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 Fortran (gfortran v4.8.4) (judge verdict: Accepted)

module ABC139

  ! <module>s to import
  use, intrinsic :: iso_fortran_env

  ! require all variables to be explicitly declared
  implicit none

  ! accessibility of <subroutine>s and <function>s in this <module>
  public :: task_C

  ! contained <subroutine>s and <function>s are below
  contains

  subroutine task_C

    ! variables for this <subroutine>
    integer(INT64) :: len_sequence

    ! STEP.01
    ! read out the given data (the number of squares)
    read(unit=INPUT_UNIT, fmt=*) len_sequence

    ! STEP.02
    ! output the answer of this task
    write(unit=OUTPUT_UNIT, fmt='(I0)', advance='yes') (len_sequence - 1_INT64) * len_sequence / 2_INT64

    ! STEP.END
    return

  end subroutine task_C

end module ABC139

program main

  ! <module>s to import
  use, non_intrinsic :: ABC139

  ! require all variables to be explicitly declared
  implicit none

  call task_C

end program main