A + B = C

Practice contests at informatics olympiads often include an "A + B" problem, where the task is to find the sum of given integers $A$ and $B$.

While preparing a city informatics olympiad, the chair of the judging committee decided to make the tests for such a problem himself. He used his own method: first choose the intended correct answers, then construct the input data that matches those answers.

Suppose the chair chose a number $C$ with $n$ decimal digits whose first digit is not zero. He now wants to find positive integers $A$ and $B$ such that their sum is $C$, and each of them also has $n$ decimal digits with a nonzero first digit. In addition, the chair wants both $A$ and $B$ to be beautiful. In his view, a number is beautiful if its decimal representation contains no two equal consecutive digits. For example, $1272$ is beautiful, while $1227$ is not.

Given a positive integer $C$, write a program that counts the pairs of beautiful positive integers $A$ and $B$ whose sum is $C$. Since the count can be large, output the remainder of this count modulo $10^9+7$.

The input file contains a single positive integer $C$. $C$ does not start with zero. The number of digits of $C$ is at most $10\,000$.

The output file must contain a single integer: the remainder of the number of desired pairs of beautiful numbers $A$ and $B$ modulo $10^9+7$.

$22$ can be written as a sum of two-digit numbers in three ways: $10 + 12$, $11 + 11$, $12 + 10$. The way $11 + 11$ does not qualify because $11$ is not beautiful. Therefore the answer for $22$ is $2$.

$200$ can be written as a sum of three-digit numbers in only one way: $100 + 100$. This way does not qualify, so the answer for $200$ is $0$.

$1000$ cannot be written as a sum of four-digit numbers, so the answer for $1000$ is also $0$.