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G. XOUR
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given an array $$$a$$$ consisting of $$$n$$$ nonnegative integers.

You can swap the elements at positions $$$i$$$ and $$$j$$$ if $$$a_i~\mathsf{XOR}~a_j < 4$$$, where $$$\mathsf{XOR}$$$ is the bitwise XOR operation.

Find the lexicographically smallest array that can be made with any number of swaps.

An array $$$x$$$ is lexicographically smaller than an array $$$y$$$ if in the first position where $$$x$$$ and $$$y$$$ differ, $$$x_i < y_i$$$.

Input

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

The first line of each test case contains a single integer $$$n$$$ ($$$1 \leq n \leq 2\cdot10^5$$$) — the length of the array.

The second line of each test case contains $$$n$$$ integers $$$a_i$$$ ($$$0 \leq a_i \leq 10^9$$$) — the elements of the array.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.

Output

For each test case, output $$$n$$$ integers — the lexicographically smallest array that can be made with any number of swaps.

Example
Input
4
4
1 0 3 2
5
2 7 1 5 6
8
1 2 1 2 1 2 1 2
4
16 4 1 64
Output
0 1 2 3 
1 5 2 6 7 
1 1 1 1 2 2 2 2 
16 4 1 64
Note

For the first test case, you can swap any two elements, so we can produce the sorted array.

For the second test case, you can swap $$$2$$$ and $$$1$$$ (their $$$\mathsf{XOR}$$$ is $$$3$$$), $$$7$$$ and $$$5$$$ (their $$$\mathsf{XOR}$$$ is $$$2$$$), and $$$7$$$ and $$$6$$$ (their $$$\mathsf{XOR}$$$ is $$$1$$$) to get the lexicographically smallest array.