

"""simple docstring"""
from __future__ import annotations




def 					a__						(						lowerCAmelCase			,	lowerCAmelCase    )	-> bool:
      if len(lowerCAmelCase    ) == 0:
            return False
      UpperCAmelCase__			:							Optional[Any]							=    len(lowerCAmelCase    ) // 2
      if a_list[midpoint] == item:
            return True
      if item < a_list[midpoint]:
            return binary_search(a_list[:midpoint]			,	lowerCAmelCase    )
      else:
            return binary_search(a_list[midpoint + 1 :]			,	lowerCAmelCase    )


if __name__ == "__main__":
    _A							=  input("""Enter numbers separated by comma:\n""").strip()
    _A							=  [int(item.strip()) for item in user_input.split(""",""")]
    _A							=  int(input("""Enter the number to be found in the list:\n""").strip())
    _A							=  """""" if binary_search(sequence, target) else """not """
    print(f'''{target} was {not_str}found in {sequence}''')




"""simple docstring"""
from __future__ import annotations

from functools import lru_cache
from math import ceil

_A							=  1_00

_A							=  set(range(3, NUM_PRIMES, 2))
primes.add(2)
_A							=  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=1_00    )
def 					a__						(						lowerCAmelCase    )	-> set[int]:
      if number_to_partition < 0:
            return set()
      elif number_to_partition == 0:
            return {1}

      UpperCAmelCase__			:							set[int]							=    set()
      UpperCAmelCase__			:							int
      UpperCAmelCase__			:							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 					a__						(						lowerCAmelCase = 50_00    )	-> 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() = }''')

