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printЛето 12

printB. 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  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

7
(.5 3 9)
()

Output for Sample Input

7.00
3.00
Source: Gordon V. Cormack, Waterloo local contest, 2007
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