






from math import sqrt


def     _A  (							SCREAMING_SNAKE_CASE__    :      int			):
    assert isinstance(lowercase__	,    lowercase__			) and (
        number >= 0
    ), "'number' must been an int and positive"

    UpperCamelCase			:Optional[int]      				=  True

    # 0 and 1 are none primes.
    if number <= 1:
        UpperCamelCase			:List[str]      				=  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:
            UpperCamelCase			:Dict      				=  False
            break

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

    return status


def     _A  (							SCREAMING_SNAKE_CASE__    :      Optional[Any]			):
    assert isinstance(lowercase__	,    lowercase__			) and (n > 2), "'N' must been an int and > 2"

    # beginList: contains all natural numbers from 2 up to N
    UpperCamelCase			:Dict      				=  list(range(2	,    n + 1			)			)

    UpperCamelCase			:Optional[int]      				=  []  # 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):
                UpperCamelCase			:List[str]      				=  0

    # filters actual prime numbers.
    UpperCamelCase			:Any      				=  [x for x in begin_list if x != 0]

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

    return ans


def     _A  (							SCREAMING_SNAKE_CASE__    :      Any			):
    assert isinstance(lowercase__	,    lowercase__			) and (n > 2), "'N' must been an int and > 2"

    UpperCamelCase			: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(lowercase__			):
            ans.append(lowercase__			)

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

    return ans


def     _A  (							SCREAMING_SNAKE_CASE__    :      Any			):
    assert isinstance(lowercase__	,    lowercase__			) and number >= 0, "'number' must been an int and >= 0"

    UpperCamelCase			:Any      				=  []  # this list will be returns of the function.

    # potential prime number factors.

    UpperCamelCase			:str      				=  2

    UpperCamelCase			:int      				=  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     _A  (							SCREAMING_SNAKE_CASE__    :      List[str]			):
    assert isinstance(lowercase__	,    lowercase__			) and (
        number >= 0
    ), "'number' bust been an int and >= 0"

    UpperCamelCase			:Union[str, Any]      				=  0

    # prime factorization of 'number'
    UpperCamelCase			:str      				=  prime_factorization(lowercase__			)

    UpperCamelCase			:Tuple      				=  max(lowercase__			)

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

    return ans


def     _A  (							SCREAMING_SNAKE_CASE__    :      Any			):
    assert isinstance(lowercase__	,    lowercase__			) and (
        number >= 0
    ), "'number' bust been an int and >= 0"

    UpperCamelCase			:Optional[int]      				=  0

    # prime factorization of 'number'
    UpperCamelCase			:Optional[int]      				=  prime_factorization(lowercase__			)

    UpperCamelCase			:List[str]      				=  min(lowercase__			)

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

    return ans


def     _A  (							SCREAMING_SNAKE_CASE__    :      Dict			):
    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     _A  (							SCREAMING_SNAKE_CASE__    :      Optional[Any]			):
    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     _A  (							SCREAMING_SNAKE_CASE__    :      int			):
    assert (
        isinstance(lowercase__	,    lowercase__			) and (number > 2) and is_even(lowercase__			)
    ), "'number' must been an int, even and > 2"

    UpperCamelCase			:Any      				=  []  # this list will returned

    # creates a list of prime numbers between 2 up to 'number'
    UpperCamelCase			:Optional[Any]      				=  get_prime_numbers(lowercase__			)
    UpperCamelCase			:str      				=  len(lowercase__			)

    # run variable for while-loops.
    UpperCamelCase			:Union[str, Any]      				=  0
    UpperCamelCase			:Union[str, Any]      				=  None

    # exit variable. for break up the loops
    UpperCamelCase			:Optional[Any]      				=  True

    while i < len_pn and loop:
        UpperCamelCase			:Union[str, Any]      				=  i + 1

        while j < len_pn and loop:
            if prime_numbers[i] + prime_numbers[j] == number:
                UpperCamelCase			:Optional[int]      				=  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     _A  (							SCREAMING_SNAKE_CASE__    :      Union[str, Any]	,    SCREAMING_SNAKE_CASE__    :      Any			):
    assert (
        isinstance(lowercase__	,    lowercase__			)
        and isinstance(lowercase__	,    lowercase__			)
        and (numbera >= 0)
        and (numbera >= 0)
    ), "'number1' and 'number2' must been positive integer."

