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- 1202

## Learning Opportunities

This puzzle can be solved using the following concepts. Practice using these concepts and improve your skills.

## Statement

## Goal

Calculate the equivalent resistance of a circuit containing only resistors.A resistor is a component used in electrical circuits. A resistor is quantified by its

**Resistance**, which is measured in Ohms. We are interested in knowing the total resistance of a circuit of only resistors. There are two key definitions needed to determine the resistance of multiple resistors.

**1. Series**

The resistance of resistors in a line is equivalent to the sum of the resistance of those resistors.

---[R_1]---[R_2]---

Resistors in series will be noted with parentheses ( R_1 R_2 R_3 ... and so on ).

The resistance of a series arrangement is: R_eq = R_1 + R_2 + R_3 + ... and so on, where R_eq is the equivalent resistance of the series arrangement.

**2. Parallel**

The resistance of resistors in branching paths of the circuit is equal to 1 over the sum of 1 over the resistance of each branching path.

+---[R_1]---+

| |

---+ +---

| |

+---[R_2]---+

Resistors in parallel will be noted with brackets [ R_1 R_2 R_3 ... and so on ].

The resistance of resistors in parallel is R_eq = 1/(1/R_1 + 1/R_2 + 1/R_3 + 1/... and so on).

A branch can be treated as a single resistor by determining its equivalent resistance.

**Example:**

`N`= 3

A 24

B 8

C 48

[ ( A B ) [ C A ] ]

This will look something like this:

+---[C]---+

| |

+--+ +--+

| | | |

| +---[A]---+ |

| |

+---[A]---[B]---+

| |

+---[Battery]---+

[

Input

**Line 1:**An integer

`N`for the number of unique resistors present in the circuit

**Next**A space separated

`N`lines:`name`and the integer resistance

`R`of a resistor

**Last line:**A space separated combination of parentheses, brackets, and names of resistors

Output

The equivalent resistance expressed as a float rounded to the nearest 0.1 Ohms.

Constraints

0 <

0 <

`N`< 100 <

`R`< 100Example

Input

2 A 20 B 10 ( A B )

Output

30.0

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