Keys 2&3 may be combined, cause there is no sense to use them separately. 
It's cost of pressing is 2, however.
For all other keys the cost is 1 though.
DP[i][n] - maximum number of A's we can produce with cost of pressings = i 
and we have string of A's with size n in a clipboard.
DP[N][any] - result. There are 

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