
'''simple docstring'''

from __future__ import annotations


class 					a_					:




							def __init__(       self				,				snake_case_ = 0					):
									_lowerCAmelCase    :					Optional[Any]							=   value
									_lowerCAmelCase    :					Node | None							=   None
									_lowerCAmelCase    :					Node | None							=   None



def 		_UpperCAmelCase			(					_lowerCamelCase  :    Node | None					, _lowerCamelCase  :    Node | None						)      ->  Node | None:
		if treea is None:
				return treea
		if treea is None:
				return treea

		_lowerCAmelCase    :					Any							=   treea.value + treea.value
		_lowerCAmelCase    :					Tuple							=   merge_two_binary_trees(treea.left					, treea.left						)
		_lowerCAmelCase    :					List[str]							=   merge_two_binary_trees(treea.right					, treea.right						)
		return treea


def 		_UpperCAmelCase			(					_lowerCamelCase  :    Node | None						)      ->  None:
		if root:
				print(root.value						)
				print_preorder(root.left						)
				print_preorder(root.right						)


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

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

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




'''simple docstring'''

def 		_UpperCAmelCase			(					_lowerCamelCase  :    list[list[int]]					, _lowerCamelCase  :    list[list[int]]						)      ->  list[list[int]]:
  _lowerCAmelCase    :					int							=   []
  _lowerCAmelCase    :					Union[str, Any]							=   len(_lowerCamelCase						)
  for i in range(_lowerCamelCase						):
    _lowerCAmelCase    :					List[str]							=   []
    for j in range(_lowerCamelCase						):
      _lowerCAmelCase    :					Union[str, Any]							=   0
      for k in range(_lowerCamelCase						):
        _lowerCAmelCase    :					Any							=   val + matrix_a[i][k] * matrix_b[k][j]
      list_a.append(_lowerCamelCase						)
    matrix_c.append(_lowerCamelCase						)
  return matrix_c


def 		_UpperCAmelCase			(					_lowerCamelCase  :    int						)      ->  list[list[int]]:
  return [[int(row == column						) for column in range(_lowerCamelCase						)] for row in range(_lowerCamelCase						)]


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


def 		_UpperCAmelCase			(					_lowerCamelCase  :    int						)      ->  int:
  if n <= 1:
    return n
  _lowerCAmelCase    :					Any							=   0
  _lowerCAmelCase    :					Dict							=   1
  for _ in range(2					, n + 1						):
    _lowerCAmelCase			,   _lowerCAmelCase    :					int							=   fiba, fiba + fiba
  return fiba


def 		_UpperCAmelCase			(					)      ->  None:
  for ordinal in "0th 1st 2nd 3rd 10th 100th 1000th".split():
    _lowerCAmelCase    :					Union[str, Any]							=   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(_lowerCamelCase						)} and using bruteforce is '
        f'{nth_fibonacci_bruteforce(_lowerCamelCase						)}\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()


