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 testcases. First line of test case is the length of array N and second line of test case are its elements.

Output:
Number of possible triangles are displayed to the user.

Constraints:
1 <= T <= 200
3 <= N <= 10⁷
1 <= arr[i] <= 10³

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

Output:
1
10

** For More Input/Output Examples Use 'Expected Output' option **