A11178. Classroom Watch

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.

The first line contains integer $n$ ( $1<=n<=10^{9}$ ).

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.

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 $x$ .