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)

// In The Name Of God
#include<bits/stdc++.h>
using namespace std;

#define F first
#define S second
#define mp make_pair
#define pb push_back
#define int long long
#define ll long long
#define for2(a,b,c) for(int (a) = (b); (a) < (c); (a)++)
#define setp cout << fixed << setprecision(15)
#define endl "\n"
#define minit(a,b) a = min(a,b)
#define maxit(a,b) a = max(a,b)
#define PII pair<int,int>
#define Vec vector<int>
#define error(x) cerr << #x << " = " << (x) << endl;
#define all(x) (x).begin() , (x).end()



int32_t main()
{
    int n; cin >> n;
    if(n == 3){
        cout << "2 "<< "5 "<< "63" << endl;
        return 0;
    }
    vector<int> v;
    v.pb(2);
    v.pb(3);
    v.pb(4);
    v.pb(9);
    n -= 4;
    vector<int> one;
    for(int i = 6; i <= 30000; i += 6) one.pb(i);
    vector<PII> two;
    for(int i = 8; i <= 30000; i += 6){
        two.pb({i,i+2});
    }
    for(int i = 15; i <= 30000; i += 12){
        two.pb({i,i+6});
    }
    while(n>1 && two.size()){
        n -= 2;
        v.pb(two.back().F);
        v.pb(two.back().S);
        two.pop_back();
    }
    while(n){
        n--;
        v.pb(one.back());
        one.pop_back();
    }
    sort(all(v));
    for(auto x : v) cout << x << ' ';
    cout << endl;
    return 0;

}