⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ㅤ⠀⠐⡖⠒⠒⠀⠀⠀⣴⡀⠀⠀⠒⠒⡖⠒⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ㅤ⠀ ⠀⡇⠀⢠⠀⠀⢰⣈⣧⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⠀⠀ㅤ⠀⠀⠀⡇⠀⠀⡀⢀⠃⠀⠘⣆⠀⠀⠀⣇⠀⠀⠀⠀⠀ ⠀⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀ㅤ⠀⠈⠉⠉⠉⠁⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢈⢷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⣦⠀⠀⠀⠀⣼⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀ ⠀⠈⢦⣻⡄⠀⠀⠀⠀⠀⣠
⠀⢸⡀⠀⠀⣼⡇⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⣿⡄⠀⠀⠀⠀⣿
⠀⠘⣿⣶⣾⣿⣿⡟⠀⠀⠀⠀⠀ ⠀ ⠀⠀⠉⠉⣿⠀⠙⠀⣿⠀⠀⠈⡇⠀⢸⡇⠀⠈⠀⠀⠀⠀⠀⠀ ⠀ ⠀⠘⣿⣿⡄⠀⢀⣼⡏
⠀⠀⠹⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ㅤ⠀⠀⣿⠀⠀⠀⣿⠒⠒⠒⡇⠀⢸⡗⠒⠂⠀⠀⠀ ⠀⠀⠀ㅤ ⠀⠀⠸⣿⣿⣴⣾⠏⠀
⠀⠀⠀⠹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ㅤ⠀⠀⠿⠀⠀⠀⠿⠀⠀⠠⠧⠀⠼⠧⠤⠤⠀⠀⠀⠀⠀⠀⠀ ㅤㅤ ⠀⠀⣿⣿⡿⠁⠀⠀
⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ㅤㅤ ⢸⣿⡟⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ㅤㅤ ⠀⠀⣾⡿⠀⠀⠀⠀⠀
⢠⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⢤⠤⢄⡀⠀⠠⣤⠄⠀⠠⡤⠀⢤⡤⠤⠤⡀⠀⠠⣤⠤⠤⡄⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⣼⠀⠀
⠘⣷⣄⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⢸⠀⢀⡿⠀⠀⣿⠀⠀⠀⡇⠀⢸⡇⠀⠀⢸⡆⠀⣿⣀⣀⠀⠀⠀⠀⢀⣼⡿⠁⠀⢀⣴⠏⠀⠀
⠀⠈⠛⢷⣦⣤⣤⣼⣿⣷⣄⠀⠀⠀⢸⠀⠙⣦⠀⠀⢿⠀⠀⢀⡇⠀⢸⡇⠀⠀⣸⠇⠀⣿⠀⠀⠀⠀⠀⣠⣾⣿⣧⣴⡾⠟⠁⠀⠀⠀
⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⣦⡀⠀⠚⠂⠀⠈⠁⠀⠈⠑⠂⠁⠉⠀⠈⠁⠀⠈⠁⠀⠀⠉⠀⠈⠁⢀⣴⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀ ⠀ ⠀⢀⣴⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀ ⠀⠀⣠⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣾⡟⠁⠀⠀⠀ ⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣾⣿⠋⠀⠀⠀⠀⠀⠀ ⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⢀⣠⣤⣾⣿⣿⣷⣤⠀⠀⠀⠀⠀ ⠀⣴⣿⣿⣿⣷⣶⣤⣄⣀⣀⣠⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⠶⠿⠛⠛⠉⠉⠉⠻⠿⠇⠀⠀⠀⠀⠀ ⠀⠹⠿⠋⠁⠀⠀⠉⠉⠙⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