


from queue import PriorityQueue
from typing import Any

import numpy as np
def 				UpperCAmelCase_					(							__snake_case     ,						__snake_case     ,						__snake_case     ,						__snake_case     ,						__snake_case     ,						__snake_case     ,						__snake_case     ,						__snake_case     ,						__snake_case     ,						)     ->			float | int:







 """simple docstring"""


 for nxt, d in graph[v]:
  if nxt in visited_forward:
   continue
  _lowercase							      =cst_fwd.get(__a     ,						np.inf						)
  _lowercase							      =cst_fwd[v] + d
  if new_cost_f < old_cost_f:
   queue.put((new_cost_f, nxt)						)
   _lowercase							      =new_cost_f
   _lowercase							      =v
  if nxt in visited_backward:
   if cst_fwd[v] + d + cst_bwd[nxt] < shortest_distance:
    _lowercase							      =cst_fwd[v] + d + cst_bwd[nxt]
 return shortest_distance
def 				UpperCAmelCase_					(							__snake_case     ,						__snake_case     ,						__snake_case     ,						__snake_case						)     ->			int:







 """simple docstring"""


 _lowercase							      =-1

 _lowercase							      =set()
 _lowercase							      =set()
 _lowercase							      ={source: 0}
 _lowercase							      ={destination: 0}
 _lowercase							      ={source: None}
 _lowercase							      ={destination: None}
 _lowercase							      =PriorityQueue()
 _lowercase							      =PriorityQueue()

 _lowercase							      =np.inf

 queue_forward.put((0, source)						)
 queue_backward.put((0, destination)						)

 if source == destination:
  return 0

 while not queue_forward.empty() and not queue_backward.empty():
  _lowercase							      =queue_forward.get()
  visited_forward.add(__a						)

  _lowercase							      =queue_backward.get()
  visited_backward.add(__a						)

  _lowercase							      =pass_and_relaxation(
      __a     ,						__a     ,						__a     ,						__a     ,						__a     ,						__a     ,						__a     ,						__a     ,						__a     ,						)

  _lowercase							      =pass_and_relaxation(
      __a     ,						__a     ,						__a     ,						__a     ,						__a     ,						__a     ,						__a     ,						__a     ,						__a     ,						)

  if cst_fwd[v_fwd] + cst_bwd[v_bwd] >= shortest_distance:
   break

 if shortest_distance != np.inf:
  _lowercase							      =shortest_distance
 return shortest_path_distance


UpperCAmelCase__   	=							{
    '''B''': [['''C''', 1]],
    '''C''': [['''D''', 1]],
    '''D''': [['''F''', 1]],
    '''E''': [['''B''', 1], ['''G''', 2]],
    '''F''': [],
    '''G''': [['''F''', 1]],
}
UpperCAmelCase__   	=							{
    '''B''': [['''E''', 1]],
    '''C''': [['''B''', 1]],
    '''D''': [['''C''', 1]],
    '''F''': [['''D''', 1], ['''G''', 1]],
    '''E''': [[None, np.inf]],
    '''G''': [['''E''', 2]],
}

if __name__ == "__main__":
  import doctest

  doctest.testmod()








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() = }')

