
from __future__ import annotations

from collections import Counter
from random import random




class 				_lowerCamelCase :





     """simple docstring"""







     def __init__(							self  )  ->   int:




           """simple docstring"""







           UpperCamelCase__    :   int					=				{}






     def    __SCREAMING_SNAKE_CASE			(							self						,						__SCREAMING_SNAKE_CASE  )  ->   None:




           """simple docstring"""







           UpperCamelCase__    :   Any					=				{}






     def    __SCREAMING_SNAKE_CASE			(							self						,						__SCREAMING_SNAKE_CASE						,						__SCREAMING_SNAKE_CASE						,						__SCREAMING_SNAKE_CASE  )  ->   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  )
           UpperCamelCase__    :   List[Any]					=				probability






     def    __SCREAMING_SNAKE_CASE			(							self  )  ->   list[str]:




           """simple docstring"""







           return list(self.connections  )






     def    __SCREAMING_SNAKE_CASE			(							self						,						__SCREAMING_SNAKE_CASE  )  ->   str:




           """simple docstring"""







           UpperCamelCase__    :   Union[str, Any]					=				0
           UpperCamelCase__    :   str					=				random()

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


def 							SCREAMING_SNAKE_CASE_      (			UpperCamelCase__ ,		UpperCamelCase__ ,		UpperCamelCase__		):
      UpperCamelCase__    :   List[str]					=				MarkovChainGraphUndirectedUnweighted()

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

      UpperCamelCase__    :   str					=				Counter(graph.get_nodes()		)
      UpperCamelCase__    :   int					=				start

      for _ in range(UpperCamelCase__		):
            UpperCamelCase__    :   Optional[int]					=				graph.transition(UpperCamelCase__		)
            visited[node] += 1

      return visited


if __name__ == "__main__":
    import doctest

    doctest.testmod()




def 							SCREAMING_SNAKE_CASE_      (			UpperCamelCase__ = 5_0_0_0_0_0_0_0		):
      UpperCamelCase__    :   Any					=				set()
      UpperCamelCase__    :   Any					=				int((limit - 2_4) ** (1 / 2)		)

      UpperCamelCase__    :   Dict					=				set(range(3 ,		prime_square_limit + 1 ,		2		)		)
      primes.add(2		)
      for p in range(3 ,		prime_square_limit + 1 ,		2		):
            if p not in primes:
                  continue
            primes.difference_update(set(range(p * p ,		prime_square_limit + 1 ,		UpperCamelCase__		)		)		)

      for primea in primes:
            UpperCamelCase__    :   Dict					=				primea * primea
            for primea in primes:
                  UpperCamelCase__    :   str					=				primea * primea * primea
                  if square + cube >= limit - 1_6:
                        break
                  for primea in primes:
                        UpperCamelCase__    :   Dict					=				primea * primea * primea * primea
                        UpperCamelCase__    :   Tuple					=				square + cube + tetr
                        if total >= limit:
                              break
                        ret.add(UpperCamelCase__		)

      return len(UpperCamelCase__		)


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


