⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢧⣄⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⢀⠄⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⡐⠀⠀⢸⡇⠀⠀⠀⠀⢀⠔⠁⠀⠀ ⠀⠀⠀⢿⣷⣄⠀⠀⠀⣠⣾⠃⢀⣴⠛⢧⠀⠀⠀⠀⢀⣾⠇⠀⣤⠞⢷⡀⠀⢸⡇⠀⠀⢀⣴⠋⠀⠀⡀⠀ ⠀⠀⠀⠀⣿⡿⢧⣤⡾⢻⣿⠀⢼⣏⠰⢸⡷⠀⣠⡾⠛⣿⡀⠠⣿⠘⢘⣿⠀⢹⡇⠀⠰⣿⠁⠀⣠⣾⡇⠀ ⠀⠀⠀⠀⣿⣧⡾⠛⢷⣼⣿⠀⢂⣿⠒⢻⡄⠂⢿⠃⡄⢿⠁⠃⣸⠓⠺⣇⠀⢺⡇⢠⡄⠉⣷⣾⠛⠻⡇⠀ ⠀⠀⠀⠀⣾⡏⠀⠀⠀⠙⣿⠀⢸⡏⣼⠸⣿⠀⣼⡆⡇⣸⡄⢰⣿⢸⢀⣿⠀⢸⡇⠨⣿⡿⠋⠙⣦⡀⠀⠀ ⠀⠀⠀⠀⣼⡇⠀⠀⠀⢠⣿⠀⢿⣧⢙⢸⣿⠀⣿⡃⠇⣾⡄⢠⣿⢸⠐⣿⠀⢸⡇⠰⠋⠀⠀⣠⠞⠀⠀⠀ ⠀⠀⠀⢠⡿⠁⠀⠀⠀⠘⢿⠀⠈⠻⣶⠞⠁⢠⡿⠃⠀⠻⠃⠀⠻⣦⡴⢋⡄⢸⡇⠀⠀⢀⠔⠁⠀⠀⠀⠀ ⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠋⠀⢀⠞⠀⠀⠀⠀⠑⠀⠀⠈⠡⢸⡇⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣬⣤⣿⣧⣤⣤⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⣿⡟⠉⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀ ⠀⠘⢦⡀⠀⠀⠀⠀⠀⢠⡖⣀⣤⠊⠠⣦⠀⣀⣼⣿⣷⣄⠀⣴⠀⠱⣤⡀⠀⠘⢦⡀⠀⠀⠀⠀⣰⠏⠀⠀ ⠀⠀⠘⢿⣶⡀⠀⢀⣴⡏⣾⡿⠙⣿⡆⡇⠱⢿⣿⠀⣿⣿⡎⢸⢰⣿⠛⢿⣷⢰⣦⢻⣦⠀⠠⣾⡏⠀⠀⠀ ⠀⠀⠀⢸⣿⢿⣶⡿⣿⡇⣿⣇⣀⣿⡇⡇⢰⡈⠻⠀⣿⣿⡇⢸⢸⣿⣀⣸⣿⠰⣿⠸⣿⣇⢠⣿⠇⠀⠀⠀ ⠀⠀⠀⢈⣿⡾⠻⣷⣿⡇⣾⡟⠉⣿⡆⡇⢸⣮⣢⠐⠫⡻⡗⢸⢰⣿⠉⢻⣷⢸⣿⠀⢸⣿⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠸⣿⡇⠀⠙⣿⡅⣿⡇⠀⣿⡇⡇⢸⣿⣿⠀⣦⡙⠇⢸⢾⣿⠀⢸⣿⠰⣿⢰⣿⠁⢈⣿⡆⠀⠀⠀ ⠀⠀⠀⢸⣿⠇⠀⢰⣿⠁⠻⢧⣤⣿⠃⡇⣼⣷⣿⠀⣷⣕⢄⢸⠺⣿⣤⣼⢟⣼⣿⣘⣟⣤⢜⣿⡇⠀⠀⠀ ⠀⠀⠀⢸⣿⣆⡀⠀⠛⠳⡀⡼⠋⠀⠠⢟⣿⠋⢸⠀⡇⠙⢿⡻⠀⠀⠙⢧⠉⠉⣿⠉⠉⢍⠘⣿⡇⠀⠀⠀ ⠀⠀⠀⣸⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⢸⣠⡇⠀⠀⠓⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠙⣿⣇⠀⠀⠀ ⠀⠀⢰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄⠀⠀ ⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀

⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀ ⠀⠀⡄⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢰⠀⠀ ⠀⠀⠀⣇⣿⠙⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠓⠀⠀⡇⣠⢸⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣸⠀⠀⠀ ⠀⠀⠀⡇⣿⠘⢍⠉⠉⣿⠉⠉⢧⠙⠀⠀⡻⢿⠙⡇⠀⢸⠋⣿⢟⠠⠀⠋⡼⡀⠳⠛⠀⡀⣆⣿⢸⠀⠀⠀ ⠀⠀⠀⡇⣿⢜⣤⣟⣘⣿⣼⢟⣼⣤⣿⠺⢸⢄⣕⣷⠀⣿⣷⣼⡇⠃⣿⣤⢧⠻⠁⣿⢰⠀⠇⣿⢸⠀⠀⠀ ⠀⠀⠀⡆⣿⢈⠁⣿⢰⣿⠰⣿⢸⠀⣿⢾⢸⠇⡙⣦⠀⣿⣿⢸⡇⡇⣿⠀⡇⣿⡅⣿⠙⠀⡇⣿⠸⠀⠀⠀ ⠀⠀⠀⠀⡀⣿⣿⢸⠀⣿⢸⣷⢻⠉⣿⢰⢸⡗⡻⠫⠐⣢⣮⢸⡇⡆⣿⠉⡟⣾⡇⣿⣷⠻⡾⣿⢈⠀⠀⠀ ⠀⠀⠀⠇⣿⢠⣇⣿⠸⣿⠰⣿⣸⣀⣿⢸⢸⡇⣿⣿⠀⠻⡈⢰⡇⡇⣿⣀⣇⣿⡇⣿⡿⣶⢿⣿⢸⠀⠀⠀ ⠀⠀⠀⡏⣾⠠⠀⣦⢻⣦⢰⣷⢿⠛⣿⢰⢸⡎⣿⣿⠀⣿⢿⠱⡇⡆⣿⠙⡿⣾⡏⣴⢀⠀⡀⣶⢿⠘⠀⠀ ⠀⠀⠏⣰⠀⠀⠀⠀⡀⢦⠘⠀⡀⣤⠱⠀⣴⠀⣄⣷⣿⣼⣀⠀⣦⠠⠊⣤⣀⡖⢠⠀⠀⠀⠀⠀⡀⢦⠘⠀ ⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡉⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠉⡟⣿⠉⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡄⣤⣤⣧⣿⣤⣬⣤⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢺⡇⢸⠡⠈⠀⠀⠑⠀⠀⠀⠀⠞⢀⠀⠋⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠋⠠⠀⠀ ⠀⠀⠀⠀⠁⠔⢀⠀⠀⡇⢸⡄⢋⡴⣦⠻⠀⠃⠻⠀⠃⡿⢠⠁⠞⣶⠻⠈⠀⢿⠘⠀⠀⠀⠁⡿⢠⠀⠀⠀ ⠀⠀⠀⠞⣠⠀⠀⠋⠰⡇⢸⠀⣿⠐⢸⣿⢠⡄⣾⠇⡃⣿⠀⣿⢸⢙⣧⢿⠀⣿⢠⠀⠀⠀⡇⣼⠀⠀⠀⠀ ⠀⠀⡀⣦⠙⠋⡿⣿⠨⡇⢸⠀⣿⢀⢸⣿⢰⡄⣸⡇⡆⣼⠀⣿⠸⣼⡏⢸⠀⣿⠙⠀⠀⠀⡏⣾⠀⠀⠀⠀ ⠀⡇⠻⠛⣾⣷⠉⡄⢠⡇⢺⠀⣇⠺⠓⣸⠃⠁⢿⡄⠃⢿⠂⡄⢻⠒⣿⢂⠀⣿⣼⢷⠛⡾⣧⣿⠀⠀⠀⠀ ⠀⡇⣾⣠⠀⠁⣿⠰⠀⡇⢹⠀⣿⢘⠘⣿⠠⡀⣿⠛⡾⣠⠀⡷⢸⠰⣏⢼⠀⣿⢻⡾⣤⢧⡿⣿⠀⠀⠀⠀ ⠀⡀⠀⠀⠋⣴⢀⠀⠀⡇⢸⠀⡀⢷⠞⣤⠀⠇⣾⢀⠀⠀⠀⠀⢧⠛⣴⢀⠃⣾⣠⠀⠀⠀⣄⣷⢿⠀⠀⠀ ⠀⠀⠁⠔⢀⠀⠀⠀⠀⡇⢸⠀⠀⡐⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠄⢀⠀⠂⡠⠀⠀⠀⠀⠀⠀⠀⣄⢧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