Palindrome Counting

TopicDifficultyCompanies
Mathematical
HARD

In how many different ways can the palindrome "WAS IT A CAT I SAW" be read in the diamond shaped arrangement shown in the figure? You may start at any W and go in any direction on each step - up, down, left or right - through adjacent letters. The same letter can be used more than once in the same sequence.

puzzle

The Answer is an integer. Just put the number without any decimal places.
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