URI Online Judge | 2673
# Serial and Parallel Resistors

**Timelimit: 1**

By Hamilton José Brumatto, UESC Brazil

An association of resistors always results in an equivalent resistor. This association can be in parallel, in series or hybrid. See example of a parallel association:

This parallel association is equivalent to a resistor of 10 Ω. We can also consider series associations, as the example below, which results in an equivalent resistance of 40Ω.

Finally, a hybrid association, with series and parallel. The association below results in 50Ω.

To better represent an association we will consider the equivalent resistance Req of a series association between resistors R1 and R2 represented as: Req = R1 - R2. Similarly for the parallel association: Req = R1 | R2. There is no precedence between associations, except when explicitly expressed in parentheses, for example: R1 - R2 | R3 is equivalent to (R1-R2) | R3, and R1 | R2 - R3 is equivalent to (R1 | R2 - R3) These two circuits can be drawn, respectively, as:

In this way a hybrid association is represented by an expression that follows the following rule, considering R the nominal value of a resistance in Ohms (Ω):

*exp* := **R**;

*exp* := *exp* - *exp*;

*exp* := *exp* | *exp*;

*exp* := ( *exp* ).

The hybrid circuit of the third figure above could be represented by the expression:

R_{eq} = 20 - (20 | 20) - 20 = 50

You have been asked for a program where, given the expression of an association, calculate the equivalent resistance.

The input contains several test cases, each test case occupying a line of a maximum of 300 symbols (there is no blank space) and represents a valid expression for the association of resistors, where each resistor value is represented by an integer **R** (0 < **R** < 10000). The end of the test cases coincides with the end of the input.

For each test case, the equivalent resistance value with three decimal digits is expected on a single line.

Input Sample | Output Sample |

20-20 |
40.000 |