CF1744F.MEX vs MED

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题目描述

You are given a permutation $p_1, p_2, \ldots, p_n$ of length $n$ of numbers $0, \ldots, n - 1$ . Count the number of subsegments $1 \leq l \leq r \leq n$ of this permutation such that $mex(p_l, p_{l+1}, \ldots, p_r) > med(p_l, p_{l+1}, \ldots, p_r)$ .

$mex$ of $S$ is the smallest non-negative integer that does not occur in $S$ . For example:

$mex({0, 1, 2, 3}) = 4$
$mex({0, 4, 1, 3}) = 2$
$mex({5, 4, 0, 1, 2}) = 3$

$med$ of the set $S$ is the median of the set, i.e. the element that, after sorting the elements in non-decreasing order, will be at position number $\left \lfloor{ \frac{|S| + 1}{2} } \right \rfloor$ (array elements are numbered starting from $1$ and here $\left \lfloor{v} \right \rfloor$ denotes rounding $v$ down.). For example:

$med({0, 1, 2, 3}) = 1$
$med({0, 4, 1, 3}) = 1$
$med({5, 4, 0, 1, 2}) = 2$

A sequence of $n$ numbers is called a permutation if it contains all the numbers from $0$ to $n - 1$ exactly once.

输入格式

The first line of the input contains a single integer $t$ $(1 \leq t \leq 10^4$ ), the number of test cases.

The descriptions of the test cases follow.

The first line of each test case contains a single integer $n$ ( $1 \leq n \leq 2 \cdot 10^5$ ), the length of the permutation $p$ .

The second line of each test case contains exactly $n$ integers: $p_1, p_2, \ldots, p_n$ ( $0 \leq p_i \leq n - 1$ ), elements of permutation $p$ .

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

输出格式

For each test case print the answer in a single line: the number of subsegments $1 \leq l \leq r \leq n$ of this permutation such that $mex(p_l, p_{l+1}, \ldots, p_r) > med(p_l, p_{l+1}, \ldots, p_r)$ .

输入输出样例

输入#1

8
1
0
2
1 0
3
1 0 2
4
0 2 1 3
5
3 1 0 2 4
6
2 0 4 1 3 5
8
3 7 2 6 0 1 5 4
4
2 0 1 3

输出#1

说明/提示

The first test case contains exactly one subsegment and $mex({0}) = 1 > med({0}) = 0$ on it.

In the third test case, on the following subsegments: $[1, 0]$ , $[0]$ , $[1, 0, 2]$ and $[0, 2]$ , $mex$ is greater than $med$ .

In the fourth test case, on the following subsegments: $[0, 2]$ , $[0]$ , $[0, 2, 1]$ and $[0, 2, 1, 3]$ , $mex$ greater than $med$ .

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