





"""simple docstring"""


import math
from timeit import timeit





def 				a__      (	_UpperCAmelCase						)     ->	int:

 '''simple docstring'''






 snake_case__     				=					0
 snake_case__     				=					abs(snake_case__						)
 while True:
  snake_case__     				=					n // 1_0
  digits += 1
  if n == 0:
   break
 return digits





def 				a__      (	_UpperCAmelCase						)     ->	int:

 '''simple docstring'''






 return 1 if n == 0 else math.floor(math.log(abs(snake_case__						)						,  1_0						) + 1						)





def 				a__      (	_UpperCAmelCase						)     ->	int:

 '''simple docstring'''






 return len(str(abs(snake_case__						)						)						)





def 				a__      (	)     ->	None:

 '''simple docstring'''






 from collections.abc import Callable

 def benchmark_a_function(_UpperCAmelCase						,  _UpperCAmelCase						) -> None:
  snake_case__     				=					f"{func.__name__}({value})"
  snake_case__     				=					timeit(f"__main__.{call}"						,  setup="import __main__"						)
  print(f"{call}: {func(snake_case__						)} -- {timing} seconds"						)

 for value in (2_6_2_1_4_4, 1_1_2_5_8_9_9_9_0_6_8_4_2_6_2_4, 1_2_6_7_6_5_0_6_0_0_2_2_8_2_2_9_4_0_1_4_9_6_7_0_3_2_0_5_3_7_6):
  for func in (num_digits, num_digits_fast, num_digits_faster):
   benchmark_a_function(snake_case__						,  snake_case__						)
  print()


if __name__ == "__main__":
   import doctest

   doctest.testmod()
   benchmark()









def 			__lowerCamelCase     (						snake_case__			,snake_case__						)				->    Dict:






						"""simple docstring"""





						if not root or root not in binary_tree_mirror_dictionary:
												return
						_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE       =    binary_tree_mirror_dictionary[root][:2]
						_SCREAMING_SNAKE_CASE       =    [right_child, left_child]
						binary_tree_mirror_dict(snake_case__			,snake_case__						)
						binary_tree_mirror_dict(snake_case__			,snake_case__						)

def 			__lowerCamelCase     (						snake_case__			,snake_case__ = 1						)				->    dict:






						"""simple docstring"""





						if not binary_tree:
												raise ValueError("""binary tree cannot be empty"""						)
						if root not in binary_tree:
												_SCREAMING_SNAKE_CASE       =    F'root {root} is not present in the binary_tree'
												raise ValueError(snake_case__						)
						_SCREAMING_SNAKE_CASE       =    dict(snake_case__						)
						binary_tree_mirror_dict(snake_case__			,snake_case__						)
						return binary_tree_mirror_dictionary


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

