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.Scanner;
import java.lang.Math;

public class Z1{
    public static void main(String[] args){
    Scanner sc = new Scanner(System.in);
    int a = sc.nextInt();
    float b = (float)a/2;
    double d = b-0.5;
    long c = Math.round(d);
    System.out.println(c);
    for (int i =0 ; i<c-1;i++){
    System.out.print(2+" ");
    }
    if (b==Math.round(b+0.1)){
    System.out.print(2);
    }
    else System.out.print(3);
}

}