Shrug Kaomojis

Copy & Paste Shrug Kaomoji Emojis & Symbols ¯\_(ツ)_/¯ | ¯\(º_o)/¯ | ¯\_ ⍩⃝_/¯

ʅ(◞‿◟)ʃ
Your votes help make this page better.
With great power comes great responsibility!

Related Text & Emojis

🤷🤷‍♀🤷‍♂️
😐🤷😔🙁😑😕😶🙃
T^T
( ͡° ͜ʖ ͡°)>👉🏻(c" ತ,_ತ)
-.^-^.-
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢫⣭⡑⢦⠀⠀⠀⠀⠀⠀⠀⠀⡠⢚⣭⣝⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⣧⡿⠀⠳⡀⠀⠀⠀⠀⢀⡞⠁⠸⣶⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⡀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠴⣋⠉⠉⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠁⠀⠀⠈⠳⣄⠔⠒⠚⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠒⠒⠒⠀⠒⠒⡟⠰⠀⠂⠐⡏⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡾⠋⠀⠳⢄⣀⣀⣠⡞⠙⢦⣄⡤⠞⠀⠀⠘⢷⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⢁⠞⠁⠀⠀⠀⢀⣼⣿⠟⠛⠛⠛⣷⣦⡀⠀⠀⠀⠀⠱⣄⡙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⡴⠁⠀⠀⠀⠀⠀⣾⣿⣿⣷⣶⣶⣾⣿⣿⣿⠀⠀⠀⠀⠀⠈⢻⣧⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⡜⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢹⡀⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠤⡄⠀⡰⠟⠛⠋⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢻⣿⣿⣧⡀⠀⡤⢤⠀⠀⠀ ⢰⡒⡒⡟⠒⠛⣾⠁⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠈⠉⠁⢱⠞⠓⠺⡆⠀⣢ ⣯⠤⠭⠟⠛⠀⢸⣄⠔⠒⢶⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⢷⠖⠲⣄⡼⠀⠈⠚⠧⠤⢬ ⠘⠢⠤⠦⢤⡤⠀⠉⠀⢀⠈⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠈⢀⠀⠈⠀⢠⣤⠤⠤⠤⠚ ⠀⠀⠀⠀⡼⠙⠲⠤⢴⡿⣄⡀⠀⠀⠉⠓⠦⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠖⠋⠀⠀⠀⣀⠼⡶⠤⠴⠊⢹⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⢀⣠⣼⣀⠀⠉⠓⠦⢄⣀⡀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⣀⣠⠤⠒⠋⠁⢀⣵⠀⠀⠀⠘⡇⠀⠀⠀ ⠀⠀⠀⠠⡇⠀⣾⣿⣇⠈⠑⠢⢄⣀⠀⠀⠉⠉⠙⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠊⠉⠉⠀⠀⢀⣠⠤⠚⠁⢈⡇⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠨⡇⠀⠹⣿⠉⠓⠤⣀⠀⠈⠉⠒⠲⠤⠤⠤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⡤⠤⠤⠔⠒⠋⠉⠀⢀⡠⠖⠉⢱⠀⣤⣶⡇⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⡟⠳⢄⡀⠈⠉⠒⠤⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠖⠊⠁⠀⣠⠔⢻⠀⢿⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⢷⡄⠀⣿⢄⡀⠉⠓⠤⣄⡀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⢀⣀⠤⠖⠉⠀⣀⢾⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣦⣿⡀⠙⠢⢄⡀⠀⠈⠉⠑⠒⠢⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠔⠒⠒⠉⠉⠀⠀⣠⠴⠊⠁⣸⡄⠀⡎⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⠟⢿⠦⣀⠀⠈⠉⠒⠦⠤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠤⠒⠊⠉⠀⢀⡤⢺⣿⠇⡸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⡀⠈⢦⠀⠉⠒⠤⢄⣀⡀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣀⡀⠤⠖⠊⠁⣠⠟⠋⡴⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⢦⣤⣽⣦⣤⣀⠀⠀⠉⠉⠙⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠊⠉⠉⠁⠀⢀⣠⡴⠚⢁⡠⠊⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣌⡙⠛⢷⣶⣦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣶⡶⠟⠛⣉⠤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢺⠀⠀⠈⡯⠭⠭⠭⣭⣍⣉⣭⠭⠭⠭⢽⡏⠀⠀⣿⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠼⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠻⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⡶⣿⣶⠶⣾⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣾ ⣿⣿⣧⣾⣿⣧⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢟⣫⣽⡿⠿⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠻⠿⢿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠉⠻⢿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠇⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⢹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⡿⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠈⠉⠛⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠈⢻⣷⣄⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠈⠙⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣽⣿⣷⠀⠀⠀⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⡏⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⣀⣠⣴⡾⠿⠟⠋⠉⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⡇⠀⠀⠀⠀⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠘⠿⠶⠶⠶⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⡇⠀⠀⠀⠀⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⠟⠃⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⡇⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⡿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣾⠿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⣇⠀⠀⠀⠀⢿⡇⠀⣀⣤⣤⣶⣾⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣶⣿⠿⠟⠛⠛⠉⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⠻⠟⠛⠉⠁⠀⠀⠀⠀⢀⣀⣤⣤⣤⣶⣿⠿⠿⠿⢿⣯⣤⣤⣄⡀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠿⠟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⠷⣦⣄⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣵⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠀⠀⠀⣾⣿⠀⠀⢀⣠⣴⣶⣄ ⠀⠀⠀⠀⠀⠹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠏⠀⠀⠀⠀⣿⣿⣶⣾⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣤⣤⣤⣀⣀⣀⠀⠀⣀⣤⣶⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠟ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠿⠿⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⢻⣿⣶⠀⠀⠀⠀⠀⣿⠛⠿⠿⠿⠛⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⠈⢻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠋⠀⠘⣿⡏⢷⣄⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣿⡆⠀⠙⢿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⡿⠟⠁⠀⠀⠀⠀⢹⣿⠀⠙⢷⣄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣤⣶⣾⣿⣿⠇⠀⠀⠀⢙⣿⣿⣷⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣶⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀⠻⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣼⡏⣿⡏⠛⠛⠿⣿⣿⣷⣶⣶⣤⣤⣤⣤⣤⣶⣶⣶⣿⣿⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⡿⠛⠻⣿⠀⠀⠀⢠⣿⠀⢸⣷⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣾⠇⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⣰⡿⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⣿⠃⠀⠀⠀⠸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⣰⡿⠀⠀⠀⠀⠐⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡃⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠒⠋⣩⠿⢿⣏⠻⠓⠲⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠾⢁⣴⠿⣿⠿⣞⣷⡍⢹⣽⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠉⠀⠀⠹⣆⠈⠉⠀⠘⠛⠙⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⣠⠖⠛⣳⣿⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠻⠤⠼⢿⣿⠀⠀⠀⢀⣶⠛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⢀⡀⠀⠀⠀⠐⠒⠋⡁⠀⠀⠀⠀⢿⣟⠻⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⣿⠙⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣁⡴⠚⠙⠉⠙⣦⡾⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢀⠀⢸⡟⠁⠀⠀⠘⡿⠒⠛⡇⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠘⢦⣈⠀⠀⠀⠀⠀⠀⢀⠀⣇⢰⠃⣠⡴⠒⠒⢶⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⢶⣟⠷⣤⣀⠀⣀⡀⠀⠉⠁⠀⠀⠀⠀⠈⣇⣨⣿⠞⠁⠀⠀⣄⢸⠀⣸⣧⣄⡀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠈⠳⡌⠙⠳⣤⡙⠦⣄⠀⠠⢤⣀⣀⡴⢿⣿⠛⢳⡀⠀⠀⣿⣾⢸⠏⠀⠀⠙⠲⢶⣏⣉⠉⠉⠙⢦⡤⠤⠞⠋⠉⠙⢲⡄⠀ ⠀⠀⠀⢀⣀⣠⣄⣀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠘⣆⠀⠻⣟⠲⣬⣙⠦⠀⠀⠀⢠⠏⡿⣆⠈⣧⠀⠀⢸⣿⡸⡆⠀⠀⠀⠀⠀⠀⠈⠙⠲⠀⠛⣳⡦⠴⣶⣒⠒⠒⠋⠀ ⠀⠀⠀⣿⣁⣀⣀⣼⠷⣦⣴⡞⠉⠙⢦⡀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠘⢧⡈⠛⢟⡓⠒⠦⠤⣤⡧⢸⡄⠘⠂⠀⠀⢻⡇⢿⠰⢦⣀⠀⠘⠻⣍⣓⣶⣶⣿⣛⠲⠶⠤⢬⣙⡳⣄⠀ ⠀⠀⢀⡤⠞⣉⣡⠴⣶⢧⣀⠙⠷⡞⠉⠉⠉⠉⠉⢳⡄⠀⠀⠸⡄⠀⠀⠹⣆⠀⠙⠲⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢻⣼⡀⠀⠉⢷⣶⣤⣤⣅⣀⣀⣀⣉⣙⣿⠶⢤⡈⠉⠻⣆ ⠀⣴⡿⠖⣻⠵⣶⡾⠿⠤⠼⠟⠓⠳⢤⡀⠀⠀⠀⠀⡇⠀⠀⠀⢳⣤⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠐⠟⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠸⠹⣷⡀⠀⠀⠀⠉⠙⠛⠒⠚⠋⠉⠙⠛ ⣼⣋⣀⣼⣧⠴⠿⠤⠤⠤⠤⠤⣤⣤⣤⣧⠤⠆⠀⠀⢷⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠙⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⣿⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⡏⠓⠂⠀⠀⠘⣇⠀⠀⢸⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⢹⡟⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢹⠀⠀⠀⠀⠀⠸⡆⠀⢸⠛⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⢤⣼⡇⠀⠀⠀⠀⠀⢻⣄⡜⠀⠀⠈⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⢹⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡇⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⢸⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣧⣀⣀⣀⣀⣀⣀⣽⣷⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣧⣀⣀⣸⣀⣼⣤⣀⣀⣀⣀⣀⣀⣀⢀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⠉⠁⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⣿⣉⣉⣉⣉⣩⣯⣅⣤⣾⣿⣏⣹⣄⣀⣀⣼
