You are given two arrays A and B consisting of N integers each.

Index K is named fair if the four sums (A[0], ..., A[K-1]), (A[K], ... + A[N-1]), (B[0], ... + B[K-1]) and (B[K], ... + B[N-1]) are all equal. In other words, K is the index where the two arrays, A and B, can be split (into two non-empty arrays each) in such a way that the sums of the resulting arrays' elements are equal.

For example, given arrays A = [0,4,-1,0,3] and B = [0,-2,5,0,3], index K = 3 is fair.

The sums of the four subarrays are all equal: 0 + 4 + (-1) = 3; 0 + 3 + 3; 0 + (-2) + 5 = 3 and 0 + 3 = 3. On the other hand, index K = 2 is not fair, the sums of the subarrays are: 0 + 4 + (-1) = 3; 0 + 3 + 3; 0 + (-2) + 5 + 0 + 3 = 8.

Write a function:

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

which, given two arrays of integers A and B, returns the total number of fair indexes.

Examples

1. Given A = [0,4,-1,0,3] and B = [0,-2,5,0,3], your function should return 2. The fair indexes are 3 and 4. In both cases, the sums of elements of the subarrays are equal to 3.
2. Given A = [2,-2,-3,3] and B = [0,0,4,-4], your function should return 1. The only fair index is 2. Index 4 is not fair as the subarrays containing indexes from K to N - 1 would be empty.
3. Given A = [4,-1,0,3] and B = [-2,6,0,4], your function should return 0. There are no fair indexes.
4. Given A = [3,2,6] and B = [4,1,6], your function should return 0