⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢖⣈⠭⠵⠲⠭⢍⡐⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢊⡴⠋⠀⠀⠀⠀⠀⠀⠈⠑⠢⣍⡒⠤⢄⣀⣀⣀⣀⣀⢤⠤⠔⠒⣂⣈⣉⣀⡲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⣡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠉⠒⠒⡖⠒⠒⠒⠒⠋⠉⡀⠀⠀⠀⠀⠈⠳⣌⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⢌⠑⠒⠠⠤⠤⠤⠤⠤⢚⡡⠚⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠜⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⠭⣑⣒⣒⡒⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠳⡝⢏⠙⠒⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢦⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⢒⡡⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠳⡙⣄⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢚⡥⠖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⡜⢆⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢡⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣌⣆⠀⢀⣀⣀⣘⣄⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⡠⠀⣒⣒⣒⣒⣒⣒⣚⣉⣉⣩⣉⣩⡉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡠⠐⣫⠥⠐⠶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠓⠛⠛⠛⠛⠋⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣷⡖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣨⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡝⡇⠀⠀⠈⡇⠀⠀⠀⠀⠀⣠⣴⣶⠶⠿⠿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⠿⠛⠛⠛⠛⣿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠻⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠛⠋⠁⠀⠀⠀⠘⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠹⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⡷⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣇⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠿⢿⣷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣷⣧⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠉⠙⠻⠿⣷⣦⣤⣄⣀⣀⣀⣀⣠⣴⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢹⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡏⣿⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡛⠛⠷⠶⢶⣤⣤⣄⣀⣀⠈⠉⠙⠛⠛⠛⠋⢹⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⣿⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠻⠷⠶⣶⣦⣤⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⣿⠏⠀⠀⠀⣀⣀⣀⡀⠀ ⠀⠀⠀⠀⠀⣷⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢸⣧⣶⣶⣶⣾⣿⣿⣿⣿⣧ ⠀⠀⠀⠀⠀⢹⣿⡄⣾⡆⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⢶⣶⠶⠶⢶⣶⣶⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⢠⣶⣿⣿⣿⣾⣿⣾⣿⣄⣀⣇⣀⣀⠀⣠⠤⠤⠤⠤⠠⠤⠤⠤⠤⠤⠠⠀⠠⠀⠠⠀⠀⠐⠀⠒⠒⠒⠒⢒⠒⠒⢒⣒⣒⣊⣉⣉⣉⣉⣉⣩⣭⣽⣤⠀⠀⠀⠈⠻⣿⣿⣿⡿⠁ ⣿⣿⣿⣿⣿⣿⡟⠋⠙⠒⠓⠀⠐⠒⠒⠒⠒⠐⢲⡖⠒⠒⠒⠒⠛⠛⠓⠊⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⢹⣇⠀⠀⠀⢀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⢠⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