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: Wrong Answer)

#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define pb push_back
#define F first
#define S second
#define all(x) x.begin(),x.end()
#define maxi 1e18
#define pll pair<ll,ll>
map<ll,ll> pos,pos1;
int main(){
   /*ll a,b;
    cin>>a>>b; //ll giv=a;
    //ll ans;
    ll ans=0,giv=0;
    while(giv+a<b){
        giv+=a-1;
        ans++;
    }
    cout<<ans+1;*/
    ll n;
    cout<<n*(n-1)/2;
}