Codeforces 215B Olympic medal (math AH)

Title Link: Http://codeforces.com/problemset/problem/215/B

Description

The World Programming Olympics medal is a metal disk, consisting of both parts:the first part are 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 a 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 Would take one of possible values of x_{1,? X2,?...,? xn} . It is jury to decide which particular value R₁ would take. Similarly, the Olympic jury decided that P₁ Would take one of possible value of y_{1,? Y2,?...,? Ym} , and P₂ Would take a value from list z_{1,? Z2,?...,? Zk} .

According to most ancient traditions the ratio between the outer ring mass m outand the inner disk mass m inMust equal, where A,? B is 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 of that would maximize radius r₂. Help the jury find the sought value of R₂. Value R₂ doesn ' t has the to is an integer.

Medal have a uniform thickness throughout the area, the thickness of the inner disk are the same as the thickness of the out ER ring.

Input

The first input line contains an integerNand a sequence of integers x_{1,? X2,?...,? xn} . The second input line contains an integermand a sequence of integers y_{1,? Y2,?...,? Ym} . The third input line contains an integerkand a sequence of integers z_{1,? Z2,?...,? Zk} . The last line contains and integersAandB.

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

Output

Print a single real number-the sought value r₂ with absolute or relative error of in most 10 ^{?-? 6}. It's guaranteed that solution that meets the problem requirements exists.

Sample Input

Input

3 1 2 31 23 3 2 11 2

Output

2.683281573000

Input

4 2 3 6 42 1 23 10 6 82 1

Output

2.267786838055

Hint

In the first sample the jury should choose the following values: r_1?=?3, p_{1?=? 2}, p_2?=?1.

Test instructions
A kind of medal consists of inner circle and outer ring, outer ring radius is r1, density is P1, inner circle radius is r2, density is p2; a mass ratio of outer ring and inner circle is given (A/b)!

Give a series of r1,p1,p2! Choose the r1,p1,p2 from which the maximum R2 is required!

Ps:

The height of the inner circle and outer ring are the same, the formula! After simplification:

((r1^2-r2^2) *P1)/(R1^2*P2) = A/b;

Directly find the largest r1,p1, and the smallest P2;

The code is as follows:

#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\n", ans);    }    return 0;}

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Codeforces 215B Olympic medal (math AH)