About me:
• Specialties: Embedded Systems, Operating Systems, and Networking
• Operating Systems: Fedora (daily driver), bare-metal (custom x86_64 kernel development), NixOS (sandboxing)
• Tools: Docker, FUSE, Git, GNU Make, Jupyter Notebook, Kubernetes, OKDShift, Vim
On the web:
• Github: aln730
• Mail : arnsg730@proton.me
• Discord: @aiubnf
• Resume
▶ Cool stuff/
┣━ Nand2Tetris
┣━ wiki.osdev
┣━ Cool Embedded Systems Guide
┣━ Internet Protocol Journal
┣━ OKD is based
┣━ KATTIS
┣━ Meshtastic: An opensource, off-grid, decentralized mesh network
┗━ beej.us/guide/bgnet/
▶ Gamer hax/
┣━ sh -c "$(curl -fsSL https://raw.githubusercontent.com/ohmyzsh/ohmyzsh/master/tools/install.sh)"
┣━ git clone https://github.com/zsh-users/zsh-autosuggestions ${ZSH_CUSTOM:-~/.oh-my-zsh/custom}/plugins/zsh-autosuggestions
┣━ git clone --depth 1 https://github.com/junegunn/fzf.git ~/.fzf
┗━ sudo dnf thefuck
▶ Favorite Sofware/
┣━ KiCad EDA: Schematic Capture & PCB Design Software
┣━ Wireshark: An open-source network protocol analyzer
┗━ HeSuVi: Headphone Surround Virtualizations for Equalizer APO
▶ 
Sign my guestbook :> (Write stuff, idc. Could be anything, your favorite memory with me, or any kind of yap.)
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(my configuration files)/
▶ Misc Stuff/
┣━ Nick Stacky
┣━ Learning how to wirewrap circuits
┣━ gameOfLife (I made this)
┗━ Gallery
"The thing about perfection is that it's unknowable. It's impossible, but it's also right in front of us all the time."
— Kevin Flynn
(my configuration files)/
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡶⠶⢖⣶⣾⢋⣙⠛⠻⢋⡉⠉⣽⠄⠀⠀⢠⣾⣧⣾⣿⣿⢟⣴⣆⣴⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⢟⣻⣾⣿⠿⢛⣲⡶⢶⣦⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠶⠞⠛⢩⣿⡇⢠⣶⣿⡿⣿⣿⠿⠀⠰⠿⠁⠀⠉⢀⣀⣀⣨⣿⠟⣿⢿⣵⣿⣿⣿⣯⣿⣿⣿⣿⣿⢟⣿⣿⣿⠟⢛⣱⣾⣿⣟⣷⣾⡿⣫⣵⣿⣻⣷⡎⣭⣿⢛⡛⣲⣶⢶⣶⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠘⠛⠛⠋⠙⠛⠛⣉⠛⠛⠛⠋⠉⠙⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣋⡁⠀⠀⠀⠃⣬⣭⠀⢛⣥⡄⢀⣿⡿⣿⣤⣤⠀⠀⠀⠀⣿⠛⣿⡿⠡⣞⣷⣿⣿⣿⠟⠛⣻⣿⢻⣿⢟⡁⢸⣿⢹⣿⣶⣿⣿⢹⡟⣿⣿⠁⣸⣿⢿⣿⣿⣯⣴⣿⣿⢟⣿⣟⣡⣾⢟⣡⣤⣿⣻⣿⡿⠛⣷⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠶⠶⢶⣿⣿⡶⠀⠀⠀⠀⠐⠲⣿⣿⣷⣼⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠈⢉⠉⠙⢳⣿⣿⣶⣤⣀⠰⠀⣼⣿⣷⣄⠙⠿⢿⣿⣐⡒⠀⣀⣀⢿⣦⣿⣵⣾⠿⡻⣧⣠⣿⣤⡀⠹⣿⡄⢿⣿⣁⠈⢻⣧⣻⣿⠉⠁⢸⣷⣿⣿⡄⢻⣿⣾⣿⣿⣿⣿⣽⣿⣸⣿⣿⣿⣿⣾⣿⣿⣿⣛⣵⡾⠿⢋⣴⣿⡿⢿⣶⠶⢶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⢾⣧⣼⣿⣿⣧⣀⣤⡶⣶⣤⣼⣿⣿⣷⣼⡿⣻⣿⡀⠰⠀⠀⠀⠀⠀⠉⠙⠃⠀⢠⣿⡟⢻⣯⡉⠀⠀⠙⣿⡏⣿⣦⡀⠀⢻⣯⠻⠇⢻⣿⣄⠋⠹⣿⣿⣶⣴⣿⣿⣧⡝⢿⣄⠘⠿⠿⣏⠉⠀⣤⣿⣽⣿⡜⠷⢼⣿⠃⣿⣇⡸⣿⠹⣿⡇⠙⢧⣿⣿⣿⢿⣷⢿⣿⣿⣟⣹⣿⣿⣿⣧⣼⣿⣛⣫⣶⡿⢋⣴⣿⡿⠋⠙⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡶⠞⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⢠⣤⠄⠀⠀⣤⠄