



"""simple docstring"""
def 					lowerCamelCase_		(UpperCamelCase__						:						Dict	,			UpperCamelCase__						:						Any	,			UpperCamelCase__						:						Optional[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(A__				)





def 					lowerCamelCase_		(UpperCamelCase__						:						int	,			UpperCamelCase__						:						Tuple	,			UpperCamelCase__						:						Dict				):

    def count_of_possible_combinations_with_dp_array(
        UpperCamelCase__						:						List[Any]	,			UpperCamelCase__						:						Dict				) -> int:
        if target < 0:
            return 0
        if target == 0:
            return 1
        if dp_array[target] != -1:
            return dp_array[target]
        _UpperCAmelCase				:    int											=       sum(
            count_of_possible_combinations_with_dp_array(target - item	,			A__				)
            for item in array				)
        _UpperCAmelCase				:    List[str]											=       answer
        return answer

    _UpperCAmelCase				:    Union[str, Any]											=       [-1] * (target + 1)
    return count_of_possible_combinations_with_dp_array(A__	,			A__				)





def 					lowerCamelCase_		(UpperCamelCase__						:						int	,			UpperCamelCase__						:						List[str]	,			UpperCamelCase__						:						int				):
    _UpperCAmelCase				:    List[Any]											=       [0] * (target + 1)
    _UpperCAmelCase				:    Optional[int]											=       1

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

    return dp_array[target]


if __name__ == "__main__":
  import doctest

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




'''simple docstring'''
import math






def      UpperCamelCase_				(      A__						):
	return math.sqrt(A__						) * math.sqrt(A__						) == num






def      UpperCamelCase_				(      A__						):
	a_      				=						0
	a_      				=						n
	while left <= right:
		a_      				=						(left + right) // 2
		if mid**2 == n:
			return True
		elif mid**2 > n:
			a_      				=						mid - 1
		else:
			a_      				=						mid + 1
	return False


if __name__ == "__main__":
		import doctest

		doctest.testmod()
