Some Special Three-Digit Numbers

How many 33 digit numbers NN are there such that the digits of NN and 3N3N are all even?

Details and assumptions

All of the digits of NN and 3N3N are even. For example, N=200N=200, 3N=6003N=600 will be a valid solution. However, N=600N=600, 3N=18003N=1800 will not be valid, due to the '1' in 18001800.

There is not restriction on the number of digits of 3N3N.

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