Some Special Three-Digit Numbers

How many $$3$$ digit numbers $$N$$ are there such that the digits of $$N$$ and $$3N$$ are all even?

Details and assumptions

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

There is not restriction on the number of digits of $$3N$$.

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