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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.InputMismatchException;
import java.util.List;
import java.util.StringTokenizer;

public class Main {

	public static void main(String[] args) throws IOException {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskX solver = new TaskX();
		solver.solve(1, in, out);
		out.close();
	}

	static int INF = 1 << 30;
	static int modP = 1000000007;

	static class TaskX {
		public void solve(int testNumber, InputReader in, PrintWriter out) {

			int N = in.nextInt();

			List<Integer> nums = new ArrayList<>();
			for (int k = 11; k < 10000; k++) {
				nums.add(6 * k + 2);
				nums.add(6 * k + 3);
				nums.add(6 * k + 4);
				nums.add(6 * k + 6);
			}

			List<Integer> list = new ArrayList<>();
			list.add(2);
			list.add(5);
			list.add(20);
			list.add(30);
			list.add(63);

			long sum = 0;
			for (int i : list) {
				sum += i;
			}

			if (N == 3) {
				list.remove((Integer)30);
				list.remove((Integer)20);
			} else if (N == 4) {
				list.remove((Integer)30);
			} else if (N == 5) {
				;
			} else {
				int j = 0;
				list.clear();
				while (list.size() < N) {
					sum += nums.get(j);
					list.add(nums.get(j));
					nums.remove(j);
				}
				long mod = sum % 6;
				if (mod == 2) {
					for (int src : list) {
						if (src % 6 == 2) {
							list.remove((Integer)src);
							break;
						}
					}
					for (int tar : nums) {
						if (tar % 6 == 0) {
							list.add(tar);
							break;
						}
					}
				} else if (mod == 3) {
					for (int src : list) {
						if (src % 6 == 3) {
							list.remove((Integer)src);
							break;
						}
					}
					for (int tar : nums) {
						if (tar % 6 == 0) {
							list.add(tar);
							break;
						}
					}
				} else if (mod == 5) {
					for (int src : list) {
						if (src % 6 == 3) {
							list.remove((Integer)src);
							break;
						}
					}
					for (int tar : nums) {
						if (tar % 6 == 4) {
							list.add(tar);
							break;
						}
					}
				}
			}


			for (int i = 0; i < list.size(); i++) {
				if (i == 0) {
					out.print(list.get(i));
				} else {
					out.print(" " + list.get(i));
				}
			}
			out.print("\n");


		}
	}

	static class InputReader {
		BufferedReader in;
		StringTokenizer tok;

		public String nextString() {
			while (!tok.hasMoreTokens()) {
				try {
					tok = new StringTokenizer(in.readLine(), " ");
				} catch (IOException e) {
					throw new InputMismatchException();
				}
			}
			return tok.nextToken();
		}

		public int nextInt() {
			return Integer.parseInt(nextString());
		}

		public long nextLong() {
			return Long.parseLong(nextString());
		}

		public double nextDouble() {
			return Double.parseDouble(nextString());
		}

		public int[] nextIntArray(int n) {
			int[] res = new int[n];
			for (int i = 0; i < n; i++) {
				res[i] = nextInt();
			}
			return res;
		}

		public long[] nextLongArray(int n) {
			long[] res = new long[n];
			for (int i = 0; i < n; i++) {
				res[i] = nextLong();
			}
			return res;
		}

		public InputReader(InputStream inputStream) {
			in = new BufferedReader(new InputStreamReader(inputStream));
			tok = new StringTokenizer("");
		}

	}

}