⠃⠀⢶⣶⣦⣤⡔⠿⠏⣴⠶⣴⣿⣿⣷⠆⠙⢻⣿⠏⠙⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣽⣿⣦⠒⠀⠀⠀⠀⠀⢹⣤⣾⠟⣿⣴⣿⣿⢿⣦⠀⠀⠛⠿⣿⡝⣿⣄⠀⠛⣷⣄⠰⣽⠻⣧⡶⣿⠿⣿⣷⣼⡻⣿⣿⣼⡿⣷⡄⠀⠹⡆⠀⠀⠀⠉⠁⠐⠇⠸⢿⣧⣾⡿⢿⣿⣿⣿⣧⠀⠛⠙⠛⣿⠿⢿⣷⡝⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣿⣿⡟⠀⣠⣾⣿⣧⠈⣙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠾⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⡀⠘⠛⠀⠀⠘⠛⠁⠾⠛⠀⠀⠀⠀⠀⠀⠞⠛⠀⠀⢸⣿⠁⢀⣼⠟⠁⢠⣿⠋⣿⠉⠀⠛⢃⣥⣴⣿⢿⣿⣠⣿⠏⣿⣇⣼⡇⣹⣿⣰⡿⢻⣿⣠⣶⠆⣀⣸⣶⠿⣛⢀⣾⡿⣟⠀⣿⠀⣿⡆⠃⠀⠀⠘⣿⠈⣿⡀⠀⠈⢻⡆⠙⠇⢹⣇⠘⠃⢹⣿⠘⣷⠹⣿⠉⣿⡜⣿⡟⠃⠀⠀⠀⠀⣀⢳⣦⡀⠈⢻⣾⣫⣾⣾⣝⠛⠛⠉⠀⠀⠀⠀⠀⠀⠘⢻⣷⡜⢿⣿⣿⣏⣿⣿⣍⡻⣿⣿⣤⣾⣿⣿⠰⢿⣿⣿⣿⣷⣿⣿⠟⢋⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠶⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⠂⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢠⣾⢿⣦⡘⣉⡀⠀⣛⣡⡾⠛⠀⣀⣴⠟⠻⣿⣵⡿⠻⢿⣧⡄⡉⠻⣯⣾⠟⠻⣿⣴⠏⠙⢿⣤⠾⠛⢿⣄⠾⠋⢋⣡⡾⠛⢷⣦⡾⠟⢷⣆⠀⠘⢿⣧⠀⠈⠿⣦⠀⠘⢿⣄⠀⠈⢿⣆⠀⠈⢿⣆⡙⠀⢿⣆⢸⣷⢸⣇⠀⠀⠀⠀⠀⠀⠰⠾⠀⠀⠀⠘⠟⢹⣮⢻⣷⠖⠀⠀⠀⠀⠀⢀⣶⡀⠀⢹⣿⣇⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣛⣿⣏⣭⣾⣿⣿⠿⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡶⠶⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣰⠀⠀⠀⣴⠟⠁⠀⣴⡿⠋⠀⠹⣿⠏⠁⠀⠹⣿⠀⠀⠀⢿⠃⠀⣦⠙⣿⠀⣠⡜⣿⡄⣿⠀⢹⡇⠀⣶⠘⣿⠀⠀⠈⣿⠀⠀⠀⢻⠀⠀⠈⠛⠀⠀⠀⢿⠀⠀⠀⢹⡆⠀⠀⣿⡀⠀⠀⢻⡆⠀⠀⠹⣷⠀⠀⠹⣷⢀⡄⠻⣷⡉⠀⠙⣿⡿⣾⡿⣷⡀⠀⠀⠀⠀⠀⣰⣦⡀⠀⣠⣦⡀⡿⣸⡟⠀⠀⠀⠀⠀⢀⡿⢿⡟⠀⠀⢹⣿⣯⡿⣷⣾⡿⠁⣼⣯⣹⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣶⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣥⠀⠀⠀⢀⠀⠀⠀⠀⣄⠀⠀⠀⢹⡇⠀⠀⠀⣯⡀⠀⠀⢸⣆⢸⡟⢰⣿⣤⣿⢠⣿⣿⡟⢀⣾⣷⣄⢙⡸⣿⣄⠀⣸⣿⣆⠀⠀⢾⣦⠀⠀⢸⣧⡀⠀⢸⣦⠀⠀⠈⣧⣀⡀⠘⣷⣰⠄⠸⣿⡄⠘⠃⣿⣆⠀⠀⢿⣿⣿⠀⣿⡇⢿⠀⣿⡇⠸⡇⢸⣿⠀⠀⠀⠀⠀⢻⡟⢿⡆⢻⣿⣷⣾⡿⠃⠀⠀⠀⠀⢀⣿⣡⣿⢁⣼⣿⣿⠇⣽⡇⣿⡇⠀⠀⠙⣻⣿⣷⣄⣿⣟⠉⣿⣿⣿⣿⣏⣽⣿⣿⠛⢩⣭⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠾⠛⠉⠀⠀⠀⠀⢀⣤⡦⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⣠⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄⠀⠀⠘⢷⣄⠀⠀⠻⣷⡄⠀⠘⢿⣦⡀⢷⣽⠻⣦⡀⢠⡙⣿⣾⠛⠈⢿⣷⣿⠀⠙⣿⡟⢿⡞⣿⣟⢻⣮⢻⣿⠿⣇⠙⣷⠘⣷⠸⣷⡀⠀⠙⣿⡄⠀⠹⣷⡄⠀⠘⢻⡿⣷⡙⣿⣶⣿⡈⢿⣆⢿⡌⢿⣆⢠⡜⢿⣿⠼⠟⢿⣼⣿⠟⢿⣤⣻⣾⣿⣆⠀⠀⠀⠀⣾⣇⣸⡇⢸⡟⢸⣿⠀⠀⠀⠀⢀⣿⠿⣿⡟⣡⣾⣿⠟⠃⣀⣿⣾⡿⠁⠀⣠⣴⣟⠻⣾⣿⡛⢿⣾⣿⣻⣿⣿⣿⣿⣿⣿⣆⣿⣯⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠟⠉⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⣠⣀⠀⠀⠀⢶⣦⡀⠀⠈⠻⣶⣄⠀⣀⡻⣶⡄⠀⠈⠻⣷⠀⠀⠀⢻⣇⠀⢀⡘⣿⡆⠀⡀⢹⣇⠀⠙⠃⣿⣇⣈⠁⢸⣇⢀⣤⡄⣿⣧⣴⡆⢿⣷⣾⡇⣸⣿⠀⠇⠈⣿⣾⣿⠀⣿⡆⢿⣆⣿⣧⢶⡆⢹⣷⣤⡄⢹⣷⣤⡄⢸⣿⣼⣷⢸⣿⣿⣇⢸⣿⣼⣯⡈⣿⣘⣛⡊⣿⡇⢀⣴⣿⡇⠀⠀⢻⠏⢿⣮⣿⣦⡀⣀⣠⣿⣿⣿⢿⣿⣣⣿⣿⣄⠀⢠⣦⣸⣯⣴⡟⠸⣿⣡⣿⣰⡿⢻⣿⠁⠀⠀⢺⣿⣤⣹⣦⣹⡟⠛⣿⣏⣿⣿⣯⣹⣿⣿⣿⣿⣿⠋⣽⡟⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋⢁⠀⠀⠀⠀⢠⣤⣤⠰⠟⢫⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⡀⠀⠀⠻⣦⣄⠀⢈⡛⣷⣄⠀⢰⡝⠻⠆⠀⠀⠈⣿⣆⣉⡅⢹⣿⣄⠀⠀⢿⣆⠀⠀⠘⣿⡾⠿⠁⢿⣧⡀⠁⠘⢿⣦⡀⠀⠻⣿⣍⠀⣘⢿⣧⡉⢀⡙⣿⣿⣷⣼⢿⣿⣿⣿⢻⣧⡀⠀⠹⣿⣿⣾⠿⣿⣾⣿⣿⣿⣷⣷⣾⢿⣿⡴⠈⢿⣧⣰⣎⢿⣿⣿⣼⢿⣿⣿⣾⠿⣧⢻⣷⠿⣿⠛⠛⢿⣧⣾⡏⢿⣿⡛⠃⢰⣦⠀⣭⣻⣯⣯⣭⣙⣃⣀⣿⡏⣿⡿⣿⠈⣿⡄⣿⡟⣷⡌⠛⠀⠀⢸⣿⣿⣿⣧⣾⣿⡄⠀⢀⣿⣷⣿⣵⡿⢹⣷⢰⡿⠿⠈⢿⣿⡟⢿⣿⣾⣿⣡⡼⠏⠀⠀⠀⠀⢀⣀⣴⢾⣿⡍⠁⢀⣬⣿⣷⣄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⠁⠀⠚⢛⣁⣤⡀⢀⣽⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠘⠻⣦⣄⠀⣤⠙⠛⣴⡗⠀⠈⣿⣆⣈⢻⣞⣿⡀⠀⠀⠸⣷⡄⠘⠃⢿⣿⣿⡇⣈⢻⣷⣄⠀⠘⢻⣷⣄⠀⠙⢿⣦⡀⣤⣝⢿⣦⠀⣤⡛⣷⡄⢿⣿⢿⡆⠻⣧⡹⣿⣿⣿⡞⣿⡎⢻⣧⢻⣿⣿⣷⠹⣿⣤⣶⡎⣿⡋⣿⣮⣿⣿⣿⡇⢿⣿⣿⡇⣿⡇⢸⣯⢻⣿⣿⣿⢻⣿⣿⣧⢹⣿⣿⣧⠹⣿⣿⣧⢹⣧⣸⣮⡻⣿⣷⣦⠻⣿⣦⣌⢻⣷⣀⣿⢿⣧⡉⠉⢿⣿⣿⢡⣿⣧⣿⡀⣿⣷⣸⡇⢸⣧⡀⣀⠀⡀⣿⠈⣿⣿⣿⠙⣿⢀⣼⣿⣤⣾⣿⣷⣾⣿⣼⣿⠛⢠⣾⢿⣧⢈⣿⣿⠛⣿⣷⣶