
"""simple docstring"""


from math import sqrt






def    _snake_case					(		snake_case__ :  int  ):
	assert isinstance(snake_case__						,   snake_case__  ) 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(snake_case__  )  )  ) + 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(snake_case__						,   snake_case__  ), "'status' must been from type bool"

	return status






def    _snake_case					(		snake_case__ :  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     = list(range(2						,   n + 1  )  )

	A     = []  # 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     = 0

    # filters actual prime numbers.
	A     = [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    _snake_case					(		snake_case__ :  int  ):
	assert isinstance(snake_case__						,   snake_case__  ) 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(snake_case__  ):
			ans.append(snake_case__  )

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

	return ans






def    _snake_case					(		snake_case__ :  str  ):
	assert isinstance(snake_case__						,   snake_case__  ) 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(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    _snake_case					(		snake_case__ :  str  ):
	assert isinstance(snake_case__						,   snake_case__  ) and (
	    number >= 0
	), "'number' bust been an int and >= 0"

	A     = 0

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

	A     = max(snake_case__  )

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

	return ans






def    _snake_case					(		snake_case__ :  Tuple  ):
	assert isinstance(snake_case__						,   snake_case__  ) and (
	    number >= 0
	), "'number' bust been an int and >= 0"

	A     = 0

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

	A     = min(snake_case__  )

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

	return ans






def    _snake_case					(		snake_case__ :  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    _snake_case					(		snake_case__ :  List[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    _snake_case					(		snake_case__ :  int  ):
	assert (
	    isinstance(snake_case__						,   snake_case__  ) and (number > 2) and is_even(snake_case__  )
	), "'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(snake_case__  )
	A     = len(snake_case__  )

	# 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(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    _snake_case					(		snake_case__ :  str						,   snake_case__ :  Union[str, 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     = 0

	while numbera != 0:
		A     = numbera % numbera
		A     = numbera
		A     = rest

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

	return numbera






def    _snake_case					(		snake_case__ :  Tuple						,   snake_case__ :  List[str]  ):
	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     = 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(snake_case__  )
		A     = prime_factorization(snake_case__  )

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

	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(snake_case__  )
				A     = prime_fac_a.count(snake_case__  )

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

			else:
				A     = 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     = 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    _snake_case					(		snake_case__ :  int  ):
	assert isinstance(snake_case__						,   snake_case__  ) 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(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    _snake_case					(		snake_case__ :  int						,   snake_case__ :  Any  ):
	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     = 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(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    _snake_case					(		snake_case__ :  int  ):
	assert isinstance(snake_case__						,   snake_case__  ) 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(snake_case__  )

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

	return ans






def    _snake_case					(		snake_case__ :  Tuple  ):
	assert isinstance(snake_case__						,   snake_case__  ) and (
	    number > 1
	), "'number' must been an int and >= 1"

	A     = 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    _snake_case					(		snake_case__ :  str						,   snake_case__ :  List[str]  ):
	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     = 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    _snake_case					(		snake_case__ :  Any  ):
	assert isinstance(snake_case__						,   snake_case__  ) 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    _snake_case					(		snake_case__ :  List[str]  ):
	assert isinstance(snake_case__						,   snake_case__  ) 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

"""simple docstring"""


import pytest
import requests

from datasets.utils.file_utils import http_head

from .utils import OfflineSimulationMode, RequestWouldHangIndefinitelyError, offline






@pytest.mark.integration
def    _snake_case					(		):
	with offline(OfflineSimulationMode.CONNECTION_TIMES_OUT  ):
		with pytest.raises(snake_case__  ):
			requests.request('GET'						,   'https://huggingface.co'  )
		with pytest.raises(requests.exceptions.ConnectTimeout  ):
			requests.request('GET'						,   'https://huggingface.co'						,   timeout=1.0  )






@pytest.mark.integration
def    _snake_case					(		):
	with offline(OfflineSimulationMode.CONNECTION_FAILS  ):
		with pytest.raises(requests.exceptions.ConnectionError  ):
			requests.request('GET'						,   'https://huggingface.co'  )






def    _snake_case					(		):
	with offline(OfflineSimulationMode.HF_DATASETS_OFFLINE_SET_TO_1  ):
		with pytest.raises(snake_case__  ):
			http_head('https://huggingface.co'  )