class Solution:
    def maxProduct(self, nums: List[int]) -> int:

        max_prod_prev = 1
        min_prod_prev = 1
        max_so_far = -math.inf

        for n in nums:

            max_prod_ending_here = max(n, max_prod_prev*n, min_prod_prev*n)
            min_prod_ending_here = min(n, min_prod_prev*n, max_prod_prev*n)
            max_prod_prev, min_prod_prev = max_prod_ending_here, min_prod_ending_here
            max_so_far = max(max_so_far, max_prod_ending_here)

        return max_so_far