Symmetry

Given a point $p$ and a line $L$ in the plane, the reflection of $p$ across $L$ is the point $p'$ such that the segment $pp'$ is perpendicular to $L$ and its midpoint lies on $L$. If $p$ lies on $L$, then $p' = p$.

For a set of points in the plane, an axis of symmetry is a line such that the reflection of every point of the set across that line is again a point of the set. Given a set of points, decide whether at least one axis of symmetry exists.

The first line contains the number of test cases $K$ ($1 \le K \le 10$).

The first line of each test case contains the number of points $N$ ($1 \le N \le 100000$). Each of the next $N$ lines contains the coordinates $X$ and $Y$ of one point, separated by a single space ($-10000 \le X, Y \le 10000$). Each coordinate has at most $6$ digits after the decimal point. No two points of one test case have the same location. The sum of $N$ over all test cases is at most $200000$.

Because the coordinates are real numbers, the input satisfies the following. If an axis of symmetry exists, the reflection of every point coincides exactly with a point of the set. If no axis of symmetry exists, then for every line $L$ there is at least one point whose reflection across $L$ is farther than $10^{-6}$ from every point of the set.

For each test case, print YES on its own line if the set has at least one axis of symmetry, and NO otherwise.