⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣯⡀⠉⢻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣌⣿⣇⣤⣴⣶⣶⣶⣶⣶⣶⣶⠿⠟⠋⠁⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣠⣴⣶⣿⣿⣿⡿⠋⠉⢀⣀⣤⣀⣀⠀⠀⠀⠀⠀⠀⢸⣿⣄⠈⡡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠀⠀⠀⢸⣷⣬⣤⣦⣃⣤⣿⡿⡿⠁⠴⠀⣉⣍⣀⠀⣴⡟⠛⢉⣻⣿⣿⣶⡆⠀⠀⣴⣿⣿⣯⣿⣅⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⡀⣀⣄⣴⣾⣿⣻⢿⡿⠛⠋⠁⠀⠀⢀⣶⡿⠋⣉⣿⣿⣟⣵⡾⠟⠋⠁⠀⠀⠀⠀⠀⠉⠉⠉⠻⣿⣿⣗⢳⣄⣤⢀⠀⠀⠀⠀⠀⠀⠀ ⣣⣦⣟⢟⠋⡏⣉⡞⠟⢿⣿⣭⣔⣿⠇⠀⠀⠀⣼⣯⣴⠟⠋⢹⡿⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧⣊⠃⠛⣝⢦⣠⠀⠀⠀⠀ ⡷⣟⠉⣫⡽⡋⠉⠁⠈⠁⣽⣿⠻⠋⠀⠀⠀⠀⢻⣿⠁⠀⠀⣿⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣤⣾⣏⡉⣭⣫⣿⡤ ⢏⣻⡿⣖⣀⣀⡀⠀⠀⣰⣿⠃⠀⣠⡄⠀⠀⠀⢹⣿⡇⠀⣰⣿⣷⠀⢿⣧⠀⠀⠀⣶⡀⢠⣶⡀⠀⠀⠀⠀⣶⣦⣀⡀⣀⣼⣿⠟⠁⠉⠛⣺⣮⣭ ⠀⠀⠀⠋⢽⣿⣿⣦⣴⣿⠏⠀⣀⣿⠃⠀⠀⣠⣾⣿⠃⢠⣿⣏⠻⣷⣌⣿⣧⡀⠀⣿⡇⠀⢿⣷⡄⠀⠀⠀⢻⣟⠻⣿⣟⠋⠁⠀⠀⢀⢌⣁⠜⢯ ⠀⠀⠀⠀⠸⢿⣿⣍⠉⠁⠀⠘⣿⡏⠀⠀⣤⣿⣿⣿⡿⠿⣿⣿⣶⣬⡙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠺⣿⡀⠈⣿⡆⡤⡯⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⢿⣷⣦⣤⣤⣿⡇⠀⠘⣿⡿⠁⠻⣷⡀⢸⣿⣆⠈⢠⣴⠎⢁⣿⣿⢁⣴⣿⠃⠹⣿⡄⠀⠀⣿⣧⣀⢸⣿⠁⢠⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⢻⣷⠀⣸⣿⣁⣀⣀⣻⣷⣼⣿⣿⣆⠀⠀⢀⣼⣿⣿⣼⣿⣏⣀⣀⣹⣿⣀⢀⣿⡟⣿⣇⢿⣷⣼⣿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣶⣤⣿⢻⣿⡀⢸⣿⡿⠛⠛⠛⢹⣿⣿⣿⣿⣿⣿⣿⣆⠀⣼⣿⣿⣿⣿⣿⣿⣿⠙⠛⠛⠛⠿⣿⠀⣼⣿⡀⣩⣿⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣟⠁⠘⣿⣧⠈⣿⣷⣤⣀⠀⠘⣿⣹⡿⢿⣿⡟⠘⠿⣾⡟⠈⢿⣿⠻⣿⣩⡟⠀⠀⣀⣴⣾⡏⢠⣿⠻⣿⡟⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣾⣿⣦⣻⣯⠻⣿⠻⠶⠙⠿⠿⠿⠟⠀⠀⣀⢹⣿⠀⠈⠻⠿⠿⠛⠁⠰⠾⠿⣿⣿⣷⣿⠋⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠿⢿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣤⣽⣿⣆⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⣀⣀⣠⣤⡀⠀⠀⠀⠀⠀⣠⣿⠟⢿⣧⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠉⠻⣿⣿⣦⣄⠀⠀⠀⠀⠙⠛⠿⠛⠻⠿⠛⠁⠀⠀⢀⣤⣾⣿⣋⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷⣦⣤⣄⠀⠀⠀⠀⢀⣤⣤⣴⣾⣿⡿⠛⠛⠻⣿⣿⠋⠀⠀⠀-⠀⠀hi⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣶⣾⢿⣿⣿⣶⣶⣶⣿⣿⣿⣭⣬⣿⣿⣦⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣾⣿⣿⣿⡿⠛⠛⠻⠿⣿⣿⣭⣭⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⠟⠋⢿⣿⣽⠿⠋⠀⠀⠀⠀⣰⣿⣿⣿⠙⠻⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⢠⡄⠈⢿⣇⠀⠀⠀⠀⠀⢸⣿⣿⡟⢹⣧⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⢀⣴⣾⠃⠀⠘⣿⣧⠀⠀⠀⣰⣿⣿⡟⠀⠀⢹⣷⡄⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⢠⣼⣿⠀⠀⠀⠘⣿⣦⠀⣰⣿⣿⡟⠀⠀⠀⠀⣿⡇⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⣿⣿⠀⠀⠀⠀⠈⣿⣦⣿⣿⡟⠀⠀⠀⠀⠀⣿⡇⠀⠀⠈⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠈⣿⣿⡟⠀⠀⠀⠀⠀⠀⣿⡷⡆⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⣿⠛⣿⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⡀⠀⠀⠀⠀⠀⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡀⠀⠀⠀⣠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⣶⣤⣤⣤⣤⣀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣠⣽⣿⣦⣴⣾⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠉⠙⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣻⣿⡿⠟⠻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠃⠀⠀⢠⣿⣿⣿⣿⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠉⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⣸⣿⣿⣿⡇⣬⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣆⠀⠀⠀⠀⠀⠹⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠁⠀⠀⠀⢰⣿⣿⣿⡟⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⠀⠀⠀⠀⠀⠘⣿⣧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣿⡟⠀⠀⠀⠀⢀⣿⣿⣿⡟⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣆⠀⠀⠀⠀⠀⠈⢿⣷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⣾⣿⠁⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⣦⣤⣤⣀⣻⣷⣀⣀⣀⢀⣀⣀⢀⣀⣀⣀⣤⣤⣴⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢹⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⢀⣼⡿⢿⣷⣄⡀⠀⠀⣾⣿⣿⣿⢳⣶⢉⣿⣿⠛⠛⠿⣿⣿⣿⠿⠿⣿⣿⡿⠿⢿⣿⣯⡁⠀⢿⣿⣿⣆⠀⠀⠀⣀⣴⣿⠿⣿⣆⠀⠀⠀ ⠀⠀⣠⣿⡟⠁⠀⠈⠛⢿⣷⣶⣿⣿⣿⠃⣾⠃⣼⣿⡿⢻⡆⠀⣿⣿⡆⢸⡆⢹⣿⡇⣀⠸⣿⣿⣷⡀⠀⠹⣿⣿⣧⣴⣿⠟⠛⠁⠀⠙⢿⣷⡀⠀ ⢀⣾⣿⣿⣷⣄⠀⠀⠀⢀⡀⠉⣽⣿⠃⢸⠏⣰⣿⣿⠃⣾⠇⠀⣿⣿⠀⢸⡇⢸⣿⣧⢹⡄⢹⣿⢿⣷⠀⠀⢹⣿⣍⠉⣀⡀⠀⠀⢀⣤⣾⣿⣿⡆ ⠘⠻⣿⣿⣾⣿⣷⢦⣴⣿⣿⣾⣿⠋⠀⠀⢠⣿⣿⡏⢰⡟⠀⢸⣿⣿⠀⠀⠁⣿⣿⣿⠈⠁⠈⣿⡇⠻⣧⠀⠀⢻⣿⣆⣿⣿⣦⣶⣾⣿⣧⣿⣿⠇ ⠀⠀⠉⠙⢿⣿⣿⣿⠟⠙⢿⣿⡏⠀⠀⢀⣾⣿⣿⠃⢸⡇⠀⢸⣿⣿⠀⠀⠀⢸⣿⣿⡄⠀⠀⢻⣿⣸⡿⠀⠀⠘⣿⣿⠟⠉⢻⣧⣿⣿⠿⠋⠁⠀ ⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⣾⡿⠀⠀⠀⣼⣿⣿⡿⠀⠈⠁⠀⢸⣿⣿⠀⠀⠀⢸⣿⣿⡇⠀⠀⠘⣿⣿⣗⢢⡄⠀⠸⣿⣆⠀⠀⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⣸⣿⣿⣿⠇⢸⡟⠀⠀⢸⣿⣿⡄⠀⠀⢸⣿⣽⣿⠀⠀⠀⢻⣿⣿⣿⣿⡆⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⠇⠀⠀⢠⣿⣿⣿⣿⠀⠠⠀⠀⠀⢸⣿⣿⡇⠀⠀⢸⣿⣿⣿⡀⠀⠀⢸⣿⣿⣿⣿⣿⡆⠀⢿⣿⡤⡀⡀⠀⠀⠀⢀⡤ ⠀⠀⠀⠀⠀⠀⠀⠸⢿⣷⣤⡀⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣾⣿⣿⣧⠀⠀⠸⣿⣿⣿⣇⠀⠀⠀⣿⣿⣿⣿⣿⣷⣴⣤⣿⡗⣄⡭⠷⠾⡷⣋⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⣿⣿⣿⣿⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⠟⠇⢙⠵⠌⠉⠁⠉⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠻⣿⣿⣄⡀⠀⠀⠀⢠⣿⣿⣿⣿⣇⡀⠀⣿⣿⣿⣿⡇⠀⣠⣼⣿⣿⣻⣿⡋⠤⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠉⠛⠻⠿⠿⠿⠿⠿⠿⣿⡿⠿⣿⡿⠿⠿⢿⡿⠿⠿⣛⠛⢉⡀⢻⣿⠿⠦⠦⣤⣀⣠⣀⣀⣠⡾⠿⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣿⠃⠀⣿⣇⠱⡠⠖⠣⠀⢀⠖⠉⡴⠊⣹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⡷⠗⠋⠏⠏⠓⠁⠉⠉⠁⢰⣿⠀⠀⢸⣿⠉⠈⢄⡤⠚⣅⡤⠃⠀⠀⣿⡇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠨⠎⡀⠡⢔⠁⠑⡄⣀⡔⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠘⣿⣇⠔⠁⠰⠀⠀⢡⡞⠣⠄⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⣇⠀⠀⠀⢀⡼⠯⡀⢑⡤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