





'''simple docstring'''

from collections import defaultdict
from math import gcd







def  a__    (    lowercase :					int = 1500000				)		->		int:





     """simple docstring"""

     _UpperCamelCase       =	defaultdict(lowercase				)
     _UpperCamelCase       =	2
     while 2 * euclid_m * (euclid_m + 1) <= limit:
          for euclid_n in range((euclid_m % 2) + 1, lowercase, 2				):
               if gcd(lowercase, lowercase				) > 1:
                    continue
               _UpperCamelCase       =	2 * euclid_m * (euclid_m + euclid_n)
               for perimeter in range(lowercase, limit + 1, lowercase				):
                    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 gc
import unittest

from diffusers import FlaxControlNetModel, FlaxStableDiffusionControlNetPipeline
from diffusers.utils import is_flax_available, load_image, slow
from diffusers.utils.testing_utils import require_flax


if is_flax_available():
   import jax
   import jax.numpy as jnp
   from flax.jax_utils import replicate
   from flax.training.common_utils import shard
@slow
@require_flax
class     __lowerCAmelCase					(   unittest.TestCase			):






       """simple docstring"""





       def snake_case__						(							self       :		List[str]					)   ->					Optional[int]:

            '''simple docstring'''




            super().tearDown()
            gc.collect()





       def snake_case__						(							self       :		int					)   ->					Union[str, Any]:

            '''simple docstring'''




            _UpperCamelCase   ,    _UpperCamelCase       =	FlaxControlNetModel.from_pretrained(
                '''lllyasviel/sd-controlnet-canny'''	,			from_pt=lowerCAmelCase__	,			dtype=jnp.bfloataa					)
            _UpperCamelCase   ,    _UpperCamelCase       =	FlaxStableDiffusionControlNetPipeline.from_pretrained(
                '''runwayml/stable-diffusion-v1-5'''	,			controlnet=lowerCAmelCase__	,			from_pt=lowerCAmelCase__	,			dtype=jnp.bfloataa					)
            _UpperCamelCase       =	controlnet_params

            _UpperCamelCase       =	'''bird'''
            _UpperCamelCase       =	jax.device_count()
            _UpperCamelCase       =	pipe.prepare_text_inputs([prompts] * num_samples					)

            _UpperCamelCase       =	load_image(
                '''https://huggingface.co/datasets/hf-internal-testing/diffusers-images/resolve/main/sd_controlnet/bird_canny.png'''					)
            _UpperCamelCase       =	pipe.prepare_image_inputs([canny_image] * num_samples					)

            _UpperCamelCase       =	jax.random.PRNGKey(0					)
            _UpperCamelCase       =	jax.random.split(lowerCAmelCase__	,			jax.device_count()					)

            _UpperCamelCase       =	replicate(lowerCAmelCase__					)
            _UpperCamelCase       =	shard(lowerCAmelCase__					)
            _UpperCamelCase       =	shard(lowerCAmelCase__					)

            _UpperCamelCase       =	pipe(
                prompt_ids=lowerCAmelCase__	,			image=lowerCAmelCase__	,			params=lowerCAmelCase__	,			prng_seed=lowerCAmelCase__	,			num_inference_steps=50	,			jit=lowerCAmelCase__	,			).images
            assert images.shape == (jax.device_count(), 1, 768, 512, 3)

            _UpperCamelCase       =	images.reshape((images.shape[0] * images.shape[1],) + images.shape[-3:]					)
            _UpperCamelCase       =	images[0, 253:256, 253:256, -1]

            _UpperCamelCase       =	jnp.asarray(jax.device_get(image_slice.flatten()					)					)
            _UpperCamelCase       =	jnp.array(
                [0.167969, 0.116699, 0.081543, 0.154297, 0.132812, 0.108887, 0.169922, 0.169922, 0.205078]					)
            print(f"""output_slice: {output_slice}"""					)
            assert jnp.abs(output_slice - expected_slice					).max() < 1e-2







       def snake_case__						(							self       :		Union[str, Any]					)   ->					Union[str, Any]:

            '''simple docstring'''




            _UpperCamelCase   ,    _UpperCamelCase       =	FlaxControlNetModel.from_pretrained(
                '''lllyasviel/sd-controlnet-openpose'''	,			from_pt=lowerCAmelCase__	,			dtype=jnp.bfloataa					)
            _UpperCamelCase   ,    _UpperCamelCase       =	FlaxStableDiffusionControlNetPipeline.from_pretrained(
                '''runwayml/stable-diffusion-v1-5'''	,			controlnet=lowerCAmelCase__	,			from_pt=lowerCAmelCase__	,			dtype=jnp.bfloataa					)
            _UpperCamelCase       =	controlnet_params

            _UpperCamelCase       =	'''Chef in the kitchen'''
            _UpperCamelCase       =	jax.device_count()
            _UpperCamelCase       =	pipe.prepare_text_inputs([prompts] * num_samples					)

            _UpperCamelCase       =	load_image(
                '''https://huggingface.co/datasets/hf-internal-testing/diffusers-images/resolve/main/sd_controlnet/pose.png'''					)
            _UpperCamelCase       =	pipe.prepare_image_inputs([pose_image] * num_samples					)

            _UpperCamelCase       =	jax.random.PRNGKey(0					)
            _UpperCamelCase       =	jax.random.split(lowerCAmelCase__	,			jax.device_count()					)

            _UpperCamelCase       =	replicate(lowerCAmelCase__					)
            _UpperCamelCase       =	shard(lowerCAmelCase__					)
            _UpperCamelCase       =	shard(lowerCAmelCase__					)

            _UpperCamelCase       =	pipe(
                prompt_ids=lowerCAmelCase__	,			image=lowerCAmelCase__	,			params=lowerCAmelCase__	,			prng_seed=lowerCAmelCase__	,			num_inference_steps=50	,			jit=lowerCAmelCase__	,			).images
            assert images.shape == (jax.device_count(), 1, 768, 512, 3)

            _UpperCamelCase       =	images.reshape((images.shape[0] * images.shape[1],) + images.shape[-3:]					)
            _UpperCamelCase       =	images[0, 253:256, 253:256, -1]

            _UpperCamelCase       =	jnp.asarray(jax.device_get(image_slice.flatten()					)					)
            _UpperCamelCase       =	jnp.array(
                [[0.271484, 0.261719, 0.275391, 0.277344, 0.279297, 0.291016, 0.294922, 0.302734, 0.302734]]					)
            print(f"""output_slice: {output_slice}"""					)
            assert jnp.abs(output_slice - expected_slice					).max() < 1e-2



