The advice for dealing with cougars (a/k/a mountain lions, panthers, painters, and "Uh oh, we're in trouble!") is never to run -- they'll outrun you and taking the prey from behind and biting the spinal cord at the back of the neck is how they usually kill. Instead, if you see one, try to make yourself as large as possible: open your coat flasher-style, for example. And stand your ground.

If you're attacked, guard your spine and soft tissue areas (belly, neck, genitals, etc.).

Better yet, wear a full suit of plate armor.

Don't mess with cougars. On the other hand, it's not likely you'll come across one.