Problem Description

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:
1) An integer represents itself
2) 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?

Input

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

Output

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

7
(.5 3 9)
()

7.00
3.00

Author

Gordon V. Cormack