Given an array where each element is the money a person have and there is only Rs. 3 note. We need to check whether it is possible to divide the money equally among all the persons or not. If it is possible then find Minimum number of transactions needed.

**Input:**

The first line of input consists of an integer T denoting the number of test cases Each test case contains an integer N denoting the size of the array. Then in the next line are N space separated elements of the array.

**Output: **

For each case in a new line print the minimum number of transactions if it is possible to divide the money else print "-1" without quotes.

**Constraints:**

1<=T<=500

1<=N<=1000

1<=elements of array <=10^6

**Example:**

**Input:**

2

3

5 8 11

4

1 2 3 4

**Output:**

1

-1

**Explanation:**

In first example third person will give a 3 rs note to first person so that all will have same amount of money.

In second example it is not possible to divide the money.

Author: Ayush jha

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