Yet Another Minimization Problem

Description:

Input:

Each test case consists of several test cases. The first line contains a single integer $$$t$$$ ($$$1 \leq t \leq 40$$$) — the number of test cases. The following is a description of the input data sets.

The first line of each test case contains an integer $$$n$$$ ($$$1 \leq n \leq 100$$$) — the length of both arrays.

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \leq a_i \leq 100$$$) — elements of the first array.

The third line of each test case contains $$$n$$$ integers $$$b_1, b_2, \ldots, b_n$$$ ($$$1 \leq b_i \leq 100$$$) — elements of the second array.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$100$$$.

Output:

For each test case, print the minimum possible total cost.

Sample Input:

3
1
3
6
4
3 6 6 6
2 7 4 1
4
6 7 2 4
2 5 3 5

Sample Output:

0
987
914

Note:

In the second test case, in one of the optimal answers after all operations $$$a = [2, 6, 4, 6]$$$, $$$b = [3, 7, 6, 1]$$$.

The cost of the array $$$a$$$ equals to $$$(2 + 6)^2 + (2 + 4)^2 + (2 + 6)^2 + (6 + 4)^2 + (6 + 6)^2 + (4 + 6)^2 = 508$$$.

The cost of the array $$$b$$$ equals to $$$(3 + 7)^2 + (3 + 6)^2 + (3 + 1)^2 + (7 + 6)^2 + (7 + 1)^2 + (6 + 1)^2 = 479$$$.

The total cost of two arrays equals to $$$508 + 479 = 987$$$.