Four Points

You are given four different integer points p_1, p_2, p_3 and p_4 on 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 OX and OY axes (a square with side 0 is allowed).

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

Input

The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of test cases.

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

All points are different in one test case.

Output

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

Example

Input

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

Note

In 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.

inputFormat

Input

The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of test cases.

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

All points are different in one test case.

outputFormat

Output

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

Example

Input

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

Note

In 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.

样例

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

</p>