## Problem Description

Given the value of N, you will have to find the value of G. 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 20000 lines of inputs. Each line contains an integer N (1<N <1000001). The meaning of N is given in the problem statement. Input is terminated by a line containing a single zero.

## Output

For each line of input produce one line of output. This line contains the value of G for the corresponding N. The value of G will fit in a 64-bit signed integer.

## Sample Input

10
100
200000
0

## Sample Output

67
13015
143295493160

## Source

Contest for 2010 lecture II