B'You 're playing a game called Osu! Here 's a simplified version of it. There are n clicks in a game. For each click there are two outcomes: correct or bad. Let us denote correct as "O", bad as "X", then the whole play can be encoded as a sequence of n characters "O" and "X". Using the play sequence you can calculate the score for the play as follows: for every maximal consecutive "O"s block, add the square of its length (the number of characters "O") to the score. For example, if your play can be encoded as "OOXOOOXXOO", then there 's three maximal consecutive "O"s block "OO", "OOO", "OO", so your score will be 22 xe2 x80 x89+ xe2 x80 x8932 xe2 x80 x89+ xe2 x80 x8922 xe2 x80 x89= xe2 x80 x8917. If there are no correct clicks in a play then the score for the play equals to 0. You know that the probability to click the i-th (1 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89i xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89n) click correctly is pi. In other words, the i-th character in the play sequence has pi probability to be "O", 1 xe2 x80 x89- xe2 x80 x89pi to be "X". You task is to calculate the expected score for your play. The first line contains an integer n (1 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89n xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89105) -- the number of clicks. The second line contains n space-separated real numbers p1, xe2 x80 x89p2, xe2 x80 x89..., xe2 x80 x89pn (0 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89pi xe2 x80 x89 xe2 x89 xa4 xe2 x80 x891). There will be at most six digits after the decimal point in the given pi. Print a single real number -- the expected score for your play. Your answer will be considered correct if its absolute or relative error does not exceed 10 xe2 x80 x89- xe2 x80 x896. For the first example. There are 8 possible outcomes. Each has a probability of 0.125. So the expected score is '...