⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠔⠀⠀⠐⠀⠲⠴⠦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠰⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⢤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⠋⠁⠀⠀⠀⠀⠉⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣤⢦⣤⣀⠂⠀⢀⡀⠀⠀⠀⠀⠀⠈⠻⣷⠶⠤⣤⣀⡀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠀⢀⣻⣿⣤⣄⠀⠤⢀⠠⠀⡠⠀⠀⠻⣇⠀⠀⡘⠻⠿⣟⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣍⠛⠍⡉⡡⠉⠙⠿⣦⣄⠐⢂⠔⠀⠁⠀⡈⢷⡐⠀⠀⠀⠄⠉⠑⠮⢴⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⠘⠃⠀⠀⠀⠉⠉⡿⢷⣄⡁⠳⡄⢀⠸⣇⠰⠀⠄⠐⠀⠌⠀⡀⠈⠳⢵⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣴⣦⣴⣀⠀⢠⡗⠒⣏⢻⣤⡐⢂⡄⠹⣆⠡⢀⠀⠌⠈⠄⠄⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣧⣠⠈⢳⠋⡟⠀⣿⡏⣯⢟⣦⡜⢦⢹⣆⠌⠀⠄⠐⠀⡤⠀⠀⢁⠀⠀⠑⢗⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢧⠈⣧⡇⠀⣿⡇⡏⣿⠈⠻⣦⣁⣻⣄⠂⠌⠀⠡⡇⣀⠠⠀⠐⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡤⡀⠀⠀⠀⠀⠀⠀⠀⠠⡇⣸⠀⡟⣇⠀⢸⣿⣿⢪⣧⠀⠙⢷⣞⢻⡄⢀⠘⣀⡇⠠⠀⠠⠀⠄⠠⠀⢀⠉⠻⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣤⣄⣀⣀⣀⣿⢿⣴⡿⣽⠀⠈⣷⢹⣿⣟⠀⠀⠈⢻⣜⣿⠀⡘⠄⣯⠀⡄⠀⠡⠐⠀⠄⠁⠠⠀⠘⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢹⣏⣎⢷⣾⠀⠀⣿⢸⡇⠙⣦⡀⠀⠀⢿⣿⡇⠐⠂⣿⠀⢄⠀⠄⡁⠌⠠⢁⠐⢀⠀⠈⢯⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣴⣶⣖⣄⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢸⣾⡟⠀⢀⡿⠈⢷⡄⠘⢷⣄⠐⠘⣿⣯⢈⠥⣿⢈⡟⠀⠌⡀⢄⠃⠌⠂⡀⠀⢀⠈⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣾⡣⠶⣾⠃⢫⣿⡟⠁⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣟⣹⡇⠀⢠⣯⠀⠈⠀⠀⢹⠛⠷⣴⡺⣿⠨⢜⣿⢸⢃⣥⠂⠜⠀⢌⠐⠡⠀⠀⠀⠀⠈⣟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣀⠀⣠⠟⡏⠳⡌⢳⣐⡿⢤⠚⣉⣷⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣿⠀⠀⣾⣋⠙⠃⠀⠀⣹⠁⠀⠀⠙⢿⡖⡌⣿⣾⣋⢆⠘⠠⢉⠠⢀⠡⠀⠀⠠⠁⠀⠹⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢤⢄⣘⣧⣉⠚⢾⠀⢧⠀⢸⢸⠉⠒⣄⢻⣶⣬⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⢠⡾⠋⠀⠀⠀⠀⢰⡿⠀⢀⣀⣠⣿⣧⡿⠛⢯⣍⠏⠛⠒⢦⠁⠀⠀⠂⠀⠀⢀⠀⠀⢹⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠚⢒⣿⠿⢿⠟⢩⠟⠢⡳⡸⡏⢠⣿⢻⡮⠓⣿⣎⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣠⣄⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠋⠀⠀⢀⣤⠴⠶⠻⠦⠤⠿⣌⠻⣖⣨⠻⣦⡌⠹⣞⢡⠀⡐⣈⠣⠈⠁⠀⠈⠀⢂⠐⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⠥⣤⠋⣳⣼⣆⣀⠘⣽⣳⡟⢁⣠⡶⠟⠉⣠⡿⠁⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉⠁⠀⠀⠀⠀⠈⠉⠛⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⠀⠀⢠⣿⣫⢆⡀⠀⠀⠀⢀⣸⡆⠘⢷⡤⠌⢻⣆⡹⣧⢢⠁⠄⠂⢁⠀⠐⠀⠠⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣺⣿⡾⣛⣿⣿⣿⢷⡤⣟⣷⣏⣤⢔⡶⠞⠁⠀⠀⠀⠀⠀⣠⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢱⡄⠀⠀⠀⠀⠀⣠⣶⠟⠉⠀⠀⠀⣀⣾⣿⣵⠥⠚⠉⠉⠙⡏⠁⢹⠀⠈⣷⡄⡈⢿⣤⠙⣧⡅⢆⠉⠄⠒⡠⠁⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⡎⢟⣾⣋⣴⣿⡏⠀⠘⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢇⡀⣠⡤⠞⠚⠉⢙⣆⣧⠶⠟⠋⠀⠉⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⠸⣧⠐⠈⣿⡰⠘⣧⡘⢄⠂⡐⢀⠀⠄⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣸⡷⢶⣝⢧⣨⣯⠖⣶⡟⢷⣷⣴⣽⡿⣆⣀⣀⣀⣀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