


'''simple docstring'''

from math import sqrt





def __snake_case					(      UpperCAmelCase_						:						int		):
 assert isinstance(UpperCAmelCase_					,				UpperCAmelCase_		) 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(UpperCAmelCase_		)		)		) + 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(UpperCAmelCase_					,				UpperCAmelCase_		), "'status' must been from type bool"

 return status





def __snake_case					(      UpperCAmelCase_						:						List[Any]		):
 assert isinstance(UpperCAmelCase_					,				UpperCAmelCase_		) 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(UpperCAmelCase_		)		):
  for j in range(i + 1					,				len(UpperCAmelCase_		)		):
   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(UpperCAmelCase_					,				UpperCAmelCase_		), "'ans' must been from type list"

 return ans





def __snake_case					(      UpperCAmelCase_						:						Optional[int]		):
 assert isinstance(UpperCAmelCase_					,				UpperCAmelCase_		) 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(UpperCAmelCase_		):
   ans.append(UpperCAmelCase_		)

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

 return ans





def __snake_case					(      UpperCAmelCase_						:						List[str]		):
 assert isinstance(UpperCAmelCase_					,				UpperCAmelCase_		) 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(UpperCAmelCase_		)

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

 else:
  ans.append(UpperCAmelCase_		)

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

 return ans





def __snake_case					(      UpperCAmelCase_						:						Dict		):
 assert isinstance(UpperCAmelCase_					,				UpperCAmelCase_		) and (
     number >= 0
 ), "'number' bust been an int and >= 0"

 lowerCamelCase_      =  0

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

 lowerCamelCase_      =  max(UpperCAmelCase_		)

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

 return ans





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

 lowerCamelCase_      =  0

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

 lowerCamelCase_      =  min(UpperCAmelCase_		)

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

 return ans





def __snake_case					(      UpperCAmelCase_						:						List[Any]		):
 assert isinstance(UpperCAmelCase_					,				UpperCAmelCase_		), "'number' must been an int"
 assert isinstance(number % 2 == 0					,				UpperCAmelCase_		), "compare bust been from type bool"

 return number % 2 == 0





def __snake_case					(      UpperCAmelCase_						:						Dict		):
 assert isinstance(UpperCAmelCase_					,				UpperCAmelCase_		), "'number' must been an int"
 assert isinstance(number % 2 != 0					,				UpperCAmelCase_		), "compare bust been from type bool"

 return number % 2 != 0





def __snake_case					(      UpperCAmelCase_						:						List[str]		):
 assert (
     isinstance(UpperCAmelCase_					,				UpperCAmelCase_		) and (number > 2) and is_even(UpperCAmelCase_		)
 ), "'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(UpperCAmelCase_		)
 lowerCamelCase_      =  len(UpperCAmelCase_		)

 # 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(UpperCAmelCase_					,				UpperCAmelCase_		)
     and (len(UpperCAmelCase_		) == 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_						:						Optional[Any]					,				UpperCAmelCase_						:						int		):
 assert (
     isinstance(UpperCAmelCase_					,				UpperCAmelCase_		)
     and isinstance(UpperCAmelCase_					,				UpperCAmelCase_		)
     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(UpperCAmelCase_					,				UpperCAmelCase_		) and (
     numbera >= 0
 ), "'number' must been from type int and positive"

 return numbera





def __snake_case					(      UpperCAmelCase_						:						List[Any]					,				UpperCAmelCase_						:						int		):
 assert (
     isinstance(UpperCAmelCase_					,				UpperCAmelCase_		)
     and isinstance(UpperCAmelCase_					,				UpperCAmelCase_		)
     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(UpperCAmelCase_		)
  lowerCamelCase_      =  prime_factorization(UpperCAmelCase_		)

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

 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(UpperCAmelCase_		)
    lowerCamelCase_      =  prime_fac_a.count(UpperCAmelCase_		)

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

   else:
    lowerCamelCase_      =  prime_fac_a.count(UpperCAmelCase_		)

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

   done.append(UpperCAmelCase_		)

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

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

   done.append(UpperCAmelCase_		)

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

 return ans





def __snake_case					(      UpperCAmelCase_						:						Tuple		):
 assert isinstance(UpperCAmelCase_					,				UpperCAmelCase_		) 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(UpperCAmelCase_		):
   ans += 1

