"""simple docstring"""



class 	__UpperCAmelCase						:







			'''simple docstring'''





			def __init__( self      ,			snake_case_       ):







										'''simple docstring'''


										A__					:    Union[str, Any]														= data
										A__					:    int
										A__					:    Node





def    _A(		lowerCAmelCase       ):
							A__					:    List[str]														= 0
							A__					:    Tuple														= x

def    _A(		lowerCAmelCase ,     lowerCAmelCase       ):
							A__							,       A__					:    str														= find_set(lowerCAmelCase       ), find_set(lowerCAmelCase       )
							if x == y:
														return

							elif x.rank > y.rank:
														A__					:    int														= x
							else:
														A__					:    Tuple														= y
														if x.rank == y.rank:
																					y.rank += 1

def    _A(		lowerCAmelCase       ):
							if x != x.parent:
														A__					:    List[Any]														= find_set(x.parent       )
							return x.parent

def    _A(		lowerCAmelCase       ):
							A__					:    Dict														= ({0, 1, 2}, {3, 4, 5})
							for s in sets:
														if node.data in s:
																					return s
							A__					:    Dict														= F'''{node.data} is not in {sets}'''
							raise ValueError(lowerCAmelCase       )

def    _A(		):
							A__					:    Union[str, Any]														= [Node(lowerCAmelCase       ) for i in range(6       )]
							for v in vertex:
														make_set(lowerCAmelCase       )

							union_set(vertex[0] ,     vertex[1]       )
							union_set(vertex[1] ,     vertex[2]       )
							union_set(vertex[3] ,     vertex[4]       )
							union_set(vertex[3] ,     vertex[5]       )

							for nodea in vertex:
														for nodea in vertex:
																					if find_python_set(lowerCAmelCase       ).isdisjoint(find_python_set(lowerCAmelCase       )       ):
																												assert find_set(lowerCAmelCase       ) != find_set(lowerCAmelCase       )
																					else:
																												assert find_set(lowerCAmelCase       ) == find_set(lowerCAmelCase       )


if __name__ == "__main__":
				test_disjoint_set()






"""simple docstring"""



from __future__ import annotations

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

_UpperCamelCase         =		TypeVar("T", bound=bool)
class 	__UpperCAmelCase						(Generic[T]    ):







			'''simple docstring'''





			def __init__( self      ,			snake_case_       ):







										'''simple docstring'''


										A__					:    T														= value
										A__					:    RandomizedHeapNode[T] | None														= None
										A__					:    RandomizedHeapNode[T] | None														= None





			@property
			def 		lowerCamelCase				( self       ):







										'''simple docstring'''


										return self._value





			@staticmethod
			def 		lowerCamelCase				( snake_case_      ,			snake_case_       ):







										'''simple docstring'''


										if not roota:
																	return roota

										if not roota:
																	return roota

										if roota.value > roota.value:
																	A__							,       A__					:    Union[str, Any]														= roota, roota

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

										A__					:    Dict														= RandomizedHeapNode.merge(roota.left      ,			snake_case_       )

										return roota





class 	__UpperCAmelCase						(Generic[T]    ):







			'''simple docstring'''





			def __init__( self      ,			snake_case_ = ()       ):







										'''simple docstring'''


										A__					:    RandomizedHeapNode[T] | None														= None

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





			def 		lowerCamelCase				( self      ,			snake_case_       ):







										'''simple docstring'''


										A__					:    Dict														= RandomizedHeapNode.merge(self._root      ,			RandomizedHeapNode(snake_case_       )       )





			def 		lowerCamelCase				( self       ):







										'''simple docstring'''


										A__					:    List[str]														= self.top()

										if self._root is None:
																	return None

										A__					:    str														= RandomizedHeapNode.merge(self._root.left      ,			self._root.right       )

										return result





			def 		lowerCamelCase				( self       ):







										'''simple docstring'''


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





			def 		lowerCamelCase				( self       ):







										'''simple docstring'''


										A__					:    List[Any]														= None





			def 		lowerCamelCase				( self       ):







										'''simple docstring'''


										A__					:    int														= []
										while self:
																	result.append(self.pop()       )

										return result





			def __bool__( self       ):







										'''simple docstring'''


										return self._root is not None


if __name__ == "__main__":
				import doctest

				doctest.testmod()





