𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Wednesday, November 17, 2021 ┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅ Generated Thu 18 Nov 02:40:31 GMT 2021 Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖) Full hyperlinks for navigation omitted but are fully available in the originals The corresponding HTML versions are at 𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈 Latest in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕 and older bulletins can be found at 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕-𝒂𝒓𝒄𝒉𝒊𝒗𝒆𝒔 Full IPFS index in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔 and as plain text in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔/𝒕𝒙𝒕 Gemini index for the day: gemini://gemini.techrights.org/2021/11/17/ ╒═══════════════════ 𝐑𝐄𝐂𝐄𝐍𝐓 𝐁𝐔𝐋𝐋𝐄𝐓𝐈𝐍𝐒 ════════════════════════════════════╕ Previous bulletins in IPFS (past 21 days, in chronological order): QmR26bCkmAgeJHsLEpDDduxsZtvTiPxLdppYuH4w8mzfdo Qmex86DPLV4yK5WC34kReVXbdEtRT7fvt7mBVzMTGbSCct QmUF9ey4dzyvtaKZQVc5QTVyN1uh5C8nqhzm5bDtAjMpUH QmQQsCU87GH58r3ULuJPn4a3DUUCqjRgtvTnrTgEzE32uB QmXo7j8hPUpwapnbFNNyHpSzJw8jxwrfGCZfVzhG6m46Fc QmWRUGR4iW5rnmLQnw9FgqKFSzKTya3pneRJvmK2VknwKJ QmRj8aGQBLtRqtiYJQreD9xtEMzqDcpaLPjFYLoe48xgQ5 QmceuRQeatSitbW6vADhod8yMXLWphJhT1uYZmcy4rjm6f QmewryoNvgmB7zLqV7RQ2PTLYkagYXvBASicFQi1ESPiHm QmViJLHdiRf7wrstUaHcTaXuiWpGyTkptFkDjYAFoJBJoj QmVzPu6Qip7yK3FGSsrMzEt3zNmqWufLFF5CZNmsVbHZLd QmYTFyk7SSEVeJPYyyFr91pb7fbKnpS4kiFjty9U136upV QmYKBd728JBm11x2JbtET9sF2KJXtKjGPDD1jVnpt7fLqz QmQba8m7JeAYTn4JDwkhe5nDZfnw9TnSASsQqLF7LBYEg2 QmT9Hh5LgzS2eg26pkvFLpdGLNAEURRLod8DffDCczhxy1 QmdEutfCAc7HzKtnLt7k7b2dajGSqfBSGnEPAuD2bontJM QmSuWrcnwPk5e1gVWiJbTq7uxUkNn8DzRVm659JmGTFR5W QmRDvU3Bb1mJHK7qGvaLg5kKvJ9tXx4qDntaaZU2EPXgnr QmXnPPSuiAbypBs2W4Hu14xEgjjptzNmzCptadFdRv7xt5 Qmed7VnZALGrUYrCRnPW72Zg4XmWFjZQUFe7BHLQ4EWp12 Qmak6N1wRPKAPf9DxMtCC9P4rZVS2rKi58Zcinr7iLRtd5 ╒═══════════════════ 𝐈𝐍𝐃𝐄𝐗 ═══════════════════════════════════════════════════╕ ⦿ Debian Expulsion Lies and Blackmail | Techrights ⦿ [Meme] Edge’s Edgy Security | Techrights ⦿ Totally Legit Gemini Search (TLGS), a Search Provider Just Announced for Gemini Space, Will Help Move More of Us Off the World Wide Web | Techrights ⦿ Video: Getting Off the Web and Away From Mozilla Firefox | Techrights ⦿ Check Your Inputs (Including Microphone) to Avoid Disaster | Techrights ⦿ IRC Proceedings: Tuesday, November 16, 2021 | Techrights ⦿ Bruce Schneier: Microsoft Edge is Apparently a Password Stealer Too, Even on GNU/Linux | Techrights ䷼ Bulletin articles (as HTML) to comment on (requires login): http://techrights.org/2021/11/17/debian-expulsion-lies-and-blackmail/#comments http://techrights.org/2021/11/17/edge-steals/#comments http://techrights.org/2021/11/17/firefox-and-totally-legit-gemini-search-tlgs/#comments http://techrights.org/2021/11/17/getting-off-the-web/#comments http://techrights.org/2021/11/17/glfer-in-action/#comments http://techrights.org/2021/11/17/irc-log-161121/#comments http://techrights.org/2021/11/17/microsoft-password-stealer/#comments ䷞ Followed by Daily Links (assorted news picks curated and categorised): http://techrights.org/2021/11/17/cockpit-257-released/#comments http://techrights.org/2021/11/17/oracle-linux-8-5/#comments http://techrights.org/2021/11/17/qubes-os-4-1-rc2/#comments ䷩ 𝚕𝚒𝚗𝚎 67 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2021/11/17/debian-expulsion-lies-and-blackmail/#comments Gemini version at gemini://gemini.techrights.org/2021/11/17/debian-expulsion-lies-and-blackmail/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.17.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Debian_Expulsion_Lies_and_Blackmail⠀✐ Posted in Debian, Deception at 6:02 pm by Guest Editorial Team By Daniel_Pocock Rogue members of the Debian ecosystem continue to spread untrue statements about expulsions. It is easy to prove these expulsions are not only untrue but also impossible. Debian is not an organization. Debian is simply a trademark. The US_trademark database_shows_the_trademark_is_registered_to_another_organization,_Software_in the_Public_Interest,_Inc. Most Debian Developers, myself included, have never been members of Software in the Public Interest, Inc. If we are not members and if we can not join, we can’t be expelled. Imagine making a movie and then removing the names of some people from the credits and putting other names in their place. Is that “expulsion”? Or is that simply stealing credit for somebody else’s work? Removing names from the list of Debian Developers is much like removing somebody’s name from the credits in a movie. It is wrong. █ ䷩ 𝚕𝚒𝚗𝚎 116 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2021/11/17/edge-steals/#comments Gemini version at gemini://gemini.techrights.org/2021/11/17/edge-steals/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.17.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ [Meme]_Edge’s_Edgy_Security⠀✐ Posted in Deception, Microsoft, Security at 6:24 pm by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Send_me_all_your_passwords_for_free_entry⦈_ Summary: Microsoft’s password_stealer is more of that old tradition of crushing real security and handing over all your data — even_passwords — to_the_NSA ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⠛⢻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣭⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣶⡸⣿⣿⢏⣶⢸⣿⠋⣿⡿⢛⣩⣹⣿⠛⣛⣹⡿⣛⣭⣛⢿⣿⢛⣭⣿⣿⠟⣫⣍⡛⣿⣏⢈⣙⣉⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣷⠙⠏⣼⣿⢸⣿⠀⣿⡇⣿⣿⣿⣿⠀⣿⣿⠀⣿⣿⣿⢈⣿⣦⣍⠻⣯⢸⣿⣿⡇⢸⣿⢸⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣧⣼⣿⣿⣼⣿⣤⣿⣷⣬⣭⣽⣿⣤⣿⣿⣷⣬⣭⣥⣾⣿⣭⣭⣴⣿⣦⣭⣭⣴⣿⣿⣼⣿⣿⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⣀⣠⣴⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡿⠋⠉⠉⠉⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢰⣦⠀⢹⣿⣿⣧⣤⣄⣠⣾⣦⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣡⣿⣿⡿⣿⣿⣿⣷⣿⠛⡛⠛⠓⠿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⠛⠁⠀⢀⣿⣿⣶⠲⣿⣿⠿⢿⠟⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡤⠄⠀⠀⠀⠀⠀⠀⠀⢀⣦⡈⠉⠘⠀⠉⠙⠻⠿⢵⣿⣿⠂⠀⠸⠿⣿⠃⢠⣾⣍⣁⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⠀⢠ ⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠓⠂⠀⣟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⡀⠀⠀⠀⠀⠀⠀⠻⠿⠃⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣧⣤⣴⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣤⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⠟⡙⣿⡿⣽⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⣿⣿⡇⢸⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣶⣆⠀⣼⡆⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣧⣼⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⠁⠀⢿⣦⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿ 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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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⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣤⣴⣶⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣿⣷⣀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠈⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡿⠿⠟⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢍⠭⠍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⠿⠛⠛⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣼⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣭⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⢠⣴⣶⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⣿⣿⣿ ⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣏⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠛⠟⠋⠉⣿⣿⣿⣷⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠿⠿⠙⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣴⣶⣶⣦⠀⣶⣶⣶⡆⣶⣶⠀⣶⡆⢰⣶⣶⣶⣄⠀⠀⢰⣶⣶⠀⣶⣶⡆⢰⣶⣶⡆⠀⠀⢰⣶⣶⣦⠀⣶⣶⠀⠀⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⣿⣧⣘⠛⠀⣿⣿⣀⡀⣿⣿⣇⣿⡇⢸⣿⡇⣿⣿⠀⠀⢸⣿⣿⣶⣿⣿⡇⢸⣿⣇⡀⠀⠀⢸⣿⢿⣿⠀⣿⣿⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣈⡻⢿⣷⡀⣿⣿⠛⠃⣿⡿⣿⣿⡇⢸⣿⡇⣿⣿⠀⠀⢸⣿⢹⣿⡇⣿⡇⢸⣿⡟⠃⠀⠀⣾⣿⣸⣿⡄⣿⣿⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣧⣼⣿⠇⣿⣿⣤⡄⣿⡇⢹⣿⡇⢸⣿⣧⣿⡿⠀⠀⢸⣿⠸⣿⠇⣿⡇⢸⣿⣧⣤⠀⠀⣿⣿⢻⣿⡇⣿⣿⣤⡄⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣷⡄⠉⠉⠁⠀⠉⠉⠉⠁⠉⠁⠈⠉⠁⠈⠉⠉⠉⠀⠀⡦⠌⠉⠀⠉⠀⠉⠁⠈⠉⠉⠉⠀⠈⠉⠉⠈⠉⠉⠉⠉⢉⣁⣉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿ ⡏⢠⣤⡄⣤⣤⢀⣤⣶⣦⣄⢠⣤⡄⢠⣤⡄⣤⣤⣤⣤⡀⠀⠀⣤⣤⣤⣤⠀⣤⣤⣤⡀⢀⣤⣶⣦⣄⢀⣤⣶⣦⣄⢠⣤⡄⣤⣤⡄⣤⣤⠄⣤⣴⣦⣄⠁⣤⣤⣤⣤⡀⣤⣤⣤⣤⡄⢀⣤⣶⣦⣄⢻⣿⣿⣿⣿⣿ ⣷⠈⣿⣧⣿⠇⢸⣿⡇⣿⣿⢸⣿⡇⢸⣿⡇⣿⣿⢸⣿⡇⠀⠀⣿⣿⢸⣿⡇⣿⡿⣿⡇⢸⣿⣇⠛⠛⢸⣿⣇⠛⠛⢸⣿⡇⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⡇⣿⣿⡏⣿⣿⢸⣿⣇⠛⠛⢠⣿⣿⣿⣿⣿ ⣿⡆⢸⣿⡿⠀⢸⣿⡇⣿⣿⢸⣿⡇⢸⣿⡇⣿⣿⢻⣿⡅⠀⠀⣿⣿⠿⠟⢱⣿⡇⣿⣧⠀⠙⠿⣿⣦⠀⠙⠿⣿⣦⠈⣿⣷⣿⢿⣧⣿⡿⢸⣿⡇⣿⣿⠀⣿⣿⢻⣿⡄⣿⣿⡇⣿⣿⠀⠙⢿⣿⣦⠘⣿⣿⣿⣿⣿ ⣿⡇⢸⣿⡇⠀⢸⣿⣇⣿⡿⠸⣿⣧⣼⣿⠁⣿⣿⢸⣿⡇⠀⠀⣿⣿⠀⠀⢸⣿⡟⣿⣿⠸⣿⣇⣿⣿⠸⣿⣇⣿⣿⠀⣿⣿⣿⢸⣿⣿⡇⠸⣿⣇⣿⣿⠀⣿⣿⢸⣿⡇⣿⣿⣧⣿⣿⢸⣿⣇⣿⣿⠀⣿⣿⣿⣿⣿ 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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 1918 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2021/11/17/firefox-and-totally-legit-gemini-search-tlgs/#comments Gemini version at gemini://gemini.techrights.org/2021/11/17/firefox-and-totally-legit-gemini-search-tlgs/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.17.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Totally_Legit_Gemini_Search_(TLGS),_a_Search_Provider_Just_Announced_for Gemini_Space,_Will_Help_Move_More_of_Us_Off_the_World_Wide_Web⠀✐ Posted in Free/Libre_Software at 11:45 am by Dr. Roy Schestowitz Video_download_link | md5sum 7eb4b3a6838dfa20f824d31556da50be http://techrights.org/videos/librewolf-and-tlgs.webm Summary: The state of the Internet isn’t great, but it’s a lot worse when it comes to the Web; it became a hub of spying and malicious activity, so in this video I explain why we’re moving away from Firefox and, where possible, embrace gemini:// as well THE World Wide Web is not in a healthy state. The committee which controls the World Wide Web is stacked by monopolies. It has gone_on_for_about_a_decade already and years ago they added DRM (EME) on top of it. Mozilla too went along with that agenda… In the video above I mostly discuss why I’m giving up on Mozilla; the ‘last straw’ or the breaking point was some time this month and it isn’t limited to Mozilla’s latest controversial ambition. It’s trying to relay (or grab) people’s mail (links [1-3] at the bottom). So at the start of the week both Ryan and I started documenting some essential facts and more of us in IRC started moving from Firefox to something else. We don’t typically use Firefox as a primary Web browser regardless, but why ever use it if Firefox is controlled by surveillance ogres? For that matter, I am truly concerned about Thunderbird, as the video above explains. It’s being gutted. There are no forks of it, so Mozilla still controls (or harms) millions of existing Thunderbird users (along with extension developers). Mozilla’s CEO, the Chef and Baker, didn’t think too highly of Thunderbird. She actually dismissed if not blasted Thunderbird about a decade back. She insinuated that people moving to Gmail is OK (spoiler: Google’s money pays her over 3 million dollars a year). She attacked the very concept of decentralised E-mail. Gmail is antithetical to it. She does not (or does not wish to) understand Thunderbird users. The way I see it, today’s Mozilla milks the “goodwill ambassador” status of Firefox (which the community advocated, free of charge, for the benefit of Mozilla Corporation) in the same way frauds and charlatans who run the Linux Foundation milk_"Linux" (which they do not even use!!!) to death… Why would you trust Mozilla with your E-mail? Of with your passwords? Of your browsing history? It handles bugs (by taking data from users), sure, but that’s for the technical staff, not the sales executives at Mozilla. They hired_from companies_like_Facebook and the_Board_includes_Microsoft (no wonder Mozilla increasingly acts like Microsoft’s slave [1, 2, 3]). The company is circling down the drain and now it (mis)uses Firefox as a brand to entice you to give them DNS queries (through partners), Internet traffic (VPN), and even your emails (Mozilla is spying_on_people; don’t be misled by the PR). I’ve had enough! “One noteworthy downside is that by default LibreWolf is very strict — even too strict by “Libre” standards — to the point of being unusable for most people.”Both my wife and I have migrated our data from Firefox to LibreWolf. Earlier today I nearly completed the migration and Ryan posted some tips last night [4]; applicable only for newer versions of Firefox, i.e. not the ESR in Debian (it lacks export option for passwords, for instance). One noteworthy downside is that by default LibreWolf is very strict — even too strict by “Libre” standards — to the point of being unusable for most people. And it defaults to a_Microsoft_'proxy'_for_search. Maybe we’ll do a HowTo related to this one day. Moreover, LibreWolf pretends to be “FirefoxDesktop on Windows” (or something to that effect) even when you use it on GNU/Linux, which means that Web statistics will inevitably give a false impression of Microsoft Windows being bigger than it actually is (not a new problem). I get to the main point of the video only in the last 5 minutes or so (the sound quality will improve as we_adapt_to_a_new_workflow). One hour before recording the video we found another new encouraging development in Gemini Space (or Geminispace). “After some testing by my friends and talking to René,” said_the_announcement around_1PM, “I’m excited to share my new search provider for the Gemini protocol, TLGS” (already quite good and accessible at gemini://tlgs.one). So far, based on some tests (e.g. searches_about_Techrights and Mozilla in the video above), the TLGS capsule/search engine works better than the other (existing) ones… Based on this_page, TLGS Search has indexed (for search) 80,000 pages so far… it’s a great start! “‘Fixing’ the World Wide Web is too ambitious an aspiration because once something enters the formal specifications/standards it’s very difficult to undo.”That’s quite a lot and it doesn’t include much cruft. We hope that a bunch of notable scandals, both large and small, will encourage people to reassess their choice of Web browsers and maybe explore a move to Gemini. There’s already a lot of good material there. No spying, no advertising, no affiliate marketing in links. Totally Legit Gemini Search (TLGS), as_per_its_site, “is an experimental search engine for contents served over the Gemini Protocol. It crawls and indexes textual contents that it encounters in the Geminispace. And provides a [sic] interface for people to look for what they need. The interface is heavly [sic] inspired by GUS and geminispace.info.” The World Wide Web was great in the 1990s. Then it was abused by Microsoft, it sort of recovered for a while (owing largely to Firefox), but now it seems beyond redemption. ‘Fixing’ the World Wide Web is too ambitious an aspiration because once something enters the formal specifications/standards it’s very difficult to undo. Tim Berners-Lee had a chance to say “No!” to DRM and other nasty stuff. But he missed that chance, wilfully… █ Related/contextual items from the news: 1. ⚓ Firefox_Relay_is_Now_Out_of_Beta_&_Adds_New_Premium_Plan_to_Help Protect_Your_Real_Email_Address_–_It’s_FOSS_News⠀⇛ Firefox Relay aims to help you protect your real email address by providing email aliases. While good options like Simplelogin, and AnonAddy already exists, Mozilla’s Firefox Relay can encourage more users to use email aliases. For a while, it was in the beta phase with limited access to features. Now, as per the official announcement, it is available for all users, out of beta, and introduces a premium plan to unlock all features. 2. ⚓ Support.Mozilla.Org:_Introducing_Firefox_Relay_Premium⠀⇛ If you’re a fan of Firefox Relay, you may have been waiting for the day when you can add more aliases. After a long wait, you can now celebrate because we’re launching Firefox Relay Premium today. As a refresher, Firefox Relay is a free service available at relay.firefox.com where you’ll get five email aliases to use whenever you sign-up for an online account. Today, Firefox Relay is launching as a premium subscription where you can unlock unlimited aliases and additional features. 3. ⚓ The_Mozilla_Blog:_Firefox_Relay_now_available_with_more_email_aliases with_Premium_service,_protecting_your_identity_and_email_addresses_from spammers⠀⇛ Today, Firefox Relay, a privacy-first and free product that hides your real email address to help protect your identity, is available with a new paid Premium service offering. The release comes just in time for the holiday season to help spare your inbox from being inundated with emails from e-commerce sites, especially those sites where you may shop or visit a few times a year. In real life you have a phone number where family and friends can call and reach out to you directly. You likely have it memorized by heart and it’s something you’ve had for years. In your online life your email address is like your phone number, it’s a personal and unique identifier. Your email address has become the way we login and access almost every website, app, newsletter, and hundreds of other interactions we have online every single day. That means your email address is in the hands of hundreds, if not thousands, of third parties. As you think more about your email address and the places it’s being used, Firefox Relay can help protect and limit where it’s being shared. Firefox Relay is a free service available at relay.firefox.com where you’ll get five email aliases to use whenever you sign-up for an online account. Over the last year, the team has been experimenting with Firefox Relay, a smart, easy solution that can preserve the privacy of your email address. Firefox Relay was initially rolled out to a beta phase for early adopters who like to test new products. We heard back from beta testers who provided feedback where we improved the free service and added a new paid Premium service that we’re introducing today. 4. ⚓ How_to_backup_your_passwords_from_Firefox_and_import_them_into_a_fresh copy,_or_LibreWolf,_without_Firefox_Sync.⠀⇛ Mozilla implemented support for importing CSV-formatted password lists generated by Firefox or other Web browsers, but it’s hiding by default. It’s fairly clear that Mozilla wants everyone to be pressured to create an account to use their Web browser. That way all of your browsing data is stored on a server you have no control over, and Mozilla may not either. (We don’t know if they farm this out to Clown Computing partners like Microsoft or Amazon.) To enable password import in Firefox or LibreWolf, type about: config into the address bar and hit enter, agree that you’ll be careful. Search for this entry: browser.bookmarks.addedImportButton Double click to make it True. Now you are able to import passwords in CSV format. You should be able to export passwords from another browser and into Firefox or LibreWolf (where there is no Firefox Sync, due to privacy reasons), without needing any pesky Sync servers. ䷩ 𝚕𝚒𝚗𝚎 2172 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2021/11/17/getting-off-the-web/#comments Gemini version at gemini://gemini.techrights.org/2021/11/17/getting-off-the-web/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.17.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Video:_Getting_Off_the_Web_and_Away_From_Mozilla_Firefox⠀✐ Posted in Free/Libre_Software at 12:21 pm by Dr. Roy Schestowitz Video_download_link | md5sum 24f4bd1a60c0d7e7cca1158d46ac8065 http://techrights.org/videos/web-alternatives-and-librewolf.webm Summary: The Web has gone too far and Mozilla is acting like little but a Microsoft/Google subsidiary; this is why over the past 1+ years we’ve divested and reduced focus on the Web, which for the time being ought to be accessed by community-led_projects (Mozilla Corporation doesn’t qualify as one) FURTHER to our_previous_post, we thought it would be worthwhile showing in the form of a video the sorts of settings one needs to adjust in LibreWolf after installing it, assuming a smooth migration from Mozilla Firefox is desirable. To be most frank, ultimately it will be a good idea to get off the Web, where possible (or to the extent feasible), in favour of something like Gemini Protocol. When browsers become merely a canvas to throw anything at (even megabytes of JavaScript frameworks with hundreds of net sockets) we’re basically recreating Adobe Trash (Flash), this time with a fake ‘standards’ consortium to usher it in, calling it “open” as if monoculture has legitimacy (all the major browsers are Chromium clones and Firefox is financially connected to Google; it helps give an illusion of fair competition). █ ䷩ 𝚕𝚒𝚗𝚎 2217 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2021/11/17/glfer-in-action/#comments Gemini version at gemini://gemini.techrights.org/2021/11/17/glfer-in-action/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.17.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Check_Your_Inputs_(Including_Microphone)_to_Avoid_Disaster⠀✐ Posted in Free/Libre_Software, GNU/Linux at 3:49 am by Dr. Roy Schestowitz Video_download_link | md5sum f0c1543d7b0c93f548668e77ec4e07dc http://techrights.org/videos/checking-the-microphone-input.webm Summary: It’s far too easy to lose audio data when it is not visible (while recording it), so we’ve embraced glfer YESTERDAY was the first time in a very long time (maybe half a year) that we lost work or lacked some sound in a recording. The protocols were meant to be robust, but if during a recording something happens to the sound it is hard to see it (visually). We we’ve decided to embrace or to move_to_adopt signal (such as microphone) visualisation software (spectrogram). It’s widely used in some studios which record extensively not for posing but for purely practical purposes. A lot of mistakes and accidents can be prevented this way. Hopefully yesterday was the very last time such an incident happened. In the video above I show the software as it appears on my desktop (Debian 10 with KDE). █ ䷩ 𝚕𝚒𝚗𝚎 2261 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2021/11/17/irc-log-161121/#comments Gemini version at gemini://gemini.techrights.org/2021/11/17/irc-log-161121/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.17.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ IRC_Proceedings:_Tuesday,_November_16,_2021⠀✐ Posted in IRC_Logs at 2:38 am by Needs Sunlight Also available via the Gemini protocol at: * gemini://gemini.techrights.org/tr_text_version/irc-log-techrights- 161121.txt * gemini://gemini.techrights.org/tr_text_version/irc-log-161121.txt * gemini://gemini.techrights.org/tr_text_version/irc-log-social-161121.txt * gemini://gemini.techrights.org/tr_text_version/irc-log-techbytes- 161121.txt Over HTTP: 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇HTML5_logs⦈_ #techrights_log_as_HTML5 #boycottnovell_log_as_HTML5 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇HTML5_logs⦈_ #boycottnovell-social_log_as_HTML5 #techbytes_log_as_HTML5 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇t 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇text_logs⦈_ #techrights_log_as_text #boycottnovell_log_as_text 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇t 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇text_logs⦈_ #boycottnovell-social_log_as_text #techbytes_log_as_text Enter_the_IRC_channels_now =============================================================================== § IPFS Mirrors⠀➾ CID Description Object type IRC log for  QmSKAE2m3WA9pjvfYQ7SCxdAxTGakQGSAcPp5YonH3J9JX #boycottnovell 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #boycottnovell  QmWWumJRtgYZFGgtiDNJ1ewxD1aHav4agFAeSrBhFUxy2r (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ as plain/ASCII text) IRC log for #boycottnovell-  Qmda7t9AFatxyNEDTZJcMnKU96JwwAeknk5k7NXqqhRbYB social 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #boycottnovell-  QmNzCxLVwJF8SRwBiJuMu5KMLHSFk4LBVpGjXUXXyWTZMD social 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ (full IRC log as plain/ASCII text) IRC log for  QmdYhHgk2aTi9PHK1ikkrtBSsrBBqzW3sc7QecQ5agV6dm #techbytes 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #techbytes  QmVRCKkyLge9pWzxF9PRj98DFH68n8gFx77hmT71WrGtF4 (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ as plain/ASCII text) IRC log for  QmdXgdLESwxKdWZSHWVZ46oYBHxnJ7aHSeRMNFugGCR1U8 #techrights 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #techrights  QmdQti8T4jjVyWmk5Z4oWN2Qiis84C2J89zpANirF7yiLA (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ as plain/ASCII text) 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈ § Bulletin for Yesterday⠀➾ Local_copy | CID (IPFS): QmcNLdXKwxdD6cLvdgRCUDzCTD4PfjtBzdq6btKA1VdHeD ䷩ 𝚕𝚒𝚗𝚎 2390 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2021/11/17/microsoft-password-stealer/#comments Gemini version at gemini://gemini.techrights.org/2021/11/17/microsoft-password-stealer/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.17.