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)

#![allow(non_snake_case,unused_imports,dead_code)]
use std::io::Read;
use std::cmp::max;
use std::cmp::min;
use std::str::FromStr;
use std::collections::HashMap;
use std::collections::HashSet;
use std::collections::BinaryHeap;

fn main() {
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();
    let mut buf_it = buf.split_whitespace();

    let N = buf_it.next().unwrap().parse::<usize>().unwrap();
    let mut ans = HashSet::new();
    ans.insert(2);
    ans.insert(3);
    let mut i = 4;
    while ans.len() < N-1{
        if i%2==0 || i%3==0{ans.insert(i);}
        i+=1;
    }
    let S:usize = ans.iter().sum();
    let mut ans2 = ans.iter().map(|&a| a).collect::<Vec<_>>();
    for i in 1..30001{
        if ans.contains(&i) { continue;}
        let mut check = gcd(i,S) > 1;
        for j in 0..N-1{
            if !check { break;}
            check = gcd(ans2[j],S + i - ans2[j]) > 1;
        }
        if check {
            ans2.push(i);
            break;
        }
    }
    println!("{}",ans2.len());
    
    let mut out = String::new();
    for tmp in ans2{
        out += &(tmp.to_string());
        out += " ";
    }
    let l = out.len();
    println!("{}",&out[..l-1]);
    
}

fn gcd(x:usize,y:usize) -> usize{
    if y==0{return x;}
    gcd(y,x%y)
}