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 PyPy3 (2.4.0) (judge verdict: Time Limit Exceeded)

#!/usr/bin/env python
import logging
logging.basicConfig(level=logging.DEBUG)
logging.disable(logging.CRITICAL)


def main():
    N = int(input())
    # N % 1 == 0
    ans = 0
    for i in range(1, N):
        logging.debug('%d %d' %(i, i+1))
        logging.debug('adding to ans: %d' % (i % i+1))
        ans += (i % (i+1))

    return ans

if __name__ == '__main__':
    print(main())