

from __future__ import annotations

from collections.abc import Generator


def   __SCREAMING_SNAKE_CASE					():
						snake_case_   =	{}
						snake_case_   =	2
						while True:
												snake_case_   =	factor_map.pop(SCREAMING_SNAKE_CASE__  ,		SCREAMING_SNAKE_CASE__       )
												if factor:
																		snake_case_   =	factor + prime
																		while x in factor_map:
																								x += factor
																		snake_case_   =	factor
												else:
																		snake_case_   =	prime
																		yield prime
												prime += 1


def   __SCREAMING_SNAKE_CASE					(SCREAMING_SNAKE_CASE__ = 1E10       ):
						snake_case_   =	sieve()

						snake_case_   =	1
						while True:
												snake_case_   =	next(SCREAMING_SNAKE_CASE__       )
												if (2 * prime * n) > limit:
																		return n
												# Ignore the next prime as the reminder will be 2.
												next(SCREAMING_SNAKE_CASE__       )
												n += 2


if __name__ == "__main__":
					print(solution())


from collections import deque

from .hash_table import HashTable





class 	snake_case_   (		__A					):







			'''simple docstring'''

			def __init__(     self :				int							,   *_UpperCamelCase :				int							,   **_UpperCamelCase :				Tuple							)      ->Tuple:
									super().__init__(*_UpperCamelCase							,   **_UpperCamelCase							)







			def 				snake_case__(     self :				Dict							,   _UpperCamelCase :				List[str]							,   _UpperCamelCase :				Dict							)      ->Tuple:
									snake_case_   =	deque([]							) if self.values[key] is None else self.values[key]
									self.values[key].appendleft(_UpperCamelCase							)
									snake_case_   =	self.values[key]







			def 				snake_case__(     self :				List[Any]							)      ->str:
									return (
									    sum(self.charge_factor - len(_UpperCamelCase							) for slot in self.values							)
									    / self.size_table
									    * self.charge_factor
									)







			def 				snake_case__(     self :				Dict							,   _UpperCamelCase :				Union[str, Any]							,   _UpperCamelCase :				Optional[int]=None							)      ->str:
									if not (
									    len(self.values[key]							) == self.charge_factor and self.values.count(_UpperCamelCase							) == 0
									):
															return key
									return super()._collision_resolution(_UpperCamelCase							,   _UpperCamelCase							)