⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢏⠙⠉⠋⠙⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢼⣣⠁⢁⠉⠀⠀⣦⢽⠀⠀⠀ ⠀⣠⡤⣤⣠⡤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⡴⠁⠐⠃⠀⠀⠀⢷⣾⠀⠀⠀ ⡒⠋⠀⠀⠑⠨⢽⣿⣻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠤⠤⢠⠤⠴⠋⢠⡜⠀⡠⢒⢅⣴⠀⠀⢛⢿⠀⠀⠀ ⢻⠀⠀⠀⠀⠀⠀⠈⠳⣟⠻⢴⣄⣴⡶⠖⠲⠶⠚⠙⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠘⢿⣅⣠⣼⠣⠐⡂⡅⠚⠃⠀⠀⢘⢸⠀⠀⠀ ⢿⡇⠃⠀⠀⠀⠀⠀⠀⠈⠳⣼⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠈⠛⣀⢀⣪⣺⣄⠄⠀⠀⠀⠼⢾⠀⠀⠀ ⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠡⡿⠃⠀⠀⢀⢞⡄⡎⠀⠀⠀ ⠀⢹⣇⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢖⡴⡺⠉⢰⡇⠀⠀⠀ ⠀⠀⢿⡅⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠗⠀⢊⠂⣾⠁⠀⠀⠀ ⠀⠀⢸⡇⠑⢓⡲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣩⣽⣿⣿⣷⣤⣠⢄⠒⠡⠀⠀⠀⠠⠒⣀⠐⡌⢣⡀⠀⠀ ⠀⠀⢸⣇⠰⠋⠀⠀⠀⠀⠀⢸⣾⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠔⣿⣿⣷⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠒⠡⠃⠀⠀⠳⡀⠀ ⠀⠀⣻⠇⠀⠀⠀⠀⠀⠠⠞⠛⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠨⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠙⡄ ⠀⢠⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⢀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⢰⡞⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣾⣿⠿⢿⣿⣿⣶⣆⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠈ ⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣿⣿⣷⣶⣿⣿⣿⣿⡿⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠂⠀⠀ ⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠘⢽⣿⣿⣿⣿⣿⣿⣟⢴⠑⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀ ⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠦⠈⣹⢻⣿⣿⣿⣿⣿⣴⠅⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠉⡁⠀⠃⣉⣽⣷⣯⣭⣅⡄⡐⢠⡤⠴⠟⠁⠀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠇⠘⠀⠀⠀⠀⠀⡀⠀⠀⡠⡲⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸ ⠀⠈⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⢂⢠⠏ ⠀⠀⢨⣗⣂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣤⣉⡵⠋⠀ ⠀⠀⠀⠙⢳⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⣡⡤⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠚⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠿⣤⣢⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢶⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⣀⣀⣠⣤⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