Problem Statement  
You are standing on some arbitrary point in the infinite plane. You are given a String[] commands that contains the commands you have to execute. Each character of each element of commands is one command. The commands must be executed in the given order: first you execute all commands in the first element of commands one by one, then those in the second element, etc. There are only three types of commands: 'S' means "step forward", 'L' means "turn 90 degrees to the left", and 'R' means "turn 90 degrees to the right". All your steps have the same length. You will be executing the commands forever: after you execute the last character of the last element of commands, you will always start from the beginning again. We say that your path is bounded if there is some positive real number R such that while executing the infinite sequence of steps you will never leave the circle with radius R steps and center at your starting location. Given the String[] commands, your method should determine whether your path will be bounded or not. Return the String "bounded" (quotes for clarity) if the path is bounded and "unbounded" if it is not.  
Definition  
 
Constraints  
  commands will contain between 1 and 50 elements, inclusive.  
  Each element in commands will contain between 1 and 50 characters, inclusive.  
  Each character in each element of commands will be one of 'S', 'L', and 'R'.  
Examples  
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