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 JAVA):

Solution:
import java.io.*; 
import java.util.*; 
public class test {
    public static void main (String[] args) { 
    Scanner sc=new Scanner(System.in);
    int c=0;
      int n=sc.nextInt();
      int m=n;
       if (n % 2 == 1) {
           c++;
        n -= 3; 
    } 
     while (n>0) {
         c++;
        n -= 2; 
    }
    System.out.println(c); 
    int[] a=new int[c];
    if (m % 2 == 1) {
        System.out.print( "3 "); 
        m -= 3; 
    } 
     while (m>0) {
        System.out.print( "2 "); 
        m -= 2; 
    }
        
    }
}