Three points $$O(0,0)$$, $$P(a, a^2)$$, $$Q(-b, b^2)$$, $$a > 0$$, $$b > 0$$, are on the parabola $$y = x^2$$. Let $$S_1$$ be the area of the region bounded by the line PQ and the parabola, and $$S_2$$ be the area of the triangle OPQ. If the minimum value of $$\frac{S_1}{S_2}$$ is $$\frac{m}{n}$$, $$\gcd(m, n) = 1$$, then $$m + n$$ is equal to: