Maximum Product of Array Splitting

You are given an array of integers. Your task is to split this array into two non-empty subarrays at a point such that the product of the sums of the two subarrays is maximized. Formally, if the array is A of length N and you split it at position i (where 1 ≤ i < N), let S_L = \(\sum_{j=0}^{i-1} A[j]\) and S_R = \(\sum_{j=i}^{N-1} A[j]\). You need to maximize the product \(S_L \times S_R\). If the array cannot be split into two non-empty subarrays (i.e. when N < 2), output -1.

Note: There may be several ways to split the array. You only need to output the maximum product of the sums.

inputFormat

The first line contains a single integer T representing the number of test cases.

For each test case, the first line contains an integer N denoting the number of elements in the array.

The second line contains N space-separated integers, representing the elements of the array.

Input is given from standard input (stdin).

outputFormat

For each test case, output a single line containing the maximum product of the sums of the two non-empty subarrays. If the array cannot be split, output -1.

Output should be written to standard output (stdout).

## sample

4
5
1 2 3 4 5
3
1 1 1
4
10 5 1 2
1
1

54
2
80
-1

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