A14956 | Inversion Graph

You are given a permutation $p_1, p_2, \dots, p_n$ . Then, an undirected graph is constructed in the following way: add an edge between vertices $i$ , $j$ such that $i < j$ if and only if $p_i > p_j$ . Your task is to count the number of connected components in this graph.

Two vertices $u$ and $v$ belong to the same connected component if and only if there is at least one path along edges connecting $u$ and $v$ .

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).

Each test contains multiple test cases. The first line contains a single integer $t$ ( $1 \le t \le 10^5$ ) — the number of test cases. Description of the test cases follows.

The first line of each test case contains a single integer $n$ ( $1 \le n \le 10^5$ ) — the length of the permutation.

The second line of each test case contains $n$ integers $p_1, p_2, \dots, p_n$ ( $1 \le p_i \le n$ ) — the elements of the permutation.

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

For each test case, print one integer $k$ — the number of connected components.