Professor Octastichs has invented a new programming language, Carl. An expression in Carl 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 Carl expressions. An integer represents itself and (p e1 e2) represents x + y where x is the value of e1 and y is the value of e2 with probability p, otherwise it represents x - y.

Given a Carl expression, what is its expected value?

Input

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

Output

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

Score

Score is the length of your source program.

Example

Input:
7
(.5 3 9)
()

Output:
7.00
3.00