⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⠢⡑⠌⢆⡃⠘⡠⢈⠱⠌⢓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣵⠚⣠⢂⠱⢈⠆⡌⠱⠠⢃⠈⣈⠒⠬⢷⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢛⡹⠗⣠⠊⠤⣁⠒⢀⠆⡑⢌⠢⡀⠕⠢⢴⣻⣏⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢊⡑⢢⢁⡚⢁⣞⠰⡠⠁⠎⡐⢌⠢⡑⣌⠨⢑⡮⠗⡙⢾⣟⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢄⡘⢄⠢⡀⢊⠜⢣⠁⡜⣰⣌⡆⡱⣒⣤⢳⠐⡱⠐⡌⠌⢟⢯⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠣⢀⠘⡀⠇⠀⡃⠜⡠⠠⠃⡧⠿⡄⡿⠿⠟⡛⢸⡠⢣⠘⠸⢠⠿⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⢀⠃⡌⠤⠁⠌⡰⢁⠆⡰⢁⠢⡑⢌⠲⡱⢨⠥⣿⣿⡤⢉⠆⡡⢀⠈⢛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢂⠄⡒⠠⡑⠠⡑⠰⡈⠄⡂⠌⡆⠍⣬⠓⡥⡜⣰⣿⣿⣷⣮⠂⡔⢩⠀⠒⠄⢂⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢌⠰⡈⠢⢌⠡⠂⡔⠈⠥⡘⠄⠁⡏⠐⡰⣣⣾⠧⣡⣿⣿⠏⠀⢠⠁⠜⢠⠂⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡐⢌⠰⣁⠃⠄⠃⢠⠘⠀⡃⠬⣙⡀⠃⠄⢀⠀⣸⣿⣿⣿⣿⢀⡄⣿⡎⠸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠰⠈⠐⢠⡉⢠⠀⠰⣁⢆⢃⡆⣄⣤⣸⣿⣿⣿⣿⣿⣿⣯⠄⢣⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠄⠐⡜⠸⡧⠂⠵⡐⡌⣻⢾⣿⣿⣿⣿⣿⣿⡿⠟⠁⢈⠂⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⡀⠀⠘⡀⠀⠈⠀⠳⡈⡈⢟⣭⣽⣯⣍⡽⠇⡀⠀⠀⡁⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠁⠀⠄⠁⠀⠀⠀⢠⡄⠑⢱⣰⣿⣿⣿⣵⣿⠘⢠⣶⣿⣗⡂⠀⠡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠈⠠⢈⠀⠀⢠⠿⡏⡀⠈⡺⡿⡻⢛⠏⠇⠁⣿⣿⣿⡿⣵⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠈⠄⡀⢠⣖⢿⣻⡽⠻⣿⢧⡀⠀⠨⢻⡢⣸⣿⣿⣿⠏⣾⡄⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠠⠁⠀⣰⣳⢾⣏⣷⣻⢷⡙⢿⣻⣽⣦⣟⡧⣿⣿⣿⣟⣞⢯⣷⡀⠀⠀⣃⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠁⢠⠇⣟⣯⢞⡶⣯⣟⣧⡀⠙⡣⢿⡎⣼⣿⣿⡿⣿⡾⣿⣿⡷⣄⠀⠰⠠⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠈⢀⠀⢈⣇⠹⢞⡏⠉⢳⣯⢘⠝⠁⠉⢋⣵⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣦⠂⠁⢂⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⣸⠷⣠⣅⡚⠒⠛⠈⠀⠀⣠⣶⣿⣿⣿⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⡂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⢠⣏⢧⢃⡿⣿⣿⣿⣶⣴⣾⣿⣿⣿⠟⢋⡜⢟⣿⣿⢿⣿⣿⣿⣿⣿⣿⡧⡀⠀⠅⠢⠀⡀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⠀⢠⠘⠀⠀⡄⠀⠛⢨⣾⠁⠈⣿⣿⣿⣿⣿⠛⣿⠐⣾⠋⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣦⣬⠀⠃⠀⠂⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡄⣈⠂⠀⠰⡟⢻⠟⣾⣷⣟⠀⢼⣿⣿⠟⠉⠀⣀⣀⠀⣠⣶⣛⣛⡿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⡖⠡⠈⠊⠄⠂⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠒⠄⠢⠁⠀⠀⠀⠀⢀⣿⣿⣿⣿⣙⣿⣷⠌⠋⠁⠀⠄⠰⡏⢅⣺⣿⣍⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⠃⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣛⡏⢔⠋⠙⠢⢀⡤⣵⣿⣿⣿⣿⣿⣮⣯⢿⣟⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠛⠿⣿⠿⠿⠛⠃⠀⠄⠡⠐⠈⣽⣿⣿⣿⣿⣿⣿⣿⣷⣿⡟⠿⣿⣿⣿⣿⡿⡿⠟⠁⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