For a given n calculate the value of G, where
Here GCD(i,j) means the greatest common divisor of integers i and j.
For those who have trouble understanding summation notation, the meaning of G is given in the following code:
Consists of no more than 20000 lines. Each line contains one integer n (1<n≤4⋅106). Input is terminated by a line containing a single zero and should not be processed.
For each input number n print in a separate line the corresponding value of G. The value of G fits in a 64-bit signed integer.