


import functools
from math import sqrt
from time import time







def   lowerCamelCase(      a__		,*a__		,**a__):
				_SCREAMING_SNAKE_CASE	     =time()
				_SCREAMING_SNAKE_CASE	     =func(*__UpperCamelCase		,**__UpperCamelCase)
				_SCREAMING_SNAKE_CASE	     =time()
				if int(end - start) > 0:
								print(f"{func.__name__} runtime: {(end - start):0.4f} s")
				else:
								print(f"{func.__name__} runtime: {(end - start) * 1000:0.4f} ms")
				return output







def   lowerCamelCase(      a__):
				if n < 0:
								raise Exception('''n is negative''')
				if n == 0:
								return [0]
				_SCREAMING_SNAKE_CASE	     =[0, 1]
				for _ in range(n - 1):
								fib.append(fib[-1] + fib[-2])
				return fib







def   lowerCamelCase(      a__):

				def fib_recursive_term(a__) -> int:
								if i < 0:
												raise Exception('''n is negative''')
								if i < 2:
												return i
								return fib_recursive_term(i - 1) + fib_recursive_term(i - 2)

				if n < 0:
								raise Exception('''n is negative''')
				return [fib_recursive_term(__UpperCamelCase) for i in range(n + 1)]







def   lowerCamelCase(      a__):

				@functools.cache
				def fib_recursive_term(a__) -> int:
								if i < 0:
												raise Exception('''n is negative''')
								if i < 2:
												return i
								return fib_recursive_term(i - 1) + fib_recursive_term(i - 2)

				if n < 0:
								raise Exception('''n is negative''')
				return [fib_recursive_term(__UpperCamelCase) for i in range(n + 1)]







def   lowerCamelCase(      a__):
				if n < 0:
								raise Exception('''n is negative''')
				# Cache must be outside recursuive function
				# other it will reset every time it calls itself.
				_SCREAMING_SNAKE_CASE	     ={0: 0, 1: 1, 2: 1}  # Prefilled cache

				def rec_fn_memoized(a__) -> int:
								if num in cache:
												return cache[num]

								_SCREAMING_SNAKE_CASE	     =rec_fn_memoized(num - 1) + rec_fn_memoized(num - 2)
								_SCREAMING_SNAKE_CASE	     =value
								return value

				return [rec_fn_memoized(__UpperCamelCase) for i in range(n + 1)]







def   lowerCamelCase(      a__):
				if n < 0:
								raise Exception('''n is negative''')
				if n >= 1475:
								raise Exception('''n is too large''')
				_SCREAMING_SNAKE_CASE	     =sqrt(5)
				_SCREAMING_SNAKE_CASE	     =(1 + sqrt_a) / 2
				return [round(phi**i / sqrt_a) for i in range(n + 1)]


if __name__ == "__main__":
							snake_case_  :	int							  =							30
							time_func(fib_iterative, num)
							time_func(fib_recursive, num)  # Around 3s runtime
							time_func(fib_recursive_cached, num)  # Around 0ms runtime
							time_func(fib_memoization, num)
							time_func(fib_binet, num)





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			: Union[str, Any]				,_UpperCamelCase			: T						)		->   None:


         '''simple docstring'''





         SCREAMING_SNAKE_CASE__								=value
         SCREAMING_SNAKE_CASE__								=None
         SCREAMING_SNAKE_CASE__								=None




     @property
     def   __A				(	self			: Optional[Any]						)		->   T:


         '''simple docstring'''





         return self._value




     @staticmethod
     def   __A				(	_UpperCamelCase			: RandomizedHeapNode[T] | None				,_UpperCamelCase			: RandomizedHeapNode[T] | None						)		->   RandomizedHeapNode[T] | None:


         '''simple docstring'''





         if not roota:
             return roota

         if not roota:
             return roota

         if roota.value > roota.value:
             SCREAMING_SNAKE_CASE__			,		SCREAMING_SNAKE_CASE__								=roota, roota

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

         SCREAMING_SNAKE_CASE__								=RandomizedHeapNode.merge(roota.left				,_UpperCamelCase						)

         return roota






class       __a					( Generic[T]     ):


     """simple docstring"""


     def __init__(	self			: Any				,_UpperCamelCase			: Iterable[T] | None = ()						)		->   None:


         '''simple docstring'''





         SCREAMING_SNAKE_CASE__								=None

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




     def   __A				(	self			: Union[str, Any]				,_UpperCamelCase			: T						)		->   None:


         '''simple docstring'''





         SCREAMING_SNAKE_CASE__								=RandomizedHeapNode.merge(self._root				,RandomizedHeapNode(_UpperCamelCase						)						)




     def   __A				(	self			: Dict						)		->   T | None:


         '''simple docstring'''





         SCREAMING_SNAKE_CASE__								=self.top()

         if self._root is None:
             return None

         SCREAMING_SNAKE_CASE__								=RandomizedHeapNode.merge(self._root.left				,self._root.right						)

         return result




     def   __A				(	self			: Optional[Any]						)		->   T:


         '''simple docstring'''





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




     def   __A				(	self			: Optional[int]						)		->   None:


         '''simple docstring'''





         SCREAMING_SNAKE_CASE__								=None




     def   __A				(	self			: List[Any]						)		->   list[Any]:


         '''simple docstring'''





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

         return result




     def __bool__(	self			: Tuple						)		->   bool:


         '''simple docstring'''





         return self._root is not None


if __name__ == "__main__":
    import doctest

    doctest.testmod()






