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  1. Prepare
  2. Mathematics
  3. Geometry
  4. Points on a Rectangle

Points on a Rectangle

You are given queries where each query consists of a set of points on a two-dimensional plane (i.e., ). For each set of points, print YES on a new line if all the points fall on the edges (i.e., sides and/or corners) of a non-degenerate rectangle which is axis parallel; otherwise, print NO instead.

Input Format

The first line contains a single positive integer, , denoting the number of queries. The subsequent lines describe each query in the following format:

  1. The first line contains a single positive integer, , denoting the number of points in the query.
  2. Each line of the subsequent lines contains two space-separated integers describing the respective values of and for the point at coordinate .

Constraints

Output Format

For each query, print YES on a new line if all points lie on the edges of some non-degenerate rectangle which is axis parallel; otherwise, print NO instead.

Sample Input

2
3
0 0
0 1
1 0
4
0 0
0 2
2 0
1 1

Sample Output

YES
NO

Explanation

We perform the following queries:

  1. In the first query, all points lie on the edges of a non-degenerate rectangle with corners at , , , and . Thus, we print YES on a new line.
  2. In the second query, points , , and could all lie along the edge of some non-degenerate rectangle, but point would have to fall inside that rectangle. Thus, we print NO on a new line.