




'''simple docstring'''






from __future__ import annotations

import math
import random

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









'''simple docstring'''






from __future__ import annotations

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

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



class  A		(			Generic[T]		):




				'''simple docstring'''





				def __init__(self			,  _UpperCAmelCase      )     ->	None:
							__UpperCamelCase				:      T									=       value
							__UpperCamelCase				:      RandomizedHeapNode[T] | None									=       None
							__UpperCamelCase				:      RandomizedHeapNode[T] | None									=       None
				@property
				def 	a_	(self      )     ->	T:
							return self._value





				@staticmethod
				def 	a_	(_UpperCAmelCase			,  _UpperCAmelCase      )     ->	RandomizedHeapNode[T] | None:
							if not roota:
										return roota

							if not roota:
										return roota

							if roota.value > roota.value:
										__UpperCamelCase		, __UpperCamelCase				:      int									=       roota, roota

							if random.choice([True, False]      ):
										__UpperCamelCase		, __UpperCamelCase				:      Dict									=       roota.right, roota.left

							__UpperCamelCase				:      Any									=       RandomizedHeapNode.merge(roota.left			,  _UpperCAmelCase      )

							return roota







class  A		(			Generic[T]		):




				'''simple docstring'''





				def __init__(self			,  _UpperCAmelCase = ()      )     ->	None:
							__UpperCamelCase				:      RandomizedHeapNode[T] | None									=       None

							if data:
										for item in data:
													self.insert(_UpperCAmelCase      )
				def 	a_	(self			,  _UpperCAmelCase      )     ->	None:
							__UpperCamelCase				:      str									=       RandomizedHeapNode.merge(self._root			,  RandomizedHeapNode(_UpperCAmelCase      )      )
				def 	a_	(self      )     ->	T | None:
							__UpperCamelCase				:      Dict									=       self.top()

							if self._root is None:
										return None

							__UpperCamelCase				:      List[str]									=       RandomizedHeapNode.merge(self._root.left			,  self._root.right      )

							return result
				def 	a_	(self      )     ->	T:
							if not self._root:
										raise IndexError("Can't get top element for the empty heap."      )
							return self._root.value
				def 	a_	(self      )     ->	None:
							__UpperCamelCase				:      int									=       None
				def 	a_	(self      )     ->	list[Any]:
							__UpperCamelCase				:      int									=       []
							while self:
										result.append(self.pop()      )

							return result





				def __bool__(self      )     ->	bool:
							return self._root is not None


if __name__ == "__main__":
				import doctest

				doctest.testmod()



