Grid-based movement with auto-move

Hi, Im working on grid-based movement, that will **continously** move a game object at a constant speed in one of 4 directions. For example, if I press A it keeps moving left until I press D, so that it starts moving right, but in a grid-based way, so that I cannot turn other direction before it reaches another grid (center, I guess?). The problem is that I have a script that allows to walk in a grid-based way, but Im having a hard time implementing auto-moving.

Here`s the script

Vector3 pos;
float speed = 2f;

// Use this for initialization
void Start () {
	pos = transform.position;
}

// Update is called once per frame
void FixedUpdate () {

	if (Input.GetKey (KeyCode.A) && transform.position == pos) {
		pos += Vector3.left;
	} 
	if (Input.GetKey (KeyCode.D) && transform.position == pos) {
		pos += Vector3.right;
	} 
	if (Input.GetKey (KeyCode.W) && transform.position == pos) {
		pos += Vector3.up;
	} 
	if (Input.GetKey (KeyCode.S) && transform.position == pos) {
		pos += Vector3.down;
	} 

	transform.position = Vector3.MoveTowards(transform.position, pos, Time.deltaTime * speed);

}

I would suggest using a variable like Vector3 dir that stores the direction you want your object to go in. To change value, simply put the following, changing as needed:

if(Input.GetKeyDown(KeyCode.A){ dir = Vector3.left; } else if(Input.GetKeyDown(KeyCode.D){ dir = Vector3.right; } and so on and so forth. Then, just put

transform.position += dir; at the end.

Also, you may have a reason for this, but I would suggest using the Input.GetButtonDown() function instead of the Input.GetKeyDown() function since it makes your code a little more flexible.