⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢻⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣿⣿⣿⣿⣶⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣷⣿⣿⣿⣿⣿⣿⣻⣷⣈⣿⣿⣦⠀⠀⠀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠙⢻⣿⡟⠹⣿⣿⣿⣻⣿⢿⡿⣿⣶⣴⣾⣿⢿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡆⠀⠀⢰⣄⣄⠀⠀⠀⠀⠀⢀⣴⣿⣷⣶⡀⠀⢀⣺⣿⣷⣾⣿⡿⣷⣟⣾⢿⣽⢯⣿⣽⣻⢾⣟⣷⣻⣟⡿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣁⣀⣴⣿⣿⣿⣧⣤⣤⣶⣾⣿⣿⣟⣯⡿⣿⣿⣿⣿⣿⢿⣽⣳⣿⣳⣯⢿⣻⡾⣟⣷⢯⣟⣿⢾⣯⢷⡿⣽⡷⣯⣿⣷⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣄⣀⣠⣤⠀⠀⠀⠀⠀⠀⣤⣤⣿⣿⢯⣷⢿⡿⣿⣟⡿⣯⣟⣿⣻⣿⣽⣻⣽⡾⣽⣳⡿⣯⢿⡽⣯⣟⡿⣞⣿⢾⡽⣯⣟⣯⢿⣻⡾⣟⡿⣾⣻⡾⣿⣽⢯⣟⣷⣯⢿⣿⣶⣤⣴⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣹⣿⣿⢿⣿⣿⣅⠀⠀⢀⣀⣤⣿⣿⡿⣽⢿⣾⣻⣽⢷⣻⣽⣟⣾⢷⣻⣽⣾⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⡿⣽⣯⢿⣯⢿⣽⣻⢯⣟⡿⣽⡷⣿⡽⣷⢯⣿⣻⡾⣽⢿⡾⣽⣻⢿⡿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣯⡿⣞⣿⣻⣿⣿⡿⣿⢿⡿⣯⣟⣿⣻⣾⡽⣯⡿⣯⣷⣻⣽⣟⣯⡷⣟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣟⣷⣻⣟⣾⢿⡽⣯⡿⣯⣟⣯⣿⣳⡿⣯⣿⣳⡿⣽⣟⣯⣿⣻⡽⣿⣽⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠛⠛⠛⣿⣿⢯⣷⣟⡷⣯⣿⡽⣯⣿⣳⣿⣳⢿⡾⣽⡷⣟⣿⢾⣽⣳⣯⢿⣽⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⡾⣟⣾⢯⣟⣿⣳⣿⡽⣯⣷⣻⢷⡿⣽⣞⣯⣿⣽⢾⣻⣞⣯⡿⣷⣻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣯⢿⣳⣯⢿⡷⣯⣿⣽⣞⡿⣾⡽⣿⣽⢯⣟⣿⢾⣻⣽⢷⣻⢿⣾⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣟⡿⣽⣻⣟⣾⣽⢾⣻⡷⣯⣟⣯⡿⣯⣟⣷⣻⢾⣟⣯⣟⡷⣿⣽⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣻⢾⣟⣯⣟⣯⡿⣷⣻⡾⣽⣻⢷⣟⡿⣾⣻⣟⣾⣟⣯⢿⣯⢿⣻⡾⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢷⣻⢿⣽⡷⣯⡿⣞⣿⣽⣻⣽⡾⣯⣟⣷⢿⡽⣯⣿⢾⣻⡾⣿⣽⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣟⣾⡽⣿⣞⡿⣞⣯⣿⣳⡿⣽⢿⡽⣿⣞⣿⡽⣷⢯⣷⣻⣽⢿⣾⣻⢯⣟⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣟⣯⣿⢾⣽⢿⣽⣻⢷⣯⣟⡷⣿⣽⣻⢾⣟⣿⣳⣯⡿⣷⣟⡷⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣻⢾⣯⣟⣷⣻⣽⢿⣽⣞⣯⢿⣯⣟⣿⣳⡿⣞⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠻⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣟⣾⢯⣿⣞⣯⣷⢿⡽⣷⣻⣟⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⢯⣷⢿⣻⣾⡽⣯⣟⣾⣟⡷⣯⣿⣻⡾⣽⡾⣯⣟⡿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣟⡾⣟⣷⣯⣟⣾⣟⡿⣽⡷⣯⣿⣧⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢿⣽⣻⣽⣻⣽⢾⣻⣽⣾⣻⣞⣿⣽⢾⡷⣟⣯⡿⣷⣻⣟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⢿⣻⣾⣳⣯⡷⣿⣽⢯⣟⣷⣯⣟⣿⣻⣟⣿⣻⣟⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣾⣿⢿⣽⡿⣞⣯⣷⢿⣽⣻⢯⣷⢯⣷⢿⣽⣾⣻⣽⢿⣽⣻⢷⣻⣽⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣯⣟⡿⣾⣽⣳⣿⣽⢾⣟⡿⣞⣷⢿⣞⣷⢿⣞⣷⣟⡷⣯⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣴⣿⣿⣿⣦⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢿⣻⣯⣟⡿⣾⣽⢿⣽⣾⣻⣽⢯⡿⣯⡿⣽⣻⣾⣳⡿⣽⣻⡾⣯⡿⣯⣷⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣷⣻⣽⡷⣯⣟⣾⡽⣿⣞⡿⣯⣟⣯⡿⣾⣻⣽⡾⣯⢿⣯⣟⣿⣶⣶⣶⣶⡄⠀⠀⠀⣸⣿⣿⣿⣻⣞⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡾⣟⡿⣾⣽⣻⢷⣯⡿⣞⣷⣯⣟⡿⣽⡷⣿⣻⢷⣯⡷⣿⣻⢷⡿⣽⣻⢷⣻⣾⣷⣶⣤⣤⣤⣤⣤⣤⣤⣦⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣴⣤⣦⣤⣤⣤⣤⣤⣤⣤⣾⣿⣳⣿⣳⢿⣯⣟⣾⣟⣷⣻⣽⣟⣾⢯⣟⣷⣟⡷⣟⣿⣻⡾⣽⡾⣯⢿⣽⢿⣿⣷⣴⣿⣿⣿⣳⣯⡷⣿⣿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣽⣻⢷⣯⣟⡿⣾⣽⣟⣷⣻⢾⣟⣯⢿⣳⣿⣻⣾⡽⣷⣟⣯⣿⣻⣽⣟⣯⡷⣿⣽⣻⣟⣿⣻⣟⣿⣻⣟⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣯⣟⣿⣻⣟⣿⣻⣟⡿⣽⣳⡿⣾⡽⣟⣾⣽⣳⡿⣞⣯⣷⢿⣽⣻⣟⣾⣽⣻⢯⣷⢿⣽⣻⣽⣟⡿⣾⣟⣾⢯⣿⣽⣳⡿⣽⣞⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⢯⣷⢿⣻⣾⣽⣻⢷⣻⣾⡽⣯⣿⢾⣻⢿⣽⡾⣷⢯⣿⣳⣯⣟⣾⣽⢾⣻⣾⡽⣷⢯⣷⢿⣞⣷⢿⣞⣷⣻⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣽⡾⣷⣻⡾⣷⣻⡾⣟⡿⣽⣻⢷⣿⣻⣽⢾⣯⣟⡿⣽⡾⣯⣷⢿⣞⡿⣞⡿⣯⣟⡿⣞⣯⣷⣻⣽⡷⣯⣟⡿⣞⣷⡿⣽⣟⣾⣿⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⢯⡿⣯⣟⡿⣞⣷⢿⣻⣟⣾⣽⣷⣻⣯⢿⣻⣾⣽⢯⣿⣳⣟⡷⣯⣟⣾⢿⣽⣞⣿⡽⣿⣽⣻⡾⣯⣿⢾⣯⣟⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣯⢿⣳⡿⣽⡷⣿⣽⣻⣽⢿⡽⣟⣾⣽⡾⣟⣷⣻⣽⢿⡽⣷⣯⢿⡾⣟⣿⡽⣟⣾⣟⡿⣽⡾⣯⣷⣟⣯⡿⣽⣟⣯⡿⣽⣾⣻⣾⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣻⣽⣻⣽⣟⣾⣟⣯⢿⣯⣟⣾⣽⢾⣳⣯⣟⡿⣽⡾⣽⣻⢷⣯⢿⣽⢿⣽⡾⣟⣷⣻⣾⣻⢷⣯⣷⢿⣻⢾⣟⣾⣽⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣾⣻⢿⣽⣻⣽⣻⢷⣯⣟⣾⣟⡿⣯⣟⣾⣽⢿⣽⣻⢾⣟⣿⣳⢿⣯⣟⡿⣞⣿⢯⣷⣻⣽⢿⡽⣷⣻⣾⣽⣻⣽⣾⣿⠿⣿⣾⢷⣻⣿⣷⣦ ⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣷⢯⣟⣾⢯⣷⣻⢷⣯⣟⡿⣾⣽⣻⢾⣟⣯⡷⣟⣿⣽⣻⣽⢯⣿⢾⡿⣽⣻⣾⡽⣿⣽⣳⣯⣟⡿⣾⣽⣻⢯⣿⢾⣻⣞⣿⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣻⣯⡷⣟⣷⢿⣻⣾⣽⣳⣯⣿⣽⢾⣻⡾⣯⣷⢿⣻⡾⣯⣟⡿⣾⣽⣻⢯⣟⣯⣷⢿⡽⣯⡿⣯⣷⣟⣾⣽⡿⠋⠀⠁⠘⢿⣿⣿⠾⢿⣿ ⠀⠀⠀⠀⢰⣿⣿⣿⣳⡿⣽⣻⢯⣟⣯⣷⢿⣻⣾⣽⣻⢷⣯⣟⡿⣾⢯⣟⣿⣞⡷⣿⣽⣻⣽⣯⣟⣿⣳⣯⢿⣳⣯⣟⣾⣽⣻⢷⣯⣟⡿⣽⣻⢯⣟⣾⢿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣯⡷⣿⣽⣻⣽⣻⣽⣾⣳⣟⣷⣻⢾⣟⣯⢿⡷⣯⡿⣯⣿⣷⣿⣻⡷⣯⣟⡿⣽⣻⢾⣻⢿⣽⣻⢷⣻⣾⣻⣿⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁ ⠀⠀⠀⢠⣾⣿⣿⢷⣻⣽⣟⣯⡿⣯⣿⣾⠿⢿⣾⣷⣟⣯⣷⣟⡿⣽⣻⣟⣾⣽⣻⢷⣯⣟⣾⢷⣯⡷⣿⣽⣻⢯⣷⢿⣽⢾⣻⣟⣾⡽⣟⣯⣿⣻⣽⢯⡿⣯⢿⡽⣯⢿⡽⣯⢿⣽⣿⣷⣯⢿⣳⣯⣟⡷⣟⣷⢯⣟⣾⢯⣟⡿⣾⢯⣿⡽⣟⣿⡿⠋⠹⣿⣿⣿⣽⢾⣟⡿⣽⣟⣯⣿⣳⣿⣻⣽⡾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣯⣟⣯⣷⢯⣿⣽⠟⠁⠀⠀⠀⠀⠈⠉⠙⠻⠛⠻⣿⣷⢯⣟⣾⢯⣿⣞⣯⣟⡿⣾⣽⢷⣯⣟⡿⣽⣻⡾⣟⡿⣞⣯⣿⣻⣽⣞⡿⣾⣻⢿⣽⣻⢿⣽⣟⣿⡿⠟⠉⠉⣿⣿⢯⣟⣷⣻⣟⡿⣾⣻⢯⣟⣯⡿⣽⣟⣯⣷⢿⣻⣿⡀⠀⠀⠀⠸⣿⣾⢿⣽⣻⣟⣾⣽⢾⣻⡾⣽⣳⣿⣳⣿⣷⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⢿⣿⣾⡽⣷⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣻⣿⡿⣯⣟⣯⡷⣿⡽⣾⣟⣷⣯⢿⣞⣯⣿⣻⢷⣟⡿⣽⣟⡷⣯⣷⣟⣾⣟⡷⣿⢯⡿⣽⡿⣾⣽⣿⡆⠀⠀⠘⢿⣿⢯⣿⣞⡿⣞⡿⣷⣻⡿⣽⢯⣟⡿⣾⣽⢾⣟⣯⣿⣿⡀⠀⠀⠈⢽⣿⣻⣾⣽⢾⣟⣾⣿⣽⡿⠿⢿⣾⣽⣾⣽⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢹⣿⣿⠯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⣟⣷⢿⣽⣻⢷⣿⣳