HZNUOJ

Smeech

Tags:
Time Limit:  1 s      Memory Limit:   128 MB
Submission:5     AC:5     Score:99.68

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:

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.

Input

Please Input Input Here

Output

Please Input Output Here

Samples

input
7 (.5 3 9) ()
output
7.00 3.00