


"""simple docstring"""



def     __lowerCAmelCase		(		lowercase    :    int		,				lowercase    :    list[int]		,				lowercase    :    int					)      ->		int:


    """simple docstring"""





    def count_of_possible_combinations(lowercase    :    int					) -> int:
        if target < 0:
            return 0
        if target == 0:
            return 1
        return sum(count_of_possible_combinations(target - item					) for item in array					)

    return count_of_possible_combinations(lowercase					)







def     __lowerCAmelCase		(		lowercase    :    int		,				lowercase    :    list[int]		,				lowercase    :    int					)      ->		int:


    """simple docstring"""





    def count_of_possible_combinations_with_dp_array(
        lowercase    :    int		,				lowercase    :    list[int]					) -> int:
        if target < 0:
            return 0
        if target == 0:
            return 1
        if dp_array[target] != -1:
            return dp_array[target]
        snake_case       : Dict    =       sum(
            count_of_possible_combinations_with_dp_array(target - item		,				lowercase					)
            for item in array					)
        snake_case       : int    =       answer
        return answer

    snake_case       : Dict    =       [-1] * (target + 1)
    return count_of_possible_combinations_with_dp_array(lowercase		,				lowercase					)







def     __lowerCAmelCase		(		lowercase    :    int		,				lowercase    :    list[int]		,				lowercase    :    int					)      ->		int:


    """simple docstring"""





    snake_case       : Union[str, Any]    =       [0] * (target + 1)
    snake_case       : Optional[Any]    =       1

    for i in range(1		,				target + 1					):
        for j in range(lowercase					):
            if i - array[j] >= 0:
                dp_array[i] += dp_array[i - array[j]]

    return dp_array[target]


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  __snake_case       =       3
  __snake_case       =       5
  __snake_case       =       [1, 2, 5]
  print(combination_sum_iv(n, array, target))









"""simple docstring"""



import math
from collections.abc import Iterator
from itertools import takewhile







def     __lowerCAmelCase		(		lowercase    :    int					)      ->		bool:


    """simple docstring"""





    if 1 < number < 4:
        # 2 and 3 are primes
        return True
    elif number < 2 or number % 2 == 0 or number % 3 == 0:
        # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
        return False

    # All primes number are in format of 6k +/- 1
    for i in range(5		,				int(math.sqrt(lowercase					) + 1					)		,				6					):
        if number % i == 0 or number % (i + 2) == 0:
            return False
    return True







def     __lowerCAmelCase		(		)      ->		Iterator[int]:


    """simple docstring"""





    snake_case       : Optional[int]    =       2
    while True:
        if is_prime(lowercase					):
            yield num
        num += 1







def     __lowerCAmelCase		(		lowercase    :    int = 200_0000					)      ->		int:


    """simple docstring"""





    return sum(takewhile(lambda lowercase					: x < n		,				prime_generator()					)					)


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





