Simple Quadratic Factorization

In this problem, you are given a quadratic polynomial in one variable (x) of the form (x^2 + bx + c) (with the coefficient of (x^2) always equal to 1). The input polynomial may be written in a simplified format where:

• The term for \(x^2\) is always present as "x^2".
• If the coefficient of \(x\) is 1 or -1, the number 1 is omitted (i.e. written as "x" or "-x").
• If either the \(x\) term or the constant term has a coefficient of 0, that term is completely omitted.

Your task is to factorize the given polynomial into two linear factors with integer constants. That is, for a polynomial

[ x^2 + bx + c, ]

find two integers (m) and (n) such that:

[ m+n = b, \quad m \times n = c. ]

Then, output the factorization in the format:

[ (x + m)(x + n), ]

where the linear factors are printed according to the following rules:

• If the constant part is 0, output the factor as simply "x".
• If the constant is positive, print it as "x+constant".
• If the constant is negative, print it as "x-abs(constant)".

It is guaranteed that the input polynomial can be factorized in this manner with integer factors. Note that the input expression will always be in a simplified format (for example, omitting the coefficient 1).

inputFormat

A single line containing a quadratic polynomial expressed in the simplified format (e.g. x^2+5x+6, x^2-3x+2, or x^2+4).

outputFormat

A single line containing the factorization of the polynomial in the format (factor1)(factor2) without any extra spaces. For example, if the input is x^2+5x+6, the output should be (x+2)(x+3).

sample

x^2+5x+6

(x+2)(x+3)