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:

$$\begin{cases} b_i = (a_i \text{ and } a_1) + (a_i \text{ and } a_2) + \cdots + (a_i \text{ and } a_n), \\ c_i = (a_i \text{ or } a_1) + (a_i \text{ or } a_2) + \cdots + (a_i \text{ or } a_n). \end{cases}$$

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 bi (0 ≤ bi ≤ 109) — elements of the array b.

Third line contains n integers ci (0 ≤ ci ≤ 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 ai — elements of the array a. If there are multiple possible solutions, you may print any of them.

见题面 Input 部分

见题面 Output 部分