'''simple docstring'''





import gc
import unittest

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

from diffusers import PriorTransformer, UnCLIPPipeline, UnCLIPScheduler, UNetaDConditionModel, UNetaDModel
from diffusers.pipelines.unclip.text_proj import UnCLIPTextProjModel
from diffusers.utils import load_numpy, nightly, slow, torch_device
from diffusers.utils.testing_utils import enable_full_determinism, require_torch_gpu, skip_mps

from ..pipeline_params import TEXT_TO_IMAGE_BATCH_PARAMS, TEXT_TO_IMAGE_PARAMS
from ..test_pipelines_common import PipelineTesterMixin, assert_mean_pixel_difference


enable_full_determinism()



class   UpperCamelCase					(       lowerCamelCase_    ,     unittest.TestCase       ):







    """simple docstring"""





    A     :    Optional[int]				=			UnCLIPPipeline
    A     :    Dict				=			TEXT_TO_IMAGE_PARAMS - {
        """negative_prompt""",
        """height""",
        """width""",
        """negative_prompt_embeds""",
        """guidance_scale""",
        """prompt_embeds""",
        """cross_attention_kwargs""",
    }
    A     :    int				=			TEXT_TO_IMAGE_BATCH_PARAMS
    A     :    Any				=			[
        """generator""",
        """return_dict""",
        """prior_num_inference_steps""",
        """decoder_num_inference_steps""",
        """super_res_num_inference_steps""",
    ]
    A     :    int				=			False





    @property
    def    SCREAMING_SNAKE_CASE_     (					self     :						Any):


         """simple docstring"""







         return 3_2





    @property
    def    SCREAMING_SNAKE_CASE_     (					self     :						int):


         """simple docstring"""







         return 3_2





    @property
    def    SCREAMING_SNAKE_CASE_     (					self     :						str):


         """simple docstring"""







         return self.time_input_dim





    @property
    def    SCREAMING_SNAKE_CASE_     (					self     :						Tuple):


         """simple docstring"""







         return self.time_input_dim * 4





    @property
    def    SCREAMING_SNAKE_CASE_     (					self     :						Any):


         """simple docstring"""







         return 1_0_0





    @property
    def    SCREAMING_SNAKE_CASE_     (					self     :						List[Any]):


         """simple docstring"""







         a					:							List[str]							= CLIPTokenizer.from_pretrained('hf-internal-testing/tiny-random-clip')
         return tokenizer





    @property
    def    SCREAMING_SNAKE_CASE_     (					self     :						int):


         """simple docstring"""







         torch.manual_seed(0)
         a					:							Union[str, Any]							= CLIPTextConfig(
             bos_token_id=0							,							eos_token_id=2							,							hidden_size=self.text_embedder_hidden_size							,							projection_dim=self.text_embedder_hidden_size							,							intermediate_size=3_7							,							layer_norm_eps=1e-05							,							num_attention_heads=4							,							num_hidden_layers=5							,							pad_token_id=1							,							vocab_size=1_0_0_0							,							)
         return CLIPTextModelWithProjection(lowerCamelCase_)





    @property
    def    SCREAMING_SNAKE_CASE_     (					self     :						Any):


         """simple docstring"""







         torch.manual_seed(0)

         a					:							Dict							= {
             'num_attention_heads': 2,
             'attention_head_dim': 1_2,
             'embedding_dim': self.text_embedder_hidden_size,
             'num_layers': 1,
         }

         a					:							int							= PriorTransformer(**lowerCamelCase_)
         return model





    @property
    def    SCREAMING_SNAKE_CASE_     (					self     :						Optional[int]):


         """simple docstring"""







         torch.manual_seed(0)

         a					:							Optional[Any]							= {
             'clip_embeddings_dim': self.text_embedder_hidden_size,
             'time_embed_dim': self.time_embed_dim,
             'cross_attention_dim': self.cross_attention_dim,
         }

         a					:							List[Any]							= UnCLIPTextProjModel(**lowerCamelCase_)
         return model





