


'''simple docstring'''

def __snake_case					(      UpperCAmelCase_						:						int = 50000000		):
 lowerCamelCase_      =  set()
 lowerCamelCase_      =  int((limit - 24) ** (1 / 2)		)

 lowerCamelCase_      =  set(range(3					,				prime_square_limit + 1					,				2		)		)
 primes.add(2		)
 for p in range(3					,				prime_square_limit + 1					,				2		):
  if p not in primes:
   continue
  primes.difference_update(set(range(p * p					,				prime_square_limit + 1					,				UpperCAmelCase_		)		)		)

 for primea in primes:
  lowerCamelCase_      =  primea * primea
  for primea in primes:
   lowerCamelCase_      =  primea * primea * primea
   if square + cube >= limit - 16:
    break
   for primea in primes:
    lowerCamelCase_      =  primea * primea * primea * primea
    lowerCamelCase_      =  square + cube + tetr
    if total >= limit:
     break
    ret.add(UpperCAmelCase_		)

 return len(UpperCAmelCase_		)


if __name__ == "__main__":
     print(f'''{solution() = }''')







'''simple docstring'''

import math





def __snake_case					(      UpperCAmelCase_						:						float					,				UpperCAmelCase_						:						float		):
 return math.pow(UpperCAmelCase_					,				2		) - a





def __snake_case					(      UpperCAmelCase_						:						float		):
 return 2 * x





def __snake_case					(      UpperCAmelCase_						:						float		):
 lowerCamelCase_      =  2.0

 while start <= a:
  lowerCamelCase_      =  math.pow(UpperCAmelCase_					,				2		)

 return start





def __snake_case					(      UpperCAmelCase_						:						float					,				UpperCAmelCase_						:						int = 9999					,				UpperCAmelCase_						:						float = 0.00_0000_0000_0001		):

 if a < 0:
  raise ValueError("math domain error"		)

 lowerCamelCase_      =  get_initial_point(UpperCAmelCase_		)

 for _ in range(UpperCAmelCase_		):
  lowerCamelCase_      =  value
  lowerCamelCase_      =  value - fx(UpperCAmelCase_					,				UpperCAmelCase_		) / fx_derivative(UpperCAmelCase_		)
  if abs(prev_value - value		) < tolerance:
   return value

 return value


if __name__ == "__main__":
     from doctest import testmod

     testmod()



