



"""simple docstring"""
def       _snake_case						(						UpperCamelCase						:		Any						):
 return [
     {
         0: [1, 2],
         1: [0, 2],
         2: [0, 1, 3, 5],
         3: [2, 4],
         4: [3],
         5: [2, 6, 8],
         6: [5, 7],
         7: [6, 8],
         8: [5, 7],
     },
     {
         0: [6],
         1: [9],
         2: [4, 5],
         3: [4],
         4: [2, 3],
         5: [2],
         6: [0, 7],
         7: [6],
         8: [],
         9: [1],
     },
     {
         0: [4],
         1: [6],
         2: [],
         3: [5, 6, 7],
         4: [0, 6],
         5: [3, 8, 9],
         6: [1, 3, 4, 7],
         7: [3, 6, 8, 9],
         8: [5, 7],
         9: [5, 7],
     },
     {
         0: [1, 3],
         1: [0, 2, 4],
         2: [1, 3, 4],
         3: [0, 2, 4],
         4: [1, 2, 3],
     },
 ][index]

def       _snake_case						(						UpperCamelCase						:		dict[int, list[int]]						):
 UpperCAmelCase	:					Optional[int]	=	0
 UpperCAmelCase	:					Dict	=	len(UpperCamelCase						)  # No of vertices in graph
 UpperCAmelCase	:					Union[str, Any]	=	[0] * n
 UpperCAmelCase	:					Optional[Any]	=	[False] * n

 def dfs(UpperCamelCase						:		Optional[Any]			,		UpperCamelCase						:		Tuple			,		UpperCamelCase						:		int			,		UpperCamelCase						:		Union[str, Any]						):
  UpperCAmelCase	:					Tuple	=	True
  UpperCAmelCase	:					Any	=	id_
  id_ += 1
  for to in graph[at]:
   if to == parent:
    pass
   elif not visited[to]:
    dfs(UpperCamelCase			,		UpperCamelCase			,		UpperCamelCase			,		id_						)
    UpperCAmelCase	:					Dict	=	min(low[at]			,		low[to]						)
    if id_ <= low[to]:
     bridges.append((at, to) if at < to else (to, at)						)
   else:
    # This edge is a back edge and cannot be a bridge
    UpperCAmelCase	:					Optional[Any]	=	min(low[at]			,		low[to]						)

 UpperCAmelCase	:					list[tuple[int, int]]	=	[]
 for i in range(UpperCamelCase						):
  if not visited[i]:
   dfs(UpperCamelCase			,		-1			,		UpperCamelCase			,		id_						)
 return bridges


if __name__ == "__main__":
      import doctest

      doctest.testmod()





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

def       _snake_case						(						UpperCamelCase						:		int						):
 UpperCAmelCase	:					Any	=	[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						):
    UpperCAmelCase	:					str	=	False

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

def       _snake_case						(						UpperCamelCase						:		int = 800800			,		UpperCamelCase						:		int = 800800						):
 UpperCAmelCase	:					Union[str, Any]	=	degree * loga(UpperCamelCase						)
 UpperCAmelCase	:					int	=	int(UpperCamelCase						)
 UpperCAmelCase	:					Union[str, Any]	=	calculate_prime_numbers(UpperCamelCase						)

 UpperCAmelCase	:					Dict	=	0
 UpperCAmelCase	:					Optional[int]	=	0
 UpperCAmelCase	:					Dict	=	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() = }""")
