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⠀⠤⠆⠀⠀⣀⣀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⠵⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠚⠉⠀⠀⠀⠐⠒⠀⠀⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠐⡀⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⢀⠀⠀⠠⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠋⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠀⠐⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠐⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠈⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣶⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⣿⣿⣿⣿⣿⣷⣤⣠⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⡄⠀⠀⣀⡤⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣦⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡀⠀⠉⠉⠛⠿⣿⣿⡄ ⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠉⠙⠛⠻⢿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠉⠁ ⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⠿⠛⠛⠿⠿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣷⣄⠀⠀⠀⠀ ⠀⢀⣴⣾⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣷⠀⠀⠀ ⠴⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠍⠀
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⠌⠂⠄⠂⠌⠠⠐⡀⢂⠰⠀⠂⠄⢂⠰⠀⠆⡀⠆⠐⠠⠁⠄⢂⠰⠀⠡⢀⠢⠐⡀⠆⠐⠠⠐⡀⠆⠰⢀⠰⠀⠂⠌ ⠁⢂⠈⠒⢈⠀⡑⠀⢂⠀⠃⠘⠀⢂⠠⠁⠂⢄⢠⣈⠀⢃⠈⠄⠐⠂⡁⠂⡐⠐⠀⡘⠀⠃⠐⡀⠒⢀⠂⠐⠈⡁⠰ ⠂⠂⢀⠡⢀⠂⣀⠁⢂⢈⠀⡉⢀⡁⢀⠁⠂⠸⣿⣿⡀⡄⢈⠐⢈⠀⡄⢁⠐⢈⠀⡁⠈⡄⢁⠀⡁⢠⠈⡈⠐⡀⢁ ⠄⢡⠀⠆⠠⠀⡄⠰⢠⠀⠆⡜⠀⠀⠆⣤⣼⣤⣿⣿⣷⠀⡄⠘⢠⠀⡄⢠⠘⢠⠀⢣⠰⠀⠘⠀⠰⢠⠀⡄⠃⡄⠣ ⡀⠁⠌⡀⢈⠄⠠⢁⠠⢈⠀⠄⡁⢂⠠⠉⢉⠉⢻⣿⣿⣇⠠⠁⡈⢀⢁⠠⠁⡈⢀⠂⡀⠡⢈⠁⡁⠠⠁⣀⠁⡐⠈ ⠂⡁⠠⡐⠠⡀⢡⠀⡄⢠⠈⢄⠠⠀⣀⣶⣶⣶⣾⣿⣿⣿⣆⠂⠠⠀⡠⢀⠁⠤⠀⡐⠠⢁⠠⡀⠄⠡⡀⢄⠠⠐⡈ ⡁⠤⠁⠄⠐⠠⠀⠄⠄⠠⠄⠂⠄⢂⠠⠉⠉⠉⠀⣿⣿⣿⣿⣟⠛⠀⠤⠀⠄⢢⣄⠂⠄⠂⠄⡀⠆⠐⠠⠠⠀⠆⠄ ⡀⠕⠀⠊⠐⠠⠁⠂⢂⠰⠀⠒⠀⠂⠠⣀⣃⣀⣃⣻⣿⣿⣿⣿⡆⠠⠐⡀⠂⢸⣿⣆⢈⠀⠒⠀⠂⠌⠄⠒⠀⠢⢌ ⠀⢂⠈⠂⠑⡀⠑⠀⢂⠐⠂⠁⠌⠐⠀⠿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣄⠂⢀⠁⢸⣿⣿⡆⠐⠈⡀⠁⢂⠐⠈⡀⢁⠊ ⠁⠂⠠⢁⢈⠀⠡⠈⡀⠈⠄⠁⠂⣁⣀⣂⣐⣠⣾⣿⣿⣿⣿⣿⣿⣿⣤⣄⣊⣸⣿⣿⣿⣄⣁⣤⣥⠤⠖⢒⠀⢂⢁ ⡀⢁⠁⡄⢈⠀⡁⢀⣠⣶⣾⣿⣿⠿⠹⣿⡍⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⡄⢀⠆⡀⡄⡈⢀ ⠄⠌⠀⡁⢈⠀⢁⣴⣿⣿⣿⣿⡄⠀⠀⣸⡟⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⡿⠟⠋⢹⣿⣿⣿⠀⡀⠄⢈⡀⢁⠠⢁⠨ ⠄⡁⠠⢁⠠⢈⠠⠉⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⠐⡀⢻⣿⣿⠀⠄⣈⠠⢀⢈⡀⠄⡈ ⠁⡐⠀⢂⠠⠄⠠⠂⡁⢂⠐⠠⢀⠂⠐⡀⠂⡐⠀⠠⠀⠈⣿⣿⣿⣿⣿⡄⠄⠠⠐⡀⢿⣿⡆⠄⠠⢀⠂⠠⠀⠄⡀ ⠂⠄⠌⠠⠐⠀⠒⠀⠔⠀⠂⠔⠀⠂⠡⠄⠒⠠⣿⣿⡿⠿⢿⣿⣿⣿⣿⡇⠐⢀⠂⠄⠈⠛⠃⡀⠆⠠⠂⠡⠐⠂⠠ ⠁⡐⠠⠁⢈⠂⠡⠈⠐⠈⡐⠈⠄⠃⠐⠀⢂⠐⠀⡀⠄⠂⠀⢿⣿⣿⣿⣟⠛⡀⠀⠊⠠⠁⠐⠀⠂⠐⠁⠂⠄⠃⠔ ⠁⠂⢀⠁⢂⠠⢁⠈⡁⢈⠀⡁⠂⡁⢈⠂⡁⠈⠄⢀⣤⣭⣶⣾⣿⣿⣿⡇⠀⡀⠁⡁⢂⠁⡘⠀⡑⠈⡁⢈⠀⡁⠢ ⠂⢁⠂⡉⠀⡄⢈⠀⡐⢈⠀⠄⡁⡐⠀⠄⣈⠐⢈⠠⠉⡉⠉⠉⢹⣿⣿⡇⠐⢈⠁⢠⠀⡁⠠⠁⣀⠂⡁⢈⠀⡁⠌ ⡁⠌⠀⡁⠠⠁⡈⠄⡁⢈⠘⡀⢁⡁⠘⡀⢉⠀⠌⡀⠠⢁⣤⣧⢼⣿⣿⣇⠘⢈⠀⠌⢀⡁⢃⠀⡉⢀⡁⠌⢀⡁⠃ ⠀⠁⡁⡈⠠⢁⠠⢀⡁⢈⡀⠌⡀⠄⢈⡀⠌⡀⡁⠠⠁⠂⠠⠀⠀⢻⣿⣿⠠⠀⠌⡈⠀⡄⠠⠁⡠⠀⡄⢈⠀⡄⠬ ⠁⡁⡀⠄⠡⠀⠤⠀⠄⠠⠀⠤⠀⠌⠠⠀⠤⢀⠐⠠⠁⠤⠁⠌⢂⠀⠉⠉⢁⠂⠄⠄⠡⠀⠤⠁⠄⠠⠄⠠⠂⠄⡡ ⠁⠄⠀⠆⠠⠁⢂⠐⠌⠠⠁⢂⠐⠄⠂⠡⠐⠀⠢⠐⠄⠂⡐⠄⠂⠐⠈⠄⠂⠰⠀⠌⠐⠄⠂⠄⠌⠐⡀⠢⠅⠂⠢
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