OMM 2012 Problem 4

The following process is applied to each positive integer: the sum of its digits is subtracted from the number, and the result is divided by $9$ . For example, the result of the process applied to $938$ is $102$ , since $\frac{938-(9 + 3 + 8)}{9} = 102.$ Applying the process twice to $938$ the result is $11$ , applied three times the result is $1$ , and applying it four times the result is $0$ . When the process is applied one or more times to an integer $n$ , the result is eventually $0$ . The number obtained before obtaining $0$ is called the house of $n$ .

How many integers less than $26000$ share the same house as $2012$ ?