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Bruce_Schneier:_Microsoft_Edge_is_Apparently_a_Password_Stealer_Too,_Even_on GNU/Linux⠀✐ Posted in GNU/Linux, Microsoft, Security at 1:43 pm by Guest Editorial Team Guest post by Ryan, reprinted with permission from the_original Bruce Schneier: Microsoft_Edge_is_apparently_a_password_stealer_too,_even_on GNU/Linux. According to people who have contacted Bruce Schneier, Microsoft Edge is a password stealer on top of all of the other nasty things it does (It’s_as private_as_a_dodgy_browser_from_a_Russian_search_engine,_as_I_discussed yesterday.). Mr. Schneier added that Microsoft Edge encourages the user to also add their passports and other sensitive documents and trust the company with all of the major security breaches in personal and “cloud” computing with those too. █ ䷩ 𝚕𝚒𝚗𝚎 2429 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.17.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Links_17/11/2021:_Brave_Does_Digital_Currencies,_Cockpit_257_Released⠀✐ Posted in News_Roundup at 6:41 am by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈ § Contents⠀➾ * GNU/Linux o Distributions o Devices/Embedded * Free_Software/Open_Source * Leftovers * § GNU/Linux⠀➾ o § Desktop/Laptop⠀➾ # ⚓ Phytium_D2000:_Mini_PC_with_Chinese_eight-core_processor and_Radeon_GPU⠀⇛ Basically, some Linux distributions such as Ubuntu Kylin, OpenSUSE or Debian run on the PC. The x86-64 emulator Box86, possibly with the Windows-to-Linux translator Wine, enables games that would otherwise not run on ARM CPUs. o § Kernel Space⠀➾ # ⚓ Google_Proposes_“Page_Table_Check”_For_Fighting_Some_Types Of_Linux_Memory_Corruption_–_Phoronix⠀⇛ Last week Google engineers uncovered a reference count underflow issue affecting all Linux kernels going back to v4.14 in 2017. This issue led to memory leaking from one process to another and only uncovered by accident. To address this class of memory corruption issues moving forward, Google is proposing a new “Page Table Check” feature moving forward. o § Instructionals/Technical⠀➾ # ⚓ How_to_design_a_business_card_with_Inkscape⠀⇛ A new design is needed for a business card with a company logo, the person’s name, job title, email and phone contacts, as well as the company name and address. In this article you will learn how to install Inkscape, how to create a new document, design a simple logo, type texts, and how to lay out the logo and the text to finalize the card. # ⚓ How_to_backup_your_passwords_from_Firefox_and_import_them into_a_fresh_copy,_or_LibreWolf,_without_Firefox_Sync.⠀⇛ Mozilla implemented support for importing CSV- formatted password lists generated by Firefox or other Web browsers, but it’s hiding by default. It’s fairly clear that Mozilla wants everyone to be pressured to create an account to use their Web browser. That way all of your browsing data is stored on a server you have no control over, and Mozilla may not either. (We don’t know if they farm this out to Clown Computing partners like Microsoft or Amazon.) To enable password import in Firefox or LibreWolf, type about:config into the address bar and hit enter, agree that you’ll be careful. Search for this entry: browser.bookmarks.addedImportButton Double click to make it True. Now you are able to import passwords in CSV format. You should be able to export passwords from another browser and into Firefox or LibreWolf (where there is no Firefox Sync, due to privacy reasons), without needing any pesky Sync servers. # ⚓ How_to_add_Brave_Search_to_GNOME_Web_and_switch_from DuckDuckGo⠀⇛ How to add Brave Search to GNOME Web and switch from DuckDuckGo. In this article, we explore Brave Search. A new search engine from the company that makes the Brave Web browser. Perhaps you hop around browsers like I do and want to use Brave Search in GNOME Web, but all you get when you ask Brave how to add it is this. # ⚓ How_to_Integrate_ONLYOFFICE_Docs_with_Alfresco_on_Ubuntu⠀⇛ If your team and you work with content a lot, it might be a good idea to use an ECM (Enterprise Content Management) system. Taking into consideration a vast array of available solutions, it’s very difficult to choose the right tool for your purposes and needs. One of the best software tools in this category is Alfresco. Using it, you can easily store and collaborate on content with your teammates. In this guide, you will learn how to enable document editing within Alfresco with the help of ONLYOFFICE Docs. # ⚓ How_to_Install_Latest_LAMP_Stack_in_RHEL-based Distributions⠀⇛ If you are a system administrator, a developer, or a DevOps engineer, chances are that at some point you’ve had to set up (or work with) a LAMP (Linux / Apache / MySQL or MariaDB / PHP) stack. The web and database servers, along with the well- known server-side language, are not available in their latest versions from the major distributions’ official repositories. If you like to play or work with cutting-edge software, you will need to either install them from a source or use a third-party repository. # ⚓ How_to_Monitor_Docker_Containers_with_Zabbix_Monitoring Tool⠀⇛ Docker is arguably one of the most cherished DevOps tools that streamline the development, deployment, and shipping of applications inside containers. The concept of containerization entails leveraging container images. These are small, lightweight, and standalone executable packages that include everything that is needed to run an application including the source code, libraries and dependencies, and configuration files. By doing so, the application can run in almost any computing environment; traditional IT infrastructure, cloud, and a myriad of Linux / UNIX flavors. o § Games⠀➾ # ⚓ Nvidia’s_new_open_source_upscaling_SDK_could_benefit_AMD gamers_as_much_as_its_own⠀⇛ Nvidia’s image scaling and sharpening feature, Nvidia Image Scaling, has been updated today to improve performance and image quality. Though there’s more here of interest to gamers, even AMD ones. This upscaling feature is also being made open-source and cross-platform, meaning it could soon play nicely with AMD and Intel GPUs. o § Desktop Environments/WMs⠀➾ # § GNOME Desktop/GTK⠀➾ # ⚓ 50,000_rules_is_not_enough_for_Safari_Content Blockers_and_I’m_not_hopeful_that_the_situation_will improve_for_GNOME_Web,_despite_“WebExtensions” coming.⠀⇛ GNOME Web uses WebkitGTK, which is basically an improved version of the one that Safari has. (No DRM modules and support for open media codecs.) However, it has some of the same limitations. One of these is using Content Blockers for the ad blocking. GNOME Web previously had one that was much, much worse, and caused many bugs, and ate RAM like it was going out of style, and was only partially compatible with Adblock Plus. So deleting it out of the browser and moving to use Webkit Content Blockers was a win by that measure. However, Apple is such a piece of shit company that they designed the scheme so that you’re limited to 50,000 rules. To put that in perspective, in most of my browsers, I have twice that many, and no, they don’t slow the browser down at all, because uBlock- Origin is efficient. o § Distributions⠀➾ # § IBM/Red Hat/Fedora⠀➾ # ⚓ Fedora_Community_Outreach_Revamp_–_Halloween_Update⠀⇛ The Fedora Community Outreach Revamp (FCOR) has been underway since summer of 2020. The co-leads, Mariana Balla and Sumantro Mukherjee, along with Marie Nordin, set out to repair broken bridges around Fedora’s outreach. We have made significant steps as a team towards completing the deliverables set out in the Fedora Objective. We are hoping to wrap things up in the next six months. As we move towards the close of 2021, we want to share the latest work that we have accomplished. # ⚓ Friday’s_Fedora_Facts:_2021-45⠀⇛ Here’s your weekly Fedora report. Read what happened this week and what’s coming up. Your contributions are welcome (see the end of the post)! Fedora Linux 33 will reach end of life on Tuesday 30 November. Nominations for the F35 elections cycle are now open. # ⚓ Fedora_Linux_36_wallpaper_brainstorming!⠀⇛ That’s right!!! We are officially ready to start brainstorming for Fedora 36 Wallpaper ideas because our candidate with a K last name has been chosen (drum roll please) and it’s Deepika Kurup! Ideas and progress are going to be documented on Design issue 789. If you want to help us brainstorm an approach, join us at 1830 UTC Wednesday in #fedora-design on Matrix. # ⚓ Contribute_at_the_Fedora_Linux_36_Test_Week_for Kernel_5.15_–_Fedora_Community_Blog⠀⇛ The kernel team is working on final integration for kernel 5.15. This version was released just recently and will arrive soon in Fedora. As a result, the Fedora kernel and QA teams have organized a test week from Sunday, November 14, 2021 through Sunday, November 21, 2021. Refer to the wiki page for links to the test images you’ll need to participate. Read below for details. # ⚓ Contribute_at_the_Fedora_Linux_36_Test_Week_for Kernel_5.15⠀⇛ The kernel team is working on final integration for kernel 5.15. This version was just recently released, and will arrive soon in Fedora. As a result, the Fedora kernel and QA teams have organized a test week from Sunday, November 14, 2021 through Sunday, November 21, 2021. Refer to the wiki page for links to the test images you’ll need to participate. Read below for details. # ⚓ CPE_Weekly_Update_–_Week_of_November_08th_–_12nd⠀⇛ # ⚓ Call_for_F36_Test_Days_–_Fedora_Community_Blog⠀⇛ It’s time to start thinking about Test Days for Fedora Linux 36. A Test Day is an event aimed getting together interested users and developers to test a specific feature or area of the distribution. You can run a Test Day on just about anything for which it would be useful to do some fairly focused testing in ‘real time’ with a group of testers; it doesn’t have to be code. For instance, we often run Test Days for l10n/i18n topics. For more information on Test Days, see the wiki. # ⚓ Cockpit_257⠀⇛ Formerly, cockpit-tls, the process responsible for handling encryption on HTTPS connections to cockpit, would directly read the certificate file for itself. This required the private key file to be owned by the cockpit-ws user (or group) that this process ran as. Users sometimes want to share the same key file with several different services, making this arrangement awkward. It also required additional configuration steps in the case of automatically-issued certificates. Cockpit now reads the certificate and key files as the root user, allowing them to be installed with any set of permissions. # ⚓ Fedora_Community_Blog:_Upcoming_Mindshare_Committee Election:_What_to_know⠀⇛ We released Fedora Linux 35 and that means it’s time for the elections for various governing bodies in Fedora. This includes the Mindshare Committee. One seat is open on the Committee this election to serve two release cycles (one year). We invite you to vote in the upcoming Mindshare Committee election, and even run for the seat if you are inspired! Participating on the Mindshare Committee takes 1-3 hours weekly, as well as the expectation that you will attend any face-to-faces (virtual or in-person) if possible. This is an opportunity to support the Fedora Project in an organizational capacity, and you don’t need a lot of experience. Each Fedoran’s perspective is valuable to the work that Mindshare does. We would love to have you be a part of the Committee. Maybe you know someone who wants to be more involved in Fedora and would be a good fit. Make sure to get consent from the nominee if you decide to nominate someone. If you or someone you know is interested in running, add those names to the Mindshare Election wiki page. The Election Wrangler will reach out to you with next steps. # ⚓ Remi_Collet:_Enterprise_Linux_9_Repository⠀⇛ Red Hat Enterprise Linux 9 Beta is released and CentOS 9 Stream is available, so my repository is already open and (mostly) fully populated. As EPEL is not yet ready, for now you have to enable “remi” repository which provides lot of packages usually available in EPEL. o § Devices/Embedded⠀➾ # § Open Hardware/Modding⠀➾ # ⚓ ESP32-POE_and_ESP32-POE-ISO_back_in_stock⠀⇛ We are glad that this week we shipped all backlog orders and now the boards are again for sale! # ⚓ STMP157-OLinuXino-LIME2_Open_Source_Hardware Industrial_Grade_Linux_computer_is_in_mass_production with_4_variants⠀⇛ STMP157-OLinuXino-LIME2 Open Source Hardware Linux computer running Mainline Linux is in mass production in four variants: [...] # ⚓ Raspberry_Pi_3_vs_4:_Which_One_Should_You_Get?⠀⇛ Raspberry Pi is an inexpensive single-board computer useful for many things. And, until Raspberry Pi 4, it was not an impressive option as a quick desktop replacement. So, yes, Raspberry Pi 4 changed the game with its new capabilities. But, how does it compare to Raspberry Pi 3? Is Raspberry Pi 3 still worth considering? Or, should you go for the latest and greatest Raspberry Pi 4? In this article, we try to get you some answers to that by highlighting some key differences between the two. First, let us look at the specifications both offer. # ⚓ Hacking_a_USB_battery_bank_to_gather_telemetry_| Arduino_Blog⠀⇛ USB battery banks are a dime-a-dozen and useful for recharging all of those devices in your life. But the typical cheap battery banks don’t provide you with much information about their status. You usually just get a few LEDs that provide a very general idea of how much battery life remains. Keenan Johnson needed more info for an upcoming project and so he hacked a USB battery bank to gather telemetry. The most useful data about a USB battery bank is its voltage at any given time, which tells you approximately how much longer the batteries will last. But there is other telemetry that Johnson wanted to have, including the charging current and output current. This USB battery bank contains an HT66F018 microcontroller to monitor the battery cells and control charging/ discharging, but it runs custom firmware and doesn’t make the telemetry accessible through a standard interface like I2C or SPI. # § Mobile Systems/Mobile Applications⠀➾ # ⚓ The_best_Android_apps_in_2021⠀⇛ # ⚓ 5_Android_settings_to_change_immediately_to_get_more out_of_your_phone_–_CNET⠀⇛ # ⚓ An_Android_user_can_now_use_their_smartphone_to_get applications_onto_some_of_their_TVs_–_NotebookCheck.net News⠀⇛ # ⚓ Nasty_new_Android_malware_cleaning_out_bank_and crypto_accounts_|_Tom’s_Guide⠀⇛ # ⚓ Google_Classroom_for_Android_gets_offline_mode,_and more_–_9to5Google⠀⇛ # ⚓ A_Japanese_toaster_company_makes_the_most_unique Android_phone_of_the_year_|_Ars_Technica⠀⇛ # ⚓ Android_fast_charging_is_leaving_iPhones_in_the dust⠀⇛ # ⚓ How_To_Create_&_Set_A_Reminder_Directly_From_An Android_Notification⠀⇛ # ⚓ PS5_DualSense_support_comes_to_Android_12_– 9to5Google⠀⇛ # ⚓ Android_12L_will_arrive_in_the_first_half_of_2022⠀⇛ # ⚓ Nokia_Mobile_releases_new_Android_11_build_for_Nokia 5.4_with_October_Security_update_–_Nokiapoweruser⠀⇛ o § Free, Libre, and Open Source Software⠀➾ # § Web Browsers⠀➾ # § Chromium⠀➾ # ⚓ Brave_embeds_a_cryptocurrency_wallet_right_in the_browser⠀⇛ Brave version 1.32 includes a dedicated wallet built right into the browser, in which users can store their private keys for various cryptocurrency holdings. (Read our review of Brave 1.0.) The company claims that the direct integration is more secure than a third-party browser plugin, but also allows users to connect with hardware wallet devices like Trezor and Ledger. Brave’s wallet also provides real-time market information as well as the ability to buy and pay via various cryptocurrencies. * § Leftovers⠀➾ o ⚓ In_Resemblance_of_the_Living⠀⇛ Alone I spirit myself away looking at the many flowers born on the balcony, certainly not thanks to me, the gardener was the wind. They skin me with precision, their beauty sinks in with the same noble knife used by the missing. I remember your laughter whirling all around when I confessed that flowers frighten me. Mine is a young pain, it’ll take patience, waiting as the bird at the edge of a field just barely sown. I loved you with a human love, like taking off one’s clothes at night and putting them back on in the morning. Now in these boundless days I write you an invisible letter to tell you there’s a wonderful path a pearl that goes rolling fast down a tree-lined avenue towing lightness with it, towing wakefulness. o ⚓ You_Couldn’t_Lose_Me⠀⇛ It was like waking up in California— the awkward blossoms, the sky an aggressive blue. I remember the smell from your armpits, the greenhouse windows covered in white paint, where the air was heavy. The silver weeds. A small herd of farm animals at the Agricultural College wore the field to dust. The wind was hot and fresh on our faces. The donkey looked so dumb trying to walk. It was simple: Beneath your shirt was skin. I remember that first year, pulling your briefs from the hamper. o ⚓ PBS_Taps_Maribel_Lopez_to_Lead_Digital_Studios⠀⇛ PBS has hired Maribel Lopez, an executive producer and managing director at a PBS member station in Minnesota, to lead its digital studios, which produces original and short-form content on social platforms like YouTube. Lopez begins on December 13 and replaces Brandon Arolfo, who exited PBS earlier this year to join Travel + Leisure as vp creative and content. Lopez will join PBS from Twin Cities PBS, where she is the executive producer of Sound Field, a music education series on YouTube that is produced for PBS Digital Studios, and the managing director of Racism Unveiled, a multimedia storytelling project that explores racism in Minnesota. o § Education⠀➾ # ⚓ Our_math_skills_are_keeping_us_from_bigger,_juicier burgers⠀⇛ As QSR Magazine explains, back in the 1980s when the McDonald’s Quarter Pounder was the burger to beat, A&W had the great idea to debut a 1/3 Pound Burger at the same price as a Quarter Pounder. More meat for your dollar—what could go wrong? Unfortunately, the burger was a total flop, for reasons that A&W didn’t see coming. In focus groups following the disastrous launch of the 1/3 Pound Burger, customers indicated that they thought 1/ 3 pound of meat was smaller than 1/4 pound, because 4 is a bigger number than 3. So people considered the burger a rip-off, not a deal. A&W, perhaps embittered by the hard-learned lessons of the past, is still stuck on winning Americans over with a big, juicy burger. So it has decided to rebrand the 1/3 Pound Burger in a way that Americans of all math skill levels will be drawn to: the 3/9 lb. Burger. # ⚓ ‘Democracy_in_freefall’_at_Australian_universities⠀⇛ The Greens say the combination of federal and state legislation and “active steps” by university management has left staff and students with little say in decisions that affect them. Such decisions have been outsourced to “a small group of unelected senior managers” and governing body appointees who “have entrenched a corporate university model”. “The collapse of democracy on university campuses has had devastating consequences for staff and students,” Dr Faruqi said. “Funding cuts, fee hikes, systemic wage theft and rampant casualisation have all followed. # ⚓ Progressives_Can_No_Longer_Cede_School_Boards_to_the_GOP⠀⇛ In 1996, conservative Christian activist Ralph Reed declared, “I would rather have a thousand school board members than one president and no school board members.” As today’s school board meetings devolve into screaming matches and fistfights over mask requirements, vaccine mandates, and anti- racist curriculums, conservatives are once again growing their influence within one of the most underrated power structures in American politics. # ⚓ Cubans_Say_They_Are_More_Excited_About_School_Reopening Than_Regime_Change⠀⇛ “If you build it, they will come,” said Kevin Costner in the Field of Dreams. In Cuba, they didn’t come. Dissidents on the island, with their U.S. backers, had been working feverishly for months to turn the unprecedented July 11 protests into a crescendo of government opposition on November 15. They built a formidable structure, with sophisticated social media (including an abundance of fake news), piles of cash from Cuban Americans and the U.S. government, and declarations of support from a bipartisan Congress and all the way up to the White House. o § Hardware⠀➾ # ⚓ Blacksmith⠀⇛ We demonstrate that it is possible to trigger Rowhammer bit flips on all DRAM devices today despite deployed mitigations on commodity off-the- shelf systems with little effort. This result has a significant impact on the system’s security as DRAM devices in the wild cannot easily be fixed, and previous work showed real-world Rowhammer attacks are practical, for example, in the browser using JavaScript, on smartphones, across VMs in the cloud, and even over the network. o § Health/Nutrition/Agriculture⠀➾ # ⚓ The_FDA’s_Lax_Oversight_of_Research_in_Developing_Countries can_do_Harm_to_Vulnerable_Participants⠀⇛ My study highlighted loopholes in the agency’s oversight processes that exploited vulnerable people and led to faulty data for drug approval decisions. Until the early 2000s, participants in FDA-reviewed research trials came almost entirely from the U.S. But a 2010 report from the Department of Health and Human Services found that 78% of research participants were enrolled overseas. Faster research subject recruitment and lower expenses – paired with these regulatory loopholes – seem to be driving this shift. It isn’t clear how often these gaps allow problematic trials to slip through the system, because trials that go wrong can simply not be disclosed, and there are virtually no on-site inspections. # ⚓ Massive_COVID_Surge_Rattles_Europe,_Putting_US_at_Risk Ahead_of_Thanksgiving⠀⇛ # ⚓ One_Major_Reason_the_U.S._Hasn’t_Stopped_Syphilis_From Killing_Babies⠀⇛ In public health, a “sentinel event” is a case of preventable harm so significant that it serves as a warning that the system is failing. The alarms are now blaring. A growing number of babies are being born with syphilis after their mothers contract the sexually transmitted disease and the bacteria crosses the placenta. These cases are 100% preventable: When mothers who have syphilis are treated with penicillin while pregnant, babies are often born without a trace of the disease. But when mothers go untreated, there is a 40% chance their babies will be miscarried, be stillborn or die shortly after birth. Those who survive can be born with deformed bones or damaged brains, or can suffer from severe anemia, hearing loss or blindness. # ⚓ US_and_UK_Press_Mock_New_Zealand’s_Incredibly_Successful Covid_Response⠀⇛ When New Zealand’s Prime Minister Jacinda Ardern announced the country’s transition away from its coronavirus elimination strategy, also known as “zero-Covid,” US and British media outlets framed the decision as a recognition of the inevitable failure of an irrational goal. # ⚓ Millions_of_Afghans_Face_Starvation_as_US_and_the_West