clamping camera's rotation

I have it set up to where the camera should only go to certain point before it stops rotating, but when I try, the camera will not move up or down. please help.

code c#

Vector3 rot = transform.eulerAngles;

     float vertical = Input.GetAxis ("Mouse Y") * rotateSpeed;
     target.transform.Rotate (-vertical, 0, 0);
     
     float desiredAngle = target.transform.eulerAngles.y;
     Quaternion rotation = Quaternion.Euler (desiredAngle, 0, 0);
     transform.position = target.transform.position - (rotation * offset);
     rot.x = Mathf.Clamp(rot.x + vertical, vertical, -vertical);
     transform.eulerAngles = rot;
     
     
     transform.LookAt (target.transform);