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 $k$.