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.

The first line contains integer $ n $ ( $ 1

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 $ .