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>
using namespace std;
#define finish(x) return cout << x << endl, 0
#define ll long long

int n;
vector <int> a;

void del(int x){
    for(int i = 0 ; i < n ; i++){
        if(a[i] == x){
            a.erase(a.begin() + i);
            return;
        }
    }
}
int main(){
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cin >> n;
    if(n == 3) finish("2 5 63");
    if(n == 4) finish("2 5 20 63");
    if(n == 5) finish("2 5 20 30 63");
    int sum = 0;
    int cur = 1;
    while((int)a.size() < n){
        if(cur % 2 && cur % 3){
            cur++;
            continue;
        }
        a.push_back(cur);
        sum += cur;
        sum %= 6;
        cur++;
    }
    if(sum == 2){
        del(8);
        while(cur % 6) cur++;
        a.push_back(cur);
    }
    else if(sum == 3){
        del(9);
        while(cur % 6) cur++;
        a.push_back(cur);
    }
    else{
        del(9);
        while(cur % 6 != 4) cur++;
        a.push_back(cur);
    }
    for(auto &i : a) cout << i << " ";
    cout << endl;
}