Given an array (a_1, a_2, \ldots, a_n), you can apply the following operation any number of times (possibly zero): Choose an integer (k \geq 1) such that (2k+1 \le m) and (2k+1) indices, (i_1, i_2, \ldots, i_{2k+1}) ((1 \le i_1 \lt i_2 \lt \ldots \lt i_{2k+1} \le m)), where (m) is the current length of the array. Then, remove the (i_{k+1})-th element from the array. Let (b_1, b_2, \ldots, b_m) be the remaining array after all operations. What is the maximum possible value of (\gcd(b_1, b_2, \ldots, b_m)), where (\gcd) of an array of integers denotes the greatest common divisor (GCD) of them? Each test contains multiple test cases. The first line contains the number of test cases (t) ((1 \le t \le 500)). The description of the test cases follows. The first line of each test case contains (n) ((1 \le n \le 100)), denoting the size of the array. The second line of each test case contains (n) integers (a_1, a_2, \ldots, a_n) ((1 \le a_i \le 10^9)). For each test case, output a single integer — the maximum possible value. In the first test case, the given array is (2, 4, 6, 7, 8, 9, 10). Choosing indices (1, 3, 4, 6, 7) results in the removal of (a_4 = 7) and the array (2, 4, 6, 8, 9, 10). Then, choosing indices (2, 5, 6) results in the removal of (a_5 = 9) and the array (2, 4, 6, 8, 10). You can't get an answer greater than (2).