
'''simple docstring'''





from math import floor, sqrt
def 	snake_case_							(				_a  :				str      ):
      snake_case_    							=				0.0
      snake_case_    							=				1.0
      snake_case_    							=				int(sqrt(_SCREAMING_SNAKE_CASE      )      )
      snake_case_    							=				root
      snake_case_    							=				0
      while integer_part != 2 * root:
            snake_case_    							=				denominator * integer_part - numerator
            snake_case_    							=				(n - numerator**2) / denominator
            snake_case_    							=				int((root + numerator) / denominator      )
            period += 1
      return period
def 	snake_case_							(				_a  :				Any = 10_000      ):
      snake_case_    							=				0
      for i in range(2			,       n + 1      ):
            snake_case_    							=				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()))}""")



import gc
import unittest

import numpy as np
import torch
from transformers import CLIPTextConfig, CLIPTextModel, CLIPTokenizer

from diffusers import (
    AutoencoderKL,
    DDIMParallelScheduler,
    DDPMParallelScheduler,
    StableDiffusionParadigmsPipeline,
    UNetaDConditionModel,
)
from diffusers.utils import slow, torch_device
from diffusers.utils.testing_utils import (
    enable_full_determinism,
    require_torch_gpu,
)

from ..pipeline_params import TEXT_TO_IMAGE_BATCH_PARAMS, TEXT_TO_IMAGE_IMAGE_PARAMS, TEXT_TO_IMAGE_PARAMS
from ..test_pipelines_common import PipelineLatentTesterMixin, PipelineTesterMixin


enable_full_determinism()
class    _UpperCamelCase(   SCREAMING_SNAKE_CASE		,						SCREAMING_SNAKE_CASE		,						unittest.TestCase				):
						__A:						Optional[Any]				   =      StableDiffusionParadigmsPipeline
						__A:						Optional[int]				   =      TEXT_TO_IMAGE_PARAMS
						__A:						Dict				   =      TEXT_TO_IMAGE_BATCH_PARAMS
						__A:						Any				   =      TEXT_TO_IMAGE_IMAGE_PARAMS
						__A:						List[Any]				   =      TEXT_TO_IMAGE_IMAGE_PARAMS

						def 						a__ (					self		:			Optional[Any]			):
													torch.manual_seed(0			)
													_UpperCAmelCase  :			str	       =		UNetaDConditionModel(
													    block_out_channels=(32, 64)	,						layers_per_block=2	,						sample_size=32	,						in_channels=4	,						out_channels=4	,						down_block_types=("DownBlock2D", "CrossAttnDownBlock2D")	,						up_block_types=("CrossAttnUpBlock2D", "UpBlock2D")	,						cross_attention_dim=32	,						attention_head_dim=(2, 4)	,						use_linear_projection=_lowerCamelCase	,						)
													_UpperCAmelCase  :			Dict	       =		DDIMParallelScheduler(
													    beta_start=0.0_00_85	,						beta_end=0.0_12	,						beta_schedule="scaled_linear"	,						clip_sample=_lowerCamelCase	,						set_alpha_to_one=_lowerCamelCase	,						)
													torch.manual_seed(0			)
													_UpperCAmelCase  :			Tuple	       =		AutoencoderKL(
													    block_out_channels=[32, 64]	,						in_channels=3	,						out_channels=3	,						down_block_types=["DownEncoderBlock2D", "DownEncoderBlock2D"]	,						up_block_types=["UpDecoderBlock2D", "UpDecoderBlock2D"]	,						latent_channels=4	,						sample_size=1_28	,						)
													torch.manual_seed(0			)
													_UpperCAmelCase  :			Optional[Any]	       =		CLIPTextConfig(
													    bos_token_id=0	,						eos_token_id=2	,						hidden_size=32	,						intermediate_size=37	,						layer_norm_eps=1E-05	,						num_attention_heads=4	,						num_hidden_layers=5	,						pad_token_id=1	,						vocab_size=10_00	,						hidden_act="gelu"	,						projection_dim=5_12	,						)
													_UpperCAmelCase  :			Tuple	       =		CLIPTextModel(_lowerCamelCase			)
													_UpperCAmelCase  :			Dict	       =		CLIPTokenizer.from_pretrained("hf-internal-testing/tiny-random-clip"			)

