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>
using namespace std;

#define IOS ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define ll long long
#define vi vector<ll>
#define sll(x) scanf("%lld",&x)
#define prll(x) printf("%lld ",x)
#define pri(x) printf("%d ",x)
#define si(x) scanf("%d",&x)
#define el printf("\n")
#define pb push_back
#define f first
#define s second
#define arrondi(a) (long long)floor(a+0.5);
#define NIL -1
ll N=500005;
ll MAX=9223372036854775807;
ll MOD=1000000007;
long double PI =4*atan(1);

int main()
{
	IOS;
    cout.precision(30);
    ll n,m,k,a,b,c,x,y; string s,t;
    cin >> n;
    cout << n*(n-1)/2;
    return 0;
}