L. Permutation Recovery
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

There are two hidden permutations $$$a$$$ and $$$b$$$ of size $$$n$$$.

A permutation of length $$$n$$$ is an array consisting of $$$n$$$ distinct integers from $$$1$$$ to $$$n$$$ in arbitrary order. For example, $$$[2, 3, 1, 5, 4]$$$ is a permutation, but $$$[1, 2, 2]$$$ is not a permutation ($$$2$$$ appears twice in the array), and $$$[1, 3, 4]$$$ is also not a permutation ($$$n=3$$$ but there is $$$4$$$ in the array).

For each $$$i$$$ from $$$1$$$ to $$$n$$$, you are given the values $$$a_{b_i}$$$ and $$$b_{a_i}$$$. Recover any possible permutations $$$a$$$ and $$$b$$$, or determine that none exist.

Input

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

The first line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 2\cdot 10^5$$$) — the size of the two permutations.

The second line of each test case contains $$$n$$$ integers. The $$$i$$$-th of these is $$$a_{b_i}$$$ ($$$1 \le a_{b_i} \le n$$$). It is guaranteed that these $$$n$$$ integers are distinct.

The third line of each test case contains $$$n$$$ integers. The $$$i$$$-th of these is $$$b_{a_i}$$$ ($$$1 \le b_{a_i} \le n$$$). It is guaranteed that these $$$n$$$ integers are distinct.

It is guaranteed that the sum of $$$n$$$ across all test cases is at most $$$2\cdot 10^5$$$.

Output

For each test case, the first line of output should contain "YES" if there is a solution, and "NO" otherwise. You can print this in any case (upper or lower). For example, the strings "yEs", "yes", "Yes", and "YES" will be recognized as positive responses.

If you print "YES", print two additional lines of output:

The first line should contain $$$n$$$ integers $$$a_1, a_2, \cdots a_n$$$ ($$$1 \le a_i \le n$$$) — a valid permutation $$$a$$$.

The second line should contain $$$n$$$ integers $$$b_1, b_2, \cdots b_n$$$ ($$$1 \le b_i \le n$$$) — a valid permutation $$$b$$$.

If there are multiple solutions, you may print any.

Example
Input
6
3
3 1 2
2 3 1
2
1 2
2 1
5
1 2 3 4 5
1 2 3 4 5
1
1
1
6
4 5 1 2 3 6
1 2 3 4 5 6
10
3 7 5 8 9 1 4 10 6 2
7 8 1 5 10 9 2 3 4 6
Output
YES
2 1 3 
3 2 1 
NO
YES
5 4 3 2 1 
5 4 3 2 1 
YES
1 
1 
NO
YES
8 2 4 6 1 5 10 7 9 3 
10 8 6 1 9 5 3 7 4 2
Note

The given solution to the first sample case is $$$a=[2, 1, 3]$$$, $$$b=[3, 2, 1]$$$. This gives $$$$$$a_{b_1} = a_3 = 3 \quad\quad a_{b_2} = a_2 = 1 \quad\quad a_{b_3} = a_1 = 2$$$$$$ $$$$$$b_{a_1} = b_2 = 2 \quad\quad b_{a_2} = b_1 = 3 \quad\quad b_{a_3} = b_3 = 1$$$$$$ which matches the input values $$$a_b=[3, 1, 2]$$$ and $$$b_a=[2, 3, 1]$$$.

In the second sample case, it can be shown that there are no valid permutations $$$a$$$ and $$$b$$$.