Tom is jumping around a $4\times4$ grid of circles with the following conditions:

- He starts from any of the 16 circles.
- He always jumps in a straight line from one circle to any other circle.
- Each subsequent jump is farther than the last.
- He doesn't visit a circle already visited.

The maximum number of circles that he can step on is $m,$ and the number of ways of doing so is $r.$

Find the value of $mr.$

$$

**Note:** The grid is fixed on the ground, so a method obtained by rotating another is considered different.

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