Let $A=\left[\begin{array}{lll}0 & 1 & 2 \\ a & 0 & 3 \\ 1 & c & 0\end{array}\right]$, where $a, c \in R$. If $A^3=A$ and the positive value of a belongs to the interval $(n-1$, $n]$, where $n \in N$, then $n$ is equal to $\_\_\_\_$ .
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