Assault Rifle Dot Art

Copy & Paste Assault Rifle Dot Art Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣶⣶⣆⣀⢙⣳⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣦⣤⣬⣭⣿⣿⣿⣿⣬⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢀⠜⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀ ⢸⣿⣶⡶⠿⢿⣿⣿⣷⣶⣿⣿⡟⠛⠛⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⢿⡿⢿⣿⣿⣿⣿⠿⣿⢿⠿⠛⠇⠈⠛⠋⠉⠁⠈⠉⠉⠁⠈⠉⠉⠉⠀ ⢸⣿⡇⠁⠈⠉⣠⣾⡿⠋⠉⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡿⡿⠛⢿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⡇⢀⣴⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠆⠃⠀⠠⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡟⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣀⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⡀⣠⣾⣿⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣦⣄⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣶⣿⠟⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣼⣿⠟⠁⢀⣴⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢺⣿⣅⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣀⣴⣿⣿⣿⣿⣶⣶⡄ ⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠴⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠉⠙⠛⠛⠛⠻⠟⠃ ⠀⠀⢀⣴⣿⣿⣿⣿⠛⠛⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣴⣿⣿⣿⣿⣿⠇⠀⠀⠘⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠸⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡄⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡸⠿⣿⣿⠿⠀⠀⠀⠀⠀⠀⢀⢴⠀⠀⠀⠀⠀⠀ ⢠⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢾⠶⠤⠶⠴⠶⠆ ⠘⡟⠁⣩⡿⠋⠉⠀⠀⣿⣿⠿⠻⣿⣿⡇⠀⠀⢸⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠷⠞⠁⠀⠀⠀⠀⣴⣿⠏⠁⠀⣿⣿⡇⠀⠀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠶⠶⠶⠶⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣾⣿⣿⣤⣤⣤⣤⣤⣤⣤⣼⣀⣠⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⢀⠜⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠉⠿⠏⠉⠉⠉⠉⠉⠙⠛⠛⠃ ⢸⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⣿⣿⣿⠟⠉⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠛⠉⠉⠙⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡟⠀⠀⠀⠀⠀⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠃⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣄⡇⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠿⠿⠛⢻⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠋⠉⠉⠉⠉⠉⠙⠋ ⢸⡿⠿⠋⠋⠀⠀⠀⠀⣿⡿⠉⠹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⢀⣴⢀⡀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣾⣦⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣾⣿⠋⠹⣿⣿⣦⣠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡠⣲⣿⣿⠛⠁⠀⠀⠈⠙⣿⣿⣧⡳⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣤⣮⣾⣿⣿⣿⣧⣀⠀⠀⣠⣾⣿⣿⣿⣿⣾⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⠝⠻⢿⣿⠋⣿⣿⡿⠛⢭⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣾⠛⠋⢻⡇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣿⠏⠙⠙⣷⣄⠀⠀⠀⠀ ⠀⠀⢀⣼⠟⠁⠀⠀⠸⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⠀⠀⠀⠈⢻⣷⣄⠀⠀ ⣤⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⣶ ⠙⢿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣦⣤⣴⣤⣤⣄⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣻⣿⣦⣀⠀⢀⣀⣀⣏⣹⠀ ⢠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠭⠭⠽⠽⠿⠿⠭⠭⠭⠽⠿⠿⠛ ⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⢻⣿⣿⣿⡟⠏⠉⠉⣿⢿⣿⣿⣿⣇⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁⠀⠀⠀⢠⣿⣿⣿⠋⠑⠒⠒⠚⠙⠸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⣿⣿⣴⣤⣴⣤⣶⣴⣦⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣤⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠒⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿ ⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠋⠉⠁⠁⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠛⠛⠙⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⠏⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠟⠂⠀⠀⢺⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣋⣀⣀⣀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⡤⠤⠤⢤⡤ ⣿⣿⣿⠿⠟⠉⠉⠀⣹⣿⣋⣻⣿⡇⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠀⠀⠀⠀⠀ ⠈⠉⠀⠀⠀⠀⠀⣴⡿⠁⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣦⣤⣤⡀⠀⠀⣶⠀ ⢸⣿⣿⣿⣿⣿⣿⡿⢿⣿⡿⠟⢻⣿⣿⡟⠛⠛⠛⠉⠙⠛⠋⠀⠈⠉⠀⠈⠉⠁ ⢸⣿⠿⠟⠋⠉⠀⢀⣾⡿⠉⠀⠈⠸⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠹⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡀⢀⣠⡾⠛⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⣷⣿⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡪⡒⣡⡮⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣰⣷⡼⣧⢑⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⢶⣵⢟⡽⣻⠴⠻⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡵⡗⢝⠅⢾⣿⣗⢀⡕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⢤⣿⣗⠫⣾⣷⣻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣠⣪⡿⣿⣝⠈⠉⣿⡟⡅⠈⠻⣿⣟⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⣟⢯⣯⣿⠋⠀⠀⠀⢹⡇⡇⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠙⠿⡿⠀⠀⠀⠀⠘⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⢻⣤⣀⡠⢖⣠⣤⠄⠠⠤⢀⡀⠀⣀⡀⠠⡀⠄⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠉⠉⠛⠙⠲⠮⢀⣉⣀⣐⡛⣢⠒⠚⠯⢍⠖⠂⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡻⡒⢀⣤⢌