🤷🏻‍♀️¯\_(ツ)_/¯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠸⣿⣿⣿⣿⠇⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣧⣈⠛⠛⣁⣼⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣶⣾⣷⡀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⣾⣷⣶⣦⣄⠀ ⠀⠛⠉⠉⠘⣿⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⣿⠃⠉⠉⠛⠀ ⠀⠀⠀⠀⠀⢹⣿⣾⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣷⣿⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣿⡿⠁⠘⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⢿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠿⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣗⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⣠⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣶⡶⡄⠀⠀⠀⠀⠀⠈⣏⣯⠀⠀⠀⠀⠀⠀⢾⣶⣖⣤⡀⠀⠀⠀⠀ ⠀⠀⢸⣹⠋⣹⣿⠀⠀⠀⠀⠀⠀⠻⠿⣦⡀⠀⠀⠀⠀⡰⣤⣼⣯⡇⠀⠀⠀⠀ ⠀⠀⠈⠋⠀⠙⠪⣷⣤⢀⡶⢤⡀⠀⣰⠋⢿⡄⠀⢠⢾⡖⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⡗⠀⢹⣾⣷⣤⣤⢧⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡽⠛⠉⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⣀⡴⠀⣠⡾⠓⢦⣄⠈⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠤⢤⣤⡴⠖⠋⣿⠟⠋⠁⠀⠷⡄⠘⣷⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠃⠀⠀⠀⣤⣤⠀⠀⢀⣤⡄⠀⢸⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡞⠀⢸⠀⠀⠀⠀⠻⠿⠀⢀⠘⠿⠇⠀⡼⢻⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⠾⠁⠀⢸⡄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠰⡇⠈⠳⣄⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⢤⣀⠀⢹⣁⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⢀⡇⢀⣀⠴⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⢶⠪⡉⠉⠉⣳⢦⣀⠀⠀⠀⠀⠀⣀⡴⡏⠉⠉⢠⠖⣦⡄⠀⠀ ⠀⠀⠀⠀⠀⠛⠒⢦⠱⣄⣾⣅⢀⣼⠙⢷⡒⠚⣻⠃⣧⣬⣆⡰⢃⠔⠚⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠣⣌⡤⠛⡟⠋⠀⣄⣉⣉⣡⠀⡟⠻⢌⡠⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠱⣀⣀⡞⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣦⣤⣤⣤⣤⣤⣤⣤⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡇⣿⠀⠉⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣿⠀⢸⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠿⠿⠀⠸⠿⠿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⠄⠤⢰⠆⢰⡆⢰⡶⢶⡖⣶⣾⠃⣶⢲⡖⢲⠀⠀⠀⠀⠒⠆⢾⠠⠀⠠⠆⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⡄⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠒⠛⠋⠙⡇⠀⠀⠀⠀⠘⡄⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⣰⠛⠉⠉⠓⠂⠀⠀⣿⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠋⠙⠓⠦⣄⡀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠁⢀⣤⣤⢶⣦⣄⡀⠛⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠙⠻⣇⠀⠀⠀⠀⢀⡀⠀⠀⠀⢠⡟⣵⣶⡶⢤⣈⠻⣦⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⡞⠁⠀⠀⠀⠘⢹⡇⠀⣿⣷⣍⢷⡘⣧⢻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡄⠀⢣⡀⠀⠀⠀⢘⣿⠟⢋⣉⡙⠓⠀⠀⠀⠀⠈⣷⢶⣿⣼⣿⣧⢷⢸⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⡀⠀⠻⣦⡀⠀⣾⢃⡾⠻⣧⣝⢦⠀⠀⠀⠀⠀⠈⠣⣟⠿⠿⣟⣼⠟⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠱⣄⠀⠈⠁⠀⡏⢸⡀⣠⡿⣿⣯⣇⠀⢀⡴⠊⢩⠀⠈⢉⣩⠿⠇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⣿⢸⡿⣿⣷⣿⣿⡟⠀⠈⠒⠂⢀⣠⠶⠋⠁⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣦⣳⣙⠿⢟⣽⠃⠀⣄⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⣠⣿⣀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠛⠉⠙⠳⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡙⠛⠟⠛⠁⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠈⠛⢦⡀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠹⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠀⠀⠈⠳⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱ ⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠉⠳⣦⣤⡤⠴⠶⠒⠉⠁⠀⠈⢣⡀⠀⠀⠀⠀⠀⠙⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈ ⠀⠀⡠⠊⠉⢩⠉⠙⠶⣄⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠖⠋ ⢀⡞⠁⠀⢠⠏⠀⠀⠀⠈⢳⣄⡞⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀ ⡼⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⣴⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢦⣀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀ ⣧⡀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⣠⡾⠁⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠈⠙⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣀⠀⠀⠀⡇⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠀⠀⠙⠀⠀⢠⠃⢰⣄⠪⡼⢴⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢇⠀⠒⠀⠀⠀⠊⣀⠽⠋⠀⢰⣿⡂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⢌⣀⡠⠤⢒⠪⠛⡡⠊⡠⢊⡠⠶⡁⠀⠀ ⠀⠀⣀⡤⢀⣤⡤⠀⠀⡀⠀⡇⠀⠀⠀⡀⠔⠊⠁⠂⡁⣔⠮⠊⠁⠀⠀⠈⢂⠀ ⠀⡜⠋⠀⠀⠁⠲⣿⣏⣄⠀⠣⣀⡀⠁⢀⣀⡠⢴⡺⠋⠁⠀⠀⠱⣄⠀⠀⠀⢣ ⢸⠀⢠⡴⡔⠀⠀⣈⡠⠃⠉⢽⠅⠶⠘⡆⠥⠂⠁⠀⠀⠀⠀⠀⠀⢫⢣⠀⠀⠀ ⢸⠋⠀⣸⡔⠀⢀⣠⠈⡆⠀⠈⡲⠂⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠆⠀⠀ ⢺⣥⡄⠉⠺⣣⠮⠓⣰⠉⠈⠢⠇⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⡀⡀⠀ ⠀⠛⢛⡷⠀⠀⠀⠀⠁⠀⠉⠢⡀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢋⠓⠛ ⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀ ⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀ ⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⠴⠖⠒⠛⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠀⠀⢀⣽⣿⣿⡿⢷⣽⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⣅⡄⠀⠀⠀⠀⠋⣴⠿⣷⣯⣝⢮⣻⣿⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⠿⠛⠻⠦⠀⠀⠀⠀⢹⣤⣾⣉⣿⣷⣳⣿⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣴⠾⣯⣟⢦⠀⠀⠀⠀⠀⠳⣟⣿⣿⣿⣽⡿⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⢠⡿⣿⣿⣇⠀⣠⡖⠊⣽⠿⢏⣩⡽⠟⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣠⡤⠖⠒⠒⠒⣶⣶⠆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⣟⣿⣷⣿⡷⡇⠀⣿⠒⠀⠀⠀⣸⡏⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⢰⡞⢉⣽⠀⠀⡴⠀⠀⢀⣆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣝⣌⣛⣿⡿⠁⠀⣸⡶⠿⠷⢤⣯⠀⠀⠀⠀⣼⡿⣄⣀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⣀⠝⠁⢸⡶⠋⠀⣄⠤⠂⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⠛⠛⠋⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⢿⡳⣄⣼⣿⠀⠀⢦⣀⠀⠈⠁⠀⢠⡾⠁⠀⢀⡇⠀⡰⠋ ⠀⠀⠀⠀⠀⠀⠐⣶⣶⡒⠒⠒⠒⠒⠒⠦⣤⡀⠀⠀⠀⠀⠈⣳⡶⠶⠦⣄⡀⠀⠀⠀⠀⠀⣀⡤⠚⠋⠀⡄⠀⠀⣨⡗⠋⡟⢏⢳⡄⠀⠈⠙⠒⢦⡤⢾⣥⣤⡤⠾⠓⠋⠀⠀ ⢠⣆⠀⠀⣿⣄⠀⢸⣆⡉⢑⡶⠀⠀⠀⠀⠈⠻⡄⠀⠀⢠⡞⠁⠀⠀⠀⠈⠹⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⢹⡉⠉⠉⠀⠘⣷⡈⢦⡉⠲⢤⣀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡟⢦⣀⣿⠈⠳⣼⡇⠙⠿⣄⡀⠀⠀⠀⠀⠀⢳⣄⢀⡏⢿⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠉⢻⡤⢽⡶⢤⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢳⡀⠘⣿⠀⠀⠈⢷⡀⠀⠈⠙⠀⢀⡴⠇⠀⣸⣿⣿⣅⡘⠳⠴⠋⢧⠀⠀⢰⡇⠀⠀⠀⠀⢷⡀⠀⠀⠀⣿⢳⣦⡀⠀⠀⠁⠀⠸⣻⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠙⠦⠼⣧⣀⣀⣈⣳⡦⣤⠴⠚⠉⠀⠀⣰⣯⡏⢻⣄⠁⠀⠀⠀⢘⣷⠴⣏⢹⡀⠀⠀⠀⢸⠙⠲⠤⠴⠏⠈⣧⠙⠳⠤⠤⠴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠘⢧⣀⣠⡴⠚⢁⡞⢁⣿⡁⠀⠀⠀⣰⠟⠁⠀⣿⠀⠻⣤⣀⣴⠟⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⡤⢶⡿⠶⣯⡀⠀⠀⠀⣴⠃⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣟⠇⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⠤⠤⠔⠋⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠖⠛⠉⠉⠉⠙⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢀⣰⠀⠀⠀⠀⠀⣾⣶⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⣰⡶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡼⣿⣇⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⣼⠀⠀⣶⢧⡀⢀⡾⣋⢀⣿⣠⣶⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣀⣸⡎⣷⡞⠁⢨⡾⠋⠁⣴⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⡄⠀⠀⣠⣤⠤⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠈⣙⣷⠾⠃⣠⠆⠀⣤⡾⢟⣶⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠛⠁⣠⠞⠁⠀⠀⢻⣯⣾⣯⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠛⣩⠟⠉⠀⣠⠞⠁⠀⣠⠖⠁⠀⠡⣠⡾⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠶⢤⣄⣀⣠⡤⠶⠖⠛⠋⢁⣠⠞⠋⠀⣀⡴⠎⠁⠀⣠⠞⡁⢀⣠⡶⠛⠻⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠚⠁⢀⣠⠴⠛⠁⠀⢀⡴⢚⣡⡴⠟⠋⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⡤⠶⠂⢀⣤⣶⣶⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠁⠀⠀⠀⠉⠁⠀⢀⣤⢞⣯⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀ ⠀⠀⠀⣠⡶⣫⠵⠂⠐⠚⠛⠿⠟⠉⢀⣤⣶⣦⣴⠞⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⢀⡤⣶⣿⣶⠟⠋⠀⠀⠀⠀⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀ ⠀⠀⣰⠏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣞⡽⣿⡅⣠⣆⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⠾⠟⣫⠵⠋⠁⠀⠀⠀⠀⠀⠀⠀⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠹⡆ ⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣋⡵⠞⠁⡟⢷⣄⣀⣀⣈⣟⠻⠶⠦⠤⣤⡤⠶⢛⡿⠟⠋⠁⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡳⣄⠀⠀⠀⠀⠀⠀⠀⢻ ⠀⣿⠀⠀⠀⢀⣤⢶⣢⣤⠶⠄⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⠉⢉⣿⣃⡤⠤⣖⣻⠽⣿⠋⠁⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠙⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⣇⣀⠀⠀⠚⡿⠋⣭⡾⠂⠀⠀⠀⠀⢤⣤⣶⡟⠁⠀⠀⠒⠋⠹⣿⠒⠒⠊⠉⠀⠀⢻⡄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠸⣧⠀⠀⠀⠀⠀⠀ ⢰⣿⠿⠋⠁⠀⠀⢸⢃⣠⡄⠀⠀⠀⠀⠀⠀⣀⠝⢳⡄⠀⠀⠀⠀⠻⠦⣤⡶⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⢻⠀⠀⠀⠀⠀⠀ ⠠⣯⠀⠀⠀⠀⠠⢿⣿⡵⠂⢀⠀⠀⣠⣶⣻⠇⠀⢀⡟⢀⡀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣿⠀⠀⠀⠀⠀⠀ ⣤⢿⡟⠀⢀⣀⠀⠛⢣⡤⣞⡯⠄⡠⠿⣋⡥⠆⢀⣿⠛⠋⠙⠻⣄⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⢸⣟⣻⣟⡏⠀⠀⠀⠘⢯⣤⣞⠵⠚⠉⠀⢀⣸⠃⠀⠀⠀⠀⠙⠃⠛⠃⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢀⡄⠀⡀⠀⠀⢠ ⠀⠈⢙⣿⣿⣥⠶⢤⠀⠀⠀⠉⠁⠀⠀⠀⠀⠘⠛⠛⠙⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⢻⣧⡴⣿⣴⣦⣼ ⠀⠀⠈⠛⠙⠓⣻⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠉⠉⠛⠉ ⠀⠀⠀⢀⣴⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀ ⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀ ⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀ ⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀ ⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣻⣫⠢⠀⠀⠀⠀⡔⣽⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠑⣀⣀⠎⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠉⠢⡀⠬⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢏⠉⠁⢨⢇⠈⣈⠉⢢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡀⢊⠊⠀⠀⢩⣿⠛⠒⣿⣄⠀⠀⠑⢅⡢⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣿⡐⠁⠀⠀⠀⢻⣿⣿⣿⣿⡿⠀⠀⠀⠈⢃⢨⣦⠀⠀⠀⠀⠀ ⢀⢀⡖⣄⠜⠉⢡⠁⠀⠀⠀⠀⠀⠉⠉⡉⠉⠀⠀⠀⠀⠀⠀⡟⠿⠷⣀⠖⡄⢀ ⡯⠽⠒⠈⠤⠐⡔⢆⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⢠⠣⠀⢄⠇⠒⠣⢬ ⠈⠉⢱⠣⠀⡴⡀⠈⠒⠤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠒⠁⢀⣢⠀⠤⠏⠉⠁ ⠀⠀⠈⢀⣴⠣⢄⠁⠒⠠⠤⢀⣉⣉⣉⣉⣉⣉⣀⠠⠤⠐⠊⣁⠜⡆⠀⢸⠀⠀ ⠀⠀⠀⠘⢟⠑⠤⣈⠁⠒⠀⠤⠤⠤⠤⠤⠤⠤⠤⠄⠐⠂⢉⠠⠒⣁⢠⣼⠀⠀ ⠀⠀⢰⠀⠧⡁⠢⠄⡈⠀⠒⠂⠀⠀⠀⠀⠀⠀⠐⠒⠀⢉⡀⠔⠊⣸⠈⡋⠀⠀ ⠀⠀⠈⣿⣶⣈⠐⠠⢀⣈⠁⠒⠒⠒⠒⠒⠒⠒⠒⠈⢉⡀⠤⠒⢁⣼⢀⠃⠀⠀ ⠀⠀⠀⠘⢅⠣⡁⠂⠤⢀⣈⡉⠀⠀⠀⠀⠀⠀⠉⣉⡀⠤⠐⠈⠴⢋⠊⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠾⣓⠦⣤⣄⣀⣈⣉⣉⣉⣉⣁⣀⣠⣤⠴⢒⡡⠐⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⡁⠀⠙⠛⠛⠋⠙⠛⠛⢻⠀⢸⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⠀⡀⠀⢀⣎⣁⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣈⣑⡄⠀⢀⠀⠀⠀⢀ ⣿⣏⣿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠶⠶⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠀⠀⠀⠀⢀⣴⣦⡉⠉⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠛⢡⡾⣷⣤⡀⠀⠙⢧⡀⠀⠀⣀⣤⣦⣄⡀⠀⠀⠀⠀⠀⣠⣤⣤⡶⣶⣦⣄⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢃⣴⠳⠂⠀⠀⠀⠀⠀⠀⢿⡄⠻⣿⡿⠀⠀⠀⠹⣆⣼⠋⠀⠀⠈⠙⢦⡀⠀⠀⣾⠛⣿⠿⢛⣋⣭⡭⣽⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢨⣿⡟⢻⡆⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠈⢳⡄⠀⢻⣄⣿⠿⠛⢯⡀⠀⠈⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣿⡘⢗⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢿⡁⠀⠀⠘⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⣸⠀⠈⠉⠉⠀⠀⡀⠀⠀⠀⠀⣠⣧⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠘⣧⠀⠘⣇⠀⠀⠀⢹⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⠈⠙⠳⣿⡄⠀⠀⠀⠀⠀⢷⡤⠴⠞⠛⠉⠹⠇⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⡀⠀⠀⠀⠀⢹⡆⠀⢹⡄⠀⠀⠀⢿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠘⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢳⡄⠀⠀⠀⠀⢻⡀⢸⡇⠀⠀⠀⠸⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠈⣷⠀⠀⠀⠀⠈⢷⣼⠁⠀⠀⠀⢀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡀⠀⠀⠻⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢸⠁⠀ ⠀⠀⠀⠀⠀⠀⣠⣿⣿⠀⠹⣦⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠈⠻⠶⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⣀⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀⢸⡟⣧⡀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀ ⠀⠀⠀⣀⣠⡾⠿⠞⠙⠃⠀⢹⡆⠀⠀⠀⣧⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠳⣤⣀⣀⠀⢀⣠⡾⠃⠀⠀ ⠀⢀⣾⣿⣭⣽⠆⠀⠀⢀⣠⠾⢻⡆⠀⠀⣿⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀ ⢠⡞⢉⣠⣤⣤⣤⣦⡾⠋⠁⠀⠀⢿⡄⠀⢸⡆⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⠿⠿⠟⠀⠀⠀⢿⡃⠀⠀⠀⠀⠈⠻⣤⣈⣷⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢷⣄⣀⠀⠀⠀⠀⠀⠀⣀⣴⠋⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣶⡄⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⡿⣿⣿⣿⣿⣷⣄⣯⢳⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⠞⠛⠉⠉⠉⠛⠛⠳⢮⣤⣝⡖⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⣠⣤⣶⣶⣤⣀⠀⠀⠙⠛⠻⢷⣌⠻⣦⡀⢀⣀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣅⠀⠾⠟⠉⠀⠈⠛⢿⣿⣶⣶⣤⣄⠀⠙⢷⡘⢟⣉⣭⣯⣝⣷⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⢀⡾⢡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⣧⠀⢼⡇⠘⠛⠋⢻⣿⣿⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡀⠻⣤⡹⣦⣼⣧⠋⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⢰⣤⣾⣿⡿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡛⠾⠿⠌⠻⡿⠃⠀⠀⠀⣼⡿⠀⠀⢀⣶⠀⠀⠀⠀⠀⠀⠐⠶⣶⣶⣿⠛⠛⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠶⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣼⡿⠀⠀⠀⠀⢠⣣⣀⠀⠀⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⡀⠀⠀⠀⠀⢀⣤⠶⠶⢶⣤⣶⡀⠀⠀⠀⠀⠀⠀⢴⣷⣾⣧⣤⣿⣃⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⠞⠉⠉⠻⣦⠀⠐⠦⠤⣶⠇⠀⠀⠀⠀⣿⣷⣶⣶⣶⣤⣉⠻⣦⠀⠀⠀⠀⠀⠈⠉⠛⠁⠈⠻⣞⡛⠉⠉⠀⠀⠀⠀⠀ ⠀⢀⣠⣀⠀⠀⡇⠀⠀⠀⠀⡟⠀⢀⣠⠿⠷⢶⣄⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⢷⣦⡀⠀⠀⠀⠀ ⢰⡟⠁⠈⢻⣄⣿⡀⠀⠀⠀⡇⢀⡾⠁⠀⠀⠀⣿⠀⠀⠀⢀⡀⠙⠻⠿⠿⠿⠋⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⢀⣠⣹⡆⠉⠁⠀⠀⠀⠀ ⢸⣅⠀⠀⠀⠹⣾⠁⠀⠀⠀⣿⣾⠃⠀⠀⠀⣰⡿⢖⣢⣆⠀⠙⠲⣶⣤⣄⣀⠀⠀⠀⠀⣸⠏⠁⠀⠈⢻⣧⣾⠋⠀⠉⢿⣦⠀⠀⠀⠀⠀ ⠀⠙⢳⣄⠀⠀⠀⠐⠒⠀⠀⠉⠁⠀⠀⢀⡼⠋⠀⢸⡍⢿⣦⡀⠀⠀⠉⠓⠛⠃⠀⠀⠀⢻⡇⠀⠀⠀⢸⣿⠇⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⢀⡴⠛⢿⡆⠙⢿⣶⣄⣀⠀⠀⠀⢀⣀⠀⣼⡇⠀⠀⠀⢸⣽⠀⠀⠀⠀⡾⢁⣤⡤⣶⣄⠀ ⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣥⣾⣿⣶⣴⡛⠁⠀⠀⠀⠉⠉⠛⠛⠛⠋⠁⣵⠈⣷⠀⠀⠀⠈⠋⠀⠀⠀⠈⢷⣛⠁⠀⠀⠹⡇ ⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠯⠤⣬⣽⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣿ ⠀⠀⠀⠈⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠶⠶⠶⠾⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠞⠛⠁ ⠀⠀⠀⠀⠀⣿⣷⣦⣤⣜⣳⣶⡶⣤⡀⠀⣠⣾⠛⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠃⠈⠉⠛⠿⠿⣿⡇⠘⢿⣿⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣀⡀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣏⡀⠀⠀⢀⣀⣤⡿⣿⣦⣀⣷⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣯⣬⣭⡝⠲⣆⠀⣀⣠⣤⣶⠟⣧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⠛⠻⠿⣿⣿⠿⠛⠃⢸⡿⣟⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⡉⠉⠙⣿⣁⣼⣿⣿⠿⠿⠛⠁⠀⢨⣿⣄⠀⠀⠀⠀ ⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⣠⡿⢡⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣠⣾⣿⠋⢈⣿⡄⠀⠀⢀⣴⣿⡿⠛⢷⣦⡀⠀ ⠀⠀⠀⠘⢷⣤⣀⣠⣤⣴⣾⠏⣠⡟⢠⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⣶⠿⢿⣿⣿⣧⠀⢸⡿⠿⠶⠾⠿⡟⠋⣀⣠⣾⡿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠸⠉⠀⠀⢭⡁⠒⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡔⡉⠀⠀⠆⠀⠀⠀⠈⣡⠀⠘⠌⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⢡⠁⠀⠀⡀⠀⠀⠀⠀⠃⡆⠀⠈⡤⠋⠁⠢⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠈⠈⣀⣀⠠⠇⠐⠒⣟⣿⣟⢽⠀⠀⢸⡀⠀⠀⠈⡄⠀⠀ ⠀⠀⠀⠀⠀⢸⠱⣿⢿⣿⡅⠀⠀⠀⠸⣧⡿⠘⡄⠀⢸⣿⣄⠀⡄⢱⠀⠀ ⠀⠀⠀⠀⠀⠸⠀⢸⠘⠻⠃⠀⡀⠠⠤⠀⠀⠀⠃⠀⢸⠜⡟⢦⡜⡾⠀⠀ ⠀⠀⠀⠀⠀⠀⡄⢆⠀⠀⠀⠘⣄⠀⣀⠆⠀⢀⣴⠀⢸⠀⠇⠀⠈⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠡⠀⠁⢆⠠⣤⣤⡤⠀⢰⡎⡇⣿⠀⢸⢀⠀⢀⢴⣀⣀⡀ ⢠⠄⢒⢓⢤⡀⠀⣆⠀⠸⠒⠛⠋⠉⠩⢾⠳⡓⢻⠀⠸⢸⡠⠎⠂⢀⠠⠂ ⠈⠑⠀⠠⠁⠈⣆⠇⢂⠀⢃⠀⠀⠑⠧⠈⠔⠁⠀⢀⠆⣼⠀⠓⡂⠁⠀⠀ ⠀⠀⠀⠈⠤⠊⠸⠀⡜⠕⠄⣆⠀⠀⠀⠀⠀⠀⣇⡾⢠⠃⠈⡙⠁⠀⠀⠀ ⠀⠀⠀⠀⠘⡄⠀⢳⠀⠈⣶⠋⢠⠀⠀⠀⠀⡌⠱⣧⠃⠀⠰⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠱⡀⠀⠃⡰⠉⠒⠊⠀⠀⠈⠁⠑⠊⠃⠀⢠⡃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠁⠉⠉⠁⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠂⠐⣲⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡤⠀⠀⠀⢏⢷⠄⠘⢤⠖⠑⢦⡀⢠⢾⢿⣓⣢ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣏⠇⠀⠀⠀⠁⠀⠀⠸⠀⠀⠀⢡⠘⡎⠉⢆⠀ ⠀⠀⠀⠀⠀⠀⠀⠠⠒⠒⠸⡄⠀⠀⠄⠔⠚⠄⠀⠀⠀⡇⠀⠀⠈⢆⠀⠀⠘⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢆⠀⠘⡦⠀⠀⠀ ⠀⠀⣠⡾⡅⠆⠀⠀⠀⠀⢰⠀⠈⠒⠠⠤⠄⠀⠤⠐⠁⠀⠀⠈⠣⡀⠀⠀⣰⠀ ⢠⢾⣅⣀⠠⠚⡄⢠⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠉⠈⠁⠀ ⠛⠋⠀⢫⠀⠀⠘⠺⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢣⡀⠀⠀⠀⡠⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀
⠀⢀⠔⣂⡀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⢂⣮⣉⣹⣅⡀⠈⣇⣠⢀⣤⣠⣀⣤⣀⣄⢀⡠⣄⣀ ⠀⠘⢲⡞⠒⡶⡹⠀⡇⢸⠀⢸⠀⠀⣿⠀⡇⢸⡇⢸⠀ ⠠⡈⠉⠙⠛⠂⠁⠘⢃⠼⠀⠙⠊⠀⠙⠈⠃⠈⣟⣙⡧ ⠀⠀⠀⠀⠈⡴⠦⡔⡔⠂⠀⠠⢀⣠⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢼⡇⡇⠀⠐⡖⢺⡗⠂⡔⢦⠑⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣹⣿⣁⣀⠀⣇⢸⣇⢀⣏⣁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠨⠀⠀⠀⠁⢀⡁⠀⠁⠀⠈⠐⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠰⡐⢢⣠⣼⣧⡄⡠⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠂⠁⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡘⢸⠃⠸⡇⠆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠣⠭⠀⠠⠭⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠒⠒⠶⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢻⡟⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣀⡼⠛⠳⢦⣄⣀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⢾⡟⠋⠀⠀⠀⠀⠈⠉⠛⠓⠶⠶⡿⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣇⢸⡇⠀⠀⠿⠀⠀⠀⠀⠸⠀⠀⠀⡇⢨⡇⠀⠀⠀⠀⠀⠀ ⢀⣀⡀⠀⠀⠀⠀⠉⠛⣧⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣼⠛⠋⠀⠀⠀⠀⠀⣀⡀ ⣿⣉⠙⠛⠛⠛⠛⢦⡀⠈⢷⣄⠀⠈⠋⠙⠃⠀⣠⡾⠃⢀⣴⠟⠛⠛⠛⠋⣉⣿ ⠈⠉⠙⠛⢻⡆⠀⠈⡇⠀⠀⢹⡟⠶⢤⡤⠶⢿⡏⠀⠀⢸⡇⠀⠀⡟⠛⠋⠉⠁ ⠀⠀⠀⠀⣿⠛⠛⠛⢻⡶⠞⠛⣧⣀⠀⠀⢀⣼⠟⠳⢶⡿⠛⠛⠛⢻⡄⠀⠀⠀ ⠀⠀⠀⢠⡏⠀⠀⠀⢸⡇⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⢀⡇⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⢀⡄⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⡀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⢀⡟⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⡇⠀⠀⠀⢠⡗⠀⠀⠀ ⠀⠀⠀⠀⠻⢶⣤⠴⠞⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠻⢶⣤⠴⠟⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠐⢶⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⠞⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠇⢀⠳⡈⠒⣄⣀⡀⠀⠵⢰⠭⢦⣾⠁⡜⡀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⠘⠢⠹⡜⣉⠞⠳⠄⠐⢊⠄⠚⠨⣲⠷⢳⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠡⠈⢀⠔⢿⠄⠀⠀⢢⢇⠆⠀⠀⢸⢢⢁⡀⠀⠤⡀⠀ ⠀⠀⠀⠀⡐⠊⡄⠀⠈⠢⢼⣀⣀⣠⣈⠠⡥⠖⠂⠉⠹⣞⣉⣀⡼⠃⠀ ⠀⠀⠀⠀⠈⢐⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠐⠀⠀⠀ ⠀⠀⠀⢀⣀⡀⠉⠐⢢⢀⠀⠀⠒⠖⠒⡒⠲⠈⢍⠭⠋⠀⠀⣀⡀⠀⠀ ⠀⠀⠀⠘⣾⣧⣀⠀⡁⠀⠑⠀⠀⠀⠀⠀⡼⠁⢁⠘⠀⠀⣸⣯⠇⠀⠀ ⢰⣶⣦⣠⣯⣹⡆⠳⣇⠀⠀⡀⠀⠀⠀⠀⢿⠆⢸⠀⣶⣿⡿⣿⣄⣠⣿ ⠀⠉⠛⠿⣿⣿⠙⢦⣼⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠇⡟⣿⢳⣿⣯⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠱⣇⢀⠇⠀⠀⠀⠀⠀⡆⠀⠸⣷⣏⠛⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠉⠁⠀⠀⠀⠀⠀⠂⠀⠀⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠶⠒⠚⠉⠉⠙⠒⠒⠲⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⠁⠀⡸⠀⠀⠀⠀⠀⠀⠈⢦⣠⡀⠀⠈⠙⡲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠈⣇⢳⠀⠀⠀⠉⢆⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡘⣇⠀⠀⠀⠈⢷⡀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢏⡄⢰⠇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⡀⠀⠀⠀⠀⢳⡀⠈⢳⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⡞⠀⡏⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⣷⠀⠀⠀⠀⠀⢳⢀⡼⠋⠉⠉⠉⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢸⠁⢸⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣸⡇⣸⡆⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⡟⠀⣸⠀⠀⠀⠀⠀⠀⠀⢣⣀⣀⠤⠤⠴⢚⣿⢟⣿⣿⡻⢷⣞⣧⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⡇⠀⣷⢀⣤⣤⣤⣴⡒⠛⠉⠁⠀⠀⠀⠀⢼⢁⣿⣿⣿⣿⣮⠹⣾⠀⠀⠀⠀⠀⢸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠆⡇⢰⣾⣿⢯⣿⣿⣯⡙⠆⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇⠈⣿⣿⠀⢹⡇⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠿⢻⣿⡟⢻⣿⡟⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡟⠀⠀⣷⠀⠀⠀⠀⠀⣟⣾⢟⣧⡀⠀⠀⠹⡄⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⣯⡇⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢹⠀⠀⠀⠀⢠⡏⢸⣿⣿⣷⣄⠀⠀⢻⡄⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⢸⡄⠀⠙⠛⠛⠋⠀⠀⠀⠀⣀⣤⡤⠤⠤⢤⣄⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠘⣿⠞⢻⡇⠙⠿⣷⣄⠈⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⣴⡏⠁⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡟⠀⠀⡇⠀⠀⠈⠛⠢⣽⠅⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⣠⡿⠀⠀⠀⠠⡏⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⠴⠚⠁⠀⠀⢀⣀⢴⡞⣿⣿⠀⠀⠀⠀⡧⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠉⠓⣦⠤⢤⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣾⣿⡇⢸⠀⡟⢹⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⢀⣴⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⢸⡆⠀⠀⢻⣏⣿⣽⣿⣇⠀⠀⠀⢀⣿⣿⠇⢸⠀⣷⢸⠀⠀⠀⠀⡇⠀⣼⠀⠀⠀⣰⠏⠾⠤⠤⠴⠂⠤⠤⡄ ⠀⢀⣀⣤⣤⣿⡙⠦⣄⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⣿⡤⠴⠾⣿⣿⡟⠉⠉⠉⠉⣹⡘⣯⢿⣆⣼⡦⠟⢿⠀⠀⠀⢰⡇⠀⡇⠀⢀⣴⠁⢰⠀⠀⠀⠀⠀⣠⠜⠁ ⣾⡏⠀⠀⣠⠆⠱⡄⢘⡷⢄⡀⠀⠀⢨⣷⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠱⣄⠀⠀⣰⠃⢧⡇⠀⢻⣆⠀⠀⢸⠀⠀⠀⣹⠁⢸⣇⡴⠋⡏⠀⠀⠀⠀⣃⡴⠚⠁⠀⠀ ⠙⠳⢦⣀⠁⠀⠀⢠⡞⠁⠀⠙⢆⠀⢸⠃⢳⡀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠈⠳⣤⣇⡀⢸⡇⢀⡠⠏⠀⠀⡏⠀⠀⠀⡏⠀⢸⣿⠁⠀⠧⠤⣤⡴⠚⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠉⠉⢹⠋⠀⠀⠀⠀⣸⡇⡟⠀⠀⢱⣄⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠈⠛⠯⠝⠉⠛⠋⠀⠀⠀⡇⠀⠀⣾⠁⠀⣾⣏⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣦⠀⠀⢀⡾⠉⣿⠃⠀⠀⢸⣏⢢⡀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⣴⡧⠀⢠⡟⠉⠓⠒⠒⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣧⡴⠋⠀⠀⠹⡀⠀⢀⡎⠙⢦⠙⠦⣄⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣀⢼⣹⣯⠀⡼⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⢧⠀⡼⠁⠀⠈⢦⠀⢈⣷⠿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡇⢸⠃⢸⡼⠃⠀⠀⠀⢀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠘⣷⠃⠀⠀⠀⠀⢧⣾⠃⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⢹⣸⡀⣼⠃⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡄⠀⠀⠀⠘⣷⡄⠀⠀⢀⣾⣿⡀⠀⠀⢨⡷⠦⠤⠤⠤⠤⣤⣤⣤⣸⠀⠀⣠⣿⡟⠁⠀⠀⠀⠠⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢳⡀⠀⠀⠀⠙⡇⠀⠀⣾⠁⠀⠙⠲⢶⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠚⠉⠉⡇⠀⠀⠀⠀⢦⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⣀⣀⣷⣀⣀⣀⣀⣀⣴⣸⣇⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣇⣀⣀⣀⣐⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣷⡆⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡿⠿⠿⢿⣿⣶⡏⢢⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢀⣠⣤⣤⣀⠈⠙⠛⠳⣯⠲⣄⡀⢀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠐⠛⠉⠀⠙⠻⠷⣶⣶⣄⠈⠳⡌⢋⣭⣿⣽⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⢠⡀⣸⠳⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠹⡧⠘⠃⠈⣁⣸⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⠾⣷⡝⣿⠇⠀⠀⢠⡿⠀⠀⣤⠀⠀⠀⠀⠀⠤⣤⣤⡿⠿⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡶⠾⠷⠀⠀⠀⠀⠀⠀⠈⠁⠀⢰⡟⠀⠀⠀⢠⣆⡀⠈⣹⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⠤⣄⠀⠀⡈⢉⣢⠀⠀⠀⢠⣞⣋⣛⠒⢷⣄⠀⠀⠀⠀⠸⠿⡿⠺⣿⣴⡤⠄⠀⠀⠀⠀ ⠀⠀⡀⠀⠀⡏⠀⠀⢸⡇⠀⢉⣿⣥⡀⠀⠀⠸⣿⣿⣿⣿⣶⣹⠆⠀⠀⠀⠀⠀⠀⠀⠨⣷⣦⣀⠀⠀⠀⠀ ⢀⡞⠉⠙⣆⣷⠀⠀⢸⡇⡴⠁⠀⠀⣻⠀⠀⠀⡈⠛⠿⠿⠟⠉⠀⠀⢀⣠⠤⣤⡀⠀⣠⣬⣆⠉⠀⠀⠀⠀ ⠘⢧⡀⠀⠈⠿⠀⠀⠰⠿⠃⠀⠀⣰⠟⢩⢾⡄⠈⠙⠶⣦⣄⠀⠀⠀⣏⠀⠀⠈⣿⡞⠀⠀⠙⣇⠀⠀⠀⠀ ⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⣠⠾⣄⠻⣦⣄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⡇⠀⠀⣰⠃⣀⣀⡀⠀ ⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⣸⣥⢾⣧⣴⡋⠀⠀⠉⠙⠓⠒⠚⠉⡆⢹⠀⠀⠀⠛⠁⠀⠀⠷⡊⠁⠀⢹⡆ ⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠙⠓⠲⣾⡋⠀⠀⠀⠀⠀⠀⠀⢀⣈⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠇ ⠀⠀⠀⠀⢹⣆⣀⡠⣤⣄⣀⠀⠀⣀⡾⠃⠀⠀⠀⠀⠀⢰⠟⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⠀⠀ ⠀⠀⠀⢠⡏⠉⠛⠿⢿⣿⠘⢷⣾⡿⠀⠀⠀⠀⠀⠀⠀⠘⣆⣀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀ ⠀⠀⠀⣾⣄⣀⣀⣠⣼⡿⣷⣤⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣹⣿⣧⣬⡭⢳⣦⣠⣤⣶⠟⢳⡄⠀⠀⠀⠀ ⠀⠀⠀⣇⠉⠙⠛⠋⠁⣠⡏⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠙⠂⠀⣸⣷⠿⢻⡏⠉⠁⢀⣴⡿⢦⣀⠀⠀ ⠀⠀⠀⢻⣄⣀⣀⣤⣾⢋⣼⢩⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢤⣴⣾⣿⣿⠀⢸⠿⢤⣶⢿⠟⢁⣠⡿⣧⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⡞⣹⣉⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣋⣉⣓⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⣿⣈⣷⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⢸⣯⣼⢿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠋⠀⠀⠹⣆⠀⠀⠀⠀⠀⣠⡞⠀⠀⠈⠛⠳⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣀⣀⣀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣋⠉⠉⠉⠙⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⠉⠀⠀⠀⠈⠳⣄⢀⣠⠤⠤⢽⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣀⣀⣀⣽⣏⣀⣀⣀⣀⣙⡟⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡼⢿⠀⠀⠀⠀⠀⠉⠁⣼⡄⠈⠁⠀⠀⢀⡇⠈⢳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⡿⠋⠀⠈⠳⣄⣀⣀⣀⣠⠖⠁⠙⠦⣤⣤⠴⠋⠀⠀⠀⠙⢿⡳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⢀⡞⠁⠀⠀⠀⠀⠀⢈⣭⣿⡿⠟⠛⠛⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠹⣄⠉⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⡴⠋⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣦⣀⣀⣀⣠⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠈⢷⣷⣤⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡇⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⣹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⢣⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢰⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣤⣄⠀⠀⢠⣾⠿⠿⠛⢡⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡞⣿⣿⣿⣿⣆⠀⠀⢀⣤⣄⠀⠀⠀⠀ ⠀⣠⠤⢤⣿⠤⠼⣇⣠⠋⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠈⠛⠛⠛⠛⢧⣀⡾⠤⢼⣆⠀⢀⡀ ⣸⠧⠴⠤⣇⣀⣀⠈⢯⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⡀⠀⠀⠀⠀⢸⡇⢀⣀⣈⡧⠤⠤⢿ ⢳⠖⠒⠒⠋⠉⠉⠀⠸⣤⠶⠋⠉⢻⡏⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⢷⠋⠉⠳⣦⡼⠁⠈⠁⠉⠓⠒⠐⣶ ⠘⠲⠤⠤⢤⣄⣠⣤⠀⠈⠀⠀⢀⡈⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠟⠁⠀⠈⢁⠀⠀⠈⠀⠠⣤⣤⣤⠤⠤⠴⠛ ⠀⠀⠀⠀⠀⢸⡟⠷⣄⣀⣀⣤⣟⡀⠀⠀⠀⠀⠙⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠶⠋⠁⠀⠀⠀⠀⢘⣦⣄⣀⣀⡴⠟⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⠁⠀⠀⠉⠁⣾⠉⠙⠶⢄⣀⠀⠀⠀⠀⠉⠉⠓⠲⠶⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠶⠶⠚⠋⠉⠀⠀⠀⠀⢀⣀⠴⠚⠉⠹⡀⠉⠁⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡏⠀⠀⢠⣶⣾⠿⣤⡀⠀⠀⠉⠙⠒⠦⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠖⠚⠉⠁⠀⠀⣠⠾⣷⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠰⡇⠀⢰⣿⣿⣿⠀⠀⠈⠓⢦⣄⡀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⣀⡤⠞⠋⠁⠀⢸⡆⠀⠀⠀⠸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢈⡇⠀⠈⢿⣿⠋⠙⠦⣄⠀⠀⠀⠉⠙⠒⠦⠤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡤⠤⠖⠛⠋⠁⠀⠀⣀⡤⠞⠋⣧⠀⢀⣠⣼⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⣽⢦⣀⠀⠈⠙⠲⠤⣄⣀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⣀⡠⠶⠊⠉⠀⠀⣠⢿⠀⣾⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠉⠲⢤⡀⠀⠀⠈⠉⠙⠒⠲⠤⣤⣤⣄⣀⣀⣀⡀⡀⢀⢀⠀⡀⡀⢀⣀⣀⣀⣤⣤⠤⠴⠒⠚⠉⠁⠀⠀⢀⣠⠔⠋⠁⢸⠀⠙⠿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣦⠀⠀⣿⠷⣄⠀⠀⠈⠙⠲⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠚⠋⠀⠀⢀⡴⢻⠀⠀⠀⣼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⣿⣦⣽⡀⠈⠑⠶⣄⡀⠀⠀⠀⠉⠉⠓⠲⠶⠤⠤⠤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡤⠤⠤⠴⠶⠒⠋⠉⠁⠀⠀⠀⣀⡤⠚⠉⠀⣼⡀⠀⢠⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⣿⢦⡀⠀⠀⠉⠓⠶⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠖⠋⠁⠀⠀⣠⢾⣿⡇⠀⡼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠘⣆⠉⠒⢦⣄⡀⠀⠀⠈⠉⠉⠓⠒⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠒⠒⠒⠋⠉⠁⠀⠀⠀⢀⣤⠔⠋⢁⣾⡿⠃⡼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠈⢧⡀⠀⠀⠙⠓⠦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠒⠛⠉⠀⠀⣠⠟⠋⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣤⣝⡷⣤⣀⡀⠀⠀⠀⠈⠉⠉⠙⠒⠒⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠒⠒⠚⠉⠉⠉⠁⠀⠀⠀⣀⣠⡶⠞⠁⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⡌⠙⠿⢷⣶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⣴⣶⠿⠟⠉⢀⣤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⣤⣌⣹⠛⠛⠛⢯⡭⢿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⠯⣭⠝⠛⠛⢻⣉⣤⠤⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢸⠛⠒⠒⠒⠲⠶⠶⠤⠤⠶⠶⠒⠒⠒⠺⣿⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠾⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠸⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠉⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠉⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣶⣶⣶⣶⣶⣶⣶⣶⣾⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣶⣶⣶⣶⣶⣶⣶⣶⣾⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤ ⣿⣿⣿⠟⢽⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣶⣾⣾⣿⣎⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣿⣿⣿
⠀⠀⣠⣤⣶⣿⣿⣿⣿⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⣿⣿⣿⣿⡿⢿⣿⣟⣶⣾⣿⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⢿⣿⣿⡇⠀⠈⠙⠻⠿⠏⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣟⣾⡟⣿⡇⠀⠀⠀⠀⢀⣀⣿⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣷⣾⣷⡞⠉⠀⠀⠈⣇⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡿⣿⣿⡿⠛⠀⠀⠀⠀⠈⠉⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⣿⡇⣰⣿⡇⠀⠀⠀⡀⠀⠤⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⢈⡏⠾⣿⣿⡶⡌⠀⠀⣤⢊⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⠁⠃⠀⠰⠛⠓⢠⠁⠆⣰⡈⠑⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢀⡂⣀⣤⠄⡀⢤ ⡇⠀⠀⠀⠀⠀⠀⠀⢷⠄⠀⠐⣀⠐⠂⣸⡆⠀⠀⠀⡰⠀⠀⠀⠈⠤⠐⠁⠀⠀ ⠁⢀⡀⠀⠀⠀⠀⠀⢀⣜⠀⠀⠀⠀⠀⢻⠀⠀⠀⠌⠃⡀⠀⠀⠀⠂⠀⠀⠀⠀ ⠀⠀⠉⠓⠆⠐⠂⠉⢡⡜⠀⠀⠀⠀⠀⢸⠀⢀⠊⠀⠀⠈⠐⡣⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡤⠊⢁⣀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠎⠀⣤⠾⠻⠿⣷⣴⠃⠀⠀⠀⠐⢳⣴⡟⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⠋⠀⣸⣇⠀⠀⠀⣸⣃⣀⠀⠀⠀⠀⢸⣿⡇⠀⣠⡀⠀⠀⣤⡀⢀⣤⠀⠀⣠⣄⠀⠀⣤⣀⠀⠁⠀⢀⣤⣄⡀⠀⡀⠀⠀ ⢰⠁⢠⣾⠙⠿⠿⠿⡿⠿⠛⠿⢿⣷⣄⠀⢸⣿⡷⠋⢿⣿⠀⠛⣿⣿⠛⢿⠓⠚⢿⣿⠋⠘⣿⡟⠁⠀⣿⣏⠉⠻⣿⠿⠿⠀⠀ ⠈⠀⠈⠿⣷⣶⣶⣾⣿⡿⢿⣿⡆⢹⣿⠀⢸⣿⡇⠀⢸⣿⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿⠀⠀⣿⡇⠀⠀⣿⡏⠀⠀⣿⠀⠀⠀⠀ ⠀⠁⢀⣠⣤⣤⣼⣁⡀⠀⣠⠿⢃⡼⠃⠀⢸⣿⡇⠀⢸⣿⠀⠀⣿⣏⠀⡀⠀⠀⣿⣿⠀⣠⣿⡇⠀⠀⣿⣇⠀⣠⣿⡀⠀⠀⠀ ⢸⠀⠸⣏⣉⣉⣛⡿⠿⢿⣷⠖⠋⠀⠀⠐⠺⡿⠗⠂⣼⡿⠀⠘⠻⣿⠖⠃⠀⠀⠹⠿⠟⠉⢿⠟⠒⠀⠙⢿⡗⠉⢿⣷⡀⠀⡆ ⠈⢦⣀⠉⠉⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣶⣶⣮⡿⠇⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠀⣀⡀⠀⠀⣤⢍⣁⣀⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠊⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⡟⠛⠻⢻⡿⢩⣿⡏⠀⡀⠀⠀⠀⣸⠏⠀⢀⣴⢿⣶⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⠁⠀⢀⣾⡇⢸⣿⡆⠀⡀⠀⠀⣠⣅⠀⣀⣸⣿⣀⡀⠀⠀⢀⣤⡀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣤⢼⣿⡇⠘⣿⡇⠀⠀⠀⠘⣿⡟⠛⠉⢹⣿⠉⠁⠀⣾⡏⠻⣷⣤⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠠⢤⣿⡇⣸⡿⠁⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⣿⣇⣤⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⢀⣿⣱⣋⣀⣀⡀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣤⠾⠛⠛⠛⠛⠿⣿⠷⠋⠀⢿⡿⠎⠈⠻⢿⡷⠃⠘⠿⢿⡷⠞⠁⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⣀⠀⠀⠀⠀⠠⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣴⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠠⢤⣦⡀⠀⠀⣀⣼⣿⣧⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠘⣿⣤⣾⣿⣿⣿⣿⣿⣧⣀⣾⠏⠉⢁⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠘⠛⠉⢹⣿⣿⣿⡏⠻⠿⠁⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠆⠀⣼⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠛⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢸⣿⠇⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣾⣿⠀⠀⠈⣿⡇⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣴⣿⡏⠀⠀⠀⢹⣿⣄⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠉⠉⢀⠀⠀⢦⣀⠉⠉⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢝⡻⣯⣥⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⢀⠠⣱⠀⠈⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⡀⠈⠙⠛⠀⠰⣾⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⡡⢐⢢⡇⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢂⡀⠀⠂⡉⠀⠀⠁⢇⣃⠤⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⣆⣠⠀⠀⢸⣏⢃⠀⢂⡞⠐⠀⠀⠒⠠⡀⡐⠀⠀ ⠀⢸⡤⣕⡆⢆⠱⠄⠀⡀⢀⠈⢌⠣⠐⠂⠛⡈⠀⠸⢃⠢⢀⡢⠴⠶⠗⣊⠵⡄ ⡰⠓⢻⣞⠘⠓⠢⠀⠀⠁⠀⢴⠀⠑⠄⠀⠀⠃⠀⠀⠹⠀⠈⠻⠀⠈⠙⠓⠃⠈ ⠉⠁⠀⠀⠀⠀⠉⠐⠀⠘⠀⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠐⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠂⡇⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⡱⠀⠀⠀⠀⠀ ⠀⠀⠀⠒⠒⠒⠲⣷⣶⣶⣶⣷⡶⠒⠒⠒⠒⠒⠒⠒⠒⠒⡖⢒⣓⣗⣒⣲⣒⣰
