




"""simple docstring"""





from __future__ import annotations

from collections.abc import Iterator
from typing import Any

class  __lowercase    :


				'''simple docstring'''


				def __init__(				self				:       List[Any] ,SCREAMING_SNAKE_CASE_				:       Any ):
										snake_case__    :   Any							     =   data
										snake_case__    :   Node | None							     =   None





				def __str__(				self				:       Union[str, Any] ):
										return F'''{self.data}'''







class  __lowercase    :


				'''simple docstring'''


				def __init__(				self				:       Optional[int] ):
										snake_case__    :   Node | None							     =   None
										snake_case__    :   Node | None							     =   None

				def __iter__(				self				:       Optional[int] ):
										snake_case__    :   Optional[int]							     =   self.front
										while node:
																yield node.data
																snake_case__    :   Optional[int]							     =   node.next

				def __len__(				self				:       Any ):
										return len(tuple(iter(self ) ) )

				def __str__(				self				:       Union[str, Any] ):
										return " <- ".join(str(SCREAMING_SNAKE_CASE_ ) for item in self )

				def  _lowerCamelCase   (				self				:       List[str] ):
										return len(self ) == 0

				def  _lowerCamelCase   (				self				:       Optional[int] ,SCREAMING_SNAKE_CASE_				:       Any ):
										snake_case__    :   int							     =   Node(SCREAMING_SNAKE_CASE_ )
										if self.is_empty():
																snake_case__    :   List[Any]							     =   node
										else:
																assert isinstance(self.rear ,SCREAMING_SNAKE_CASE_ )
																snake_case__    :   Union[str, Any]							     =   node
																snake_case__    :   int							     =   node

				def  _lowerCamelCase   (				self				:       int ):
										if self.is_empty():
																raise IndexError('''dequeue from empty queue''' )
										assert isinstance(self.front ,SCREAMING_SNAKE_CASE_ )
										snake_case__    :   List[str]							     =   self.front
										snake_case__    :   str							     =   self.front.next
										if self.front is None:
																snake_case__    :   Optional[Any]							     =   None
										return node.data





				def  _lowerCamelCase   (				self				:       Optional[int] ):
										snake_case__    :   Optional[Any]							     =   None


if __name__ == "__main__":
							from doctest import testmod

							testmod()








"""simple docstring"""





from __future__ import annotations

import math
import random

def 						lowerCAmelCase							(	lowerCamelCase ,     lowerCamelCase ,     lowerCamelCase						):
						'''simple docstring'''


						snake_case__    :   Tuple							     =   d * e - 1
						snake_case__    :   Optional[int]							     =   0
						snake_case__    :   Tuple							     =   0
						while p == 0:
												snake_case__    :   Optional[int]							     =   random.randint(2 ,     n - 1						)
												snake_case__    :   Tuple							     =   k
												while True:
																		if t % 2 == 0:
																								snake_case__    :   List[Any]							     =   t // 2
																								snake_case__    :   Union[str, Any]							     =   (g**t) % n
																								snake_case__    :   Dict							     =   math.gcd(x - 1 ,     lowerCamelCase						)
																								if x > 1 and y > 1:
																														snake_case__    :   Union[str, Any]							     =   y
																														snake_case__    :   str							     =   n // y
																														break  # find the correct factors
																		else:
																								break  # t is not divisible by 2, break and choose another g
						return sorted([p, q]						)


if __name__ == "__main__":
							import doctest

							doctest.testmod()


