
from __future__ import annotations

from collections import Counter
from random import random
class       _lowerCAmelCase  :

 """simple docstring"""

 def __init__(						self			:			Union[str, Any]   ):






      """simple docstring"""



      UpperCamelCase						    =					{}

 def      __lowerCAmelCase  (						self			:			Tuple					, SCREAMING_SNAKE_CASE__			:			str   ):






      """simple docstring"""



      UpperCamelCase						    =					{}

 def      __lowerCAmelCase  (						self			:			Optional[Any]					, SCREAMING_SNAKE_CASE__			:			str					, SCREAMING_SNAKE_CASE__			:			str					, SCREAMING_SNAKE_CASE__			:			float   ):






      """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						    =					probability

 def      __lowerCAmelCase  (						self			:			str   ):






      """simple docstring"""



      return list(self.connections   )






 def      __lowerCAmelCase  (						self			:			Any					, SCREAMING_SNAKE_CASE__			:			str   ):






      """simple docstring"""



      UpperCamelCase						    =					0
      UpperCamelCase						    =					random()

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




def  __lowerCamelCase					( _lowercase						,     _lowercase						,     _lowercase			)       ->      dict[str, int]:
     UpperCamelCase						    =					MarkovChainGraphUndirectedUnweighted()

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

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

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

     return visited


if __name__ == "__main__":
 import doctest

 doctest.testmod()




def  __lowerCamelCase					( _lowercase = 50000000			)       ->      int:
     UpperCamelCase						    =					set()
     UpperCamelCase						    =					int((limit - 24) ** (1 / 2)			)

     UpperCamelCase						    =					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						,     _lowercase			)			)			)

     for primea in primes:
          UpperCamelCase						    =					primea * primea
          for primea in primes:
               UpperCamelCase						    =					primea * primea * primea
               if square + cube >= limit - 16:
                    break
               for primea in primes:
                    UpperCamelCase						    =					primea * primea * primea * primea
                    UpperCamelCase						    =					square + cube + tetr
                    if total >= limit:
                         break
                    ret.add(_lowercase			)

     return len(_lowercase			)


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


