B. Permutation Swaptime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given an unsorted permutation p_1, p_2, \ldots, p_n. To sort the permutation, you choose a constant k (k \ge 1) and do some operations on the permutation. In one operation, you can choose two integers i, j (1 \le j < i \le n) such that i - j = k, then swap p_i and p_j.What is the maximum value of k that you can choose to sort the given permutation?A permutation is an array consisting of n distinct integers from 1 to n in arbitrary order. For example, [2, 3, 1, 5, 4] is a permutation, but [1, 2, 2] is not a permutation (2 appears twice in the array) and [1, 3, 4] is also not a permutation (n = 3 but there is 4 in the array).An unsorted permutation p is a permutation such that there is at least one position i that satisfies p_i \ne i.InputEach test contains multiple test cases. The first line contains the number of test cases t (1 \le t \le 10^4). The description of the test cases follows.The first line of each test case contains a single integer n (2 \le n \le 10^{5}) — the length of the permutation p.The second line of each test case contains n distinct integers p_1, p_2, \ldots, p_n (1 \le p_i \le n) — the permutation p. It is guaranteed that the given numbers form a permutation of length n and the given permutation is unsorted.It is guaranteed that the sum of n over all test cases does not exceed 2 \cdot 10^{5}.OutputFor each test case, output the maximum value of k that you can choose to sort the given permutation.We can show that an answer always exists.ExampleInput
733 1 243 4 1 274 2 6 7 5 3 191 6 7 4 9 2 3 8 561 5 3 4 2 6103 10 5 2 9 6 7 8 1 4111 11 6 4 8 3 7 5 9 10 2Output
1
2
3
4
3
2
3
NoteIn the first test case, the maximum value of k you can choose is 1. The operations used to sort the permutation are:   Swap p_2 and p_1 (2 - 1 = 1) \rightarrow p = [1, 3, 2]  Swap p_2 and p_3 (3 - 2 = 1) \rightarrow p = [1, 2, 3] In the second test case, the maximum value of k you can choose is 2. The operations used to sort the permutation are:   Swap p_3 and p_1 (3 - 1 = 2) \rightarrow p = [1, 4, 3, 2]  Swap p_4 and p_2 (4 - 2 = 2) \rightarrow p = [1, 2, 3, 4] 
733 1 243 4 1 274 2 6 7 5 3 191 6 7 4 9 2 3 8 561 5 3 4 2 6103 10 5 2 9 6 7 8 1 4111 11 6 4 8 3 7 5 9 10 2
1 2 3 4 3 2 3 
['math', 'number theory', '*900']