### 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 (0-based) 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

 Class: SequenceSync Method: getLength Parameters: String[] Returns: int Method signature: int getLength(String[] transitions) (be sure your method is public)

### 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 k-1 inclusive. Here k is the number of elements in transitions.

### Examples

0)

 ```{"1 1 1 1", "1 1 1 2", "0 2 2 2"}```
`Returns: 2`
 The string "33" forces the machine into state 2.
1)

 ```{"1 1 1 1", "2 2 2 2", "3 3 3 3", "0 0 0 0"}```
`Returns: -1`
 There are no strings that work here.
2)

 `{"0 0 0 0"}`
`Returns: 0`
 A string of length 0 works here.
3)

 ```{"1 1 1 0", "2 2 2 1", "3 3 3 2", "4 4 4 3", "5 5 5 5", "6 6 6 6", "7 7 7 0", "0 0 0 8", "8 8 8 8", "9 9 9 8"}```
`Returns: 15`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=4506

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=6537&pm=4506