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1035. Smeech

Ограничения: время – 1s/2s, память – 64MiB Ввод: input.txt или стандартный ввод Вывод: output.txt или стандартный вывод copy
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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\ e_1\ e_2)` where `p` is a real number between 0 and 1 (inclusive) and `e_1` and `e_2` are Smeech expressions. The value represented by a Smeech expression is as follows:
  • An integer represents itself
  • With probability `p`, `(p\ e_1\ e_2)` represents `x+y` where `x` is the value of `e_1` and `y` is the value of `e_2`; otherwise it represents `x-y`.
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.

Sample Input

(.5 3 9)

Output for Sample Input

Source: Gordon V. Cormack, Waterloo local contest, 2007