⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢔⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣵⣢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣽⢛⠟⣻⢟⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⡛⠛⢿⡽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠎⡱⢣⠞⣡⢟⣽⠋⣼⣹⠁⠀⢟⣯⢯⣳⡝⣾⢿⡄⠈⢪⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢮⠉⠀⢡⡟⣼⣟⡾⠁⣸⡿⡟⠀⠀⢸⢿⡄⢳⡹⢞⣷⢻⡀⠀⢩⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⡎⠀⠀⣿⣸⣟⠎⡁⣨⡿⣷⠀⠀⠀⢸⢸⣷⡀⢳⠘⣿⣇⢧⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣧⠁⠀⢸⢡⡷⢎⡜⣰⡟⢁⣿⠀⠀⠀⢸⢸⠈⢷⡀⢃⠙⣽⡼⡀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣸⣸⢩⠮⣴⠿⠾⠃⢻⠀⠀⠀⡇⡞⠷⠮⣿⣎⢆⢹⣧⡇⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⣿⣯⣾⣣⣤⢀⡀⢰⠀⠀⢀⢧⡇⢀⡀⣠⣙⣞⣎⣿⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⣿⣿⠿⣿⣿⣿⣦⣸⠀⠀⣸⠸⢀⣴⣿⣿⣿⢿⣿⣿⡁⠀⢸⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡇⠈⠓⠿⠿⠋⠀⢸⢀⢀⣏⠇⠈⠂⠿⠿⠧⠊⢸⣿⠇⢰⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⡇⣷⠀⠀⠀⠀⠀⠀⡞⡸⣼⡏⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⢹⡌⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢱⢹⣇⠀⠀⠀⠀⢀⢇⢷⡟⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⠀⢸⠀⣇⢇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠘⣿⡄⠀⠀⠀⡘⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢸⠀⢸⡄⣿⡼⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡸⢠⣿⣿⣆⠀⢠⣳⡟⠒⢶⣴⡔⠀⠀⠀⢀⣼⣿⣿⢸⠀⠘⡃⢰⢻⣣⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣇⢸⣿⣿⣿⣷⣮⡏⠀⠀⠈⠉⠀⠀⣠⣶⣿⣿⣿⢸⢸⠀⠀⡄⢸⡎⣻⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⡟⣿⣿⡿⣿⣿⣿⣷⣦⣀⣀⣤⣾⣿⣿⣆⢹⡟⢸⢸⠀⠀⡇⠀⣿⡐⣻⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⡇⡇⣿⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡇⠈⢸⠀⢀⡇⠀⢻⣧⠸⢿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠚⣿⠀⠀⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣾⠀⠀⡇⡀⢸⣿⡄⢛⣿⡄⠀⠀⠀ ⠀⠀⠀⠀⡜⠕⠀⢿⡄⠀⡇⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣿⠀⢰⡇⡇⠀⢻⣧⠈⣿⡇⠀⠀⠀ ⠀⠀⢠⠎⠀⠀⢰⣿⡇⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⢿⡇⠘⢷⢁⡀⠈⣿⡀⣹⡟⠢⡀⠀ ⠞⣩⠇⠀⠀⠀⣸⡿⠃⠀⠃⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⡇⢸⡜⣿⡄⢿⣸⡇⠀⢸⡇⣿⠃⠀⢹⠀ ⠀⣿⠀⠀⠀⠀⣿⠀⣼⠀⢸⣿⣸⠉⠉⠩⢝⣛⡛⢿⣿⣿⣿⣿⠉⡭⠔⢿⣿⡸⣧⠹⣷⡘⢏⣤⠀⢸⣇⡿⠀⠀⠀⡧ ⠀⣿⡆⠀⠀⢰⣿⠀⣟⡀⢸⡟⣿⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠈⢿⣗⢽⣧⡙⣿⣜⣿⡀⢸⠈⡟⣦⡀⢸⡷ ⠀⠘⣷⡀⠀⢸⣿⡀⣿⡇⢸⣧⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣭⣛⣻⢿⣿⣧⢸⢸⡇⢹⡇⣾⠃ ⣀⠀⠘⣿⣤⣾⣿⣇⣸⣧⣼⡏⠳⣝⠦⣀⣀⣰⠀⠀⠀⢄⢠⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣈⠉⠛⢿⣿⣿⡇⢸⣿⣧⣴ ⠿⣷⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣭⣿⣓⠬⣻⣧⣼⠘⣯⠁ ⠀⠀⠉⠙⠻⢿⣿⣿⢿⣿⣿⣿⣟⣛⠉⠉⠉⠙⠛⠛⠿⠿⠟⠟⠋⠉⠀⠀⠀⠀⠀⠀⠉⠙⢿⣦⡈⠙⡿⣿⣿⡆⣽⡆ ⠀⠀⠀⠀⠀⣼⠟⠁⠈⠉⠀⠀⠀⠀⠉⠉⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⣍⡺⣿⣧⢸⡇ ⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡛⢿⣿⣼⠳ ⠀⣠⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⣙⢿⠀ ⣭⠤⢴⡾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⣧ ⣿⣭⣿⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡎⢻⡽ ⠀⠠⣶⣧⡀⠀⣦⣤⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣀⠀⠀⢀⠠⣀⣀⣀⡀⣤⣄⣴⣶⣷⣿⡄⣼⣿⣿⡀⣷ ⠀⠈⢻⣿⣾⡀⠀⠈⠉⠻⣽⡖⡄⠀⠀⠀⠀⢀⣱⢺⣷⣿⣷⣷⣾⣿⡾⡫⣵⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⢻⢻⣇⣿ ⠀⢠⡾⣟⣿⣿⣄⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠉⠈⢛⣿⣿⣏⠉⠉⠉⠈⠉⠉⠉⠉⠉⠀⠉⠉⢁⡰⢻⡿⠀⣏⣿⠏ ⠀⠑⠱⣼⣿⣿⡄⠹⣶⣤⣤⣀⣀⣀⣀⣀⣠⣤⣴⣾⣿⣿⣿⣿⣷⣶⣤⣤⣀⣀⣀⣀⣤⣤⣴⣾⡿⠀⠘⣧⢀⣿⡏⠀