Freeze_Government_Funds⠀⇛ # ⚓ “Hell_on_Earth”:_Millions_of_Afghans_Face_Starvation_as U.S._&_West_Freeze_Billions_in_Gov’t_Funds⠀⇛ Humanitarian and economic conditions are rapidly deteriorating in Afghanistan, where the U.N. estimates that more than half of the population suffers from acute hunger. The country has fallen into an economic crisis after the U.S. and other Western countries cut off direct financial assistance to the government following the Taliban takeover in August. Taliban leaders are also unable to access billions of dollars in Afghan national reserves that are held in banks overseas. “Forty million civilians were left behind when the NATO countries went for the door in August,” says Jan Egeland, secretary general of the Norwegian Refugee Council, who recently visited Afghanistan and with refugees in Iran, where as many as 5,000 Afghans are fleeing everyday. “They told me very clearly, ‘We believe we will starve and freeze to death this harsh winter unless there is an enormous aid operation coming through.’” # ⚓ ‘Reckless’_FDA_and_Big_Pharma_Greed_Blamed_for_Medicare Premium_Hike⠀⇛ Medicare Part B recipients will soon be hit with one of the biggest premium increases in the history of the government program, a hike driven in large part by the Food and Drug Administration’s scandalous approval of a costly—and, according to many experts, dubious—Alzheimer’s drug. “Medicare’s inability to negotiate lower drug prices means that Big Pharma companies can charge whatever they want.” # ⚓ Amazon_to_Pay_CA_$500K_After_Being_Accused_of_Breaking COVID_Workplace_Rules⠀⇛ # ⚓ Elizabeth_Warren_Urges_Biden_to_Free_People_Imprisoned_on Marijuana_Charges⠀⇛ # ⚓ Why_Biden_Should_Legalize_Marijuana_Right_Now⠀⇛ # ⚓ Two_‘forever_chemicals’_more_toxic_than_previously_thought: EPA_drafts⠀⇛ The drafts found the safe levels of ingestion for chemicals perfluorooctanoic acid (PFOA) and perfluorooctanesulfonic acid (PFOS) are much lower than the agency had found in prior assessments. The agency also found that PFOA is “likely” carcinogenic to humans. This is a step up from before, as it has previously said that there is “suggestive” evidence that the substance can cause cancer. o § Integrity/Availability⠀➾ # § Proprietary⠀➾ # ⚓ On_the_recent_vulnerability_in_Diebold_Nixdorf_ATMs⠀⇛ First of all, it should be said that the firmware is encrypted with keys that are known only to the vendor. An attacker can exploit the vulnerabilities described by Positive Technologies (one in each device) to upload firmware to the dispenser without knowing the encryption keys (they will be mentioned below as KEY0 and KEY1). That is, having a clean code, an attacker can modify it however he likes, encrypt it again, upload it to the ATM, and then withdraw cash bypassing the existing USB traffic encryption algorithms. Well, now let’s move on to the details… # ⚓ Convictions_of_eight_former_subpostmasters_in Scotland_under_review⠀⇛ About 60 former subpostmasters in England, Wales and Northern Ireland convicted of theft and false accounting have already had their convictions overturned, including 39 in a landmark Court of Appeal hearing in April this year. There are likely to be many more. Between 2000 and 2015, 736 were convicted of crimes based on evidence from the faulty Horizon system. # ⚓ Post_Office_board_‘appalling’_and_‘short-sighted’, said_minister_researching_Horizon_project_in_2000⠀⇛ A government minister researching the Horizon project in 2000 said that, given the choice, he would have sacked the entire Post Office board. The Horizon project saw the Post Office branch network computerised, but the system led to subpostmasters being wrongly blamed and even imprisoned because of unexplained accounting shortfalls that were actually caused by software errors. # ⚓ Post_Office_Horizon_IT_Inquiry_demands_more evidence⠀⇛ The Post Office Horizon IT Inquiry took place in London on Monday 8 November. Chaired by Sir Wyn Williams, the process’ aim is to provide a public summary of the failings which occurred with the Horizon IT system at the Post Office leading to the suspension, termination of subpostmasters’ contracts, prosecution and conviction of subpostmasters. The Inquiry had been made statutory earlier this year in light of the quashing of sentences of subpostmasters who had been wrongly convicted due to errors made by the Horizon system. # ⚓ New_malware_‘SharkBot’_attacking_banking_apps_on Android_phones⠀⇛ New Delhi, Cybersecurity researchers have discovered a new Android Trojan that can circumvent multi-factor authentication on banking apps on smartphones, putting users’ financial data and money at risk. Called ‘SharkBot’, the Android malware has been found in attacks across Europe and the US, focused on stealing funds from mobile phones running the Google Android operating system. # § Security⠀➾ # § Privacy/Surveillance⠀➾ # ⚓ Podcast_Episode:_What_Police_Get_When They_Get_Your_Phone⠀⇛ # ⚓ EU’s_Latest_Internet_Regulatory_Madness: Destroying_Internet_Security_With_Its Digital_Identity_Framework⠀⇛ The EU is at it again. Recently Mozilla put out a position paper highlighting the latest dangerous move by busybody EU regulators who seem to think that they can magically regulate the internet without (1) understanding it, or (2) bothering to talk to people who do understand it. The issue is the Digital Identity Framework, which, in theory, is supposed to do some useful things regarding interoperability and digital identities. This could be really useful in enabling more end user control over identity and information (a key part of my whole Protocols, Not Platforms concept). But the devil is in the details, and the details are a mess. # ⚓ Google_Allegedly_Boasted_of_Slowing_Down and_Delaying_ePrivacy_Regulation,_Accused of_Colluding_with_Facebook⠀⇛ The amended complaint now includes 17 states. Its 173 pages offer one of the best descriptions of how the online advertising model works, and how deeply embedded Google is in every aspect of the system. Of particular interest to readers of this blog are some fairly stunning allegations about Google’s attempts to limit protection for its users’ privacy. For example, one section claims: # ⚓ Meta_and_Microsoft_move_to_tie_Workplace and_Teams_closer_together⠀⇛ Although the two companies compete in a variety of ways (Microsoft’s Viva Connections also provides social network capabilities, for instance, and both recently unveiled competing visions for immersive collaboration) Wednesday’s move is an acknowledgement that many customers now rely on a range of tools to support employee collaboration. # ⚓ EU_snooping_laws_could_see_YOUR_private messages_being_read_–_stark_warning⠀⇛ Even though the new proposals are only intended to affect individuals living in the EU, as many chat services are worldwide, the “obligation” placed on service providers may extend to “all users”, Patrick Breyer, a Pirate Party MEP and privacy campaigner, told the Express. # ⚓ Facebook’s_Algorithm_Is_Broken._We Collected_Some_Spicy_Suggestions_On_How_To Fix_It.⠀⇛ If the algorithm is to blame, can Facebook change the algorithm to make it better? What would that look like? To find out, I interviewed 12 leading experts on data and computer science, as well as former Facebook employees, and asked them to propose changes that could help the algorithm suck less. What I got was a range of ideas about how Facebook could start to solve this problem, or whether a solution is even possible. Some are more radical than others, so I’ve categorized these ideas from mild to spicy (though we know Facebook CEO Mark Zuckerberg prefers it sweet). # ⚓ Apple_“Privacy”._Safari_sends_32_requests to_Google_and_Apple_servers_because_you typed_a_5_letter_word_in_the_address_bar.⠀⇛ “Safari sends typed text both to a Google server clients1.google.com and to an Apple server api-glb- dub.smoot.apple.com. Data is initially sent to both every time a new letter is typed, although transmission to clients1.google.com stops shortly after the first word “leith” is complete. The result is 7 requests to clients1.google.com and 25 requests to api-glb- dub.smoot.apple.com, a total of 32 requests” # § Confidentiality⠀➾ # ⚓ Ninth_Circuit_Tells_NSO_Group_It Isn’t_A_Government,_Has_No_Immunity From_WhatApp’s_Lawsuit⠀⇛ Long before its current run of Very Bad News, Israeli malware purveyor NSO Group was already controversial. Investigations had shown its exploits were being used to target journalists and activists and its customer list included governments known mostly for their human rights abuses. o § Defence/Aggression⠀➾ # ⚓ Refugees_Face_Tear_Gas,_Water_Cannons_as_Violence_Escalates at_Poland-Belarus_Border⠀⇛ A group of migrants trapped in freezing conditions at the Belarus-Poland border faced water cannons and tear gas by Polish border guards on Tuesday amid an ongoing humanitarian and political crisis. Polish forces put the blame for the violence, which took place near the Bruzgi-Kuznica border crossing, on some of the thousands of migrants throwing objects. # ⚓ U.S._and_Its_Allies_Are_Fueling_Worldwide_Erosion_of Democracy,_Analysis_Shows⠀⇛ “Much of the world’s backsliding is not imposed on democracies by foreign powers, but rather is a rot rising within the world’s most powerful network of mostly democratic alliances.” # ⚓ Let’s_Stop_Handing_the_Pentagon_Blank_Checks⠀⇛ Even as Congress moves to increase the Pentagon budget well beyond the astronomical levels proposed by the Biden administration, a new report from the Congressional Budget Office (CBO) has outlined three different ways to cut $1 trillion in Department of Defense spending over the next decade. A rational defense policy could yield far more in the way of reductions, but resistance from the Pentagon, weapons contractors, and their many allies in Congress would be fierce. # ⚓ Opinion_|_America’s_Terrible_God_Is_a_Weapons-Maker⠀⇛ Who is America’s god? The Christian god of the beatitudes, the one who healed the sick, helped the poor, and preached love of neighbor? Not in these (dis)United States. In the Pledge of Allegiance, we speak proudly of One Nation under God, but in the aggregate, this country doesn’t serve or worship Jesus Christ, or Allah, or any other god of justice and mercy. In truth, the deity America believes in is the five-sided one headquartered in Arlington, Virginia. # ⚓ Historian_Alfred_McCoy_Predicts_the_U.S._Empire_is Collapsing_as_China’s_Power_Grows⠀⇛ President Joe Biden’s virtual summit Monday with Chinese President Xi Jinping follows the two countries’ announcement just days earlier they will work together to confront the climate emergency after Xi did not attend the U.N. climate summit in Glasgow. Tension has been mounting between the two superpowers, especially over Taiwan and Hong Kong, with some speculating that a new Cold War is developing. “The United States, in the immediate future, is faced with the possibility of fighting a war over Taiwan … that it would probably lose,” says Alfred McCoy, professor of history at the University of Wisconsin-Madison in an extended interview about U.S.-China relations. “China is also working to break the U.S. geopolitical hold over the Eurasian landmass.” McCoy is a prolific author and his newest book is out today: “To Govern the Globe: World Orders and Catastrophic Change.” # ⚓ German_project:_Drones_for_non-governmental_maritime rescue⠀⇛ Searchwing has developed a waterproof drone that can be hand-launched from a ship. In a two-hour mission, the aircraft flies up to 120 kilometres. For real-time transmission, members are working on a new model. # ⚓ US_Congress_to_punish_lawmaker_over_violent_clip⠀⇛ Arizona Congressman Paul Gosar faces a formal censure on Wednesday in the Democratic-controlled Congress. It came after he posted then deleted an anime video that Democrats say promoted violence against President Joe Biden and lawmaker Alexandria Ocasio- Cortez. # ⚓ They_attack_Spanish_gendarmes_and_shout:_“Here_we_Arabs have_the_say!”⠀⇛ This is what happened last weekend when two trainee community service officers were “cornered” at the Ébano discotheque in Peñíscola after being recognised as members of the police corps.At the discotheque, a group of five people of different nationalities, mainly Moroccans, who are known criminals in the area, recognised the civilian officers and started harassing them inside the club. “We are waiting for you outside,” was the threat. In view of this, the officers decided not to leave the discotheque but to wait until it was closed, believing that they had left the discotheque but were waiting for them. When the club was closed, they appeared and shouted:”We Arabs have the say here”, pointed out that the Guardia Civil had no business in this place and started to attack the officers. # ⚓ Michael_Flynn_Pushed_Defense_Department_to_Seize_Ballots, Overturn_Trump’s_Loss:_Report⠀⇛ According to the book, after the election, Flynn placed a call to Ezra Cohen, a senior intelligence official who had previously worked under Flynn. Cohen was traveling in the Middle East at the time, but Flynn urged him to get back to the United States because, as Karl writes, there was going to be an “epic showdown” over the election results. Flynn told Cohen that “he needed to get orders signed, that ballots needed to be seized, and that extraordinary measures needed to be taken to stop Democrats from stealing the election.” (To be clear, this is projection on Flynn’s part: The actions he urged Cohen to take would be an effort to steal an election. There’s no evidence of widespread voter fraud.) o § Environment⠀➾ # ⚓ Climate_Deniers_Are_Using_These_Four_Major_Scare_Tactics_to Stop_Climate_Action⠀⇛ When fossil fuel companies found out about the link between their product and climate change decades ago, they did everything they could to hide it. They lied, manipulated, and deceived.  Today, denying the reality of climate change isn’t as easy, and it is certainly more controversial. But that doesn’t mean climate deniers — fossil fuel companies, lobbyists, and their allies opposed to climate action — have moved past the lies.  # ⚓ China_and_Solutions_to_Climate_Change⠀⇛ Last year, President Xi Jinping, pledged that China’s CO2 emissions would peak before 2030, and China would become carbon neutral before 2060. China has a track history of setting ambitious, nearly impossible goals and then achieving them–often before deadline–so this pledge is significant. Under the CPC, China has already created “an economic miracle” in transforming China into the largest economy in the world. It ended extreme poverty while creating the largest middle class in the world.  It has virtually eradicated Covid through non-pharmaceutical methods, while vaccinating up to 20 million people daily, and pledging the largest number of vaccines (2.2 Billion) and distributing over 1 Billion-to the rest of the world. It has also been applying this incredible focus and national resolve to tackle Climate change. # ⚓ Opinion_|_The_People_vs._COP26:_Time_for_Politicians, Billionaires_to_Listen⠀⇛ Of all the speeches and political grandstanding at the 2021 United Nations Climate Change Conference in Glasgow (COP26), the words of Mexican President, Andres Manuel Lopez Obrador, were the most profound and least hypocritical. # ⚓ Glasgow’s_“Conference_of_the_Polluters”_Again_Confirms_that Global_Arson_Needs_Local_Fire_Extinguishers⠀⇛ The United Nations COP26 Glasgow Climate Pact signed on November 14 is another confirmation of what we learned in Durban in 2011, at the 17th UN climate summit. As expressed by Indigenous activist Ta’Kaiya Blaney (from the Tla A’min Nation in western Canada): ‘COP26 is a performance. It is an illusion constructed to save the capitalist economy rooted in resource extraction and colonialism.’ Swedish youth leader Greta Thunberg was also clear: ‘The COP26 is over. Here’s a brief summary: Blah, Blah, Blah. But the real work continues outside these halls. And we will never give up, ever.’ # ⚓ ‘We_Are_in_a_Climate_Emergency’:_Historic_Floods_in_BC, Washington_Follow_Scientists’_Warnings⠀⇛ After a summer that featured the “world’s most extreme heatwave in modern history,” which experts linked to human-caused global heating, the Pacific Northwest was inundated with floodwaters Monday, fueling fresh calls for ambitious action to combat the climate emergency. The recent rain and subsequent flooding—which came on the heels of the COP26 climate summit in Scotland—led to evacuations, power outages, rescues, school closures, and stranded vehicles in Washington state and British Columbia, Canada. # ⚓ Opinion_|_Forget_Any_COP26_Promises_Your_Heard._Just_Look at_the_$6_Trillion_in_Fossil_Fuel_Subsidies⠀⇛ It sounds incredible: while politicians have been cackling about the climate emergency and profiling in empty promises to halt it, they have spent six trillion US dollars from taxpayers’ money to subsidise fossil fuels in just one year: 2020. And they are set to increase the figure to nearly seven trillion by 2025. # ⚓ The_People_vs._COP26:_Time_for_Politicians,_Billionaires_to Listen⠀⇛ Lopez Obrador raged against the “technocrats and neoliberals” – world leaders who hold the future of humanity in their hands. This was a direct reference to leaders of the powerful countries that “increase their fuel production, at the same time that they hold summits for the protection of the environment,” while arriving in Glasgow on private jets. Indeed, hypocrisy continues to define what is meant to be a collective global fight against climate change and its ravaging, often deadly consequences. # ⚓ Opinion_|_The_Mixed_Blessings_of_the_Glasgow_Climate_Pact⠀⇛ The pact creates a timeline to bring nations back to the table with higher commitments to reduce greenhouse gas emissions, references the reduction of fossil fuels, and allocates more funding from developed nations to developing nations.  # ⚓ Lying_in_Public_Life:_The_Scott_Morrison_Formula⠀⇛ Prior to heading to Glasgow, Morrison, having done his bit of crossdressing on the climate change front, was coy.  He refused to reveal the modelling that went into the fabulous predictions of net- neutral utopia.  But on his return, and after any sense of jet lag had been overcome, he was happy to promote the scanty details of an enterprise verging on a hoax. Such efforts have become the stock and trade of a man habitually committed to the advertising message.  At best, it is simple dissimulation; at worse – and here, we find ourselves on difficult territory – it is mendacious.  Little wonder, then, that critics have been coming out of late with a sort of adamant righteousness against the Australian prime minister’s relationship with lying. # ⚓ Why_Some_Polluter’s_Victims_Hate_Enviros_More_Than Polluters⠀⇛ Environmental groups have utterly failed to organize citizens to lobby environmental enforcers to go after big polluters. Meanwhile, citizens see every day that government brings the full force of the law down on average citizens without mercy. This undermines efforts to strengthen the laws and provides evidence to conservatives, populists and nationalists that liberals and strong government advocates are really on the side of the banksters, hedge funds and big guys. Neoliberalism and win-win have created people like Trump, who can persuade people the fix is in. And that fix includes the entire edifice of partnerships, consensus and win- win to keep corporations on top and average people in thrall to anything that purports to bring people together. Bad actors and ivory tower academics have always tried to lure activists into consensus and partnerships, but from Alinsky’s words there is no escape: “All change means movement, movement means friction and friction means heat. You’ll find consensus only in a totalitarian state, communist or fascist… conflict is the vital core of an open society…” # § Energy⠀➾ # ⚓ Opinion_|_How_‘Low_Carbon’_Energy_Became_the_New_‘Low Tar’_Cigarette⠀⇛ The top executives of ExxonMobil, Shell, Chevron, and BP America were put in the hot seat last month, when the House Oversight and Reform Committee grilled them under oath about their companies’ well-documented campaigns to spread disinformation and deceive the public about the role their products play in causing climate change.  # ⚓ ‘Lighting_the_Fuse_on_a_Massive_Carbon_Bomb’:_Biden Rebuked_on_Eve_of_Drilling_Lease_Sale⠀⇛ Climate and environmental campaigners on Tuesday took President Joe Biden to task on the eve of his administration’s scheduled oil and gas drilling auction of 80 million acres in the Gulf of Mexico—a move that comes just days after the U.S. leader pleaded for “every nation to do its part” to combat the climate emergency at the U.N.-backed climate summit in Glasgow, Scotland. “Continued leasing for dirty and dangerous offshore drilling is a disaster for our environment, our economy, and our climate.” # ⚓ Forgive_Humans,_Not_Oil_Companies⠀⇛ # ⚓ Let’s_get_students_off_the_plane_and_on_to_the train⠀⇛ Despite this, university students around Europe are not travelling in an environmentally friendly way when using the European Union’s student exchange programme Erasmus+. Taking the plane is the standard procedure when students go to study abroad. To limit the carbon footprint of international exchange, we have to give the students a better opportunity to get off the plane and on the train. # ⚓ Swedish_Regulators_Call_for_EU_Ban_on_ [Cryptocurrency]_Mining,_Power_Company_Defends Industry⠀⇛ Alarmed by the rising energy needs of cryptocurrency mining, Sweden’s financial and environmental regulators have recently proposed an EU-wide ban on proof-of-work coin minting. The Swedish officials believe this would encourage a move towards a more energy- efficient extraction of bitcoin while supporting the transition towards climate neutrality in Sweden and Europe. A state-run power company warns, however, that restrictions could have an adverse effect on global carbon emissions. # ⚓ Why_is_India_clinging_to_coal?⠀⇛ India has another reason for hanging on to coal: politics. The black stuff is big business, making it ripe for graft. In the 1990s and 2000s mining contracts were handed out to government cronies at knockdown prices, a scandal that became known as “Coalgate”. Mining also provides a rich seam of votes. According to one study, between 10- 15m Indians depend on coal for their livelihood, many of them miners in the country’s poorest states, Jharkhand and Chhattisgarh. o § Finance⠀➾ # ⚓ UN_Food_Chief_Details_How_Mega-Rich_Like_Elon_Musk_Could Spend_Just_$6.6_Billion_to_Avert_Deadly_Famine⠀⇛ “While there’s $400 trillion of wealth in the world today, shame on us that we let a single child die of hunger.” # ⚓ The_Trucker_Shortage:_Why_Don’t_We_Let_the_Market_Work?