𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Monday, January 03, 2022 ┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅ Generated Tue 4 Jan 02:40:39 GMT 2022 Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖) Full hyperlinks for navigation omitted but are fully available in the originals The corresponding HTML versions are at 𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈 Latest in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕 and older bulletins can be found at 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕-𝒂𝒓𝒄𝒉𝒊𝒗𝒆𝒔 Full IPFS index in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔 and as plain text in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔/𝒕𝒙𝒕 Gemini index for the day: gemini://gemini.techrights.org/2022/01/03/ ╒═══════════════════ 𝐑𝐄𝐂𝐄𝐍𝐓 𝐁𝐔𝐋𝐋𝐄𝐓𝐈𝐍𝐒 ════════════════════════════════════╕ Previous bulletins in IPFS (past 21 days, in chronological order): QmUQmiHKq1wV1JkS2hwXEf1etD3jM43Afc68V6omxpqaCi QmbheKKYhpyw3SvZSmHbavdgcv1PSaRtPdaQ746tgUFXbp QmZqoL722Mk7hDJcSz2oBxydXY7S2G5r4ByHgRdKBw7dUH QmTZSRzHEP7hwr4tL7ky23HxA9Z3tUBjQrfwYPAieSYsGe QmRKnWzns1EsWaoxUGG5KEEhiyhSELGYVdfVqSB5Ay4qhc QmZdVw5kGwFeXoGNexLWZDS8MJxeGKAeup4JpiAnmE946y QmYdAKSfCu9puR3SWGWwGW19Uzo1jj4L1aYpeGqpC5FCp6 QmZP4LnsTHrznHVdokybFZafDLWJqRPKyvvberG4dVRasQ QmfL4kPLDVa6CGiB1yXozobGCQ5fTPahv8T7hPstsxvkie QmP2Y5UBBDqcCEECSknvoPU6WVjL4V93dQMbKj34jYv56N QmTTqHT1gu1SWzp4ejhsMMHeEr1cnaDHeAQnawx8obkmR5 QmVjqVfy1bLLkjPbYtUagNsq6vfXCToNocEPu1s2Cvo3ab QmXVB3t7bvESJpBXVnHEH2koE5NY8MqsHXWVco5dbnNW1M QmUnmYrNuwB9WxrYeqcbFyf8Bew66hMkdU1YVc9WsKh4JC QmYjUQnBiQsqQMypkyvfTj7b9arksYuzUe1BzJ9a6JUTk4 QmarLrYBMcbMFgab1qAkPGRjRr57niwUpd5PEPbMp8225S QmYYUiUwcwdiuMNs9EXu5Ci3ELNhZcY4b7JsFUZqp7drnc QmTWhb5PucmgsMLVAJufczuFnxY37RcgjXGMTczMdhndPd QmVgY18p35Thp6aWh7cRUuoocqLYGYFW2QnLEJhuqn69Kw QmcN2LseMFZtt5HtSJMT5h9HDZa4ZNy6B7uWe7gK8fPeF9 QmfH2by4K6HCiZyvyGQ1L5syH6ZSfcHH12ph6TDo82aovk ╒═══════════════════ 𝐈𝐍𝐃𝐄𝐗 ═══════════════════════════════════════════════════╕ ⦿ My Year as a Digital Vegan — Part X — Happy New Year: Thoughts for 2022 and Beyond | Techrights ⦿ [Meme] A ’Good’ Consumer | Techrights ⦿ Software Freedom Makes the World a Greener Place, Too | Techrights ⦿ IRC Proceedings: Sunday, January 02, 2022 | Techrights ⦿ Stop Cheering/Calling for Social Control Media Censorship, Quit Getting ’Information’ From It Instead | Techrights ⦿ Microsoft GitHub Exposé — Part XIII — Nihilistic Death Cults With Substance Abuse and Sick Kinks | Techrights ⦿ In Picture: Microsoft Windows Market Share in a Freefall in 2022 | Techrights ䷼ Bulletin articles (as HTML) to comment on (requires login): http://techrights.org/2022/01/03/article-on-digital-rights-in-2021-part-10/#comments http://techrights.org/2022/01/03/good-consumer/#comments http://techrights.org/2022/01/03/green-freesw-not-greenwashing/#comments http://techrights.org/2022/01/03/irc-log-020122/#comments http://techrights.org/2022/01/03/popularising-censorship/#comments http://techrights.org/2022/01/03/sick-kinks-balabhadra-alex-graveley/#comments http://techrights.org/2022/01/03/windows-share-in-2022/#comments ䷞ Followed by Daily Links (assorted news picks curated and categorised): http://techrights.org/2022/01/03/kde-2022-roadmap/#comments http://techrights.org/2022/01/03/mdadm-4-2/#comments http://techrights.org/2022/01/03/ubuntudde-remix-21-10/#comments ䷩ 𝚕𝚒𝚗𝚎 67 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/01/03/article-on-digital-rights-in-2021-part-10/#comments Gemini version at gemini://gemini.techrights.org/2022/01/03/article-on-digital-rights-in-2021-part-10/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.03.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ My_Year_as_a_Digital_Vegan_—_Part_X_—_Happy_New_Year:_Thoughts_for_2022_and Beyond⠀✐ Posted in Free/Libre_Software at 5:48 pm by Dr. Roy Schestowitz By Dr. Andy Farnell Series parts: 1. My_Year_as_a_Digital_Vegan_—_Part_I_—_2021_in_Review 2. My_Year_as_a_Digital_Vegan_—_Part_II_—_Impact_of_a_‘COVID_Year’ 3. My_Year_as_a_Digital_Vegan_—_Part_III_—_Lost_and_Found;_Losing_the_Mobile Phone_(Cellphone) 4. My_Year_as_a_Digital_Vegan_—_Part_IV_—_Science_or_Scientism? 5. My_Year_as_a_Digital_Vegan_—_Part_V_—_Change_in_Societal_Norms_and Attitudes 6. My_Year_as_a_Digital_Vegan_—_Part_VI_—_The_Right_Words 7. My_Year_as_a_Digital_Vegan_—_Part_VII_—_Staying_the_Course_and_Fake_It Till_You_Make_It? 8. My_Year_as_a_Digital_Vegan_—_Part_VIII_—_Who_Teaches_the_Teachers? 9. My_Year_as_a_Digital_Vegan_—_Part_IX_—_Hard_Reckonings:_The_Nine_Circles of_E-Waste 10. YOU ARE HERE ☞ Happy New Year: Thoughts for 2022 and Beyond 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Andy Farnell⦈ Summary: Dr. Andy Farnell (above) offers some positive words of encouragement and optimism as this series concludes Thanks for reading my review of 2021, my first official year as a Digital Vegan. Lest you think that it’s in any way a negative philosophy, let me change your mind. The most frequent critical personal comment I get is that I’m by_far too_much_an_optimist. “…the European Patent Office (EPO) looks lost to all hope of reform.”I feel optimistic that many techno-doom stories are passing teacup storms. It’s the spirit of our age that we ruminate on our worst nightmares, egged on by fear- mongers. AI isn’t a thing. Machine learning ain’t all it’s puffed up to be. Its dark faces are mainly manifestations of existing malevolent social cybernetics now illuminated by computing progress. We ought to attack those root causes and the maniacs pushing them, not attack promising technologies. Face recognition may be banned in Europe within a year along with killer drones and illegal mass surveillance. I can imagine a future when the CCTV cameras in our streets are taken down – perhaps only because visual surveillance has shifted to more effective and invisible modes. With respect to rights, “to be forgotten”, “to repair and reverse engineer what we own”, “to choose free software”, “to use end-to-end encryption free from backdoors”… Europe is on the right track. Certainly there is corruption_in_Europe – so bad in fact that the European Patent Office (EPO) looks lost to all hope of reform. However, if the new government of Germany is really what it seems, it may be time to put some faith in the rule of law and institutions again, however weak they seem now. In 2022 the ECJ is likely to let individuals bring actions against foreign tech-giants. Unexpectedly our UK DPA has not diverged from GDPR and the Online Safety Bill, despite some authoritarian attacks on speech and privacy, bolsters other rights and is empowering against big-tech abusers. “E-waste will come into mainstream discourse in 2022 and campaigns to “not buy a new phone” will likely meet brutal resistance and disinformation from the industry and become a speech/censorship battleground.”Going forward, we’ll figure out how to recycle our phones more and use them less. E-waste will come into mainstream discourse in 2022 and campaigns to “not buy a new phone” will likely meet brutal resistance and disinformation from the industry and become a speech/censorship battleground. Regardless, because of rising environmental and ethical awareness the technological society will have to find a place for all four ‘R’s, recycling, reuse, reduction and rejection. All-together these support resilience through functional diversity. A technological society without space for dissent and abstinence will fail. Other things I am hopeful for, 5G and anti-vac paranoia will fade with renewed popular belief in science and continued total_absence_of_evidence (which is not evidence of absence) of harm. Maybe Bezos, Branson and Musk will stop their dick-waving so that personal vanity space_tourism where each passenger’s trip unleashes a lifetime_CO2 use, becomes a mark of shame, not pride. Further along, in post-pandemic boom, I think the passing of paranoia and closer human contact will unleash a new wave of humanist thinking around tech. Education and health-care can undergo healing and restoration. And the world, albeit a warmer one, will keep turning. I’ll still be a Digital Vegan – an Electronic Epicurean – because it’s a philosophy of celebrating good technology. That means rejecting bad technology, and much of my thought will still be defined by what I don’t do. Like rejecting people who behave as if it’s only a means to dominate and extract rent from others. Like eschewing uncritical and stuck behaviours, passive assent to technological abuse, and helpless claims it’s all “inevitable”. It means embracing smaller groups, less travel, slower technology, more meaningful technology geared toward conviviality. “The bad-old world died a little, not you.”Yes, Digital Veganism is also about “changing the world” and “social justice”, but changing the world is not about stopping bulldozers, Neo-Luddism, blocking traffic, daubing slogans, toppling statues, vandalising 5G masts, shouting down speakers, DDOSing servers, or handing out pamphlets. Those are easy things because they externalise struggle. The really hard stuff is the little things that actually change our own lives and souls in a way that is dangerously infectious. I act because I am following my heart (The Path, The Way, The Force) and assert that is a good_enough_reason on_its_own. I don’t need to justify why I think Microsoft, Facebook and Google are grotesquely immoral catastrophes for humanity (although I could write a book on it). I simply refuse to let them touch my life, and that’s the end of it. Take courage. If your Digital Vegan thing pisses-off even your closest friends for a while, you’re probably in to something real. Follow that moral instinct. Do things that are embarrassing, make yourself feel small, excluded or weird in a world where social non-conformity feels like death. Then realise, you’re still alive and it didn’t hurt. It felt good. The bad-old world died a little, not you. “The system relies on you being a hopelessly lazy and insecure narcissist who cares more about the judgement of others than your love for them.”Now watch those friends congratulating you. They want to be a little more like you. These repeated acts of social self-immolation are deadly to the status quo. The system relies on you being a hopelessly lazy and insecure narcissist who cares more about the judgement of others than your love for them. It needs you to be comfortable and greedy for the latest powerful hardware, for skin-deep accolades, and rituals of conspicuous waste – not a soldier who adapts, improvises and overcomes to achieve more with less. It cannot adapt to fatal strategies. Instead, make it awkward for others to not support you in what are very reasonable and modest requests, so that the absurdity of our silent acquiescence is forced to a head. Don’t_feed_the_machine. As philosopher Rick Roderick put it “People aren’t afraid of dying any more, they’re afraid of being seen wearing the wrong trainers.” Put on a pair of the wrong trainers and join me in a little mischievous Digital Veganism in 2022. █ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠻⠛⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣠⣼⣿⣿⣿⣷⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⡀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⢿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣷⣹⣿⣿⣿⣿⣏⣏⣀⣀⠒⠀⠀⠀⠀⣀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡏⠉⣹⣿⣿⣿⣿⣿⣿⣧⣀⡀⣀⣤⠴⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠐⠟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣄⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠁⢀⣾⣿⣿⣿⠃⠀⠄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠈⠉⠉⠉⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢟⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⠀⠸⣿⣿⣹⠏⠈⠃⠀⠀⠀⠀⠀⠀⠓⠐⠂⠈⠁⠀⠀⠀⠀⠀⠀⠈⠉⠻⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⣿⣿⣝⢻⣿⣿⣿⡿⠁⠀⢰⡝⠻⣿⠇⡀⠀⠀⠀⠀⠀⠀⠻⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠛⠢⡤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⢿⣯⣷⣶⣿⠁⠀⠈⠛⣿⣶⣿⠟⠋⠀⠀⠀⢾⡇⠀⠉⠁⠀⠀⠀⠀⠀⢀⣀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠓⠒⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢿⣷⣾⣛⢯⣿⣿⡟⠀⠀⠀⠀⠙⠛⣤⡞⠋⠀⠀⠀⣽⡧⠀⣤⠀⠀⠀⠀⠀⠀⠘⠻⢿⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢠⣿⠦⣀⠀⠀⠀⠀⠀ ⣿⠻⣿⣿⣿⣿⣿⢏⣁⣶⢋⡽⠻⣿⣿⣿⡙⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢰⡟⣿⡆⢹⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⡀⠫⠵⡄⠀⠀⠀ ⠿⠦⠟⠛⠐⠛⣽⡿⣻⣶⣿⠀⡴⠋⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡄⠀⠈⡏⢿⣧⠀⠘⢿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⢙⢢⠀⠀ ⠀⠀⠀⢀⣶⠀⠏⢱⣿⣿⣿⣿⣷⠀⠐⠸⠇⠀⠀⠂⠀⠀⠀⠀⡿⠀⠀⠃⠀⠀⠇⠈⡎⣆⠀⠈⠙⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀ ⠀⠀⢀⣿⢻⠀⢨⣃⠙⣿⠿⠛⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀ ⠀⠀⠸⠉⣮⠀⣿⣿⠂⠉⠀⠀⠀⣷⠀⠠⡄⠀⠀⢠⠀⠀⠀⠀⣶⠀⠀⣸⡀⠀⠀⠀⠈⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠓⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡄ ⠀⠀⠀⢀⣿⠀⠀⣙⢦⡀⠀⣤⡀⢿⡇⠀⢉⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⣤⠀⠀⠀⠀⠘⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢃⠀⢠⠄⠀⠈⠥⠂⠀⣼⠀⠀⠀⠀⠃ ⠀⠀⠀⠸⣿⣇⠀⠿⠂⢙⡆⠉⣡⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢹⠀⠀⠀⠀⠀⡌⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡒⠀⠈⠀⠀⠀⠂⠀⣠⠁⠀⠀⠀⠀⠠ ⠀⠀⣄⠀⢻⣿⡄⠀⢠⠘⣷⣄⠙⣇⠈⠇⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⣛⡞⠀⠀⠀⠀⠀⠀⢠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⣶⠚⠀ ⠀⠀⢹⡆⠀⠉⢷⠀⠈⠳⣌⠿⠀⠈⠀⠀⠀⠀⠀⠀⡄⠀⠀⠘⠁⠀⠀⠀⠀⠷⠀⠀⠀⠀⠈⠀⠀⠰⠦⠀⠀⠔⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠈⠀⠀ ⠀⢀⣼⣷⡄⠀⢰⠄⠀⠀⠘⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠠⠀⡄⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠘⢤⣴⠀⠀⣀⣦⡤⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠁⠀⠀ ⠀⣾⣿⣿⣷⣄⠀⠀⠱⣶⣀⠀⠁⣀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠿⠂⠀⠀⠀⠀⠈⠁⠆⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠀⠀⡂⠙⠉⠀⠀⠀⠀⠁⠀⢀⣴⠀⠀⠀⣤⠀⠐ ⢠⣿⡟⠛⣻⣿⡅⠀⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡄⠀⠀⠀⠀⠃⠀⠆⠄⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠘⠆⠀⠀⠀⠀⠀⠀⢡⢼⣿⠀⠀⠀⠉⠀⠀ ⣼⣿⣷⡄⢿⣿⣧⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠤⠀⠀⠀⢻⣷⠀⠀⠀⡄⠀⠀⠂⡄⠖⠋⠈⠁⠀⠀⠀⠀⣀⡀ ⣿⣿⣿⡿⠿⣿⣿⢿⠛⣛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠘⠀⠂⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠟⠃ ⣿⢭⣿⡶⢲⣿⣿⣿⣏⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣶⣶⠷⠹⣟⡀⠀⠀⠀⠀ ⣿⣼⣿⠁⢸⣿⣿⣿⣿⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠛⠛⠒⠄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠿⠛⢛⣉⣤⠐⡆⢹⡇⠀⠀⠀⠀ ䷩ 𝚕𝚒𝚗𝚎 266 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/01/03/good-consumer/#comments Gemini version at gemini://gemini.techrights.org/2022/01/03/good-consumer/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.03.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ [Meme]_A_‘Good’_Consumer⠀✐ Posted in Free/Libre_Software, Hardware at 9:55 am by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Computer_5_years_old,_time_to_get_a_new_one⦈_ Summary: It may be worthwhile reminding people that Free software makes the world a better place ecologically, too [1, 2] ⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣟⣷⡆⠀⠈⠙⠳⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⣰⣶⣀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠅⠏⠀⠀⠀⢀⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣭⣭⣽⣷⣶⣶⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⡀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠃⠀⣶⣶⣤⣾⣟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣔⠀⠄ ⣿⣿⣿⣿⣿⣿⠀⣿⣿⠿⠏⠁⠀⠀⠹⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠁⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⠀⣿⣿⡤⣀⠀⠀⠀⠀⠿⠟⢻⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣴⡿⠛⠀⠈⢷⣄⣀⣄⠀⠀⣸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⠟⠻⠋⠉⠹⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣤⣄⣤⣴⣆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡿⠿⠿⠿⣿⣿⣭⣽⣿⣷⣠⡆⣿⡟⣿⣿⣿⣿⣿⣻⣿⣿⡀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⣿⣶⣮⣿⡿⠿⢿⣿⣿⡇⣘⣿⣿⡌⠹⠧⢀⣼⣿⣿⣿⣷⡀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⡿⠀⠀⢿⣿⣿⣿⣿⣿⡿⠋⠉⣹⡶⠸⢛⢻⣿⣦⣤⣾⠛⢿⣿⠻⢙⠛⠳⠀⠀⠀ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡄⠀⢀⣾⣿⣿⣿⣿⣯⣿⣿⡶⠍⠉⠁⠀⠼⢿⣿⣿⣿⣦⠈⠉⠉⣬⣠⣤⡀⣠⡄ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⣶⣶⣶⣿⣿⣿⢿⣿⣿⣧⢠⣿⡿⠿⡏⠳⠿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠛⠛⠛⠿⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⡿⡌⢿⣿⣿⣆⣾⠗⠀⠀⠀⠀⠹ ⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢀⣤⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣷⢯⣿⣿⣿⣿⡆⠀⠀⠶⠀⠀⠀ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⢸⣿⣿⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣿⣿⡟⠓⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⢹⣾⣿⣛⣿⣿⣧⡄⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⣼⠋⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⢷⡍⠁⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠤⠀⠀⠀⠀⢀⠼⠛⠉⣉⠉⠘⠃⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⡟⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠌⠉⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣧⣤⣄⣠⣴⣾⣿⣿⣿⣿⣷⣿⣗⠀⠀⠀⠀⠀⠀⠀ ⣿⣟⣿⣻⢻⠃⢠⢀⡄⠒⠆⣤⢀⣠⢀⡄⣠⣤⣴⣠⡶⠛⢲⢻⡄⣿⣟⠟⢲⢒⡀⢐⣖⣤⣄⣀⣀⣀⡀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⣛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀ ⣿⣿⣿⠛⢻⠨⢥⣾⣺⣾⣾⣿⣭⣽⢸⡗⣯⣿⣿⣿⣇⠀⢰⠀⡇⣭⣏⣭⣽⠈⣙⠦⢍⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣄⠀⠀⠀⠀⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡖⠀ ⠛⢿⢿⣷⠿⣿⢿⠸⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣭⣀⣉⡁⡈⠉⡩⠑⠛⣛⠸⠛⠂⢱⣾⣶⣮⣭⣭⣛⣛⡛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠁⠀⣀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀ ⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⡟⢿⡷⠀⠀⠈⠙⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣧⣄⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⡇⠞⠀⠀⠀⢀⣤⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣭⣭⣿⣶⣶⣾⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢎⡃⠀⠀⠀ ⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠃⠀⢾⣿⣶⣿⣯⡁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠂⠉⠀ ⣿⣿⣿⣿⣿⠀⣿⣿⠿⠛⠀⠀⠀⠈⣿⣿⢿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⣤ ⣿⣿⣿⣿⣿⠀⣿⣿⡶⢦⡀⠀⠀⠀⠙⠛⢹⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿ ⣿⣿⣿⣿⣿⣴⡿⠋⠀⠀⠹⣦⣤⣤⣄⣀⣸⣿⡃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿ ⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡿⠛⠛⠋⠀⠘⠃⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣤⣤⣤⣶⣾⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⠿⠿⣿⣿⣧⣶⣿⣿⣤⡖⣼⣿⣻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠛⢿⣿⣿⣷⣿⣿⡛⠻⣿⣿⣿⢬⣿⣿⣧⠘⠛⠂⣴⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠇⠀⠸⣿⣿⣿⣿⣿⣟⡋⠁⢠⣿⣟⢛⢿⣿⣷⣶⣼⡛⠻⣿⢛⡛⡛⠛⠀⠀⢀⠀ ⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣧⠀⢀⣼⣿⣿⣿⣿⣯⣿⣿⡿⠒⠉⠁⠀⢺⣽⣿⣿⣿⣷⣄⠈⠀⢠⣤⣶⡆⢠⣦⣢ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⡄⣿⣿⠻⠏⠙⠚⢿⠿ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡛⠛⠛⠛⢃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⢁⣨⣿⣿⣷⡼⠟⠀⠀⠀⠀⠘⠇ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠈⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⢀⣤⣾⣿⢿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢿⠏⣿⣿⣿⣿⣷⠀⠀⠚⠃⠀⠀⠀ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣾⣿⣿⣿⠉⠁⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠃⠀⠈⣿⣿⣋⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⢸⡏⢈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠹⠿⣆⣉⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠀⠀⠀⢀⣄⣛⠁⣀⡐⠒⠛⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⣿⠁⣼⡟⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣷⣶⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀ ⣿⣟⣿⣻⢻⠀⢠⢠⡔⣒⡆⣤⢠⣤⢠⡆⣲⣶⣦⣎⡽⠛⢻⠃⡜⣿⣟⣛⣫⢁⣰⢒⣖⣤⣤⣤⣀⣀⣀⣀⣠⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣋⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀ ⣿⣏⣿⠙⢻⠨⢥⣾⣺⣿⣿⣿⣭⣽⢸⡗⣯⣿⣿⡇⣇⠀⢰⠀⡇⣭⣏⣭⣽⢐⣛⠦⢍⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⡄⡀⠀⠀⠉⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡟⠀⠀ ⠉⢿⢿⣷⠟⣿⢿⠾⢿⣿⣿⣿⣿⢿⣿⠿⣿⣿⣯⣭⣤⣉⡁⡈⢉⡩⣙⠛⠑⠚⠋⢰⣷⣿⣶⣶⣬⣭⣭⣙⣛⣻⠿⢿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀ ⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⢻⣿⠟⠀⠀⠀⠈⠑⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣦⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣛⣛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⡀⠀⠀⠀⠀ ⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡄⠁⣠⣀⠀⣰⣶⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⡂⠀⠀⢀ ⣿⣿⣿⣇⢸⣿⣿⣿⡿⠟⠀⠈⣿⣿⣿⣿⣷⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠂⠂⠀ ⣿⣿⣿⣷⢸⣿⣿⠛⠁⠀⠀⠀⠈⣿⣿⣻⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣶ ⣿⣿⣿⡏⢸⣿⡿⠛⢦⣄⠀⠀⠀⠉⠉⢸⣿⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿ ⣿⣿⣿⣿⡿⠋⠀⠀⠀⠹⣷⣶⣶⣄⣤⣼⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿ ⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠉⠁⠀⠋⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡿ ⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣧⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⠛⢻⣿⣿⣾⣿⣿⣧⡼⢢⣿⣯⣿⣿⡿⠿⢟⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⣿⣟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠉⢹⣿⣿⣿⣿⣿⣟⣛⣿⣿⡿⣷⣽⣿⣿⣆⠙⠃⣰⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠃⠀⠐⢿⣿⣿⣿⣿⣿⣍⣁⠀⢾⣿⣹⢏⣿⣿⣷⣶⣯⡉⢻⣟⣛⢉⠉⠑⠀⠀⢠⠀ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⣰⣿⣿⣿⣿⣿⣾⣿⣿⠛⠀⢀⡀⢀⣿⣿⣿⣿⣿⣷⡀⠀⣀⣶⣴⣶⡄⣼⣷⡞ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⠹⣿⣿⣷⠸⣻⡟⠻⠋⢙⠛⣿⠃ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⠉⠉⠛⠋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⡇⣶⣿⣿⣿⣧⠿⠃⠀⠀⠀⠀⠹⠀ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⣠⣾⣿⡿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣹⣿⣿⣿⣿⡆⠀⠐⠛⠀⠀⠀⠀ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢠⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠏⠉⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠀⠀⢸⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⡏⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠟⢷⣀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠿⠿⠒⠀⠀⣀⣀⣠⣊⣉⣀⣄⡀⠈⠃⠀⠀⠀⠀⠀⠀ ⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⣿⠁⣼⡟⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠒⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣷⣶⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⣿⣟⣿⠳⢠⠀⢠⢠⡔⣒⡆⣴⣠⣴⢢⡖⣲⣤⣾⡋⡿⢛⠣⣸⡟⣿⡟⡉⣡⢀⣴⢖⣖⣤⣤⣀⣀⣀⣀⣠⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⣽⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀ ⠉⠛⣿⠶⢾⢨⣥⣿⣿⣿⣿⣿⣭⣽⢸⡗⣯⣿⢿⠀⣇⠀⢰⢩⡇⣭⡷⣭⣹⢘⢻⠦⢍⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣀⠀⠀⠈⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡇⠀⠀ ⠀⢾⠿⣿⠿⣿⢿⢿⣿⣿⣾⣿⣿⢿⣿⣿⣿⣭⣭⣭⡀⢉⡁⣈⢉⡻⠻⠙⠛⠊⠉⢲⣷⣶⣶⣮⣭⣭⣙⣛⣻⠿⠿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀ ⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⠻⣿⠟⠀⠀⠀⠈⠑⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣆⢀⡀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣛⣛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡍⠀⠀⠀⠀⠀ ⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡄⠁⣠⣀⠀⣰⣶⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣤⡄⣀⠀⡀ ⣿⣿⣿⣇⢸⣿⣿⣿⡿⠟⠀⠈⣿⣿⣿⣿⣷⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠧⠀⠀⠀ ⣿⣿⣿⡧⢸⣿⡿⠉⠁⠀⠀⠀⠈⣿⣿⣻⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣶ ⣿⣿⣿⡏⢸⣿⡿⠛⢦⣄⠀⠀⠀⠉⠉⢸⣿⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿ ⣿⣿⣿⣿⡿⠉⠀⠀⠀⠹⣷⣶⣶⣄⣤⣼⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿ ⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠉⠁⠀⠋⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠿ ⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣧⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⠛⢻⣿⣿⣾⣿⣿⣧⡼⢠⣿⣏⢿⣿⡿⠿⢟⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠉⢹⣿⣿⣿⣿⣿⣟⣛⣻⣿⢿⣷⣹⣿⣿⣆⠙⠁⣰⣾⣿⣿⣿⣿⣄⡀⠐⠀⠀⠀ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠃⠀⠐⢿⣿⣿⣿⣿⣿⣝⣁⠀⣼⣿⢙⠋⣿⣿⣷⣶⣯⠉⢻⣟⣙⢉⠉⠑⠀⠀⠐⠄ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⣰⣿⣿⣿⣿⣿⣾⣿⣿⠛⠀⢀⣀⢀⣹⣿⣿⣿⣿⣷⡀⠀⣀⣶⣴⣶⡀⣼⣾⡞ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣷⠸⣿⡟⠻⠋⢙⠛⣿⠃ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡜⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⠉⠙⠙⠋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠻⡇⣕⣿⣿⣿⣧⠿⠃⠀⠀⠀⠀⠹⠀ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⣠⣾⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣡⣿⣿⣿⣿⡆⠀⠐⠛⠀⠀⠀⠀ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢠⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⣿⣿⠏⠉⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠀⠀⢸⣿⣿⣭⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⢸⡏⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⣷⣀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠿⠿⠒⠀⠀⣀⣀⣠⣊⣉⣀⣄⡂⠈⠃⠀⠀⠀⠀⠀⠀ ⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⣿⠁⣸⡟⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠂⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣶⣦⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀ ⣿⣟⣿⠣⢠⠀⢠⣠⣔⣒⡆⣴⣠⣴⢢⡖⣲⣴⣾⡋⡽⢛⠣⣼⡟⣿⡟⡉⣡⢀⣶⢖⣖⣤⣤⣀⣀⣀⣀⣠⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢹⡙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀ ⠉⠛⣿⠶⢾⢨⣥⣿⣾⣿⣿⣿⣭⣽⢸⡗⣯⣿⢿⠀⣇⠀⢰⢩⡇⣭⣿⣭⣹⢘⣻⠦⢍⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣄⡀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡇⠀⠀ ⠀⣾⠿⣿⠿⣿⢿⢿⣿⣿⣾⣿⣿⢿⣿⣿⣿⣭⣭⣭⡀⢉⡁⡈⢉⡹⠻⠙⠛⠊⢉⢲⣷⣶⣶⣮⣭⣭⣙⣛⣻⠿⠿⣿⣿⣿⣿⣿⣿⣿⠟⠈⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀ ⣿⠀⣿⣿⣿⣿⣿⣿⡸⠏⠀⠀⠀⢀⣀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⣻⣿⣿⣿⣿⣿⣷⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡦⣒⠀⠀ ⣿⡆⣿⣿⣿⣿⣿⣿⠃⠰⣾⣷⣴⣾⣿⡁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣔⡠ ⣿⡇⣿⣿⣿⡿⠋⠁⠀⠀⠻⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⠈⠁⢀ ⣿⡇⣿⣿⣷⣄⠀⠀⠀⠀⠀⠿⡿⢺⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿ ⣿⣧⣿⡿⠛⠀⠙⣦⣀⣀⣀⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿ ⣿⡿⠋⠀⠀⠀⠀⠈⣿⣿⣿⣷⣶⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿ ⡟⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢀⣠⠘⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠛ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⡆⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣷⡀⢀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠐⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠟⠛⠉⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣉⣉⣿⣿⣿⣿⣿⣿⣷⡟⣼⣿⣿⠿⣿⠟⠟⣣⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣟⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⣿⣿⣿⣿⣿⣿⣭⣭⡿⠿⣿⣗⢾⣿⣿⣦⠉⠁⣴⣿⣿⣿⣿⣿⣦⣄⠈⠀⠀⣄ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⠂⠀⢻⣿⣿⣿⣿⣿⣯⣥⣀⣴⠿⣿⣟⣿⣿⣿⣿⣿⣧⡈⠻⡿⠽⠣⠀⡙⡀⠀⣠⣸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⣠⣿⣿⣿⣿⣿⣷⣿⣿⠟⠋⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⡄⠀⣀⣶⣴⣿⡆⣼⣿⣿ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⡕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⡸⣻⣏⠻⠃⢈⠙⢻⠑ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡯⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠉⠉⠙⠛⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢹⢇⣿⣿⣿⣿⣧⠟⠃⠀⢀⠀⠀⠘⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠁⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⣠⣶⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠸⣿⣼⣿⣿⣿⣿⡇⠀⠀⠛⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡟⠉⠁⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⡟⠀⠀⢿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠀⠀⠀⠀⠀⣿⠁⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢿⢿⣆⡁⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠿⠷⠆⠀⠀⣀⣀⣔⣊⣉⣀⣄⡒⠊⠃⠀⠀⠀⠀⠀⠀ ⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣾⡏⢠⣿⠃⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠴⠀⠀⠀⠀⡀⠀⠀⢹⣿⣿⣿⣿⣿⣷⣶⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀ ⣿⠄⣤⠀⢠⠀⣠⣠⣄⣒⡆⣤⣠⣤⢰⡖⣲⡿⢳⣚⡿⢒⣿⠿⡟⣛⣷⡀⣠⢀⣤⢔⣖⣀⣀⣀⣀⣀⣀⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣋⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀ ⢿⣶⣿⣶⣿⢨⣥⣿⣺⣿⣿⣿⣭⣽⢸⡗⣯⡁⢸⠃⣇⢰⣿⢩⡇⣭⡗⣙⣿⠸⢿⣶⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣄⡀⠀⠀⠉⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⢿⠿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⢿⣿⣯⣤⣉⣍⣩⡀⢉⡑⡚⠛⡿⠹⠟⠋⠸⣟⣲⣷⣾⣭⣭⣛⣛⡻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠠ ⣿⣿⣿⣿⣿⡇⠀⣴⣦⣄⣠⣼⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣥⣦⡤⣀ ⣿⣿⣿⡿⠋⠀⠀⠸⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠷⠛⠊ ⣿⣟⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢀ ⣿⡿⠟⠶⣄⠀⠀⠀⠀⠉⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢨ ⠁⠀⠀⠀⠙⣷⣶⣶⣦⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⠿⠟⠿⠏⠉⡸⠃⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣯⣀⣀⣠⣴⣶⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣻⣿⣿⣷⢀⣤⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣦⣤⣸⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⠻⣿⣋⠋⣱⣿⣿⣿⣷⡄⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⢹⣿⣿⣿⣿⣿⣷⣤⡾⠟⢻⣿⣿⣿⣿⣿⣧⣀⣀⣼⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⢈⣿⣿⣿⣿⣿⠿⣶⣤⣤⣾⠿⠟⠙⢿⣿⣿⣿⣿⣷⡀⠹⠿⠴⠅⠄⢠⠁⠀⣀⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣁⣤⣤⣄⣼⣿⣿⣿⣿⣿⣿⣆⠀⣄⣼⣷⣿⣧⢠⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡟⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⡴⢻⣿⠙⠋⠀⡉⠹⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠹⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠉⠉⠉⠙⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢹⢣⣿⣿⣿⣿⣧⠿⠛⠀⢀⡀⠀⠀⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⣠⣶⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠸⣞⣼⣿⣿⣿⣿⣇⠀⠀⠛⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⣿⣿⡿⠉⠉⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠏⠀⠀⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠀⠀⠀⠀⠀⣿⠁⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢿⣿⣆⡁⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠀⠀⠀⣀⣀⣔⣊⣉⣀⣐⡒⠚⡛⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡟⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠤⠬⠍⢀⠀⣀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠄⣤⠠⢠⠀⢠⢀⣄⣒⡆⣤⣠⣺⢰⡟⢳⡾⣿⠀⣼⣻⣿⠷⡖⣒⣄⡄⣠⢀⣄⢔⣒⢀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⢹⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀ ⣤⣶⣿⣿⣿⢨⣥⣿⣺⣿⣿⣿⣭⣽⢸⡗⢫⡙⢹⢈⣇⣷⣾⢙⡇⠭⡧⣿⣿⢸⣿⣶⣝⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣄⣀⡀⠀⠀⠈⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⢟⣩⠉⡤⢉⡍⢹⡛⢿⡷⡾⠛⡿⠷⠓⣿⢺⣏⣠⣗⣛⣛⡻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠓⠀⢀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀ ⡿⠋⠀⠀⢹⣿⣿⣿⣿⣿⣧⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣏⠽ ⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠈⠈⠀⠀ ⣀⠀⠀⠀⠀⠈⠻⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠙⣷⣄⣀⣤⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠈⣿⣿⣿⣿⣶⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠈⠉⠀⠀⠋⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣧⣴⣿⣿⣧⣴⡆⣾⣿⣻⣿⣿⣿⣿⣿⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣷⣶⣦⣿⣿⠿⠿⣿⣿⣿⣿⣘⣿⣿⣯⡹⠿⠥⢁⣼⣿⣿⣿⣿⣇⠀⠀⠄⠀⠀ ⠀⠀⠀⠀⠈⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⡷⠶⠛⠉⣿⣿⣾⣟⣿⣿⣧⣤⣤⡾⠻⣿⣿⠿⣿⡻⠷⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠈⠀⢀⣿⣿⣿⣿⣿⡿⣿⣶⣤⣬⠟⠛⠣⠚⣼⣿⣿⣿⣿⣿⣄⠘⠛⠒⠂⠂⢀⣆⠀⢀⡀ ⠀⠀⠀⠀⠀⠀⣹⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢁⣠⣤⣤⣤⣾⣿⣿⣿⢻⣿⣿⣧⠀⣤⣼⣷⣿⢿⣆⣾⣷ ⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢼⣿⣿⣿⡆⢻⣿⡈⠛⠁⠬⠉⢿ ⠀⠀⠀⠀⠀⠰⣿⡟⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⠉⠉⠉⠙⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⢹⢡⣮⣾⣿⣿⣧⠞⠛⠀⠀⡀⠀⠀⠘ ⠀⠀⠀⠀⠀⢸⣿⡁⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⣠⣶⣿⣿⠏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠸⣾⣼⣿⣿⣿⣿⣷⠀⠀⠘⠛⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⣿⣿⣿⠉⠉⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠃⠀⠀⣿⣿⣿⣽⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠿⡿⠀⠀⠀⠀⠀⢸⡟⠉⣹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠙⣿⣟⠆⠉⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡦⠀⠀⠀⢀⣀⣔⣛⡉⢉⣀⠒⠒⡛⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠇⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢠⡤⠈⠉⠁⠀⠀⠀⠀⠘⣻⣿⣿⣭⣿⣿⣿⣤⣤⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⡁⠀⠀⠀⠀⠀⠀⠀ ⠀⠄⣤⠀⢠⠀⠠⢀⡔⢒⡖⣷⡻⣻⢂⡞⣻⡄⣾⣲⣶⣲⡶⠤⡄⣀⡄⡀⣠⠀⠀⠔⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠉⠉⠛⠛⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀ ⣶⣶⣿⣶⣾⢨⣥⣿⣺⣿⣿⣿⡍⢸⠀⡗⢯⣑⣿⡯⣧⠶⢾⢹⡇⣭⡧⣿⣿⢸⣿⣶⣍⢻⣷⣾⣿⣿⣿⣿⣶⣶⣶⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠟⠋⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣶⠄⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢡⠍⢩⠉⠄⢹⣿⣿⡿⣿⡷⣼⣿⡯⢩⣟⣿⠚⡛⠲⢷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⢀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀ ⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⠁⠈⠁⠀⠀⠊⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣴⣦⣤⣴⣶⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⡆⢀⣤⢸⣿⡿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣍⣉⣉⢿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣾⣿⣇⠿⢿⣿⠟⠿⢻⣼⣿⣿⣿⣇⡀⠀⠀⠀⠀ ⣿⡩⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⢻⣿⣿⣿⣿⣿⣿⣏⣉⣛⣿⡿⢿⣿⣶⣿⣿⣿⣷⡈⠛⠋⣰⣾⣿⣿⣿⣿⣿⣧⣄⠀⠚⠂ ⣿⣯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣄⠀⠸⣿⣿⣿⣿⣿⣿⣿⣛⠋⠀⢀⣿⣿⣿⢿⣿⣿⣿⣿⣶⣾⣟⠛⢻⣿⡟⠻⡭⠛⠙⠷⠀⠀ ⣿⣯⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣻⣿⣿⣾⡿⠍⠉⠁⠀⠪⣿⣿⣿⣿⣿⣿⣧⡀⠉⠉⠉⣈⡃⣠⣄⠂⢠ 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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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⠀⠀⠀⠀⠀⢸⣿⣿⣾⠁⠀⠀⠀⠀⢘⣿⣿⡟⡿⠉⠋⠉⠉⠉⠉⢉⣭⣿⣿⣄⠀⠀⠀⣿⣿⣿⠏⠠⣿⠟⠻⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⡄⠀⢠⢘⣻⣿⠗⠒⠆⣤⠀⢠⢈⠉⣙⠁⠉⢁⠔⠒⢂⢀⡄⣹⡍⡉⣩⢉⠑⠒⣒⢻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⡇⠀⢸⢨⣥⢿⡀⠀⠀⣿⠀⢸⠘⠀⠉⢰⡆⢸⡀⢧⣤⢨⡇⣤⡇⣿⣿⢸⣟⢦⡍⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡟⠛⣿⠿⠛⠉⠙⠛⢿⣿ ⠀⠎⠻⣶⠋⢿⣿⣾⢾⣿⡾⠁⣥⢡⢈⢠⠚⣶⢷⣞⠗⡖⢲⡺⢲⡿⢲⠛⣷⠺⣟⢲⣶⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣷⣷⢀⣀⣤⣴⣶⣾⣿ ⣶⠞⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⡿⠛⠛⠛⠛⠟⢛⡛⠻⣿⣿⠟⣛⡛⠻⠟⠛⠛⠛⠛⠛⠛⠿⣿⠟⠛⠛⢿⣿⠿⠛⠻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⡿⠟⣛⡛⠿⠟⠛⠟⠛⠛⠛⠛⠻⣿⣿ ⣿⡀⠿⣿⣿⠛⣿⣿⢸⣿⣿⣸⣿⡇⢸⣿⠿⢃⡀⠟⣿⡿⠃⣾⡟⣿⣷⠘⠁⣾⡟⣿⣧⢸⣿⡟⠛⢻⣿⡿⢃⡇⢸⣿⣿⡄⠛⢸⣿⣇⣿⡇⣿⣿⠛⢹⣿⢸⣿⡇⣿⣿⠈⢠⣿⡟⣿⡆⣿⣿⣸⣿⢸⣿⡟⠇⣼⣿ ⣿⣿⠀⣿⣿⠀⣿⣿⢸⣿⣿⣿⣿⡇⢸⣿⣶⢈⣿⠀⣿⡇⠀⣿⡇⣿⣿⠀⠀⣿⣧⣭⣭⢸⣿⣷⡆⢸⣿⡇⣿⠇⣿⡏⣿⡇⠀⢸⣿⣿⣿⡇⣿⣿⣶⢸⣿⣼⣿⣷⣿⡇⢀⢸⣿⡇⣿⡇⣿⣿⣿⣿⢸⣿⣷⡆⣿⣿ ⣿⣿⠀⣿⣿⠀⣿⣿⢸⣿⢹⡿⣿⡇⢸⣿⣤⡜⣿⠀⣿⡇⠀⣿⣇⣿⡿⠀⠀⣿⣇⣿⣿⢸⣿⣧⡄⢸⣿⡇⣿⠀⣿⡿⣿⣷⠀⢸⣿⠸⣿⡇⣿⣿⣤⠘⣿⣿⡟⣿⣿⡇⣼⠸⣿⣇⣿⡇⣿⡏⢿⣿⢸⣿⣧⡄⢿⣿ ⣿⣿⣄⣉⣩⣤⣍⣉⣈⣉⣈⣁⣉⣁⣈⣉⣉⣥⣿⣧⣉⣡⣶⣌⣉⣉⣥⣘⣃⣈⣉⣉⣉⣈⡉⠉⠁⠈⢉⣵⣿⣮⣉⣡⡉⠉⠀⡈⠉⠀⠉⣡⣉⣉⣉⣤⣉⣉⣤⣉⣉⣵⣿⣧⣍⣉⣉⣤⣍⣩⣌⣉⣬⣉⣉⣡⣾⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢿⣿⡟⠁⠀⠀⠀⠀⠀⠉⠛⠿⣿⣷⣄⠀⠀⠃⠀⠀⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣯⡿⣿⣧⡤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣟⣻⡛⠀⢀⡐⢀⣂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⣼⡇⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⠘⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢀⡐⠂⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣉⣉⣉⣹⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣛⠛⠛⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢀⡀⠃⠁⠀⠀⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣼⢣⠀⠴⠀⠴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠀⢸⡟⢡⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠘⠀⠀⠑⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠀⠈⠀⠀⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⡄⠀⢠⠀⠀⢠⢟⣿⡟⣤⠀⢠⠀⠀⣹⠻⡏⢉⠟⣛⣛⢩⡍⣹⡍⡉⣩⢉⡙⠛⣛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⡇⠀⢸⠀⠀⠸⣺⣿⡿⣿⠀⢸⠘⠀⠉⠰⠇⢸⡀⣿⣯⢸⡇⣭⡇⣿⣿⢸⣟⢦⡍⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠉⠉ ⠀⠎⠻⣶⠉⢿⠍⠰⣿⣿⡾⢻⣥⢥⡜⢶⠒⣶⢷⣞⠗⡖⢲⡾⢲⡿⣲⠛⣷⠺⣟⢲⣶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⣴⣷⣿ ⣶⠞⠛⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⡿⠛⠛⠛⠻⠟⢛⡛⠻⣿⣿⠟⣛⡛⠻⠟⠛⠛⠛⠛⠛⠛⠿⣿⠟⠛⠛⢿⣿⠿⠛⠻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⡿⠟⣛⡛⠿⠟⠛⠟⠛⠛⠛⠛⠻⣿⣿ ⣿⡀⠿⣿⣿⠟⣿⣿⢸⣿⣿⣸⣿⡇⢸⣿⠿⢃⡀⠿⣿⡿⠇⣾⡟⣿⣷⠘⠁⣾⡟⣿⣧⢸⣿⡿⠛⢿⣿⡿⢃⡇⢸⣿⣿⡄⠛⢸⣿⣇⣿⡇⣿⣿⠟⢹⣿⢸⣿⡇⣿⣿⠈⢠⣿⡟⣿⡆⣿⣿⣸⣿⢸⣿⡿⠇⣼⣿ ⣿⣿⠀⣿⣿⠀⣿⣿⢸⣿⣿⣿⣿⡇⢸⣿⣶⢈⣿⠀⣿⡇⠀⣿⡇⣿⣿⠀⠀⣿⣧⣭⣭⢸⣿⣷⡆⢸⣿⡇⣿⠇⣿⡏⣿⡇⠀⢸⣿⣿⣿⡇⣿⣿⣶⢸⣿⣼⣿⣷⣿⡇⢀⢸⣿⡇⣿⡇⣿⣿⣿⣿⢸⣿⣷⡆⣿⣿ ⣿⣿⠀⣿⣿⠀⣿⣿⢸⣿⢹⡿⣿⡇⢸⣿⣤⡜⣿⠀⣿⡇⠀⣿⣇⣿⡿⠀⠀⣿⣇⣿⣿⢸⣿⣧⡄⢸⣿⡇⣿⠀⣿⡿⣿⣷⠀⢸⣿⠸⣿⡇⣿⣿⣤⠘⣿⣿⡟⣿⣿⡇⣼⠸⣿⣇⣿⡇⣿⡏⢿⣿⢸⣿⣧⡄⢿⣿ ⣿⣿⣄⣉⣩⣤⣍⣉⣈⣉⣈⣁⣉⣁⣈⣉⣉⣥⣿⣧⣉⣡⣶⣌⣉⣉⣥⣘⣃⣈⣉⣉⣉⣈⡉⠉⠁⠈⢉⣵⣿⣮⣉⣡⡉⠉⢀⡈⠉⠀⠉⣁⣉⣉⣉⣤⣉⣉⣤⣉⣉⣵⣿⣷⣍⣉⣉⣤⣍⣩⣌⣉⣬⣉⣉⣡⣾⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠉⠛⠿⣿⣷⣄⠀⠀⠂⠀⠀⠙⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣯⡝⣿⣧⡦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣟⣛⡛⠀⢀⡐⢀⣂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⣼⡇⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⠘⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢀⡐⠂⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣉⣉⣉⣹⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡅⢀⡀⠁⠀⠀⠀⠉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢾⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣼⠡⠄⠲⠒⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⢭⡍⢹⡟⢡⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠉⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡟⠀⠈⠀⠀⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⡄⠀⢠⠀⠀⢠⢟⣿⡟⣤⠀⢠⠀⠀⣹⠻⡏⢉⠟⣛⣋⢡⡍⣹⡍⡉⣩⢉⠙⠛⣛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⡇⠀⢸⠀⠀⠸⣸⣿⡿⣿⠀⢸⠘⠀⢉⠸⠇⢸⡀⣿⣯⢸⡇⣭⡇⣿⣿⢸⣟⢦⡍⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠉⠉ ⠀⠎⠻⣶⠉⢿⠍⠰⣿⣿⡾⢹⣥⢩⣈⢦⠒⣶⢷⣞⠗⡖⢲⡺⢲⡿⣲⠛⣷⠺⣟⢲⣶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣬⣿⣿ ⠀⠟⠃⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⡿⠛⠛⠛⠛⠟⢛⡛⠻⣿⣿⠟⣛⡛⠿⠟⠛⠛⠛⠛⠛⠛⢿⣿⠟⠛⠛⢿⣿⠿⠛⠻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⡿⠟⣛⡛⠿⠟⠛⠟⠛⠛⠛⠛⠻⣿⣿ ⠀⠀⠿⣿⣿⠟⣿⣿⢸⣿⣿⣸⣿⡇⢸⣿⠿⢃⡀⠿⣿⡿⠇⣾⡟⣿⣷⠘⠃⣾⡟⣿⣧⢸⣿⡿⠛⢿⣿⡿⢃⡇⢸⣿⣿⡄⠉⢸⣿⣇⣿⡇⣿⣿⠟⢹⣿⢸⣿⡇⣿⣿⠈⢠⣿⡟⣿⡆⣿⣿⣸⣿⢸⣿⡿⠇⣿⣿ ⢘⣿⠀⣿⣿⠀⣿⣿⢸⣿⣿⣿⣿⡇⢸⣿⣶⢘⣿⠀⣿⡇⠀⣿⡇⣿⣿⠀⠀⣿⣧⣭⣭⢸⣿⣷⡆⢸⣿⡇⢸⠇⣿⡏⣿⡇⠀⢸⣿⣿⣿⡇⣿⣿⣶⢸⣿⣼⣿⣷⣿⡇⢀⢸⣿⡇⣿⡇⣿⣿⣿⣿⢸⣿⣷⡆⣿⣿ ⢈⣿⠀⣿⣿⠀⣿⣿⢸⣿⢹⡿⣿⡇⢸⣿⣤⡜⣿⠀⣿⡇⠀⣿⣇⣿⡿⢠⡀⣿⣇⣿⣿⢸⣿⣧⡄⢸⣿⡇⢸⠀⣿⡿⣿⣧⠀⢸⣿⠸⣿⡇⣿⣿⣤⠘⣿⣿⡟⣿⣿⡇⣼⠸⣿⣇⣿⡇⣿⡏⢿⣿⢸⣿⣧⡄⢿⣿ ⠀⣿⣤⣉⣉⣄⣉⣉⣈⣉⣈⣁⣉⣁⣌⣉⣉⣥⣿⣧⣉⣡⣶⣌⣉⣉⣥⣾⣷⣌⣉⣉⣉⠈⠉⠉⠁⠈⠉⠁⢸⣮⣉⣁⠉⠉⠀⠈⠉⠀⣉⣁⣉⣉⣉⣤⣉⣉⣤⣉⣉⣵⣿⣷⣍⣙⣉⣤⣍⣩⣬⣉⣬⣉⣉⣡⣾⣿ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢷⡄⠀⠉⠀⠀⠈⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡌⠉⢉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠈⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣃⠀⣘⠃⢚⣚⣓⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡏⢰⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣤⣤⡄⣀⠐⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⢈⣉⣉⣉⣏⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣉⠑⠏⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡟⠛⠛⠻⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣦⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⣈⠈⠉⠁⢉⠚⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⠀⠀⣹⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢠⣟⣴⠴⢶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠻⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣾⠛⡓⠀⣰⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠄⡄⠀⢠⠀⠀⢀⠄⠂⠟⣿⣿⣧⠀⠀⢀⠨⡍⢩⠟⣛⣛⢩⡍⣹⡍⡉⣩⢉⠙⠛⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⡇⠀⢸⠀⠀⠸⡀⠀⢸⣿⣭⢽⠀⠀⠉⠐⠇⠸⠀⢿⣭⢹⡇⣭⡇⣿⣿⢸⣟⢦⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⢿⣿⡟⠋ ⠀⠎⠻⣶⠉⢿⠍⠰⢼⠿⢾⣿⣿⢡⣾⣤⡒⣶⢷⣞⠖⡖⢲⡾⢲⡿⣲⠛⣷⠺⣟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣠ ⣿⠀⠈⠛⠀⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⡿⠛⠛⠛⠛⠟⢛⡛⠿⣿⣿⠟⣛⡛⠿⠟⠛⠛⠛⠛⠛⠛⢿⣿⠟⠛⠛⢿⣿⠿⠛⠻⠛⠛⠛⠛⠛⠛⠛⠟⠛⠛⠛⠛⢿⡿⠟⣛⡛⠿⠟⠛⠟⠛⠛⠛⠛⠻⣿⣿ ⣿⠀⠿⣿⣿⠟⣿⣿⢸⣿⣿⣸⣿⡇⢸⣿⠿⢃⡄⠿⣿⡿⠇⣾⡟⣿⣷⠘⠃⣾⡟⣿⣧⢸⣿⡿⠛⢿⣿⡿⠃⠏⢸⣿⣿⡄⠀⢸⣿⣇⣿⡇⣿⣿⠿⢹⣿⢸⣿⡇⣿⣿⠈⢡⣿⡟⣿⡆⣿⣿⣸⣿⢸⣿⡿⠇⣿⣿ ⣿⡀⠀⣿⣿⠀⣿⣿⢸⣿⣿⣿⣿⡇⢸⣿⣶⢈⣿⠀⣿⡇⠀⣿⡇⣿⣿⠀⠀⣿⣧⣭⣭⢸⣿⣷⡆⢸⣿⡇⠐⠀⣿⡏⣿⡇⠀⢸⣿⣿⣿⡇⣿⣿⣶⢸⣿⣼⣿⣷⣿⡇⢀⢸⣿⡇⣿⡇⣿⣿⣿⣿⢸⣿⣷⡆⣿⣿ ⣿⡄⠀⣿⣿⠀⣿⣿⢸⣿⢹⡿⣿⡇⢸⣿⣤⡜⣿⠀⣿⡇⠀⣿⣇⣿⣿⢠⡀⣿⣇⣿⣿⢸⣿⣧⡄⢸⣿⡇⠤⠀⣿⡿⣿⣷⠀⢸⣿⠸⣿⡇⣿⣿⣤⠘⣿⣿⡟⣿⣿⡇⣼⠸⣿⣇⣿⡇⣿⡏⢿⣿⢸⣿⣧⡄⢿⣿ ⣿⡇⣀⣉⣉⣤⣉⣉⣈⣉⣌⣁⣉⣡⣈⣉⣉⣥⣿⣧⣉⣡⣶⣌⣙⣉⣥⣿⣷⣌⣉⣉⠉⠈⠉⠉⠁⠈⠉⠁⠛⢈⣉⣁⠉⠉⠀⡈⠉⠀⣉⣡⣉⣉⣉⣤⣉⣉⣤⣍⣉⣵⣿⣷⣍⣙⣉⣤⣍⣭⣬⣩⣬⣉⣉⣡⣾⣿ ⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠈⠁⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢨⠈⣠⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠐⠛⠀⣛⣛⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣄⣽⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣀⣤⣤⣤⢀⡐⠂⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ 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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 1987 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/01/03/green-freesw-not-greenwashing/#comments Gemini version at gemini://gemini.techrights.org/2022/01/03/green-freesw-not-greenwashing/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.03.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Software_Freedom_Makes_the_World_a_Greener_Place,_Too⠀✐ Posted in Free/Libre_Software, Hardware at 9:28 am by Dr. Roy Schestowitz Video_download_link | md5sum b9818d9e345d7dc111adbe5628e972f2 http://techrights.org/videos/e-pollution.webm Summary: We probably need to improve our messaging along the lines of energy consumption and rejection of planned_obsolescence in advocacy of free-as-in- freedom software THE so-called ‘Linux’_Foundation is a total disgrace that is greenwashing the worst offenders and the biggest polluters on the planet, especially Microsoft [1, 2]. It’s even plastered all over the_2021_annual_report. But then again, it’s not about software freedom but about openwashing and reputation laundering. The so-called ‘Linux’ Foundation should never even be called “Linux” anything; it’s a misleading name. Similarly, FSFE_was_repeatedly_asked by_the_FSF_to_rename,_as_it_had_violated_an_agreement_on_the_use_of_the_name. FSFE is a bunch of self-serving_dictators bankrolled by Gulag and Microsoft. They try to censor actual proponents of software freedom, who aren’t doing this for a salary but altruism and ideology. Same_as_the_OSI, which they_colluded with_(against_volunteers_and_lifelong_activists). “We need to think or rethink how we use (or reuse, recycle) technology; as gemini:// is 100% Free software (all software I’ve ever seen for it was liberally licensed) and works across many platforms — including very old ones — one stepping stone towards lowering “footprint” (energy and surveillance) is to encourage adoption of it.”My rants about fake NGOs aside (the IRS needs_to_bust them_for_misuse_of_tax_exemption_status; maybe_it_already_does), the video above concerns Dr. Andy Farnell’s excellent_article_from_last_night. I show this article as GemText over gemini:// because I wish to encourage more people to adopt Gemini, which is vastly better for the environment, both in terms of system requirements and the energy it takes to load a page. Incidentally, those who use gemini:// to access Techrights did not notice the 4-hour downtime of the Web site yesterday (due to electric outage) and benefited from a secure connection that does not involve a CA like the_so-called_'Linux'_Foundation's Let's_Encrypt. We need to think or rethink how we use (or reuse, recycle) technology; as gemini:// is 100% Free software (all software I’ve even seen for it was liberally licensed) and works across many platforms — including very old_ones — one stepping stone towards lowering “footprint” (energy and surveillance) is to encourage adoption of it. There are many other things one can do in order to lessen human suffering; in the video above I show my PDA, which is a model made in 2002, i.e. 20 years ago. It still works. My alarm clock and stereo were made in the 1990s and I use them every day. We need to demand from companies that they use components made to last, not to break after about 5 years, spurring another wave of sales (bad for the planet, not just for the wallet). To make matters worse, some of the CAs are spurring further obsolescence; it’s a known issue which we were reminded of last year because many old devices ceased to work with the Web. There was no workaround because the so-called ‘Linux’ Foundation with its silly CA had a “cert” expire (last year wasn’t the first time) and then the software relying upon that “cert” — somewhere further up the chain — panicked over n nothing; Gemini does not force such a reliance on third party CAs, so it’s not bad for the environment like the Web is. █ ䷩ 𝚕𝚒𝚗𝚎 2068 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/01/03/irc-log-020122/#comments Gemini version at gemini://gemini.techrights.org/2022/01/03/irc-log-020122/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.03.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ IRC_Proceedings:_Sunday,_January_02,_2022⠀✐ Posted in IRC_Logs at 2:35 am by Needs Sunlight Also available via the Gemini protocol at: * gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-020122.gmi * gemini://gemini.techrights.org/irc-gmi/irc-log-020122.gmi * gemini://gemini.techrights.org/irc-gmi/irc-log-social-020122.gmi * gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-020122.gmi Over HTTP: 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇HTML5_logs⦈_ #techrights_log_as_HTML5 #boycottnovell_log_as_HTML5 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇HTML5_logs⦈_ #boycottnovell-social_log_as_HTML5 #techbytes_log_as_HTML5 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇t 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇text_logs⦈_ #techrights_log_as_text #boycottnovell_log_as_text 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇t 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇text_logs⦈_ #boycottnovell-social_log_as_text #techbytes_log_as_text Enter_the_IRC_channels_now =============================================================================== § IPFS Mirrors⠀➾ CID Description Object type IRC log for  QmeFMLBRmWeVpkUb8AucJYiFU1Co2yCoXpV7i8USA1oN6w #boycottnovell 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #boycottnovell  QmdQYBGzgQSsKacFZDZio2cmoqE585BxfAQgGnY6sUhEyC (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ as plain/ASCII text) IRC log for #boycottnovell-  QmSfhPfV2Fu3pEzbc99TDMyFEiKGuYtVDzcszRp92Kf6ud social 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #boycottnovell-  Qmb7W5GQPtLiZ5eapjNJQrgwCxVVahbRyadvwHFKHHCWPd social 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ (full IRC log as plain/ASCII text) IRC log for  QmR4d6wFUzemF9NXLHTgS8V5MVHaFUpYiSLcUfWcTvxXh5 #techbytes 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #techbytes  QmUF3D788EiAZp6Z1cuDFVS9Vm5ouJFs26RLvxeCGeTnF4 (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ as plain/ASCII text) IRC log for  QmQFAXnAmktDdhMbhetAbqhh3LYRRxntdFfCtKz2KEccEn #techrights 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #techrights  QmVdtFNabLwFSaqLzszYpnAz2sFuCVPwpVs5yekXc6j6Hq (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ as plain/ASCII text) 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈ § Bulletin for Yesterday⠀➾ Local_copy | CID (IPFS): QmfH2by4K6HCiZyvyGQ1L5syH6ZSfcHH12ph6TDo82aovk ䷩ 𝚕𝚒𝚗𝚎 2195 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/01/03/popularising-censorship/#comments Gemini version at gemini://gemini.techrights.org/2022/01/03/popularising-censorship/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.03.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Stop_Cheering/Calling_for_Social_Control_Media_Censorship,_Quit_Getting ‘Information’_From_It_Instead⠀✐ Posted in Deception at 6:15 am by Dr. Roy Schestowitz Video_download_link | md5sum f54e3e1e7143f3e545f86f0d9cb85ffe http://techrights.org/videos/unintended-consequences.webm Summary: Don’t rush to congratulate Twitter for more and more censorship; many of those who get muzzled are nowhere as unpopular as what media likes to focus on and many are wrongly accused using totally bogus grounds/pretexts THE BAIT is alluring. We’re meant to be bite. But hang on. It’s a trap. Censorship is being hailed, promoted, and openly celebrated by online platforms and media outlets owned by the rich and powerful, who also_deny_our_privacy rights. The surveillance is a tool of social control (oppression) and it is celebrated by those who do the surveillance, knowing they’re exempted. “Speaking for myself, I spend barely a minute a day in social control media sites.”I was unhappy to discover just to what degree our government nowadays promotes online censorship, e.g. towards the end of this reasonably_new_or_very recent_media_segment from ITV News (UK). Are they really protecting us? They highlight the worst of the worst (like vandals and people who reject vaccination in general) because they love straw man arguments. it’s well- crafted propaganda. Speaking for myself, I spend barely a minute a day in social control media sites. I am only a ‘passive user’ (like passive smoker) of the thing, basically never retrieving actual (mis/dis/)information from it anymore. I stopped a number of years ago after I had experienced too many cases of false claims going ‘viral’, leading to injustice (like lynch mobs with ‘mob justice’ or campaigns of defamation). As the video above notes, last_week_I_was_wrongly_suspended_by_Twitter (5 days already!). Well, you cannot really appeal (it is there for the pretence of due process or placeholder for the most part) as there’s an unreasonable response time and by the time they might respond — if ever — it is already too late. “Misinformation on Twitter and Facebook — or in social control media at large, YouTube and TikTok included (videos) — does not show that we need more censorship but that we need less of social control media.”The media likes to highlight the least popular politicians to make online censorship seem not just necessary but also commendable. It’s slanted as a matter of public safety or combating violence. The media does not mention all the false possitives (errors) unless it’s a very high-profile example, such as silencing of victims and misuse of “COVID-19″ for censorship of dissent. Sadly, a lot of people are cheering this while ignoring ‘collateral damage’. The media barely tells them about this ‘collateral damage’ and people who become voiceless (banned or suspended) cannot tell their story, either. Misinformation on Twitter and Facebook — or in social control media at large, YouTube and TikTok included (videos) — does not show that we need more censorship but that we need less of social control media. We need to reject the very concept of it and go back to a Web that’s not so centralised, barely controlled by corrupt_businesspeople. They should not be herding us to control what we think and determine what’s ‘permissible’ speech based on fear (of speaking out and potentially losing all our fake ‘friends’ or ‘followers’, based on arbitrary decisions made in some other country). █ ䷩ 𝚕𝚒𝚗𝚎 2282 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/01/03/sick-kinks-balabhadra-alex-graveley/#comments Gemini version at gemini://gemini.techrights.org/2022/01/03/sick-kinks-balabhadra-alex-graveley/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.03.