
'''simple docstring'''


from math import sqrt



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

   UpperCamelCase	  =	True

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

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

   return status



def 			__snake_case  (     _UpperCAmelCase       :							Tuple):
   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
   UpperCamelCase	  =	list(range(2,   n + 1))

   UpperCamelCase	  =	[]  # 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):
            UpperCamelCase	  =	0

    # filters actual prime numbers.
   UpperCamelCase	  =	[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  (     _UpperCAmelCase       :							str):
   assert isinstance(__snake_case,   __snake_case) and (n > 2), "'N' must been an int and > 2"

   UpperCamelCase	  =	[]

   # 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  (     _UpperCAmelCase       :							List[Any]):
   assert isinstance(__snake_case,   __snake_case) and number >= 0, "'number' must been an int and >= 0"

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

   # potential prime number factors.

   UpperCamelCase	  =	2

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

   UpperCamelCase	  =	0

   # prime factorization of 'number'
   UpperCamelCase	  =	prime_factorization(__snake_case)

   UpperCamelCase	  =	max(__snake_case)

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

   return ans



def 			__snake_case  (     _UpperCAmelCase       :							Optional[Any]):
   assert isinstance(__snake_case,   __snake_case) and (
       number >= 0
   ), "'number' bust been an int and >= 0"

   UpperCamelCase	  =	0

   # prime factorization of 'number'
   UpperCamelCase	  =	prime_factorization(__snake_case)

   UpperCamelCase	  =	min(__snake_case)

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

   return ans



def 			__snake_case  (     _UpperCAmelCase       :							Union[str, 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  (     _UpperCAmelCase       :							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  (     _UpperCAmelCase       :							Union[str, Any]):
   assert (
       isinstance(__snake_case,   __snake_case) and (number > 2) and is_even(__snake_case)
   ), "'number' must been an int, even and > 2"

   UpperCamelCase	  =	[]  # this list will returned

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

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

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

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

      while j < len_pn and loop:
         if prime_numbers[i] + prime_numbers[j] == number:
            UpperCamelCase	  =	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  (     _UpperCAmelCase       :							Union[str, Any],   _UpperCAmelCase       :							int):
   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."

   UpperCamelCase	  =	0

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

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

   return numbera



def 			__snake_case  (     _UpperCAmelCase       :							Optional[int],   _UpperCAmelCase       :							List[Any]):
   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."

   UpperCamelCase	  =	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'
      UpperCamelCase	  =	prime_factorization(__snake_case)
      UpperCamelCase	  =	prime_factorization(__snake_case)

   elif numbera == 1 or numbera == 1:
      UpperCamelCase	  =	[]
      UpperCamelCase	  =	[]
      UpperCamelCase	  =	max(__snake_case,   __snake_case)

   UpperCamelCase	  =	0
   UpperCamelCase	  =	0

   UpperCamelCase	  =	[]  # 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:
            UpperCamelCase	  =	prime_fac_a.count(__snake_case)
            UpperCamelCase	  =	prime_fac_a.count(__snake_case)

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

         else:
            UpperCamelCase	  =	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:
         UpperCamelCase	  =	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  (     _UpperCAmelCase       :							Optional[Any]):
   assert isinstance(__snake_case,   __snake_case) and (n >= 0), "'number' must been a positive int"

   UpperCamelCase	  =	0
   UpperCamelCase	  =	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  (     _UpperCAmelCase       :							Optional[int],   _UpperCAmelCase       :							Optional[int]):
   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'"

   UpperCamelCase	  =	p_number_a + 1  # jump to the next number

   UpperCamelCase	  =	[]  # 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  (     _UpperCAmelCase       :							Dict):
   assert isinstance(__snake_case,   __snake_case) and (n >= 1), "'n' must been int and >= 1"

   UpperCamelCase	  =	[]  # 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  (     _UpperCAmelCase       :							Union[str, Any]):
   assert isinstance(__snake_case,   __snake_case) and (
       number > 1
   ), "'number' must been an int and >= 1"

   UpperCamelCase	  =	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  (     _UpperCAmelCase       :							Any,   _UpperCAmelCase       :							int):
   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.
   UpperCamelCase	  =	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  (     _UpperCAmelCase       :							Tuple):
   assert isinstance(__snake_case,   __snake_case) and (n >= 0), "'n' must been a int and >= 0"

   UpperCamelCase	  =	1  # this will be return.

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

   return ans



def 			__snake_case  (     _UpperCAmelCase       :							str):
   assert isinstance(__snake_case,   __snake_case) and (n >= 0), "'n' must been an int and >= 0"

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

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


lowercase__       : Dict         =       logging.getLogger(__name__)


@dataclass
@add_start_docstrings(TrainingArguments.__doc__				)
class 					SCREAMING_SNAKE_CASE       (a__				):
     lowerCAmelCase						     =			field(default=a__   ,						metadata={'''help''': '''Whether to use SortishSampler or not.'''}				)
     lowerCAmelCase						     =			field(
         default=a__   ,						metadata={'''help''': '''Whether to use generate to calculate generative metrics (ROUGE, BLEU).'''}				)
     lowerCAmelCase						     =			field(
         default=a__   ,						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.'''
             )
         }   ,						)
     lowerCAmelCase						     =			field(
         default=a__   ,						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.'''
             )
         }   ,						)
     lowerCAmelCase						     =			field(
         default=a__   ,						metadata={
             '''help''': '''Model id, file path or url pointing to a GenerationConfig json file, to use during prediction.'''
         }   ,						)


     def 				SCREAMING_SNAKE_CASE    (		self):

          '''simple docstring'''






          __A		:					List[Any]						=			super().to_dict()
          for k, v in d.items():
               if isinstance(_UpperCAmelCase		,      _UpperCAmelCase):
                    __A		:					List[Any]						=			v.to_dict()
          return d