Minimum Triangulation

You are given a regular polygon with $n$ vertices labeled from $1$ to $n$ in counter-clockwise order. The triangulation of a given polygon is a set of triangles such that each vertex of each triangle is a vertex of the initial polygon, there is no pair of triangles such that their intersection has non-zero area, and the total area of all triangles is equal to the area of the given polygon. The weight of a triangulation is the sum of weigths of triangles it consists of, where the weight of a triagle is denoted as the product of labels of its vertices.

Calculate the minimum weight among all triangulations of the polygon.

Input

One integer $n(3\le n\le 500)$ — the number of vertices in the regular polygon.

Output

Print the minimum weight among all triangulations of the given polygon.

Examples

In the first test case a triangle with labels $1,2,3$ is given. Its weight is $1\cdot 2\cdot 3=6$.

The second test case is a square with labels $1,2,3,4$. We shall get the minimum weight for a triangulation with the diagonal $(1,3)$. It is equal to $1\cdot 2\cdot 3+1\cdot 3\cdot 4=6+12=18$.