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 (1.14.1) (judge verdict: Accepted)

package main

import (
	"bufio"
	"fmt"
  	"os"
  	"strconv"
)

var sc = bufio.NewScanner((os.Stdin))

func nextLine() string {
	sc.Scan()
	return sc.Text()
}

func nextInt() int {
	l := nextLine()
	i, e := strconv.Atoi(l)
	if e != nil {
		panic(e)
	}
	return i
}

func main() {
	sc.Split(bufio.ScanWords)
	N := nextInt()

	fmt.Printf("%d\n", ABC139D(N))
}

// ABC139D ...
func ABC139D(N int) (res int) {
	return N * (N - 1) / 2
}