$2016$ numbers written on the board: $\frac{1}{2016}, \frac{2}{2016}, \frac{3}{2016}, ..., \frac{2016}{2016}$. In one move, it is allowed to choose any two numbers $a$ and $b$ written on the board, delete them, and write the number $3ab - 2a - 2b + 2$ instead. Determine what number will remain written on the board after $2015$ moves.