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: Accepted)

# coding: utf-8
class Case04

  def initialize
  end

  def show
    p self.instance_variables
        .map{ |sym| [sym, self.instance_variable_get(sym)] }
        .to_h
  end
  
  # 実行する
  def execute
    read
    solve
    output
  end

  # 読込
  def read
    @n = gets.chomp.to_i
  end

  # 回答
  def solve
    # @result = (1..@n-1).reduce(0) {|r, x| r + x}
    @result = (@n-1) * @n / 2
  end
  
  # 出力
  def output
    puts @result
  end

end

Case04.new.execute if $0 == __FILE__