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Microsoft_GitHub_Exposé_—_Part_XIII_—_Nihilistic_Death_Cults_With_Substance Abuse_and_Sick_Kinks⠀✐ Posted in Microsoft at 12:08 am by Dr. Roy Schestowitz Series parts: 1. Microsoft_GitHub_Exposé_—_Part_I_—_Inside_a_Den_of_Corruption_and Misogynists 2. Microsoft_GitHub_Exposé_—_Part_II_—_The_Campaign_Against_GPL_Compliance and_War_on_Copyleft_Enforcement 3. Microsoft_GitHub_Exposé_—_Part_III_—_A_Story_of_Plagiarism_and_Likely Securities_Fraud 4. Microsoft_GitHub_Exposé_—_Part_IV_—_Mr._MobileCoin:_From_Mono_to Plagiarism…_and_to_Unprecedented_GPL_Violations_at_GitHub_(Microsoft) 5. Microsoft_GitHub_Exposé_—_Part_V_—_Why_Nat_Friedman_is_Leaving_GitHub 6. Microsoft_GitHub_Exposé_—_Part_VI_—_The_Media_Has_Mischaracterised_Nat Friedman’s_Departure_(Effective_Now) 7. Microsoft_GitHub_Exposé_—_Part_VII_—_Nat_Friedman,_as_GitHub_CEO,_Had_a Plan_of_Defrauding_Microsoft_Shareholders 8. Microsoft_GitHub_Exposé_—_Part_VIII_—_Mr._Graveley’s_Long_Career_Serving Microsoft’s_Agenda_(Before_Hiring_by_Microsoft_to_Work_on_GitHub’s_GPL Violations_Machine) 9. Microsoft_GitHub_Exposé_—_Part_IX_—_Microsoft’s_Chief_Architect_of_GitHub Copilot_Sought_to_be_Arrested_One_Day_After_Techrights_Article_About_Him 10. Microsoft_GitHub_Exposé_—_Part_X_—_Connections_to_the_Mass_Surveillance Industry_(and_the_Surveillance_State) 11. Microsoft_GitHub_Exposé_—_Part_XI_—_Violence_Against_Women 12. Microsoft_GitHub_Exposé_—_Part_XII_—_Life_of_Disorderly_Conduct_and_Lust 13. YOU ARE HERE ☞ Nihilistic Death Cults With Substance Abuse and Sick Kinks 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GitHub: Where everything comes to die⦈ Summary: ‘Mr. Copilot’ Graveley is deserving of attention he wishes not to have; after repeatedly assaulting women we take stock of his past mischiefs and oddest fetishes A week ago we reflected upon a number of things, without yet introducing much new information (it was Christmas after all). We reminded people that Miguel_de Icaza, who is extremely unhappy about this series (he spoke about it), is rather close to Balabhadra (Alex) Graveley — a subject we shall revisit later in the year. Well, de Icaza and his other half have_family_in_Brazil_and Mexico; it’s worth noting that Mr. Graveley lived in Brazil. He also “mentioned a Portuguese language film that I was disturbed by Alex’s [Graveley] obsession with,” a source has told us. 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GitHub Project Managers⦈ That film_is_called_Talk_to_Her, a film “about a male nurse raping a woman in a coma, but it’s a romance” [or so we're meant to think] and as Wikipedia puts it: “Talk to Her (Spanish: Hable con ella) is a 2002 Spanish drama written and directed by Pedro Almodóvar, and starring Javier Cámara, Darío Grandinetti, Leonor Watling, Geraldine Chaplin, and Rosario Flores. The film follows two men who form an unlikely friendship as they care for two women who are both in comas.” “It’s relevant,” our source has added, because “Alex kept asking me to get blackout drunk to fulfill a kink.” As someone put it in IRC a few moments ago, “potentially poison yourself with alcohol so he can “fulfill a kink”.” “The problem with the media bosses is, they usually believe the rich person or the large corporation, which means that smear campaigns against the accuser/ s can be rather effective.”The source stressed that “Alex is a really bad dude. Nat [Friedman] seems to have been good at maintaining a wholesome persona publicly…” We’ve already shown that Alex Graveley and Nat Friedman are very close; even Miguel de Icaza confirmed this. Our source has said that “journalists think it’s a non-issue” and have in fact suppressed this information. We’ll come to that much later in this series. Where was the BBC when Jimmy_Savile was abusing unconscious or dead kids (necrophilia)? Why is the BBC still operating like nothing major happened? Remember Microsoft pays many sites for “advertising” and Bill Gates is repeatedly bribing the BBC, so don’t expect to see any coverage there about his ties to Jeffrey Epstein — strong_ties_that_he_can_no_longer_publicly_deny. But back to our main topic, it is far from normal to do all those things. As we’ll explain later in this series, there’s a problem also with hard drugs and alcohol, which can contribute or accentuate an eccentric persona. “Serial abuse only stops when someone gets exposed and reported/arrested (in spite of attempts to shame the victim or accuse the victim of lying).”The problem with the media bosses is, they usually believe the rich person or the large corporation, which means that smear campaigns against the accuser(s) can be rather effective. Just read up on what Harvey_Weinstein did to media giants and how he suppressed the story about him for many years. Very similar tactics… it ranges from woman-shaming, e.g. by spying on them, to spiking stories etc. by threats and lawsuits. Weinstein has so many victims, but they had to group/ confront the publishers in large numbers in order to break the media’s silence. Weinstein hired spies who targeted the victims, as has been documented in the media only after he had been exposed. Our source notes that “there’s lots of women that don’t want to talk about what Alex [Graveley] did to them” and we’ll give some examples in the future. Serial abuse only stops when someone gets exposed and reported/arrested (in spite of attempts to shame the victim or accuse the victim of lying). “I don’t think Dropbox has dirty hands,” our source said. “They just wanted his [Graveley's] patents and fired him for abuse.” In future parts we’ll bring up stories about substance abuse and some anecdotes about misogyny from the_self-described_"Chief_Architect_of_GitHub_Copilot". █ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Balabhadra_(Alex)_Graveley:_Affidavit_and_Application_for Arrest_page_1⦈_ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⣤⣀⡀⠀⠀⠀⠘⠛⠓⠐⠿⠿⣿⣷⣶⣦⣤⣤⣤⠀⠀⣤⣄⠤⢄⣀⡄⠈⢻⣿⣿⠋⢁⣀⣀⣽⡏⢙⣿⠛⢻⣿⠉⢹⣯⡄⠀⣠⣤⣤⣤⣤⡄⠀⣠⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢰⣿⣿⣿⣿⣿⣷⠀⠈⣿⡇⠀⣾⡟⠛⢻⡏⠉⣏⠀⢈⣹⡀⠘⠛⠃⠀⡏⠉⣿⡏⠉⡇⠀⣉⡉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠘⢿⣿⣿⣿⣿⠟⠀⢰⣿⣧⠀⢿⣷⡆⢸⡇⠀⣿⠀⢸⣿⠂⢸⣿⡇⠀⡗⠀⣿⡇⠀⡇⠀⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⠦⢼⣿⣿⠀⠀⣠⣿⣿⣿⣶⣤⣤⣤⣼⣧⣤⣿⣦⣤⣼⣤⣼⣿⣧⣤⣿⣤⣤⣤⣤⣧⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡟⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⡿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⡿⠿⡿ ⠷⣿⣷⣷⣯⣄⣍⠻⣿⣿⣿⣯⣽⡽⢿⣿⣿⣿⣿⡿⡿⢿⣿⣟⠛⠻⢿⢿⣿⣿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣛⣿⣟⣿⣿⣷⣶⢶⣿⣿⣿⣷⣷⣬⣵⣶⣷⣴⣲⣆⣌ ⠞⢅⣵⣒⣾⣬⠺⡟⣿⣾⣿⡯⣷⣽⣗⣿⣗⣝⣿⣯⣮⣿⡞⣿⢭⣓⣿⣏⡿⡈⣿⢿⢷⣿⠏⣿⢿⣿⣻⡿⣽⣿⣿⢯⣿⣿⣫⣿⣟⣯⣿⣿⢻⡿⢷⣿⣿⣿⣟⢹⣟⢻⢿⡯⣿⣿⢻⣯⣻⣿⣿⢿⠿⠙⠯⠿⠿⠛ ⠋⠃⠀⠈⠚⡁⠓⠱⠿⠆⠘⠛⠑⠮⠿⠡⠿⠹⣿⡧⣪⠿⠡⠿⣭⣏⣿⣭⣿⣤⣿⣤⣆⣼⣠⠿⣬⣆⠫⠿⠷⠸⢿⣶⣶⣿⣌⠷⣯⠿⢿⠖⠼⢧⠶⣿⡄⣼⣧⣼⣧⡼⣴⡿⢇⡝⢧⠼⠫⠏⠍⠛⢻⡂⠄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡀⣀⣀⣀⠀⢀⣀⡀⠀⠀⠀⠀⣴⠒⣲⢨⡖⠺⣍⢻⣿⠩⣵⡟⢻⡟⡻⣻⣷⡺⡙⠲⠖⢺⣞⢏⡷⠒⣮⢳⣄⣲⡞⢲⡌⣲⣖⢲⡖⣲⣄⠉⠌⠉⠁⠁⠒⣁⠀⠀⠀⠄⠀⠀⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠈⠀⠐⠀⠀⠈⢿⣩⡢⡸⣇⣢⡟⣸⡘⠟⣸⣇⣸⣏⣅⣠⣉⣻⠆⠈⠐⣸⡟⢘⣯⣖⡿⠀⠋⣹⣏⣹⠇⣸⡏⣸⣏⣫⠀⠀⠀⠈⠀⠉⠁⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠤⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠘⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⣿⣿ ⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠁⠀⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠋⠀⠀⠻⣿⢠⡘⢿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣷⣶⣶⣶⣶⣶⣖⣶⣖⣀⣀⣨⣭⡭⠭⠭⠉⠉⠉⢉⢻⣿⣿⣿⠁⠀⢀⣀⣠⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⣸⠀⠁⣿⢳⣄ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢸⣿⣿⣿⡀⠀⠸⡿⡿⠇⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣾⠀⠀⠻⠁⢠⣼⠀⠛ ⣿⣿⣿⣿⣿⠿⠿⠋⠉⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣏⠙⣿⣿⠟⠻⠿⠿⣿⣿⡯⢀⣸⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⡌⢀⠀ ⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠙⣿⣿⣿⢿⣿⡿⠋⠉⠁⠀⠈⠉⡁⠉⠉⠁⠀⠀⠀⠀⠈⠙⣿⡟⠛⢻⣿⣿⣿⠁⠀⢀⡀⣲⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⣿⣿⣿⡆⠀⠀⠀⠀⠀⣴⣶⣦⡀⠀⠈⣿⡇⠀⠀⠈⠉⠀⠀⠀⠀⠀⢠⣤⣶⣤⣤⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠁⠀⢸⣿⣿⣿⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣻⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⡇⠀⠀ ⣿⣿⣿⡇⠀⠀⠀⠀⢾⡟⠛⣿⡇⠀⠀⣸⣿⡆⠀⠀⠀⣰⣶⠀⠀⢠⣛⡛⠛⠛⠛⠛⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⠛⠛⠛⠀⠀⠀⠀⠀⢀⣏⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠙⣿⣿⣿⣿⣿⣦⣄⠀⠀⡇⠀⠀ ⣿⣿⣿⡇⠀⠀⠀⠀⠈⢻⡿⣿⠋⢀⣴⣿⣿⠇⠀⠀⢸⣿⣿⠀⠀⠰⣶⣆⣀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠄⠀⣤⠀⠀⠀⠀⠀⢘⠋⠀⠀⠀⠀⠀⠀⢰⣿⣷⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⢀⡇⠀⠀ ⣿⣿⣿⣿⡀⠀⡀⠐⠤⣨⣳⣿⣿⣿⣿⡿⠋⠀⠀⠀⣾⣿⣿⣇⠀⠀⠻⢿⣿⠀⠀⢸⣿⠀⠀⢠⣶⠀⠀⢸⠉⠁⠀⠀⠈⠛⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢸⡇⠀⠀ ⣿⣿⣿⣿⣧⡀⠈⢤⣀⢀⣾⣿⣿⣷⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⢀⣸⣿⠀⠀⣸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⣾⣿⡏⣿⣿⣿⠏⠈⠁⠀⠀ ⣿⣿⣿⡏⢿⣿⣦⣀⠉⠉⣿⣿⣿⣿⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠀⠘⣿⣿⣿⢸⣿⡏⠀⠀⠀⠀⠀ ⣿⣿⣿⡇⠸⣿⣿⣿⣷⣶⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⠿⡟⠋⠀⣾⣿⣿⡇⠈⣧⣇⣀⣀⣰⣷⣤ ⣿⣿⣿⡇⠀⠀⠀⠀⠀⢩⢝⣉⣡⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠞⠋⠀⠀⠀⠀⠀⣀⣿⣿⠟⠣⠀⣼⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⠁⠀⠀⠀⠰⣶⣶⣾⣿⣿⣿⣷⣿⣿⣿⠿⠿⠿⠟⠻⠛⠛⠛⢃⣼⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠀⠀⠀⠘⣧⠀⠀⣤⣤⡀⠀⠀⠀⠀⣹⡇⠀⠀⠀⠀⠀⣤⣶⣶⣾⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡏⣰⡀⢰⣧⣀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡄⠀⠀⠀⢸⡏⠉⠁⠀⢸⣿⣧⣄⡀⠀⣼⣿⡇⠀⠉⠛⢿⣷⣦⣀⠀⢉⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⣿⣤⣤⣤⣼⣧⣤⣀⣀⠘⣿⡿⠿⠿⠖⠣⠿⠀⠀⠀⠀⠈⠻⠟⣁⠉⠀⡀⢀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠻⣿⣿⠿⠛⠛⣿⣿⣿⣿⣿⢹⡏⠐⣿⡇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⣭⣽⣿⣭⣭⣍⡛⠻⢿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢹⣿⣿⣿⣿⠀⠀⠀⣿⡇⠈⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣿⣿⡷⣾⣿⣿⣿⣿⣿⡧⣿⣷⡇⢸⣿⣿⣿⣿⣿ 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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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⢻⣿⣿⡄⠀⠙⣿⣶⣶⣤⣄⣾⣿⣿⣿⣿⠗⠿⠏⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⡇⢸⡀⢧⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⡇⠀⠃⠉⠀⠀⠀⠀⣀⣀⣬⣤⣄⠀⠀⢠⣿⣿⣿⣿⣿ ⠙⢿⣟⠃⠀⠀⠈⢿⣿⣿⡿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠁⠸⠣⠸⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣟⠏⢇⣠⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣧⣀⣸⣿⣿⣿⣿⣿ ⠀⠀⠉⠀⠀⠀⠀⠀⠈⠀⠀⠹⠙⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣯⣥⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠉⠉⢻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⠟⠋⢉⣽⡿⠛⠁⠀⠀⠀⠀⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⠀⢠⠺⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢻⣿⡟⠀⠘⢿⣿⡟⢠⣌⠻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣷⣶⣄⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣄⠙⠁⠀⠀⣀⠙⠁⣾⣿⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿ ⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢭⡤⠏⣿⣿⣿⣷⠄⠀⠀⠉⠉⠙⠀⠈⠘⢿⣧⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠟⠛⠻⣿⡿⠃⠀⢸⣿⣿⣿⣿⣿⡿⠿⠛⠁⠰⠇⠀⠀⠈⠈⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣄⣠⣾⣿⣧⣀⠀⠚⠛⠛⠛⠛⠋⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄⠀⢸⣿⣿⣿⣿⣿⡶⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣶⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠛⣟⠛⠃⠀⠈⠻⠟⢿⣿⣿⣇⠀⠀⠀⠘⣍⣽⣿⣦⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⢸⣿⣿⣿ ⣦⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣛⠛⠋⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⣠⣾⣶⣾⣿⣶⠇⢀⡀⣠⣤⣴⠿⠿⣿⣿⡿⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⠿⠿⠿⡷⠀⠀⠀⢸⣿⣿⣿ ⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⣿⣿⣿⣭⡼⠀⠀⠀⠀⠀⠀⣶⣤⣴⣿⣾⣾⠛⢿⣿⡿⠀⠀⠀⢀⣠⣿⣿⡏⠈⠉⠀⢀⠀⠈⠉⠀⠀⠁⠀⠀⠉⠿⠁⠀⠀⠀⠘⢻⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⡀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣦⣤⣿⣤⣤⣴⣾⣿⣿⣿⣿⡇⠈⠀⣺⣾⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣤⡀⢀⣰⣔⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣧⡆⠀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣶⢾⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠈⠛⡛⠛⣿⣿⣿⣿⣧⡤⡀⣴⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠟⠘⣿⠋⠉⠁⠀⣀⣀⡀⠀⢸⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢿⡏⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣴⣂⣴⣿⣿⣿⣿⣷⣾⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡿⢻⣿⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣯⣿⣧⣯⣷⣤⣼⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⣿⡏⣸⣿⢣⣼⠀⠀⠀⠄⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡟⠻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠿⣿⣿⣿⣿⣿⣿⣧⡤⠼⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⠀⠀⣿⣿⠻⠃⠚⢿⣇⠀⠀⢀⠀⠀⠀⣀⣰⣿⣿⣿⣿⣿⣿⡆⠙⠛⢿⣆⠙⢿⣿⣿⣿⣿ ⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣭⣤⣤⣄⣀⣙⣟⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⢀⣨⠁⠀⣈⢿⣽⣿⣿⠁⠸⣿⣿⣟⣉⠁⠀⢿⣧⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠙⢷⠐⢹⣿⣿⣿ ⣿⣿⣿⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀⣾⣿⡿⠿⢋⣡⣶⣿⠟⣴⣿⣿⡏⠀⠀⢹⣿⡟⣿⣿⠀⢸⡇⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠿⠿⠿⠀⠀⠀⠀⠀⠀⡀⠻⣿⣿ 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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 3470 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/01/03/windows-share-in-2022/#comments Gemini version at gemini://gemini.techrights.org/2022/01/03/windows-share-in-2022/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.03.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ In_Picture:_Microsoft_Windows_Market_Share_in_a_Freefall_in_2022⠀✐ Posted in Microsoft, Windows at 12:43 pm by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Windows_share_in_2022⦈_ Summary: Vista 11 was released 3 months ago; the market share of Windows? Falling faster than before and even_Windows/Microsoft_fan_sites_are_throwing_in the_towel ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀ ⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀ ⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ䷩ 𝚕𝚒𝚗𝚎 3549 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.03.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Links_3/1/2022:_KDE’s_2022_Roadmap_and_Resignation_of_Solus_Lead_Developer⠀✐ Posted in News_Roundup at 8:04 am by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈ § Contents⠀➾ * GNU/Linux o Distributions o Devices/Embedded * Free_Software/Open_Source * Leftovers * § GNU/Linux⠀➾ o § Audiocasts/Shows⠀➾ # ⚓ Double_Server_Jeopardy_|_LINUX_Unplugged_439⠀⇛ Our new server setup is bonkers, but we love it. o § Kernel Space⠀➾ # ⚓ Intel_releases_patch_for_Alder_Lake’s_Thread_Director_Linux support_to_increase_performance_and_energy_efficiency⠀⇛ Website Phoronix reports that the current firmware in Linux uses an algorithm to plan which of the Performance or Efficiency cores utilized by the ITMT/Turbo Boost Max 3.0 driver are accessed at the time. In turn, due to the nature of Linux choosing to lean more towards higher performance, such as what is found in Golden Cove’s clock speed, while at the same time lessening the utilization of the energy-efficient Gracemont cores. Enter the Intel Hardware Feedback Interface—a table created by the HFI to help provide information for both the performance and energy efficiency of the computer’s processor. The HFI table, working together with the OS and the hardware, is constantly updated depending on any changes in the operating conditions or any actions from external factors at the time. An example of this process is the thermal limits reached by the operating system or changes made by the thermal design power. o § Instructionals/Technical⠀➾ # ⚓ How_to_Install_EndeavourOS_Step_by_Step_with_Screenshots⠀⇛ EndeavourOS is a terminal-centric Arch-based Linux distribution that provides a cool and elegant desktop environment and prides itself in having a vibrant community of opensource developers. Like all rolling releases, it’s an evolving distribution that aims at provides the best and the latest software packages. If you fancy an Arch-based distribution with a beginner-friendly User Interface, then EndeavourOS is the go-to Linux flavor. In this guide, we will journey through a step-by- step installation of EndeavourOS with screenshots. # ⚓ [Fixed]_Host_is_not_allowed_to_connect_to_this_MySQL server⠀⇛ Application developers may encounter difficulties connecting to a database hosted on a server other than the local server. In this article, we will resolve a common error that occurs when connecting to a MySQL database remotely from outside the network or from another host. # ⚓ How_to_Install_and_Manage_Podman_Containers_in_RHEL Systems⠀⇛ Most of us are familiar with Docker as a popular Container runtime for major Linux distributions. However, when it comes to the RHEL-based distributions such as CentOS, Rocky Linux, and AlmaLinux, Docker is not officially supported. This Linux system has instead found favor in a Podman-based Container management library called libpod. This library adapts to the same functional implementation as Kubernetes’ Container Pod concept. Therefore, it is the libpod project that provides the Podman tool making it viably easy to manage Containers, Container Images, and Pods. We can officially and uniquely define Podman as a library tool that does not need a Container daemon to manage Containers and Pods. The podman tool hosts created Containers and Pods as part of their child processes. # ⚓ How_to_Install_Maldet_(Linux_Malware_Detect)_on_Debian_11 Bullseye_–_LinuxCapable⠀⇛ Linux Malware Detect (LMD), also known as Maldet, is a malware scanner for Linux released under the GNU GPLv2 license. Maldet is quite popular amongst sysadmins and website devs due to its focus on the detection of PHP backdoors, dark mailers, and many other malicious files that can be uploaded on a compromised website using threat data from network edge intrusion detection systems to extract malware that is actively being used in attacks and generates signatures for detection. In the following tutorial, you will learn how to install and use Maldet on Debian 11 Bullseye Desktop or Server. # ⚓ How_to_Install_OpenJDK_17_on_Debian_11_Bullseye_– LinuxCapable⠀⇛ Java is a general-purpose, class-based, object- oriented multipurpose programming language that is popular due to the design of having lesser implementation dependencies, meaning that the compiled Java code can be run on all platforms that support Java without the need for recompilation. Java is also fast, secure, and reliable, therefore. It is widely used for developing Java applications in laptops, data centers, game consoles, scientific supercomputers, cell phones, etc. The tutorial will look at installing the OpenJDK version instead of the default Oracle JDK. The difference between these two is licensing. OpenJDK is an entirely free open-source Java with a GNU General Public License, and Oracle JDK requires a commercial license under the Oracle Binary Code License Agreement. Other differences are release schedules and other factors that come into play; however, performance is pretty much the same. In the following tutorial, you will learn how to install the latest OpenJDK 17 LTS on Debian 11 Bullseye. # ⚓ How_to_Deploy_Kubernetes_Cluster_on_Linux_With_k0s⠀⇛ K0s, pronounced kzeros, is a fully-fledged open- source Kubernetes distribution developed by team Lens – the Kubernetes IDE project. K0s is highly configurable and flexible to cover various Kubernetes uses like local and private data centers, IoT and public cloud clusters, and hybrid deployments. It is a simple, solid and certified Kubernetes distribution that can be deployed on any infrastructure. This means that K0s can run on any private or public cloud environment. k0s is distributed as a single binary with zero host OS dependencies besides the host OS kernel. It works with any operating system without additional software packages or configuration. Any security vulnerabilities or performance issues can be fixed directly in the k0s distribution. # ⚓ Modern_Linux_Tools:_Command-Line_Help_–_Invidious⠀⇛ A few of my favorite modern Unix tools: – TLDR: Show well-documented, useful examples of commands. – mcfly: better shell history reverse-search (ctrl- r). # ⚓ How_to_Burn_CD/DVD_in_Linux_Using_Brasero⠀⇛ Frankly speaking, I cannot recall the last time I used a PC with a CD/DVD drive. This is thanks to the ever-evolving tech industry which has seen optical disks replaced by USB drives and other smaller and compact storage media that offer more storage space such as SD cards. However, that doesn’t mean that CDs and DVDs are no longer used. A fairly small percentage of users still run old PCs which still support DVD / DC drives. Some of them still deem it fit to burn their files on CDs or DVDs for their own reasons. o § Desktop Environments/WMs⠀➾ # § K Desktop Environment/KDE SC/Qt⠀➾ # ⚓ KDE_Gets_A_2022_Roadmap_–_Plasma_Wayland_To_Shine, Updated_Breeze_Icons⠀⇛ # ⚓ KDE_roadmap_for_2022⠀⇛ Another year, another roadmap! Last year’s was a smashing success, as we delivered on everything. So here’s what I think we can expect in 2022. As always, this is not an official planning document or a promise; it’s just me giving you a sneak peak of some things that are in progress or about to start, and that I think will be feasible to complete before the year’s end! The Languages and Formats pages in System Settings have long been problematic because their scopes overlapped. Not for long! Han Young is working on merging them together into one new page that handles both, making it clear what applies when and making it harder or impossible to mess up your system by choosing incompatible settings. This is in progress and I expect it to be completed sometime in the first half of 2021. o § Distributions⠀➾ # ⚓ Solus_Lead_Dev_Resigns,_Joins_Serpent_OS_and_Plans_to_Fork Budgie_Under_a_New_Organization⠀⇛ The co-lead of Solus Project has decided to leave and move on to work on something else, unhappy with the current state of Solus and lack of acknowledgement for the issues raised. # § Debian Family⠀➾ # ⚓ A_custom_Debian_installer:_v-i⠀⇛ I’m doing a (custom) Debian installer (just a hobby, won’t be useful and reliable like the official one) for my Thinkpad X220 laptop. This has been brewing since August 2018, and is starting to get ready. I’d like no feedback on things people like/dislike in the official installer, as my installer resembles it not at all. I’ve currently installed Debian on my X220, with full disk encryption, and it seems to boot and allow me to log in via SSH. This implies that I’ll get something else to be stubborn about within a few months, and I’d like to let someone else make it work other people’s computers. Any volunteers are welcome, but I won’t promise I’ll have much energy to help. To be clear, my installer only works on my X220. Not your X220, and not on any other computer. But it’d probably be feasible to make it work on other PCs. o § Devices/Embedded⠀➾ # § Mobile Systems/Mobile Applications⠀➾ # ⚓ Android_12_One_UI_4.0_already_out_for_the_Galaxy_A52? Find_out_more!_–_SamMobile⠀⇛ # ⚓ A_developer_got_Android_12_booting_on_the_legendary Samsung_Galaxy_S_III⠀⇛ # ⚓ Realme_GT_Master_Edition_gets_Android_12_but_in_beta, should_you_install_it?