
"""simple docstring"""







import timeit



class 				UpperCAmelCase_	:
 """simple docstring"""




 def __init__( self       : Any     ,   a_       : Optional[Any] )->					Optional[Any]:



      """simple docstring"""

      if isinstance(lowerCAmelCase__     ,   lowerCAmelCase__ ):  # Initializes a matrix identical to the one provided.
           UpperCAmelCase_						:    List[Any]    					=  arg
           UpperCAmelCase_						:    Optional[int]    					=  len(lowerCAmelCase__ )
      else:  # Initializes a square matrix of the given size and set values to zero.
           UpperCAmelCase_						:    Optional[Any]    					=  arg
           UpperCAmelCase_						:    Union[str, Any]    					=  [[0 for _ in range(self.n )] for _ in range(self.n )]






 def __mul__( self       : Optional[int]     ,   a_       : Optional[int] )->					Optional[int]:



      """simple docstring"""

      UpperCAmelCase_						:    int    					=  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_			(					lowercase						, lowercase      )     ->							str:


     """simple docstring"""







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




def 			A_			(					lowercase						, lowercase						, lowercase      )     ->							Optional[Any]:


     """simple docstring"""







     if n == 1:
          return fa
     elif n == 2:
          return fa
     UpperCAmelCase_						:    int    					=  Matrix([[1, 1], [1, 0]]      )
     UpperCAmelCase_						:    Optional[Any]    					=  modular_exponentiation(lowercase						, n - 2      )
     return fa * matrix.t[0][0] + fa * matrix.t[0][1]




def 			A_			(					lowercase						, lowercase						, lowercase      )     ->							Any:


     """simple docstring"""







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

     UpperCAmelCase_						:    str    					=  fa
     UpperCAmelCase_						:    Optional[Any]    					=  fa
     n -= 2

     while n > 0:
          UpperCAmelCase_						:    Dict    					=  fn_a + fn_a, fn_a
          n -= 1

     return fn_a




def 			A_			(					)     ->							Optional[int]:


     """simple docstring"""







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




def 			A_			(					)     ->							Tuple:


     """simple docstring"""







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




def 			A_			(					)     ->							Dict:


     """simple docstring"""







     matrix_exponentiation_time()
     simple_fibonacci_time()


if __name__ == "__main__":
       main()



"""simple docstring"""







from __future__ import annotations



class 		UpperCAmelCase_	:
 """simple docstring"""




 def __init__( self       : Any     ,   a_       : int = 0 )->					None:



      """simple docstring"""

      UpperCAmelCase_						:    Tuple    					=  value
      UpperCAmelCase_						:    Node | None    					=  None
      UpperCAmelCase_						:    Node | None    					=  None




def 			A_			(					lowercase						, lowercase      )     ->							Node | None:


     """simple docstring"""







     if treea is None:
          return treea
     if treea is None:
          return treea

     UpperCAmelCase_						:    int    					=  treea.value + treea.value
     UpperCAmelCase_						:    List[str]    					=  merge_two_binary_trees(treea.left						, treea.left      )
     UpperCAmelCase_						:    List[str]    					=  merge_two_binary_trees(treea.right						, treea.right      )
     return treea




def 			A_			(					lowercase      )     ->							None:


     """simple docstring"""







     if root:
          print(root.value      )
          print_preorder(root.left      )
          print_preorder(root.right      )


if __name__ == "__main__":
       lowercase_						    =					Node(1)
       lowercase_						    =					Node(2)
       lowercase_						    =					Node(3)
       lowercase_						    =					Node(4)

       lowercase_						    =					Node(2)
       lowercase_						    =					Node(4)
       lowercase_						    =					Node(6)
       lowercase_						    =					Node(9)
       lowercase_						    =					Node(5)

       print("Tree1 is: ")
       print_preorder(treea)
       print("Tree2 is: ")
       print_preorder(treea)
       lowercase_						    =					merge_two_binary_trees(treea, treea)
       print("Merged Tree is: ")
       print_preorder(merged_tree)

