CF1486B.Eastern Exhibition

You and your friends live in $n$ houses. Each house is located on a 2D plane, in a point with integer coordinates. There might be different houses located in the same point. The mayor of the city is asking you for places for the building of the Eastern exhibition. You have to find the number of places (points with integer coordinates), so that the summary distance from all the houses to the exhibition is minimal. The exhibition can be built in the same point as some house. The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is $|x_1 - x_2| + |y_1 - y_2|$, where $|x|$ is the absolute value of $x$.

你和你的朋友们住在 $n$ 座房屋中。每座房屋位于二维平面上的一个整数坐标点处。不同房屋可能位于同一个点上。市长向你们征集东方展览馆的建设地点。你需要找出满足“所有房屋到展览馆的总距离最小”的地点（即整数坐标点）的数量。展览馆可以建在某座房屋所在的位置。两点 $(x_1, y_1)$ 与 $(x_2, y_2)$ 之间的距离定义为 $|x_1 - x_2| + |y_1 - y_2|$，其中 $|x|$ 表示 $x$ 的绝对值。

First line contains a single integer $t$ $(1 \leq t \leq 1000)$ — the number of test cases.

The first line of each test case contains a single integer $n$ $(1 \leq n \leq 1000)$. Next $n$ lines describe the positions of the houses $(x_i, y_i)$ $(0 \leq x_i, y_i \leq 10^9)$.

It's guaranteed that the sum of all $n$ does not exceed $1000$.

第一行包含一个整数 $t$（$1 \leq t \leq 1000$）——测试用例的数量。

每个测试用例的第一行包含一个整数 $n$（$1 \leq n \leq 1000$）。接下来的 $n$ 行描述房屋的位置 $(x_i, y_i)$（$0 \leq x_i, y_i \leq 10^9$）。

保证所有 $n$ 的总和不超过 $1000$。

For each test case output a single integer - the number of different positions for the exhibition. The exhibition can be built in the same point as some house.

对于每个测试用例，输出一个整数——展览馆可选的不同位置的数量。展览馆可以建在与某座房屋相同的位置上。

Here are the images for the example test cases. Blue dots stand for the houses, green — possible positions for the exhibition.

First test case.

Second test case.

Third test case.

Fourth test case.

Fifth test case.

Sixth test case. Here both houses are located at $(0, 0)$.

以下是示例测试用例的图片。蓝色圆点表示房屋，绿色表示展览可能的位置。

第一个测试用例。

第二个测试用例。

第三个测试用例。

第四个测试用例。

第五个测试用例。

第六个测试用例。此时两座房屋均位于 $(0, 0)$。