⣤⡟⢈⣉⠓⠢⠠⠤⢄⣀⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠈⠀⠠⣢⠋⢹⡙⢗⠼⣏⠑⠦⡀⠀⠀⠀⠀⢹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠐⠀⣐⠔⠁⠐⠀⡉⠘⢤⡴⠇⠀⠈⠳⢄⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢶⣦⠀⠀⢀⣤⡾⣷⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠙⣷⣴⠟⣫⣶⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣦⣾⠟⣡⡾⠛⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣴⡿⠋⠀⠙⢿⣿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠻⠟⠉⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠋⠀⠀⠀⠀⠀⢀⣤⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡾⠟⠁⠀⠀⠀⠀⠀⢀⣴⠿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣷⠀⠀⠀⠀⠀⣠⣾⡟⠁⠀⠈⠙⠿⣶⣤⣄⣀⣀⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⠟⠁⠀⠀⠀⢰⡾⠋⣿⡿⣶⣄⡀⠀⠀⠀⠈⠉⠉⠉⢻⡇⠀ ⠀⠀⠀⠀⠀⣰⣿⣧⣀⣠⣄⠀⠘⣿⣴⡿⠀⠀⠙⠻⢷⣦⣤⣀⣀⣀⣀⣸⡇⠀ ⠀⠀⠀⣠⣾⠟⠁⠉⣹⡟⣿⡄⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠁⠀ ⢀⣤⡾⠋⠁⠀⠀⣰⡿⠁⠸⣷⡀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣏⠀⠀⠀⠀⣰⡿⠁⠀⠀⢹⣧⠀⠀⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠻⣦⡀⠀⣰⡟⠁⠀⠀⠀⠀⢻⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⢿⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢶⣶⣶⠼⣦⣤⣼⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣯⠿⠟⠛⠻⢶⣿⣯⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⣺⡿⠿⠷⠶⠒⢶⣶⠖⠀⠉⡻⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⢻⣭⣫⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣖⡿⠋⢙⣿⠿⢿⠿⣿⡦⠄⠀⠀⠀⣠⣾⠟⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣰⣿⣴⣿⡿⠿⠿⠿⢿⣦⣄⠀⠀⠀⣠⣾⣿⠃⠀⢀⣸⡿⣳⣶⣲⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣽⡿⣛⣵⠾⠿⠿⠷⣦⣌⠻⣷⣄⢰⣿⠟⠁⠀⢠⣾⠿⢡⣯⠸⠧⢽⣄⠀⠀⠀⠀⠀ ⠀⢸⡇⡟⣴⡿⢟⣽⣾⣿⣶⣌⠻⣧⣹⣿⡿⠋⠀⠀⠀⣾⠿⡇⣽⣿⣄⠀⠀⠉⠳⣄⢀⡀⠀ ⠀⢸⠇⢳⣿⢳⣿⣿⣿⣿⣿⣿⡆⢹⡇⣿⡇⠀⡆⣠⣼⡏⢰⣿⣿⣿⣿⣦⠀⠀⠀⠈⠳⣅⠀ ⠀⣸⡀⢸⣿⢸⣿⣿⣿⣿⣿⣿⡇⣸⡇⣿⡇⠀⡟⣻⢳⣷⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⣧ ⢰⡟⡿⡆⠹⣧⡙⢿⣿⣿⠿⡟⢡⣿⢷⣿⣧⠾⢠⣿⣾⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠘ ⠀⠻⡽⣦⠀⠈⠙⠳⢶⣦⡶⠞⢻⡟⡸⠟⠁⢠⠟⠉⠉⠙⠿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡴ ⠀⠀⢸⣿⡇⠀⠀⣀⣠⠀⢀⡀⠸⣹⠇⠀⣰⡟⡀⠀⠈⠛⠻⢿⣻⣿⡿⠀⠀⠀⠀⠀⠀⡠⠁ ⠀⠀⢸⣿⣇⣴⢿⣿⣿⣿⣮⣿⣷⡟⠀⣰⣿⢰⠀⣀⠀⠀⠀⢀⣉⣿⡇⠀⠀⠀⠀⠀⣸⠃⠀ ⠀⠀⢸⣿⡟⣯⠸⣿⣿⣿⣿⢈⣿⡇⣼⣿⠇⣸⡦⣙⣷⣦⣴⣯⠿⠛⢷⡀⠀⠀⠀⣰⡟⠀⠀ ⠀⠀⠘⣿⣿⡸⣷⣝⠻⠟⢋⣾⣟⣰⡏⣠⣤⡟⠀⠀⠈⠉⠁⠀⠀⠀⠀⢻⣶⠀⢀⣿⠁⠀⠀ ⠀⠀⠀⢸⡿⣿⣦⣽⣛⣛⣛⣭⣾⣷⡶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁⢸⢻⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣀⣀⣀⣀⣀⣠⣤⠶⠛⠁⢀⣾⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⣻⣿⣿⣿⣿⣿⣿⣎⣿⡅⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡷⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠻⢿⣿⣿⣟⣂⣀⣀⣀⣀⣀⣀⣤⠴⠋⠁⣾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣷⡄⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣤⣤⣤⣤⣄⣤⣤⡤⠴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢦⣤⣴⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣆ ⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠏⠉⠉⠉⠉⠉⠉⠉⠉ ⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣾⣿⣿⣿⣿⣿⢿⣿⠛⠿⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣾⣿⣿⠁⠀⠈⠇⠀⢿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⣿⡇⠀⠀⠀⠈⠂⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣤⣄⣴⣶⣿⣿⣶⣶⣦⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣶⣀⣶⣆⣶⣦ ⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⠛⠛⢿⣿⣿⣿⣿⣿⠛⡟⠛⢿⡿⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⣿⣿⣿⣿⣧⣀⣀⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠙⠛⠿⠿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⠀⢀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣆ ⠀⠀⠀⠀⠀⠀⠀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢀⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃ ⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⠏⢻⠟⠉⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⡿⠛⠛⢄⡈⢢⣀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣶⣾⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⡟⠙⠻⣿⣿⡿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣿⡟⠀⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡀⠀⠀⠹⣇⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠻⣦⣄⣀⣉⣳⣦⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⢿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣀⡀⠀⠀⣤⣤⣤⣾⣿⣿⣿⣷⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⢀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣶⣶⠀⠀⣶⣶⡆⠀⢰⣶⣦⠀ ⠀⢰⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣶⣿⣿⣿⡇ ⠀⠀⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇ ⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⢴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀ ⠀⠈⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⡿⠿⠿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠸⠀⠀⠀⠈⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣴⣾⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠻⡏⠁⠴⠟⠟⠻⣦⣤⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡆⠙⢄⠀⠀⠀⢠⠿⢾⣿⠳⢤⡀⠀⠀ ⠀⠀⠀⠀⣶⣿⣿⡀⠀⠳⣆⠀⣠⢾⣻⣿⣿⣷⣿⣄⠀ ⠀⣠⡴⠊⢉⣼⣇⡿⡆⠀⠘⣿⣷⢟⣽⣶⣾⣿⣿⢿⡄ ⡾⠋⠀⠀⣿⣿⣿⣧⣽⡆⠀⣿⣿⢼⣿⣿⣿⣿⣿⢘⡇ ⡇⠀⠀⠀⢹⣿⣿⣿⠿⣷⡀⠻⣽⣮⣙⣛⣻⠿⠋⣻⡇ ⢷⡄⠀⠀⠈⣿⡯⠔⠒⠈⣿⡄⢹⣇⡀⢡⣄⡀⢸⡏⠀ ⠀⢿⡀⠀⢀⡿⢶⣄⣠⣴⣿⢷⣄⣿⢽⣿⣿⣿⣿⡇⠀ ⠀⠈⠣⣴⡏⠀⠀⠈⠁⠀⠘⢾⣿⣿⣮⠭⣽⣿⣿⠇⠀ ⠀⠀⠀⣿⠉⢀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡏⠀⠀ ⠀⠀⠀⠘⡇⠀⠉⠑⠒⠒⠒⠚⣻⣻⣿⣿⣿⣿⡗⠀⠀ ⠀⠀⠀⠀⠹⡤⢀⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠁⠀⠀ ⠀⠀⠀⠀⠀⠱⡄⠈⠉⠉⠉⠉⠉⢩⣷⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠦⣀⣀⣀⣀⣀⣼⠟⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣶⣿⣶⡾⣶⣦⣽⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣯⠿⢿⡻⢿⢿⣿⣽⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣞⣻⣿⡿⢷⡾⢛⣿⣿⠿⣨⢙⣿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣻⣿⣣⢟⡽⣺⠟⡦⡙⢢⣵⡿⢃⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣾⡿⣻⣽⣿⡿⣿⢿⣿⣯⠷⢏⠚⠀⣵⣿⡟⢁⣎⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⣿⣵⣿⣿⣿⢿⡿⣿⣶⣵⡪⠝⠀⣠⣿⣿⠋⣠⢣⣾⣿⣷⣶⣶⡄⠀⠀⠀⠀⠀⠀ ⠀⢠⣾⣿⣿⣿⣿⡿⡿⠿⢿⣶⣝⢿⣷⣌⣾⣿⠟⡁⠆⣽⣿⠿⢱⣯⠿⣧⣽⣄⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣽⣿⢻⣽⣿⣿⣶⣌⠻⣧⣽⣿⡿⢋⡘⢠⢃⣿⠿⣟⣽⣿⣟⡶⣥⣻⣳⣦⢄⡀⠀ ⠀⢸⣿⣟⣿⢳⣿⣿⣿⣿⣿⣿⡧⢹⣧⣿⡷⢀⣿⣠⣿⡿⣼⣿⣿⣿⣿⣿⣳⢧⣋⠿⣳⣧⠀ ⠀⣹⣿⣻⣿⣸⣿⣿⣿⣿⣿⣿⣟⣸⡿⣿⡷⢩⡿⣿⣻⣷⣿⣿⣿⣿⣿⣿⢯⡷⣩⠝⡑⢚⣧ ⢸⣟⡿⣷⢿⣧⡙⢿⣿⣿⢿⡿⣣⣿⣿⣿⣧⡿⢧⣿⣿⣿⣿⣿⣿⣿⣿⡯⢏⡳⢅⡲⢌⠢⢼ ⠈⠻⣽⣯⣻⡽⣿⣿⣶⣾⣷⡿⣿⡟⣾⠿⣡⣺⣿⢛⡝⣻⠿⣿⣿⣿⣿⡝⢢⠳⢌⠲⣅⠣⣾ ⠀⠀⢹⣟⡷⣻⢗⣯⣾⠳⣯⣽⢿⣻⠟⣰⣳⣿⡇⡝⢚⠛⡻⣿⣿⣿⡿⣜⠡⡎⣄⠳⣌⣹⡃ ⠀⠀⢸⣯⣷⣽⢿⣿⣿⣿⣮⣿⣿⡟⣸⣳⣿⢹⣷⣭⣎⠱⡒⣬⣽⣿⣟⢢⠏⡐⢄⢻⣼⠇⠁ ⠀⠀⢸⣷⡿⣿⢸⣿⣿⣿⣿⢼⣿⡇⣿⣿⡟⣾⣷⣻⣿⣧⣽⣿⢿⣛⢿⣤⠣⡘⠄⣿⡿⠀⠀ ⠀⠀⠘⣿⣿⡹⣷⣝⡿⣟⣫⣾⡿⣼⣿⣿⣾⡟⢀⠂⠍⠩⠍⢆⠯⣜⠫⢿⣷⡭⣞⣿⠁⠀⠀ ⠀⠀⠀⢹⡿⣿⣮⣽⣛⣻⣻⣭⣾⣷⣷⢟⡫⢅⡢⢜⡠⢁⠜⡠⢉⠌⣹⣾⣿⣿⡟⠁⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⢎⡵⢫⡜⣣⢞⡱⣊⠥⣋⣜⣼⢣⢾⣻⠅⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣾⣧⣛⣦⣏⣲⣥⣾⠶⢛⢥⣣⣿⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣷⢭⠎⡍⣍⠩⣉⠉⢤⠠⡘⡄⢪⣿⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⡳⣜⢦⣛⡴⡛⢆⢣⠑⣬⣳⡿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⢿⣿⣿⣿⣿⣾⣵⣫⣞⣵⣮⣽⣮⣾⠛⣡⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣷⣯⢎⡥⣍⠭⣩⢋⡭⡙⢆⠲⢬⣳⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣾⠽⣜⢮⣛⡦⢏⠶⣙⢎⡹⣲⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣾⣯⣿⣽⣯⣾⡽⠶⠟⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣄⣀⣀⣀⣰⣦⣼⣟⣛⣯⣭⣽⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⢛⣿⣛⣛⣛⣻⣟⣛⡛⠛⠻⠿⠿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⡆ ⢰⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣾⣿⡿⠿⢹⣀⠨⣿⣿⣿⡿⠿⠿⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⣀⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⣿⠃⠀⠀⠀⠀⣀⣀⣀⣀⣀⣰⣟⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠻⣿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀ ⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢷⣴⢹⠇⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠙⠾⣀⣀⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠻⢿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀ ⣼⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⠀⠀⠀⠀⠀⠀ ⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⣿⣿⣶⡆⠀⠀⠀⠀ ⣿⣿⣄⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿ ⠈⠻⢿⣷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⠿⠇⠀⠀⠀⠀ ⠀⠀⠀⠙⣿⣿⠛⠛⠛⣿⣿⠛⠛⠛⢻⣿⠛⠛⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⣿⣀⣀⣀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⣿⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣤⣤⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠛⠛⣿⣿⣿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⢘⣀⠀⣷⣿⣤⠴⠛⠓⠒⠒⠊⠒⠀⠀⠁⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⢷⣄⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⢾⣡⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⠀⠀⠸⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡤⣤⣤⡀⠀⣠⠈⣷⡀⠀⠀⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⣿⡿⠁⠀⠀⠀⠀⣀⣀⣀⣀⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠟⠉⠀⠀⠀⠉⠙⠿⣧⣀⣹⣧⠀⠀⢸⡇⠀⠀⠀⠀ ⠀⠀⡇⠀⢸⣿⣿⣁⣀⢀⡤⠞⠛⠉⠉⠉⠛⠳⢾⣝⠀⠀⠀⠀⠀⠀⠀⠸⠟⠁⣠⣴⠦⠀⠀⠀⠀⠀⠘⣿⠉⢻⡄⠀⠸⣿⠀⢰⡀⠀ ⠀⢸⡇⠀⣸⣿⡇⠀⣽⠟⠁⠀⠀⠀⣀⣤⣄⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣀⣾⡀⠀⠀⠀⠀⠹⡆⠈⣷⠀⠀⣿⡀⢸⣇⠀ ⠀⣸⡇⠀⣿⣿⡷⣾⠋⠀⠀⠀⠀⢸⣿⣿⣄⣰⣆⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠙⠃⠀⠀⠀⠀⠀⡇⠀⣿⣇⠀⣿⡇⢸⣿⠀ ⠀⣿⡇⢰⣿⣿⡧⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠶⠀⠀⠀⠀⠀⢠⡇⠀⡿⣿⠀⣿⡇⢸⣿⠀ ⠀⣿⡇⣸⣿⣿⠃⣿⠀⠀⠀⠀⠀⠘⢶⣿⣿⣥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⢸⡃⣿⣦⣿⣧⣿⣿⠀ ⠀⣿⡇⣿⣿⣿⠀⠘⣇⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣮⣹⣄⣸⣷⠿⠁⠙⠻⢿⣿⠀ ⠀⣿⣇⣿⣿⣿⡀⠀⠈⠷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⢀⣾⡟⠁⠀⡀⠀⠀⠀⠈⢧ ⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⣹⣶⣦⣴⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡁⠀⠀⢠⣿⣿⠁⣠⣾⣿⣷⣤⠤⡀⠀ ⠀⢿⣿⣿⣿⣿⣿⡀⢀⡴⠛⠁⠀⠀⠀⠉⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠳⠀⣰⣯⣾⠉⠀⢿⣿⣿⣿⣿⣿⠀⠀ ⡆⢸⣿⣿⣿⣿⠻⢷⡉⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⠀⠀⢀⣼⣿⣿⣿⢸⠀⡘⢿⣿⣿⣿⡟⡀⠀ ⣿⠈⣿⣿⣿⣿⡄⠀⢿⡄⠀⠀⠀⢀⣀⣴⠞⠁⠀⠀⠈⠉⠒⠂⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡀⣧⠈⠑⠶⠶⠒⠉⠀⠀ ⣿⣆⢻⣿⣿⣿⣿⣶⣦⣿⡀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⣿⡜⣇⣀⠀⠀⠀⢄⣀⣴ ⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢸⣿⣿⣿⣿⡿⠸⣿⣤⣤⣤⣼⣏⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠿⣿⢸⡿⢿⢿⡿⠀⡜⢿⣿⣿⣿⡿⣸⡿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠙⠲⣶⣤⣄⣀⠀⠀⠀⠀⠀⣀⣠⣶⡾⠋⠀⠀⣿⣿⣿⡆⣾⣿⡀⠈⢲⡿⢯⠭⠴⡟⠀ ⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⢀⣿⣧⣬⣎⡞⣿⣟⣶⣶⢔⡠⠈⠀⡟⠀ ⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡏⠻⢿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠈⠉⠙⠛⠛⠋⠀⠀⠀⣠⠔⠛⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠁⠀⡀⠁⠀ ⠀⠀⢿⣿⣿⣿⣿⣿⡌⠻⢿⣆⠈⠉⡠⢉⣿⠋⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⣠⠿⢿⣿⡏⠉⠉⠙⣿⣿⠁⠀⠀⠉⠁⠒ ⠀⠀⠘⣿⣿⣿⣿⣿⣷⡀⠀⠉⣳⣆⣴⠏⠁⠀⠉⠙⢦⣄⡀⠀⠀⢀⣠⡴⠚⠋⠀⠀⠀⣰⠃⠀⠀⢙⢷⡀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢿⣿⣿⣿⣿⣷⠀⠐⣻⡞⠁⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠸⣦⣤⠔⠁⢸⣧⣤⣾⣿⣿⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣧⣠⡟⠀⠤⢀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣄⠀⢸⣷⠢⠴⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣗⣷⢶⣾⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⣶⠾⠻⠛⠦⠀⢙⠿⡿⠀⠀⠀⠀⠀ ⠀⠀⢀⣤⠔⣿⡿⡿⡤⠀⠀⢀⡤⠋⢠⠃⠀⠀⠀⠀⠀ ⠀⣠⣾⣿⣿⣿⣛⠷⣄⠀⣴⠟⠁⣠⡾⡵⣶⡀⠀⠀⠀ ⠀⡿⣿⣿⣷⣶⣯⡻⣞⣿⠋⠀⢰⢿⣸⣧⡈⠉⠢⢀⠀ ⠀⡇⣿⣿⣿⣿⣿⡷⣿⣿⢀⣶⣿⣼⣿⣿⡷⠀⠀⠈⢦ ⢸⣿⠈⠻⣿⣛⣛⣵⣿⡿⢂⡾⠿⣿⣿⣿⡇⠀⠀⠀⢀ ⠀⢸⡆⢀⣠⣄⢀⣸⡏⢀⣾⠀⠐⠒⢿⣿⠀⠀⠀⢀⠈ ⠀⢸⣿⣿⣿⣿⡿⣿⣀⡾⣷⣶⣤⣠⡶⠿⡀⠀⢀⡞⠀ ⠀⠘⣿⣿⣯⠭⢽⣿⣿⡶⠏⠀⠈⠁⠀⠀⢸⣦⡼⠁⠀ ⠀⠀⢹⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣀⠉⣿⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣟⣟⠒⠒⠒⠒⠂⠉⠀⢰⡏⠀⠀⠀ ⠀⠀⠀⠻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡀⠠⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣾⡍⠉⠉⠉⠁⠉⠁⢀⠎⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢻⣧⣀⣀⣀⣀⣀⠴⠋⠀⠀⠀⠀⠀⠀