_–_Technology_News⠀⇛ # ⚓ Latest_OnePlus_9/9_Pro_Android_12_update_fixes_5G connectivity_issues_–_PhoneArena⠀⇛ # ⚓ How_To_Set_Up_An_Android_Phone_For_An_Emergency Situation⠀⇛ # ⚓ Realme_achives_831%_growth_among_5G_Android smartphone_brands:_Counterpoint⠀⇛ # ⚓ Best_way_to_mark_SMS_text_messages_as_read_on_Android phone⠀⇛ o § Free, Libre, and Open Source Software⠀➾ # ⚓ Best_Free_and_Open_Source_Alternatives_to_Cisco_DNA Center⠀⇛ Cisco Systems, Inc. is an American multinational technology corporation that focuses on networking hardware and software. It has over 75,000 employees with its headquarters in San Jose, California. Cisco has been participating in open source development for almost 30 years including founding projects like OpenDaylight, FD.io, VPP, PNDA, SNAS, and OpenH264, and contributing to projects like OPNFV, Kubernetes, OpenStack, Ansible, Chef, Puppet, Maven, and many others. Cisco has also been a key contributor to the Linux kernel over the years, accounting for about 0.5% of total kernel commits, and is a Platinum Member of the Linux Foundation and Premium Sponsor of the Open Source Initiative. From a software perspective, Cisco’s main focus is developing proprietary programs. In this series we look at free and open source alternatives to their products. # ⚓ 2021’s_Top_Ten:_What_You_Read_on_FOSS_Force⠀⇛ 1. A German State Is Saying Goodbye Windows, Hello Linux: The state parliament of Schleswig-Holstein in Northern Germany has already produced plans to make the state government almost 100% open source by the end of 2026. * § Leftovers⠀➾ o § Health/Nutrition/Agriculture⠀➾ # ⚓ Industrialized_Farming_Has_Unleashed_an_Insect_Apocalypse⠀⇛ # ⚓ Doctors_Are_Urging_Medicare_to_Deny_Coverage_for Controversial_Alzheimer’s_Drug⠀⇛ # ⚓ Expect_an_‘Unprecedented_Number_of_Social_Disruptions’_Amid Omicron_Surge:_Health_Experts⠀⇛ As the ultra-transmissible Omicron variant causes Covid-19 cases in the United States and around the world to explode at an unprecedented rate, public health experts are warning that the first month of 2022 is likely to be defined by more suffering and widespread disruptions of daily life. “Omicron is truly everywhere,” Megan Ranney, a professor of emergency medicine at Brown University’s School of Public Health, told CNN on Friday night. “What I am so worried about over the next month or so is that our economy is going to shut down, not because of policies from the federal government or from the state governments, but rather because so many of us are ill.” # ⚓ [Old] Bigger_vehicles_are_directly_resulting_in_more_deaths of_people_walking⠀⇛ To put it simply, pickup trucks and SUVs are two to three times more likely than smaller personal vehicles to kill people walking in the event of a crash. Recent research from the University of Wisconsin-Milwaukee found the share of pedestrian deaths involving trucks, vans, and SUVs has increased from 22 to 44 percent since the mid- 1980s. More SUVs and trucks in the fleet = more pedestrian injuries becoming deaths instead. You don’t need a PhD to see why trucks and SUVs are more likely to kill people walking: They’re taller, have worse visibility, and are more likely to produce head/neck injuries than leg injuries. # ⚓ [Old] America’s_car_crash_epidemic⠀⇛ Oslo, incredibly, virtually eliminated traffic deaths in 2019 by aggressively reducing speeds, banning cars from the city center, and building out a robust bike path network. Very slow speeds and car-free zones are becoming the norm in many European cities. Americans might imagine that Europeans are somehow naturally predisposed to dense development that deprioritizes cars, but that isn’t exactly true. Car-centric development came to Europe in the mid- 20th century, just as it did to the US. The Netherlands’ car fatality rate was once higher than America’s; now it’s one-third of it. In the 1970s, a citizens movement called “Stop de Kindermoord,” or “Stop Murdering Children,” protested the country’s epidemic of death by cars. “They were just sick and tired of kids being killed in the streets,” says Jason Slaughter, a Canadian immigrant in Amsterdam who runs Not Just Bikes, an urban planning YouTube channel. Combined with the 1973 oil crisis, public outcry helped transform Dutch streets. o § Integrity/Availability⠀➾ # § Proprietary⠀➾ # ⚓ Tesla_recalls_475,000_vehicles_due_to_camera_and front_trunk_issues⠀⇛ Two voluntary recall reports were filed with the National Highway Traffic Safety Administration, with Tesla stores and service centers notified last week of the recalls. All Model 3 cars made between 2017 and 2020, a total of 356,309 vehicles, are being recalled due to a cable that, over time, may separate after wear and tear, blocking the rear-view camera feed. # ⚓ Tesla_recalls_nearly_half_a_million_Model_3_and_Model S_cars⠀⇛ According to documents submitted to the National Highway Traffic Safety Administration (NHTSA), there are 475,318 vehicles subject to the recall, comprising 356,309 Model 3 vehicles and 119,109 Model S vehicles. Tesla estimates that only 1 percent of the Model 3 vehicles will actually display the defect, compared to 14 percent of the recalled Model S vehicles. # ⚓ Tesla_recalls_nearly_500,000_cars_to_fix_safety defects⠀⇛ Both issues increase the chances of an accident. Tesla will inspect the recalled cars and make any needed repairs at no cost to owners. o § Defence/Aggression⠀➾ # ⚓ Opinion_|_Here’s_Why_the_UN_General_Assembly_Criticizes Israel_More_Than_All_Other_States_Combined⠀⇛ Again in 2021, the United Nations General Assembly overwhelmingly passed 14 resolutions aimed at criticizing Israel (and supporting the Palestinians). On every resolution, only a handful of countries (among them the USA, Canada, and a sprinkle of small Pacific island nations) stood with Israel. Some others abstained. # ⚓ Opinion_|_With_One_Exception,_Biden_Has_Barely_Altered Foreign_Policies_Inherited_From_Trump⠀⇛ The Biden administration’s foreign policy in its first year was mostly defined by an unwillingness to make major policy changes and to take significant political risks to follow through on the president’s campaign pledges. # ⚓ In_the_footsteps_of_the_women_who_escaped_a_Nazi_death march⠀⇛ When Gwen Strauss’ great-aunt revealed she had led a group of nine Resistance women in an escape from a Nazi death march in 1945, Gwen wanted to find out more. It set her on a path that would see her retrace the women’s steps and ensure the bravery of their work was recognised over 75 years later. o § Environment⠀➾ # ⚓ Opinion_|_The_Critique_of_Apocalyptic_Profit-Seeking_in “Don’t_Look_Up”_Hits_Close_to_Home⠀⇛ I’m often accused of being an “easy laugh” when it comes to political satire. I love political cartoons, movies, and TV shows, even those on the other side of the ideological spectrum if they’re funny and make me laugh at my own biases. # ⚓ 2022:_COP27,_Climate_Delay,_and_the_Future_of_the_North Sea⠀⇛ Another year has come and gone, and with it a crucial climate conference and the battle over a controversial new oilfield.  The year in British politics has ended in dramatic fashion, with a number of scandals coming hot on the heels of the UK-hosted COP26 summit, and another wave of Covid sweeping through the country. o § Finance⠀➾ # ⚓ “Localization”_Can_Help_Free_the_Planet_From_Neoliberal Globalization⠀⇛ # ⚓ Staten_Island_Amazon_Workers_Pause_Unionization_Battle,_But the_Fight_Isn’t_Over⠀⇛ # ⚓ Review:_Crashed_by_Adam_Tooze⠀⇛ The histories of the 2008 financial crisis that I have read focus almost exclusively on the United States. They also stop after the bank rescue and TARP or, if they press on into the aftermath, focus on the resulting damage to the US economy and the widespread pain of falling housing prices and foreclosure. Crashed does neither, instead arguing that 2008 was a crisis of European banks as much as American banks. It extends its history to cover the sovereign debt crisis in the eurozone, treating it as a continuation of the same crisis in a different guise. In the process, Tooze makes a compelling argument that one can draw a clear, if wandering, line from the moral revulsion at the propping up of the international banking system to Brexit and Trump. Qualifications first, since they are important for this type of comprehensive and, in places, surprising and counterintuitive history. Adam Tooze is Kathryn and Shelby Cullom Davis Professor of History at Columbia University and the director of its European Institute. His previous books have won multiple awards, and Crashed won the Lionel Gelber Prize for non-fiction on foreign policy. That it won a prize in that topic, rather than history or economics, is a hint at Tooze’s chosen lens. [...] The institution that saved the European banks was the United States Federal Reserve. This was an act of economic self-protection, not largesse; in the absence of dollar liquidity, the fire sale of dollar assets by European banks in a desperate attempt to cover their loans would have exacerbated the market crash. But it’s remarkable in its extent, and in how deeply this contradicts the later public political position that 2008 was an American recession caused by American banks. 52% of the mortgage-backed securities purchased by the Federal Reserve in its quantitative easing policies (popularly known as QE1, QE2, and QE3) were sold by foreign banks. Deutsche Bank and Credit Suisse unloaded more securities on the Fed than any American bank by a significant margin. And when that wasn’t enough, the Fed went farther and extended swap lines to major national banks, providing them dollar liquidity that they could then pass along to their local institutions. o § AstroTurf/Lobbying/Politics⠀➾ # ⚓ Twitter_Boots_Marjorie_Taylor_Greene_From_Platform_for COVID_Misinformation⠀⇛ # ⚓ Trump_Appointee_Resigns_as_FDIC_Chair_After_Failing_to Stymie_Policy_Review⠀⇛ # ⚓ Twitter_permanently_suspends_Marjorie_Taylor_Greene’s personal_account⠀⇛ Greene said, in a statement Sunday through her office, that she was suspended for tweeting statistics from the Vaccine Adverse Event Reporting System. # ⚓ Twitter_Permanently_Bans_Marjorie_Taylor_Greene’s_Personal Account_Over_Deadly_Covid_Disinformation⠀⇛ Twitter has banned for good the personal account of Rep. Marjorie Taylor Greene because the Georgia Republican—a longtime purveyor of anti-vaccine and other dangerous conspiracies—refused to stop spreading deadly disinformation about the coronavirus pandemic. “We permanently suspended Marjorie Taylor Greene for repeated violations of our Covid-19 misinformation policy,” Twitter said Sunday in a statement, as first reported by CNN’s Donie O’Sullivan. “We’ve been clear that, per our strike system for this policy, we will permanently suspend accounts for repeated violations of the policy.” o § Censorship/Free Speech⠀➾ # ⚓ A_Digital_Manhunt:_How_Chinese_Police_Track_Critics_on Twitter_and_Facebook⠀⇛ The contractor said he used the rankings to classify infractions on dossiers he submitted to his bosses in China’s security apparatus. In a sample document reviewed by The Times, he listed key details about each person he looked into, including personal and career information and professional and family connections to China, as well as a statistical analysis of the reach of the person’s account. His approach was corroborated by procurement documents and guides for online security workers. Over the past year, he said, he had been assigned to investigate a mix of Chinese undergraduates studying in the United States, a Chinese American policy analyst who is a U.S. citizen and journalists who previously worked in China. Those caught up in the dragnet are often baffled at how the authorities linked them to anonymous social media accounts on international platforms. o § Civil Rights/Policing⠀➾ # ⚓ Settler-Colonialism_in_a_Cross-Cultural_Perspective⠀⇛ This is in diametrically opposed and tragic contrast to the Native American tribes of New England the seeds of whose destruction were sown beginning with intermittent contact with murderous, disease-ridden, and slave-trading European explorers and elevated to a foregone conclusion with the arrival of the Mayflower in November 1620 and the Great Puritan Migration that followed. This ignominious history is not only academic but also intensely personal, as I am both a permanent resident of Vietnam and a direct and collateral descendant of settler-colonizers, both saints and strangers, who arrived in their New World in 1610 and 1620. If they hadn’t been there at that fleeting moment in history, I wouldn’t be here in this unique genetic form. That said, it is a painful reality that gives me pause. # ⚓ Fighting_For_You_From_Coast_to_Coast:_2021_In_Review⠀⇛ We helped win a huge victory in for all Californians this year, finally securing an historic $6 billion investment for broadband infrastructure for the state of California. Building on the work and community support we started building in 2020 for investment to close the digital divide, we were able to help bring those efforts across the finish line. EFF has vocally supported efforts to expand and improve broadband infrastructure to bring access to 21st-century broadband technology to every community. For years, internet service providers have carved up the state, neglecting low-income and rural communities. It’s become abundantly clear that the market alone will not close the digital divide; that’s why we need policy. The struggles many people had while learning and working remotely in the pandemic made it clearer than ever that California needed to change the status quo. California’s new broadband program approaches the problem on multiple fronts. It empowers local public entities, local private actors, and the state government itself to be the source of the solution. Through a combination of new construction, low-interest loans, and grants, this money will allow communities to have more input on where and how networks are built. # ⚓ How_Woody_Harrelson_(Unwittingly)_Helped_Nab_A_Shoplifter⠀⇛ The photo manipulation can include sitcom-sounding practices, like the copying and pasting of random stock images of eyes and lips onto people’s faces. Unsurprisingly, this may confuse the recognition algorithms, so the matches produced by these Frankenstein-ian aesthetic amalgamations may not always be 100% faithful. Also, we’re no fancy big- city law folk or anything, but this sounds legally iffy. o § Internet Policy/Net Neutrality⠀➾ # ⚓ Opinion_|_To_Curb_Facebook’s_Political_Power,_Take_Away_Its Section_230_Protection⠀⇛ I have been engaging on Twitter recently on my ideas on repealing Section 230. Not surprisingly, I provoked a considerable response. While much of it was angry ad hominems, some of it involved thoughtful comments, especially those from Jeff Koseff and Mike Masnick, the latter of whom took the time to write a full column responding to my proposals on repeal. o § Monopolies⠀➾ # ⚓ Antitrust_Law_and_the_Right_to_Settle:_The_Case_of_Pay-for- Delay_Settlements⠀⇛ In the spring of 2021, pay-for-delay settlements took over the legal scene on the both sides of the Atlantic. In March, following the line of reasoning it had elaborated in Generics, the Court of Justice of the European Union (CJEU) decided Lundbeck. It dismissed the appeals brought against the homonymous decision of the European Commission (EC), which had fined a number of patent settlements in which brand-name drug manufactures had paid generic drug producers to delay their entry in the market of citalopram-based antidepressant medications. A few weeks later, in the US, the Court of Appeals for the Fifth Circuit decided Impax. It affirmed the decision of the Federal Trade Commission (FTC), which, in its first post-Actavis patent settlement case, had fined a generic drug producer for having accepted payments to delay the entry in the market of an opioid named oxymorphone. Meanwhile, some House representatives introduced a new bill on pay-for-delay settlements which has not yet passed. At first glance, one might be tempted to place these settlements at the heart of the interface between antitrust and patent law. The aforementioned rulings – which, in the United States and the European Union are not anomalous but follow a recent case law – have instead used the case of pay-for-delay settlements to establish when antitrust law should limit firms’ right to settle. The paper discusses such a shift in perspective. # § Patents⠀➾ # ⚓ With_emergence_of_the_Omicron,_Canada_must_finally waive_COVID-19_vaccine_patents:_Singh [Ed: Patents are killing millions of people at the moment]⠀⇛ NDP leader Jagmeet Singh says the emergence of the Omicron variant means the Liberal government must finally back international calls to waive patents on COVID-19 vaccines. “With what we’re seeing in the Omicron variant, is that unless and until we do our part in tackling the global pandemic, meaning we help people around the world, we will not be able to beat this pandemic,” Singh told reporters on Parliament Hill Tuesday. [...] The WTO said in a press release Monday that “members expressed unanimous support for maintaining the momentum of the discussions on a common intellectual property (IP) response to COVID-19.” That includes the proposal by India and South Africa asking for a patent waiver. It said delegations are “committed to continue engaging in various configurations in the coming weeks to try and harvest any outcome that may still be possible.” Conservative leader Erin O’Toole said in the spring that he supports a temporary suspension to intellectual property rules, as dozens of MPs from all parties, including Liberals, signed an open letter calling on the government to support the waiver. “Opponents of the waiver proposal argue that patent monopolies are necessary to allow firms to recover their investments in research and development. However, given that COVID-19 vaccine development was primarily financed through public investment and advanced market commitments, we strongly believe this justification does not apply,” the letter said. Asked how much of a difference he believes Canada’s voice could make on this issue, given that it’s an international decision, Singh said “it’s a part of our fight. It’s a part of what Canada can do.” # ⚓ Research_on_Healthcare_Innovations_in_India:_Before, During_and_Beyond_COVID-19 [Ed: Just put aside patents and do actual research with life-saving, not money, as motivator]⠀⇛ The healthcare sector is one of the fastest- growing sectors globally as well as in India, with innovations being one of the key drivers of this growth, especially during this novel coronavirus disease (COVID-19) pandemic. Given its importance for the present and future, healthcare innovations have emerged as an important area of research and practice. The Indian innovation ecosystem is a vibrant space and India has emerged as the world’s third-largest startup economy. However, there has been no systematic collation and understanding of the literature on healthcare innovations in the Indian context. This study aims to fill this gap and help understand the existing scope and nature of research on healthcare innovations in India to identify research gaps for future studies. A scoping review of published peer-reviewed literature from the Scopus database was performed on healthcare innovations in India in the last 26 years (1996-2021). The selected studies were analysed using multidimensional criteria and an iterative inductive approach, followed by a narrative synthesis to present the findings using a multiparadigmatic framework. The review found that the concept of healthcare innovation was not uniform across these studies. Theory building studies and studies on the healthcare innovation ecosystem and policies have been limited. The studies identified changes in design, services, products, technology, organization, system interaction and conceptual elements as innovations. Healthcare innovations are important in public health, clinical practice, pharmaceuticals, medical devices and Indigenous System of Medicine (ISM), but are affected by the international and national policies affecting the ecosystem. The need for inclusive and convergent innovation as a driver for equity and increasing the translational rate of healthcare technologies also emerges from the analysis. The review identified research gaps and proposed key areas for future research across different domains of healthcare innovation. # ⚓ Patent_Enforcement_and_Subsequent_Innovation ][Ed: On mythology of litigation as key to innovation]⠀⇛ How does patent enforcement affect subsequent innovation? I exploit patent infringement litigation in the United States to analyze the effect of patent enforcement on cumulative innovation. The results imply that subsequent innovation increase after a case is filed in a court. While there is a strong increase during the litigation period, the relative effect size decreases in the years following the closure of the case. Further results imply that signals about the value of the patent and reductions in asymmetric information are particular driver of the increase in follow-on innovation. Although there is a general positive effect, subsequent innovation show a low degree of novelty and are close to the litigated patents in terms of technological proximity and general similarity. # ⚓ Court_says_Intel_can_contest_parts_of_Qualcomm_mobile patents [Ed: Why devices are so expensive (lots and lots of patent thickets including many on software)]⠀⇛ Intel Corp got a new chance to challenge two Qualcomm Inc smartphone patents on Tuesday, when a U.S. appeals court held that a U.S. Patent and Trademark Office tribunal had wrongly rejected Intel’s arguments that parts of the patents were invalid. The two rulings by the U.S. Court of Appeals for the Federal Circuit also said Qualcomm’s 2019 global settlement of a related patent dispute with Apple Inc over iPhones, iPads and other devices using Intel modem chips didn’t prevent the court from hearing Intel’s appeals. Qualcomm sued Apple for allegedly infringing several patents in 2017, and Intel challenged the validity of the two patents at issue at the Patent Trial and Appeal Board in 2018. One of the patents relates to receiving data transmissions, the other to data processing. The PTAB invalidated some parts of both patents in 2020, but found others valid. Intel appealed the board’s decisions on the surviving parts of the patents. # ⚓ Fighting_For_A_More_Open,_Balanced_Patent_System: 2021_in_Review⠀⇛ But there’s reason for hope. Patent trolls have finally been seen as the problem they are, and both courts and Congress seem to be moving away from simplistic misconceptions like believing they can create more innovation just by handing out more patents.  This year, EFF fought hard for increased transparency in the patent system that will allow us to call out the worst actors, and ultimately get a more balanced patent system. We also worked to defend and strengthen patent review systems that allow the worst patents to be kicked out of the system more efficiently.  Patent cases in particular suffer from a problem of overzealous secrecy. In 2019, EFF intervened in a court case called Uniloc v. Apple to defend the public’s right to know the details of what’s going on in patent cases. This case was an egregious one, in which a patent troll that had sued hundreds of companies was sealing up court records showing whether it even had the right to sue at all.  # ⚓ Apple_sued_for_$7.5M_over_alleged_LED,_mini_LED patent_infringement⠀⇛ Apple has become the target of another patent infringement lawsuit, this time by an LED producer claiming Apple infringes on patents relating to LED packaging and mini LED technology with its iPad Pro. Filed at the Intellectual Property and Commercial Court of Taiwan, the lawsuit by New Century Optoelectronics accuses Apple of infringing on a total of nine LED patents. The patents relate to both LED and Mini LED, largely in the context of packaging, referring to how chips and wires are encased and protected. # ⚓ What_to_watch_for_in_patent_law_in_2022 [Ed: Patent maximalists on patent law in media owned by billionaires who rely on state-enforced monopolies]⠀⇛ This year could bring big shifts in patent law, with a landmark U.S. Supreme Court case about patent eligibility, a new U.S. Patent and Trademark Office director, and significant changes to the PTO’s Patent Trial and Appeal Board all potentially in store. Will the Supreme Court or U.S. lawmakers take up patent eligibility? American Axle and Manufacturing Inc v. Neapco is the biggest chance in years for the Supreme Court to take up the contentious question of when an invention can be patented. The case, involving an invention related to quieting noisy driveshafts, produced an even split at the Federal Circuit, and all of its judges have asked the high court to weigh in. The confusion around patent eligibility could also inspire Congress to take action – a bipartisan group of U.S. senators said in a March letter that it was “past time that Congress act to address this issue.” # ⚓ Moderna_Drops_After_Losing_Appeal_Over_Drug-Delivery Patents [Ed: No sympathy for these monopolisers and grifters who storm the media, turning news into marketing with misinformation and hate speech]⠀⇛ Moderna Inc. shares plunged after the pharmaceutical company lost an appeal of a patent ruling involving a rival’s drug- delivery technology, which could make its Covid-19 vaccine vulnerable to infringement suits. A three-judge panel of the U.S. Court of Appeals for the Federal Circuit on Wednesday affirmed decisions by the Patent Trial and Appeal Board on two Arbutus Biopharma Corp. patents. The court said Moderna had no standing to appeal the ruling on one patent because it hadn’t developed its Covid vaccine until after it filed the appeal — the pandemic hadn’t yet begun. The panel also affirmed the board’s finding that Moderna hadn’t proven the second patent covers an obvious invention. # ⚓ Who_Invented_Covid-19_Vaccines?_Drugmakers_Battle Over_Patents [Ed: Nobody invented them, but some robber barons_monopolise_them_using_patents, acquired on the backs of taxpayers]⠀⇛ A high-stakes legal battle is taking shape over lucrative patent rights for Covid-19 vaccines, with drug companies pitted against each other and government and academic scientists over who invented what. # ⚓ Can_natural_disasters_affect_innovation?_Evidence from_Hurricane_Katrina⠀⇛ Studies of the geography of innovation have focused on how spatial proximity to human and material resources and institutions affect collaboration, knowledge flows, the demand and competition for invention, and the economic value of invention. I study a different source of the geographical determinants of innovation: exposure to large shocks. I conduct an inductive assessment, theoretically grounded on recent evidence that large exogenous shocks produce enduring fluctuations in risk aversion, to explain why Hurricane Katrina in the U.S. could have changed innovation outcomes. The difference- in-difference estimates show that, after an immediate fall, affected counties exhibit substantial increases in the growth rate of patenting and the quality of innovation compared to counterfactual counties. This correlation persists 10 years after the shock and is robust to measures of agglomeration and urbanization, firm resources, wealth, actual and expected income, education, external assistance, public policy, business cycles, and other county- and state-level factors. To account for the confounds of selective migration and network affiliation, I use narrowly georeferenced information to construct histories of inventors between 1999 and 2015 that allow me to follow the “Katrina effect” across geographies. The estimates imply that shock-affected individuals not only were more likely to patent, but became more skewed toward high-technology sectors. # ⚓ U.S._government_must_face_patent_case_over_armored vehicles [Ed: Even the military builds up patent monopolies that taxpayers needs to pay for, in spite of the taxpayers subsiding these companies]⠀⇛ The U.S. government and defense contractors Oshkosh Corp and General Dynamics shouldn’t have been allowed to escape claims that they infringed another contractor’s patents for an armored vehicle, a U.S. appeals court said Friday. A unanimous panel of the U.S. Court of Appeals for the Federal Circuit revived Ideal Innovations Inc’s case at a lower court, finding factual questions about its research agreement with the U.S. Army justified a trial. The U.S. Department of Justice, Oshkosh, and General Dynamics declined to comment. Ideal Innovations and its attorney Ahmed Davis of Fish & Richardson didn’t immediately respond to a request for comment. # ⚓ USPTO_announces_PPH_pilot_program_with_the_National Institute_of_Industrial_Property_of_France [Ed: USPTO liaising with deeply_corrupt_INPI to promote litigation agenda at the expense of science]⠀⇛ USPTO announces PPH pilot program with the National Institute of Industrial Property of France The United States Patent and Trademark Office (USPTO) will commence a Patent Prosecution Highway (PPH) pilot program with the National Institute of Industrial Property of France (INPI) on December 1, 2021. Under the pilot, a PPH request may be submitted to the USPTO based on a patent application that was filed in the INPI on or after May 22, 2020. # ⚓ Biden’s_PTO_pick_calls_for_clarity_on_patent- eligibility_controversy [Ed: Biden is propping_up_a Microsofter_who_is_promoting_software_patents]⠀⇛ Winston & Strawn partner Kathi Vidal said in a Wednesday hearing before the Senate Judiciary Committee that she would focus on “strengthening the value of IP” if confirmed to head the U.S. Patent and Trademark Office, and addressed questions about divisive issues such as patent eligibility and PTO patent- challenge procedures from senators on both sides of the aisle. “We can work together to build an intellectual property system that is more predictable, reliable and transparent,” Vidal said. Patent attorneys have said Vidal, who leads Winston & Strawn’s Silicon Valley office, is “eminently qualified” and a “safe pick” for the role. She has extensive experience as a patent litigator, and has represented companies including Microsoft Corp, Tesla Inc, Intel Corp, Dell Corp and Spotify Technologies SA. # ⚓ [Older]_India_to_push_for_patent_waiver_for_COVID-19 vaccines_at_WTO [Ed: Everybody should speak about these mad and unjust patents on vaccines; the patent monopolies kill far more people than so-called 'unvaccinated' people do]⠀⇛ India will lead demands for an intellectual property rights waiver for COVID-19 vaccines and supplies at a World Trade Organization (WTO) meeting next week, two government officials said. A year after India and South Africa introduced a proposal https:// www.reuters.com/article/us-health- coronavirus-wto/india-and-south-africa-ask- wto-to-waive-rules-to-aid-covid-19-drug- production-idUSKBN26P0H1 to temporarily waive intellectual property rights on COVID-19 vaccines and therapies at the WTO, negotiations are deadlocked in the face of opposition from some developed countries. # ⚓ After_winning_$1_bln_in_Apple_case,_Caltech_sues Samsung_over_same_patents⠀⇛ The California Institute of Technology has made Samsung its latest target for allegedly infringing its Wi-Fi patents following its $1.1 billion win against Apple and Broadcom last year, according to a complaint filed in East Texas federal court Friday. Caltech said in the new lawsuit that Samsung’s Galaxy phones, tablets, and watches use Wi-Fi chips that infringe five of its data-transmission patents, in addition to other Wi-Fi-enabled Samsung products including televisions and refrigerators. Samsung didn’t immediately respond to a request for comment, nor did Caltech or its attorney Daniel Shih of Susman Godfrey. # ⚓ Apple_quietly_filed_2_patents,_and_it_may_hint_that the_giant_has_a_drone_in_the_works⠀⇛ A patent application published last month suggests Apple may be working to develop a drone. The giant had previously filed two other patent applications, indicating some effort had been made to keep the project quiet. 9to5Mac explained that there are two ways a company can try and conceal patent applications. It can delay the date that a patent application is made public, and it can submit the application in another country. It appears that Apple did both these things. # ⚓ NTRB_Stock_Alert:_The_Patent_News_Sending_Nutriband Soaring⠀⇛ Nutriband (NASDAQ:NTRB) stock is soaring 170% in mid-morning trading after the company announced today that it was granted a patent for “abuse deterrent” technology, called Aversa. The patent was granted by South Korea’s Korean Intellectual Property Office, or KIPO. # § Trademarks⠀➾ # ⚓ Trademark_application_filed_in_bad_faith_–_Commentary –_Lexology⠀⇛ This article discusses a controversy that emerged between the members of a company regarding a sign that was used by the company. One member of the company filed a trademark application covering the sign with the Hungarian Intellectual Property Office (HIPO), which registered the mark in that member’s favour. The company requested a review of the HIPO’s decision, alleging that the member had filed the application in bad faith. # ⚓ Virtual_battles ⠀⇛ The reality around us is moving more and more to the virtual world. # ⚓ Trademark_procedures_and_strategies:_Germany [Ed: "worldtrademarkreview" is nowadays composed by litigation firms like Team UPC/COHAUSZ & FLORACK (basically chronic liars) instead of actual journalists ]⠀⇛ The following are enforceable in Germany: German trademarks, EU trademarks, German trademarks based on international registrations, names and non-registered trade designations. German trademarks are governed by the Trademark Act, which implements the EU Trademark Directive (89/104/EEC) and the Regulation on Trademark-Related Administrative Proceedings. # ⚓ 2021_Wrap_up_–_EUTMs_in_Luxembourg⠀⇛ 2021 has yet again been a busy year for the General Court when it comes to decisions dealing with EU trademarks. It would also have been busy for the Court of Justice; however, alas, also in 2021 the CJEU has not allowed a single appeal in EUTM matters to proceed, rejecting 47 appeals as not being “significant with respect to the unity, consistency or development of EU law”, including in the MONOPOLY case (order of 1 December 2021, C-373/21 P). This is a shame as this practice deprives the IP community of necessary guidance on essential questions of EU IP laws. After all, the case law of the GC is far from consistent. There is, however, a shimmer of hope: in Community design law, the CJEU has only just allowed the first appeal to proceed (10 December 2021, C-382/21-P). This is the appeal brought by the EUIPO in The KaiKai Company, where the GC had stated that priority for a Community design could be claimed from an earlier patent, and that the priority period depended on the nature of the right from which priority was claimed, allowing therefore 12 months for the priority claim rather than 6 months. That decision contains so many fundamental(ly wrong) statements that it is a relief that the EUIPO’s appeal has finally taken the hurdle of admission. More on this case in 2022! Back to EU trademarks. Of the reported General Court decisions from 2021 – and this analysis is based solely on the cases reported on eSearch Case Law, the EUIPO’s case law database – 130 concerned relative grounds, half that number absolute grounds. 15 cases dealt with procedural issues, and 17 each focused on issues of genuine use of trade marks or bad faith. Quite a number of cases were closed without judgment. # ⚓ Champagne,_lipstick,_energy_drinks:_the_five_most- read_Legal_Updates_of_the_year⠀⇛ # ⚓ Around_the_IP_Blogs⠀⇛ Lise Charles (WTR) provides an overview of the most-read posts on Word Trademark Review (WTR) on European trade mark case law over the past year, including analyses of cases dealing with issues such as unconventional signs (i.e., colour marks and 3D marks) (MHCS v EUIPO | Case T-274/20 and Guerlain v EUIPO | Case T-488/20), the risks of using a mark in a manner other than that registered (Fashioneast Sàrl v EUIPO | Case T-297/20) and taking unfair advantage of the reputation of a well-known mark (Asolo Ltd. v EUIPO | Case T-509/19) and the importance of presenting valid arguments for the existence of a link between the marks – even in the case of marks with an exceptional reputation (Puma v EUIPO | Case T-71/20). # ⚓ The_Future_of_Trademark_Exhaustion_is_Still_Unclear for_Brands_Post-Brexit⠀⇛ The United Kingdom’s withdrawal from the European Union has brought with it an array of legal and procedural developments – and still-impending changes – that stand to have a significant impact on the workings of fashion brands and luxury goods groups. Among the critical legal tenets whose new post- Brexit reality is still being decided by lawmakers in the UK is the issue of trademark exhaustion – or in other words, the limitation of a trademark holder’s ability to exercise control over a trademark-bearing product once it releases – or authorizes the release of – that product into the market. Hardly an uncommon issue, trademark exhaustion (better known as the First Sale Doctrine in the U.S.) has been argued in an array of fashion and luxury-centric cases, particularly in light of the relatively recent rise of the $30 billion-plus secondary market. Earlier this year, for instance, reseller Crepslocker pushed back in the since-settled trademark case that Chanel filed against it, arguing that Chanel lacked “any proper basis” for its objections to Crepslocker’s sale of authentic Chanel goods and use of the Chanel trademarks, as its “rights in the goods have been exhausted by the consented sale from its authorized outlets in the UK or the EU.” The issue was also raised in an interesting case over Ferrari’s Testarossa trademark, and a number of cases centering on the distribution of high-end cosmetics and fragrances in the EU. (In the U.S., the First Sale doctrine has been recently raised as a defense to trademark cases waged by Chanel, Nike, and iPhone accessories maker OtterBox, among others.) # ⚓ DOUBLE_STANDARD_ON_REPUTATION._CAN_ANYONE_GUESS_WHY? –_Kluwer_Trademark_Blog⠀⇛ With Messi (see cases C-449/18P and C-474/18P MESSI) and Miley Cyrus (case T‑368/20 MILEY CYRUS), we learnt that reputation or renown of (personal) names is a factor which should be taken in consideration when comparing marks and which may ultimately exclude confusion with an earlier similar mark. However, two recent cases seem to indicate that a different standard applies for (corporate) names. Why is anyone’s guess. The first case T-353/20, decided on 10 November 2021, concerns Associazione Calcio Milan Spa (AC MILAN), one of the most famous football clubs in Europe and perhaps in the world, which filed an EUTM application for the following figurative mark in Class 16. [...] Inditex argued that consumers would associate ZARA with the name of the famous retailer specialized in fast fashion, and that therefore, the conceptual difference with the earlier marks counteracted the visual and phonetic similarities. However, also in this case, the GC stated that the reputation of the contested mark was irrelevant, and that reputation was relevant only in respect of the earlier mark (§ 145). There is little doubt that the AC MILAN name and team probably rivals Lionel Messi in renown in the area of football. Also ZARA’s renown in the fashion world likely outclasses the (arguable) renown of Miley Cyrus. The double standard therefore appears inexplicable as the only difference between MESSI and MILEY CYRUS on the one hand and AC MILAN and ZARA on the other is not the degree of fame, but rather that the latter two are not celebrities’ (personal) names. However, the reasons why the reputation of the contested mark should be relevant in case of celebrities, but not in case of companies’ names (be they a soccer team or a store chain) are unfathomable. # ⚓ Around_the_IP_Blogs⠀⇛ The Kluwer Trademark Blog posted an article questioning the understanding of reputation for trade marks based on the standards of reputation or renown of personal names and reputation of corporate names. # § Copyrights⠀➾ # ⚓ Practice_points_on_licence_agreements_|_IP_Draughts⠀⇛ wordle licenceOver the last few days, IP solicitor @Ellen_Lambrix has been writing an interesting set of articles on IP licensing, on LinkedIn. This has prompted IP Draughts to try to catalogue some of the articles on this blog on licensing over the last decade. Here’s a very quick and dirty set of links. IP Draughts has probably missed a fair few articles of relevance. Try doing word searches in the search box of this blog – near the bottom of the right hand column. # ⚓ The_interface_between_NFTs_and_the_public_domain⠀⇛ 2021 has been the year of the NFT here at Llama Towers. It seems like there’s no shortage of stories coming out of the NFT scene, so to avoid having to rename the blog to “NFT Weekly News” I haven’t been reacting to the latest occurrence with the same enthusiasm as earlier in the year. But there are a few developments that fall squarely in Yours Truly’s expertise and research interests, and require further analysis. The latest debate to catch my eye has been the growing discussion of what exactly is an NFT for from a copyright perspective, and whether they are actually being used to free up works. A very good example of the interface between NFTs and public domain was done by photographer Cath Simard. In 2017 she took the photo shown above of a road in Hawaii and she posted it on her Instagram account. The picture was an instant hit, and started getting shared all over the internet, often without any attribution. After years of having her picture infringed online, Simard decided to try something different, she created a website called #FreeHawaiiPhoto where she offered the picture as an NFT with a reserve price of Ξ100 ETH. If someone bought the picture at a minimum of the reserved price, Simard promised to make the picture available to download for free for everyone in the world. The price was met and the NFT purchased by a collector, making this the first public domain image powered by an NFT… until you look at the small print. # ⚓ EU_copyright_law_round_up_–_fourth_trimester_of_2021 [Ed: Copyrights in Europe do not serve the public, the system is "captured" by special interests, including foreign ones that control the likes of FSFE]⠀⇛ Welcome to the fourth and final trimester of 2021 round up of EU copyright law! We started this rubric in the beginning of 2021. In this series, we update readers every three months on developments in EU copyright law. This includes Court of Justice (CJEU) and General Court judgments, Advocate Generals’ (AG) opinions, and important policy developments. You can read the first, second and third trimester round ups here, here and here. The end of 2021 has been particularly busy. This becomes quite evident when one looks at the number of institutional policy reports that have been issued in the past three months. # ⚓ The_5_Worst_Copyright_Decisions_of_2021_–_Copyright Lately⠀⇛ Remembering another frustrating year with a countdown of 2021’s most unsatisfying copyright rulings. I don’t know about you, but my 2021 actually made 2020 look pretty, prettay, prettaay good by comparison. This was the year we actually had to try to pretend everything was back to normal when, frankly, it was anything but. So, forget all the “best of” lists that I’m sure are clogging up your feeds right now. Here are my personal picks for the copyright opinions from 2021 that, much like the year itself, leave a little something to be desired. [...] In a July 2021 order in Nicklen v. Sinclair Broadcast Group, Inc., Southern District of New York Judge Jed Rakoff denied a motion to dismiss filed by Sinclair in a dispute over Paul Nicklen’s video of a starving polar bear. Relying on the server test, Sinclair unsuccessfully argued that it and its affiliates didn’t infringe the copyright in Nicklen’s video because they only embedded it on their websites from Instagram or Facebook, as opposed to maintaining a copy of the video on a Sinclair-controlled server. Judge Rakoff held that the fact that Sinclair didn’t actually possess a copy of Nicklen’s video didn’t mean that Sinclair wasn’t responsible for displaying it. With the decision, Rakoff became the second SDNY judge to reject the server test, joining a view shared by then-judge Katherine Forrest in 2018’s Goldman v. Breitbart News Network. Battle lines have been firmly drawn between the Ninth Circuit, which has explicitly adopted the server test, and a growing number of district court judges within the Second Circuit (although the appellate court itself hasn’t yet weighed in). Regardless of what you may think about the server test generally, the court’s opinion in Nicklen doesn’t sufficiently focus on or evaluate what’s actually going on behind the scenes when a website uses embed code to instruct a visitor’s web browser to fetch the contents of a post directly from Instagram’s own servers. The court also gave short shrift to arguments about what would happen if the server test were abolished, merely noting that the “speculations” offered by Sinclair “seem farfetched.” Finally, the court failed to fully recognize a key distinction between Goldman, which involved a photograph that appeared the moment the defendant’s website was loaded, and the video at issue in Nicklen, which required a viewer to take the volitional act of affirmatively clicking on the video within the embedded social media post in order to play it. # ⚓ MetaBirkins_Creator_Says_He_Received_a_Cease_&_Desist from_Hermès,_Claims_Fair_Use⠀⇛ Hermès appears to have made good on its claims about non-fungible tokens (“NFTs”) that were marketed as MetaBirkins without its authorization. Creator Mason Rothschild revealed in an open letter to Hermès that he posted on his Instagram account on December 22 that he received a cease-and-desist letter from the French luxury goods brand. In a separate open letter to OpenSea, Rothschild confirmed that the MetaBirkins have been removed from the NFT platform, potentially as a result of trademark-centric takedown requests lodged by Hermès, which said in a statement earlier this month that it views the one hundred MetaBirkins NFTs as “infring [ing] upon [its] trademark rights, and an example of fake Hermès products in the metaverse.” In his letter to Hermès, Rothschild argues that the MetaBirkins NFTs are shielded from Hermès’ trademark claims, asserting that “the First Amendment gives me every right to create art based on my interpretations of the world around me.” Additionally, he claims that the MetaBirkins – which currently boast a trade volume of $1.1 million, according to the MetaBirkins Rarible page – are “also a commentary on fashion’s history of animal cruelty, and its current embrace of fur-free initiatives and alternative textiles.” # ⚓ Volvo_Settles_Copyright_Lawsuit_After_Reposting Photos_for_Instagram_Ad_Campaign [Ed: Robber barons do not respect copyright law, either; they rely on selective enforcement and misuse of words like "pirate"]⠀⇛ Volvo has settled a copyright-centric lawsuit after being sued in a California federal court last year for using another party’s photos for an alleged Instagram ad campaign. Photographer Jack Schroeder and model Britni Sumida accused the Swedish automaker of copyright infringement for using photos that Schroeder had taken of Sumida posing alongside a Volvo S60 as part of “a global advertising campaign” on Instagram without their authorization. After unsuccessfully attempting to get Volvo to cease its use of the images, Schroeder and Sumida filed suit in June 2020, setting out claims of copyright infringement, unfair competition, and misappropriation of likeness, with the latter resulting from Volvo’s unauthorized use of images featuring Sumida. In response to the lawsuit, Volvo filed an unsuccessful motion to dismiss in August, arguing that Schroeder and Sumida are actually the ones who were in the wrong due to their use of the Volvo “brand, image, reputation and substantial social media reach of a venerable automotive company to promote themselves professionally.” Volvo asserted that the plaintiffs’ claims that it “impermissibly shared [the] photographs and misappropriated Sumida’s image rights as part of an unauthorized ‘global advertising campaign’ are false and disingenuous,” as there was “no such advertising campaign.” Instead, Volvo claimed that it “simply used basic social media sharing/publishing platform features to re-post” Schroeder’s images of its S60 sedan “after Schroeder and others had already published (and tagged Volvo in) the photos on their own public social media accounts.” The crux of Volvo’s argument was that by posting the photos on Instagram in the first place, Schroeder granted it an implied license to re-post the photos in accordance with Instagram’s licensing terms. [...] This case may be on the brink of coming to a close, but it, nonetheless, raises one of a number of questions that have come hand-in- hand with allegedly unauthorized use of imagery first posted on Instagram and other social media platforms. The overarching issue centers on Instagram’s terms and whether they provide users with a license that could shield them from copyright infringement liability should they use images first shared on its platform without the copyright holder’s consent. This has seen brands like Volvo come under fire for resharing copyright-protected imagery to their own accounts, but maybe more commonly, cases have come about in connection with publications’ practice of embedding imagery into online articles using social media sharing tools without the copyright holders’ authorization, prompting claims of copyright infringement. In terms of embedded imagery, this issue has been at the center of an array of cases in furtherance of what Frankfurt Kurnit Klein & Selz PC’s Craig Whitney recently called “one of the most hotly litigated issues in copyright law over the past two-plus years.” In one noteworthy case, Nicklen v. Sinclair Broadcast Group, Inc., a New York federal district court found that the unauthorized re-posting of copyright protected content online could run afoul of copyright law by infringing the copyright holder’s exclusive right to display the work regardless of whether a copy was created and stored on the alleged infringer’s own server – or whether the image was re-posted by using Instagram’s API. # ⚓ The_European_Audiovisual_Observatory_publishes_the Mapping_report_on_national_remedies_against_online piracy_of_sports_content [Ed: European Audiovisual Observatory is uses propaganda term "piracy", which reveals whose pockets it is in; when your drug regulator is controlled by Big Pharma and the copyright cartels do 'studies' in Federal clothing you become disillusioned about this whole concept of regulation]⠀⇛ The European Audiovisual Observatory (“EAO”) has recently published the Mapping report on national remedies against online piracy of sports content (“Report”), conducted at the request of the European Commission. Through a comparative perspective, the Report examines the scope of protection of audiovisual sports content in the national framework of the 27 EU member states and the UK. In particular, the Report relies on an extensive review of the EU law, Court of Justice of the European Union (“CJEU”) decisions and case law concerning remedies against online piracy, starting from the results of a questionnaire submitted to international experts from relevant institutions, universities and law firms. [...] Regarding the entitlement to the rights, the recording and broadcast of a sports event are protected by related rights, which are respectively granted to producers of audiovisual works for the first fixation of the film and to broadcasting organisations for the transmission of broadcast signals for public reception. On the other hand, in some countries, domiciliary rights (also called “house rights”) are held by the sports event organisers. With regard to the entitlement to take action, the differences between countries show that in some the sports clubs can take legal action on the basis of the domiciliary rights in the case of unauthorised recordings made within the premises of the venue or the place of the event; in others, federations and leagues can act on the same basis in the case of illegal broadcasting or streaming of the event. # ⚓ YouTube’s_Innovative_Content_ID_is_No_Substitute_For Humankind’s_Greatest_Gift⠀⇛ YouTube has made massive strides towards solving millions of copyright claims that plague its platform. The automated Content ID system is by no means perfect but does provide a way for rightsholders and alleged infringers to amicably settle their differences. What it doesn’t have is the human ability to spot opportunities for cooperation and innovation. Sadly, humans can struggle with that too. ䷩ 𝚕𝚒𝚗𝚎 5564 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.03.