E. Four Pointstime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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?InputThe 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.OutputFor each test case, print the single integer — the minimum number of steps to make a square.ExampleInput
3
0 2
4 2
2 0
2 4
1 0
2 0
4 0
6 0
1 6
2 2
2 5
4 1
Output
8
7
5
NoteIn the first test case, one of the optimal solutions is shown below:    Each point was moved two times, so the answer 2 + 2 + 2 + 2 = 8.In the second test case, one of the optimal solutions is shown below:    The answer is 3 + 1 + 0 + 3 = 7.In the third test case, one of the optimal solutions is shown below:    The answer is 1 + 1 + 2 + 1 = 5.
3
0 2
4 2
2 0
2 4
1 0
2 0
4 0
6 0
1 6
2 2
2 5
4 1

8 7 5 
['brute force', 'constructive algorithms', 'flows', 'geometry', 'greedy', 'implementation', 'math', 'ternary search', '*2400']