CF1637D.Yet Another Minimization Problem

You 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.

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 $100$ .

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

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 $508 + 479 = 987$ .