Construct the state diagram for a two$-$input eight$-$state machine that is to produce an output z $=1$ whenever the last string of five input contains exactly three $1$s and string starts with two $1$s$.$ After each string that starts with two $1$s$,$ analysis of the next string will not start until the end of this string of five symbols, whether it produces an output value $1$ or not. For example, if the input sequence is $11011010$ then the output sequence is $00000000,$ while an input sequence $10011010$ produces an output sequence $00000001.$