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 Scala (2.11.7) (judge verdict: Wrong Answer)

import java.util.Scanner



object Main {

  def read(): Int = {
    scala.io.StdIn.readInt()
  }


  def solve(n: Int): Int = {
    val iSeq: Seq[Int] = 1 to n
    val pSeq: Seq[Int] = iSeq.takeRight(n-1) ++ iSeq.take(1)
    val modSeq = for(i <- 0 until iSeq.length) yield {
      iSeq(i) % pSeq(i)
    }
    modSeq.sum
  }


  def main(args: Array[String]): Unit = {
    val n = read()
    println(solve(n))
  }

}