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: Wrong Answer)

#include <bits/stdc++.h>
#define endl '\n'

using namespace std;
template<class T, class T2> inline void chkmax(T &x, const T2 &y) { if(x < y) x = y; }
template<class T, class T2> inline void chkmin(T &x, const T2 &y) { if(x > y) x = y; }
const int MAXN = (1 << 20);

int n;

void read()
{
	cin >> n;
}

void solve()
{
	vector<int> answer; 
	
	int c = 0;
	n -= 2;
	answer.push_back(3);
	answer.push_back(9);

	if(n == 1)
	{
		answer.push_back(2);
		for(int x: answer) cout << x << " ";
		return;
	}

	while(n >= 2 && c + 4 <= 30000)
	{
		answer.push_back(c + 2);
		answer.push_back(c + 4);
		c += 6;
		n -= 2;
	}

	c = 12;
	while(n >= 2 && c + 3 + c + 9 <= 30000)
	{
		answer.push_back(c + 3);
		answer.push_back(c + 12);
		c += 12;
		n -= 2;
	}

	c = 0;
	while(n)
	{
		answer.push_back(c + 6);
		c += 6;
		n -= 1;
	}

	for(int x: answer) cout << x << " ";
	cout << endl;
}

int main()
{
	ios_base::sync_with_stdio(false);
	cin.tie(NULL);

	read();
	solve();
	return 0;
}