Problem:
Score : 600 points

Problem Statement

Nagase is a top student in high school. One day, she's analyzing some properties of special sets of positive integers.

She thinks that a set S = \{a_{1}, a_{2}, ..., a_{N}\} of distinct positive integers is called special if for all 1 \leq i \leq N, the gcd (greatest common divisor) of a_{i} and the sum of the remaining elements of S is not 1.

Nagase wants to find a special set of size N. However, this task is too easy, so she decided to ramp up the difficulty. Nagase challenges you to find a special set of size N such that the gcd of all elements are 1 and the elements of the set does not exceed 30000.

Constraints

3 \leq N \leq 20000

Input

Input is given from Standard Input in the following format:

N

Output

Output N space-separated integers, denoting the elements of the set S. S must satisfy the following conditions :

The elements must be distinct positive integers not exceeding 30000.

The gcd of all elements of S is 1, i.e. there does not exist an integer d > 1 that divides all elements of S.

S is a special set.

If there are multiple solutions, you may output any of them. The elements of S may be printed in any order. It is guaranteed that at least one solution exist under the given contraints.

Sample Input 1

3

Sample Output 1

2 5 63

\{2, 5, 63\} is special because gcd(2, 5 + 63) = 2, gcd(5, 2 + 63) = 5, gcd(63, 2 + 5) = 7. Also, gcd(2, 5, 63) = 1. Thus, this set satisfies all the criteria.

Note that \{2, 4, 6\} is not a valid solution because gcd(2, 4, 6) = 2 > 1.

Sample Input 2

4

Sample Output 2

2 5 20 63

\{2, 5, 20, 63\} is special because gcd(2, 5 + 20 + 63) = 2, gcd(5, 2 + 20 + 63) = 5, gcd(20, 2 + 5 + 63) = 10, gcd(63, 2 + 5 + 20) = 9. Also, gcd(2, 5, 20, 63) = 1. Thus, this set satisfies all the criteria.

Solution in Rust (1.15.1) (judge verdict: Wrong Answer)

fn read_line() -> String {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().to_owned()
}

fn reads<T>() -> Vec<T>
where
    T: std::str::FromStr,
    <T as std::str::FromStr>::Err: std::fmt::Debug,
{
    read_line()
        .split_whitespace()
        .map(|w| w.parse().unwrap())
        .collect()
}

fn main() {
    let n: i32 = reads()[0];

    if n == 3 {
        println!("2 5 63");
        return;
    } else if n == 4 {
        println!("2 5 20 63");
        return;
    }

    let mut m2 = 0;
    let mut m3 = 0;
    let mut m6 = 0;

    for i in 2..30001 {
        if i % 6 == 0 {
            m6 += 1;
        } else if i % 2 == 0 {
            m2 += 1;
        } else if i % 3 == 0 {
            m3 += 1;
        }
    }

    let mut u2 = 0;
    let mut u3 = 0;
    let mut u6 = 0;

    u2 += 3;
    m2 -= 3;
    u3 += 2;
    m3 -= 2;

    let mut rest = n - 5;
    if n == 20000 {
        rest -= 2;
    }

    while rest > 0 {
        if m2 >= 3 && rest >= 3 {
            u2 += 3;
            m2 -= 3;
            rest -= 3;
        } else if m3 >= 2 && rest >= 2 {
            u3 += 2;
            m3 -= 2;
            rest -= 2;
        } else if m6 >= 1 {
            u6 += 1;
            m6 -= 1;
            rest -= 1;
        }
    }

    let mut ans = vec![];
    if n == 20000 {
        ans.push(5);
        ans.push(7);
    }

    for i in 2..30001 {
        if i % 6 == 0 && u6 > 0 {
            ans.push(i);
            u6 -= 1;
        } else if i % 2 == 0 && u2 > 0 {
            ans.push(i);
            u2 -= 1;
        } else if i % 3 == 0 && u3 > 0 {
            ans.push(i);
            u3 -= 1;
        }
    }

    for i in 0..ans.len() {
        if i > 0 {
            print!(" ");
        }
        print!("{}", ans[i]);
    }
    println!();
}