Counting Domino Spots

Compute the total number of spots over all distinct unordered pairs of mark values from 0 to N.

Easy3MathCombinatoricsNo attempts yetTime limit2sMemory limit512 MB

Problem

Dominoes are pieces used in many tile games. Each domino piece has two marks, and each mark carries 00 or more spots. The size of the set decides how many spots a mark can carry: in a set of size NN, every mark carries between 00 and NN spots, inclusive.

Two pieces are the same piece if their two marks carry the same numbers of spots, whatever the reading order. A piece with marks of 22 and 88 spots is the same as a piece with marks of 88 and 22 spots. A proper domino set never holds the same piece twice. The complete set of size NN holds one copy of every possible piece whose marks carry at most NN spots. For example, the complete set of size 22 consists of 66 pieces.

the complete domino set of size 2

Write a program that computes the total number of spots on all pieces of the complete set of size NN.

Input

The first and only line contains the size NN of the complete set. (1N10001 \le N \le 1000)

Output

Print the total number of spots in the complete set of size NN.