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: Wrong Answer)

using System;
using System.Collections.Generic;

namespace ABC
{
    class ABC096D
    {
        public static int N = 0;
        static void Main(string[] args)
        {
            N = int.Parse(Console.ReadLine());//長さ

            var ans = findArray();

            ans.Sort();
            for (int i = 0; i < ans.Count-1; ++i) {
                Console.Write("{0} ",ans[i]);
            }
            Console.WriteLine(ans[ans.Count - 1]);
        }

        static List<int> findArray()
        {
            var ans = new List<int>(N);

            int mem = 0;
            while (true)
            {
                ans.Clear();
                //数列作成
                {
                    for (int i = mem; i < 55555; ++i)
                    {
                        if (isPrime(i) == true)
                        {
                            ans.Add(i);
                            if (ans.Count == N) break;
                        }
                    }
                    //ans.Add(2);
                    //ans.Add(3);
                    //ans.Add(5);
                    //ans.Add(7);
                    //ans.Add(11);
                    //ans.Add(13);
                    ////ans.Add(31);
                }


                //判定
                {
                    if (checkCondition(ans) == true)
                    {
                        break;
                    }
                    else
                    {
                        ;//答えではない
                        mem = ans[ans.Count - 1];
                    }
                }
            }

            return ans;
        }

        static bool checkCondition(List<int> ary)
        {
            var _subAry = new List<int>(5) { 0,0,0,0,0 };

            for (int i0 = 0; i0 < ary.Count; ++i0)
            {
                _subAry[0] = ary[i0];
                for (int i1 = i0+1; i1 < ary.Count; ++i1)
                {
                    _subAry[1] = ary[i1];
                    for (int i2 = i1 + 1; i2 < ary.Count; ++i2)
                    {
                        _subAry[2] = ary[i2];
                        for (int i3 = i2 + 1; i3 < ary.Count; ++i3)
                        {
                            _subAry[3] = ary[i3];
                            for (int i4 = i3 + 1; i4 < ary.Count; ++i4)
                            {
                                _subAry[4] = ary[i4];
                                if(isSumPrime(_subAry) == true)
                                {
                                    return false;
                                }
                            }
                        }
                    }
                }
            }
            return true;
        }

        static bool isSumPrime(List<int> x)
        {
            int sum = x[0] + x[1] + x[2] + x[3] + x[4];
            return isPrime(sum);
        }

        static bool isPrime(int x)
        {
            int max = (int)Math.Sqrt(x);
            for(int i = 2; i < max+1; ++i)
            {
                if(x % i == 0)
                {
                    return false;
                }
            }
            return true;
        }
    }
}