CSES - Sum of Divisors

Time limit: 1.00 s
Memory limit: 512 MB

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:

Output: