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)

N = int(input())
max = 0

init = list(range(1, N+1))
all = []


def helper(input):
    if len(input) == N:
        all.append([i for i in list])
        return

    for i in range(1, N+1):
        if i not in input:
            input.append(i)
            helper(input)
            input.pop()


list = []
helper(list)

for i in all:
    sum = 0
    for j in range(N):
        sum += i[j] % (j+1)
    if sum > max:
        max = sum

print(max)