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)

$debug = false
flag = ARGV.shift
if flag == "-d"
  $debug = true
end

def dputs str
  p str if $debug
end

def max(n, m)
  if n > m
    return n
  else
    return m
  end
end

def min(n, m)
  if n < m
    return n
  else
    return m
  end
end

def gets_all_int
  return gets.chomp.split.map{|v| v.to_i}
end

## start

N = gets_all_int[0]

#puts (N-1).downto(1).to_a.inject(0, :+)
puts ((N-1) * N)/2