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D. Zigzags

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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 $$$a_j = a_l$$$;

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.

Example

Input

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

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 $$$a_3 = a_6$$$.

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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