𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Tuesday, December 21, 2021 ┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅ Generated Wed 22 Dec 02:41:17 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/2021/12/21/ ╒═══════════════════ 𝐑𝐄𝐂𝐄𝐍𝐓 𝐁𝐔𝐋𝐋𝐄𝐓𝐈𝐍𝐒 ════════════════════════════════════╕ Previous bulletins in IPFS (past 21 days, in chronological order): QmThpqmVrTBjQ3aKEp3yrZKJUdKapNAGts5Lu3eYkGeBwf QmQPL4aU5VkHzGprihFtysZx7tMGqLPQa11SU2s4ao6H6r QmWDLoPpML1exaPTP8wfzYiKd4whiRGaCCqWNHJQ8Tgfgg QmXP9uUCLGPXq5XphWSHwKkEcNvzBUFmcGuun1rgVhDoMf QmbcSKJZiufM2XfxxnB92wQE323m9MsiAMo5YFmwFPu8VN QmWmC3AgPDFykej4Jpay8nnpKKVGMMEfv8MjggJ9Qw5Lm9 QmNPpiGqWGFQNEECwNKt72LSricBeH2VuxSzamtqTrESHV QmUNbGTar72DvDUxqyAh6Jdzfvu4JHUqaTFKqWpu9P64bk QmXFHTXDoB1z4Af36pfwwfrJcsZWK4nkbqqF2EndNyJ9YA QmcFJuq5PVoQgjijbLaMibeRbgr4h5pFcpzBYWqLap1cNu QmSBPP9JjsnqHFcHfShHhNsQwTc4eHz66BF5ihuBjaxpKM QmPrW6GPykdMyQtg8txV2DXmRYjghF1TQPv6CJcwVUx6iy QmVNVya1kBzPYdBdJekAHEpk3m857qJsnQet4QNxycPonK QmUQmiHKq1wV1JkS2hwXEf1etD3jM43Afc68V6omxpqaCi QmbheKKYhpyw3SvZSmHbavdgcv1PSaRtPdaQ746tgUFXbp QmZqoL722Mk7hDJcSz2oBxydXY7S2G5r4ByHgRdKBw7dUH QmTZSRzHEP7hwr4tL7ky23HxA9Z3tUBjQrfwYPAieSYsGe QmRKnWzns1EsWaoxUGG5KEEhiyhSELGYVdfVqSB5Ay4qhc QmZdVw5kGwFeXoGNexLWZDS8MJxeGKAeup4JpiAnmE946y QmYdAKSfCu9puR3SWGWwGW19Uzo1jj4L1aYpeGqpC5FCp6 QmZP4LnsTHrznHVdokybFZafDLWJqRPKyvvberG4dVRasQ ╒═══════════════════ 𝐈𝐍𝐃𝐄𝐗 ═══════════════════════════════════════════════════╕ ⦿ Links 21/12/2021: EasyOS 3.1.17 and IPFire 2.27 - Core Update 162 | Techrights ⦿ [Meme] Will You Trust These Clowns With Your Confidential Data? | Techrights ⦿ Microsoft’s Team Mono: One Happy Family | Techrights ⦿ IRC Proceedings: Monday, December 20, 2021 | Techrights ⦿ Saturday Morning Breakfast Cereal on ’Intellectual Property’ | Techrights ⦿ Team Mono is on the Run | Techrights ⦿ The Microsoft Shuffle: Making One’s Own Products Intentionally Defective | Techrights ⦿ EPO’s Privacy Violations Being ’Normalised’ | Techrights ䷼ Bulletin articles (as HTML) to comment on (requires login): http://techrights.org/2021/12/21/easyos-3-1-17/#comments http://techrights.org/2021/12/21/epo-clowns-data/#comments http://techrights.org/2021/12/21/happy-mono-family/#comments http://techrights.org/2021/12/21/irc-log-201221/#comments http://techrights.org/2021/12/21/smbc-comics-ip/#comments http://techrights.org/2021/12/21/team-mono-gone-into-hiding/#comments http://techrights.org/2021/12/21/the-microsoft-shuffle-making-ones-own-products-intentionally-defective/#comments http://techrights.org/2021/12/21/the-unlawful-normalised/#comments ䷞ Followed by Daily Links (assorted news picks curated and categorised): http://techrights.org/2021/12/21/elementary-os-6-1-release/#comments http://techrights.org/2021/12/21/qubes-os-4-1-rc3/#comments http://techrights.org/2021/12/21/wordpress-5-9-beta-4/#comments ䷩ 𝚕𝚒𝚗𝚎 70 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2021/12/21/easyos-3-1-17/#comments Gemini version at gemini://gemini.techrights.org/2021/12/21/easyos-3-1-17/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.21.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Links_21/12/2021:_EasyOS_3.1.17_and_IPFire_2.27_–_Core_Update_162⠀✐ Posted in Site_News at 12:45 pm by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈ § Contents⠀➾ * GNU/Linux o Distributions o Devices/Embedded * Free_Software/Open_Source * Leftovers * § GNU/Linux⠀➾ o ⚓ What_Is_A_Linux_Distribution?⠀⇛ Many people are still strangers to the “Linux” topic, although it directly or indirectly powers most of the world’s computers, servers, and many other devices. Linux usage has seen immense growth in the past decade, but one area where it still has to see some improvements is in Desktop computing (Linux Distributions). As of writing this article, the Linux desktop market stands at 2.5%, which is no surprise considering the market is dominated by Windows and macOS. One of the reasons Linux desktop isn’t that popular is because of people not knowing what it is or if it exists in the first place. If you’re one of them, let’s look at what’s a Linux Distribution in this article. o § Kernel Space⠀➾ # ⚓ Intel_i9-12900K_Alder_Lake_Linux_Performance_In_Different P/E_Core_Configurations_–_Phoronix⠀⇛ One of the much requested Linux benchmarks since the debut of Intel Alder Lake last month has been for seeing the Core i9 12900K in different core configurations with its mix of P and E cores. Now that the Linux kernel activity has begun settling down around Alder Lake, here are those benchmarks for reference purposes with toggling Hyper Threading and different P and E core counts enabled. o § Benchmarks⠀➾ # ⚓ AMD_Ryzen_7_PRO_5850U_–_Windows_vs._Linux_Performance Review⠀⇛ With the Lenovo ThinkPad T14s Gen2 powered by the Ryzen 7 PRO 5850U prior to blowing the default Microsoft Windows installation on the device I ran some benchmarks for seeing how the performance stacks up against various Linux distributions. Going up against Windows 11 on this AMD Zen 3 laptop were Clear Linux, Fedora Workstation 35, Ubuntu 20.04.3 LTS, Ubuntu 21.10, and Arch Linux. The Lenovo ThinkPad T14s Gen2 (20XF004WUS) being tested shipped with Windows 10 but on initial boot was quickly prompted for moving to Windows 11. So with that this Windows 11 testing on the installation configured by Lenovo was compared to Arch Linux in its latest rolling state as of earlier this month, Clear Linux 35400, Fedora Workstation 35, Ubuntu 20.04.3 LTS, and Ubuntu 21.10 for seeing how the various operating systems compare in their default / out-of-the-box state on this current-generation Lenovo ThinkPad. o § Applications⠀➾ # ⚓ Open_source_desktop_publishing_with_Scribus⠀⇛ One of my favorite shelves at my local comic book store is the zine rack. Filled with self-published booklets that are too niche, too quirky, or just too individual for any company to spend money on producing, zines are produced by one or two people who have something to say and want to express themselves through text and graphics. Zines are usually created by cutting out blocks of text and graphics and literally pasting them to a master page. Once everything has been laid out, each page is scanned and printed on a copy machine, and distributed to comic book stores, used book stores, Infoshops, and libraries. When you’re a computer nerd like me, though, you have easier access to a computer than you do scissors and glue, and my first choice for desktop publishing with open source is Scribus. There are different tools for different jobs, but there can be a lot of overlap. You can produce books for online distribution as a comic book archive or djvu file, Epub, or even good old HTML. However, if you’re producing a book for print, then at least one of your targets must be PDF (or at least Postscript) because that’s what printers use. When I’m working on something with more graphics than typed content, or I just need maximum flexibility for layout, I use Scribus because its canvas is freeform, and it can link to external assets rather than import them. o § Instructionals/Technical⠀➾ # ⚓ How_to_Install_Python_3.11_on_Pop!_OS_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, and one of the many is the popular PIP package manager. # ⚓ How_to_Install_PostgreSQL_14_in_Rocky_Linux_and_AlmaLinux⠀⇛ Dependability and resilience are some of the key attributes that define PostgreSQL as the go-to Relational Database Management System (RDBMS) for both web-based and desktop-based software application projects. Also, since PostgreSQL continues to find shelter under the umbrella of its global developer community, bugs and user issues related to database software’s life cycle are easily fixed thanks to its open-source status. Therefore, PostgreSQL is a brand name in numerous enterprises invested in e-commerce platforms, financial transactions, and web traffic statistics. Also, the open-source nature of PostgreSQL embraces the addition of several programming languages’ functions to make its usability dynamic. These programming languages include the likes C/C++, Python, and Java. # ⚓ How_to_Install_Opera_Browser_on_Pop!_OS_20.04_– LinuxCapable⠀⇛ Opera is a freeware, cross-platform web browser developed by Opera Software and operates as a Chromium-based browser. Opera offers a clean, modern web browser that is an alternative to the other major players in the Browser race. Its famous Opera Turbo mode and its renowned battery saving mode are the best amongst all known web browsers by quite a margin, along with a built-in VPN and much more. # ⚓ Host_Multiple_Websites_on_One_server_using_Docker Containers⠀⇛ Docker is an extremely useful platform that enables developers to easily develop and deploy applications. In this article, we’ll look at how to use Docker containers to host multiple websites on a single server. One of the most significant benefits of using Docker containers is that they are lightweight, faster, and easier to manage. This month, I moved two of my custom-built applications from two separate servers to a single server, each in its own Docker container. It’s easier to manage both applications, and it’s also reduced my production costs. # ⚓ Install_ISPConfig_on_CentOS_8_–_Unixcop_the_Unix_/_Linux the_admins_deams⠀⇛ In this tutorial we will install ISPConfig on CentOS 8. ISPConfig is an open source control panel for Linux. It has user friendly web interface. Using ISPConfig users can manage their websites, email addresses, FTP accounts, DNS records, databases and shell accounts. Administrator, Reseller, Client, and Email-user are the four different levels of user access ISPConfig. Each of the user level have different kind of address. # ⚓ How_to_Install_balenaEtcher_on_Pop!_OS_20.04_– LinuxCapable⠀⇛ balenaEtcher is a free and open-source flashing utility tool famous for writing image files such as .iso and .img files and zipped folders onto storage media to create live SD cards and USB flash drives. balenaEtcher has cross-platform support on Linux, BSD, macOS, and Windows and is developed by balena and licensed under Apache License 2.0. In the following tutorial, you will learn how to install baelnaEtcher on Pop!_OS 20.04 LTS and create a Linux distribution boot disk. # ⚓ [Updated]_10_Wget_(Linux_File_Downloader)_Command_Examples in_Linux⠀⇛ In this article, we are going to review the wget utility which retrieves files from World Wide Web (WWW) using widely used protocols like HTTP, HTTPS, FTP, and FTPS. # ⚓ OpenFaaS:_Classic_and_of-watchdog_templates_–_Anto_./ Online⠀⇛ OpenFaaS (Function as a Service) is a popular serverless framework. However, unlike other serverless function providers, OpenFaaS has very few restrictions on providing and receiving data. This guide will show you the primary differences between the Classic and of-watchdog templates. # ⚓ smxi:_Manage_Debian_Systems_Interactively_in_Terminal⠀⇛ smxi is an interactive console script that helps you maintain your Debian installation. You can use it to install upgrades, install graphics drivers, upgrade kernels and much more. I know that you can do it all with their respective commands. This smxi script gives you everything at one place and in an interactive manner. smxi is limited to only direct derivates of Debian. Only distributions like AntiX, Aptosid, Epidemic, Linux Mint Debian Edition (LMDE), Mepis are supported. It also supports the testing and Sid branches of Debian. That means Ubuntu and Ubuntu- based distributions are NOT supported as there are many differences between Ubuntu and Debian. o § Games⠀➾ # ⚓ This_hilarious_Doom_mod_takes_aim_at_NFTs_|_GamingOnLinux⠀⇛ NFTs, they’re freaking everywhere and NFT bros have become some of the most annoying people on the planet and so of course there’s now a Doom mod to mock them. ICYMI: Valve banned NFT games on Steam. It’s not a particularly fleshed-out mod, with the main aim of it just being pure mockery. You get to run around with your trusty camera, taking snaps of everything. Like running around and right click - > saving on images that would be NFTs. Released by modder “Ultra Boi” last week, it’s certainly been turning some heads across the internet, especially because of just how toxic things have become around the NFT community. # ⚓ Proton_Experimental_sees_new_fixes_for_DEATHLOOP,_Forza Horizon_5_|_GamingOnLinux⠀⇛ Valve has put out another small upgrade to Proton Experimental, with it focused on improving a couple of popular games. What is Proton? It’s a compatibility layer designed to run Windows games from Steam on Linux. See more about it in our full guide. The release that went up on December 20 fixed up the Xbox login window behaviour for Forza Horizon 5, worked around a bunch of graphical glitching in DEATHLOOP and also fixed Mount & Blade II: Bannerlord occasionally getting stuck in a loop displaying errors. Not only that though, this release should also speed up the “wind-down” of Proton after you exit a game. So that should make the whole experience a fair bit smoother. See the Proton Experimental changelog to see all the current differences to the normal Proton releases. # ⚓ My_favourite_2021_games_played_on_Linux_|_GamingOnLinux⠀⇛ Here we are, the year is ending so here’s a few of what I consider to be my favourite games played on Linux that had a release during 2021. As always, these are highly personal and are only based on what I actually played. There’s masses in my backlog I haven’t yet, that I will likely kick myself during 2022 for not getting around to earlier. The trouble is also, that most of my favourites were released back in 2020 and earlier – because newer simply isn’t always better! So many games had huge upgrades across 2021 too that sucked me back in. However, these are my personal standouts. # ⚓ Level_up_your_Steam_experience_with_a_browser_extension_– Firefox_Add-ons_Blog⠀⇛ With more than 120 million users worldwide and 50,000+ games in its ecosystem, Steam is an extraordinarily eclectic gaming distribution platform. Given its broad reach, it makes sense that different users have different ways they’d like to adjust and optimize their personal Steam experience. That’s where browser extensions come in… # ⚓ Great_News!_80%_of_Steam’s_Top_100_Games_Now_Run_on_Linux⠀⇛ All thanks to Proton and Steam Play, gaming on Linux is better than ever. o § Distributions⠀➾ # § New Releases⠀➾ # ⚓ Elementary_OS_6.1_Jolnir_Available_to_Download_and Upgrade_–_itsfoss.net⠀⇛ Elementary OS 6.1 Jolnir Available to Download and Upgrade, The elementary team have announced the release of elementary OS 6.1 which carries the codename “Jolnir”. The new release features the same base operating system as 6.0, though with a number of evolutionary improvements. Some of these changes affect the distribution’s software centre: “AppCenter continues to fill out with apps from developers—and since the move to Flatpak, all apps that have been released for OS 6 will continue to be available on OS 6.1 and beyond. You can currently find over 90 curated apps in AppCenter, and developers have continued to push out rapid and frequent updates to their apps with new features and bug fixes, as they’re in control of their own update schedule. Our shift from Debian packages to Flatpak for both curated and non- curated apps also means we’re able to lean more on Flatpak features, and we’ve been using this as an opportunity to make AppCenter much more engaging and informative right from the start – directly addressing feedback about the discoverability of the wide variety of apps in AppCenter.” Additional information is available in the project’s release announcement. # ⚓ Linux-Distribution:_Detailverbesserungen_in Elementary_OS_6.1_(Jólnir)_–_Market_Research_Telecast [Ed: Automated translation]⠀⇛ The developers of Elementary OS list numerous smaller improvements that they have incorporated in version 6.1 (Jólnir). The Linux distribution focuses on an attractive appearance and uniform usability and therefore relies on its own desktop called Pantheon. # ⚓ EasyOS_3.1.17_released⠀⇛ Very important enhancements; now have Qt5 libraries, and three powerful media applications. # ⚓ IPFire_2.27_–_Core_Update_162_released⠀⇛ Just before Christmas, it is time for the last release of the year: IPFire 2.27 – Core Update 162. It comes with a brand-new kernel based on Linux 5.15, and it will be the last release supporting the i586 architecture. Before we talk about what is new, I would like to ask you for your support. IPFire is a small team of people and like many of our open source friends, we’ve taken a hit this year and would like to ask you to help us out. Please follow the link below where your donation can help fund our continued development: https://www.ipfire.org/donate. # ⚓ IPFire_Linux_Firewall_Distro_Is_Now_Powered_by_Linux Kernel_5.15_LTS⠀⇛ IPFire 2.27 Core Update 162 is here less than a month after the Core Update 161 release as the last update of the year and also the first update to be powered by the latest and greatest Linux 5.15 LTS kernel series. Until now, IPFire was powered by the Linux 5.10 LTS kernel series, since mid-August 2021, but even if Linux kernel 5.10 LTS is supported until the end of 2026, the devs decided to move to Linux kernel 5.15 LTS, which is supported only until October 2023, since it offers better hardware support and some cool new features. # § IBM/Red Hat/Fedora⠀➾ # ⚓ Red_Hat_donates_$10,000_to_OBS_Studio,_Flatpak_to_be official_for_Linux⠀⇛ Little bit of good news to start Tuesday, as the excellent livestreaming and recording software OBS Studio got another good donation recently, this time from Red Hat. Red Hat certainly aren’t the first big company to help fund OBS development, software that has become essential for so many different uses. Nice to see a bigger Linux and open source company jump in though with the confirmation of the $10,000 donation on Twitter. This actually puts Red Hat in the top 5 of companies who have donated to OBS via their OpenCollective campaign. # § Canonical/Ubuntu Family⠀➾ # ⚓ Linux_Mint_20.3_Una_Install_Guide_[Multi_boot, btrfs]⠀⇛ This is Linux Mint 20.3 Una full install guide from Download to ready updated desktop. Real PC install with real multiboot setup. # ⚓ The_beautiful_Linux_distro_elementary_OS_6.1_is_out now⠀⇛ elementary OS is easily one of the best looking Linux distributions around, with such an incredible attention to the finer details and a big new release is up now. With elementary OS 6.1 the developers focused on addressing feedback from the previous release, new and more useful office productivity features and expanding compatibility with a larger range of hardware. o § Devices/Embedded⠀➾ # ⚓ Qualcomm_IPQ8072_networking_SBC_supports_dual_10GbE,_WiFi 6⠀⇛ DR8072 V01 is a networking SBC based on Qualcomm IPQ8072 communication processor, with two 10GbE interfaces, one through an SFP cage and the other through an RJ45 connector, plus four Gigabit Ethernet ports, and 4×4 MIMO WiFi 6 connectivity (AX3700). Based on Qualcomm AP.HK09 reference design, the board follows Wallys Communications’ DR8072A embedded router board introduced earlier this year, also based on Qualcomm IPQ8072, but equipped with two 2.5 GbE interfaces and WiFi 6 connectivity. # ⚓ UP_Xtreme_i11_Edge_Compute_Enabling_Kit_Review_–_Part_1_: Unboxing_and_Teardown⠀⇛ AAEON’s UP Xtreme i11 Edge Compute Enabling Kit is an industrial mini PC based on the UP Xtreme i11 Edge single board computer powered by a choice of Tiger Lake processors and designed for edge applications for the industry. I recently got contacted by AAEON who sent me a version of the Edge Compute Enabling Kit with an Intel Core i7-1185GRE SoC, 16GB RAM, and a 128GB SSD pre-loaded with Ubuntu. I’ll start the review by checking out package content and interfaces, and teardown the hardware, before testing is with Ubuntu next month. # § Mobile Systems/Mobile Applications⠀➾ # ⚓ Google’s_Android_12_Go_Edition_Packs_Major Improvements_Over_Predecessor⠀⇛ # ⚓ Google_Pixel_Android_12_bugs,_problems,_&_issues tracker⠀⇛ # ⚓ OnePlus_Android_12_(OxygenOS_12)_bugs,_issues_tracker &_current_status⠀⇛ # ⚓ Nvidia_hints_Android_11_rollout_for_Shield_TVs_could happen_soon_–_Android_Community⠀⇛ # ⚓ LG_Android_11_update_(LG_UX_10)_list_of_eligible devices_&_release_date⠀⇛ # ⚓ ICYMI:_Android_has_an_SOS_feature_that_could_save your_life_–_Ausdroid⠀⇛ # ⚓ How_to_set_a_screen_lock_on_Pixel_and_other_Android devices_–_9to5Google⠀⇛ # ⚓ Top_10_Best_Free_Play_Pass_Games_On_Android_–_2021⠀⇛ # ⚓ Best_video_editing_apps_for_Android_|_Business Insider_India⠀⇛ # ⚓ Android_Phone’s_Haptic_Feedback,_How_to_Disable_and Adjust_the_Feature_|_Tech_Times⠀⇛ o § Free, Libre, and Open Source Software⠀➾ # ⚓ Top_7_Open_Source_eCommerce_Platforms⠀⇛ Open source software have been fantastic in solving a lot of business use cases. For example, we have open source ERP solutions, open source project management tools, open source survey software and much more of other use cases. All of these cases share the same benefits open source brought to them, and in today’s article we’ll be seeing some of the top open source eCommerce platforms for establishing an online shop. We’ll also see the usage marketshare of each of these solutions. All those statistics are provided by builtWith (Products with no mentioned stats means that they are less than >1% for top 1M sites). # ⚓ Open_Source_‘Matter’_Hopes_To_Make_Sense_Of_The_Fractured, Messy_Smart_Home_Sector⠀⇛ If you’ve spent any meaningful time trying to build a “smart home” you’ve probably run face first into no shortage of problems. Gear is expensive, frequently complicated, and more often than not different devices don’t play well together. It’s a sector filled with various walled gardens by gatekeepers looking to lock you into one ecosystem, placing the onus on consumers to figure out which devices work with other devices and ecosystems, forcing the end user to spend countless calories trying to fix interoperability issues when they inevitably arrive. # § Funding⠀➾ # ⚓ Intel_has_boosted_their_commitment_to_Blender_as_a Corporate_Patron⠀⇛ Intel was already a pretty high backer of the free and open source 3D creation suite Blender but now they’re going in for even more as a Corporate Patron. ICYMI: recently Blender 3.0 was release. Previously down as a Corporate Gold member, this increase will see Intel give at least €120K a year to the Blender Foundation to better support one of the biggest and most important FOSS projects around. This means Intel joins the ranks of AMD, NVIDIA, AWS, Epic MegaGrants, Unity, Facebook and Decentraland at the same level (with many more in lower funding levels). # § FSF⠀➾ # § GNU Projects⠀➾ # ⚓ GIMP_2.10.30_Improves_Support_for_PSD_and_AVIF Files,_Supports_Modern_Linux_Distros⠀⇛ GIMP 2.10.30 comes three months after GIMP 2.10.28 to further improve support for various file formats, including AVIF, DDS, HEIF, PBM, PSD, and RGBE. For the AVIF file format, this release improves the export functionality to favor the AOM (Alliance for Open Media) encoder, which uses the AV1 (AOMedia Video 1) open and royalty-free video coding format. # § Programming/Development⠀➾ # § Perl/Raku⠀➾ # ⚓ Rakudo_Weekly_News:_2021.51_Transiting⠀⇛ Arne Sommer was inspired by public transport developments in their native Oslo. This resulted in a cool new module Transit::Network, but also a serious blog post: Planning Public Transportation with Raku (/r/rakulang comments), a semi-serious Reindeer Express blog post, and a followup on the original: Bugs R Us – A Transit:: Network Update (/r/rakulang comments). And Arne was still being able to find the time to do a blog post for the Weekly Challenge: Stealthy Calculator. # § Python⠀➾ # ⚓ Prevent_Python_dependency_confusion_attacks with_Thoth⠀⇛ Python became popular as a casual scripting language but has since evolved into the corporate space, where it is used for data science and machine learning applications, among others. Because Python is a high-level programming language, developers often use it to quickly prototype applications. Python native extensions make it easy to optimize any computation-intensive parts of the application using a lower-level programming language like C or C++. For applications that need to scale, we can use Python Source-to-Image tooling (S2I) to convert a Python application into a container image. That image can then be orchestrated and scaled using cluster orchestrators such as Kubernetes or Red Hat OpenShift. All of these features together provide a convenient platform for solving problems using Python-based solutions that scale, are maintainable, and are easily extensible. As a community-based project, the main source of open-source Python packages is the Python Package Index (PyPI). As of this writing, PyPI hosts more than 3 million releases, and the number of releases available continues to grow exponentially. PyPI’s growth is an indicator of Python’s popularity worldwide. However, Python’s community-driven dependency resolvers were not designed for corporate environments, and that has led to dependency management issues and vulnerabilities in the Python ecosystem. This article describes some of the risks involved in resolving Python dependencies and introduces Project Thoth’s tools for avoiding them. * § Leftovers⠀➾ o ⚓ What’s_New_in_the_New_West_Side_Story?⠀⇛ As I sat through a screening of West Side Story at a Lincoln Square movie theater—literally in the same neighborhood portrayed in the film—I couldn’t escape a growing realization. These days, we are trapped in a cycle of repetition, one in which the gnarled conflicts and perhaps small triumphs of the postwar era repeat themselves over and over again, sometimes with profound new expression and sometimes just as shiny objects of entertainment consumption. In Steven Spielberg’s new “reimagining” of West Side Story, we get a film that offers a far more inclusive vision of postwar America, but one that still retains its flawed view of working- class tribalism. o ⚓ NBA_and_NFL_to_America:_Drop_Dead⠀⇛ In March 2020, one positive Covid-19 case, Utah Jazz center Rudy Gobert, put the NBA season on hold. The league canceled games, and entered a “bubble” alongside the WNBA at the Walt Disney World Resort in Orlando. The move sent an unmistakable message to the United States that the “normal” world was over, that we would need to reimagine our lives to minimize contagion and death. o § Education⠀➾ # ⚓ Protect_Students⠀⇛ # ⚓ Culture_Wars:_the_Assault_on_Education⠀⇛ The Trump administration and Senate Republicans stacked the Supreme Court and innumerable federal judgeships with conservatives. They secured the appointment of three judges to the Supreme Court, 54 to federal appeals court and 174 to the district courts. The current legal battle regarding the Texas “Heartbeat” Act (Senate Bill 8) may well reverse the landmark Roe v. Wade (1973) decision acknowledging a woman’s right to determine her pregnancy. Most troubling, conservative culture values were once championed by a minority of religious activists but, during Trump’s presidency, they became the anchor for the larger white nationalist and rightwing movement.  In the wake of the January 6th effort to seize the Capitol, the culture wars strongly influenced Trump’s “Stop the Steal” movement but the more troubling rightwing movement that is manifesting itself in an ever-growing number of social or cultural domains. o § Health/Nutrition/Agriculture⠀➾ # ⚓ The_Dirty_Secret_of_America’s_Clean_Dishes⠀⇛ Hollie Walker cherished the simplicity of her life in White Stone, South Carolina, a tiny community on the outskirts of Spartanburg. In the quiet of the country, she and her husband raised their two sons in a yellow house on 37 acres of secluded land, where they hiked in the woods and swam in their lake. Today, the area is home to a one-room post office, two churches, and a shooting range open three days a week. For years in the 1990s, Walker worked behind the counter at the post office. There used to be a bar called the White Stone Mall on the same stretch of highway, where Walker would sip beers, shoot pool and chat with workers getting off their shifts from a chemical plant across the street. She didn’t know much about the German-owned company, BASF, that operated the plant. After BASF expanded its site in the 2000’s, demolishing the bar in the process, she had little reason to stop along that highway, except when the railroad gates halted traffic. # ⚓ The_Nazi_Language_of_German_Anti-Vaxxers⠀⇛ For months, German politicians – from ex-chancellor Merkel (conservative) to newly elected social- democratic chancellor, Olaf Scholz – have been trying to convince Germans of the need to get a Corona vaccination. As a consequence of their endless appeal to common sense, about 30% of Germans still remain unvaccinated. By mid-December 2021, infection rates and Covid-19 deaths were on the rise again. Yet, there are way too many Germans who are simply not interested in facts about the pandemic. Beyond Germany’s anti-vaxxers, there are also plenty of people who still deny the existence of the Coronavirus pandemic despite ample evidence to the contrary. Recently however, the proportion of people in the camp of believers of a global Corona conspiracy myths, while also denying the existence of the virus, has actually fallen, somewhat. # ⚓ Medical_Racism_Is_Fueling_the_Black_Overdose_Crisis, Advocates_Say⠀⇛ # ⚓ Health_Care_and_Our_Heroes:_Kaiser_Permanente_in_COVID Time⠀⇛ Kaiser’s origins are in the Bay Area, and it still is based in Oakland, today it has 39 nine hospitals and some 700 medical facilities. In recent years, it has expanded to Washington State, Oregon, Hawaii, Colorado, Maryland, Virginia and Georgia. Since just before COVID its membership has grown by 600,000 and it now employs some 300,000 workers, including 80,000 nurses and doctors. In 2020, its profits were $6.4 billion. In 2021, its net worth was $43.3 billion, according to the California Department of Managed Health Care. It returned $500 million in pandemic relief funding to the federal government in 2020. Kaiser management is doing OK as well; the CEOs bring home salaries that favorably compare to its workers: 231-1!  Greg Adams, the chief executive in Oakland received $17.3 million in total compensation in 2020. He and the 100 top executives have the benefit of eight separate retirement plans. o § Integrity/Availability⠀➾ # § Proprietary⠀➾ # ⚓ Delaware_Court_Says_Dominion_Voting_Systems_Can Continue_Suing_Fox_News_For_$1.6_Billion_In Defamation⠀⇛ Another one of Dominion Voting Systems’ many, many lawsuits against Trump loyalists will be allowed to continue. (For a pretty comprehensive rundown of Dominion’s election- related defamation lawsuits, check out these comments by Techdirt reader RP.) # § Security⠀➾ # § Privacy/Surveillance⠀➾ # ⚓ NSO_Group_Facing_Even_More_Money_Problems As_Debt_Manager_Says_Sayonara_And_State_Of Oregon_Seeks_To_Terminate_Its_Investment⠀⇛ NSO Group spent years supplying some of the world’s most untrustworthy governments with powerful spyware capable of completely compromising targeted devices. It managed to weather a few years of reports tying its malware to surveillance of journalists and activists, but all hell broke loose earlier this year, resulting in a steady stream of reports linking its tools to surveillance of government officials, journalists, dissidents, government critics, religious leaders, and, in one incredible case, the ex-wife of the king of Dubai. o § Defence/Aggression⠀➾ # ⚓ GOP_January_6_Panel_Member_Says_Trump_Could_Be_Subpoenaed, Face_Charges⠀⇛ # ⚓ Bringing_Out_the_Big_Guns⠀⇛ How did a small, landlocked country without significant natural resources become Africa’s “most inspiring success story”? A hint: Stats about “natural resources” usually don’t include bullets. # ⚓ Opinion_|_New_York_Times_Reporting_on_Airstrikes_Should Give_Daniel_Hale_More_Credit⠀⇛ The New York Times recently came through with a display of reporting that should be commended. On December 18, the paper announced its release of hundreds of the Pentagon’s confidential reports of civilian casualties caused by U.S. airstrikes in the Middle East. This followsits high profile investigations into the U.S. drone murder of the Ahmadi family during the Afghanistan withdrawal, and an American strike cell in Syria that killed dozens of civilians with airstrikes. # ⚓ The_Mainstream_Media_Seems_to_Want_More_War_for_the_United States⠀⇛ For its part, the Senate overwhelmingly passed a $768 billion defense bill that exceeded the requests of both Biden’s White House and the Pentagon.  The bill included significant increases for countering China; bolstering Ukraine; and modernizing strategic nuclear forces, including hundreds of billions of dollars for replacing the silo-based intercontinental ballistic missiles that mar the landscape of the American West. If the United States was concerned with nuclear stability and safety, it would abandon all silo- based missiles, which are the most vulnerable.  Significant reductions of nuclear forces, moreover, would increase U.S. national security; contribute to the lessening of an arms race with Russia and China; and fulfill our treaty obligations to the Non-Proliferation Treaty of 1968, which has been observed in the breach. o § Environment⠀➾ # § Wildlife/Nature⠀➾ # ⚓ Mexican_Gray_Wolves_Belong_in_the_Wild,_Wherever_They Roam⠀⇛ Almost as soon as the Department dropped him off on the Apache-Sitgreaves National Forest, Anubis started running towards his new territory in northern Arizona. He’s a young male wolf, and following his instinct to seek out new terrain and possible mates. Since his return, he’s been successfully crossing the I-40 boundary, avoiding cars, and staying out of conflict with livestock. Mexican gray wolves belong in the Coconino and Kaibab National Forests and in the Grand Canyon region, where prey is widely available and there’s plenty of open space for native wildlife to survive and thrive. The only reason Mexican wolves aren’t allowed to wander in suitable wolf habitats is a wholly political decision to keep them south of I-40 and within a limited recovery area for the sake of appeasing ranchers and the anti-wolf states to our north. But in the context of climate change and species adaptation, as well as an recovering population of wolves in the established range, it makes a lot of sense that Anubis and others would be expanding into new turf. # § Overpopulation⠀➾ # ⚓ Opinion_|_Time_for_a_Climate_Insurgency?⠀⇛ Since the end of the feudal era the world order has been largely structured by the nation-state system. Individuals have been willing to kill and die for their countries. The pursuit of individual and collective interests has occurred largely within a national framework. # ⚓ Life_Circa_2050_Will_Be_Bad._Really_Bad.⠀⇛ When midnight strikes on New Year’s Day of 2050, there will be little cause for celebration. There will, of course, be the usual toasts with fine wines in the climate- controlled compounds of the wealthy few. But for most of humanity, it’ll just be another day of adversity bordering on misery—a desperate struggle to find food, water, shelter, and safety. o § Finance⠀➾ # ⚓ 2021_Saw_Gaps_in_Racial_and_Economic_Inequality_Widen._But There’s_Still_Hope.⠀⇛ # ⚓ Lessons_from_the_Great_Resignation:_Can_Quitters_be Winners?⠀⇛ The first is the headline item (actually, subhead) that although the quitters’ mental health improved, their finances were not necessarily better after they left their jobs. There is an obvious point here that people should recognize. It is unlikely that, even in a good labor market, people who leave near minimum wage jobs will suddenly find themselves flush with money. If someone is earning $10 an hour, even a 20 percent increase (in excess of inflation) only gets them to $12 an hour. That sort of increase likely means a big difference in their standard of living, but still leaves them far short of a comfortable middle-class existence. In some cases, the modest gains from the tighter labor market may give them the ability to get additional education or training that will let them enter a higher paying occupation, but we shouldn’t expect that a tight labor market alone will mean that workers in the lowest paying jobs are now financially secure. o § AstroTurf/Lobbying/Politics⠀➾ # ⚓ Georgia_Senator_Wants_to_Ban_Ballot_Drop_Boxes_After_Voting to_Install_Them⠀⇛ # ⚓ In_Historic_Win,_Chile_Votes_for_Socialism_Over_Fascism⠀⇛ # ⚓ Russia_expels_two_German_diplomats,_decries_allegations_of state_involvement_in_Khangoshvili_murder⠀⇛ The Russian Foreign Ministry has declared two German diplomats persona non grata in a “symmetrical response” to Berlin’s expulsion of two Russian diplomats last week, according to a ministry statement released on Monday, December 20. # ⚓ A_separate_peace_A_dispatch_from_the_Prigorodny_District, where_violence_broke_out_between_Ingush_and_Ossetian residents_thirty_years_ago_—_and_nobody_has_forgotten⠀⇛ The Prigorodny District is a disputed territory on the border between the Russian republics of North Ossetia and Ingushetia. Violence broke out there 30 years ago — and to this day, Ingush and Ossetian neighbors in Prigorodny avoid speaking to one another and send their children to separate schools. In a dispatch from Prigorodny, Meduza special correspondent Sasha Sivtsova examines why the conflict, which was triggered by state repressions, is still going on after so many years. o § Civil Rights/Policing⠀➾ # ⚓ Opinion_|_I’m_18_With_a_Full-Ride_College_Scholarship._But as_a_Dreamer,_I_Worry_About_Being_Deported⠀⇛ In 2005, when I was two years old, my mom brought me across the border from San Luis Potosí, Mexico. We came to reunite with my dad, who was already here and had started his own concrete business in the New Orleans suburbs, where we still reside.  