Codeforces Round 944 (Div. 4) |
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Finished |
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, $$$x_i < y_i$$$.
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 $$$2 \cdot 10^5$$$.
For each test case, output $$$n$$$ integers — the lexicographically smallest array that can be made with any number of swaps.
441 0 3 252 7 1 5 681 2 1 2 1 2 1 2416 4 1 64
0 1 2 3 1 5 2 6 7 1 1 1 1 2 2 2 2 16 4 1 64
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.
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