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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        sc.close();
        long sum = 0;
        int tmp = 2;
        StringBuilder sb = new StringBuilder();
        ArrayList al = new ArrayList<Integer>();

        if(n == 3){
            System.out.println("2 5 63");
            return;
        }
        if(n == 4){
            System.out.println("2 5 20 63");
            return;
        }
        if(n == 5){
            System.out.println("2 5 30 60 63");
            return;
        }

        for(int i=0; i<n; i++){
            while(true){
                if(tmp%2==0 || tmp%3==0){
                    al.add(tmp);
                    
                    sum += tmp;
                    tmp++;
                    break;
                }
                tmp++;  
            }
        }
        
        if(sum % 6 == 0){

        }else if(sum % 6 == 2){
            al.removeAll(Arrays.asList(new Integer[]{8}));
            al.add(29994);
        }else if(sum % 6 == 3){
            al.removeAll(Arrays.asList(new Integer[]{9}));
            al.add(29994);
        }else if(sum % 6 == 5){
            al.removeAll(Arrays.asList(new Integer[]{9}));
            al.add(29998);
        }

        for(int i=0; i<n; i++){
            sb.append(al.get(i));
            sb.append(" ");       
        }
        System.out.println(new String(sb));
    }
}