Let L be the set of all strings in $\{0,1\}*$ that contain at least two occurrences of the substring $000.$ Hint: The shortest string in L has the length $4$; for example, the substring $"0000"$ contains two occurrences of the substring $000.$

Describe a DFSM over the alphabet $\backslash$Sigma $=\{0,1\}$ that accepts the language L$.$ You may either draw the DFSM or describe it formally, but the states Q$,$ the start state q$0,$ the accepting states F$,$ and the transition function $\backslash$delta must be clearly specified.