Circles P and Q are externally tangent at T, the radius of P is 12 and the radius of Q is 2. PTQ¯ extended intersects Q at B. A lies on circle P such that AP¯⊥PB¯. R lies on AB¯ such that RT¯⊥PB¯, and S is the intersection of circle Q and AB¯. The length of RS¯ can be written in simplest form as mn. What is m+n?