





'''simple docstring'''







from __future__ import annotations

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

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



class 							__SCREAMING_SNAKE_CASE			(       Generic[T]      ):
      '''simple docstring'''



      def __init__(							self    : Dict   ,UpperCamelCase    : T  )		->  None:
           _lowercase							:      T  						=							value
           _lowercase							:      RandomizedHeapNode[T] | None  						=							None
           _lowercase							:      RandomizedHeapNode[T] | None  						=							None

      @property
      def   _lowerCamelCase		(							self    : Tuple  )		->  T:
           return self._value



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

           if not roota:
                return roota

           if roota.value > roota.value:
                _lowercase							:      Optional[int]  						=							roota, roota

           if random.choice([True, False]  ):
                _lowercase							:      Optional[int]  						=							roota.right, roota.left

           _lowercase							:      Any  						=							RandomizedHeapNode.merge(roota.left   ,UpperCamelCase  )

           return roota



class 							__SCREAMING_SNAKE_CASE			(       Generic[T]      ):
      '''simple docstring'''



      def __init__(							self    : List[Any]   ,UpperCamelCase    : Iterable[T] | None = ()  )		->  None:
           _lowercase							:      RandomizedHeapNode[T] | None  						=							None

           if data:
                for item in data:
                     self.insert(UpperCamelCase  )

      def   _lowerCamelCase		(							self    : List[Any]   ,UpperCamelCase    : T  )		->  None:
           _lowercase							:      int  						=							RandomizedHeapNode.merge(self._root   ,RandomizedHeapNode(UpperCamelCase  )  )

      def   _lowerCamelCase		(							self    : int  )		->  T | None:
           _lowercase							:      Optional[Any]  						=							self.top()

           if self._root is None:
                return None

           _lowercase							:      List[Any]  						=							RandomizedHeapNode.merge(self._root.left   ,self._root.right  )

           return result

      def   _lowerCamelCase		(							self    : Any  )		->  T:
           if not self._root:
                raise IndexError('Can\'t get top element for the empty heap.'  )
           return self._root.value

      def   _lowerCamelCase		(							self    : Tuple  )		->  None:
           _lowercase							:      Any  						=							None

      def   _lowerCamelCase		(							self    : Tuple  )		->  list[Any]:
           _lowercase							:      Optional[int]  						=							[]
           while self:
                result.append(self.pop()  )

           return result



      def __bool__(							self    : List[str]  )		->  bool:
           return self._root is not None


if __name__ == "__main__":
    import doctest

    doctest.testmod()






'''simple docstring'''







from __future__ import annotations

import math
import random

def 		SCREAMING_SNAKE_CASE      (					lowerCAmelCase__     :	int       ,  lowerCAmelCase__     :	int       ,  lowerCAmelCase__     :	int)			->						list[int]:

     '''simple docstring'''




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