
from typing import List, Optional, Tuple, Union

import PIL
import torch
from torchvision import transforms

from diffusers.pipeline_utils import DiffusionPipeline, ImagePipelineOutput
from diffusers.schedulers import DDIMScheduler
from diffusers.utils import randn_tensor


A     :	Optional[Any]    = transforms.Compose(
    [
        transforms.Resize((2_5_6, 2_5_6)),
        transforms.ToTensor(),
        transforms.Normalize([0.5], [0.5]),
    ]
)


def     __lowerCAmelCase			(			a__  )       ->  int:





				if isinstance(a__						,    torch.Tensor  ):
								return image
				elif isinstance(a__						,    PIL.Image.Image  ):
								__a										=    [image]

				__a										=    [trans(img.convert('''RGB'''  )  ) for img in image]
				__a										=    torch.stack(a__  )
				return image







class 			__A( SCREAMING_SNAKE_CASE_			):




				def __init__(     self		,     _snake_case		,     _snake_case				)    ->      List[Any]:


								'''simple docstring'''




								super().__init__()

								# make sure scheduler can always be converted to DDIM
								__a										=    DDIMScheduler.from_config(scheduler.config				)

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




				def 				SCREAMING_SNAKE_CASE_		(     self		,     _snake_case				)    ->      Any:


								'''simple docstring'''




								if strength < 0 or strength > 1:
												raise ValueError(F"""The value of strength should in [0.0, 1.0] but is {strength}"""				)




				def 				SCREAMING_SNAKE_CASE_		(     self		,     _snake_case		,     _snake_case		,     _snake_case				)    ->      Tuple:


								'''simple docstring'''




								__a										=    min(int(num_inference_steps * strength				)		,     __UpperCAmelCase				)

								__a										=    max(num_inference_steps - init_timestep		,     0				)
								__a										=    self.scheduler.timesteps[t_start:]

								return timesteps, num_inference_steps - t_start




				def 				SCREAMING_SNAKE_CASE_		(     self		,     _snake_case		,     _snake_case		,     _snake_case		,     _snake_case		,     _snake_case		,     _snake_case=None				)    ->      List[str]:


								'''simple docstring'''




								if not isinstance(__UpperCAmelCase		,     (torch.Tensor, PIL.Image.Image, list)				):
												raise ValueError(
												    F"""`image` has to be of type `torch.Tensor`, `PIL.Image.Image` or list but is {type(__UpperCAmelCase				)}"""				)

								__a										=    image.to(device=__UpperCAmelCase		,     dtype=__UpperCAmelCase				)

								if isinstance(__UpperCAmelCase		,     __UpperCAmelCase				) and len(__UpperCAmelCase				) != batch_size:
												raise ValueError(
												    F"""You have passed a list of generators of length {len(__UpperCAmelCase				)}, but requested an effective batch"""
												    F""" size of {batch_size}. Make sure the batch size matches the length of the generators."""				)

								__a										=    init_latents.shape
								__a										=    randn_tensor(__UpperCAmelCase		,     generator=__UpperCAmelCase		,     device=__UpperCAmelCase		,     dtype=__UpperCAmelCase				)

								# get latents
								print('''add noise to latents at timestep'''		,     __UpperCAmelCase				)
								__a										=    self.scheduler.add_noise(__UpperCAmelCase		,     __UpperCAmelCase		,     __UpperCAmelCase				)
								__a										=    init_latents

								return latents




				@torch.no_grad()
				def __call__(     self		,     _snake_case = None		,     _snake_case = 0.8		,     _snake_case = 1		,     _snake_case = None		,     _snake_case = 0.0		,     _snake_case = 50		,     _snake_case = None		,     _snake_case = "pil"		,     _snake_case = True		,     )    ->      Union[ImagePipelineOutput, Tuple]:


								'''simple docstring'''




								self.check_inputs(__UpperCAmelCase				)

								# 2. Preprocess image
								__a										=    preprocess(__UpperCAmelCase				)

								# 3. set timesteps
								self.scheduler.set_timesteps(__UpperCAmelCase		,     device=self.device				)
								__a										=    self.get_timesteps(__UpperCAmelCase		,     __UpperCAmelCase		,     self.device				)
								__a										=    timesteps[:1].repeat(__UpperCAmelCase				)

