⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠈⠋⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⢦⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⡿⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠸⣷⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⡧⢕⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣿⣿⡄⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⠏⠃⠈⠉⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠐⣿⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣴⣶⡆⠀⠀⠀⠀⠀⠀⠀⣴⣴⣴⣄⣿⣿⣇⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣦⣤⣤⠌⣻⣦⣤⡀⢀⣤⡠⢔⡀⢀⣀⣉⢻⢿⣿⠇⠀⠀⠀
⠀⠀⠀⠀⢿⣿⠋⡟⠙⠛⠚⠘⠋⢉⠁⠈⠙⠋⠃⠿⠟⠛⠩⠹⣿⡿⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⡎⡐⠙⠓⠚⠉⠠⣾⡆⠀⢰⠀⠒⠒⠒⠂⡀⢺⣿⠇⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⡁⠀⠀⠀⡤⠔⡎⠂⠀⠈⡖⣀⡀⠀⠀⠨⠄⢿⠂⠀⠀⠀⠀
⠀⠀⠀⠀⠈⣷⣿⣧⣠⡖⠁⠀⣿⣧⣀⣀⣠⣷⠀⠉⢦⣤⣤⣷⡗⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢻⣸⠉⠛⢿⣶⣄⡨⠻⢿⣿⣿⣅⣄⣶⣾⠿⠛⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⢿⣦⠀⠀⠈⠻⢍⠙⠉⠋⠋⠉⡿⠋⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠞⣦⠀⢬⢧⣄⣀⡁⠉⣀⣠⡽⠁⠀⡼⠅⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣄⡉⠛⠛⠛⠛⠛⠋⠀⢠⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⠈⠀⠀⢀⢀⣤⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⠼⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠈⠋⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⢦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⡿⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠸⣷⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⡧⢕⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⠏⠃⠈⠉⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠐⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣴⣶⡆⠀⠀⠀⠀⠀⠀⠀⣴⣴⣴⣄⣿⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣦⣤⣤⠌⣻⣦⣤⡀⢀⣤⡠⢔⡀⢀⣀⣉⢻⢿⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⠋⡟⠙⠛⠚⠘⠋⢉⠁⠈⠙⠋⠃⠿⠟⠛⠩⠹⣿⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⡎⡐⠙⠓⠚⠉⠠⣾⡆⠀⢰⠀⠒⠒⠒⠂⡀⢺⣿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⡁⠀⠀⠀⡤⠔⡎⠂⠀⠈⡖⣀⡀⠀⠀⠨⠄⢿⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣷⣿⣧⣠⡖⠁⠀⣿⣧⣀⣀⣠⣷⠀⠉⢦⣤⣤⣷⡗⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣸⠉⠛⢿⣶⣄⡨⠻⢿⣿⣿⣅⣄⣶⣾⠿⠛⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢿⣦⠀⠀⠈⠻⢍⠙⠉⠋⠋⠉⡿⠋⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠞⣦⠀⢬⢧⣄⣀⡁⠉⣀⣠⡽⠁⠀⡼⠅⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣄⡉⠛⠛⠛⠛⠛⠋⠀⢠⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⠈⠀⠀⢀⢀⣤⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⠼⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