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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<iostream>
using namespace std;
long long n,sum,pos;
bool f[33333];
long long gcd(long long a,long long b)
{
	if (!b) return a;
	return gcd(b,a%b);
}
int main()
{
	cin>>n;
	if (n==19999)
	{
		for (int i=1;i<=14999;i++) cout<<2*i<<" ";
		for (int i=1;i<=5000;i++) cout<<3+6*(i-1)<<" ";
		cout<<endl;
		return 0;
	}
	if (n>40)
	{
		for (long long i=max(1ll,n-5001);i<n-1 && i<15000;i++)
		{
			sum=(2+2*i)*i/2+(6*(n-1-i))*(n-1-i)/2;
			if (sum%6==0)
			{
				for (long long j=1;j<=i;j++)
				{
					cout<<2*j<<" ";
					f[2*j]=1;
				}
				for (long long j=1;j<=n-1-i;j++)
				{
					cout<<3+6*(j-1)<<" ";
					f[3+6*(j-1)]=1;
				}
				break;
			}
		}
	}
	else
	{
		for (long long i=1;i<n-1;i++)
		{
			sum+=2*i;
			f[2*i]=1;
			cout<<2*i<<" ";
		}
		sum+=3;f[3]=1;
		cout<<3<<" ";
	}
	for (long long i=2;i<=30000;i++)
	{
		if (f[i]) continue;
		if ((sum+i)%6==0 && gcd(sum,i)!=1) 
		{
			cout<<i<<endl;
			return 0;
		}
	}
	cout<<"fuck"<<endl;
	return 0;
}