A16196 | Chips on the Board

You are given a board of size $n \times n$ ( $n$ rows and $n$ colums) and two arrays of positive integers $a$ and $b$ of size $n$ .

Your task is to place the chips on this board so that the following condition is satisfied for every cell $(i, j)$ :

- there exists at least one chip in the same column or in the same row as the cell $(i, j)$ . I. e. there exists a cell $(x, y)$ such that there is a chip in that cell, and either $x = i$ or $y = j$ (or both).

The cost of putting a chip in the cell $(i, j)$ is equal to $a_i + b_j$ .

For example, for $n=3$ , $a=[1, 4, 1]$ and $b=[3, 2, 2]$ . One of the possible chip placements is as follows:

 White squares are emptyThe total cost of that placement is $(1+3) + (1+2) + (1+2) = 10$ .

Calculate the minimum possible total cost of putting chips according to the rules above.

The first line contains a single integer $t$ ( $1 \le t \le 10^4$ ) — the number of test cases.

The first line of each test case contains a single integer $n$ ( $1 \le n \le 3 \cdot 10^5$ ).

The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ( $1 \le a_i \le 10^9$ ).

The third line contains $n$ integers $b_1, b_2, \dots, b_n$ ( $1 \le b_i \le 10^9$ ).

The sum of $n$ over all test cases doesn't exceed $3 \cdot 10^5$ .

For each test case, print a single integer — the minimum possible total cost of putting chips according to the rules.