⠀⢀⡠⡖⠒⠒⠢⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⢡⠰⠀⠀⠀⠀⠈⠉⠚⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣾⢬⢃⡅⢢⢀⠄⠀⠀⢀⠀⠀⢞⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⣯⣯⣜⢲⡍⡐⠠⠂⠀⠀⠀⠀⠉⢰⠒⠤⠤⢄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⢯⣷⣞⣵⢣⠌⣄⠀⠀⢀⠄⢂⠀⠀⠀⠀⠀⠈⠙⠂⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⣿⣮⢳⡜⢢⡜⣥⢠⠂⠀⠀⣤⠀⠈⠀⠀⠀⠀⠘⠑⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢵⣧⣞⡶⣇⡜⡄⠁⢐⠁⠀⠀⠀⠀⠀⠀⢞⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠻⣿⣿⣿⠿⣿⣞⠂⠀⠀⠀⠀⠀⠀⠀⠁⠁⢑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣇⠀⠘⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠛⡇⠠⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡄⣤⣸⡴⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠐⠒⠆⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠭⠶⡄⡀⠀⠀⠀⠀⠀⠀⡀⠄⠀⡨⠀⢒⠚⠶⣌ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠴⠒⢀⡀⠀⢹⠢⣠⠶⠀⠨⠋⢁⣢⣽⣷⣶⡸⣘⠂⡥ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⡠⠀⡔⡮⠀⣐⣶⡱⣜⢶⣹⣷⣳⣯⣿⣿⣿⣤⣿⠷⠟⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⡃⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠢⠱⢇⡐⣝⡀⣼⣿⣷⣻⡽⣯⣿⣾⣿⣿⣿⡿⠟⠉⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠸⠊⢠⠂⣀⣠⠄⠐⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠒⠙⡇⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠠⠂⢁⠆⣠⣾⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⢎⣠⢎⠈⠀⠁⠀⠐⠃⠈⠻⣿⣿⣿⣿⣿⠟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠀⡇⠀⠀⠀⠀⠀⠀⡈⣠⣞⡮⢾⣿⣿⣿⣿⡏⡀⠀⠀⠀⠀⠀⠀⡔⡈⣿⣧⡆⢀⠀⠄⡌⠀⠀⢆⠀⢉⢻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⢐⠀⠀⡁⠄⢂⠀⢀⡀⢂⣴⠞⠋⠀⠀⠀⠙⢿⣿⡇⠇⠀⠠⡀⠀⠀⠈⠤⠈⣽⣿⣿⣯⡂⡀⡄⡠⠀⢀⢀⠈⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡄⠀⠜⠀⠄⡠⠘⡀⠄⣀⣼⠿⠃⠀⠀⠀⠀⢀⠄⠘⣿⡇⠀⠘⢄⠇⠀⠀⠀⡄⢀⣿⣿⣿⣿⣧⣧⣿⢣⢇⡀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠠⢂⠉⡐⡄⢁⢐⣚⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡃⡎⠀⠀⡀⠀⠀⠀⠀⣜⠛⠿⠛⠿⠿⠿⠿⠿⠛⠾⠿⠞⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⡔⣇⢂⢔⠀⠐⣝⣔⣾⠋⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠃⠀⠀⠀⠑⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣿⡰⢚⠤⣡⠦⣱⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡄⠀⢀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠛⠻⠟⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣳⡐⢂⠀⠀⠀⠀⣨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣝⣦⠐⣂⣰⣵⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