⠀⠀⠀⠀⠀⢠⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣶⣿⣿⡟⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢻⣿⣿⣿⣯⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣼⣿⣿⠿⠛⠛⠛⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⡟⣿⣿⡟⠀⠀⠀⠀⠀⠀⠙⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡿⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠳⠝⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⠇⠀⠀⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡹⢳⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣾⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⢹⡀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⡿⠃⠀⠀⠀⠈⠙⠛⠓⠒⢦⡄⠀⠀⠀⠀⠀⢻⡜⣧⠀⠀⠀⠀⠀⠀
⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⢷⣿⠀⠀⠀⠀⠀⠀
⠀⠀⣿⠀⡄⡀⠀⠀⠀⠀⢁⣠⣀⣦⠀⠀⠘⢧⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀
⠀⠈⠻⠿⠷⠀⠀⠀⠀⠾⠿⠿⠛⠁⠀⠀⠀⠈⢧⠀⠀⠀⠙⡇⠀⠀⠀⠀⠀
⠀⢰⣆⠀⢠⡄⢠⣀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠘⢧⠀⠀⠀⣷⠀⠀⠀⠀⠀
⠀⠘⣿⡄⠈⢳⣟⣋⠀⠀⠀⠀⢰⡉⠉⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀
⠀⠀⠹⣿⣷⣾⣿⣿⣤⣤⣐⣤⣾⡷⠖⠶⠂⠀⢀⡾⠀⠀⠀⢸⡄⠀⠀⠀⠀
⠀⠀⠀⢻⣿⡟⠛⠂⣉⠙⠉⢙⣧⡤⠀⠀⠀⠐⠉⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀
⠀⠀⠀⠈⢿⡛⠶⠤⢬⣤⣲⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠈⢻⡄⠀⠈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⡇⠈⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⢀⣠⡇⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣴⢿⡅⠀⠀⠰⠧⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⢯⣉⣽⣷⣤⣀⠀⠀
⠀⢀⣴⢻⣿⣿⡇⠰⣇⡀⠀⠀⠀⠀⠀⢀⣼⡿⠁⠀⢠⣾⠻⣯⢤⡈⠻⣷⡄
⣀⣾⣿⣼⠋⣾⣧⢀⣿⣿⠀⠀⠀⢀⣴⠟⠋⠀⢀⣴⡿⣻⣾⠻⣦⣥⣾⣿⡇
⠙⠏⠋⠀⠰⢿⣿⣿⣿⣿⣦⣤⡞⠋⠁⠀⢀⣴⢿⣿⣿⠟⠉⠀⠙⢿⡿⠿⠁
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡟⠛⠉⠉⠉⣹⡿⢿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡿⠻⣿⣿⡻⣿⣦⣀⣼⡟⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⡷⢀⡀⣿⣟⠛⠿⠿⢻⣇⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣼⣏⢘⣛⣿⣿⠀⠀⠀⠀⣿⡄⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠐⠛⠷⠤⠴⠞⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