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 Go (1.6) (judge verdict: Runtime Error)

package main

import (
  "fmt"
  )

func main(){
  var n,ans int64
  fmt.Scan(&n)
  p := make([]int64, n)
  var i int64 = 0
  for i = 0; i<n;i++ {
    p[i]=n-i
  }
  tmp := n
  var l int64
  for l = 1; l < n; l++ {
    ans += (p[l]%tmp)
    tmp--
  }
  fmt.Println(ans)
}