Anton goes to school, his favorite lessons are arraystudying. He usually solves all the tasks pretty fast, but this time the teacher gave him a complicated one: given two arrays b and c of length n, find array a, such that:

$\text{[math]}$

where a and b means bitwise AND, while a or b means bitwise OR.

Usually Anton is good in arraystudying, but this problem is too hard, so Anton asks you to help.

Input

The first line of the input contains a single integers n (1 ≤ n ≤ 200 000) — the size of arrays b and c.

The second line contains n integers b_i (0 ≤ b_i ≤ 10⁹) — elements of the array b.

Third line contains n integers c_i (0 ≤ c_i ≤ 10⁹) — elements of the array c.

Output

If there is no solution, print - 1.

Otherwise, the only line of the output should contain n non-negative integers a_i — elements of the array a. If there are multiple possible solutions, you may print any of them.

Anton and School

Examples