GCD | judge.

Given the value of N , you will have to find the value of G. The definition of G is given below: G = i<N ∑ i=1 j≤N ∑ j=i+1 GCD(i, j) Here GCD(i, j) means the greatest common divisor of integer i and integer j. For those who have trouble understanding summation notation, the meaning of G is given in the following code: G=0; for(i=1;i<N;i++) for(j=i+1;j<=N;j++) { G+=GCD(i,j); } /*Here GCD() is a function that finds the greatest common divisor of the two input numbers*/

Input

The input file contains at most 100 lines of inputs. Each line contains an integer N (1 < N < 501). The meaning of N is given in the problem statement. Input is terminated by a line containing a single zero. This zero should not be processed.

Output

For each line of input produce one line of output. This line contains the value of G for corresponding N .

#11417GCD

Input

Output