Maximum AND
Description
You 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).
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 $10^5$.
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.
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.
3
5
1 0 0 3 3
2 3 2 1 0
3
1 1 1
0 0 3
8
0 1 2 3 4 5 6 7
7 6 5 4 3 2 1 0
2
0
7