SP31502 UNIHW - University Homework

Hugo had quite a bad day today. His favourite university subject, mathematical analysis, was taught by his least liked substitute teacher - he always gave out an abnormaly large amount of homework. Today was no different. The teacher wrote **N** numbers on the board, and after a long, thoughtful pause he told the class with a grin: "Well then, kids. For today's homework you will do this harmless exercise. As you can see, I've written quite a few numbers on the board, and your task is to find which smallest non-empty subset of them has the greatest product. That should keep you busy for today's evening!". Sigh. How could someone even come up with such a boring, time-consuming and impractical task. If only there was someone who would help Hugo and do it for him.

The first line of input contains the number **1 : the number of test cases. **T** cases follow. The first line of each case contains the number **1 : how many numbers the teacher wrote on the board. The second line contains **N** integers; their absolute value will not exceed **10 $ ^{9} $** . You may assume that in any input file, the sum of **N** across all test cases does not exceed **3\*10 $ ^{5} $** .****

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