⠀ ⠀⠀⠀⠀⠀⠀⠤⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠤⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠠⢤⣤⣤⠄⠄⠀⠀⢤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⠉⠉⠉⠉⠛⠻⣿⣷⡄⠀⠀⠀⠀⢀⣾⡟⣿⡄⠀⠀⠀⠀⠀⠀⢸⣿⡏⠉⠉⠉⠉⠉⠻⣿⡆⠀⠀⢸⣿⡏⠀⠀⠀⣠⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⠀⠀⠀⠀⠀⠀⠈⢿⣿⠀⠀⠀⢠⣿⡟⠀⢻⣿⣄⠀⠀⠀⠀⠀⠸⣿⡇⠀⢀⣀⣀⣀⣤⣿⠇⠀⠀⢸⣿⡇⠀⣠⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⣠⣿⠟⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠈⣿⡇⠀⠀⠻⣿⣟⠛⠋⠀⠀⠀⢸⣿⡇⠈⠉⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣗⠀⠀⠀⠀⢀⣠⣾⣿⠏⠀⣰⣿⠏⠀⠀⠀⠀⠀⠹⣿⣦⠀⠀⠀⢰⣿⡇⠀⠀⠀⠙⣿⣦⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠘⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠼⠿⠿⠿⠿⠿⠿⠿⠿⠋⠁⠠⠼⠿⠿⠄⠀⠀⠀⠀⠀⠠⠾⠿⠧⠀⠀⠾⠿⠷⠤⠀⠀⠠⠿⠿⠷⠄⠀⠠⠾⠿⠿⠦⠀⠀⠀⠴⠿⠿⠦⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠀⠀⠀⠀⠙⣿⣿⣿⠃⠀⠀⢀⠤⠞⠚⠛⠿⣿⣿⣶⣾⠀⠀⠀⢀⡴⠞⠛⠛⠿⣿⣿⣦⡀⠀⠈⠹⣿⣿⣿⠁⠀⠀⠈⢻⣿⡿⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⣿⣆⠀⠀⢀⣾⡟⣿⡟⠀⠀⢠⡞⠀⠀⠀⠀⠀⢀⠝⣿⣿⡄⠀⢀⡟⠀⠀⠀⠀⠀⠀⠙⣿⣿⡄⠀⠀⣿⡇⢻⣷⡄⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⢿⣧⣠⣿⠏⠀⣿⣧⠀⠀⣼⣧⠀⠀⠀⠀⠀⠀⠀⠈⢿⡗⠀⣾⣇⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⣿⡇⠀⠹⣿⣆⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢻⣿⠋⠀⠀⣿⣿⠀⠀⢹⣿⣦⡀⠀⠀⠀⠀⠀⠀⣸⠇⠀⢻⣿⣦⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⣿⡇⠀⠀⠘⢿⣷⡘⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⠀⠀⠀⠁⠀⠀⢠⣿⣿⠀⠀⠀⠻⣿⣷⣦⣄⣀⣀⣀⡴⠋⠀⠀⠀⠻⣿⣷⣦⣄⣀⣀⣀⡴⠋⠀⠀⢠⣿⣧⠀⠀⠀⠈⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠈⠙⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠁⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠀⠀⠀⠁⠉⠉⠉⠀⠀⠀⠀⠁⠛⠛⠛⠛⠙⠈⠀⠀⠀⠀⠀⠀⠁⠛⠛⠛⠛⠙⠈⠀⠀⠀⠉⠉⠉⠉⠈⠀⠀⠀⠀⠁⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⢻⠈⠀⠀⠀⣧⣿⢠⠀⠀⠋⡴⣀⣀⣀⣄⣦⣷⣿⠻⠀⠀⠀⠋⡴⣀⣀⣀⣄⣦⣷⣿⠻⠀⠀⠀⣿⣿⢠⠀⠀⠁⠀⠀⠀⣧⣿⢰⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⣿⡘⣷⢿⠘⠀⠀⡇⣿⠀⠀⠇⣼⠀⠀⠀⠀⠀⠀⠀⣦⣿⢻⠀⠇⣸⠀⠀⠀⠀⠀⠀⡀⣦⣿⢹⠀⠀⣿⣿⠀⠀⠋⣿⢻⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⣿⢸⠀⣆⣿⠹⠀⡇⣿⠀⠀⡇⣿⠈⠀⠀⠀⠀⠀⠀⠀⣇⣾⠀⡗⢿⠈⠀⠀⠀⠀⠀⠀⠀⣧⣼⠀⠀⣧⣿⠀⠏⣿⣠⣧⢿⠈⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⣿⢸⠀⠀⡄⣷⢻⡇⣿⠀⠀⡄⣿⣿⠙⠀⠀⠀⠀⠀⠀⡟⢀⠀⡄⣿⣿⠝⢀⠀⠀⠀⠀⠀⡞⢠⠀⠀⡟⣿⡟⣾⢀⠀⠀⣆⣿⡏⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⡿⣿⢻⠈⠀⠀⠁⣿⣿⣿⠹⠈⠀⡀⣦⣿⣿⠿⠛⠛⠞⡴⢀⠀⠀⠀⣾⣶⣿⣿⠿⠛⠚⠞⠤⢀⠀⠀⠃⣿⣿⣿⠙⠀⠀⠀⠀⣿⣿⣿⠹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠄⠦⠿⠿⠴⠀⠀⠀⠦⠿⠿⠾⠠⠀⠄⠷⠿⠿⠠⠀⠀⠤⠷⠿⠾⠀⠀⠧⠿⠾⠠⠀⠀⠀⠀⠀⠄⠿⠿⠼⠠⠁⠋⠿⠿⠿⠿⠿⠿⠿⠿⠼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⢿⠘⠀⠀⠀⣇⣿⢸⠀⠀⠀⠀⣦⣿⠙⠀⠀⠀⡇⣿⢰⠀⠀⠀⣦⣿⠹⠀⠀⠀⠀⠀⠏⣿⣰⠀⠏⣿⣾⣠⢀⠀⠀⠀⠀⣗⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⠻⠉⠈⡇⣿⢸⠀⠀⠀⠋⠛⣟⣿⠻⠀⠀⡇⣿⠈⠀⠀⠀⠀⣆⣿⠹⠀⠀⠀⠟⣿⣠⠀⠀⣿⣼⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠟⣾⣠⠀⡇⣿⢸⠀⠀⠇⣿⣤⣀⣀⣀⢀⠀⡇⣿⠸⠀⠀⠀⠀⠀⣄⣿⢻⠀⡟⣿⢠⠀⠀⠀⣿⢿⠈⠀⠀⠀⠀⠀⠀⣏⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣼⣠⠀⠀⠀⡏⣿⢸⠀⠀⡆⣿⠻⠉⠉⠉⠉⠉⡏⣿⢸⠀⠀⠀⠀⠀⠀⡄⣿⡟⣾⢀⠀⠀⠀⠀⡄⣷⣿⠻⠛⠉⠉⠉⠉⣏⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡄⣤⣤⢤⠀⠀⠄⠄⣤⣤⢤⠠⠀⠀⡀⣄⣤⣤⣤⣤⣤⣤⣤⣤⠤⠀⠀⠀⠀⠀⠀⡀⣤⣤⠠⠀⠀⠀⠀⠀⠀⡀⣄⣤⣤⣤⣤⣤⣤⣤⣤⠤⠀⠀⠀⠀⠀⠀ ⠀