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 Rust (1.15.1) (judge verdict: Accepted)

use std::cmp::max;
use std::io;
fn main() {
    let mut buft = String::new();
    io::stdin().read_line(&mut buft).unwrap();
    let n: i64 = buft.trim().parse().unwrap();
    buft.clear();
    let mut ans : i64 = 0;
    // ans += 1;
    ans += (1 + n-1) * (n-1) / 2;
    println!("{}", ans);
}