PERIDOT :3 Emojis & Text

⠀⠀⠀⠀⠀⣴⢿⡇⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡾⢃⢸⠁⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠏⢁⡆⠈⢸⡆⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⡷⡀⠀⢳⡄⠘⣗⣿⠷⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠏⠀⠈⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⢿⡄⡸⣧⡀⠹⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⠋⠀⠀⠀⠀⠀⠀⠙⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⢀⠀⠻⣝⡏⣧⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠘⢠⠀⠈⠳⣮⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⠘⣇⠀⠘⡏⠳⣄⠀⢹⣆⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⠀⢸⡄⠀⠻⠰⠈⢷⠀⢻⡄⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣧⠀⠙⠄⠀⠧⣴⣸⣧⣬⡷⢸⣧⣬⡷⠀⠀⠀⠀⠀⠀⢠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠴⠾⠶⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⢶⣛⣛⣛⣿⡛⠷⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⢿⡍⠹⣍⣩⡿⠀⠈⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠙⠷⠛⠉⠀⣠⣤⣤⡀⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣼⡟⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⣞⣿⢯⣗⣦⠀⠀⠀⣠⢞⡵⣶⠲⣝⢧⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⡦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠉⠉⠉⠉⠉⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢹⡟⢡⢶⡈⣿⣧⠀⢠⣯⡿⡰⠏⠧⠸⡞⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⠰⣏⠈⢡⢿⢹⠀⢸⣸⡟⡷⢀⡐⡇⡇⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣹⡀⠧⠞⠾⣼⣾⠀⠸⡟⣧⠛⠉⠙⢳⣇⡷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⡀⠀⠀⠀⠀⠀⠀⢸⡟⢿⣷⣄⣀⡤⣿⡿⠶⢧⡹⣜⠷⣤⡤⢞⡼⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⢸⣿⣮⡙⠲⠶⢚⡾⢷⡄⠀⠙⢿⣟⠛⠛⢋⣡⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣄⠀⠀⠀⠸⣿⠈⠻⢦⡴⠋⠀⠀⠁⠀⠀⠀⠈⠛⠚⠋⠁⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⣤⡀⠀⠀⠀⢀⣴⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣴⠟⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣷⣌⠻⣿⡀⠀⠠⣦⡀⢀⣀⡀⢀⣰⡆⠀⠀⢠⣿⣥⡿⠋⠀⢀⣠⣾⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⣾⣿⣿⣧⣈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣽⣷⡄⠀⠈⠙⠛⠉⠉⠉⠉⠀⠀⠀⢿⣿⠏⣀⣤⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣤⡾⣿⣿⣿⣹⡟⣿⡆⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣷⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀ ⣼⠟⣉⣤⣾⣿⣿⣿⣿⣿⣿⡆⠀⠈⢿⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣦⣄⣀⣠⣤⡶⠟⠋⢹⣟⣿⣿⣿⣿⡟⠛⠛⠛⠛⠶⠶⠶⠶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣶⡄⠀⠈⠉⠛⠛⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠛⠛⠛⣽⢿⣿⣿⣿⣿⣦⠀⠀⣠⣿⣿⣿⣿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⣁⢈⣿⣿⣿⠿⣻⣽⣿⣿⣿⠛⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢸⣿⣿⣿⣧⠈⠀⣰⣿⣿⣿⣿⠋⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣍⠉⢉⣿⣷⣿⣿⣿⣿⣿⣿⣦⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠈⣿⣿⣿⣿⡇⢰⣿⣿⣿⣿⠃⠀⠀⠘⠛⣿⠛⠛⠛⢻⡿⠿⠻⠷⣆⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢻⣯⣉⣡⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠿⢿⣻⣷⣶⣶⣦⣤⣤⣤⣤⡤⠤⠴⠶⠶⠾⠛⠛⠙⣿⡀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢠⡿⠀⠀⢾⣿⠛⢷⣄⠀⢻⡆⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⣿⣭⣤⣿⣯⣿⣿⣿⣿⠿⢯⣤⣤⣀⣀⣀⠀⠈⠉⠉⠉⠉⠉⠙⠛⠓⠲⠶⠶⠤⠤⢤⣽⣷⡄⠙⢿⣿⡟⠈⠻⣿⠇⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠻⣆⠀⠙⢷⣬⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠛⠷⣾⣿⣿⡛⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠐⠓⠒⠶⠦⢤⣤⣄⣀⣀⣀⣀⡀⠀⠛⢿⣆⠈⢿⣇⠀⢰⡟⠀⠀⠀⢀⣰⡿⣥⣤⣤⣄⣀⣀⣙⣷⣄⡀⠙⣿⠀⠀⠀⢸⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣀⠀⢀⣠⣤⣀⣈⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠺⠿⣿⣶⣿⣷⣿⣷⣶⣶⣾⣿⡏⠀⠀⠀⠀⠀⠉⠉⠉⢉⣿⠿⠛⠿⠇⠀⠀⠈⢿⣌⠙⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠛⠛⢻⠏⠉⠛⢿⣏⠀⠒⠲⠦⠤⠠⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠛⠓⠲⠶⠤⢤⣤⣼⠏⢀⡀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠉⠉⠛⠳⠶⠶⠶⠦⠤⠤⠄⠀⠀⠀⠀ ⠀⠀⠀⠃⠀⣶⣄⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠐⠲⠤⢤⣤⣀⣀⣀⡀⠀⠀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⢠⣿⣄⣨⡇⠀⠀⠀⠀⠀⠀⢸⡷⠤⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡂⣤⡄⢿⣦⠈⢿⣷⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⣽⣿⠿⠛⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⢿⣦⣀⠀⠀⠀⠈⣽⠿⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣧⠙⣿⡀⢻⣧⣄⣿⠲⠶⠶⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠛⠉⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠉⠻⢷⣦⣄⣀⢿⣧⣀⣴⠇⣰⡇⣰⣧⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣴⡿⢷⣴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠒⠒⠶⠶⣤⣤⣤⣠⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣭⡉⠙⠛⠛⠻⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠ ⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣴⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣿⣿⣿⣿⡿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⢿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣞⡁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⢰⢆⣾⠟⠁⠸⡇⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡾⠟⠛⠋⠁⠒⠲⠦⠤⠬⣽⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠉⠉⠙⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡍⠛⢦⠀⠀⠀⠀⠀⢸⡏⠀⠀⣠⡿⠀⢠⣴⣶⡿⣟⠛⠋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣤⣀⠀⠀⠀⣼⠇⠀⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⣀⡀⠄⠀⠀⢀⠀⠠⠖⠋⠐⠀⠘⣧⠀⠀⠀⠀⢸⡇⢀⣼⠟⠀⠀⠀⠀⢹⣧⠀⠈⡇⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠛⢷⣦⡄⢿⡄⠀⠀⣼⣿⡗⠒⠶⠦⠀⠀⠀⢀⣤⣶⠛⠉⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠉⠛⠓⠲⠦⠤⣤⣤⣀⣀⠀⠀⠛⣀⠀⠀⠀⢸⣧⡟⠁⠀⠀⠀⠀⠀⠈⣿⡄⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠻⣦⢰⡏⣿⡏⠀⠀⠀⣠⣴⠞⠋⠉⠙⠛⠛⠳⠶⠶⢦⣤⣤⣀⣀⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠉⠀⠛⠐⠾⠶⢦⣤⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠈⠛⠉⣿⢇⣤⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⡯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡉⠉⠛⠛⠶⠶⠤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠁⠀⠑⠒⠀⠀⠀⠀⠉⠉⠙⠛⠒⠲⠦⠤⣄⣀⣀⡀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡽⠟⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⠒⠦⢤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠛⠁⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡶⠶⢦⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠶⢦⣴⡿⠟⠋⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠾⠋⠁⠀⠀⠀⠀⠡⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠈⠉⠉⠙⠛⠻⠷⠶⢶⣤⣤⣀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠋⠀⠀⠀⠈⠳⣽⡆⠀⠀⠀⠀⣀⣀⣠⣼⡏⠀⠀⠀⠀⠈⣵⡷⢀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⢛⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠓⠶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⣶⡶⠶⠶⢿⡿⠿⠿⠿⠟⠛⠛⠙⠻⠃⣠⣶⣀⣴⡿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣷⣤⣀⡀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠙⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢰⣿⣿⣤⢉⣩⡾⠟⠛⠳⠶⢦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣷⣶⣯⣤⣄⣀⣀⣀⣠⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⢀⣤⣀⣨⣿⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠳⠶⢶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣉⣉⣉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣷⣶⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠉⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⣀⣤⣤⣤⣀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⣿⣿⣿⣿⣿⠟⣁⣀⣀⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠇⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⡿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠟⠁⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠤⢤⡄⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⠻⣇⠀⠀⠀⠀⠀⠀⠀⣰⡶⠀⣠⠞⠋⠉⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡄⣠⠞⠋⠉⠉⣳⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢻⡻⣽⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣴⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠙⠿⠛⠁⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠉⢳⡆⠀⠀⠀⠀⠀⠀⠀⠀⢻⡎⠙⠻⠿⣿⣿⣟⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠛⢧⡀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⡶⠂⣼⠉⠀⠀⠀⠈⢉⣩⣿⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⢀⣠⣤⡴⠶⠊⠻⡀⠀⠀⠀⠱⣦⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢀⡼⠁⢠⠇⠀⠀⣀⡴⠊⠉⠀⠀⠀⠈⠙⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⠀⠙⢦⣙⢦⡀⠀⠈⢢⣀⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⢀⡞⠁⣠⠏⠀⢀⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⠃⢠⠟⠀⣰⠏⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠞⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡞⠁⠀⡞⣴⠏⠀⡴⠃⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⡾⠃⠀⢿⠈⠛⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣰⣶⠿⠛⠛⠁⠀⣸⣷⠋⢠⡞⠁⢸⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀ ⠀⠀⠀⠀⣼⠁⠀⠀⢸⡆⠀⠀⠀⠉⠙⢿⠙⣛⢻⢿⡉⠉⠉⠀⠀⠀⠀⠀⠀⣰⣿⠇⣴⠋⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀ ⠀⠀⠀⢰⡇⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠈⢧⠘⣾⠈⠳⠦⣄⣀⣀⣠⠤⠖⠋⠁⣸⡾⠁⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀ ⠀⠀⠀⣿⠇⠀⠀⠀⣆⠈⢧⠀⠀⠀⠀⠀⠈⢳⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢇⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⠙⢧⠸⣇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⢳⣼⡄⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⢸⡇⠀⠀⠀⡟⠀⠀⢀⣤⣄⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⡀ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠙⣷⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⢰⠃⠀⠹⢷⣀⠀⠈⣇⠀⠀⣸⣇⡴⠞⠋⠉⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠗ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⢸⡇⠀⢀⡟⠀⠀⠀⠀⠙⢿⡄⢹⠀⢠⣿⠛⠒⠛⠛⠉⠛⠛⠳⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠺⣇⠀⠀⠀⠀⠀⠸⢳⠀⠸⠀⠀⠀⠀⠀⢀⣠⠞⠻⣆⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⠳⣆⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣶⣄⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⡟⠛⠛⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡟⠛⠋⠀⠙⠳⠺⣿⣿⣿⣿⣿⣦⠀⠀⠀⣠⣶⣶ ⠀⠀⠀⠀⠀⠀⣗⣵⡄⠠⣖⠤⡀⣹⣿⣿⣿⣿⡿⠀⣠⣾⣿⣿⣿ ⠀⠀⠀⠀⠀⣰⠀⠙⠃⠐⠛⠀⠐⠟⠀⠈⣿⡟⢁⣴⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣠⠿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⣦⣀⣀⣀⡀⠄⣀⢼⠛⢻⡃⠀⠈⢻⣿⣿⠏⠀ ⠀⠀⠀⠀⠀⢀⣰⣿⣿⣀⢀⡰⠞⠉⣉⣠⠼⠭⢆⣴⣿⡿⠁⠀⠀ ⠀⠀⠀⢀⠔⠁⠨⣹⣿⣿⣻⣷⠶⡉⠅⠀⠀⡠⠂⢘⡏⠀⠀⠀⠀ ⠀⠀⠀⠊⡀⠀⠈⢹⢿⣿⣿⣿⠑⠤⠀⠀⡐⠀⠀⠀⠡⠀⠀⠀⠀ ⠀⠀⢸⠀⣏⠭⠲⣾⠟⢁⣸⣿⠀⡸⠐⡀⠀⣀⡀⠀⠀⢁⠀⠀⠀ ⠀⢀⠊⡆⠀⠀⠀⡎⠉⠁⠠⠼⣰⠡⠄⠚⠈⠀⠀⠀⠀⠀⡆⠀⠀ ⠀⢊⢀⠳⡗⡱⡟⡏⠒⠄⠀⠀⢰⠀⠰⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀ ⠀⣸⣅⡒⠂⠀⠇⡿⡅⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⣀⠔⠁⠀⠀⠀ ⡰⣻⣿⣿⠀⠀⠀⡇⠙⢧⠤⢶⠊⠁⠀⠐⠒⣒⡞⠀⠀⠀⠀⠀⠀ ⡆⠀⠸⣿⠄⢀⢲⠓⠀⠀⠈⠙⡇⣀⢐⢂⣁⡤⠊⠀⠀⠀⠀⠀⠀ ⢣⣔⣲⣿⡖⠛⠋⢙⠉⠉⠉⠉⠉⠉⠉⠻⡒⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⣿⣿⡇⠀⠀⠈⢔⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠛⡇⠀⠀⠐⠪⢆⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣡⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀

⣿⣿⣿⣿⣿⣿⡏⢛⣿⣿⡟⠉⠈⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠟⢛⡳⠤⠴⡺⠿⡛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡿⠋⢠⠁⠀⢀⠠⢁⡠⠃⡀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣶⡟⡃⢖⠋⠁⠉⣀⣀⡠⠈⠑⠂⢇⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣷⣶⡎⠀⠁⠀⣀⠠⠐⠒⡢⠀⠘⡄⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡙⠒⠩⠿⠘⢄⠀⢐⣁⠜⠀⢠⠃⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⢄⠀⠀⠀⠀⠉⠁⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠀⠑⢄⠀⠀⠀⢶⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⡿ ⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠈⠐⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢢⣽⡟⠄ ⣿⣿⣿⣿⣿⠋⠰⡀⠀⠤⠀⠀⠀⠀⠸⢀⠔⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣿⠃⠀ ⣿⣿⣿⣿⣧⠇⡄⠈⣢⣀⣀⠀⣀⣀⢴⡎⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⣿⣿⣿⣿⣿⣿⣠⣾⣿⣿⣿⣿⣿⡆⣀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄

⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣾⣿⣿⡿⠟⠛⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣥⣤⠀⠘⠿⠛⠓⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀ ⠘⣿⣿⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠛⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠘⠻⡆⢀⣀⣀⠄⠠⠒⠈⠁⠀⠿⠿⠀⠀⠀⣿⣿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⠁⠀⠺⣷⠄⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠁⠀⠀⠀⠀⢀⢠⠂⢰⠀⠀⠀⠀⡏⢛⠻⠯⠤⠤⣀⠀⠀⠀⠀ ⠀⠀⠸⡀⠀⠰⣒⡈⢀⣀⠰⠁⠀⠀⠀⡘⠠⢃⠃⡠⠊⠁⠀⠑⣄⠀⠀ ⠀⠀⠀⡱⣄⠀⠀⠈⠁⠀⠀⠀⣀⡔⢰⡐⠡⠂⠌⠀⠀⠀⠀⠀⠈⡄⠀ ⠀⠀⡜⠀⠇⠉⠒⢆⣠⢄⠒⠋⠉⣀⢞⠔⠁⡟⠀⠀⠀⠀⠀⠀⠀⢰⠀ ⠀⢰⠀⠀⡜⡄⠀⠈⢪⠀⠉⠉⠉⠀⡏⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠸⠄ ⠀⢸⠀⠀⠈⢲⠀⠀⠈⡆⠀⡀⢄⠀⢀⠀⡘⡀⠤⠦⠤⠄⠀⠀⠀⠈⠠ ⠀⢸⠀⠀⠀⠀⡇⠀⠀⢤⢠⠁⠀⢙⠼⣠⠋⠈⠉⠁⠒⢤⠀⠀⠀⡀⠀

⬜⬜🏿⬜⬜⬜⬜🏿⬜⬜ ⬜🏿🟫🏿⬜⬜🏿🟫🏿⬜ ⬜🏿🟫🟫🟫🟫🟫🟫🏿⬜ 🏿🟫🟫🟫🟫🟫🟫🟫🟫🏿 🏿🟫🏻🏻🟫🟫🏻🏻🟫🏿 🏿🟫🏻🏻🟫🟫🏻🏻🟫🏿 🏻🏿🟫🟫🟫🟫🟫🟫🏿🏻 🏿🏻🏿🏿🟫🟫🏿🏿🏻🏿 ⬜🏿🏻🏻🏻🏻🏻🏻🏿⬜ ⬜⬜🏿🏿🏿🏿🏿🏿⬜⬜

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⣤⣄⣀⢀⣠⣴⣶⣾⣿⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⣀⣤⣤⣤⣀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣤⣶⣤⠀⠀⠘⠿⠿⠿⠿⠟⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⣿⣿⣿⡇⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠟⠁⠈⠙⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⢿⣿⡇⠀⠀⠀⠀⠀⢀⡀⠀⣀⡤⠖⠒⠒⠒⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢣⠀⡠⠴⠒⢤⣞⡁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢈⡇⠀⠀⠀⠸⣿⣽⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣼⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⣠⢤⣀⠀⠀⠀⠀⠀⠈⢻⣿⢿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⡋⠀⠀⡿⠀⠀⠀⠀⠀⠀⢀⠇⠀⡬⢹⠛⠓⠒⠒⠒⢦⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡀⠀⠀⠀⣠⣤⠔⠚⢏⠀⠀⠙⢦⡜⠀⠀⠀⠀⠀⠀⢀⠎⠀⡼⠁⡞⠀⢀⡠⠖⠋⠉⠀⠉⠲⡀⠀⠀⠀⠀ ⠀⠀⠀⠈⣧⠀⠀⠀⠙⠮⠷⣄⣀⠵⠤⠒⠉⠀⠀⠀⠀⠀⠀⠠⡞⢀⠞⠀⡜⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀ ⠀⠀⠀⠀⢈⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠀⣸⢡⠎⢀⠞⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀ ⠀⠀⠀⡰⠃⠸⡉⠳⢤⣀⣀⠀⠀⠀⠀⠀⣀⣠⡶⠟⠛⠁⢀⣯⠋⡰⠋⢰⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀ ⠀⠀⢰⠃⠀⠀⢇⠀⠀⠀⠉⢯⠩⣹⢯⡉⠁⠀⠀⠀⢀⡠⠿⣇⡜⠁⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀ ⠀⠀⡏⠀⠀⢀⠘⡆⠀⠀⠀⠀⢣⣹⠀⠉⠙⠒⠒⠉⠁⠀⢰⡏⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀ ⠀⢰⠇⠀⠀⠈⢧⡸⡄⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⠀ ⠀⢸⠀⠀⠀⠀⠀⠻⣷⠀⠀⠀⠀⠈⣇⠀⠀⢀⠠⢦⡀⠀⠀⡇⠀⠀⡞⠀⣀⣤⠶⠶⠤⠤⣄⠀⠀⠀⠀⠀⠀⢐⠀⢄ ⠀⢸⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢹⠀⠀⡼⠀⠀⠙⢦⡀⢱⠀⢰⣷⣋⠥⠤⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠸⡆⠰⠁⠀⠀⠀⢀⡽⠺⣄⡟⠀⠀⠀⠀⠀⠀⠀⠉⠓⢆⠀⠀⠀⠀⠀⡎⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠠⠄⢀⡤⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠚⢅⠈⠡⡀⠄⠊⠀⠉⠉⢂⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⢓⡆⠀⡇⠀⡇⠎⠉⣥⠈⠂⠀⠣⣥⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢄⢀⡠⠁⢠⠀⡄⠘⠣⠀⠀⡠⠊⡘⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠄⢀⠔⠁⠀⠈⠉⠁⠀⠈⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢥⡀⠀⠀⠘⠤⠆⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢢⠀⡀⠤⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣄⣤⣤⣤⡀⠀⠀⠀⢀⣠⡜⠀⠣⢄⡀⠀⠀⠀⠀⠀⣠⣾⠀⣀⣤⡶ ⢶⣶⣼⣿⣿⣿⡗⢄⠀⠀⡎⠈⣼⣦⡀⢀⣽⢆⠀⠀⢀⣿⣛⣟⣿⠽⠛⠁ ⠈⠉⠉⠛⠉⠀⢻⣦⠱⢼⠁⣼⣿⣿⣿⣿⣿⡇⢆⣴⣿⡟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣷⣯⡷⠉⢻⣿⣿⠿⣿⣧⣣⣿⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠋⢨⠀⡉⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠐⠀⠉⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢞⣷⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⢁⣵⣿⣿⣷⣌⠹⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣞⣡⣤⠒⠉⠁⡐⠐⡀⠉⢱⠐⠮⢻⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⠀⠀⡐⠀⠀⠐⡀⢸⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⠀⡐⠀⠀⠀⠀⠐⡘⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀ ⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡐⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀ ⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀ ⠀⣾⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⢻⡀ ⢸⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠺⣇ ⢸⠃⠙⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⢀⠔⠁⣿ ⢸⡄⠀⠈⠻⣿⡟⠀⣀⣠⣤⣶⡈⠁⠀⣿⣿⣷⣶⣤⣄⣀⠀⢡⠀⡴⠃⠀⠀⡿ ⠘⣇⠀⠀⠀⢸⣶⣿⣿⣿⣿⣿⣿⣦⡀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⢸⡇ ⠀⠹⣆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢠⡟⠀ ⠀⠀⠙⣦⡀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠋⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣴⠟⠀⠀ ⠀⠀⠀⠀⠙⠿⠿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠉⠻⠿⢿⣿⣿⡿⠿⠛⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⠿⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⡏⠀⠀⠀⢣⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣟⠧⠤⠤⠔⠋⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⢀⣶⠤⠒⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⢿⣆⣠⣤⣤⣤⣤⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⢿⢿⠀⠀⠀⢀⣀⣀⠘⣿⠋⠁⠀⠙⢇⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⢇⡞⠘⣧⠀⢖⡭⠞⢛⡄⠘⣆⠀⠀⠀⠈⢧⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀ ⠀⠀⣠⣿⣛⣥⠤⠤⢿⡄⠀⠀⠈⠉⠀⠀⠹⡄⠀⠀⠀⠈⢧⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⣼⡟⡱⠛⠙⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠹⣧⡀⠀ ⢸⡏⢠⠃⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠸⣷⡀ ⠸⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿⠇ ⠀⣿⡄⢳⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢹⡇⠘⣇⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⡟⠀⠀ ⠀⢸⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢳⣼⠟⠀⠀⠀ ⠀⠸⣧⣀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⣴⡿⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⢷⣄⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣠⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⣀⣀⣠⣤⠾⠷⣦⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠄⠀⠢⠤⠄⣀⠀⡀⡀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢣⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠀⠀⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠄⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⠀⠰⡀⠀⠐⡀⠀⠀⡄⠀⠀⠀⠀⠀⠄⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⡖⢠⠬⠔⠤⠬⠦⠄⠈⠢⡄⡰⠀⠀⠡⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⢀⡤⠊⠀⠈⠀⠀⠀⠐⠂⠀⠀⠀⡇⠀⠀⠀⠀⠐⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠢⢀⣀⡐⠒⣀⣀⠴⠁⠀⠀⠀⠀⠀⠀⡄⠀⠀ ⣿⣿⣿⣿⣿⡟⠀⠀⠠⠐⠀⠐⢄⠀⠀⡀⠀⡇⠀⠠⠒⠀⠂⠄⠀⠀⠀⢸⣿⣿ ⣿⣿⣿⣿⣿⣇⠀⠀⠁⠀⠀⠀⣴⡿⠥⠤⠤⠄⢿⣆⠀⠀⠀⠈⡄⠀⣠⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣆⡀⠣⣀⣀⣰⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⣀⠔⠀⠀⠈⢿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠹⣧⠸⣿⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢇⢿⠀⣿⡸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⢠⠃⣠⠶⠋⠉⠙⠻⡟⠛⠓⠦⣤⣀⠀⠀⠀⠀⠀⢸⣇⢸⡘⢷⡈⠧⠙⣦⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣶⡴⣾⡏⠀⠀⠀⠀⠀⡽⠀⠀⣠⣴⣿⣷⣦⡀⠀⠀⠈⠻⣄⠑⠀⠁⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠷⣄⠀⠀⠀⠀⣠⡾⠋⠰⣅⡘⠲⠤⠤⠔⠋⠀⠀⢰⣱⢻⡿⢿⢻⠻⣦⠀⠀⢰⡛⠳⣄⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠈⠓⠦⣴⣾⠏⠀⠀⢠⡾⢀⡤⢖⣒⡲⣄⠀⠀⢈⡼⠋⠀⣸⢞⠀⡎⣧⡀⠈⠙⠲⣌⠙⠒⠚⠉⠑⠢⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣤⠶⢿⣇⠀⠀⠀⣸⠃⠀⠀⢀⡿⠃⡏⢰⢩⣦⣽⢸⠆⠴⠋⠀⠀⠀⢸⠘⠀⡇⠈⢷⠀⠀⠀⠀⠙⠲⢤⣀⣀⣀⢀⡼⠿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⣩⠶⣿⡿⣿⡄⠀⠐⠃⠀⠀⠀⠘⢦⠀⢣⡘⠣⠭⠴⠋⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⢸⣧⠀⠉⠻⣄⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡞⢁⡼⠃⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠉⠂⠀⠀⢰⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠈⢧⡀⠀⠀⠙⢦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠾⢯⡑⣿⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⡀⢰⠀⢸⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡆⠀⣿⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠙⣆⠀⠀⠀⠙⢦⡀⠀⠀ ⠀⠀⠀⢀⣾⡷⣶⣆⢣⢹⡆⠀⢠⡴⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢇⠀⡇⠀⠀⠀⠀⢀⣤⣴⣶⣶⡿⠟⠛⠋⠁⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⡉⠀⠀⠀⢈⣧⡀⠀⠀⠀⠹⣦⡀ ⠀⠀⠀⢼⡇⢇⢸⡈⠛⠛⣇⢠⠏⢠⠟⠀⠙⢦⣄⠀⠀⠀⠀⠀⠸⣄⣁⡀⠀⠀⠀⠘⢿⣭⠽⠋⠀⠀⠀⠀⣰⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⢧⠀⠀⠀⠀⠉⠿⡄⠀⠀⠀⠈⠳ ⠀⠀⠀⢸⡇⠈⠺⠃⠀⠀⠙⠟⠀⣿⠀⠀⠀⠀⠈⠳⢦⣀⠀⠀⠀⠀⠀⣉⣷⠆⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠃⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣿⣸⣇⣀⣀⣀⣀⣠⣼⠦⠀⠀⠀⠀ ⠀⠀⠀⠈⢷⠀⠀⠙⢦⡀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣄⣀⠠⠯⢤⣄⣀⣀⣤⣤⣤⡋⡹⢋⡙⢦⣀⣠⠴⠚⠋⡉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⠀⠀⠀⠘⣧⠀⠀⠀⢳⠀⣠⠏⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠉⠉⣁⣠⣽⣧⣎⣀⠀⠙⢳⣄⡀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠤⠶⠚⠋ ⠈⠳⣄⠀⠀⠈⠳⣄⠀⠀⣘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠉⠀⠀⠀⠈⠉⠛⣆⢸⡏⠛⠛⠳⣤⠈⠙⣶⠶⠒⠒⠺⣟⠉⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢷⡄⠀⠀⠈⢧⡾⠉⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢧⠀⠀⠀⢸⡄⣇⠈⢷⡀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢈⣹⢀⡀⠀⠈⢷⡀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⣄⠘⠲⠤⠤⣬⠇⢸⡀⠈⢳⡄⠀⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢦⠙⢦⠀⠘⠿⣄⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⢀⣠⡴⠋⠀⠀⡀⠀⠀⢀⣀⣴⣾⣷⣀⠀⠀⠀⠀⠉⠉⠙⠒⠒⠀⠀⠀⠑⠢⠀⢳⡀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡹⡇⢿⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⢀⠀⢀⡤⠤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⡇⢁⢧⠸⡞⢇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⢀⣨⣶⠃⠀⠀⠀⣣⠀⢈⣹⣶⣄⠀⠀⠀⠷⡘⠎⠃⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠦⡀⠀⠀⠀⡴⠋⢽⡈⠢⠤⠤⠒⠁⠀⣎⣾⡿⡟⡷⣄⠀⢠⡚⠦⡀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠈⠓⢶⡟⠁⠀⣴⢇⠔⡪⢽⣢⡀⢀⡴⠃⠀⡟⡀⡞⢇⠀⠉⠳⢌⠉⠉⠉⠑⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⡶⢖⣫⣽⣇⠀⠀⡌⠀⠀⢰⡋⢸⠸⡸⠗⡳⠃⠉⠀⠀⠀⡇⠀⠃⠘⡇⠀⠀⠀⠉⣲⠒⠶⣴⠉⠓⢆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⢋⡏⢳⡉⠃⠀⠀⠀⠀⠀⢱⡈⠓⠄⠁⢠⠀⠀⠀⠀⠀⠇⠀⠀⠀⢹⡀⠀⠀⠀⢹⣧⠀⠈⢣⡀⠀⠑⢤⡀⠀⠀⠀ ⠀⠀⠀⢀⡴⠮⡑⡾⠀⠀⢷⡄⠀⠀⠀⠀⠀⠀⢣⠀⡀⠆⢸⠀⠀⠀⠀⠀⣠⣶⣷⠄⣸⠀⠀⠀⠀⠀⠙⣆⡀⠀⠙⢆⠀⠀⠑⢄⠀⠀ ⠀⠀⢠⡞⡷⡧⣰⣹⠀⣠⢞⡟⢦⡀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⢠⣶⣿⡿⠛⠉⠁⢠⠇⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠨⣧⡀⠀⠀⠳⣄ ⠀⠀⢸⡇⠣⡇⠀⠘⣦⠇⡜⠁⠀⠙⠦⣀⠀⠀⠈⠓⠒⢤⡀⠀⠈⠛⠉⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⢸⢱⠀⠀⠀⠈⠱⡄⠀⠀⠈ ⠀⠀⠀⣧⠀⠐⢄⠀⠀⢰⡇⠀⠀⠀⠀⠈⠑⠢⢄⣀⠀⣹⣁⣀⣀⣀⣀⣄⢒⠟⠳⣄⢀⡠⠔⠒⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀ ⢆⠀⠀⠘⢆⠀⠀⢃⢠⠎⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⢉⣡⡬⠿⢬⣀⠈⢻⣄⣀⡈⠲⢄⠀⠀⠀⠀⢀⣀⣀⡤⠤⠔⠒⠋ ⠀⠱⣄⠀⠈⠢⡀⣠⠽⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⠀⠀⠀⠈⢹⠀⡇⠉⠉⢲⢠⠹⣞⠉⠉⢫⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⢣⠀⠀⠘⣇⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⠀⠀⠀⠀⠀⠀⠘⡇⠱⣀⣀⢘⡎⡆⠘⣆⠀⠈⢧⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠻⡜⢦⡀⠸⢆⠀⠀⠙⢦⡀⠀⠀⠀⠀⣀⡤⠊⠀⠀⠀⠀⣀⣠⣾⣄⠀⠀⠀⠉⠓⠒⠤⠀⠀⠑⠄⠘⣆⠀⢸⡆⠀⠀⠀⠀⠀

