






'''simple docstring'''




def    __lowercase		(     __lowercase  ,    __lowercase  ,    __lowercase			)			->		Any:

      '''simple docstring'''


      def count_of_possible_combinations(__lowercase			) -> 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    __lowercase		(     __lowercase  ,    __lowercase  ,    __lowercase			)			->		Dict:

      '''simple docstring'''


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

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

def    __lowercase		(     __lowercase  ,    __lowercase  ,    __lowercase			)			->		int:

      '''simple docstring'''


      _A     	=      [0] * (target + 1)
      _A     	=      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_				   =   3
    lowerCamelCase_				   =   5
    lowerCamelCase_				   =   [1, 2, 5]
    print(combination_sum_iv(n, array, target))








from math import isqrt, loga







def 						lowerCamelCase__      ( __A    :int		):


       """simple docstring"""




       __snake_case       	=							[True] * max_number
       for i in range(2	,isqrt(max_number - 1		) + 1		):
              if is_prime[i]:
                     for j in range(i**2	,__A	,__A		):
                            __snake_case       	=							False

       return [i for i in range(2	,__A		) if is_prime[i]]







def 						lowerCamelCase__      ( __A    :int = 8_0_0_8_0_0	,__A    :int = 8_0_0_8_0_0		):


       """simple docstring"""




       __snake_case       	=							degree * loga(__A		)
       __snake_case       	=							int(__A		)
       __snake_case       	=							calculate_prime_numbers(__A		)

       __snake_case       	=							0
       __snake_case       	=							0
       __snake_case       	=							len(__A		) - 1
       while left < right:
              while (
                  prime_numbers[right] * loga(prime_numbers[left]		)
                  + prime_numbers[left] * loga(prime_numbers[right]		)
                  > upper_bound
              ):
                     right -= 1
              hybrid_integers_count += right - left
              left += 1

       return hybrid_integers_count


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

