


'''simple docstring'''
def   __snake_case							(							lowerCamelCase_			:					List[str]    ):
				'''simple docstring'''




				__magic_name__							=			(1 + 24 * n) ** 0.5
				return ((1 + root) / 6) % 1 == 0




def   __snake_case							(							lowerCamelCase_			:					int = 5000    ):
				'''simple docstring'''




				__magic_name__							=			[(i * (3 * i - 1)) // 2 for i in range(1						,	lowerCamelCase_    )]
				for i, pentagonal_i in enumerate(lowerCamelCase_    ):
								for j in range(lowerCamelCase_						,	len(lowerCamelCase_    )    ):
												__magic_name__							=			pentagonal_nums[j]
												__magic_name__							=			pentagonal_i + pentagonal_j
												__magic_name__							=			pentagonal_j - pentagonal_i
												if is_pentagonal(lowerCamelCase_    ) and is_pentagonal(lowerCamelCase_    ):
																return b

				return -1


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





import gc
import unittest

from parameterized import parameterized

from diffusers import FlaxUNetaDConditionModel
from diffusers.utils import is_flax_available
from diffusers.utils.testing_utils import load_hf_numpy, require_flax, slow


if is_flax_available():
		import jax
		import jax.numpy as jnp







@slow
@require_flax
class 							lowerCAmelCase__   ( unittest.TestCase						):

						def 			A_					(      self							,				a							,				a					)       ->   Optional[int]:


								'''simple docstring'''

								return F'gaussian_noise_s={seed}_shape={"_".join([str(a					) for s in shape]					)}.npy'

						def 			A_					(      self					)       ->   List[Any]:


								'''simple docstring'''

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

						def 			A_					(      self							,				a=0							,				a=(4, 4, 64, 64)							,				a=False					)       ->   Optional[int]:


								'''simple docstring'''

								_UpperCamelCase         =						jnp.bfloataa if fpaa else jnp.floataa
								_UpperCamelCase         =						jnp.array(load_hf_numpy(self.get_file_format(a							,				a					)					)							,				dtype=a					)
								return image

						def 			A_					(      self							,				a=False							,				a="CompVis/stable-diffusion-v1-4"					)       ->   Any:


								'''simple docstring'''

								_UpperCamelCase         =						jnp.bfloataa if fpaa else jnp.floataa
								_UpperCamelCase         =						"""bf16""" if fpaa else None

								_UpperCamelCase     ,						_UpperCamelCase         =						FlaxUNetaDConditionModel.from_pretrained(
								    a							,				subfolder="""unet"""							,				dtype=a							,				revision=a					)
								return model, params

						def 			A_					(      self							,				a=0							,				a=(4, 77, 7_68)							,				a=False					)       ->   Tuple:


								'''simple docstring'''

								_UpperCamelCase         =						jnp.bfloataa if fpaa else jnp.floataa
								_UpperCamelCase         =						jnp.array(load_hf_numpy(self.get_file_format(a							,				a					)					)							,				dtype=a					)
								return hidden_states

						@parameterized.expand(
						    [
						        # fmt: off
						        [83, 4, [-0.2323, -0.1304, 0.0813, -0.3093, -0.0919, -0.1571, -0.1125, -0.5806]],
						        [17, 0.55, [-0.0831, -0.2443, 0.0901, -0.0919, 0.3396, 0.0103, -0.3743, 0.0701]],
						        [8, 0.89, [-0.4863, 0.0859, 0.0875, -0.1658, 0.9199, -0.0114, 0.4839, 0.4639]],
						        [3, 10_00, [-0.5649, 0.2402, -0.5518, 0.1248, 1.1328, -0.2443, -0.0325, -1.0078]],
						        # fmt: on
						    ]					)
						def 			A_					(      self							,				a							,				a							,				a					)       ->   Any:


								'''simple docstring'''

								_UpperCamelCase     ,						_UpperCamelCase         =						self.get_unet_model(model_id="""CompVis/stable-diffusion-v1-4"""							,				fpaa=a					)
								_UpperCamelCase         =						self.get_latents(a							,				fpaa=a					)
								_UpperCamelCase         =						self.get_encoder_hidden_states(a							,				fpaa=a					)

								_UpperCamelCase         =						model.apply(
								    {"""params""": params}							,				a							,				jnp.array(a							,				dtype=jnp.intaa					)							,				encoder_hidden_states=a							,				).sample

								assert sample.shape == latents.shape

								_UpperCamelCase         =						jnp.asarray(jax.device_get((sample[-1, -2:, -2:, :2].flatten())					)							,				dtype=jnp.floataa					)
								_UpperCamelCase         =						jnp.array(a							,				dtype=jnp.floataa					)

								# Found torch (float16) and flax (bfloat16) outputs to be within this tolerance, in the same hardware
								assert jnp.allclose(a							,				a							,				atol=1e-2					)







						@parameterized.expand(
						    [
						        # fmt: off
						        [83, 4, [0.1514, 0.0807, 0.1624, 0.1016, -0.1896, 0.0263, 0.0677, 0.2310]],
						        [17, 0.55, [0.1164, -0.0216, 0.0170, 0.1589, -0.3120, 0.1005, -0.0581, -0.1458]],
						        [8, 0.89, [-0.1758, -0.0169, 0.1004, -0.1411, 0.1312, 0.1103, -0.1996, 0.2139]],
						        [3, 10_00, [0.1214, 0.0352, -0.0731, -0.1562, -0.0994, -0.0906, -0.2340, -0.0539]],
						        # fmt: on
						    ]					)
						def 			A_					(      self							,				a							,				a							,				a					)       ->   Any:


								'''simple docstring'''

								_UpperCamelCase     ,						_UpperCamelCase         =						self.get_unet_model(model_id="""stabilityai/stable-diffusion-2"""							,				fpaa=a					)
								_UpperCamelCase         =						self.get_latents(a							,				shape=(4, 4, 96, 96)							,				fpaa=a					)
								_UpperCamelCase         =						self.get_encoder_hidden_states(a							,				shape=(4, 77, 10_24)							,				fpaa=a					)

								_UpperCamelCase         =						model.apply(
								    {"""params""": params}							,				a							,				jnp.array(a							,				dtype=jnp.intaa					)							,				encoder_hidden_states=a							,				).sample

								assert sample.shape == latents.shape

								_UpperCamelCase         =						jnp.asarray(jax.device_get((sample[-1, -2:, -2:, :2].flatten())					)							,				dtype=jnp.floataa					)
								_UpperCamelCase         =						jnp.array(a							,				dtype=jnp.floataa					)

								# Found torch (float16) and flax (bfloat16) outputs to be within this tolerance, on the same hardware
								assert jnp.allclose(a							,				a							,				atol=1e-2					)



