"""simple docstring"""





from collections import defaultdict
from math import gcd





def 				a_     (      _lowerCAmelCase  : int = 150_0000     ):





       '''simple docstring'''

       lowercase__			:		defaultdict       =	defaultdict(_lowerCAmelCase     )
       lowercase__			:		int       =	2
       while 2 * euclid_m * (euclid_m + 1) <= limit:
              for euclid_n in range((euclid_m % 2) + 1   , _lowerCAmelCase   , 2     ):
                     if gcd(_lowerCAmelCase   , _lowerCAmelCase     ) > 1:
                            continue
                     lowercase__			:		Tuple       =	2 * euclid_m * (euclid_m + euclid_n)
                     for perimeter in range(_lowerCAmelCase   , limit + 1   , _lowerCAmelCase     ):
                            frequencies[perimeter] += 1
              euclid_m += 1
       return sum(1 for frequency in frequencies.values() if frequency == 1     )


if __name__ == "__main__":
       print(f'''{solution() = }''')








"""simple docstring"""





import tempfile

import numpy as np
import torch
from transformers import AutoTokenizer, TaEncoderModel

from diffusers import DDPMScheduler, UNetaDConditionModel
from diffusers.models.attention_processor import AttnAddedKVProcessor
from diffusers.pipelines.deepfloyd_if import IFWatermarker
from diffusers.utils.testing_utils import torch_device

from ..test_pipelines_common import to_np

class 		lowercase					:





      def     _snake_case			(       self )		->     List[Any]:
            torch.manual_seed(0 )
            lowerCAmelCase  						=       TaEncoderModel.from_pretrained("""hf-internal-testing/tiny-random-t5""" )

            torch.manual_seed(0 )
            lowerCAmelCase  						=       AutoTokenizer.from_pretrained("""hf-internal-testing/tiny-random-t5""" )

            torch.manual_seed(0 )
            lowerCAmelCase  						=       UNetaDConditionModel(
                sample_size=32      ,						layers_per_block=1      ,						block_out_channels=[32, 64]      ,						down_block_types=[
                    """ResnetDownsampleBlock2D""",
                    """SimpleCrossAttnDownBlock2D""",
                ]      ,						mid_block_type="""UNetMidBlock2DSimpleCrossAttn"""      ,						up_block_types=["""SimpleCrossAttnUpBlock2D""", """ResnetUpsampleBlock2D"""]      ,						in_channels=3      ,						out_channels=6      ,						cross_attention_dim=32      ,						encoder_hid_dim=32      ,						attention_head_dim=8      ,						addition_embed_type="""text"""      ,						addition_embed_type_num_heads=2      ,						cross_attention_norm="""group_norm"""      ,						resnet_time_scale_shift="""scale_shift"""      ,						act_fn="""gelu"""      ,						)
            unet.set_attn_processor(AttnAddedKVProcessor() )  # For reproducibility tests

            torch.manual_seed(0 )
            lowerCAmelCase  						=       DDPMScheduler(
                num_train_timesteps=1_000      ,						beta_schedule="""squaredcos_cap_v2"""      ,						beta_start=0.0_001      ,						beta_end=0.02      ,						thresholding=lowercase      ,						dynamic_thresholding_ratio=0.95      ,						sample_max_value=1.0      ,						prediction_type="""epsilon"""      ,						variance_type="""learned_range"""      ,						)

            torch.manual_seed(0 )
            lowerCAmelCase  						=       IFWatermarker()

            return {
                "text_encoder": text_encoder,
                "tokenizer": tokenizer,
                "unet": unet,
                "scheduler": scheduler,
                "watermarker": watermarker,
                "safety_checker": None,
                "feature_extractor": None,
            }





      def     _snake_case			(       self )		->     int:
            torch.manual_seed(0 )
            lowerCAmelCase  						=       TaEncoderModel.from_pretrained("""hf-internal-testing/tiny-random-t5""" )

            torch.manual_seed(0 )
            lowerCAmelCase  						=       AutoTokenizer.from_pretrained("""hf-internal-testing/tiny-random-t5""" )

            torch.manual_seed(0 )
            lowerCAmelCase  						=       UNetaDConditionModel(
                sample_size=32      ,						layers_per_block=[1, 2]      ,						block_out_channels=[32, 64]      ,						down_block_types=[
                    """ResnetDownsampleBlock2D""",
                    """SimpleCrossAttnDownBlock2D""",
                ]      ,						mid_block_type="""UNetMidBlock2DSimpleCrossAttn"""      ,						up_block_types=["""SimpleCrossAttnUpBlock2D""", """ResnetUpsampleBlock2D"""]      ,						in_channels=6      ,						out_channels=6      ,						cross_attention_dim=32      ,						encoder_hid_dim=32      ,						attention_head_dim=8      ,						addition_embed_type="""text"""      ,						addition_embed_type_num_heads=2      ,						cross_attention_norm="""group_norm"""      ,						resnet_time_scale_shift="""scale_shift"""      ,						act_fn="""gelu"""      ,						class_embed_type="""timestep"""      ,						mid_block_scale_factor=1.414      ,						time_embedding_act_fn="""gelu"""      ,						time_embedding_dim=32      ,						)
            unet.set_attn_processor(AttnAddedKVProcessor() )  # For reproducibility tests

            torch.manual_seed(0 )
            lowerCAmelCase  						=       DDPMScheduler(
                num_train_timesteps=1_000      ,						beta_schedule="""squaredcos_cap_v2"""      ,						beta_start=0.0_001      ,						beta_end=0.02      ,						thresholding=lowercase      ,						dynamic_thresholding_ratio=0.95      ,						sample_max_value=1.0      ,						prediction_type="""epsilon"""      ,						variance_type="""learned_range"""      ,						)

