E. Every Queen
time limit per test
2 seconds
memory limit per test
1024 megabytes
input
standard input
output
standard output

There are $$$n$$$ chess queens on an infinite grid. They are placed in squares with coordinates $$$(x_1, y_1), (x_2, y_2), \ldots, (x_n, y_n)$$$. Your task is to find a square that all queens attack, or report that no such square exists.

A queen in square $$$(x_i, y_i)$$$ attacks square $$$(x, y)$$$ if at least one of the following conditions is satisfied:

  • $$$x_i = x$$$;
  • $$$y_i = y$$$;
  • $$$|x_i - x| = |y_i - y|$$$.

Note that in this problem, the queens do not block each other. For example, if there are queens in squares $$$(1, 1)$$$ and $$$(2, 2)$$$, both of them attack square $$$(3, 3)$$$. Moreover, you can choose a square that already contains a queen. For example, square $$$(1, 1)$$$ would be a valid answer in this case.

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^5$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$, denoting the number of queens ($$$1 \le n \le 10^5$$$).

The $$$i$$$-th of the following $$$n$$$ lines contains two integers $$$x_i$$$ and $$$y_i$$$, denoting the coordinates of the square containing the $$$i$$$-th queen ($$$-10^8 \le x_i, y_i \le 10^8$$$). No two queens share the same square.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$10^5$$$.

Output

For each test case, if an answer exists, print "YES" in the first line. Then, in the second line, print two integers $$$x$$$ and $$$y$$$, denoting the coordinates of a square attacked by every queen ($$$-10^9 \le x, y \le 10^9$$$).

If no such square exists, print a single line containing "NO" instead.

It can be shown that if an answer exists, there also exists an answer that satisfies $$$-10^9 \le x, y \le 10^9$$$. If there are multiple answers, print any of them.

Example
Input
3
2
1 1
2 2
4
0 1
1 0
3 1
4 0
5
0 1
1 0
1 2
2 2
4 2
Output
YES
1 1
NO
YES
-1 2