


from typing import Dict, Iterable, Optional, Union

import numpy as np

from ...image_processing_utils import BaseImageProcessor, BatchFeature, get_size_dict
from ...image_transforms import normalize, rescale, resize, to_channel_dimension_format, to_pil_image
from ...image_utils import (
    IMAGENET_STANDARD_MEAN,
    IMAGENET_STANDARD_STD,
    ChannelDimension,
    ImageInput,
    PILImageResampling,
    make_list_of_images,
    to_numpy_array,
    valid_images,
)
from ...utils import TensorType, is_pytesseract_available, is_vision_available, logging, requires_backends


if is_vision_available():
						import PIL

# soft dependency
if is_pytesseract_available():
						import pytesseract

_UpperCAmelCase			:  int     =logging.get_logger(__name__)



def 			lowerCAmelCase (		lowerCAmelCase_ ,   lowerCAmelCase_ ,   lowerCAmelCase_ )-> Dict:
				return [
				    int(1_000 * (box[0] / width) ),
				    int(1_000 * (box[1] / height) ),
				    int(1_000 * (box[2] / width) ),
				    int(1_000 * (box[3] / height) ),
				]



def 			lowerCAmelCase (		lowerCAmelCase_ ,   lowerCAmelCase_ ,   lowerCAmelCase_ )-> List[Any]:
				lowerCAmelCase_ :      str    				=				to_pil_image(lowerCAmelCase_ )
				lowerCAmelCase_ :      Tuple    				=				pil_image.size
				lowerCAmelCase_ :      Any    				=				pytesseract.image_to_data(lowerCAmelCase_ ,   lang=lowerCAmelCase_ ,   output_type='''dict''' ,   config=lowerCAmelCase_ )
				lowerCAmelCase_ :      Dict    				=				data['''text'''], data['''left'''], data['''top'''], data['''width'''], data['''height''']

				# filter empty words and corresponding coordinates
				lowerCAmelCase_ :      Dict    				=				[idx for idx, word in enumerate(lowerCAmelCase_ ) if not word.strip()]
				lowerCAmelCase_ :      int    				=				[word for idx, word in enumerate(lowerCAmelCase_ ) if idx not in irrelevant_indices]
				lowerCAmelCase_ :      Tuple    				=				[coord for idx, coord in enumerate(lowerCAmelCase_ ) if idx not in irrelevant_indices]
				lowerCAmelCase_ :      List[Any]    				=				[coord for idx, coord in enumerate(lowerCAmelCase_ ) if idx not in irrelevant_indices]
				lowerCAmelCase_ :      Optional[int]    				=				[coord for idx, coord in enumerate(lowerCAmelCase_ ) if idx not in irrelevant_indices]
				lowerCAmelCase_ :      int    				=				[coord for idx, coord in enumerate(lowerCAmelCase_ ) if idx not in irrelevant_indices]

				# turn coordinates into (left, top, left+width, top+height) format
				lowerCAmelCase_ :      str    				=				[]
				for x, y, w, h in zip(lowerCAmelCase_ ,   lowerCAmelCase_ ,   lowerCAmelCase_ ,   lowerCAmelCase_ ):
								lowerCAmelCase_ :      str    				=				[x, y, x + w, y + h]
								actual_boxes.append(lowerCAmelCase_ )

				# finally, normalize the bounding boxes
				lowerCAmelCase_ :      Optional[Any]    				=				[]
				for box in actual_boxes:
								normalized_boxes.append(normalize_box(lowerCAmelCase_ ,   lowerCAmelCase_ ,   lowerCAmelCase_ ) )

				assert len(lowerCAmelCase_ ) == len(lowerCAmelCase_ ), "Not as many words as there are bounding boxes"

				return words, normalized_boxes







class 				snake_case__(							UpperCAmelCase__							):







						'''simple docstring'''




