⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⢉⡠⣖⠊⠓⢦⡙⢦⠀⠀⠀⣞⡤⣶⠆⠀⣠⣾⠥⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⡴⠋⢁⢘⡄⠀⠀⢳⠀⣇⠀⠉⠛⡰⠃⠀⠀⠉⣠⠞⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⡇⠀⢸⢸⠀⠀⠀⣸⠀⡟⠀⢀⠜⠁⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⣠⠖⡱⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢰⠞⣳⢭⣓⠓⠚⠒⠒⠉⣁⡼⣉⣲⠋⣀⣀⣠⣞⣁⣀⡀⠀⠀⠀⠀⢀⠞⣡⣊⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠺⣾⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣆⠀⠀⠀⠀⠀⠀⢤⠀⠀⢸⡖⠒⠒⠒⠒⠒⣒⠒⠒⠒⠒⠒⠒⠲⠤⠤⠤⢄⣀⡀⠀ ⠀⠀⠀⢀⣀⣀⣀⠀⠀⣀⡠⠤⠔⠒⢒⡞⠁⠀⣸⠦⠔⠀⠀⠀⠒⢿⣆⠀⠀⢧⠀⠀⠀⠀⠀⣈⣧⡤⠤⠤⠤⢄⡀⠀⠀⠀⠀⠀⠈⠉ ⠄⠀⠀⠀⠀⠀⠀⠉⠉⠉⠒⠒⠤⣴⣋⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠠⠤⠗⠒⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⢰⡶⠚⠉⠙⢦⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⠶⠤⢄⣀⠀⠀⠀⠀⠀ ⠀⠀⢀⣠⠴⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡰⠋⠀⠀⠀⢣⠀⢳⡀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠙⡄⠀⠠⠌⠽⠦⣄⠀⠀ ⠚⠉⠁⠀⠀⠀⠙⢲⢄⡀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⣴⡀⠀⠸⢇⠀⢳⣀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠙⠢ ⠀⠀⠀⠀⠀⠀⣠⠋⠀⠈⠑⠦⣀⠀⠀⠀⡼⠀⠀⠀⠉⠃⠀⠀⡀⠀⠀⢿⣤⣀⡀⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠈⠓⠒⡾⠁⠀⠆⠀⠀⠀⠀⠈⠇⠀⠀⠘⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⢺⠃⢰⠀⠰⢡⠇⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⢤⣎⡮⣶⡟⠀⢸⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠨⣧⣬⣠⡂⢃⢠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⡌⠑⠉⠑⠈⠁⠀⣈⣿⠀⠀⠸⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣏⡈⠀⠀⠊⢀⠀⢋⡆⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀ ⠀⠀⠀⠀⡃⡭⠃⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠂⠈⠀⠑⣁⡀⠀⠀⠀⠀⠀⢣⠀⠀⠀

⠀⠀⠀⢣⠀⠀⠀⠀⠀⡀⣁⠑⠀⠈⠂⠀⠀⠀⠃⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇⢹⠀⠀⠀⠀⠀⠃⡭⡃⠀⠀⠀⠀ ⠀⠀⠀⡀⢱⠀⠀⠀⠀⠀⠀⡆⢋⠀⢀⠊⠀⠀⡈⣏⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠸⠀⠀⣿⣈⠀⠁⠈⠑⠉⠑⡌⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⠸⠀⠀⠀⠀⠀⠀⠀⡀⠄⢠⢃⡂⣠⣬⣧⠨⠀⠀⠀⠀⠀⠀⠀⠀⠏⢠⠀⢸⠀⡟⣶⡮⣎⢤⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢻⠀⠀⠀⠀⠀⠀⠀⠇⢡⠰⠀⢰⠃⢺⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⣿⠘⠀⠀⠇⠈⠀⠀⠀⠀⠆⠀⠁⡾⠒⠓⠈⠀⠀⠀⠀⠀⠃⣠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠁⠋⠖⠤⡀⣀⣤⢿⠀⠀⡀⠀⠀⠃⠉⠀⠀⠀⡼⠀⠀⠀⣀⠦⠑⠈⠀⠋⣠⠀⠀⠀⠀⠀⠀ ⠢⠙⠀⠀⠀⠀⠀⡀⠹⠀⠀⠀⠁⠚⡤⣀⠀⠀⠀⠀⠀⠀⣀⢳⠀⢇⠸⠀⡀⣴⠀⠁⡞⠀⠀⠀⠀⠀⠀⠀⡀⢄⢲⠙⠀⠀⠀⠁⠉⠚ ⠀⠀⣄⠦⠽⠌⠠⠀⡄⠙⠚⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⢳⠀⢣⠀⠀⠀⠋⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠴⣠⢀⠀⠀ ⠀⠀⠀⠀⠀⣀⢄⠤⠶⢑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠳⠈⢦⠙⠉⠚⡶⢰⠂⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣠⠀⠀⠀⠀⠀ ⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⢤⠳⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⢄⠢⠑⠈⠀⠀⠀⠀⠀⠀⠀⠉⠉⠊⠒⠗⠤⠠⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⡤⣋⣴⠤⠒⠒⠉⠉⠉⠀⠀⠀⠀⠀⠀⠄ ⠉⠈⠀⠀⠀⠀⠀⡀⢄⠤⠤⠤⡤⣧⣈⠀⠀⠀⠀⠀⢧⠀⠀⣆⢿⠒⠀⠀⠀⠔⠦⣸⠀⠁⡞⢒⠒⠔⠤⡠⣀⠀⠀⣀⣀⣀⢀⠀⠀⠀ ⠀⡀⣀⢄⠤⠤⠤⠲⠒⠒⠒⠒⠒⠒⣒⠒⠒⠒⠒⠒⡖⢸⠀⠀⢤⠀⠀⠀⠀⠀⠀⣆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠈⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⣾⠺⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⣊⣡⠞⢀⠀⠀⠀⠀⡀⣀⣁⣞⣠⣀⣀⠋⣲⣉⡼⣁⠉⠒⠒⠚⠓⣓⢭⣳⠞⢰⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠋⡱⠖⣠⠀⠀⠀⠀⠀⠀⠁⠞⣠⠀⠀⠁⠜⢀⠀⡟⠀⣸⠀⠀⠀⢸⢸⠀⡇⡿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠞⣠⠉⠀⠀⠃⡰⠛⠉⠀⣇⠀⢳⠀⠀⡄⢘⢁⠋⡴⡏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠥⣾⣠⠀⠆⣶⡤⣞⠀⠀⠀⢦⡙⢦⠓⠊⣖⡠⢉⡖⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