Problem:
Score: 400 points

Problem Statement

Print a sequence a_1, a_2, ..., a_N whose length is N that satisfies the following conditions:

a_i (1 \leq i \leq N) is a prime number at most 55 555.

The values of a_1, a_2, ..., a_N are all different.

In every choice of five different integers from a_1, a_2, ..., a_N, the sum of those integers is a composite number.

If there are multiple such sequences, printing any of them is accepted.

Notes

An integer N not less than 2 is called a prime number if it cannot be divided evenly by any integers except 1 and N, and called a composite number otherwise.

Constraints

N is an integer between 5 and 55 (inclusive).

Input

Input is given from Standard Input in the following format:

N

Output

Print N numbers a_1, a_2, a_3, ..., a_N in a line, with spaces in between.

Sample Input 1

5

Sample Output 1

3 5 7 11 31

Let us see if this output actually satisfies the conditions.

First, 3, 5, 7, 11 and 31 are all different, and all of them are prime numbers.

The only way to choose five among them is to choose all of them, whose sum is a_1+a_2+a_3+a_4+a_5=57, which is a composite number.

There are also other possible outputs, such as 2 3 5 7 13, 11 13 17 19 31 and 7 11 5 31 3.

Sample Input 2

6

Sample Output 2

2 3 5 7 11 13

2, 3, 5, 7, 11, 13 are all different prime numbers.

2+3+5+7+11=28 is a composite number.

2+3+5+7+13=30 is a composite number.

2+3+5+11+13=34 is a composite number.

2+3+7+11+13=36 is a composite number.

2+5+7+11+13=38 is a composite number.

3+5+7+11+13=39 is a composite number.

Thus, the sequence 2 3 5 7 11 13 satisfies the conditions.

Sample Input 3

8

Sample Output 3

2 5 7 13 19 37 67 79

Solution in C# (.NET Core 3.1.201) (judge verdict: Wrong Answer)

using System;
using System.Numerics;
using System.Linq;
using System.Collections.Generic;
using System.Text;
using System.Collections;

namespace debug
{
    class main
    {
        static void Main(string[] args)
        {
            //問題クラスを展開
            ProgramD a = new ProgramD();
            a.main();//実行する

        }

    }

    //ABC097
    class ProgramA
    {
        public void main()
        {
            //入力
            string[] s = Console.ReadLine().Split(' ');
            int a = int.Parse(s[0]);
            int b = int.Parse(s[1]);
            int c = int.Parse(s[2]);
            int d = int.Parse(s[3]);


            if (Math.Abs(a-b)<= d && Math.Abs(c - b) <= d)
                Console.WriteLine("Yes");
            else if(Math.Abs(c - a) <= d)
                Console.WriteLine("Yes");
            else
                Console.WriteLine("No");

        }
    }

    class ProgramB
    {
        public void main()
        {
            //入力
            int x = int.Parse(Console.ReadLine());

            for (int i = x; i > 0; i--)
            {
                for(int j = 2; j <= Math.Sqrt(x);j++)
                {
                    if(i % j == 0)
                    {
                        int t = i;
                        while (t % j == 0)
                            t /= j;

                        if(t == 1)
                        {
                            Console.WriteLine(i);
                            return;
                        }
                    }
                }

            }


            Console.WriteLine(1);
        }

        
    }

    class ProgramC
    {
        public void main()
        {

            //入力
            string s = Console.ReadLine();
            int k = int.Parse(Console.ReadLine());

            List<string> ans = new List<string>();

            //kが5文字以下が答えの候補なので入れて考えてみる
            for(int j = 1; j <= 5;j++)
                for (int i = 0;i < s.Length + 1 - j;i++)
                {
                    if(!ans.Contains(s.Substring(i, j)))
                        ans.Add(s.Substring(i, j));
                }
            
            //ソートする
            ans.Sort();

            //答え出力
            Console.WriteLine(ans[k -1]);

        }

        
    }



    class ProgramD
    {
        public void main()
        {

            //入力
            int n = int.Parse(Console.ReadLine());

            List<int> a = new List<int>(230);

            for (int i = 0; i < 1000; i++)
                a.Add(i + 2);

            //Union-find
            for(int i = 2;i <= Math.Sqrt(1000);i++)
            {
                List<int> t = new List<int>(1000);
                foreach (var s in a)
                {
                    if (s % i == 0)
                        t.Add(s);
                }

                foreach (var s in t)
                {
                    a.Remove(s);
                }


            }
            //要素数-1を足し合わせる。（前のところで友だちは除いているので友だち候補のみ残る）
            for (int i = 0; i < n; i++)
            {
                //答
                Console.Write(a[i] + " ");
            }


            
        }
    }

    


}