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)


#[allow(dead_code)]
fn rd() -> String {
    let mut input = String::new();
    std::io::stdin().read_line(&mut input).unwrap();
    input.trim().to_owned()
}

/// 1行の文字を空白で分割してVec<T>にする。
#[allow(dead_code)]
fn rd_vec<T : std::str::FromStr>() -> Vec<T> {
    rd().split_whitespace().map(|x| x.parse().ok().unwrap()).collect()
}

/// 1つの要素を入力で受け取る
#[allow(dead_code)]
fn rd_one<T : std::str::FromStr>() -> T {
    rd().parse().ok().unwrap()
}

/// 複数回read_splitを行う
#[allow(dead_code)]
fn rd_vec_mul<T : std::str::FromStr>(count : i32) -> Vec<Vec<T>> {
    (0..count).map(|_| rd_vec()).collect()
}

/// Vecを1列で出力する
#[allow(dead_code)]
fn op_vec<T : std::fmt::Display>(item : Vec<T>, splitter : char) {
    let cnt = item.len();
    let mut c = 0;
    for i in item.iter() {
        c+=1;
        if cnt > c {print!("{}{}", i, splitter);} else {println!("{}", i);}
    }
}

fn main() {
    let input : i64 = rd_one();
    let answer : i64 = input * (input - 1) / 2;
    
    println!("{}", answer);
}