bee 1472 - Triangles

It will be give to you N points on a circle. You must write a program to determine how many distinct equilateral triangles can be constructed using the given points as vertices.

The figure below illustrates an example: (a) shows a set of points, determined by the lengths of the circular arcs that have adjacent points as extremes; and (b) shows the two triangles which can be built with these points.

Input

The input contains several test cases and ends with EOF. The first line of a test case contains an integer N ( 3 ≤ N ≤ 10⁵), the number of points given. The second line contains N integers X_i(1 ≤ X_i ≤ 10³) for 1 ≤_i ≤ N, representing the lengths of the circular arcs between two consecutive points in the circle: for 1 ≤ i ≤ (N − 1), X_i represents the length of the arc between points _i and _i + 1; X_N represents the length of the arc between points N and 1.

Output

For each test case your program must output a single line, containing a single integer, the number of distinct equilateral triangles that can be constructed using the given points as vertices.

Sample Input	Sample Output
8 4 2 4 2 2 6 2 2 6 3 4 2 1 5 3	2 1