⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⢠⣤⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣰⣿⣯⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠛⣿⢻⣦⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣸⠻⢸⣇⠈⠙⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⢋⡟⠀⠀⣿⠀⢘⢂⣀⠀⠀⠀
⠀⠀⠀⠀⢀⣾⠡⠀⠀⢻⣶⣄⠀⢠⡙⠃⠀⠀⠀⠀⠀⠀⠀⢸⡏⢀⡞⠁⠀⢀⡿⠀⠀⠉⢹⡀⠀⠀
⠀⠀⠀⢀⣼⠿⠀⠀⠀⠀⢷⠈⠳⣆⣻⣄⠀⠀⠀⠀⠀⠀⠀⡾⣰⣏⡄⠀⠀⣸⠁⠀⠀⠀⠘⢸⡇⠀
⠀⠀⠀⢸⢿⠀⠀⠀⠀⠀⠸⠧⠀⠈⣳⣽⡄⠀⠀⠀⠀⠀⢸⡿⢻⠋⠀⠀⠰⠿⠀⠀⠀⠀⠀⠸⣿⡄
⠀⠀⠀⢸⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⢦⡀⠀⠀⠀⠀⣠⠖⠒⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇
⠀⠀⠀⢸⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣤⣷⣄⠀⠀⢸⠧⠤⠤⠞⠁⡀⠀⠀⠠⡀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⢸⢲⠀⠀⠀⠀⠀⠀⠀⠸⠧⠀⠀⠀⠀⠛⠀⠀⠉⠀⠀⠀⠀⠾⠃⠀⠀⡰⠙⡄⠀⠀⠀⣻⡇
⠀⠀⠀⠸⢿⣀⠀⠀⠀⠀⣀⣤⣤⠶⢖⠀⠀⠀⠐⠶⠖⠀⠀⠀⢐⢶⣦⢤⣤⣔⣁⡀⠘⡆⠀⢀⣿⠀
⠀⠀⠀⢀⣸⣿⣶⠖⠛⠹⣛⣩⣽⣾⣿⡿⢦⣤⣤⠶⠶⣤⣤⡴⠞⠙⣟⢿⣶⢤⡀⠉⠉⠹⣷⣿⣧⠀
⢀⣴⡿⠛⠉⢹⢾⠄⢠⠞⣋⡤⠟⣹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡈⠻⣍⠓⢦⣄⠸⡇⠀⠀
⠈⠁⠀⠀⠀⠀⠈⢽⣧⡾⠋⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠈⠻⣤⡈⠙⢷⣦⡀
⠀⠀⠀⠀⠀⠀⢰⡿⠋⢹⣷⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠻⣤⠘⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣻⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⢀⡶⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣷⣿⠇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⣁⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢙⣽⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠹⡟⣄⠀⡀⢀⡀⠀⡀⠀⠀⠀⢀⠀⠠⣤⠀⣠⣯⣴⡟⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢴⣿⣎⣣⣝⡏⢻⣶⣾⣧⡶⣰⣿⣧⣶⣿⣶⠛⠛⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⣿⣿⠷⣿⣿⣿⣻⡇⣿⣿⣸⣿⣯⣏⣳⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⢄⣿⡾⠿⠟⠁⠻⣿⣿⣹⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