⠀⇛ But the drop in pay is just part of the story. The industry is far less unionized than it was back in the 1970s, when President Carter began to deregulate trucking. Not having a union means that truckers have far less control over their working conditions. That’s a big deal in trucking. Without a union to stand behind them, truckers can be forced to work irregular shifts and long hours. They can be forced to drive in all sorts of weather. They can also be forced to drive trucks that they don’t think are safe due to bad brakes or other issues. # ⚓ Biden_Administration_Is_Playing_With_Fire_by_Failing_to Regulate_Cryptocurrency⠀⇛ # ⚓ Infrastructure_Bill_Passes⠀⇛ Yes, Democrats improved their mid-term prospects. Those shovel-ready projects bring in votes— Assuming that enough back-ordered shovels Can get unloaded from the jammed up boats. # ⚓ Where_“Defund”_Isn’t_Dead⠀⇛ A few months ago, Salley May showed up at a mosque in Harlem where a woman was having a mental health crisis, holding children inside and refusing to allow people in or out. About 50 onlookers had gathered outside, as well as a large number of police officers. # ⚓ ‘It’s_About_Giving_People_Tools_So_We_Can_Reach Transparency_Critical_Mass’⠀⇛ # ⚓ After_Bipartisan_Bill,_Progressives_Demand_Fast_Passage_of Build_Back_Better_Act⠀⇛ # ⚓ ‘We_Need_to_Get_Our_Priorities_Right’:_Bernie_Sanders_a ‘No’_on_$778_Billion_Pentagon_Budget_Vote⠀⇛ On Tuesday, the eve of a likely U.S. Senate vote on the 2022 National Defense Authorization Act, Sen. Bernie Sanders said he would vote against the legislation because it enriches the military- industrial complex at the expense of desperately needed social programs and climate action. “Meanwhile, the Senate has spent month after month discussing the Build Back Better Act and whether we can afford to protect the children, the elderly, the sick, the poor, and the future of our planet.” o § AstroTurf/Lobbying/Politics⠀➾ # ⚓ Critics_Warn_Corporate_Democrats_Obsessing_Over_CBO_Are Peddling_a_‘Right-Wing_Scam’⠀⇛ As House members await the Congressional Budget Office’s cost assessment of the Build Back Better package, outside progressives are attempting to hammer home their view that right-wing Democrats’ expressed concerns about the looming CBO deficit projection are completely cynical—and should be treated as such. “The whole ‘pay for’ thing is a right-wing scam, and Democrats are dumb for playing by GOP rules that the GOP doesn’t itself follow.” # ⚓ Digital_Democracies:_How_Liberal_Governments_Can_Adapt_In The_Technological_Age⠀⇛ At the turn of the last millennium, there was a wave of optimism surrounding new technologies and the empowerment of the modern digital citizen. A decade later, protestors across North Africa and the Middle East leveraged platforms such as Facebook and Twitter to bring down authoritarian regimes during the revolutions of the Arab Spring and it was believed these technologies would bring about a new flourishing of the worldwide liberal democratic order. # ⚓ Trump_Could_be_Re-Elected_in_the_2024,_Yet_Democrats_are Still_Obsessing_Over_the_Steele_Dossier⠀⇛ In 2016, Hillary Clinton tried to put unrelenting focus on Trump’s failings, convinced that these were so flagrant that they would alienate the majority of voters. The demonisation backfired because it gifted Trump millions of hours of free television time as his every word was covered by the media, while Clinton’s speeches were cut or ignored. Assisted further by Clinton’s comically inept campaign, Trump was able to win an election that he had expected to lose. Five years on and the Democrats have just been defeated at the polls in a series of closely watched elections for much the same reasons as they lost in 2016. They pursued their old strategy of portraying Trump as the source of all evil. In the Virginia gubernatorial election, in which the Democrats suffered their worst reverse, the Democratic candidate Terry McAuliffe failed to win in a state carried by Joe Biden with a large majority. A former governor with an undistinguished record, he was regarded by many as a party hack close to the Clintons and with a limited appetite for campaigning. He portrayed his Republican opponent Glenn Youngkin as a dyed-in-the-wool Trump supporter, although Youngkin had distanced himself from the former president. # ⚓ With_No_Change_in_Votes,_GOP_Would_Win_Through Gerrymandering⠀⇛ # ⚓ ‘A_Damn_Shame’:_Ohio_Senate_Approves_‘Extreme’ Gerrymandered_Map_Favoring_GOP⠀⇛ Ohio’s Republican-dominated Senate on Tuesday approved a congressional district map that critics say is designed to benefit the GOP—a move that sparked swift criticism of the state’s lawmakers and bolstered demands for Congress to pass federal legislation to protect voting rights and outlaw gerrymandering. Unveiled late Monday by Republican state lawmakers, the new map was advanced by the Ohio Senate Local Government and Elections Committee before being approved by the full upper chamber. It still needs approval from the Ohio House and GOP Gov. Mike DeWine. # ⚓ Meta_goes_into_lockdown⠀⇛ The pulling of the talks highlights how a barrage of leaks and external scrutiny has chilled the flow of information inside the company formerly known as Facebook. Many of the changes appear designed to thwart the next Frances Haugen, who worked in the Integrity organization responsible for making the social network safer before she quit earlier this year, taking thousands of internal documents with her. Those documents served as the basis for a series of damning stories in The Wall Street Journal and dozens of other news outlets, including The Verge. Some of them, such as internal research showing Instagram and Facebook can have negative effects on young people, have led to congressional hearings and lawsuits. And as the bad press continues, Meta executives have argued that the documents were cherry-picked to smear the company and paint an incomplete story. # ⚓ Group_behind_cyberattacks_on_multiple_governments_linked_to Belarus⠀⇛ Researchers for cybersecurity company Mandiant made the attribution as part of a new report, assessing with “high confidence” that the activity of what has been labeled the “Ghostwriter” information campaign was “aligned with Belarusian government interests.” A cyber espionage group, which Mandiant labeled “UNC1151,” was also linked to the Belarusian government. Mandiant in April had reported that UNC1151 was helping conduct Ghostwriter influence operations. # ⚓ The_Coolest_Member_of_the_Senate_Is_Retiring⠀⇛ At the time, Leahy was the youngest senator ever elected from Vermont. He took office as one of the two youngest Democrats in the chamber. The other was Delaware Senator Joe Biden. Now, Biden is the 78-year-old president of the United States, and Leahy is the 81-year-old president pro tempore of the Senate, making him the third person in the current line of succession to the presidency. # ⚓ The_1619_Project_and_the_Denial_of_the_Enslavement_of Blacks_in_Islam⠀⇛ If there is going to be an accusation of racism against Blacks as a cause of slavery, then perhaps the “1619 Project” advocates should look at the Islamic world were an estimated 529,000 to 869,000 black men, women and children are still slaves. Pope St. Zachary (741-752) is documented for saying: “Wherever Islam goes slavery follows, and specifically the horrible institution of sex slavery, as that was the primary reason for it.” And while thre might have been a times where Muslims were told to treat their slaves decently, or promised a great reward in heaven if they choose to free a slave. But there is NOT A SINGLE VERSE in the Quran or the hadiths that abolishes slavery: [...] o § Misinformation/Disinformation⠀➾ # ⚓ Facebook_Whistleblower_Testifies_Before_‘Grand_Committee_On Disinformation’;_Which_Includes_Countries_That_Lock_People_Up For_Criticizing_The_Gov’t⠀⇛ It didn’t get as much press as some of Facebook whistleblower Frances Haugen’s other high profile talks to government inquisitors, but last week, Haugen testified before the rather Orwellian International Grand Committee on Disinformation. This is a bizarre “committee” set up by regulators around the world, but its focus — and its members — are kind of notable. Considering that tons of evidence shows that cable news is a much larger vector of disinformation flows to the general public, it seems notable that the “International Grand Committee on Disinformation” seems to only want to pay attention to online disinformation. I mean, it’s right in the group’s mission: o § Censorship/Free Speech⠀➾ # ⚓ 100+_Global_Donors_Pen_Letter_to_‘Stand_With’_Palestinian Rights_Groups_Outlawed_by_Israel⠀⇛ More than 100 global philanthropic foundations and individual donors on Tuesday joined a growing chorus of human rights advocates who have condemned Israel for its recent decision to label six prominent Palestinian civil society groups as “terrorist organizations,” and stressed that the apartheid regime’s move will not affect their funding decisions. “The cynical weaponization of anti-terrorism laws poses an existential threat both for Palestinian human rights defenders and those defending human rights globally.” # ⚓ Drag_queens_are_being_swatted_while_streaming_on_Twitch. They_want_it_to_stop.⠀⇛ Since September, six members of the streaming group Stream Queens, a collective of drag queens who stream mostly horror video games on Twitch, have been swatted, according to members of the group. Swatting can be deadly. In 2017, Andrew Finch, of Wichita, Kansas, was killed during a swatting raid. Tyler Barriss, who called in the false report, was sentenced to 20 years in prison. # ⚓ “Censorship_is_never_okay_at_any_cost”,_says_Naomi_Osaka, joins_Djokovic_and_Cornet_in_expressing_concern_for_Peng Shuai’s_safety⠀⇛ Naomi Osaka has joined a growing list of high- profile tennis stars to have expressed concerns regarding the safety of fellow player Peng Shuai. The Chinese player has been facing censorship in her country following her allegations of sexual abuse against the country’s Vice Premier of Zhang Gaoli. # ⚓ Science_Round-Up:_Has_religious_satire_shaped_our_culture more_than_religion_itself?⠀⇛ But that might not be so. In a new paper, ‘The Gospel of Deviance’, satire researcher Dennis Meyhoff Brink from the University of Copenhagen has traced the early roots of religious criticism to the 1100s and argues that satire actually played a greater role in the spread of democratic values ​​in medieval Europe than Christianity itself. # ⚓ Germany:_Because_he_drew_a_Mohammed_caricature_as_a_Muslim, he_is_now_threatened_by_his_own_family,_a_lot_of_other Muslims_and_the_German_courts⠀⇛ But: It is possible that Slim is now even being investigated. “Irrespective of a possible endangerment of the person concerned, the Offenburg public prosecutor’s office is currently examining whether the publication of the person concerned could in turn be punishable.” Meaning: Did Mohammed Ali Slim insult religious societies with the publication? # ⚓ Arrested_in_my_pyjamas:_I_became_a_Russian_political prisoner_at_23⠀⇛ I was working as an editor at DOXA, an online student magazine in Moscow. Three other editors and I released a three-minute video in which we criticised universities for illegally expelling protesters. As my sign off, I said, “the government has declared war on young people. But we will definitely win.” We showed the script to lawyers, who said it didn’t contain criminal content. [...] The judge placed me and the other editors under house arrest. We were also banned from using the [Internet] and making phone calls. Two weeks later, after we appealed, the court let us go out for a two-hour walk each morning. # ⚓ The_Islamophobia_Industry⠀⇛ MT: What is the Islamophobia industry? DB: There are two #Islamophobia Industries. One is run by Muslims to fight Islamophobia – what they refer to as the irrational fear of Islam. I would suggest that for many, fear of Islam is rational. The other is the one about which I write: the Industry set out to silence anyone who criticizes or questions Islam. This Industry has managed to turn Islam, a religion and political ideology, into a race. By doing that they can legally stop any criticism because race is immutable; one, obviously, cannot change one’s race, so attacking race is forbidden. # ⚓ The_Jihad_on_Mimicry⠀⇛ After the Muslim mob had had its fill, it was the Muslim authorities’ turn: at least four of the teenagers were arrested on the charge of “insulting Islam,” detained for 45 days and subjected to “ill- treatment,” according to one human rights group. Then, in early 2016, three of these Christian teenagers were sentenced to five years imprisonment. The fourth defendant, 15, was handed a juvenile detention for an indefinite period. They “have been sentenced for contempt of Islam and inciting sectarian strife,” explained their defense lawyer, Maher Naguib: “The judge didn’t show any mercy. He handed down the maximum punishment.” # ⚓ American_Fascism_on_Trial_in_Kenosha⠀⇛ Two of the martyrs, Anthony Huber and Joe Joe Rosenbaum, were killed by the cop-and Trump- worshipping teen vigilante Kyle Rittenhouse, in Kenosha, Wisconsin, on August 25, 2020. They died trying to prevent Rittenhouse from murdering people marching for Black lives and against the brutal and outrageous Kenosha police shooting of the 29-year- old Black man Jacob Blake. Closing arguments in Rittenhouse’s murder trial are being made today (Monday, November 15th). Most legal experts following the trial expect Rittenhouse to escape conviction on the most serious charges. Contrary to what his defense team claims, Kyle Rittenhouse didn’t come to Kenosha with a fully loaded and illegally owned military assault rifle just to protect used car dealerships. He hooked up in Kenosha with the Boogaloo Bois, a neo-Nazi network that wants to spark a genocidal race war. He later partied and made white- supremacist hand signals with the Proud Boys. # ⚓ The_Rittenhouse_effect:_Republicans_want_a_Stasi_of_their own⠀⇛ One of the most prominent groups advocating for this heavy-handed censorship is the misleadingly named “Moms for Liberty,” which presents as a “parents rights” group, but is in fact a racist organization dedicated to banning books about Martin Luther King Jr. and replacing them with books that insist there was no racial component to American slavery. Now the New Hampshire branch of Moms for Liberty is taking it to the next level. As Insider reports, the group is offering a $500 bounty to any person who reports a teacher supposedly breaking the law banning “critical race theory.” o § Freedom of Information/Freedom of the Press⠀➾ # ⚓ India’s_Increasingly_Despotic_Crackdown_on_Journalists⠀⇛ Pesky journalists such as Varadarajan, and a new crop of similarly doughty media platforms that provide space for views that don’t echo the established narrative, are a thorn in the side of despotic power. By contributing to a diversity of views, these journalists threaten the echo chamber that despotic power builds to fortify itself. The price they pay is intimidation, and worse. Knocks on the door by personnel from the UP Police—with its formidable track record of 124 deaths in nearly 6,500 “encounters” in three-and-a-half years under Adityanath (at the time)—can be daunting. # ⚓ China,_US_agree_to_ease_restrictions_on_journalists⠀⇛ Under this, both governments will increase the validity of journalist visas from three months to one year, provided they are eligible under all applicable laws and regulations. Both countries have also pledged to allow journalists to freely depart and return, which they had previously been unable to do. o § Civil Rights/Policing⠀➾ # ⚓ Not_Just_a_Kid_From_the_Projects⠀⇛ Growing up, I didn’t know that I came from a lower class. Once, I even had a birthday party at a Build-a-Bear workshop! My dad worked for a theater and we were able to watch movies and got popcorn for free, while my mom stayed at home and helped translate for Spanish-speaking parents of kids who went to my school. I come from a big family; I have four siblings, two nieces, two nephews, and more cousins than I can count. My house is always full of smiles and laughter that help make the small space feel big. My home was a haven for me, but school was a different story. This story was produced for Student Nation, a program of the Nation Fund for Independent Journalism, which is dedicated to highlighting the best of student journalism. For more Student Nation, check out our archive or learn more about the program here. StudentNation is made possible through generous funding from The Puffin Foundation. If you’re a student and you have an article idea, please send pitches and questions to [email protected]. # ⚓ Concern_Grows_for_Mexican_Land_Defender_Irma_Galindo Barrios,_Missing_Nearly_3_Weeks⠀⇛ Human rights defenders in Mexico’s Oaxaca state and beyond are demanding the safe return of an Indigenous forest defender who disappeared nearly three weeks ago after years of activism against illegal logging and corrupt local officials who enable and profit from it. “Irma has revealed the depredation of the forest, as well as the corruption and collusion between loggers and authorities who illegally act against those who defend the territory.” # ⚓ Minneapolis_May_Have_Rejected_That_Referendum_on_the Police⠀⇛ The voters’ decisive rejection earlier this month of the public safety amendment that would have replaced the troubled police department here has left the city’s progressives battered and bruised. But politicians and activists on both sides of the issue agree that some crucial aspects in the referendum will remain unavoidable in any plan to reform policing. # ⚓ Native_American_Heritage_Month⠀⇛ # ⚓ Supreme_Court_Takes_A_Pass_On_A_Chance_To_Firmly_Establish A_Right_To_Record_Police_Officers⠀⇛ After taking some positive steps towards trimming the growth of qualified immunity it had itself encouraged for years, the Supreme Court decided to reverse course. Two more cases on the court’s “shadow docket” were sent back to the appellate levels with instructions to reverse the stripping of qualified immunity from government employees accused of rights violations. # ⚓ “Critical_Race_Theory”_Is_White_History⠀⇛ For more than a year now, conservatives have been waging war against the misdefined conception of critical race theory that they themselves created. The right-wing campaign against so-called CRT largely amounts to a round-robin chorus of hysterical voices asking, Won’t someone think of the poor white children?! “CRT tries to make kids feel bad because of the color of their skin,” Representative Ron Nate, cosponsor of Idaho’s anti- CRT law, stated just after the bill passed in May. Florida Governor Ron DeSantis, who successfully led the state school board to ban CRT from public school classrooms last summer, tweeted in June that “Critical Race Theory teaches kids to hate our country and to hate each other.” Texas Governor Greg Abbott signed a bill muzzling history educators over lessons that might make students “feel discomfort, guilt, anguish, or any other form of psychological distress on account of the individual’s race or sex.” In pursuit of that goal, Republican senators in Texas recently drafted and approved yet another anti-CRT bill—after ditching language inserted by outnumbered and outvoted Democrats that would have required teaching “the history of white supremacy,” including slavery and the Ku Klux Klan, “and the ways in which it is morally wrong.” “We don’t want to teach those little white children that they should feel guilty because of what previous white people did generations ago,” Senator Bryan Hughes explained to a local news outlet about why he filed the bill. # ⚓ Stay_Outraged,_Patriots!⠀⇛ # ⚓ Nicaragua_Has_a_Public_Relations_Problem,_Not_a_Democracy Problem⠀⇛ US President Joe Biden hectored Nicaragua about their November 7 elections accusing them of “a pantomime election that was neither free nor fair, and most certainly not democratic.” Three days earlier, the US lavished a $650mil arms deal on Saudi Arabia, a monarchy where they don’t even pretend to have elections for higher office. Clearly more than democracy is at issue with the US offensive against Nicaragua. At issue is what Biden described as “the arbitrary imprisonment of nearly 40 opposition figures since May, including seven potential presidential candidates.” An objective investigation reveals: (1) the motivation for the arrests had nothing to do with the election and (2) the effects of the arrests had no impact on the election. # ⚓ Dave_Chapelle_Should_Read_Adolph_Reed_Jr.⠀⇛ He then preceded to go on a rant about being canceled, which just means one blogger doesn’t like you and you get that parlayed into millions of dollars based on the unhinged rage of rich white people. This was in theory the very same crowd Chapelle was critiquing but as always the thesis of liberalism being bourgeois just missed the mark. Dave Chapelle may have been right to recognize that his original fan base was a bunch of racist white liberals but he has only been a reactionary thus far, moving from white liberalism to white conservativism, which pays even better. That being said Chapelle as always is doing something a little more than the typical reactionaries. That doesn’t mean his transphobia is any less dangerous. # ⚓ “We_Will_Be_Kicked_Out_and_No_One_Will_Care”⠀⇛ # ⚓ DEA_Racks_Up_Two_Forfeiture_Losses_In_One_Week,_Returns $100,000_In_Stolen_Cash_To_Victims⠀⇛ In the past week, the federal government has twice (!) been forced to return money it stole from travelers just because it could. In both cases, American citizens were trying to board domestic flights at US airports. And in both cases, despite it not being illegal to carry large amounts of cash on domestic flights, the government decided the cash had to have been illegally obtained, and moved forward with forfeiture proceedings. # ⚓ Italy:_14-year-old_Bangladeshi_girl_beaten_by_her_family for_refusing_to_wear_the_burqa⠀⇛ It happened on Saturday afternoon when the Bangladeshi girl, after refusing to wear the traditional Islamic female dress that covers the whole body, including the head, except for a slit for the eyes, was beaten by her older brother. But when she arrives at the Carabinieri of Ostia, she reports further assaults on her, always because she did not want to conform to Islamic culture. It is alleged that these assaults were not only related to her brother, but also to her mother. The Rome Juvenile Prosecutor’s Office opened an investigation for assault and ill-treatment. The girl was first taken to Grassi hospital, where she was diagnosed with a head injury, and then taken to a facility with protection. # ⚓ Muslim_farmer_recruits_gang_and_kills_two_Christian_farmers over_irrigation_water⠀⇛ Mukhtar Masih (70 yrs) and his sons leased six acres of land belonging to a Christian family now living abroad from March 2021. The Christian family had a desire to work together to earn a decent living through farming. Unbeknown to them the land had previously been leased to Muhammad Qadir who was angry not over the loss of the lease but that he now had to farm alongside ritually impure Christians. o § Internet Policy/Net Neutrality⠀➾ # ⚓ EFF’s_New_Series_of_How_to_Fix_the_Internet_Podcast_Tackles Toughest_Issues_in_Tech⠀⇛ # ⚓ Opinion_|_Future_FCC_Leaders_Must_Repair_the_Harms_That Agency_Policies_Have_Inflicted_on_Black_and_Brown Communities⠀⇛ As the U.S. Senate is set to hold confirmation hearings on the nominations of Jessica Rosenworcel and Gigi Sohn to respectively become the next chairwoman and commissioner of the Federal Communications Commission, it’s important to remember the political stakes that await them at the agency. # ⚓ EFF’s_How_to_Fix_the_Internet_Podcast_Offers_Optimistic Solutions_to_Tech_Dystopias⠀⇛ # ⚓ Report:_US_ISPs_Aren’t_Transparent_About_Prices_And_Speeds, And_Regulators_Generally_Don’t_Care⠀⇛ By now we’ve well established that regional monopolization, limited competition, and the (state and federal) corruption that enables both (aka regulatory capture) are why US broadband is spotty, expensive, and slow. With neither competent regulatory oversight nor meaningful competition to drive improvements, regional dominant broadband providers simply… don’t bother. The end result goes beyond high prices to substandard customer service, privacy violations, net neutrality violations, and unnecessary surcharges, usage caps, and fees they often don’t clearly disclose. o § Digital Restrictions (DRM)⠀➾ # ⚓ Netflix’s_Expanded_Viewing_Data_Move_Is_Mainly_a_Flex⠀⇛ More broadly, Netflix is flexing here: It’s underscoring the fact that it operates the biggest subscription-video service on the planet (with 213.6 million paid subs as of Q3). The streamer is giving notice to the industry, customers