						SCREAMING_SNAKE_CASE__      :  List[Any]					=							["""pixel_values"""]




						def __init__(				self   ,						__lowercase = True   ,						__lowercase = None   ,						__lowercase = PILImageResampling.BILINEAR   ,						__lowercase = True   ,						__lowercase = 1 / 2_5_5   ,						__lowercase = True   ,						__lowercase = None   ,						__lowercase = None   ,						__lowercase = True   ,						__lowercase = None   ,						__lowercase = ""   ,						**__lowercase   ,						)					->    None:
										super().__init__(**__lowercase							)
										lowerCAmelCase_ :      List[str]    				=				size if size is not None else {'''height''': 2_2_4, '''width''': 2_2_4}
										lowerCAmelCase_ :      Any    				=				get_size_dict(__lowercase							)

										lowerCAmelCase_ :      Dict    				=				do_resize
										lowerCAmelCase_ :      Optional[Any]    				=				size
										lowerCAmelCase_ :      Optional[Any]    				=				resample
										lowerCAmelCase_ :      Optional[int]    				=				do_rescale
										lowerCAmelCase_ :      Union[str, Any]    				=				rescale_value
										lowerCAmelCase_ :      List[Any]    				=				do_normalize
										lowerCAmelCase_ :      Any    				=				image_mean if image_mean is not None else IMAGENET_STANDARD_MEAN
										lowerCAmelCase_ :      List[str]    				=				image_std if image_std is not None else IMAGENET_STANDARD_STD
										lowerCAmelCase_ :      Tuple    				=				apply_ocr
										lowerCAmelCase_ :      Dict    				=				ocr_lang
										lowerCAmelCase_ :      Union[str, Any]    				=				tesseract_config




						def 						lowercase_ (				self   ,						__lowercase   ,						__lowercase   ,						__lowercase = PILImageResampling.BILINEAR   ,						__lowercase = None   ,						**__lowercase   ,						)					->    np.ndarray:
										lowerCAmelCase_ :      Union[str, Any]    				=				get_size_dict(__lowercase							)
										if "height" not in size or "width" not in size:
														raise ValueError(f"""The size dictionary must contain the keys 'height' and 'width'. Got {size.keys()}"""							)
										lowerCAmelCase_ :      List[str]    				=				(size['''height'''], size['''width'''])
										return resize(__lowercase   ,						size=__lowercase   ,						resample=__lowercase   ,						data_format=__lowercase   ,						**__lowercase							)




						def 						lowercase_ (				self   ,						__lowercase   ,						__lowercase   ,						__lowercase = None   ,						**__lowercase   ,						)					->    np.ndarray:
										return rescale(__lowercase   ,						scale=__lowercase   ,						data_format=__lowercase   ,						**__lowercase							)




						def 						lowercase_ (				self   ,						__lowercase   ,						__lowercase   ,						__lowercase   ,						__lowercase = None   ,						**__lowercase   ,						)					->    np.ndarray:
										return normalize(__lowercase   ,						mean=__lowercase   ,						std=__lowercase   ,						data_format=__lowercase   ,						**__lowercase							)




						def 						lowercase_ (				self   ,						__lowercase   ,						__lowercase = None   ,						__lowercase = None   ,						__lowercase=None   ,						__lowercase = None   ,						__lowercase = None   ,						__lowercase = None   ,						__lowercase = None   ,						__lowercase = None   ,						__lowercase = None   ,						__lowercase = None   ,						__lowercase = None   ,						__lowercase = None   ,						__lowercase = ChannelDimension.FIRST   ,						**__lowercase   ,						)					->    PIL.Image.Image:
										lowerCAmelCase_ :      List[Any]    				=				do_resize if do_resize is not None else self.do_resize
										lowerCAmelCase_ :      List[str]    				=				size if size is not None else self.size
										lowerCAmelCase_ :      str    				=				get_size_dict(__lowercase							)
										lowerCAmelCase_ :      str    				=				resample if resample is not None else self.resample
										lowerCAmelCase_ :      Tuple    				=				do_rescale if do_rescale is not None else self.do_rescale
										lowerCAmelCase_ :      Union[str, Any]    				=				rescale_factor if rescale_factor is not None else self.rescale_factor
										lowerCAmelCase_ :      Any    				=				do_normalize if do_normalize is not None else self.do_normalize
										lowerCAmelCase_ :      Union[str, Any]    				=				image_mean if image_mean is not None else self.image_mean
										lowerCAmelCase_ :      Optional[int]    				=				image_std if image_std is not None else self.image_std
										lowerCAmelCase_ :      Optional[Any]    				=				apply_ocr if apply_ocr is not None else self.apply_ocr
										lowerCAmelCase_ :      Dict    				=				ocr_lang if ocr_lang is not None else self.ocr_lang
										lowerCAmelCase_ :      int    				=				tesseract_config if tesseract_config is not None else self.tesseract_config

