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# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ABC96_D
{
    public static class Combination
    {
        public static IEnumerable<T[]> Enumerate<T>(IEnumerable<T> items, int k, bool withRepetition)
        {
            if (k == 1)
            {
                foreach (var item in items)
                    yield return new T[] { item };
                yield break;
            }
            foreach (var item in items)
            {
                var leftside = new T[] { item };

                // item よりも前のものを除く （順列と組み合わせの違い)
                // 重複を許さないので、unusedから item そのものも取り除く
                var unused = withRepetition ? items : items.SkipWhile(e => !e.Equals(item)).Skip(1).ToList();

                foreach (var rightside in Enumerate(unused, k - 1, withRepetition))
                {
                    yield return leftside.Concat(rightside).ToArray();
                }
            }
        }
    }
    class Program
    {
        public static class Combination
        {
            public static IEnumerable<T[]> Enumerate<T>(IEnumerable<T> items, int k, bool withRepetition)
            {
                if (k == 1)
                {
                    foreach (var item in items)
                        yield return new T[] { item };
                    yield break;
                }
                foreach (var item in items)
                {
                    var leftside = new T[] { item };

                    // item よりも前のものを除く （順列と組み合わせの違い)
                    // 重複を許さないので、unusedから item そのものも取り除く
                    var unused = withRepetition ? items : items.SkipWhile(e => !e.Equals(item)).Skip(1).ToList();

                    foreach (var rightside in Enumerate(unused, k - 1, withRepetition))
                    {
                        yield return leftside.Concat(rightside).ToArray();
                    }
                }
            }
        }
        static IEnumerable<int> Primes(int maxnum)
        {
            yield return 2;
            yield return 3;
            var sieve = new BitArray(maxnum + 1);
            int squareroot = (int)Math.Sqrt(maxnum);
            for (int i = 2; i <= squareroot; i++)
            {
                if (sieve[i] == false)
                {
                    for (int n = i * 2; n <= maxnum; n += i)
                        sieve[n] = true;
                }
                for (int n = i * i + 1; n <= maxnum && n < (i + 1) * (i + 1); n++)
                {
                    if (!sieve[n])
                        yield return n;
                }
            }
        }


        public static long[] comb(int[] b)
        {
            var ret = new long[5];

            for (int i = 0; i < b.Length; i++)
            {
                for (int j = 0; j < b.Length; j++)
                {

                }
            }

            return ret;
        }

        static void Main(string[] args)
        {

            var n = int.Parse(Console.ReadLine());

            var a = new int[n];

            a[0] = 2;
            a[1] = 3;
            a[2] = 5;
            a[3] = 7;
            a[4] = 11;

            for (int i = 5; i < n; i++)
            {
                var nums = Enumerable.Range(1, i).ToArray();
                var comb = Combination.Enumerate(nums, 4, false);
                var ss = new List<long>();
                foreach (var item in comb)
                {
                    //Console.WriteLine(String.Join(",", item.Select(x => x.ToString())));
                    ss.Add(a[item[0] - 1] + a[item[1] - 1] + a[item[2] - 1] + a[item[3] - 1]);
                }
                foreach (var j in Primes(55555))
                {
                    if (a[i - 1] < j)
                    {
                        var count = 0;
                        foreach (long item in ss)
                        {
                            for (int l = 2; l < item + j; l++)
                            {
                                if ((item + j) % l == 0)
                                {
                                    count++;
                                    break;
                                }
                            }

                        }
                        if (count == ss.Count)
                        {
                            a[i] = j;
                            break;
                        }
                    }
                    //if (a[i] < j && ) ;

                }
                //next:;

            }

            Console.WriteLine(String.Join(" ", a.Select(x => x.ToString()).ToArray()));
        }
    }
}