Mathia, the great magician, showed his audiences 9 cards, each displaying a distinct digit from 1 to 9 (inclusive), before putting 3 cards to each of his 3 top hats.

Afterwards, by yelling "Abracadabra!", the card "$$a$$" popped up magically from the first hat, where $$a$$ was prime. Then with the second "Abracadabra!", the card "$$b$$" popped up from the second hat, and when he put it next to the previous card, the 2-digit number $$\overline{ab}$$ was also prime. Then after calling out the third card "$$c$$", the 3-digit $$\overline{abc}$$ was also prime and is the sum of $$\overline{ab}$$ and a cube.

After a long applause, the magician began the second round of incantations in the same fashion. This time, the card "$$d$$" was a composite number. The 2-digit number $$\overline{de}$$ was also a composite number, and the 3-digit number $$\overline{def}$$ was composite and a difference between two squares, both greater than $$1$$.

Last but not least, the grand finale started with the card "$$g$$" being a perfect square. The 2-digit number $$\overline{gh}$$ was also a perfect square, and the 3-digit number $$\overline{ghi}$$ was a sum of two different squares.

By revealing all the 9 cards, what is the value of the 9-digit number $$\overline{abcdefghi}$$? O

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