⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣾⣿⣿⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣾⣶⣿⣶⣶⣴⣬⡙⡛⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⠼⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⢶⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠀⠀⠀⣨⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠈⢿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣹⢿⡈⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠘⠀⠀⣠⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡀⠀⢻⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⠼⡏⢹⣘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⢠⣽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⠋⢻⣿⡳⠄⠹⣿⣿⣿⢿⣿⣿⣿⣿⣿⣟⣹⣾⣷⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢿⣿⣿⣦⠀⠈⢿⣿⣾⣿⣿⢿⣿⣿⣿⣷⣿⣥⣂⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣮⢿⣿⠟⠇⠀⠀⠙⠛⣦⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣇⠀⠀⢸⣄⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠆⠀⠀⠀⠀⠀⠀⠰⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣷⣄⠀⠀⣶⣤⡀⠀⠀⢄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣠⣾⡏⡆⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣦⣜⠛⠁⣠⣴⣾⢿⣿⣿⣿⣿⣿⡿⠛⠋⠉⠛⠷⠦⣤⣄⣠⣴⣿⡿⠿⢃⠇⠀⠀⠀⠀⠀⡀⠀⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠿⠛⠻⠿⠿⣿⣿⡛⠁⢸⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣹⡏⡁⡀⡜⠀⠀⠀⠀⠀⠀⠘⢿⣦⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣿⡟⠀⠀⠠⢤⣤⣴⠟⢩⡧⠀⢸⣿⣿⡏⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠊⢁⣣⠃⠀⠀⠀⠀⠀⠀⠀⠀⠳⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⡇⣿⡟⠀⠀⠀⠀⢠⠾⢻⡃⠗⠀⣀⣿⣿⡿⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠁⠀⠀⠀⠠⡶⣆⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⢻⡇⠠⡆⢀⡴⠋⠀⠈⠀⠀⠀⢩⣿⣿⠁⢀⡇⠀⠀⠀⠦⡀⠀⠀⠀⠀⣸⡿⠆⠀⠀⠀⠀⠀⠀⠀⠳⢿⣷⣄⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⡇⣼⠁⢠⣷⠛⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⡇⠀⠀⡀⡆⠈⣳⣤⣤⣶⠟⠁⠐⢄⠀⠀⠸⣷⡦⠀⠀⠀⠉⢻⣆⡀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣴⠏⠁⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⠰⣇⣠⣶⣷⠿⠾⠿⠛⠉⠀⠐⢲⣼⣾⡆⠀⡐⡛⣷⡀⠀⠀⠀⠘⣏⣿⣦⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡾⠹⠏⠀⣠⣴⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠙⣿⣧⣤⣻⣁⣿⣿⡀⠀⠀⠀⢻⡈⢻⣷⣆⠀⡠⠀⠛⣷⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠋⠂⠀⠀⠀⠀⢀⣠⣤⣶⠟⠉⠀⠀⢸⣟⣿⣿⣿⢿⡏⠈⣷⠀⠀⠀⠘⣇⠀⠙⢿⣧⠀⠀⠀⠈⠻⣷⣄⡀⠀ ⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⡣⠊⠀⢀⣠⣶⣶⡾⠿⠟⠋⡏⠀⠀⠀⠀⢸⠿⠻⠿⣿⣾⡇⠀⢻⣧⠀⠀⠀⣿⠀⠀⠈⢿⣦⠀⠀⠀⠀⠉⢿⣿⣶ ⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⡎⠀⠀⠀⣿⣷⣰⣶⣾⣿⡿⠏⢩⠀⠀⠀⡰⠃⠀⠀⠀⠀⣿⠀⠀⢠⢠⣿⠃⠀⠈⡏⠇⠀⠀⠙⡆⠀⠀⠀⠻⢷⡄⠀⠀⠀⠀⠈⢻ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡆⢠⠒⠀⢸⡇⠀⣀⣼⣿⣿⣿⣿⣿⣿⡇⢸⡜⠀⠀⢠⠇⠀⠀⠀⠀⢸⡟⠀⠀⠀⢸⡏⠀⠀⠀⢿⡼⡀⠀⠀⣿⠀⠀⠀⠀⠀⠉⠛⠿⠶⠶⣾⣿ ⠀⠀⠀⠀⠘⢿⣿⣿⣿⠿⠟⠳⣧⣤⡀⣸⡆⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣸⡅⠀⠀⣼⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⢸⠃⠀⠀⠀⠈⣷⠀⠂⢠⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡏⠁⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡞⠁⠀⠀⠀⠀⢠⣿⡇⠀⠀⡗⡚⠀⠀⠀⠀⠀⢸⡧⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢉⡽⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⢠⢸⡇⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠟⠋⠁⢀⣼⠁⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⢀⣻⣤