and Wall Street that it has an engine capable of producing a surprise hit like “Squid Game,” which (Netflix says) was viewed an astronomical 1.6 billion hours over its first 28 days of release. It will be interesting to see if Netflix rivals like Amazon, Disney and HBO Max follow suit by releasing their own metrics. o § Monopolies⠀➾ # § Patents⠀➾ # ⚓ Tax_Money_Lost_to_Abuses_by_the_Rich_Could_Pay_to Vaccinate_the_World_3_Times_Over⠀⇛ Ending abuses of the global tax system by the super-rich and multinational corporations would allow countries to recoup nearly half a trillion dollars in revenue each year—enough to vaccinate the world’s population against Covid-19 three times over. That estimate is courtesy of The State of Tax Justice 2021, a new report that argues rich countries—not the “palm-fringed islands” on the European Union’s tax haven blacklist—are the primary enablers of offshoring by large companies and tax evasion by wealthy individuals. # ⚓ Opinion_|_Climate_Emergency,_Vaccine_Monopolies,_and Fiscal_Blindness:_The_Fight_Against_Inequality_Is_the Only_Way_Out⠀⇛ 2021 will perhaps be remembered as the year when the great powers demonstrated their inability to assume their responsibilities to prevent the world from sinking into the abyss. I am thinking of course of the 26th United Nations Climate Change Conference (COP26) in Glasgow. After having used up the available atmospheric space to develop, the industrialized countries reaffirmed their refusal to honour this climate debt, even though global warming has become an existential issue. # ⚓ We_Could_Vaccinate_the_World_3_Times_Over_If_the_Rich Paid_the_Taxes_They_Owe⠀⇛ # ⚓ ‘Far_From_Enough’:_Pfizer’s_Covid_Drug_License Excludes_Almost_Half_of_the_Global_Population⠀⇛ While many observers called Pfizer’s new licensing agreement allowing generic drug manufacturers to produce its promising Covid- 19 treatment a welcome step, public health experts also condemned the deal for shutting out nearly half of the world’s population—and asked why the pharmaceutical giant remains unwilling to share vaccine know-how and technology. “Billions of people will still be left without as the deal excludes many developing countries.” # ⚓ Pfizer_Will_Allow_Its_Covid_Pill_to_Be_Made_and_Sold Cheaply_in_Poor_Countries⠀⇛ Under the agreement, Pfizer will grant a royalty-free license for the pill to the Medicines Patent Pool, a nonprofit backed by the United Nations, in a deal that will allow manufacturers to take out a sublicense. They will receive Pfizer’s formula for the drug, and be able to sell it for use in 95 developing countries, mostly in Africa and Asia, once regulators authorize the drug in those places. The organization reached a similar deal with Merck for its Covid antiviral pill, molnupiravir, to be made and sold inexpensively in 105 poorer countries. # ⚓ Spotlight:_patent_enforcement_and_invalidity procedures_in_Netherlands⠀⇛ # ⚓ Spotlight:_patent_enforcement_and_invalidity procedures_in_Switzerland [Ed: These patents should never_get_granted_in_the_first_place]⠀⇛ Switzerland is a signatory to the European Patent Convention, so Swiss national patents and European patents granted by the European Patent Office coexist in Switzerland. The granting authority for Swiss national patents is the Federal Institute of Intellectual Property (IPI) in Berne, which also maintains the register for Swiss national patents and the Swiss parts of European patents.6 Unlike European patents, Swiss national patents are granted without the IPI examining whether the invention is new and inventive in light of the prior art.7 Despite this difference, a Swiss national patent confers the same rights on its proprietor as the Swiss part of a European patent. Under Swiss law, supplementary protection certificates (SPCs) for medicinal products and plant protection products may be granted on the basis of Swiss national and Swiss parts of European patents. The Swiss regime8 for SPCs closely follows the corresponding legislation of the European Union; however, because Switzerland is not a member of the European Union, judgments of the European Court of Justice on the interpretation and application of the EU legislation on SPCs are not binding in Switzerland. A Swiss SPC’s maximum term of protection is five years. Swiss lawmakers also partially followed the European Union’s endeavours to improve the health of children by incentivising pharmaceutical companies to perform paediatric tests for their drugs by extending already granted SPCs by an additional six months (paediatric extensions).9 The Swiss legislator, however, went one step further and decided to grant the benefit of an additional six-month exclusivity period not only to those who have already been granted an SPC but also to those who, for whatever reason, have not previously obtained an ordinary SPC (paediatric certificate).10 The detailed regulations for the paediatric extensions and the paediatric certificate can be found in the Federal Ordinance on Patents.11 # ⚓ German_Federal_Patent_Court_points_to_solution_for Dabus_inventions [Ed: Those are not inventions, it's just some troll from England rick-rolling patent offices and courts for a PR blitz/stunt in the media]⠀⇛ Courts around the globe have dealt with the inventions of Stephen Thaler’s artificial intelligence (AI) system Dabus. The German Federal Patent Court has now come to a pragmatic decision over DE1020191281202. According to the court, the listed inventor must be a natural person, even if the AI has identified both the problem and the solution. At the same time, however, the AI system itself can be additionally named. # § Copyrights⠀➾ # ⚓ GTA_Modders_to_Court:_Our_Game_Fixes_&_Enhancements Are_Fair_Use,_Not_Piracy⠀⇛ In response to a lawsuit filed by Take-Two Interactive, four men behind the popular re3 and reVC Grand Theft Auto fan projects claim their work is protected under fair use. Among other things they fixed bugs, something the plaintiff stopped doing years ago. They also improved the games which, if anything, enhanced the market for the original games, which are required for the mods to run. # ⚓ CANAL+_Sends_Preemptive_Takedown_Notice_to_Pirate Sites_Ahead_of_TV-Show_Premiere⠀⇛ Copyright holders commonly ask pirate sites to remove infringing content. That typically happens after it appears online but the Polish branch of media giant CANAL+ is trying to get ahead of the curve. The company is asking sites to prevent the illegal distribution of an upcoming TV show, or face legal consequences. # ⚓ Rockstar’s_GTA_Retro_Games_Was_Completely_Broken_And Support_Was_Ghosting_Everyone⠀⇛ You may recall that a couple of months ago we discussed Rockstar and Take2, the game studio and publisher behind the Grand Theft Auto series, taking down a fan-made GTA4 mod that aimed to put all of the cities from previous games in one massive map. While this was a labor of love by dedicated fans of the GTA series, it escaped nobody’s attention that this action was taken on a mod started in 2014 just as Rockstar was about to release GTA Trilogy, consisting of remastered versions of GTA3, Vice City, and San Andreas. The very cities the mod looked to input into GTA4. In other words, the fan project was only shut down when the game companies decided to try to make money off this retro love themselves. # ⚓ CC_Community_Spotlight_Series:_Meet_the_co-founders of_Fine_Acts,_Pavel_and_Yana⠀⇛ In the weeks leading up to #GivingTuesday on November 30th, we’re spotlighting leaders in the Open Movement and encouraging you to support our Better Sharing, Brighter Future campaign.  # ⚓ Chief_Keef_Changed_the_Music_Industry:_It’s_Time_He Gets_the_Credit_He_Deserves⠀⇛ The track displayed a rawness unlike anything else that was released at the time, and you couldn’t stroll down the streets of Chicago’s South Side without hearing Bang’s lyrics pulsing from the stereos of cars rolling by: Yet he was almost completely unknown outside of Chicago. His Facebook profile had less than 2,000 followers, he claimed his occupation was “smokin’ dope” and he still lived with his grandmother. ䷩ 𝚕𝚒𝚗𝚎 5049 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.17.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Links_18/11/2021:_Oracle_Linux_8.5_and_Firebird_3.0.8⠀✐ Posted in News_Roundup at 7:53 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⠀➾ # ⚓ Tuxedo_Nano_Pro_Gen_11_is_a_compact_Linux_desktop_with_AMD Ryzen_4000U⠀⇛ The Tuxedo Nano Pro Gen 11 is a mini PC that measures 4.6″ x 4.3″ x 1.9″ and ships with a choice of Ubuntu Linux or the Ubuntu-based Tuxedo_OS. It’s the latest in a line of Linux PCs from Tuxedo Computers, and the company says the little desktop is one of the smallest available with an AMD Ryzen 4000U processor. It’s available from Tuxedo for 640 Euros and up, taxes included. o § Audiocasts/Shows⠀➾ # ⚓ FLOSS_Weekly_656:_Switching_to_Linux_–_and_Much_Else_– Intel_on_Linux,_System76⠀⇛ Doc Searls, Jonathan Bennett and Aaron Newcomb are together on FLOSS Weekly taking a look at the challenges of switching to Linux, even though Linux runs on many things used in everyday life. System76 has decided to build a non-Gnome desktop for its distro. Why? Bennett addresses the allegations of Intel being optimized for Windows 11, but not taking Linux into consideration. It’s a fun discussion on this episode of FLOSS Weekly. # ⚓ Linux_overview_|_Lubuntu_21.10_–_Invidious⠀⇛ In this video, I am going to show an overview of Lubuntu 21.10 and some of the applications pre- installed. # ⚓ Video:_What_is_the_MiSTer?⠀⇛ I’m guessing, given the fact that I’ve posted a considerable amount of content on it already, that you know what the MiSTer is. Here’s a presentation from the Retro World Expo 2021 (just a few days ago) by two prominent retro YouTubers. # ⚓ Just_Say_No_to_M1_|_Coder_Radio_440⠀⇛ We get some spicy emails, dig into why Mike just picked up another Linux laptop, and then share our real thoughts on Web3. # ⚓ The_Future_of_Pop_OS_–_Invidious⠀⇛ System76 looks to be ditching GNOME and building its own Desktop Environment. # ⚓ Streamlabs_Rips_Off_OBS,_Lightstream_and_Elgato_– Invidious⠀⇛ Streamlabs is in the news today due to several companies claiming that Streamlabs copied their work. Those companies include Lightstream, Elgato and OBS, the maker of the free and open source Open Broadcaster Software. Additionally, OBS claims that Streamlabs is using the OBS name without their permission. # ⚓ StreamLabs_OBS_Accused_Of_Stealing_OBS_Name_–_Invidious⠀⇛ For the longest time I thought that StreamLabs OBS was a partnership with OBS but apparently that’s not the case and OBS is not happy about them using the name, along with this they’ve allegedly been copying other competitors. o § Kernel Space⠀➾ # ⚓ Linux_5.17_To_Continue_With_I/O_Optimizations,_5~6% Improvement_Pending_For_NVMe_–_Phoronix⠀⇛ The recently-ended Linux 5.16 merge window saw significant I/O improvements driven primarily by maintainer Jens Axboe’s recent focus on relentlessly optimizing the block and IO_uring code for record-setting per-core IOPS. As good as those improvements are, Linux 5.17 should be even better. Linux 5.16 saw much of Axboe’s work merged around the I/O optimizations in his quest for maximizing the per-core IOPS out of his new Ryzen 9 5950X system with dual Intel Optane NVMe solid-state drives. But there is still more work pending that in turn should be ready for Linux 5.17. # ⚓ Intel_AMX_support_in_5.16⠀⇛ The x86 instruction set is large, but that doesn’t mean it can’t get bigger yet. Upcoming Intel processors will feature a new set of instructions under the name of “Advanced Matrix Extensions” (AMX) that can be used to operate on matrix data. After a somewhat bumpy development process, support for AMX has found its way into the upcoming 5.16 kernel. Using it will, naturally, require some changes by application developers. AMX (which is described in this document) is meant to be a general architecture for the acceleration of matrix operations on x86 processors. In its initial form, it implements a set of up to eight “tiles”, which are arrays of 16 64-byte rows. Programmers can store matrices in these tiles of any dimension that will fit therein; a matrix of 16×16 32-bit floating-point values would work, but other geometries are supported too. The one supported operation currently will multiply the matrices stored in two tiles, then add the result to a third tile. By chaining these operations, multiplication of matrices of any size can be implemented. Evidently other operations are meant to come in the future. While AMX may seem like a feature aimed at numerical analysis, the real target use case would appear to be machine-learning applications. That would explain why 16-bit floating-point arithmetic is supported, but 64-bit is not. The design of AMX gives the kernel control over whether these features can be used by any given process. There are a couple of reasons for this, one being that AMX instructions, as one might imagine, use a lot of processor resources. A process doing heavy AMX work on a shared computer may adversely affect other processes. But AMX also cannot be supported properly unless both the kernel and the user-space process are ready for it. # ⚓ The_balance_between_features_and_performance_in_the_block layer⠀⇛ Back in September, LWN reported on a series of block-layer optimizations that enabled a suitably equipped system to sustain 3.5 million I/ O operations per second (IOPS). That optimization work has continued since then, and those 3.5 million IOPS would be a deeply disappointing result now. A recent disagreement over the addition of a new feature has highlighted the potential cost of a heavily optimized block layer, though; when is a feature deemed important enough to outweigh the drive for maximum performance? Block subsystem maintainer Jens Axboe has continued working to make block I/O operations go faster. A recent round of patches tweaked various fast paths, changed the plugging mechanism to use a singly linked list, and made various other little changes. Each is a small optimization, but the work adds up over time; the claimed level of performance is now 8.2 million IOPS — well over September’s rate, which looked good at the time. This work has since found its way into the mainline as part of the block pull request for 5.16. So far, so good; few people will argue with massive performance improvements. But they might argue with changes that threaten to interfere, even in a tiny way, with those improvements. Consider, for example, this patch set from Jane Chu. It adds a new flag (RWF_RECOVERY_DATA) to the preadv2() and pwritev2() system calls that can be used by applications trying to recover from nonvolatile-memory “poisoning”. Implementations of nonvolatile memory have different ways of detecting and coping with data corruption; Intel memory, it seems, will poison the affected range, meaning that it cannot be accessed without generating an error (which then turns into a SIGBUS signal). An application can respond to that error by reading or writing the poisoned range with the new flag; a read will replace the poisoned data with zeroes (allowing the application to obtain whatever data is still readable), while a write will overwrite that data and attempt to clear the poisoned status. Either way, the application can attempt to recover from the problem and continue running. # ⚓ 5.16_Merge_window,_part_1⠀⇛ As of this writing, Linus Torvalds has pulled exactly 6,800 non-merge changesets into the mainline repository for the 5.16 kernel release. That is probably a little over half of what will arrive during this merge window, so this is a good time to catch up on what has been pulled so far. There are many significant changes and some large- scale restructuring of internal kernel code, but relatively few ground-breaking new features. # § Graphics Stack⠀➾ # ⚓ Mesa_21.3_Graphics_Stack_Is_Here_with_Zink,_RADV,_and Panfrost_Improvements⠀⇛ Mesa 21.3 is here three and a half months after Mesa 21.2 to further improve Linux’s number one graphics stack. It brings many great improvements, starting with official OpenGL ES 3.1 compliance for Collabora’s Panfrost driver, threaded shader compilation for the Iris driver, OpenGL ES 3.2 support for the Zink driver, and support for AV1 videos for the Video Acceleration API (VA-API ). # ⚓ Intel_Developing_Universal_Scalable_Firmware_As_Next- Gen_Firmware_Platform_–_Phoronix⠀⇛ Universal Scalable Firmware intends to extend its scope beyond just system firmware but is also planned for use by Intel discrete graphics processors. USF is also designed to offer greater firmware security than the status quo. The key planned features/ components right now include a Universal Payload that can work across different operating systems and boot loaders, the Platform Orchestration Layer with simplified ACPI support and interfaces with the Rust programming language and configured with YAML, and the SoC FSP. Intel is hoping USF will reduce development costs, improve firmware quality and security, and push forward other new firmware innovations. # ⚓ Mesa_21.3_Released_With_Radeon_RADV_Ray-Tracing,_Much Better_Zink_–_Phoronix⠀⇛ Mesa 21.3 is now out as the latest quarterly feature release to this collection of open- source graphics drivers. Mesa 21.3 as the Q4’2021 update brings a number of exciting improvements and new features like: - Radeon RADV ray-tracing support landed along with experimental shader-based ray- tracing for older Radeon GPUs. Note though that this RADV ray-tracing code hasn’t yet been well optimized and the performance is likely to be slow and there may still be various game issues. In any case, at least it’s finally maturing now in mainline in experimental form. # ⚓ Copper_Aims_To_Improve_Mesa’s_Zink_Efficiency_In_2022 –_Phoronix⠀⇛ Following the news from last week of experimental Zink code running Wayland’s Weston compositor over this Mesa-based OpenGL-on-Vulkan implementation, developer Mike Blumenkrantz has opened up about some of the ongoing work to improve the efficiency of Zink and making such advancements a reality. In particular, the ongoing Zink Gallium3D improvements by Blumenkrantz and others along with the work of Red Hat’s Adam Jackson on the new “Copper” DRI interface extension. The “Copper” effort has been ongoing for a while and should allow for some simplifications to the architecture for how Zink functions and in turn allow for greater efficiency as well as broader platform coverage. With that, the ability to handle Wayland compositors like Weston. # ⚓ NVIDIA_470.62.12_Vulkan_Beta_Driver_For_Linux_Updates Video_Support_–_Phoronix⠀⇛ NVIDIA today released their latest Vulkan beta drivers for Windows and Linux. With the NVIDIA 470.62.12 beta driver released today there is updated Vulkan Video API support based on the upstream spec as of the newly-released Vulkan 1.2.199. There are some subtle changes to the Vulkan Video capabilities for specification compliance. NVIDIA’s Vulkan beta driver remains the leading driver for Vulkan Video API support right now and they were quick in supporting the provisional extensions since their debut earlier this year. Finally at least Vulkan Video is seeing movement by Mesa drivers. o § Instructionals/Technical⠀➾ # ⚓ How_To_Install_NumPy_on_Ubuntu_20.04_LTS_–_idroot⠀⇛ In this tutorial, we will show you how to install NumPy on Ubuntu 20.04 LTS. For those of you who didn’t know, NumPy (Numerical Python) is an open- source library for the Python programming language. It is used for scientific computing and working with arrays. It offers the following and much more. 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 NumPy 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. # ⚓ Debugging_a_weird_‘file_not_found’_error⠀⇛ Yesterday I ran into a weird error where I ran a program and got the error “file not found” even though the program I was running existed. It’s something I’ve run into before, but every time I’m very surprised and confused by it (what do you MEAN file not found, the file is RIGHT THERE???!!??) So let’s talk about what happened and why! # ⚓ PostgreSQL_and_Undelete⠀⇛ Earlier this week, I updated pg_dirtyread to work with PostgreSQL 14. pg_dirtyread is a PostgreSQL extension that allows reading “dead” rows from tables, i.e. rows that have already been deleted, or updated. Of course that works only if the table has not been cleaned-up yet by a VACUUM command or autovacuum, which is PostgreSQL’s garbage collection machinery. # ⚓ How_to_install_RPM_fusion_on_AlmaLinux_8_/_Rocky_Linux_8⠀⇛ RPM Fusion is a repository specifically for Fedora Linux. It is an amalgamation of the software repositories Livna, Freshrpms, and Dribble to bundle resources. Among other things, the repo provides packages for multimedia and the required codecs. The repo is divided into “free” and “non- free“. # ⚓ How_to_format_USB_drive:_Mac,_Windows,_Ubuntu⠀⇛ USB keys will sometimes display less memory than is actually available, even after the drive has been completely wiped. When this happens, it’s helpful to reformat your USB flash drive to restore your device to its full capacity. Formatting your USB will open up the drive’s storage space and even increase its efficiency. USB keys can be formatted in several different ways. # ⚓ How_to_install_Parsec_on_a_Chromebook_in_2021⠀⇛ Today we are looking at how to install Parsec on a Chromebook. Please follow the video/audio guide as a tutorial where we explain the process step by step and use the commands below. # ⚓ How_to_install_Flowblade_Video_Editor_on_Elementary_OS_6.0 –_Invidious⠀⇛ In this video, we are looking at how to install Flowblade Video Editor on Elementary OS 6.0. o § Desktop Environments/WMs⠀➾ # § GNOME Desktop/GTK⠀➾ # ⚓ Sam_Thursfield:_Status_update,_November_2021⠀⇛ I am impressed with the well-deserved rise of Sourcehut, a minimalist and open source alternative to Github and Gitlab. I like their unbiased performance comparison with other JavaScript-heavy Git forges. I am impressed by their substantial contributions to Free Software. And I like that the main developers, Drew DeVault and Simon Ser, both post monthly status update blog posts on their respective blogs. o § Distributions⠀➾ # § IBM/Red Hat/Fedora⠀➾ # ⚓ Release_Notes_for_Oracle_Linux_8.5⠀⇛ Oracle® Linux 8: Release Notes for Oracle Linux 8.5 provides information about the new features and known issues in the Oracle Linux 8.5 release. This document may be updated after it is released. # ⚓ Getting_started_with_Red_Hat_Insights_and_OpenSCAP for_compliance_reporting⠀⇛ Sysadmins trying to ride herd over tens, hundreds or thousands of systems need tools to help keep systems in compliance with policies and security standards. In this post we’ll look at using Red Hat Insights compliance service to manage compliance at scale. Verifying that your organization’s systems satisfy your compliance requirements is something that takes time and effort. Too often it’s only done on an ad hoc basis. That approach may work for organizations with a limited number of hosts, but performing this task at scale is problematic with complex environments and limited resources. Fortunately, organizations that use Red Hat Enterprise Linux (RHEL) in a standard operating environment (SOE) can take advantage of Red Hat Insights and its Compliance service to proactively and efficiently manage their regulatory compliance requirements at scale. Combining Red Hat Insights with Red Hat Smart Management and the Red Hat Ansible Automation Platform to create an automated process for compliance configuration, validation, and remediation can lessen the administrative burden of your compliance workload. # ⚓ Red_Hat_OpenShift_extends_High_Performance_Computing_ (HPC)_infrastructure_from_edge_to_exascale⠀⇛ Massive amounts of data are racing towards us at an unheard of velocity. But processing this data quickly, at a centralized location, is no longer possible for most organizations. How might we better act on this data to preserve its relevance? The answer lies in acting on the data as close to the source as possible. This means making data-driven decisions or getting answers to the most pressing questions in real-time, across all of your computing environments – from the edge to the exascale. If you’re processing massive amounts of data at scale with multiple tasks running simultaneously, you are likely already using high-performance computing (HPC). Oil & gas exploration, complex financial modeling and DNA mapping and sequencing are just a few modern workstreams that have massive data requirements and rely on HPC to drive breakthrough discoveries. With HPC, running advanced and computational problems and simulations in parallel on highly optimized hardware and super fast networks can help deliver answers and create outcomes more quickly. Because of HPC’s sheer scale, it would be challenging for the traditional datacenter infrastructure to deliver similar results. And also because its massive scale “just works,” HPC has largely gone unchanged over the past 20 years. Today, however, we are seeing HPC undergo a transformation as it faces increased demand from the applications running on it. # § Canonical/Ubuntu Family⠀➾ # ⚓ FSearch_is_an_‘Everything_Search_Engine’_Alternative for_Ubuntu⠀⇛ If you’re looking for a super fast file search tool for Ubuntu that’s similar to the Everything Search Engine on Windows you’re in the right place. FSearch is exactly what you’re looking for. The utility’s developer, Christian Boxdörfer, is even upfront about the inspiration, explaining on the project homepage: “ [Everything Search Engine] provides instant results as you type for all your files and lots of useful features (regex, filters, bookmarks, …). On Linux however I couldn’t find anything that’s even remotely as fast and powerful.” Christian says he a slew of Linux file search tools (including standalone ones like Catfish and ANGRYSearch, as well as the file-finding features baked into file managers like Nautilus) first, as he didn’t want to create “yet-another” file-search tool for Linux. Sadly, none of them were what he wanted, or catered to different use cases. So he built his own. o § Devices/Embedded⠀➾ # § Open Hardware/Modding⠀➾ # ⚓ Video:_$5,000_Raspberry_Pi_Server?