Description:
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 Format:
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 Format:
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.
Note:
None