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 $*n*$ ($1 ≤ *n* ≤ 10^{9}$).

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.

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 $*x*$.