⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡾⠿⢷⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣇⣤⣘⡇⠀⠀⠀⡀⠀⠀⠀⠀⠀⡁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣯⣿⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠍⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣉⠿⣅⣿⠀⠀⠀⠀⠁⠂⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣿⠷⣄⡸⢿⡆⠀⠀⠠⠠⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡴⠋⠓⢾⣇⢀⠈⡀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣸⣟⣦⣤⡖⢋⣿⡆⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢻⣍⡟⠻⣽⡇⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⢸⣿⠿⣯⣿⣿⠾⣽⣧⠐⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄⠀⠀⠀⡂⠀⣿⣯⠷⣿⡟⣿⡿⢏⣿⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠆⠀⠀⢀⠐⣟⣟⣛⣻⣿⣿⣛⣛⣟⣟⣛⣻⣻⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠁⠀⠀⢹⣯⣽⣽⣭⣿⣿⣿⣿⣿⣽⣭⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠅⠀⢸⣏⣷⡞⢹⡏⠉⠉⣯⠓⣮⣏⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠌⠂⡠⠂⠁⠀⠀⢠⡿⣏⣀⣽⣾⠁⠀⠀⣿⢾⣁⣈⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠧⠟⢯⣀⡿⠀⠀⠀⠹⣇⣸⠛⠦⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⢳⣤⠔⢻⠃⠀⠀⠀⠀⣿⠓⢤⣴⠛⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡖⠋⠉⣦⣼⠀⠀⠀⠀⠀⢸⣦⠋⠉⠓⣾⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣭⣿⣯⣭⣽⣿⣿⣯⣯⣭⣽⣿⣿⣯⣿⣿⣿⣿⣿⣭⣭⣽⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣀⣀⣀⣤⣽⣭⣬⣤⣭⣯⣭⣭⣽⣬⣽⣯⣅⣁⣭⣉⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣯⣤⣽⣄⣿⣥⣽⣧⣽⣧⣽⣯⣿⣤⣿⣄⣽⣅⣼⣧⣜⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡖⠲⠶⠶⣶⡶⢶⣶⡶⠶⠶⠶⠶⠶⣶⣶⣶⢶⣶⡶⠶⠶⠖⣻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠈⣳⡴⠖⠋⣹⣷⣏⡽⢿⣿⣂⣀⣀⣙⣻⡿⣍⣳⣿⡉⠓⢶⣴⡁⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⠖⠋⠁⠹⣆⢰⣯⡿⠞⣛⣉⡭⠵⠷⠿⠿⣭⣝⠳⠾⣍⣧⣠⡞⠁⠉⠓⢾⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠏⠙⣇⣀⣤⠴⢻⡟⣡⣴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠉⠻⠷⣬⡛⣿⠦⢤⣄⣠⠟⠘⣷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣏⡴⠖⠛⢻⡄⢀⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡆⠀⣼⠛⠓⢦⣌⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⠛⢷⡀⠀⠀⠀⢹⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣾⠁⠀⠀⠀⣠⠏⢿⡄⠀⠀⠀ ⠀⠀⢀⣾⠃⠀⠀⢳⣤⠴⠚⣹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠙⠳⢤⣼⠁⠀⠀⢻⣆⠀⠀ ⠀⢠⡟⢁⣀⠴⠚⠉⠻⣆⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⢀⡞⠉⠙⠶⣤⡀⠻⣧⠀ ⢰⣿⣾⣋⣀⣀⣀⣀⣀⣈⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⣀⣐⣤⣤⣀⣉⣗⣾⣷