⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠖⣲⣤⣴⠶⠲⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⡴⣾⣿⣿⣽⡿⠍⣦⠝⠣⡤⢈⣋⣍⣷⣿⣷⣲⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣧⡿⠿⠿⣿⣿⣧⡀⢙⣷⠶⣿⢿⣻⠿⠿⣹⣎⣿⣷⡹⢗⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⣭⠷⠞⠛⢛⣿⡟⠉⠉⢘⣽⣾⢠⣾⣶⡿⣭⡙⢿⣿⡷⠦⣝⡆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣴⣿⣿⣿⣾⣿⣿⡿⢻⣿⣶⡞⢸⣿⣿⡿⢿⣿⣿⣿⣷⡜⣿⣿⡿⣯⠙⠇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣾⣿⣿⣿⣿⢹⣿⡛⢿⣭⣽⣿⣧⠸⠷⣿⣡⡞⣽⣯⣛⢿⣿⣟⢿⣿⢞⣳⠗⢤⡀⠀⠀⠀⠀⠀
⠀⢀⣸⣿⢿⣿⣿⠣⣸⣿⣙⠒⢛⡋⠉⠉⠙⠒⠉⠁⠁⠉⠉⠛⠶⣽⣟⣮⡻⣿⣿⢯⣤⣌⠑⠦⣄⠀⠀
⢠⣿⣡⢾⣼⣿⡏⠑⣼⣯⣙⣧⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡾⢥⡾⢿⡛⢿⡆⠀⠋⣧⡀
⢻⣯⠇⣼⣿⡟⢠⣿⠿⢋⣾⠃⠀⡉⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡄⢹⠀⢣⡤⢤⣾⡇
⠈⠹⣿⡧⣿⣰⣏⣁⡀⣸⠇⠀⡀⣡⣠⣶⣶⣄⠀⠀⠀⠀⠀⣀⣤⣶⢤⣀⠀⠈⣿⣷⡸⣦⠘⠉⢘⡇⠀
⠀⠀⣹⣿⣾⣿⣿⢻⣽⡟⢐⣂⣿⠿⠳⢽⣿⣿⠋⠀⠀⢀⡞⠋⠉⠉⠉⠪⣦⠈⢹⣿⡧⣙⡶⢤⡼⠁⠀
⠀⠀⣾⣿⣿⣿⡿⣿⣿⣏⣸⡿⠷⠠⡄⣈⣿⡿⢲⠋⠀⠀⠑⠀⠀⠀⠀⠀⠘⠤⢸⣿⣿⠷⢿⢿⣅⠀⠀
⠀⠀⣼⣿⣿⣿⣿⣿⣿⠇⠹⠋⠙⠓⠋⠉⢆⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡉⠈⠺⠿⣿⡀⠀
⠀⢰⡏⣙⡿⠃⢿⢸⣿⠀⠈⠀⠀⠀⠀⢌⠂⣌⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣀⠀⠐⢻⡇⠀
⠀⠘⠻⣷⠃⣀⣸⢾⣿⠀⢢⠀⢂⠀⠀⠢⣿⣿⡟⠻⠤⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣌⠣⢄⣸⡇⠀
⠀⠀⢠⣿⡸⣿⣿⣿⣿⡇⢠⡄⠆⠀⠀⠀⣘⣻⣤⣤⣼⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⣷⣦⣻⠃⠀
⠀⠀⠀⣿⣷⣿⣿⣿⣿⣇⠀⠐⡀⠂⠀⠀⣟⠛⣛⣻⣿⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡿⣿⠀⠀
⠀⠀⠀⣿⣿⣽⣫⣟⣿⡟⠠⠀⠄⡡⠀⠁⠩⠟⢁⠀⡀⠀⠀⠉⠙⠂⠀⠀⠀⠀⠀⢠⣿⣿⢋⠉⡿⠀⠀
⠀⠀⠀⠘⢿⣿⣿⣟⣻⡏⠀⢀⠂⠰⠀⠌⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⢻⠀⢀⡇⠀⠀
⠀⠀⠀⠀⠈⠻⣿⣽⣿⠇⢁⠀⠘⠠⢌⠂⠌⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡟⢈⣧⠀⣸⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⢿⣿⠀⡈⠠⢀⠡⢈⠣⢈⠵⡨⣄⣀⢀⡀⠀⠀⠀⠀⠀⣠⠌⣿⠁⢩⠋⡶⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⢀⠐⢢⠐⢢⣀⡉⢒⡱⢎⠷⣫⢖⡩⢄⣤⠴⠚⠁⢰⡿⣈⠆⡸⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠂⠌⠢⠜⠠⡄⠉⠓⠘⠚⠚⠓⠋⠉⠉⠀⠀⠀⢠⢸⣷⣸⣿⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣽⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡞⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⡴⠋⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠑⣦⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠛⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠠⠄⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