'''simple docstring'''


def    _lowerCamelCase       ( lowerCamelCase_   :				dict      ,	lowerCamelCase_   :				int  ):



     """simple docstring"""





     if not root or root not in binary_tree_mirror_dictionary:
          return
     UpperCAmelCase_  ,     UpperCAmelCase_				:  List[str]  = binary_tree_mirror_dictionary[root][:2]
     UpperCAmelCase_				:  Union[str, Any]  = [right_child, left_child]
     binary_tree_mirror_dict(__lowerCamelCase      ,	__lowerCamelCase  )
     binary_tree_mirror_dict(__lowerCamelCase      ,	__lowerCamelCase  )


def    _lowerCamelCase       ( lowerCamelCase_   :				dict      ,	lowerCamelCase_   :				int = 1  ):



     """simple docstring"""





     if not binary_tree:
          raise ValueError('binary tree cannot be empty'  )
     if root not in binary_tree:
          UpperCAmelCase_				:  Union[str, Any]  = F'''root {root} is not present in the binary_tree'''
          raise ValueError(__lowerCamelCase  )
     UpperCAmelCase_				:  Optional[int]  = dict(__lowerCamelCase  )
     binary_tree_mirror_dict(__lowerCamelCase      ,	__lowerCamelCase  )
     return binary_tree_mirror_dictionary


if __name__ == "__main__":
 snake_case__	:     Union[str, Any]      =    {1: [2, 3], 2: [4, 5], 3: [6, 7], 7: [8, 9]}
 print(f'''Binary tree: {binary_tree}''')
 snake_case__	:     List[Any]      =    binary_tree_mirror(binary_tree, 5)
 print(f'''Binary tree mirror: {binary_tree_mirror_dictionary}''')







'''simple docstring'''

import timeit





class 				lowercase    :


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


   def __mul__( self					:						int ,		__lowerCAmelCase					:						List[str])   ->       Union[str, Any]:
         lowercase_     			=   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 __a			(						__lowerCamelCase      :    List[str]			,		__lowerCamelCase      :    Dict					)						->				Optional[Any]:
      '''simple docstring'''


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


def __a			(						__lowerCamelCase      :    Tuple			,		__lowerCamelCase      :    Tuple			,		__lowerCamelCase      :    List[Any]					)						->				Dict:
      '''simple docstring'''


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


def __a			(						__lowerCamelCase      :    List[Any]			,		__lowerCamelCase      :    Union[str, Any]			,		__lowerCamelCase      :    List[str]					)						->				Optional[Any]:
      '''simple docstring'''


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

      lowercase_     			=   fa
      lowercase_     			=   fa
      n -= 2

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

      return fn_a


def __a			(						)						->				str:
      '''simple docstring'''


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


def __a			(						)						->				Optional[Any]:
      '''simple docstring'''


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


def __a			(						)						->				Tuple:
      '''simple docstring'''


      matrix_exponentiation_time()
      simple_fibonacci_time()


if __name__ == "__main__":
       main()






