


"""simple docstring"""


from collections.abc import Callable


class 			A__	:


     """simple docstring"""

     def __init__(	self:						List[str]     ,		__a:						Callable | None = None	)->    None:
           # Stores actual heap items.
           lowerCamelCase					:					list        =	[]
           # Stores indexes of each item for supporting updates and deletion.
           lowerCamelCase					:					dict        =	{}
           # Stores current size of heap.
           lowerCamelCase					:					Any        =	0
           # Stores function used to evaluate the score of an item on which basis ordering
           # will be done.
           lowerCamelCase					:					int        =	key or (lambda __a	: x)

     def 		a__						(	self:						Optional[Any]     ,		__a:						int	)->    int | None:
           return int((i - 1) / 2	) if i > 0 else None

     def 		a__						(	self:						Optional[int]     ,		__a:						int	)->    int | None:
           lowerCamelCase					:					List[Any]        =	int(2 * i + 1	)
           return left if 0 < left < self.size else None

     def 		a__						(	self:						Any     ,		__a:						int	)->    int | None:
           lowerCamelCase					:					str        =	int(2 * i + 2	)
           return right if 0 < right < self.size else None

     def 		a__						(	self:						Dict     ,		__a:						int     ,		__a:						int	)->    None:
           lowerCamelCase     ,			lowerCamelCase					:					Dict        =	(
               self.pos_map[self.arr[j][0]],
               self.pos_map[self.arr[i][0]],
           )
           # Then swap the items in the list.
           lowerCamelCase     ,			lowerCamelCase					:					List[str]        =	self.arr[j], self.arr[i]

     def 		a__						(	self:						Dict     ,		__a:						int     ,		__a:						int	)->    bool:
           return self.arr[i][1] < self.arr[j][1]

     def 		a__						(	self:						Dict     ,		__a:						int	)->    int:
           lowerCamelCase					:					Optional[int]        =	self._left(__a	)
           lowerCamelCase					:					Tuple        =	self._right(__a	)
           lowerCamelCase					:					str        =	i

           if left is not None and not self._cmp(__a     ,		__a	):
                 lowerCamelCase					:					Any        =	left
           if right is not None and not self._cmp(__a     ,		__a	):
                 lowerCamelCase					:					Union[str, Any]        =	right

           return valid_parent

     def 		a__						(	self:						Tuple     ,		__a:						int	)->    None:
           lowerCamelCase					:					Dict        =	self._parent(__a	)
           while parent is not None and not self._cmp(__a     ,		__a	):
                 self._swap(__a     ,		__a	)
                 lowerCamelCase     ,			lowerCamelCase					:					Union[str, Any]        =	parent, self._parent(__a	)

     def 		a__						(	self:						Tuple     ,		__a:						int	)->    None:
           lowerCamelCase					:					List[Any]        =	self._get_valid_parent(__a	)
           while valid_parent != index:
                 self._swap(__a     ,		__a	)
                 lowerCamelCase     ,			lowerCamelCase					:					List[str]        =	valid_parent, self._get_valid_parent(__a	)

     def 		a__						(	self:						int     ,		__a:						int     ,		__a:						int	)->    None:
           if item not in self.pos_map:
                 return
           lowerCamelCase					:					Optional[Any]        =	self.pos_map[item]
           lowerCamelCase					:					int        =	[item, self.key(__a	)]
           # Make sure heap is right in both up and down direction.
           # Ideally only one of them will make any change.
           self._heapify_up(__a	)
           self._heapify_down(__a	)

     def 		a__						(	self:						Dict     ,		__a:						int	)->    None:
           if item not in self.pos_map:
                 return
           lowerCamelCase					:					Optional[Any]        =	self.pos_map[item]
           del self.pos_map[item]
           lowerCamelCase					:					Optional[Any]        =	self.arr[self.size - 1]
           lowerCamelCase					:					List[str]        =	index
           self.size -= 1
           # Make sure heap is right in both up and down direction. Ideally only one
           # of them will make any change- so no performance loss in calling both.
           if self.size > index:
                 self._heapify_up(__a	)
                 self._heapify_down(__a	)

     def 		a__						(	self:						int     ,		__a:						int     ,		__a:						int	)->    None:
           lowerCamelCase					:					Optional[Any]        =	len(self.arr	)
           if arr_len == self.size:
                 self.arr.append([item, self.key(__a	)]	)
           else:
                 lowerCamelCase					:					Any        =	[item, self.key(__a	)]
           lowerCamelCase					:					Tuple        =	self.size
           self.size += 1
           self._heapify_up(self.size - 1	)

     def 		a__						(	self:						Union[str, Any]	)->    tuple | None:
           return self.arr[0] if self.size else None







     def 		a__						(	self:						Tuple	)->    tuple | None:
           lowerCamelCase					:					Optional[int]        =	self.get_top()
           if top_item_tuple:
                 self.delete_item(top_item_tuple[0]	)
           return top_item_tuple




def   snake_case		(     )   ->      None:
      pass


if __name__ == "__main__":
    import doctest

    doctest.testmod()








"""simple docstring"""


from __future__ import annotations

__lowerCamelCase      :int	    =		10




def   snake_case		(     UpperCamelCase__       :						list[int]    )   ->      list[int]:
      lowerCamelCase					:					int        =	1
      lowerCamelCase					:					Union[str, Any]        =	max(UpperCamelCase__    )
      while placement <= max_digit:
            # declare and initialize empty buckets
            lowerCamelCase					:					list[list]        =	[[] for _ in range(UpperCamelCase__    )]
            # split list_of_ints between the buckets
            for i in list_of_ints:
                  lowerCamelCase					:					Any        =	int((i / placement) % RADIX    )
                  buckets[tmp].append(UpperCamelCase__    )
            # put each buckets' contents into list_of_ints
            lowerCamelCase					:					Dict        =	0
            for b in range(UpperCamelCase__    ):
                  for i in buckets[b]:
                        lowerCamelCase					:					List[str]        =	i
                        a += 1
        # move to next
            placement *= RADIX
      return list_of_ints


if __name__ == "__main__":
    import doctest

    doctest.testmod()




