

"""simple docstring"""


from __future__ import annotations

from functools import lru_cache
from math import ceil

a					:Optional[int]    = 100

a					:Optional[int]    = set(range(3, NUM_PRIMES, 2))
primes.add(2)
a					:int

for prime in range(3, ceil(NUM_PRIMES**0.5), 2):
  if prime not in primes:
    continue
  primes.difference_update(set(range(prime * prime, NUM_PRIMES, prime)))




@lru_cache(maxsize=100							)
def  _lowercase					(    __lowerCAmelCase							)       ->				set[int]:
      if number_to_partition < 0:
            return set()
      elif number_to_partition == 0:
            return {1}

      SCREAMING_SNAKE_CASE__   :      set[int]      		=	set()
      SCREAMING_SNAKE_CASE__   :      int
      SCREAMING_SNAKE_CASE__   :      int

      for prime in primes:
            if prime > number_to_partition:
                  continue
            for sub in partition(number_to_partition - prime							):
                  ret.add(sub * prime							)

      return ret




def  _lowercase					(    __lowerCAmelCase = 5000							)       ->				int | None:
      for number_to_partition in range(1  ,					__lowerCAmelCase							):
            if len(partition(__lowerCAmelCase							)							) > number_unique_partitions:
                  return number_to_partition
      return None


if __name__ == "__main__":
  print(f'{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}')




