


'''simple docstring'''






from __future__ import annotations

import math


def       _snake_case     (  A )		->					bool:

							if 1 < number < 4:
														# 2 and 3 are primes
														return True
							elif number < 2 or number % 2 == 0 or number % 3 == 0:
														# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
														return False

							# All primes number are in format of 6k +/- 1
							for i in range(5				,					int(math.sqrt(A ) + 1 )				,					6 ):
														if number % i == 0 or number % (i + 2) == 0:
																					return False
							return True


__UpperCAmelCase					       =							[num for num in range(3, 100_001, 2) if not is_prime(num)]


def       _snake_case     (  A )		->					list[int]:
							if not isinstance(A				,					A ):
														raise ValueError('''n must be an integer''' )
							if n <= 0:
														raise ValueError('''n must be >= 0''' )

							lowerCAmelCase__      =			[]
							for num in range(len(A ) ):
														lowerCAmelCase__      =			0
														while 2 * i * i <= odd_composites[num]:
																					lowerCAmelCase__      =			odd_composites[num] - 2 * i * i
																					if is_prime(A ):
																												break
																					i += 1
														else:
																					list_nums.append(odd_composites[num] )
																					if len(A ) == n:
																												return list_nums

							return []


def       _snake_case     (  )		->					int:
							return compute_nums(1 )[0]


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



'''simple docstring'''






import unittest

import numpy as np
import torch

from diffusers import VersatileDiffusionImageVariationPipeline
from diffusers.utils.testing_utils import load_image, require_torch_gpu, slow, torch_device


__UpperCAmelCase					       =							False




class 	a__       (							unittest.TestCase						):





							'''simple docstring'''






							pass




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





							'''simple docstring'''






							def 						__SCREAMING_SNAKE_CASE							(	self     ) ->							str:
														lowerCAmelCase__      =			VersatileDiffusionImageVariationPipeline.from_pretrained('''shi-labs/versatile-diffusion'''     )
														pipe.to(lowerCamelCase_     )
														pipe.set_progress_bar_config(disable=lowerCamelCase_     )

														lowerCAmelCase__      =			load_image(
														    '''https://huggingface.co/datasets/hf-internal-testing/diffusers-images/resolve/main/versatile_diffusion/benz.jpg'''     )
														lowerCAmelCase__      =			torch.manual_seed(0     )
														lowerCAmelCase__      =			pipe(
														    image=lowerCamelCase_      ,					generator=lowerCamelCase_      ,					guidance_scale=7.5      ,					num_inference_steps=50      ,					output_type='''numpy'''      ,					).images

														lowerCAmelCase__      =			image[0, 2_53:2_56, 2_53:2_56, -1]

														assert image.shape == (1, 5_12, 5_12, 3)
														lowerCAmelCase__      =			np.array([0.0_441, 0.0_469, 0.0_507, 0.0_575, 0.0_632, 0.0_650, 0.0_865, 0.0_909, 0.0_945]     )

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