Each Digit Once in Powers of N

NN is an integer. The numbers N3N^3 and N4N^4 together consist of all of the digits 0,1,2,3,4,5,6,7,8,90,1,2,3,4,5,6,7,8,9 exactly once. What is the value of N2N^2?

Details and assumptions

The number 12=01212 = 012 does not contain the digit 0.

Each digit (0 to 9) appears in either N3N^3 or N4N^4 exactly once, and doesn't appear in both of them. For example, if N=2N=2, then N3N^3 and N4N^4 together consist of the digits 1,6,81, 6, 8 exactly once.

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