A15313. Maximum AND

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.