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;
const int inf = (int)1e9;
int n;
int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  cin >> n;
  if (n % 2 == 0) {
    cout << n / 2;
    cout << '\n';
    for (int i = 0; i < n / 2; ++i) {
      cout << "2 ";
    }
    return 0;
  }
  n -= 3;
  cout << n / 2 + 1;
  cout << '\n';
  cout << "3 ";
  for (int i = 0; i < n / 2; ++i) {
    cout << "2 ";
  }
  return 0;
}