													_UpperCAmelCase  :			Optional[int]	       =		{
													    "unet": unet,
													    "scheduler": scheduler,
													    "vae": vae,
													    "text_encoder": text_encoder,
													    "tokenizer": tokenizer,
													    "safety_checker": None,
													    "feature_extractor": None,
													}
													return components

						def 						a__ (					self		:			Dict	,						_lowerCamelCase		:			str	,						_lowerCamelCase		:			int=0			):
													if str(_lowerCamelCase			).startswith("mps"			):
																				_UpperCAmelCase  :			Tuple	       =		torch.manual_seed(_lowerCamelCase			)
													else:
																				_UpperCAmelCase  :			Optional[int]	       =		torch.Generator(device=_lowerCamelCase			).manual_seed(_lowerCamelCase			)
													_UpperCAmelCase  :			str	       =		{
													    "prompt": "a photograph of an astronaut riding a horse",
													    "generator": generator,
													    "num_inference_steps": 10,
													    "guidance_scale": 6.0,
													    "output_type": "numpy",
													    "parallel": 3,
													    "debug": True,
													}
													return inputs

						def 						a__ (					self		:			Optional[Any]			):
													_UpperCAmelCase  :			Union[str, Any]	       =		"cpu"  # ensure determinism for the device-dependent torch.Generator
													_UpperCAmelCase  :			List[str]	       =		self.get_dummy_components()
													_UpperCAmelCase  :			List[Any]	       =		StableDiffusionParadigmsPipeline(**_lowerCamelCase			)
													_UpperCAmelCase  :			List[str]	       =		sd_pipe.to(_lowerCamelCase			)
													sd_pipe.set_progress_bar_config(disable=_lowerCamelCase			)

													_UpperCAmelCase  :			List[Any]	       =		self.get_dummy_inputs(_lowerCamelCase			)
													_UpperCAmelCase  :			int	       =		sd_pipe(**_lowerCamelCase			).images
													_UpperCAmelCase  :			Tuple	       =		image[0, -3:, -3:, -1]
													assert image.shape == (1, 64, 64, 3)

													_UpperCAmelCase  :			str	       =		np.array([0.47_73, 0.54_17, 0.47_23, 0.49_25, 0.56_31, 0.47_52, 0.52_40, 0.49_35, 0.50_23]			)

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

						def 						a__ (					self		:			Optional[Any]			):
													_UpperCAmelCase  :			Dict	       =		"cpu"  # ensure determinism for the device-dependent torch.Generator
													_UpperCAmelCase  :			Dict	       =		self.get_dummy_components()
													torch.manual_seed(0			)
													_UpperCAmelCase  :			str	       =		DDPMParallelScheduler()
													torch.manual_seed(0			)
													_UpperCAmelCase  :			int	       =		StableDiffusionParadigmsPipeline(**_lowerCamelCase			)
													_UpperCAmelCase  :			Any	       =		sd_pipe.to(_lowerCamelCase			)
													sd_pipe.set_progress_bar_config(disable=_lowerCamelCase			)

													_UpperCAmelCase  :			int	       =		self.get_dummy_inputs(_lowerCamelCase			)
													_UpperCAmelCase  :			Dict	       =		sd_pipe(**_lowerCamelCase			).images
													_UpperCAmelCase  :			str	       =		image[0, -3:, -3:, -1]
													assert image.shape == (1, 64, 64, 3)

