[ICPC2022 Jinan R] Stack Sort

你有一个 $n$ 项的数组 $a$ 和 $m$ 个栈，满足： - $1\leq a_i\le n$，每一项各不相同。 - 对于 $i=1,2...n$，使 $a_i$ 成为任意一个栈的栈顶。 - 在每一项入栈后有一种方法使得 $1,2...,n$ 可以按照递增顺序依次出栈。 求 $m$ 的最小值。

You are given a permutation with $n$ numbers, $a_1, a_2, \dots, a_n (1\leq a_i\leq n, a_i\neq a_j\textrm{ when }i\neq j)$. You want to sort these numbers using $m$ stacks. Specifically, you should complete the following task: Initially, all stacks are empty. You need to push each number $a_i$ to the top of one of the $m$ stacks one by one, in the order of $a_1,a_2,\ldots, a_n$. $\textbf{After pushing all numbers in the stacks}$, you pop all the elements from the stacks in a clever order so that the first number you pop is $1$, the second number you pop is $2$, and so on. **If you pop an element from a stack $S$, you cannot pop any element from the other stacks until $S$ becomes empty.** What is the minimum possible $m$ to complete the task?

The first line contains one integer $T~(1\le T \le 10^5)$, the number of test cases. For each test case, the first line contains one positive integer $n~(1\le n \le 5 \times 10^5)$. The next line contains $n$ integers $a_1,\ldots, a_n~(1 \le a_i\le n)$ denoting the permutation. It is guaranteed that $a_1,\ldots, a_n$ form a permutation, i.e. $a_i\neq a_j$ for $i \neq j$. It is guaranteed that the sum of $n$ over all test cases is no more than $5\times 10^5$.

For each test case, output the minimum possible $m$ in one line.

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

3
1
4