XOR

Given a multiset S of non-negative integers, divide it into two multisets A and B in a way that minimizes |xor(A) - xor(B)|. Here xor(X) denotes the bitwise XOR of all elements of X.

Note that one of the multisets A and B can be empty, and XOR of an empty multiset is 0.

It is enough to output the minimum possible value of |xor(A) - xor(B)|.

Input

First line contains the number of test cases z (1 ≤ z ≤ 50). The descriptions of the testcases follow, two lines per test case.

The first line of every test case contains an integer n (1 ≤ n ≤ 10^5) - the size of the multiset.

The second line contains n integers x[i] (0 ≤ x[i] ≤ 10^18) - elements of the multiset.

Output

For each test case output one integer: the smallest possible difference of XORs.

Examples