⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⣼⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⣿⠟⠿⠿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠤⠤⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠘⠀⠀⠀⠀⢀⣀⡤⠤⠤⠤⢤⣀⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠤⠖⠒⠒⠢⠤⢄⣔⠒⠒⠒⠠⠤⢀⡀⣇⠀⣤⣤⣇⠀⠀⠀⠀⢀⡤⠒⠊⠉⠀⠀⠀⠀⠀⠸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠈⠙⢷⣿⣿⣿⣀⣠⠴⠞⠛⠛⠛⠛⠛⠛⠲⠦⣤⣄⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣠⠴⠒⠛⠛⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢳⣠⠴⠋⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣧⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣠⢤⡀⠀⠀⠀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣄⣀⡀⠀⠀⡇⠀⢠⠎⠀⠀⡇⠀⠀⠀
⠀⠀⠀⠀⢧⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡉⠈⠉⠓⠦⡇⠀⡏⠀⠀⢠⠇⠀⠀⠀
⠀⠀⠀⠀⠸⡄⠀⢠⠏⠀⢀⡀⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠈⠲⠀⠀⢠⡟⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢧⠀⣼⠀⢀⡞⡇⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠹⣷⣄⡀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⢻⣿⣦⣀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢤⡷⠷⠶⠞⠀⠷⠶⣶⠂⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠈⢻⣿⣗⠂⡤⢀⣿⡇⠀⠀⠀⠀⠀⢿⣿⣿⣟⠦⣄⣰⠏⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢹⣦⡀⠀⠀⠀⠈⠳⣤⡀⠀⢠⡇⢳⠀⠀⠀⠀⠀⢠⡀⠀⡠⢧⣿⣠⠴⠋⠈⠙⠿⣿⣷⣿⣿⠀⠀⠀⠀⠀⠈⣿⣿⣿⡆⠀⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⢀⣠⡀⣠⣶⡶⠾⠟⢀⣾⠃⠈⢧⠀⠀⠀⠀⠀⠙⣦⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⡟⠛⠿⠏⣿⡆⠀⢀⣿⠟⠶⠶⠾⢧⠀⡦⢤⣄⣀⣀⣙⣧⠀⠀⠀⠀⠀⠀⠀⣀⣠⡀⢸⡇⠀⣸⠀⠀⠀⠀⠸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢹⡧⢠⣿⠋⠀⠀⠀⠀⠀⠳⠇⠸⠿⠛⠉⠁⠀⠀⠀⠤⢒⣤⣶⡿⠛⠉⠀⢸⣇⣾⣿⠀⠀⠀⠀⠀⠹⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⡆⠀⠀⠀⠘⡿⠛⠁⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠛⠛⠛⠉⢸⣿⣿⡏⠀⠀⢰⡇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⡇⠰⣄⡀⠀⢹⡀⢰⣶⠶⠿⣿⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠇⠀⣰⣿⠇⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠹⣿⣦⣀⣳⡀⢀⣤⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⠆⠀⠀⠀⠀⠀⠀⢀⣚⣋⣹⣟⣠⣾⣿⣿⠀⢀⣴⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⣿⣇⠠⣄⢹⣿⣿⣿⣷⣌⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠊⠀⠀⠀⠀⠀⠀⣀⠴⠒⠉⠉⠀⠈⠉⠛⢿⣿⣿⡏⢠⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀
⠀⡴⠤⣄⠀⢸⠏⠀⢹⡆⠹⣆⣛⣻⣿⣿⣿⣷⠴⠒⠒⠲⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠈⣇⠀⠀⠑⠾⠀⠀⣼⠃⠀⠈⢿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⣀⣀⣀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠉⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀
⠀⠈⠳⣄⠀⠀⠀⢠⣿⣶⣶⣦⣄⣹⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣅⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣼⣦⣤⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠙⠦⣤⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠚⢿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣯⠀⢸⡤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣷⠏⠀⠀⠀⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠷⠄⠀
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣿⣿⣿⣿⣿⣿⣿⠟⠘⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣛⣿⣿⣿⣿⣷⣶⣶⣿⣿⣏⣓⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣜⣁⣀⣸⣿⣿⣿⣿⡛⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