CodeForces 215B Olympic Medal（数学啊）

题目链接：http://codeforces.com/problemset/problem/215/B

Description

The World Programming Olympics Medal is a metal disk, consisting of two parts: the first part is a ring with outer radius of r₁ cm, inner radius of r₂ cm, (0 < r2 < r1) made of metal with density p₁ g/cm³. The second part is an inner disk with radius r₂ cm, it is made of metal with density p₂ g/cm³. The disk is nested inside the ring.

The Olympic jury decided that r₁ will take one of possible values of x₁, x₂, ..., x_n. It is up to jury to decide which particular value r₁ will take. Similarly, the Olympic jury decided that p₁ will take one of possible value of y₁, y₂, ..., y_m, and p₂ will take a value from listz₁, z₂, ..., z_k.

According to most ancient traditions the ratio between the outer ring mass m_out and the inner disk mass m_in must equal , where A, B are constants taken from ancient books. Now, to start making medals, the jury needs to take values for r₁, p₁, p₂ and calculate the suitable value of r₂.

The jury wants to choose the value that would maximize radius r₂. Help the jury find the sought value of r₂. Value r₂ doesn't have to be an integer.

Medal has a uniform thickness throughout the area, the thickness of the inner disk is the same as the thickness of the outer ring.

Input

The first input line contains an integer n and a sequence of integers x₁, x₂, ..., x_n. The second input line contains an integer m and a sequence of integers y₁, y₂, ..., y_m. The third input line contains an integer k and a sequence of integers z₁, z₂, ..., z_k. The last line contains two integers A and B.

All numbers given in the input are positive and do not exceed 5000. Each of the three sequences contains distinct numbers. The numbers in the lines are separated by spaces.

Output

Print a single real number — the sought value r₂ with absolute or relative error of at most 10^- 6. It is guaranteed that the solution that meets the problem requirements exists.

Sample Input

Input

3 1 2 3
1 2
3 3 2 1
1 2

Output

2.683281573000

Input

4 2 3 6 4
2 1 2
3 10 6 8
2 1

Output

2.267786838055

Hint

In the first sample the jury should choose the following values: r₁ = 3, p₁ = 2, p₂ = 1.

题意：
一种奖牌由内圆和外环组成，外环的半径为r1， 密度为p1。内圆的半径为r2，密度为p2；给出一种外环和内圆的质量比（A/B）！

给出一系列的r1,p1,p2！分别从中选出r1,p1,p2；要求最大的r2是多少！

PS:

内圆和外环的高度都是一样的，公式！化简后得：

（(r1^2 - r2^2）*p1）/ (r1^2*p2)  = A/B。

直接找最大的r1,p1,和最小的p2;

代码例如以下：

#include <cstdio>
#include <cmath>
int main()
{
    int n, m, k;
    double r1, r2, p1, p2;
    while(~scanf("%d",&n))
    {
        double tt;
        r1 = 0;
        for(int i = 0; i < n; i++)
        {
            scanf("%lf",&tt);
            if(tt > r1)
                r1 = tt;
        }
        scanf("%d",&m);
        p1 = 0;
        for(int i = 0; i < m; i++)
        {
            scanf("%lf",&tt);
            if(tt > p1)
                p1 = tt;
        }
        scanf("%d",&k);
        p2 = 5000+47;
        for(int i = 0; i < k; i++)
        {
            scanf("%lf",&tt);
            if(tt < p2)
                p2 = tt;
        }
        int A, B;
        scanf("%d%d",&A,&B);
        double ans = sqrt((r1*r1*p1*B)/(p1*B+p2*A));
        printf("%lf
",ans);
    }
    return 0;
}