
"""simple docstring"""


from math import sqrt






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

			lowerCamelCase_					=  True

			# 0 and 1 are none primes.
			if number <= 1:
						lowerCamelCase_					=  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_					=  False
									break

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

			return status






def  lowercase						(	lowerCAmelCase__						):
			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_					=  list(range(2	,n + 1						)						)

			lowerCamelCase_					=  []  # 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_					=  0

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

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

			return ans






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

			lowerCamelCase_					=  []

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

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

			# potential prime number factors.

			lowerCamelCase_					=  2

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

			lowerCamelCase_					=  0

			# prime factorization of 'number'
			lowerCamelCase_					=  prime_factorization(lowerCAmelCase__						)

			lowerCamelCase_					=  max(lowerCAmelCase__						)

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

			return ans






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

			lowerCamelCase_					=  0

			# prime factorization of 'number'
			lowerCamelCase_					=  prime_factorization(lowerCAmelCase__						)

			lowerCamelCase_					=  min(lowerCAmelCase__						)

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

			return ans






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

			lowerCamelCase_					=  []  # this list will returned

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

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

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

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

						while j < len_pn and loop:
									if prime_numbers[i] + prime_numbers[j] == number:
												lowerCamelCase_					=  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  lowercase						(	lowerCAmelCase__	,lowerCAmelCase__						):
			assert (
			    isinstance(lowerCAmelCase__	,lowerCAmelCase__						)
			    and isinstance(lowerCAmelCase__	,lowerCAmelCase__						)
			    and (numbera >= 0)
			    and (numbera >= 0)
			), "'number1' and 'number2' must been positive integer."

			lowerCamelCase_					=  0

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

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

			return numbera






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

			lowerCamelCase_					=  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_					=  prime_factorization(lowerCAmelCase__						)
						lowerCamelCase_					=  prime_factorization(lowerCAmelCase__						)

			elif numbera == 1 or numbera == 1:
						lowerCamelCase_					=  []
						lowerCamelCase_					=  []
						lowerCamelCase_					=  max(lowerCAmelCase__	,lowerCAmelCase__						)

			lowerCamelCase_					=  0
			lowerCamelCase_					=  0

			lowerCamelCase_					=  []  # 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_					=  prime_fac_a.count(lowerCAmelCase__						)
												lowerCamelCase_					=  prime_fac_a.count(lowerCAmelCase__						)

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

									else:
												lowerCamelCase_					=  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_					=  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  lowercase						(	lowerCAmelCase__						):
			assert isinstance(lowerCAmelCase__	,lowerCAmelCase__						) and (n >= 0), "'number' must been a positive int"

			lowerCamelCase_					=  0
			lowerCamelCase_					=  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  lowercase						(	lowerCAmelCase__	,lowerCAmelCase__						):
			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_					=  p_number_a + 1  # jump to the next number

			lowerCamelCase_					=  []  # 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  lowercase						(	lowerCAmelCase__						):
			assert isinstance(lowerCAmelCase__	,lowerCAmelCase__						) and (n >= 1), "'n' must been int and >= 1"

			lowerCamelCase_					=  []  # 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  lowercase						(	lowerCAmelCase__						):
			assert isinstance(lowerCAmelCase__	,lowerCAmelCase__						) and (
			    number > 1
			), "'number' must been an int and >= 1"

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

			lowerCamelCase_					=  1  # this will be return.

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

			return ans






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

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

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

			return ans





"""simple docstring"""


import logging
from dataclasses import dataclass, field
from pathlib import Path
from typing import Optional, Union

from .generation.configuration_utils import GenerationConfig
from .training_args import TrainingArguments
from .utils import add_start_docstrings


A_    							=					logging.getLogger(__name__)




@dataclass
@add_start_docstrings(TrainingArguments.__doc__			)
class  __lowerCamelCase  ( lowerCAmelCase			):
				a__:      bool          =    field(default=lowerCAmelCase						,	metadata={'help': 'Whether to use SortishSampler or not.'}			)
				a__:      bool          =    field(
				    default=lowerCAmelCase						,	metadata={'help': 'Whether to use generate to calculate generative metrics (ROUGE, BLEU).'}			)
				a__:      Optional[int]          =    field(
				    default=lowerCAmelCase						,	metadata={
				        'help': (
				            'The `max_length` to use on each evaluation loop when `predict_with_generate=True`. Will default '
				            'to the `max_length` value of the model configuration.'
				        )
				    }						,	)
				a__:      Optional[int]          =    field(
				    default=lowerCAmelCase						,	metadata={
				        'help': (
				            'The `num_beams` to use on each evaluation loop when `predict_with_generate=True`. Will default '
				            'to the `num_beams` value of the model configuration.'
				        )
				    }						,	)
				a__:      Optional[Union[str, Path, GenerationConfig]]          =    field(
				    default=lowerCAmelCase						,	metadata={
				        'help': 'Model id, file path or url pointing to a GenerationConfig json file, to use during prediction.'
				    }						,	)




				def        UpperCAmelCase__						(				self   ):
							lowerCamelCase_					=  super().to_dict()
							for k, v in d.items():
										if isinstance(UpperCAmelCase							,						UpperCAmelCase   ):
													lowerCamelCase_					=  v.to_dict()
							return d



