P13585 [NWRRC 2023] Every Queen

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.

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 $10^5$.

For each test case, if an answer exists, print $\tt{YES}$ 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 $\tt{NO}$ 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.