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.
Please Input Input Here
Please Input Output Here