⠀⠀⠀⠀⣠⠾⣿⡍⠓⠒⠚⠒⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⡏⠀⠈⠻⣦⠀⠀⠀⠀⠀⠉⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠁⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⡇⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠈⢦⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠈⡿⡄⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⡃⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠙⢆⠀⠙⣽⡶⠤⠤⠤⠤⢤⣀⣹⣄⣀⣵⣿⣤⣤⣄⣀⡠⢾⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⠗⠋⠉⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠉⠁⠀⠀⠀⠠⢶⣋⠀⠀⠀⠀⠀⠀⠀⠀⢐⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⢀⣼⠟⠁⢠⠀⠀⠀⠀⠀⠈⠳⣤⡀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠓⠲⢤⡀⠀⠀⠀⠈⠉⠓⣾⠃⠀⢀⡇⠀⠀⢠⠀⠀⠀⠀⠀⠹⣶⡾⠗⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠶⣲⡞⠁⠀⠀⢸⣷⢀⡠⠟⠀⠀⠀⠀⠀⠀⠘⣿⣦⢠⣴⠖⠉⠉⠀⠀⠀⠀⢧⠀⠀⠐⠒⠇⠀⠀⠀⣠⠦⠤⠤⠤⠤⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⡿⠀⠀⠀⢀⣽⣿⣿⠤⣤⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⢰⡟⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢧⡄⠀⣰⠏⣼⡟⠁⢀⠀⠹⡄⠀⠀⢠⣀⣤⣾⣿⡿⣿⣿⣿⠛⣳⡆⢠⠀⠀⢿⠀⠒⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡁⠀⢃⣴⡟⢀⡞⠁⣀⡀⠹⡄⠀⠀⠘⣿⣿⠷⡞⢻⣧⣬⡶⠟⠁⣾⠇⠂⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⡏⠀⢸⣿⡇⢸⠀⡜⢠⡦⢤⣧⠀⠀⠀⠹⣆⠀⢳⣾⣿⡉⠀⠀⠀⢯⠀⠀⠀⠻⣷⠀⠀⠰⣴⡿⠳⠤⠴⢄⣀⡀⠄⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡞⠋⠀⢻⡆⠘⣞⣷⡸⡀⢣⢸⣹⠻⣿⣀⡠⠶⠖⠚⠛⠛⠑⠉⣻⣆⣀⣴⢿⠀⠀⠀⣈⠛⢳⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠉⠀⡀⠀⠈⢧⠀⢸⣹⣧⣷⣸⣦⣯⡿⠏⠁⣠⣤⣤⣀⣀⠀⠀⠀⢸⣟⠁⠘⡾⠀⠀⠀⣸⡟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠐⠚⠁⠀⢀⡾⠁⠀⢀⣼⡇⢀⠉⠉⠙⢽⣯⠉⠀⢠⣾⣿⣿⣿⣿⡟⠀⠀⢠⡏⠘⡆⢀⠇⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠠⣿⡒⢀⡈⣁⣀⠀⠁⡻⣦⠀⠈⠙⠻⣿⡿⠋⠀⠀⣠⠎⠀⠀⢹⡟⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠉⢧⣼⣅⠈⠉⠙⢦⣀⠈⠀⠀⠀⠀⠀⢀⠴⠊⠉⣿⠉⠑⣲⣾⠀⠀⠀⢀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⣠⠄⠈⠃⢻⣧⠀⠀⠀⠙⢗⣦⡤⠤⠤⢴⠟⠦⣄⣀⢸⣀⡴⢻⡟⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⡖⠋⠀⠀⠀⣴⠋⠀⠀⠀⠀⢻⣧⣀⠀⠀⠀⠉⠻⣷⣄⣸⠀⣀⣀⠼⠛⠁⠀⡞⠁⠀⣀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢩⡇⠀⠀⠀⠀⠀⠙⠷⣄⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⢸⢅⡤⠚⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠐⣏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⢩⡀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠙⠒⠶⠶⠒⠉⠁⠀⣀⣨⠧⠖⠊⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣛⣚⡛⠚⠛⠛⠉⠉⠀⠀⠀⠀⢈⡿⠥⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠒⠒⠒⢻⡄⢀⣀⣀⣀⣀⣀⣀⠤⠔⠒⣏⠉⢻⠀⠀⠉⠑⠲⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠊⠉⠁⢠⢀⠄⠀⠀⣸⠶⣔⠲⢤⣄⠀⠉⠀⠀⠀⠀⠸⡄⣈⡷⠤⠤⠖⠢⠤⣌⡙⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠞⠉⠀⠀⠀⠀⠀⠀⠓⠈⠠⠶⣿⣏⣀⣈⣳⣄⠀⠉⠲⠶⠶⢒⡲⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣾⠏⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠊⠉⠙⠒⠲⠤⣀⡴⠋⠉⠂⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣔⡏⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢄⣀⡀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢦⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣤⠴⠒⠚⠋⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠉⠓⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠈⣆⠀⠀⠀⠀⠀⠀
⠀⢔⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⢤⣿⠀⣀⡾⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠈⠳⡄⠀⠀⠀⠀