Problem:
Score : 400 points

Problem Statement

For an integer N, we will choose a permutation \{P_1, P_2, ..., P_N\} of \{1, 2, ..., N\}.

Then, for each i=1,2,...,N, let M_i be the remainder when i is divided by P_i.

Find the maximum possible value of M_1 + M_2 + \cdots + M_N.

Constraints

N is an integer satisfying 1 \leq N \leq 10^9.

Input

Input is given from Standard Input in the following format:

N

Output

Print the maximum possible value of M_1 + M_2 + \cdots + M_N.

Sample Input 1

2

Sample Output 1

1

When the permutation \{P_1, P_2\} = \{2, 1\} is chosen, M_1 + M_2 = 1 + 0 = 1.

Sample Input 2

13

Sample Output 2

78

Sample Input 3

1

Sample Output 3

0

Solution in Common Lisp (SBCL 1.1.14) (judge verdict: Time Limit Exceeded)

(let* ((n (read))
       (lst (loop :for k :from 1 :upto n :collect k)))
  (defun rotate ()
    (setf lst (cons (car (last lst)) (subseq lst 0 (1- n)))))
  (rotate)
  (princ (reduce #'+ (mapcar #'mod lst (loop :for k :from 1 :upto n :collect k)))))