⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣋⣿⣷⣤⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠫⠉⠉⠈⠙⢻⡟⢿⣿⣯⣭⣭⣴⡶⠶⠶⢶⣤⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠋⡶⠴⠖⢁⣀⣤⣀⡤⠀⠉⠛⢿⡆⠀⠀⠀⠀⠀⠉⠙⢷⣝⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⣴⣶⠟⡿⡉⠙⠿⣦⣀⡀⢹⡆⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⡂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢋⣼⠏⢀⣤⣾⡿⠋⣼⠋⠁⠀⠀⠬⢿⡿⢿⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⣠⣾⡿⠁⣼⠏⠀⠀⣀⠠⠤⠴⢖⣸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡝⣧⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⢠⣻⡿⠁⣼⠏⠀⠀⢱⡟⠋⠉⠉⠉⢀⡄⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⠀⠘⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⢠⣏⡿⠁⣰⠃⠀⠀⢂⣾⠁⠀⠀⠀⣰⠟⠝⣠⡞⠁⠀⠀⠀⠀⠀⢠⠄⢠⡾⠁⢀⣾⠃⢼⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢇⣾⠀⣾⠾⠁⢠⡟⠀⠀⠀⢸⠇⠀⠀⢀⠜⣡⠎⣴⠏⣠⠆⠀⡀⠀⠀⡐⠋⡰⠋⠀⣰⠟⠃⠀⢸⣿⣿⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⣹⣾⢣⡆⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⡾⢫⡞⠁⠌⠁⠀⠋⠉⣼⡟⠛⠛⠛⠒⢚⡿⣶⣷⣶⣿⣿⣛⣧⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⣿⠏⣠⣿⠁⢸⠁⠀⢸⠁⠀⠀⠀⡇⣀⠀⠀⠟⠁⠉⡀⠀⠀⠀⢀⣰⠾⣿⠁⠀⠀⢀⣠⣿⣾⣿⣾⣿⣟⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣶⠟⣣⣾⣿⣾⣿⣿⠀⢼⠀⣠⣾⠀⠀⠀⢀⣟⢿⣷⣦⣄⡀⠊⠀⠀⢀⣼⠏⠀⠀⠘⢷⣤⣠⣿⣿⡿⣵⡿⣿⢣⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠛⣿⢉⣿⡟⠀⡈⠀⣷⠉⠀⢢⢸⢸⠟⢿⣿⣿⣿⣿⣶⣤⣴⠟⠀⠀⠀⠀⠀⣠⡿⢿⣿⣏⣴⣿⣾⣷⡿⣧⣿⣿⠋⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⢸⣿⠇⢸⡇⢠⣽⠀⢰⢸⡈⣼⠀⠘⠿⠿⠿⣿⣿⣿⣧⠀⠀⢀⣴⣶⣾⣯⣶⡾⣿⣿⣿⣿⣧⣿⣵⣿⣿⠃⠀⠀⠀⠀ ⡀⡀⠀⠀⠀⠀⢰⠀⣠⣾⣿⣾⣸⢿⠀⣼⡇⢸⣿⠀⣸⢸⡇⣿⠀⠀⠀⠀⠀⠈⠉⠓⢿⣦⣴⡿⢿⡿⠹⠿⠛⢇⣼⣿⣿⣿⣿⣰⣿⣿⡏⠀⠀⠀⠀⠀ ⡇⠇⠀⠀⠀⠀⢸⣾⣿⠛⣻⣗⣧⣿⠀⣿⡗⠈⣿⠀⣿⢰⣇⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣷⣴⣴⣏⣴⣿⣿⣿⣿⣿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀ ⡇⠁⠀⢸⠀⢠⣾⣿⣏⣰⠟⠻⣿⣿⣿⠿⢿⣦⣿⣤⣿⣼⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣟⠻⢿⣿⣿⣿⣟⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⢸⣴⣿⣿⣿⣿⠏⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⣤⡿⠿⠿⠦⢶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⠉⠀⠀⠀⠀⠀⣀⡙⠻⣿⣦⣀⠀⠀⠀⠀⠀⠀ ⠀⢰⠀⣼⣿⣼⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⢷⡄⠀⠀⠀⠀⠀⠀⠙⢿⣶⣌⢻⣿⣧⡀⠀⠀⠀⠀ ⠀⠸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⡐⠀⠸⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣭⢻⣿⣦⡀⠀⠀ ⠀⢠⣿⣿⣿⣿⠏⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣁⣤⡻⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣽⣿⣷⡄⠀ ⠀⢸⣿⣿⣿⣿⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣿⣿⣹⣇⠁⢈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣿⣿⡀ ⠀⠈⠉⢿⣿⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣍⣡⣻⡏⢸⣉⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡷