⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢠⣶⣌⠢⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠁⢸⡏⠙⡄⠈⠻⣿⣶⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⠀⠈⠑⠙⠂⠀⠀⠀⠀⠀⠀⠈⠊⠽⠶⠄⣀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⡁⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⡀⠀⠑⠚⠉⢉⣀⣤⢙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⠁⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠻⡍⡹⢋⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡞⣾⣿⣿⡖⣴⣿⣿⣿⣿⣟⠿⢿⣿⣿⠉⠛⢿⣿⣿⠻⣿⣿⣿⣿⣷⡄⠙⢁⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡞⢸⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣶⣤⣉⠁⢰⣄⡈⠛⢷⡀⠙⠻⣿⣿⡞⣄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⢀⣿⣅⠈⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣿⣿⣶⣄⡀⢠⣀⠀⠙⠃⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⣿⢸⢯⢿⡀⠈⣿⣿⣏⣬⣿⠿⣯⣷⣿⢿⡿⣝⢯⣿⢿⣿⣿⣿⣾⣿⣷⣄⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⣿⣿⣚⣾⠁⢠⣿⡏⣿⣿⣿⣿⣷⣄⠁⠚⠳⢽⣪⣟⣽⣽⠳⢿⠾⣿⣿⣿⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⢹⣿⣿⣿⣟⠟⠀⣸⣿⠀⢱⣿⣿⣧⣈⣟⣧⠀⠀⠀⠀⠈⠉⠓⠻⣬⣷⣿⣿⣏⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⢃⣿⣿⣿⣿⣿⣷⡖⣿⣿⠀⠀⠹⣾⡿⠟⠁⠋⠀⠀⠀⠀⠀⣠⣶⠛⡟⢻⣶⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡼⣸⣿⣿⣿⣿⣿⡏⣧⢿⣿⣷⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠋⣠⣾⡷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⢇⡟⣿⣿⣿⣿⣿⡇⣿⣞⣿⣿⣿⣦⣄⠀⠀⠀⢀⣀⣀⠂⠀⠈⠓⠂⠀⣰⣿⡿⡙⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣼⠃⣿⡏⣿⣿⣿⣷⣿⣿⣾⣿⣿⣿⢻⠉⠒⠄⣀⠈⣉⣀⣀⣀⠀⠤⢺⣿⣿⣿⡤⠔⠊⠉⠀⠉⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢨⣿⠀⡿⢱⢹⣿⣿⣿⣿⣿⣿⣿⢳⡆⠀⠣⠠⠚⠁⠀⠀⠀⠀⠠⠂⠀⠞⠉⢹⠋⠀⠀⠀⢢⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡟⠀⢷⢸⣯⣿⣿⣿⣿⠟⠿⣿⠿⠓⢢⠒⠧⡠⢀⡀⠠⢀⠔⠁⠔⠊⠀⠀⠈⠀⠀⠀⢀⣸⠀⠀⠀⡤⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡚⠒⣦⡀⠀ ⣿⣿⠀⢸⡈⣿⣿⣿⣿⣿⢀⠊⠁⠀⠀⠀⢡⠄⡈⢺⡕⠊⠁⠀⠀⠈⠉⠉⠐⠢⢄⡈⠉⠁⢹⡆⠀⣰⠩⠮⢳⡀⠀⠀⠀⠀⠀⠀⠀⣼⢄⠘⣆⢸⣷⠀ ⣿⣿⣄⠨⣧⢻⣿⣿⣿⣿⣯⠀⠑⢌⠂⣄⡸⠤⣬⡻⡁⠀⠠⢄⡀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⡟⡄⠓⠒⣸⢹⣇⣀⣀⣤⡤⠴⠚⣼⣿⡟⡇⢸⢸⣿⠆ ⣿⣿⣿⢦⣿⣧⢿⣯⣿⣿⣧⠀⠀⠦⣷⠏⠉⠐⠈⠻⣗⢤⡐⠺⠉⡁⠀⠀⠀⠀⠀⠻⠿⣃⡜⠁⠈⢄⠀⠀⠁⠘⡌⠀⠀⠀⠀⠀⠉⣽⠃⡇⢸⣸⣿⠀ ⢿⣿⣿⣿⣿⣿⣿⣿⣞⣿⣿⡀⠀⠀⠉⢻⡀⠀⠀⠀⢹⡦⠚⠑⠒⠨⠵⢮⣷⣶⠁⠖⠉⠀⠉⢳⠒⠛⡏⠂⢤⠤⠞⠀⠀⠀⢀⡀⠀⢙⢲⠁⣾⣿⠏⠀ ⠸⣿⣿⣯⠻⣿⣿⣿⡽⣞⣿⣧⡄⠠⠔⠉⣧⠀⠀⣠⠊⠀⠀⠀⡌⠀⣠⠗⠊⢊⠢⡀⠀⠀⠀⡜⠀⠀⢸⠀⠀⡆⠀⠀⠀⢔⡃⢈⡝⠘⡇⢀⣷⡿⠀⠀ ⠀⠻⣿⣿⣆⠙⢿⣿⣿⣧⣛⣿⣳⣤⣀⣼⣿⣏⠁⠆⠀⠀⠀⢰⡅⢸⣒⣚⣁⠈⡄⢈⠔⠒⠓⠤⣀⣀⡸⢀⡐⠀⠀⠀⠀⠆⠓⠛⡛⢸⣠⣾⡿⠃⠀⠀ ⠀⠀⠙⠿⣿⣦⡀⢻⢿⡿⣿⢼⡷⣟⣾⣿⣿⣏⠙⠛⠢⠀⠤⡎⠀⠀⠈⠒⠮⣤⠗⠁⠀⠀⠀⠀⡥⠤⢍⣀⣨⣭⠗⠋⠐⠛⠐⠒⠋⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠛⣺⣯⣿⡽⣿⣟⣯⢞⣾⣿⣵⣼⣄⣠⢺⠩⡇⠀⠀⠀⠀⠀⢹⣦⡀⠀⠀⢀⣰⣵⣾⡿⠟⠛⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⣟⣿⣿⣾⡿⠛⡉⣉⣭⣙⡻⣖⠳⢀⠀⠀⠀⣠⡾⣤⣉⠐⠈⠛⠓⠚⠓⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⢞⣫⠏⣼⣿⠏⣿⢿⣿⡟⠀⡰⠊⠡⣠⢳⢱⠘⢇⠈⠹⡟⢻⣟⣉⣡⣶⣛⣖⣦⡤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠒⠶⠿⣟⣾⠟⢁⣾⠟⠁⠀⢿⣺⣿⡁⡜⡡⣑⣄⡈⢀⠞⣠⣿⣧⡀⠈⢯⣻⣷⣼⠼⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⠓⠛⣧⣡⣓⣙⡣⠚⣁⣾⡟⣧⡿⠋⢢⣜⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⣠⣶⢿⣳⡿⠏⢁⠢⡈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⠛⠀⠄⡁⢂⠁⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣌⣀⣈⣤⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