





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)							-> int:




    """simple docstring"""




    def count_of_possible_combinations(_SCREAMING_SNAKE_CASE				) -> 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(_SCREAMING_SNAKE_CASE				)





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)							-> int:




    """simple docstring"""




    def count_of_possible_combinations_with_dp_array(
        _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				) -> 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							,     _SCREAMING_SNAKE_CASE				)
            for item in array				)
        _A     =							answer
        return answer

    _A     =							[-1] * (target + 1)
    return count_of_possible_combinations_with_dp_array(_SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)							-> int:




    """simple docstring"""




    _A     =							[0] * (target + 1)
    _A     =							1

    for i in range(1							,     target + 1				):
        for j in range(_SCREAMING_SNAKE_CASE				):
            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							:			str         =			3
 __A							:			Tuple         =			5
 __A							:			int         =			[1, 2, 5]
 print(combination_sum_iv(n, array, target))












import numpy as np





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE				)							-> np.array:




    """simple docstring"""




    return (2 / (1 + np.exp(-2 * vector				))) - 1


if __name__ == "__main__":
 import doctest

 doctest.testmod()