⣀⡤⠖⠒⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⣨⢟⠉⣠⠤⣀⡴⢪⠉⠹⡄⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⣷⠀⠘⡇⠀⠀⢻⣎⠁⠘⣷⢁⠸⣷⡈⢳⠀⠄⠂⡀⠂⠈⠀⠀⠄⢹⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠸⠛⠸⣶⡾⠟⢰⠋⠂⠈⢷⡘⣷⣿⣿⣷⣿⠿⠿⠿⢿⣽⣷⢄⣼⠃⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠙⡟⣦⡀⠀⠀⠀⠀⣿⡏⡾⣿⣻⠁⠀⢸⠀⠀⢳⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⣸⡄⠀⡇⠀⠀⠀⣿⠤⢀⢹⡧⠂⠈⢷⡄⠹⣆⠠⠀⠀⠐⠀⠂⠀⠸⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣚⡡⣴⢿⣸⡟⠻⣦⡈⣿⣟⡿⡇⠀⣿⡛⢤⣘⠌⣿⢋⣻⣿⠶⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⢀⠀⠰⡈⠻⠷⣶⡿⠀⠀⠘⣻⣇⠀⣟⠀⠀⢸⡆⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢳⡀⡷⠀⠀⠀⠘⣧⡅⡀⢿⡥⠀⡈⢻⣄⠘⢷⣀⠱⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠋⠁⠀⠈⠋⠃⠀⢻⡏⣿⣿⣥⣧⣌⢷⡽⣲⣽⣾⢣⣾⣿⣿⠀⠀⠀⠀⠀⢸⡇⡆⣄⠀⡴⠈⠈⠳⡱⣼⡖⣐⣺⣷⠇⣠⡾⡟⠀⠀⢸⢦⡀⠀⡇⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⣾⠀⠈⢧⡗⠀⠀⠀⠀⢹⣤⠐⠸⣧⢡⠄⡀⠙⣷⡀⠛⣦⡀⢃⠈⠀⢀⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⣒⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⢸⣷⣿⣟⠝⢻⣿⣾⣷⣿⣿⣿⣾⣿⡏⣿⡀⠀⠀⠀⠀⠸⣇⣧⣹⡦⠓⠀⢀⠀⠑⠻⠷⢿⡿⣯⠔⠻⣗⣧⠀⠀⢸⢸⡇⠀⣇⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⢠⡏⠀⠀⠸⡇⠀⠀⠀⠀⠸⣏⠔⠠⣿⣘⡀⠅⢂⠙⣷⡀⠹⢧⡈⠄⠀⢈⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⣸⣹⡗⢕⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⡇⣾⣿⣾⠃⠀⠀⠀⢸⣿⡿⣿⣿⣷⣿⣿⣿⣧⠀⠀⠀⠀⠀⠙⠯⣍⣀⡀⠈⡋⠀⠀⠀⠀⡌⠉⡇⠀⠀⠑⠘⠦⣤⠾⠜⡇⠀⢿⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⣸⠁⠀⠀⠀⣇⠀⠀⠀⠀⠀⣿⠈⠄⢹⡇⢸⡘⠠⠄⠀⠻⣆⡈⠛⣦⡀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠑⢶⣼⣾⠈⣉⡇⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢻⣾⣿⢻⡲⠀⢀⣀⣨⣿⣿⡹⣽⢿⠻⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠈⠹⢤⣉⣥⡏⢀⣠⠞⠀⣸⠇⠀⢀⠀⠀⠀⠀⠀⡼⠁⠀⠸⡆⠀⠀⠀⠀⠀⠳⡀⠀⠀⡿⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⢸⡏⡀⠠⣷⠸⢁⠆⠌⡠⠠⢀⠓⢦⡀⠐⠀⢹⡇⠀⠀⠀⠀⠀⣀⣤⣴⢟⡿⣿⣚⠙⣹⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢫⣞⢴⣼⣿⣱⣻⠳⠟⠛⢙⣻⣿⣷⣯⣟⣮⢳⢜⣾⣸⣿⠵⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⡝⠛⠶⠤⠞⠁⠀⠀⠀⠉⠑⠒⠲⠾⣇⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠈⣷⢁⠒⢸⡇⢃⠖⢈⠰⠐⢀⠠⠀⠙⢧⠀⣹⡇⠀⠀⠀⢠⣿⢻⠙⣿⣽⢹⡏⣏⡙⠗⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣠⡶⣴⡀⠀⢀⣀⠹⣮⡿⣿⡟⠛⠫⣧⣄⣢⣭⣿⣿⣽⣽⣿⣷⣿⡗⢝⡽⠑⢍⠳⠦⣄⡀⠀⠀⠀⠀⢸⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢸⡖⡀⠄⣿⠐⡜⡀⠀⠁⢂⠈⠀⠂⠀⠀⢸⣆⠀⠀⠀⠸⣟⣻⣿⡟⠹⣧⣇⣭⡒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣠⡟⢀⡿⡇⠀⠉⢗⣶⣻⣧⣿⣷⣶⣦⡈⣹⣿⣿⣿⣿⣿⢿⣿⣟⡷⡔⠁⠀⣀⣀⣨⣯⣶⣭⣿⣶⣶⣦⣼⡆⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢿⡂⠀⠀⠀⠀⠀⠸⣷⠀⠀⢺⡇⣱⠁⢁⠀⠡⠀⠠⠀⠈⠂⢸⣿⠀⠀⢀⣀⣿⢯⣍⣤⡼⠏⡤⢾⠏⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⣾⣦⣿⠚⢿⣢⠀⠀⠈⠿⣽⡿⢿⡍⣿⣿⡏⠀⠒⠿⣏⠀⣻⢿⡯⣿⠎⣈⣍⣩⣭⠤⠦⠔⠧⠰⠭⢑⡷⠋⠁⠉⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠒⠎⣇⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠐⢺⡇⠀⠀⠀⠀⠀⢀⣿⠆⠈⠐⣧⠉⡴⢃⠈⠄⠂⠂⠀⠀⡀⠘⣿⠀⠀⠿⣭⣄⡸⢿⠟⠷⢿⣖⠋⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣧⣀⣟⣧⣨⣿⡝⢶⡀⠂⣯⡰⣧⢳⢸⡟⢧⣤⠀⠲⣿⢀⣿⣛⠉⡓⣯⠀⠉⡠⠤⠢⠤⠴⠂⣠⣾⡛⠦⡀⠀⠀⢈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢹⡄⠀⠀⠀⠀⢸⡇⠀⠀⠁⠀⠌⣸⡇⠀⠀⠀⠀⢠⡾⠋⠀⠄⣀⠙⠀⠄⢂⢂⡐⠀⠀