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: Time Limit Exceeded)

#n = int(input())
#L = list(map(int, input().split()))
import math
import sys
import fractions
sum = 0
for i in range(5*10**8):
    sum += i
N = int(input())
if N >=5*10*8:
    for i in range((5*10**8),N):
        sum += i
else:
    for i in range(0,N,-1):
        sum -= i

print(sum)