⠀⠀⠀⠀⠀⠀⢠⡾⢫⡂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣤⣦⠀⠀⠀⠘⣹⠁⠀⠀⠰⠶⣠⡀⠀⠀ ⠀⠸⠇⠟⣄⡀⣀⠀⢉⢶⡀⢀⣔⠵⠗⠁⠀⠀ ⠀⠀⠀⠀⠈⠁⣇⡹⠿⠴⠣⠌⡁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⢀⡠⢴⡦⠔⢋⠒⣄⡆⠀⠀⠀ ⠀⠀⠀⠀⢸⢰⠁⠀⢨⡄⠀⣤⡅⢸⡅⠀⠀⠀ ⠀⠀⠀⣠⠇⠸⡀⠀⠈⠁⠐⠈⠁⡆⠣⣀⠀⠀ ⠀⠀⠀⢑⡠⠜⢤⡀⠀⠀⠉⠀⣠⠧⠄⣊⡀⠀ ⠀⠀⠀⠛⢌⢆⢶⣩⡗⢆⣐⠎⣯⢆⢌⠌⠃⠀ ⠀⠀⠀⠀⠀⠑⠊⡏⠀⢖⢒⠆⡇⠑⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠓⠖⡖⠒⡖⠚⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⡇⢰⣇⠀⠀⠀⠀⠀⠀ ⣤⡀⡄⢠⢠⢤⢤⣼⢩⢥⢬⠉⠁⠤⢠⠀⠤⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⠟⠉⠁⠀⠀⠀⠀⠀⠉⠙⠻⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠁⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢀⣿⡟⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣠⣴⡿⠋⠀⠀⠈⠙⠻⠿⣷⣦⣤⣄⣀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⢶⣾⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⣿⡇⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠠⣤⡄⠀⠀⠀⠀⣿⠀⠙⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⡀⣿⡇⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⢀⣿⠀⣠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣴⣶⣦⣤⣄⣤⣤⣤⣤⣄⣀⠀⠀⠀⢻⣷⡄⠀⠀⠀⠀⠀⣠⣤⣤⣤⡀⠀⠀⠀⠀⢀⣼⡿⠁⠀⠀⢀⣀⣤⣤⣤⣤⣄⣤⣤⣶⣶⣄ ⣿⣏⠀⠉⠙⠛⠛⠛⠛⠛⠛⠿⣷⣄⠀⠀⠙⢿⣦⡀⠀⠀⠀⠙⠉⠉⠉⠁⠀⠀⢀⣴⣿⠟⠀⠀⢠⣾⡿⠛⠛⠛⠛⠛⠛⠋⠉⠀⣸⣿ ⠈⠛⠿⢷⣶⣦⣤⣤⣤⠀⠀⠀⠘⣿⡄⠀⠀⠀⠙⢿⣷⣤⣀⠀⠀⠀⠀⣀⣠⣴⣿⠟⠁⠀⠀⠀⣿⡏⠀⠀⠀⢠⣤⣤⣤⣶⡾⠿⠟⠋ ⠀⠀⠀⠀⠀⠈⠉⢹⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣸⣿⠙⠻⠿⠿⠿⠿⠟⠛⢹⣿⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⢸⣿⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⠿⠿⠿⠿⠿⠿⣿⣦⣤⣶⡾⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⣶⣦⣤⣿⡿⠿⠿⠿⠿⠿⣿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡟⠉⠁⠀⠀⠻⣿⣶⣤⣄⣠⣤⣴⣾⠟⠁⠀⠀⠉⢛⣿⠁⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⢨⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣷⣄⡀⠀⠀⠀⣠⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⣀⣼⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠉⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠉⢳⣆⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠸⣦⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⢳⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠛⣍⣹⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠈⣷⠴⠚⠛⢶⣄⣀⣀⣀⣀⣚⣀⠀⠀⠀⠀⠀⢀⣴⠄⠀⠀⢸⣍⢀⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⣸⡦⠶⣛⣛⠉⠉⠈⢻⡛⢮⣉⠙⠛⡶⣤⣴⡛⠁⠀⠀⠀⠀⠁⠀⠈⠛⠗⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⣠⠖⣋⠥⢿⣿⠀⠀⠀⠀⠀⢈⣷⠀⠙⣷⡴⣿⣿⣟⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠿⠓⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠈⡵⠚⠁⠀⣿⠸⡇⠀⣀⣤⠖⡋⢻⣦⡀⠈⠀⠉⣷⣿⣿⣎⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠟⠀⠀⠀⠀⣿⠒⣻⡿⠿⠋⢉⣿⣿⣿⢶⣀⠀⠀⣿⣿⣽⣞⣆⢻⣷⡴⠛⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⢀⣤⠿⡾⠋⠀⡜⠁⣸⢿⣿⣯⠴⣟⣧⠀⢿⣻⡁⢻⣿⡄⢻⣧⠀⠀⢻⣆⠀⠀⣠⠶⠛⠻⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⢀⣴⠟⠁⣸⠁⠀⢸⠁⠀⣯⣭⣥⣶⣿⡿⢻⣧⠘⢿⣷⣞⣿⣯⢸⣿⢦⠀⠀⠹⣦⠊⠀⠀⠀⠀⢘⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⠀⠀⣠⡟⠁⠀⠀⣿⠀⠀⢽⡀⠀⣿⣛⣫⣷⡞⣷⡼⣿⠀⠈⢻⣿⣿⣹⢸⡟⠘⢧⡀⠀⠉⠀⢀⣴⠳⣤⣾⠿ ⠀⠀⠀⣀⣠⣄⡀⠀⠀⢠⠟⠀⣿⠀⢠⠏⠀⠀⠀⠀⠙⣇⠀⠀⢧⡀⢸⣿⢋⣵⣾⣿⣧⡟⠀⠀⠀⠙⠷⣏⣼⠃⠀⠀⢻⣄⣀⣰⠟⠀⠀⠀⠀⠀ ⠀⢀⣾⠛⠀⠈⢻⡀⢠⡟⠀⢀⡼⣆⠘⡄⠀⠀⠀⠀⠀⠘⠳⣄⣀⣳⣤⠽⠞⠛⠛⠛⠉⢁⣀⣤⣤⠴⠒⣾⠏⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⣾⠃⠀⠀⠀⠀⢳⡏⠀⢀⡞⠀⠹⣆⠹⡄⠀⠀⠀⠀⠀⠒⠛⠉⠱⣇⣀⣤⡴⠖⠚⠋⠉⠉⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠙⠛⠋⢻⡄⠀⠀⠀⢠⠞⠀⠀⠀⠈⠳⣼⣆⠀⠀⠀⠀⠀⠀⠀⢠⡟⠉⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣦⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⣠⡤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡟⠒⠲⠶⠶⠶⠖⢶⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠶⠶⠦⠤⠤⣀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⡀⣀⠀⠀⢀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠉⠉⠉⠉⠉⠉⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⣀⣀⣀⣀⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⣤⠄⣿⡤⣤⡤⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠙⣺⠏⣧⡈⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠉⢁⣶⣶⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣩⡄⠀⠀⠀⢩⡟⢿⣿⡿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣛⣭⣝⠃⠀⠀⠀⢷⣿⣾⣿⣿⣿⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⠋⣿⣿⣷⠀⢀⡤⢰⡿⡟⣿⡿⠃⠀⣇⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⣤⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣿⣿⠀⣟⠂⠀⠀⡾⠁⠀⠀⢠⠇⠀⠀⠀⠀⡔⠉⠀⠀⠠⣖⣉⡇⠀⡴⠀⠀⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢿⣿⡿⠃⠀⠼⠛⠛⠒⠇⠀⠀⣠⡿⠲⣤⡀⠀⣼⠁⠀⠀⠀⠠⠞⠁⡿⠋⠀⡄⠀⡼ ⠀⠀⠀⠀⠀⣤⡤⠤⠤⠤⠤⣄⡀⠀⠀⠀⠈⢢⣤⣤⣀⠀⠀⠀⠀⠀⢀⡠⠞⠋⠀⠀⢹⡽⢿⡿⣄⠈⠓⠦⢄⣀⣼⣃⣀⣰⠧⠞⠁ ⢠⡀⠀⣦⡀⢸⣍⣑⡦⠀⠀⠀⠈⢣⠀⠀⣠⡊⠁⠀⠈⠙⠶⠒⠒⠊⠉⠀⠀⠈⢟⠒⠋⠀⢻⡘⢌⠓⠤⢀⡴⠃⠀⠈⠀⠀⠀⠀⠀ ⢸⠳⢤⡇⠙⢾⡄⠙⠢⡄⠀⠀⡀⠈⣧⣤⠃⣇⠀⣰⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⢸⣆⠀⠀⠀⠽⠒⣿⣲⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠣⣄⣳⡀⠀⠳⣄⣀⣠⠴⠊⠁⣰⣿⢿⠒⠈⠉⠀⢧⣀⡼⣆⠀⠀⠈⡷⢄⣀⡼⠙⡗⠦⣀⣀⣀⠽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠉⠉⠁⠙⢧⣀⡠⠞⣩⢃⡾⠁⠀⠀⣰⠏⠀⣷⠘⢦⣀⡴⠃⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣶⣾⡓⠺⠄⠀⠀⡼⠁⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢄⣀⣀⡠⠎⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣰⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣉⣬⣉⠑⠺⢕⢤⣀⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⠀⠁⠀⠈⠛⠓⡄⠱⠑⠺⣾⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⢲⠯⠻⠇⠀⢰⠀⢠⠀⠀⠀⠤⣼⠛⠋⠀⠀ ⠀⠀⠀⢀⣀⡀⠘⠩⠅⠀⢠⠤⠤⢤⠉⠀⠀⣶⡦⡜⣀⡀⠀⠀ ⢀⠤⡀⡁⠀⠓⢀⠭⢥⠀⠘⢿⣿⣶⠇⠀⠀⠀⠀⠸⠶⠄⠀⠀ ⠸⡀⠘⠇⡀⠴⠃⠀⡴⡲⡀⠲⢤⣄⠀⢰⠉⠙⣦⠊⠙⡄⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⣘⣔⡳⠙⠢⠄⣀⠠⢸⠀⠀⠽⠀⢰⡡⠠⡄ ⠀⠸⣀⠀⠀⠀⠈⠋⢽⠋⠀⠀⠀⢀⣀⣺⠀⠀⠀⠀⠀⠁⣀⠇ ⠀⠀⡘⠶⢮⣶⠢⣤⡎⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀ ⠀⢰⠧⣤⣤⠞⣷⠦⠀⠀⠀⠀⠀⠨⡹⠿⣇⣦⣤⠶⠛⣄⠀⠀ ⠀⠘⣄⣀⣀⡴⡛⡓⠀⠀⠀⠀⠀⣼⣤⣴⡟⢸⢆⣤⠾⢋⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠄⡀⠀⠀⠀⡔⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠈⢆⠀⢰⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠈⠆⢠⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⡤⡀⠀⠀⠀ ⠀⠀⠀⠀⠰⠀⠀⠀⠸⣚⡲⠤⢤⡬⢄⣀⣠⠂⠀⠇⠽⡁⠀⠀⠀ ⠀⠀⠀⠀⠀⠡⡀⢐⠜⡷⠁⢀⡨⡌⠒⢿⣿⢦⡀⠀⠀⠘⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠜⠁⢀⣧⠟⡍⣽⣟⣆⢸⡟⣧⢳⠈⢆⠀⡠⠤⡀ ⠀⠀⠀⠀⢀⣼⠀⡴⠁⡆⢸⠀⣿⣾⣏⡇⠻⣿⣾⠣⡈⠊⢠⢄⡇ ⢀⠔⠲⣀⠎⡸⠸⠀⠀⠘⢄⣣⠫⠾⠛⣃⠠⢭⡞⠀⠑⠒⠁⠀⠀ ⠚⠒⡄⠉⡰⠁⠑⢥⡀⠀⠀⢨⠒⠉⠁⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠈⠀⠀⠀⠀⠈⠐⡒⠠⠤⢶⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢤⠤⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡶⡸⠠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀ ⠀⠀⣴⠋⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⣴⣿⠋⠙⢶⣄⠀⠀⢸⣇⠀⠀⠀⠀ ⠀⢰⠏⠀⢀⣾⣿⡟⠀⠉⠻⣆⠀⠀⠀⠀⣿⠋⠀⠀⢀⣹⡧⠀⠀⣿⠀⠀⠀⠀ ⠀⣾⠀⠀⣼⠿⠋⠀⠀⠀⠀⢘⣧⠀⠀⠀⠘⠂⠖⠚⠉⣁⡀⠀⠀⣿⠀⠀⠀⠀ ⠀⢿⠀⠀⣿⠀⢀⣀⣤⠶⠚⠋⠁⠀⢀⣀⣠⡤⠶⡒⠋⠁⠀⠀⢠⡟⠀⠀⠀⠀ ⠀⠸⣇⠀⠀⠙⠉⠁⢠⠤⠴⠖⠚⠛⠛⠳⢤⣀⠀⣿⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀ ⠀⠀⠻⣄⠀⠀⠀⠀⠸⣆⡀⠀⠀⠀⠀⠀⢀⣬⠟⠁⠀⠀⣠⡾⠁⠀⣧⣤⣶⣶ ⠀⠀⠀⠹⣆⠀⠀⠀⠀⠈⠛⠓⠲⠶⠶⠞⠋⠀⠀⠀⣀⡴⢻⣄⠀⠀⡿⠿⠟⠋ ⠀⠀⣠⣷⠘⠷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋⠀⠈⡏⠳⣄⡇⠀⠀⠀ ⣴⣿⣿⡟⠀⢰⢻⡛⠛⠲⠶⠶⠶⠶⠶⠒⠛⠉⠀⠀⠀⠀⠀⢹⡀⠘⠃⠀⠀⠀ ⠈⠀⠀⢷⠀⡎⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣸⠁⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠋⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣿⣟⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣷⡞⠉⢩⣧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣯⠿⠃⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⡻⣄⠀⠀⠀⠀⠀⠀⠀⠘⣷⣸⡆⠀⠀⠀⠀⠀⠀⠀⠸⡿⢿⣯⣓⣤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣺⢱⡏⢉⣷⣽⠀⠀⠀⠀⠀⠀⠀⠀⠿⣭⡷⢀⠀⠀⠀⠀⠀⠀⢀⡦⣤⣬⡟⣹⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⠿⠇⠘⢧⣙⢶⡄⡀⠀⣀⣀⠀⠀⠀⠀⣼⠛⣷⠀⠀⠀⠀⣠⣋⡴⠳⠟⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣯⠟⠸⣇⠈⠳⣦⣀⣼⢃⠈⠙⣷⠀⠀⠻⣽⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠀⣀⣼⡯⠿⠯⠶⠖⠻⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣽⠟⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣄⡀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⢀⡤⣶⠋⣀⣴⡾⠏⡈⠙⢶⣄⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠤⣤⣤⣴⠾⠟⠉⣾⣿⠛⠉⠀⠀⠀⢷⡄⠀⢹⡷⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢸⠇⠀⠀⠀⠀⢨⣤⡀⠀⠀⠀⢀⣀⣀⠀⠀⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⢸⠀⠀⠀⠀⠀⢾⣿⣷⠀⠀⠀⣿⢯⣻⠀⠀⣿⢿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⢸⡄⠀⠀⠀⠀⠈⠙⠁⠀⠠⠇⠈⠛⠉⠀⢰⡇⠸⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⢿⡀⠀⠙⠷⣤⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⣏⡉⠀⠀⠀⠀⠀⠀⠀⠈⠻⠇⠀⠀⠀⠀⢸⠇⠀⠀⣠⡾⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣈⣉⡓⠲⠾⠿⢶⣄⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⢀⣴⠿⠶⠚⠋⣩⣀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡏⠟⠈⢣⡀⠀⢀⡤⠞⠛⢦⣤⣀⡀⠀⢀⣀⣤⡼⣟⠳⡄⠀⠀⢰⠋⠸⠯⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠙⠳⡄⠻⣄⣼⣷⣄⣠⢾⣇⠙⢯⡉⠉⣉⡟⠀⣿⣤⣾⣆⡴⠃⡴⠊⠉⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⣠⠟⢹⡗⠋⠀⢀⣀⣉⣙⣉⣀⠀⢻⠙⢦⡈⣠⠞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢸⡇⠀⠀⠘⡆⠀⠀⢀⡏⠀⢸⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠘⠒⠒⠛⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠭⢭⣯⠯⡿⠽⣽⠿⣿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⡇⠀⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢤⡇⠀⢸⡦⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣾⡇⠀⢸⣷⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⢉⡍⠉⠉⠁⠀⠈⠉⠉⠉⠉⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀ ⣸⡷⢠⠷⡰⡿⠀⢿⢾⢸⡏⠟⢽⡙⢿⢿⣟⠁⣹⡝⣿⣻⢻⡇⠀⠀⠀⠀⢸⠉⠇⠸⡇⠌⠈⠁⠏⠉⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⡈⠀⠐⡿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢽⣩⠀⠀⣻⣿⣿⠇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣾⣿⠀⣃⡉⡑⠁⢀⡆⠀⠀⡔⠉⠀⢔⢽⡠⠀⢠ ⠀⠀⢀⡀⠀⠀⣀⠀⠀⠩⣉⣁⠀⠁⠀⢁⡠⠊⠉⡆⣼⡄⠢⠀⣁⡜⢀⡇⠌ ⢄⠐⢄⡯⢕⠀⠀⠑⡀⣴⠁⠀⠉⠋⠉⠁⠀⠘⡍⠁⠣⣫⣐⡰⠁⠀⠀⠀⠀ ⠣⠱⣀⣱⢀⠥⠒⡠⡟⡂⠁⢑⡤⢣⠀⠘⠢⠠⠛⡢⠄⠠⠛⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠱⣮⡴⠜⠀⢠⠊⠀⡇⠑⠊⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠒⠠⠐⠁⠀⠀⢡⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡶⠒⢦⣀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠙⢦⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⢧⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠘⣆⠀⢧⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⢹⣄⠼⢦⣀⠀⠀⠀⢠⠃⠀⠀⠀⠀⢀⡀⠀⠀⡾⠁⣶⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⢀⣧⠴⣲⠛⠉⠉⢿⠻⣉⠓⢲⣤⣴⡋⠀⠀⠀⠁⠀⠙⠓⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠠⢚⠵⢚⢿⠀⠀⠀⢀⣸⡆⠘⠷⠿⣿⣿⡻⣦⡀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠞⠁⠀⢸⡬⣧⣴⡾⢿⣬⣿⣆⠀⠀⣿⣿⣿⡎⢿⣄⡠⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⢀⡼⡶⠋⢡⠂⢸⢿⣿⠽⣷⡄⢿⣿⠙⣿⡌⣿⠀⠈⢧⠀⠀⣠⠴⠲⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⢀⡴⠋⢠⠃⠀⡏⠀⣿⣽⣶⣿⡟⣿⡈⢿⣷⣿⣧⣹⠷⡀⠈⢳⠊⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⢀⡔⢿⠀⢠⠏⠀⠀⠸⡆⠀⢣⠀⢻⡿⢿⣯⣿⣻⠀⠀⠻⣿⡟⣿⠀⠙⣄⠀⢀⡴⠋⠛⠛⠁ ⠀⢀⡾⠋⠙⡄⢀⡞⠀⣸⡄⢸⠀⠀⠀⠀⠙⢦⡀⣳⣈⡧⠿⠟⠛⠛⢀⣀⣠⠤⣽⠏⠀⠀⠈⠑⠋⠀⠀⠀⠀⠀ ⢠⣿⣀⣀⠀⠸⠞⠀⡰⠁⠹⣌⢧⠀⠀⠀⠀⠚⠋⠙⣧⣠⠤⠖⠚⠉⠉⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠉⠙⢆⠀⢀⡴⠁⠀⠀⠈⠛⢷⡀⠀⠀⠀⠀⠰⠏⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⠤⣤⣤⣤⢤⡴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠗⠀⠀⠠⠤⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠤⠤⠤⠤⠄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⢹⠉⠉⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡶⣆⣸⡦⢤⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠼⠃⠳⠴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣦⠀⠀⠀⣰⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣆⠀⠀⠀⣴⣶⣶⣶ ⠛⠻⣿⣿⡀⠀⢠⣿⣿⠏⠀⠀⢀⠀⢤⣴⣆⠀⠀⠀⠹⣿⣿⡄⠀⢀⣿⣿⠟⠛ ⠀⠀⢿⣿⣧⠀⢸⣿⡟⠀⠸⣿⡿⠄⠘⠋⠉⣠⣤⣄⠀⢻⣿⡇⠀⣼⣿⡿⠀⠀ ⠀⠀⠸⣿⣿⡀⢸⣿⣇⠀⠀⠁⠀⠀⠀⠀⣠⣿⣿⠇⠀⣸⣿⡇⢀⣿⣿⠇⠀⠀ ⠀⠀⠀⣿⣿⣇⣸⣿⣿⡀⠀⠀⠀⢀⣤⣾⣿⡿⠋⠀⢀⣿⣿⣇⣸⣿⣿⠀⠀⠀ ⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⡀⠀⠀⠘⡿⠟⠋⠀⠀⢀⣾⣿⣿⣿⣿⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣶⣶⣶⣶⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠿⠛⠛⠉⠉⠉⠉⠉⠛⠛⠻⢿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠉⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠘⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠘⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⣼⣿⡟⠻⢿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣀⣤⣾⡿⠋⠀⠀⠀⠈⠙⠻⢿⣿⣷⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⣿⣷⣶⣶⣤⣤⣾⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⢿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⢿⣿⠛⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⡆⠀⠀⠀⠀⠀⢸⣿⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣆⠀⢸⣿⡆⠀⠀⠀⠀⠀⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⣸⣿⠀⢠⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣾⣿⣿⣿⣶⣶⣴⣶⣶⣶⣶⣶⣶⣤⡄⠀⠀⠀⠀⢻⣿⣦⡀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣷⣶⣆⠀⠀⠀⠀⠀⠀⣠⣿⡿⠃⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣦ ⣿⣿⡁⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⣿⣷⣄⠀⠀⠀⠙⢿⣿⣆⡀⠀⠀⠀⠀⠉⠉⠀⠈⠉⠁⠀⠀⠀⠀⣠⣾⣿⠟⠀⠀⠀⢀⣶⣿⠿⠛⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⣹⣿ ⠘⢿⣿⣿⣶⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠈⢻⣿⡆⠀⠀⠀⠈⠛⢿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⠟⠁⠀⠀⠀⢠⣾⣿⠃⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣴⣾⣿⡿⠟ ⠀⠀⠀⠈⠉⠛⠻⠿⠿⢿⣿⡇⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣤⣤⣤⣤⣤⣴⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⡿⠿⠿⠟⠛⠋⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣇⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⢀⣿⣿⡆⠈⠉⠛⠛⠛⠛⠛⠋⠉⠀⢸⣿⣄⡀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⠿⠿⠿⡿⣿⣿⣿⣿⣤⣴⣶⣿⡿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢿⣿⣷⣶⣤⣼⣿⡿⢿⠿⠿⠿⠿⡿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠛⠉⠀⠀⠈⢿⣿⣦⣄⣀⡀⠀⠀⣀⣠⣴⣾⡿⠋⠀⠀⠉⠙⠻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠿⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢺⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⣄⣀⣀⣀⣤⣾⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⣷⣦⣀⣀⣀⣀⣤⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢉⡛⢿⠿⠿⠿⢟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⡿⠿⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⣦⡙⠲⣄⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⢀⢤⡀⠀⣀⣴⠚⠁⡿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠈⢷⡄⠀⠙⢦⡀⣀⣀⠀⡠⠋⣾⠾⢢⣧⠤⣼⣶⣿⠇⠀⣸⠃⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⣧⡈⢻⡄⢠⡟⡟⣠⢿⡏⠀⠘⣁⣠⠴⠇⢀⣈⣿⡙⢦⣀⡿⣾⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠙⣕⠀⢿⡞⢠⣷⠃⠀⠉⠉⠉⠉⠀⣠⠞⠉⠀⠀⠉⠢⡻⠷⠇⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠘⠁⠈⣠⣿⣿⢀⡤⠒⠚⠛⠲⡄⣿⢰⡄⠀⠀⠀⠀⢻⣄⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣁⣀⣠⡞⠁⠈⣽⠋⠀⠀⠀⠸⠆⣿⠈⢦⡁⠀⠀⠀⢀⣾⣸⣧⠤⣤⣒⣒⣊⣉⣻⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⡰⠚⠫⠤⣀⠀⠀⠀⠙⠶⣼⣧⡀⠀⠀⠀⣀⠴⢃⣀⣀⣙⡶⠶⠒⠋⠉⠀⣿⡛⠉⠀⠀⢀⣰⡟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠯⣉⠉⠉⠁⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠋⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠉⠓⠛⠋⣩⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠖⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠤⣄⡀⠀⠀⠀⠀⠀⠠⡄⢤⢰⠒⢶⠶⣲⠲⣖⣺⠋⣩⠝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠖⢿⣶⠀⠀⠀⠀⡴⠛⠒⢤⡀⠀⠀⠀⠙⠋⠀⠳⠞⠀⣈⣤⢀⠴⠛⠇⠀⠀⠀⠀⢠⣶⢶⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⣿⣀⣀⠀⠀⡇⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⣈⡼⠥⠄⣀⠀⢸⠀⠀⠀⢀⣿⣇⣸⠇⠀⠀⠀⠀ ⢀⣠⣄⠀⠀⠀⣾⡿⠿⣇⠈⢷⡄⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡤⠤⢬⠓⢸⡄⣠⣾⣿⣿⣿⡋⠀⠀⢀⣴⡆ ⠸⣿⣶⣿⣗⣲⣿⣷⣶⣿⣧⠀⠙⣾⡄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢷⣽⡄⠘⡆⠀⣷⣿⣿⣿⠛⢿⡷⣄⣠⣿⣾⡏ ⠀⠈⠛⠿⣿⣿⣷⣬⣿⣼⠛⣶⣀⠘⣷⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⣻⡇⣷⠘⣦⣾⣷⠛⣻⡿⠋⠀ ⠀⠀⠀⠀⠈⠉⠙⠿⣿⠏⠀⠈⠻⣷⡾⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⣏⢸⣿⣇⣿⢛⣻⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡇⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⡀⠀⠀⢻⣿⣾⡉⠛⠛⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⡾⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠈⡟⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣷⡀⠀⠀⠘⠟⠀⠀⠀⠀⢀⡇⠀⣴⡀⠀⡴⠋⣹⣀⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠤⢄⣹⣹⡞⠀⢵⠋⢁⣼⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⡄⠀⠐⠒⠂⠀⠀⠀⠀⠐⠃⢀⣠⡾⠛⢁⠜⠀⢴⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠻⠀⠀⠀⠀⠀⠀⣀⣠⠴⣺⠟⠁⣀⠔⠁⢀⠔⠀⢛⣩⠿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠲⠤⠤⠤⠤⠒⠒⢉⡡⠔⠋⣀⠤⠊⠁⣠⠔⣁⣠⠴⠚⠳⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠉⠠⠴⠊⠁⢀⡤⣊⡵⠞⠋⠀⠀⠀⠀⠈⠳⡄⠀⠀ ⠀⠀⢀⣤⣶⠏⠁⠴⢾⡿⠛⢁⣠⣀⣠⠄⠀⠀⢸⠀⠀⠀⠀⢀⡠⠔⠋⠁⠀⠀⠀⠀⣀⣤⣾⡿⠟⠉⠀⠀⣤⠀⠀⠀⠀⠀⠀⠙⣆⠀ ⠀⢀⡞⠉⠀⠀⠀⠀⠀⠀⠲⢿⣿⣿⣄⣤⠀⠀⠘⣆⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⣻⠝⠋⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⠘⣆ ⠀⡾⠀⠀⠀⢀⠀⢀⡀⠀⠀⠐⠻⠛⠁⣼⠓⠦⠤⣤⡟⠙⢓⣲⣶⣚⠿⠛⢉⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⢦⠀⠀⠀⠀⠀⠸ ⢠⡇⠀⠀⢾⡿⢚⣿⠁⠀⠀⢀⣀⣠⠾⠃⠀⠤⠴⣿⠋⠭⠖⠋⠙⡇⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢷⠀⠀⠀⠀⠀ ⢸⡿⠛⠂⠀⢠⣏⣠⠀⠀⠀⠀⠉⣉⠓⣆⠀⠀⠀⠙⢦⣤⠆⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠘⡇⠀⠀⠀⠀ ⠀⣧⡀⠀⠀⢺⡿⢚⣠⠄⠠⣶⡿⠃⢀⣾⡤⣄⡀⠀⣼⠁⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣸⠃⠀⠀⠀⠀ ⠋⣻⣤⣴⡆⠀⠐⢿⣟⣡⣮⠵⠚⠁⣸⠁⠀⠀⠙⠆⠷⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀ ⠀⠙⣿⣿⡵⠦⠀⠀⠉⠉⠀⠀⠀⠘⠛⠒⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠶⣿⡴⣧⣤⣼ ⠀⠀⠉⠉⣹⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠉⠉⠁ ⠀⠀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀ ⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀ ⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣻⣽⠿⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠿⢿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠿⣦⣄⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀⠈⠙⢷⣄⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⠇⠀⠀⠀⢀⣼⣿⣿⣿⠍⠉⠛⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠏⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡿⠀⠀⠀⢀⣾⣿⣿⣿⠏⠀⠀⠀⠀⠙⢿⣧⡀⠀⠀⠀⠀⠀⠀⣿⡋⠀⠀⠀⠀⢀⣠⣤⡾⠿⠃⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⡇⠀⠀⠀⣼⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀⠀⠀⠀⠀⠀⠹⣧⣤⣤⡶⠟⠛⠉⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⡇⠀⠀⠀⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠖⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⡇⠀⠀⠀⣿⠁⠀⠀⠀⣀⣤⣴⣾⠟⠛⠉⠁⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⡶⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣧⠀⠀⠀⠙⠠⣶⠶⠟⠛⠉⠁⠀⠀⠀⣀⣀⣤⣤⣶⣶⣟⣛⠛⠉⠉⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠾⠟⠛⠋⠉⠉⠀⠀⠈⠉⠉⠛⠳⢦⣄⠀⢀⣿⡇⠀⠀⠀⠀⠀⢠⣿⠏⠀⢀⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣵⡿⠋⠀⠀⠀⠀⠀⣠⣿⠏⠀⠀⣾⡇⢀⣀⣤⣶⣦ ⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠛⠁⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⢿⣶⣾⠿⠟⠋⠀⠀⠀⠀⠀⠀⢀⣴⡿⢿⣧⠀⠀⠀⠀⣿⢿⣿⣿⠿⠛⠁ ⠀⠀⠀⠀⠀⣤⡈⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋⠀⠘⣿⠳⣄⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣸⣿⡇⠀⠙⢿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠿⠋⠀⠀⠀⠀⢻⡄⠘⢷⡄⣿⠀⠀⠀⠀⠀⠀ ⢀⣴⣾⣿⣿⣿⡇⠀⠀⢰⡏⣿⠿⢿⣶⣦⣤⣤⣀⣀⣀⣀⣠⣤⣤⣴⣶⡾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⡿⠟⣿⠁⠀⠀⣾⠀⣿⡀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⡇⠀⢸⡇⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⢀⣿⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⢸⡇⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⠀⠨⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⡹⠛⣿⣝⢓⢲⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠘⠵⠛⠹⡏⠳⠗⠰⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⢀⡤⠤⣽⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠸⠤⠾⣿⠁⠀⠀⣴⢻⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠠⡄⠀⠀⠐⠉⡡⠀⠀⠀⠹⡯⡛⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠈⠀⠀⠀⡸⢁⡠⠤⠤⣄⡇⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢀⠀⢰⠟⠉⠀⢲⡦⠞⡇⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠈⠣⢌⣀⠀⠀⠀⠀⡀⢇⡎⣠⠔⠒⢲⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠻⣝⠳⣤⡐⢄⡀⠀⠀⠀⠀⠀⣷⣼⣟⠀⠀⢰⣈⢠⡾⠒⢤⣀⣀⠤⠤⠤⣀⠀⢀⡠⠤⢄⡀⠀ ⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠈⠣⡀⠹⡦⢍⡲⢄⠉⠒⢊⡽⣯⠈⣇⠀⠈⣿⣸⡀⠀⠀⠈⠉⠒⠢⡄⠼⢯⣉⣠⠤⠤⠵⠀ ⠀⠀⢼⣉⣉⣉⠷⡤⣔⠒⠚⣄⠀⠀⠀⠀⠀⠱⡀⠘⢆⠙⢷⡒⠦⠬⢤⠇⡇⠘⠀⠀⠹⡇⡇⢦⣀⠀⠲⣆⣒⣴⣶⣛⠶⠬⢭⣒⢦⡀ ⠀⢀⠴⣋⡥⢞⣲⠣⣄⣑⡏⠁⠀⠈⠉⡇⠀⠀⢣⠀⠀⠳⣄⠉⠒⠀⠀⠀⢰⠀⠀⠀⠀⠹⣵⠀⠈⠿⣶⡶⠦⠤⠤⢤⣽⡗⢢⣄⣉⣧ ⣰⠟⢩⡞⣩⣛⣉⣉⣉⡉⠉⢢⢀⡀⠀⢠⠀⠀⠈⣾⠀⠀⠈⠓⢤⡀⠀⠀⠉⠀⠀⠀⠀⠀⢹⡀⠀⠀⠁⣿⡄⠀⠀⠀⠀⠉⠁⠀⠀⠀ ⠑⠚⠉⠉⠁⠀⠀⠀⠀⢹⠉⢻⠣⠄⠀⠘⣆⠀⢀⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⢸⡾⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⡆⠀⠀⠀⠘⡄⢸⠓⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⢲⡇⠀⠀⠀⠀⢳⣼⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢰⠘⡄⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠹⣟⢉⣉⣉⣹⣏⣩⣽⣿⣻⣉⣉⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡼⠀⠀⢀⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠉⠀⢠⠗⠠⠄⠀⡆⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠉⠉⠂⢄⡔⠁⠀⠀⠀⠀⢀⣴⣒⡒⢤⡁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⡀⠀⠀⢁⣀⣠⣞⠀⠀⠘⣞⢹⢮⡳⡱⣺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢆⠘⣄⠀⣰⡫⢶⡢⡁⠀⠀⠘⢽⡾⢿⣷⠃⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠢⡀⠁⣇⡧⣼⣻⣶⠠⢂⠉⢀⡩⠛⠃⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠑⢿⣵⣟⣻⠏⢠⡤⠚⠁⠀⠀⠀⣠⢇⡀⠀⠀⢀⠤⠒⠐⠢⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠳⣉⣁⡀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠈⢦⡴⠁⠀⠀⠀⠀⢡ ⠀⢀⠤⠤⢄⡀⠀⠀⠔⠁⠀⠈⠓⠒⠒⠂⠉⠀⠈⢆⠀⠀⠀⠑⠀⠀⠀⠀⢀⡠ ⠠⠁⢠⠃⠀⠈⢢⡌⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⡠⠊⠁⠀ ⡇⡠⠁⠀⠀⠀⠀⠧⠀⠀⠀⡠⠺⡀⠀⠀⠀⠀⠀⠀⠀⢏⠒⠤⠔⠉⠀⠀⠀⠀ ⠈⠒⢄⡀⠀⠀⠀⠀⠀⢀⠜⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠒⢄⡀⠀⡠⠃⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠘⢿⣝⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⢋⣿⠃⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠻⣷⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⢠⠶⡿⣠⡀⢠⠞⠑⢦⡀⣠⣶⡟⠁⠐⢸⠇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⢠⡀⠹⣷⡀⠀⠈⠻⣦⣀⣠⣤⣀⢀⡴⠁⣰⠟⠽⠃⣯⠞⠛⢶⣿⣿⣿⠁⠀⢠⡿⠀⡄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⣧⡀⠙⣷⡀⠀⣾⢿⡟⢁⣼⣽⡏⠀⠐⠋⠀⣀⣴⠿⠀⠀⢀⣹⣏⠻⣦⡀⣸⣧⢾⠄⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢻⡑⠆⠘⣷⣼⠃⢸⢡⡟⠀⠙⠗⠒⠒⠛⠋⠉⠀⣠⠶⠛⠉⠉⠉⠓⢬⠻⣿⠴⡧⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠹⣦⠀⠹⠃⢠⣿⡾⠀⠀⠀⣀⣀⣀⣀⡀⠀⣸⠃⣀⠀⠀⠀⠀⠀⠀⢳⡉⠈⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠈⠀⢀⣴⠿⣿⡷⢠⡴⠋⠉⠀⠀⡈⠻⣆⢹⡆⢿⡄⠀⠀⠀⠀⠀⢸⡿⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣁⣀⣀⣴⡟⠁⠀⠈⣿⠋⠀⠀⠀⠀⠀⠿⠀⣿⠂⠿⣄⠀⠀⠀⠀⠀⢀⡼⣃⣽⣦⠤⠴⣖⣒⣋⣉⣉⣉⢹⣦⠀⠄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡴⢶⣯⣉⠁⠀⠀⠀⠀⠈⠛⢦⣀⢺⡇⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠈⠓⢦⣤⣤⠶⠛⠋⠉⢸⣷⠿⠋⠉⠉⠀⠀⠀⣨⣿⠏⠀⠀⠤ ⠀⠀⠀⠀⠀⠀⠀⢸⣦⠤⠤⠤⠭⠷⠆⠀⠀⠀⠀⠀⠙⠻⢿⣶⣤⣤⣤⣴⣾⣭⠤⠶⠒⠚⠻⠟⠋⠁⠀⠀⠀⠀⠀⠈⠻⠷⢤⣤⣤⡤⠴⢞⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡬⠽⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠤⢤⡤⢤⡤⣤⠤⢤⠤⡤⢴⠶⣖⠒⢶⠒⠛⣩⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠈⣩⡷⢤⣀⠀⠀⠀⠀⠀⠈⠳⣼⠀⠘⣆⣸⠇⠈⠚⠀⠈⠑⣫⡴⣟⠁⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣏⣀⣹⣿⡇⠀⠀⠀⠀⢰⠃⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠴⢒⡟⠁⠚⠁⠀⢸⡄⠀⠀⠀⠀⢀⣾⡟⠉⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣤⣤⣤⡀⠀⢸⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠿⠤⠤⠤⣄⠀⠀⡇⠀⠀⠀⠀⣸⣿⣇⣀⡿⠀⠀⠀⠀⠀⠀ ⢀⣀⣀⡀⠀⠀⠀⢰⣿⡿⢿⣧⠀⠈⢿⣄⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⣤⠤⠤⠤⣤⠟⠀⣇⠀⣠⠾⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣴⡆ ⢿⣿⣦⣽⣶⠲⢤⣾⣿⣤⣤⣿⣷⡄⠈⠹⣦⣿⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣌⡳⡄⠀⢸⡄⠀⢹⢸⣿⣾⢿⣿⠿⣿⡻⣄⠀⢀⣴⣫⣾⡟ ⠈⠻⣿⣿⣿⣷⣾⣿⠙⠿⣷⠉⣿⣿⣀⠀⠘⣿⣇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠀⠀⣧⠀⢸⣼⠟⣿⠚⣯⠀⢸⣇⣹⣷⣾⣿⣿⡿⠁ ⠀⠀⠈⠙⠛⢿⣿⣿⣿⣶⣿⣷⡏⠈⢷⣶⣄⠘⢿⡄⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢨⣿⠀⣿⣇⢹⣷⣿⣿⣏⣀⣼⡿⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⡿⠁⠀⠀⠙⣿⣳⡹⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣧⢸⡇⢸⣿⣿⡘⣿⠋⢙⣿⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⡀⠀⠀⠀⢸⣼⣷⣼⠏⠻⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⣤⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠓⠀⠀⠀⠈⣯⣻⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠻⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⠲⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⠀⠀⠀⠀⠀⠸⣆⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡶⠶⠟⠛⠉⠉⠉⠙⣿⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠁⠀⠀⠀⠀⠀⠀⣠⠾⠛⠛⠓⠦⠤⠀⠀⠀⣿⡄⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⠤⠤⣤⣀⡀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⠀⠀⠀⢀⣀⣀⠀⠀⠀⣿⠇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠉⠙⠳⣦⣀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠛⠛⠛⠿⣶⣄⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠙⢯⡄⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⢰⡿⣹⣿⣿⡒⠶⣤⡈⠙⣷⡄⠀⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠋⠀⠀⠀⠀⠀⠘⠁⡟⠀⠘⣿⣷⣮⡹⣦⡈⢿⡈⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣇⠀⠈⢧⠀⠀⠀⠀⠀⠀⠰⣶⣿⡿⠟⠛⠻⢶⡄⠀⠀⠀⠀⠀⠀⣿⣄⣼⣟⢉⣿⣷⡞⣷⠈⣷⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡆⠀⠈⢷⣄⠀⠀⠀⠀⣴⡿⢁⣠⣶⠶⢶⣄⠀⠀⠀⠀⠀⠀⠀⠸⣯⢻⣿⣿⣿⣿⣿⢸⣇⣿⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠈⠻⣷⣄⠀⢸⣿⢠⡾⠉⠹⣿⣦⡙⢧⠀⠀⠀⠀⠀⠀⣀⡈⠳⣍⣛⣛⣛⣩⣾⠟⠁⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⢸⡇⢸⡄⢀⣸⡿⢿⣿⣸⣇⠀⠀⣠⠞⠋⢁⡤⠀⠀⠀⣀⣼⠿⠗⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⢸⣧⢸⡟⣿⣿⣷⣾⣿⣇⡿⠀⠈⠳⠤⠤⠀⠀⣠⣴⠞⠋⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢶⣾⣿⡈⢷⡸⣿⣿⣿⡿⣼⠃⠀⠀⠀⠀⣠⡴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠶⠶⣦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣮⣻⣮⣍⣩⡾⠋⠀⠀⢸⣶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠶⣦⣄⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁⠀⠀⠀⠀⠈⠳⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣌⠉⠙⠛⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠁⠀⠀⠀⠙⢷⡄⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠻⣆⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠉⠉⠉⠳⣶⣄⣀⣀⣀⣀⣀⣤⡴⠖⠋⠁⠀⠐⢦⡀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⣠⠶⠶⠶⠶⣤⣀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡼ ⠀⠀⣠⠟⠁⠀⠀⡼⠀⠀⠈⠻⣦⡀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠁⠀ ⠀⣼⠃⠀⠀⠀⡼⠁⠀⠀⠀⠀⠈⠻⣦⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⠀ ⢸⠃⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡷⣤⡀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⢀⣤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠈⠙⠲⢤⣄⣤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣦⡘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣠⡞⠋⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠙⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⡴⠏⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣤⣀⣀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣇⠀⠀⠀⠀⣸⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠘⠷⣤⣤⠾⠃⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠟⠋⠉⠁⠈⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠁⠈⠉⠙⠻⣿ ⣿⣤⣶⣶⣧⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⣼⣶⣶⣤⣿ ⣿⣿⣿⣿⣿⡆⠀⠁⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠈⠀⢰⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡀⠀⢀⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⡀⠀⢀⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣷⣀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣀⣾⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠴⠶⠶⠶⠶⢤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡉⠙⠲⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠙⠳⠦⠀⠈⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⣠⣤⣤⣄⣀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢀⣾⠛⠻⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢠⣾⡝⢷⡀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⢋⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡄⠀⠉⠁⢸⡇⠀⠀⠀⠀⠹⣧⠀⠀⣠⣴⠾⠛⠛⠛⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢠⠟⢉⡀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⠶⠶⠟⠁⠀⠀⠀⠀⠀⠹⣦⣾⠋⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⣟⠀⠿⠟⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢻⣄⠀⢀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⣼⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⢸⡇⠀⠸ ⠀⠀⠀⣀⣀⣀⣀⡀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⢸⡇⠀⠀ ⣠⡶⠛⠉⠈⠉⠉⠙⢷⣄⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡤⠶⠖⠛⠋⠉⠁⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠈⣿⢦⣤ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⢀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⢸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⢶⡀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣸⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠶⢤⣤⣤⣤⣤⣤⣤⣤⡤⠶⠞⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠒⠲⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣤⢞⣦⡀⠙⠲⣄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡠⡤⠀⠀⠀⠀⠀⣾⢹⣿⡇⠀⠈⢣⢀⡴⠋⠉⠳⣄⠀⠀⢠⠾⡿⡿⠟⣛⣓⣆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢨⣿⠒⡆⠀⠀⠀⠀⠘⠓⠚⠁⠀⠀⠀⢿⠀⠀⠀⠀⠈⢧⡀⢹⣄⡷⠖⢯⠁⠈⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣝⡽⠃⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠈⣇⠀⢻⠀⠀⠈⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⢦⣠⡇⠀⠀⠀⠀⣄⢀⣀⡤⠾⣇⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠸⡄⠈⣇⠀⠀⢸⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠈⢿⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⣄⠀⠀⠀⢳⠀⢸⠀⠀⠀⢧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢹⡀⠀⠀⠈⢧⡟⠀⠀⠀⣸⠀ ⠀⠀⠀⠀⠀⢠⣶⠦⡄⠀⠀⠀⡇⠀⠀⠀⠀⢤⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠏⠀⠀⠀⠀⠻⣄⠀⠀⠈⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⢀⣴⣿⠿⡄⠹⡄⠀⠀⣷⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⠓⠒⠶⠶⠤⠤⠤⠴⠖⠋⠀⠀⠀⠀⠀⠀⢸⠈⢧⡀⠀⠀⠀⠀⣼⠁⠀ ⠀⢠⣞⣛⣢⠀⠀⢀⣠⢷⡄⠀⢸⠀⠀⠀⠀⢸⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⠙⠓⠒⠋⠁⠀⠀ ⣰⢋⣡⡤⠤⢴⡖⠋⠀⠀⢷⡀⠘⡆⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠛⠋⠀⠀⠸⡇⠀⠀⠀⠀⠓⠦⠗⠀⠀⠀⡼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣄⣀⠀⠀⠀⠀⢀⣠⠞⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
\_('_')_/
⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠒⠁⠒⢂⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠔⢁⣉⡀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡆⣪⢭⡀⠀⠀⠀⠀⢠⡘⠋⠆⠀⠱⡄⣠⠔⠒⠤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⢸⠱⠂⠇⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⢹⠁⠀⠀⠀⠐⡄⠀⠀⠀⡠ ⠀⠀⠀⠀⢸⠈⠑⠊⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠹⡀⠀⢰⠀ ⠔⠂⠀⠐⢼⡀⠀⠀⠀⠠⡐⠂⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠘⠂ ⠀⠀⠀⠀⠀⢡⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠈⡄⢠⠀ ⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⢢⠀⠀⠀⠘⡜⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⠄⣀⣀⣀⣀⡠⠤⠒⠉⠀⠀⠀⠀⠀⢂⠀⠀⠀⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣷⣿⣿⣷⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣽⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣭⣐⢤⣶⣽⣿⣿⣿⣷⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡟⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢿⣿⣿⣮⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠷⣿⣻⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⢿⠿⣏⠀⣸⡿⣿⣿⡍⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡿⡀⣣⣿⣿⣿⣿⣿⣿⠀⠀⣀⡤⠄⠀⠀⠀⠀⠀⠀⠉⠉⠳⣿⣿⣼⣿⡿⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⠇⡧⣿⣿⡟⢿⢻⣿⣿⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡟⢿⡇⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣶⣿⣿⣿⢱⡎⣼⣿⡟⡄⠀⠠⠤⣄⠀⠀⠀⠀⠀⠠⣶⣷⠶⣾⡿⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣹⣿⣧⠈⣿⣻⣷⣶⡾⠛⠋⠀⠀⠀⠀⠀⠀⢻⣧⡈⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡏⣿⣿⣿⣷⢻⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠈⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣻⣇⣿⣿⣿⢸⡿⡹⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠈⢹⣿⣿⣿⣿⣷⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡿⠀⢸⡄⢹⣿⣿⣿⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠻⢿⣿⣿⠠⣀⣿⢻⣿⣿⣿⡇⠈⡆⠀⠀⠀⠀⣀⣠⠤⠴⠒⠒⠚⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠹⡟⠷⠦⣽⣧⣿⣿⣿⣳⠀⢹⡀⠐⠚⠉⠁⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⢀⣸⠤⠶⠴⢿⠾⣿⣿⣿⣟⣶⢧⠤⠤⠤⠤⠤⠴⣞⡋⠀⢀⣀⣀⣀⣀⡀⠀⠘⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣳⡰⠋⢀⠀⠀⠀⠘⣇⠹⣿⣿⢻⡈⡉⡍⠓⠒⠤⣄⠀⢧⠉⠙⠛⢦⡄⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠁⠀⠸⣀⣀⣤⠤⠼⠖⠛⠛⠓⠷⣧⠘⡄⠀⠀⡏⢧⡈⢦⠀⠀⢸⠘⢆⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠚⠉⣁⡤⠋⠀⣀⣤⣶⡶⠞⢋⣉⠭⠶⣤ ⢿⠇⠀⠀⠸⣇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠹⣿⡀⠀⣧⠀⠙⠮⠷⡄⠸⣆⡈⢳⡀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠘⠛⠒⠖⣩⠴⠋⣡⠴⢚⡭⠔⢀⡗⠁ ⣾⠀⠀⠀⠀⠈⣩⠷⠚⠉⠉⠐⠦⣄⡀⠀⠀⠸⣿⣆⢸⠀⠀⠀⠀⢡⠀⢠⠓⠦⢷⣤⠀⢠⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⣀⣀⣀⠙⠲⠋⣡⠔⠉⢀⡴⠋⠀⠀ ⡏⠀⠀⠀⣠⠞⠁⠀⣠⠴⠚⠀⢀⠀⠉⠀⠀⠀⠙⡎⢻⡀⠀⠀⠀⠘⢦⡎⠀⠀⠀⠸⡀⣸⣿⠋⠀⠀⠀⠀⠀⠀⢀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⣠⠖⠁⠀⠀⠀⠀ ⡇⠀⢠⡞⠁⣀⠴⠋⠀⢀⡤⠒⠉⠀⣀⣤⠀⠀⠀⢸⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠁⢣⠀⠀⠀⠀⠀⠀⢀⠏⢿⡃⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠈⢳⡾⠉⠀⣀⠔⠋⠀⣀⠔⠋⠁⠀⠀⣀⣤⣼⠤⣾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢿⠇⠀⠀⠀⠀⢀⡞⠀⠀⠙⢦⡀⠀⠀⠀⡠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠒⠾⣅⣀⡴⠚⠧⠤⠴⠒⠋⠉⠉⠉⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣼⠀⠀⠀⠀⣤⢟⠀⠀⠀⠀⠀⠉⠓⠦⣴⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⠀⠀⢀⡼⠀⠐⣆⣀⠀⠀⢀⣀⡀⢒⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⣰⠃⠈⠠⡀⠀⠀⠀⠀⠀⠀⢀⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠤⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⡆⠀⠀⠀⠀⠀⣤⡀⠉⠓⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠸⡹⡄⠀⠀⢣⡙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⡰⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢣⢱⠀⠀⠀⠑⡄⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡝⢠⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠸⡀⡇⠀⠀⠀⠘⡀⣸⠖⠒⠒⠤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢳⠁⡌⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣀⣀⣀⣇⣸⡀⠀⠀⠀⢹⡁⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠘⠀⡇⠀⠀⠀⣀⡠⠷⠖⠒⠒⠉⡿⣻⣿⣿⡿⢿⡇⠀⠀⠀⢘⣧⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷⣆⢠⣷⣿⣿⣿⡓⠄⠀⠀⠀⠀⠀⠑⣿⡏⢻⣿⠈⣷⠀⠀⠀⠈⣿⣷⡀⠀⠀⠀⠀⢸⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⢻⣿⢻⣿⣛⣿⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠟⠀⢸⠀⠀⠀⠀⣿⣿⣷⡄⠀⠈⣆⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⣟⠈⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⣇⣼⣿⢿⣦⡀⠘⣦⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡼⠀⠀⠀⠀⠀⠀⣴⠒⠉⠉⠉⠉⢢⠀⠀⠀⠀⢇⠀⠀⠀⡟⠁⢹⠀⠉⠻⠧⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠸⡀⠀⠀⠀⠀⠀⠀⠻⡀⠀⠀⠀⣠⠏⠀⠀⠀⢀⣼⠀⠀⠀⡇⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠑⠤⣀⡀⠀⠀⠀⠀⠉⠒⠐⠊⠁⠀⣠⡤⢾⢹⣿⠀⠀⠀⡇⠀⡇⠀⠀⠀⢀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⢿⠉⠑⣶⣶⣶⣶⡆⠀⠀⢸⣿⡇⢸⢀⣿⠀⠀⠀⡇⠀⡇⠀⠀⡠⢻⣃⣀⡀⣀⣀ ⠀⣀⣠⠤⢾⡒⢄⡀⠀⠀⠀⢱⠀⠀⠀⠘⡦⠤⠾⠿⡿⠋⠉⠐⢲⢸⠿⣧⡼⠼⢿⠄⠀⢀⡇⢸⠁⢀⡜⠁⠆⠀⠀⠀⣠⠞ ⢺⣇⠀⠠⠂⠐⢀⡟⠢⡀⠀⢸⢧⠀⠀⠀⢃⠀⠀⠀⠈⢢⡀⢠⠋⣿⠀⠘⡦⠀⢸⠀⠀⢸⠀⢸⡶⠉⡇⠀⠀⣠⠔⠊⠀⠀ ⠀⠉⠓⠢⠤⣤⠎⠀⠀⠘⡆⡼⠀⢣⡀⠀⠘⡄⠀⠀⠀⠀⠙⠷⡤⠼⠤⠞⠁⠀⡜⠀⢀⡞⠀⣼⡇⠀⠉⠑⢻⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⡄⠀⢠⠞⢻⠃⠀⢠⣟⢦⡀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣼⠁⢠⡏⠓⠢⠤⡴⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⡖⠁⠀⠘⡆⠀⡜⠘⢦⠙⠦⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⢺⡽⣄⡞⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠸⡴⠀⠀⠈⢣⣠⠏⠉⢦⠀⠀⠀⠀⠀⠀⠀⢠⠛⢣⣸⠀⡿⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⢳⣄⠀⠀⣸⣿⠀⠀⢀⡦⠀⠠⠄⠀⣀⠀⣸⠀⢀⣿⠞⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠉⢦⠀⠀⠀⠙⠀⢠⠏⠀⠉⠒⠞⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠘⡆⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⠓⠒⠚⠓⠒⠒⠒⠚⠛⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠓⠒⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠎⢀⠖⠛⠻⢶⠇⠀⠀⠀⢰⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠋⣠⣾⣦⣤⣤⣿⣶⣤⣀⠀⢸⣿⣠⣴⡆⢀⣴⣦⣼⣦⣀⣴⣦⠠⣶⡦⠀⣠⡴⢶⣦⣤⡄⠀ ⠈⠀⢿⣦⣬⣥⣿⣶⣶⡌⢻⡆⢸⣿⠀⢸⡇⠀⢸⣿⠀⠁⠀⣾⡇⠀⣿⠃⠀⣿⡇⠀⣿⠁⠀⠀ ⠀⠀⣠⣤⣼⣧⣀⣀⡼⢃⠞⠁⢸⣿⠀⢸⡇⠀⣸⣏⢀⠀⠀⣿⣇⣠⣿⡅⠀⣿⣇⢀⣿⡀⠀⠀ ⢠⠈⠣⠤⠜⠛⠙⠛⠋⠁⠀⠀⠉⠛⢁⡼⠃⠀⠉⠛⠉⠀⠀⠈⠋⠁⠙⠋⠀⠈⣿⣃⣙⣷⠀⠀ ⠀⠉⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⢀⡒⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠚⠉⠉⠉⠉⠠⠂ ⠀⠀⠀⠀⠀⠀⠀⠁⡞⠛⠛⣷⢻⣿⠉⠀⠀⠀⢠⠆⠀⣤⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⢰⣿⢸⣿⠀⠀⠀⢠⣶⡄⢴⣿⡶⠄⢀⡤⣶⡄⠙⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠠⠀⢉⣹⣿⢰⡿⠀⠀⠀⠈⣿⠀⠀⣿⠀⠀⢸⣇⣨⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢨⣿⣞⣀⣀⠀⠀⢠⣿⠀⠀⣿⡀⠀⢸⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠛⠉⠉⠉⠻⠟⠁⠀⠻⠋⠈⠛⠛⠁⠉⠛⠛⠉⡠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠁⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠠⣤⡀⠀⣀⣿⣿⣀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠘⢷⡾⣿⣿⣿⣿⣧⡾⠋⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⣸⣿⣿⣇⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢰⡿⠀⠀⣿⡆⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢀⣼⡇⠀⠀⢹⣧⡀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣈⣁⠄⠀⠐⠤⣈⣡⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
¯\_(- o -)_/¯
⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣟⢯⣽⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠙⠛⠿⣿⣿⣿⣿⣿⠟⣿⣿⣯⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⠛⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠉⠻⠿⣄⣿⣿⣿⣮⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣄⣿⣿⢿⣿⣿⡤⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⡏⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣷⣿⣿⡏⡆⢼⣿⡇⠀⢠⣀⠀⠀⠀⠀⢠⣶⠤⣿⠇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣷⣸⣿⣷⡶⠛⠉⠀⠀⠀⠀⠀⢷⡎⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⢿⣿⣿⣧⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⠷⠤⠶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠙⣿⣿⣿⣿⡇⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡟⠀⢧⣹⣿⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣯⠙⢿⣿⣄⢸⡿⣿⣿⣇⠈⡄⠀⡠⠤⠒⠒⠉⠉⣠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⣣⠬⠭⢿⢿⣿⣿⣦⡼⣄⣀⣀⣀⣤⡔⠊⠁⢀⣀⣀⠀⠀⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣦⠊⠁⠀⠀⠘⡄⢻⣿⣯⢉⠙⠒⠂⣤⡀⢏⠉⠛⣥⡀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠃⠀⢠⠄⠐⠒⠛⠈⠉⠉⠛⢬⣆⠀⢸⠑⣌⢆⠀⢱⠙⢄⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠉⢁⣤⣊⡡⢤⡶⠟⣋⠥⠐⢚⡶ ⡝⠀⠀⠈⠓⣠⠤⠒⠂⢄⡀⠀⠀⢻⣆⢸⠀⠈⠉⢱⠈⠳⢌⣦⡀⠀⣿⡀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠐⠯⠔⣊⠔⠊⡠⠊⠀ ⡇⠀⠀⡠⠊⠁⡠⠔⠂⢀⠈⠁⠀⠀⢻⠻⡄⠀⠀⠘⢦⠃⠀⠀⢣⢰⡿⠃⠀⠀⠀⠀⢀⣰⡇⠀⠀⠀⠀⠀⠉⠉⠁⠀⢁⠴⠊⠀⠀⠀ ⡃⠀⣞⢀⠔⠋⢀⡤⠒⢁⡠⠄⠀⠀⠀⡇⣱⠀⠀⠀⠀⠀⠀⠀⠘⡅⣡⠀⠀⠀⠀⢀⠎⠻⡀⠀⠀⠀⠀⢀⠤⠔⠒⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠘⠧⢤⡔⠋⣠⢔⡋⣀⠤⠤⠶⠛⠉⡟⠀⠀⠀⠀⠀⠀⠀⠀⢱⣹⠀⠀⠀⢀⠞⠀⠀⠈⠒⠤⣀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⡹⠀⢤⣀⠀⠀⢀⡀⢰⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠈⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠖⠒⠒⠲⠦⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⣈⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⢀⣀⣈⠁⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⡖⠳⠦⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⢩⣟⢦⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⣡⡶⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡀⠀⣸⠇⠀⠀⠀⢻⡄⢀⡴⠞⠋⠉⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠇⣰⠁⣴⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⢳⡟⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⢻⡀⠉⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⢀⡞⠁ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⢸⠀⠘ ⠀⣀⡤⠤⠤⣤⡀⢸⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⣠⡤⠴⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⢸⡀⠀ ⠞⠁⠀⠀⠀⠀⠙⢶⣧⠀⠀⠀⠀⠀⠀⠀⢻⡋⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⢸⠋⠓ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⢳⡞⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠨⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⢤⣄⣀⣀⣀⣀⣤⡤⠴⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⠀⠀⠀⠀⠀⠀⠀⠀
_/-(🙂)-\_¯\_(ツ)_/¯
૮ ˶ᵔ xᵔ˶ ა
😐😐😑😐
¯\_(ツ)_/¯🤷‍♀️🤷‍♂️
🤷🏻‍♀️
🐀🌈💕🌱🤷‍♀️
🤷🤷‍♂️🤷‍♀️¯\_(ツ)_/¯
🤷‍♂️
If you'd like to report a bug or suggest a feature, you can provide feedback here. Here's our privacy policy. Thanks!