⣤⣤⣴⠾⠟⠋⢀⣸⣿⡿⠆⠀⠀⠀⠈⢻⣦⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⠁⠀⠀⠀⢀⡘⠛⠛⠋⠙⠻⣿⣤⠀⠀⣴⣆⡘⠃⠀⠀⠀⠈⠙⢣⡄⠀⠀⠈⢿⡆⠀⠀⠀⣿⣆⠀⠀⠸⣿⣏⠈⠛⠹⢿⣆⡀⠀⣘⠿⣦⡔⣶⣍⢿⣷⠹⣷⣍⣿⣆⠀⣷⡜⣿⣦⣶⣆⢻⣇⣼⣿⣼⣿⢀⣹⣿⣿⣇⠸⣿⢼⣿⣤⣿⡇⣿⣿⣿⡇⣻⣧⣾⣿⢸⣿⣿⣿⣶⣿⣿⣛⠁⣿⣿⣿⣿⣿⣿⣿⣇⣾⣿⣿⡇⢸⣿⣘⣏⠈⣿⣿⣿⢸⣿⣿⣿⠈⣿⣿⣿⣇⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣧⣻⣿⣿⡇⢹⣿⣿⣯⣿⣿⣿⡏⢿⣿⣿⣜⣿⣿⣧⡸⣿⣹⣿⢸⣿⣿⣆⣿⣿⣿⡄⣿⣧⣭⣼⣿⣿⣿⡟⣿⣽⡿⠀⣾⣿⡅⠀⢛⣻⣿⠿⠿⣿⢻⣧⣠⣾⣛⡀⣿⣴⡿⣛⡁⠀⠀⠀⠀⣀⠀⠀⠹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡶⠟⠋⠁⠀⠀⠀⢀⣠⣶⠿⠋⣀⠀⠀⠀⠀⠀⢻⣧⠐⢫⣿⣿⡷⡄⢀⡀⣀⣤⠸⣷⣄⠀⠀⠘⢿⣦⡀⠀⢈⡻⣷⣄⠀⣙⣻⣷⣄⢺⣦⡙⣷⣄⣻⣷⠸⣷⣈⣿⣿⣿⣧⣸⣿⢸⣿⣤⡝⠃⣿⣿⣿⡁⠸⣿⣿⣉⡙⢿⣿⣿⣷⣿⣿⣿⣿⣯⡿⣿⣿⣧⣿⣿⣿⣿⣯⣿⣿⣿⣿⡻⣿⣿⣿⣏⢿⣿⣿⣟⢿⣿⣿⣯⢻⣿⣿⣯⣻⣿⣷⣮⡻⣿⣿⣦⡻⣿⣿⣿⡻⣿⣿⣦⡻⣿⣿⣧⡿⣿⣿⣦⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⢸⣿⣿⣿⢿⣿⣿⣷⢸⣿⣿⣿⠘⣿⢿⣇⢻⣿⣿⣷⢹⣿⣿⡏⢿⣿⣶⡹⣿⡿⠉⣿⣿⣿⣵⣿⣿⣷⣾⣿⣿⣦⣰⣾⣿⠏⣿⣦⠻⣮⣛⣿⣿⣿⣿⣿⣿⡾⠟⣃⣴⣶⣾⣟⣋⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡶⠾⠋⠉⠀⠀⠀⠀⠀⢠⡄⠛⠋⠀⠀⠀⢻⣷⡄⠀⠀⠀⠀⢿⣧⠈⣿⡉⠻⡇⠘⢷⣧⡀⣶⣍⠻⣷⣶⠀⠀⣉⢿⣦⠈⣿⡎⢿⣦⣸⣿⠸⣿⣿⣿⡇⢹⣿⣿⣿⣆⢿⣿⣿⣇⡻⣿⣿⣿⣈⡻⣿⣿⣷⣮⡿⣿⣷⣶⣯⢻⣿⣿⣷⡝⣿⣿⣿⣮⢿⣿⣿⣿⡹⣿⣿⣿⡏⣿⣿⣿⣯⢻⣿⣿⡇⢻⣿⣿⣿⣮⣿⣿⣿⣷⣿⣿⣿⡆⢿⣿⣿⣧⣿⣿⣿⡇⢹⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣷⢹⣿⣿⣿⠹⣿⣿⣷⣹⣿⣿⣿⡹⣿⣿⣿⢻⣿⣷⣾⣿⣿⣿⣎⢿⣿⣿⣾⣿⣿⣏⡸⣿⣿⣿⠀⣿⣾⣿⢠⣿⣿⣿⢈⣿⣿⣇⢸⣿⣿⡇⢹⣿⣿⣿⠉⣿⣯⡀⣽⣿⣟⣿⣿⣿⡿⢿⡿⣴⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⠿⠿⠿⠂⠀⠀⠙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠛⠋⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣤⠄⢀⣿⡇⣶⡀⠀⠀⠀⣿⠃⣘⠻⠾⣿⡿⣶⣍⢻⣿⡙⢷⡎⣿⣧⣤⣿⠀⣿⣷⣿⣷⢸⣿⣿⣿⣤⡻⣿⣿⣿⣮⣿⣿⣿⣿⣾⣿⣿⣿⣿⣮⢻⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣷⣿⣿⣿⣿⢸⣿⣿⣿⣇⣿⣿⣿⡇⣿⣿⣿⣿⢸⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡁⣿⣿⣿⡿⣿⣿⣿⡄⣿⣿⣿⡟⣿⣿⣿⡈⣿⣿⣷⠙⣿⣿⣆⢻⣿⣿⣌⢿⣿⣿⡼⣿⣿⣇⢸⣿⣿⡇⣼⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⢰⣾⣿⡏⠉⣷⣯⡍⣯⣿⣿⣻⣿⣿⡿⣤⣿⣿⣶⣶⣶⠿⠿⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠶⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠘⣂⡀⠀⠀⠀⠈⢹⣗⡿⠃⠀⠀⠀⢻⣷⡟⣿⣆⢻⣿⣿⣿⣧⣿⣿⣾⣇⠸⣿⣿⣿⣀⣙⢿⣿⣿⣷⣝⠻⣿⣿⣿⣿⣻⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡿⢿⣿⣿⣿⠛⣿⣿⣿⣧⣿⣿⣿⣯⣽⣿⣿⣿⣾⣽⣿⣿⣿⣿⣿⣿⣿⣶⡻⣿⣿⣷⣽⣿⣿⣷⣝⢿⣿⣿⣮⢻⣿⣿⣿⢻⣿⣿⣧⣻⣿⣿⣿⣿⣿⣿⣷⣝⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣮⡿⣿⣿⣿⡿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣏⢿⣿⣿⣇⣿⣿⣿⣇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⠀⣿⣿⣿⡌⣿⣿⣷⠹⣿⣿⣧⢻⣿⣷⡽⣿⣿⣶⣿⣿⡟⣹⣿⣿⣿⣼⣿⣿⣧⠀⣿⣿⣧⣿⣿⣿⣿⣛⣿⣷⣿⠋⣀⣭⣤⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⢾⡛⢉⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠃⠀⠐⠒⢀⢀⣼⡿⠁⠀⢛⡁⠀⠀⢀⡀⢠⣿⠇⠀⠀⠀⠀⢼⣿⣿⣿⣿⠘⢿⣿⣿⣿⣼⡻⠿⣻⣿⣦⡝⢿⣿⣿⣷⣼⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡟⠹⣿⣿⣿⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢸⣿⣿⣿⢎⣿⣿⣿⡇⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣇⢻⣿⣿⣿⢸⣿⣿⡇⢹⣿⣿⣿⢸⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡽⣿⣿⣷⠻⣿⣿⣇⢿⣿⣿⣆⣿⣿⣿⡇⣿⣿⣿⢠⣿⣿⣿⢸⣿⣿⣧⣹⣿⣿⡟⠉⢹⣿⣿⣿⣿⣿⠙⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⠀⠻⣟⣥⣤⣤⣤⣀⣀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠋⠉⣠⡾⠛⠋⠈⠈⠀⠀⠀⠾⡃⠆⠀⠰⠀⣀⠀⠁⠀⠀⠀⠈⣨⡿⠀⠘⢣⣬⠁⠀⠀⠈⢁⣿⣿⠀⠀⠀⠀⠀⣼⣿⣯⡻⣿⣶⣶⡉⢿⣿⣿⣿⡶⢿⣿⣿⣷⡸⣿⣿⣿⠇⠻⣿⣿⣿⣭⡻⣿⣿⣷⣍⡛⢿⣿⣿⣎⢩⣿⣿⣿⣟⣿⣿⣿⣿⢻⣿⣿⣿⡟⣿⣿⣿⣿⣽⣿⣿⡏⢸⣿⣿⡿⠹⣿⣿⣿⣟⣿⣿⣿⣇⣻⣿⣿⣿⣽⣿⣿⣯⣼⣿⣿⣿⣼⣿⣿⣿⣯⠻⣿⣿⣷⡿⣿⣿⣧⡿⣿⣿⣷⣿⣿⣿⣿⣼⣿⣿⣿⣜⣿⣿⣿⣼⣿⣿⣧⢸⣿⣿⣿⣾⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣨⣿⣿⣿⣼⣿⣿⣷⢸⣿⣿⣷⢹⣿⣿⣮⢻⣿⣿⡝⣿⣿⣿⡿⣿⣿⣾⣿⣿⣿⣼⣿⣿⣯⣿⣿⣿⣀⣴⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⡟⣩⣶⣿⣩⣿⣾⡿⣿⡿⢿⣿⣿⣯⣭⣭⣿⣽⣛⡇
