

SCREAMING_SNAKE_CASE_            = [sum(int(c, 10) ** 2 for c in i.__str__()) for i in range(100000)]

def 							__SCREAMING_SNAKE_CASE							(			lowerCAmelCase:					int	)				->    int:
				_UpperCAmelCase    :						Optional[int]							=      0
				while number:
								# Increased Speed Slightly by checking every 5 digits together.
								sum_of_digits_squared += DIGITS_SQUARED[number % 10_0000]
								number //= 10_0000

				return sum_of_digits_squared


# There are 2 Chains made,
# One ends with 89 with the chain member 58 being the one which when declared first,
# there will be the least number of iterations for all the members to be checked.

# The other one ends with 1 and has only one element 1.

# So 58 and 1 are chosen to be declared at the starting.

# Changed dictionary to an array to quicken the solution
SCREAMING_SNAKE_CASE_            = [None] * 10000000
SCREAMING_SNAKE_CASE_            = True
SCREAMING_SNAKE_CASE_            = False

def 							__SCREAMING_SNAKE_CASE							(			lowerCAmelCase:					int	)				->    bool:

				if CHAINS[number - 1] is not None:
								return CHAINS[number - 1]  # type: ignore

				_UpperCAmelCase    :						Union[str, Any]							=      chain(next_number(_lowerCAmelCase	)	)
				_UpperCAmelCase    :						int							=      number_chain

				while number < 1000_0000:
								_UpperCAmelCase    :						Dict							=      number_chain
								number *= 10

				return number_chain

def 							__SCREAMING_SNAKE_CASE							(			lowerCAmelCase:					int = 1000_0000	)				->    int:
				for i in range(1					, _lowerCAmelCase	):
								if CHAINS[i] is None:
												chain(i + 1	)

				return CHAINS[:number].count(_lowerCAmelCase	)


if __name__ == "__main__":
					import doctest

					doctest.testmod()
					print(F'''{solution() = }''')





def 							__SCREAMING_SNAKE_CASE							(			lowerCAmelCase:					str					, lowerCAmelCase:					str	)				->    bool:
				_UpperCAmelCase    :						Optional[Any]							=      len(lowerCAmelCase	) + 1
				_UpperCAmelCase    :						Optional[int]							=      len(lowerCAmelCase	) + 1

				# dp is a 2d matrix where dp[i][j] denotes whether prefix string of
				# length i of input_string matches with prefix string of length j of
				# given pattern.
				# "dp" stands for dynamic programming.
				_UpperCAmelCase    :						List[str]							=      [[0 for i in range(lowerCAmelCase	)] for j in range(lowerCAmelCase	)]

				# since string of zero length match pattern of zero length
				_UpperCAmelCase    :						List[Any]							=      1

				# since pattern of zero length will never match with string of non-zero length
				for i in range(1					, lowerCAmelCase	):
								_UpperCAmelCase    :						Dict							=      0

				# since string of zero length will match with pattern where there
				# is at least one * alternatively
				for j in range(1					, lowerCAmelCase	):
								_UpperCAmelCase    :						Tuple							=      dp[0][j - 2] if pattern[j - 1] == "*" else 0

				# now using bottom-up approach to find for all remaining lengths
				for i in range(1					, lowerCAmelCase	):
								for j in range(1					, lowerCAmelCase	):
												if input_string[i - 1] == pattern[j - 1] or pattern[j - 1] == ".":
																_UpperCAmelCase    :						Optional[Any]							=      dp[i - 1][j - 1]

												elif pattern[j - 1] == "*":
																if dp[i][j - 2] == 1:
																				_UpperCAmelCase    :						List[str]							=      1
																elif pattern[j - 2] in (input_string[i - 1], "."):
																				_UpperCAmelCase    :						str							=      dp[i - 1][j]
																else:
																				_UpperCAmelCase    :						int							=      0
												else:
																_UpperCAmelCase    :						List[Any]							=      0

				return bool(dp[-1][-1]	)


if __name__ == "__main__":
					import doctest

					doctest.testmod()
					# inputing the strings
					# input_string = input("input a string :")
					# pattern = input("input a pattern :")

					SCREAMING_SNAKE_CASE_            = 'aab'
					SCREAMING_SNAKE_CASE_            = 'c*a*b'

					# using function to check whether given string matches the given pattern
					if match_pattern(input_string, pattern):
										print(F'''{input_string} matches the given pattern {pattern}''')
					else:
										print(F'''{input_string} does not match with the given pattern {pattern}''')