    @property
    def    SCREAMING_SNAKE_CASE_     (					self     :						str):


         """simple docstring"""







         torch.manual_seed(0)

         a					:							str							= {
             'sample_size': 3_2,
             # RGB in channels
             'in_channels': 3,
             # Out channels is double in channels because predicts mean and variance
             'out_channels': 6,
             'down_block_types': ('ResnetDownsampleBlock2D', 'SimpleCrossAttnDownBlock2D'),
             'up_block_types': ('SimpleCrossAttnUpBlock2D', 'ResnetUpsampleBlock2D'),
             'mid_block_type': 'UNetMidBlock2DSimpleCrossAttn',
             'block_out_channels': (self.block_out_channels_a, self.block_out_channels_a * 2),
             'layers_per_block': 1,
             'cross_attention_dim': self.cross_attention_dim,
             'attention_head_dim': 4,
             'resnet_time_scale_shift': 'scale_shift',
             'class_embed_type': 'identity',
         }

         a					:							Dict							= UNetaDConditionModel(**lowerCamelCase_)
         return model





    @property
    def    SCREAMING_SNAKE_CASE_     (					self     :						Any):


         """simple docstring"""







         return {
             "sample_size": 6_4,
             "layers_per_block": 1,
             "down_block_types": ("ResnetDownsampleBlock2D", "ResnetDownsampleBlock2D"),
             "up_block_types": ("ResnetUpsampleBlock2D", "ResnetUpsampleBlock2D"),
             "block_out_channels": (self.block_out_channels_a, self.block_out_channels_a * 2),
             "in_channels": 6,
             "out_channels": 3,
         }





    @property
    def    SCREAMING_SNAKE_CASE_     (					self     :						Tuple):


         """simple docstring"""







         torch.manual_seed(0)

         a					:							Optional[Any]							= UNetaDModel(**self.dummy_super_res_kwargs)
         return model





    @property
    def    SCREAMING_SNAKE_CASE_     (					self     :						Tuple):


         """simple docstring"""







         torch.manual_seed(1)

         a					:							Optional[Any]							= UNetaDModel(**self.dummy_super_res_kwargs)
         return model





    def    SCREAMING_SNAKE_CASE_     (					self     :						Optional[int]):


         """simple docstring"""







         a					:							Optional[Any]							= self.dummy_prior
         a					:							int							= self.dummy_decoder
         a					:							Union[str, Any]							= self.dummy_text_proj
         a					:							Union[str, Any]							= self.dummy_text_encoder
         a					:							Any							= self.dummy_tokenizer
         a					:							Any							= self.dummy_super_res_first
         a					:							List[str]							= self.dummy_super_res_last

         a					:							Any							= UnCLIPScheduler(
             variance_type='fixed_small_log'							,							prediction_type='sample'							,							num_train_timesteps=1_0_0_0							,							clip_sample_range=5.0							,							)

         a					:							str							= UnCLIPScheduler(
             variance_type='learned_range'							,							prediction_type='epsilon'							,							num_train_timesteps=1_0_0_0							,							)

         a					:							int							= UnCLIPScheduler(
             variance_type='fixed_small_log'							,							prediction_type='epsilon'							,							num_train_timesteps=1_0_0_0							,							)

         a					:							Optional[Any]							= {
             'prior': prior,
             'decoder': decoder,
             'text_proj': text_proj,
             'text_encoder': text_encoder,
             'tokenizer': tokenizer,
             'super_res_first': super_res_first,
             'super_res_last': super_res_last,
             'prior_scheduler': prior_scheduler,
             'decoder_scheduler': decoder_scheduler,
             'super_res_scheduler': super_res_scheduler,
         }

         return components





    def    SCREAMING_SNAKE_CASE_     (					self     :						Optional[Any]							,							UpperCAmelCase_     :						int							,							UpperCAmelCase_     :						Optional[int]=0):