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⣾⠁⢀⠀⠀⣎⣿⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠈⠉⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⢀⠎⠁⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⢰⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⢘⣸⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡾⡇⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠅⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⣠⡾⡇⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⠓⠃⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⣎⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣫⡄⢻⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⢀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠀⠀⠀⣾⠑⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢨⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣧⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣷⡄⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⡏⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⡿⠟⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⣀⣠⣶⣾⠟⠉⠀⠀⣰⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣋⣁⣠⣤⣴⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠃⠀⠈⠉⢿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⣽⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⢤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⠋⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⣘⣶⢤⣶⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢹⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢠⢎⣼⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣹⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⣠⣧⣾⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⠿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡗⢿⣿⣿⣿⣿⠏⠀⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡝⢿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⢇⣠⣿⣿⣿⣿⣿⣿⢿⣷⣿⣿⣿⣿⠼⠟⠁⢘⣻⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⢿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠞⣾⣿⣾⡏⢹⣿⡿⡄⠙⣾⠿⠿⠛⠀⠀⢀⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁ ⠀⠀⠀⠀⠀⠀⠀⣰⢏⣴⣿⣿⣿⡷⢸⣿⡇⠘⢾⡁⠀⠀⠀⠀⢤⣍⠛⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⣧⣾⣿⣿⣿⣿⣷⣿⣿⡇⠀⢸⠈⠁⠀⠀⠀⠼⠋⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡤⣞⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⡀⢸⠀⠀⠀⠶⠶⡶⢀⣼⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡤⢋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣾⣅⡀⠀⠀⠀⣠⣿⣿⣿⣿⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣽⣿⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⠠⠘⣿⡹⣿⣿⣷⣦⣾⣿⣿⣿⣿⣿⣇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠊⣱⠿⣻⠏⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠐⠀⠸⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀ ⡜⢡⡞⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣹⣖⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠈⠁⠀⠀ ⢠⡏⠀⠀⣠⠖⣋⣉⣉⣙⣛⡟⠛⠒⠺⣿⡉⠉⠀⠀⠉⠉⠉⠀⠀⠙⠛⠻⠿⠿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡏⠀⠀⢰⢡⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣶⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⡟⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣧⣄⣠⠤⠤⠤⠤⢶⣦⣄⠀⠀⠀⢠⠤⡄⠀⠀⣽⠀⠈⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⣹⠁⠉⠙⠒⠶⢦⣄⡠⠤⠝⠳⣄⠀⠀⠀⠀⠀⢀⡟⡀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠱⠀⢰⡇⡇⠀⠀⠀⠀⢻⣦⡀⠀⡘⠀⢰⠃⠀⠀⠀⠀⠐⢤⠏⠙⠷⣦⡀⠹⣦⡀⠀⠀⣠⡾⡞⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣷⣷⡇⠀⠀⠀⠀⢸⣿⣿⣦⣧⠀⡏⢀⢀⠴⠋⠁⠀⠀⠀⠀⠀⠈⠻⣷⡿⣿⣿⣾⣿⢤⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠐⠁⠈⠀⠀⠀⠀⠀ ⠀⠀⣿⠟⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⡇⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣾⣿⣿⢾⠿⠿⠿⢷⣶⣶⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⡇⠀⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡝⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠋⠀⠈⣆⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀ ⠀⢸⡀⠀⠻⡆⠀⠀⠀⢸⡏⠻⣿⣿⣿⣿⣿⣦⣤⣀⣀⣀⣠⣤⣶⣿⠟⠋⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠀⠀⠀⠀⠀ ⠀⠀⢧⠀⢠⢹⠀⠀⠀⢸⠇⠀⠹⣿⣿⠹⣿⡟⠉⠉⠉⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠳⢼⠈⣇⠀⠀⢸⠀⠀⠀⢻⡿⠀⠸⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⢸⠀⢸⡀⠀⣸⠀⠀⢀⠞⠁⠀⢀⡏⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⣿⣆⠀⠀⢸⠃⡆⡇⠀⡿⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠈⢳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⡑⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⣿⣿⣄⡀⠘⠀⣷⡄⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠙⢦⡈⠙⠒⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣷⠄⠀⡇⠁⠀⢸⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠈⠁ ⣿⣿⣿⣿⠀⢠⠇⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⣷⣄⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠀⢸⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠀⢸⠀⠀⢸⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡟⠹⡄⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠀⢸⠀⠀⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⡰⠷⠶⣦⣤⣀⣈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⣿⣿⡏⠀⠀⠘⡄⠀⠀⠀⠀ ⣿⣿⣿⣿⠀⠈⠀⢰⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢰⢃⣀⣀⣤⣤⣟⡛⡻⠿⢿⣶⣶⣦⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⢹⡀⠀⠀⠀ ⣿⣿⣿⣿⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⡼⠛⠉⠉⠉⢹⢉⡻⣟⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢳⠀⠀⠀ ⣿⣿⣿⣿⠀⡟⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⠃⠀⠀⠀⠀⢼⡞⠋⠁⠀⠀⠈⠉⠛⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⡆⠀⠀ ⡾⠙⠛⠿⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢷⠀⠀ ⠀⠀⠀⠀⠀⡷⢿⣿⣿⣿⣿⣿⡿⠟⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⠀⠀⠀⢀⠀⢀⠀⠀⠉⠹⢿⣿⣿⣿⣿⣿⣷⣶⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⢠⠃⠼⢿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⣀⠈⠻⣿⣿⣿⣿⣿⠀⠠⠀⠀⢸⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⣿⣿⣿⣿⣿⣿⣿⢿⠉⠈⠀⠃⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣴⣤⣠⣁⣋⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣿⣰⠀⠀⠉⠟⣾⣶⣠⣀⠀⠀⠀⠀⣀⣦⣷⣿⣿⣿⣿⣿⣿⣿⢿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⠟⡿⣼⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⣿⣿⣿⣿⣿⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⢷⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⡏⡄⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