⡆⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠲⠿⣿⣯⣭⣍⠉⠉⠉⠉⠉⠁⢲⣦⢮⡐⠊⠉⢱⣮⠀⠈⠃⢔⣢⣼⣿⣷⡦⠾⠦⠲⣶⣶⣉⣶⣶⣶⣶ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣤⣤⣍⣙⠻⢿⣿⣦⣄⡀⠀⠘⣿⡻⣿⣿⡟⠛⠙⠀⢀⣴⣿⡿⠟⠉⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿ ⡇⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠉⠀⠀⠀⠀⠈⠑⠨⡙⠿⣿⣶⣄⣿⣷⣿⠀⣮⠀⡀⢰⣿⡿⠋⠀⠀⠀⠀⠀⢀⠀⠀⠀⢿⣿⣿⣿⣿⣿ ⡇⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣬⡻⢿⣿⣿⠃⣀⡼⠷⡽⣿⡟⠀⢀⡀⠀⢠⣥⣴⣶⣶⣦⣄⣿⣿⣿⣿⣿⣿ ⡇⠀⣰⡟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣽⣿⣜⢿⡇⠀⢰⡟⢀⠖⠁⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⣰⡿⢡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢻⣷⣕⢠⡿⠑⠁⠀⠀⠀⠀⢀⣀⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢹⣿⢱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⡠⠁⠀⢀⣤⣶⣿⣿⣿⣿⣿⣶⣍⠻⣿⢃⣶⣿⣿⣷⣄⠀⠈⠙⠿⣗⡀⠙⢿⣿⣿⣿⣿⣿⣿ ⢻⡧⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⠃⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣷⣤⣾⣿⣿⣿⡿⠟⠃⠀⠀⠀⠈⠻⣷⢄⠙⢿⣿⣿⣿⣿ ⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡑⠄⠉⠻⢿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣽⣿⣿⣿⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⡀⠀⠉ ⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠓⠐⠒⣸⣄⣠⠀⣼⣿⣿⣿⣿⣴⡇⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣷⣶⣶⣦⣰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⠿⠿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣉⡀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠑⠦⣤⣑⠄⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣴⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠂ ⡡⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠟⠉⠀⠉⠀⠀⠙⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠈⠙⠲⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠛⠁⠀⠀⢤⣬⣤⠀⠀⣈⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠉⠑⠲⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣷⣦⠀⠈⠉⠈⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣷⣶⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣄⡀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶ ⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⢆⣠⣴⣾⠿⠟⠛⢛⣿⣿ ⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⡠⣶⡿⣫⠾⠛⠉⢁⣀⣤⣴⣶⣿⣿⠿