# Your mind will explode #1

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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