# A discrete mathematics problem by Shenal Kotuwewatta

Peter created a cool problem to post on Brilliant, but he don't have a cool name for that.

So he decided wrote a simple program which outputs a string of 7 letters.

(The letters are from A-Z, and the same letter may be repeated.)

Call a name pronounceable if vowels and consonants appear alternatively in that name. The probability that the name of Peter's problem is pronounceable is $$\frac{p}{q}$$ where $$p$$ and $$q$$ are coprime positive integers. What is the last $$3$$ digits of $$p+q$$?

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