






'''simple docstring'''
from __future__ import annotations

from collections import Counter
from random import random


class 							_UpperCAmelCase    :




    def __init__(      self	:							Dict      ):






       '''simple docstring'''






       lowercase_						:     Optional[Any]							     =  {}




    def 					lowerCAmelCase__					(      self	:							Any	,  a	:							str      ):






       '''simple docstring'''






       lowercase_						:     Tuple							     =  {}




    def 					lowerCAmelCase__					(      self	:							str	,  a	:							str	,  a	:							str	,  a	:							float      ):






       '''simple docstring'''






       if nodea not in self.connections:
          self.add_node(a      )
       if nodea not in self.connections:
          self.add_node(a      )
       lowercase_						:     str							     =  probability




    def 					lowerCAmelCase__					(      self	:							Dict      ):






       '''simple docstring'''






       return list(self.connections      )





    def 					lowerCAmelCase__					(      self	:							List[str]	,  a	:							str      ):






       '''simple docstring'''






       lowercase_						:     int							     =  0
       lowercase_						:     List[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				):


   """simple docstring"""




   lowercase_						:     Optional[Any]							     =  MarkovChainGraphUndirectedUnweighted()

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

   lowercase_						:     List[str]							     =  Counter(graph.get_nodes()				)
   lowercase_						:     Any							     =  start

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

   return visited


if __name__ == "__main__":
 import doctest

 doctest.testmod()












'''simple docstring'''
def 		__SCREAMING_SNAKE_CASE       (	_UpperCamelCase = 100				):


   """simple docstring"""




   lowercase_						:     Dict							     =  n * (n + 1) * (2 * n + 1) / 6
   lowercase_						:     int							     =  (n * (n + 1) / 2) ** 2
   return int(square_of_sum - sum_of_squares				)


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




