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::io::Read;
use std::cmp;

fn main() {
    let mut buf = String::new();

    // 標準入力から全部bufに読み込む
    std::io::stdin().read_to_string(&mut buf);

    // 読み込んだStringを空白で分解する
    let mut iter = buf.split_whitespace();

    // 入力を受け取る
    let n: usize = iter.next().unwrap().parse().unwrap();

    println!("{}", (n * (n - 1)) / 2);
}