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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