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.*;
import java.util.*;

public class BachgoldProblem 
{
    public static void main(String[] args) 
    {
        Scanner input = new Scanner( System.in );
        
        int sumOfPrime = input.nextInt();
        
        StringBuilder output = new StringBuilder();
        
        for( int i = 0; i < ( ( sumOfPrime / 2 ) - 1 ); i++ )
        {
            output.append( "2 " );
        }
        
        if( sumOfPrime % 2 == 0 )
        {
            output.append( "2" );
        }
        else
        {
            output.append( "3" );
        }
        
        System.out.println( sumOfPrime / 2 );
        
        System.out.println( output );
        
    }
}