Get Total Balanced

You are given an array of positive integer capacities. A contiguous segment of length at least 3 is balanced if and only if its left-end capacity, its right-end capacity, and the sum of all capacities between the two ends are all equal. Find the number of balanced segments.

输入格式

The first line contains n (1..100000), and the second line contains n capacities (1..10⁹).

输出格式

Output one integer, the answer required by the problem.

样例 1

输入：

5
9 3 3 3 9

输出：

2

样例 2

输入：

2
1 1

输出：

0

样例 3

输入：

3
2 2 2

输出：

1

样例说明

Example 1 contains two balanced segments: the whole [9,3,3,3,9] and the middle [3,3,3].