The diagram above shows a \(4\times4\) rectangular array of points, each of which is \(1\) unit away from its nearest neighbors.

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 \(mr\).

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