⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣄⣀⡀⠀⠀⣀⣀⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠚⠛⠿⣿⣶⣤⣠⣤⣶⠿⠛⠉⠉⠀⠀⣈⣤⣽⣿⡿⠋⠉⠀⠀⠈⠉⢻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⡿⠋⠁⠀⠀⣠⣤⣴⣿⣿⠟⠋⠀⠀⠘⠶⣄⡀⠀⠀⠀⣿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠋⠀⠀⠀⠀⣾⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠘⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠲⢤⣄⣀⣀⣠⣴⣾⣿⠿⣿⣿⣷⣦⠀⠀⠀⠙⢿⣿⣿⣿⣦⡀⠀⠀⠀⠀⣠⣾⣿⣿⠿⣷⣦⣄⣀⣀⣠⣄⡴⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠉⠛⠿⠷⣦⣤⡴⠶⠚⠛⠋⠛⠿⢶⣤⡴⠾⠿⠛⠋⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⡶⠿⠟⠛⠛⠛⣋⣿⡿⠟⠛⠛⠻⠶⣦⣄⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⣶⣿⣿⣛⡉⠀⠀⠀⠀⢀⣤⣾⢟⣋⣀⣀⣀⣀⣀⣀⣀⣙⣿⣦⠀ ⠀⠀⣠⣾⣿⢿⣿⣿⣿⣿⣿⡆⢀⣠⣶⠟⢫⣾⣿⣿⣿⣿⡟⣭⣭⣭⣭⣭⣭⢻⡇ ⢀⣼⣿⠟⠁⠈⢿⣿⣿⣿⣿⣿⡄⠉⠁⢀⣿⣿⣿⣿⣿⡿⣸⣿⣿⣿⣿⣿⡏⣼⠇ ⢸⣿⡟⠀⠀⣠⣼⣿⣿⣿⣿⣏⣀⡀⠀⣀⣙⣿⣿⣿⣿⢣⣿⣿⣿⣿⣿⣿⣾⠏⠀ ⢸⣿⣧⣴⡿⠟⠁⠸⣿⣿⣿⣿⣿⣧⣸⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⠟⠁⠀⠀ ⠈⠻⣿⣿⣦⣀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣩⣭⡿⠟⠋⠀⠀⠀⠀⠀ ⠀⠀⠈⠛⠿⣿⣿⣷⣶⣶⣤⣤⣤⣤⣤⣴⣶⡶⠾⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⡶⠿⠟⠛⠛⠛⣋⣿⡿⠟⠛⠛⠻⠶⣦⣄⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⣶⣿⣿⣛⡉⠀⠀⠀⠀⢀⣤⣾⢟⣋⣀⣀⣀⣀⣀⣀⣀⣙⣿⣦⠀ ⠀⠀⣠⣾⣿⢿⣿⣿⣿⣿⣿⡆⢀⣠⣶⠟⢫⣾⣿⣿⣿⣿⡟⣉⣉⣉⣉⣉⣉⢻⡇ ⢀⣼⣿⠟⠁⠈⢿⣿⣿⣿⣿⣿⡄⠉⠁⢀⣿⣿⣿⣿⣿⡿⣸⣿⣿⣿⣿⣿⡏⣼⠇ ⢸⣿⡟⠀⠀⣠⣼⣿⣿⣿⣿⣏⣀⡀⠀⣀⣙⣿⣿⣿⣿⢣⣿⣿⣿⣿⣿⣿⣾⠏⠀ ⢸⣿⣧⣴⡿⠟⠁⠸⣿⣿⣿⣿⣿⣧⣸⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⠟⠁⠀⠀ ⠈⠻⣿⣿⣦⣀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣩⣭⡿⠟⠋⠀⠀⠀⠀⠀ ⠀⠀⠈⠛⠿⣿⣿⣷⣶⣶⣤⣤⣤⣤⣤⣴⣶⡶⠾⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣶⣿⣿⣷⣄⠀⠀⢠⠖⠛⣿⣿⣦⡀⠀⠀⠀⢀⣤⣶⣿⠟⠉⣿⣷⣦⡀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣇⢰⠇⠀⣾⣿⣿⣿⡷⠀⢀⣶⣿⣿⣿⠋⢠⣾⣿⣿⣿⣷⠀ ⠀⠀⠹⣿⣿⣿⡿⠟⢿⢸⠀⠀⠻⣿⣿⡿⠃⢠⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⡿⠀ ⠀⠀⠀⠀⠉⠁⠀⠀⢸⣿⣆⠀⠀⠀⠠⡀⠀⣿⣿⣿⣿⣿⢃⣀⣀⣙⣛⣻⣯⡴⠆ ⠀⣠⣶⣿⣿⣷⡄⠀⣼⣿⣿⣷⣤⣤⣴⣿⡀⣿⣿⣿⣿⣿⠈⠀⠹⣿⣿⣿⣿⠇⠀ ⢠⣿⣿⣿⣿⣿⡇⢰⠇⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⡆⠀⠀⢻⣿⣿⣿⠀⠀ ⠈⢿⡏⠙⠛⠋⣠⠏⠀⢹⣿⣿⣿⣿⣿⡿⠀⠈⠻⣿⣿⣿⣷⡀⠀⢸⡿⠋⡿⠀⠀ ⠀⠈⠛⠲⠶⠚⠁⠀⠀⠀⠙⠻⠿⠟⠋⠀⠀⠀⠀⠈⠙⠛⠿⠿⠒⠋⠀⠠⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢠⣶⣿⣿⣷⣄⠀⠀⢠⠖⠛⣿⣿⣦⡀⠀⠀⠀⢀⣤⣶⣿⠟⠉⣿⣷⣦⡀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣇⢰⠇⠀⣾⣿⣿⣿⡷⠀⢀⣶⣿⣿⣿⠋⢠⣾⣿⣿⣿⣷⠀ ⠀⠀⠹⣿⣿⣿⡿⠟⢿⢸⠀⠀⠻⣿⣿⡿⠃⢠⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⡿⠀ ⠀⠀⠀⠀⠉⠁⠀⠀⢸⣿⣆⠀⠀⠀⠠⡀⠀⣿⣿⣿⣿⣿⢃⣀⣀⣙⣛⣻⣯⡴⠆ ⠀⣠⣶⣿⣿⣷⡄⠀⣼⣿⣿⣷⣤⣤⣴⣿⡀⣿⣿⣿⣿⣿⠈⠀⠹⣿⣿⣿⣿⠇⠀ ⢠⣿⣿⣿⣿⣿⡇⢰⠇⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⡆⠀⠀⢻⣿⣿⣿⠀⠀ ⠈⢿⡏⠙⠛⠋⣠⠏⠀⢹⣿⣿⣿⣿⣿⡿⠀⠈⠻⣿⣿⣿⣷⡀⠀⢸⡿⠋⡿⠀⠀ ⠀⠈⠛⠲⠶⠚⠁⠀⠀⠀⠙⠻⠿⠟⠋⠀⠀⠀⠀⠈⠙⠛⠿⠿⠒⠋⠀⠀⠷⠀⠀