1455E · Four Points

Problem: You are given four different integer points $p_1$, $p_2$, $p_3$ and $p_4$ on $\mathit{XY}$ grid.

In one step you can choose one of the points $p_i$ and move it in one of four directions by one. In other words, if you have chosen point $p_i = (x, y)$ you can move it to $(x, y + 1)$, $(x, y - 1)$, $(x + 1, y)$ or $(x - 1, y)$.

Your goal to move points in such a way that they will form a square with sides parallel to $\mathit{OX}$ and $\mathit{OY}$ axes (a square with side $0$ is allowed).

What is the minimum number of steps you need to make such a square?

Input Format: The first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases.

Each test case consists of four lines. Each line contains two integers $x$ and $y$ ($0 \le x, y \le 10^9$) — coordinates of one of the points $p_i = (x, y)$.

All points are different in one test case.

Output Format: For each test case, print the single integer — the minimum number of steps to make a square.

Note: In the first test case, one of the optimal solutions is shown below:

In the second test case, one of the optimal solutions is shown below:

In the third test case, one of the optimal solutions is shown below: