⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡶⢦⣀⣸⡟⡈⠙⠷⣄⡀⢀⣠⡾⠋⠀⢹⠀⣠⡴⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⣤⣤⣟⣘⣀⣉⡛⠡⠅⠀⠀⠈⠻⠛⠁⠀⠀⠀⡘⠟⠋⠀⡈⣻⣦⣤⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣰⠏⢀⠤⠤⠒⠂⠐⠒⠬⠕⣢⣔⡐⢆⡠⣂⠤⠒⠈⠉⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀
⠀⠀⡶⢛⠋⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢟⠿⣶⡄⠀⠀
⠀⠀⣷⠎⡴⠁⠀⠀⠀⢀⠶⡢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⢆⠀⠀⠀⠀⠀⡈⢄⡿⠁⠀⠀
⠀⢀⡏⢸⠀⠀⠀⠀⢠⠎⣆⡱⡄⠱⡉⠑⡦⠄⣀⢀⡠⢴⠖⢩⠃⢀⠇⢈⣦⠀⠀⠀⠀⢱⡈⣷⠀⠀⠀
⠀⣼⢁⡏⠀⠀⠀⢠⠁⠀⠀⠈⠉⠒⠑⠤⣱⣀⠀⡏⢀⣎⠤⠧⠐⠛⠉⠀⠀⢣⠀⠀⠀⠀⣇⣿⡇⠀⠀
⢀⣿⢸⠁⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠘⣷⢸⢨
⣸⢻⢸⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⣶
⠻⣼⢸⠀⠀⢰⠁⡴⣲⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⠲⡄⠱⠀⠀⠀⢸⣮⡿⠀
⠀⣿⢸⡀⠀⡌⠀⡇⣿⣿⣿⣯⣈⣿⢱⠒⠆⠀⠀⠀⠑⠒⢲⢹⣿⣉⣿⣿⣿⡇⡇⠀⡇⠀⠀⢸⡏⠀⠀
⠀⡏⠸⡇⢀⠃⠀⢻⠹⣿⣿⣿⣿⠋⡜⠀⠀⠀⠀⠀⠀⠀⠘⡌⢿⣿⣿⣿⡿⢁⠇⠀⢃⠀⢸⢸⣿⠀⠀
⢸⣵⠀⡇⡼⠀⠀⠀⠑⢤⣉⣉⡠⠞⠁⠀⠀⣀⣀⣀⡀⠀⠀⠑⠦⣉⣉⣉⡤⠊⠀⠀⢸⠀⢸⢸⣹⠀⠀
⠘⠙⣷⡇⣷⠀⠀⠀⠀⠐⠀⢀⠔⠒⠉⠉⠀⠀⠀⠀⠀⠉⠉⠒⠢⢄⠀⢄⠀⠀⠀⠀⢸⡇⣷⣼⠛⠀⠀
⠀⠀⠉⢻⠟⢧⡀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⣠⡿⣧⡿⠛⠀⠀⠀
⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣴⠏⠀⠘⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣴⠟⠉⡷⢤⣣⠀⠄⠠⣄⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠄⣢⣣⠔⡏⠛⢦⣄⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣴⠟⠁⠀⠀⢸⡀⠉⢳⣤⣀⠉⠀⠀⠀⠀⠀⠀⠀⠓⢀⣤⣶⡿⠃⣸⠁⠀⠀⠙⢷⣄⠀⠀⠀⠀
⠀⣴⠟⠁⠀⠀⠀⠀⠈⢇⠀⠀⠙⢮⣍⠁⠒⠒⠒⠒⠒⣒⣉⡵⠞⠋⠀⢠⠇⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀
⢸⡟⠀⠀⠀⠀⠀⠀⠀⢸⠑⢤⣀⣀⠙⠳⢼⣿⣿⣟⣿⣯⣭⣶⡀⣠⠖⢹⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀
⠘⣿⡂⡀⠀⠀⣀⣀⡰⠛⠀⠎⠄⠠⠑⠒⠒⠒⠒⠒⠒⠒⢚⠁⠈⠙⡆⠘⠾⣄⣀⠀⠀⠀⢀⣲⡟⠀⠀
⠀⠈⠙⠛⠛⠛⠉⣿⣎⠢⠀⠦⡄⠀⡠⠀⠀⠂⠀⠄⠀⠀⠠⠀⠀⡴⠁⠠⢪⡟⡿⠿⢿⣷⠛⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⠸⡑⠠⡑⠵⣀⠀⢂⡀⡂⠂⠄⠂⠘⠌⢂⡼⠒⡡⠐⣽⠃⠰⢊⠤⡹⢷⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠹⣆⠈⠢⣈⢐⠌⣹⠁⠒⠢⠥⠵⠖⠒⣾⡧⡕⠉⡠⠞⢸⣤⠤⠴⠒⠳⣿⣽⢦⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠈⠳⡶⡨⠀⠀⠀⠀⠀⠀⠀⢿⠷⡲⠙⠁⢠⡿⠻⣦⠀⠀⠈⠙⣿⣯⣻⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⣨⣈⡣⠒⠲⣄⠤⠤⠤⢒⣈⣀⣤⠶⠞⠀⠀⠘⢷⡀⠀⠀⠈⣚⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠚⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠶⠶⠋⠀