three arrays

Problem Description

There are three integer arrays $a, b, c$. The lengths of them are all $N$. You are given the full contents of $a$ and $b$. And the elements in $c$ is produced by following equation: $c[i] = a[i]\ XOR\ b[i]$ where $XOR$ is the bitwise exclusive or operation. Now you can rearrange the order of elements in arrays $a$ and $b$ independently before generating the array $c$. We ask you to produce the lexicographically smallest possible array $c$ after reordering $a$ and $b$. Please output the resulting array $c$.

Input

The first line contains an integer $T$ indicating there are $T$ tests. Each test consists of three lines. The first line contains one positive integer $N$ denoting the length of arrays $a, b, c$. The second line describes the array $a$. The third line describes the array $b$.

• $T \le 1000$
• $1 \le N \le 10^5$
• integers in arrays $a$ and $b$ are in the range of $[0, 2^{30})$.
• at most $6$ tests with $N > 100$

Output

For each test, output a line containing $N$ integers, representing the lexicographically smallest resulting array $c$.

Sample Input

1

3

3 2 1

4 5 6

Sample Output

4 4 7

Source

2019 Multi-University Training Contest 5