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++ (GCC 9.2.1) (judge verdict: Accepted)

#include<bits/stdc++.h>

#define IOS ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define endl "\n"
#define ll long long
#define pii pair<int,int>
#define all(x) begin(x), end(x)
#define loop(i,n) for(int i=0; i<n; i++)
#define rep(i,a,b,c) for(int i=a; i<b; i+=c)
#define brep(i,a,b,c) for(int i=a; i>b; i-=c)
#define tc(t) int t; cin>>t; while(t--)
#define sz(v) int((v).size())
#define pb push_back

const int maxm = 1000000000 + 7;


using namespace std;


int main()
{

#ifndef ONLINE_JUDGE
	freopen("input.txt", "r", stdin);
	freopen("output.txt", "w", stdout);
#endif

	ll n;
	cin>>n;

	cout<<n*(n-1)/2<<endl;





}