⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣔⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠏⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠁⠀⠀⣰⡇⠀⠀⠀⢠⣄⠀⠀⠀⠀⡴⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢦⢀⠇⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⣴⣾⣿⣇⠀⠀⠀⡜⠘⡆⠀⠀⣠⢸⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⣾⡀⣇⠀⠀⠀⠀⠀⠀⠀⢀⡤⣴⣾⠃⠀⠀⠀⢸⡿⠘⣿⣿⣿⣶⡟⠁⢠⣇⣴⠎⡼⠀⠀⠀⠀⠀
⠀⠀⠀⢠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠈⠻⣿⣦⣀⣀⣠⣶⡏⢰⣿⣿⠀⠀⠀⠀⠀⠀⢸⡿⠟⣿⡿⠀⠀⠀⣤⣿⣿⣿⠀⡠⠞⣠⡀⠀⠀
⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠈⢻⣿⣿⠻⣿⡇⠀⠿⠟⠀⠀⠀⠀⠀⠀⠸⠁⠀⣿⣿⡼⠿⡿⠹⣿⡞⠁⠀⠀⡴⠁⢹⠀⠀
⠀⠀⠀⢸⠀⠸⡀⠀⠀⠀⠀⢴⠢⡀⠀⠀⠀⢣⠀⠀⢿⣿⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢠⣿⠃⠀⣾⠃⣰⢿⠀⣠⢲⡞⠀⢀⠎⠀⠀
⠀⠀⠀⠀⠢⡀⢱⡄⠀⠀⠀⠸⣆⠈⢻⣷⡓⢬⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢰⣴⡿⠃⠀⠀⣇⢰⡏⠈⢦⡇⢸⡷⣤⠏⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠻⣿⠦⣤⣤⣤⣿⣿⣾⣿⡟⡾⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣿⠏⠀⠀⣼⡇⠘⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡈⠳⢤⡉⠙⢿⣯⡻⢿⠃⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⣼⡟⠀⢀⠞⣿⡇⠀⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣄⠀⠀⠘⢯⠓⢗⠿⣆⠀⠹⣿⣦⠀⠀⠓⢄⠀⠀⢰⣄⣄⢀⠊⠁⡷⠊⠀⡇⠀⠀⣸⡇⠀⠀⢸⠀⡰⡏⠀⢿⡇⢠⠇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠹⡌⠓⠤⣀⣘⡇⠀⠀⠈⢢⡀⢻⣿⣇⠀⠀⠀⠀⠀⠀⠉⠟⠂⠀⠀⠀⠀⢠⢀⠀⠀⠁⠁⠀⠀⢸⠀⢣⠀⠘⡷⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠉⠙⠒⢬⣿⣿⣶⣤⣰⡷⠹⠈⠁⠀⠑⢠⠄⠀⠀⠀⠀⠀⡀⢀⠂⠀⠀⣷⠁⠀⠀⠀⣠⣤⡀⢸⠂⡸⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⡏⠿⣿⣿⠀⣠⣤⡶⠆⡀⣄⣆⠀⠀⡀⠀⠀⣇⢞⠀⠀⠀⠑⠀⠀⠀⠀⣠⣾⣿⣿⡇⠀⣄⠁⠈⡎⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢶⢢⣤⣀⡇⠘⠸⣿⡾⣝⠛⠇⡨⣒⠍⣿⣶⢌⣀⠜⠀⠹⣾⡀⠀⠀⢀⢠⣮⢻⣿⣿⣿⡇⢀⠉⠀⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⢫⠁⠀⠙⣿⣶⣤⣀⠀⠚⠀⢹⠉⣆⡄⣀⠀⠀⠀ ⢀⢙⠿⣿⣿⣷⣶⣿⣿⡿⣏⢔⡀⠀⢠⠠⣌⠳⢄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣸⡄⠀⠀⢸⡇⠈⠉⠀⠈⠁⠁⠊⢉⡟⣻⢠⡕⠀⠑⢬⡒⢬⣭⣿⣿⣯⠽⠞⠋⢠⠀⠈⢳⣄⠑⢄⠳⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠫⣙⣷⣤⣘⢷⣤⣬⣔⣠⣤⣴⡟⠙⠣⠈⠛⣧⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⡀⠘⠧⣈⠆⢸⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠣⡈⣿⣿⡼⠛⣻⠛⠛⠋⠀⠀⠀⠀⢠⣇⡠⠂⢀⣴⣷⢸⣷⡀⠀⠀⠀⢸⠢⣄⠀⡀⠻⣶⣦⠀⢰⠊⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣠⡄⢠⢃⠤⠤⢀⠠⠀⠀⠀⠸⣧⣁⠀⣈⣯⣵⠟⡋⠉⠑⠢⡿⠀⠈⠙⠦⣀⣀⣀⣠⠎⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢗⡴⠃⠀⠀⠀⡇⠀⠀⡀⠀⢈⣏⠉⠉⠉⢁⡎⠀⠀⠀⠀⠡⠈⡇⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠉⠀⠀⠀⠀⣀⣴⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⣄⠀⠀⠀⠀⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣤⠒⠒⠊⠉⠀⠀⠀⣀⡄⠊⠻⢿⡀⠈⠟⠙⠛⠉⠉⠉⠛⠈⠋⠀⢸⣷⣦⠀⠀⠀⠀⠈⠑⠒⠠⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠒⠊⠉⠀⠑⢄⡀⠀⠀⠀⠀⡀⠤⠒⠒⠒⢦⢄⡀⠀⠈⠉⣠⠏⠑⠒⠲⠶⠖⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⡁⡰⠀⠀⠀⠀⠀⠂⠀⠀⠈⣡⠖⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⢄⣀⣠⣀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