



"""simple docstring"""







def 				UpperCamelCase_    (    lowerCAmelCase__      :				Optional[int]						)						->   Dict:

  """simple docstring"""




  lowerCAmelCase_   :				Union[str, Any]								= [False] * len(lowerCAmelCase__						)
  lowerCAmelCase_   :				Optional[Any]								= [-1] * len(lowerCAmelCase__						)

  def dfs(lowerCAmelCase__      :				List[Any]    ,   lowerCAmelCase__      :				Optional[Any]						):
    lowerCAmelCase_   :				Optional[Any]								= True
    lowerCAmelCase_   :				Optional[int]								= c
    for u in graph[v]:
      if not visited[u]:
        dfs(lowerCAmelCase__    ,   1 - c						)

  for i in range(len(lowerCAmelCase__						)						):
    if not visited[i]:
      dfs(lowerCAmelCase__    ,   0						)

  for i in range(len(lowerCAmelCase__						)						):
    for j in graph[i]:
      if color[i] == color[j]:
        return False

  return True


# Adjacency list of graph
lowercase__		:				str          =	{0: [1, 3], 1: [0, 2], 2: [1, 3], 3: [0, 2], 4: []}
print(check_bipartite_dfs(graph))












"""simple docstring"""
from math import isqrt, loga






def 					A__				(			UpperCamelCase       ):
							A		=  [True] * max_number
							for i in range(2					,  isqrt(max_number - 1       ) + 1       ):
														if is_prime[i]:
																					for j in range(i**2					,  UpperCamelCase					,  UpperCamelCase       ):
																												A		=  False

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






def 					A__				(			UpperCamelCase = 800_800					,  UpperCamelCase = 800_800       ):
							A		=  degree * loga(UpperCamelCase       )
							A		=  int(UpperCamelCase       )
							A		=  calculate_prime_numbers(UpperCamelCase       )

							A		=  0
							A		=  0
							A		=  len(UpperCamelCase       ) - 1
							while left < right:
														while (
														    prime_numbers[right] * loga(prime_numbers[left]       )
														    + prime_numbers[left] * loga(prime_numbers[right]       )
														    > upper_bound
														):
																					right -= 1
														hybrid_integers_count += right - left
														left += 1

							return hybrid_integers_count


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


