





"""simple docstring"""
from math import sqrt

def 		_SCREAMING_SNAKE_CASE			(_UpperCAmelCase					:    Any = 100_0000			):
 lowerCAmelCase    				= 0
 lowerCAmelCase    				= 0
 lowerCAmelCase    				= 42

 while num_cuboids <= limit:
  max_cuboid_size += 1
  for sum_shortest_sides in range(2  ,     2 * max_cuboid_size + 1			):
   if sqrt(sum_shortest_sides**2 + max_cuboid_size**2			).is_integer():
    num_cuboids += (
        min(lowerCAmelCase_  ,     sum_shortest_sides // 2			)
        - max(1  ,     sum_shortest_sides - max_cuboid_size			)
        + 1
    )

 return max_cuboid_size


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










"""simple docstring"""






from ..utils import DummyObject, requires_backends



class     UpperCAmelCase    (	metaclass=__SCREAMING_SNAKE_CASE  ):
   A__		:	Optional[int]           =  ['''torch''', '''scipy''']



   def __init__(       self    :	Any							,       *__lowerCamelCase    :	List[Any]							,       **__lowerCamelCase    :	Any				):



     """simple docstring"""
     requires_backends(self							,       ['''torch''', '''scipy''']				)



   @classmethod
   def    __UpperCAmelCase    (       cls    :	Dict							,       *__lowerCamelCase    :	List[str]							,       **__lowerCamelCase    :	Tuple				):



     """simple docstring"""
     requires_backends(cls							,       ['''torch''', '''scipy''']				)





   @classmethod
   def    __UpperCAmelCase    (       cls    :	int							,       *__lowerCamelCase    :	Union[str, Any]							,       **__lowerCamelCase    :	Tuple				):



     """simple docstring"""
     requires_backends(cls							,       ['''torch''', '''scipy''']				)





