Permutation Sort

题意翻译

你需要对一个长度为 $n$ 的全排列进行一些操作，每次你都可以选择一个区间（当然是连续的）进行任意的交换（你想把这个区间排成什么样都行），请问最少需要多少次操作才能使得这个排列是升序的？

题目描述

You are given a permutation $ a $ consisting of $ n $ numbers $ 1 $ , $ 2 $ , ..., $ n $ (a permutation is an array in which each element from $ 1 $ to $ n $ occurs exactly once). You can perform the following operation: choose some subarray (contiguous subsegment) of $ a $ and rearrange the elements in it in any way you want. But this operation cannot be applied to the whole array. For example, if $ a = [2, 1, 4, 5, 3] $ and we want to apply the operation to the subarray $ a[2, 4] $ (the subarray containing all elements from the $ 2 $ -nd to the $ 4 $ -th), then after the operation, the array can become $ a = [2, 5, 1, 4, 3] $ or, for example, $ a = [2, 1, 5, 4, 3] $ . Your task is to calculate the minimum number of operations described above to sort the permutation $ a $ in ascending order.

输入输出格式

输入格式

The first line contains a single integer $ t $ ( $ 1 \le t \le 2000 $ ) — the number of test cases. The first line of the test case contains a single integer $ n $ ( $ 3 \le n \le 50 $ ) — the number of elements in the permutation. The second line of the test case contains $ n $ distinct integers from $ 1 $ to $ n $ — the given permutation $ a $ .

输出格式

For each test case, output a single integer — the minimum number of operations described above to sort the array $ a $ in ascending order.

输入输出样例

输入样例 #1

3
4
1 3 2 4
3
1 2 3
5
2 1 4 5 3

输出样例 #1

1
0
2

说明

In the explanations, $ a[i, j] $ defines the subarray of $ a $ that starts from the $ i $ -th element and ends with the $ j $ -th element. In the first test case of the example, you can select the subarray $ a[2, 3] $ and swap the elements in it. In the second test case of the example, the permutation is already sorted, so you don't need to apply any operations. In the third test case of the example, you can select the subarray $ a[3, 5] $ and reorder the elements in it so $ a $ becomes $ [2, 1, 3, 4, 5] $ , and then select the subarray $ a[1, 2] $ and swap the elements in it, so $ a $ becomes $ [1, 2, 3, 4, 5] $ .