⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠶⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⣠⣒⡘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⢰⠃⠀⠉⠻⠀⠀⠀⠀⢀⣀⡀⠀⢀⢀⠠⠐⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠤⠀⠀⠠⠤⠀⡀⠀⠀⠠⠄⠀⢣⠀⠀⢨⡀⠀⠀⠀⡀⠄⠒⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢈⣱⣄⡀⢧⠤⠒⠋⠉⠉⠉⠉⠉⠒⠲⠤⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠸⠀⢀⠠⠒⠉⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀
⠀⠀⠀⠘⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⠀⠀⠀⡀⠀⡔⠁⠈⡄⠀⠀
⠀⠀⠀⠀⡆⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⠀⠈⠁⠢⡇⠘⠀⠀⢰⠀⠀⠀
⠀⠀⠀⠀⢡⠀⢠⠃⠀⣤⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠣⡀⠀⠀⠈⠀⠀⢠⠃⠀⠀⠀
⠀⠀⠀⠀⢀⣂⣼⣀⡜⢸⣀⣠⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠱⣄⡄⠀⠀⠀⢧⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⡠⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠑⣤⠀⠀⠀⠀⠪⣀⠀⠀⠘⢣⠀⠀⠀⠀⢀⠀⠀⠀⢸⢀⡠⠊⠑⠤⣀⡀⠸⡄⠀⠀⠀⠀⢣⠀⢱⡀⠙⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⢀⣠⢀⣴⠒⠚⠃⢀⠇⠈⢆⠀⠀⠀⠀⠑⢄⢀⠇⠁⠀⠀⠀⠀⠀⠉⠉⡇⠀⠀⠀⠀⠀⢣⠀⢧⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡏⠉⠈⠋⠸⠀⠀⢈⠟⠙⠒⠊⢦⢰⠒⡤⢤⡤⠵⠀⠀⠀⠀⠀⣀⣤⡦⠀⡇⠀⠀⠀⠀⠀⠈⢧⠈⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⡇⡀⠀⠀⠀⣆⡤⠋⠀⠀⠀⠀⠀⠉⠀⠉⠁⠀⠀⠀⠀⣨⣶⣿⣯⣥⠤⠄⡇⠀⠀⠀⠀⡀⠀⠘⡆⢸⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⢠⡇⠀⠀⠀⢩⠀⢠⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⠃⣠⠂⠀⢀⡇⠀⠀⢳⠀⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⢣⠀⣀⠤⠞⠋⠁⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣚⣉⡇⠀⢀⣾⠃⠀⣀⣸⡆⢸⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⠜⢄⠠⡀⣀⡀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠐⠂⠁⠀⠀⠀⠀⠀⠔⠂⠀⠀⠀⠀⠉⠲⣿⡏⠀⣾⣿⣿⣧⣼⡇⠀⠀⠀⠀
⠀⠌⠁⠢⡀⠇⠀⢸⠀⠙⢤⡉⠓⢒⠖⠉⠉⠉⠉⠀⠂⠄⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⣿⣿⠏⠸⣇⠀⠀⠀⠀
⠀⠘⢄⠀⠈⠀⠀⣎⣀⡀⠀⠹⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠖⢂⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣅⣀⡹⠋⠀⠀⣿⠀⠀⠀⠀
⠀⠀⠀⠁⠢⢄⣼⣿⣿⣿⣷⣶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠼⣾⠿⠳⡽⠀⠀⠀⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠸⣯⠻⣿⣿⣿⡀⢸⠄⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠘⣦⣸⡏⠀⠀⠀⣿⣿⣄⠀⠀
⠀⠀⠀⠀⠀⠀⢿⣷⣄⠉⢹⣿⠃⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡏⢻⣷⠀⢀⡞⠛⠛⠛⠋⠀
