⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠉⠉⠉⠲⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢠⡏⣽⠀⢰⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠤⠤⠤⠤⠤⠤⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⢯⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⣉⡤⠴⠒⠒⠚⠉⠙⠒⠒⠲⠤⣌⡉⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠘⡇⠸⣄⠈⠑⣄ ⠀⠀⠀⠀⠀⠀⢀⡴⢋⡤⠞⠋⠀⠀⠀⠀⠀⡤⠤⠲⠼⠦⠤⠤⢤⣉⠓⢦⣈⠳⣄⠀⠀⠀⠀⠀⠀⢧⡀⠘⢦⣈⡗⠀⢺ ⠀⠀⠀⠀⠀⡰⢋⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠷⣌⠳⡄⠀⠀⠀⠀⡰⠃⢀⡴⢦⡄⠀⡏ ⠀⠀⠀⢀⠞⣠⠞⠁⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠙⢆⠘⢆⠀⠀⡴⠁⢠⠎⢠⠎⠀⣰⠃ ⠀⠀⢠⠋⣰⣯⠀⠀⠀⠀⠀⣰⠃⢀⠀⢀⡴⠃⢠⠏⠀⠀⠀⠀⠀⠰⡀⠀⠀⠈⢣⡈⢧⠈⣆⠀⡇⠀⢯⡀⢣⡀⠘⣅⠀ ⠀⢠⠋⣰⢳⡇⠀⠀⠀⠀⢠⠃⠀⡼⢀⡞⠀⠀⣿⣿⢀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⢱⡌⣧⠘⣆⣇⠀⠀⠱⣄⢱⡄⠈⡆ ⠀⡞⢠⢧⣿⠀⠀⠀⠀⠀⡟⠀⢠⡇⣼⠃⠀⣸⣿⣿⣾⡇⠀⣧⡀⠀⠀⢷⠀⢰⢰⡀⢳⡸⡄⢻⠃⠀⡖⢲⠌⠉⢀⡴⠃ ⢀⠁⣾⡿⢻⠀⠀⠀⠀⢀⡇⠀⢸⢡⣿⣠⡾⠁⢻⢻⢻⡇⠀⣿⢷⣄⠀⢸⡇⠘⡆⢇⢸⣧⣧⠀⠀⢸⠁⢸⠀⢸⠁⠀⠀ ⠈⠀⣿⡇⢸⠀⠀⡆⠀⢸⡇⠀⣿⣿⣽⠏⠀⠀⢸⡎⣆⢿⠀⢻⡈⠻⣷⣤⣿⠀⡇⢸⡀⣿⢸⠀⠀⢸⡀⢸⡀⠘⢤⡀⠀ ⢰⠀⣿⠀⢸⣇⣼⡇⠀⢸⡇⠀⣿⣿⠟⠒⠒⠒⠉⢿⠘⢮⢳⣼⠉⠑⠚⠻⣿⣇⡇⠈⣧⣿⣼⠀⡆⠀⢣⡀⠳⡄⠀⢹⠀ ⠀⠣⣈⣠⡀⣿⡿⠀⠀⠈⣿⡀⢻⡟⠀⠀⠀⠀⠀⠘⣇⠈⣿⣿⣦⣄⣀⠀⢠⣿⡇⠀⣿⣿⣿⠀⣿⡦⠀⢉⡛⠁⢀⣾⠀ ⠀⢀⡜⠋⣠⡞⠁⢀⣼⠁⡿⢷⡸⣿⣴⣤⣄⣀⣀⣀⠘⢦⡸⣿⣄⣤⣤⣶⣿⣿⠃⠀⡿⢸⡿⢰⠋⠀⡰⠋⡸⠃⢀⡿⠀ ⠀⠘⢧⡙⠛⠶⢾⣿⣿⣼⠁⣠⣿⠃⠋⡴⠛⣯⠇⠀⠀⠀⠙⠿⣧⣈⣞⠧⣹⡟⢀⢰⡇⠚⢁⡏⠀⡜⠁⡞⠁⠀⡞⠀⠀ ⠀⠀⠀⠈⠉⠛⢆⠹⣿⣹⡟⢻⣿⢧⣀⠀⠈⣿⡀⣠⡤⢤⣤⣄⣠⣾⠁⠀⢸⠀⣸⡾⢠⡖⠉⢣⡀⠙⢆⠘⢦⠀⠙⡄⠀ ⠀⠀⠀⠀⠀⠀⠘⡆⠸⠿⠿⣿⠟⣿⢻⠁⠀⣯⣉⣿⣯⣹⣿⣿⣿⡏⠀⢶⣇⣼⡿⢁⡜⠀⠀⠀⡹⠂⠈⠳⠼⠃⢀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠲⠴⠦⣤⢀⣯⣿⠀⠀⣿⣿⣿⣿⣿⣿⣹⣿⠃⠀⡿⢋⣄⠴⠋⠀⠀⠀⠀⡇⠀⠿⠇⠀⣰⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⡏⠸⡀⠀⣿⡿⣿⣿⣿⡾⣷⠸⣄⣀⣷⠀⡇⠀⠀⠀⠀⠀⢸⠁⠀⠒⡆⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠸⣿⣄⠈⠉⣁⠇⠙⣿⡿⠀⢻⣄⡀⢀⠞⢠⠇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠰⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣉⣛⠿⠭⠥⠤⠤⠿⠧⠴⠾⠃⣭⣡⡤⠃⠀⠀⠀⠀⠀⠀⠸⣄⡀⠀⠀⣰⠃⠀⠀⠀

