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)

//#pragma warning disable
using System.Collections;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Text;
using System;
using System.Numerics;
using System.Threading.Tasks;
using static System.Math;
using static System.Console;
class Z { static void Main() => new K(); }
class K
{
	int F() => int.Parse(ReadLine());
	long FL() => long.Parse(ReadLine());
	int[] G() => ReadLine().Split(new char[] { ' ', '\t' }, StringSplitOptions.RemoveEmptyEntries).Select(int.Parse).ToArray();
	long[] GL() => ReadLine().Split(new char[] { ' ', '\t' }, StringSplitOptions.RemoveEmptyEntries).Select(long.Parse).ToArray();
	public const int MOD = 1000000007;
	public K()
	{
		//for (var i = 3; i < 1000; i++) Solve(i);
		SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
		WriteLine(string.Join(" ", Solve(F())));
		Out.Flush();
	}
	IList<int> Solve(int N)
	{
		if (N == 3) return new[] { 2, 3, 25 };
		var M = 30000;
		var good = new SortedSet<int>();
		for (var p = 2; p <= M; p += 2) good.Add(p);
		for (var p = 3; p <= M; p += 3) good.Add(p);
		var ans = new HashSet<int>();
		var tmp = good.ToArray();
		for (var i = 0; i < N - 2; i++) ans.Add(tmp[i]);
		var s = ans.Sum(i => (long)i);
		for (var j = 0; j < 6; j++)
			for (var k = j; k < 6; k++)
				if ((s + j + k) % 6 == 0)
					for (var a = j; a <= M; a += 6)
						if (!ans.Contains(a))
							for (var b = k; b <= M; b += 6)
								if (!ans.Contains(b) && a != b && GCD(s + b, a) > 1 && GCD(s + a, b) > 1 && a > 1 && b > 1)
								{
									ans.Add(a);
									ans.Add(b);
									return ans.ToList();
								}
		return null;
	}
	public static long GCD(long a, long b)
	{
		var n = (ulong)Abs(a); var m = (ulong)Abs(b);
		if (n == 0) return (long)m; if (m == 0) return (long)n;
		int zm = 0, zn = 0;
		while ((n & 1) == 0) { n >>= 1; zn++; }
		while ((m & 1) == 0) { m >>= 1; zm++; }
		while (m != n)
		{
			if (m > n) { m -= n; while ((m & 1) == 0) m >>= 1; }
			else { n -= m; while ((n & 1) == 0) n >>= 1; }
		}
		return (long)n << Min(zm, zn);
	}
}