import math
from timeit import timeit


def SCREAMING_SNAKE_CASE				(     lowercase_:	int				):
       _UpperCamelCase     :       Tuple  						=  0
       _UpperCamelCase     :       Union[str, Any]  						=  abs(snake_case__				)
       while True:
              _UpperCamelCase     :       Dict  						=  n // 10
              digits += 1
              if n == 0:
                     break
       return digits


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


def SCREAMING_SNAKE_CASE				(     lowercase_:	int				):
       return len(str(abs(snake_case__				)				)				)


def SCREAMING_SNAKE_CASE				(     ):
       from collections.abc import Callable

       def benchmark_a_function(lowercase_:	Callable		,						lowercase_:	int				) -> None:
              _UpperCamelCase     :       Any  						=  F"{func.__name__}({value})"
              _UpperCamelCase     :       List[str]  						=  timeit(F"__main__.{call}"		,						setup='import __main__'				)
              print(F"{call}: {func(snake_case__				)} -- {timing} seconds"				)

       for value in (262144, 1125899906842624, 1267650600228229401496703205376):
              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()




import math
from collections.abc import Generator


def SCREAMING_SNAKE_CASE				(     lowercase_:	int				):
       _UpperCamelCase     :       Generator  						=  (i for i in range(1		,						(max_n + 1)				))
       for i in (n for n in numbers if n > 1):
              for j in range(2		,						lowercase_				):
                     if (i % j) == 0:
                            break
              else:
                     yield i


def SCREAMING_SNAKE_CASE				(     lowercase_:	int				):
       _UpperCamelCase     :       Generator  						=  (i for i in range(1		,						(max_n + 1)				))
       for i in (n for n in numbers if n > 1):
              # only need to check for factors up to sqrt(i)
              _UpperCamelCase     :       Any  						=  int(math.sqrt(lowercase_				)				) + 1
              for j in range(2		,						lowercase_				):
                     if (i % j) == 0:
                            break
              else:
                     yield i


def SCREAMING_SNAKE_CASE				(     lowercase_:	int				):
       _UpperCamelCase     :       Generator  						=  (i for i in range(1		,						(max_n + 1)		,						2				))
       # It's useless to test even numbers as they will not be prime
       if max_n > 2:
              yield 2  # Because 2 will not be tested, it's necessary to yield it now
       for i in (n for n in numbers if n > 1):
              _UpperCamelCase     :       Tuple  						=  int(math.sqrt(lowercase_				)				) + 1
              for j in range(3		,						lowercase_		,						2				):
                     # As we removed the even numbers, we don't need them now
                     if (i % j) == 0:
                            break
              else:
                     yield i


def SCREAMING_SNAKE_CASE				(     ):
       from timeit import timeit

       _UpperCamelCase     :       Optional[Any]  						=  'from __main__ import slow_primes, primes, fast_primes'
       print(timeit('slow_primes(1_000_000_000_000)'		,						setup=lowercase_		,						number=1000000				)				)
       print(timeit('primes(1_000_000_000_000)'		,						setup=lowercase_		,						number=1000000				)				)
       print(timeit('fast_primes(1_000_000_000_000)'		,						setup=lowercase_		,						number=1000000				)				)


if __name__ == "__main__":
 UpperCAmelCase					=				int(input('''Calculate primes up to:\n>> ''').strip())
 for ret in primes(number):
  print(ret)
 benchmark()



