Maximum AND

3000ms

262144K

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).

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.

Sample Input:

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

Sample Output:

2
0
7

Informação

Provedor Codeforces

Código CF1721D