Consider Simon's problem with the case $n=3.$

$($a$)$ Find the state after passing through the first Hadamard gate.

$($b$)$ Assuming that the function $f$ satisfies $f(000)=f(111)=000,f(001)=f(110)=001,f(010)=f(010)=010,f(011)=f(100)=011,$ find the state after passing the $F$ gate.

$($c$)$ Find the status after passing through the second Hadamard gate.

$($d$)$ Write down all the measurements you can get from the first three qubits.

$($e$)$ Turn the circuit twice to show that the secret strings can be obtained from this result when the measurements of $011$ and $101$ are obtained respectively.