										lowerCAmelCase_ :      int    				=				make_list_of_images(__lowercase							)

										if not valid_images(__lowercase							):
														raise ValueError(
														    '''Invalid image type. Must be of type PIL.Image.Image, numpy.ndarray, '''
														    '''torch.Tensor, tf.Tensor or jax.ndarray.'''							)

										if do_resize and size is None:
														raise ValueError('''Size must be specified if do_resize is True.'''							)

										if do_rescale and rescale_factor is None:
														raise ValueError('''Rescale factor must be specified if do_rescale is True.'''							)

										if do_normalize and (image_mean is None or image_std is None):
														raise ValueError('''If do_normalize is True, image_mean and image_std must be specified.'''							)

										# All transformations expect numpy arrays.
										lowerCAmelCase_ :      List[Any]    				=				[to_numpy_array(__lowercase							) for image in images]

										# Tesseract OCR to get words + normalized bounding boxes
										if apply_ocr:
														requires_backends(self   ,						'''pytesseract'''							)
														lowerCAmelCase_ :      Union[str, Any]    				=				[]
														lowerCAmelCase_ :      Any    				=				[]
														for image in images:
																		lowerCAmelCase_ :      List[str]    				=				apply_tesseract(__lowercase   ,						__lowercase   ,						__lowercase							)
																		words_batch.append(__lowercase							)
																		boxes_batch.append(__lowercase							)

										if do_resize:
														lowerCAmelCase_ :      Union[str, Any]    				=				[self.resize(image=__lowercase   ,						size=__lowercase   ,						resample=__lowercase							) for image in images]

										if do_rescale:
														lowerCAmelCase_ :      List[Any]    				=				[self.rescale(image=__lowercase   ,						scale=__lowercase							) for image in images]

										if do_normalize:
														lowerCAmelCase_ :      List[str]    				=				[self.normalize(image=__lowercase   ,						mean=__lowercase   ,						std=__lowercase							) for image in images]

										lowerCAmelCase_ :      Union[str, Any]    				=				[to_channel_dimension_format(__lowercase   ,						__lowercase							) for image in images]

										lowerCAmelCase_ :      Union[str, Any]    				=				BatchFeature(data={'''pixel_values''': images}   ,						tensor_type=__lowercase							)

										if apply_ocr:
														lowerCAmelCase_ :      str    				=				words_batch
														lowerCAmelCase_ :      str    				=				boxes_batch
										return data



from math import sqrt



def 			lowerCAmelCase (		lowerCAmelCase_ )-> bool:
				assert isinstance(lowerCAmelCase_ ,   lowerCAmelCase_ ) and (
				    number >= 0
				), "'number' must been an int and positive"

				lowerCAmelCase_ :      str    				=				True

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

				for divisor in range(2 ,   int(round(sqrt(lowerCAmelCase_ ) ) ) + 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(lowerCAmelCase_ ,   lowerCAmelCase_ ), "'status' must been from type bool"

				return status



def 			lowerCAmelCase (		lowerCAmelCase_ )-> List[str]:
				assert isinstance(lowerCAmelCase_ ,   lowerCAmelCase_ ) and (n > 2), "'N' must been an int and > 2"

				# beginList: contains all natural numbers from 2 up to N
				lowerCAmelCase_ :      Optional[Any]    				=				list(range(2 ,   n + 1 ) )

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

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

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

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

				return ans



def 			lowerCAmelCase (		lowerCAmelCase_ )-> int:
				assert isinstance(lowerCAmelCase_ ,   lowerCAmelCase_ ) 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(lowerCAmelCase_ ):
												ans.append(lowerCAmelCase_ )

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

				return ans



def 			lowerCAmelCase (		lowerCAmelCase_ )-> Optional[Any]:
				assert isinstance(lowerCAmelCase_ ,   lowerCAmelCase_ ) and number >= 0, "'number' must been an int and >= 0"

				lowerCAmelCase_ :      Union[str, Any]    				=				[]  # this list will be returns of the function.

