B. AND Sortingtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given a permutation p of integers from 0 to n-1 (each of them occurs exactly once). Initially, the permutation is not sorted (that is, p_i>p_{i+1} for at least one 1 \le i \le n - 1). The permutation is called X-sortable for some non-negative integer X if it is possible to sort the permutation by performing the operation below some finite number of times:   Choose two indices i and j (1 \le i \lt j \le n) such that p_i \& p_j = X.  Swap p_i and p_j. Here \& denotes the bitwise AND operation.Find the maximum value of X such that p is X-sortable. It can be shown that there always exists some value of X such that p is X-sortable.InputThe input consists of multiple test cases. The first line contains a single integer t (1 \le t \le 10^4)  — the number of test cases. Description of test cases follows.The first line of each test case contains a single integer n (2 \le n \le 2 \cdot 10^5)  — the length of the permutation.The second line of each test case contains n integers p_1, p_2, ..., p_n (0 \le p_i \le n-1, all p_i are distinct)  — the elements of p. It is guaranteed that p is not sorted.It is guaranteed that the sum of n over all cases does not exceed 2 \cdot 10^5.OutputFor each test case output a single integer — the maximum value of X such that p is X-sortable.ExampleInput
4
4
0 1 3 2
2
1 0
7
0 1 2 3 5 6 4
5
0 3 2 1 4
Output
2
0
4
1
NoteIn the first test case, the only X for which the permutation is X-sortable are X = 0 and X = 2, maximum of which is 2.Sorting using X = 0:   Swap p_1 and p_4, p = [2, 1, 3, 0].  Swap p_3 and p_4, p = [2, 1, 0, 3].  Swap p_1 and p_3, p = [0, 1, 2, 3]. Sorting using X = 2:   Swap p_3 and p_4, p = [0, 1, 2, 3]. In the second test case, we must swap p_1 and p_2 which is possible only with X = 0.
4
4
0 1 3 2
2
1 0
7
0 1 2 3 5 6 4
5
0 3 2 1 4

2 0 4 1 
['bitmasks', 'constructive algorithms', 'sortings', '*1100']