Let the positive numbers $$a_1, a_2, a_3, a_4$$ and $$a_5$$ be in a G.P. Let their mean and variance be $$\frac{31}{10}$$ and $$\frac{m}{n}$$ respectively, where $$m$$ and $$n$$ are co-prime. If the mean of their reciprocals is $$\frac{31}{40}$$ and $$a_3 + a_4 + a_5 = 14$$, then $$m + n$$ is equal to _____.