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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠙⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠛⣿⣿⣿⣟⣯⣿⣿⣽⣿⣿⣽⣾⣿⣿⢿⣿⡮⣟⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣿⣾⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣳⡳⡯⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⣟⠯⡫⢓⡳⣕⣗⢽⢽⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣟⣯⣿⣾⣿⣿⣿⣷⣿⣿⣟⣿⣷⢯⢯⢷⣝⣧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⣟⣗⢟⠨⢂⢔⢵⢋⠪⡀⢎⣗⣿⣿⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠠⢀⠀⠀⠄⡀⠀⠠⠀⠀⡀⡀⡁⡀⡠⢀⠐⠀⢁⠀⠈⡀⠠⢀⠀⡀⠀⡀⡀⡀⡀⢀⠀⠀⡀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣻⣿⣟⣿⣿⣿⣯⣿⣗⡷⣽⢽⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⣿⣿⡿⡽⣾⡳⡱⢡⡨⡮⣳⢢⢁⢀⢣⣳⣿⡏⠀⠄⠀⠄⢁⠀⠨⠀⠅⢀⠐⠀⠡⠐⢀⠐⠈⡀⠐⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠬⢄⢄⠂⠀⠄⠂⠀⠄⠀⡀⠀⠄⠂⠀⡐⠀⡂⠀⢹⣿⣿⡿⣟⣯⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣷⢯⣧⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⢿⣽⣿⣿⡻⢸⡪⡮⡚⠭⣞⡵⡕⡅⡎⣞⣾⡿⠀⠈⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢒⢄⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡾⣇⠀⠀⠀ ⠀⠀⠀⣾⡿⣝⣷⣿⣿⡕⢨⢺⢥⠈⡎⣿⠸⣣⡪⡞⣵⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢇⠂⠄⡀⠀⠐⠌⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⣿⣿⢿⣿⡿⣿⣯⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀ ⠀⠀⣸⣿⣽⣿⣟⣿⣿⣽⡨⣻⣕⡱⣽⣪⠂⡱⣗⣽⣾⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⡀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠂⡁⡑⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣾⣿⣿⣻⣿⡇⠀⠀ ⠀⠀⣿⣿⣻⣿⣿⣿⣿⢿⣳⣯⠳⡻⣿⣷⣣⡿⢻⣷⣿⣿⡀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠂⠀⠀⠔⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⠰⡈⠘⢆⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣽⣿⣯⣿⣿⣿⣿⣻⣯⣷⣿⣿⣿⣿⣿⢿⣿⣿⣿⡇⠀⠀ ⠀⠀⣻⣿⣿⣿⣿⣾⣿⣿⣿⣿⡽⣜⣽⡟⣕⢔⣽⣾⣟⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⡠⠊⠀⠀⠀⠀⠀⠀⢀⠐⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠐⠀⠦⠇⠀⡂⢣⠀⠀⣠⣴⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣯⣿⠅⠀⠀ ⠀⠀⠸⣿⣿⣾⣿⣿⢿⣿⣿⣿⣿⣽⣾⣯⣯⣿⣽⣿⣿⣿⣿⣿⣷⣦⣄⣀⡀⡀⣐⣁⡤⠐⠀⠀⠀⠀⠀⠀⠀⢀⠔⠐⠀⠀⠀⠀⠀⠀⠀⠢⡁⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⢀⣀⣀⣬⣴⣶⣿⣿⣿⣿⡿⣟⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⡿⣿⣟⣯⣿⣿⣿⣿⣻⣿⠏⠀⠀⠀ ⠀⠀⠈⢿⣿⡿⣟⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣽⣿⣿⣿⣿⣿⡿⠏⠁⢀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠨⠀⠀⠀⠀⠀⠀⠀⠅⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⢿⣻⣿⣯⣷⣿⣿⣿⣿⣿⣟⣿⣽⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣻⣿⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⢿⣿⣻⣷⣿⣿⣾⣿⣿⣿⣾⣿⣿⣿⣿⢿⣯⣿⣿⣹⣥⣶⡞⠀⠀⠀⠀⠀⠀⠠⠁⡀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠡⠀⠀⠑⢄⠀⠀⠀⠀⡁⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⣟⣿⣿⣻⣿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⣿⣿⣿⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢠⢁⢀⠀⠁⠀⠘⡀⠀⠀⠀⠀⠀⢐⠀⠀⠄⠀⠑⠐⢄⠠⢐⠀⠀⠀⠀⠠⡈⢿⣿⡿⣿⣻⣿⣟⣿⣿⣻⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠿⢟⣿⣿⣽⣾⣿⣿⣿⣟⣯⣿⣿⣿⣿⣿⣿⣿⣻⣽⣿⣟⠀⠀⠀⡀⢀⢀⣆⣦⣲⣴⣦⣢⣄⡅⠀⠀⠀⠀⠀⠰⠠⣤⣼⣬⣵⣵⣤⣮⣼⠀⡀⠀⠀⠀⣿⣦⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣾⣿⣿⣿⣟⣿⣾⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⢿⣿⣿⣿⣟⣯⣿⣿⣻⣿⣿⣿⣗⠀⠀⠐⠀⠀⠐⠉⠀⡸⡛⣛⣛⢛⢏⠂⠀⡀⠀⠀⠨⠙⢉⠝⡝⢝⠝⡝⢧⠐⠨⠀⠈⠀⠠⣿⣿⣿⣿⣿⣿⡿⣿⣽⣿⣽⣷⣿⣿⣿⡿⡿⠽⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠙⠛⠛⠻⠻⢿⣻⣷⠀⠀⢈⠀⠀⢸⠀⠀⠇⢕⢐⢐⠅⡹⠀⠠⠈⢄⠀⠀⡂⠨⢊⠌⠢⡡⠡⢓⠈⠀⠀⠀⠀⢸⣿⣿⣿⡿⣿⣻⡿⠿⠟⠟⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⡂⡑⢐⠨⢐⠐⡐⠠⠂⠌⣿⡀⠠⠀⠠⠀⠐⠀⡀⠄⢂⠅⡂⠂⠅⡂⡂⠔⠠⢑⢐⠨⢐⠐⡨⠨⢘⠀⡀⠄⠀⠄⠠⠀⠐⣼⢁⢂⢂⠂⠅⡂⡂⠢⠨⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡐⠨⢐⢐⢐⠠⠀⠐⠀⡁⡂⠅⠅⠅⣻⣿⡀⠐⠀⡈⠀⠂⢀⠀⢸⢐⠠⠡⡁⠢⠠⠡⢑⢐⢐⠨⢐⠨⢐⢈⣺⠀⡀⠠⠐⠀⠐⠀⣱⣿⢐⠐⡐⠨⢐⠐⠄⠅⠅⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠠⢑⢐⢐⠠⠀⠂⠁⠠⠀⡂⠅⡡⠡⠸⣿⣷⡄⠁⠀⠄⠁⡀⠀⣽⡐⠨⢐⠨⠨⠨⠨⢐⠠⠂⢌⢐⢐⢐⠠⣿⡇⠀⠠⠀⡈⠀⣢⣿⡯⢐⠨⠠⢑⠠⠡⠡⢁⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠨⢐⠐⡐⠨⢈⠔⠡⢐⢀⠂⢅⠐⠌⢂⢻⣿⣿⣮⡀⠐⠀⣀⣮⣿⡎⠨⢐⠨⢐⢁⢊⢐⠨⢈⠔⡀⡂⡂⢌⣿⣿⡀⠐⢀⣠⣾⣿⣿⡇⠅⠌⡨⢐⠨⢈⠌⡐⠨⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠨⠐⠨⠠⢑⠐⡨⢈⠐⠄⡊⡐⠨⠨⢐⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⡑⡐⠨⢐⠠⠂⡂⠌⡐⡐⡐⡐⠄⢱⣿⣿⣿⣿⣿⣿⣿⣿⡿⠠⠡⢁⢂⠂⢌⢐⢐⠨⠐⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠐⠄⠅⠅⡂⢂⠅⡑⠠⢑⠐⡘⠿⣿⣿⣾⣷⣿⣿⠇⡂⠌⠌⡐⠨⠐⢄⢑⠐⡐⠠⠂⠅⡂⣿⣿⣿⣭⣿⣿⢿⢛⠐⡨⠈⠔⠠⡁⡂⡂⡂⠌⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠐⢁⠂⠌⠌⠐⠨⢐⢐⠨⠙⠻⠽⡛⠍⡐⠄⠅⠅⠌⠌⢌⠐⠀⠀⠀⠈⠨⢐⢐⢈⠻⠷⠿⠛⠍⠅⡂⠌⠄⠅⠅⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠈⠐⠠⠨⠨⠨⢐⠠⡁⠂⠁⠅⠡⠡⠁⠂⠈⠀⠀⠀⠀⠀⢂⠂⡂⠂⠅⠌⠌⠌⠐⠄⠅⠅⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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