Boolean Product of Boolean Matrices

While setting problems, Ukje suddenly wanted to write a twisted one. Unfortunately, many contestants in this contest are new to programming, so he could not. Still, Ukje could not give up his urge to torment the freshmen.

"Ha ha! Can the freshmen really solve this one?"

The task is simple. You are given two $N \times N$ Boolean matrices (matrices made only of 0s and 1s) $A=[a_{ij}]$ and $B=[b_{ij}]$. Compute their Boolean product $C=[c_{ij}]$ and count the 1s in $C$. The Boolean product is computed as follows.

$c_{ij} = (a_{i1} \land b_{1j}) \lor (a_{i2} \land b_{2j}) \lor \cdots \lor (a_{in} \land b_{nj})$

Here $x_{ij}$ is the element in row $i$, column $j$ of matrix $X$, $\land$ is logical AND, and $\lor$ is logical OR. Now, start coding!

The first line contains the matrix size $N$ ($1 \le N \le 300$). The next $N$ lines contain the Boolean matrix $A$, and the $N$ lines after that contain the Boolean matrix $B$. Each of these lines contains $N$ integers, each 0 or 1, separated by spaces.

Print the number of 1s in the matrix $C$, the Boolean product of $A$ and $B$.

The Boolean product for sample 1 is:

1 1 1
1 1 1
0 0 1

So the number of 1s is 7.

The Boolean product for sample 2 is:

0 0
1 1

So the number of 1s is 2.