Meximization

1000ms

262144K

Description:

You are given an integer $$$n$$$ and an array $$$a_1, a_2, \ldots, a_n$$$. You should reorder the elements of the array $$$a$$$ in such way that the sum of $$$\textbf{MEX}$$$ on prefixes ($$$i$$$-th prefix is $$$a_1, a_2, \ldots, a_i$$$) is maximized.

Formally, you should find an array $$$b_1, b_2, \ldots, b_n$$$, such that the sets of elements of arrays $$$a$$$ and $$$b$$$ are equal (it is equivalent to array $$$b$$$ can be found as an array $$$a$$$ with some reordering of its elements) and $$$\sum\limits_{i=1}^{n} \textbf{MEX}(b_1, b_2, \ldots, b_i)$$$ is maximized.

$$$\textbf{MEX}$$$ of a set of nonnegative integers is the minimal nonnegative integer such that it is not in the set.

For example, $$$\textbf{MEX}(\{1, 2, 3\}) = 0$$$, $$$\textbf{MEX}(\{0, 1, 2, 4, 5\}) = 3$$$.

Input:

The first line contains a single integer $$$t$$$ $$$(1 \le t \le 100)$$$ — the number of test cases.

The first line of each test case contains a single integer $$$n$$$ $$$(1 \le n \le 100)$$$.

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ $$$(0 \le a_i \le 100)$$$.

Output:

For each test case print an array $$$b_1, b_2, \ldots, b_n$$$ — the optimal reordering of $$$a_1, a_2, \ldots, a_n$$$, so the sum of $$$\textbf{MEX}$$$ on its prefixes is maximized.

If there exist multiple optimal answers you can find any.

Sample Input:

3
7
4 2 0 1 3 3 7
5
2 2 8 6 9
1
0

Sample Output:

0 1 2 3 4 7 3 
2 6 8 9 2 
0

Note:

In the first test case in the answer $$$\textbf{MEX}$$$ for prefixes will be:

$$$\textbf{MEX}(\{0\}) = 1$$$
$$$\textbf{MEX}(\{0, 1\}) = 2$$$
$$$\textbf{MEX}(\{0, 1, 2\}) = 3$$$
$$$\textbf{MEX}(\{0, 1, 2, 3\}) = 4$$$
$$$\textbf{MEX}(\{0, 1, 2, 3, 4\}) = 5$$$
$$$\textbf{MEX}(\{0, 1, 2, 3, 4, 7\}) = 5$$$
$$$\textbf{MEX}(\{0, 1, 2, 3, 4, 7, 3\}) = 5$$$

The sum of $$$\textbf{MEX} = 1 + 2 + 3 + 4 + 5 + 5 + 5 = 25$$$. It can be proven, that it is a maximum possible sum of $$$\textbf{MEX}$$$ on prefixes.

Informação

Provedor Codeforces

Código CF1497A