CF1400D 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 $ .