No submission language available for this problem.

Description

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.

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

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 $[1,2,4,3]$.