Eighth-grader Vova is on duty today in the class. After classes, he went into the office to wash the board, and found on it the number n. He asked what is this number and the teacher of mathematics Inna Petrovna answered Vova that n is the answer to the arithmetic task for first-graders. In the textbook, a certain positive integer x was given. The task was to add x to the sum of the digits of the number x written in decimal numeral system.

Since the number n on the board was small, Vova quickly guessed which x could be in the textbook. Now he wants to get a program which will search for arbitrary values of the number n for all suitable values of x or determine that such x does not exist. Write such a program for Vova.

Input

The first line contains integer n (1 ≤ n ≤ 109).

Output

In the first line print one integer k — number of different values of x satisfying the condition. 

In next k lines print these values in ascending order.

Examples

Input

21


Output

1
15


Input

20


Output

0

Note

In the first test case x = 15 there is only one variant: 15 + 1 + 5 = 21.

In the second test case there are no such x.
import java.io.*;
import java.util.*;

public class Main
 {
    class Reader 
    {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;
 
        public Reader()
        {
            din = new DataInputStream(System.in);
            if (System.getProperty("ONLINE_JUDGE") == null) 
            {
            try 
            {
                System.setOut(new PrintStream(new FileOutputStream("output.txt")));
                din = new DataInputStream(new FileInputStream("input.txt"));
            }
              catch (Exception e) {
            }
        }
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }
 
        public Reader(String file_name) throws IOException
        {
            din = new DataInputStream(
                new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }
 
        public String readLine() throws IOException
        {
            byte[] buf = new byte[200]; // line length
            int cnt = 0, c;
            while ((c = read()) != -1) {
                if (c == '\n') {
                    if (cnt != 0) {
                        break;
                    }
                    else {
                        continue;
                    }
                }
                buf[cnt++] = (byte)c;
            }
            return new String(buf, 0, cnt);
        }
 
        public int nextInt() throws IOException
        {
            int ret = 0;
            byte c = read();
            while (c <= ' ') {
                c = read();
            }
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
 
            if (neg)
                return -ret;
            return ret;
        }
 
        public long nextLong() throws IOException
        {
            long ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }
 
        public double nextDouble() throws IOException
        {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
 
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
 
            if (c == '.') {
                while ((c = read()) >= '0' && c <= '9') {
                    ret += (c - '0') / (div *= 10);
                }
            }
 
            if (neg)
                return -ret;
            return ret;
        }
 
        private void fillBuffer() throws IOException
        {
            bytesRead = din.read(buffer, bufferPointer = 0,
                                 BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }
 
        private byte read() throws IOException
        {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }
 
        public void close() throws IOException
        {
            if (din == null)
                return;
            din.close();
        }

    }

Reader read;
public static void main(String[] args) throws IOException
    
    {
        Main obj = new Main();
        obj.run();
        //obj.read = new Reader();
        
    }
        public int getParent(int parent[], int src)
    {
        if(parent[src] != src)
        {
            int ultimateparent = getParent(parent, parent[src]);
            parent[src] = ultimateparent;
            return ultimateparent;
        }
        return src;
    }

    public void union(int parent[], int i, int j, int rank[])
    {

        int root1 = getParent(parent, i);
        int root2 = getParent(parent, j);
        if(rank[root1] == rank[root2])
        {
            parent[root1] = root2;
            rank[root2]++ ;
        }
        else if(rank[root1] > rank[root2])
        {
            parent[root2] = root1;
        }
        else // rank[root2] > rank[root1]
        {
            parent[root1] = root2;
        }
    }
    public String ns() throws IOException
    {
        return(read.readLine());
    }
    public int ni() throws IOException
    {
        return(read.nextInt());
    }
    public double nd() throws IOException
    {
        return(read.nextDouble());
    }
    public long nl() throws IOException
    {
        return(read.nextLong());
    }
    public int[] ai(int n) throws IOException
    {
        int arr[] = new int[n];
        for(int i = 0; i<n; i++)
            arr[i] = read.nextInt();
        return(arr);
    }
    public double[] ad(int n) throws IOException
    {
        double arr[] = new double[n];
        for(int i = 0; i<n; i++)
            arr[i] = read.nextDouble();
        return(arr);
    }
    public long[] al(int n) throws IOException
    {
        long arr[] = new long[n];
        for(int i = 0; i<n; i++)
            arr[i] = read.nextLong();
        return(arr);
    }


//---------------------------------------------------------------------------------------------------------------

    private int sumOfigits(long n)
    {
        int sum = 0;
        while(n != 0)
        {
            sum += (n%10);
            n/= 10;
        }
        return(sum);
    }


    int count = 0;
    public void run() throws IOException
    {
        read = new Reader();
        
        long n = nl();
        int count = 0;
        StringBuilder sb = new StringBuilder();
        for(long i = Math.max(0, n-85); i<= n; i++)
        {
            if(i + sumOfigits(i) == n)
                {
                    count ++;
                    sb.append(i).append("\n");
                }
        }
        System.out.println(count);
        System.out.println(sb.toString());

    }

}