⠀⇛ # ⚓ Finally,_A_Piano_BBQ_Grill_That_You_Can_Drive_Around the_Workshop⠀⇛ It’s a truth universally acknowledged that sometimes a little music can add much to a nice afternoon picnic. It’s also well-known that meat cooked over hot coals should be turned regularly to allow for even cooking. This barbecue grille project from [Handy Geng] delivers on both counts. The project uses a full 88 motors, activated by pressing keys on an electronic piano. The technique used is simple; rather than interface with the keyboard electronically or over MIDI, instead, a microswitch is installed under each individual key. # ⚓ This_tinyML_system_helps_soothe_your_dog’s_separation anxiety_with_sounds_of_your_voice_|_Arduino_Blog⠀⇛ Due to the ongoing pandemic, Nathaniel Felleke’s family dog, Clairette, had gotten used to having people around her all the time and thus developed separation anxiety when the family would leave the house. But thanks to some clever thinking, Felleke came up with the idea to automatically detect when his dog started to bark and play some sounds of his family speaking to calm her down. # ⚓ Arduino_Library_Makes_Digital_Rain_Like_It’s_1999_| Hackaday⠀⇛ There’s going to be a new Matrix movie in theaters next month, and you know what that means: we’re about to see a whole new generation get obsessed with the franchise’s iconic “Digital Rain” effect. Thanks to modern advertisement technology, expect to see lines of glittering text pouring down the displays of everything from billboards to gas pumps pretty soon. # ⚓ Nixie_Tube_Indicator_Tells_You_How_Many_Tasks_You’ve Got_Left_to_do⠀⇛ For busy people, keeping track of all the tasks on your to-do list can be a daunting task in itself. Luckily there’s software to help you keep organized, but it’s always nice to have a physical artifact as well. Inspired by some beautiful nixie clock designs, [Bertrand Fan] decided to build a nixie indicator that tells him how many open items are on his to-do list, giving a shot of instant gratification as it counts down with each finished task. o § Free, Libre, and Open Source Software⠀➾ # § SaaS/Back End/Databases⠀➾ # ⚓ Firebird_3.0.8_sub-release_is_available⠀⇛ Firebird Project is happy to announce general availability of Firebird 3.0.8 — the latest point release in the Firebird 3.0 series. This sub-release offers many bug fixes and also adds a few improvements, please refer to the Release Notes for the full list of changes. # § Programming/Development⠀➾ # ⚓ Concurrency_in_Julia⠀⇛ The Julia programming language has its roots in high-performance scientific computing, so it is no surprise that it has facilities for concurrent processing. Those features are not well-known outside of the Julia community, though, so it is interesting to see the different types of parallel and concurrent computation that the language supports. In addition, the upcoming release of Julia version 1.7 brings an improvement to the language’s concurrent-computation palette, in the form of “task migration”. # § Perl/Raku⠀➾ # ⚓ Vale,_David⠀⇛ David H. Adler passed away yesterday. David was a gentleman and a scholar: a gentle, warm, erudite, funny, clever, and deeply kind man. And one who has made a vast contribution to our Perl and Raku communities over more than quarter of a century. # § Python⠀➾ # ⚓ Late-bound_argument_defaults_for_Python⠀⇛ Python supports default values for arguments to functions, but those defaults are evaluated at function- definition time. A proposal to add defaults that are evaluated when the function is called has been discussed at some length on the python-ideas mailing list. The idea came about, in part, due to yet another resurrection of the proposal for None-aware operators in Python. Late-bound defaults would help with one use case for those operators, but there are other, stronger reasons to consider their addition to the language. In Python, the defaults for arguments to a function can be specified in the function definition, but, importantly, they are evaluated in the scope where the function is defined. So default arguments cannot refer to other arguments to the function, as those are only available in the scope of the function itself when it gets called. * § Leftovers⠀➾ o § Hardware⠀➾ # ⚓ SCPI:_On_Teaching_Your_Devices_The_Lingua_Franca_Of Laboratories⠀⇛ One could be excused for thinking sometimes that the concept of connecting devices with other devices for automation purposes is a fairly recent invention. Yet for all the (relatively) recent hype of the Internet of Things and the ‘smart home’, laboratories have been wiring up their gear to run complicated measurement and test sequences for many decades now, along with factories doing much the same for automating production processes. Much like the chaotic universe of IoT devices, lab equipment from different manufacturers feature a wide number of incompatible protocol and interface standards. Ultimately these would coalesce into IEEE-488.1 (GPIB) as the physical layer and by 1990 the first Standard Commands for Programmable Instruments (SCPI) standard was released that built on top of IEEE-488. o § Integrity/Availability⠀➾ # § Proprietary⠀➾ # ⚓ VMware_pulls_vSphere_update_that_only_made_things worse⠀⇛ So this is awkward for VMware. The virtualization giant has pulled an update to its flagship vSphere suite because it didn’t fix the problems it was released to address, and may have made them worse. The upgrade was vSphere 7 Update 3b, which on November 15 was the subject of a VMware blog post headed “Important Update.” It offered a fix for issues that could cause vSphere to crash, or prevent some upgrades from completing successfully. That post has been taken down – but The Register retrieved it [PDF] from Google’s cache. # ⚓ DRM_on_Motorcycles⠀⇛ Zero Motorcycles announced their groundbreaking new battery “technology”, in which they sell you a large capacity battery in a motorcycle with powerful motors and advanced traction control systems, and then lock all that away behind a software paywall that you can unlock (for a fee) in their app. # ⚓ Magnanimous_Apple_will_allow_people_to_fix_their iPhones_using_parts_bought_from_its_Self_Service_Repair program⠀⇛ # ⚓ Apple_announces_self_service_repair_program,_starting with_iPhone_12_and_13⠀⇛ This is a major win for right-to-repair, and I’m very happy Aplpe caved to regulatory, shareholder, and public pressure. Momentum behind right-to-repair has been growing for years now, and it’s satisfying to see it bear fruit. Of course, we’ll have to wait and see if there’s any catch – insane NDAs, crazy high prices, little to no stock – but if not, this could be a model for other companies to follow. # ⚓ Is_your_Apple_Mac_running_macOS_Monterey_leaking memory?_It_may_be_due_to_mouse_cursor_customization⠀⇛ # § Security⠀➾ # ⚓ Freexian’s_report_about_Debian_Long_Term Support,_October_2021⠀⇛ Every month we review the work funded by Freexian’s Debian LTS offering. Please find the report for October below. # ⚓ Secure_development:_New_and_improved_Linux Random_Number_Generator_ready_for_testing⠀⇛ The Linux Random Number Generator (LRNG), which relies on several computing functions to act as a source of entropy, is designed to be a drop-in replacement for the long-established / dev/random function. The technology is designed to offer both API (application programming interface) and ABI (application binary interface) compatibility with its /dev/ random predecessor, while offering several performance and utility advantages. # ⚓ CISA_Adds_Four_Known_Exploited_Vulnerabilities to_Catalog [Ed: Microsoft is a_threat_to_National Security]⠀⇛ CISA has added four new vulnerabilities to its Known Exploited Vulnerabilities Catalog, which require remediation from federal civilian executive branch (FCEB) agencies by December 1, 2021. CISA has evidence that threat actors are actively exploiting the vulnerabilities listed in the table below. These types of vulnerabilities are a frequent attack vector for malicious cyber actors of all types and pose significant risk to the federal enterprise. # ⚓ How_has_Abcbot_been_targeting_Linux? [Ed: "This botnet mainly targets systems and web servers with wear passwords, which makes it easier for the botnet to deploy the DDoS attack," so it does not sound like a Linux issue]⠀⇛ Reportedly, a new kind of botnet called Abcbot has been observed in the dark web world. According to the sources, this botnet has some worm-like propagation features to infect Linux systems. The main target of the botnet is to launch malicious denial-of- service (DDoS) attacks on the devices. # ⚓ GitHub_fixes_authorisation_vulnerability_in_the NPM_JavaScript_package_registry⠀⇛ # ⚓ The_inside_story_of_ransomware_repeatedly masquerading_as_a_popular_JS_library_for_Roblox gamers⠀⇛ Since early September, Josh Muir and five other maintainers of the noblox.js package, have been trying to prevent cybercriminals from distributing ransomware through similarly named code libraries. # ⚓ Rowhammer_defenses_in_RAM_chips_can_still_be defeated_•_The_Register⠀⇛ Boffins at ETH Zurich, Vrije Universiteit Amsterdam, and Qualcomm Technologies have found that varying the order, regularity, and intensity of rowhammer attacks on memory chips can defeat defenses, thereby compromising security on any device with DRAM. o § Defence/Aggression⠀➾ # ⚓ Russian_Anti-Satellite_Weapon_Test_Draws_Widespread Condemnation_|_Hackaday⠀⇛ On the morning of November 15, a Russian missile destroyed a satellite in orbit above Earth. The successful test of the anti-satellite weapon has infuriated many in the space industry, put astronauts and cosmonauts alike at risk, and caught the attention of virtually every public and private space organisation on the planet. It’s yet another chapter in the controversial history of military anti-satellite operations, and one with important implications for future space missions. Let’s examine what happened, and explore the greater context of the operation. o § Environment⠀➾ # § Wildlife/Nature⠀➾ # ⚓ MintCast:_Whitney_Webb_Discusses_Global_Elites’ Stealth_Takeover_of_Nature⠀⇛ As world leaders, celebrities, business moguls and activists alike descend on Scotland for the COP26 climate summit, behind the scenes powerful financial groups are attempting to rewrite the rules of international trade and to privatize nature under the guise of sustainability. While high politics has understandably made the headlines, a cartel of international bankers is attempting to use the crisis to rewrite international capitalism for their own benefit. o § Finance⠀➾ # ⚓ Linux_Unveils_a_Blockchain-Based_Platform_–_All_About_It! [Ed: Inappropriately using/riding the Linux brand]⠀⇛ By now, you have heard the hype about blockchain technology. The inherent capabilities of blockchain are vast in its ability to securely, transparently, and efficiently transmit information. The need to improve service delivery in the insurance industry led the Linux Foundation (LF) and AAIS (the American Association of Insurance Services) to use this distributed ledger to launch OpenDIL (Open Insurance Data Link). So what is OpenIDL, and what is its aim? Here, we will discuss that and more. o § Civil Rights/Policing⠀➾ # ⚓ Chiwenga_and_his_wife_saga!_No_wonder_white_people_have_a low_opinion_of_Africans_and_their_empty_philosophy_of_Ubuntu –_Bulawayo24_News⠀⇛ General Constantine Chiwenga could be a head of state anytime if Mnangagwa became incapacitated or for any other reason. We have people in the government in 2021 who could be well described as primitive and backward: Some fossils of five hundred years left behind by time, this is the calibre of leadership who have no values of Ubuntu. ䷩ 𝚕𝚒𝚗𝚎 6140 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.17.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Links_17/11/2021:_Proxmox_VE_7.1,_Qubes_OS_4.1_RC2,_Microsoft_Stealing People’s_Passwords⠀✐ Posted in News_Roundup at 4:43 pm by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈ § Contents⠀➾ * GNU/Linux o Distributions o Devices/Embedded * Free_Software/Open_Source * Leftovers * § GNU/Linux⠀➾ o ⚓ Tux’s_Favorite_Recipes:_Enticing_Snippets_from_the_New_‘Linux Cookbook,_2nd_Edition’⠀⇛ In Why I Wrote the Linux Cookbook, 2nd Edition, I discussed how much Linux has changed in a short time, and how I updated the Linux Cookbook to include some of these changes. Now I will share some snippets from the new book, so you can get a taste of how fabulous it is, and inspire you to dash out and buy many copies. o ⚓ Sick_of_Windows?_Here’s_how_easy_it_is_to_install_Linux⠀⇛ Linux isn’t nearly as challenging as you’ve been led to believe. In fact, it’s just as easy to use as any other operating system. But what about the installation? Wouldn’t installing an operating system be a challenge that’s way above the paygrade of the average user? Not necessarily. And now that you know how to test-drive Linux, it’s time you learned how to install the open- source operating system. Like the previous entry in this series, I’m going to focus on elementary OS because it’s one of the more user friendly distributions, and the installation is fairly indicative of the average Linux installation. o § Desktop/Laptop⠀➾ # ⚓ The_5_best_Linux_desktops_for_beginners_in_2021⠀⇛ Some people still insist that using Linux is hard. Sure, it was difficult — when I started with the Linux desktop back in the 1990s. But that was a long time ago. Today, the easiest desktop of all, Chrome OS, is simply Linux with the Chrome web browser on top of it. The more full-featured Linux desktop distributions are as easy to use in 2021 as Windows or macOS. Yes, you can get a lot more from Linux if you know how to do shell programming and the like. But that’s also true of Windows and PowerShell. With both operating systems, you don’t need to know the deep ins and outs of either one to get your work done. # ⚓ AWS_adds_Linux_app_streaming_alongside_Windows_to_‘greatly lower’_cost⠀⇛ Amazon Web Services has added support for streaming Linux applications and desktops to its AppStream service, which was previously Windows-only, claiming that it will “greatly lower the total streaming cost.” AppStream 2.0 has been running since late 2016 and enables users to stream GUI applications or entire desktops to a local PC either via a web browser or using a Windows client. Although running applications remotely has some drawbacks – such as latency, dependency on a strong internet connection, and potential snags accessing local resources like printers and storage – it also has advantages. # ⚓ Unsplash_Wallpapers_Is_An_Unsplash_Desktop_Open_Source App⠀⇛ You may have heard about Unspalsh; a very famous online service that provides high-quality images and wallpapers under a semi-open license. Unsplash is important for website creators, app designers and basically anyone who wants to get free wallpapers without having to deal with licensing issues (No attribution required, and even commercial usage of Unsplash images is allowed). It was a revolution in stock images when it first started. For the average user, though, nothing more is needed than setting these beautiful wallpapers as a background image for his/her operating system’s desktop. And for that, a desktop application is going to be needed. o § Audiocasts/Shows⠀➾ # ⚓ In_Conversation_with_Matthias_Ettrich,_Founder_of_KDE⠀⇛ On occasion of KDE’s 25th anniversary, Matthias Ettrich, the founder of KDE, talked to Lydia Pintscher, Vice President of KDE e.V., about how KDE came to be, what has changed since and how he sees the future of Linux desktops., To learn more about KDE, the Free Software we create, the Community and the history of our project, visit our 25th Anniversary site. # ⚓ mintcast_374_–_Mounted_Archery⠀⇛ First up in the news, Linux Mint Monthly News, Firefox 94 released, Steam OS announcement, System76 Desktop announcement, Intel has been doing this for a long time and Nvidia released a fix In security, A Dutch newspaper gets hacked, Azure is vulnerable, and AMD and Intel have more security flaws Then in our Wanderings, Joe works on an xbox, Josh remodels a bathroom, Tony got a new phone and Norbert tells us about running arch # ⚓ Three_Tumbleweed_Temptations_|_LINUX_Unplugged_432⠀⇛ Can we live with openSUSE Tumbleweed? We try three different builds and prepare ourselves for our journey into SUSE land. Our setups, what we liked, and what we still need to figure out. o § Kernel Space⠀➾ # ⚓ Sound_Open_Firmware_For_AMD_Audio_Hardware_Arrives, Initially_For_Renoir_ACP_–_Phoronix⠀⇛ Back in 2018 Intel founded Sound Open Firmware as their effort to provide an open-source audio DSP firmware and software development kit. AMD has begun supporting Sound Open Firmware too now, initially for the Renoir audio co-processor (ACP). Sound Open Firmware as a Linux Foundation project has been maturing over the past three years and now supports a wide-range of Intel hardware with other audio hardware also becoming supported. Ultimately it’s about having open-source audio DSP firmware and a SDK to better support modern audio processing. In the SOF documentation it’s summed up rather broadly, “The Sound Open Firmware SDK is comprised of many ingredients that can be customized for use in the firmware/software development lifecycle. Customization allows for a “best fit” development approach where the SDK can be optimized for a particular process or environment. Some SDK ingredients are optional while there can be more than once choice for other ingredients.” # ⚓ Linux_5.17_To_Support_Temperature_Monitoring_For_New_AMD Zen_Generation_–_Phoronix⠀⇛ The Linux 5.17 kernel next year will support temperature monitoring for a “new generation” of AMD Zen processors. While AMD has often been late to the game in supporting CPU temperature reporting under Linux for Zen processors, it’s nice to see them out in front ahead of their next launch. Even in cases where new IDs simply need to be added to the k10temp driver, unfortunately they have often not added them until post-launch or in some cases where those in the community (including cases like I when getting hands on review samples) have the hardware and find the support not working until making some trivial driver alterations. # ⚓ Linux_5.14.19⠀⇛ I'm announcing the release of the 5.14.19 kernel. All users of the 5.14 kernel series must upgrade. The updated 5.14.y git tree can be found at: git://git.kernel.org/pub/scm/linux/kernel/git/ stable/linux-stable.git linux-5.14.y and can be browsed at the normal kernel.org git web browser: https://git.kernel.org/?p=linux/kernel/git/stable/ linux-s... thanks, greg k-h # ⚓ Linux_5.4.160⠀⇛ # § Graphics Stack⠀➾ # ⚓ NVIDIA_Looks_To_Improve_Power_Management_For_Linux VFIO_PCIe_Devices_–_Phoronix⠀⇛ NVIDIA is looking to enable run-time power management for the VFIO PCI Linux driver to allow for better power-savings. For PCIe devices assigned to the vfio_pci driver for passing through to a guest virtual machine, a NVIDIA engineer sent out a patch series allowing for run-time power management. The VFIO PCI driver code currently has very limited power management handling and with this series the hope is moving the PCIe device from D3hot to D3cold state when appropriate to save on power consumption. o § Instructionals/Technical⠀➾ # ⚓ Sending_logs_from_syslog-ng_store_box_to_Splunk_–_Blog_– syslog-ng_Community_–_syslog-ng_Community⠀⇛ One of the most popular applications to feed Splunk with syslog messages is syslog-ng. However not everyone is happy to work on the command line anymore. This is where syslog-ng store box (SSB), an appliance built around syslog-ng, can help. The SSB GUI provides you not only with an easyto-use interface to configure most syslog-ng features, but also a search interface and complete log life cycle management. It can forward log messages to several destinations, recently also to Splunk’s HTTP Event Collector (HEC). From this blog you can learn about how SSB fits into your logging infrastructure and how to configure SSB for Splunk. # ⚓ Clean_empty_job_groups_in_openQA_–_openQA_bites⠀⇛ In this blog post I present you a small script, which can help you to remove empty job groups from your own openQA instance. This is helpful if you have a development instance with a lot of job groups, that you never use. This script can help you to tidy the list of dangling job groups. # ⚓ How_to_check_if_an_RHEL_system_is_vulnerable_to_a_CVE⠀⇛ Most companies scan infrastructure devices for vulnerability every quarter, but the duration may vary depending on the company’s ITSM policy. After the security scan, if the security team finds vulnerabilities in a specific support group, such as Linux, Windows, Middleware or Network, it will be sent to them. Once assigned, the team will create a CR (Change Request) based on the environment such as TEST, DEV, UAT or PROD and mitigate it to make their systems more secure. # ⚓ How_to_Install_MariaDB_10.7_on_Ubuntu_20.04_– LinuxCapable⠀⇛ MariaDB is one of the most popular open-source databases next to its originator MySQL. The original creators of MySQL developed MariaDB in response to fears that MySQL would suddenly become a paid service due to Oracle acquiring it in 2010. With its history of doing similar tactics, the developers behind MariaDB have promised to keep it open source and free from such fears as what has happened to MySQL. MariaDB has become just as popular as MySQL with developers, with features such as advanced clustering with Galera Cluster 4, faster cache/ indexes, storage engines, and features/extensions that you won’t find in MySQL. In the following tutorial, you will learn how to install MariaDB 10.7 on Ubuntu 20.04 LTS Focal Fossa. # ⚓ How_to_Install_PHP_8.1_on_Fedora_35_–_LinuxCapable⠀⇛ PHP 8.1 is a significant update of the PHP language that will be “officially” released on November 25, 2021. This is a standard upgrade going forward from the existing PHP 8.0 release with the new PHP 8.1 is bringing enums, fibers, never return type, final class constants, intersection types, read-only properties amongst the long list of new features and changes. In the following tutorial, you will learn how to import the REMI Module and install PHP 8.1 on your Fedora 35 system. # ⚓ How_to_install_a_full_desktop_on_a_Multipass_virtual machine_for_easier_Linux_development_–_TechRepublic⠀⇛ Multipass is still one of my favorite virtual machine systems. With this command-line tool, I can very quickly spin up a virtual instance of Ubuntu in seconds. These VMs can be used for testing, development and other use cases. # ⚓ How_to_Install_PHP_8.1_on_Rocky_Linux_8_–_LinuxCapable⠀⇛ PHP 8.1 is a significant update of the PHP language that will be “officially” released on November 25, 2021. This is a standard upgrade going forward from the existing PHP 8.0 release with the new PHP 8.1 is bringing enums, fibers, never return type, final class constants, intersection types, read-only properties amongst the long list of new features and changes. In the following tutorial, you will learn how to import the REMI Module and install PHP 8.1 on your Rocky Linux system. # ⚓ How_to_Install_MongoDB_with_Podman_on_Rocky_Linux_8_– NextGenTips⠀⇛ In this tutorial I will be showing you how to install MongoDB with Podman on Rocky Linux. Mongodb is an open source NoSQL database that provides high throughput for data driven applications. Unlike relational databases such as MySQL, Oracle and SQL server which store data in tables according to a rigid schema, MongoDB stores data in documents with flexible schema. Podman is a daemonless, open source, Linux native tool designed to make it easy to find, run, build, share and deploy applications using Open Container Initiative (OCI) containers and container images. # ⚓ How_To_Install_Hugo_on_Debian_11_–_idroot⠀⇛ In this tutorial, we will show you how to install Hugo on Debian 11. For those of you who didn’t know, Hugo is a free and open-source website framework written in developed in Go. Hugo provides a reliable and modern static site generator. It is capable of generating a site at a speed of less than 1 ms per page. It works by shipping pre-made templates to make a quick work of SEO, analytics, commenting e.t.c. Hugo sites can run without any expensive run times like PHP, Python, Ruby and don’t need any database. 