				# potential prime number factors.

				lowerCAmelCase_ :      Any    				=				2

				lowerCAmelCase_ :      List[str]    				=				number

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

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

				else:
								ans.append(lowerCAmelCase_ )

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

				return ans



def 			lowerCAmelCase (		lowerCAmelCase_ )-> List[Any]:
				assert isinstance(lowerCAmelCase_ ,   lowerCAmelCase_ ) and (
				    number >= 0
				), "'number' bust been an int and >= 0"

				lowerCAmelCase_ :      Union[str, Any]    				=				0

				# prime factorization of 'number'
				lowerCAmelCase_ :      Optional[int]    				=				prime_factorization(lowerCAmelCase_ )

				lowerCAmelCase_ :      Dict    				=				max(lowerCAmelCase_ )

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

				return ans



def 			lowerCAmelCase (		lowerCAmelCase_ )-> str:
				assert isinstance(lowerCAmelCase_ ,   lowerCAmelCase_ ) and (
				    number >= 0
				), "'number' bust been an int and >= 0"

				lowerCAmelCase_ :      Union[str, Any]    				=				0

				# prime factorization of 'number'
				lowerCAmelCase_ :      int    				=				prime_factorization(lowerCAmelCase_ )

				lowerCAmelCase_ :      Union[str, Any]    				=				min(lowerCAmelCase_ )

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

				return ans



def 			lowerCAmelCase (		lowerCAmelCase_ )-> Dict:
				assert isinstance(lowerCAmelCase_ ,   lowerCAmelCase_ ), "'number' must been an int"
				assert isinstance(number % 2 == 0 ,   lowerCAmelCase_ ), "compare bust been from type bool"

				return number % 2 == 0



def 			lowerCAmelCase (		lowerCAmelCase_ )-> List[str]:
				assert isinstance(lowerCAmelCase_ ,   lowerCAmelCase_ ), "'number' must been an int"
				assert isinstance(number % 2 != 0 ,   lowerCAmelCase_ ), "compare bust been from type bool"

				return number % 2 != 0



def 			lowerCAmelCase (		lowerCAmelCase_ )-> List[Any]:
				assert (
				    isinstance(lowerCAmelCase_ ,   lowerCAmelCase_ ) and (number > 2) and is_even(lowerCAmelCase_ )
				), "'number' must been an int, even and > 2"

				lowerCAmelCase_ :      Union[str, Any]    				=				[]  # this list will returned

				# creates a list of prime numbers between 2 up to 'number'
				lowerCAmelCase_ :      List[Any]    				=				get_prime_numbers(lowerCAmelCase_ )
				lowerCAmelCase_ :      Any    				=				len(lowerCAmelCase_ )

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

				# exit variable. for break up the loops
				lowerCAmelCase_ :      int    				=				True

				while i < len_pn and loop:
								lowerCAmelCase_ :      Tuple    				=				i + 1

								while j < len_pn and loop:
												if prime_numbers[i] + prime_numbers[j] == number:
																lowerCAmelCase_ :      Union[str, Any]    				=				False
																ans.append(prime_numbers[i] )
																ans.append(prime_numbers[j] )

												j += 1

								i += 1

				# precondition
				assert (
				    isinstance(lowerCAmelCase_ ,   lowerCAmelCase_ )
				    and (len(lowerCAmelCase_ ) == 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 			lowerCAmelCase (		lowerCAmelCase_ ,   lowerCAmelCase_ )-> Optional[int]:
				assert (
				    isinstance(lowerCAmelCase_ ,   lowerCAmelCase_ )
				    and isinstance(lowerCAmelCase_ ,   lowerCAmelCase_ )
				    and (numbera >= 0)
				    and (numbera >= 0)
				), "'number1' and 'number2' must been positive integer."

				lowerCAmelCase_ :      List[str]    				=				0

				while numbera != 0:
								lowerCAmelCase_ :      int    				=				numbera % numbera
								lowerCAmelCase_ :      Union[str, Any]    				=				numbera
								lowerCAmelCase_ :      Tuple    				=				rest

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

				return numbera



def 			lowerCAmelCase (		lowerCAmelCase_ ,   lowerCAmelCase_ )-> Any:
				assert (
				    isinstance(lowerCAmelCase_ ,   lowerCAmelCase_ )
				    and isinstance(lowerCAmelCase_ ,   lowerCAmelCase_ )
				    and (numbera >= 1)
				    and (numbera >= 1)
				), "'number1' and 'number2' must been positive integer."

