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.util.*;
public class Solution
{
    public static void sieve(int n,int[] a)
    {
        int k=0;
        boolean[] visited=new boolean[n+1];
        for(int i=2;i<=n;i++)
        {
            if(!visited[i])
            {
                a[k]=i;
                k++;
            }
            for(int j=2*i;j<=n;j=j+i)
            {
                visited[j]=true;
            }
        }
    }
    public static void main(String[] args)
    {
        Scanner sc=new Scanner(System.in);
        int n=sc.nextInt();
        int count=0;
        int i=0;
        int[] a=new int[n+1];
        ArrayList<Integer> arr=new ArrayList<Integer>();
        sieve(n,a);
        while(n>0)
        {
            if(n-a[i]>=0 && n-a[i]!=1)
            {
                n-=a[i];
                arr.add(a[i]);
                count++;
               //t.print(a[i]+" ");
            }
            else
            {
                i++;
            }
        }
        System.out.println(count);
        for(i=0;i<count;i++)
        {
            System.out.print(arr.get(i)+" ");
        }
    }
}