At a recent magic show, the magician has 10 cards, each assigned a distinct integer from 1 to 10 (inclusive). After randomly shuffling the cards, he claims that they are now in order, which the audience disbelieves. Let $$p$$ be the probability that exactly 9 of the cards are arranged in order. What is the value of $$\lfloor 1000p \rfloor$$?

Details and assumptions

The function $$\lfloor x \rfloor: \mathbb{R} \rightarrow \mathbb{Z}$$ refers to the greatest integer smaller than or equal to $$x$$. For example $$\lfloor 2.3 \rfloor = 2$$ and $$\lfloor -5 \rfloor = -5$$.

The card is in order if it's position in the sequence corresponds to the numerical value of the card. As an explicit example, the sequence 1 , 3, 5, 7, 9, 10, 6, 8, 2, 4 has 2 cards (listed in bold) that are in order.

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