




from __future__ import annotations

from functools import lru_cache
from math import ceil

a_   		=     100

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 					__SCREAMING_SNAKE_CASE   (  lowercase_      )       ->	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 					__SCREAMING_SNAKE_CASE   (  lowercase_ = 50_00      )       ->	int | None:

    """simple docstring"""


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


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












def 					__SCREAMING_SNAKE_CASE   (  lowercase_					,     lowercase_ = False      )       ->	str:

    """simple docstring"""


    if not isinstance(lowercase_					,     lowercase_      ):
        __UpperCamelCase  		=						F"Expected string as input, found {type(lowercase_      )}"
        raise ValueError(lowercase_      )
    if not isinstance(lowercase_					,     lowercase_      ):
        __UpperCamelCase  		=						F"Expected boolean as use_pascal parameter, found {type(lowercase_      )}"
        raise ValueError(lowercase_      )

    __UpperCamelCase  		=						input_str.split('''_'''      )

    __UpperCamelCase  		=						0 if use_pascal else 1

    __UpperCamelCase  		=						words[start_index:]

    __UpperCamelCase  		=						[word[0].upper() + word[1:] for word in words_to_capitalize]

    __UpperCamelCase  		=						'''''' if use_pascal else words[0]

    return "".join([initial_word, *capitalized_words]      )


if __name__ == "__main__":
 from doctest import testmod

 testmod()






