


from math import ceil, sqrt

def       lowercase_		(		_A			:    str = 1000000						):

      """simple docstring"""




      lowerCamelCase__		:				List[Any]    =  0

      for outer_width in range(3    ,					(limit // 4) + 2						):
            if outer_width**2 > limit:
                  lowerCamelCase__		:				Tuple    =  max(ceil(sqrt(outer_width**2 - limit						)						)    ,					1						)
            else:
                  lowerCamelCase__		:				Any    =  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() = }')







import unittest

from diffusers.pipelines.pipeline_utils import is_safetensors_compatible

class     _A       (	unittest.TestCase    ):



       def 		_lowerCamelCase			(		self							:     List[Any]):


           '''simple docstring'''

           __a						       =				[
               '''safety_checker/pytorch_model.bin''',
               '''safety_checker/model.safetensors''',
               '''vae/diffusion_pytorch_model.bin''',
               '''vae/diffusion_pytorch_model.safetensors''',
               '''text_encoder/pytorch_model.bin''',
               '''text_encoder/model.safetensors''',
               '''unet/diffusion_pytorch_model.bin''',
               '''unet/diffusion_pytorch_model.safetensors''',
           ]
           self.assertTrue(is_safetensors_compatible(__SCREAMING_SNAKE_CASE))



       def 		_lowerCamelCase			(		self							:     Optional[Any]):


           '''simple docstring'''

           __a						       =				[
               '''unet/diffusion_pytorch_model.bin''',
               '''unet/diffusion_pytorch_model.safetensors''',
           ]
           self.assertTrue(is_safetensors_compatible(__SCREAMING_SNAKE_CASE))



       def 		_lowerCamelCase			(		self							:     Optional[Any]):


           '''simple docstring'''

           __a						       =				[
               '''safety_checker/pytorch_model.bin''',
               '''safety_checker/model.safetensors''',
               '''vae/diffusion_pytorch_model.bin''',
               '''vae/diffusion_pytorch_model.safetensors''',
               '''text_encoder/pytorch_model.bin''',
               '''text_encoder/model.safetensors''',
               '''unet/diffusion_pytorch_model.bin''',
               # Removed: 'unet/diffusion_pytorch_model.safetensors',
           ]
           self.assertFalse(is_safetensors_compatible(__SCREAMING_SNAKE_CASE))



       def 		_lowerCamelCase			(		self							:     Dict):


           '''simple docstring'''

           __a						       =				[
               '''text_encoder/pytorch_model.bin''',
               '''text_encoder/model.safetensors''',
           ]
           self.assertTrue(is_safetensors_compatible(__SCREAMING_SNAKE_CASE))



       def 		_lowerCamelCase			(		self							:     Union[str, Any]):


           '''simple docstring'''

           __a						       =				[
               '''safety_checker/pytorch_model.bin''',
               '''safety_checker/model.safetensors''',
               '''vae/diffusion_pytorch_model.bin''',
               '''vae/diffusion_pytorch_model.safetensors''',
               '''text_encoder/pytorch_model.bin''',
               # Removed: 'text_encoder/model.safetensors',
               '''unet/diffusion_pytorch_model.bin''',
               '''unet/diffusion_pytorch_model.safetensors''',
           ]
           self.assertFalse(is_safetensors_compatible(__SCREAMING_SNAKE_CASE))



       def 		_lowerCamelCase			(		self							:     Tuple):


           '''simple docstring'''

           __a						       =				[
               '''safety_checker/pytorch_model.fp16.bin''',
               '''safety_checker/model.fp16.safetensors''',
               '''vae/diffusion_pytorch_model.fp16.bin''',
               '''vae/diffusion_pytorch_model.fp16.safetensors''',
               '''text_encoder/pytorch_model.fp16.bin''',
               '''text_encoder/model.fp16.safetensors''',
               '''unet/diffusion_pytorch_model.fp16.bin''',
               '''unet/diffusion_pytorch_model.fp16.safetensors''',
           ]
           __a						       =				'''fp16'''
           self.assertTrue(is_safetensors_compatible(__SCREAMING_SNAKE_CASE     ,		variant=__SCREAMING_SNAKE_CASE))



       def 		_lowerCamelCase			(		self							:     Dict):


           '''simple docstring'''

           __a						       =				[
               '''unet/diffusion_pytorch_model.fp16.bin''',
               '''unet/diffusion_pytorch_model.fp16.safetensors''',
           ]
           __a						       =				'''fp16'''
           self.assertTrue(is_safetensors_compatible(__SCREAMING_SNAKE_CASE     ,		variant=__SCREAMING_SNAKE_CASE))



       def 		_lowerCamelCase			(		self							:     Optional[Any]):


           '''simple docstring'''

           __a						       =				[
               '''unet/diffusion_pytorch_model.bin''',
               '''unet/diffusion_pytorch_model.safetensors''',
           ]
           __a						       =				'''fp16'''
           self.assertTrue(is_safetensors_compatible(__SCREAMING_SNAKE_CASE     ,		variant=__SCREAMING_SNAKE_CASE))



       def 		_lowerCamelCase			(		self							:     Union[str, Any]):


           '''simple docstring'''

           __a						       =				[
               '''safety_checker/pytorch_model.fp16.bin''',
               '''safety_checker/model.fp16.safetensors''',
               '''vae/diffusion_pytorch_model.fp16.bin''',
               '''vae/diffusion_pytorch_model.fp16.safetensors''',
               '''text_encoder/pytorch_model.fp16.bin''',
               '''text_encoder/model.fp16.safetensors''',
               '''unet/diffusion_pytorch_model.fp16.bin''',
               # Removed: 'unet/diffusion_pytorch_model.fp16.safetensors',
           ]
           __a						       =				'''fp16'''
           self.assertFalse(is_safetensors_compatible(__SCREAMING_SNAKE_CASE     ,		variant=__SCREAMING_SNAKE_CASE))



       def 		_lowerCamelCase			(		self							:     Dict):


           '''simple docstring'''

           __a						       =				[
               '''text_encoder/pytorch_model.fp16.bin''',
               '''text_encoder/model.fp16.safetensors''',
           ]
           __a						       =				'''fp16'''
           self.assertTrue(is_safetensors_compatible(__SCREAMING_SNAKE_CASE     ,		variant=__SCREAMING_SNAKE_CASE))



       def 		_lowerCamelCase			(		self							:     List[str]):


           '''simple docstring'''

           __a						       =				[
               '''text_encoder/pytorch_model.bin''',
               '''text_encoder/model.safetensors''',
           ]
           __a						       =				'''fp16'''
           self.assertTrue(is_safetensors_compatible(__SCREAMING_SNAKE_CASE     ,		variant=__SCREAMING_SNAKE_CASE))





       def 		_lowerCamelCase			(		self							:     List[str]):


           '''simple docstring'''

           __a						       =				[
               '''safety_checker/pytorch_model.fp16.bin''',
               '''safety_checker/model.fp16.safetensors''',
               '''vae/diffusion_pytorch_model.fp16.bin''',
               '''vae/diffusion_pytorch_model.fp16.safetensors''',
               '''text_encoder/pytorch_model.fp16.bin''',
               # 'text_encoder/model.fp16.safetensors',
               '''unet/diffusion_pytorch_model.fp16.bin''',
               '''unet/diffusion_pytorch_model.fp16.safetensors''',
           ]
           __a						       =				'''fp16'''
           self.assertFalse(is_safetensors_compatible(__SCREAMING_SNAKE_CASE     ,		variant=__SCREAMING_SNAKE_CASE))





