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: Accepted)

package main

import (
	"math/rand"
	"time"
	"os"
	"bufio"
	"fmt"
	"strconv"
)

var(
	inf = 10000000071000000
	stdin = bufio.NewReader(os.Stdin)
	mod = 1000000007
	mod9 = 1000000009
	//////////////////////////////////
	stack []byte
)

func init()  {
	rand.Seed(time.Now().UnixNano())
}

type zahyo struct {
	x int
	y int
}

func main() {
	n := goint()
	c := (n-1)*n/2
	fmt.Println(c)
}


//||||||||||||||||||||||||||入力|||||||||||||||||||||||||||||||||||||||

//次のスペースか改行まで読み込む
func gostring() string {
	byte_ls := make([]byte,0)
	for  {
		b, _ := stdin.ReadByte()
		if b == 32 || b == 10 || b == 0{
			return string(byte_ls)
		} else if b == 13 {
			continue
		} else {
			byte_ls = append(byte_ls,b)
		}
	}
}

//上の関数のintバージョン
func goint() int {
	n,_ := strconv.Atoi(gostring())
	return n
}

//数字一行
func intLine(n ,a int) []int {
	ls := make([]int,n)
	for i,_ := range ls{
		ls[i] = goint() + a
	}
	return ls
}

//|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

func sum(a ...int) int {
	ans := 0
	for i:=0;i<len(a);i++{
		ans += a[i]
	}
	return ans
}

func min(a ...int) int {
	ans := a[0]
	for i:=1;i<len(a);i++{
		if ans > a[i]{
			ans = a[i]
		}
	}
	return ans
}

func abs(n int) int {
	if n >= 0{
		return n
	} else {
		return -n
	}
}

func max(a ...int) int {
	ans := a[0]
	for i:=1;i<len(a);i++{
		if ans < a[i]{
			ans = a[i]
		}
	}
	return ans
}

func intList(n,k int) []int {
	ls := make([]int,n)
	for i:=0;i<n;i++{
		ls[i] = k
	}
	return ls
}