Draw the state diagram of a T$-$decider for the language $\{$w $|$ w contains $2-$times as many $0\text{'}$s as $1\text{'}$s$\}.$ Test your diagram on each of the following inputs and for those inputs that are rejected, indicate the last state from which the q$\_$reject state is reached.

$110100000$

$1101000$

$01010$