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;
using System.Linq;
using System.Linq.Expressions;

class Program{

    const long MOD =1000000007;

    static void Main(string[] args)
    {
        // main ↓
        // 6k + 1 && prime -> absolutely OK
        int n = ScanOneInt();
        int cnt = 0;
        for (int i = 1; 6*i+1 <= 55555; i++)
        {
            if (isPrime(6*i+1))
            {
                Console.Write((6 * i + 1) + " ");
                cnt++;
            }
            if(cnt == n)
            {
                Console.WriteLine("");
                break;
            }
        }
        // main↑
    }
    
    

    static T[] Ruiseki<T>(T[] array)
    {
        // i 番目の要素までの累積和 -> r[i]
        // 0 r[0] r[0] + r[1]... と続く
        T[] res = new T[array.Length];
        for (int i = 0; i < array.Length; i++)
        {
            if (i==0)
            {
                res[i] = array[i];
            }
            else
            {
                res[i] = (dynamic)res[i - 1] + (dynamic)array[i];
            }
        }
        return res;
    }

    static T[] RuisekiRev<T>(T[] array)
    {
        T[] res = new T[array.Length];
        for (int i = array.Length-1; i >= 0; i--)
        {
            if (i == array.Length-1)
            {
                res[i] = array[i];
            }
            else
            {
                res[i] = (dynamic)res[i + 1] + (dynamic)array[i];
            }
        }
        return res;
    }

    static int Nibutan(long[] array, long k)
    {
        int low = 0 ;
        int high = array.Length-1;
        int mid = high;

        while (low < high)
        {
            mid = (low + high) / 2;
            if(array[mid] >= k) // k以上の最小index.ココを変えるだけ
            {
                high = mid;
            }
            else
            {
                low = mid + 1;
            }
            mid = (low + high) / 2;
        }
        return mid;
    }   

    static int ScanOneInt()
    {
        return int.Parse(Console.ReadLine());
    }

    static long ScanOneLong()
    {
        return long.Parse(Console.ReadLine());
    }

    static string[] ScanStringArray(int lines)
    {
        string[] str = new string[lines];
        for (int i = 0; i < lines; i++)
        {
            str[i] = Console.ReadLine();
        }
        return str;
    }

    static int[] ScanIntArray(int t)
    {
        string[] str = Console.ReadLine().Split(' ');
        int[] ar = new int[t];
        for (int i = 0; i < t; i++)
        {
            ar[i] = int.Parse(str[i]);
        }
        return ar;
    }

    static string[] ScanStringArrayInOneLine(int t)
    {
        string[] str = Console.ReadLine().Split(' ');
        return str;
    }

    static Tuple<int,int> ScanTuple()
    {
        int[] tmp = ScanIntArray(2);
        return new Tuple<int, int>(tmp[0], tmp[1]);
    }

    static long[] ScanLongArray(int t)
    {
        string[] str = Console.ReadLine().Split(' ');
        long[] ar = new long[t];
        for (int i = 0; i < t; i++)
        {
            ar[i] = long.Parse(str[i]);
        }
        return ar;
    }

    static double[] ScanDoubleArray(int t)
    {
        string[] str = Console.ReadLine().Split(' ');
        double[] ar = new double[t];
        for (int i = 0; i < t; i++)
        {
            ar[i] = double.Parse(str[i]);
        }
        return ar;
    }

    static int[,] ScanIntSquareArray(int h, int w)
    {
        int[,] resAr = new int[h, w];
        for (int i = 0; i < h; i++)
        {
            int[] ar = ScanIntArray(w);
            for (int j = 0; j < w; j++)
            {
                resAr[i, j] = ar[j];
            }
        }
        return resAr;
    }

    static int[,] CombModMake()
    {
        int[,] res = new int[2005, 2005];
        for (int i = 0; i < 2005; i++)
        {
            for (int j = 0; j < 2005; j++)
            {
                if (i == 0 || i < j)
                {
                    res[i, j] = 0;
                }
                else if (j == 0 || i == j)
                {
                    res[i, j] = 1;
                }
                else
                {
                    res[i, j] = (res[i - 1, j] + res[i - 1, j - 1]) % (int)MOD;
                }
            }
        }
        return res;
    }

