Six chairs sit in a row.  Six people randomly seat themselves in the chairs. Each person randomly chooses either to set their feet on the floor, to cross their legs to the right, or to cross their legs to the left.  There is only a problem if two people sitting next to each other have the person on the right crossing their legs to the left and the person on the left crossing their legs to the right.  The probability that this will [b]not[/b] happen is given by $\frac{m}{n}$ where $m$ and $n$ are relatively prime positive integers. Find $m+n$.

Let's think step by step and output the final answer within \boxed{}.
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