Zigzags

Description:

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.

Sample Input:

2
5
2 2 2 2 2
6
1 3 3 1 2 3

Sample Output:

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 $$$a_3 = a_6$$$.