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

\(1\le n\le10^{6}\)