A13729. Zigzags

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.

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 $a_3 = a_6$ .