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.Scanner;

class Solver{
	Scanner sc =new Scanner(System.in);
	
	
	void run(){
		int n = sc.nextInt();
		
		int[] ans = new int[n];
		int count = 64;
		ans[0] = 2;
		ans[1] = 5;
		ans[2] = 63;
		
		long sum = 0;
		for(int i = 3;i < n-1; i++){
			for(;count % 2 != 0 && count % 5 != 0 && count % 3 != 0;count++){}
			ans[i] = count;
			sum += count;
			count++;
		}
		
		if(n > 3){
			ans[n-1] = (count / 30 + 2) * 30 - (int)(sum%30);
		}
		for(int i = 0;i < n-1; i++){
			System.out.print(ans[i]);
			System.out.print(" ");
		}
		System.out.println(ans[n-1]);

		
	}
}

public class Main {
	public static void main(String[] args){
		Solver s  = new Solver();
		s.run();
	}
}