⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠒⡄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠋⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠚⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⣀⣤⣶⠶⠟⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠳⠶⣦⣤⣀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⠀⠢⡀⠀⠀⠁⠀⢀⣠⡴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣿⣿⠟⠋⠀⠈⣿⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⡀⠀⣿⣿⣧⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣿⣿⣿⠟⠷⣄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⣤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣇⠂⠀⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢁⡾⠃⠀⠀⠀⠀⠀⠀⠀⣰⠂⠀⠀⠀⡀⠀⢀⡼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⣸⠃⢠⡟⠁⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⢀⣿⠇⠀⠀⠀⠀⠀⡀⠀⢠⣿⠀⠀⢀⢠⣿⣠⡏⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣠⣼⣿⠀⠀⠀⠀⠶⡶⠃⠀⣾⢏⠀⢀⣸⣾⣿⡟⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣱⣿⣿⡏⠀⠀⠀⠀⠀⠁⠂⢸⣟⣴⣴⠾⠋⠘⠟⠀⠀⠀⠀⢄⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣟⣿⡇⠀⣾⣿⠰⠂⠀⠀⣿⠛⠉⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠉⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⢈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠈⢱⣿⠘⣿⡇⠀⠷⠈⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⢠⣿⣿⣷⣦⣀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⢠⡾⠁⠚⠁⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⢿⣧⠀⠀⠀⠐⠀⠀⢸⡇⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⣿⣷⣄⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⢀⠙⢿⣦⡠⡀⠀⠀⠄⢸
⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⢸⣿⡀⠀⠀⣀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⠇⠀⢰⣇⣨⡿⢶⣄⠀⣿⠀⢀⣠⣴⣶⣿⣿⡀⠀⠉⣿⣷⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠈⣿⣧⠀⢠⡿⣧⣄⣀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠃⠀⠀⠈⠉⠁⠀⠀⠙⠻⠇⠀⢸⣿⣿⣿⣿⣿⡇⠀⣸⣿⡇⠃⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠸⣿⣦⣿⣿⣦⣉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⢠⣿⡏⠀⠀⢀⠀⣸
⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀⢀⣾⡿⣿
⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⢀⣯⣿⣿⣯⣤⡀⠈⠙⠿⠶⣤⣄⡀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣴⣿⣿⢡⡿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢠⣿⣿⣿⣷⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠛⠁⣾⠃
⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⢀⠢⣼⣿⣻⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣤⣴⣿⠃⠀⠐⢰⡟⠀
⠀⠀⠀⠀⣾⠃⠀⠀⠀⢠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⣹⣿⣿⣿⣿⡏⠂⠀⠀⣾⡇⠀