For the longest time, I didn’t even know I was undocumented. But that changed two years ago, when I realized I couldn’t get a driver’s license like my other friends. # ⚓ Introducing_‘Department_One’_Exiled_human_rights_lawyer Ivan_Pavlov_launches_new_legal_group_to_take_on_Russia’s treason_and_espionage_cases⠀⇛ Exiled human rights lawyer Ivan Pavlov has launched a new legal group that specializes in defending those accused of treason and espionage in Russia. Pavlov, who fled abroad to escape criminal charges in September, previously led Team 29 — a similar human rights initiative that tackled some of Russia’s most challenging political prosecutions. The group disbanded in July 2021, to protect its members and supporters from persecution. Pavlov’s new project, dubbed “Pervy Otdel” (which translates as “First Department” or “Department One”) also aims to take on cases that are handled “behind closed doors” and will function in cooperation with colleagues working “on the ground” in Russia. # ⚓ The_Things_Musicians_At_Territorial_Prison_Carry:_‘Battle Cry’_Video_Premiere⠀⇛ The Colorado Territorial Correctional Facility was constructed in the late 1800s when the state of Colorado was still a territory. It is the oldest prison in the state’s prison system. It is also is the site, where the first compilation album for Die Jim Crow Records was recorded.Die Jim Crow is the first record label in the United States dedicated to incarcerated musicians. The label recorded seven musicians at Territorial in Cañon City in April 2018.The tracks laid down during these sessions represented an array of genres—Americana, indigenous Nahuatl chant, blues, and hip hop, etc—and matched the diversity of the musicians, who were indigenous, Black, queer Jewish, and white. Some of these men are serving life sentences.“In the 150 years since the prison’s construction, ‘TLAXIHUIQUI’ is the first recorded music to make it outside the forbidding walls of Territorial into the free world,” according to Die Jim Crow Records. [...] Newton shared, “Just me growing up the way I was, in an abusive environment and me not knowing how to deal with that, growing up in that environment.”Opening up even more, Newton added, “My mom had me when she was 14. My father was 19. And he took off immediately, so you grow up in that kind of world where it’s watching your mom do drugs and come in and out of these abusive relationships.”“I think you have to be honest about the brokenness in everybody, especially your own [self], before you can move forward. You gotta look yourself in the mirror.”  # ⚓ Human_rights_project_Gulagu.net_releases_more_footage_of torture_in_Russian_prisons⠀⇛ Activists from Gulagu.net (No to the Gulag) have obtained and released new footage further evidencing the torture and abuse of inmates in Russian prisons.  # ⚓ “A_Big_Relief”:_Haitian_Immigrant_Rights_Leader_Jean Montrevil_Wins_Victory_in_Fight_to_Stay_in_U.S.⠀⇛ Longtime immigrant rights leader Jean Montrevil has been granted three years of protection from deportation as part of a settlement for the First Amendment lawsuit Montrevil filed against the U.S. government that argued federal immigration officials targeted him for deportation due to his activism. Montrevil was abruptly deported to Haiti in 2018 but was allowed under the Biden administration to return home to New York in October to reunite with his family. We speak with Jean Montrevil, who says the news has given him “peace of mind” to enjoy the holiday season without fear of getting detained or deported, as well as Montrevil’s lawyer Alina Das, who attributes the highly unusual decision to the strength of the immigrant rights movement. “It is the power of organizing that brought the government to the negotiating table,” says Das. o § Internet Policy/Net Neutrality⠀➾ # ⚓ The_Law_Bytes_Podcast,_Episode_113:_The_Year_in_Canadian Digital_Law_and_Policy⠀⇛ o § Monopolies⠀➾ # § Patents⠀➾ # ⚓ Judge_Albright_Names_Lawyer_For_Patent_Trolls_As_New Magistrate_Judge_For_Waco⠀⇛ With the transformation of his Waco courtroom into the venue for more than 25% of all patent cases in the United States, Judge Albright can’t keep up with all the business he’s “drummed up” for his courtroom. He’s made heavy use of technical advisors—one of whom made more than $700,000 in the first half of 2021 alone—as well as deferring almost all non-patent cases to his magistrates for all pre-trial proceedings. # § Software Patents⠀➾ # ⚓ Patent_Awarded_To_Clearview_AI_For_Its Innovative,_Web-Scraping_Fuckery⠀⇛ Clearview AI has begun travelling the long road back to semi-respectability. ䷩ 𝚕𝚒𝚗𝚎 1448 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2021/12/21/epo-clowns-data/#comments Gemini version at gemini://gemini.techrights.org/2021/12/21/epo-clowns-data/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.21.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ [Meme]_Will_You_Trust_These_Clowns_With_Your_Confidential_Data?⠀✐ Posted in Europe, Patents at 10:59 am by Dr. Roy Schestowitz With diplomatic immunity comes unacceptable behaviour (also at WIPO) 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Watching_over_your_private_data_at_EPO⦈_ Summary: The EPO does_not_take_privacy_seriously; it cares only about optics, not legality ⣿⣿⣿⣿⣿⣿⡟⠛⠀⠀⠀⢋⣻⣿⣿⣿⣟⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡟⠁⠀⠀⠠⢘⣛⠖⡛⢿⠟⠩⢥⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⡿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡿⠟⠋⠁⠖⠀⠀⢰⣿⣿⣿⠄⢸⠀⣶⣦⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⢉⣉⣤⣾⣿⣿⣿⣿⣯⠛⠻⣿⠿⠋⠉⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⠿⠿⠋⠉⢉⣀⣹⢰⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠗⣠⣬⠁⣿⡿⠀⣿⣿⣿⣿⣿⠿⡿⠿⠇⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡟⠃⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⣿⣿⣿⣿⣿⣿ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣥⡈⠩⠏⠀⣼⠇⠀⢻⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠉⠉⠿⠿⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⠻⠟⠿⢿⡿⣧⠻⠿⣿⣿⣿⣿⣿ ⢸⣶⣤⣄⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣼⠟⠀⠀⢸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡄⠀⢀⣠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⡀⠈⠙⠀⠀⠀⠀⠀⠉⣀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠻⣿⣿ ⣿⣦⣭⣍⣛⡛⠷⢤⡀⠈⠛⠻⣻⠿⠓⠁⠀⠀⠀⠈⠛⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠞⢩⡿⢟⢿⣟⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆⡀⢠⣷⣤⣤⣾⣿⡿⢧⡀⠀⢀⠄⠀⠀⠀⠀⠀⠘⣿ ⢸⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠋⠰⠦⠀⢴⣿⡟⡴⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠙⠛⠋⠁⣈⠛⠛⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⣀⢹ ⣇⢻⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣶⣿⣷⣦⣤⡄⣤⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠀⠀⠀⠈⠉⢀⡀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡾⠿⢿⡌ ⣿⣷⡙⢿⣿⣿⣿⣿⣿⣿⣥⣍⣛⣛⣿⣿⣿⠟⣼⣿⣿⡿⠿⢿⢳⠀⠀⠀⠀⠀⠀⠀⣀⢀⣈⠁⠈⠉⣁⣀⡀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⢀⢰⣿⡿⠛⠉⠀⠀⠀⠠⠔⠞⠛⠋⠀⠀⠀⠀⢒⣋⣭⣴⣶⣶⣿⣿⡇ ⣿⣿⣿⣦⠙⠻⣿⣿⣿⣿⣿⣿⡿⡿⣿⠟⣫⣾⢹⣶⣾⠿⠿⣿⢸⡇⣾⢠⢉⡀⡶⠀⣿⣿⡏⠉⠀⣿⡏⠉⠀⠀⣿⠃⣠⠭⢰⡆⡀⣰⢊⡍⢷⣉⡶⢛⢷⡁⠀⠀⣀⣀⠶⠄⠀⠀⠀⠀⢀⠸⢿⣿⣿⣿⣿⣿⡿⣰ ⣿⣿⣿⢣⡷⠡⠄⠈⠉⠉⠉⠉⠎⣠⠀⣾⣿⣿⣤⡄⣿⢰⡆⣿⢸⡇⣿⢸⢸⡇⣀⡼⠏⢸⡇⠀⠂⣿⠃⠀⠀⠀⣿⡄⣶⣿⢸⡇⢣⡇⣼⡇⡜⣿⢠⣿⡏⣷⠁⣼⠛⡻⠓⣿⢛⣃⢞⣵⡹⣄⣸⣿⣿⣿⣿⡟⣱⣿ ⣿⣿⡏⠈⡆⣦⢻⣷⡜⢿⣿⡇⢠⡇⠀⠻⠛⠝⠻⡇⣿⢸⡇⣿⢸⡇⣿⢸⢸⡇⢻⣧⠠⢸⡷⠶⠂⣿⠷⠆⣠⣤⠹⣷⠹⣿⢸⡇⡘⡇⡟⣸⡇⣏⢸⣿⡇⣿⣾⡇⡸⡿⠇⣿⢰⢢⣿⢋⣴⣿⣿⣿⣿⠿⣫⣾⣿⣿ ⣿⣿⡇⢸⣦⡊⠁⠱⠶⠶⠶⠀⠰⠂⠀⠀⠃⠒⠶⠆⣿⢰⡆⣿⣶⣥⣿⢸⢸⡇⣧⢻⣧⣸⣇⡐⠃⣿⣀⡚⢋⣬⣧⢻⡇⢿⢸⡇⡇⢧⠸⡿⣸⢿⠸⣿⢇⡿⢿⡄⠰⡎⠀⣿⠸⠸⣿⠸⣿⠿⢟⣋⣥⣾⣿⣿⣿⣿ ⣿⣿⡇⣸⣿⣿⢸⣿⣿⣿⡿⠀⣾⠀⠀⠀⢠⣾⣿⡇⠿⠈⡇⠛⢠⣌⣛⣸⣈⣁⣿⣧⣉⣈⣉⡁⢦⣉⣉⣡⣾⣿⡿⣸⡇⣸⠈⠁⣴⣦⡛⠚⢁⣌⠳⠭⠞⢡⡜⣧⣀⡇⠀⡿⠟⠁⠹⣧⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⣿⣿⣿⡆⢭⣭⣭⡅⢀⡍⠀⠀⣥⣀⣀⣭⡅⢶⡆⢹⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣝⣛⣛⡛⣱⡿⠀⣠⠄⣶⡝⣿⣿⣿⣿⣿⣷⣶⣾⢟⣩⣬⣙⠃⡀⠷⠶⠀⣱⡿⢈⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣌⠻⣿⣿⠸⣿⣿⠁⢸⣇⣴⣾⣿⣿⣿⣿⡇⢰⡆⣤⡄⣤⢭⣭⣝⣿⣛⡛⣛⣛⠿⣿⠿⠿⠿⠿⣿⣿⠌⠋⢠⡾⢋⣾⣿⣷⠸⣿⣿⣿⣿⣿⡟⣱⣿⣿⣿⣿⣿⣷⣶⡆⣶⣌⣡⣿⣦⡙⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣷⣮⡄⣿⣿⢀⣴⣶⣶⣶⣶⣶⠀⢸⡇⢸⣿⣿⣿⣿⣼⣿⣏⢹⡟⢹⣿⣿⣇⣿⣻⡿⣿⣧⣿⣼⡆⣶⣶⣦⠛⣹⣿⣯⣥⡍⣭⣭⣭⡏⣀⣀⡈⠙⠻⠿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣌⢿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣷⢸⡟⢸⣿⣿⣿⣿⣿⡿⠸⠀⠇⠸⠿⠿⠿⡇⣿⢿⣿⣿⡇⢸⣿⣶⣾⣿⣿⡇⣿⣿⣿⣿⣇⣿⢿⣿⠀⣿⣿⣿⢸⣷⣿⢹⣿⡅⣿⣿⡿⣷⣶⣶⣦⣭⡙⠘⠻⠿⣿⣿⣿⣿⣿⣎⢿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⣿⣿⣿⣿⣿⡟⠰⣶⣴⢦⣤⣤⣠⣤⣠⡄⣤⣀⡠⡶⣀⣉⡉⠈⠉⠉⠁⠛⠙⠋⠛⠋⠻⠛⠏⢀⠻⠿⠟⠸⠿⡟⣼⣯⣼⣿⣼⡇⣿⣿⣿⣿⣿⡇⣿⣷⣦⣔⡪⠭⣙⠛⢿⡎⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⣿⣿⣿⣿⣿⣧⠀⣿⡟⢸⡿⣿⣿⣿⣿⡇⣿⣿⡟⠀⣿⣿⣿⣿⣿⣷⣿⣿⣿⣸⡿⣶⣶⡴⣶⣶⣴⣶⡞⢣⣤⣤⡀⣠⣄⣀⣀⣙⢛⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣷⡆⣠⢀⢡⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⠀⠿⣇⣹⣷⡿⠹⣿⣿⢿⣿⣼⡇⠀⣿⡏⢁⣿⢿⡧⣿⡇⣿⣿⣷⣿⣿⡇⣿⡇⣿⡷⠄⢸⣿⣿⡇⣿⣿⡏⣿⡏⣿⣿⡇⣿⣿⢻⣿⣿⣿⣿⣿⣿⣵⣇⣿⣾⣿⣿⣿⣿ ⠿⠿⠿⠿⠿⠿⠿⠿⠏⠼⠿⠿⠿⠿⠿⠿⠀⠸⠿⠿⠿⠿⠿⠿⠿⠷⠶⠾⠿⠿⠿⠿⠿⠯⠼⠧⠿⠧⠟⠛⠘⠛⠿⠷⠿⠀⠿⠷⠆⠸⣿⣿⢿⣿⣿⡇⣿⢧⣿⣿⡇⠿⠿⠸⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠿⠿⠛⠛⠻⠒⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿ ䷩ 𝚕𝚒𝚗𝚎 1502 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2021/12/21/happy-mono-family/#comments Gemini version at gemini://gemini.techrights.org/2021/12/21/happy-mono-family/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.21.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Microsoft’s_Team_Mono:_One_Happy_Family⠀✐ Posted in Microsoft, Mono at 5:50 am by Dr. Roy Schestowitz Balabhadra (Alex) Graveley, Miguel de Icaza, Nat Friedman, and Stephanie Friedman as captured by their own photographs [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], which might disappear at a later point 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Balabhadra_(Alex)_Graveley,_Miguel_de_Icaza⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Miguel_de_Icaza,_Nat_Friedman,_Stephanie_Friedman⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Balabhadra_(Alex)_Graveley_shot_by_Stephanie_Friedman⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Balabhadra_(Alex)_Graveley_kissed_by_Stephanie_Friedman⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Balabhadra_(Alex)_Graveley_stands_by_Stephanie_Friedman⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Miguel_de_Icaza,_Nat_Friedman,_Stephanie_Friedman⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Balabhadra_(Alex)_Graveley,_Miguel_de_Icaza_at_wedding⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Balabhadra_(Alex)_Graveley,_Miguel_de_Icaza_at_dinner⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Balabhadra_(Alex)_Graveley_shot_by_Stephanie_Friedman_in_the street⦈_ Summary: Now that the Friedmans are deleting their own photos we must preserve some of the key photos, which connect them to a massive liability (they knew what he had done) Nat Friedman has deleted_his_Flickr_account. It happened recently, but the exact date is difficult to pinpoint. But Stephanie’s Flickr account is still up. She’s the wife of Nat and will be the subject of a later part in the long- running series that may in fact run until springtime. It’s an ongoing and fast- developing story. Microsoft’s Chief Architect of GitHub Copilot, Balabhadra (Alex) Graveley, was in the docket yesterday after assaulting women (not the first time!) and there’s certainly a lot more to come for us to integrate into the series. “It’s an ongoing and fast-developing story.”For the sake of ensuring the integrity of the series (along with evidence) we’ve captured key photos and share some of them above. We’ll come back to that later. Alleging that this is a privacy violation would be ludicrous given that they’ve shared all this publicly for over a decade and people who engage in misconduct don’t deserve exemptions from self-incriminating things, more so if they themselves upload everything online in bulk. █ ⠀⠀⠘⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢤⠄⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠕⡟⠹⠸⠹⠹⠸⡹⠈⠛⠏⡏⠇⡏⣿⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢺⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡟⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠿⠿⠟⡟⠛⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢿⣿⡇⢸⣿⣿⡏⡹⡉⡏⡟⡟⡟⡟⡟⠟⠏⣿⢻⢹⠻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⣷⣦⣧⣧⣷⣧⣽⣸⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⢀⣷⣤⡀⢉⢷⣌⣿⣿⡷⢿⣶⣷⣦⣤⣷⣶⣷⣾⣶⣿⣶⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⡯⡟⣻⠛⡟⡟⢟⢻⢹⠛⠟⠟⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣤⣴⣿⣿⣿⣿⣦⣜⢿⣿⣿⡇⢈⠹⡟⡉⠋⢝⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣷⣿⣶⣿⣾⣾⣿⣾⣾⣿⣼⣿⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢏⠙⣻⢿⣿⣿⣿⣿⣿⠃⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⢀⢤⣰⡿⠿⠿⢿⡄⠀⡜⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀ ⠈⠀⠀⠀⠂⠸⠿⠻⣿⠃⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⢿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠛⠁⠀⠀⣀⣼⣿⠀⢡⣴⣤⣤⣄⣆⣀⣀⠀⠀⠀ ⠀⠀⠠⣤⣤⠄⠔⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⣹⣿⣿⣿⣿⣿⡆⠀⠀⢰⣿⣤⣦⣴⣾⣿⣿⡆⠘⢿⣿⣿⣿⣿⣿⣿⣷⣄⠀ ⠀⠀⡀⠉⠉⠃⠀⠈⠻⢿⣿⣿⣿⣿⣿⣯⣉⣈⡩⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⣛⣛⣀⣶⣿⣿⣿⣿⣿⣿⡁⠀⠁⠠⣿⣿⠏⡍⠉⠉⠻⠁⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡆ ⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠠⡀⠀⠉⠁⠀⠀⠀⠀⠀⠀⣠⠀⢸⣿⣿⣿⣿⣿⢿⣿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣼⠟⣰⣮⣿⣿⣿⣿⡟⢚⢿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠁⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣦⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣀⡀⠀⠞⢁⣴⣿⣿⣿⠿⣿⣿⠁⠀⠘⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⠿⣋⣴⣿⣿⢉⠁⠀⠛⠛⠡⠾⠿⠿⠚⠐⢺⣿⣟⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣇⣀⣠⣶⣿⣿⣿⣿⣿⣿⠿⢃⣤⣾⣿⣿⣿⡿⠒⠐⢂⡀⠀⠀⠀⠀⠉⠻⠤⠖⠄⠏⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠐⠁⠀⠩⣿⣿⣿⣿⣯⢸⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣋⣤⣾⣿⣿⣿⣿⠛⠋⠐⢍⡭⠡⠄⠀⠀⠀⠀⠀⠀⠨⠴⣟⠀⠀⠀⠀⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣶⣐⣿⣿⣆⠀⠐⢄⠀⠸⣿⣿⣿⣿⠰⣿⣿⡿⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣋⣵⣷⣄⠀⠀⠑⠂⠀⠊⠁⠀⠀⠀⢀⢐⠈⠹⠗⠀⠀⢒⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢶⣶⣶⣶⣿⣿⣖⣿⣿⣿⣿⣿⡄⠀⠑⠁⠀⠙⢿⣿⣾⠀⠼⠙⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣤⣾⣿⣿⢿⣿⡄⠀⠀⠀⠀⠄⠀⢀⣠⠔⣿⣿⣿⣿⣯⢤⣤⣼⣦⣾ ⢑⢦⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣭⣭⣭⣽⢹⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠈⣿⣿⣀⠈⢀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⣻⣿⣿⣿⣿⣿⣵⣿⣿⠇⠀⠀⠀⢀⡠⠬⠉⣂⠭⠚⣿⣿⣿⣾⣿⣿⣾⣿⣿ ⠐⢕⣗⢄⠀⠀⠀⠡⡀⠀⠀⠀⢄⠈⠙⢻⣿⣮⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣿⣿⡟⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⢶⣦⣴⣲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⣠⣀⣽⣿⣷⡀⠀⠀⠀⠢⠀⡀⠀⠈⠲⢄⠉⢿⣿⣿⣿⣿⣿⣿⡀⠀⣴⣤⡀⠹⣿⡇⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⣩⣶⣾⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⣀⠀⠀⠚⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠊⠈⢠⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣷⡌⢿⣿⢿⡄⠹⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣡⣶⣿⣿⡿⠋⠀⠋⠉⡡⠀⠀⠀⣄⢠⣄⣀⠲⢨⣀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⢿⣿⣿⣿ ⣬⣙⠿⣿⣿⣿⣿⣿⣶⣀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣧⣤⣿⣿⡿⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠿⢿⡿⠋⠁⠀⠀⠀⠀⠁⠀⠀⠩⣖⠸⣾⣿⣿⣧⣴⣿⡗⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⠿⠿⠿⠿ ⣿⣿⣿⣾⣿⣿⡿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣫⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠆⠀⠑⢬⣷⣿⣿⣿⣿⣿⣿⣿⣦⣐⡀⠀⠲⣄⣤⣀⡀⣀⡀⠀⣀⣀ ⠛⢛⣛⣻⣿⠿⣿⣿⡻⢿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠈⣻⣿⣿⣿⣿⢽⠟⢿⣿⣿⣷⣔⣮⣿⣿⣿⢽⣿⣾⣟⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⡟⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣌⠃⡗⡷⢸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣅⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿ 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⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠛⠉⠉⠉⠉⠉⠙⢿⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡞⢀⣀⣠⣤⣤⣀⡀⠀⠀⠙⠛⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣄⠀⣰⣿⣿⣿⡿⣻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣉⡁⠈⣻⣿⣿⣿⣏⣹⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣯⠉⠙⢿⢋⠀⠠⠄⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣦⣴⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⣷⣾⣶⣿⡧⣬⣽⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣺⣿⣿⡿⢶⡒⠛⠿⠃⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⠇⠁⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⠏⠐⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣴⣶⣶⣶⠂⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠛⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣸⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣠⣿⣿⣿⣿⣷⣦⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠦⣠⡤⢤⣤⣤⣄⠀⣀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣶⣶⣾⡗⢞⣋⣙⡿⣴⣦⣤⣍⡉⠂⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠛⠽⢿⡯⠉⠁⠈⢩⠾⡻⣽⣭⣽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣯⣍⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃ ⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣸⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀ ⠀⠀⠀⢀⠀⠀⠀⠉⠙⠻⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⢻⣿⣿⣿⣿⣿⣿⣿⣧⡆⠀ ⠀⠀⢰⣶⣤⣤⣤⣤⣀⣰⣿⣧⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡏⠈⠛⠿⢿⠁⠀⠀⠀⠀⠸⠙⠻⠿⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⣀⣠⣾⣿⣿⣿⣿⣿⢿⣭⣿⡇⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡓⣿⣿⣿⣿⣿⣿⣿⣿⣷⡙⣟⠇⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡒⣄⠘⣻⣿⣿⣿⣿⣿⣿⣟⢵⣼⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠿⣿⣿⣿⣿⣿⣿⣿⣦⣕⡹⢾⣯⣭⣙⣿⣿⣿⣿⡟⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠙⠻⢿⡿⣿⣿⣿⢿⠂⠀⠉⢻⣿⣿⣿⣿⣿⣧⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠛⠫⣣⠑⠀⢸⢄⠉⠻⡝⣿⣿⠟⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠀⠈⠈⠀⠀⠀⠀ ⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠡⠂⠇⠐⡆⢀⢰⡇⠿⠁⠰⠻⠐⠷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤ 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⣛⣩⣭⣭⣵⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠔⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⡞⣿⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠂⠀⠀⠨⢸⠿⠁⣿⠀⠻⣿⣯ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⡀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢊⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⢿⣮⣻⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠁⠀⠈⠁⠀ ⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⡇⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡡⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣛⡥⠁⣿⠿⠿⠟⢛⣛⣋⣩⣭⣴⣖⡹⠿⣿⣿⣇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⢀⡆⠀⠀⠀⠀⠀⡀⢀⣿⣿⣿⣿⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠟⣿⠟⡔⠀⣶⣶⣿⣿⣿⡿⠿⣿⣛⣻⣯⡅⠐⢿⣿⣿⠀⠼⢿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠉⠀⠀⠀⠀⠀⣿⡃⡀⠀⠀⠀⠘⢁⡈⣁⠴⠒⢌⣫⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⢋⢎⡜⠀⣭⣽⣷⣶⣾⣿⣿⣿⣿⣿⣿⢷⠀⠸⡿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⢹⡟⢟⠀⠀⠠⢸⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⡰⢣⠞⠔⡀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣶⠀⠀⢢⠀⠐⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠈⢻⣛⡀⠀⠀⠬⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠞⡱⢋⢎⣼⡇⢹⣿⣿⣿⣿⣿⣿⡿⠿⠏⠹⠋⠀⠀⢸⣆⡀⠀⣦⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣨⠜⣿⢽⡷⠡⣼⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡞⣱⢣⣾⣿⡇⠸⠻⠟⠋⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⣹⡄⠀⢻⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠂⠀⠀⠸⢛⣚⠣⢤⣾⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡼⣡⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠹⣿⣷⠈⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠈⢟⣽⣣⡄⠈⠻⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠻⡀⢧⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠐⠀⠀⠿⠉⠀⠈⠀⢹⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠰⡐⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠋⠀⠀⢼⣿⣿⣉⣀⠀⠁⣿⠈⢿⣦⠀⠀⡀⢸⠀⠀⢐⣒⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⠀⠀⢀⣬⣿⣿⣿⣿⡷⠀⠘⠀⢸⣿⣤⣀⠇⠘⠤⠂⠐⠚⠒⢀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣼⣿⣻ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⡯⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⠈⢿⠟⢻⣿⡿⣿⣳⣦⣵⣿⣿⠀⠀⠀⢨⠛⠒⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠿⠿⢿⣟⣻⣿⣿⣿⣿⣯⣿⣿⣷⣿⡇⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡳⡥⡀⠀⠀⢜⡿⢟⣭⣿⡹⣿⣿⡆⠀⠀⠘⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠊⠚⠢⠀⠠⡾⢿⣿⢊⠀⢻⣿⣇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⣻⣿⣿⣿⣿⣷⣿⣟⣿⣿⣭ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠺⣿⡶⠾⠷⡖⠿⠦⠶⠾⠿⠟⠀⠸⡿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢹⣿⣿ ⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣭⣿⢸⡇⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠘⠇⠀⠀⠀⠀⠍⡉⠟⢈⡀⠀⠀⠁⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠞⠓⠛ ⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠇⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠐⠀⠀⠀⠀⠁⠏⢯⣚⡗⣤⣤⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠹⢿⠁⣿⣿⣻⣿⣿⠿⠿⠿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠘⠀⠀⠀⠀⡀⠀⡫⠿⣼⣯⠽⡄⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⡟⠀⣿⠿⠿⠿⢛⣛⣛⣭⢹⣿⠀⣟⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠄⠀⢀⠀⠈⡀⢀⠂⠘⢎⣾⣯⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢈⢊⠂⣶⣾⠿⠿⢿⣛⣛⣿⣽⣷⣄⡿⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠁⠀⠐⠃⣈⡩⢫⠄⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡵⡡⡁⢰⣿⣿⣿⣿⡿⡟⢻⣿⡿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣼⠗⡀⠀⠐⣨⠸⠀⢸⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢜⣼⣇⢸⣿⣿⣿⠿⠿⠛⠋⣿⡗⢈⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣘⢿⡟⣠⢬⠄⢉⢌⠀⢸⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣷⠈⠉⠁⠀⠀⠀⠀⠀⠈⠁⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⡽⡛⢰⢭⡅⢄⠈⡐⢗⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠋⣤⢾⡷⣕⠀⢠⠆⠘⣻⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣔⠷⠊⠀⢸⡬⠀⢺⣯⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣰⣦⣤⣄⣀⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⢀⢀⢐⠀⠇⡰⡃⠈⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡿⣳⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣼⡇⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠔⢸⢀⠈⡁⢠⣾⣄⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢻⣿⡿⠃⠀⠉⠉⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢻⣿⠈⢿⣿⡟⣿⣿⣿⡆⠀⣾⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⠀⠀⣸⣿⣿⣿⣿⣿ ⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣍⠛⠋⠛⠻⢿⣿⣷⠀⠀⠀⠀⠀⠘⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣟⡟⠀⠀⠀⠀⠈⠟⠀⢸⣿⣧⣯⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢻⣿⡆⢠⣿⣿⣿⣿⣿⣿ ⠁⠈⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣤⣶⣦⢻⣿⡆⠀⠀⠀⠀⠀⠹⣿⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⢹⣿⣷⣾⣾⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠘⠻⠏⠈⣭⣿⣿⣿⣿⡟⢸⣿⣿⣿⠿⢿⣿⠈⢿⠃⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣿⠿⣿⣿⣿⣿⢻⣿⠀⠀⣸⣿⣭⣇⢸⣿⣷⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⣡⣶⣶⣤⡈⠛⢻⣿⣿⡝⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⢀⣿⡿⡹⢿⣿⣳⣿⣿⣿⣿⣿⣿⠋⠀⢀⣴⣿⣿⣿⣿⣿⡟⢛ ⠀⠀⡟⠀⠁⠁⠁⠀⠈⠿⠀⠀⠻⣿⡟⠁⢠⡗⢿⡄⠀⠀⠀⠀⠀⠀⠀⠤⣤⡤⠀⣸⣿⣿⣿⣿⣿⣧⡌⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢈⣿⣿⡇⠀⣿⣿⣿⣿⣟⣿⣿⣿⣄⣠⣾⣿⣿⣿⡿⠓⠟⢃⣸ ⠀⠀⠙⠂⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠁⠀⢀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠘⠝⠁⠀⢿⣿⣿⣿⣿⣿⣿⣧⡀⣈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠈⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⢴⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⡟⠻⢿⣿⣷⢻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⢸⣟⣿⣿⣿⣶⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⣷⣿⣿⡇⣸⣿⣭⡆⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡀⣠⣾⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⣾⣿⣿⣿⣷⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡇⢿⣿⣿⡇⠀⠀⠀⠀⢠⣾⣿⣼⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠹⣿⣵⣾⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠛⠛⠛⠀⠀⣦⠀⠀⠸⣿⠇⢿⣿⣿⣿⣿⣿⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠥⣸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣟⣛⣤⣾⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⡻⣿⣿⣷⣆⠀⠀⠀⠘⠳⠀⡄⢿⠈⢸⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⡿⣏⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣼⣿⣿⣿⣧⡀⠀⠀⠀⢨⣿⠜⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⡿⡧⣾⣿⣿⡿⠁⢸⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣸⣷⣓⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣾⢱⣿⣿⡿⠁⠀⠘⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣻⣷⣼⣿⣿⣷⠀⠀⠀⢳⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣳⣿⣿⣿⣿⣿⣾⡆⠀⠀⢨⣿ ⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢟⣿⢯⣿⣿⣿⣿⣿⣟⠀⢀⣾⣿ ⢻⣿⣿⣿⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⣷⠾⣿⣷⣿⣿⣿⣿⣿⠀⣼⣿⣿ ⣼⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⢹⣟⣿⢿⣿⣿⣿⢗⣿⠀⣿⣿⣽ 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⠀⠀⠀⣾⣿⣶⣶⣶⣶⣶⣦⣶⣤⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣶⣶⡀⠀⠀⠀⠀⢿⡁⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢧⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠻⣿⡇⡀⠀⠀⠀⠘⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢻⠀⠐⠇ ⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⡯⣿⢿⢿⡿⡿⣿⢿⢿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⠳⠢⠁⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠈⠀⠀⠈ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣧⣿⣼⢀⣧⣧⣿⣼⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢁⢍⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⢸⡀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⣿⣿⣿⡷⣿⡿⣿⣿⣿⣥⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣬⡞⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⢐⣏⣇⣟⣱⣋⣟⣸⣿⡟⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠋⠀⠀⠀⠀⠈⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡟⡀⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠿⠿⠿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠁⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡟⢿⡿⣿⠛⣿⢿⡟⡿⣿⠋⢹⡇⠀⢸⢿⢻⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣀⣇⣽⣹⣸⣀⣏⣇⣇⣛⣸⡀⢀⡇⠀⠀⣸⣸⣇⣿⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠿⠛⠛⠈⠻⣿⣿⡿⣿⠟⣿⡟⣿⣿⣿⣿⣿⢿⡇⣿⣷⣴⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣇⠀⠀⠀⠀⠀⠀⣼⣶⣶⠄⣀⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⠈⢻⡸⣟⣤⡘⠇⣇⢥⣽⣌⣿⢀⡇⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠠⢹⣛⠻⢿⣿⣿⣍⣽⣿⣿⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⣀⠀⠀⠀⠀⠀⠙⠋⢹⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⢙⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⢨⢿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣶⡄⠉⠘⠛⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠀⠀⠀⠀⠀⠀⢸⣸⣿⢿⣿⣿⣿⢏⣶⣿⣿⣿⣿⡟⢀⠄⠀⠀⢀⣍⣛⣟ ⣿⣿⣿⠿⠟⠛⠉⢉⣿⣿⣿⣿⣿⣿⣷⣦⣶⠀⠀⠀⠀⠀⠈⠉⠩⣿⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⣤⣀⣀⣾⠿⠛⠂⠠⣴⣾⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⡀⢉⣍ ⠉⠁⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢩⠛⠻⣿⣷⣦⣤⣤⣤⣽⣿⣿⣏⣉⣉⣼⣷⣶⡇⠀⠀⠀⠀⠘⣥ ⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣵⣤⣤⣤⣴⣾⠈ ⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠁⠈⠁⣾⠿⠋⠦⠀⠀⠘⠛⠛⢛⣛⡛⢛⢿⣿⢿⣿⣿⠿⢿⡿⡇⠙⠻⢿⣿⣿⡄⣿⣿⣿⣿⣿⡆ ⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣍⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡀⠉⠉⠉⠉⠉⠅⠀⠀⠈⠁⠈⠀⠀⠉⠈⠚⠄⠀⠙⠋⠀⠈⠉⠉⠉⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠛⠛⠏⠛⠛⠻⠀⠀⠛⠿⠛⠓⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⣠⡈⠉⠶⠧⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠙⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡇⠀⠀⠀⠀⢹⣟⠛⠓⠒⠒⠒⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠻⠋⣹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣄⣀⣀⣠⣼⣿⣧⠀⢀⠀⢠⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠿⣿⣿⣿⣿⣿⡿⠙⡻⢿⣿⣿⢹⣿⣿⣿⣿⣥⣇⣸⣿⣿⣿⣿⣿⡇⠀⠸⣾⣿⠍⣹⣿⣿⣿⣿⣿⣿⣷⠦⠀⠠⠿⣾⣿⡿⠃⠈⠻⣿⣿⣿⠀⡆⢸⡇⢠⡇⢠⠀⠀⠀⣌⣿⡿⠏⠟⠻⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⣿⣷⣿⡍⣟⣿⠇⠀⠀⠈⢉⣛⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣾⡇⠚⢻⣿⣿⣿⣿⣿⣿⣿⣶⡇⠀⠿⢾⣿⡟⡀⠀⠀⠈⠙⢿⣀⡇⣼⡇⢸⡇⢸⠀⡀⠀⠀⠈⠃⠚⠀⠘⢻⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠿⣿⢹⣿⣿⣿⣆⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⡇⠐⢿⣿⣿⣿⣿⣿⣟⣿⡷⡅⠼⠻⢾⣿⡇⠃⠀⠀⡞⣿⡀⢸⡇⢿⡇⣼⡇⢸⠀⡇⢰⣦⣤⣀⡀⠀⠀⠀⠻⣿⣿⣿⣿⣿ ⠀⠀⠀⣿⣿⣿⣽⣟⡻⠇⠀⠀⠀⠀⣶⡎⡇⢹⠛⠇⢹⠛⣿⣿⣿⣿⣿⣿⡇⠀⠘⣿⡇⣵⣾⣿⣿⣿⣿⣿⣿⣷⣿⡇⠀⠿⢿⣿⡇⠀⠀⠼⠁⠸⠧⢼⡇⠀⠑⢿⡇⣿⠀⡇⢸⣿⣿⣿⣿⣄⠀⠀⠂⢏⠛⣽⣿⣿ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⡇⡇⢸⣐⡆⢸⣸⡿⢿⣿⣿⣿⣿⡇⠀⠀⣿⡇⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠈⠿⣺⣿⡗⠀⠀⢤⡔⢲⡆⢸⡇⠀⠀⠀⠙⠻⣰⡇⠸⠛⠛⠛⠻⢿⡇⣠⣥⡀⢂⠹⣿⣿ ⠀⠀⠀⣾⣿⣭⣿⣿⣿⡇⠀⠀⠀⢀⣿⣭⣥⣬⣭⣥⣼⣿⣤⣾⣿⣿⣿⣿⣧⣄⣀⠛⠅⣀⠛⠙⣻⣿⣿⣿⣿⣇⠀⠯⠐⠿⢾⣷⡦⠀⠀⠀⠗⢺⡇⢸⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⣀⠀⠉⠛⠿⣿⣄⠁⣙⢙ ⠀⠀⠀⣿⣿⣿⢻⣿⣿⡇⠀⠀⠀⢸⣿⣿⡿⠛⠛⠋⠋⠛⠛⠙⠻⣿⣿⣿⣿⣿⣏⠀⡀⠸⣸⣷⣶⣭⣟⡻⠿⣿⣿⣇⠻⠿⢿⣿⣝⠀⠀⠀⠀⠉⠉⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠿⠧⠄⠀⠀⠈⢿⣧⡈⢧ ⠀⠀⠀⣭⣭⣿⣹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⡇⠉⠀⠉⢾⣿⣿⣿⣿⣿⣿⣶⣮⣽⣟⡻⢿⡯⣗⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⣿⣿⡟⣏ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣀⣀⣤⡀⠘⠿⢿⡇⠀⠀⠲⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣋⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣿⠷⣤⣴⣆⠄⠰⣿⣿⣧⣿ ⠀⠀⠀⣻⠻⢛⣻⣿⣿⡇⢠⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠿⣿⣿⣿⣷⠀⠀⠈⠀⣂⠄⠤⡄⠈⢉⣙⡛⠿⠿⣿⣿⣿⣿⡿⡏⣛⢶⡟⡇⡂⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠂⢸⣿⠳⣒⣚⣛⣿⠃⠀⠀⠈⠻⣇⣽ ⠀⠀⠀⣼⣽⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣛⡂⠒⠀⣐⢿⠀⠀⠀⠀⠀⠀⣟⡅⠀⣿⡇⠀⠀⠉⡆⠀⠀⠈⠉⠉⠹⠥⠶⣿⠓⠀⠂⠀⠀⠀⠨⣿⣿⣷⣶⣤⣄⡀⠀⠀⠙⢻⣿⣿⡿⠗⡄⠀⠀⠀⠀⢙⣿ ⠀⠀⠀⠛⠼⢿⣿⣿⣿⠀⢤⢀⡀⠀⣴⢆⣄⠀⣿⣿⣷⣥⣤⣥⣿⣧⣼⡖⠁⠀⠀⢻⡇⠀⣿⡇⠀⠀⢸⠇⠀⠀⠀⠀⠤⠽⢏⢀⢉⠀⠀⠀⠀⠀⠀⠀⠏⠛⠛⠿⢿⣿⣿⠀⡿⢄⠀⢈⣁⣀⣼⣷⣀⣧⣠⡀⡀⢻ ⠀⠀⠀⢽⢟⣿⣶⣶⣲⢀⣞⡹⠂⠀⠈⠿⠿⢿⣿⣿⣿⣿⣿⣯⡍⢩⣿⡧⠀⠀⡆⣾⡇⣤⣿⡇⢀⡀⢸⠀⠀⠁⢰⠀⠂⠘⠗⠈⠀⠀⠀⠀⣿⣿⡧⠀⠂⠀⠀⠀⠀⠀⠀⠀⣷⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣎⣺ ⠀⠀⠀⡀⡨⠿⣿⣿⠿⢼⣷⣤⡄⠀⠀⠀⢰⡈⠻⢿⢿⣯⣭⡭⠉⠩⠉⠁⠀⠀⢧⣿⡇⠉⣽⡅⢈⠟⢸⠀⠀⡆⣿⠀⠀⠸⢿⠐⠂⠀⠀⠀⢿⣿⣷⠀⠀⢀⣤⣶⣶⣶⣿⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢂⣷⣮⣿⡇⢀⣀⠉⢹⣿⠀⠀⠀⢸⣿⣄⠀⠈⠻⠿⠷⠒⠆⠀⠀⠀⠀⢸⣯⠃⠀⣿⡿⢿⣶⠸⠚⢿⣷⣿⠀⠀⠀⠙⢈⠀⠀⠀⠀⢠⣿⡏⢀⣾⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠈⣗⣩⡡⢀⢘⠛⠀⠀⢫⠀⣀⠄⣾⣿⣿⣦⣤⣠⠀⣰⣾⣦⣄⡀⠀⣀⣈⣗⡁⠀⠛⣙⣿⣿⡀⣈⣘⡝⣿⠀⠀⠀⠀⠄⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠭⠉⠁⣄⣀⡄⠀⣶⣤⣾⣧⣶⡀⠈⠙⠻⠿⠿⠇⠀⠟⢹⣇⣿⣿⣿⣿⣿⣿⣧⡀⠀⢫⡛⠻⠇⣿⣏⠃⣿⠈⠁⠈⠀⠀⠀⠀⠀⣴⣾⣿⠿⡿⢿⣿⣿⡿⣿⣿⣿⢿⣧⠈⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢀⡄⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡘⣿⣿⣿⣿⣷⣄⠀⠇⠈⠀⣿⠟⠆⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠂⡅⢸⠲⠈⡇⡗⠂⢹⠸⠎⡄⠀⠹⢲⠈⡃⡆⢸⢸⡞⠳⢹⣿ ⠀⠀⠀⡅⢩⣾⣿⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⡀⣸⡟⣿⣿⣿⡷⣹⣿⣿⡿⣿⣿⢷⡄⠀⠀⠻⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⢿⡷⣯⠐⠉⣿⣿⣿⣿⣿⣿⣄⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠁⣸⣿⣿⣧⡙⢧⠙⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣷⣿⣿⣿⣾⣟⣹⠋⠁⣿⣿⡟⠉⠀⠀⣿⡁⠄⡏⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⠿⠁⠉⠀⠀⠀⠘⢩⣹⡍⢩⡇⢻⣿⣦⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣿⣟⣿⡿⠿⣦⣅⡀⠀⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣭⠀⠀⣹⣿⣷⣀⣀⠀⠹⠧⠂⠇⠀⣠⣶⣿⣿⣿⣿⣿⠿⠃⠁⠀⠀⠀⠀⠀⢸⣦⣾⣾⣶⣵⣿⣿⣿⣷⡀⠈⠿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢿⡛⠧⡙⠢⠉⠈⠁⠀⠀⣺⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⢫⣿⣿⣏⠉⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⡿⠛⣡⣾⣿⡀⠀⠀⠀⠀⠀⠸⠛⡛⡟⠟⠟⣷⢸⢻⠻⡛⣆⡀⠈⠻⣿⣿⣿⣿ ⠀⠀⠀⢀⣈⠻⢶⣬⠀⠄⠀⠀⠀⠀⠁⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⠟⣋⣴⡊⠀⠀⠀⠀⢼⣿⣿⣿⣆⠀⢀⣴⠿⠛⠻⠿⠟⢋⣡⣶⣟⣿⣿⣿⠀⠀⠀⠀⠀⢀⡀⣤⣷⣼⣧⣭⣯⣼⣬⣽⣳⣼⣿⣦⣀⠀⠻⣿⣿ ⠀⠀⠀⠉⢠⣤⣤⣤⣶⠟⠉⠐⠀⠀⠀⠀⠠⢊⣵⣿⣿⣿⣿⠋⠥⠏⠻⠓⠂⠀⠀⠀⠀⢸⡿⢿⣛⣋⣺⠋⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⣀⡤⠖⠋⠁⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠈⠻ ⠀⠀⠀⠀⠈⣝⣉⣷⣶⣿⣿⣵⣦⣄⡀⢀⣤⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠶⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⣈⠉⠁⠋⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀ ⠀⠀⠀⠀⠀⣹⣯⣿⣿⣭⡽⣿⢿⣫⣷⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⣀⣼⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⠀⠀⣷⣶⠻⠷⢒⣴⣾⣿⣿⣿⣿⡿⢟⣿⡿⢁⣴⣾⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢸⡏⠀⢰⣿⣿⣿⠟⢋⠀⢉⣴⣿⠟⠠⠿⠛⢛⣿⣿⣿⣿⠿⠟⠿⠛⠛⠉⠁⠀⠀⠔⠛⠁⠀⠀⠀⠀⠀⠀⢀⣰⡇⠀⠀⠀⠿⠷⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠈⡀⠀⠈⣹⢏⣁⡔⣁⡴⠟⠟⠁⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢳⣶⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⠿⠛ ⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠋⠰⠛⠿⠓⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠉⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠂⠁⠀⣁⣠⠄⠂⠈⠃⠉⢩⠁⡄⠄⡄⠉⠙⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⢿⢿⢽⢿⢿⡿⡏⣿⢿⢿⡿⡿⡿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣸⣿⣸⣟⣸⣜⣶⣆⣃⣻⣸⣀⣇⣯⣲⣸⣘⣃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣗⣽⣏⣺⣯⣿⣯⣾⣯⣿⣯⣯⣻⣏⣿⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣛⣼⣿⡾⣿⣿⣿⣿⣤⣵⣿⣽⣿⣿⣬⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ䷩ 𝚕𝚒𝚗𝚎 1870 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2021/12/21/irc-log-201221/#comments Gemini version at gemini://gemini.techrights.org/2021/12/21/irc-log-201221/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.21.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ IRC_Proceedings:_Monday,_December_20,_2021⠀✐ Posted in IRC_Logs at 2:55 am by Needs Sunlight Also available via the Gemini protocol at: * gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-201221.gmi * gemini://gemini.techrights.org/irc-gmi/irc-log-201221.gmi * gemini://gemini.techrights.org/irc-gmi/irc-log-social-201221.gmi * gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-201221.gmi Over HTTP: 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇HTML5_logs⦈_ #techrights_log_as_HTML5 #boycottnovell_log_as_HTML5 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇HTML5_logs⦈_ #boycottnovell-social_log_as_HTML5 #techbytes_log_as_HTML5 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇t 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇text_logs⦈_ #techrights_log_as_text #boycottnovell_log_as_text 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇t 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇text_logs⦈_ #boycottnovell-social_log_as_text #techbytes_log_as_text Enter_the_IRC_channels_now =============================================================================== § IPFS Mirrors⠀➾ CID Description Object type IRC log for  QmShAR7utG3EqWKeKzKkLhfkSrPT4invJs9uBRg8yd19eL #boycottnovell 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #boycottnovell  QmNrCjrYz8xJeuZcqZrsoHBqfEM5LXLdt7RQFLdTsPgmS8 (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ as plain/ASCII text) IRC log for #boycottnovell-  QmY5dCyNJnxLBHHivXpSj1uAFTMoptWqwEoUcnW9624R92 social 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #boycottnovell-  QmbtY89tKBiEzJVsP6yCbRyjkGLqFxgactcnBCqadWUNHy social 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ (full IRC log as plain/ASCII text) IRC log for  QmRt7auYUBJEUHDNja23yG52TkKp4C1fFqRAWvHJu8LAtJ #techbytes 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #techbytes  QmVci9BxpEFh7B7zJy19qk5azUZUDq4rS2anf49nCDknra (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ as plain/ASCII text) IRC log for  QmT7ACW3u8TFiCGEoR3PgrBKqR1r3cBhVhCvJJMPq6CxDu #techrights 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #techrights  Qme8uC65qJYqxiGTzAciVQxB3NfLfQ1ykr5pDDNVzmjnHF (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ as plain/ASCII text) 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈ § Bulletin for Yesterday⠀➾ Local_copy | CID (IPFS): QmZP4LnsTHrznHVdokybFZafDLWJqRPKyvvberG4dVRasQ ䷩ 𝚕𝚒𝚗𝚎 1997 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2021/12/21/smbc-comics-ip/#comments Gemini version at gemini://gemini.techrights.org/2021/12/21/smbc-comics-ip/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.21.