⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣼⣿⣿⣿⣿⠟⣿⣿⣿⣭⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⣿⣿⡋⠃⢀⡭⠼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣿⡿⡿⠿⡿⡴⠻⡉⠉⠉⢿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⡀⠅⢴⡃⠤⠰⡀⠁⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣖⠰⣶⡋⡭⠭⠛⠁⠀⠀⢀⢆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⣿⡖⣦⡓⣂⠀⣀⠄⠀⠀⢀⣾⡟⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡤⣰⣎⣴⣿⣷⣿⣝⡒⢚⣡⣀⡠⡦⣽⣿⣯⣿⡯⡶⣢⡀⠀⠀⠀⠀⠀ ⢸⣷⡾⣿⣿⣿⣿⣿⡛⠭⠟⠻⠝⣮⣾⣿⡿⢟⣿⣾⣹⢞⡌⠣⡀⠀⠀⠀ ⢹⣿⣧⣿⣿⣿⣿⣿⣿⣦⣤⣰⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⡾⠀⠐⡀⠀⠀ ⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⠟⠛⠀⠠⢽⣿⣿⣿⣧⢔⡵⠎⡄⠀ ⣿⣿⣿⣿⣿⠋⣻⣿⣿⣿⣿⣿⣇⠂⠀⠀⠀⠀⠀⠻⢿⣿⣿⣏⡼⣀⢷⡀ ⢿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⠓⢁⠰ ⠈⣟⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⢀⡀⠀⠀⠀⠀⠘⠉⠚⠀⠀ ⠀⠀⠀⠴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡡⠉⠣⡆⡠⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣦⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠻⠺⢿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠃⠀⠀⠀⠈⠈⠙⠿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣅⡀⠀⠀⠀⠀⣀⣤⣄⣄⠩⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⣿⣿⡾⣽⣦⠀⠚⢫⣥⣤⣄⣀⡀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⠳⠏⣨⠀⠄⠀⠦⠉⠘⠁⠀⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢨⣿⣿⣿⠀⠀⡟⠀⠠⡀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⣿⣿⣿⣇⠀⢷⣰⠶⠇⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⣴⢴⣤⣄⠄⠀⣀⣼⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣯⠛⠙⠈⣨⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣭⢧⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀ ⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⡀⢐⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀ ⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⡴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢷⡄ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠣⣪⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠘⠠⢻ ⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣑⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠁⠉⠀⠌⡳ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠠⠀⠀⡐⢨⡱ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡁⠀⡀⠠⢐⢣⣽

⠀⠀⠀⠀⠀⠀⣠⡎⠀⠀⠀⠀⢠⡐⠠⠀⠀⠀⠉⠻⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⠀⢀⡀⣀⣺⣎⡕⣄⠌⣂⢤⣂⠈⠻⣿⣝⢶⡄⠀⠀⠀⠀ ⠀⠀⠀⣀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⣮⠚⢻⣧⢻⡀⠀⠀⠀ ⠀⠀⠈⣰⡏⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⣾⣿⢣⠘⡄⠀⠀ ⠀⣰⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠄⣈⡄⠀ ⠀⣿⣿⣿⣿⡇⡤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣶⠀⣆⠃⠀ ⠀⣿⢺⢹⣿⠁⢠⢤⣴⣄⠀⠀⠀⠀⢀⣀⠉⠙⠲⠄⠀⠀⣰⣿⣿⣿⣿⣿⠂⠀ ⠀⣿⣼⣾⣿⠀⠈⠁⠉⠘⠁⠀⠀⠈⠧⠹⠗⡶⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠃⠀ ⠀⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡟⣸⣿⣽⣿⡏⠀⠀ ⠀⠀⢻⣿⣿⠀⠀⡀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⣼⣽⣷⣿⣿⣿⡟⠀⣠⣯ ⠀⠀⠀⠙⢻⢇⠘⠢⣄⡄⠠⠖⠀⠀⠈⠠⠀⠀⠀⢰⣿⣿⣿⣿⣿⡿⠁⣰⠛⡋ ⠀⠀⠀⠀⢿⠈⢄⠀⠙⢠⠥⠠⡩⠍⠉⠁⡠⠀⣠⢿⡿⣿⣿⣿⠟⠀⢰⠙⠶⡾ ⠀⠀⠀⠀⠸⣇⣼⡄⠠⠀⠀⠀⠀⠀⠀⠘⢀⡜⠁⢸⣣⣿⠋⠀⠀⢀⡟⢲⣼⡧ ⣀⣠⣶⣿⣿⣿⣿⡗⠄⠀⠀⠀⠀⢀⣤⠒⠁⠀⢀⠇⡸⣿⣿⣦⣄⣼⢱⣿⣿⣷ ⣿⣿⣿⣿⣿⣿⣿⡇⠈⠲⠤⠤⠾⠋⠀⠀⠀⡠⠞⠊⠁⢻⣿⣿⣿⣇⣾⣿⠛⣿ ⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⣹⣾⣿⣿⣿⠋⣸⠇ ⣿⣿⣿⣿⡇⣿⣿⣿⡾⣄⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⣼⠃⠈⠛⢿⡏⣴⣏⠀ ⣿⣿⣿⣿⡇⣿⣿⣿⣷⢻⣷⣄⡀⠀⠀⠀⢈⣂⠀⠀⠰⠇⡠⠀⢀⣖⣿⣿⣿⣧ ⣿⣿⣿⣿⣇⣿⣿⣿⣿⣟⣿⣿⣿⣷⣶⣶⣿⣿⣆⠀⢿⡞⢀⣔⣿⡭⢹⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⣿⣽⣿⠂⡗⣿⡿⠗⠉⠀⠀⠙⢟⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣶⣶⣶⢄⡀⣰⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣷⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⢀⡴⢺⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⢀⣸⣿⣿⣿⣿⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠂⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⣿⣿⡟⠉⠉⠉⠙⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⣼⣿⣾⣿⣿⣿⣟⣿⣾⣿⣷⣿⠃⠀⡸⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⢸⣿⣿⣻⣿⣿⣻⣿⣿⣿⠟⢻⣇⣆⢠⣷⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠉⢿⣿⣿⣯⣿⣿⣿⠇⢠⣿⣿⢁⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠈⠛⣿⣿⡿⢿⠃⠀⣾⢁⣿⣾⠿⣃⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠘⣿⣧⣼⣤⣼⣿⠶⠿⠷⡿⣟⣻⣟⢯⠗⠀⠀⠐⠐⣶⣿⣿⠿⠿⠿⠄⠰⡄⠘⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⣼⡭⡝⣿⡏⠁⠀⣴⣶⣾⣿⣿⠷⣿⡟⢿⣶⣶⣴⣾⡿⢻⠟⣿⣿⣿⣿⡚⠓⡶⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⢸⣇⡇⡃⣇⠀⠀⠁⠀⠀⠀⠀⠠⠿⠋⣼⡟⠉⠹⣿⡈⠙⠺⠈⠉⠈⠉⠉⠀⠁⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠻⣳⡇⠙⣤⡀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⢎⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⢳⢁⠀⠀⠙⠛⠒⠒⠒⠒⠒⠟⠙⠃⠀⡀⠁⠈⢛⠻⣤⣤⣀⣀⣀⣤⣴⠟⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠸⡐⠀⠀⠀⠀⠀⠀⠀⠀⣠⡎⠀⡀⠘⠀⠀⠀⠀⠰⠀⠀⠉⠉⠀⠘⠀⢠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⢠⠾⠁⠉⠚⠛⢀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠐⠉⠀⠀⢀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠁⣀⡀⠀⠈⠁⠛⡣⠴⠃⠁⢤⠀⠀⠠⠀⠀⢞⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡟⣄⠀⠀⠀⠀⠈⠁⠛⠿⡿⢾⠷⠶⠻⠴⠂⠀⠀⠀⢠⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⢀⠤⠒⠉⢸⠁⠘⣆⠀⠀⠀⠀⠀⠀⠀⣁⢈⡀⠨⠁⠀⠀⠀⠀⢀⣸⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣀⣤⡤⠒⠋⠀⠀⠀⠀⠘⠀⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⠘⠸⠅⠀⠀⠀⠀⣠⠞⢻⣿⠀⠛⣶⣄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠙⣿⣆⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠠⠆⠀⢀⣠⣾⣿⠁⠸⣿⡆⠀⠘⣿⡀⠉⣶⠤⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠙⢹⡇⣰⡖⣦⣠⣶⣾⣿⣿⠿⠋⠁⢀⣤⢻⣿⠀⠀⠹⣷⠀⢹⡆⠀⠀⠉⠙⠒⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠸⣿⡆⠀⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⠀⢘⡈⠛⠉⠉⠛⠛⠋⠁⠀⠀⠀⢺⡇⢸⣿⠀⠀⠀⢻⣧⠀⣿⡀⠀⠀⠀⠀⠀⠀⠓⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⠀⠘⣿⡇⠀⠀⠈⣿⣆⢡⡇⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡄⠀⠀⠀⠹⣿⣄⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⣷⠀⠀⠀⠘⣿⡞⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣷⡄⠀⠀⠀⠘⣿⣦⠀⠀⠀⠀⠀⢩⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠐⠀⣿⣿⠀⠀⠀⠀⠸⣿⡿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⢻⣷⡀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⣿⣿⠀⠀⠀⠀⠀⢹⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠈⢿⣧⠀⠀⠀⠀⠘⣿⣦⠀⠀⠀⠀⠀⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢻⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠈⣿⣇⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⡀⠖⣿⡇⠀⠀⠀⠀⠀⠀⠀⠛⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⢸⣿⡄⠀⠀⠀⠀⠻⣿⣄⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠠⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠻⣿⡄⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢻⣇⠀⠄⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠹⣿⣄⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⢰⣾⠂⠀⠀⣲⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡘⣿⣴⠇⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⢳⡆⠀⠀⠤⣺⡏⠀⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣼⡷⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡤⠀⠀⠀⠈⣟⣐⡂⢠⣿⡀⠀⠀⢪⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⣟⠀⠀⠀⠀⠀⠀⠀⢳⣠⣾⣿⣿⣶⣿⣿⣷⣦⡀⢸ ⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣄⠀⠀⠀⠀⠁⢀⣾⠇⡠⢀⣰⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⠀⠀⠀⠀⠀⠀⠀⢂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼ ⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡀⠀⠀⢀⣿⣿⣷⡝⢗⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣤⣰⣿⣧⣼⡟⡃⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣧⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡏⢸⡇⣶⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧⣠⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿ ⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣸⣿⣿⣶⣀⡀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿ ⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠛⣼⣿⣿⣿⣿⣿⣿⣿⣿⡶⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣦⣄⡀⠀⠀⠀⠀⢀⣀⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠟⠁⢀⣺⣿⣿⣻⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣶⡞⠉⠁⠀⠀⠀⢂⣿⣿⣧⢾⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