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 javax.print.attribute.standard.PrintQuality;
        import java.io.*;
        import java.lang.reflect.Array;
        import java.math.BigInteger;
        import java.util.*;
        import java.lang.*;
        import static java.lang.Math.*;
        public class main implements Runnable {

            public static void main(String[] args) {
                new Thread(null, new main(), "Check2", 1 << 28).start();// to increse stack size in java
            }
            void init(ArrayList <Integer> adj[], int n){
                for(int i=0;i<=n;i++)adj[i]=new ArrayList<>();
            }
            static long mod = (long) (1e9 + 7);
            public void run() {
                InputReader in = new InputReader(System.in);
                PrintWriter w = new PrintWriter(System.out);

                int n=in.nextInt();

                     ArrayList <Integer> ans=new ArrayList<>();
                     for(int i=0;i<=100;i++){
                         int p=n-i;
                         if(p<0)break;
                         int cur=p;
                         int pp=p;
                         while (p>0){
                             cur+=p%10;
                             p/=10;
                         }

                         if(cur==n){
                             ans.add(pp);
                         }
                     }
                     if(ans.size()==0){
                         w.println(0);
                     }
                     else{
                         w.println(ans.size());
                         Collections.sort(ans);
                         for(Integer ne:ans)w.println(ne);
                     }





                w.close();
            }

           
            static class InputReader
            {
                private InputStream stream;
                private byte[] buf = new byte[1024];
                private int curChar;
                private int numChars;
                private SpaceCharFilter filter;

                public InputReader(InputStream stream)
                {
                    this.stream = stream;
                }

                public int read()
                {
                    if (numChars==-1)
                        throw new InputMismatchException();

                    if (curChar >= numChars)
                    {
                        curChar = 0;
                        try
                        {
                            numChars = stream.read(buf);
                        }
                        catch (IOException e)
                        {
                            throw new InputMismatchException();
                        }

                        if(numChars <= 0)
                            return -1;
                    }
                    return buf[curChar++];
                }

                public String nextLine()
                {
                    BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
                    String str = "";
                    try
                    {
                        str = br.readLine();
                    }
                    catch (IOException e)
                    {
                        e.printStackTrace();
                    }
                    return str;
                }
                public int nextInt()
                {
                    int c = read();

                    while(isSpaceChar(c))
                        c = read();

                    int sgn = 1;

                    if (c == '-')
                    {
                        sgn = -1;
                        c = read();
                    }

                    int res = 0;
                    do
                    {
                        if(c<'0'||c>'9')
                            throw new InputMismatchException();
                        res *= 10;
                        res += c - '0';
                        c = read();
                    }
                    while (!isSpaceChar(c));

                    return res * sgn;
                }

                public long nextLong()
                {
                    int c = read();
                    while (isSpaceChar(c))
                        c = read();
                    int sgn = 1;
                    if (c == '-')
                    {
                        sgn = -1;
                        c = read();
                    }
                    long res = 0;

                    do
                    {
                        if (c < '0' || c > '9')
                            throw new InputMismatchException();
                        res *= 10;
                        res += c - '0';
                        c = read();
                    }
                    while (!isSpaceChar(c));
                    return res * sgn;
                }

                public double nextDouble()
                {
                    int c = read();
                    while (isSpaceChar(c))
                        c = read();
                    int sgn = 1;
                    if (c == '-')
                    {
                        sgn = -1;
                        c = read();
                    }
                    double res = 0;
                    while (!isSpaceChar(c) && c != '.')
                    {
                        if (c == 'e' || c == 'E')
                            return res * Math.pow(10, nextInt());
                        if (c < '0' || c > '9')
                            throw new InputMismatchException();
                        res *= 10;
                        res += c - '0';
                        c = read();
                    }
                    if (c == '.')
                    {
                        c = read();
                        double m = 1;
                        while (!isSpaceChar(c))
                        {
                            if (c == 'e' || c == 'E')
                                return res * Math.pow(10, nextInt());
                            if (c < '0' || c > '9')
                                throw new InputMismatchException();
                            m /= 10;
                            res += (c - '0') * m;
                            c = read();
                        }
                    }
                    return res * sgn;
                }

                public String readString()
                {
                    int c = read();
                    while (isSpaceChar(c))
                        c = read();
                    StringBuilder res = new StringBuilder();
                    do
                    {
                        res.appendCodePoint(c);
                        c = read();
                    }
                    while (!isSpaceChar(c));

                    return res.toString();
                }

                public boolean isSpaceChar(int c)
                {
                    if (filter != null)
                        return filter.isSpaceChar(c);
                    return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
                }

                public String next()
                {
                    return readString();
                }

                public interface SpaceCharFilter
                {
                    public boolean isSpaceChar(int ch);
                }
            }







        }