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