⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠢⠀⠀⠀⠀⠀⠀⠠⠂⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⡇⠀⢠⡐⣀⠀⠀⣀⠀⠑⣄⠀⠀⠀⠀⠠⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠇⠀⠘⠂⠤⢠⠇⣿⠀⣼⠏⢠⠀⠈⠃⠤⠀⠀⠁⢁⠀ ⠀⠀⣀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢱⠆⢡⠂⠀⢀⠠⠈⢆⡿⠀⢀⡴⠛⠀⠀⠘⠀⡀⠀⠀⠈⠀ ⢀⣼⣷⣵⣼⣯⡷⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠊⣁⠀⠀⡴⠆⡀⠀⡀⠀⠀⢃⠀⠃⠀⢂⠀⠀⠱⠇⢈⡀⠸⢐⡣⠒⠉⠃⠠⢣⠃⠀⠀⢀⠀ ⠈⢺⣿⢿⣿⠟⢿⣄⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢇⡾⠁⠀⠀⠀⠀⠈⠁⢦⠀⠀⠀⢆⠀⠢⠀⠀⠀⠅⠀⡜⠻⠓⠚⠁⠀⠀⡀⠴⠃⠀⠀⠀⡘⠀ ⠀⠀⡻⣟⣅⠀⠀⡙⢧⡀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⢎⣿⣦⣦⣤⣶⣶⣄⢀⣼⠀⠀⠀⠀⠢⠀⠀⠀⠈⢢⡞⠙⠷⣶⠂⠠⠀⠀⠠⡀⠀⠀⡀⠑⢅⠀ ⠀⠀⠑⠄⣫⣳⣄⠀⣀⢨⣧⣀⣟⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⡿⠛⠛⠀⠻⢟⡿⠋⠀⠀⠀⠀⠀⠐⢄⠀⢀⠌⠀⠰⠹⠁⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠱ ⠀⠀⠀⠀⠘⠻⢿⣟⠻⣟⣧⡟⠀⡀⠀⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣇⠀⢀⡤⣆⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀ ⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣟⣼⣲⣿⣿⣿⣿⡿⠧⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣦⣤⣃⡀⣠⣤⣄⣀⣀⡠⠔⠂⠉⠁⠀⣠⡷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⢯⣟⣿⣿⣿⣯⡂⠀⠀⠀⠀⠀⣠⡴⣶⢶⡿⢋⣻⣿⣿⣽⣿⣿⣿⡟⠉⢁⠀⣠⣰⣶⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢤⡄⣴⣿⢺⢿⣯⣿⣭⣭⡳⠀⠀⠀⠀⢘⢿⣋⢵⠝⠻⢹⣿⣀⡹⣫⣞⣞⣿⣶⣷⠷⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣾⣷⢼⣿⣎⠿⠛⢻⣿⣿⣟⣦⠀⠀⢠⡿⠛⢻⡆⣠⡾⠋⢋⡿⡝⡚⣋⣾⣿⣃⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⠋⠀⠁⠀⠀⠀⣻⣿⣿⣿⣿⣗⢴⡇⢀⣠⣿⢸⣯⡀⠀⢸⢻⡇⢐⣶⠃⠋⠹⢧⡊⠀⡦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣟⠉⢮⣿⣿⣿⣿⣿⢸⣿⡷⠴⣃⣾⢹⢺⠎⠀⠀⠀⠀⠀⠈⠡⢆⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⠟⢹⣄⣸⣾⣿⣇⣏⡿⡟⣿⢷⣶⣼⣯⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣴⣙⣻⢿⡟⢽⢏⡆⣹⣣⢿⡎⣶⡯⠗⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣅⠠⣀⡾⣞⣡⢏⣸⣠⢸⠫⡅⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠝⣾⣿⠆⡎⡼⣡⢆⡞⡿⣿⢀⠹⠦⠀⠀⠀⠀⠀⠀⢀⡤⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢹⢡⢯⣾⣅⣷⢛⣿⣿⣴⠞⠓⢀⠀⠀⠀⠸⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⣞⣷⣻⣿⣿⣿⣿⣿⣧⠀⠘⣧⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⢸⣿⣮⣾⣿⣿⣿⣝⣢⣏⠷⠑⡀⠋⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⢼⣿⣻⣿⣿⣿⣿⣯⣷⣿⣳⣆⣡⠀⢘⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