⡿⣾⡽⣯⣟⣷⢯⣟⡿⣾⣻⣟⣾⢿⣽⡾⣽⡾⣽⣻⣽⢿⣽⣯⢿⣷⠟⠉⠀⠀⠀⢸⣿⡿⣟⣾⣽⣻⢿⣽⣻⢷⣟⣯⡿⣯⢿⣳⣯⣿⢾⣻⣞⣿⡇⠀⠀⠀⠀⢻⣿⣾⣽⣻⣿⠉⠉⠛⠀⠀⠀⣽⣿⣾⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⣿⡋⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣾⣟⣯⢿⣻⣞⣯⣿⢾⣽⣻⢷⣟⣯⡿⣾⣻⢯⣿⢷⣻⣽⡾⣟⡷⣿⢯⣟⡿⣽⢯⣿⣾⡽⠿⠇⠀⠀⠀⠀⢀⣿⣿⣻⢯⣟⣾⢯⣿⡽⣯⣿⢾⣯⢿⣽⣟⣯⡷⣟⣯⡿⣽⡿⠁⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⢀⣸⣿⡏⣸⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣾⣻⢿⡽⣯⣷⣟⣯⣷⢿⣯⣟⡷⣿⡽⣯⣿⣽⣻⢯⣷⣟⡿⣽⣻⣯⢿⣽⣟⣯⡿⣿⣄⠀⠀⠀⠀⠀⠀⠈⠘⢿⣿⣯⡿⣽⣻⢷⣻⣟⣾⣟⣾⣟⡷⣯⡿⣽⢿⣽⣻⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⣿⣿⣿⣿⣷⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣳⢿⣯⢿⣷⣻⣾⣽⢾⣟⣾⣽⣻⢷⣟⡿⣞⣷⢿⣻⢷⣯⢿⣻⢷⣻⣯⣷⣻⣽⣻⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⡽⣟⣿⣾⣷⣯⣷⣟⡿⣽⣟⣯⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣿⣿⣷⣿⣯⣟⡿⣞⣷⣟⣾⢯⣿⣞⡷⣿⢯⣿⡽⣿⣽⣻⢯⣿⢾⣟⣯⣿⣻⣞⣷⣟⡷⣿⣻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠹⢿⣿⣿⠛⣿⣥⣿⣿⣞⣿⣽⡾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣻⣟⣯⣷⢿⣽⣻⣾⣽⣻⣽⢿⣞⣿⣳⣯⣟⡿⣽⣻⣾⣻⣞⣷⢿⣻⢾⣿⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠙⣿⢻⣿⣿⢾⣽⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠛⣿⣷⣻⣽⡾⣯⣷⣟⡷⣯⣟⣾⣯⢿⣞⣯⡷⣟⣿⡽⣷⢯⣷⢿⣽⣻⢯⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣟⡿⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⢿⣿⣳⡿⣽⡾⣽⣻⣽⢯⣷⣻⣯⣟⣿⡿⢿⡷⣿⣯⡿⣯⣿⢾⣿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣯⣿⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣯⣟⣯⣿⣻⣽⣯⣿⣳⣿⡟⠋⠈⠀⠀⠀⠘⡿⠿⠿⣾⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣯⣷⣿⠟⠻⠍⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠛⠉⠉⢀⣀⣀⣀⣀⡀⣀⠀⠀⠀⠀⠀⡀⢀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