				lowerCAmelCase_ :      Dict    				=				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_ :      Tuple    				=				prime_factorization(lowerCAmelCase_ )
								lowerCAmelCase_ :      str    				=				prime_factorization(lowerCAmelCase_ )

				elif numbera == 1 or numbera == 1:
								lowerCAmelCase_ :      List[Any]    				=				[]
								lowerCAmelCase_ :      List[Any]    				=				[]
								lowerCAmelCase_ :      str    				=				max(lowerCAmelCase_ ,   lowerCAmelCase_ )

				lowerCAmelCase_ :      str    				=				0
				lowerCAmelCase_ :      List[str]    				=				0

				lowerCAmelCase_ :      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_ :      str    				=				prime_fac_a.count(lowerCAmelCase_ )
																lowerCAmelCase_ :      List[str]    				=				prime_fac_a.count(lowerCAmelCase_ )

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

												else:
																lowerCAmelCase_ :      Dict    				=				prime_fac_a.count(lowerCAmelCase_ )

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

												done.append(lowerCAmelCase_ )

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

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

												done.append(lowerCAmelCase_ )

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

				return ans



def 			lowerCAmelCase (		lowerCAmelCase_ )-> Dict:
				assert isinstance(lowerCAmelCase_ ,   lowerCAmelCase_ ) and (n >= 0), "'number' must been a positive int"

				lowerCAmelCase_ :      Optional[int]    				=				0
				lowerCAmelCase_ :      Optional[int]    				=				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(lowerCAmelCase_ ):
												ans += 1

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

				return ans



def 			lowerCAmelCase (		lowerCAmelCase_ ,   lowerCAmelCase_ )-> Dict:
				assert (
				    is_prime(lowerCAmelCase_ ) and is_prime(lowerCAmelCase_ ) and (p_number_a < p_number_a)
				), "The arguments must been prime numbers and 'pNumber1' < 'pNumber2'"

				lowerCAmelCase_ :      str    				=				p_number_a + 1  # jump to the next number

				lowerCAmelCase_ :      Dict    				=				[]  # this list will be returns.

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

				while number < p_number_a:
								ans.append(lowerCAmelCase_ )

								number += 1

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

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

				# 'ans' contains not 'pNumber1' and 'pNumber2' !
				return ans



def 			lowerCAmelCase (		lowerCAmelCase_ )-> List[str]:
				assert isinstance(lowerCAmelCase_ ,   lowerCAmelCase_ ) and (n >= 1), "'n' must been int and >= 1"

				lowerCAmelCase_ :      List[str]    				=				[]  # will be returned.

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

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

				return ans



def 			lowerCAmelCase (		lowerCAmelCase_ )-> List[Any]:
				assert isinstance(lowerCAmelCase_ ,   lowerCAmelCase_ ) and (
				    number > 1
				), "'number' must been an int and >= 1"

				lowerCAmelCase_ :      Tuple    				=				get_divisors(lowerCAmelCase_ )

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

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



def 			lowerCAmelCase (		lowerCAmelCase_ ,   lowerCAmelCase_ )-> Any:
				assert (
				    isinstance(lowerCAmelCase_ ,   lowerCAmelCase_ )
				    and isinstance(lowerCAmelCase_ ,   lowerCAmelCase_ )
				    and (denominator != 0)
				), "The arguments must been from type int and 'denominator' != 0"

				# build the greatest common divisor of numerator and denominator.
				lowerCAmelCase_ :      List[str]    				=				gcd(abs(lowerCAmelCase_ ) ,   abs(lowerCAmelCase_ ) )

				# precondition
				assert (
				    isinstance(lowerCAmelCase_ ,   lowerCAmelCase_ )
				    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 			lowerCAmelCase (		lowerCAmelCase_ )-> List[Any]:
				assert isinstance(lowerCAmelCase_ ,   lowerCAmelCase_ ) and (n >= 0), "'n' must been a int and >= 0"

				lowerCAmelCase_ :      Tuple    				=				1  # this will be return.

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

				return ans




def 			lowerCAmelCase (		lowerCAmelCase_ )-> Tuple:
				assert isinstance(lowerCAmelCase_ ,   lowerCAmelCase_ ) and (n >= 0), "'n' must been an int and >= 0"

				lowerCAmelCase_ :      Tuple    				=				0
				lowerCAmelCase_ :      Optional[Any]    				=				1
				lowerCAmelCase_ :      Tuple    				=				1  # this will be return

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

				return ans