
"""simple docstring"""

from collections import defaultdict

from graphs.minimum_spanning_tree_prims import prisms_algorithm as mst






def 							A						(    )				->     Dict:
 __UpperCamelCase  ,     __UpperCamelCase      =	9, 1_4  # 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, 1_4],
     [3, 4, 9],
     [5, 4, 1_0],
     [1, 7, 1_1],
 ]

 __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 math import isqrt






def 							A						(    snake_case				:int		)				->     list[int]:
 __UpperCamelCase      =	[True] * max_number
 for i in range(2    , isqrt(max_number - 1		) + 1		):
  if is_prime[i]:
   for j in range(i**2    , snake_case    , snake_case		):
    __UpperCamelCase      =	False

 return [i for i in range(2    , snake_case		) if is_prime[i]]






def 							A						(    snake_case				:int = 1_0**8		)				->     int:
 __UpperCamelCase      =	calculate_prime_numbers(max_number // 2		)

 __UpperCamelCase      =	0
 __UpperCamelCase      =	0
 __UpperCamelCase      =	len(snake_case		) - 1
 while left <= right:
  while prime_numbers[left] * prime_numbers[right] >= max_number:
   right -= 1
  semiprimes_count += right - left + 1
  left += 1

 return semiprimes_count


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



