⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⠤⠤⢤⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⡤⠄⠒⠛⠉⡉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢄⠀⠀⠀⠀⠀⠀⠈⢉⠙⠓⠒⠠⢄⡀⠀⠀ ⢰⠋⠀⠀⡠⢤⣒⠋⠀⣀⠔⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡠⠟⠂⠀⣁⡂⠡⠦⣑⣤⠖⣁⡼⠿⢂⠀⠄⢈⢆⠀ ⢸⡎⣖⠲⠥⢍⣈⣃⣐⠡⠍⠓⠬⣁⠆⠀⠀⠀⠀⠄⠠⠀⠨⡯⣠⠈⣀⡠⣶⠭⢧⠀⠩⢉⣉⣁⡛⠧⠽⠒⢀⡏⡞⠀ ⠈⣇⢸⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠉⠉⠉⠁⠀⠀⠀⠀⠀⡀⢸⠇⡇⠀ ⠀⣿⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⣾⢸⡆⠀ ⠀⢸⢢⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢸⠀⠀ ⠀⠘⡄⣾⣆⠀⣀⣠⠤⠐⠂⢤⠤⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠭⠭⢉⡑⠒⠢⣄⠀⢀⣼⡇⡄⠀⠀ ⠀⠀⠇⢯⡿⡿⠋⢐⣢⢔⡊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡲⢄⠒⠩⠻⣶⡟⡇⠀⠀ ⠀⠀⢸⢸⢙⠦⣄⣨⠐⢏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢬⣑⣢⣤⠞⣹⢧⠃⠀⠀ ⠀⠀⠈⡸⡄⢢⠀⠉⠉⠛⠛⠓⠒⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠛⠛⠉⠉⠀⠀⠀⣿⢸⠀⠀⠀ ⠀⠀⠀⡇⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠸⠀⠀⠀ ⠀⠀⠀⣇⣿⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⠀⠀⠀ ⠀⠀⠀⢸⢹⠀⠇⣀⣤⣤⣤⡶⣶⣶⣶⣶⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣔⣢⡤⠬⠤⢤⣤⣽⣧⣯⢤⡀⠀ ⠀⠀⠀⠸⠘⡄⢸⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⣄⣄⣄⣀⣠⣀⣪⢷⣿⡟⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⡟⣦ ⠀⠀⠀⠀⡇⣇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠈⠉⠹⣾⣿⠁⠄⠀⢰⣿⣿⣿⣿⣿⣿⡿⢱⠟ ⠀⠀⠀⠀⢷⢻⠀⠈⠙⠻⠾⠿⠿⠿⠿⠿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠲⣿⠛⠛⠻⡿⣿⠋⠒⠉⠀ ⠀⠀⠀⠀⢸⢸⡎⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢶⣴⡴⣦⢴⣤⢶⡦⠀⠀⠀⠀⠀⡟⠀⠀⢸⠇⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡎⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣾⠉⠛⠉⠋⠹⣼⠃⠀⠀⠀⠀⠀⡇⠀⠀⣿⢠⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⢃⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢱⢸⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⢰⡏⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⡌⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠃⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣾⢀⠆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢣⣇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⢸⡘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⡇⡜⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣮⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⡿⠅⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡏⣷⣄⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢀⣀⢀⠞⢀⣸⣿⢃⠅⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⡿⣿⣽⣒⠩⠥⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡬⣕⣺⣯⢿⣿⢸⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡰⣿⣾⡂⠈⠉⠉⠉⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⢸⡟⣼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠃⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢇⢿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢇⠀⠙⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠓⠁⣰⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠄⣀⡀⠈⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⢉⣀⣀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡉⠉⠉⠉⠑⠒⠲⣶⢦⣀⠀⡀⠒⠒⠒⠒⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