⠀⠀⣿⣿⣷⡀⠀⣿⣿⡀⠀⢱⣄⠀⠀⠀⠀⠀⢀⠄⠀⢀⣀⡤⢀⣀⠐⣿⣿⠀⠀⠀⠀⣶⠀⠀⠀⠁⠀⠈⠁⢠⡀⠀⠀⠀⠀⡀⠀⢨⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⠀⠀⠀⣠⣤⣤⣤⣄⠀⠀ ⠀⠀⣿⣿⣿⣷⣼⣿⣿⣷⠀⠈⣿⣆⠀⠀⢀⣴⣟⣠⣴⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢰⣿⡄⠀⠀⠀⠀⠀⠀⣴⣷⡀⠀⠀⣶⣿⠀⣸⡇⢸⣶⣶⣿⣶⣶⣼⡆⠀⣼⣿⠀⠀⠀⢠⣾⢿⣿⣿⡿⣷⡀ ⠀⠀⣿⣿⠉⢿⣿⣿⠻⣿⡇⠘⣿⣿⡄⢠⣾⣿⣿⣿⡿⠛⠉⠉⠉⠉⠙⢿⣿⡀⠀⠀⢸⣿⣀⣀⣠⣤⣴⣴⣴⣿⣿⣷⠀⣼⣿⣿⠀⣿⣷⣿⠟⠉⠉⠉⣻⣿⡷⢀⣿⡟⠃⠀⠀⠘⣿⣷⣽⣫⣾⣿⠃ ⠀⢀⣿⣿⠀⠀⢻⡇⠀⢻⣿⡀⢹⣿⣿⣿⡿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⣿⣿⢻⣿⣟⣉⣉⡤⢼⣿⢻⣿⣷⣿⣿⣿⣠⣿⣿⡏⠀⠀⠀⣠⣿⢹⡇⣸⣿⡇⠀⠀⠀⠀⠘⠻⠿⠿⠟⠁⠀ ⠂⢸⣿⣿⠀⠀⠀⠀⠀⠈⣿⣧⣨⣿⣿⠏⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣶⣾⣿⣿⢿⣿⠿⠛⠋⠀⣿⡇⠀⢿⣿⡟⣿⣿⣿⣿⢻⣿⣦⣄⣨⣿⠿⢿⣿⣿⣿⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠁⠀⠀⢿⣿⣇⠀⠀⠀⠀⠀⠀⠉⠉⢿⣿⠉⢸⣿⡇⢸⣿⣠⣤⣤⣰⣿⠃⠀⣼⡟⠀⣿⣿⣿⡇⠀⠉⠛⠻⢿⠃⠀⢠⣿⣿⣿⣶⣾⣿⣷⣶⣶⣤⣤⣀⣀⠀⠀ ⡆⠀⠀⠁⠀⠀⠀⠀⠀⢠⣿⡿⢿⡄⠀⠀⠀⠈⠻⣿⣶⣄⣀⣀⣀⣀⣤⠖⢹⣿⣀⣸⣿⣇⣘⣿⠟⠋⠉⢽⡿⠀⠀⠙⠀⠀⢻⣿⡿⠃⠀⠀⠀⠀⠀⣠⡤⠄⠿⠛⣿⠛⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀ ⣇⠀⠀⠀⠀⠐⢄⠀⢠⣿⠟⠁⣿⣿⣦⣀⣀⣀⣀⣈⠙⠛⠻⠿⠿⠿⢃⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⡀⠀⠀⠀⢹⠏⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⠃⠉⠒⠢⢄⡀⠀⣱⣿⠁⠐⠚⣿⣿⣿⠛⠛⠛⠛⠛⢿⣷⣤⠀⢀⣴⣿⡿⠛⠹⠅⣿⡿⠉⠉⣿⣿⣿⣷⣄⠀⢠⡇⠀⠀⠀⠸⠀⠀⠀⠀⢀⣾⠀⢀⣿⣿⣧⢐⣿⡇⠀⣠⣴⣾⣿⣿⣿⣿⣿⣶⣶⣾ ⡄⠀⠀⠀⠀⠀⡔⠃⠈⠳⣦⡀⢿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⠏⠀⠀⠀⠀⠛⠁⠀⠀⡇⠙⢿⣿⣿⡄⣾⣿⣶⣶⣄⠀⣀⣀⠀⢀⣾⢿⡆⢸⣿⠏⣿⣿⣿⣧⣴⣶⣾⣿⣿⡟⠛⠛⠛⠋⠙⢛ ⠄⠀⠀⠀⠠⠊⠀⠀⠀⠀⠈⠿⣿⣿⣿⡀⠀⠀⠀⢀⣤⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⢘⣿⣿⣿⣿⣿⡿⠛⣿⣾⡿⣿⣇⣼⠇⠈⣿⣼⣿⣷⡿⢿⣿⡏⠉⠉⠙⣿⣿⣧⣀⣀⣀⠀⠀⠈ ⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣤⣴⣾⣿⡿⠛⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣸⣿⣿⣿⣿⣿⠁⠀⣿⠟⠀⢻⣿⡿⠛⠻⣿⣿⣿⣿⡶⠾⢿⡇⠀⠀⠀⣿⣿⠟⠻⠟⠛⠋⠀⠀ ⠆⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⣿⣿⣿⣿⣿⣿⣿⣏⡁⠀⠀⢿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⣿⣿⣿⢿⣿⡏⠀⠀⠋⠀⠀⣿⠿⠀⠀⠀⠸⣿⡿⠻⣿⣷⣿⣷⣶⣶⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢹⣿⣿⠉⠻⢿⣿⣤⡀⠘⣿⣿⣿⣿⣶⣤⣄⣀⣀⣀⣠⣴⣿⣿⣿⡿⠁⠈⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⠇⠀⠀⠉⠛⠛⠛⠻⢿⣿⣿⣶⣶⣶⡶⠶⠦⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠙⢿⣿⣦⡈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠉⠙⠻⠄⠀⠀⠉⠉⠉⠩⠽⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡁⠀⠀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡆⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡥⢞⣻⣿⠋⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡀⠀⠀⠀⠘⢯⣿⣿⡁⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣶⣶⣾⢿⣿⣿⣿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⣿⣿⣿⣿⠋⢉⣻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣆⣾⣿⣿⣿⠁⢀⢹⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣤⡏⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠓⣿⣽⣿⣿⣹⣿⣿⣹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⢸⡁⣿⠬⡿⢩⢸⠁⣽⢨⡇⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⢠⣤⣄⠀⣄⡀⣤⡤⠀⣦⣄⡀⣄⡀⣄⣀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠇⣿⠀⡇⠸⠰⠇⠿⠉⡗⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣽⡇⢸⣿⣽⠀⣿⣏⣿⡆⠀⣿⠿⣷⣿⡃⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠁⠘⠛⠉⠙⠙⠉⠛⠙⠀⠟⠀⠙⠛⠋⠻⠛⠹⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠛⠛⠛⢛⣛⣿⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⣀⢀⣀⡀⣀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