Employees

At the factory, each of the $N$ items can be processed on one of two machines: $A$ or $B$. Each item has a serial number from $1$ to $N$. The items are processed sequentially, in the order of their serial numbers. The number of items is always even.

There are rules that determine on which machine an item can be processed:

1. If, at the current moment, the number of items processed on machine $B$ is equal to the number of items processed on machine $A$, then the next item must be processed on machine $A$.

2. In total, the same number of items must be processed on each machine.

Each factory worker suggests a sequence for processing the items. All such sequences are different and must satisfy rules $1$ and $2$.

Write a program that, given the number of items $N$, determines the maximum possible number of factory workers.