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 (3.8.2) (judge verdict: Accepted)

#139D

#ここから試験用コード
'''
import itertools

for N in range(1,13):
    l = [i for i in range(1,N+1)]

    ans = 0
    ans_permutation = list()

    for permutation in itertools.permutations(l, N):
        temp_ans = 0
        permutation = [0] + list(permutation)
        for i in range(1,N+1):
            temp_ans += i%permutation[i]

        if ans <= temp_ans:
            if ans < temp_ans:
                ans_permutation = list()
            ans = temp_ans    
            ans_permutation.append(list(permutation)[1:])

    print(N,ans,ans_permutation)
    
#試験用コードの結果
# 1  0 [[1]]
# 2  1 [[2, 1]]
# 3  3 [[1, 3, 2], [2, 3, 1]]
# 4  6 [[2, 3, 4, 1]]
# 5 10 [[1, 3, 4, 5, 2], [2, 1, 4, 5, 3], [2, 3, 4, 5, 1]]
# 6 15 [[2, 3, 4, 5, 6, 1]]
# 7 21 [[1, 3, 2, 5, 6, 7, 4], [1, 3, 4, 5, 6, 7, 2], [2, 3, 1, 5, 6, 7, 4], [2, 3, 4, 5, 6, 7, 1]]
# 8 28 [[2, 1, 4, 5, 6, 7, 8, 3], [2, 3, 4, 5, 6, 7, 8, 1]]
# 9 36 [[1, 3, 4, 5, 6, 7, 8, 9, 2], [2, 3, 4, 1, 6, 7, 8, 9, 5], [2, 3, 4, 5, 6, 7, 8, 9, 1]]
#10 45 [[2, 3, 4, 5, 6, 7, 8, 9, 10, 1]]

#いずれにも最初は2,3...、最後は1となるパターンがある
#上記パターン時は ((N-1)+1)*(N-1)/2 が答え。
'''
N = int(input())
print(N*(N-1)//2)