            torch.manual_seed(0 )
            lowerCAmelCase  						=       DDPMScheduler(
                num_train_timesteps=1_000      ,						beta_schedule="""squaredcos_cap_v2"""      ,						beta_start=0.0_001      ,						beta_end=0.02      ,						)

            torch.manual_seed(0 )
            lowerCAmelCase  						=       IFWatermarker()

            return {
                "text_encoder": text_encoder,
                "tokenizer": tokenizer,
                "unet": unet,
                "scheduler": scheduler,
                "image_noising_scheduler": image_noising_scheduler,
                "watermarker": watermarker,
                "safety_checker": None,
                "feature_extractor": None,
            }





      def     _snake_case			(       self )		->     Union[str, Any]:
            lowerCAmelCase  						=       self.get_dummy_components()
            lowerCAmelCase  						=       self.pipeline_class(**lowercase )
            pipe.to(lowercase )
            pipe.set_progress_bar_config(disable=lowercase )

            lowerCAmelCase  						=       self.get_dummy_inputs(lowercase )

            lowerCAmelCase  						=       inputs["""prompt"""]
            lowerCAmelCase  						=       inputs["""generator"""]
            lowerCAmelCase  						=       inputs["""num_inference_steps"""]
            lowerCAmelCase  						=       inputs["""output_type"""]

            if "image" in inputs:
                  lowerCAmelCase  						=       inputs["""image"""]
            else:
                  lowerCAmelCase  						=       None

            if "mask_image" in inputs:
                  lowerCAmelCase  						=       inputs["""mask_image"""]
            else:
                  lowerCAmelCase  						=       None

            if "original_image" in inputs:
                  lowerCAmelCase  						=       inputs["""original_image"""]
            else:
                  lowerCAmelCase  						=       None

            lowerCAmelCase						,		lowerCAmelCase  						=       pipe.encode_prompt(lowercase )

            # inputs with prompt converted to embeddings
            lowerCAmelCase  						=       {
                """prompt_embeds""": prompt_embeds,
                """negative_prompt_embeds""": negative_prompt_embeds,
                """generator""": generator,
                """num_inference_steps""": num_inference_steps,
                """output_type""": output_type,
            }

            if image is not None:
                  lowerCAmelCase  						=       image

            if mask_image is not None:
                  lowerCAmelCase  						=       mask_image

            if original_image is not None:
                  lowerCAmelCase  						=       original_image

            # set all optional components to None
            for optional_component in pipe._optional_components:
                  setattr(lowercase      ,						lowercase      ,						lowercase )

            lowerCAmelCase  						=       pipe(**lowercase )[0]

            with tempfile.TemporaryDirectory() as tmpdir:
                  pipe.save_pretrained(lowercase )
                  lowerCAmelCase  						=       self.pipeline_class.from_pretrained(lowercase )
                  pipe_loaded.to(lowercase )
                  pipe_loaded.set_progress_bar_config(disable=lowercase )

            pipe_loaded.unet.set_attn_processor(AttnAddedKVProcessor() )  # For reproducibility tests

            for optional_component in pipe._optional_components:
                  self.assertTrue(
                      getattr(lowercase      ,						lowercase ) is None      ,						f'`{optional_component}` did not stay set to None after loading.'      ,						)

            lowerCAmelCase  						=       self.get_dummy_inputs(lowercase )

            lowerCAmelCase  						=       inputs["""generator"""]
            lowerCAmelCase  						=       inputs["""num_inference_steps"""]
            lowerCAmelCase  						=       inputs["""output_type"""]

            # inputs with prompt converted to embeddings
            lowerCAmelCase  						=       {
                """prompt_embeds""": prompt_embeds,
                """negative_prompt_embeds""": negative_prompt_embeds,
                """generator""": generator,
                """num_inference_steps""": num_inference_steps,
                """output_type""": output_type,
            }

            if image is not None:
                  lowerCAmelCase  						=       image

            if mask_image is not None:
                  lowerCAmelCase  						=       mask_image

            if original_image is not None:
                  lowerCAmelCase  						=       original_image

            lowerCAmelCase  						=       pipe_loaded(**lowercase )[0]

            lowerCAmelCase  						=       np.abs(to_np(lowercase ) - to_np(lowercase ) ).max()
            self.assertLess(lowercase      ,						1e-4 )





      def     _snake_case			(       self )		->     Optional[int]:
            lowerCAmelCase  						=       self.get_dummy_components()
            lowerCAmelCase  						=       self.pipeline_class(**lowercase )
            pipe.to(lowercase )
            pipe.set_progress_bar_config(disable=lowercase )

            lowerCAmelCase  						=       self.get_dummy_inputs(lowercase )
            lowerCAmelCase  						=       pipe(**lowercase )[0]

            with tempfile.TemporaryDirectory() as tmpdir:
                  pipe.save_pretrained(lowercase )
                  lowerCAmelCase  						=       self.pipeline_class.from_pretrained(lowercase )
                  pipe_loaded.to(lowercase )
                  pipe_loaded.set_progress_bar_config(disable=lowercase )

            pipe_loaded.unet.set_attn_processor(AttnAddedKVProcessor() )  # For reproducibility tests

            lowerCAmelCase  						=       self.get_dummy_inputs(lowercase )
            lowerCAmelCase  						=       pipe_loaded(**lowercase )[0]

            lowerCAmelCase  						=       np.abs(to_np(lowercase ) - to_np(lowercase ) ).max()
            self.assertLess(lowercase      ,						1e-4 )






