code: 
  
  
  from math import floor, sqrt
  
  
  
  
  
  def lowerCamelCase    (    lowerCAmelCase       :			int	):
  
  
  
  
  
  	"""simple docstring"""
  
  
  
  
  
  
  
  	__magic_name__ :					Optional[int]  			=  0.0
  	__magic_name__ :					List[Any]  			=  1.0
  	__magic_name__ :					Union[str, Any]  			=  int(sqrt(lowerCAmelCase	)	)
  	__magic_name__ :					Dict  			=  root
  	__magic_name__ :					Optional[int]  			=  0
  	while integer_part != 2 * root:
  		__magic_name__ :					List[Any]  			=  denominator * integer_part - numerator
  		__magic_name__ :					str  			=  (n - numerator**2) / denominator
  		__magic_name__ :					Union[str, Any]  			=  int((root + numerator) / denominator	)
  		period += 1
  	return period
  
  
  
  
  
  def lowerCamelCase    (    lowerCAmelCase       :			int = 1_0000	):
  
  
  
  
  
  	"""simple docstring"""
  
  
  
  
  
  
  
  	__magic_name__ :					Optional[int]  			=  0
  	for i in range(2	,	n + 1	):
  		__magic_name__ :					str  			=  sqrt(lowerCAmelCase	)
  		if sr - floor(lowerCAmelCase	) != 0 and continuous_fraction_period(lowerCAmelCase	) % 2 == 1:
  			count_odd_periods += 1
  	return count_odd_periods
  
  
  if __name__ == "__main__":
  							print(F'{solution(int(input().strip()))}')
style_context: 
  
  
  '''simple docstring'''
  
  import random
  import unittest
  
  import numpy as np
  import torch
  
  from diffusers import DDIMScheduler, LDMSuperResolutionPipeline, UNetaDModel, VQModel
  from diffusers.utils import PIL_INTERPOLATION, floats_tensor, load_image, slow, torch_device
  from diffusers.utils.testing_utils import enable_full_determinism, require_torch
  
  
  enable_full_determinism()
  class _lowerCamelCase (		unittest.TestCase							):
  
  
  
  		'''simple docstring'''
  
  
  
  
  
  
  
  		@property
  		def      __lowerCAmelCase	(      self	:		Union[str, Any]    )						->				List[Any]:
  			__magic_name__ :					Union[str, Any]  			=  1
  			__magic_name__ :					str  			=  3
  			__magic_name__ :					Optional[Any]  			=  (32, 32)
  
  			__magic_name__ :					Dict  			=  floats_tensor((batch_size, num_channels) + sizes						,  rng=random.Random(0    )    ).to(_A    )
  			return image
  
  
  
  
  
  
  
  		@property
  		def      __lowerCAmelCase	(      self	:		Optional[Any]    )						->				List[str]:
  			torch.manual_seed(0    )
  			__magic_name__ :					Dict  			=  UNetaDModel(
  			    block_out_channels=(32, 64)						,  layers_per_block=2						,  sample_size=32						,  in_channels=6						,  out_channels=3						,  down_block_types=('DownBlock2D', 'AttnDownBlock2D')						,  up_block_types=('AttnUpBlock2D', 'UpBlock2D')						,  )
  			return model
  
  
  
  
  
  
  
  		@property
  		def      __lowerCAmelCase	(      self	:		Any    )						->				Optional[int]:
  			torch.manual_seed(0    )
  			__magic_name__ :					Union[str, Any]  			=  VQModel(
  			    block_out_channels=[32, 64]						,  in_channels=3						,  out_channels=3						,  down_block_types=['DownEncoderBlock2D', 'DownEncoderBlock2D']						,  up_block_types=['UpDecoderBlock2D', 'UpDecoderBlock2D']						,  latent_channels=3						,  )
  			return model
  
  
  
  
  
  
  
  		def      __lowerCAmelCase	(      self	:		Optional[int]    )						->				int:
  			__magic_name__ :					Dict  			=  'cpu'
  			__magic_name__ :					str  			=  self.dummy_uncond_unet
  			__magic_name__ :					Optional[int]  			=  DDIMScheduler()
  			__magic_name__ :					Optional[Any]  			=  self.dummy_vq_model
  
