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FYI, there is a problem with this definition. You can have overlap of the "top" nodes. For instance, when looking "to the left", you could have a branch "poke" out that coincides with another branch. In this case both nodes would appear to be at both the same level and height. My assumption (in my solution) for a tie was the the "left-most" branch was the highest--that is the branch that originated from the "most" left position (in this case that would be how I drew it).
Now, that's some Editorial-grade insight take notes, lads!