Problem C: Center of symmetry

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.

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 ≤ n ≤ 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 ≤ x, y ≤ 10000000.

For each set of input data print yes if the set of points has a center of symmetry and no otherwise.

Sample input

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

Output for sample input

yes

Adapted from VI AMPwPZ by P. Rudnicki
ACPC 2003