# Oozy rat in a sanitary zoo

**Discrete Mathematics**Level 5

Consider the palindromic phrase

\[\text{OOZYRATINASANITARYZOO}\]

In how many ways can \(\text{OOZYRATINASANITARYZOO}\) be read if you start at any \(O\) and are restricted to read only up, down, left or right to adjacent letters?

*Note:* You are allowed to use the same letter twice, and you each case is counted twice since you can read a case from one direction, but it can also be read from the opposite direction.

You may use a calculator for the final step