Code HDU

HDU - 5212 

http://acm.hdu.edu.cn/showproblem.php?pid=5212

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 1010) 

For each case: 

The first line contains an integer N(1≤N≤10000)N(1≤N≤10000). 

The next line contains NN integers a1,a2,...,aN(1≤ai≤10000)a1,a2,...,aN(1≤ai≤10000). 

Output

For each case: 

Print an integer,denoting what the function returns.

Sample Input

51 3 4 2 4

Sample Output

64          

Hint

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

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