For -1<r<1, let S(r) denote the sum of the geometric series

12+12 r+12 r^{2}+12 r^{3}+\cdots

Let a between -1 and 1 satisfy S(a) S(-a)=2016. Find S(a)+S(-a).

For -1<r<1, let S(r) denote the sum of the geometric series

12+12 r+12 r^{2}+12 r^{3}+\cdots

Let a between -1 and 1 satisfy S(a) S(-a)=2016. Find S(a)+S(-a).