



from math import sqrt






def      _A				(UpperCamelCase		:      int )  ->bool:



			'''simple docstring'''







			assert isinstance(UpperCamelCase      ,			UpperCamelCase ) and (
			    number >= 0
			), "'number' must been an int and positive"

			lowerCamelCase__ :      Union[str, Any]								=		True

			# 0 and 1 are none primes.
			if number <= 1:
						lowerCamelCase__ :      Dict								=		False

			for divisor in range(2      ,			int(round(sqrt(UpperCamelCase ) ) ) + 1 ):
						# if 'number' divisible by 'divisor' then sets 'status'
						# of false and break up the loop.
						if number % divisor == 0:
									lowerCamelCase__ :      str								=		False
									break

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

			return status






def      _A				(UpperCamelCase		:      str )  ->Union[str, Any]:



			'''simple docstring'''







			assert isinstance(UpperCamelCase      ,			UpperCamelCase ) and (n > 2), "'N' must been an int and > 2"

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

			lowerCamelCase__ :      Any								=		[]  # this list will be returns.

			# actual sieve of erathostenes
			for i in range(len(UpperCamelCase ) ):
						for j in range(i + 1      ,			len(UpperCamelCase ) ):
									if (begin_list[i] != 0) and (begin_list[j] % begin_list[i] == 0):
												lowerCamelCase__ :      Any								=		0

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

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

			return ans






def      _A				(UpperCamelCase		:      Optional[int] )  ->int:



			'''simple docstring'''







			assert isinstance(UpperCamelCase      ,			UpperCamelCase ) and (n > 2), "'N' must been an int and > 2"

			lowerCamelCase__ :      Optional[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(UpperCamelCase ):
									ans.append(UpperCamelCase )

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

			return ans






def      _A				(UpperCamelCase		:      Dict )  ->Optional[int]:



			'''simple docstring'''







			assert isinstance(UpperCamelCase      ,			UpperCamelCase ) and number >= 0, "'number' must been an int and >= 0"

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

			# potential prime number factors.

			lowerCamelCase__ :      Any								=		2

			lowerCamelCase__ :      Any								=		number

			if number == 0 or number == 1:
						ans.append(UpperCamelCase )

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

			else:
						ans.append(UpperCamelCase )

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

			return ans






def      _A				(UpperCamelCase		:      List[str] )  ->str:



			'''simple docstring'''







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

			lowerCamelCase__ :      List[str]								=		0

			# prime factorization of 'number'
			lowerCamelCase__ :      Union[str, Any]								=		prime_factorization(UpperCamelCase )

			lowerCamelCase__ :      List[Any]								=		max(UpperCamelCase )

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

			return ans






def      _A				(UpperCamelCase		:      Optional[Any] )  ->int:



			'''simple docstring'''







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

			lowerCamelCase__ :      Optional[Any]								=		0

			# prime factorization of 'number'
			lowerCamelCase__ :      List[Any]								=		prime_factorization(UpperCamelCase )

			lowerCamelCase__ :      List[str]								=		min(UpperCamelCase )

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

			return ans






def      _A				(UpperCamelCase		:      Optional[Any] )  ->int:



			'''simple docstring'''







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

			return number % 2 == 0






def      _A				(UpperCamelCase		:      str )  ->Optional[Any]:



			'''simple docstring'''







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

			return number % 2 != 0






def      _A				(UpperCamelCase		:      List[Any] )  ->List[str]:



			'''simple docstring'''







			assert (
			    isinstance(UpperCamelCase      ,			UpperCamelCase ) and (number > 2) and is_even(UpperCamelCase )
			), "'number' must been an int, even and > 2"

			lowerCamelCase__ :      str								=		[]  # this list will returned

			# creates a list of prime numbers between 2 up to 'number'
			lowerCamelCase__ :      List[Any]								=		get_prime_numbers(UpperCamelCase )
			lowerCamelCase__ :      Dict								=		len(UpperCamelCase )

			# run variable for while-loops.
			lowerCamelCase__ :      Dict								=		0
			lowerCamelCase__ :      List[Any]								=		None

			# exit variable. for break up the loops
			lowerCamelCase__ :      int								=		True

			while i < len_pn and loop:
						lowerCamelCase__ :      List[str]								=		i + 1

						while j < len_pn and loop:
									if prime_numbers[i] + prime_numbers[j] == number:
												lowerCamelCase__ :      Tuple								=		False
												ans.append(prime_numbers[i] )
												ans.append(prime_numbers[j] )

									j += 1

						i += 1

			# precondition
			assert (
			    isinstance(UpperCamelCase      ,			UpperCamelCase )
			    and (len(UpperCamelCase ) == 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				(UpperCamelCase		:      str      ,			UpperCamelCase		:      Optional[int] )  ->Optional[Any]:



