⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⠛⢁⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠀⠀⠠⣄⡀⠀⠀⠀⠀⣾⠀⢹⡄⠀⣀⠈⠻⣿⣿⣿⣿⡿⢛⠀⢻⡀⠀⠀⠀⢀⣠⠄⠀⠀⠀ ⢤⣅⢀⣀⣠⡙⠲⣤⡀⢰⠏⠀⢸⣇⡤⠃⠀⠀⠀⠉⠉⢶⢰⡟⠀⠘⣧⠀⣀⡴⢛⣧⣄⠀⢀⣶ ⠀⠉⠉⠁⠀⠙⢦⡀⠙⠻⠆⠀⣼⢿⡆⢤⣤⣤⣤⣤⣤⣀⣿⢿⡀⠀⠛⠛⠁⣠⠞⠁⠀⠉⠉⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⣶⣾⠃⣸⣿⣤⣅⣃⣘⣁⣤⣾⣧⠈⢷⣶⣤⣤⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⠀⢀⠀⣉⢙⣁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣉⣉⡁⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣴⠃⣴⣾⣿⡟⠋⠉⠉⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠉⠉⠉⠹⣿⣿⣶⣄⠀⠀⠀ ⠀⠀⠓⠘⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠖⠀⠀ ⠀⠀⠀⠐⠂⠙⢿⣿⣦⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠋⠠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠹⣄⠉⠙⠓⠶⡦⠄⣤⣿⣿⣿⣿⡆⢠⠤⠶⠶⠚⠉⢀⣿⠁⠊⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⢀⣶⣀⠀⣠⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡏⢁⡿⠓⠦⠀⠀⢠⠖⠻⣅⠉⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠀⣠⠀⠀⠀⠀⢧⠀⠘⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠤⠴⠃⠀⠀⠀⠀⠈⠳⠤⠼⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠛⠼⠤⠳⠈⠀⠀⠀⠀⠃⠴⠤⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣥⣿⠘⠀⢧⠀⠀⠀⠀⣠⠀⠟⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡷⠉⣅⠻⠖⢠⠀⠀⠦⠓⡿⢁⡏⢳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⡴⣠⠀⣀⣶⢀⠀⠀⠀⠀⠀⠀⣄⣠⢀⠀⣄⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠊⠁⣿⢀⠉⠚⠶⠶⠤⢠⡆⣿⣿⣿⣿⣤⠄⡦⠶⠓⠙⠉⣄⠹⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠋⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⣀⣦⣿⢿⠙⠂⠐⠀⠀⠀ ⠀⠀⠖⠟⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣿⠘⠓⠀⠀ ⠀⠀⠀⣄⣶⣿⣿⠹⠉⠉⠉⠉⠉⠛⡿⣿⣿⣿⣿⣿⣿⠻⠙⠉⠉⠉⠉⠋⡟⣿⣾⣴⠃⣴⢠⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡁⣉⣉⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣁⢙⣉⠀⢀⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠞⣤⣤⣶⢷⠈⣧⣾⣤⣁⣘⣃⣅⣤⣿⣸⠃⣾⣶⣀⢦⠳⠈⠀⠀⠀⠀⠀⠀ ⠀⠉⠉⠀⠁⠞⣠⠁⠛⠛⠀⡀⢿⣿⣀⣤⣤⣤⣤⣤⢤⡆⢿⣼⠀⠆⠻⠙⡀⢦⠙⠀⠁⠉⠉⠀ ⣶⢀⠀⣄⣧⢛⡴⣀⠀⣧⠘⠀⡟⢰⢶⠉⠉⠀⠀⠀⠃⡤⣇⢸⠀⠏⢰⡀⣤⠲⡙⣠⣀⢀⣅⢤ ⠀⠀⠀⠄⣠⢀⠀⠀⠀⡀⢻⠀⢛⡿⣿⣿⣿⣿⠻⠈⣀⠀⡄⢹⠀⣾⠀⠀⠀⠀⡀⣄⠠⠀⠀⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠀⠀⣀⡟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⢁⠛⠒⠖⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⣿⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⣿⣿⣿⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