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: Runtime Error)

def mapt(fn, *args):
    return tuple(map(fn, *args))


def Input():
    return mapt(int, input().split(" "))


def main():
    n = int(input())
    if n == 1: print(0); exit()
    k = list(range(1, n+1))
    list1 = [i+1 for i in range(2, n)]
    a = [1] + list1[:] + [2]
    b = [2] + list1[:] + [1]
    ans = 0
    for row in (a, b):
        r = 0
        for x, y in zip(k, row):
            r += x % y
        ans = max(ans, r)
    print(ans)



main()