⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣰⣾⠁⠀⢦⣾⣤⠆⠀⠻⣧⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣼⠏⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀
⠀⠀⢀⣸⣿⠃⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢿⣧⡀⠀⠀
⠀⢰⣾⣿⡁⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢀⣿⣿⠖⠀
⠀⠀⠈⠻⣿⣦⣄⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀
⠀⠀⠀⠀⠈⠻⢿⣷⣄⡀⠀⣿⡇⠀⣠⣾⣿⠟⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣿⣧⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⣻⣿⠈⠙⢿⣿⣦⡀⠀⠀⠀⠀
⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⣽⣿⠀⠀⠀⠙⢿⣿⣦⣄⠀⠀
⠀⣠⣴⣿⡿⠋⠀⠀⠀⠀⠀⢼⣿⠀⠀⠀⠀⠀⠈⢻⣿⣷⣄
⠈⠙⢿⣿⣦⣄⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁
⠀⠀⠀⠙⢿⣿⣷⣄⠀⠀⠀⢸⣿⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀
⠀⠀⠀⠀⠀⠙⢻⣿⣷⡄⠀⢸⣿⠀⠀⣼⣿⣿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣦⣸⣿⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣴⣦⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⢠⠘⣿⣿⡇⠠⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀
⣼⣱⣿⣿⡇⢰⠆⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣎⢸⣿⡄⢠⡀⠀
⠙⠦⣍⠩⠰⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠈⠳⠬⠑⠸⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣀⣉⣏⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⡀⠀⠀⠀
⠀⠀⠀⠀⣀⣀⣀⣷⡆⠛⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⡇
⠀⠀⠀⠀⠹⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠠⠬⢍⡹⣿⣿⠿⠁⠘⠀
⠀⠀⠀⠀⠀⠀⠑⠓⠛⠛⠺⠟⠉⠁⢹⣿⣿⡟⠀⣤⢀⡀⢀⠳⠍⠀⠐⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⢻⡸⣿⡆⣇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⣧⢹⣿⣸⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⢇⣾⣷⡼⡄⠀⠀⠀⢸⣿⣿⠀⠀⠀⡝⢀⣿⣇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠸⡼⣿⣿⡇⣇⠀⠀⠀⢸⣿⣿⠀⠀⢠⢁⣿⣿⡏⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠱⡜⢿⣿⡜⣆⠀⠀⢸⣿⣿⠀⡤⣣⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⣮⢿⣿⣮⠢⠀⢸⣿⣿⣧⣼⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢻⣿⡇⠀⣸⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⡀⠀⠀⠀⠀⢠⡀⢠⣘⣓⣠⣤⣾⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡾⢺⣷⣾⠙⡧⠈⢳⡸⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣠⣷⣿⣿⢷⡆⠀⠀
⣧⣿⠛⡏⢸⠀⠀⠀⢷⡸⠿⠛⣁⢰⣿⣿⠀⠀⠀⠀⠀⠀⢹⡟⣿⡿⢃⣸⠀⠀
⠈⠙⠦⣁⠟⠀⠀⠀⠀⠙⠐⠀⢡⣾⠇⣿⠀⠀⠀⠀⠀⠀⠀⠙⠧⠔⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠹⡿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