⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡼⠀⠀⠀⠀⢀⢠⡶⠥⠿⣛⣫⣦⠀⠸⡀⠀⠀⠀⠀⢠⢃⣠⡤⠶⢖⣤⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⣰⠁⠀⠀⠀⢠⣷⠋⡀⠀⠀⠀⠀⠉⣧⠀⠂⠀⠀⠀⡌⢹⠕⠁⠀⠀⠀⡝⠳⡀⠀⠀⠀⠀⠸⠀⠀⠀⠀ ⠀⡆⠀⠀⠀⢠⠃⣧⠀⡇⠀⠀⠀⠀⠀⠱⡅⠀⠣⡀⡘⠀⡏⠀⠀⠀⠀⠀⢹⠀⣪⡆⠀⠀⠀⠨⠀⠀⠀⠀ ⠀⡇⠀⠀⢠⠏⣼⠃⠀⡇⠀⠀⠀⠀⠀⠀⢹⠀⠀⢲⠃⢸⠀⠀⠀⠀⠀⠀⢸⠀⠸⣽⡀⠀⠀⠨⠀⠀⠀⠀ ⠀⢸⠀⠀⠈⠣⡸⡄⠀⢸⡀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠀⢸⠀⠀⠀⠀⠀⢠⠟⠀⣰⡟⣅⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⢧⠀⠀⠀⠈⠻⡆⠀⢳⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢸⡀⠀⠀⠀⢀⠏⣳⣞⠤⠋⠹⠀⠀⡞⠀⠀⠀⠀ ⠀⠀⠈⢇⠀⠀⠀⡟⣿⡀⠰⢵⣤⡄⣀⡠⠃⠀⠀⠀⠀⣄⡣⠀⠀⣤⣏⢠⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠈⢧⠀⠀⢇⡧⣿⣄⠀⠈⠉⠁⠀⠀⠀⠀⠀⠐⠈⠙⠋⠉⠀⡠⢻⠁⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠇⠀⠈⠓⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀ ⠀⠀⠀⠀⢸⠀⢀⣠⡄⠀⠈⠻⠗⢦⣰⠚⠉⠉⠉⠑⢦⢀⡠⠤⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀ ⠀⠀⠀⠀⠸⠊⠉⠀⡇⠀⠀⢹⠀⠈⠉⢱⠒⠾⠴⢲⠉⢱⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠑⠤⣠⠏⠀⠀⠀⢸⠀⠜⠀⠀⠀⠀⠀⡰⠂⡇⢀⠴⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⠀⠀⠡⡀⠀⠀⠀⠈⠣⠷⠀⠀⠀⣠⠎⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢦⣉⠑⠐⠚⠃⠀⠀⢠⣇⡠⠄⠒⠫⢠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠠⠜⠉⠀⠀⠈⠧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠉⠉⠐⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠄⠁⠀⠀⠀⠀⠀⠀⠈⠳⠦⣤⣀⣠⣤⢴⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⡎⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢄⠑⠀⠀⠀⠀⠀⠀⠀⠁⠛⠾⢴⣤⣠⣀⣤⠦⠳⠈⠀⠀⠀⠀⠀⠀⠁⠄⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠐⠉⠉⠴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠧⠈⠀⠀⠉⠜⠠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠫⠒⠄⡠⣇⢠⠀⠀⠃⠚⠐⠑⣉⢦⠔⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠀⠀⠎⣠⠀⠀⠀⠷⠣⠈⠀⠀⠀⡀⠡⠀⠀⣀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠴⢀⡇⠂⡰⠀⠀⠀⠀⠀⠜⠀⢸⠀⠀⠀⠏⣠⠤⠑⠀⠀⢄⠘⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠊⡠⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢱⠉⢲⠴⠾⠒⢱⠉⠈⠀⢹⠀⠀⡇⠀⠉⠊⠸⠀⠀⠀⠀ ⠀⠀⠀⠋⡠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠔⠤⡠⢀⢦⠑⠉⠉⠉⠚⣰⢦⠗⠻⠈⠀⡄⣠⢀⠀⢸⠀⠀⠀⠀ ⠀⠀⡄⢳⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⢿⠓⠈⠀⠇⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠁⢻⡠⠀⠉⠋⠙⠈⠐⠀⠀⠀⠀⠀⠁⠉⠈⠀⣄⣿⡧⢇⠀⠀⢧⠈⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⢠⣏⣤⠀⠀⡣⣄⠀⠀⠀⠀⠃⡠⣀⡄⣤⢵⠰⡀⣿⡟⠀⠀⠀⢇⠈⠀⠀ ⠀⠀⠀⠀⡞⠀⠀⠹⠋⠤⣞⣳⠏⢀⠀⠀⠀⡀⢸⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⢳⠀⡆⠻⠈⠀⠀⠀⢧⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⣅⡟⣰⠀⠟⢠⠀⠀⠀⠀⠀⢸⠀⠈⠀⠀⢸⠀⠀⠀⠀⠀⡀⢸⠀⡄⡸⠣⠈⠀⠀⢸⠀ ⠀⠀⠀⠀⠨⠀⠀⡀⣽⠸⠀⢸⠀⠀⠀⠀⠀⠀⢸⠃⢲⠀⠀⢹⠀⠀⠀⠀⠀⠀⡇⠀⠃⣼⠏⢠⠀⠀⡇⠀ ⠀⠀⠀⠀⠨⠀⠀⠀⡆⣪⠀⢹⠀⠀⠀⠀⠀⡏⠀⡘⡀⠣⠀⡅⠱⠀⠀⠀⠀⠀⡇⠀⣧⠃⢠⠀⠀⠀⡆⠀ ⠀⠀⠀⠀⠸⠀⠀⠀⠀⡀⠳⡝⠀⠀⠀⠁⠕⢹⡌⠀⠀⠀⠂⠀⣧⠉⠀⠀⠀⠀⡀⠋⣷⢠⠀⠀⠀⠁⣰⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⣤⢖⠶⡤⣠⢃⢠⠀⠀⠀⠀⡀⠸⠀⣦⣫⣛⠿⠥⡶⢠⢀⠀⠀⠀⠀⡼⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡜⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣠⠀⠀⠀⠀