



from math import ceil, sqrt
def 							UpperCAmelCase__		(				_SCREAMING_SNAKE_CASE   :	int = 1_0_0_0_0_0_0				)->int:
      _lowerCAmelCase 			=  0

      for outer_width in range(3     ,				(limit // 4) + 2				):
            if outer_width**2 > limit:
                  _lowerCAmelCase 			=  max(ceil(sqrt(outer_width**2 - limit				)				)     ,				1				)
            else:
                  _lowerCAmelCase 			=  1
            if (outer_width - hole_width_lower_bound) % 2:
                  hole_width_lower_bound += 1

            answer += (outer_width - hole_width_lower_bound - 2) // 2 + 1

      return answer


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




from ...utils import (
    OptionalDependencyNotAvailable,
    is_torch_available,
    is_transformers_available,
    is_transformers_version,
)


try:
    if not (is_transformers_available() and is_torch_available()):
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    from ...utils.dummy_torch_and_transformers_objects import ShapEPipeline
else:
    from .camera import create_pan_cameras
    from .pipeline_shap_e import ShapEPipeline
    from .pipeline_shap_e_img2img import ShapEImgaImgPipeline
    from .renderer import (
        BoundingBoxVolume,
        ImportanceRaySampler,
        MLPNeRFModelOutput,
        MLPNeRSTFModel,
        ShapEParamsProjModel,
        ShapERenderer,
        StratifiedRaySampler,
        VoidNeRFModel,
    )