starting with printed string x, find the minimum number of operations required to print x n times if only 2 operations are allowed
- op1 - copy (copies everthing that is printed to copyspace)
- op2 - print (appends current copyspace to printed string)

ex -
for n = 6
| steps | op | copyspace (after op) | printed string (after op) |
| -------- |------- | --------------------:| ------------------------: |
| 0 (start) | | | x |
| 1 | copy | x | x |
| 2 | paste | x | xx |
| 3 | copy | xx | xx |
| 4 | paste | xx | xxxx |
| 5 | paste | xx | xxxxxx |

samples -

f(1) = 0 -- noop
f(2) = 2 -- cp
f(3) = 3 -- cpp
f(4) = 4 -- cppp
f(6) = 5 -- cpcpp
f(9) = 6 -- cppcpp