  			__magic_name__ :					Tuple  			=  LDMSuperResolutionPipeline(unet=_A						,  vqvae=_A						,  scheduler=_A    )
  			ldm.to(_A    )
  			ldm.set_progress_bar_config(disable=_A    )
  
  			__magic_name__ :					Optional[int]  			=  self.dummy_image.to(_A    )
  
  			__magic_name__ :					List[Any]  			=  torch.Generator(device=_A    ).manual_seed(0    )
  			__magic_name__ :					str  			=  ldm(image=_A						,  generator=_A						,  num_inference_steps=2						,  output_type='numpy'    ).images
  
  			__magic_name__ :					List[Any]  			=  image[0, -3:, -3:, -1]
  
  			assert image.shape == (1, 64, 64, 3)
  			__magic_name__ :					Optional[Any]  			=  np.array([0.8678, 0.8245, 0.6381, 0.6830, 0.4385, 0.5599, 0.4641, 0.6201, 0.5150]    )
  
  			assert np.abs(image_slice.flatten() - expected_slice    ).max() < 1E-2
  
  
  
  
  
  
  
  		@unittest.skipIf(torch_device != 'cuda'						,  'This test requires a GPU'    )
  		def      __lowerCAmelCase	(      self	:		List[Any]    )						->				List[Any]:
  			__magic_name__ :					Union[str, Any]  			=  self.dummy_uncond_unet
  			__magic_name__ :					Tuple  			=  DDIMScheduler()
  			__magic_name__ :					Union[str, Any]  			=  self.dummy_vq_model
  
  			# put models in fp16
  			__magic_name__ :					Optional[int]  			=  unet.half()
  			__magic_name__ :					int  			=  vqvae.half()
  
  			__magic_name__ :					Optional[Any]  			=  LDMSuperResolutionPipeline(unet=_A						,  vqvae=_A						,  scheduler=_A    )
  			ldm.to(_A    )
  			ldm.set_progress_bar_config(disable=_A    )
  
  			__magic_name__ :					str  			=  self.dummy_image.to(_A    )
  
  			__magic_name__ :					Union[str, Any]  			=  ldm(_A						,  num_inference_steps=2						,  output_type='numpy'    ).images
  
  			assert image.shape == (1, 64, 64, 3)
  
  
  
  
  
  
  
  @slow
  @require_torch
  class _lowerCamelCase (		unittest.TestCase							):
  
  
  
  		'''simple docstring'''
  
  
  
  
  
  
  
  		def      __lowerCAmelCase	(      self	:		str    )						->				Dict:
  			__magic_name__ :					Tuple  			=  load_image(
  			    'https://huggingface.co/datasets/hf-internal-testing/diffusers-images/resolve/main'
  			    '/vq_diffusion/teddy_bear_pool.png'    )
  			__magic_name__ :					Dict  			=  init_image.resize((64, 64)						,  resample=PIL_INTERPOLATION['lanczos']    )
  
  			__magic_name__ :					List[Any]  			=  LDMSuperResolutionPipeline.from_pretrained('duongna/ldm-super-resolution'						,  device_map='auto'    )
  			ldm.set_progress_bar_config(disable=_A    )
  
  			__magic_name__ :					int  			=  torch.manual_seed(0    )
  			__magic_name__ :					Optional[Any]  			=  ldm(image=_A						,  generator=_A						,  num_inference_steps=20						,  output_type='numpy'    ).images
  
  			__magic_name__ :					List[str]  			=  image[0, -3:, -3:, -1]
  
  			assert image.shape == (1, 256, 256, 3)
  			__magic_name__ :					int  			=  np.array([0.7644, 0.7679, 0.7642, 0.7633, 0.7666, 0.7560, 0.7425, 0.7257, 0.6907]    )
  
  			assert np.abs(image_slice.flatten() - expected_slice    ).max() < 1E-2