⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡓⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠙⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⡶⠤⠤⢤⣄⣀⢀⣠⡴⠚⠉⠁⣠⡤⠖⠒⠉⠉⠑⠒⢀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⡄⠀⠀⠀⠈⠉⠀⠀⣠⢖⣯⣷⠷⠄⣀⣤⠤⠴⢲⡟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⠋⠓⡆ ⠀⠀⠙⣦⡀⠀⠀⠀⡴⠋⠀⠞⡿⠂⠈⠙⠳⣄⠀⢠⣿⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠙⡿⠀⢠⡏ ⠀⢀⡼⠁⠀⠀⢀⡞⠁⠀⢀⡾⠀⠀⠀⠀⠀⠈⢻⡿⣿⡀⣿⣯⣹⡇⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠻⠃ ⢀⡞⠀⠀⠀⠀⣼⠀⠀⢀⣾⣧⠀⢰⣿⡟⢢⠀⠀⡇⠈⢿⣽⣛⡛⣁⡰⠿⣶⠶⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠒⠢⢤⠇⠀ ⠾⣄⡀⠀⠀⠀⡏⠀⠀⣸⠃⢻⣦⠘⣿⣿⣾⠃⢠⠇⠀⢠⣶⣶⡏⠡⣴⠾⣷⡶⠒⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⣠⠋⠀⠀ ⠀⠀⠉⠉⠙⢦⣷⠀⠀⡏⠀⠀⠉⠻⠶⠦⠤⠖⠃⠀⠀⠀⢉⣭⣅⠀⠀⠀⢳⡾⠁⠀⢀⣠⠴⠋⠁⠀⠀⢀⡴⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣦⣠⠃⠀⠀⠀⠀⠐⢢⠶⠒⠒⠒⠒⠚⣉⣠⡿⠀⢀⣴⠯⠔⠒⠉⠉⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠻⣯⡇⢀⠀⠀⠀⠘⢦⣰⡖⠒⣋⣿⡿⢛⣡⡴⠋⠀⠀⠀⠀⠀⢀⣀⠤⠖⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⣻⠏⠀⠀⠀⣀⣀⣈⣙⣭⣥⢾⡛⣏⠁⠀⠀⡤⠤⠔⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡟⠉⠉⢉⡽⡏⠉⠁⠀⠀⠀⠀⢣⠘⡆⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡞⡑⠀⠀⡰⠋⠀⠘⣆⠀⠀⠀⠀⠀⠈⣇⠸⡄⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⢡⠇⠀⡼⠁⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠸⡄⢱⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⢠⣇⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⢳⠈⡇⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⢸⡏⠳⣄⠀⠀⠀⠀⢳⣆⠀⠀⠀⠀⠘⣇⢸⡀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠈⣇⠀⠈⠳⣄⠀⠀⠀⢿⠀⠀⠀⣀⣀⣼⣨⣧⣴⣶⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⠈⡆⠀⢿⠷⣄⠀⠀⠉⠒⠴⣿⠿⠿⠿⠿⠿⠿⠛⡍⠉⢙⠁⠁⠣⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⡷⠒⠋⠉⠀⠈⠙⠲⣤⣀⠀⠸⣦⣶⣖⠀⠀⠀⢠⣇⠀⢻⣦⡀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠱⣠⠖⠉⠉⢹⡆⠀⠀⠈⠉⠙⠛⢿⣿⣿⣄⢠⣿⣿⠀⠈⣿⣿⣶⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣼⣆⣥⡿⠃⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠀⡄⠸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢹⠀⢱⠀⢹⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡿⠘⠒⠛⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢻⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣤⠤⠤⠖⠚⣉⣡⠿⢿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠒⠒⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢳⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠸⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⣿⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢿⣿⣿⣿⣷⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