⡸⢸⡆⢻⠀⣔⡾⠛⠋⠀⠀⠀⠀⠀⢀⠀⠀⠀⠨⡍⠳⣝⢿⡲⣝⠮⣕⢦⠈⠹⣷⣄⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⣸⡇⢸⠀⡼⠀⠀⠀⠀⠀⠀⠀⢀⠀⢧⠀⠀⠀⢰⠀⠈⢦⠘⢾⣆⠈⣯⢧⠀⠈⠪⡳⡼⣷⡀⠀⠀⠐⣿⣶⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⣏⢻⠈⣷⠃⠀⠀⠀⠀⠀⠀⠀⡎⠀⢸⠀⠀⠀⡸⢀⠎⠀⢳⡈⠿⡆⠸⡌⣆⠀⠀⠹⡽⡌⢷⡄⠀⠀⠀⠉⢰⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⣿⢻⣄⠇⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⢸⠀⢰⠰⣣⠊⠀⠀⠀⢳⠠⢻⠀⠹⣼⡀⠀⠀⢧⢱⠀⢻⡆⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢆⢻⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⢀⣧⢞⡡⠀⠀⠀⠀⠈⡆⠘⡇⠀⢻⣇⠀⠀⢸⢸⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⡼⣦⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣞⠵⠋⠀⠀⠀⠀⠀⠀⣷⠀⣿⠀⠀⠈⠀⠀⣾⢸⠀⠀⠀⠈⠙⠲⠴⣤⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢣⡇⠀⠤⢄⡀⡿⠈⡆⠀⣀⠤⠂⣠⠔⠋⠉⠛⠛⢉⣙⡶⣄⣠⠴⠚⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴ ⠀⢹⠠⠤⠖⢒⡆⠀⠀⠀⠀⠀⠀⣰⠋⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⠀⢨⢱⠀⠀⠀⠘⢹⢱⡇⠀⠙⠖⠋⠀⠀⠀⠀⠀⠀⠫⠴⠊⠁⠀⠀⠀⠀⠘⣇⠀⠀⠀⣶⠶⠚⠋⠉⠀ ⣀⣸⠀⠀⠴⠋⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠙⠚⠛⠓⠲⠤⠄⠸⠀⣸⡼⠀⠀⠀⣠⢾⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠻⠦⡄⠀⠙⠶⡶⠚⠓⠄ ⡼⠃⠀⠀⠀⠀⣠⠔⠀⠀⡔⣸⠀⠠⠤⠤⢤⣀⣀⣀⣀⣀⣀⣀⣀⣸⢀⣇⣇⡀⠀⠀⣾⣿⣏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⡼⣷⡶⠤⢼⢳⠉⢳⠀ ⠁⠀⠀⢀⠔⠋⠀⠀⠀⠀⣼⢿⡀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠀⠀⢠⣇⣾⠏⠀⠉⢹⣽⢿⣿⠟⠉⠙⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⠁⠀⢸⢽⡟⠵⡺⠋⣸⠀⠀⠀ ⠀⠀⠔⠉⠀⠀⠀⠀⠀⣸⠃⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⠀⠀⠀⢸⠐⠉⠀⣀⢠⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣏⣿⡃⠀⠀⠀⢳⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⢬⠏⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠙⠿⠄⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⣄⡀⠀⠀⣀⡿⣤⣰⠏⠙⠓⠦⣤⣀⣸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢁⡟⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣧⡀⠀ ⠀⠀⠀⠀⠀⠀⣠⣿⣴⠋⠀⠀⠀⠀⠀⠀⣀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀ ⠀⠀⠀⠀⠀⣰⢻⡞⠁⠀⣀⣠⢴⠊⠻⢉⣅⢹⣆⠐⣏⠓⢤⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳ ⠀⠀⠀⠀⢰⢣⣟⣤⡖⡾⡁⡿⣬⡞⠑⠋⠀⠉⠈⠀⠈⠉⠹⡵⣄⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣯⡿⣽⢏⣸⣏⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢎⡷⢄⡀⠀⢸⢻⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢴⣿⡟⠾⡿⢄⢷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⡧⣄⢸⡇⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡬⡿⠀⠀⠉⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡈⡿⠃⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡾⢱⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠁⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠃⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⠏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⣤⣤⣤⣤⣾ ⠋⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣀⣀⣀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣶⣿⣦⣴⣶⣤⣄⣀⣀⣀⠤⠤⠤⠤⠤⠤⠴⠶⠾⠟⠛⠛⠻⢿⣿⣿⣿⣿ ⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠰⡶⠄⠀⠀⠀⠀⠐⠶⠖⠚⠁⠀⠙⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣀⠤⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