
"""simple docstring"""





from collections import defaultdict

from graphs.minimum_spanning_tree_prims import prisms_algorithm as mst



def  lowerCamelCase__						(     )				->						Any:


					"""simple docstring"""





					_UpperCamelCase					,    _UpperCamelCase									=    9, 14  # noqa: F841
					_UpperCamelCase									=    [
					    [0, 1, 4],
					    [0, 7, 8],
					    [1, 2, 8],
					    [7, 8, 7],
					    [7, 6, 1],
					    [2, 8, 2],
					    [8, 6, 6],
					    [2, 3, 7],
					    [2, 5, 4],
					    [6, 5, 2],
					    [3, 5, 14],
					    [3, 4, 9],
					    [5, 4, 10],
					    [1, 7, 11],
					]

					_UpperCamelCase									=    defaultdict(__snake_case      )
					for nodea, nodea, cost in edges:
										adjancency[nodea].append([nodea, cost]      )
										adjancency[nodea].append([nodea, cost]      )

					_UpperCamelCase									=    mst(__snake_case      )

					_UpperCamelCase									=    [
					    [7, 6, 1],
					    [2, 8, 2],
					    [6, 5, 2],
					    [0, 1, 4],
					    [2, 5, 4],
					    [2, 3, 7],
					    [0, 7, 8],
					    [3, 4, 9],
					]

					for answer in expected:
										_UpperCamelCase									=    tuple(answer[:2]      )
										_UpperCamelCase									=    tuple(edge[::-1]      )
										assert edge in result or reverse in result








"""simple docstring"""





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  lowerCamelCase__						(     __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__						(     __snake_case = 50_00      )				->						int | None:


					"""simple docstring"""





					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() = }""")






