Factors
Create a program that factors a polynomial with integer coefficients into irreducible polynomials—those that cannot be further factored into binomials with integer coefficients. You do not need to represent numbers as arrays of their digits, as long as you allocate 4 bytes for storing integers.
**Input Data**
The input consists of a natural number, the degree of the polynomial **n** (**n** < **100**), followed by (**n** + **1**) integers representing the coefficients of the polynomial, listed in descending order from degree **n** to **0**.
**Output Data**
The first line should display the sign of the leading coefficient of the polynomial and the greatest common divisor of all its coefficients. Each subsequent line should contain the following integers in the specified order:
the multiplicity of the divisor in the factorization of the original polynomial;
the degree of the polynomial divisor;
the coefficients of the polynomial in descending order of degree, ensuring the leading coefficient is positive.
Starting from the second line, as the line number increases, the leading coefficient of the binomial (the third number) should not decrease. For binomial divisors with the same leading coefficient, list the binomial of the lower degree first. For binomial divisors of the same degree and leading coefficient, list the binomial with a negative constant term (the last number of the line) first. The polynomial divisor that is not a binomial (the remainder after dividing the polynomial by all its binomial divisors, considering their multiplicity) should be recorded on the last line.
Each number should have no more than two digits.