Hen Hao randomly selects two distinct squares on a standard $8 \times 8$ chessboard. Given that the two squares touch (at either a vertex or a side), the probability that the two squares are the same color can be expressed in the form $\frac{m}{n}$ for relatively prime positive integers $m$ and $n$. Find $100m + n$.

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