




'''simple docstring'''


from __future__ import annotations

from pprint import pformat
from typing import Generic, TypeVar

__lowercase							:   int					=     TypeVar('''T''')

class 	__lowercase				(  Generic[T]    ):

			def __init__(self			,   A = True      ):
								lowerCamelCase_					:      dict[T, list[T]]     =		{}  # dictionary of lists
								lowerCamelCase_					:      Union[str, Any]     =		directed

			def        UpperCAmelCase__ (self			,   A			,   A      ):

								if not self.directed:  # For undirected graphs
													# if both source vertex and destination vertex are both present in the
													# adjacency list, add destination vertex to source vertex list of adjacent
													# vertices and add source vertex to destination vertex list of adjacent
													# vertices.
													if source_vertex in self.adj_list and destination_vertex in self.adj_list:
																		self.adj_list[source_vertex].append(snake_case_      )
																		self.adj_list[destination_vertex].append(snake_case_      )
													# if only source vertex is present in adjacency list, add destination vertex
													# to source vertex list of adjacent vertices, then create a new vertex with
													# destination vertex as key and assign a list containing the source vertex
													# as it's first adjacent vertex.
													elif source_vertex in self.adj_list:
																		self.adj_list[source_vertex].append(snake_case_      )
																		lowerCamelCase_					:      List[str]     =		[source_vertex]
													# if only destination vertex is present in adjacency list, add source vertex
													# to destination vertex list of adjacent vertices, then create a new vertex
													# with source vertex as key and assign a list containing the source vertex
													# as it's first adjacent vertex.
													elif destination_vertex in self.adj_list:
																		self.adj_list[destination_vertex].append(snake_case_      )
																		lowerCamelCase_					:      Any     =		[destination_vertex]
													# if both source vertex and destination vertex are not present in adjacency
													# list, create a new vertex with source vertex as key and assign a list
													# containing the destination vertex as it's first adjacent vertex also
													# create a new vertex with destination vertex as key and assign a list
													# containing the source vertex as it's first adjacent vertex.
													else:
																		lowerCamelCase_					:      Tuple     =		[destination_vertex]
																		lowerCamelCase_					:      Tuple     =		[source_vertex]
								else:  # For directed graphs
													# if both source vertex and destination vertex are present in adjacency
													# list, add destination vertex to source vertex list of adjacent vertices.
													if source_vertex in self.adj_list and destination_vertex in self.adj_list:
																		self.adj_list[source_vertex].append(snake_case_      )
													# if only source vertex is present in adjacency list, add destination
													# vertex to source vertex list of adjacent vertices and create a new vertex
													# with destination vertex as key, which has no adjacent vertex
													elif source_vertex in self.adj_list:
																		self.adj_list[source_vertex].append(snake_case_      )
																		lowerCamelCase_					:      List[str]     =		[]
													# if only destination vertex is present in adjacency list, create a new
													# vertex with source vertex as key and assign a list containing destination
													# vertex as first adjacent vertex
													elif destination_vertex in self.adj_list:
																		lowerCamelCase_					:      List[str]     =		[destination_vertex]
													# if both source vertex and destination vertex are not present in adjacency
													# list, create a new vertex with source vertex as key and a list containing
													# destination vertex as it's first adjacent vertex. Then create a new vertex
													# with destination vertex as key, which has no adjacent vertex
													else:
																		lowerCamelCase_					:      Dict     =		[destination_vertex]
																		lowerCamelCase_					:      List[Any]     =		[]

								return self






			def __repr__(self      ):
								return pformat(self.adj_list      )




'''simple docstring'''


import itertools
import math




def lowercase_	(   _lowercase				)     ->							bool:
					'''simple docstring'''

					if 1 < number < 4:
										# 2 and 3 are primes
										return True
					elif number < 2 or number % 2 == 0 or number % 3 == 0:
										# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
										return False

					# All primes number are in format of 6k +/- 1
					for i in range(5			,       int(math.sqrt(_lowercase				) + 1				)			,       6				):
										if number % i == 0 or number % (i + 2) == 0:
															return False
					return True




def lowercase_	(   )     ->							Optional[int]:
					'''simple docstring'''

					lowerCamelCase_					:      Union[str, Any]     =		2
					while True:
										if is_prime(_lowercase				):
															yield num
										num += 1




def lowercase_	(   _lowercase = 10_001				)     ->							int:
					'''simple docstring'''

					return next(itertools.islice(prime_generator()			,       nth - 1			,       _lowercase				)				)


if __name__ == "__main__":
					print(f'{solution() = }')


