


"""simple docstring"""




import math

def        lowercase							(		lowerCAmelCase__ :     int			) ->      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(lowerCAmelCase__			) + 1			)    ,					6			):
				if number % i == 0 or number % (i + 2) == 0:
						return False
		return True

def        lowercase							(		lowerCAmelCase__ :     float = 0.1			) ->      int:
		__a           =			3
		__a           =			3

		while primes / (2 * j - 1) >= ratio:
				for i in range(j * j + j + 1    ,					(j + 2) * (j + 2)    ,					j + 1			):
						primes += is_prime(lowerCAmelCase__			)
				j += 2
		return j


if __name__ == "__main__":
				import doctest

				doctest.testmod()













"""simple docstring"""




import torch

from diffusers import DiffusionPipeline

class  _UpperCAmelCase  (   UpperCAmelCase__		):



      '''simple docstring'''

      def __init__(     self					,      snake_case_					,      snake_case_  ):

        """simple docstring"""

        super().__init__()

        self.register_modules(unet=snake_case_					,      scheduler=snake_case_  )

      def __call__(     self  ):

        """simple docstring"""

        A_  :       Optional[Any]										=  torch.randn(
            (1, self.unet.config.in_channels, self.unet.config.sample_size, self.unet.config.sample_size)					,      )
        A_  :       List[str]										=  1

        A_  :       List[str]										=  self.unet(snake_case_					,      snake_case_  ).sample
        A_  :       Optional[int]										=  self.scheduler.step(snake_case_					,      snake_case_					,      snake_case_  ).prev_sample

        A_  :       List[Any]										=  scheduler_output - scheduler_output + torch.ones_like(snake_case_  )

        return result