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: Wrong Answer)

using System;
using System.Collections.Generic;
class Program
{
	static void Main(string[] args)
	{
		int N = int.Parse(Console.ReadLine());
		int[]A = new int[N];
		if(N==3){
			A[0]=2;
			A[1]=5;
			A[2]=63;
		} else if(N==4){
			A[0]=2;
			A[1]=5;
			A[2]=20;
			A[3]=63;
		} else {
			for(var i=0;i<N/8;i++){
				A[i*8] = (i+1)*12+2;
				A[i*8+1] = (i+1)*12+3;
				A[i*8+2] = (i+1)*12+4;
				A[i*8+3] = (i+1)*12+6;
				A[i*8+4] = (i+1)*12+8;
				A[i*8+5] = (i+1)*12+9;
				A[i*8+6] = (i+1)*12+10;
				A[i*8+7] = (i+1)*12+12;
			}
			if(N%8==1){
				A[N/8*8] = 12;
			} else if(N%8==2){
				A[N/8*8] = 12;
				A[N/8*8+1] = 6;
			} else if(N%8==3){
				A[N/8*8] = 12;
				A[N/8*8+1] = 8;
				A[N/8*8+2] = 4;
			} else if(N%8==4){
				A[N/8*8] = 12;
				A[N/8*8+1] = 9;
				A[N/8*8+2] = 6;
				A[N/8*8+3] = 3;
			} else if(N%8==5){
				A[N/8*8] = 12;
				A[N/8*8+1] = 10;
				A[N/8*8+2] = 9;
				A[N/8*8+3] = 3;
				A[N/8*8+4] = 2;
			} else if(N%8==6){
				A[N/8*8] = 12;
				A[N/8*8+1] = 10;
				A[N/8*8+2] = 9;
				A[N/8*8+3] = 6;
				A[N/8*8+4] = 3;
				A[N/8*8+5] = 2;
			} else if(N%8==7){
				A[N/8*8] = 12;
				A[N/8*8+1] = 10;
				A[N/8*8+2] = 9;
				A[N/8*8+3] = 8;
				A[N/8*8+4] = 4;
				A[N/8*8+5] = 3;
				A[N/8*8+6] = 2;
			}
		}
		Console.Write(A[0]);
		for(var i=1;i<N;i++){
			Console.Write(" "+A[i]);
		}
	}
}