Problem Statement  
State machines occur frequently in computer science literature. At any given point in time, a state machine is in a particular state p. After receiving an input symbol, the machine updates its state. The potential input symbols in this problem are 0, 1, 2, or 3. The String[] transitions describes how the state machine M behaves. Each element of transitions will contain 4 space delimited integers. The integers in element i (0based) describe how M reacts to input while in state i. For example, if element 3 is "0 4 2 3", then M will transition from state 3 to state 0, 4, 2, or 3 depending on whether 0, 1, 2, or 3 are received as input, respectively. Our state machine M is unfortunately out of control. We do not know which state M is currently in. To rectify the situation, we want to find a string s and a state h such that, after feeding s into M one symbol at a time, M will definitely be in state h. Considering all possible pairs of s and h, return the length of the shortest s. If no such pairs exist, return 1.  
Definition  
 
Constraints  
  transitions will contain between 1 and 20 elements inclusive.  
  Each element of transitions will have the form "w x y z" where w, x, y, and z are integers, without extra leading zeros, between 0 and k1 inclusive. Here k is the number of elements in transitions.  
Examples  
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