P17642 [ICPC 2019 Yinchuan R] Largest Common Submatrix

You are given two $n \times m$ matrices, and the elements of each matrix are ranged from $1$ to $n \times m$ and pairwise distinct. You need to find the common submatrix with the largest size between these two matrices. Example: Matrix $A$: $$ \begin{array}{ccc} 1 & 2 & 3\\ 4 & 5 & 6\\ 8 & 7 & 9\\ \end{array} $$ Matrix $B$: $$ \begin{array}{ccc} 5 & 6 & 1\\ 7 & 9 & 3\\ 2 & 4 & 8\\ \end{array} $$ Largest common submatrix: $$ \begin{array}{cc} 5 & 6\\ 7 & 9\\ \end{array} $$

The first line of input contains two integers $n~(1 \le n \le 1000)$ and $m~(1 \le m \le 1000)$, denoting the number of rows and columns of each matrix. Each of the next $n$ lines contain $m$ integers per line, denoting the first matrix $A=(a_{i,j})_{n\times m}$. And again, each of the next $n$ lines contains $m$ integers per line, denoting the second matrix $B=(b_{i,j})_{n\times m}$. It is guaranteed that $1 \le a_{i,j}, b_{i,j} \le n \times m$, and $a_{i_1,j_1} \ne a_{i_2,j_2} \wedge b_{i_1,j_1} \ne b_{i_2,j_2}$ always holds for each pair of $(i_1, j_1)$ and $(i_2, j_2)$, where $i_1 \ne i_2 \vee j_1 \ne j_2$.

Output an integer representing the size of the largest common submatrix.

Largest common submatrix in the sample test: $$\displaystyle \begin{array}{cc} 5 & 6\\ 1 & 2\\ \end{array}$$