CF1721D 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.