Terry the Tiger lives on a cube-shaped world with edge length 2. Thus he walks on the outer surface. He is tied, with a leash of length 2, to a post located at the center of one of the faces of the cube. The surface area of the region that Terry can roam on the cube can be represented as \frac{p \pi}{q}+a \sqrt{b}+c for integers a, b, c, p, q where no integer square greater than 1 divides b, p and q are coprime, and q>0. What is p+q+a+b+c ? (Terry can be at a location if the shortest distance along the surface of the cube between that point and the post is less than or equal to 2.)