
import random

from .binary_exp_mod import bin_exp_mod




def 	_SCREAMING_SNAKE_CASE					(		_lowerCamelCase :			List[Any]						,  _lowerCamelCase :			List[str]=1_000)					->    Dict:






							'''simple docstring'''





							if n < 2:
														return False

							if n % 2 == 0:
														return n == 2

							# this means n is odd
							__UpperCamelCase	:   Union[str, Any]			   =					n - 1
							__UpperCamelCase	:   Tuple			   =					0
							while d % 2 == 0:
														d /= 2
														exp += 1

							# n - 1=d*(2**exp)
							__UpperCamelCase	:   Dict			   =					0
							while count < prec:
														__UpperCamelCase	:   List[str]			   =					random.randint(2						,  n - 1)
														__UpperCamelCase	:   Union[str, Any]			   =					bin_exp_mod(_lowerCamelCase						,  _lowerCamelCase						,  _lowerCamelCase)
														if b != 1:
																					__UpperCamelCase	:   int			   =					True
																					for _ in range(_lowerCamelCase):
																												if b == n - 1:
																																			__UpperCamelCase	:   Tuple			   =					False
																																			break
																												__UpperCamelCase	:   List[Any]			   =					b * b
																												b %= n
																					if flag:
																												return False
																					count += 1
							return True


if __name__ == "__main__":
		lowercase  :					Union[str, Any]													=       abs(int(input('Enter bound : ').strip()))
		print('Here\'s the list of primes:')
		print(', '.join(str(i) for i in range(n + 1) if is_prime_big(i)))

class  lowerCamelCase__							:




	'''simple docstring'''




	def __init__(					self		:int						)		-> Dict:
								__UpperCamelCase	:   Union[str, Any]			   =					{}







	def    _lowerCamelCase				(					self		:str						)		-> None:
								print(self.vertex						)
								for i in self.vertex:
															print(a     ,   " -> "     ,   " -> ".join([str(a						) for j in self.vertex[i]]						)						)







	def    _lowerCamelCase				(					self		:List[Any]     ,   a		:int     ,   a		:int						)		-> None:
								# check if vertex is already present,
								if from_vertex in self.vertex:
															self.vertex[from_vertex].append(a						)
								else:
															# else make a new vertex
															__UpperCamelCase	:   Optional[Any]			   =					[to_vertex]







	def    _lowerCamelCase				(					self		:Tuple						)		-> None:
								# visited array for storing already visited nodes
								__UpperCamelCase	:   Dict			   =					[False] * len(self.vertex						)

								# call the recursive helper function
								for i in range(len(self.vertex						)						):
															if not visited[i]:
																						self.dfs_recursive(a     ,   a						)







	def    _lowerCamelCase				(					self		:Any     ,   a		:int     ,   a		:list						)		-> None:
								# mark start vertex as visited
								__UpperCamelCase	:   int			   =					True

								print(a     ,   end=" "						)

								# Recur for all the vertices that are adjacent to this node
								for i in self.vertex:
															if not visited[i]:
																						self.dfs_recursive(a     ,   a						)


if __name__ == "__main__":
		lowercase  :					Dict													=       Graph()
		g.add_edge(0, 1)
		g.add_edge(0, 2)
		g.add_edge(1, 2)
		g.add_edge(2, 0)
		g.add_edge(2, 3)
		g.add_edge(3, 3)

		g.print_graph()
		print('DFS:')
		g.dfs()

		# OUTPUT:
		# 0  ->  1 -> 2
		# 1  ->  2
		# 2  ->  0 -> 3
		# 3  ->  3
		# DFS:
		#  0 1 2 3