    // int, long両方で出来るGCDを作った
    static T GCD<T>(T a, T b)
    {
        if((dynamic)a % (dynamic)b == 0)
        {
            return b;
        }
        else
        {
            return GCD((dynamic)b, (dynamic)a % (dynamic)b);
        }
    }

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


public class Pair<T,U>: IComparable where T : IComparable<T> where U: IComparable<U>
{
    public T Item1;
    public U Item2;

    public int  CompareTo(object obj)
    {
        Pair<T,U> pair = (Pair<T, U>)obj;
        return Item1.CompareTo(pair.Item1);
    }
    public Pair(T t, U u)
    {
        Item1 = t;
        Item2 = u;
    }

}

// 計算量: Push -> O(logN), Peek -> O(1)。Clear() -> O(logN)
// ToArray()で配列化
public class PriorityQueue<T> where T : IComparable
{
    private IComparer<T> _comparer = null;
    private int _type = 0;
    private T[] _heap;
    private int _sz = 0;
    private int _count = 0;

    /// <summary>
    /// Priority Queue with custom comparer
    /// </summary>
    public PriorityQueue(int maxSize, IComparer<T> comparer)
    {
        _heap = new T[maxSize];
        _comparer = comparer;
    }

    /*
     -> Item: _heap(ヒープを持つ.sizeはmaxSize)
     -> Item: _type -> 0:asc(昇順), 1:desc(降順)
     */
    public PriorityQueue(int maxSize, int type = 0)
    {
        _heap = new T[maxSize];
        _type = type;
    }

    private int Compare(T x, T y)
    {
        if (_comparer != null) return _comparer.Compare(x, y);
        return _type == 0 ? x.CompareTo(y) : y.CompareTo(x);
        // typeが0なら昇順, 1なら降順にソートするCompare
    }

    public void Push(T x)
    {
        _count++;

        //node number
        var i = _sz++;

        while (i > 0)
        {
            //parent node number
            var p = (i - 1) / 2;
            if (Compare(_heap[p], x) <= 0) break;
            _heap[i] = _heap[p];
            i = p;
        }

        _heap[i] = x;
    }

    public T Pop()
    {
        _count--;

        T ret = _heap[0];
        T x = _heap[--_sz];

        int i = 0;
        while (i * 2 + 1 < _sz)
        {
            //children
            int a = i * 2 + 1;
            int b = i * 2 + 2;

            if (b < _sz && Compare(_heap[b], _heap[a]) < 0) a = b;

            if (Compare(_heap[a], x) >= 0) break;

            _heap[i] = _heap[a];
            i = a;
        }

        _heap[i] = x;

        return ret;
    }

    public int Count()  // O(1)
    {
        return _count;
    }

    public T Peek() // O(1)
    {
        return _heap[0];
    }

    public bool Contains(T x)   // O(N)なので注意
    {
        for (int i = 0; i < _sz; i++) if (x.Equals(_heap[i])) return true;
        return false;
    }

    public void Clear()
    {
        while (Count() > 0) Pop();
    }

    public IEnumerator<T> GetEnumerator() // なにこれ
    {
        var ret = new List<T>();

        while (Count() > 0)
        {
            ret.Add(Pop());
        }

        foreach (var r in ret)
        {
            Push(r);
            yield return r;
        }
    }

    public T[] ToArray()
    {
        T[] array = new T[_sz];
        int i = 0;

