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设 $A =\left(\begin{array}{cccc}1 & -1 & -1 & -1 \\ -1 & 1 & -1 & -1 \\ -1 & -1 & 1 & -1 \\ -1 & -1 & -1 & 1\end{array}\right), f(x)=1+x+x^2+\cdots+x^{2 n+1}$, 则 $f( A )=$
                        
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