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;

namespace agc022_b
{
	class Program
	{
		static void Main(string[] args)
		{
			int n = int.Parse(Console.ReadLine());
			if (n == 3) Console.WriteLine("2 5 63");
			else
			{
				int[] x = new int[] { 2, 3, 4, 6, 8, 9, 10, 12 };
				bool first = true;
				for (int i = 0; i < n / 8; i++)
				{
					foreach (int a in x)
					{
						if (first) first = false;
						else Console.Write(" ");
						Console.Write(i * 12 + a);
					}
				}
				int end = n / 8 * 12;
				if (first) first = false;
				else Console.Write(" ");
				switch (n % 8)
				{
					case (0): break;
					case (1):
					{
						Console.Write((end + 6));
						break;
					}
					case (2):
					{
						Console.Write((end + 2) + " " + (end + 4));
						break;
					}
					case (3):
					{
						Console.Write((end + 4) + " " + (end + 6) + " " + (end + 8));
						break;
					}
					case (4):
					{
						Console.Write((end + 2) + " " + (end + 3) + " " + (end + 4) + " " + (end + 9));
						break;
					}
					case (5):
					{
						Console.Write((end + 2) + " " + (end + 3) + " " + (end + 6) + " " + (end + 9) + " " + (end + 10));
						break;
					}
					case (6):
					{
						Console.Write((end + 2) + " " + (end + 3) + " " + (end + 6) + " " + (end + 9) + " " + (end + 10) + " " + (end + 12));
						break;
					}
					case (7):
					{
						Console.Write((end + 2) + " " + (end + 3) + " " + (end + 4) + " " + (end + 6) + " " + (end + 8) + " " + (end + 9) + " " + (end + 10));
						break;
					}
				}
			}
		}
	}
}