

import unittest

import numpy as np
import torch

from diffusers import DDPMPipeline, DDPMScheduler, UNetaDModel
from diffusers.utils.testing_utils import enable_full_determinism, require_torch_gpu, slow, torch_device


enable_full_determinism()






class 							A_				(	unittest.TestCase      ):


     @property
     def 						UpperCAmelCase						(							self    :	str      )							->			Optional[Any]:
      torch.manual_seed(0      )
      __lowerCAmelCase:     str     			=   UNetaDModel(
          block_out_channels=(3_2, 6_4)    ,						layers_per_block=2    ,						sample_size=3_2    ,						in_channels=3    ,						out_channels=3    ,						down_block_types=('DownBlock2D', 'AttnDownBlock2D')    ,						up_block_types=('AttnUpBlock2D', 'UpBlock2D')    ,						)
      return model


     def 						UpperCAmelCase						(							self    :	str      )							->			int:
      __lowerCAmelCase:     Any     			=   'cpu'
      __lowerCAmelCase:     int     			=   self.dummy_uncond_unet
      __lowerCAmelCase:     int     			=   DDPMScheduler()

      __lowerCAmelCase:     Optional[Any]     			=   DDPMPipeline(unet=UpperCAmelCase    ,						scheduler=UpperCAmelCase      )
      ddpm.to(UpperCAmelCase      )
      ddpm.set_progress_bar_config(disable=UpperCAmelCase      )

      __lowerCAmelCase:     Optional[Any]     			=   torch.Generator(device=UpperCAmelCase      ).manual_seed(0      )
      __lowerCAmelCase:     List[Any]     			=   ddpm(generator=UpperCAmelCase    ,						num_inference_steps=2    ,						output_type='numpy'      ).images

      __lowerCAmelCase:     Optional[int]     			=   torch.Generator(device=UpperCAmelCase      ).manual_seed(0      )
      __lowerCAmelCase:     List[Any]     			=   ddpm(generator=UpperCAmelCase    ,						num_inference_steps=2    ,						output_type='numpy'    ,						return_dict=UpperCAmelCase      )[0]

      __lowerCAmelCase:     List[str]     			=   image[0, -3:, -3:, -1]
      __lowerCAmelCase:     Optional[int]     			=   image_from_tuple[0, -3:, -3:, -1]

      assert image.shape == (1, 3_2, 3_2, 3)
      __lowerCAmelCase:     List[Any]     			=   np.array(
          [9.9_56E-01, 5.7_85E-01, 4.6_75E-01, 9.9_30E-01, 0.0, 1.000, 1.1_99E-03, 2.6_48E-04, 5.1_01E-04]      )

      assert np.abs(image_slice.flatten() - expected_slice      ).max() < 1E-2
      assert np.abs(image_from_tuple_slice.flatten() - expected_slice      ).max() < 1E-2


     def 						UpperCAmelCase						(							self    :	Optional[int]      )							->			str:
      __lowerCAmelCase:     int     			=   self.dummy_uncond_unet
      __lowerCAmelCase:     Union[str, Any]     			=   DDPMScheduler(prediction_type='sample'      )

      __lowerCAmelCase:     Optional[int]     			=   DDPMPipeline(unet=UpperCAmelCase    ,						scheduler=UpperCAmelCase      )
      ddpm.to(UpperCAmelCase      )
      ddpm.set_progress_bar_config(disable=UpperCAmelCase      )

      __lowerCAmelCase:     Optional[int]     			=   torch.manual_seed(0      )
      __lowerCAmelCase:     Tuple     			=   ddpm(generator=UpperCAmelCase    ,						num_inference_steps=2    ,						output_type='numpy'      ).images

      __lowerCAmelCase:     Optional[int]     			=   torch.manual_seed(0      )
      __lowerCAmelCase:     List[str]     			=   ddpm(generator=UpperCAmelCase    ,						num_inference_steps=2    ,						output_type='numpy'      )[0]

      __lowerCAmelCase:     List[str]     			=   image[0, -3:, -3:, -1]
      __lowerCAmelCase:     List[Any]     			=   image_eps[0, -3:, -3:, -1]

      assert image.shape == (1, 3_2, 3_2, 3)
      __lowerCAmelCase:     Optional[Any]     			=   1E-2 if torch_device != 'mps' else 3E-2
      assert np.abs(image_slice.flatten() - image_eps_slice.flatten()      ).max() < tolerance







@slow
@require_torch_gpu
class 							A_				(	unittest.TestCase      ):


     def 						UpperCAmelCase						(							self    :	Union[str, Any]      )							->			Optional[int]:
      __lowerCAmelCase:     Dict     			=   'google/ddpm-cifar10-32'

      __lowerCAmelCase:     int     			=   UNetaDModel.from_pretrained(UpperCAmelCase      )
      __lowerCAmelCase:     List[str]     			=   DDPMScheduler.from_pretrained(UpperCAmelCase      )

      __lowerCAmelCase:     Tuple     			=   DDPMPipeline(unet=UpperCAmelCase    ,						scheduler=UpperCAmelCase      )
      ddpm.to(UpperCAmelCase      )
      ddpm.set_progress_bar_config(disable=UpperCAmelCase      )

      __lowerCAmelCase:     List[str]     			=   torch.manual_seed(0      )
      __lowerCAmelCase:     str     			=   ddpm(generator=UpperCAmelCase    ,						output_type='numpy'      ).images

      __lowerCAmelCase:     List[str]     			=   image[0, -3:, -3:, -1]

      assert image.shape == (1, 3_2, 3_2, 3)
      __lowerCAmelCase:     Union[str, Any]     			=   np.array([0.4200, 0.3588, 0.1939, 0.3847, 0.3382, 0.2647, 0.4155, 0.3582, 0.3385]      )
      assert np.abs(image_slice.flatten() - expected_slice      ).max() < 1E-2








from math import floor, sqrt







def _a				( SCREAMING_SNAKE_CASE	:    int	)					->					int:

 """simple docstring"""






 __lowerCAmelCase:     Optional[int]     			=   0.0
 __lowerCAmelCase:     Any     			=   1.0
 __lowerCAmelCase:     List[str]     			=   int(sqrt(SCREAMING_SNAKE_CASE	)	)
 __lowerCAmelCase:     Union[str, Any]     			=   root
 __lowerCAmelCase:     List[str]     			=   0
 while integer_part != 2 * root:
  __lowerCAmelCase:     List[str]     			=   denominator * integer_part - numerator
  __lowerCAmelCase:     Optional[int]     			=   (n - numerator**2) / denominator
  __lowerCAmelCase:     Union[str, Any]     			=   int((root + numerator) / denominator	)
  period += 1
 return period







def _a				( SCREAMING_SNAKE_CASE	:    int = 1_00_00	)					->					int:

 """simple docstring"""






 __lowerCAmelCase:     Optional[int]     			=   0
 for i in range(2					,      n + 1	):
  __lowerCAmelCase:     List[str]     			=   sqrt(SCREAMING_SNAKE_CASE	)
  if sr - floor(SCREAMING_SNAKE_CASE	) != 0 and continuous_fraction_period(SCREAMING_SNAKE_CASE	) % 2 == 1:
   count_odd_periods += 1
 return count_odd_periods


if __name__ == "__main__":
  print(f"{solution(int(input().strip()))}")





