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|| || || the graphic designer practice deconstructed to its rawer shape || ||
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Welcome !
Softwares, when they are text-based, requires to learn their language. Like the virtual terminal, which is the most primary software, as it communicates directly with the shell.
Unlike AIs, which receive prompts in all human languages and then translate them into machine language, the terminal requires its user to have precise knowledge of possible commands. Jean-Louis Frechin, digital designer, says it beautifully : “interfaces must be rough to keep us alert and explicit to be understood”. The terminal interface is demanding. But this quality, added to that of being open-source, gives back its full capabilities to the user.
It is still a step toward DTP click-interactions, but it can offer similar possibilities.
In this #3 issue of the series, we stepped fully in the front-end area. In the following page we will get closer to the intermediary command languages. We will look how the terminal can be completed by other softwares or packages for images editing.
The terminal is the primary software which gives access to the Operating System of the computer. It is a very direct way to connect to the power and core of the hardware. It takes input, pass them on to the shell, and receives the outputs back to display them on its interface.
It is based on a command-line interface (CLI), which requires from users to know the commands.
As scary as it can look, once its language learned, the terminal becomes the most powerful tool for :
To get a first contact with the terminal, we will try to learn the basic navigation commands of the terminal.
Open your terminal window. Type this command before starting :
cd Desktop\the_treasure_hunt
Rules are simple. In one these two building is hidden a potato-computer !! Your goal is to find it by navigating in the folders through your terminal interface. From building, to stairs, to doors, to rooms.
☖ ⇨ ≡ ⇨ ⊓ ⇨ ⊡ ⇨ ?
On your way, you might encounter some hints. Check what is inside to get closer to your goal!
cd path/to/directory -> to move forward in the files
cd .. <- to move backwards
ls : to see what is inside a folder
cat "file.txt" : to reveal the inside of a document
start "img.jpg" (windows), open "img.jpg" (macos) : to show the image
| command | description | options | example |
|---|---|---|---|
| cd | change directory to the specified path | cd /path/to/directory | |
| pwd | print working directory : display the current working directory | pwd | |
| ls | list files of the current directory | -a : list all files, including hidden files -l : long format with detailed informations -h : list file sizes in a human-readable format |
ls (-option) |
| mkdir | create a new directory | mkdir directory_name | |
| touch | create an empty file | /!\ only for Mac ! | touch name.format |
| rm | remove files or directory | rm name.format | |
| cp | copy the file to the specified directory | cp name.format path/to/dir | |
| mv | move/ rename file or directory | mv name.format newname.flmr OR mv name.format path/to/dir | |
| cat | display the content of a file | cat name.format | |
| head | display the first few lines of a file | -n : specify the number of lines to display | head (-n x) name.format |
| tail | display the last few lines of a file | idem | tail (-n x) filename.format |
