






from math import sqrt



def 			_SCREAMING_SNAKE_CASE						( __lowercase   :			int    )						->      bool:





    """simple docstring"""

    assert isinstance(__lowercase			,				__lowercase    ) 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(__lowercase    )    )    ) + 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(__lowercase			,				__lowercase    ), "'status' must been from type bool"

    return status



def 			_SCREAMING_SNAKE_CASE						( __lowercase   :			Dict    )						->      List[str]:





    """simple docstring"""

    assert isinstance(__lowercase			,				__lowercase    ) 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(__lowercase    )    ):
        for j in range(i + 1			,				len(__lowercase    )    ):
            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(__lowercase			,				__lowercase    ), "'ans' must been from type list"

    return ans



def 			_SCREAMING_SNAKE_CASE						( __lowercase   :			Any    )						->      List[Any]:





    """simple docstring"""

    assert isinstance(__lowercase			,				__lowercase    ) 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(__lowercase    ):
            ans.append(__lowercase    )

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

    return ans



def 			_SCREAMING_SNAKE_CASE						( __lowercase   :			int    )						->      int:





    """simple docstring"""

    assert isinstance(__lowercase			,				__lowercase    ) 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(__lowercase    )

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

    else:
        ans.append(__lowercase    )

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

    return ans



def 			_SCREAMING_SNAKE_CASE						( __lowercase   :			Optional[Any]    )						->      Optional[Any]:





    """simple docstring"""

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

    __A         =	0

    # prime factorization of 'number'
    __A         =	prime_factorization(__lowercase    )

    __A         =	max(__lowercase    )

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

    return ans



def 			_SCREAMING_SNAKE_CASE						( __lowercase   :			List[Any]    )						->      Any:





    """simple docstring"""

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

    __A         =	0

    # prime factorization of 'number'
    __A         =	prime_factorization(__lowercase    )

    __A         =	min(__lowercase    )

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

    return ans



def 			_SCREAMING_SNAKE_CASE						( __lowercase   :			Tuple    )						->      Optional[Any]:





    """simple docstring"""

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

    return number % 2 == 0



def 			_SCREAMING_SNAKE_CASE						( __lowercase   :			str    )						->      List[Any]:





    """simple docstring"""

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

    return number % 2 != 0



def 			_SCREAMING_SNAKE_CASE						( __lowercase   :			List[str]    )						->      str:





    """simple docstring"""

    assert (
        isinstance(__lowercase			,				__lowercase    ) and (number > 2) and is_even(__lowercase    )
    ), "'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(__lowercase    )
    __A         =	len(__lowercase    )

    # 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(__lowercase			,				__lowercase    )
        and (len(__lowercase    ) == 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 			_SCREAMING_SNAKE_CASE						( __lowercase   :			Optional[Any]			,				__lowercase   :			Union[str, Any]    )						->      Dict:





    """simple docstring"""

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

    return numbera



def 			_SCREAMING_SNAKE_CASE						( __lowercase   :			Dict			,				__lowercase   :			List[Any]    )						->      Dict:





    """simple docstring"""

    assert (
        isinstance(__lowercase			,				__lowercase    )
        and isinstance(__lowercase			,				__lowercase    )
        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(__lowercase    )
        __A         =	prime_factorization(__lowercase    )

    elif numbera == 1 or numbera == 1:
        __A         =	[]
        __A         =	[]
        __A         =	max(__lowercase			,				__lowercase    )

    __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(__lowercase    )
                __A         =	prime_fac_a.count(__lowercase    )

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

            else:
                __A         =	prime_fac_a.count(__lowercase    )

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

            done.append(__lowercase    )

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

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

            done.append(__lowercase    )

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

    return ans



def 			_SCREAMING_SNAKE_CASE						( __lowercase   :			List[str]    )						->      Optional[int]:





    """simple docstring"""

    assert isinstance(__lowercase			,				__lowercase    ) 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(__lowercase    ):
            ans += 1

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

    return ans



def 			_SCREAMING_SNAKE_CASE						( __lowercase   :			Dict			,				__lowercase   :			Optional[int]    )						->      Tuple:





    """simple docstring"""

    assert (
        is_prime(__lowercase    ) and is_prime(__lowercase    ) 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(__lowercase    ):
        number += 1

    while number < p_number_a:
        ans.append(__lowercase    )

        number += 1

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

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

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



def 			_SCREAMING_SNAKE_CASE						( __lowercase   :			Optional[int]    )						->      List[str]:





