1780: Smeech

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?

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.

Please Input Input Here

Please Input Output Here

7
(.5 3 9)
()

7.00
3.00