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Saturday_Morning_Breakfast_Cereal_on_‘Intellectual_Property’⠀✐ Posted in Intellectual_Monopoly at 12:35 pm by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Saturday_Morning_Breakfast_Cereal_on_'Intellectual Property'⦈_ Source (from today): Saturday_Morning_Breakfast_Cereal_–_Fire ⡏⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⣭⣭⠭⡭⠭⠭⡭⢭⡭⣭⠭⡭⠭⡭⡭⢭⡭⣭⣭⡭⡭⣭⣭⣭⣭⣭⡭⡭⠭⢭⡭⠭⠭⢭⡭⢭⡭⣭⢩⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⡤⠠⠄⣀⣤⡄⢠⢭⣭⣭⣭⣭⣉⢹ ⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠻⣗⣩⣏⣗⣫⣭⣯⣾⣗⣩⣏⣇⣫⣩⣷⣾⣿⣦⣽⣺⣾⣳⣬⣬⣼⣭⣀⣳⣿⣩⣯⣩⣳⣚⣽⠾⠿⠶⠦⢭⣙⡛⠿⢿⣿⣿⣿⣿⣿⣿⣧⢴⢹⠗⠟⠃⠈⣾⣿⣿⣿⣿⣿⢸ ⠀⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿⣿⣷⣶⣭⣭⣭⣭⣭⣭⣭⣭⠍⠉⠉⠉⠉⠉⠉⠉⠉⠉⢭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣶⣶⣾⣿⣿⣷⣶⣶⣶⣤⣤⣤⣉⣙⣛⠿⣿⣿⠀⠀⠂⠐⠀⢀⢄⣮⣍⣛⠿⣿⢸ ⡄⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⣶⣤⣀⣀⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣅⣀⢀⠀⣠⣾⢸⣟⣛⠿⠿⢶⢸ ⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣴⣶⣶⣶⣖⣿⡄⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⡙⢿⡿⠿⢟⣛⣫⣵⣾⡿⢻⣿⡿⣳⣿⣿⣎⣛⡬⣿⣿⣷⢸ ⡇⣿⣿⣟⢿⣿⣿⣿⢇⣟⣧⠿⠿⠿⠿⠿⠿⠿⣿⣿⣇⠀⠀⢱⣿⢹⣿⠿⠿⠇⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡲⠟⣿⣋⣩⣭⣭⣭⣴⣶⣾⡞⣿⣣⣿⣿⣿⣿⣿⡇⠀⠀⠉⢸ ⡇⠉⠉⠁⠀⠀⠀⣰⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⡄⠈⠉⠘⠁⠀⠀⠀⢠⣶⣦⣶⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠉⠉⠁⠀⢡⡿⡿⣱⣿⣿⣿⣿⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣇⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣇⠈⠉⠉⠛⠛⠿⠿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⣱⣿⣿⣿⣿⣿⠂⠀⠀⢸ ⠃⠀⠀⠀⠀⡆⠈⢿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣄⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⡛⣽⠀⠀⠀⢸ ⠀⠀⠀⢰⣴⡇⠀⢸⣿⣿⣿⣿⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣻⣿⢿⢒⢚⡿⣿⣿⣿⣿⣷⢻⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⠟⠹⠋⠀⠀⠀⢸ ⠀⠀⠀⠘⣿⣿⣶⣿⣿⣿⣿⣿⣶⡌⢰⣿⢩⣶⣄⠀⢀⣀⣿⢩⣴⡱⡩⣊⣾⣿⠿⢝⣪⣬⣭⣽⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣩⣶⠗⢼⣆⠀⠀⠀⠀⢸ ⠀⠀⣤⣴⣿⣿⡿⢿⢷⡻⣿⣿⣿⠇⠀⠀⡑⠐⠛⠻⢿⣿⣿⢼⠿⠋⠥⣽⣟⣿⣿⠿⢿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠙⠃⠀⠀⠀⢸ ⠀⢸⣿⣿⣿⡟⣼⣿⣾⡇⣿⡿⠁⠀⢠⣶⡇⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠠⣐⣶⣶⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠈⢻⣿⣿⣿⠌⣿⣿⣧⣿⣧⣀⣠⣿⠋⠾⣿⣿⣿⣶⣍⠳⣄⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⣿⣿⣝⣿⣝⢿⣿⣿⢿⠟⣿⡿⠟⠀⠀⠈⠛⠿⣿⣿⠇⠉⠀⠀⠐⣿⣿⣿⡿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠉⠋⠻⠟⠫⣻⡯⠿⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸ ⡟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⣛⣛⣛⣛⣛⣛⣛⢻⣿⢩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣉⣉⣉⣉⣉⣉⣙⣛⣛⡛⣛⣛⢻ ⡇⣯⣲⣽⣢⡷⢾⣟⣛⣯⣧⣿⣩⣝⢳⣸⡲⣟⢿⢿⡷⢾⡶⣷⣺⡿⣉⣹⣻⣿⡇⣿⣿⣿⣿⣿⣿⣿⢸⡇⢸⣮⣞⣷⣿⣻⣧⣝⣗⣗⣿⣽⣻⣿⣯⣿⣮⣿⣻⣯⣟⣾⣤⣽⣷⣽⣏⣿⣷⣵⣻⣾⣟⣿⡇⡿⠿⢸ ⡇⣯⣏⡿⣛⣭⡯⣽⢝⡏⢯⣭⣯⣛⣿⢫⣽⣿⣿⣹⡙⡿⢻⣿⣻⣿⣿⣿⣿⠟⣱⣿⣿⣿⣿⣿⣿⣿⢸⡇⣸⢙⢿⢽⢽⣏⡻⣯⣏⡻⢿⣻⡿⣿⢗⡯⡯⣻⢏⣻⣿⣯⣫⢿⢉⣯⣿⢫⢏⠻⣻⣿⣿⣿⡇⣶⣿⢸ ⡇⣛⣛⡻⠿⣿⣿⡿⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠿⠿⠟⣛⣫⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⣿⠫⢽⢯⢭⣭⠯⢯⣿⣟⣽⣫⢛⠿⣝⣽⢫⡝⢍⡿⣭⡿⡯⠿⣽⡿⢯⠿⢭⢯⣭⣟⣽⣿⢇⣿⣿⢸ ⡇⣿⣿⣿⣿⡜⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⠿⠶⠿⠾⠶⠶⠿⢶⣿⣷⣾⣶⣿⣾⣷⣾⣶⣿⣿⣿⣿⣷⣾⣾⣿⣷⣿⣿⣾⣶⣾⠿⠟⣫⣾⣿⣿⢸ ⡇⣿⣿⣿⣿⣿⡜⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠲⠦⡙⣿⣿⡀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⣾⣿⣿⣿⣿⣿⢸ ⡇⣿⣿⣿⣿⣿⣿⣌⠌⣿⣿⣿⣿⣿⣿⡿⣛⣭⣭⣶⣾⣭⣭⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠋⠙⣿⣿⣿⣿⢸ ⡇⣿⣿⣿⣿⣿⣿⣿⣦⠸⣿⣿⣿⣿⢫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠈⠉⠛⠻⠿⢿⣿⠋⠀⢰⣷⣼⣿⣿⣿⠈ ⡇⣿⣿⣿⣿⣿⣿⣿⣿⣷⣹⣿⡿⠟⠚⠛⠿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠊⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢿⣿⣿⣿⣿⠀ ⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⣿⣶⣦⣄⡉⠛⠛⠋⣁⣤⠶⢾⡆⡾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⡇⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣼⣿⣿⣿⣿⠀ ⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣶⠆⣿⣧⣼⣿⣿⣿⣼⣿⣿⣿⣲⣾⣧⠸⡇⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⡇⣷⠀⡄⠀⠀⠀⠀⢈⢽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣭⣿⠿⠁⠀⢸ ⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⠀⠘⠛⠟⠛⠻⣿⣿⡟⠉⠉⠉⠉⠛⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⢸⣾⠁⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⠀⠀⠀⢸ ⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢽⡿⢿⠿⠿⠿⣿⣿⣿⡇⢸⡇⢰⣻⡆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠛⠋⢀⣠⡤⠄⠀⢸ ⡇⣿⣿⣿⣿⣿⣿⢋⣵⣶⣶⣶⠆⠀⠀⠀⠀⠉⠉⠉⠓⠒⠒⠒⠂⠀⠀⠀⠈⣾⣶⣿⣷⡇⢜⡻⣿⡇⢸⡇⢸⠻⠷⠀⣀⠀⢠⣾⣿⣿⣧⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠉⠀⠀⠀⢸ ⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⡟⣿⢸⣿⣮⡃⣸⡇⠰⠛⠁⠘⣿⡀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⣿⣿⣿⣿⡿⢳⣿⣿⢏⣬⢻⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣜⢧⢹⣿⡇⣿⡇⠀⠀⠀⠀⠘⣽⣿⢏⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⣿⣿⣿⢋⣴⣿⣿⡿⢸⡟⡼⢟⣫⡵⢞⠋⣁⣀⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣟⣿⣟⠜⢰⣿⡃⣿⡇⠀⠀⠀⣀⣠⠈⠁⠈⠙⠛⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⣿⡿⣣⣾⣿⣿⡟⣵⣿⣷⣾⣿⣯⡤⠶⡛⠭⣁⡀⠀⠀⠀⣄⣠⣴⣿⣿⣿⣿⣿⣿⢿⣿⢸⢠⣿⡇⣿⣇⠀⠀⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠿⠡⠿⠿⠿⠿⠷⠝⠿⠿⠿⠿⠿⠷⠶⠋⠭⠢⠾⠢⠶⠿⠿⠿⠿⠿⠿⠵⠿⠿⠟⠾⠿⠾⠜⠿⠇⢻⣿⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠛⠛⠛⠛⠛⣛⣛⣛⣛⣛⣓⣒⣒⡒⠒⠒⠒⠒⠒⠒⠒⠶⠶⠶⠒⠒⠒⠒⠒⠒⠒⠒⠛⠛⠛⠛⠿⢿⣿⠛⠛⠛⠛⠛⠛⠛⠛⢛⣛⣛⣛⣛⣛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻ ⡇⡿⢝⢿⡿⣟⣻⢿⣿⢿⣻⣯⣿⡿⣿⣿⣝⡿⣿⣏⣏⡹⣟⣯⣿⣻⣛⡿⢫⣏⣯⣋⣿⢹⠏⡻⣹⣿⢸⣿⢸⢛⢯⣟⢿⣏⣟⡯⡯⣿⣏⡯⡏⣿⣙⢿⣿⣿⢋⡻⣿⢿⣻⣿⢟⢋⡿⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⣟⢿⣿⡿⡟⣿⣟⡟⣟⣿⣿⣿⣿⢿⡻⣿⣿⡟⣿⠛⡿⢿⢻⣿⡟⢿⣻⠿⣿⣿⡿⣿⡿⠿⣻⢻⣿⢸⣿⢸⡿⢿⣿⣿⣽⡿⢿⡿⠯⡛⣯⣽⡿⣟⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⣟⣳⡷⣳⡟⡻⣿⣷⢾⣿⢿⣷⢿⣾⡿⣷⢾⣷⢿⠿⣶⡷⣾⣿⣿⣷⣿⣷⣿⣶⣿⣿⣾⣶⣿⣿⣿⢸⣿⠸⠾⣿⣶⣿⣿⣿⣷⣾⣾⣷⣿⣿⣿⣿⣿⠿⠟⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⣷⣾⡯⣽⢷⠧⡮⢽⠷⢽⣿⠧⣾⣷⠿⣿⣮⣽⣷⣽⠽⣿⡿⣿⠿⡿⢿⡿⣿⢿⣿⣿⡿⡿⢿⣿⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠉⠙⠛⠿⣿⣻⢷⣦⡀⠀⠀⠀⠀⢸ ⡇⣧⣼⣛⣟⣻⣛⣏⣷⣧⣧⣼⣉⣯⣻⣛⣿⣟⣝⣿⣽⣛⣷⣕⣿⣹⣮⣵⣟⣻⣻⣟⣻⣛⣟⣻⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⠀⠀⠀⠀⠀⢀⣾⡇⣴⣿⣿⣿⣶⣄⡀⠉⠛⠛⢉⡀⠀⠀⠀⢸ ⡇⣗⣾⡳⣿⡶⣿⣆⣏⣾⣄⢾⣿⣲⣷⢾⡷⣛⢏⣻⣖⣷⢾⣇⣺⡷⣁⣢⣿⣿⣿⣿⣿⡿⠿⢛⣡⡆⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⡿⠄⠀⠀⢸ ⡇⣿⡿⢫⣽⣽⣿⣝⣯⣹⣝⣹⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⢛⣋⣩⣤⣶⣾⣿⣿⡇⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣧⣠⣿⣿⣿⣿⣿⡟⣿⣧⣤⠀⠀⢸ ⡇⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠛⠛⠛⠛⣛⣛⣛⣋⣉⣭⠹⣿⠏⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⠀⠀⢹⣿⣿⣽⣿⣿⣿⣿⣿⣿⣜⢿⣿⡇⠀⢸ ⡇⠀⠀⠀⣤⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡇⡏⣸⣿⣿⣿⣿⣿⡿⣋⣭⣬⣍⠻⣿⣿⡇⣿⡇⠀⠀⠺⢛⣩⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠯⠻⣇⠀⠀⢹⠿⠿⠿⠛⠛⠻⢿⣿⣿⣎⠿⢿⠀⢸ ⡇⣀⣀⣴⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠁⣴⣿⣿⣿⣿⡿⠏⠾⣿⡿⠟⠛⢇⠛⣿⡇⣿⣿⠀⣽⢫⣿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣽⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⡉⠛⠛⠂⠀⠀⢸ ⡇⣿⣿⣛⣛⣽⠟⢉⣡⣬⣱⣤⠀⠀⠀⠀⠀⢹⣿⣿⢃⣾⣿⣿⣿⣿⣿⣷⠔⣶⣤⣴⣾⣙⠋⠔⣸⡇⣿⣿⠀⠁⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⠿⠗⠀⠀⠀⠀⢸ ⡇⣤⣈⡉⠁⢀⣰⣿⡟⢻⣿⣿⡄⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⡟⠸⠿⢹⠿⠛⠛⠁⢰⣿⡇⣿⣿⢀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠂⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⣉⣿⡟⣵⣿⣿⣿⣿⣛⣻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠿⢛⡃⠀⠀⠀⠀⠀⠀⠀⣨⣭⡅⣿⣿⢸⣦⣄⠀⠀⢀⣴⣿⠿⠟⣛⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⣿⡟⣼⣿⣿⢿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢡⣾⣿⣷⠀⠀⠀⠀⠀⢀⣠⣿⢯⡇⣿⣿⢸⣿⣿⣿⣿⠟⣡⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠙⠁⠿⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⡿⣿⣿⣷⣶⢢⣶⣶⣾⡿⣋⣭⡃⣿⣿⢸⣿⣿⣿⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣄⠀⠀⠀⡀⠀⢀⠀⢀⣴⢸ ⡇⠀⠀⠀⠀⢠⣤⠶⠶⠒⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣋⠋⣼⣧⣿⣿⡟⣡⣾⡿⣃⣿⠜⣵⢟⡇⣿⣿⠸⢛⣩⣥⣾⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣴⣿⣿⣿⣶⢻⣼⣿⣿⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠤⣀⣤⣴⣶⣾⣿⣿⣧⢲⣶⣶⣶⣦⣍⠻⣿⣿⣿⣿⢤⣉⡂⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣫⣴⣿⢟⣷⣿⣿⣿⣿⣿⡿⣧⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣟⣻⣭⣷⣾⣿⣿⣧⢻⣿⣿⣿⣿⣷⡘⣿⣿⣫⣾⣿⠁⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣋⣴⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣯⣾⣿⢸ ⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⣉⣉⣉⣉⣈⣉⣉⣉⣉⣉⣁⣉⣉⣉⣉⣁⣥⣿⣿⣬⣭⣭⣭⣭⣭⣭⣭⣭⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣼ ⡇⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡭⣭⣭⡭⢭⠭⡭⢭⡭⣭⣭⡭⢭⣭⢭⠭⣭⢭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣬⣥⢈ ⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣌⣃⣣⣈⣠⣉⣌⣫⣛⣠⣓⣌⣳⣮⣸⣾⣜⣫⣼⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⡿⣿⣿⢿⣿⣿⠀ ⡇⡶⡒⢖⣶⣒⣶⡲⢒⠒⣲⣶⢖⣲⣲⢶⣶⣖⣲⡒⣶⣖⡶⡒⣶⠶⡖⣒⣒⣲⣖⣒⣒⡶⣶⣖⣶⢶⠶⣲⣶⡆⣶⣶⣶⣶⣶⣶⣶⡆⣶⣶⣶⣲⢶⡒⣶⣿⣿⡻⡛⣟⢻⣿⡛⣖⢲⣲⣒⣖⠒⡖⢲⡖⢲⣶⣶⠀ ⡇⣿⢾⡯⢿⣭⢿⡵⣶⣷⣵⣿⡯⡴⣶⡷⣿⣷⣿⢾⡿⣯⣷⠾⡿⣶⣷⣾⢿⡿⣧⡴⣮⡷⢽⠯⣿⣷⣴⣥⣿⢃⣟⣵⣿⢟⣼⣿⣿⡇⣿⣿⣿⣷⢿⡮⣿⣷⣾⣿⣷⢷⣽⣿⡷⣷⣽⣶⣷⣾⡶⣵⢿⣷⣽⣿⣿⠀ ⡇⣿⣿⣼⣿⣿⣿⣟⣿⣵⣯⣾⣯⣮⣿⣿⣾⣿⣿⣶⣟⣯⣽⣧⣯⣿⣿⣿⣷⣟⣿⣿⣻⣼⣿⣻⣿⣿⡿⠟⣡⣾⡿⣹⣣⣾⣿⣿⡿⣣⡙⢿⣿⣿⣿⣥⣾⣾⣽⣿⣼⣵⣽⣿⣯⣾⣾⣿⣷⣯⣿⣿⣽⣾⣿⣿⣿⠀ ⡇⣶⢲⡶⣰⢆⣶⢆⣶⢠⣶⣶⡶⣠⣤⣤⣤⣤⡭⣩⣭⢹⣿⡿⢩⣭⣭⣭⣭⣭⣭⠍⣭⣭⣥⣤⠄⣴⣶⣿⣿⣿⣷⣿⣿⣿⣿⣯⣾⡿⣿⣶⣦⣬⣭⣭⣭⣭⣭⣭⣭⡭⣩⣭⣍⢻⣿⢫⣭⣭⣭⣭⣥⣤⣶⣶⣶⠀ ⡇⣿⣿⣱⣟⣾⣧⣾⢧⡿⣿⣏⣼⣿⣿⢏⣿⣿⢣⣿⡇⣼⡟⢡⣾⣿⣿⢏⣾⣿⢏⣾⣿⣿⡿⣡⣾⣿⣿⡟⣿⣿⣿⢟⡽⢫⣾⣿⢏⣾⣿⣿⣿⣯⡿⣿⣵⣿⣿⣿⣿⣿⣿⢻⣿⠸⢃⣾⣿⣿⣿⣿⣻⣿⣿⣿⣿⠀ ⡇⣿⢱⡟⣽⣏⣾⣤⡿⢙⣫⣬⡛⣿⣟⣾⣿⣧⣿⣿⢃⡟⢠⣿⢟⣿⢏⣾⡿⣿⣿⣿⢿⣿⣾⣿⣿⣿⢟⣼⣿⣿⣫⢞⣴⣿⡿⣣⣿⣿⢟⣿⡿⠟⣛⡛⠿⣿⣿⣿⣾⣿⣳⣿⠏⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⡇⣧⠿⣿⢋⣥⣵⣶⣾⡿⢿⠉⠀⢸⣿⣿⢋⣿⣿⡟⠈⢤⣿⣏⡾⣿⣿⢯⡾⢫⡾⣡⣿⣿⣿⣿⣿⢫⣾⡿⣿⡿⣵⣿⣿⣿⣿⣿⡿⣣⡾⣫⣶⣿⣿⣿⣿⣎⠛⢿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣵⣿⠀ ⡇⡿⣰⢣⣿⡿⠻⠋⠙⠁⠀⠀⢨⡜⣿⣿⣞⣼⣿⣧⢢⡿⣹⣿⢱⣿⣷⡟⣵⣿⣾⣿⣿⣿⣿⡿⣵⣿⡟⣵⣿⡿⣽⣿⢻⣿⣿⣿⣿⡏⣬⡙⠛⣋⣩⣭⡹⠛⣀⠈⠻⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⢏⣾⣿⣿⠀ ⡇⠧⠁⠟⠉⠀⠀⠀⠀⠀⠀⠀⣘⣠⢾⣿⢏⣿⣿⡿⣾⣵⣿⢣⣿⣿⡿⣾⣿⢟⣿⣿⣿⣿⢏⣼⣿⣟⣼⣧⣟⣼⣿⢣⣿⣿⡏⣿⣿⢱⣭⣿⣹⣿⣿⣽⡇⠐⠝⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀ ⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡌⢋⣾⣿⣿⣱⡿⣹⢧⣿⣿⡟⣼⣿⢏⣼⣿⢟⣿⣿⣿⣿⣟⢼⣿⢏⣿⣻⢇⣿⣿⣟⣼⣿⠟⠸⠿⣳⠿⠟⠛⠛⠃⠀⢀⣠⣾⣿⣿⣿⣧⣿⣿⣿⣿⣿⢿⣼⣿⣿⣿⣿⣿⠀ ⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⠘⣿⡿⢏⡿⢡⡟⣿⣿⣿⣿⣿⢏⣾⡿⣡⣿⣿⣿⣿⣿⢊⣾⣿⡾⣱⡟⣾⣿⣿⣿⣿⡿⠀⠀⠀⠀⠴⠶⠂⠀⠀⠀⢹⡿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⡇⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣛⣴⡿⣱⠾⠣⠿⠣⠿⠿⠿⢿⢏⣿⣿⣾⣿⢿⣿⣿⠿⣣⣿⡿⡱⣱⣿⢿⣿⣿⣾⡿⠟⡃⠀⠀⠀⠀⠀⠈⠳⠆⠀⠀⣶⠾⡶⣢⣉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⠀ ⡇⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠹⡙⣶⣊⣋⢟⠿⡻⡿⢻⡿⢸⢿⣿⣿⢋⣾⣿⣣⣾⠟⣜⣴⣿⡿⢣⣿⣿⣿⢏⣴⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣷⡿⣸⣿⣿⣿⣦⣝⠯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⡇⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⢾⣟⡽⢻⣛⣾⣿⣃⡾⠜⢈⣾⡿⣱⣿⣿⣿⡿⣑⠼⣿⢫⣿⣣⣿⣿⣿⣏⣾⣿⣿⣿⣿⡿⣓⣤⣶⣤⣶⣶⣿⣿⣿⣟⣼⣿⣿⣿⣿⣿⠧⢿⣿⣿⣿⣿⣧⣿⣿⣿⣿⠀ ⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣷⣩⣿⣯⣏⣈⢶⠿⢞⣤⠊⣸⡟⣿⣿⢿⣿⣿⠇⣿⡿⢶⣍⠙⣿⣿⣿⢟⣵⣿⡇⣿⡿⣋⡾⣿⣿⣿⣿⡿⣇⣿⡟⣿⢫⣿⣿⡿⣛⣭⠶⣿⣆⢝⢿⣿⣿⣿⣿⣿⣿⣿⠀ ⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠧⠻⠿⠿⠟⠸⠿⠿⠿⠠⠿⠴⠿⠷⠿⠿⠹⠇⠿⠟⠳⠮⠙⠼⠿⠱⠿⠿⠿⠱⠟⠽⠷⠿⠿⠿⠿⠿⠿⠿⠿⠵⠿⠸⠿⠿⠏⠰⠖⠫⠽⠿⠦⠣⠹⠿⠿⠿⠷⠿⠿⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ䷩ 𝚕𝚒𝚗𝚎 2101 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2021/12/21/team-mono-gone-into-hiding/#comments Gemini version at gemini://gemini.techrights.org/2021/12/21/team-mono-gone-into-hiding/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.21.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Team_Mono_is_on_the_Run⠀✐ Posted in Microsoft at 11:21 am by Dr. Roy Schestowitz Video_download_link | md5sum 5b7264e232fbbcc90d91dc1c70064131 http://techrights.org/videos/github--evasion.webm Summary: The so-called ‘Team Mono‘ — a collective of Microsoft operatives who use .NET as their Trojan horse inside GNU/Linux — has gone into hiding, but it might be too late for them… THE above video was recorded while I was extremely tired and I forgot to turn on noise removal, so the quality of audio is relatively poor (mostly background noise). Nevertheless, the video goes through the latest ‘evidence tampering’ by the Friedmans, who knew very well about the bad behaviour (including sick kinks and fetishes) of a GitHub manager, a longtime family friend who went too far by once again suffocating a woman, repeatedly too. Can’t help himself, can he? Those horrific kinks and fetishes will be covered later in the series, but the key point is, the Friedmans and Miguel_de_Icaza knew all about these problems but chose to look the other way, even in recent years. Not too long before the arrest, Nat Friedman said that his longtime buddy had changed, in effect enabling his buddy to find more victims, whom he nearly killed. Friedman and he coordinated their attack on copyleft (by misusing “fair use” — using “hey hi” (AI) hype as a workaround against copyright law) and even arranged for him a high-salary job at Microsoft. Is Microsoft still protecting him [1, 2]? Hard to tell, but this month he deleted his Microsoft LinkedIn and his Twitter accounts. Friedman deleted his Flickr account after more than 15 years, as we noted_last_night. These people are hiding. █ ䷩ 𝚕𝚒𝚗𝚎 2151 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2021/12/21/the-microsoft-shuffle-making-ones-own-products-intentionally-defective/#comments Gemini version at gemini://gemini.techrights.org/2021/12/21/the-microsoft-shuffle-making-ones-own-products-intentionally-defective/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.21.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ The_Microsoft_Shuffle:_Making_One’s_Own_Products_Intentionally_Defective⠀✐ Posted in Deception, Microsoft at 8:59 pm by Guest Editorial Team Original_by_Mitchel_Lewis_at_HackerNoon/Medium, resposted here due to reported suppression attempts; reprinted with permission 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Microsoft guns⦈ In my previous_post, I covered how Microsoft and their partners have a vested interest in keeping their products artificially defective and complex. But I didn’t get a chance to dive as far as I would have liked into how Microsoft could go about intentionally keeping their solutions artificially defective or the negative impact that these methods seem to have elsewhere within their company. Without involving employees though, there are only a few ways that a company can intentionally create defective products without making it look intentional. Obviously, its not as simple as their employees dropping random 💩 emojis into their code at night. “In fact, as a former Microsoft employee myself, I can confirm that no one in this world hates defects and unnecessary complexity more than Microsoft employees and that great efforts are made to address such problems there. But, while the quality of an IT solution can absolutely reflect the quality and dedication of the engineers that made it, the quality of the environments where these solutions are produced are of equal importance and are reflected in the product just the same.”Certainly, Microsoft could just as well be ignorant and inept with regard to quality software engineering best practices and just accidentally make $89 billion dollars per year. They could also just be dated, as this business model was much more justifiable in the 80’s and 90’s when they had no real competition and the productivity boost that their products offered at the time was unparalleled. Without an intricate understanding of quality engineering though, Microsoft, as a premier software development firm throughout the world, could not get to the level that they are presently at nor could they capitalize on such a dynamic that benefits off of artificially defective products to the degree that they do. It goes without saying, but Microsoft doesn’t actually instruct their employees to create defective software. In fact, as a former Microsoft employee myself, I can confirm that no one in this world hates defects and unnecessary complexity more than Microsoft employees and that great efforts are made to address such problems there. But, while the quality of an IT solution can absolutely reflect the quality and dedication of the engineers that made it, the quality of the environments where these solutions are produced are of equal importance and are reflected in the product just the same. Along with hiring top talent, tech companies, as with others, can nurture their desired end result by adjusting their environment accordingly. This happens to be why modern technology companies tend to spend a significant amount of revenue tuning their work environment with extravagant office perks and progressive management practices. “By reducing vendor headcount, they can increase workload of their employees at scale while reducing morale which can increase the probability of defects occurring within their products in turn.”Regardless of how passionate and dedicated they may be, Microsoft employees, unlike Sr. leadership, have little to no influence on environmental variables such as headcount, workload, schedules, resources, morale, management, standards, or ideologies being leveraged; all of which influence the overall quality of their products. As such and just as companies can streamline their environment with this understanding in order to maximize quality, Microsoft can easily apply the same same logic inversely and make subtle changes to the aforementioned environmental variables in order to stifle quality. In doing this and almost as if they can turn a dial, Microsoft leadership can modulate the morale of employees at scale, increasing the tendency for them to be less motivated, more apathetic, less productive, and more error-prone without ever having to tell them to do anything but to do their best; all by simply making subtle changes to their environment. For instance and since they depend heavily on vendors, which are almost as numerous as their full-time employees, leadership can easily modulate stress and pressure on their teams by increasing or reducing vendor headcount indiscriminately. It doesn’t matter how great of an employee they are, as people are worked harder and stretched thinner, they tend to cut corners in order to meet deadlines and among other things, they generally become more error-prone. By reducing vendor headcount, they can increase workload of their employees at scale while reducing morale which can increase the probability of defects occurring within their products in turn. “…while employee layoffs always seem to make the news, Microsoft’s vendor attrition seldom generates any buzz and they can modulate pressure on remaining employees and vendors with impunity.”On top of modulating the pressure on their employees with variable vendor resources, Microsoft can also limit the quality of their products to various degrees by limiting the quality of their environment elsewhere. Besides simply laying off a ton of QAs and SDETs, they can also leverage antiquated leadership that often come attached with antiquated organizational and managerial practices. This kind of leadership often results in frequent re-orgs, tenurocracy, thick management structures, change resistance, complex roles, and a rat race for a review system. When combined with adjusting their vendor headcount and lowering the bar with leadership, such practices can have a significant negative impact on productivity and morale which again can have a limiting effect in the overall quality of their products that they just would not have otherwise. In comparison to having their employees complicit in the sabotage of their products, operating like this can be beneficial for several reasons. For starters, it would be impossible to keep a lid on such a foul if their employees were complicit in it. Conveniently though, making environmental changes in order to make your products artificially defective can be incredibly difficult to correlate, which also distances them from complicity in the matter from a legal perspective. Since so few people are well-versed on the subject of defect density, finding someone with a deep enough understanding of it in order to make such correlations can be quite challenging while also making a plea of ignorance to the subject incredibly easy, believable, and convenient; even for a software engineer. Also, while employee layoffs always seem to make the news, Microsoft’s vendor attrition seldom generates any buzz and they can modulate pressure on remaining employees and vendors with impunity. However, there are drawbacks inherent to operating like this. “The Playstation 4 has outsold Xbox One 2:1, Windows Phone was a complete bust along with their Nokia acquisition, they’re having trouble giving away Windows 10 for free, their health band lasted three minutes, Consumer Reports recently pulled their recommendation for the Surface line of products, Groove is going away, and no one seems to give a damn about their soon to be released Invoke speaker.”One unfortunate consequence of Microsoft optimizing their organization in order to make products that are more prone to defects is that doing so also makes their products less competitive in markets where innovation and quality take precedence over the influence of their partners, such as retail markets. To no surprise and presumably for this reason, Microsoft has been experiencing difficulty in reaching retail consumers. The Playstation 4 has outsold Xbox One 2:1, Windows Phone was a complete bust along with their Nokia acquisition, they’re having trouble giving away Windows 10 for free, their health band lasted three minutes, Consumer Reports recently pulled their recommendation for the Surface line of products, Groove is going_away, and no one seems to give a damn about their soon to be released Invoke speaker. In order to supplement their defective products in retail markets, Microsoft has to spend more on marketing as well as charging significantly more for support than the likes of Apple. For instance, Microsoft also had to give the NFL $400 million dollars to use their Surfaces for 5 years. Relative to their revenue in 2016, Microsoft spent 1/6th of their revenue on Marketing in comparison to Apple spending only 1/107th of their revenue. Also, a three year AppleCare hardware warranty with unlimited software support costs less than a call to Microsoft for a single Windows support case. 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Microsoft_Surfaces_fail⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Microsoft_Surfaces_fail⦈_ Further and by embracing their own solutions when better solutions are available, Microsoft also limits themselves in the same way that other businesses are limited by their products. Not only are Microsoft products more costly with regard to productivity loss, management, and support, there are much more productive and efficient tools available for such work which their competition is using. For a comparison, Apple employees equipped with Apple solutions generate 3x the amount of revenue per employee than Microsoft employees equipped with Microsoft solutions. Certainly, other environmental variables also contribute to this disparity, but the quality and efficiency of tools have a significant impact on the overall quality of the end product, just as the quality and efficiency of weapons influence the outcome of wars. This is yet another reason why IBM switched to Macs and why many startups are standardizing with Apple products to this day. While most would consider Microsoft products to be a standard within industry, they are failing to see them for the monopoly that they are with the help of their partners. From the perspective of productivity software, they fit the profile quite well and there is not a realm of science that could justify the organizational moves and methodologies that Microsoft relies on outside their actions being that of a monopoly or of an inept company. Fortunately, as the IT industry improves its ability to engineer higher quality, more efficient, less expensive, and simpler solutions, Microsoft will eventually be forced to adapt or collapse. Credit where its due, they are trying incredibly hard to diversify their revenue outside of their partner network, but Microsoft’s many blunders throughout these efforts have forced them to revert back to their monopolistic tendencies and depend on artificially defective solutions in order to keep their partner network and investors happy, now more than ever. “Without an incredibly high level understanding of engineering best practices, software defect density and the consequences of deviating from them, Microsoft wouldn’t have been able to operate at the level that they do, let alone realize and capitalize on their partner dynamic which is presently responsible for 95% of their revenue.”In summary, this is just one of many ways that monopolies work and to no surprise, Microsoft seems to have a monopoly in the same industries that their partners thrive on. Working in the industry that they built, Microsoft cannot claim to be ignorant of the relationship between the quality of the environment and the quality of their products or of the stimulating effects that their defective software can have on their partners and their own business at the expense of industry as a whole. Without an incredibly high level understanding of engineering best practices, software defect density and the consequences of deviating from them, Microsoft wouldn’t have been able to operate at the level that they do, let alone realize and capitalize on their partner dynamic which is presently responsible for 95% of their revenue. To make such a claim would essentially be the equivalent of saying that they make $89 billion dollars per year by accident. █ ⣿⠛⢛⣉⣉⣉⣉⣉⣉⣛⣋⣉⣉⣉⣉⣉⣉⣉⠙⠛⠋⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡙⢋⢉⣉⣉⣉⣉⣉⣉⡉⢹ ⣿⠀⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸ ⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡿⢿⣿⡿⣿⠿⢿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸ ⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠁⡈⡏⢹⠁⠶⠃⡀⠎⠀⢸⠄⠐⠋⠴⢀⠀⣒⣶⢐⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⣄⢀⣀⣀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡶⠿⣶⣶⣿⣶⣿⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠ ⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⣷⣶⣶⣶⣾⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣁⡀⡘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸ ⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣡⣶⣾⣿⣇⢱⣷⣬⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸ ⣿⠀⣿⣿⣤⣤⣤⣤⣤⣤⣭⣭⣭⣭⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣡⣴⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣶⣌⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸ ⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣉⣴⣿⣿⣿⣿⠿⢛⣋⣩⡅⠀⣍⣉⡛⠿⣿⣿⣶⣍⠛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸ ⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣩⣴⣿⣿⣿⣿⣿⠟⣡⣾⣿⣿⠿⢡⣦⡙⢿⣿⣷⣬⠙⢿⣿⣷⣌⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣩⣶⣾⣿⣿⣿⣿⣿⡟⣡⣾⣿⣿⡿⠏⠀⣾⣿⣷⣎⠹⠋⡁⠈⣠⠻⣿⣿⣿⣦⣙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣋⣴⣿⣿⣿⣿⣿⣿⣿⣿⡏⡴⣿⣿⣿⠟⢡⣼⣷⡌⢻⣿⣿⣦⠙⢿⣿⣿⡇⢻⣿⣿⣿⣿⣷⣌⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀ ⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⠀⣀⣉⠃⠐⣿⣿⣿⡇⠰⣿⣿⣿⠇⠰⣿⣿⣿⠘⠻⢿⣿⣿⠿⣿⣿⣶⣍⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⣿⣿⡇⢨⡇⠸⣿⠏⢠⡇⢹⣿⠋⣸⡁⢹⣿⡟⢰⣦⡄⠀⠁⠀⠀⠙⠻⢿⣷⣦⣙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣋⣴⣿⣿⣿⣿⣿⠿⠟⠛⠉⢻⣿⣿⣿⣿⣿⣿⣇⠙⡟⠁⠹⡏⠘⡟⠃⢸⠇⠘⡟⠀⣿⠃⢸⣿⠇⣾⣿⣧⣀⣠⣤⣤⣤⣤⣾⣿⣿⣿⣧⡌⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠ ⣿⠀⣿⣿⣿⣿⣿⣿⡿⠿⠛⠁⠚⠿⢿⣿⣿⣿⣧⠄⠀⠀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣧⡁⢠⣼⣥⣤⣤⣤⣴⠤⢤⣧⣤⣧⣤⡤⢋⣾⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⡿⠟⣋⣭⡄⠈⢍⣘⠻⢿⣿⣿⣿⣿⡇⠀ ⣿⠀⣿⣿⣿⡿⢃⣥⣶⣿⢀⠸⢿⡷⠆⠈⠻⠟⠃⠀⠀⣸⣿⣿⣿⣿⣿⣿⡿⠛⠉⣿⡿⠋⠀⣈⣙⠻⠿⣿⡁⠀⣾⣿⠿⠛⣋⣴⣿⣿⣿⣿⣿⣿⣀⠀⠈⠛⢿⣿⡟⠃⣤⣼⣿⣿⡏⣀⠘⢿⣿⣦⡘⢿⣿⣿⡇⠀ ⣿⠀⣿⣿⠋⠄⠻⢿⣿⢃⣾⣷⣤⡀⠠⣤⣶⡀⢾⣷⣤⣾⣿⣿⣿⣿⠉⠁⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣷⣶⣶⣦⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠏⡀⢁⣀⣈⣻⠟⣰⣿⡆⢎⠻⠛⠉⠂⠹⣿⡇⢰ ⣿⠀⣿⠇⣦⣤⣤⣤⠅⢸⣿⣿⣿⣷⡄⢸⣿⣿⡘⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣶⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣤⢰⣿⣿⣿⣿⠃⣼⣿⣿⣟⠀⣣⠰⣶⣶⣧⢹⡇⢸ ⣿⠀⣿⢸⣿⣿⡿⠋⡄⣆⠻⣿⣿⠏⠄⠎⢿⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡿⠟⢻⠏⣤⠹⣿⣿⠟⣠⠹⣷⡘⢿⣿⢸⡇⢸ ⣿⠀⣿⡈⣿⣿⠀⣾⡆⢸⡆⢸⡅⣰⡀⣥⠀⣽⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠄⠀⡿⠠⣿⡄⢹⣯⠀⣿⢀⣿⠀⢸⡟⣸⡇⢸ ⣿⠀⣿⣧⡙⠁⠀⠹⠀⠨⠁⠈⠀⠉⠀⠈⠀⡽⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡛⠁⡀⣋⢀⣀⣁⡀⣀⣀⣃⣀⠘⣀⣿⣿⠘ ⣿⠀⣿⣿⣷⣄⡒⠶⣶⣶⣶⡂⠀⣾⣶⠷⢋⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣍⡛⠿⢿⣿⠿⠿⠟⣋⣥⣾⣿⣿⣿⠀ ⣿⠀⣿⣿⣿⣿⣿⣷⣶⣤⣭⣤⣤⣭⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⠀ ⣿⣀⠛⠛⠛⠛⠻⠛⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⣉⣉⣉⣉⣉⠉⠉⠉⢉⢋⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⣿⣿⣇⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⣿⣿⣿⠑⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⣸⣿⣿⢻⡟⣛⣛⡛⣿⣿ ⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⠀⠙⢿⣿⠀⠀⠀⠀⠀⠈⠳⣄⡀⡂⠂⡰⠋⠀⠀⠀⠀⠀⣿⣿⠇⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠀⠀⠀⠀⠀⠀⠙⢦⣄⣀⣤⠞⣿⣿⣿⣼⣧⣬⣥⣥⣿⣿ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⢹⡿⣷⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⡈⢿⡿⠋⠀⠀⠀⠀⢀⣤⡴⠿⣿⡿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠛⠃⠀⠀⠀⠀⠀⠀⣀⣙⣛⣀⡀⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿ ⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⡏⠠⣶⣦⡄⠀⢠⠀⢀⣤⣤⣤⣄⣁⡈⠈⠀⠁⣀⣀⡀⠀⢀⣠⣄⡀⠀⠉⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⠀⢸⣶⣤⣤⣀⣉⠉⠉⠉⠉⣿⡟⠿⢹⡿⢻⣿⣿⣿⣿ ⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠛⠛⠃⠀⣄⢡⠈⠙⠛⠀⠀⣿⣿⣇⠀⠋⣿⣿⡇⢠⣿⣶⣿⣿⣿⣶⣀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⢉⣿⣿⡿⠀⢸⣿⠙⠂⠉⣿⣷⣆⠠⣾⣿⣧⠀⠚⠀⠸⣋⣽⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⣿⣘⠀⠸⣷⡶⠶⣿⡿⠇⠀⠀⣿⣿⠆⠘⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠿⣿⣿⣿⣿⣿⣿⡟⣼⣿⠋⠁⢀⣾⣿⡄⢰⣶⣾⣿⠿⠀⣤⣟⠉⠀⠀⠀⢉⣭⣽⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⠿⣿⣿⠀⢠⣿⡇⠀⣀⣀⣀⠀⠀⣿⣿⣇⠀⠹⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠈⠙⠻⢿⣟⣿⡇⢻⣿⣆⠀⣾⣿⣿⣇⢸⣿⠀⢠⣀⡀⢿⣿⣿⠆⠀⣴⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠈⢱⣤⣀⠉⠻⠶⣾⣿⣿⠀⠰⠿⠛⢁⢀⡶⢻⣥⣷⣶⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠙⠛⠆⠀⢻⣿⣇⠙⣿⣿⣿⣎⠛⠿⢾⣿⣿⢸⣿⣿⣧⣶⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣄⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣶⣤⠀⢀⣤⣤⣴⠾⠋⠁⠀⠀⠩⢻⣽⣿⣻⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣇⢹⣿⣿⣿⣿⣿⣶⣾⣭⣬⣭⣭⣭⣥⣴⡿⡛⣛⣫⣽ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠙⣻⣿⣿⡟⠀⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠈⠒⠛⠁⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠑⠊⠉⠉⠉ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⣄⠀⢰⣿⣷⣿⣿⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢦⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣡⣤⣶⢀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠙⠛⠻⢿⡿⠟⠿⠿⢿⣿⣿⣦⡍⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢶⡤⠀⠀⠀⢀⣀⣀⣀⣭⣻⣿⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣟⡻⢿⡿⠿⠿⠟⠂⠀⠀⠀ ⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣤⣤⣠⡟⣿⡿⣿⣿⣿⣠⡍⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⢽⠞⠛⠙⠿⣿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣠⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡷⡀⢀⠀⡄⠀⠀⠋⡉⣉⡽⢻⡟⣷⣿⣶⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡏⠡⠀⠀⠀⠀⠀⠀⠛⠻⠿⣿⣿⣿⣿⣾⣿⣦⣿⡇⠀⠀⠀⠀⣼⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣷⣿⣒⣟⣾⣿⣿⣿⣯⣿⣟⣿⣿⣿⡿⠀⠀⠀ ⣿⣽⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⢠⣘⣀⠀⢿⣿⣻⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⢿⢿⡿⠝⠗⠀⠀⠀⣀⣀⣠⣤⠤⠶⠖⠚⠛⠃⠀⠀⠀⠀⠀⠀⠀⢀⠺⠻⡿⡷⣯⣶⣿⢿⣻⣟⣿⣿⣿⣿⣿⣿⣭⠀⠀⠀ ⣿⣿⣿⣺⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢸⣿⣿⣿⣯⣿⣷⣿⣿⣮⣿⣦⣿⣿⣶⣀⣀⣀⣤⣤⠴⠶⠖⠛⠋⠉⣉⡀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣾⣿⣿⡾⣛⣻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⣿⣿⣿⣫⣻⣻⣹⣙⣉⣏⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣮⣟⣽⡿⣟⣽⣿⣿⣿⣿⣿⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠟⠻⠟⣿⣾⣿⣿⣿⣿⣧⡇⠻⣿⠿⢿⡿⡿⠿⠟⠀⠀⠀ ⣿⣿⣿⣿⣿⢟⡿⣿⣿⠿⢿⢿⠀⠀⠀⠀⠿⣿⣿⣟⣿⢻⠿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⢰⣶⣤⣶⣿⣿⣿⣿⣿⣿⣿⣷⣄⣠⣬⣤⣤⣶⣼⡇⠀⠀⠀ ⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣿⣿⣇⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⣿⣿⣿⠑⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⣸⣿⣿⢻⡟⣛⡛⡛⣿⣿ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⠀⠙⢻⣿⠀⠀⠀⠀⠀⠈⠳⣄⡀⡂⠂⣰⠏⠀⠀⠀⠀⠀⣿⣿⠇⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠀⠀⠀⠀⠀⠀⠙⢦⣀⣀⣠⠜⣿⣿⣿⣼⣧⣬⣥⣥⣿⣿ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⢰⡿⣷⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⡈⠻⡿⠋⠀⠀⠀⠀⠀⣀⠴⠿⢿⣿⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠙⠃⠀⠀⠀⠀⠀⠀⣀⣙⣛⣁⡀⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⡏⠠⣶⣦⡄⠀⢠⡀⢀⣤⣤⣤⣄⣁⡈⠉⠀⠁⣀⣀⡀⠀⠀⡀⢄⣀⠀⠀⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣆⠀⢸⣦⣤⣄⣀⣉⠉⠉⠉⠉⣿⡟⠿⢸⡿⢿⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠛⠛⠃⠀⣄⢱⠀⠙⠛⠀⠀⣿⣿⣧⠀⠛⣿⣿⡇⠀⣶⣾⣿⣿⣿⣷⡆⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⢉⣻⣿⡿⠀⢸⣿⡙⠋⠉⣿⣷⣄⠠⣶⣿⡧⠀⠒⠀⠸⣛⣝⣿⣿ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⣀⣿⣘⠀⠰⣷⣶⠶⣿⡿⠇⠀⠀⣿⣿⠆⡀⢹⣿⣿⣿⣿⣿⣿⣇⠀⠀⢨⢿⣿⣿⣿⣿⣿⡟⣼⣿⠋⠁⢀⣾⣿⡇⢰⣶⣾⣿⠿⠀⣠⣏⠉⠀⠀⠀⢉⣭⣽⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠐⠿⣿⣿⠀⢠⣿⡇⠀⢀⣀⣀⠀⠀⣿⣿⣇⠀⠀⢿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠙⠛⢿⣟⣿⡇⢻⣿⣆⠀⣾⣿⣿⣇⢸⣿⠀⢠⣀⡀⢿⡿⢷⠆⠀⣰⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⢱⣤⣀⠉⠻⠶⢾⣿⣿⠀⠰⠾⠛⢁⢀⡴⠞⣯⣿⣶⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠙⠛⠓⠀⢻⣿⣇⠙⣿⣿⣿⣎⠛⠿⣾⣿⣿⢸⣿⣿⣧⣶⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣄⡀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣶⣤⠄⢀⣤⣤⣴⡾⠓⠁⠀⠀⠈⢻⣽⣻⣽⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣇⢹⣿⣿⣿⣿⣿⣶⣮⣭⣬⣭⣭⣭⣥⣴⡿⡛⣛⣫⣽ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠙⣻⣿⣿⡟⠀⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠓⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠑⠊⠉⠉⠉ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⣄⡀⢠⣿⣷⣿⣿⣶⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠻⢢⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣡⣤⣶⢀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠙⠛⠻⢿⡿⠿⠿⠿⢿⣿⣿⣶⡍⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣤⠀⠀⠀⠀⣀⣁⣉⣭⡿⣿⢿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣻⣿⣿⣟⠻⢿⡿⠟⠿⠟⠂⠀⠀⠀ ⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣠⣤⣨⡟⣻⡿⣿⣿⣿⣡⡍⠓⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢽⠞⠛⠙⠿⣿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⡀⢀⠀⡄⠀⠀⢋⡉⣉⡽⢿⡟⢷⣷⣶⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡟⠡⠀⠀⠀⠀⠀⠀⠛⠻⠿⣿⣿⣿⣿⣾⣿⣦⣿⣶⡄⠀⠀⠀⣼⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣷⣾⣖⣟⣾⣿⣿⣿⣯⣿⣟⣿⣿⣿⡿⠀⠀⠀ ⣿⣽⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⢠⡘⣀⠀⢿⣿⣻⣿⣿⣾⣻⣿⣿⣿⡄⠀⠀⣿⣿⡿⠻⠇⠀⠀⠀⠀⢀⣀⣀⢤⡤⠴⠶⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⡿⡟⣿⣴⣿⢿⣻⣟⢿⣿⣿⣿⣿⣿⣭⠀⠀⠀ ⣿⣿⣿⣺⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢸⣿⣿⣿⣯⣿⣵⣿⣿⣮⣿⣦⣿⣿⣿⣀⡀⢀⣀⣀⣤⡤⠶⠖⠚⢛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣿⣿⡾⢛⣛⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⣿⣿⣿⣫⣻⣻⣹⣙⣉⣏⣿⡇⠀⠀⠀⠘⣿⣿⣟⣿⣾⣟⣽⡿⣟⣽⡿⣿⣿⣿⣿⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠿⠻⠟⣯⣾⣿⣿⣿⣿⣧⡏⠻⣿⠿⣿⡿⡿⠿⠟⠀⠀⠀ ⣿⣿⣿⢿⣿⢟⡿⠿⡿⠿⡿⢿⠀⠀⠀⠀⠿⣿⣿⣟⣿⢻⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢰⣶⣤⣶⣻⣿⣿⣿⣿⣿⣿⣷⣄⣠⣬⣤⣤⣶⣴⡇⠀⠀⠀ ⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣿⣿⣇⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⣿⣿⡿⠈⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⣼⣿⣿⢻⡟⣛⡛⡛⣿⣿ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⢿⠀⠈⠻⣿⠀⠀⠀⠀⠀⠀⠑⢤⣀⣀⣂⡰⠃⠀⠀⠀⠀⠀⣿⣿⠇⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠀⠀⠀⠀⠀⠀⠙⢦⣤⣤⡤⠞⣽⣿⣿⣼⣧⣬⣥⣥⣿⣿ ⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⠿⣿⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⣻⣿⡉⡀⠀⠀⠀⠀⠀⠐⠛⠛⠿⡿⢟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠊⠃⠀⠀⠀⠀⠀⠀⣠⣝⣋⣀⡀⣿⣿⣿⣯⣿⣿⣿⢿⣿⣿ ⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡏⠠⣶⣶⡆⠀⢰⡀⢠⣤⣶⣦⣤⣤⣀⠀⠀⢁⣀⣀⡀⠀⠀⣠⣐⣐⠀⡀⠈⠈⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣆⠀⢸⣷⣦⣤⣤⣀⠀⠉⠀⠁⣿⡟⠻⢹⡟⢛⣿⣿⣿⣿ ⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠛⠉⠃⠀⣤⢱⠀⠉⠙⠂⠀⣿⣿⣷⠀⠉⣿⣿⡇⠀⢸⣿⣿⣿⣿⣷⣦⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⢩⣻⣿⡿⠀⢸⣿⠉⠀⠈⣿⣿⣆⠰⣾⣿⣧⠀⠋⠀⢼⣩⣽⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⣿⣬⠀⠸⣿⡿⠶⠾⠿⠃⠀⠀⣿⣿⠃⠐⠀⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⡟⢿⣿⣿⣿⣿⡏⣾⣿⠋⠁⢀⣿⣿⡆⢸⣷⡾⠿⠟⠀⣴⣏⡉⠀⠀⠀⣨⣭⣽⣿⣿ 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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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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢆⠀⠀⠀⠀⠐⠀⠄⠀⠀⠀⠀⢀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠄⠀⠀⢀⠀⠀⣄⢀⢀⠀⠀⠀⠠⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣛⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⠀⠀⠀⣸⣇⠀⠳⠼⢸⣟⢳⡇⡧⢰⠀⣶⡆⣦⡖⡂⡀⠀⠀⠀⠀⠀⠀⠀⢀⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡟⠀⠀⠀⢠⣿⣿⡄⠀⠀⠀⠀⠈⣁⣉⣉⣉⠁⠁⠁⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⢠⣿⣿⣿⣷⡄⠀⠀⠀⣴⣮⣭⣭⣭⣍⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠨⠿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⣯⣿⣿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⣿⣿⣿⣿⣿⡆⠀⠀⠀⢻⣿⡟⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⢶⣶⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠉⠁⠀⠀⠀⠀⠀⠀⠘⣿⣷⣀⣀⣐⣶⣶⡆⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣷⢻⠋⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣥⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠎⠻⠿⡿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠋⠉⠁⠀⢀⣠⣴⣿⣿⣿⡿⠏⠊⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡪⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⢩⣻⣽⣅⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⢀⣴⣾⡿⠋⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣻⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣷⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠹⣿⣿⣿⣿⡿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⡀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠉⢻⣧⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠋⠿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠌⢿⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢠⠤⣤⡤⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⣿⣧⣴⢼⠀⠀⠀⠀⠀⠀⠘⠭⠚⣿⠸⠤⠧⠧⠅⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠅⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⡿⠊⠀⢧⡀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠻⠛⠟⠒⢾⣿⣿⣶⣦⡴⠖⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⣉⣁⣉⠀⠀⠀⠀⠀⠀⠒⠐⠒⠒⠐⠀⠀⠀⠀⢸⣿⣿⡄⠠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣿⣿⣿⣷⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣶⣤⣄⣀⣀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣀⣀⣀⣠⣤⣶⡿⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣇⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢦⠈⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠙⢇⡟⠿⠻⣿⣿⣿⣿⠧⠬⠊⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠳⣶⣤⣀⡀⠈⢹⢃⠟⡋⠏⠉⠉⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⠉⠉⠉⠁⢀⣠⡾⢋⣿⣿⣿⣿⣿⣿⣿⢏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠉⠛⠿⢷⣍⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣶⡶⠿⠛⢁⣴⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠄⠀⠀⠀⠀⠐⠀⠠⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠠⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣟⠃⠀⠀⠀⣸⡆⠀⠳⠸⣸⣟⢳⡇⡧⢰⠀⡶⡄⣆⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢠⣿⣿⡀⠀⠀⠀⠀⢈⣁⣉⣉⠉⠁⠁⠁⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣿⣗⡀⠀⠀⢠⣿⣿⣿⣷⡄⠀⠀⠀⣦⣬⣭⣭⣍⣉⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠙⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⡄⠀⠀⠀⢻⣿⡟⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣤⣸⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⠉⠉⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⣀⣴⣦⡆⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⡯⠻⠂⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⡿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠏⠉⠁⠀⠀⣀⣴⣿⣿⣿⠿⠉⠀⠁⠀⠰⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⢩⠟⣿⣆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⢀⣤⣶⠟⠋⠉⠈⠁⠀⠀⠀⠀⠀⠀⠈⣽⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣷⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣶⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠯⠙⢿⣇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⠻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⢨⣸⣿⠀⢀⢄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢠⠤⣤⡤⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠈⣿⣿⣶⣿⡘⠠⡀⠀⠀⠀⠀⠘⠉⣾⣿⣼⡤⠧⠧⠅⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⢿⣿⣿⡉⠀⣠⣧⡀⠀⠀⠀⠀⠀⠿⠟⠛⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠁⠈⠀⠘⣿⣿⣿⣿⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣉⣁⣀⡀⠀⠀⠀⠀⠀⠀⠂⠒⠒⢺⣿⣿⡇⠀⣀⣄⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⣸⣿⣿⣇⣀⣀⣀⡀⡀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠚⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠐⠂⠀⠀⠀⣀⣴⠀⠘⣿⢿⣿⣷⣿⣷⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣿⠏⠀⠀⢘⡼⢿⣿⣿⣿⣿⣿⣿⡿⢟⠿⠇⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢳⡀⠉⠛⠻⠿⢿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠟⠋⠁⠀⠀⠀⠈⢨⠸⠉⠉⡩⠟⡿⡿⠓⠂⠀⣰⢻⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠙⠷⣶⣤⣀⡀⢘⡐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⣴⠞⢃⣾⣿⣿⣿⣿⣿⠣⠃⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠈⠉⠛⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣶⠿⠿⠛⠋⢀⣴⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠃⠀⠀⠀⠀⠀⠀⡤⢀⢀⣀⡀⡀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⣸⣇⠀⠑⠺⠌⢗⢸⡇⣇⣸⡄⣞⡇⡧⡆⡄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡓⠀⠀⠀⠀⢠⣿⣿⡄⠀⠀⠀⠀⠠⢀⣀⣀⣀⣀⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣤⣤⡀⠀⠀⢠⣿⣿⣿⣿⠀⠀⠀⠀⢰⣦⣦⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣦⠀⢿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⡟⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣲⢦⡂⣌⣹⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣇⠈⠉⠀⠀⠀⠀⠀⠀⠀⢈⣿⣷⣀⣀⣀⣶⣶⡆⠀⠀⠀⠀⢀⣴⣿⣿⡿⠛⠓⠒⠀⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠯⠋⠹⠿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠏⠉⠀⠀⢀⣠⣰⢿⣿⠟⠉⠀⠀⠀⠀⢐⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⢠⣻⣭⣅⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⣀⣴⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⡀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣾⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠅⠉⢿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠋⠽⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⢱⢀⣦⣽⡏⠀⡀⡄⠀⠀⠀⠀⠀⠀⢀⣀⣛⣛⢢⠤⣤⡤⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡐⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⣹⣿⣿⣾⣫⠏⢠⠀⠀⠀⠀⠀⠘⢭⣾⣿⣼⣤⣧⠧⠅⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⢸⣿⣿⡿⠁⣴⣿⣦⡀⠀⠀⠀⠀⠿⠟⠛⠋⠉⠙⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠘⠋⠀⠀⠀⢿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣈⣈⣉⣉⣁⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⢺⣿⣿⡇⠀⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠜⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⣸⣿⣿⣇⣀⣀⡀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡀⠀⠀⠀⢠⠁⠄⠀⠀⠀⢀⠀⢡⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⣀⣀⣀⣠⣤⣶⡟⠀⠸⣿⣿⣿⣷⣿⣯⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⢿⣽⣻⣿⣿⣿⣿⣿⣿⡿⢝⠿⠇⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢳⡀⠉⠙⠛⠿⢿⣿⣻⠷⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠡⠽⠉⠉⢻⣟⣿⡿⠓⠒⠁⣰⢻⣿⣿⣿⣿⡿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠙⠿⣶⣤⣄⡀⢸⡁⠋⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣠⣴⠞⢃⣾⣿⣿⣿⣿⠑⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⠛⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⡶⠿⠿⠛⠋⢀⣴⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⡤⢀⢀⣀⡀⡀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣸⡇⠀⠓⠸⠼⣗⢹⡇⣗⢸⡀⣟⡆⣧⡆⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡓⠀⠀⠀⠀⢠⣿⣿⡄⠀⠀⠀⠀⠠⢄⣀⣁⣀⣀⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣶⣣⡀⠀⠀⢠⣿⣿⣿⣷⠀⠀⠀⠀⣶⣶⣤⣤⣤⣬⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣦⠀⢿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⡟⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⢤⡂⢈⣻⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⠉⠁⠀⠀⠀⠀⠀⠀⠈⣿⣷⡀⢀⣀⣴⣶⡆⠀⠀⠀⠀⢀⣴⣾⣿⣿⠿⠷⠓⠀⣽⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠛⠿⡿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠏⠉⠀⠀⢀⣠⣰⣿⣿⡟⠏⠁⠀⠀⠀⢰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠩⣻⣯⡆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⢀⣴⣾⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣝⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣶⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⡀⠀⠀⠀⠀⠀⠀⣿⣿⠭⠙⣿⡆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠋⠽⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⢸⣿⣿⡇⠀⢀⣴⣾⣿⡅⢀⡀⡄⠀⠀⠀⠀⠀⠀⢀⣘⣋⣛⢻⠦⣤⡤⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠠⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢰⠏⢸⣿⣿⣿⣿⡵⠃⡆⠀⠀⠀⠀⠀⠘⣭⣾⣿⣼⣤⣧⣧⡅⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢻⠀⠘⣿⣿⣿⢯⣠⣴⣿⣤⡀⠀⠀⠀⠸⠿⠛⠛⠛⠛⢿⠿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠟⠃⠈⠈⢻⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀ ⣉⡁⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠀⠀⠀⠀⠀⢸⣿⣿⡇⠠⣄⣄⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣺⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾⣿⣿⣷⣿⣿⣿⣿⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠂⣿⣿⣿⣿⣿⣷⣶⣄⣀⢀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠘⠂⠀⠀⠀⢀⣤⠀⢠⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣿⡿⠃⠀⠰⣿⣿⣿⣿⣯⣧⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢿⣿⣿⣿⣿⣿⣿⣟⣿⡟⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠿⠇⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢷⡀⠉⠛⠻⠿⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢻⡟⡟⠝⣻⣿⣿⢿⠓⠂⠋⣰⢻⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠙⠷⣶⣤⣀⡀⢸⡽⠋⣖⡝⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠀⢌⠁⠐⠈⠉⠉⠀⠀⣀⣤⠾⢋⣾⣿⣿⣿⠓⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⠉⠛⢻⠂⠀⠂⠁⠅⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢈⡂⢠⣤⣶⣶⠿⠿⠛⠋⠁⣴⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⣤⢀⢀⣀⡀⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠑⠀⠀⠀⢸⡆⠀⠓⠸⢼⣗⢹⡇⡯⢸⠀⣟⡆⣦⡆⡄⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣓⠀⠀⠀⠀⢠⣿⣿⡀⠀⠀⠀⠀⠀⣀⣉⣉⣉⣁⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣻⣧⡀⠀⠀⢀⣾⣿⣿⣷⠀⠀⠀⠀⣤⣤⣤⣥⣭⣭⣥⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⢿⣿⣿⣿⣿⡄⠀⠀⠀⢸⣿⡟⠛⠿⠿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⣤⡀⢰⢻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⠋⠉⠉⠀⠁⠀⠀⠀⠘⣿⣷⠀⠀⠀⣤⣤⡆⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⡢⠣⠀⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⠻⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⢀⣤⣾⣿⣿⡛⠉⠀⠀⠀⠱⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⢹⢟⣛⡂⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⢀⣠⣶⡾⠛⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⣝⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣦⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣴⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⡀⠀⠀⠀⠀⠀⠀⣾⣿⡛⠻⣿⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⡻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠠⠀⠀⠀⢸⣿⣿⡇⠀⠰⣿⣿⣯⣠⣤⣰⠀⠀⠀⠀⠀⠀⠀⢀⣀⣚⣛⢹⠿⣷⡦⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⡐⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⣿⣿⣿⣿⡷⠋⣸⡀⠀⠀⠀⠀⠀⠘⢭⣾⣿⣼⣤⣧⣧⣽⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⣿⠿⣿⠷⢤⣾⣿⣷⣄⣀⠀⠀⠀⠀⠈⠉⠉⠉⠻⠿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⣶⠏⠉⠀⠀⢸⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⠀ ⣀⣀⣀⣀⣀⣈⣁⣀⣀⣉⠀⠀⠀⠀⠀⠀⠐⠒⢺⣿⣿⣇⣀⣤⣦⣴⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⡀⣠⣤⣀⣀⣀⡀⠀⠀⠀⠀⢸⣿⣿⡇⠠⠇⠀⠁⠀⠀⢿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡠⡀⠀⠀⠀⠀⠀⠐⠛⣿⣿⣿⣿⣿⣿⣶⣤⣀⣸⣿⣿⣇⣀⣀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣦⣤⣄⣀⣀⣤⣤⣴⣶⠏⠀⠘⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⡿⠿⠿⠛⠁⠀⠀⠘⣿⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⣿⣿⣿⣿⣿⣿⣿⡟⠫⠙⠃⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠹⣆⣀⠈⠉⠙⠛⢿⣟⣻⡿⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡎⢹⣿⡿⣽⣿⡿⠿⠟⠉⠁⢀⣼⢹⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠛⠿⣶⣦⣤⠘⣟⠑⢏⢿⠀⠀⠀⠀⠀⠀⠀⠀⡲⠟⠁⠰⠁⠀⠀⢀⣀⣀⣠⣴⡾⠋⣡⣿⣿⣿⠉⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢆⠀⠀⠀⠈⠉⢭⠂⣀⠀⠉⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠁⠰⡾⠿⠟⠛⠛⠉⠁⢠⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣖⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⢀⠀⠀⡖⢠⢠⡤⣄⡄⣈⢁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠁⠀⠀⠀⣸⣇⠀⠉⠘⠚⠯⠸⠇⠧⣸⠀⡯⡇⡷⡇⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⢙⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⠀⠀⠀⠀⢰⣿⣿⡄⠀⠀⠀⠀⠐⠠⠤⠤⠤⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣧⡄⠀⠀⢠⣿⣿⣿⣿⠆⠀⠀⠀⢶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠆⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢻⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⡏⠙⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⠶⡀⠝⣻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣧⠀⠁⠀⠀⠀⠀⠀⠀⠀⢈⣿⣷⣀⣀⣀⣶⣶⡆⠀⠀⠀⠀⢀⣴⣿⣿⣿⠛⠗⠐⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠯⠙⠻⠿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⠉⠀⠀⢀⣠⣴⣿⣿⡿⠋⠁⠀⠀⠀⢘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠩⣻⣯⡆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⢀⣴⣾⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣦⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⡀⠀⠀⠀⠀⠀⠀⣿⣿⠥⠙⣿⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠏⠻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⢀⠀⠀⠀⢸⣿⣿⡇⠐⢾⣿⣿⣧⣤⡔⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⢺⠿⣿⡷⣄⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠃⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢘⡒⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⣾⣿⣿⣿⣿⠞⢁⡆⠀⠀⠀⠀⠀⠀⠘⠉⢾⣿⣼⣤⣧⣧⣽⣿⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⣾⣿⡿⠿⡥⣴⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⢀⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿ ⣀⣁⣉⣉⣉⡁⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠂⠀⢸⣿⣿⡇⢀⣤⣤⣤⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⢀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠏ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣻⠀⠀⠀⠀⡤⠐⠀⠀⠀⠀⢀⠘⠛⣿⣿⣿⣿⣿⣷⣦⣄⣀⣸⣿⣿⣇⣀⡀⠀⣠⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀ 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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 6567 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2021/12/21/the-unlawful-normalised/#comments Gemini version at gemini://gemini.techrights.org/2021/12/21/the-unlawful-normalised/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.21.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ EPO’s_Privacy_Violations_Being_‘Normalised’⠀✐ Posted in Deception, Europe, Patents at 10:41 am by Dr. Roy Schestowitz Video_download_link | md5sum a7b1588e28c65c7a480647e2d7e76fd8 http://techrights.org/videos/dpr-epo.webm Summary: The EPO has chosen to use mindless hype and buzzwords to justify its abuses of the personal dignity and basic human rights of staff and stakeholders Yesterday we published a couple_of_posts (the second_was_just_a_meme) after a document had made the rounds, showing that the EPO persists with the same violations of privacy that we_covered_early_in_the_year. Instead of accepting that the problem was the privacy abuses they treated the whole thing like that problem was a lack of framework to retroactively legalise these abuses by cloudwashing and other buzzwords (e.g. Data Protection Board (DPB), Data Protection Rules (DPR), and Data Protection Officer (DPO)). The above video was recorded when I was very tired and I even forgot to turn on the noise remover, but it goes through some of the key points nonetheless. █ ䷩ 𝚕𝚒𝚗𝚎 6608 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.21.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Links_21/12/2021:_elementary_OS_6.1_Released_and_Tor_Browser_11.0.3⠀✐ Posted in News_Roundup at 2:22 am by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈ § Contents⠀➾ * GNU/Linux o Distributions o Devices/Embedded * Free_Software/Open_Source * Leftovers * § GNU/Linux⠀➾ o § Server⠀➾ # ⚓ NGINX_vs._Apache:_Comparision_of_web_servers_to_host_your website⠀⇛ If you are visiting a website then most probably one of the two web servers – Apache or Nginx has been serving that for you. To make several different websites available to visitors, the host needs web server software. The key task of a webserver is to take the requests and analyzes them to return the requested documents in the browser. Here we will learn about two popular web servers Apache and Nginx by comparing them; we will learn about their features in detail and which is better suited for which purposes. o § Audiocasts/Shows⠀➾ # ⚓ Endless_OS_4.0.0_Quick_overview_#Shorts_–_Invidious⠀⇛ A Quick overview of Endless OS 4.0.0 # ⚓ Linux_Action_News_220⠀⇛ The nasty Log4Shell vulnerability isn’t solved yet, this week saw a new round of attacks and patches. Plus how the work to port Linux to the Apple M1 resulted in fixing a bug that impacted all Linux distros. # ⚓ LHS_Episode_#445:_Year-End_Round_Table_2021⠀⇛ Hello and welcome to Episode 445 of Linux in the Ham Shack. In this final episode of 2021, we invite listeners to join us via Discord for a discussion of amateur radio, technology, open source software and hardware and the year in review. We even depart briefly into hedonism as well. We hope you enjoy this community-driven content, have a safe and happy holiday season and join us again when we re- start the show on January 6, 2022. # ⚓ Gramma:_Fixing_YoUr_Grammar_right_In_The_Terminal_– Invidious⠀⇛ Do you ever find that your grammar is horrible, well I do so lucky there’s a tool to address that and that tool is Gramma so you can fix it right from the terminal # ⚓ You’ve_heard_of_Liminal_spaces,_now_what_about_Liminal Operating_Systems?_–_Invidious⠀⇛ # ⚓ MakuluLinux_Shift_Gen_2_Ubuntu_Run_Through_–_Invidious⠀⇛ In this video, we are looking at MakuluLinux Shift Gen 2 Ubuntu. Enjoy! # ⚓ Late_Night_Linux_–_Episode_156_–_Late_Night_Linux⠀⇛ We look back at some of the biggest stories and trends of 2021 including Linux on Mars, gaming, Arm, drama, and NFTs. # ⚓ 257:_You_Down_With_IDEs?_Yea_You_Know_Me!_–_Destination Linux⠀⇛ This week’s episode of Destination Linux, we discuss our favorite IDE’s and text editors for writing code and discuss some of the future tools and enhancements to several popular options. Then we’re going to discuss Kdenlive’s new features which are going to give you geek chills. Plus we’ve also got our famous tips, tricks and software picks. All of this and so much more this week on Destination Linux. So whether you’re brand new to Linux and open source or a guru of sudo. This is the podcast for you. # ⚓ elementary_OS_6.1_Jolnir_–_What’s_new?_–_Invidious⠀⇛ o § Kernel Space⠀➾ # ⚓ There’s_a_new_Linux_kernel,_but_you_probably_shouldn’t_use it_right_now_|_TechRadar [Ed: WHo the heckwrites these misleading headlines?]⠀⇛ If you’re feeling like having a slow week ahead of Christmas then you’re not alone: Linux creator Linus Torvalds has used his weekly post to assure us that Linux 5.16 is coming, but probably after the festive season. “Things are calming down, and rc6 is fairly small. That’s normal for this time in the release schedule, but it’s also normal for this time of year,” Torvalds wrote. “And I expect that the next two weeks will be very quiet, and smaller still. But maybe people are bored, maybe people are staying in due to covid picking up again, we’ll just see.” # ⚓ Linux_5.16_is_coming_after_a_slight_delay,_offers_improved support_for_Surface_devices⠀⇛ According to the announcement, we can expect the usual peppering of filesystem updates, general kernel additions, and improvements to networking. However, there are lots of driver updates and two of them target Microsoft’s Surface line of devices. One relates to the button array on the Surface Go 3 but isn’t explained clearly. Apparently, it properly implements the five-button array on the tablet itself. The other solves a multitouch issue with the non-pro Type Cover of the Surface 3. The problem only affected this variant. Looking forward at 5.16, Mac users can expect improved support for Apple’s M1 chip, while gamers can expect the already available Nintendo Switch Pro controller driver to be merged into the mainline kernel. This means you’ll finally be able to use the Switch Pro Controller outside of Steam with no extra effort. Stable support for Intel’s Alder Lake graphics is also a notable feature. # § Graphics Stack⠀➾ # ⚓ Meet_wxrd,_a_standalone_Wayland_compositor_for xrdesktop⠀⇛ From its inception, an important use case for xrdesktop was that applications that are already running on the 2D desktop should be seamlessly available in VR at the press of a button. Although it is possible to implement something like this in a desktop agnostic fashion with pure xlib/xcb proof of concept: x3d, for performance and robustness reasons we opted for code integration into window managers. Typically, window managers have an internal abstraction of the windows they manage that is much easier to reliably consume than the raw X11 protocol. The first two window manager integrations we started out with were a patchset for gnome- shell and a kwin plugin. The window manager integration approach unfortunately suffers several drawbacks. Most importantly however, not everyone is running kwin or gnome-shell, and adding integration into more and more window managers would result in an unmaintainable mess. Each window manager is shipped in a different version on different distributions too. The gnome-shell patchset needs to be adjusted for every major version change. The kwin plugin needs to be compiled for a specific kwin version, meaning an Ubuntu PPA with an updated KDE version would break a packaged version of the plugin. While the ability to mirror already running 2D applications without good performance has been a unique feature of xrdesktop, which is enjoyed by our users and will still be maintained, we have also heard many voices who desire a more native XR solution, especially looking at standalone devices. # ⚓ Collabora_announce_wxrd,_a_standalone_Wayland compositor_for_xrdesktopx⠀⇛ Working with Virtual Reality and Linux just got a lot more interesting, with the clever hackers at Collabora announcing their new standalone Wayland compositor for xrdesktop called wxrd. For those that didn’t see our previous coverage on it: xrdesktop is a way to turn your desktop into a VR space, allowing you to interact with windows and do some pretty cool stuff with a VR HMD. It does this with patches and integrations for window managers like the defaults of GNOME and KDE Kwin but “suffers several drawbacks” and isn’t then an option for others. It gets messier with all the different versions across different Linux distributions. o § Applications⠀➾ # ⚓ HP’s_Linux_Imaging_&_Printing_Software_HPLIP_3.21.12_Adds Fedora_35,_MX_Linux_21_Support_|_UbuntuHandbook⠀⇛ HPLIP, HP’s inkjet and laser printers drivers for Linux, released 3.21.12 a few days ago with new Linux Distros support. The released added Fedora 35, MX Linux 21, and Elementary OS 6 support. Since HPLIP package in these Linux Distros’ own repositories is always old, users may now easily install the latest version via the official script by HP. o § Instructionals/Technical⠀➾ # ⚓ SSH_agent_restriction⠀⇛ OpenSSH 8.9 will include an experimental set of agent restrictions that meet the above requirements, though with some caveats (discussed below). These are built around some two simple agent protocol extensions and a small modification to the public key authentication protocol. These extensions allow the user to add destination constraints to keys they add to a ssh-agent and have ssh enforce them. For example, this command: [...] # ⚓ Restrict_users_to_a_network_interface_on_Linux⠀⇛ If for some reasons you want to prevent a system user to use network interfaces except one, it’s doable with a couple of iptables commands. The use case would be to force your user to go through a VPN and make sure it can’t reach the Internet if the VPN is not available. # ⚓ How_to_Install_and_set_up_Nginx_as_a_proxy_OpenSUSE_Leap 15.3⠀⇛ Nginx is a web server that can also be used as a reverse proxy, load balancer, mail proxy and HTTP cache. It started out as a web server designed for maximum performance and stability. Nginx has grown in popularity since its release due to its light- weight resource utilization and its ability to scale easily on minimal hardware. Nginx excels at serving static content quickly and is designed to pass dynamic requests off to other software that is better suited for those purposes. In this guide we are going to learn how to install Nginx in OpenSUSE Leap 15.3 and set it up as a proxy server. We will set up an Nginx virtual host that proxies a request from a domain to a service listening on a port. # ⚓ How_to_Install_&_Enable_EPEL_/_EPEL_Next_Repository_on Rocky_Linux_8_–_LinuxCapable⠀⇛ EPEL, which stands for Extra Packages for Enterprise Linux, is an open-source and free repository that provides extra packages for Enterprise Linux. The EPEL repository was created because Fedora contributors wanted to use Fedora packages they maintain on RHEL and other compatible distributions such as Rocky Linux, CentOS, AlmaLinux, to name a few. The EPEL repository is also known for bringing additional packages and updated packages that may be behind in the core repository, along with dependencies required by other external repositories, for example, the Remi PHP repository. In the following tutorial, you will learn how to install the EPEL repository along with the EPEL Next repository, which is the next testing version that can come into use for newer packages when major upgrades occur to the core distribution on Rocky Linux 8. # ⚓ How_To_Install_Wine_on_Fedora_35_–_idroot⠀⇛ In this tutorial, we will show you how to install Wine on Fedora 35. For those of you who didn’t know, Wine (an acronym for “Wine Is Not an Emulator”) is open-source software. By using a wine you can install/run Windows applications/tools on Linux. As we know that Linux does not support windows executable so WineHQ is a solution to run Windows applications and Linux systems. 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 WineHQ on a Fedora 35. # ⚓ How_to_use_the_procs_command_to_show_the_active_processes in_Linux?_–_Unixcop_the_Unix_/_Linux_the_admins_deams⠀⇛ Hello, friends. Now in this post, I will show you how to install and use the procs command to show processes in Linux from the terminal. So, let’s get to it. # ⚓ How_to_install_Ultimaker_Cura_slicer_on_Linux⠀⇛ Ultimaker Cura is one of the best 3d printer slicer applications out there. It has dozens of excellent features like material estimation, support for a wide variety of printers (even ones not made by Ultimaker,) and much more. This guide will show you how to install Ultimaker Cura on Linux. # ⚓ How_to_install_Pesterchum_on_a_Chromebook⠀⇛ Today we are looking at how to install Pesterchum 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_Open_Broadcaster_Studio_on_Linux_|_FOSS Linux⠀⇛ The popularity of streaming in today’s world has, in one way or the other, skyrocketed the popularity of this Open Broadcasting Software (OBS). Nowadays, several game broadcasting and streaming software are available in the market. Nonetheless, most of them are either paid for or are not that appealing for use. But, to your rescue, the open-source community has offered you OBS as the most immediate solution. OBS is a free-and feature-rich, cross-platform, open-source live streaming software used for recording purposes among the masses. This software started as a small project but gained its fame via its users’ stability and ease of use. By now, it is regarded as a vital component of the computer system for users who like to do stuff like recording and video streaming on their workstations. # ⚓ How_to_Set_Up_a_Local_Kubernetes_Instance_With_MicroK8s_on Ubuntu⠀⇛ DevOps has greatly changed the way software engineers and developers develop and deploy applications. One of the technologies at the heart of this revolution is Kubernetes. Let’s explore how you can install a local instance of Kubernetes on Ubuntu using MicroK8s (MicroKates). With this setup in place, you can easily host container applications in a secure, reliable, and highly scalable manner. # ⚓ 6_SSH_Authentication_Methods_and_How_to_Use_Them_–_ByteXD⠀⇛ As more companies migrate their services to the cloud and more people continue to work remotely, a secure connection is needed to connect to a remote computer over a network. One of the most utilized encryption protocols to mitigate cyber threats such as password sniffing is SSH (Secure Shell). SSH was designed and developed to replace unsecured protocols such as rlogin, rsh, and telnet to connect two remote hosts. # ⚓ How_to_Use_Double_Bracket_Conditional_Tests_in_Linux⠀⇛ Conditional tests branch the flow of execution of Linux Bash scripts according to the result of a logical expression. Double bracket conditional tests simplify the syntax considerably—but still have their own gotchas. # ⚓ How_To_Stop_and_Start_AWS_EC2_Spot_Instances_–_CloudSavvy IT⠀⇛ Spot instances are AWS’s way to sell off unused server capacity when demand isn’t high. They are much cheaper, but come with a lot of restrictions, such as being interruptable and more complicated to start, stop, and run for longer periods of time. # ⚓ Commands_to_install_Apache_Web_server_on_Ubuntu_22.04_or 20.04_LTS⠀⇛ If you want to learn how to run and access a website from a remote location, we need a Web server and what it be more practical than starting with Apache if you are new to the hosting world. Here in this tutorial, we will learn the command to install and start Apache web server on Ubuntu 22.04 LTS Jammy JellyFish or Ubuntu 20.04 LTS focal fossa. Apache is the most widely used web server on the Internet. And can be easily configured because of its flexible nature and ability to expand features with the help of a large number of modules. It has been developed and maintained under the Apache foundation. Usually, the Apache web server is installed with PHP and MySQL/MariaDB. Although, Apache itself delivers only static HTML pages. However, when combined with PHP (PHP Hypertext Preprocessor) like scripting language it can serve the Dynamic HTML pages generated from database contents. # ⚓ How_to_Install_Centreon_Monitoring_Tool_on_Rocky_Linux_8⠀⇛ Centreon is an open-source tool that can monitor your entire infrastructure including network, system, and application. Using Centreon you can set notifications depending on thresholds, set email alerts, easily add any system for monitoring. # ⚓ Wi-Fi_not_working?_It’s_time_to_consult_the_lovely_people on_those_fine_Linux_forums⠀⇛ Welcome to another edition of Who, Me? in which a Register reader makes the impossible possible and actually gets Wi-Fi working on Linux. To be fair to the Penguinistas choking on their mince pies, our tale is set more than 10 years ago, when making Wi-Fi work under Windows could be challenging, let alone on everyone’s favourite open-source OS. Our story comes from a reader we’ll call “Erik” (for that was not his name) who was trying to pop a new version of Linux on his laptop. He was a big SUSE fan but distro-curious, also tinkering with Ubuntu at the time. Alas, exactly which distribution and version is lost to time, so for the purposes of this story we’ll go with “Linux.” The install went well, but all the bells and whistles of Erik’s laptop did not seem to be supported. Most importantly, the Wi-Fi. Naturally, he hit the forums in search of help. # ⚓ Fresh_liveslak_ISO_images,_setup2hd_can_now_install_a_basic firewall⠀⇛ New ISO’s for Slackware Live Edition (based on liveslak-1.5.1) are available for download. You’ll find SLACKWARE (32bit/64bit), XFCE (32bit/64bit), DAW, LEAN, CINNAMON and MATE updated images (see below for download locations). I also refreshed the ‘bonus’ section with nvidia and broadcom-sta drivers matching the installed kernel, and other useful stuff. All 32bit ISOs will boot a SMP kernel from now on, since the non-SMP kernels still refuse to execute the init script in the initramfs. o § Games⠀➾ # ⚓ 80%_of_Steam’s_top_100_games_now_work_on_Linux⠀⇛ Proton has made enormous strides toward game compatibility through advances in related technologies like DXVK, which enable DirectX 9, 10, and 11 games to run through the Vulkan API. In fact, the project is so far along that Amazon has thrown its hat in the ring, working toward streaming Proton enabled games through Luna. The progress of this effort is updated all the time on ProtonDB, and today they crossed a major milestone as user reports on the site reveal that 80% of the top 100 games on Steam now run on Linux, and by extension, Steam Deck. # ⚓ How_To_Play_0_A.D._(and_WIN!)_–_DT_LIVE_–_Invidious⠀⇛ 0 A.D is a free and open source real-time strategy game, similar in spirit to Age of Empires. I am not much of a gamer, and 0 A.D is not something that I often win at, but I do enjoy playing this game. And I love promoting open source games, especially those that are native to Linux. # ⚓ Fast-paced_strategic_action_in_Sky_Fleet_is_out_now_| GamingOnLinux⠀⇛ Melding together elements of a fast-paced action game with the tactics of a tower defence game, Sky Fleet is officially out now. Taking place in the clouds, you speed around various floating islands as you battle for supremacy while also grabbing some resources. o § Desktop Environments/WMs⠀➾ # § K Desktop Environment/KDE SC/Qt⠀➾ # ⚓ Latte_Dock_|_Plasma_LookNFeel_support⠀⇛ As the title implies from now on Plasma LookNFeel packages can contain and apply Latte Layouts. What that means is that distros and designers can include their latte layouts inside their own Plasma LookNFeel package and Plasma will auto adjust everything in order to load or unload the latte layout. The relevant approved merged reguest can be found here. What will happen is that Latte will automatically switch to the provided layout. In case the looknfeel package does not contain any latte layout then we can guess that Latte is not needed and for that reason is closed. You can of course restart Latte afterwards if you want to. The Latte approach is pretty safe concerning your data and your layouts. When you apply a new layout through LookNFeel packages then your current latte layout is not removed or touched at all, it just remains inactive with the same name and you can reenable it whenever you want to from Latte Layouts Editor. # ⚓ Kate_is_a_fantastic_text_editor!⠀⇛ Kate is the KDE Advanced Text Editor, and it’s one of the many, many goodies one gets when using the Plasma Desktop. You can install Plasma yourself (like I do on FreeBSD, thanks maintainers!), or there are Linux distributions such as KDE Neon and Kubuntu that ship with it by default for you. Others usually give you the option to replace their default desktop with it too, like Debian. Like other KDE applications, you can also run it on whatever desktop you want. o § Distributions⠀➾ # § New Releases⠀➾ # ⚓ elementary_OS_6.1_Available_Now⠀⇛ Just over four months ago we announced elementary OS 6 Odin with new ways to be in control and express yourself, a slew of innovative new features, and a focus on gettability and inclusivity. So far, OS 6 has been downloaded from our website over 250,000 times—and as always, that’s not including downloads from third parties or direct downloads via torrent that bypass our download page! # ⚓ elementary_OS_6.1_Released,_This_is_What’s_New⠀⇛ Available to download from today is elementary OS 6.1, the first point-release in the 6.x series. This milestone rolls together all of the post-release updates, fixes, and encements dished out to the distro since its debut, resulting in a nice, new, shiny .iso image. # ⚓ Elementary_OS_6.1_Has_Been_Released⠀⇛ The developers of elementary OS have been hard at work delivering the first point release for Odin (the sixth iteration of the distribution). Normally a point release wouldn’t receive a new name and identity, but the developers felt there was enough polish added to warrant the change. With the new release of elementary OS, comes an AppCenter that continues to fill out with applications. Since elementary OS has added Flatpak support, you’ll find over 90 curated apps in the AppCenter. The shift from Debian packages to Flatpak has made it possible for developers to push out rapid and frequent updates. And thanks to the added Flatpak support, along with curated apps you’ll find plenty of non-curated apps to fill in the gaps. The AppCenter itself has received plenty of attention with a reworked home page and banners featuring the most recently released applications. # ⚓ elementary_OS_6.1_“Jólnir”_Officially_Released,_This Is_What’s_New⠀⇛ Dubbed “Jólnir,” elementary OS 6.1 comes more than four months after elementary OS 6 “Odin” and it’s built on top of the Ubuntu 20.04.3 point release of the Ubuntu 20.04 LTS (Focal Fossa) long-term supported operating system series and powered by Linux kernel 5.11. Highlights of elementary OS 6.1 include a redesigned quick window switcher (Alt+Tab) that no longer relies on the dock to switch between apps (you can see in action below), animated dialogs, improved File Chooser portal, a new App Chooser, as well as a much- improved dark style. # ⚓ elementary_OS_6.1_Release_Enhances_the_Desktop Experience_and_Brings_AppCenter_Upgrades_–_It’s_FOSS News⠀⇛ elementary OS 6.0 was an exciting release. If you haven’t explored that yet, I suggest you go through the features introduced with elementary OS 6. After four months of its release, elementary OS 6.1 is here! You can get started by downloading it. But, before that, you may want to explore the exciting new changes mentioned here. # ⚓ elementary_OS_6.1_Available_Now_⋅_elementary_Blog⠀⇛ Just over four months ago we announced elementary OS 6 Odin with new ways to be in control and express yourself, a slew of innovative new features, and a focus on gettability and inclusivity. So far, OS 6 has been downloaded from our website over 250,000 times—and as always, that’s not including downloads from third parties or direct downloads via torrent that bypass our download page! # ⚓ elementary_OS_6.1_is_Now_Available⠀⇛ Elementary today announced the availability of elementary OS 6.1, the latest update to its Linux-based distribution. “Just over four months ago we announced elementary OS 6 Odin with new ways to be in control and express yourself, a slew of innovative new features, and a focus on gettability and inclusivity,” elementary founder and CEO Danielle Foré writes. “So far, OS 6 has been downloaded from our website over 250,000 times, and as always, that’s not including downloads from third parties or direct downloads via torrent that bypass our download page.” Elementary OS 6.0 was released back in August, and since then, the firm has supported it with monthly OS updates. But elementary OS 6.1—codenamed Jólnir—is a bigger functional update for existing users that combines the changes in the previous monthly updates and adds new features that focus on addressing feedback, adding office productivity functionality, and expanding hardware compatibility. # § BSD⠀➾ # ⚓ Clang_upgraded_to_version_13⠀⇛ After much preparatory work in base and ports, clang(1) has been upgraded to version 13.0.0 (on the relevant platforms). # § Arch Family⠀➾ # ⚓ Arch_No-Systemd_…_yes_but_how?_Is_systemd_so different_than_ALL_the_other_inits?⠀⇛ So where are we in the struggle against IBM domination? Ground zero, we are just starting to realize the task involved in achieving something of substance.. While we are contemplating how to attack the monster more and more upstream is getting comfortable taking it for granded, that if it is linux as the end user, systemd, libs, logind, udevd, are all there, so don’t bother writing something more generic and unix like in nature. It is in ALL LINUX … now and it will be more and more later. # § IBM/Red Hat/Fedora⠀➾ # ⚓ Prevent_auto-reboot_during_Argo_CD_sync_with_machine configs_|_Red_Hat_Developer⠀⇛ Nodes in Red Hat OpenShift can be updated automatically through OpenShift’s Machine Config Operator (MCO). A machine config is a custom resource that helps a cluster manage the complete life cycle of its nodes. When a machine config resource is created or updated in a cluster, the MCO picks up the update, performs the necessary changes to the selected nodes, and restarts the nodes gracefully by cordoning, draining, and rebooting them. The MCO handles everything ranging from the kernel to the kubelet. However, interactions between the MCO and the GitOps workflow can introduce major performance issues and other undesired behavior. This article shows how to make the MCO and the Argo CD GitOps orchestration tool work well together. # ⚓ Exploring_new_opportunities_in_open_source:_From_RHEL user_to_quality_engineer⠀⇛ Red Hat’s Products and Technologies organization is doing game-changing work in the IT industry, so we’re taking a closer look at some of the talented Red Hatters from around the world who are enabling our continued evolution. In showcasing their unique stories, it’s clear that there’s no one path to finding success as a Red Hatter. For each of us, it’s about open collaboration and building something together. As a principal software quality engineer in Beijing, Red Hatter Shi Wei often sees how his role impacts the company. “Each year at Red Hat Summit, there are usually one or two presentations that are directly related to a project I’m working on, which makes me feel that my daily work is closely related to Red Hat’s success. It’s nice to feel like a part of that.” Even before joining the company, Wei was a part of the open source community. “My Linux journey started with Red Hat. I clearly remember using my first Linux distribution—Red Hat Linux 9—for the first time. It really made an impact on my career path. In my previous position, I was an operations and maintenance engineer, working on Unix business support systems for a telecommunications provider. My whole career has been about Unix and Linux. So, when I joined Red Hat, I was excited to be a part of the team behind these products.” # ⚓ 8_ways_to_enjoy_the_holidays_with_your_team⠀⇛ When I first started my company, I didn’t know what I was getting myself into. I’d never built a startup or run a nonprofit before. But the pandemic had just begun, and I knew I needed to do something to help the 40 percent of Americans who couldn’t afford a $400 emergency long before COVID-19 further destroyed our social safety nets. So I reached out to my neighbors, my co- workers, and my friends of friends. A few weeks in, we secured a team of more than 30 passionate individuals who worked on nights and weekends building a functioning platform to help the people who needed it most. Everyone was remote, and everyone was a volunteer, so I learned quickly that building a community online was not only harder than doing so in an office, but that it was even more important. Community is what makes the late nights easier. It’s what helps us show up for each other on the tough days. And it’s what allows us to celebrate all of our wins, whether it’s a successful campaign or helping a neighbor, even from afar. # ⚓ Digital_transformation:_4_tips_to_speed_your_progress |_The_Enterprisers_Project⠀⇛ While digital transformation has been an IT industry priority for years, the pandemic accelerated the transition. Companies looked to run operations from anywhere and anytime, increase nimbleness, and build protection from disruption. Remote work and contactless retail transactions are two prime examples. While the operational impact of the pandemic is slowly waning, it’s clear that many attitudes and expectations have permanently shifted for both employees and customers. Shoppers, for example, now expect a seamless experience between online and in-store buying – and many prefer the convenience of curbside pickup. Employees have proven their ability to work and remain productive from anywhere and anytime with connected devices, applications, and connectivity. All of this means that the strong demand for digital transformation isn’t lessening. Organizations should be examining all aspects of their operations for opportunities to enact digital change that can unlock benefits for employees and deliver valuable interactions and experiences for their customers. # ⚓ AlmaLinux_Announces_Codenotary_As_Its_First_Platinum Member⠀⇛ AlmaLinux OS Foundation has announced that Codenotary has joined its governance board as the first Platinum member. As a former CentOS user, Codenotary is investing in AlmaLinux to support its growth. o § Devices/Embedded⠀➾ # ⚓ Edge_AI_system_combines_octa-core_Arm_SoC_with_Hailo- 8_NPU⠀⇛ Axiomtek’s rugged “RSC100” edge AI system runs Linux on an octa-core Arm processor accompanied by a Hailo-8 NPU. Highlights include 4GB LPDDR4, 16GB eMMC, 2x GbE, 2x CAN, 2x mini-PCIe, and 2x M.2. Axiomtek announced the latest embedded computing vendor to bundle Hailo’s up to 26-TOPS, 3-TOPS per Watt Hailo-8 NPU. The compact, fanless RSC100 (Plato) embedded computer runs Yocto 3.0 on an unnamed, octa-core Arm SoC and is designed for edge AI applications including “smart” city, retail, agriculture, and transportation. # § Open Hardware/Modding⠀➾ # ⚓ Monitoring_the_vintage_server_room_(and_reverse- engineering_USB_sensors)⠀⇛ Part of the task of any home server room, vintage or otherwise, is monitoring. After all, you’re now your own L1, L2 and L3 support. A camera passively observes the room that can be remotely viewed. The main server can generate alerts if it fails over to a UPS (power outage, blown supply, etc.). If the WAN connection goes down, an SMS gateway can communicate with me by text message and I can query it about the state of the internal network. I use an SMSEagle for that, basically a Raspberry Pi in a cool case with an LTE modem running modified Raspbian (which I naturally have modified further). All of the systems can send it alerts for broadcast via its internal APIs. # ⚓ Raspberry_Pi_Weekly_Issue_#380_–_More_Raspberry_Pi hardware_in_space⠀⇛ Tomorrow, 21 Dec, new Raspberry Pi hardware is due to launch to the International Space Station. It will let young people run a greater range of experiments in space as part of the Raspberry Pi Foundation’s Astro Pi programme. You can watch live. # ⚓ My_Fairphone_App:_Your_digital_sustainability_tool_– Fairphone⠀⇛ I’d like to kick things off with a quote from tech reviewer Marques Brownlee: “We only have one earth. Hot take – we should be taking better care of it!” For the better part of a decade, we’ve worked to normalize this idea in the electronics industry. However, when your goal is to set new standards and reshape an entire industry, you’re looking at a long road ahead. There’s never been another traveller on this road, and it’s up to us to count the miles, remember the bumps and know that this is how change happens: a crazy, impossible thing simply gets done. And in doing so, proves that the people who believe in impossible things aren’t crazy at all; they just choose to see a little further down the road. So, here’s something new for everyone who’s along for this ride: We’ve completely redesigned the My Fairphone App, from the ground up, to be your individual guide to a more sustainable lifestyle. Track and reduce your CO2 emissions, get to know your Fairphone and everything that happens behind the scenes, connect with like-minded people and sustainable businesses in your area or join our green challenges. The app is available for download, so you’ve got two options: Give it a go right now and see for yourself, or stick around for an overview of the updated features. o § Free, Libre, and Open Source Software⠀➾ # § Web Browsers⠀➾ # § Mozilla and Tor⠀➾ # ⚓ Debian_11.2_ships,_but_there_are_still_Firefox problems.