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)

/**
            ▄█▀ ▀█▀ ▄▀▄ █▀ █▄█▄█ ▄▀▄ █▀ ▄█▀
            <⇋⇋⇋⋛∰≓⊂(⌒,_ゝ⌒)⊃≓∰⋛⇋⇋⇋>

    ♔♕♖♗♘♙ ☜❷☞✪ ィℋ६ ≈ ᗫẵℜℵĬŊĞ ✪☜❷☞ ♚♛♜♝♞♟
    ♔♕♖♗♘♙                             ♚♛♜♝♞♟
                ˙·٠•●♥ Ƹ̵̡Ӝ̵̨̄Ʒ ♥●•٠·˙
**/

#include <bits/stdc++.h>

#define fr first
#define sc second
#define pb push_back
#define mk make_pair
#define sz(s) (int)s.size()
#define all(s) s.begin(), s.end()

using namespace std;

const int N = 1e5 + 5;

int n, a[N], u[N];

main()
{
    cin >> n;
    u[2] = 1;
    u[3] = 1;
    a[1] = 2;
    a[2] = 3;
    int sum = 5;
    for( int i = 3; i <= n; i++ )

        for( int k = 4; k <= 30000; k++ )

            if( !u[k] and sum != k )
            {
                int fl = 0;
                for( int j = 1; j < i; j++ )
                    if( __gcd( a[j], sum + k - a[j] ) == 1 )
                    {
                        fl = 1;
                        break;
                    }
                if( fl ) continue;

                a[i] = k;
                u[k] = 1;
                sum += k;
                break;
            }

    for( int i = 1; i <= n; i++ )
        cout << a[i] << ' ';
}