Problem: Bachgold problem is very easy to formulate. Given a positive integer n represent it as a sum of maximum possible number of prime numbers. One can prove that such representation exists for any integer greater than 1.

Recall that integer k is called prime if it is greater than 1 and has exactly two positive integer divisors — 1 and k. 

Input

The only line of the input contains a single integer n (2 ≤ n ≤ 100 000).

Output

The first line of the output contains a single integer k — maximum possible number of primes in representation.

The second line should contain k primes with their sum equal to n. You can print them in any order. If there are several optimal solution, print any of them.

Examples

Input

5


Output

2
2 3


Input

6


Output

3
2 2 2

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
double EPS = 1e-9;
int INF = 100005;
long long int mod = 1000000007;
long long TES = 1000007;
long long INFF = 1000000000000000005LL;
double PI = acos(-1);
int dirx[8] = {-1, 0, 0, 1, -1, -1, 1, 1};
int diry[8] = {0, 1, -1, 0, -1, 1, -1, 1};
void solve() {
  int n;
  scanf("%d", &n);
  if (n % 2 == 1) {
    int t = n / 2;
    cout << "\n" << t << "\n";
    for (int(i) = (0); (i) < (t - 1); ++(i)) cout << "2 ";
    cout << "3\n";
  } else {
    int t = n / 2;
    cout << "\n" << t << "\n";
    for (int(i) = (0); (i) < (t); ++(i)) cout << "2 ";
    cout << "\n";
  }
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  ;
  cout << fixed;
  cout << setprecision(9);
  solve();
}