⡄⣷⣿⣿⣿⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⣇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⣧⣿⣿⣿⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢨⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⡇⣼⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⠿⠻⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠑⣾⠀⠀⠀⠓⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣼⢀⠀⠀⠀⠀⡀⢦⠈⠀⠀⠀⠀⠀⠀⠀⠀⡯⣿⢠⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⢻⡄⣫⣷⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡞⣎⠀⠀⠀⠀⠀⠀⠀⠀⣄⠙⠀⠀⠀⠀⠀⠃⠓⣿⢰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⡇⡾⣠⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠏⣹⠅⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⠀⠀⠀⠀⡇⡾⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠃⣸⢘⠀⡀⣄⠦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠇⣸⢰⠀⠀⠀⣿⢰⠀⠀⠀⠀⠀⠀⠁⠎⢀⡄⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡄⣿⠉⠈⠀⠀⠀⣇⢸⠀⠀⠀⠀⠀⠀⠀⣿⣎⠀⠀⢀⠁⣾⠀⠀⠀⠀⠀⠀⠃⡼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣤⣻⢀⠀⠀⠀⡀⣿⠘⠀⠀⠀⠀⠀⠁⣾⢀⠀⠀⠀⡟⢀⠀⠀⠀⠀⠀⠁⣼⢀⠁⠋⠟⠿⠿⠻⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢳⠀⠀⠀⠀⣟⢸⠀⠀⠀⠀⠀⡇⢸⢠⠀⠀⠇⣼⠀⠀⠀⠀⠀⠀⡽⢉⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢹⠀⠀⠀⡧⢸⠀⠀⠀⠀⠀⡚⡗⠀⠀⡇⣿⢠⠀⠀⠀⠀⠁⡞⣤⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠛⠙⠀⠀⠀⠀⠀⠀⠁⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣹⢠⠂⠀⣷⠈⠀⠀⠀⠃⢸⠀⠀⠀⡇⣼⠀⠀⠀⠀⠀⣼⠀⠀⡅⣸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣴⡆⣸⡀⣤⣧⠳⠟⠿⣿⣿⣿⢿⠘⠀⠀⠀⠀ ⣿⣾⠶⠶⠿⠛⠉⠀⠀⠀⠀⠀⣿⠀⠀⡀⡼⢿⠀⠀⠀⡏⢸⠀⠀⠀⡟⢸⠀⠀⠀⠀⠇⢠⠀⠀⡜⢸⡇⣿⣿⣿⣿⣿⣿⣼⣀⠀⡇⢸⠀⠒⢠⡆⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⢻⠈⠀⠀⠀⠀⡄⢷⠻⠀⠀⠀⡆⠙⠀⠀⠇⡏⠈⠀⠃⣿⢠⢠⠀⠀⣿⠀⠀⠀⠀⠃⡰⠀⠀⠀⢩⠏⡿⣿⣾⣶⣰⣷⣿⠀⠀⠀⡎⢀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠸⠀⠀⠀ ⣶⣿⢿⠉⠀⠀⠀⠀⣦⢿⠈⠀⠀⣿⠀⠀⠀⣧⢻⠀⡇⣾⣿⠿⠻⠿⢸⠀⠀⠀⠀⡏⠋⠟⠿⡾⣶⣶⣠⢀⠀⠊⡣⡿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⢠⠀⠀⠀ ⠀⡀⣄⣷⠻⠈⠀⠀⠀⣧⢿⠙⠀⣇⠘⠀⠀⠀⣷⠈⡏⢿⣿⣿⣿⣟⢸⠀⠀⠉⠟⣶⣤⣠⢀⠀⠀⠀⠀⠂⠋⠋⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣾⣠⠀⠀⠀⠀ ⠀⠀⠀⠀⣄⣷⠛⠀⡠⠀⣆⣷⢻⡈⢻⠀⠀⠀⡀⣿⣿⣁⣻⣤⣧⣿⠙⠟⣴⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⡾⣴⣠⠀⠏⠹⡾⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣆⠻⠈⠀⠀⠀⣦⣿⣏⠘⠀⠀⠀⡀⣷⡛⡐⠀⡆⣾⣼⢲⠐⠀⠉⠛⠿⠾⠿⣷⣶⣠⣇⠰⠀⠀⠏⣿⣼⠀⠀⠀⠀⠀⠀⠀⠁⠏⣴⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡄⢷⠙⠀⠀⠀⡀⣆⢻⠉⠀⠀⠀⡦⣷⠸⠀⠀⢄⠐⠁⠟⣶⣤⣤⣳⠈⡆⡀⠀⠀⡇⠀⠀⠃⣿⣼⠀⠀⠀⠀⠀⠀⠀⠛⣷⢠⠁⣼⡇⠸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⠹⠀⠀⠀⠀⣄⣷⢿⠳⠀⠀⠀⠀⠀⠀⠀⠆⡿⣸⠀⠀⠀⠀⡀⠦⠀⠀⠀⡇⢀⠁⣿⣿⢩⠀⠀⠀⠈⠀⠋⡴⢀⡆⠠⡇⢻⡇⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢻⠀⠀⠀⠀⠀⣆⡶⠠⠀⠀⠀⠁⠀⠀⠃⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢠⡿⣿⣿⣀⠀⠗⡃⢻⠾⢠⠀⠀⠀⠀⡟⣿⡇⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⠳⠀⠀⠀⠀⠀⠀⠀⠀⠃⣣⢁⠊⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡏⣿⣿⢸⠀⡧⢩⠟⣴⣤⢤⠠⠀⠀⡟⣿⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣦⢿⠘⠀⠀⠀⠀⠀⠀⡜⡀⡁⡏⣹⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣿⣿⣿⢸⠁⡛⣿⣿⠿⠿⠻⠛⠿⣿⣿⣿⣿⣿⣿⠸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣸⠀⡀⠀⠀⠀⠀⠀⠇⢃⠿⡿⣿⣴⣠⣄⣤⠦⠷⠛⠉⠋⠛⡿⣿⣿⣿⣿⣿⢿⣾⣴⣠⠁⠛⣜⣦⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⡆⡏⣾⣠⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢄⠀⠀⡀⣤⣶⠀⠀⣄⣷⣿⣿⣿⣿⣿⢹⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠰⠀⠀⠀⠀⠀⠀⠆⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⣄⢸⠀⠀⣇⣿⣿⣿