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#### LongestNonnegativeSumSlice

Given an array consisting of the integers -1, 0 and 1, find the longest slice with a non-negative sum.

You are given an array A consisting of the integers −1, 0 and 1. A slice of that array is any pair of integers (P, Q) such that 0 ≤ P ≤ Q < N. Your task is to find the longest slice of A whose elements yield a non-negative sum.

Write a function:

class Solution { public int solution(int[] A); }

that, given an array A of length N, consisting only of the values −1, 0, 1, returns the length of the longest slice of A that yields a non-negative sum. If there's no such slice, your function should return 0.

For example, given A = [−1, −1, 1, −1, 1, 0, 1, −1, −1], your function should return 7, as the slice starting at the second position and ending at the eighth is the longest slice with a non-negative sum.

For another example, given A = [1, 1, −1, −1, −1, −1, −1, 1, 1] your function should return 4: both the first four elements and the last four elements of array A are longest valid slices.

Write an efficient algorithm for the following assumptions:

• N is an integer within the range [2..100,000];
• each element of array A is an integer within the range [−1..1].