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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