There is a pack of 27 distinct cards, and each card has three values on it. The first value is a shape from $\{\Delta,\square,\odot\}$; the second value is a letter from $\{A,B,C\}$; and the third value is a number from $\{1,2,3\}$.  

In how many ways can we choose an unordered set of 3 cards from the pack, so that no two of the chosen cards have two matching values?  

For example, we can choose $\{\Delta A1, \Delta B2, \odot C3\}$, but we cannot choose $\{\Delta A1, \square B2, \Delta C1\}$.

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