You and your friend are playing a game. The game goes as follows:

- At the start, you are given a positive integer $N$.
- You choose a positive factor $n$ of $N$, where $n \neq N$.
- You compute $N - n$ and give the result to your friend.
- Your friend repeats the above procedure with the integer she is given and gives the result to you, and so forth.

For example, if you are given $N = 12,$ you can choose $n = 3$ and give $N - n = 9$ to your friend. Then, $N = 9$.

Play continues in this fashion until one person is given $N = 1$, at which point that person loses.

Given that you and your friend will both play optimally, how many positive integers $N \leq 2015$ are there such that, when given at the start, you will always win?