



import math
from timeit import timeit




def       UpperCAmelCase__	(							__snake_case							)				->	int:
  _A          =      0
  _A          =      abs(__snake_case							)
  while True:
    _A          =      n // 10
    digits += 1
    if n == 0:
      break
  return digits




def       UpperCAmelCase__	(							__snake_case							)				->	int:
  return 1 if n == 0 else math.floor(math.log(abs(__snake_case							)  ,			10							) + 1							)




def       UpperCAmelCase__	(							__snake_case							)				->	int:
  return len(str(abs(__snake_case							)							)							)




def       UpperCAmelCase__	(							)				->	None:
  from collections.abc import Callable

  def benchmark_a_function(__snake_case  ,			__snake_case							) -> None:
    _A          =      F'''{func.__name__}({value})'''
    _A          =      timeit(F'''__main__.{call}'''  ,			setup='''import __main__'''							)
    print(F'''{call}: {func(__snake_case							)} -- {timing} seconds'''							)

  for value in (262_144, 1_125_899_906_842_624, 1_267_650_600_228_229_401_496_703_205_376):
    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()




from __future__ import annotations




def       UpperCAmelCase__	(							__snake_case  ,			__snake_case  ,			__snake_case  ,			__snake_case							)				->	int:

  # Base Case
  if counter == 0 or capacity == 0:
    return 0

  # If weight of the nth item is more than Knapsack of capacity,
  #   then this item cannot be included in the optimal solution,
  # else return the maximum of two cases:
  #   (1) nth item included
  #   (2) not included
  if weights[counter - 1] > capacity:
    return knapsack(__snake_case  ,			__snake_case  ,			__snake_case  ,			counter - 1							)
  else:
    _A          =      capacity - weights[counter - 1]
    _A          =      values[counter - 1] + knapsack(
        __snake_case  ,			__snake_case  ,			__snake_case  ,			counter - 1							)
    _A          =      knapsack(__snake_case  ,			__snake_case  ,			__snake_case  ,			counter - 1							)
    return max(__snake_case  ,			__snake_case							)


if __name__ == "__main__":
    import doctest

    doctest.testmod()