Problem Description

WLD likes playing with codes.One day he is writing a function.Howerver,his computer breaks down because the function is too powerful.He is very sad.Can you help him?

The function:


int calc
{
  
  int res=0;
  
  for(int i=1;i<=n;i++)
    
    for(int j=1;j<=n;j++)
    
    {
      
      res+=gcd(a[i],a[j])*(gcd(a[i],a[j])-1);
      
      res%=10007;
    
    }
  
  return res;

}

Input

There are Multiple Cases.(At MOST $10$)

For each case:

The first line contains an integer $N(1 \leq N \leq 10000)$.

The next line contains $N$ integers $a1,a2,...,aN(1 \leq ai \leq 10000)$.

Output

For each case:

Print an integer,denoting what the function returns.

5
1 3 4 2 4

64

Hint

gcd(x,y) means the greatest common divisor of x and y.