405208: GYM101845 E Equilateral Triangles

Yeison drew an equilateral triangle of side length n cm. Then for each side of the triangle he drew n - 1 lines parallel to it, with 1 cm of separation between them. Now the big triangle contains n² equilateral small triangles of side length 1.

Let S be the set of all points that are vertices of any of the small triangles, now he is interested in knowing how many different pairs of points {a, b} where contain some other point and c ≠ b in the line segment ab, two pairs {a₁, b₁} and {a₂, b₂} are considered equal if a₁ = a₂ and b₁ = b₂ or if a₁ = b₂ and b₁ = a₂, two pairs are different if they are not equal.

For n = 3 the triangle drew by him would be the following:

Help Yeison to solve this problem.

The input consist of a single integer n (1 ≤ n ≤ 50) - the length of the triangle drew by Yeison.

Print one single integer - the answer of the problem.

2

3

3

12