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;
inline void boost() {
  ios_base::sync_with_stdio();
  cin.tie(0);
}
const long long MAX = 1e5 + 111;
const long long mod = 1e9 + 7;
map<string, int> maap;
vector<int> g[MAX];
int main() {
  boost();
  int n;
  cin >> n;
  cout << n / 2 << "\n";
  for (int i = 1; i <= n / 2; i++) {
    if (i == n / 2 && n % 2 == 1) {
      cout << 3;
      break;
    }
    cout << 2 << " ";
  }
  exit(0);
}