Tokitsukaze and Strange Inequality Codeforces Solution | Codeforces Problem Solution 2022

Tokitsukaze and Strange Inequality Codeforces Solution | Codeforces Problem Solution 2022

C. Tokitsukaze and Strange Inequality

time limit per test

1.5 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

Tokitsukaze has a permutation 𝑝$p$ of length 𝑛$n$. Recall that a permutation 𝑝$p$ of length 𝑛$n$ is a sequence 𝑝1,𝑝2,…,𝑝𝑛$p_1,p_2,\dots ,p_n$ consisting of 𝑛$n$ distinct integers, each of which from 1$1$ to 𝑛$n$ (1≤𝑝𝑖≤𝑛$1\le p_i\le n$).

She wants to know how many different indices tuples [𝑎,𝑏,𝑐,𝑑]$[a,b,c,d]$ (1≤𝑎<𝑏<𝑐<𝑑≤𝑛$1\le a<b<c<d\le n$) in this permutation satisfy the following two inequalities:

𝑝𝑎<𝑝𝑐$p_a<p_c$ and 𝑝𝑏>𝑝𝑑$p_b>p_d$.

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Note that two tuples [𝑎1,𝑏1,𝑐1,𝑑1]$[a_1,b_1,c_1,d_1]$ and [𝑎2,𝑏2,𝑐2,𝑑2]$[a_2,b_2,c_2,d_2]$ are considered to be different if 𝑎1≠𝑎2$a_1\ne a_2$ or 𝑏1≠𝑏2$b_1\ne b_2$ or 𝑐1≠𝑐2$c_1\ne c_2$ or 𝑑1≠𝑑2$d_1\ne d_2$.

Input

The first line contains one integer 𝑡$t$ (1≤𝑡≤1000$1\le t\le 1000$) — the number of test cases. Each test case consists of two lines.

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The first line contains a single integer 𝑛$n$ (4≤𝑛≤5000$4\le n\le 5000$) — the length of permutation 𝑝$p$.

The second line contains 𝑛$n$ integers 𝑝1,𝑝2,…,𝑝𝑛$p_1,p_2,\dots ,p_n$ (1≤𝑝𝑖≤𝑛$1\le p_i\le n$) — the permutation 𝑝$p$.

It is guaranteed that the sum of 𝑛$n$ over all test cases does not exceed 5000$5000$.

Output

For each test case, print a single integer — the number of different [𝑎,𝑏,𝑐,𝑑]$[a,b,c,d]$ tuples.

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