CF442B.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.

安德烈还需要一道题目来举办一场编程竞赛。他有 $n$ 位朋友，他们总是乐于帮忙。他可以请其中一些人来出题。安德烈知道每位朋友的一个数值——即如果他向该朋友请求出题，这位朋友成功出题的概率。

请帮助安德烈选择应向哪些人请求出题。由于他仅需要一道题目，因此如果无人成功出题，或有多于一位朋友成功出题，安德烈都会非常沮丧。你需要选出一个合适的人选集合，使得安德烈不沮丧的概率最大化。

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.

第一行包含一个整数 $n$（$1 \leq n \leq 100$）—— 表示安德烈的朋友人数。
第二行包含 $n$ 个实数 $p_i$（$0.0 \leq p_i \leq 1.0$）—— 表示第 $i$ 个朋友能想出一道题的概率。
这些概率的小数点后最多有 6 位数字。

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.

输出一个实数——Andrey 在最优选择朋友的情况下不会生气的概率。若输出答案与正确答案的差值不超过 $10^{-9}$，则视为正确。

In the first sample the best strategy for Andrey is to ask only one of his friends, the most reliable one.

In the second sample the best strategy for Andrey is to ask all of his friends to come up with a problem. Then the probability that he will get exactly one problem is 0.1·0.8 + 0.9·0.2 = 0.26.

在第一个样例中，安德烈的最佳策略是仅向他的一位朋友求助，即最可靠的朋友。

在第二个样例中，安德烈的最佳策略是向他所有的朋友求助以提出一个问题。此时，他恰好获得一个问题的概率为 $0.1\cdot 0.8 + 0.9\cdot 0.2 = 0.26$。