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;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace AGC022B {
    class Program {
        static void Main(string[] args) {
            int N = int.Parse(Console.ReadLine());
            int[] ans = new int[N];
            if (N == 3) {
                ans[0] = 2;
                ans[1] = 5;
                ans[2] = 63;
            } else {
                int div = N / 8;
                int rem = N % 8;
                for (int i = 0; i < div; i++) {
                    ans[i * 8] = 12 * i + 2;
                    ans[i * 8 + 1] = 12 * i + 3;
                    ans[i * 8 + 2] = 12 * i + 4;
                    ans[i * 8 + 3] = 12 * i + 6;
                    ans[i * 8 + 4] = 12 * i + 8;
                    ans[i * 8 + 5] = 12 * i + 9;
                    ans[i * 8 + 6] = 12 * i + 10;
                    ans[i * 8 + 7] = 12 * i + 12;
                }
                switch (rem) {
                    case 0:
                        break;
                    case 1:
                        ans[div * 8] = 12 * div + 6;
                        break;
                    case 2:
                        ans[div * 8] = 12 * div + 3;
                        ans[div * 8 + 1] = 12 * div + 9;
                        break;
                    case 3:
                        ans[div * 8] = 12 * div + 3;
                        ans[div * 8 + 1] = 12 * div + 9;
                        ans[div * 8 + 2] = 12 * div + 6;
                        break;
                    case 4:
                        ans[div * 8] = 12 * div + 3;
                        ans[div * 8 + 1] = 12 * div + 9;
                        ans[div * 8 + 2] = 12 * div + 2;
                        ans[div * 8 + 3] = 12 * div + 4;
                        break;
                    case 5:
                        ans[div * 8] = 12 * div + 3;
                        ans[div * 8 + 1] = 12 * div + 9;
                        ans[div * 8 + 2] = 12 * div + 2;
                        ans[div * 8 + 3] = 12 * div + 4;
                        ans[div * 8 + 4] = 12 * div + 6;
                        break;
                    case 6:
                        ans[div * 8] = 12 * div + 3;
                        ans[div * 8 + 1] = 12 * div + 9;
                        ans[div * 8 + 2] = 12 * div + 2;
                        ans[div * 8 + 3] = 12 * div + 4;
                        ans[div * 8 + 4] = 12 * div + 8;
                        ans[div * 8 + 5] = 12 * div + 10;
                        break;
                    case 7:
                        ans[div * 8] = 12 * div + 3;
                        ans[div * 8 + 1] = 12 * div + 9;
                        ans[div * 8 + 2] = 12 * div + 2;
                        ans[div * 8 + 3] = 12 * div + 4;
                        ans[div * 8 + 4] = 12 * div + 8;
                        ans[div * 8 + 5] = 12 * div + 10;
                        ans[div * 8 + 6] = 12 * div + 6;
                        break;
                }
            }
            Console.WriteLine(string.Join(" ", ans));
        }
    }
}