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F. Anton and School

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputAnton 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.

Examples

Input

4

6 8 4 4

16 22 10 10

Output

3 5 1 1

Input

5

8 25 14 7 16

19 6 9 4 25

Output

-1

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

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