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.Text;
using System.Threading.Tasks;
using System.IO;

namespace Contest
{
    class Scanner
    {
        private string[] line = new string[0];
        private int index = 0;
        public string Next()
        {
            if (line.Length <= index)
            {
                line = Console.ReadLine().Split(' ');
                index = 0;
            }
            var res = line[index];
            index++;
            return res;
        }
        public int NextInt()
        {
            return int.Parse(Next());
        }
        public long NextLong()
        {
            return long.Parse(Next());
        }
        public string[] Array()
        {
            line = Console.ReadLine().Split(' ');
            index = line.Length;
            return line;
        }
        public int[] IntArray()
        {
            return Array().Select(int.Parse).ToArray();
        }
        public long[] LongArray()
        {
            return Array().Select(long.Parse).ToArray();
        }
    }

    class Program
    {
        private int N;
        private void Scan()
        {
            var sc = new Scanner();
            N = sc.NextInt();
        }

        public void Solve()
        {
            if (N == 3)
            {
                Console.WriteLine("2 5 63");
                return;
            }
            long sum = 0;
            List<int> ans = new List<int>();
            Scan();
            var p = new int[] { 2, 3, 4, 6 };
            for (int i = 0; ans.Count < N; i++)
            {
                foreach (var j in p)
                {
                    sum += 6 * i + j;
                    ans.Add(6 * i + j);
                    if (ans.Count >= N)
                    {
                        break;
                    }
                }
            }

            switch (sum%6)
            {
                case 2:
                    for (int i = N - 1; i >= 0; i--)
                    {
                        if (ans[i] % 2 == 0)
                        {
                            ans[i] += 4;
                            break;
                        }
                    }
                    break;
                case 3:
                    for (int i = N - 1; i >= 0; i--)
                    {
                        if (ans[i] % 3 == 0)
                        {
                            ans[i] += 3;
                            break;
                        }
                    }
                    break;
                case 5:
                    for (int i = N - 1; i >= 0; i--)
                    {
                        if (ans[i] % 2 == 0)
                        {
                            ans[i] -= 2;
                            break;
                        }
                    }
                    for (int i = N - 1; i >= 0; i--)
                    {
                        if (ans[i] % 3 == 0)
                        {
                            ans[i] -= 3;
                            break;
                        }
                    }
                    break;
            }
         
            Console.WriteLine(string.Join(" ",ans));
        }

        static void Main(string[] args)
        {
            new Program().Solve();
        }
    }
}