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$2x^{21}-2x^{20}+2x^{18}-2x^{17}+2x^{15}-2x^{14}+2x^{12}-2x^{11}+2x^{9}-2x^{8}+2x^{6}-2x^{5}+x^{3}-x^{2}+1+\frac{-x+2}{x^2+x+1}$