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 (2.7.1) (judge verdict: Accepted)

n = gets.chomp.to_i
# if n % 2 == 0
#     mae = ((1 + han) * han) / 2
#     (han+1..n).each do |i|
#         aikata = n + 1 - i
#         iko = i % aikata
#         ans += iko
#     end
# elsif n % 2 != 0
#     mae = ((1 + han) * han) / 2
#     (han+2..n).each do |i|
#         aikata = n + 1 - i
#         iko = i % aikata
#         ans += iko
#     end
# end
# p mae
# puts ans + mae
saigo = n- 1
puts (1 + saigo) * saigo / 2