| find | search for files or directory | -name : search by name / -type : search by types | find /path/to/search name "*.txt" |
| start | display the image in the default application | /!\ on macos use "open" instead | start "img.jpg" |
Packages are a collection of code and programs ressources, that can be invoked by a command to execute a specific action. Some are a part of the initial OS and others can be downloaded by the users for specific tasks.They can be installed directly from the terminal or downloaded online.
Packages call packages. It means that each new tool installed often required previous packages, called dependancies, to run properly. We'll look here at the main packages to install, to start.
As you see along this zines, each OS requires a different behavior. The methodology stays the same, but the packages and the name of the commands will change.
We will download :
/!\ if an error occurs, the terminal gives precious indications about what went wrong and how to fix it !
Chocolatey, the windows package manager :
To install it, open a window terminal shell as an administrator and run :
Set-ExecutionPolicy Bypass -Scope Process -Force; [System.Net.ServicePointManager]::SecurityProtocol = [System.Net.ServicePointManager]::SecurityProtocol -bor 3072; iex ((New-Object System.Net.WebClient).DownloadString
('https://community.chocolatey.org/install.ps1'))
the command can be copied from chocolatey.org/install
Python, as Pip should already be installed. Verify by :
pip --version
ImageMagick
choco install imagemagick
Homebrew, the macos package manager :
To install it, simply open a terminal window and run :
/bin/bash -c "$(curl -fsSL https://raw.githubusercontent.com/Homebrew/install/HEAD/install.sh)"
/!\ if an error occurs after that, read what the terminal indicates you to do -> there is often a text to copy / or the computer password to fill in
Python
brew install python
To check the version installed, run :
python3 --version
ImageMagick
brew install imagemagick
Vim
brew install vim
One of the most complete and efficient tool for images-editing is the package imagemagick. The instructions to install it are in the previous pages.
As a command-line tool, fo each actions executed we need to to know the specific command and its variations. The official website imagemagick.org is a great reference.
To edit an image, we always need to be in its directory. But how does a command work ?
magick original-image.jpg -command new-image.jpg
magick : calls the package
original-image.jpg : call the file you want to change (sometimes we'll need it in png)
-"command" : type here the name of the command and its variations
new-image.jpg : type in a new image name, to create a new one
To print the image type
2printer.exe -src "2output.jpg" -prn "Canon LBP2900"
| action | command | options |
|---|---|---|
| format conversion | magick 1.jpg 1.png | possible to give a new name to the file |
| size conversion | magick 1.jpg -resize x% 1output.jpg | it will resize it to x% of the original image |
| images transformation | ||
| Threshold effect | magick 2.jpg -threshold x% 2output.jpg | 0% is very light / 100% is very dark |
| Blur effect | magick 3.png -blur ?x? 3output.png | 1x1 is the sharpest / 0x8 is the blurriest |
| Brightness and contrast | magick 4.jpg -brightness-contrast "l"x"c" 4output.jpg | l is the number you want to increase light with / c idem but for contrast |
Resizing the image : a usefull for a lightweight web integration
Threshold effect : the image has to be converted in .jpg first
