We Need the Zero
Description
There is an array $a$ consisting of non-negative integers. You can choose an integer $x$ and denote $b_i=a_i \oplus x$ for all $1 \le i \le n$, where $\oplus$ denotes the bitwise XOR operation. Is it possible to choose such a number $x$ that the value of the expression $b_1 \oplus b_2 \oplus \ldots \oplus b_n$ equals $0$?
It can be shown that if a valid number $x$ exists, then there also exists $x$ such that ($0 \le x < 2^8$).
Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 1000$). The description of the test cases follows.
The first line of the test case contains one integer $n$ ($1 \le n \le 10^3$) — the length of the array $a$.
The second line of the test case contains $n$ integers — array $a$ ($0 \le a_i < 2^8$).
It is guaranteed that the sum of $n$ over all test cases does not exceed $10^3$.
For each set test case, print the integer $x$ ($0 \le x < 2^8$) if it exists, or $-1$ otherwise.
Input
Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 1000$). The description of the test cases follows.
The first line of the test case contains one integer $n$ ($1 \le n \le 10^3$) — the length of the array $a$.
The second line of the test case contains $n$ integers — array $a$ ($0 \le a_i < 2^8$).
It is guaranteed that the sum of $n$ over all test cases does not exceed $10^3$.
Output
For each set test case, print the integer $x$ ($0 \le x < 2^8$) if it exists, or $-1$ otherwise.
5
3
1 2 5
3
1 2 3
4
0 1 2 3
4
1 2 2 3
1
1
6
0
3
-1
1
Note
In the first test case, after applying the operation with the number $6$ the array $b$ becomes $[7, 4, 3]$, $7 \oplus 4 \oplus 3 = 0$.
There are other answers in the third test case, such as the number $0$.