

from __future__ import annotations

from functools import lru_cache
from math import ceil

SCREAMING_SNAKE_CASE		:Dict						=     100

SCREAMING_SNAKE_CASE		:str						=     set(range(3, NUM_PRIMES, 2))
primes.add(2)
SCREAMING_SNAKE_CASE		: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=1_0_0			)
def 			lowerCAmelCase(      SCREAMING_SNAKE_CASE_			)->						set[int]:



    """simple docstring"""






    if number_to_partition < 0:
        return set()
    elif number_to_partition == 0:
        return {1}

    UpperCamelCase_			  =						set()
    UpperCamelCase_			  =						42
    UpperCamelCase_			  =						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 			lowerCAmelCase(      SCREAMING_SNAKE_CASE_ = 5_0_0_0			)->						int | None:



    """simple docstring"""






    for number_to_partition in range(1			,						SCREAMING_SNAKE_CASE_			):
        if len(partition(SCREAMING_SNAKE_CASE_			)			) > number_unique_partitions:
            return number_to_partition
    return None


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



from __future__ import annotations

import math




def 			lowerCAmelCase(      SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			)->						int:



    """simple docstring"""






    if depth < 0:
        raise ValueError("Depth cannot be less than 0"			)

    if len(SCREAMING_SNAKE_CASE_			) == 0:
        raise ValueError("Scores cannot be empty"			)

    if depth == height:
        return scores[node_index]

    if is_max:
        return max(
            minimax(depth + 1			,						node_index * 2			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			)			,						minimax(depth + 1			,						node_index * 2 + 1			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			)			,						)

    return min(
        minimax(depth + 1			,						node_index * 2			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			)			,						minimax(depth + 1			,						node_index * 2 + 1			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			)			,						)




def 			lowerCAmelCase(      )->						None:



    """simple docstring"""






    UpperCamelCase_			  =						[9_0, 2_3, 6, 3_3, 2_1, 6_5, 1_2_3, 3_4_4_2_3]
    UpperCamelCase_			  =						math.log(len(SCREAMING_SNAKE_CASE_			)			,						2			)
    print("Optimal value : "			,						end=""			)
    print(minimax(0			,						0			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			)			)


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 main()
