



from __future__ import annotations

from functools import lru_cache
from math import ceil

UpperCAmelCase_		 =					1_0_0

UpperCAmelCase_		 =					set(range(3, NUM_PRIMES, 2))
primes.add(2)
UpperCAmelCase_		 =					42

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 	SCREAMING_SNAKE_CASE_							(	_snake_case	:int				)  ->     set[int]:
   if number_to_partition < 0:
      return set()
   elif number_to_partition == 0:
      return {1}

   _A      =       set()
   _A      =       42
   _A      =       42

   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 	SCREAMING_SNAKE_CASE_							(	_snake_case	:int = 5_000				)  ->     int | None:
   for number_to_partition in range(1	,   _snake_case				):
      if len(partition(_snake_case				)				) > number_unique_partitions:
         return number_to_partition
   return None


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








UpperCAmelCase_		 =					2_5_6
# Modulus to hash a string
UpperCAmelCase_		 =					1_0_0_0_0_0_3

def 	SCREAMING_SNAKE_CASE_							(	_snake_case	:str	,   _snake_case	:str				)  ->     bool:
   _A      =       len(_snake_case				)
   _A      =       len(_snake_case				)
   if p_len > t_len:
      return False

   _A      =       0
   _A      =       0
   _A      =       1

   # Calculating the hash of pattern and substring of text
   for i in range(_snake_case				):
      _A      =       (ord(pattern[i]				) + p_hash * alphabet_size) % modulus
      _A      =       (ord(text[i]				) + text_hash * alphabet_size) % modulus
      if i == p_len - 1:
         continue
      _A      =       (modulus_power * alphabet_size) % modulus

   for i in range(0	,   t_len - p_len + 1				):
      if text_hash == p_hash and text[i : i + p_len] == pattern:
         return True
      if i == t_len - p_len:
         continue
      # Calculate the https://en.wikipedia.org/wiki/Rolling_hash
      _A      =       (
          (text_hash - ord(text[i]				) * modulus_power) * alphabet_size
          + ord(text[i + p_len]				)
      ) % modulus
   return False

def 	SCREAMING_SNAKE_CASE_							(	)  ->     None:
   _A      =       '''abc1abc12'''
   _A      =       '''alskfjaldsabc1abc1abc12k23adsfabcabc'''
   _A      =       '''alskfjaldsk23adsfabcabc'''
   assert rabin_karp(_snake_case	,   _snake_case				) and not rabin_karp(_snake_case	,   _snake_case				)

   # Test 2)
   _A      =       '''ABABX'''
   _A      =       '''ABABZABABYABABX'''
   assert rabin_karp(_snake_case	,   _snake_case				)

   # Test 3)
   _A      =       '''AAAB'''
   _A      =       '''ABAAAAAB'''
   assert rabin_karp(_snake_case	,   _snake_case				)

   # Test 4)
   _A      =       '''abcdabcy'''
   _A      =       '''abcxabcdabxabcdabcdabcy'''
   assert rabin_karp(_snake_case	,   _snake_case				)

   # Test 5)
   _A      =       '''Lü'''
   _A      =       '''Lüsai'''
   assert rabin_karp(_snake_case	,   _snake_case				)
   _A      =       '''Lue'''
   assert not rabin_karp(_snake_case	,   _snake_case				)
   print('''Success.'''				)


if __name__ == "__main__":
   test_rabin_karp()



