Breaking Sticks

You have $N$ sticks, of integral lengths $A_1, A_2, ..., A_N$. You can take any stick of length $X$ and break it into $2$ **positive integer** lengths $Y$ and $Z$ such that $Y + Z = X$, i.e. now instead of the stick of length $X$, you obtained one stick of length $Y$ and another of length $Z$. One such action is called a **break**. Find the maximum number of **breaks** you can perform. ### Inpu