Imagine you have a special keyboard with the following keys:

1. A

2. Ctrl+A

3. Ctrl+C

4. Ctrl+V

where CTRL+A, CTRL+C, CTRL+V each acts as one function key for “Select All”, “Copy”, and “Paste” operations respectively.

If you can only press the keyboard for N times (with the above four keys), please write a program to produce maximum numbers of A. If possible, please also print out the sequence of keys.

That is to say, the input parameter is N (No. of keys that you can press), the output is M (No. of As that you can produce).

Example:-

For N = 8 the answer is M = 9, where S = { A, A, A, CTRL+A, CTRL+C, CTRL+V, CTRL+V, CTRL+V }.

For N = 9 the answer is M = 12, where S = { A, A, A, CTRL+A, CTRL+C, CTRL+V, CTRL+V, CTRL+V, CTRL+V }.

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