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

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