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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Linq;//リストの使用
using System.Collections.Generic;
class Program
{
	static void Main()
	{
		long n = long.Parse(Console.ReadLine());
    long[] answer = new long[n];
    long sumMemo = 0;
    string answerMemo = "";
    
    if(n == 3) Console.WriteLine("2 5 63");
    else if(n == 4) Console.WriteLine("2 5 20 63");
    else if(n == 5) Console.WriteLine("2 5 20 30 63");
    else
    {
      for(long i = 0; i < n; i++)
      {
      long memo = i/4;
        if(i%4 == 0) answer[i] = 6*memo+2;
        if(i%4 == 1) answer[i] = 6*memo+3;
        if(i%4 == 2) answer[i] = 6*memo+4;
        if(i%4 == 3) answer[i] = 6*memo+6;
      sumMemo += answer[i];
      }
      if(sumMemo%6 == 2) answer[4] = 30000;
      if(sumMemo%6 == 3) answer[5] = 30000;
      if(sumMemo%6 == 5) answer[5] = 29998;

      answerMemo = answer[0].ToString();
      for(long i = 1; i < n; i++)
      {
        answerMemo += " "+answer[i].ToString();
      }
      Console.WriteLine(answerMemo);
    }
	}
}