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;
long long n, w[300000], menor[300000], peso[300000], painho[300000];
vector<long long> adj[300000];
void pd(int x, int pai) {
  peso[x] = w[x];
  menor[x] = -2000000000;
  painho[x] = pai;
  for (int i = 0, y; i < ((int)adj[x].size()); i++) {
    y = adj[x][i];
    if (y == pai) continue;
    pd(y, x);
    menor[x] = max(menor[x], menor[y]);
    peso[x] += peso[y];
  }
  menor[x] = max(menor[x], peso[x]);
}
int main() {
  int n;
  cin >> n;
  vector<int> ans;
  if (n % 2 == 1) {
    ans.push_back(3);
    n -= 3;
  }
  while (n) {
    ans.push_back(2);
    n -= 2;
  }
  cout << ans.size() << endl;
  for (int i = 0; i < ans.size(); i++) cout << ans[i] << " ";
  cout << endl;
}