You are given n coins, with i-th coin having probability of landing heads when tossed. Your task is to calculate the probability of obtaining more heads than tails after tossing all n coins.

Input

The first line contains a single integer n (1 β€ n β€ 2000), representing the number of coins.

The second line contains n real numbers with two decimal places (0 β€ β€ 1), representing the probabilities of the i-th coin landing heads.

Output

The program should print a single floating-point number representing the probability of obtaining more heads than tails after tossing all the n coins.