1999 AIME Problem 5

For any positive integer x_{}, let S(x) be the sum of the digits of x_{}, and let T(x) be |S(x+2)-S(x)|. For example, T(199)=|S(201)-S(199)|=|3-19|=16. How many values of T(x) do not exceed 1999?

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.