{"trustable":true,"sections":[{"title":"","value":{"format":"HTML","content":"\u003cdiv class\u003d\"problem_par\"\u003e\u003cdiv class\u003d\"problem_par_normal\"\u003eVasya, nicknamed Ferrari, has to solve an equation of fourth degree with integer \r\ncoefficients \u003ci\u003ex\u003c/i\u003e\u003csup\u003e4\u003c/sup\u003e+\u003ci\u003eax\u003c/i\u003e\u003csup\u003e3\u003c/sup\u003e+\u003ci\u003ebx\u003c/i\u003e\u003csup\u003e2\u003c/sup\u003e+\u003ci\u003ecx\u003c/i\u003e+\u003ci\u003ed\u003c/i\u003e \u003d 0. \r\nVasya wants to factorize the polynomial in the left part of this equation to the \r\nmaximal possible number of multipliers with integer coefficients to reduce the \r\nproblem to solving several equations of lower degree.\r\n\u003c/div\u003e\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cdiv class\u003d\"problem_par\"\u003e\u003cdiv class\u003d\"problem_par_normal\"\u003e4 integers: \u003ci\u003ea\u003c/i\u003e, \u003ci\u003eb\u003c/i\u003e, \u003ci\u003ec\u003c/i\u003e, \u003ci\u003ed\u003c/i\u003e\u0026nbsp;— the coefficients of the polynomial, \r\nwith absolute values not exceeding 20000.\r\n\u003c/div\u003e\u003c/div\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cdiv class\u003d\"problem_par\"\u003e\u003cdiv class\u003d\"problem_par_normal\"\u003eIf the polynomial can\u0027t be factorized to multipliers with integer coefficients, \r\nyou 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\u0027t delimit the multipliers with spaces and output monomials with zero coefficients. Coefficients and degrees equal to 1 should be omitted, except the monomial “1”.\r\n\u003c/div\u003e\u003c/div\u003e"}},{"title":"Sample","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e0 0 0 0\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e(x)(x)(x)(x)\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003cbr\u003e\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e-4 -3 24 45\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e(x2+3x+3)(x2-7x+15)\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003cbr\u003e\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e1 1 1 1\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eIrreducible\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}