





from graphs.minimum_spanning_tree_kruskal import kruskal





def      lowerCAmelCase_ (       )     ->		str:







  """simple docstring"""





  lowerCamelCase__:      Optional[int]			  =9
  lowerCamelCase__:      Union[str, Any]			  =[
      [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],
  ]

  lowerCamelCase__:      Optional[Any]			  =kruskal(__a	,    __a		)

  lowerCamelCase__:      str			  =[
      [7, 6, 1],
      [2, 8, 2],
      [6, 5, 2],
      [0, 1, 4],
      [2, 5, 4],
      [2, 3, 7],
      [0, 7, 8],
      [3, 4, 9],
  ]

  assert sorted(__a		) == sorted(__a		)








import itertools
import math





def      lowerCAmelCase_ (       __a		)     ->		bool:







  """simple docstring"""





  if 1 < number < 4:
    # 2 and 3 are primes
    return True
  elif number < 2 or number % 2 == 0 or number % 3 == 0:
    # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
    return False

  # All primes number are in format of 6k +/- 1
  for i in range(5	,    int(math.sqrt(__a		) + 1		)	,    6		):
    if number % i == 0 or number % (i + 2) == 0:
      return False
  return True





def      lowerCAmelCase_ (       )     ->		str:







  """simple docstring"""





  lowerCamelCase__:      Optional[int]			  =2
  while True:
    if is_prime(__a		):
      yield num
    num += 1





def      lowerCAmelCase_ (       __a = 10001		)     ->		int:







  """simple docstring"""





  return next(itertools.islice(prime_generator()	,    nth - 1	,    __a		)		)


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

