⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⢀⣿⣿⣿⣻⣾⡷⣿⡿⣽⣿⣳⣿⣟⣷⡿⣾⣷⢿⣳⣿⡾⣷⣿⢾⣿⣟⣷⣿⡇⠀⠀⠐⠀⠁⠀⠐⠀⠐⠀⠐⠀⠀⠂⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢯⣿⡷⣿⣟⣿⣟⣷⣿⣻⣾⢿⣽⣿⣾⡿⣿⣳⣿⡿⣽⣿⣻⣾⢿⣿⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣟⣿⡷⣿⢿⣽⡿⣾⡿⣽⡿⣽⣿⣻⣾⣷⢿⣟⣿⣽⡿⣟⣷⣿⣻⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣾⣿⣿⡇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣻⣿⣽⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠉⡉⠈⠉⠉⠉⠉⠉⠉⠹⠋⠛⠻⠿⠿⠿⢿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢰⣷⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣾⣿⣶⣮⡀⠀⠀⠀⠀⣰⣾⣿⣶⣹⡀⠀⠀⠀⠀⠀⠘⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⣿⣿⣿⠛⠃⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⢯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠁⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣛⢾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⣼⣧⠀⠀⠀⠀⡀⠀⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡛⢿⣿⣿⡟⣼⣻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣷⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣶⣶⡄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣾⢟⡱⣜⣷⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⣽⣷⡞⣿⠃⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠄⢀⣴⣿⣿⣾⠿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣷⣦⣤⣤⣀⣀⣀⣀⣀⣤⣤⣤⣶⣿⡿⠟⠇⢸⡏⠀⠀⠀⣿⣧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣾⠿⡛⡍⣆⣳⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣿⣿⣿⠿⠿⠛⡋⠁⠀⠀⠀⠉⠀⠀⠀⠀⣿⣿⣷⣦⡀⠀⠀⠀⠀ ⣤⣶⠿⣡⢣⡑⣚⣼⣹⣿⡇⠀⠀⠀⠀⠀⢠⡄⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⡀⠄⠀ ⣿⢃⠳⢤⠣⡜⣰⢿⣹⣿⡇⠀⠀⠀⠀⠀⢸⡇⡟⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⠉⠉⠉⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣾⣟⣿⣿⣷⣂ ⣿⣈⠳⣌⢳⣘⣧⣟⣿⣿⡇⠀⠀⠀⠀⠰⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠿⠿⠿⠿⠟⠻⠿ ⣿⣮⣗⣮⣳⣿⠯⣼⣿⣿⡇⠀⠀⠀⢠⢸⣿⠇⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⢘⣁⠀⣀⣤⣠⣠⣤⡀⠀⠠⠶⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠙⠻⣿⣿⣹⣿⣿⣿⣧⠀⠀⠀⠈⣿⠇⠀⠀⠀⢰⡟⠛⠲⠦⣤⠤⠤⠶⠶⠒⠆⠐⠂⠐⠒⠚⠓⠂⣴⣲⣲⣶⣾⡟⠋⠉⠉⣿⣿⣿⣿⣧⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⠀⠀⠀⢰⡟⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠒⠒⡐⠠⢉⠌⡥⢃⣽⡟⠈⠉⠉⠉⠛⠛⠛⠻⣿⡀⠀⠀⠘⣿⣿⣦⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠟⠳⣄⣰⡿⠁⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠉⡀⡐⢨⠐⡄⠣⢌⠒⡄⠣⢼⣇⣀⠀⢀⣀⣀⣀⣀⣤⣿⡇⠀⠀⠀⣿⡏⣉⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⡿⠿⠛⠉⠀⠀⠀⠈⢈⡿⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠄⠒⠈⠂⠰⢁⠂⠐⡈⠐⠢⠐⡡⢂⠱⢀⠣⢌⠛⣛⠻⣛⠻⡍⢯⠹⡍⡽⣿⡀⠀⠀⣿⣷⠀⠎⠄⡡⠀⠀ ⠀⠀⠀⢸⣟⠀⠀⠀⠀⠀⢀⣀⣀⣼⡇⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠆⡄⠡⠑⡈⠔⡀⢃⠌⡒⢌⠲⠄⠣⡔⢱⡘⢆⠳⢌⠒⣽⣇⠀⠀⠻⠛⠿⣮⡐⠀⠁⠀ ⠀⠀⠀⠀⠙⢳⣶⡖⠛⠋⠉⠉⠀⣿⠃⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠂⠈⠐⠈⠂⡜⠐⡌⠒⢨⠑⠈⠂⢰⠈⠂⠂⢡⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡿⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠈⠤⢂⠐⡀⠄⢠⠀⠂⠄⠡⠈⠄⠰⠈⠐⠀⠈⠛⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