⠀⠀⢀⣀⣀⢠⣤⣤⣴⣶⣶⣾⣿⡄⠀⢠⣤⡿⠖⠻⣿⡟⠛⠋⢀⠀⠈⠋⠀⠀⠀⠀⣠⣾⠟⠁⠠⡧⠀⣿⠇⠠⠀⢀⡘⢻⣿⠀⠀⠀⠀⣴⡿⢿⣿⣿⣮⣿⣿⣿⠀⢻⣿⣿⡟⠘⢿⣿⣿⣡⣌⡛⠋⣤⣤⣌⠻⣿⣿⣿⡌⢿⣿⣿⡇⠸⣿⣿⣿⠀⣿⣿⣿⡿⠻⣿⣿⢟⣜⠻⣿⣿⣷⣟⢿⣿⣧⣬⠛⢻⣿⣿⣍⢻⣿⣿⣿⡻⣿⣿⣿⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⢹⣿⣿⣷⠹⣿⣿⣿⡾⣿⣿⣿⡟⣿⣿⣿⣜⣿⣿⣿⡞⣿⣿⣿⠘⣿⣿⣿⡿⣿⣿⣷⡿⣿⣿⣷⡿⣿⣿⣿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣾⣿⣿⡿⣿⣿⣿⡟⣼⣿⣿⣿⣼⣿⣿⡎⣿⣿⣿⢹⣿⣿⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿⣿⣿⣿⣿⣛⡁⠿⣿⣶⣬⣭⣟⠛⠉⠉⢉⣽⠇
⢰⣶⣌⠻⣯⣀⢷⣿⣿⣿⣿⠉⠿⣿⠛⣿⡿⠟⠛⢀⣄⠘⠛⠛⠴⠀⠘⠓⠀⣠⣶⡿⠛⣁⠀⠰⠿⠃⠀⠀⠛⢀⣴⠟⠃⠻⠳⢶⣶⢦⢀⣿⠁⠀⠉⠉⢙⣻⣿⠿⢠⣤⣭⡉⢰⣿⣿⣧⠘⣿⣿⣿⡆⣿⣿⡿⠀⠻⣿⣿⣃⡘⠻⣿⣧⣤⣍⠛⢫⣶⣶⡝⢫⣶⣶⠈⠁⣿⣿⣿⡌⣿⣿⣿⡇⢸⣿⣿⡇⢸⣿⣿⡿⠀⣿⣿⣿⠇⢿⣿⣿⠃⢿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⡿⠸⣿⣿⣿⣾⣿⣿⣿⣄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣧⣿⣿⣿⠀⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣽⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣎⢿⣿⣷⣽⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠿⣿⣿⠿⣿⣶⣶⣿⠛⠛⠿⠿⢿⣷⡟⠁⠀
⡀⠙⠿⠿⠈⠻⣧⡛⠛⠿⠉⠀⣨⣭⣃⡀⠶⣠⡄⣀⣀⣀⣀⠻⠟⠀⢀⡀⢀⡉⠹⠶⠶⣿⣿⣶⣶⡶⠀⠀⠀⠛⠁⠀⠀⢀⣀⣠⣶⢧⣾⠋⠀⠀⠀⠀⠸⠿⠿⠷⠸⣿⣿⣿⢚⣿⣿⠟⢀⣛⡿⠟⣴⣾⣍⠁⣠⣶⣮⠹⣿⣿⣷⠀⢹⣿⣿⡆⠰⣿⣿⡇⠰⢿⣿⠇⠀⠻⣿⣿⣇⡛⢿⣿⣃⣈⡛⠟⢁⣤⡝⠛⢡⣶⣮⠉⢡⣶⣶⠉⣱⣶⣦⠉⣡⣶⣄⠈⣁⣤⣄⠙⣻⣷⣶⣬⣻⣿⣿⣿⢹⣿⣿⣷⢿⣿⣿⣿⢹⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣯⢿⣿⣿⣟⢻⣿⣿⣟⢿⣿⣷⣿⣿⣿⣧⣿⣿⣿⣧⣿⣿⣿⣋⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⡿⢰⣿⣿⣿⣸⣿⣿⡿⣸⣿⣿⣷⣿⣿⣿⡏⣿⣿⣿⠹⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⢻⡆⠀⠀⠀⠀⠈⠙⠷⣮⣛⠿⣿⣷⣦⣄⣴⠿⠋⠀⠀⠀
⠻⢶⣄⠀⠀⠀⠾⠻⣷⣴⣶⣶⣭⣭⣭⣁⣀⡉⢀⠉⠉⠉⢉⣀⠶⠆⠀⠀⠈⠁⠀⠘⠲⠶⠶⠀⠀⠀⠀⢰⠆⠀⠀⠀⠀⠈⠉⠉⢁⣼⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣿⣿⣿⣦⣝⣛⡛⢀⣉⣉⠉⢠⣬⣉⠉⢠⣤⣿⠍⠰⣶⡾⠉⠀⠶⡶⠀⠀⠿⠿⠈⠿⠿⠿⠃⠙⠻⠿⠟⠀⠘⠿⠇⠀⠘⠿⠟⠀⠈⠻⠋⠀⠉⠙⠋⢀⡉⠉⠉⣀⡈⠉⢉⣬⣭⣉⡉⣛⣙⡻⠿⣟⣼⡿⠿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣸⣿⣿⣿⢼⣿⣿⣿⢾⣿⣿⣿⢹⣿⣿⣇⢻⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣰⣿⣿⣿⣼⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⣷⡄⠀⠀⠀⠀⠀⠀⠈⠙⢷⣾⣽⣿⡿⠋⠀⠀⠀⠀⠀
⠀⠀⠙⠛⠶⣤⣄⣀⠀⢉⡉⠈⠛⠛⢶⣭⠉⠛⠛⠛⠀⠛⠛⠋⠀⠀⠀⠀⠀⠀⠰⢶⣶⣶⠦⠤⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⢿⣿⣶⣶⣿⣿⠶⠶⠾⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠺⠷⠶⠶⠿⠷⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣯⣼⣻⡿⠟⢸⣿⡿⠾⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⢤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⣀⣤⣤⣤⣤⣤⣤⣴⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⣄⣀⣤⣀⣈⠉⠉⠉⠙⠛⠛⠃⠿⢿⣿⡷⣿⣿⣿⣷⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⢹⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠗⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠓⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠒⠛⠛⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣌⡻⣦⠉⠉⠉⠉⠙⠻⢶⣤⣀⣤⣦⣶⣶⣶⣶⣾⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠿⠆⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣠⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣷⡀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠛⠿⠷⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⢀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⣭⣥⣝⠻⣯⠻⣿⡿⠿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⠻⣿⠆⠘⠛⠀⢀⣠⣤⡴⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠀⠀⠀⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠶⠦⢤⣤⣌⣛⣛⣈⠻⣿⣯⠻⣿⣿⣙⠿⣿⣿⠿⣿⣿⣿⢿⣿⣿⠻⣿⣿⡟⢿⣿⣿⠻⢿⠿⠛⠿⣿⣯⠹⠿⠿⠉⢻⣿⣌⠛⣿⣷⣈⣉⣡⣤⣤⠤⠶⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠗⠤⠉⠉⠉⠉⠉⠁⠴⠶⠶⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠶⠿⠿⠉⠙⣋⣉⣉⣁⡴⠶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠻⠾⠿⠶⠶⠿⣭⣤⣌⣡⣤⣌⡙⠟⠃⠉⠻⠟⠈⠛⠻⣀⣙⣿⣤⣄⣀⠰⠤⠀⡼⠶⠶⠶⠶⠶⠾⠿⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⣖⣛⡿⣭⢽⣉⠀⠉⠉⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡟⠋⣤⣄⣶⡿⠿⢛⣿⣿⣿⡿⠖⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⡾⣟⣫⣭⣴⣴⣿⠟⣋⢉⣀⣀⣠⣤⣤⠂⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⣞⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢉⣩⣵⣿⣎⠃⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⢶⡻⣯⣭⣀⡀⢀⢀⡈⠉⠉⠓⠶⢄⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⠤⠤⣤⣤⠤⡤⠤⣤⣤⣤⣤⣤⣤⣤⣤⢤⣤⣤⣤⣤⡤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⡤⠟⣃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⢿⣿⠇⠘⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⣀⢼⣿⣿⣤⣿⣿⣿⢧⢇⣿⡿⠿⠇⠀⠀⠀⠀⠀⠀⠛⠧⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣤⣶⣶⣶⣶⣶⣶⣿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣷⣾⣷⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣶⣯⡹⣿⣿⣯⡿⠟⣩⠒⠷⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡛⢉⣥⣰⣤⣧⣴⡾⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⣀⣤⢖⣩⣿⣿⣿⣿⣿⣿⣿⣯⣿⡿⢋⣜⣢⣵⣦⣶⣰⣄⣀⣀⠀⠀⠈⠑⢦⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣖⣾⣿⣿⣽⣷⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣶⣿⣫⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣬⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⢿⡼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⠰⠖⠉⠐⠚⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢷⣷⣿⣿⣿⣿⣿⣷⡟⠀⠀⣠⠏⠀⠀⠀⣠⡴⡚⣉⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢮⡵⣿⣿⣿⣿⣿⣯⣷⣿⣹⣆⢀⠀⠀⠀⠀⠙⢦⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⡤⣶⣶⡾⣟⣿⣿⣿⣯⣿⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠰⣙⡛⣿⠿⡝⣿⣿⣿⣿⣟⣿⡛⠟⢻⢏⣿⣿⣿⣿⠿⣿⣿⣿⣿⣷⣾⣿⢻⢿⠿⣿⣿⠿⢿⠷⣻⣯⡋⠿⠀⢹⣿⣿⠿⡏⢿⣿⣿⡿⡿⢳⣿⢿⡿⡿⢷⣝⠻⠏⠱⢫⣿⠿⡿⢿⢿⣼⡿⣿⠿⣹⣿⡿⢿⠿⣿⣿⠿⣿⡿⣡⡜⠻⢿⢿⣿