


import math







def        lowerCAmelCase_  (      __lowerCamelCase			):
       __snake_case	:    int											=     [True] * n
       __snake_case	:    Optional[int]											=     False
       __snake_case	:    Dict											=     False
       __snake_case	:    List[Any]											=     True

       for i in range(3							,			int(n**0.5 + 1			)							,			2			):
              __snake_case	:    Optional[Any]											=     i * 2
              while index < n:
                     __snake_case	:    Union[str, Any]											=     False
                     __snake_case	:    Tuple											=     index + i

       __snake_case	:    str											=     [2]

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

       return primes







def        lowerCAmelCase_  (      __lowerCamelCase = 9_9_9_9_6_6_6_6_3_3_3_3			):
       __snake_case	:    Dict											=     math.floor(math.sqrt(SCREAMING_SNAKE_CASE_			)			) + 1_0_0
       __snake_case	:    Any											=     prime_sieve(SCREAMING_SNAKE_CASE_			)

       __snake_case	:    int											=     0
       __snake_case	:    List[Any]											=     0
       __snake_case	:    Tuple											=     primes[prime_index]

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

              __snake_case	:    Union[str, Any]											=     last_prime**2
              __snake_case	:    Any											=     next_prime**2

              # Get numbers divisible by lps(current)
              __snake_case	:    Union[str, Any]											=     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)
              __snake_case	:    str											=     upper_bound - next_prime
              while current > lower_bound:
                     matches_sum += current
                     current -= next_prime

              # Remove the numbers divisible by both ups and lps
              __snake_case	:    str											=     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
              __snake_case	:    int											=     next_prime
              prime_index += 1

       return matches_sum


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





def        lowerCAmelCase_  (      __lowerCamelCase							,			__lowerCamelCase			):
							if number < 0 or shift_amount < 0:
														raise ValueError("both inputs must be positive integers"			)

							__snake_case	:    Dict											=     str(bin(__lowerCamelCase			)			)
							binary_number += "0" * shift_amount
							return binary_number







def        lowerCAmelCase_  (      __lowerCamelCase							,			__lowerCamelCase			):
							if number < 0 or shift_amount < 0:
														raise ValueError("both inputs must be positive integers"			)

							__snake_case	:    List[str]											=     str(bin(__lowerCamelCase			)			)[2:]
							if shift_amount >= len(__lowerCamelCase			):
														return "0b0"
							__snake_case	:    Union[str, Any]											=     binary_number[: len(__lowerCamelCase			) - shift_amount]
							return "0b" + shifted_binary_number







def        lowerCAmelCase_  (      __lowerCamelCase							,			__lowerCamelCase			):
							if number >= 0:  # Get binary representation of positive number
														__snake_case	:    Optional[int]											=     "0" + str(bin(__lowerCamelCase			)			).strip("-"			)[2:]
							else:  # Get binary (2's complement) representation of negative number
														__snake_case	:    Tuple											=     len(bin(__lowerCamelCase			)[3:]			)  # Find 2's complement of number
														__snake_case	:    Any											=     bin(abs(__lowerCamelCase			) - (1 << binary_number_length)			)[3:]
														__snake_case	:    Optional[Any]											=     (
														    "1" + "0" * (binary_number_length - len(__lowerCamelCase			)) + binary_number
														)

							if shift_amount >= len(__lowerCamelCase			):
														return "0b" + binary_number[0] * len(__lowerCamelCase			)
							return (
							    "0b"
							    + binary_number[0] * shift_amount
							    + binary_number[: len(__lowerCamelCase			) - shift_amount]
							)


if __name__ == "__main__":
			import doctest

			doctest.testmod()

