






from typing import Dict, Optional

import numpy as np

import datasets


A        =			'\nIoU is the area of overlap between the predicted segmentation and the ground truth divided by the area of union\nbetween the predicted segmentation and the ground truth. For binary (two classes) or multi-class segmentation,\nthe mean IoU of the image is calculated by taking the IoU of each class and averaging them.\n'

A        =			'\nArgs:\n    predictions (`List[ndarray]`):\n        List of predicted segmentation maps, each of shape (height, width). Each segmentation map can be of a different size.\n    references (`List[ndarray]`):\n        List of ground truth segmentation maps, each of shape (height, width). Each segmentation map can be of a different size.\n    num_labels (`int`):\n        Number of classes (categories).\n    ignore_index (`int`):\n        Index that will be ignored during evaluation.\n    nan_to_num (`int`, *optional*):\n        If specified, NaN values will be replaced by the number defined by the user.\n    label_map (`dict`, *optional*):\n        If specified, dictionary mapping old label indices to new label indices.\n    reduce_labels (`bool`, *optional*, defaults to `False`):\n        Whether or not to reduce all label values of segmentation maps by 1. Usually used for datasets where 0 is used for background,\n        and background itself is not included in all classes of a dataset (e.g. ADE20k). The background label will be replaced by 255.\n\nReturns:\n    `Dict[str, float | ndarray]` comprising various elements:\n    - *mean_iou* (`float`):\n        Mean Intersection-over-Union (IoU averaged over all categories).\n    - *mean_accuracy* (`float`):\n        Mean accuracy (averaged over all categories).\n    - *overall_accuracy* (`float`):\n        Overall accuracy on all images.\n    - *per_category_accuracy* (`ndarray` of shape `(num_labels,)`):\n        Per category accuracy.\n    - *per_category_iou* (`ndarray` of shape `(num_labels,)`):\n        Per category IoU.\n\nExamples:\n\n    >>> import numpy as np\n\n    >>> mean_iou = datasets.load_metric("mean_iou")\n\n    >>> # suppose one has 3 different segmentation maps predicted\n    >>> predicted_1 = np.array([[1, 2], [3, 4], [5, 255]])\n    >>> actual_1 = np.array([[0, 3], [5, 4], [6, 255]])\n\n    >>> predicted_2 = np.array([[2, 7], [9, 2], [3, 6]])\n    >>> actual_2 = np.array([[1, 7], [9, 2], [3, 6]])\n\n    >>> predicted_3 = np.array([[2, 2, 3], [8, 2, 4], [3, 255, 2]])\n    >>> actual_3 = np.array([[1, 2, 2], [8, 2, 1], [3, 255, 1]])\n\n    >>> predicted = [predicted_1, predicted_2, predicted_3]\n    >>> ground_truth = [actual_1, actual_2, actual_3]\n\n    >>> results = mean_iou.compute(predictions=predicted, references=ground_truth, num_labels=10, ignore_index=255, reduce_labels=False)\n    >>> print(results) # doctest: +NORMALIZE_WHITESPACE\n    {\'mean_iou\': 0.47750000000000004, \'mean_accuracy\': 0.5916666666666666, \'overall_accuracy\': 0.5263157894736842, \'per_category_iou\': array([0.   , 0.   , 0.375, 0.4  , 0.5  , 0.   , 0.5  , 1.   , 1.   , 1.   ]), \'per_category_accuracy\': array([0.        , 0.        , 0.75      , 0.66666667, 1.        , 0.        , 0.5       , 1.        , 1.        , 1.        ])}\n'

A        =			'\\n@software{MMSegmentation_Contributors_OpenMMLab_Semantic_Segmentation_2020,\nauthor = {{MMSegmentation Contributors}},\nlicense = {Apache-2.0},\nmonth = {7},\ntitle = {{OpenMMLab Semantic Segmentation Toolbox and Benchmark}},\nurl = {https://github.com/open-mmlab/mmsegmentation},\nyear = {2020}\n}'



def 					_lowerCamelCase(			lowerCAmelCase__				:		str    ,    lowerCAmelCase__				:		List[Any]    ,    lowerCAmelCase__				:		str    ,    lowerCAmelCase__				:		bool    ,    lowerCAmelCase__				:		Optional[Dict[int, int]] = None    ,    lowerCAmelCase__				:		bool = False    ,    ):





				'''simple docstring'''







				if label_map is not None:
								for old_id, new_id in label_map.items():
												SCREAMING_SNAKE_CASE_   :	Union[str, Any]													=   new_id

