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*<sub class="lower-index">*i*</sub> (0.0 ≤ *p*<sub class="lower-index">*i*</sub> ≤ 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.
n = int(input())
dp = [0] * n
a = list(map(float, input().split()))
dp[0] = [a[0], 1 -a[0]]
for i in range(1, n):
    dp[i] = dp[i - 1]
    if dp[i][0] < dp[i][0] * (1 - a[i]) + dp[i][1] * a[i]:
        dp[i] = [dp[i][0] * (1 - a[i]) + dp[i][1] * a[i], dp[i][1] * (1 - a[i])]
    if a[i] > dp[i][0]:
        dp[i] = [a[i], 1 - a[i]]
print(dp[n - 1][0])