⠀⠀⠀⡌⠀⠀⠀⣰⠁⠈⡇⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⡇⠀⠀⢠⠃⠀⠀⡇⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢑⣦⣤⠒⠚⠺⢍⠉⠉⠉⠀⠒⠒⠚⡦⠤⣀⠀⠀⠀⠀⠀⠀⢀⠀⡇
⠀⢠⠀⠀⢀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣀⠤⠚⠁⠀⠈⠑⢦⣀⠀⠉⠢⢖⣄⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰
⠀⢸⠀⠀⡜⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⡇⠀⠀⠀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⠀⠉⠛⢖⣤⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠘⠀⢰⠃⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠘⣣⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⡀⠈⠙⢳⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈
⠀⠀⣀⡯⠒⠀⠐⠒⠢⠤⡘⡆⠀⠀⠀⠀⠱⣇⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠀⠀⠀⠀⣀⣀⣀⣬⣷⣦⣤⣆⡀⠀⠀⠀⠀⠀⠀⡇⠀
⠔⠋⢸⠃⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠹⣆⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⠿⠿⣿⡿⠋⠁⠀⠀⠀⠀⡇⠀
⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠹⣆⠀⠸⡄⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠁⠀
⠀⢀⡇⠀⠀⠀⠀⠀⠀⠄⢀⣀⡸⡄⠀⠀⠀⠀⠀⠹⣦⠀⣇⠀⠀⠀⠀⢈⡿⠟⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⡇⠀⠀⠀⢀⣀⣀⣤⣤⣤⣬⣹⡄⠀⠀⠀⠀⠀⠘⢷⣸⡄⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠠⠏⠘⡆⠀⠀⠀⠀⠀⠀⠐⠀
⠀⢸⣇⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⡀⠀⠀⠀⠀⠀⠈⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⣿⣿⣿⣿⣿⡿⢿⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢰⠀
⣠⣾⣿⣟⠛⠉⢹⣿⣿⣿⣿⣿⣿⣿⣷⠹⡄⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠋⠀⠀⣀⠰⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀
⠘⠁⣿⣿⣆⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡇⠹⣄⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠉⠓⠴⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⢸⠀
⠀⠀⢿⣜⢿⣧⡀⠀⠛⢻⣿⣿⣿⣿⣿⡇⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀
⠀⠀⢸⣿⣎⠛⠀⠀⠀⠹⣿⠟⠋⠉⠛⡇⠀⠀⠀⠹⣄⠐⣄⡀⠀⠀⠀⠀⠀⠈⠑⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀
⠀⠀⢸⢿⣿⡄⠀⠀⠀⠀⠈⠓⠶⠒⠈⠁⢰⣿⡶⠃⠈⠳⢌⢯⡑⠒⠤⠤⠤⠤⠤⠤⠒⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀
⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠑⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀
⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀
⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀
⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀
⠀⠀⠀⢸⣿⣿⣿⣏⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢸⠀⠀⠀⠀⠀⠸⠀
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⢹⢸⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⡿⠃⣿⢸⠀⠀⠀⠀⠀⣇⠀
⠀⠀⠀⠀⣿⣿⣿⡟⣿⣿⣿⣿⠿⠟⠛⠉⠉⠉⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣞⢣⢟⣷⣮⡟⠁⠀⡇⢸⠀⠀⠀⠀⠀⢿⠀
⠀⠀⠀⠀⣿⣿⣿⣇⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡿⠋⣠⣿⣿⠟⠉⠀⠀⠀⡇⢸⠀⠀⠀⠀⢰⡸⠀
⠀⠀⠀⠀⣿⣿⣿⠋⠀⠀⠀⣀⣀⠤⠴⠒⠚⠛⠃⠻⡟⠋⢩⣷⣶⣤⣀⣀⣀⣀⣤⣶⣿⡿⠿⠿⠛⡁⣭⡿⠋⠀⠀⠀⠀⠀⢀⡇⣾⠀⠀⠀⠀⠸⡇⠀
⠀⠀⠀⠀⣿⣿⠏⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢿⢯⡿⣆⠀⠠⠛⠉⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⠀⣷⠁⠀