CF1689B.Mystic Permutation

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?

Monocarp 是一个住在 ByteLand 的小男孩，他热爱编程。

最近，他找到了一个长度为 $n$ 的排列。他需要构造一个“神秘排列”——这是一个全新的排列，且在每个位置上都与原排列不同。

更准确地说，若原排列为 $p_1,p_2,\ldots,p_n$，新排列为 $q_1,q_2,\ldots,q_n$，则必须满足

$$p\_1\\neq q\_1, p\_2\\neq q\_2, \\ldots ,p\_n\\neq q\_n.$$

Monocarp 害怕字典序过大的排列。你能帮他找出字典序最小的神秘排列吗？

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.

输入数据包含多个测试用例。第一行包含一个整数 $t$（$1\leq t\leq 200$），表示测试用例的数量。随后是各测试用例的描述。

每个测试用例的第一行包含一个正整数 $n$（$1\leq n\leq 1000$），表示排列的长度。

每个测试用例的第二行包含 $n$ 个互不相同的正整数 $p_1, p_2, \ldots, p_n$（$1 \leq p_i \leq n$）。保证 $p$ 是一个排列，即对所有 $i \neq j$，均有 $p_i \neq p_j$。

保证所有测试用例中 $n$ 的总和不超过 $1000$。

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

对于每个测试用例，输出 $n$ 个正整数——字典序最小的神秘排列。如果这样的排列不存在，则输出 $-1$。

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

在第一个测试用例中，可能的神秘排列有 $[2,3,1]$ 和 $[3,1,2]$。其中字典序更小的是 $[2,3,1]$。

在第二个测试用例中，$[1,2,3,4,5]$ 是字典序最小的排列，且它也是神秘排列。

在第三个测试用例中，可能的神秘排列有 $[1,2,4,3]$、$[1,4,2,3]$、$[1,4,3,2]$、$[3,1,4,2]$、$[3,2,4,1]$、$[3,4,2,1]$、$[4,1,2,3]$、$[4,1,3,2]$ 和 $[4,3,2,1]$。其中最小的一个是 $[1,2,4,3]$。