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)

use std::io::*;
use std::str::FromStr;

fn main() {
    let n: usize = read();

    let mut ans: Vec<usize> = 
        match n {
            3 => vec![2, 5, 63],
            4 => vec![2, 5, 20, 63],
            5 => vec![2, 5, 20, 30, 63],
            _ => Vec::new(),
        };

    if n > 5 {
        let po = [2, 3, 4, 6];
        let mut cnt = 0;
        let mut bai = 0;
        while cnt < n {
            let kiso = 6 * bai;
            for i in 0..4 {
                ans.push(kiso + po[i]);
                cnt += 1;
                if cnt == n {
                    break;
                }
            }
            bai += 1;
        }
        let mut sum = 0;
        for i in 0..n {
            sum += ans[i];
        }
        match sum % 6 {
            2 => {
                for i in 0..n {
                    if ans[i] == 8 {
                        ans[i] = (bai-1) * 6 + 6;
                    }
                }
            },
            3 => {
                for i in 0..n {
                    if ans[i] == 9 {
                        ans[i] = (bai-1) * 6 + 6;
                    }
                }
            },
            5 => {
                for i in 0..n {
                    if ans[i] == 9 {
                        ans[i] = (bai-1) * 6 + 4;
                    }
                }
            },
            _ => {},
        }
    }

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

fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.unwrap() as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().unwrap()
}