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