



'''simple docstring'''




def     lowerCAmelCase_       (     _lowerCamelCase:       List[Any]	,				_lowerCamelCase:       Optional[int] ):
		__SCREAMING_SNAKE_CASE	:		Optional[int]   	=		[]
		__SCREAMING_SNAKE_CASE	:		str   	=		len(lowercase_ )
		for i in range(lowercase_ ):
				__SCREAMING_SNAKE_CASE	:		str   	=		[]
				for j in range(lowercase_ ):
						__SCREAMING_SNAKE_CASE	:		Dict   	=		0
						for k in range(lowercase_ ):
								__SCREAMING_SNAKE_CASE	:		Dict   	=		val + matrix_a[i][k] * matrix_b[k][j]
						list_a.append(lowercase_ )
				matrix_c.append(lowercase_ )
		return matrix_c


def     lowerCAmelCase_       (     _lowerCamelCase:       int ):
		return [[int(row == column ) for column in range(lowercase_ )] for row in range(lowercase_ )]


def     lowerCAmelCase_       (     _lowerCamelCase:       str ):

		if n <= 1:
				return n
		__SCREAMING_SNAKE_CASE	:		Optional[Any]   	=		identity(2 )
		__SCREAMING_SNAKE_CASE	:		Dict   	=		[[1, 1], [1, 0]]
		__SCREAMING_SNAKE_CASE	:		Dict   	=		n - 1
		while n > 0:
				if n % 2 == 1:
						__SCREAMING_SNAKE_CASE	:		Optional[Any]   	=		multiply(lowercase_	,				lowercase_ )
				__SCREAMING_SNAKE_CASE	:		Union[str, Any]   	=		multiply(lowercase_	,				lowercase_ )
				__SCREAMING_SNAKE_CASE	:		int   	=		int(n / 2 )
		return res_matrix[0][0]


def     lowerCAmelCase_       (     _lowerCamelCase:       Any ):

		if n <= 1:
				return n
		__SCREAMING_SNAKE_CASE	:		Tuple   	=		0
		__SCREAMING_SNAKE_CASE	:		Optional[int]   	=		1
		for _ in range(2	,				n + 1 ):
				__SCREAMING_SNAKE_CASE	,						__SCREAMING_SNAKE_CASE	:		List[Any]   	=		fiba, fiba + fiba
		return fiba


def     lowerCAmelCase_       (     ):

		for ordinal in "0th 1st 2nd 3rd 10th 100th 1000th".split():
				__SCREAMING_SNAKE_CASE	:		List[str]   	=		int("""""".join(c for c in ordinal if c in """0123456789""" ) )  # 1000th --> 1000
				print(
				    F"{ordinal} fibonacci number using matrix exponentiation is "
				    F"{nth_fibonacci_matrix(lowercase_ )} and using bruteforce is "
				    F"{nth_fibonacci_bruteforce(lowercase_ )}\n" )
		# from timeit import timeit
		# print(timeit("nth_fibonacci_matrix(1000000)",
		#              "from main import nth_fibonacci_matrix", number=5))
		# print(timeit("nth_fibonacci_bruteforce(1000000)",
		#              "from main import nth_fibonacci_bruteforce", number=5))
		# 2.3342058970001744
		# 57.256506615000035


if __name__ == "__main__":
						import doctest

						doctest.testmod()
						main()





'''simple docstring'''




from __future__ import annotations

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

UpperCamelCase__	:     str    =			TypeVar('''T''', bound=bool)






class 						_UpperCamelCase  (							Generic[T]   ):


			'''simple docstring'''

			def __init__(							self					:			str							,					lowerCAmelCase__					:			T						):





					"""simple docstring"""






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

			@property
			def UpperCamelCase__ (							self					:			Any						):





					"""simple docstring"""






					return self._value



			@staticmethod
			def UpperCamelCase__ (							lowerCAmelCase__					:			RandomizedHeapNode[T] | None							,					lowerCAmelCase__					:			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	:		List[str]   	=		roota, roota

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

					__SCREAMING_SNAKE_CASE	:		Tuple   	=		RandomizedHeapNode.merge(roota.left							,					lowerCAmelCase__						)

					return roota






class 						_UpperCamelCase  (							Generic[T]   ):


			'''simple docstring'''

			def __init__(							self					:			Optional[int]							,					lowerCAmelCase__					:			Iterable[T] | None = ()						):





					"""simple docstring"""






					__SCREAMING_SNAKE_CASE	:		RandomizedHeapNode[T] | None   	=		None

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

			def UpperCamelCase__ (							self					:			Dict							,					lowerCAmelCase__					:			T						):





					"""simple docstring"""






					__SCREAMING_SNAKE_CASE	:		Dict   	=		RandomizedHeapNode.merge(self._root							,					RandomizedHeapNode(lowerCAmelCase__						)						)

			def UpperCamelCase__ (							self					:			Union[str, Any]						):





					"""simple docstring"""






					__SCREAMING_SNAKE_CASE	:		Tuple   	=		self.top()

					if self._root is None:
							return None

					__SCREAMING_SNAKE_CASE	:		Union[str, Any]   	=		RandomizedHeapNode.merge(self._root.left							,					self._root.right						)

					return result

			def UpperCamelCase__ (							self					:			Union[str, Any]						):





					"""simple docstring"""






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

			def UpperCamelCase__ (							self					:			List[Any]						):





					"""simple docstring"""






					__SCREAMING_SNAKE_CASE	:		List[str]   	=		None

			def UpperCamelCase__ (							self					:			Optional[Any]						):





					"""simple docstring"""






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

					return result



			def __bool__(							self					:			List[Any]						):





					"""simple docstring"""






					return self._root is not None


if __name__ == "__main__":
						import doctest

						doctest.testmod()