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:

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 $*b*_{*i*}$ ($0 ≤ *b*_{*i*} ≤ 10^{9}$) — elements of the array $*b*$.

Third line contains $*n*$ integers $*c*_{*i*}$ ($0 ≤ *c*_{*i*} ≤ 10^{9}$) — 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.