
from math import sqrt





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

    snake_case__						=				True

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

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

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

    return status





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

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

    snake_case__						=				[]  # this list will be returns.

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

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

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

    return ans





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

    snake_case__						=				[]

    # 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(__lowerCAmelCase							):
            ans.append(__lowerCAmelCase							)

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

    return ans





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

    snake_case__						=				[]  # this list will be returns of the function.

    # potential prime number factors.

    snake_case__						=				2

    snake_case__						=				number

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

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

    else:
        ans.append(__lowerCAmelCase							)

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

    return ans





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

    snake_case__						=				0

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

    snake_case__						=				max(__lowerCAmelCase							)

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

    return ans





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

    snake_case__						=				0

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

    snake_case__						=				min(__lowerCAmelCase							)

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

    return ans





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

    return number % 2 == 0





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

    return number % 2 != 0





def 	SCREAMING_SNAKE_CASE__    (      __lowerCAmelCase							):
    assert (
        isinstance(__lowerCAmelCase    ,		__lowerCAmelCase							) and (number > 2) and is_even(__lowerCAmelCase							)
    ), "'number' must been an int, even and > 2"

    snake_case__						=				[]  # this list will returned

    # creates a list of prime numbers between 2 up to 'number'
    snake_case__						=				get_prime_numbers(__lowerCAmelCase							)
    snake_case__						=				len(__lowerCAmelCase							)

    # run variable for while-loops.
    snake_case__						=				0
    snake_case__						=				None

    # exit variable. for break up the loops
    snake_case__						=				True

    while i < len_pn and loop:
        snake_case__						=				i + 1

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

            j += 1

        i += 1

    # precondition
    assert (
        isinstance(__lowerCAmelCase    ,		__lowerCAmelCase							)
        and (len(__lowerCAmelCase							) == 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__    (      __lowerCAmelCase    ,		__lowerCAmelCase							):
    assert (
        isinstance(__lowerCAmelCase    ,		__lowerCAmelCase							)
        and isinstance(__lowerCAmelCase    ,		__lowerCAmelCase							)
        and (numbera >= 0)
        and (numbera >= 0)
    ), "'number1' and 'number2' must been positive integer."

    snake_case__						=				0

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

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

    return numbera





def 	SCREAMING_SNAKE_CASE__    (      __lowerCAmelCase    ,		__lowerCAmelCase							):
    assert (
        isinstance(__lowerCAmelCase    ,		__lowerCAmelCase							)
        and isinstance(__lowerCAmelCase    ,		__lowerCAmelCase							)
        and (numbera >= 1)
        and (numbera >= 1)
    ), "'number1' and 'number2' must been positive integer."

    snake_case__						=				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'
        snake_case__						=				prime_factorization(__lowerCAmelCase							)
        snake_case__						=				prime_factorization(__lowerCAmelCase							)

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

    snake_case__						=				0
    snake_case__						=				0

    snake_case__						=				[]  # 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:
                snake_case__						=				prime_fac_a.count(__lowerCAmelCase							)
                snake_case__						=				prime_fac_a.count(__lowerCAmelCase							)

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

            else:
                snake_case__						=				prime_fac_a.count(__lowerCAmelCase							)

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

            done.append(__lowerCAmelCase							)

    # iterates through primeFac2
    for n in prime_fac_a:
        if n not in done:
            snake_case__						=				prime_fac_a.count(__lowerCAmelCase							)

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

            done.append(__lowerCAmelCase							)

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

    return ans





def 	SCREAMING_SNAKE_CASE__    (      __lowerCAmelCase							):
    assert isinstance(__lowerCAmelCase    ,		__lowerCAmelCase							) and (n >= 0), "'number' must been a positive int"

    snake_case__						=				0
    snake_case__						=				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(__lowerCAmelCase							):
            ans += 1

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

    return ans





def 	SCREAMING_SNAKE_CASE__    (      __lowerCAmelCase    ,		__lowerCAmelCase							):
    assert (
        is_prime(__lowerCAmelCase							) and is_prime(__lowerCAmelCase							) and (p_number_a < p_number_a)
    ), "The arguments must been prime numbers and 'pNumber1' < 'pNumber2'"

    snake_case__						=				p_number_a + 1  # jump to the next number

    snake_case__						=				[]  # this list will be returns.

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

    while number < p_number_a:
        ans.append(__lowerCAmelCase							)

        number += 1

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

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

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





def 	SCREAMING_SNAKE_CASE__    (      __lowerCAmelCase							):
    assert isinstance(__lowerCAmelCase    ,		__lowerCAmelCase							) and (n >= 1), "'n' must been int and >= 1"

    snake_case__						=				[]  # will be returned.

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

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

    return ans





def 	SCREAMING_SNAKE_CASE__    (      __lowerCAmelCase							):
    assert isinstance(__lowerCAmelCase    ,		__lowerCAmelCase							) and (
        number > 1
    ), "'number' must been an int and >= 1"

    snake_case__						=				get_divisors(__lowerCAmelCase							)

    # precondition
    assert (
        isinstance(__lowerCAmelCase    ,		__lowerCAmelCase							)
        and (divisors[0] == 1)
        and (divisors[len(__lowerCAmelCase							) - 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__    (      __lowerCAmelCase    ,		__lowerCAmelCase							):
    assert (
        isinstance(__lowerCAmelCase    ,		__lowerCAmelCase							)
        and isinstance(__lowerCAmelCase    ,		__lowerCAmelCase							)
        and (denominator != 0)
    ), "The arguments must been from type int and 'denominator' != 0"

    # build the greatest common divisor of numerator and denominator.
    snake_case__						=				gcd(abs(__lowerCAmelCase							)    ,		abs(__lowerCAmelCase							)							)

    # precondition
    assert (
        isinstance(__lowerCAmelCase    ,		__lowerCAmelCase							)
        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__    (      __lowerCAmelCase							):
    assert isinstance(__lowerCAmelCase    ,		__lowerCAmelCase							) and (n >= 0), "'n' must been a int and >= 0"

    snake_case__						=				1  # this will be return.

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

    return ans





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

    snake_case__						=				0
    snake_case__						=				1
    snake_case__						=				1  # this will be return

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

    return ans





from __future__ import annotations





def 	SCREAMING_SNAKE_CASE__    (      __lowerCAmelCase    ,		__lowerCAmelCase							):
    if len(__lowerCAmelCase							) == 0:
        return False
    snake_case__						=				len(__lowerCAmelCase							) // 2
    if a_list[midpoint] == item:
        return True
    if item < a_list[midpoint]:
        return binary_search(a_list[:midpoint]    ,		__lowerCAmelCase							)
    else:
        return binary_search(a_list[midpoint + 1 :]    ,		__lowerCAmelCase							)


if __name__ == "__main__":
     __magic_name__            =  input('''Enter numbers separated by comma:\n''').strip()
     __magic_name__            =  [int(item.strip()) for item in user_input.split(''',''')]
     __magic_name__            =  int(input('''Enter the number to be found in the list:\n''').strip())
     __magic_name__            =  '''''' if binary_search(sequence, target) else '''not '''
     print(F'''{target} was {not_str}found in {sequence}''')



