
"""simple docstring"""


from math import sqrt






def    _snake_case					(		snake_case__ :  int  ):
	assert isinstance(snake_case__						,   snake_case__  ) and (
	    number >= 0
	), "'number' must been an int and positive"

	A     = True

	# 0 and 1 are none primes.
	if number <= 1:
		A     = False

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

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

	return status






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

	# beginList: contains all natural numbers from 2 up to N
	A     = list(range(2						,   n + 1  )  )

	A     = []  # this list will be returns.

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

    # filters actual prime numbers.
	A     = [x for x in begin_list if x != 0]

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

	return ans






def    _snake_case					(		snake_case__ :  int  ):
	assert isinstance(snake_case__						,   snake_case__  ) and (n > 2), "'N' must been an int and > 2"

	A     = []

	# 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(snake_case__  ):
			ans.append(snake_case__  )

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

	return ans






def    _snake_case					(		snake_case__ :  str  ):
	assert isinstance(snake_case__						,   snake_case__  ) and number >= 0, "'number' must been an int and >= 0"

	A     = []  # this list will be returns of the function.

	# potential prime number factors.

	A     = 2

	A     = number

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

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

	else:
		ans.append(snake_case__  )

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

	return ans






def    _snake_case					(		snake_case__ :  str  ):
	assert isinstance(snake_case__						,   snake_case__  ) and (
	    number >= 0
	), "'number' bust been an int and >= 0"

	A     = 0

	# prime factorization of 'number'
	A     = prime_factorization(snake_case__  )

	A     = max(snake_case__  )

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

	return ans






def    _snake_case					(		snake_case__ :  Tuple  ):
	assert isinstance(snake_case__						,   snake_case__  ) and (
	    number >= 0
	), "'number' bust been an int and >= 0"

	A     = 0

	# prime factorization of 'number'
	A     = prime_factorization(snake_case__  )

	A     = min(snake_case__  )

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

	return ans






def    _snake_case					(		snake_case__ :  Any  ):
	assert isinstance(snake_case__						,   snake_case__  ), "'number' must been an int"
	assert isinstance(number % 2 == 0						,   snake_case__  ), "compare bust been from type bool"

	return number % 2 == 0






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

	return number % 2 != 0






def    _snake_case					(		snake_case__ :  int  ):
	assert (
	    isinstance(snake_case__						,   snake_case__  ) and (number > 2) and is_even(snake_case__  )
	), "'number' must been an int, even and > 2"

	A     = []  # this list will returned

	# creates a list of prime numbers between 2 up to 'number'
	A     = get_prime_numbers(snake_case__  )
	A     = len(snake_case__  )

	# run variable for while-loops.
	A     = 0
	A     = None

	# exit variable. for break up the loops
	A     = True

	while i < len_pn and loop:
		A     = i + 1

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

			j += 1

		i += 1

	# precondition
	assert (
	    isinstance(snake_case__						,   snake_case__  )
	    and (len(snake_case__  ) == 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    _snake_case					(		snake_case__ :  str						,   snake_case__ :  Union[str, Any]  ):
	assert (
	    isinstance(snake_case__						,   snake_case__  )
	    and isinstance(snake_case__						,   snake_case__  )
	    and (numbera >= 0)
	    and (numbera >= 0)
	), "'number1' and 'number2' must been positive integer."

	A     = 0

	while numbera != 0:
		A     = numbera % numbera
		A     = numbera
		A     = rest

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

	return numbera






def    _snake_case					(		snake_case__ :  Tuple						,   snake_case__ :  List[str]  ):
	assert (
	    isinstance(snake_case__						,   snake_case__  )
	    and isinstance(snake_case__						,   snake_case__  )
	    and (numbera >= 1)
	    and (numbera >= 1)
	), "'number1' and 'number2' must been positive integer."

	A     = 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'
		A     = prime_factorization(snake_case__  )
		A     = prime_factorization(snake_case__  )

	elif numbera == 1 or numbera == 1:
		A     = []
		A     = []
		A     = max(snake_case__						,   snake_case__  )

	A     = 0
	A     = 0

	A     = []  # 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:
				A     = prime_fac_a.count(snake_case__  )
				A     = prime_fac_a.count(snake_case__  )

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

			else:
				A     = prime_fac_a.count(snake_case__  )

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

			done.append(snake_case__  )

    # iterates through primeFac2
	for n in prime_fac_a:
		if n not in done:
			A     = prime_fac_a.count(snake_case__  )

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

			done.append(snake_case__  )

