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 sp <<" "
#define el <<"\n"
#define S second
#define F first
#define mp make_pair
#define pb push_back
#define pf push_front
#define pob pop_back
#define obit __builtin_popcount
#define pof pop_front
#define mod (int)1e9 + 7
#define For(i,a,n) for(i=a;i<n;i++)

using namespace std;

typedef long long ll;
typedef unsigned long long ul;
typedef unsigned short int us;
typedef short int ss;
typedef long double ld;

int main(){
    ios_base::sync_with_stdio(0);
    cin.tie(NULL);
    /*
#ifndef ONLINE_JUDGE
    freopen("input.txt","r",stdin);
    freopen("output.txt","w",stdout);
#endif
    //*/
    ll a;
    cin>>a;
    cout<<(a*(a-1))/2;
    return 0;
}