
"""simple docstring"""




import math



def     __magic_name__		(					UpperCamelCase     :		float							,		UpperCamelCase     :		float     )     ->						float:
    return math.pow(UpperCamelCase							,		2     ) - a



def     __magic_name__		(					UpperCamelCase     :		float     )     ->						float:
    return 2 * x



def     __magic_name__		(					UpperCamelCase     :		float     )     ->						float:
    a__		=			2.0

    while start <= a:
        a__		=			math.pow(UpperCamelCase							,		2     )

    return start



def     __magic_name__		(					UpperCamelCase     :		float							,		UpperCamelCase     :		int = 9999							,		UpperCamelCase     :		float = 0.00_0000_0000_0001     )     ->						float:

    if a < 0:
        raise ValueError('math domain error'     )

    a__		=			get_initial_point(UpperCamelCase     )

    for _ in range(UpperCamelCase     ):
        a__		=			value
        a__		=			value - fx(UpperCamelCase							,		UpperCamelCase     ) / fx_derivative(UpperCamelCase     )
        if abs(prev_value - value     ) < tolerance:
            return value

    return value


if __name__ == "__main__":
    from doctest import testmod

    testmod()




"""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))


