Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

bitmasks

dfs and similar

divide and conquer

greedy

sortings

*1800

No tag edit access

The problem statement has recently been changed. View the changes.

×
D. Maximum AND

time limit per test

3 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou are given two arrays $$$a$$$ and $$$b$$$, consisting of $$$n$$$ integers each.

Let's define a function $$$f(a, b)$$$ as follows:

- let's define an array $$$c$$$ of size $$$n$$$, where $$$c_i = a_i \oplus b_i$$$ ($$$\oplus$$$ denotes bitwise XOR);
- the value of the function is $$$c_1 \mathbin{\&} c_2 \mathbin{\&} \cdots \mathbin{\&} c_n$$$ (i.e. bitwise AND of the entire array $$$c$$$).

Find the maximum value of the function $$$f(a, b)$$$ if you can reorder the array $$$b$$$ in an arbitrary way (leaving the initial order is also an option).

Input

The first line contains one integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases.

The first line of each test case contains one integer $$$n$$$ ($$$1 \le n \le 10^5$$$) — the size of arrays $$$a$$$ and $$$b$$$.

The second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$0 \le a_i < 2^{30}$$$).

The third line contains $$$n$$$ integers $$$b_1, b_2, \dots, b_n$$$ ($$$0 \le b_i < 2^{30}$$$).

The sum of $$$n$$$ over all test cases does not exceed $$$10^5$$$.

Output

For each test case print one integer — the maximum value of the function $$$f(a, b)$$$ if you can reorder the array $$$b$$$ in an arbitrary way.

Example

Input

351 0 0 3 32 3 2 1 031 1 10 0 380 1 2 3 4 5 6 77 6 5 4 3 2 1 0

Output

2 0 7

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Apr/20/2024 09:31:42 (l3).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|