





"""simple docstring"""





from math import sqrt
def  __A   (_SCREAMING_SNAKE_CASE			)					->bool:





  """simple docstring"""


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

  lowerCAmelCase__			:Tuple											=							True

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

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

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

  return status
def  __A   (_SCREAMING_SNAKE_CASE			)					->Dict:





  """simple docstring"""


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

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

  lowerCAmelCase__			:List[Any]											=							[]  # this list will be returns.

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

    # filters actual prime numbers.
  lowerCAmelCase__			:Union[str, Any]											=							[x for x in begin_list if x != 0]

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

  return ans
def  __A   (_SCREAMING_SNAKE_CASE			)					->int:





  """simple docstring"""


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

  lowerCAmelCase__			:Dict											=							[]

  # 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(_SCREAMING_SNAKE_CASE			):
      ans.append(_SCREAMING_SNAKE_CASE			)

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

  return ans
def  __A   (_SCREAMING_SNAKE_CASE			)					->List[Any]:





  """simple docstring"""


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

  lowerCAmelCase__			:List[str]											=							[]  # this list will be returns of the function.

  # potential prime number factors.

  lowerCAmelCase__			:Optional[Any]											=							2

  lowerCAmelCase__			:Any											=							number

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

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

  else:
    ans.append(_SCREAMING_SNAKE_CASE			)

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

  return ans
def  __A   (_SCREAMING_SNAKE_CASE			)					->List[Any]:





  """simple docstring"""


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

  lowerCAmelCase__			:Any											=							0

  # prime factorization of 'number'
  lowerCAmelCase__			:Dict											=							prime_factorization(_SCREAMING_SNAKE_CASE			)

  lowerCAmelCase__			:Tuple											=							max(_SCREAMING_SNAKE_CASE			)

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

  return ans
def  __A   (_SCREAMING_SNAKE_CASE			)					->List[Any]:





  """simple docstring"""


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

  lowerCAmelCase__			:int											=							0

  # prime factorization of 'number'
  lowerCAmelCase__			:Optional[int]											=							prime_factorization(_SCREAMING_SNAKE_CASE			)

  lowerCAmelCase__			:List[Any]											=							min(_SCREAMING_SNAKE_CASE			)

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

  return ans
def  __A   (_SCREAMING_SNAKE_CASE			)					->Dict:





  """simple docstring"""


  assert isinstance(_SCREAMING_SNAKE_CASE     ,   _SCREAMING_SNAKE_CASE			), "'number' must been an int"
  assert isinstance(number % 2 == 0     ,   _SCREAMING_SNAKE_CASE			), "compare bust been from type bool"

  return number % 2 == 0
def  __A   (_SCREAMING_SNAKE_CASE			)					->Tuple:





  """simple docstring"""


  assert isinstance(_SCREAMING_SNAKE_CASE     ,   _SCREAMING_SNAKE_CASE			), "'number' must been an int"
  assert isinstance(number % 2 != 0     ,   _SCREAMING_SNAKE_CASE			), "compare bust been from type bool"

  return number % 2 != 0
def  __A   (_SCREAMING_SNAKE_CASE			)					->Optional[int]:





  """simple docstring"""


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

  lowerCAmelCase__			:List[str]											=							[]  # this list will returned

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

  # run variable for while-loops.
  lowerCAmelCase__			:Tuple											=							0
  lowerCAmelCase__			:Optional[Any]											=							None

  # exit variable. for break up the loops
  lowerCAmelCase__			:int											=							True

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

    while j < len_pn and loop:
      if prime_numbers[i] + prime_numbers[j] == number:
        lowerCAmelCase__			:Union[str, Any]											=							False
        ans.append(prime_numbers[i]			)
        ans.append(prime_numbers[j]			)

      j += 1

    i += 1

  # precondition
  assert (
      isinstance(_SCREAMING_SNAKE_CASE     ,   _SCREAMING_SNAKE_CASE			)
      and (len(_SCREAMING_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  __A   (_SCREAMING_SNAKE_CASE     ,   _SCREAMING_SNAKE_CASE			)					->int:





  """simple docstring"""


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

  lowerCAmelCase__			:Dict											=							0

  while numbera != 0:
    lowerCAmelCase__			:Dict											=							numbera % numbera
    lowerCAmelCase__			:Optional[int]											=							numbera
    lowerCAmelCase__			:Optional[Any]											=							rest

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

  return numbera
def  __A   (_SCREAMING_SNAKE_CASE     ,   _SCREAMING_SNAKE_CASE			)					->List[str]:





  """simple docstring"""


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

  lowerCAmelCase__			:Union[str, 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'
    lowerCAmelCase__			:List[Any]											=							prime_factorization(_SCREAMING_SNAKE_CASE			)
    lowerCAmelCase__			:str											=							prime_factorization(_SCREAMING_SNAKE_CASE			)

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

  lowerCAmelCase__			:List[Any]											=							0
  lowerCAmelCase__			:Tuple											=							0

  lowerCAmelCase__			:Optional[int]											=							[]  # 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__			:Optional[int]											=							prime_fac_a.count(_SCREAMING_SNAKE_CASE			)
        lowerCAmelCase__			:int											=							prime_fac_a.count(_SCREAMING_SNAKE_CASE			)

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

      else:
        lowerCAmelCase__			:List[str]											=							prime_fac_a.count(_SCREAMING_SNAKE_CASE			)

