\begin{array}{c|c} f & (f(0),f(1),f(2)) \\ \hline[br]0 & (0,0,0) \\[br]1 & (1,1,1) \\[br]2 & (2,2,2) \\[br]x & (0,1,2) \\[br]x+1 & (1,2,0) \\[br]x+2 & (2,0,1) \\[br]2x & (0,2,1) \\[br]2x+1 & (1,0,2) \\[br]2x+2 & (2,1,0) \end{array}
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