Problem Statement  
John and Brus are training for a card game tournament. During his offtime, Brus likes to occupy himself with the following game. The game is played with a subset of a standard deck of 52 distinct cards. Each card can be represented by a twocharacter string, where the first character is the rank ('2''9', 'T', 'J', 'Q', 'K', or 'A') and the second character is the suit ('S' for Spades, 'C' for Clubs, 'D' for Diamonds or 'H' for Hearts). All Spades and Clubs are black, and all Diamonds and Hearts are red. For example, the Jack of Spades is black and is represented as "JS", and the Nine of Hearts is red and is represented as "9H". You are given a String[] cards containing the subset of the deck that Brus is playing with. Each element of cards represents a single card. He wants to place all of these cards in a line such that every pair of neighboring cards has the same rank or the same color (or both). Return the number of different ways he can do this modulo 1234567891.  
Definition  
 
Constraints  
  cards will contain between 1 and 50 elements, inclusive.  
  Each element of cards will contain exactly two characters, where the first character is '2''9', 'T', 'J', 'Q', 'K' or 'A', and the second character is 'S', 'C', 'D' or 'H'.  
  All elements of cards will be distinct.  
Examples  
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