⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠁⢀⡤⠒⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠘⠀⠀⢀⡤⠒⠲⠦⠴⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣠⠊⢀⣞⡁⣀⣀⣄⢠⣀⠢⡨⣡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠊⠁⠀⣾⡿⠿⢇⡯⢿⡸⣿⠥⣿⡾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣂⠀⠀⣿⠰⠶⣤⠀⣠⠦⠙⢯⢀⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡣⠀⢸⠴⠒⠦⠀⠴⠒⠲⡜⠞⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⣸⡄⢂⣔⠀⠀⠀⠀⠀⠀⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠖⠚⢷⣽⢷⠔⠒⠚⠀⠀⢀⡔⠀⣿⠏⠉⠑⠒⠒⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⡀⠀⡄⠀⠉⢸⣧⣀⣀⣠⣴⠏⣠⣼⡾⠀⠀⠀⠀⡄⢀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⢱⠀⡇⠀⠀⠀⠸⣿⣿⣿⢏⣰⣿⠏⠀⠀⠀⠆⠀⢀⠇⢀⡆⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢐⡿⢄⠀⠀⢀⠀⠞⣧⠀⣄⠀⠀⡌⠛⠯⠿⠋⠀⠀⠀⢀⠌⠀⣰⠋⣠⠎⠀⣠⠼⣷⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠔⠉⠀⠈⠳⣄⠀⠁⠘⣿⠀⠸⣎⠞⠷⠶⠖⣡⡾⡴⠀⢀⠊⡀⢀⣏⢜⡏⠀⠔⠁⠀⠀⠳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⠛⠒⠛⠓⣦⣠⣿⣦⣴⢶⣿⡀⠀⠘⢁⣠⣥⣭⣄⣰⠃⠀⠃⡴⠀⠸⣿⠋⢢⡏⠀⠀⣠⣴⠤⠌⢣⡀⠀⠀⠀ ⠀⠀⠀⣠⣯⡀⠀⠀⠀⠘⣿⠋⠈⠁⠘⣿⡷⠄⠀⡜⣭⣹⣿⣿⣿⣷⡁⡜⠀⢀⣼⣿⡧⠹⠟⢳⡴⠁⠀⠀⠀⠀⢹⡄⠀⠀ ⠀⢀⣾⠿⡻⣷⡄⠀⠀⠀⠸⣷⣦⣄⣴⡿⡄⠘⢦⣿⣿⣿⣿⣿⣿⣿⡇⠀⡴⠋⣻⣿⣀⣤⣠⡞⠁⠀⠀⠀⠀⣰⣿⣤⠀⠀ ⢀⡿⠉⠍⠀⡸⣷⡄⠀⠀⠀⢻⡎⢟⢯⡉⢞⢦⡈⢻⣿⣿⣿⣿⡿⣟⣴⠏⣠⣿⣿⣿⠿⢟⡟⠀⠀⠀⠀⣠⣾⣟⡋⢿⣧⠀ ⢸⡗⠠⡃⢀⠤⣻⣿⣧⠀⠀⠈⢧⠂⠈⢿⣄⠁⠳⣤⣭⣿⣿⣿⣿⢿⣿⠿⢋⣿⠏⠀⠁⡾⠀⠈⠀⢀⣾⣿⡥⠀⠁⠊⣿⡆ ⠘⣇⠐⠀⠢⠀⠈⠿⣿⣷⡀⠁⠸⣆⠒⢘⣿⣷⣄⠘⢿⣿⣿⣿⡿⠿⠃⣴⣿⡋⢀⠀⡼⠁⠀⢀⣴⣿⠟⠋⢀⠀⠁⢸⡿⠁ ⠀⠹⣦⣑⠀⠠⠄⠢⡉⣿⣿⡄⠀⠹⡄⠒⠘⣿⣻⣷⣄⠉⠻⠉⠀⣀⣴⣿⡓⠀⡂⡜⠀⠀⣰⣿⣟⡦⡐⡁⠂⠎⠀⣿⡇⠀ ⠀⠀⠙⢿⣷⢦⡁⢀⢰⣿⣿⡟⠀⠀⢱⠧⣀⢹⢿⢿⠿⡟⢒⠚⡙⣽⡻⢃⡴⢻⠞⠀⠀⣴⣿⡯⠁⢀⣀⡤⢶⣻⣿⠋⠀⠀ ⠀⠀⠀⠀⠘⠷⣤⣀⣿⠿⡟⠀⠀⠀⢸⣕⠀⡁⠻⠼⠴⠿⡒⠻⡿⠵⠿⠋⠀⡚⠀⠀⠨⣿⣿⠑⠚⣩⠽⢞⡯⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⢣⣀⠚⠧⠀⠀⠀⢸⢹⢷⣤⣁⠀⠂⠐⠀⠁⠀⢂⣀⣤⡗⠀⠀⠀⢸⠟⠀⠀⣀⡴⠟⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣿⢱⡆⣈⢾⣶⢾⡏⣏⡈⣿⣿⣿⣿⣿⣿⣿⡿⢏⣹⣷⠀⣀⡀⡾⣷⠾⢏⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣐⡟⠫⢋⣈⣵⣿⣟⣥⣯⡓⠻⣿⠉⠉⠡⣿⢚⡩⣼⣿⣯⣷⣼⣶⡥⢴⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣼⢶⣷⡞⢟⠘⠛⠛⠶⣶⣤⣾⣿⣷⣶⣼⣧⣄⣮⣷⠿⠋⠉⣉⣽⣶⠾⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠚⠪⠤⠥⠤⠥⠖⠒⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠓⠲⠾⢧⣀⣛⣻⣏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