You are given an integer array nums. Pick one contiguous, non-empty subarray and return the largest product you can make from its elements.

The difficult part is that multiplication is not monotonic here:

• a large positive product can become very negative after multiplying by a negative value
• a very negative product can become the new best product after multiplying by another negative value
• a zero breaks the chain and starts a new segment

That is why the solution must remember both the strongest and weakest product that end at each index.