			'''simple docstring'''







			assert (
			    isinstance(UpperCamelCase      ,			UpperCamelCase )
			    and isinstance(UpperCamelCase      ,			UpperCamelCase )
			    and (numbera >= 0)
			    and (numbera >= 0)
			), "'number1' and 'number2' must been positive integer."

			lowerCamelCase__ :      Dict								=		0

			while numbera != 0:
						lowerCamelCase__ :      Optional[int]								=		numbera % numbera
						lowerCamelCase__ :      Tuple								=		numbera
						lowerCamelCase__ :      List[str]								=		rest

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

			return numbera






def      _A				(UpperCamelCase		:      Dict      ,			UpperCamelCase		:      List[str] )  ->Optional[int]:



			'''simple docstring'''







			assert (
			    isinstance(UpperCamelCase      ,			UpperCamelCase )
			    and isinstance(UpperCamelCase      ,			UpperCamelCase )
			    and (numbera >= 1)
			    and (numbera >= 1)
			), "'number1' and 'number2' must been positive integer."

			lowerCamelCase__ :      Optional[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'
						lowerCamelCase__ :      int								=		prime_factorization(UpperCamelCase )
						lowerCamelCase__ :      List[str]								=		prime_factorization(UpperCamelCase )

			elif numbera == 1 or numbera == 1:
						lowerCamelCase__ :      Any								=		[]
						lowerCamelCase__ :      Any								=		[]
						lowerCamelCase__ :      Any								=		max(UpperCamelCase      ,			UpperCamelCase )

			lowerCamelCase__ :      List[Any]								=		0
			lowerCamelCase__ :      Tuple								=		0

			lowerCamelCase__ :      List[str]								=		[]  # 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:
												lowerCamelCase__ :      str								=		prime_fac_a.count(UpperCamelCase )
												lowerCamelCase__ :      Optional[int]								=		prime_fac_a.count(UpperCamelCase )

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

									else:
												lowerCamelCase__ :      int								=		prime_fac_a.count(UpperCamelCase )

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

									done.append(UpperCamelCase )

    # iterates through primeFac2
			for n in prime_fac_a:
						if n not in done:
									lowerCamelCase__ :      List[Any]								=		prime_fac_a.count(UpperCamelCase )

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

									done.append(UpperCamelCase )

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

			return ans






def      _A				(UpperCamelCase		:      Optional[int] )  ->Optional[int]:



			'''simple docstring'''







			assert isinstance(UpperCamelCase      ,			UpperCamelCase ) and (n >= 0), "'number' must been a positive int"

			lowerCamelCase__ :      Union[str, Any]								=		0
			lowerCamelCase__ :      str								=		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(UpperCamelCase ):
									ans += 1

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

			return ans






def      _A				(UpperCamelCase		:      List[Any]      ,			UpperCamelCase		:      List[Any] )  ->Any:



			'''simple docstring'''







			assert (
			    is_prime(UpperCamelCase ) and is_prime(UpperCamelCase ) and (p_number_a < p_number_a)
			), "The arguments must been prime numbers and 'pNumber1' < 'pNumber2'"

			lowerCamelCase__ :      List[str]								=		p_number_a + 1  # jump to the next number

			lowerCamelCase__ :      List[str]								=		[]  # this list will be returns.

			# if number is not prime then
			# fetch the next prime number.
			while not is_prime(UpperCamelCase ):
						number += 1

			while number < p_number_a:
						ans.append(UpperCamelCase )

						number += 1

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

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

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






def      _A				(UpperCamelCase		:      Optional[Any] )  ->int:



			'''simple docstring'''







			assert isinstance(UpperCamelCase      ,			UpperCamelCase ) and (n >= 1), "'n' must been int and >= 1"

			lowerCamelCase__ :      int								=		[]  # will be returned.

			for divisor in range(1      ,			n + 1 ):
						if n % divisor == 0:
									ans.append(UpperCamelCase )

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

			return ans






def      _A				(UpperCamelCase		:      str )  ->int:



			'''simple docstring'''







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

			lowerCamelCase__ :      List[str]								=		get_divisors(UpperCamelCase )

