<image>The diagram below shows a $ 4\times4$ rectangular array of points, each of which is $ 1$ unit away from its nearest neighbors.
<image1>Define a growing path to be a sequence of distinct points of the array with the property that the distance between consecutive points of the sequence is strictly increasing. Let $ m$ be the maximum possible number of points in a growing path, and let $ r$ be the number of growing paths consisting of exactly $ m$ points. Find $ mr$.