Zigzags
Description
You are given an array $a_1, a_2 \dots a_n$. Calculate the number of tuples $(i, j, k, l)$ such that:
- $1 \le i < j < k < l \le n$;
- $a_i = a_k$ and $a_j = a_l$;
The first line contains a single integer $t$ ($1 \le t \le 100$) — the number of test cases.
The first line of each test case contains a single integer $n$ ($4 \le n \le 3000$) — the size of the array $a$.
The second line of each test case contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le n$) — the array $a$.
It's guaranteed that the sum of $n$ in one test doesn't exceed $3000$.
For each test case, print the number of described tuples.
Input
The first line contains a single integer $t$ ($1 \le t \le 100$) — the number of test cases.
The first line of each test case contains a single integer $n$ ($4 \le n \le 3000$) — the size of the array $a$.
The second line of each test case contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le n$) — the array $a$.
It's guaranteed that the sum of $n$ in one test doesn't exceed $3000$.
Output
For each test case, print the number of described tuples.
Samples
2
5
2 2 2 2 2
6
1 3 3 1 2 3
5
2
Note
In the first test case, for any four indices $i < j < k < l$ are valid, so the answer is the number of tuples.
In the second test case, there are $2$ valid tuples:
- $(1, 2, 4, 6)$: $a_1 = a_4$ and $a_2 = a_6$;
- $(1, 3, 4, 6)$: $a_1 = a_4$ and $a_3 = a_6$.