Problem:
Score : 200 points

Problem Statement

Given is a sequence of N integers A_1, \ldots, A_N.

Find the (multiplicative) inverse of the sum of the inverses of these numbers, \frac{1}{\frac{1}{A_1} + \ldots + \frac{1}{A_N}}.

Constraints

1 \leq N \leq 100

1 \leq A_i \leq 1000

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 \ldots A_N

Output

Print a decimal number (or an integer) representing the value of \frac{1}{\frac{1}{A_1} + \ldots + \frac{1}{A_N}}.

Your output will be judged correct when its absolute or relative error from the judge's output is at most 10^{-5}.

Sample Input 1

2
10 30

Sample Output 1

7.5

\frac{1}{\frac{1}{10} + \frac{1}{30}} = \frac{1}{\frac{4}{30}} = \frac{30}{4} = 7.5.

Printing 7.50001, 7.49999, and so on will also be accepted.

Sample Input 2

3
200 200 200

Sample Output 2

66.66666666666667

\frac{1}{\frac{1}{200} + \frac{1}{200} + \frac{1}{200}} = \frac{1}{\frac{3}{200}} = \frac{200}{3} = 66.6666....

Printing 6.66666e+1 and so on will also be accepted.

Sample Input 3

1
1000

Sample Output 3

1000

\frac{1}{\frac{1}{1000}} = 1000.

Printing +1000.0 and so on will also be accepted.

Solution in C (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>
 
int gcd(int a,int b)
{
  if(b==0)
      return a;
  
  else
      return gcd(b,a%b);
}

int main()
{
 
  int n;
  scanf("%d",&n);
  int a[n],i;
  for(i=0;i<n;++i)
       scanf("%d",&a[i]);
  
  int ans=a[0];
  int sum=0;
  for(i=1;i<n;++i)
  {
    ans=(ans*a[i])/(gcd(ans,a[i]));
  }
  
  for(i=0;i<n;++i)
  {
    sum+=ans/a[i];
  }
  
  double ans1=(double)ans/sum;
  
  printf("%lf",ans1);
  
}