

from math import sqrt



def       __lowerCAmelCase      (						A    ):
	assert isinstance(A       ,     A    ) 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(A    )    )    ) + 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(A       ,     A    ), "'status' must been from type bool"

	return status



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

	return ans



def       __lowerCAmelCase      (						A    ):
	assert isinstance(A       ,     A    ) 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(A    ):
			ans.append(A    )

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

	return ans



def       __lowerCAmelCase      (						A    ):
	assert isinstance(A       ,     A    ) 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(A    )

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

	else:
		ans.append(A    )

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

	return ans



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

	UpperCAmelCase_       				=			0

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

	UpperCAmelCase_       				=			max(A    )

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

	return ans



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

	UpperCAmelCase_       				=			0

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

	UpperCAmelCase_       				=			min(A    )

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

	return ans



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

	return number % 2 == 0



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

	return number % 2 != 0



def       __lowerCAmelCase      (						A    ):
	assert (
	    isinstance(A       ,     A    ) and (number > 2) and is_even(A    )
	), "'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(A    )
	UpperCAmelCase_       				=			len(A    )

	# 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(A       ,     A    )
	    and (len(A    ) == 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       __lowerCAmelCase      (						A       ,     A    ):
	assert (
	    isinstance(A       ,     A    )
	    and isinstance(A       ,     A    )
	    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(A       ,     A    ) and (
	    numbera >= 0
	), "'number' must been from type int and positive"

	return numbera



def       __lowerCAmelCase      (						A       ,     A    ):
	assert (
	    isinstance(A       ,     A    )
	    and isinstance(A       ,     A    )
	    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(A    )
		UpperCAmelCase_       				=			prime_factorization(A    )

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

	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(A    )
				UpperCAmelCase_       				=			prime_fac_a.count(A    )

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

			else:
				UpperCAmelCase_       				=			prime_fac_a.count(A    )

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

			done.append(A    )

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

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

			done.append(A    )

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

	return ans



def       __lowerCAmelCase      (						A    ):
	assert isinstance(A       ,     A    ) 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(A    ):
			ans += 1

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

	return ans



def       __lowerCAmelCase      (						A       ,     A    ):
	assert (
	    is_prime(A    ) and is_prime(A    ) 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(A    ):
		number += 1

	while number < p_number_a:
		ans.append(A    )

		number += 1

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

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

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



def       __lowerCAmelCase      (						A    ):
	assert isinstance(A       ,     A    ) 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(A    )

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

	return ans



def       __lowerCAmelCase      (						A    ):
	assert isinstance(A       ,     A    ) and (
	    number > 1
	), "'number' must been an int and >= 1"

	UpperCAmelCase_       				=			get_divisors(A    )

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

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



def       __lowerCAmelCase      (						A       ,     A    ):
	assert (
	    isinstance(A       ,     A    )
	    and isinstance(A       ,     A    )
	    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(A    )       ,     abs(A    )    )

	# precondition
	assert (
	    isinstance(A       ,     A    )
	    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       __lowerCAmelCase      (						A    ):
	assert isinstance(A       ,     A    ) 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       __lowerCAmelCase      (						A    ):
	assert isinstance(A       ,     A    ) 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


from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_torch_available,
)


_a:    List[str] 							=			{
    """configuration_encodec""": [
        """ENCODEC_PRETRAINED_CONFIG_ARCHIVE_MAP""",
        """EncodecConfig""",
    ],
    """feature_extraction_encodec""": ["""EncodecFeatureExtractor"""],
}

try:
				if not is_torch_available():
								raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
				pass
else:
				_a:    List[Any] 							=			[
				    """ENCODEC_PRETRAINED_MODEL_ARCHIVE_LIST""",
				    """EncodecModel""",
				    """EncodecPreTrainedModel""",
				]

if TYPE_CHECKING:
				from .configuration_encodec import (
				    ENCODEC_PRETRAINED_CONFIG_ARCHIVE_MAP,
				    EncodecConfig,
				)
				from .feature_extraction_encodec import EncodecFeatureExtractor

				try:
								if not is_torch_available():
												raise OptionalDependencyNotAvailable()
				except OptionalDependencyNotAvailable:
								pass
				else:
								from .modeling_encodec import (
								    ENCODEC_PRETRAINED_MODEL_ARCHIVE_LIST,
								    EncodecModel,
								    EncodecPreTrainedModel,
								)

else:
				import sys

				_a:    int 							=			_LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)