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.

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.

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 $$$508 + 479 = 987$$$.

Yet Another Minimization Problem

Examples