Problems
Smeech
Smeech
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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 \textbf{(p e_1 e_2)} where \textbf{p }is a real number between \textbf{0} and \textbf{1} (inclusive) and \textbf{e_1} and \textbf{e_2} are Smeech expressions. The value represented by a Smeech expression is as follows:
\begin{itemize}
\item An integer represents itself
\item With probability \textbf{p}, \textbf{(p e_1 e_2) }represents \textbf{x + y }where \textbf{x }is the value of \textbf{e_1} and \textbf{y }is the value of \textbf{e_2}; otherwise it represents \textbf{x - y}.
\end{itemize}
Given a Smeech expression, what is its expected value?
\InputFile
Consists of several Smeech expressions, one per line, followed by a line containing \textbf{( )}.
\OutputFile
For each expression, output its expected value to two decimal places.
Input example #1
7 (.5 3 9) ()
Output example #1
7.00 3.00