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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
#define ll long long int
using namespace std;
/*
ll npr(ll n, ll r, ll mod){
    ll val = 1;
    for(ll i=n; i<=(n-r+1); i++){
        ll k = i%mod;
        val = val*k;
        val = val%mod;
    }
return val;
}
*/
int main(){
    ll n;
    cin>>n;
    ll sum = 0;
    /*for(ll i=1; i<=n; i++){
        sum = sum + npr(n , i,  i);
        cout<<sum<<endl;
    }*/
    ll k = n;
    if(n%2 == 0){
        k = n/2;
        sum = (k)*(n-1);
    }
    else{
        k = (n-1)/2;
        sum = (k)*(n);
    }
    cout<<sum;



return 0;
}