Two ladders of different lengths cross in a narrow alley (see graphic below). The rungs of the ladders are spaced a foot apart, from end to end, and the alley is an integer number of feet wide. The ladders cross exactly where there are rungs, i.e., integer number of feet from intersection point to ends of ladders. If no ladder is greater than \(30\) feet in length, how wide is the alley?

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