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;
int main() {
  int userInput, i, finalResult;
  string multi = "";
  cin >> userInput;
  while (!(userInput >= 2 && userInput <= 100000)) {
    cin >> userInput;
  }
  cout << userInput / 2 << "\n";
  if (userInput == 3) {
    cout << userInput;
  } else {
    for (i = 1; i <= userInput / 2; i++) {
      finalResult = userInput - (2 * i);
      multi += to_string(2) + " ";
      if (finalResult == 0) {
        cout << multi;
      }
      if (finalResult == 3) {
        cout << multi << "3";
      }
    }
  }
  return 0;
}