




import timeit




class        snake_case__				:
				"""simple docstring"""



				def __init__( self							:	Optional[int]   , __lowerCamelCase							:	Dict				)   ->	int:
							if isinstance(__lowerCamelCase   , __lowerCamelCase				):  # Initializes a matrix identical to the one provided.
										a       =     arg
										a       =     len(__lowerCamelCase				)
							else:  # Initializes a square matrix of the given size and set values to zero.
										a       =     arg
										a       =     [[0 for _ in range(self.n				)] for _ in range(self.n				)]





				def __mul__( self							:	Union[str, Any]   , __lowerCamelCase							:	List[str]				)   ->	Any:
							a       =     Matrix(self.n				)
							for i in range(self.n				):
										for j in range(self.n				):
													for k in range(self.n				):
																matrix.t[i][j] += self.t[i][k] * b.t[k][j]
							return matrix




def      __magic_name__							(					A						:   int,    A						:   Any  ):






			'''simple docstring'''







			a       =     Matrix([[1, 0], [0, 1]]  )
			while b > 0:
						if b & 1:
									matrix *= a
						a *= a
						b >>= 1
			return matrix




def      __magic_name__							(					A						:   str,    A						:   Dict,    A						:   str  ):






			'''simple docstring'''







			if n == 1:
						return fa
			elif n == 2:
						return fa
			a       =     Matrix([[1, 1], [1, 0]]  )
			a       =     modular_exponentiation(A,    n - 2  )
			return fa * matrix.t[0][0] + fa * matrix.t[0][1]




def      __magic_name__							(					A						:   Optional[Any],    A						:   Dict,    A						:   Optional[int]  ):






			'''simple docstring'''







			if n == 1:
						return fa
			elif n == 2:
						return fa

			a       =     fa
			a       =     fa
			n -= 2

			while n > 0:
						a       ,						a       =     fn_a + fn_a, fn_a
						n -= 1

			return fn_a




def      __magic_name__							(					):






			'''simple docstring'''







			a       =     "\nfrom random import randint\nfrom __main__ import fibonacci_with_matrix_exponentiation\n"
			a       =     "fibonacci_with_matrix_exponentiation(randint(1,70000), 1, 1)"
			a       =     timeit.timeit(setup=A,    stmt=A,    number=100  )
			print("With matrix exponentiation the average execution time is ",    exec_time / 100  )
			return exec_time




def      __magic_name__							(					):






			'''simple docstring'''







			a       =     "\nfrom random import randint\nfrom __main__ import simple_fibonacci\n"
			a       =     "simple_fibonacci(randint(1,70000), 1, 1)"
			a       =     timeit.timeit(setup=A,    stmt=A,    number=100  )
			print(
			    "Without matrix exponentiation the average execution time is ",    exec_time / 100  )
			return exec_time




def      __magic_name__							(					):






			'''simple docstring'''







			matrix_exponentiation_time()
			simple_fibonacci_time()


if __name__ == "__main__":
		main()












class        snake_case__				:
				"""simple docstring"""



				def __init__( self							:	List[str]   , __lowerCamelCase							:	int				)   ->	None:
							a       =     data
							a       =     42
							a       =     42




def      __magic_name__							(					A						:   Node  ):






			'''simple docstring'''







			a       =     0
			a       =     x




def      __magic_name__							(					A						:   Node,    A						:   Node  ):






			'''simple docstring'''







			a       ,						a       =     find_set(A  ), find_set(A  )
			if x == y:
						return

			elif x.rank > y.rank:
						a       =     x
			else:
						a       =     y
						if x.rank == y.rank:
									y.rank += 1




def      __magic_name__							(					A						:   Node  ):






			'''simple docstring'''







			if x != x.parent:
						a       =     find_set(x.parent  )
			return x.parent




def      __magic_name__							(					A						:   Node  ):






			'''simple docstring'''







			a       =     ({0, 1, 2}, {3, 4, 5})
			for s in sets:
						if node.data in s:
									return s
			a       =     F"""{node.data} is not in {sets}"""
			raise ValueError(A  )




def      __magic_name__							(					):






			'''simple docstring'''







			a       =     [Node(A  ) for i in range(6  )]
			for v in vertex:
						make_set(A  )

			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(A  ).isdisjoint(find_python_set(A  )  ):
												assert find_set(A  ) != find_set(A  )
									else:
												assert find_set(A  ) == find_set(A  )


if __name__ == "__main__":
		test_disjoint_set()






