You are given a multiplicative function $f(x)$, where $f(p^k)=p^k-p^{k-1}$ when $p$ is prime. Determine $\sum _{i=1}^{N}f(i)$ modulo ${10}^9+7$.

Input Specification

The only line contains an integer, $N$ $(1\le N\le {10}^{10})$.

Output Specification

Output $\sum _{i=1}^{N}f(i)$ modulo ${10}^9+7$.

Sample Input

5

Sample Output

10