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Professor Octastichs has invented a new programming language, Smeech. An expression in Smeech may be a positive or negative integer, or may be of the form (p e1 e2) where p is a real number between 0 and 1 (inclusive) and e1 and e2 are Smeech expressions. The value represented by a Smeech expression is as follows:
Given a Smeech expression, what is its expected value?
Input consists of several Smeech expressions, one per line, followed by a line containing ().
For each expression, output its expected value to two decimal places.
7 (.5 3 9) ()
Waterloo Local Contest, 2007.9.29
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