⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠛⠒⠒⠛⠛⠛⠛⠯⣍⡻⣟⠶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⣆⠀⠈⠙⠋⠣⣝⡆⣀⡤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠖⠋⠳⡄⠀⠀⠀⠀⠀⠒⠒⠒⠢⠬⣃⠀⠀⠀⠀⣀⣹⣿⢏⣉⠲⡙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢣⠀⠀⠀⠘⠂⡠⠤⠔⠒⠒⠒⠒⠂⠀⠀⠈⠛⢻⡀⡿⠇⠀⠀⠈⠙⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⡏⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⠒⢏⢦⠀⡀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⡇⡇⣄⠀⠀⠀⠸⡦⠤⠤⠆⠋⠁⢀⡄⠀⢰⠀⠀⠀⠹⡄⢹⠀⠀⠀⣄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⣆⠀⡇⡇⢸⢆⠀⠀⠀⠳⡀⠀⠀⠀⢀⠞⠁⢠⠊⡇⠀⠀⠀⣿⠀⡃⠀⡆⢹⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠇⣿⢧⡇⡇⠀⠳⡕⢤⠀⠀⠑⣄⠀⠘⠁⢀⡏⢠⠇⠀⢀⣔⠋⠼⡞⣰⡇⠀⡇⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠆⣿⠀⠛⣿⡀⠀⠈⢢⣉⡶⠒⣆⢆⠀⠀⠃⠀⠈⠀⣠⠔⠋⠀⣠⠟⣏⣷⠀⡗⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣌⣻⡆⠀⠙⠂⠀⠀⠈⠁⠀⠀⡇⢱⠀⠀⠀⠀⠈⠁⠀⡀⠀⠈⠁⠀⣿⡟⡾⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⢸⠀⠀⠀⡇⠀⠀⢯⠀⠀⠀⠀⢸⡇⠷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠐⠋⡅⡇⠀⡇⠀⠀⢸⡀⠀⠀⡇⠀⠀⠀⢤⣿⡷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⢰⢹⢁⠋⠀⠀⠀⢺⠀⠀⠀⡃⠀⠀⠀⣷⠘⡌⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠋⡏⡞⠀⠀⠀⠀⠀⠇⠀⠀⢹⠀⠀⠀⡇⡇⢹⣀⢱⡛⠶⠶⠴⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡀⠀⠀⠀⣀⣴⣿⠀⠀⡀⠀⣄⠀⠀⠀⠀⢸⠀⠀⠀⡇⢧⠀⣯⠟⠳⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⠚⠛⠛⢦⢷⠁⠀⠀⡇⠀⢳⠀⠀⠀⠀⢸⠀⠀⠘⡖⡕⣌⣙⣦⣀⢳⠙⠂⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡴⠾⡽⠃⡤⠀⡏⠀⠀⢸⠀⠀⠀⠀⢹⠀⠀⠈⠃⢧⠻⡄⠀⠀⡇⠀⢸⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠁⠉⠉⠶⠮⠵⠋⡇⣞⠀⠀⠀⡏⢰⠀⠀⠀⡟⡆⠀⠀⠀⣿⠀⠈⣆⡞⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⡀⠀⠀⠀⠀⠀⠀⠀⣼⣏⡞⡤⠖⠟⠁⡇⠀⢠⠇⣹⠁⠀⢀⡿⠃⠀⠀⡇⠀⠀⢀⢼⠀⠀⠀ ⠀⠀⠀⠀⠠⠴⠒⠒⠒⠒⠒⠿⢇⠀⠀⠀⠀⠀⠀⠀⣴⣏⣰⠁⠀⠀⠀⠀⡞⠀⣠⠋⠀⡇⢠⠏⣸⠀⢠⠃⠀⠊⠁⠈⠦⡄⠀⠀ ⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⣾⠃⠀⠸⠙⠢⡀⡖⣣⠞⠋⠀⣴⡟⠁⠈⠁⠀⠀⠀⠀⠀⡅⠀⠀⠀⠹⡄ ⠀⠀⠴⡾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠉⣿⣅⠀⠀⡔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸ ⠀⡠⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠁⠒⠢⣀⡀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⢱ ⢋⡡⠤⠤⠔⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠂⠀⠸⠁⠀⠀⠀⠀⠀⠀⢣⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠢⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠚⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠊⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠤⠔⠊⠁⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡖⠒⠒⠒⠒⠒⠒⠒⢦⣀⣀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠙⣆⡼⠁⡤⠇⠀⠀⠀ ⠀⠀⠀⠀⢀⡏⢀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⢿⠙⠁⠈⠻⡄⠀ ⠀⠀⢀⡞⢁⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⢧⠀⠀⠀⠀⠱ ⠀⢠⠏⣠⡏⢸⠁⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⢶⣳ ⠀⠸⠋⣹⠀⣸⠀⠀⠀⠀⡇⠀⠀⡴⠋⠳⣄⠀⠀⠀⠏⠀⠀⣸⡇⠀⠀⠀⣏⣿ ⠀⠀⠀⡇⠀⡇⠀⠀⠀⡜⡇⣠⠞⠓⠚⠋⠀⠉⠉⡤⡶⣆⣯⠇⡇⠀⠀⢸⠈⠁ ⠀⠀⢠⠃⢀⡏⠀⠀⡏⠀⠉⠀⠀⣸⠟⢻⡟⠀⠀⠃⠀⠀⡟⠁⡜⣀⠀⢸⠀⠀ ⠰⠾⠭⠤⠆⢻⠀⠀⡇⠀⢠⠀⠀⠀⠀⠈⠉⠀⠀⣠⠤⣿⠇⠰⠟⢹⢰⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⢧⡀⡇⠀⠀⣀⣠⠄⠀⠀⠀⠀⣰⠋⡇⣸⠁⠀⠀⠀⣸⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠳⡟⢦⡀⠀⠀⠀⠀⣠⠴⠋⢀⣿⡟⣉⣧⡴⠒⠒⢲⠀⠀⠀ ⢀⣀⠀⠀⡖⠳⡀⠀⠀⠀⣀⣉⠛⠚⡏⠀⠀⠀⠀⠀⢠⠿⠁⢀⣀⡤⠄⡼⠀⠀ ⢸⠀⠹⡄⡇⠀⡇⠀⣀⣰⠁⠀⠀⠀⢸⠀⡀⠀⢀⡴⠟⠚⠉⠀⠀⠀⠀⠹⡄⠀ ⠀⣇⠀⠘⠿⠀⢽⡀⡇⠀⠀⠀⢸⡀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇ ⠀⣸⡓⣄⠀⠀⠀⠘⡏⠀⠀⠀⠀⠀⣇⠤⠖⠒⠒⠒⠒⠦⠤⣤⣤⣀⡀⡏⠀⠀ ⠀⣇⠘⠂⢹⠀⢀⣠⠇⢰⣖⠀⠀⣶⠶⠖⢠⣶⣶⣾⡄⠀⢰⡖⠲⣤⠶⣦⠀⠀ ⠀⠀⠉⠓⠋⠉⠉⠁⠀⠀⢹⡇⠀⢸⡷⠶⠆⣿⣤⣤⡿⠀⠀⠘⢦⡀⢀⡼⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠇⠿⠶⠆⠸⠇⠀⠿⠇⠀⠀⠀⠈⠙⠁⠀⠀