    UpperCamelCase			:int      				=  0

    while numbera != 0:
        UpperCamelCase			:Optional[Any]      				=  numbera % numbera
        UpperCamelCase			:Optional[Any]      				=  numbera
        UpperCamelCase			:Union[str, Any]      				=  rest

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

    return numbera


def     _A  (							SCREAMING_SNAKE_CASE__    :      Any	,    SCREAMING_SNAKE_CASE__    :      Optional[int]			):
    assert (
        isinstance(lowercase__	,    lowercase__			)
        and isinstance(lowercase__	,    lowercase__			)
        and (numbera >= 1)
        and (numbera >= 1)
    ), "'number1' and 'number2' must been positive integer."

    UpperCamelCase			:List[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'
        UpperCamelCase			:List[Any]      				=  prime_factorization(lowercase__			)
        UpperCamelCase			:int      				=  prime_factorization(lowercase__			)

    elif numbera == 1 or numbera == 1:
        UpperCamelCase			:Any      				=  []
        UpperCamelCase			:Optional[Any]      				=  []
        UpperCamelCase			:int      				=  max(lowercase__	,    lowercase__			)

    UpperCamelCase			:str      				=  0
    UpperCamelCase			:List[str]      				=  0

    UpperCamelCase			: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:
                UpperCamelCase			:Tuple      				=  prime_fac_a.count(lowercase__			)
                UpperCamelCase			:Any      				=  prime_fac_a.count(lowercase__			)

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

            else:
                UpperCamelCase			:Optional[int]      				=  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:
            UpperCamelCase			:int      				=  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     _A  (							SCREAMING_SNAKE_CASE__    :      Union[str, Any]			):
    assert isinstance(lowercase__	,    lowercase__			) and (n >= 0), "'number' must been a positive int"

    UpperCamelCase			:List[Any]      				=  0
    UpperCamelCase			:List[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(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     _A  (							SCREAMING_SNAKE_CASE__    :      int	,    SCREAMING_SNAKE_CASE__    :      Tuple			):
    assert (
        is_prime(lowercase__			) and is_prime(lowercase__			) and (p_number_a < p_number_a)
    ), "The arguments must been prime numbers and 'pNumber1' < 'pNumber2'"

    UpperCamelCase			:Optional[Any]      				=  p_number_a + 1  # jump to the next number

    UpperCamelCase			:Optional[int]      				=  []  # 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     _A  (							SCREAMING_SNAKE_CASE__    :      Optional[Any]			):
    assert isinstance(lowercase__	,    lowercase__			) and (n >= 1), "'n' must been int and >= 1"

    UpperCamelCase			:Union[str, Any]      				=  []  # 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     _A  (							SCREAMING_SNAKE_CASE__    :      Union[str, Any]			):
    assert isinstance(lowercase__	,    lowercase__			) and (
        number > 1
    ), "'number' must been an int and >= 1"

    UpperCamelCase			:str      				=  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     _A  (							SCREAMING_SNAKE_CASE__    :      List[str]	,    SCREAMING_SNAKE_CASE__    :      Tuple			):
    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.
    UpperCamelCase			:Union[str, Any]      				=  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     _A  (							SCREAMING_SNAKE_CASE__    :      Optional[int]			):
    assert isinstance(lowercase__	,    lowercase__			) and (n >= 0), "'n' must been a int and >= 0"

    UpperCamelCase			:List[str]      				=  1  # this will be return.

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

    return ans



def     _A  (							SCREAMING_SNAKE_CASE__    :      str			):
    assert isinstance(lowercase__	,    lowercase__			) and (n >= 0), "'n' must been an int and >= 0"

    UpperCamelCase			:Union[str, Any]      				=  0
    UpperCamelCase			:Union[str, Any]      				=  1
    UpperCamelCase			:Union[str, Any]      				=  1  # this will be return

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

    return ans








'''simple docstring'''

from dataclasses import dataclass, field
from typing import ClassVar, Dict

from ..features import Features, Value
from .base import TaskTemplate


@dataclass(frozen=A )
class 	lowerCAmelCase  (   A ):
       # `task` is not a ClassVar since we want it to be part of the `asdict` output for JSON serialization
       lowerCAmelCase_												=			field(default="summarization" ,      metadata={"include_in_asdict_even_if_is_default": True} )
       lowerCAmelCase_												=			Features({"text": Value("string" )} )
       lowerCAmelCase_												=			Features({"summary": Value("string" )} )
       lowerCAmelCase_												=			"text"
       lowerCAmelCase_												=			"summary"







       @property
       def       snake_case (				self      :			int   ):







            """simple docstring"""







            return {self.text_column: "text", self.summary_column: "summary"}


