⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣀⣀⡀⢀⣀⣀⠀⠀⣀⠀⣀⣀⡀⢀⣀⣀⡀⣀⣀⣀⠀⠀⣀⠀⣀⠀⣀⠀⣀⠀⣀⡀⠀⣀⡀⠀⢀⣀⠀⢀⡀⠀⣀⠀ ⣀⢀⣀⣀⡀⣀⠀⣀⠀⠀⠀⠀
⠀⠀⠀⢸⣯⣽⠇⢸⡧⠄⢀⠀⣿⠀⣿⠤⠄⣿⠁⠉⡃⠀⣿⡇⠀⠀⣿⠶⣿⠀⣿⠀⣿⠀⣿⢷⣰⢿⡇⢀⣿⢻⡄⢸⡿⣦⣿⠀⣿⠀⢹⡏⠀⠘⣷⠏⠀⠀⠀⠀
⠀⠀⠀⠘⠃⠙⠃⠘⠓⠒⠙⠛⠛⠀⠛⠒⠂⠙⠓⠛⠃⠀⠛⠃⠀⠀⠛⠀⠛⠀⠙⠛⠛⠀⠛⠈⠋⠘⠃⠚⠋⠉⠛⠘⠃⠈⠛⠀⠛⠀⠘⠃⠀⠀⠛⠀⠀⠀⠀⠀
⠀⠀ ⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀ ⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣀⡀⠀⠀⠈⣿⡷⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀ ⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣷⡆⠀⢀⣾⡿⠟⠀⠀⣾⣿⡇⠀⠀⠀⠀⢀⣼⡿⠿⠀⠀⠀⠀⢀⣤⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏⠉⠁⣴⣿⣿⠇⠀⠀⠀⣿⣿⣇⠀⠀⠀⣴⣿⣿⡗⠀⠀⠀⠀⣴⣿⣿⠏⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣴⣿⣿⣿⡀⠀⠀⢿⣿⣿⠦⢄⡀⠀⢹⣿⣏⠳⠀⠀⠹⣿⣿⡷⠤⢤⠀⣴⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡿⠂⠀⠀⢿⣿⣿⡉⠙⠆⠀⠸⣿⣿⣆⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⢿⣿⣧⡀⠀⠀⢿⣿⣿⡄⠙⠃⠀⠀⣠⣶⣾⣿⠗⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣴⣿⡿⠛⣿⣧⡀⠀⠀⠘⣿⢿⣷⠀⠀⠀⠀⣻⡟⣿⡆⠀⠀⣸⡏⢹⡇⠀⠀⠀⣸⡿⢻⣷⠀⠀⢘⣿⢿⣷⠀⠀⢠⣾⣿⠟⢻⣿⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣸⡿⢻⡆⠘⠻⡟⢦⠀⢸⠏⢸⣿⠀⠀⢀⡾⠋⠀⣿⠁⠀⠀⡿⠀⢸⡇⠀⢀⣼⠋⠀⢸⡇⠀⠀⣸⠏⠸⡟⠀⠀⢀⣿⠟⣷⠈⠛⢿⠳⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠧⠀⠸⠧⠀⠀⠷⠀⠀⠿⠦⠌⠿⠤⠀⠙⠧⠀⠀⠿⠦⠄⠀⠿⠤⠸⠷⠄⠈⠳⠄⠀⠸⠷⠤⠀⠟⠢⠤⠿⠤⠀⠻⠅⠀⢿⡀⠀⠘⠆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣟⣻⡆⢸⣟⡋⠛⣿⡟⢻⣿⠀⣿⠀⣿⣛⣷⢸⣿⣄⣿⠀⠘⢻⡟⠃⣴⠟⠛⣷⠀⠀⣾⣧⣠⣿⡇⣴⠟⠛⢷⡄⣿⣦⣸⡇⣿⣤⡟⠁⣿⣛⠃⠀⠀⠀
⠀⠀⠀⢸⡏⠻⡄⢸⣧⡤⠀⢿⠇⠈⠿⣤⠿⠀⡿⠹⣧⠸⡇⠙⢿⠀⠀⠸⡇⠀⠻⢦⣴⠟⠀⠀⡿⠘⠟⠸⡧⠙⢧⣤⠾⠁⣿⠈⢿⡇⢿⠛⢷⠄⣿⣥⡄⠀⠀⠀