Lexicographically Smallest XOR Array

Problem Description

You are given two arrays $\{A\}$ and $\{B\}$, both of length $N$. You may rearrange the order of array $\{B\}$ arbitrarily, and define

Find, among all possible arrays $\{X\}$, the lexicographically smallest one.

Input Format

The first line contains an integer $N$.

The second line contains $N$ space-separated integers, the array $\{A\}$.

The third line contains $N$ space-separated integers, the array $\{B\}$.

Output Format

Output one line of $N$ space-separated integers — the lexicographically smallest $\{X\}$.

Sample Input 1

3
520 1314 61
1389 104 577

Sample Output 1

73 79 85

Sample Input 2

3
8 4 13
17 2 7

Sample Output 2

10 3 28

Sample Input 3

3
0 0 0
17 2 7

Sample Output 3

2 7 17

Constraints

• $1 \le N \le 2 \times 10^3$
• $0 \le A_i, B_i < 2^{30}$

Hint

It is obvious that $X_i \ge 0$.