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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠑⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠁⠀⢸⠀⣠⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⡀⡜⠉⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠠⠄⠄⠄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢸⠋⠀⡇⠀⠀⠀⠀ ⠀⠀⡖⠉⠀⠀⢹⠀⠀⢀⠃⢀⠤⢤⠀⠀⠀⠀⡠⠐⠁⠁⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⣠⠤⢤⡄⠀⠀⠰⡃⠀⡏⠀⣤⠀⠀⠀ ⠀⠀⠀⠅⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⡏⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠸⡠⠖⠛⠀⠀⠀⠃⠀⣎⠊⠀⡃⠀ ⠀⠀⠀⠨⡢⣀⠀⠀⠀⠀⠀⠀⡔⠋⠁⡠⠕⠀⠁⠁⡁⠀⠡⠀⠀⠃⠀⠡⠀⠁⠐⠁⡀⠀⠀⡇⠁⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⠀⠀⠀⠀⠈⠓⠢⠤⠤⠔⠒⠉⠀⠠⠁⠌⠀⡄⡀⠇⠈⠛⠑⢑⢜⠁⡀⠀⠈⠈⠀⠀⠘⠊⣆⠄⠀⠀⠀⠀⠀⠀⡀⡀⠂⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢊⡆⠂⠀⠁⠀⠀⠆⠄⠀⡀⠀⠀⠘⠀⠌⢀⠀⠀⠀⢃⡀⠀⠉⡉⠈⠈⠁⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡁⢀⠀⠸⡅⠀⠠⠀⢅⠑⠈⠀⢂⠀⠀⠀⠀⠀⠠⢐⠀⠀⠀⠀⢡⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡈⠰⠀⠄⠀⢂⡫⠡⠍⠁⡁⡃⡒⡃⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⢴⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠈⠄⠤⠆⠆⡀⡀⠒⠁⠍⡊⠀⠀⠀⠁⠀⠀⠀⠘⠀⠐⠀⠀⠀⠅⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠌⠬⡆⣀⡩⡔⠒⠤⠂⢲⠀⠀⠄⢀⠈⠁⠀⠀⠐⠀⠀⠃⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠡⠭⡀⣂⠅⡰⢌⠃⣌⠀⢀⠠⠀⢀⠁⠂⠀⠁⠀⠀⠅⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠀⠀⠁⠀⠄⠒⠈⠁⠢⣢⣑⡠⡁⠌⠂⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⠐⢀⠀⠀⠀⡐⠌⠀⢈⢀⠀⠀⠀⡈⠓⠒⢣⢡⠞⠂⠐⠄⠀⠀⠀⠀⠀⠀⠂⠅⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⣂⣀⠀⡀⢢⣀⢐⠀⠐⠀⠀⠀⠀⠀⠀⠌⠀⠀⠌⠨⠁⠉⠒⠢⠀⠀⢨⠀⠀⠀⠀⠀⢀⠤⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢈⠀⠄⠀⠄⠂⠀⡰⠈⢀⡆⠁⢂⢀⠀⠀⠀⠀⠀⢀⡨⠀⠀⠀⠀⠀⠀⠅⠀⢱⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⡌⠁⠀⠀⠀⠁⠈⠀⠂⠁⠁⠁⠀⠀⠀⠀⠀⠀⠈⡑⠐⠊⠀⢁⠀⠀⠀⠁⠢⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠐⡂⠄⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠀⡆⠁⠀⢠⠳⡇⠀⠀⡗⡆⠀⡶⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢀⠀⢂⠂⠂⠢⡀⠀⠨⠀⠀⠂⠀⠀⠈⠀⡀⠔⠁⠁⠀⢘⠀⢽⠀⠀⡏⠀⢣⡇⠈⡃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⡖⢢⡇⠀⡇⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣆⠘⠂⠀⠀⠀⠀⣀⡤⠖ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠉⠉⠉⠙⠒⠦⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠻⡄⠀⠀⠀⠠⣾⡿⣷⣄⠈⢱⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⣸⣾⣇⡀⠀⢀⢀⠀⠀⠟⡿⣷⣀⠙⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡉⢹⣼⠛⣷⣦⣴⢔⠀⠀⠀⠀⢸⠢⣀⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⣷⣾⣿⣷⣿⣿⣿⡾⣧⣤⣄⢄⢀⠈⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣟⡀⢻⢻⣿⣿⣨⣭⣥⣄⡈⠉⠉⣛⠛⣾⣿⣿⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣗⢰⣿⣿⢻⡏⢀⣀⠉⣻⣶⠟⠓⠶⠿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⢇⣧⣾⣿⡇⠘⢷⣌⣉⣠⠏⢸⡀⠶⠀⢠⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣟⡇⠀⠀⠉⠉⢡⡀⠈⡟⠶⣶⣾⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⡿⠏⠻⡇⠀⠀⠉⢑⠒⠷⠮⢄⣰⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠚⠉⠉⠉⠢⣀⠀⠀⠉⢛⣴⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⡤⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠘⡆⠤⠤⢤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠳⣄⠀⠀⣇⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢬⣳⠴⢻⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠈⣆⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠸⡄⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡠⠤⠴⢾⡁⠀⠀⢱⡀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⢳⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠦⣳⠀⠀⢣⠀⠀⠀⠀⠀⠀ ⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⡏⠀⠹⡄⠀⠘⡇⠀⠀⠀⠀⠀ ⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠓⢤⡀⢇⢸⢸⡹⠀⠀⠀⠀⠀ ⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⡇⠀⠀⠀⠱⡼⣞⣾⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣄⠀⠀⠀⠀⢀⣀⠤⢶⣟⢧⣼⠁⠀⠀⠀⡼⠤⢄⣉⡎⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠲⠖⠒⠊⠉⠀⢠⠛⠉⢳⠃⠀⠀⠀⡴⠿⢶⣢⡝⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢠⡎⠀⠀⠀⡼⠁⠀⠀⡽⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⠞⠀⠀⢀⡞⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⠲⢀⣾⣿⣿⣷⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣿⣿⠿⠟⢃⣾⣿⣿⣿⡍⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣝⣿⣹⣿⣿⣿⣀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠙⠛⠛⠛⠛⠻⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⢻⣿⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⣠⣶⣾⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢰⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄⠀⠀ ⠀⠀⣀⣤⣴⣶⣶⣿⡟⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀ ⠀⢰⣿⡟⠋⠉⣹⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⠯⡀ ⠀⢸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢳⢃⣿ ⠀⣸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⡿⠿⠿⠛⢻⣿⡇⡼⢫⡽ ⠀⣿⣿⠁⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⢽⣹ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⢿ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣯⢡ ⠀⢿⣿⡆⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠈⠉⠀ ⠀⠸⣿⣧⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀ ⠀⠀⠛⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣰⣿⣿⣷⣶⣶⣶⣶⠶⠀⢠⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⣽⣿⡏⠁⠀⠀⢸⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⢹⣿⡆⠀⠀⠀⣸⣿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣄⣀⣠⣴⣿⣿⠁⠀⠈⠻⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠿⠿⠿⠿⠻⠛⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠏⡿⣿⣿⣿⣿⠻⠈⠀⠁⣿⣿⣴⣠⣀⣄⣦⣿⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠇⣿⣸⠀⠀⠀⡆⣿⢹⠀⡇⣿⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⣿⢸⠀⠀⠁⡏⣿⣽⠀⡇⣿⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⢠⠀⠶⣶⣶⣶⣶⣷⣿⣿⣰⠀⠀⠀⠀⠀⣇⣿⣿⣿⣿⢿⠛⠀⠀ ⠀⠀⠀⠃⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⠀⡀⣧⣿⠸⠀ ⠀⠉⠈⡇⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⠀⠀⡆⣿⢿⠀ ⢡⣯⣧⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⠀⠀⠀⣿⣿⠀ ⢿⣿⢸⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⠀⠀⠀⣿⣿⠀ ⣹⢽⠀⣧⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⠀⠀⠁⣿⣿⠀ ⡽⢫⡼⡇⣿⢻⠛⠿⠿⡿⣿⣿⣿⣿⠿⠻⠉⠀⠀⠀⠀⠀⡇⣿⣿⠀⠀⡇⣿⣸⠀ ⣿⢃⢳⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⠀⠀⠀⠀⡇⣿⣿⠀⠀⡇⣿⢸⠀ ⡀⠯⣿⣿⣿⣶⣶⣶⣶⣤⣤⣤⣦⣷⣿⣿⣿⣿⠘⠀⠀⠀⡇⣿⣹⠉⠋⡟⣿⢰⠀ ⠀⠀⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿⣿⢸⠀⠀⠀⡟⣿⣶⣶⣴⣤⣀⠀⠀ ⠀⠀⡄⣷⢿⠙⠈⠀⠀⠀⠀⠀⠀⠀⠁⣯⣿⣿⢰⠀⠀⠁⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣄⣿⣿⣿⢿⠿⠿⠿⣿⣿⣿⣾⣶⣠⠀⠀⠀⡏⣿⣸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡄⣿⣿⢻⠈⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠋⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⣤⣷⣿⢿⠻⠛⠛⠛⠛⠙⠉⠛⡿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣤⣦⣶⣤⣤⣤⣤⣤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠦⠲⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⠌⠤⠠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠰⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠊⠒⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡏⣿⢻⠭⢫⠉⠟⡿⢿⠛⣛⣿⠽⠻⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠋⡟⣿⣿⣿⣿⣿⣿⣿⣿⣾⣦⣶⣷⣿⢿⣿⢻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠂⠙⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣻⠉⠈⠈⠁⡄⢀⣀⣂⢻⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠂⣟⣿⣿⣿⣿⣿⣿⣿⣾⠲⠒⠓⠙⡈⠀⠀⠀⠃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⣀⣟⣿⣿⣿⣿⣿⣿⣻⡈⢀⠲⠉⠀⠀⠀⠀⡌⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡟⣷⣿⣿⣿⣿⣿⣿⣿⣿⠘⠀⠀⠀⠀⡀⣀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⣦⣷⣿⣭⣻⣟⣶⣤⢀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣈⣀⣁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⡈⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠋⡛⠓⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠀⠀⠀⠁⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠟⣿⣼⢧⣿⣿⣿⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠈⠀⠀ ⣦⠹⠀⠀⡀⢀⠀⠟⠿⠿⠙⠀⠀⠀⠀⠳⠈⠀⠀⡀⣀⣤⣿⢿⠙⣦⣿⣿⣿⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⣿⠸⠀⠀ ⠀⣄⠹⠀⠀⠀⡇⣹⡷⣿⣿⢿⠸⠀⠀⠀⢧⠙⠀⠀⠀⠀⠀⣀⣤⣶⣴⣤⣀⡠⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⢿⣿⣿⢈⠀⡿ ⠀⠀⡀⢦⠀⠀⠀⣄⣿⣿⣿⣾⢸⠀⣦⠻⠈⣿⢳⠷⠈⠀⠀⠀⠀⠀⠀⠀⠁⠋⡬⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣼⢀⡟⣿⣿⢸⠀⣠ ⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢻⣇⣼⣦⢾⠘⠀⠀⠀⠀⠀⣥⣤⠢⠐⠀⠀⠀⠀⠀⠀⠀⠁⠂⡟⢰⠀⠉⠟⠻⡍⢸⠀⠀ ⠀⡀⢻⠈⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⣎⠀⣧⠸⣄⣰⠰⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠋⡾⣶⣿⣿⣿⣿⣙⣀⣀⣿⢸⠀⠀ ⠀⠀⡀⣤⠲⠛⠉⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⡇⠹⠀⣀⢄⡤⠠⠀⠒⠘⠀⠀⠀⠀⠀⠁⠟⣿⢺⣦⡛⣯⣿⣿⣿⢹⠣⡌⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⣤⢤⠳⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣴⣷⣿⠙⣤⠛⣛⣿⣿⣿⣿⢸⢀⡆⠻⠀ ⠀⠀⠀⠀⠀⠒⠋⠙⠉⠀⡀⣀⠢⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⡍⣭⠌⠀⣄⣷⠘⠀⣦⣵⣬⣤⣷⢸⠀⢧⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣤⣤⠰⠋⠛⠛⠙⠋⠚⠴⣤⣤⣠⣀⣀⣄⣠⣀⢀⠀⠀⡀⢦⠻⠀⣿⠘⠀⠁⠀⠀⡀⢰⠀⡟⣼⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢠⠀⠋⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⡙⣧⠙⠀⠀⢐⠀⠇⠹⡿⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⡿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⣳⠦⠘⠀⠷⡿⣟⣸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠋⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡛⢈⠄⡇⣾⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⣁⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⣠⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣃⢔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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