⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠹⡁⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⠀⠀⠀⠘⡄⠁⠀⠀⠀⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⣧⠀⠀⠘⡀⠘⣄⢣⣠⠀⠀⢠⠆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⡇⡇⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢹⠀⠀⠀⢣⢀⢹⣮⡇⢀⡴⡏⠀⠀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣼⣷⡇⠀⠀⢾⠀⠀⡆⠀⠀⠀⠀⢰⡀⠀⠀⠀⣧⠀⢀⡨⡆⠀⠀⢰⠸⠀⣿⣿⣥⠄⠁⠀⠀
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢠⣴⠇⠀⢰⠉⣿⡇⠀⠀⡿⠀⠀⣿⡀⡀⠀⠀⢸⡇⠀⢀⠀⣿⡏⠁⠀⡇⢸⠀⢸⠘⡀⠉⣻⢎⢦⠀⠀⠀
⠀⠀⣰⢻⠄⠀⠀⠀⠀⠀⠸⡟⠀⢠⠃⠀⣿⣇⠈⠁⢹⡇⠀⢿⣿⢻⠈⠀⣿⡇⠀⣼⠀⣿⣤⣦⣾⡇⣸⠀⢸⢰⣇⣤⣿⠈⣆⢣⡀⠀
⠀⢀⡏⠺⡄⠀⠀⠀⠀⠀⠇⢣⢠⠏⠀⠀⠹⠉⣀⣤⣾⣷⣶⣾⣯⣿⡀⠀⣿⡇⠀⣯⠴⢻⣿⣏⢰⢃⡿⢀⣿⣿⢿⢻⡟⠀⡏⢆⢳⡀
⣾⣼⡀⠛⣇⡆⠀⠀⠀⠀⠘⡈⣿⠒⠲⢿⠋⠉⠉⡿⢛⣿⠛⠋⠉⠉⠁⠀⠉⠀⠀⠁⠀⣼⣿⡏⢸⣾⠈⠉⠁⠿⠀⢸⠃⢀⠃⠘⡄⠱
⢹⡟⠣⢤⣹⠘⠀⠀⠀⠀⠀⢱⡸⡀⠀⠙⠷⣄⡀⠹⣌⣋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠋⠀⣾⣿⡄⠀⠀⠸⡀⡜⠀⢸⠀⠀⠸⡀
⠈⣿⡄⠀⠀⠙⣧⠀⠀⠀⠀⠀⢳⣳⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣷⠀⠀⠀⢷⡇⠀⣾⠀⠀⠀⢻
⠀⢹⡇⠀⠀⠀⢹⢆⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢀⣿⡘⢿⣇⠀⠀⠈⡇⠀⡇⠀⠀⣠⣿
⠀⠈⣷⠀⠀⠀⠘⣎⢣⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡸⢻⣣⠀⠻⣆⠀⠀⠸⣶⡇⢀⣼⣿⣿
⠀⠀⢻⡀⠀⠀⠀⡏⢢⠣⡀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⡴⠁⠀⠳⡃⠀⠹⣆⠀⠀⠹⡷⣿⣿⣿⣿
⠀⠀⠸⡇⠀⠀⠀⢸⠀⢻⣷⡀⠀⠀⠀⢀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⣻⡿⠷⠶⠆⠀⠱⡄⠀⠘⢆⠀⠀⠱⡘⢿⣿⣿
⠀⠀⠀⣷⠀⠀⠀⠘⡄⠀⣿⢿⣄⠀⠀⠀⢣⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠉⢠⡞⠁⠈⠢⡀⠀⠀⠀⠈⢦⠀⠀⢣⡀⠀⠘⡄⠹⡏
⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⣿⣎⢟⢆⠀⠀⠀⠳⡈⢦⣄⣀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠿⢂⡀⠀⠱⡄⠀⠀⠀⣸⠑⢄⠀⠁⠀⠀⠘⢆⠈
⡆⠀⠀⠀⡇⠀⠀⠀⢰⠀⢸⣿⡎⢆⠳⡀⠀⠀⠱⡈⢻⣿⣿⡖⠒⠤⠤⠴⠋⠀⢀⣠⣿⣷⣄⠀⠘⡄⠀⢀⡇⠀⣾⣷⣤⡀⠀⠀⠈⢣
⣹⡄⠀⠀⢰⠀⠀⠀⢸⠀⢸⣿⣿⡘⣷⡱⡄⠀⠀⠘⣄⠙⢿⡿⢦⠉⡷⠀⠀⣠⣿⣿⣿⣿⣿⣆⠀⠘⣦⣼⠁⣸⡿⢹⣿⣿⡦⢄⠀⠀
⣇⢷⠀⠀⠈⡆⠀⠀⢸⠀⢸⣿⣿⣇⢹⣿⣿⣄⠀⠀⠈⢆⠈⢣⣞⣉⣀⣀⣼⢿⣿⣿⣿⣿⣿⣿⣆⠀⢹⡟⢠⡿⠃⢸⣿⠏⠀⠀⠙⠦
⣿⡜⡆⠀⠀⢱⠀⠀⢸⠀⢸⣿⣿⣿⠀⣿⣿⣿⡆⡀⠀⠀⢣⠀⠹⡟⢏⣹⠇⡸⢻⣿⣿⣿⣿⣿⣿⣦⠀⢷⣾⠃⠀⣿⡋⠳⠘⢦⠀⠀
⣿⣷⢹⡀⠀⠀⠀⠀⢸⠀⣦⡈⠻⣿⡇⢸⣿⣿⣿⣧⠀⠀⠀⢡⡀⠘⠄⡟⠀⠁⠀⠹⣿⣿⣿⣿⣿⣿⣷⣬⡇⠀⣾⡟⢣⡀⠀⠀⠑⢄
⣿⣿⡆⢷⠀⠀⠀⠀⡘⢀⣧⠙⢆⠈⠃⠀⣿⣿⢿⣿⡆⠀⠀⠀⠱⡀⠘⡿⣄⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠀⠻⣼⣿⡧⡀⠱⡀⠀⠈⠢
⠘⢿⣿⡌⣧⠀⠀⠀⡧⡜⠈⠳⣄⠑⢾⠀⡏⢁⠜⢿⡇⠀⠀⠀⠀⠱⡀⠰⡄⠉⠢⢄⡀⠹⡉⠉⠉⠙⠋⠀⠀⣽⡿⢥⡈⠢⣌⢦⡀⠀