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.Collections.Generic;
using System.Linq;
using System.IO;
using System.Text;
using static System.Math;
using static System.Array;
using static AtCoder.Tool;
namespace AtCoder
{
    class AC
    {
        const int MOD = 1000000007;
        const int INF = int.MaxValue / 2;
        const long SINF = long.MaxValue / 2;
        const double EPS = 1e-8;
        static readonly int[] dx = { 0, 1, 0, -1 };
        static readonly int[] dy = { 1, 0, -1, 0 };
        //static List<List<int>> G = new List<List<int>>();
        //static List<List<Edge>>G = new List<List<Edge>>();
        //static List<Edge> E = new List<Edge>();
        static void Main(string[] args)
        {
            //var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            //Console.SetOut(sw);
            var cin = new Scanner();

            var N = int.Parse(Console.ReadLine());
            if (N == 3) { Console.WriteLine("2 5 63");return; }
            var D2 = new List<Queue<int>>();
            for (var i = 0; i < 3; i++) D2.Add(new Queue<int>());
            var D3 = new Queue<int>();
            for(var k = 30000; k >= 2; k--)
            {
                if (k % 2 == 0)
                {
                    D2[k % 3].Enqueue(k);
                }
                else if (k % 3 == 0) { D3.Enqueue(k); }
            }
            var ans = new List<int>();
            int res = 20000 - N;
            //Console.WriteLine(res);
            int de = Min(4998, res - (res % 2));
            for (var i = 0; i < de; i++)
            {
                D3.Dequeue();
            }
            res -= de;
            //Console.WriteLine(res);
            int rem = res % 3;
            res = Max(0, (res - rem) / 3);
            //Console.WriteLine($"{res} {rem}");
            for(var i = 0; i < res; i++)
            {
                foreach(var q in D2) { q.Dequeue(); }
            }
            if (rem == 1) { D2[0].Dequeue(); }
            else if (rem == 2) { D2[1].Dequeue();D2[2].Dequeue(); }
            foreach(var q in D2)
            {
                foreach(var k in q)
                {
                    ans.Add(k);
                }
            }
            foreach (var k in D3) { ans.Add(k); }

            /*Func<int, int, int> gcd = null;
            gcd = (a, b) =>
            {
                int A = Max(a, b);
                int B = Min(a, b);
                if (B == 0) { return A; }
                if (A % B == 0) { return B; }
                return gcd(B, A % B);
            };
            ans.Sort();
            int g = 0;
            for(var i = 0; i < ans.Count(); i++)
            {
                g = gcd(g, ans[i]);
            }
            Console.WriteLine($"{g} {ans.Count()} {ans.Max()}");
            Console.Write($"{ans.Count(x => x % 3 == 0 && x % 2 != 0)} ");
            Console.Write($"{ans.Count(x => x % 2 == 0 && x % 3 == 0) % 3} ");
            Console.Write($"{ans.Count(x => x % 2 == 0 && x % 3 == 1) % 3} ");
            Console.Write($"{ans.Count(x => x % 2 == 0 && x % 3 == 2) % 3} \n");*/
            Console.WriteLine(string.Join(" ", ans));

            //Console.Out.Flush();
        }
        
        struct Edge
        {
            public int from;

            public int to;
            public long dist;
            public Edge(int t, long c)
            {
                from = -1;
                to = t;
                dist = c;
            }
            public Edge(int f, int t, long c)
            {
                from = f;
                to = t;
                dist = c;
            }

        }
    }
    public class Scanner
    {
        public int[] ReadSplitInt()
        {
            return ConvertAll(Console.ReadLine().Split(), int.Parse);
        }
        public long[] ReadSplitLong()
        {
            return ConvertAll(Console.ReadLine().Split(), long.Parse);
        }
        public double[] ReadSplit_Double()
        {
            return ConvertAll(Console.ReadLine().Split(), double.Parse);
        }
    }
    public static class Tool
    {
        static public void Initialize<T>(ref T[] array, T initialvalue)
        {
            for (var i = 0; i < array.Length; i++)
            {
                array[i] = initialvalue;
            }
        }
        static public void Swap<T>(ref T a, ref T b)
        {
            T keep = a;
            a = b;
            b = keep;
        }

        static public void Display<T>(T[,] array2d, int n, int m)
        {
            for (var i = 0; i < n; i++)
            {
                for (var j = 0; j < m; j++)
                {
                    Console.Write($"{array2d[i, j]} ");
                }
                Console.WriteLine();
            }
        }

        static public long LPow(int a, int b)
        {
            return (long)Pow(a, b);
        }
    }
}