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⠀⠀⠀⠀⠀⠀⠏⣰⢞⡠⢀⠁⠀⠀⠀⡀⣀⢀⠀⠀⠄⠀⠐⠈⡀⠀⠄⠀⠀⣆⡿⣿⡿⣿⣱⠠⢀⠀⠁⠐⠄⡀⠀⠀⡀⠀⣀⣀⣀⠀⠠⠄⠂⠁⡀⠣⣬⠹⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡞⢁⡇⢀⠈⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠂⠈⠀⢈⠀⡄⣿⣿⣰⠀⠁⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⣆⡈⢷⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⡞⢈⢀⠻⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⡇⢸⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢌⠂⢯⠀⠀⠀⠀ ⠀⠀⠀⠇⢔⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠢⠈⡇⠠⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡄⢹⠀⠀⠀ ⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡇⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀ ⠀⠀⡿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣞⠈⠀ ⠀⠟⣿⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣷⢻⠈ ⠀⣽⢀⡿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⢿⣌⢸ ⠀⢸⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢠⣿⢸⢸ ⠀⢃⣿⢿⣴⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢰⠰⣏⢿⢠ ⠀⣏⣷⣄⠌⡑⢧⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⣷⡌⠆⠈⣷⠀ ⠀⣧⠁⢠⡛⠑⠠⣴⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣇⢀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⣶⣻⣿⢉⢠⡘⡇⠀ ⠋⣿⠻⢀⣿⡈⡑⡌⠃⣄⠺⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⡇⢈⡄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⣂⠑⢂⣌⣿⢇⡜⠃⣿⠻ ⣾⡽⣿⠛⣿⡌⠐⡿⢠⡟⣰⡘⠡⣟⠿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡇⠐⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠟⡻⢚⣁⣎⢻⡠⢷⠌⡄⣯⠹⣟⢿⣶ ⢱⡄⡷⣯⣿⢿⡿⣸⠏⣸⡡⠟⣯⣟⣿⣇⣻⠢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⠀⡄⠸⠀⡀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⣟⣻⣯⣳⣯⠻⠙⣆⢻⡄⢷⣿⣿⡿⣾⣨⡆ ⡀⠘⠀⣛⢟⣿⣏⣿⣡⠌⣤⣖⢶⣤⣠⣱⡀⢄⡙⠐⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠃⢹⠄⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠎⢋⡴⠀⣊⣄⣤⣖⣲⣄⠳⡌⢧⣿⣬⠳⣿⠀⠀⢘ ⠀⡂⠈⡗⢾⣽⢞⣼⣀⠀⠀⠀⠀⠀⠀⡄⠈⠐⡈⠦⢜⠈⠀⠀⠀⠀⠀⠀⡌⡁⠀⡌⣷⠠⠀⢲⠀⠀⠀⠀⠀⠀⠂⡡⠕⢠⠈⠀⢘⠀⠀⠀⠀⠀⠀⣀⠤⣻⣍⠷⣾⠃⡔⠀ ⠀⠀⡀⡵⣯⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠄⠂⡀⡳⠨⠀⠀⠀⠀⠀⢸⠠⠀⠐⠂⠀⠂⢠⠀⠀⠀⠀⠀⠊⢟⣠⠂⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⣕⣿⢰⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠄⠁⡆⡐⠱⠀⠀⠀⠀⢡⠄⡈⠀⠐⢀⠀⢩⠀⠀⠀⠀⠆⢈⣥⠂⠄⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢀⠡⠀⠠⠐⠀⢡⠀⠀⠀⡇⠀⠋⠛⠓⠑⡌⢀⠀⠀⠀⠞⢀⠁⠀⠐⠄⡀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠙⠀⠠⠄⠀⢀⠉⠢⠈⠈⡄⡸⢧⢊⠉⣶⣸⠸⠀⠀⡝⠀⡀⠀⠠⠄⠀⠋⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⡀⢀⠠⢙⠝⢚⠿⣳⣝⢻⣯⠱⢾⠍⡻⠄⡀⣀⢀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣿⣿⣿⣿⣴⢡⠈⠀⣄⣦⣿⣿⣿⣿⣿⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⣿⣿⣿⣼⠀⠇⡃⣛⣛⢟⠠⡀⣧⣿⣿⣿⣿⣿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⣿⣿⣿⣿⣿⣿⢀⠄⡀⣀⡿⢺⡁⠠⠁⡈⣿⣿⣿⣿⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣿⠀⢀⠀⢤⠂⠀⠀⠀⡀⢀⡿⣿⣿⣿⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⢬⡥⣿⢸⠀⠀⣽⣤⢿⡯⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⣽⣦⣷⢻⣾⣶⣤⣯⣿⣿⣿⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⢿⢹⣤⢠⢫⡿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣿⣿⣿⣿⠹⠏⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣾⣷⣿⣿⣶⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