Algebra Level 5

How many unordered triplets $$(x,y,z)$$ are in the range $$[0,2]$$ and satisfy the system of equations: $\left\{\begin{array}{l}2x^2-4x+2=y\\ 2y^2-4y+2=z\\ 2z^2-4z+2=x\end{array}\right.$

Details and Assumptions:

An unordered triplet means that $$(1,2,3)$$ is the same as $$(3,2,1)$$ or $$(1,3,2)$$.

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