Pinely Round 2 (Div. 1 + Div. 2) |
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Finished |
You are given a permutation$$$^{\dagger}$$$ $$$p_1, p_2, \ldots, p_n$$$ of integers $$$1$$$ to $$$n$$$.
You can change the current permutation by applying the following operation several (possibly, zero) times:
For example, if the permutation used to be $$$[6, 4, 3, 5, 2, 1]$$$ and you choose $$$x = 4$$$, then you will first write down $$$[3, 2, 1]$$$, then append this with $$$[6, 4, 5]$$$. So the initial permutation will be replaced by $$$[3, 2, 1, 6, 4, 5]$$$.
Find the minimum number of operations you need to achieve $$$p_i = i$$$ for $$$i = 1, 2, \ldots, n$$$. We can show that it is always possible to do so.
$$$^{\dagger}$$$ A permutation of length $$$n$$$ 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).
Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 1000$$$). The description of the test cases follows.
The first line of each test case contains one integer $$$n$$$ ($$$1 \le n \le 100\,000$$$).
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 $$$p_1, p_2, \ldots, p_n$$$ is a permutation.
It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$100\,000$$$.
For each test case, output the answer on a separate line.
51122 166 4 3 5 2 133 1 21910 19 7 1 17 11 8 5 12 9 4 18 14 2 6 15 3 16 13
0 1 4 1 7
In the first test case, $$$n = 1$$$ and $$$p_1 = 1$$$, so there is nothing left to do.
In the second test case, we can choose $$$x = 2$$$ and we immediately obtain $$$p_1 = 1$$$, $$$p_2 = 2$$$.
In the third test case, we can achieve the minimum number of operations in the following way:
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