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: Wrong Answer)

import sys
read = sys.stdin.readline
import time
import math
import itertools as it
def inp():
    return int(input())
def inpl():
    return list(map(int, input().split()))
start_time = time.perf_counter()
# ------------------------------

n = inp()
print(int(0.5*(n-1)*(1+n-1)))

# -----------------------------
end_time = time.perf_counter()
print('time:', end_time-start_time, file=sys.stderr)