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>
#define rep(i,n) for(int i=0;i<n;i++)
#define FOR(i,start,end) for(int i=start;i<=end;i++)
const int INF = 1001001001;
typedef long long ll;
const ll MOD=1000000007;
using namespace std;
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }
template<class T>auto MAX(const T& a) { return *max_element(a.begin(),a.end()); }
template<class T>auto MIN(const T& a) { return *min_element(a.begin(),a.end()); }
template<class T, class U>U SUM(const T& a, const U& v) { return accumulate(a.begin(),a.end(), v); }
template<class T, class U>U COUNT(const T& a, const U& v) { return count(a.begin(),a.end(), v); }
template<class T, class U>int LOWER(const T& a, const U& v) { return lower_bound(a.begin(),a.end(), v) - a.begin(); }
template<class T, class U>int UPPER(const T& a, const U& v) { return upper_bound(a.begin(),a.end(), v) - a.begin(); }
int GCD(int a, int b) { return b ? GCD(b, a%b) : a; }
int LCM(int a, int b) { int g = GCD(a, b); return a / g * b; }

int main(void){
    // Your code here!
    int n;
    cin >> n;
    int res = n*(n-1)/2;
    if (n>2)cout << res << endl;
    else if (n == 2) cout << 1 << endl;
    else cout << 0 << endl;
}