⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠊⠉⠉⠉⠀⠀⠈⠉⠉⠉⠓⠒⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢰⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⢋⡵⠃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⢀⡴⠋⠀⠀⠀⠀⠈⠓⠒⣦⡀⠀⠀⣀⣀⣤⡄⠀⠢⠤⢬⣙⣦⣀⠀⠀⠀⠀⠀⠈⠉⠢⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠋⠀⠀⢠⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠹⢏⣀⡀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀ ⠀⠀⠀⣠⠎⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀ ⠀⠀⣰⠃⠀⠀⠀⠀⢸⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠈⠳⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠟⠋⠉⠉⠛⠛⠛⠷⣦⣄⠀⠀⠀⠀⠈⠉⠉⠑⠲⢄⡀⠀⠀⠀⢸⡀ ⢀⡇⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⡇ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⣰⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⣳ ⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⢿ ⡇⠀⠀⠀⠀⢠⡇⠀⠀⠀⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⣿ ⡇⠀⠀⠀⠀⢸⢹⠀⠀⠀⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋ ⢧⠀⠀⠀⠀⢸⠈⡇⠀⠀⢹⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀ ⠸⡄⠀⠀⠀⢸⡀⠘⣄⠀⠸⡆⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⠀⠀⢀⣤⡼⠁⠀⠉⢧⡀⠀ ⠀⢧⠀⠀⠀⠀⣇⠀⠈⠛⣟⠋⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠀⠀⢰⠋⠀⠀⠀⠀⠂⠀⣿⠀ ⠀⠈⢇⠀⠀⠀⠘⡄⠀⠀⠘⢦⠀⠀⠀⠀⠀⠙⢿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡿⠋⠀⠀⣠⢤⣠⡏⠀⠀⠀⠀⠀⠀⢰⡟⠀ ⠀⠀⠈⢦⠀⠀⠀⠹⡄⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠷⢶⣶⠾⠿⠟⠋⠁⠀⠀⣠⠞⠃⠘⡿⠀⠀⢀⠀⠀⠀⢠⡿⠁⠀ ⠀⠀⠀⠈⠣⡀⠀⠀⠹⡄⠀⠀⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠁⠀⠀⡴⠃⢀⡴⠃⠀⠀⢀⡾⠁⠀⠀ ⠀⠀⠀⠀⠀⠙⢶⣀⠀⠸⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⣠⠎⣀⠴⠋⠀⠀⠀⢠⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠓⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠃⠀⠀⠀⢀⣴⠿⠗⠋⠁⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⣀⡀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣉⠛⠙⠒⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⣄⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠦⠶⠤⠦⠶⠖⠛⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