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 Hugo static site generator on a Debian 11 (Bullseye). # ⚓ How_To_Find_All_Files_Containing_Specific_Text_On_Linux From_The_Command_Line_–_Linux_Uprising_Blog⠀⇛ This article explains how to find all files containing specific text on Linux. For this we’ll use grep, a standard Unix program. grep is a command-line utility which prints lines that match a given pattern, and should be installed by default. Let’s start simple. Say you want to search for the word text (case-sensitive!) in all the files in the current directory and its subdirectories. To do this, you need to open the terminal, navigate to the folder where you want to perform the search, and run… # ⚓ 20_one-line_Linux_commands_to_add_to_your_toolbox_|_Enable Sysadmin⠀⇛ Many Linux users have experienced a lasting sense of accomplishment after composing a particularly clever command that achieves multiple actions in just one line or that manages to do in one line what usually takes 10 clicks and as many windows in a graphical user interface (GUI). Aside from being the stuff of legend, one-liners are great examples of why the terminal is considered to be such a powerful tool. # ⚓ What_is_a_Hypervisor?_What’s_Difference_Between_Type_1_& 2?⠀⇛ Before you see difference between Type 1and Type 2 Hypervisor and which one is better (if that’s even a case), let’s first see what a Hypervisor is. # ⚓ Monitoring_bandwidth_on_Linux_with_Nethogs_–_Unixcop_the Unix_/_Linux_the_admins_deams⠀⇛ Hello, colleagues. It is the task of any computer scientist to know how to manage the bandwidth of a computer. Especially if this computer is a server or a production computer that needs to know how the bandwidth is spent. So, in this post, you will learn how to monitor bandwidth in Linux. For this, we will use a CLI tool called NetHogs. Sounds interesting? So, let’s go for it. # ⚓ How_to_Install_Python_3.11_on_Ubuntu_20.04_–_LinuxCapable⠀⇛ Python is one of the most popular high-level languages, focusing on high-level and object- oriented applications from simple scrips to complex machine learning algorithms. Python is famous for its simple, easy-to-learn syntax, emphasizes readability, and reduces program maintenance costs and more straightforward conversion to newer releases. Python supports modules and packages. One of the many is the popular PIP package manager. # ⚓ How_to_install_MongoDB_4.4_on_Fedora_35_–_NextGenTips⠀⇛ In this tutorial we are going to explore how to install MongoDB on fedora 35. MongoDB is a free and open source document database designed for ease of application development and scaling. Every record in a mongoDB document, which is a data structure composed of field and pair values. MongoDB stores documents in collection. Collections are analogous to tables in relational databases. # ⚓ How_to_use_grep_to_search_for_strings_in_files_on_the shell⠀⇛ The grep command, which stands for global regular expression print, is one of the most versatile commands in a Linux terminal environment. It is an immensely powerful program that allows the user to sort input according to complex rules, which makes it a rather popular link in numerous command chains. The grep command is primarily used to search text or any file for lines that contain a match to the specified words/strings. By default, grep displays the matched lines, and it can be used to search for lines of text that match a regular expression(s), and it outputs only the matched lines. # ⚓ How_to_create_an_SQS_Queue_on_AWS⠀⇛ Amazon Simple Queue Service (SQS) is a managed message queuing service of AWS which enables us to decouple and scale microservices, distributed systems, and serverless applications. Using SQS, we can send, store, and receive messages between software components at any volume, without losing messages. Standard queues offer maximum throughput, best-effort ordering, and at least-once delivery. FIFO queues are designed to guarantee that messages are processed exactly once, in the exact order that they are sent. SQS Eliminates administrative overhead, provides Reliably delivery of messages, keeps sensitive data secure, and scales elastically and cost- effectively. Security, Durability, Availability, Scalability, Reliability, Customization are a few of the benefits of using SQS. There are 2 types of SQS Queues on AWS. # ⚓ How_To_Install_Apache_with_Let’s_Encrypt_on_RHEL_8⠀⇛ In terms of popularity and usage, the Apache webserver engine tops all other web server software systems, and for good reasons. The Apache Software Foundation ensured that this cross-platform web server software is attributed as free, open-source, and easy to configure. Its user-friendly footprints make it an ideal web server software alternative even for beginners that want to experience how their websites/applications will perform under HTTP and HTTPS protocols. # ⚓ 3_interesting_ways_to_use_the_Linux_cowsay_command_| Opensource.com⠀⇛ Most of the time, a terminal is a productivity powerhouse. But there’s more to the terminal than commands and configurations. Among all the outstanding open source software out there, some of it has been written just for fun. I’ve written about fun commands before, but this article is about just one: the venerable cowsay command. o § Games⠀➾ # ⚓ SteamVR_Overlay_not_working_on_Arch_or_Manjaro_Linux? Here’s_a_fix_|_GamingOnLinux⠀⇛ Sadly, SteamVR on Linux continues to have quite a lot of quirks and over time it’s gotten a little rough, here’s a way to fix the SteamVR Overlay not working. One of the most annoying bugs right now is how the SteamVR Overlay doesn’t seem to work. Not just that, but even the settings menu from the main SteamVR menu doesn’t seem to work either. This appears to be a problem on any Arch-like Linux distribution (EndeavourOS, Manjaro etc) and seems to originate with the vrwebhelper. # ⚓ Baba_Is_You_gets_a_level_editor,_new_levels_and_more_| GamingOnLinux⠀⇛ Baba Is You, the puzzle game where you push word blocks around to link them and change all the rules has a big free update out now with a level editor. I’ve said it before and I’ll say it again: it’s absolutely amazing. It’s easily one of the best puzzle games ever made. Don’t just take my word for it, on Steam it has an Overwhelmingly Positive score from over 12,000 players. It’s good! This new free update brings with it a level editor, online level sharing with codes and built-in options to view them, a curated Featured Levels list, two new fully level packs from the developer with over 150 new puzzles and more. # ⚓ Duke_Smoochem_3D_is_turning_into_a_hilarious_look_at Britain_in_Doom⠀⇛ What started off as a joke, Duke Smoochem 3D now seems to be turning into something of an actual game. The joke was around former UK Secretary of State for Health and Social Care, Matt Hancock, who was famously captured on CCTV kissing an aid which broke COVID-19 social distancing restrictions. [...] Meanwhile, if you’re after another good bit of retro-fuelled gaming with a British edge to it, there was also the Thatcher’s Techbase release from September that sees you take down an evil reincarnation of Maggie Thatcher. # ⚓ The_Polaris_15_and_17_from_Tuxedo_Computers:_Linux_Notebook Full_Review_–_Invidious⠀⇛ Tuxedo Computers sent over both the 15″ and 17″ versions of their new 3rd-gen Polaris notebook, and in this video I’ll review both! I’ll compare the two models side-by-side, and I’ll give you my thoughts # ⚓ Ready,_player_anyone?_China’s_gaming_ban_left_cloud providers_looking_for_someone_to_play_with⠀⇛ China’s decision to limit minors to three hours of gaming each week has proven problematic for the nation’s clouds, which find themselves with unused capacity. So said Steve Brazier, CEO of channel-centric analyst firm Canalys, at the company’s Asia-Pacific Forum “25 to 30 per cent of Chinese cloud capacity was for gaming,” Brazier said. Chinese clouds like Alibaba are now trying to figure out what to do with that capacity. Some have even deferred datacentre builds as a result, Brazier said. # ⚓ Experiences_of_configuring_and_using_a_‘hackendeck’ homemade_Steam_Deck⠀⇛ Valve recently released information about developing for the Steam Deck if you didn’t have a Dev-Kit which is an engineering verification test build (EV2) version of their device. Included in the documentation is a suggestion to build your own Steam Deck, or ‘hackendeck’ using a mini PC. Whilst I didn’t have the exact brand they picture in the article I did have a mini PC with the required specifications so I set about following the instructions to see how it performed. # ⚓ Everything_we_learned_from_the_Steam_Deck_Developer’s Conference_–_Invidious⠀⇛ # ⚓ First-person_shooter_RPG_‘Beyond_Sunset’_looks_awesome_in the_new_trailer_|_GamingOnLinux⠀⇛ With a graphical style inspired by classic DOS games, Beyond Sunset is probably one of the absolute most promising looking retro shooters coming. “SUNSET CITY, CALIFORNIA – 20XX: You’ve been awakened from cryostasis. Your name, your identity, your memories… All lost in the confusing fog of hypersleep. Not only a stranger in a strange place, you begin to manifest powerful abilities. Lightning-fast reactions. Innate combat skills. Near-supernatural agility. You’re not like everyone else. # ⚓ Kingdom_Come:_Deliverance_gets_shown_off_on_the_Steam_Deck |_GamingOnLinux⠀⇛ Sadly, this is a game that was supposed to offer up native Linux support years ago as a result of the Kickstarter crowdfunding campaign. When the release was coming up, the developer cancelled both Linux and macOS support for launch and then just never ported it. A huge shame but at least with Steam Play Proton around there is another option to play Windows versions on Linux through Steam. # ⚓ Sci-fi_point_and_click_adventure_Warp_Frontier_released_for Linux_|_GamingOnLinux⠀⇛ Originally released in September, developer Brawsome has now ported over their space sci-fi point and click adventure War Frontier over to Linux. “Vincent Cassini, decorated war hero, but still just a Captain in the police force he started, is patrolling the orbital slums of his home planet Cetus, when he stumbles across a lead in a war crime that resulted in the mysterious disappearance of thousands of Cetans, including his first wife and best friend. Captain Cassini and his robot partner MAC, must ally with morally questionable characters to stop an old enemy before their crimes are erased forever. # ⚓ Squid_Game_knock-off_Crab_Game_now_has_a_Linux_version_| GamingOnLinux⠀⇛ Squid Game, the huge Netflix hit, was always going to inspire others and it clearly did with the free multiplayer title Crab Game and the developer has now put up a Linux build on Steam. It looks completely ridiculous of course but it’s surprisingly fun to play and watch. Crab Game has been quite a big hit on Twitch too, with tens of thousands watching people spectacularly fail at it. # ⚓ Take_down_the_enemy_capital_ship_in_Deep_Space_Battle_Sim out_now_|_GamingOnLinux⠀⇛ Deep Space Battle Simulator, a game where two opposing sides battle it out in space with their capital ships has now left Early Access on Steam. It’s a round-based multiplayer first-person online game, one that allows a fair amount of freedom in how each team goes about conquering the other side. Each team is made up of actual players (8-16 on each side), who will fly around in fighters and board the enemy ship to try and take it down. A fun idea if you’re a space sci-fi fan. # ⚓ You’ll_be_able_to_save_the_bees_together_online_in_APICO_| GamingOnLinux⠀⇛ APICO is an upcoming casual wholesome game about saving the bees, breeding them and building up your own beekeeping dream and the developer recently revealed online multiplayer support. o § Desktop Environments/WMs⠀➾ # ⚓ JWM_version_2.4.0_compiled⠀⇛ JWM, Joe’s Window Manager, has been in the pups since the very early days. JWM is not just a window manager, it also manages one or more trays and one or more menus. # § K Desktop Environment/KDE SC/Qt⠀➾ # ⚓ Evolving_3D_desktop_effects_in_Plasma⠀⇛ The latest Plasma release dropped a few desktop effects: the cube family, CoverSwitch and FlipSwitch. All of those effects were written back in 2008, the early days of KDE 4.x and the early days of desktop effects in KWin. The effects were implemented by me and when Vlad asked about removing them I saw the need for this and supported this step for technical reasons. With this blog post I want to share a little bit of why it was needed to remove them and why this means that they can come back in better ways than ever before. To really understand this we need to time travel back to 2008 and the years before when desktop effects were introduced. This can help to understand how the hardware architecture changed and how that influenced design decisions in the effects API which are nowadays problematic. First of all CPUs. The Intel Core 2 Duo architecture was launched in 2006 as the brand new thing which had multiple (namely 2) cores which slowly replaced the NetBurst architecture which dominated Desktop computing for the beginning of that decade. # § GNOME Desktop/GTK⠀➾ # ⚓ Clapper_–_GNOME_media_player_built_using_GJS_with GTK4_toolkit⠀⇛ GTK is a free and open-source cross-platform widget toolkit for creating graphical user interfaces (GUIs). Offering a complete set of widgets, GTK is used from small one-off tools to complete application suites. GTK 4.0 was released in December 2020 with components that rely on GTK4 following promptly. The GNOME desktop is built on the GTK toolkit. GNOME 40 released in March 2021 supports GTK4. Many distros include GNOME 40 such as Ubuntu 21.10, Arch, Debian, Fedora, and Gentoo to name a few. # ⚓ Cinnamon_5.2_Desktop_Environment_Released,_This_Is What’s_New⠀⇛ Cinnamon 5.2 is packed with an improved Menu applet that now features better keyboard navigation for RTL (Right-to-Left) languages, symbolic icons for all apps, the ability to hide the app buttons by default and when the menu is closed, support for displaying completion results only when the file system path entry is enabled, and the ability to show refreshed menu items while the menu is open. # ⚓ China_has_now_used_a_major_Safari/Webkit_zero_day vulnerability_against_Hong_Kong_activists_for_at_least the_second_time.⠀⇛ On GNOME Web (especially in Flatpak), it’s actually quite a bit safer because of advanced Linux sandboxing techniques, and additional hardening options available to the GNU Compiler, which simply either don’t exist or are broken, or fake (report success, do nothing) in Apple’s Clang/LLVM. In many cases, the browser would simply crash rather than arbitrary code execution. I really can’t tell you how much I dislike Clang/LLVM. Apple switched over to it from GCC not due to maturity or technical excellence, but to get away from the GNU GPLv3, and now it’s democracy protesters in China who get to pay for that. When Fedora’s engineering steering committee was debating switching to LLVM based on anti- GNU FUD coming from Mozilla, I was preparing to apply two patches to Firefox (someone else quickly wrote them to make Firefox build on GCC with the features Mozilla said weren’t possible in GCC 8, to justify their switch to an inferior compiler) and build it under some other name and put it in my COPR repo instead. Now I don’t use Fedora or Firefox. If that had been the only thing going wrong with it, I might have groused a little and stayed in the end, but IBM has moved Fedora in a direction where it’s even less stable than Debian Sid! And Mozilla has turned into a political party of extremism (wokeness/corporate leftism) and Cancel Culture, and a thrall of Big Tech. # ⚓ Strong_passwords,_2FA,_and_GNOME_Authenticator.⠀⇛ About a year ago, I noticed that I kept getting emails that some of my accounts had been taken over. Nothing very important. An old Disney rewards account I signed up for to get free DVDs forever ago, an unused Spotify account from I don’t know when. But it got me thinking about security. Up until that point, I had dodged bullets. I hated passwords, I used bad practices without even considering it (like reusing weak passwords over and over again), and I decided to clean house. o § Distributions⠀➾ # ⚓ MX_Linux_MX-21_KDE_–_Now,_here’s_a_verily_splendid_distro⠀⇛ Luck is a combination of two factors: probability and time. Case in point, my foray with MX Linux MX- 21 KDE. As you well know, I’m a great fan of this small yet feisty distro. So far, I’ve mostly tested (and liked) the Xfce flavors. My one quick brush with its KDE build was largely unsuccessful. In fact, with the release of MX-21 Wildflower, I wasn’t even thinking of testing the KDE version. But then, as luck would have it, the official download page didn’t have the Xfce release available for my Lenovo IdeaPad box. To be able to run on modern systems with UEFI, AMD Ryzen processors and NVMe, you need the AHS release – I discovered this with MX-19.3. However, at the time of writing, or rather testing, there was only the regular Xfce edition sans modern stuff, the Xfce AHS in almost-but-not-quite Release Candidate (4), and the KDE version, with all the right bits in place! So I thought, let’s go for it. # § New Releases⠀➾ # ⚓ Qubes_OS_4.1-rc2_has_been_released!⠀⇛ We’re pleased to announce the second release candidate for Qubes 4.1! Qubes 4.1-rc2 contains fixes for bugs that were discovered in the first release candidate (4.1-rc1). For existing Qubes 4.1- rc1 users, a regular update is sufficient to upgrade to 4.1-rc2. # § PCLinuxOS/Mageia/Mandriva/OpenMandriva Family⠀➾ # ⚓ Audacity_»_PCLinuxOS⠀⇛ Audacity is an open source, freely distributed, cross-platform and easy-to-use software project designed from the offset to act as an audio editor and recorder for personal computers. Updated to 3.1.2. # § IBM/Red Hat/Fedora⠀➾ # ⚓ CentOS_Alternative_Rocky_Linux_8.5_Is_Out_Now⠀⇛ Rocky Linux 8.5 is now availlable for the download. Based on Red Hat Enterprise Linux 8.5. It inherits many of the new features from RHEL 8.5. This is the first release of Rocky Linux with official Rocky Linux signed Secure Boot shim. # ⚓ Customize_Python_dependency_resolution_with_machine learning_|_Red_Hat_Developer⠀⇛ It has not been that long since pip, the Python package installer, introduced a new resolver. A resolver is a critical piece of programming infrastructure, responsible for locating and selecting versions of packages to use when building an application. The new pip resolver uses a backtracking algorithm that works considerably better than the old one, according to community feedback. This article introduces a new cloud-based Python dependency resolver created by Project Thoth. Running in the cloud, Thoth uses reinforcement learning techniques and your desired criteria to resolve Python library dependencies. Moreover, a pluggable interface lets you fix underpinning and overpinning issues (that is, where specified versions of packages are too strict or too lax) and make additional adjustments to the resolution process. The process takes into consideration the runtime environment, hardware, and other inputs to the cloud-based resolver. # ⚓ From_Godot_to_RPM_–_Fedora_Magazine⠀⇛ With more games being developed with the Godot engine, we need to learn how to package these games for Fedora. Developing a game is complex. The requirements for each game differ. In the past developers created new game engines for each game. Over time game engines become more generic. They adapt to cover a style of game. Some engines can create a wide variety of games. Godot is a well known open source game engine. Both open source and closed source games use the system. The Godot packages for Fedora run these games but no RPM package examples exist. Much of the packaging is the same regardless of the application. RPM spec files need summary, version, license, description, etc. For build requirements, you need the godot- headless package. Godot publishes a pck file but requires a graphical user interface to run. Godot headless builds a project without needing a graphical user interface. # ⚓ Managing_persistent_volume_access_in_Kubernetes_|_Red Hat_Developer⠀⇛ Data storage gets complex in the world of containers and microservices, as we discussed in Part 1 of this series. That article explained the Kubernetes concept of a persistent volume (PV) and introduced Red Hat OpenShift Data Foundation as a simple way to get persistent storage for your applications running in Red Hat OpenShift. Beyond the question of provisioning storage, one must think about types of storage and access. How will you read and write data? Who needs the data? Where will it be used? Because these questions sound a bit vague, let’s jump into some specific examples. I ran the examples in this article on Developer Sandbox for Red Hat OpenShift, a free instance of OpenShift that you can use to begin your OpenShift and Kubernetes journey. # ⚓ The_office’s_next_chapter:_How_CIOs_can_shape_a positive_workplace_experience_|_The_Enterprisers Project⠀⇛ When the pandemic hit, the first wave of transformation was about moving employees home and supporting remote workers. The result of that transformation has forever changed our workforce – today, people are able to get work done from anywhere. It’s also forever changed the role of the physical workplace. The office will always have an important role in work. And as employees continue to return to the office, it’s time to think about how we can make it a place where people want to be – not just need to be – and a place where they can work effectively. Creating an enticing workplace experience is nothing new; years ago, tech companies in Silicon Valley began offering perks such as chef-prepared meals in the cafeteria and massages to attract and retain top talent. Today, the pandemic has employees reflecting on what benefits are important to them and which jobs align with their values, wants, and needs in a career. The perks that get them excited to come into the workplace might change. After working from home, for example, they likely crave time for collaboration and socializing in the workplace. And it’s up to us to help rethink that workplace experience with sustainability and employee needs in mind. After the warp-speed transformation CIOs have experienced over the last two years, now is not the time to slow down. As you look toward the near future, focus on improving the workplace experience, including by leveraging data from sensors and forming stronger cross- functional partnerships that can drive your organization forward. # ⚓ 3_things_CIOs_should_know_about_developers_in_the cloud_era⠀⇛ What do today’s developers wish CIOs and IT leaders knew about the realities of the cloud era? What do developers want in order to advance their careers? For my first episode hosting Red Hat’s livestreaming show, In The Clouds, I was excited to dig into these and related questions around the role of developers in the enterprise. I was joined by the leaders of the Red Hat Developer Business Unit: Vice President and General Manager Mithun T. Dhar and Senior Director of Developer Marketing and Strategy Ignacio Riesgo Pablo. We had an excellent discussion about how Red Hat works with developers and the unique culture and opportunities that brought all three of us to join the company. # § Debian Family⠀➾ # ⚓ Proxmox_VE_7.1_released!