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.
/*

LANG: JAVA
TASK: combo
 */
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Random;

public class combo
{
	public static void main(String[] args) throws Exception
	{
		BufferedReader bR = new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(bR.readLine());
		int min = n-(""+n).length()*9;
		ArrayList<Integer> working = new ArrayList<Integer>();
		for (int i = Math.max(min,1); i < n; i++)
		{
			if(sumDigits(i)+i==n)
			{
				working.add(i);
			}
		}
		System.out.println(working.size());
		for(int wor : working)
		{
			System.out.println(wor);
		}
	}

	public static int sumDigits(int i)
	{
		if(i==0)
		{
			return 0;
		}
		return  i % 10 + sumDigits(i / 10);
	}

	static int minCoins(int coins[], int m, int V)
	{
		// table[i] will be storing the minimum number of coins
		// required for i value. So table[V] will have result
		int[] table = new int[V + 1];
		// Base case (If given value V is 0)
		table[0] = 0;
		// Initialize all table values as Infinite
		for (int i = 1; i <= V; i++)
			table[i] = Integer.MAX_VALUE;
		// Compute minimum coins required for all
		// values from 1 to V
		for (int i = 1; i <= V; i++)
		{
			// Go through all coins smaller than i
			for (int j = 0; j < m; j++)
				if (coins[j] <= i)
				{
					int sub_res = table[i - coins[j]];
					if (sub_res != Integer.MAX_VALUE && sub_res + 1 < table[i])
						table[i] = sub_res + 1;
				}
		}
		return table[V];
	}

	static long fibbonaci(int n)
	{
		if (n < 2)
		{
			return 1;
		}
		return fibbonaci(n - 1) + fibbonaci(n - 2);
	}

	static int findMinDiff(int[] array)
	{
		int min = Integer.MAX_VALUE;
		for (int a = 0; a < array.length - 1; a++)
		{
			min = Math.min(min, array[a + 1] - array[a]);
		}
		return min;
	}

	static int numUppercase(String a)
	{
		int num = 0;
		char[] thing = a.toCharArray();
		for (char c : thing)
		{
			if (c >= 'A' && c <= 'Z')
			{
				num++;
			}
		}
		return num;
	}

	static char whichChar(char[][] array, int startX, int endX, int startY,
			int endY)
	{
		char test = array[startY][startX];
		for (int x = startX; x < endX; x++)
		{
			for (int y = startY; y < endY; y++)
			{
				if (array[y][x] != test)
				{
					return '-';
				}
			}
		}
		return test;
	}

	public static void shuffle(int[] array)
	{
		Random random = new Random();
		for (int i = array.length - 1; i > 0; i--)
		{
			int index = random.nextInt(i + 1);

			int temp = array[index];
			array[index] = array[i];
			array[i] = temp;
		}
	}

	public static int[] readInt(BufferedReader bR) throws Exception
	{
		String temp[] = bR.readLine().split(" ");
		int[] readArr = new int[temp.length];
		for (int a = 0; a < temp.length; a++)
		{
			readArr[a] = Integer.parseInt(temp[a]);
		}
		return readArr;
	}

	public static double[] readDouble(BufferedReader bR) throws Exception
	{
		String temp[] = bR.readLine().split(" ");
		double[] readArr = new double[temp.length];
		for (int a = 0; a < temp.length; a++)
		{
			readArr[a] = Double.parseDouble(temp[a]);
		}
		return readArr;
	}

	public static long[] readLong(BufferedReader bR) throws Exception
	{
		String temp[] = bR.readLine().split(" ");
		long[] readArr = new long[temp.length];
		for (int a = 0; a < temp.length; a++)
		{
			readArr[a] = Long.parseLong(temp[a]);
		}
		return readArr;
	}
}
