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: Accepted)

#インポート
import sys
 
#入力用
def ILI(): return list(map(int, sys.stdin.readline().rstrip().split()))
def ISI(): return map(int, sys.stdin.readline().rstrip().split())
def II(): return int(sys.stdin.readline().rstrip())
def ISS(): return sys.stdin.readline().rstrip().split()
def IS(): return sys.stdin.readline().rstrip()
 
N = II()
sum = N*(1+N)//2
print(sum-N)