⠀⠀⠀⠀⠀⢸⣁⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡄⠀⠀⠠⣄⣀⠀⠀⠀⢀⠤⡀⠀⠀⠀⡠⠃⠁⠉⠉⠉⠁⠁⠁⠂⠐⠀⠁⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⡠⠋⠑⢄⡀⣀⠜⠀⠀⠀⠀⠀⠀⠁⠢⣀⡘⠀⠀⠉⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⡀⠄⠄⠌⠭⠁⠤⠠⠠⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠢⢄⡄⠒⠁⡡⠈⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠁⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⡀⢄⢄⠀⠌⠀⠀⠀⠀⡀⠀⠀⣰⠀ ⠠⠤⠄⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⣀⣝⡑⣀⠤⠊⠁⠔⠀⠀⠠⠁⠀⠀⡀⡀⠥⡀⢀⠈⢄ ⠀⢀⠄⠂⠒⠒⠒⠢⡀⠀⠀⠀⠀⠀⡀⠅⠅⠶⠦⠆⣒⠒⠂⢡⠀⠀⠀⠀⠀⢸⠀⠀⠤⠤⡤⡊⣀⡀⡠⡡⠄⠤⠄⠗⢄⣀⣡⡄⡄⡀ ⡄⠁⠀⢰⡦⡄⠀⠀⠑⡀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠑⠄⠨⠀⠀⠀⠀⠀⢐⠀⡆⠁⠁⠀⠀⠀⠀⠙⡀⠀⠀⢀⠂⠁⠀⠀⠀⠀⠑ ⠆⠀⠀⠀⠉⠁⠀⠀⠀⡃⠀⠀⡃⠀⠀⠀⢀⠤⡀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠐⠀⡂⠀⠀⣟⡀⠀⠀⠀⠁⢆⢐⠁⠀⠏⣿⠀⠀⠀⠀ ⡃⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⡂⠀⠀⠀⠘⡓⠃⠀⠀⠀⠀⡭⠀⠀⠀⠀⠀⠨⠀⡁⠀⠀⠉⠁⠀⠀⠀⠀⣸⠐⠀⠀⠂⠀⠀⠀⠀⠀ ⠁⠢⣀⠀⠀⠀⠀⣀⡎⠀⠀⠀⠃⢄⠀⠀⠀⠀⠀⠀⠀⢀⠌⢀⠀⠀⠀⠀⠀⢈⠀⠁⣄⠀⠀⠀⠀⡀⡀⠊⠀⠘⣀⠀⠀⠀⠀⢀⠀⠄ ⠀⠀⠀⠈⠁⠁⠉⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⠄⠄⠄⠌⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠁⠁⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣸⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠰⠮⡧⢧⠍⣄⡀⡀⡀⣀⠀⠀⠀⠀⠀⠀⠀⡁⠀⡠⠃⠀⠀⠕⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⠛⡟⠛⠛⠛⣟⡋⠒⠀⠣⢤⠀⠀⠀⠀⠀⠀⣄⠔⠁⠀⠀⠀⡁⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠢⡀⡀⠀⠀⠀⡇⠀⠀⠀⠀⠈⢳⠀⠀⢸⠀⠀⢀⢀⠤⠚⡁⠀⠀⠀⠀⠀⡂⠀⠀⠁⢄⠀⠀⠀⠀⢀⡧⠷⣽⡗⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠑⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⢹⠈⠀⠁⠀⠀⠀⡅⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠁⠉⠐⠐⡞⡋⡛⡛⡗⠋⡒⠀⠂⠂⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠔⠒⠛⠙⡄⠀⠀⡔⠒⢺⠀⠀⢸⠀⠀⠀⠀⠀⠈⠁⠁⠒⠐⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣀⡀⣘⣀⠀⠀⠀⠀ ⠀⠀⡠⠏⠀⠀⠀⠀⠃⠀⠀⠁⠀⢸⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡗⠦⡠⠊⠀⠀⠀⠀⢳⠀⠀⠀ ⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣋⡠⠞⢏⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡠⠖⠉⠁⠀⠁⠀⠀⡇⠀⠀⠀⠀⠀⠘⡆⠀⠀ ⠀⡞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⠀⠇⡆⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢀⠇⠀⠀ ⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⢀⠎⠀⠀⠀ ⠀⠀⠉⢆⡀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠆⢄⣀⡀⣆⡀⠀⡀⢂⣀⡀⠤⠂⠊⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠑⠒⠦⠤⠔⢣⡀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠀⠀⠀⠀⡀⢣⠔⠤⠦⠒⠑⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠊⠂⠤⡀⣀⢂⡀⠀⡀⣆⡀⣀⢄⠆⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⡀⢆⠉⠀⠀ ⠀⠀⠀⠎⢀⠀⠀⠀⠀⠃⡠⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⠀⠀⠇⢀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⡆⠇⠀ ⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀ ⠀⠀⡆⠘⠀⠀⠀⠀⠀⡇⠀⠀⠁⠀⠁⠉⠖⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢏⠞⡠⣋⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⠀⠀⠀⢳⠀⠀⠀⠀⠊⡠⠦⡗⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⠀⠀⢸⠀⠁⠀⠀⠃⠀⠀⠀⠀⠏⡠⠀⠀ ⠀⠀⠀⠀⣀⣘⡀⣀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠐⠒⠁⠁⠈⠀⠀⠀⠀⠀⢸⠀⠀⢺⠒⡔⠀⠀⡄⠙⠛⠒⠔⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠂⠂⠀⡒⠋⡗⡛⡛⡋⡞⠐⠐⠉⠁⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⡅⠀⠀⠀⠁⠀⠈⢹⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠑⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⡗⣽⠷⡧⢀⠀⠀⠀⠀⢄⠁⠀⠀⡂⠀⠀⠀⠀⠀⡁⠚⠤⢀⢀⠀⠀⢸⠀⠀⢳⠈⠀⠀⠀⠀⡇⠀⠀⠀⡀⡀⠢⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⡁⠀⠀⠀⠁⠔⣄⠀⠀⠀⠀⠀⠀⢤⠣⠀⠒⡋⣟⠛⠛⠛⡟⠛⠈⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠕⠀⠀⠃⡠⠀⡁⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⡀⣄⠍⢧⡧⠮⠰⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⣸⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠁⠁⠉⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠌⠄⠄⠄⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠈⠀⠀⠀ ⠄⠀⢀⠀⠀⠀⠀⣀⠘⠀⠊⡀⡀⠀⠀⠀⠀⣄⠁⠀⢈⠀⠀⠀⠀⠀⢀⠌⢀⠀⠀⠀⠀⠀⠀⠀⢄⠃⠀⠀⠀⡎⣀⠀⠀⠀⠀⣀⠢⠁ ⠀⠀⠀⠀⠀⠂⠀⠀⠐⣸⠀⠀⠀⠀⠁⠉⠀⠀⡁⠀⠨⠀⠀⠀⠀⠀⡭⠀⠀⠀⠀⠃⡓⠘⠀⠀⠀⡂⠀⠀⠃⢀⠀⠀⠀⠀⠀⠀⠀⡃ ⠀⠀⠀⠀⣿⠏⠀⠁⢐⢆⠁⠀⠀⠀⡀⣟⠀⠀⡂⠀⠐⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⡀⠤⢀⠀⠀⠀⡃⠀⠀⡃⠀⠀⠀⠁⠉⠀⠀⠀⠆ ⠑⠀⠀⠀⠀⠁⠂⢀⠀⠀⡀⠙⠀⠀⠀⠀⠁⠁⡆⠀⢐⠀⠀⠀⠀⠀⠨⠄⠑⠀⠀⠀⠀⠀⠀⠀⠊⢀⠀⠀⡀⠑⠀⠀⡄⡦⢰⠀⠁⡄ ⡀⡄⡄⣡⣀⢄⠗⠄⠤⠄⡡⡠⡀⣀⡊⡤⠤⠤⠀⠀⢸⠀⠀⠀⠀⠀⢡⠂⠒⣒⠆⠦⠶⠅⠅⡀⠀⠀⠀⠀⠀⡀⠢⠒⠒⠒⠂⠄⢀⠀ ⢄⠈⢀⡀⠥⡀⡀⠀⠀⠁⠠⠀⠀⠔⠁⠊⠤⣀⡑⣝⣀⠀⠀⠀⠀⠀⡀⢄⠑⠀⠀⠀⠀⠀⠀⣀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄⠤⠠ ⠀⣰⠀⠀⡀⠀⠀⠀⠀⠌⠀⢄⢄⡀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠂⠁⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠈⡡⠁⠒⡄⢄⠢ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠠⠠⠤⠁⠭⠌⠄⠄⡀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠈⠉⠀⠀⡘⣀⠢⠁⠀⠀⠀⠀⠀⠀⠜⣀⡀⢄⠑⠋⡠⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⠁⠀⠐⠂⠁⠁⠁⠉⠉⠉⠁⠃⡠⠀⠀⠀⡀⠤⢀⠀⠀⠀⣀⣄⠠⠀⠀⡄⠣⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣁⢸⠀⠀⠀⠀⠀