🙋♀️,🍒, ⬆️
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢉⡀⠄⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⠤⠊⠁⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡠⠊⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠕⠁⠀⠀⠀⠠⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⡀⢄⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠛⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⡠⢐⣤⣾⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠁⠀⠀⡀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⡠⠔⠪⠶⠿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠠⠤⠤⠄⣀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣀⣀⣀⣀⣤⣤⠍⠉⠀⠀⠀⠀⠀⢐⠈⠁⣂⠀⠀⠀⡀⠑⠢⡀⠀⠀⠀⠀⠀⠈⠑⠢⡀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⡠⠄⠀⠀⠀⢠⠃⠀⡆⠘⣆⠀⠀⠸⡀⠀⡌⠢⡀⠀⢀⠀⠑⠄⡀⠈⠢⡀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⡠⠊⠀⠀⠀⠀⢠⡇⠀⠀⢸⠀⢹⡆⠀⠀⣷⡀⠸⡀⠰⡀⠀⢀⠀⠀⠈⠢⡀⠘⢆⠀⠀⠘⢆⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⡠⠊⠀⠀⠄⠀⠀⣾⠟⠀⠀⠀⠀⡆⠀⡟⣄⠀⠸⡗⡄⠱⡀⠹⡀⠈⢆⠀⠀⠀⠑⢄⠀⠣⡀⠀⠀⢢⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⠊⠀⠀⠀⡄⠀⠀⣸⠏⢰⢸⠀⠀⠀⠱⠀⠿⡌⠢⡀⢳⡈⠢⣱⠀⢱⠀⠈⠄⠀⠀⠀⠈⢂⠀⠱⡀⠀⠀⢣⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⡇⠀⣰⠏⠀⢸⢸⠀⠀⠀⠈⠓⠶⠥⢀⣈⡴⣧⣀⠈⠳⡄⢇⠀⠰⠀⠀⠀⠀⠀⠱⡄⢳⠀⠀⠀⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⡌⠀⢠⡇⠀⣿⠀⠀⡜⢨⡇⠀⠀⠈⡆⢠⠀⢠⣴⣾⣷⣿⣶⣦⡌⣿⡄⠀⡇⠀⠀⠀⠀⠀⠘⡄⠃⠀⠀⢸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⡇⠀⢸⣇⣸⡇⠀⡰⠃⡀⡿⡀⠀⢀⣧⣽⣾⣿⣿⣿⣿⠟⣻⠿⠿⠿⢷⠀⢱⠀⠀⠀⠀⠀⠀⠱⡘⠀⠀⠀⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠀⠀⠀⢳⠀⠸⣯⢻⣴⣾⣤⣭⣵⡇⠘⠄⠀⢰⣾⠋⠀⢿⣷⣻⣼⣷⠄⠀⠀⢸⡆⡜⠀⠀⠀⠀⢠⠃⢠⠇⡇⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠘⡄⣀⣿⣾⣿⣿⣿⡿⡿⠏⠀⠈⢢⣸⡇⠀⠀⠘⠛⢍⠉⢹⠀⡀⠀⡾⢰⠁⠀⠀⠀⠀⡜⠀⣼⠀⢟⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⡄⠀⠀⠀⢣⠀⢸⠏⠀⢻⣿⣿⡿⡇⠀⠀⠀⠉⠀⠀⢂⠀⠱⡀⠀⢸⠀⠁⡸⠁⠁⠀⠀⠀⠀⡜⠀⡸⣿⠀⢹⠀⡅⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢱⠀⠀⠀⠀⠣⡈⢆⠀⠈⢉⠑⠄⢡⠀⠀⠀⠀⠀⠀⠀⠉⠂⠑⠒⠃⠀⢠⠗⠀⠀⠀⢀⣠⡞⠀⡰⢡⡇⠳⢤⡶⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢣⡀⠀⠀⠀⠑⢌⢆⠀⠀⠣⣀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠔⠋⠀⢀⡠⠔⣫⠋⢀⠜⠀⣸⠇⠐⡋⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢱⣄⠀⠀⠀⡀⠑⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣤⣶⣮⠧⠴⠚⡁⠔⠁⢸⠀⣿⠀⠀⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ 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⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⢻⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⡦⠀⠈⢂⠳⡀⠘⣿⣆⠳⠌⠃⠐⡘⣔⢫⣿⣏⢢⠀⠙⣿⣿⠓⢄⠀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡟⢉⢀⣴⡘⠻⠿⣿⣿⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠙⣅⠀⠀⠡⠈⠢⠸⣿⣭⣳⠶⣤⡱⣬⣻⢾⡇⠀⢣⠀⠈⢇⠀⠀⢳⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡿⠀⣀⣀⡉⣉⠱⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠙⠦⡀⠀⠀⠀⠙⢯⣿⣿⡲⣍⠷⣯⣿⢷⠀⠀⢣⡀⠀⠱⡄⣸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠤⠄⢶⣚⡷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠹⣷⣽⣞⡿⣽⣿⠈⢧⠀⠀⠱⡀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡟⠱⡄⢲⣶⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⣀⡠⠘⣟⣿⣽⣿⡯⢀⠘⣧⠀⠀⠱⡀⠀⠈⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡁⠀⠈⢬⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⣿⡾⣿⣿⡇⢀⠂⢹⠣⡀⠀⠘⡄⠀⠈⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣷⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢠⣿⣿⣿⣿⣷⡄⠐⠈⢧⠑⡀⠀⠰⡀⠀⠘⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣷⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣿⣿⣿⣿⣿⣿⣧⡈⠐⠘⡆⠘⡄⠀⠱⡀⠀⠹⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠈⠄⢹⡀⠘⡄⠀⠱⠀⠀⢻⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠛⠛⢷⣈⡐⠠⣷⠀⢡⠀⠀⢣⠀⠘⣿⣿⣿ ⣿⣿⣿⣟⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠒⠀⡆⢳⡜⠀⠳⣜⡄⠀⢸⡆⠀⢿⣿⣿ ⣿⣿⣿⣿⣟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡛⠛⠤⡟⠀⠘⡇⠀⠀⠘⡇⠤⠤⣿⠀⢸⣿⣿ ⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡛⢦⠈⠂⠄⣈⡇⢰⠇⠀⠀⢰⠁⠀⢀⣿⡄⢸⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⢄⠉⠢⡤⠇⠀⣼⠀⠀⢀⠆⠀⢀⣾⣿⡇⢸⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⡱⠖⠃⠀⡰⠃⠀⣤⠋⠀⣤⣿⣿⣟⡇⢸⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣟⠁⠀⢀⡔⠊⠀⠀⣼⢃⣠⣾⣿⣿⣿⡼⠃⢸⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠺⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠋⢈⡽⢉⠏⠀⠀⢀⣜⣷⣿⣿⣿⣿⣿⠏⠁⡀⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣚⡉⠹⣯⠀⠀⣀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠁⣐⡞⠀⡌⠀⠀⣠⡿⠋⢸⣿⣿⣿⠋⠀⢠⠚⢀⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⠉⠛⠚⢿⡶⢤⣙⣀⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⢄⡏⠀⢰⠀⢀⣾⡉⠄⡐⢸⣿⠟⠁⡠⠊⣥⣶⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠈⠢⣝⣦⠀⠈⢭⣿⣧⣄⣀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡇⠠⢁⡞⠀⠀⡇⢠⣿⣿⣇⠐⠠⢸⣿⢀⠌⣠⣾⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⢷⠀⡿⠀⡀⠸⡇⣾⣿⣿⣿⣦⠁⣼⣿⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣧⣄⠀⠈⠻⣿⣿⣿⣿⣏⡜⣱⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠿⠋⠀⠀⢸⣸⢛⠀⠀⠀⢹⣿⡿⠋⠁⠀⣷⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣄⣀⡈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠖⠚⣉⠭⠕⠋⠀⠀⠀⠀⠀⢸⡇⢸⣆⠀⠀⠀⣿⡇⠀⠀⣾⣿⣿⣿⣷⡀⠙⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣴⣿⣿⣷⣄⠀⠘⢿⣤⡀⢿⣿⣿⣿⣿⣿⣶⣤⣭⣽⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⣿⠋⠈⠉⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠿⠟⠃⠀⠀⣻⣷⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣶⣶⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣑⣑⣑⣌⣡⣊⣇⣲⣣⣪⣣⣘⣅⣪⣸⣔⣢⣔⣢⣕⣎⣱⣛⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣄⣀⣀⣀⣀⣀⣤⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣠⣀⣀⣀⣀⣀⣄⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣽⣫⣹⣏⣺⣱⣝⣹⣌⣽⣿⣿⣿ ⠀⢑⠪⡣⢪⠢⡐⢅⡘⡅⡨⢅⡌⡪⢸⠱⡪⢰⢆⢣⢕⡸⢑⡊⣕⠻⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠁⡂⢒⡐⣒⡀⡀⢀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠟⠙⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢿⡺⡣⡎⢗⡼⢱⢧⠢⣳⣷⣿ ⠀⠨⡃⠪⡣⢪⠪⠇⡒⢔⢂⡐⡅⢌⢪⢜⡰⢢⢐⡃⡔⢢⠕⠪⡇⡸⣇⠾⠈⡀⡀⡀⡀⡀⠁⠐⡀⡀⡀⡀⠂⡀⠈⡀⡀⡀⡀⡀⡀⡀⡀⡀⠄⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢩⠌⠤⠆⡂⡀⠐⡠⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡟⣿⣿⣿⠻⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢽⡱⡝⡫⡝⣏⣹⣜⢜⣌⣟ ⠀⢘⠔⡂⢑⡣⡰⡌⢌⡆⡢⡑⢆⢔⡂⢐⠆⡣⢸⢇⡕⢱⡣⢜⡰⢅⡪⢕⡪⢻⡀⡀⡀⡀⡀⡀⠄⠐⡀⠁⡀⠒⡐⠑⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠭⠬⠥⠬⠥⠤⡀⡀⡀⡀⡀⠋⡀⡀⡀⡀⡀⡀⡀⡀⡏⣿⣿⣿⣿⣿⠈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣻⢎⡗⢮⡳⢳⡹⢝⢞⡢ ⠀⢑⡘⡨⡊⡇⠩⠌⢕⢎⢔⡪⢕⡲⢰⢡⢅⢇⠬⢇⢪⡣⡎⢸⡣⡜⢣⡞⢥⣷⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠲⠉⢂⢡⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠁⠇⠣⡀⡀⡀⠠⡀⡀⡀⡀⡀⠊⠒⡀⡀⡀⡀⡀⡀⡀⡀⣶⣿⣿⣿⣿⢿⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣻⣜⢪⡎⡱⣎⣜⢕⡇ ⠀⡪⡘⢑⠕⠱⡨⢕⢨⡃⡒⠡⢑⢔⢨⠪⠢⢅⠢⡑⢕⡇⢒⡣⢕⢣⣠⡀⣣⡜⠘⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢄⢆⠈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠠⠂⡀⠃⡀⡀⢀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣤⣳⣟⠈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢿⡝⣸⣎⣪⢎⢭⡏ ⠀⢌⠨⠌⠪⡱⡑⠔⢎⡜⣃⠌⢅⢌⢌⢰⠨⡑⡕⢔⢅⢌⢢⢘⠎⣿⡀⡀⢣⡡⢟⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡜⡀⡀⡀⠰⡀⠁⠈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠉⠈⡀⡀⡀⡀⡀⡀⡀⡀⡅⣿⢿⠛⠉⠈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⢻⡇⣺⣎⣱⣇ ⠀⢌⠪⠸⠰⠢⡢⡃⡑⢔⢆⢔⡊⢐⠨⠔⡃⢪⡇⡪⢜⢨⢌⢰⢌⢸⡀⡀⢹⣨⣎⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢠⠄⠐⠐⡀⡀⠄⡀⡠⡀⡀⡀⡀⡀⠉⠾⣣⢰⡪⣜⠙⡀⡀⡀⡀⡀⡀⠟⣿⣿⣿⣿⣷⣿⣸⢥⠷⠛⠉⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣷⣗⡟⢺⡳⡮ ⠀⠢⡣⢪⢑⠣⠪⡢⡑⡑⡜⢌⠪⠡⡑⠇⢑⡨⡃⠪⠱⢊⠱⡣⢪⣿⡀⡀⡄⡎⢱⢸⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡰⢀⡂⢐⡁⠐⡆⠃⢀⡼⡀⡀⡀⡀⡀⡿⢬⡐⡑⢎⠱⡎⣱⠻⠉⠉⠖⠋⣿⣿⣿⣿⣿⡇⢃⣿⠃⠇⡏⢸⡝⣮⠙⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣷⣝⢝⢳⡳ ⠀⡘⢜⢌⡪⢜⢣⡘⠨⡑⢆⠣⢌⠌⠢⡢⡎⡘⠌⠢⡎⢑⡊⡘⡕⣇⡀⡀⡀⣆⠙⣏⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣒⢂⣐⠂⡒⣒⡇⠁⡀⡀⡀⡀⠁⣷⢸⠁⡜⢣⡘⢃⡜⢣⡖⢴⢋⣿⣾⣿⣿⣿⣿⣾⡿⣿⢠⡴⣸⢮⢻⢽⣻⣝⢷⠙⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⢽⡯⣽ ⠀⠨⡑⢌⡂⢅⡊⠣⡪⢢⢌⢢⡢⢡⡁⢊⠪⢘⡑⡘⢅⡊⠢⠣⡪⢜⢷⡀⡀⡀⣆⡝⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡇⡀⡀⡀⡀⣾⡕⢪⢇⡸⢇⡸⢇⡸⢠⣿⣡⣿⣡⣿⣿⣿⣿⣿⢇⢸⢸⣩⡿⢇⣯⣻⣯⣯⢿⣯⣟⢿⠈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⠻⠙⣀⣀ ⠀⠪⠱⢕⢰⡊⢑⠢⡣⢪⡕⢔⢆⡐⢁⡐⢨⢐⡐⢨⡂⢅⡃⡱⡑⡕⡱⠹⡀⡀⡀⣆⢸⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡇⡀⡀⡀⡇⢢⡕⢪⡎⢱⡇⢝⡮⢣⠳⢇⣯⠧⣿⣿⣷⣿⣿⣵⠐⢿⡿⣿⢃⣿⣿⣿⣸⠿⠷⣌⢿⢻⣧⠙⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⣿⣿⣿⣿ ⠀⠢⠢⢆⡢⢢⡆⠢⠆⠸⠅⡐⡆⠢⡑⡑⢌⡨⡨⠢⡢⠆⢔⢌⢆⡢⢌⣌⠙⡀⡀⡀⣆⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⠧⢸⡇⢏⡫⡿⡿⢿⡾⡝⡜⣶⡆⣜⣠⣺⠳⡼⠟⣿⣧⣧⢣⣿⣿⣿⣿⣿⡙⣦⡶⣟⣿⢊⣷⠹⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠇⣿⣿⣿⣿⣿ ⠀⡑⡑⠅⢨⢡⡃⡌⡅⠱⡨⡑⡎⡢⢔⢌⠨⠨⠨⡑⠌⡡⡘⠔⠪⢢⡑⠔⡡⠻⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢱⡀⡀⣿⢙⡆⣖⣻⢟⣿⣿⣿⣿⢳⣿⣗⢷⣝⢦⡽⣟⡞⣿⣿⡇⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢸⢸⣿⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡟⣿⣿⣿⣿⣿ ⠀⢌⢌⡊⢅⢸⢆⢢⠣⢌⡅⢌⢌⢍⠅⠪⡐⡐⡐⢕⡣⢔⡌⡢⢡⢍⠩⠌⠕⠱⢷⠈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡇⣜⢣⢗⢿⣜⣿⡿⣿⣿⡏⣿⣯⣻⢽⢹⢶⢨⣧⡎⣫⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼⢱⣿⠸⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⣿⣾⣾⣿⣿ ⠀⢍⢇⡨⡑⡘⡃⡑⡕⢜⠣⠨⠢⡪⢨⡅⡰⢌⢌⡐⢎⢛⡤⣀⠉⠛⠚⠓⠉⣀⣀⣤⠲⠈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢿⡸⠸⣺⣿⠆⣌⣿⣱⣿⣿⣿⣿⢿⡿⣨⣿⢰⣿⣿⣿⣿⣿⡎⣿⣿⣿⣿⣿⡏⣿⣿⣿⣜⣿⣿⢹⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠁⣿⣯⣿⣿⣾⣯ ⠀⠙⢦⢍⢨⠜⡣⠌⡅⡩⡕⡨⡅⢌⠥⠄⢌⠢⠡⢊⡴⠞⣥⢨⢂⠢⡫⡖⡤⣤⢤⠒⡀⡀⢀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠐⡀⡀⡀⡀⡀⡿⣻⣽⢿⠛⠈⡀⡀⣇⢪⢌⣺⣽⢸⣿⡆⣼⡜⣿⣿⣿⣿⣿⢽⣷⡇⣷⣿⣿⡿⣿⣿⣧⣿⣿⣿⣾⣸⣿⣿⣿⡿⣿⣿⣿⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡏⣿⣿⣽⣻⣿⡯ ⠀⡀⣵⠙⢦⡘⡂⡅⢇⡑⡘⢅⡨⡕⡱⢌⢌⢍⡨⢐⢸⠌⡊⢘⠞⣠⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠁⡀⡀⡀⡀⡀⡀⣿⣾⣻⣾⣻⢿⣧⡀⡀⢷⢨⢿⣷⢸⣿⡀⢻⣿⣯⣿⣿⣿⣽⣭⢸⢻⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢸⣿⣿⣿⣿⣿⣿⣿⠃⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⣿⣿⣿⣿⣿⣷ ⠀⡊⢆⢌⣗⡙⡢⢌⢇⢔⢌⡊⢑⠔⢨⠢⠢⡐⡐⡈⢐⠔⢏⣠⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠄⡀⡀⡀⡀⡀⡇⣽⣗⣗⣿⣿⣿⣇⡀⡀⡀⢽⣻⢿⢡⣿⡏⣿⣧⡝⣿⣿⣿⡇⣿⣿⣿⡘⣿⣿⣿⣿⣿⣿⣿⣿⣌⣷⣿⣮⣿⣿⣿⣿⣾⠁⣿⢻⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⣿⣯⣿⣌⣽⣯ ⠀⢂⠣⡨⠱⣌⢷⡉⠲⡌⠰⡑⠔⢔⢊⡱⡑⡑⡑⢌⠢⡞⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡏⢾⡯⡽⣿⡷⣿⡯⡀⡀⠁⡈⣿⣿⡿⢡⣿⣿⡾⢼⣿⣿⣿⢻⣷⣿⣿⣿⡻⣤⣿⣿⣿⣿⣿⣿⣿⣿⠿⣝⡙⣶⣽⡴⠋⣿⣿⣻⠻⡀⡀⡀⡀⡀⠈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡇⣿⣿⣾⣿⡿⣿⣿ ⠀⡀⢕⢩⡌⢣⠵⢌⢷⡈⠳⢅⢅⡨⠡⢜⢡⢘⢜⠢⠯⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⢽⣗⣺⣟⡿⣿⣿⡀⡀⡽⡜⠑⢣⢠⣶⣤⣤⣦⢷⣿⣾⣿⣿⣿⠿⡛⣛⣭⣷⡛⠯⣓⣭⣭⣾⣾⣷⣿⣽⡁⣿⣼⡟⣿⣾⡫⣿⣿⠹⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠈⠐⡀⠢⢄⡩⢜⠢⡄⠯⣌⠳⠢⠅⡡⡕⠰⡰⢅⢀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠁⣷⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠉⠈⡀⣿⢿⡽⡯⣺⣿⣿⣿⡀⡾⡆⡢⣾⠁⣿⣿⣿⣥⠤⡀⡁⣦⣿⣿⣿⣿⣿⣿⣻⣿⡘⣿⣿⣷⣿⣿⣿⣶⣥⡏⣭⣿⣿⡘⣿⢸⣿⣿⣿⣿⠹⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⣿⣿⣿⢛⡘⣿⣿ ⠀⠸⡀⡀⢸⠅⠸⡄⢪⢕⠪⡢⠻⣌⠝⡂⢆⡊⡑⣰⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠋⢬⣸⠁⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡇⣿⢽⡽⡮⡿⣿⣿⣿⡇⡔⢣⡟⡀⣿⣿⣿⣿⣿⣿⠻⡇⡀⡣⣧⣿⣿⣿⣳⣿⣿⢸⣿⣿⢿⠛⠟⡿⣿⣿⣿⣿⣿⣿⢟⣿⢿⣿⣿⣿⣾⢟⠹⡀⡀⡀⡀⠁⡀⡀⡀⡀⡀⡀⡀⡀⡀⠍⣿⣿⣿⣿⣿⢱⣿⣿ ⠀⢸⡀⡀⣹⢊⢌⢈⠑⣄⢳⡣⠪⣆⠳⣄⡙⠔⣼⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠏⢰⢇⡀⡤⠘⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⡽⡯⣽⣷⣻⣿⣿⣿⡘⣿⠔⣸⡀⣿⣿⣿⣿⣿⠟⣫⡇⡀⡀⣧⣆⣿⣿⣿⣿⣶⣥⣈⣤⡀⡀⡀⣿⣸⡀⣿⣷⣿⣿⣮⣿⣿⣿⣴⣋⣿⣻⣿⠹⡀⡀⡀⡀⠠⡀⡀⡀⡀⡀⡀⡀⡀⣿⢿⣍⣿⣿⣿⣿⣿⣿ ⠀⢸⡀⡀⡇⢕⢕⡨⡑⡌⢌⡌⢳⡣⠑⣦⠑⣦⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠃⣣⢣⡿⠃⢣⣷⠈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⣽⣗⣳⣝⣺⣿⣿⣿⣿⣿⢸⢹⡀⣇⣿⣿⣿⣿⡗⣍⡏⢀⡀⡀⢰⣥⣈⠑⣠⠈⡀⠙⠳⡀⡀⡀⣿⡀⣄⡄⣷⣧⣷⣿⣿⠿⣿⣿⣿⣿⡇⣿⣿⠹⡀⡀⡀⡀⠐⡀⡀⡀⡀⡀⡀⡀⡆⣿⣿⢿⣝⣿⣿⣿⣿ ⠀⢳⡀⡀⡇⠆⡐⠔⡕⠨⢑⢐⠔⣈⡱⢆⡞⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢸⠇⡎⣿⡇⡐⠣⡧⠹⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⣿⡾⡿⣷⢽⣿⣿⣿⣿⣿⢻⣿⡀⡀⣼⣿⣤⣁⡆⣍⡿⠆⠘⡀⡀⢼⢣⡟⠄⡔⠇⣼⠙⡀⢄⠑⣤⡀⠄⡼⡀⣿⣿⣿⣿⣿⣿⡿⠿⣿⡯⣿⣿⣿⢻⡀⡀⡀⡀⠈⡀⡀⡀⡀⡀⡀⡀⣆⣿⣿⣯⣿⣝⣿⣿ ⠀⡇⡀⡀⡀⢅⢑⡁⢘⢅⢘⡑⡌⠢⢅⣍⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡟⠸⡣⢔⢷⣼⡢⢅⢆⣌⢷⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⡽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⡀⢷⢕⡨⢀⢌⢌⢿⢻⢼⡀⠇⡪⢆⢸⣼⡀⡇⡀⡀⣀⠲⠉⡀⠦⡟⠐⡿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣶⣿⣴⢟⣿⣿⠿⠙⠈⠑⡀⡀⡀⡀⡀⡀⡀⡙⣿⣿⣿⡿⣿⡷ ⠀⡇⡀⡀⡀⢕⡱⢂⠪⡐⢔⡑⢑⠔⡈⢠⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡇⢪⠣⢌⣇⣺⢜⠪⢐⢆⢕⡈⠢⠈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠑⢹⡀⡄⢝⡪⢒⠔⡇⡿⣨⣿⠙⣤⡭⢭⢠⢠⠋⣿⡀⡀⠄⡀⡀⣄⠓⡀⡿⣿⣿⣿⣿⣿⢿⡎⡿⣙⣈⡯⣴⠟⣿⣿⣿⣿⣿⣿⣿⠹⠐⡀⡀⡀⡀⡀⡀⡀⢿⣙⣦⣿⣿⣿ ⠀⡇⡀⡀⡀⡺⢕⠨⢂⡂⠰⢌⡢⠨⡞⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢻⡡⡒⡇⣀⣤⡦⢲⡫⡍⢱⣳⠣⢍⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠁⡀⠈⡀⡀⡀⡀⡀⡀⠈⡀⣷⣿⣿⣿⣿⣿⣿⣿⣠⡹⢖⡴⡞⡀⡀⣾⡐⠱⠁⡏⣴⡄⢴⠰⣼⠻⣾⡇⡯⣻⣿⡀⣄⠲⠉⡀⡼⠁⡿⣿⡀⣿⣿⣿⣿⣿⣿⡻⣭⣬⣥⡿⣿⣿⣿⣇⣿⣿⣿⣿⣿⡈⡀⡀⡀⡀⡀⡀⡀⡄⡻⣿⢿⡛⣬ ⠀⡇⡀⡀⡀⣣⢌⢂⡐⢅⡁⡐⠢⢑⢀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡻⢸⡊⣜⠙⡀⡀⡀⡀⣀⡀⢖⣛⣪⠳⠈⡀⡀⡀⡀⡀⡀⠕⡂⡀⡀⡀⡀⡀⠈⡀⡀⠨⡎⠱⣦⣿⣿⣿⣶⣠⡀⠂⡄⢵⢸⢸⢻⡀⣷⡄⠁⡷⣾⡀⠁⠒⢲⣖⣷⢀⡟⣰⣿⣿⢀⢤⠒⠈⣀⢣⣿⣿⣿⢹⠻⣦⣿⣿⣿⣿⣿⣾⠟⣿⣿⣿⣿⢡⣿⢏⣿⣿⣿⣿⣿⠻⠈⠂⠉⡀⡀⡀⡀⣇⡻⡿⣾⡿ ⠀⡆⡀⡀⡀⡄⠔⡅⠡⠑⡐⢌⢄⣏⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢷⠩⠅⢌⣣⠷⠙⡀⡀⡀⡀⡀⡀⣀⣤⠲⡀⡀⡀⡀⠈⡀⢅⡐⡀⡀⡀⡀⠂⡀⡀⠢⢸⢕⡎⢢⠐⠁⡀⠈⠸⠐⡀⢾⡂⢔⢏⡀⡇⡀⢧⢫⣻⠒⣌⠐⠦⣶⡰⣿⢸⠒⡇⣰⡀⠐⡼⣾⢈⣭⣶⣿⣿⣿⣥⣶⠥⣛⣍⣩⢛⡿⣿⣿⣾⣫⡿⣛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠍⠂⡀⡀⣿⠽⡿⣿ ⠀⡀⢘⡀⡀⡀⢜⠡⡊⠌⠂⠄⠌⢸⡀⡀⡀⡀⡀⡀⡀⡀⠟⣦⠘⡀⡀⡀⡀⡀⡀⡀⣇⠳⠈⣀⢳⡙⡄⠨⢅⢌⣎⠮⠓⠉⡀⡀⡀⡀⡀⡀⡀⡀⡀⠐⡀⠁⢀⡀⡀⡀⡀⡀⡀⠂⠅⠢⠐⣅⠈⢈⢠⢁⠅⠨⡀⣵⡋⣿⣼⡇⡇⡀⡇⢿⡟⡈⣠⣿⣿⣼⡀⣧⣿⠿⣻⠈⣿⡀⣄⡀⡇⡌⣶⣷⡀⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡙⡀⣿⡹⣿ ⠀⡀⢸⡀⡀⡀⢇⡂⡊⠌⠠⠌⡃⡀⡀⡀⡀⡀⡀⡀⡀⡼⡞⣌⡜⠸⡀⡀⡀⡀⡀⡀⡆⡪⢸⣎⣮⠼⢆⢐⡂⢇⢔⡅⢌⣂⣪⡙⠶⠚⠙⠈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡁⠖⢦⠣⡇⡀⠳⠆⢠⡘⢀⠃⣿⣿⣿⡀⣀⡿⡀⡇⣤⠄⢿⢸⣿⣿⠄⠠⣿⢁⠉⡀⢻⣼⡁⣦⠈⡇⣿⣾⣹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⣷⡝ ⠀⡀⢸⡀⡀⡀⠄⠢⠪⠨⠨⠅⡯⡀⡀⡀⡀⡀⡀⡀⡀⢷⣚⡛⢛⢠⡀⡀⡀⡀⡀⡀⡅⠓⢦⢝⠪⡢⡌⡢⠅⠨⡐⡑⡘⡍⢨⡐⢔⡙⡱⢌⣣⣼⠙⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠠⠔⠣⡜⡅⠆⡇⠄⡀⢨⠠⡇⣾⣿⡀⡀⠈⣿⡀⢸⠸⣻⠂⠲⡖⢰⣁⠁⢰⠙⡀⠋⣿⠂⢉⣥⢸⡖⣀⡇⠙⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣭⣭⣶⣿⣿⢿⣦ ⠀⡀⢿⡀⡀⡀⡀⡱⡢⠢⠢⡐⢸⡀⡀⡀⡀⡀⡀⡀⡀⡆⡉⣋⡏⡀⡀⡀⡀⡀⡀⡀⠂⡑⣕⠳⣦⢝⠪⡑⡂⡆⢑⡣⢨⡊⡌⠢⡑⢘⢕⡙⡗⢇⡹⢿⡀⡀⡀⡀⡀⡀⡀⡀⡀⡂⢄⢠⡄⢠⠄⡇⡀⠁⢀⡀⡇⢻⢀⡀⡰⠛⣿⠚⢿⣿⡼⣿⣿⣿⡀⡀⣿⠂⠇⣿⣿⣿⠢⡀⣀⡀⠟⣰⣿⠻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡿⣿⣿⣿⣼⣷⣿⣿⣿ ⠀⡀⣿⡀⡀⡀⡀⢆⠢⠡⠡⢁⢀⡀⡀⡀⡀⠁⠟⠳⠉⠋⣴⠷⢳⡀⡀⡀⡀⡀⡀⡀⡁⡢⡳⡑⣓⠳⣤⢁⠛⡀⢔⢆⢪⡑⢑⡌⢅⢅⣊⠸⢬⡙⢳⢌⢹⡀⡀⡀⡀⡀⡀⡀⡀⡧⣿⣴⣿⣿⡀⡅⡀⡈⡀⡀⡇⣿⣿⠉⡾⣿⣿⢹⣖⢧⡟⣶⣦⣿⢹⡀⣷⠈⡀⣿⣿⣿⢣⡀⡀⡇⣼⠃⡝⡟⠿⡿⣿⣿⠋⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿⣿⣿⣿⣿⣿⡘⣿⣿ ⠀⡀⣿⡀⡀⡀⡀⡀⡑⡢⢊⡇⡀⡀⡀⡀⡀⣏⠰⠟⡇⡇⣭⡶⡧⡀⡀⡀⡀⡀⡀⡀⡇⡀⡀⣄⢜⢄⠟⣣⠳⣦⠈⢆⡸⢆⠢⢆⢔⢌⢨⢎⡣⢇⢮⣌⣷⡀⡀⡀⡀⡀⡀⡀⡀⡇⣿⣀⣾⣿⠂⠂⠙⡀⡀⠡⡇⣿⢀⠽⡇⣴⣐⣅⢷⡿⢸⣩⣙⡀⣎⠹⡀⢻⠉⣿⣡⣅⡰⠄⠞⣴⠰⢿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⠿⣦⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣾⢏⣿⣿ ⠀⡀⡇⡀⡀⡀⡀⡀⢇⢔⢌⣼⡀⡀⡀⡀⡀⡁⢶⠓⣶⠟⠶⠼⢻⡀⡀⡀⡀⡀⡀⡀⡸⠋⡮⡣⡑⡀⢹⣶⣮⢰⢾⢍⡘⠔⡅⡪⢜⡊⢕⡌⡱⡘⡆⢣⠺⢪⡀⡀⡀⡀⡀⡀⡀⡇⡀⠥⡦⡇⡀⡀⡇⡀⡀⠟⣿⣿⠃⢩⣾⠡⠨⢄⢣⣿⣟⣾⣿⣿⣿⢽⣛⣧⣯⢾⡛⠿⠸⠕⢣⣱⣿⣿⢩⡈⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣶⣤⣶⣿⣿⣿⣿⣿⡆⣿⣿⣿⣾⡃⣿⣿⣿ ⠀⡀⡇⡀⡀⡀⡀⡀⢅⠨⢟⡀⡀⡀⡀⡀⡀⣦⡶⡘⡟⡇⡀⢨⡭⡀⡀⡀⡀⡀⡀⡀⣠⡀⢕⠱⡪⢰⡋⣡⠻⣷⠈⠳⢤⡫⢕⠸⠨⠆⡠⢂⡣⢱⡘⡣⢜⣧⡀⠟⡀⡀⡀⡀⡀⡇⠈⡇⠨⣆⢸⡀⡀⡀⡀⣿⣾⣀⠦⠛⣀⣠⠢⢸⡻⣷⡻⣦⣷⣿⢿⣔⢠⣿⣷⢻⡀⡀⠁⢇⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⢿⣌⣿⣴⠻⣦⣿⣿⣿⣿⣿⣿⣿⠾⣯⣛⠛⣛⣦⣿ ⠀⡀⡇⡀⡀⡀⡀⡀⡀⡞⡀⡀⡀⡀⡀⡀⡀⠃⡶⡖⠻⡀⣼⢭⢻⡀⡀⡀⡀⡀⡀⠃⡀⡀⡀⠟⠳⡀⢸⣿⢦⢸⢾⢌⣕⠳⣄⡙⠕⢌⡨⠣⡪⢆⠣⡎⢔⠟⣿⣿⠘⡀⡀⡀⡀⡇⢸⠦⠖⡇⢸⡀⡀⡀⡀⡇⡀⡀⠠⠛⠁⠈⠈⢸⢞⠻⣷⣿⣌⠿⠱⡿⣼⠑⠱⣿⢿⠈⢄⠏⣿⣼⣧⣿⣿⠟⡟⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣻⣶⣍⣴⣿⣿⣦⢾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⣿ ⠀⡀⡂⢸⡀⡀⡀⠊⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣴⣿⡿⡟⠠⣭⣭⡀⡀⡀⡀⡀⡀⡸⡀⡀⡇⢂⣶⣭⡀⣿⣭⣧⡀⢱⢕⢌⣣⠻⣤⠝⡂⢐⡊⢰⡅⢌⣌⢻⠶⣧⢿⡀⢀⡀⡀⡀⢸⡛⡃⠐⣸⣀⠘⡀⠉⡄⡀⡀⡀⡆⡀⢃⢁⢘⣨⣀⢦⣌⣶⣿⣿⣿⣶⢊⡧⡀⣷⣿⡇⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⠿⣎⣿⣴⡛⣧⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⡻⣦⣿ ⠀⡀⡀⢸⠁⠊⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣽⣷⣠⡿⣥⣁⣅⠐⡀⡀⡀⡀⡀⡀⡀⡀⠁⣗⠒⢳⣷⣉⠩⣋⢰⢎⣄⡙⢎⣈⣕⠙⢦⠪⡣⢪⠣⡸⢗⣧⠛⠒⡹⠸⡀⡀⡀⡀⣿⣗⠇⠇⢸⡀⢸⡀⡀⡀⡀⡀⡀⡀⡿⣿⣿⢸⢠⡇⡃⢇⣱⠸⠳⠤⡀⣈⣄⠟⢠⠆⣿⠻⣧⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣻⣶⣬⣶⣿⣿⣶⢿⣿⣿⣿⣿⣿⣿⣿⢿⣛⣛⣍⣛⡿⣿ ⠀⡀⠈⢴⢀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠈⡀⠃⡶⡖⣤⡗⣃⡃⣇⡀⡀⡀⡀⡀⢸⡀⡀⡀⡃⣶⠃⡶⡇⣙⠭⣿⠌⡹⣑⡑⢣⡘⢎⢌⣕⡙⢳⢌⡎⢕⡸⡈⣦⠎⣝⣧⡀⡀⡀⡀⣧⠛⣿⡛⢹⡀⢠⠁⠈⡀⡀⡀⡀⡀⡄⣽⢹⢸⡀⡀⡁⠐⡈⢠⡀⢈⠂⡈⡀⣿⡀⠠⣆⣿⡀⣿⠟⡛⣿⣿⡇⣿⣿⣿⢾⠲⡶⢿⡄⣿⣿⣿⣿⣿⣿⠸⡀⠗⣿⣿⣃⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠁⣴⡙⠳⡟⣃⣇⣃⠇⣁⡤⣧⡀⡀⡀⡀⡞⢸⢀⡀⡀⠃⣶⡗⠶⣌⡹⣅⣿⢀⡣⢒⡱⢎⢄⡣⢸⠰⢄⠼⡄⠜⢩⡕⢿⢱⢍⠛⢹⢸⡀⣄⡀⡀⢀⡀⡀⡀⡀⡀⡇⣿⣸⣿⠾⡀⡀⡀⣿⣿⢸⡀⡀⡀⡀⢰⡂⡀⡀⡀⢸⡀⡇⠈⡂⡀⣿⡀⣿⣿⣽⣈⣿⡄⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡉⡀⢙⣿⡟⡘⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣸⣻⠳⠸⢸⣃⢡⣴⣧⡌⡤⡟⡀⡀⡀⠏⢨⣇⠄⡀⡀⣄⣧⡘⡾⠟⡧⢋⣇⡀⢜⡪⢑⡊⣑⠘⣄⡆⡰⠠⢳⣇⢫⠹⡏⡄⣥⠂⡭⣿⡀⡀⣆⠁⡀⠔⠠⡀⡀⡀⡏⣬⢤⣶⢸⣿⣤⣀⣀⣤⣿⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠋⣾⢸⡀⡀⣿⡀⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⡄⡁⣿⣬⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⠯⣭⡿⢋⡿⡟⣇⠇⠷⣉⣇⡀⡀⠃⢢⠡⡌⡀⡀⡀⡀⡾⡭⢿⡄⠻⣿⡏⡀⢕⡪⢕⢪⡰⣇⠁⡀⡀⡀⡆⡀⠁⠂⠄⡀⣿⣸⢻⣷⠈⠨⡀⠄⢠⠈⡀⡀⡀⡀⣿⣛⣁⡏⢸⡀⡀⡀⡀⡀⡆⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣰⡀⢧⡀⡀⣾⠇⣿⠹⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⡄⠉⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣷⠟⣃⢰⣦⡟⡀⠾⣅⠛⣿⡏⡀⠃⢄⡑⡑⠨⡀⡀⡀⡿⢉⣒⠓⡇⠲⣒⣶⠘⡎⢱⡎⢱⡌⡢⠘⡀⡀⡀⡀⠸⡀⡀⡀⡀⣇⢿⣿⠷⢀⡀⡀⠉⡀⡀⡀⡀⡀⡀⣿⣼⡀⡿⡀⡀⡀⡀⡀⡀⡀⢧⡀⡀⡀⡀⡀⡀⡀⡀⠟⡀⡀⡀⡀⡀⡀⣿⣿⣿⣿⣿⣿⠃⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠍⣏⣿⣰⠿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡇⢃⠲⣥⡟⠇⢈⡃⣿⠅⢩⠋⢀⡀⡀⡀⡀⠲⡀⡀⡀⡀⣽⡷⣀⡀⢻⠋⣶⠁⢜⡪⢕⡪⡕⢸⡧⡀⡀⡀⡀⢇⡀⡀⡀⡀⡀⢐⠂⣁⢲⢡⠔⡀⡀⡀⡀⡀⡀⡀⣿⢻⡏⣇⡀⡀⡀⡀⡀⡀⡀⡀⠻⡀⡀⡀⡀⡀⡀⡀⢠⡀⡀⡀⡀⡀⠇⣿⣿⣿⣿⣿⢿⠻⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡁⣿⣿⢿⣹⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣇⠁⣟⡀⣻⢈⣟⣇⠈⡉⠯⢠⡀⡀⡀⡀⡀⡀⡀⡀⣳⡖⡖⣤⠐⣯⡇⠛⡀⡢⡔⢢⡑⢊⡑⢌⠈⡀⡀⡀⡄⡀⡀⡀⡀⡀⠄⠂⢠⢠⡄⠙⢤⠓⡀⡀⡀⡀⡀⢸⠴⠳⣿⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠍⡞⣿⠶⡒⡖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣏⡿ ⠀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣀⡀⡀⡀⣀⠉⡀⣈⢀⡀⡀⡀⠂⡀⡀⡀⡀⡀⡀⣿⣁⣖⡇⡆⠾⠾⠶⢁⢜⠪⡇⢪⡘⢌⡇⢫⡀⡀⡀⡀⠸⡀⡀⡀⡀⡀⠠⡢⡀⠁⡀⡀⣀⡀⡀⡀⡀⡀⣿⠘⡏⢸⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡃⣟⣿⢻⠋⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⡿⣿⣿⣿⣿ ⠀⠐⠉⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠁⠐⡀⠂⡠⡀⡀⠂⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⠇⠃⠃⣿⡆⣤⣿⡂⡕⡸⡐⡅⢌⠪⠆⡢⡀⡀⡀⡀⢧⡀⡀⡀⡀⡠⡞⡀⠠⢄⡀⠢⡀⡀⡀⡀⡀⠁⢸⣿⣟⢸⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢡⡐⣿⣰⣶⡅⣿⣿⣿⣿⣽⢟⡿⣿⣿⣿⣿⣿⣿⡿ ⠀⡀⡣⡇⡀⠤⠢⠒⠛⠛⠋⠛⠊⠓⠶⣣⣕⢼⠑⡀⡀⠁⠐⡀⡀⡀⡀⡀⡀⡀⡀⡀⠂⡀⡿⣈⣘⣖⠟⣠⣄⠶⡀⡐⢅⢇⡔⢊⡑⢘⠢⢸⡀⡀⡀⡆⡀⡀⡀⡀⠃⡀⡐⡰⠈⠈⠠⡀⡀⡀⡀⡀⡇⢤⣿⡿⢨⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⢛⡿⣟⢷⠛⡿⣤⣛⡿⣿⣿⣿⣿⣾⣟⣳⣟⢿⢽⣝ ⠀⡀⡆⡅⡀⡀⡀⡀⡀⡀⠤⢪⠰⢕⡚⡬⢕⡪⡑⡨⠦⠙⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣷⣂⢚⠓⣷⢍⣬⡏⡀⠦⠱⢌⢅⠆⡐⠅⢅⣇⡀⡀⡀⡀⠘⡀⡀⡀⢀⡀⡀⠔⠄⡀⡀⡀⡀⡀⡀⡀⡀⣤⣶⣶⠰⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠂⠧⡇⣿⣽⣦⣿⣿⠙⣛⠛⠘⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⡟⣧⣄⠿⡀⢸⣿⣿⣽⢵⣯⣽⢮⡮⡵⢝⢝⡪⡇ ⠀⡀⡀⡇⠈⡀⠈⡀⡀⡀⡀⡀⣀⠲⢕⢆⢮⡚⠤⡏⢒⡑⣕⠳⠌⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣄⣤⣀⡀⡀⣤⡀⡀⡀⡀⠤⠌⠡⡐⠨⠔⠨⠈⡀⡀⡀⢹⡀⡀⡐⠠⡀⠎⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠈⣤⣤⡀⣇⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⢶⠶⡶⠋⣬⣆⡶⠃⢽⡯⡳⡳⣞⣫⡳⡳⡞⣕⢎⡣⡕ ⠀⡀⡀⡇⢸⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣄⢲⡩⢕⢵⡙⢢⡪⢔⢈⣌⠛⠈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢣⢌⢍⡌⢆⢳⡀⡀⡀⡇⡀⡀⠁⠢⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠃⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⡿⣿⣿⣿⣿⣿⣿⣿⣾⣯⢻⡾⣿⣞⣳⣮⣻⣯⢷⡽⡺⣜⣏⣗⣜⢕⣣⡗⣺⢕⢪⢕⡪⢕⡪ ⠀⡀⡀⡇⢸⡀⡀⡀⡀⡀⢀⠂⡀⡀⡀⡀⡀⡀⢄⠦⡊⡐⠇⡙⠢⠪⡪⡌⢦⠑⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢕⠡⡑⡐⡀⡀⡀⡜⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡰⡀⠃⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⢷⣿⣿⣿⣶⣵⡺⢯⣽⣝⣗⢽⡻⣳⣳⢜⣕⣼⣮⣪⣇⡵⣪⢸⡕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕ ⠀⡀⡀⡇⢸⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠁⡀⡀⡀⡀⡀⣀⡢⡑⡐⠢⣉⢒⠨⠨⣂⠧⠉⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢄⠂⠪⢸⡀⠇⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠉⠛⡵⢔⠙⠈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠈⠨⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣧⣙⡏⣗⣻⡯⢽⣻⣺⡳⡵⢣⢝⡝⡹⢜⢪⡱⢜⢧⡸⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪ ⠀⡀⡀⡇⢸⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠐⡀⡀⡀⡀⡀⡀⠤⣑⣌⠱⢌⠱⢈⠅⣔⠻⠈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡄⠳⣔⠁⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠁⠛⡾⣕⢪⡕⢪⢳⡂⡄⣙⢰⡄⣀⢋⣴⡄⣽⠿⠈⡀⡀⡀⡀⡀⡀⡄⡀⡄⡀⣿⣿⣿⣿⣿⣾⣿⣿⣵⢳⡳⡺⡺⢵⢽⢺⢗⢵⣪⢸⢕⡇⣝⣎⣕⣎⢧⡺⣕⢮⢵⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕ ⠀⡀⡀⡇⢸⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡠⠱⡉⡐⣩⠊⢌⡓⢘⡇⢥⠙⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠈⡄⢀⡀⡀⡀⡀⠉⠊⠂⠤⢀⡀⡀⡽⢪⡕⢪⡕⢪⡕⢹⢱⠁⡀⡀⡸⡀⠐⠸⡌⢟⣽⠻⠈⡀⡀⡀⡀⡀⢷⡀⡀⣿⣻⣟⣿⣿⣮⢕⡧⢯⡹⣜⣱⡝⣎⢱⡪⣕⡸⡎⡱⢜⡣⢜⡣⣕⢪⡕⢪⡕⢪⡔⢣⡜⢣⡜⢣⡜⢣⡘⡃⡜⢜⡪⢕⡪⢕⡪ ⠀⡀⡀⡇⢸⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠂⡀⡀⡀⡀⡂⢕⢒⠢⡁⢆⢸⡃⢄⠣⡪⡅⠧⠙⡀⡀⡀⡀⡀⡀⡀⡀⠈⠐⠑⠉⠉⠉⠘⠎⢀⠸⡀⡀⡀⡀⡀⡀⡀⢿⡎⢳⡜⢣⡜⢣⡜⠘⡀⡀⡀⡄⡀⡀⠄⡄⣎⢸⣻⣯⠘⡀⡀⡀⡀⡀⠈⡀⣿⣺⣵⢪⡕⡮⢵⢪⡱⡎⣣⢞⡱⢎⡱⢎⡱⢎⡱⢎⡱⢎⡱⢎⡱⢎⡱⢎⡱⢎⡱⢎⡱⢎⡱⢎⡱⢎⠱⡎⢕⡪⢕⡪⢕⡪⢕ ⠀⡀⡀⡇⢸⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠢⡰⠢⠢⠔⣌⠪⣉⢔⢮⡑⢢⡙⠥⣪⠺⠈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢻⡀⡀⡀⡀⡀⡀⡀⡇⡎⢳⡜⢣⡜⢣⡜⣧⡀⠈⡀⡀⢄⠉⠑⢢⡇⡜⢎⡺⣗⠹⡀⡀⡀⡀⢷⡇⢿⡺⢕⡪⢕⡪⢕⡪⣕⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⢪⡒⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪ ⠀⡀⡀⡇⢸⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡑⠌⢂⠌⢂⠪⠰⡅⣎⠱⢉⡲⠽⣉⡢⢍⠱⢜⠑⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡇⡀⡀⡀⡀⡀⡀⡀⡀⡼⢣⡜⡇⣎⢱⡎⢱⢹⢂⡀⡀⡀⡀⢢⠈⠐⣿⣆⢗⣻⡷⠹⡀⡀⡀⡄⡆⣿⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕ ⠀⡀⡀⡇⢸⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠨⠂⡑⢨⢌⢊⡅⢌⡨⢐⡇⣸⠣⢍⣲⠫⣌⠲⠪⡕⠮⠉⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠈⡀⡀⡀⡀⡀⡀⡀⢽⡣⢜⡸⢇⡸⢇⡸⣇⡀⡈⢤⠲⠒⠙⠉⣃⣆⢻⣳⣾⡳⡽⠹⡀⡀⡀⠸⣽⢫⡜⢣⡜⢇⡸⢇⡸⢇⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪ ⠀⡀⡀⡇⢸⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢑⢑⡂⠨⠌⡌⢂⢔⢰⡡⢌⡑⢇⡸⣇⠺⣌⣳⠺⣌⡓⡪⣱⠺⠈⡀⡀⡀⡀⡀⡀⡀⢸⡀⡀⡀⡀⡀⡀⡀⣇⡎⡕⢮⢱⡎⢱⡎⢱⢹⡀⡀⡀⡀⡀⢁⠨⢘⣿⡸⡹⡯⡽⣝⠻⡀⡀⢀⣺⡆⢣⡎⢱⡎⢱⡎⢱⡎⡣⢜⡣⡓⢜⡣⢜⡣⢜⡣⢜⡣⢜⡣⢜⡣⢜⡣⢜⡣⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕ ⠀⡀⡀⡇⢸⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡊⡢⠪⠨⠢⡄⡡⢆⠢⡇⢜⢪⡕⡪⢱⡎⢱⣎⡓⢦⢝⡛⢤⡙⢊⢕⠓⡀⡀⡀⡀⡀⣇⡀⡀⡀⡀⡀⡀⡀⡀⡪⢕⡪⢕⡪⢕⡪⢕⡧⡀⠐⡀⡀⠐⡈⡐⠄⡆⣿⡆⣗⢺⢎⡵⠻⡀⡀⣺⢕⡪⡕⢪⡕⢪⡕⢪⡕⢎⡱⢎⡕⢪⡕⢪⡕⢪⡕⡪⢕⡪⢕⡪⢕⠪⡕⢪⡕⢪⢕⠪⡕⢪⡕⢪⡕⢪⡕⢪⢕⡪⢕⡪⢕⡪ ⠀⡀⡀⡇⢻⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡇⠂⠅⠁⢌⠢⡡⢘⡒⡱⢎⠣⡱⢌⡣⢕⡪⢕⡪⢕⡪⠵⣙⢆⢜⡙⠤⢝⡐⢶⠑⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣹⢎⡱⢎⡱⢎⡱⢎⡱⠸⠂⡀⠈⡀⠄⡀⠨⡐⣯⢿⢷⣺⡝⣎⣜⠻⡀⣯⢸⡇⣜⢢⡇⢸⡇⢸⡇⢳⡸⢇⡳⢸⡇⢸⡇⢸⡇⢜⡣⢜⡣⢜⡣⢜⡣⢘⡇⢸⡣⢜⡣⢜⡣⢸⡇⢸⡇⢜⡪⢕⡪⢕⡪⢕ ⠀⡀⡀⡇⡯⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡇⠌⡁⡑⢨⡊⡑⡑⠑⡑⠪⡣⡎⡣⢕⡨⢇⢸⡎⢱⡎⢱⡎⣱⠫⣉⡢⠜⡑⢢⣄⣝⠾⠉⢸⡀⡀⡀⡀⡀⡀⡀⡆⢜⡣⢜⡣⢜⡣⢸⡇⣿⡀⡀⡀⡀⡀⡀⢈⠈⢧⡾⠹⢻⡳⢳⣕⣿⡇⡞⢕⡪⢕⠪⡕⢪⡕⢪⡕⡪⢕⡪⢕⡪⢕⢪⡕⢪⡕⡪⢕⡪⢕⡪⢕⠪⡕⢪⡕⢪⢕⡪⢕⡪⢕⡪⢕⢪⡕⢪⢕⡪⢕⡪⢕⡪ ⠀⡀⡀⡇⣏⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡇⠌⡨⡁⢑⡂⠄⡨⠌⡢⢡⠨⡑⠪⠣⠎⠥⢪⢕⡪⢕⡪⢕⡪⢕⡪⢕⠙⢁⢄⠰⡁⡳⡜⢣⡀⡀⡀⡀⡀⡀⡀⡀⢽⢜⡣⢜⡣⢜⡣⢜⡣⡀⡀⡀⡀⡀⡀⢀⠄⡀⣞⣯⡌⣕⢣⢗⡵⣪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕
⠀⣌⣌⣎⣪⣑⣑⣜⣎⣔⣅⣎⣣⣸⣕⣸⣕⣪⣕⣎⣣⣎⣳⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣀⣀⣀⣀⣀⣢⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣀⣀⣀⣀⣀⣀⣂⣂⣐⣀⣀⣀⣀⣀⣀⣄⣘⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣧⣎⣝⣹⣪⣇⣕⣫⣕⣿⣿⣿⣟ ⠀⢃⡑⡘⢑⡑⢘⡐⢃⡑⡌⢌⠔⠢⡑⢜⢱⠪⡰⡅⢪⡱⢌⡣⢾⢉⡀⡀⡀⠠⡀⡀⠠⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣄⡀⢀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠁⢂⡂⡐⢢⡀⡀⢀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠁⠻⠈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣷⢮⡳⡹⢇⡕⣫⢮⠪⢦⣯⣟ ⠀⢅⢨⢅⢌⡢⢢⠱⡒⢑⡘⢍⡪⢅⡨⢕⢱⡪⢸⡑⢣⡎⡰⢅⡪⡕⣮⠙⡀⡀⡀⡀⡀⠁⠐⡀⡀⡀⡀⡎⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡐⠂⠐⠆⠆⡀⠐⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠃⣿⣿⣿⣿⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣷⢭⢣⢕⡇⢝⡎⣕⡹⣔⡿ ⠀⡢⡃⢔⢪⠱⡢⢅⢣⡪⢢⠬⢌⠨⢌⢪⢇⡕⡸⢑⡘⡔⢢⡑⢎⡸⢆⡱⣿⡀⡀⡀⡀⡀⡀⠐⠨⡀⠂⡀⠰⡐⠈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠏⠬⠬⠥⠜⠤⠠⠐⡀⡀⠁⠒⡀⡀⡀⡀⡀⡀⡀⡀⣿⣿⣿⣿⣿⢻⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣷⢝⡎⠵⢮⡣⡝⢝⢮⠪ ⠀⢕⠱⡑⡕⡱⠬⡌⡪⡸⠔⢅⢌⠪⡢⢅⡪⠕⢣⠕⠣⡱⢔⠣⡜⢇⡺⢥⣇⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠄⠦⠙⠡⠐⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠁⠇⠆⡀⡀⡀⢐⡀⡀⡀⡀⡀⠔⠠⡀⡀⡀⡀⡀⡀⡀⣄⣶⣿⣿⣿⣿⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣧⢮⡳⢕⡝⢮⢳⡹⡇ ⠀⢘⠣⡪⡘⢅⠣⠪⡲⢕⡣⢕⠪⡢⡑⡘⢐⠢⡕⢱⡨⢅⡎⢕⡱⣰⡀⣺⡑⢹⡀⡀⡀⠁⡀⡀⡀⡀⡀⡀⡀⡀⡀⢀⢆⠈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠠⠈⡀⠨⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣤⡻⢹⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣧⡽⣖⢳⡹⡜⡲⡇ ⠀⢌⢎⢜⠸⠨⢑⠢⡑⢜⡆⡐⢔⢌⠨⡂⢅⡌⠪⠣⡑⡌⡐⢊⡟⡀⡀⣻⣁⡷⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡜⡀⠁⡀⢠⠈⠂⠐⡀⡀⡀⡀⡀⡀⡀⡀⠉⠉⠛⠈⡀⡀⡀⡀⡀⡀⡀⠁⡿⣿⢿⠻⠙⠉⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣦⣟⡎⢮⣗⢵⡇ ⠀⠢⡃⢸⡆⢑⢅⢑⡑⢕⡌⢊⠪⢒⠢⠡⡑⢐⠡⢘⢜⢣⡪⡘⣗⡀⡀⣇⡸⡕⠘⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠉⢌⠡⠡⠬⡀⡀⢈⠁⢀⡀⡀⡀⡀⠁⠞⣥⠵⠊⡕⣮⠘⡀⡀⡀⡀⡀⠋⣿⣿⣿⣾⣭⣿⣼⢸⣮⠷⠛⠈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣦⣻⡻⢗⡳⡝ ⠀⡊⠣⠱⡨⡊⠆⠢⡢⢣⢪⠢⠢⡱⡑⠔⢌⢌⡨⠌⠪⡢⠅⠢⡇⡀⡀⡀⣳⢕⢿⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡄⡀⢀⡀⠊⠠⢁⠇⡀⢰⡀⡀⡀⡀⠋⣸⡀⠜⢣⡸⢇⡸⣇⠺⠓⠴⣛⣿⣿⣿⣿⣿⢸⢡⣿⢁⠃⢜⡫⣗⣳⠻⠈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣆⢽⣫⢮⡖ ⠀⢐⡅⣃⢪⡆⡔⠨⢊⡢⢣⠪⠢⠢⢑⢑⠢⠢⠢⢢⢢⡑⠕⢆⠡⢹⡀⡀⡀⣻⡖⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣄⢀⢀⡀⣀⣀⡄⠇⡀⡀⡀⡀⠏⣱⢎⠆⡔⢣⡜⢣⡜⢴⣉⢚⣿⣾⣿⣿⣿⣿⣿⡟⡏⢰⣰⣿⢽⡯⣽⢯⣟⣟⠻⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣦⣷⣻⣟ ⠀⠪⢅⢍⠪⡕⡪⠅⠨⡐⢇⡣⡊⡑⢑⢕⢔⡂⡐⢨⡨⡑⠎⢣⠬⣆⠈⡀⡀⡀⠽⠸⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠈⡀⡀⡀⡀⡀⡇⡀⡀⡀⠁⢸⡇⢸⣆⣇⢸⡇⢸⡇⡿⣱⡿⣡⡿⣿⣿⣿⣿⢸⣿⠄⢋⣿⡏⣿⢿⡿⢿⣶⣟⣟⣾⠙⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡟⣿⠿⠛⠉ ⠀⢆⡑⢕⢱⡒⢔⡊⢑⠔⣂⡱⡂⡂⢅⢌⢌⢌⡊⡘⡑⢑⡨⡔⡨⡌⣧⡀⡀⡀⡀⣷⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡆⡀⡀⡀⡿⢘⡇⢸⢺⡕⡳⡺⢳⢗⢿⣾⢸⣾⣿⣴⣾⣶⣪⢩⣧⡇⡿⢋⣿⣿⣿⢻⣷⣟⠳⣿⢿⡧⢻⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⣟⣻⣻⣯ ⠀⡘⠢⢅⢨⠌⡨⠌⠨⡈⠅⢆⡡⡑⡑⢃⠪⠢⠢⠢⡢⢔⢌⠕⠱⡑⡅⣮⠈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠈⡀⡀⢿⡰⢇⢸⣟⣞⣿⣿⣿⣿⠇⣙⢋⣦⢻⣯⢽⣶⡿⣷⡐⡹⢇⣿⣿⣿⣿⣿⢿⡛⣉⣿⣷⠌⣦⢻⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠃⣿⣿⣿⣿⣿ ⠀⢌⡒⡑⡃⢒⠪⠢⠐⠄⠢⠢⡣⢔⢌⢢⡡⡑⡕⡨⡑⡑⠕⠪⠄⠢⡢⡑⣜⠙⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢃⡀⡀⣿⢣⡚⢐⣬⣟⣿⣾⣿⣿⣟⣿⣟⣝⠻⣿⡯⡇⣜⣿⠇⣿⣻⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢨⣿⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡏⣿⣿⣿⣿⡿ ⠀⢌⢌⢌⢨⢅⢅⡂⡐⡊⡅⡨⡊⢕⢪⡅⠬⢡⢕⠬⡢⢕⢫⢖⡤⠶⢖⠖⠲⡹⠻⠈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡆⡎⢱⠢⣞⡹⣶⣻⣿⢱⣾⣿⣿⢿⡾⡛⢟⢡⢿⠟⣿⣿⣿⢸⣿⣿⣿⣿⣿⣷⣿⣿⣿⢹⡟⣿⠘⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⢿⣿⣿⢿⣿ ⠀⠦⢍⡪⢕⡪⡣⡢⡂⢐⡂⢑⠕⢔⠡⡑⡑⢌⢌⢌⡞⢉⠛⠷⣮⣱⣑⣮⠻⠙⡀⡀⠤⠈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠁⠛⠛⠉⡀⡀⡀⡀⣹⢇⡇⢯⣷⣇⡘⣿⡱⣻⣿⣿⣿⣿⣷⣇⡘⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⡿⣿⣿⣿⢇⣿⣿⢸⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠁⣿⣿⣿⣾⣾⣿ ⠀⣕⡙⢦⢌⠪⡢⠆⢔⡨⠔⢌⢌⢌⡡⠕⡪⢜⠢⡡⡼⠢⡢⠱⠫⡴⣀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠠⡀⡀⡀⡀⡀⣿⡯⣿⣿⣿⠮⠙⡀⡆⢏⡕⡽⣿⡀⣿⡇⡇⡎⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣵⣛⢸⣿⣿⣿⣿⣿⣿⣿⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡇⣿⣿⡽⣿⣽⣿ ⠀⠔⡌⢵⡙⡦⡨⡑⡑⢑⠜⢢⠆⡕⡔⢌⠪⠱⠕⢜⠆⡑⡫⣠⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⣯⣯⣯⣽⣿⡗⡀⡀⣦⢍⢕⣿⡇⣿⡿⡸⣿⣿⣿⣷⣼⣿⡿⡟⠸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢻⣿⣿⣿⣿⣿⣿⢠⣟⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⣿⣿⣿⣷⣻⣿ ⠀⠌⡂⢦⢈⢷⡉⢲⠨⢐⠌⢌⢌⢌⢕⠬⡑⡑⡐⢌⢊⡾⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠐⡀⡀⡀⡀⡇⣯⡯⡷⣯⢯⣿⡇⡀⡀⡀⢷⡯⣾⡿⢡⣿⣿⣿⣏⣿⣿⢿⣷⣿⣿⣿⡝⣷⣿⣿⣿⣿⣿⣿⢿⣛⣭⠳⣷⣿⣿⣿⢀⡿⣿⢷⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⣿⣿⣿⢯⣿⣿ ⠀⠂⡑⠨⢢⠕⢌⢮⡈⠳⢌⢢⠢⡢⢡⢔⢌⢌⢊⠢⡾⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡟⡿⡯⢿⡽⢮⣿⣿⡀⡀⡝⠪⣧⢃⣰⣿⣿⣿⣿⡯⣿⣿⣿⠻⣍⣬⣶⣷⢿⣎⣽⣾⣿⣿⣿⣿⣿⣿⣿⣇⡻⣞⠋⣿⣿⣱⣟⢿⡀⡀⡀⡀⡀⠈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡇⣿⣿⢻⡿⣿⣿⣿ ⠀⡀⡁⣃⢄⢱⠇⠵⣌⢷⣈⠳⠢⡱⡊⡑⠕⢕⢕⡟⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠟⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⡷⣗⣟⡿⡿⣿⣿⡀⠟⠰⡢⣾⢀⡽⠿⠿⠛⠈⣄⣷⣿⣻⣿⣿⣿⣿⣿⠿⣌⣿⠿⣷⢿⡿⠿⡿⣿⣣⡿⣿⢻⣧⣿⣅⣿⣿⣿⢿⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⣿⣿⣿⣴⣮⣿⣿ ⠀⢐⡀⡀⢊⠱⢈⡍⢎⠸⡄⠳⣄⢹⢌⡢⢅⡂⢇⢀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡾⡾⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢀⡀⠁⣿⡿⡺⣗⣗⣿⣿⣿⡏⢜⡣⢟⡀⣾⣯⣿⠟⢿⠛⡀⢸⡀⣷⣽⣿⣿⣿⢻⣿⣿⣿⣿⡻⣭⣭⣋⠟⣿⣿⣿⣿⣿⢫⣿⢸⣿⣿⣿⣿⢫⡀⡀⡀⡀⠂⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⣿⣿⣿⣿⢸⣿⣿ ⠀⢸⡀⡀⢸⡑⠑⠌⢌⡓⡕⠪⣢⠳⣄⡙⡘⡑⣰⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠁⣼⠣⢀⡇⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡟⣳⢿⣟⡿⢿⣿⣿⣿⡇⢿⢡⢸⡀⣿⣿⣿⣿⣼⣋⢌⢸⡀⣆⣌⣿⣿⢿⣿⣿⣿⡴⣶⣴⢀⡀⣿⣾⣤⣿⣿⣿⢿⣿⣿⣟⣿⣿⣥⡿⣵⢿⡀⡀⡀⡀⠠⡀⡀⡀⡀⡀⡀⡀⡀⡟⡻⣷⣿⣿⣿⣿⣿⣿ ⠀⢸⡀⡀⢽⡂⡐⢌⢌⢅⢈⠱⡕⠸⣤⠓⢦⣼⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣺⡑⣟⡀⠸⢿⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⣫⣺⣗⣿⣻⣿⣿⣿⢻⣿⡀⢸⡀⣿⣿⣿⣿⢸⠟⢐⣼⡀⡀⣧⣷⣶⣤⣋⡀⡤⢑⠉⡀⡀⡀⣿⢀⠢⣆⡟⣿⣿⢿⣛⣛⠟⣿⣿⣿⣯⣿⢿⡀⡀⡀⡀⠠⡀⡀⡀⡀⡀⡀⡀⡄⣿⣿⡻⣮⣿⣿⣿⣿ ⠀⢸⡀⡀⢇⠰⢌⢢⠢⢅⡰⢌⡁⢓⡢⠑⣴⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡽⡑⡕⣿⡇⡣⡘⢯⠈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⣯⢯⡯⣻⣟⣿⣿⣿⣿⣯⢸⢸⡀⡇⣿⣿⣶⢸⣼⡒⢻⠃⡀⡀⣿⢎⢱⢰⢁⡀⣿⡀⣀⠲⠈⣶⡀⠂⠊⡀⣿⣿⣻⢿⣟⣽⣭⣛⠿⣿⣿⣿⢿⠈⡀⡀⡀⠡⡀⡀⡀⡀⡀⡀⡀⣆⣿⣯⣿⡻⣮⣿⣿ ⠀⡗⡀⡀⠆⠌⡂⠌⡘⡑⠌⡂⠄⢌⠑⡶⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡇⢇⢑⡂⣿⣽⠣⢔⠣⣦⠛⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣧⣗⣷⣻⣽⣻⣿⣿⣿⣿⣿⢻⣷⡀⡀⢺⠑⢎⠇⣼⣰⡏⡄⡀⡀⣽⡜⣟⠇⢀⡀⢰⡀⢤⠓⠈⣄⠓⠇⠌⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠟⢿⠻⠉⠠⠑⡀⡀⡀⡀⡀⡀⡀⣜⣿⣿⢿⣟⡻⣽ ⠀⡇⡀⡀⡀⡐⡐⠨⢅⢕⠨⢑⠨⡐⠇⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡇⢜⢌⠆⡧⢽⢸⠥⢎⣢⠓⡆⠙⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡪⠘⡀⢷⡸⢢⠊⣙⠻⣾⠣⠉⠆⣒⡖⣶⢶⡀⡟⡀⡀⡀⡀⡀⢦⠉⡀⠟⣿⣿⣿⣿⣿⠛⢏⣿⣤⣣⠿⠶⠟⣿⣿⣿⣿⣿⣿⠻⢂⡀⡀⡀⡀⡀⡀⡀⡻⣭⣷⣿⣿⡿ ⠀⡇⡀⡀⡀⠸⠱⢸⢪⢨⢌⠰⡨⡐⢰⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡽⠣⢑⣇⣤⢶⢲⢏⡑⠡⠘⢜⢑⠐⡀⡀⡀⡀⡀⡀⡀⠈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠁⣷⣿⣿⣿⣿⣿⣿⣿⣡⠳⡞⢶⢻⡀⠇⠿⣡⣃⢉⣿⣵⡳⠃⣇⠻⣧⢀⢹⣿⣿⡀⠤⠑⠈⡀⠟⡀⡟⣿⣀⣿⣿⣿⣿⣿⣿⣝⣶⣶⠰⣿⣿⣿⣼⣿⣿⣿⣿⣿⢹⠐⡀⡀⡀⡀⡀⡀⡄⡻⣿⠻⣍⣶ ⠀⡇⡀⡀⡀⢽⡪⢔⢔⢔⠠⠐⡂⠏⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢹⢊⠑⢮⠉⡀⡀⡀⣀⣤⣆⠻⡪⠦⠙⡀⡀⡀⡀⡀⡀⠄⢂⠐⡀⡀⡀⡀⡀⡀⡀⠨⡇⠑⣦⣿⣿⣿⣾⣤⢀⡀⣣⣪⢐⡕⠘⡀⡻⡢⠃⢭⢹⡀⠋⢑⡀⡖⣸⠁⢾⣷⣿⢸⠦⠑⠈⢄⠱⡿⣿⣿⡸⡹⣷⣿⣿⣿⣿⣿⣾⡟⣿⣿⣿⣾⢏⣾⣿⣿⣿⣿⣿⠻⠌⠂⠈⡀⡀⡀⡀⣇⡹⣿⣿⣟ ⠀⡇⡀⡀⡀⡇⢅⢕⠢⠢⡐⠌⠄⢸⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠐⢳⡢⢌⢸⣴⠓⠉⡀⡀⡀⡀⡀⣀⣤⢶⠘⡀⡀⡀⠈⡀⢀⢐⠈⡀⡀⡀⡀⡀⡀⡑⢜⡱⢎⠰⠂⠄⠠⡀⠘⠄⡀⢺⣂⢔⢟⠃⣿⡀⡝⠎⣋⠝⠓⢂⠿⢾⡿⣿⠄⡀⣾⡀⠂⠞⡿⢠⣬⣷⣿⣿⣿⣤⣶⠲⣍⣭⣭⣛⣿⣿⣿⣾⣫⡿⣛⡿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡙⠨⠐⡀⡀⣿⡹⣿⣟ ⠀⡀⠨⡀⡀⡀⡣⡢⡨⠨⢑⠨⡃⡀⡀⡀⡀⡀⡀⡀⡀⠃⡴⠙⡀⡀⡀⡀⡀⡀⡀⡆⠳⠈⣄⡳⢝⡢⠆⢪⣑⢼⠲⠙⠈⡀⡀⡀⡀⡀⡀⡀⡀⠂⠈⢐⡀⡀⡀⡀⡀⡀⡀⡄⢄⢪⢑⣬⠈⣈⢠⢈⡂⠨⡀⢶⡏⣿⢰⡿⣿⡀⣿⠸⣲⢫⡟⣿⣿⢀⡄⣿⠿⣿⢸⣿⡀⡄⡀⡄⡌⣺⢷⠠⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡙⡀⣿⠹⣿ ⠀⡀⢸⡀⡀⡀⣳⡪⡪⢜⡑⢐⡟⡀⡀⡀⡀⡀⡀⡀⠇⢣⣩⡻⢻⡀⡀⡀⡀⡀⡀⡆⡘⢌⣡⢬⠳⡪⠅⡊⢘⡨⡌⢃⡰⢦⢌⠻⠛⠉⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡂⠆⢦⢇⠇⡀⠓⠆⣈⠸⡀⠇⣿⣿⣼⠐⢃⢿⠃⣾⢷⡷⡌⣇⣿⢰⢤⡟⣸⠊⡀⣧⣿⡁⣤⠘⡀⣿⣶⣹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠙⣧⡝ ⠀⡀⢸⡀⡀⡀⡆⢕⢨⢈⢑⠨⢸⡀⡀⡀⡀⡀⡀⡀⣆⡙⠓⣉⡴⡀⡀⡀⡀⡀⡀⡀⠳⠦⡙⢕⡸⢍⠢⠣⠪⢨⡔⢅⢌⡅⢍⠳⣌⢏⡱⣎⠷⠈⡀⡀⡀⡀⡀⡀⡀⡀⡀⠄⡐⡑⡜⡅⠊⡇⠄⢀⢐⡀⡇⡷⣮⡀⡀⡆⣿⡀⠏⠆⣾⠖⠲⣶⡈⠸⣾⠙⠈⠉⡿⢠⠙⣌⣼⡆⣠⡃⠹⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⣭⣶⣿⣿⢿⣦ ⠀⡀⢻⡀⡀⡀⡀⢰⠌⡊⢐⠅⡀⡀⡀⡀⡀⡀⡀⡀⡀⢻⣉⠁⢰⡀⡀⡀⡀⡀⡀⡀⡑⣕⠳⢦⡪⢣⠪⠰⡃⢪⠱⢌⢪⠱⡌⡨⡑⠪⣌⢹⡕⣮⠈⡀⡀⡀⡀⡀⡀⡀⡀⡀⠄⡠⢄⠡⢄⡇⡀⠃⡀⡀⡇⠹⡀⡀⣡⠟⣿⡖⡷⢹⣇⣿⣿⣹⠈⠿⢠⡀⣿⣿⣿⠈⠘⡀⡀⠟⣸⡿⠻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣽⣶⣿⣿⣿ ⠀⡀⣿⡀⡀⡀⡀⡳⢑⢐⠨⡇⡀⡀⡀⡀⡀⠛⠶⠙⠈⡶⠤⣾⠘⡀⡀⡀⡀⡀⡀⡀⢠⡗⢕⡲⠳⢦⠋⠛⡀⡌⠪⠢⡱⠜⡅⢇⢇⢪⡣⠺⣌⡏⣷⡀⡀⡀⡀⡀⡀⡀⡀⡇⣿⣼⣷⣿⡀⡅⡀⠐⡀⡀⡇⣿⣿⠋⣷⣻⣿⠌⣾⣼⣾⣤⣶⣿⡀⣌⠻⡀⣧⣿⣿⢰⡀⡀⠃⣼⠃⡙⡟⠿⣿⣿⣿⠟⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⣿⣿⣿⣿⣿⣿⡘⣿⣿ ⠀⡀⣿⡀⡀⡀⡀⡂⢘⠕⡐⣼⡀⡀⡀⡀⡀⢾⠏⢠⢸⣹⢮⠅⢸⡀⡀⡀⡀⡀⡀⠇⡀⡀⣄⡘⡀⡟⢋⢳⣧⡀⠆⡑⡱⢕⢌⢇⡑⢣⡸⢐⡢⠳⢦⢹⡀⡀⡀⡀⡀⡀⡀⡇⣿⠱⣴⣿⡀⠆⠑⡀⡀⠐⡿⣾⡀⢸⣯⣁⡊⣌⠿⢽⡅⢛⠉⠉⣇⠈⡇⠉⡟⣠⣑⣼⡈⠏⣴⠕⢿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠟⡙⣿⣿⣿⣿⡝⣿⣿⣿⣿⣿⣾⢏⣿⣿ ⠀⡀⡧⡀⡀⡀⡀⡀⢱⡑⠕⢀⡀⡀⡀⡀⡀⣞⣦⣾⢻⠤⣿⣦⠘⡀⡀⡀⡀⡀⡀⡔⠃⡧⡨⠃⡀⢹⣴⣌⢡⢰⠩⠇⢨⢌⠢⡃⠌⡣⠔⠆⠢⡣⣜⡙⡀⡀⡀⡀⡀⡀⡀⡀⢸⢥⡬⡏⠘⡀⡇⡀⡀⠿⣿⢿⡆⠘⢱⠕⢄⠡⡁⢨⣿⣺⣿⣿⣷⡿⣕⣽⣿⠷⠿⠾⠣⣹⣵⣿⣿⢹⠉⣿⣿⣿⣿⢸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⣱⣦⡏⣿⣿⣿⣿⢹⣷⣿⣿⣶⠋⣿⣿⣿ ⠀⡀⡇⡀⡀⡀⡀⡀⡍⢌⡼⡀⡀⡀⡀⡀⡀⢤⢻⠃⢠⢹⣩⡁⢸⡀⡀⡀⡀⡀⡀⢨⡀⣇⢜⢢⢐⠟⢋⠳⢧⡀⠳⢤⡫⢢⡐⠢⠪⠸⠪⠢⡰⡊⢇⢸⢰⠟⡀⡀⡀⡀⡀⡀⢸⡇⡑⡄⢸⡀⡀⡀⡀⣿⣴⡀⢤⠲⡀⣄⡧⡀⡘⣿⡹⣳⣻⢶⡾⡭⡟⡄⣿⠈⡀⡀⡱⣡⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣼⡟⢻⣧⣾⠟⡙⣿⣿⣿⣿⣿⣿⣿⣾⣻⢟⠿⠻⣌⣿ ⠀⡀⡇⡀⡀⡀⡀⡀⡇⣠⡀⡀⡀⡀⡀⡀⡀⠾⢭⣤⠘⡟⣋⣇⡀⡀⡀⡀⡀⡀⠃⡀⡀⡀⠞⢯⡀⢹⣶⣎⢡⢰⡑⣲⠳⣄⡝⠪⠢⠥⡱⡕⢌⡎⢔⠛⣾⣾⢶⡀⡀⡀⡀⡀⢸⢼⡴⡀⢸⡀⡀⡀⡀⡇⡀⡀⡀⠸⠓⠃⡇⠂⣭⡙⣿⢿⣦⠴⡟⣿⠂⡅⣆⣿⠻⡀⠟⣿⣹⣍⣿⣿⡿⡿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⡙⣩⣍⠏⡌⣵⣶⡏⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣵⣿ ⠀⡀⡇⠘⡀⡀⠁⠄⡀⡀⡀⡀⡀⡀⡀⡀⡀⡟⣆⣶⢀⣹⣂⣛⢰⡀⡀⡀⡀⡀⡸⡀⡀⡆⠉⣭⣟⡀⢹⣚⣿⡁⡳⢜⣉⣒⠳⣤⡙⡈⡂⡌⢎⡣⢳⣷⡤⣠⣮⠈⡀⡀⡀⡀⣿⢿⠇⠸⢸⡀⠸⡀⠓⡀⡀⡀⡀⣇⡀⡖⡟⡀⡀⡀⢦⣅⣮⣶⣶⣴⠃⡈⢰⣄⣷⣱⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣼⠟⠻⣧⣾⠟⡙⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⢿⣌⣿ ⠀⡀⠄⢸⠙⠠⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡦⣈⣸⡆⠈⠘⠸⢸⡀⡀⡀⡀⠁⡀⡀⡀⠃⡦⠭⢧⣧⠛⠿⠾⠁⢕⢌⣙⢕⣈⣕⠙⣢⡌⢣⡕⢇⢱⡘⢧⢬⣶⢷⡀⡀⡀⡀⣿⠦⡆⡄⢸⡀⢸⡀⡀⡀⡀⡀⡀⡀⣿⣿⣷⡀⡀⢸⠡⡀⣇⡀⠙⡀⠓⠈⠏⢸⡀⣿⣿⡄⣿⣾⣷⣿⣿⡇⣿⣿⣿⣿⣼⣿⣤⣿⣿⣿⣿⣿⣿⡙⣩⣌⠋⡎⣴⣶⡇⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⠿⣿⣿ ⠀⠘⠔⢀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠋⠈⡀⣽⢉⣋⣼⢹⠸⢹⢰⡀⡀⡀⡀⣺⠠⡀⡀⠇⣭⡇⣤⡟⠲⣒⣷⡀⡣⢎⠱⢣⡘⢕⣁⣕⡘⡳⢅⡌⢆⢷⣡⢻⠇⣹⠸⡀⠹⡀⡄⢿⣿⠶⢲⡀⢀⠃⠛⠉⡀⡀⡀⡀⡄⣟⡏⡀⡀⢀⠠⡁⢀⡸⠣⠄⠳⠘⣧⢸⡀⡀⣿⢸⣿⡿⠿⣿⣿⡇⣿⣿⣿⣽⢩⣭⢻⡇⣿⣿⣿⣿⣿⣿⠌⠠⣿⣾⢠⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡾⠞⡙⠻⢹⠸⢡⣰⢠⣰⡘⢸⡀⡀⡀⡞⡧⡀⡀⡀⠏⣡⣇⣁⡀⠷⠞⣹⠔⠣⠜⡢⢕⢌⠪⠆⠥⡈⣏⢧⡪⢡⡌⡈⢣⠆⡴⣷⡀⠐⠹⡀⡀⡀⡀⡀⡀⡀⡇⣿⠤⣿⢸⠋⡀⠏⣿⣿⠈⡀⡀⡀⠄⡀⡀⡀⡀⣾⡀⠁⢿⡀⡀⣷⢸⣿⣿⣿⠻⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⠿⠾⡿⢿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡆⡌⣵⣶⡏⡀⣹⣽⠈⢲⣛⠿⢀⡀⡀⠏⠪⡥⡀⡀⡀⡀⣃⢡⣴⣷⣆⡿⡇⠄⡡⢎⠸⡕⢸⠈⡀⣀⢀⠐⠈⢶⠶⢤⢤⢹⠹⣛⡿⠈⢸⡀⡀⠃⢂⡀⡀⡀⡀⣿⠙⣀⣙⢡⣤⡀⡀⡀⣄⢸⡀⡀⡀⡀⡀⡀⡀⡀⢸⠟⣴⣧⡀⡀⡇⡀⣿⣶⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡓⢘⡿⢿⠇⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢸⣰⡋⡀⣤⠂⢠⢻⣈⢻⠸⢸⡀⠃⢊⢌⡈⡀⡀⡀⠁⣸⠛⣿⠃⣶⣬⡿⠕⡪⢕⡪⡕⡸⢳⠠⡀⡀⡀⢳⠐⠠⡀⡀⡇⣿⣧⡸⢻⠂⡀⡀⠂⠐⡀⡀⡀⡀⣿⢽⠤⡺⡀⡀⡀⡀⡀⡀⣆⡀⡀⡀⡀⡀⡀⡀⡀⡀⣼⡀⡀⡀⡀⡄⠃⣿⢿⣿⣿⣿⣶⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠶⡿⣿⠾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢧⢲⣿⡀⣾⣻⣶⢛⣶⣦⠶⢹⠊⡀⡀⠕⠢⠨⡀⡀⣆⠽⣃⣟⡷⣈⣻⣟⡀⢎⢕⠪⡕⡪⡔⠈⡀⡀⡀⡆⡀⡀⡀⡀⡀⣿⣴⣹⠃⠈⡀⠼⡀⡀⡀⡀⡀⡀⣽⢲⠉⣿⡀⡀⡀⡀⡀⡀⡀⢳⡀⡀⡀⡀⡀⡀⡀⠗⡀⡀⡀⡀⡀⡀⣿⣿⣿⣿⣿⣾⠄⣦⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠨⠭⣯⣹⡇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢻⣺⠃⣼⢹⢭⣋⣾⠨⠤⢼⢻⡀⡀⡀⡀⡀⢀⡀⡀⠛⢷⣇⠉⡀⣬⣷⢀⡪⢜⡪⢔⡣⢜⢪⢻⡀⡀⡀⡀⠘⡀⡀⡀⡀⡄⢂⠋⡃⢀⣠⢻⢠⡀⡀⡀⡀⡀⢸⢰⡤⣿⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠇⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⢶⣿⣿⣴⡬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣶⣴⣠⡄⣦⣴⢀⢷⠟⠶⢠⡀⡀⡀⡀⡀⡀⡀⡀⣟⣛⠓⠗⠇⣴⡴⣧⠄⡣⢎⡕⢪⠱⠎⡜⡀⡀⡀⡀⢣⡀⡀⡀⡀⡀⠐⢁⢠⠐⢄⠒⣙⡀⡀⡀⡀⡀⢹⢒⣇⢸⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢨⠩⣏⣻⢐⣒⣟⣿⣿⣿⣿⣿⣿⣿⣿⣾⣭⢟⡿⣿ ⠀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠒⢀⠔⡀⡀⡀⠐⡀⡀⡀⡀⡀⡀⡀⣿⡄⣆⡆⠟⣁⣉⠈⠌⠪⡣⢐⡅⢎⢪⠣⠸⡀⡀⡀⡆⡀⡀⡀⡀⠁⢀⢰⠃⠃⡀⠂⢠⡀⡀⡀⡀⡀⣾⡿⡿⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣡⣌⣿⣿⣿⣿⣿⣿⣯⣻⡿⣿⣿⣷⣿⣯ ⠀⡀⠵⠓⡀⠈⡀⡀⡀⡀⡀⡀⡀⡀⠉⠛⠳⡈⡀⡀⡀⡀⠂⡀⡀⡀⡀⡀⡀⡀⡀⡀⠠⡯⡓⡖⡗⣇⠛⠿⣨⠢⠢⡅⢆⡔⡢⢆⢢⡧⡀⡀⡀⡀⠘⡀⡀⡀⡀⡸⡀⢂⢀⡀⠌⡀⡀⡀⡀⡀⡇⢸⣿⣿⡀⡀⡀⡀⠰⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣲⣴⡿⣻⡀⠭⣿⣿⣵⣯⢿⣿⣿⣿⣾⣿⣷⣻⢽⣗ ⠀⡀⢇⡇⡀⡀⡀⡀⣄⣓⣣⣘⠪⢍⠲⡢⢱⢜⢭⠙⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣟⢂⢰⠖⣏⠐⠞⡟⠃⡔⡊⡑⡑⡑⢌⡪⢰⠈⡀⡀⡀⢹⡀⡀⡀⠁⠈⠠⢰⠠⡐⡀⡀⡀⡀⡀⡀⡆⠟⣿⣿⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠅⣼⣷⣿⣿⣿⣿⣬⣶⣤⣀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣘⣿⣾⣿⣉⢿⣿⣿⡿⣿⣿⣺⢽⢷⡽⣫⣵⣕⣇ ⠀⡀⡀⡇⡀⡀⡀⡀⡀⡀⡀⠤⡙⢆⣣⠲⣌⠔⡡⡌⡨⠦⠉⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡄⡗⢻⠶⡀⣦⠟⣤⡀⡀⠦⠨⠅⢅⠆⠜⡪⢹⡀⡀⡀⡇⡀⡀⠁⠁⡀⡀⠰⠠⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢸⡿⣿⠈⣧⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠉⣭⢸⣷⡟⢸⣿⣞⣯⡿⣝⡻⣝⣝⡞⢼⡮⣣⢎⡕ ⠀⡀⡀⡇⡀⡀⡀⠐⡀⡀⡀⡀⡀⡀⢢⡋⡱⢜⠒⡌⣑⡑⡌⣪⠳⠈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢲⡌⠌⢐⡃⣔⡀⡀⡀⡀⡀⡀⢀⠁⡠⡠⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠛⣿⠿⠛⠛⡟⣿⣿⣿⣿⢀⡏⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⣛⢟⢿⠺⠛⠯⣳⡯⠪⠮⢯⣯⣗⣞⣪⢵⢯⡺⡕⢎⡳⢜⡣ ⠀⡀⡀⡇⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢦⢍⠢⢆⡑⠤⡩⡑⡑⣔⠓⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠕⠌⡂⠄⢸⡀⡀⡀⢰⠐⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠁⡀⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⣾⣿⣿⣿⣿⣿⣽⣫⢟⣻⣗⣻⣳⡽⢷⡯⣽⢧⡺⡳⡱⡣⡎⡪⢱⡪⢕⡪⢕⡪⢕⡪⢕⡪ ⠀⡀⡀⡇⠠⡀⡀⡀⡀⡀⡀⡀⡀⠐⡀⡀⡀⡀⡀⡀⢤⢓⡪⢜⡘⠤⠩⡑⢱⢮⠙⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣄⠨⠅⡇⡀⡀⡜⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠁⠛⠙⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠍⡀⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣪⢞⡳⣫⣟⣳⣽⢮⢮⣣⢮⢮⣗⣪⣎⢕⡜⢕⡎⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕ ⠀⡀⡀⡇⠨⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠁⡀⡀⡀⡀⡀⣄⡒⡊⠔⡑⢄⢅⢌⣱⠲⠉⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡓⠂⠘⠎⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠁⠋⠾⣵⢎⡱⠹⢡⣧⠦⠠⠇⠴⠠⠛⠓⠛⠈⡀⡀⡀⡀⡀⡀⡀⠸⡀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣋⡝⡳⡮⡮⡵⣝⢮⢧⣪⢵⡸⢪⡳⣝⣎⣕⣪⣕⢪⡕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪ ⠀⡀⡀⡇⢘⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠁⠘⡠⢌⠢⣁⢔⠨⡂⣬⠓⠈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡄⡶⡀⡀⡀⡀⡀⡀⠁⠈⠐⠠⡀⣽⢣⡜⢣⡜⢣⡜⠘⠈⣀⡀⡀⣄⠄⡂⠈⣳⣕⠿⠈⡀⡀⡀⡀⡀⣧⡀⡀⣷⣷⣯⣟⣻⣾⣵⢎⡳⡺⡕⢮⡸⡪⡗⢳⡺⣕⣸⣇⣪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕ ⠀⡀⡀⡇⢸⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠁⡀⡀⠁⢕⢕⢕⠙⠢⡱⠪⢌⡒⠔⡆⢤⠑⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠉⡀⡀⡀⠉⡀⠔⣿⢀⡀⡀⡀⡀⡀⡀⣿⢜⡣⢜⡣⢜⡣⣝⠄⣇⡀⡀⢣⡀⠡⠱⠑⡽⣯⣯⠹⡀⡀⡀⡀⡀⠸⡀⡇⢯⡾⣵⢪⡗⢵⡪⡱⡪⢕⡣⢕⡪⡕⢪⡕⢪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪ ⠀⡀⡀⡯⢸⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢼⡑⡑⢆⡐⢢⡑⠤⣣⠚⡌⡑⡜⡱⠮⠉⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡇⡀⡀⡀⡀⡀⡀⡀⡆⡏⢸⡇⢸⡇⢸⢇⢿⡀⡀⡀⡀⢳⡂⡀⠈⢻⢳⢿⣗⢻⡀⡀⡀⡀⡇⡀⡇⢎⢳⡜⡣⢜⡣⢜⡣⢜⡣⢜⡣⢜⡣⢜⡣⢜⡣⢜⡣⢝⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕ ⠀⡀⡀⡯⢸⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢺⠢⢰⢅⢰⡨⢌⡢⢇⡘⢤⢝⡑⢤⢙⡑⣌⠚⠈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠈⡀⡀⡀⡀⡀⡀⡀⢻⡜⢣⡜⢣⡜⢣⡜⠘⠑⡀⡀⡀⢄⠍⣃⡆⠹⡻⡿⣺⢷⡀⡀⡀⡀⠘⡇⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪ ⠀⡀⡀⣇⢸⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢽⠨⠅⡑⠌⠆⢪⡘⢑⡡⢎⠼⣑⢦⢽⣑⠦⢝⢸⢔⠑⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢸⡀⡀⡀⡀⡀⡀⡀⣻⡎⢱⡎⢱⡎⢱⡎⣷⡀⢢⠢⠑⠉⠉⢉⠩⣻⡌⣺⡽⣕⢷⡀⡀⡀⢣⡇⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕ ⠀⡀⡀⡇⢸⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢵⢐⠆⢐⠅⠌⠢⠰⡡⡊⢆⡕⢸⡎⠵⡙⡦⠯⣉⢒⠣⡕⠮⠉⡀⡀⡀⡀⡀⡀⡀⣇⡀⡀⡀⡀⡀⡀⡀⡇⢣⡜⢣⡜⢣⡜⢣⡜⠘⢀⡀⡀⡀⠅⡐⡄⡆⣿⣧⣗⣳⢵⢿⡀⡀⠄⡇⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪ ⠀⡀⡀⡇⢸⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡹⠂⡅⠨⡊⢜⡣⡌⠢⡐⢅⡪⢇⡪⢜⡣⣜⠧⣍⣖⠪⣍⡲⢌⣔⠲⠈⡀⡀⡀⡀⡄⡀⡀⡀⡀⡀⡀⡀⡀⡹⢎⡱⢎⡱⢎⡱⢎⢷⡀⡀⠐⡀⠂⠨⠢⠰⣿⢹⡽⣗⢵⡹⢿⡀⡀⡇⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕ ⠀⡀⡀⡇⢸⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢆⢂⡀⢌⡂⢆⢑⢜⢌⡕⣊⢜⠪⡕⢪⡕⢪⡕⢪⣕⠚⢬⣓⠪⢌⡑⡐⢦⠛⡀⡀⡀⠸⡀⡀⡀⡀⡀⡀⡀⣿⢱⡎⢱⡎⢱⡎⢱⡎⠈⢀⡀⡀⡀⢈⡀⡀⡣⣿⡜⣝⢟⢽⡫⢿⡀⡇⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪ ⠀⡀⡀⡇⢸⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢨⠨⠂⠨⡐⢕⡪⢪⠱⡣⢪⠸⢎⠸⡎⢕⡨⢇⡸⢇⡸⢇⢼⡑⢄⢲⠒⡄⡈⡱⢮⠙⢧⡀⡀⡀⡀⡀⡀⡀⡄⢜⡣⢜⡣⢜⡣⢜⡣⢻⡀⡀⡀⡀⠂⠄⠅⡀⣟⣿⣆⢝⢺⡸⣓⡀⠺⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕ ⠀⡀⡀⡇⢯⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠅⡀⠄⠠⠄⢈⠨⡨⢌⡢⢢⠡⡈⢅⢪⢇⡪⢱⡪⢕⡪⢕⡪⢕⡪⠳⠈⣀⢆⠘⣤⢙⡎⡀⡀⡀⡀⡀⡀⡀⡀⣻⡸⢇⡸⢇⡸⢇⡸⣇⡀⢐⡀⡀⡀⡀⡀⠐⣇⣽⢻⣻⢜⣪⢜⡇⡎⢱⡎⢱⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⢪⡕⢪⡑⢎⡱⢎⡱⢎⡱⢎⡱⢎⡱⢎⡱
⠀⣷⣾⣷⣾⣷⣾⣶⣷⣾⣷⣾⣷⣷⣾⣷⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣾⣾⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣿⣾⣷⣾⣷⣿⣿⣿ ⠀⠢⠢⠅⡱⠪⢆⢱⢜⡪⠇⠪⠆⠣⡱⢜⡱⢜⣵⠛⡀⡀⡀⡀⡀⠐⡀⡀⡀⡀⡀⠈⡀⡀⡀⠤⡀⠠⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠎⠢⠰⠰⡀⠠⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠛⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣄⢻⡕⡫⡜⡪⡳⣅⣟⣿ ⠀⡂⠆⠢⡐⡌⡢⢑⡘⢆⢔⠪⡱⢣⠱⠜⡨⢕⠪⡑⣎⠷⠈⡀⡀⡀⡀⡀⡀⡀⡀⢀⠑⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡠⠄⠤⢠⠂⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⣿⣿⢹⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣄⡻⡪⡕⢏⡹⣜⡘⡷ ⠀⡑⡑⡃⡑⢑⢇⢪⠢⡢⡅⡢⢱⠪⡪⡆⢕⢇⠱⢌⢣⡝⣯⡀⡀⡀⡀⡀⠠⡀⠠⡉⡀⠪⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣡⡠⢄⡠⡈⡀⢀⡀⡤⠈⡀⡀⡀⡀⡀⡆⣿⣿⣿⣿⠈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡄⣝⣎⢵⡫⡝⡺⡳ ⠀⡑⢜⢌⢨⢌⢌⡕⢌⡨⡑⡑⢕⢌⡐⢆⢣⡪⢣⡓⣠⠏⣇⠈⡀⡀⡀⡀⡀⡀⡀⡀⡀⠄⠆⠈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡌⡀⢂⠈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣀⣦⣿⢹⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡄⢿⡲⢆⡣⢕⡝ ⠀⠣⠪⡢⢢⠢⠅⠨⠌⢅⡂⢢⢅⢌⡘⡑⡜⡰⡕⣿⡀⣧⣁⢹⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠁⠃⡀⡀⡄⠁⠂⡀⠈⡀⡀⡀⡀⡀⠉⠛⠈⡀⡀⡀⡀⡀⡀⢟⣿⠿⠛⠉⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡄⣿⡎⢮⡪⡇ ⠀⢅⢌⢌⡡⡂⡑⡑⡑⠕⢕⠰⡨⠕⠪⠢⡐⡊⡑⢿⡀⡀⡫⣗⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠋⠃⠚⠒⠁⡀⠘⡜⡀⡀⡀⠁⠷⣂⣱⡪⣕⠙⡀⡀⠉⠋⣿⣿⣿⣣⣇⣸⡇⣇⠾⠙⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⡳⢕⡇ ⠀⡨⡑⠜⠢⡑⢑⠨⠌⠌⢌⢌⡌⠌⢌⠢⡣⠌⢌⡧⡀⡀⣆⡍⠘⡀⡀⡀⡀⡀⡀⠠⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠄⠲⠴⢢⠶⠆⠃⡀⡀⡀⠃⣪⢁⣸⢇⡸⢇⡺⣲⢋⣿⣿⣿⣿⣿⡼⣾⡎⡜⡫⡻⢝⣯⠙⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡿⢽⠯ ⠀⠢⡑⡑⡑⢑⡨⠔⢌⠪⠪⠢⠢⠢⠡⠡⢃⠪⠢⠱⢹⡀⡀⣆⢻⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢀⡀⡀⡀⡀⡇⡀⡀⡀⣸⡇⢎⡱⢎⡱⢎⡿⣣⣶⠟⣿⣿⣿⢸⢸⠡⡿⡟⣻⣟⡿⢿⡿⢿⠈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡟⠻⡙⣈ ⠀⡑⢔⢌⢌⢨⢑⠕⢂⠇⡑⡑⡑⡑⢌⢌⢢⢔⢌⢎⡜⠙⡀⡀⣆⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡇⡀⡀⡏⢘⡇⡇⢹⡫⡹⢫⢸⣿⣧⣿⣏⣴⣜⠛⢻⣿⠏⣿⣿⣿⣦⣽⣆⢿⣧⠙⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⣿⣿⣿ ⠀⢌⢌⠪⠢⠢⡢⢔⢌⡌⢌⢌⢌⢌⠢⠢⡑⢂⠣⠌⠪⡥⠙⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠈⡀⣷⡕⢖⡏⣯⣿⣿⣿⡟⠽⡙⢶⣿⣞⡷⣯⡇⢋⣿⣿⣿⣿⣿⠿⡿⣿⠃⣷⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠃⣿⣿⣿⣿ ⠀⠢⠢⢅⢌⡨⡑⡑⠕⠰⠪⠢⠢⠢⡑⡑⢅⢃⡫⡛⢛⠫⡹⢿⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢀⡀⡇⡒⡗⢿⣎⣿⣿⣼⣿⣿⢿⣯⣬⢊⢿⣫⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⢇⡿⢸⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡏⣿⣿⣾⣿ ⠀⢆⢌⠢⠢⠢⡢⢔⢌⢌⡨⡁⡑⡑⢆⢕⡴⠋⠖⠮⣧⠯⠛⠉⡀⠤⠈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠋⠛⠉⡀⡀⡀⡿⣺⣺⣿⢷⣧⠨⣿⣿⣿⣿⢹⢿⡟⣿⣽⣿⢻⣿⣿⣿⣿⣿⣿⣿⡏⣿⢿⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⣿⣷⣿⣗ ⠀⣆⡙⡢⡑⡑⡑⡑⠕⠪⢅⢌⢌⢌⢌⢃⣰⠔⢋⡴⣀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢀⡀⡀⡀⠇⣿⣷⣿⣿⠾⡀⡆⢹⢽⣿⡇⢸⡞⡎⣿⣿⣿⣾⡞⣎⣿⣿⣿⣿⣿⣿⣣⠿⡇⣿⣿⣿⣿⣿⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⣻⣾⣿⣿ ⠀⢂⠢⢦⡙⢳⢌⢌⢊⡡⡘⢐⠡⠨⠆⢅⢌⡼⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡇⣷⣿⣽⣾⢸⡀⡀⣇⢾⣿⡿⡇⢻⣻⣿⣿⢸⣿⣿⢿⣷⣿⣿⣿⣿⣿⡹⣶⢻⣷⣿⣿⣿⢁⣿⠈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡇⣿⣿⣻⣿⣟ ⠀⠃⠪⢥⡊⢦⡙⠳⡡⡑⢑⠢⢢⠢⡑⡑⣴⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠄⡀⡀⡀⡿⡯⣿⢿⡿⣿⡀⡀⢾⣆⢣⢡⣿⣿⣿⣿⣿⣿⣍⣶⣶⣿⡙⣮⣷⣿⣿⣿⣿⢿⣜⣝⣼⠋⣿⣭⣿⠈⡀⡀⡀⠐⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⣿⣻⣿⣿⣿ ⠀⡀⣀⡙⢢⡣⡘⢦⣈⢕⢌⢌⡢⡢⢔⡼⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠃⠸⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠡⡀⡀⣿⣟⣿⣞⣿⣿⡀⡿⡑⣟⠁⢻⠿⠲⡀⣤⣿⣿⣿⣿⣿⣾⡻⣷⢿⣿⠿⠿⢿⣴⠾⣯⠛⣿⢸⣿⣿⣿⠈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⣿⣿⣩⣷⣿ ⠀⠐⡀⢧⢰⡁⡢⢪⡑⢶⣌⠝⡪⡐⡏⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠏⣏⠁⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠃⢾⣿⣞⡿⣿⣿⡇⠸⡏⢀⣿⣿⢿⣿⢿⡇⡀⣝⣿⣿⣾⡿⣿⡇⣿⠿⣒⠿⣿⣿⣾⣿⣼⣿⢺⣿⣿⣾⣟⠈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡏⣿⣿⣿⣿⡟⣿ ⠀⢸⡀⡇⠅⠅⡂⡁⡆⢆⡑⠳⣄⡛⢀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠏⢔⢸⢸⠹⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡇⢯⣽⣷⣯⣿⣿⠹⣿⣗⡀⣿⣽⣿⢸⣋⡇⡀⡀⡸⣿⣾⣷⣠⠝⡀⡀⡀⡇⢰⠈⣽⣿⣿⣭⣥⣭⢟⣿⠧⣿⠈⡀⡀⠄⡀⡀⡀⡀⡀⡀⣷⢿⣝⣿⣿⣿⣿ ⠀⢸⡀⡄⢅⢕⢕⠪⡢⡑⢦⢭⣍⠠⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠏⢣⠪⢠⣹⡌⠻⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡇⡽⣯⣽⣪⣿⣿⣿⣿⡇⡀⣇⣿⣾⢱⡎⣇⡀⡀⢀⠽⠪⢰⠌⡟⡀⠤⠑⣷⡀⠐⡀⡿⣿⣿⣿⣯⣭⣛⡯⣿⣿⠙⡀⡀⠄⡀⡀⡀⡀⡀⡀⣿⣿⣿⣝⣿⣿ ⠀⢸⡀⡀⢕⢕⠨⢂⡐⢐⢅⠣⢠⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣽⢌⠨⡀⢔⢨⡊⢦⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡇⣽⣯⣿⣾⣿⣿⣿⣿⠨⠈⡀⠹⡎⡇⣹⠏⠑⡀⠃⢑⡯⡎⡀⣼⡀⣄⠓⡀⠦⡸⠏⣿⣿⣿⣴⣷⣿⣿⣾⣷⣴⢟⣿⠿⠙⢀⡀⡀⡀⡀⡀⠄⣧⣿⢿⣟⣻ ⠀⡧⡀⡀⠸⢐⡂⡂⢑⠪⡐⡼⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣳⢅⠨⡀⠫⠪⠣⡪⠘⠬⠈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⣿⣿⣻⣿⣿⣿⣥⢜⢷⡀⣭⢣⡒⠰⣿⠘⠤⣛⣓⣘⣈⠿⢘⠙⡀⡀⡀⢦⠏⣶⣿⣿⣿⣿⡝⢿⠛⣭⢛⣿⣿⣿⣿⣿⣿⡀⡀⡀⡀⡀⡀⣆⠻⣍⣶⣿ ⠀⡇⡀⡀⢺⠢⢕⠪⡑⠌⠡⢀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡹⢕⣮⠈⡀⣀⣤⢶⢧⣎⠲⠈⡀⡀⡀⡀⠂⠊⠈⠂⡀⡀⠠⡀⢅⠣⣄⣿⣿⣿⣿⣤⡀⣱⠿⣾⠈⡇⢂⡀⣳⢀⡀⡡⡇⣿⡀⣼⣿⢿⠓⠈⢄⣰⡟⣿⢹⣝⣿⣿⣿⣿⣿⢡⠿⣿⣿⣱⣾⣿⣿⣿⢿⠈⡀⡀⡀⡀⡀⣷⣬⣿⠯ ⠀⡇⡀⡀⡆⠡⢐⠢⢑⡂⣞⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢷⡌⡨⢦⠓⠈⡀⡀⡀⡀⣄⢶⡀⡀⡀⠈⠄⢨⡀⡀⡀⠂⡀⡂⢜⡱⠄⠠⠁⠁⢣⡀⡆⢸⢅⢚⠘⠸⢻⡏⢚⢨⢈⡶⣇⣿⠂⡇⢀⡀⡼⣴⡥⣶⣿⣿⡥⢶⣉⣭⣭⢟⣿⣿⣵⢟⣻⡿⣿⣿⣿⣿⣿⣿⠿⠙⠈⡀⡀⣿⣦⣟ ⠀⡇⡀⡀⡀⡘⠅⠢⢅⠡⢠⡀⡀⡀⡀⡀⠁⣡⢦⡀⡀⡀⡀⡀⡀⢽⠙⣉⢦⡘⡑⠕⣱⢵⠳⠙⠈⡀⡀⡀⡀⡀⠂⠄⡀⡀⡀⡀⡀⡀⠠⡨⡐⢈⡀⠁⠰⠠⡀⢛⣿⢀⢰⡀⣇⢼⠘⢏⣿⣼⡀⣿⣴⣷⡇⠡⣈⡀⢹⣹⣼⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⡈⢿⡧ ⠀⡀⡀⡀⡀⢵⡂⠂⠡⢇⡀⡀⡀⡀⡀⡀⢹⢴⣶⢼⡀⡀⡀⡀⡀⢌⢕⢌⠡⠕⠪⠢⢆⢔⢌⠪⠵⣌⣽⠾⠓⠈⡀⡀⡀⡀⡀⡀⡀⡀⡁⠊⠐⢡⣇⠈⡇⢈⡇⣿⣰⡀⣿⠸⣹⢇⣸⢩⣿⠒⠃⣠⣄⠡⣾⠈⡛⡀⣾⢣⣧⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠻⣷ ⠀⡀⡀⡀⡀⡅⡂⠌⡈⡯⡀⡀⡀⡀⡀⡀⡆⡍⣀⡀⡀⡀⡀⡀⡀⢽⢶⣌⠱⢐⡨⡑⡑⡑⠕⠪⠢⡑⠪⢌⡹⣜⠹⡀⡀⡀⡀⠄⡀⡀⠄⢠⡄⡠⡃⡀⡰⡀⣿⡌⡀⡡⡟⠸⠟⠯⠿⠿⢸⡀⡿⡀⣿⣿⢹⠈⣄⠁⡾⡿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠟⣿⣿⢼⣷⣿⢿ ⠀⡀⢸⡀⡀⡀⢕⠪⠡⢸⡀⡀⡀⠃⠵⠺⠇⣭⡼⠘⡀⡀⡀⡀⡀⢀⢦⣑⢮⣀⠞⠙⢄⢌⢌⢌⢊⡢⡢⡕⠪⢌⡝⠈⡀⡀⡀⡀⡀⡀⣿⣩⣿⢸⡇⡀⡀⡀⣟⣿⠒⣯⡿⢻⣤⢻⣥⣍⣧⡀⣦⡀⣧⣿⣼⢠⡀⣾⠃⡻⢿⡿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢣⣿⣿⣿⣿⣿⣯⣿ ⠀⡀⢸⡀⡀⡀⣇⢑⡃⡀⡀⡀⡀⡆⡏⠋⡅⠯⠟⢀⡀⡀⡀⡀⡀⡀⠋⡘⢐⣸⣻⠻⠸⠪⠢⠆⡑⡑⢑⠢⠢⡐⠣⢧⡀⡀⡀⡀⡀⡀⣼⠍⡟⢸⡀⢸⡀⠁⣿⢀⣸⡼⠑⠨⣆⡆⠿⢿⠿⣍⠒⢿⣽⡌⣩⡀⢱⠱⣿⣼⣶⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣧⣿⣿⢿⣧⣿⣿⣽⢗⣿⣿ ⠀⡀⢹⡀⡀⡀⡂⢐⡼⡀⡀⡀⡀⡦⠳⢃⣇⡆⡀⢸⡀⡀⡀⡀⠇⡀⡳⢜⠰⣏⡫⠦⢈⣍⠳⡘⡊⢑⡨⡊⢆⢣⡪⣕⡀⠛⡀⡀⡀⡀⢸⡓⡔⢸⡀⣀⡀⣿⣾⠂⣛⠤⠴⢺⠨⠻⣦⣿⢿⣖⢁⣖⢻⣀⣀⠫⣡⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣡⡙⣿⠵⢜⣿⣿⣿⣿⢿⡻⢗⠭⣛⣮⣿ ⠀⡀⣿⡀⡀⡀⠁⣰⡀⡀⡀⡀⡀⠇⣭⢦⠁⣡⣄⡀⡀⡀⡀⡀⣸⡀⠁⠴⠁⢹⣭⣥⢸⣈⢧⣌⠳⡰⢊⠕⡇⡸⢔⠋⣶⣶⡀⡀⡀⡀⢸⠤⠧⢽⠈⡀⡀⡇⡀⡀⠗⠓⠒⢸⣿⣍⣿⣍⠭⡿⣸⡀⣧⢿⠈⠟⣿⣉⣿⣿⠿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣭⣅⡟⣶⣮⡏⣿⣿⣿⣿⢸⣿⣿⣾⣽⣿ ⠀⡀⣿⡀⠁⠰⡀⡀⡀⡀⡀⡀⡀⠄⠙⣏⡏⠻⠶⢈⡀⡀⡀⠁⡀⡀⡆⣘⠟⠋⢰⡆⠈⡢⢕⢌⢮⢌⠝⡂⠕⡪⡕⣇⣈⣇⢹⡀⡀⡀⣿⢷⡿⣿⡀⡀⡀⡀⡀⡀⡀⠉⢫⢸⡀⡀⢡⣛⣡⣥⢂⠒⢁⣌⣯⣽⣿⣿⣿⣿⡘⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⡟⢿⣧⢏⢻⣷⣿⣿⣿⣿⡻⣮⣶⣶⢱⣿ ⠀⡀⣞⡄⡀⡀⡀⡀⡀⡀⡀⡀⡀⠃⢴⢲⡟⣥⢸⢐⡀⡀⡀⠸⡀⡀⡇⠐⠛⡇⣨⣇⡀⡱⡑⢔⠢⢌⠳⣄⢙⡨⢎⢹⣦⠊⣽⠈⠇⡀⣇⡉⢻⣿⡀⡀⠈⡀⡀⡀⡀⣧⣿⣸⡀⢸⡀⡀⠊⢠⡁⢠⣿⡀⡄⣿⡀⣿⡙⣿⢸⣿⣿⣿⣚⡖⠸⣿⣿⣿⣿⣿⠘⢀⣿⠟⠺⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠋⢋⢮⡏⣘⣱⠧⣏⣘⠘⡀⡀⠏⢸⡀⡀⡟⢬⢴⣄⢙⣟⢀⠌⡡⢎⢆⢱⠢⣌⠩⠽⡌⡕⠃⢙⡾⢻⡇⢳⡀⡀⡀⡀⡀⡀⣿⣰⣿⠁⠈⠏⣿⢻⡀⡀⡀⡀⢠⡀⠆⡀⡇⠘⠨⣧⡀⣿⣿⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⠚⣿⡟⢏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢻⣩⣭⢰⣾⣻⡄⡳⡶⡀⡀⠃⡪⢳⡀⡀⡀⣽⡽⣧⣧⢰⡀⡣⢜⡅⢪⡀⡀⡁⡀⡀⡤⣤⢠⠟⣓⡷⡀⡀⡀⠎⣰⡀⡀⡀⠺⡀⣓⡔⢀⡀⡀⣧⡀⡀⡀⡀⡀⡀⠆⠟⣠⢸⡀⡇⠃⣼⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⢸⣿⠰⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⢘⡯⣧⢻⠋⣤⣏⢸⢠⡀⢦⠣⡏⡀⡀⡟⡄⡅⡇⣈⣏⠌⡣⢜⡢⢇⢹⡀⡀⡀⢸⢀⡀⡀⣷⡛⠛⢠⡀⠉⠃⡀⡀⡀⡀⡇⡀⣿⡀⡀⡀⡀⡀⠸⡀⡀⡀⡀⡀⡀⣸⡀⣀⡀⡀⡿⣿⣿⣿⣿⣏⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣘⣿⣼⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡇⠟⣅⡷⡴⠡⣿⠂⠘⢸⡀⡀⡀⡷⡀⡀⠉⣌⣘⡄⠲⣶⠁⡨⢇⡱⢌⡢⡀⡀⡀⡇⡀⡀⡀⡀⠂⣁⣦⠞⢹⠅⡀⡀⡀⠁⡏⣆⣼⡀⡀⡀⡀⡀⡄⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠁⣿⣿⣿⣿⠿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣛⣿⢻⢒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣦⢴⡀⠦⠴⡄⠒⠲⢠⡀⡀⡀⡀⡀⡀⢾⢚⢒⢃⢠⢭⠘⢎⢕⡌⢡⡊⢸⡀⡀⡀⡀⡀⡀⡀⢁⢁⡀⣄⠒⣏⡀⡀⡀⡇⣂⣥⢰⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢬⢭⣿⣚⣒⣿⣿⣿⣿⣿⣿⣿⣾⣫⢟⡿ ⠀⠈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡤⠔⢀⡀⡀⡀⡀⡀⡀⡀⡀⣻⢈⠠⡿⡖⠷⠂⠢⡱⢕⠬⠨⡇⡀⡀⡀⢸⡀⡀⡀⢀⢠⠠⢠⠁⡀⡀⡀⡀⡇⢏⣧⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣉⣿⣸⠐⣿⣿⣿⣿⣯⢟⡿⣿⣽⣿⣗ ⠀⡀⡀⢸⠤⠐⠒⠛⠛⠙⠖⠬⣪⢵⠙⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣻⣃⣁⡗⣂⢼⡀⡑⡑⢑⠢⡢⢐⠈⡀⡀⢇⡀⡀⡀⡔⡀⡰⡀⢠⡀⡀⡀⡀⣿⣿⡏⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠏⣿⣿⣿⣿⣾⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠲⠖⣻⢿⠶⣼⣟⢿⣯⣿⣳⣫⣪⣝⣞⡧ ⠀⡀⢠⢸⡀⡀⡀⡀⣄⢓⢎⠸⢁⡔⡣⣪⠧⠉⡀⡀⡀⡀⡀⡀⡀⡀⣧⠍⡛⣄⡗⠾⡀⣄⡙⢂⢄⡡⡑⢫⡀⡀⡄⡀⡀⠄⠠⡀⠠⡀⡀⡀⡀⡀⡀⡀⣀⣀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣇⢳⣿⣄⣿⢿⠿⡿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⢴⣌⡙⣼⢸⣽⢽⣞⣯⡳⣗⡪⣕⢎⡕ ⠀⡀⢈⢸⡀⡀⠐⡀⡀⡀⡀⢤⢓⡨⠱⢌⢒⡕⣪⠻⠈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢄⡘⢁⢑⡌⡀⡀⡀⠘⠁⡀⡌⡠⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠉⠿⠿⠿⠛⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣾⣧⣻⠾⠳⠛⡾⡺⠙⡜⣕⣕⢮⣣⣎⣕⣪⢕⢪⡕ ⠀⡀⠠⢸⡀⡀⡀⡀⠄⡀⡀⡀⡀⡀⢄⠲⣐⠣⡌⢑⡨⢥⠓⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠦⢕⡪⢸⡀⡀⢠⢀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡸⡀⣏⣿⣿⣿⣿⣿⣿⣿⢻⡟⣿⣿⣶⣬⣓⠾⢯⣳⣞⢯⢽⣺⡳⡺⣝⢮⣕⣪⢕⡪⢕⡪⢕⡪⢕⡪ ⠀⡀⡀⢸⡀⡀⡀⡀⡀⡀⡀⡀⠂⡀⡀⡀⡀⢄⠲⢪⠣⡨⢊⡕⢵⠙⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡙⡎⡀⢠⡀⡀⡀⡀⡀⡀⡀⡀⠁⠛⠾⣧⢄⠃⠛⡀⠙⠈⠈⠉⠈⡀⡀⡀⡀⡀⡀⢐⡀⣿⣿⣿⣿⣿⣿⣿⣾⣬⣍⠮⡪⡪⣕⢧⡸⣕⣎⢗⢳⢎⡕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡸⢕⡪⢕ ⠀⡀⡀⢸⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣃⡨⢢⠒⡠⠍⣨⠲⠉⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢆⢰⡀⡀⡀⡀⠁⠈⠐⠠⣿⡱⢎⡱⢎⢷⢡⣠⡀⠇⣄⡆⡄⣝⠻⠈⡀⡀⡀⡀⠸⡀⣿⣯⣽⣻⡷⣫⡹⣇⣝⣜⡱⢪⠵⡎⡱⢎⢱⡎⢱⡎⢱⡎⢱⡎⢰⡇⢸⡌⢡⡊⢕⡪⢕⡪⢕⡪ ⠀⡀⡀⢸⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢐⡀⡀⡅⢌⣂⡂⢨⠆⢑⡢⢌⣎⠓⡀⡀⡀⡀⡀⡀⠁⠐⠐⠉⠃⠈⡰⢸⡀⡀⡀⡀⡀⣇⢣⡜⢣⡜⢣⢻⡆⡀⡀⠉⠡⢘⣍⡎⣿⠙⡀⡀⡀⡆⡀⣇⣵⣪⡕⣪⢕⡪⡕⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⢪⠕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕ ⠀⡀⡀⢸⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡇⠨⡐⡐⢌⣈⠃⠬⠕⣍⢲⡪⢵⠙⡀⢀⡀⡀⡀⡀⡀⡀⡀⡀⡇⡀⡀⡀⡀⡀⡀⢝⡪⢕⡪⢕⡪⠘⡀⡀⡀⡕⡀⡄⡜⣯⡽⠹⡀⡀⡀⠸⡇⡱⢎⡱⢎⡱⢎⡱⢎⡱⢎⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪ ⠀⡀⡀⢸⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡇⢌⡈⠐⠂⡘⠨⡪⢝⡚⡤⠳⡌⡱⣑⠪⠈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢿⡳⡸⢇⡸⢇⢿⡀⠒⠉⡀⣄⢠⣷⣇⣧⡮⠻⡀⡀⢇⡇⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕ ⠀⡀⡀⣻⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡇⡁⠌⠠⢐⠨⠔⠡⡃⡎⢣⢜⡑⣦⠻⢬⢕⢦⠚⠈⡀⡀⡀⡀⡀⠸⡀⡀⡀⡀⡀⣧⠱⡎⢱⡎⢱⡎⠈⡀⡀⡀⠄⠠⡔⢻⢱⢺⣎⠻⡀⡀⡇⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪ ⠀⡀⡀⡿⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡇⡂⢐⠅⠢⢢⢅⡇⡪⢱⡘⢎⡱⢎⢵⣙⢶⡚⡢⢝⢬⠙⡀⡀⡀⢣⡀⡀⡀⡀⡀⡄⢕⡣⢜⡣⢜⡣⢻⡀⡀⡀⡀⠄⡀⣷⡸⣝⢮⢼⢻⡀⣿⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕ ⠀⡀⡀⣯⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡇⠨⡑⠊⠔⡂⡐⢅⠨⡌⢅⡎⢸⡇⢸⡇⣸⠣⣉⠦⢘⠄⣌⠯⠉⡄⡀⡀⡀⡀⡀⡀⢽⢕⡪⢕⡪⢕⡪⠈⡀⡀⡀⡀⠁⡆⣿⢆⡪⡳⡝⢸⡏⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪ ⠀⡀⡀⣿⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡆⠂⡐⢅⠡⠱⡂⢅⢨⠜⡌⢅⠪⠕⡪⢕⡪⢕⡪⣕⠙⣀⠤⠑⢦⡣⠈⡀⡀⡀⡀⡀⡇⡇⢸⡇⢸⡇⢸⢸⡀⡀⡀⡀⡀⡀⣽⢿⣳⢎⢣⢱⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕
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