
'''simple docstring'''





import math
from timeit import timeit

def   A			(							A_				:       int							):
						snake_case							:  List[str]			=     0
						snake_case							:  Any			=     abs(A_							)
						while True:
												snake_case							:  List[Any]			=     n // 10
												digits += 1
												if n == 0:
																		break
						return digits

def   A			(							A_				:       int							):
						return 1 if n == 0 else math.floor(math.log(abs(A_							)     ,				10							) + 1							)

def   A			(							A_				:       int							):
						return len(str(abs(A_							)							)							)

def   A			(							):
						from collections.abc import Callable

						def benchmark_a_function(A_				:       Callable     ,				A_				:       int							) -> None:
												snake_case							:  Optional[int]			=     F"""{func.__name__}({value})"""
												snake_case							:  Optional[int]			=     timeit(F"""__main__.{call}"""     ,				setup='''import __main__'''							)
												print(F"""{call}: {func(A_							)} -- {timing} seconds"""							)

						for value in (262144, 1125899906842624, 1267650600228229401496703205376):
												for func in (num_digits, num_digits_fast, num_digits_faster):
																		benchmark_a_function(A_     ,				A_							)
												print()


if __name__ == "__main__":
						import doctest

						doctest.testmod()
						benchmark()






'''simple docstring'''

from __future__ import annotations

_A					:     Union[str, Any]      ='''Alexander Joslin'''







def     __UpperCamelCase					(				_lowercase       )			->      int:

	if number <= 0:
		_lowercase       :							Optional[Any]  	=		f'''n must be greater than 0. Got n = {number}'''
		raise ValueError(_lowercase       )

	_lowercase       :							List[str]  	=		[number + 1] * (number + 1)

	# starting position
	_lowercase       :							str  	=		0
	for i in range(1,					_lowercase       ):
		_lowercase       :							Union[str, Any]  	=		min(table[i + 1],					table[i] + 1       )
		# check if out of bounds
		if i * 2 <= number:
			_lowercase       :							Optional[Any]  	=		min(table[i * 2],					table[i] + 1       )
		# check if out of bounds
		if i * 3 <= number:
			_lowercase       :							Any  	=		min(table[i * 3],					table[i] + 1       )
	return table[number]


if __name__ == "__main__":
		import doctest

		doctest.testmod()
