Navigating menus using Joystick

I have a menu system in my game. The menu works with arrow keys on the keyboard and with the joystick/d-pad on an xbox controller. Since the joystick uses an axis I can not use Input.GetButtonDown, I have to use Input.GetAxis("Vertical"). I have Vertical mapped to the xbox joystick, the d-pad, and the arrow keys to cover both in 1 command.

The problem I was having then, was when I would hold down the joystick it would rapidly move ( I mean 10/second ) since this is in the Update() function.

As an attempt to solve the problem I have added a boolean value. When 0 < input > 0 it calls the MoveUp or MoveDown function appropriately. Within those two functions I have a value that turns false, and in MoveUp/Down function if this value is false it does not continue.

(I also have a counter which is an int. It only goes from 1 to 3 each representing an item in the menu, I only have 3 at this time.

Please I am open to any improvements to this code.)

 function Update(){
     var inputY = Input.GetAxis("Vertical");
 
     if (inputY > 0){
         MoveUp();
     } else{
         canMoveUp = true;
     }
     
     if (inputY < 0){
         MoveDown();
     } else{
         canMoveDown = true;
     }
 }
 
 function MoveUp(){
     if (canMoveUp == true){
         if (count == 3){
             count = 2;
             canMoveUp = false;
         } else if (count == 2){
             count = 1;
             canMoveUp = false;
         }
         
         if (count == 1){
             count = 1;
             canMoveUp = false;
         }
     }
 }
 
 function MoveDown(){
     if (canMoveDown == true){
         if (count == 1){
             count = 2;
             canMoveDown = false;
         } else if (count == 2){
             count = 3;
             canMoveDown = false;
         }
         
         if (count == 3){
             count = 3;
             canMoveDown = false;
         }
     }
 }

Now, I have a problem with this code. If I am holding down the down key (or holding the joystick down), I'm essentially calling this MoveDown function every frame. I believe this causes some lag on the system because if I let go and try to move down again rapidly, there is some delay (1-2secs). It is a minor bug, but since my menu systems are working 100% at this point. I'd like to refine and fix this bug.