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)

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn main() {
    let mut n: usize = read();
    let mut ans: Vec<usize> = vec![2, 3, 25];
    let thirty_times = (1..16).map(|x| x * 30).collect::<Vec<_>>();
    let two_times = (226..15001).map(|x| x * 2).collect::<Vec<_>>();
    let three_times = (75..4995).map(|x| x * 6 + 3).collect::<Vec<_>>();
    let five_times = (15..999).map(|x| x * 30 + 5).collect::<Vec<_>>();

    /*
    println!("{:?}", thirty_times);
    println!("{:?}", two_times.len());
    println!("{:?}", three_times.len());
    println!("{:?}", five_times.len());
    println!("{:?}", (&three_times[0..10], &three_times[0..10].iter().sum::<i32>()));
    */
    n -= 3;

    let two_times_nums = std::cmp::min(two_times.len(), (n / 15) * 15);
    n -= two_times_nums;
    for i in 0..two_times_nums {
        ans.push(two_times[i]);
    }
    let three_times_nums = std::cmp::min(three_times.len(), (n / 10) * 10);
    n -= three_times_nums;
    for i in 0..three_times_nums {
        ans.push(three_times[i] as usize);
    }
    let five_times_nums = std::cmp::min(five_times.len(), (n / 6) * 6);
    n -= five_times_nums;
    for i in 0..five_times_nums {
        ans.push(five_times[i] as usize);
    }
    for i in 0..n {
        ans.push(thirty_times[i] as usize);
    }


    println!("{}", ans.iter().map(|x| x.to_string()).collect::<Vec<_>>().join(" "));
}