⠀⇛ Yesterday, Debian released the 11.2 update. Notably missing is Firefox 91.x ESR, which replaced Firefox 78 ESR upstream months ago. It’s available, but masked. I had to use a special command to bring it in. sudo apt-get -t=bullseye install firefox-esr At this point, the security situation has gone from bad, to seriously bad. There are now 17 unpatched CVEs (some of which have multiple actual defects attached to them) which affect Debian 11’s Firefox 78.15 ESR, which has been unmaintained for over 2.5 months. If anyone is still using this, they need to move over to a browser which is current with its security patches. Debian has been bumping WebkitGTK, so GNOME Web is safe to use (or you can install it from Flatpak), and Brave bumps their browser to be in line with Chromium’s latest updates. The fact is that this is mostly Mozilla’s fault because they chose to depend on an entirely new version of Mesa out of nowhere in the middle of an ESR series. Firefox ESR 91.2 would have built on Debian 11, but Firefox 91.3+ needs new system packages. But the fact remains that Debian _chose_ to depend on Firefox, they _chose_ to make it their default browser even though Mozilla has gone insane and nothing they release is stable, so Debian owns this mess. # ⚓ New_Release:_Tor_Browser_11.0.3⠀⇛ Tor Browser 11.0.3 is now available from the Tor Browser download page and also from our distribution directory This release updates Firefox to 91.4.1esr and picks up a number of bug fixes. In particular, this release should fix various extension related and crash issues Windows users were experiencing. Additionally, Linux users especially on Ubuntu and Fedora systems were reporting fonts not properly rendering, which should be solved by this release. # ⚓ Tor_in_2022⠀⇛ It has become a tradition for me to write a blog post at the end of each year, sharing my vision for the Tor Project for the upcoming year. Before talking about what I see for us in 2022, I want to reflect on 2021 and how this has been a year of resilience for Tor. I’m very proud of every single person who contributed to Tor, the Tor Project staff, our core contributors, our community, and our supporters. 2020 was a year of sacrifice, but none of the stones thrown in our way stopped us from looking ahead and dreaming of a greater future. And in 2021, we bounced back to continue to shape this greater future. # ⚓ My_Firefox_bookmarklet_to_see_links_I’ve visited_more_reliably⠀⇛ I want to make links that I’ve already visited be clearly visible in Firefox, so that I can avoid re-reading links that I’ve already read. My first solution to this was to use the Firefox Stylus addon to write a brute force rule for frequently visited sites, which forced the a:visited colour to the special ‘VisitedText’ colour that Firefox provides. Later, when I wrote about bookmarklets versus addons, it occurred to me that a bookmarklet was a great use for this in general; I don’t always need it and don’t necessarily want it, but a bookmarklet would let me try to fix sites with a click and then said I didn’t know enough to write it. In a comment on that entry, seth shared a bookmarklet to do a large scale restyling. I took that and turned it into a simpler version that duplicated my Stylus effort. # § Education⠀➾ # ⚓ Why_R?_2021_Conference_Summary⠀⇛ The fifth edition of Why R? Conference (2021.whyr.pl) finished last week. The post presents the highlights of the conference and the overall summary. You can find all videos from the conference on youtube.com/ WhyRFoundationVideos channel. Numbers Sponsors Keynotes Discussion Panels People behind the scenes What’s next? – Webinars! Donate # § FSFE⠀➾ # ⚓ Fernanda_Weiden,_Google,_FSFE_&_Wikipedia_vanity pages⠀⇛ Fernanda Weiden (nanda) has a vanity page in Wikipedia. Weiden is a Brazilian/German system administrator. She currently works for Facebook, the page history tells us somebody created the page in 2006 during the time Weiden worked for Google. There is an alert about notability on the Talk page but nobody has acted on it. The user who created Weiden’s vanity page is Tobias Conradi, banned indefinitely for having multiple accounts. Wikipedia has a policy on notability. Women like Frances Haugen, the Facebook whistleblower who testified before the US Congress and Timnit Gebru, the ethics boss sacked by Google are notable. The actions of Haugen and Gebru are brave and commendable. In the absence of such actions, people make crude and derogatory speculation about how Weiden attended a number of tech conferences, showed her belly button (photo) and Wikipedia bosses allowed her to break the rules. # § FSF⠀➾ # § Licensing/Legal⠀➾ # ⚓ TikTok’s_new_Live_Studio_app_allegedly_violates OBS’_licensing_policy⠀⇛ Ben Torell, the business developer for OBS, later replied to that tweet in agreement, but noted that OBS is open to working with TikTok: “We have a commitment to dealing with GPL violations in good faith, and in the case of TikTok/ByteDance we would be happy to have a friendly working relationship with them as long as they comply with the license.” The Trump Media and Technology Group (TMTG) got in trouble for a similar reason in October, as it failed to make the source code for Truth, Donald Trump’s upcoming social network, publicly available after using the open-source Mastodon to build the site. # ⚓ Beware_The_CopyLEFT_Trolls [Ed: Corbet adds: “Techdirt looks at the problem of copyleft trolls, and those who target users of Creative Commons materials in particular.”]⠀⇛ For years we’ve covered the problems of copyright trolls — abusive schemes in which aggressive lawyers and schemers leverage copyright to shake down hundreds or thousands of people over what may be accidental or incidental infringement. In some cases, copyright trolls have gone even further, deliberately seeding their own works in order to find people to demand money from. # § Openness/Sharing/Collaboration⠀➾ # § Open Data⠀➾ # ⚓ xj_—_HTML_to_JSON⠀⇛ This, xj, is a Unix filter that reads XML (or permissively parses HTML) and outputs JSON. Perfect for piping directly into jq, gron or json2tsv. # § Programming/Development⠀➾ # ⚓ What_Are_the_Best_Programming_Languages_for_Linux Devs?⠀⇛ If you are on the path to becoming a Linux developer, surely you will understand that computer science and programming are a core part of this journey. Even though Linux holds a small market share compared to others, it’s a great operating system with automation capabilities, access to devices and software endpoints via the command line because everything is a file. Also, more than half of OS that run the majority of servers are Linux. But if you want to write software for Linux, not just use it, you need to learn a suitable language. So the question is, which language or languages should you learn in order to propel yourself forward in your beginning career and deepen your understanding of the Linux world? Let’s take a closer look! # ⚓ The_Essential_AI_Frameworks_You_Should_Know_– Embedded_Computing_Design⠀⇛ Open Source frameworks are open source software, that is, the source code that composes it is published openly, under a free use license that allows people who use it to use and modify it without having any type of license for Copyright. This means that a developer can use an open source code and use it in the same way, reduce it, modify it, and improve it. They are based on the collaborative methodology. # ⚓ OBS_Studio_and_dependencies_compiled⠀⇛ I installed the last three in a running Easy, but not libglvnd as it has libraries that conflict with the mesa package. I read somewhere that it is a dependency, but I don’t understand what it does. Anyway, left it out. OBS Studio version 27.x requires wayland, or at least the wayland libraries even if you are not using wayland. So I chose 26.1.2, and it compiled fine, no issues. Runs also. It checks out the host system capabilities at first startup, and the only thing that failed was “Checking if mpv can decode to png: fail”, but success with mpv decoding to jpeg. I don’t know if that will be an issue in practice. # § Perl/Raku⠀➾ # ⚓ Day_20_–_Create_beautiful_text_charts_–_Raku Advent_Calendar⠀⇛ Every number corresponded to the gifts wrapped by every elf in the department in alphabetical order, starting with Alabaster Snowball, and continuing with Bushy Evergreen. But numbers don’t sing, and that made Santa not sing either. A simple way to check visually what was going on was needed. # § Shell/Bash/Zsh/Ksh⠀➾ # ⚓ Backlog:_Language_FAQs⠀⇛ I’d like to answer these questions more authoritatively, but the “narrative style” with links has proven effective. And most topics came from reader questions anyway. Leave a comment if anything is unclear! # § Java⠀➾ # ⚓ The_Real_Fix_for_Log4j_Isn’t_a_Patch.⠀⇛ The log4j exploit requires unrestricted outbound traffic. Again, we’re not there yet – few organizations have outbound whitelists for every service, and in many cases, we don’t have the right architecture to isolate certain restrict different parts of the same process (e.g. first-party application code should be able to reach out to the [Internet], but third-party libraries like loggers should not). # ⚓ Log4j_flaw_needs_immediate_remediation⠀⇛ After nearly two years of adopting major network and security changes wrought by COVID-19 and hybrid work, weary IT network and security teams didn’t need another big issue to take care of, but they have one: Stemming potential damage from the recently disclosed vulnerability in open source Java-logging Apache Log4j software. Log4j or Log4Shell has been around a long time—it was released in January, 2001—and is widely used in all manner of enterprise and consumer services, websites, and applications. Experts describe the system as an easy-to-use common utility to support client/server application development. # ⚓ Guide:_How_To_Detect_and_Mitigate_the_Log4Shell Vulnerability_(CVE-2021-44228_&_CVE-2021-45046)⠀⇛ A few days ago, a serious new vulnerability was identified in Apache log4j v2 and published as CVE-2021- 44228. We were one of the first security companies to write about it, and we named it “Log4Shell”. * § Leftovers⠀➾ o § Science⠀➾ # ⚓ WTF_happened_to_John_Ioannidis_revisited:_The_Carl_Sagan effect⠀⇛ Earlier this month, I noted the publication of an article by John Ioannidis, Alangoya Tezel, and Reshma Jagsi that caught my interest in BMJ Open, the BMJ’s open-access journal. Titled, Overall and COVID-19-specific citation impact of highly visible COVID-19 media experts: bibliometric analysis. To boil the paper down to its essence, Ioannidis examined the citation impact in the scientific literature of “highly visible COVID-19 media experts” in the US, Denmark, Greece, and Switzerland and concluded that most were not highly cited overall and few had published much on COVID- 19 in particular. It’s a terrible analysis for the simple reason that its premise is flawed to the point where the results are, in essence meaningless, as I will explain. However, I did see this article as a good launching off point, a “teachable moment” if you will, to discuss science communication in the age of the deadliest global pandemic in over a century. Ioannidis was once one of my scientific heroes but since COVID-19 hit has disabused me of any previous hero worship, likely forever, although, truth be told, I had intermittently been unimpressed with his takes dating back years. In any event, this paper, published in late October but only seemingly finding an audience on social media last week (which is how I became aware of it) illustrates a problem that all of us who try to communicate science and medicine to the public face. o § Education⠀➾ # ⚓ Reflections_On_An_Academic_Life⠀⇛ For this reason I have been paying close attention to what is happening in China in recent years because it is there that some of the most obvious contradictions of sustaining capitalism are playing out before our very eyes. Global capital was saved from a grand depression in 2007–2008 by the huge expansion of urban and infrastructural investment in China. This stimulated a massive demand for raw materials such that producers in Latin America, South Asia, and Australia could exit crisis conditions very quickly. In the same way that Haussmann had helped Louis Bonaparte solve the economic problems of 1848–1850 through the rebuilding of Paris, and Robert Moses had done much the same for the United States after 1945 in creating metropolitan regions around strong processes of suburbanization, so the Chinese did something similar but at an unprecedented scale that had them consuming more cement between 2012 and 2014 than the United States had consumed in the preceding 100 years. Cement production, it also turns out, is a major source of greenhouse gas emissions! # ⚓ Purdue_President_Condemns_Tactics_Used_to_Censor_Chinese Students_on_U.S._Campuses⠀⇛ The letter from Purdue University President Mitch Daniels last week was unflinching, unapologetic and unusual. In a Dec. 15 letter to faculty, staff and students, Daniels described his regret that he’d had to learn from a ProPublica article that a Chinese graduate student had been harassed by other Chinese students and that his parents in China had been visited by the Ministry of State Security — all because the graduate student had spoken out “on behalf of freedom and others martyred for advocating it.” # ⚓ University_president_warns_Chinese_students_not_to_harass other_Chinese_on_campus⠀⇛ A U.S. university president who is a former governor of Indiana has condemned Chinese nationalist students in his state who harassed a Chinese pro-democracy graduate student for openly praising Tiananmen Square protesters. Mitch Daniels, president of Purdue University, a public land-grant research university in West Lafayette, Indiana, sent an email to members of the campus community on Wednesday, saying that the treatment of the student, Kong Zhihao — whom Daniels did not name in the message — was “unacceptable and unwelcome.” The incident stems from a November report by the U.S. media organization ProPublica about how the Chinese government is threatening Chinese students at American universities who openly criticize Beijing, and harassing their families back home. o § Hardware⠀➾ # ⚓ 9_Best_Laptops_for_Car_Tuning_in_2022⠀⇛ Just like you know what setting would work best when tuning a car, we know what laptop would work smoothly or efficiently with the software solutions you’ll use. In case you trust us already, then you can jump to the list. If not, read the minimum and recommended specs we followed to find out good- quality laptops that’ll suit your tuning work. # ⚓ Forget_RGB,_this_E-Ink_monitor_focuses_on_16_eye-pleasing shades_of_gray⠀⇛ Dasung says that the screen has zero flickering and does not emit blue light, instead using a more old- fashioned front light to illuminate its surface (again, very much like some e-reader designs). While the refresh rate isn’t specified, the display can operate in text, graphic, or video modes, with the company boasting a “turbo” system for high- speed refresh and low latency. Presumably no matter how fast the E-ink panel is going, it’s somewhat less than the standard 60 hertz, but it’ll make reading PCWorld reviews amazingly comfortable. o § Health/Nutrition/Agriculture⠀➾ # ⚓ Emerging_Omicron_Variant_Has_Health_Officials_Urging_World Vaccination⠀⇛ # ⚓ “Get_This_Thing_Out_of_My_Chest”⠀⇛ For the roughly 2,000 Americans who rely on it to keep their hearts going, the implanted pump is impossible to ignore. They feel it pressing inside their ribs when they lean over. Or they ache from the weight of its controller strapped to their shoulders. Some can even hear the device’s whirring hum deep inside their chests. # ⚓ Trump_White_House_Deliberately_Undermined_Efforts_to Contain_COVID,_Report_Says⠀⇛ # ⚓ Covid_Testing_Rackets_and_Flying_Again⠀⇛ The passengers on this Melbourne to Brisbane flight were taking a moment to compose themselves.  The customary hard cushion seating, cool, slightly refrigerated, touched the skin, imposing itself upon the visitor.  The cafeteria, plastic tray tables that must be put up prior to lift-off and descent.  The sardine can phenomenon of being kept close and packed.  The mandatory wearing of fitted facemasks, a rule constantly subverted by people nibbling snacks or sneaking a drink or too.  People were flying again. The mother and her child were awaiting to travel to the Queensland capital.  She, weary and bleary- eyed, seemed fascinated with another toy her son had also taken on as hand luggage: a classic example of macho moronic strength, an elastic muscle man who could be abused and distorted into any shape of your preference.  “Look,” she squealed, “I can tie his arms up.”  Just what a traveller needs: a bit of cruelty inflicted on a plastic figure by a desperate human. # ⚓ Dr._Carlos_del_Rio_on_Omicron_Surge,_COVID_Testing_Crisis_& the_Need_to_Vaccinate_the_World⠀⇛ With the emergence of the highly transmissible Omicron variant, the United States is now averaging over 130,000 new COVID-19 cases a day, and health officials warn the U.S. could see a million new cases a day by February. We speak with health expert Dr. Carlos del Rio, who says that vaccination complemented by booster shots is the best defense against severe illness. “Everybody’s going to get infected. You’re going to be exposed to this virus because it’s essentially going to be everywhere,” says del Rio. # ⚓ Most_of_Illinois_is_vaccinated,_daily_cases_more_than double_from_last_month,_while_state_officials_celebrate_the third_year_of_“15_days_to_slow_the_spread”.⠀⇛ With most of Illinois vaccinated and daily cases more than doubled from a month ago, state officials celebrate the third year of 15 days to slow the spread. [...] They’ve managed to figure out that their business model is fucked from a social disease but they offer to segregate the vaxxed from the unvaxxed because you feel safer if you’re in a room exclusively with people who are vaxxed but can spread it anyway and are just as contagious. o § Integrity/Availability⠀➾ # § Proprietary⠀➾ # ⚓ The_Extortion_Economy_Podcast:_Exploring_the_Secret World_of_Ransomware⠀⇛ Ransomware is proliferating across the country, disabling computer systems and harming critical infrastructure — hospitals, city governments, schools, even an oil pipeline. The technology that enables ransomware may be new, but extortion and ransom are not. # ⚓ Nokia_wins_5-year_nationwide_5G_RAN_deployment_deal from_Elisa_Estonia⠀⇛ Finnish telecom equipment maker Nokia Monday said it has been selected by Elisa Estonia, a subsidiary of Elisa Finland, for nationwide 5G Radio Access Network (RAN) deployment. Nokia will also replace the existing 4G infrastructure under the five-year deal. Under the deal, Nokia will provide equipment from its ReefShark System on Chip (SoC)- powered AirScale equipment portfolio covering Elisa’s nationwide radio network across the country. Deployment is expected to roll out next year following the completion of Estonia’s spectrum auction in early 2022. # ⚓ The_smart_way_to_switch_to_a_new_Android_phone⠀⇛ Here’s how to transfer data, apps, contacts, and more from your old Android phone to a new one, along with tips for a smooth transition. # § Security⠀➾ # ⚓ Security_updates_for_Monday⠀⇛ Security updates have been issued by Debian (apache-log4j2, firefox-esr, libssh2, modsecurity-apache, and tang), Fedora (lapack, log4j, rust-libsqlite3- sys, rust-rusqlite, xorg-x11-server, and xorg-x11-server-Xwayland), Mageia (bind, botan2, chromium-browser-stable, dovecot, hiredis, keepalived, log4j, matio, mediawiki, olm, openssh, pjproject, privoxy, vim, and watchdog), openSUSE (barrier, nim, and python- pip), Oracle (ipa and samba), Scientific Linux (ipa and samba), SUSE (log4j), and Ubuntu (apache-log4j2, htmldoc, python3.6, python3.7, python3.8, and python3.8, python3.9). # ⚓ Yes,_fun_browser_extensions_can_have vulnerabilities_too!⠀⇛ What’s the worst possible vulnerability a browser extension could possibly have? If the extension connects to a local application, facilitating Remote Code Execution in that application would be pretty bad. But if it’s only the sandboxed browser extension, then granting attackers access to each and every website is probably as bad as it goes. The only way to top this should be making the access permanent, surviving even a browser restart. Somehow the fun browser extension “Meow, The Cat Pet” ended up in that exact spot. Despite having merely 200 thousand users, it is promoted prominently in the “Fun” category of the Chrome Web Store. Yet up until recently it had a Cross-Site Scripting vulnerability. This vulnerability would have allowed any website to inject JavaScript code which would have executed in the context of websites visited by the user. A one-time visit to a malicious website would have been sufficient to compromise the browser integrity permanently. # ⚓ More_on_NSO_Group_and_Cytrox:_Two_Cyberweapons Arms_Manufacturers⠀⇛ Citizen Lab published another report on the spyware used against two Egyptian nationals. One was [cracked] by NSO Group’s Pegasus spyware. The other was [cracked] both by Pegasus and by the spyware from another cyberweapons arms manufacturer: Cytrox. # ⚓ WordPress_5.8.2_Debian_packages_–_Dropbear⠀⇛ After a bit of a delay, WordPress version 5.8.2 packages should be available now. This is a minor update from 5.8.1 which fixes two bugs but not the security bug. # § Privacy/Surveillance⠀➾ # ⚓ Boston_City_Councilors_Seek_Review_of Surveillance_Tech_Purchase_by_Police⠀⇛ Boston city councilors are calling for a review of the city Police Department’s purchase of controversial surveillance technology, after an investigation by WBUR and ProPublica revealed the transaction, which had been hidden from public view. Councilor At-Large Julia Mejia said the Boston Police Department should stop using its cell site simulator, or “stingray,” which can track real-time cell phone location, until a public hearing can be held to learn more about the use of the device and how it was purchased. Critics have suggested the technology could threaten constitutional rights, and members of Congress have called for measures to restrain its use. # ⚓ Govt_Panel’s_Report_on_Data_Protection Bill_Recommends_Tougher_Norms_for_Social Media_Platforms⠀⇛ The report, however, did not recommend any major dilution of the contentious exemption clause, which gives powers to the government to keep any of its agencies outside the purview of the law. # ⚓ House_report_on_data_bill_tabled, Opposition_flags_concern_|_Latest_News India_–_Hindustan_Times⠀⇛ The report of the joint parliamentary committee studying the proposed data protection law was tabled in both houses of parliament on Thursday, after almost two years of deliberations, but continued to cause concern among civil society members and opposition leaders that the proposals will be inadequate in protecting individual privacy and give the state far-reaching powers. The report carries several suggestions that in effect give the government a wider berth on obligations and private companies a stricter guardrail to follow, as reported by HT on November 23, while also suggesting new mechanisms to regulate social media companies. Among some of the new proposals is a plan to “age-gate” content and access to digital services for children, requiring companies to appoint guardians of data and needing those that deal primarily with services for children to to register themselves with the government. # § Confidentiality⠀➾ # ⚓ Open_Source_Pwned_Passwords_with FBI_Feed_and_225M_New_NCA_Passwords is_Now_Live!⠀⇛ In the last month, there were 1,260,000,000 occasions where a service somewhere checked a password against Have I Been Pwned’s (HIBP’s) Pwned Password API. 99.7% of the time, that check went no further than one of hundreds of Cloudflare edge nodes spread around the world (95% of the world’s population is within 50ms of one). It looks like this: [...] o § Defence/Aggression⠀➾ # ⚓ Opinion_|_The_Pentagon’s_20-Year_Killing_Spree_Has_Always Treated_Civilians_as_Expendable⠀⇛ Top U.S. officials want us to believe that the Pentagon carefully spares civilian lives while making war overseas. The notion is pleasant. And with high-tech killing far from home, the physical and psychological distances have made it even easier to believe recent claims that American warfare has become “humane.” # ⚓ Pakistan_is_opening_a_dangerous_Pandora’s_box_with_the Taliban⠀⇛ Discourteous remarks about Afghanistan made by Pakistani Prime Minister Imran Khan at the recent Organization for Islamic Cooperation (OIC) meeting were an insult to the Afghan nation reeling from the Taliban takeover. In his remarks, Khan described the non-monolithic Taliban group as a predominately ethnic Pashtun movement, implicitly casting millions of Pashtuns as the Taliban’s adherents. The prime minister, meanwhile, said girls’ education is antithetical to Afghan values and went on to discuss “Islamophobia” in the West — an epiphenomenon supposedly linked to the recent refugee influx, which Khan wants to champion as a savior. For Pakistani leaders, such calculated tirades are no accident. These recurring talking points are indicative of Pakistan’s long-running designs to create a new, false narrative about post-American Afghanistan. With the Taliban’s victory, Pakistan no longer makes secret what it wants in Afghanistan, a country which Islamabad now treats as an extension of Pakistan. # ⚓ Hong_Kong:_Pro-Beijing_candidates_sweep_‘patriot’-only election_amid_low_turnout⠀⇛ All candidates were also vetted by a largely pro- Beijing committee before they could be nominated. # ⚓ Uganda_buys_Chinese_arms_for_war_on_ADF⠀⇛ The Independent has established that globally renowned Chinese military contractors are working with Uganda Peoples Defence Forces (UPDF) and could make a difference in taking the battle to the ADF. An investigation by The Independent has so far yielded two names of major Chinese contractors that have recently supplied the UPDF; China North Industries Corporation (Norinco) and Poly Technologies Inc. # ⚓ Mosul_museum_restores_artefacts_destroyed_by_Islamic_State jihadists_in_Iraq⠀⇛ Ancient artefacts in the museum were smashed into little pieces when Islamic State group fighters seized the northern city of Mosul in 2014 and made it their seat of power for three years. o § Environment⠀➾ # ⚓ 9_Don’t-Miss_Environmental_Interviews_of_2021⠀⇛ # § Energy⠀➾ # ⚓ ‘Speed_Bump_on_the_Road_to_Climate_Catastrophe’: Critics_Warn_Biden_Car_Emission_Rules_Not_Enough⠀⇛ Finalized rules targeting emissions from cars and light trucks announced by the Biden administration Monday drew tepid welcome mixed with rebuke from climate groups who said the new standards, while an improvement, fail to meet the urgency of the planetary crisis. “Storms, wildfires, and heatwaves have grown far worse over the past decade, so auto pollution rules must be far stronger.” # ⚓ Ground_Flare_At_Mammoth_New_Exxon_SABIC_Plastics Plant_Likened_to_A_Harmless_‘Barbecue’_In_Corporate Video⠀⇛ This story is part of a collaboration between DeSmog and Public Health Watch. “The normal flare plus the BBQ is on,” Elida Castillo, the program director of Chispa Texas, an environmental advocacy group, wrote to me in a text on December 6. It was an update about a new, giant plastics plant built on the line between two small Texas cities just northeast of Corpus Christi: Portland and Gregory. # ⚓ The_New_Get-Rich-Faster_Job_in_Silicon_Valley:_ [Cryptocurrency]_Start-Ups⠀⇛ Ms. Carter is part of a wave of executives and engineers leaving cushy jobs at Google, Amazon, Apple and other large tech companies — some of which pay millions of dollars in annual compensation — to chase what they see as a once-in-a-generation opportunity. That next big thing is [cryptocurrency], they said, a catchall designation that includes digital currencies like Bitcoin and products like nonfungible tokens, or NFTs, which rely on the blockchain. # ⚓ [Old] Bitcoin_energy_consumption_worldwide_from February_2017_to_October_19,_2021⠀⇛ Bitcoin’s annualized footprint in electricity consumption reached an all-time high in June 2021, now believed to be higher than the power consumption of Finland. This according to a source that tries to estimate the energy consumption of both Bitcoin (BTC) as well as Bitcoin (BTH). It does by assuming that miner costs and income are the same thing: The higher the miner income, the more powerful machinery it can support. Essentially, the source first calculates how much miners earn, then estimates how much of this income is spent on electricity and how much per kWH, to finally be converted into consumption figures. The main reason this figure is an estimate, is due to the decentralized nature of Bitcoin or cryptocurrencies in general: There is no central authority that tracks how many computers there are or where miners submit figures. # ⚓ [Old] Bitcoin_vs._Ethereum:_Which_Uses_the_Most Power?⠀⇛ The vast amount of energy that cryptocurrencies use has long been a point of contention between enthusiasts and critics. It’s no secret that blockchain activity, from mining coins to conducting transactions, is far from eco-friendly. Some [cryptocurrencies] now use more electricity than entire cities or even countries. The two biggest players in the [cryptocurrency] game, Bitcoin and Ethereum, are both guilty of this. But which requires more energy, and is either one doing anything to improve? # ⚓ [Old] Bitcoin_used_more_power_in_2021_than_all_of 2020_as_climate_debate_on_[cryptocurrency]_mining_heats up⠀⇛ Bitcoin has already used more power so far this year than it did in all of 2020, a new study has suggested, as the debate on the impact of cryptocurrency mining on the environment heats up. Bitcoin is set to use 91TWh of energy by the end of this year, according to a Bloomberg report, which noted this is as much energy as Pakistan. Last year, Bitcoin was estimated to have consumed about 67TWh of electricity. # ⚓ [Old] Why_You’re_Paying_Bitcoin’s_Energy_Bill⠀⇛ Millions of people who have neither mined nor traded a bitcoin are nevertheless paying for bitcoins to exist. That’s because the vast computing power needed to create new bitcoins consumes enormous amounts of electricity and has driven up energy bills for residents and businesses, according to University of California at Berkeley’s Matteo Benetton and Adair Morse and Chicago Booth’s Giovanni Compiani. # ⚓ Twilight_of_the_coal_boom_as_banks_run_out_of_excuses to_fund_coking_coal⠀⇛ Coking coal is headed the way of thermal coal, despite the present frenzy in exports and coal company profits. Diplomatic tension between China and Australia, pressure to act on climate, and the rise in scrap steel recycling, mean banks are running out of excuses to finance “methane super-emitters”. Energy finance analysts Simon Nicholas and Soroush Basirat on the findings of a special investigation into recycling. # § Wildlife/Nature⠀➾ # ⚓ Squirrel_privilege_is_real:_Intergenerational_wealth drives_animal_inequality,_study_says⠀⇛ “In North American red squirrels (Tamiasciurus hudsonicus), a mother may store spruce cones on her territory and privilege her daughter by bequeathing a rich territory to her; daughters who receive these resources survive longer and reproduce earlier than those without,” the researchers wrote. They note that this squirrel privilege can perpetuate for many generations, and perpetuate what humans might call class divisions among animals. “Intergenerational transfer of material wealth can drive inequality within family lineages of animals,” the researchers wrote. # § Overpopulation⠀➾ # ⚓ More_Than_130_Groups_Call_on_CFTC_to_Shut_Down ‘Dystopian’_Water_Futures_Market⠀⇛ Warning Wall Street against commodifying what has been treated since ancient history as “a common right for everyone,” more than 130 civil society groups on Monday demanded that federal regulators shut down the Chicago Mercantile Exchange’s water futures market. Food & Water Watch organized the petition, which was sent to the Commodity Futures Trading Commission (CFTC), a year after the Chicago Mercantile Exchange (CME) opened the world’s first market for water futures contracts, based on water rights in drought- plagued California. # ⚓ Water_Scarcity_Fuels_Violence_and_Mass_Displacement in_Cameroon⠀⇛ “While over 85,000 people have fled to Chad in recent days, at least 15,000 Cameroonians left their homes but remain within their country,” UNCHR Spokesperson Matthew Saltmarsh said, adding that the figures could be much higher given that humanitarian organizations cannot easy access to the area. So far, the violent clashes have caused at least 44 deaths and more than 100 injured. # ⚓ [Old] Opinion:_Overpopulation,_not_climate_change, caused_California’s_water_crisis⠀⇛ California has grown from 10 million to at least 40 million since 1950, making it necessary to move water over long distances to where people live and work. Close to two thirds of the state’s population is bunched in a few water-dependent coastal counties. # ⚓ [Old] The_Effects_of_Overpopulation_on_Water Resources_and_Water_Security⠀⇛ As the global population is expected to keep growing in the coming decades, the negative impact that humans will have on earths finite resources, especially water, will become increasingly apparent as areas of the world will start to experience drastic shortages of water, leading to instability in food production, industry, social order, and political and military control. In order to limit the amount of chaos and conflict that will ensue over limited water resources, there needs to be compromise and cooperation between all countries, not just the nations that are water stressed, to provide water management techniques, newer and more efficient technology to conserve as much water as possible, and strict security and enforcement of all regulations to prevent groups and individuals using water to gain power. o § Finance⠀➾ # ⚓ Record-High_81_Jurisdictions_Set_to_Raise_Minimum_Wages_in 2022:_Report⠀⇛ Efforts to raise the federal minimum wage to $15 an hour may have stalled, but a report out Monday shows that a record number of states, cities, and counties are set to boost their minimum wages in 2022—an indication that grassroots organizing for a higher pay floor is continuing to bring results across the United States. “Twenty states have refused to raise their wage floors above the federal rate for over a decade.” # ⚓ Inflation_Comes_From_Printing_Money_For_The_Rich⠀⇛ In general people of all political spectrums are far to the left of most politicians in both parties. Alienation from the Democratic Party comes not from supposed neoliberalism or wokeism, the two most common tropes by the reactionary right. Rather the alienation from the Democrats comes from their commitment to the state as a means to consolidate corporate power. Many conflate this with communism, and in the context of communism being understood as state capitalism historically, people aren’t wrong. So how does a party like the Republican Party, who is so cruel towards the working class, even stay afloat? How has their extremism not collapsed on itself? If the Republicans governed on their own the country would have no function at all. Both parties know this and both use it to keep power. # ⚓ Opinion_|_A_Consumer-Free_Christmas⠀⇛ Confession time: this year, I don’t want to buy my kids anything for Christmas. Big one, right? Okay, let me soften that just a bit. I have bought a few modest, useful things. But that’s it!  