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 Python (3.4.3) (judge verdict: Runtime Error)

def get_max(n):
    if n==1:
        return 0
    if n % 2 == 0:
        return (n/2+(n-1))*n/2/2-1 + get_max((n-1)/2)
    else:
        return ((n-1)/2+(n-1))*(n+1)/2/2 + get_max((n-1)/2)

def main():
    N = int(input())
    print(int(get_max(N)))


if __name__ == '__main__':
    main()