⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠛⠻⣷⣤⣠⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠈⠉⠉⠉⠉⠛⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⢹⣿⠀⢀⣤⣶⣶⡄⣠⣶⢶⣦ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡾⠿⠿⠿⠿⢶⣦⣤⣠⣿⠋⠀⠀⣼⣇⣴⠿⠋⠀⣿⣿⠟⠁⣼⡟ ⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⡄⠀⢀⣿⡿⠋⠀⠀⢰⣿⠃⠀⢰⣿⠁ ⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠈⠛⠁⠀⠀⠀⠙⠃⠀⠀⣿⠇⠀ ⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁⠀⠀⠀⡴⠶⢦⣄⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀ ⠀⠀⢠⣿⠏⠀⠀⠀⣠⣶⣶⣦⣤⣤⣴⣶⡾⠟⠋⠁⣠⣴⣷⢲⣾⣟⢷⣶⣽⡇⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀ ⠀⢠⣿⠃⠀⠀⠀⣰⡿⠁⠀⠀⠀⣾⡇⠀⠀⠀⠀⣸⠿⣧⡿⠘⠷⠟⠈⠋⠈⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀ ⢠⣿⠃⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⠀⠀⢀⣤⣤⣤⣀⣠⣿⠃⠀⠀⠀⠀ ⣾⡏⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⡋⠀⠀⠀⠀⠘⣿⣭⣭⣿⠟⠿⣶⣄⠀⠀⠀ ⠻⣷⣤⣤⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣤⣄⣀⣀⣀⣤⣤⣶⠾⠟⠋⠁⠙⢿⣦⣄⣀⣀⣀⡀⠉⠉⠀⢀⣀⣠⣿⡇⠀⠀ ⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠟⠁⠙⠷⠶⠶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣶⠀⠀⣀⣀⠀⣀⣀ ⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠛⣷⣶⠶⢶⣦⣄⣀⣾⠋⠀⣿⣠⡾⠏⣿⣾⠋⣿ ⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠉⠻⣷⡀⢀⣿⠏⠀⢠⡿⠁⢰⡏ ⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⢀⣀⠀⠀⠀⠘⣷⠈⠁⠀⠀⠈⠁⠀⣿⠁ ⠀⢀⡾⠃⠀⢀⣤⣄⣀⣀⣠⣴⠾⠋⣀⣤⣤⡽⣭⣷⡄⠀⠀⣿⠀⠀⠀⠀⠀⠀⣸⡇⠀ ⢀⣿⠃⠀⢀⣾⠁⠉⠉⣿⠉⠀⠀⣼⢿⠟⠻⠟⠙⠋⠁⠀⣸⡏⠀⠀⠀⠀⠀⢠⡟⠀⠀ ⣾⠃⠀⢀⣾⠃⠀⠀⠀⢿⡄⠀⠀⢿⠀⠀⠀⠀⠀⠀⣀⣼⠏⠀⠀⣴⡶⣦⣴⣟⡁⠀⠀ ⣿⣀⣠⡾⠃⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⣀⣠⣴⠾⠻⣧⣀⠀⠀⠘⠛⠛⠋⠉⢻⡆⠀ ⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠉⠀⠀⠀⠈⠙⠛⠛⠻⠿⠶⠿⠟⠛⠁⠀