The numbers, in order, of each row and the numbers, in order, of each column of a $4\times 4$ array of integers form an arithmetic progression of length $4$. The numbers in positions $(4,4)$, $(1,4)$, $(4,1)$ and $(2,3)$ are $16$, $19$, $16$, and $16$, respectively. What number is in position $(2,2)$?