⠀⠀⢀⡴⠖⠋⠉⠉⠉⠉⠓⢦⣀⡤⠖⠚⠉⠉⠙⠳⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠔⠁⠀⠀⣀⣠⠤⠤⢤⣤⣀⠐⡀⠀⣀⣀⣀⣀⣀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀ ⠏⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣬⣽⣿⣏⠉⠉⠈⠉⣉⣙⣳⣞⣿⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⡴⠞⠛⠉⠁⠀⠀⠈⠉⠻⣶⠞⠛⠉⠉⠉⢉⠉⠛⢷⡀⠀⠀⠀ ⠀⠀⠀⢰⣿⡉⠀⠀⠀⠀⠀⣶⣿⣷⠄⠀⣿⠀⠀⠀⠀⢀⣿⣿⡆⠀⣿⣤⠀⠀ ⠀⠀⠀⠀⠉⠙⠳⠤⣤⣀⣀⣈⣙⣁⣤⣴⡿⠤⣤⣤⣤⣤⣿⣽⣧⣴⡿⢿⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⠛⣋⡿⠟⠉⠀⠀⠀⢀⡀⣀⣠⣤⣿⡿⠛⠃⠓⠳ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣾⡯⢀⢠⣶⣶⡌⢹⣾⣿⣿⣽⣾⣿⡇⡌⣶⣶⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠘⠘⠻⠟⠃⠀⢹⣿⣿⣿⣿⣿⣇⠘⠙⠋⠀ ⠀⠀⢀⣤⡶⢻⣿⣛⣻⣿⣿⡿⠷⠶⠲⡖⠒⠚⠛⠛⡿⠛⠛⠛⣻⡏⠀⠀⠀⠀ ⠀⠀⠘⢿⣀⣈⣉⣉⣿⠟⠻⣷⣶⡀⢀⣤⣐⣦⣤⣶⣿⣿⣿⡿⣿⣿⣀⣀⣀⠔ ⠀⠈⠳⢮⠉⠉⢹⡟⠁⠀⠀⣿⣿⡇⣿⣿⡿⠟⠛⠙⢿⣿⡏⠈⠙⢂⠀⠀⠀⠀ ⣀⡀⠀⠀⠀⠀⢸⡄⡀⠀⠀⣿⣿⣇⣿⠁⠀⠀⠀⠀⢸⣿⡇⠀⣠⠆⠀⠀⠀⠀ ⠿⠿⢷⣤⣭⣭⣽⣿⡁⢀⣴⠟⠿⠿⠿⣶⣄⣀⣀⣄⣼⣿⠏⠉⠹⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡅⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⣰⠇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠿⠛⠟⠻⠿⠶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣴⡟⢋⠡⣀⠒⠄⠣⢘⠰⣀⠒⢠⠉⡙⠿⣦⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣼⠟⠡⡐⢠⠡⠠⠘⡄⢃⠢⡐⢄⠊⡄⢒⠠⢂⠌⠹⣷⡀⠀⠀⠀⠀ ⠀⠀⢰⣿⠃⡌⢰⠐⠂⡄⣷⣷⠀⡎⠐⠐⠈⣶⣶⠈⠐⠂⡌⠐⠈⣿⡄⠀⠀⠀ ⠀⢠⣿⠖⡐⢈⡄⣢⣴⣿⠿⢋⠐⠤⠡⢡⢁⠹⢿⣷⣦⣁⡌⡑⠤⠙⣿⡀⠀⠀ ⠀⣾⠇⡰⢀⠻⡿⠟⢋⢉⠰⡀⡉⢄⠃⡄⢊⠐⡠⢉⠛⠿⣿⣷⣆⢁⢺⣷⠀⠀ ⠀⣟⡣⠐⣂⠡⠐⣨⣄⠨⠐⡠⢁⣂⣌⡐⡈⢂⢁⠂⣌⣰⣿⡛⡿⣶⣬⣿⢆⡀ ⠀⣿⡁⠥⠐⡈⢅⠈⢻⣿⣷⣶⣿⠟⢉⢻⣿⣶⣾⣿⠟⣰⣯⡹⣦⡙⣿⣿⣧⣽ ⠀⣿⡇⢐⠡⢌⠠⢃⠂⡌⠙⡉⢡⠈⠆⡄⠨⠙⣉⣴⢾⣿⣿⣷⡘⣿⣿⣿⣿⣿ ⠀⠘⣿⡄⠊⡄⠒⡠⠡⠘⡠⣁⣆⣨⣐⣠⣑⣢⣿⡌⢻⣿⣿⡿⣷⢻⣯⢿⣿⣳ ⠀⠀⠘⢿⣄⠘⠤⢁⠢⠑⡐⢛⠛⡛⢛⠛⡛⢛⠠⢿⢰⣻⣯⢴⣹⣿⣼⣻⣾⢧ ⠀⠀⠀⠘⢧⣘⠠⠘⡀⠇⡘⡀⢃⠸⢀⢃⡘⢀⠃⠼⣧⡿⢛⠛⠻⣿⣿⢿⣟⣧ ⠀⠀⠀⠀⠀⠛⢿⢦⣁⡒⠠⢁⠆⠒⠄⠢⠄⢃⠘⣠⣰⡿⢦⣟⣷⣭⣿⣿⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⣶⣎⣶⣼⣱⣞⡶⠿⠛⢻⡇⣒⣶⣮⣼⣿⣿⣿⠿ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣳⣜⣦⣝⣾⣿⠋⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠗⣼⣤⣬⣴⣶⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣾⠟⠉⠁⣀⣀⠀⠀⡙⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣇⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡐⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⢠⡶⡿⠿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⢤⣤⣤⣀⣰⢚⣧⣻⣄⠀⠀⠈⠻⣖⢄⡀⠀⠀⠀⢀⣠⣶⣾⣿⢿⣿⣿⣶⣤⣀⠀⠀ ⠀⠀⠀⢀⣠⢶⣫⣭⠶⠛⡷⠞⠉⠉⠉⠉⠉⢙⣿⠷⠾⣿⣿⡏⢿⣷⢀⠀⠀⠙⢷⣝⠀⣠⣾⡿⢋⣵⡶⠿⠿⠿⢿⣿⣝⢿⣷⡀ ⣀⡴⣾⡿⠟⠉⠁⠀⢠⡾⠋⠳⣄⠀⠀⣠⡶⠋⠁⠀⠀⣰⣿⣧⢸⡟⣿⡆⠀⠀⠀⠙⣾⣿⡏⣴⡟⢁⣴⣶⣾⣿⣶⣝⢿⣷⠉⠃ ⣽⣟⣡⣶⡀⠀⠀⠀⣿⣀⣀⣠⣿⡷⠞⠉⠀⠀⠀⠀⣾⣿⣿⣿⣿⣧⠈⢷⣦⡀⠀⠀⢹⣿⠀⡏⢠⣿⣿⣿⣿⣿⣿⣿⣦⠋⠀⠀ ⣵⠋⢹⣿⠀⠀⠀⠀⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⣏⢿⡇⠀⠀⢸⣿⠀⣧⡘⣿⣿⣿⣿⣿⣿⣿⠟⣠⠀⠀ ⣀⣠⣾⣿⠀⠀⠀⠀⠻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣧⣿⠿⣷⣄⠀⠀⣿⣇⠙⢷⣌⠙⠛⠛⠛⣛⣧⡾⠃⠀⠀ ⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠙⠻⣄⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠟⠋⠁⠀⠀⠈⠻⣦⠀⠈⢻⡄⠀⠈⠙⠛⠛⠛⠋⠉⠀⠀⣀⡄ ⣿⣿⡟⠀⠀⠀⠀⠀⢀⣠⣾⠃⠈⢧⡀⠀⠀⠀⠀⠀⢠⣻⣿⠁⠀⠀⠀⠀⠀⠀⢰⣿⣷⡀⠀⢿⡄⠀⠀⣀⣠⣶⣶⣤⣀⠀⣿⡇ ⠛⠉⣅⠀⠀⣀⣤⣶⡿⠟⠁⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⣼⣿⡄⠀⠀⠀⠀⠀⠀⢸⡇⣿⣷⣄⠈⣷⡞⢸⣿⣿⣿⣿⣯⢻⣯⣿⣇ ⠀⠈⠛⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⣠⠞⠀⠀⠀⠀⠙⠛⠛⠋⠉⠙⣷⡸⣝⢿⣆⢻⣿⡘⠿⣿⣿⠟⣣⣾⠿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡶⢾⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣯⣽⣦⣝⡻⠷⠶⠶⠟⣋⢰⣿⣿⡿ ⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠉⠛⠚⠛⠉⠉⠈⣿⣿⠁ ⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢲⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀
⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣇⣀⣤⣤⣤⣴⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄ ⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋ ⠀⠀⠀⢀⣴⣿⣿⣿⣿⢿⠟⠛⡟⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠙⠀ ⠀⣠⣴⣿⣿⡿⠛⠉⠉⠣⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⣠⣤⣴⣴⣶⣶⣶⣶⣶⣶⣶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⠃⠈⠉⢻⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠙⣿⠀⠀⠀⣿⡏⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⣷⡀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⣀⣈⣩⡶⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⠿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡴⣖⢲⡤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣋⡉⠁⠙⠓⠒⠶⠦⣤⣤⣄⠀⠀⠀⠀⢀⡤⠴⠒⠚⠋⠛⠛⠛⠒⠒⠒⠦⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠳⢿⣟⣻⣿⣂⣶⣦⣤⣤⣀⡈⠃⣷⠀⣀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡿⡟⣿⣿⣿⣮⠉⢩⡟⠳⠿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠓⠒⡎⢛⣿⣿⡃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣷⠠⣿⣿⣶⣿⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣾⢿⣿⣿⡿⠁⠀⠀⠀⠀⠈⢀⣿⣦⡀⠀⣤⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠐⢁⡀⣾⣿⠛⠀⠐⣿⡿⠃⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠸⠟⠹⣧⠀⠀⢀⣻⠇⠸⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠳⢤⠴⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠘⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠀⣿⡀⠀⠀⠀⠀⠀⢠⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⣗⣀⠀⠀⠀⢀⡞⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣟⣇⠈⠛⠳⠶⠖⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣾⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣾⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣷⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡶⣄⣀⡀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⡿⠽⠟⠋⠀⠀⠀⠉⠉⠉⠋⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢤⡼⣿⣶⣶⣾⣿⣿⣷⣶⡀⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⣿⠭⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠪⢽⣗⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⡯⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠮⣕⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⢾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢼⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡴⣧⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡳⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡜⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡼⣄⠀⠀⠀⠀⠀ ⠀⢀⡾⡽⠃⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⢳⡹⡆⠀⠀⠀⠀ ⠀⣸⣱⠃⠀⠀⠀⠀⣴⣶⣾⣿⣿⠶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣿⣿⣿⣷⣦⡀⠀⠀⠀⠈⢷⣱⡀⠀⠀⠀ ⢠⣧⡟⠀⠀⠀⠀⠀⠘⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣿⣯⣵⣷⡀⠀⠀⠘⡿⡇⠀⠀⠀ ⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⢻⣍⣿⣄⡀⠀⣳⣿⡀⠀⠀ ⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣄⡀⠀⠀⠀⠀⠀⢀⣤⣤⣠⣤⣀⠀⠀⠀⠀⠀⠀⣀⣤⠀⢸⣮⠳⡀⠀⠀⠀⢙⣿⣿⣯⠙⠳⣄ ⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣟⠛⠿⠿⠿⠛⣿⠟⠁⠀⠹⣯⡛⠛⠿⠿⠟⢛⣿⠟⠀⣨⣿⠀⠙⣆⠀⠀⢸⣻⣿⣿⣶⣤⡙ ⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣶⡾⠟⠁⠀⠀⠀⠀⠈⠙⠷⣶⣶⠾⠋⠁⢠⣾⣿⡙⣧⠀⠈⢳⣠⣾⣿⡿⢛⣿⣿⡿ ⠈⣏⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢉⣿⣿⣿⡟⣧⡀⠀⣿⣿⢑⣿⣿⣿⣷⠁ ⠀⠸⡎⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⢸⣿⣿⣿⣿⣮⡇⠀⢿⣿⠘⣿⣿⣿⡿⢀ ⠀⠀⠻⡞⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⠙⣧⠀⠀⠀⢻⣿⣿⠿⠛⠻⣆⠘⢧⠀⠈⠉⠭⠒⠈ ⠀⠀⠀⢹⣏⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠘⣧⠀⠀⠸⣿⠃⠀⠀⠀⣙⣆⠀⠀⠀⣠⣤⠄⠀ ⠀⠀⠀⠀⠙⢦⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢀⣴⠟⠶⣤⣶⠿⣿⢻⣆⢿⣼⣿⣿⠆⠀ ⠀⠀⠀⠀⠀⠈⠱⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⣯⠀⠀⠀⠀⠀⠈⣿⣿⣮⡓⠍⢁⣠⣾ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⣭⣢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣀⠀⠂⠀⠀⠀⢹⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠾⣕⡲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢴⣺⡇⠀⠉⠉⠉⠛⠋⠉⢻⣿⣿⣿⣿⣿⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠬⣿⣖⣒⠤⠤⠤⠤⠤⠤⠤⠤⣐⣒⣾⠯⠗⠛⢻⠥⠀⠀⠀⠐⠀⠀⠀⣼⣿⣿⣿⡿⢛⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠈⣦⣤⠀⠈⠛⠛⠛⠛⠛⢻⣯⣿⡷⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⡻⣆⣀⣀⣤⣀⣀⣸⣿⣟⠀⠀⠀
⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⡿⣿⣿⣷⣿⣿⣿⣿⣾⡳⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⣿⠿⠓⢋⠩⠉⢄⠠⢀⠄⣀⢀⠉⡉⠛⠓⠯⢿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠛⡉⢄⠂⠜⣀⠣⠉⡄⢊⠔⠨⡀⠎⠰⣀⠣⢌⡐⠠⢈⠙⠾⣟⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⠟⡉⢐⡐⠰⠈⠌⢂⡐⠠⢃⠐⣈⠐⠡⠘⣀⠃⡄⠒⠠⠘⡐⠂⠌⡐⢈⠛⢿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣿⡿⠛⠠⡘⠠⠀⠇⡘⠸⢀⠠⠃⡜⢠⠀⠜⢃⠣⢀⠜⣀⠛⠄⢣⢀⠛⢠⠘⡀⠄⡀⠘⣿⢧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⠟⢀⠡⢂⠅⠡⠃⡌⠐⡁⢢⣀⣃⠐⢂⡉⢌⠂⣁⢊⠐⢂⣉⡌⢄⠢⠉⢄⠂⢅⠘⠠⢁⠘⢻⣳⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡾⣿⠋⠄⢃⠘⡀⠎⡐⠡⢀⢃⣴⣿⣿⡿⠈⠤⠐⠤⠡⠄⢢⠈⠼⣿⣿⣦⡠⢉⠐⠌⢂⠌⢡⠂⠌⠄⢿⣽⣄⠀⠀⠀⠀⠀ ⠀⠀⢀⡾⣿⠣⡉⠄⠃⠌⡐⠐⣠⣡⣶⣿⣿⡿⠋⠠⡁⢆⠩⢐⠡⢘⠠⠌⠠⠙⢿⣿⣿⣦⣌⣄⠃⠌⠠⠉⢆⡈⠄⣻⡽⡆⠀⠀⠀⠀ ⠀⠀⣾⣹⠇⠠⡑⡈⠴⣿⣿⣿⣿⣿⠿⠟⢉⠠⠌⢂⠑⡠⢊⠐⠌⢂⠑⡨⠑⡈⠄⡈⠻⢿⣿⣿⣿⣿⣶⣅⢂⡐⠐⡈⢷⣻⡀⠀⠀⠀ ⠀⢠⣿⡟⠈⡅⢒⡀⠆⠹⢛⠋⡉⠄⢂⠌⢂⢂⡉⠤⢁⠰⡀⢎⡐⢡⠈⡄⡑⢈⠤⢁⠂⡄⠠⠉⢯⣿⣯⣿⣷⣆⠡⠈⠼⣿⣇⠀⠀⠀ ⠀⢸⡷⡇⡑⠌⡄⠢⢘⠠⠉⢄⢡⠌⢂⠘⠠⠂⠔⠢⢈⡐⢀⠂⡐⠠⠁⡔⠈⡄⠢⠌⡐⠠⠡⠈⣿⢿⡟⣻⣯⣿⣦⣅⣒⣿⣿⡀⠀⠀ ⠀⢸⣟⡇⢈⠖⠠⡑⢂⠢⢁⠂⠌⣿⣦⣌⣡⠘⢠⢁⣂⣴⣾⡶⣵⣷⣬⣀⣡⢈⡐⣐⣠⣵⣾⡓⢹⣯⠿⣔⠣⢞⣼⣻⣿⣿⣯⠽⢳⣦ ⠀⢸⣿⡇⠰⠎⡰⠀⢇⠰⠁⠎⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣿⣿⡆⢿⣷⠈⢰⢿⣿⣿⣿⣿⣆⣹ ⠀⢸⣷⡇⢂⠱⢀⠃⢢⠐⠡⢊⠄⠡⢈⠻⠿⣿⣯⡿⠟⢋⠐⡈⠔⠠⠙⠻⢷⣿⣽⠾⠟⠡⣨⣾⣿⣻⣿⠠⠹⣿⣦⣿⣿⠿⣿⣿⣿⣿ ⠀⠘⣯⣷⡀⠃⡌⢨⠐⡈⢅⠢⢈⠅⢢⠐⡠⠀⡔⢠⠈⡄⢊⠔⡉⢄⠃⡌⠠⡀⠄⣂⣼⡿⣻⣿⣿⣿⣟⣧⡱⣈⣿⣿⢻⣿⣿⣿⣯⢿ ⠀⠀⢹⣞⣧⠐⠨⠄⡑⢨⠀⠆⢡⠈⠔⡨⢐⠡⠐⡠⠁⠌⡐⠠⢂⠂⠌⠠⠑⢠⣸⡟⢡⢛⣿⣿⣿⣿⣿⣾⣟⠦⣿⣿⡼⣿⣿⣿⡿⣻ ⠀⠀⠀⠻⣞⣧⠁⡘⡐⢂⡁⠊⢄⠊⡰⠐⡈⢂⣡⣶⣥⣮⣤⣵⣤⣬⣦⣵⣬⣿⠛⣷⡌⢎⠜⣿⣿⣿⡿⣛⢿⣮⠽⣿⣻⡽⣯⣽⡾⣟ ⠀⠀⠀⠀⠻⣎⢷⢀⠰⠁⠤⡉⢄⠂⡁⢆⢁⠂⠹⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠠⠙⣿⡐⢮⢽⣿⡳⣉⠜⣬⣻⣧⣹⣳⢟⣵⣯⣟⡦ ⠀⠀⠀⠀⠀⠙⣮⡳⠂⡉⠔⡐⡈⠤⠡⢈⠤⢉⠰⠐⡠⢂⠔⡠⢂⠔⡠⢂⠔⡈⢆⠡⢹⣇⢼⣾⢿⠿⣧⣿⠿⣿⣿⣧⣿⣾⣿⣿⢯⣗ ⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣌⠐⡈⠄⠣⠄⠂⢆⠨⠐⡁⠂⡔⠐⠂⡔⠠⠂⡔⢈⠄⢢⠀⠛⠛⣯⢋⠚⡠⢀⡆⡹⣿⣿⣮⣟⣾⣹⣯⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣬⣷⣴⠈⡄⠉⠒⢨⠀⠃⡔⢡⠀⢣⢡⡄⠃⢡⠐⢨⠐⢡⠈⠂⢹⣿⣧⣧⢹⢻⢱⠓⣦⢻⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢭⣳⡦⣥⣂⠂⡉⡐⠐⡈⠌⣀⠂⠔⡈⢂⠑⢂⠰⣀⣮⣴⣿⣏⡘⡙⠛⠿⠻⢿⢻⣿⣿⣿⣿⣿⣿⣧ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⢭⣟⣷⣶⡥⢶⡴⣤⢬⢦⡴⣥⣾⣶⣟⡯⠿⠛⣯⢷⠤⣩⢙⡶⣟⢦⣏⣿⣿⣿⣿⣿⢿⡽ ⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠘⣧⣶⡝⣛⢻⢛⡟⢻⣛⣿⣿⣿⣷⠋⢀ ⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣻⣦⣋⣞⣼⣗⣞⣾⣿⣟⠁⣀⠀
⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡀⣈⡉⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣾⣧⣉⠁⣠⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣷⡀⠀⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢿⣿⣿⣿⣿⣿⣿⡟⢁⣾⣿⣿⣦⠈⢿⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠛⠛⠛⠛⢉⣴⣿⣿⣿⣿⣿⠇⢸⠀⠁⠶⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⡉⠙⠛⢁⣠⣿⠀⡇⣴⠄⣁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠑⢠⡤⢉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣄⠉⢉⣠⠈⠛⠒⣤⡈⠛⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⡄⢻⣧⠀⠀⠈⣴⠙⣂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⢸⡄⠹⣇⠀⠀⢠⣦⠈⡁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠟⠀⠹⣆⠀⠀⠠⣦⠈⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⣶⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠶⠀⣠⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣔⡾⠿⠛⠛⠛⠶⠖⣢⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⡤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣦⡀⠀⠀⠀⠀ ⠀⢀⡾⠃⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀ ⢀⡾⠀⠀⠀⠀⣀⣤⣾⠟⠁⠀⠀⠀⠀⠀⠈⠻⣷⣤⣀⡀⠀⠀⠀⢷⡀⠀⠀ ⣼⠇⠀⠀⠘⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣿⣧⣄⠀⠐⣧⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡙⠛⠢⢤⣿⠤⡀ ⣿⠀⠀⠀⠀⠀⠀⠻⣗⠒⠒⣺⠟⠉⠻⣗⠒⠒⣺⠟⢠⣇⠘⢆⠀⣿⣿⣦⣜ ⢿⡄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠈⠉⠉⢡⢔⣿⣿⢃⠈⢿⣿⣿⣿⡋ ⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠁⠘⣿⣿⣿⣇⢸⠟⠿⠿⠡ ⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠟⠈⠆⠀⢸⡏⠀⣈⣆⠀⢀⣤⠀ ⠀⠀⠈⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⡏⠉⠉⠙⢿⣿⡛⢋⣠ ⠀⠀⠀⠀⠉⠲⣢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡗⠠⠤⠤⢤⣿⣿⣿⡟ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠖⣠⣠⣠⣤⣤⡶⠾⠛⢻⠇⠀⢀⣀⣀⣿⣿⣟⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⣀⡀⣰⣿⠋⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣤⡤⣤⠤⣾⣿⣽⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣀⣠⣤⣤⣀⠀⣀⣼⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆ ⣼⣿⣿⣿⣿⣧⣤⣿⠿⠉⠿⠿⠿⠛⠛⠛⠛⠛⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠿⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡿⢿⠷⢶⣄⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡿⠁⠘⠶⣾⠟⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠈⢿⣿⠿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⡀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠙⣷⡀⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣦⣤⣤⣤⣤⡶⠋⠀⠀⠀⠀⠀⣸⡇⣿⣾⣉⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⢶⣦⣤⡾⠟⠀⣿⢸⠋⣻⠾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣮⡟⢛⡶⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⠻⣶⡶⠟⣷⣤⣭⠛⢷⣤⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣴⣿⢻⡄⠘⣿⣿⣷⠋⣦⠽⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣼⣿⣿⡇⢻⣆⠸⣿⣿⡟⠙⣷⢾⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⣾⣿⣿⣿⣿⣠⣿⣆⠹⣿⣿⣟⠙⣷⠿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠏⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠹⣿⣿⣿⠉⣻⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣉⣿⠟⢿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡴⠶⠾⠿⠛⠟⠻⠿⠿⠶⠶⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⢶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⢾⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠙⢻⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠛⣷⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⣄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠈⠛⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠛⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣿⣿⣾⢿⣇⠀⠀⠀⢀⣠⣤⣤⣤⣬⣙⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⣋⣁⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣟⣛⣉⣽⠉⢻⣆⣠⡶⠟⢛⣩⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣟⠻⠷⣦⣄⠀⠀⠀⠀⠀⠀⢸⣷⠀ ⠀⠀⠀⠀⠀⣠⣤⣶⣟⣋⡭⣿⠃⢠⡿⢙⠋⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠣⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠙⢷⡄⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⠀⢰⣿⣿⣧⣤⣻⡿⠁⣠⡿⠁⢸⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⣼⣿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠈⢿⡆⠀⠀⠀⠀⣿⡆ ⠀⠀⢀⣴⣿⣽⣯⣭⣍⠍⠀⣰⡿⠁⢠⡾⠿⣮⠝⠛⠻⣿⣿⣿⣿⣿⣯⠏⠀⠻⣿⣿⣿⣄⢠⣤⠤⣾⠿⠟⠀⠈⠳⠿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠸⣷⠀⠀⠀⠀⢹⣇ ⠀⣴⣿⣿⣿⣶⣾⣿⣻⣿⣾⡿⠁⠀⢸⡿⣭⣿⣿⣶⣃⣀⣙⣻⣾⣂⣀⠀⠀⠀⣀⣀⣹⣿⠠⣤⢤⣦⣤⣀⠀⠀⢠⣤⣤⣶⣶⣿⣿⠋⠉⣀⣠⣤⡄⠀⣿⠃⠀⠀⠀⣸⣯ ⢸⣿⣿⣟⣿⣿⣿⣦⡹⣯⣿⡇⠀⣤⣼⢃⣿⣿⣿⣿⣟⣿⡙⠀⠉⠻⣿⣧⠀⣴⣿⣿⣿⡇⠀⠀⠐⣿⣿⣿⠆⢸⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣿⠲⡾⣛⠻⢛⡷ ⢸⣿⡟⣾⣿⣿⣿⣿⣷⢹⣿⣷⠀⠘⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⢀⣿⣿⠀⣿⣿⣿⣿⠁⠀⠀⠀⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠃⢠⠕⢡⠣⠰⣟ ⠈⣿⣿⣝⣿⣿⣿⡿⢏⣿⢿⣿⠃⣸⠟⠿⠛⠿⣿⣿⡗⠀⣀⣀⣀⣼⣿⣿⣯⣿⣿⠟⠃⠀⠀⠀⠀⠘⠿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⣰⢋⡜⢆⢣⢘⣯ ⠀⠈⠻⣿⣷⣶⣶⣷⠿⣿⣿⠃⢰⣏⠈⠉⠉⠙⠛⣿⣯⠐⠀⠀⢹⣿⣿⠿⠟⠉⠀⠀⠀⣀⣀⣀⡀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⣠⢞⡓⢭⡘⡌⠆⣸⡧ ⠀⠀⠀⢹⣿⣫⣭⣭⡻⢿⣧⢠⣿⣯⡴⣾⣅⣀⣴⣟⠻⣬⣓⣤⣿⠉⠀⠀⠀⠀⣠⣾⠟⠛⠛⠛⢿⣶⡄⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉⣰⠶⡒⣍⠲⢬⡘⢆⡳⢈⠄⣿⠁ ⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿⣼⣿⡜⡟⠉⠉⠉⠱⠶⠥⣼⣟⠉⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢣⠱⣌⠚⡤⣙⢢⡱⠉⣼⡏⠀ ⠀⠀⠀⠀⣿⣧⣿⣿⣟⣼⡿⣿⢿⣿⠄⢀⣀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⢧⠘⢧⢠⢃⠼⠃⣸⡿⠀⠀ ⠀⠀⠀⠀⢻⣯⣽⣿⣿⣭⣿⣿⡋⠉⡉⠬⣉⠏⡉⢀⣤⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣢⠙⡆⢣⠞⠐⣼⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣷⣧⡽⠧⠷⠶⠚⠋⠁⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡜⢓⣨⠞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣶⣶⠂⠀⣀⢐⡲⠆⠀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡾⣭⣳⣌⣣⣴⠶⠛⢷⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣯⣯⣙⡉⢉⣉⡉⠁⣀⣀⣴⠟⠛⠳⠶⣦⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⠶⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣭⣥⣫⣟⣖⣰⠟⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⣾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⢠⣦⣤⣶⣾⣽⣯⣭⣭⣽⣯⣭⣿⣯⣿⣽⣿⣿⣿⣿⣿⣷⣯⣧⣴⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⣀⡀ ⢐⣶⣶⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡭⣕⣥⣦⣤⣵⣴⣤⡊⣷⣜⣷⢢⣶⡴⠴⢮⣊⢓⣴⣶⣾⣿⣿⡓⣿⡿⢿⢯⣯⣽⡹⠟⠻⠿⢛⠟⡛⢻⣿⣿⣿⣟⡿⢟⣻⠻⣿⣷⣴⢦⠤⢤⡤⢤⣴⣶⣿⡿⣿⣮⢹⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⣻⣿⣭⣭⣭⣯⣭⣭⣭⣭⣭⣭⣭⣭⣽⣭⣭⣿⣿⡻⣯⢱⣿⢙⣿⣿⢝⣿⡿⢀⣀⡈⢠⡻⢍⠀⠠⡂⣳⣿⣿⣟⣿⣟⣅⣿⣇⣧⠠⡈⣷⣷⢫⠚⡆⣶⡌⠙⡏⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠘⠓⠒⠗⠒⠒⠒⠚⠛⠒⣻⣿⢿⠵⡒⠍⢎⡉⠓⡖⣇⣿⣗⣾⣚⣿⣛⣿⣾⣿⣿⣾⣷⣶⣶⣿⣿⣾⣿⢿⠋⠛⠛⠛⠛⠛⠚⠞⠚⠓⠒⠯⣰⠸⣧⢀⠃⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠚⠍⠞⠀⠀⠁⠈⣿⣿⣿⣽⣿⠿⣿⣿⠛⠛⣿⣿⣯⣿⣿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠟⢛⣳⣄⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⡏⠙⠠⠤⠯⠑⢛⣵⣟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣿⣿⣿⣯⣇⠀⠀⠀⠀⠀⠈⢒⡿⡯⡧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⠙⡍⠏⡯⣧⠀⠀⠀⠀⠀⠀⠈⣾⣿⠽⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣖⣃⣃⣐⣀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⢀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡶⠷⢶⡾⠿⠿⠿⠿⠿⠿⡿⠶⠶⠶⢶⢶⠦⠤⠤⠤⠤⠤⠤⠤⢄⡀ ⢠⡤⣤⢤⣤⣶⣶⣶⣲⣶⣶⣶⣶⣲⣶⢿⢸⠙⠒⡶⢲⢦⠖⠖⡾⡶⣶⠗⢶⣖⣶⠖⠒⠒⠒⢠⣶⣶⣶⣶⣶⢶⡾⠿⡿⡛⣿⠿⠿⠿⠍⠉⠉⠉⣩⡍⣻⡇ ⠈⠉⠀⠉⠉⠛⠛⣛⣿⠛⣛⡛⣿⣿⣿⣾⣼⡧⣴⣦⣤⣧⣠⣦⣭⣦⣤⣴⣿⣿⣿⣟⣫⣿⣽⣽⡟⠞⠈⠛⢃⣾⣷⢾⣾⡷⣶⣦⣼⣽⣽⣷⣤⡿⣿⢿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⢻⣿⠿⡿⣿⣿⣿⣶⣶⣶⣶⣷⣊⣁⣠⣌⣉⣉⣿⡼⢹⣗⡀⠀⠀⣤⣼⡟⠀⠸⣟⣾⢏⠀⠀⠀⠀⢸⠋⣯⠿⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁⢸⣿⣿⣶⣶⣶⢻⣿⣿⠟⠉⠉⠎⢹⡦⣀⢀⣠⣦⣷⡿⠟⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣾⣿⡿⠀⠀⠀⠈⢆⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣷⣿⠇⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣌⢁⣰⣴⣰⣲⣲⣰⣠⡠⣤⣤⣰⣬⣩⢿⣿⣻⣿⡿⣹⡿⣿⢿⣿⢛⡛⡛⠛⣛⣿⣿⣿⣿⣷⡖⡤⣤⢤⡤⡤⢤⣶⡾⣶⡞⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣯⣭⠭⡯⢭⡭⡭⡭⣉⣉⣿⠿⣿⠿⣿⡵⡞⣿⣟⢛⣿⣃⢌⣙⡌⡩⠀⣐⣔⣯⣽⣟⣿⣼⣇⣷⢢⡮⠦⠉⡫⠈⠌⣨⢹⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢰⠷⠿⡵⡡⡠⠃⠏⠷⣾⣿⡾⠿⢿⣿⡿⢷⣿⣿⣯⣷⣿⠿⠏⠉⠉⠉⠉⠉⠉⠉⠉⢷⣧⡿⣟⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⡟⠛⠄⠜⠫⢿⣻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⠀⠀⠀⠀⠈⠽⣓⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣈⠎⠉⢻⠀⠀⠀⠀⠀⠘⠛⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠂⠐⠈⠉⠉⠑⠲⠤⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢩⠷⣄⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠁⠐⠤⠦⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠒⠁⠢⠀⠀⠀⠀⠒⠒⠌⠭⠥⣋⣐⣚⣓⣲⡧⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠘⢿⣦⣄⡀⠀⠀⢀⡇⠀⣼⣿⣿⣧⡶⢁⣴⣿⣟⡁⢀⣠⣬⣿⣿⢿⣿⣿⣦⣤⣀⣀⠀⢀⠀⠂⠀⡀⠀⠀⢀⣿⣿⡿⢁⣱⠀⠀⠀⠀⡹⠉⣿⣿⣿⣿⣿⣿⣿⣿⡏⠈⠀⠀⠀⣈⣍⣥⠾⠚⢿⣿⣿⡿⠿⠿⣤⣶⣾⠟⣛⣋⡭⢿⢻⣾⣟⣧⣿⡿⠿⠋⢉⣁⣤⣤⣴⣶⣿⣽⣿⡿⣿⣿⡏⢰⣿⣤⡶⠛⠻⠷⣤⣧⠀⠠⣶⣾⠏⠀⠀⠀⢀⣳⣾⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣾⣮⣛⠿⢷⣦⣎⡀⣸⣿⢷⣿⠁⢠⣾⡿⠋⠀⠠⠾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣷⣶⡇⠀⠀⠁⣸⣿⣿⠟⠛⢛⠓⠀⢀⡜⠁⠈⢫⣿⣿⣿⣿⣿⣿⣿⣤⣶⡖⠚⣋⣁⣤⣶⣶⣬⣿⣿⣿⣧⠤⠄⠐⢯⣥⡟⠁⠀⠀⢘⡴⢿⣾⣻⣵⣶⡶⠿⠟⠿⠷⣅⠙⢛⣛⠿⠯⡿⢿⣯⡿⣿⣿⣿⣷⣾⢻⡟⣿⣷⣄⣀⣉⣄⣤⠴⢲⣚⣽⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡟⠉⠁⣟⣷⡷⣂⠈⠉⠻⠿⣴⣿⣔⣻⠟⠳⠀⣔⢛⣿⣿⣿⣿⣿⡿⢷⣿⡿⠋⡀⠠⢲⠆⠀⠀⠑⢠⠀⠀⠉⢿⣟⣀⣀⡄⠀⢠⡋⠀⢀⡤⠻⣇⡀⠛⢿⣻⡋⢻⣧⠘⠿⡉⢉⣁⣿⠿⠿⠋⣿⡛⠻⣿⡠⠴⠖⠚⠉⠉⣁⣠⣤⢨⣀⣾⡽⢿⣿⡅⡷⠤⢀⠀⢠⡏⢉⡇⣐⣴⣶⣧⡾⠀⠉⣿⡁⢹⢦⡟⢸⡇⣿⡿⢟⣯⣽⣿⣿⣻⣭⣿⢿⣿⣿⣿⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡠⣾⡇⠀⠀⠀⠬⡷⠄⢿⣶⣦⣄⡸⠿⣌⠉⠀⠀⡮⣉⣿⣿⣿⣿⣿⠋⠀⢸⣿⠁⠘⠀⡴⣋⡄⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠦⠀⢏⣀⣰⣻⠄⠀⠀⢁⣷⠀⢻⣧⡀⠉⠉⠀⠘⢄⠀⢸⣿⡷⠀⠀⠀⠀⣴⣶⣿⣿⣿⣿⣿⣿⣏⠻⣧⣘⣿⢿⡾⣄⣀⡵⢾⠀⢘⣾⣫⣶⣮⣽⡇⠀⢐⣇⣇⣾⣭⣧⡼⠧⢛⣇⣌⣹⣿⣿⣿⡿⣿⣿⣿⡏⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠈⠛⠭⣛⠒⠦⣄⣿⣿⡟⣿⣿⣿⣿⣾⣷⣶⡾⠚⠉⠻⢿⣿⣿⣿⠀⠈⢸⣿⠀⠀⣶⣻⣿⡇⠘⠀⠀⠀⠀⠀⢀⡏⠀⣴⠀⠀⠀⠀⠸⡄⠀⠘⣿⣷⠃⡀⠀⢨⣿⣿⠭⣿⣷⡀⢀⣠⣤⣼⢷⣿⣽⣧⠤⢴⠖⢻⣿⠛⣛⣉⣭⣤⣿⣿⣿⣤⣿⡗⠚⠚⠋⠁⠀⠀⡸⢶⠶⠿⠛⠉⣻⣇⠀⣄⣿⣭⣿⠿⡟⣰⣿⣿⣍⡉⠙⢿⣿⢿⣷⡶⠾⠛⠈⠃⠈⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠻⣆⠀⠈⠛⠢⠭⣌⡡⠾⠟⢿⣿⣿⡛⢿⣿⣦⡄⠀⠀⠙⠻⣾⡀⠠⠈⢻⣆⢠⡉⠉⠛⣣⠞⠀⠀⠀⠀⠀⢸⡇⢀⡇⠀⠀⠀⠀⡴⠁⣠⠟⠙⠿⠉⠀⣠⡾⡻⠻⣯⠙⣿⣿⣿⣟⣯⣿⣿⣿⡿⠛⣢⠈⣧⡀⣻⣻⣿⠿⠝⠻⡋⠉⠉⠣⣀⣠⣤⣤⡤⠤⠔⡛⡐⠈⢀⣀⣴⣾⣟⣸⣛⣻⡿⣏⣿⣠⡛⠿⠿⠿⠍⠉⠉⢹⣿⢀⣿⡿⣶⣷⡄⠁⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⠀⠀⠸⡇⠀⠀⠀⢀⠈⢻⣷⣷⡈⠉⠻⣇⠀⢿⣿⣿⣶⣄⠀⠀⣨⣿⠶⢤⡀⢹⣄⡉⠀⠘⢠⠆⠀⠀⠀⠀⠀⣼⠁⣸⠇⠀⠀⠀⣀⣵⣾⣅⡀⠀⣈⣶⣾⣿⡟⠃⣁⣼⣶⣿⣿⣿⣿⣯⣿⣿⣛⣟⣿⣿⠛⠋⠉⠉⠀⣀⣀⣤⡴⠧⠖⢒⣋⣉⣹⣿⣿⣦⣠⣽⣺⡿⣿⣟⣉⣻⠟⢧⣸⣸⣾⣿⡽⢿⠟⣿⣿⣿⣶⣾⣶⣿⣿⠿⣏⠉⠀⣼⣇⣹⣦⡠⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢣⡈⠢⡀⠁⠀⠀⠀⠠⠤⠼⠿⢿⡿⠤⣘⣿⠀⠀⠻⣿⣟⡟⣷⣼⠟⣡⣾⣶⣝⣿⣿⣿⣷⣶⣋⣀⣀⣀⣀⣀⣶⠿⠿⠿⠖⠒⠒⠋⠁⠈⢿⡇⢀⣴⣿⠟⠉⣀⣤⡾⢋⠴⣿⢛⣵⣿⣿⡿⠿⢝⣿⣶⡇⠀⢢⣴⢶⠞⠛⠉⠉⠀⠀⠀⢠⠃⢈⣧⣸⠧⠖⠛⠋⠉⠀⠀⠀⠈⣿⣍⣀⣀⣀⣀⣛⡿⣿⣿⡿⠟⠉⢹⣿⢻⣿⣿⠿⠦⠾⠤⣦⣬⣿⣿⣿⣷⣾⡁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢣⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⠀⢸⣿⣶⡈⢻⣾⣿⢟⣵⣿⣿⣿⣿⣿⣿⣟⠻⠍⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⡿⠟⢇⣠⣾⢛⣽⣶⣣⣴⣿⣿⣿⡿⢿⣤⠾⠿⣿⣿⣷⣰⡸⣿⡏⡋⠀⠀⠀⠀⠀⣀⡘⣄⡈⠿⠿⠂⠀⠀⠀⠀⠀⢠⣤⣴⣿⣮⡿⠿⠷⠶⠿⣦⣿⠁⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀⠀⡖⠀⠀⠉⢿⣭⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢃⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣦⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⣠⠶⠛⠉⠳⣿⣿⣿⣿⣯⣭⠿⡿⠃⠀⢳⣏⣿⣿⡞⢹⣧⠁⠛⢧⡇⠀⢀⣀⡠⢊⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⣼⠛⣿⠀⢴⠀⠀⠀⢸⣿⣃⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⣏⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠀⠈⢆⣠⣤⣤⣤⣴⣶⣶⣶⠦⠤⠤⠄⠀⠈⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣰⣿⣿⣿⣫⣭⣿⢣⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⡴⠾⣶⣭⣤⢶⣶⣿⢿⣿⠙⣿⣿⣿⠏⠀⠄⠀⣀⣾⣿⠉⢹⣴⣋⣿⣄⡤⠤⣷⠆⢉⠌⢠⣾⡇⣟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣹⣿⣸⡇⣀⡉⠀⠀⠀⣞⣿⣿⡄⠀⠀⣿⣿⢿⡄⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠈⢿⡛⢆⠙⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠼⠿⠿⠟⠛⠿⠍⢍⣠⣤⣬⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⡈⠉⠉⠻⣿⣿⣿⣼⣤⣤⣦⡖⢉⣿⡟⠋⣭⣴⣃⣀⣴⣿⣦⣶⣯⣾⡇⣤⣸