A14963 | 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.