⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣀⣠⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⠞⠉⠀⠀⠀⣈⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠈⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡞⠁⠀⠀⠀⠀⠈⠉⠉⢻⢋⠉⠋⠉⠙⣛⠛⠛⡿⠉⠉⢹⡏⠉⠻⠏⢩⣉⣩⣍⣙⡿⢷⣄⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⠁⠀⠀⠀⠀⠀⠀⢀⣠⡾⣏⡤⠶⠶⠶⠿⠦⢤⣀⣰⠀⠈⢰⣤⠖⠊⠉⠉⠀⠀⠈⠉⠺⢿⣦⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⢠⣾⣏⡵⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠚⠉⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠛⣧⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⡄⠀⠀⠀⠀⡾⢩⠏⠀⠀⣰⣦⣄⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣴⡿⠛⠋⠉⠙⠛⢷⣤⠀⢹⡄⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠦⣤⣤⣴⢇⡎⠀⢀⣾⠟⠀⠀⠉⠉⠻⣿⣿⣿⣿⡄⠀⠀⢠⡿⠋⠀⠀⢀⠀⢹⣿⣿⣿⣷⡀⣧⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⢰⢸⠁⠀⢸⣿⠀⠀⠀⢰⣦⣴⣿⣿⣿⣿⣷⠀⡀⣼⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣇⢃⡜⠀⠀⢸⣯⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡟⠀⠁⢹⣇⠀⠀⠀⠘⠿⣿⣿⣿⡿⣿⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡄⡇⠀⠀⠀⠻⣧⡀⠀⠀⠈⠙⠛⢛⣿⡿⠁⠀⢀⠈⢿⣦⡀⠀⠀⠀⠀⠉⣁⣾⠟⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⢻⡇⠀⠀⠀⠀⠉⠻⠶⣶⣤⣴⡶⠿⠋⠀⣴⣶⠞⠒⢶⣿⡿⠶⢶⣶⡶⠾⠟⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣷⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣾⡄⠀⠀⠀⠀⠀⠀⢰⡖⠛⠋⠉⠉⠉⠉⠙⠛⠒⠲⠤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠼⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⢨⡇⠀⠉⡿⠲⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⡇⠀⢀⡏⠀⠀⡏⠉⠙⣿⠶⠶⢤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣤⡤⠤⢶⡶⠛⠋⣿⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠶⠛⢧⣄⣸⡇⠀⠀⣷⠀⠀⣿⠀⠀⢠⡇⠀⠀⢸⠁⠀⣸⠁⠀⢸⡇⠀⢸⡇⠀⠀⣿⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠃⠀⠀⠀⠈⠉⠓⠶⠴⣇⣀⣀⡿⠀⠀⢸⠃⠀⠀⣿⠀⠀⡟⠁⠀⢸⠁⠀⢸⡇⠀⢀⣇⡴⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣭⣽⡷⠒⢾⡦⠤⢤⣿⣀⣀⣇⣀⣀⣿⣠⣤⠼⠶⠖⠋⠉⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⢰⡆⠀⣠⡴⣾⠃⠟⠉⠁⠀⡼⢻⡶⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡟⠀⠀⠀⠀⣠⠶⠶⣾⡶⢦⠀⠀ ⠀⣾⠀⠀⠀⠀⠀⣸⣡⠾⡇⠀⠸⣇⠀⠀⠀⠀⠠⣾⡃⠀⠀⠀⠙⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⢀⡴⠛⢻⡸⣦⣙⣧⠼⢷⡄ ⢠⠇⠀⠀⢀⣤⠞⠋⠁⠀⢳⡄⠀⠘⣦⡀⠀⣀⣴⣿⣧⠀⣤⣴⣿⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡤⠞⠋⣧⠀⠈⢷⣤⠿⡤⠤⠞⣧ ⣼⢀⣤⠞⠋⠀⠀⠀⠀⠀⠀⠻⣄⣀⣠⡽⠛⠓⡦⠈⠁⠀⠉⢉⣭⣀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡟⠉⠀⠀⠀⠈⢧⡀⠀⠙⣦⠿⠒⠛⠁ ⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠁⠀⠀⠀⢧⣦⣇⢠⡇⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⣀⡽⠗⠛⠁⠀⠀⠀⠀ ⡿⠀⠀⠀⠀⠀⢀⣠⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⢤⣀⣀⡤⠶⠋⠉⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣣⠴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⢤⣄⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⣀⠀⠀⠀⠀⢀⣀⣤⡶⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠈⠉⠉⠉⠉⠉⢹⡆⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⢀⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⢸⣅⡀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⣽⣭⣭⡵⠟⠀⠀⠀⠀⠀⠀⠀⠸⢮⣝⣉⣉⣉⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡇⠀⢸⣤⣄⣀⠀⠀⠀⠀⠀⠀⣀⣸⠀⠀⣯⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡿⣿⣿⣿⢶⣦⡀⠀⣼⣿⣿⣿⣿⣿⢿⣿⣿⡷⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣟⣵⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣽⣫⣾⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢮⣝⡛⠿⢿⣿⣿⣿⣿⣿⠿⠿⢿⡯⣝⡛⠿⢿⣿⣿⣿⣿⣿⣿⠿⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠒⠒⠒⠒⠛⠛⠉⠀⠀⠉⠙⠛⠒⠒⠒⠒⠒⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