This problem was created by CodeWars user "SleepingCode".

Description:

When we attended middle school were asked to simplify mathematical expressions like "3x-yx+2xy-x" (or usually bigger), and that was easy-peasy ("2x+xy"). But tell that to your pc and we'll see!

Write a function:

simplify(poly) that takes a string in input, representing a multilinear non-constant polynomial in integers coefficients (like "3x-zx+2xy-x"), and returns another string as output where the same expression has been simplified in the following way ( -> means application of simplify):

All possible sums and subtraction of equivalent monomials ("xy==yx") has been done, e.g.: "cb+cba" -> "bc+abc", "2xy-yx" -> "xy", "-a+5ab+3a-c-2a" -> "-c+5ab"

All monomials appears in order of increasing number of variables, e.g.: "-abc+3a+2ac" -> "3a+2ac-abc", "xyz-xz" -> "-xz+xyz"

If two monomials have the same number of variables, they appears in lexicographic order, e.g.: "a+ca-ab" -> "a-ab+ac", "xzy+zby" ->"byz+xyz"

There is no leading + sign if the first coefficient is positive, e.g.: "-y+x" -> "x-y", but no restrictions for -: "y-x" ->"-x+y"

N.B. to keep it simplest, the string in input is restricted to represent only multilinear non-constant polynomials, so you won't find something like '-3+yx^2'. Multilinear means in this context: of degree 1 on each variable.

Warning: the string in input can contain arbitrary variables represented by lowercase characters in the english alphabet.