Given an unsorted array of positive integers. Find the number of triangles that can be formed with three different array elements as lengths of three sides of triangles. 

Input: 
The first line of the input contains T denoting the number of test cases. The first line of each test case contains an integer represents N and the second line contains N space-separated integers.

Output:
For each test case, print the number of possible triangles in a separate line.

Constraints:
1 <= T <= 10
3 <= N <= 10³
1 <= arr[i] <= 10⁵

Example:
Input:
2
3
3 5 4
5
6 4 9 7 8

Output:
1
10