Practice Parsing and Algebra with the exercise "Expand the polynomial"

Learning Opportunities

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

Parsing
Algebra
Output formatting
Mathematics

Statement

Goal

You are given a polynomial that is partially or fully factorized and you have to write a code that fully expands it.
For example, if you are given (x-1)*(x+2)=x²+x-2, its coefficients that are 1 1 -2 and you have to write x^2+x-2.

Input

A partially or not factorized polynomial.

Output

The expanded polynomial written in the standard way:
* x^1 is written x
* 1x^3 is written x^3
* 0x^2 and x^0 are not written

Constraints

All the coefficients are integers (positive, null or negative).
All coefficients are in decreasing order: (x^3 then x^2 then x^1 then x^0)

Example

Input

(x-1)*(x+2)

Output

x^2+x-2

Solve it

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