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D. Lucky Permutation
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given a permutation$$$^\dagger$$$ $$$p$$$ of length $$$n$$$.

In one operation, you can choose two indices $$$1 \le i < j \le n$$$ and swap $$$p_i$$$ with $$$p_j$$$.

Find the minimum number of operations needed to have exactly one inversion$$$^\ddagger$$$ in the permutation.

$$$^\dagger$$$ 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).

$$$^\ddagger$$$ The number of inversions of a permutation $$$p$$$ is the number of pairs of indices $$$(i, j)$$$ such that $$$1 \le i < j \le n$$$ and $$$p_i > p_j$$$.

Input

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases. The 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 second line of each test case contains $$$n$$$ integers $$$p_1,p_2,\ldots, p_n$$$ ($$$1 \le p_i \le n$$$). It is guaranteed that $$$p$$$ is a permutation.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.

Output

For each test case output a single integer — the minimum number of operations needed to have exactly one inversion in the permutation. It can be proven that an answer always exists.

Example
Input
4
2
2 1
2
1 2
4
3 4 1 2
4
2 4 3 1
Output
0
1
3
1
Note

In the first test case, the permutation already satisfies the condition.

In the second test case, you can perform the operation with $$$(i,j)=(1,2)$$$, after that the permutation will be $$$[2,1]$$$ which has exactly one inversion.

In the third test case, it is not possible to satisfy the condition with less than $$$3$$$ operations. However, if we perform $$$3$$$ operations with $$$(i,j)$$$ being $$$(1,3)$$$,$$$(2,4)$$$, and $$$(3,4)$$$ in that order, the final permutation will be $$$[1, 2, 4, 3]$$$ which has exactly one inversion.

In the fourth test case, you can perform the operation with $$$(i,j)=(2,4)$$$, after that the permutation will be $$$[2,1,3,4]$$$ which has exactly one inversion.