"""simple docstring"""







from __future__ import annotations

from collections.abc import Iterable, Iterator
from typing import Any, Generic, TypeVar

SCREAMING_SNAKE_CASE						=    TypeVar('T', bound=bool)



class 			_lowerCamelCase      (Generic[T]  ):







				def __init__(			self     :							List[Any]      ,       lowerCamelCase_     :							T    ):

					"""simple docstring"""






					_lowercase			:     T      					=				value
					_lowercase			:     SkewNode[T] | None      					=				None
					_lowercase			:     SkewNode[T] | None      					=				None







				@property
				def 				__UpperCAmelCase       (			self     :							Tuple    ):

					"""simple docstring"""






					return self._value







				@staticmethod
				def 				__UpperCAmelCase       (			lowerCamelCase_     :							SkewNode[T] | None      ,       lowerCamelCase_     :							SkewNode[T] | None    ):

					"""simple docstring"""






					if not roota:
						return roota

					if not roota:
						return roota

					if roota.value > roota.value:
						_lowercase					,   _lowercase			:     Tuple      					=				roota, roota

					_lowercase			:     Optional[int]      					=				roota
					_lowercase			:     Union[str, Any]      					=				roota.right
					_lowercase			:     List[Any]      					=				roota.left
					_lowercase			:     List[str]      					=				SkewNode.merge(lowerCamelCase_      ,       lowerCamelCase_    )

					return result



class 			_lowerCamelCase      (Generic[T]  ):







				def __init__(			self     :							Dict      ,       lowerCamelCase_     :							Iterable[T] | None = ()    ):

					"""simple docstring"""






					_lowercase			:     SkewNode[T] | None      					=				None
					if data:
						for item in data:
							self.insert(lowerCamelCase_    )







				def __bool__(			self     :							Dict    ):

					"""simple docstring"""






					return self._root is not None







				def __iter__(			self     :							List[Any]    ):

					"""simple docstring"""






					_lowercase			:     list[Any]      					=				[]
					while self:
						result.append(self.pop()    )

					# Pushing items back to the heap not to clear it.
					for item in result:
						self.insert(lowerCamelCase_    )

					return iter(lowerCamelCase_    )







				def 				__UpperCAmelCase       (			self     :							int      ,       lowerCamelCase_     :							T    ):

					"""simple docstring"""






					_lowercase			:     Tuple      					=				SkewNode.merge(self._root      ,       SkewNode(lowerCamelCase_    )    )







				def 				__UpperCAmelCase       (			self     :							Any    ):

					"""simple docstring"""






					_lowercase			:     Tuple      					=				self.top()
					_lowercase			:     Dict      					=				(
					    SkewNode.merge(self._root.left      ,       self._root.right    ) if self._root else None
					)

					return result







				def 				__UpperCAmelCase       (			self     :							Dict    ):

					"""simple docstring"""






					if not self._root:
						raise IndexError('Can\'t get top element for the empty heap.'    )
					return self._root.value







				def 				__UpperCAmelCase       (			self     :							int    ):

					"""simple docstring"""






					_lowercase			:     Optional[int]      					=				None


if __name__ == "__main__":
						import doctest

						doctest.testmod()




"""simple docstring"""







from __future__ import annotations

import math
import random


def   __lowerCAmelCase(		__UpperCAmelCase  ,__UpperCAmelCase  ,__UpperCAmelCase      ):






	"""simple docstring"""





	_lowercase			:     Optional[int]      					=				d * e - 1
	_lowercase			:     int      					=				0
	_lowercase			:     Union[str, Any]      					=				0
	while p == 0:
		_lowercase			:     int      					=				random.randint(2  ,n - 1      )
		_lowercase			:     str      					=				k
		while True:
			if t % 2 == 0:
				_lowercase			:     List[Any]      					=				t // 2
				_lowercase			:     int      					=				(g**t) % n
				_lowercase			:     Tuple      					=				math.gcd(x - 1  ,__UpperCAmelCase      )
				if x > 1 and y > 1:
					_lowercase			:     List[str]      					=				y
					_lowercase			:     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()