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

	return ans






def    _snake_case					(		snake_case__ :  int  ):
	assert isinstance(snake_case__						,   snake_case__  ) and (n >= 0), "'number' must been a positive int"

	A     = 0
	A     = 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(snake_case__  ):
			ans += 1

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

	return ans






def    _snake_case					(		snake_case__ :  int						,   snake_case__ :  Any  ):
	assert (
	    is_prime(snake_case__  ) and is_prime(snake_case__  ) and (p_number_a < p_number_a)
	), "The arguments must been prime numbers and 'pNumber1' < 'pNumber2'"

	A     = p_number_a + 1  # jump to the next number

	A     = []  # this list will be returns.

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

	while number < p_number_a:
		ans.append(snake_case__  )

		number += 1

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

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

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






def    _snake_case					(		snake_case__ :  int  ):
	assert isinstance(snake_case__						,   snake_case__  ) and (n >= 1), "'n' must been int and >= 1"

	A     = []  # will be returned.

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

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

	return ans






def    _snake_case					(		snake_case__ :  Tuple  ):
	assert isinstance(snake_case__						,   snake_case__  ) and (
	    number > 1
	), "'number' must been an int and >= 1"

	A     = get_divisors(snake_case__  )

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

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






def    _snake_case					(		snake_case__ :  str						,   snake_case__ :  List[str]  ):
	assert (
	    isinstance(snake_case__						,   snake_case__  )
	    and isinstance(snake_case__						,   snake_case__  )
	    and (denominator != 0)
	), "The arguments must been from type int and 'denominator' != 0"

	# build the greatest common divisor of numerator and denominator.
	A     = gcd(abs(snake_case__  )						,   abs(snake_case__  )  )

	# precondition
	assert (
	    isinstance(snake_case__						,   snake_case__  )
	    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    _snake_case					(		snake_case__ :  Any  ):
	assert isinstance(snake_case__						,   snake_case__  ) and (n >= 0), "'n' must been a int and >= 0"

	A     = 1  # this will be return.

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

	return ans






def    _snake_case					(		snake_case__ :  List[str]  ):
	assert isinstance(snake_case__						,   snake_case__  ) and (n >= 0), "'n' must been an int and >= 0"

	A     = 0
	A     = 1
	A     = 1  # this will be return

	for _ in range(n - 1  ):
		A     = ans
		ans += fiba
		A     = tmp

	return ans




'''simple docstring'''

import faiss  # noqa: F401 # Here to have a nice missing dependency error message early on
import numpy  # noqa: F401 # Here to have a nice missing dependency error message early on
import requests  # noqa: F401 # Here to have a nice missing dependency error message early on
import sklearn  # noqa: F401 # Here to have a nice missing dependency error message early on
import tqdm  # noqa: F401 # Here to have a nice missing dependency error message early on
from mauve import compute_mauve  # From: mauve-text

import datasets


__lowerCAmelCase		     =  '''\
@inproceedings{pillutla-etal:mauve:neurips2021,
  title={MAUVE: Measuring the Gap Between Neural Text and Human Text using Divergence Frontiers},
  author={Pillutla, Krishna and Swayamdipta, Swabha and Zellers, Rowan and Thickstun, John and Welleck, Sean and Choi, Yejin and Harchaoui, Zaid},
  booktitle = {NeurIPS},
  year      = {2021}
}

'''

__lowerCAmelCase		     =  '''\
MAUVE is a library built on PyTorch and HuggingFace Transformers to measure the gap between neural text and human text with the eponymous MAUVE measure.

MAUVE summarizes both Type I and Type II errors measured softly using Kullback–Leibler (KL) divergences.

For details, see the MAUVE paper: https://arxiv.org/abs/2102.01454 (Neurips, 2021).

This metrics is a wrapper around the official implementation of MAUVE:
https://github.com/krishnap25/mauve
'''

