Problem Statement

Consider the following operations on an $H\times W$ matrix $A = (A_{i,j})$ ($1\leq i\leq H, 1\leq j\leq W$).

• Row-sort: Sort every row in ascending order. That is, sort $A_{i,1},\ldots,A_{i,W}$ in ascending order for every $i$.
• Column-sort: Sort every column in ascending order. That is, sort $A_{1,j},\ldots,A_{H,j}$ in ascending order for every $j$.

You are given an $H\times W$ matrix $B = (B_{i,j})$. Find the number of $H\times W$ matrices $A$ that satisfy both of the following conditions, modulo $998244353$.

• Performing row-sort and then column-sort on $A$ produces $B$.
• Performing column-sort and then row-sort on $A$ produces $B$.

Constraints

• $1\leq H, W\leq 1500$
• $0\leq B_{i,j}\leq 9$
• $B_{i,j}\leq B_{i,j+1}$, for any $1\leq i\leq H$ and $1\leq j\leq W - 1$.
• $B_{i,j}\leq B_{i+1,j}$, for any $1\leq j\leq W$ and $1\leq i\leq H - 1$.
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

H W
B_{1,1} B_{1,2} \ldots B_{1,W}
\vdots
B_{H,1} B_{H,2} \ldots B_{H,W}

Output

Print the number of matrices $A$ that satisfy the conditions, modulo $998244353$.