⣿⣿⣿⡅⠁⢨⡑⠊⠘⣿⣿⣿⣿⣿⣟⡿⣿⣿⡿⠿⢷⣦⣄⣀⣀⣀⠉⣀⠉⣀⠂⣉⠛⠿⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡿⠿⠃⣀⣀⣴⣏⣤⠴⠚⠉⡒⣞⣵⣿⣿⢿⣩⠿⠻⠿⡿⢛⡻⣍⣢⣦⣴⣶⣿⣿⣿⢿⡿⢻⠿⡍⠏⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣴⢶⣶⣖⣻⣿⣿⣽⣿⣶⣷⣾⣽⣯⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣷⡽⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣹⢿⣿⣿⣿⣻⣿⣶⣿⣏⠿⣟⠿⣿⣿⡻⣿⣿⣿⣿⡿⣿⣾⣿⣿⠛⣿⣿⢟⣿⠹⣷⣾⣦⠉⠙⣿⣿⣿⣿⡿⣿⢷⣶⠃⠘⢿⡞⣿⠋⠙⣿⣿⣿⣿⡟⢻⡟⠛⠛⠙⢿⡿⣿⣟⡛⢿⡿⡿⢿⡛⢿⡛⠉⠉⠀⢷⡛⢻⡟⠛⢿⡻⢷⠀⠈⢻⡅⠂⠀⠙⢿⣭⠙⣿⣿⣯⣯⡀⠀⠀⢹⣯⣿⣿⣿⣿⣾⣶⣄⠀⠁⡀⠀⠂⠚⠙⠿⢿⣿⠿⠿⠿⣾⢿⡿⣿⠿⢟⡻⣽⣿⣦⣄⣀⡀⠉⢿⣭⢷⣹⣦⢧⣼⢧⣻⣷⡿⣿⢟⣟⢻⠛⡍⢦⡑⢎⡰⣈⠥⡘⢄⢊⣄⡠⠀⠀⠀⠀⠀⠈
⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣶⣖⣾⣿⣽⣿⣿⣿⣿⣿⣿⡿⣿⣿⢻⣟⣿⣿⣏⠿⠩⡽⣽⣧⡿⣉⡉⠛⣯⣿⣹⣿⣿⣿⣿⣿⣿⣽⣿⢳⡍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣿⣿⣿⣿⣿⣿⣷⣿⣟⡿⢿⣷⣹⣿⣿⣿⣷⣩⢿⣿⣿⣷⣽⣿⣿⣿⣷⣸⣿⣃⣙⡷⣹⣿⣛⢿⣧⣹⣿⣟⣷⣇⣸⣿⣛⠿⢿⣨⣿⣉⡶⢟⣊⣷⣜⡹⣆⡘⣿⣟⢏⣻⣀⣿⣄⣀⣀⣈⣷⣹⢛⡿⣌⣷⣿⣈⣛⣈⠿⣤⣀⣀⣀⣿⣮⣷⣄⠀⠳⣜⠣⣄⠀⣻⣦⣀⣀⣀⣉⡀⠀⠛⠿⣏⡃⠀⠀⢀⣙⡻⠿⢿⣿⠻⠛⠿⣇⡄⠀⠀⡉⠁⠒⣦⣈⠉⠠⣄⠀⠛⠈⢡⣍⣎⣳⣼⣿⣿⣿⣿⣿⣿⣷⣦⣖⠡⠉⢊⢉⣼⣶⣿⣶⣿⣼⣧⡖⢮⠙⠞⠓⠚⠋⠙⣀⣋⣴⣫⣗⢣⡁⠄⠀⠀⠀⠈⠀
⣿⣿⣶⣶⢶⣿⣭⣭⣭⣿⣯⣯⣿⣽⣯⣿⣽⣿⣷⣶⣾⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣫⣥⣍⣻⣿⣿⣿⣷⣯⣯⣿⣿⣴⣦⣖⢳⠰⣹⣿⡔⢡⠓⠀⢹⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢿⣿⣿⣿⣟⣿⣿⣿⣿⣟⣿⠿⢿⣿⣿⣿⣿⣿⣿⣼⢿⣿⣿⣿⣏⢿⣿⣿⣿⣟⢿⣿⣷⣿⣞⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠩⣽⣻⣿⣌⠻⣿⣿⣿⣿⡹⣿⣿⣿⣦⡻⣎⢥⣀⢀⢻⣿⣿⣿⣧⣽⣤⠀⠀⣀⠻⣷⡄⡉⣦⣙⣧⠁⠈⢴⡁⣼⣿⣦⣰⡈⠂⢘⣧⣄⡘⣿⡳⣤⣄⡹⣆⠀⠀⠈⠻⡗⠚⠁⠘⣿⠛⠛⢛⣿⡟⠿⣿⣿⡿⡏⠉⠀⠘⢻⣿⡿⣷⣼⣷⣄⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⡈⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡾⠷⠞⡟⠿⠿⣿⣳⢏⡎⠧⣃⠀⠀⠀⠀⠀⢰
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣃⠗⣾⡟⠠⢌⠀⢡⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣛⢿⡣⢹⣿⣿⣿⣿⣿⣿⣿⣿⡷⠼⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⡩⣿⣿⣯⣿⣿⣿⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣧⣹⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣧⣭⢼⣿⣿⣿⣿⣿⣿⣿⣿⣤⣌⣾⣿⣿⣶⣿⣿⣿⣷⣄⡚⣿⣸⣿⣿⣿⣿⡆⢼⣿⣿⣷⣾⣷⣿⣿⣷⣾⢿⣦⡄⠐⠛⠲⡄⠀⠿⢷⣦⣤⡼⢿⣦⠶⠾⣷⣯⠖⠚⢶⣶⣾⣿⣷⣾⣿⣿⣧⡀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠣⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡡⠠⠄⠀⢀⠂⡀⠉⠑⠻⠟⡸⠄⠀⠀⠀⠀⠀⡜
⠀⠙⢿⣍⣈⣡⣤⣤⣤⣏⣱⣒⣆⣣⣙⣘⣃⠫⠙⠏⠻⠹⡛⠟⢿⠻⡟⢿⢻⣿⣿⣿⣿⣿⣟⣻⣻⣽⣿⢿⡻⢿⠿⣿⢿⣿⡟⣛⠱⢏⣴⡿⠀⡡⠈⢠⣾⠏⠉⣭⠍⡿⣿⣟⣿⠿⣛⢻⡁⣍⣶⣭⣧⣜⢻⣿⣿⣿⣿⣿⣯⣽⣧⣚⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠠⢻⣿⣿⣿⣿⣿⣧⢂⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣶⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠶⣻⣿⣿⣿⣿⣷⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⠽⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣳⣿⣿⣿⣿⣷⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⢤⣷⣀⣦⣀⠈⠛⢿⣿⣾⣷⣯⣽⣿⡆⠀⣸⣿⣿⣿⣿⣾⣿⣿⣿⣷⡄⠀⠀⠙⠛⣿⣿⣿⠟⠋⠁⠲⠙⠀⡄⠀⡉⠉⠛⠛⠛⠻⠋⡙⠉⡉⠀⠁⡈⣀⣃⠈⠐⠁⠀⠂⠀⠐⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠈⠉⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠶⠶⠶⠦⠤⢧⣴⣬⣤⣑⣨⣌⡉⠍⡋⠹⠙⠻⠟⠿⣋⠛⢬⠳⢎⠲⠙⢎⣿⣇⢋⠒⣼⡿⠁⠐⠃⣠⡾⠏⠀⠐⣭⢒⡥⠟⣿⢯⡔⢫⢮⡗⡉⠿⢿⣟⡿⣜⣻⣿⣿⣿⡟⠿⣿⢿⣿⠬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢪⠝⡿⣿⣿⣟⡿⢾⢆⣻⣿⣿⣿⣿⣿⣿⣿⡿⢇⣻⣿⣿⣿⣿⢾⣿⣿⣿⣿⣿⣿⡶⣻⣿⣿⣿⣿⣿⣧⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣏⣿⣿⣿⣿⣿⣇⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢳⣾⣽⣿⣿⣿⣶⡤⣈⠝⡻⢻⠿⣿⣿⡥⢆⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠐⠀⠀⢹⠋⢉⣤⣶⣤⣄⣂⠀⠁⠀⠁⠒⠂⠐⠒⠒⠒⠓⠒⢳⢶⣶⡷⣿⡿⣶⣶⡶⡖⢦⡄⢀⠀⠀⠀⠀⢠⠏⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠓⠷⠶⢤⣬⣁⣙⡛⠛⠟⠾⢷⣷⣾⣿⣿⢿⡿⠋⠀⣀⣴⣾⠛⠁⠀⠀⠈⠡⢋⠀⠀⡀⠰⠊⢤⠖⠸⠮⢷⣬⠭⢲⣭⣦⡼⠲⣶⣽⣶⣭⠺⣥⣯⣽⣹⠬⠭⠝⣾⣿⣿⠭⣧⣔⣠⢮⢤⠥⣛⡿⣷⢬⣤⣌⠻⣿⣝⣻⢻⡟⣿⣍⣠⢡⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣥⠫⠝⡛⢿⣿⣧⠉⠌⢻⣿⣿⡿⣿⡿⣿⣿⣿⠋⠻⣏⠈⠉⠙⠻⣿⠉⠉⠉⠙⣿⡿⢿⢿⡿⣿⣿⣿⣿⡟⢿⠭⠙⠛⠿⣿⡿⠨⢟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢮⣵⣭⡞⣱⢻⣷⡘⢦⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠘⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠠⠢⢤⣤⣆⡔⣦⣮⠵⣳⡝⣮⡱⢧⣘⠣⡌⢸⠀⡇⠀⢠⡏⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠲⠶⢦⣦⣥⣀⣤⣤⡶⠿⠟⠋⠀⠀⠸⣆⢀⠁⠀⠁⠀⡀⠀⠀⠀⠘⣷⣄⠀⠀⢻⣷⣄⡀⠀⠠⣧⡀⠀⠀⢉⠲⣤⠀⢂⢱⣿⣷⣤⡀⢉⠛⣆⣀⠈⢉⡙⣶⡚⠍⡑⢸⣧⡌⣉⠛⡌⢿⡀⠥⢘⡻⠿⣅⠆⠻⣼⣿⣿⢿⡿⢿⣿⣿⢻⠐⢤⢿⣗⢢⢡⡌⢻⣿⡇⡤⠄⠸⢿⣿⣽⣧⡻⣿⣧⠀⠀⠘⣷⡄⠀⠠⠘⢷⡀⠠⠀⠈⢿⣤⣆⣥⣹⣷⣍⢩⣃⠈⠳⣄⠀⠀⠙⢷⡀⠈⠀⠀⠛⠛⠻⠻⢿⣿⣿⣿⠏⠛⢻⣿⣿⣿⣿⣿⣿⣿⡷⣾⣿⣿⣿⣷⣿⣾⡽⠺⡔⣉⢯⣉⡟⠹⣿⣟⠉⠠⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣶⣦⣤⣤⣄⣄⣸⣜⣳⡜⡻⢷⡻⢶⣻⢧⠞⡣⠄⢠⠀⠇⢠⠟⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⢧⣴⣀⡄⠐⠀⠙⣧⣬⡧⢄⡀⠀⠠⠈⠤⠀⠘⢿⣇⠀⠀⠙⢿⣷⠀⠀⠀⠙⡀⠀⠠⠀⠉⢣⡈⠙⠙⠻⣿⡏⠀⠂⠈⢷⡀⠈⠀⠈⢿⣔⠒⠁⠈⣿⣆⠘⠂⠈⢷⣀⠈⠀⠀⠻⣎⠀⠘⠛⢻⣆⠘⠈⠙⠻⣧⡀⠀⠀⠻⣧⠰⠞⠳⠞⣷⡄⠀⠀⠘⢷⡀⠀⡐⢻⣿⣆⠀⠀⠈⣿⣤⠀⠀⠈⠻⣆⠀⠀⠄⢹⣄⠀⠁⠀⠉⠻⠿⠶⢦⠈⠂⠀⠀⠀⣻⣄⠀⠀⢀⠀⣀⠀⠀⢉⡿⣧⠀⡒⡄⢺⣿⣿⢿⣿⣿⠟⢱⡉⠿⣿⣿⣿⣿⣿⡿⣱⠫⣔⠢⡜⢀⠂⠀⠂⠂⠐⠂⠀⠀⠋⠿⣿⣿⣿⣿⣿⣮⣵⣃⠫⠵⣿⣅⣀⠀⠀⠀⠈⠉⠉⠛⠿⠿⠷⡷⢣⣅⡎⠐⠁⠄⠀⠀⣰⠏⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠶⢦⣼⡆⡙⢿⡷⣷⣦⣀⠀⠀⠀⠀⡙⠀⠀⠀⠀⠘⢧⠀⠀⠀⠘⠢⠀⠀⠀⠘⠁⡀⠀⡀⠘⢷⡄⣀⠀⠈⢻⠄⠀⠀⠸⡿⣦⣀⣀⣴⣿⣷⡄⢀⡈⠻⣧⡀⠀⠀⠻⢷⠀⡀⠀⠽⣧⡄⠀⠀⠞⣷⡄⢀⠀⠸⢷⡀⠀⠀⠘⢿⣆⠀⠀⡼⠷⣤⠀⠀⠀⠿⣦⠀⠀⢿⣿⣷⣄⠀⠀⠙⢶⠀⠀⠀⠹⣆⠀⠀⠰⣶⡶⣤⣀⠀⠀⠀⠀⠀⢸⣿⣇⡀⢀⠀⢸⣦⡔⣋⡔⣿⣧⣝⣾⢳⣾⣿⣭⣾⣥⣿⣣⣿⣾⠿⠻⢯⣝⡛⠓⠛⠛⠛⠿⠿⢾⣳⠶⢦⣌⣀⣀⠀⠐⠀⠀⡀⠉⠛⠿⢯⡏⠛⠙⠲⢤⣀⣈⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣇⠌⠻⣌⠳⣝⠓⢶⣄⡀⠀⠈⠅⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠛⠆⠀⢀⠀⢊⠡⠀⠀⠀⠹⠋⠁⠀⠀⠹⣧⡀⠀⠀⠘⢷⡄⠀⠀⠀⠠⣀⠀⠀⠈⠻⣆⠀⠀⠈⠻⠆⠀⠀⠈⠛⢄⠀⠀⠀⠛⣦⠀⠀⠀⠋⠀⡀⠀⠀⠈⠀⠀⠀⠙⢻⣿⠀⠀⠀⠈⠀⠀⠀⠀⠈⠳⡄⠀⢿⣎⣝⣿⡇⠀⠀⢀⢠⠠⢿⡿⡧⢆⡚⡴⢿⣿⡾⣭⣏⡿⢿⢿⣿⣦⣄⣉⠛⠻⢿⣟⡿⢷⣦⣄⠀⠀⠙⠳⢶⣶⣷⡶⡄⠀⠈⠳⣄⠀⠈⠉⠛⠶⣦⡀⠁⠠⠀⠤⠀⠀⠀⠐⢦⣄⠀⢈⡙⢿⣶⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠈⢇⠈⠳⣤⡌⠻⢶⣤⣤⣀⡄⢂⠁⠀⠁⠀⠠⠀⠁⠀⠐⠀⠀⠀⠈⡀⠂⠀⢀⠀⠐⠀⡀⠀⠂⠡⠐⠈⠀⠈⠈⠀⠄⠀⠈⠹⠀⠀⠀⠊⠻⣦⡀⠀⠀⠘⠀⠀⠀⠀⠙⢧⠀⠄⡀⠀⠠⠀⠀⠀⠀⠐⠀⠀⠀⠈⡿⠀⠀⠀⠀⠐⠀⡀⠀⢀⠠⠀⠀⠀⠉⡷⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀⢀⠙⢟⠻⠁⡰⣈⠴⣊⡔⣎⡷⣱⣾⣾⠧⠞⠛⠳⣌⡛⠿⣮⣼⣙⠿⢿⣽⠿⣦⣤⣜⣿⣾⣿⣶⣤⡈⠀⠒⠶⣿⣿⣿⡵⡀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠈⠓⠦⣄⠀⠈⠘⠶⣄⠀⢹⣧⠾⣜⣦⡝⡮⡟⡽⢛⡋⠥⠚⠀⠀⠀⡀⠀⣠⠾⡁⠊⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠈⠷⣤⡈⠙⠶⡀⠙⢯⡛⢿⠷⠿⢶⣦⣍⣤⢀⡤⢀⡄⣀⢀⠠⢀⠠⠁⠀⡀⠀⠰⠀⠡⠐⡀⠁⡁⠰⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠈⠻⣶⣄⣘⣛⡳⠦⣤⣤⣀⡀⠀⠀⠐⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⡀⠀⢀⠀⠀⠄⠀⠐⠀⠠⠀⢀⠐⠠⠐⡠⠁⢘⢀⢢⠀⢥⡚⢠⡗⣪⡵⣶⣹⣾⡵⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠈⠙⠲⣍⡻⠿⣿⣤⡉⠁⠻⢿⣿⣿⣿⣿⣿⣿⣿⢦⡄⠀⠈⠉⠛⠿⢷⣄⡀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