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: $$f([2, 3, 4, 2, 1, 5, 6]) + f([1, 2, 3, 4, 5, 6, 5]) = 6 + 6 = 12$$
样例
3
5
1 2 4 4 4
1 3 3 5 2
7
2 2 4 4 5 5 5
1 3 3 2 1 6 6
7
12 3 3 4 5 6 4
1 2 13 8 10 13 7
9
1 3 4 5 2
1 2 3 4 4
12
2 3 4 2 1 5 6
1 2 3 4 5 6 5
14
12 3 13 8 10 6 4
1 2 3 4 5 13 7
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