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⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⢠⡿⠋⠀⠀⣴⣿⣿⡅⠀⠀⠀⠙⢻⣿⡄⠸⠿⠇⠀⢿⣆⠀⢰⣦⡀⠀⠉⠻⣿⣿⡿⣷⣦⣄⡘⢿⣿⣄⠀⠀⠀⠀⠉⢉⣤⠉⠛⢿⣶⣄⠀⠀⣴⣶⣾⣿⢸⣿⣿⣿⡄⠀⢸⣧⠈⠹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⣠⣾⠿⠋⠉⠀⣠⡄⠀⠀⠈⠻⢿⣶⣶⣶⠆⠘⣿⡆⠈⣿⢿⣦⠀⠀⠈⠻⣿⣦⡉⢿⣿⣄⠻⣿⣷⣄⣤⣄⠀⣼⡏⠀⣀⠀⢻⣿⣷⣠⣿⡏⠉⣵⡿⠙⣿⣿⣿⡆⠸⣿⣷⡄⠸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡿⠀⢀⣼⡿⠀⢀⣾⠟⠁⣀⣤⣴⣾⠿⠁⠀⠀⠀⠀⠀⣠⣿⠏⠀⣰⣿⠇⠀⣿⣿⣿⣇⠀⠀⠀⠙⣿⣷⡄⢻⣿⣆⠀⠉⠉⠉⠙⠛⠋⢠⣾⡿⠀⠈⠹⣿⡿⠟⠀⣾⡿⣷⣄⠸⣿⣿⣿⣆⠈⠙⢿⣦⣹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⡇⢠⣿⠏⠀⢰⡿⠁⢠⣾⣿⠋⠉⠀⠀⠀⣀⣀⣤⣤⣶⣿⣇⠀⢸⣿⠃⢻⣦⣹⣿⡙⣿⣷⣄⣰⣦⡈⠿⣿⣦⢻⣿⡾⢾⡇⣠⣤⣀⣰⣿⡟⠁⠀⠀⠀⢿⣿⠀⠀⢿⣷⣿⣿⣦⡈⠻⢿⣿⣷⣄⡀⠉⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⣿⠟⠀⠸⢿⣧⠀⠀⣴⣧⣾⠏⠀⠀⠀⢀⣴⡿⠛⠉⣿⣅⣰⡿⢿⣷⣜⣿⡄⠘⢿⡏⢿⣷⡀⠙⠻⠟⠻⠿⠿⢿⣿⡌⠙⠿⣾⣽⡟⠉⠛⠛⢹⣷⠀⠀⠀⠀⠘⣿⡄⠀⠈⠉⠘⣿⣿⣿⣄⠀⠉⠙⠛⠿⢶⣆⠘⢿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣾⠿⠁⢸⣇⢀⣿⡿⠀⢸⣿⣿⠃⠀⠀⣠⣄⣿⣫⣴⣾⢿⣿⣿⠿⠻⠿⠟⢿⣿⣷⢀⣿⣿⠀⠻⣿⡄⢸⣆⠀⠀⠀⠀⣿⣷⠀⠀⣤⡄⢠⣄⠀⠀⠘⣿⣷⡆⠀⠀⠀⣿⡇⠀⣿⣦⡀⠈⢻⣿⡿⢷⡄⠀⠀⠀⠀⣿⡄⠀⠉⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣏⡀⠀⣸⣿⠈⢻⣿⠀⣾⡟⠃⠀⠀⣰⣿⣹⣿⠟⠉⣰⣿⠟⠁⠀⠀⠀⠀⣸⣿⢉⣾⣿⠋⠀⠀⣿⡇⠀⠻⠆⠀⠀⠀⠈⣿⡄⠀⣿⡇⠈⣿⡄⠀⠀⠸⣿⣇⠀⠀⠀⣿⡇⢶⡙⢿⣿⣦⠀⠻⣿⡌⣿⡄⠀⠀⠀⠸⣷⠀⠀⠀⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⢻⣿⣄⣿⣅⠀⣸⡿⠀⠿⠃⠀⢀⣴⡿⣱⣿⠃⠀⣼⣿⠃⠀⠀⠀⠀⠀⣴⣿⢃⣿⣿⠇⠀⠀⢀⣿⣥⣤⣀⣀⠀⠀⠀⠀⣿⡇⠀⣿⡇⢠⣿⠇⠀⠀⣰⣿⠃⠀⠀⠀⣿⡇⢘⣷⠀⠙⣿⣷⡀⠈⢻⣾⣧⠀⠀⠀⠀⣿⡆⢀⣿⠀⠹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⣿⡎⣻⣿⣿⠇⢀⣠⣾⣿⣿⠟⢠⣿⠃⠀⣾⡿⠁⠀⠀⠀⠀⠀⣼⡿⢁⣾⣿⣿⠀⠀⠀⠾⠛⠉⠉⠛⠻⢿⣶⡄⢀⣿⡇⣸⣿⠁⢸⣿⠀⠀⣼⡿⢁⡀⠀⠀⠀⢿⣧⡘⣿⣦⡀⠘⣿⡇⠀⠀⣹⣿⡄⠀⠀⢠⡀⣰⣿⠟⠀⣰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⡿⢿⣿⣿⣿⣿⣿⠿⢟⣽⠇⣾⣿⠀⣸⣿⠁⠀⠀⠀⠀⠀⢸⣿⣁⣼⡟⣸⣿⡆⠀⢀⣴⣾⠿⣿⣶⣤⠈⠻⠿⣸⣿⠁⣽⡇⢀⣾⡇⠀⣼⣿⣷⣿⣿⣿⣷⣄⠀⠙⢿⣤⣿⣿⡄⣼⡇⠀⣴⡿⣹⡿⠂⣰⡿⠀⢿⠇⢀⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡇⠀⢸⣿⠉⢁⣄⢠⣾⡟⣀⣿⣿⣾⣿⣷⣤⡀⠀⠀⠀⠀⣿⡇⠃⢻⣷⣿⡇⠀⢰⣿⣟⣁⣤⣤⣬⣿⣿⣤⣀⠿⠇⣀⢿⣄⢸⣿⠁⣼⡿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠈⣉⣵⣿⣷⠟⢋⣴⡿⠁⣸⡿⠁⠀⠀⣠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⡿⢁⠀⢸⣿⢠⣜⢿⡿⢋⣼⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣿⡇⠀⢸⡇⠻⣿⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣛⢿⣿⣿⣿⣦⣿⡇⠙⢿⣿⣿⢿⣿⣿⡿⠀⠀⢀⣼⣿⢿⡿⠁⣠⣿⠏⢀⣴⡿⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣾⡿⢁⣿⠀⢸⣿⡼⣿⣆⠀⣨⣿⠋⣿⡟⠻⣿⣿⠙⠛⠁⠀⠀⠀⢿⣿⡄⢸⣷⠀⠀⠉⠉⠿⠿⣿⣿⣿⠟⠛⠛⠿⠿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣄⠀⠙⢻⣾⣿⡿⠁⠀⠀⣿⠟⠋⠘⠿⢸⡟⠁⢰⡿⠋⠀⠀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⡏⢀⣼⠇⠀⢸⣿⣇⠙⢿⣾⡿⠃⢀⣿⡏⠀⠙⣿⣧⡀⠀⠀⠀⠀⠀⠹⢿⣦⣍⣀⣀⣀⣀⣤⣾⣿⠟⠁⠀⠀⠀⠀⠀⠐⣿⣿⠉⠉⠙⢿⣿⣎⣿⣿⠿⠿⣿⣿⡏⠀⠀⠀⣸⡿⠀⢀⣴⡿⣿⠁⠀⣿⡇⠀⠀⢸⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⣡⣾⣿⠀⠀⠘⢿⣿⣦⣀⣉⣁⣠⣾⣿⣧⣄⡀⠈⢿⣿⡆⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣤⣀⠀⠘⠻⡿⠿⠃⠀⠀⣼⣿⣤⣤⣾⡿⠃⠀⣾⠏⢠⣿⠀⠀⣿⣧⠀⠀⠈⠉⠛⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⠛⢿⣷⣿⣦⣀⡙⠿⣿⣿⣿⣿⡏⠀⣼⡟⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⣭⣿⣿⠿⢿⣿⡿⢿⣷⣶⣾⣿⠿⠿⠛⠁⣀⡀⢸⣿⠀⠈⢿⣧⡀⠈⠉⣸⣿⢀⣄⠀⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢿⣿⡀⠀⠈⠉⠛⠛⠿⣷⣼⣿⣿⣿⣇⠀⣿⣷⣿⣿⣿⣷⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⢛⣿⢿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢈⣿⠏⠀⢸⣿⡇⣼⡿⢀⣿⣷⣶⣶⣦⠀⢻⣧⠘⣿⣧⣄⠀⠙⠻⠶⠟⠛⣡⣿⠇⠀⠀⠈⢻⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⢿⡷⠀⠀⠀⣤⣄⣤⣾⣿⣿⣿⣿⣿⣆⠹⣿⣿⣿⣿⣿⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⣼⣏⣰⣿⣿⣿⣿⣿⣷⠀⠀⠀⢠⣾⡟⠀⠀⢸⣿⣿⣿⢁⣾⠏⠉⠀⠸⣿⣧⠸⣿⣦⡀⠉⢻⣿⣷⣶⣶⣶⣿⡟⠁⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠋⣿⣿⡜⠻⣷⣮⣛⣿⡿⠁⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠸⠟⢀⠘⣿⣿⡿⠿⣿⣿⠋⠀⠀⣀⣴⡿⠋⠀⠀⠀⣾⣿⣿⢇⣾⠏⠀⠀⠀⠀⠙⣿⣧⠈⣹⣿⡇⠀⠹⣿⣿⣿⣿⠟⠁⠀⠀⠀⣠⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠈⠉⠿⠛⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠾⠿⠿⢿⣿⣷⣶⠶⠾⠛⠁⠀⠀⠀⠀⢀⣿⣿⣏⣼⡏⠀⠀⠀⠀⠀⠀⢸⣿⡀⣿⢻⡗⠀⠀⠈⠉⢉⣠⣤⣴⣶⣶⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡇⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣾⠟⠀⠀⠀⠀⠀⠀⣠⣴⠿⢣⡟⣿⠁⢀⣄⣀⢸⣿⡋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠋⠀⠀⠀⠀⠀⣠⣾⠟⣡⣴⠿⠁⢛⣤⣾⠟⠿⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⠀⠀⠀⣠⣾⣿⠃⣿⡟⠁⠀⢀⣾⠋⠀⠀⠀⠀⠙⠛⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⢸⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣤⣾⣿⣿⠁⠀⣿⣿⣶⡄⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⣏⠉⠁⠉⠁⢀⣴⣿⠿⠻⣿⣿⣧⣀⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⢸⣿⣤⣀⣀⣰⡿⠋⠁⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠟⠀⢸⣿⡝⢿⣿⢿⣃⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣶⠀⠀⠀⠿⠟⠛