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문제

Bobo has a set $P$ of $\frac{n(n + 1)}{2}$ points: $\{ (x, y) : 1 \leq x \leq y \leq n, \ x, y \in \mathbb{Z} \}$. He would like to know the number of distinct lines passing through at least two points in $P$, taken modulo $(10^9+7)$.

입력

The input contains zero or more test cases, and is terminated by end-of-file.

Each test case is a single line containing an integer $n$ ($2 \leq n \leq 2 \cdot 10^9$).

It is guaranteed that the number of test cases does not exceed $10^5$, and the sum of all $n$ does not exceed $2 \cdot 10^9$.

출력

For each test case, output an integer which denotes the number of distinct lines.

예제 입력 1

2
3
5

예제 출력 1

3
9
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