Problem Statement  
"Hangman for two" is a game based on the popular Hangman game.
In this version of the game, the computer randomly selects a word from
its word database and displays a line of dashes,
each of which represents one character of the selected word. Then two
players alternately try to find out the selected word. Each turn, the current player may guess one character. If the character occurs in the word, all occurrences of this character are displayed and the current player may continue guessing, otherwise the other player continues. Whenever the current player thinks he knows the word, he can also guess the word directly instead of guessing a character (but only during his turn). If he is right, the game stops and he has won, otherwise the other player continues with guessing either a character or a word. Now, two players want to try out this game. As they know the word database the computer uses, they try to use this information to find a strategy for maximizing the probability of winning. They ask you if you can tell them the probability that the starting player wins, if both players use a strategy for maximizing their probability of winning the game.  
Definition  
 
Notes  
  You can assume the probability that the computer selects a certain word is 1 / number of words.  
  The probability for winning is the same as the number of words for which the strategy used guarantees a win, divided by the total number of words.  
Constraints  
  words contains between 1 and 10 elements, inclusive.  
  Each element of words consists of between 1 and 50 lowercase letters, inclusive.  
  Each element of words contains the same number of characters.  
  All elements of words are distinct.  
Examples  
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