⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣒⣊⣉⣁⠀⠈⠉⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠉⠀⠀⠀⠀⠉⠓⢄⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⣀⠀⠀⣀⠤⠤⠐⠒⠂⠒⠒⠒⠒⠚⠧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠠⣄⡀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠋⣉⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠟⠒⠒⡲⠋⠁⠀⡤⢳⠀⠀⠀⢳⡀⡤⠒⡒⠤⢤⡀⠀⠀⠀⠙⣄⠀⠀⡆⠀⠸⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⡇⠈⡇⠀⠀⢼⠛⠦⡀⢷⣄⠀⠀⠀⠀⠰⡀⠈⢆⠀⢹⠀⠀⢧⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⡔⠀⠀⢠⡇⣞⡟⡄⠀⢸⡇⠀⠑⢌⣎⠑⢄⠀⠀⠀⢣⠀⠘⡆⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⣴⠁⢸⡄⠈⡇⢹⠀⠙⣄⢸⡄⠀⣀⣤⣽⣦⣤⣹⢦⡀⠘⡦⣄⠸⣸⠀⠀⢸⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡔⠁⢸⠀⢠⡇⢠⢷⣼⠀⣀⡘⢆⡇⠀⢻⡿⠿⠛⠋⢹⡤⠈⠲⣷⣿⠷⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⢸⠀⣯⢱⢸⠀⢿⣾⣿⡷⠈⢻⡄⠀⠀⠀⠀⠀⢨⡇⠀⠀⢸⠁⢀⠏⠀⠀⢸⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⢹⡈⢿⡄⠀⡛⠁⠀⠄⠀⠀⢀⠀⠀⠀⠀⡼⢀⡀⠀⡿⠖⠛⠤⡀⠀⢸⠂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠀⢧⣿⡁⢰⢧⠀⠀⠠⠴⠦⠎⠀⠀⠀⢠⠃⡜⠀⢠⠇⠀⠀⠀⠈⢦⢸⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⢷⠙⢾⡜⠳⠤⢄⣀⠀⠀⠀⠀⣀⣼⡞⠀⢀⣾⠂⠀⠀⠀⠀⠘⣹⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⡟⠉⡽⢉⠽⢫⣿⠇⠀⣼⠇⠀⠀⠀⠀⠀⠘⡏⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⣾⠀⢾⡀⠈⣠⠟⡏⢀⡜⢸⠀⠀⠀⠀⠀⠀⠀⣧⢳⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⠇⢀⣬⡗⠈⠁⠀⢁⡎⣇⢸⠀⠀⠀⠀⠀⠀⠀⠉⢿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣯⣴⣿⣿⣿⢻⢒⡄⡟⠀⠸⡼⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⢹⢹⣿⣻⡟⠯⠞⠀⠃⠀⠀⠃⠀⢀⡤⠔⠒⠋⠉⡏⣀⢼⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡉⣼⣿⢣⠋⡇⠀⠀⠀⠀⠀⠀⢸⠎⠁⠀⠀⠀⠀⢀⠏⠁⠘⡆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⠖⠒⣲⠖⠉⠓⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⢿⡈⢸⢰⡁⠀⠀⣠⠆⠀⠀⠘⡆⠀⠀⠀⠀⠀⢸⢇⠀⠀⢹⠀⠀⠀
⠀⠀⠀⠀⢀⠞⠁⠀⡜⠁⠀⠀⠀⠀⠀⠉⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠈⠃⠀⠙⢁⡤⠞⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣸⢸⡄⠀⠈⣇⠀⠀
⠀⠀⠀⣠⠋⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⢀⡤⠤⠬⡏⠀⢀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⣧⠆⠀⠀⠀⠀⠀⢸⠅⠀⠀⢸⡀⠀
⠀⢀⡜⠁⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢭⡓⢦⡇⠀⠀⠀⠘⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⡇⠀
⣠⠋⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠙⣖⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⢸⡀