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Links_3/1/2022:_New_Rescuzilla_and_MDADM_4.2⠀✐ Posted in News_Roundup at 12:27 pm by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈ § Contents⠀➾ * GNU/Linux o Distributions o Devices/Embedded * Free_Software/Open_Source * Leftovers * § GNU/Linux⠀➾ o § Desktop/Laptop⠀➾ # ⚓ 9_Reasons_Why_Techies_Are_in_Love_With_Linux⠀⇛ You might not be a Linux user but have a nerdy friend who won’t shut up about it. Why would they get so excited about an operating system? Read on to find out why so many technical people are so in love with Linux. o § Server⠀➾ # ⚓ Best_Linux_Distros_for_Servers_–_Linux_Stans⠀⇛ You can use pretty much any Linux distro as a server, however, some distros are specialized and configured in a way that makes them a lot better and easier to work on out of the box when it comes to servers. So, technically, all Linux distros are for servers, and you can use any distro for your server. o § Audiocasts/Shows⠀➾ # ⚓ OBS_Studio_27.2_enters_Beta_with_official_Flatpak_support_| GamingOnLinux⠀⇛ Ready for 2022, the OBS team is preparing a major new release of the free and open source livestreaming and recording software OBS Studio. OBS Studio 27.2 has two Beta versions out bringing in some major new features. For Linux users, it’s a big one too as it brings along our previously reported plans for official Flatpak support. This means users of any Linux distribution will be able to grab the officially supported package with all the bells and whistles. o § Kernel Space⠀➾ # ⚓ A_set_of_patches_has_been_published_that_speed_up_the assembly_of_the_Linux_kernel_by_50-80%⠀⇛ Ingo Molnar ( by Ingo Molnar is ), a well-known Linux kernel developer and author of CFS Task Scheduler (Completely Fair Scheduler), proposed for discussion of Linux kernel development mailing list a series of patches, affecting more than half of all the files in the kernel source and provides an increase in the total rebuilding core speed 50-80% depending on the settings. The implemented optimization is remarkable in that it is associated with the addition of the largest set of changes in the history of kernel development – 2297 patches were proposed for inclusion at once, changing more than 25 thousand files (10 thousand header files in the directories “include /” and “arch / * / include / “and 15 thousand source files). The performance gain is achieved by changing the method of handling header files. It is noted that over thirty years of kernel development, the state of header files has taken on a depressing form due to the presence of a large number of cross- dependencies between files. The restructuring of the header files took over a year and required a significant redesign of the hierarchy and dependencies. During the restructuring, work was done to separate the type definitions and APIs for different kernel subsystems. Among the changes made are: separation of high- level header files from each other, exclusion of inline functions that bind header files, allocation of header files for types and APIs, provision of a separate assembly of header files (about 80 files had indirect dependencies that interfere with assembly, exposed through other header files), automatic addition of dependencies to “.h” and “.c” files, step-by-step optimization of header files, use of the “CONFIG_KALLSYMS_FAST = y” mode, selective consolidation of C files into assembly blocks to reduce the number of object files. # ⚓ MDADM_4.2_Released_For_Managing_Linux_Software_RAID_– Phoronix⠀⇛ The mdadm utility for managing Linux software RAID arrays is out with a new release — its first in more than three years. MDADM 4.1 was released long before the pandemic even got started… All the way back in October 2018. As such with MDADM 4.2 now available, it’s a rather big update. Meta’s Jes Sorensen released MDADM 4.2 just before the new year. Jes summed up v4.2 as, “The release includes more than two years of development and bugfixes, so it is difficult to remember everything. Highlights include enhancements and bug fixes including for IMSM RAID, Partial Parity Log, clustered RAID support, improved testing, and gcc-9 support.” # ⚓ New_Linux_Patch_Series_Proposes_Gating_“Legacy_PCI”_Support –_Phoronix⠀⇛ A patch series sent out by IBM would introduce a new “LEGACY_PCI” Kconfig option for gating legacy PCI device support, including PCI devices attached to PCI-to-PCIe bridges and PCIe devices using legacy I/O spaces. Sent out over the holidays were a set of 32 patches proposing new LEGACY_PCI and HAS_IOPORT options for the Linux kernel. The justification for the patch series is IBM’s s390 architecture not supporting legacy PCI devices nor PCI I/O spaces. The interesting aspect for non-s390 Linux users is on the LEGACY_PCI toggle to which it has already been successfully tested on x86_64 hardware and AArch64 (ARM64) too. o § Applications⠀➾ # ⚓ Pinta_2.0_Graphics_and_Photo_Editor_Released_–_itsfoss.net [Ed: Mono makes this problematic]⠀⇛ The release of the open raster graphics editor Pinta 2.0 has been published , which is an attempt to rewrite the Paint.NET program using GTK. The editor provides a basic set of drawing and image processing capabilities, targeting novice users. The interface is simplified as much as possible, the editor supports an unlimited rollback buffer, allows you to work with multiple layers, is equipped with a set of tools for applying various effects and adjusting images. The Pinta code is licensed under the MIT license. The project is written in C # using Mono and the Gtk # binding. Binary assemblies prepared for Linux ( Flatpak , Snap), macOS and Windows. o § Instructionals/Technical⠀➾ # ⚓ Complete_guide_on_Inode_number_in_Linux_with_an_examples_– TREND_OCEANS⠀⇛ I’m going to ask you a question. What do you see when you pass the ls -l command? A list of files with a bunch of details like permission, number of files, file owner, group owner, size, date & time along with a file name, and more number of data can be accessed using different parameters, but have you ever imagined where all data get stored, and what we call for this data type? This type of data is called meta-data, which is useful to store all information of files except file name and data of a file. And meta-data is a part of Inode. Now, what is an inode? # ⚓ 13_examples_of_how_DevOps_facilitated_transformation_in 2021_|_Opensource.com⠀⇛ Tools of the trade continue to rank as a top read for Opensource.com readers. Nimisha Mukherjee, an engineering manager with Red Hat, wrote 13 open source tools for developers. She breaks tools down by Inner loop, the most common tasks developers do, and Outer loop, where the developers’ code goes through continuous integration and delivery (CI/CD) for deployment to production. Implementing a DevOps toolchain also ranked high on our reader’s interests. A first-time contributor, Tereza Denkova, Marketing Associate at Accedia, an IT professional services company, wrote How to implement a DevOps toolchain and eloquently tied it to innovation. # ⚓ 10_tutorials_to_sharpen_your_command-line_skills_|_Enable Sysadmin⠀⇛ The command-line interface (also known as the CLI) might be the most powerful yet intimidating aspect of Linux. It gives you unparalleled power and complete access to what the operating system can do for you. Linux inherited the Unix design and its ability to compose more complex commands from simple tools. # ⚓ How_To_Install_HTTP_Git_Server_on_Ubuntu_20.04_LTS_– idroot⠀⇛ In this tutorial, we will show you how to install HTTP Git Server on Ubuntu 20.04 LTS. For those of you who didn’t know, HTTP Git Server is an open- source project that uses an Nginx webserver to serve Git repositories over your Local Area Network (LAN). HTTP Git Server is surprisingly easy to set up and manage. 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 HTTP Git Server on Ubuntu 20.04 (Focal Fossa). You can follow the same instructions for Ubuntu 18.04, 16.04, and any other Debian-based distribution like Linux Mint. # ⚓ How_to_Install_Odoo_15_on_Ubuntu_20.04_with_Nginx_–_AWS⠀⇛ Install Odoo 15 on Ubuntu 20.04 with Nginx – AWS. In this tutorial you are going to learn how to install and setup Odoo with Nginx reverse proxy and connect it with PostgreSQL in Amazon RDS. Odoo is a management self hosted software to run a business with a top notch user experience. The applications within Odoo are perfectly integrated with each other, allowing you to fully automate your business processes easily. # ⚓ New_Year’s_resolutions_for_Linux_sysadmins_in_2022_| Network_World⠀⇛ Even after using Linux for more than 30 years, I often find myself discovering some command that I didn’t know about or didn’t realize how much I could do with it. 2021 was the first year that I used the cheat command or used the –help option for commands more often that I read their man pages. I also started using the bpytop command fairly often. And, whenever I ran across a command I wasn’t previously familiar with, I took the time to look it up, install it (if needed) on one or more of my Linux systems and play with it. Considering that I’m seeing nearly 2,000 files just in /usr/bin on my Fedora system, I’m not surprised that, even after 30+ years, I’m not familiar with all of them. o § Games⠀➾ # ⚓ Steam_ended_2021_with_a_slightly_lower_Linux_user_share ending_the_recent_growth⠀⇛ After 7 months of seeing the Linux user share on Steam continue to grow, December saw 2021 end with it dropping slightly. The results can be seen on our Steam Tracker, which shows some trends over time, taken from the official opt-in Steam Hardware Survey. December 2021 saw the Linux user share at 1.11%. Something we’ve seen a few times, is that when the number of Simplified Chinese language users rises on Steam, the Linux numbers drop and it appears to be what has happened once again this time. It’s not always the case, as we have seen times where Linux has risen regardless but it is often the cause. # ⚓ Steam_On_Linux_Ended_2021_At_1.11%_Marketshare_–_Phoronix⠀⇛ After a reporting snafu over the weekend, Valve has now made available the December 2021 results of the Steam Survey. This metric has been quite interesting to monitor with the increases since Steam Play (Proton) was first introduced but particularly in recent months since the announcement of the Linux-powered Steam Deck causing more excitement around Linux gaming and more people trying out the current state of Steam Play. # ⚓ Check_Out_The_Top_11_New_Games_to_Play_on_Linux_With_Proton Since_December_2021_–_Boiling_Steam⠀⇛ We are back with our usual monthly update! Boiling Steam looks at the latest data dumps from ProtonDB to give you a quick list of new games that work (pretty much?) perfectly with Proton since December 2021 – all of them work out of the box or well enough with tweaks… # ⚓ Online_Linux_Gaming_is_not_ready_for_prime_time._|_Reacting to_Linux_Daily_Driver_Challenge_ep_5_–_Invidious⠀⇛ That’s not to say there are *no* Linux gamers out there. But if you’re an average PC boy and you play popular online multiplayer games, then you’re in for a bad time with Linux. # ⚓ OpenRGB_gets_greatly_expanded_hardware_support_in_the_0.7 release_|_GamingOnLinux⠀⇛ Controlling all your fancy RGB lighting on Linux can sometimes be a hassle but OpenRGB thankfully can reduce that pain and a new release is out now with OpenRGB 0.7. Since every vendor decides to have their own applications, usually proprietary and Windows-only, OpenRGB is becoming something of an essential item if you want to control your hardware on Linux since it’s vendor agnostic. # ⚓ Heroic_Games_Launcher_2.0.0_brings_a_much_improved_login system_for_Epic_Games_|_GamingOnLinux⠀⇛ Ending 2021 with quite the bang, the unofficial Epic Games Store app Heroic Games Launcher put up a big new release improving lots of features. One of the major annoyances previously was the login system, that used an external browser and needed some copy / pasting to actually get in. That’s been replaced with a new system that directly interfaces with the Epic Store making it much simpler to get going. There’s also a new design for the app, with it using a sidebar instead of a navbar along the top which does look quite a bit nicer. # ⚓ Orontes_Games_creator_of_DRAG_gets_acquired_by_iRacing_| GamingOnLinux⠀⇛ Seems DRAG from Orontes Games has been noticed as something special as iRacing has acquired the team. Lead developers Christian Folkers and Thorsten Folkers have officially joined the iRacing team, and the statement makes it clear that DRAG will continue to be developed. Not only that, the Folkers will also be developing additional games and bring their expertise and proprietary tech to iRacing. o § Distributions⠀➾ # ⚓ Trouble_in_Solus_Linux_land_as_their_Experience_Lead quits⠀⇛ Joshua Strobl, who was Experience Lead for the Solus Linux distribution, has officially quit but work on the Budgie desktop environment continues. Announcing the departure on Twitter, Strobl linked to a longer statement that went over some rather vague issues that probably won’t make much sense to anyone who isn’t close to Strobl or the project. These include problems “which affect the ability to contribute to Solus, both from myself and others in the community”. # ⚓ systemd_and_ipv6_–_why_should_it/they_not_be_disabled? Ever?_|_systemd-free_linux_community⠀⇛ Yours, mine, … my ISP’s, …..? It has taken nearly 2.5 decades (since 1998) to transition from ipv4 to ipv6.Is the day ipv4 will be globally terminated and disabled/banned by all servers? As far as I know there is no foreseeable date for when this can be done, or will it ever. According to our beloved spyware author, google,com, only 30% of all public servers have ipv6 ability. The ONLY servers recently found to have ipv6 ONLY ability, are test servers where if you can not reach them, it means you have no ipv6 ability enabled. A good test for us, we will explain later, or maybe not! Talk to a teenager with a relatively good aptitude in math, explain to them the scheme of 255.255.255.255 and also explain why this wouldn’t it be enough of addressing, how should we go about it? I suspect the vast majority would say add another (5th) batch of (0-255) numbers or 2^8 power, and increase the quantity by 250+ times. For every single ipv4 address there can be now 256 subdomains. Instead this illogical scheme of an undetermined number of digits, alphanumeric, colons, was devised as a solution. Few people still today, even networking engineers, can really explain you what does a specific ipv6 address really mean. Ipv4 addressing scheme, like tel- numbers, made sense to even 12 year olds. Ipv6 scheme only makes sense to encryption mathematicians. But was it your problem the internet was running out of IP addresses? It wasn’t mine. Did you experience a problem ever, of a dns providing you with an IP that matched two different servers? No, and no. So why are we exposing ourselves to connectivity we have little understanding about, vulnerabilities of a different variety than we know how to handle with ipv4, software that provide the ability to directly communicate through an ipv6 channel, but provide unknown protection for having such ability, and software we wouldn’t imagine they had their own networking functionality, that they actually do. This is a totally different protocol, not an expanded/modified protocol. # § New Releases⠀➾ # ⚓ Neptune_7.0_Released_as_a_Classic_KDE-Based_Linux Distro⠀⇛ The project’s latest release, Neptune 7.0 “Faye”, is based on Debian 11.2 “Bullseye” and includes KDE’s Plasma 5.20 desktop. Neptune is a Linux distro for desktops based fully upon the Debian stable branch, except for a newer kernel and some drivers. In addition, Neptune’s devs package and maintain the KDE Plasma desktop as well as KDE Frameworks and KDE Applications. Overall it’s very well-behaved and functional, a great derivative of Debian 11, featuring a nice more modern Plasma implementation. Now with their latest Faye version, Neptune Linux comes with another great release, helping make Linux more accessible for a broader audience from beginners to gamers. So let’s give it a shot and see what’s new. # ⚓ A_new_release_of_Rescuzilla_is_here_to_help_you recover_your_backed-up_data⠀⇛ There are two ways you can use Rescuezilla. The first is the traditional method of downloading the ISO, burning the ISO to a USB drive, booting the USB drive, and using the included tools to back up or restore your data. The tool also allows you to easily clone one drive to another, which makes for an outstanding method of rescuing your data from a failing server. The Rescuezilla GUI is straightforward enough that just about anyone can successfully back up data or clone a drive. That traditional method should be a part of every admin’s skillset (and fortunately, it really is just as easy as booting a USB drive and following the steps). # § Arch Family⠀➾ # ⚓ Arch_Linux’s_Archinstall_Preparing_Better_Btrfs Support,_More_Fixes⠀⇛ One of the great successes for Arch Linux in 2021 was “archinstall” debuting on the Arch Linux install media as a convenient and quick installer for this enthusiast-minded Linux distribution. This year that easy Arch Linux installer is getting into even better shape. Archinstall 2.3.1-rc1 has been released as a test version to showcase the latest Arch Linux installation enhancements. One of the big changes for this point release is continuing to improve the Btrfs file-system support, especially with accommodating more complex file-system configurations. This pull was merged for Archinstall 2.3.1 that now has Btrfs sub-volume support working that can fix various existing issues with the installer as well as paving the way for more Btrfs-driven features moving forward. # § IBM/Red Hat/Fedora⠀➾ # ⚓ Farewell_CentOS_and_Hello_Rocky_Linux⠀⇛ I remember when I first heard of CentOS (Community Enterprise Operating System) Linux all those many years ago. At the time, the latest release was at a 4.x. I did not initially touch the distro, nor was I an early adopter. I was subscribed to Red Hat and downloading / registering RHEL (Red Hat Enterprise Linux). It would not be until 6 was released that I finally decided to opt for CentOS rather than RHEL. Fast forward to the present and version 8.3 is not only the latest release but as of December 31, 2021, already EOL’d by Red Hat in favor of their CentOS Stream model which takes the distribution away from its original purpose: to provide a free and open-source community-supported computing platform, functionally compatible with its upstream source, RHEL. Although, to most folks, it was just a freely available version of RHEL. Under this model, a version of CentOS was released shortly after a RHEL release of the same version literally containing the same package sources / versions but stripped of the Red Hat branding. It was binary compatible. # ⚓ New_Community_Manager_at_OpenSource.com_to_Focus_on Accessibility_–_FOSS_Force⠀⇛ “I am privileged to be here at Opensource.com as the new community manager,” she said. “I’m looking forward to working with existing correspondents and contributors, and also bringing in new contributors and increasing the diversity of thoughts and ideas shared here on Opensource.com.” Although the duties associated with the position of community manager varies from organization to organization, in 2020 Opensource.com published an article on community management that might serve as insight into how Red Hat, or at least it’s Opensource.com website, defines the role. # ⚓ Digital_transformation:_4_do’s_and_don’ts_for_2022_| The_Enterprisers_Project⠀⇛ Digital transformation is never easy, but it is unavoidable – especially as we approach a post-COVID workforce. By laying out a strategy ahead of time and investing in data and analytics to inform your decision-making as you progress, it is possible to execute transformation with less disruption. # § Debian Family⠀➾ # ⚓ My_Debian_Activities_in_December_2021_–_Thorsten Alteholz⠀⇛ This month I accepted 412 and rejected 44 packages. The overall number of packages that got accepted was 423. # § Canonical/Ubuntu Family⠀➾ # ⚓ Canonical_hiring_a_Desktop_Gaming_Product_Manager_for Ubuntu_Linux_|_GamingOnLinux⠀⇛ It seems Canonical, creator of Ubuntu, is finally looking to get serious and improve Ubuntu gaming with a new Desktop Gaming Product Manager job waiting to pull someone in. Currently, Ubuntu is still the most popular Linux distribution on Steam, but the likes of Manjaro have been creeping up towards it pretty closely so perhaps with moves like this Canonical can keep Ubuntu on top. Not only that, but more and more people are recommending users install something else often Pop!_OS and even Valve moved away from a Debian base for SteamOS 3 with it being based on Arch Linux and so they suggest developers go with Manjaro. According to the job advert, Canonical want to “make Ubuntu the best Linux desktop for gaming” and they “work with partners in the silicon world to ensure the latest graphics drivers and tweaks are built-in for optimal frame rates and latency, as well as with partners in the gaming industry to ensure that mechanisms such as anti-cheat capabilities are available to ensure fairness and product availability”. # ⚓ Papirus_Icon_Set_Updated_with_45_New_Icons_–_OMG! Ubuntu!⠀⇛ A swathe of new glyphs have been added to the hugely popular Papirus icon set, enhancing its phenomenally broad coverage even further. We already consider the Papirus icon pack to be one of the best icon themes for Ubuntu (regardless of which flavour you use) and with this update the popularity of it is only certain to continue. So what have designers delivered in this, their first update to the set this year? A total of 45 new icons, including symbols for Linux Mint’s sticky notes tool, GTK4 Reddit client Headlines, Overwatch (when installed through Lutris), and the promising new GTK image viewer ImageRoll (which we’ll be talking about more shortly). The changes don’t stop there, though. # ⚓ What_Do_You_Want_to_See_From_Ubuntu_in_2022?_–_OMG! Ubuntu!⠀⇛ In my happy new year post I looked back at what Ubuntu had been up to in 2021 and touched on what’s planned for 2022, like the brand-new Ubuntu desktop installer, Flutter based apps, and planned long-term support release. And the recent job posting for a dedicated desktop game lead suggests that Canonical is aware that Ubuntu could use a bit more oomph in its tank if it’s to keep pace with other desktop Linux distros. But forget all that; we know what we think we’ll see from Ubuntu in 2022, but I want to hear from you: what do you want to see Ubuntu (in any of its shades) do this year? # ⚓ UbuntuDDE_Remix_21.10_–_Ubuntu_with_Beautiful_Deepin Desktop_is_Out!