Array Reodering

Description:

Input:

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 1000$$$) — the number of test cases.

The first line of the test case contains a single integer $$$n$$$ ($$$2 \le n \le 2000$$$) — the number of elements in the array.

The second line of the test case contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 10^5$$$).

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2000$$$.

Output:

For each test case, output a single integer — the maximum number of good index pairs if you can reorder the array $$$a$$$ in an arbitrary way.

Sample Input:

3
4
3 6 5 3
2
1 7
5
1 4 2 4 1

Sample Output:

4
0
9

Note:

In the first example, the array elements can be rearranged as follows: $$$[6, 3, 5, 3]$$$.

In the third example, the array elements can be rearranged as follows: $$$[4, 4, 2, 1, 1]$$$.