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문제

You will be given 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.

 

입력

The first line of the input contains an integer N, the number of points given. The second line contains N integers Xi, representing the lengths of the circular arcs between two consecutive points in the circle: for 1 ≤ i ≤ (N − 1), Xi represents the length of the arc between between points i and i + 1; XN represents the length of the arc between points N and 1.

Restrictions

  • 3 ≤ N ≤ 105
  • 1 ≤ Xi ≤ 103, for 1 ≤ i ≤ N

출력

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.

예제 입력 1

8
4 2 4 2 2 6 2 2

예제 출력 1

2

예제 입력 2

6
3 4 2 1 5 3

예제 출력 2

1