⠭⠵⠖⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⡠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀
⠀⠂⠀⠀⠀⠀⠀⢀⡀⠀⠀⠁⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⠀⠔⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠳⢦⣀⠀⠀⠀⠁⠀⠈⣐⠲⠶
⠀⠀⣀⠠⣒⣼⡵⠋⠀⠀⠀⡴⢃⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠣⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠀⠐⠁⠢
⡶⠞⠊⣽⡵⠟⠁⠀⠀⣀⡞⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⠑⢄⠀⠀⠀⠀⠉⠒⠤⢀⠀⠀
⠀⣠⢟⠟⠁⠀⠀⢀⠄⡼⢀⠀⠀⢠⠀⠀⡔⠀⠠⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠁⠢⡀⠀⠀⠠⢀⣀⠀⠀
⡼⠡⠂⠀⠀⣀⡴⡱⢊⠁⠀⠀⠀⠂⠀⡜⠀⣆⢠⣼⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⡀⡀⠀⢦⡀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠣⡐⢄⡑⠂⠀⠀⢹⣿⢟
⠀⠁⢀⠤⢊⠏⡰⢁⠊⠀⠄⠀⠀⠀⢰⠃⠘⢨⣽⣿⠀⣸⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠐⠀⠤⡀⠀⠣⠂⠀⠀⢆⠀⠀⠐⡄⠀⠁⠂⢢⠀⠀⠀⠀⢀⠑⣄⠀⠀⠻⣦⡈⠢⠈⠢⣀⠢⡀⢣⠑
⣠⠔⠁⠠⠂⠐⡡⠃⢀⠔⠀⠀⠀⠀⡎⠀⡇⡞⣿⣿⠀⢿⣼⢠⣸⣇⠀⠘⣤⡀⠀⢃⣆⠐⡌⣶⠄⠀⢷⣀⠀⠈⢷⣄⡠⠽⣴⡀⠀⠳⡃⠀⠀⠈⠪⢢⡈⢵⣄⠀⠹⡷⡄⠀⢡⡙⢇⠠⠀⢣
⠁⠀⠀⠀⠰⡴⠁⠀⠙⠀⡄⠀⡄⢀⠇⢀⢁⣿⣿⣿⡾⡞⣿⢸⣿⡿⡄⠀⢹⢳⠀⠘⡼⣆⢸⣼⣿⣦⠈⢿⣧⠀⠈⢿⣷⣄⠹⣧⡀⠀⠙⣄⠠⡀⠀⠈⢳⣄⢻⣷⣤⡙⣌⢦⡀⢳⣮⡳⣤⠀
⠀⠀⠀⢀⡖⠁⠀⠀⠀⠸⠀⠐⠇⡀⢀⣾⣼⣿⣿⣿⣿⣧⣿⡆⣿⣷⣷⡀⠈⣿⣧⠀⢷⣏⢦⢹⣼⡿⣷⣌⢟⢷⡄⠘⣿⣿⣦⡙⣷⡀⡀⠘⣄⠩⣂⠀⠸⣿⠿⠷⠀⢀⡝⠾⢟⢄⠻⡏⠛⠊
⠀⠀⠀⡜⠑⠀⠀⠀⠀⠀⢀⠜⢠⠇⣿⣿⣿⡏⢹⢹⣿⣿⣿⣽⣿⡟⣿⣷⠀⢹⣿⢧⢸⣿⡀⣳⣯⢷⣟⣿⣯⣿⣻⣦⣹⣍⣿⣿⣾⣷⣄⠀⠺⣆⠹⣦⣷⣽⣰⣦⣀⠹⣧⠀⢸⣾⣏⠙⠄⠀
⠀⠀⢠⠅⠀⠀⠀⠀⠀⠀⡞⠀⡜⢰⢹⣿⢻⣇⠀⠈⣿⣿⣿⣾⣿⣇⠻⡇⢣⢸⣿⠈⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣿⠿⣿⡿⣿⣿⣦⡀⠣⠣⡸⢷⣽⣿⣞⢿⠀⢻⠀⠀⣏⢿⡄⠀⠀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⢰⠁⢀⠁⣸⣿⡁⠆⢻⣆⠀⠙⢿⣿⣿⣿⡈⠀⠻⡌⢻⣏⠆⠼⢿⠁⠀⢿⣿⣿⣿⣿⣿⡿⠁⠀⠈⣰⡟⠃⠀⣹⣿⣝⣠⣷⠉⢢⡝⠘⢻⠟⠀⣼⠀⠀⣿⢦⢻⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣼⠀⢸⣿⣷⠀⠀⠻⣦⡀⠀⠉⠉⠀⠁⠀⠀⠁⠈⠻⠀⠀⠈⠀⢀⠈⠙⠻⠿⠟⠋⠀⠀⣠⡾⠋⠀⠀⠐⢻⣿⡍⣽⡇⣀⠼⠑⡠⠐⢀⠌⠈⢀⡴⠋⠀⠈⠋⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠰⢸⠘⢹⣧⠀⠀⠈⠻⠷⡶⠤⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣶⣶⣤⣤⣶⡶⠟⠋⠀⠠⠐⠀⠀⣸⣿⣇⣿⡿⠤⡤⠂⢀⡴⢃⣠⣾⡍⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⠀⢹⢿⡄⠀⠀⡆⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢲⣾⣿⣿⣿⣿⡶⠒⠀⠀⠈⠁⠐⢤⡀⠀⣿⣿⡿⢿⠴⠒⠒⢛⣴⢻⡋⠉⢿⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⣷⢀⠐⠀⠀⠀⠀⠻⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠋⠉⠁⠀⠀⠀⡇⠀⠀⢠⣄⣤⣿⡇⠀⠀⠀⣠⡞⠹⠋⠸⠀⠀⠀⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠃⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⠀⠀⠰⠆⠀⠀⠁⠀⡀⣸⣿⣟⣿⣿⡷⣶⠏⣿⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⢰⡇⠀⣀⣴⠟⠀⣿⣿⣿⣿⣿⣧⣿⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢?