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

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