for the rest of the array we will rely on the previous entries to compute new ones
for ( N = 1 ; N <= 20 ; N ++ ) cout << " Maximum ▁ Number ▁ of ▁ A ' s ▁ with ▁ " << N << " ▁ keystrokes ▁ is ▁ " << findoptimal ( N ) << endl ; }