								# 4. Prepare latent variables
								__a										=    self.prepare_latents(__UpperCAmelCase		,     __UpperCAmelCase		,     __UpperCAmelCase		,     self.unet.dtype		,     self.device		,     __UpperCAmelCase				)
								__a										=    latents

								# 5. Denoising loop
								for t in self.progress_bar(__UpperCAmelCase				):
												# 1. predict noise model_output
												__a										=    self.unet(__UpperCAmelCase		,     __UpperCAmelCase				).sample

												# 2. predict previous mean of image x_t-1 and add variance depending on eta
												# eta corresponds to η in paper and should be between [0, 1]
												# do x_t -> x_t-1
												__a										=    self.scheduler.step(
												    __UpperCAmelCase		,     __UpperCAmelCase		,     __UpperCAmelCase		,     eta=__UpperCAmelCase		,     use_clipped_model_output=__UpperCAmelCase		,     generator=__UpperCAmelCase		,     ).prev_sample

								__a										=    (image / 2 + 0.5).clamp(0		,     1				)
								__a										=    image.cpu().permute(0		,     2		,     3		,     1				).numpy()
								if output_type == "pil":
												__a										=    self.numpy_to_pil(__UpperCAmelCase				)

								if not return_dict:
												return (image, latent_timestep.item())

								return ImagePipelineOutput(images=__UpperCAmelCase				)




'''simple docstring'''





from math import sqrt
def    _SCREAMING_SNAKE_CASE  (       UpperCamelCase			):



    """simple docstring"""





    assert isinstance(UpperCamelCase							,    UpperCamelCase			) and (
        number >= 0
    ), "'number' must been an int and positive"

    lowerCAmelCase__ :  int							      =					True

    # 0 and 1 are none primes.
    if number <= 1:
        lowerCAmelCase__ :  Optional[Any]							      =					False

    for divisor in range(2							,    int(round(sqrt(UpperCamelCase			)			)			) + 1			):
        # if 'number' divisible by 'divisor' then sets 'status'
        # of false and break up the loop.
        if number % divisor == 0:
            lowerCAmelCase__ :  Any							      =					False
            break

    # precondition
    assert isinstance(UpperCamelCase							,    UpperCamelCase			), "'status' must been from type bool"

    return status
def    _SCREAMING_SNAKE_CASE  (       UpperCamelCase			):



    """simple docstring"""





    assert isinstance(UpperCamelCase							,    UpperCamelCase			) and (n > 2), "'N' must been an int and > 2"

    # beginList: contains all natural numbers from 2 up to N
    lowerCAmelCase__ :  List[str]							      =					list(range(2							,    n + 1			)			)

    lowerCAmelCase__ :  str							      =					[]  # this list will be returns.

    # actual sieve of erathostenes
    for i in range(len(UpperCamelCase			)			):
        for j in range(i + 1							,    len(UpperCamelCase			)			):
            if (begin_list[i] != 0) and (begin_list[j] % begin_list[i] == 0):
                lowerCAmelCase__ :  List[Any]							      =					0

    # filters actual prime numbers.
    lowerCAmelCase__ :  List[Any]							      =					[x for x in begin_list if x != 0]

    # precondition
    assert isinstance(UpperCamelCase							,    UpperCamelCase			), "'ans' must been from type list"

    return ans
def    _SCREAMING_SNAKE_CASE  (       UpperCamelCase			):



    """simple docstring"""





    assert isinstance(UpperCamelCase							,    UpperCamelCase			) and (n > 2), "'N' must been an int and > 2"

    lowerCAmelCase__ :  List[str]							      =					[]

    # iterates over all numbers between 2 up to N+1
    # if a number is prime then appends to list 'ans'
    for number in range(2							,    n + 1			):
        if is_prime(UpperCamelCase			):
            ans.append(UpperCamelCase			)

    # precondition
    assert isinstance(UpperCamelCase							,    UpperCamelCase			), "'ans' must been from type list"

    return ans
def    _SCREAMING_SNAKE_CASE  (       UpperCamelCase			):



    """simple docstring"""





    assert isinstance(UpperCamelCase							,    UpperCamelCase			) and number >= 0, "'number' must been an int and >= 0"

    lowerCAmelCase__ :  Optional[Any]							      =					[]  # this list will be returns of the function.

