

"""simple docstring"""


a					:dict[tuple[int, int, int], int]    = {}




def  _lowercase					(    __lowerCAmelCase  ,					__lowerCAmelCase  ,					__lowerCAmelCase							)       ->				int:

      # if we are absent twice, or late 3 consecutive days,
      # no further prize strings are possible
      if late == 3 or absent == 2:
            return 0

      # if we have no days left, and have not failed any other rules,
      # we have a prize string
      if days == 0:
            return 1

      # No easy solution, so now we need to do the recursive calculation

      # First, check if the combination is already in the cache, and
      # if yes, return the stored value from there since we already
      # know the number of possible prize strings from this point on
      SCREAMING_SNAKE_CASE__   :      Dict      		=	(days, absent, late)
      if key in cache:
            return cache[key]

      # now we calculate the three possible ways that can unfold from
      # this point on, depending on our attendance today

      # 1) if we are late (but not absent), the "absent" counter stays as
      # it is, but the "late" counter increases by one
      SCREAMING_SNAKE_CASE__   :      Optional[Any]      		=	_calculate(days - 1  ,					__lowerCAmelCase  ,					late + 1							)

      # 2) if we are absent, the "absent" counter increases by 1, and the
      # "late" counter resets to 0
      SCREAMING_SNAKE_CASE__   :      int      		=	_calculate(days - 1  ,					absent + 1  ,					0							)

      # 3) if we are on time, this resets the "late" counter and keeps the
      # absent counter
      SCREAMING_SNAKE_CASE__   :      Any      		=	_calculate(days - 1  ,					__lowerCAmelCase  ,					0							)

      SCREAMING_SNAKE_CASE__   :      Optional[int]      		=	state_late + state_absent + state_ontime

      SCREAMING_SNAKE_CASE__   :      Dict      		=	prizestrings
      return prizestrings




def  _lowercase					(    __lowerCAmelCase = 30							)       ->				int:
      return _calculate(__lowerCAmelCase  ,					absent=0  ,					late=0							)


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







"""simple docstring"""


def  _lowercase					(    __lowerCAmelCase  ,					__lowerCAmelCase							)       ->				bool:
      SCREAMING_SNAKE_CASE__   :      Optional[Any]      		=	len(__lowerCAmelCase							) + 1
      SCREAMING_SNAKE_CASE__   :      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.
      SCREAMING_SNAKE_CASE__   :      Dict      		=	[[0 for i in range(__lowerCAmelCase							)] for j in range(__lowerCAmelCase							)]

      # since string of zero length match pattern of zero length
      SCREAMING_SNAKE_CASE__   :      Dict      		=	1

      # since pattern of zero length will never match with string of non-zero length
      for i in range(1  ,					__lowerCAmelCase							):
            SCREAMING_SNAKE_CASE__   :      Union[str, Any]      		=	0

      # since string of zero length will match with pattern where there
      # is at least one * alternatively
      for j in range(1  ,					__lowerCAmelCase							):
            SCREAMING_SNAKE_CASE__   :      int      		=	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] == ".":
                        SCREAMING_SNAKE_CASE__   :      Any      		=	dp[i - 1][j - 1]

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

  a					:Any    = "aab"
  a					:Optional[Any]    = "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}')




