






def    __magic_name__    (	SCREAMING_SNAKE_CASE = 1_000_000				)     ->    int:
							_lowercase							:   str 							=   set(range(3     ,     SCREAMING_SNAKE_CASE     ,     2				)				)
							primes.add(2				)
							for p in range(3     ,     SCREAMING_SNAKE_CASE     ,     2				):
														if p not in primes:
																					continue
														primes.difference_update(set(range(p * p     ,     SCREAMING_SNAKE_CASE     ,     SCREAMING_SNAKE_CASE				)				)				)

							_lowercase							:   Tuple 							=   [float(SCREAMING_SNAKE_CASE				) for n in range(limit + 1				)]

							for p in primes:
														for n in range(SCREAMING_SNAKE_CASE     ,     limit + 1     ,     SCREAMING_SNAKE_CASE				):
																					phi[n] *= 1 - 1 / p

							return int(sum(phi[2:]				)				)


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






"""simple docstring"""




def     __magic_name__		(					UpperCamelCase     :		int							,		UpperCamelCase     :		list[int]							,		UpperCamelCase     :		int     )     ->						int:

    def count_of_possible_combinations(UpperCamelCase     :		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(UpperCamelCase     )



def     __magic_name__		(					UpperCamelCase     :		int							,		UpperCamelCase     :		list[int]							,		UpperCamelCase     :		int     )     ->						int:

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

    a__		=			[-1] * (target + 1)
    return count_of_possible_combinations_with_dp_array(UpperCamelCase							,		UpperCamelCase     )



def     __magic_name__		(					UpperCamelCase     :		int							,		UpperCamelCase     :		list[int]							,		UpperCamelCase     :		int     )     ->						int:
    a__		=			[0] * (target + 1)
    a__		=			1

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

    return dp_array[target]


if __name__ == "__main__":
    import doctest

    doctest.testmod()
    a		:       Optional[Any]     						=       3
    a		:       List[str]     						=       5
    a		:       Dict     						=       [1, 2, 5]
    print(combination_sum_iv(n, array, target))


