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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Web;

namespace Competitive
{
    internal class Solution
    {
        public int N;
        public void Run()
        {
            int[] A3 = new int[] { 2, 5, 63 };
            int[] A4 = new int[] { 2, 5, 20, 63 };
            int[,] V = new int[,]
            {   { 2, 3,4,6,8,9,10,12 },
                { 6, 0,0,0,0,0,0,0 },
                { 2, 4,0,0,0,0,0,0 },
                { 2, 4,6,0,0,0,0,0 },
                { 2, 4,6,12,0,0,0,0 },
                { 2, 3,4,6,9,0,0,0 },
                { 2, 3,4,8,9,10,0,0 },
                { 2, 3,4,6,8,9,10,0 }
            };

            N = Input.ReadInt();
            if (N == 3)
            {
                Console.WriteLine(string.Join(" ", A3));
            }
            else if (N == 4)
            {
                Console.WriteLine(string.Join(" ", A4));
            }
            else
            {
                List<int> ret = new List<int>();
                int C = N / 6;
                int M = N % 6;
                for (int i = 0; i < C; i++)
                {
                    for(int j = 0; j < 8; j++)
                        ret.Add(V[0, j] + 12 * i);
                }

                {
                    for (int j = 0; j < 8; j++)
                    {
                        int v = V[M, j];
                        if (v != 0)
                            ret.Add(v + 12 * C);
                    }
                }

                Console.WriteLine(string.Join(" ", ret));   
            }
        }
    }

    // libs ----------


    // common ----------

    internal static class Input
    {
        public static string ReadString()
        {
            string line = Console.ReadLine();
            return line;
        }

        public static int ReadInt()
        {
            string line = Console.ReadLine();
            return int.Parse(line);
        }

        public static int[] ReadIntArray()
        {
            string line = Console.ReadLine();
            return line.Split(' ').Select(int.Parse).ToArray();
        }

        public static long ReadLong()
        {
            string line = Console.ReadLine();
            return long.Parse(line);
        }

        public static long[] ReadLongArray()
        {
            string line = Console.ReadLine();
            return line.Split(' ').Select(long.Parse).ToArray();
        }

        public static double[] ReadDoubleArray()
        {
            string line = Console.ReadLine();
            return line.Split(' ').Select(double.Parse).ToArray();
        }
    }

    internal class Program
    {
        public static void Main(string[] args)
        {
            var s = new Solution();
            s.Run();
        }
    }
}