													_UpperCAmelCase  :			Optional[Any]	       =		np.array([0.35_73, 0.44_20, 0.49_60, 0.47_99, 0.37_96, 0.38_79, 0.48_19, 0.43_65, 0.44_68]			)

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

						def 						a__ (					self		:			List[str]			):
													super().test_inference_batch_consistent(batch_sizes=[1, 2]			)

						def 						a__ (					self		:			List[str]			):
													super().test_inference_batch_single_identical(batch_size=2	,						expected_max_diff=3E-3			)






						def 						a__ (					self		:			Optional[Any]			):
													_UpperCAmelCase  :			int	       =		"cpu"  # ensure determinism for the device-dependent torch.Generator
													_UpperCAmelCase  :			Tuple	       =		self.get_dummy_components()
													_UpperCAmelCase  :			Dict	       =		StableDiffusionParadigmsPipeline(**_lowerCamelCase			)
													_UpperCAmelCase  :			str	       =		sd_pipe.to(_lowerCamelCase			)
													sd_pipe.set_progress_bar_config(disable=_lowerCamelCase			)

													_UpperCAmelCase  :			Optional[int]	       =		self.get_dummy_inputs(_lowerCamelCase			)
													_UpperCAmelCase  :			Optional[Any]	       =		"french fries"
													_UpperCAmelCase  :			Tuple	       =		sd_pipe(**_lowerCamelCase	,						negative_prompt=_lowerCamelCase			)
													_UpperCAmelCase  :			Optional[Any]	       =		output.images
													_UpperCAmelCase  :			Union[str, Any]	       =		image[0, -3:, -3:, -1]

													assert image.shape == (1, 64, 64, 3)

													_UpperCAmelCase  :			Optional[Any]	       =		np.array([0.47_71, 0.54_20, 0.46_83, 0.49_18, 0.56_36, 0.47_25, 0.52_30, 0.49_23, 0.50_15]			)

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







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

						def 						a__ (					self		:			int			):
													super().tearDown()
													gc.collect()
													torch.cuda.empty_cache()

						def 						a__ (					self		:			Tuple	,						_lowerCamelCase		:			Optional[int]=0			):
													_UpperCAmelCase  :			Union[str, Any]	       =		torch.Generator(device=_lowerCamelCase			).manual_seed(_lowerCamelCase			)
													_UpperCAmelCase  :			List[str]	       =		{
													    "prompt": "a photograph of an astronaut riding a horse",
													    "generator": generator,
													    "num_inference_steps": 10,
													    "guidance_scale": 7.5,
													    "output_type": "numpy",
													    "parallel": 3,
													    "debug": True,
													}
													return inputs






						def 						a__ (					self		:			Any			):
													_UpperCAmelCase  :			str	       =		"stabilityai/stable-diffusion-2-base"
													_UpperCAmelCase  :			List[str]	       =		DDIMParallelScheduler.from_pretrained(_lowerCamelCase	,						subfolder="scheduler"			)
													_UpperCAmelCase  :			Union[str, Any]	       =		StableDiffusionParadigmsPipeline.from_pretrained(_lowerCamelCase	,						scheduler=_lowerCamelCase	,						safety_checker=_lowerCamelCase			)
													pipe.to(_lowerCamelCase			)
													pipe.set_progress_bar_config(disable=_lowerCamelCase			)
													pipe.enable_attention_slicing()

													_UpperCAmelCase  :			Optional[Any]	       =		self.get_inputs()
													_UpperCAmelCase  :			List[str]	       =		pipe(**_lowerCamelCase			).images
													_UpperCAmelCase  :			Tuple	       =		image[0, -3:, -3:, -1].flatten()

													assert image.shape == (1, 5_12, 5_12, 3)

													_UpperCAmelCase  :			Union[str, Any]	       =		np.array([0.96_22, 0.96_02, 0.97_48, 0.95_91, 0.96_30, 0.96_91, 0.96_61, 0.96_31, 0.97_41]			)

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




