题目描述

点击这里查看pdf

We call a matrix "01 Square" if and only if it's a $N\ imes N$ matrix and its elements are all $0$ or $1$.

For two 01 Squares $X$,$Y$, we define two operators $X\ imes Y$ and $X\\odot Y$. The value of them are also 01 Square matrices and calculated below(we use $Z$ to abbreviate $X\ imes Y$ and $D$ to abbreviate $X\\odot Y$):

Now MianKing has two 01 Squares $A,B$, he wants to solve the matrix equation below:

$A\ imes C=B\\odot C$

You need to help MainKing solve this problem by calculating how many 01 Squares $C$ satisfy this equation.

The answer may be very large, so you only need to output the answer module $998244353$.

输入格式

The first line has one integer $N$

Then there are $N$ lines and each line has $N$ integers, the j-th integer of the i-th line denotes $A_{i,j}$

Then there are $N$ lines and each line has $N$ integers, the j-th integer of the i-th line denotes $B_{i,j}$

$1\\leq N\\leq 200$ $A_{i,j} \\in \\{0,1\\}$

$B_{i,j} \\in \\{0,1\\}$

输出格式

Output the answer module $998244353$.

样例

2 
0 1 
1 1 
1 0 
0 1 

2 

3 
1 0 0 
0 1 0 
0 0 1 
1 1 1 
1 1 1 
1 1 1 

512 

4 
0 1 0 1 
0 1 1 0 
0 1 1 1 
1 0 0 1 
1 0 1 1 
0 1 1 1 
1 0 0 1 
1 1 1 0 

8 

提示

Form 2020ICPC济南赛站