⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠾⠿⠛⠛⠛⠛⠛⠛⠛⠛⠿⠷⣶⣤⣀⠀⣀⣴⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢨⣛⣿⣿⣿⣿⡾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣄⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⡾⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣀⠀⠀⠈⢻⣿⣿⣿⣿⣀⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⠏⠀⠀⣴⠂⠀⠀⡇⠀⢰⢇⠀⠀⠀⠀⠀⠀⣴⠀⠀⢹⢷⡀⠀⠀⠀⢻⡿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠏⠀⠀⣼⠃⠀⢀⡾⡇⠀⢸⠸⠀⠀⠀⠀⠀⠀⢿⠰⡄⠀⢏⢿⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣾⣻⣷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡿⠀⢄⣀⡇⠀⢠⡿⠑⣇⠀⠈⡜⡄⠀⠀⣄⠀⠀⢸⣆⢻⣄⢸⠘⣷⡀⠀⢀⠘⣿⣿⣿⣿⣿⣿⢋⠙⠿⣧⣄⠀⠀⠀⠀⠀ ⠀⠀⣾⠇⠀⠀⣸⡇⢠⡿⡷⣝⣿⡄⠀⣷⢱⠠⠀⢻⣔⠀⢈⣿⣷⡿⣿⣄⢺⡇⠂⠠⢀⢹⣿⣿⣿⣿⣽⣧⠆⣠⡉⢻⣷⡀⠀⠀⠀ ⠀⢠⣿⠈⠀⠠⢙⣇⣾⡵⠁⠀⡙⣿⡀⢿⣷⣃⠀⠈⢿⢶⣯⣻⣏⠻⣾⣿⣷⣷⠀⡁⠂⢸⣿⡿⠿⢛⣫⣿⣣⡟⠀⠄⢹⣿⠀⠀⠀ ⠀⢸⣿⠀⠈⣰⣸⣿⣯⣶⣶⡶⣯⣝⠿⢮⣿⡛⠧⣤⣜⣧⣬⣿⢿⢿⠿⣿⣿⣿⣀⣴⡡⠒⣿⢞⣿⢛⠩⢡⡾⠃⢀⠂⢸⣿⣄⠀⠀ ⠀⢸⣿⠀⢸⡇⢹⡿⠋⣼⢏⡇⢭⡛⣿⠄⠉⠁⠀⠀⠉⠿⣽⢏⡏⠘⢷⣸⣷⣿⣯⠈⠀⠡⣿⠛⢿⣇⣘⣾⠑⠀⣀⢒⣼⠛⢻⣷⡄ ⠀⣼⣿⠀⢸⣧⢸⡇⠠⣿⡚⠀⠈⢓⣻⡇⠀⠀⠀⠀⠀⠁⣿⠭⣄⠀⣠⠒⣿⡿⣯⠆⠀⢡⡿⠱⠈⣿⣼⠃⢀⡄⢠⡾⢃⡸⠋⠘⣿ ⢰⡿⢹⠀⠀⢿⡆⣷⠀⢻⣜⢧⢸⠱⣼⠃⠀⠀⠀⠀⠀⠀⠹⣧⡉⠇⣇⣼⣿⣧⡟⠀⠀⢸⡇⣡⢡⣿⠇⡠⡹⠀⣾⢑⠞⠀⠀⣰⡿ ⠸⣿⢸⡇⠀⠀⣿⢿⣧⠀⠙⠻⠿⠋⠁⢀⣠⣤⣶⠶⢶⣦⠀⠌⠙⠛⠉⣱⣿⢿⣷⠂⢈⣾⣁⣡⣿⣿⠰⢁⡇⣸⣯⠂⠀⠀⠰⢿⣧ ⠀⠻⣿⣧⠀⠸⣇⠀⠙⠶⠰⠇⢘⡄⠀⠈⣧⠂⡔⣈⢲⡿⠈⠀⠲⠐⠊⠋⢁⣿⠃⠀⠈⣿⡛⠋⠁⢿⣎⣾⡼⣿⠃⠀⢰⡀⢠⣿⠇ ⠀⠀⣹⡏⠀⡠⠙⢷⣤⣄⡀⠠⠎⠀⠀⠀⢻⡇⡰⢀⢻⡇⠀⠁⠀⣀⣤⣶⡿⠃⢡⠀⢀⣿⠇⠀⠀⠈⠻⠿⢿⣿⡇⢀⣾⣷⣿⡇⠀ ⠀⠀⢻⣇⠀⡅⠌⡈⢿⣿⠛⠿⢶⣶⣶⣶⣤⣿⣴⣷⣾⣷⡶⠿⠿⠛⢹⣿⠑⡈⣚⣴⡿⣿⡄⠀⠀⠀⠀⠀⠀⠘⢿⣼⣿⡈⠉⠀⠀ ⠀⠀⠈⢛⣿⣶⣦⣥⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣲⡟⠿⡊⢀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀ ⠀⠀⠀⢸⡏⠉⡎⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⢢⣥⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣷⣄⡃⠌⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡬⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣮⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