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 Java8 (OpenJDK 1.8.0) (judge verdict: Runtime Error)

import java.util.*;
class Main{ 
public static void main(String[] args) {
        Scanner scn =new Scanner(System.in);
        int N=scn.nextInt();
        int[] pi=new int[N];
        for (int i = 0; i <N; i++) {
            pi[i]=i;
        }
        int sum=0;
        for(int j=1;j<N-1;j++){
            sum+=(j)/pi[j+1];
        }
        sum+=N;
        System.out.println(sum);
    }
}