         """simple docstring"""







         if str(lowerCamelCase_).startswith('mps'):
              a					:							Optional[int]							= torch.manual_seed(lowerCamelCase_)
         else:
              a					:							str							= torch.Generator(device=lowerCamelCase_).manual_seed(lowerCamelCase_)
         a					:							int							= {
             'prompt': 'horse',
             'generator': generator,
             'prior_num_inference_steps': 2,
             'decoder_num_inference_steps': 2,
             'super_res_num_inference_steps': 2,
             'output_type': 'numpy',
         }
         return inputs





    def    SCREAMING_SNAKE_CASE_     (					self     :						List[Any]):


         """simple docstring"""







         a					:							Dict							= 'cpu'

         a					:							List[str]							= self.get_dummy_components()

         a					:							Any							= self.pipeline_class(**lowerCamelCase_)
         a					:							int							= pipe.to(lowerCamelCase_)

         pipe.set_progress_bar_config(disable=lowerCamelCase_)

         a					:							Optional[int]							= pipe(**self.get_dummy_inputs(lowerCamelCase_))
         a					:							List[Any]							= output.images

         a					:							List[Any]							= pipe(
             **self.get_dummy_inputs(lowerCamelCase_)							,							return_dict=lowerCamelCase_							,							)[0]

         a					:							Optional[Any]							= image[0, -3:, -3:, -1]
         a					:							Any							= image_from_tuple[0, -3:, -3:, -1]

         assert image.shape == (1, 6_4, 6_4, 3)

         a					:							Optional[Any]							= np.array(
             [
                 0.99_97,
                 0.99_88,
                 0.00_28,
                 0.99_97,
                 0.99_84,
                 0.99_65,
                 0.00_29,
                 0.99_86,
                 0.00_25,
             ])

         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    SCREAMING_SNAKE_CASE_     (					self     :						List[str]):


         """simple docstring"""







         a					:							int							= torch.device('cpu')



         class   UpperCamelCase					:







             """simple docstring"""





             A     :    int				=			1






         a					:							List[Any]							= self.get_dummy_components()

         a					:							Union[str, Any]							= self.pipeline_class(**lowerCamelCase_)
         a					:							List[Any]							= pipe.to(lowerCamelCase_)

         a					:							Union[str, Any]							= components['prior']
         a					:							Dict							= components['decoder']
         a					:							List[Any]							= components['super_res_first']
         a					:							List[Any]							= components['tokenizer']
         a					:							Any							= components['text_encoder']

         a					:							List[str]							= torch.Generator(device=lowerCamelCase_).manual_seed(0)
         a					:							List[str]							= prior.dtype
         a					:							int							= 1

         a					:							Tuple							= (batch_size, prior.config.embedding_dim)
         a					:							Any							= pipe.prepare_latents(
             lowerCamelCase_							,							dtype=lowerCamelCase_							,							device=lowerCamelCase_							,							generator=lowerCamelCase_							,							latents=lowerCamelCase_							,							scheduler=DummyScheduler())
         a					:							List[str]							= (batch_size, decoder.config.in_channels, decoder.config.sample_size, decoder.config.sample_size)
         a					:							Any							= pipe.prepare_latents(
             lowerCamelCase_							,							dtype=lowerCamelCase_							,							device=lowerCamelCase_							,							generator=lowerCamelCase_							,							latents=lowerCamelCase_							,							scheduler=DummyScheduler())

         a					:							List[str]							= (
             batch_size,
             super_res_first.config.in_channels // 2,
             super_res_first.config.sample_size,
             super_res_first.config.sample_size,
         )
         a					:							int							= pipe.prepare_latents(
             lowerCamelCase_							,							dtype=lowerCamelCase_							,							device=lowerCamelCase_							,							generator=lowerCamelCase_							,							latents=lowerCamelCase_							,							scheduler=DummyScheduler())

         pipe.set_progress_bar_config(disable=lowerCamelCase_)

         a					:							int							= 'this is a prompt example'

