Pen and paper please

A pattern recognizer has the following specifications:

a$)$ a single input and a single output.

b$)$ The output is $1$ if and only if the input has completed the sequence $1010$ NO$-$OVERLAP is ALLOWED $(15$ points$)$ USE D flip$-$flops and any necessary external gates.

a$)$ show the STATE DIAGRAM $(5$ points$)$

b$)$ show the STATE TRANSITION TABLE and the input to the flipflops. $(5$ points$)$

c$)$ Indicate the necessary Boolean functions in their SIMPLIFIED form. $(5$ points$)$

d$)$ NO NEED TO DRAW the CIRCUIT!!!