Monocarp is a little boy who lives in Byteland and he loves programming.

Recently, he found a permutation of length $n$. He has to come up with a mystic permutation. It has to be a new permutation such that it differs from the old one in each position.

More formally, if the old permutation is $p_1,p_2,\ldots,p_n$ and the new one is $q_1,q_2,\ldots,q_n$ it must hold that $$p_1\neq q_1, p_2\neq q_2, \ldots ,p_n\neq q_n.$$

Monocarp is afraid of lexicographically large permutations. Can you please help him to find the lexicographically minimal mystic permutation?

Input

There are several test cases in the input data. The first line contains a single integer $t$ ($1\leq t\leq 200$) — the number of test cases. This is followed by the test cases description.

The first line of each test case contains a positive integer $n$ ($1\leq n\leq 1000$) — the length of the permutation.

The second line of each test case contains $n$ distinct positive integers $p_1, p_2, \ldots, p_n$ ($1 \leq p_i \leq n$). It's guaranteed that $p$ is a permutation, i. e. $p_i \neq p_j$ for all $i \neq j$.

It is guaranteed that the sum of $n$ does not exceed $1000$ over all test cases.

Output

For each test case, output $n$ positive integers — the lexicographically minimal mystic permutations. If such a permutation does not exist, output $-1$ instead.

Note

In the first test case possible permutations that are mystic are $[2,3,1]$ and $[3,1,2]$. Lexicographically smaller of the two is $[2,3,1]$.

In the second test case, $[1,2,3,4,5]$ is the lexicographically minimal permutation and it is also mystic.

In third test case possible mystic permutations are $[1,2,4,3]$, $[1,4,2,3]$, $[1,4,3,2]$, $[3,1,4,2]$, $[3,2,4,1]$, $[3,4,2,1]$, $[4,1,2,3]$, $[4,1,3,2]$ and $[4,3,2,1]$. The smallest one is $[1,2,4,3]$.

Samples

4
3
1 2 3
5
2 3 4 5 1
4
2 3 1 4
1
1

2 3 1
1 2 3 4 5
1 2 4 3
-1