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: Runtime Error)

use std::io;

fn main() {
    let mut s = String::new();
    io::stdin().read_line(&mut s).ok();
    let n: i32 = s.trim().parse().ok().unwrap();
    let mut v: Vec<i32> = Vec::new();
    for i in 1..(n+1) {
        v.push(i);
    }

    let mut m: Vec<i32> = Vec::new();
    m.push(v[v.len()-1]);
    let mut t: Vec<i32> = v.clone().into_iter().map(|i| i-1).collect();
    m.append(&mut t[1..].to_vec());

    let mut ans: i32 = 0;

    for i in 0..(m.len()) {
        ans += m[i] % v[i];
    }

    println!("{}", ans);
}