#include <bits/stdc++.h>
int main() {
  int tests;
  std::cin >> tests;
  for (int t = 0; t < tests; ++t) {
    std::size_t n;
    std::cin >> n;
    std::vector<std::size_t> as(n);
    std::vector<std::vector<std::size_t>> sums(n + 1);
    sums[0].resize(n);
    std::vector<std::vector<std::size_t>> indices(n);
    for (std::size_t i = 0; i < n; ++i) {
      std::cin >> as[i];
      --as[i];
      sums[i + 1] = sums[i];
      ++sums[i + 1][as[i]];
      indices[as[i]].push_back(i);
    }
    long long quadruples = 0;
    for (std::size_t j = 1; j < n - 2; ++j) {
      std::size_t aj = as[j];
      for (std::size_t k = j + 1; k < n - 1; ++k) {
        std::size_t ak = as[k];
        auto prefix = sums[j][ak];
        auto suffix = sums.back()[aj] - sums[k + 1][aj];
        quadruples += prefix * suffix;
      }
    }
    std::cout << quadruples << '\n';
  }
  return 0;
}

### Prompt

Construct a CPP code solution to the problem outlined:

You are given an array a_1, a_2 ... a_n. Calculate the number of tuples (i, j, k, l) such that: 

  * 1 ≤ i < j < k < l ≤ n; 
  * a_i = a_k and a_j = a_l; 

Input

The first line contains a single integer t (1 ≤ t ≤ 100) — the number of test cases.

The first line of each test case contains a single integer n (4 ≤ n ≤ 3000) — the size of the array a.

The second line of each test case contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 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. 

### Response

```cpp
#include <bits/stdc++.h>
int main() {
  int tests;
  std::cin >> tests;
  for (int t = 0; t < tests; ++t) {
    std::size_t n;
    std::cin >> n;
    std::vector<std::size_t> as(n);
    std::vector<std::vector<std::size_t>> sums(n + 1);
    sums[0].resize(n);
    std::vector<std::vector<std::size_t>> indices(n);
    for (std::size_t i = 0; i < n; ++i) {
      std::cin >> as[i];
      --as[i];
      sums[i + 1] = sums[i];
      ++sums[i + 1][as[i]];
      indices[as[i]].push_back(i);
    }
    long long quadruples = 0;
    for (std::size_t j = 1; j < n - 2; ++j) {
      std::size_t aj = as[j];
      for (std::size_t k = j + 1; k < n - 1; ++k) {
        std::size_t ak = as[k];
        auto prefix = sums[j][ak];
        auto suffix = sums.back()[aj] - sums[k + 1][aj];
        quadruples += prefix * suffix;
      }
    }
    std::cout << quadruples << '\n';
  }
  return 0;
}

```