⠀⠀⠀⠃⣰⠀⠀⡀⣄⠸⠀⠀⠀⠀⠀⠀⠃⡤⣡⣭⠃⠾⠴⠧⠿⠤⠤⠥⠭⠿⣛⣉⠢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠰⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠇⢠⠞⢀⡀⣄⢻⠀⡿⣿⠙⠇⣁⠉⠈⣄⣿⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⡆⠒⠀⠁⢸⠀⠀⠀⠀⠀⡇⠀⣷⣀⣄⠸⣷⡾⣿⣿⣿⡿⣿⠀⡀⠸⡏⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠋⣰⠀⠇⠿⠀⡇⠀⠀⠀⠀⠋⠴⣄⢋⡿⠀⠃⣿⣹⣿⣿⣿⣿⣿⣿⠀⠀⣿⣯⢀⣤⠦⠴⠲⠙⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⢀⠃⠼⠳⠈⠂⡹⠀⠀⠀⡜⢁⡿⣼⣇⢶⠀⡏⣿⣿⣿⣹⣯⣿⣉⣯⠀⠁⢻⣿⠟⣿⠿⠿⠸⡆⠘⠀⠀⠀⠀⠀⠀ ⠀⡄⠙⠀⢦⠘⢆⠙⡀⢣⠉⡖⢠⡾⣸⠀⢸⠀⠁⣾⣠⣄⣤⢤⡤⣠⡀⣿⠈⠀⣀⢧⣿⢻⡟⣹⣿⠹⢆⠛⠉⠈⠀⠀⠀ ⠀⠀⡞⠀⠁⡞⠁⡜⠀⡏⢁⠚⡇⢰⢀⡟⣹⠧⣞⣈⣧⠿⠙⠀⠀⠀⠇⣯⠛⡴⠋⠃⣿⣠⠁⣼⣿⣿⢾⠶⠛⡙⢧⠘⠀ ⠀⡿⢀⠃⡸⠋⡰⠀⠋⢰⡿⢸⡿⠀⠃⣿⣿⣶⣤⣤⣄⣿⡸⢦⠘⣀⣀⣀⣄⣤⣴⣿⡸⢷⡿⠁⣼⢀⠁⡞⣠⠋⡜⢀⠀ ⠀⣾⢀⠁⡛⢉⠀⡦⣿⠀⣿⣿⣿⠀⡇⣿⢠⠀⣀⣄⣦⣿⣿⠈⣇⠘⠀⠀⠀⠀⠀⡟⢻⡀⣿⠈⠀⠀⡿⣿⡀⣠⣈⠣⠀ ⠀⢹⠀⡄⠳⡀⢣⠀⡆⠀⣼⣿⣧⠈⡇⣇⣿⠻⠚⠑⠉⣼⢳⢮⠘⢿⠉⠒⠒⠒⠟⣿⣿⠀⡇⢸⠀⡇⣼⣇⢸⠀⣿⠀⢰ ⠀⡀⢤⠘⡀⢸⡀⢸⠀⠀⢸⣿⡀⢸⡇⠀⣿⣤⣷⠻⡈⢻⠀⢿⣆⡎⢸⠀⠀⠏⣽⣿⣿⠀⡇⢸⠀⡆⠀⠀⢸⡇⣿⠀⠈ ⠀⠀⠁⢸⠀⢸⠁⢸⠀⠀⣧⣧⢸⢇⡆⠘⡇⢸⠀⣄⢷⣿⠀⡇⢻⢻⢻⠁⡾⣠⣿⢡⢸⠀⡇⢀⠀⠀⠀⠀⢻⡿⣾⠁⢀ ⠃⡴⢀⠉⠌⢲⡖⠀⠃⢻⡄⡸⢳⡀⢰⢰⠀⢷⠀⠀⡀⣧⠀⡇⣾⣿⣿⣸⠀⠃⣼⡇⢠⠀⡟⠀⠀⠀⠀⠀⣿⢧⢠⡞⠀ ⡆⠈⡄⢱⣄⠱⠀⠀⣇⣆⠘⣧⡌⢱⠀⠀⠀⡀⠱⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⡞⢀⡼⠀⠃⢠⠀⠀⠀⠀⡇⢳⣰⠋⢠⠀ ⠀⣅⠘⡀⢣⡀⢯⠀⡇⠀⣆⠈⢧⡈⢣⠈⠀⠀⡀⠰⠀⠀⠀⠀⠀⠏⢠⠃⡴⢀⠀⢀⠃⣰⠀⠀⠀⠀⠀⣯⣰⠋⢠⠀⠀ ⠃⣰⠀⠎⢠⠎⢠⠁⡴⠀⠀⢆⠘⢆⠙⣄⠠⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠆⣠⠀⠀⠀⠀⠁⠞⣠⠞⢀⠀⠀⠀ ⡏⠀⡄⢦⡴⢀⠃⡰⠀⠀⠀⠀⡄⠳⣌⠷⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡴⢋⡰⠀⠀⠀⠀⠀ ⢺⠀⡗⣈⢦⠘⡀⢧⠀⠀⠀⠀⠀⠀⣄⠳⣈⢦⠓⣉⢤⠤⠤⠦⠼⠲⠤⡤⠀⠀⠀⠀⠀⠋⠞⡤⢋⡴⢀⠀⠀⠀⠀⠀⠀ ⣄⠑⠈⣄⠸⡇⠘⡀⢸⠀⠀⠀⠀⠀⠀⠀⡀⢤⠒⡉⣌⠤⠲⠒⠒⠙⠉⠚⠒⠒⠴⡤⣉⠊⠔⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⢯⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠄⠤⠤⠤⠤⠤⠤⠤⡀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⢰⠀⣽⡏⢠⠃⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠲⠉⠉⠉⠉⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