    # potential prime number factors.

    lowerCAmelCase__ :  Dict							      =					2

    lowerCAmelCase__ :  Dict							      =					number

    if number == 0 or number == 1:
        ans.append(UpperCamelCase			)

    # if 'number' not prime then builds the prime factorization of 'number'
    elif not is_prime(UpperCamelCase			):
        while quotient != 1:
            if is_prime(UpperCamelCase			) and (quotient % factor == 0):
                ans.append(UpperCamelCase			)
                quotient /= factor
            else:
                factor += 1

    else:
        ans.append(UpperCamelCase			)

    # precondition
    assert isinstance(UpperCamelCase							,    UpperCamelCase			), "'ans' must been from type list"

    return ans
def    _SCREAMING_SNAKE_CASE  (       UpperCamelCase			):



    """simple docstring"""





    assert isinstance(UpperCamelCase							,    UpperCamelCase			) and (
        number >= 0
    ), "'number' bust been an int and >= 0"

    lowerCAmelCase__ :  Optional[int]							      =					0

    # prime factorization of 'number'
    lowerCAmelCase__ :  List[str]							      =					prime_factorization(UpperCamelCase			)

    lowerCAmelCase__ :  Any							      =					max(UpperCamelCase			)

    # precondition
    assert isinstance(UpperCamelCase							,    UpperCamelCase			), "'ans' must been from type int"

    return ans
def    _SCREAMING_SNAKE_CASE  (       UpperCamelCase			):



    """simple docstring"""





    assert isinstance(UpperCamelCase							,    UpperCamelCase			) and (
        number >= 0
    ), "'number' bust been an int and >= 0"

    lowerCAmelCase__ :  List[Any]							      =					0

    # prime factorization of 'number'
    lowerCAmelCase__ :  List[str]							      =					prime_factorization(UpperCamelCase			)

    lowerCAmelCase__ :  Optional[int]							      =					min(UpperCamelCase			)

    # precondition
    assert isinstance(UpperCamelCase							,    UpperCamelCase			), "'ans' must been from type int"

    return ans
def    _SCREAMING_SNAKE_CASE  (       UpperCamelCase			):



    """simple docstring"""





    assert isinstance(UpperCamelCase							,    UpperCamelCase			), "'number' must been an int"
    assert isinstance(number % 2 == 0							,    UpperCamelCase			), "compare bust been from type bool"

    return number % 2 == 0
def    _SCREAMING_SNAKE_CASE  (       UpperCamelCase			):



    """simple docstring"""





    assert isinstance(UpperCamelCase							,    UpperCamelCase			), "'number' must been an int"
    assert isinstance(number % 2 != 0							,    UpperCamelCase			), "compare bust been from type bool"

    return number % 2 != 0
def    _SCREAMING_SNAKE_CASE  (       UpperCamelCase			):



    """simple docstring"""





    assert (
        isinstance(UpperCamelCase							,    UpperCamelCase			) and (number > 2) and is_even(UpperCamelCase			)
    ), "'number' must been an int, even and > 2"

    lowerCAmelCase__ :  Dict							      =					[]  # this list will returned

    # creates a list of prime numbers between 2 up to 'number'
    lowerCAmelCase__ :  Dict							      =					get_prime_numbers(UpperCamelCase			)
    lowerCAmelCase__ :  Optional[Any]							      =					len(UpperCamelCase			)

    # run variable for while-loops.
    lowerCAmelCase__ :  List[str]							      =					0
    lowerCAmelCase__ :  List[Any]							      =					None

    # exit variable. for break up the loops
    lowerCAmelCase__ :  Any							      =					True

    while i < len_pn and loop:
        lowerCAmelCase__ :  List[Any]							      =					i + 1

        while j < len_pn and loop:
            if prime_numbers[i] + prime_numbers[j] == number:
                lowerCAmelCase__ :  Optional[Any]							      =					False
                ans.append(prime_numbers[i]			)
                ans.append(prime_numbers[j]			)

            j += 1

        i += 1

    # precondition
    assert (
        isinstance(UpperCamelCase							,    UpperCamelCase			)
        and (len(UpperCamelCase			) == 2)
        and (ans[0] + ans[1] == number)
        and is_prime(ans[0]			)
        and is_prime(ans[1]			)
    ), "'ans' must contains two primes. And sum of elements must been eq 'number'"

    return ans
def    _SCREAMING_SNAKE_CASE  (       UpperCamelCase							,    UpperCamelCase			):



