

"""simple docstring"""

import heapq



def 			SCREAMING_SNAKE_CASE       (   lowercase__				,				lowercase__				,				lowercase__      ) ->	Union[str, Any]:
 lowerCAmelCase__      :							str    =							[(0, start)]  # cost from start node,end node
 lowerCAmelCase__      :							Dict    =							set()
 while heap:
  ((lowerCAmelCase__) ,	(lowerCAmelCase__))      :							List[Any]    =							heapq.heappop(lowercase__      )
  if u in visited:
   continue
  visited.add(lowercase__      )
  if u == end:
   return cost
  for v, c in graph[u]:
   if v in visited:
    continue
   lowerCAmelCase__      :							Optional[int]    =							cost + c
   heapq.heappush(lowercase__				,				(next_item, v)      )
 return -1


_UpperCamelCase       =						{
    'A': [['B', 2], ['C', 5]],
    'B': [['A', 2], ['D', 3], ['E', 1], ['F', 1]],
    'C': [['A', 5], ['F', 3]],
    'D': [['B', 3]],
    'E': [['B', 4], ['F', 3]],
    'F': [['C', 3], ['E', 3]],
}
_UpperCamelCase       =						{
    'B': [['C', 1]],
    'C': [['D', 1]],
    'D': [['F', 1]],
    'E': [['B', 1], ['F', 3]],
    'F': [],
}
_UpperCamelCase       =						{
    'B': [['C', 1]],
    'C': [['D', 1]],
    'D': [['F', 1]],
    'E': [['B', 1], ['G', 2]],
    'F': [],
    'G': [['F', 1]],
}

_UpperCamelCase       =						dijkstra(G, """E""", """C""")
print(short_distance)  # E -- 3 --> F -- 3 --> C == 6

_UpperCamelCase       =						dijkstra(Ga, """E""", """F""")
print(short_distance)  # E -- 3 --> F == 3

_UpperCamelCase       =						dijkstra(Ga, """E""", """F""")
print(short_distance)  # E -- 2 --> G -- 1 --> F == 3

if __name__ == "__main__":
    import doctest

    doctest.testmod()









"""simple docstring"""

from itertools import product



def 			SCREAMING_SNAKE_CASE       (   lowercase__ = 1_5      ) ->	int:
 lowerCAmelCase__      :							float    =							0.0
 lowerCAmelCase__      :							float
 lowerCAmelCase__      :							int
 lowerCAmelCase__      :							int
 lowerCAmelCase__      :							int
 lowerCAmelCase__      :							int
 lowerCAmelCase__      :							tuple[int, ...]

 for series in product(range(2      )				,				repeat=lowercase__      ):
  lowerCAmelCase__      :							Optional[int]    =							series.count(1      )
  lowerCAmelCase__      :							Dict    =							num_turns - num_blue
  if num_red >= num_blue:
   continue
  lowerCAmelCase__      :							Dict    =							1.0
  for ind, col in enumerate(lowercase__				,				2      ):
   if col == 0:
    prob *= (ind - 1) / ind
   else:
    prob *= 1 / ind

  total_prob += prob

 return int(1 / total_prob      )


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






