Siraj has a dataset consisting of $N$ 2D cartesian points. Siraj wants to find out a straight line of the form $y = mx$ so that when he takes orthogonal projection of those data points on this line, the average distance of the projected points from the origin is the maximum. As Siraj has got only $5$ minutes to do this, he needs your help in finding out $m$. It can be shown that $m$ can be written in the form $p/q$ where $p$ and $q$ are integers and coprime. You have to find $pq^{-1}$ modulo $10^9+7$.
In the first line, you will be given a single integer $N$, the size of the dataset. In the following $N$ lines each, you will be given a pair of integers $(x,y)$, the data points.
$1 \leq N \leq 10^5$, $1 \leq x,y \leq 10^4$
Print a single integer, $pq^{-1}$ mod $10^9+7$.
| Input | Output |
|---|---|
3 1 1 3 3 2 2 | 1 |