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 Ruby (2.3.3) (judge verdict: Wrong Answer)

# frozen_string_literal: true
n = gets.to_i

def keisan(n)
  all = (1..n).inject(:+)

  while n > 0
    wari = (n / 2) + 1
    honto = n % wari
    all = honto + all - n
    n = wari - 1
  end

  all
end

if n == 2
  p 1
elsif n == 1
  p 0
else
  p keisan(n)
end