Construct the ladder logic diagram $($LD$)$ for the operation of the parking gate system illustrated in Figure P$1$

Figure P$1$

When a car enters, the vehicle sensor $(x0)$ turns $ON.$

When the vehicle sensor turns $ON,$ a ticket is issued $($Y$0).$

When the ticket is taken, the ticket sensor $($X$1)$ turns ON$.$

When the ticket sensor turns ON$,$ the gate opens $($Y$1),$ and Gate close limit sensor $($X$3)$ turns OFF.

When the gate is fully open, the gate open limit sensor $($X$2)$ turns ON$,$ and the gate stops.

When the car passes the gate, the vehicle sensor turns OFF $($X$0).$

When the vehicle sensor turns OFF, the timer counts $3$ seconds for safety, and then the gate closes $($Y$2),$ and the gate open limit sensor $($X$2)$ turns OFF.

When the gate is fully closed, the gate close limit sensor turns ON$,$ and the gate stops.

$\backslash$table$[[$External Device,Input$/$output$,$Tag $($Address$)],[$Vehicle Sensor,Input,X$0],[$Ticket Sensor,Input,X$1],[$Gate Open Limit Sensor,Input,X$2],[$Gate Close Limit Sensor,Input,X$3],[$Issue Ticket,Output,Y$0],[$Gate Opening Motor,Output,Y$1],[$Gate Closing Motor,Output,Y$2]]$