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: Accepted)


#![allow(non_snake_case)]
fn main() {
    let s = std::io::stdin();
    let mut sc = Scanner { stdin: s.lock() };
    let N:usize = sc.read();
    if N == 3{
        println!("2 5 63");
        return
    }
    if N == 4{
        println!("2 5 20 63");
        return
    }
    let template: Vec< Vec<usize>> = vec![vec![],
                                          vec![3],
                                          vec![0,2],
                                          vec![0,2,3],
                                          vec![0,2,4,6],
                                          vec![0,1,2,3,5],
                                          vec![1,2,3,4,5,7],
                                          vec![0,1,2,3,4,5,6]
    ];
    let mut nums:Vec<usize> = vec![];
    for i in 0..5000{
        nums.push(i*6+2);
        nums.push(i*6+3);
        nums.push(i*6+4);
        nums.push(i*6+6);
    }
    nums.sort();
    let quotient = N/8;
    let remainder = N%8;
    let mut ans:String = "".to_string();
    for i in 0..quotient{
        for j in 0..8{
            ans.push(' ');
            ans.push_str(&nums[i*8+j].to_string());
        }
    }
    for i in 0..remainder{
        ans.push(' ');
        ans.push_str(&nums[quotient*8+template[remainder][i]].to_string());
    }
    println!("{}", ans.trim());
        


}

pub struct Scanner<R> {
    stdin: R,
}

impl<R: std::io::Read> Scanner<R> {
    pub fn read<T: std::str::FromStr>(&mut self) -> T {
        use std::io::Read;
        let buf = self
            .stdin
            .by_ref()
            .bytes()
            .map(|b| b.unwrap())
            .skip_while(|&b| b == b' ' || b == b'\n')
            .take_while(|&b| b != b' ' && b != b'\n')
            .collect::<Vec<_>>();
        unsafe { std::str::from_utf8_unchecked(&buf) }
        .parse()
            .ok()
            .expect("Parse error.")
    }
    pub fn vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read()).collect()
    }
    pub fn chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
}