Brightness and constrast
Blur effect
Edges tracing
Background removing
and so many more possibilities !
Ascii converter is a command-line tool that converts images into ascii art and prints them out onto the terminal.
It can be downloaded via Homebrew for Mac, or following these instructions for Windows.
Mac
brew install TheZoraiz/ascii-image-converter/ascii-image-converter
Ascii technic exists because old computers didn't have enough graphical power to display images, as we can today. Pixels are very heavy, compared to text-characters, which have been chosen as a lightweight alternative. This quality gives them a bit of a revival today : they can be a great help in website eco-conception.
| action | command | options |
|---|---|---|
| classic conversion | ascii-image-converter image.jpg | |
| setting the height | ascii-image-converter image.jg -H "height" | set height in character length, width is adapted to ratio |
| Braille effect | ascii-image-converter image.jpg -b | or --braille |
| Dither | ascii-image-converter image.jpg -b --dither | it helps to make the brialle more visible |
| Color effect | ascii-image-converter image.jpg -C --color-bg | |
| Images saving | ascii-image-converter img.png --save-img . | the image will be saved under this name "image-name"-ascii-art.png, in the directory |
Setting the height
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mediamonster@netre
Braille effect
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠉⠁⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠐⠿⢿⣿⣿⣿⣿⣿⡏⣛⣻⣭⣥⣷⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣠⣖⣀⣀⣀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⢸⣿⣿
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⣿⣿⣿⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿
⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡈⠻⠗⢆⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⣄⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡏⠉⠒⡀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⡟⠀⠀⢀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⠀⣀⢾⣦⣀⣀⣀⡀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠁⠀⢠⣿⣦⠴⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣛⠃⠃⠀⠀⠀⠘⣆⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠇⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠈⢿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠰⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠙⢿⣿⣿⣷⠆⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠉⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⠋⢻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣦⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡾⠽⠽⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣧⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⣾⡿⢿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⢀⣼⣿⣇⣠⣿⣿⣿⣿⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠆⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠻⡟⠛⠋⠀⠻⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣴⠀⠀⠀⣰⣶⣶⣶⡦⠀⢰⣶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⢸⠖⠂⠒⠂⠀⠀⠀⠂⠂⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⠀⢸⡏⠀⠀⠀⠚⠟⠋⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⢈⣧⠀⠀⠀⢾⠂⠀⢤⣤⣤⣤⠀⠀⡤⠤⠤⡄⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⢨⣇⡀⠀⡃⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⢤⠤⠤⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠅⠀⠸⠿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⢸⡇⠀⠀⣿⡆⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠄⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠉⠀⠀⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡿⠀⠀⠀⠏⠉⠀⠀⣻⠀⠀⠀⠂⠀⠋⠉⠁⠀⠀⠁⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⣿⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⠀⠀⣴⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⢘⠃⠀⠀⣿⠀⠀⣾⠆⠀⢸⡟⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣆⠀⠀⠀⠃⠀⠀⠿⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣯⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⢀⠀⠀⠀⣀⠀⠀⣀⡀⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⣼⣛⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⠀⣶⡦⠀⠀⢸⡀⠀⠀⣯⠀⠀⣿⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⢰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠻⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠇⠀⠀⣶⣶⣶⣿⠀⠐⠲⣶⣶⣶⡖⠀⠀⠐⢲⣿⠛⠛⠋⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠙⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠉⠁⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣀⣴⣶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠇⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣇⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣄⣤⣤⣤⣤⣤⣴⣶⣿⣿⡿⠋⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⣶⣶⣦⣄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠐⢿⣤⠄⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠙⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠃⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣾⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠈⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠿⢿⣿⣿⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠹⣿⣿⣶⣿⣿⣿⣿⣿⣿⣷⣦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣄⣀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣙⣻⣖⣈⡉⠛⠛⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣶⣭⣿⣳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⢀⣤⣤⣶⣶⣦⣄⠀⠀⠀⠀⠀⢠⣶⣿⡿⣿⣿⣿⣿⡿⣿⣿⣷⡄⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⡿⣦⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠟⣶⠠⢬⠤⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠠⠄⣂⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⠿⠻⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⣿⣿⣿⣿⡿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣽⢿⠀⣴⣾⣿⣿⣿⡛⠛⣫⣿⡶⣶⣮⡙⠛⢛⣽⣷⣶⣶⣤⠀⠀⣴⣿⢿⣿⣷⣆⡷⣴⣿⣿⣿⣿⣮⣦⣾⣿⣿⣿⣿⣿⡿⠻⡿⠿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣯⣿⣭⣿⣿⣿⢉⣿⣇⣿⣿⣿⣟⠛⣿⣿⣿⣷⣿⣿⡄⣼⣿⣿⣺⣿⣿⡄⢠⣿⣿⣷⣿⣿⣧⠀⣿⣿⣧⣿⣿⣧⠀⣾⣿⣿⣿⣿⣿⡀⢰⣿⣿⣿⣿⢿⣿⠿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢺⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡇⠈⢿⣿⣿⣿⣿⠟⠀⣿⣿⣿⣿⣿⠿⠀⣻⣿⣿⣿⣽⡾⠇⠀⣿⣿⣿⣿⠿⠏⠀⠸⣿⣿⣟⡿⢿⠁⠀⢻⣿⣿⣿⢻⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⣠⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣥⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⣵⣶⢶⣿⣿⢿⣿⣿⣶⣶⣿⣿⡿⢿⢟⣵⣶⣿⣿⣿⡿⡿⣿⣶⣶⣶⣯⡛⠏⣿⡷⣶⣿⣿⡍⠙⣽⣿⡟⣿⣿⣿⡈⢉⣾⣿⣿⣿⣿⣿⣿⣷⠀⢠⣾⣿⣿⣿⣿⣆⠀⣴⣿⣿⣷⣿⡈⣷⣾⣿⠃⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⣐⣄⣶⣟⣥⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣵⣯⣿⣿⡆⢸⣿⣷⣿⣿⣿⣷⠀⣼⣿⣧⣿⣿⣿⣇⢸⣿⣧⣿⣹⣿⣧⢠⣿⣧⣿⣾⣿⣿⠰⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢺⣿⣿⣿⣿⣿⣿⠞⢿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣟⣿⣇⠀⠀⢈⠔⢻⡋⠑⡻⣿⣍⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⡀⠸⣿⣿⣿⣿⠿⠇⢸⣿⣿⣿⣿⣿⣟⠀⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⣟⣈⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⢿⣿⣁⣬⣿⡿⣿⣿⣿⣭⣤⣤⣿⣿⣿⣿⣧⣤⣶⣦⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢿⣙⣿⣿⣿⣯⣤⣼⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠿⠟⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣵⣿⣿⢷⣿⣿⡿⢿⣿⢟⣿⣿⣿⣿⠻⣿⣿⣻⡿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣷⣾⣺⣿⡉⣹⣿⣿⣿⣿⣿⣿⣿⡌⢱⣿⣿⣿⣿⣿⣷⠈⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠹⠋⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣟⣿⣫⣇⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⢠⣿⣿⣿⣾⣿⣿⡇⣾⣿⣷⣿⣿⣿⣿⡄⣿⣿⣷⣾⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⠇⢿⣿⣿⣿⣿⣯⣿⡇⢻⣿⣿⣿⣿⣛⣩⣾⡇⢸⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣠⣿⣿⣿⣿⣿⣿⣿⡿⠋⠈⠛⠋⢂⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠿⠿⠿⢿⣿⠟⠃⠸⣿⣿⣿⣿⣿⠿⠁⢿⣿⣿⣿⣿⠿⠿⠀⢻⣿⣿⣿⡿⠿⠃⠀⢿⣿⣿⣿⡿⠟⠀⠸⣿⣿⣿⡿⠿⠛⠀⠘⣿⣿⣿⣿⠿⠏⠉⠀⠸⣿⣿⣿⠿⢿⣿⠀⢘⣿⣿⣿⣍⣉⠉⠛⢛⣿⣿⣷⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠪⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⣛⣋⣡⣥⣾⡿⠿⠛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣰⣾⣿⣿⣿⣿⣦⠈⠉⣻⣾⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠁⢠⣿⣿⣿⣻⣿⣿⣇⢀⣾⣿⣿⣷⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡿⢿⣿⣧⣤⣀⣀⠀⠀⠀⠀⠀⣠⣶⡀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠋⢹⡿⢡⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⣿⣿⣿⣿⣿⡿⠟⠋⠋⢻⣿⣿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠠⣠⣻⣿⣿⣿⣿⡿⠟⠁⠀⣻⣿⣿⣿⣿⣿⣷⣾⣷⣿⣿⣿⣷⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠁⣸⣿⠿⠛⠛⠛⠉⠈⠋⠀⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠻⠿⠿⠿⠻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠀⠀⠈⢿⡿⠋⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣷⣦⣤⣤⣄⣤⡒⣻⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢶⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⢿⣿⣿⣿⣽⣿⣿⣿⣏⣀⣈⣻⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀
⣿⣿⣿⣿⣿⣟⣼⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣀⡀⡀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠀⠀⢀⣤⣶⣦⣄⣀⣀⠀⠀⠀⡀⣀⣠⣠⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠿⣿⣿⡄⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣠⣴⣴⣶⣶⣶⣦⣤⣦⣤⣄⣤⣤⣤⣤⣤⣤⣠⡴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣴⣤⣤⣴⣤⣶⣠⣴⣦⣦⣴⣶⣶⣶⣴⣤⣾⣾⡿⠟⢻⣿⣿⣿⣿⣿⣿⣾⣿⠟⠀⠀⠈⠃⣾⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣾⣿⣃⣀⣸⣿⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠈⢹⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⠟⠛⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⠛⠋⠉⣉⣻⣿⣿⡿⣿⠛⠀⠀⠈⠉⣻⣿⣿⣿⣿⣿⣿⣷⣦⣤⣴⣶⣿⣿⣿⣿⣋⣽⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠛⠉⠀⠀⠀
⣿⣿⣿⣿⡿⠿⠿⠛⠟⠿⠛⠛⠛⣿⢻⠿⠛⣿⠿⠷⠶⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠓⠻⠛⠿⠿⠿⠿⠟⣿⢿⠿⠿⠿⠿⠿⠿⠿⠟⣿⠿⠷⠛⠛⠛⠛⠿⠿⠿⠿⠻⠿⠛⠛⠛⠿⠻⠟⠻⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠛⠻⠻⠂⠀⠈⠉⠉⠉⠛⠉⠿⠋⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠀⠟⣿⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀
Dither effect
⠀⠀⡀⣀⢀⢀⢀⠠⠀⡐⡾⡽⣯⣻⡪⡎⡆⡂⡂⠄⢂⢌⢎⢆⢇⢇⢯⣗⡯⣿⣻⣟⣿⡽⣯⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⢿⡿⣟⣿⣟⣿⣟⣿⣻⣟⣟⣿⡽⣿⢽⣻⡽⣯⢿⣽⣻⣿⣿⢿⢽⢽⡽⣽⢽⡿⣽⢽⢽
⡿⡽⣝⣎⢎⢢⠂⠄⢅⢐⢽⢯⣗⡷⣽⣺⣪⡪⢌⢌⢔⠰⣝⣕⣗⢽⢵⣳⣟⣿⣟⣯⣷⣿⣻⣟⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣻⣿⣟⣿⣯⣿⣯⣿⣷⣿⣷⣿⣷⣿⡿⣿⢿⣻⣿⣟⣯⣿⢷⡿⣽⡷⣿⡽⣷⣻⡯⣿⢽⡯⡿⣽⢾⣽⣿⣿⢯⣟⣽⣺⢽⢽⡯⡯⡯⡯
⡿⣽⣳⡳⣝⡎⡎⡎⡢⡡⣫⣟⡷⡯⣗⣗⣗⢽⡸⡢⡱⡱⣳⡳⠳⠫⠛⢊⢛⠻⠻⢿⢿⣾⢯⣿⣽⣾⣿⣿⣻⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⢿⡿⢟⠿⠽⠿⠿⢿⣿⣿⣿⣿⣫⣿⣾⣿⣿⣟⣿⣿⣿⣿⡿⣟⣿⣽⣿⣽⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⢿⡿⣿⢿⣻⣿⣻⣿⣽⣿⣾⣿⣾⣷⡿⣿⢿⡿⠟⠗⡛⠹⣙⢻⢻⢯⡿⣷⣟⣯⡷⣿⢽⡯⡿⡽⡯⣟⣾⣿⣿⢽⣺⣺⣺⢽⡽⣯⢯⢯⣻
⣿⡽⡾⡽⡵⣝⢮⡪⡪⡪⡺⣾⢽⡯⣟⣾⣺⣳⠝⠞⠘⡈⣈⣠⠀⠀⠌⠢⠣⢫⢫⢢⠣⡪⣛⢯⣿⣻⣿⣻⣿⣿⣿⣿⣿⣻⣿⡿⠟⠋⡈⠀⠄⡐⠨⡨⢪⠪⡢⣢⡮⣔⠡⠡⠩⡉⡫⡛⡿⣿⣿⣿⣷⣿⣿⣿⡿⢿⡿⠟⠋⠍⠄⠅⡂⡢⡑⢔⢐⢐⢐⠠⡑⢭⢹⡻⡿⣯⣿⣾⣿⣾⣟⣿⠟⠉⠄⡑⠅⡂⢅⢂⢪⢸⢸⡹⣳⣯⡷⣟⣯⢿⡽⣯⣟⣯⡯⣿⣿⣯⣟⣞⣞⢾⢽⡽⣯⢯⣟⣞
⣷⣻⢯⢿⢽⢽⢵⢝⢮⡳⡽⣽⢯⡿⣽⡾⠗⠁⠁⠀⠀⠈⠙⠈⠀⠁⠌⠌⢌⠢⡣⡣⡫⣞⣯⡷⣽⢽⣿⡿⣿⣿⣿⣿⢿⣿⠛⠡⠈⠈⠀⠀⡂⠢⡑⡌⡆⡧⣪⢢⢩⢢⢱⢱⢱⢱⡱⣕⡧⣗⡽⡽⣿⣿⣿⣿⡿⠃⠀⠈⡀⠅⠌⡂⢆⢆⢎⢜⢢⢱⢰⢱⢸⢜⡮⡾⣽⣽⣻⣿⣾⣿⠊⠁⠀⠐⠀⢐⢐⠐⢔⢸⢰⢱⢕⣝⣞⣞⣿⢯⣿⢽⡯⣷⣻⣺⡽⣿⣿⣗⣗⣗⡯⡯⡯⣿⢽⣳⣳⣳
⣿⣺⢿⡽⣯⢯⡯⣯⡳⣝⢾⣽⣿⡿⠙⠁⣄⡂⠐⠀⠀⢀⠀⠀⢐⠨⡨⡪⣲⣹⢼⣪⡯⣞⣗⣿⢽⣻⣺⡻⠿⠿⢿⣿⠟⢀⠄⠀⠀⠀⠀⡐⢌⢜⢜⢜⡮⣟⡮⡧⣣⡳⡹⣕⢗⡷⣽⣳⡿⣯⢿⢽⢝⣯⡾⠋⠀⠀⠀⠀⠀⢌⢐⠅⡇⡣⡣⡣⡣⡳⣕⡵⡯⣯⣿⡽⣟⣷⣷⢻⣷⠃⠀⠀⠀⠀⠐⢀⠂⢕⢱⢱⢱⡳⣝⣾⣺⣿⣽⣿⣟⣯⣟⣷⣻⢾⡽⣿⣿⣗⣟⡾⡽⡽⡯⣟⣟⣞⣞⣞
⣿⢾⣻⣽⣿⣟⣯⡷⣯⢯⣗⣿⡯⢁⢜⠜⠖⠡⠀⠀⠀⠀⠫⡠⡡⢱⢱⢹⡺⡪⣟⣞⡯⣟⡷⣯⢯⣗⣗⢯⣢⡣⡖⠀⠀⠘⠀⠀⠀⢀⠐⢌⢢⢣⡳⣽⣽⣟⣯⣟⢮⢾⢽⣺⣯⣿⣯⣿⣟⣯⡯⣯⡣⣟⢄⠄⠀⠀⠀⠠⠨⡐⡰⡱⡱⡕⣗⣝⢮⣳⣳⢽⣻⣿⡷⣿⣿⣿⣞⡧⡃⡰⡨⣐⠨⠀⠌⡐⡈⢆⢣⢣⢳⡹⣺⣺⣳⢿⣻⡿⣿⡿⣿⡾⣽⢯⣟⣿⣿⣳⣗⡯⡿⡽⣽⢯⣗⡷⣳⢯
