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