Statement

Pompieru is hungry and wants to cook the famous Half-Pound Sandwich. He is given a list of N ingredients, each one with an integer flavor-value V_i. However, the Half-Pound Sandwich is very special, with some specific rules in its receipt: (1) Ingredients are used in the order they are given. The first ingredient used must be the first one in the list, and so on. (2) The sandwich consists of one or more levels. Each level must include one or more consecutive ingredients, and each ingredient must be part of exactly one level. (3) The total flavor value of each level must be positive. Given the rules above, determine the maximum number of levels the sandwich can have.