CF1805A We Need the Zero

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](https://en.wikipedia.org/wiki/Bitwise_operation#XOR). 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.

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 $ .