





"""simple docstring"""




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

UpperCamelCase_									=TypeVar("""KEY""")
UpperCamelCase_									=TypeVar("""VAL""")




@dataclass(frozen=_lowerCAmelCase     ,    slots=_lowerCAmelCase    )
class 			_a						(				Generic[KEY, VAL]    ):
				UpperCamelCase								=   42
				UpperCamelCase								=   42




class 			_a						(				_Item    ):






				def __init__(			self		:   Union[str, Any]							)     ->				None:




										'''simple docstring'''



										super().__init__(_SCREAMING_SNAKE_CASE,			_SCREAMING_SNAKE_CASE							)






				def __bool__(			self		:   Union[str, Any]							)     ->				bool:




										'''simple docstring'''



										return False

UpperCamelCase_									=_DeletedItem()




class 			_a						(				MutableMapping[KEY, VAL]    ):






				def __init__(			self		:   Union[str, Any],			lowerCAmelCase__		:   Tuple = 8,			lowerCAmelCase__		:   str = 0.75							)     ->				None:




										'''simple docstring'''



										_UpperCamelCase      : Any         =   initial_block_size
										_UpperCamelCase      : list[_Item | None]         =   [None] * initial_block_size
										assert 0.0 < capacity_factor < 1.0
										_UpperCamelCase      : Optional[Any]         =   capacity_factor
										_UpperCamelCase      : Union[str, Any]         =   0






				def     snake_case     (			self		:   Optional[Any],			lowerCAmelCase__		:   str							)     ->				int:




										'''simple docstring'''



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






				def     snake_case     (			self		:   int,			lowerCAmelCase__		:   Union[str, Any]							)     ->				int:




										'''simple docstring'''



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






				def     snake_case     (			self		:   Tuple,			lowerCAmelCase__		:   Dict,			lowerCAmelCase__		:   int,			lowerCAmelCase__		:   Tuple							)     ->				bool:




										'''simple docstring'''



										_UpperCamelCase      : Union[str, Any]         =   self._buckets[ind]
										if not stored:
																_UpperCamelCase      : int         =   _Item(_SCREAMING_SNAKE_CASE,			_SCREAMING_SNAKE_CASE							)
																self._len += 1
																return True
										elif stored.key == key:
																_UpperCamelCase      : Tuple         =   _Item(_SCREAMING_SNAKE_CASE,			_SCREAMING_SNAKE_CASE							)
																return True
										else:
																return False






				def     snake_case     (			self		:   Dict							)     ->				bool:




										'''simple docstring'''



										_UpperCamelCase      : Union[str, Any]         =   len(self._buckets							) * self._capacity_factor
										return len(self							) >= int(_SCREAMING_SNAKE_CASE							)






				def     snake_case     (			self		:   Tuple							)     ->				bool:




										'''simple docstring'''



										if len(self._buckets							) <= self._initial_block_size:
																return False
										_UpperCamelCase      : Optional[int]         =   len(self._buckets							) * self._capacity_factor / 2
										return len(self							) < limit






				def     snake_case     (			self		:   str,			lowerCAmelCase__		:   Any							)     ->				None:




										'''simple docstring'''



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






				def     snake_case     (			self		:   List[str]							)     ->				None:




										'''simple docstring'''



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






				def     snake_case     (			self		:   int							)     ->				None:




										'''simple docstring'''



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






				def     snake_case     (			self		:   Optional[int],			lowerCAmelCase__		:   List[str]							)     ->				Iterator[int]:




										'''simple docstring'''



										_UpperCamelCase      : Union[str, Any]         =   self._get_bucket_index(_SCREAMING_SNAKE_CASE							)
										for _ in range(len(self._buckets							)							):
																yield ind
																_UpperCamelCase      : str         =   self._get_next_ind(_SCREAMING_SNAKE_CASE							)






				def     snake_case     (			self		:   Optional[int],			lowerCAmelCase__		:   int,			lowerCAmelCase__		:   str							)     ->				None:




										'''simple docstring'''



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






				def __setitem__(			self		:   int,			lowerCAmelCase__		:   Tuple,			lowerCAmelCase__		:   int							)     ->				None:




										'''simple docstring'''



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

										self._add_item(_SCREAMING_SNAKE_CASE,			_SCREAMING_SNAKE_CASE							)






				def __delitem__(			self		:   Optional[int],			lowerCAmelCase__		:   List[Any]							)     ->				None:




										'''simple docstring'''



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






				def __getitem__(			self		:   Any,			lowerCAmelCase__		:   Any							)     ->				VAL:




										'''simple docstring'''



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






				def __len__(			self		:   Tuple							)     ->				int:




										'''simple docstring'''



										return self._len






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




										'''simple docstring'''



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






				def __repr__(			self		:   str							)     ->				str:




										'''simple docstring'''



										_UpperCamelCase      : Tuple         =   ''' ,'''.join(
										    f"""{item.key}: {item.val}""" for item in self._buckets if item							)
										return f"""HashMap({val_string})"""










"""simple docstring"""




from __future__ import annotations

from random import choice





def 	a_    (							_lowercase       ):
						return choice(_lowercase       )





def 	a_    (							_lowercase	,						_lowercase       ):
						_UpperCamelCase      : Optional[int]         =   random_pivot(_lowercase       )

						# partition based on pivot
						# linear time
						_UpperCamelCase      : Union[str, Any]         =   [e for e in lst if e < pivot]
						_UpperCamelCase      : int         =   [e for e in lst if e > pivot]

						# if we get lucky, pivot might be the element we want.
						# we can easily see this:
						# small (elements smaller than k)
						# + pivot (kth element)
						# + big (elements larger than k)
						if len(_lowercase       ) == k - 1:
												return pivot
						# pivot is in elements bigger than k
						elif len(_lowercase       ) < k - 1:
												return kth_number(_lowercase	,						k - len(_lowercase       ) - 1       )
						# pivot is in elements smaller than k
						else:
												return kth_number(_lowercase	,						_lowercase       )


if __name__ == "__main__":
						import doctest

						doctest.testmod()



