




from math import sqrt

def      A      (      _SCREAMING_SNAKE_CASE = 100_0000    )	-> Union[str, Any]:
       lowerCamelCase   :      str			 =					0
       lowerCamelCase   :      Optional[int]			 =					0
       lowerCamelCase   :      Any			 =					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 __future__ import annotations




def    UpperCAmelCase__       (lowerCAmelCase_  ,						lowerCAmelCase_ = None  ,						lowerCAmelCase_ = None   ):




					'''simple docstring'''


					if start is None:
										__SCREAMING_SNAKE_CASE						   =				0

					if end is None:
										__SCREAMING_SNAKE_CASE						   =				len(lowerCAmelCase_   ) - 1

					if start >= end:
										return

					__SCREAMING_SNAKE_CASE						   =				(start + end) // 2

					slowsort(lowerCAmelCase_  ,						lowerCAmelCase_  ,						lowerCAmelCase_   )
					slowsort(lowerCAmelCase_  ,						mid + 1  ,						lowerCAmelCase_   )

					if sequence[end] < sequence[mid]:
										__SCREAMING_SNAKE_CASE   ,  __SCREAMING_SNAKE_CASE						   =				sequence[mid], sequence[end]

					slowsort(lowerCAmelCase_  ,						lowerCAmelCase_  ,						end - 1   )


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

		testmod()
