$N$ is an integer. The numbers $N^3$ and $N^4$ together consist of all of the digits $0,1,2,3,4,5,6,7,8,9$ exactly once. What is the value of $N^2$?

**Details and assumptions**

The number $12 = 012$ does not contain the digit 0.

Each digit (0 to 9) appears in either $N^3$ or $N^4$ exactly once, and doesn't appear in both of them. For example, if $N=2$, then $N^3$ and $N^4$ together consist of the digits $1, 6, 8$ exactly once.

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