    # turn into Numpy arrays
				SCREAMING_SNAKE_CASE_   :	Optional[int]													=   np.array(lowerCAmelCase__      )
				SCREAMING_SNAKE_CASE_   :	str													=   np.array(lowerCAmelCase__      )

				if reduce_labels:
								SCREAMING_SNAKE_CASE_   :	Optional[int]													=   255
								SCREAMING_SNAKE_CASE_   :	Optional[int]													=   label - 1
								SCREAMING_SNAKE_CASE_   :	Dict													=   255

				SCREAMING_SNAKE_CASE_   :	List[Any]													=   label != ignore_index
				SCREAMING_SNAKE_CASE_   :	str													=   np.not_equal(lowerCAmelCase__    ,    lowerCAmelCase__      )
				SCREAMING_SNAKE_CASE_   :	Tuple													=   pred_label[mask]
				SCREAMING_SNAKE_CASE_   :	Tuple													=   np.array(lowerCAmelCase__      )[mask]

				SCREAMING_SNAKE_CASE_   :	Optional[Any]													=   pred_label[pred_label == label]

				SCREAMING_SNAKE_CASE_   :	Optional[Any]													=   np.histogram(lowerCAmelCase__    ,    bins=lowerCAmelCase__    ,    range=(0, num_labels - 1)      )[0]
				SCREAMING_SNAKE_CASE_   :	int													=   np.histogram(lowerCAmelCase__    ,    bins=lowerCAmelCase__    ,    range=(0, num_labels - 1)      )[0]
				SCREAMING_SNAKE_CASE_   :	str													=   np.histogram(lowerCAmelCase__    ,    bins=lowerCAmelCase__    ,    range=(0, num_labels - 1)      )[0]

				SCREAMING_SNAKE_CASE_   :	str													=   area_pred_label + area_label - area_intersect

				return area_intersect, area_union, area_pred_label, area_label



def 					_lowerCamelCase(			lowerCAmelCase__				:		Optional[int]    ,    lowerCAmelCase__				:		Union[str, Any]    ,    lowerCAmelCase__				:		List[str]    ,    lowerCAmelCase__				:		bool    ,    lowerCAmelCase__				:		Optional[Dict[int, int]] = None    ,    lowerCAmelCase__				:		bool = False    ,    ):





				'''simple docstring'''







				SCREAMING_SNAKE_CASE_   :	Optional[int]													=   np.zeros((num_labels,)    ,    dtype=np.floataa      )
				SCREAMING_SNAKE_CASE_   :	List[str]													=   np.zeros((num_labels,)    ,    dtype=np.floataa      )
				SCREAMING_SNAKE_CASE_   :	Tuple													=   np.zeros((num_labels,)    ,    dtype=np.floataa      )
				SCREAMING_SNAKE_CASE_   :	Optional[int]													=   np.zeros((num_labels,)    ,    dtype=np.floataa      )
				for result, gt_seg_map in zip(lowerCAmelCase__    ,    lowerCAmelCase__      ):
								SCREAMING_SNAKE_CASE_							,       SCREAMING_SNAKE_CASE_							,       SCREAMING_SNAKE_CASE_							,       SCREAMING_SNAKE_CASE_   :	Dict													=   intersect_and_union(
								    lowerCAmelCase__    ,    lowerCAmelCase__    ,    lowerCAmelCase__    ,    lowerCAmelCase__    ,    lowerCAmelCase__    ,    lowerCAmelCase__      )
								total_area_intersect += area_intersect
								total_area_union += area_union
								total_area_pred_label += area_pred_label
								total_area_label += area_label
				return total_area_intersect, total_area_union, total_area_pred_label, total_area_label



def 					_lowerCamelCase(			lowerCAmelCase__				:		int    ,    lowerCAmelCase__				:		List[str]    ,    lowerCAmelCase__				:		Tuple    ,    lowerCAmelCase__				:		bool    ,    lowerCAmelCase__				:		Optional[int] = None    ,    lowerCAmelCase__				:		Optional[Dict[int, int]] = None    ,    lowerCAmelCase__				:		bool = False    ,    ):





				'''simple docstring'''







				SCREAMING_SNAKE_CASE_							,       SCREAMING_SNAKE_CASE_							,       SCREAMING_SNAKE_CASE_							,       SCREAMING_SNAKE_CASE_   :	int													=   total_intersect_and_union(
				    lowerCAmelCase__    ,    lowerCAmelCase__    ,    lowerCAmelCase__    ,    lowerCAmelCase__    ,    lowerCAmelCase__    ,    lowerCAmelCase__      )

