Long long ago, there was a kingdom named Kingdom C. There were n cities in Kingdom C, and every pair of cities was connected by a two-way road. Unfortunately, some of those roads may have been destroyed in a heavy rain.
You are given a String roads. The probability that the road connecting city i and city j is still available after the heavy rain is d/8, where d is the j-th digit of the i-th element of roads.
The king of Kingdom C is very sad, and he wants to know the probability of the following scenario: Every city is reachable from the capital (city 0), but if you were to destroy any one of the remaining roads, there would be at least one city that is not reachable from the capital. Return the probability of this scenario as a double.