        foreach (var r in this)
        {
            array[i++] = r;
        }

        return array;
    }
}

public class GenericOperation<T>
{
    public GenericOperation()
    {
        var availableT = new Type[]
        {
            typeof(int), typeof(uint), typeof(short), typeof(ushort), typeof(long), typeof(ulong), typeof(byte),
            typeof(decimal), typeof(double)
        };
        if (!availableT.Contains(typeof(T)))
        {
            throw new NotSupportedException();
        }
        var p1 = Expression.Parameter(typeof(T));
        var p2 = Expression.Parameter(typeof(T));
        Add = Expression.Lambda<Func<T, T, T>>(Expression.Add(p1, p2), p1, p2).Compile();
        Subtract = Expression.Lambda<Func<T, T, T>>(Expression.Subtract(p1, p2), p1, p2).Compile();
        Multiply = Expression.Lambda<Func<T, T, T>>(Expression.Multiply(p1, p2), p1, p2).Compile();
        Divide = Expression.Lambda<Func<T, T, T>>(Expression.Divide(p1, p2), p1, p2).Compile();
        Modulo = Expression.Lambda<Func<T, T, T>>(Expression.Modulo(p1, p2), p1, p2).Compile();
        Equal = Expression.Lambda<Func<T, T, bool>>(Expression.Equal(p1, p2), p1, p2).Compile();
        GreaterThan = Expression.Lambda<Func<T, T, bool>>(Expression.GreaterThan(p1, p2), p1, p2).Compile();
        GreaterThanOrEqual = Expression.Lambda<Func<T, T, bool>>(Expression.GreaterThanOrEqual(p1, p2), p1, p2).Compile();
        LessThan = Expression.Lambda<Func<T, T, bool>>(Expression.LessThan(p1, p2), p1, p2).Compile();
        LessThanOrEqual = Expression.Lambda<Func<T, T, bool>>(Expression.LessThanOrEqual(p1, p2), p1, p2).Compile();
    }

    public Func<T, T, T> Add { get; private set; }
    public Func<T, T, T> Subtract { get; private set; }
    public Func<T, T, T> Multiply { get; private set; }
    public Func<T, T, T> Divide { get; private set; }
    public Func<T, T, T> Modulo { get; private set; }
    public Func<T, T, bool> Equal { get; private set; }
    public Func<T, T, bool> GreaterThan { get; private set; }
    public Func<T, T, bool> GreaterThanOrEqual { get; private set; }
    public Func<T, T, bool> LessThan { get; private set; }
    public Func<T, T, bool> LessThanOrEqual { get; private set; }
}

class Segtree<T>
{
    int n;
    T[] tree;
    Func<T, T, T> f;
    T exnum;
    public Segtree(int m, Func<T, T, T> f, T ex)
    {
        this.f = f;
        exnum = ex;
        n = 1;
        while (n < m) n <<= 1;  // resize calc
        tree = new T[(n << 1) - 1]; // resize
        for (int i = 0; i < tree.Length; i++) tree[i] = ex; // init
    }
    public Segtree(int m, T ini, Func<T, T, T> f, T ex) : this(m, f, ex)
    {
        for (int i = 0; i < m; ++i) tree[i + n - 1] = ini;
        All_update();
    }
    public void Assign_without_update(int j, T x)
    {
        tree[j + n - 1] = x;
    }
    public void Update(int j, T x)
    {
        int i = j + n - 1;
        tree[i] = x;
        while (i > 0)
        {
            i = (i - 1) >> 1;
            tree[i] = f(tree[(i << 1) + 1], tree[(i << 1) + 2]);
        }
    }
    public void All_update()
    {
        for (int i = n - 2; i >= 0; i--)
            tree[i] = f(tree[(i << 1) + 1], tree[(i << 1) + 2]);
    }
    public T Look(int i) { return tree[i + n - 1]; }

    // [s, t)
    public T Run(int s, int t) { return Query(s, t, 0, 0, n); }
    T Query(int s, int t, int k, int l, int r)
    {
        if (r <= s || t <= l) return exnum;
        if (s <= l && r <= t) return tree[k];

        return f(Query(s, t, (k << 1) + 1, l, (l + r) >> 1), Query(s, t, (k + 1) << 1, (l + r) >> 1, r));
    }
}