
"""simple docstring"""




class 		a__						:
   def __init__(      self    ):
          # numbermap keys are the number and its values are lists of indexes sorted
          # in ascending order
          lowercase   :    dict[int, list[int]]			=							{}
          # indexmap keys are an index and it's values are the number at that index
          lowercase   :    dict[int, int]			=							{}
   def       __magic_name__      (      self     ,   _a     ,   _a    ):
          if isinstance(_a     ,   (range, str)    ):
                 lowercase   :    int			=							list(_a    )
          elif not isinstance(_a     ,   _a    ):
                 raise TypeError(
                     "binary_search_delete() only accepts either a list, range or str"    )

          lowercase   :    Any			=							0
          lowercase   :    Union[str, Any]			=							len(_a    ) - 1

          while low <= high:
                 lowercase   :    str			=							(low + high) // 2
                 if array[mid] == item:
                        array.pop(_a    )
                        return array
                 elif array[mid] < item:
                        lowercase   :    Optional[Any]			=							mid + 1
                 else:
                        lowercase   :    int			=							mid - 1
          raise ValueError(
              "Either the item is not in the array or the array was unsorted"    )
   def       __magic_name__      (      self     ,   _a     ,   _a    ):
          if isinstance(_a     ,   (range, str)    ):
                 lowercase   :    Optional[Any]			=							list(_a    )
          elif not isinstance(_a     ,   _a    ):
                 raise TypeError(
                     "binary_search_insert() only accepts either a list, range or str"    )

          lowercase   :    Dict			=							0
          lowercase   :    List[Any]			=							len(_a    ) - 1

          while low <= high:
                 lowercase   :    List[Any]			=							(low + high) // 2
                 if array[mid] == index:
                        # If the item already exists in the array,
                        # insert it after the existing item
                        array.insert(mid + 1     ,   _a    )
                        return array
                 elif array[mid] < index:
                        lowercase   :    int			=							mid + 1
                 else:
                        lowercase   :    int			=							mid - 1

        # If the item doesn't exist in the array, insert it at the appropriate position
          array.insert(_a     ,   _a    )
          return array
   def       __magic_name__      (      self     ,   _a     ,   _a    ):
          # Remove previous index
          if index in self.indexmap:
                 lowercase   :    Union[str, Any]			=							self.indexmap[index]
                 if len(self.numbermap[n]    ) == 1:
                        del self.numbermap[n]
                 else:
                        lowercase   :    Tuple			=							self.binary_search_delete(self.numbermap[n]     ,   _a    )

        # Set new index
          lowercase   :    Optional[Any]			=							number

          # Number not seen before or empty so insert number value
          if number not in self.numbermap:
                 lowercase   :    Dict			=							[index]

          # Here we need to perform a binary search insertion in order to insert
          # The item in the correct place
          else:
                 lowercase   :    Union[str, Any]			=							self.binary_search_insert(
                     self.numbermap[number]     ,   _a    )

   def       __magic_name__      (      self     ,   _a    ):
          return self.numbermap.get(_a     ,   [-1]    )[0]


if __name__ == "__main__":
   import doctest

   doctest.testmod()




"""simple docstring"""




from __future__ import annotations

_A      :	List[str]       		=	"""Alexander Joslin"""


def   __magic_name__     (				__snake_case    :	int  )			->    int:

       if number <= 0:
              lowercase   :    Optional[Any]			=							f"""n must be greater than 0. Got n = {number}"""
              raise ValueError(__snake_case  )

       lowercase   :    List[str]			=							[number + 1] * (number + 1)

       # starting position
       lowercase   :    Optional[Any]			=							0
       for i in range(1					,			__snake_case  ):
              lowercase   :    str			=							min(table[i + 1]					,			table[i] + 1  )
              # check if out of bounds
              if i * 2 <= number:
                     lowercase   :    int			=							min(table[i * 2]					,			table[i] + 1  )
              # check if out of bounds
              if i * 3 <= number:
                     lowercase   :    Optional[int]			=							min(table[i * 3]					,			table[i] + 1  )
       return table[number]


if __name__ == "__main__":
   import doctest

   doctest.testmod()


