Express each of X, Y and Z in terms of a,b,c,p,q and r so that the equation given below becomes an identity.

(a^{3}+b^{3}+c^{3} - 3abc)(p^{3}+q^{3}+r^{3} - 3pqr) = X^{3}+Y^{3}+Z^{3} - 3XYZ

__Note__: Disregard any permutations. For example, if (X, Y, Z) = (α, β, γ), then (X, Y, Z) = (β, γ, α) is invalid.

Contrary to the comments posited, there does exist a

*general solution* to the given problem.

I will wait for a week before officially posting the solution.

I regret my inability to provide any hint, as positing that would render this problem to less than D1 in light of the comment received until now.