    """simple docstring"""

    assert isinstance(__lowercase			,				__lowercase    ) 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(__lowercase    )

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

    return ans



def 			_SCREAMING_SNAKE_CASE						( __lowercase   :			List[Any]    )						->      List[Any]:





    """simple docstring"""

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

    __A         =	get_divisors(__lowercase    )

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

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



def 			_SCREAMING_SNAKE_CASE						( __lowercase   :			Dict			,				__lowercase   :			List[Any]    )						->      Dict:





    """simple docstring"""

    assert (
        isinstance(__lowercase			,				__lowercase    )
        and isinstance(__lowercase			,				__lowercase    )
        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(__lowercase    )			,				abs(__lowercase    )    )

    # precondition
    assert (
        isinstance(__lowercase			,				__lowercase    )
        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 			_SCREAMING_SNAKE_CASE						( __lowercase   :			Optional[Any]    )						->      int:





    """simple docstring"""

    assert isinstance(__lowercase			,				__lowercase    ) 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 			_SCREAMING_SNAKE_CASE						( __lowercase   :			Union[str, Any]    )						->      Tuple:





    """simple docstring"""

    assert isinstance(__lowercase			,				__lowercase    ) 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












from collections import OrderedDict
from typing import Any, Mapping, Optional

from ... import PreTrainedTokenizer, TensorType, is_torch_available
from ...configuration_utils import PretrainedConfig
from ...onnx import OnnxConfigWithPast
from ...utils import logging


__a      :       List[Any]				  =   logging.get_logger(__name__)

__a      :       List[str]				  =   {
    "EleutherAI/gpt-neo-1.3B": "https://huggingface.co/EleutherAI/gpt-neo-1.3B/resolve/main/config.json",
    # See all GPTNeo models at https://huggingface.co/models?filter=gpt_neo
}


class       __lowercase      (	lowercase_  ):







     '''simple docstring'''
     SCREAMING_SNAKE_CASE   						=				"gpt_neo"
     SCREAMING_SNAKE_CASE   						=				["past_key_values"]
     SCREAMING_SNAKE_CASE   						=				{"num_attention_heads": "num_heads", "num_hidden_layers": "num_layers"}




     def __init__(				self       :			Optional[Any] ,	UpperCamelCase_       :			List[Any]=50_257 ,	UpperCamelCase_       :			Union[str, Any]=2_048 ,	UpperCamelCase_       :			List[str]=2_048 ,	UpperCamelCase_       :			Optional[int]=24 ,	UpperCamelCase_       :			Any=[[["global", "local"], 12]] ,	UpperCamelCase_       :			Tuple=16 ,	UpperCamelCase_       :			List[Any]=None ,	UpperCamelCase_       :			Optional[Any]=256 ,	UpperCamelCase_       :			List[str]="gelu_new" ,	UpperCamelCase_       :			str=0.0 ,	UpperCamelCase_       :			Optional[Any]=0.0 ,	UpperCamelCase_       :			str=0.0 ,	UpperCamelCase_       :			List[Any]=0.1 ,	UpperCamelCase_       :			str=1e-5 ,	UpperCamelCase_       :			Optional[Any]=0.02 ,	UpperCamelCase_       :			Union[str, Any]=True ,	UpperCamelCase_       :			Union[str, Any]=50_256 ,	UpperCamelCase_       :			Dict=50_256 ,	**UpperCamelCase_       :			Union[str, Any] ,	):


         """simple docstring"""



         __A         =	vocab_size
         __A         =	max_position_embeddings
         __A         =	hidden_size
         __A         =	num_layers
         __A         =	num_heads
         __A         =	intermediate_size
         __A         =	window_size
         __A         =	activation_function
         __A         =	resid_dropout
         __A         =	embed_dropout
         __A         =	attention_dropout
         __A         =	classifier_dropout
         __A         =	layer_norm_epsilon
         __A         =	initializer_range
         __A         =	use_cache

         __A         =	bos_token_id
         __A         =	eos_token_id

         __A         =	attention_types
         __A         =	self.expand_attention_types_params(UpperCamelCase_				)

         if len(self.attention_layers				) != self.num_layers:
             raise ValueError(
                 """Configuration for convolutional module is incorrect. """
                 """It is required that `len(config.attention_layers)` == `config.num_layers` """
                 F"but is `len(config.attention_layers) = {len(self.attention_layers				)}`, "
                 F"`config.num_layers = {self.num_layers}`. "
                 """`config.attention_layers` is prepared using `config.attention_types`. """
                 """Please verify the value of `config.attention_types` argument."""				)

