D. Yet Another Minimization Problemtime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given two arrays a and b, both of length n.You can perform the following operation any number of times (possibly zero): select an index i (1 \leq i \leq n) and swap a_i and b_i.Let's define the cost of the array a as \sum_{i=1}^{n} \sum_{j=i + 1}^{n} (a_i + a_j)^2. Similarly, the cost of the array b is \sum_{i=1}^{n} \sum_{j=i + 1}^{n} (b_i + b_j)^2.Your task is to minimize the total cost of two arrays.InputEach 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.OutputFor each test case, print the minimum possible total cost.ExampleInput
3
1
3
6
4
3 6 6 6
2 7 4 1
4
6 7 2 4
2 5 3 5
Output
0
987
914
NoteIn 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.
3
1
3
6
4
3 6 6 6
2 7 4 1
4
6 7 2 4
2 5 3 5

0 987 914 
['dp', 'greedy', 'math', '*1800']