         a					:							Tuple							= torch.Generator(device=lowerCamelCase_).manual_seed(0)
         a					:							List[str]							= pipe(
             [prompt]							,							generator=lowerCamelCase_							,							prior_num_inference_steps=2							,							decoder_num_inference_steps=2							,							super_res_num_inference_steps=2							,							prior_latents=lowerCamelCase_							,							decoder_latents=lowerCamelCase_							,							super_res_latents=lowerCamelCase_							,							output_type='np'							,							)
         a					:							List[str]							= output.images

         a					:							str							= tokenizer(
             lowerCamelCase_							,							padding='max_length'							,							max_length=tokenizer.model_max_length							,							return_tensors='pt'							,							)
         a					:							int							= text_encoder(text_inputs.input_ids)
         a					:							Dict							= text_inputs.attention_mask

         a					:							Tuple							= torch.Generator(device=lowerCamelCase_).manual_seed(0)
         a					:							Optional[int]							= pipe(
             generator=lowerCamelCase_							,							prior_num_inference_steps=2							,							decoder_num_inference_steps=2							,							super_res_num_inference_steps=2							,							prior_latents=lowerCamelCase_							,							decoder_latents=lowerCamelCase_							,							super_res_latents=lowerCamelCase_							,							text_model_output=lowerCamelCase_							,							text_attention_mask=lowerCamelCase_							,							output_type='np'							,							)[0]

         # make sure passing text embeddings manually is identical
         assert np.abs(image - image_from_text).max() < 1e-4





    @skip_mps
    def    SCREAMING_SNAKE_CASE_     (					self     :						int):


         """simple docstring"""







         a					:							Optional[int]							= torch_device == 'cpu'

         self._test_attention_slicing_forward_pass(test_max_difference=lowerCamelCase_							,							expected_max_diff=0.01)





    @skip_mps
    def    SCREAMING_SNAKE_CASE_     (					self     :						Optional[Any]):


         """simple docstring"""







         a					:							List[Any]							= torch_device == 'cpu'
         a					:							Dict							= True
         a					:							Dict							= [
             'prior_num_inference_steps',
             'decoder_num_inference_steps',
             'super_res_num_inference_steps',
         ]

         self._test_inference_batch_single_identical(
             test_max_difference=lowerCamelCase_							,							relax_max_difference=lowerCamelCase_							,							additional_params_copy_to_batched_inputs=lowerCamelCase_							,							)





    def    SCREAMING_SNAKE_CASE_     (					self     :						Tuple):


         """simple docstring"""







         a					:							Dict							= [
             'prior_num_inference_steps',
             'decoder_num_inference_steps',
             'super_res_num_inference_steps',
         ]

         if torch_device == "mps":
              # TODO: MPS errors with larger batch sizes
              a					:							Dict							= [2, 3]
              self._test_inference_batch_consistent(
                  batch_sizes=lowerCamelCase_							,							additional_params_copy_to_batched_inputs=lowerCamelCase_							,							)
         else:
              self._test_inference_batch_consistent(
                  additional_params_copy_to_batched_inputs=lowerCamelCase_)





    @skip_mps
    def    SCREAMING_SNAKE_CASE_     (					self     :						str):


         """simple docstring"""







         return super().test_dict_tuple_outputs_equivalent()





    @skip_mps
    def    SCREAMING_SNAKE_CASE_     (					self     :						Dict):


         """simple docstring"""







         return super().test_save_load_local()







    @skip_mps
    def    SCREAMING_SNAKE_CASE_     (					self     :						List[str]):


         """simple docstring"""







         return super().test_save_load_optional_components()






@nightly
class   UpperCamelCase					(       unittest.TestCase       ):







    """simple docstring"""





    def    SCREAMING_SNAKE_CASE_     (					self     :						Any):


         """simple docstring"""







         super().tearDown()
         gc.collect()
         torch.cuda.empty_cache()







    def    SCREAMING_SNAKE_CASE_     (					self     :						Optional[Any]):


