#P1677A. Tokitsukaze and Strange Inequality
Tokitsukaze and Strange Inequality
Description
Tokitsukaze has a permutation $p$ of length $n$. Recall that a permutation $p$ of length $n$ is a sequence $p_1, p_2, \ldots, p_n$ consisting of $n$ distinct integers, each of which from $1$ to $n$ ($1 \leq p_i \leq n$).
She wants to know how many different indices tuples $[a,b,c,d]$ ($1 \leq a < b < c < d \leq n$) in this permutation satisfy the following two inequalities:
Note that two tuples $[a_1,b_1,c_1,d_1]$ and $[a_2,b_2,c_2,d_2]$ are considered to be different if $a_1 \ne a_2$ or $b_1 \ne b_2$ or $c_1 \ne c_2$ or $d_1 \ne d_2$.
The first line contains one integer $t$ ($1 \leq t \leq 1000$) — the number of test cases. Each test case consists of two lines.
The first line contains a single integer $n$ ($4 \leq n \leq 5000$) — the length of permutation $p$.
The second line contains $n$ integers $p_1, p_2, \ldots, p_n$ ($1 \leq p_i \leq n$) — the permutation $p$.
It is guaranteed that the sum of $n$ over all test cases does not exceed $5000$.
For each test case, print a single integer — the number of different $[a,b,c,d]$ tuples.
Input
The first line contains one integer $t$ ($1 \leq t \leq 1000$) — the number of test cases. Each test case consists of two lines.
The first line contains a single integer $n$ ($4 \leq n \leq 5000$) — the length of permutation $p$.
The second line contains $n$ integers $p_1, p_2, \ldots, p_n$ ($1 \leq p_i \leq n$) — the permutation $p$.
It is guaranteed that the sum of $n$ over all test cases does not exceed $5000$.
Output
For each test case, print a single integer — the number of different $[a,b,c,d]$ tuples.
Samples
3
6
5 3 6 1 4 2
4
1 2 3 4
10
5 1 6 2 8 3 4 10 9 7
3
0
28
Note
In the first test case, there are $3$ different $[a,b,c,d]$ tuples.
$p_1 = 5$, $p_2 = 3$, $p_3 = 6$, $p_4 = 1$, where $p_1 < p_3$ and $p_2 > p_4$ satisfies the inequality, so one of $[a,b,c,d]$ tuples is $[1,2,3,4]$.
Similarly, other two tuples are $[1,2,3,6]$, $[2,3,5,6]$.