We all know how much Monica loved candies in her childhood. And, her excessive competitiveness is no big secret! There have been various incidents where the Gellars had brought home some candies (say $n$). Monica always wanted to have more candies than Ross. Now, the Gellars actually gave the candies randomly to both of them. Inspite of the randomness, Monica got more candies than Ross every single time! Now, we want to calculate the probability that Monica had more candies than Ross at every instant that the candies were being distributed. Let the probability of that be $F(n)$. Calculate $x = \sum_{i=1}^{1000000000}F(i)$. Submit $\lfloor x \times 1000000\rfloor$.