No new games, no new toys, no new clothes (other than socks)… nothing. They already have too much. We have too much. Our nation is drowning in stuff and, in reality, need almost none of it. # ⚓ Warning_of_‘Humanitarian_Collapse,’_Dozens_of_House_Dems Urge_Biden_to_Unfreeze_Afghan_Funds⠀⇛ Warning that the U.S. freeze on Afghanistan’s central bank reserves and sanctions risk deadly “economic pain and humanitarian collapse,” 46 House Democrats on Monday implored President Joe Biden and Treasury Secretary Janet Yellen to “urgently” lift financial restrictions on the Taliban-ruled nation. “United Nations officials are warning that millions of Afghans could run out of food before winter, with one million children at risk of starvation.” o § AstroTurf/Lobbying/Politics⠀➾ # ⚓ Lessons_from_the_Presidency_in_the_Philippines⠀⇛ Most notably, legendary boxer and Philippine Senator Manny Pacquiao has recently filed his candidacy to run as the next president. Other candidates include Ferdinand Marcos Jr. (son of the infamous dictator), police chief Ronald “Bato” Dela Rosa, Vice President Leni Robredo, Senator Panfilo “Ping” Lacson, and Mayor of Manilla Francisco “Isko” Moreno. There is even speculation that Duterte’s daughter Sara will run as president while Rodrigo will run as her vice, despite Duterte declaring he will retire from politics. The race for presidency in the country is already producing high levels of tension and anxiety as the elected candidate could bring the country to new heights or repeat its dark and corrupt history. # ⚓ NY_AG_Letitia_James_‘Undeterred’_in_Trump_Probe_After Former_President_Sues⠀⇛ New York Attorney General Letitia James hit back at Donald Trump Monday after he sued her amid a tightening probe of his allegedly fraudulent business practices, with the Empire State’s top prosecutor reminding the twice-impeached ex- president that he is not in charge of the investigation—and that “no one is above the law.” “Neither Mr. Trump nor the Trump Organization get to dictate if and where they will answer for their actions.” # ⚓ ‘We_Will_Bury_Neoliberalism’:_Global_Celebration_Follows Leftist_Victory_in_Chile⠀⇛ Socialist Gabriel Boric’s victory in Chile’s high- stakes presidential election Sunday was hailed by progressives worldwide as an inspiring example of how a democratic groundswell can overcome deeply entrenched forces of reaction and chart a path toward a more just, equal, and sustainable future. “If Chile was the cradle of neoliberalism, it will also be its grave.” # ⚓ Progressives_Demand_Floor_Vote_to_Spotlight_Manchin’s ‘Contempt’_for_His_Constituents⠀⇛ In a letter sent to colleagues Monday morning, Senate Majority Leader Chuck Schumer (D-N.Y.) announced that “the Senate will, in fact, consider the Build Back Better Act, very early in the new year, so that every member of this body has the opportunity to make their position known on the Senate floor, not just on television.” # ⚓ “Unacceptable”:_Rep._Jamaal_Bowman_Slams_Manchin_After Senator_Says_No_to_Build_Back_Better_Plan⠀⇛ President Biden’s signature $1.75 trillion Build Back Better package appears to be dead after Democratic Senator Joe Manchin of West Virginia announced on Fox News this Sunday he would not support the plan to expand the social safety net and combat the climate crisis. Without Manchin, Senate Democrats do not have enough votes to pass the landmark legislation, which has already been approved by the House. We speak with Congressmember Jamaal Bowman, who is one of six progressive Democrats in the House who correctly predicted that his party’s decision to vote on the infrastructure bill prior to the Build Back Better package — as opposed to voting on them together — would risk throwing the $1.75 trillion package into jeopardy. “Special interests have been heavily involved in the negotiation process for Build Back Better throughout this entire year,” says Bowman. President Biden “all but promised that he would be able to deliver Manchin,” continues Bowman, “and as we can see, that has not happened.” # ⚓ There_Must_be_a_Vote_on_Build_Back_Better⠀⇛ I also find it amusing that Sen. Manchin indicates his worry about the deficit after voting just this week for a military budget of $778 billion, four times greater than Build Back Better over ten years and $25 billion more than the president requested. ⚓ As_World_Burns,_Climate_Campaigners_Denounce_Manchin_as_‘Fossil-Fueled Sociopath’⠀⇛ In the wake of Sen. Joe Manchin’s repudiation of the Build Back Better climate and social investment bill, campaigners on Monday implored President Joe Biden to take executive action to meaningfully address the planetary emergency. “At the end of the day, Manchin cares less about his constituents than he does about the fossil fuel industry.” ⚓ Sanders_and_the_Squad_Knew_Manchin_Couldn’t_Be_Trusted⠀⇛ President Joe Biden and Senate Democratic leaders were shocked when West Virginia Senator Joe Manchin screwed his fellow Democrats over on Sunday, with an announcement that, after months of tortured, behind-closed-doors negotiations, he would vote against Biden’s Build Back Better agenda. White House press secretary Jen Psaki ripped into Manchin, scorching the West Virginian for making a “sudden and inexplicable reversal in his position” and accusing the senator of a “breach of his commitments.” ⚓ Why_Spending_$2_Trillion_on_Child_Care,_Health_Care_and_Fighting_Climate Change_Won’t_Make_Inflation_Any_Worse_Than_it_Already_is⠀⇛ The Senate is currently considering a roughly US$2 trillion bill passed by the House that would spend money on health care, education, fighting climate change and much else over the next decade. But Republicans and a handful of Democrats like Sen. Joe Manchin of West Virginia argue the risk that more spending could push inflation even higher is too great. As an economist, I believe these concerns are likely overblown. Here’s why. ⚓ AOC_Warned_About_Manchin’s_Betrayal._Democratic_Leaders_Chose_to_Ridicule Her.⠀⇛ ⚓ Manchin_Says_He_Opposes_Sick_Leave_Because_People_Will_Use_It_for_Hunting Trips⠀⇛ ⚓ Displaying_‘Inhuman_Disdain’_for_Working_Families,_Manchin_Said_Child_Tax Credit_Would_Be_Used_for_Drugs⠀⇛ As 36 million families across the U.S. appeared unlikely to receive any further child tax credit payments after the New Year following Sen. Joe Manchin’s refusal to support the Build Back Better Act, progressives on Monday were outraged over reports that the threat to the payments stems from the right-wing senator’s belief that parents might use the money for drugs or other uses he deems unnecessary. According to HuffPost, before Manchin (D-W.Va.) announced Sunday that he “cannot get there” to support the $1.75 trillion investment in social spending and climate policy, the senator privately told colleagues that “he thought parents would waste monthly child tax credit (CTC) payments on drugs instead of providing for their children.” ⚓ AOC_to_Democratic_Leaders:_Time_to_‘Take_the_Kid_Gloves_Off’_With_Manchin⠀⇛ Congresswoman Alexandria Ocasio-Cortez on Monday suggested Sen. Joe Manchin’s explanation for why he’s opposing the Build Back Better Act is baseless as she called for a different “environment of pressure” by Democratic leadership to confront his obstruction. “Make him take that vote.” ⚓ Because_Manchin_Says_He_Can’t,_Experts_Explain_How_Build_Back_Better_Would Help_West_Virginians⠀⇛ Congressional colleagues and outside critics Monday continued to call “bullshit” on Sen. Joe Manchin after the West Virginia Democrat claimed his “no” vote on the Democrats’ signature Build Back Better legislation is because he finds it impossible to explain to the people in his state how it will improve their lives. In his statement on Sunday, Manchin said, “I have always said, ‘If I can’t go back home and explain it, I can’t vote for it.’ Despite my best efforts, I cannot explain the sweeping Build Back Better Act in West Virginia and I cannot vote to move forward on this mammoth piece of legislation.” ⚓ Brandon_Just_Wants_to_Drive_His_Racecar⠀⇛ But the hot slogan of the American right doesn’t turn out to be something you can easily shake off. Now Mr. Brown finds himself facing a threat to his vocation: He’s an athlete on the cusp of breaking out in a sport that relies on corporate sponsors, a group that likes nothing less than the whiff of divisive partisanship. “Our whole navigation is, you want to appeal to everybody, because, all in all, everybody is a consumer,” Mr. Brown said after our drive. “I have zero desire to be involved in politics.” He had reached out to me, through a spokesman for his team, because he realized that waiting out the storm wasn’t working. But as his name took on a new meaning, his silence on the matter seemed to be a political statement. And for most athletes these days — and many others — politics can be hazardous to your ability to make money. § Misinformation/Disinformation⠀➾ * ⚓ Buying_Influence:_How_China_Manipulates_Facebook_and_Twitter⠀⇛ Now, a new set of documents reviewed by The New York Times reveals in stark detail how Chinese officials tap private businesses to generate content on demand, draw followers, track critics and provide other services for information campaigns. That operation increasingly plays out on international platforms like Facebook and Twitter, which the Chinese government blocks at home. The documents, which were part of a request for bids from contractors, offer a rare glimpse into how China’s vast bureaucracy works to spread propaganda and to sculpt opinion on global social media. They were taken offline after The Times contacted the Chinese government about them. * ⚓ Children_barred_from_Christmas_market_and_Santa_arrested?_Nope,_these viral_stories_are_fake⠀⇛ Since early December, social media users have been sharing a photo and video that they claim show restrictive Covid safety measures taking the fun out of Christmas celebrations in Europe. But the photo and video were taken out of context to produce fake news. * ⚓ Data:_How_TikTok_Dominated_2021⠀⇛ In September, TikTok started testing an integration with Square that allows sellers to send users directly from TikTok videos to their Square Online stores. A month prior, TikTok and Shopify announced a partnership that allows users to buy products directly from select profiles for the first time. § Censorship/Free Speech⠀➾ * ⚓ Saudi_Arabia_jails_Yemeni_man_for_15_years_for_apostasy:_Human_Rights Watch⠀⇛ Human Rights Watch said on Monday a Saudi court had sentenced a Yemeni man to 15 years for apostasy, urging the kingdom to prioritise decriminalising blasphemy amid a modernisation drive. The rights group said that Ali Abu Luhum, 38, had been accused of making comments “via two anonymous Twitter accounts”, which prosecutors argued were registered with phone numbers linked to him. * ⚓ Egypt_sentences_activist_Alaa_Abdel_Fatah_to_5_years_in_prison⠀⇛ The activist, who had been previously imprisoned for five years, was a major figure in the 2011 revolution, which led to the ouster of long-time former President Hosni Mubarak who had held power for three decades. * ⚓ United_Arab_Emirates_Moves_Needle_Forward_Against_Film_Censorship_With New_Rating_Category⠀⇛ The United Arab Emirates has announced the addition of a new over-21 age classification to its motion picture rating system that could become a milestone in moving the needle against censorship across West Asia. The new rating will allow uncut versions of international movies to be shown in UAE cinemas, though details remain vague. * ⚓ UAE_halts_censorship_of_‘adult_content’_in_cinemas⠀⇛ “According to this classification, the movies will be screened in cinemas according to their international version, and the classification is given based on the standards of media content in the country.” * ⚓ Online_content_moderation:_Can_AI_help_clean_up_social_media?⠀⇛ Two days after it was sued by Rohingya refugees from Myanmar over allegations that it did not take action against hate speech, social media company Meta, formerly known as Facebook, announced a new artificial intelligence system to tackle harmful content. Machine learning tools have increasingly become the go-to solution for tech firms to police their platforms, but questions have been raised about their accuracy and their potential threat to freedom of speech. § Freedom of Information/Freedom of the Press⠀➾ * ⚓ Using_Assange_to_Send_a_Three-Part_Message⠀⇛ The first message is to people within the national-security establishment who might be tempted, out of a crisis of conscience, to reveal dark-side activities of the national- security establishment. By doing everything they could to destroy Assange’s life and even maybe bring about his death, the national-security establishment sends a powerful message to would-be leakers: “This is what will happen to you if you disclose our dark-side secrets to the American people. We will hunt you down, we will persecute you, we will prosecute you, we will destroy you, and we might even kill you.” How many people within the national-security establishment are willing to undergo that price for revealing dark-side secrets of the Pentagon, the CIA, and the NSA? I’d venture to say not very many at all. * ⚓ The_Prosecution_of_Julian_Assange_Absolutely_Threatens_Freedom_of_the Press⠀⇛ That understanding is supposed to infuse the public discourse about press freedom in the United States. But it only rarely does. Too frequently, prominent political and media voices go silent—or, at least, soft—when real fights over the First Amendment are being fought. It’s particularly concerning that there isn’t a louder outcry now, from across the political spectrum, regarding the prosecution of Assange. One notable exception is US Representative Ro Khanna, the California Democrat who has worked with US Senator Ron Wyden (D-Ore.) to address at least some of the abuses associated with the Espionage Act. * ⚓ What_the_Pandora_Papers_Mean_in_Fight_Against_Corruption⠀⇛ Reporting by the International Consortium of Investigative Journalists revealed how the files exposed the hidden offshore finances of 35 current and former world leaders, including Azerbaijan’s President Ilham Aliyev. The Azeri leader has denied any wrongdoing, telling the Italian newspaper la Repubblica that only “five percent of (the reporting) could be true, the rest is a lie.” Since the release of the Pandora Papers, investigative journalist Khadija Ismayilova has been reporting on findings related to Azerbaijan. § Civil Rights/Policing⠀➾ * ⚓ Opinion_|_CBP_Does_Little_to_Stop_Mistreatment_of_Pregnant_People_in Custody⠀⇛ * ⚓ Indian_Christians_fear_attacks_or_jail_over_conversions⠀⇛ This isn’t an isolated incident – a report by the Evangelical Fellowship of India (EFI) listed 39 cases of threats or violence against Christians from January to November this year in Karnataka. These include alleged attacks on pastors by members of right- wing Hindu groups, and even instances where they reportedly physically prevented them from holding religious services. Christians are a tiny minority in overwhelmingly Hindu India. * ⚓ Addressing_loopholes_in_digital_and_data_rights_in_Africa:_This_is_what it_will_take⠀⇛ … This year has seen several African governments clamping down on their citizens’ data and digital rights. Many have used the Covid-19 pandemic and election misinformation as reasons to infringe on these liberties, which global institutions such as the UN define as human rights. With the number of Africans connected to digital technologies growing exponentially, and an internet penetration rate of around 43% across Africa, governments, state institutions and private companies are increasingly collecting, processing and sharing data about our online activity. And while this practice itself is not nefarious, as it can help improve service delivery, across the continent, online rights are increasingly being curbed. § Internet Policy/Net Neutrality⠀➾ * ⚓ Open_RAN_Technology_Could_Play_Key_Role_in_Narrowing_Digital_Divide⠀⇛ “We are very much looking at open RAN as another tool in that Swiss army knife of connectivity solutions.” The utility of open RAN is significant, McRae said, in both low-density and urban regions alike. “We are looking at things like neutral hubs, where can we build a solution that allows multiple operators to connect in rural locations,” he said. * ⚓ What_victories_for_digital_rights_happened_this_year?_Test_your knowledge_with_this_quiz⠀⇛ In 2021, activists across the world won major digital rights victories — defending free expression, privacy, and other rights we must protect online. When governments, companies, and others infringe these rights, it affects marginalized communities the most, and inequalities are replicated in digital spaces. So while 2021 was a year of hardship — from the continuation of the pandemic to internet shutdowns that left many in the dark — we can be proud of what we achieved together. § Monopolies⠀➾ * ⚓ US_giant_Microsoft_is_accused_of_NHS_‘takeover_by_stealth’_by_elbowing UK_firms_out_of_millions_of_pounds_of_contracts_by_giving_remote-meeting software_to_the_Health_Service⠀⇛ * ⚓ UK_Government_looking_into_claims_free_pandemic_gift_of_Microsoft_Teams to_NHS_actually_an_anti-competitive_trojan_horse⠀⇛ Now the UK Government is apparently looking the gift horse in the mouth, after rivals complained that it is hurting their competitiveness. ‘This looks like “NHSwashing” to rival companies – gaining lucrative leverage over health infrastructure under the guise of charity,’ a source complained. ‘Microsoft may have claimed to save the NHS millions of staff hours – but the price will be much higher later on down the line. ‘Their licence renewals will not only be incredibly expensive. but it will be too late to find a system that is cheaper and frankly better. This “NHSwashing” is a useful distraction, but the Microsoft anti-trust case is growing.’ * § Copyrights⠀➾ o ⚓ Judge_Recommends_$83_Million_‘Piracy’_Damages_Award_Against YouTube_Rippers⠀⇛ In a detailed report and recommendation, Virginia Magistrate Judge Theresa Buchanan concludes that the RIAA is entitled to more than $82 million in piracy damages from YouTube rippers FLVTO and 2Conv. The sites and their Russian operator are liable for willful and repeated copyright infringement, which resulted in significant losses for the music industry. o ⚓ RipRequests_Dead_After_RIAA_‘Hand_Delivers’_Piracy_Cease-and- Desist⠀⇛ Last month, RipRequests, a popular Discord server specializing in music piracy, went down after receiving a complaint relating to an early leak of Adele’s album ’30′. Its operator now says that the RIAA turned up at his home this weekend to hand-deliver a cease-and-desist notice. ䷩ 𝚕𝚒𝚗𝚎 9628 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.21.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Links_21/12/2021:_GIMP_2.10.30_and_Qubes_OS_4.1_RC3⠀✐ Posted in News_Roundup at 5:26 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⠀➾ # ⚓ 5_Best_linux_distros_for_Day_Trading_(Stock_or_Forex)⠀⇛ Trading become a popular way to invest especially after COVID. However, if you are a Trader who is switching to Linux and thinking about which Linux distro you should use for stocks or Forex day trading, then here are options to consider. Well, trading can be done on any operating system even on Android or iOS; the thing which creates the problem is the availability of the Trading software for Linux OS by the brokers. Well, there are only a few brokers who offer Linux clients otherwise only for Windows. Therefore, the only solution left is either use a web-based trading platform or use Wine on Linux to install your Trafing software meant for Windows. For example, if you are a Forex trader then it is possible to easily install MT4 or MT5 on a Linux system. Hence, here is a list of Linux distributions that are popular and easy to use. o § Audiocasts/Shows⠀➾ # ⚓ MakuluLinux_Shift_Gen_2_Ubuntu⠀⇛ Today we are looking at MakuluLinux Shift Gen 2 Ubuntu. It is based on Ubuntu 21.10, Linux Kernel 5.11, and uses about 1.6GB of ram when idling. Enjoy! # ⚓ Zorin_OS_16_Lite_overview_|_Breathe_new_life_into_your_old and_low-spec_computers_–_Invidious⠀⇛ o § Kernel Space⠀➾ # ⚓ Linux_5.17_Will_Add_Ethernet_Support_For_AMD_Yellow_Carp_ (Rembrandt)⠀⇛ AMD’s Yellow Carp enablement has been going back to early summer for this next-generation APU that is better known as Rembrandt for the Ryzen 6000 mobile series. While there has already been the graphics support to land, sensor support, and various other functionality, only coming now with the next kernel cycle will be Ethernet support. Coming seemingly late compared to the other Rembrandt / Yellow Carp feature code introduced prior cycles is now having Ethernet support, especially with wired network connectivity still rather important to many users. This Yellow Carp Ethernet support doesn’t require some shiny new driver either but is being added onto the existing and-xgbe driver. As well, Yellow Carp uses an existing PCI ID (0x14b5) but requires a few changes for properly supporting. # ⚓ AVX-Optimized_SM3_Hashing_For_The_Linux_Kernel_Nets_Up_To 38%_Improvement_–_Phoronix⠀⇛ An Alibaba engineer is proposing a standalone SM3 crypto library within the Linux kernel and with optimizations for x86_64 AVX usage nets up to a 38% performance improvement for this crypto algorithm. SM3 is another Chinese hashing function standard for digital signatures and other use-cases similar to SHA256 and part of the Chinese Commercial Cryptography suite. There has been SM3 hashing code in the Linux kernel since 2017 as well as support within Arm’s TrustZone CryptoCell “CCREE” driver. # ⚓ Systemd_250_Piles_On_Yet_More_Features_With_New_Release Candidate_–_Phoronix⠀⇛ It was just over one week ago the systemd 250 release candidate was issued (along with a brown paper bag 250-rc2 fix-up release). Systemd 250 has a ton of changes for this init system and more while today systemd 250-rc3 was released with yet more changes in tow. Besides fixes and other maintenance items in systemd 250-rc3, more minor feature work has continued to land during the release candidate phase. # § Graphics Stack⠀➾ # ⚓ WXRD_Is_A_New_Wayland_Compositor_Focused_On_XR/VR Use-Cases⠀⇛ For the Valve-funded Xrdesktop has allowed GNOME and KDE desktops to be VR-aware, Collabora has been developing WXRD as a standalone Wayland compositor for XR/VR use- cases. WXRD is a standalone Wayland compositor for the xrdesktop to offer better integration than what can be achieved using the existing patches around KDE KWin and GNOME Shell integration. WXRD is built atop the wl-roots Wayland support library as well as WXRC as a Wayland XR compositor for VR headsets. WXRC hasn’t seen too much activity lately while now Collabora is pushing ahead with WXRD as the new XR/VR Wayland compositor. # ⚓ LLVM’s_HIPSPV_Coming_Together_For_AMD_HIP_To_SPIR- V_For_OpenCL_Execution_–_Phoronix⠀⇛ Last week I wrote about the interesting HIPSPV back-end for LLVM to take AMD HIP code — which generally starts off as NVIDIA CUDA code to begin with before the HIP-ification — and to be able to output that from the LLVM compiler stack as the SPIR-V intermediate representation used across OpenCL and Vulkan drivers. The goal with this is to be able to take AMD HIP code and ultimately be able to run it on Intel graphics processors but potentially other vendors/drivers too given the vendor-neutral SPIR-V. More of that HIPSPV work is now hitting mainline LLVM. # ⚓ Raspberry_Pi_“V3DV”_Vulkan_Driver_Now_Works_On Android_–_Phoronix⠀⇛ The open-source Broadcom “V3DV” Vulkan driver within Mesa that is most notably used by the Raspberry Pi can now run on Android. For those making use of Google’s Android on the Raspberry Pi 4 and newer as an alternative to conventional Linux distributions, V3DV can now work there too for providing Vulkan API support. This support now upstream in Mesa was based on earlier work by Android-RPi and Lineage-RPi developers. Some of this Android-specific support code was based as well on the open- source Intel “ANV” and Qualcomm “TURNIP” Mesa Vulkan drivers too. # ⚓ Vulkan_1.2.203_Released_With_Many_Documentation Updates,_New_Extensions ⠀⇛ Vulkan 1.2.203 is out with many fixes/updates to the specification documentation to end out the year as well as introducing three new extensions. For being just another two-week update to the Vulkan API, Vulkan 1.2.203 does come with a large number of fixes/clarifications — 11 changes stemming from internal issues and another five public GitHub issues. o § Applications⠀➾ # ⚓ The_8_Best_Open-Source_Writing_Software_for_Linux⠀⇛ Improve your writing and craft better content with these free and open-source writing apps for Linux. Writers are always looking for some exciting tools to compile their written pieces. Despite the various options in the market, there is always an ongoing need to look for open-source options, which won’t burn a hole in the pocket. If you are a Linux user, you are in luck, for there are plenty of excellent open-source apps that you can use on your machine. A majority of these apps offer premium-grade type features for free. If you’re raring to go, then check out these top open-source writing tools enlisted below. o § Instructionals/Technical⠀➾ # ⚓ ssh_authentication_using_FIDO/U2F_hardware_authenticators⠀⇛ From OpenSSH 8.2 release it supports authentication using FIDO/U2F. These tokens are required to implement the ECDSA-P256 “ecdsa-sk” key type, but some (say Yubikey) also supports Ed25519 (ed25519- sk) keys. In this example I am using a Yubikey 5. I am going to generate a non-discoverable key on the card itself. Means along with the card, we will also have a key on disk, and one will need both to authenticate. If someone steals you Yubikey, they will not be able to login just via that. # ⚓ Install_Arduino_Software_(IDE)_on_Linux_–_TREND_OCEANS⠀⇛ Arduino is open-source by design, meaning anyone can use this board architecture to design their own custom-made Arduino. It is used to create a device that can interact with the environment using sensors and actuators. Millions of boards are sold to big industries and factories every year to automate environment relative tasks. These include checking room temperature, delivering equipment using an IR sensor, etc. # ⚓ Commands_to_Check_your_Linux_Kernel_Version_– buildVirtual⠀⇛ What version of Linux am I running? Have you ever been staring at a CLI prompt wondering how to check what version of Linux or which Kernel version you are running on your Linux system? If so, read on, as we will go through a bunch of commands to show you how to get this information. # ⚓ What_Is_SSH_Tunneling_and_How_Does_It_Work?_–_ByteXD⠀⇛ In this tutorial we’ll explain how to use SSH port forwarding and create a secure tunnel over the network, i.e., SSH Tunneling. Have you ever used a VPN (Virtual Private Network)? We use VPN to access regionally restricted contents, secure browsing, and many more. VPN allows public internet users to connect to a private network and browse the internet as if they (public users) were on the private network. Thus, it is called a “Virtual” Private Network. On the other hand, SSH (Secure Shell) is a protocol that uses the client-server communication model to provide a secure channel for operating network services. SSH provides encryption and can secure any network services over an unsecured network. When we hear about SSH, we generally think of it as being a tool used for remote login and command execution. However, SSH can be used in many ways other than this – transfer files, forward local or remote ports (used as a tunnel), etc. # ⚓ Let_it_snow_’21_–_Et_tu,_Cthulhu⠀⇛ Amidst the holidays that perhaps aren’t turning out exactly as hoped, one can take comfort in small tokens of continuity – like the fact that xsnow is still being actively maintained. Thanks, everyone, for all the good software. Let’s extract the best from the year to come. # ⚓ How_to_install_Telnet_server_&_client_on_Debian_11_Bullseye linux_–_Linux_Shout⠀⇛ Telnet has been around since 1969. Telnet is originally an abbreviation for “Telecommunication Network” and describes a protocol from the TCP/IP world with which text-based commands can be executed on remote computers. Using it the user can have remote access to the remote computer using Telnet client-server architecture via IP address. A suitable telnet client is available for almost all operating systems. It is still used to configure old hardware, especially industrial and scientific devices to diagnose and resolve technical problems. # ⚓ Install_HPLIP_3.21.12_In_Fedora_/_Elementary_OS_/_MX_Linux |_Tips_On_UNIX⠀⇛ This tutorial will be helpful for beginners to install HPLIP 3.21.12 in Fedora 35, MX Linux 21, and Elementary OS 6. HPLIP – HP Linux Image and Printing, developed by HP for Printing, scanning, and faxing with HP inkjet and laser-based printers in Linux platforms. The latest version of HPLIP 3.21.12 contains new Distro support only and the hplip installer is available for download from SourceForge. # ⚓ Install_Ubuntu_20.04_|_22.04_Cloud_Image_(Minimal)_on VirtualBox⠀⇛ Do you want to run minimal Ubuntu 20.04 Cloud Image on VirtualBox? Then here is a simple and quick tutorial to do that… Ubuntu 20.04 LTS is the popular server and desktop Linux operating system, however, the standard image of it is around 1GB or more, which would not be a cup of tea forever body. Especially those who want to run Ubuntu to test some Linux server applications but without investing much hardware resources. Earlier there was minimal ISO image available by Ubuntu developers, however not after 18.04. Therefore, we have another option that is a cloud Image, available to use by cloud platforms. But we can use the same on VirtualBox and here are the simple steps to do that. # ⚓ How_to_install_Go_1.18_on_Fedora_35_–_NextGenTips⠀⇛ In this tutorial, we are going to explore how to install go on Fedora 35. Golang is an open-source programming language that is easy to learn and use. It is built-in concurrency and has a robust standard library. It is reliable, builds fast, and efficient software that scales fast. Its concurrency mechanisms make it easy to write programs that get the most out of multicore and networked machines, while its novel-type systems enable flexible and modular program constructions. Go compiles quickly to machine code and has the convenience of garbage collection and the power of run-time reflection. # ⚓ How_to_create_an_event_in_AWS_Cloudwatch_to_trigger_a Lambda_Function⠀⇛ Amazon CloudWatch Events describe changes in AWS resources. We can match events and route them to one or more target functions. CloudWatch Events come to know about operational changes as they occur, e.g. if a defined resource in the Cloudwatch Rule has been created then the rule would come to know about it and in return it will trigger a target function. Before we proceed and create an event rule, let’s understand basics of it. # ⚓ How_to_Install_Bugzilla_Bug_Tracker_on_Debian_11⠀⇛ Bugzilla is a free and open-source bug tracking system that allows us to track the bugs and collaborate with developers and other teams in our organization. It helps us to keep track of bugs, issues, and other change requests in their products effectively. It was adopted by thousands of organizations across the globe due to its robust features. It is written in Perl and uses MySQL/ MariaDB as a database backend. In this article, I will explain how to install Bugzilla on Debian 11. # ⚓ How_to_Install_Vivaldi_Browser_on_Pop!_OS_20.04_– LinuxCapable⠀⇛ Vivaldi is a freeware, cross-platform web browser developed by Vivaldi Technologies. It had grown from the downfall of Opera with many disgruntled when it changed from the Presto layout engine to a Chromium-based browser. This platform angered traditional Opera users. Since then, Vivaldi has become one of the most popular alternative Internet Browsers amongst the big three Chrome, Firefox, and Edge. Vivaldi promotes itself as a leading browser with faster navigation, clever bookmarking, more intelligent browsing, extensive tab management, and a more visual approach. In the following tutorial, you will learn how to install Vivaldi Browser on Pop!_OS 20.04 LTS. # ⚓ How_to_Quickly_Deploy_Redis_as_a_Docker_Container_– CloudSavvy_IT⠀⇛ Redis is an in-memory key-value store which can save abstract data structures with high performance. The open-source software is typically used for database, messaging, and caching functions. Docker is the leading toolkit for packaging applications into containers. It lets you isolate software components into independent environments with their own filesystem. In this guide, we’ll use Docker to quickly deploy Redis using the official image on Docker Hub. Compared to bare metal installation, Docker enables a simpler set up procedure and won’t pollute your host with new packages. Make sure you’ve got a functioning Docker installation on your host before you continue. # ⚓ How_to_Automatically_Turn_Off_AWS_EC2_Instances⠀⇛ A common use case for EC2 On-Demand and Spot Instances is using powerful machines for short- term, one-off tasks. However, if you were to leave these machines running on accident, you may end up with a very large bill. Luckily, AWS has tools to prevent that. # ⚓ How_To_Install_Centreon_Monitoring_on_AlmaLinux_8_– idroot⠀⇛ In this tutorial, we will show you how to install Centreon Monitoring on AlmaLinux 8. For those of you who didn’t know, Centreon is an open-source tool that can monitor your entire infrastructure including network, system, and application. Centreon drives business performance excellence aligning IT operations with business objectives. Using Centreon you can set notifications depending on thresholds, set email alerts, easily add any system for monitoring. 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 Centreon monitoring on an AlmaLinux 8. You can follow the same instructions for Fedora, RHEL, CentOS, and Rocky Linux distributions. # ⚓ Debug_Bash_Scripts_–_OSTechNix⠀⇛ Debugging helps you to fix the errors in your program. In this article, we will discuss various methods to debug bash scripts in Linux and Unix operating systems. o § Games⠀➾ # ⚓ Free_games_on_Linux:_How_to_start_games_from_the_Epic_Games Store_–_Market_Research_Telecast [Ed: Automated translation from German]⠀⇛ You don’t look in the mouth of a given horse: Epic Games’ strategy of expanding its user base with free games is having an effect even on many die- hard Linux gamers. A good 150 games have already gathered in this way in the author’s Epic Games account. In many cases, the collected games can also be played under Linux with the help of Wine, but a Linux version of the Epic Games Launcher is not in sight. Open source tools such as Heroic Games Launcher, Legendary or Lutris fill the gap. With the help of the compatibility layer Wine (or its Fork Proton), the tools pretend Windows games to have a suitable operating system environment. # ⚓ 80_Percent_of_Steam’s_Top_100_Games_Run_‘Nearly_Flawlessly’ on_Linux⠀⇛ Thanks to Valve’s ProtonDB compatibility layer, 80% of Steam’s top 100 games are now playable within Linux operating systems. The new milestone was achieved today and shows how committed Valve is to get as many games as possible to run on Linux from the Steam library. That’s due in no small part to the new Steam Deck running on Valve’s own Linux- based SteamOS. But the accolades don’t stop there. If you go to protondb.com you can see that 75% of the top one- thousand most popular Steam games are also playable within Linux. This means there’s a good chance most of your favorite Steam titles are probably playable on Linux already, making Linux adoption even easier than before. o § Distributions⠀➾ # § New Releases⠀➾ # ⚓ elementary_OS_6.1_“Jólnir”_Officially_Released⠀⇛ elementary unveiled elementary OS 6.1. This is the first point-release in the 6.x series. elementary OS 6.1 is based on Ubuntu 20.04.3 and powered by Linux kernel 5.11. It includes all of the monthly OS updates since the OS 6 release. # ⚓ Qubes_OS_4.1-rc3_has_been_released!