




def 							_UpperCAmelCase  (UpperCamelCase_ : int      ,    UpperCamelCase_ : bool = False       ):
				'''simple docstring'''
				if n == 2:
								return True
				if not n % 2 or n < 2:
								return False
				if n > 5 and n % 10 not in (1, 3, 7, 9):  # can quickly check last digit
								return False
				if n > 3317044064679887385961981 and not allow_probable:
								raise ValueError(
								    """Warning: upper bound of deterministic test is exceeded. """
								    """Pass allow_probable=True to allow probabilistic test. """
								    """A return value of True indicates a probable prime."""       )
				# array bounds provided by analysis
				_lowerCAmelCase    :    Any										=      [
				    2047,
				    1373653,
				    25326001,
				    3215031751,
				    2152302898747,
				    3474749660383,
				    341550071728321,
				    1,
				    3825123056546413051,
				    1,
				    1,
				    318665857834031151167461,
				    3317044064679887385961981,
				]

				_lowerCAmelCase    :    Any										=      [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41]
				for idx, _p in enumerate(UpperCamelCase_      ,    1       ):
								if n < _p:
												# then we have our last prime to check
												_lowerCAmelCase    :    int										=      primes[:idx]
												break
				_lowerCAmelCase					,    _lowerCAmelCase    :    int										=      n - 1, 0
				# break up n -1 into a power of 2 (s) and
				# remaining odd component
				# essentially, solve for d * 2 ** s == n - 1
				while d % 2 == 0:
								d //= 2
								s += 1
				for prime in plist:
								_lowerCAmelCase    :    Dict										=      False
								for r in range(UpperCamelCase_       ):
												_lowerCAmelCase    :    str										=      pow(UpperCamelCase_      ,    d * 2**r      ,    UpperCamelCase_       )
												# see article for analysis explanation for m
												if (r == 0 and m == 1) or ((m + 1) % n == 0):
																_lowerCAmelCase    :    Union[str, Any]										=      True
																# this loop will not determine compositeness
																break
								if pr:
												continue
								# if pr is False, then the above loop never evaluated to true,
								# and the n MUST be composite
								return False
				return True




def 							_UpperCAmelCase  ():
				'''simple docstring'''
				assert not miller_rabin(561       )
				assert miller_rabin(563       )
				# 2047

				assert not miller_rabin(838201       )
				assert miller_rabin(838207       )
				# 1_373_653

				assert not miller_rabin(17316001       )
				assert miller_rabin(17316017       )
				# 25_326_001

				assert not miller_rabin(3078386641       )
				assert miller_rabin(3078386653       )
				# 3_215_031_751

				assert not miller_rabin(1713045574801       )
				assert miller_rabin(1713045574819       )
				# 2_152_302_898_747

				assert not miller_rabin(2779799728307       )
				assert miller_rabin(2779799728327       )
				# 3_474_749_660_383

				assert not miller_rabin(113850023909441       )
				assert miller_rabin(113850023909527       )
				# 341_550_071_728_321

				assert not miller_rabin(1275041018848804351       )
				assert miller_rabin(1275041018848804391       )
				# 3_825_123_056_546_413_051

				assert not miller_rabin(79666464458507787791867       )
				assert miller_rabin(79666464458507787791951       )
				# 318_665_857_834_031_151_167_461

				assert not miller_rabin(552840677446647897660333       )
				assert miller_rabin(552840677446647897660359       )
				# 3_317_044_064_679_887_385_961_981
				# upper limit for probabilistic test


if __name__ == "__main__":
	test_miller_rabin()







def 							_UpperCAmelCase  (UpperCamelCase_ : str       ):
				'''simple docstring'''
				_lowerCAmelCase    :    List[str]										=      [int(UpperCamelCase_       ) for i in ip_va_address.split("""."""       ) if i.isdigit()]
				return len(UpperCamelCase_       ) == 4 and all(0 <= int(UpperCamelCase_       ) <= 254 for octet in octets       )


if __name__ == "__main__":
	_lowerCamelCase      :  List[str]      						=						input().strip()
	_lowerCamelCase      :  int      						=						"valid" if is_ip_va_address_valid(ip) else "invalid"
	print(F'''{ip} is a {valid_or_invalid} IP v4 address.''')

