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문제

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:

  • An integer represents itself
  • With probability p, (p e1 e2) represents x+y where x is the value of e1 and y is the value of e2; otherwise it represents x-y.

Given a Smeech expression, what is its expected value?

입력

Input consists of several Smeech expressions, one per line, followed by a line containing (). 

출력

For each expression, output its expected value to two decimal places.

예제 입력

7
(.5 3 9)
()

예제 출력

7.00
3.00

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