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

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






def      _A				(UpperCamelCase		:      int      ,			UpperCamelCase		:      Any )  ->List[Any]:



			'''simple docstring'''







			assert (
			    isinstance(UpperCamelCase      ,			UpperCamelCase )
			    and isinstance(UpperCamelCase      ,			UpperCamelCase )
			    and (denominator != 0)
			), "The arguments must been from type int and 'denominator' != 0"

			# build the greatest common divisor of numerator and denominator.
			lowerCamelCase__ :      Tuple								=		gcd(abs(UpperCamelCase )      ,			abs(UpperCamelCase ) )

			# precondition
			assert (
			    isinstance(UpperCamelCase      ,			UpperCamelCase )
			    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				(UpperCamelCase		:      int )  ->str:



			'''simple docstring'''







			assert isinstance(UpperCamelCase      ,			UpperCamelCase ) and (n >= 0), "'n' must been a int and >= 0"

			lowerCamelCase__ :      int								=		1  # this will be return.

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

			return ans






def      _A				(UpperCamelCase		:      List[Any] )  ->str:



			'''simple docstring'''







			assert isinstance(UpperCamelCase      ,			UpperCamelCase ) and (n >= 0), "'n' must been an int and >= 0"

			lowerCamelCase__ :      str								=		0
			lowerCamelCase__ :      List[Any]								=		1
			lowerCamelCase__ :      Dict								=		1  # this will be return

			for _ in range(n - 1 ):
						lowerCamelCase__ :      List[str]								=		ans
						ans += fiba
						lowerCamelCase__ :      Optional[int]								=		tmp

			return ans








from __future__ import annotations

import string
from itertools import cycle, product
from pathlib import Path

_lowercase     							=						(
    string.ascii_letters + string.digits + string.punctuation + string.whitespace
)
_lowercase     							=						[ord(letter) for letter in string.ascii_lowercase]
_lowercase     							=						{ord(char) for char in VALID_CHARS}

_lowercase     							=						["the", "be", "to", "of", "and", "in", "that", "have"]






def      _A				(UpperCamelCase		:      list[int]      ,			UpperCamelCase		:      tuple[int, ...] )  ->str | None:



			'''simple docstring'''







			lowerCamelCase__ :      str								=		""
			lowerCamelCase__ :      int
			lowerCamelCase__ :      int
			lowerCamelCase__ :      int

			for keychar, cipherchar in zip(cycle(UpperCamelCase )      ,			UpperCamelCase ):
						lowerCamelCase__ :      str								=		cipherchar ^ keychar
						if decodedchar not in VALID_INTS:
									return None
						decoded += chr(UpperCamelCase )

			return decoded






def      _A				(UpperCamelCase		:      list[int] )  ->list[str]:



			'''simple docstring'''







			lowerCamelCase__ :      list[str]								=		[]
			for key in product(UpperCamelCase      ,			repeat=3 ):
						lowerCamelCase__ :      Union[str, Any]								=		try_key(UpperCamelCase      ,			UpperCamelCase )
						if encoded is not None:
									possibles.append(UpperCamelCase )
			return possibles






def      _A				(UpperCamelCase		:      list[str]      ,			UpperCamelCase		:      str )  ->list[str]:



			'''simple docstring'''







			return [possible for possible in possibles if common_word in possible.lower()]






def      _A				(UpperCamelCase		:      str = "p059_cipher.txt" )  ->int:



			'''simple docstring'''







			lowerCamelCase__ :      list[int]
			lowerCamelCase__ :      list[str]
			lowerCamelCase__ :      str
			lowerCamelCase__ :      str
			lowerCamelCase__ :      str								=		Path(UpperCamelCase ).parent.joinpath(UpperCamelCase ).read_text(encoding="""utf-8""" )

			lowerCamelCase__ :      str								=		[int(UpperCamelCase ) for number in data.strip().split(""",""" )]

			lowerCamelCase__ :      Optional[Any]								=		filter_valid_chars(UpperCamelCase )
			for common_word in COMMON_WORDS:
						lowerCamelCase__ :      Optional[int]								=		filter_common_word(UpperCamelCase      ,			UpperCamelCase )
						if len(UpperCamelCase ) == 1:
									break

			lowerCamelCase__ :      Union[str, Any]								=		possibles[0]
			return sum(ord(UpperCamelCase ) for char in decoded_text )


if __name__ == "__main__":
				print(F'''{solution() = }''')



