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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.io.StreamTokenizer;
 
 
public class Main{
	static StreamTokenizer sc=new StreamTokenizer(new BufferedReader(new InputStreamReader(System.in)));
	static int nextint() throws IOException {
		sc.nextToken();
		return (int)sc.nval;
	}
	static long nextLong() throws IOException {
		sc.nextToken();
		return (long)sc.nval;
	}
	static String nextLine() throws IOException{
		sc.nextToken();
		return sc.sval;
	}

	public static void main(String args[]) throws IOException {
		PrintWriter out=new PrintWriter(System.out);
		int n=nextint();
		int dp[]=new int[100010];
		dp[2]=1;
		dp[3]=1;
		if(n<4) {
			out.println(1);
		}else {
			for(int i=4;i<=n;i++) {
				dp[i]=dp[i-2]+1;
			}
			out.println(dp[n]);
		}
		if(n%2==0) {
			for(int i=0;i<n/2;i++) {
				out.print(2+" ");
			}
		}else {
			for(int i=0;i<n/2-1;i++) {
				out.print(2+" ");
			}
			out.print(3+" ");
		}
		out.flush();
		out.close();
	}
}