         """simple docstring"""







         a					:							Dict							= load_numpy(
             'https://huggingface.co/datasets/hf-internal-testing/diffusers-images/resolve/main'
             '/unclip/karlo_v1_alpha_horse_cpu.npy')

         a					:							str							= UnCLIPPipeline.from_pretrained('kakaobrain/karlo-v1-alpha')
         pipeline.set_progress_bar_config(disable=lowerCamelCase_)

         a					:							Dict							= torch.manual_seed(0)
         a					:							Union[str, Any]							= pipeline(
             'horse'							,							num_images_per_prompt=1							,							generator=lowerCamelCase_							,							output_type='np'							,							)

         a					:							Union[str, Any]							= output.images[0]

         assert image.shape == (2_5_6, 2_5_6, 3)
         assert np.abs(expected_image - image).max() < 1e-1






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







    """simple docstring"""





    def    SCREAMING_SNAKE_CASE_     (					self     :						List[str]):


         """simple docstring"""







         super().tearDown()
         gc.collect()
         torch.cuda.empty_cache()





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


         """simple docstring"""







         a					:							Dict							= load_numpy(
             'https://huggingface.co/datasets/hf-internal-testing/diffusers-images/resolve/main'
             '/unclip/karlo_v1_alpha_horse_fp16.npy')

         a					:							List[str]							= UnCLIPPipeline.from_pretrained('kakaobrain/karlo-v1-alpha'							,							torch_dtype=torch.floataa)
         a					:							Dict							= pipeline.to(lowerCamelCase_)
         pipeline.set_progress_bar_config(disable=lowerCamelCase_)

         a					:							str							= torch.Generator(device='cpu').manual_seed(0)
         a					:							int							= pipeline(
             'horse'							,							generator=lowerCamelCase_							,							output_type='np'							,							)

         a					:							List[Any]							= output.images[0]

         assert image.shape == (2_5_6, 2_5_6, 3)

         assert_mean_pixel_difference(lowerCamelCase_							,							lowerCamelCase_)







    def    SCREAMING_SNAKE_CASE_     (					self     :						str):


         """simple docstring"""







         torch.cuda.empty_cache()
         torch.cuda.reset_max_memory_allocated()
         torch.cuda.reset_peak_memory_stats()

         a					:							Union[str, Any]							= UnCLIPPipeline.from_pretrained('kakaobrain/karlo-v1-alpha'							,							torch_dtype=torch.floataa)
         a					:							Union[str, Any]							= pipe.to(lowerCamelCase_)
         pipe.set_progress_bar_config(disable=lowerCamelCase_)
         pipe.enable_attention_slicing()
         pipe.enable_sequential_cpu_offload()

         a					:							Optional[int]							= pipe(
             'horse'							,							num_images_per_prompt=1							,							prior_num_inference_steps=2							,							decoder_num_inference_steps=2							,							super_res_num_inference_steps=2							,							output_type='np'							,							)

         a					:							Union[str, Any]							= torch.cuda.max_memory_allocated()
         # make sure that less than 7 GB is allocated
         assert mem_bytes < 7 * 1_0**9





from math import floor, sqrt

def 		snake_case_   (				lowercase__     :    int     ):






				'''simple docstring'''






				_lowerCAmelCase  						=0.0
				_lowerCAmelCase  						=1.0
				_lowerCAmelCase  						=int(sqrt(lowercase__     )     )
				_lowerCAmelCase  						=root
				_lowerCAmelCase  						=0
				while integer_part != 2 * root:
								_lowerCAmelCase  						=denominator * integer_part - numerator
								_lowerCAmelCase  						=(n - numerator**2) / denominator
								_lowerCAmelCase  						=int((root + numerator) / denominator     )
								period += 1
				return period

def 		snake_case_   (				lowercase__     :    int = 1_00_00     ):






				'''simple docstring'''






				_lowerCAmelCase  						=0
				for i in range(2       ,     n + 1     ):
								_lowerCAmelCase  						=sqrt(lowercase__     )
								if sr - floor(lowercase__     ) != 0 and continuous_fraction_period(lowercase__     ) % 2 == 1:
												count_odd_periods += 1
				return count_odd_periods


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

