Professor Amit Gupta has given you a mathematical programming assignment. It goes as follows:
\(F(x,y)\) = sum of numbers that divide both x and y, i.e., sum of the common divisors of x and y.
Given the value of N, you are required to calculate the value of S.

\(S=\sum_{i=1}^{N}\) \(\sum_{j=i}^{N}\) \(F(i,j)\).

As the value of S can be large, find it modulo \(10^{9}+7\).

Input
Input contains only one number N.

Output
Output contains only one number, the value of S modulo \(10^9+7\).

Constraints
\(1\le N \le 10^{15}\)