_|_UbuntuHandbook⠀⇛ For those looking for a best looking Linux system, I would recommend Deepin and Zorin OS 16. And, I personally prefer the former one a bit more for the desktop appearance. Deepin is based on Debian. It’s great, but for those stick to most recent NVIDIA drivers, Ubuntu PPAs, and/or the Ubuntu communities, then UbuntuDDE Remix is a good choice. UbuntuDDE Remix is a Ubuntu flavor that uses the Deepin Desktop Environment. It includes all the goodies from Ubuntu while having the beautiful desktop appearance. o § Devices/Embedded⠀➾ # ⚓ Another_Homebrew_Linux_Board_Success_Story_|_Hackaday⠀⇛ It’s truly incredible what the hobbyist is now capable of. While it would have seemed all but impossible a few years ago, we’re happy to report that yet another dedicated hardware hacker has managed to spin up their own custom Linux single- board computer. Creator [Ian Kilgore] tells us the only goal when developing CATFOOD (yes, that’s the name) was to gain confidence with at-home board production, so it looks like a success to us. # § Open Hardware/Modding⠀➾ # ⚓ Save_big_on_this_Raspberry_Pi_and_Arduino_training [Ed: A bit spammy]⠀⇛ # ⚓ ESP32_CAN_board_fits_into_OBD-II_dongle,_supports auto_shutdown_–_CNX_Software⠀⇛ RejsaCAN-ESP32 is a small board based on ESP32-WROOM-32 WiFi (and Bluetooth) module with a CAN interface that fits into a 3D printed OBD-II dongle for easy installation into most cars. Magnus Thomé has already published several automotive projects, notably for car racing with a system that checks real-time tire temperature, and he designed RejsaCAN-ESP32 board so that it can be plugged directly into his car with support for 5-15V input voltage, and also includes an auto-shutdown option to prevent battery drain by monitoring the battery voltage in the car. o § Free, Libre, and Open Source Software⠀➾ # ⚓ Apache_Month_in_Review:_December_2021⠀⇛ # ⚓ The_Apache_Weekly_News_Round-up:_week_ending_31_December 2021_:_The_Apache_Software_Foundation_Blog⠀⇛ Here we are –the last day of the year– we wish everyone a happy new year. Thank you for your dedicated readership: below is our final weekly round-up for 2021; we’ll be back in your inbox in 2022… # § Web Browsers⠀➾ # § Mozilla⠀➾ # ⚓ Cameron_Kaiser:_Updates_to_TenFourFox_on_Github [Ed: TenFourFox does not care about freedom at all because it is outsourced to Microsoft's proprietary software prison]⠀⇛ Happy New Year (I’d like to say nothing can be worse than 2021 was, but I don’t want to tempt 2022). Fortunately, we’re starting the year off right with new changesets on Github for the TenFourFox rolling release. # § Productivity Software/LibreOffice/Calligra⠀➾ # ⚓ LibreOffice_project_and_community_recap:_December 2021_–_The_Document_Foundation_Blog⠀⇛ Happy new year, everyone! Here’s our summary of updates, events and activities in the LibreOffice project in the last four weeks of 2021 – click the links to learn more… # § Programming/Development⠀➾ # § Python⠀➾ # ⚓ Telegram_bots_in_Python_made_easy⠀⇛ A while ago I set out to get some teenagers interested in programming, and thought about a good way to achieve that. A way that allows them to get started with very little friction, build something that’s relevant in their currently live quickly, and avoids frustration. They were old enough to have their own smartphone, and they were already happily chatting with their friends, using the Telegram messenger. I have already experimented a bit with writing bots for Telegram (e.g. @Umklappbot or @Kaleidogen), and it occurred to me that this might be a good starting point: Chat bot interactions have a very simple data model: message in, response out, all simple text. Much simpler than anything graphical or even web programming. In a way it combines the simplicity of the typical initial programming exercises on the command- line with the impact and relevance of web programming. But of course “real” bot programming is still too hard – installing a programming environment, setting up a server, deploying, dealing with access tokens, understanding the Telegram Bot API and mapping it to your programming language. * § Leftovers⠀➾ o § Hardware⠀➾ # ⚓ Edge-Mounted_Meters_Give_This_Retro_Frequency_Counter_Six Decades_Of_Display_|_Hackaday⠀⇛ With regard to retro test gear, one’s thoughts tend to those Nixie-adorned instruments of yore, or the boat-anchor oscilloscopes that came with their own carts simply because there was no other way to move the things. But there were other looks for test gear back in the day, as this frequency counter with a readout using moving-coil meters shows. We have to admit to never seeing anything like [Charles Ouweland]’s Van Der Heem 9908 electronic counter before. The Netherlands-based company, which was later acquired by Philips, built this six-digit, 1-MHz counter sometime in the 1950s. The display uses six separate edge-mounted panel meters numbered 0 through 9 to show the frequency of the incoming signal. The video below has a demo of what the instrument can do; we don’t know if it was restored at some point, but it still works and it’s actually pretty accurate. Later in the video, he gives a tour of the insides, which is the real treat — the case opens like a briefcase and contains over 20 separate PCBs with a bunch of germanium transistors, all stitched together with point-to-point wiring. o § Health/Nutrition/Agriculture⠀➾ # ⚓ Kushal_Das:_2021_blog_review⠀⇛ A major part of the year went to thinking if we can survive the year, India’s medical system broke down completely (the doctors and staff did some amazing job using whatever was available). Everyone I know lost someone in COVID, including in our family. All 3 of us were down in COVID from the end of April & the recovery was long. For a few days in between I could not remember any name. # ⚓ Keeping_The_Philippines’_Surface_Waters_Clean_With_Kabooms |_Hackaday⠀⇛ [Rich] over at Tropical Ocean Cleanup on YouTube has been working hard to prevent plastic waste from getting into the waters around the Philippines. Even as a mostly one-man crew, he’s collecting large sums of plastic waste using a boom system which he fittingly made out of waste: old tires and empty plastic bottles. This Kaboom system is a low- cost method of capturing any waste so that it can be collected and properly disposed of. In addition [Rich] also installs containers where locals can dispose of their plastic trash. The Kaboom system is detailed by [Rich] in this video (also linked after the break). As a shoestring budget project, it relies heavily on donations and local support to install more of these booms. It is however a highly effective way to prevent such common plastic waste from making it into the oceans in the first place. Having these booms made out of waste items that are commonly found where humans roam should make this a snap. o § Integrity/Availability⠀➾ # ⚓ What_is_This_Y2K22_Bug?_What_Problem_is_it_Causing_for Sysadmins?_–_It’s_FOSS_News⠀⇛ The turn of the new year has triggered errors in Microsoft Exchange mail servers, causing thousands, possibly millions, of emails around the world to not get sent and staying stuck on email transport queues, in some cases even causing entire servers to crash. The server administration community has dubbed this bug “Y2K22” due to its similarity to the infamous Y2K bug, a date-related bug which was feared to cause many computer systems and potentially the world economy itself to collapse at the turn of this century. # § Proprietary⠀➾ # § Security⠀➾ # ⚓ Security_updates_for_Monday_[LWN.net]⠀⇛ Security updates have been issued by Debian (thunderbird), Fedora (kernel, libopenmpt, and xorg-x11-server), Mageia (gegl, libgda5.0, log4j, ntfs- 3g, and wireshark), openSUSE (log4j), and Red Hat (grafana). # ⚓ blog.ipfire.org_–_Changes_to_our_donation process⠀⇛ We have had many conversations with other Open Source projects over the years and it looks like everyone has their own donation process – simply because donations do not exist in German tax law. # ⚓ Koch:_A_New_Future_for_GnuPG⠀⇛ He concludes with a request for individuals who have been donating to GnuPG to redirect their generosity toward another deserving project. This is good news; GnuPG ran on a shoestring for far too long. o § Internet Policy/Net Neutrality⠀➾ # ⚓ Telangana_HC_issues_notice_in_challenge_to_FRT⠀⇛ Mr. S.Q. Masood, a prominent social activist from Hyderabad has filed a petition challenging the deployment of Facial Recognition Technology in the State of Telangana. In the petition, he has argued that the deployment of the technology is not backed by law, unnecessary, disproportionate, and is being done without any safeguards in place to prevent misuse. The petition was listed for hearing before a bench led by the Chief Justice of the Telangana High Court. The bench has issued notice on the petition after hearing submissions from Mr. Manoj Reddy who represented Mr. Masood in court. The case will now be taken up after court vacations which end on 15th January, 2022. IFF provided legal support in the drafting of the petition. ䷩ 𝚕𝚒𝚗𝚎 6669 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.03.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Links_4/1/2022:_UbuntuDDE_Remix_21.10_and_Libreboot’s_Binary_Blob_Policy⠀✐ Posted in News_Roundup at 9:30 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⠀➾ # ⚓ The_Most_Popular_Linux_Distro_That_Doesn’t_Exist_– Invidious⠀⇛ I have had it with Windows! I’m tired of waiting longer for my web browser to open than it takes to brew a cup a coffee. I hear good things about Linux but…which Linux distro should is the best? # ⚓ Update_Everything_On_Linux_With_Topgrade_–_Invidious⠀⇛ Managing all the different package managers you have on Linux can be a massive pain, whether it’s the system packages, pip, cargo, vim plugins, zsh plugins, the AUR and countless others. But what if I said there was way and they way is topgrade. o § Kernel Space⠀➾ # ⚓ Cleaning_up_the_Linux_kernel’s_‘Dependency_Hell’:_This developer_is_proposing_2,200_commit_changes_|_ZDNet⠀⇛ Last year, Linux’s source code came to a whopping 27.8 million lines of code. It’s only gotten bigger since then. Like any 30-year old software project, Linux has picked up its fair share of cruft over the years. Now, after months of work, senior Linux kernel developer Ingo Molnar is releasing his first stab at cleaning it up at a fundamental level with his “Fast Kernel Headers” project. The object? No less than a comprehensive clean-up and rework of the Linux kernel’s header hierarchy and header dependencies. Linux contains many header, .h, files. To be exact there are about 10,000 main .h headers in the Linux kernel with the include/ and arch/*/include/ hierarchies. As Molnar explained, “Over the last 30+ years they have grown into a complicated & painful set of cross- dependencies we are affectionately calling ‘Dependency Hell’.” To bring rhyme and reason to all this, Molnar is proposing to make 2,200 commit changes to the code. That’s a lot of commits! Why so many? Well, Molnar continued, it turns out there’s a lot more mess in all that code than he thought there was when he started his clean-up project in late 2020. # ⚓ Intel_Is_Bringing_A_Feature_Upgrade_To_Linux_That_Will_Make Windows_Users_Jealous_|_HotHardware⠀⇛ Ever since BIOS updates became possible, the process required rebooting the PC. Even when motherboard manufacturers moved completely to UEFI, this remained the case. Intel is now changing that, thanks to a new part of the ACPI specification called Platform Firmware Runtime Update and Telemetry (PFRUT). This allows for firmware updates to a PC’s BIOS or UEFI without forcing a reboot. Windows users, though, will be disappointed. The feature is Linux-only, at least for now. Intel’s been working on PFRUT for some time, previously under the moniker “Seamless Update.” The idea is to reduce downtime, especially for servers that should ideally remain available 100 percent of the time. Servers can undergo BIOS/UEFI updates “on the fly,” keeping critical workloads fully operational the whole time. # § Graphics Stack⠀➾ # ⚓ AMD_Threadripper_3990X_+_RX_5700_XT_System76_Thelio Major_Performance_After_2_Years⠀⇛ Next month marks two years since AMD introduced the Ryzen Threadripper 3990X 64- core / 128-thread processor. All of our testing of the 3990X on Linux over the past two years has been with the System76 Thelio Major, which continues holding up well with that US-assembled workstation with hand- crafted enclosure from Colorado. With System76 having recently released Pop!_OS 21.10 as the latest update to their Ubuntu Linux derived operating system and upcoming two year anniversary of the 3990X, it made for an interesting time to see how the performance of the Ryzen Threadripper 3990X and Radeon RX 5700 XT within that workstation has evolved. # ⚓ Mike_Blumenkrantz:_New_Year_New_Me⠀⇛ Zink Somehow the driver is still in the tree, still builds, and still runs. It’s a miracle. Thus, since there were obviously no other matters more pressing than not falling behind on MesaMatrix, I spent the morning figuring out how to implement ARB_sparse_texture. Was this the best decision when I didn’t even remember how to make meson clear its dependency cache? No. No it wasn’t. But I did it anyway because here at SGC, we take bad ideas and turn them into code. Your move, 2022. o § Applications⠀➾ # ⚓ The_16_Best_Free_Linux_Screen_Recorders_Available_ (Download)_–_DekiSoft⠀⇛ This article will share with you the 16 best and top-of-the-line Linux screen recorders that are free to download. We made sure we also choose open- source choices! o § Instructionals/Technical⠀➾ # ⚓ How_To_Install_and_Use_WhatsApp_for_Linux_(Easy_Guide)_– DekiSoft⠀⇛ Whatsapp which is a popular messaging application does not provide users with a desktop client. The best thing is that they took this problem into consideration and launched WhatsApp Web. # ⚓ Splitting_files_on_Linux_by_context_|_Network_World⠀⇛ The csplit command is unusual in that allows you to split text files into pieces based on their content. The command allows you to specify a contextual string and use it as a delimiter for identifying the chunks to be saved as separate files. As an example, if you wanted to separate diary entries into a series of files each with a single entry, you might do something like this. # ⚓ How_To_Make_Bootable_Windows_10/11_USB_with_WoeUSB_(Linux) –_DekiSoft⠀⇛ This is a tool which is used to create a bootable Window 10 USB drive on Linux and is CLI based known as WoeUSB. This is under active development and a graphic user interface known as WoeUSB-frontend- wxgtk which at the moment is not maintained. An independent python port of this known as WoeUSB- ng is also available which is maintained actively. This supports to the creation of a bootable Windows USB from Linux with support for both UEFI booting and Legacy PC. Its filesystem can either be FAT32 or NTFS, whereas the source can be either a disk image or physical installation disk. The best thing is that it supports non-ASCII filenames. # ⚓ TWRP_101:_Uninstall_TWRP_Recovery_(Restore_To_Stock Recovery)_–_DekiSoft⠀⇛ There is one quality you need to qualify when it comes to custom development, and it is to unlock the bootloader of the device. Once this is done, you have opened floodgates to a plethora of customizations. We suggest that you get hold of TWRP recovery before you make your steps in the flashing community. This is not a compulsory requirement but only a recommendation. This guide explains the steps required to Uninstall TWRP on Android without getting stuck in a boot loop and bricking your smartphone. # ⚓ How_To_Install_Laravel_on_Fedora_35_–_idroot⠀⇛ In this tutorial, we will show you how to install Laravel on Fedora 35. For those of you who didn’t know, Laravel is one of the most popular PHP frameworks in the world, and it’s great for developers looking to build modern web applications. So, many developers use it to make their most popular applications. 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 Laravel PHP Framework on a Fedora 3 # ⚓ How_to_install_sudo_on_Debian_or_Ubuntu_Linux_–_Linux Shout⠀⇛ Whether you are using Debian 11 Bullseye, 10 Buster, Ubuntu 20.04, 18.04, 22.04, or any other minimal server version of the same base, here are there steps to install sudo Debian Linux. The command sudo, we used before other program calls to execute them. The key purpose of it is to authorize the users to run the program on behalf of and with the rights of another user to perform tasks that are reserved for administrators. When we run the command with sudo, it asks for the password of the current user before executing the program. This checks whether the user that entered the command is the group of authorized users defined in the /etc/sudoers file or not. The target user is root assumed by default. # ⚓ How_to_Install_Xfce_Desktop_on_Debian_11_Bullseye_– LinuxCapable⠀⇛ Xfce is a lightweight free, open-source desktop environment for UNIX-like operating systems. It is designed to be fast and light on system resources while visually appealing than the default desktop environments that ship with most operating systems. Xfce is very popular with older systems with hardware as a key feature in its design is to conserve both memory and CPU cycles. In the following tutorial, you will learn how to install Xfce on your Debian 11 Bullseye desktop. # ⚓ Classic_SysAdmin:_How_to_Kill_a_Process_from_the_Linux Command_Line⠀⇛ The first step in killing the unresponsive process is locating it. There are two commands I use to locate a process: top and ps. Top is a tool every administrator should get to know. With top, you get a full listing of currently running process. From the command line, issue top to see a list of your running processes (Figure 1). # ⚓ How_to_migrate_from_CentOS_8_to_AlmaLinux_(conversion)_– nixCraft⠀⇛ already wrote about migrating from CentOS 8 to CentOS Stream. I also have a guide about migrating from CentOS 8 to Rocky Linux. Today, I am working on another side project with my partner, and I wanted to try out AlmaLinux. Hence, this quick post will list steps to convert existing VM or bare metal server from CentOS 8 to AlmaLinux 8. The server currently acts as API for mobile apps, including PostgreSQL, Redis, Python+Django, Apache web server, and SELinux and firewalld. # ⚓ How_to_install_Mayhem_Cars_2_on_a_Chromebook⠀⇛ Today we are looking at how to install Mayhem Cars 2 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_Share_Data_Between_Docker_Containers_–_CloudSavvy IT⠀⇛ Docker containers are intentionally isolated environments. Each container has its own filesystem which can’t be directly accessed by other containers or your host. Sometimes containers may need to share data. Although you should aim for containers to be self- sufficient, there are scenarios where data sharing is unavoidable. This might be so a second container can access a combined cache, use a file-backed database, create a backup, or perform operations on user-generated data, such as an image optimizer container that processes profile photos uploaded via a separate web server container. In this guide, we’ll look at a few methods for passing data between your Docker containers. We’ll assume you’ve already got Docker set up and are familiar with fundamental concepts such as containers, images, volumes, and networks. # ⚓ Using_OATH_in_FreeIPA_|_Zamir’s_Board⠀⇛ OATH has been the choice of Two-factor authentication (2FA) for many companies and websites. And it’s also exists in FreeIPA. As a user, it’s pretty straight forward to enable OATH token in FreeIPA on you own given your organization has enabled the choice for you. Firstly, login into FreeIPA with your own account. Click your own users from the ‘Active users’ table. Click the drop-down button ‘Action’ then you’ll see ‘Add OTP Token’. Click it. # ⚓ How_to_install_sudo_on_Debian_or_Ubuntu_Linux_–_Linux Shout⠀⇛ Whether you are using Debian 11 Bullseye, 10 Buster, Ubuntu 20.04, 18.04, 22.04, or any other minimal server version of the same base, here are there steps to install sudo Debian Linux. The command sudo, we used before other program calls to execute them. The key purpose of it is to authorize the users to run the program on behalf of and with the rights of another user to perform tasks that are reserved for administrators. When we run the command with sudo, it asks for the password of the current user before executing the program. This checks whether the user that entered the command is the group of authorized users defined in the /etc/sudoers file or not. The target user is root assumed by default. # ⚓ How_to_install_Nitrux_1.8.0_–_Invidious⠀⇛ In this video, I am going to show how to install Nitrux 1.8.0 # ⚓ How_to_install_Docker_CE_on_Ubuntu_22.04_LTS_Jammy Jellyfish⠀⇛ Docker is an open-source project that gives us the ability to easily run applications in isolated containers. Those who are using Ubuntu 22.04 LTS and want to install Docker CE to run containers of various Linux apps can follow this tutorial. Another benefit of Docker containers is they can build on one another and communicate with one another. Examples of these applications would be an Apache server or a MySQL database. As compared to normal virtual machines we do not need every container to run a complete operating system. I mean if we want to run a separated web server from the database server, we would have to start two complete virtual machines including the operating system. This is not the case with docker, in it, the underlying kernel will be the same and two independent containers can be started for respective servers without installing the full- blown operating system instead a lightweight Docker image will do the work. # ⚓ How_to_easily_update_a_tar_file_from_the_Linux_file_manager –_TechRepublic⠀⇛ Instead of re-creating your tar archives when you need to add files, why not simply append those files? Jack Wallen shows you how from the command line and a GUI file manager on Linux. # ⚓ How_To_Install_Go_on_Fedora_35_–_idroot⠀⇛ In this tutorial, we will show you how to install Go Browser on Fedora 35. For those of you who didn’t know, Go is an open-source programming language developed by a team at Google that makes it easy to build simple, reliable, and efficient software. Golang is very useful for writing lightweight microservices, infrastructure like networked servers, and also tools and systems for developers. It can also be used for generating APIs that interact with front-end applications. 