⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⢀⠀⠀⠀⠀⠙⠻⣿⡇⠀⠀⣿⡇⠀⢸⣿⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠙⣄⠀⠀⠈⢢⡀⠀⠲⡀⠙⢧⠀⠀⣿⡇⠀⢸⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⠀⠀⠀⠀⠀⣴⠆⠀⠌⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠙⣦⡀⠙⡄⠘⢧⠀⣿⡇⠀⢸⣿⠀⠀
⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠘⢷⡀⠈⠆⠘⣇⢿⠀⠀⢸⣿⠀⠀
⡰⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⢠⠏⠀⠀⠘⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢹⢷⡀⠀⠀⠘⢧⠀⠈⡄⠸⡞⠂⠀⢸⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⢀⡋⠀⠀⠀⢀⡆⠀⠀⠀⠀⠘⡄⠀⠀⠸⡎⡇⠻⡄⠀⠀⠘⡆⠀⠘⠀⢻⠀⠀⠘⢋⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⡀⠀⠀⠀⡀⢘⣷⠀⠀⠀⠀⠀⢇⠀⠀⠀⡇⠇⠀⠙⣆⠀⠀⢱⠀⠀⢃⠈⣇⠀⠀⢸⠄⠀
⢀⠤⠒⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⡇⢸⠟⣇⢳⡀⠀⠀⠸⡀⠀⢀⣿⠀⠀⠀⠘⣆⠀⠀⠇⠀⢸⠀⢸⡄⠀⢸⠀⠀
⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⠀⠀⠀⡘⠀⠀⠀⠀⠇⠘⠀⠘⡄⢣⡀⠀⠀⠃⠀⠌⢸⡆⣀⠤⠖⠚⡟⠀⢠⣀⠀⡇⢸⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⡆⠀⠀⠀⡇⠀⠀⠀⣸⠀⠆⠀⠀⠘⢄⠳⣄⠀⠈⢆⡤⣾⠏⠀⠀⠀⠀⠸⡄⠘⠿⣷⣇⢸⣧⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠁⠀⠀⢠⠆⠀⠀⠀⡟⢀⣀⡤⠤⠤⠀⣳⣽⣿⠦⣜⣦⡛⠀⠀⠀⠀⠀⠀⢻⡀⡇⠈⣿⣿⣿⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡄⠀⠀⢸⠀⡀⠄⡾⠃⠇⠀⠀⠀⠀⠚⠋⠁⠉⠓⠀⠉⠉⠀⣀⣠⣤⣤⣶⣦⣷⣇⣴⠟⢿⣿⣷⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣤⡀⠀⢸⠃⣀⣴⡿⠁⠀⡜⡘⡌⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣵⣿⣿⡿⣏⡥⠀⢨⣿⡟⠃⠀⢸⣿⢸⡄⠀⠀
⠀⠀⠀⠀⠀⣰⣿⠻⢿⣦⣾⣾⡟⠋⡇⢀⡌⣴⣿⣶⣾⣿⡿⠟⠻⡟⠂⠀⠀⠀⠀⠀⠹⣟⠛⠃⣿⠀⠀⢾⣿⡇⠀⠀⢸⣿⢸⡇⠀⠀
⡉⠛⠀⠀⣠⢿⣿⠀⣠⣿⡿⣿⣤⣀⣵⣿⣿⣿⣿⣿⡟⠧⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⠴⡃⠀⠤⢺⣿⡇⠀⠀⢸⣿⢸⡇⠀⠀
⢳⡀⠀⡞⣱⣟⢿⣾⠟⠁⢷⠀⠙⢿⠇⠛⣦⣻⡏⠉⠀⢀⡏⠀⠀⠀⠀⠀⠀⢠⠒⠐⢄⠀⠈⠛⠉⠀⠀⣾⢿⣇⠀⠀⣾⣿⣸⠃⠀⠀
⠳⣵⣄⣇⢹⣄⠸⠁⠀⠈⢠⠀⠀⠈⠀⠀⠈⠉⠙⠒⢋⣩⡥⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠁⠀⠀⠀⠀⠀⡿⢿⣿⠀⢀⣿⡏⣿⠀⠀⠀
⠀⠈⠻⣿⣦⢹⣆⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢀⡇⠸⣿⠀⣸⣼⠇⡿⠀⠀⠀
⠀⠀⠀⠈⠙⢷⣮⣧⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠀⢹⣄⣿⠏⢸⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠛⣷⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢫⠞⠁⠀⢸⡿⠟⠀⣿⡇⢰⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⡆⡇⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠁⠀⠀⡰⡿⠁⠀⢸⣿⡇⠸⡀⠀
⢹⡄⠀⠀⠀⠀⠀⠀⠈⣿⡄⠁⢰⠀⢰⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢒⡼⠟⠁⠀⠀⠀⠀⡔⣰⠁⠀⡄⣸⠏⠛⢶⣭⣓
⠀⣿⠀⠀⠀⠀⣀⣠⣤⡾⠳⠀⠀⠆⠈⠀⠀⠀⠀⠉⠳⠶⣦⣤⣀⡀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⢀⡞⣰⠃⠀⠀⣷⡿⠀⠀⠀⠈⠙
⢠⣏⣤⣶⣾⣿⣿⠟⠋⠀⠀⠣⠀⠠⠀⡆⠀⠀⠀⠀⠀⠀⠈⢙⡿⠋⠙⠻⢿⡛⠿⠀⠀⠀⣀⠤⠔⠚⠛⢷⡀⠀⠀⣿⡇⠀⠀⠀⠀⠀
⠋⣿⣿⣿⡽⠋⠁⠀⠀⠀⠀⠀⠣⡀⠃⢰⠀⠀⠀⠀⠀⠀⣠⡊⠀⠀⠀⠀⠀⠹⣄⡠⠖⠋⠁⠀⠀⠀⠀⠀⠸⡄⠀⢹⡧⢤⣄⠀⠀⠀