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: Time Limit Exceeded)

=begin
a = gets.split("").map{|x| x.to_s}
b = gets.split("").map{|x| x.to_s}
count = 0
3.times do |i|
  if a[i] == b[i]
    count += 1
  end
end

p count
=end

=begin
a = gets.split(" ").map{|x| x.to_i}
if a[1] == 1
  p 0
  exit()
end
a[1] -= a[0]
ans = 1
while true
  break if (a[1] <= 0)
  a[1] -= a[0] - 1
  ans += 1
end
p ans
=end

=begin
n = gets.to_i
a = gets.split(" ").map{|x| x.to_i}
max = 0

count = 0

(n - 1).times do |i|
  if a[i] >= a[i + 1]
    count += 1
  else
    if(max < count)
      max = count
    end
    count = 0
  end
end
if(max < count)
  max = count
end

p max
=end

input = gets.to_i
a = (1..input).to_a
ar = a.rotate(1)
sum = 0
(a.size).times do |i|
  sum += a[i] % ar[i]
end
p sum