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.

Example

Input:
10
100
200000
0

Output:
67
13015
143295493160

Time limit has been changed. Some AC solutions get TLE.

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	Francky: 2015-12-30 20:15:34 Description updated and corrected.
	iam_ss: 2015-12-25 22:03:02 Welcome to The World Of Number Theory..... Amazing Question!!!
	Deepak : 2015-12-10 19:28:22 very strict time limit..
	Ankit Sultana: 2015-07-22 21:59:19 Had to change a few long long's to ints to get AC. Relax the time limit!!!
	Madhav: 2015-04-09 16:01:45 very good question !!
	/* Nitin Jaiman */: 2015-03-23 20:45:48 Same logic passed in c++ but giving TLE in java.
	RISHABH: 2015-02-08 14:44:53 time problem Last edit: 2015-02-08 14:53:39
	Sayak Haldar: 2015-01-24 12:55:53 if you are getting tle, change your long long datatype into int in some places...may be that will help(scanf,printf takes more time while we are dealing with long long)
	Rishav Goyal: 2014-06-19 13:52:49 w**********k is wrong with spoj!! AC in 2 sec. even with max N=4000000 on UVA but tle on spoj with max N=1000000. its disappointing .!! Last edit: 2015-01-11 16:49:36
	Yu Zhijingcheng: 2014-03-20 16:29:59 Look here if you got TLE 1. N is in the range [1, 1000000] 2. The input may end with EOF instead of 0 in the sample input.