Run diagonally!
Imagine a right angled triangle...
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Note the diagonal edge is longer than the edges adjacent to the right angle? Essentially the distance covered by running sideways and forwards at the same is greater than the distance you could have achieved in the same time by running only forwards (or only sideways).
Praise Pythagoras and be safe from pumas!
Edit: I've also always imagined adding a jump when starting running seems to give a head start too.
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