Christmas Streak 31/88: A Bit Farther

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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