





from math import sqrt


def  SCREAMING_SNAKE_CASE   ( _UpperCAmelCase = 100_0000				)    ->  int:
    lowerCamelCase__					:   int      				=	0
    lowerCamelCase__					:   int      				=	0
    lowerCamelCase__					:   int

    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(_UpperCAmelCase		,			sum_shortest_sides // 2				)
                    - max(1		,			sum_shortest_sides - max_cuboid_size				)
                    + 1
                )

    return max_cuboid_size


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












from ..utils import DummyObject, requires_backends

class      lowerCAmelCase							(      metaclass=__UpperCamelCase    ):
 UpperCAmelCase__									=	["""torch""", """transformers""", """onnx"""]
 def __init__(   self						:   Tuple    ,  *UpperCAmelCase						:   str    ,  **UpperCAmelCase						:   Optional[int]			)    ->			List[str]:
     requires_backends(self    ,  ['torch', 'transformers', 'onnx']			)
 @classmethod
 def   A_			(   cls						:   Union[str, Any]    ,  *UpperCAmelCase						:   Dict    ,  **UpperCAmelCase						:   List[str]			)    ->			int:
     requires_backends(cls    ,  ['torch', 'transformers', 'onnx']			)







 @classmethod
 def   A_			(   cls						:   Any    ,  *UpperCAmelCase						:   List[Any]    ,  **UpperCAmelCase						:   Tuple			)    ->			Union[str, Any]:
     requires_backends(cls    ,  ['torch', 'transformers', 'onnx']			)


class      lowerCAmelCase							(      metaclass=__UpperCamelCase    ):
 UpperCAmelCase__									=	["""torch""", """transformers""", """onnx"""]
 def __init__(   self						:   List[Any]    ,  *UpperCAmelCase						:   Union[str, Any]    ,  **UpperCAmelCase						:   Dict			)    ->			Any:
     requires_backends(self    ,  ['torch', 'transformers', 'onnx']			)
 @classmethod
 def   A_			(   cls						:   str    ,  *UpperCAmelCase						:   Union[str, Any]    ,  **UpperCAmelCase						:   Union[str, Any]			)    ->			Tuple:
     requires_backends(cls    ,  ['torch', 'transformers', 'onnx']			)







 @classmethod
 def   A_			(   cls						:   List[Any]    ,  *UpperCAmelCase						:   str    ,  **UpperCAmelCase						:   Dict			)    ->			str:
     requires_backends(cls    ,  ['torch', 'transformers', 'onnx']			)


class      lowerCAmelCase							(      metaclass=__UpperCamelCase    ):
 UpperCAmelCase__									=	["""torch""", """transformers""", """onnx"""]
 def __init__(   self						:   Dict    ,  *UpperCAmelCase						:   Dict    ,  **UpperCAmelCase						:   Dict			)    ->			Optional[int]:
     requires_backends(self    ,  ['torch', 'transformers', 'onnx']			)
 @classmethod
 def   A_			(   cls						:   Optional[Any]    ,  *UpperCAmelCase						:   Union[str, Any]    ,  **UpperCAmelCase						:   Any			)    ->			Any:
     requires_backends(cls    ,  ['torch', 'transformers', 'onnx']			)







 @classmethod
 def   A_			(   cls						:   List[str]    ,  *UpperCAmelCase						:   Any    ,  **UpperCAmelCase						:   Dict			)    ->			Tuple:
     requires_backends(cls    ,  ['torch', 'transformers', 'onnx']			)


class      lowerCAmelCase							(      metaclass=__UpperCamelCase    ):
 UpperCAmelCase__									=	["""torch""", """transformers""", """onnx"""]
 def __init__(   self						:   Union[str, Any]    ,  *UpperCAmelCase						:   Optional[int]    ,  **UpperCAmelCase						:   Optional[int]			)    ->			Any:
     requires_backends(self    ,  ['torch', 'transformers', 'onnx']			)
 @classmethod
 def   A_			(   cls						:   List[Any]    ,  *UpperCAmelCase						:   Dict    ,  **UpperCAmelCase						:   int			)    ->			Dict:
     requires_backends(cls    ,  ['torch', 'transformers', 'onnx']			)







 @classmethod
 def   A_			(   cls						:   Dict    ,  *UpperCAmelCase						:   Dict    ,  **UpperCAmelCase						:   Optional[int]			)    ->			Optional[int]:
     requires_backends(cls    ,  ['torch', 'transformers', 'onnx']			)


class      lowerCAmelCase							(      metaclass=__UpperCamelCase    ):
 UpperCAmelCase__									=	["""torch""", """transformers""", """onnx"""]
 def __init__(   self						:   List[str]    ,  *UpperCAmelCase						:   List[Any]    ,  **UpperCAmelCase						:   List[str]			)    ->			Optional[int]:
     requires_backends(self    ,  ['torch', 'transformers', 'onnx']			)
 @classmethod
 def   A_			(   cls						:   List[Any]    ,  *UpperCAmelCase						:   Optional[Any]    ,  **UpperCAmelCase						:   Optional[Any]			)    ->			str:
     requires_backends(cls    ,  ['torch', 'transformers', 'onnx']			)







 @classmethod
 def   A_			(   cls						:   List[Any]    ,  *UpperCAmelCase						:   Optional[int]    ,  **UpperCAmelCase						:   Any			)    ->			Any:
     requires_backends(cls    ,  ['torch', 'transformers', 'onnx']			)


class      lowerCAmelCase							(      metaclass=__UpperCamelCase    ):
 UpperCAmelCase__									=	["""torch""", """transformers""", """onnx"""]
 def __init__(   self						:   List[str]    ,  *UpperCAmelCase						:   Tuple    ,  **UpperCAmelCase						:   Optional[int]			)    ->			Optional[Any]:
     requires_backends(self    ,  ['torch', 'transformers', 'onnx']			)
 @classmethod
 def   A_			(   cls						:   Union[str, Any]    ,  *UpperCAmelCase						:   List[Any]    ,  **UpperCAmelCase						:   Optional[Any]			)    ->			Tuple:
     requires_backends(cls    ,  ['torch', 'transformers', 'onnx']			)







 @classmethod
 def   A_			(   cls						:   Tuple    ,  *UpperCAmelCase						:   List[str]    ,  **UpperCAmelCase						:   List[str]			)    ->			Tuple:
     requires_backends(cls    ,  ['torch', 'transformers', 'onnx']			)





