Maximum Camera Angle Rotation

For now panning the camera above and under the player results in a full 360 all around it. I wish to be able to stop the rotation on the top and the bottom of the player.

This is my camera script so far...

 public class CameraController : MonoBehaviour
 {
 public float turnSpeed = 4.0f;
 public Transform player;


 private Vector3 offset;


 void Start()
 {
     offset = new Vector3(player.position.x, player.position.y + 8.0f, player.position.z + 7.0f);
 }

 void LateUpdate()
 {
     offset = Quaternion.AngleAxis(Input.GetAxis("Mouse X") * turnSpeed, Vector3.up) * offset;
     offset = Quaternion.AngleAxis(Input.GetAxis("Mouse Y") * turnSpeed, Vector3.left) * offset;

     transform.position = player.position + offset;

     transform.LookAt(player.position);
 }