⢄⣀⠀⠈⠀⠻⢿⣯⣷⡻⡗⡽⡌⠷⢘⠤⠂⢀⠀⢀⣴⠾⠣⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣤⠈⠛⠂⠀⠀⠀⠈⣷⢸⣧⠀⠀⠀⠉⠉⠛⠛⠛⠚⣿⣾⣧⣭⣶⣼⢢⡕⢢⠐⢠⠂⣤⢠⠐⢠⠁⢠⠐⠀⠁⠂⠁⠀⠀⠀⠀⠁⠀⢠⠀⠀⠈⠛⢳⡍⠙⠓⠒⢲⣮⠛⠛⣶⣦⡌⠀⠀⡄⠐⠂⠈⡔⠀⢰⠀⠀⢠⠀⠁⢠⠁⠀⠁⠁⠈⠀⠁⢠⠈⡆⠈⣦⢡⡎⡔⢢⡎⣼⢣⣿⣿⣭⣿⣿⡗⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⡄⠉⠛⢳⣤⠀⠉⠛⢻⢻⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢲⣦⡄⠀⠉⢹⠛⣿⣧⠉⢡⠘⠀⠀⢠⣶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣀⣀⠀⢀⣠⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠿⠷⠾⠷⠧⠽⠦⢷⣵⣮⣴⣦⣵⣘⣶⣸⣴⣂⣦⡦⣄⢆⣈⢞⣽⣦⡀⠈⠳⣄⢦⣀⠀⠈⢍⡛⠻⢶⣬⣄⡡⢌⡡⣄⣣⡐⣬⡰⢬⣜⣤⣆⣜⣤⣭⣸⣵⣮⣶⣽⡶⠮⠾⠼⠷⠿⠛⠛⠋⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠈⠙⠶⣄⣀⠀⠀⠀⠈⠉⠉⠻⢶⣾⣟⢺⠇⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠤⠥⠤⠬⠥⠴⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠙⠋⠉⠋⠛⠛⠻⣅⠀⠈⠙⠻⣷⣄⠀⠹⣶⣄⠈⠙⢿⡏⠙⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀⠈⠻⣷⣦⣴⣶⣤⡀⠀⠀⠙⠯⢸⠀⠀⢠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀⠶⢬⣝⣆⠐⢦⣭⣁⠁⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⢤⡉⠿⡟⢏⠹⠟⠷⠀⠁⠀⢀⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠓⠮⣬⣟⣛⡂⠀⢉⠀⠀⡼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠛⠳⠬⠥⠤⠤⠤⠶⠛⡉
⠀
........'''''. ..'',,,,,,,,,;;;;;;;;;;;;;;;;;;;;;;;;;;,.. ..';:cc::;,.. .;;;;, .''''''.'
,:'........,dc ,loc;;;,,,,,,,,,,,;;;;;;;;;;;;;;;;;;;;;;;cod1' 'codlc:,,,,;:loxxc' ..xx;;;dd. cx,....,o'
,c. .x: ,ol'... .,oo' .:ol,. ..':xkl. ..kk. ..ckl. cO. 'o'
;l. .kc cx:.. .......................................;d, .cd:. ... .'oO1. .'kk. .'lkc. lO. 'd'
.;,,,,,,,,;;c;'ko.. ;ddllllllllooooooooooodddddddddddddddddddxxdo. .dc. .,:oodddxdl;. .;kO,.'Ok. ..'dk:. lO. 'd'
,x: . .kd............................................ol. ,dl,......'ckOc.....,OO''OO. ..;xx' l0. .d'
,kc . .ko.. ....,kdlclllxd'.:kdooodddddddddddddxx':x... .lo............1Kx.....;0d'OO. ..cko. .......o0. ,d'
,kc . .kd.. .....:Kd.....O0,.oK;...............:kc.dc.....ck'.............1Xc.....k0,OO. .,Ox,xc'''',':. ,x'
,k: . .kd.. ...:0d.....O0,.oK;.............;dd,..d:.....lO..............cKc.....x0,0O. .......;0x;0: ,x'
,k: . kd.. .;0d.....O0,.,kd,.....':::cloc'....co. ,ko............,OO.....,0x'0O. ..ox:,,'';:''dx; ,x,
,x: ko.. ;0d.....O0'...ckd;.....'oxc........o, .ox;.........1Ox......xK;,OO. ..oO, ..;xd. ,x,
,x: xo.. ;0o. .k0'.....:xo,.....'ld;......'o'. .'colc::cldd1' ..xK:.'OO. ..oO, .cxc. ,x'
,x; xo.. ;Oo. .k0'. .;dd;. .:o;. .lc. ....... .;Ox' .'OO. ..lO, .cd; ,x'
,x; xl . ,Oo. .k0'. .,od;, .:dc. 'cc'. .'lkk; .'Ok. ..lO, .ld; ,d'
,d; xl . ,kl. .xO.. 'dd;. .:o:. .;ll;'........':okxc. .'kk. ..lk, .'oo. ,d,
.c;;''',;, .oo::cccl:. 'ldigitalllc. ..,;:ccllllc:'. .:c:::::ll. .,,',,c.