⣿⣿⡿⣿⣯⣿⢷⣿⣽⢽⣺⡽⠃⠀⠁⠀⠀⠀⠀⠀⡀⠡⢐⠔⡜⡔⡆⡧⡽⣞⡮⡮⡯⡯⡿⣝⣗⣗⣝⢧⣳⠉⠀⠀⠀⠀⠀⠀⡐⡠⡊⡆⣗⣗⣯⣷⣿⣻⣽⣾⣻⣽⢿⣽⣯⣷⣿⣷⣿⣯⣟⣮⣿⣟⡆⡆⡠⢐⠨⡈⡆⡎⡜⣜⢜⣞⣞⡮⣗⡷⡽⣯⣿⣾⣿⣿⣿⣿⣯⣯⣷⣿⣽⣎⡎⣎⠪⡐⠨⢂⢇⢇⢧⢫⡺⡪⡾⣽⣳⡿⣿⡿⣿⣿⡯⣿⣺⣿⣿⣳⣗⡯⡿⡽⣽⣟⡾⣝⣗⡯
⣿⢷⣿⣿⣻⣾⡿⣷⣻⣽⠇⠐⠩⡢⠊⠀⠀⠠⢀⠡⡀⡪⡢⡣⣣⡳⣝⡾⣽⣽⣟⣿⣽⣟⣯⣟⣞⢞⣮⣻⢪⠀⡀⢀⠠⢀⢂⠅⡆⡕⡕⣕⣗⣯⣷⣿⢿⣿⣿⣽⢿⡾⣟⣯⣿⣿⡿⣿⣿⣾⢿⣾⣿⣿⣺⡸⡸⡨⡪⡪⡪⡪⡪⣮⣳⣳⣗⡿⣯⣟⣿⣽⣾⣷⣿⣿⣟⣯⣿⣯⣿⣿⣷⡷⡯⣎⢎⢢⢡⢱⢱⢱⢱⢵⡹⡽⣽⣻⣽⣿⣿⣿⣿⣷⣿⡯⣿⣿⣿⣺⢾⢽⢽⢯⢷⡯⡯⣗⣗⡯
⡿⣟⣿⣾⢿⣯⣿⢿⣽⠇⠀⠀⠀⠀⠀⡀⠄⢅⢢⢱⢱⢱⡱⣝⢮⣞⡷⣟⣿⡾⣟⣯⣿⣟⣷⡷⣯⣟⣾⣟⡆⡕⡐⡐⢌⠢⡢⡣⣣⡳⣝⣞⣷⣻⣽⣾⣿⣿⣾⣿⢿⣻⣿⢿⣿⣻⣿⣿⣷⣿⣿⣿⢿⣿⡾⣝⣮⡺⣜⢮⢮⡫⣯⣺⣺⣞⣷⡿⣿⣽⡿⣾⣿⣯⣿⣟⣿⣿⡿⣿⣿⣿⢿⣿⣻⢮⣳⡱⡕⣕⢵⡱⣳⡳⡽⣯⣿⣻⣿⡿⣟⣯⣿⣿⣿⣻⣽⣿⣿⣺⢽⢯⢿⢽⣻⡽⡯⣗⡷⡯
⣿⢿⣻⣽⣿⢿⣽⡿⣿⠁⡀⠄⢑⢺⢐⢔⢱⢱⢱⡣⣳⡳⣽⣺⣽⢾⣻⣿⣻⣿⣿⡿⣟⣯⣿⣻⣽⣿⣿⣿⣺⢜⢌⢎⢆⢧⡳⣝⣞⣞⣷⣻⡾⣟⣿⣟⣿⣯⣿⡿⣿⣿⣻⣿⢿⣻⣿⣷⣿⣟⣷⣿⣿⣿⣿⣻⣞⡾⣵⣫⣗⣽⣺⣺⣳⣟⣷⣿⣿⣽⣿⣿⣷⣿⡿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣻⣽⡺⡮⣳⣳⣳⢯⣺⣺⣻⣯⣿⣿⣻⣿⣿⣿⣿⣿⣻⣽⣿⣿⡷⡯⡿⡽⡯⣯⢿⡽⣽⣳⢯⣻
⣿⢿⣿⣻⣽⣿⣟⣿⣿⡂⢄⢡⢃⠢⡣⡣⡣⣣⡳⣝⡾⣽⣻⣾⣻⣿⣻⣟⣿⣽⣾⣿⣿⡿⣿⣻⣿⣿⣾⣿⣯⣯⣳⢵⢽⣺⣽⣳⣻⣞⣷⣟⣿⣻⣟⣿⣻⣯⣿⢿⣻⣽⣟⣿⢿⣿⣻⣾⣿⣻⣿⣿⣿⣿⣿⣻⣾⣯⣷⢷⡷⣷⣻⡾⣯⣿⣯⣷⣿⣽⣿⣾⢿⣷⣿⣿⣟⣿⣿⣿⣿⣿⣯⣿⣟⣷⣻⣽⣳⢽⢽⣻⣗⣯⣿⣽⣷⣿⣿⣿⣿⣿⢿⣻⣿⡿⣽⣿⡿⣝⡯⡿⡽⣽⣻⣽⣳⢽⢽⣺
⣿⣻⣽⣿⣻⣽⡿⣵⣳⣳⡌⡆⡇⡕⣕⢵⢝⣞⡮⣷⣻⣿⣽⣾⣿⢿⣻⣟⣿⣻⣯⣷⣿⢿⣿⢿⣻⣽⣿⣿⣿⣷⣯⡿⣽⢿⣾⣽⢷⣟⣷⢿⣽⣯⣿⣻⣽⣿⢾⣿⣟⣯⣿⣻⣿⣯⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣾⢿⣻⣿⣽⣯⡿⣿⢾⣻⣾⣿⣽⣾⣿⣿⣟⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣽⡷⣗⣯⢯⣟⡾⣽⢷⣿⣻⣿⣟⣿⣿⣯⣿⣿⣿⣿⢯⣿⣿⣯⢷⣻⢽⢯⣯⢷⣗⡯⡯⣟⣞
⣿⣻⣯⣿⣻⣟⣿⣿⣽⣷⣿⡜⡎⣞⡮⡯⣳⣳⢿⣽⢾⡷⣿⢷⡿⣟⣿⣻⣟⣿⣯⣿⣻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣻⣽⣟⣿⣯⡿⣟⣿⣾⣻⣽⣿⣾⣿⣯⣿⣿⣽⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣿⡾⣿⢿⡿⣿⣻⣾⣿⣽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢯⣿⡽⣷⣻⣟⣿⣻⣿⣻⣿⣿⡿⣿⣿⣿⣿⢯⡿⣿⣿⣽⢽⣺⢯⣟⡾⣟⡾⡽⡯⣗⣯
⣿⣯⣿⣽⣿⣻⣿⢾⣿⢾⣷⡿⣎⡳⡽⣽⣳⣻⢽⢾⣻⣟⣿⣻⣟⣿⣻⣽⡿⣷⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⡿⡿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⣿⣿⣿⣿⢿⣟⣯⣿⣿⡿⣿⣟⣿⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣻⣿⣟⣿⣾⣿⣷⡿⣟⣯⣿⣟⣿⣟⣿⣿⣷⣿⣿⣿⢿⡽⣯⢿⣿⣿⣞⣯⢯⣟⣞⣿⣽⢽⢯⢯⣗⡷
⣿⣾⣯⣷⣿⢿⣽⣿⣟⣿⣷⡿⣿⣷⣝⡪⢎⢮⢫⣟⢷⣻⢷⣟⣯⣿⣟⣯⣿⣿⣯⣿⣿⣯⣿⣿⡿⣿⡿⣿⣻⣽⣾⣯⢷⣻⡽⣗⣯⢿⣽⣟⣿⣻⣿⣻⣯⣿⣾⣿⣾⣿⣾⣿⣾⣿⣿⣿⣿⢿⣷⣿⣿⣿⣿⢿⣯⣿⢿⣽⣯⣷⢿⣻⡾⣯⡿⣯⣿⢿⣽⣿⣻⣿⣻⣯⣿⣷⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣷⣿⣿⣿⣯⣿⣟⣿⣿⣽⣾⣿⣿⣾⣯⢿⣽⣻⣿⣿⢾⢽⣽⣺⣳⢿⣺⢽⢯⣟⡾⡽
⣿⣾⣯⣿⣾⣿⢿⣷⡿⣿⡾⣿⣻⣷⡿⠛⠂⢁⢋⢞⣯⣿⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣟⣿⣿⣿⢿⣿⣻⣷⣟⣿⣽⢿⣽⡾⣿⢾⣽⣯⡿⣾⣟⣯⣿⣯⣿⣽⣾⢿⣽⢿⡾⣟⣷⡿⣿⣻⣽⣷⣿⡾⣿⣻⣾⢿⡷⣿⡾⣿⣻⣟⣯⣿⢿⣽⡿⣯⣿⣻⣽⡿⣟⣿⣯⣿⣷⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⢿⡿⣿⢿⣿⣿⣿⣿⣾⣿⣳⣿⣿⣿⢽⣻⣺⣳⢯⣿⢽⢯⣟⡾⡽⣽
⣿⣾⢿⣾⢿⣾⣿⣟⣿⣟⣿⣟⡿⠉⠀⠀⠀⡂⢕⢝⢵⣟⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣽⣿⢿⣻⣿⣽⣾⣿⣿⣽⣾⣿⣽⣾⣿⣷⣿⣿⣿⣷⣷⣿⣿⣾⣿⣾⣾⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⡿⣞⣿⣷⣿⣿⣿⣿⣟⡷⡯⣗⢿⢽⢯⣟⣯⡷⣟⣯⣿⣿⣽⣿⣾⣿⡿⣽⣳⣻⢾⡽⣯⢿⣽⣺⢽⣽⣳
⣿⣽⣿⣻⣿⢿⣾⢿⣯⣿⣷⠎⠀⠀⠀⠀⠁⠍⠎⢎⢎⢮⢺⡺⡷⣿⣿⣿⣿⣿⣿⡿⣞⣿⡿⣿⣟⣿⣿⣿⣯⢳⢽⣿⢿⣿⢿⣿⣻⣿⣽⣿⣻⣿⣻⣟⣿⣟⣿⣟⣿⢿⣻⣿⣽⣿⣽⣷⣿⣯⣿⣟⣿⣿⣻⣿⣽⣾⣿⢿⣽⣿⣽⣷⣿⣷⣿⣿⣽⣿⣿⣽⣿⣯⣿⣿⣿⢿⣿⣿⣿⡿⣽⣳⣿⡿⣷⣿⣿⣳⢯⢯⣪⠳⣝⣗⣗⣷⣻⣯⢿⣽⣿⢿⣷⣿⣿⡿⣽⢾⡽⣽⢽⡿⣽⣺⢾⢽⣺⣞
⣿⢿⣾⢿⣻⣿⣻⣿⣟⣷⠏⠀⠀⠀⠀⠀⠀⢁⠈⠢⡑⡕⣕⢯⣟⣿⣽⣿⣟⣿⣿⣿⢯⣷⢿⣿⣿⣿⣿⡷⣿⣺⣿⡿⣿⣻⣟⣯⣿⢾⡷⣿⣽⢾⣯⢿⣳⣿⡽⣯⣿⣻⣯⣷⢿⡷⣟⣿⣾⣻⣷⢿⣯⣿⣻⣽⣿⣽⡿⣟⣿⣯⣿⣯⣿⣽⣾⣯⣷⣻⣾⣿⣾⣯⣷⣿⣾⣿⣿⣿⢿⡯⣗⣯⣷⣿⣿⣿⣟⡾⣝⢽⡻⡱⡳⣵⣳⣳⢷⣻⣟⣯⣿⣿⣿⣷⣿⢿⡽⡯⡿⣽⣻⣯⢷⢯⢿⢽⣺⣞
⣿⣿⣻⣿⢿⣻⣿⣽⡿⡟⢀⠐⢀⠀⠠⠀⠈⢀⠠⡱⡸⣪⡾⣯⣿⣽⣿⣻⣿⣿⣿⣿⣯⣟⣿⣽⣾⣿⣿⣿⢿⣿⣻⣿⣻⣯⣿⣽⢾⣟⣿⣽⢾⣻⡽⡿⡽⣾⡻⣽⢾⢯⢷⢟⣿⣻⣟⣷⢿⣽⡾⣟⣿⡾⣿⣽⣾⣯⣿⣟⣯⣷⡿⣷⢿⣽⡾⡯⡯⣿⢽⣯⢿⡽⣿⣽⢯⣿⣿⢿⣿⡯⣗⣯⣿⣟⣿⣿⣳⡻⡮⡳⣝⢮⣻⣺⡺⣞⣟⣿⡿⣿⣿⣿⣿⣽⣿⡿⣽⢯⣟⣷⣻⣞⣯⢿⣽⣻⣞⡾
⣿⣽⣿⣽⣿⣿⣻⣽⣿⡇⡐⠨⢀⠨⠐⡈⡐⠄⣎⢮⢾⣽⢿⣯⣿⣽⣿⣿⣻⣷⣿⣿⣷⣿⡽⣟⣿⣿⣿⣿⣻⣟⣯⣿⣽⢷⡿⣞⣿⡽⣾⡽⣯⣟⣮⣟⣞⣾⣺⣿⣳⣿⣽⣻⣿⣿⣯⣿⣻⡷⣿⣻⡷⣿⣯⣷⢿⡾⣷⣟⣯⣷⡿⣟⣿⣽⣟⣯⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⣟⢞⣞⣯⣿⣿⣿⣗⡯⣯⡫⣞⣵⣳⣳⢯⡿⣽⣟⣿⣿⣿⣷⣿⣿⡿⣿⢽⡯⡷⣯⣟⡷⣯⣟⣾⣺⢾⢽
⣿⣯⣷⣿⢿⣾⡿⣿⣾⢕⢌⠌⡀⠂⠅⠢⡘⡜⣜⢾⣽⢾⣿⣿⣿⣽⣷⣿⣿⢿⣿⣿⣿⣾⢿⣿⢿⣻⣿⣯⣿⣻⣽⡷⣟⣯⡿⣯⡷⣟⢗⣿⣗⣿⡺⡪⣫⣫⣻⡿⣯⣫⢯⢯⣻⣯⣿⣯⣿⣻⣽⣯⣿⣻⡾⣯⣿⣻⣯⣟⣷⢳⣿⣿⡿⣞⣯⣷⢷⣽⣾⣽⣾⣽⣽⣽⣽⣾⣿⣿⣻⣗⢽⣺⣿⢿⣷⣿⣿⣽⢮⣻⣺⣺⣺⣺⢯⣿⣻⣽⣿⣿⣟⣿⣿⣿⣿⣻⣽⣻⡽⣷⣻⡯⣷⣻⣞⣞⡯⣟
⣿⣯⣿⣻⣿⣻⣿⣟⣯⣏⢇⠅⠠⢈⢌⢪⢪⢺⡺⣽⢾⣿⣻⣾⣿⣿⣻⣯⣿⣿⣿⣿⡿⣿⣟⣿⣿⣿⣿⣿⣯⡿⣷⣟⣿⣳⡯⡷⣿⣯⣺⣿⣿⣺⣳⡽⣷⣷⣷⣿⣷⣿⣿⣿⣿⡿⣿⣿⣾⣯⡷⣿⣞⣯⣿⣻⣾⢳⢽⣿⡾⢽⢿⣻⣿⣳⣻⣽⣻⣝⣟⣟⣿⣿⣻⣻⣻⣻⣿⣟⣿⣗⢽⣺⣿⣿⡿⣿⣿⣿⣯⡿⣾⣺⡾⣽⢿⣽⣿⡿⣿⣿⢿⣿⣿⣟⣯⣷⣻⣗⣿⢽⣯⣟⣷⣳⣟⡾⡽⣯
⣿⣯⣿⣻⣽⣿⣷⣿⡿⣿⡜⠠⠨⢐⢎⢮⣪⡳⡽⡽⣽⢾⣟⣿⣷⣿⣿⢿⣟⣯⣿⣿⣿⣿⣿⣻⣽⣿⣿⣿⣾⢿⣻⢞⣽⣯⡯⣻⢿⣷⢯⣷⣿⣯⡷⣻⡫⣟⣯⣻⣻⢯⣻⣽⣺⣿⢿⣷⢿⡾⣟⣿⣞⡿⣾⡽⡾⣝⣿⢿⣯⣳⣟⣿⣿⡳⣿⣿⣷⣿⣾⣯⣿⣷⣯⣿⣽⣿⣻⣿⢿⡳⣝⡾⣿⣾⣿⣿⣿⣿⣿⣿⣯⣷⡿⣟⣿⣟⣷⣿⣿⣿⡿⣟⣯⣿⡿⣞⣷⣟⣾⣻⣷⣻⣞⡷⡯⡿⣽⣳
⣿⣯⣿⣟⣿⣷⡿⣷⣿⣿⣿⡌⢌⢜⢜⣕⢧⡫⡾⣽⣻⣟⣿⣿⣽⣾⣿⣿⢿⣿⣿⣿⣿⣽⣿⢿⣻⣿⣿⣷⣿⢿⣻⡽⣻⣿⣝⣞⣿⣿⡹⣺⣟⣿⣽⡾⣿⢿⣾⣿⣽⣿⣿⣾⣷⣿⣿⣿⡿⣟⣿⣳⡿⣽⢷⣟⣟⢺⣺⣿⣿⡷⣿⣿⣿⢽⣻⣿⣿⣿⣻⡿⡿⡿⣿⡿⣟⣿⡿⣿⣿⡯⣪⢿⣻⣿⣻⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⢿⣿⣿⣿⣿⣟⣯⣿⣿⡿⣯⣷⣻⢾⣽⣾⣳⡯⣿⢽⡯⡷⣯
⣿⣯⣷⣿⡿⣷⣿⣿⣟⣷⣿⣿⡰⡱⡱⣕⢷⢽⡽⣯⣿⣽⣿⣾⢿⣯⣷⣿⣿⣿⣾⣿⣿⣟⣿⣿⡿⣟⣿⣽⣾⣿⣿⢽⣻⣿⣷⣞⣷⣿⣮⣻⣟⣿⣿⣟⣿⣻⣿⣽⡿⣯⣿⣽⣿⣽⢿⣷⢿⡿⣯⣿⡽⣟⣯⢿⣪⡺⣟⣿⣷⣻⣗⣿⣿⢽⣻⣿⣷⣯⣷⡿⣽⣿⣽⣯⣿⣿⢿⣿⢾⡯⣺⣻⣿⢿⣿⣿⣿⣿⣿⣿⣳⢿⣝⣟⡾⣯⢿⣽⢿⣻⣿⣟⣿⣿⣟⣷⣻⣞⣯⣷⢿⣺⡯⣿⢽⢯⣟⡷
⣿⣿⣽⣷⣿⣿⢿⣾⣿⣟⣿⣾⣷⡙⣞⢮⢯⣯⣟⣿⢾⣻⣾⣟⣿⣯⣿⣻⣿⣟⣿⣿⣟⣿⣿⣯⣿⣿⣿⣿⣿⢿⣾⡯⣿⣿⣿⣞⣿⣿⣿⣺⣿⣿⢿⣽⣯⣷⢿⣾⣻⣯⡿⣾⢷⣟⣿⣽⣟⣿⣻⣾⣻⣯⣟⣯⢷⣻⡿⣿⢿⣿⢿⣿⣿⢽⣿⣿⢿⣻⣿⢿⡿⣿⣻⣿⣿⣾⣿⣿⢿⣏⢮⣷⣿⣿⢿⣿⣿⣿⣟⣞⣾⡳⡳⣕⢯⢯⣟⣾⢿⣿⡿⣿⣟⣿⣽⣾⣻⣞⡷⣿⡯⣷⣻⣽⣻⡽⣗⡿
