⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣵⣾⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠈⠻⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣷⣤⡄⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⡄⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠟⡀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⢸⡗⠴⢦⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢠⡞⠁⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢦⡄⠀⠀⠀⣠⣿⣿⣷⠀⣷⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⣠⠏⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣦⡄⠀⠀⠀⠀⠀⢘⣆⣿⠀⣠⠞⢿⣿⣿⣟⡀⡿⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⢻⣄⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠙⢦⡀⠀⢀⡴⠟⣽⣧⠞⠁⢸⣟⡿⠋⢸⣧⠃⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣝⡳⣄⡀⠀⢸⢷⡀⠀⠀⠀⠀⢠⡟⠁⠀⢠⡞⣡⡴⢋⡴⠟⠋⠙⢷⣄⣠⣿⢣⠞⠙⡿⠀⢰⠇⠀⠀⠀⠀⠀⠀⢀⣼⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡛⠟⠳⠬⠧⠙⢦⣀⠀⢠⡟⠀⠀⠰⠟⠛⠁⣴⠋⢀⣠⣴⣶⣿⡿⣽⣿⡏⠀⠀⡇⠀⣼⠀⠀⠀⠀⠀⠀⢠⣾⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢪⣷⡤⢤⣄⡀⠀⠀⠉⠙⠛⠀⠀⠀⠀⠀⢀⣾⣡⠶⢻⣅⣴⣿⡟⢀⣿⡟⢻⠀⢀⡇⠀⡏⠀⠀⠀⠀⠀⣠⣿⡿⢁⠀⠀⢰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢸⣼⣦⣤⣬⣽⣶⣄⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠁⣀⣤⠿⠛⠋⠀⣼⢹⢧⠈⠀⡾⠃⢸⠃⠀⠀⠀⠀⢰⣿⡟⢀⡏⠀⠀⢸⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠈⣏⡷⣄⣈⣿⣼⣿⣷⡄⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⢀⡟⣿⢸⡴⠞⠁⠀⣸⠀⠀⠀⠀⢰⣿⡟⢱⠋⠀⠀⠀⠀⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⡄⠀⢀⣾⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠏⠀⠀⠀⠀⣿⠀⠀⠀⢀⣿⣿⢠⡏⠀⠀⠀⠀⠀⠀ ⡶⠀⠠⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣾⣿⠇⠀⠀⢸⡿⡄⠀⠀⠀⠀⠀⢰⣟⡁⠀⠀⠀⠀⠀⣰⡦⠀⠀⠀⠀⠀⢸⡇⢫⠀⠀⠀⠀⠀⡟⠀⠀⠀⣸⣿⡇⡜⠀⠀⠀⠀⠀⠀⢀ ⣧⣄⠀⠀⠀⠀⠀⠀⠀⠘⢿⠟⣿⣿⣿⠏⠀⠀⠀⡼⠀⣿⣦⡀⠀⠀⠀⠀⠈⣁⣀⣤⣤⣴⣾⡏⠀⠀⠀⠀⠀⣠⢾⡇⢸⡀⠀⠀⠀⠀⡇⠀⠀⢠⣿⡿⢠⠁⠀⠀⠀⠀⠀⠠⠋ ⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡟⠀⠀⠀⢠⠇⢠⠇⠈⠛⢦⣄⠀⠀⠀⠉⣿⣭⣭⣶⡿⠁⠀⠀⠀⣠⠞⠉⢸⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⢸⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⡄ ⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⣠⠴⠶⢶⡞⢀⣾⣀⠀⠀⠀⠈⠙⠶⣄⣀⠉⠉⠉⠁⠀⠀⣀⡴⡿⠁⠀⠀⣸⡇⠈⣿⣷⣦⡤⠴⠟⠒⠒⠲⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠀⠀⠀⡜⠁⣼⠃⠈⠙⠓⠶⠤⣄⣀⣀⡉⣻⡷⠤⠤⠴⠛⠁⠀⡇⠀⢀⣾⡿⠁⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⢧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠀⠀⠀⠀⡼⠁⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠀⠀⠀⠀⠀⠀⠀⠓⠚⣻⣿⣷⡀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡏⠀⠀⠀⠀⣼⠁⢰⠏⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⣿⣿⡇⠀⢸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡾⠃⢸⠁⠀⠀⠀⣰⠃⣰⠃⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⠏⠀⢀⡾⠀⠀⠀⢰⠋⣰⢣⡞⠁⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡟⣁⣀⠀⢸⡇⠀⠀⠀⡞⣰⣿⠋⠀⠀⢀⣀⣤⡴⠛⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢸⠃⢸⠃⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⠛⠉⠉⠉⠉⠉⠉⠛⠛⠚⠛⠛⠛⠒⠒⠛⠛⠛⠋⠁⣴⡇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣸⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⣼⡷⣤⣀⠀⠀⠀⠀⠀ ⠀⣼⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢹⣤⣤⣤⣴⣶⣾⣿⣿⣦⣀⠉⠙⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠤⠤⣧⣏⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⢳⡈⠻⢿⣿⣤⣀⣀ ⣴⢻⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠈⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢳⠀⠀⠀⠈⠉⠉ ⠁⣾⠀⠈⠙⠲⢶⠶⢶⣦⣀⠀⠀⣇⠀⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀ ⠀⠇⠀⠀⠀⠀⢸⡄⠈⣧⠹⠆⢀⣸⣀⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢠⡞⠁⣀⡄⠀⠀⠀⠀⠀⠀⠀⢀⣴⠗⠀⢸⠃⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀ ⠀⠄⠀⠀⠀⠀⠸⡇⠀⠘⠓⢶⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡏⢀⡾⠋⠀⣠⡤⢤⣤⣤⣶⠖⠋⠁⠀⠀⡾⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⢸⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠚⢁⣴⣾⣿⣿⠋⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⡿⢷⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⢸⡀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣸⠁⠸⡇⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀ ⢀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠈⡇⠀⡇⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢠⠇⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⣷⠀⡇⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⡟⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠸⡄

⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠁⠀⠀⠀⠀⠀⠉⠛⠿⣦⡀⠀⠑⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⢞⠀⡠⠊⠀⠀⠀⠀⠀⢠⡀⠀⠈⢹⠠⡀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢐⢡⠃⠀⡁⠀⠀⠀⢲⢄⠀⠀⣫⢆⢔⣿⢇⡇⡆⠀⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠈⠚⣷⣄⣱⢄⠀⠰⠁⡰⠕⠞⢊⣱⣼⡗⢸⢀⠁⠀⠀⣠⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣖⣢⣄⠉⠁⠀⢀⠎⢊⡿⠟⣾⠁⡸⠘⠀⠀⣴⢯⠀⠀ ⠀⠀⠀⠀⣠⣤⡀⣰⠈⡗⠚⠚⠃⡀⠀⠀⠀⠀⠀⢰⢹⠊⠀⡆⠀⣸⢏⠃⠀⠀ ⣅⠁⠀⠀⠹⢿⣿⠃⢀⢓⢄⠀⠈⢃⣀⢤⡎⠀⢀⣼⢰⠀⠀⡇⠀⡿⡀⠀⠀⠐ ⠿⠇⠀⠀⠀⢀⡧⠄⡜⡬⢀⡉⠢⠄⡉⠉⡀⢴⠁⣸⠘⣶⠤⠓⠚⢇⠀⠀⠀⠐ ⠀⠀⠀⠀⣠⠋⠀⡐⡐⢀⠀⠀⠉⠁⠁⠀⠀⢘⣶⣿⠀⡿⠀⠀⠀⠀⠡⠀⠀⠀ ⠀⠀⢠⠊⡌⠀⡰⣐⠄⠀⠁⠂⢀⣀⣤⣶⣾⣿⣿⣿⠀⡇⠀⠀⠀⠀⢰⠀⠀⠀ ⠀⡴⠁⠀⠃⠤⠿⠧⠤⠶⢊⡏⢿⣿⣿⣿⣿⣿⣿⣿⠀⣣⠁⠀⠀⠀⣆⣀⠀⠀ ⢼⢣⡀⠀⠀⠀⡐⠘⣿⣿⣿⣿⣦⣬⣍⠉⠉⠉⠉⠉⠉⠣⠀⠀⠀⡜⠘⡌⠑⠒ ⠘⠀⠈⡍⢏⣀⣧⣤⣿⣿⣿⣿⣿⣟⡡⢂⠄⠀⠀⣀⠴⢀⠃⠀⢰⠁⠀⠘⡀⠀ ⠀⠀⠀⢧⠀⠃⢻⣿⣿⣿⣿⣿⣿⣿⣷⣧⣮⣽⡿⠁⠀⢸⠀⢀⠳⠀⠀⠀⠰⠀ ⠀⠀⠀⠈⡄⢸⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠀⡌⠀⡆⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣵⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣦⡀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠁⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣦⡀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢙⡧⠠⣄⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⣠⠏⠀⢠⠏⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⢷⢦⠀⠀⣠⣾⣿⡆⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⢰⠃⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⡽⠲⡀⠀⠀⢀⣼⣾⣀⠔⢭⣿⡿⢳⣼⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⣷⣄⡀⠀⢷⣄⠀⠀⠀⢀⡞⠁⠀⡼⣀⠴⣫⠶⠛⢧⡀⣸⣿⡔⢺⡇⢀⠇⠀⠀⠀⠀⠀⣰⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠓⠾⠏⠳⣄⣀⡜⠀⠀⠚⠋⢡⠞⢁⡤⣶⣾⡟⣿⣟⠀⢸⠄⢸⠀⠀⠀⠀⢀⣼⡿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⡗⠒⠢⣄⡀⠀⠉⠀⠀⠀⠀⣠⡿⠚⠙⣷⡿⠟⢸⣿⠙⠀⣸⠀⡇⠀⠀⠀⢀⣾⠟⡠⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢸⡿⣋⣹⣟⣷⣄⠀⠀⠀⠀⠀⠛⠒⠒⠉⠁⠀⠀⡾⣿⣇⡴⠁⠀⡇⠀⠀⢀⣾⡟⡔⠁⠀⠀⠓ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⣶⡄⣀⣼⠁⠀⣿⠁⠉⠁⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡿⠁⠀⠀⢸⠀⠀⠀⣼⡿⡰⠁⠀⠀⠀⠀ ⡟⠀⠂⠀⠀⠀⠀⢿⣿⣿⣿⣿⠃⠀⠀⡟⢦⠀⠀⠀⠀⠺⠄⠀⠀⠀⣠⡞⠀⠀⠀⠀⢠⡇⡇⠀⠀⠀⢸⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⣠ ⣿⣇⡀⠀⠀⠀⠀⠈⠉⢸⣿⠏⠀⠀⣸⠀⡏⠑⢦⡀⠀⠀⠐⣾⣿⣿⡿⠁⠀⠀⣀⠴⠉⡇⢹⠀⠀⠀⢸⠀⠀⣸⣿⠘⠀⠀⠀⠀⠀⡀ ⠿⠿⠇⠀⠀⠀⠀⠀⠀⢀⣯⡤⠄⢴⠇⣸⣀⡀⠀⠉⠓⠦⣀⡉⠉⠉⠀⢀⡤⡾⠁⠀⣰⡇⢸⣷⣦⠤⠞⠒⠒⠺⣧⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⡎⢠⠃⠀⠉⠙⠒⠂⠤⠤⣽⠓⠒⠊⠉⠀⣧⣀⣼⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⢀⡞⢠⠇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⡇⠀⡿⠃⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠋⡼⠀⠀⠀⡞⢠⠏⠀⠀⠈⠑⠦⡀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⣿⣿⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠟⠁⢠⠇⠀⠀⡸⣰⣯⠏⠀⠀⠀⢀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀ ⠀⢀⡼⠧⠶⠦⠾⠦⠤⠤⠷⠿⠥⠤⠤⠶⠿⠋⣸⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⡇⡜⠀⠀⠀⠀⠀⠀⣸⣄⠀⠀⠀⠀⠀ ⠀⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⣤⣤⣤⣴⣾⣿⣦⣈⠙⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠤⠼⣟⠁⠀⠀⠀⠀⠀⢠⠟⢏⠻⠷⣦⣀⣀ ⠞⡏⠳⣄⡀⠀⠀⠀⠀⠘⡆⢹⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⢀⡞⠀⠈⢆⠀⠀⠀⠀ ⠀⡇⠀⠀⠈⡏⠹⡟⣆⠀⢃⢸⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⡴⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢸⠆⠀⠀⠀⡼⠁⠀⠀⠈⢆⠀⠀⠀ ⠀⠀⠀⠀⠀⢧⠀⠹⢶⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠋⡰⠋⢁⣠⢤⣤⣤⡴⠚⠁⠀⡼⠀⠀⠀⢰⠃⠀⠀⠀⠀⠈⡆⠀⠀ ⠀⠀⠀⠀⠀⢸⡀⠀⠈⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣉⣴⣾⣿⡟⠀⠀⠀⠀⡇⠀⠀⢀⠟⡇⠀⠀⠀⠀⠀⠸⠀⠀ ⠀⠀⠀⠀⠀⠀⢧⠀⠀⡇⢸⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢠⠇⠀⠀⡼⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠀⠀⠀⠀⠀⠘⡆⠀⣣⢸⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢸⠀⠀⣰⠁⠀⠈⣇⠀⠀⠀⠀⠀⠈⡄

⡄⠸⠀⠀⠀⠀⠀⠀⠀⡄⢸⠀⠀⠀⡟⢀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠀⡇⠀⣷⠀⠀⣧⠘⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠇⢠⠀⠀⠁⢸⠀⠀⠀⠀⠀⠀⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⡇⠀⡇⠈⠀⡀⢷⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⡇⠸⠁⣸⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⡀⢸⠀⠀⡆⠸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡆⠘⠀⠀⠀⠀⠀⠀⠀⢷⡿⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠋⣿⣿⣾⣴⢁⠚⠀⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⠀⢸⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣧⠈⠀⠀⠀⠀⠀⠀⡏⢠⠀⠀⠀⠀⡾⠀⠀⠁⠋⠖⣶⣤⣤⢤⡤⣠⠀⠋⡾⢀⡏⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⢶⠓⠘⠀⡇⠸⠀⠀⠀⠀⠄⠀ ⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠇⣸⠀⠀⠀⠀⠃⢸⠀⠗⣴⢀⠀⠀⠀⠀⠀⠀⠀⡄⣀⠁⡞⢠⠋⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣷⣀⣸⢀⠆⠹⣧⠈⡄⢸⠀⠀⠀⠀⠇⠀ ⠀⠀⠀⠀⡀⢷⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠁⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⡇⠀⣇⠀⠀⣀⣦⢶⠶⢶⠲⠙⠈⠀⣾⠁ ⠉⠉⠈⠀⠀⠀⢳⠀⠀⡏⢠⠀⠀⠀⠀⠀⠀⢷⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣦⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠈⡆⠸⠀⠀⠀⠀⠀⠀⠀⡀⣦⠘⢻⣴ ⣀⣀⣤⣿⢿⠻⡈⢳⠏⣸⠀⠀⠀⠀⠀⠀⠀⠀⣏⣧⠤⠤⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠛⠛⠛⠛⠙⠉⣀⣦⣿⣿⣾⣶⣴⣤⣤⣤⢹⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣼⠀ ⠀⠀⠀⠀⠀⣀⣤⡷⣼⠀⠀⠀⠀⠀⠀⠀⠀⡏⢠⣸⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⡇⣴⠁⠋⠛⠛⠛⠒⠒⠛⠛⠛⠚⠛⠛⠉⠉⠉⠉⠉⠉⠛⣴⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡏⢀⠀⠀⠀⠀⠀⠀⠀⠃⢸⠃⢸⠀⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡟⠛⡴⣤⣀⢀⠀⠀⠋⣿⣰⡞⠀⠀⠀⡇⢸⠀⣀⣁⡟⣠⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠁⡞⢣⣰⠋⢰⠀⠀⠀⡾⢀⠀⠏⣴⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⣿⣿⣿⣿⣿⣿⣿⣾⣶⣤⣠⢀⠀⠀⠀⠀⠀⡀⢤⠳⠉⠀⠀⠀⠀⠃⣰⠃⣰⠀⠀⠀⠁⢸⠃⡾⢠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢸⠀⡇⣿⣿⣿⣿⣴⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠀⠀⠏⢰⠁⣼⠀⠀⠀⠀⡏⠞⣠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⢸⠀⡀⣷⣿⣻⠚⠓⠀⠀⠀⠀⠀⠀⠀⠛⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃⢰⠁⡼⠀⠀⠀⠀⡟⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⢧⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⢹⠀⠁⡿⣾⢀⠀⡇⠀⠁⠛⠴⠤⠤⡷⣻⡉⣀⣀⣄⠤⠶⠓⠙⠈⠃⣼⠁⡜⠀⠀⠀⠋⡿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠀⠀⠀⠀⠀⠀⠀⠀⣇⢿⠲⠒⠒⠟⠴⡤⣦⣷⣿⠈⡇⣸⠀⠀⠁⡿⡴⣀⠀⠀⠁⠉⠉⠉⣀⣄⠶⠙⠈⠀⠀⠀⣀⣾⢀⡞⢶⠶⠴⣠⣟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿ ⡄⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⢸⠀⠀⡇⠀⠀⠀⠀⡇⢸⠀⢸⠉⠞⣠⠀⠀⠀⠁⡿⣶⣭⣭⣿⠉⠀⠀⠀⣄⢦⠛⠈⠇⢠⠇⢠⠀⠀⠀⡟⣿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿ ⠋⠠⠀⠀⠀⠀⠀⠁⢠⡿⣿⢠⠀⠀⡇⠀⠀⠀⠀⡀⢸⡇⢾⣠⠀⠀⠀⠀⠀⡏⣾⣴⣤⣤⣀⣁⠈⠀⠀⠀⠀⡀⣦⣿⠀⡼⠀⠀⠀⠏⣿⣿⣿⠟⢿⠘⠀⠀⠀⠀⠀⠀⠀⣄⣧ ⢀⠀⠀⠀⠀⠀⠀⡜⡇⣿⣸⠀⠀⠀⡟⠀⠀⠀⠀⠀⢫⡇⢸⠀⠀⠀⠀⠀⡦⣰⠀⠀⠀⠀⠀⡁⣟⢰⠀⠀⠀⠀⠀⡄⡿⢸⠀⠀⠇⣿⣾⣿⣿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠠⠀⡶ ⠀⠀⠀⠀⠀⠀⡏⢠⣿⣿⢀⠀⠀⠀⣿⠀⠀⠀⠀⠏⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠀⠀⠀⠀⠀⠀⠁⣿⢸⠀⠀⣾⢀⠀⡄⣷⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⠀⠀⠀⠀⠋⢱⡟⣿⢰⠀⠀⠀⠀⣸⠀⠁⠞⡴⢸⣿⡟⢀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⡄⣷⣿⣼⣿⣈⣄⡷⣏⠈⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⢸⠀⠀⡏⢀⡟⣿⢰⠀⠀⠀⠀⠃⢸⠃⡾⠀⠈⢧⢹⣼⠀⠋⠛⠿⣤⣀⠁⠋⣾⢀⠀⠀⠀⠀⠀⠀⠀⣄⣶⣽⣬⣤⣦⣼⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠀⠀⢁⡿⣿⣠⠀⠀⠀⠀⠀⡏⠀⡇⢀⠀⢻⡟⣿⢀⡟⣿⣴⣅⢻⠶⣡⣾⢀⠀⠀⠀⠀⠀⠛⠙⠉⠀⠀⡀⣄⢤⡤⣷⢪⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⡿⣾⢠⠀⠀⠀⠀⠀⠀⣼⠀⡇⠀⠀⡏⣿⣽⡿⣿⣶⣴⣠⢀⠋⣴⠁⠛⠟⠰⠀⠀⡟⢠⠀⣀⢦⠙⠧⠬⠳⠟⡛⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⣼⢀⠀⠀⠀⠀⠀⠀⠇⢰⠀⡿⠙⠞⢣⣿⣠⣄⢷⠙⠋⠟⡴⢋⡴⣡⡞⢠⠀⠁⡟⢠⠀⠀⠀⠀⡀⢷⢸⠀⡀⣄⡳⣝⠶⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡄⣠⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠃⣧⢸⠋⡿⣟⢸⠁⠞⣧⣽⠟⡴⢀⠀⡀⢦⠙⠁⡾⢀⠀⠀⠀⠀⠀⠀⠀⣦⠘⠀⠀⠀⣄⢻⡀⢷⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠾⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣾⠀⡿⡀⣟⣿⣿⢿⠞⣠⠀⣿⣆⢘⠀⠀⠀⠀⠀⡄⣦⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠏⣠⠁⡾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⣷⠀⣷⣿⣿⣠⠀⠀⠀⡄⢦⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀⠀⠁⡞⢠⠋⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡀⢦⠴⡗⢸⠀⠀⠀⠀⠀⠀⠀⣄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡾⢠⠀⠀⡀⠟⡿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠹⠀⠀⠀⠀⡄⣿⠿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣠⠀⠀⠀⠀⠋⡿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠘⠀⠀⠀⠀⡄⣤⣷⣿⠿⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⡿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠻⠈⠀⠀⠀⠀⠀⣦⣷⣿⣿⣿⠻⠙⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠿⣾⣵⡞⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡄⠈⠀⠀⠀⠀⠀⣇⠈⠀⠁⣰⠀⠀⢸⠀⠀⠀⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠀⢸⣣⠀⡆⠘⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡼⠀⠀⠇⢠⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⢸⡇⠀⠀⢧⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⠀⠀⠀⠀⠀⡇⠟⢀⠀⠀⡇⠀⠀⠀⠀⡟⣿⣾⣴⣉⣄⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡆⠈⠀⡀⢸⠀⠀⠀⠀⠀ ⠀⠀⡆⠈⠀⠀⠀⠀⠃⢰⠀⠀⠀⡼⠀⠁⠚⡴⣤⣤⢤⣠⢁⠋⡰⠋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⢶⠹⠀⢧⠀⠀⠀⠀⠀ ⠀⠀⠀⢆⠈⠀⠀⠁⡼⠀⠀⠀⠆⢸⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⡴⢁⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣀⢸⢃⠀⣆⡟⠹⡏⠈⠀⠀⡇⠀ ⠀⠀⠀⠀⢆⠈⠀⡞⢀⠀⠀⠀⠀⢳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣤⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⢹⡆⠘⠀⠀⠀⠀⡀⣄⠳⡏⠞ ⣀⣀⣦⠷⠻⢏⠟⢠⠀⠀⠀⠀⠀⠁⣟⠼⠤⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠛⠙⣈⣦⣿⣾⣴⣤⣤⣤⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣾⠀ ⠀⠀⠀⠀⠀⣄⣸⠀⠀⠀⠀⠀⠀⡜⡇⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⣸⠋⠿⠶⠤⠤⠥⠿⠷⠤⠤⠦⠾⠦⠶⠧⡼⢀⠀ ⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣤⣤⣀⢀⠀⠀⠀⠏⣯⣰⡸⠀⠀⠇⢠⠁⠟⣠⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⣿⣿⣿⣿⣿⣶⣴⣤⣀⢀⠀⠀⠀⡀⠦⠑⠈⠀⠀⠏⢠⡞⠀⠀⠀⡼⠋⡴⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠃⡿⠀⡇⣿⣿⣴⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠇⢠⡞⢀⠀⠀⠏⣼⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⠱⠀⠀⠀⠀⠀⠀⣿⣿⠀⡇⣿⣼⣀⣧⠀⠉⠊⠒⠓⣽⠤⠤⠂⠒⠙⠉⠀⠃⢠⡎⢀⠀⠁⠞⣠⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠀⠀⠀⠀⠀⠀⣧⠺⠒⠒⠞⠤⣦⣷⢸⡇⣰⠀⠁⡾⡤⢀⠀⠉⠉⡉⣀⠦⠓⠉⠀⡀⣀⣸⠇⢴⠄⡤⣯⢀⠀⠀⠀⠀⠀⠀⠇⠿⠿ ⡀⠀⠀⠀⠀⠀⠘⣿⣸⠀⠀⢸⠀⠀⠀⢹⡇⠉⠴⣀⠀⠀⠁⡿⣿⣿⣾⠐⠀⠀⡀⢦⠑⡏⠀⣸⠀⠀⠏⣿⢸⠉⠈⠀⠀⠀⠀⡀⣇⣿ ⣠⠀⠀⠀⠀⠀⠃⣿⢰⠀⠀⢸⠀⠀⠀⡇⡇⢠⠀⠀⠀⠀⡞⣠⠀⠀⠀⠄⠺⠀⠀⠀⠀⢦⡟⠀⠀⠃⣿⣿⣿⣿⢿⠀⠀⠀⠀⠂⠀⡟ ⠀⠀⠀⠀⠁⡰⡿⣼⠀⠀⠀⢸⠀⠀⠁⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠁⠉⠁⣿⠀⠁⣼⣀⡄⣶⣿⣾⠀⠀⠀⠀⠀⠀⠀ ⠓⠀⠀⠁⡔⡟⣾⢀⠀⠀⡇⠀⠁⡴⣇⣿⡾⠀⠀⠁⠉⠒⠒⠛⠀⠀⠀⠀⠀⣄⣷⣟⣹⣋⡿⢸⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡠⠟⣾⢀⠀⠀⠀⡇⠀⣸⠀⠙⣿⢸⠟⡿⣷⠙⠚⡿⣠⠀⠀⠀⠀⠉⠀⡀⣄⠢⠒⡗⢿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⡿⣼⢀⠀⠀⠀⠀⢸⠄⢸⠀⣟⣿⡟⣾⣶⡤⢁⠞⢡⠋⠚⠀⠀⡜⣀⣄⠳⠏⠾⠓⠋⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡏⣰⠀⠀⠀⠀⠀⠇⢀⡇⢺⡔⣿⣸⡀⢧⠛⠶⣫⠴⣀⡼⠀⠁⡞⢀⠀⠀⠀⣄⢷⠀⡀⣄⣷⠮⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⣼⢳⡿⣿⢭⠔⣀⣾⣼⢀⠀⠀⡀⠲⡽⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀⠃⢰⡁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡆⣿⣾⣠⠀⠀⢦⢷⠈⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠏⢠⠀⠏⣠⠋⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⣄⠠⡧⢙⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⢠⠀⠀⠇⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠈⠀⠀⡀⣦⢿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠁⠟⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⠀⠀⠀⡀⣦⣿⣿⠿⠛⠉⠈⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣵⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⡆⠀⡌⠀⠈⠀⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠀⢸⡄⠈⠀⠀⠀ ⠀⠰⠀⠀⠀⠳⢀⠀⢸⠀⠁⡿⣽⣮⣧⣷⣿⣿⣿⣿⣿⣿⣿⢻⠃⠀⢧⠀⠀⠀ ⠀⡀⠘⠀⠁⢰⠀⠃⢀⠴⣀⠀⠀⠄⢂⡡⣟⣿⣿⣿⣿⣿⣤⣧⣀⢏⡍⠈⠀⠘ ⠒⠑⡌⠘⡜⠀⠀⠀⠣⠉⠉⠉⠉⠉⠉⣍⣬⣦⣿⣿⣿⣿⠘⡐⠀⠀⠀⡀⢣⢼ ⠀⠀⣀⣆⠀⠀⠀⠁⣣⠀⣿⣿⣿⣿⣿⣿⣿⢿⡏⢊⠶⠤⠧⠿⠤⠃⠀⠁⡴⠀ ⠀⠀⠀⢰⠀⠀⠀⠀⡇⠀⣿⣿⣿⣾⣶⣤⣀⢀⠂⠁⠀⠄⣐⡰⠀⡌⠊⢠⠀⠀ ⠀⠀⠀⠡⠀⠀⠀⠀⡿⠀⣿⣶⢘⠀⠀⠁⠁⠉⠀⠀⢀⡐⡐⠀⠋⣠⠀⠀⠀⠀ ⠐⠀⠀⠀⢇⠚⠓⠤⣶⠘⣸⠁⢴⡀⠉⡉⠄⠢⡉⢀⡬⡜⠄⡧⢀⠀⠀⠀⠇⠿ ⠐⠀⠀⡀⡿⠀⡇⠀⠀⢰⣼⢀⠀⡎⢤⣀⢃⠈⠀⢄⢓⢀⠃⣿⢿⠹⠀⠀⠁⣅ ⠀⠀⠃⢏⣸⠀⡆⠀⠊⢹⢰⠀⠀⠀⠀⠀⡀⠃⠚⠚⡗⠈⣰⡀⣤⣠⠀⠀⠀⠀ ⠀⠀⢯⣴⠀⠀⠘⡸⠁⣾⠟⡿⢊⠎⢀⠀⠁⠉⣄⣢⣖⢿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠇⣠⠀⠀⠁⢀⢸⡗⣼⣱⢊⠞⠕⡰⠁⠰⠀⢄⣱⣄⣷⠚⠈⠀⠀⠀⠀⠀⠀ ⠐⠀⠀⠀⠀⡆⡇⢇⣿⢔⢆⣫⠀⠀⢄⢲⠀⠀⠀⡁⠀⠃⢡⢐⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⡀⠠⢹⠈⠀⡀⢠⠀⠀⠀⠀⠀⠊⡠⠀⢞⢠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⠑⠀⡀⣦⠿⠛⠉⠀⠀⠀⠀⠀⠁⠋⡾⢠⠀⠀⠀⠀⠀⠀⠀⠀