CF1682B.AND Sorting

You 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.

The 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 $2 \cdot 10^5$ .

For each test case output a single integer — the maximum value of $X$ such that $p$ is $X$ -sortable.

In 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 $X = 0$ .