12 1 s 64 MB

Given is a set of n points with integer coordinates. Your task is to decide whether the set has a center of symmetry.

A set of points $S$ has the center of symmetry if there exists a point s (not necessarily in $S$) such that for every point $p$ in $S$ there exists a point $q$ in $S$ such that $p-s = s-q$.

A set of points $S$ has the center of symmetry if there exists a point s (not necessarily in $S$) such that for every point $p$ in $S$ there exists a point $q$ in $S$ such that $p-s = s-q$.

The first line of input contains a number $c$ giving the number of cases that follow. The first line of data for a single case contains number $1 \leq n \leq 10000$. The subsequent $n$ lines contain two integer numbers each which are the $x$ and $y$ coordinates of a point. Every point is unique and we have that $ -10000000 \leq x, y \leq 10000000$.

For each set of input data print

`yes`

if the set of points has a center of symmetry and `no`

otherwise.## Sample Input | ## Sample Output |
---|---|

1 8 1 10 3 6 6 8 6 2 3 -4 1 0 -2 -2 -2 4 | yes |