Middle equals the sum of its neighbours

Count the groups of three consecutive elements where the first plus the third equals the middle one.

Reported in: Cognizant GenC (memory-based)

Input

First line: N. Second line: N integers.

Output

The number of such groups.

Constraints

1 ≤ N ≤ 10^5.

Example 1

Input:
5
1 3 2 -1 -3

Output:
3

Example 2

Input:
4
1 1 1 1

Output:
0

Hint: Check a[i] + a[i+2] == a[i+1] for every i from 0 to N−3.

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