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For a string $x=a_0a_1 \ cdots a_{n-1}$ over the alphabet $\{0, 1, 2\}$, define $val(x)$ to be the value of $x$ interpreted as a ternary number, where $a_0$ is the most significant digit. More formally, $val(x)$ is given by $$ \Sigma_{0 \leq i < n} 3^{n-1-i} \cdot a_i.$$

Design a finite automaton that accepts exactly the set of strings $ x \in \{0, 1, 2\}^*$ such that $val(x)$ is divisible by 4.
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