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;

public class Codeforces749A {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int kol2 = 0;
        int kol3 = 0;
        if(n%2 == 0){
            kol2 = n/2;
        }
        else{
            kol3++;
            kol2 = (n-3)/2;
        }
       /** int kol2 = n / 2;
        int kol3 = (n % 2) / 3;
        int q = n / 3;
        int w = (n % 3) / 2;
        if (kol3 + kol2 <= q + w) {
            if (n - w * 2 - q * 3 == 0) {
                kol2 = w;
                kol3 = q;
            }
        }
        **/
        System.out.println(kol2 + kol3);
        for (int i = 0; i < kol2; i++) {
            System.out.print(2 + " ");
        }
        for (int i = 0; i < kol3; i++) {
            System.out.print(3 + " ");
        }
    }
}