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

 return ans





def __snake_case					(      UpperCAmelCase_						:						str					,				UpperCAmelCase_						:						Optional[Any]		):
 assert (
     is_prime(UpperCAmelCase_		) and is_prime(UpperCAmelCase_		) 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(UpperCAmelCase_		):
  number += 1

 while number < p_number_a:
  ans.append(UpperCAmelCase_		)

  number += 1

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

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

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





def __snake_case					(      UpperCAmelCase_						:						Union[str, Any]		):
 assert isinstance(UpperCAmelCase_					,				UpperCAmelCase_		) 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(UpperCAmelCase_		)

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

 return ans





def __snake_case					(      UpperCAmelCase_						:						Optional[int]		):
 assert isinstance(UpperCAmelCase_					,				UpperCAmelCase_		) and (
     number > 1
 ), "'number' must been an int and >= 1"

 lowerCamelCase_      =  get_divisors(UpperCAmelCase_		)

 # precondition
 assert (
     isinstance(UpperCAmelCase_					,				UpperCAmelCase_		)
     and (divisors[0] == 1)
     and (divisors[len(UpperCAmelCase_		) - 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_						:						Optional[Any]					,				UpperCAmelCase_						:						Dict		):
 assert (
     isinstance(UpperCAmelCase_					,				UpperCAmelCase_		)
     and isinstance(UpperCAmelCase_					,				UpperCAmelCase_		)
     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(UpperCAmelCase_		)					,				abs(UpperCAmelCase_		)		)

 # precondition
 assert (
     isinstance(UpperCAmelCase_					,				UpperCAmelCase_		)
     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(UpperCAmelCase_					,				UpperCAmelCase_		) 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 __snake_case					(      UpperCAmelCase_						:						Dict		):
 assert isinstance(UpperCAmelCase_					,				UpperCAmelCase_		) 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"""






from ...configuration_utils import PretrainedConfig
from ...utils import logging


lowerCAmelCase__  :  int						     =	logging.get_logger(__name__)

lowerCAmelCase__  :  str						     =	{
    'facebook/xglm-564M': 'https://huggingface.co/facebook/xglm-564M/resolve/main/config.json',
    # See all XGLM models at https://huggingface.co/models?filter=xglm
}
class 				snake_case       ( __UpperCAmelCase				):




					"""simple docstring"""

					snake_case__				    = "xglm"
					snake_case__				    = ["past_key_values"]

					snake_case__				    = {
					    "num_attention_heads": "attention_heads",
					    "hidden_size": "d_model",
					    "num_hidden_layers": "num_layers",
					}







					def __init__(				self   :	Any    ,lowerCamelCase__   :	Any=256_008    ,lowerCamelCase__   :	Optional[Any]=2_048    ,lowerCamelCase__   :	List[str]=1_024    ,lowerCamelCase__   :	List[str]=4_096    ,lowerCamelCase__   :	Tuple=24    ,lowerCamelCase__   :	Optional[int]=16    ,lowerCamelCase__   :	int="gelu"    ,lowerCamelCase__   :	Dict=0.1    ,lowerCamelCase__   :	int=0.1    ,lowerCamelCase__   :	List[Any]=0.0    ,lowerCamelCase__   :	List[str]=0.0    ,lowerCamelCase__   :	Optional[Any]=0.0_2    ,lowerCamelCase__   :	List[str]=True    ,lowerCamelCase__   :	Optional[Any]=True    ,lowerCamelCase__   :	str=2    ,lowerCamelCase__   :	Dict=1    ,lowerCamelCase__   :	Optional[int]=0    ,lowerCamelCase__   :	Tuple=2    ,**lowerCamelCase__   :	List[Any]    ,):
									UpperCAmelCase__             =							vocab_size
									UpperCAmelCase__             =							max_position_embeddings
									UpperCAmelCase__             =							d_model
									UpperCAmelCase__             =							ffn_dim
									UpperCAmelCase__             =							num_layers
									UpperCAmelCase__             =							attention_heads
									UpperCAmelCase__             =							activation_function
									UpperCAmelCase__             =							dropout
									UpperCAmelCase__             =							attention_dropout
									UpperCAmelCase__             =							activation_dropout
									UpperCAmelCase__             =							layerdrop
									UpperCAmelCase__             =							init_std
									UpperCAmelCase__             =							scale_embedding  # scale factor will be sqrt(d_model) if True
									UpperCAmelCase__             =							use_cache

									super().__init__(
									    pad_token_id=lowerCamelCase__    ,bos_token_id=lowerCamelCase__    ,eos_token_id=lowerCamelCase__    ,decoder_start_token_id=lowerCamelCase__    ,**lowerCamelCase__    ,)



