606第三周周三赛 E - Andrey and Problem

E - Andrey and Problem

Time Limit:2000MS     Memory Limit:262144KB     64bit IO Format:%I64d & %I64u

Submit  Status  Practice  CodeForces 442B

Description

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.

Input

The first line contains a single integer n(1 ≤ n ≤ 100) — the number of Andrey's friends. The second line contains n real numbersp_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.

Output

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.

Sample Input

Input

4
0.1 0.2 0.3 0.8

Output

0.800000000000

Input

2
0.1 0.2

Output

0.260000000000

Hint

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.

分析：

这个题可以用搜索，第一层循环是选择事件次数的循环，第二层是选择这些事件成功的概率，第三层就是算每个事件的概率。

因为是恰巧只有也成功，所以第三层循环要乘以所有不成功的概率。

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#include<stdio.h>
#include<string.h>
#include<string>
#include<algorithm>
using namespace std;
int cmp(double a,double b)
{
    return a>b;
}
int main()
{
    double a[105],sum,ans,ax;
    int n,i,j,k;
    scanf("%d",&n);
    for(i=0; i<n; i++)
        scanf("%lf",&a[i]);
    sort(a,a+n,cmp);
    for(i=0; i<=n; i++)
    {
        sum=0;
        for(j=0; j<i; j++)
        {
            ans=a[j];
            for(k=0; k<i; k++)
                if(j!=k)
                    ans*=(1-a[k]);
            sum+=ans;
        }
        ax=max(ax,sum);
    }
    printf("%.12lf\n",ax);
    return 0;
}