A15334 | Madoka and The Best University

Madoka wants to enter to "Novosibirsk State University", but in the entrance exam she came across a very difficult task:

Given an integer $n$ , it is required to calculate $\sum{\operatorname{lcm}(c, \gcd(a, b))}$ , for all triples of positive integers $(a, b, c)$ , where $a + b + c = n$ .

In this problem $\gcd(x, y)$ denotes the [greatest common divisor](https://en.wikipedia.org/wiki/Greatest_common_divisor) of $x$ and $y$ , and $\operatorname{lcm}(x, y)$ denotes the [least common multiple](https://en.wikipedia.org/wiki/Least_common_multiple) of $x$ and $y$ .

Solve this problem for Madoka and help her to enter to the best university!

The first and the only line contains a single integer $n$ ( $3 \le n \le 10^5$ ).

Print exactly one interger — $\sum{\operatorname{lcm}(c, \gcd(a, b))}$ . Since the answer can be very large, then output it modulo $10^9 + 7$ .