				# compute metrics
				SCREAMING_SNAKE_CASE_   :	List[Any]													=   {}

				SCREAMING_SNAKE_CASE_   :	Any													=   total_area_intersect.sum() / total_area_label.sum()
				SCREAMING_SNAKE_CASE_   :	Tuple													=   total_area_intersect / total_area_union
				SCREAMING_SNAKE_CASE_   :	List[Any]													=   total_area_intersect / total_area_label

				SCREAMING_SNAKE_CASE_   :	Tuple													=   np.nanmean(lowerCAmelCase__      )
				SCREAMING_SNAKE_CASE_   :	List[Any]													=   np.nanmean(lowerCAmelCase__      )
				SCREAMING_SNAKE_CASE_   :	Dict													=   all_acc
				SCREAMING_SNAKE_CASE_   :	Tuple													=   iou
				SCREAMING_SNAKE_CASE_   :	str													=   acc

				if nan_to_num is not None:
								SCREAMING_SNAKE_CASE_   :	Optional[int]													=   {metric: np.nan_to_num(lowerCAmelCase__    ,    nan=lowerCAmelCase__      ) for metric, metric_value in metrics.items()}

				return metrics


@datasets.utils.file_utils.add_start_docstrings(_DESCRIPTION ,	_KWARGS_DESCRIPTION						)
class 							__a							(  datasets.Metric						):





		'''simple docstring'''



		def   __snake_case			(						self       ):
						return datasets.MetricInfo(
						    description=_DESCRIPTION ,    citation=_CITATION ,    inputs_description=_KWARGS_DESCRIPTION ,    features=datasets.Features(
						        # 1st Seq - height dim, 2nd - width dim
						        {
						            'predictions': datasets.Sequence(datasets.Sequence(datasets.Value('uint16'       )       )       ),
						            'references': datasets.Sequence(datasets.Sequence(datasets.Value('uint16'       )       )       ),
						        }       ) ,    reference_urls=[
						        'https://github.com/open-mmlab/mmsegmentation/blob/71c201b1813267d78764f306a297ca717827c4bf/mmseg/core/evaluation/metrics.py'
						    ] ,    )






		def   __snake_case			(						self ,    UpperCamelCase__ ,    UpperCamelCase__ ,    UpperCamelCase__ ,    UpperCamelCase__ ,    UpperCamelCase__ = None ,    UpperCamelCase__ = None ,    UpperCamelCase__ = False ,    ):
						SCREAMING_SNAKE_CASE_   :	Union[str, Any]													=   mean_iou(
						    results=UpperCamelCase__ ,    gt_seg_maps=UpperCamelCase__ ,    num_labels=UpperCamelCase__ ,    ignore_index=UpperCamelCase__ ,    nan_to_num=UpperCamelCase__ ,    label_map=UpperCamelCase__ ,    reduce_labels=UpperCamelCase__ ,    )
						return iou_result







from math import sqrt



def 					_lowerCamelCase(			lowerCAmelCase__				:		int      ):





				'''simple docstring'''







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

				SCREAMING_SNAKE_CASE_   :	Dict													=   True

				# 0 and 1 are none primes.
				if number <= 1:
								SCREAMING_SNAKE_CASE_   :	Optional[int]													=   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:
												SCREAMING_SNAKE_CASE_   :	Dict													=   False
												break

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

				return status



def 					_lowerCamelCase(			lowerCAmelCase__				:		int      ):





				'''simple docstring'''







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

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

				SCREAMING_SNAKE_CASE_   :	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):
																SCREAMING_SNAKE_CASE_   :	str													=   0

    # filters actual prime numbers.
				SCREAMING_SNAKE_CASE_   :	int													=   [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__				:		List[str]      ):





				'''simple docstring'''







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

				SCREAMING_SNAKE_CASE_   :	int													=   []

				# 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__				:		Union[str, Any]      ):





				'''simple docstring'''







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

				SCREAMING_SNAKE_CASE_   :	Optional[int]													=   []  # this list will be returns of the function.

				# potential prime number factors.

				SCREAMING_SNAKE_CASE_   :	Optional[Any]													=   2

				SCREAMING_SNAKE_CASE_   :	List[Any]													=   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__				:		Any      ):





				'''simple docstring'''







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

				SCREAMING_SNAKE_CASE_   :	int													=   0

				# prime factorization of 'number'
				SCREAMING_SNAKE_CASE_   :	Optional[Any]													=   prime_factorization(lowerCAmelCase__      )

				SCREAMING_SNAKE_CASE_   :	Dict													=   max(lowerCAmelCase__      )

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

				return ans



def 					_lowerCamelCase(			lowerCAmelCase__				:		Optional[Any]      ):





				'''simple docstring'''







