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;
typedef long long ll;
typedef pair<ll, ll> p_ll;

template<class T>
void debug(T itr1, T itr2) { auto now = itr1; while(now<itr2) { cout << *now << " "; now++; } cout << endl; }
#define repr(i,from,to) for (int i=(int)from; i<(int)to; i++)
#define all(vec) vec.begin(), vec.end()
#define rep(i,N) repr(i,0,N)
#define per(i,N) for (int i=(int)N-1; i>=0; i--)

const ll MOD = pow(10,9)+7;
const ll LLINF = pow(2,61)-1;
const int INF = pow(2,30)-1;

vector<ll> fac;
void c_fac(int x=pow(10,6)+10) { fac.resize(x,true); rep(i,x) fac[i] = i ? (fac[i-1]*i)%MOD : 1; }
ll inv(ll a, ll m=MOD) { ll b = m, x = 1, y = 0; while (b!=0) { int d = a/b; a -= b*d; swap(a,b); x -= y*d; swap(x,y); } return (x+m)%m; }
ll nck(ll n, ll k) { return fac[n]*inv(fac[k]*fac[n-k]%MOD)%MOD; }
ll gcd(ll a, ll b) { if (a<b) swap(a,b); return b==0 ? a : gcd(b, a%b); }
ll lcm(ll a, ll b) { return a/gcd(a,b)*b; }


int main() {
  ll N; cin >> N;
  ll sum = 0;
  ll result[N];

  if (N==3) { cout <<  "2 3 25" << endl; return 0; }
  else if (N==4) { cout <<  "2 3 5 20" << endl; return 0; }
  else if (N==5) { cout <<  "2 3 5 20 30" << endl; return 0; }
  else {
    rep(i,N) {
      if (i%4==0) result[i] = 6*(i/4) + 2;
      else if (i%4==1) result[i] = 6*(i/4) + 3;
      else if (i%4==2) result[i] = 6*(i/4) + 4;
      else if (i%4==3) result[i] = 6*(i/4) + 6;
      sum += result[i];
    }
    if (sum%6==1) {
      if (result[N-1]%2==1) { result[N-1] += 9; result[(N-1)/4*4+1] += 8; }
      else { result[N-1] += 8; result[(N-1)/4*4+1] += 9; }
    }
    else if (sum%6==2) {
      if (result[N-1]%2==1) { result[N-1] += 10; result[(N-1)/4*4+1] += 0; }
      else { result[N-1] += 0; result[(N-1)/4*4+1] += 10; }
    }
    else if (sum%6==3) {
      if (result[N-1]%2==1) { result[N-1] += 9; result[(N-1)/4*4+1] += 0; }
      else { result[N-1] += 0; result[(N-1)/4*4+1] += 9; }
    }
    else if (sum%6==4) {
      if (result[N-1]%2==1) { result[N-1] += 0; result[(N-1)/4*4+1] += 8; }
      else { result[N-1] += 8; result[(N-1)/4*4+1] += 0; }
    }
    else if (sum%6==5) {
      if (result[N-1]%2==1) { result[N-1] += 9; result[(N-1)/4*4+1] += 10; }
      else { result[N-1] += 10; result[N/4*4+1] += 9; }
    }
  }
  debug(result,result+N);
  // cout << result << endl;
  return 0;
}