Vasya, nicknamed Ferrari, has to solve an equation of fourth degree with integer
coefficients x4+ax3+bx2+cx+d = 0.
Vasya wants to factorize the polynomial in the left part of this equation to the
maximal possible number of multipliers with integer coefficients to reduce the
problem to solving several equations of lower degree.
4 integers: a, b, c, d — the coefficients of the polynomial,
with absolute values not exceeding 20000.
If the polynomial can't be factorized to multipliers with integer coefficients,
you should output a single line “Irreducible”. In the other case output the factorization of the polynomial as a product of several polynomials with integer coefficients, enclosed in parentheses. You shouldn't delimit the multipliers with spaces and output monomials with zero coefficients. Coefficients and degrees equal to 1 should be omitted, except the monomial “1”.
0 0 0 0
-4 -3 24 45
1 1 1 1
Problem Author: Igor Chevdar
Problem Source: Ural SU Contest. Petrozavodsk Winter Session, January 2008