__lowerCAmelCase		     =  '''
Calculates MAUVE scores between two lists of generated text and reference text.
Args:
    predictions: list of generated text to score. Each predictions
        should be a string with tokens separated by spaces.
    references: list of reference for each prediction. Each
        reference should be a string with tokens separated by spaces.
Optional Args:
    num_buckets: the size of the histogram to quantize P and Q. Options: \'auto\' (default) or an integer
    pca_max_data: the number data points to use for PCA dimensionality reduction prior to clustering. If -1, use all the data. Default -1
    kmeans_explained_var: amount of variance of the data to keep in dimensionality reduction by PCA. Default 0.9
    kmeans_num_redo: number of times to redo k-means clustering (the best objective is kept). Default 5
    kmeans_max_iter: maximum number of k-means iterations. Default 500
    featurize_model_name: name of the model from which features are obtained. Default \'gpt2-large\' Use one of [\'gpt2\', \'gpt2-medium\', \'gpt2-large\', \'gpt2-xl\'].
    device_id: Device for featurization. Supply a GPU id (e.g. 0 or 3) to use GPU. If no GPU with this id is found, use CPU
    max_text_length: maximum number of tokens to consider. Default 1024
    divergence_curve_discretization_size: Number of points to consider on the divergence curve. Default 25
    mauve_scaling_factor: "c" from the paper. Default 5.
    verbose: If True (default), print running time updates
    seed: random seed to initialize k-means cluster assignments.
Returns:
    mauve: MAUVE score, a number between 0 and 1. Larger values indicate that P and Q are closer,
    frontier_integral: Frontier Integral, a number between 0 and 1. Smaller values indicate that P and Q are closer,
    divergence_curve: a numpy.ndarray of shape (m, 2); plot it with matplotlib to view the divergence curve,
    p_hist: a discrete distribution, which is a quantized version of the text distribution p_text,
    q_hist: same as above, but with q_text.
Examples:

    >>> # faiss segfaults in doctest for some reason, so the .compute call is not tested with doctest
    >>> import datasets
    >>> mauve = datasets.load_metric(\'mauve\')
    >>> predictions = ["hello there", "general kenobi"]
    >>> references = ["hello there", "general kenobi"]
    >>> out = mauve.compute(predictions=predictions, references=references) # doctest: +SKIP
    >>> print(out.mauve) # doctest: +SKIP
    1.0
'''

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







							def 				__lowercase     (				self   :			Optional[Any]						):
									return datasets.MetricInfo(
									    description=_DESCRIPTION      ,citation=_CITATION      ,homepage='https://github.com/krishnap25/mauve'      ,inputs_description=_KWARGS_DESCRIPTION      ,features=datasets.Features(
									        {
									            'predictions': datasets.Value('string'      ,id='sequence'						),
									            'references': datasets.Value('string'      ,id='sequence'						),
									        }						)      ,codebase_urls=['https://github.com/krishnap25/mauve']      ,reference_urls=[
									        'https://arxiv.org/abs/2102.01454',
									        'https://github.com/krishnap25/mauve',
									    ]      ,)







							def 				__lowercase     (				self   :			Tuple      ,_UpperCAmelCase   :			Optional[Any]      ,_UpperCAmelCase   :			Dict      ,_UpperCAmelCase   :			Any=None      ,_UpperCAmelCase   :			Tuple=None      ,_UpperCAmelCase   :			List[str]=None      ,_UpperCAmelCase   :			Optional[Any]=None      ,_UpperCAmelCase   :			Any="auto"      ,_UpperCAmelCase   :			Tuple=-1      ,_UpperCAmelCase   :			Union[str, Any]=0.9      ,_UpperCAmelCase   :			List[Any]=5      ,_UpperCAmelCase   :			Optional[int]=500      ,_UpperCAmelCase   :			int="gpt2-large"      ,_UpperCAmelCase   :			int=-1      ,_UpperCAmelCase   :			Tuple=1024      ,_UpperCAmelCase   :			Any=25      ,_UpperCAmelCase   :			int=5      ,_UpperCAmelCase   :			Optional[int]=True      ,_UpperCAmelCase   :			Optional[int]=25      ,):
									_a	: Any								=				compute_mauve(
									    p_text=_UpperCAmelCase      ,q_text=_UpperCAmelCase      ,p_features=_UpperCAmelCase      ,q_features=_UpperCAmelCase      ,p_tokens=_UpperCAmelCase      ,q_tokens=_UpperCAmelCase      ,num_buckets=_UpperCAmelCase      ,pca_max_data=_UpperCAmelCase      ,kmeans_explained_var=_UpperCAmelCase      ,kmeans_num_redo=_UpperCAmelCase      ,kmeans_max_iter=_UpperCAmelCase      ,featurize_model_name=_UpperCAmelCase      ,device_id=_UpperCAmelCase      ,max_text_length=_UpperCAmelCase      ,divergence_curve_discretization_size=_UpperCAmelCase      ,mauve_scaling_factor=_UpperCAmelCase      ,verbose=_UpperCAmelCase      ,seed=_UpperCAmelCase      ,)
									return out




