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Language: Polynomial
Description In the present problem, we always assume that all the polynomials mentioned have the following properties (take f(x) for example ):
(1) 0 < deg(f) <= 20, so we can assume that f(x) has the following form: f(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+...+a_{1}x+a0 (an!=0 and 1<=n<=20)(2) ai ( i=0,1,...,n ) is integer, and ?2^31<=ai<=2^31-1; (3) an = 1. We call a polynomial G(x) "good" polynomial, when there is no polynomial F(x) such that F^{2}|GGiven a polynomial f(x), it is known that f(x) can be factorized as follow: f(x)=Gt
^{mt}G_{t-1}^{mt-1}...G1^{m1} (Gi is good and mt>m_{t-1}>...>m1>=1)It抯 easy to prove that this way of factorizing is unique. You job is to factorize the given polynomials in this way. To make input and output easy, a polynomial f(x) f(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+...+a_{1}x+a0 (an!=0 and 1<=n<=20)is represented as _{n-1} ... a1 a0In this representation, we use (n+2) integers, which are separated by single blanks. Input The first line of the input contains a single integer T (1 <= T <= 20), the number of test cases. Then T cases follow. Every case gives a polynomial in a single line. Output For each test case, output the corresponding result in the following form (where the meaning of those characters is taken as just mentioned):
t m _{t} G_{t}
m _{t-1} G_{t-1}
... m _{1} G_{1}Sample Input 2 5 1 -3 4 -4 3 -1 2 1 -1 -2 Sample Output 2 3 1 1 -1 1 2 1 0 1 1 1 2 1 -1 -2 Hint 补充：
如果f=a1^n1*...at^nt(n1>...>nt) 那么要求a1,a2...at两两互质 Source |

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