A9513 | Andrey and Problem

Andrey needs one more problem to conduct a programming contest. He has $n$ friends who are always willing to help. He can ask some of them to come up with a contest problem. Andrey knows one value for each of his fiends — the probability that this friend will come up with a problem if Andrey asks him.

Help Andrey choose people to ask. As he needs only one problem, Andrey is going to be really upset if no one comes up with a problem or if he gets more than one problem from his friends. You need to choose such a set of people that maximizes the chances of Andrey not getting upset.

The first line contains a single integer $n$ $(1<=n<=100)$ — the number of Andrey's friends. The second line contains $n$ real numbers $p_{i}$ $(0.0<=p_{i}<=1.0)$ — the probability that the $i$ -th friend can come up with a problem. The probabilities are given with at most 6 digits after decimal point.

Print a single real number — the probability that Andrey won't get upset at the optimal choice of friends. The answer will be considered valid if it differs from the correct one by at most $10^{-9}$ .