⣿⣿⣿⠁⣀⠀⠀⠀⣽⣿⠇⡠⠴⢿⣾⣯⠉⢺⡿⢹⡠⠂⣴⠿⢿⣇⣹⢹⠀⠀⠠⡀⠀⠀⢀⣶⠟⠋⠉⠉⠉⠙⣿⣉⡓⠲⢴⣿⣜⣯⣳⠀⣴⣿⣿⣍⡀⠀⠀⠀⠀⠁⠀⠀⠀⡠⠀⠀⠘⢷⣀⡇⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣤⢸⢷⡾⣶⣤⣦⣀⡀⠀⠀⠀⠀⠙⠓⠛⠳⣦⣶⣴⣶⡤⢄⣠⡞⡀⢀⠐⡀⠀⠀⢹⣯⢻⡿⠟⠻⣿⣷⠾⢿⣇⣼⠉⢰⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣷⣿⣿⣿⠄⠀⠁⣰⣾⣿⣾⣾⣤⡤⠚⠛⠛⠷⣾⢉⣻⣤⣼⠋⠈⢸⣿⣿⠸⠀⠀⡴⣃⣴⡾⣿⣿⣷⢦⡀⠀⠀⠀⣿⡬⠟⠗⠚⠿⣿⣿⢿⣯⡛⣿⡿⠉⠀⠀⠀⠀⠇⠀⢀⡄⠀⠀⠀⠀⠀⠙⣧⡠⠄⢐⡄⠀⠀⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡣⠃⠀⠀⠈⠓⠘⠋⠙⠛⠿⢷⣤⣄⠐⠄⡆⠁⠉⠙⠛⠃⠀⠋⠁⠑⡀⠁⢣⠀⠀⠈⣿⣼⣿⣶⣷⣾⣯⠀⢸⣿⣿⡀⢸⣏⣿⣿⠿⣿⣿⣿⣿⣇⢀⣽⣿⣿⣿⠀⠀⣸⣿⠿⠞⠋⠉⠀⠀⠀⠀⠀⣀⣿⣿⠉⣿⠀⠀⠀⢰⢹⢻⢸⣂⠜⢑⣿⣿⣻⣿⣵⣿⡇⣿⣄⢀⢀⣿⡇⠀⠀⠀⠀⠘⠻⣴⡏⢳⣼⣀⡀⠀⠀⠀⠰⠀⠀⡇⠀⢀⠀⠀⠀⠁⠀⢿⣶⠻⡿⡃⠀⠃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠳⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⠊⠀⠀⠉⠠⣄⣿⡟⠻⡏⢱⣀⣿⣄⣼⠟⡟⢻⣏⣯⣿⣶⣾⣫⣽⣿⣿⠋⢁⣾⣿⠉⡿⠀⠂⠉⠀⠀⠀⠀⢀⠀⢠⣤⣞⣟⣻⣿⣿⠀⣾⡀⠒⠀⠀⢿⢸⣼⣧⠚⠉⣿⣿⣻⣿⣿⣿⣷⣿⣿⣄⠘⡆⢹⣤⠔⠒⠒⠂⠀⠙⣧⣼⡇⠉⣿⡀⠀⠁⠲⠃⡐⠁⠀⣸⠀⠀⢠⣇⠀⠀⣿⣿⠿⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢰⣆⡀⠀⠀⠈⠑⠀⠀⠀⠀⡠⠈⠀⣀⣤⡶⠦⣀⠈⠿⣧⠼⣷⣿⢯⠏⣹⣸⡆⣧⣿⣿⣿⠟⠟⠋⠉⠀⠀⢠⢤⠟⠋⡿⣸⠃⠀⠀⠀⠀⠀⠀⠒⠉⠀⠟⠙⡠⢻⣿⣿⣿⠀⣿⡇⠀⠈⣃⣸⣼⣏⠙⢶⣴⣿⣮⣽⡟⣿⣿⣿⣿⠋⠛⣦⣿⠛⣧⢧⡄⠀⠀⡄⠀⠘⣧⠑⣰⠟⠇⠐⡀⠀⠀⠇⠈⠂⢸⠀⠀⠀⣸⡀⠀⠙⣷⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⠉⠈⠐⠹⣿⠉⠐⠿⠅⠀⠈⠉⠉⠀⠨⠄⠠⠆⠀⠀⠀⡠⠊⠀⠀⠀⠡⢰⣍⣁⠶⠧⠀⠰⡠⣹⣿⣸⠘⢿⠃⣇⣿⣘⡾⠃⠀⠀⠀⡀⠀⠀⣾⡿⠀⣸⢧⠃⠀⠀⠀⣠⠤⡤⠀⠀⠀⡰⠂⡜⠀⡏⣿⣿⣿⡄⡿⠁⠀⠀⣧⣽⡿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠀⠀⣿⢻⣧⠻⣆⢳⠅⠄⠀⠀⠀⠹⣘⠣⢤⣜⣷⠈⢶⡂⠀⠀⠀⠠⠀⠀⠀⡭⠠⠀⠀⢸⢟⣉⣥⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠀⡀⡀⠑⠳⠶⠤⣉⡀⠀⢀⠴⠶⣿⡚⠓⠒⣤⡄⠐⡦⢡⣖⠀⢐⣮⣖⣤⠔⠒⢿⣿⠀⠀⠁⠀⠐⢘⣛⡻⢇⣼⣿⣿⣿⠋⠀⠀⠀⠀⠙⠃⠛⢲⣿⣇⡀⣿⡞⠀⠀⠀⠀⠀⠀⠀⢀⡀⣴⠖⠈⣀⡞⠁⢻⣿⣿⡇⠇⢀⡠⠞⢋⣡⢴⡾⠿⠿⠿⠿⣿⣿⣿⡿⠟⠋⠁⠀⠀⣿⣸⣿⠀⣹⣆⠀⠀⠀⠀⠀⠀⠸⡍⠐⢿⣿⡵⠀⣱⢀⠀⠀⠀⠆⠀⠀⡇⢠⠤⠴⠿⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣧⠘⠥⠤⠤⠔⠂⣴⡄⢹⢿⠀⠀⠀⠀⠀⠉⠉⠛⢦⢴⡋⣩⠽⡟⢿⠟⠀⠀⠀⠀⠈⠁⠀⠐⠄⠠⡀⠻⣿⣶⣤⣉⠛⠁⠀⠂⠀⠀⠈⠀⠀⠀⢈⢹⣷⣷⡿⠁⠀⠀⠀⠀⠀⠀⢐⠃⣠⠏⢀⡴⠋⠧⣴⣿⣛⣍⣧⡗⣡⣴⣾⣿⣿⡿⠃⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⠀⠒⡿⢧⢆⠀⠀⠀⠀⠀⠀⢹⣆⠉⣿⣟⡵⣯⡤⡡⠀⠀⠀⡤⠀⡹⢃⣤⡖⢊⡔⠀⢀⠞⠉⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣧⠀⢤⠤⠖⠾⣄⣾⠋⠉⠹⠤⣀⠀⠀⠀⢀⣤⡿⠣⡀⠀⠀⠈⠉⠀⠀⠀⠊⢵⣄⠀⠀⠀⠇⠀⠻⣄⠘⢿⠮⡙⢿⢷⣶⣄⡀⠂⠀⡀⠀⠀⢈⠹⣿⣿⠃⠀⠀⠀⠀⠀⠀⢠⠆⠠⠃⢠⠟⠀⠀⣰⣿⣿⡟⠿⠉⢹⣌⠛⣿⠟⠉⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⠀⢠⠃⠀⠀⣿⣿⣾⡂⡷⠈⢎⣀⡀⠀⣀⡀⠀⢀⠻⣆⣰⣏⣿⣿⣗⣇⢱⣶⠀⣡⡎⣀⠜⠋⣀⡈⠀⡆⠁⣄⡠⢊⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⣿⡆⠀⢑⣶⡤⣈⠙⣶⠃⡈⠑⠛⠲⣆⣴⣮⠿⠃⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⡷⠋⠘⢶⣌⠣⡈⠶⣻⣿⣿⣃⠀⠀⠀⡀⢄⡎⠰⣿⠃⠀⠀⠀⠀⠀⠀⢠⠏⠀⢣⣴⠋⠀⠀⠀⣿⣿⣿⣿⢄⠀⠀⣉⠗⠁⠀⠀⠀⠀⠀⡇⠐⢺⣿⣿⣿⣿⡀⢸⠀⡀⠀⣿⣻⠈⡧⣸⠀⠘⡅⡨⠊⠁⠀⠀⠀⠀⠻⣧⣘⢻⣿⣿⡿⠊⢹⣧⡀⠀⠠⠶⠛⡡⢃⢢⠸⣞⡡⠖⠛⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣷⡤⠈⢧⡀⠀⠀⠉⠀⠀⠀⠏⡑⠛⢿⠛⠀⠀⠐⠀⠈⠄⠀⢤⣀⣠⡄⣄⣀⣤⣠⣿⣿⣶⠃⠀⠀⠈⠻⣷⣰⡶⠿⣽⡗⠚⠀⢄⣸⣧⢤⠗⠙⠇⠀⠀⠀⠀⠀⠀⠀⡜⠀⣸⣿⠁⠀⠀⠀⣰⣿⣿⣿⣿⣾⣿⣿⣿⠄⠀⠠⠀⠰⠀⢤⠁⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠴⣿⣟⣿⠃⣴⠀⡄⢹⠀⠀⠀⠀⠀⠀⠀⠀⢈⢫⡹⠿⠿⠟⠋⠉⠀⡛⣮⡁⠤⠐⢁⠁⢐⣊⠁⠀⡆⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⣿⣧⠀⠀⠀⢀⣀⡀⠀⣄⣠⡎⠀⠀⠀⠀⠀⡀⠠⣀⣀⠚⢄⡶⠦⠽⣷⣿⣽⣿⡯⣿⣿⣿⣿⣦⡀⡄⠀⣨⣏⣿⡀⠢⠗⠠⠴⢍⡉⠋⠊⠁⢸⠠⠄⡀⣀⡀⠀⠀⠘⠁⢠⡏⡸⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠒⠀⠀⡆⠀⡈⣿⣿⣿⣿⣧⠀⠀⠀⠀⣿⣋⣏⠉⢿⣃⠁⠤⢷⠀⠀⠔⠂⠀⠐⢤⡈⠀⠙⢖⠆⠀⠀⠀⠀⣸⢋⡿⡆⠠⢻⠀⡿⠟⠀⠘⠣⡈⠄⠀⠀⠀⠀⠀⠀⢀⠅⠀⠀⠀⠀⠀⠐⠀⠀⠀⠄⠀⠙⠳⠆⠀⠀⠰⠂⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⠀⠐⢶⠛⢅⣀⠙⣿⡳⠀⠀⠀⠀⠀⢰⠟⠛⠀⠚⡲⠚⠗⠀⢰⣴⣿⣟⠛⠒⠟⠏⠈⠙⠿⣿⣦⣨⣼⣽⡿⣷⣄⠁⠀⠀⠲⡄⢀⡒⢠⣁⠄⣠⡔⢸⣄⣷⠪⣲⡀⠈⣠⠇⢀⣴⣿⣿⡿⠿⠟⣿⣿⣋⣤⣶⠤⠀⠀⠀⠀⠐⠀⢰⠀⢆⠑⢿⣿⣿⣿⣿⠀⠀⠒⠠⣿⠀⢿⠀⢸⡇⣰⣦⢊⢧⡀⠀⠀⢀⣀⣀⡈⢴⠒⠈⢻⣦⣤⡤⢞⡽⠀⡧⣣⠀⠀⠀⠀⠀⠀⠀⠀⢤⠰⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣠⣰⣥⠀⠀⠀⠀⠀⠀⠐⠤⡄⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡿⠄⡠⠚⠀⠐⢄⣜⠁⠀⠐⢦⠀⠤⠴⠉⠐⢄⠀⠀⢰⡄⠈⢄⣼⠛⠓⠇⢤⣀⡄⠀⠀⣤⣤⡻⠻⣄⠙⢿⣿⣿⣿⡀⠀⠀⢀⡈⠂⣘⠾⠧⠄⠀⠿⠂⠀⠀⠷⠏⣏⢫⣭⣶⡿⠛⠉⠀⢀⣤⡾⢋⡩⠿⠋⠁⠀⠀⠀⠀⠀⠀⠉⢾⡀⠀⠀⠸⣿⣿⣿⣿⡆⠀⠀⠀⡟⠀⣸⢀⡃⠈⢠⡋⡌⠘⢗⡤⠎⠁⠀⠀⠠⠀⠡⠄⢸⡌⢢⡈⣓⣷⡿⣓⣿⣧⣖⠀⠀⠰⠾⠇⠀⠈⠢⠑⡀⠀⠀⠀⠘⠀⠀⢠⠀⢀⠀⡄⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠠⠀⠀⠀⠀⠁⠹⠀⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⠰⢀⠎⠀⠯⢿⠦⡜⣷⡀⠀⠀⠀⠀⣀⠀⠀⢧⠀⠘⡟⠋⠀⠀⠘⢿⣅⠀⢠⣾⡷⡀⠀⠙⢷⣌⣿⣿⣿⣵⡆⢀⠉⠈⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⣦⣿⠿⢋⣽⣿⡿⣿⣿⣷⠚⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢿⣿⣿⣿⣇⠐⠀⠀⣯⣿⣽⣛⡂⢀⠈⠸⠀⠉⡿⣅⠔⠒⠀⠀⠐⠢⢀⠁⠘⡗⠈⠻⣯⣤⣶⣿⣿⣧⣾⣆⠄⠀⠀⠀⠀⡄⠐⠧⠁⣀⣀⡀⢄⢴⡌⠢⡑⠍⡅⠁⢀⠀⢈⣀⠀⡄⢀⠀⠀⡀⠀⠆⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⢂⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠟⡃⣀⢢⣼⣓⡞⠀⠀⠀⡰⠀⢇⠘⣿⠀⠀⠀⠀⠈⠲⠤⡈⡆⠀⢘⣄⣤⠀⠀⣸⣿⣖⢾⣿⣿⡿⠀⠀⠈⢏⣷⣏⢉⢹⠙⠂⡝⢃⠃⠀⠀⠀⠀⠀⠀⠀⠘⣄⣦⠖⢦⠸⡽⣿⣿⣷⠙⠀⠐⠨⡀⠀⣀⣤⠤⠖⢂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠟⢻⡧⡽⠀⠀⣧⣤⣬⣧⡼⠂⠀⢀⠔⠊⠀⢳⡀⠀⠀⠀⠀⠀⠀⠑⠒⡟⠀⠀⠈⠻⣦⣿⡿⢛⣯⣹⣧⡀⠀⠀⠈⢀⢠⠀⠡⠙⡏⠀⠈⠿⠃⡈⠀⡐⡄⠒⠘⡄⠸⣄⠀⣅⣸⡀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢨⠀⠀⢀⠀⠫⣽⡞⠀⢴⣦⣤⣍⢐⠉⣭⠿⡄⠀⠀⠀⠀⠀⠀⠀⢘⠀⢻⣷⡜⠶⠚⡟⠁⣾⣿⡟⢅⣄⣼⡤⠄⣀⠳⡏⠀⢺⠳⠤⣈⠉⠀⠄⠀⡀⠀⠀⠀⠀⠀⠤⡈⠑⢼⠦⠀⢘⢿⣿⣏⠁⠀⠤⠘⠀⢸⠟⠩⠀⢌⠁⠀⠀⠀⠠⠀⠂⠀⢀⠠⠀⠀⣷⣾⣿⠛⠃⠀⠀⡗⠮⣿⣏⡃⠀⠈⠀⠁⡀⠄⢈⠡⠀⠀⠀⠀⠀⡀⠀⠘⡃⠀⠀⠀⠀⠀⠙⢦⠀⢉⣿⠿⣷⡞⠀⠐⢟⠟⢡⠄⢧⡈⠁⠀⠂⠈⠁⠈⠁⡀⢼⡆⡋⠀⡨⠁⠈⠈⠉⠁⠈⠁⠀⠀⠀⠀⡠⠶⠂⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⢀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡶⠷⢶⠾⠿⠿⠿⠿⠿⠿⡿⠶⠶⠶⢶⢶⠦⠤⠤⠤⠤⠤⠤⠤⢄⡀ ⢠⡤⣤⢤⣤⣶⣶⣶⣲⣶⣶⣶⣶⣲⣶⢿⢸⠙⠒⡶⢲⢦⠖⠖⡾⡶⢶⠗⢶⣖⣶⠖⠒⠒⠒⢠⣶⣶⣶⣶⣶⢶⡾⠿⡿⡛⣿⠿⠿⠿⠍⠉⠉⠉⣩⡍⣻⡇ ⠈⠉⠀⠉⠉⠛⠛⣛⣿⠛⣛⡛⣿⣿⣿⣾⣼⡧⣴⣦⣤⣧⣠⣦⣭⣦⣤⣴⣿⣿⣿⣟⣫⣿⣽⣽⡟⠞⠈⠛⢃⣾⣷⢾⣾⡷⣶⣦⣼⣽⣽⣷⣤⡿⣿⢿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⢻⣿⠿⡿⣿⣿⣿⣶⣶⣶⣶⣷⣊⣁⣠⣌⣉⣉⣿⡼⢹⣗⡀⠀⠀⣤⣼⡟⠀⠸⣟⣾⢏⠀⠀⠀⠀⢸⠃⣯⠿⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁⢸⣿⣿⣶⣶⣶⢻⣿⣿⠟⠉⠉⠎⣹⡦⣀⢀⣠⣦⣷⡿⠟⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣾⣿⡿⠀⠀⠀⠈⢆⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣷⣿⠇⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
ᡕᠵ᠊ᡃ່࡚ࠢ࠘ ⸝່ࠡࠣ᠊߯᠆ࠣ࠘ᡁࠣ࠘᠊᠊ࠢ࠘𐡏 三三ᕕ( ⌓̈ )ᕗ
⢄⡀⠀⠀⡤⡤⠤⠤⠤⣄⣤⣄⠀⠀⠀⠀⠀⡴⡆ ⡴⣟⡉⣉⡭⢭⡟⢻⢻⠛⠛⡗⣒⡿⠿⠭⠷⠆⠀ ⠘⡇⠀⢰⣇⡼⠃⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⣇⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣤⣤⣀⣄⣤⣠⣤⣤⡤⠤⠤⢤⣀⣤⡀⠀⠀⣰⠀⠀ ⢰⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⠿⣿⣿⣿⠿⠧⠴⠛⠛⠒⠛⠉⠉⠋⠉⠉⠉⠉⠙ ⢸⣿⣿⠿⠏⠉⠁⠀⢰⣿⠁⠀⠉⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⠀⠀⠀⠈⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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