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⣼⣿⣷⡋⠁⠠⠤⠔⠉⠉⠉⠉⠁⠀⣀⣠⠤⠴⠟⠂⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠙⠿⠧⠄⠀⠀⠖⠒⠐⠒⠋⠋⠉⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀ ⠈⠂⠀⠀⠀⠀⢀⣠⠤⠶⠛⠉⣼⣿⣿⣿⣿⣿⠿⠿⠿⠇⠀⠀⠀⠹⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀ ⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠁⡤⠚⠉⠙⢦⠀⠀⠀⠀⣀⠤⢤⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠒⠈⢫⠖⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠇⣼⡇⠀⠀⠀⠈⡧⠀⢠⡊⠀⠀⠀⠈⣦⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀ ⠠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠰⡟⠁⠀⠀⠀⣸⡅⢰⣿⡇⠀⠀⠀⠀⢸⡇⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⢣⣀⢀⣰⡾⠙⠀⢸⡏⠀⠀⠀⠀⢠⠏⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠶⣄⠀⠀⣰⠋⠀⠀⠀⠀⠀⠈⠉⣿⣿⣶⠀⠈⠳⣄⣀⣀⡴⠋⠀⠀⣾⣿⣿⡿⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⢤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡟⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡇⠀⠉⠁⠀ ⠀⠀⠀⢀⠀⠠⠚⠉⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀ ⢀⠤⠀⠀⠀⠀⠀⠀⠀⢽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣤⣴⣾⣿⣿⣿⣿⣛⣉⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠘⠉⠉⠉⠑⠒⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠚⣻⠁⠀⠀⣧⠟⢻⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⡟⢹⢿⠒⠒⠒⠛⠛⠛⠋⠉⢀⡼⠁⠀⠀⣰⠋⠀⡟⢹⣿⣀⡴⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⡴⠀⡜⢠⠇⢸⡀⠀⣀⣀⣀⣀⠤⠖⠉⠀⠀⣀⡔⠁⢀⡾⠁⡼⠀⠈⠉⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠀⠀⠀⢀⡽⠁⠀⡼⠁⢠⠃⡾⢠⠏⠓⠤⣀⣀⣀⣀⣀⣀⠤⠔⣻⠋⠀⣰⠟⢁⠞⠁⠀⠀⢀⡤⠒⠀⠉⠳⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⡸⠁⠀⢸⠀⣳⠏⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⣰⠁⣠⠞⢁⡴⠃⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡿⠀⠀⢠⠇⠀⠀⣸⠀⡟⠀⣠⠞⠁⠈⠺⣷⡀⠀⠀⢠⡧⠞⢁⡴⠋⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀ ⠀⠀⠀⠀⠀⣸⠁⠀⠀⡞⠀⠀⠀⠁⢷⢃⡞⠁⠀⠀⠀⠀⠘⠳⣄⠀⡎⣠⠔⠁⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀ ⠀⠀⠀⠀⢐⡏⠀⠀⢸⠃⠀⠀⠀⠀⡿⠉⠀⠀⠀⠀⠀⠰⣖⣋⣉⣹⠟⠁⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄ ⠀⠀⠀⠀⢸⠃⠀⠀⣾⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧

⠀⠉⠐⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔ ⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀ ⠀⠀⠀⠀⠀⢠⠚⠂⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⢰⡁⠀⠀ ⠀⠀⠀⠀⠀⠈⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀ ⢄⣀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀ ⠀⠀⠈⠉⠀⠀⠀⠀⢸⡀⠀⢀⠤⠤⡀⠀⠀⠀⠀⠀⠀⢀⠤⠠⡃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢣⡀⢠⡌⢢⠀⠀⠀⠀⢠⡆⣶⣤⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠈⠈⠉⠈⠀⠀⠀⠀⠀⠉⠉⢀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⢔⠶⢒⡠⠗⠂⠤⣀⠀⠀⣴⣾⣶⣦⣄⣤⣶⣶⡄⠘⣄⡀⠀⡀ ⠀⠀⠀⠀⡔⠁⠀⠀⠃⠠⠒⠉⠉⠉⠑⢦⠻⣿⣿⣿⣿⣿⣿⣿⠏⠉⠈⠑⠆⠀ ⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⡠⡖⠒⠒⢚⣀⠈⠙⠛⠿⠟⢉⡣⠤⢒⠖⢄⠀⠀ ⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⢇⠸⠆⠠⣧⣴⣤⣤⣦⣤⣶⣤⣼⠠⣎⠀⢸⠀⠀ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠓⠒⠈⠉⠉⠉⠛⠛⠻⣀⠀⠈⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⢄⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠤⣀⠔⠊⠁⠀⠀⡼⠢⠬⢑⣶⣒⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠓⢤⡀⠀⠈⢣⣀⡀⠴⠊⠀⠀⠀⠀⠀⠈⠳⡀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠥⣄⠀⠀⠹⡀⠀⠈⡇⠀⡤⠒⢒⢦⡀⠐⢄⠀⠀⠘⡄⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠰⠾⠃⠀⠀⡇⠀⠀⡇⠘⠀⠀⡋⢹⢧⠀⠠⠴⠖⠒⢚⡶⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⢀⡼⠀⠀⢰⠁⢰⠀⠀⠳⠊⡜⠀⠀⠀⠀⡠⠊⡇⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠒⠒⠉⠀⠀⣠⠃⠀⠀⠳⠤⡠⠔⠁⠀⠀⠠⠎⠀⠀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠤⣤⠚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢒⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡘⡄⠀⠀⠀⠀⠀⠈⢇⠀⢠⠆⠀⠈⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀⠈⠉⠁⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢢⠀⠀⣀⣀⡠⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⢀⣀⠀ ⠀⠀⠀⠀⣶⣶⣶⣾⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣠⣶⡶⣏⠀⠀⠘⠒⠲⣦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣋⡀⢀⣴⣿⣿⡿⠃ ⢠⣶⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⢰⠇⠘⢁⡙⣧⣀⠀⠀⠀⢈⣿⣦⠀⠀⠀⠀⠀⢰⣿⡿⠾⡯⢽⣿⣟⣿⠿⠛⠁⠀ ⠈⠻⢿⣿⣿⣿⣿⣿⡷⠚⢻⣧⡌⠳⣄⠀⢀⡿⠀⠀⣼⣵⣿⣿⣷⣦⣴⣿⣿⡎⢧⠀⠀⢀⣴⣿⣷⡶⠖⠒⠒⠛⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⢻⣶⣷⡨⠳⣼⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⢧⣴⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣶⣤⡛⢷⣴⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⠏⠸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣾⡏⠀⠀⠹⣿⣿⡿⡿⠛⢻⢿⡿⣶⢦⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⡟⠁⠀⡁⠀⠀⠇⡇⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢇⡠⠄⠓⠤⠞⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠀⠉⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣶⣿⣿⣿⣿⣿⣷⣦⡀⢀⣀⣠⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠐⠒ ⠀⠀⠀⠀⠀⣀⣴⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡼⠋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀ ⠀⠀⢀⡟⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀ ⠀⠀⢸⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠛⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⣰⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣇⡀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣆⠀ ⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣠⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⢿⣧⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡆ ⠘⣿⣿⣿⣿⣿⣿⠀⠀⠀⣾⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠀⠀⣿⢟⡻⣿⣿⣿⣿⡇ ⢀⣿⣿⣿⣿⡿⢿⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠄⠀⠀⠀⠀⣾⡏⠀⣽⣿⣿⡿⠀ ⢸⣿⣿⣿⡿⠤⣼⡄⠀⠀⠀⠀⠰⠟⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠀⠻⣇⣰⣿⣿⡿⠃⠀ ⠀⢿⣿⣿⣧⠀⢣⠇⠀⠀⠠⢤⡀⠀⠀⠀⠀⢀⣠⠴⠒⢒⣻⣷⠀⠀⡰⠋⠀⠀⠀⠀⠈⢻⣿⠟⠁⠀⠀ ⠀⠈⠻⢿⣿⣷⠏⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⡟⠀⣠⠞⠉⠀⡇⠀⢰⠁⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢳⠞⠁⠀⠀⡼⠁⠀⠘⡄⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠈⠳⣄⣠⠞⠁⠀⠀⠀⠘⠦⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⠤⠤⢤⣄⣀⡤⠤⠤⠴⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⣠⠔⠒⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠒⠢⢄⡇⢠ ⠀⡼⠇⠀⠀⠀⢀⠨⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠐⢧⣸ ⠰⣅⠀⠀⢀⡠⢧⡀⠀⠈⠂⠀⢀⣀⠠⠤⠤⠄⣀⡀⠀⠐⠋⠀⣸⣀⠀⢠⡟⠁ ⠀⠙⢷⣀⠡⠄⠀⠀⢀⠄⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⠀⠀⠤⠔⠋⠀⠀ ⠀⠀⠀⢣⡀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀ ⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀ ⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⢰⠖⠒⠒⠶⠒⠒⢒⡆⠀⠀⣶⠒⠒⠶⠒⠂⠠⡤⢸⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠁⠒⠀⠀⠀⠒⠁⠀⠀⠀⠀⠑⠂⠤⠤⠄⠊⠁⣸⠀⠀⠀ ⠀⠀⠀⠼⠓⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠙⣆⠀⠀ ⠀⠀⠀⠀⠤⠚⠢⡄⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣷⡄⠀⠀⢳⡀ ⠀⠀⠀⠀⠀⢀⡠⢄⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠉⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠒⢄⠀⠀⠀⠀⣠⠞⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣶⣶⣶⣶⣶⣶⣿⣿⣿⡇⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⣿⠿⠿⣿⣿⣿⡇⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠋⠁⠀⠀⠀⠀⠈⢉⡉⠁⠀⠀⠀⠀⠸

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⠟⠉⠙⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣔⣿⣿⡿⢿⠃⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⢛⣺⡀⠠⣴⡿⠿⣟⡛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣠⠞⠉⠀⠀⠀⠀⡿⠀⠀⢱⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⢠⠃⠀⠀⠀⢀⡠⠊⠀⣠⡴⠋⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣭⣭⣿⡿⠧⣄⣴⡟⠑⠒⠒⠊⠁⠀⠀⠀⠈⠙⠻⠭⠤⢶⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣧⠤⠒⠉⡞⠀⢀⠀⠀⠠⠤⠤⠤⠒⠉⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡼⠁⠉⠁⠀⠀⠀⠀⢀⣀⠤⠄⠒⠂⢄⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⣀⣤⡄⠀⡰⠊⠁⠀⠀⢀⠤⠒⢺⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⠉⠁⠒⠫⠿⠀⠱⣀⠀⠀⠰⡃⣀⡴⠃⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠁⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⢤⡤⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⡿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠈⠓⢦⣀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣿⡟⠁ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣩⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣤⣶⣿⡿⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣈⣻⣿⠃⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠳⡄⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⡇⠀⡰⠋⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣇⣼⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡰⠁⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣇⢠⠃⠀⣀⣤⣿⣷⣶⣦⣤⣤⣤⣴⠒⠊⠹⣇⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠊⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄

⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⠒⠒⠒⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⡀⠀⢀⣠⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣧⠀⠀⠀⠀⠀⠀⡏⠀⠀⠇⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣇⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⣄⠸⣆⣀⣀⡀⢸⠃⠀⢀⠁⠀⢀⣴⣿⣿⣿⣿⣿⠿⠛⠋⠉⠉⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀ ⠈⢿⣇⠀⠀⠈⢹⠀⠀⢸⠀⢠⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀ ⠀⠀⢹⣆⠀⠀⢸⠀⠀⡸⠀⢸⣿⣿⣿⡟⠁⣤⣤⣀⡀⠀⠀⣠⣤⣤⣶⣶⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠹⡆⠀⡄⠀⠀⡇⠀⠘⢿⣿⣿⠃⠈⠻⢿⣿⡿⠇⠀⠻⠿⠿⠛⠁⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⠀⠃⠀⠀⡇⠀⠀⠈⠻⢿⠀⣄⣀⣀⡢⣄⠀⠀⠀⣠⢖⣀⣤⡤⠤⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⡅⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠈⠛⢯⠟⠁⠸⠟⠋⠁⠀⠀⠀⢠⣿⣿⣿⠟⠛⢿⣿⣿⣏⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⡈⣷⠇⠀⢸⠃⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⢸⢰⢲⡆⠀⠀⠀⠀⠀⠀⠸⢿⡿⠁⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⡏⠉⠉⠉⠉⠻⡄⠀⢸⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠈⠓⠛⠁⢀⣠⣤⠄⠠⣄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠳⣄⠀⠀⠀⠀⣇⠀⢸⠀⠀⠀⣿⠀⠀⠀⢠⠄⢠⠄⠀⠀⢶⠊⠉⠀⢸⠀⠀⣸⠀⠀⠀⢀⣠⣾⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠈⠳⠄⠀⠀⣻⠀⠸⠀⠀⠀⠘⣆⠀⠀⠘⢦⡈⡇⠀⠀⠈⡄⠀⠀⢀⣦⠞⠁⠀⢀⣀⣾⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⠀⡄⠀⢀⣠⡤⠼⢶⣄⠀⠀⠉⠛⠒⠤⠤⠷⠒⠚⠉⠀⠀⠀⠀⠚⡏⠉⣽⢧⣀⠤⠤⠤⣤⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⠀⡇⢠⠏⢹⠀⠀⠀⠘⡏⢳⡶⢤⠤⠤⠤⠤⠤⠤⠔⠒⠁⠀⠀⢀⣇⣼⠃⡜⠀⠀⢀⡼⠁⠀⢳⡄⠀⠀ ⠀⠀⠀⠀⠀⢀⡏⠀⣇⡏⠀⢸⡀⠀⠀⠀⢱⠈⣧⡸⢦⣀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⡾⠃⡼⠁⠀⢀⡞⠀⠀⠀⠈⢳⠀⠀ ⠀⠀⠀⠀⢀⡾⠁⢀⡿⠀⠀⠈⡇⠀⠀⠀⠈⢇⢸⡇⠀⠈⠙⠒⠲⠤⠔⠒⠋⠁⠀⡟⢁⡜⠁⠀⠀⡞⠀⠀⠀⠀⠀⢸⡆⠀ ⠀⠀⢀⣤⢾⠁⠀⢸⡇⠀⠀⠀⢹⠀⠀⠀⠀⠈⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡧⠊⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠰⡇⠀ ⠟⠛⢻⡇⢸⠀⠀⢸⠇⠀⠀⠀⠀⡇⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠳⢦⣼⠁⡏⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⢧⠀ ⠀⠀⢸⡆⡇⠀⠀⣼⠀⠀⠀⠀⢀⠇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡄ ⠀⠀⢸⠀⠃⠀⢀⡏⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⣧ ⠀⠀⡠⠀⠀⠀⢸⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⢸

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⢸⣿⣯⣷⠏⠉⢉⣤⣤⡤⠏⠉⠉⠉⠉⠉⢀⣁⣀⠠⣀⣀⣰⣬⠷⠂⠒⠒⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣷⣶⣤⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⣿⣿⡅⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⡤⠤⠖⠚⠉⠉⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⡀⠀⠀ ⠀⠀⠈⠉⠉⠉⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⠋⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠠⠴⠒⠋⠉⠉⠀⠀⢰⣿⣿⣿⣿⣿⣿⠟⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡟⠀⣤⠞⠋⠉⠛⢦⡀⠀⠀⠀⠀⢀⣀⡤⣄⣀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⣠⡔⠻⡝⢤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡿⠀⣼⡅⠀⠀⠀⠀⠀⢷⡀⠀⠀⡴⠋⠁⠀⠀⠉⢣⡀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⠇⠀⠀⠀⠀⠀⡾⠃⡀⣼⣷⠀⠀⠀⠀⠀⠀⣯⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠵⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢿⠁⠀⠀⠀⠀⢀⣼⣗⠀⣧⣿⡟⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠐⠂⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠁⠀⠘⣆⠀⠀⢀⣶⣯⠑⠀⠀⣼⡉⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠳⢦⣄⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠈⠛⠛⢻⣿⣶⣤⡄⠀⠻⢷⡀⠀⠀⠀⢀⡰⠋⠀⠀⣰⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⠇⠀⠀⠀⠙⠒⠒⠒⠋⠀⠀⠀⠀⣿⣿⣿⣿⡟⠉⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠉⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⠴⠟⠋⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀ ⠩⠅⠀⡀⠴⠚⠉⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣧⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⡿⠧⠤⠤⠤⠤⠀⠀⠀⠒⠒⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠉⠉⠀⠀⠉⠉⠙⣲⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣀⣠⡶⠶⡾⠁⠀⠀⣸⣏⡛⢿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣿⣷⢦⣤⣤⣀⣀⣀⣠⣤⣔⣒⣿⠿⠟⠀⢀⡼⠃⠀⠀⠀⣁⡟⠁⢸⡟⣿⡿⠛⢋⣁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⠉⣴⠃⣼⠃⡇⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣠⠟⠀⢀⡾⠀⢸⠷⠦⣼⣋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣶⡞⠉⢠⡶⠀⢰⠃⢰⠃⢠⣇⠀⠀⣤⣀⣀⣀⣠⣤⠖⠋⠁⠀⠀⠀⣀⡼⠃⠀⢠⡾⠁⢠⡟⠀⠀⠈⠉⠛⠶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠀⠀⠀⠈⠀⠀⠒⠀⠀⣨⡿⠉⠀⢀⡟⠀⢀⡏⢠⡏⢀⡞⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠶⣻⠏⠀⢀⣴⡟⠁⣰⠟⠀⠀⠀⠀⠀⣠⠴⠂⠉⠛⢶⣤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⢀⡟⠀⠀⢸⠇⢸⢇⡿⠁⠀⠀⠈⠉⠛⠛⠚⠛⠛⠋⠉⠁⠀⣴⠃⠀⣠⡾⠋⢀⡾⠁⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠎⠻⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⣼⠁⠀⠀⢸⠀⠘⣼⠁⠀⠀⣠⡴⢟⡲⣄⠀⠀⠀⠀⠀⠀⣼⠃⣠⡾⠋⢀⡴⠋⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⣰⠇⠀⠀⠀⣼⡆⢸⡇⠀⣠⠞⠋⠀⠀⠙⢮⢳⡀⠀⠀⠀⢠⣷⠞⠁⣀⡴⠋⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⢀⡟⠀⠀⠀⠘⠁⣷⡾⢀⡼⠋⠀⠀⠀⠀⠀⠀⠳⢷⡄⠀⢀⡟⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀ ⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⣼⠃⠀⠀⠀⠈⠀⢸⡷⠞⠁⠀⠀⠀⠀⠀⠀⣀⣤⠤⠿⠶⢾⣥⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀ ⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠰⡿⠀⠘⠀⠀⠀⢀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠶⠤⠤⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄ ⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠠⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣄⣠⣴⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠴⠒⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣅⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡾⠁⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠏⠉⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀ ⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⣶⣦⡀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀ ⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣴⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠿⣿⣴⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠐⣿⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠁⠀⠀⣾⡿⢟⢿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⠀⠀⠀⠀⠀⠀⣸⣟⠋⠀⢻⣿⣿⣿⣿⠇⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⠟⠉⣿⠀⠀⠀⠀⠀⠀⠀⣰⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠇⠀⠀⠀⠀⠀⠀⣿⡽⠁⢀⣿⣿⣿⣿⡟⠀⠀⠀ ⠀⠸⣿⣿⣿⣿⣿⠘⢻⣿⡆⠀⠀⠀⠀⠀⠀⠙⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠁⠀⠊⠻⣦⣾⣿⣿⣿⠏⠀⠀⠀⠀ ⠀⠀⢻⣿⣿⣿⣿⠀⠈⣠⡇⠀⠄⠒⠲⢦⣀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠶⠛⠋⣉⣹⡇⠀⠀⠀⡼⠋⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⣿⣿⣿⣷⣴⠏⠀⠀⠀⠀⠀⠀⠉⢇⠀⠀⠀⠀⠀⣿⠁⠀⣀⡴⠟⠉⢠⡇⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠛⠻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⣿⢀⡴⠋⠀⠀⠀⣼⠃⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢹⡏⠀⠀⠐⠀⣰⠇⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠹⢦⣄⣤⡾⠃⠀⠀⠀⠀⠀⠘⠦⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠒⠦⠤⢤⣤⣤⣤⡤⠤⠴⠒⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⣿⣿⣿⡟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣷⣦⣼⣿⣦⣤⣽⣿⣿⣷⡀⠀⠀⠀⠀ ⠀⠀⡀⢸⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⡄⣼⣿⣿⣿⠿⠄⠾⠿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⡆⠑⣿⡟⠄⠒⠄⠀⡔⠀⠠⡀⠹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⡇⠀⠹⣿⠀⢰⣸⠀⡰⠆⠀⡇⢀⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀ ⠀⠀⠀⢸⠀⡇⠃⡠⠃⡂⣤⠿⠆⠑⢀⠪⡀⠸⠿⠋⠙⣿⣿⣿⠿⠁⠀⠀⠀ ⠀⠀⡇⢸⠀⣗⣴⠁⠈⠉⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣿⣿⠋⠀⠀⠀⠀⠀ ⠀⠀⡇⢸⠀⠉⢺⠀⠀⠀⢀⣠⡤⢀⠀⠀⠀⠀⠰⣴⣾⣿⡿⠉⠉⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠳⢄⠀⠈⠓⠒⠚⠁⠀⡀⠀⠀⣿⣿⢻⡇⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⢀⡠⡏⠐⠒⠒⠒⠀⠉⠀⢀⡔⢁⠜⢹⠣⠤⢿⣀⠀⠀⠀ ⠀⠀⠀⢸⢀⢴⠊⠁⠇⢧⢀⠓⠒⠒⠒⠂⠈⡙⡠⠊⡠⠃⠀⡠⠊⠀⠑⠄⠀ ⠀⠀⡄⡸⠃⢸⠀⠀⠘⢄⡏⠀⠀⠀⠀⠀⢠⠉⡠⠊⠀⠀⡰⠁⠀⠀⠀⠈⢆ ⠀⠀⡷⠁⠀⡆⠀⠀⠀⠀⡇⠀⠈⢢⠀⠀⡔⠉⠀⢀⢀⡀⡇⠀⠀⠀⠀⠀⠘ ⢠⠎⠀⠀⢰⠀⠀⠀⠀⠀⠁⠀⠀⠀⠓⠄⡇⢀⠔⢁⡀⠬⠣⣄⠠⠄⣀⡀⠀

⠀⢀⣀⣀⡀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡘⠀⡃⠀⠀⢠⣶⣿⣿⣿⣷⣶⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⢣⠀⠀⠀⡅⠀⠁⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀ ⢦⡇⠀⠤⡇⢠⠀⣠⣾⣿⡿⠛⠉⠉⠉⠉⠙⠻⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀ ⠀⢹⡄⠀⠀⢸⠀⣿⣿⡏⣤⣄⣀⢀⣤⣤⡦⠀⠘⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⢱⠰⠀⠘⠀⠙⢿⢀⣈⣉⡉⠀⢉⢍⣀⣀⠀⣸⣿⣿⣿⣿⡟⠀⠀⠀ ⠀⠀⠘⣼⠀⡄⠀⠀⡨⠀⠀⠉⣛⣁⠋⠁⠀⠀⢼⣿⠋⠙⣿⣿⠀⠀⠀⠀ ⡏⠉⠁⢣⠀⡇⠀⡜⠀⠀⠀⠀⠐⠛⣀⠤⠀⢤⠀⠁⠀⢠⣿⣿⠀⠀⠀⠀ ⠈⠢⠀⠸⠀⡇⠀⠱⡀⠀⢍⢋⠉⢹⠀⠀⣆⠜⠀⣀⣶⣿⠿⠃⠀⠀⠀⠀ ⠀⠀⠀⠈⠆⠀⡤⠖⠓⢤⢀⣉⠐⠒⠃⢉⣀⠀⠀⡁⡼⡂⠒⢒⠖⢄⠀⠀ ⠀⠀⠀⣸⢠⡜⠀⡄⠀⠘⡸⣼⠢⡀⠀⠀⠀⣀⢔⡿⡱⠁⢠⠃⠀⠘⡆⠀ ⠀⢀⣰⠁⢸⠁⠀⢁⠀⠀⠡⡇⠀⠀⠈⠉⠁⠀⢸⠔⠁⢀⠇⠀⠀⠀⢇⠀ ⣏⣹⢸⠀⢸⠀⠀⠈⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡆⠀⠀⠘⠀⠀⠀⠀⢸⠀ ⠀⢹⠘⠀⠈⠀⠀⢠⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠈⡀ ⠀⠘⠀⠀⠇⠀⠀⡸⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⡃

⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣠⣤⣤⣤⣤⣤⣀ ⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⠉⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠁⠀⠀⠀⠉⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣥⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣄⡤⠀⠀⣰⠏⣰⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⣴⠇⡸⠉⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠏⢰⣿⣷⡄⠀⠈⣳⣤⠴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡴⠛⠁⠀⠀⠸⣿⣿⠇⠀⡾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣾⣿⣿⣿⣿⣿⢿⣽⠏⠀⠀⠀⠀⠀⠀⠘⠯⣤⣼⢻⡗⣾⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢷⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠃⡿⠂⠀⠀⠀⠀⠀⠉⠛⠶⠶⠶⠶⠛⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠒⠒⠂⠒⢲⣶⣶⣶⣶⣤⣤⣤⠤⢠⠤⠤⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠻⠿⣿ ⣷⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠘ ⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠋⠉⠀⠬⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠤⠤⠤⠤⠤⠶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠙⢿⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣅⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣤⠤⣄⣀⣤⡴⠟⠁⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⠋⠉⠙⠻⢶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢾⠟⠋⣁⡴⠟⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⣶⣤⣤⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⣀⣤⣤⣴⠾⠟⠛⠉⠀⣾⠀⠀⡏⠀⢀⣠⠴⠖⠛⠛⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⡾⣛⣁⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⣀⣀⣈⢉⢙⡛⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⣀⣀⠀⠀⠀⣴⣿⡧⠤⠟⣻⠟⠁⢀⡀⠀⠀⠀⠀

⠾⣿⠁⠒⣊⡉⠉⠀⠤⠐⠒⠁⢀⣴⣾⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣀⠀⠀⠀⠀⠀ ⠠⠀⠀⠀⣀⠠⠔⣺⣿⣿⣿⠿⣿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀ ⠀⢠⠀⠀⠀⠀⠀⢿⣿⠏⡀⠄⡀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠫⠂⠀⠀⠀⠀⠈⡏⣾⠀⠀⢰⠀⡔⠁⠈⢢⠀⠈⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀ ⠉⢀⠀⠀⠀⠀⢀⠔⠃⢄⠀⣤⠛⢸⠃⠀⠀⡘⠀⣠⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀ ⠀⠀⠉⠒⢄⠰⠁⠀⠀⠀⠉⠿⠇⠈⠂⠤⠐⠁⢸⣿⡟⠋⠛⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣿⣿⣿⣿⠇⠐⠀ ⠀⠄⠂⠉⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣤⣾⣿⣿⣛⣁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠁⠈⠉⠂⠀⢀⡀⡄⠀⡿⢿⣿⣿⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠤⠘⢇⢲⠒⠒⠒⠛⢁⠔⠁⢀⠏⡸⠹⢭⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠞⢁⠊⡘⡌⡜⢄⣐⣒⣈⣁⠠⡔⢁⡔⡡⠃⠀⢀⠝⠲⢄⠀⠀⠀ ⠀⠀⠀⢀⠎⠀⠆⠀⡇⡟⢀⠤⢆⡄⠀⠀⣜⠴⡫⠞⠀⠀⡔⠁⠀⠀⠀⠑⡄⠀ ⠀⠀⠀⡞⠀⡸⠀⠀⢡⡡⠃⠀⠀⠙⣆⣰⡡⠊⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⡀ ⠀⠀⢠⠁⢀⡇⠀⠀⢸⠀⠀⠀⠀⠁⠒⠊⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢣

⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡟⣻⣏⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠀⠁⢠⡤⠎⠀⢈⠄⡁⣦⡀⠀⠣⡋⠊⠈⢌⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠁⠠⡴⠋⢸⡠⡐⢄⠀⠘⠩⡏⢣⠘⠫⡂⠐⠂⠑⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⡺⣿⠇⠠⠁⠀⢇⠈⡜⠘⠈⠀⠀⠃⠀⢇⠀⠈⢱⠒⠎⠑⠄⠀⠀⠀ ⠀⠀⡠⢾⢞⠀⢣⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⣴⡦⡸⠀⠀⠈⢣⡀⠑⡄⠙⢦⠀ ⠀⢸⠹⡁⠙⡔⡝⠁⠠⡀⠀⠂⠤⡀⠘⠛⠋⠀⡠⠃⠀⠀⠀⢨⠆⠀⠘⢄⠀⠑ ⡀⠈⠆⠐⠄⠰⠇⠀⠀⠈⠐⠠⠨⠥⠤⠤⢴⣘⠳⢤⠒⠈⡉⠉⠉⠉⠉⢀⡀⠀ ⠀⢄⠀⢠⡠⢇⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠀⠀⠉⠸⠉⠑⡜⢖⠀⢫⠁⠀⠀⠀ ⠀⠈⢇⡀⠡⡀⠑⢄⠀⠀⠀⣀⠔⠁⠀⢀⣤⠀⠀⠂⠡⠄⠃⠄⢣⠀⣇⠀⠀⠀

⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤ ⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠐⢲⣿⣿⣿⣿⡿⠟⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⡿⠟⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢋⠀⠀⠀⠀⠠⣾⣦⣀⡀⠀⠀⢻⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢠⢳⡑⠄⡀⡀⠀⠀⠈⠛⠛⠃⠀⠀⠈⣿⣿⣿⣿ ⣠⣤⣤⣤⣤⣤⣤⣤⣤⡤⠊⠁⠸⡇⣴⣁⠀⠠⡀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿ ⠛⠛⠛⠛⠛⠛⠛⢛⡟⠀⠀⠀⠀⠀⠉⠊⠀⠀⠈⠑⠒⠀⠀⠀⣰⣿⣿⣿⣿⣿ ⣤⣤⣿⣷⣶⣤⣔⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠛⠉⠉⠙ ⠀⠀⠀⠀⣀⣀⣀⣸⡀⠀⠀⠀⠐⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⡠⠤⠊⠉ ⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⠉⠓⠒⠢⠤⠤⠤⠤⠖⠒⠋⢁⣇⠨⡤⠒⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠹⣿⣿⣿⠀⠀⠀⢿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣦⣤⣿⣿⣿⣶⣦⣤⣘⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠄⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣯⠉⣩⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠄⠀⡇⣾⣿⣿⣿⠿⠿⠛⠉⠉⠀⠈⠉⠉⠉⠉⠁⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠘⣿⣿⣿⢃⡴⠒⠒⢄⠀⠀⢠⠚⠉⠈⠱⡄⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⢹⣿⣿⡞⠀⠀⠀⠈⡆⠀⡏⢀⣀⠀⠀⢸⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠛⡇⡇⠀⠀⢿⣆⡿⠀⢇⠸⠿⠀⠀⣸⠃⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠇⠀⣀⡇⠘⣄⣀⣀⣿⣷⡀⠘⠢⢄⣀⠴⠃⠀⢸⣿⣿⡿⠛⠻⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡄⠀⢸⠀⠀⡇⠀⠀⣰⠋⠀⡴⣢⢮⠅⠉⠉⠁⠀⠀⠠⠂⢼⠟⠁⠀⠙⠋⠀⠀⠀⠘⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⢸⠀⠀⡟⢢⣰⠃⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⢸⠀⠀⢷⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⣿⠆⠒⠒⠒⠒⠂⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⢀⣤⡶⡶⠤⣄⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠻⠿⠴⠶⠶⠾⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣾⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠀⠀⠀⠀⣿⠛⠛⣧⣸⣿⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡴⡏⠉⠉⢻⠒⠒⠚⠋⠉⠉⠀⠀⠀⠀⢀⡼⠁⠀⡴⠃⢹⡿⠤⠤⢀⣿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣠⠴⠚⣿⠀⣇⠀⠀⣼⣀⠀⠀⣀⣀⣀⣀⡠⠤⠒⡟⠀⣠⠞⠁⢀⡞⠀⠀⠀⠀⣡⠟⠙⢦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⣠⠞⡏⠀⠀⠀⢹⠀⢻⡄⣸⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⢰⢁⠴⠉⠀⣰⠋⠀⠀⠀⣰⠋⠀⠀⠀⠀⠙⢇⠀⠀ ⠀⠀⠀⡀⠀⢸⡴⠃⠀⣥⠀⠀⠀⠈⢧⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⠀⣠⠞⠁⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠈⢧⠀ ⠀⠀⠀⡇⢠⡟⠁⠀⢠⠏⠀⠀⠀⠀⠀⠳⣼⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⡜⢀⡴⠊⠁⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇ ⠀⠀⠀⣿⠏⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠙⣆⠀⠀⠀⢠⠏⠁⠀⠀⠀⢀⣀⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⢀⡴⠃⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠈⢷⡀⠀⢸⠀⠀⠀⢀⡖⠋⠀⠉⠳⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⠟⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠙⠂⣼⠀⢀⡴⠋⠀⣠⡤⠔⠒⠊⠑⣾⡉⠙⠒⠦⢤⣀⣀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⢴⣶⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣤⡀⠀⠀⠁ ⠀⠀⢠⠎⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀ ⠀⠀⣧⣾⣿⣿⣿⣿⡿⠿⠿⠛⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⡆⠀ ⢀⣾⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡀⠀ ⢸⣿⣿⣿⣿⠁⠀⢀⣀⠀⠀⠀⠀⠀⢠⣦⣤⡀⠀⣿⣿⣿⣿⡄ ⠈⢿⣿⣿⣿⠀⢠⠟⠛⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⢼⡿⣿⣿⡇ ⠀⣿⣿⡟⣹⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠙⠁⢀⠀⠿⣀⣿⡿⠁ ⠀⠹⣿⣇⡹⠀⠀⠂⠀⠀⠀⠔⢂⠭⢻⠀⡔⠀⠀⠀⠘⡟⠁⠀ ⠀⠀⠈⠉⡁⠀⠀⠀⢰⠀⠀⡖⠁⢀⠆⠀⢇⠀⠀⠀⢀⠃⠀⠀ ⠀⠀⠀⠀⠱⡀⠀⠄⠁⠀⠀⠈⠒⠁⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠐⠤⢀⣀⠀⠀⠀⠀⣀⡀⠤⠐⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡀⢀⣀⣀⣀⣀⣀⣄⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣶⣦⣀⣀⣴⣶⣾⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣧⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⣧⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⡇⠀⠀⠀⠀⠀⢈⡇⠀⠀⢀⡇⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣀⢿⡤⢤⣀⣀⣀⢸⡇⠀⠀⢰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡿⠟⠉⠉⠀⠀⠀⠀⠀⠈⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⣿⡆⠀⠀⠀⠈⢻⡇⠀⠀⣼⠀⠀⣸⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀ ⠐⠀⠘⣿⡄⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⣄⡀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣿⡄⠀⠀⣼⠀⠀⠀⡏⠀⠀⣿⣿⣿⣿⣿⠃⠀⣿⣿⣷⣶⣦⣤⠀⢠⣾⣿⣿⣿⣿⡿⠃⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⠀⠀⡗⠀⠀⠀⡇⠀⠀⠘⢿⣿⣿⡟⠀⠀⠙⠻⠿⠿⠿⠋⠀⠈⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀ ⠠⡀⠀⠀⠀⢹⡇⠀⡇⠀⠀⢠⠃⠀⠀⠀⠈⠻⢿⡇⠀⣄⣀⣀⡰⢦⡀⠀⠀⠀⠀⢀⡴⠛⣀⣀⣀⣀⣀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀ ⡆⠀⠀⠀⠀⠈⣧⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠉⠙⢻⠷⣝⣷⠶⠀⠀⣿⠶⠟⠋⠁⠀⠀⠀⠀⣰⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠂⠀⣿⣀⡇⠀⠀⢸⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⢸⡏⢀⣤⠀⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠟⠁⠀⠀⠙⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⣥⣤⣤⣤⣤⣤⣸⣿⠁⠀⠀⢸⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⢸⡟⣇⢹⡳⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠋⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⡏⠁⠀⠈⠉⠉⠉⢻⠀⠀⠀⣼⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠘⠛⠁⠀⢀⣠⣤⠶⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⢷⣄⠀⠀⠀⠀⠀⠘⡇⠀⠀⡏⠀⠀⠀⢸⡷⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣠⡤⠴⠚⠉⠀⢻⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢧⡀⠀⠀⠀⢀⣷⠀⠀⡇⠀⠀⠀⠈⣷⠀⠀⠀⠀⢿⡄⠀⢸⠀⠀⠀⠀⢹⠀⠀⠀⠀⠘⡇⠀⣰⠟⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠂⠀⠀⠈⣼⠀⢰⡇⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠙⢤⣘⡆⠀⠀⠀⠘⣆⠀⠀⠀⣀⡷⠞⠁⠀⠀⠀⣠⣴⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⢸⡇⠀⠀⣀⣤⠤⠬⣿⣦⡀⠀⠀⠀⠉⠙⠒⠶⠶⠶⠿⠒⠛⠉⠁⠀⠀⠀⠀⠀⠐⠛⡇⠀⣸⡿⣄⣠⣤⠤⠤⠶⣤⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣻⠁⢸⠀⢀⡾⠋⡇⠀⠀⠀⠀⢹⡟⢶⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠤⠶⠀⠀⠀⠀⢠⠇⣰⡟⢁⡟⠀⠀⠀⠀⡴⠋⠀⠙⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⣸⢀⡿⠀⠀⡇⠀⠀⠀⠀⠈⣧⠈⣿⠀⣿⡍⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣼⡿⠀⡼⠁⠀⠀⢀⡾⠁⠀⠀⠀⢻⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⡿⣼⠁⠀⠀⣻⠀⠀⠀⠀⠀⢹⡄⢻⡇⡟⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠞⢩⣿⠟⠀⡼⠁⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⣷⡏⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⢧⠀⢿⠃⠀⠀⠈⠉⠓⠒⠒⠒⠒⠒⠋⠉⠀⠀⣸⠃⢀⡾⠁⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀ ⠀⠀⠀⠀⢀⣴⡏⠀⠀⠀⣿⠁⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠈⣦⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣠⠏⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠠⣇⠀⠀ ⣤⣤⣶⢾⡏⠀⡇⠀⠀⢠⡟⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀ ⣇⠀⠆⣿⡇⢠⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠛⠳⣶⣿⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄⠀⠀⠀⠀⠀⢼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀ ⠀⠀⠀⢹⡆⣸⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀ ⠀⠀⠀⢸⠉⡿⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀ ⠀⠀⠀⣸⠀⡇⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧ ⠀⠀⠀⡿⠀⠇⠀⠀⣸⠃⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣟⣋⡉⠀⠀⢀⣤⣀⣉⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⠀⠀⠸⢿⣿⣿⣿⣿⠏⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠿⠛⠉⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⠤⠒⠺⠿⣷⡀⠀⣏⠀⠀⠀⠻⠿⠿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣇⠀⠀⢀⠞⠋⠀⠀⠙⣄⠀⠀⠀⢀⠜⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠒⠒⢺⣰⠘⡆⠀⠀⠀⠉⠉⠉⠁⠀⢸⣿⣿⣿⠟⠉⠀⠈⠙⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠘⠿⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠚⠉⠉⠉⢲⣄⠀⠀⠀⠀⠀⠈⠲⣤⣴⣾⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⣖⠿⣅⣠⡤⠤⠒⠂⠉⢁⣨⠇⠀⠀⠀⠀⠀⠀⡟⠛⢿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠈⠓⠒⠛⠒⠊⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠘⡆⠀⢹⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢴⠇⠀⢈⡇⠹⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡶⠦⠤⣤⠤⠤⠤⠒⠀⠀⠀⠀⠀⠀⣠⣴⡏⠀⠀⠀⠀⠀⠘⠁⠀⡿⣆⠀⠐⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠒⠒⣲⣾⠁⢠⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢁⡞⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢹⠉⠓⢦⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⡆⠀⣹⠀⢸⣀⣀⠀⠀⠀⣀⣀⣤⡟⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠹⡄⠀ ⠀⠀⠀⠀⠠⣄⠀⠀⢀⡼⠁⠀⠀⠀⡇⠀⢿⠀⡏⠀⠀⠉⠉⠉⠀⢀⡞⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢷⠀⠀⠀⠀⢹⠀ ⠦⠀⠀⠀⠀⠨⠷⠤⣼⠑⠀⠀⡆⠀⢇⠀⠘⣼⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⣇⢀⡠⠴⠒⠒⠒⠒⠒⠢⢤⡀⣸⠂⠀⠀⠀⠘⡇ ⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⣼⠁⠀⠸⡄⢀⠇⠀⠀⠀⠀⠀⠀⢰⡇⢀⡴⠊⣸⠁⠀⠀⠀⠀⠀⠀⢀⣀⡀⡈⢣⣄⡀⠀⠀⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠔⠒⠒⠒⠚⠒⠢⠤⠤⣀⡀⠀⢀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⢧⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠳⢄⡀⠀⠀⠘⢦⡀⠀⠀⠙⢄⠀⠀⠀⠠⢄⠀⠀⠀⠸⡄⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠉⠉⢰⡖⠒⠛⠓⠒⠤⠤⠿⠦⠤⣤⠤⠽⢶⡤⣀⠇⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⢀⡴⠋⠀⠀⠘⡇⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⠞⠁⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⣀⡀⠀⠀⠒⠒⠀⠀⣀⣀⡴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀ ⣤⣤⣴⣷⣶⣶⣶⣶⣶⣶⠃⠀⠀⠀⠀⢀⡀⠤⠤⢀⡀⠀⠀⠉⠉⢹⠀⠀⡾⠉⠉⠀⠀⢀⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠸⣶⣤⣤⣤ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠙⢦⣀⣀⣀⠼⠀⠀⠧⣀⣀⣠⠖⠁⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⢠⣾⣿⣏⣀⣀⣀⣀⣀⣀⣿⣿⣧⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣠⣾⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢣⠀⠀⠀⠀⠀⠀⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡆⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠻⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠈⠳⢤⣀⣀⣀⣸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⣀⣄⠴⠃⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⣠⣶⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠿⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡾⠇⠀⠺⠿⠿⠿⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣋⠡⢤⣄⠀⡖⠂⠰⡶⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠣⣀⡐⣁⠀⠑⠤⠠⠔⢡⣾⣿⠿⠿⢿⣿⣿⣿⡋⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠊⠀⠀⠸⠟⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠈⣿⣿⣿⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⡄⠀⠀⢀⡠⠔⢊⣁⠨⠶⡀⠀⠀⠈⣶⣾⣿⣿⣿⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠐⢄⠀⠈⠚⠛⠒⠀⠀⠉⠀⠀⠀⠀⡇⠈⠉⢹⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠑⠢⡤⢀⡀⠀⠠⠀⠀⠀⢀⣴⠁⠘⠀⠰⠀⣦⠀⠄⠀⠀ ⠀⠀⠀⠉⠉⠉⢉⡩⢻⠀⠀⡇⠀⠀⠀⠀⡠⢣⠃⠀⠀⠀⠀⠐⢀⠉⠐⢄⠀ ⠀⠀⠀⢄⠀⣰⠁⠀⠀⠘⢠⠉⠁⠀⠈⠩⠁⠂⠀⠀⠀⠀⠀⠀⠘⡀⠀⠈⡄ ⠉⠀⠈⠉⢩⠋⢀⠇⠘⡀⡌⠀⠀⠀⢀⠇⡡⢲⠂⠉⠀⠀⠈⡁⠲⣁⠀⠀⡇

⠀⠈⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠ ⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⡴⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠈⠉⠙⠲⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠃⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⢿⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠙⠒⠒⠲⠄⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡀⠀⠀⡴⠚⠛⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠉⢳⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⢸⡁⠀⠀⠀⣀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⣴⡀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠑⢤⣀⢸⣿⣧⠀⣷⠀⠀⠀⠀⠀⠀⠀⠘⢧⣸⣿⡿⠏⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢇⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣤⡤⠤⠒⣲⣿⣤⣀⣀⡀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣤⣄⡀⠀⢀⣠⣤⣶⣤⡀⠀⠘⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠡⠞⠁⢀⡴⠋⠁⠀⢀⣀⣈⣉⣳⣄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣠⠼⣶⣒⠀⠀⠘⠀ ⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠋⠀⠀⡤⠚⠁⠀⠀⠀⠈⠉⠑⢦⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠈⠓⠦⠀⠀ ⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡽⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⠿⢻⡇⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣯⠀⠀⠀⠉⠉⣠⡤⠤⠤⠤⠤⠭⠟⠛⠯⠤⠤⣀⡓⠒⠋⠁⡞⠉⢧⡀⠀⠀⠀ ⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠈⢧⣀⣀⣄⣾⣀⣰⣄⣀⣀⣰⣄⣀⢀⣠⣄⠀⠀⣹⠀⢀⡼⠁⠀⠀⢷⠀⠀⠀ ⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠚⠉⠁⠀⢘⣏⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠣⠤⢄⣤⠿⠀⠀⠀ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠙⠒⠲⠶⠶⠶⠶⠶⠒⠚⠛⠛⠉⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠴⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢳⡀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⡿⠗⠀⠠⠄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠈⠑⢶⣶⡄ ⢀⣶⣦⣸⠀⢼⣟⡇⠀⠀⢀⣀⠀⠘⡿⠃ ⠀⢿⣿⣿⣄⠒⠀⠠⢶⡂⢫⣿⢇⢀⠃⠀ ⠀⠈⠻⣿⣿⣿⣶⣤⣀⣀⣀⣂⡠⠊⠀⠀ ⠀⠀⠀⠃⠀⠀⠉⠙⠛⠿⣿⣿⣧⠀⠀⠀ ⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀ ⠀⠀⠀⣷⣄⡀⠀⠀⠀⢀⣴⡟⠿⠃⠀⠀ ⠀⠀⠀⢻⣿⣿⠉⠉⢹⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀

⣿⣿⣿⢿⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⡿⣽⣻⡽⢯⡿⣽⣫⡟⣽⣫⢟⣽⢫⡟⣽⢫⡟⣭⡻⣭⢻⡭⢯⡽⣭⢯⡽⣭⠻⣜⡣⢟⣜⡣⢟⡜⣣⢛⡜⣣⢛⡜⣣⢏⡼⣡⢏⡼⣡⢏⡼⣡⢏⡼⡱ ⣿⣷⣻⣟⣾⣳⢿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⡷⣯⣟⡷⣯⡽⣯⢷⣏⡷⣽⣣⢯⣟⢮⣯⢽⣚⡷⣹⢧⣻⡜⣧⣛⢧⡻⣜⢮⡳⣭⢻⡔⣏⡳⢎⡝⢮⠼⣱⢫⠼⣱⢫⡜⡱⢎⠶⡱⢎⠶⡱⢎⠶⡱⢎⠶⣙ ⣿⢿⣽⡾⣷⣟⣯⢿⡾⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻⣞⣯⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣽⣻⢾⣽⣻⢾⣽⢾⣯⢷⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⢯⣟⡷⢯⣟⡷⣻⣵⡻⣾⣱⢷⣫⠷⣞⢯⡞⣧⢟⡼⣏⢷⣣⢟⡵⣫⢞⡽⣎⢷⡹⣞⢣⡞⣱⢭⡛⡼⣙⡞⣥⣋⢗⣣⠳⣜⡹⢎⡳⣙⢎⡳⣙⢎⡳⣙⢮⡹⣒ ⣿⣯⣷⢿⣳⣯⣟⣯⡿⣽⢯⣿⢾⣽⣻⢾⣽⣻⣞⡷⣯⢷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢯⣷⣟⡿⣞⡿⣞⣯⡿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣾⣽⣿⣾⣿⣿⣾⣿⣷⣿⣷⣯⣟⣾⣭⢿⡹⣾⣹⢮⣏⢷⣫⢞⡵⣫⢷⡹⣎⢷⡹⣎⠷⡭⢮⡕⣏⠶⣹⢱⢣⠞⡴⣩⠞⡴⣋⠶⣙⢮⡱⣍⢮⡱⣍⢮⡱⡍⢶⣑⢣ ⣿⡾⣽⡿⣽⡾⣽⣳⡿⣯⣟⣾⣻⢾⣽⣻⣞⡷⣯⢿⡽⣯⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣟⣾⣽⣻⡽⣟⣯⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣛⡾⣼⢣⡟⣮⢳⡝⣮⢳⡝⣮⠳⣭⢛⡼⢣⢞⡬⡳⣍⢎⢧⡛⡴⢣⡛⡴⣍⢞⡱⢎⡵⣊⠶⡱⢎⡖⣱⡙⢦⡍⡖ ⣿⣻⣽⣟⡷⣟⣯⡷⣟⡷⣯⢷⣻⣟⣾⣳⢯⡿⣽⢯⣟⡷⣯⢷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⣟⣯⡷⣯⣷⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣵⣫⢞⡵⣏⢾⡱⢯⡞⡵⣛⢦⣛⡼⣍⠾⣰⠳⡜⣎⠶⡹⣜⢣⡝⡲⣍⢮⡱⢫⠴⣩⠞⣡⠳⡜⡥⣚⢥⡚⡜ ⣿⣽⣳⣯⣟⣯⡷⣟⣯⢿⡽⣯⢷⣻⢾⡽⣯⢿⣽⣻⢾⣽⣻⢯⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⢿⡽⣞⣯⢿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡽⢮⡝⣧⡛⣵⡩⢖⣣⠞⣬⠳⣥⢛⡼⣌⢳⡱⢎⢧⡚⡵⣊⠶⣉⢧⢛⡤⣛⠴⣋⠼⡱⡜⣆⢧⡙ ⣿⢾⣽⡾⣽⣳⣟⣯⣟⣯⢿⡽⣯⣟⣯⢿⣽⣻⢾⣽⣻⢾⣽⣻⡞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⢿⡽⣯⣟⣯⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⢟⠶⣙⢦⡛⡵⢪⡝⢦⡛⡴⣋⠶⣩⢖⡹⢎⠶⡹⠴⣩⠞⡱⢎⡣⠞⡴⢋⡼⣡⠣⡵⣈⠦⣙ ⣿⢯⣷⣟⣯⡷⣯⣷⣻⣞⣯⣟⣷⣻⣞⡿⣾⣽⣻⢾⡽⣻⡞⣷⡻⢷⣛⣾⣳⣟⣾⣳⣯⡿⣽⢯⡿⣽⣳⣟⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣟⣿⢻⡽⢺⡝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢯⡹⣆⠻⣜⢣⠞⣥⢛⡴⣩⢞⡱⢎⡵⢋⡞⣱⢋⠶⣉⠷⡩⢞⡱⣘⠣⢖⡡⢓⡴⣉⠖⣡ ⣿⣻⢷⣻⡾⣽⢷⣯⢷⣻⢾⡽⣞⡷⣯⣟⣷⣳⢯⣟⢾⣳⢟⣳⣟⣯⣟⣾⣳⡽⣞⡷⣯⢿⡽⣯⣟⣷⣻⣞⣿⣿⣿⡟⢥⠲⡝⣾⣟⣿⣿⣻⣿⣟⣿⣯⢿⣞⣷⣻⣽⣚⠷⣘⢧⡚⡕⢦⢫⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⢣⡭⢳⢬⢣⡛⡴⣋⠶⡱⢎⡵⢋⡜⣣⠞⡥⢫⡜⡱⢎⡱⢎⠴⢣⡙⢦⡙⢦⠱⣌⠚⡤ ⣿⣽⣻⢷⣻⢯⣟⡾⣯⣟⣯⢿⣽⣻⢷⣻⢮⣽⣳⢯⣻⣭⡟⣷⣞⣳⣞⡷⣯⢿⡽⣽⣏⣯⣟⣷⣻⣞⣷⣻⣿⣿⠫⠄⣉⣳⣽⣼⣿⣿⣿⢿⣟⣿⢯⣟⡿⣞⣷⡳⢞⡜⢢⠏⡖⡩⢞⡥⣛⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢣⢞⡱⢎⢧⡙⢶⡩⢞⡱⣋⠶⣩⠞⣡⠞⣱⠣⡜⡱⢊⠖⡩⢎⡱⡘⠦⡑⢎⡱⢌⡓⡔ ⣿⢾⣽⣻⣯⢿⣽⣻⢷⣻⣞⣯⢷⡯⣟⣞⡿⣼⢏⣯⢷⣳⣻⣳⣞⢷⣫⣟⡷⣯⣟⢷⣻⢮⡽⣞⣷⡻⣞⣿⣿⠁⠳⢾⣧⣽⣞⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⣿⡝⣮⢞⡳⣎⠳⡵⢊⡴⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢮⠳⣍⠶⣙⢦⡙⣎⠵⣊⠗⡱⢎⡱⣊⠥⡓⣬⢱⡉⢎⡱⢊⠴⣡⠣⣙⠢⡑⠦⡱⢌ ⣿⢯⣟⡷⣯⣟⣾⡽⣯⢷⣻⣞⣯⣽⣻⣼⣛⣾⣛⡾⣏⡷⣏⡷⣞⣯⢷⢯⡽⣶⢯⣛⣧⢿⡽⣳⢾⣽⣻⣿⠃⢉⡷⣿⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⡿⣯⢟⡞⣞⡳⣜⣫⡑⠳⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢌⡳⢬⢳⡩⢖⡹⡸⡜⡡⢏⡕⢎⡱⣉⠖⡱⢢⠱⡘⠦⡑⣍⠲⢄⠳⣄⢣⡙⢆⡱⢊ ⣿⣯⢿⡽⣷⣻⣞⡿⣽⢯⣷⣻⢮⢷⣳⣳⠿⣜⣯⢷⣏⡿⣽⣹⢯⣞⣯⢯⣟⡾⣽⣛⣾⣫⡽⢯⣷⣫⣿⡟⢠⣯⣄⢿⣿⣿⣿⡧⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡱⢦⡝⢳⡒⠦⡄⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⡱⣋⠶⣙⢎⡵⢱⠱⣙⠲⡘⢎⡱⢌⢎⡑⢣⠱⣡⢣⡑⠦⡙⣌⢃⢆⠣⡜⠢⣅⠣ ⣿⣞⣿⡽⣷⢯⡿⣽⣻⣟⡶⣯⢟⣯⣗⡯⣿⠽⣞⣯⢾⣝⡧⣟⡧⢿⣜⡯⢾⡽⣞⡽⣶⢏⣿⣛⡶⣯⣿⠇⠿⢱⣿⢸⣿⣿⣡⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣎⠧⡝⢲⠱⣌⡠⢘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠳⣍⢞⡱⢎⠴⣋⢜⣢⡙⡱⢣⠜⡌⠦⣙⢂⠳⡐⠦⣑⢣⠱⡌⠎⡜⢢⡑⢣⠆⢣ ⣿⡾⣽⣻⡽⣯⣟⣷⣻⠾⣝⣳⣟⣞⡾⣽⢞⡿⣽⣺⣝⣮⡽⣞⡽⣏⡾⣝⣯⠾⣽⣹⢞⣟⣮⢿⣱⢯⣿⠀⣐⡊⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣜⢣⠷⢤⡡⠉⠆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⡵⣊⢮⡱⢍⡲⢩⡒⢤⢣⡑⢣⠚⢬⡑⢢⢍⠲⣉⠖⡡⢎⠱⡘⡜⣠⠣⣘⢂⢎⡡ ⣿⡽⣷⢯⣟⣷⣻⢾⣽⣻⡽⣳⢾⣝⡾⣭⢿⣹⢧⢷⢾⣱⡟⡾⣵⢏⣷⢻⡼⣻⡵⢯⣾⣹⢮⣯⣻⣿⣧⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣶⣭⡞⢣⢏⣬⡱⡌⢒⡠⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⢲⠍⣦⠱⡎⡜⣡⠚⡔⢢⡙⢢⡙⢦⡘⢥⢊⠵⡨⠜⡐⢎⠱⡐⢆⡡⢒⡡⢊⠴⡐ ⣿⣳⣟⡾⣽⢯⣟⡾⣽⣫⢷⣻⣞⣽⣳⣛⣞⢯⣞⠾⣼⢏⣷⡳⡽⣞⡽⣞⢧⡿⣱⠾⣭⡟⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠾⢞⡩⣇⠣⠌⡑⢺⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⡑⢎⡴⢩⡒⢥⠣⣍⠲⣑⠪⡑⢎⡱⢨⠱⡌⢚⠤⢃⠲⡑⡌⢆⠓⡌⢃⠎⡱⠘⡄⢣ ⣿⡽⣞⡿⣽⣻⢾⣽⣳⢯⣟⡵⣞⣧⢷⡻⣼⢏⣾⢻⡽⣺⢧⢿⣹⢾⣹⡞⣯⠾⣝⡯⣗⢿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣖⣿⢯⢀⢒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡶⡷⣎⠷⣤⢓⡒⣩⢒⣿⣿⣿⣿⡟⡹⠋⢴⣆⡘⣿⣷⣏⢲⡘⢥⡙⢆⠳⣨⠱⠌⡥⣙⠢⣅⠣⢃⠍⡆⠣⠍⠦⡑⠌⡌⠱⡈⠆⡜⢠⠃⡜⢠ ⣿⡽⣯⣟⡷⣯⣟⡾⣵⣻⠾⣽⣻⡼⣳⢏⣷⢻⢮⣏⡷⣏⢿⡺⣽⣚⣧⢟⣧⢿⣹⢾⣹⢾⣹⢟⡿⢥⣼⣿⣿⣿⣿⣿⣿⣿⣿⢳⠚⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣭⡛⠿⡵⣉⠞⣩⠳⢦⡀⢎⣽⣿⣿⣿⣇⢠⣅⠮⠿⢿⠿⣿⣗⠦⣙⢢⡙⣌⠳⣄⠫⡜⡰⢡⠣⡔⢩⢊⠜⡰⢩⠘⡰⢁⠞⡄⢣⠑⡌⠔⡡⢊⠔⡡ ⣿⣽⣳⣯⣟⡷⣯⣟⣳⣽⢻⣳⣭⠷⣏⣟⡮⣟⡽⢮⣗⢯⡯⢷⡳⣏⣾⢫⣞⣳⢯⢾⣹⡞⣽⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭⣇⡋⡔⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢮⡓⢦⡙⣷⡳⣬⣦⢥⡛⣤⡙⣦⣿⣿⣿⣿⣏⣿⢸⣿⣿⣿⣿⣾⣿⡜⣌⠣⣜⠰⢣⢌⡱⢢⢙⣂⠳⢌⡡⠎⢆⡑⢢⠡⡑⢊⠴⡈⢆⠱⣈⠒⡡⠎⡰⢁ ⣿⣞⣷⣻⢾⣽⣳⢯⣷⢫⣯⢷⣚⣯⡽⣞⡵⣯⢽⡻⣼⣛⠾⣯⢽⡳⣽⢻⡼⣽⡺⣏⡷⣽⢣⣟⡞⣿⣾⣥⣿⣿⣿⣯⣿⡳⢷⡈⡑⠌⢠⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣶⣍⢏⡞⣴⣙⣦⡹⢆⣿⣴⣽⣾⣿⣿⣿⣿⠐⡻⢷⢩⣿⣿⣿⣿⣿⡗⣨⠱⣌⠹⣂⠎⡔⢣⢌⠢⢃⠆⢢⠍⢢⠘⡄⢣⠘⣐⠢⡑⢌⠢⡁⢎⠰⡁⢆⠡ ⣿⢾⣳⣯⢿⡾⣽⣻⣼⣻⢞⣽⣹⢶⣻⢼⣻⢼⣳⡻⣵⣫⢟⡮⣗⣻⡼⣳⡽⣖⣻⡝⣾⡱⣟⢮⣽⡟⢻⣿⣿⣿⣟⣿⣯⢳⣦⣷⣶⣿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣼⣆⢳⣎⠿⣖⣾⣿⣾⣿⣿⣿⣿⣿⡀⣟⢈⣦⣹⣿⣿⢿⣿⠓⡤⢓⣌⢣⠱⡊⢜⡂⢎⡱⢊⡜⢄⠚⡄⢣⠘⡄⢃⠆⡱⢈⠆⡱⢈⠆⡱⢈⠄⡃ ⣿⢯⣟⡾⣯⣟⡷⣯⢶⣏⣟⡮⣗⣻⡼⣏⡾⡽⢶⡻⣵⢫⣾⡹⣞⡵⣫⢷⣹⢞⡵⣻⢖⣻⡝⣾⣿⠁⠰⠟⣿⣯⢸⣿⣯⡧⣴⣠⣴⣶⣦⣄⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣮⣷⣾⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣟⠃⢿⣿⠟⣽⣿⣿⠣⡙⡔⢣⠜⣢⠣⢍⠢⡙⢄⢢⠡⡘⢄⠣⡘⢄⠣⡘⢄⠊⡄⠣⡐⢄⠃⡔⢠⠃⡌⡐ ⣿⢯⡿⣽⣻⢾⡽⢯⡷⣞⢧⣟⣭⠷⣝⡾⣱⠿⣭⢗⣯⢳⡞⣵⡻⣼⣛⢮⡗⣯⡝⣧⡟⣧⢻⡞⣿⠀⠀⣦⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣛⣷⠿⣫⣾⢃⠧⡱⡘⢥⠚⣄⠳⣈⠱⡈⢆⠢⡑⢌⠢⡑⢌⠢⡑⠰⡈⢆⠡⢃⠌⡂⠜⡠⢂⠅⢢⠁ ⣿⢯⣿⣳⣟⣯⣟⣯⠷⣏⡿⡼⣞⢯⣻⠼⣏⣟⢮⣻⡜⣯⢞⣳⡽⣣⢯⣳⢻⡼⣽⢲⡟⣼⡳⣏⢿⣆⠀⢿⣿⣿⣿⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⢟⣿⢅⠺⡰⢡⡙⠤⢋⠤⠓⡄⢣⠘⡄⢣⠘⡄⢣⠘⠤⡑⢨⠑⠌⡄⢃⠢⡘⠄⡃⠔⣁⠊⡄⢃ ⣿⣻⣞⡷⣿⢮⡽⣞⣿⡹⣞⡽⣞⢯⣳⢻⡝⣮⢟⡶⣻⡝⣞⣧⢻⡵⣫⣗⢯⣳⡭⢷⣫⢷⡹⣎⡯⢿⣆⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⢻⡯⢌⢣⡑⢧⠘⡥⢋⠌⡓⢌⠢⡑⢌⠢⡑⢌⠢⢉⠆⢡⠂⡜⡐⢌⠂⡅⠢⡑⠌⢒⡀⠣⠌⡄ ⣿⣳⢯⡿⣽⣏⡿⣽⣲⢟⡽⣞⣭⢷⣫⢟⡼⣏⡾⣳⢧⣛⢷⡺⣝⡾⡵⣞⢯⡖⣯⡳⣝⡮⢷⡹⣞⣻⣿⡄⣿⣿⣿⡟⢛⣫⣿⣿⣿⣿⣿⣿⠟⣿⠛⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣹⡟⣌⠲⣡⠊⡕⢢⠡⢚⠰⡈⠖⡡⢊⠔⠡⢂⠱⡈⢌⠂⡅⢒⡈⢄⠣⡐⢡⠂⢍⠂⡌⢡⠒⠠ ⣿⡽⣯⣟⡷⣯⢷⣳⡽⢾⣹⡞⡽⣎⡷⣫⡽⣞⡵⣛⣮⢟⣮⢽⣣⢟⣵⢫⡾⣹⢖⣯⢳⡝⣧⢻⡜⣷⣿⣿⣿⣿⣿⣴⣿⡿⡏⢻⣿⣟⣤⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠠⢚⡯⣐⠣⢆⠹⣠⢃⠣⢌⠢⡑⠌⠴⢁⢊⠱⡈⢆⠘⡠⢃⡘⢄⡘⢄⠢⢑⢂⠩⢄⠊⡔⠡⠌⡡ ⣿⣽⣳⣯⣟⣷⣛⣶⢻⡝⣧⡻⣝⢾⣱⣏⢷⣹⢞⡽⣎⢿⡜⣧⣛⠾⣜⢯⣳⣛⠾⣜⢧⡻⣜⢧⡻⣜⣿⣿⣿⣿⣿⣿⡟⠳⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠌⡐⢫⢄⠫⡜⢠⢃⠌⡒⢌⠢⢑⠊⡄⠣⢌⠰⡐⡈⢆⠡⢂⠔⡂⠔⡈⢆⠡⢊⠰⡈⠒⢄⠣⡘⠠ ⣿⣞⣷⣻⣞⡾⣝⡾⢯⣽⢺⡵⣏⡟⣶⡹⣞⡽⣚⡷⣹⢮⡻⣵⢫⡟⡽⣎⠷⣭⣛⢮⡳⣝⢮⡳⣝⡞⡶⣿⣿⣿⣿⡿⠈⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠬⣙⠆⢳⠘⠤⣉⠆⡱⢈⢆⠡⢊⠰⡁⢆⠡⢂⠱⣀⠣⠌⢒⡈⢆⠡⢂⠱⡈⠤⢡⠉⡂⢆⠡⡁ ⣿⢾⣽⣳⢯⣟⡽⣞⡿⣜⣳⡽⣺⡝⣶⢫⢷⡹⣝⠾⣭⣳⢻⣜⡳⣽⢳⣭⣛⢶⣭⢳⡝⣮⢳⡝⣮⣝⡳⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡈⠴⣈⢏⠰⣉⠒⡡⢊⠔⡡⢈⠆⡡⢒⠈⡔⡈⢆⠡⡐⢂⡑⠢⡐⢂⠅⡊⠔⡠⢃⠢⡑⠨⠄⡃⠔ ⣿⣻⢾⣽⣳⢾⣹⣳⢽⡺⣵⢫⢷⡹⣞⡽⢮⣽⣚⢯⣳⢭⣳⢭⣳⢭⣳⢮⡝⡾⣜⢧⡻⣜⢧⡻⢶⣭⢳⢧⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⡐⢈⠲⢡⢎⡱⢄⡩⢐⠡⢊⠄⣃⠰⢁⠢⡑⠰⡈⢄⠃⡔⣁⠢⡑⢄⠃⡌⠰⣁⠒⡄⢃⠌⡑⢌⠰⢁ ⣿⣽⣻⢾⡽⣞⣧⢟⣞⣳⡭⣟⢮⢷⡹⣞⣳⢮⡝⣾⣱⢻⡜⣧⣛⢮⡳⣏⢾⣱⢏⡾⣱⢏⡾⣹⢳⣎⡟⡾⣴⢛⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠭⡀⢡⠌⡡⢂⡅⢺⡔⡨⢔⡡⢊⡅⢒⠠⡑⣈⠒⡈⢅⠒⣈⠒⡐⢄⠒⡨⠐⡌⠰⣁⢂⠒⡈⢆⡘⠰⢈⠢⢁ ⣿⢾⡽⣯⢷⣻⢮⣛⣮⢳⣝⣮⣛⢮⢷⡹⣎⢷⣹⠶⣭⣳⣛⠶⣭⡳⣝⡞⣧⣛⢮⣳⡝⣮⢳⣝⡳⢮⣝⡳⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⡁⠞⡌⠐⡤⠂⠤⢡⠘⣐⠣⣏⡐⠆⡔⣡⠈⡆⡑⠰⣀⠃⡜⢠⢊⡐⢌⠰⣈⠂⡅⢃⠌⡡⢐⢂⠱⢈⠆⢌⠡⢊⠄⠡ ⡿⣯⣟⡷⢯⢷⣫⠷⣭⢷⣚⢶⡹⢮⡳⣝⢮⣳⢭⣛⢶⣣⢏⡟⡶⣝⢮⣝⠶⣭⡳⢧⣻⣜⡳⢮⣝⡳⢮⣽⣟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣍⡳⢍⢦⣹⡰⢬⠑⡠⠨⠰⢀⣋⠄⠳⣼⡄⣙⠰⢠⡘⠤⣁⠣⡐⢌⡐⢢⠐⡰⢈⠢⠄⡃⠔⣈⠢⠑⡂⢌⠢⡁⢎⠠⠃⡄⢊⠐ ⣿⢷⣯⣟⢯⢷⣫⣟⢮⣳⡝⣮⣛⢧⣛⢮⡳⣝⡮⣝⣮⢳⣏⣞⡳⣝⠾⣜⡻⢶⣹⢳⡳⢮⣝⡳⢮⣝⡳⣞⢿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣭⢻⣌⠳⣭⢖⣦⠳⣌⢌⠡⢁⠒⢡⠈⢎⠡⠜⣷⡈⠜⣠⠘⡰⢀⢣⠘⡄⠒⡄⢣⠐⡡⢂⠱⢈⠒⡠⢁⠣⢘⠠⢂⠅⢊⠐⠡⠐⠂⠌ ⣿⣻⢶⢯⣛⡾⡵⣞⢯⢶⡹⣖⢯⡞⣭⣳⢻⣜⡳⣝⢮⡳⣞⡼⣳⢭⣛⣮⡝⣧⢏⡷⣹⢳⢮⣝⡳⣎⠷⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⣽⣳⢮⡳⣎⡳⡼⡞⡴⢫⡜⠌⢦⠉⠈⠄⡐⠂⡜⢨⢽⣿⡔⢂⠱⣀⠃⢆⠱⣈⠱⡈⢆⠱⣀⠣⡘⢄⠣⡐⢡⠊⡄⠣⢌⠘⡀⢊⠡⠌⠡⢈ ⣟⡷⢯⣟⡽⣺⣝⢾⡹⣎⢷⡹⢮⣝⠶⣭⡳⢮⣝⢮⡳⣝⢮⡳⣝⢮⣳⢮⣝⢮⡻⡼⣭⣛⠾⣜⡳⣭⣛⠶⣭⢿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣏⣟⡳⢞⡥⢯⡽⣭⢳⢧⡹⢜⣣⡙⢾⡀⠎⠡⠀⢄⠡⡀⠣⢎⢿⣿⣧⣖⡠⢉⠆⡒⠤⡑⡈⢆⠱⣀⠣⡘⢄⠣⡘⢄⠣⡘⠰⡈⠆⡁⠢⠐⡈⢂⠁ ⣯⣟⣟⣮⡽⣳⢞⣯⢳⡝⣮⢽⡳⣎⡟⡶⣝⢯⡞⣧⣛⢮⢷⡹⣞⢧⣛⠾⣜⢧⡻⣵⢣⣏⠿⣜⡳⢧⣏⠿⣜⡧⣏⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⢾⡸⣹⡍⣞⣱⠞⣥⢻⢦⡙⣦⠧⡙⢦⡑⢎⠡⡀⠆⠰⢀⢣⠘⡼⣷⣏⡿⣿⣶⣾⣤⣵⣠⡑⣈⠒⠤⢑⠰⡈⢆⠱⡈⢆⠡⢃⠜⡠⠑⣂⠑⡠⠁⠌ ⣷⣻⡼⢶⣻⢵⣫⢞⣧⢻⡜⣧⢻⡼⣹⢳⡝⣮⡝⡶⣭⣛⢮⣳⡝⣮⣝⡻⣜⢧⡻⣜⡳⣞⡽⢮⣝⡳⣎⠿⣜⡳⣝⠾⣭⣛⠿⡿⢿⠿⣿⢿⣿⠋⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣞⡧⢷⡩⡜⠶⣥⢯⡙⣧⣾⠵⣣⠝⣌⠣⡜⢢⠡⡁⠂⠅⣂⠢⠘⢤⢫⡝⣻⣷⣻⢞⣽⣻⣟⣿⡿⣿⣶⣮⣴⣡⣈⠆⡑⠌⢢⠁⢎⡐⠡⡀⠎⢠⢁⠂ ⣷⣳⢻⣏⣞⢧⣛⡾⣜⢧⡻⣜⣧⢻⡵⣫⢾⡱⣏⢷⣣⢟⣮⢳⡝⡶⣭⢳⡝⣮⢳⣭⢳⡝⣞⡳⢮⡝⣾⡹⢧⡻⣜⡻⢶⡍⡷⣍⣛⠮⡵⢎⣽⠀⠀⠀⠀⢮⣿⣿⣿⣿⣿⣿⡿⡞⣥⢳⡉⢳⡜⣦⢿⡻⣌⠷⣢⠝⣠⠒⡌⢠⠃⡔⢁⠂⠴⢈⡑⢎⡳⢼⢯⡷⣯⣟⣮⢷⣻⣾⣟⡿⣽⣿⣻⣿⣿⣿⣷⣾⣤⣉⡤⠘⢠⠁⡌⠂⡄⢂ ⡷⢯⣛⣞⢮⡻⣜⡳⣝⢮⢷⡹⣎⢷⡹⢧⣏⢷⡹⣎⢷⣫⢞⣧⢻⡵⣫⢷⡹⣎⢷⡺⣝⠾⣱⢏⡳⣝⢶⣹⢳⡝⣧⣛⢧⠞⡵⢎⢧⡛⣜⢣⢾⡃⠀⠀⠀⠠⣼⣿⣿⣿⣿⣟⣷⡻⣬⢓⣌⠶⣹⣯⣗⣳⣭⠳⡆⣍⠲⠠⠄⠃⡜⠐⡌⡀⢂⠬⠑⡎⡵⢋⡞⣹⢳⣻⣾⣿⢿⣟⣾⣟⣷⣿⣿⣽⣷⡿⣯⣿⣿⣿⣿⣿⣦⣴⣀⠡⠐⠂ ⣟⢯⡽⣎⣯⢳⡭⣗⢯⡞⣧⢻⡜⣯⣝⡳⢮⣏⢷⡹⣎⢷⣫⢞⣧⢻⡵⣫⢷⡹⣎⠷⣭⢻⡥⣏⢷⡹⣎⢷⣫⢞⡵⣭⠺⡭⣝⢮⢣⡝⣬⠓⡾⡇⠀⠀⠀⠐⢼⣽⣿⣿⣿⣿⣷⣿⠶⣏⢬⣛⣷⣻⣞⡷⣊⠷⣉⠦⣁⠣⣘⠐⡈⠱⣀⠖⠡⠀⡝⡘⡔⠫⡔⢣⡞⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣾⢿⣟⣷⡿⣯⣿⣿⢿⣿⣿⣿⣾⣤ ⣯⣛⢾⡱⣏⢷⡹⣎⢷⡹⣎⢷⣛⠶⣭⣛⠷⣎⢯⡳⡽⣎⢷⣫⢞⣧⢻⡵⣫⠷⣭⢻⡜⣧⢳⡝⣎⢷⡹⣎⢷⣋⠾⣜⢫⡵⣚⡬⢳⡜⢦⡛⡴⣧⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣯⡿⣜⡶⣹⣾⢯⣟⣳⡽⢎⡕⢢⠰⣁⠣⡜⢀⠡⡘⢠⠁⢆⠐⡤⢩⠓⣬⢓⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣿⣻⣿⣿ ⡷⣭⡗⣯⠽⣎⢷⣫⢞⡵⣫⡞⣭⣛⠶⣭⢻⡼⣣⢟⡵⣫⢞⡵⣫⢞⣧⢻⡵⣻⡜⣧⢻⣜⡳⢞⡭⡞⣵⢫⡞⣭⢻⢬⡳⣜⡱⢺⡱⢎⢧⡙⡖⣿⠀⠐⠄⢀⠀⠀⠉⣿⣿⣿⣿⣿⣟⡷⣏⣷⣿⣿⢿⣻⡝⢮⡜⣡⠓⠬⣑⠜⣨⠂⡁⢃⡚⢤⡈⢠⢃⡝⢦⣛⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣽⣿⣽⣿ ⣟⡵⣻⣜⡻⣜⢧⣛⢮⡳⢧⡻⣵⢫⡟⡼⢧⡻⣵⢫⡞⣵⢫⡞⣵⢫⡞⣧⣛⢶⡹⣎⢷⣪⠽⣹⢼⣙⢮⣳⢹⡜⣣⢳⣙⠦⣝⢣⡝⢎⢶⣭⡿⠛⠀⠀⠀⢹⠆⣄⣀⠿⣿⣿⣿⣿⣯⣿⡽⣾⣿⣯⡿⣧⣛⢧⡚⡥⢊⠶⣩⢎⡡⢚⠄⢃⠜⡢⣄⠣⡘⣬⢣⠿⣽⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣯⢞⡵⣎⡷⣹⢎⣯⢳⡽⣳⡝⣮⢳⡽⣹⢧⡻⣜⢧⡻⣜⢧⣻⡜⣧⣛⢶⡹⣎⢷⡹⢶⣩⢏⠷⡮⣝⡞⣬⡓⣞⣱⢫⡜⣹⢬⣳⡾⠟⠋⠁⠀⢀⠀⠀⠀⢸⡅⣦⢉⡉⢿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡿⣖⡻⢦⡛⣌⢏⡾⡵⢪⡕⢯⣌⢣⣌⡱⢎⡧⣙⣤⢏⡿⣵⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢷⣫⢞⡵⣫⢗⡯⣞⢧⡻⣵⢻⡜⣧⢻⡵⣫⢷⡹⣎⢷⡹⣎⢷⡹⢶⡹⣎⢷⡹⢎⡗⣯⣜⢫⢷⡹⡖⣽⠲⣝⡼⢲⣍⣾⠟⠋⡁⢀⠀⠀⠀⢰⣿⠀⠀⠀⠈⡇⠸⣧⣌⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⣥⣋⢷⡙⣞⣮⡽⣽⢳⣚⠷⣜⡲⣬⡳⢯⣶⢻⣼⣻⣞⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡼⣫⢞⡵⣫⢞⡽⣎⠷⣭⢳⡝⣮⢷⡹⢧⣏⢷⡹⣎⢷⡹⢮⡝⣧⢳⡝⡮⡝⣏⡞⢶⢎⡿⢬⡳⣝⠮⣝⣲⣽⠟⠋⠀⠠⠀⢀⡀⢀⡈⢷⣾⣿⠀⠀⢠⠀⢻⡄⢽⣷⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⡍⣎⢿⣼⣳⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⣱⣏⣞⡳⣝⢮⣳⢭⡟⣼⢫⡞⣵⢫⣝⡳⣎⢷⡹⣞⢧⣛⢧⢻⡜⣳⠞⡵⣋⢶⡹⣚⢮⡜⢧⣛⡼⣹⣶⠟⢡⣀⠈⢒⠠⣇⢢⣽⣦⣿⣿⣿⣿⠃⠀⠈⢣⠀⢳⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⡼⣣⢟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣻⢯⣟⡳⡽⣎⢷⣛⣾⣳⣿⣿⣿⣿⣿⣿⣿ ⣳⢯⡽⣹⢧⡻⣜⢯⡞⣵⢫⡞⣵⢫⡞⣽⢣⡟⡼⢧⡻⣜⡻⣜⢮⣓⢏⡖⢧⠻⣜⡣⢟⣬⢓⡮⢫⣵⡿⠋⠀⠈⢻⣤⣚⡤⢿⡞⣿⣻⣿⣿⣿⠏⠀⠀⠀⠈⡆⠸⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⡵⣿⣿⣿⣧⣻⣾⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⡿⣟⣿⣯⣿⣟⡿⣿⣻⣿⣽⣟⣷⣿⢾⣟⡾⣽⣳⢧⣻⣼⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿ ⢯⡞⣵⢏⡾⣱⢯⡞⡽⣎⢷⡹⣎⢷⡹⣎⢷⡹⣝⢧⡟⣼⡱⢏⡶⢭⡺⣜⢫⣝⡲⢭⣓⢮⡹⣼⡟⠃⠀⠀⠀⣐⡠⠞⣿⡽⢎⡽⣶⢿⣾⢏⡆⠀⠀⠀⠀⠀⠑⠀⣧⠀⢺⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣝⡮⣝⡾⣿⣳⣿⣟⣿⣿⣽⣷⣿⣿⣿⣿⣷⣿⣿⣿⣯⣿⣾⣟⣷⣿⣻⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡼⣣⡟⣼⢣⡟⣼⢳⡝⣮⢳⡝⣮⢳⡝⣾⡱⣏⠾⣜⢧⡝⡞⣜⡣⢗⣎⠳⣎⣵⣫⣼⣶⠟⣉⣠⠀⠀⠀⢀⡿⣷⢍⣙⣧⣿⣾⣿⣫⣝⣾⣤⣄⣲⣤⣹⣦⠲⠤⣄⠀⠈⢿⣿⣿⣿⣿⣿⠃⢤⣿⣿⡿⢫⣙⢮⣳⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡷⢯ ⣞⡳⣝⢾⡱⣏⣞⢧⡻⣜⢧⡻⣜⢧⡟⣼⢣⡝⣮⣛⡼⢎⣞⡹⡲⣍⣷⡾⠟⢋⢉⣥⣶⣾⣿⣿⣿⣿⠿⡩⢞⣷⠟⠉⡐⢎⠛⡍⢯⡽⣻⣿⡻⢿⣿⣿⣿⣿⣷⣦⣜⣦⡀⠹⣿⣿⣿⣿⠏⢀⣿⡿⠉⢁⠣⣞⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣟⣿⣟⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠾⣝⢯ ⣯⣝⢾⣣⢟⡼⣎⡷⣹⢎⣯⢳⡝⣮⡝⣮⢳⡝⢶⡹⣜⣫⣖⣽⠿⢋⡡⢴⠶⣞⡾⣞⣷⣿⣾⣿⣿⣟⡶⣡⣿⠋⠀⠀⢁⠢⠕⡚⢡⢎⡱⠭⣽⠿⣟⢿⡻⣝⣮⣿⣿⣿⣷⡧⣿⣿⣿⡋⢥⣿⡏⣠⣄⣠⣔⣫⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣟⡿⣿⣾⣿⣿⡿⣟⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣽⣯⢿⡽⣞ ⡷⢮⣳⡝⣮⢳⡝⣾⡱⣏⡞⣧⣛⢶⣽⣮⡷⠿⢛⠛⡫⢍⠋⡅⣎⢱⡙⣎⠿⣜⣻⡽⣿⣾⣿⣿⣿⣿⣿⣿⠏⢀⢠⡐⣠⠉⠒⠬⡁⢎⡰⢿⣬⡻⣜⣯⢷⣻⣿⣿⣿⣿⣿⣷⣉⡟⢦⡑⣮⢯⣴⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣻⡾⣿⣟⣯⡿⣿⣿⣯⣟⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡷⣯⡿⣽⢯ ⣽⢳⢧⡻⣜⢧⡻⢶⣹⢮⣽⡶⠿⠛⠉⠀⠐⠤⠣⡘⠐⢊⠒⡌⢂⠧⣜⡎⣷⣹⡾⣽⣷⡿⣿⣿⣿⣿⠿⣡⠲⣌⢶⡹⢿⣆⣙⣲⠱⣮⢙⠶⣣⢿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠥⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⢷⣯⣟⣷⣿⣳⣯⢿⡽⣷⣿⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⡷⣟⣯⣿ ⣳⢯⡞⣵⣫⢞⣽⣳⠟⠋⠁⠀⠀⠀⠀⠐⠠⠂⢀⠈⠄⢡⠘⡰⣍⡞⣴⢯⡷⣯⣟⣿⡾⣟⡿⡹⣍⢆⡳⢣⡽⣘⣮⡟⣽⣿⣿⢣⠷⣌⣯⣛⣷⣻⢾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣶⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣯⢷⡿⣜⢯⢾⣭⢿⡿⣿⡿⣿⣾⢿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣻⣿⣾ ⣟⢮⣽⢺⣵⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠢⡜⢢⡝⢲⣟⡾⣽⣯⣿⣿⣻⡽⣛⢥⢳⡱⢎⢎⣝⢣⡻⣵⣳⡿⣟⣿⣞⣯⢿⣝⡶⣛⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣟⡾⣞⡯⣝⢿⣫⡗⣾⣯⣿⡽⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⣿⣷⣿ ⣻⢞⣼⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠔⣠⠒⣭⠳⡜⣧⣿⣟⣷⣯⢷⣫⢇⡧⣙⢎⢣⠳⡞⡼⣌⢷⣻⢽⣯⢿⡽⣯⣟⡞⡿⣮⣽⢳⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠘⢦⡈⢿⣞⣿⣿⣿⣿⣷⡿⣿⣟⡾⣽⣟⡾⣽⢣⡟⣽⣺⢷⣻⢽⣳⣯⣿⢿⣻⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿ ⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢬⡸⣔⢫⢖⣻⣾⣿⠿⣝⡾⣡⠧⣍⠞⣰⠙⢎⡲⢥⣛⣼⣻⡼⢯⡟⣞⢯⣿⣱⢿⡜⣷⡝⣾⢻⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢳⣄⡆⣹⣜⣿⣿⣿⣿⣿⣿⣿⢿⣟⣿⣳⢏⡷⣭⢗⣯⣛⣷⢻⣾⢯⣿⣻⣽⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢆⡞⠶⣱⣮⣾⣿⣿⢿⡽⣛⡮⢱⡡⣚⡜⡸⢣⢛⣤⡝⣫⣼⠶⡽⢾⡹⡞⡭⢞⠶⢭⢞⡹⣞⡽⣮⢿⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⣻⣽⢻⡼⣾⢿⣿⣿⢿⣻⣿⣿⣾⣳⢯⡻⣼⢛⡾⢧⣻⣼⣻⣾⢿⣽⣿⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⡌⣞⣬⣿⣿⣿⣿⣿⣯⣿⡟⢧⠘⡅⣶⢩⠞⣱⢛⣼⢲⡝⣣⢟⡽⢞⡹⢻⡱⣛⢮⣙⣧⢫⡷⣭⢷⣯⣟⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣰⣿⣿⣻⣿⣯⣿⣿⣿⣿⣿⣟⣮⢷⡏⣯⢳⣭⢻⡼⣟⣧⣿⣹⣽⣻⣯⣿⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⡜⣰⣿⣿⣿⣻⣽⣯⢿⣿⣯⠳⡜⢠⢛⡘⢤⡃⣞⡥⢏⡞⡶⣙⢮⣟⡼⡳⣍⣳⣫⡝⣮⣝⣮⣻⡽⢯⣿⣾⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡷⢧⣿⣿⣿⣿⢯⣟⡾⣽⢻⡯⣟⣳⡛⢾⣳⣽⡽⣞⡿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⡘⡼⣼⣿⣻⣷⢿⣽⣿⣽⣿⣿⣦⠃⡄⠙⠦⠸⠀⡗⡌⢲⡛⣜⠶⣙⡞⣼⣱⢯⣝⣣⢿⣝⣯⣟⣾⣳⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣼⣿⣋⢿⡟⣞⣻⣞⡷⣹⢏⡷⣫⢷⣹⣛⣷⣻⣽⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⡉⣥⢻⣽⣷⢿⣷⣯⣿⣿⣿⣿⣿⣿⠂⠄⠡⠒⠐⠈⠳⢐⡚⡡⢜⡭⢻⡴⣛⢶⣭⡞⣧⣟⣯⢿⣭⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⢿⠙⣇⣿⢫⡝⣭⣓⣮⠷⣳⢾⣱⢟⣯⣟⣯⣷⣻⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣟⡷⣯⣿⣿ ⠀⠀⣀⣄⣠⠌⢦⡱⣯⣿⣻⣾⡿⣯⣿⣿⣿⣿⣿⣿⡏⠙⠀⠀⠀⡰⣃⡤⢋⣜⣍⣫⣜⣣⣷⣻⣟⣶⡿⣟⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡉⠁⡫⢜⠣⢯⣜⣦⠳⣬⠷⣽⣚⣷⣞⣳⣾⣷⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣹⣿⣽⣯⣿

⠀⢀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣠⣤⣤⣤⣤⣀⠲⢦⣄⡀⠀⠀ ⡶⢟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠰⣷⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⡛⢷⣔ ⣾⡿⠟⠋⠉⠁⠀⡀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢻⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣛⣛⣛⣛⣉⢉⣉⡀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣝ ⠃⠀⠀⠀⠀⠀⠀⣛⣛⣛⣛⣛⣛⢛⡛⠛⠛⠛⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣓⣀⠀⠀⠀⠀⠀⠈⢻ ⠀⠀⠀⢀⣤⡾⠛⢻⣿⣿⣿⡿⣿⡟⢻⣿⠳⠆⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠐⠛⣿⡟⢻⣿⣿⣿⣿⢿⣟⠛⠻⣦⣀⠀⠀⠀⠀ ⠀⠀⢴⠿⣧⣄⣀⣘⣿⣿⣿⣿⣿⡿⣀⡙⢷⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⡖⠀⣾⣋⣀⣺⣿⣿⣿⣿⣿⣏⣀⣤⣴⠿⢷⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠆⠀⠀⢀⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣾⠿⠛⠋⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠈⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⣄⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⢀⠀⢀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣉⣩⣤⠴⠶⠶⠒⠛⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠤⠶⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡍⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣫⣭⣷⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠶⠖⠚⠛⠛⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠛⠉⡁⠀⠀⠙⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡷⠷⢿⣦⣤⣈⡙⢿⣿⢆⣴⣤⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⡀⣸⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣟⣩⣤⣴⣤⣌⣿⣿⣿⣦⣹⣿⢁⣿⣿⣄⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⠋⠻⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠛⢦⣽⣿⣿⢻⣿⣿⣿⣿⠋⠁⠘⣿⣿⣿⣿⣿⣿⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠁⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⣿⣯⣼⣿⡿⠟⠃⠀⠀⠀⣿⣿⣿⣿⣿⡛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣧⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠟⠃⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⢁⣀⣀⣀⣀⣀⣠⣀⣀⢀⢀⢀ ⠀⠀⢿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠛⠛⠙⢻⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠘⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡟⢿⣿⣆⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡼⠁⢀⣀⡀⠀⠀⠀⣦⣄⠀⣠⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⣬⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣰⣿⡿⠿⠦⢤⣴⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠒⣿⣿⣿⡿⠟⠹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡖⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⣾⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⣀⣀⣤⣴⣶⣶⣾⣿⣷⣦⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⣿⣿⡛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡟⠛⠛⠻⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠓⢁⣬⣿⠇⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢰⡿⣻⠇⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢐⣯⠞⠁⠀⠀⠀⠀⠀⠀⣄⠱⣄⠀⠀⠀⠀⠸⡧⠟⠆⠀⠀⠀⠀⠘⠿⢿⠿⠿⣿⡿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠂⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣦⣼⡏⠳⣜⢿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣷⣦⣤⣀⣀⣀⣴⣿⣿⣿⣿⣿⡿⠻⠆⠸⣎⣧⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⡄⠀⣿⢹⡇⢸⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡔⠡⠞⠀⣀⣀⣀⣄⣀⡀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠊⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠁⠈⠉⠉⠛⠿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀ ⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠏⠀⠀⠀⠀⠀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠘⡟⠁⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠘⠿⣿⣷⣦⠀⠀⠀⣾⣿⠿⢋⡀⠀⢹⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠻⣿⣿⣿⣿⡿⠿⠿⣿⣿⣧⡀⠀⠘⠒⠲⠶⢤⣉⠉⠀⠀⠦⣌⠗⠛⠙⠊⠉⠁⠀⠈⠳⣄⠀⠀⠀ ⠀⠀⠀⢰⣿⣿⡏⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠐⠒⠢⢤⣁⣀⣠⡆⣼⢀⣠⡴⠶⡶⢦⣀⠀⠀⠘⡆⠀⠀ ⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⣰⠋⢹⠁⠘⡇⠹⡍⢯⠀⡿⠀⡇⢸⠘⡆⠀⠀⣿⠀⠀ ⠀⠀⠀⠸⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⡇⠀⢸⠀⠀⡇⠀⡇⢸⠀⠁⠈⠁⠎⢀⠇⠀⢠⠏⠀⠀ ⠀⠀⠀⠀⠈⠿⣿⣿⣿⡶⠟⠓⠒⠒⠤⣼⡀⠀⠁⠀⠉⠀⠈⠁⠈⠁⣸⠀⠀⠀⠀⠀⣼⡀⣠⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⠏⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠙⠧⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⣀⡤⠴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢀⡴⠊⠁⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀ ⠀⠀⠀⠀⠀⠀⡼⢻⡀⡰⠋⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⢀⡇⠈⣿⠁⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇ ⠀⠀⠀⠀⠀⢸⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠈⠲⢄⣀⠀⠀⠀⣀⡴⠋⠀ ⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠱⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⡀⠈⢹⠉⠉⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠙⠲⢄⣀⠀⠀⠀⠀⠀⣀⡤⠞⠁⠈⠑⠒⠤⠤⠅⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡼⠇⠀⠀⠀⠘⡆⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢼⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⢀⡼⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢠⠞⠀⢹⡄⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⡿⣯⡷⡴⢦⣤⡠⣶⡶⠀⢷⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡾⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⣼⣥⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⠀⠈⢧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡇⠀ ⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⠛⢦⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠳⠀⢳⡀⢹⡇⠀⠀⠀⠀⠀⡾⡇⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠘⠀⠀⠹⣼⡇⠀⠀⠀⠀⢠⠇⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⡾⠀⠀⠀ ⠀⠀⢠⡏⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢸⠁⠀⠀⠀ ⠀⠀⡾⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⡟⠀⠀⠀⠀ ⠀⣴⠓⣾⣳⣀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠃⠀⠀⠀⠀⠀⠀⢸⡇⢀⠇⠀⠀⠀⠀ ⣾⠃⠀⠀⠀⠑⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⠀⠀ ⠹⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⠀ ⠀⢳⡄⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⠀⠀⠀⠀⠀ ⠀⠀⣷⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡏⠀⠀⠀⠀⠀ ⠀⢀⡇⢹⣄⠀⠀⠀⠀⣀⠉⠓⠶⢄⡀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣸⣧⠀⠀⠀⠀⠀ ⠀⣴⣿⠋⠘⣆⠀⢰⠶⠤⢍⣛⣶⠤⠿⣷⣦⡀⠒⠚⡟⠀⠀⠀⠀⠈⠛⠢⠤⡄⠀⠀⢀⡴⢯⠴⣳⠇⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⠘⢦⡈⠻⣖⠤⣤⣉⣉⣹⣯⣭⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⣫⣼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⣄⠉⢦⡀⠀⠀⠈⠉⠁⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣷⢚⡝⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣷⠇⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⢄⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⠢⢃⣀⣠⣀⡀⠀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀ ⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⠿⠛⠛⠙⠛⠻⢿⣿⣿⣿⡆⠀⠀⠀ ⢀⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡇⠀⠀⠀ ⠸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣀⡀⠀⠀⢀⣤⡄⠘⡋⠀⠀⠀⠀ ⠀⠻⣿⣿⣿⠿⣿⣧⠀⠠⠤⠝⡛⠃⠠⡙⠯⠶⠀⠑⠂⡄⠀⠀ ⠀⠀⣼⣿⠁⠀⠘⠿⠇⠀⠀⠠⢦⠤⠰⡾⠔⡖⡖⡦⡀⠈⡄⠀ ⠀⠀⢹⣿⣄⡀⢀⠀⠀⢠⠤⠇⢸⠀⠇⡇⡇⠃⠃⢃⠃⢠⠃⠀ ⠀⠀⠀⠙⢛⠟⠉⠈⠉⠺⡄⠀⠀⠀⠀⠀⡇⠀⠀⠘⠲⡁⠀⠀ ⠀⠀⠀⠀⠸⠀⠀⢀⠤⢰⠃⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠈⢄⠀ ⠀⠀⠀⠀⢷⢀⠔⠁⠀⡌⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⡆ ⠀⠀⠀⢸⠀⢣⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⠉⠦⡀⠀⠀⠀⡴⠁ ⠀⠀⠀⠘⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⣠⢃⡀⠀⠎⢱⠀⠉⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⠉⠒⠂⠀⠐⠊⠁⠀⠈⠁⠀⢸⠀⠀⠀⠀

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⠋⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⠿⠿⠛⠛⠛⠛⠉⠛⠛⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿ ⣷⣄⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠛⠉⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠛⠿⡗⠀⠀⢠⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣴⣿⣿⣿⣿ ⠈⠛⢶⣤⡀⠀⢀⣶⡿⠋⠁⣠⡴⠖⠛⠉⠉⠉⠉⠉⠉⠛⠲⣶⣀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠈⠙⢻⣿⠏⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢠⡿⢉⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿ ⠀⠀⠀⢀⡾⣧⡾⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠉⠁⠀⠀ ⠀⠀⠀⣸⠀⠙⠃⠀⣷⣤⢴⠖⠊⠉⠉⠉⠓⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣠⠟⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡟⠀⠀⠳⢄⣀⣀⣆⣀⣤⣤⣶⣾⠿⠛⣇⠀⠀⠀⠀⠀⠀⠀⣼⣃⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⠀⢻⡁⠀⢀⡀⠒⠐⣛⣿⣿⣿⡉⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠶⣄⡀⠀⠀⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢨⣑⣾⣿⣿⡏⠱⡀⠉⠁⠈⢿⣯⣤⠀⠀⠀⣰⠇⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⣰⣿⣿⠿⠿⠗⠒⠒⠒⠶⠦⢤⣤⣀⡀ ⠀⠀⠀⠐⠻⣿⣷⣄⢣⠀⠀⠀⠈⠻⣇⣀⠤⠚⢣⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙ ⠀⠀⠀⠀⠀⠹⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⠳⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⠀⠀⠀⠀⠀⠀⢀⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠃⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⢀⣾⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡀⠀⠀⠀⢀⣀⣀⡠⠤⠔⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠶⢾⣇⠀⠀⠀⠀⢀⣠⠞⠋⠉⠛⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢤⣄⣀⣀⡀⣀⣀⣀⣤⠴⠞⠛⢷⣄⠀⠀⠈⢻⣷⠀⣠⡴⠋⠁⠀⠀⠀⠀⢸⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡼⠛⣉⣀⠀⠀⠀⠀⢿⣧⡀⠀⠈⣿⣟⠁⠀⠀⠀⠀⠀⠀⢀⠇⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⣤⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣟⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣫⣿⡾⠀⠀⢰⣶⣬⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡇⠉⠉⠀⠀⠀⠀⠉⠛⠃⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡶⠒⢦⠀⠀⢀⣠⣤⡀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠧⣿⣷⠃⠀⠘⣷⡄⠉⠢⢄⣾⣿⠟⠻⢿⣿⣿⣿⣿⠃⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠈⠙⠁⠀⠘⠛⠛⠐⠀⠸⣿⠏⠀⠀⠈⣿⣿⠟⠁⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⢧⣾⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣦⣀⠉⠁⠀⠀⠀⠀⣀⡤⠀⢀⣼⡶⡿⠷⡿⠋⠀⠀⠀⠙⢻⣿⣿⣿⣿⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣽⣿⡒⠒⠒⠒⠉⢁⣤⡾⠿⠵⠓⠀⠀⡿⠶⣄⠀⠀⢀⣾⣿⣿⡿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣇⣻⣿⣦⣀⠀⣀⣴⠟⠉⠀⢈⣀⣀⣴⡾⠿⠤⠿⣀⣴⣿⣿⣾⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⢀⡟⠻⣷⣿⢿⣿⣿⣿⣥⣠⣴⠞⠉⡃⠀⠀⠀⠀⢀⡤⠂⠙⣿⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡰⠇⠀⠀⠀⣉⡲⣿⢹⣯⣿⣾⡟⣿⣟⡡⠔⠊⠁⠀⠀⠀⢠⠊⠀⠀⠀⠾⡁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡼⠁⢀⠀⠀⡋⠀⠀⣿⢸⣿⣿⣿⡇⣿⡋⠓⠦⣀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣇⠈⢿⠛⠙⢁⣀⣸⣷⣾⡿⠋⠉⡗⣿⡇⠀⠀⣾⢄⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠇⠀⣾⠔⠊⠉⠙⢿⣿⠋⣀⣤⡴⠽⣿⠀⠀⡼⠃⠈⠳⣈⠀⣀⠤⠤⠤⠀⡀⠀⠀⢣⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠟⢠⠞⠁⠀⠱⡄⢱⢶⠋⠉⠁⠀⠀⣀⣻⡆⠸⠁⢀⡴⠒⠿⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⢠⠇⡄⢸⠀⡄⢘⣀⢤⣌⣾⣀⢔⠀⠉⠉⠀⠉⠑⡟⠉⠉⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⢸⡀⣧⠘⢿⣿⠉⡼⢻⠘⣇⠈⠛⠒⠒⠀⠀⠀⠀⢹⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀ ⠀⠀⠀⣷⠊⠳⣼⣣⠔⠁⢸⠀⣿⣗⠲⢄⠀⠀⠀⠀⠀⢸⡇⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀ ⠀⢀⣼⣿⣷⣤⡬⠀⠀⠀⠈⠀⡇⠹⣶⣀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠸⡄⠀⠀⠀⠀⢀⡦⠚⠁⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⡟⣿⣿⣿⡇⠀⠀⠀⠠⠀⣧⠀⠘⠮⣥⣤⠴⢶⡏⠙⠥⠤⠤⠐⠛⠛⠛⠒⣺⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠉⠉⢀⣿⣇⠀⠀⢀⢀⠀⣿⡀⠀⠀⠙⠒⠲⢾⣷⠀⠀⠀⠀⠀⣤⠖⠊⠉⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣽⠀⠀⠀⠘⢿⣿⠦⠀⢈⠏⣿⠅⠁⠀⠀⠀⠈⠉⠀⠘⣇⡄⣀⣋⣁⣀⡤⢴⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⡀⢠⠤⢤⣾⣿⣧⣾⠵⠾⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠒⢿⡻⠦⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⣿⣶⣿⣿⣿⡧⠂⠀⠀⠀⠀⢇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠸⣆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣟⠀⠀⠀⠀⠲⢄⣈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⠁⠀⠀⠀⠀⠀⠈⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠁⠈⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿ ⡀⠀⠀⠀⠀⠀⣠⡼⠟⠛⠉⠉⠉⠉⠑⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿ ⠙⠦⣄⣀⣶⠟⣃⠤⠒⠊⠉⠉⠒⠲⢄⡀⠀⠀⠙⢿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿ ⠀⠀⢀⡟⡣⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⠀⠀⡜⢶⠁⡀⣀⠠⠤⠤⡀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢻⣿⣿⡏⠉⠉⠉⠁⠀ ⠀⠀⣧⠂⡀⠉⠁⠀⠀⠀⣈⡄⠀⠀⠀⠀⢀⠟⠀⠀⠀⠘⣿⣿⣿⠀⠀⠀⠀⠀ ⢀⠀⡇⠀⡈⠶⣾⣶⡞⠛⠉⢰⠀⠀⠀⠀⠚⠒⠤⣀⠀⢠⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠥⣿⣿⠑⡈⠀⠹⣶⠀⣠⣆⡴⠁⠀⠀⠀⠀⠀⠈⣆⡾⠟⠛⠉⠉⠙⠒⠢⢤ ⠀⠀⠀⢻⠛⠁⠀⠀⠈⠁⠀⠁⠀⢀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠋⠓⠂⠀⠀⠀⠀⠀⡀⠄⠋⠀⠀⠀⣰⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⡄⠀⠀⠀⠐⠂⠈⠁⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⠢⣀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⢽⡀⠀⠀⡠⠖⠒⢢⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠐⡒⣒⠖⢊⠉⠈⢱⣄⠀⢻⡔⠉⠀⠀⠀⡘⡸⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⡶⠁⣠⣴⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⣿⣴⣿⠿⠋⣁⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣾⣿⡿⠟⠋⠉⠀⣀⣀⣀⣨⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣴⠂ ⠈⠉⠁⠀⠀⣀⣴⣾⣿⣿⡿⠟⠛⠉⠉⠉⠉⠉⠛⠻⠿⠿⠿⠿⠿⠿⠟⠋⠁⠀ ⠀⠀⠀⢀⣴⣿⣿⣿⡿⠁⠀⢀⣀⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⣿⡿⠁⢀⣴⣿⠋⠉⠉⠉⠉⠛⣿⣿⣶⣤⣤⣤⣤⣶⠖⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⡇⢀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠸⣿⣿⣿⣿⡇⠈⢿⣿⣿⠇⠀⠀⠀⠀⠀⢠⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⣿⣿⣷⡀⠀⠉⠉⠀⠀⠀⠀⠀⢀⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣷⣄⡀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣋⣠⡤⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣀⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢟⠛⠉⠀⠀⠀⠀⣀⣀⣀⣈⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣿⣿⣷⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠋⠁⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠤⣤⣀⣀⣀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣀⡤⠶⠛⢿⣿⣿⣠⠀⠀⣿⠀⠀⠀⠀⠸⢿⣿⠟⡇⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢀⣤⠞⠋⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⣴⠃⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⢷⡀⠀⠀⣸⠁⠠⡄⠀⠀⠀⠘⠲⢤⣤⣤⠤⠚⠁⠀⣼⣿⣿⣿⣿⣿⠿⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠉⠉⠉⢹⢹⣅⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠸⢾⡻⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠖⠉⠁⠀⠀⠉⢙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠑⢶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⣤⣶⣖⠋⠁⢀⣀⣀⡤⠴⠖⠚⠉⠁⢻⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠹⣦⣈⣙⣻⣟⣡⡤⠤⠤⠤⠶⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⣟⠛⠛⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⢸⠀⠀⠈⣷⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣬⣳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢸⣼⠀⠀⠀⣸⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣶⣤⣀⣀⣀⣀⣀⣀⣠⠴⠂⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⠁⠀⠀⠀⠀⠀⠀⠠⠏⠀⠀⣿⣖⠒⠒⠲⠂⠀⠀⠀⠀ ⠒⠂⠀⠐⠶⠶⠶⠶⠤⠤⠤⠤⠤⣤⣄⣀⣀⣀⣀⡾⠃⠀⠀⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣡⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⢹⡶⢦⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⢻⠇⢀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⢨⡇⠠⠀⠙⢳⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⢸⠀⠸⣸⠀⠀⣧⣄⣀⡀⠀⠀⢀⣀⣀⣤⢴⡟⠁⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠻⡆⠀ ⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⣾⠀⠀⣿⠀⣸⠃⠈⠉⠉⠉⠉⠉⠉⠉⢀⡾⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⢳⠀ ⣀⠀⠀⠀⠀⠀⠈⠳⣄⠀⢀⡾⣥⠀⠀⢀⡀⠀⢹⠀⠀⢻⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⡀⠀⢸⡄⠀⠀⠀⢀⣀⣀⣀⣤⣀⣀⣀⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡆ ⠉⠁⠀⠁⠀⠈⠉⠛⠛⠛⢻⠇⠃⠀⠀⣸⠇⠀⠸⡄⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⡨⢧⣤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣰⠏⠀⠀⠀⠀⠀⠀⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠇⠀⣠⡏⠀⠀⠀⢷⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⢀⡴⠛⢁⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⡄⣙⡦⣄⡀⠀⠀⠀⠀⣿

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠙⠛⠛⠛⠛⠻⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⢻⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⣠⣶⣾⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢰⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄⠀ ⠀⠀⣀⣤⣴⣶⣶⣿⡟⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀ ⠀⢰⣿⡟⠋⠉⣹⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⠀ ⠀⢸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀ ⠀⣸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⡿⠿⠿⠛⢻⣿⡇⠀⠀ ⠀⣿⣿⠁⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⢿⣿⡆⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀ ⠀⠸⣿⣧⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀ ⠀⠀⠛⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣰⣿⣿⣷⣶⣶⣶⣶⠶⠀⢠⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⣽⣿⡏⠁⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⢹⣿⡆⠀⠀⠀⣸⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣄⣀⣠⣴⣿⣿⠁⠀⠈⠻⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠴⠶⠶⠶⠶⠶⠶⠶⠶⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⡄⠀⠀⠀ ⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀ ⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀ ⣿⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢹⡄ ⡏⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇ ⣿⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢸⡇ ⢹⡆⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣾⠀ ⠈⢷⡀⢸⡇⠀⢀⣠⣤⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣤⣄⠀⠀⣿⠀⣼⠃⠀ ⠀⠈⢷⣼⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⡾⠃⠀⠀ ⠀⠀⠈⣿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠃⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠘⢿⣿⣿⣿⣿⡿⠃⠀⢠⠀⣄⠀⠀⠙⢿⣿⣿⣿⡿⠏⠀⠀⢘⡇⠀⠀⠀ ⠀⠀⠀⢻⡄⠀⠀⠀⠈⠉⠉⠀⠀⠀⣴⣿⠀⣿⣷⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠈⠻⣄⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣟⠳⣦⡀⠀⠀⠀⠸⣿⡿⠀⢻⣿⡟⠀⠀⠀⠀⣤⡾⢻⡏⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡄⢻⠻⣆⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⢀⡾⢻⠁⢸⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⡆⢹⠒⡦⢤⠤⡤⢤⢤⡤⣤⠤⡔⡿⢁⡇⠀⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡇⠀⢣⢸⠦⣧⣼⣀⡇⢸⢀⣇⣸⣠⡷⢇⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣷⠀⠈⠺⣄⣇⢸⠉⡏⢹⠉⡏⢹⢀⣧⠾⠋⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠈⠉⠙⠓⠚⠚⠋⠉⠁⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⠦⣤⣤⣤⡤⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀ ⠀⠀⠀⢀⣠⠤⠤⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠶⠤⣄⡀⢸⣿⠀⢀ ⠀⢀⡴⡋⠁⠀⠀⠀⠀⠈⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠙⢾⡟⢀⣾ ⢠⡿⡽⠁⠀⠀⠀⠀⠀⠀⣀⣠⣌⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠱⢿⠐⢹ ⣼⠁⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠵⠚⠛⠓⣄⠀⠀⠀⠀⢰⣼⠹⠀ ⢻⣼⠀⠀⠀⠀⣠⡴⠞⠺⠦⣄⠀⠀⠀⠀⠀⠀⢀⣀⡠⠴⠶⠶⠒⠒⠒⠶⠶⠦⠤⣄⣀⠀⠀⠁⠀⠀⢀⡤⠿⠤⣀⠀⢠⣻⠟⠀⠀ ⠈⠻⣿⠤⡀⠀⢿⡀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⡀⠀⠀⠀⠀⠀⢠⡷⠟⠁⠀⠀⠀ ⠀⠀⠈⠛⣶⠊⠉⠉⠃⠀⠀⢀⣴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⣄⡀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠁⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢣⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⢀⣠⣀⣀⣀⣀⣠⣀⣀⣤⣤⣀⣀⡄⠀⠀⠀⠀⢠⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠸⣏⠉⠁⠀⠀⠘⠃⠀⠀⠀⠀⣨⠿⠀⠀⠀⠀⢛⣍⠁⠀⠘⠛⠁⠀⠈⠉⠉⢉⡟⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠙⠒⠤⠤⠄⠠⠠⠤⠴⠛⠁⠀⠀⠀⠀⠀⠀⠈⠙⠢⠤⢄⣀⣀⣀⠤⠖⠋⠀⢠⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⠚⠉⠙⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠨⡷⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣼⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣶⣿⣿⣿⣿⣿⣿⣶⣶⣤⣴⣾⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠈⢨⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢺⢇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠚⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣠⡵⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⣶⠛⠉⠀⠀⠀⠀⠀⠀⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠛⠁⠈⠉⠉⠀⠀⠈⠙⠻⠿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⣀⠀⠀⠀ ⠀⣿⣁⢈⠉⠉⣉⣉⡧⠀⠀⣼⠋⠁⠀⠘⠢⡾⠋⠉⠉⢳⠀ ⠐⠛⢻⣯⠀⢠⠋⠉⠀⠀⢸⣷⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇ ⠀⠀⢸⡿⠀⢸⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀ ⢴⣯⣉⣁⣀⡈⠒⠒⡀⠀⠀⠈⠻⣧⡀⠀⠀⠀⢀⡠⠊⠀⠀ ⠈⠉⠉⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠉⠢⡠⠒⠁⠀⠀⠀⠀ ⢰⣖⠒⡀⠀⢠⣴⠒⡂⢀⣀⣀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠙⣦⠈⢄⡾⠃⡜⣴⠟⢉⢥⡈⢢⢶⣯⢀⠁⠀⢰⡯⠉⡇ ⠀⠀⠈⢿⡬⢁⠌⢠⡿⠁⠆⠈⡇⢸⣿⣇⢸⠀⠀⢸⡇⠀⡇ ⠀⠀⠀⢸⡯⢻⠀⢸⡇⠀⡀⢸⠇⢸⣿⠃⢈⠀⠀⣿⡀⠀⡇ ⠀⠀⠀⣾⠁⠘⠀⢸⣧⠀⠈⠁⢀⠎⣿⠀⢺⠀⣰⡿⠀⢠⠁ ⠀⠀⠀⠛⠒⠃⠀⠈⠛⠳⠶⠖⠋⠀⢿⣄⡀⠉⠁⠀⡠⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⣇⣠⢖⣖⢦⡤⠴⢶⣶⠄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢤⡀⠀⠀⠀⠀⠀⢾⠀⠈⢁⡿⣿⡏⣆⠀⠈⠉⣷⡆⠀⡿⡷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠀⠀⠀⠉⠙⠒⠦⠤⣤⣼⡄⠀⡞⠀⠘⣿⢸⡄⠀⠀⠘⣆⡴⠃⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⡀⠀⠀⡴⠊⠁⡴⠒⠒⠒⠚⠙⢦⡀⢀⣀⣀⣯⣈⣿⢸⠁⠀⠀⠹⡇⢹⠀⣠⣾⣿⣶⠀⢀⣼⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡴⢋⣠⡍⠉⠉⠀⠀⠉⢳⠀⠀⠀⠀⠀⢀⡿⠏⠀⢀⣀⣄⡈⠙⣆⠀⠀⢀⣽⠸⣿⠟⠉⢠⣏⡤⠼⠷⠶⣏⡉⠙⠒⠒⠒⠚⠛⠓⣆⠀⠀⠀⠀⠀⠀⠀ ⠈⠉⠉⣼⡟⢠⠞⠉⠙⠲⣄⡳⣄⠀⠀⡴⠁⠀⠀⠀⢀⣴⣿⢿⡦⠼⢦⡤⠿⠿⠷⣿⣀⡴⢟⣉⣤⣆⡀⠀⠘⠻⣄⠀⣠⠴⢤⡀⠀⢹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠴⠃⠀⠀⠀⠀⠀⠉⠁⠀⣼⡄⠀⠀⠀⠀⣸⣿⡋⠀⠀⠀⣇⠀⠀⠀⠀⣨⠇⠀⠈⢿⣿⣷⠤⠄⠀⠀⣸⡏⠀⠀⡼⠉⠃⠈⢧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠁⠀⠀⠀⠀⣿⣿⣷⠤⣀⣀⣈⣹⣶⣿⣉⠁⠀⠀⢀⣠⣿⣿⡇⠀⠀⠀⢹⡁⠀⡼⠁⡠⠤⢄⠀⠑⠲⣤⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⣿⣿⣿⣄⣼⣯⣿⣿⣿⣿⣿⣿⣻⡟⢉⣿⣿⣿⡇⠀⠀⠀⠀⢧⠺⠓⠋⠀⠀⠈⢧⠀⢢⡈⢿⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⢣⣀⠹⣶⠿⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⡼⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⢹⡿⠿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣤⠞⠁⠀⠀⢀⡤⠞⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢻⣿⣿⡟⢻⣿⣯⣀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⣩⣄⢸⣿⣿⠇⠀⣿⡏⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣅⣈⣿⣡⣿⡤⠤⠞⠁⣨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄⠀⠀⠀⠀⠀⠀⢀⣏⢀⢀⣀⣀⣀⣀⡤⠴⠚⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠓⠦⢤⣤⠤⢴⣿⣭⣭⣭⣿⣛⣉⣀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⡿⠀⠀⠀⢹⡍⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⣙⠆⠀⠀⢀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⢀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠥⣄⣀⣈⣛⡲⠖⠒⢲⣯⣍⠓⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠦⣄⣀⣈⡷⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠿⠛⠉⠉⠉⠉⠉⠙⠻⢿⣦⡀⠀⠀⢀⣴⡾⠿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⢀⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣠⣾⠑⣄⠀⠀⠈⠛⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣦⡀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠀⢹⣇⠀⠀⠀⠀⠙⠷⣶⣶⣤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⣠⣶⠿⠋⠀⢀⣄⠈⠙⢿⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⠀⠀ ⠀⠀⠀⣴⣿⠟⠛⠉⠁⠀⠀⠀⢸⣿⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀ ⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇ ⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇ ⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠿⣿⣶⡀⠀⣿⣷⡀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⣴⣟⠿⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠻⣆⠈⢿⣷⠀⢿⣿⣿⡄⠀⠀⠀⠀⣠⠞⠁⠀⠀ ⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⣼⡟⠛⣷⡄⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢹⡇⠀⣿⡇⠈⣿⣿⣿⣦⣀⣤⠞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢠⣿⡇⠀⢘⣷⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣾⡟⠀⣿⡇⠀⠈⣿⡍⠉⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢿⣧⡀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠘⣿⣿⣦⣼⣿⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠃⢠⣿⠁⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⢠⣿⠀⠀⠀⢿⣿⣿⣿⠏⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣅⣴⡿⣁⡀⣠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⣠⣾⣿⣷⣄⠀⠈⢿⣿⣯⣤⡾⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠈⠻⣯⣀⣤⠶⠦⢤⣤⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁⠀⠙⠻⣷⣦⣄⠉⠉⠉⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠘⣿⠁⠀⠀⠀⠈⠻⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠶⠬⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠉⠁⠀⠉⢻⡇⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠈⢻⣇⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣦⣤⣤⣴⣿⠇⠀⠀⢀⣴⣿⠃⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠸⣿⣦⣀⠀⠀⠀⠀⠈⠻⠟⠛⠛⣩⣉⠉⠀⣀⣠⣴⣿⣿⠋⠀⠀⠀⠀⠀⠞⠻⢦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⣶⣤⣤⣤⡤⠶⠾⠿⠛⠛⠛⠛⠻⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠶⣿⣿⣷⣄⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⠀⠀⠀⠀⢿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣤⣴⣶⣶⣶⣿⣿⡿⠿⣷⣦⡀⠀⠀⠀⠀⢀⡞⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⣤⣴⣾⣿⣿⣿⣿⣿⣿⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠈⢿⣿⣶⣤⣤⣤⡞⠁⠀⠀⠀ ⢀⣄⠀⠀⠀⠀⠀⣾⡄⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⣀⣀⣀⣀⣴⣾⣿⡟⠉⠉⠉⣟⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠉⠀⠀⠀⠀⠀ ⢸⢷⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡟⡿⠀⠀⠀⢰⣿⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠈⣧⠀⠀⠀⠀⢸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⡿⠋⠀⡇⠀⠀⠀⢸⣿⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡄⠈⢷⣄⡀⠀⠸⣿⣿⣆⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣟⣀⡀⢰⠇⠀⠀⠀⢸⣿⣆⠀⠘⠻⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣆⠀⠙⠳⢶⣤⣿⣿⣿⡆⠀⠀⠀⠀⠀⣾⣿⠿⠛⠉⠉⠻⣾⠀⠀⠀⠀⠘⠛⡟⢷⣄⢰⡄⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠻⢶⣤⣄⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣽⣄⣀⠀⢸⣿⡀⢻⣇⠀⠀⢐⣦⠀⢹⡀⢿⣤⣿⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⢿⣿⣿⣿⣿⣿⠟⠛⠿⣿⣿⡿⠿⣿⠿⠻⣿⣿⣿⢿⣷⣾⠿⣿⠋⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠉⠀⡀⠄⡒⠈⠭⠭⠥⠈⠐⣚⣛⠛⠛⠛⡲⢦⣀⠀⠀⠀ ⠀⠀⠀⣰⠃⠀⠔⡨⡢⠑⠈⠉⠁⠉⠄⠀⠀⠀⡲⠀⠀⠐⢄⠀⠈⢷⠀⠀ ⠠⣤⣿⣛⡛⠛⣻⢿⣛⣟⡻⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⢿⣿⣿⣿⡟⢦⡀ ⡴⠛⢡⡶⠒⡖⠦⢭⣿⣮⣱⣎⣿⣿⡿⠏⠀⠙⡿⠷⠿⣾⢿⣿⢭⡞⡐⣷ ⡇⠀⢺⠠⢾⡟⠲⢤⣀⡀⠠⠤⠄⡖⢂⣀⠀⠀⠙⣦⣄⠉⠉⢰⡄⠠⢃⣿ ⠹⣎⡪⠀⠀⢷⡦⣄⣯⡉⠓⠲⣤⣵⣉⣀⡀⠶⠞⠁⣀⣨⣴⢿⣷⠈⣰⠃ ⠀⠈⢳⡀⠀⠀⠻⣌⡟⠛⠷⣶⣧⣄⣀⣹⣏⣉⣻⣉⣉⣧⣸⣷⣿⠀⣿⠀ ⠀⠀⠀⠳⣄⠀⠀⠈⠳⢤⡀⣸⠉⠉⠛⡿⠻⠿⡿⠿⣿⢿⡿⣿⡟⠀⣿⠀ ⠀⠀⠀⠀⠈⠳⣅⡪⢔⡠⢉⡛⠲⠦⠤⠧⣤⣤⣧⡴⠧⠾⠖⠛⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣅⡒⠡⠶⠀⣠⡤⠤⠤⠤⠤⠤⠐⢁⠠⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣄⣀⡀⠀⠉⠉⠉⠉⠀⢀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠒⠒⠚⠉⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢛⣽⣡⡶⠟⠉⣠⠞⠉⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣄⠙⠶⣤⡀⠀⠀⠀⡤⠶ ⠿⠿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢉⡴⠋⡴⠋⠀⣠⡾⠃⠀⠀⢰⣷⠀⢸⣷⡀⠀⠀⢳⣄⠀⠀⠀⠀⠙⢶⣄⡀⠀⠀⠀⠀⠈⠛⢷⣄⠈⠻⣦⠀⠸⠃⠀ ⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⣰⠟⢀⡜⠀⢀⡼⠋⠀⠀⠀⢀⣿⡿⡄⠀⢷⢳⡀⠀⠈⢻⣦⡀⢦⣄⠀⠀⠙⠿⣖⠶⢤⣀⣀⣀⣀⣨⠽⣗⠊⢳⡄⠀⠀ ⣠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⢀⡾⠁⣠⠞⠀⢠⣾⠁⠀⠀⠀⠀⡼⢀⢿⡿⡀⠈⢷⡹⢦⡀⡀⢿⠙⢦⣈⢻⣦⣄⣀⠈⠳⠄⢰⡄⠙⢦⡀⠀⠙⣷⡀⠻⣦⡀ ⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⣠⡟⠁⣰⠋⠀⠀⣞⡟⠀⠀⠀⠀⣼⢣⡟⠀⠻⣷⡜⣎⢻⣮⡳⣽⣌⣧⠀⠉⠳⢷⡈⠙⠛⠳⠦⣄⣱⣄⠀⠳⣄⠀⠘⣿⢆⠙⣇ ⠁⠀⠀⠀⠀⠀⢀⣴⠶⠲⠶⣦⣄⠀⣾⠃⣰⡿⠁⢰⠇⠀⠀⣾⡽⠀⠀⠀⠀⣼⣡⠏⠀⠀⠀⠈⠻⣮⣿⣷⡙⠾⣽⣿⣧⡀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠉⠛⢤⡙⣄⠀⠈⣿⢧⠹ ⡀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠈⠻⣿⡟⣰⣿⠁⢀⡏⠀⠀⢰⢯⠇⠀⠀⢀⡼⣱⠏⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⡄⠀⠉⠉⠁⠀⠀⠀⣀⡤⢶⠟⠀⠀⠀⠀⠀⠱⣌⢧⠀⠘⣏⣧ ⣇⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠘⢿⣷⡏⠀⣸⠀⠀⠀⡾⣿⢸⠀⠀⣼⡼⠃⠀⠀⢠⣤⣄⣀⣀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⣴⠟⣡⠔⠋⣀⣀⠀⠀⠀⠀⣠⠈⢻⣷⠀⢸⠘ ⣿⡄⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢀⣨⣿⠁⢠⡏⠀⠀⢠⣷⡏⡞⠀⢸⡟⠁⠀⠀⠀⠈⠳⠤⣄⣈⠙⠳⣄⡀⠀⠀⠀⠀⠀⠿⠗⣫⣵⣾⣿⣷⠿⠿⢿⣿⣿⡋⠀⠀⢹⡇⠸⣦ ⣿⠇⠀⠀⠀⠀⡇⠀⢠⣶⣤⣄⣶⠟⠉⣽⠀⢸⠇⠀⠀⢸⣹⠇⡇⠀⡾⠀⠀⠀⠀⣠⠤⠤⠤⢤⣍⣙⠓⠚⠃⠀⠀⠀⠀⠀⠠⣾⣿⡿⣛⣉⣀⠀⠀⠀⠈⠙⢿⣷⡾⠗⣇⠀⡿ ⠀⠀⠀⠀⠀⠀⢿⡀⠀⠙⢹⣽⡏⠀⠀⠿⠀⢸⠀⠀⢀⣿⣿⢠⡇⢀⣧⣀⠀⣀⣤⣶⣶⣿⠿⠿⢿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠸⠋⣾⣿⣿⣽⣇⠀⠀⠀⠀⠀⢻⣧⠀⢿⣀⡇ ⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⢹⠀⠀⠀⠀⠀⢸⠀⡠⠞⠛⣿⣸⠁⢸⠈⢉⣿⡿⠛⠁⠀⠀⣠⣾⣶⣶⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠉⡿⠛⠂⠀⠀⠀⠀⠀⣿⠀⢸⣿⠀ ⡀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⢸⠀⠀⠀⠀⠀⠸⠿⠁⠀⠀⠸⣿⡇⣾⣿⣿⠏⠀⠀⠀⠀⢸⣿⣿⠛⣾⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣛⣻⡿⠁⠀⠀⠀⠀⢀⡟⠀⢸⣿⠀ ⠻⣦⣀⠀⠀⠀⠀⠀⣹⣦⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⣿⣿⡿⠀⠀⠀⠀⠀⠸⣿⣿⣶⣯⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠠⠎⠀⠀⢸⣿⠀ ⣷⣬⡿⠶⠶⣤⣄⠀⢿⡟⣧⣸⡻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⢿⣷⠀⠀⠀⠀⠀⠀⠙⢷⣴⡾⠟⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠁⠀⠀⠀⠀⠀⠉⠛⢿⣧⡘⢷⣧⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢿⣧⡀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢀⣀⠀⠀⠀⠀⠀⠀⠉⢿⣮⣿⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣙⣿⠟⢻⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠞ ⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠘⢿⣧⣀⠈⠳⡄⠀⠀⠀⠀⣀⣀⡀⠀⠀⠘⣿⣿⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀ ⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆⠀⠙⢦⡀⢠⡾⣿⣭⢿⠟⢶⣤⡹⣿⠴⠇⠀⠀⠀⠀⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣏⡇⠀ ⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⡈⣿⣧⠀⠀⠁⣏⠙⢮⠻⣷⡅⠈⢳⠙⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⢀⣤⡆⡇⣿⡟⣦⡀⠀⢳⡁⢷⣄⠘⠋⠂⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⢻⡏⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣶⣿⢻⠇⢃⣿⣇⠈⠛⢦⣄⡓⠈⠻⣷⣄⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡇⣟⠷⠖⠁ ⣧⠀⠀⠀⠀⣀⣤⣾⣿⡿⣿⠏⢾⢘⣾⠛⠻⣆⠀⠀⣽⢻⠻⠷⣶⣭⣄⣀⣀⣰⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠿⢿⣿⡇⡿⠀⠀⠀ ⠙⢿⡄⢀⣾⠻⡜⣟⡜⠀⢻⣆⣬⠞⠃⠀⠀⢹⣧⠀⣿⢸⡄⠀⠘⣯⢹⣿⣿⣿⡿⡏⠉⠉⠙⣿⣷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⠟⠀⠀⠀⢸⠇⠛⠁⠀⠀⠘ ⠀⢘⣿⣾⢩⢧⠱⠘⣱⣶⠛⠉⠀⠀⠀⠀⠀⠀⣿⣤⣿⠘⡇⠀⠀⠈⢧⣽⣿⣿⡅⠹⡄⠀⠀⣿⣿⢿⣝⠿⠷⡦⣤⣶⣶⣶⣶⢶⡾⣿⣻⣿⣿⡇⠀⠀⠀⣠⡞⣀⡴⠀⠀⠀⠀ ⡄⠈⠋⣿⣆⠈⣳⠞⠉⠀⠀⣠⢶⠀⠀⠀⢀⣴⣿⠃⢹⣆⡇⠀⠀⠀⠀⠙⢻⣿⣇⠀⠙⠷⣄⡈⠻⣦⡙⠳⣤⣀⠀⠈⢻⣷⡺⢷⣚⡏⠉⠿⣿⣷⣀⠶⠾⢛⡿⠹⡇⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⠇⠀⠀⢠⠞⠁⣼⢀⣤⣾⡿⠋⠁⠀⢸⠹⣽⠀⠀⠀⠀⠀⠀⠈⠛⠶⢤⣤⣀⣙⣦⣤⠟⠓⠲⠮⢭⣛⣒⣛⢷⣔⣊⣓⣠⠴⠟⠁⠀⠀⢀⡼⠁⣸⣷⠀⢠⡀⠀ ⣤⣶⣿⣿⣾⣿⠀⠀⢀⡞⠀⣰⡿⣟⠋⡿⣷⣄⠀⠀⠈⣧⢻⣧⠀⠀⠀⠀⠀⠀⠘⢦⣀⣒⣲⡾⠟⠙⢳⡀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⢀⣿⡜⣦⠸⣷⡀ ⣶⣻⣿⣿⣿⣿⣆⡀⣼⡷⠛⢹⣇⢹⡆⠹⣞⣟⣦⠀⠀⠸⣎⢻⣆⠀⠀⠀⠀⠀⠀⠀⠙⠻⣧⣄⣀⠀⠀⢻⡒⠦⣤⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢸⡁⢀⣾⣿⣿⣿⣧⡙⣿ ⣿⣻⠝⠚⠁⠀⠉⠉⠁⠀⢀⣾⣿⢈⣿⠀⣌⢮⡋⠀⠀⠀⠙⣷⡽⣦⠀⢠⣄⠀⠀⠀⠀⠈⠑⠚⠯⣭⣉⣽⠃⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⢸⣧⣿⣿⣿⣿⣿⣿⣿⠞ ⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡷⠋⣸⠏⠀⠈⢳⣿⡄⠀⠀⠀⣿⣿⣾⣷⣄⠹⢿⣶⣶⣤⣤⣤⠴⠶⣻⣷⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣿⣶⣿⣿⣿⣿⣿⡦ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣃⣤⢞⣣⢴⠃⠀⠀⠙⠃⠀⠀⠀⣼⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⡧⢤⣀⣸⣟⣛⡷⢶⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⡴⢇⣀⣿⣿⣿⠿⢿⣿⣿⣿ ⠀⠀⠀⠀⠀⢀⣠⡴⢿⣻⣩⣞⣑⣚⣡⠔⣀⠀⠀⠀⠀⠀⢠⣿⡃⢋⢻⢿⣿⣻⣿⣷⣌⢻⡇⠀⠀⠀⠉⠻⣟⣷⠔⢿⣿⣿⠿⠟⠛⠙⣯⠙⠛⠛⠋⠙⠁⢹⡿⠿⠿⠛⠉⠉⣻

⠀⠈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀ ⢀⠀⠈⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀ ⠠⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀ ⣾⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⢛⣿⣯⣿⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠛⢿⣿⡆⠀⠀ ⠀⠀⠀⡀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠟⣿⣿⣿⡿⠀⠀⣋⡼⠟⠛⠒⠚⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠈⠛⠂⠀ ⠀⠀⠂⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⠏⢠⣿⢿⣿⠁⠀⠀⢀⣠⣤⣤⣤⣄⣀⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀ ⠀⢈⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⠃⠀⣿⣿⣿⡿⠃⠀⢸⡟⣼⠛⠒⣶⣾⣿⣟⣛⣟⣉⣛⠿⣿⣾⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀ ⣠⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣦⣿⣿⡿⠁⠀⠀⢼⣿⣇⣴⣾⡿⠟⠉⢀⣾⡿⢿⣿⢻⣿⣿⠟⢿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠙⢿⣧⠀⠀⠀ ⣍⢧⣼⣿⠟⢋⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠟⠛⠓⣶⣿⣿⣿⣿⣿⡆⠀⠀⠈⠻⣿⣡⠿⠷⠶⠶⠾⠷⠶⠶⠿⠿⠿⠋⠀⢸⣸⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣷⠀⠀⠙⠂⠀⠀ ⣮⢿⡯⠃⢠⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⣿⣅⠀⠀⢸⣟⣭⣿⢷⡿⠋⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣟⣿⣿⠃⢻⣿⣿⣆⠀⠀⠀⠀⠀ ⠧⢞⢇⣠⣿⣿⣿⢿⣿⣿⣿⣿⡿⣿⠁⠈⠛⠿⠟⠛⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡟⢽⡟⠀⣸⣿⣿⣿⡀⠀⠀⠀⠀ ⠉⠁⢠⠿⠟⠉⢀⣾⣿⣿⣿⣿⣇⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⣿⣿⡿⢻⡇⠟⠁⢰⣿⡇⠈⠻⣇⢀⣀⠀⠠ ⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⢿⣏⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠋⢀⣿⡟⢠⣾⠃⣠⣤⣿⣿⣿⠚⠛⠙⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⠟⠋⠁⠘⣿⠢⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡄⠰⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⢸⣏⣦⣻⣿⢻⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠻⣦⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⣉⣵⣿⣿⠈⢻⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡏⠀⠈⢿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⡤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⢿⣿⡇⠀⠀⠘⢷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠖⠋⠉⣁⣠⣤⣤⣤⣤⠄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣴⡿⣿⣿⣿⡿⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⣿⣿⣿⡇⠒⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⢠⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⠁⠀⢁⣾⠏⢸⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠇⠀⢄⣀⣾⣧⣶⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠋⢸⣿⣿⣿⡻⣦⣀⡀⠀⠀⠀⠀⣀⣀⣠⣴⢾⣫⣠⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⣾⣇⣀⣉⣙⣻⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣴⡿⠫⠉⠛⣟⠓⠶⣦⢤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⡀⠈⠀⠁⠄⢄⢀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠐⠈⡂⠀⠀⢀⣀⣃⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⡠⠐⢀⢢⠀⠒⡈⠠⠄⠠⣉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠐⠆⠈⠁⢛⠂⠤⠁⢀⠁⠄⠠⠌ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣤⣤⣄⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢐⠀⠀⠀⠅⡁⣐⡀⡀⠤⡂⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡴⡾⠛⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⠜⠠⠉⢀⠀⠀⢄⢉⠈⠠⠉⠀⡰⢁⠠⠄ ⣀⣤⣤⣤⢤⣤⣤⠾⠉⠉⢀⠈⣂⠉⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠅⠁⠀⡄⡁⠈⢄⠀⠥⠿⠆⡠⠛⠀⠀⡤⢿⡃

⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀ ⢸⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⡏ ⢸⣟⣻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⡇ ⠘⣿⣽⣾⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⢳⣟⡿⠿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣯⣽⣿⡏⠀ ⠀⠸⣿⡿⠿⢿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣻⣿⣿⣿⣿⡛⣿⣿⡇⠀ ⠀⠀⣿⣟⣿⣿⣿⣽⣿⣿⣿⣿⣾⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⠀⠀ ⠀⠀⠸⣿⣧⣬⣽⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣤⣴⣶⣶⣶⣶⣶⣴⣶⣶⣾⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣾⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠸⣿⣿⣿⣿⣯⣿⣿⣯⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡟⠀⠀⠀ ⠀⠀⠀⠀⡯⣷⣏⣿⣿⣿⣿⣿⣽⣿⣾⣿⣿⣿⣿⣿⣷⣿⣿⡟⠿⠏⢹⠿⣿⢿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⣷⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢩⡇⢠⣿⡇⠀⠀⣿⠀⢸⡟⣿⢋⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣍⣿⣿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣷⣿⣏⣿⡇⣯⣿⠻⠘⠁⠈⠀⠀⠀⠀⠈⠀⠘⢧⣿⣾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⣧⣿⣿⢿⡿⣝⣿⣿⡍⢿⡓⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡟⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⢇⣸⡿⠒⠶⢯⣒⠉⠹⠿⣿⣿⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡏⠛⣹⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣯⣼⡁⣠⣴⣶⡾⣿⣿⣿⣧⡹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢉⣿⣿⣿⣿⣿⣷⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⣾⣽⢿⡟⠛⢿⣿⣀⢲⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣻⣿⣿⣿⣿⣄⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀ ⠀⢰⣿⡧⣶⣦⣀⡀⢻⣿⣷⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⣛⠋⠞⠋⠐⢻⣿⣿⣿⣿⣾⣿⢟⣋⣠⣼⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀ ⠀⣼⢸⡷⣿⣿⣿⣿⣿⣿⣬⣉⣽⡏⠀⠀⠀⠀⡀⢀⣀⡆⡀⠀⣠⣾⣷⣯⠁⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀ ⢸⣧⣼⣇⣙⣿⣿⣿⣿⡿⠟⢻⡿⠂⠀⠀⠀⠀⢻⣧⢿⣿⣿⠾⣷⣾⣿⡷⢐⣶⠶⠟⢁⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀ ⢸⠉⠽⠒⣚⠛⣻⣿⣿⣷⣶⡞⠁⠀⠀⠀⠀⠀⢈⣻⡷⢹⡇⢀⣿⣿⣿⠖⠋⠈⠙⠛⠲⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀ ⢸⣖⠂⣰⣿⣿⠟⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣙⣿⣿⢾⣯⡀⠀⠀⠀⢀⣀⡉⠉⠙⠻⣿⣿⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠘⢿⣿⢿⣛⣁⡀⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡤⡈⣿⠀⠀⠃⠀⠀⠀⠀⠈⠉⠛⠶⣤⣬⣙⠿⠿⠿⣶⣼⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠘⠿⠯⠝⠲⠯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢵⣾⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠤⣙⣻⠿⣓⣾⢿⣉⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀ ⠀⠀⠀⢦⡀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣽⣿⣿⣿⠛⠛⠿⢿⣦⣀⠀⠀⠂⠀⠀⠀⠄⠀⠀⠀⠈⠻⠿⣿⣯⠟⢷⣦⣭⠙⠛⣿⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠹⣶⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠛⠋⠀⠀⢀⠄⠂⠹⠻⢷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⢀⣽⠶⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⡀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠌⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠤⠞⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠤⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠤⠤⠖⠒⠒⠒⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀ ⠀⠀⠀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⢿⢤⣄⠀ ⠀⣴⠦⣿⠁⠙⡆⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠻⢿⡸⡄⠀⠘⡄⢹⡀ ⠀⡟⠀⡏⠀⢀⣇⡿⠉⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠈⢿⣧⠀⠀⢣⠈⡇ ⢰⡇⢰⠀⠀⢼⡿⠁⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠈⢿⠀⠀⢸⠀⡇ ⢸⡇⢸⠀⠀⠘⡇⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⡀⠀⠈⠀⣇ ⠀⡇⢸⠀⠀⢸⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⢣⠀⠀⠇⣿ ⠀⣿⢸⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⣠⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠯⠉⢳⡄⠀⣀⡴⠛⠀⠀⡸⠀⣸⡴⠏ ⠀⠙⢮⣧⠀⢧⠀⠀⠉⢷⣤⣀⢸⡁⠀⠉⡙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠤⢄⣼⣧⣾⣿⠃⠀⠀⠀⡇⣰⠏⠀⠀ ⠀⠀⠀⠙⣦⠘⡄⠀⠀⠈⣿⣿⣿⡗⠾⠥⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠈⠉⣸⣿⣿⠛⠀⠀⠀⢸⢠⡏⠀⠀⠀ ⠀⠀⠀⠀⠸⣆⢣⠀⠀⠀⠙⣿⣿⣿⡄⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢀⣀⣀⣤⡿⢻⡏⠀⠀⠀⠀⡜⣸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣼⡄⠀⠀⠀⠀⢿⣍⠻⡖⠶⠊⠈⢧⣄⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠈⢹⣃⣴⠟⠁⠀⠀⠀⢠⣷⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠈⠻⢗⢿⠀⠀⠀⠀⢻⣷⣄⠀⠀⠀⠀⣾⢻⠀⠀⠀⠀⢸⠁⠁⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠸⠟⢻⠀⠀⠀⠀⡏⠋⠃⠀⠀⠀⡜⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⠀⠀⠀⠙⠀⠀⠀⠀⠀⢸⡆⠀⠀⢸⢇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠐⠃⢳⠀⠀⡇⠈⠁⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⢸⣷⢸⣿⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⠀⠀⠀⠀⠀⠀⣀⠜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⢄⣀⠀⠀⣾⣿⠀⣿⡄⣀⡠⠔⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠙⠃⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣿⣿⠿⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠉⠉⠙⠛⠛⠿⢿⣿⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣇⠀⠀⠀ ⠀⠀⢰⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠀⠀ ⠀⢀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⠀ ⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⣿⣿⡄ ⢰⣿⡿⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⣀⠀⠀⠀⠀⡇⠀⠀⢸⣿⣇ ⢸⣿⡇⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⡇⠀⠀⠈⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠛⠛⠁⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⣿⣿ ⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⢀⣿⣿ ⢸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⢸⣿⡏ ⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⢀⣿⣿⠃ ⠀⠘⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀ ⠀⠀⠹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⠀⠀ ⠀⠀⠀⠹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀ ⠀⠀⠀⠀⠙⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣾⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⢿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣬⣿⣿⡿⠿⠛⠻⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡟⣿⣿⡿⠁⠀⠀⠀⠀⠀⠙⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠁⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠻⠞⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠳⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠙⠰⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣌⢹⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⡄⠀⣀⣤⠴⠶⠖⠒⠒⠒⢶⣦⣀⠀⠀⠀⠸⣎⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⣷⣶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⢹⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⢸⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠈⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣸⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⢺⣿⣿⣿⠃⡀⠰⠃⢸⣶⣦⣴⡤⠀⠀⠀⠀⡆⠘⣸⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⠀⠙⠋⠉⠁⠁⠀⠐⠛⠿⠛⠋⡁⢀⣠⡶⠄⠁⠀⢻⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠄⠐⠀⠈⢧⣠⡴⠀⣀⠀⠈⣳⡿⠿⢭⣁⡆⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣷⣀⣿⣷⣼⣿⣮⣶⣶⣶⡾⣯⣗⢦⣾⠟⠁⠀⠀⣺⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⣯⡽⢿⣿⣄⣿⣉⣻⣏⣻⣼⠿⠛⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣄⠀⠀⠉⣿⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀⢀⣼⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⢿⠁⠀⠀⠠⠿⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⢿⡄⣽⣷⣤⣀⠀⠀ ⠀⠀⣴⠟⣿⣿⡇⠰⣶⣀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⢀⣼⠿⣯⡀⡄⠙⣷⣄ ⢀⣼⣿⣼⠋⢸⣿⣀⣿⣿⠆⠀⠀⢀⣤⡿⠋⠀⢀⣰⣿⣿⣾⡿⣦⣙⣾⣷⣿ ⠘⠏⠛⠁⠀⢸⣿⣿⣿⣿⣦⣤⡖⠛⠁⠀⠀⣰⣿⣿⣿⡟⠉⠀⠈⢿⣿⠿⠃ ⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡿⠛⠋⠉⢉⣭⡽⢾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠻⣿⣿⣻⣿⣦⣤⣼⡟⠉⠂⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⢦⡒⣿⣿⠛⠿⠿⠻⣿⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⣎⣻⣿⣿⠆⠀⠀⠀⢻⡆⠠⠈⠁⢻⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠛⠿⠦⠴⠞⠛⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀

⠰⣖⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⣧⣽⠟⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⡇⠀⠀⠙⢷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠙⠻⣦⣄⠀⠀⠀⠀⠸⣧⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣷⡀⣠⣤⣤⣽⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⣀⣤⣤⣽⠷⠶⠶⠶⠶⠿⠀⠀⠈⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢷⣏⢀⣈⣙⣷⣝⢿⣆⠀⠀⠀⠀⠀⠀⠀⢈⣿⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣾⡄⠈⠻⣿⣷⡙⢷⣄⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠙⢿⣿⣆⠙⢷⣄⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠻⣿⣦⠈⠻⣧⠀⠀⠀⠀⠀⣠⡄⢀⣾⠏⠈⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⢻⡹⣷⡀⠙⣷⡀⠀⠀⠀⠛⢁⡾⠃⠀⠀⣼⠇⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣾⠀⠙⣷⡀⠈⢻⣄⠀⠀⠀⢸⣿⣿⣷⡾⠋⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠘⢷⡀⠀⠙⣷⡀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⣬⠇⠀⠀⢸⢿⣄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠛⠲⣦⣠⣿⡀⠙⢦⡀⠀⠀⠀⣠⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⢀⣿⡉⠱⣝⢆⠀⠻⣆⣰⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⣦⣴⡶⠶⠟⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣀⣀⣴⠟⠙⢿⣄⠘⢯⡳⢠⡿⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⣿⠀⠀⠀⠹⣧⣀⣱⣿⣇⠀⣀⣠⣞⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⢿⣦⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠈⢻⣤⠀⠉⠛⠉⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠘⣿⣄⢹⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⣿⠃⢀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⣰⣟⣤⠿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠙⢷⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢦⣤⣄⣀⡀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣭⡙⡶⣤⡀⠀⢨⢿⣄⠀⠀⠀⠀⠀⢹⣧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃⠈⠙⠷⠞⠀⠙⢷⣄⠀⠀⣠⣾⠋⠻⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣋⠙⢮⠳⡀⠹⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠳⣝⢆⢹⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠮⣯⣷⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⢦⡄⠀⠀⠀⠀⣀⣀⡀⠀⣼⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠟⠁⢸⡇⠀⠀⢠⣾⣿⠏⠙⠶⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⣴⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⢚⣻⣞⣿⡟⣿⡞⡟⢺⢻⢻⣿⢻⣿⣿⣿⣿⣿⣿⠿⢿⣿⣻⣽⠿⣿⠛⠛⠛⠛⠿⠦⣭⣽⣿⣿⣿⣿⣿⣻⣿⣻⣿⣿⣞⣟⣻⣟⣿⣿ ⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⠿⢿⣿⣿⢿⣿⢿⠿⢿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠒⠀⢸⢿⢸⢸⡞⠐⠰⣤⣿⠿⠁⠀⠀⠀⠀⠀⠀⣠⣤⣠⣦⣤⣤⣤⣀⡄⠀⠀⠀⠀⣀⠀⣀⡘⣟⠉⠈⠛⠃⠛⣇⠩⠆⡈⢺⣿⢀⣿ ⠀⠀⠘⠘⠘⢘⠃⠀⢠⣿⣯⢆⣠⠀⠀⠀⢀⡀⣰⣿⠿⠛⠿⠛⠛⠛⠟⣿⠀⣶⡗⣀⣽⣧⠸⣿⣿⡀⠀⠀⠀⠀⠱⣷⣶⣶⣾⣥⣤⣿ ⣧⠠⢤⣼⡤⣼⣾⡼⠯⣽⡿⣾⡟⡼⢀⣼⣿⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣿⣿⣳⣿⡄⣿⣿⣷⣯⣤⡤⣴⣧⣬⣭⣿⣿⣿⣿⣿ ⡆⠃⡀⢩⣿⠯⠍⠈⠉⣿⣿⣿⣹⣛⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⣽⣿⣿⠉⣉⣊⠭⢹⠻⠛⢹⣯⣿⣿⣿ ⠁⠉⠉⠃⠂⠠⠠⣄⡈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⣼⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠙⣿⣺⢏⡉⢋⡙ ⠀⠀⠀⠀⠀⠠⠤⠔⢲⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⡻⢿⣶⠀⠰⣾⠟⢻⠟⣿⡿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠒⠶⣶⠒⡿⣺⣽⣺⣝⣻ ⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⠘⣿⣙⣿⣷⣧⣀⠀⠀⠈⠁⣠⢴⣶⣿⣧⣈⣹⣿⣿⣿⣿⣿⣷⣤⠀⠀⣿⠀⠿⣒⠭⣺⢍⡒ ⠉⠀⠀⠀⠀⠀⠀⣡⣿⣿⣿⣿⣿⣿⡎⠁⠉⢹⣿⣿⠛⠋⠀⠀⠀⠺⠟⠋⢹⣿⣯⠉⠁⢿⣿⣿⣿⣿⡛⠿⠟⠙⠉⢙⡏⠀⠉⠒⠈⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⢋⣧⠀⠀⠀⠈⣀⣈⢀⡠⠦⢤⡀⢀⣀⠒⠊⢀⣀⣤⣴⠻⢿⣿⣿⠿⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⣲ ⠀⠀⠀⠀⠀⠀⠀⠾⠟⢹⣿⣿⣿⢀⣿⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠉⠓⠚⠛⠉⠉⠉⢀⣿⡰⣾⣿⣇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣆⢻⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣽⣿⢣⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⢸⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⢿⣿⣿⣿⣦⡀⠀⠀⠀⠒⠒⠒⠀⠀⠲⠀⠀⠀⢀⣴⣿⣿⣿⣿⢾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⢿⣿⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢸⠏⡧⢸⡟⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠙⢦⣀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣿⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡇⠀⡀⠀⠘⣟⠓⠒⠒⠋⠁⠀⣠⠄⣿⠛⠛⢮⡅⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋⡇⠀⢰⡆⠀⢸⠀⠀⠀⡤⠀⠀⡯⠀⣿⣸⠁⠈⢷⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠓⢦⡧⠀⠘⡇⠀⢸⡀⠀⠐⠃⠀⢰⡇⠀⢿⠏⠀⠀⠀⠙⠿⣿⣦⣄⣀⣀⡀⠀⠀⠀⢀⠀⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⣾⣿⠏⠀⠀⠙⢦⡀⢿⠀⠈⢳⡄⠀⠀⠀⣸⢀⡰⠋⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣯⣭⣟⣛⡛⠛⠛⠛ ⣤⣤⡶⠶⠶⣛⣻⣿⣿⣿⠟⠉⣸⡟⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⡟⣾⠇⠈⠻⣟⠿⣿⣿⣿⣶⣶ ⠀⠀⠰⣶⣿⡿⠟⢉⡼⠋⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣄⣠⢖⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡧⣿⠀⠀⠀⠘⢦⡀⠀⠉⠙⠈ ⣠⡶⣟⣟⣋⣀⡴⠋⠀⠀⠀⠀⢸⣽⡄⠀⠀⠀⠀⠀⠀⠀⢀⣠⡼⣻⠏⠳⣦⠀⠀⠀⠀⠀⠀⠀⢠⣿⣱⡏⠀⠀⠀⠀⠀⠹⣦⣀⡀⠀

⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡞⡛⢦⡘⣷⢿⠆⠀⢀⡇⡀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠳⠿⠟⢧⡙⠀⠀⠀⣼⠷⣦⣄⠘⣷⠶⠆⠀⣴⠶⢦⣄⣠⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡿⠛⠶⠆⠀⠁⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⡤⢤⣤⡀⠀⠀⠀⠀⠀⢀⡴⠶⠛⠛⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡼⡿⠁⠀⠀⠈⠻⣶⠒⠒⠛⢳⣿⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣧⠃⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣽⠷⠀⠀⢶⡤⠀⠀⠀⠀⠀⠀⠀⠀⢶⠾⠂⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⠃⠀⠀⠀⠀⡀⠀⠀⢀⣀⡀⠀⢀⣀⣸⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀ ⠀⢀⡾⣧⡀⠀⠀⠀⠙⠛⠛⢿⡿⢿⣟⡋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀ ⠀⣼⠁⠈⠻⠦⢀⣠⡴⠊⠉⠁⠀⠀⠀⠈⠉⠒⠢⣦⡄⠀⠀⠀⠀⠀⣸⣧⣀⠀⠀ ⢀⣽⣄⠀⠀⠀⠈⣻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣄⣀⣀⣤⡶⠋⠀⠙⢷⡄ ⣼⠃⠙⠛⠶⢶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠈⣷ ⠹⣦⡀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣠⡼⠋ ⠠⠼⠿⠓⠒⠚⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠓⠚⠛⠳⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠒⠒⠛⠉⠉⠉⠉⠙⠛⠒⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡒⣲⡄⠀⠀⠀⠀⠀⡸⠁⠀⣀⡤⠖⠒⠒⢦⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⡙⠋⠀⠀⠀⠀⠀⢰⠃⢀⠞⢁⣤⣶⣶⣶⣦⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣋⠁⠀⠀⠀⠀⠀⠀⣾⢀⡎⣰⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢳⡀⠀⠀⠀⠀⠀⢸⣼⢰⣿⣿⣿⣟⣁⣹⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡼⢁⣀⠀⠀⠀⠀⠀⢿⣸⣿⣿⣿⣿⣁⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣈⠋⠟⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀ ⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⣄⣤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀ ⠻⣯⡉⠉⠙⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠀⠀⠀ ⠀⠈⢻⣄⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢤⣀⣀⣀⣀⣠⣤⠴⠞⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⡄⠀⠀⠀⠘⣧⡀⠀⠀⣀⣤⡴⠶⠲⡶⠶⠶⢶⣤⡿⠀⠀⠀⠀⠠⠤⣀⣀⣀⣀⣠⣤⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⡀⠀⠀⠀⠈⢷⡶⠟⡿⠦⠤⠤⡞⠁⢴⣉⡽⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣷⠀⠀⢀⡴⢯⠑⠺⡧⣤⠀⠺⣭⡗⠀⢵⡏⣲⠄⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⢃⢀⡞⢁⣼⠁⠀⠉⠁⠀⠀⠀⠛⠃⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣇⢘⣿⡍⠉⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⢶⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⣆⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠴⢋⡟⠀⠀⠸⣏⣹⡿⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡏⠀⠀⠀⠈⢷⡦⢤⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢠⠧⠒⠉⠁⣠⠏⠀⠀⢸⣉⡿⠋⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⢹⡦⣬⠇⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⣀⣤⠾⣧⡀⠀⠀⢀⠟⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⡇⡼⠀⠀⠀⠀⠀⠀⠀⠀⢠⡗⠛⠉⠀⠀⠈⠻⣦⣀⡏⠀⢀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣄⣠⠖⣆⢠⠖⢶⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠙⠛⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠻⠶⠾⠿⠖⠋⢹⡁⠀⠀⠀⢀⡤⣀⣰⠛⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣤⣠⣏⣀⣸⣧⣶⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠤⠤⠖⠒⠒⠒⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠞⡉⠉⠀⠀⠀⠀⠀⠀⠀⢀⡤⠆⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣾⠞⠉⠙⠲⠤⡄⠀⠀⠀⠘⠧⠴⠒⠚⠁⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡴⠧⣄⠀⠀⠀⢰⣧⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀ ⣾⠀⠀⢸⠀⠀⣀⡿⠤⢤⣀⡴⠲⢤⣤⡤⠒⠢⣤⢤⡴⠒⠲⢄⢑⣄⠀⠀⠀⠀⠀ ⠈⠓⠒⠚⠀⡼⠂⠁⠀⠀⠉⠁⠀⠀⠉⠁⠀⠀⠈⠈⠁⠀⠀⠈⠉⠟⠛⠒⠢⡀⠀ ⠀⠀⠀⠀⠘⢇⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⢀⠀⠀⣉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠹⡆ ⠀⠀⠀⠀⠀⠸⣠⣤⢤⣤⣦⣴⣾⣿⡟⠋⠙⠛⠋⠈⠛⠉⠢⣄⣀⠀⡀⠀⠀⣠⠃ ⠀⠀⠀⠀⠀⢰⡟⠐⠂⢹⣿⣿⣿⣿⠁⣠⣶⠢⣴⠀⠀⠀⠀⢉⣙⠛⢿⣶⠉⠀⠀ ⠀⠀⠀⠀⠀⣾⡇⠀⠀⢺⣿⣿⣿⡿⣸⣿⣿⠧⢹⡅⠀⠀⢰⣿⣬⢧⣸⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣷⡀⠖⣿⣿⣿⣿⡇⠻⢿⠟⠁⢸⠁⠀⠀⢸⣿⡾⢸⣿⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣷⣤⣿⣿⣿⣿⡇⠀⠈⠉⠉⠁⠀⠀⠘⠋⠙⠒⠂⢹⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣠⣤⣤⣤⣀⠀⠀⢀⣾⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⢷⣶⢬⣩⠇⠀⣠⣾⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠓⠢⠤⣀⣉⣋⣥⣴⣾⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣿⡿⠋⠀⠙⣏⠉⠛⢿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡦⠔⠲⠤⠇⠀⠀⠀⠀⢠⠏⠀⠀⠈⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⡟⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⣿⣿⠀⢸⣿⣿⣿⣿⠒⠤⠴⠛⠚⠒⠊⡤⠀⠀⠀⠀⠀⡞⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⡏⢀⡞⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⢰⡇⠀⠀⠀ ⠀⠀⠀⢰⣿⣿⣿⠁⡞⠀⠘⣿⣿⣿⣧⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⡟⠀⢷⠀⠀⠈⢿⣿⣿⣧⡀⠀⠀⢸⠃⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⢻⣿⣿⠃⠀⠈⣧⠀⠀⠀⠙⠿⠿⠷⠄⠀⡾⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀ ⠀⠀⠀⠀⠛⡏⠀⠀⠀⣹⣷⣶⣤⡤⠤⢤⣤⣤⣴⠇⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣁⡜⣿⡯⠀⢄⠁⠀⠀⢀⡈⠋⠁⠀⠛⠁⠊⠁⢻⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣧⢀⣀ ⡿⠿⠿⣿⣿⣿⣿⣿⣿⢯⠙⠻⣄⢁⣷⠻⠁⢠⠈⣆⢀⠀⠚⠀⢀⠀⠀⢀⣀⠤⠒⠉⠐⠒⠈⣿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⢉ ⣷⣦⣄⡀⠉⠻⢿⣏⡏⡞⡀⠀⠸⣿⡇⠀⠀⣼⡆⡆⢸⡀⠀⠀⠂⠀⢀⣞⣁⣀⠄⠀⢀⡐⡃⢸⣀⠀⣸⣿⣿⣿⡿⢛⣩⣴⣾⣷⣿⣿ ⣿⣿⣿⣿⣷⣦⣤⣿⠁⠁⠸⡸⡀⠈⢣⣐⡠⢭⣶⡯⠤⢿⣯⠁⠈⠉⣿⡉⠠⣄⣈⣵⣄⠉⡥⠚⠉⠉⠁⠨⡿⣫⣴⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡿⣿⡷⠿⡆⠀⢀⣃⣧⠔⠋⠁⠀⣸⣧⣴⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡷⣜⣆⡀⠀⡠⠀⠏⣿⣿⣿⣿⣿⣿⣿⡿⢛ ⣿⣿⣿⣿⣇⡿⢃⠀⠘⡿⠛⠙⣟⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠝⢷⣆⠀⡸⡾⢻⣿⣿⣿⣿⣿⣿⢞⣭ ⣿⣿⡿⠿⣇⡃⠤⡤⠈⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣦⢻⡉⢿⡟⠛⠛⠭⣙⡿⣶⣿⣿⣦⡀⠀⠈⢹⣿⣿⣿⣿⡿⠛⣙ ⣿⣿⣧⠀⠀⢙⣤⣞⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠿⡇⢻⠙⣷⠻⡀⢣⠀⠀⠀⠀⠉⠻⢿⣿⡟⡑⡄⢐⡿⣿⣿⣿⣫⣴⣿⣿ ⠶⠶⢿⣆⣠⡿⢿⣿⣿⣿⡿⢿⣿⣿⠃⠀⣿⡌⠉⠀⠀⠀⢀⣏⣼⣄⣠⣧⡇⢸⠀⠀⠀⠀⠀⠀⠄⠙⢿⡇⣰⡼⢄⣿⡿⢟⣫⣭⣴⣾ ⣿⣿⣶⡞⡿⢁⣿⡟⡿⠋⠀⣾⣿⡇⠀⢀⣿⣷⡄⠐⠀⢀⣼⣿⣿⢻⣿⣿⣿⢿⣦⣔⣶⣶⣤⠤⢄⣈⠲⣿⠙⢢⠾⠷⠾⠿⣿⣿⣿⣾ ⣿⣿⣿⣅⣁⣾⠏⢰⠁⠀⢰⣿⣿⡇⠀⣾⣸⣷⣿⣦⣼⣿⣿⣿⣿⣾⣿⣿⣿⣼⣿⣿⣧⠀⠉⠉⠒⣺⡷⢼⣿⣯⣀⡀⠐⠀⠀⠈⠙⣿ ⠀⢠⣤⣠⣿⠟⠀⣼⠀⠀⣼⣿⣿⣿⣦⣿⣇⢯⣿⣿⣿⣿⣿⣷⢻⣷⣿⣿⣿⣿⣿⣿⡟⣧⡀⣦⣸⣻⣧⢸⣧⠈⢻⣿⣳⣤⡀⠀⠀⠈ ⠀⢸⡿⠁⣸⢀⣼⣿⣶⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⣻⣿⣯⣼⣿⣿⣿⣿⣿⣿⡏⡌⡻⡆⢎⢿⣿⣷⣤⣀⠀⡀ ⣀⣼⣦⣄⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⡿⠿⢛⣟⠻⣝⣿⣿⣿⣿⣿⣧⠙⣏⢹⡘⡎⢿⣿⣿⣿⣿⣮ ⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⡆⠻⣿⣿⣿⣿⣿⣿⣿⡟⢘⡿⢻⠀⢈⢉⣿⣰⡿⣿⣿⣿⣿⣿⣿⡇⠻⢸⡇⠸⣯⢿⣿⣿⣿⠟ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⠚⠛⠋⣿⠁⢸⣿⣿⣿⠿⣿⣿⠁⢀⣾⡍⡀⢻⠋⢇⠹⠥⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⣿⡿⢿⠉⢱⠆⢼⡇⠀⠙⠈⠿⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⣹⡇⠀⢀⣿⢻⣨⣿⡿⡁⠁⠈⣆⠘⣆⠀⠀ ⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⠧⢼⣯⠴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣾⣿⣿⢸⡟⠛⢲⡇⠀⠀⠘⡄⠻⡄⠀ ⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣏⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣾⣿⢲⣬⡟⠀⠀⠀⢳⠀⠸⡀ ⣭⠭⠿⣿⠀⣿⡿⢸⣿⣿⣿⡟⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠤⠀⠀⠀⠀⠀⠸⢸⣿⣿⣿⣿⣿⠹⢞⠉⠓⠒⠤⠤⠼⠤⠤⠱ ⣿⣿⣿⡇⠀⢿⡇⢸⣿⣿⣿⣷⠀⠸⢷⡀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⢠⣸⣿⣿⣿⣿⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⣿⣿⡇⠀⠘⡗⢸⣿⣿⣿⣿⡆⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢺⣿⢻⣿⣿⣿⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⣿⡇⠀⠀⢣⢸⣿⣿⣿⣿⡇⠢⡀⠊⣁⣬⠷⠦⣄⣀⠀⠀⠀⠀⠀⠀⢀⣴⣟⠀⣼⣿⠜⣿⣿⣿⡿⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⣇⠀⠀⠘⣿⣿⣿⣿⣗⢧⢀⡶⠋⢁⣠⣴⣴⣟⡟⠉⠓⢲⣦⣤⣾⡿⠉⣭⣭⠉⣹⡇⢹⣿⣿⡇⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣺⣿⣿⠀⠀⠀⢹⣿⣿⣿⣿⠘⣾⣠⣾⣿⣿⣿⣿⣿⢰⣦⠶⣿⢻⣿⣿⣧⡰⠏⢸⢟⡘⣿⠈⣿⣿⡷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⣿⣿⠀⠀⠀⠀⠿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣣⣿⣿⢿⣿⣾⠟⣿⣿⠿⠶⠒⠋⠹⡌⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠈⠱⡀⠈⠙⢆⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠢⢄⠈⠣⡀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⣀⡤⠤⠖⠂⠒⠲⠐⠒⠒⠦⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡘⠦⣄⠀⠀⠀⠉⣲⡤⠒⠉⠁⠀⠀⠀⠀⣠⠔⠊⣁⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⡀⠙⢦⡈⢳⣄⡠⣞⡡⠔⠒⠉⠉⠓⠢⣄⣫⠴⠛⠁⠠⢄⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢍⣒⣤⠽⠾⠛⠋⠁⠀⢀⣠⣤⣶⠄⠀⠙⠣⣤⡀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⠉⢑⠆⠀⢀⡠⠞⠋⠉⠁⡟⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⡉⠒⠦⣀⡠⠞⠁⢀⠐⠉⡴⠀⠀⢀⡾⠀⠀⠀⢆⠀⠀⠀⠘⢷⡀⠀⠀⠀⢇⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡹⠖⠚⣉⣠⠴⠚⠁⢀⡜⡇⠀⣠⣿⠃⠀⠀⠀⢸⡀⠀⠀⠀⡈⢇⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀ ⠀⠀⠐⠢⠶⠾⠷⠒⠒⠫⣡⢀⠞⠀⠀⡞⠀⣇⡴⢹⡏⠀⠀⠀⠀⣘⢧⠰⡀⠀⠱⡘⠂⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⢆⢉⣓⣦⣤⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⡏⠀⠀⣼⢁⡴⢻⠀⣸⠃⠀⠀⠀⢀⣸⡌⣆⠱⡀⠀⠹⡄⠀⠀⠀⠀⠈⠢⢄⣀⡀⠀⢀⡙⢄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠖⠉⣿⠟⡇⠀⢰⣿⣿⠉⣿⣇⢻⢰⡇⠀⠀⢸⡇⠘⣞⣆⢳⣄⠤⠝⣦⠀⠀⠀⠀⠀⠀⠀⢀⡡⠋⠀⠀⠙⠢⣄⣀ ⠀⠀⠀⢀⡠⠊⠁⠀⢸⡏⠀⣇⠀⣼⢿⠹⣀⣿⣿⢿⡟⢹⣆⠀⣸⣇⣤⣼⣿⣿⣿⣦⡀⠈⠳⡄⠒⡲⠴⣶⡾⠍⢢⡤⣤⣤⣤⡤⠚⠉ ⠀⠀⢠⡏⠀⠀⠀⠀⢸⠁⢰⢻⣴⡏⢻⠀⠈⠓⠚⠸⣧⠘⣿⠉⢹⢿⣻⢿⡇⠉⠹⣟⣏⣲⣤⣈⠲⣧⠤⠤⠤⠤⣈⣿⣿⣿⡟⢧⠀⡀ ⠀⠀⠘⣧⠀⠀⠀⠀⠘⢀⡶⠋⢸⡃⠘⡆⠀⠀⠀⠀⠹⠀⠘⣇⡸⠘⠃⠾⠤⠤⠴⠋⡏⠀⠀⠈⢩⣨⣵⠶⠐⠒⠂⠤⠄⣈⣉⡽⠆⠀ ⠀⠀⠀⢻⣄⠀⠀⡴⠋⠁⡜⠀⠈⠣⠀⣹⣄⠀⣔⠒⠤⠤⣀⣈⣧⣀⠀⠀⠀⠀⠈⣼⠁⠀⠀⠀⢸⣋⣁⣀⣠⡤⣶⠞⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⠀⣀⡇⠀⣼⡇⠀⠀⠀⣰⣇⠈⢲⣯⡭⣖⣒⠀⠢⠤⠬⣧⢀⣠⣴⣾⡏⠀⠀⠀⠀⠸⡿⠛⠛⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⠀⠀⠀⢨⣷⣿⣿⣴⣿⠀⣀⣴⣾⣿⣿⡄⠀⢻⣷⣄⣀⣉⣑⣶⣶⣾⣿⠟⣫⣿⠀⠀⠀⡇⠀⠀⢳⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡄⠐ ⣽⡀⠀⠀⣨⣿⠿⣿⣿⣿⡿⠏⠠⣿⣿⣿⣿⣄⠀⢾⣿⠉⠀⠁⢹⡿⢋⣠⢾⠏⡌⠀⡆⠀⡇⡀⢀⡞⠀⢀⣀⣤⣶⣿⣿⣿⣿⣿⣧⣄ ⣇⠘⣄⡞⡏⠀⣸⠿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⠋⠒⠾⢿⣿⠞⠁⡟⠀⡇⠀⡇⢰⣿⢠⣾⣶⣾⡿⠟⠛⠛⠛⠛⠛⠋⠉⠉⠉ ⣾⣟⠻⣼⡇⠀⢿⣆⠘⣌⠙⠻⡧⠤⠀⠤⢴⠾⣿⠛⠋⠉⣶⠤⢄⣙⢳⡤⠷⢤⣸⣤⣹⣼⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡏⡽⠇⣸⣿⡄⠀⠈⢳⡼⠷⡞⠀⠀⠀⠀⠀⢳⣇⠀⠀⠀⠻⣄⣀⣼⣿⡂⠀⠀⠻⣿⣿⣿⣿⠿⣿⣿⠀⢀⣀⡼⠀⠀⠀⠀⠀⠀⠀⢀ ⣿⠃⣰⠃⢈⠻⣿⢦⡀⡇⠀⠱⣄⠀⠀⠀⠀⠀⠙⠧⣄⡀⠀⠘⣇⠀⠀⠙⠢⣄⡠⢾⣿⣿⣿⠀⠈⠉⣉⣽⣋⣀⣀⣀⣀⣴⣦⣴⣶⣿ ⡟⠀⡃⠀⠀⡇⢻⡀⢳⠇⠀⣠⣼⣿⣿⣆⠀⠀⠀⢀⣴⣿⣿⣗⠛⢦⡀⠀⠀⢠⠉⠛⠛⠽⡟⠢⡀⠀⠀⠀⠀⠀⣀⡭⢽⣿⣿⣿⣟⠁ ⢡⣄⢣⡆⠀⣇⠀⢳⡀⢠⣾⣿⣿⣿⣿⣿⣧⢠⣾⣻⣿⢿⣿⡗⠽⣶⣿⣆⣐⠋⢀⡤⣤⣤⣿⣆⣈⣑⣒⣦⡶⣿⠁⢀⣼⣿⣿⣿⡿⢿ ⣒⠛⠉⢧⠀⠈⠢⣌⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢡⠞⠿⣿⣆⢹⡿⠿⠯⣿⢿⡖⠚⢁⣠⢴⣼⡃⢻⣿⢃⣽⠞⠉⠸⢹⣿⠋⠁⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠍⣉⢷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠟⠉⠉⢾⡅⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢀⡇⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡏⠀⠀⠀⠈⢻⡄⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⣹⣁⣀⣀⣒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠻⣦⡄⢻⣆⠀⠠⡤⣤⣤⣶⠎⠛⠋⠉⠀⠀⠀⠀⠀⠉⠉⠒⠤⣶⣀⠀⢀⣀⣀⢀⡰⣳⣄⠀⠀ ⠀⠀⡜⠀⡀⠀⠀⡀⠀⠀⠀⠸⣧⣀⣽⠀⢠⠞⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡀⠀⠈⠛⢍⣧⠀⠀⠉⠈⠁⢸⠀⠀ ⠀⡸⠁⠀⡏⠣⡜⠻⣀⡤⠒⠒⠛⢧⣾⣶⣿⠎⠀⠀⠀⠀⠀⡀⠀⠐⢄⠀⠀⠀⠀⠀⠘⡄⠀⠀⢪⢻⣄⡀⠀⠀⣠⠇⠀⠀ ⣰⠃⠀⠀⢣⡀⠸⠔⢄⡀⠀⠀⠀⣿⢿⣿⡏⠀⠀⠀⢀⠀⢰⢧⠀⠀⠈⡇⠀⠀⠀⢠⠀⡝⠄⠀⠀⢳⣧⠈⠓⠋⠁⠀⠀⠀ ⠏⠀⠀⠀⠹⣷⣄⣀⡀⠉⠉⢉⣴⣿⣿⣿⢠⠀⠀⠀⢸⡀⢸⠀⠳⡀⠠⠃⠀⢀⣠⣏⡴⠁⠈⠂⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠚⠻⢿⣿⣿⡇⢸⣀⠐⡀⢸⢳⣾⢁⣀⣼⠧⢴⡒⠛⣮⣉⠉⠑⠒⢲⡖⠀⢀⣈⡽⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⠖⠲⡀⠀⠀⠀⠀⠀⠈⠛⣿⠁⢸⣧⠀⢱⣸⣤⡿⠛⣭⣿⣧⠀⠈⠉⠚⠻⣿⣶⣤⣨⡇⠀⠀⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣷⡀⠹⣄⠀⠀⠀⠀⣤⣠⣋⠀⣼⢿⠀⠀⠻⣿⡁⠘⢤⢿⣿⡇⠀⠀⠀⠀⠉⠛⢿⡿⢿⡄⢀⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢻⡀⠙⣧⠀⣤⣜⣏⢻⣿⣦⣟⢸⣷⣄⡀⠈⠻⢆⡈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⣸⡇⡇⠀⠀⠀⠀⠀ ⣿⡒⠦⣄⣀⠀⠳⠴⠿⠀⠹⣄⣉⣙⣙⣿⣿⣯⣿⡉⠻⣷⠤⠔⣛⠀⠀⠀⠐⠒⠒⠒⠀⠀⠀⢀⣼⠛⡟⠿⠃⠀⠀⠀⠀⠀ ⠈⠓⠦⣄⡈⠙⢿⣶⣤⣀⢠⡞⠉⢻⣉⣹⣿⠙⣿⠿⣦⠈⠦⣀⡙⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⢻⠘⠞⠁⠀⠀⠀⣀⣠⡀⠀ ⠀⠀⠰⢯⣀⠀⠀⠙⣻⣿⣿⣷⣀⠀⣉⣽⠟⢿⣿⠀⠈⠉⠉⠀⠈⣉⣷⣶⠶⣾⣿⣿⢷⠤⡀⠈⢆⠀⠀⢀⣶⢿⣭⣴⠃⠀ ⠀⠀⠀⠀⠉⠹⣿⣛⣩⣿⡟⣻⠟⡞⠛⠛⠲⢿⡇⠀⠀⠀⠀⠀⢰⣇⠀⠹⣎⣻⣯⣿⢯⣧⣸⡷⢮⡷⢴⠿⣅⡼⣿⣿⡆⠀ ⠀⠀⠀⠀⠀⠀⣠⠞⠁⠙⣋⣻⠿⣧⣀⣤⣦⢸⣿⠀⠀⠀⠀⣿⣿⣝⣿⣶⣾⣿⣽⣿⣿⣿⣿⡀⠀⠀⠀⢀⣨⠄⠺⢏⠀⠀ ⠀⠀⠀⠀⠀⣸⠁⣠⠖⠋⠁⠀⣠⠞⠙⢻⣿⣾⣿⣶⠦⡄⠀⣿⣿⣭⣿⣿⣿⣟⣿⣿⣹⣿⣿⠙⠒⠦⠺⡯⠤⢀⣀⠀⠑⡄ ⠀⠀⠀⠀⠀⠷⠞⠀⠀⣠⣿⡞⠁⠀⢠⡾⣿⡿⣿⠛⠀⢣⠀⡾⢿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⡇⣠⠔⠀⠉⠢⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⠀⢀⣼⡄⠈⠁⠀⠀⠀⠀⣿⣥⡞⠋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⠋⠀⠀⠀⠀⠀⠀ ⠂⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⣾⣹⣿⡆⠀⣤⣀⠀⠎⠉⠙⠓⢾⣻⠁⢨⡿⢿⣿⣿⣿⣿⠟⢿⣿⣝⣦⣀⡀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⣽⣿⣿⣿⣿⣧⣀⣿⣿⣍⣷⣤⣤⣄⣠⣿⣤⡾⢣⡖⠋⣼⣏⢁⣀⣙⣹⡏⣹⡿⠛⠀⠀⠀⠀ ⠿⠤⠤⠴⠆⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠙⠛⢻⣛⣏⣉⣴⣿⡋⠀⠀⠸⣿⠛⠿⠋⣿⡟⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡰⠁⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡵⠁⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⣱⠇⠀⠀⠀⠀⡰⠃⠀⠀⠀⢀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⢡⡏⠀⠀⠀⢀⠞⠀⠀⢀⣤⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡀⠀⠀⠀⠀⠀⢀⣾⣿⡇⡾⠀⠀⠀⡠⠋⠀⢀⣶⠗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⣰⠇⠀⠀⠀⠀⠀⠀⠀⠁ ⢁⣾⠤⢲⠀⠀⢀⣾⣿⣿⢸⠁⠀⢀⡴⠁⣠⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢒⡭⢀⡞⢹⠀⠀⠀⠀⠀⠀⠀⠘⠀ ⠛⢁⡴⠋⠀⠀⣾⣿⣿⡇⡌⠀⢀⣾⢡⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⢒⡀⠠⠐⢈⠤⠒⢁⡔⠋⢠⣾⠀⠀⠀⠀⠀⠀⠀⠀⢈ ⠶⢍⣀⣀⣀⣼⣿⡿⠟⣥⠃⢀⣾⣧⠟⠀⠀⠀⢀⣀⣠⣤⣤⣶⠶⠛⠓⣀⡈⠥⠐⢀⠞⠁⣠⠔⠁⣠⣴⠟⢹⠀⠀⠀⠀⠀⠀⠀⠀⢄ ⠒⠤⣀⡀⢀⣀⡀⢀⣰⣿⠀⢸⡞⠛⡶⠛⠛⢻⣿⣿⣿⣗⠒⠒⠂⠉⠉⠀⠀⢀⠔⢁⡤⠊⢀⣤⣾⠗⠁⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠒⠉⠉⠉⠀⠉⠉⠹⡏⠀⢸⠇⠀⡇⠀⠀⣿⣿⣿⡇⣹⣷⡀⠀⠀⠀⣠⢖⠁⠂⣁⠤⣺⣿⠟⠁⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢸⠀⠀⢇⠀⠸⣏⢹⣿⣿⠇⠸⠟⠢⣠⣾⣛⠥⠒⢉⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⡆⠀⠈⠣⣀⠻⠿⠿⠋⠀⠀⠀⠚⢹⠉⢀⡠⠔⠋⠁⠀⣀⣀⣀⣀⣀⣤⣤⠄⠤⢴⠇⠙⣦⡀⠀⠀⠘ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠳⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠀⠀⠘⠿⠛⠉⣿⣿⣿⠋⢹⠙⠳⣶⣾⠀⢠⡿⢸⣷⡦⣄ ⠇⠲⠄⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⣿⣿⣶⡏⠀⠀⣸⣿⠅⣼⡟⢉⡷⠀⠈ ⡤⠊⠀⠀⠀⠀⠀⠀⠀⢀⠻⡀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣉⣿⠏⠀⢀⡴⢻⠁⢠⣿⢃⢼⣃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠎⠀⣧⠀⠀⠀⠱⡄⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠭⠭⠅⠀⠀⠉⣠⡞⠀⣾⠟⠃⠀⠈⠓⢄ ⠀⠀⠀⠀⠀⠀⢀⣾⠋⢀⣼⠿⡄⠀⠀⠀⠹⡀⠀⠙⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣡⠃⣸⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣟⣡⡴⠟⠃⠀⡇⠀⠀⠀⠀⣷⡀⠀⠀⢈⡒⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢺⣿⣾⡏⣰⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡔⠛⠉⠁⠀⠀⠀⣰⠁⠀⠀⢀⡼⠃⠙⢦⡀⠀⠈⠁⠀⠀⠀⠀⢀⣀⣀⠤⣤⣶⠋⠀⢀⣾⣿⡟⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⡲⠀⢰⠋⠀⠀⠀⠀⠀⢀⡔⢁⣀⠤⠒⢻⣇⠀⠀⠀⠈⠉⠙⠿⠛⠋⢉⡉⠁⠀⠀⣴⠏⢸⠀⠀⣀⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⡌⢀⣀⣤⡤⢲⠖⠋⠉⠀⠀⠀⠀⠈⢿⣷⢄⠀⠀⠀⠀⢀⡠⠔⠉⠀⠀⣠⡾⢃⣠⠼⢲⠟⠉⠘⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡟⠁⠀⠀⠳⡇⠀⠀⠀⠀⠀⠀⢣⠀⠀⠻⣮⣧⣀⡠⠔⠋⠉⠐⠒⢂⣾⠟⡝⠉⠀⠀⣇⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠾⢧⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠙⢿⣌⠀⠀⠀⠀⠀⠀⣼⠃⠘⡄⠀⠀⠀⠈⠢⡀⠀⠈⡇⠈⠑⠂⠀⠀⠀⠀⠀⠀⠀ ⠋⠀⠀⠣⠀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠙⠷⣦⡀⠀⠀⠀⡏⠀⠀⠘⢦⡀⠀⠀⠀⠘⢄⠀⢱⠖⠺⠟⡶⠦⣀⠀⠀⠀⠀ ⠀⠐⠲⠤⠤⢶⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣼⠅⢘⣦⣀⠀⠈⡗⠤⣄⡀⠈⡆⠸⠒⠉⠁⠀⠀⠀⠑⢦⣀⠀

⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣶⣦⡀⢀⡀⠀⣀⣤⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⡿⠿⠽⣿⣿⣿⣾⣿⢿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠏⠀⠀⠀⠀⠭⣿⣿⢻⣟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⣿⣧⠖⠴⡀⠀⡢⡤⢏⣿⣿⣝⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡷⣿⡷⠀⠀⣴⣬⡆⢻⡟⣣⠱⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⡇⠀⠀⠀⠀⠀⠉⠀⣾⣯⢧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣄⠀⠀⠀⠀⢀⢼⣿⢿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢿⢿⣅⡒⢒⣈⣵⣿⠻⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢜⣿⣇⣿⣿⣿⠟⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⣸⣽⠛⣿⣿⡟⠀⠀⠳⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢃⣴⣿⣿⣿⣿⠉⡇⠀⢸⠀⢡⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⣿⣿⣷⠛⣿⣷⣶⠁⠀⠈⣠⠁⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⢲⠀⢿⣿⣻⣿⣿⣿⣿⠀⠀⡜⠸⠀⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡎⠘⢀⣿⣿⣿⡏⣻⣿⣿⠂⡐⠀⡀⠀⢰⡀

⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀ ⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀ ⠀⠀⠀⣰⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠳⡀⠀ ⠀⠀⢠⣿⣿⣏⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡋⠀⠀⢡⠀ ⠀⠀⢸⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢡⣿⠻⣿⣿⣿⠻⣿⣷⣄⣠⣧⠇ ⠀⠀⣸⣿⣿⣿⣿⣷⣤⣀⡀⠀⢀⣀⣴⡿⠃⠀⢘⣿⣿⣄⡼⣿⣿⣿⣿⣾ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠿⢥⣤⡴⠇⢽⣿⣿⠋⢹⣿⣿⣿⣿ ⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⣯⡉⡻⡋⠀⠈⣿⣿⢃⢆⣿⣿⣿⣿ ⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣯⠘⢧⡙⠛⢛⠐⠁⠀⠀⡘⣿⠁⢸⣿⣿⣿⠏ ⠀⠀⠀⠀⣙⣿⣿⣿⣿⣿⣿⡄⢄⠈⠉⠁⠀⠀⠀⠀⡡⡟⢠⣿⡿⠟⠁⠀ ⠀⠉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⠢⡀⠀⠀⠀⡀⠄⠂⣧⣿⣏⠀⠀⠀⠀ ⣤⣶⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⡿⡕⠺⢦⣄⡀⠀⢀⢼⣿⣿⣿⣆⠀⠀⠀ ⠉⣉⣯⠽⡾⠟⠋⢂⠀⢻⣿⣿⣿⣬⣦⣔⡝⠈⠙⡁⠀⠹⣿⣿⣷⠑⢄⠀ ⠠⠉⠁⠺⡀⠀⠀⠀⢂⠀⠳⣹⢿⣿⣿⠉⣯⠒⠢⢅⡀⠀⠘⢆⢻⣧⠀⠉ ⠁⠀⠀⠀⠘⠀⠀⠀⠀⠃⠘⠛⠒⠛⠛⠃⠘⠒⠒⠒⠃⠀⠀⠚⠀⠋⠀⠀

⠀⢻⠀⣧⢸⣠⡣⠋⢧⢰⢸⢣⠀⡟⣤⡀⢠⢯⠁⠀⠀⠀⠀⠀⠀⠀ ⣼⣾⠀⣿⣳⣿⣡⣀⣾⣷⡌⣸⣧⣼⡝⣷⣞⡟⡙⠂⠀⠀⠀⠀⠀⠀ ⣿⡟⢻⣏⣿⣿⣿⢿⣿⠙⢿⣿⣿⣿⣿⣎⣿⢲⡆⠀⠀⠀⠀⠀⠀⠀ ⣿⡾⠿⢏⢸⣏⡿⠈⢿⣶⣤⣿⣿⣿⣿⣧⢨⠟⢇⠀⠀⠀⠀⠀⠀⠀ ⠂⠀⠁⠈⠮⢸⡎⠀⠀⠛⠉⠹⣿⡯⢙⣧⠛⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠰⢻⣧⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⡀⠀⠀⣀⣀⣀⠀⠀⢠⣾⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣆⠀⠙⠩⠭⠍⠩⠿⠋⠀⣰⢿⡇⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⡿⠦⣀⠀⠀⢀⣠⡴⢾⢿⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡘⢧⠀⠈⠓⠶⠛⠁⡠⣿⣟⡴⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠵⠈⣦⠀⢀⡠⠔⠈⠀⡧⢸⠀⠀⢿⣶⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡱⡋⡎⠁⠀⢠⠀⠀⡡⢁⣠⣄⢸⢽⣧⠀⠁⠂⠄⡀⠀⠀⠀⠀⠀ ⣾⣫⣰⠏⠀⠀⠘⡀⠤⣿⣿⣿⠘⣾⡇⣻⠐⢄⠀⠀⠈⠢⢀⠀⠀⠀ ⢻⡈⢶⠑⣄⣠⠊⠀⣰⠋⢸⣿⣾⣿⡇⠈⡆⠀⠈⠠⡀⠤⠀⠑⠄⠀ ⢈⣛⣄⡈⡀⡐⣤⡞⠃⠀⣼⡿⠛⠿⠀⣸⠀⢰⠀⠀⠁⠄⠀⠀⠈⢆

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⢿⣷⣿⣿⣟⠛⠈⠻⣏ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⡿⠟⣿⠉⢿⡀⣤⣶⣯⣿⣾⣿⣜⣧⣤⣤⣽ ⣿⣿⣿⠿⢿⣿⠉⢁⣏⣡⣤⢿⣷⣶⣦⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢿⣏⣿⣀⣼⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣾⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⢿⣿ ⣿⣿⣿⣿⠒⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⣿⣿⣿⣿⠇⠈⠻⣿⡎⢟ ⣿⣿⣿⠙⡄⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢿⣿⣿⣿⣠⣤⣦⣼⣷⣈ ⣿⣯⡟⠀⠘⣄⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣭⣭⣿⣿⡉ ⢿⣿⣇⢀⣉⣤⣾⠛⣁⢹⣿⣿⣿⡿⢹⣿⡿⠃⠈⠳⣼⠟⠅⣿⣽⣿⡿⡝⠻⣧ ⠈⠻⣿⣷⣿⡿⣻⣿⣟⠻⣿⣿⡟⠙⠚⣿⡁⠂⠀⠒⢁⠀⠀⢿⡇⠻⠵⠃⣠⠏ ⣤⣿⢿⣿⣿⣿⣿⣿⣋⣖⠣⡈⠙⠂⠀⠸⠀⠀⠀⠀⠁⠀⠀⠈⠹⢄⣀⡠⠼⠄ ⣿⡃⠀⣿⡿⠻⡙⢸⡟⢿⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠ ⣿⣃⠀⠙⣧⡄⠋⠁⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣷⠞⠋⠉⠑⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣅⠀⠉⢈⢀⠤⢊⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠈⠉⢛⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏ ⣤⣤⡾⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢠ ⣿⣿⣿⡄⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿ ⣿⣿⣿⣷⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿ ⣿⣿⣿⣧⣃⠀⠀⠈⠐⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠁⣿⣿ ⣿⣿⣿⣿⣿⡄⠀⣀⣠⣄⣀⠀⠉⠀⠒⢦⡤⠤⠀⣀⣀⢀⣀⠤⠊⡔⠁⠀⢹⣿ ⣿⣿⣿⣿⣿⣶⣿⣿⣿⠿⢯⣿⣶⣦⣤⣀⠉⢲⢄⠀⠀⠀⢀⣠⠊⠀⠀⢠⣏⣻ ⣿⣿⣿⣿⣿⣿⣿⢋⣠⣾⣿⣿⣿⣿⣿⣿⢷⣿⣷⣗⡀⣠⣊⣥⣴⣶⠿⣟⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢁⣴⣿⣿⣿⣿⣿⣿⣿⡿⠋⣰⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢉⣿⣿⣿⣿⣿⣧⣼⣿⣿⡿⢷⣾⣿⣿⣿⣿ ⣿⠁⢿⣿⣿⣿⣿⣿⣿⣿⠏⢁⣼⣿⣿⢿⣿⣿⣿⣿⣿⣿⡟⠀⣼⣿⣿⣿⣿⣿ ⡿⠀⠀⠝⢿⣿⣿⣿⡿⡧⣼⣿⣿⠟⢡⣿⣿⣿⣿⢹⣿⣿⣤⣤⣿⣿⣽⣿⣿⣿ ⡇⠀⠀⡀⣉⣼⡿⢿⣀⣿⣿⢿⣿⠀⣾⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⠠⠄⠀⠀⠄⠄⠊⠉⠐⢄⠀⠀ ⢀⠔⠈⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⠐⢠⠀ ⠎⠔⠁⠈⡆⠠⠂⠀⠀⠀⠀⠀⠀⣤⡔⡀⠀⢀⠃ ⠀⠀⠀⠀⢃⢠⣶⢦⡀⣠⡶⢦⢸⣷⡇⢃⠀⡸⠀ ⠳⡀⡀⠀⡌⠘⣿⣟⡷⣿⡇⠘⣇⠉⠁⠸⠔⠁⠀ ⠀⠈⠣⠀⢡⣀⡀⠉⡠⢿⣷⣴⡯⢃⠤⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠐⠐⠐⠰⢍⡱⠎⠁⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠜⠢⠄⠤⣀⠏⢴⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠠⣀⠈⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠰⣎⡠⠄⠓⠀⠠⠔⠁⠀⠀⠀⠀

⠀⠀⠀⢀⣀⢠⡠⣄⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣲⡘⠛⠈⣀⠈⠃⠁⠳⠀⡀⠀⠀⠀⠀⠀⠀ ⠈⢿⡉⣵⡦⠶⠿⣴⣃⡄⠀⠀⠇⡀⠀⠀⠀⠀⠀ ⠀⠠⣵⠀⠀⠀⠀⠘⠶⡅⠰⡇⠀⢿⠀⠀⠀⠀⠀ ⠀⠀⡍⠀⣴⢷⡲⠀⠀⢰⣰⣿⣆⢈⡇⠀⠀⠀⠀ ⠀⠀⢻⠇⠀⠉⠀⠀⠀⠸⢸⠛⠟⡸⠁⠀⠀⠀⠀ ⠀⠀⢳⠀⢀⠀⠠⠀⠀⠀⡜⠀⡷⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠊⠀⠀⠀⠀⠀⠚⠁⠀⠃⢡⣀⠀⠀⠀⠀ ⠀⠀⠀⠸⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⣿⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⢀⢎⣿⣿⣢⢀⡀

⡖⢲⢲⣶⣶⣶⣶⣶⡖⣲⣶⣲⣶⣶ ⡇⣧⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⣿ ⣧⡿⢽⣿⣟⠲⣿⢿⢿⡟⣹⣿⣿⣿ ⣿⡇⠈⠻⡿⠃⢸⠇⠀⠑⠻⢿⣿⣿ ⣿⣁⠀⠀⠀⠉⠈⠀⠀⢠⡤⢤⣉⣿ ⣿⢸⡀⠀⠀⠀⠀⠀⠀⠘⢃⣷⣿⣿ ⠛⠓⠓⠐⠒⠒⠀⠀⠀⠀⠚⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠉⠉⠙⠻⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⡎⠀⠀⠀⢀⣠⣴⣾⣿⢿⣿⣷⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠛⠧⠀⣠⣶⣿⣿⣿⣿⡏⠈⠙⢿⣿⣷⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣟⣿⣿⠀⣧⡀⠘⣿⢿⡟⢿⣦⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⢡⣸⡟⣈⣿⣿⣦⢸⡇⠀⣿⣾⣿⣌⠛⢿⣿⡿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡏⢿⣿⡿⢾⣿⠀⢿⣿⡇⢹⣇⡀⣻⡇⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⣿⣿⣹⣿⣿⢿⣿⡘⣿⣇⣸⣿⣇⢸⣿⠁⡀⣿⠈⢹⡇⢠⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠰⣿⣿⣿⣾⣿⡟⢻⣿⣷⣿⣿⣿⡟⢿⣾⣿⠀⠀⣿⣆⣻⡇⣶⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡁⠈⢻⡜⣿⣿⣿⡇⢈⣻⣿⣇⣁⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⢿⣿⣿⣿⡟⠉⠉⠃⠈⠻⣿⣿⠉⠉⢹⣿⣿⣿⢻⣿⣿⡿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠈⢿⣿⣿⠇⠀⠀⠀⠀⠀⠈⠈⠀⠀⣼⣿⠟⣿⣈⡟⢻⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⣆⠀⠀⠀⢶⣖⣲⠀⠀⠀⠸⢏⡴⠿⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⢀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡖⠦⠄⠒⠉⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣠⠇⠠⠔⢁⡇⡨⠛⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤ ⠀⠀⠀⠀⠀⠀⠀⣀⠠⠒⠉⠁⠠⡀⠙⠢⢄⡠⠜⠋⠀⡠⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿ ⠀⠀⠀⠀⠀⠀⣏⠁⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠈⠫⣓⢤⡀⠀⠀⠀⠀⠀⣰⣿⣯⣾⣿ ⠀⠀⠀⠀⠀⡜⠘⠀⠀⠀⠀⠀⠀⠀⠱⡉⠢⠤⠔⠁⠀⠀⠀⠀⠀⠀⠀⢀⠴⠻⡄⠀⠀⢀⣾⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠠⡀⠀⠀⠀⠀⡔⠁⠀⠀⠸⡀⠀⣿⣿⣷⣿⣿⣿⢻ ⠀⠀⠀⠀⣸⠀⡇⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢱⠀⠀⢀⡜⠀⠀⠀⡀⠀⡇⠈⣿⣿⣿⣿⡇⡟⢸ ⠀⠀⠀⢀⠇⣀⡁⡇⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠈⡇⠀⡿⠁⠀⠀⢀⠇⠀⠸⣾⣿⣿⡟⡏⠉⠂⠸ ⠀⠀⠀⡎⠀⣿⢁⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠁⠀⠀⠀⡜⠀⠀⠆⣿⣿⢿⠷⠀⠀⠀⠀ ⠀⠀⡸⠀⠀⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠘⡀⠀⠀⡸⠁⠀⢸⠀⠈⣿⡈⣇⠀⠀⣶⠤ ⠀⢠⠃⠀⠀⣏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡇⠀⣰⠁⠀⠀⠸⠇⠀⠘⡀⠈⢧⡀⠉⠀ ⢀⡎⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡽⣧⣴⠃⠀⠀⠀⠀⠀⠀⠀⢱⡪⠋⢑⡲⠲

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⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠃⠀⠀⠀ ⠀⠀⢻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀ ⠀⠀⠘⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠇⠀⠹⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⠀⠀⠀⠘⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⣿⣿⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⠀⠀⠀⠀⠀⠘⣿⣿⣿⡄⠀⠀⠀⠀⢀⣿⣿⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⣠⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣆⠀⠀⠀⣸⣿⣿⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⣰⣿⣿⡿⠁⠀⠀⠀⢠⣿⡀⠀⠀⠀⠈⢿⣿⣿⣆⠀⢀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⣿⡆⣰⣿⣿⡿⠁⠀⠀⠀⢠⣿⣿⣷⡄⠀⠀⠀⠈⢿⣿⣿⣆⣸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⢠⣿⣿⣿⣿⣿⡄⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠁⠀⠀⠀⣰⣿⣿⡿⠛⣿⣿⣿⣄⠀⠀⠀⠈⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⠀⠀⣰⣿⣿⡿⠁⠀⠘⢿⣿⣿⣆⠀⠀⠀⢀⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡇⠀⠀⣴⣿⣿⡿⠁⠀⠀⠀⠈⢿⣿⣿⣆⠀⠀⣸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⣿⣿⡟⣿⣿⣿⠀⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣆⢀⣿⣿⡿⢻⣿⣿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⢀⣾⣿⣿⠟⠀⢻⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣾⣿⣿⡇⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀ ⠀⠀⠘⠛⠛⠋⠀⠀⠈⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣋⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠟⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣜⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡤⠄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⡼⣙⡁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠉⠁⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠀⣀⣷⠃⠀⠀⠈⠲⣄⠀⠘⢦⠀⠐⠪⡀⠀⠀⣲⠇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣀⡤⠼⢿⢠⣔⡤⠀⠀⠈⢷⠀⠀⠳⡀⠀⠹⣆⠉⠀⠀⠀⡇⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠛⣿⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠞⡡⣊⣥⡼⠼⠟⠙⠳⣄⠘⣦⣗⢄⠀⠙⡆⠠⣜⣖⠀⡀⣾⡧⣺⡃⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢙⣿⣶⣟⣿⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⡼⣹⠟⠁⠀⠀⠀⠀⠀⠈⠳⣌⢫⡓⢦⡲⣤⡀⠈⢙⡶⣿⣫⠞⢉⣷⠂⠀⠀⠀⠀⢀⣾⡟⠉⢹⣿⣿⣿⣿⣿⣿⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⣰⠃⢰⢡⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⢷⡓⣦⣝⣦⣹⣷⣤⣉⠛⠿⣦⡫⠃⠀⠀⠀⠀⠀⣸⣻⣇⣀⣼⡏⢿⡟⣿⣤⣿⠿ ⠀⣀⣤⣶⣾⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢿⠀⢸⢸⡇⠀⣀⠤⠤⠄⠀⠀⠀⠀⠀⢀⣿⢿⣿⣿⣿⠇⠉⠛⢽⠲⣤⡙⣆⠀⠀⠀⠀⠀⣿⣿⡿⣿⡿⠁⣼⠀⣿⣿⠋⠀ ⠀⣿⣉⣿⠉⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⠀⡎⠀⢸⢸⢳⣾⣷⣶⣤⡀⠀⠀⠀⠀⠀⡿⢻⣿⣿⣿⡟⠀⠀⢰⠾⠓⠈⢯⠛⣷⡄⠀⠀⠀⣿⣿⡇⠀⡇⢠⠇⠘⣿⣿⡆⠀ ⠀⢹⣿⠻⣦⣤⣴⣿⡛⢷⣦⡀⠀⠀⠀⠀⠀⠀⢳⢰⠈⣿⠈⢿⡻⢾⣿⣧⠀⠀⠀⠀⠀⣧⣀⡠⠐⠉⠰⡖⠀⡞⠀⠀⠀⠘⡆⢸⡘⠄⠀⣸⣿⣥⡇⢰⢁⡾⠲⣴⠋⡼⢿⡄ ⠀⣻⡿⢶⣟⣻⣟⠻⣿⡾⢿⠟⢦⡀⠀⠀⠀⠀⢸⠸⠀⠸⡄⠈⢯⠈⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⣇⡇⠀⠀⢠⣿⣾⠟⣿⣿⡿⠀⠀⣇⣼⣷⣿⣷ ⢰⣿⣄⣠⣿⠋⠘⣦⡹⣿⠾⣷⣶⡿⣦⡀⠀⠀⠀⠂⢧⠀⢷⠀⠈⢧⠀⠀⠠⡀⠀⣀⡤⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⡼⠁⠀⣠⣿⣿⣿⡴⠋⠈⡇⠀⢀⡟⣸⣿⣁⣿ ⢸⣏⣻⣿⡿⠿⣶⡼⠷⢾⣆⣷⢻⣷⣼⣿⣷⣄⠀⠀⠈⢆⠈⢧⠀⠀⠳⢄⡀⠈⣉⠥⠤⠄⠀⠀⢀⣴⣾⡿⠀⠀⠀⠀⠀⢠⠇⢀⣾⣿⣿⠃⡿⠁⠀⡼⠀⠀⣼⠟⠁⠈⣻⣿ ⠈⢻⣿⣻⡗⢦⣾⡆⠀⠀⠙⢿⣤⣿⢿⣿⠳⡾⢧⡀⠀⠈⢦⠈⠃⠀⠀⠀⠉⠳⣮⢭⣁⣀⣤⠾⣿⠟⠻⣧⠀⠀⠀⠀⠀⠋⣰⣿⢛⡧⣼⡿⠁⠀⡴⠁⠀⣰⡿⠲⡊⢹⣿⣿ ⠀⢸⣿⣿⣇⣀⣾⣿⣄⡀⠀⠀⠙⢄⠀⠈⠻⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢷⣄⡀⠠⠞⠁⠀⠀⢘⡶⠋⠉⠉⠉⠙⣿⣿⠎⢀⡞⠀⢀⡼⠁⢀⡼⠋⠀⣰⣧⣾⣟⠁ ⠀⢸⣟⣿⣧⢉⣻⡄⠀⠉⠑⠶⢤⣈⠑⢤⣀⠀⠙⠿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢠⠧⠀⠉⠉⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⢘⣏⣠⠎⢀⡴⠋⣀⡴⠋⠀⣀⣼⣋⣤⠼⣿⡄ ⠀⠈⢿⣷⣹⣯⢉⣿⣶⣤⣀⣀⠀⠀⠉⠙⠚⠻⠶⠦⠬⣽⣿⣷⣦⠴⠒⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⢀⣿⣡⣴⣫⠴⢚⣁⡤⠴⠚⠛⢾⡥⣤⣴⣿⠇ ⠀⠀⠘⢿⣽⣿⣭⡉⣏⠁⠀⠈⠉⠉⠉⠉⠉⠉⣉⣩⣽⠟⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⢭⣍⣉⣀⡀⢀⣀⣤⠾⠳⢤⣿⠋⠀ ⠀⠀⠀⠀⠀⠉⠛⣿⡉⢛⣶⣤⣤⣤⡤⠖⠊⣩⠕⡿⠁⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⢀⣿⣿⠳⡌⠓⢦⣀⠀⠉⢹⣟⠓⠲⣤⣾⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢷⡋⠉⣰⣏⠁⣀⣤⠞⠁⣸⠃⠀⢸⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⣼⠃⣿⠀⣿⡄⠀⢹⠛⢿⣭⠽⠗⠒⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠤⠽⠿⣏⣻⣀⣠⣿⠀⢀⣿⡇⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣴⣧⡴⢋⠟⠒⢻⣤⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠙⢭⡿⠛⣹⠟⢻⡇⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⣯⠟⠋⠉⠉⠉⠉⠀⠀⢴⣶⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣶⡆⠀⢉⣑⡿⠶⣻⡇⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣼⡥⠚⠉⠙⠒⢤⣀⠀⠀⠀⢡⡸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢯⡈⠉⣀⡴⠋⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠆⠀⠀⠀⠀⠈⠉⠙⠊⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠒⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠉⠉⠲⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣄⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢹⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⣦⡀⠀⠈⢯⣇⠀⠀⠀⠀⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣤⠈⢿⣧⠀⠀⠀⠀⢦⡈⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡛⢿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣈⣓⣈⣹⣇⣀⣀⣀⣀⣙⣶⠤⠨⠷⣶⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⢶⣶⡦⠴⠶⠾⠿⠷⠿⠟⠇⠰⠶⠤⣖⣲⡖⠒⠒⠒⠒⠒⠒⠒⠒⠒ ⠀⠉⠀⠉⢿⡟⣿⣹⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⠺⢄⠀⠀⠀⠇⡄⠀⠀⣀⣀⣠⣤⠤⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⢦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠁⠧⠇⢀⠰⠀⠀⠀⠄⠀⠺⠿⣛⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀⠀⠀⠀ ⠀⢀⣀⣀⣴⣶⣶⣶⣶⣆⣠⠤⠤⠤⠴⠆⣤⣖⣒⣒⢚⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠐⢲⢖⣶⡶⠶⢶⣶⠟⣿⠛⡘⠶⢾⠓⠒⠒⠚⠓⠓⠀⠀⣰⣿⢟⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⢿⠉⠹⣿⣿⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠋⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡜⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⠀⢸⢸⡄⡇⢸⠀⠀⠀⠀⠀⣠⣿⠿⣻⣷⣻⠟⢁⡾⠃⠀⢀⢠⡆⠀⠀⠀⢠⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⣼⢸⡇⣷⢸⠀⠀⠀⠀⠠⠟⠁⣺⣷⣯⠁⣠⠋⡰⠀⢀⡾⣾⡇⢠⡄⢀⡾⡏⣴⠀⠀⠀⠀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⢷⣵ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⡇⣿⢸⠀⠀⠀⠀⠀⠀⠘⢿⣿⢣⣿⢃⡞⠁⠀⣸⣿⠁⡇⢸⡇⢸⣿⣼⠁⠀⡀⢰⣿⢻⠘⡇⠀⠀⠀⠀⠀⠀⠀⠰⣄⠳⣤⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠙⡿⡇⢹⢨⠀⠀⠀⠀⠀⠀⠀⣾⣯⣾⢃⣞⣤⠀⣰⣿⡃⠀⣧⢸⡇⣾⣿⢁⣼⢿⠇⣼⠃⠈⣇⢹⠠⣆⠀⠀⠀⢠⡀⠀⠙⣷⣜⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⣷⡇⢸⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⣿⣿⣾⢣⣰⣿⠟⠻⠦⣿⣾⣿⣿⢋⣾⣿⡏⣸⣏⣀⠀⠙⡟⡇⢿⢠⠀⠀⠸⡿⣆⣀⠈⣿⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⡇⢸⢀⠀⠀⠀⠀⠀⠀⠘⠃⠀⡏⣿⡏⣾⣿⡯⢶⣶⣿⠿⢿⣿⣯⡞⢸⣿⢱⢟⣻⣭⣭⣍⣹⣿⣸⣸⢰⢠⡀⢹⡽⣜⣄⡿⣿ ⠀⠀⠀⢸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡘⡇⣸⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢷⣿⣼⣿⡽⠀⠘⣿⣿⠀⢈⣿⡞⠀⣿⣣⡏⢨⡿⣿⡿⡍⠉⠛⣿⡇⢸⣿⢻⠈⣿⢻⣻⡅⣿ ⠀⠀⣠⠾⣟⣛⣳⣦⣀⡀⢀⣠⡄⠀⢸⠀⣴⠇⡇⠿⠐⠀⢀⣀⣠⣤⡿⠤⠂⠀⠀⢹⣟⣿⡇⠀⠙⠛⠛⠛⠛⠛⠀⠀⣿⡿⠀⠀⢠⣝⣿⣃⣀⣀⣨⢿⣿⢸⣾⣸⣿⣿⡿⣷⣿ ⣶⣶⣿⣤⡟⠛⠉⠛⠻⣿⣿⣇⣀⣀⡜⠀⢀⡀⠃⠀⠀⡶⠭⠟⠛⠉⠀⠀⠀⠀⢀⡾⠋⡿⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠁⠀⢸⣿⢸⡿⣿⠃⠹⣿⣿⢻ ⢹⣿⡏⢹⠀⠀⠀⠀⠀⠀⠙⠳⢽⣿⣶⣿⠟⠃⠀⠀⠰⠀⠀⠀⠀⠀⠀⣀⣠⣤⣾⣶⣿⠃⠀⠀⠀⠀⠀⠀⠀⣼⣅⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⡿⠋⡄⠀⡿⣼⣿ ⢻⢿⣷⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣯⣷⣧⣄⣀⣤⡴⠶⠶⠶⠺⠿⠿⠿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠙⠺⠆⠉⠁⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢰⣷⠞⠁⣰⠃⠙⣯ ⣸⣏⣿⡀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠋⠀⠀⠀⠀⣠⠴⣲⣶⣤⣄⠀⠀⠉⠻⢿⡄⠀⠀⠀⠀⠈⢲⡀⠀⠀⠀⣰⠟⣏⠁⢉⠹⡏⢭⡝⣷⣄⠀⣿⣡⣴⣿⠁⠀⠀⠀ ⠛⠻⡮⣿⡉⢱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⡞⠁⣰⣿⣿⣿⣿⣷⡀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠿⠶⣤⣶⣽⠟⠙⣷⣽⣶⠋⠉⢹⠿⢹⣴⣿⣳⡞⢹⡀⠀⠀⠀ ⠀⠀⠻⢿⢷⣤⣼⣟⠲⢤⣀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⢧⠀⢻⣿⣿⣿⣿⣯⡇⠀⠀⠀⠀⠀⠉⠳⣤⠀⠀⠀⣰⠏⠀⠀⣀⣤⣞⣛⣷⣶⣤⣤⣤⡿⠀⠈⠙⠳⢦⣄⡀⠀⠀ ⢀⢤⡤⠬⠷⣿⣽⣾⡷⣶⣯⣙⠲⢤⣀⡀⡇⠀⠀⠀⠀⠀⠘⢧⣀⣙⣛⣛⡭⠞⠁⠀⠀⢀⡀⠀⠀⠀⠈⠷⣄⣸⠃⠀⠀⠸⡿⣻⠿⢯⣅⠋⠀⠉⠻⣄⠀⠀⠀⠀⠀⠈⠙⠳⣦ ⠛⠛⠛⠛⠛⠛⠋⠙⣻⣶⣿⣟⡻⣶⣬⣉⣷⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⢸⡇⠀⢀⣀⣴⠻⣧⡀⠀⠙⠳⣄⠀⠀⠘⢧⡀⠀⠀⣀⣤⠔⠒⣺ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⣿⣿⣿⣷⣟⣝⡻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠘⣷⡾⢫⣷⣷⡀⠈⠙⣆⠀⠀⠙⠇⠀⠀⠈⢻⣄⡞⠉⠘⢋⣋⡴ ⠀⠀⠀⠀⠀⠀⠀⣾⢹⠀⣿⣿⣿⣿⣿⠛⠓⢿⣄⠀⠀⠀⠀⠀⠀⠀⢠⡦⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⢹⡿⠋⡿⠛⡇⠀⠀⠈⠁⠀⠀⢠⠀⠀⠀⣸⡿⢁⣼⣴⠋⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠿⡆⠳⣝⣛⣿⣻⠏⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⠀⠀⠀⠀⠘⢻⠇⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⢀⣴⡿⢃⣯⡾⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠉⠳⣤⣀⣀⣠⠶⣯⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⢠⣟⡞⠁⣼⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠘⠛⠶⣄⡀⠀⠀⠀⣸⠁⠀⠉⠀⠀⠙⠣⠤⠤⣤⠤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣻⠏⠀⣼⢻⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠙⣶⠶⠾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠰⣿⠏⠀⣸⠁⡞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣦⠀⠀⠀⠀⠀⠀⠀⣧⠀⢀⣿⣸⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⢸⡄⠘⢀⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠘⡇⠀⠀⠀⠀⠀⠀⢸⣇⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⢻⡒⠋⠓⠶⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠈⢷⠀⠀⠀⠀⠈⠉⠛⠛⠒⠒⠒⠛⡏⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⢹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⠆⠁⠀⢀⡇⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠔⠉⠀⠀⠀⣼⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⢯⠇⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⢸⡇⢀⣤⣀⠀⠀⠀⠀⣷⠀⠀⠀⠀⣀⣤⣤⣤⣴ ⠀⠀⣀⣠⣤⣤⣀⣀⢀⠏⠀⠀⠀⠀⠀⣻⡄⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣠⡞⠀⠀⠀⠀⢀⡼⠟⠋⠀⠉⠳⢦⣀⠀⠸⣄⣴⣾⣿⣿⣿⣿⣿⣿ ⢀⣴⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠠⡴⠊⠁⢳⡄⠀⠀⠀⠀⠀⠀⢸⡗⠶⢤⣤⣤⣄⣀⣀⣀⡇⠀⠀⠀⠀⣿⣀⣀⣀⣤⠶⠋⢀⡠⠖⠀⣀⠀⠀⠈⠙⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣾⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠙⠿⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢀⡟⠀⠀⠀⠀⠀⠴⠶⠒⠂⠀⢤⣤⣤⣬⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢠⠟⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⡀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⣿⠀⠀⢀⣀⣀⣀⣀⣀⣸⣞⣋⣀⣙⣹⣄⡀⠀⠀⠀⠀⠀⠰⠶⠒⠊⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡶⠒⠚⠛⠛⣆⣠⡿⠛⠛⠉⠉⠁⠀⢸⡀⠀⠀⠀⠀⠉⠉⠛⠙⠳⢤⣄⣀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠟⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀⠉⠓⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