

'''simple docstring'''



from __future__ import annotations

from collections import Counter
from random import random







class 		lowerCAmelCase__  :



 """simple docstring"""



 def __init__(						self   :			Tuple     )    ->					Any:


      """simple docstring"""




      __SCREAMING_SNAKE_CASE      = {}
 def  UpperCAmelCase__						(						self   :			Union[str, Any]   ,				__SCREAMING_SNAKE_CASE   :			str     )    ->					None:


      """simple docstring"""




      __SCREAMING_SNAKE_CASE      = {}
 def  UpperCAmelCase__						(						self   :			int   ,				__SCREAMING_SNAKE_CASE   :			str   ,				__SCREAMING_SNAKE_CASE   :			str   ,				__SCREAMING_SNAKE_CASE   :			float     )    ->					None:


      """simple docstring"""




      if nodea not in self.connections:
           self.add_node(__SCREAMING_SNAKE_CASE     )
      if nodea not in self.connections:
           self.add_node(__SCREAMING_SNAKE_CASE     )
      __SCREAMING_SNAKE_CASE      = probability
 def  UpperCAmelCase__						(						self   :			Tuple     )    ->					list[str]:


      """simple docstring"""




      return list(self.connections     )


 def  UpperCAmelCase__						(						self   :			Tuple   ,				__SCREAMING_SNAKE_CASE   :			str     )    ->					str:


      """simple docstring"""




      __SCREAMING_SNAKE_CASE      = 0
      __SCREAMING_SNAKE_CASE      = random()

      for dest in self.connections[node]:
           current_probability += self.connections[node][dest]
           if current_probability > random_value:
                return dest
      return ""







def   a__			(    a__ ,       a__ ,       a__		):




     """simple docstring"""


     __SCREAMING_SNAKE_CASE      = MarkovChainGraphUndirectedUnweighted()

     for nodea, nodea, probability in transitions:
          graph.add_transition_probability(a__ ,       a__ ,       a__		)

     __SCREAMING_SNAKE_CASE      = Counter(graph.get_nodes()		)
     __SCREAMING_SNAKE_CASE      = start

     for _ in range(a__		):
          __SCREAMING_SNAKE_CASE      = graph.transition(a__		)
          visited[node] += 1

     return visited


if __name__ == "__main__":
  import doctest

  doctest.testmod()









'''simple docstring'''



from math import isqrt







def   a__			(    a__		):




     """simple docstring"""


     return all(number % divisor != 0 for divisor in range(2 ,       isqrt(a__		) + 1		)		)







def   a__			(    a__ = 10**6		):




     """simple docstring"""


     __SCREAMING_SNAKE_CASE      = 0
     __SCREAMING_SNAKE_CASE      = 1
     __SCREAMING_SNAKE_CASE      = 7
     while prime_candidate < max_prime:
          primes_count += is_prime(a__		)

          cube_index += 1
          prime_candidate += 6 * cube_index

     return primes_count


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






