You are given a set \(S\) of distinct positive integers of size \(n\) (\(n\) is always even). Print the minimum positive integer \(k\) that is greater than 0 such that after replacing each element \(e\) of the set \(S\) with \(e⊕k\), set \(S\) remains the same.

Print -1 if there is no such \(k\).

Note: It is guaranteed that \(\frac{n}{2}\) is odd.

Input format

The first line contains a single integer \(t\ (1\le t \le 100)\) denoting the number of test cases.
The first line of each test case contains a single integer \(n\ (2 \le n \le 1e5)\) denoting the number of elements in the set.
The second line of each test case contains \(n\) integers \(e\ (1 \le e \le 1e9)\).

Output format

Print \(t\) lines each containing a single line that contains \(k\).