





'''simple docstring'''




from math import sqrt






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

     __A						:			Dict								=	True

     # 0 and 1 are none primes.
     if number <= 1:
          __A						:			Optional[int]								=	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:
               __A						:			Dict								=	False
               break

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

     return status






def 	_lowerCAmelCase      (  __snake_case  :			Union[str, Any]      )					->					List[str]:
     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
     __A						:			Union[str, Any]								=	list(range(2			,							n + 1      )      )

     __A						:			Tuple								=	[]  # 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):
                    __A						:			Tuple								=	0

    # filters actual prime numbers.
     __A						:			Optional[Any]								=	[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 	_lowerCAmelCase      (  __snake_case  :			List[str]      )					->					str:
     assert isinstance(__snake_case			,							__snake_case      ) and (n > 2), "'N' must been an int and > 2"

     __A						:			Any								=	[]

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

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

     # potential prime number factors.

     __A						:			Union[str, Any]								=	2

     __A						:			Dict								=	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 	_lowerCAmelCase      (  __snake_case  :			int      )					->					Dict:
     assert isinstance(__snake_case			,							__snake_case      ) and (
         number >= 0
     ), "'number' bust been an int and >= 0"

     __A						:			int								=	0

     # prime factorization of 'number'
     __A						:			Optional[Any]								=	prime_factorization(__snake_case      )

     __A						:			str								=	max(__snake_case      )

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

     return ans






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

     __A						:			str								=	0

     # prime factorization of 'number'
     __A						:			Optional[int]								=	prime_factorization(__snake_case      )

     __A						:			str								=	min(__snake_case      )

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

     return ans






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

     __A						:			Dict								=	[]  # this list will returned

     # creates a list of prime numbers between 2 up to 'number'
     __A						:			List[str]								=	get_prime_numbers(__snake_case      )
     __A						:			List[Any]								=	len(__snake_case      )

     # run variable for while-loops.
     __A						:			Optional[int]								=	0
     __A						:			List[Any]								=	None

     # exit variable. for break up the loops
     __A						:			List[Any]								=	True

     while i < len_pn and loop:
          __A						:			Dict								=	i + 1

          while j < len_pn and loop:
               if prime_numbers[i] + prime_numbers[j] == number:
                    __A						:			int								=	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 	_lowerCAmelCase      (  __snake_case  :			Union[str, Any]			,							__snake_case  :			List[Any]      )					->					List[Any]:
     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."

     __A						:			str								=	0

     while numbera != 0:
          __A						:			List[str]								=	numbera % numbera
          __A						:			Any								=	numbera
          __A						:			Optional[int]								=	rest

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

     return numbera






def 	_lowerCAmelCase      (  __snake_case  :			Optional[Any]			,							__snake_case  :			List[str]      )					->					Dict:
     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."

     __A						:			int								=	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						:			List[str]								=	prime_factorization(__snake_case      )
          __A						:			Optional[int]								=	prime_factorization(__snake_case      )

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

     __A						:			int								=	0
     __A						:			Union[str, Any]								=	0

     __A						:			Union[str, Any]								=	[]  # 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						:			Dict								=	prime_fac_a.count(__snake_case      )
                    __A						:			Any								=	prime_fac_a.count(__snake_case      )

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

               else:
                    __A						:			Tuple								=	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:
               __A						:			List[str]								=	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 	_lowerCAmelCase      (  __snake_case  :			List[str]      )					->					str:
     assert isinstance(__snake_case			,							__snake_case      ) and (n >= 0), "'number' must been a positive int"

     __A						:			List[str]								=	0
     __A						:			Optional[Any]								=	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 	_lowerCAmelCase      (  __snake_case  :			str			,							__snake_case  :			Dict      )					->					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'"

     __A						:			Dict								=	p_number_a + 1  # jump to the next number

     __A						:			Union[str, Any]								=	[]  # 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 	_lowerCAmelCase      (  __snake_case  :			Any      )					->					Tuple:
     assert isinstance(__snake_case			,							__snake_case      ) and (n >= 1), "'n' must been int and >= 1"

     __A						:			Any								=	[]  # 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 	_lowerCAmelCase      (  __snake_case  :			Tuple      )					->					Optional[Any]:
     assert isinstance(__snake_case			,							__snake_case      ) and (
         number > 1
     ), "'number' must been an int and >= 1"

     __A						:			Any								=	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 	_lowerCAmelCase      (  __snake_case  :			Any			,							__snake_case  :			Dict      )					->					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.
     __A						:			str								=	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 	_lowerCAmelCase      (  __snake_case  :			List[Any]      )					->					str:
     assert isinstance(__snake_case			,							__snake_case      ) and (n >= 0), "'n' must been a int and >= 0"

     __A						:			Union[str, Any]								=	1  # this will be return.

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

     return ans







def 	_lowerCAmelCase      (  __snake_case  :			Union[str, Any]      )					->					Dict:
     assert isinstance(__snake_case			,							__snake_case      ) and (n >= 0), "'n' must been an int and >= 0"

     __A						:			Optional[int]								=	0
     __A						:			Dict								=	1
     __A						:			Union[str, Any]								=	1  # this will be return

     for _ in range(n - 1      ):
          __A						:			List[Any]								=	ans
          ans += fiba
          __A						:			Union[str, Any]								=	tmp

     return ans






'''simple docstring'''




from ...utils import (
    OptionalDependencyNotAvailable,
    is_torch_available,
    is_transformers_available,
    is_transformers_version,
)


try:
  if not (is_transformers_available() and is_torch_available()):
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  from ...utils.dummy_torch_and_transformers_objects import ShapEPipeline
else:
  from .camera import create_pan_cameras
  from .pipeline_shap_e import ShapEPipeline
  from .pipeline_shap_e_img2img import ShapEImgaImgPipeline
  from .renderer import (
      BoundingBoxVolume,
      ImportanceRaySampler,
      MLPNeRFModelOutput,
      MLPNeRSTFModel,
      ShapEParamsProjModel,
      ShapERenderer,
      StratifiedRaySampler,
      VoidNeRFModel,
  )