Break the Stick

Chef has a stick of length $N$. He can break the stick into $2$ or more parts such that the [parity](https://en.wikipedia.org/wiki/Parity_(mathematics)) of length of each part is same. For example, a stick of length $11$ can be broken into three sticks of lengths $\{3, 3, 5\}$ since each part is odd, but it cannot be broken into two sticks of lengths $\{5, 6\}$ since one is even and the other is