Create a deterministic state diagram which accepts all binary strings in the following set $($and rejects all others$)$:

$\{w|w$ does not contain $an$ even$-$length run $of0s\}$

$($A "run" is a maximal group of consecutive identical symbols, so e$.$g$.0000010$ consists of a length$-5$ run of $0$s

followed by a length$-1$ run of $1s$ and then a length$-1$ run of $0$ s$.$ Examples for your state diagram: $,11,00000,$

and $00010110001$ should all be accepted, while $00$ and $11100101000$ should be rejected. A string is

"accepted" if the state diagram ends up in a Goal State $($aka "end", "final", or "accepting" state$)$ after the whole

string is read, and the string is rejected otherwise.$)$

Hint: it is possible to solve this using just $4$ states, though you are welcome to use more.