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 <algorithm>
#include <cmath>
#include <cstdio>
#include <cstring>
#include <deque>
#include <iostream>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <utility>
#include <vector>

#define CK(N, A, B) (A <= N && N < B)
#define REP(i, a, b) for (int i = a; i < b; i++)
#define RREP(i, a, b) for (int i = (b - 1); a <= i; i--)
#define F first
#define S second
#define ll long long

const int INF = 1e9;
const long long LLINF = 1e18;

using namespace std;

int dy[] = {0,1,0,-1};
int dx[] = {1,0,-1,0};
int dy8[] = {0,1,1,1,0,-1,-1,-1};
int dx8[] = {1,1,0,-1,-1,-1,0,1};

/*==================================================*/
/*variable*/
int N;
set<int> st;
/*==================================================*/
/*function*/

/*==================================================*/

int main(){
    cin>>N;

    if(N <= 5){
        switch (N) {
            case 3:
                cout<<2<<" "<<5<<" "<<63<<endl;
                break;
            case 4:
                cout<<2<<" "<<5<<" "<<63<<" "<<20<<endl;
                break;
            case 5:
                cout<<2<<" "<<5<<" "<<63<<" "<<20<<""<<30<<endl;
                break;
            default:
                cout<<"EORROR!"<<endl;
                break;
        }
        return 0;
    }

    int num = 0;
    int sum = 0;
    int cnt = 0;
    while(cnt < N){
        num++;
        if(num % 2 == 0 || num % 3 == 0){
            st.insert(num);
            sum += num;
            cnt++;
        }
    }

    int nextn = num;
    while(true){
        nextn++;
        if(nextn % 6 == 0){
            break;
        }
    }
    int nextf = num;
    while(true){
        nextf++;
        if(nextf % 6 == 4){
            break;
        }
    }

    switch (sum % 6){
        case 0:
            break;
//        case 1:
//            st.erase(14);
//            st.insert(nextn - 7);
//            break;
        case 2:
            st.erase(8);
            st.insert(nextn);
            break;
        case 3:
            st.erase(9);
            st.insert(nextn);
            break;
//        case 4:
//            st.erase(9);
//            st.insert(nextn + 5);
//            break;
        case 5:
            st.erase(9);
            //st.insert(nextn + 4);
            st.insert(nextf);
            break;
        default:
            cout<<"ERROR!"<<endl;
            break;
    }

    auto it = st.begin();
    while(it != st.end()){
        cout<<(*it);
        if(it != st.end()) cout<<" ";
        it++;
    }
    cout<<endl;

    return 0;
}