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 Go (Golang) programming language on a Fedora 35. o § Games⠀➾ # ⚓ GOG_have_one_last_free_game_during_their_sale_with_Iratus: Lord_of_the_Dead_|_GamingOnLinux⠀⇛ While the GOG Winter Sale shall be ending soon, they have one last freebie for you with the rather good turn-based tactical roguelike RPG Iratus: Lord of the Dead. How to claim the latest free game: head to the GOG.com website and scroll down a bit to find the giveaway banner. The giveaway ends January 5th at 2 PM UTC. # ⚓ Not_Actually_A_DOS_Game_looks_like_a_retro_delight_| GamingOnLinux⠀⇛ Do you love retro games (or just retro-styled) and you’re a fan of dungeon crawling? Check out the recent release of Not Actually A DOS Game for your latest fix. Taking the visuals of classics like Rogue, it spices things up a bit to make the style a little more approachable with a slightly more modern interface and some small effects. The result is a game that should appeal to classic roguelike fans while giving some nice quality-of-life adjustments like tooltips, stat comparisons and more. Overall it certainly seems like a solid entry. # ⚓ Best_12_Linux_ASCII_Games_That_are_Modern_Looking_– DekiSoft⠀⇛ A decade back terminal-based games were quite popular when you did not have visual masterpieces such as Red Dead Redemption 2, Spiderman, and God of War, or Grand Theft Auto 5. Most were played on DOS or hacker-like screens. The Linux platform carries its own share of good games but keeps in mind that these are not always the “latest and the greatest”, there are ASCII games to which we can never say no to or turn our back. Most of the collection below can also be played online or in the browser depending on your setup. Please remember: Installing such games is time- consuming and you may encounter some games which require building from source. o § Distributions⠀➾ # ⚓ An_Inferno_Diary⠀⇛ At the end of 2020 I decided to finish the contracting gig I was doing with the aim of spending less time every day stressing about things I couldn’t really influence while not making a sustainable income. I figured that, if I wasn’t going to make the big bucks, I might as well work on things I enjoyed. Isn’t the gig economy wonderful? Anyway, that’s a story for another time. Today, I’m mentioning something I started during December, which is a diary about my recent experiences with the Inferno operating system. It started because I felt I was doing bits and pieces with Inferno from time to time, and there wasn’t much to show if the activities didn’t lead to finished products. # § New Releases⠀➾ # ⚓ KaOS_Linux_Sees_First_2022_ISO_Release_with_Initial ZFS_Support,_Latest_KDE_Goodies⠀⇛ Still powered by the Linux 5.14 kernel series, which reached end of life about one and a half months ago, KaOS Linux 2022.01 is here with the latest KDE Plasma 5.23.4 desktop environment, which is accompanied by the latest KDE Frameworks 5.89 and KDE Gear 21.12 software suites. KaOS Linux’s first 2022 ISO release also comes with the latest and greatest Calamares graphical installer (version 3.2.49.1), which received initial support for the ZFS file system. This implementation, along with the ZFS (Zettabyte File System) userspace utilities from the KaOS repositories, will allow you to use ZFS on KaOS Linux through the linux-next kernel. # § IBM/Red Hat/Fedora⠀➾ # ⚓ Matrix_Digital_Rain_On_The_IBM_PC_With_A_High Persistence_Monitor_|_Hackaday⠀⇛ Unless you’ve been hiding under a rock for the last 20-odd years, you will have come across The Matrix series of movies, and the cool green ‘digital rain’ effect used frequently. This inspired [Oli Wright] to wonder what it would look like if instead of running the animation on a modern display, using a digitally produced phosphor persistence effect, it was implemented on some retro PC hardware, using an actual high- persistence phosphor Green Monochrome monitor. (Video embedded, below) As luck would have it, [Oli] owns a 40-year-old IBM PC 5150 as well as the matching IBM 5151 monitor, so it was a simple matter to implement the effect in 8088 assembler to create falling sequences of characters. The final binary is less than 256 bytes! # ⚓ My_2022_Focus⠀⇛ My biggest frustration is the fatigue I have from working from home and being in our apartment so much. # § Debian Family⠀➾ # ⚓ Debian’s_approach_to_Rust_–_Dependency_handling⠀⇛ I have been involved in Debian for a very long time. And I’ve been working with Rust for a few years now. Late last year I had cause to try to work on Rust things within Debian. When I did, I found it very difficult. The Debian Rust Team were very helpful. However, the workflow and tooling require very large amounts of manual clerical work – work which it is almost impossible to do correctly since the information required does not exist. I had wanted to package a fairly straightforward program I had written in Rust, partly as a learning exercise. But, unfortunately, after I got stuck in, it looked to me like the effort would be wildly greater than I was prepared for, so I gave up. Since then I’ve been thinking about what I learned about how Rust is packaged in Debian. I think I can see how to fix some of the problems. Although I don’t want to go charging in and try to tell everyone how to do things, I felt I ought at least to write up my ideas. Hence this blog post, which may become the first of a series. # ⚓ Debian_Community_News:_Albanian_women,_Brazilian women_&_Debian_Outreachy_racism_under_Chris_Lamb⠀⇛ We previously looked at the vast amounts of money spent on travel for Albanian women to come to DebConf19 in Curitiba and many other events. Before DebConf19, Debian tried to organize a warm-up event, MiniDebConf Curitiba in the location that would host DebConf proper. Local women had found Chris Lamb so difficult to deal with that they had to start their own crowdfunding campaign to get there. Lamb only had eyes for Albanian women like the woman who won an Outreachy internship. Renata blogs about the crowdfunding campaign for five women: Alice, Anna e So, Miriam Retka, Ana Paula and Luciana. # ⚓ Paul_Wise:_FLOSS_Activities_December_2021⠀⇛ This month I didn’t have any particular focus. I just worked on issues in my info bubble. # § Canonical/Ubuntu Family⠀➾ # ⚓ UbuntuDDE_Remix_21.10_Released_with_Latest_Deepin Desktop_Environment⠀⇛ Based on the Ubuntu 21.10 (Impish Indri) operating system release, UbuntuDDE Remix 21.10 is powered by the same kernel as upstream, Linux 5.13, and features the latest Deepin Desktop Environment (DDE) and related software packages available at the moment of writing. In addition, UbuntuDDE Remix 21.10 comes with an updated DDE Store to version 1.2.3 for a better package management experience, the Calamares graphical installer to make the installation of the distribution easier, as well as updated artwork from both the Ubuntu 21.10 and Deepin Linux distributions. # ⚓ Ubuntu_Fridge_|_Ubuntu_Weekly_Newsletter_Issue_716⠀⇛ Welcome to the Ubuntu Weekly Newsletter, Issue 716 for the week of December 26, 2021 – January 1, 2022. o § Devices/Embedded⠀➾ # ⚓ The_PinePhone_Keyboard_Case_is_Now_Available_to_Buy⠀⇛ PinePhone owners can finally get their hands on a physical keyboard case designed exclusively for use with the FOSS-friendly handset. This official keyboard accessory is compatible with all version of the PinePhone released to date, from the early batch of BraveHeart devices through to the ‘convergence’ edition, as well as the forthcoming PinePhone Pro. Don’t picture some sort of generic bluetooth keyboard with a feeble phone holder here. Oh no; this thing is custom engineered for this device, and this device only. You pop the PhonePhone’s back cover off to attach the PinePhone keyboard, which connects through the phone’s internal pogo pins (added to enable the creation add-ons such as this one). A 6000mAh battery and USB Type-C port are built-in to the keyboard (which lets charge the keyboard and phone batteries simultaneously). # ⚓ PinePhone_official_keyboard_case_is_finally_available_to purchase⠀⇛ Pine64 is a tech company that has been selling Linux-powered hardware for years, including the entry-level PinePhone and upcoming PinePhone Pro. Pine64 has been working with the PinePhone community for months to create an official keyboard attachment, and two months after the design was finalized, you can finally buy one to create the fun-sized pocket Linux PC of your dreams. The new keyboard case is compatible with both the PinePhone and upcoming PinePhone Pro, and takes the place of the original back casing. Since the PinePhone already has internal pogo pins designed for accessories, there’s no added bulk or fiddling with Bluetooth connections. It looks more like a tiny laptop than a phone with a keyboard. # § Open Hardware/Modding⠀➾ # ⚓ Neatly_fold_your_t-shirts_with_an_Arduino-powered robot_|_Arduino_Blog⠀⇛ Folding t-shirts isn’t a fun process for many people, and even worse, it’s difficult to get them looking the exact same way when the pile of folded clothing is completed. So in order to make it easier, mechanical engineering students Pietro Oppici, Corentin Vandebroek, Stefano Pontoglio, and Quentin Bertieaux set out to build a robot of their own that could quickly and precisely fold shirts to perfection and drop them below. They also wanted it to be able to detect what kind of tee was present so the robot could adjust its folding style to match. After designing and fabricating a mechanism consisting of birch and MDF wooden panels held together with 3D-printed hinges, the team opted to use an Arduino Uno board as the brains of the operation. From there, they attached a series of NEMA17 stepper motors, three of which were high torque for fast folding, and a servo motor for the final fold. A set of five DRV8825 drivers were then connected to the Uno, which delivered current from the 12V power supply to the motors. # ⚓ This_Samsung_Ballie-inspired_spherical_robot_gets around_on_a_couple_of_wheels_|_Arduino_Blog⠀⇛ Back in early 2020, Samsung demonstrated their Ballie robot concept at CES, and although it never got off the ground, it inspired Derek Lieber to create his own version of a gyroscopically stabilized robot that moves with a pair of hemispherical “wheels” on each side. Lieber’s project, which he calls “Ballbot2”, is based around a single Arduino Mega connected to a set of two LM6234 drivers that take the incoming 5V PWM signals and boost them up to the 12V required by the motors. Speaking of motors, the ones for the Ballbot2 aren’t the typical geared DC or steppers, but rather gimbal motors that use copper coils surrounding a central magnet to turn it. Detecting the current orientation of the magnetic field is done by utilizing four Hall effect sensors to sense its position and then send it in a digitized format to the Arduino for further processing and feedback. He mounted an XBee module to a custom shield, along with the two driver ICs, before attaching it to the Mega. The XBee allows for the robot to be remotely operated with a secondary XBee module, which reads data from a joystick and transmits it wirelessly. # ⚓ Homemade_thermal_battery_system_keeps_the_shop_cool with_Arduino_|_Arduino_Blog⠀⇛ When trying to cool off a space, most people reach for an air conditioning unit that uses a pump, compressor, refrigerant, and a radiator to move heat from inside a room to the outside air. But in a break from this typical model, YouTuber Curtis in Seattle came up with a system that pumps water between a series of radiators/box fans and a set of five 55-gallon drums to move heat away from a room during the day. Curtis employed an Arduino Uno to calculate temperatures via input from four DS18B20 sensors, activate relays, log data, and display the indoor, outdoor, battery, and ground measurements on an LCD module. The components are all housed in a vintage movie projector. # ⚓ Need_A_Small,_Cheap_Ammeter?_Blinkenlights_To_The Rescue!_|_Hackaday⠀⇛ You know how it is. You’ve got that new project running, and while it doesn’t consume much power, it also doesn’t give much indication of whether it’s functioning or just sitting there with a dead battery. What you need is an ammeter to check power consumption, even from across the room. And it just so happens that [Manuka] has Just The Circuit You Need, complete with a demonstration in the video after the break! Oh sure, you could grab a cheap ammeter at your favorite tool import store or site, but those are bulky and take batteries. You could put in an LED that gets dimmer as voltage drops. But wait- is that the sun shining on it? or is it on? Or has something gone awry and it’s consuming too much power? # § Mobile Systems/Mobile Applications⠀➾ # ⚓ Top_8_Ways_to_Fix_Android_Phone_Not_Receiving_Texts⠀⇛ # ⚓ Get_more_out_of_your_Android_phone_by_changing_these settings_–_CNET⠀⇛ # ⚓ Speed_up_that_Android_phone_by_clearing_your_browser cookies_and_cache_–_CNET⠀⇛ # ⚓ Developer_Releases_Android_12_Custom_ROM_For_Galaxy S9_&_Note_9⠀⇛ # ⚓ Developer_brings_Android_12_to_the_Samsung_Galaxy_S3 –_9to5Google⠀⇛ # ⚓ Is_it_time_for_Samsung_to_ditch_Tizen_in_favor_for Android_TV?_–_SamMobile⠀⇛ # ⚓ How_To_Set_Up_Automatic_Email_Reminders_In_Gmail_For Android_&_Desktop⠀⇛ # ⚓ Lenovo_Legion_Y700_Android_gaming_tablet_has_an_8.8 inch_120_Hz_display_–_Liliputing⠀⇛ o § Free, Libre, and Open Source Software⠀➾ # ⚓ Apache_in_2021_–_By_The_Digits⠀⇛ The Apache Software Foundation’s (ASF) merit-driven “Contributor-Committer-Member” progression is the central governing process across the Apache ecosystem. Following the ASF’s incorporation in 1999, the core Apache Group of 21 individual Members grew with developers who contributed code, patches, or documentation. Some of these contributors were subsequently granted Committer status by the Membership, and provided access to: 1) commit code directly to Apache repositories; 2) vote on community-related decisions; and 3) propose an active user for Committership. Today, ASF Committers contribute not just code and documentation, but also an array of initiatives that provide value across the greater Apache ecosystem, including Project promotion and community development through mentoring, events, and diversity and inclusion programs. Those Committers who demonstrate merit in the Foundation’s growth, evolution, and progress are nominated for ASF Membership by existing members. More than 630,000 individuals have contributed to the ASF to date. During 2021, 724 individuals new to the ASF contributed to Apache projects and initiatives. # § FSF⠀➾ # § GNU Projects⠀➾ # ⚓ Libreboot_Binary_blob_policy⠀⇛ Libreboot intentionally de-blobs coreboot, which is to say that it does not include binary blobs. The coreboot software otherwise requires binary blobs on most systems that it has support for. Libreboot’s version of coreboot is entirely free, on its consequently reduced set of supported mainboards. Libreboot is designed to comply with the Free Software Foundation’s Respects Your Freedom criteria and the GNU Free System Distribution Guidelines (GNU FSDG), ensuring that it is entirely Free Software. It was decided that a formal policy should be written, because there is quite a bit of nuance that would otherwise not be covered. Libreboot’s policies in this regard were previously ill defined. # § Programming/Development⠀➾ # ⚓ LLVM/Clang_Adds_Support_For_ARMv9.3-A_–_Phoronix⠀⇛ It was nearly one year ago that Arm announced the Armv9 architecture as the successor to ARMv8 that was introduced a decade ago. Since then Arm has been working on adding Armv9 support to the open-source compilers such as GCC and LLVM/Clang. That initial Armv9 support has been in place for months now while on the LLVM/Clang today it received support for Armv9.3-A as the latest iteration. Last September Arm outlined their 2021 Architecture Developments with optimized memcpy functions, non-maskable interrupts, Pointer Authentication updates, PMU updates, and other changes. Those 2021 updates are rolled into the form of Armv8.8-A and then in the Armv9 world as Armv9.3-A. # ⚓ Intel_IGC_1.0.9933_Brings_DG2/Alchemist_&_Xe_HPC Improvements,_More_SPIR-V_Plumbing⠀⇛ Starting off a new year Intel’s open-source compute stack developers have published the Intel Graphics Compiler (IGC) 1.0.9933 release that is used for their OpenCL / oneAPI Level Zero support on Linux and also used by their graphics driver on Windows. Notable with today’s IGC 1.0.9933 release is DG2 (Alchemist) and Xe HPC “Ponte Vecchio” support within IGC’s Vector Compute “VC” backend. The IGC compiler and associated open-source Compute-Runtime components have been seeing a lot of DG2 and Xe HPC “PVC” enablement over the past two months, following all the Linux kernel driver work that continues to happen for enabling these forthcoming GPUs/accelerators on fully open- source driver stacks. # ⚓ Botond_Ballo:_2021_C++_Standardization_Highlights⠀⇛ The ISO C++ Standards Committee (also known as WG21) has not met in person since its February 2020 meeting in Prague, which I wrote about here. However, the committee and its subgroups have continued their work through remote collaboration, and a number of notable proposals have been adopted into C++23, the next language version, in this way, with many others in the pipeline. In this post, I will outline some of the highlights of the committee’s work in 2021. (The post will also cover some material from the latter part of 2020, a period when remote collaboration was already underway but which I have not covered in any previous post.) I’ve been less involved in the committee than before, so this post will not be as comprehensive as my previous trip reports, but I hope to share the proposals I’ve found most notable. # § Rust⠀➾ # ⚓ Birger_Schacht:_Introducing_carl⠀⇛ For some time now I wanted to learn Rust, but I either didn’t have the time or couldn’t come up with a nice beginner project. Given that I recently found myself to be without a job and we had another lockdown in the part of the world I happen to live in, I decided to give that idea another go (no pun intended). There is apparently a trend to reimplement existing Unix tools in Rust (see exa, a ‘modern replacement for ls’, delta, a syntax highlighting pager for git, diff and grep output, bat, a ‘cat clone with wings’, zellij, a terminal workspace, ripgrep, a line- oriented search tool …). I looked around what else was out there, but what I wasn’t able to find was an implementation of cal(1) in Rust (maybe I wasn’t looking hard enough, feel free to point anything out to me I might have overlooked). No cal in Rust even though a calendar implementation would provide the potential to go over the top with terminal colors, which is also very important when writing reimplementations of older CLI tools! So I started writing and soon had a simple prototype of a cal reimplementation. * § Leftovers⠀➾ o ⚓ Homemade_Scrapyard_Security_Mech_Gives_Uncle_Super_Powers_| Hackaday⠀⇛ [Handy Geng] is back again with another bonkers build, that we just can’t not cover. His Uncle came to visit the workshop one day and said he’d love to go there every day, and could even watch over it when [Handy Geng] was away. But being an older chap and needing a stick to get around, he would not be much use if ‘bad guys’ decided to pay a visit. The obvious solution was to build a ride-on security mech which Uncle could ride on, (video, embedded below) and use to defend the shop from bandits. The build starts with him unloading a large pair of tracked wheel units from his truck, which caused a chuckle around these parts when we tried to imagine the scrap yard he’d just visited! The build video is more of a spot-weld-come-assembly log, with the less interesting sub assembly construction omitted. If he’d included all the details, this video would have been hours long. Though, we’d probably watch that anyway. o ⚓ TFT35_Dual_Mode_3D_Print_Control_–_Hands_On_|_Hackaday⠀⇛ I was rebuilding one of my 3D printers — again — and decided I needed a display upgrade. A color screen is nice, but there are some limitations. I also found there are ways around these limitations, so I wanted to share my thoughts on a dual-mode color touch screen LCD controller for your 3D printer. The screen in question is a TFT35 from BigTree Tech. It is similar to an MKS screen, but it can operate in two different modes, as you will see. A few years ago, I picked up an Anet A8 which was very inexpensive, especially on sale. Not the best printer, though, because it has that cheap acrylic frame. No problem. A box full of aluminum extrusion later, the printer was reborn. Over time, I’ve completely reworked the extrusion system and the Y-axis, leaving only the motors, bearings, and the controller/display as the original. o § Hardware⠀➾ # ⚓ 2021:_As_The_Hardware_World_Turns_|_Hackaday⠀⇛ Well, that didn’t go quite as we expected, did it? Wind the clock back 365 days, and the world seemed to be breathing a collective sigh of relief after making it through 2020 in one piece. Folks started getting their COVID-19 vaccines, and in-person events started tentatively putting new dates on the calendar. After a rough year, it seemed like there was finally some light at the end of the tunnel. Turns out, it was just a another train. New variants of everyone’s favorite acute respiratory syndrome have kept the pandemic rolling, and in many parts of the world, the last month or so has seen more new cases of the virus than at any point during 2020. This is the part of the Twilight Zone episode were we realize that not only have we not escaped the danger, we didn’t even understand the scope of it to begin with. o § Integrity/Availability⠀➾ # § Proprietary⠀➾ # § Security⠀➾ # ⚓ High_Security_Shipping:_Anti-interdiction_in 2021⠀⇛ We offer a lot of unique, high-security features at Purism (I discuss the most secure options for the Librem 14 in this post). One of the most interesting things we offer is our anti- interdiction service, an add-on service that we custom-tailor for each customer to add multiple levels of tamper detection to an order. With anti- interdiction in place, a customer can detect any attempt to tamper with the package, the computer hardware, or the firmware during shipping. In 2021 we saw more anti-interdiction orders than ever before. In this post I wanted to talk through some of the highlights of anti-interdiction in 2021 including some of the most common anti- interdiction steps our customers choose. [...] These steps allow the customer to detect whether someone has opened the package during shipping, and therefore the laptop should get extra scrutiny. Pictures of the motherboard allow the custom to have a “known good” state for the motherboard, RAM, and disk in case they are concerned that an attacker may have replaced or added to the laptop during shipment. In addition to these steps, we also offer additional, optional measures and work with each customer (over GPG- encrypted email if they prefer) to determine their particular threats, and decide which combination of additional anti-interdiction measures are appropriate. It’s always interesting to see which measures customers pick, and which threats they are facing. Our average customer doesn’t necessarily face specific threats, but instead wants the highest level of protection possible for extra peace of mind. They might not know for sure that someone is targeting them, but if someone does tamper with their laptop during shipping, they’d like to know about it. [...] One of the more unique options for anti-interdiction orders is painting glitter nail polish on the bottom screws. The principle behind this measure starts with the fact that you have to remove the bottom case screws to tamper with the laptop motherboard. If you were to cover those screws with some sort of paint, someone would have to disturb the paint to access that hardware and then attempt to repaint it. Glitter nail polish leaves behind a unique, random, 3-dimensional pattern of glitter that, once disturbed, is incredibly difficult and time-consuming to replace. We provide each anti- interdiction customer who selects this option pictures of these glitter patterns on request so they can compare them with the laptop they receive. They can also compare the laptop against pictures whenever their laptop is left unattended. o § Finance⠀➾ # ⚓ Why_Is_the_UK’s_National_Health_Service_Being_Run_by_Former Bankers?⠀⇛ o § Monopolies⠀➾ # § Patents⠀➾ # ⚓ The_Antitrust_Conduct_Cases_To_Watch_In_2022⠀⇛ U.S. antitrust enforcers carried out dramatic efforts to combat anticompetitive conduct last year, and all signs show that the aggressive efforts will continue in 2022. Among the areas to watch will be criminal and civil cases accusing companies of anticompetitive collusion to restrict their workers’ wages and mobility. Important developments in the cases against Big Tech and a key decision on the intellectual property strategies of pharmaceutical giants are also expected. # ⚓ USPTO_News_Briefs⠀⇛ In a notice of proposed rulemaking published last month in the Federal Register (86 Fed. Reg. 71209), the U.S. Patent and Trademark Office is proposing to issue patents electronically through its patent document viewing systems (i.e., Patent Center and Patent Application Image Retrieval (PAIR)). As a result of the proposed changes to the rules, the Office would no longer issue patents on paper or physically deliver patents by mailing them to the correspondence address, and 37 C.F.R. § 1.315, which states that “[t]he patent will be delivered or mailed upon issuance to the correspondence address of record,” would be removed and reserved. Currently, the Office issues “letters patent” as paper copies bound with a cover sheet that has both an embossed seal and the signature of the USPTO Director. Under the proposed process, the Office would issue patents electronically under a new digital USPTO seal and with a digital signature from the USPTO Director. The notice indicates that the electronic issuance of patents will allow the Office to issue patents approximately two weeks faster than the current process. Stakeholders and patentees, however, would still have the option of ordering certified copies or paper presentation copies of patents. ╘══════════════════════════════════════════════════════════════════════════════╛ ¶ Lines in total: 8077 ➮ Generation completed at 02:41, i.e. 75 seconds to (re)generate ⟲