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## Learning Opportunities

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

## Statement

## Goal

Story:Louise is learning calculus in her maths courses and she likes the idea. When doing her homework, she is not sure and she wants to check her answers with yours. Could you create a program so that we can check the answers?

Calculate, evaluate the partial derivative of a given formula.

For instance,

given the function formula "(5*(x*(y^2)))"

and "y x", the variables in respect with you must derive it

So here f(x,y) = 5xy²

and you have to calculate:

d²f(x,y)

----------

dxdy

it gives you the formula 10*y,

At last "x 2 y 6" means x=2, y=6,

gives you the values with which you must evaluate the obtained derivative

So the answer should be 60

Note:

To simplify the task, only consider

Negative power has no parenthesis.

e.g. (((18*(x^

`var`s may be in other forms other than x, y, and z. Similar to identifiers in many programming languages, the

`var`would be some letter followed by letters, numbers or underscore.

link about calculus rules:

**https://en.wikipedia.org/wiki/Differentiation_rules**

The rules needed here:

a'=0

(a*x)'=a

(x^a)'=a*x^(a-1) (when a is not 0)

(u+v)'=u'+v'

(u*v)'=u'*v+v'*u

Input

**Line 1**:

`formula`

**Line 2**: list of

`var`s for partial derivative, separated by space, length of the list will be 1, 2 or 3.

**Line 3**:

`var`s' values, paired and separated by space

Output

The result (always an

`integer`).Constraints

All numbers are integers.

You can assume that the second argument of ^ is constant, to be simple and avoid "ln" or "e^x".

e.g.:

will appear:

(x^y)

x

x 1 y 1

won't appear (this could be too complex):

(x^y)

y

x 1 y 1

**Line 2**would give a list from 1 to 3 different/same`var`s to do partial derivative.You can assume that the second argument of ^ is constant, to be simple and avoid "ln" or "e^x".

e.g.:

will appear:

(x^y)

x

x 1 y 1

won't appear (this could be too complex):

(x^y)

y

x 1 y 1

Example

Input

(5*(x*y)) x x 2 y 6

Output

30

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