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)

from itertools import product, permutations,combinations
#from operator import itemgetter
#from bisect import bisect_left,bisect
#from heapq import heappop,heappush
#from fractions import gcd
#from math import ceil,floor,sqrt,cos,sin,pi
#from copy import deepcopy
import numpy as np

N = int(input())

# 元配列を生成
N_array = np.arange(1,N+1, dtype=np.int)

# 順列を生成
per = list(permutations(N_array))

# count配列を生成
count = np.zeros(len(per), dtype=np.int)


for i in range(len(per)):
	for j in range(len(per[i])):
		rem = N_array[j] % per[i][j]
		count[i] += rem

print(count.max())