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 Kotlin (1.0.0) (judge verdict: Wrong Answer)

fun main(args: Array<String>) {
  val n = readLine()!!.toInt()
  val numList: MutableList<Int> = mutableListOf()
  val shiftedList: MutableList<Int> = mutableListOf()
  
  for (i in 1..n) {
    numList.add(i)
    if (i == n) {
      shiftedList.add(1)
    } else {
      shiftedList.add(i+1)
    }
  }
  var sum = 0
  numList.forEachIndexed { i,e ->
    val sub = shiftedList.get(i)
    sum += e % sub
  }
  println(sum)
}