four- day week is well within your grasp.” # ⚓ Afghans_‘marry_off’_baby_girls_for_dowries_as_starvation looms⠀⇛ Child marriage has increased in tandem with soaring poverty since the Taliban seized power 100 days ago on August 15, with reports of destitute parents even promising baby girls for future marriage in exchange for dowries, women’s rights activists said. They predicted the rate of child marriage — which was prevalent even before the Taliban’s return — could nearly double in the coming months. # ⚓ Couple_Flogged_Publicly_for_Extramarital_Affair_in_Sharia- Compliant_Indonesia⠀⇛ Any moral offense, such as like homosexuality, gambling, drinking alcohol, closeness between people of the opposite gender if not related or married, or public display of affection is eligible to be tried under Sharia. # ⚓ Afghanistan:_Taliban_unveil_new_rules_banning_women_in_TV dramas⠀⇛ The Taliban seized power in Afghanistan in mid- August and many fear they are gradually imposing harsh restrictions. o § Internet Policy/Net Neutrality⠀➾ # ⚓ Techdirt_Podcast_Episode_306:_Lessons_From_The_First Internet_Ages⠀⇛ Earlier this month Mike participated in a content series and virtual symposium on Lessons From The First Internet Ages, hosted by the Knight Foundation, alongside several important figures from the history of the internet. On this week’s episode, the creators and curators of the event — John Sands, Mary Anne Franks, and Eric Goldman — to reflect on the writings and conversations from the event and the lessons to be learned. # ⚓ FAA_Blocks_5G_Deployments_Over_Safety_Concerns_Despite_No Actual_Evidence_Of_Harm⠀⇛ A few weeks back, both Verizon and AT&T announced they’d be pausing some aspects of their 5G deployments over FAA concerns that those deployments would create significant safety hazards. The problem: there’s absolutely no evidence that those safety concerns are legitimate. o § Monopolies⠀➾ # ⚓ EU_Parliament_Takes_First_Step_Towards_a_Fair_and Interoperable_Market⠀⇛ However, we didn’t like that the DMA proposals missed the mark from the end-user perspective, in particular the lack of interoperability obligations for platforms. The Commission met us half-way by introducing a real-time data portability mandate into the DMA, but it failed to go the full distance. Would it lead to a measurable behavioral change of Facebook if frustrated users could only benefit from data portability if they continued being signed up to Facebook’s terms of service? We doubt it. In today’s vote, the Internal Market Committee (IMCO) of the EU Parliament overwhelmingly agreed to preserve most of the proposed anti-monopoly rules and agreed on key changes of the Commission’s Proposal. We’ll analyze them in more details in the coming weeks, but some elements are striking. One is that the Committee opts for an extremely high threshold before platforms will be hit by the rules (market capitalization of at least €80bn) which means that only a few, mainly U.S based, firms would legally be presumed to act as gatekeepers and hold an entrenched and durable position in the internal market. Members of Parliament also agreed on incremental improvements on the ban of mixing data, added clarification on the limits of targeted ads, including substantial protection of minors, and introduced an ambitious dark patterns prohibition in the DMA’s anti-circumvention provision. It also added a prohibition on new acquisitions as a possible punishment for systematic non-compliance with the anti-monopoly rules. On interoperability, Members of Parliament followed the strong recommendation by EFF and other civil society groups to not settle for the low-hanging fruits of data portability and interoperability in ancillary services. Focusing on the elephant in the room – namely, messaging services and social networks – the DMA’s lead committee proposes key provisions that would allow any providers of “equivalent core platform services” to interconnect with the gatekeeper’s number independent interpersonal communication services (like messaging apps) or social network services upon their request and free of charge. To avoid discrimination, interconnection must be provided under objectively the same conditions and quality that are available or used by the gatekeeper, its subsidiaries, or its partners. The objective is a functional interaction with these services while guaranteeing a high level of security and data protection. # § Copyrights⠀➾ # ⚓ BookTok_Shows_How_Fans_Can_Power_Sales;_Imagine_What Could_Be_Done_Without_Copyright_Anxiety⠀⇛ A little while back, the Guardian covered the rising literary power of BookTok – short videos on TikTok devoted to the pleasures and pains of reading. As well as plenty of background information about the BookTok phenomenon, it has the following perceptive comment from Kat McKenna, a marketing and brand consultant specializing in children’s and young adult books: # ⚓ CC_Community_Spotlight_Series:_Angela_Oduor_Lungati, Achal_Prabhala_and_Cecília_Olliveira⠀⇛ Giving Tuesday is only a week away! We hope you’ll join us next Tuesday, 30 November in celebrating our Better Sharing, Brighter Future campaign.  # ⚓ Founder_of_Piracy_&_Subtitling_Site_YYeTs_Sentenced to_3.5_Years_in_Prison⠀⇛ Following pressure from Hollywood, more than a dozen people behind famous Chinese piracy and subtitling site YYeTs.com were arrested in February. After a legal process in China, the founder of the platform – also known as Renren Yingshi – has been sentenced to 3.5 years in prison and a US$235,000 fine. The site itself remains online although accessing content is hit and miss. # ⚓ Court_Orders_Telegram_to_Block_Access_to_Piracy Channels_With_Millions_of_Members⠀⇛ A Portuguese court has ordered the messaging app Telegram to block access to more than a dozen piracy-related channels with millions of members in total. The court recognizes that the measure may not be perfect but concludes that it’s better than taking no action at all. Rightsholders are happy with the injunction that was issued without hearing Telegram. ╘══════════════════════════════════════════════════════════════════════════════╛ ¶ Lines in total: 10052 ➮ Generation completed at 02:42, i.e. 102 seconds to (re)generate ⟲