⣿⣷⣿⢿⣽⣾⣿⣿⣷⣿⣿⣯⣿⣿⣌⢯⣻⢾⡽⣾⣻⣯⣷⢿⡷⣿⢾⣿⣽⣿⣿⣿⡿⣿⣷⣿⢿⣽⣿⣿⢿⣿⢿⣽⣻⣿⣗⣗⣿⢿⣲⣳⣟⣿⣿⣯⣷⣟⣿⣞⣿⣺⢿⣽⢿⡽⣷⣻⡾⣯⣗⢯⣷⣿⡺⣽⣯⣷⢟⣿⣻⣟⣿⣻⣾⣻⣾⣿⣿⡿⣿⣟⣺⢿⣿⣿⣽⣿⣽⣾⣿⡳⡽⣾⢿⣾⣿⣿⣿⣟⣞⢞⡚⣎⢯⡺⣝⣗⣟⣾⣿⣿⣿⣿⣿⣟⣷⣟⡾⣗⣿⣯⢿⡽⣞⡷⣯⢿⡽⣯
⣿⣿⣾⣿⡿⣟⣿⣾⡿⣷⣿⣯⣿⣾⣿⣷⣱⢫⢯⡳⣗⣷⣻⣯⣿⣻⣿⣷⣿⣿⣿⣿⢿⣟⣿⣾⣿⣿⣿⣿⡿⣿⣿⢿⡾⣿⣿⡮⣿⣿⣧⢷⣿⢿⣻⣷⣿⣽⢾⣳⣯⣟⣯⡿⣽⢿⡽⣷⣻⣽⡲⣽⣻⣽⡯⣾⣿⣯⣳⣿⣿⡪⣯⣿⣞⢼⣾⣿⣾⣿⣟⣷⡾⣿⣿⣻⣿⣻⣯⣿⢿⣇⢯⡿⣿⣻⣾⣿⣿⣺⢪⡣⡣⡪⣺⡪⣗⣗⣯⣷⣿⣷⣿⣿⣯⣿⢷⣻⢿⣽⢾⣻⣽⣻⡽⣯⢿⡽⣯⢷
⣿⣷⣿⣯⣿⣿⣿⣻⣿⣿⣯⣿⣿⣽⣾⡟⠋⠀⢁⢏⡷⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⣯⣷⣿⣿⣷⣿⣿⢿⣟⡿⣿⣟⣯⣿⣿⣟⢯⡿⣿⣿⡿⣾⢯⣿⣻⡺⣽⣾⣻⣽⢿⣽⢯⡷⣟⣞⣾⢿⡿⡽⣿⣾⣿⣺⣽⣿⣪⣿⣽⣗⣽⣯⣿⣿⢯⣿⣷⣿⣿⣽⣿⣻⣿⣻⣟⣿⢮⣳⢿⣿⣻⣿⣿⡳⣕⢇⢇⠕⣝⢞⡮⣗⣯⣷⣿⣯⣿⣿⣻⣿⣿⣻⣟⣿⣾⣻⣯⣷⢯⣿⢽⡯⣿⢽⣻
⣿⣿⣾⡿⣯⣷⣿⣿⢿⣾⣿⢿⣾⡿⠋⠐⠀⠀⠂⠕⡝⡽⡽⣟⣿⣿⣻⣷⣿⣿⣿⣿⡿⣿⢿⣿⣻⣯⣿⣿⣽⣾⣿⡿⣽⣟⣿⣯⣾⣿⣯⢳⢿⡿⣿⣻⣟⣿⣳⣷⣹⣿⢿⣿⢾⣻⣽⣟⣿⢽⣻⣞⣿⣻⣞⣿⣾⣟⣯⣿⣿⢯⣿⣻⡿⣽⢿⣿⡿⣝⣿⣿⣽⣾⣿⡾⣿⣽⣿⣻⣿⡣⡯⣿⣻⣽⣿⡳⡽⡜⡜⡔⡵⣕⢽⣺⢽⡾⣿⣾⣿⣿⣻⣿⣿⣿⣻⣿⣻⣿⣻⣿⣻⣿⢿⣿⢿⣿⢿⣿
⣿⣿⣾⣿⣿⢿⣯⣿⣿⣿⣻⣿⡟⠁⠀⠀⠀⠀⠡⢑⢸⢸⡹⡽⣽⣾⣿⣿⣿⣿⣿⣿⣿⢿⣻⣿⣻⣿⣿⣯⣿⣯⣿⢿⣯⣿⣿⣳⣻⣯⣿⣟⣿⣿⣿⢿⣯⣿⣳⣗⣗⣿⡿⣿⣿⣻⡷⣿⢾⣻⣝⣞⣿⢪⣗⣿⣿⢯⢾⣯⣿⢵⣟⣿⡽⡾⣿⣿⣿⣽⡿⣟⣿⣟⣷⣿⣿⣻⣾⣟⣿⢎⣟⣿⣻⣿⣟⢎⢗⢝⢜⡎⣞⢼⢽⣺⣯⣿⣿⢿⣷⣿⣿⣿⣯⣿⡿⣿⣿⣻⣿⣻⣿⣻⣿⢿⡿⣿⡿⣿
⣿⣿⣾⣿⣽⣿⡿⣿⣽⣾⣿⠻⠀⠀⠀⠀⡀⠂⠨⡐⡕⡕⡭⡯⣷⣿⢾⣿⣾⣿⣯⣿⣿⣿⣻⣿⣽⣷⣿⣿⢾⣯⣿⣿⣳⣯⣿⣗⣽⣾⣿⡯⣯⣷⣿⣿⢷⣟⡷⣗⣝⣾⣿⣿⣽⣿⣻⣟⣿⣽⢷⣻⣿⡱⣯⣿⣿⡿⣿⣻⣿⣽⣾⣿⣯⣿⢿⣯⣿⣺⣿⣿⣿⢿⣟⣯⣿⣯⣿⣻⣿⢕⣟⣾⣿⣽⣷⡹⣪⢳⠵⣝⡮⣯⣟⣷⡿⣿⣾⣿⣿⣿⣟⣯⣿⣟⣿⣿⣟⣿⣿⢿⣻⣿⡿⣿⣿⡿⣿⣿
⣿⣿⣾⣿⣻⣽⣿⣿⡿⣿⣾⠃⠠⠈⠄⡡⡐⢌⠢⡣⡣⣫⣺⢽⣳⣿⣿⣿⣽⣾⣿⣿⣿⣿⣻⣽⣾⣿⣿⣿⣟⣯⣷⡿⣿⢾⣿⣿⣺⣟⣿⡯⣿⣿⢿⣻⣿⣯⢿⣳⡵⣟⣷⣿⣷⣿⣯⡿⣷⣻⢿⣽⢾⢯⣯⣷⣿⣿⢿⣿⣻⣽⣿⣽⣿⣾⣿⢿⣗⣯⣷⣿⢿⣻⣟⣿⣽⣷⣿⣻⣿⢕⣯⣷⣿⣽⣿⣞⡮⣳⢽⣳⢿⣽⣯⣿⡿⣿⣿⣿⣟⣯⣿⣿⢿⣻⣿⣟⣿⣿⣻⣿⣿⡿⣿⣿⣷⣿⣿⣿
⣿⣿⣾⣿⢿⣿⣻⣷⣿⣿⡿⠀⠌⠄⡁⠂⢌⠢⡱⡱⣱⡳⣽⢽⣯⣷⣿⣯⣿⣟⣿⣽⣿⣿⢿⣻⣿⣾⣿⣿⡿⣟⣿⣿⣻⣯⣿⣿⣳⢿⣿⡿⣽⣿⡿⡽⡵⣝⣝⣷⣻⡽⡽⡽⣝⣞⣷⣿⣽⢽⣳⣵⣻⣺⣷⣻⣾⡿⣿⣯⡿⣿⢾⡿⣾⡷⣿⢿⣻⣽⣿⣻⣿⣻⣽⡿⣾⢷⣿⣻⣯⡳⣵⢿⣾⣻⣿⣿⣿⣽⣽⣾⣻⣯⣿⣟⣿⣿⣿⣷⣿⡿⣟⣿⣿⣿⢿⣿⣟⣿⣿⢿⣷⣿⣿⣿⣾⣿⢿⣾
⣿⣿⣷⣿⣿⣿⢿⣿⣻⣿⢿⠈⠄⢅⠢⡑⡔⡕⣕⣕⢷⢽⣽⢿⣽⣯⣷⣿⣯⣿⣟⣿⣿⣿⣿⡿⣿⣾⣿⣿⣿⣿⣿⡿⣷⣿⣾⣿⣽⣿⣾⣿⣟⣾⣿⢿⣻⣿⣾⢿⣻⣿⣽⣿⢿⣾⣿⣟⣟⣿⣻⡾⣟⣿⣻⣟⣿⡿⣿⣷⣿⢿⣿⣻⣿⣻⣿⢿⣟⣯⣿⣯⣿⣯⣿⣻⣟⣿⣯⣿⡷⣝⢾⣻⣽⣟⣿⣿⣟⢯⢗⢯⣻⡻⣟⣿⣿⣿⣿⣟⣿⣿⣿⡿⣿⣾⣿⣿⢿⣟⣿⣿⡿⣿⣽⣾⣿⣾⣿⣿
⣿⣷⣿⣯⣷⣿⣿⣿⢿⣿⣿⡨⡘⡜⡌⡎⡮⣺⣪⣞⣯⣿⣻⣟⣯⣿⣽⣾⣯⣷⣿⣿⣽⣿⣷⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣯⣷⣿⣷⣿⣿⣻⣿⡿⣿⣾⣿⣿⣿⣻⣽⣿⣿⣽⣿⣷⣿⣯⣿⣿⣿⣿⣽⣿⣿⣿⣷⣿⣿⣿⣻⣽⣿⣽⣿⣿⣿⣷⣿⣷⣿⣯⣿⣿⢿⣟⡯⢏⢮⣟⣯⣷⣿⣿⢳⢕⢝⢜⢕⢎⢮⡳⣽⣺⢷⡿⣿⣿⢿⣷⣿⣿⣿⣽⣾⣿⣿⣿⣟⣿⣿⣿⣟⣯⣿⣿⣻
⣿⣿⣯⣿⣿⢿⣯⣿⣿⣿⠻⡑⡜⡜⣞⡷⣝⣗⡷⣯⡷⣿⢽⡯⣟⣷⣟⣷⢿⣽⣷⣿⣿⣿⣿⣿⣷⣿⣿⢿⣿⡿⣟⣿⣟⣿⣻⣯⡿⣟⡿⣯⢿⣻⣟⣿⣻⣟⢿⢽⢿⡽⣟⣿⣻⣟⣿⣻⣟⣿⢿⡿⣿⣟⣿⢿⣟⣿⣟⣯⡿⣽⢯⣟⣯⢿⢽⣻⣞⣗⣿⣺⣳⣻⣺⣳⢯⣟⡮⣧⣳⣽⢾⣻⡾⣿⡪⡎⢮⢪⠢⡱⡱⣣⡻⣺⣺⣯⣿⣿⣽⣿⣿⡿⣿⣽⣿⡿⣟⣿⣽⣿⣿⣻⣽⣿⡿⣟⣿⣿
⣿⣿⣽⣿⢿⣿⣿⢟⠏⢔⢱⢑⢕⣕⢗⡯⡷⣯⣟⣷⣻⢽⢽⢯⢿⣺⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⣯⣿⣽⢷⣟⣯⣿⢽⢯⣳⢳⡣⡳⢵⢝⣝⣗⢿⣽⡾⣗⣷⢷⣻⡾⣽⢯⣟⣷⣻⣞⣯⢷⣷⡻⣞⢯⢯⡻⡮⡯⣯⣻⣳⢷⣻⢾⢾⢷⣟⣷⣿⣻⣾⣻⣷⢿⡾⣟⣯⣿⡗⡕⡕⡝⢔⢱⢱⡱⣣⣻⣺⢾⣾⣻⣾⣿⡿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣟⣿⣿⡿⣿⣿⣿⣿⣿
⣿⣿⣟⣿⡿⡛⠡⠢⡑⢅⢇⢇⢇⢳⡫⣯⣟⣗⣷⡳⡯⡯⣯⢿⢽⣯⣷⣿⣾⣿⣿⣿⣿⡿⣟⣿⣻⣟⣿⣻⣟⣿⣿⣿⣿⣿⣽⣿⣿⣻⡺⣝⢵⢱⠱⡱⢍⢷⣕⢧⣗⡿⣾⢿⣿⣿⣿⣿⣟⣿⣻⣽⣾⡷⡿⡺⡝⡎⡞⡜⡎⡮⡺⣜⢵⡳⣳⢽⡽⣯⡿⣽⣻⣻⣟⣟⡿⣿⣻⣽⣿⣿⣿⣿⣟⢎⢎⢎⢪⢢⢣⡣⣏⣞⣞⣾⣻⡷⣿⣯⣷⣿⣿⣿⣯⣿⣿⣿⣷⣿⣟⣿⣿⣻⣿⣿⣷⣿⣷⣿
⣿⣿⠟⢋⠐⢌⢘⠌⠜⡌⢆⢇⢇⢇⢪⢳⣳⣗⡷⣻⡯⡿⣵⣻⣽⢾⣾⣿⢿⣻⣿⢽⣞⡿⡽⣽⣺⣽⢽⣷⣻⣽⣾⣿⣿⣿⢿⣻⣪⢺⢪⢪⢪⢂⢇⢕⢕⢗⡽⣳⢷⣻⣟⣿⢿⣽⣾⣿⣿⣿⣿⣿⢯⢫⢪⢣⠣⡃⡣⢣⢣⢳⡹⣜⢵⡯⣯⢯⣿⣯⣿⣳⣟⣾⣳⣿⣽⣟⣿⣿⣿⣿⢿⣿⣗⢵⢱⢱⢱⢱⡱⣕⢗⣵⣳⣟⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣻⣷⣿⣿⣻⣿⡿⣿⡿⣿⣾⣿⣟⣿
⠛⡁⠌⢄⢑⢐⠔⢅⠣⡪⡊⡆⡇⡇⡇⣗⢗⣗⡯⣗⡿⣽⣳⣻⣞⣿⣟⣿⣻⡻⡪⡳⡱⣝⢽⣺⣺⣞⣿⣽⣿⣿⣽⣿⣻⣿⣝⢎⢮⣪⣪⢺⢜⢎⢮⣪⡳⣽⣺⣽⣟⣯⣿⣻⡿⣯⣷⣿⣿⣿⣿⢯⣣⢣⠣⡡⡑⡌⡜⡜⡜⡮⣺⣪⣗⣿⣻⣟⣷⣿⣾⣿⣽⣯⣿⣾⣷⣿⣻⣾⣷⡿⣟⣿⣞⢎⢮⡣⡳⡵⣹⡪⣟⣞⣾⣯⣿⣷⣿⣿⣿⣿⣽⣿⣷⣿⣿⣿⣟⣿⣿⢿⣿⣿⣿⣿⣿⣽⣿⣿
⢐⠨⠨⠐⠄⢕⠨⠢⡑⡔⢕⢱⢱⢱⢱⢪⢫⢾⢝⣗⣟⣞⣾⣺⣗⡿⣝⡞⣞⢼⢸⡸⡜⡮⣳⣳⣗⣿⢾⣻⣾⣯⣷⣿⣿⣷⢯⢯⡳⣕⣮⡳⣝⢽⡱⡧⣻⣺⣺⢾⣽⣯⡿⣯⣿⣿⣽⣿⣿⣿⣿⣽⡪⡪⡣⡣⡪⡪⡪⡮⢮⣫⣞⣾⣺⡾⣯⣿⣟⣯⣷⣿⣷⢿⣻⣾⣷⢿⣯⣿⣿⣿⡿⣯⣿⡽⣕⢯⢯⣺⣪⢯⣗⣿⢷⣿⣯⣿⣿⢿⣿⣿⣿⣿⡿⣟⣿⣽⣿⣿⣿⣿⣿⣿⣽⣷⣿⣿⡿⣿
⢐⠌⠌⠜⡈⡢⠡⡃⡪⡨⡊⢎⢢⢣⢣⢣⢣⡋⢙⠺⣺⣺⣞⣷⣿⢸⢪⢺⣪⡎⣇⢧⡫⣞⣗⣷⣻⣽⢿⣻⣽⣾⡿⣾⣿⣿⣯⣯⣯⡷⣗⣯⡯⣗⡯⣯⣗⣷⣻⣽⢷⣯⡿⣿⣽⣾⣿⣿⣿⣿⣿⣷⣝⣎⢧⡳⣹⡪⣳⢽⢵⣳⣗⡿⣾⢿⣟⣷⣿⣻⣯⣷⡿⣟⣿⣽⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣽⣳⣳⣳⣗⣿⣞⣿⣟⣿⣽⣿⣿⣿⣿⣿⣯⣷⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⣿⣿⣿⢿⣿⣿
⢐⠌⠌⢌⠢⠨⠢⡑⢔⢑⠜⡌⡎⡎⡎⡮⡪⠐⡌⡎⡞⡾⣿⣿⣿⣇⢇⢗⢝⡝⣜⢮⡺⡵⣻⣺⢽⣾⣻⣯⣿⣾⣿⣿⣿⣿⣿⣽⣾⣿⣿⣯⣿⣯⡿⣷⡿⣞⣿⣾⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢮⣳⣝⡮⡾⡵⣯⣟⣾⣳⣿⣻⣿⡿⣿⢾⣯⣷⣿⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣾⣷⣿⣿⣽⣿⣿⣻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿
⢐⠌⢌⠢⠡⡑⡑⢌⠢⡡⢣⢱⢸⢸⢸⢸⠀⢎⢎⢎⢎⢯⡳⡯⣿⣻⢷⣕⡵⣕⢧⡳⣝⢽⣺⣺⣽⣷⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⢿⣽⣟⣷⣿⣽⢿⣾⣻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢻⣛⢯⡛⣟⣟⢿⢿⣿⣿⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿
⢐⠌⢔⠨⠨⡂⡊⡢⡑⢜⢰⠡⡣⡱⡱⡁⢜⢜⢪⠢⣃⢗⢝⢔⡷⡯⠯⠷⣟⣾⣵⣯⣾⣽⣾⣾⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⢿⠿⠿⢯⠿⡿⠿⠿⢿⢻⠿⡻⠿⠿⠿⣿⣽⣾⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⢍⢎⡳⡸⡢⡳⡱⣙⡳⢧⢏⡗⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢐⠌⡐⢌⢂⠢⠪⡐⠜⢌⢢⠣⡱⡸⡨⢐⢕⠱⡡⢫⢩⢪⠪⡊⠐⡈⠜⠄⠀⡼⡺⣽⣻⣟⠟⡙⡙⡙⢙⠻⣿⣿⡿⣿⣻⡯⢣⢑⢥⢅⡅⢅⢅⣑⡄⠅⠍⣿⣻⣯⢷⡿⡍⠢⡑⢕⢇⢗⠺⡸⡘⢖⠵⡱⠺⡸⠪⢎⢂⣟⣿⣻⣿⣻⣿⣻⣿⣿⣿⢿⣿⣿⣿⢿⣻⣿⣽⣿⠱⡑⡐⡈⠇⡏⡎⡞⡜⡜⡬⡹⣺⣲⡹⣻⡾⣷⣟⣷⢿⣯⣿⣯⣿⣯⣿⢿⣿⣿⣷⣿⣿⣿⣽⣿⣿⣽⣿⣿⣾⣿
