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 $10^9+7$ .
The only input line has an integer $n$ .
Print $\sum_{i=1}^n \sigma(i)$ modulo $10^9+7$ .