Problem: Dima loves representing an odd number as the sum of multiple primes, and Lisa loves it when there are at most three primes. Help them to represent the given number as the sum of at most than three primes.

More formally, you are given an odd numer n. Find a set of numbers pi (1 ≤ i ≤ k), such that

  1. 1 ≤ k ≤ 3
  2. pi is a prime
  3. <image>



The numbers pi do not necessarily have to be distinct. It is guaranteed that at least one possible solution exists.

Input

The single line contains an odd number n (3 ≤ n < 109).

Output

In the first line print k (1 ≤ k ≤ 3), showing how many numbers are in the representation you found.

In the second line print numbers pi in any order. If there are multiple possible solutions, you can print any of them.

Examples

Input

27


Output

3
5 11 11

Note

A prime is an integer strictly larger than one that is divisible only by one and by itself.

Solution (in JAVA):

Solution:

/* 
Keep solving problems. 
*/
import java.util.*;
import java.io.*;

public class CF584D {

    BufferedReader br;
    PrintWriter out;
    StringTokenizer st;
    boolean eof;
    final long MOD = 1000L * 1000L * 1000L + 7;

    void solve() throws IOException {
        int n = nextInt();
        int m = 10000 + 10;
        boolean[] seive = new boolean[m];
        Arrays.fill(seive, true);
        for(int i = 2; i < m; i++) {
            if(seive[i]) {
                for(int j = 2; j * i < m; j++) {
                    seive[i * j] = false;
                }
            }
        }

        if(n < m) {
            if(seive[n]) {
                outln(1);
                out(n);
                return;
            }
        }
        for(int i = 2; i < m; i++) {
            if(n - i < m) {
                if(n - i >= 2 && seive[i] && seive[n - i]) {
                    outln(2);
                    out(i + " " + (n - i));
                    return;
                }
            }
        }

        for(int i = n - 1; ; i--) {
            boolean tmp = isPrime(i);
            if(tmp) {
                int need = n - i;
                for(int j = 2; j < m; j++) {
                    if(need - j >= 2 && seive[j] && seive[need - j]) {
                        outln(3);
                        out(i + " " + j + " " + (need - j));
                        return;
                    }
                }
            }
        }

    }
    boolean isPrime(int num) {
        for(int i = 2; i * i <= num; i++) {
            if(num % i == 0) {
                return false;
            }
        }
        return true;
    }

    void shuffle(int[] a) {
        int n = a.length;
        for(int i = 0; i < n; i++) {
            int r = i + (int) (Math.random() * (n - i));
            int tmp = a[i];
            a[i] = a[r];
            a[r] = tmp;
        }
    }
    private void outln(Object o) {
        out.println(o);
    }
    private void out(Object o) {
        out.print(o);
    }
    public CF584D() throws IOException {
        br = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        solve();
        out.close();
    }
    public static void main(String[] args) throws IOException {
        new CF584D();
    }

    public long[] nextLongArr(int n) throws IOException{
        long[] res = new long[n];
        for(int i = 0; i < n; i++)
            res[i] = nextLong();
        return res;
    }
    public int[] nextIntArr(int n) throws IOException {
        int[] res = new int[n];
        for(int i = 0; i < n; i++)
            res[i] = nextInt();
        return res;
    }
    public String nextToken() {
        while (st == null || !st.hasMoreTokens()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (Exception e) {
                eof = true;
                return null;
            }
        }
        return st.nextToken();
    }
    public String nextString() {
        try {
            return br.readLine();
        } catch (IOException e) {
            eof = true;
            return null;
        }
    }
    public int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }
    public long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }
    public double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }
}