Given an array of distinct integers. The task is to count all the triplets such that sum of two elements equals the third element.

Input:
The first line of input contains an integer T denoting the number of test cases. Then T test cases follow. Each test case consists of two lines. First line of each test case contains an Integer N denoting size of array and the second line contains N space separated elements.

Output:
For each test case, print the count of all triplets, in new line. If no such triplets can form, print "-1".

Constraints:
1 <= T <= 100
3 <= N <= 10⁵
1 <= A[i] <= 10⁶

Example:
Input:
2
4
1 5 3 2
3
3 2 7
Output:
2
-1

Explanation:
Testcase 1: There are 2 triplets: 1 + 2 = 3 and 3 +2 = 5

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