CF1863B.Split Sort

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:

• choose some $x$ ($2 \le x \le n$);
• create a new permutation by:
  • first, writing down all elements of $p$ that are less than $x$, without changing their order;
  • second, writing down all elements of $p$ that are greater than or equal to $x$, without changing their order;
• replace $p$ with the newly created permutation.

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).

给你一个 $1$ 到 $n$ 的排列$^{\dagger}$ $p_1, p_2, \ldots, p_n$。

你可以通过多次（可能为零次）执行以下操作来改变当前排列：

• 选择某个 $x$（满足 $2 \le x \le n$）；
• 按如下方式构造一个新排列：
  • 首先，按原顺序写出 $p$ 中所有小于 $x$ 的元素；
  • 然后，按原顺序写出 $p$ 中所有大于或等于 $x$ 的元素；
• 将 $p$ 替换为该新构造的排列。

例如，若当前排列为 $[6, 4, 3, 5, 2, 1]$，且你选择 $x = 4$，则你首先写出 $[3, 2, 1]$，再在其后追加 $[6, 4, 5]$。因此初始排列将被替换为 $[3, 2, 1, 6, 4, 5]$。

求使 $p_i = i$（对所有 $i = 1, 2, \ldots, n$）成立所需的最少操作次数。可以证明，这一目标总能实现。

$^{\dagger}$ 长度为 $n$ 的排列是指由 $1$ 到 $n$ 中互不相同的 $n$ 个整数以任意顺序组成的数组。例如，$[2,3,1,5,4]$ 是一个排列，但 $[1,2,2]$ 不是排列（数组中 $2$ 出现了两次），$[1,3,4]$ 也不是排列（此时 $n=3$，但数组中出现了 $4$）。

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 $100\,000$.

每个测试包含多个测试用例。第一行包含测试用例的数量 $t$（$1 \le t \le 1000$）。随后是各测试用例的描述。

每个测试用例的第一行包含一个整数 $n$（$1 \le n \le 100\,000$）。

每个测试用例的第二行包含 $n$ 个整数 $p_1, p_2, \ldots, p_n$（$1 \le p_i \le n$）。保证 $p_1, p_2, \ldots, p_n$ 是一个排列。

保证所有测试用例的 $n$ 值之和不超过 $100\,000$。

For each test case, output the answer on a separate line.

对于每个测试用例，在单独的一行上输出答案。

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:

1. $x = 4$: $[6, 4, 3, 5, 2, 1] \rightarrow [3, 2, 1, 6, 4, 5]$;
2. $x = 6$: $[3, 2, 1, 6, 4, 5] \rightarrow [3, 2, 1, 4, 5, 6]$;
3. $x = 3$: $[3, 2, 1, 4, 5, 6] \rightarrow [2, 1, 3, 4, 5, 6]$;
4. $x = 2$: $[2, 1, 3, 4, 5, 6] \rightarrow [1, 2, 3, 4, 5, 6]$.

在第一个测试用例中，$n = 1$ 且 $p_1 = 1$，因此无需任何操作。

在第二个测试用例中，我们可以选择 $x = 2$，从而立即得到 $p_1 = 1$、$p_2 = 2$。

在第三个测试用例中，我们可通过以下方式实现最少的操作次数：

1. $x = 4$：$[6, 4, 3, 5, 2, 1] \rightarrow [3, 2, 1, 6, 4, 5]$；
2. $x = 6$：$[3, 2, 1, 6, 4, 5] \rightarrow [3, 2, 1, 4, 5, 6]$；
3. $x = 3$：$[3, 2, 1, 4, 5, 6] \rightarrow [2, 1, 3, 4, 5, 6]$；
4. $x = 2$：$[2, 1, 3, 4, 5, 6] \rightarrow [1, 2, 3, 4, 5, 6]$。