⣿⣿⠘⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⠀⠀⠀⠀⠀⠀⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⣦⠛⠙⠀⠀⠇⠟⣿⢿⣮⣿⣿⣿⣿⣿⠸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⢸⠀⠀⠀⠀⠀⡇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣸⣂⣥⣿⣷⣿⣿⣿⢿⣿⣿⣾⣿⢿⠈⠀⣦⣿⣿⢿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⠀⠀⠀⠀⠁⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣾⣷⣾⣹⣟⣿⣿⣿⣿⣿⢿⣿⣿⣿⠹⠄⡳⣿⢻⠋⣿⣿⣿⣿⢿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣽⢠⠀⠀⠀⠁⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣘⢹⡏⠼⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⢻⠀⡀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣾⣠⠀⠀⠘⠃⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⡈⢿⣹⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⣿⣿⢿⠈⡇⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣨⠀⠀⠀⠟⡾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣠⠀⢶⠁⡟⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣿⣿⠼⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣼⠀⠀⠀⠃⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣿⢿⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠘⠀⠃⡾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⢿⡛⡙⣬⣴⣶⣶⣿⣶⣾⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣾⣶⣴⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢸⠀⠀⠠⠀⣿⣿⣿⣿⣿⠻⠈⣀⠦⠒⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⣿⣿⣿⣿⣿⢿⠼⠃⢠⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⣶⣷⣿⣿⣿⣿⣿⢿⠹⠉⠀⠀⢀⠀⢀⠀⠀⠀⠤⠢⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠇⠿⠿⠿⠟⡿⣿⣿⣿⣿⣿⢿⡷⠀⠀⠀⠀⠀ ⠀⠀⢷⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠘⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠙⠀⠀⠀⠀⠀⠀⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⠀⠿⠛⠙⡾ ⠀⠀⡆⠘⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠟⠛⠉⠈⠀⠀⠁⠋⡞⢼⠀⠀⠀⠀⠃⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⡟⠀⣿⣿⣿⣿ ⠀⠀⠀⢳⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⡻⢉⢹⠉⠉⠉⠛⡼⠀⠀⣦⣿⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⣿⣿⣿⣿ ⠀⠀⠀⡀⢹⠀⠀⠁⡟⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣶⣤⣤⣦⣶⣶⢿⠿⡻⡛⣟⣤⣤⣀⣀⢃⢰⠀⠀⠀⡀⣦⣿⣿⣿⣿⣿⢰⠀⠈⠀⣿⣿⣿⣿ ⠀⠀⠀⠀⡄⠘⠀⠀⡏⣿⣿⣿⣿⣴⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣈⣀⣤⣦⠶⠷⡰⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣾⠀⠀⢸⠀⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⡄⠹⡟⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣷⢸⠀⠀⢸⠀⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⡄⣿⣿⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⢸⠀⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣄⣷⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢹⠇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠇⢠⠀⣿⣿⣿⣿ ⠁⠈⠀⠀⠀⠀⠀⠀⡀⢳⠈⠀⠀⠀⠀⠀⠀⡆⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⢸⠀⠁⡇⠀⠄⣷⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠒⠙⡈⢦⠙⠀⠀⠀⠀⠀⠀⣆⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⡄⣷⠀⠘⡀⣄⣿⣿ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⣀⢦⡑⠫⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢳⠈⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⡿⠀⡇⡆⠃⢸⠀⠀⣆⣿ ⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠳⠈⠀⡏⢀⠀⠁⠞⢀⠀⠀⣸⠀⡀⢸⠀⢸⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢹⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⣿⠸⠀⡿⢻⠀⠀⠀⢸⠀⠀⣇⠈⢼⠳⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠉⠉⡟⣿⠹⣿⣿⠹⠀⠇⢸⠀⠀⠀⢹⢠⠀⢧⠀⠀ ⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⠀⠀⠀⠀⡄⠸⠀⠀⠀⠀⠋⠟⣿⣶⣤⣠⣀⣀⣀⣤⣦⣿⣿⣿⣿⣿⠻⡏⢸⠀⠀⠀⡆⠻⠀⡀⢸⠀ ⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⣆⠈⠀⠋⡿⣾⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⡝⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⣿⠀⡇⢰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡞⣶⣶⢷⠿⠿⠿⢾⣿⣿⣾⢙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣾⡇⣦⣿⣿⣿⣿⢸⠀⠀⠀⠀⡇⠟⣿⠀⠀ ⠀⠀⠀⠀⠀⠈⠁⠐⠀⠀⠀⠀⠀⠀⠋⣰⠀⠀⠀⠀⢤⣿⣾⣿⣿⡿⣷⠻⠈⠀⠀⠀⠀⠀⠁⠋⠴⢀⢀⡏⠀⣧⣦⣿⣿⢸⠀⠀⠀⠀⡇⣷⣷⢠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⡞⡾⣠⠀⠀⡀⣦⠹⡀⣦⠷⠙⠏⢤⠐⠀⠀⠀⠀⠃⢰⠀⡘⠀⡀⣦⢻⠀⠀⠀⠀⡇⡇⢰⠀⠱ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⡀⡟⢀⠀⠀⠀⠀⠀⣄⠳⠝⠤⡠⣄⢦⠶⠒⠙⠉⠁⣹⠁⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢷⠛⠈⠀⣽⠀⠀⡄⠤⢠⠀⠀⠀⣄⣦⢶⠤⠤⠤⠤⣠⣄⣧⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⢦⣶⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠹⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⢡⢰⠀⠀⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣆⣿⣿⣿⠿⠿⠻⠛⠙⠀⠀⠉⠉⠉⠀⠀⠉⡉⣿⠺⠒⠛⡟⣛⣙⣉⣉⣋⠖⣠⠀⠀⡏⢠ ⠀⠀⠁⠈⠄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣖⣹⢀⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠁⡞⢡⡜ ⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣧⠸⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⠏⣻⠿⣱⠊ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣇⣿⣿⣿⣿⣿⣾⣦⣷⣿⣿⡹⣿⠘⠠⣿⣿⣿⣿⣿⣿⣿⣿⢟⡿⣿⣽⣴⣠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠙⣿⣿⣿⣿⣠⠀⠀⠀⡀⣅⣾⣿⢿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢋⡤⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣼⢀⡶⠶⠶⠀⠀⠀⢸⡀⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣡⣞⡤⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠋⠼⠀⠀⠀⠁⠈⢸⠀⡇⣿⣿⣷⣿⣿⣿⣿⣾⣧⡴⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⠛⣍⢤⠀⠀⠀⠀⡁⢾⠘⡇⣿⢸⡷⣿⣿⣿⣴⢏⣰⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⢀⠀⠀⠛⠿⠿⣾⠙⡄⡿⣿⢹⡏⣾⣿⣾⠞⣼⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⣿⣿⢿⠸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣻⢘⠁⠟⠼⣿⣿⣿⣿⣷⢿⣿⣿⣿⣿⣿⣿⣠⢇⢰⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⣿⣿⣿⢿⡝⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⢿⠀⠏⣿⣿⣿⣿⢿⡗⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⣿⣿⣿⣿⢻⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⠿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣾⣧⣠⠀⠃⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⣿⣿⣿⣹⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣼⢎⢠⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⣿⣿⣿⢹⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣾⣶⢤⣶⣘⣎⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⣿⣿⣿⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣶⣿⣿⣿⣿⣿⣿⣿⣸⠀⠀⠋⡔⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣤⣤⣤⢤⡠⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡏⣽⣭⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣟⣿⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