    """simple docstring"""





    assert (
        isinstance(UpperCamelCase							,    UpperCamelCase			)
        and isinstance(UpperCamelCase							,    UpperCamelCase			)
        and (numbera >= 0)
        and (numbera >= 0)
    ), "'number1' and 'number2' must been positive integer."

    lowerCAmelCase__ :  int							      =					0

    while numbera != 0:
        lowerCAmelCase__ :  Any							      =					numbera % numbera
        lowerCAmelCase__ :  str							      =					numbera
        lowerCAmelCase__ :  List[str]							      =					rest

    # precondition
    assert isinstance(UpperCamelCase							,    UpperCamelCase			) and (
        numbera >= 0
    ), "'number' must been from type int and positive"

    return numbera
def    _SCREAMING_SNAKE_CASE  (       UpperCamelCase							,    UpperCamelCase			):



    """simple docstring"""





    assert (
        isinstance(UpperCamelCase							,    UpperCamelCase			)
        and isinstance(UpperCamelCase							,    UpperCamelCase			)
        and (numbera >= 1)
        and (numbera >= 1)
    ), "'number1' and 'number2' must been positive integer."

    lowerCAmelCase__ :  int							      =					1  # actual answer that will be return.

    # for kgV (x,1)
    if numbera > 1 and numbera > 1:
        # builds the prime factorization of 'number1' and 'number2'
        lowerCAmelCase__ :  int							      =					prime_factorization(UpperCamelCase			)
        lowerCAmelCase__ :  Any							      =					prime_factorization(UpperCamelCase			)

    elif numbera == 1 or numbera == 1:
        lowerCAmelCase__ :  Optional[Any]							      =					[]
        lowerCAmelCase__ :  Dict							      =					[]
        lowerCAmelCase__ :  List[str]							      =					max(UpperCamelCase							,    UpperCamelCase			)

    lowerCAmelCase__ :  Tuple							      =					0
    lowerCAmelCase__ :  str							      =					0

    lowerCAmelCase__ :  List[Any]							      =					[]  # captured numbers int both 'primeFac1' and 'primeFac2'

    # iterates through primeFac1
    for n in prime_fac_a:
        if n not in done:
            if n in prime_fac_a:
                lowerCAmelCase__ :  int							      =					prime_fac_a.count(UpperCamelCase			)
                lowerCAmelCase__ :  Any							      =					prime_fac_a.count(UpperCamelCase			)

                for _ in range(max(UpperCamelCase							,    UpperCamelCase			)			):
                    ans *= n

            else:
                lowerCAmelCase__ :  Any							      =					prime_fac_a.count(UpperCamelCase			)

                for _ in range(UpperCamelCase			):
                    ans *= n

            done.append(UpperCamelCase			)

    # iterates through primeFac2
    for n in prime_fac_a:
        if n not in done:
            lowerCAmelCase__ :  Optional[int]							      =					prime_fac_a.count(UpperCamelCase			)

            for _ in range(UpperCamelCase			):
                ans *= n

            done.append(UpperCamelCase			)

    # precondition
    assert isinstance(UpperCamelCase							,    UpperCamelCase			) and (
        ans >= 0
    ), "'ans' must been from type int and positive"

    return ans
def    _SCREAMING_SNAKE_CASE  (       UpperCamelCase			):



    """simple docstring"""





    assert isinstance(UpperCamelCase							,    UpperCamelCase			) and (n >= 0), "'number' must been a positive int"

    lowerCAmelCase__ :  Optional[Any]							      =					0
    lowerCAmelCase__ :  Tuple							      =					2  # this variable holds the answer

    while index < n:
        index += 1

        ans += 1  # counts to the next number

        # if ans not prime then
        # runs to the next prime number.
        while not is_prime(UpperCamelCase			):
            ans += 1

    # precondition
    assert isinstance(UpperCamelCase							,    UpperCamelCase			) and is_prime(
        UpperCamelCase			), "'ans' must been a prime number and from type int"

    return ans
def    _SCREAMING_SNAKE_CASE  (       UpperCamelCase							,    UpperCamelCase			):



    """simple docstring"""





    assert (
        is_prime(UpperCamelCase			) and is_prime(UpperCamelCase			) and (p_number_a < p_number_a)
    ), "The arguments must been prime numbers and 'pNumber1' < 'pNumber2'"

    lowerCAmelCase__ :  Dict							      =					p_number_a + 1  # jump to the next number

    lowerCAmelCase__ :  List[Any]							      =					[]  # this list will be returns.

