Three fair six-sided dice are labeled with the numbers $\{1, 2, 3, 4, 5, 6\},$ $\{1, 2, 3, 4, 5, 6\},$ and $\{1, 2, 3, 7, 8, 9\},$ respectively. All three dice are rolled. The probability that at least two of the dice have the same value is $\frac{m}{n},$ where $m, n$ are relatively prime positive integers. Find $100m + n.$

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