You are given two arrays $$$a$$$ and $$$b$$$ of length $$$n$$$. You can perform the following operation an unlimited number of times:

Choose an integer $$$i$$$ from $$$1$$$ to $$$n$$$ and swap $$$a_i$$$ and $$$b_i$$$.

Let $$$f(c)$$$ be the number of distinct numbers in array $$$c$$$. Find the maximum value of $$$f(a) + f(b)$$$. Also, output the arrays $$$a$$$ and $$$b$$$ after performing all operations.

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^4$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 10^5$$$) — the length of the arrays.

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \le a_i \le 2n$$$) — the elements of array $$$a$$$.

The third line of each test case contains $$$n$$$ integers $$$b_1, b_2, \ldots, b_n$$$ ($$$1 \le b_i \le 2n$$$) — the elements of array $$$b$$$.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$10^5$$$.

Output

For each test case, print a single integer in the first line — the maximum value of $$$f(a) + f(b)$$$.

In the second line, print $$$n$$$ integers — the elements of array $$$a$$$ after performing the operations.

In the third line, print $$$n$$$ integers — the elements of array $$$b$$$ after performing the operations.

Note

In the first test case, after applying three operations with $$$i=2$$$, $$$i=4$$$, and $$$i=5$$$, we obtain $$$a = [1, 3, 4, 5, 2]$$$ and $$$b = [1, 2, 3, 4, 4]$$$. After that, $$$f(a) + f(b) = 5 + 4 = 9$$$. It can be shown that it is not possible to achieve a greater answer.

In the second test case, after applying the operations: $$$$$$f([2, 3, 4, 2, 1, 5, 6]) + f([1, 2, 3, 4, 5, 6, 5]) = 6 + 6 = 12$$$$$$

Two Arrays

Examples