The numbers, in order, of each row and the numbers, in order, of each column of a $5\times 5$ array of integers form an arithmetic progression of length $5$. The numbers in positions $(5,5)$, $(2,4)$, $(4,3)$, and $(3,1)$ are $0$, $19$, $16$, and $4$, respectively. What number is in position $(1,2)$?