D. Minimum Triangulationtime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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.InputThe first line contains single integer n (3 \le n \le 500) — the number of vertices in the regular polygon.OutputPrint one integer — the minimum weight among all triangulations of the given polygon.ExamplesInput
3
Output
6
Input
4
Output
18
NoteAccording to Wiki: polygon triangulation is the decomposition of a polygonal area (simple polygon) P into a set of triangles, i. e., finding a set of triangles with pairwise non-intersecting interiors whose union is P.In the first example the polygon is a triangle, so we don't need to cut it further, so the answer is 1 \cdot 2 \cdot 3 = 6.In the second example the polygon is a rectangle, so it should be divided into two triangles. It's optimal to cut it using diagonal 1-3 so answer is 1 \cdot 2 \cdot 3 + 1 \cdot 3 \cdot 4 = 6 + 12 = 18.
3

6 
['dp', 'greedy', 'math', '*1200']