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CSES Problem Set

Sum of Divisors


Task | Statistics


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
Example

Input:
5

Output:
21