    # if number is not prime then
    # fetch the next prime number.
    while not is_prime(UpperCamelCase			):
        number += 1

    while number < p_number_a:
        ans.append(UpperCamelCase			)

        number += 1

        # fetch the next prime number.
        while not is_prime(UpperCamelCase			):
            number += 1

    # precondition
    assert (
        isinstance(UpperCamelCase							,    UpperCamelCase			)
        and ans[0] != p_number_a
        and ans[len(UpperCamelCase			) - 1] != p_number_a
    ), "'ans' must been a list without the arguments"

    # 'ans' contains not 'pNumber1' and 'pNumber2' !
    return ans
def    _SCREAMING_SNAKE_CASE  (       UpperCamelCase			):



    """simple docstring"""





    assert isinstance(UpperCamelCase							,    UpperCamelCase			) and (n >= 1), "'n' must been int and >= 1"

    lowerCAmelCase__ :  List[Any]							      =					[]  # will be returned.

    for divisor in range(1							,    n + 1			):
        if n % divisor == 0:
            ans.append(UpperCamelCase			)

    # precondition
    assert ans[0] == 1 and ans[len(UpperCamelCase			) - 1] == n, "Error in function getDivisiors(...)"

    return ans
def    _SCREAMING_SNAKE_CASE  (       UpperCamelCase			):



    """simple docstring"""





    assert isinstance(UpperCamelCase							,    UpperCamelCase			) and (
        number > 1
    ), "'number' must been an int and >= 1"

    lowerCAmelCase__ :  Optional[int]							      =					get_divisors(UpperCamelCase			)

    # precondition
    assert (
        isinstance(UpperCamelCase							,    UpperCamelCase			)
        and (divisors[0] == 1)
        and (divisors[len(UpperCamelCase			) - 1] == number)
    ), "Error in help-function getDivisiors(...)"

    # summed all divisors up to 'number' (exclusive), hence [:-1]
    return sum(divisors[:-1]			) == number
def    _SCREAMING_SNAKE_CASE  (       UpperCamelCase							,    UpperCamelCase			):



    """simple docstring"""





    assert (
        isinstance(UpperCamelCase							,    UpperCamelCase			)
        and isinstance(UpperCamelCase							,    UpperCamelCase			)
        and (denominator != 0)
    ), "The arguments must been from type int and 'denominator' != 0"

    # build the greatest common divisor of numerator and denominator.
    lowerCAmelCase__ :  int							      =					gcd(abs(UpperCamelCase			)							,    abs(UpperCamelCase			)			)

    # precondition
    assert (
        isinstance(UpperCamelCase							,    UpperCamelCase			)
        and (numerator % gcd_of_fraction == 0)
        and (denominator % gcd_of_fraction == 0)
    ), "Error in function gcd(...,...)"

    return (numerator // gcd_of_fraction, denominator // gcd_of_fraction)
def    _SCREAMING_SNAKE_CASE  (       UpperCamelCase			):



    """simple docstring"""





    assert isinstance(UpperCamelCase							,    UpperCamelCase			) and (n >= 0), "'n' must been a int and >= 0"

    lowerCAmelCase__ :  str							      =					1  # this will be return.

    for factor in range(1							,    n + 1			):
        ans *= factor

    return ans




def    _SCREAMING_SNAKE_CASE  (       UpperCamelCase			):



    """simple docstring"""





    assert isinstance(UpperCamelCase							,    UpperCamelCase			) and (n >= 0), "'n' must been an int and >= 0"

    lowerCAmelCase__ :  List[Any]							      =					0
    lowerCAmelCase__ :  Any							      =					1
    lowerCAmelCase__ :  Optional[Any]							      =					1  # this will be return

    for _ in range(n - 1			):
        lowerCAmelCase__ :  Dict							      =					ans
        ans += fiba
        lowerCAmelCase__ :  str							      =					tmp

    return ans