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

				SCREAMING_SNAKE_CASE_   :	Optional[int]													=   0

				# prime factorization of 'number'
				SCREAMING_SNAKE_CASE_   :	Union[str, Any]													=   prime_factorization(lowerCAmelCase__      )

				SCREAMING_SNAKE_CASE_   :	Optional[Any]													=   min(lowerCAmelCase__      )

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

				return ans



def 					_lowerCamelCase(			lowerCAmelCase__				:		Optional[int]      ):





				'''simple docstring'''







				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__				:		Optional[int]      ):





				'''simple docstring'''







				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__				:		Optional[Any]      ):





				'''simple docstring'''







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

				SCREAMING_SNAKE_CASE_   :	Any													=   []  # this list will returned

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

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

				# exit variable. for break up the loops
				SCREAMING_SNAKE_CASE_   :	Optional[Any]													=   True

				while i < len_pn and loop:
								SCREAMING_SNAKE_CASE_   :	Optional[int]													=   i + 1

								while j < len_pn and loop:
												if prime_numbers[i] + prime_numbers[j] == number:
																SCREAMING_SNAKE_CASE_   :	List[str]													=   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__				:		str    ,    lowerCAmelCase__				:		List[Any]      ):





				'''simple docstring'''







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

				SCREAMING_SNAKE_CASE_   :	int													=   0

				while numbera != 0:
								SCREAMING_SNAKE_CASE_   :	List[str]													=   numbera % numbera
								SCREAMING_SNAKE_CASE_   :	Optional[int]													=   numbera
								SCREAMING_SNAKE_CASE_   :	List[Any]													=   rest

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

				return numbera



def 					_lowerCamelCase(			lowerCAmelCase__				:		int    ,    lowerCAmelCase__				:		Optional[Any]      ):





				'''simple docstring'''







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

				SCREAMING_SNAKE_CASE_   :	Optional[Any]													=   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'
								SCREAMING_SNAKE_CASE_   :	Tuple													=   prime_factorization(lowerCAmelCase__      )
								SCREAMING_SNAKE_CASE_   :	List[Any]													=   prime_factorization(lowerCAmelCase__      )

				elif numbera == 1 or numbera == 1:
								SCREAMING_SNAKE_CASE_   :	List[Any]													=   []
								SCREAMING_SNAKE_CASE_   :	Optional[Any]													=   []
								SCREAMING_SNAKE_CASE_   :	int													=   max(lowerCAmelCase__    ,    lowerCAmelCase__      )

				SCREAMING_SNAKE_CASE_   :	Union[str, Any]													=   0
				SCREAMING_SNAKE_CASE_   :	Any													=   0

				SCREAMING_SNAKE_CASE_   :	Optional[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:
																SCREAMING_SNAKE_CASE_   :	int													=   prime_fac_a.count(lowerCAmelCase__      )
																SCREAMING_SNAKE_CASE_   :	Tuple													=   prime_fac_a.count(lowerCAmelCase__      )

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

												else:
																SCREAMING_SNAKE_CASE_   :	List[Any]													=   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:
												SCREAMING_SNAKE_CASE_   :	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__				:		Any      ):





				'''simple docstring'''







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

				SCREAMING_SNAKE_CASE_   :	Optional[int]													=   0
				SCREAMING_SNAKE_CASE_   :	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__				:		List[str]    ,    lowerCAmelCase__				:		Optional[int]      ):





				'''simple docstring'''







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

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

				SCREAMING_SNAKE_CASE_   :	List[Any]													=   []  # 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__				:		Optional[Any]      ):





				'''simple docstring'''







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

				SCREAMING_SNAKE_CASE_   :	Optional[Any]													=   []  # 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__				:		int      ):





				'''simple docstring'''







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

				SCREAMING_SNAKE_CASE_   :	int													=   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__				:		Dict    ,    lowerCAmelCase__				:		str      ):





				'''simple docstring'''







				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.
				SCREAMING_SNAKE_CASE_   :	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__				:		Tuple      ):





				'''simple docstring'''







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

				SCREAMING_SNAKE_CASE_   :	Optional[Any]													=   1  # this will be return.

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

				return ans



def 					_lowerCamelCase(			lowerCAmelCase__				:		Tuple      ):





				'''simple docstring'''







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

				SCREAMING_SNAKE_CASE_   :	List[Any]													=   0
				SCREAMING_SNAKE_CASE_   :	Union[str, Any]													=   1
				SCREAMING_SNAKE_CASE_   :	int													=   1  # this will be return

				for _ in range(n - 1      ):
								SCREAMING_SNAKE_CASE_   :	Optional[Any]													=   ans
								ans += fiba
								SCREAMING_SNAKE_CASE_   :	List[str]													=   tmp

				return ans