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: Accepted)

import java.util.Scanner;
import java.util.StringJoiner;
import java.util.TreeSet;

class Main {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);

        if (scanner.hasNextLine()) {
            int N = Integer.parseInt(scanner.nextLine());

            if (N == 3) {
                System.out.println("3 5 22");
            } else {
                int c6p3 = ((N - 1) / 8) * 2 + 2;
                int c6p2 = (N - c6p3 - 1) / 3 + 1;
                int c6p6 = N - c6p3 - c6p2 - c6p2;

                TreeSet<Integer> set = new TreeSet<>();
                for (int i = 0; i < c6p3; ++i) {
                    set.add(i * 6 + 3);
                }
                for (int i = 0; i < c6p2; ++i) {
                    set.add(i * 6 + 2);
                    set.add(i * 6 + 4);
                }
                for (int i = 0; i < c6p6; ++i) {
                    set.add(i * 6 + 6);
                }
                StringJoiner joiner = new StringJoiner(" ");
                for (Integer v: set) {
                    joiner.add(v.toString());
                }
                System.out.println(joiner.toString());
            }
        }
    }
}