⠀⡁⠀⠁⣿⡇⠀⠀⡀⡉⠉⠁⠀⠀⠐⣿⠤⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡿⢫⣸⣯⠉⣟⢎⠫⡿⣽⠧⢼⣿⢸⣷⠋⡿⣆⡐⠃⣼⣇⠏⣇⣡⡉⢷⡀⣴⡯⢷⣶⡒⣾⢿⡋⢻⣦⣷⣤⡖⣋⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠳⣆⢻⠀⠀⠀⠀⢸⠁⠀⠀⠠⠌⣀⠠⣷⠀⠀⣀⣴⠛⣷⠀⢎⡔⡀⠰⢡⣦⣴⣿⣧⠐⠈⠀⢀⠠⠁⢸⡟⢾⣿⢮⣉⣛⠻⣔⡄⡀⢸⣷⠘⠆⢀⠄⢊⡆⢣⠀⠀⠀⠀⠀
⠀⠘⡅⢠⣿⢿⡶⠟⠊⣧⢻⣿⣰⢻⣧⣾⣿⣴⢣⣿⢷⣸⣃⣉⣫⣭⣉⡉⠙⠳⢹⣿⣯⣿⣽⠏⠀⠉⠻⢿⣄⢸⠒⢢⢸⡻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣷⡈⢧⠀⠀⠀⢹⠆⠀⡀⢂⠒⠀⠄⢹⣴⠟⠉⠀⠀⢽⡄⠈⠖⠀⣡⣿⡽⣯⢻⢻⣔⣶⡟⢀⠂⢀⠈⣷⠠⣎⡀⡉⢙⡿⠋⣹⡷⢿⣯⠳⡌⣣⣾⣵⣇⡘⠠⡀⠀⠀⠀
⠀⣼⣷⣾⣯⠈⣧⡤⣜⣙⣾⢿⢃⣿⡵⠿⣬⡏⡟⣿⣼⣿⣠⠉⠹⣶⡥⢿⣳⣤⣸⣤⣴⠞⠁⠀⠀⠀⠀⠀⣹⡎⡄⡇⣸⠁⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢘⢣⠈⣧⠀⠀⢸⡇⠠⠐⠠⠐⠆⡀⠁⠙⢷⣄⠀⠀⠈⣷⠀⠌⡰⣿⣿⡙⡟⡜⣻⡾⣹⠁⢀⡀⠀⠀⢸⣇⠐⣴⢁⣾⠴⠞⢹⡇⢨⢿⣦⢿⣧⣠⡤⠴⠛⡛⠀⠀⠀⠀
⠀⣯⡀⣾⣿⣟⣿⡋⠲⢏⣻⣿⣼⠷⢠⣴⡮⣧⣧⣷⠞⠉⠈⢿⣀⠉⢿⣭⣤⠄⠀⣱⡦⠶⣆⠀⠀⠀⠀⣰⡿⢠⢽⡰⣇⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⡶⠚⡁⠎⠀⠣⠘⢧⡀⠘⡇⡀⡐⠡⡘⢡⠀⠀⠈⢀⠩⢻⣶⣄⡸⣿⢿⣟⠛⢦⣹⣽⣡⣿⣵⣟⡈⠄⠀⠀⡐⠀⢻⡄⠹⠒⠒⠒⢂⠆⢳⡏⢸⣿⠳⠾⢷⢀⡴⢻⠃⠇⠀⠀⠀
⠀⠀⠁⢻⡇⡇⠈⣳⠀⠀⣱⠿⠉⠴⣸⠏⠀⠠⠺⢷⠊⠉⠀⣻⠓⣻⢭⣥⠤⣶⣮⣵⣶⣿⣭⣦⠀⣀⣠⠞⡡⠂⠀⡇⣾⠈⠉⠉⠋⢙⡗⠒⢺⡉⠙⠋⠁⢠⠧⡄⢃⠀⠀⠀⠡⡈⢳⡄⣯⠀⠀⠂⠜⠰⡈⢄⠂⢀⠂⡁⢻⡎⠙⣿⢀⣼⣿⣛⡽⣋⣿⡿⢶⣦⣿⣷⣥⠒⠀⡀⠈⢿⣦⣀⣒⣀⣡⠞⢫⡽⣿⢯⣉⣙⡶⣿⣴⣋⣀⣑⠂⠀⠀
⢤⣤⣤⣦⣇⣷⡶⠏⠚⠛⠧⠤⢴⡾⢿⣂⠀⢀⡄⠻⢷⡀⢠⡾⣲⢿⣇⡛⣾⠃⠀⠀⠀⣤⠞⠛⣛⣉⠤⠊⠀⠀⠀⢃⢷⠀⠀⠀⠀⣾⠘⡗⢄⠻⣤⠀⠀⠀⠀⠹⡆⢆⠀⠀⠀⠐⠄⠻⣿⡀⠀⢁⠊⢄⡑⠇⡌⠒⠀⠄⠡⣻⡀⡿⢸⡿⣻⠟⡟⢩⣇⢹⣝⣷⡠⢂⡄⠠⠄⠁⠰⠘⣿⡙⢿⣾⠖⠛⡏⣰⣟⢨⡿⠛⣿⣡⢿⡉⠛⣮⠭⠛⠁
⠀⠈⠓⠺⣿⠚⠁⠀⠀⢀⣀⡀⣾⣂⣙⣻⠶⠻⠷⢦⣀⣽⣫⢿⡱⡱⡹⡗⣯⡀⠀⢠⣼⢡⢖⠉⠀⠀⠀⠀⠀⠀⠀⢸⠘⡇⠀⠀⠀⠘⡇⡃⠀⠡⠘⢦⡀⠀⠀⠀⢹⡜⢄⠀⠀⠀⠘⡄⢹⡇⠀⠀⠠⠆⡐⢎⡐⠉⠌⢁⡂⠜⣧⡷⠿⠛⡏⣼⡇⣸⢻⣾⣿⡿⠇⡥⢈⠂⡅⡈⠄⠁⠘⣷⡠⢈⠛⢾⣟⡁⠘⢷⡇⠸⠛⠁⠈⠓⠦⣽⠀⠀⠀
⠠⢤⣀⣄⣻⣦⣴⣒⣿⣟⡁⠘⠉⠈⣡⣵⠲⢤⡀⡰⢋⡝⢩⣿⣖⣗⡧⣄⠸⡙⡄⠉⠉⠳⣤⠢⠀⠀⠀⠀⠀⠀⠀⠀⢆⠻⡄⠀⠀⠀⡇⡇⠀⠀⠈⠂⡙⢦⣀⢀⠠⡷⣥⠠⠀⠀⠀⢣⠘⣟⠠⢂⠀⢢⠙⣁⡒⡡⢆⡐⠬⡐⢹⣷⣀⡌⣿⠇⢻⣽⠙⣱⣿⠃⠌⡱⠆⠩⠄⠑⠢⠉⢀⠘⣷⡣⣈⠠⠈⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⠙⡀⠀⠀
