⣀⡿⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣿⣇⡀⠀⠀ ⠀⠟⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠙⠆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⡇⠀⠀⢸⣿⠀⣴⡄⠀⢸⣿⣿⣿⡇⠀⠀⣤⣤⣼⣿⣿⣿⠀⣶⡄⠀⢸⣿⠀⠀⠀⠳⢤⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠚⠒⠒⡗⠂⠀⢸⣿⠀⣤⣀⠀⢹⣭⣭⣿⡇⠀⠀⣤⣤⣼⣭⣭⣿⠀⢰⣦⠀⠘⣿⠀⠀⢠⠎⠁⠙⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢸⣿⣤⣤⣤⣤⣾⣿⣿⣿⣧⣤⣤⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡵⡅⡯⠅⣞⡇⡷⢾⢳⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠋⠙⡆⡖⠉⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢹⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⢲⡴⠛⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣰⠋⠈⡇⠀⠀⡇⠀⢀⡤⣄⢀⡴⠲⣄⠉⠉⡆⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⡤⠤⣄⠀⠈⠳⠔⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣄⣀⣀⡞⠁⠀⠀⢣⡀⠀⠀⠲⣄⡖⠀⠀⠀⣀⡇⡏⠀⠀⠀⠀⠙⣆⠀⢀⡞⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡽⠁⠀⠀⠀⡿⡅⠀⠀⠹⡄⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣆⣤⡖⠀⠀⠀⠀⠀⠀⣀⣀⣠⠞⢠⠇⠀⠀⠀⠀⡇⠙⡆⠀⠀⢀⣳⡄⠞⠙⠻⠄⠰⠋⠳⣄⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠐⠓⣗⡟⠷⣄⠀⠀⠀⠀⠀⠻⣧⡴⠋⢹⢧⣀⣠⠤⡎⠉⠳⡌⠙⡏⢁⡞⠁⠀⢧⡤⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⡇⠀⡃⠀⠀⠀⠉⢹⡁⠀⠀⠀⢀⡴⡅⠙⣦⣄⠀⢀⣧⡳⣠⣤⣤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⣰⣿⡇⠀⣧⣄⠀⠀⠀⠀⣼⣿⣿⣿⣝⣆⠈⢷⡃⡤⣄⠀⠀⠉⠙⠚⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣺⣿⢷⣄⣈⣿⣿⣿⣀⣠⣿⣿⡦⠀⠀⠀⣼⣿⣿⣟⣁⡳⣄⠀⣠⣿⣷⣶⣦⡤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣸⣀⣀⣇⣀⠀⠒⢲⠒⠂⢠⢾⠀⡞⢳⠀⡆⢰⠆⢰⣆⠀⡇⠐⠒⢲⠚⡴⠒⠀⡆⠀⢰⠀⢤⠤⡤⢴⡄⢠⡦⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⡏⠒⢺⠓⠂⢰⡀⣸⠀⠰⠋⠉⡇⢧⣠⠀⡏⠳⡄⡼⠀⠿⠄⢸⣀⡞⠀⣗⣒⡀⣇⣀⢸⣀⣸⡀⡏⠁⢹⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣀⣸⣇⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡜⠋⠳⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠟⢿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