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For a binary string, $x = a_0,a_1, · · · ,a_n−1$ define $val(x)$ to be the value of x interpreted as a binary number, where $a_0$ is the most significant bit. More formally, $val(x)$ is given by         

$\sum_{0\leq i<n}2^{n-1-i}\cdot a_{i}$

How many minimum states will be in a finite automaton that accepts exactly the set of binary strings x such that val(x) is divisible by either $4$ or $ 5?$
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