⢒⠗⣚⣿⢿⣿⣭⠟⠒⠒⠿⣶⣤⣼⠁⢸⡀⢀⡝⣠⣞⢰⣫⢴⢿⢞⢫⣻⠄⣧⠙⡀⠀⠀⠸⣇⢑⢀⡀⠀⠀⠀⠀⠀⢈⡄⢳⡀⠀⠰⡇⢁⠀⠀⠀⠀⠐⡦⣽⠋⠀⢁⡏⢸⠀⠀⢀⠊⣰⢿⡆⠈⠀⠒⠡⠖⣐⢳⠠⢉⠄⡰⢊⢬⣯⣽⣶⣀⠈⢉⣰⣿⣧⠾⣓⠳⠶⠶⣼⠔⠁⡐⠀⠀⠈⢳⣵⢧⣡⠐⠀⢈⡿⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀
⣣⠊⡿⢩⡞⠉⣿⡆⠀⠀⠀⠀⠚⠛⡾⠻⡇⣼⢻⣥⠛⢿⠈⢟⣿⣻⡿⣥⣀⢸⠀⢡⡤⠿⠺⠛⠺⢖⣦⣑⠢⠀⠀⡔⢡⠶⠚⠙⠂⠀⣱⠞⠄⠀⠀⠀⡜⣠⠇⣀⣠⠞⢐⠃⠀⢠⠂⣤⡟⠳⣦⣅⠠⠀⢡⢉⡔⢃⠨⠅⡃⡔⠌⠤⠿⣍⠉⡙⢳⣦⣿⣟⠋⠛⢿⡶⠶⠛⡁⢬⡶⣿⢻⠄⢰⠀⠙⢳⣆⠻⢣⡟⠁⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀
⠥⠀⣿⡋⠀⠀⢸⣇⣠⣤⠖⣲⡖⠛⠓⠆⠐⣯⢫⠉⣌⣿⣄⢸⣿⣰⠷⣕⣾⣸⡀⠁⠀⢀⣤⣴⢲⣬⣄⠛⢹⠂⠕⢧⡙⠛⠒⠒⠚⣉⠡⠊⠀⠀⠀⠀⠣⡙⠓⠛⣉⠔⠁⠀⠀⠈⠢⡉⠙⠛⢛⡛⠳⠶⡦⢾⣤⣃⡆⢭⠰⡐⢚⡂⣌⣻⣦⣬⣷⣻⣿⣍⠷⣦⣀⢹⣦⡐⠀⣾⣻⣿⡽⣦⡟⡧⢀⣶⣿⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡐⠀
⠀⢡⠈⡅⠀⠀⢸⠟⢀⡟⡼⠉⣷⠀⠀⠀⠀⠈⠉⠛⢉⣠⡽⣿⣯⣾⠸⣟⣡⠼⠽⠃⠀⣹⠖⣿⣺⣷⣏⣿⠚⠉⣳⣤⣌⢋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠐⠛⠐⠤⠤⢈⡙⠛⢒⠓⢾⠟⠩⠉⢩⡿⢛⣿⣃⣈⣳⣶⡿⠽⠿⣤⣐⠉⠉⠡⠀⣸⣿⡟⠋⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡀⣬⠏⡰⠁⠀
⠀⠀⡇⣧⡜⠛⣿⢠⣼⣷⣷⣴⣿⡄⠀⠀⠀⠀⠀⢰⠋⠀⣴⢻⡇⢻⣶⡌⡇⠀⠀⠀⠀⢹⠛⣿⡇⠈⣿⡟⠀⠀⠁⠀⠙⡆⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡝⢠⡏⢠⣤⣶⠛⣦⢸⣿⣷⡄⠀⠀⠙⣶⠀⠈⠉⠙⠛⠛⠛⢩⣿⠀⠀⣴⣿⣯⣿⣶⠀⠀⠀⠀⠀⣽⠉⡔⠁⠀⠀
⠀⠀⠐⢀⠳⡆⠘⢉⠻⠀⠈⠉⠈⠁⠀⠀⠀⠀⢠⣯⠤⠛⠁⢸⡅⣸⠇⠙⠁⠀⢤⡀⠀⠘⣾⣽⣿⠀⠀⠀⠀⠀⠀⠈⠑⢛⣄⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠈⠀⠞⣛⣩⣥⣤⣜⣹⠳⣿⣧⠿⣓⡶⠶⠺⢿⣀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠻⣟⣹⡽⠋⠀⢀⣠⡤⠋⡁⠐⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢉⠙⠚⣤⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠁⠀⠀⠀⠀⠀⠻⣗⢶⣯⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠹⠦⣌⠐⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣠⡶⢦⡄⠀⠈⠙⢶⣀⠰⢮⡻⣿⣠⣴⠿⠶⢶⣦⠶⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⣀⣀⡴⠚⣉⠉⠔⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠑⠢⢀⠻⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡿⣆⣠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡵⢦⣘⣧⣁⠐⠂⠂⡄⠠⠀⢀⡀⠀⠀⠀⠀⢀⣀⠀⢀⠀⠀⠀⠀⠀⡌⣴⣫⡿⣟⣻⣵⡄⣶⣅⠉⢛⠿⣛⢻⡗⠛⠳⢮⡤⠭⣷⣄⢠⡀⢠⢀⡀⣄⣠⣰⡤⠟⠓⣃⠄⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢈⠓⣧⢠⡄⣄⠀⢀⠀⠀⣀⠀⡄⠀⣰⢢⠄⠀⠀⠀⠀⠀⠀⣿⡟⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠏⠛⠙⠳⠶⠿⣺⡄⠢⡀⡠⢂⣱⣖⣞⣦⡑⠄⠀⠀⠀⠐⢄⠛⠛⠋⣿⣻⠀⣯⠆⠀⡟⢈⣥⠟⠀⠀⠀⠀⠀⢀⣰⠞⢉⠭⠭⠭⠭⠤⠤⠁⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠨⠅⠉⢉⡓⠹⠶⠷⠓⣚⡙⢻⡰⣏⡄⠀⠀⠀⠀⠀⢸⣿⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣾⣽⣈⠉⣛⣾⢿⢟⢧⠈⡄⠀⠀⠀⠀⠑⡀⣸⠟⠁⠀⢻⣧⠀⣷⠋⠀⠀⠀⠀⠀⠀⣀⡟⢁⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠈⠐⠠⢀⠓⢧⣀⠀⠀⠀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢙⡟⠹⠾⢾⡧⠟⢩⡇⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠸⣾⠄⠀⠀⠀⠀⠀⠀⣄⡦⠋⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢀⡋⠳⠼⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⠯⣷⡆⠈⣹⡂⢼⠀⠀⠀⠀⢀⡊⠀⠀⠀⠀⠀⠀⢻⣫⡄⢀⠀⣄⡦⠗⢋⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠠⡉⠳⢴⠀⡀⢳⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠘⠃⠰⢼⠁⢠⠀⠀⠀⡐⠑⠀⠀⠀⠀⠀⢀⣠⡬⠝⠲⠝⠋⡡⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠨⢉⠙⣛⢛⡙⠊⠓⠚⢦⡤⣄⣀⣄⣄⣀⣀⠀⠀⠀⠀⠀⢀⢀⠀⡀⠀⢀⠀⣀⢀⣤⡞⠋⡀⣨⠁⠀⢎⢠⠤⠴⠆⠶⠤⣒⡚⠡⠄⠒⠂⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠈⣁⡐⠢⡤⢤⡤⠀⠈⡒⠚⠭⠽⠦⠰⠒⠛⠒⠉⠛⠉⣋⠉⠩⠥⠤⢓⠈⠀⠀⠀⠀⠉⠈⠉⡉⠉⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