⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⣡⣔⠯⣿⡿⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡮⣿⣿⣍⣍⡙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡡⣾⢯⢒⡿⠤⣄⡹⡿⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡮⡳⠓⠉⠀⡠⠖⠚⠛⣮⣗⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣝⠈⡗⢁⠜⠀⠀⠀⠀⢷⢬⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣏⡿⠁⠀⡀⠎⠀⠀⠀⠀⠀⠃⣟⡭⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡷⠂⣾⠍⠁⠀⠀⠀⠀⠀⢸⠀⠘⣇⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣿⢣⡄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⢯⢯⣄⠀⠀⠀⠀⠀⠀⠀⠀⡱⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢺⢻⡄⠀⠀ ⠀⠀⠀⠀⠀⢀⣸⡏⠁⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡹⢵⠄⠀⠀⠰⣄⣐⡮⠝⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠀⠀ ⠀⠀⠀⠀⠛⡺⢧⠂⠀⠀⠱⡄⠀⠀⠀⠀⠀⠔⠒⠒⢄⠀⢸⡀⠀⠀⠀⠘⢢⠀⠀⠀⠀⠀⠀⡞⣉⣭⣭⣢⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠜⣡⠇⠀⠀⠀⠀⠙⣄⠀⠀⢀⣧⡾⣳⣦⣄⡡⡀⢇⠀⠀⠀⠀⠀⠓⡀⠀⠀⠀⠀⡷⣿⡿⠛⡿⣷⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⢣⠀⠸⡯⣿⠏⠀⠹⣯⡣⣸⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⣟⣯⠀⠀⠸⣿⣗⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠘⡾⣿⡄⠀⠀⢻⣷⢺⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⢿⣿⡂⣀⢴⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡜⢽⣯⡲⣄⣼⣿⡎⠀⠀⠀⠀⠀⢀⠀⠀⠀⠳⢤⣀⣙⣿⣷⣿⡿⡟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠙⠫⠽⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢫⣣⡀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⡀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⢀⢀⣴⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⣬⣿⣿⣿⠗⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣆⣦⡤⣀⣀⣀⣀⡀⣀⣀⣤⣤⡤⣀⢀⣀⣤⣾⣿⣯⣾⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠒⠐⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣟⣛⣟⠿⠷⠾⠿⣿⣿⣿⣿⣿⣿⡿⢛⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠁⠀⠂⠐⠒⠄⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠯⠽⠾⠿⠷⠯⠭⠭⠤⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