Subset Multiplication

In mathematics, especially in set theory, set A is a subset of set B, or equivalently B is a superset of set A if A is contained inside B, that is, all elements of A are also elements of B.

You’re given a set of N positive integers. How many ways can you select two disjoint non-empty subsets, such that the multiplication of elements in both subsets is equal.

Input

Input starts with an integer T (T ≤ 3), denoting the number of test cases.
Each case contains an integer N (1 ≤ N ≤ 25) denoting the number of elements of an array. The next line contain array A (1 ≤ A[i] ≤ 25) of N distinct numbers.

Output

For each test case print the required answer on a line by itself.

Sample

Input	Output
2 1 1 6 1 2 3 4 5 6	0 6
For the second case, the valid combinations are: {2, 3} and {6} {1, 2, 3} and {6} {2, 3} and {1, 6} {3, 4} and {2, 6} {1, 3, 4} and {2, 6} {3, 4} and {1, 2, 6}