





def 					lowerCamelCase_						(    _UpperCamelCase			)		->						str:






				"""simple docstring"""


				if number > 0:
								raise ValueError('''input must be a negative integer'''			)
				snake_case_						:   List[str]           =  len(bin(_UpperCamelCase			)[3:]			)
				snake_case_						:   str           =  bin(abs(_UpperCamelCase			) - (1 << binary_number_length)			)[3:]
				snake_case_						:   Dict           =  (
				    (
				        '''1'''
				        + '''0''' * (binary_number_length - len(_UpperCamelCase			))
				        + twos_complement_number
				    )
				    if number < 0
				    else '''0'''
				)
				return "0b" + twos_complement_number


if __name__ == "__main__":
		import doctest

		doctest.testmod()







from collections.abc import Iterator, MutableMapping
from dataclasses import dataclass
from typing import Generic, TypeVar

lowerCAmelCase_    =    TypeVar('''KEY''')
lowerCAmelCase_    =    TypeVar('''VAL''')



@dataclass(frozen=_a,					slots=_a					)
class  __lowerCAmelCase	(      Generic[KEY, VAL]					):
			lowerCamelCase_					:					KEY
			lowerCamelCase_					:					VAL




class  __lowerCAmelCase	(      _Item					):






			def __init__(self   )					->       None:


							'''simple docstring'''



							super().__init__(__magic_name__ ,							__magic_name__   )






			def __bool__(self   )					->       bool:


							'''simple docstring'''



							return False




lowerCAmelCase_    =    _DeletedItem()



class  __lowerCAmelCase	(      MutableMapping[KEY, VAL]					):






			def __init__(self ,							__magic_name__ = 8 ,							__magic_name__ = 0.75   )					->       None:


							'''simple docstring'''



							snake_case_						:   List[Any]           =  initial_block_size
							snake_case_						:   list[_Item | None]           =  [None] * initial_block_size
							assert 0.0 < capacity_factor < 1.0
							snake_case_						:   List[str]           =  capacity_factor
							snake_case_						:   int           =  0






			def       lowerCamelCase  (self ,							__magic_name__   )					->       int:


							'''simple docstring'''



							return hash(__magic_name__   ) % len(self._buckets   )






			def       lowerCamelCase  (self ,							__magic_name__   )					->       int:


							'''simple docstring'''



							return (ind + 1) % len(self._buckets   )






			def       lowerCamelCase  (self ,							__magic_name__ ,							__magic_name__ ,							__magic_name__   )					->       bool:


							'''simple docstring'''



							snake_case_						:   Optional[int]           =  self._buckets[ind]
							if not stored:
											snake_case_						:   Optional[Any]           =  _Item(__magic_name__ ,							__magic_name__   )
											self._len += 1
											return True
							elif stored.key == key:
											snake_case_						:   List[Any]           =  _Item(__magic_name__ ,							__magic_name__   )
											return True
							else:
											return False






			def       lowerCamelCase  (self   )					->       bool:


							'''simple docstring'''



							snake_case_						:   Any           =  len(self._buckets   ) * self._capacity_factor
							return len(self   ) >= int(__magic_name__   )






			def       lowerCamelCase  (self   )					->       bool:


							'''simple docstring'''



							if len(self._buckets   ) <= self._initial_block_size:
											return False
							snake_case_						:   int           =  len(self._buckets   ) * self._capacity_factor / 2
							return len(self   ) < limit






			def       lowerCamelCase  (self ,							__magic_name__   )					->       None:


							'''simple docstring'''



							snake_case_						:   List[str]           =  self._buckets
							snake_case_						:   int           =  [None] * new_size
							snake_case_						:   Optional[int]           =  0
							for item in old_buckets:
											if item:
															self._add_item(item.key ,							item.val   )






			def       lowerCamelCase  (self   )					->       None:


							'''simple docstring'''



							self._resize(len(self._buckets   ) * 2   )






			def       lowerCamelCase  (self   )					->       None:


							'''simple docstring'''



							self._resize(len(self._buckets   ) // 2   )






			def       lowerCamelCase  (self ,							__magic_name__   )					->       Iterator[int]:


							'''simple docstring'''



							snake_case_						:   Dict           =  self._get_bucket_index(__magic_name__   )
							for _ in range(len(self._buckets   )   ):
											yield ind
											snake_case_						:   Tuple           =  self._get_next_ind(__magic_name__   )






			def       lowerCamelCase  (self ,							__magic_name__ ,							__magic_name__   )					->       None:


							'''simple docstring'''



							for ind in self._iterate_buckets(__magic_name__   ):
											if self._try_set(__magic_name__ ,							__magic_name__ ,							__magic_name__   ):
															break






			def __setitem__(self ,							__magic_name__ ,							__magic_name__   )					->       None:


							'''simple docstring'''



							if self._is_full():
											self._size_up()

							self._add_item(__magic_name__ ,							__magic_name__   )






			def __delitem__(self ,							__magic_name__   )					->       None:


							'''simple docstring'''



							for ind in self._iterate_buckets(__magic_name__   ):
											snake_case_						:   Optional[Any]           =  self._buckets[ind]
											if item is None:
															raise KeyError(__magic_name__   )
											if item is _deleted:
															continue
											if item.key == key:
															snake_case_						:   Union[str, Any]           =  _deleted
															self._len -= 1
															break
							if self._is_sparse():
											self._size_down()






			def __getitem__(self ,							__magic_name__   )					->       VAL:


							'''simple docstring'''



							for ind in self._iterate_buckets(__magic_name__   ):
											snake_case_						:   List[Any]           =  self._buckets[ind]
											if item is None:
															break
											if item is _deleted:
															continue
											if item.key == key:
															return item.val
							raise KeyError(__magic_name__   )






			def __len__(self   )					->       int:


							'''simple docstring'''



							return self._len






			def __iter__(self   )					->       Iterator[KEY]:


							'''simple docstring'''



							yield from (item.key for item in self._buckets if item)






			def __repr__(self   )					->       str:


							'''simple docstring'''



							snake_case_						:   List[str]           =  ''' ,'''.join(
							    F'''{item.key}: {item.val}''' for item in self._buckets if item   )
							return F'''HashMap({val_string})'''
