200753: [AtCoder]ARC075 F - Mirrored

Problem Statement

For a positive integer $n$, we denote the integer obtained by reversing the decimal notation of $n$ (without leading zeroes) by $rev(n)$. For example, $rev(123) = 321$ and $rev(4000) = 4$.

You are given a positive integer $D$. How many positive integers $N$ satisfy $rev(N) = N + D$?

Constraints

• $D$ is an integer.
• $1 ≤ D < 10^9$

Input

Input is given from Standard Input in the following format:

$D$

Output

Print the number of the positive integers $N$ such that $rev(N) = N + D$.

Sample Input 1

63

Sample Output 1

2

There are two positive integers $N$ such that $rev(N) = N + 63$: $N = 18$ and $29$.

Sample Input 2

75

Sample Output 2

0

There are no positive integers $N$ such that $rev(N) = N + 75$.

Sample Input 3

864197532

Sample Output 3

1920