CF875A.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.

八年级学生沃瓦今天在班里值日。下课后，他走进办公室擦黑板，发现黑板上写着一个数字 $n$。他问这是什么数字，数学老师伊娜·彼得罗夫娜告诉沃瓦：$n$ 是一道面向一年级学生的算术题的答案。教科书中给出某个正整数 $x$，题目要求将 $x$ 与其在十进制表示下的各位数字之和相加。

由于黑板上的数字 $n$ 很小，沃瓦很快猜出了教科书中可能的 $x$ 值。现在，他希望编写一个程序：对于任意给定的 $n$，找出所有满足条件的 $x$，或判定这样的 $x$ 不存在。请为沃瓦编写这样一个程序。

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

第一行包含一个整数 $n$（$1 \leq n \leq 10^9$）。

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.

第一行输出一个整数 $k$ —— 满足条件的不同 $x$ 值的个数。

接下来的 $k$ 行按升序输出这些值。

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.

在第一个测试用例中，$x = 15$，只有一种可能：$15 + 1 + 5 = 21$。

在第二个测试用例中，不存在满足条件的 $x$。