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Is there a classification of all products of different cyclotomic polynomials with non-negative coefficients?

Clearly if the cyclotomic polynomials have only nonnegative coefficients, their products have only nonnegative coefficients too. But the example $\Phi_2(x)\Phi_6(x)=(x+1)(x^2-x+1)=x^3+1$ shows that other solutions are possible too. I am interested in all such possibilities, when no cyclotomic polynomial appears more than once.

Notice that what I am interested in are cyclotomic polynomials being different in the product. This is why this is different from

Products of Cyclotomic Polynomials with Nonnegative Coefficients

where it is claimed that the general answer is unmanageable but relies on an example with products of multiples of same cyclotomic polynomials.

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