⠀⇛ we’re excited to announce the release of Proxmox Virtual Environment 7.1. It’s based on Debian 11.1 “Bullseye” but using a newer Linux kernel 5.13, QEMU 6.1, LXC 4.0, Ceph 16.2.6, and OpenZFS 2.1. and countless enhancements and bugfixes. Proxmox Virtual Environment brings several new functionalities and many improvements for management tasks in the web interface: support for Windows 11 including TPM, enhanced creation wizard for VM/container, ability to set backup retention policies per backup job in the GUI, and a new scheduler daemon supporting more flexible schedules.. # § Canonical/Ubuntu Family⠀➾ # ⚓ The_future_of_documentation_at_Canonical⠀⇛ We’ve understood the importance of this for some time, but actually finding a way to express those values in our practice is less easy. One thing that has made it difficult at Canonical is the complexity of our engineering, product and services portfolio. Our software spans a range from single- purpose command-line tools to vertical ecosystems composed of dozens of discrete component products, created by dozens of independent engineering and product teams. We’ve been able to create unified and coherent software product lines, but we’ve been less successful doing the same for documentation. We want to do better for our documentation users – this is how we’re going to do it. # ⚓ Ubuntu_Maker_Canonical_Planning_To_Vastly_Improve_Its Documentation⠀⇛ Back in the day Ubuntu’s Wiki was a great resource for Linux documentation but less so these days while the Arch Linux Wiki is often viewed as a gold standard for open-source documentation. Canonical though is now hoping to radically improve the documentation for Ubuntu and its other software offerings. o § Devices/Embedded⠀➾ # ⚓ Tiger_Lake-U_module_offers_quad_displays_and_PCIe_Gen4⠀⇛ Aaeon’s “COM-TGUC6” Compact Type 6 module runs on an 11th Gen ULP “E” and “GRE” processors with up to 32GB DDR4, quad display support, 2.5GbE, 4x USB 3.2 Gen2, PCIe Gen3 x5, and PCIe Gen4 x4. Aaeon has launched its COM-TGUC6 COM Express Compact Type 6 module, which it teased over a year ago. The module joins other Tiger Lake ULP3 (Tiger Lake-U) based Compact Type 6 entries including Adlink’s cExpress-TL, Kontron’s COMe-cTL6, Portwell’s PCOM-B656VGL, and Congatec’s Conga-TC570 and more industrial Conga-TC570r. # § Open Hardware/Modding⠀➾ # ⚓ Orange_Pi_R1_Plus_LTS_is_a_cheaper_dual_GbE_SBC_with YT8531C_Ethernet_transceiver⠀⇛ It’s been a while since Shenzhen Xunlong Software released a new Orange Pi board. But the wait is over… sort of, as Orange Pi R1 Plus LTS is a low-cost version of Orange Pi R1 Plus SBC that replaced the Realtek RTL8211E PHY with a YT8531C Ethernet PHY that offers the exact same features but at a lower price. That means the new single board computer is still designed for headless operation, for example a router or firewall, with a Rockchip RK3328 processor, 1GB RAM, dual Gigabit Ethernet, and a USB 2.0 port. # ⚓ Cramming_A_DS_Inside_A_Gameboy_|_Hackaday⠀⇛ Many holiday recipes and console hacks share a common theme: cramming a thing inside another thing. Whether it’s turducken or a Nintendo DS inside a Gameboy, the result is always unexpected. The chassis for this mod is a humble Gameboy color with a Gameboy SP screen tackled on the top to serve as the secondary display. Unfortunately, this mod lost touch screen functionality, limiting some of the games you can play. [TheRetroFuture] received the custom handheld from [GameboyCustom], which was somewhat damaged in shipping. The original screw mounts had to be removed and the case glued back together to fit the DS motherboard. So for [TheRetroFuture] to get inside to start troubleshooting involved a razor blade and patience. Testing various points and swapping components got [TheRetroFuture] closer to the root problems. The fix ended up being a few wires that came loose during shipping. Finally, after reseating a display connection and some careful soldering, it booted and started playing games. # ⚓ NTP,_Rust,_And_Arduino_Make_A_Phenomenal_Frequency Counter_|_Hackaday⠀⇛ Making a microcontroller perform as a frequency counter is a relatively straightforward task involving the measurement of the time period during which a number of pulses are counted. The maximum frequency is however limited to a fraction of the microcontroller’s clock speed and the accuracy of the resulting instrument depends on that of the clock crystal so it will hardly result in the best of frequency counters. It’s something [FrankBuss] has approached with an Arduino-based counter that offloads the timing question to a host PC, and thus claims atomic accuracy due to its clock being tied to a master source via NTP. The Rust code PC-side provides continuous readings whose accuracy increases the longer it is left counting the source. The example shown reaches 20 parts per billion after several hours reading a 1 MHz source. # § Mobile Systems/Mobile Applications⠀➾ # ⚓ T-Mobile,_Verizon,_Sprint_&_AT&T_Android_12_update tracker:_Eligible…⠀⇛ # ⚓ PS5_DualSense_controller_support_has_finally_landed on_Android_12_|_TechRadar⠀⇛ # ⚓ Verizon_and_T-Mobile_Galaxy_S21_eSIM_support_unlocked by_Samsung’s_Android_12_update_–_PhoneArena⠀⇛ # ⚓ Check_out_this_Android_12L_deep_dive_for_all_the finer_details_and_tiny_tweaks⠀⇛ # ⚓ Android_12_makes_saving_and_sharing_images_easier than_ever_before⠀⇛ # ⚓ Samsung_Android_12_update:_These_devices_have_One_UI 4.0_–_9to5Google⠀⇛ # ⚓ Android_12_on_the_Galaxy_S21_has_a_lag_issue_– SamMobile⠀⇛ # ⚓ A_20-second_tweak_for_smarter,_simpler_Android security_|_Computerworld⠀⇛ # ⚓ Gmail_For_Android_Finally_Gets_Updated_Material_You Widget ⠀⇛ # ⚓ 3_Android_Apps_That_Let_You_Use_Multiple_Search Engines_at_the_Same_Time⠀⇛ # ⚓ 8_Common_Mistakes_Slowing_Down_Your_Android_Phone_ (And_What_to_Do_Instead)⠀⇛ # ⚓ Android_Auto_bug_is_bad_news_for_Samsung_Galaxy_S21 owners_|_T3⠀⇛ # ⚓ Android_12_broke_Amazon_Appstore,_company_aware_& working_on_a_fix⠀⇛ # ⚓ Redmi_Note_8_Android_11_Update_for_Indian_Users Reportedly_Ready_|_Technology_News⠀⇛ # ⚓ OnePlus_rolling_out_Android_November_security_patch update:_When_will_your_phone_get_it⠀⇛ # ⚓ CarPlay,_Android_Auto_Offer_Alluring_Potential_for Restaurant_Mobile_Apps_|_QSR_magazine⠀⇛ # ⚓ Xiaomi_Said_to_Be_Working_on_New_Compact_Android Phones_With_Snapdragon_870_SoC⠀⇛ # ⚓ Realme_Pad_Android_tablet_launches_in_Europe_–_Geeky Gadgets⠀⇛ # ⚓ 5_Android_settings_to_change_immediately_to_get_more out_of_your_phone_–_CNET⠀⇛ # ⚓ Gmail_for_Android_gets_a_brand_new_Material_You widget⠀⇛ o § Free, Libre, and Open Source Software⠀➾ # § Web Browsers⠀➾ # § Mozilla⠀➾ # ⚓ Karl_Dubost:_Browser_regression_and_tools⠀⇛ In simplified terms, there is a regression when a code used to work and is not working properly after a specific release. For websites, a webpage would stop having the right behavior after updating to a new version of the browser. # ⚓ Firefox_Relay_is_Now_Out_of_Beta_&_Adds_New Premium_Plan_to_Help_Protect_Your_Real_Email Address_–_It’s_FOSS_News⠀⇛ Firefox Relay aims to help you protect your real email address by providing email aliases. While good options like Simplelogin, and AnonAddy already exists, Mozilla’s Firefox Relay can encourage more users to use email aliases. For a while, it was in the beta phase with limited access to features. Now, as per the official announcement, it is available for all users, out of beta, and introduces a premium plan to unlock all features. # ⚓ Safeguard_Your_Email_Address_from_Spam_Using Firefox_Relay._Here’s_How.⠀⇛ You can now protect your email addresses from spammers using Firefox Relay with premium service + unlimited aliases. Everything you need to know. # ⚓ Support.Mozilla.Org:_Introducing_Firefox_Relay Premium⠀⇛ If you’re a fan of Firefox Relay, you may have been waiting for the day when you can add more aliases. After a long wait, you can now celebrate because we’re launching Firefox Relay Premium today. As a refresher, Firefox Relay is a free service available at relay.firefox.com where you’ll get five email aliases to use whenever you sign-up for an online account. Today, Firefox Relay is launching as a premium subscription where you can unlock unlimited aliases and additional features. # § Productivity Software/LibreOffice/Calligra⠀➾ # ⚓ Use_atan2_function_instead_of_atan_–_EasyHack⠀⇛ When working with shapes and charts in LibreOffice, there are several occasions that you have to calculate tan -1 x . But is atan function always the best choice? Here we discuss using atan2 function instead of atan in C++ code. When used in correct place, atan2 can have a lot of benefits when calculating atan ( y / x ). # ⚓ OSS_News:_Enterprise_Linux,_Microsoft_Replacements, Fuzzy_Linux_Solutions ⠀⇛ The Document Foundation on Nov. 4 announced the release and general availability of LibreOffice 7.1.7 as the last point release in the LibreOffice 7.1 office suite series. The LibreOffice 7.1 office suite was released in February. It is supported until the end of November, after which the LibreOffice 7.1 series reaches the end of life. No new maintenance updates will be published. LibreOffice 7.1.7 is a minor update to address 27 bugs across the office suite’s various core components. You can see details about them in the RC1 and RC2 changelogs. This renders your installation vulnerable and outdated. No new maintenance releases for the 7.1 series will be issued. It is being replaced with LibreOffice 7.2, which is supported until June 12th, 2022. You can download it here. Or you can wait for it to be available in the various Linux distribution repositories. LibreOffice 7.2 brings many new features and improvements, as well as better support for proprietary formats created with the MS Office suite. The latest point release is LibreOffice 7.2.2, but version 7.2.3 is expected to arrive by the end of the month. # ⚓ Collabora_Online_Partners_Shine_at_Open_Source Experience_Paris_2021⠀⇛ The Open source Experience 2021 in Paris was wonderful. Of course we met a large number of people, but various of Collabora Online partners too! We love to tell you about them. # § Programming/Development⠀➾ # ⚓ Nasah_Kuma:_open_source_is_flexible⠀⇛ I had as main objective when I started my Coding Experience(CE) to get to grips with C or C++ since I am convinced that understanding one or both languages will help me become a better developer. Cog is developed in C which explained my excitement when I was introduced to the project. The first couple of tasks assigned to me were challenging but quite beginner-friendly. Like it usually happens to many developers, I got stuck on an issue. After weeks of working on it, I couldn’t complete it. My mentor and I had a couple of meetings/coding sessions which helped me move ahead though not to the point of finishing the work. I could feel that there was a knowledge gap I had to bridge in C which studies and practice hadn’t given me that ability yet. Cutting the long story short I got really exhausted and anxious and suggested to my mentor that we move to something else and revisit this issue later. After a couple of days, I was presented with a new program that can help me make the most of the CE. It turns out I will be moving back to contributing actively on GJS since there was good progress when I previously contributed to it. The only difference is most of my contributions will be in C++ and will probably include more core stuff. # ⚓ Hacking_Multiplication_with_Karatsuba’s_Algorithm⠀⇛ People tend to obsess over making computer software faster. You can, of course, just crank up the clock speed and add more processors, but often the most powerful way to make something faster is to find a better way to do it. Sometimes those methods are very different from how a human being would do the same task, but it suits the computer’s capabilities. [Nemean] has a video explaining a better multiplication algorithm known as Karatsuba’s algorithm and it is actually quite clever. You can see the video below. To help you understand the algorithm, the video shows a simple two-digit by two-digit multiplication. You can see that the first and last digits are essentially the result of one multiplication. It is all the intermediate digits that add together. The only thing that might change the first digit is a carry. # § Rust⠀➾ # ⚓ Rust_Foundation_appoints_Rebecca_Rumbul_as executive_director_|_ZDNet⠀⇛ Today, the Rust Foundation, an independent non-profit organization dedicated to supporting the Rust language, announced Dr. Rebecca Rumbul would be the new organization’s first Executive Director and CEO. * § Leftovers⠀➾ o § Hardware⠀➾ # ⚓ Tuned_Out⠀⇛ We’ve lost a lot of things in recent years, but one that we haven’t talked about too much is the demise of the children’s radio station. Yes, this is not exactly a surprise—how is radio going to compete with YouTube and Roblox? But back in April, the only real player in the kid-centric terrestrial radio space, Radio Disney, which started life on the airwaves 25 years ago this week, quietly wound down as Disney made the decision to focus on, well, every other part of being Disney. But it’s worth noting that Radio Disney was not the only one to embrace this phenomenon. Kids’ music makes a lot of money even to this day—it’s part of the reason why traditionally adult-centric bands like They Might Be Giants have embraced it. Today’s Tedium looks back at the many attempts to sell kids on radio—a market that has basically faded away by this point. o § Integrity/Availability⠀➾ # § Proprietary⠀➾ # ⚓ Splunk_CEO_jumps_ship,_share_price_slumps_despite surging_growth⠀⇛ # § Security⠀➾ # ⚓ Hardware_security_flaw_impacts_Intel_Apollo Lake_&_Gemini_Lake_processors_–_CNX_Software⠀⇛ A few years go the Spectre and Meltdown hardware security vulnerabilities impacted a wide range of processors from Intel, AMD, Arm, and others. But a newly discovered hardware security flaw impacts specifically the Atom, Celeron, and Pentium from the Apollo Lake, Gemini Lake, Denverton … low-power processors we often feature on CNX Software. # ⚓ Alibaba’s_Linux-based_cloud_servers_exploited for_use_by_cryptojackers_|_SC_Media [Ed: But is it the fault of "Linux"? No. Journalism has become a mixture of FUD and advertising.]⠀⇛ # ⚓ Free_Android_Penetration_Testing_Toolkit_&_Risk Assessment_–_blackMORE_Ops⠀⇛ zANTI is an Free Android Penetration Testing Toolkit & Risk Assessment application that functions as a mobile penetration testing toolkit that lets you assess the risk level of a network using your mobile device for free download. zANTI lets security managers assess the risk level of a network with the push of a button. This easy to use mobile toolkit enables IT Security Administrators to simulate an advanced attacker to identify the malicious techniques they use in the wild to compromise the corporate network. # ⚓ Security_updates_for_Wednesday⠀⇛ Security updates have been issued by CentOS (389-ds-base and libxml2), Debian (atftp, axis, and ntfs-3g), Fedora (digikam, freerdp, guacamole- server, and remmina), openSUSE (java- 11-openjdk, kernel, samba, and tomcat), SUSE (firefox, java-11-openjdk, kernel, libarchive, samba, and tomcat), and Ubuntu (accountsservice, hivex, and openexr). # ⚓ Google_launches_open_source_fuzzing_tool_to tackle_SolarWinds-style_attacks⠀⇛ Google has announced a new open source project designed to assist software developers find vulnerabilities in their code, without much effort, in order to help enhance the security of the software supply chain. # ⚓ Is_Microsoft_Stealing_People’s_Bookmarks?⠀⇛ I received email from two people who told me that Microsoft Edge enabled synching without warning or consent, which means that Microsoft sucked up all of their bookmarks. Of course they can turn synching off, but it’s too late. Has this happened to anyone else, or was this user error of some sort? If this is real, can some reporter write about it? [...] It’s actually worse than I thought. Edge urges users to store passwords, ID numbers, and even passport numbers, all of which get uploaded to Microsoft by default when synch is enabled. # ⚓ Iranian_Government-Sponsored_APT_Cyber_Actors Exploiting_Microsoft_Exchange_and_Fortinet Vulnerabilities⠀⇛ CISA, the Federal Bureau of Investigation (FBI), the Australian Cyber Security Centre (ACSC), and the United Kingdom’s National Cyber Security Centre (NCSC) have released a joint Cybersecurity Advisory highlighting ongoing malicious cyber activity by an advanced persistent threat (APT) group that FBI, CISA, ACSC, and NCSC assess is associated with the government of Iran. FBI and CISA have observed this Iranian government-sponsored APT exploit Fortinet and Microsoft Exchange ProxyShell vulnerabilities to gain initial access to systems in advance of follow-on operations, which include deploying ransomware. # ⚓ Linux_has_a_serious_security_problem_that_once again_enables_DNS_cache_poisoning⠀⇛ The sleight of hand worked because DNS at the time relied on a transaction ID to prove the IP number returned came from an authoritative server rather than an imposter server attempting to send people to a malicious site. The transaction number had only 16 bits, which meant that there were only 65,536 possible transaction IDs. Kaminsky realized that hackers could exploit the lack of entropy by bombarding a DNS resolver with off-path responses that included each possible ID. Once the resolver received a response with the correct ID, the server would accept the malicious IP and store the result in cache so that everyone else using the same resolver—which typically belongs to a corporation, organization, or ISP—would also be sent to the same malicious server. # § Privacy/Surveillance⠀➾ # ⚓ Disparity_in_the_data_collection_policies of_some_pan-African_firms_in_Uganda_raises privacy_concerns_·_Global_Voices⠀⇛ The Unwanted Witness report revealed that most of the personal data collected online violates privacy rights, with no regards for the safety and dignity of citizens. # ⚓ Lenovo_violates_the_United_States_CAN- SPAM_Act_of_2003.⠀⇛ If you give Lenovo your email address to make an order, they’ll start sending you unsolicited emails every day or two, and they’ll ignore your unsubscribe requests even though they said it was processed. This violates the CAN-SPAM Act of 2003. I’ll be lodging complaints with the Illinois Attorney General and the Federal Trade Commission shortly. o § Environment⠀➾ # § Wildlife/Nature⠀➾ # ⚓ Tales_From_The_Crypt_#286⠀⇛ Whitney Webb joins Marty Bent to discuss how the Davos class wants to securitize natural assets. o § Internet Policy/Net Neutrality⠀➾ # ⚓ No_centralised,_verifiable_record_on_internet_shutdowns, says_parliamentary_panel:_Reports⠀⇛ In its report, the committee on information and technology noted that there were no rules to dictate these clampdowns. # ⚓ No_verifiable_records_of_Internet_shutdowns_available: parliamentary_panel_–_The_Hindu⠀⇛ There were no verifiable, centralised records of Internet shutdowns in the country. Neither the Ministry of Home Affairs nor the Department of Telecom maintain such a record, the parliamentary standing committee on information and technology pointed out in its report adopted on Tuesday. The committee, headed by senior Congress leader Shashi Tharoor, pressed for a detailed study on the economic impact owing to frequent and prolonged Internet shutdowns. Advocacy group Access Now, in a study published in March last, reported that India topped the list of countries that resorted to government imposed Internet clampdown. The report, as per sources, said that in absence of the database there was no mechanism to review whether the Internet clampdowns followed the laid down rules or the Supreme Court guidelines. o § Digital Restrictions (DRM)⠀➾ # ⚓ Microsoft_brings_Windows_Media_Player_back_from_the_dead because_their_“modern”_apps,_Groove_and_Movies_and_TV, flopped.⠀⇛ The Microsoft news has taken a break from puffing up Microsoft Fake Linux for Windows and the trojan horse malware, Edge, to ooh and aah over the resurrection of….Windows Media Player. I wonder why anyone would want to use Windows Media Player instead of VLC. VLC can do almost anything and Windows Media Player is like the Internet Exploder of media players. To get Windows Media Player to do much of anything, you need pirate codec packs that probably come with viruses. o § Monopolies⠀➾ # § Copyrights⠀➾ # ⚓ 28_New_Prints_Up_On_Our_Online_Shop_–_The_Public Domain_Review⠀⇛ New delights for your walls, including works by Blake, Grandville, Redon, Hiroshige, and lots of stunning Japanese firework illustrations. # ⚓ Imaging_Inscape:_*The_Human_Soul*_(1913)_–_The_Public Domain_Review⠀⇛ In The Human Soul: Its Movements, Its Lights, and the Iconography of the Fluidic Invisible, originally published in French in 1896, Dr. Hippolyte Baraduc (1850–1909) postulates the existence of “the fluidic invisible” — a “vital cosmic force”, which he calls Odic liquid, that extends across the universe and “saturates the organism of living beings and constitutes our fluidic body”. Instead of all things being composed of one elementary substance, as in philosophical accounts of the monad, in this cosmic vision, we all live in a sea that we cannot see, which Baraduc names Somod. ╘══════════════════════════════════════════════════════════════════════════════╛ ¶ Lines in total: 8212 ➮ Generation completed at 02:41, i.e. 87 seconds to (re)generate ⟲