⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠉⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡄⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠜⠻⠍⠹⠉⠉⠉⠉⠉⠉⠙⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠢⢄⠀⠱⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠈⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠜⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠈⠂⢄⡈⠉⠓⠒⠦⠤⠤⠖⠒⠒⠚⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡀⠤⠀⠀⠀⠀⠀⠨⢐⠲⢀⠀⠤⠤⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⡄⠀⠀⠀⠀⠀⠀⠐⠂⠤⢁⠊⠢⡀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢄⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠢⠱⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠰⢧⠀⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡰⡄⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁⠇⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠀⠁⠒⠂⠂⠒⠂⠒⠒⠚⠉⠁⠀⠀⢠⣐⠄⡞⠁⡤⡤⠍⢁⡒⠠⠄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠎⡆⠀⠈⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣥⠘⠁⠀⠀⠁⠀⠀⠈⠉⠒⠤⡑⣄ ⠀⠀⠀⠀⠀⠀⢀⠜⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠃⠼⢃⡀⢸⠀⠀⠀⠉⠐⠀⠀⠈⠟ ⠀⠀⠀⠀⣠⣶⣴⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⣟⡐⠋⢀⡸⠀⠀⢀⠠⠄⠀⠀⠀⠀ ⠀⠀⢀⣴⣿⣽⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠃⢋⣤⡠⠞⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢼⣿⣿⣿⣙⣿⣹⣿⠀⠂⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡟⣒⢭⠓⢀⡉⣁⣀⣖⡤⢄⡀⠀⠀⠀⠀ ⠀⠀⠈⠻⢿⣽⣿⣿⣿⣿⠀⡙⠒⠌⠢⢀⣭⠣⢤⠘⠃⠚⢏⣴⠏⣀⣿⣟⣿⣿⣿⣜⣻⣾⣤⡈⢂⠀⠀⠀ ⠀⠀⠀⠂⢄⠀⠉⠉⠁⠀⡀⠘⠂⠐⠶⠄⠁⢴⡦⠀⣤⠆⠛⢼⢸⣿⣿⣿⣿⣿⣟⣿⠿⣽⢟⣿⢾⠇⠀⠀ ⠀⠈⠀⠀⠀⠈⢉⠔⠊⠁⢸⠈⠂⢶⣤⠀⣾⠋⢠⡴⠀⠰⡂⣜⢠⡙⡿⣿⣿⣶⣿⣹⣾⡿⣿⠿⠊⢀⠀⠀ ⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⣇⠀⠀⠈⠐⠛⠀⠀⣀⡀⢸⠑⢹⠎⣽⣯⣭⣿⡻⢿⣿⢟⣯⡶⠑⠀⢀⠄⠀ ⠠⣐⠢⣄⡊⠀⠀⠀⠀⠀⣀⡆⡘⡷⠀⠘⠿⢀⣬⡁⠀⡫⢘⡽⠈⠭⣻⡿⣿⣿⣿⠿⠛⢉⠔⢁⠔⠁⠀⠀ ⠀⠀⠉⠐⠮⢁⠂⠄⣀⠀⠀⠳⡫⣉⠒⠒⠓⠒⠒⠲⢊⣰⠞⣃⠀⠀⠁⠀⠀⠀⠀⢀⠔⠁⠐⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠑⠠⠍⡂⠤⢀⠙⠫⠥⠶⠖⠽⠟⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠴⢁⠀⠁⠀⠀⠀⠀⠀⠀