⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⡇⡴⠶⠒⠒⠛⠛⠛⠛⠛⣛⣒⣲⣶⣶⣤⣄⣀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⣻⣿⣿⣿⡇⣀⡠⠴⠖⠋⢉⡉⢉⠉⢈⣓⡲⣄⠙⠉⠺⢯⣹⣿⣿⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠋⠀⢠⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠈⠉⠳⡄⠀⠙⠊⠛⠢⠤⢄⣿⣿⣿⡿⣟⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠀⠀⠀⣠⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢸⣿⣿⣿⡇⠈⠳⣌⡛⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⣰⠎⣽⣿⡿⣛⡯⠵⠒⠒⢤⠀⠀⠀⠔⠒⠒⠒⢀⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠈⠛⣄⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⢀⠞⠁⠀⣫⠵⠋⠁⣀⣤⠴⠖⠲⠶⢮⡹⢭⣶⣄⡀⠀⠈⠉⠲⣄⠀⣸⣿⣿⣿⣿⡈⢧⠀⠀⠀⠈⢳⡀⠙⢷⣆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⣰⠃⠀⡠⠎⠁⠀⠐⠋⡁⡠⠊⠀⠀⠀⠈⠳⡄⢀⠙⠿⣲⣄⠀⠀⠈⢗⢌⠻⣿⣿⣿⡇⠈⢧⠀⠀⠀⠀⠹⣄⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⡼⠁⣠⠞⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⡞⠀⠀⠀⢻⣦⠙⢦⡈⠙⢧⡀⠀⠸⣦⠳⡌⢿⣿⡁⠀⠈⠧⠀⠀⠀⠀⠘⣆⠀⠘⢿⡄⠀⠀⠀⠀⠀
⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⡼⢁⡴⠁⢀⠀⠀⠀⢠⡾⠃⠀⠀⠀⢸⠇⠀⠀⠀⠀⢻⣇⠀⢻⢦⡀⠑⠄⠀⣿⡆⠘⢆⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠈⢿⡄⠀⠀⠀⠀
⠀⠀⣸⠟⠀⠀⠀⠀⠀⢰⢁⠎⠀⣰⡞⠀⠀⢠⣿⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢿⠀⠘⣇⠙⢆⠀⠀⠘⣴⠀⠘⢧⢧⠀⠀⠀⡄⠀⠀⠀⠀⠸⡾⡀⠀⠈⣿⡀⠀⠀⠀
⠀⢠⡟⠀⠀⠀⠀⠀⢠⡏⡞⠀⣠⡟⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⡆⠀⢸⡀⢨⢣⡀⠀⡏⡆⠀⠈⡞⡇⠀⠀⣷⠀⠀⠀⠀⠀⢳⢧⠀⠀⠸⣷⠀⠀⠀
⠀⣿⠁⠀⠀⠀⠀⠀⣾⢹⠁⠀⣿⠁⠀⢠⣿⣿⡇⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠻⠀⠀⡇⠀⢧⠱⡄⠀⢿⠀⠀⠸⡼⡀⠀⢸⠀⠀⠀⠀⠀⢸⢸⡆⠀⠀⢻⡇⠀⠀
⢰⡟⠀⠀⠀⠀⠀⢸⣏⡏⠀⢸⡏⠀⣠⡟⢹⣹⢱⠀⠀⠀⠀⠀⠈⣧⠀⠀⢶⠀⠀⠀⠀⠀⠀⢸⠀⠈⢇⠘⢄⢸⠀⠀⠀⢳⢧⠀⠘⢰⠀⠀⠀⠀⠈⡇⢣⠀⠀⠈⣿⠀⠀
⢸⠃⠀⠀⠀⠀⢀⡟⢿⠃⠀⣿⠀⣰⡟⠁⠸⣾⢸⠀⠀⠀⠀⠀⠀⢹⠀⠀⣻⣣⠀⠀⠀⠀⠀⠸⡇⠀⠘⡆⢸⠀⡆⠀⠀⠘⢾⡄⠀⡜⠀⠀⠀⠀⠀⡇⢸⡀⠀⠀⢿⡇⠀
⢸⠀⠀⠀⠀⠀⢸⠏⡟⠀⠀⡏⣴⠏⠀⣄⠀⣿⡞⡆⠀⠀⠀⠀⠀⢸⡇⠀⢹⢿⣷⡀⠀⠀⠀⠀⢇⠀⠀⠹⡜⠀⣷⡀⠀⠀⠀⢇⠀⡆⡄⠀⠀⠀⠀⡇⠀⣇⠀⠀⢸⡇⠀
⣿⠀⠀⠀⠀⠀⡟⠀⡇⠀⢰⣿⠋⢀⠀⠈⢳⣿⣧⢻⠀⠀⠀⠀⠀⠈⣇⠀⠈⠀⠙⣷⡀⠀⠀⠠⣾⠀⠀⠀⢹⠀⡏⢷⡀⠀⠀⢸⡰⡄⡇⠀⠀⠀⠀⡇⠀⣿⠀⠀⢸⡇⠀
⢸⠀⠀⠀⠀⢸⠇⠀⠃⠀⣾⠿⣾⠟⠛⣿⣿⣟⡏⣎⢇⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠈⠳⡀⠀⠀⠘⡆⠀⠀⠈⣇⡇⠈⢷⡀⠀⠸⣷⢇⡄⠀⠀⠀⠀⣧⠀⢹⠀⠀⢸⡇⠀
⢸⡀⠀⠀⠀⢸⠀⠀⠀⠀⢻⢿⣧⠀⢸⣸⢳⡿⣿⠘⡼⡄⠀⠀⠀⠀⢸⣇⢀⠀⠀⢀⠀⠘⠢⡀⠀⢿⢆⠀⠀⡟⣿⣄⠈⢳⡀⠀⣿⣮⡷⠀⠀⠀⠀⠿⡆⠘⡄⠀⣸⠃⠀
⢸⣧⠀⠀⠀⣸⠀⢰⠀⠀⢸⠰⠟⢦⡀⠻⣿⣾⠿⣧⠰⡹⡄⠀⠀⠀⠀⣼⢽⢉⣉⣉⣉⣍⠉⠙⢦⣘⡾⣷⣄⡇⠘⢿⠆⠀⣷⡄⣿⡿⢭⠀⠀⠀⢀⠀⣇⠀⡇⠀⡟⠀⠀
⠀⣿⡀⠀⠀⡏⠀⠸⠀⠀⠸⠂⠀⠈⠉⠁⠒⠂⠀⠘⣆⠳⠹⡄⠀⠀⠀⠸⣼⣴⠶⠛⣻⢯⡟⡷⣾⣝⣷⡬⡙⡇⢀⣈⠳⣦⣽⣿⣿⣶⠈⣧⠀⠀⢸⠀⣿⠀⣇⣰⡇⠀⠀
⠀⠸⣧⠀⠀⡇⠀⢰⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⣠⡟⣦⠀⠉⠀⠀⠀⠀