E - Olympic Medal CodeForces - 215B(数学思维)-白红宇

E - Olympic Medal CodeForces - 215B(数学思维)

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发布时间：2019-05-25

本文共 2626 字，大约阅读时间需要 8 分钟。

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, …, xn. 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, …, ym, and p2 will take a value from list z1, z2, …, zk.

According to most ancient traditions the ratio between the outer ring mass mout and the inner disk mass min 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, …, xn. The second input line contains an integer m and a sequence of integers y1, y2, …, ym. The third input line contains an integer k and a sequence of integers z1, z2, …, zk. 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.

Examples

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

Note

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

说了一大堆,就是一个大盘子中间挖去了一块,然后呢,这两个的密度还不同.已经给你了r1,p1,p2,(r1就是盘子的直径),让你去求r2(内圆的直径).要求是内外的比值一定要等于A/B.就是推公式…会得到r2^2=(Bp1r1r1)/(Ap2+Bp1).开始我看到这里的时候,我就想,暴力一发,然后就t了,这么做复杂度是O(mnk),肯定会爆的.然后继续看式子.上下同时除以p1不就好了吗,这么做复杂度是O(nm).就可以啦.

代码如下:

#include
   
    #include
    
     #include
     
      #include
      
       #include
       
        using namespace std;const int maxx=5e3+10;double r[maxx];double p1[maxx];double p2[maxx];double a,b;int n,m,k;int main(){	scanf("%d",&n);	for(int i=0;i
        
         m) { m=x; } } printf("%.12lf\n",m);}

努力加油a啊,(^o)/~

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