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.

见题面 Input 部分

见题面 Output 部分

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.