Sum of Divisors

Let \sigma(n) denote the sum of divisors of an integer n. For example, \sigma(12)=1+2+3+4+6+12=28. Your task is to calculate the sum \sum_{i=1}^n \sigma(i) modulo 10^9+7.

Input

The only input line has an integer n.

Output

Print \sum_{i=1}^n \sigma(i) modulo 10^9+7.

Constraints

$1 \le n \le 10$^{12}$

Example

Input

5

Output

21