⠀⠀⠀⠀⠀⠀⠈⣿⣿⡆⠘⣿⡀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢦⣤⣤⣶⣿⣇⡿⢻⣆⡜⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⢧⣽⣿⣶⣤⣤⣼⣿⠒⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠈⣿⣿⣿⠿⠋⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢱⡀⠤⠀⠒⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣈⣤⣲⠃⣠⠏⠀⢃⠀⠀⠀⠀⠀⢀⡼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡎⠉⠉⠉⠑⠒⢠⡀⢀⣀⣀⣀⠀⠀⠀⡠⢊⡜⣡⢾⢡⡖⠀⠀⢣⠀⠀⢀⡰⠋⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡀⣀⡤⠴⠖⠛⠓⠒⢳⠎⠞⠛⠑⠋⠑⠒⠶⢒⡡⠖⠋⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣀⠜⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⠉⠁⠀⠉⠲⣄⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⠆⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⢀⠈⢳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠹⣌⣴⠃⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢚⠁⠀⠀⠈⠛⢲⠖⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣽⠁⠀⠰⡲⠴⠃⠣⠤⡄⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢙⠕⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⣼⣀⠀⢀⣫⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠰⡀⠀⠀⡟⡄⠀⠀⠀⠀⠀⠁⠰⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡏⠀⠸⠀⠀⠀⢸⡰⠃⠀⠀⠀⠀⠠⠧⢧⠄⠀⠀⠀⠀⠣⠀⣀⠇⠘⢏⠂⢀⠑⡄⠀⠀⣇⠀⠀⢳⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡇⠀⡄⠀⠀⠀⠀⠀⠀⠀⢠⢼⠀⡜⠀⠈⢂⢠⢀⠀⢀⠀⠳⡘⠀⠀⠀⠑⠃⠑⢴⡀⠀⠸⠀⢀⡤⠚⠛⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣼⣷⠀⢱⠀⠀⠀⠀⠀⢀⢠⠃⠘⢊⣀⣠⣤⡤⠍⠀⠁⠚⢹⡲⠁⠄⣢⣶⣦⣴⡀⠀⢱⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⡄⢸⠀⠀⠀⠀⠀⢸⡾⣄⣰⠟⠛⠉⠉⠉⠃⠀⠀⠀⠸⠀⠀⠈⠀⠀⠀⠈⠙⠟⢹⠀⠞⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣷⣸⠀⠀⠀⡇⡄⠘⡇⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⡀⠀⢸⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠙⠁⠀⢳⠀⠀⠤⠄⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠈⠀⡸⠀⠀⠀⢇⢀⡤⠂⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢿⣿⣿⠇⠀⠀⢁⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠉⢹⠀⠀⠀⠀⠀⠀⡠⢃⡀⠀⠀⠸⣁⠀⢀⠄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠘⡄⠀⠀⠀⠠⡬⠷⠀⠀⠀⠀⠀⠀⠀⡇⢀⣀⣸⠀⠀⠀⠀⣀⠤⠛⠉⢀⣠⠂⠐⢵⣖⠕⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⣿⡇⢰⠀⠀⠀⠀⠐⠄⣀⠀⠈⠑⠢⣤⠀⠀⠀⠀⠈⠉⠁⠀⠀⢀⣀⠠⢴⠞⠉⠉⠉⠁⠀⠀⠠⢖⣷⣍⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣇⠰⠐⠀⠀⠀⠀⠀⠈⠫⡉⠉⠫⢒⠒⠒⠲⣖⠒⠒⠒⣴⡹⠉⠀⡰⠁⠠⠁⠀⠀⠀⠀⢠⠁⢸⣿⣿⣦⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣄⠁⠀⠤⠀⠀⠀⠀⠀⠐⡄⠀⠠⢣⠄⣀⣀⡉⠒⢒⣞⣁⡰⢒⡇⠀⢂⡇⠀⠀⠀⣐⣡⣡⣿⣿⣿⣿⣷⢄⠤⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣷⣬⣓⢤⣆⠀⠀⠀⣠⢷⡆⢀⡞⠀⠀⠀⠉⠉⢻⠶⣏⠒⠦⡳⣀⡇⠉⢢⣴⠋⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠀⠙⡖⣎⠀⠀⣷⠫⢄⠀⠀⠀⢸⠀⢹⠀⠘⣆⠀⠘⣎⣣⡠⠞⢣⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀
⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠀⠀⠋⠙⠀⠀⠛⠀⠀⠉⠒⠂⠈⠂⠈⠂⠀⠘⠂⠀⠘⠚⠁⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