def A__  (			lowercase:     int,		lowercase:     list					)				->		Dict:
							_enforce_args(lowercase,		lowercase					)
							if n == 0:
														return 0
							A						:     Optional[int]         =float('-inf'					)
							for i in range(1,		n + 1					):
														A						:     Union[str, Any]         =max(
														    lowercase,		prices[i - 1] + naive_cut_rod_recursive(n - i,		lowercase					)					)

							return max_revue



def A__  (			lowercase:     int,		lowercase:     list					)				->		Optional[Any]:
							_enforce_args(lowercase,		lowercase					)
							A						:     Dict         =[float('-inf'					) for _ in range(n + 1					)]
							return _top_down_cut_rod_recursive(lowercase,		lowercase,		lowercase					)



def A__  (			lowercase:     int,		lowercase:     list,		lowercase:     list					)				->		Optional[Any]:
							if max_rev[n] >= 0:
														return max_rev[n]
							elif n == 0:
														return 0
							else:
														A						:     Dict         =float('-inf'					)
														for i in range(1,		n + 1					):
																					A						:     int         =max(
																					    lowercase,		prices[i - 1] + _top_down_cut_rod_recursive(n - i,		lowercase,		lowercase					),		)

														A						:     str         =max_revenue

							return max_rev[n]



def A__  (			lowercase:     int,		lowercase:     list					)				->		Optional[int]:
							_enforce_args(lowercase,		lowercase					)

							# length(max_rev) = n + 1, to accommodate for the revenue obtainable from a rod of
							# length 0.
							A						:     Dict         =[float('-inf'					) for _ in range(n + 1					)]
							A						:     List[Any]         =0

							for i in range(1,		n + 1					):
														A						:     Dict         =max_rev[i]
														for j in range(1,		i + 1					):
																					A						:     List[str]         =max(lowercase,		prices[j - 1] + max_rev[i - j]					)

														A						:     int         =max_revenue_i

							return max_rev[n]



def A__  (			lowercase:     int,		lowercase:     list					)				->		int:
							if n < 0:
														A						:     Tuple         =F'n must be greater than or equal to 0. Got n = {n}'
														raise ValueError(lowercase					)

							if n > len(lowercase					):
														A						:     Dict         =(
														    'Each integral piece of rod must have a corresponding price. '
														    F'Got n = {n} but length of prices = {len(lowercase					)}'
														)
														raise ValueError(lowercase					)



def A__  (			)				->		List[str]:
							A						:     Optional[Any]         =[6, 10, 12, 15, 20, 23]
							A						:     List[str]         =len(lowercase					)

							# the best revenue comes from cutting the rod into 6 pieces, each
							# of length 1 resulting in a revenue of 6 * 6 = 36.
							A						:     Union[str, Any]         =36

							A						:     Dict         =top_down_cut_rod(lowercase,		lowercase					)
							A						:     Tuple         =bottom_up_cut_rod(lowercase,		lowercase					)
							A						:     Union[str, Any]         =naive_cut_rod_recursive(lowercase,		lowercase					)

							assert expected_max_revenue == max_rev_top_down
							assert max_rev_top_down == max_rev_bottom_up
							assert max_rev_bottom_up == max_rev_naive


if __name__ == "__main__":
				main()







import math



def A__  (			lowercase:     int					)				->		list:
       A						:     Optional[Any]         =[True] * n
       A						:     Tuple         =False
       A						:     List[Any]         =False
       A						:     Dict         =True

       for i in range(3,		int(n**0.5 + 1					),		2					):
              A						:     Dict         =i * 2
              while index < n:
                     A						:     Dict         =False
                     A						:     Dict         =index + i

       A						:     Tuple         =[2]

       for i in range(3,		lowercase,		2					):
              if is_prime[i]:
                     primes.append(lowercase					)

       return primes



def A__  (			lowercase:     int = 999_966_663_333					)				->		int:
       A						:     Optional[int]         =math.floor(math.sqrt(lowercase					)					) + 100
       A						:     Optional[int]         =prime_sieve(lowercase					)

       A						:     Optional[Any]         =0
       A						:     List[Any]         =0
       A						:     Union[str, Any]         =primes[prime_index]

       while (last_prime**2) <= limit:
              A						:     Tuple         =primes[prime_index + 1]

              A						:     Optional[int]         =last_prime**2
              A						:     Tuple         =next_prime**2

              # Get numbers divisible by lps(current)
              A						:     int         =lower_bound + last_prime
              while upper_bound > current <= limit:
                     matches_sum += current
                     current += last_prime

              # Reset the upper_bound
              while (upper_bound - next_prime) > limit:
                     upper_bound -= next_prime

              # Add the numbers divisible by ups(current)
              A						:     List[Any]         =upper_bound - next_prime
              while current > lower_bound:
                     matches_sum += current
                     current -= next_prime

              # Remove the numbers divisible by both ups and lps
              A						:     Any         =0
              while upper_bound > current <= limit:
                     if current <= lower_bound:
                            # Increment the current number
                            current += last_prime * next_prime
                            continue

                     if current > limit:
                            break

                     # Remove twice since it was added by both ups and lps
                     matches_sum -= current * 2

                     # Increment the current number
                     current += last_prime * next_prime

              # Setup for next pair
              A						:     List[str]         =next_prime
              prime_index += 1

       return matches_sum


if __name__ == "__main__":
    print(solution())