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

      done.append(_SCREAMING_SNAKE_CASE			)

    # iterates through primeFac2
  for n in prime_fac_a:
    if n not in done:
      lowerCAmelCase__			:Tuple											=							prime_fac_a.count(_SCREAMING_SNAKE_CASE			)

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

      done.append(_SCREAMING_SNAKE_CASE			)

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

  return ans
def  __A   (_SCREAMING_SNAKE_CASE			)					->Optional[int]:





  """simple docstring"""


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

  lowerCAmelCase__			:Optional[Any]											=							0
  lowerCAmelCase__			:Tuple											=							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(_SCREAMING_SNAKE_CASE			):
      ans += 1

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

  return ans
def  __A   (_SCREAMING_SNAKE_CASE     ,   _SCREAMING_SNAKE_CASE			)					->str:





  """simple docstring"""


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

  lowerCAmelCase__			:Tuple											=							p_number_a + 1  # jump to the next number

  lowerCAmelCase__			:Any											=							[]  # this list will be returns.

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

  while number < p_number_a:
    ans.append(_SCREAMING_SNAKE_CASE			)

    number += 1

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

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

  # 'ans' contains not 'pNumber1' and 'pNumber2' !
  return ans
def  __A   (_SCREAMING_SNAKE_CASE			)					->Dict:





  """simple docstring"""


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

  lowerCAmelCase__			:int											=							[]  # will be returned.

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

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

  return ans
def  __A   (_SCREAMING_SNAKE_CASE			)					->Optional[Any]:





  """simple docstring"""


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

  lowerCAmelCase__			:List[Any]											=							get_divisors(_SCREAMING_SNAKE_CASE			)

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

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





  """simple docstring"""


  assert (
      isinstance(_SCREAMING_SNAKE_CASE     ,   _SCREAMING_SNAKE_CASE			)
      and isinstance(_SCREAMING_SNAKE_CASE     ,   _SCREAMING_SNAKE_CASE			)
      and (denominator != 0)
  ), "The arguments must been from type int and 'denominator' != 0"

  # build the greatest common divisor of numerator and denominator.
  lowerCAmelCase__			:Any											=							gcd(abs(_SCREAMING_SNAKE_CASE			)     ,   abs(_SCREAMING_SNAKE_CASE			)			)

  # precondition
  assert (
      isinstance(_SCREAMING_SNAKE_CASE     ,   _SCREAMING_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  __A   (_SCREAMING_SNAKE_CASE			)					->Any:





  """simple docstring"""


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

  lowerCAmelCase__			:str											=							1  # this will be return.

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

  return ans




def  __A   (_SCREAMING_SNAKE_CASE			)					->int:





  """simple docstring"""


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

  lowerCAmelCase__			:int											=							0
  lowerCAmelCase__			:Any											=							1
  lowerCAmelCase__			:Tuple											=							1  # this will be return

  for _ in range(n - 1			):
    lowerCAmelCase__			:Any											=							ans
    ans += fiba
    lowerCAmelCase__			:int											=							tmp

  return ans







'''simple docstring'''







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


lowerCAmelCase_					:    Dict      	=			logging.get_logger(__name__)

lowerCAmelCase_					:    int      	=			{
    'bigcode/gpt_bigcode-santacoder': 'https://huggingface.co/bigcode/gpt_bigcode-santacoder/resolve/main/config.json',
}
class 				__SCREAMING_SNAKE_CASE  (lowerCamelCase_      ):






				"""simple docstring"""







				__a            ='gpt_bigcode'
				__a            =['past_key_values']
				__a            ={
				    'hidden_size': 'n_embd',
				    'max_position_embeddings': 'n_positions',
				    'num_attention_heads': 'n_head',
				    'num_hidden_layers': 'n_layer',
				}




				def __init__(  self     :					Optional[Any]					,				__a     :					Tuple=5_02_57					,				__a     :					str=10_24					,				__a     :					Dict=7_68					,				__a     :					Tuple=12					,				__a     :					str=12					,				__a     :					Optional[int]=None					,				__a     :					Dict="gelu_pytorch_tanh"					,				__a     :					Tuple=0.1					,				__a     :					Tuple=0.1					,				__a     :					Union[str, Any]=0.1					,				__a     :					Tuple=1e-5					,				__a     :					str=0.02					,				__a     :					Dict=True					,				__a     :					Union[str, Any]=True					,				__a     :					Optional[int]=5_02_56					,				__a     :					Optional[int]=5_02_56					,				__a     :					Union[str, Any]=True					,				__a     :					Dict=True					,				__a     :					Union[str, Any]=True					,				**__a     :					List[Any]					,				):
								_a								= vocab_size
								_a								= n_positions
								_a								= n_embd
								_a								= n_layer
								_a								= n_head
								_a								= n_inner
								_a								= activation_function
								_a								= resid_pdrop
								_a								= embd_pdrop
								_a								= attn_pdrop
								_a								= layer_norm_epsilon
								_a								= initializer_range
								_a								= scale_attn_weights
								_a								= use_cache
								_a								= attention_softmax_in_fpaa
								_a								= scale_attention_softmax_in_fpaa
								_a								= multi_query

								_a								= bos_token_id
								_a								= eos_token_id

								super().__init__(bos_token_id=__a					,				eos_token_id=__a					,				**__a					)
