Problem:
Score: 400 points

Problem Statement

Print a sequence a_1, a_2, ..., a_N whose length is N that satisfies the following conditions:

a_i (1 \leq i \leq N) is a prime number at most 55 555.

The values of a_1, a_2, ..., a_N are all different.

In every choice of five different integers from a_1, a_2, ..., a_N, the sum of those integers is a composite number.

If there are multiple such sequences, printing any of them is accepted.

Notes

An integer N not less than 2 is called a prime number if it cannot be divided evenly by any integers except 1 and N, and called a composite number otherwise.

Constraints

N is an integer between 5 and 55 (inclusive).

Input

Input is given from Standard Input in the following format:

N

Output

Print N numbers a_1, a_2, a_3, ..., a_N in a line, with spaces in between.

Sample Input 1

5

Sample Output 1

3 5 7 11 31

Let us see if this output actually satisfies the conditions.

First, 3, 5, 7, 11 and 31 are all different, and all of them are prime numbers.

The only way to choose five among them is to choose all of them, whose sum is a_1+a_2+a_3+a_4+a_5=57, which is a composite number.

There are also other possible outputs, such as 2 3 5 7 13, 11 13 17 19 31 and 7 11 5 31 3.

Sample Input 2

6

Sample Output 2

2 3 5 7 11 13

2, 3, 5, 7, 11, 13 are all different prime numbers.

2+3+5+7+11=28 is a composite number.

2+3+5+7+13=30 is a composite number.

2+3+5+11+13=34 is a composite number.

2+3+7+11+13=36 is a composite number.

2+5+7+11+13=38 is a composite number.

3+5+7+11+13=39 is a composite number.

Thus, the sequence 2 3 5 7 11 13 satisfies the conditions.

Sample Input 3

8

Sample Output 3

2 5 7 13 19 37 67 79

Solution in C++ (GCC 9.2.1) (judge verdict: Accepted)

/*#include <boost/multiprecision/cpp_dec_float.hpp>
#include <boost/multiprecision/cpp_int.hpp>

#include <boost/rational.hpp>
*/
#include <bits/stdc++.h>
using namespace std;
#define _GLIBCXX_DEBUG
#define rep(i, n) for (ll i = 0; i < (ll)(n); i++)
using ll = long long;
using ld = long double;
using pll = pair<ll,ll>;
#define rep2(i, s, n) for (ll i = (s); i < (ll)(n); i++)
#define rep3(i, n) for (ll i = 1; i < (ll)(n+1); i++)
#define rep4(i, s, n) for (ll i = (s); i < (ll)(n+1); i++)
#define repr(i,n) for (ll i = (n-1); i>=0;i--)
#define repr3(i,n) for(ll i = (n);i>0;i--)
#define repr4(i,s,n) for(ll i = (n);i>=(s);i--)
#define stlen(s) ll s.size()-1
#define all(v) v.begin(), v.end()
#define allr(v) v.rbegin(), v.rend()
#define cout(n) cout<<std::fixed<<std::setprecision(n)
using Graph = vector<vector<int>>;
using Graphw = vector<vector<pair<ll,ll>>>;
using mat = vector<vector<ll>>;
using vec = vector<ll>;
#define INF1  INT_MAX;
#define INF2  LLONG_MAX;
#define PI  3.14159265358979323846;
#define MOD 1000000007;
/*
namespace mp = boost::multiprecision;
// 任意長整数型
using Bint = mp::cpp_int;
// 仮数部長が32の浮動小数点数型
using Real32 = mp::number<mp::cpp_dec_float<32>>;
// 仮数部長が1024の浮動小数点数型
using Real1024 = mp::number<mp::cpp_dec_float<1024>>;
// 有理数型
using Rat = boost::rational<Bint>;
*/
const int mod = 1000000007;



int main(){

// エラトステネスのふるい
    int MAX = 101010;
    vector<int> is_prime(MAX, 1);
    is_prime[0] = 0, is_prime[1] = 0;
    for (int i = 2; i < MAX; ++i) {
        if (!is_prime[i]) continue;
        for (int j = i*2; j < MAX; j += i) is_prime[j] = 0;
    }

    int N;
    cin>>N;
    vector<int> ans;
    int p=2;
    while(ans.size()<N){
        if((p%5==2)&&(is_prime[p]))ans.push_back(p);
        p++;

    }
    rep(i,N){
        cout<<ans[i];
        if(i!=N-1)cout<<" ";
        else cout<<endl;
    }

return 0;
}