⢻⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⠿⠃⠀⠀⠀⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣀⠀⢙⡿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠉⠙⠿⠿⠿⠃⠈⠹⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⣦⡌⠙⠻⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣄⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠿⠿⠶⠤⣤⣤⣤⣄⣠⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠇⠙⢿⣷⡆⢀⣾⡿⢡⣿⣿⣧⠀⠀⠀⢀⣾⠟⠀⠈⢿⣿⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠻⠟⠁⠀⠀⣤⣶⡿⢛⣡⣤⣶⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣿⠀⠀⢸⣿⣿⣿⡟⢰⣾⣿⢿⡿⠀⠀⢠⣿⡇⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢋⣠⣤⡄⠀⠀⠈⠙⠋⠘⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⠀⠀⢸⣿⣿⡿⠀⣸⣿⣿⢸⡇⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠛⠛⣻⣯⣶⣾⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⡏⣠⣴⣾⠿⠟⠀⠀⣿⣿⣿⢻⡇⠀⣿⣿⡇⠀⠀⠀⢀⣠⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠛⠁⠀⠀⠀⠀⢀⣤⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢿⣿⠋⠀⠀⠀⠀⠀⣿⣿⣿⣼⡇⠀⢿⣿⠀⢀⣤⣶⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠁⠀⠀⠀⢀⣠⣾⣿⣯⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀ ⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⣼⣿⣿⢸⣿⢸⡇⠀⠀⠀⠀⠀⢰⣿⢻⣿⣿⠁⠀⠘⠛⠃⠘⠿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠟⠀⠀⠀⠀⣰⡟⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀ ⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢰⣿⣿⣿⣼⡟⠸⠷⠶⣦⡄⠀⠀⣿⡏⣼⡟⣿⡄⠀⠀⠀⠀⠀⣶⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠋⠀⠀⠀⠀⣰⡟⢀⣾⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠛⢿⣿⣿⡇⠀⠀⠀⣼⡇⠀⠀⢻⣧⢿⣧⣿⡅⠀⠀⠀⠀⢠⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⢠⣿⢀⣾⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣷⡄⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀ ⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⢠⣿⡇⠀⠀⠸⣿⣦⣿⣿⡆⠀⠀⠀⠀⠀⠿⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣇⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