⢐⠡⠨⡐⡐⢅⠕⢌⠪⡊⡢⢣⠣⡣⢁⢎⢂⣇⢎⠆⢦⡧⣇⠂⡂⡆⡎⣦⣳⣫⢝⣌⠪⡀⢔⢔⡲⡰⣔⣵⡻⡫⣛⢛⢝⠃⡐⢅⠣⢩⠨⡂⡢⡘⢌⢌⣼⢽⣞⡾⣯⣟⢀⢂⢮⣲⣲⢵⢵⣜⣼⣰⣕⣼⡸⣜⣼⣺⣞⣿⣺⣗⣿⣺⣽⡽⣾⣳⣟⣿⡽⣷⣻⣟⣿⢽⢞⢛⢜⢌⢌⢌⠢⡨⠘⠜⡜⡜⡜⡜⡜⡔⡕⣵⣿⣻⡾⣗⣯⣿⣾⢷⣟⣷⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢐⠅⢕⠨⠨⡂⢅⢕⢑⢌⢎⢪⢪⠊⡔⡝⠜⠭⡰⣸⣲⣮⡂⠠⡡⠡⠉⢪⣞⡮⡛⢊⡉⡂⠳⣽⡺⡝⠪⡚⡺⠻⣮⡲⡂⠂⣌⢌⡊⢳⣽⣺⠺⡚⡝⡹⠺⡯⣿⢋⠧⣑⡄⡑⣯⡷⡯⢫⢋⡚⡚⢷⣳⡷⢛⢙⣊⢓⠻⣾⣻⠋⡆⡇⡢⡉⣟⣞⠗⡱⡩⡪⠨⠳⡯⡏⡀⢙⠎⡞⢜⣐⣷⣸⣜⣜⢔⢕⣕⢼⣸⣼⡾⣿⡿⣿⣿⣿⣿⢾⣯⡿⣽⣞⣿⣳⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢐⠅⡢⢑⢑⢌⠢⢢⢑⢢⠱⡡⡃⠰⡑⡜⡳⡑⡬⡆⡇⢕⠀⠥⠨⠒⡠⣳⣱⠇⠹⠊⠗⢁⢜⢮⣿⠈⢾⢑⠁⡂⡳⣗⠇⠁⠏⡚⢄⣔⢿⡃⢜⠨⠇⠌⡨⣿⣟⢀⢅⠫⡐⣔⡯⣿⢁⠑⢝⢐⢠⣝⣯⠇⡂⠯⢜⢑⢄⣿⣟⢄⢑⣓⢕⡴⡵⣯⢕⢘⠸⡸⡨⡼⣽⣆⡊⡆⣳⢽⣽⣻⣽⣾⣿⣯⣿⣳⡷⣿⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⢽⡾⣗⣿⣺⢽⣿⣿⣿⣾⣿⣿⣯⣿⣿⣾⣿⣿
⢐⠅⢌⠢⡂⢆⠕⢅⠕⢅⢣⠱⢀⠇⡇⢑⢌⡦⡪⢨⠨⡂⠀⡆⡮⣚⢮⡳⣿⢄⢕⡵⣽⣺⢽⣺⣎⢆⢦⣢⣖⡯⣫⣿⢨⢸⢜⣮⣗⣯⣿⢕⢰⡨⣎⡮⡾⣽⣿⣢⡣⡯⡯⣗⣟⣿⣢⡣⣗⡯⣗⣗⣿⡇⣎⢮⣺⣞⡽⣾⡿⣆⢧⢗⣯⢯⣟⣿⣯⢮⡺⣺⢽⣺⣽⣿⡞⢊⢌⢲⡬⢨⢙⠻⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣻⣽⣧⣿⡿⡿⣾⢽⢯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢐⢅⢑⠌⢌⠢⡑⢅⠕⡅⢇⠣⡪⢪⢸⠸⢻⠻⡫⡢⠣⢀⢢⢢⢐⢄⢂⠐⠀⢂⠀⢍⣷⣟⢏⢋⣋⠙⢳⣳⣳⠫⣩⢩⠉⡚⣽⣞⡾⢚⢙⣉⢊⠺⣳⡽⢝⢘⣍⢑⠹⢯⣟⠇⢭⠩⡨⠘⣳⣟⠇⠕⢴⣢⠂⢍⢾⣗⠋⡢⡪⣔⢔⣔⢤⢙⣿⣟⠑⡔⢼⡐⠌⣹⡿⠏⡀⢐⠍⡅⣿⠨⡣⣑⣽⣿⣿⣿⠿⡽⠯⠿⢝⢗⠿⢽⢾⣻⢾⡯⣷⢷⢷⣻⣻⢽⡽⡯⣟⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿
⠰⡐⢔⠡⡡⡑⢌⠆⡕⢜⠐⡜⡜⠌⡆⣱⣱⡑⡌⠢⠁⡠⡐⡄⡄⡄⡄⡄⡅⣄⢦⢯⢾⡇⠢⢚⠸⢐⢰⢽⡆⠂⠮⠺⡀⣔⢗⣿⠇⠂⢟⢘⠀⡢⣹⡏⡀⠫⢔⢗⢠⣫⡿⢀⠙⢅⠫⣐⢮⢿⢀⢅⢍⢌⡬⣜⢽⣇⠂⢌⢪⢨⢡⣑⢔⡼⣺⣇⠢⡨⡢⣥⡳⣪⣯⣖⡐⡠⡑⡬⣢⣳⣼⢾⣽⣿⣿⣷⢑⢕⢭⢮⡪⡦⡣⡕⢽⣽⣯⢿⡽⣽⣻⣾⢽⣳⣻⢽⡳⣝⣿⣿⣿⣻⣯⣿⣾⣿⣿⣿
⢨⠨⡂⢕⢐⠅⡕⡑⡜⢌⠰⡱⢡⢃⠣⢙⠪⠫⡨⡨⠐⠜⠜⡚⠎⠗⠽⠮⡻⠮⡯⡟⣿⣗⡵⡵⣵⣫⢯⣻⣇⢕⢵⢵⢝⡮⡯⣿⡅⡕⣔⣖⢵⣝⣾⣷⡸⣸⡺⣪⢗⠷⡿⡢⣝⢮⡫⡮⠗⣟⠇⠮⣺⢽⡺⡎⡛⡓⡑⡑⠵⣝⢷⢽⣝⠾⡻⠟⠮⣺⣺⡵⠯⠳⠻⠳⡓⠔⠕⢝⢚⢝⢚⠛⠯⣿⣿⣿⡢⢑⢭⢑⢕⢍⡪⣑⢕⣿⣿⣿⣽⣳⢗⢯⢻⢺⣺⣻⢽⣺⡺⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡐⢅⢊⠢⡂⢇⠪⡢⡑⡁⡎⡪⡩⡢⣮⣟⣮⢪⢊⠢⠁⠨⠢⠬⠨⠌⠄⠅⠂⢂⠐⠀⠄⡐⣿⣻⡓⠍⢥⡩⠌⢙⣽⡺⠑⣔⠖⠔⠈⢺⣺⠎⡑⣄⢢⠂⡈⢷⡽⠡⠢⡑⠔⡐⢘⣷⠝⠀⠅⠯⠳⡏⢌⣿⡝⠀⡃⡪⡐⡌⡂⣸⣻⡏⠠⡣⡑⡅⠕⡘⣷⠃⢈⠪⢏⠯⡪⡳⠱⡱⡂⢆⠢⡑⢅⢿⣿⣿⡧⣿⡾⣟⣯⣷⣿⣯⣿⣺⣿⣷⡟⢐⢕⢕⠱⡱⢰⢑⢻⡪⣟⣞⣿⣿⣿⣿⣿⣿⣿⣿
⠨⡂⡪⡨⠪⡘⡌⢆⠅⢜⠔⡜⢔⢜⢌⠪⡪⠢⠡⡑⠠⡡⡡⡨⢠⠡⡨⡀⡅⡄⣂⢅⣔⣞⢮⣟⢀⢑⢃⢙⡠⣎⢾⡃⢈⢘⢊⢃⣡⡪⣾⡁⡐⡘⣑⢠⣪⢽⣯⠠⡑⡌⣆⣖⡧⣿⡢⠡⡨⣪⡲⡮⡷⣽⡦⡡⢢⢲⣲⣞⡾⣵⣻⣗⠄⢕⡘⣌⢢⣜⣿⡅⠢⡡⣣⣱⡰⣌⣎⡆⣎⢆⡧⣞⣾⣟⣿⣿⣿⣻⡿⣿⢿⣻⣟⡷⣟⣿⣻⣻⠐⢄⠈⢆⢇⢕⡱⣱⣵⣿⣾⣺⡽⣿⣿⣿⣿⣿⣿⣿
⡑⡌⢆⢎⢊⠆⡕⠅⢪⢊⠎⡜⣠⠝⡑⠕⡌⢌⠌⠄⠕⠡⢑⠡⠑⠉⠪⣷⣻⡮⣗⡯⣞⣾⣻⣷⡢⡧⣗⡯⣟⣞⣿⣪⢢⣣⡳⡽⣮⢯⣿⣎⡎⣞⢮⣻⣺⣽⣷⣇⣇⢯⣳⣳⣯⣿⣿⣸⣪⣳⣫⣯⣯⣿⡿⣜⢜⡵⣳⣳⣯⡷⣿⣷⢕⡵⣽⣺⣽⣺⣾⡿⠜⠮⠳⡳⢿⣽⣞⡾⢕⢫⢩⢋⢙⠽⣿⣿⣿⣿⣿⣯⣟⡷⡯⡯⣗⣗⢷⢽⢕⣅⢣⡣⣗⣿⣾⣿⣾⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿
⠢⡊⢆⠪⡂⢇⠎⣨⠶⡶⠿⢝⢇⣮⣾⡽⡷⡱⢑⠁⢈⢊⠂⠊⠂⠃⡰⣝⣿⠏⡑⢌⢂⢂⠡⢙⣿⣽⡗⠩⠁⠅⠩⠈⠌⠠⠉⠍⠨⢉⠅⠅⠩⠈⠌⠨⠨⠨⠨⢀⠢⢁⠂⠅⠌⠌⠌⠄⡂⢔⠠⢂⢂⠢⠨⡐⡐⢌⢂⢂⠢⡨⡂⡢⡑⡐⡐⢄⢻⣾⡟⠀⡣⡇⡧⡪⡂⢵⡿⠡⠈⢆⢍⠧⡑⡐⣽⣿⣿⡿⣷⣿⣳⡟⡽⣝⣞⢮⢯⢮⣳⣕⢷⢝⣟⢿⢾⢿⢿⣻⡿⣽⣗⡯⣿⣿⣿⣿⣿⣿
⠱⡘⢌⢪⠨⡢⠁⣽⢡⢣⠣⡃⢅⣆⠕⢍⢎⢊⠂⢠⢢⢦⣪⢦⣪⣮⡿⡼⣞⠁⠪⠨⠨⠐⡀⡼⡼⣽⠀⢂⠡⠁⠅⠡⠁⠅⠡⠁⠅⡂⠌⡨⢈⠌⠨⠨⠠⠡⡁⠢⡁⠢⠡⠡⠡⠡⠡⡁⡂⠢⡑⡐⠄⠅⢕⢐⢌⢂⠢⠢⡑⡐⢔⢐⠔⢌⢌⠢⣱⣻⡂⠅⢌⢢⡊⣆⢮⡾⣵⣧⢑⢔⣵⣵⡾⣾⣿⣽⣾⣟⣿⣺⣗⡯⣎⣺⣪⣳⣳⣳⣿⣿⣝⢷⢽⡹⡽⣝⣝⣗⢯⢗⢷⢝⣞⣿⣿⣿⣽⣿
⡑⠜⢌⠢⠣⠊⣼⠳⡱⡡⢣⠪⡨⡱⢉⠢⡂⠆⢌⢪⣟⣿⣽⢿⣯⣷⡿⣿⡇⣜⣼⣼⣼⣼⣺⣽⣾⣿⢠⢢⣪⣪⣪⣪⣎⡮⣎⣮⣎⣮⣲⣜⡴⣕⣵⣱⣕⣵⣜⣖⣼⡼⣼⢼⣼⢼⣜⣦⢧⣳⣼⣜⣮⣧⣧⣗⣶⣵⣳⣳⣵⢷⣵⢷⣽⣺⣮⢿⣾⣻⣿⣎⢮⣞⣿⣻⣿⢿⣿⣿⣳⣻⣯⣷⣿⣿⣿⣽⣿⣿⣿⣷⡯⣟⣞⡮⣯⣻⣻⡻⡯⣷⢽⣳⡳⢽⣝⣞⢮⢮⢯⢯⡫⣗⢗⢽⣿⣿⣿⣿
⡘⠜⢌⢪⢑⠡⣏⢇⢕⠸⡠⣮⡾⡌⡎⡪⢨⠨⡐⡽⣞⣷⣟⣿⢷⣟⣿⣿⢮⢾⡾⣷⢿⡾⣟⣿⣾⣿⣜⣷⣟⣷⡿⣷⣟⣿⣟⣷⡿⣷⢿⣽⣿⣻⣽⣯⣿⢷⣿⣯⣿⣻⣿⣟⣿⣟⣿⣽⣿⣿⣽⣯⣿⣾⣯⣿⣷⣿⣻⣟⣿⣟⣿⣿⣻⣯⣿⣿⣯⣿⣿⣿⣽⣿⣽⣿⣻⣿⣿⣿⣿⣽⣿⣟⣿⣽⣾⣿⣿⣿⣿⡷⣿⣻⣺⢽⣺⣺⡺⡮⣯⣳⣳⡳⣳⡳⡿⡾⡽⡽⣕⢷⣝⢮⢯⢧⡻⣿⣿⣿
⢌⠪⡪⡨⢂⢪⢗⢅⢣⢑⣨⡢⡱⡑⢕⢌⢆⢣⠪⡹⡻⣻⣻⣻⢿⣻⢿⣻⣟⡿⡿⣿⢿⣿⣿⣿⣿⣿⢾⡷⣿⡿⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⢿⣿⢿⣿⢿⣿⣿⣾⣿⣿⢿⣿⢿⣿⢿⣿⣿⣾⣿⡿⣿⢿⣟⣿⣾⣿⢿⣿⢿⡿⣿⢿⡿⣿⢿⣻⣟⣿⣻⣯⢿⡽⡽⡯⣟⣿⣻⡯⣿⢫⡫⣫⢿⢽⢯⣟⡷⡿⣞⡿⣽⣳⢯⣻⡺⡮⣯⣺⣺⢺⡪⣮⡳⣽⡹⡽⣝⣝⢮⣳⠳⣝⣗⣗⢽⢽⣿⣿
⡘⡌⢆⠅⡂⢽⠸⣈⣢⣑⡱⡱⡑⡜⡌⡆⡕⡅⠃⣅⣮⡎⡎⡮⣫⡺⣝⣞⢮⢯⡫⡯⣻⣺⣺⣺⡳⡯⡿⣝⣗⢯⣟⣞⢯⢯⣟⣗⣟⣞⣗⢿⢽⢯⢿⣝⢯⢗⣟⣞⢷⡻⣯⣻⢽⢽⢯⣗⣟⣞⣗⢿⢽⢯⢯⣟⢾⢽⣫⢿⣝⡯⡿⡽⣝⡯⡯⣗⣯⢳⢱⣱⣽⡽⡽⣝⣗⢗⣗⢯⢷⢕⣼⣻⣿⣿⣽⡳⡯⡯⣗⡯⣗⢯⣳⣳⢽⢽⣺⡪⣮⡳⣝⢮⢯⣺⡪⡯⣺⡺⡽⡽⡵⡽⣾⢾⢕⣽⣿⣿
⢌⠪⡢⡡⠨⡘⡜⢌⠝⢜⠜⡔⡑⢖⢕⢌⠆⡕⢵⣿⣾⣿⢾⡸⡢⡫⡪⡪⣣⡳⡹⡪⡺⡜⣜⣜⢮⢏⡞⣞⢜⣗⢕⢗⡝⣕⢧⢳⢕⢇⣯⡫⣫⡨⣷⡽⡭⡣⡷⣝⢗⣝⢞⢮⡫⣫⡳⣳⢳⢵⢽⡹⣝⢝⣕⢗⣝⢗⡽⣕⢥⣿⣾⡽⡾⣞⣝⢮⡺⡴⣵⣿⣿⣿⣿⡺⣜⣗⢽⡹⡪⡯⡺⣝⢯⢯⢗⢯⢯⡻⡪⣞⢯⡳⡳⣝⡗⣗⢗⣝⢮⢯⡺⣝⣕⢧⡫⣯⣺⣪⣳⣝⣮⣫⣮⢷⣻⣾⣿⣿
⢸⢘⢔⢕⣧⡳⣮⢷⣝⣮⣮⣖⣮⢖⡾⣴⢵⣜⡬⡮⣝⣮⣣⣇⣇⣇⣧⣣⣣⣕⣵⣱⣵⣧⣷⡵⣵⢵⢵⡵⡵⣼⢜⣼⣸⣜⡮⣧⢧⢯⢮⡮⣖⣭⢧⣷⣷⣽⢾⢮⣧⣳⣝⣮⢮⣮⣞⣮⡮⣧⣳⡵⣕⣷⣵⣳⣵⣳⣽⢼⣺⣲⣵⣽⣺⡾⣼⣺⣺⣞⣞⣮⣿⡾⣾⣽⣾⣺⣵⣯⢧⣿⣾⣾⣽⢷⣻⣽⣗⣯⣟⣷⣯⣿⣟⣮⢏⣿⣽⣾⣿⣷⣿⣿⣾⣿⣿⣿⣾⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿
⢸⠰⡑⢝⢾⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣯⣿⣷⣿⣷⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣟⣿⣿⣿⣿⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿
⢸⢘⠜⡔⡅⡝⣳⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⢨⠪⡊⡎⢮⣺⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
To mark everyone's entrance in the noob community, it is better that every participant can archive their achievements digitally and on paper.
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