Need help with EE/ compE question

Design a sequence recognizer. In this problem you will be designing a sequential circuit for a sequence recognizer. You will develop a state diagram with one input variable X and one output variable Z. The output is 1 if and only if the last four input bits are 0010 or 0001. Note that sequences may overlap. Sample input: 1 0 0 1 1 0 0 0 0 1 0 0 1 0 1 1 1 0 1 0 0 1 0 Sample output: 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 1 Please draw the state diagram. Label each are with X/Z. Label the initial state with S0 and other states with S1, S2, S3, etc. And then explain the purpose of each state. Use a minimum number of states