Maximize Colours

For the human eye, primary colours are red, green, and blue. Combining $1$ drop each of **any two primary** colours produces a new type of secondary colour. For example, mixing red and green gives yellow, mixing green and blue gives cyan, and, mixing red and blue gives magenta. You have $X, Y,$ and $Z$ drops of red, green, and blue colours respectively. Find the **maximum** total number of **di