A monkey starts at $(0,0)$ on the $xy$-plane in period $1$. From any position $(x,y)$ in a period, the monkey can only jump to $(a,b)$ in the next period, where $a\in\{x+1,x,x-1\}$ and $b\in\{y+1,y,y-1\}$. How many possible positions can the monkey be in period $2$?