Let the matrix $A=\left[\begin{array}{lll}1 & 0 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 0\end{array}\right]$ satisfy $A^n=A^{n-2}+A^2-1$ for $n \geqslant 3$. Then the sum of all the elements of $A^{50}$ is:
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