⠀⇛ The third release candidate for Qubes 4.1 is here! There are no major changes to report. We’ve just focused on fixing bugs that were discovered and reported in the second release candidate. If you’re currently using either any Qubes 4.1 release candidate, a regular update is sufficient to upgrade to the latest one. Otherwise, read on for more about how to get started with testing Qubes 4.1-rc3. # ⚓ Elementary_OS_6.1_Jolnir_Released,_Adds_a_Lot_of Quality_Improvements⠀⇛ Elementary announced the availability of Elementary OS 6.1, the first point-release in the 6.x series. Here’s what’s new. Elementary OS 6.1 Jolnir has been released. It’s the follow up to Elementary 6 Odin, which released four months ago. In that time period they boasted 240,000 downloads not including torrents. Of course Elementary OS 6 users already have all the new features because this distribution is a rolling release. But for newcomers there’s a ton of new stuff to take a look so let’s begin. # ⚓ EasyOS_most_likely_staying_with_Xorg⠀⇛ Yes, unfortunately. Linux development is controlled by techies — “breaking things is the new norm”. Yes, true. I think that by the time I get to thinking of moving to Wayland, I’ll be pushing up daisies. ChromeOS, yes, watching that. Apparently there are still issues with running Linux apps. Don’t recall, think it runs Debian in a container, so the whole techie-driven ecosystem is still there. # ⚓ Little_fixes_for_3.1.17⠀⇛ Oops, the “update” script was broken. I had created a folder at ibiblio.org, amd64/ releases/dunfell/2022, thinking that in future will group the releases by year. However, that upsets the update. Have removed that folder, until I fix the script. I did an “erase session” to get rid of a lot of junk from development work, then clicked on “update” on the desktop — that’s when I discovered the problem. Now fixed, and did an update from 3.1.15 to 3.1.17. # § BSD⠀➾ # ⚓ FreeBSD_jails_made_simple_using_BastilleBSD_|_Random thoughts_of_Peter_‘CzP’_Czanik⠀⇛ I wish I had BastilleBSD twenty years ago. I had a part-time sysadmin job – running web servers. PHP started to become popular by the turn of the century. Using jails on FreeBSD seemed to be a safe environment to run PHP- enabled web servers. However, there were no tools yet to work with jails. I had to write many scripts to build and update jails. # § Arch Family⠀➾ # ⚓ 3_Best_Arch-based_Linux_Distributions_for_Everyday Desktop_Usage⠀⇛ Here I’ve created a list of the 3 best Arch- based user-friendly Linux distributions that you should try out. Arch Linux is a rolling release, bleeding edge operating system used mostly by advanced Linux users. From installing to managing, Arch Linux lets you handle everything, giving you all the power and control you’ll ever need. This is probably one of the reasons why Arch has a cult following in the Linux community. Unfortunately, Arch comes with its drawbacks in the form of the complicated installation procedure, for example. You will need also to use command line more than any other distribution. So you really want to use Arch Linux, but you are a little bit scared about its complexity? Well, then give Arch a try from a different angle. While Arch Linux itself isn’t a good pick for beginners, a lot of the distributions based on it are definitely very user-friendly. Here is a list of the 3 best Arch-based distributions to check out. # § IBM/Red Hat/Fedora⠀➾ # ⚓ Looking_at_Fedora_Linux_33_bugs⠀⇛ At Nest, I delivered a talk called “Exploring Our Bugs“. But a single snapshot isn’t very useful. Building on the work there, let’s make this a regular thing. With the recent Fedora Linux 33 end-of-life, I’ve added F33 bugs to the bug exploration notebook. Here’s a few of my key findings. # ⚓ Download_CentOS_Stream_9_ISO_or_Cloud_Image_files_– Linux_Shout⠀⇛ The next major release from CentOS Stream is here, this successor of CentOS 8 will give us a glimpse of what lies ahead in RHEL 9 for users. Here are the links to download the CentOS 9 Stream ISO Images. CentOS Stream is designed as a continuous delivery distribution to provide every single stable version of Red Hat Enterprise Linux (RHEL). It is because to make the Red Hat better and bug-free the company decided to repurpose CentOS as an upstream for its enterprise distribution. Which earlier was a downstream stable replica of RHEL and was popular among the server users because of the stability. However, as per the announcement, the packages before including in the CentOS stream will go through several series of automated and manual tests and checks to ensure that the strict standards for inclusion in RHEL are met. Also, the updates in the unreleased minor version of RHEL will be the same as the ones published in the Stream, in short, the main key of having CentOS stream by the company is to make RedHat more stable and robust. Well, this rolling release system is based on Fedora 34 and forms the basis of the upcoming RHEL 9 (Red Hat Enterprise Linux). The latter has been in beta since the beginning of November. # § Debian Family⠀➾ # ⚓ Thomas_Lange:_New_ISO_images_using_Debian_11⠀⇛ I’ve created new ISO images for FAI. Now, they install Debian 11 using kernel 5.10. The ISOs are available from https://fai-project.org/fai-cd There’s also a Ubuntu version of the FAI CD which installs Ubuntu LTS 20.04 in two variants. A desktop and a server installation is available. # § Canonical/Ubuntu Family⠀➾ # ⚓ It’s_your_Loki_day:_The_Reg_takes_Elementary_OS Jólnir_for_a_quick_test_drive⠀⇛ A new minor version of Elementary OS, a rather modernist and minimalist Ubuntu derivative, fixes a lot of small details. The Register took it for a quick spin. Fans of American Gods might recognise that Odin, the Allfather of the Norse gods, has many names – and “Jólnir” is one of them. Elementary OS 6.1 makes quite substantial changes for a point release, but if you were already running 6.0 and you update regularly, you probably already have it. o § Devices/Embedded⠀➾ # ⚓ Hark!_A_VR_headset_powered_by_Linux_that_you_can_maybe_buy one_day⠀⇛ The thing you didn’t even know you wanted is here: SimulaVR have been working hard on bringing Linux to the VR world and the result is the SimulaVR One and, well, it actually looks pretty cool. Now, you might be thinking, do we need Linux in a VR headset? It’s a good question and the answer, in our view, is why not. The year of Linux has been coming for a while and SimulaVR might have just found the missing piece. # ⚓ Strap_This_Linux-Powered_NUC_to_Your_Face_for_Virtual Productivity⠀⇛ The SimulaVR Simula One probably isn’t going to wind up on our gaming-focused list of the best VR headsets, but it’s certainly unique. Its goal is to function as a VR workstation, by replacing your physical monitors with a virtual environment to get work done. The Simula One runs a Linux operating system on a small intel NUC attached to the headset itself. Since the headset isn’t aimed at gamers, high graphics horsepower is not required. So the team behind SimulaVR opted to use an Intel NUC 11 compute element equipped with a Core i7-1165G7 processor. It’s a quad-core hyperthreaded CPU with a peak boost of 4.7GHz and Intel Iris Xe integrated graphics. # § OpenStreetMap⠀➾ # ⚓ Should_you_contribute_open_data_to_OpenStreetMap_for free?⠀⇛ Facebook uses OSM world wide. They do a lot of quality-assurance (QA) work on OSM data as they were burned by a malicious user changing the name of New York City to Jewtroplis. As part of their work they now release a dataset called Daylight. Daylight is basically OSM data (+ other Open Data, like the Bing buildings) delayed with QA tests. They employ nobody in the OSM community. Amazon do a lot of work globally to help their delivery drivers, mainly by mapping new residential roads and driveways. They employ nobody in the OSM community. Ordnance Survey, the National mapping agency in Great Britain (GB), now uses OSM for all data outside of GB, and some data inside. Comically, some of the OSM data they use inside GB is because they couldn’t agree on a licensing agreement with themselves. They employ nobody in the OSM community. [...] I’ve been working on a Places dataset by scraping Linked Data and Microdata from first party websites. But due to issues with the source data going off spec means I basically have to write some code for each site anyway. Plus, I don’t have the resources to do a large scale web crawl to find independent shop websites. And even then, this data is probably covered by Database rights in the UK and European Union so it can’t be used in OSM without the data owners permission. It’s surprisingly hard to get companies to give you permission to copy data from there website, it’s basically free advertising for them, but they are still reluctant. In the UK we’ve reached a mid-point, we use the dataset for QA, and to identify areas that need an independent survey to collect missing data. Depending on the interpretation of Database rights, even that may be infringing. # § Mobile Systems/Mobile Applications⠀➾ # ⚓ The_Android_Auto_hack_your_Tesla_craves_is_ready_for you_to_try_it_out⠀⇛ # ⚓ Will_the_Galaxy_S9_or_S9+_get_Android_12_and_One_UI 4?_–_SamMobile⠀⇛ # ⚓ Google_offers_Lenovo_P12_Pro_discount_to_test_Android 12L_–_9to5Google⠀⇛ # ⚓ How_to_add_medical_information_to_your_Android phone⠀⇛ # ⚓ Having_problems_with_Google_Meet_for_Android?_We_help you_solve_them_–_How_smart_Technology_changing_lives⠀⇛ # ⚓ Google_pushes_developers_to_adapt_Android_apps_for Chromebooks_|_Ars_Technica⠀⇛ o § Free, Libre, and Open Source Software⠀➾ # § FSF⠀➾ # § GNU Projects⠀➾ # ⚓ GIMP_2.10.30_Released⠀⇛ GIMP 2.10.30 is once again mostly a bugfix release, with many fixes and incremental improvements, not so much on the “new feature” side. # ⚓ GIMP_2.10.30_Released_With_Better_Adobe_PSD Support,_Improved_Portals_Integration⠀⇛ GIMP 3.0 still isn’t ready for release and won’t be in 2021 but the GIMP 2.10.30 release is out today in time for working on your Christmas photos or holiday cards. GIMP 2.10.30 is primarily a maintenance/bug-fix release but does carry some improvements worth noting. GIMP 2.10.30 includes changes such as… # ⚓ GIMP_2.10.30_Bugfix_Release_Now_Available⠀⇛ GIMP 2.10.30 ships with many fixes and incremental improvements, but not so much on the new feature side. For years now, GIMP has been one of the best free alternatives for commercial image editing suites like Photoshop. It is a bitmap/pixel-based image manipulation program for photo editing and retouching and creating images and animations. There’s still some time to go before seeing the long-awaited GIMP 3.0 release for this open source image manipulation program but at least out today is GIMP 2.10.30 for bettering the current stable series. Let’s see what’s new! # ⚓ GIMP_2.10.30_Released!_Improved_file_format support,_Prefer_Freedesktop_API_| UbuntuHandbook⠀⇛ GIMP image editor got a new bug-fix release for the current 2.10 stable series today. Here’s what’s new and how to install it in Ubuntu 20.04 & Ubuntu 21.10. GIMP 2.10.30 improved several file format supports. PSD support received various types of improvements allowing it to load more sub-cases of PSD. And, AVIF export now favors AOM encoder. Color picking from Colors dockable can now use the Freedesktop API when available. The screenshot plugin for GNOME 41 has been dropped due to restricted API. And, in KDE it uses in priority the Freedesktop API. # § Programming/Development⠀➾ # ⚓ Dirk_Eddelbuettel:_RcppSMC_0.2.6_on_CRAN:_Compiler Update⠀⇛ A new maintenance RcppSMC release 0.2.6 arrived at CRAN yesterday. It chiefly updates the code to comply with g++-11 which default to C++17 – which brings us std::data(). And if one is not careful, as we weren’t in three files, this can clash with other uses of data as I tweeted a good week ago. Otherwise some JSS URLs now sport the preferred shorter doi form. RcppSMC provides Rcpp-based bindings to R for the Sequential Monte Carlo Template Classes (SMCTC) by Adam Johansen described in his JSS article. Sequential Monte Carlo is also referred to as Particle Filter in some contexts. The package features the Google Summer of Code work by Leah South in 2017, and by Ilya Zarubin in 2021. # ⚓ Heaptrack_v1.3.0_Release_–_KDAB⠀⇛ Version 1.3.0 of the KDE Heaptrack project was just released by KDAB’s Milian Wolff. Heaptrack is a heap memory profiler on Linux- based operating systems. It can help you find hotspots that need to be optimized for reducing memory usage, memory leaks, allocation hotspots, and temporary allocations. Included in this release is a special new feature that NetworkRADIUS.com hired KDAB to develop: support for custom suppression files, including support for per-application embedded default suppression lists. This can be done by the same API that is already used by LSAN: __lsan_default_suppressions. KDAB is always more than happy to make improvements to products for their customers. And this change even made it into the very next release! Thanks to NetworkRADIUS.com for bringing this forward. This release also brings you filtering by time ranges. All you have to do to filter by time range is select a range of time and right click. The ability to see the difference between the two time points that results from this action is a very helpful new feature in the workflow of the heap memory analysis. # ⚓ 802.11ah_WiFi_HaLow_development_board_to_launch_for $99_(Crowdfunding)_–_CNX_Software⠀⇛ When 802.11.ah WiFi operating in the 900 MHz frequency range for low-power long-range communication was announced in 2014, then named WiFi HaLow in 2016, I naively assumed it would soon compete against other LPWAN standards like LoRaWAN or Sigfox. However, over the next few years, we did not see much interest in the wireless standard. But it may be picking up now, as Gateworks recently announced a Newracom NRC7292 based 802.11ah WiFi HaLow Mini PCIe module for their Arm Linux SBC’s, and a company called Teledatics is about to launch Halo TD-XPAH 802.11ah Hallow development board featuring an AzureWave AW-HM482 module. # ⚓ Jonathan_Dowland:_Vim_plugins_by_Tim_Pope⠀⇛ I’ve been using Vim as my main text editor for 18 years, but for most of that time I’ve been using something very close to the default configuration: my vimrc contained not much more than preferences for indentation and how to visually indicate white space characters like tabs. Last but not least, I’ve used a single colour scheme for most of that time: Zenburn. # ⚓ Mold_1.0_Released_As_A_Modern_High-Speed_Linker Alternative_To_GNU_Gold,_LLVM_LLD⠀⇛ Mold 1.0 is a production-ready, high-speed linker alternative to GNU’s Gold or LLVM’s LLD that currently is supported on Linux systems and written by the original LLD author. Rui Ueyama who previously spearheaded LLD as the LLVM linker has been recently designing Mold. Mold 1.0 marks the project’s first stable and production-ready release. Mold 1.0 doesn’t add any shiny new linker features over LLD or Gold, but that it’s much faster. Currently Linux systems are supported while plans are underway to extend the linker to macOS followed by Windows. # ⚓ Zstd_1.5.1_Released_With_Even_More_Performance Improvements_–_Phoronix⠀⇛ Zstandard 1.5.1 is now available as the latest release of this widely-used data compression algorithm backed by Facebook that delivers on great performance. With the new release, performance is even better. # ⚓ REST_vs_SOAP:_What’s_the_Difference_between_REST_API and_SOAP_API?⠀⇛ In this article, we have discussed difference between REST API and SOAP API. Comparing REST vs SOAP API, REST works with plain text, JSON, XML and HTML whereas SOAP work only with XML formats. Moreover, SOAP API needs more bandwidth for its usage whereas REST API doesn’t need much bandwidth. # ⚓ Red_Hat_Developer_roundup:_Best_of_December_2021⠀⇛ Welcome to our monthly recap of all the articles published in December 2021! This month’s highlights include two quick guides for developers looking to integrate their favorite tools with Red Hat OpenShift Streams for Apache Kafka, an elegant process for performance testing microservices on Kubernetes, a Quarkus developer’s guide to Java 17 language features, and more. # ⚓ The_Origins_of_C⠀⇛ C has influenced the shape of almost every programming language developed since the 1980s, says Richard Jensen. In this article, Jensen offers a brief look at the language’s history, which begins in England with a colleague of Alan Turing and a program that played checkers. # § Qt⠀➾ # ⚓ QStringView_Diaries:_QAnyStringView_–_A_Variant String-View⠀⇛ In Qt, the vast majority of strings are held in QString objects, and most functions take strings by const QString& and return by QString. This works fine in practice, because QString is so readily created from string literals that for the most part, you don’t need to pay attention. The compiler will helpfully convert string literals to QString when calling such functions. It doesn’t convert std:: string, nor even std::u16string, but who cares about those? 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇:)⦈ # ⚓ Qt_for_MCUs_2.0_released⠀⇛ A new major update of Qt for MCUs is now available. Download version 2.0 to benefit from the many improvements we have made based on your feedback in the last two years. Qt for MCUs 2.0 also includes new features such as text rendering in any language, new APIs for management and optimizations of graphical resources, and more. * § Leftovers⠀➾ o ⚓ Never_trash_READABLE_data!_|_Stop_at_Zona-M⠀⇛ One of the countless, unexpected effects of the COVID lockdowns was and still is, says Wired a great increase of the amounts of highly sensitive data found in old, even really old computers. Like the case of a collector of vintage hardware buying this year a computer only sold in 1995 and 1996, and discovering it was still full of “all sorts of personal files, like tax records and letters to mom”. For both funny and worrying details do read the full piece. Here, I only need to motivate you with a quote from a security , but the gist is all in this declaration from a security consultant they interviewed: “If you don’t properly dispose of your old hardware, you effectively pass the buck to someone else to protect your data. And once that happens, it’s done. It’s a problem you can’t retrospectively fix. o § Hardware⠀➾ # ⚓ HDD_Vending_Machine_Works_Like_A_Vending_Machine_Should⠀⇛ The concept of vending machines in hackerspaces is nothing new, but [iooner] took it a step further – as hackers ought to. Putting HDDs into the rotating spring of a repurposed vending machine, right where you’d expect to see a Granola bar, isn’t revolutionary – but we don’t remember anybody doing it before this. And, with how heavy a typical HDD is, you are guaranteed to never encounter the “it just won’t fall down” issue that’s omnipresent with the snack-loaded machines. Nothing could illustrate the premise of this concept better than [iooner]’s video does, and hackerspaces acquiring and having fun with consumer-facing equipment is always fun to watch. A stereotypical hackerspace vending machine sells resistor packs and Arduino boards, but you wouldn’t see it venture into the realm of data storage and distribution. Given how cheap HDDs are nowadays, this concept could benefit us in a variety of applications – selling new HDDs to members for regular data storage use, or distributing hacking magazine archives and Wikipedia dumps, even exclusive release things like recordings of hackerspace lectures. # ⚓ “Window_To_The_World”_Brings_Far-Off_Places_To_Your_Home_| Hackaday⠀⇛ For those who love travelling around the world, life hasn’t been great for the past two years. World-wide lockdowns and travel restrictions have kept many people stuck inside their own homes when they would rather be jetting off to distant cities. If you’re one of those bothered by Wanderlust, [Alex Shakespeare] might have a solution for you: a window that shows a live image from another location around the world. o § Integrity/Availability⠀➾ # § Proprietary⠀➾ # § Pseudo-Open Source⠀➾ # § Privatisation/Privateering⠀➾ # ⚓ Need_for_surveillance_reform_stronger than_ever_in_light_of_the_Draft_Data Protection_Bill,_2021⠀⇛ The Joint Parliamentary Committee Report on the Personal Data Protection Bill, 2019 (PDP Bill) is here. The report, however, fails to tackle head-on one of the most pressing issues facing the country presently: surveillance reform. This leaves out any regulation or oversight over projects such as the National Intelligence Grid (NatGrid) or the CCTNS (Crime and Criminal Tracking Network System) which has databases on lakhs of Indians. Why should surveillance be regulated? Surveillance refers to the continuous or intermittent monitoring of a person or a group of people, usually without their knowledge, for the purpose of gathering information about their activities. There are two forms of surveillance, first targeted surveillance (Example: spyware such as Pegasus) and second, mass surveillance (Example: NatGrid, CCTNS, CMS & AFRS). Regulation of the surveillance by government authorities is an oft- debated topic. While one constituency argues for national security, the other places individual privacy as a more important priority. However, these interests can be reconciled by specific legislative choices which have been ignored by the Joint Parliamentary Committee in the proposed Data Protection Bill, 2021 (read our explainer here). Surveillance regulation when well crafted does not harm national security, but enhances our fundamental rights along with institutional processes that ensure such capabilities are not used for political purposes. This principle of accountability and oversight in surveillance practices has been recognised by many liberal democracies. # § Linux Foundation⠀➾ # ⚓ Linux_Foundation_Releases_Report_on Data_and_Storage_|_Enterprise_Storage Forum⠀⇛ The Linux Foundation is sharing a report on enterprise use of data and storage as they relate to cloud services and workloads. The Linux Foundation released the 2021 “Data and Storage Trends” report “in the era” of cloud-native, edge computing, the Internet of Things (IoT), and 5G solutions, according to the foundation last month. # § Security⠀➾ # ⚓ Enterprise_Linux_Security_Episode_12_–_An Inside_Job?_–_Invidious⠀⇛ Earlier this year, Ubiquiti allegedly suffered a breach, which seemed to reinforce the hesitation some customers have with using the UniFi platform, given that it has a cloud-connected controller. Now, months later, an unexpected bombshell was dropped – it looks like the company wasn’t compromised by an outside attacker after all, recent developments seem to point to the whole fiasco being an inside job! # ⚓ Enterprise_Linux_Security_Episode_13_– Log4Shell_–_Invidious⠀⇛ The Log4Shell vulnerability is making its rounds all over security news sites, and with good reason – it’s quite easy to execute. In this episode, Jay and Joao discuss the vulnerability that exists within log4j, as well as some ways to keep your server safe. # ⚓ The_Log4Shell_Vulnerability,_and_CrowdSec’s Community_Response_–_Invidious⠀⇛ TheLog4Shell vulnerability is taking the Internet by storm, and it’s already being used for real-world attacks. In this video, Jay discusses the details around Log4Shell vulnerability in Log4j, and also CrowdSec’s community- based response to the situation. # ⚓ Security_updates_for_Tuesday⠀⇛ Security updates have been issued by Mageia (log4j), openSUSE (chromium, log4j, netdata, and nextcloud), Oracle (kernel and kernel-container), Red Hat (kernel, kernel-rt, log4j, openssl, postgresql:12, postgresql:13, and virt: rhel and virt-devel:rhel), Slackware (httpd), SUSE (xorg-x11-server), and Ubuntu (firefox). o § Misinformation/Disinformation⠀➾ # ⚓ What_is_disinformation,_why_it_spreads,_and_how_to_stop_it –_Access_Now⠀⇛ What is disinformation? Disinformation is false or misleading information, created to influence people. It can take many different forms and existed well before the internet. Every country struggles with the spread of disinformation online, whether you live in a functioning democracy or under an authoritarian regime. It often surrounds divisive political subjects, such as migration, vaccination, or policies on gender, sexuality, race, religion, and more. As communications moved online, so did disinformation. The advertising business models of large online platforms, which exploit our personal data in order to profit from it, have contributed to the rapid spread of disinformation. During the global pandemic, we have witnessed how disinformation, often manufactured and spread by politicians and other public figures, can incite violence and discrimination against marginalised groups. Disinformation has been linked to low vaccination rates, the silencing of marginalised voices, and the undermining of the public’s trust in journalism. As UN Special Rapporteur Irene Khan writes, “Essentially, disinformation is a modern way in the digital era of making money by purposefully spreading lies.” o § Censorship/Free Speech⠀➾ # ⚓ Certain_“fact_checks”_are_nothing_more_than_opinion_|_Stop at_Zona-M⠀⇛ It seems that the labels attached as fact-checking classifications to articles shared on Facebook are, said Facebook lawyers, nothing but protected opinions. Personally, I know nothing about the lawsuit in which Facebook’s (sorry, Meta’s) lawyers made such a statement. I just agree with the author of the email where I discovered this story that it is“an interesting line of defense. I don’t know if, as the article linked above puts it, such a position could possibly become “a looming legal disaster for Facebook”. But… o § Civil Rights/Policing⠀➾ # ⚓ Submission_to_the_Toronto_Police_Services_Board’s_Use_of New_Artificial_Intelligence_Technologies_Policy_–_The_Citizen Lab⠀⇛ Below is an excerpt of the joint submission between the Women’s Legal Education and Action Fund (LEAF) and the Citizen Lab to the Toronto Police Services Board. You can find the full letter here. Citizen Lab has conducted in-depth analysis of the human rights impacts of emerging technologies in the areas of predictive policing and algorithmic surveillance. Its findings and law reform recommendations are found in a report that was released in 2020 by the Citizen Lab and the International Human Rights Program, titled To Surveil and Predict: A Human Rights Analysis of Algorithmic Policing in Canada. Read the full report and our explanatory guide that provides a summary of research findings as well as questions and answers from the research team. We also provide a fact sheet of our key investigative findings here. o § Monopolies⠀➾ # ⚓ UK’s_Competition_and_Markets_Authority:_Digital_Mega- Watchdog?_–_Disruptive_Competition_Project⠀⇛ In the wake of Brexit, the UK’s Competition and Markets Authority (CMA) has been flexing its muscles as the world’s “mega-watchdog” competition enforcer. The CMA has lately been extremely active, widening its territorial jurisdiction, with a renewed focus on merger control in digital markets. In the words of the CMA’s Chief Executive, Dr Andrea Coscelli, the UK is “in a very strong position to lead” global competition enforcement, “because the upside [of leaving the EU] is that you take back control – genuinely – of the decisions.” Given the CMA’s global ambitions, Brexit provides the opportunity: the CMA now has jurisdiction over merger cases that were previously reserved to the European Commission. Extended Jurisdictional Scope The CMA’s global ambitions have resulted in a series of cases stretching the boundaries of its jurisdictional thresholds. The UK’s “share of supply” test is inherently flexible, looking for only an “increment” in a “share of supply” where one party has an existing presence of significance. It is designed to allow intervention where revenue- based thresholds may fall short. That being said, the CMA can now be said to routinely investigate cases even where one of the merging parties has no UK sales of relevance. In each of Sabre/Farelogix (2020) and Roche/Spark (2020), the acquired company had no UK revenues. In the former case, the acquired company had no direct UK customers (and the parties ultimately took the CMA to court over the issue, though ultimately losing). In the latter, the CMA established the threshold “share of supply” based on the share of specialist researchers employed by the parties in the UK. More recently, in Facebook/GIPHY (2021), not only did the target have no UK revenue, it was not even a horizontal competitor to the acquirer (and in fact was a long-standing and contractually bound supplier). The CMA is clearly willing (and able) to find the “share of supply” test met by looking up and down the value chain in the relevant industry to find an overlap and an “increment”. # ⚓ The_CMA_Puts_Facebook_into_a_GIPHY_Paradox_–_Disruptive Competition_Project⠀⇛ In May 2020, Facebook completed its acquisition of GIPHY, unaware that this seemingly harmless transaction would trigger ‘the nuclear option’. In June 2020, as a result of investigations, the UK’s Competition and Markets Authority (CMA) served its initial enforcement order, mandating that Facebook keep its business and GIPHY’s businesses separate from one another until the conclusion of the CMA’s investigation. Nearly a year and a half later, on 30 November 2021, the CMA issued its final decision, ordering Facebook (now Meta) to divest GIPHY. This divestment order represents more than just a ‘break-up’, it puts Meta in an impossible catch-22, and reveals the inherent contradictions and unrealistic expectations of the current ‘tech- lash’. [...] GIPHY “relied on regular rounds of external funding” (para. 6.10) and its “monetisation model was flawed because advertisers on digital media wanted to monitor return on investment closely” (para. 7.58). The GIFs company “lacked a meaningful user base of its own” (para. 7.51) and, according to Facebook’s submission it was unable to provide the recognizable constituent elements of a robust digital advertising business (para. 5.11). According to an objective reading of the facts of the CMA’s investigation, it does not appear that GIPHY was the attractive emerging business that the CMA depicted it to be, but rather a company struggling to generate revenue or interest from investors. GIPHY’s acquisition, to put it into the words of the tech industry analyst Benedict Evans, rather “represent[s] the recycling of talent and capital from ideas that didn’t go all the way into new ideas that might.” # ⚓ KOL367_|_Disenthrall_with_Patrick_Smith:_Fisking Strangerous_Thoughts’_Critique_of_“Intellectual_Communism”⠀⇛ I appeared on Patrick Smith’s Disenthrall channel (Disenthrall Youtube channel) to discuss and rebut—to fisk, really—an article by one “Strangerous Thoughts” from 2010 criticizing my IP abolitionism—or my “intellectual communism,” as he called it. # § Patents⠀➾ # ⚓ EPO_consults_users_on_grace_periods_for_patents [Ed: When EPO says "users" it means patent maximalists (who hijacked the EPO); it does not bother asking the general public (the public interest) or check the EPC, which it routinely violates; EPO has become a corrupt mafia totally out of control]⠀⇛ A randomly selected group of applicants for European patents are being surveyed this winter on the novelty requirement under the European Patent Convention (EPC) and the lack of a so-called “grace period” in the European patent system. The survey, which will explore the impact of the strict novelty requirement on the filing and business practices of EPO applicants, will be complemented by a consultation of user and stakeholder associations. The resulting feedback, which will be analysed by the EPO and published in a study in the spring of 2022, will provide important input for evidence-based discussions. # § Software Patents⠀➾ # ⚓ “It_is_transparency_which_is_the_secret_of patent_pool_MPEG_LA’s_success” [Ed: JUVE’s editor, Mathieu Klos, who helps promote crimes for Team UPC, is now boosting the_world’s_worst patent_trolls and mentions Microsoft’s]⠀⇛ Hisense has now taken a licence from MPEG LA’s AVC/H.264 patent pool. The Chinese smartphone, tablet and TV manufacturer joins telecom giants Huawei, ZTE and TCL and becomes one of over 6,000 licensees that MPEG LA has signed up since the 1990s. The patents in this program, and indeed many of the pool’s programs, are standard essential. The litigation strategy pursued by the team around patent attorney Gottfried Schüll from Cohausz & Florack and Krieger Mes lawyer Axel Verhauwen has helped shape the case law around FRAND in recent years. This strategy differs in at least two key aspects from the typical, not to say clichéd, approach of many other NPEs. Firstly, MPEG LA stands out with its comparatively transparent handling of licensing agreements. The publication of licensing conditions contributes to the pool’s respectability. At the same time, this also seems to increase the successful conclusion of licences. Secondly, the pool often files its lawsuits in batches. This approach initially causes less of a stir than the impressive number of lawsuits filed by Intellectual Ventures, for example. However, it has also meant that setbacks in the past have been less severe. The EPO recently revoked one of Intellectual Ventures’ core patents, which is the subject of numerous lawsuits in France and Germany. This was a troubling outcome for Intellectual Ventures, whose ongoing series of lawsuits are already plagued by setbacks due to invalid patents. # ⚓ Jeffrey_M._Gross_entity_Callstat_Solutions patent_challenged⠀⇛ On December 17, 2021, Unified filed a petition for inter partes review (IPR) against U.S. Patent 6,236,983, owned by Callstat Solutions LLC, an NPE and an entity of Jeffrey M. Gross. The ‘983 patent relates to collecting information about a computer system and applying rules to the collected information. It has been asserted against cybersecurity and client management software, including software sold by BMC Software, McAfee, and Check Point Software. ䷩ 𝚕𝚒𝚗𝚎 11510 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.21.