CF875A.Classroom Watch

普及/提高-

通过率：0%

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题目描述

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.

输入格式

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

输出格式

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.

输入输出样例

输入#1
```
21
```
输出#1
```
1
15
```
输入#2
```
20
```
输出#2
```
0
```

说明/提示

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 $x$ .

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