Given an unsorted list of integers, find the smallest missing positive integer. For example, for the list [3, 4, -1, 1], the smallest missing positive integer is 2. For the list [1, 2, 0], the smallest missing positive integer is 3. For the list [-1, -3, 4, 2], the smallest missing positive integer is 1.
Implement the function smallest_missing_positive_integer using the provided smallest_missing_positive_integer function to find the smallest missing positive integer in the given list.