code: def bin_insert(list, element):
      
  
      if not list:
          list.append(element)
          return
  
      lower = 0
      upper = len(list) - 1
  
      while lower <= upper:
          center = (lower + upper) // 2
          if element < list[center]:
              upper = center - 1
          elif element > list[center]:
              lower = center + 1
          elif element == list[center]:
              return
  
      if element < list[upper]:
          list.insert(upper, element)
      elif element > list[upper]:
          list.insert(upper + 1, element)
docs: bin_insert(list, element)
  
      Insert ELEMENT into LIST.  LIST must be sorted, and ELEMENT will
      be inserted to that LIST remains sorted.  If LIST already contains
      ELEMENT, it will not be duplicated.