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Links_22/12/2021:_Harvester_1.0,_RapidDisk_8.0.0,_and_WordPress_5.9_Beta_4⠀✐ Posted in News_Roundup at 8:09 pm by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈ § Contents⠀➾ * GNU/Linux o Distributions o Devices/Embedded * Free_Software/Open_Source * Leftovers * § GNU/Linux⠀➾ o § Audiocasts/Shows⠀➾ # ⚓ WP_Briefing:_Episode_22:_A_Carol_of_Thanks⠀⇛ In this last episode of 2021, Josepha Haden Chomphosy takes the time to appreciate those who make the WordPress project a success and offers a carol of thanks. # ⚓ TikTok_Live_Studio_Allegedly_Illegal_Fork_Of_OBS_– Invidious⠀⇛ OBS can’t catch a break after the Streamlabs debacle, now TikTok is being accused of creating an illegal fork of OBS with their new TikTok Live Studio. o § Applications⠀➾ # ⚓ Theme.sh_Is_An_Interactive_Terminal_Theme_Selection_Script_ (400+_Themes)_–_Linux_Uprising_Blog⠀⇛ theme.sh is a script to easily change the terminal theme. It comes with more than 400 themes, an optional interactive theme picker, and it’s terminal agnostic. The script is available as a single portable file that includes all the 400+ themes. It can set a terminal theme directly or, if you have fzf installed on your system, it provides a terminal menu for interactive theme selection, either in a preview pane, or directly as your terminal theme if the terminal you’re using supports TRUECOLOR. You can also filter light and dark themes. To use theme.sh, you need to use any terminal with OSC 4/11 support. This includes kitty, st, Terminal.app, iTerm2, alacritty, urxvt, st with a patch, and any libvte-based terminal like GNOME Terminal, Terminator, Guake, Xfce Terminal, Mate Terminal, Konsole, etc. It looks like Windows Terminal doesn’t support this yet. Note that in my test, it didn’t properly set the background color in Tilix. It’s also worth noting that this won’t work in screen. # ⚓ RapidDisk_8.0.0_now_available_–_Random_h_Stuff⠀⇛ RapidDisk is an advanced Linux RAM Disk which consists of a collection of modules and an administration tool. Features include: Dynamically allocate RAM as block device. Use them as stand alone disk drives or even map them as caching nodes to slower local disk drives. Access those drives locally or export those volumes across an NVMe Target network. o § Instructionals/Technical⠀➾ # ⚓ Using_Admission_Controllers_to_Detect_Container_Drift_at Runtime_|_Kubernetes⠀⇛ At Box, we use Kubernetes (K8s) to manage hundreds of micro-services that enable Box to stream data at a petabyte scale. When it comes to the deployment process, we run kube-applier as part of the GitOps workflows with declarative configuration and automated deployment. Developers declare their K8s apps manifest into a Git repository that requires code reviews and automatic checks to pass, before any changes can get merged and applied inside our K8s clusters. With kubectl exec and other similar commands, however, developers are able to directly interact with running containers and alter them from their deployed state. This interaction could then subvert the change control and code review processes that are enforced in our CI/CD pipelines. Further, it allows such impacted containers to continue receiving traffic long-term in production. To solve this problem, we developed our own K8s component called kube-exec-controller along with its corresponding kubectl plugin. They function together in detecting and terminating potentially mutated containers (caused by interactive kubectl commands), as well as revealing the interaction events directly to the target Pods for better visibility. # ⚓ Stupid_RCU_Tricks:_Removing_CONFIG_RCU_FAST_NO_HZ_–_Paul_E. McKenney’s_Journal_—_LiveJournal⠀⇛ The CONFIG_RCU_FAST_NO_HZ Kconfig option was added many years ago to improve energy efficiency for systems having significant numbers of short bursts of idle time. Prior to the addition of CONFIG_RCU_FAST_NO_HZ, RCU would insist on keeping a given idle CPU’s scheduling-clock tick enabled until all of that CPU’s RCU callbacks had been invoked. On certain types of battery-powered embedded systems, these few additional scheduling- clock ticks would consume up to 40% of the battery lifetime. The people working on such systems were not amused, and were not shy about letting me know of their dissatisfaction with RCU’s life choices. Please note that “letting me know” did not take the form of flaming me on LKML. Instead, they called me on the telephone and yelled at me. Given that history, why on earth would I even be thinking about removing CONFIG_RCU_FAST_NO_HZ, let alone queuing a patch series intended for the v5.17 merge window??? The reason is that everyone I know of who builds their kernels with CONFIG_RCU_FAST_NO_HZ=y also boots those systems with each and every CPU designated as a rcu_nocbs CPU. With this combination, CONFIG_RCU_FAST_NO_HZ=y is doing nothing but placing a never-taken branch in the fastpath to and from idle. Such systems should therefore run slightly faster and with slightly better battery lifetime if their kernels were instead built with CONFIG_RCU_FAST_NO_HZ=n, which would get rid of that never-taken branch. # ⚓ BE_CAREFUL_WITH_find_+_delete_–_find_._-delete_-name_vs find_._-name_-delete⠀⇛ one neat function of find, it that what it found can be passed to another function for further processing. # ⚓ Nextcloud_–_Unable_to_Open_Photos_Library_—_Firstyear’s blog-a-log⠀⇛ It seems that Nextcloud is not sandboxed which means that macos enforces stricter permissions on what this can or can not access, which is what prevented the photos library from syncing. # ⚓ How_to_compress_PNG_image_file_in_Linux_–_Unixcop_the_Unix /_Linux_the_admins_deams⠀⇛ PNG or Portable Network Graphics is an image file format meant to replace GIF. PNG utilizes lossless image compression, which results in high-quality images though sometimes they can be relatively big. Also if you have a lot of images, and want to compress them without losing its original quality There are plenty of GUI applications available which will help you to optimize the images. Here are two simple command line utilities to optimize images and they are: PNGquant and OptiPNG are programs that optimize PNG images to smaller size without losing any information or their original quality. # ⚓ How_to_install_Runescape_on_a_Chromebook⠀⇛ Today we are looking at how to install Runescape 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_quickly_back_up_and_restore_a_database_with phpMyAdmin_–_TechRepublic⠀⇛ Many of your business processes depend on databases. Should one of those databases fail, your workflow could come to a standstill. That would cost you money, an outcome you certainly do not want. To avoid that, you need to back up those databases. I’ve already walked you through the process of doing so from the command line. This is most definitely a technique you should know. But there might be times when you want to work with a bit more efficiency, such as by way of a web-based GUI like phpMyAdmin. That, my friends, is exactly what I’m going to show you today. After you read how easy this is, you might never go back to the terminal for this task. Let’s get to work. # ⚓ How_to_install_Nvidia_graphics_drivers_on_Pop_OS⠀⇛ If a web-based GUI is better suited to your admin skills, Jack Wallen wants to show you how to back up and restore your MySQL/MariaDB databases with one of the easiest tools on the market. # ⚓ How_to_upgrade_to_Pop_OS_21.10⠀⇛ Pop_OS 21.10 is here! It comes with great new features like a brand new application launcher, Gnome Shell version 40, and many other things. In this guide, we’ll go over how to upgrade your system to the new Pop_OS 21.10. o § Games⠀➾ # ⚓ New_Proton_game_compatibility_milestone_is_great_news_for Valve’s_Steam_Deck ⠀⇛ If there’s one positive we can glean from Valve’s decision to delay the Steam Deck, it’s that the company now has some extra time to polish its handheld gaming PC good and proper. In fact, this newfound extra time has already helped improve Proton compatibility with Steam’s top games, which has just hit a new milestone. According to analysis conducted by the ProtonDB community, 80% of Steam’s top 100 games now run perfectly on Proton after a few tweaks. However, there’s still plenty of work to be done before we can expect a flawless experience using the Steam Deck, with just 35% of the top 100 either running flawlessly or natively on Linux. Compatibility could quickly rise to 88% if developers were to patch their games with Proton compatible versions of Easy Anti-Cheat or BattlEye services, which are currently leaving games like Destiny 2 and New World unplayable. That said, because the affected games currently can’t launch using Proton, there’s no way of knowing whether other issues accompany those related to anti-cheat measures. # ⚓ 75%_of_Steam’s_Top_1000_games_work_on_Linux_now_–_gHacks Tech_News⠀⇛ Valve Software, the company behind the popular Steam gaming platform and smash hits such as Dota 2, Half-Life and Team Fortress, announced plans in 2018 to improve Windows game support for Linux. Steam Play, a feature that Valve Software launched in 2010 to allow cross-platform game play on Steam, would be used to improve support. Originally launched as a way for gamers to play their games on all platforms without having to purchase games for each platform, Valve Software included a modified version of Wine, called Proton, in Steam Play. Proton improved compatibility and Linux users on Steam had access to more games using the new feature. # ⚓ 80%_of_Steam’s_100_Most_Popular_Games_Now_Run_on_Linux_with Proton_–_How_smart_Technology_changing_lives [Ed: Dubious site/source]⠀⇛ Proton has de facto been the true starting gun for the Linux Gaming. For those of you who don’t know what we’re talking about, it’s a Wine-based compatibility layer powered by Valve to make it easier to run Windows video games on Linux and macOS. Proton is served through the Steam Play feature of the Steam client, but being an open source development, it can be taken over, forked, and re- implemented by anyone who wants it, so it’s also employed by Lutris, Heroic Game Launcher, and MiniGalaxy, to name three relatively well-known projects at least. # ⚓ Steam_Deck_compatibility_with_games_is_growing,_but_it’s not_all_good_news⠀⇛ Linux can now run 80% of the top 100 most popular games on Steam using the Proton compatibility layer, and therefore by extension the same is true of the SteamOS (Linux) powered Steam Deck. This fresh milestone was reported by ProtonDB, which keeps track of compatibility via reports from gamers. At the time of writing, exactly 80% of Windows games are ranked as ‘Gold’ for Proton compatibility, which means that the titles in question run ‘perfectly’ after a little tweaking (games which run perfectly with no tweaking needed at all are rated Platinum). Essentially, Gold ratings (or above) are what you’re looking for in order to ensure that a game is a smooth experience with Proton, as Silver-rated titles, while being generally playable, have some issues. Ratings are based on player reports as mentioned, and out of 21,244 games which have been reported and included in ProtonDB’s stats, 17,649 work via Proton. # ⚓ 75%_of_Steam’s_Top_1000_Games_Work_On_Linux_Now⠀⇛ o § Desktop Environments/WMs⠀➾ # § GNOME Desktop/GTK⠀➾ # ⚓ GTK4ifying_Settings_–_Georges_Stavracas⠀⇛ It took a long time, and massive amounts of energy and sweat and blood, but as of last week, Settings is finally ported to GTK4 and uses libadwaita for platform integration. This was by far the biggest application I’ve ported to GTK4. In total, around 330 files needed to be either rewritten or at least modified as part of the porting process. It also required GTK4 ports of some dependencies, like gnome-desktop, libnma, and colord-gtk. o § Distributions⠀➾ # § Elementary OS 6.1 Run Through and Interview With Danielle Foré⠀➾ # ⚓ elementary_OS_6.1_Secrets_with_Founder_and_CEO Danielle_Foré_|_Jupiter_Extras_78⠀⇛ Big internal process improvements have resulted in a major new version of elementary OS hot on the heals of the previous release. Find out why 6.1 is a lot more than just a number. Special Guest: Danielle Foré . # ⚓ Elementary_OS_6.1_Run_Through_–_Invidious⠀⇛ In this video, we are looking at Elementary OS 6.1. Enjoy! # ⚓ Elementary_OS_6.1⠀⇛ Today we are looking at Elementary OS 6.1. It comes with Linux Kernel 5.11, based on Ubuntu 20.04, and uses about 800MB of ram when idling. Enjoy! # § SUSE/OpenSUSE⠀➾ # ⚓ Harvester_is now_production-ready_and generally available  _|_SUSE_Communities⠀⇛ 2021 has been a memorable year for the Harvester team. In May, SUSE hosted the first virtual SUSECON, where we announced the beta release of Harvester, alongside a cast of new innovative open source projects from the SUSE Rancher engineering team. In October, for the first time in two years, we were able to meet our industry peers and the community face-to- face at KubeCon North America where we announced Harvester’s plans to integrate with our leading Kubernetes management platform SUSE Rancher. [..] Harvester is a 100% free-to-use, open source modern hyperconverged infrastructure solution that is built on a foundation of cloud native solutions including Kubernetes, Longhorn and Kubevirt. It has been designed as an enterprise-ready turnkey solution that gives operators a familiar operating experience like other proprietary HCI solutions in the market. # ⚓ Technical_Insights_of_Harvester_1.0_|_SUSE Communities⠀⇛ Exactly one year ago, we announced the alpha availability of the project Harvester, an open Source Hypercoverged Infrastructure solution. During this last year, the team has been working hard on developing the project and we brought you the beta release of v0.2.0 and v0.3.0. Throughout the last year, we’ve received many queries from our users and the community, asking when Harvester will be in production. # ⚓ Digest_of_YaST_Development_Sprint_137_|_YaST⠀⇛ As you may know, YaST has the ability to update itself at the very beginning of the installation of the operating system. That makes possible to correct the installation process in case errors are detected after publishing a given release of SUSE Linux Enterprise. Recently we found there was room for improving the speed and also to simplify how the mechanism works in some scenarios. It’s hard to explain exactly what we did in only a few words… so we will not try. 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇;-)⦈ But if you don’t mind reading quite some words and watching a couple of animations, go and check the description of this pull request. Apart from the already mentioned improvements, we also extended the YaST self- update to support relative URLs. Check the details in this separate pull request. # § IBM/Red Hat/Fedora⠀➾ # ⚓ What_sysadmins_want_to_know_about_OpenShift_and Kubernetes⠀⇛ If I could summarize my philosophy of knowledge in the open source world, it would be “learn hard, share harder!” This idea drives me to give back to the community in appreciation for all it has provided me. [...] Kudos to our contributors who have gifted us with such excellent articles this year! As I said at the beginning of this article, “learn hard, share harder.” Learn, benefit, use, and be inspired by these articles, so that you can share your knowledge with others, too. # ⚓ Real-time_Analytics_News_for_Week_Ending_December 18⠀⇛ Red Hat announced updates throughout its portfolio of application services. The modularity of the Red Hat Application Services portfolio contributes to a unified environment for application development, delivery, integration, and automation. The combination of the Quarkus platform with the connectivity capabilities of Apache Camel, the intelligent decisioning of Kogito, API management with Red Hat 3scale API Management, and the power of Red Hat OpenShift enables Java developers to fully embrace cloud-and Kubernetes-native development. # ⚓ Hybrid_work_model:_4_tips_for_teams_in_2022 [Ed: IBM says you are “IBM employee 100% of the time”. Today, from IBM: we keep you under control in the workplace and also at home]⠀⇛ In 2022, the hybrid work model will be called, simply, “work.” Until it’s the norm, teams will have growing pains making the adjustment. While there is no cookie-cutter approach for all people, roles, or projects, consider these tips to smooth the transition. [...] Use milestones and deadlines to gauge your team’s progress instead of tracking time. One challenge of remote work is “appearing” to be productive and present to the management team. However, measurement should not be seen as a punitive exercise to catch people out – it should guide employees toward completing their goals. # § Debian Family⠀➾ # ⚓ Debian_11_‘Bullseye’_updated_to_11.2_with_40+ security_updates_and_60+_bugfixes⠀⇛ The Debian project has released a second update for the stable distribution Debian 11, codenamed “Bullseye”. Although the latest update is not a major revision, it includes more than 40 security updates, in addition to 60+ bug fixes. Nearly two months after releasing Debian 11.1, the team behind the Linux distro has sent out an incremental update that fixes multiple bugs, and also addresses several security issues. One of the most prominent of the patches, include a fix for actively exploited Log4j vulnerability. If you have been applying updates, you’ll automatically be on Debian 11.2. You can check to see if you have the latest updates through the graphical update tool. Alternatively, experienced users can fire up the Terminal and update Debian with the command sudo apt update && sudo apt full upgrade. # ⚓ Model_upgrade:_Linux_distribution_Debian_is_in version_11.2_(Bullseye) [Ed: Automated translation of article in German]⠀⇛ The Debian Release 11.2 “Bullseye” is not a completely new version, but mainly a package refreshment. The updated version removes security problems – it contains updates to close the Log4j gaps – and is also intended to fix some serious problems. There are new installation media to download, but a normal update also brings existing Bullseye installations to the current state. That lists the numerous security updates and package updates Debian project in the changelog on. The kernel is now about version 5.10.83-rt58. New versions of Apache, Firefox, LibreOffice, Samba, WordPress and explicitly additional apache-log4j2 also seal off vulnerabilities. # § Canonical/Ubuntu Family⠀➾ # ⚓ Ubuntu_Fridge_|_Ubuntu_Weekly_Newsletter_Issue_714⠀⇛ Welcome to the Ubuntu Weekly Newsletter, Issue 714 for the week of December 12 – 18, 2021. o § Devices/Embedded⠀➾ # ⚓ 10GbE_shows_up_on_Linux_router_board_and_M.2_module⠀⇛ Wallys announced a “DR8072 V01” router board that runs Linux on a 2.2GHz, quad -A53 Qualcomm IPQ8072A and offers 802.11ax, mini-PCIe, 4x GbE, and 10GbE SFP and copper ports. Meanwhile, Innodisk unveiled the world’s first 10GbE M.2 module. Over the last year we have seen 2.5GbE and to a lesser extent 10GbE ports extend their reach in embedded systems. Now, Wallys (or Wally’s) has announced a Linux router board with dual 10GbE ports and Innodisk has announced the Linux- compatible “EGPL-T10,” which it bills as the world’s first 10GbE M.2 module (see farther below). Wallys’ DR8072 V01 board follows its DR8072A, which similarly runs OpenWrt and other Linux distributions on the 2.2GHz, quad -A53 Qualcomm IPQ8072A. The SoC is equipped with dual-band, 4×4 802.11ax (Wi-Fi 6) for 8x streams at up to 2475 Mbps. The main difference in the boards is that the new V01 model provides dual 10GbE ports instead of dual 2.5GbE ports # ⚓ LG_All-in-One_Thin_Clients_Preloaded_with_IGEL_OS_for Release_in_2022⠀⇛ LG All-in-One thin clients preloaded with IGEL OS will ship on select LG hardware with support for Citrix, VMware Workspace ONE, Windows 365 and more. # § Open Hardware/Modding⠀➾ # ⚓ Making_music_with_a_Nano_33_IoT-based_MIDI_keyboard_| Arduino_Blog⠀⇛ As part of an assigned project in his class, Peter Ashmore and a partner were tasked with making some kind of interactive object, so they decided to go with a MIDI keyboard due to their shared enjoyment of music production. Modeled somewhat after the typical Launchpad, the team’s system incorporated a set of 13 buttons spanning one octave, as well as two buttons for controlling the current octave and a knob that regulates the volume. The team went with an Arduino Nano 33 IoT as the brains of the operation and wired up the 15 push buttons in a pull-down configuration. After they had finished soldering each component to pieces of perfboard, each element was then assembled into a custom- built chassis that was laser cut from plywood and coated in black spray paint. # ⚓ Turing-ring_is_a_DIY_Turing_machine_consisting_of_an Arduino_and_an_RGB_LED_ring_|_Arduino_Blog⠀⇛ With just an infinite tape, a head that can read or write, a state, and some rules, Turing machines (TMs) are capable of running any computer program. So, after winning a NeoPixel ring in a competition, Mark Wilson wanted to implement his own Turning machine using just a few RGB LEDs and a single Arduino Nano. When his aptly named Turing-ring starts up, an initial state and cell values on the tape can be loaded from either internal program storage or over a USB serial connection. From there, the TM can be further modified or run in order to perform a given task. Furthermore, a user can input their own states (denoted by LED colors) onto the tape by turning a rotary encoder and pressing down to confirm their choice. The speed at which the machine iterates through each step is controlled from either the menu or by rotating the dial when a program is running. # ⚓ TTGO_T-CAN485_–_An_ESP32_board_with_RS485,_CAN_bus interfaces_–_CNX_Software⠀⇛ LilyGO is regularly bringing ESP32 boards to market for specific applications, and their latest TTGO T-CAN485 connects ESP32 to CAN bus and RS485 industrial control interfaces. The board also takes 5 to 12V power input via a 2-pin terminal, comes with a microSD card for data storage, a USB Type-C port and CH340K serial chip for programming and debuggging, plus a 12-pin GPIO header, some buttons, and an RGB LED. # ⚓ The_Inspirer_Keeps_Your_Mood_Up_With_Inspirational Quotes_And_Soothing_Music_|_Hackaday⠀⇛ While some people enjoy the cold weather and long, dark nights in the Northern Hemisphere these days, others may find it hard to keep a positive mindset all through the winter. [Michael Wessel] decided he needed to do something about that and came up with The Inspirer, a desktop display that shows inspirational quotes and plays soothing music. The design is deliberately bare-bones: a strip of wood, standing upright thanks to two metal brackets, onto which a bunch of components have been screwed, glued and taped. The actual display consists of a row of 14-segment LED modules that can show basic alphanumeric characters; these displays emit white light, but [Michael] added a red color filter in front to give them a more “retro” look. o § Free, Libre, and Open Source Software⠀➾ # ⚓ The_curl_year_2021_|_daniel.haxx.se⠀⇛ I’m saving my bigger summary for curl’s 24th birthday in March, but when reaching the end of a calendar year it feels natural and even fun to look back and highlight some of the things we accomplished and what happened during this particular lap around the sun. I decided to pick five areas to highlight. # ⚓ Developer_creates_‘Quite_OK_Image_Format’_that_beats_PNGs_• The_Register⠀⇛ A developer named Dominic Szablewski has given the world a new file format with a splendid name: the Quite OK Image Format (QOI). The file format might be better than that. Szablewski explained that he decided the world needed a new image format because the likes of PNG, JPEG, MPEG, MOV and MP4 “burst with complexity at the seams.” “Every tiny aspect screams ‘design by consortium’,” he added, going on to lament the fact that most common codecs are old, closed, and “require huge libraries, are compute hungry and difficult to work with.” # ⚓ The_Apache_Weekly_News_Round-up:_week_ending_17_December 2021⠀⇛ We’re wrapping up another great week with the following activities from the Apache community… # § Web Browsers⠀➾ # § Mozilla⠀➾ # ⚓ Support.Mozilla.Org:_What’s_up_with_SUMO_– December_2021⠀⇛ December is here. As you’re sliding off into a more cozy corner of your house surrounded by your family members, let’s see what SUMO has been up to in the last month of 2021. # ⚓ William_Lachance:_Leaving_Mozilla⠀⇛ I’ve decided to leave Mozilla as an employee: my last day will be December 31st, 2021. It’s hard to overstate the impact Mozilla has had on my life over the last ten years. In particular, I’m grateful for all the interactions I’ve had with the community: the opportunity to build technology for the public good with people around the world was unique and I’m really going to miss it. Looking back over the past 10 years, I’m feeling pretty good about the impact I had through building better developer and data tooling: mozregression, Perfherder, Iodide and the Glean Dictionary stand out as particular highlights. Thanks to everyone who worked on those things with me! I am because we are. # § SaaS/Back End/Databases⠀➾ # ⚓ PostgreSQL_Weekly_News_–_December_19,_2021⠀⇛ FOSDEM PGDay 2022 will be held on line, on Feb 5-6, 2022. https://fosdem.org/2022/ A PostgreSQL Transition Guide, containing much hard-won wisdom, and available in French and English, has been published pgDay Paris 2022 will be held in Paris, France on March 24, 2022. The CfP is open through December 31, 2021 at midnight, Paris time. Citus Con, a virtual global developer event, is happening April 12-13, 2022. The CFP is now open. # § Content Management Systems (CMS)⠀➾ # ⚓ WordPress_5.9_Beta_4⠀⇛ WordPress 5.9 Beta 4 is now available for testing! This software version is still under development. Please do not run this software on a production site; install it on a test site, where you can try out the newest features and get a feel for how they will work on your site. # § Programming/Development⠀➾ # ⚓ Joey_Hess:_Volunteer_Responsibility_Amnesty_Day⠀⇛ Happy solstice, and happy Volunteer Responsibility Amnesty Day! After my inventory of my code today, I have decided it’s time to pass on moreutils to someone new. This project remains interesting to people, including me. People still send patches, which are easy to deal with. Taking up basic maintenance of this package will be easy for you, if you feel like stepping forward. [...] The other reason it’s less appealing to me is that unix tools as a whole are less appealing to me now. Now, as a functional programmer, I can get excited about actual general-purpose functional tools. And these are well curated and collected and can be shown to fit because the math says they do. Even a tiny Haskell function like this is really very interesting in how something so maximally trivial is actually usable in so many contexts. # ⚓ Vanessa_Christopher:_Everybody_Struggles⠀⇛ Before Outreachy I did not have the slightest idea of what packaging was all about as a matter of fact it was completely new to me. # ⚓ stop_defining_feature-test_macros_in_your_code_– Ariadne’s_Space⠀⇛ If there is any change in the C world I would like to see in 2022, it would be the abolition of #define _GNU_SOURCE. In many cases, defining this macro in C code can have harmful side effects ranging from subtle breakage to miscompilation, because of how feature-test macros work. # ⚓ OpenBLAS_0.3.19_Released_With_Alder_Lake_&_Sapphire Rapids_Detection⠀⇛ OpenBLAS as the popular, open-source BLAS (Basic Linear Algebra Subprograms) library implementation posted its newest release on Sunday. OpenBLAS 0.3.19 is the new release and brings CPU ID detection for the recently released Intel Alder Lake desktop processors, support for upcoming Xeon Scalable “Sapphire Rapids”, and more: - Intel CPU detection for Alder Lake and Sapphire Rapids. On the Sapphire Rapids front is also an optimized SB-GEMM kernel. # ⚓ Ravgeet_Dhillon:_Create_an_App_Information_Component in_Nuxt⠀⇛ You must have seen multiple apps which show the app’s information like app version and last updated at time in their footers or via a floating action button. In this tutorial, you’ll learn to create a component to show such kind of information in a Nuxt app. [...] That’s it! You have successfully implemented an app information component in your Nuxt app. In the same way, you can add things like Changelog, What’s New, and more to your app by taking the help of publicRuntimeConfig in a Nuxt app. # ⚓ CI/CD_platforms:_How_to_choose_the_right_continuous integration_and_delivery_system_for_your_business_– TechRepublic⠀⇛ Continuous integration and continuous delivery have become mainstays in the development scene in the past few years, making them nearly a requirement for most development workflows. In recent years, new players have come into the market and brought new workflows and platforms to enable additional steps, automated testing and even automated deployment into the mix. [...] In the software development life cycle, developers push code into a Distributed Version Control System such as GitHub, GitLab, Bitbucket or some other platform on a self-hosted system or other system. A continuous integration platform sits in between this, looking for changes pushed into the DVCS and executes builds on the codebase when certain triggers are met. Continuous integration triggers could be based around individual code pushes to a particular branch, merge of code from a pull request or based on a time-based schedule (nightly builds, weekly builds, etc.). The continuous delivery aspect of CI/CD allows software teams to easily and safely get builds into production environments by building code, testing the code and then getting those build artifacts into the production environment. With continuous delivery, builds are typically triggered manually or on a time-based schedule, tests suites are run and results are reported if there are any issues with the code; then afterward, artifacts are made available to ship into a production environment. # § Perl/Raku⠀➾ # ⚓ Writing_a_SNES_assembler_compiler/disassembler –_Day_3⠀⇛ When starting implementing the compiler part of this. I noticed that the grammar does not actually really work, especially if you introduce new lines. If I parse a file with 3 instructions, we catch the \n sometime and the asm- comment token is too greedy. Let’s change the ws rule to only capture horizontal blank (space and tab) and introduce an eol token, this makes the grammar more clear on what we are working on also. # ⚓ PDL_2.063_01_released⠀⇛ There have been a couple of developments in PDL since the last announcement on here I could find, from 2013. To hypersummarise: 64-bit indexing, native complex number support, automatic pthreading using all available CPU cores, faster installation thanks to parallel- building, memory-mapped data, repository hosted on GitHub, easy to use “with” Inline. # ⚓ Raku_Advent_Calendar:_Day_21_–_Santa_Claus_is Rakuing_Along⠀⇛ # § Shell/Bash/Zsh/Ksh⠀➾ # ⚓ Making_a_transect_into_a_point_and_circle⠀⇛ Another way to describe a straight-line transect is with its midway point plus the radius of a circle which includes the whole of the transect. In the Darwin Core scheme for recording biological data, that midway point is at decimalLatitude and decimalLongitude, and the circle’s radius, or half the length of the transect, is the coordinateUncertaintyInMeters. Given the LINESTRING WKT for a transect, you can calculate the midway point and half the transect length in a single AWK command, as explained below. * § Leftovers⠀➾ o § Science⠀➾ # ⚓ Hydrogen_Generation_Made_Easy_|_Hackaday⠀⇛ Even if you never want to generate hydrogen, [Maciej Nowak’s] video (embedded below) is interesting to watch because of the clever way the electrode is formed from stainless steel washers. You’ll need heat shrink tubing, but you ought to have that hanging around anyway. Building the electrode using the techniques in the video results in a lot of surface area which is important for an electrochemical reaction. A standard rechargeable cell provides power for the generator which resides in a modified plastic bottle. The overall build looks good even though it is all repurposed material. The chemistry inside is ordinary water and drain cleaner — potassium hydroxide. We don’t need to tell you to be careful with that and also take care of what you do with the explosive gas. We say “explosive” rather than “flammable” because this design doesn’t separate the hydrogen from the oxygen, and the resulting mix is ready to go off. The video shows a few homemade rockets using the fuel and while they aren’t going to the moon, they do pack quite a bit of energy. # ⚓ Is_Cloud_Seeding_Good,_Bad,_Or_Ugly?_|_Hackaday⠀⇛ The Chinese Communist Party celebrated its centenary on the 1st of July, 2021. For such a celebration, clear skies and clean air would be ideal. For the capable nation-state, however, one needn’t hope against the whims of the weather. One can simply control it instead! A recent paper released by Tsinghua University indicated that China had used cloud seeding in order to help create nicer conditions for its 100- year celebration. Weather modification techniques have been the source of some controversy, so let’s explore how they work and precisely what it was that China pulled off. # ⚓ Li-ion_Battery_Low-Level_Intricacies_Explained_Excellently |_Hackaday⠀⇛ There’s a lot of magic in Lithium-ion batteries that we typically take for granted and don’t dig deeper into. Why is the typical full charge voltage 4.2 V and not the more convenient 5 V, why is CC/CV charging needed, and what’s up with all the fires? [The Limiting Factor] released a video that explains the low-level workings of Lithium-ion batteries in a very accessible way – specifically going into ion and electron ion exchange happening between the anode and the cathode, during both the charge and the discharge cycle. The video’s great illustrative power comes from an impressively sized investment of animation, script-writing and narration work – [The Limiting Factor] describes the effort as “16 months of animation design”, and this is no typical “whiteboard sketch” explainer video. This is 16 minutes of pay-full-attention learning material that will have you glued to your screen, and the only reason it doesn’t explain every single thing about Lithium-ion batteries is because it’s that extensive of a topic, it would require a video series when done in a professional format like this. Instead, this is an excellent intro to help you build a core of solid understanding when it comes to Li-ion battery internals, elaborating on everything that’s relevant to the level being explored – be it the SEI layer and the organic additives, or the nitty-gritty of the ion and electron exchange specifics. We can’t help but hope that more videos like this one are coming soon (or as soon as they realistically can), expanding our understanding of all the other levels of a Li-ion battery cell. o § Hardware⠀➾ # ⚓ Keebin’_With_Kristina:_The_One_With_The_Hole-y_Keyboard_| Hackaday⠀⇛ According to Google Translate, kleks is Polish for (and I’m cherry-picking definitions here) the word ‘splash’. Well, [deʃhipu]’s hole-ful and soulful Kleks Keyboard certainly made a splash with me. [deʃhipu] knows what I’m talking about. As I said in Discord, I just love the look of those holes. They’re purely aesthetic and do a nice job of showing off [deʃhipu]’s routing skills. One might argue that those holes also functional in that they increase aerodynamics and remove a not- insignificant amount of weight for travel considerations. But yeah, they mostly are there to look cool. Upon closer inspection, I saw that the two halves are joined with a series of soldered stitches that are made from a [ggconnector] bent into a u-shape. Now it’s a toss-up as to which is my favorite feature. It seems that [deʃhipu] is never completely satisfied by this or that keyboard build, and that’s okay. That’s normal. That is . . . a big part of what this hobby is all about. Because honestly, what would be the fun in finding The One? We wonder what will happen when the droplets settle. Will [deʃhipu] be satisfied with the Kleks, or will those stylish holes become un-fillable voids? # ⚓ A_Particularly_Festive_Chip_Decapping_|_Hackaday⠀⇛ As we approach the moment in the year at which websites enter a festive silly season of scrambling to find any story with a festive angle, we’re pleased to see the ever-reliable [Ken Shirriff] has brought his own take on Christmas tech to the table with a decapping of the UM66T melody chip that has graced so many musical greeting cards. # ⚓ An_All_In_One_Cube_PC_For_A_1990s_That_Never_Quite_Happened |_Hackaday⠀⇛ When a particular device or appliance is evoked, there comes with it a set of expectations over what it might look like. A toaster, a camera, a washing machine, or a PC, will all have their own accepted form factors, and it’s rare that a manufacturer is adventurous enough to venture outside them. In the world of PCs there was a brief flowering of this type of creativity through the 1990s, and it’s that time which [ikeji]’s cube PC squarely fits in. It’s a 3D printed PC with a built-in display, keyboard, and printer, and while some might categorize it as a cyberdeck we’d say it goes further, we could easily imagine a slightly more polished version being an object of desire back when a powerful machine carried an 80486. # ⚓ The_Assassin’s_Teapot_Is_A_Mischevious_Design_|_Hackaday⠀⇛ Many films use a similar trope when it comes to poisoning. The aspiring murderer ingests a drink poured from the same vessel as that given to their intended victim to indicate the liquid is safe to imbibe. The Assassin’s Teapot is a way one could achieve such a ruse, allowing two different liquids to be poured from what is seemingly a regular teapot, as shown by [Steve Mould]. (Video after the break.) The trick is simple. Two separate cavities exist within the teapot, exiting via their own paths in the same spout. Each cavity also has an air hole in the top. If the hole for a given cavity is blocked by the pourer’s thumb, the liquid will not flow. Each cavity can be filled with its own liquid. For example, one can be filled with tea, the other with poisoned tea. The murderer blocks the hole for the poison cavity when pouring their own beverage, delivering tea to their own glass. Then, when pouring for the enemy, the hole for the tea cavity is blocked, and poison is allowed to flow into the glass of one’s target. # ⚓ Concrete_With_3D_Printed_Foam_Forms_|_Hackaday⠀⇛ The latest 3D printing application? Forming concrete. That’s according to a team at ETH Zurich who claims that construction with foam forms cuts concrete usage up to 70%. It also offers improved insulation properties. You can see a video about the process, below. Typical concrete work relies on a form often made with wood, steel, or plastic. That’s easy to do, but hard to make complex shapes. However, if you can create complex shapes you can easily put material where it adds strength and omit material where it doesn’t carry load. Using a robotic-arm 3D print technique, the researchers can lay out prefabricated blocks of foam that create forms with highly complex shapes. # ⚓ All_Hail_Your_New_Giant_555_Timer_Overlord_|_Hackaday⠀⇛ You asked for it, and now you’ve got it. It’s taken more than a decade of accumulated complaining, but this gigantic 555 timer IC has finally gathered enough psychokinetic energy to take corporeal form and demand fealty from the readers of Hackaday. Or not. The less exciting explanation is that creator [Rudraksha Vegad] was looking for a way to combine his interests in discrete electronic components and woodworking. The result is an incredible build that’s more than just a conversation starter; this desktop-sized version of the iconic integrated timer circuit is fully functional. You can even hook it up to a breadboard, assuming you’ve got some alligator clips handy. # ⚓ Know_Audio:_Mixtapes,_Tape_Loops,_And_Razor_Blades_| Hackaday⠀⇛ For the collector, ther have been a multitude of esoteric tape cartridges and cassettes over the decades, but for the purposes of a Hi-Fi system it’s likely that only two formats will be of interest. The reel-to-reel was the original tape recorder, having as its name suggests a pair of open reels of tape. Consumer and lower-end professional reel-to-reel machines used 1/4 inch wide tape running at a variety of speeds, from 15 inches per second for broadcast quality to 7.5 inches per second as a normal workaday recording medium, and 3.25 inches per second for speech recording. Its extreme ease of editing with a razor blade to cut the tape before splicing with special sticky tape made it a revolution in the broadcast world, and some of us were still doing this in the 1990s. Perhaps you’ll be more familiar with the cassette tape, a format developed at Philips in the 1960s as a dictation medium but which due to its popularity was developed into a Hi-Fi medium and then through the success of Sony’s Walkman, to the genesis of portable music players. This format takes the two reels, miniaturises them, and encases them in a plastic cassette, with a 0.15 inch wide tape containing four tracks in two stereo pairs moving at 1 7/8 inches per second. That the format could be developed to the point at which such a low tape speed could provide what eventually became a high quality system is a tribute to the work of the many engineers at the competing audio companies of the era who pushed it to its limit. o § Integrity/Availability⠀➾ # § Proprietary⠀➾ # § Pseudo-Open Source⠀➾ # § Privatisation/Privateering⠀➾ # § Linux Foundation⠀➾ # ⚓ The_Linux_Foundation’s_report_on diversity,_equity,_and_inclusion_in open_source [Ed: LWN has a conflict of interest (Corbet inside LF), so it has become Zemlin PAC or its megaphone_for_PR_purposes]⠀⇛ The Linux Foundation has announced the posting of a report on its research into diversity, equity, and inclusion in open-source communities. # § Security⠀➾ # § Privacy/Surveillance⠀➾ # ⚓ privacy_in_peril_–_criminals_abusing_tor for_malicous_behavior_should_be_blocked, right?⠀⇛ o § Monopolies⠀➾ # ⚓ Would_you_like_to_have_just_one_monthly_bill…_but_like THIS?⠀⇛ ╘══════════════════════════════════════════════════════════════════════════════╛ ¶ Lines in total: 13030 ➮ Generation completed at 02:43, i.e. 113 seconds to (re)generate ⟲