Possible groups
##### Submissions: 7343   Accuracy: 34.07%   Difficulty: Medium   Marks: 4

Given an array of positive integers of size N, we can form a group of two or three only, the group should be such that the sum of all elements in that group is a multiple of 3. Count all possible number of groups that can be generated in this way.

Input:
The first line of input contains an integer T denoting the number of test cases. The first line of each test case is N, where N is the size of array. The second line of each test case contains N elements of array.

Output:
Print number of all possible group.

Constraints:
1 ≤ T ≤ 100
1 ≤ N ≤ 106
1 ≤ Ai,j ≤ 106

Example:
Input:
2
5
3 6 7 2 9
4
2 1 3 4

Output:
8
4

Explanation:
Testcase 1:
Groups of two are: {3,6}, {3,9}, {9,6},
{7,2}, {3, 6,9},
Groups of three are: {3, 7, 2}, {7, 2, 6}, {7, 2, 9}.

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

Author: rajatjha

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