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





     @staticmethod
     def 		lowerCAmelCase_     (				UpperCamelCase_       :			str				):


         """simple docstring"""



         __A         =	[]
         for item in attention_types:
             for _ in range(item[1]				):
                 attentions.extend(item[0]				)
         return attentions



def 			_SCREAMING_SNAKE_CASE						( __lowercase   :			List[Any]			,				__lowercase   :			Any			,				__lowercase   :			int			,				__lowercase   :			int    )						->      Union[str, Any]:





    """simple docstring"""

    import torch

    __A         =	input.size()
    __A         =	len(__lowercase    )
    __A         =	shape[dimension]

    __A         =	torch.arange(0			,				__lowercase			,				__lowercase    )
    __A         =	torch.div(sizedim - size			,				__lowercase			,				rounding_mode="""floor"""    ) + 1
    __A         =	torch.arange(__lowercase    ) + low_indices[:min_length][:, None]

    __A         =	[slice(__lowercase    )] * rank
    __A         =	indices
    __A         =	input[s]

    __A         =	list(range(0			,				rank + 1    )    )
    perm.append(perm.pop(dimension + 1    )    )

    return sliced.permute(__lowercase    )



def 			_SCREAMING_SNAKE_CASE						( __lowercase   :			Dict			,				__lowercase   :			Any    )						->      Union[str, Any]:





    """simple docstring"""

    import torch

    __A         =	torch.arange(1			,				__lowercase    )
    __A         =	torch.remainder(__lowercase			,				__lowercase    )
    __A         =	remainders == 0
    __A         =	candidates[divisor_indices]
    __A         =	torch.max(__lowercase    )
    return largest_divisor, torch.div(__lowercase			,				__lowercase			,				rounding_mode="""floor"""    )






class       __lowercase      (	lowercase_  ):







     '''simple docstring'''




     @property
     def 		lowerCAmelCase_     (				self       :			Dict				):


         """simple docstring"""



         __A         =	OrderedDict({"""input_ids""": {0: """batch""", 1: """sequence"""}}				)
         if self.use_past:
             self.fill_with_past_key_values_(UpperCamelCase_ ,	direction="""inputs"""				)
             __A         =	{0: """batch""", 1: """past_sequence + sequence"""}
         else:
             __A         =	{0: """batch""", 1: """sequence"""}

         return common_inputs




     @property
     def 		lowerCAmelCase_     (				self       :			Optional[int]				):


         """simple docstring"""



         return self._config.num_heads




     def 		lowerCAmelCase_     (				self       :			Union[str, Any] ,	UpperCamelCase_       :			PreTrainedTokenizer ,	UpperCamelCase_       :			int = -1 ,	UpperCamelCase_       :			int = -1 ,	UpperCamelCase_       :			bool = False ,	UpperCamelCase_       :			Optional[TensorType] = None ,	):


         """simple docstring"""



         __A         =	super(UpperCamelCase_ ,	self				).generate_dummy_inputs(
             UpperCamelCase_ ,	batch_size=UpperCamelCase_ ,	seq_length=UpperCamelCase_ ,	is_pair=UpperCamelCase_ ,	framework=UpperCamelCase_				)

         # We need to order the input in the way they appears in the forward()
         __A         =	OrderedDict({"""input_ids""": common_inputs["""input_ids"""]}				)

         # Need to add the past_keys
         if self.use_past:
             if not is_torch_available():
                 raise ValueError("""Cannot generate dummy past_keys inputs without PyTorch installed."""				)
             else:
                 import torch

                 __A    ,	__A         =	common_inputs["""input_ids"""].shape
                 # Not using the same length for past_key_values
                 __A         =	seqlen + 2
                 __A         =	(
                     batch,
                     self.num_attention_heads,
                     past_key_values_length,
                     self._config.hidden_size // self.num_attention_heads,
                 )
                 __A         =	[
                     (torch.zeros(UpperCamelCase_				), torch.zeros(UpperCamelCase_				)) for _ in range(self.num_layers				)
                 ]

         __A         =	common_inputs["""attention_mask"""]
         if self.use_past:
             __A         =	ordered_inputs["""attention_mask"""].dtype
             __A         =	torch.cat(
                 [ordered_inputs["""attention_mask"""], torch.ones(UpperCamelCase_ ,	UpperCamelCase_ ,	dtype=UpperCamelCase_				)] ,	dim=1				)

         return ordered_inputs





     @property
     def 		lowerCAmelCase_     (				self       :			Tuple				):


         """simple docstring"""



         return 13




