Your card playing rival owns a card shuffling device, which always uses the exact same procedure to shuffle cards, the knowledge of which he unfairly leverages to his advantage. You want to level the playing field, so$,$ when he is not looking, you feed the machine the spades in order $($ace to king$).$ Right after the cards come out, your rival catches you before you can get a look and feeds the cards back into the machine $($in the same order they came out$),$ laughing maniacally as the cards are re$-$scrambled and your plan apparently foiled. After this second shuffle, the cards are in the order: J$,9,$ Q$,$ A$,$ K$,3,5,2,6,4,7,10,8.$ But the joke is on him and you can still figure out what order the cards originally came out! What was the original shuffled order?