You are given $n$ and $x \Delta y = \frac{x \times y}{\gcd(x, y) ^ 2}$.

Print the value of $\sum_{i = 1}^{n} \sum_{j = 1}^n i \Delta j \mod (10^9 + 7)$.

Input format

• First line: $n$

Output format

Print the value of $\sum_{i = 1}^n \sum_{j = 1}^n i \Delta j \mod (10^9 + 7)$.

Constraints

$1\le n\le10^{6}$