⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣄⡀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡿⣿⣶⣤⣤⣀⣀⣀⣤⣤⠤⠴⠻⢿⣿⣿⣦⣤⣀⠈⠉⠛⠛⠛⠿⠿⢿⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⠿⠿⠛⠛⠋⠉⠉⣩⣿⢿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣦⣈⠉⠛⠛⠻⠿⢿⣶⣦⣤⣤⣈⣿⣿⣿⣿⡙⠻⢷⣶⣤⣀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⣠⣾⡟⠉⢸⣿⠇⠀⠀⠀⠀⠀⠀ ⢀⣴⣾⣿⣿⠛⠛⠛⠛⠋⠛⠛⠛⠛⠛⠛⠿⠿⣷⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠿⠛⠉⠙⠻⣷⣦⣀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠉⠛⠁⠀⠀⠉⠙⠻⣿⣶⣤⡀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣦⣀⣀⣠⣶⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⠛⠿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣷⣦⣤⣤⣾⠿⠛⠉⠀⠀⣀⣤⣴⣾⣿⡿⠿⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⣠⣿⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠁⠻⣿⣦⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡀⠀⠈⠻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣶⣄⣠⣴⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⠀⠀⠀⣾⠿⠋⠁⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⢤⣿⡗⢳⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣿⣧⠀⠀⢀⣬⡿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⡿⠛⠉⠀⠀⠀⣀⣠⣤⣤⣤⣶⣶⣶⣦⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠙⣿⣷⡄⠀⠀⠀⢀⣴⣶⠿⠿⠻⠿⠿⣿⣶⣦⣄⠀⠀⣠⣿⠀⠀⠀⠀⠀⠙⢷⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣿⡇⠀⢸⣿⠁⠈⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠟⢁⣀⣤⣴⣶⠿⠿⠛⠛⠉⠉⠉⠉⠀⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢉⣉⣛⣿⣿⣿⣶⣤⣤⣀⠀⠀⠈⢿⣿⣆⣀⣾⣿⠏⠁⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣶⣿⠃⠀⠀⠀⠀⠀⠀⠀⣻⣿⡅⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⣿⣀⠀⠻⠀⠀⠀⠹⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣩⣴⣾⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⠾⠿⠛⠉⠉⠉⠉⠉⠉⠻⢿⣷⣤⡀⠀⢻⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣧⡀⠀⠀⠀⠀⠀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⡋⠀⠀⠀⠀⠀⠀⠘⢿⣷⡄⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣄⠸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⡀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⡗⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡄⠀⢀⣠⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠋⠁⠀⠀⠀⠀⣀⣤⣤⣶⣶⣦⣤⣤⣤⣀⣀⠀⠀⠀⠻⣿⣷⣻⣿⠃⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣄⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠋⠀⠀⠀⠀⣠⣶⡿⠟⠋⠉⠀⠀⠉⠉⠙⠻⠿⣿⣿⣶⣤⡀⠘⢿⢿⣿⠀⠀⠀⢀⣴⣾⡿⠿⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣦⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣤⣀⢀⣠⣤⣤⣼⡿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⠟⠃⠀⠀⠀⠀⢠⣼⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿⣿⣿⣤⠄⠀⣿⠀⠀⠀⣼⡿⠃⠀⠀⠀⠀⠻⣿⣧⡀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⠙⠻⣿⣿⣤⣄⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠉⠀⠀⠀⠀⠀⣴⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡇⠀⡟⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣆⠀⠀⠀⠀⠀⠀⠻⣿⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢿⣷⣀⠀⠉⠙⠛⠛⠿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠋⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠈⠛⠀⣸⣇⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧⠀⢷⣦⡀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇⠀⠀⣀⣤⣾⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠃⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡆⠀⠀⠟⢹⣿⡀⣀⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠙⣿⣧⠀⠹⣿⣦⡀⠀⠀⠹⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⡟⣹⣿⣶⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠟⠀⠀⠀⠀⠀⠀⠀⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡿⢀⣤⣶⠿⢿⣿⣿⣿⣿⣿⠉⠉⠛⠿⣷⣤⡀⠀⠀⠘⣿⣧⡀⠈⠻⣿⣶⣄⠀⠘⢿⣿⣦⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⡿⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠈⠉⠛⠿⠿⠟⠋⠀⠀⠀⠀⠉⠛⠻⣿⣿⣄⠀⠀⠀⠈⠓⠀⠀⠀⠘⣿⣷⡀⠀⠈⠙⢿⣷⣦⣀⠈⠛⢿⣷⣦⣀⠀ ⠀⠀⠀⠀⢠⣿⠉⠲⠶⣶⣶⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠏⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡀⠀⠀⠀⢹⣆⠀⠀⠘⢿⣷⡀⠀⠀⠀⠈⢿⣿⠻⠿⠿⠿⠿⠿⠛ ⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⢨⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣧⣾⣿⠏⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣆⠀⠀⠀⣿⣆⠀⠀⠈⢿⣷⡄⠀⠀⠀⠈⢿⣷⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⣾⣿⡟⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⣿⣿⣿⡿⠟⠛⣿⡟⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⢸⣿⡄⠀⠀⠈⢿⣿⣦⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀ ⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠠⢶⣿⣿⣿⣿⡿⠿⠟⠛⠉⠁⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣆⠀⣿⡇⠀⠀⠀⠀⠙⣿⣷⣄⠀⣤⣄⣀⣙⣿⣿⣷⡄ ⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⣰⣿⡏⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⣿⣗⠀⠀⠀⠀⠀⠈⠛⢿⣷⣄⣭⡉⠉⠉⠉⠁⠀ ⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⢀⣴⠿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡇⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠿⠿⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⣠⣾⡿⠁⠀⣿⡿⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⢻⣿⡇⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⣠⣾⡿⠋⠀⠠⣾⣿⣷⣀⣀⣀⣀⣀⠀⣸⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏⠀⢸⣿⢄⣿⡏⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴⣶⣶⣾⣿⣿⡿⠿⠛⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⢀⣼⣿⠋⠀⠀⠀⠀⢸⣿⡟⠛⠻⠿⣿⣿⣿⣿⣿⣿⢶⣶⣦⣤⣄⣀⠀⠀⠀⣠⣿⡿⠁⠀⠀⣼⣿⢸⣿⡇⣀⣤⣶⠶⢟⣛⣻⣿⣿⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⢠⣾⠟⠁⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⣿⣿⣿⣿⠿⠿⣶⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⢀⣿⣯⣾⡿⠙⠻⠿⠿⠟⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⡿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⣀⣤⣴⣾⣿⣿⣿⣿⣄⣀⠀⠀⠈⠉⢈⣽⡿⠋⠀⠀⠀⠀⠀⣼⣿⣽⣿⠃⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣶⣶⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠉⣹⣿⡟⠉⠈⠉⢿⣿⠛⠿⣿⣶⣤⣴⣿⡟⠁⠀⠀⠀⠀⠀⣸⣿⣿⣿⠋⠀⠀⠀⣠⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢿⣿⣶⡄⠀⠀⠀⠀⣸⣿⠃⠀⢰⣿⠁⠀⠀⠀⢀⣤⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠘⣿⡄⠀⠀⠀⠀⢀⣤⠖⠋⣹⣿⣷⡾⠟⠁⠀⠀⠀⠀⣺⣿⠀⠀⠀⣹⣿⣿⣿⡗⠀⠀⠀⠀⠀⢰⣿⣿⣿⠃⠀⠀⢠⣾⡿⠁⢀⣀⣤⣶⣶⣶⡿⠿⠿⣾⣶⣶⣦⣄⡈⠻⣿⣦⠀⠀⣸⣿⠃⠀⣰⣿⠃⠀⠀⠀⣠⣾⠃⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⢿⣷⠀⠀⠀⣴⣿⠿⠶⠾⠛⣿⣥⣶⡶⠶⠶⠿⠷⣶⣿⣿⣶⣴⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀⢠⣿⡿⠟⠁⠀⠀⠀⠀⠙⠁⠀⠉⣹⣿⠋⠁⠀⠀⠀⠀⠀⠀⢿⣿⠉⢻⣷⣿⣿⣧⣼⡿⠁⠀⣴⣿⠋⠀⠀⢀⣴⣿⠋⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⣷⡃⠀⠀⠀⠀⠀⠀⢹⣿⣦⠘⣿⣇⠀⠀⢿⣿⣦⣤⠀⠀⣸⡿⠁⠀⠀⠀⠀⠀⠀⢸⣿⠀⠙⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠸⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠈⠛⣿⣿⠟⠁⣠⣾⠟⠁⠀⢀⣠⣾⠟⠁⠀⠀⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⣧⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡄⠀⠀⠈⠉⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⣠⡖⠀⣹⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⠇⠀⣀⣴⣿⣿⣴⣿⠟⠁⠀⣠⣾⣿⠟⠁⠀⠀⠀⢰⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣿⣷⡀⠀⠀⠀⠀⠀⣿⣿⡀⠉⠛⠿⠀⠀⠀⣼⡆⠀⠈⣿⣷⣀⡀⠀⠀⠀⠀⠀⢸⣟⢀⣼⣿⣿⡿⠁⠀⣰⣦⣠⣴⣿⠿⢿⣿⡛⠿⢿⣷⣾⣿⡇⠘⠿⣿⣿⣶⣦⣤⣤⣤⣤⣤⣤⣼⣿⣿⣶⣾⠿⠟⢻⣿⣿⢋⣀⣴⣿⠿⠋⠀⠀⠀⠀⠀⠀⢸⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣄⠀⠀⠀⠀⠹⣿⣇⠀⠀⠀⠀⠀⠀⢻⣿⣄⠀⠙⠻⠿⠿⣿⣿⣿⣿⠶⣿⣿⣿⣿⣿⠟⠁⠀⢀⣿⡿⠛⠉⠀⢰⡆⢻⣿⣄⠀⠈⠙⣿⣷⣀⣠⣶⣶⣥⣌⠈⠉⠉⠉⠉⠉⠉⣽⣿⠋⠁⢀⣠⣼⣿⣶⡿⠿⠋⠁⠀⠀⠀⣀⣴⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠙⢿⣷⣦⣄⡀⠀⢸⣿⡆⠀⠴⠶⢿⣿⡟⠁⣀⣤⣾⠿⠋⠀⠀⠀⠀⣿⣷⠄⣻⣿⡄⠀⠀⠈⠻⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⢀⣠⣾⡿⠃⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⢀⣴⣾⠟⡯⠀⠀⣸⡿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⠘⠿⣷⣄⣀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣷⣶⣶⣶⠿⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⡿⠏⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣶⣶⣶⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⣻⡏⢸⡇⠀⢠⣿⠃⠸⣿⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⣠⡀⠀⠀⠀⠀⠈⠙⠻⣷⣦⣤⣄⠀⠀⠀⠀⠰⣶⣾⣿⡟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⣠⣾⣿⣿⣼⣿⠇⡿⠀⢠⣿⢧⣄⣀⣹⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⡿⢶⣷⣶⣶⣶⣿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁⢀⣼⡿⠱⣿⣿⣿⠏⠀⠁⠀⠛⠁⠀⠉⠛⢿⣿⣿⠆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⢰⣿⣧⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⠀⠀⠀⣤⣾⣿⠋⠀⢠⣾⡟⠀⢰⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⣼⣿⣿⡄⠀⠀⠀⣿⢿⣷⠀⠀⠀⣦⣄⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣴⣾⠿⠿⣿⣶⣦⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⣤⣾⠟⠋⢀⣠⣶⣾⡿⠁⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠁⢿⣿⡄⠀⠀⠈⢸⣿⡇⠀⠀⠀⠙⠻⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⠿⠛⢿⣇⠀⢠⣿⢿⣿⡿⠁⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⢸⣿⣿⣄⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣷⣶⣦⣤⣤⣀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣶⣾⠿⠟⠛⠉⠁⠀⠀⠘⣿⣦⣼⡟⠈⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠀⠀⠈⣿⣿⡏⠀⠀⠀⠿⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢸⣿⣿⣿⣄⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣄⠀⢸⡿⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠉⣿⣿⣄⠉⠁⠉⠁⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠁⠀⠘⠿⣿⣷⣦⣤⣴⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠉⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣆⣀⣴⡿⠟⢷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⡟⠋⠉⠀⠀⠀⢹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣤⣤⡀⢀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⠿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