



'''simple docstring'''





from __future__ import annotations

import collections
import pprint
from pathlib import Path
def    _SCREAMING_SNAKE_CASE  (       UpperCamelCase			):



    """simple docstring"""





    return "".join(sorted(UpperCamelCase			)			)
def    _SCREAMING_SNAKE_CASE  (       UpperCamelCase			):



    """simple docstring"""





    return word_by_signature[signature(UpperCamelCase			)]


_lowerCAmelCase      						=	Path(__file__).parent.joinpath('''words.txt''').read_text(encoding='''utf-8''')
_lowerCAmelCase      						=	sorted({word.strip().lower() for word in data.splitlines()})

_lowerCAmelCase      						=	collections.defaultdict(list)
for word in word_list:
 word_by_signature[signature(word)].append(word)

if __name__ == "__main__":
 _lowerCAmelCase      						=	{word: anagram(word) for word in word_list if len(anagram(word)) > 1}

 with open('''anagrams.txt''', '''w''') as file:
  file.write('''all_anagrams = \n ''')
  file.write(pprint.pformat(all_anagrams))







'''simple docstring'''





from math import sqrt
def    _SCREAMING_SNAKE_CASE  (       UpperCamelCase			):



    """simple docstring"""





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

    lowerCAmelCase__ :  int							      =					True

    # 0 and 1 are none primes.
    if number <= 1:
        lowerCAmelCase__ :  Optional[Any]							      =					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__ :  Any							      =					False
            break

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

    return status
def    _SCREAMING_SNAKE_CASE  (       UpperCamelCase			):



    """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__ :  List[str]							      =					list(range(2							,    n + 1			)			)

    lowerCAmelCase__ :  str							      =					[]  # 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__ :  List[Any]							      =					0

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

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

    return ans
def    _SCREAMING_SNAKE_CASE  (       UpperCamelCase			):



    """simple docstring"""





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

    lowerCAmelCase__ :  List[str]							      =					[]

    # 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    _SCREAMING_SNAKE_CASE  (       UpperCamelCase			):



    """simple docstring"""





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

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

    # potential prime number factors.

    lowerCAmelCase__ :  Dict							      =					2

    lowerCAmelCase__ :  Dict							      =					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    _SCREAMING_SNAKE_CASE  (       UpperCamelCase			):



    """simple docstring"""





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

    lowerCAmelCase__ :  Optional[int]							      =					0

    # prime factorization of 'number'
    lowerCAmelCase__ :  List[str]							      =					prime_factorization(UpperCamelCase			)

    lowerCAmelCase__ :  Any							      =					max(UpperCamelCase			)

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

    return ans
def    _SCREAMING_SNAKE_CASE  (       UpperCamelCase			):



    """simple docstring"""





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

    lowerCAmelCase__ :  List[Any]							      =					0

    # prime factorization of 'number'
    lowerCAmelCase__ :  List[str]							      =					prime_factorization(UpperCamelCase			)

    lowerCAmelCase__ :  Optional[int]							      =					min(UpperCamelCase			)

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

    return ans
def    _SCREAMING_SNAKE_CASE  (       UpperCamelCase			):



    """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    _SCREAMING_SNAKE_CASE  (       UpperCamelCase			):



    """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    _SCREAMING_SNAKE_CASE  (       UpperCamelCase			):



    """simple docstring"""





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

    lowerCAmelCase__ :  Dict							      =					[]  # this list will returned

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

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

    # exit variable. for break up the loops
    lowerCAmelCase__ :  Any							      =					True

    while i < len_pn and loop:
        lowerCAmelCase__ :  List[Any]							      =					i + 1

        while j < len_pn and loop:
            if prime_numbers[i] + prime_numbers[j] == number:
                lowerCAmelCase__ :  Optional[Any]							      =					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    _SCREAMING_SNAKE_CASE  (       UpperCamelCase							,    UpperCamelCase			):



    """simple docstring"""





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

    lowerCAmelCase__ :  int							      =					0

    while numbera != 0:
        lowerCAmelCase__ :  Any							      =					numbera % numbera
        lowerCAmelCase__ :  str							      =					numbera
        lowerCAmelCase__ :  List[str]							      =					rest

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

    return numbera
def    _SCREAMING_SNAKE_CASE  (       UpperCamelCase							,    UpperCamelCase			):



    """simple docstring"""





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

    lowerCAmelCase__ :  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'
        lowerCAmelCase__ :  int							      =					prime_factorization(UpperCamelCase			)
        lowerCAmelCase__ :  Any							      =					prime_factorization(UpperCamelCase			)

    elif numbera == 1 or numbera == 1:
        lowerCAmelCase__ :  Optional[Any]							      =					[]
        lowerCAmelCase__ :  Dict							      =					[]
        lowerCAmelCase__ :  List[str]							      =					max(UpperCamelCase							,    UpperCamelCase			)

    lowerCAmelCase__ :  Tuple							      =					0
    lowerCAmelCase__ :  str							      =					0

    lowerCAmelCase__ :  List[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:
                lowerCAmelCase__ :  int							      =					prime_fac_a.count(UpperCamelCase			)
                lowerCAmelCase__ :  Any							      =					prime_fac_a.count(UpperCamelCase			)

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

            else:
                lowerCAmelCase__ :  Any							      =					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__ :  Optional[int]							      =					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    _SCREAMING_SNAKE_CASE  (       UpperCamelCase			):



    """simple docstring"""





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

    lowerCAmelCase__ :  Optional[Any]							      =					0
    lowerCAmelCase__ :  Tuple							      =					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    _SCREAMING_SNAKE_CASE  (       UpperCamelCase							,    UpperCamelCase			):



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

    lowerCAmelCase__ :  List[Any]							      =					[]  # 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    _SCREAMING_SNAKE_CASE  (       UpperCamelCase			):



    """simple docstring"""





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

    lowerCAmelCase__ :  List[Any]							      =					[]  # 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    _SCREAMING_SNAKE_CASE  (       UpperCamelCase			):



    """simple docstring"""





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

    lowerCAmelCase__ :  Optional[int]							      =					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    _SCREAMING_SNAKE_CASE  (       UpperCamelCase							,    UpperCamelCase			):



    """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__ :  int							      =					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    _SCREAMING_SNAKE_CASE  (       UpperCamelCase			):



    """simple docstring"""





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

    lowerCAmelCase__ :  str							      =					1  # this will be return.

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

    return ans




def    _SCREAMING_SNAKE_CASE  (       UpperCamelCase			):



    """simple docstring"""





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

    lowerCAmelCase__ :  List[Any]							      =					0
    lowerCAmelCase__ :  Any							      =					1
    lowerCAmelCase__ :  Optional[Any]							      =					1  # this will be return

    for _ in range(n - 1			):
        lowerCAmelCase__ :  Dict							      =					ans
        ans += fiba
        lowerCAmelCase__ :  str							      =					tmp

    return ans


