code: def join_ops(ops1, ops2):
          
          i = len(ops1) - 1
          j = 0
          while i >= 0 and j < len(ops2):
              if ops1[i] == ops2[j]:
                  i -= 1
                  j += 1
              else:
                  break
          return ops1[:i + 1] + ops2[j:]
docs: For internal use.