⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠀⠀⠀⡗⠖⣄⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⢣⠀⠁⠗⢄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⢏⠀⠀⠸⠉⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⢸⡀⠈⢶⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠈⠂⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠨⡖⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡀⢈⣃⡖⡈⣆⠄⠀⠀⠀⠀⠘⠊⠢⢀⠀⠀⠀⠀⠀⠈⠁⠢⠤⣀⠀⠀⠀⣀⢀⣀⣠⡋⠘⠤⠄⠤⠤⢀ ⠀⠀⠀⠀⠑⡔⠈⠈⠑⠢⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣎⢲⢌⠉⠲⠐⠌⢇⠀⠀⠀⠀⠀⠀⠀⠉⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠈⠁⠂⠄⣀⠀⠀⠀⠀⢀⠔⠝⠸⠀⣈⣙⠐⢐⠙⠀⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠉⠉⢰⠠⣀⠢⠂⠀⠂⢣⠀⠈⠂⠀⠀⡇⠀⠙⡄⡀⠀⠀⠀⠀⠀⠀⢀⡀⠹⣄⠀⠀⠀⠀⢄⡪⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠇⠁⠀⠀⡄⠀⢃⢀⠂⢂⠠⠂⠄⠢⠜⢦⠀⠀⠀⠀⠀⠀⠀⠀⠰⠙⠳⣄⠀⣸⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢡⡆⠀⠀⠀⠀⠀⠀⠀⢨⠃⠀⠀⠀⡐⢡⠡⡼⠓⢞⠅⠔⠀⠁⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠐⠖⠒⠀⡟⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣠⠀⠀⠀⠀⠀⠀⠸⠃⠀⡇⠜⡺⠯⠋⠁⠀⠀⠈⠉⠀⠀⠛⠙⠋⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⡄⠑⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⡄⠀⠀⠀⠀⠀⠀⠀⠸⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡄⢣⠀⢀⠀⠀⠈⠀⠂⠠⠀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠙⠖⠠⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠌⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⣠⠀⠀⡐⡇⠀⠀⠀⠀⠀⣀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⡄⢀⠀⡰⣏⢀⡴⢠⢇⠾⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡱⠠⣀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡀⣀⡴⡏⠘⠊⡼⡸⠊⠀⡸⠬⠁⠀⠀⣠⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡪⠊⠀⠀⠀⡩⠆⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⣤⣿⡏⠃⡧⣠⠞⠉⠀⡀⣰⠁⠅⠀⠒⣨⠟⢤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠌⠀⠀⠀⢀⠊⠀⠘⡄⠀⠀⠀⠀⠀⠀⣾⣷⣿⡿⠳⠃⡀⠇⠁⠀⠀⠀⡈⠀⢀⡠⢴⡮⠁⡸⠃⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⠀⠀⠀⢠⠂⠀⠀⠈⠙⠇⠀⠀⠀⠀⠸⣯⡾⠋⠁⠀⠁⢀⠈⠀⠀⠈⠀⠀⠀⠡⢜⠱⠠⠞⠁⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀ ⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠈⢭⠢⠄⠠⠓⠁⠀⠀⠀⠩⢌⣪⡀⠀⣀⣀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣡⣩⢋⣀⠀⠁⠀⠀⣠⠲⠁⠀⠀⠀⠀⠀⠀⠀⠁⠂ ⢀⠀⠀⠀⠁⠢⡀⠀⠀⠀⠀⠀⠀⠈⡙⠁⠀⠀⠀⠀⢀⠀⢠⡢⠝⠓⠒⠉⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⠰⠋⠀⠉⠀⠀⠀⠀⠀⡔⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀ ⠀⠀⠈⠉⠐⠢⢈⠀⠑⠄⡀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠻⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠁⠀⠀⠄⠀⠤⠀⠀⠀⠀⠀⢐⠂⠈⠀⠀⠀⠀⠀⡀⠠⠠⠀⠠⠤⠀⠤⠀⣨⠱⠆⠒⠂⠀⠀⠀⠀⠘⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢱⠁⠀⠀⠀⠀⢀⢎⠀⡢⡶⠁⠀⠜⠀⠀⠀⠀⠀⢀⡀⠀⠒⡂⠤⠤⠤⢤⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⡀⢂⠃⠀⠀⠀⡀⠀⠋⠀⠀⢿⠁⠜⢀⡠⡄⠀⠒⠒⠊⠁⠀⠀⠀⠈⠠⠊⠑⢺⡦⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠄⡀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠈⡮⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢱⣇⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠅⠈⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⢏⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠢⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠳⠀⠀⠀⠀⠘⡿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠠⡠⢣⠀⠀⠀⠀⢣⢇⠉⡀⢄⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠠⠂⠀⣀⠴⠳⢢⠄⠀⠀⠀⠀⠀⠀⢰⡃⢖⡒⠂⠁⠀⣘⠀⠀⠀⠀⡀⠘⠀⠈⠂⠐⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠒⠤⠄⠀⣠⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠐⣀⠴⠚⠀⠀⢀⠐⣾⠀⠀⠀⠀⠀⢀⢲⢨⠚⠂⠁⠀⠉⠳⠀⠀⠀⣠⡇⠰⠃⠀⠀⠁⠀⠁⢄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠁⢒⡠⠤⢀⡀⠀⠑⠄⠆⠙⠁⢀⡀⠔⠂⡁⢰⠃⠀⠀⠀⠀⠐⡡⠁⠘⢌⡀⠀⠈⢉⠕⠄⡠⠊⠈⡔⡶⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⢕⣄⠀⠀⢀⠀⣪⠔⠁⠀⠀⠀⠀⢀⡞⠁⢠⠄⣄⣚⣣⡨⢁⣀⠎⠁⠀⠀⠑⡇⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠲⠍⡀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠘⠑⠄⣀⡐⠡⠊⠀⠀⠀⠀⢀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀ ⠢⠀⠠⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠀⠀⠀⠀⠀⢀⢐⠒⠒⠊⠴⡁⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠐⠢⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