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>
using namespace std;
const int MOD = 1e9 + 7;
const long long INF = 1e15;

#include <math.h>
#define PI 3.14159265358979323846264338327950L


int Z_algo(string s) {
    int n = s.length();
    vector<int> z(n);
    int L = 0, R = 0;
    for (int i = 1; i < n; i++) {
        if (i > R) {
            L = R = i;
            while (R < n && s[R - L] == s[R]) R++;
            z[i] = R - L; R--;
        }
        else {
            int k = i - L;
            if (z[k] < R - i + 1) z[i] = z[k];
            else {
                L = i;
                while (R < n && s[R - L] == s[R]) R++;
                z[i] = R - L; R--;
            }
        }
    }
    int mx = 0;
    for (int i = 0; i < n; i++) mx = max(mx, min(i, z[i]));
    return mx;
}
const int mxN = 1e9 +7;

int main() {
    long long n;
    cin >> n;
    n--;
    cout << ((n * (n + 1ll)) / 2ll);
    return 0;
}